Focusing Telescopes in Nuclear Astrophysics

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FOCUSING TELESCOPES IN NUCLEAR ASTROPHYSICS

Edited by: PETER VON BALLMOOS

Reprinted from Experimental Astronomy Vol. 20, Nos. 1–3, 2005

Library of Congress Cataloging-in-Publication Data is available

ISBN 1-4020-5303-7 (hardbook) ISBN 1-4020-5304-5 (eBook) ISBN 978-1-4020-5303-7 (hardbook) ISBN 978-1-4020-5304-5 (eBook)

Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands.

Printed on acid-free paper All Rights Reserved c Springer 2006 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Printed in the Netherlands

TABLE OF CONTENTS

P. von Ballmoos / Preface

1–2

Section I: Scientiﬁc Requirements and Prospects J. Kn¨odlseder / Prospects in space-based gamma-ray astronomy

3–13

S. Sazonov, E. Churazov, R. Sunyaev and M. Revnivtsev / Annihilation of positrons in the Galaxy

15–22

Richard E. Grifﬁths / Prospects and requirements for measurements of extragalactic γ -ray lines

23–30

P. Giommi and S. Colafrancesco / Non-thermal cosmic backgrounds and prospects for future high-energy observations of blazars

31–40

Andrea Comastri, Roberto Gilli and G¨unther Hasinger / Rolling down from the 30 keV peak: Modelling the hard X-ray and γ -ray backgrounds

41–47

M. D. Leising / Focusing supernova gamma rays: Questions for a high sensitivity gamma-ray telescope

49–55

M. Hernanz and J. Jos´e / Nucleosynthesis in nova explosions: Prospects for its observation with focusing telescopes

57–64

David M. Smith / Puzzles and potential for gamma-ray line observations of solar ﬂare ion acceleration

65–73

Section II: Gamma-ray Optics P. Ubertini / The INTEGRAL – HESS/MAGIC connection: A new class of cosmic high energy accelerators from keV to TeV

75–83

Brian D. Ramsey / Replicated nickel optics for the hard-x-ray region

85–92

Carsten P. Jensen, Kristin K. Madsen and Finn E. Christensen / Small d-spacing WC/SiC multilayers for future hard X-ray telescope designs

93–103

Ernst-Jan Buis, Marco Beijersbergen, Giuseppe Vacanti, Marcos Bavdaz and David Lumb / Design aspects of grazing angle multilayer mirrors for soft γ -rays

105–113

M. P. Ulmer, M. E. Graham, S. Vaynman, J. Echt, M. Farber, S. Ehlert and S. Varlese / Progress toward light weight high angular resolution multilayer coated optics

115–120

J. Tueller, H. A. Krimm, T. Okajima, S. D. Barthelmy, S. M. Owens, P. J. Serlemitsos, Y. Soong, K.-W. Chan, Y. Ogasaka, R. Shibata, K. Tamura, A. Furuzawa, Y. Tawara, H. Kunieda and K.Yamashita / InFOCµS hard X-ray imaging telescope

121–129

Fiona A. Harrison, Finn E. Christensen, William Craig, Charles Hailey, Wayne Baumgartner, C. M. H. Chen, James Chonko, W. Rick Cook, Jason Koglin, Kristin-Kruse Madsen, Michael Pivavoroff, Steven Boggs and David Smith / Development of the HEFT and NuSTAR focusing telescopes

131–137

Giovanni Pareschi and Philippe Ferrando / The SIMBOL-X hard X-ray mission

139–149

Hubert Halloin and Pierre Bastie / Laue diffraction lenses for astrophysics: Theoretical concepts

151–170

Hubert Halloin / Laue diffraction lenses for astrophysics: From theory to experiments

171–184

N. V. Abrosimov / Mosaic and gradient SiGe single crystals for gamma ray Laue lenses

185–194

P. Courtois, K. H. Andersen and P. Bastie / Copper mosaic crystals for Laue lenses

195–200

Robert K. Smither, Khaliefeh Abu Saleem, Dante E. Roa, Mark A. Beno, Peter Von Ballmoos and Gerry K. Skinner / High diffraction efﬁciency, broadband, diffraction crystals for use in crystal diffraction lenses

201–210

Niels Lund / An “ESA-affordable” Laue-lens

211–217

Alessandro Pisa, Filippo Frontera, Gianluca Loffredo, Damiano Pellicciotta and Natalia Auricchio / Optical properties of Laue lenses for hard X-rays (>60 keV)

219–228

D. E. Roa, R. K. Smither, X. Zhang, K. Nie, Y. Y. Shieh, N. S. Ramsinghani, N. Milne, J. V. Kuo, J. L. Redpath, M. S. A. L. Al-Ghazi and P. Caligiuri / Development of a new photon diffraction imaging system for diagnostic nuclear medicine

229–239

F. Frontera, A. Pisa, G. Loffredo, D. Pellicciotta, V. Carassiti, F. Evangelisti, K. Andersen, P. Courtois, L. Amati, E. Caroli, T. Franceschini, G. Landini, S. Silvestri and J. Stephen / HAXTEL: A Laue lens telescope development project for a deep exploration of the hard X-ray sky (>60 keV)

241–251

Peter von Ballmoos, Hubert Halloin, Jean Evrard, Gerry Skinner, Nikolai Abrosimov, Jose Alvarez, Pierre Bastie, Bernard Hamelin, Margarida Hernanz, Pierre Jean, J¨urgen Kn¨odlseder and Bob Smither / CLAIRE: First light for a gamma-ray lens

253–267

N. Barri`ere, P. von Ballmoos, H. Halloin, N. Abrosimov, J. M. Alvarez, K. Andersen, P. Bastie, S. Boggs, P. Courtois, T. Courvoisier, M. Harris, M. Hernanz, J. Isern, P. Jean, J. Kn¨odlseder, G. Skinner, B. Smither, P. Ubertini, G. Vedrenne, G. Weidenspointner and C. Wunderer / MAX, a Laue diffraction lens for nuclear astrophysics

269–278

Craig Brown, Nicola Rando, Alexander Short, Aleksander Lyngvi and Tone Peacock / The gamma ray lens – an ESA technology reference study

279–288

G. K. Skinner / Gamma ray Fresnel lenses – why not?

289–298

John Krizmanic, Brian Morgan, Robert Streitmatter, Neil Gehrels, Keith Gendreau, Zaven Arzoumanian, Reza Ghodssi and Gerry Skinner / Development of ground-testable phase fresnel lenses in silicon

299–306

Laurent Koechlin, Denis Serre, Gerald K. Skinner, Peter Von Ballmoos and Thomas Crouzil / Multiwavelength focusing with the Sun as gravitational lens

307–315

Section III: Focal Plane Instrumentation Tadayuki Takahashi / A Si/CdTe Compton Camera for gamma-ray lens experiment

317–331

Ernst-Jan Buis, Marco Beijersbergen, Stefan Kraft, Alan Owens, Francesco Quarati, Sytze Brandenburg and Reint Ostendorf / New scintillators for focal plane detectors in gamma-ray missions

333–339

Ezio Caroli, Natalia Auricchio, Lorenzo Amati, Yuriy Bezsmolnyy, Carl Budtz-Jørgensen, Rui M. Curado da Silva, Filippo Frontera, Alessandro Pisa, Stefano Del Sordo, John B. Stephen and Giulio Ventura / A focal plane detector design for a wide-band Laue-lens telescope

341–351

Ezio Caroli, Rui M. Curado da Silva, Alessandro Pisa, John B. Stephen, Filippo Frontera, Matilde T. D. Castanheira and Stefano del Sordo / Polarisation measurements with a CdTe pixel array detector for Laue hard X-ray focusing telescopes

353–364

C. B. Wunderer, P. von Ballmoos, N. Barri`ere, S. E. Boggs, G. Weidenspointner and A. Zoglauer / Simulated performance of dedicated Ge-strip Compton telescopes as γ -lens focal plane instrumentation

365–373

G. Weidenspointner, C. B. Wunderer, N. Barri`ere, A. Zoglauer and P. von Ballmoos / Monte Carlo study of detector concepts for the MAX Laue lens gamma-ray telescope

375–386

Steven Boggs, Mark Bandstra, Jason Bowen, Wayne Coburn, Robert Lin, Cornelia Wunderer, Andreas Zoglauer, Mark Amman, Paul Luke, Pierre Jean and Peter von Ballmoos / Performance of the Nuclear Compton Telescope

387–394

Robert Andritschke, Andreas Zoglauer, Gottfried Kanbach, Peter F. Bloser and Florian Schopper / The Compton and pair creation telescope MEGA

395–403

Section IV: Ground Facilities and Flight Systems for Focusing Telescopes M. J. Freyberg, H. Br¨auninger, W. Burkert, G. D. Hartner, O. Citterio, F. Mazzoleni, G. Pareschi, D. Spiga, S. Romaine, P. Gorenstein and B. D. Ramsey / The MPE X-ray test facility PANTER: Calibration of hard X-ray (15–50 kev) optics

405–412

Gianluca Loffredo, Filippo Frontera, Damiano Pellicciotta, Alessandro Pisa, Vito Carassiti, Stefano Chiozzi, Federico Evangelisti, Luca Landi, Michele Melchiorri and Stefano Squerzanti / The Ferrara hard X-ray facility for testing/calibrating hard X-ray focusing telescopes

413–420

Rodolphe Cl´edassou and Philippe Ferrando / SIMBOL-X: An hard X-ray formation ﬂying mission

421–434

Emmanuel Hinglais (CNES) / Distributed space segment for high energy astrophysics: Similarities and specificites

435–445

Ph. Laporte, J. Evrard and A. Laurens / The CLAIRE gondola: Testing the ﬁrst gamma-ray lens on a stratospheric balloon

447–454

Xavier Leyre, Michel Sghedoni, Francis Arbusti, Primo Attina, Peter von Ballmoos / Recent advances and low cost concept for the gammaray lens project MAX

455–464

J. Borde, P. von Ballmoos and R. Soumagne / Small-sat platforms and formation ﬂying: An opportunity for the gamma ray telescope MAX

465–482

Paul Duchon / MAX: Formation ﬂying for nuclear astrophysics

483–495

John Krizmanic, Gerry Skinner and Neil Gehrels / Formation ﬂying for a Fresnel lens observatory mission

497–503

Exp Astron (2005) 20:1–2 DOI 10.1007/s10686-006-9073-y PREFACE

Preface P. von Ballmoos

C

Springer Science + Business Media B.V. 2006

Over the last decade, a small but growing community has been pursuing various techniques for the focusing of hard X-rays and gamma-rays. The workshop Focusing Telescopes in Nuclear Astrophysics provided a ﬁrst opportunity for this young “gamma-wave” community to meet, exchange technological know-how, and discuss scientiﬁc objectives and synergies. The workshop took place in Bonifacio, Corsica, September 12–15, 2005. It brought together sixty participants with different horizons, and with competence in a wide range of disciplinesbut with the common interest in ﬁnding alternative instrumental approaches for use in nuclear astrophysics. Participants from the high energy astrophysics community emphasized the extraordinary scientiﬁc potential of nuclear astrophysics for the study of the most powerful sources and the most violent events in the Universe. Their contributions are collected in the ﬁrst part of this volume and discuss science objectives on all levels: neutron stars, X-ray binaries, pulsars, novae, supernovae, AGN, blazars, cosmology . . . but also our sun! In order to achieve the ambitious scientiﬁc goals, experimental gamma-ray astronomy must ﬁnd new ways to improve the performance of its instruments, with better sensitivity being unquestionably the foremost requirement. In the second part of this volume, the evolving “gamma-wave” community examines the options for focusing optics for hard-X and soft gamma rays. A few years back, there was no way to focus gamma-rays; today we have many: grazing incident mirrors and multilayer coatings, Laue- and Fresnel-lenses; even an optic using the curvature of space-time is proposed. In more than twenty articles various aspects of the techniques are discussed, from the theoretical basis to the ambitious mission concepts for future space observatories. A particular emphasis is on the progress in R&D for the various techniques, on results from prototypes and on ﬁrst results obtained from stratospheric balloon ﬂights. The goal of improving instrument sensitivities by up to two orders of magnitude which is the main incentive for developing focusing telescopes, also drives the development of new detector technologies. One of the focal points of the workshop was the consideration

P. von Ballmoos Centre d’Etude Spatiale des Rayonnements, Toulouse, France e-mail: [email protected] Springer

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of detectors matching the ambitious objectives of gamma ray optics and their capability of taking maximum advantage of the concentrated signal ﬂux. In the third part of this volume, a number of innovative detector concepts for focusing telescopes are discussed. Besides offering high detection efﬁciencies, these focal plane instruments will provide imaging capabilities, perform high resolution spectroscopy and measure the polarization of the incident photons. The deﬂection of photons in focusing X/γ -ray optics is only by small angles. As a consequence, telescope systems have long focal lengths and require a new class of ﬂight systems and ground facilities. Part four of this volume is dedicated to the associated challenges. Facilities for testing hard X-ray focusing telescopes on the ground and techniques for testing using stratospheric balloons are presented. The space missions that seem best adapted for X/γ -ray optics involve “formation ﬂying” of two spacecraft. Photons are collected by an optics spacecraft and are focused onto a separate detector spacecraft. Formation ﬂying missions present a number of complex challenges for spacecraft engineering which are discussed in this volume. Eleven years have past since the workshop on imaging in high energy astronomy in Capri (1994), which itself followed by the same interval a similar meeting in Southampton (1983). Eleven years is also roughly the time separating launches of successive major space missions in nuclear astrophysics – HEAO-3 (1979), GRO (1991) and then INTEGRAL (2002). One of the foremost objectives of the Gamma Wave 05 workshop was to consider the next generation of instrumentation required for nuclear astrophysics and consider implementation approaches within National and European Space Science programs. In sunny Bonifacio the Gamma-Wave community expressed their wish that the eleven year cycle continue with the launch of a major focusing X/γ -ray mission on a 2013 horizon. On behalf of the local and scientiﬁc organizing committees, we acknowledge the generous contributions of ESA, CNES, ASTRIUM and ALCATEL, which allowed the organisation of the workshop and the publication of the present volume. We thank Dolores Granat, Eric Deleage and Nicolas Barri`ere for their tireless effort behind the scenes to ensure the success of this workshop. Many thanks to Gerry Skinner, who has attempted to provide a scientiﬁc conscience for the present volume, and to Sylvia Iviglia from Springer for shepherding its completion. Finally, we thank the participants of the Gamma-Wave 05 workshop for their dedication to this project, and look forward to the exciting promise of the next phase of nuclear astrophysics instrumentation. Toulouse, July 2006 PvB

Springer

Exp Astron (2005) 20:3–13 DOI 10.1007/s10686-006-9031-8 ORIGINAL ARTICLE

Prospects in space-based gamma-ray astronomy J. Kn¨odlseder

Received: 25 November 2005 / Accepted: 22 February 2006 C Springer Science + Business Media B.V. 2006

Abstract Observations of the gamma-ray sky reveal the most powerful sources and the most violent events in the Universe. While at lower wavebands the observed emission is generally dominated by thermal processes, the gamma-ray sky provides us with a view on the non-thermal Universe. Here particles are accelerated to extreme relativistic energies by mechanisms which are still poorly understood, and nuclear reactions are synthesizing the basic constituents of our world. Cosmic accelerators and cosmic explosions are the major science themes that are addressed in the gamma-ray regime. With the INTEGRAL observatory, ESA has provided a unique tool to the astronomical community revealing hundreds of sources, new classes of objects, extraordinary views of antimatter annihilation in our Galaxy, and ﬁngerprints of recent nucleosynthesis processes. While INTEGRAL provides the global overview over the soft gamma-ray sky, there is a growing need to perform deeper, more focused investigations of gamma-ray sources. In soft X-rays a comparable step was taken going from the Einstein and the EXOSAT satellites to the Chandra and XMM/Newton observatories. Technological advances in the past years in the domain of gamma-ray focusing using Laue diffraction and multilayer-coated mirror techniques have paved the way towards a gamma-ray mission, providing major improvements compared to past missions regarding sensitivity and angular resolution. Such a future GammaRay Imager will allow to study particle acceleration processes and explosion physics in unprecedented detail, providing essential clues on the innermost nature of the most violent and most energetic processes in the Universe.

Keywords Gamma-ray astronomy astronomy · Cosmic accelerators · Cosmic explosions

J. Kn¨odlseder () Centre d’Etude Spatiale des Rayonnements, 9, avenue du Colonel-Roche, B.P. 4346, 31028 Toulouse Cedex 4, France e-mail: [email protected] Springer

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1. Why gamma-ray astronomy? As introductory remark, it is worth emphasising some unique features of gamma-ray astronomy: the speciﬁc character of the emission processes, the diversity of the emission sites, and the penetrating nature of the emission. First, the emission process that leads to gamma-rays is in general very speciﬁc, and as such, is rarely observable in other wavebands. At gamma-ray energies, cosmic acceleration processes are dominant, while in the other wavebands thermal processes are generally at the origin of the emission. For example, electrons accelerated to relativistic energies radiate gamma-ray photons of all energies through electromagnetic interactions with nuclei, photons, or intense magnetic ﬁelds. Accelerated protons generate secondary particles through nuclear interactions, which may decay by emission of high-energy gamma-ray photons. At gamma-ray energies, nuclear deexcitations lead to a manifold of line features, while in the other wavebands, it is the bound electrons that lead to atomic or molecular transition lines. For example, the radioactive decay of tracer isotopes allows the study of nucleosynthesis processes that occur in the deep inner layers of stars. The interaction of high-energy nuclei with the gas of the interstellar medium produces a wealth of excitation lines that probe the composition and energy spectrum of the interacting particles. Finally, annihilation between electrons and positrons result in a unique signature at 511 keV that allows the study of antimatter in the Universe. Second, the sites of gamma-ray emission in the Universe are very diverse, and reach from the nearby Sun up to the distant Gamma-Ray Bursts and the cosmic gamma-ray background radiation. Cosmic acceleration takes place on all scales: locally in solar ﬂares, within our Galaxy (e.g. in compact binaries, pulsars, supernova remnants), and also in distant objects (such as active galactic nuclei or gamma-ray bursts). Cosmic explosions are another site of prominent gamma-ray emission. They produce a wealth of radioactive isotopes, are potential sources of antimatter, and accelerate particles to relativistic energies. Novae, supernovae and hypernovae are thus prime targets of gamma-ray astronomy. Third, gamma-rays are highly penetrating, allowing the study of otherwise obscured regions. Examples are regions of the galactic disk hidden by dense interstellar clouds, or the deeper, inner, zones of some celestial bodies, where the most fundamental emission processes are at work. New classes of sources become visible in the gamma-ray domain, that are invisible otherwise. In summary, gamma-ray astronomy provides a unique view of our Universe. It unveils speciﬁc emission processes, a large diversity of emission sites, and probes deeply into the otherwise obscured high-energy engines of our Universe. The gamma-ray Universe is the Universe of particle acceleration and nuclear physics, of cosmic explosions and non-thermal phenomena. Exploring the gamma-ray sky means exploring this unique face of our world, the face of the evolving violent Universe.

2. Cosmic accelerators 2.1. The link between accretion and ejection As a general rule, accretion in astrophysical systems is often accompanied by mass outﬂows, which in the high-energy domain take the form of (highly) relativistic jets. Accreting objects are therefore powerful particle accelerators, that can manifest on the galactic scale as Springer

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microquasars, or on the cosmological scale, as active galactic nuclei, such as Seyfert galaxies and Blazars. Although the phenomenon is relatively widespread, the jet formation process is still poorly understood. It is still unclear how the energy reservoir of an accreting system is transformed in an outﬂow of relativistic particles. Jets are not always persistent but often transient phenomena, and it is still not known what triggers the sporadic outbursts in accreting systems. Also, the collimation of the jets is poorly understood, and in general, the composition of the accelerated particle plasma is not known (electron-ion plasma, electron-positron pair plasma). Finally, the radiation processes that occur in jets are not well established. Observations in the gamma-ray domain are able to provide a number of clues to these questions. Gamma-rays probe the innermost regions of the accreting systems that are not accessible in other wavebands, providing the closest view to the accelerating engine. Time variability and polarisation studies provide important insights into the physical processes and the geometry that govern the acceleration site. The accelerated plasma may reveal its nature through characteristic nuclear and/or annihilation line features which may help to settle the question about the nature of the accelerated plasma.

2.2. The origin of galactic soft γ -ray emission Since decades, the nature of the galactic hard X-ray (>15 keV) emission has been one of the most challenging mysteries in the ﬁeld. The INTEGRAL imager IBIS has now ﬁnally solved this puzzle. At least 90% of the emission has been resolved into point sources, settling the debate about the origin of the emission (Lebrun et al., 2004) (c.f. Figure 1). At higher energies, say above ∼300 keV, the situation is less clear. In this domain, only a small fraction of the galactic emission has so far been resolved into point sources, and the nature of the bulk of the galactic emission is so far unexplained. That a new kind of object or emission mechanism should be at work in this domain is already suggested by the change of the slope of the galactic emission spectrum. While below ∼300 keV the spectrum can be explained by a superposition of Comptonisation spectra from individual point sources, the spectrum turns into a powerlaw above this energy, which is reminiscent of

Fig. 1 The hard X-ray sky resolved into individual point sources by the IBIS telescope aboard INTEGRAL Lebrun et al. (2004). Springer

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particle acceleration processes. Identifying the source of this particle acceleration process, i.e. identifying the origin of the galactic soft gamma-ray emission, is one of the major goals of a future European gamma-ray mission. One of the strategies to resolve this puzzle is to follow the successful road shown by INTEGRAL for the hard X-ray emission: trying to resolve the emission into individual point sources. Indeed, a number of galactic sources show powerlaw spectra in the gamma-ray band, such as supernova remnants, like the Crab nebula, or some of the black-hole binary systems, like Cyg X-1 (Mc Connell et al., 2000). Searching for the hard powerlaw emission tails in these objects is therefore a key objective for a future gamma-ray mission. 2.3. The origin of the soft γ -ray background After the achievements of XMM-Newton and Chandra, the origin of the cosmic X-ray background (CXB) is now basically solved for energies close to a few keV. However, whilst the CXB is ∼85% and 80% resolved in the 0.5–2 keV and 2–10 keV bands, respectively, it is only ∼50% resolved above ∼8 keV (Worsley et al., 2005). The situation is even worse in the hard X-ray and soft gamma-ray bands. Although about 20% of the sources detected in the second IBIS catalogue are of extragalactic nature (Bassani et al., 2006) they only account for ∼1% of the background emission seen in the 20–100 keV band, i.e. where the bulk of the energy density is found. Looking from another point of view, synthesis models, which are well established and tested against observational results, can be used to evaluate the integrated AGN contribution to the soft γ -ray background. Unfortunately, they lack some key information at high energies: the absorption distribution is currently biased against low column densities due to the lack of soft gamma-ray surveys, no AGN luminosity function is available above 10 keV nor has the input spectral shape of the different classes of AGN been ﬁrmly established at high energies. Furthermore, the integrated AGN contribution changes as a function of model input parameters. As an illustration, Figure 2 shows how different results can be obtained

Fig. 2 The 0.25–400 keV cosmic X-/γ −ray background spectrum ﬁtted with synthesis models (Comastri, 2004). None of the models provides a satisfactory ﬁt of the observations. Springer

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by varying the power law energy cut-off. A large region of this parameter space is virtually unexplored because we currently lack information on large AGN samples. Observations by BeppoSAX (Risaliti, 2002; Perola et al., 2002) of a handful of radio quiet sources, loosely locate this drop-off in the range 30–300 keV; furthermore these measurements give evidence for a variable cut-off energy and suggest that it may increase with increasing photon index (Perola et al., 2002). In radio loud sources the situation is even more complicated with some objects showing a power law break and others no cut-off up to the MeV region. In a couple of low luminosity AGN no cut-off is present up to 300–500 keV. The overall picture suggests some link with the absence (low energy cut-off) or presence (high energy cut-off) of jets in the various AGN types sampled, but the data are still too scarce for a good understanding of the processes involved. One method to tackle this issue is to measure the soft gamma-ray Spectra Energy Distribution (SED, which includes a power law continuum plus high energy cut-off as well as hard tails if present) in a sizeable fraction of AGN in order to determine average shapes in individual classes and so the nature of the radiation processes at the heart of all AGN. This would provide at the same time information for soft γ -ray background synthesis models. On the other hand, sensitive deep ﬁeld observations should be able to resolve the soft γ -ray background into individual sources, allowing for the ultimate identiﬁcation of the origin of the emission.

2.4. Particle acceleration in extreme B-ﬁelds The strong magnetic ﬁelds that occur at the surface of neutron stars in combination with their fast rotation make them to powerful electrodynamic particle accelerators, which may manifest as pulsars to the observer. Gamma-ray emitting pulsars can be divided into 3 classes: spindown powered pulsars, such as normal or millisecond pulsars, accretion powered pulsars, occurring in low-mass or high-mass binary systems, and magnetically powered pulsars, known as magentars. Despite the longstanding efforts in understanding the physics of spin-down powered pulsars, the site of the gamma-ray production within the magnetosphere (outer gap or polar cap) and the physical process at action (synchrotron emission, curvature radiation, inverse Compton scattering) remain undetermined. Although most of the pulsars are expected to reach their maximum luminosity in the MeV domain, the relatively weak photon ﬂuxes have only allowed the study of a handful of objects so far. Increasing the statistics will allow the study of the pulsar lightcurves over a much broader energy range than today, providing crucial clues on the acceleration physics of these objects. Before the launch of INTEGRAL, the class of anomalous X-ray pulsars (AXPs), suggested to form a sub-class of the magnetar population, were believed to exhibit very soft X-ray spectra. This picture, however, changed dramatically with the detection of AXPs in the soft gamma-ray band by INTEGRAL (Kuiper et al., 2004). In fact, above ∼10 keV a dramatic upturn is observed in the spectra which is expected to cumulate in the 100 keV – 1 MeV domain. The same is true for Soft Gamma-ray Repeaters (SGRs), as illustrated by the recent discovery of quiescent soft gamma-ray emission from SGR 1806-20 by INTEGRAL (Molkov et al., 2005) (c.f. Figure 3). The process that gives rise to the observed gamma-ray emission in still unknown. No high-energy cut-off has so far been observed in the spectra, yet upper limits in the MeV domain indicate that such a cut-off should be present. Determining this cut-off may provide important insights in the physical nature of the emission process, and in particular, about the role of QED effects, such as photon splitting, in the extreme magnetic ﬁeld that Springer

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Fig. 3 The quiescent energy spectrum of SGR 1806-20 (lower spectrum) and the summed spectrum of all detected bursts rescaled down by a factor of 1000 (upper spectrum) (Molkov et al., 2005).

occur in such objects. Strong polarisation is expected for the high-energy emission from these exotic objects, and polarisation measurements may reveal crucial to disentangle the nature of the emission process and the geometry of the emitting region. Complementary measurements of cyclotron features in the spectra provide the most direct measure of the magnetic ﬁeld strengths, complementing our knowledge of the physical parameters of the systems.

3. Cosmic explosions 3.1. Understanding type Ia supernovae Although hundreds of Type Ia supernovae are observed each year, and although their optical lightcurves and spectra are studied in great detail, the intimate nature of these events is still unknown. Following common wisdom, Type Ia supernovae are believed to arise in binary systems where matter is accreted from a normal star onto a white dwarf. Once the white dwarf exceeds the Chandrasekhar mass limit a thermonuclear runaway occurs that leads to its incineration and disruption. However, attempts to model the accretion process have so far failed to allow for sufﬁcient mass accretion that would push the white dwarf over its stability limit (Hillebrandt and Niemeyer, 2000). Even worse, there is no ﬁrm clue that Type Ia progenitors are indeed binary systems composed of a white dwarf and a normal star. Alternatively, the merging of two white dwarfs in a close binary system could also explain the observable Springer

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Fig. 4 Simulated gamma-ray spectrum of a Type Ia supernova (Gomez-Gomar et al., 1998).

features of Type Ia events (Livio and Riess, 2003). Finally, the explosion mechanism of the white dwarf is only poorly understood, principally due to the impossibility to reliably model the nuclear ﬂame propagation in such objects (Hillebrandt and Niemeyer, 2000). In view of all these uncertainties it seems more than surprising that Type Ia are widely considered as standard candles. In particular, it is this standard candle hypothesis that is the basis of one of the fundamental discoveries of the last decade: that the expansion of the Universe is currently accelerating (Riess et al., 1998). Although empirical corrections to the observed optical lightcurves seem to allow for some kind of standardisation, there is increasing evidence that Type Ia supernovae are not an homogeneous class of objects (Mannucci et al., 2005). Gamma-ray observation of Type Ia supernovae provide a new and unique view of these events. Nucleosynthetic products of the thermonuclear runaway lead to a rich spectrum of gamma-ray line and continuum emission that contains a wealth of information on the progenitor system, the explosion mechanism, the system conﬁguration, and its evolution (c.f. Figure 4). In particular, the radioactive decays of 56 Ni and 56 Co, which power the optical lightcurve which is so crucial for the cosmological interpretation of distant Type Ia events, can be directly observed in the gamma-ray domain, allowing to pinpoint the underlying progenitor and explosion scenario. The comparison of the gamma-ray to the optical lightcurve will provide direct information about energy recycling in the supernova envelope that will allow a physical (and not only empirical) calibration of Type Ia events as standard candles. In addition to line intensities and lightcurves, the shapes of the gamma-ray lines hold important information about the explosion dynamics and the matter stratiﬁcation in the system. Measuring the line shapes (and their time evolution) will allow to distinguish between Springer

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the different explosion scenarios, ultimately revealing the mechanism that creates these most violent events in the Universe (Gomez-Gomar et al., 1998). 3.2. Understanding core-collapse explosions Gamma-ray line and continuum observations address some of the most fundamental questions of core-collapse supernovae: how and where the large neutrino ﬂuxes couple to the stellar ejecta; how asymmetric the explosions are, including whether jets form; and what are quantitative nucleosynthesis yields from both static and explosive burning processes? The ejected mass of 44 Ti, which is produced in the innermost ejecta and fallback matter that experiences the alpha-rich freezeout of nuclear statistical equilibrium, can be measured to a precision of several percent in SN 1987A. Along with other isotopic yields already known, this will provide an unprecedented constraint on models of that event. 44 Ti can also be measured and mapped, in angle and radial velocity, in several historical galactic supernova remnants. These measurements will help clarify the ejection dynamics, including how common jets initiated by the core collapse are. Wide-ﬁeld gamma-ray instruments have shown the global diffuse emission from long-lived isotopes 26 Al and 60 Fe, illustrating clearly ongoing galactic nucleosynthesis. A necessary complement to these are high-sensitivity measurements of the yields of these isotopes from individual supernovae. A future European gamma-ray mission should determine these yields, and map the line emission across several nearby supernova remnants, shedding further light on the ejection dynamics. It is also likely that the nucleosynthesis of these isotopes in hydrostatic burning phases will be revealed by observations of individual nearby massive stars with high mass-loss rates. For rare nearby supernovae, within a few Mpc, we will be given a glimpse of nucleosynthesis and dynamics from short-lived isotopes 56 Ni, and 57 Ni, as was the case for SN 1987A in the LMC. In that event we saw that a few percent of the core radioactivity was somehow transported to low-optical depth regions, perhaps surprising mostly receding from us, but there could be quite some variety, especially if jets or other extensive mixing mechanisms are ubiquitous. 3.3. Unveiling the origin of galactic positrons The unprecedented imaging and spectroscopy capabilities of the spectrometer SPI aboard INTEGRAL have now provided for the ﬁrst time an image of the distribution of 511 keV electron positron annihilation all over the sky (Kn¨odlseder et al., 2005) (c.f. Figure 5). The outcome of this survey is astonishing: 511 keV line emission is only seen towards the bulge region of our Galaxy, while the rest of the sky remains surprisingly dark. Only a weak glim of 511 keV emission is perceptible from the disk of the Galaxy, much less than expected from stellar populations following the global mass distribution of the Galaxy. In other words, positron annihilation seems to be greatly enhanced in the bulge with respect to the disk of the Galaxy. A detailed analysis of the 511 keV line shape measured by SPI has also provided interesting insights into the annihilation physics (Churazov et al., 2005). At least two components have been identiﬁed, indicating that positron annihilation takes place in a partially ionised medium. This clearly demonstrated that precise 511 keV line shape measurements provide important insights into the distribution of the various phases of the interstellar medium (ISM). While INTEGRAL has set the global picture of galactic positron annihilation, high angular resolution mapping of the galactic bulge region is required to shed light on the still Springer

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Fig. 5 First all-sky map of 511 keV electron-positron annihilation radiation as observed by the SPI telescope aboard INTEGRAL (Kn¨odlseder et al., 2005).

mysterious source of positrons. So far, no individual source of positron emission could have been identiﬁed, primarily due to the expected low levels of 511 keV line ﬂuxes. An instrument with sufﬁciently good sensitivity and angular resolution should be able to pinpoint the origin of the positrons, by providing detailed maps of the central bulge region of the Galaxy. With additional ﬁne spectroscopic capabilities, comparable to that achieved by the germanium detectors onboard the SPI telescope, the spatial variations of the 511 keV line shape will allow to draw an unprecedented picture of the distribution of the various ISM phases in the inner regions of our Galaxy. Thus, with the next generation gamma-ray telescope, galactic positrons will be exploited as a messenger from the mysterious antimatter source in the Milky-Way, as well as a tracer to probe the conditions of the ISM that are difﬁcultly to measure by other means.

4. Mission requirements The major mission requirement for the future European gamma-ray mission is sensitivity. Many interesting scientiﬁc questions are in a domain where photons are rare (say 10−7 ph cm−2 s−1 ), and therefore large collecting areas are needed to perform measurements in a reasonable amount of time. It is clear that a signiﬁcant sensitivity leap is required, say 50–100 times more sensitive than current instruments, if the above listed scientiﬁc questions should be addressed. With such a sensitivity leap, the expected number of observable sources would be large, implying the need for good angular resolution to avoid source confusion in crowded regions, such as for example the galactic centre. Also, it is desirable to have an angular resolution comparable to that at other wavebands, to allow for source identiﬁcation and hence multi wavelength studies. As mentioned previously, gamma-ray emission may be substantially polarised due to the non-thermal nature of the underlying emission processes. Studying not only the intensity but also the polarisation of the emission would add a new powerful scientiﬁc dimension to the observations. Such measurements would allow to discriminate between the different plausible emission processes at work, and would allow to constrain the geometry of the emission sites. Taking all these considerations into account, the following mission requirements derive (c.f. Table 1). The energy band should cover the soft gamma-ray band, with coverage down Springer

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Table 1 Mission requirements for the future European gamma-ray mission (sensitivities are for 106 seconds at 3σ detection signiﬁcance)

Parameter

Requirement

Energy band Continuum sensitivity Narrow line sensitivity Energy resolution Field of view Angular resolution Polarisation

50 keV – 2 MeV 10−8 ph cm−2 s−1 keV−1 5 × 10−7 ph cm−2 s−1 2 keV at 600 keV 30 arcmin arcmin 1% at 10 mCrab

to the hard X-ray band (to overlap with future X-ray observatories), and coverage of the major gamma-ray lines of astrophysical interest. A real sensitivity leap should be achieved, typical by a factor of 50–100 with respect to existing gamma-ray instrumentation. For highresolution gamma-ray line spectroscopy a good energy resolution is desirable to exploit the full potential of line proﬁle studies. A reasonably sized ﬁeld-of-view together with arcmin angular resolution should allow the imaging of ﬁeld populations of gamma-ray sources in a single observation. Finally, good polarisation capabilities, at the percent level for strong sources, are required to exploit this additional observable. Can these mission requirements be reached within the 2015–2025 time frame? We are convinced that the answer is yes. How can these mission requirements be reached? We think that the best solution is the implementation of a broad-band gamma-ray lens telescope based on the principle of Laue diffraction of gamma-rays in mosaic crystals (Von Ballmoos et al., 2004; Halloin et al., 2004; De Chiara et al., 2000). The Laue lens may eventually be complemented by a coded mask telescope or a multilayer-coated mirror telescope in order to achieve the hard X-ray coverage. The focal length of such a system would lie between a few tens and a few hundreds metres, requiring the technology of satellite formation ﬂying. We note that such a gamma-ray lens telescope is currently under study at the French space agency CNES (project MAX (Von Ballmoos et al., 2004)) and at the ESA Science Payload & Advanced Concepts Ofﬁce (project Gamma-Ray Lens), which both conﬁrm the feasibility of such a scenario. We therefore believe that a gamma-ray lens telescope in formation ﬂight conﬁguration provides the most promising instrumental concept allowing advances in the ﬁeld of space-based gamma-ray astronomy. The precise design of the gamma-ray lens telescope is currently under discussion (see http://gri.rm.iasf.cnr.it/). The artists view in Figure 6 gives an idea how the future Gamma-Ray Imager mission may look like. In this example, the lens spacecraft is composed of concentric rings of crystals, where each ring is focusing a speciﬁc narrow energy band on the (same) focal spot on the Fig. 6 Artists view of the Gamma-Ray Imager. A Laue lens, situated on the left spacecraft, is focusing gamma-rays onto a small detector, situated on the right spacecraft. Both spacecrafts are in formation ﬂight with a typical focal length between a few tens and a few hundreds metres.

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detector spacecraft. Higher energies show smaller diffraction angles and therefore are situated closer to the optical axis (inner rings). Conversely, lower energies show larger diffraction angles and therefore are situated on the outer rings. The lowest energies may require radial distances from the optical axis that exceed the available space in launcher fairings, therefore deployable lens petals may eventually be employed.

5. Conclusions The gamma-ray band presents a unique astronomical window that allows the study of the most energetic and most violent phenomena in our Universe. With ESA’s INTEGRAL observatory, an unprecedented global survey of the soft gamma-ray sky is currently performed, revealing hundreds of sources of different kinds, new classes of objects, extraordinary views of antimatter annihilation in our Galaxy, and ﬁngerprints of recent nucleosynthesis processes. While INTEGRAL provides the longly awaited global overview over the soft gamma-ray sky, there is a growing need to perform deeper, more focused investigations of gamma-ray sources, comparable to the step that has been taken in X-rays by going from the EINSTEIN satellite to the more focused XMM-Newton observatory. Technological advances in the past years in the domain of gamma-ray focusing using Laue diffraction techniques have paved the way towards a future European gamma-ray mission, that will outreach past missions by large factors in sensitivity and angular resolution. Such a future Gamma-Ray Imager will allow to study particle acceleration processes and explosion physics in unprecedented depth, providing essential clues on the intimate nature of the most violent and most energetic processes in the Universe.

References Bassani, L., et al.: ApJ 636, 65 (2006) Churazov, E., Sunyaev, R., Sazonov, S., et al.: MNRAS 357, 1377 (2005) Comastri: in: R. Maiolino and R. Mujica (eds.), Proceedings of ‘Multiwavelength AGN surveys’ (Cozumel, December 8–12 2003), (astro-ph/0406031) (2004) De Chiara, P., et al.: Proc. of SPIE/ESO Astronomical Telescopes and Instrumentation ICM, 27–31 March 2000 (2000) Gomez-Gomar, J., et al.: MNRAS 295, 1 (1998) Halloin, H., von Ballmoos, P., Evrard, J., et al.: SPIE 5168, 471 (2004) Hillebrandt, W., Niemeyer, J.C.: ARAA 38, 191 (2000) Kn¨odlseder, J., Jean, P., Lonjou, V., et al.: A&A 441, 513 (2005) Kuiper, L., Hermsen, W., Mendez, M.: ApJ 613, 1173 (2004) Lebrun, F., et al.: Nature 428, 293 (2004) Livio, M., Riess, A.G.: ApJ 594, L93 (2003) Mannucci, F., Della Valle, M., Panagia, N., et al.: A&A 433, 807 (2005) McConnell, M.L., Bennett, K., Bloemen, H., et al.: in: M.L. McConnell & J.M. Ryan (eds.), Proc. 5th Compton Symposium, AIP 510, 114 (2000) Molkov, S., Hurley, K., Sunyaev, R., et al.: A&A 433, L13 (2005) Perola, G.C., et al.: A&A 389, 802 (2002) Riess, A.G., Filippenko, A.V., Challis, P., et al.: AJ 116, 1009 (1998) Risaliti, G.: A&A 386, 379 (2002) Von Ballmoos, P., Halloin, H., Paul, J., et al.: Proc. 5th INTEGRAL Workshop, Munich 16–20 February 2004, ESA SP-552, 747 (2004) Worsley, M.A., et al.: MNRAS 357, 1281 (2005)

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Exp Astron (2005) 20:15–22 DOI 10.1007/s10686-006-9039-0 ORIGINAL ARTICLE

Annihilation of positrons in the Galaxy S. Sazonov · E. Churazov · R. Sunyaev · M. Revnivtsev

Received: 17 January 2006 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract Observations of electron-positron annihilation radiation from the Galactic Center region with the SPI instrument aboard INTEGRAL are summarized. The measured width of the 511 keV line and inferred fraction of positrons annihilating through positronium formation are consistent with the annihilation taking place in the warm ISM phase, although combinations of several ISM phases are also allowed by the data. The spatial distribution of 511 keV emission suggests that positron sources are concentrated toward the Galactic bulge and avoid the Galactic disk. Keywords Galaxy: Center . Gamma rays: Observations . ISM: General

1. Introduction The electron–positron annihilation line at 511 keV is the brightest line in the electromagnetic spectrum of the Galaxy at energies above 10 keV. It was discovered during balloon ﬂights more than 30 years ago as emission at roughly ∼476 keV from the general direction of the Galactic Center (GC) [6], and later clearly identiﬁed as a narrow e− − e+ annihilation line at 511 keV in observations by high-resolution germanium detectors [8]. Although the Galactic annihilation radiation has since then been observed by many experiments, its origin remains unclear. Several mechanisms of positron production have been proposed, including: – Radioactive β + decay of unstable isotopes, e.g. 26 Al or 56 Co, produced in supernovae or novae – Decay of π + mesons produced by interaction of cosmic rays with the ISM

S. Sazonov · E. Churazov · R. Sunyaev · M. Revnivtsev Max-Planck-Institut f¨ur Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching,Germany S. Sazonov () Space Research Institute, Profsoyuznaya 84/32, 117997 Moscow, Russia e-mail: [email protected] Springer

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– Generation of e− − e+ pairs by interaction of high-energy photons or in strong magnetic ﬁelds near black holes or radiopulsars – Annihilation of dark matter particles Although not complete, this list demonstrates the very broad range of possible mechanisms, from widely accepted (nucleosynthesis in supernovae) to more exotic (dark matter annihilation). To ﬁnd out the origin of the Galactic annihilation radiation it is crucial to (a) compare its spatial distribution with that of possible positron sources and (b) obtain constraints on the properties of the annihilation medium from the observed annihilation spectrum. The INTEGRAL observatiory with its high-resolution spectrometer SPI is designed to pursue these goals.

2. Observations and data analysis INTEGRAL is the ESA’s project with participation of Russia and the USA. The SPI instrument (Vedrenne et al., 2003) consists of 19 Ge crystals, providing energy resolution ∼2 keV near 511 keV. A 3-cm thick tungsten coded mask located 1.7 m above the detector modulates the incoming ﬂux. The ﬁeld of view is ∼16◦ -radius. We analyzed observations from February–November 2003, with a total exposure of 3.9 Ms [2]. The absolute energy scale was for each observation calibrated to better than 10 eV near 511 keV using a set of background lines (71 Ge at 198.4 keV, 69 Zn at 438.6 keV, 69 Ge at 584.5 keV, and 69 Ge at 882.5 keV). The energy resolution at 511 keV was found to be 2.1 keV (FWHM) by interpolating the observed widths of two bracketing lines, 438.6 keV and 584.5 keV. Since the instrument background contribution to the 511 keV line exceeds the useful signal from the GC region by 50–100 times, it is necessary to predict the background to better than 1 percent accuracy. To construct a model of background spectrum we used observations of the sky >30◦ away from the GC, with a total exposure of 3.7 Ms. 2.1. Galaxy map in the 511 keV line Figure 1 shows the surface brightness map of the Galaxy in the 511 keV line. By construction, only large-scale structure exceeding the size of the instrument’s FOV has been retained on this map, while any small-scale structure is strongly suppressed. Nevertheless, the global pattern of annihilation radiation is evident: the central region of the Galaxy is a powerful source of 511 keV radiation, while there is no statistically signiﬁcant annihilation signal outside this region. One can obtain better constraints on the surface brightness distribution by specifying a model distribution with several free parameters, convolving it with the angular response of the instrument, and comparing the outcome with the measured distribution. In the simplest model, the surface brightness is described by a two-dimensional Gaussian around the GC. A more ﬂexible model includes a constant component. The best agreement with the data is achieved for a Gaussian with FWHM = 6◦ . The inferred ﬂux is ∼7.6 × 10−4 phot/s/cm2 and ∼10−3 phot/s/cm2 for the model with and without a constant component, respectively. This ﬂux difference indicates that the true spatial distribution may be more complex than assumed in these simple models. Using more complicated models [7, 10] of 511 keV surface brightness distribution, in particular including components associated with the Galactic disk and bulge, leads to qualitatively the same results – the ﬂux of the central component (∼10−3 phot/s/cm2 ) is much higher than that of the disk one, unless the disk thickness exceeds a few ten degrees. Springer

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Fig. 1 Surface brightness distribution of 511 keV emission in Galactic coordinates. The effective angular resolution of the map is ∼15◦ . The apparent structure outside the central ∼25◦ region is not statistically signiﬁcant

2.2. Annihilation spectrum Figure 2 shows the measured spectrum near 511 keV. It is well ﬁt by a model consisting of a Gaussian line and a 3-photon (ortho-positronium) annihilation continuum. The ﬂux ratio of these components yields the fraction of annihilations proceeding through positronium formation: FPS =

2 , 1.5 + 2.25(F2γ /F3γ )

where F2γ and F3γ are the ﬂux in the line and in the 3-photon continuum, respectively. This expression accounts for the fact that ortho- and parapositronium are produced in 3:1 proportion and generate 3 and 2 photons, respectively. Table 1 summarized the results of our spectral analysis.

3. Constraints on the ISM parameters The two measured quantities, the line width and the ﬂux ratio of the line and 3-photon continuum, place constraints on the temperature and ionization degree of the annihilation Table 1 Best-ﬁt parameters of the annihilation spectrum in the energy range 450–550 keV. The quoted uncertainties are 1σ for a single parameter of interest. Adapted from [2]

Parameter

Value and uncertainty

E, keV FWHM, keV F2γ 10−4 phot s−1 cm−2 F3γ 10−4 phot s−1 cm−2 F3γ /F2γ FP S χ2 (d.o.f.)

510.954 [510.88–511.03] 2.37 [2.12–2.62] 7.16 ± 0.36 26.1 ± 5.7 3.65 ± 0.82 0.94 ± 0.06 192.7 (193) Springer

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Fig. 2 Spectrum of the GC annihilation radiation measured by INTEGRAL/SPI. The curves show the contributions of the 511 keV line and 3-photon continuum (not convolved with the energy response of the instrument)

medium. Using a Monte-Carlo code we simulated the formation of the annihilation spectrum in a pure hydrogen, dust-free plasma. The positrons are assumed to be born hot (with an energy higher than several hundred keV), then decelerate due to Coulomb losses in an ionized plasma or due to photoionization and atom excitation in a neutral gas, and eventually thermalize with the ambient medium. After the positron energy falls below several eV, charge exchange with neutral atoms, radiative recombination or direct annihilation with free or bound electrons occurs [1]. The predicted annihilation line has a non-Gaussian shape and contains a broad and a narrow components. In Figure 3 the effective line width and positronium fraction are shown as functions of temperature and ionization degree. These theoretical curves are compared with the constraints on the effective line width and positronium fraction provided by INTEGRAL observations. There are two families of theoretical curves. One regime corresponds to a gas with temperature below ∼6,000 K. In a cold and neutral medium about 94% of positrons form positronium in ﬂight. The remaining 6% fall below the threshold for positronium formation (6.8 eV) and then annihilate with bound electrons, forming a narrow line (FWHM = 1.7 keV, [4]. The effective width of the line arising from in-ﬂight annihilation through positronium formation is 5.3 keV, and that of the net line (sum of the broad and narrow components) is ∼4.6 keV. If the ionization degree exceeds ∼10−3 , Coulomb losses start to play an important role, decreasing the fraction of positrons forming positronium in ﬂight. For positrons falling below 6.8 eV, three processes are important: radiative recombination with free electrons and annihilation with free and bound electrons. For an ionization degree ∼10−2 and temeperatures ∼1,000 K, annihilation with bound electrons leads to a decrease of the net positronium fraction to 80–90 percent. If the ionization degree exceeds several per cent, only radiative recombination and annihilation with free electrons Springer

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Fig. 3 Positronium fraction vs. effective width of the 511 keV line for different temperatures and ionization degrees of the medium. There are two groups of theoretical curves: low-temperature (T < 5,000 K, dotted lines), and high-temperature (T > 7,000 K, solid lines). The temperature is ﬁxed for each curve and the ionization degree varies from 0 to 1 along the curves. For the low-temperature curves and for the 8,000 K one, an ionization degree of 0.01 is indicated by empty squares, and 0.1 by dark squares. Each high-temperature curve has two regimes: thin (thick) lines correspond to the ionization degrees lower (higher) than expected for collision dominated plasma. The dashed line shows the prediction for a fully ionized plasma. The rectangle represents the range of parameter values allowed by INTEGRAL data. Adapted from [2]

are important, and both the positronium fraction and line width approach the values expected for a fully ionized plasma. The second family of curves corresponds to temperatures above 7,000 K. In this regime, thermalized positrons can form positronium by charge exchange with hydrogen atoms. This process dominates over radiative recombination and direct annihilation if the plasma is not strongly ionized. The positronium fraction approaches unity. Only for a signiﬁcantly ionized plasma (∼6–10 percent) at T ≥ 8,000 K does annihilation with free electrons become important and the positronium fraction decreases with increasing ionization degree. According to the standard model [9] there are several abundant ISM phases: hot (T > a few 105 K) ionized, warm (T ∼ 8,000 K), and cold (T < 100 K) neutral. It is clear from Figure 3 that the hot phase cannot provide a dominant contribution to the observed annihilation spectrum, since the width of the line would be too large (e.g. ∼11 keV for T = 106 K, Cranell et al., 1976) while the positronium fraction too low. A similar conclusion can be drawn with respect to the cold, neutral ISM phase. In this case, the expected positronium fraction is consistent with the observed one but the expected line width (∼4.5 keV) is too large. The line width can be reduced by raising the ionization degree above 10−2 , i.e. much higher than is typical of molecular and cold HI clouds, making such a solution unlikely. Springer

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Fig. 4 Expected annihilation spectrum for an ISM with T = 8, 000 K and ionization degree of 0.1 (thick solid line). Separately shown are the contributions of the 3-photon continuum (dotted), in-ﬂight annihilation line (short-dashed), annihilation through para-positronium formation upon thermalization (thin solid), and direct annihilation of thermalized positrons (long-dashed). Adapted from [2]

On the other hand, in the warm (T ∼ 8,000–10,000 K) ISM phase, the ionization degree can vary from less than 0.1 to more than 0.8. This phase alone can therefore explain the observed line width and positronium fraction. The required ionization degree is several per cent. This conclusion is in qualitative agreement with early observations of the Galactic annihilation radiation [1]. The spectrum predicted for the annihilation in a plasma with temperature 8,000 K and ionization degree 0.1 is shown in Figure 4. This spectrum is consistent with the INTEGRAL data. Although the warm ISM model can reproduce the observations, this does not rule out more complicated solutions in which annihilation takes place in several ISM phases. For example, the observations can be explained by a combination of the cold and warm ISM phases in comparable proportions (see [2, 5]).

4. Discussion INTEGRAL has enabled the most accurate to date measurement of the spectrum of positron annihilation radiation from the GC region. The surface brightness of annihilation radiation is high in the central 5–10 degrees of the Galaxy and low outside this region. The total ﬂux from the GC region is ∼10−3 phot/s/cm2 , with a signiﬁcant uncertainty due to uncertainty in the spatial distribution of the radiation. Assuming a distance of 8.5 kpc to the annihilation site and taking into account that the fraction of annihilations occuring through positronium formation is close to unity, the observed ﬂux implies a rate of ∼2 × 1043 positron annihilations per second in the Galaxy. The Springer

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corresponding luminosity is L e+ ∼1.6 × 1037 erg/s. This imposes strong energetic constraints on the mechanisms of positron production. For an initial positron Lorentz-factor γ the minimum energy supply is γ L e+ . If positrons are generated by more energetic (or massive) particles, the minimum power required to produce the necessary number of positrons can be estimated as (E o /m e c2 )L e+ , where E 0 is the initial energy of the particles. For example, if positrons are generated by cosmic rays (through π + formation), the required energy supply is 3 × 273 × L e+ ∼1040 erg/s (this takes into account that π − and π 0 mesons are also produced). The decay of π 0 mesons should also lead to gamma radiation at energies 50–100 MeV with a luminosity ∼3 × 1039 erg/s. The Galactic disk produces less annihilation ﬂux than the GC region [7, 10], although the ratio of the two luminosities is a model-dependent quantity and in paricular strongly depends on the thickness of the disk component. The energy of the annihilation line coincides with the rest energy of electrons/positrons: E/m e c2 = 0.99991 ± 0.00015, implying that the average radial velocity of the annihilation medium relative to the Earth is less than 44 km/s. The observed width of the annihilation line implies that the velocity dispersion in the annihilation medium is less than 800 km/s. The combination of the observed line width (2.37 ± 0.25 keV) and positronium fraction (0.94 ± 0.06) can be explained by an annihilation in the warm ISM phase, with T ∼ 8,000 K and ionization degree ∼0.1. Annihilation in neither the cold (T ≤ 103 K) nor hot (T ≥ 105 K) ISM phase is consistent with the observations. A combination of several ISM phases is also allowed by the data. The limit on the fraction of annihilations occuring in a very hot (T ≥ 106 K) ISM is < 8%. We note however that positrons injected into the hot ISM can live long enough to (a) leave the Galaxy or (b) propagate into a denser ISM phase to annihilate there. Therefore, the inferred low fraction of annihilations taking place in the hot ISM phase does not necessarily imply that positrions are not produced in that phase. The above characteristics witness against a positron origin associated with Type 2 supernovae or massive stars, since these classes of object are concentrated toward the Galactic disk rather than the bulge. A positron origin due to interaction of cosmic rays with the ISM is also unlikely, in particular due to energetic considerations. The INTEGRAL data strongly favor bulgedominated populations of positron sources, such as Type la supernovae, lowmass X-ray binaries or dark matter. The continuing INTEGRAL observations will provide more stringent limits on the surface brightness distribution and spectral variations of the annihilation radiation along the Galactic plane and across it, allowing one to considerably narrow the range of physical processes responsible for positron production in the Galaxy.

References 1. Bussard, R.W. et al.: The annihilation of galactic positrons. ApJ 228, 928 (1979) 2. Churazov, E. et al.: Positron annihilation spectrum from the Galactic Centre region observed by SPI/INTEGRAL. MNRAS 357, 1377 (2005) 3. Crannell, C.J. et al.: Formation of the 0.511 MeV line in solar ﬂares. ApJ 210, 582 (1976) 4. Iwata, K., Greaves, R.G., Surko, C.M.: γ -ray spectra from positron annihilation on atoms and molecules, PhRvA 55, 3586 (1997) 5. Jean, P. et al.: Spectral analysis of the Galactic e+ − e− annihilation emission. A& A 445, 579 (2006) 6. Johnson, W.N. et al.: The spectrum of low-energy gamma radiation from the Galactic-Center region. ApJ 172, L1 (1972) 7. Kn¨odlseder, J. et al.: The all-sky distribution of 511 keV electron-positron annihilation emission. A& A 441, 513 (2005) 8. Leventhal, M. et al.: Detection of 511 keV positron annihilation radiation from the galactic center direction. ApJ 225, L11 (1978) Springer

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9. McKee, C.F., Ostriker, J.P.: A theory of the interstellar medium – three components regulated by supernova explosions in an inhomogeneous substrate. ApJ 218, 148 (1977) 10. Teegarden, B.J. et al.: INTEGRAL SPI limits on electron – positron annihilation radiation from the Galactic plane. ApJ 621, 296 (2005) 11. Vedrenne, G. et al.: SPI: The spectrometer aboard INTEGRAL. A& A 411, L63 (2003)

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Exp Astron (2005) 20:23–30 DOI 10.1007/s10686-006-9053-2 ORIGINAL ARTICLE

Prospects and requirements for measurements of extragalactic γ -ray lines Richard E. Grifﬁths

Received: 16 January 2006 / Accepted: 6 June 2006 C Springer Science + Business Media B.V. 2006

Abstract A brief summary is presented of requirements for the measurements of extragalactic γ -ray lines. The electron-positron annihilation line at 511 keV represents the best prospect, and although this line is greatly broadened in active galactic nuclei, a narrow line should be present in clusters of galaxies and radio lobes as a result of prior AGN activity. The strongest ﬂuxes should be of the order of 10−4 photons cm−2 s−1 from the closest extended sources. Keywords Extragalactic . Gamma-rays . AGN . Clusters of galaxies

1. Introduction The status of γ -ray astronomy today is quite similar to the situation in X-ray astronomy in the early to mid-1970’s following the collimated rocket experiments and the early sky survey satellites UHURU, Ariel V and EXOSAT, i.e. the X-ray astronomy era before the advent of focussing X-ray optics. Before the launch of INTEGRAL, about 400 high-energy X-ray sources were known from the previous experiments such as COS-B and the Compton Gamma-Ray Observatory carrying COMPTEL and BATSE. These all-sky or Galactic plane γ -ray experiments have located the strongest γ -ray sources to a typical precision of about a degree. Source identiﬁcations have generally depended on correlated detections in the energy range of 10–100 keV (the INTEGRAL reference catalogue – see Figure 1, from Ebisawa et al. [7]), where the corresponding detection at lower energy with X-ray telescopes has resulted in optical identiﬁcation. These γ -ray missions have not had the advantage of focussing and have therefore operated in the background-limited regime, with very little spectroscopy. With such missions, the sensitivity increases as the square root of the aperture, because the detector size is comparably large. The development of future missions of this kind is thus completely inappropriate – there cannot be order-of-magnitude improvements in sensitivity

R. E. Grifﬁths Carnegie Mellon University e-mail: grifﬁ[email protected] Springer

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Fig. 1 INTEGRAL reference catalog [7]

by pursuing such techniques and spectroscopic studies would stagnate. The development of gamma-ray astronomy can only proceed by following the lead of X-ray astronomy, and for the same reasons. In order for γ -ray astronomy to ﬂourish, especially in extragalactic work, methods of focussing or concentrating γ -rays need to be developed, so that background is drastically reduced even if the experiments remain background-limited for most targets. This reduction in background will mean that gamma-ray astronomy will ﬁnally be opened up for spectroscopic studies. Considerable progress in this direction has already been made with non-focussing instruments, and these developments will be the starting point for the science requirements summarized below. The primary targets for future γ -ray astronomy payloads are thus already generally known from the large area surveys, including the BAT instrument on the Swift satellite, or they are otherwise Targets of Opportunity within known classes of objects such as SuperNovae (SN) and Gamma Ray Bursters (GRB). With the sensitivities of previous experiments, the requirements below will show that exposure times would need to be very long (typically 106 –107 s) in order to conduct any signiﬁcant astrophysics, e.g. to search for and measure nuclear lines rather than just object detection. Measurements of line strengths are needed for comparison with astrophysical models, so that the lines need to be detected at high signiﬁcance (at least 5σ ) rather than just a marginal detection. Further, the sensitivities of future instruments need to be such that variability in the nuclear lines from transient objects (novae, supernovae and γ -ray bursts) can be observed – this implies that the required sensitivity to line ﬂux needs to be reached within a typical exposure time of 105 s, rather than 106 or 107 s. These are compelling arguments in favour of a pointed, focussing mission and an argument which eliminates future surveys of large sky areas with limited sensitivity. Observations with the Integral satellite have now set the stage for future requirements on nuclear line spectroscopy in the high energy X-ray region and at gamma-ray energies. These observations are summarised in the Integral papers collected in a special issue of Astronomy & Astrophysics (INTEGRAL Special Issue [12]). The source classes with potential γ -ray lines are as follows: (i) supernovae, especially Type Ia, (ii) galactic novae and X-ray bursters, (iii) microquasars, (iv) Galactic X-ray binaries, (v) Galactic Center, (vi) Active Galactic Nuclei (AGN), (vii) Springer

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Clusters of Galaxies, (viii) Gamma-Ray Bursters, and (ix) GRB remnants. In this paper, the expected line ﬂuxes will be reviewed for extragalactic objects, especially AGN and clusters of galaxies. 2. Extragalactic supernovae Ia For a detailed review of the γ -ray lines predicted from Type Ia supernovae, see the paper by Leising (this volume). For the availability of at least one target at all times, the requirement is to reach SN Ia at distances of 50–100 Mpc (Cappellaro and Turatto [5]), because there are about 25 SNIa’s within 100 Mpc per year, each brighter than Vmag = 16 so that they will be found with the planned large-area synoptic sky surveys. Recent estimates of the rates of SN Ia have been made by Scannapieco and Bildsten [21] and Mannucci et al. [17]. The predicted absolute line ﬂuxes have been calculated by Hoeﬂich as a function of time following the explosion. For a SNIa the expected line ﬂux in 56 N i 158keV at 20 days past onset is φ(56 N i 158keV ) = 10−2 /D 2

ph cm−2 s−1

where distance D is in Mpc. The required sensitivity to reach objects at 100 Mpc is thus better than 10−7 and approaching 10−8 ph cm−2 s−1 in this line, for integration periods not exceeding 1 day (so that the decay can be followed). Similarly, at 70 days past onset φ(56 Co847keV ) = 5 × 10−3 /D 2

ph cm−2 s−1

Relative to the peak visual magnitude m V , log(φ(56 Co847keV ) × 104 ) = 0.4[10.9 − m V ] so that for m V ∼ 16, φ(56 Co847keV ) ∼ 10−6 ph cm−2 s−1 . A sensitivity of 10−7 ph cm−2 s−1 would mean that a SNIa at V mag. 18 would have detectable nuclear line ﬂux. The astrophysics resulting from line detection alone is, of course, very limited. The optical decay curves of SN Ia already show unambiguously that radionucleides of Ni56 and Co56 are the source of energy. In order to distinguish between the various models for the supernova explosion (see [11]), line widths and ratios need to be measured as a function of time (in days). As an additional cautionary note on the use of nuclear lines for the astrophysics of SNIa, it is possible in principle to use higher energy lines to distinguish between the detonation and deﬂagration models for the initial event. However, this is very difﬁcult to achieve in practice – the emission spectra calculated in Hoeﬂich et al. show that large numbers (thousands) of counts are needed in the lines in order to make progress, and the requirements then become prohibitively difﬁcult.

3. Annihilation line from nearby galaxies Results obtained with INTEGRAL have shown the presence of extended 511 keV emission from a region around the Galactic Center [14]. There may be individual compact sources Springer

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present within the region, or it may be completely diffuse. If it is mainly diffuse, then a region of size 1 sq. deg. would contain a ﬂux of about 10−7 ph cm−2 s−1 . Apart from the intrinsic interest in the GC that this result has generated, it is also a very encouraging pointer to further possibilities for observations of the 511 keV line in the nuclear regions of other galaxies. Although the Milky Way is a giant galaxy, it is much smaller in mass than the cD galaxies at the cores of large clusters of galaxies. These can have masses a hundred times as large, and it is a reasonable assumption that the strength of the annihilation line will probably scale as the mass of the galaxy. The local-group galaxy, M31, is similar in mass to the Milky Way, but has a more massive central black hole with mass of order 1–2 ×108 M (Bender et al. [3]). If the intrinsic ﬂux from the 511 keV line is (conservatively) similar to that from the GC, then the observed ﬂux −1 from the nuclear region of M31 would be about 10−7 ph cm−2 s (the distance to the GC is 8.5 kpc; the distance to M31 is about 700 kpc or about 2 million lt-yrs.). A direct scaling with MBH mass would lead to an intrinsic ﬂux from M31 about 50 times higher than that −1 from the GC, i.e. 5 × 10−6 ph cm−2 s . If the 511 keV emission from the core of M31 has a similar intrinsic size to that in the G.C., then the line in M31 would have an angular extent of about 0.1 degs.

4. Annihilation lines from nearby AGN Firstly, much work remains to be done in the study of the high-energy continuum radiation from AGN. The Hard X-ray Detector (HXD) on the Japanese/US satellite Suzaku should accomplish much of this over the next several years (see Kawaharada et al. [13] for a description of the instrument). The Suzaku HXD has the sensitivity shown in Figure 2 and is compared with previous instruments. Before Suzaku, Beppo-SAX was exemplary for its wide spectral coverage (0.1–200 keV) with the PDS sensitivity reaching to 0.1 times the ﬂux from the nearest quasar 3C273 in the energy range 10–100 keV. Other highly successful satellites and instruments which have explored this energy range have included the X-ray Transient Explorer (XTE), the IBIS instrument on INTEGRAL and the OSSE instrument on the Gamma-Ray Observatory. The

Fig. 2 Suzaku HXD sensitivity [13]. For an updated version, see [22] – this volume Springer

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Fig. 3 Spectral energy distribution from a cluster following positron injection by an AGN at various times. The cases labelled s = 2 and 3 are for different power-law indices for positron injection spectra. From Furlanetto and Loeb [8]

HXD instrument on Suzaku has a smaller ﬁeld of view than previous instruments, and this reduces the sky ﬂuctuation noise, so that the sensitivity should be better than IBIS or SAX by a factor of about 2 or 3 when the background is well understood [9]. As described by Takahashi (this volume), the HXD will be able to measure the reﬂection spectra (in the energy range of tens of keV) in several tens of AGN, out to a redshift of ∼0.1 and high-energy cut-offs in a similar number of objects, depending on the cut-offs themselves (Perola et al. [19]). The BAT instrument on Swift will provide a few hundred possible targets for these detailed studies with Suzaku. These studies will provide a further step in the overall synthesis of the X-ray background, as described by Andrea Comastri in this volume [6]. Although the prospects are good for the measurement of AGN high-energy continua, the prospects for detection of annihilation lines are rather poor. AGN jets are strongly suspected to be sources of relativistic positrons, but the annihilation lines from the jets themselves are expected to be greatly broadened [10]. The jets are emitted at high Doppler factors δ of 10–100 where

δ=

1 γ (1 − β cos θ)

and where γ = (1−β12 )0.5 and the jet is moving with velocity v = cβ at angle θ to the line of sight (see the review by Bicknell, Wagner and Groves (2001)). Springer

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The 511 keV line is blue-shifted to:

E=

δ γth × 511 keV 1+z

where γth is the Lorentz factor representing the low-energy cutoff in the power-law energy distribution of the particles [1]. A line width of 2–3 MeV is anticipated and has probably been observed as the “MeV bump” in blazars (e.g. [4, 18]) The positrons eventually lose energy and ﬁnally annihilate in the ambient ISM where the remainder should produce a narrow line in the circumnuclear region around an AGN which has been active over the previous, say, 108 yrs. Nearby AGN such as Cen A, 3C 273, NGC 1275, and NGC 4151 represent the best prospects for line detection and the historical positron ﬂux depends on the mass and spin of the central MBH. The bulk of the positrons will presumably be annihilated in close proximity because of the ISM density near the MBH. This annihilation line radiation will thus be conﬁned to the nuclear region of the galaxy, typically less than an arcminute in size, or could also be present in radio lobes, as in the case of Cen A (see below).

5. Annihilation line from clusters of galaxies Although the observation of the annihilation line arising from the positrons from active AGN jets may be impossible, the relic positrons from inactive AGN in clusters of galaxies produce enrichment of the ICM and the resulting annihilation line from cooled positrons may be more readily observable, though spatially extended. At the ambient ICM temperature, most annihilations result in the 511 keV line, rather than in the production of positronium and a continuum, as in the case of positron emission from Galactic black holes. A detailed analysis of the annihilation lines that may be anticipated from clusters of galaxies has been performed by Furlanetto and Loeb [8] and their results are summarised here (see also Figure 3): The intrinsic widths of the 511 keV lines from clusters is predicted to be roughly 32 (TkeV )1/2 , i.e. in the range of tens to about a hundred keV. The ﬂux from a cluster of galaxies is predicted to be:

Fcl = 8 × 10−7

rmix 200kpc

3

D 100Mpc

−2 ×

n˙ lines ph cm−2 s−1 10−24 cm3 s−1

where rmix is the positron mixing radius, typically 200 kpc and n˙ line is the emissivity in the −1 511 keV line, expected to be roughly 10−24 cm3 s . Typical integrated 511 keV line ﬂuxes from clusters of galaxies might therefore be of order 10−6 (D/100Mpc)−2 ph cm−2 s−1 . At a distance of 100 Mpc, a typical cluster has an angular extent of about 3 arcmins., effectively a point source for any collecting or focussing instrument at this energy. The sensitivity requirement is thus of order 10−6 ph cm−2 s−1 . For nearby large clusters, i.e. the Virgo cluster at 20 Mpc, the possibility arises of mapping the cluster in 511 keV emission. Springer

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The integrated ﬂux from Virgo is expected to be: ne ζAGN 3 × 10−3 cm−3 0.1 τ −1 ph cm−2 s , 108 yr

FVirgo = 1.3 × 10−6 X sAGN η−1 ×

LK 1044 ergs s−1

where X sAGN is a factor varying between 1 and 10 for positron injection spectra having power law indices (s) between 2 and 3; η−1 is the contribution from past AGN activity, and may be up to a factor of ten; ζAGN is the fraction of the injected kinetic energy contained in the positron component, estimated to be typically 0.1; L K is the total mechanical (kinetic) luminosity; and τ is the lifetime of an AGN in a single duty cycle, typically about 108 yr. Similarly, the ﬂux from CenA is estimated to be: ne ζAGN 10−2 cm−3 0.1 τ LK phcm−2 s−1 , × 43 −1 10 ergs s 1.4 × 108 yr

FCenA = 10−5 X sAGN η−1

where the symbols have the same meanings as above and the unknown factors have values comparable to the quantities in the denominators beneath them. The arguments for CenA are less compelling, since this is still an active nucleus and the positrons have not had time to cool, and CenA is not in a rich cluster like Virgo with many extinct AGN.

6. Conclusions The prospects for the detection and study of extragalactic γ -ray lines are strongest for the e+ − e− annihilation line at 511 keV, but only in sources where the positrons ejected from black holes have had time to cool to ambient temperatures (the intracluster medium). This means that cD galaxies, radio lobes and clusters of galaxies are more likely to produce detectable ﬂuxes than those AGN which are still currently active. The ﬂuxes from large nearby clusters of galaxies, and also from CenA, may approach 10−4 photons cm−2 s−1 in the 511 keV line. In order to detect such lines, a careful trade-off study needs to be made between high-energy Wolter-type mirrors and Laue crystal spectrometers. Acknowledgements It is a great pleasure to acknowledge many discussions with members of the Science Payloads and Advanced Concepts Ofﬁce at the European Space & Technology Center in Noordwijk: and in particular Tony Peacock, Marcos Bavdaz, Nicola Rando, Dave Lumb and Craig Brown. This work was supported in part by the European Space Agency.

References 1. Abraham, Z., Romero, G. E., Durouchoux, P.: Proc. Fourth Integral Workshop “Exploring the Gamma-Ray Universe”, ESA-SP 459, p.131 2. Barris, B.J., Tonry, J.L.: Astrophys. J. 637, 427 (2006) 3. Bender, R. et al.: Astrophys. J. 631, 280 (2005) Springer

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4. Bottcher, M., Schlickeiser, R: Astron. Astrophys. Supp. Ser. 120, 575 5. Cappellaro, E., Turatto, M.: The inﬂuence of binaries on stellar population studies, (Dordrecht: Kluwer Academic Publishers). Astrophys. Space Sci. Library 264, 199 (2001) 6. Comastri, A.: DOI: 10.1007/s10686-006-9041-6 (2006) 7. Ebisawa, K., Bourban, G., Bodaghee, A., Mowlavi, N., Courvoisier, T. J.-L.: Astron. Astrophys. 411, L59; see also vizieR On-line Data Catalog J/A+A/411/L59 (2004) 8. Furlanetto, S.R., Loeb, A.: Astrophys. J. 572, 796 (2002) 9. Fukuzawa and the Suzaku HXD Team, 2006, in press 10. Begelman, M., Blandford, R. Rees, M.J.: Rev. Mod. Phys. 56, 255 (1984) 11. Hoeﬂich, P., Wheeler, J.C., Khokhlov, A.: Astrophys. J. 492, 228; ibid. 2004, 605, 573 (1998) 12. INTEGRAL Special Issue: Astron. Astrophys. 411, L1–L460 (2003) 13. Kawaharada, M., et al.: Proc. Soc. Photo-Optical Eng. 5501, 286 (2004) 14. Knoedlseder, J., et al.: Astron. Astrophys. 441, 513 (2005) 15. Leising, M.: DOI: 10.1007/s10686-006-9052-3 (2006) 16. Maciolek-Niedzwiecki, A., Zdziarski, A. Coppi, P.: MNRAS 276, 273. 17. Mannucci, F., Della Valle, M., Panagia, N., Cappellaro, E., Cresci, G., Maiolino, R., Petrosian, A., Turatto, M.: Astron. Astrophys. 433, 807 18. Marcowith, A., Henri, G., Pelletier, G.: MNRAS 277, 681 19. Perola, G.C., Matt, G., Cappi, M., Fiore, F., Guainazzi, M., Maraschi, L., Petrucci, P.O., Piro, L.: Astron. Astrophys. 389, 802 (2002) 20. Roland, J., Hermsen, W.: Astron. Astrophys. 297, L9 21. Scannapieco, E., Bildsten, L.: Astrophys. J. 629, L85 22. Takahashi, T., et al.: DOI: 10.1007/s10686-006-9059-9 (2006)

Springer

Exp Astron (2005) 20:31–40 DOI 10.1007/s10686-006-9061-2 O R I G I NA L A RT I C L E

Non-thermal cosmic backgrounds and prospects for future high-energy observations of blazars P. Giommi · S. Colafrancesco

Received: 27 January 2006 / Accepted: 17 July 2006 C Springer Science + Business Media B.V. 2006

Abstract We discuss the contribution of the blazar population to the extragalactic background radiation across the electromagnetic (e.m.) spectrum with particular reference to the microwave, hard-X-ray and γ -ray bands. Our estimates are based on a recently derived blazar radio LogN-LogS that was built by combining several radio and multi-frequency surveys. We show that blazar emission integrated over cosmic time gives rise to a considerable broad-band non-thermal cosmic background that dominates the extragalactic brightness in the high-energy part of the e.m. spectrum. We also estimate the number of blazars that are expected to be detected by future planned or hypothetical missions operating in the X-ray and γ -ray energy bands. Keywords Galaxies:active . Galaxies: blazar: BL Lacertae surveys

1. Introduction Active Galactic Nuclei (AGN) are well known to dominate the high-energy (soft-X-ray and beyond) high Galactic latitude sky. Their radiation integrated over cosmic time can explain most, if not all, the extragalactic background radiation (e.g. [4, 7, 17, 24]). Historically, AGN have been classiﬁed in many – sometime inconsistent or confusing – ways, depending on how they appeared in surveys performed in different energy bands and with different ﬂux limits (such ﬂux limits are often determined by the technology available at the time of the survey, or depending on some speciﬁc observational parameter, like, e.g., the ﬂux ratio between radio and optical emission, the equivalent width of their emission lines, etc.).

P. Giommi () ASI Science Data Center, C/O ESA-ESRIN, Frascati, Italy e-mail: [email protected] S. Colafrancesco INAF, Osservatorio Astronomico di Roma e-mail: [email protected] Springer

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In the following we use the widely accepted standard paradigm where AGN are powered by accretion onto a super-massive black hole, e.g. [30, 31, 33], to divide this class of sources into two broad categories deﬁned by their intrinsic emission mechanism: – AGN whose power is dominated by radiation of thermal origin produced by matter that is strongly heated in the inner parts of a disk of matter falling onto the supermassive black hole and illuminating the circumnuclear matter that is responsible for the broad line emission. We call these objets Thermal Emission Dominated AGN or TED-AGN. – AGN whose power is dominated by Non-Thermal radiation (or NTED-AGN) where most of the emission is generated through non-thermal processes, like the synchrotron and the inverse Compton mechanism, by particles accelerated in a jet of material that moves at relativistic speed away from the central black hole. The jet itself is formed converting part of the accretion energy in a way that is presently not well understood. Within this general deﬁnition the class of blazars corresponds to the small subset of NTED-AGN that are viewed at a small angle w.r.t. the jet axis (for this reason their emission is strongly ampliﬁed by relativistic effects [2, 30]), whereas Radio Galaxies are those NTED-AGN that are viewed at a large angle w.r.t. the jet axis. Here we do not distinguish between line-less objects, or BL Lacs, and broad-line Flat-Spectrum Radio Quasars, or FSRQs. When the accretion and jet emission coexist in the same object and produce similar amounts of radiation we have AGN that are a mixture of the TED and NTED type that appear like broad-line radio galaxies (e.g. 3C 120). The overall cosmic background radiation has two well understood components: the primordial black body emission peaking at microwave frequencies (the cosmic microwave background, CMB), and the X-ray apparently diffuse emission arising from the accretion onto super-massive black holes in AGN integrated over cosmic time (the cosmic X-ray background, CXB). We will show that blazars add a third non-thermal component that at low frequencies contaminates the CMB ﬂuctuation spectrum and complicates its interpretation [5], while at the opposite end of the e.m. spectrum it dominates the extragalactic background radiation [7]. In the following, we estimate the contribution of blazars to non-thermal cosmic backgrounds starting from a recently derived deep radio LogN-LogS [7]. The broad-band e.m. spectrum of a blazar is composed of a synchrotron low-energy component that peaks [in a Log(ν) − Log(ν f (ν)) representation] between the far infrared (i.e. ∼300 GHz–10 THz, corresponding to ∼ (0.12–4)10−2 eV) and the X-ray band (∼2–10 keV), followed by an Inverse Compton component that has its maximum in the hard X-ray band (∼20–100 KeV) or at higher energies, depending on the location of the synchrotron peak, and extends into the γ -ray or even the TeV band. Those blazars where the synchrotron peak is located at low energy are usually called Low energy peaked blazars or LBL, while those where the synchrotron component reaches the X-ray band are called High energy peaked blazars or HBL [19]. LBL sources are the large majority among blazars [20] and are usually discovered in radio surveys, while HBL objects are preferentially found in X-ray ﬂux limited surveys, since at these frequencies they are hundreds, or even thousands, of times brighter than LBLs of similar radio power. Springer

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Fig. 1 The blazars radio (5 GHz) LogN-LogS of [7] who built it combining several surveys as indicated in the top right part of the plot (see [7] for details)

2. The radio LogN-LogS of blazars and their contribution to extragalactic cosmic backgrounds The deep blazar radio (5 GHz) LogN-LogS shown in Figure 1 has been recently derived by [7] who showed that it can be described by a broken power law with parameters deﬁned in Equation (1): N (>S) =

5.95 10−3 × S −1.62 0.125 × S −0.9

S > 0.015 Jy S < 0.015 Jy

(1)

Once the LogN-LogS of a population of sources is known in a given energy band, it is possible to estimate their emission in other parts of the e.m. spectrum, provided that the ﬂux ratio between the two bands is known. Here we deal with ﬂux ratios and Spectral Energy Distributions (SEDs) of blazars that will be used to estimate the contribution to cosmic backgrounds at microwave frequencies and in the X-ray and γ -ray bands (see Figure 3). The distribution of f x / f r ﬂux ratios shown in Figure 2 (see [7] for details) spans about four orders of magnitudes implying that the X-ray ﬂux of blazars with the same radio ﬂux can be different by a factor up to ≈10,000! In the following we estimate the blazar contribution to the cosmic backgrounds (see Figure 3) basing our calculation on the radio LogN-LogS shown in Figure 1 and on ﬂux ratios determined in different bands, or on observed blazar SEDs. 2.1. The cosmic microwave background The contribution of blazars to the CMB has been estimated in the past from different viewpoints (e.g. [5, 29]). Here we calculate the integrated microwave background intensity as Springer

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Fig. 2 The f x / f r distribution of blazars estimated by [7]

Fig. 3 The extragalactic Cosmic Background Energy distribution at microwave, X-ray and γ -ray energies. The CMB is represented by a black-body spectrum with temperature of 2.725◦ K [16]; the CXB is taken from HEAO-1 measurements [9, 15] and has been scaled to match the more recent BeppoSAX, ASCA, and XMMNewton results in the 2–10 keV band [12,14,32]. The gamma ray background is derived from the COMPTEL data in the range 0.8–30 MeV [11] and from EGRET data in the range 30 MeV–50 GeV. We report here the results of two different analyses of the EGRET data: open circles from [26] and ﬁlled circles from [27], which uses an improved model of the Galactic diffuse gamma-ray continuum. As for the TeV diffuse background, we report the upper limits derived in the 20–100 TeV region from the HEGRA air shower data analysis [1]. In the TeV–PeV energy range, other experiments give only upper limits and there is no clear observation of a diffuse photon signal yet (see [7] for more detail)

follows Iblazars =

1 Jy

S 0.1 mJy

Springer

dN dS , dS

(2)

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35

where dN/dS is the differential of Equation (1). The minimum integration ﬂux Smin = 0.1 mJy is likely to be conservative, since blazars with radio ﬂux near or below 1 mJy are already included in the Einstein Medium Sensitivity Survey BL Lac sample [23]. The integrated intensity Iblazars is converted from 5 GHz to microwave frequencies by convolving the ﬂux value with the observed distribution of spectral slopes between 5 GHz to microwave frequencies, as estimated from the 1Jy-ARN sample (see [5] for details). The fractional contamination Iblazars /ICMB of blazars to the CMB intensity ICMB and the corresponding apparent temperature increase in the frequency range 90–300 GHz has been derived by [7]. Blazars also contribute to the CMB temperature anisotropies with a spectrum ( T )blazar = [(2π)−1 C ( + 1)]1/2 ,

(3)

where C,blazar =

Smax

dS Smin

dN 2 S . dS

(4)

The quantity on the right hand side of Equation (4) is the usual Poisson shot-noise term, [21, 28] and we neglect here the clustering term ω(I )2 (which adds to the Poissonian term) since there is not a clear estimate of the blazar clustering yet. Note, however, that the inclusion of clustering signiﬁcantly increases the amount of contamination, especially at large angular scales [8]. For the blazar population described by the LogN-LogS given in Figure 1, we found C,blazar ≈ 54.4 Jy2 sr−1 at 41 GHz and C,blazar ≈ 51.6 Jy2 sr−1 at 94 GHz. When translated into temperature units (see [5]), we found a value C,blazar ≈ 2.22 × 10−2 µK2 sr at 41 GHz and C,blazar ≈ 1.09 × 10−3 µK2 sr at 94 GHz. We show in Figure 4 the quantity ( T )blazar and

Fig. 4 The contribution of blazars to the CMB ﬂuctuation spectrum in the WMAP 41 GHz (left panel) and 94 GHz (right panel) channels, as evaluated from the LogN-LogS given in Figure 1 (solid line). We also show the angular power spectrum for the blazar population by adding an estimate of the possible contribution of radio sources with steep-spectrum at low radio frequencies which ﬂatten at higher frequencies (dashed line). The dotted line also includes the effect of spectral and ﬂux variability. Although this additional contamination may be substantial a precise estimation can only be done through simultaneous high resolution observations at the same frequency. A typical CMB power spectrum evaluated in a CDM cosmology with m = 0.3, = 0.65, b = 0.05 which best ﬁts the available data is shown for comparison Springer

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compare it to the CMB ﬂuctuation power spectrum which best ﬁts the available data. These values (shown as solid lines) have to be considered as a deﬁnite lower limit for C,blazar , since they neglect the contribution of steep-spectrum sources at low frequencies which ﬂatten at these frequencies (41 and 94 GHz, dashed lines) and the effect of ﬂux variability (dotted lines). The blazar ﬂux variability at millimeter wavelengths may be substantial (higher than factors 3–10 on time scales of weeks to years w.r.t. those seen at cm wavelengths) and could increase the amount of contamination of CMB maps when these are built over long integration periods. The contamination level shown in Figure 4 is the one expected in the case where no blazars are removed from the CMB data. We expect that a correct procedure for the derivation of the CMB power spectrum that takes into account the full point-like source contribution implied by our LogN-LogS, would both inﬂuence the shape of the expected power spectrum and increase the statistical uncertainties of the WMAP data points, especially at high multipoles, where the blazar contribution is larger. The calculations shown in Figure 4 are performed neglecting the blazar clustering and thus they must again be considered as a lower limit to the realistic angular power spectrum contributed by these sources. The effects of clustering on the CMB ﬂuctuation spectrum has been partially estimated by some authors: (e.g. [8, 25]) and they depend both on the adopted model for the source counts and on their clustering model. Based on the correlation function of [13], on that for the SCUBA sources [25] and on our blazar LogN-LogS, we expect that the contamination of the ﬁrst peak of the CMB ﬂuctuation spectrum (at the WMAP 41 GHz channel) is at a level of 20–25%. This estimate does not include possible variability effects and additional core-dominated radio sources. 2.2. The soft X-ray background We estimate the contribution of blazars to the CXB at 1 keV using two methods: (i) converting the integrated radio ﬂux calculated with Equation (2) into X-ray ﬂux using the observed distribution of f x / f r ﬂux ratios in Figure 2; and (ii) converting the integrated blazar contribution to the CMB (at 94 GHz) to X-ray ﬂux using the distribution of αµx [the microwave (94 GHz) to X-ray (1 keV) spectral slope] estimated from the subsample of blazars detected by WMAP in the 94 GHz channel, for which an X-ray measurement is available (see Figure 9 in [7]). The ﬁrst method gives a total blazar contribution to the X-ray background of 2.7 × 10−12 erg cm−2 s−1 deg−1 (about 70% of which is due to HBL sources with f x / f r > 5 × 10−12 erg cm−2 s−1 Jy−1 ) in the ROSAT 0.1–2.4 keV energy band. Assuming [7] an average blazar X-ray energy spectral index of αx = 0.7, this ﬂux converts to 2.6 × 10−12 erg cm−2 s−1 deg−1 in the 2–10 keV band, i.e. 11% of the CXB which is estimated to be 2.3 × 10−11 erg cm−2 s−1 deg−1 [22]. The distribution of αµx has an average αµx = 1.07 and a standard deviation of 0.08, corresponding only to about a factor 3 in ﬂux. This distribution is much narrower than the one of the average spectral slope between the radio and X-ray band (Figure 2), while its dispersion is comparable to that expected from blazar variability at radio and especially at X-ray frequencies. The X-ray ﬂux can therefore be estimated simply as f 1 keV =1.4×10−7 f 94 GHz (see, e.g., [7]). Since the blazar integrated emission at 94 GHz is 7.2 × 10−6 CMB94 GHz (or 0.64 Jy/deg2 ) and the cosmic X-ray background is 2.3 × 10−11 erg cm−2 s−1 [22] in the 2–10 keV band (equivalent to 2.31 µJy/deg2 at 1 keV), we have that f1 keV = 0.09 µJy/deg2 , i.e. 3.9% of the CXB for f 94 GHz = 0.64 Jy/deg2 . Considering that the αµx distribution of [7] only includes LBL objects and that HBL sources make up ≈ two thirds of the total contribution to the CXB, the percentage scales to about 12%, which is very close to the value 11% obtained with the Springer

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Fig. 5 Left: The possible contribution of LBL blazars to the cosmic background. Simple SSC energy distributions fail to reproduce the observed intensity and slope of the γ -ray background. The observed range of γ -ray emission with EGRET, normalized to radio ﬂux, indicates that the duty cycle at these energies must be low (see text for details). Right: The spectral slopes between the 5 GHz emission and the 100 keV and 1 MeV high energy ﬂuxes in the SSC distribution of LBL blazars that reproduces the observed X and γ -ray cosmic background

previous method. Both our results are in good agreement with the independent estimate of [3], who ﬁnd that the radio loud AGN content of the CXB is 13% in the XMM-Newton bright serendipitous survey. 2.3. Hard X-ray – soft γ -ray background The number of sources detected at energies larger than soft X-rays is still rather low; hence, deriving reliable distributions of ﬂux ratios between radio or microwaves and the Hard X-ray/γ -ray ﬂuxes is not currently possible. Thus, in order to estimate the blazar contribution to the high energy Cosmic Backgrounds (at E > 100 keV), we followed a different approach: we extrapolated the predicted blazar integrated intensity at microwave frequencies (Equation 2) to the hard X-ray and soft γ -ray band using a set of hypothetical SSC spectral energy distributions. Figure 5 (left panel) shows the CMB, CXB, and CGB together with three predicted SEDs from a simple homogeneous SSC models with parameters constrained to: (1) be consistent with the expected integrated ﬂux at 94 GHz; 2) have αµx equal to the mean value of the WMAP blazars ( αµx = 1.07); 3) have a radio spectral slope equal to the average value found in the WMAP sample. The three curves so constrained are characterized by synchrotron peak frequencies of νpeak = 1012.8 , 1013.5 , and 1013.8 Hz. A high value of νpeak largely overestimates the observed hard-X-ray to soft γ -ray (≈1020 − 2 × 1022 Hz or ≈500 keV–10 MeV) cosmic background, whereas a too low value of νpeak predicts a negligible contribution (see Figure 5, left panel). The case νpeak = 1013.5 Hz predicts 100% of the hard X-ray/soft gamma-ray cosmic background. Since the Log(νpeak ) values of blazars in the WMAP and other catalogs peak near 13.5, ranging from 12.8–13.7 within one sigma from the mean value, we conclude that blazars may be responsible for a large fraction (and possibly 100%) of the hard-Xray/soft γ -ray cosmic background. 2.4. γ -ray background The SSC distributions of Figure 5 predict a negligible blazar contribution to the extragalactic γ -ray background above 100 MeV. Nevertheless, it is well known that blazars are the large Springer

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majority of the extragalactic γ -ray (E > 100 MeV) identiﬁed sources detected by the EGRET experiment [10]; therefore they are likely to contribute to the γ -ray background in a signiﬁcant way. Indeed, [18] concluded that blazars should make a large fraction, if not the totality, of the extragalactic γ -ray background. However, these early calculations relied upon a very small blazar sample and had to assume no strong variability, a characteristic that was later demonstrated to be extremely common in γ -ray detected blazars. Figure 11 in [7] compares the energy distribution of the CMB, CXB, and CGB to the SED of 3C 279 (a well-known bright blazar detected by EGRET) scaled to the integrated blazar ﬂux intensity as calculated with Equation (2). Taking into account the strong variability of blazars seen across the whole e.m. spectrum, it has been shown [7] that, while the contribution to the CXB can range from a few percent to over 10% in the higher states, the predicted ﬂux at γ -ray frequencies ranges from about 100% to several times the observed cosmic background intensity. Such large excess implies that (i) either sources like 3C279 are not representative of the class of blazars or (ii) their duty cycles at γ -ray frequencies are very low. A way of quantifying the ratio between the γ -ray intensity predicted by assuming that the source is representative of the entire population and the actual background intensity is to use the f 94 GHz / f 100 MeV ) microwave (94 GHz) to γ -ray (100 MeV) slope αµγ = −Log( . Log(ν94 GHz /ν100 MeV )

For comparison, we deﬁne αµγ 100%CGB = 0.994 as the αµγ of a hypothetical source that would produce 100% of the CGB, if representative of the entire class. Any realistic source with αµγ ﬂatter than αµγ 100%CGB = 0.994 would then predict – if representative of the entire population – an integrated ﬂux in excess of the observed γ -ray background. Alternatively, its duty cycle must be lower than 100%. Figure 5 (left) shows the minimum and maximum values of αµγ among the sources detected by the EGRET experiment. 2.5. TeV background All blazars detected so far at TeV energies are of the HBL type. Therefore we estimate the blazar contribution to the TeV background as in the case of the soft γ -ray background but only considering the HBL component, and not the entire blazar population. These extreme objects have been estimated to be about 0.1% of the blazar population [7]. Using the SED of the well known TeV blazar MKN421 normalized at 94 GHz (see Figure 13 in [7]) – so that the ﬂux is scaled to 0.1% of the intensity produced by the entire population of blazars – we see that, despite HBLs are a tiny minority, their integrated X-ray ﬂux makes up a fairly large fraction of the CXB, and that their TeV emission may produce a signiﬁcant amount of extragalactic light. We note, however, that since extreme HBLs (such as those of the Sedentary survey) are very rare (one object in several thousand degrees with ﬂux above a few mJy), the extragalactic light at TeV energies should be very patchy (i.e. associated to single sources) rather than a diffuse light resulting from the superposition of many unresolved discrete sources.

3. Prospects for future high-energy observations of blazars We have seen that blazars, and in general NTED-AGN, emit non-thermal radiation across the entire e.m. spectrum. A clear understanding of the blazar content of the extragalactic high-energy sky is necessary, as new missions are planned or are under study by European and other space agencies to explore in more detail the hard X-ray and γ -ray bands. These missions will open the last energy windows (e.g. the few hundred keV-few MeV region) Springer

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Table 1 The number of blazars in the high Galactic latitude sky at different sensitivities and energy bands

Energy band Micro-wave (100 GHz) Soft X-ray (0.1−2.4 keV) Hard X-ray 50–150 keV Soft γ -ray 3–10 MeV γ -ray 100 MeV–100 GeV

Flux limit (energy band)

Flux limit (5 GHz)

No. of sources at high b (25,000 deg2 )

70 mJy 7 mJy 10−15 erg cm−2 s−1

100 mJy 10 mJy ∼0.1–10 mJy

5000 >100,000 >100,000

5 × 10−12 erg cm−2 s−1 1 × 10−13 erg cm−2 s−1 5 × 10−7 ph cm−2 s−1 1 × 10−7 ph cm−2 s−1 1 × 10−7 ph cm−2 s−1 3 × 10−9 ph cm−2 s−1

1000 mJy 20 mJy 1000 mJy 200 mJy Monte Carlo simulation

130 ≈70,000 130 2000 ≈100 ≈3000

that, for technical difﬁculties, have so far remained almost unexplored but that are extremely important for understanding the physical processes powering NTED-AGN. In the following we apply the same method used in the previous sections to estimate the number of blazars that could be detected by future microwave, X-ray and γ -ray observatories. We report the results in Table 1 where column 1 gives the energy band considered, column 2 gives the limiting sensitivity reached in that energy band, column 3 gives the corresponding 5 GHz ﬂux, and column 4 gives the number of blazars expected in the high Galactic latitude sky (≈25,000 deg2 ). Figure 2 shows that the distribution of f x / f r ratios is extremely broad reﬂecting the fact that the ﬂux in the X-ray region is deeply affected by the position of the synchrotron peak in Log(ν)−Log(ν f (ν)) plots. Blazars where the peak is located in the far infrared (i.e. LBL) have very little X-ray ﬂux, whereas extreme HBL objects can be thousands of times brighter at X-ray frequencies than LBLs of the same radio ﬂux. Figure 2 implies that a survey as deep as 10−15 erg cm−2 s−1 would detect the whole f x / f r distribution of blazars with 5 GHz ﬂux larger than 10 mJy, corresponding to well over 100,000 sources in the high Galactic latitude sky. From Figure 5 (right panel) we can see that the average slope between the 5 GHz radio ﬂux and the hard-X-ray band or the soft γ -ray band is 0.85 and 0.84, respectively. Since the ratio between the radio ﬂux and these energy bands is not expected to have a large spread around the mean value (like f x / f r ), the average slopes can be directly converted to predict the hard-X-ray and the soft γ -ray ﬂuxes. We have reported these predictions in column 2 of Table 1 A deep all sky survey in the soft X-ray band: 0.1–10 keV. From Table 1 we see that a deep all-sky X-ray survey in the soft X-ray band would allow to build a sample of >100,000 blazars that are expected to be above the limiting sensitivity of PLANCK (operating in the microwaves). Given the signiﬁcant impact of the blazar foreground emission on the CMB power spectrum, it is important to remove accurately this foreground component from the CMB. An efﬁcient way to achieve this goal is to exploit the fact that the spectral slope distribution between microwave and soft X-ray ﬂux of LBLs is very narrow (see Figure 9 of [7]) with a dispersion that is probably mostly due to intrinsic variability. The soft X-ray > ﬂux of LBLs (that are ∼ 90% of the blazar population) is therefore a very good estimator of the ﬂux at microwave frequencies and could then be used to locate and remove foreground blazars from the PLANCK and other CMB esperiments. Springer

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The extremely large sample of blazars produced by such a survey could also be used to study the statistical properties of blazars in great detail (including the spatial correlation function) and would identify a very large number of targets for the next generation γ -ray observatories (such as AGILE or GLAST), as well as for the future instruments operating in the still poorly explored MeV spectral region. The expected number of blazars at γ -ray energies above 100 MeV cannot be estimated with a simple extrapolation of the 5 GHz ﬂux (see Section 2.4), and therefore we have listed the preliminary expectations (see last row of Table 1) evaluated through a Monte Carlo method that makes use of the radio luminosity distribution of blazars and predicts γ -ray ﬂuxes taking into account the αµγ distribution of EGRET detected blazars. This method is currently under development as part of our contribution to the GLAST project. Acknowledgements It is a pleasure to thank the Organizing and Advisory Committee of this meeting for the invitation to present our results in the context of the planned and future gamma-ray experiments.

References 1. Aharonian, F.A., Akhperjanian, A.G., Barrio, J.A., et al.: APh 17, 459 (2002) 2. Blandford, R.D., Rees, M.J.: in: Pittsburgh Conference on BL Lac Objects, Wolfe, A.M. (ed.), University of Pittsburgh, Pittsburgh, p. 328 (1978) 3. Galbiati, E., Caccianiga, A., Maccacaro, T., et al.: A&A, in press, astro-ph/0410432 (2004) 4. Giacconi, R., Gursky, H., Paolini, F., Rossi, B.: Phys. Rev. Lett. 9, 439 (1962) 5. Giommi, P., Colafrancesco, S.: A&A 414, 7 (2004) 6. Giommi, P., Menna, M.T., Padovani, P.: MNRAS 310, 465 (1999) 7. Giommi, P., Colafrancesco, S., Cavazzuti, E., Perri, M., Pittori, C.: A&A 445, 843 (2006) 8. Gonzales-Nuevo, J., Toffolatti, L., Argueso, F.: ApJ 621, 1 (2005) 9. Gruber, D.E., Matteson, J.L., Peterson, L.E., Jung, G.V.: ApJ 520, 124 (1999) 10. Hartman, R.C., Bertsch, D.L., Bloom, S.D., et al.: ApJS 123, 79 (1999) 11. Kappadath, S.C.: ph. D. Thesis, University of New Hampshire, USA (1998) 12. Kushino, A., Ishisaki, Y., Morita, U., et al.: PASJ 54, 327 (2002) 13. Loan, A.J., Wall, J., Lahav, O.: MNRAS 286, 994 (1997) 14. Lumb, D.H., Warwick, R.S., Page, M., De Luca, A.: A&A 389, 93L (2002) 15. Marshall, F.E., Boldt, E.A., Holt, S.S., et al.: ApJ 235, 4 (1980) 16. Mather, J., Fixsen, D., Shafer, R.A., Mosier, C., Wilkinson, D.T.: ApJ 512, 511 (1999) 17. Moretti, A., Campana, S., Lazzati, D., Tagliaferri, G.: ApJ 588, 696 (2003) 18. Padovani, P., Ghisellini, G., Fabian, A., Celotti, A. MNRAS 260, L21 (1993) 19. Padovani, P., Giommi, P.: ApJ 444, 567 (1995) 20. Padovani, P., Perlman, E., Landt, H., Giommi, P., Perri, M.: ApJ 58, 128 (2003) 21. Peebles, P.: The large scale sturcture of the universe, in: Priceton, P.U.P. (ed.) (1980) 22. Perri, M., Giommi, P.: MNRAS 362, L61 (2000) 23. Rector, T.A., Stocke, J.T., Perlman, E.S., Morris, S.L., Gioia, I.M.: AJ 120, 1626 (2000) 24. Rosati, P., Tozzi, P., Giacconi, R., et al.: ApJ 566, 667 (2002) 25. Scott, D., White, M.: A&A 346, 1 (1999) 26. Sreekumar, P., Bertsch, D.L., Dingus, B.L., et al.: ApJ 494, 523 (1998) 27. Strong, A., Moskalenko, I., Reimer, O.: ApJ 613, 956 (2004) 28. Tegmark, M., Efstathiou, G.: MNRAS, 281, 1297 (1996) 29. Toffolatti, L., Argueso Gomez, F., de Zotti, G., et al.: MNRAS 297, 117 (1998) 30. Urry, C.M., Padovani, P.: PASP 107, 803 (1995) 31. Urry, C.M.: ASPC 290, 3 (2003) 32. Vecchi, A., Molendi, S., Guainazzi, M., Fiore, F., Parmar, A.N.: A&A 349, L73 (1999) 33. Vellieux, S.: ASPC 290, 11 (2003)

Springer

Exp Astron (2005) 20:41–47 DOI 10.1007/s10686-006-9041-6 O R I G I NA L A RT I C L E

Rolling down from the 30 keV peak: Modelling the hard X-ray and γ -ray backgrounds Andrea Comastri · Roberto Gilli · Gunther ¨ Hasinger

Received: 7 February 2006 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract We will brieﬂy discuss the importance of sensitive X-ray observations above a few tens of keV for a better understanding of the physical mechanisms associated to the Supermassive Black Hole primary emission in both radio quiet and radio loud AGN and to the cosmological evolution of the most obscured sources. Keywords X-rays . Background radiation . AGN

1. Introduction The fraction of the hard X-ray background (XRB) resolved into discrete sources by deep Chandra and XMM-Newton observations smoothly decreases from essentially 100% below 2–3 keV to about 50% in the 7–10 keV energy range [1]. The resolved fraction averaged on the standard 2–10 keV band is of the order of 80% (see Hickox and Markevitch [2] for a recent estimate). At energies greater than 10 keV, where the bulk of the background energy density is produced, the resolved fraction is negligible, being strongly limited by the lack of imaging X-ray observations. The energy dependence of the resolved fraction goes almost hand in hand with the selfconsistency of AGN synthesis models. While at relatively low energy (say below 8–10 keV) a robust model, build over the AGN uniﬁed scheme, precisely account for a large body of observational data (XRB spectral intensity, X-ray source counts, redshift distribution, etc.) at higher energies the predictive power is strongly limited by the lack of observational constraints. At present the best estimates of the key parameters, responsible of the XRB spectral intensity around and above the 30 keV peak, mainly rely on the observations obtained with the PDS A. Comastri () · R. Gilli INAF-Osservatorio Astronomico di Bologna, Italy e-mail: [email protected] G. Hasinger Max Planck f¨ur Extraterrestrische Physik, Garching, Germany Springer

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instrument onboard BeppoSAX [3, 4] and are thus limited to nearby bright (S10−100keV > 10−11 erg cm−2 s−1 ) objects. As a consequence a relatively wide portion of the model parameter space remains so far unexplored [5].

2. XRB modelling Within the framework of AGN synthesis models the key parameters responsible for the shape and intensity of the >10 keV XRB spectrum are: – the covering fraction and geometrical distribution of the cold dense gas responsible of the reﬂection “hump” peaking at 20–30 keV and observed in both type 1 and type 2 AGN. – the relative fraction of heavily obscured sources with column densities of the order of a few 1024 cm−2 (the so called “mildly” Compton thick AGN; see Comastri [6] for a review). – the high energy cut-off of the primary emission which is usually parameterized as an exponential roll-over with an e-folding energy of a few hundreds of keV. The reﬂection of hard X-rays by cold dense circumnuclear gas is a well established property of nearby Seyfert galaxies (see Pounds et al. [7] for the discovery Ginga observations and Perola et al. [8] for a spectral survey of bright AGN with BeppoSAX). For unobscured or relatively unobscured AGN the reﬂecting material is covering about 2π sr. Several independent observational evidences suggest that a fraction as large as 50% (or even higher) of the Seyfert 2 galaxies in the local Universe are obscured by Compton-thick material [3, 6, 9]. A population of Compton thick (hereinafter CT) sources has to be included in AGN synthesis models for the XRB in order to match the 30 keV intensity peak and at the same time to avoid an excessive number of Compton thin AGN which are not detected in Chandra and XMM-Newton deep surveys (see the discussion in Comastri [6]). Their relative fraction and cosmological evolution are free parameters which are tuned until a good ﬁt to the XRB spectrum is obtained. Assuming the same cosmological evolution of soft X-ray selected type 1 AGN of Hasinger et al. [10], the best ﬁt model shown in Figure 1 is obtained with a relative fraction of CT AGN which is the same of Compton thin (N H in the range 1022 –1024 cm−2 ) and twice than unobscured (N H < 1022 cm−2 ) AGN (see Gilli et al. [11] for further details). The peaked shape of the CT spectrum in a ν Fν − ν plot is due to heavy absorption at low energies and the high energy cut-off (E cut ). The latter, ﬁxed at 320 keV in Figure 1, has to be present in the high energy spectrum of all the sources (regardless of the absorption column density) otherwise the observed XRB ﬂux above about 100 keV would be exceeded. The high energy cut-off e-folding energy has been unambiguosly measured only for a bunch of nearby Seyfert galaxies. The best ﬁt values are loosely constrained in the 150–350 keV range [4, 12]. Both BeppoSAX [13] and more recent INTEGRAL observations [14] suggest a large scatter in the E cut values which span from about 50 keV up to lower limits of the order of 500 keV. While a clear bias against large values of the high energy cut-off is present, the available observations seem to indicate that such a parameter might not be the same in all the sources at variance with the assumptions of most of the synthesis models. The properties of the sources of the “unresolved” background may be inferred by subtracting from the observed broad band spectrum the energy dependent fraction of the “resolved” XRB. Such an approach has been pursued both making use of present observations [1] and exploiting the XRB synthesis models [5, 6]. In the former case the spectral shape of the ”unresolved” background is consistent with that expected from a population of obscured (N H 1023−24 cm−2 ) AGN at redshifts ∼ 0.5 − 1.5. In the latter, following a model Springer

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Fig. 1 The cosmic XRB spectrum and predicted AGN contribution (magenta solide line which includes also galaxy clusters) splitted between unobscured (red dashed line), Compton thin (blue thin line) and Compton thick (black line). For unobscured and Compton thin AGN the effect of including iron line emission is also reported and corresponds to the upper red and blue dashed curve [23]. The different XRB measurements are explained on the top left. Also shown are the resolved XRB fractions in different surveys by Worsley et al. [1]: Lockman Hole = red diamonds; CDFS = cyan crosses; CDFN = black crosses.

dependent approach, the shape of the unresolved fraction can be predicted over a much wider energy range. More speciﬁcally assuming a set of model parameters tuned to match the 2–10 keV resolved fraction and to reproduce the observed absorption distribution in deep ﬁelds the predicted XRB ﬂux and spectral shape above 10 keV are strongly dependent from the adopted of E cut value (see Figure 2 in Comastri [5]). 3. Exploring the parameter space An additional source of uncertainties comes from the possible contribution to the hard XRB / soft γ -ray backgrounds (above about 100 keV) of the population of radio-loud sources which includes, for the purposes of the present exercise, both ﬂat spectrum radio quasars (e.g. 3C 273) and BL Lac objects. We refer to Giommi et al. ([15] and these proceedings) for a detailed discussion of their contribution to the extragalactic X-ray and γ -ray bands. In the very ﬁrst approximation radio-loud sources are expected to provide the bulk of the γ -ray background above a few tens of MeV, while radio-quiet AGN dominate below 100 keV. In between their relative contribution is expected to be comparable. An attempt to estimate the contribution of radio-loud quasars to the X-ray/soft γ -ray background (from 1 keV to a few MeV) is presented here. The assumed template spectrum and cosmological evolution are as follows: – the average X-ray/γ -ray spectrum is parameterized with a single power law plus a high energy cut-off. – the input spectrum is then folded with the same luminosity function of radio-quiet AGN assuming a pure luminosity evolution of the form L(z) L(0) × (1 + z)3 normalized to account for 10% of the XRB ﬂux at 1 keV in agreement with Giommi et al. [15] and Galbiati et al. [16]. Springer

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Fig. 2 An estimate of the radio loud AGN contribution to the XRB computed for a range of slopes and high energy cut-offs (red long-dashed lines; see details in the text). The blue short dashed line represents the so far resolved fraction modeled following the prescriptions of Gilli et al. [11]. The solid black lines are the sum of the above mentioned components.

The power law slope energy index α is varied in the range 0.5–0.7 consistent with the averaged value observed in the X-ray band over a large range of redshifts [17–19] while the choiche of the E cut value is driven by the requirement of not exceeding the background ﬂux. The results for three representative pairs of α and E cut : (0.5, 800 keV); (0.6, 1 MeV) and (0.7, 2 MeV) are shown in Figure 2 (long dashed lines from top to bottom respectively). In our approach, almost by deﬁnition, the two parameters are not completely independent, the ﬂatter the power law slope, the lower the cut-off energy is. The contribution of radio loud AGN is then summed to the observationally resolved fraction in the 2–10 keV range, extrapolated to high energies following the prescriptions of the Gilli et al. [11] model (short dashed line in Figure 2). Finally the total contribution for the three α, E cut pairs is computed (solid lines). The residual unresolved background obtained by subtracting the models previously described from the total XRB ﬂux, modeled using the [20] analytical approximation, is shown in Figure 3. A comparison with the contribution of a population of CT AGN, assumed to evolve as unobscured sources [10], for two different values (100 and 320 keV) of the high energy cutoff is shown in Figure 4. The model spectra agree extremely well below the peak energy while at higher energies, depending from the E cut and α values adopted to model the contribution of radio-loud AGN, the predicted residual spectrum falls more rapidly with an over-exponential shape which is more pronounced for α = 0.5, E cut = 800 keV. At the face value these results suggest that the sources of the unresolved background are characterized by either a very peaked spectrum or are clustered over a smaller redshift range or a combination of the two. 4. Conclusions The above described exercise conﬁrm and somewhat extend the ﬁndings of Worsley et al. [1] and Comastri [5]. Even though the model dependent approach does not allow to break the Springer

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Fig. 3 The unresolved background as obtained by subtracting the contribution of both radio-quiet and radioloud AGN (long-dashed black lines) along with that predicted by the CT AGN in the Gilli et al., 2006 model for two different E cut values (magenta solid lines). The XRB spectral data in the 0.3–3 MeV range are from SMM [24], while in the 2–30 MeV from COMPTEL [25].

degeneracy between the spectral parameters and in particular among the cut-off energy and the source red-shift some preliminary conclusions may be already drawn. A population of CT AGN with a space density and cosmological evolution comparable to that of less obscured, Compton thin sources provide an excellent description of the residual XRB spectrum up to about 10–20 keV. At higher energies the residual spectrum is no longer well approximated by an exponentially cut-offed power law model folded with the redshift distribution observed in deep Chandra, and XMM-Newton ﬁelds. It can be argued that a suitable ﬁne tuning of cut-off energy and redshift distributions along with a more extended treatement of the contribution of radio-loud AGN may provide a much better ﬁt to the unresolved XRB above 30 keV. However it should be also stressed that the observational constraints used to compute the residual XRB are still subject to signiﬁcant uncertainties. Recent measurements of the XRB spectral intensity below 10 keV obtained with imaging instrument are systematically higher than the intensity originally measured by HEAO1-A2 (see Figure 1 and [21] for a recent reanalysis of the HEAO1 data), Given that the the only available observation of the intensity and location of the XRB peak is from the same A2 experiment, some doubts have been raised on the absolute ﬂux and intensity of the XRB above 10 keV. In the hard X-rays/ soft γ -rays the statistical errors as well as the relative calibration between different experiments are even larger. Before attempting a more sophisticated modelling of the broad band background spectrum from its peak down to MeV and GeV region a more robust determination of the observational framework is needed. Sensitive imaging observations down to about 10−14 erg cm−2 s−1 in the approximately 10–50 keV energy range would resolve about half of the background in that band to be compared with the present less than a few percent. A major breakthrough in the census and the study of obscured accreting black holes is expected by future hard X-ray missions and especially by Simbol-X [22]. A mission capable to explore the 100–1000 keV decade with comparably good sensitivity (i.e.the Gamma Ray Imager mission concept see Von Ballmoos and Kn¨odlseder these proceedings) would open the possibility to Springer

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investigate the origin of the primary emission mechanism in AGN, presumably responsible of the high energy cut-off, with important consequences for the scientiﬁc objectives discussed in this paper. Acknowledgements This work was partially funded by a MIUR grant (Coﬁn 03-02-23) and by ASI. AC thanks Gabriele Ghisellini for useful discussions, Filippo Frontera for the kind invitation and Peter Von Ballmoos for organizing an interesting and stimulating workshop.

References 1. Worsley, M.A., Fabian, A.C., Bauer, F.E., Alexander, D.M., Hasinger, G., Mateos, S., Brunner, H., Brandt, W.N., Schneider, D.P.: The unresolved hard X-ray background: the missing source population implied by the Chandra and XMM-Newton deep ﬁelds. MNRAS 357, 1281 (2005) 2. Hickox, R.C., Markevitch, M.: Absolute measurement of the unresolved X-ray background in the 0.5–8 keV band with Chandra ApJ in press (astro-ph/0512542) (2006) 3. Risaliti, G., Maiolino, R., Salvati, M.: The distribution of absorbing column densities among Seyfert 2 galaxies. ApJ 522, 157 (1999) 4. Matt, G.: Broad band spectral properties of AGNs and quasars, observations and theory Nuclear Physics B – Proceedings Supplements 132, 97 (2004) 5. Comastri, A.: In multiwavelength AGN surveys; proceedings of the Guillermo Haro conference held December 8–12, 2003. In: Cozumel, Mexico. Mujica, R., Maiolino, R. (eds.), World Scientiﬁc Publishing Company, Singapore, p. 323 (2004a) 6. Comastri, A.: Compton-thick AGN: The dark side of the X-Ray background in supermassive black holes in the distant universe. Barger, A.J. (eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004, p. 245 (2004b) 7. Pounds, K.A., Nandra, K., Stewart, G.C., George, I.M., Fabian, A.C.: X-ray reﬂection from cold matter in the nuclei of active galaxies. Nature 344, 132 (1990) 8. Perola, G.C., Matt, G., Cappi, M., Fiore, F., Guainazzi, M., Maraschi, L., Petrucci, P.O., Piro, L.: Compton reﬂection and iron ﬂuorescence in BeppoSAX observations of Seyfert type 1 galaxies. A&A 389, 802 (2002) 9. Guainazzi, M., Matt, G., Perola, G.C.: X-ray, obscuration and obscured AGN in the local universe. A&A 444, 119 (2005) 10. Hasinger, G., Miyaji, T, Schmidt, M.: Luminosity-dependent evolution of soft X-ray selected AGN: New Chandra and XMM-Newton surveys. A&A 441, 417 (2005) 11. Gilli, R., Comastri, A., Hasinger, G. in preparation (2006) 12. Malizia, A., Bassani, L., Stephen, J.B., Di Cocco, G., Fiore, F., Dean, A.J. BeppoSAX Average Spectra of Seyfert Galaxies. ApJ 589, L17 (2003) 13. Matt, G. et al.: One more surprise from the circinus galaxy: BeppoSAX discovery of a transmission component in hard X-rays. A&A 341, L39 (1999) 14. Soldi, S., Beckmann, V., Bassani, L., Courvoisier, T.J.L., Landi, R., Malizia, A., Dean, A.J., de Rosa, A., Fabian, A.C., Walter R.: INTEGRAL observations of six AGN in the Galactic Plane. A&A 444, 431 (2005) 15. Giommi, P., Colafrancesco, S., Cavazzuti, E., Perri, M., Pittori, C.: Non-thermal backgrounds. A&A 455, 843 (2006) 16. Galbiati, E., Caccianiga, A., Maccacaro, T., Braito, V., Della Ceca, R., Severgnini, P., Brunner, H., Lehmann, I., Page, M.J.: XMM-Newton spectroscopy of an X-ray selected sample of RL AGNs. A&A 430, 927 (2005) 17. Reeves, J.N., Turner, M.J.L.: X-ray spectra of a large sample of quasars with ASCA MNRAS 316, 234 (2000) 18. Page, K.L., Reeves, J.N., O’Brien, P.T., Turner, M.J.L.: XMM-Newton spectroscopy of high-redshift quasars. MNRAS 364, 195 (2005) 19. Lopez, L.A., Brandt, W.N., Vignali, C., Schneider, D.P., Chartas, G., Garmire, G.P.: A Chandra snapshot survey of representative high redshift radio-loud quasars from the Parkes-MIT-NRAO sample, AJ in press astro-ph/0601037 (2006) 20. Gruber, D.E.: The hard x-ray background in: The X-ray background. Collected papers and reviews from a workshop held in Laredo, Spain, September, 1990. Barcons, X., Fabian, A.C. (eds.), Cambridge University Press, Cambridge; New York, NY. p. 44 (1992) Springer

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21. Revnivtsev, M., Gilfanov, M., Jahoda, K., Sunyaev, R.: Intensity of the cosmic X-ray background from HEAO1/A2 experiment. A&A 444, 381 (2005) 22. Ferrando, P. et al.: SIMBOL-X: a formation ﬂying mission for hard X-ray astrophysics Optics for EUV, X-Ray, and Gamma-Ray Astronomy II. Citterio, O., O’Dell, S.L.(eds.), Proc. SPIE, 5900, 195 (2005) 23. Gilli, R., Comastri, A., Brunetti, G., Setti, G.: The contribution of AGN to the X-ray background: the effect of iron features New Astronomy 4, 45 (1999) 24. Watanabe, K., Hartmann, D.H., Leising, M.D., The, L.-S., Share, G.H., Kinzer, R.L.: The cosmic gamma ray background from supernovae in proceedings of the fourth compton symposium (eds.), Dermer, C. D., Strickman, M. S., Kurfess, J. D. Williamsburg, VA April 1997: AIP Conference Proceedings 410, 1223. (1997) 25. Kappadath, S.C. et al.: The preliminary cosmic diffuse γ -ray spectrum from 800 keV to 30 MeV measured with COMPTEL. A&AS 120, 619 (1996)

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Exp Astron (2005) 20:49–55 DOI 10.1007/s10686-006-9052-3 ORIGINAL ARTICLE

Focusing supernova gamma rays Questions for a high sensitivity gamma-ray telescope M. D. Leising

Received: 16 January 2006 / Accepted: 26 May 2006 C Springer Science + Business Media B.V. 2006

Abstract Despite their great intrinsic interest and extensive use as tools in other areas of astronomy, fundamental questions remain as to the nature of supernovae of all types. The radioactivity produced by nuclear fusion reactions in the explosions provides several excellent diagnostics, observable through gamma-ray emission. This great potential is largely unrealized because the ﬂuxes from events at common distances are very small. Instrument sensitivity is paramount, and gamma-ray optics offer an excellent possibility for greatly increasing collecting area, without a large increase in background rates, and reaching the required sensitivities. Here we outline some of the major open questions about supernovae and discuss how gamma-ray spectroscopy can address them, including instrument requirements for a future focusing gamma-ray telescope. Keywords Supernovae . Gamma-rays . Radioactivity

1. Introduction Supernovae have been known for thousands of years as bright new stars that appeared where none was visible before. In visible light they are intrinsically as bright as a small galaxy. Fairly homogeneous in their peak brightnesses and light curves, it has been known for a century that spectral properties of supernovae are quite inhomogenous. Over the past twenty-ﬁve years, it has become clear that two distinct and very different underlying mechanisms cause supernovae: the collapse and rebound of the cores of massive stars, and the thermonuclear runaway of electron degenerate, low mass, white dwarf stars. Most of our understanding of supernovae has come from visible light observations. This emission originates from the photospheric surface (early in the evolution) so information about the initial conditions and primary energy

Supported by NASA and CESR. M. D. Leising Department of Physics & Astronomy, Clemson University e-mail: [email protected] Springer

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input is often hidden. Later, emission is from a dilute nebula, which is often far from local thermodynamic equilibrium, so detailed quantitative information is often difﬁcult to derive. The nuclear fusion reactions that are fundamental to both types of supernovae result in, besides important energy input and new stable nuclei, radioactive nuclei that serve as clear tracers of the nuclear processing that occurs. In fact, radioactivity dominates the luminous display of the ejected material after the ﬁrst few weeks. Some of the radioactive decays result in gamma-rays from the de-excitation of the daughter nuclei. These penetrating photons can be used to count the radioactive nuclei produced, measure the ejecta kinematics, and locate the radioactive nuclei within the ejecta [3]. The observational situation depends on the radioactive lifetimes: short-lived isotopes can be observed in new supernovae, intermediate lifetimes in nearby (i.e., galactic and in the local group of galaxies) supernova remnants, and long-lived nuclei in the collective, unresolved emission of the Milky Way. Our emphasis here is mostly on thermonuclear supernovae, because that is where the impact of a gamma-ray lens on our understanding of supernovae is likely to be greatest.

2. Thermonuclear supernovae Spectroscopically classiﬁed as supernovae of Type Ia (i.e., lacking hydrogen lines but with a characteristic prominent silicon line) these are the classical thermonuclear runaway and complete disruption of a white dwarf star. When the nuclear burning becomes exothermic the temperature increases, but because the star is supported by degeneracy pressure, no structural adjustment ensues, and the burning accelerates. The nuclear ﬂame propagates in an unknown manner through the star, burns much of it to iron-peak nuclei, and destroys the white dwarf. How this compact star comes to this situation is unclear. It is presumably bound in a binary system, with a donor star that is either another white dwarf or a normal star. Favored models include a carbon-oxygen white dwarf that accretes matter until it reaches about 1.4 M , when the nuclear instability occurs near its center. More than 1 M of the star is burned, with about 0.6 M of radioactive 56 Ni produced. Just how much and where depends on how the nuclear ﬂame propagates. Complete detonations (supersonic burning fronts) are ruled out by observations but whether and how a subsonic ﬂame transitions to a detonation (known as “delayed detonation”) is unknown. Double white dwarf merger models, and lower mass white dwarfs whose explosion is triggered by a helium burning detonation in accreted surface layers, are also possible models, at least for some of the observed Type Ia supernovae. Thermonuclear supernovae are the sources of most of the iron peak elements in nature. They occur in the Milky Way galaxy at the rate of one every few centuries. They are used extensively to measure vast distances with dramatic implications for the apparent acceleration of the expansion of the universe, caused by some otherwise undetected “dark energy” [9]. Almost standard candles, their absolute magnitudes are deduced from the width in time of their visible light curves, assuming there is a one to one mapping of these properties [15]. Whether there is truly one physical parameter of the explosion that determines both is not known. Even if there is, whether the same relationship should hold exactly to redshifts approaching unity, when, for example, the metallicity of the systems was much lower than in the nearby events for which this relationship is calibrated, is also not clear [5]. Complete conﬁdence in the accuracy of using supernovae of Type Ia to measure such distances awaits better understanding of the explosions themselves, which is where gamma-ray line studies of nearby SNe Ia will prove to be so useful. Springer

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Fig. 1 The escaping gamma-ray spectrum of delayed detonation model DD202c [6] at 25 days post-explosion, as calculated by [13] At this time lines of both 56 Ni (158, 749, 812 keV) and 56 Co (847, 1238, 2599, 511 . . . keV) are prominent, as is the compton scattered continuum

The prodigious production of radioactivity is what makes these objects excellent gammaray astronomy targets. The decay chain 56

Ni (6d) −→

56

Co (77d) −→

56

Fe

produces most of the power for the optical display through the deposition (scattering and absorption) of the gamma-ray photons. The 56 Ni decays while the ejecta are still mostly thick to gamma-rays, so the escaping luminosity of its 158 and 812 keV lines (among others) is very sensitive to where within the ejected material the 56 Ni is produced. Later, after the 56 Ni has decayed away, the 56 Co lines are prominent, and eventually nearly all escape. With gamma-ray measurements we can in principle unfold the distribution of radioactive 56 Ni in mass and in velocity space. In most models some 56 Ni is ejected at speeds up to 10,000 km s−1 ; it extends up to 15,000 km s−1 in some, so energy resolution better than 1% is essential. Where the radioactivity is produced is a direct diagnostic of the burning conditions and ﬂame propagation. Deriving this requires of order 1000 photons detected in a few lines (see, e.g., Figure 1 for the prominent ones) at a few times. With peak line ﬂuxes of ∼10−5 cm−2 s−1 for even near SNe Ia, it is clear that the effective area of the telescope will have to be at least hundreds of cm2 even for zero background (which is unrealistic in this energy range.) A huge improvement in sensitivity over previous and current missions is clearly required. To illustrate the requirements for real progress with a gamma-ray spectrometer, we consider current models. Different models can be distinguished by their differing 56 Ni distributions in mass, which can be measured in the gamma-ray light curves (ﬂux vs. time), or by their 56 Ni distribution in velocity, measured by the Doppler proﬁles of the lines. A narrowﬁeld gamma-ray focuser, unless it was completely dedicated to these particular observations, will not revisit enough supernovae enough times for the former objective, so it will have to excel at the latter, and do high-precision, moderate resolution spectroscopy. For example, two mildly different models, a standard deﬂagration (model W7 of [14]) and a delayed detonation (see Figure 1) are shown at 25 days in Figure 2. A line ﬂux sensitivity of roughly 3 × 10−6 cm−2 s−1 (3σ for lines of width 25 keV) is required to clearly distinguish these two, admittedly similar, models. At this time, each of these lines would be measured at ∼ 10σ signiﬁcance. The discrimination is actually better achieved near 80 days, when the 847 keV line ﬂux is four times higher. Such sensitivities are frequently discussed for near-future instruments (e.g., for MAX; see Barriere et al. this volume) but for integration times of 106 seconds, and this is a very nearby event. Of interest for lenses is the energy bandpass required. Early on, line centroids can be shifted by 4–5% of their energies to the blue. They move back Springer

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Fig. 2 The gamma-ray spectrum near 800 keV for a delayed detonation model (solid line) and a deﬂagration model (dashed line) at 25 days at distance 10 Mpc, in units of photons cm−2 s−1 MeV−1 . The two lower energy lines are from 56 Ni, the higher one from 56 Co. The spectrum will have to be measured with high precision to distinguish these two models, especially if the distance is not well known

Fig. 3 The cumulative distribution of nearby SNe of Type Ia discovered in the past 10 years versus distance. The smooth line shows the number expected if 150 per year are homogeneously distributed within 100 Mpc. The sample is by no means complete, but suggests that one per year closer than 20 Mpc is very likely, even if only considering those discovered optically

to the rest energies at roughly 1% every 10–12 days. The expected line widths are typically 3–5% FWHM. Million second integrations present two problems: the spectra can change signiﬁcantly over such times, and the long observations severely limit the number of objects a telescope can observe. In any case, one will want to observed each supernova at least a few times in its evolution. The most information will be obtained from the nearest, most precisely measured objects, but as SNe Ia do show variety, it will be necessary to observe at least several. Therefore, the required sensitivity is that needed to make very signiﬁcant detections of supernovae that are likely to occur at the rate of a few per year. To see what ﬂuxes are to be expected at this rate, we consider the recent supernova record. Simply taking conﬁrmed SNe Ia in the ten years ending 1 July 2005, and taking distances of their host galaxies from Tully’s (1988) Nearby Galaxies Catalog, gives the cumulative distribution of SNe Ia vs distance shown in Figure 3. Clearly this sample still suffers from incompleteness (even the brightest SN display a zone of avoidance along the galactic plane, see Figure 4) but at least one SN Ia per year closer than 20 Mpc seems assured. At distance of 20 Mpc, most SN Ia models reach line ﬂuxes of at least 7 × 10−6 cm−2 s−1 . In order to discriminate among them, or to constrain the distribution of 56 Ni within the ejecta in a single observation, the lines must be measured with signiﬁcance near 25σ . Thus the instrument must have a 3σ sensitivity to broad lines near 1 × 10−6 cm−2 s−1 , to insure real Springer

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Fig. 4 The distribution on the sky, in galactic coordinates, of recent supernovae. Most searches focus on individual galaxies, and avoid the galactic plane

progress. Ideally, this would be for integration times of a few days or less. An instrument such as this would make very detailed measurements of several thermonuclear supernovae in a few year mission, clarifying the nature of the progenitor systems and the nuclear ﬂame propagation.

3. Core collapse supernovae After massive stars have exhausted all central exothermic nuclear fuels, their cores exceed the mass that can be supported by electron degeneracy pressure and collapse. After reaching nearly nuclear density, the huge gravitational binding energy (a few 1053 ergs) is released and mostly radiated as neutrinos. A fraction of this energy is coupled to the more slowly infalling mantle of the star, which is shocked, heated, and ejected. How this coupling occurs, or the explosion mechanism, is uncertain at present. Peak temperatures reach that of nuclear statistical equilibrium in the innermost ejecta, and decrease moving outward. The radioactive 56 Ni is produced in the inner few tenths of a M ejected, and more falls back into the compact remnant object. This decay chain again powers the later optical display. The ejecta kinetic energy is typically 1–2 × 1051 ergs. These events produce most of the natural abundances of the elements oxygen through calcium, and probably many heavy elements as well. Their optical spectra include absorption lines of the stellar envelope material – whatever has not been lost in stellar winds – including, sometimes, hydrogen (known as Type II supernovae), helium (Type Ib), or neither (Type Ic.) These events occur at the rate of a few per century in the Milky Way. The major questions that remain about core collapse supernovae are how the large binding energy is transferred to the star, and how important are dynamical complications, such as mixing and jets. Material near the ejection cutoff radius, and that carried outward by instabilities and jets, are highly radioactive. Thus gamma-ray lines can help clarify these questions. In general, the large ejecta masses make line ﬂuxes low because of attenuation, so opportunities will be rare. A great deal of what we know about core collapse supernovae derives from Supernova 1987A. It is one of the most remarkable and best observed objects in modern astronomy. Springer

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Table 1 Isotopes possibly detectable in galactic SN and remnants and local group SNe

Isotope

Half-life

line energy (keV)

7 Be

53 d 2.6 y 0.7 My 44 d 1.5 My 5.3 y 0.1 My

478 1275 1809 1099, 1292 59 1173, 1332 87

22 Na 26 Al 59 Fe 60 Fe 60 Co 126 Sn

Among many ﬁrsts were observations of live radioactive isotopes freshly synthesized in the explosion, which provide detailed diagnostics of the nuclear burning conditions and explosion dynamics. These included 56 Co (synthesized as 56 Ni) detected directly in γ -ray lines [12] and indirectly as the power source for the intermediate time optical light curve e.g. Bouchet et al. [1]; 57 Co (made as 57 Ni) detected directly in γ -ray lines [10], inferred from infrared spectra [16] and from the visible light curve see however Clayton et al. [4]; and 44 Ti, which possibly powers the nebula at late times [2, 11]. This was a very rare event, which we can not expect to repeat any time soon, but some of the same studies can be done on other core collapse supernovae. The 56 Ni chain will be difﬁcult to observe. Scaling from SN 1987A, even allowing that some supernovae will have lower mass envelopes at explosion, we can hope to detect the 56 Co gamma-ray lines to only 2–3 Mpc distance for line sensitivities near 10−6 cm−2 s−1 . The 57 Co line ﬂuxes are much lower still, so we must wait for a local group supernova. Some supernovae might exceed these estimates. Strong jets might carry core 56 Ni to outer region, perhaps enhancing 56 Co line ﬂuxes by up to a factor of ﬁve [7]. The longer-lived isotope 44 Ti (63 y) is produced in the innermost ejected material, even interior on average to the ejected 56 Ni. It is the source of 44 Ca in nature, after the intermediate 44 Sc decay, and is produced in the alpha-rich freezeout of nuclear statistical equilibrium. Because the initial temperature is so high, of order 1010 K, the temperature of freezeout (∼3 × 109 K) is reached at lower density than for slightly exterior regions, when a large number of free alpha particles are present to alter the equilibrium abundances. It has been detected in the supernova remnant Cas A in our galaxy [8], in an unexpectedly large quantity. A gamma-ray lens, if it includes a band at 68, 78, or 1157 keV, could determine the mass of this isotope there to 1–2%. SN 1987A again offers an interesting prospect; the ﬂuxes in these lines could be 3 × 10−6 cm−2 s−1 or more. So this isotope’s abundance could be determined to 10% or better. The Doppler line proﬁles in both of these, and possibly other supernova remnants, might show the presence of jets as higher than average speed 44 Ti. In nearby core-collapse supernovae and remnants, a number of other isotopes are possibly detectable. Some of these are listed in Table 1. The last entry is an example of one of several possible r-process isotopes (made from the rapid addition of neutrons to heavy seed nuclei.) Fluxes from these are likely to be quite low, however, the discovery of a very nearby object, or signiﬁcant enhancements by jets, could make a detection possible.

4. Summary It is apparent that gamma-ray line observations of supernovae can contribute greatly to answering fundamental questions about their nature. Instrument sensitivity is by far the most Springer

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important attribute for making real progress; a sensitivity to broad lines reaching or exceeding 10−6 cm−2 s−1 is essential. A focusing gamma-ray telescope, even with only a few narrow bands, offers a strong possibility, but if it is to achieve a number of supernova objectives, among many other interesting sources, this sensitivity will probably have to be achieved in integration times of a few 105 seconds or less – a huge challenge at present.

References 1. Bouchet, P., Danziger, I.J., Lucy, L.B.: Bolometric light curve of SN 1987A – Results from day 616 to 1316 after outburst. AJ 102, 1135–1146 (1991) 2. Chugai, N.N., Chevalier, R.A., Kirshner, R.P., Challis, P.M.: Hubble space telescope spectrum of SN 1987A at an age of 8 years: radioactive luminescence of cool gas. ApJ 483, 925 (1997) 3. Clayton, D.D., Colgate, S.A., Fishman, G.J.: Gamma-ray lines from young supernova remnants. ApJ 155, 75 (1969) 4. Clayton, D.D., Leising, M.D., The, L.-S., Johnson, W.N., Kurfess, J.D.: The Co-57 abundance in SN 1987A. ApJ 399, L141–L144 (1992) 5. Dominguez, I., Hoﬂich, P., Straniero, O., Wheeler, C.: Evolution of type Ia supernovae on cosmological time scales. Memorie della Societa Astronomica Italiana 71, 449–460 (2000) 6. Hoeﬂich, P., Wheeler, J.C., Khokhlov, A.: Hard X-rays and gamma rays from type IA supernovae. ApJ 492, 228 (1998) 7. Hungerford, A.L., Fryer, C.L., Rockefeller, G.: Gamma rays from single-lobe supernova explosions. ApJ 635, 487–501 (2005) 8. Iyudin, A.F., Diehl, R., Bloemen, H., Hermsen, W., Lichti, G.G., Morris, D., Ryan, J., Sch¨onfelder, V., Steinle, H., Varendorff, M., de Vries, C., Winkler, C.: COMPTEL observations of Ti-44 gamma-ray line emission from CAS A. A&A 284, L1–L4 (1994) 9. Knop, R.A., Aldering, G., Amanullah, R., Astier, P., Blanc, G., Burns, M.S., Conley, A., Deustua, S.E., Doi, M., Ellis, R., Fabbro, S., Folatelli, G., Fruchter, A.S., Garavini, G., Garmond, S., Garton, K., Gibbons, R., Goldhaber, G., Goobar, A., Groom, D.E., Hardin, D. Hook, I., Howell, D.A., Kim, A.G., Lee, B.C. Lidman, C., Mendez, J., Nobili, S., Nugent, P.E., Pain, R., Panagia, N., Pennypacker, C.R., Perlmutter, S., Quimby, R., Raux, J., Regnault, N., Ruiz-Lapuente, P., Sainton, G., Schaefer, B., Schahmaneche, K., Smith, E., Spadafora, A.L., Stanishev, V., Sullivan, M., Walton, N.A., Wang, L., Wood-Vasey, W.M., Yasuda, N.: New Constraints on M , , and w from an independent set of 11 high-redshift supernovae observed with the hubble space telescope. ApJ 598, 102–137 (2003) 10. Kurfess, J.D., Johnson, W.N., Kinzer, R.L., Kroeger, R.A., Strickman, M.S., Grove, J.E., Leising, M.D., Clayton, D.D., Grabelsky, D.A., Purcell, W.R., Ulmer, M.P., Cameron, R.A., Jung, G.V.: Oriented scintillation spectrometer experiment observations of Co-57 in SN 1987A. ApJ 399, L137–L140 (1992) 11. Lundqvist, P., Kozma, C., Sollerman, J., Fransson, C.: ISO/SWS observations of SN 1987A. II. A reﬁned upper limit on the mass of 44Ti in the ejecta of SN 1987A. A&A 374, 629–637 (2001) 12. Matz, S.M., Share, G.H., Leising, M.D., Chupp, E.L., Vestrand, W.T.: Gamma-ray line emission from SN1987A. Nature 331, 416–418 (1988) 13. Milne, P.A., Hungerford, A.L., Fryer, C.L., Evans, T.M., Urbatsch, T.J., Boggs, S.E., Isern, J., Bravo, E., Hirschmann, A., Kumagai, S., Pinto, P.A., The, L.-S.: Uniﬁed one-dimensional simulations of gamma-ray line emission from type Ia supernovae. ApJ 613, 1101–1119 (2004) 14. Nomoto, K., Thielemann, F.-K., Yokoi, K.: Accreting white dwarf models of Type I supernovae. III – Carbon deﬂagration supernovae. ApJ 286, 644–658 (1984) 15. Phillips, M.M.: The absolute magnitudes of Type IA supernovae. ApJ 413, L105–L108 (1993) 16. Varani, G.F., Meikle, W.P.S., Spyromilio, J., Allen, D.A.: Direct observation of radioactive cobalt decay in supernova 1987A. MNRAS 245, 570 (1990)

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Exp Astron (2005) 20:57–64 DOI 10.1007/s10686-006-9036-3

Nucleosynthesis in nova explosions: Prospects for its observation with focusing telescopes M. Hernanz · J. Jos´e

Received: 19 December 2005 / Accepted: 3 March 2006 C Springer Science + Business Media B.V. 2006

Abstract Nova explosions are caused by the explosive burning of hydrogen in the envelope of accreting white dwarfs. During the thermonuclear runaway some radioactive isotopes are synthesized, which emit γ -rays when they decay. The γ -ray signatures of a nova explosion still remain undetected, because even the best instruments like SPI onboard INTEGRAL are not sensitive enough for the dim and broad lines emitted by novae at their typical distances. A very different situation is expected with a focusing telescope, like MAX. Prospects for detectability with a future γ -ray lens telescope are presented, with a special emphasis on the important information that γ -rays would provide about the explosion mechanism and the underlying white dwarf star. Keywords Gamma-ray astronomy . Gamma-ray lines . Nucleosynthesis . Novae . Cataclysmic variables

1. Introduction Novae are one example of so-called variable stars that shine in the sky. The name nova comes from nova stella, referring to the sudden appearance of a new star, followed by its fast or relatively fast fading. It was thought during many centuries that it was really a new star, before understanding that in fact it was an already existing star that brightened considerably by some reason. Nowadays we know that a classical nova is an explosion on top of a white dwarf star in a close binary system, which leads to an increase in luminosity by 7 or more orders of magnitude, and to mass ejection to the interstellar medium of about 10−5 − 10−4 Mstar , with M. Hernanz () Institut d’Estudis Espacials de Catalunya (IEEC/ICE-CSIC), Campus UAB, Facultat de Ci`encies, Torre C5 – parell – 2a planta 08193 Bellaterra (Barcelona), Spain e-mail: [email protected] J. Jos´e IEEC and Departament de F´ısica i Enginyeria Nuclear (UPC), Sor Eulalia d’Anzizu s/n, B5 08034 Barcelona, Spain Springer

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Mstar ∼M (M is the mass of the sun, i.e. 2 × 1033 g), at typical velocities of hundreds to thousands of km/s. Novae reach intrinsic luminosities which are ∼104 −105 L . Before understanding what a classical nova really is, it is important to be aware that white dwarfs are stars which have spent all their nuclear fuel and have as only destiny cooling down (when they evolve as isolated stars), at the expenses of their internal thermal energy (associated to the ions), with the electrons forming a degenerate Fermi gas which sustains the star’s gravity, keeping it at extremely large densities with extremely small sizes (typically a solar mass within an Earth-sized sphere, i.e. radius about 1000 km; the correponding surface gravities are very large −108 –109 cm.s−2 – and also the central densities – between 106 and 109 g.cm−3 ). But the ﬁnal fate of a white dwarf can be quite different when it belongs to a close binary system, where it interacts with its companion star. Then, accretion of matter from its neighbor star can lead to a wealth of spectacular phenomena; in particular, accreting white dwarfs can explode as supernovae (thermonuclear, also called type Ia) or as classical novae. Thermonuclear supernova explosions affect the whole star and are triggered by degenerate carbon burning (see Leising’s contribution in this same volume). Classical novae explosions are powered by degenerate hydrogen burning on top of the white dwarf; since only the white dwarf’s envelope is affected, the star recovers its previous state after the explosion (some months-years later), and the phenomenon is recurrent, with a period of about 104 –105 years. The companion star of the exploding white dwarf is a low-mass main sequence star (i.e. a star like the sun but with lower mass) and the binary system is called a cataclysmic variable. The nova rate in our galaxy, the Milky Way, is hard to determine, since optical observations are hampered by dust extinction. Two approaches have been used to estimate the global galactic nova rate: either the local observed nova rate is extrapolated (see for instance [25], who obtained 35 ± 11 yr−1 ), or a comparison with the nova counts in other nearby galaxies is made (see [26] for a review of both methods). It is worth mentioning that visual extinction reduces the number of discovered galatic novae to about 5, at most, per year.

2. Main observational properties of novae The visual light curves (temporal evolution of optical luminosity) of novae display a steep maximum, followed by a continuous decrease of luminosity. The steepness of the light curve (“speed class” of the nova) determines how fast the nova declines in luminosity after the outburst. The fastest novae decrease in 2 magnitudes in less than 10 days (the magnitude is a logarithmic measure of the luminosity, such that an increase in 5 magnitudes means a decrease by a factor of 100 in luminosity); slower novae can need more than 100 days for a similar luminosity variation. An important step forward in the comprehension of the nova phenomenon was made thanks to the advent of space observatories in the ultraviolet (UV). It was discovered that simultaneous to the decrease in visual luminosity there was an increase in the ultraviolet emission, so that the global “bolometric” luminosity was constant during some weeks-months after the outburst. (e.g. Nova Ser 1970 [7], Nova Cyg 1978 [30] or Nova Aql 1982 [28]). The interpretation of such an increase, observed in many novae thanks mainly to the International Ultraviolet Explorer (IUE) satellite, is that the energy distribution shifts towards higher frequencies (energies), since deeper and thus hotter regions of the expanding envelope are successively seen; that’s because the photosphere (the visible atmosphere, emitting approximately as a blackbody) recedes as expansion proceeds. Another important piece of information comes from infrared observations (when the nova forms dust), which show an Springer

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increase in infrared (IR) luminosity when the UV one diminishes; this is interpreted as the resulting re-radiation by dust grains of the UV energy they have absorbed. In addition to light curves, spectra in different energy bands give information about velocities and chemical composition (atomic) of the ejecta. An important property of many novae is their enhancements in several atoms, mainly C, N and O, but also Ne in several cases. For instance, Nova QU Vul 1984 showed an abundance of neon 100 times solar and a global metallicity 23 times solar. Another spectacular case was Nova V1370 Aql 1982, with metallicity Z = 0.86 = 45Z and Ne mass fraction about 300 times solar (see [9] for a compilation of nova abundances deduced from optical and UV observations). The physical interpretation of these enhancements relies on some process of mixing between the accreted material (assumed to be roughly solar, since it corresponds to the envelope of a “normal” companion star) with the underlying white dwarf core. At this point it is crucial to understand that the chemical composition of the underlying white dwarf, and specially that of its most external layers, is dictated by its previous stellar evolution, which mainly depends on its progenitor’s mass. For masses between ∼9 M to 10 − 12 M , non degenerate carbon burning produces an ONe white dwarf, with mass larger than ∼1.1 M [6, 8, 24]. Lower initial masses lead to CO white dwarfs. So, novae occurring on top of ONe white dwarfs can show some neon in their ejecta, whereas this is not the case for novae on CO white dwarfs. As we will see in Section 3, the chemical composition of the white dwarf is not only important to interpret the observations, but also to understand the explosion mechanism itself.

3. Why a nova explodes: The thermonuclear runaway scenario As mentioned in Section 1, a white dwarf which accretes H-rich matter from a companion star in a binary system can be “rejuvenated” and experience an outburst (instead of cooling down to invisibility as when it is isolated). The reason is the following: when matter is accreted on top of the white dwarf, it is strongly compressed (because the gravity at the surface of white dwarfs is extremely large – see above), until reaching temperatures large enough to enable fusion of hydrogen nuclei, i.e. thermonuclear hydrogen burning. Since large densities are reached, there is electron degeneracy, meaning that matter can not respond as an ideal gas (it can not expand much) to the injection of energy by hydrogen thermonuclear burning. As a consequence of this degenerate nuclear burning, a thermonuclear runaway ensues, with an increase of temperature “without control”. Convection–in addition to usual radiation in star’s envelopes- is needed to transport heat outside the burning shell. Convective transport plays a very important role in the ﬁnal success of the explosion, since it transports some radioactive nuclei (β + -unstable) produced during hydrogen burning through the CNO cycle (see Figure 1 and [29]) to the outer envelope, where they are prevented from destruction by proton captures, thus being able to decay and release energy. This later injection of energy in the outer less dense zones provoques large envelope expansion–such that there is ejection of mass- and large increase in luminosity, the two basic properties of a nova explosion.

4. Nucleosynthesis of radioactive nuclei Hydrogen thermonuclear burning starts with the proton-proton chains [2], but once temperature is larger than ∼2 × 107 K, burning through the CNO cycle (see Figure 1) is dominant, provided that there is some carbon available. In novae, some initial carbon is in general assumed, since some mixing between solar accreted matter and the underlying core is adopted Springer

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Fig. 1 Scheme of the carbon-nitrogen-oxygen (CNO) cycle of hydrogen burning, which operates out of equilibrium in nova outbursts. The lifetimes of the β + -unstable nuclei, which act as bottlenecks of the cycle, are displayed

(however, the exact mechanism through which this mixing occurs is still not well understood; see a recent multidimensional attempt to model it in [1]). As can be seen in Figure 1, a succession of proton captures (p, γ ) and β + -decays occurs, and the cycle is closed by (p, α) reactions, where a proton is captured and an α particle is released. But in novae the CNO cycle is out of equilibrium (it is “not closed”), because the timescales of some β + -decays are longer than the evolutionary lifetime; then the corresponding nuclei act as a kind of “bottleneck” of the cycle. As mentioned above, the energy release associated to those β + -decays is the ﬁnal responsible for the atmospheric expansion, luminosity increase and mass ejection, since the nuclei (mainly 14,15 O,17 F, see Figure 1) have been transported to the outer envelope by convection, being thus preserved from destruction in the hotter shells at the envelope’s bottom. The main radioactive nuclei synthesized in novae that are relevant for the γ -ray emission are: 13 N and 18 F (positron emitters), 7 Be, 22 Na and 26 Al (see Table 1). The ﬁrst two are produced during the CNO cycle; theoretical models indicate that they are both produced in novae on CO and on ONe white dwarfs [15]. On the contrary, 22 Na and 26 Al are only produced in ONe novae; the reason is that there is the need of some seed nuclei for their synthesis through the so-called “Ne-Na” and “Mg-Al” cycles (mainly 20 Ne and 24,25 Mg for 22 Na and 26 Al, respectively; see for instance [17]). Finally, 7 Be synthesis is larger in CO novae, because the presence of a larger fraction of 12 C (as compared with ONe novae) makes the rise to temperatures around 108 K, where photodisintegration of 8 B − 8 B(γ , p)7 Be-prevents 7 Be destruction, faster [12,15]. Table 1 Radioactivities in nova ejecta

Isotope 13 N

Lifetime 862 s

Type of emission

Main disintegration process

Nova type

511 keV line &

β + -decay

CO & ONe

continuum 158 min

511 keV line &

β + -decay

CO & ONe

7 Be

77 days

continuum 478 keV line

e− -capture

CO

22 Na

3.75 years

1275 & 511 keV lines

β + -decay

ONe

26 Al

106 years

1809 & 511 keV lines

β + -decay

ONe

18 F

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It is worth mentioning at this point that the depth of the white dwarf outer core at which mixing with accreted matter occurs is unknown (or alternatively, how much mass of the external layers above the ONe core of the progenitor star is lost during thermal pulses in the prior asymptotic giant branch (AGB) phase). Therefore, since there is an outer zone with some carbon (and oxygen) on top of ONe degenerate cores, it is possible that some novae would erode this “CO buffer” instead of the ONe core itself. Then the properties of the explosion would be a bit different and a nova hosted by an ONe white dwarf could also synthesize some 7 Be [18], and would not display any neon. Since neon is observed in many novae, mixing with the core should occur in some ONe novae, but perhaps in not all of them. Also, since the size in mass of the CO buffer decreases as white dwarf mass increases, mixing with the core is favored in novae on massive white dwarfs.

5. Gamma-rays from novae The role of novae as potential γ -ray emitters was noticed long ago [ 3, 4, 19]. In addition to the very short-lived isotopes responsible of the nova explosion, other longer-lived nuclei are synthesized which are relevant for the γ -ray emission of individual novae, as well as for the radioactivity of the Galaxy (see Table 1). As mentioned in Section 4, the short-lived nuclei 13 N and 18 F are produced in similar quantities in all nova types, whereas 7 Be is mainly produced in CO novae and 22 Na and 26 Al are synthesized only in ONe novae. The role played by the radioactive nuclei ejected by novae depends on their lifetimes. The short-lived nuclei 13 N and 18 F produce an intense burst of γ -ray emission, with duration of some hours, which is emitted at peak temperature epoch, well before the nova visual maximum (see [11,13] for details), i.e. before the nova is discovered optically. This emission is related to positron annihilation, which consists of a line at 511 keV and a continuum at energies between 20 and 511 keV, related to the positronium continuum plus the comptonization of the photons emitted in the line (see Figure 2, where the spectral evolution of a CO and an ONe nova at different epochs after peak temperature is shown). The emission related to medium-lived nuclei, 7 Be and 22 Na, appears later and is different in CO and ONe novae, because of their different nucleosynthesis: CO novae display a line at 478 keV related to 7 Be decay, whereas ONe novae show a line at 1275 keV related to 22 Na decay. The long-lived isotope 26 Al is also produced by novae. The Galactic γ -ray emission observed at 1809 keV ([21] with the HEAO 3 satellite and [5] with the CGRO/COMPTEL) corresponds to the decay of 26 Al. Its distribution seems to trace a young population of massive stars and the contribution of novae is not the dominant one (see [16, 23]). However, the recent detection of 60 Fe (traditionally only attributed to core collapse supernovae) in the galactic center with the RHESSI and INTEGRAL satellites [10, 27] has shown that an extra source of 26 Al is needed to explain the low 60 Fe/26 Al ratio observed (with respect to the ratio expected if only core collapse supernovae contributed to galactic 60 Fe and 26 Al). So, there is room for Wolf-Rayet stars, AGB stars and novae to contribute to the global galactic content of 26 Al [22]. But, the contribution of Wolf-Rayet stars to 60 Fe [20] also has to be taken into account to do proper comparisons between observations and theory.

6. Discussion In summary, classical novae explosions produce γ -rays, being the signature of CO and ONe novae different. The detectability distances for the lines at 478 and 1275 keV with the Springer

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Fig. 2 Early temporal evolution of the gamma-ray spectra of a CO (dotted) and an ONe (solid) nova, at a distance of 1 kpc

INTEGRAL/SPI instrument range between 0.2 and 0.5 kpc [14]; the width of the lines (∼7 keV for the 478 keV line and ∼20 keV for the 1275 keV line), is not negligible and largely degrades the sensitivity of the SPI instrument (because it has germanium detectors, with very good energetic resolution). The continuum and the 511 keV line are the most intense emissions, but their appearence before visual maximum and their very short duration requires “a posteriori” analyses, with large ﬁeld-of-view instruments monitoring the whole sky at the appropriate energies (some hundred keVs). With future instruments of these characteristics, novae would be detectable more easily in γ -rays than visually, because of the lack of extinction. In order to improve the detectability prospects for classical novae (and the same occurs for supernovae, see Leising’s contribution in this same volume), an important step forward in sensitivity for broad and moderately broad lines (in novae, E/E∼ 1.5%) is required. The best possibility by now is a focusing γ -ray lens, since it allows for a combination of large detection area with a small detector volume, a necessary condition to increase signiﬁcantly the signal to noise ratio (see various contributions in this volume). With a sensitivity of 5 × 10−7 phot.cm−2 .s−1 for narrow lines, i.e. ∼1.5 × 10−6 phot.cm−2. s−1 for the 20 keV broad 1275 keV 22 Na line, this line could be detected up to 4 kpc, with at least one ONe nova per year. To detect virtually all (ONe) novae, the sensitivity for the 1.5 % broad line at 1275 keV should be around 3 × 10−7 phot.cm−2 .s−1 (i.e. 10−7 phot.cm−2 .s−1 for a narrow line at the same energy). The detection of novae in γ -rays would give crucial insights on the nova theory: amount of 7 Be (and of its daughter nucleus 7 Li, with a still not well known galactic origin) and of 22 Na, classiﬁcation of novae as CO or ONe (and relationship with white dwarf mass), temperature attained in the burning shells (which strongly affects the nucleosynthetic output of novae), distribution and rate of novae in the Galaxy, dynamics and effectiveness of convection in the envelope (which strongly affects the prompt emission related with electron-positron Springer

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annihilation). Therefore, a push in the technology involved in γ -ray instrumentation is essential for the study of explosive phenomena such as novae and supernovae.

Acknowledgements This work has been supported by the spanish MEC grants AYA2004-06290-C02-01 and -02 and by the catalan DURSI.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13.

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

25.

Alexakis, A. et al.: On heavy element enrichment in classical novae. Astrophys. J. 602, 931–937 (2004) Clayton, D.D.: Principles of stellar evolution and nucleosynthesis. Mc.Graw-Hill (1968) Clayton, D.D.: 7 Li gamma-ray lines from novae. Astrophys. J. 244, L97–L98 (1981) Clayton, D.D., Hoyle, F.: Gamma-ray lines from novae. Astrophys. J. 187, L101–L103 (1974) Diehl, R., et al.: COMPTEL observations of Galactic 26 Al emission. Astron. & Astrophys. 298, 445–460 (1995) Dom´ınguez, I., Tornamb´e, A., Isern, J.: On the formation of O-Ne white dwarfs in metal-rich close binary systems. Astrophys. J. 419, 268–275 (1993) Gallagher, G.S., Code, A.D.: Ultraviolet photometry from the orbiting astronomical observatory. X.Nova FH SER 197. Astrophys. J. 189, 303–314 (1974) Gil-Pons, P., Garc´ıa-Berro, E., Jos´e, J., Hernanz, M., Truran, J.W.: The frequency of occurrence of novae hosting an ONe white dwarf. Astron. & Astrophys. 407, 1021–1028 (2003) Gehrz, R., Truran, J.W., Williams, R.E., Starrﬁeld, S.E.: Nucleosynthesis in classical novae and its contribution to the interstellar medium. Pub. Astron. Soc. Paciﬁc 110, 3–26 (1998) Harris, M.J., Kn¨odlseder, J., Jean, P., Cisana, E., Diehl, R., Lichti, G.G., Roques, J.-P., Schanne, S., Weidenspointner, G.: Detection of gamma-ray lines from interstellar 60 Fe by the high resolution spectrometer SPI. Astron. & Astrophys. 433, L49–L52 (2005) G´omez-Gomar, J., Hernanz, M., Jos´e, J., Isern, J.: Gamma-ray emission from individual classical novae. Month. Not. R.A.S. 296, 913–920 (1998) Hernanz, M., Jos´e, J., Coc, A., Isern, J.: On the synthesis of 7 Li and 7 Be in novae. Astrophys. J. 465, L27–L30 (1996) Hernanz, M., Jos´e, J., Coc, A., G´omez-Gomar, J., Isern, J., Gamma-ray emission fom novae related to positron annihilation: constraints on its observability posed by new experimental nuclear data. Astrophys. J. 526, L97–L100 (1999) Hernanz, M., Jos´e, J.: γ -rays from classical novae: expectations from present and future missions. New Astron. Rev. 48, 35–39 (2004) Jos´e, J., Hernanz, M.: Nucleosynthesis in classical novae: CO versus ONe white dwarfs. Astrophys. J. 494, 680–690 (1998) Jos´e, J., Hernanz, M., Coc, A.: New results on 26 Al production in classical novae. Astrophys. J. 479, L55–L58 (1997) Jos´e, J., Coc, A., Hernanz, M.: Nuclear uncertainties in the NeNa-MgAl cycles and production of 22 Na and 26 Al during nova outburts. Astrophys. J. 520, 347–360 (1999) Jos´e, J., Hernanz, M., Garc´ıa-Berro, E., Gil-Pons, P.: The impact of the chemical stratiﬁcation of white dwarfs on the classiﬁcation of classical novae. Astrophys. J. 597, L41–L44 (2003) Leising, M.D., Clayton, D.D.: Positron annihilation gamma-rays from novae. Astrophys. J. 323, 159–169 (1987) Limongi, M., Chiefﬁ, A.: New Astron. Rev. in press (2006) Mahoney, W.A., Ling, J.C., Wheaton, W.A., Jacobson, A.S.: HEAO 3 discovery of 26 Al in the interstellar medium. Astrophys. J. 286, 578–585 (1984) Prantzos, N.: Radioactive 26Al and 60Fe in the Milky Way: Implications of the RHESSI detection of 60Fe. Astron. & Astrophys. 420, 1033–1037 (2004) Prantzos, N., Diehl, R.: Radioactive 26 Al in the galaxy: observations versus theory. Phys. Rep. 267, 1–69 (1996) Ritossa, C., Garc´ıa-Berro, E., Iben, I.: On the evolution of stars that form electron-degenerate cores processed by carbon burning. II. Isotope abundances and thermal pulses in a 10 M model with an ONe core and applications to long-period variables, classical novae, and accretion-induced collapse. Astrophys. J. 460, 489–505 (1996) Shafter, A.W.: On the nova rate in the galaxy. Astrophys. J. 487, 226–236 (1997) Springer

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26. Shafter, A.W. (2002).: The Galactic nova rate, in Classical Nova Explosions, AIP CP 637, New York. p. 462–471 (2002) 27. Smith, D.M.: The Reuven Ramaty High Energy Solar Spectroscopic Imager Observation of the 1809 keV Line from Galactic 26Al. Astrophys. J. 589, L55–L58 (2003) 28. Snijders, M.A.J., Batt, T.J., Roche, P.F., Seaton, M.J., Morton, D.C., Spoelstra, T.A.T., Blades, J.C.: Nova Aquilae 1982. Month. Not. R.A.S. 228, 329–376 (1987) 29. Starrﬁeld, S.: in Classical novae, eds. M.F. Bode & A.M Evans, Wiley. Chichester p. 39–60 (1989) 30. Stickland, D.J., Penn, C.J., Seaton, M.J., Snijders, M.A.J., Storey, P.J.: Nova Cygni 1978. I – The nebular phase. Month. Not. R.A.S. 197, 107–138 (1981)

Springer

Exp Astron (2005) 20:65–73 DOI 10.1007/s10686-006-9043-4 ORIGINAL ARTICLE

Puzzles and potential for gamma-ray line observations of solar ﬂare ion acceleration David M. Smith

Received: 14 November 2005 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract The best tool for understanding ion acceleration in solar ﬂares is gamma-ray line emission from nuclear de-excitation, positron annihilation, and neutron capture. These techniques have not yet come close to reaching their potential due to limited counting statistics in the lines. Instruments with focusing optics and large effective areas promise real breakthroughs in understanding high-energy solar processes. I discuss what can be learned from the various lines and the instrumental requirements for future focusing observations. Keywords Solar ﬂares . Gamma-rays . Particle acceleration . Nuclear astrophysics

1. Introduction The Sun is our nearest astrophysical laboratory. Its photosphere and interior give us our clearest picture of “ordinary” stellar processes, but, in addition, the remarkable particle acceleration in its corona gives us a close-up look at processes that may occur not only in other active stars (some of them stunningly more violent than our own) but also in exotic environments like the magnetospheres of pulsars and the accretion disks around black holes. Solar ﬂares outshine the rest of the Sun at many wavelengths outside the visible: radio, x-ray, and the extreme ultraviolet. We are fairly certain that they take place due to a violent reconﬁguration of the coronal magnetic ﬁelds, but the details of the process are not understood. Many models exist, and many of them may correctly explain some of the variety of ﬂares observed. An astonishing fraction of the magnetic energy released – on the order of half [2,3] – goes directly into the acceleration of electrons and ions to high energies. These nonthermal distributions of particles can reach energies of hundreds of MeV for the electrons and several GeV for the ions, energies normally associated with cosmic rays. The acceleration processes “Mama always told me not to look into the sights of the Sun; oh, but mama, that’s where the fun is. . .” [1] D. M. Smith Physics Department and Santa Cruz Institute for Particle Physics, University of California, Santa Cruz Santa Cruz, CA 95064, USA e-mail: [email protected] Springer

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are both rapidly acting and sustained: ions are accelerated to tens of MeV in seconds and to GeV energies in a time on the order of a minute, yet the latter process (which may occur much further from the surface than the ﬂare loops) can persist for hours. Flare electrons can be studied by the bremsstrahlung x-rays they emit when interacting either with chromospheric plasma (in ﬂare footpoints) or in coronal loops that have ﬁlled with hot, dense plasma in the middle and later stages of a ﬂare. The electrons and x-rays are copious, so instruments of modest size can produce excellent spectra and images of the thermal bremsstrahlung (< ∼10 keV), nonthermal bremsstrahlung (> ∼25 keV), and the transition energies where they overlap. Satellites such as the Solar Maximum Mission (SMM), Yohkoh, and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) have made major advances with this technique; Sui, Holman and Dennis [4] provide an excellent example of the state of this art. Accelerated ions, however, tend to produce fewer photons. Those at low energies (< ∼1 MeV per ion) produce little emission at all. Protons and alpha particles of several MeV can excite nuclei in the solar atmosphere to produce characteristic de-excitation lines (Figure 1), and heavier accelerated ions of comparable energy can themselves be excited into these states. At even higher energies (tens of MeV), spallation reactions occur that produce free neutrons, positrons from radioactive decay of the products, and further characteristic nuclear decay lines. The neutrons produce the narrow line at 2.223 MeV when captured by protons after thermalization, and the positrons produce annihilation photons at 511 keV or below when they annihilate with an electron after slowing down. Understanding the composition and energy spectrum of the accelerated ions at the solar surface not only constrains the acceleration process, but makes for interesting comparisons with the compositions of solar energetic particles (SEPs) in interplanetary space [6] and of cosmic rays. The many gamma-ray lines from many species should carry more information than the smooth continuum of the electron bremsstrahlung. In practice, however, we know less about ion acceleration than about the electrons due to the small number of ﬂares that have shown gamma-ray lines and the small ﬂux of line photons emitted in each case. Furthermore, the

Fig. 1 De-excitation lines observed with RHESSI from the X4.8 ﬂare of 23 July, 2002. Redshifts are required by the Gaussian ﬁts (heavy curves versus unshifted thin curves), but the statistics are insufﬁcient to make out the details of the shapes. From Smith et al. [5] Springer

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lines are more difﬁcult to detect than bremsstrahlung at keV energies due to the instrumental challenges in stopping such high energy radiation and reading out the energy to sufﬁcient precision. Theoretical modeling and sophisticated analyses of gamma-ray data from SMM and other missions have run ahead of the quality of the available data in many cases. As this paper is intended to look forward rather than review the literature, only a few citations, to recent results, are included; interested readers are encouraged to explore the references in Mandzhavidze and Ramaty [7], Ramaty and Mandzhavidze [8], and the other papers cited here. 2. Speciﬁc diagnostics 2.1. Accelerated particle spectrum; accelerated and ambient abundances The spectrum of the accelerated ions is usually deduced from line ratios, either among nuclear de-excitation lines or between them and the spallation-induced positron-annihilation and neutron-capture lines. The de-excitation lines typically have a sharp threshold for excitation, varying from about 2.5 MeV for the 1.64 MeV line of 20 Ne to about 8 MeV for the 6.13 MeV line of 16 O [9]. The positron-annihilation and neutron-capture lines originate primarily from the interactions of ions of tens of MeV per nucleon, although the former can also have a component due to pion decay, which requires ion energies of hundreds of MeV. The use of these ratios is complicated by several factors. The de-excitation lines can be stimulated by alpha particles as well as protons, and the alphainduced lines have a lower threshold in energy per nucleon [9]. Thus the alpha/proton ratio and any spectral differences between the accelerated alphas and protons [10] will affect the line ratios. The abundances of the target nuclei in the solar atmosphere can also vary with height and with location on the solar surface; unless these abundances can be measured or deduced, they make up another variable interfering with determination of the accelerated spectrum from ratios. Some lines, such as the 4.4 MeV line from excited 12 C, can be created either by simple excitation of the stable counterpart nucleus or, in the case of a very energetic proton/alpha, by spallation of a heavier nucleus (in this case oxygen). This complicates the relation between accelerated particle spectrum and abundances in generating the line. The solution to these problems lies partly in making intelligent guesses about missing information, but also in using the Doppler proﬁles of the de-excitation lines to separately constrain the alpha/proton ratio and other parameters (see below). The neutron-capture line at 2.2 MeV will fade in time as neutrons are captured not only by protons but by 3 He, which has a higher cross section. The decay time of the line emission therefore constrains the atmospheric abundance of this isotope, which is astrophysically important but extremely difﬁcult to measure [7, 11, and references therein]. A concise but rich summary of the various lines and their applications to accelerated ion spectra and abundances, with many useful references, is given by Mandzhavidze and Ramaty [7]. A particularly in-depth example of their use in a very large ﬂare is given by Murphy et al. [12]. This study included abundance variations with time, which probably suggest abundance variations with position. A true imaging gamma-ray telescope with angular resolution on the order of 5–10

could test this. 2.2. Angular distribution of accelerated particles The nuclear excited states produced by collisions between accelerated and ambient particles have such short lifetimes that the decay gamma-ray is emitted with a Doppler shift due to the Springer

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Fig. 2 Simulated line shapes for the de-excitation line of 20 Ne due to accelerated protons (dashed line) and alphas (dot-dashed line), and their sum for an alpha/proton ratio of 0.5 (solid line). The rest energy is shown by the vertical line. These shapes were calculated for a spectral index of −3.75 for the particles, a ﬂare heliocentric angle of 30 deg, and an incident particle distribution isotropic in the downward hemisphere. Models calculated by Ronald Murphy [5]

recoil from the original collision. Thus, the line proﬁles can be compared to calculations for different angular distributions of incident particles with respect to the local normal (pancake, isotropic, and beamed distributions, for example, or distributions derived from modeling collisions in the loop). Accelerated alpha particles produce greater recoil, and can thus give a broad, red “tail” to the line shape (see Figure 2); ﬁtting this tail can constrain the alpha/proton ratio independently of line ﬂuxes and ratios. Accelerated nuclei heavier than He also produce de-excitation lines, but these tend to be so broadened that they run together into a quasicontinuum. The narrow lines (Figure 1) are sufﬁciently few in number that they are not expected to overlap in most cases (for a list of expected lines and reactions, see Kozlovsky, Murphy and Ramaty [9]). Line redshifts and widths have been studied using data from SMM and RHESSI [5, 13]. The former study showed the expected loss of redshift in moving from disk center to the limb when averaging over many ﬂares, while the latter found that an individual ﬂare can have high redshifts even near the limb, suggesting a particular tilt to the loops containing the ions. More recently, asymmetric, theoretically-calculated shapes like that shown in Figure 2 have been used to ﬁt high-resolution INTEGRAL data [14]; a similar analysis of RHESSI data is in progress.

2.3. Density, temperature, and convection of the solar atmosphere Recent high-resolution RHESSI spectra (e.g., Figure 3) of the positron annihilation line in ﬂares [15, 16] show surprisingly broad and variable Doppler widths. Since the positrons mostly thermalize before annihilating, this is a direct probe of the temperature of the annihilating region. The implied temperatures are on the order of 105 K, a transitional temperature Springer

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Fig. 3 Count spectra of the solar 511 keV annihilation line from two intervals in the ﬂare of 28 October 2003. During the later part of the ﬂare, when the emission was weaker, the line was much narrower (bottom data). From Share et al. [16]

found in only a negligible layer in the quiet solar atmosphere. To stop the positrons, quite a bit of plasma must be maintained at this temperature during a ﬂare despite extremely effective cooling. The ratio between the 511 keV annihilation line and the three-photon annihilation continuum below it due to decay of ortho-positronium gives an added constraint on the density of the region, since collisions disrupt the long-lived ortho-positronium at high densities, so that more annihilations occur either via free positrons or para-positronium. This new tool is revealing a part of the ﬂare environment that has eluded all other observational techniques. Another way of studying the solar atmosphere using gamma-ray lines was proposed by Ramaty and Mandzhavidze [8], using the lines at 847 and 1238 keV from 56 Co produced in the ﬂare. This isotope, with a half-life of 78.8 days, should be produced during spallation reactions and be visible as a hot spot that moves with the solar rotation while decaying, perhaps diffusing outward and being convected to deeper layers of the Sun. The rate of fading of this radioactive tracer is a unique tool to study the rate at which material is exchanged between the chromosphere and the deeper Sun. The lines have never been observed, being on the edge of sensitivity of existing instruments. The RHESSI data from after the series of large ﬂares of October/November 2003 are currently being searched. The ﬂux predictions are shown in (Figure 4). 2.4. Location of the acceleration sites by imaging RHESSI made the ﬁrst arcsecond images of MeV gamma-rays from solar ﬂares (indeed, of any source in space), resulting in a second major surprise. The positions of the 2.2 MeV neutron-capture hot spots were found to be signiﬁcantly shifted from the sites of electron bremsstrahlung. In one case, the ion interactions seemed to be taking place at the footpoint of a larger loop [17]. In another case (Figure 5), they are shifted to footpoints further along an arcade [18]. When sampled over more ﬂares and perhaps at higher resolution, these observations have the potential to reveal differences between ion and electron acceleration and help us identify the mechanisms of both. Springer

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Fig. 4 Approximate predicted ﬂux versus time for the 847 keV line of 56 Co during and after the series of major X-ﬂares in October–November 2003. The horizontal bars show the periods when the active region is visible on the near side of the Sun. These very rough estimates are based on scaling the predictions of Ramaty and Mandzhavidze [8] to the x-ray luminosity of these ﬂares Fig. 5 Overlay of the 50, 70, and 90% contours of 35-arcsecond resolution gamma-ray images from RHESSI on a contemporaneous TRACE EUV image. The ﬂare is the X17 event of 28 October 2003, and the energy bands are the 2.2 MeV neutron capture line (dark contours) and electron bremsstrahlung at 200–300 keV (lighter contours). The primary sites of ion and electron acceleration are, surprisingly, not cospatial; both footpoints are shifted in roughly the same direction. From Hurford et al. [18]

3. Role of MAX and other focusing missions 3.1. Observational capabilities Ideally, of course, we would like to study every line at once with extremely high sensitivity. Barring that, the highest priority should be simultaneous high sensitivity and high energy Springer

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resolution in the 511 keV line and at least one of the de-excitation lines. Most of the lineshape science can then be done with unprecedented precision. A traditional, non-focusing spectrometer could then obtain sufﬁcient statistics to derive ﬂuxes (if not shapes) for the other lines in a large ﬂare, for purposes of deriving the spectrum of the accelerated particles (which would be difﬁcult with only two lines). The neutron-capture line, being the brightest in the ﬂare, will be detected with good statistics in many ﬂares even without focusing, sometimes at levels that allow studies of the decay time. An advance of at least a factor of four beyond the statistics shown in Figure 1 is necessary to resolve the widths, redshifts, and relative amplitudes of the proton and alpha components shown in Figure 2. Improvements beyond that would allow the data to be split up into many time intervals, showing changes during the ﬂare that can be compared to activity at other wavelengths. The 23 July 2002 ﬂare shown in Figure 1 was of GOES class X4.81 , which would be typically among the dozen or so largest of a given solar maximum. Its line ﬂuxes (around 20 photons/cm2 per line) therefore provide a reasonable benchmark as the best ﬂare a new mission can be conﬁdent of seeing. Typical line widths are 3–10 keV at 511 keV and 4–10 keV at 847 keV (proton and alpha components, respectively). The de-excitation lines of lighter nuclei are much broader: about 50–100 keV for the C and O lines between 4 and 7 MeV. The planned energy bands for MAX (511 keV and 847 keV) match the criteria for optimal bands for solar studies on two conditions. First, the instrumental resolution must be high enough to resolve the solar widths of both lines: ∼2 keV FWHM, i.e. a well-designed germanium detector plane. Second, the width of each band must include the full line in the broadest solar cases, meaning a total width of at least 30 keV centered around each band. A signiﬁcant additional advantage will accrue if the 511 keV band can be extended downwards as far as 450, 400, or even 350 keV: this allows increasingly effective inclusion of the orthopositronium continuum and the nuclear lines from alpha/He interactions. The latter are particularly effective probes of both the accelerated alpha fraction and the angular distribution of the accelerated ions [19]. The effective area of RHESSI from 511-847 keV is fairly constant at around 26 cm2 . With a collecting area averaging about 500 cm2 over the two bands [20] and a likely photopeak efﬁciency in the detector plane on the order of 30–50%, MAX would have almost an order of magnitude more effective area. For the long-lived 847 keV line due to radioactive decay rather than de-excitation, the predicted ﬂuxes of 1 − 10 × 10−5 ph/cm2 /s (see Figure 4) after major ﬂares can be compared to the MAX 3σ narrow-line sensitivity of ∼10−6 ph/cm2 /s [20]. This is an opportunity to make an absolutely new measurement with, for once, a signiﬁcance of more than 3σ . 3.2. Operational considerations Revolutionary solar observations could be made even without a mission dedicated to ﬂare science. A focusing gamma-ray telescope such as MAX should be designed so that solar pointing is possible. This is not difﬁcult with regard to the instrument, since even tens of layers of mylar thermal blanketing do not attenuate gamma-rays signiﬁcantly. Spacecraft design considerations, however, often require that only a limited range of pointing angles with respect to the Sun be possible (for example, to simplify thermal design or to avoid having

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The GOES satellites measure thermal x-rays from hot ﬂare plasma, and the luminosity classes (A, B, C, M, X) represent decades in x-ray luminosity. A class X4.8 event peaks at 4.8 × 10−4 W/m2 . Springer

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to articulate solar panels). Astrophysical spacecraft often choose to leave a region near the Sun inaccessible for these reasons. In most cases, however, this exclusion zone could just as easily be chosen, during the space-craft design phase, to be in the anti-Sunward direction instead. For non-solar science, that should be no worse than a solar-pointing exclusion. Most of the largest ﬂares come from active regions that produce more than one, usually at intervals of one to a few days (see, e.g., the events of June 1991 and October/November 2003). A practical and possibly even optimal pointing strategy for a non-solar mission is to wait until the ﬁrst of these giant ﬂares occurs, then point to the active region responsible for the next week or so until it goes behind the Sun. This will require the ability to decide, command, and repoint in a period of one or two days. Dedicating a few weeks per year to this mode (5–10% of the mission schedule) is likely to capture a signiﬁcant fraction (perhaps even a majority) of the largest ﬂares during that year. The requirement on the ﬁeld of view is approximately 1.5–3 arcmin in radius, based on images of the largest ﬂares seen with RHESSI (e.g. Figure 5). Pointing would have to be updated continuously in a way not necessary for cosmic operations to track both the motion of the Sun on the sky and the motion of the active region on the Sun. The latter can be tracked with ground-based solar telescopes or space-based instruments at other wavelengths. 3.3. Focusing at the neutron capture line? Imaging at 2.2 MeV would require both an energy band and an instrumental strategy not yet contemplated for a proposed mission. The Laue lens system for MAX is a concentrator, not a true imager. In the most straightforward adaptation, subsets of tuned Laue crystals could all be optimized to a very narrow energy band (the line is naturally very narrow), but focused separately on different elements of an array of focal-plane detectors covering different parts of the ﬁeld of view. A grid of 10 × 10 20-arcsec pixels, for example (each pixel consisting of a subset of Laue crystals focusing to its own detector), would cover the largest ﬂares (Figure 5) with an angular resolution somewhat better than RHESSI’s. This technique is not nearly as effective as a true telescope, since each lens segment serves only one pixel of the image, not all of it. In sensitivity, it is equivalent to a small single-pixel instrument doing a long raster scan, except that such a scan would not be possible during the minutes or tens of minutes of the ﬂare. A simple extension of RHESSI’s technique (rotating modulation collimator [RMC] imaging, with no lens) to a larger instrument might prove to be preferable for this application. In a large ﬂare, the 2.2 MeV line is often strongly source dominated even without focusing, compared to either the instrumental background or the ﬂare continuum. Thus, the only purpose for focusing is that the effective area of the collecting lens might be cheaper than adding the same collecting area using more detectors instead; background reduction is no longer a major advantage. A hybrid conﬁguration might be considered, where RMC grids sit in front of the Laue lens, which focuses the temporally modulated gamma-rays onto a small detector. Imaging would be accomplished by the grids, concentration by the (possibly corotating) lens - assuming a large lens is less expensive than a large detector array.

References 1. Springsteen, B.: Blinded By The Light, lyrics, Greetings From Asbury Park, N.J. (1973) 2. Lin, R.P., Hudson, H.S.: Non-thermal processes in large solar ﬂares. Sol. Phys. 50, 153–178 (1976) Springer

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3. Ramaty, R., Mandzhavidze, N., Kozlovsky, B., Murphy, R.J.: Solar atmospheric abundances and energy content in ﬂare accelerated ions from gamma-ray spectroscopy, ApJ 455, L193–196 (1995) 4. Sui, L., Holman, G.D., Dennis, B.R.: Determination of low-energy cutoffs and total energy of nonthermal electrons in a solar ﬂare on 2002 April 15, ApJ 626, 1102–1109 (2005) 5. Smith, D.M., Share, G.H., Murphy, R.J., Schwartz, R.A., Shih, A.Y., Lin, R.P.: High-resolution spectroscopy of gamma-ray lines from the X-class solar ﬂare of 2002 July 23, ApJ 595, L81–L84 (2003) 6. Lin, R.P.: Relationship of solar ﬂare accelerated particles to solar energetic particles (SEPs) observed in the interplanetary medium, AIP Conf. Proc. #781, 246–251 (AIP: Melville, New York) (2005) 7. Mandzhavidze, N., Ramaty, R.: Particle acceleration and abundances from gamma-ray line spectroscopy, Astron. Soc. Pac. Conf. Series. #206, 64–70, (ASP: San Francisco) (2000) 8. Ramaty, R., Mandzhavidze, N.: Gamma-Rays from solar ﬂares Proc. IAU Symp. #195, 123–132 (ASP: San Francisco) (2000) 9. Kozlovsky, B., Murphy, R.M., Ramaty, R.: Nuclear Deexcitation Gamma-Ray Lines from Accelerated Particle Interactions, ApJS 241, 523–541 (2002) 10. Toner, M.P., MacKinnon, A.L.: Do fast protons and alpha particles have the same energy distributions in solar ﬂares?, Sol. Phys. 223, 155–168 (2004) 11. Murphy, R.J., Share, G.H., Hua, X.-M., Lin, R.P., Smith, D.M., Schwartz, R,A.: Physical implications of RHESSI neutron-capture line measurements. ApJ 595, L93–L96 (2003) 12. Murphy, R.J., Share, G.H., Grove, J.E., Johnson, W.N., Kinzer, R.L., Kurfess, J.D., Strickman, M.S.: Accelerated particle composition and energetics and ambient abundances from gamma-ray spectroscopy of the 1991 June 4 solar ﬂare, ApJ 490, 883–900 (1997) 13. Share, G.H., Murphy, R.J., Kiener, J, de S´er´eville, N.: Directionality of solar ﬂare-accelerated protons and α-particles from γ -ray line measurements. ApJ 573, 464–470 (2002) 14. Kiener, J., Gros, M., Tatischeff, V., Weidenspointner, G.: Properties of the energetic particle distributions during the October 28, 2003 solar ﬂare from INTEGRAL/SPI observations, A&A in press (2005) 15. Share, G.H. et al.: High-resolution observation of the solar positron-electron annihilation line, ApJ 595, L85–L88 (2003) 16. Share, G.H., Murphy, R.J., Smith, D.M., Schwartz, R.A., Lin, R.P.: RHESSI e + −e− Annihilation radiation observations: implications for conditions in the ﬂaring solar chromosphere, ApJ 615, L169– L172 (2004) 17. Hurford, G.J., Schwartz, R.A., Krucker, S., Lin, R.P., Smith, D.M., Vilmer, N.: First gamma-ray images of a solar ﬂare, ApJ 595, L77–80 (2003) 18. Hurford, G.J., Krucker, S., Lin, R.P., Schwartz, R.A., Share, G.H., Smith, D.M.: Gamma-ray imaging of the october/november 2003 solar ﬂares, in preparation (2006) 19. Share, G.H., Murphy, R.J., Smith, D.M., Lin, R.P., Dennis, B.R., Schwartz, R.A.: Directionality of ﬂareaccelerated alpha-particles at the sun. ApJ 595, L89–L92 (2003) 20. Barriere, N.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9058-x (2006)

Springer

Exp Astron (2005) 20:75–83 DOI 10.1007/s10686-006-9057-y ORIGINAL ARTICLE

The INTEGRAL – HESS/MAGIC connection: A new class of cosmic high energy accelerators from keV to TeV P. Ubertini∗

Received: 12 April 2006 / Accepted: 27 June 2006 C Springer Science + Business Media B.V. 2006

Abstract The recent completion and operation of the High Energy Stereoscopic System [1], an array of ground based imaging Cherenkov telescopes, has provided a survey with unprecedented sensitivity of the inner part of the Galaxy and revealed a new population of very high energy gamma-rays sources emitting at E > 100 GeV. Most of them were reported to have no known radio or X-ray counterpart and hypothesised to be representative of a new class of dark nucleonic cosmic sources. In fact, very high energy gamma-rays with energies E >1011 eV are the best proof of non-thermal processes in the universe and provide a direct in-site view of matter-radiation interaction at energies by far greater than producible in ground accelerators. At lower energy INTEGRAL has regularly observed the entire galactic plane during the ﬁrst 1000 day in orbit providing a survey in the 20–100 keV range resulted in a soft gamma-ray sky populated with more than 200 sources, most of them being galactic binaries, either Black Hole Candidates (BHC) or Neutron Stars (NS) [5]. Very recently, the INTEGRAL new source IGR J18135-1751 has been identiﬁed as the soft gamma-ray counterpart of HESS J1813-178 [18] and AXJ1838.0-0655 as the X/gamma-ray counterpart of HESS J1837-069 [14]. Detection of non-thermal radio, X and gamma-ray emission from these TeV sources is very important to discriminate between various emitting scenarios and, in turn, to fully understand their nature. The implications of these new ﬁndings in the high energy Galactic population will be addressed.

Keywords Gamma-ray sources . High energy emission processes

∗ On

behalf of the IBIS Survey Team.

P. Ubertini Istituto di Astroﬁsica Spaziale e Fisica Cosmica (IASF), Roma, Italy e-mail: [email protected] Springer

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1. Introduction HESS (High Energy Stereoscopic System), a ground-based Cerenkov array telescopes has been operated since a few years and in 2004 has performed the ﬁrst Galactic plane scan with a sensitivity of a few percent of the Crab at energies above 100 GeV, resulting in the discovery of eight sources, most of which without any counterpart at different energies [1, 2]. Particular attention was devoted to HESS J1813-178, not identiﬁed with any known X/gamma ray emitter and hypothesised to be a dark particle accelerator. Independently, and at the same time, INTEGRAL discovered a new soft gamma-ray source, namely IGR J18135-1751, identiﬁed as the counterpart of HESS J1813-178. This high energy emitter, whose nature was still mysterious at the time of the discovery was then associated with the supernova remnant (SNR) G12.82 0.02 [6, 10, 18]. Even if a chance coincidence cannot be completely ruled out in view of the 2 arcmin INTEGRAL error box and the possible angular extension in the high energy, the overall characteristics of this star forming region [7] comprising SNR G12.82 0.02 are consistent with supernova/plerion origin. More recently, the MAGIC (Major Atmospheric Gamma Imaging Cerenkov telescope) collaboration has reported a positive observations of HESS J1813–178, resulting in a gamma-ray ﬂux consistent with the previous HESS detection and showing a hard power law with α = 2.1 in the range from 0.4–10 TeV [3]. The detection of a substantial number of very high energy Galactic sources emitting a large fraction of energy in the GeV to TeV range has opened a new space window for astrophysical studies related to cosmic particle acceleration. Different types of Galactic sources are known to be cosmic particle accelerators and potential sources of high energy gamma rays: isolated pulsars/pulsar wind nebulae (PWN), Supernova remnants, star forming regions, binary systems with a collapsed object like a microquasar or a pulsar etc. The HESS detection of several TeV emitters without any counterpart at different energy has made the detection of X and gamma-ray emission from these sources a key issue to disentangle the mechanisms active in the different emitting regions and, in turn, to understand the source nature. The IBIS gamma-ray imager on board INTEGRAL is a powerful tool to search for their counterpart above 20 keV in view of the arcmin Point Source Location Accuracy associated to ∼ mCrab sensitivity for exposure >1 Ms [17]. 2. HESS J1837-069 = AXJ1838.0-0655: The ﬁrst IBIS/HESS new source AXJ1838.0-0655 is located in the Scutum arm region and has been detected as a new INTEGRAL source by Bird [5] and Molkov [15] and it is detected by IBIS up to 300 keV with a high statistical signiﬁcance, exceeding 15σ . The best positional location is R.A. (2000) = 18 h 38 m 01.7 s and Dec = −06◦ 54 14.4

with an error radius uncertainty of ≤3 [14]. The IBIS data provide a good ﬁt with a simple power law with a resulting χν2 /do f = 0.3/5 with a photon index = 1.66 ± 0.23 (90% c.l) and a 20–300 keV ﬂux of 9 × 10−11 erg cm−2 s−1 [14]. HESS J1837-069 is one of the 10 very high energy sources located in the central part of the Galaxy plane, detected in the TeV range with a statistical signiﬁcance of 7–8 σ . It is located at R.A. (2000)= 18 h 37 m 42.7 s and Dec (2000) = −06 55 39 (error box of about 1–2 ) [1] and the estimated ﬂux, above 200 GeV, is 9 × 10−12 photons cm−2 s−1 . The authors suggest AXJ1838.0-0655 to be the candidate for HESS J1837-069, in view of the spatial coincidence (see Figure 2). AXJ1838.0-0655 was discovered by the Einstein satellite in X-rays and named 1E1835.30658 [11] then observed by ASCA at higher energy during the Galactic plane survey [4] with a positional uncertainty of 1 in radius, basically coincident with the position of the Springer

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Fig. 1 Left panel: from Malizia et al. [14]. The IBIS/ISGRI 20–300 keV signiﬁcance map showing the location of AX J1838.0-0655 as well as the position and extension of HESS J1837-069 (white circle) and the Einstein position (black cross). The position and uncertainty of the ASCA source is basically coincident with the central, brightest IBIS pixel. Right panel: from Aharonian et al. [1]. The emission region of HESS J1837-069 overlapped to the ASCA error box of AXJ1838.0-0655. As can be seen even if the two sources are positionally coincident the TeV emission is suggestive of an extended object

Fig. 2 The large IBIS sky region map containing AXJ1838.0-0655

original discovery. It was found to be bright in the 0.7–10 keV band at a ﬂux level of 1.1 × 10−11 erg cm−2 s−1 and a hard ( = 0.8) and absorbed (N H = 4 × 1022 cm−2 ) power law shape. The summary of the observed positions for the different component, from soft X-ray to TeV range, is shown in Figure 1 (see [14] for details). From the angular distribution it looks evident that the Einstein, ASCA and IBIS sources are the same emitting source which is also likely to be active at TeV energies. Finally [14] report the presence of a strong radio source, TXS1835-069-CUL1835-06, associated in Simbad with a candidate supernova remnant, SNR025.3-00.1 [9], positioned at the side of the IBIS error box, though not compatible Springer

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with ASCA/Einstein X-ray position. The X/gamma-ray data indicate a point source nature for this object, while the high energy results are more in line with an extended emission, (see Figure 1) suggestive of a non-thermal radiation mechanism pointing to a SNR and/or a PWN [1]

3. HESS J1813-178 and IGR J18135-1751: Same emitting region/mechanism? IGR J18135-1751 was one of the newly discovered source during the compilation of the second IBIS/ISGRI survey catalogue [5]. It was immediately clear that the soft gamma-ray excess was positionally coincident with the very high energy source named HESS J1813-178, one of the 8 unknown sources found in the HESS survey of the inner region of the Galactic plane. The source position was found at R.A. (2000) = 18 h 13 m 37.9 s and Dec (2000) = −17◦ 50 34

and has a positional uncertainty of 1–2 arcmin. The source was reported to be slightly extended, about 3 arcmin and had a statistical signiﬁcance of about 9σ . Even if the source was reported to be quite bright 12 × 10−12 photons cm−2 s−1 above 200 GeV, it was impossible to ﬁnd an evident counterpart. An archival search for soft X-ray data resulted in a possible counterpart in the ASCA archive data: AGPS273.4-17.8 at R.A. (2000) = 18 h 13 m 35.8 s and Dec (2000) = −17◦ 49 43.35

with an associated uncertainty of 1 . In the X-ray band the source is fairly bright showing a 2–10 keV ﬂux (corrected for absorption) of 1.8 × 10−11 erg cm−2 s−1 [18]. In Figure 3 is shown the IBIS/ISGRI 20–40 keV map with the location of IGR J181351751. The authors report the relative signiﬁcance contours to be 6 (for the external one), 8, 10, 20 and 40 σ , that are compatible with a point source. The extension of HESS J1813-178 as well as the position of AGPS273.4-17.8 are both contained within the internal IBIS/ISGRI contour. Also it is shown the location and the extension of W33 and the 4 nearest radio pulsars, namely PSR J1814-1744, PSR J1812-1733, PSR J1815-1738 and PSR J1811-1736. The combined IBIS-ASCA spectrum, obtained adding the two data set without the need of any normalisation, conﬁrm that HESS J1813-178 has a point like X-ray counterpart with a power law emission from 2 to 100 keV and an associated radio counterpart. The data set is strongly suggesting that it is a non-thermal source, possibly accelerating electrons and positrons which radiate through synchrotron and inverse Compton mechanism. Brogan et al. [6] have provided a possible interpretation of the HESS/ASCA spectrum by ﬁtting the broadband emission assuming that all the ﬂux originates from the shell of SNR G12.8 (see Figure 5 and Brogan et al. [6], for a detailed description). The two proposed models (corresponding to two different Nh absorption values) are shown by the red and blue lines that provide the best ﬁt to the data. The models include X-ray emission from synchrotron radiation (solid lines) and Inverse Compton processes (dashed lines), assuming a ﬁlling factor of 15% for the magnetic ﬁeld in the IC emitting region. More recently the MAGIC experiment has observed HESS J1813-178, resulting in the detection of a differential gammaray ﬂux consistent with a hard-slope power law, described as dNγ /(dAdtdE) = (3.3 ± 0.5) × 10−12 (E/TeV)−2.1±0.2 cm−2 s−1 TeV−1 [3]. The image of the MAGIC ﬁeld containing the high energy excess is shown in Figure 4. The authors quote the systematic error to be 35% in the ﬂux level determination and 0.2 for the spectral index. Within errors, the ﬂux was found steady in the timescales of weeks as well as in the year-long time span between the MAGIC and HESS pointings. They report a multiwavelength emission associated to HESS J1813-178, is shown in Figure 6, including the MAGIC data at high energies. The authors compare the hadronic and leptonic emission models with the high-energy gammaray data (see [3, 16] for details). The main conclusions are that for hadronic models the Springer

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Fig. 3 From Ubertini et al. [18]. The IBIS/ISGRI 20–40 keV signiﬁcance map showing the location of IGR J18135- 1751 and relative signiﬁcance contours; the source spatial proﬁle is compatible with the detector response to a point source. The extension of HESS J1813-178 as well as the position of AGPS273.4-17.8 are both contained within the internal IBIS/ISGRI contour. Also shown is the location (and extension) of W33, of the 4 nearest radio pulsars (PSR J1814-1744,PSR J1812-1733, PSR J1815-1738 and PSR J1811-1736) and of the ROSAT source 1WGA J1813.7-1755 (white small diamond). The ASCA-SIS image is shown as an insert on the top right side of the ﬁgure: contour levels provide marginal evidence of extended emission. In the picture is also present GX13+1 and the transient source SAX J1818.6-1703 that are ﬁeld sources not contaminating in any way IGR J18135-1751, in view of the large angular distance between the objects (see text for details). The coordinates are displayed in Galactic system [18]

observed high energy luminosity (2.5 × 1034 erg s−1 at a distance of 4 kpc) implies a matter density of ∼6 cm−3 assuming gamma-ray are generated in the whole Supernova remnant, an acceleration efﬁciency for the hadrons of ∼3% and a Supernova power of 1051 ergs with a target mass for relativistic particles of about 2 Solar masses (within or close to the SNR) to justify the observed luminosity. For leptonic models, they assume relativistic electrons distribution of dNe /(dV dE) = Ae (E/GeV)−αe exp (−E/E max,e ) GeV−1 cm−3 and obtain good ﬁts with value of αe ∼ 2.0–2.1 E max,e ∼ 20–30 TeV, assuming the cosmic microwave background as target photons. The best ﬁt to the radio synchrotron emission is α ∼ 2.0 and require a magnetic ﬁeld of 10 µG with a ﬁlling fraction of about 20% [3]. This model is not very different from the blu one in Brogan et al (see Figure 5), even if a lower ﬁlling factor E max,e is assumed.

4. Implication of the synchrotron – inverse compton scenario The detection of soft gamma-ray photons from sources emitting in the TeV range is important to understand the emission mechanisms and the particle acceleration processes present in the SNR environment. In addition, the consistency with a power law of X-Ray spectra, spanning from few keV to few hundred of keV, and the lack of X/gamma variability is Springer

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Fig. 4 From Albert et al. [3]. Sky map of gamma-ray candidate events (background-subtracted) in the direction of HESS J1813-178 for an energy threshold of about 1 TeV. Overlaid are contours of 90 cm VLA radio (black) and ASCA X-ray data (green) from Brogan et al. [6]. The two white stars denote the tracking positions W1, W2 in the wobble mode (see [3] for details)

Fig. 5 From Brogan et al. [6]. Fits to the broadband emission of HESS/ASCA source assuming that all the ﬂux originates from the shell of SNR G12.8 0.0. The diagonal black lines indicate both the uncertainty in the HESS ﬂux measurements, and the fact that no spectral information has yet been published for the TeV emission. The two models indicated by the red and blue lines show the range of parameter space that best ﬁt the data: the red model uses the spectral index from the best ﬁt ASCA Nh of 10.8 × 1022 cm−2 (black X-ray spectrum), while the blue model uses the spectral index implied by the 1σ lower limit to Nh of 8.9 × 1022 cm−2 (green X-ray spectrum). Both models include contributions from synchrotron (solid lines) and IC (dashed lines) mechanisms. The authors have assumed that the ﬁlling factor of the magnetic ﬁeld in the IC emitting region is 15% Springer

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Fig. 6 From Albert et al. [3]. Leptonic and hadronic models for the J1813-178 data. Details are given in Albert et al. [3]. Radio data are from the VLA, Bonn, Parkes, and Nobeyama observatories [6]; X-ray and hard X-ray data are from ASCA [6] and INTEGRAL [18]

compatible with a SNR or a Pulsar Wind Nebula, the latter not yet evident from observational view point. As an example, HESS J1813-1751 has a very young remnant, of the order of 300 to 3000 year, assuming a density medium of ∼1 cm−3 . The IBIS detection of soft gamma-ray photons up to ∼100 keV [19] in the Synchrotron – Inverse Compton Scenario force the lifetime of the emitting electrons to be quite short if compared to the one of the radiating electrons in the GHz frequency [12, 8, 9]. In fact, the lifetime for the high energy electrons is t1/2 ∼ 224 × (B/10 µG)−3/2 y. This model also imply the radio and X/soft gamma-ray synchrotron emission to be spatially coincident and X-ray emission that sharply drops behind the shock. Because of this effect, the X-Ray photons will be conﬁned close to the electrons acceleration region while the same electron population would eventually drift having a diffusion speed of a fraction of the light one. The detection of a substantial ﬂux of soft gamma-rays from the HESS J1813-1751 region is supportive of the red ﬁt model proposed by Sy [6], implying a lower ratio of peak emission frequencies Rν = ν pI C /ν p if compared with the blue one, not capable to ﬁt the IBIS data and, in turn, not compatible with the single source scenario. Unfortunately, the red model is unable to ﬁt the HESS data, the physical reason being the synchrotron losses, in the presence of a quite strong magnetic ﬁeld predicted by the model, constraining the density of the electrons necessary to radiate via Inverse Compton interaction with the CMB radiation. The picture improves considering that a substantially higher UV light ﬂux could be supplied by W33, a close HII region. An energy density of ∼3 eV cm−3 could be easily provided, a factor ∼10 higher than the density of ∼0.26 eV cm−3 of the CMB photons [1] (for a detailed analysis of the IC model see [19]).

5. Conclusions It is clear that both the hadronic and leptonic models so far proposed fails to easily explain the whole observational picture if the radio, X/soft gamma-rays and TeV high energy photons are produced in the same SNR region by a single physical process. In fact, to ﬁnally conﬁrm the above hypothesis it is necessary to have instruments capable to provide spatially resolved spectroscopy with a fraction of arcsec. While in the X-ray range this seems to be possible with long CHANDRA exposures it is not with the present generation of gamma ray instruments Springer

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Fig. 7 The lap in sensitivity expected from new generation gamma ray observatorysuch as MAX+ or the newly prosed Gamma Ray Imager (GRI) based on Laue Lens complemented at lower energy by a large CZD detrector (in the ﬁgure is shown the SMAX sensitivity, this conference)

in the best case providing arcmin angular resolution [13, 17]. This will be achievable with a new generation of Gamma Ray Imagers providing at the same time a factor of 10 better sensitivity, as discussed in the present conference, as shown in Figure 7. On a shorter time frame it could be possible to improve the lack of our knowledge in the blank region in between the soft gamma ray range covered by INTEGRAL and the very high energy one by HESS and MAGIC. In fact, the imminent launch of the Italian AGILE gamma-ray satellite, covering the 30 MeV–50 GeV range with a good sensitivity over a wide ﬁeld of view, and GLAST in perspective, will be a powerful tool to ﬁnally disentangle the nature of the high energy sky. Acknowledgements The author acknowledge this research has been granted by the Italian Space Agency via contract n. I/R/046/04 ASI/IASF.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Aharonian, F. et al.: Science 307, 1938 (2005) Aharonian, F. et al.: ApJ 636, 777 (2006) Albert, J. et al.: ApJ 637, L41 (2006), Bamba, A. et al.: ApJ 589, 253 (2003) Bird, A.J.: ApJ 636, 765 (2006) Brogan, C. et al.: ApJ 629, L105 (2005) Churchwell, E.: A&A Rev. 2, 79 (1990) Condon, J.J. et al.: AJ 115, 1693 (1998) Dulk, P., Slee, O.: AJPh 25, 429 (1972) Helfand, D.J., Becker, R.H., White, R.L.: astro-ph/0505392 (2005) Hertz, P., Grindlay, J.: AJ 96, (1998) Lazendic, J.S. et al.: ApJ 602, L271 (2004) Lebrun, et al.: A&A 411, L141 (2003) Springer

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Malizia, A.: ApJ 630, L157 (2006) Molkov, S. et al.: Astr. Lett. 30, 534 (2004) Torres, D.F. et al.: Phys. Rept. 382, 303 (2003) Ubertini, P. et al.: A&A 411, L131 (2003) Ubertini, P. et al.: ApJ 629, L109 (2005a) Ubertini, P. et al.: Proceedings–Conference “A Life with Stars” Amsterdam 22–26/August–Elsevier. (2005b)

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Exp Astron (2005) 20:85–92 DOI 10.1007/s10686-006-9033-6

Replicated nickel optics for the hard-x-ray region Brian D. Ramsey

Received: 11 January 2006 / Accepted: 24 February 2006 C Springer Science + Business Media, B.V. 2006

Abstract Replicated nickel optics has been used extensively in x-ray astronomy, most notably for the XMM/Newton mission. The combination of relative ease of fabrication and the inherent stability of full-shell optics, make them an attractive approach for mediumresolution, high-throughput applications. MSFC has been developing these optics for use in the hard-x-ray region. Efforts at improving their angular resolution, particularly for the very-thin-wall shells required to meet the weight budgets of future missions, are described together with the prospects for future signiﬁcant improvements. Keywords Replicated . X-ray astronomy . x-ray optics Background X rays can undergo total external reﬂection from smooth surfaces at very shallow graze angles. The critical angle in degrees, below which this takes place, is given by θ ∼ 0.93 √ λ (ρ), where λ is the wavelength of the incident x ray (nm) and ρ is the density of the reﬂecting medium (g/cm3 ). Thus at 6 keV, for example, a nickel surface will reﬂect x rays up to an angle of approximately 12 degree. This phenomenon can be used to realize an x-ray telescope. A single parabolic section, limiting graze angles to 12 degree for a parallel input beam, would focus x rays to ∼6 keV. This optic, however, would have serious off-axis image distortions, and in 1951 a combination of parabolic and hyperbolic sections was proposed that overcame this limitation. This conﬁguration, known as a Wolter-1 geometry after its proposer (Wolter, 1952), has been widely adopted for x-ray astronomy. Typically, several such reﬂector pairs would be concentrically nested to build up collection area. The power of focusing optics goes beyond the capability to produce more detailed source images. Signals from cosmic sources are extremely faint and are observed against a large background ﬂux that is dependent on the detector area and the amount of sky being viewed. B. D. Ramsey () NASA/Marshall Space Flight Center, Huntsville, Alabama, USA e-mail: [email protected] Springer

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By concentrating source ﬂux from a small area of the sky onto a tiny detector area, an x-ray telescope enables an enormous increase in signal to noise ratio, and thus in sensitivity. By way of an example, the currently operating Chandra x-ray observatory has the same collecting area as the ﬁrst x-ray satellite, UHURU, but has nearly 5 orders of magnitude more sensitivity by virtue of its focusing optics. Because of this resulting sensitivity enhancement, x-ray optics has revolutionized the ﬁeld of soft-x-ray astronomy. The situation at higher energies, above 10 keV where x-ray optics have not been employed, is quite different though. The hard-x-ray region is very important for study as in this energy regime sources transit from thermal to non-thermal emission mechanisms. In addition, nuclear lines appear and obscured objects become visible. Despite this signiﬁcance, this energy region remains relatively unexplored at high sensitivities and ﬁne angular scales. The remedy is obvious – grazing optics needs to be extended to higher energies. To do this we must accept the very small graze angles that this entails and develop techniques for efﬁciently fabricating large numbers of light-weight optics that can be heavily nested to build up useful collecting areas.

Electroformed nickel replication Process The mirror fabrication process that we are developing is electroformed nickel replication (ENR). In this, nickel mirror shells are electroformed onto a ﬁgured and superpolished aluminum mandrel from which they are later released by differential thermal contraction. This process, pioneered in Italy for x-ray mirror fabrication, has been used for soft-x-ray astronomy in such missions as XMM-Newton,1 which featured 3 mirror modules with 68 electroformed nickel shells each. The attraction of the ENR process is that the resulting full shells are inherently stable and thus can give good angular resolution. At MSFC we utilize this process and have made additional developments in high-strength nickel alloys, which permit very thin shells to be fabricated, and in plating bath stress control to achieve good ﬁgure accuracy. Application: The HERO program HERO, for High Energy Replicated Optics is a balloon program designed to demonstrate MSFC-developed hard-x-ray optics while simultaneously performing new science. The project utilizes all-in-house fabricated optics plus supporting x-ray detectors, gondola and pointing system. The optical design philosophy for HERO is to utilize a large number of shallow-grazeangle, iridium-coated full-shell mirrors, and to obtain signiﬁcant collecting area by nesting many thin shells. To reduce costs, appropriate for a balloon program, we utilize long shells (which reduces the number of mandrels) and make each a conical approximation to a true Wolter-1 conﬁguration. For mandrel fabrication, we use inexpensive grinding and simple in-house fabricated polishing machines, and for shell production use a multipart plater so that multiple shells can be electroformed simultaneously. Figure 1, below, shows a HERO mandrel being polished and a series of thin nickel shells ready for iridium coating.

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http://www.sci.esa.int/science-e/www/object/index.cfm?fobjectid = 31318. Springer

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Fig. 1 A HERO mandrel being polished and shells awaiting iridium coating

A proving ﬂight of a HERO payload took place in 2001, when the ﬁrst focused hard-x-ray images of galactic sources were obtained with just 6 replicated shells of focal length 3 m (Ramsey et al., 2002). Since that time, the payload has been re-built and now features around 100 6-m-focal-length shells giving mCrab-level sensitivity in just a 3-h observation. Table 1 gives the optics conﬁguration for HERO and Figure 2 shows the payload in New Mexico awaiting launch. Table 1 HERO current optics conﬁguration Number of modules Number of shells per module Inner, outer shell diameters Shell thickness Shell length Focal length Angular resolution (module) Field of view Effective area (total)

8 12 50, 94 mm 0.25 mm 300 mm 6m 20–25 arcsec 9 arcmin @ 40 keV 80 cm2 (40 keV) 40 cm2 (60 keV)

Quality-control tests on individual HERO shells show that they typically fall into the 13– 15 arcsec resolution range (Ramsey et al., 2003). When mounted in a 12-shell ﬂight module this degrades to 20–25 arcsec for the overall module half-power diameter, due to distortions around the spider. A new alignment technique is being developed in which the shells are held at their intersection and then lowered into the spider grooves without touching. The intervening space, between the spider groove wall and the mirror shell, is then taken up by epoxy. By ﬂoating the shells in position we hope to avoid distortions occurring when the spider contacts the shell wall and deﬂects it locally. The current plan is to re-assemble all 8 ﬂight modules using this technique before a Fall 2006 scheduled ﬂight. Application: The constellation-X program Constellation-X is the planned successor to the Chandra mission and is currently planned for launch in the 2015–2020 timeframe. It will feature a very large area of soft-x-ray telescopes, primarily for spectroscopy, and also hard-x-ray telescopes (HXT) with ∼1500 cm2 effective area at 40 keV. To meet the HXT baseline requirement, approximately 12 mirror modules Springer

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will be necessary (assuming 10 m focal length) with each module housing ∼80–90 nested mirror shells. Currently, different technologies are being assessed for the HXT optics. MSFC is collaborating with the Smithsonian Astrophysical Observatory and the Observatory of Brera, Italy, in the development of a prototype unit using ENR technology (see Figure 3). For this, MSFC will produce 2 shells, one 150 mm diameter to be coated with iridium, and one 230 mm in diameter, to be coated with multilayers. Both will be just 100 micron thick to meet the stringent Constellation-X weight budget. The Observatory at Brera will produce two additional multilayer-coated shells and the 4-shell prototype will assembled at Brera and tested in Germany in late 2006.

Fig. 2 The HERO payload in Fort Sumner, New Mexico.

Fig. 3 Con-X prototype 4-shell module

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Table 2 Typical mirror shell error budget

Surface error type Delta-delta radius Average radius P Average radius H Average axial sag Axial slope (mid freq) Roundness Circumferential slope (mid freq) P-H tilt P-H decenter Total ∗ Measurement

Image RMS diameter sensitivity

Allocation per shell

Image RMS diameter arcsec

5.4 arcsec/micron rms 0.04 arcsec/micron 0.11 arcsec/micron 12.5 arcsec/micron 8 arcsec/arcsec rms 0.15 arcsec/micron rms 8.3·10−3 arcsec/arsec rms 2 arcsec/arcsec 3.4·10−2 arcsec/micron

0.4 micron rms 2 micron 2 micron 0.3 micron 0.8 arcsec 3 micron rms 6 arcsec rms 0.5 arsec∗ 0.5 micron

2.2 0.08 0.22 3.5 8.0 0.5 0.05 1.0 0.02 9.0

limit

Further ENR developments Typical mirror shells fabricated to date at MSFC have half-power-diameters (HPD) in the 13–15 arcsec range so it is natural to ask if this can be signiﬁcantly improved upon. To answer this, we have developed a budget showing the contributions of various sources of error to the overall mirror performance (ignoring mounting errors). The total, derived by taking the square root of the summed squares of each individual component, is given as an overall RMS diameter. This can be converted to a half power diameter, assuming a Gaussian ﬂux distribution, by multiplying by 1.35. The error budget is shown in Table 2. The allocation per shell for each error type is obtained from measurements of typical shells. It is evident from this table that two components, namely the average axial sag and the axial slope are the dominant contributors. The average axial ﬁgure sag represents the departure of the mandrel ﬁgure from the perfect Wolter-1 shape. In our case it represents the limit of the conical approximation that we use in all our mandrels to facilitate fabrication; this requires just two straight cuts rather than a hyperbolic/parabolic ﬁguring. Thus this component can be controlled as necessary simply by ﬁguring the mandrel. The major component in the error table is the mid-frequency axial slope. This error is a measure of the mm- to cm-scale variations in the axial ﬁgure of the replicated shell. These variations may be present in the mandrel and carried over through replication, or may come about during electroforming of the shell. Figure 4 (left) shows axial ﬁgure proﬁles for a mandrel and for the shell replicated from it. While the mandrel has small ﬁgure variations, at the 100-nm level, there are relatively large variations, micron-level, in the resulting shell ﬁgure. We identify two contributors to these ﬁgure variations. The ﬁrst is simply due to changes in the mandrel shape with temperature. The mandrel is fabricated at room temperature while the plating bath is at ∼45 ◦ C. Small variations in thermal expansion coefﬁcient at different points in the mandrel can lead to changes in shape as the mandrel is heated. These differences can come about if, for example, the mandrel is made of a solid piece of aluminum but has not been thermally conditioned (cycling from high temperatures down to cryogenic levels) sufﬁciently to relieve residual stresses before ﬁnal machining. They can also come about if the mandrel is hollow and the end caps are made from the same aluminum but which has been processed in a different manner to the cylindrical body. This latter effect is shown in Figure Springer

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1500

0.8 mandrel shell mirror

1000

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Height, µm

Height, nm

0.4 500

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0.2 0.0 -0.2 -0.4

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Fig. 4 Typical axial ﬁgure proﬁle of a mandrel and the resulting shell (left) and the effect of temperature on a mandrel ﬁgure (right)

4 (right), where a mandrel is measured at two temperatures showing a distinct change in shape. The second contributor to axial ﬁgure variations, and the most difﬁcult to eliminate is stress imparted during electroforming; this can have a signiﬁcant effect on very-thin-walled shells. Note that there are also stresses imparted by applied coatings, particularly multilayers, and these stresses (∼5·106 Pa) are an order of magnitude larger than typical controlled plating bath stresses, but as the coating thicknesses are very tiny, relative to the shell thickness, their effects are quite small. Tests at MSFC have shown that 1-micron-thick multilayers (100 bilayers), deposited on 100-micron-thick shells, have no measurable effect on the overall shell ﬁgure. To control the plating bath stress we ﬁrst adjust the chemistry of the bath so that the bath stress is relatively insensitive to the plating current density. Then, using computer models of the plating bath, we ﬁne tune the layout of shields and the bath electrodes to generate as uniform an electric ﬁeld as possible along the full plated length of the mandrel. A uniform ﬁeld ensures that there are no departures in plating current density that would in turn affect the stress of the plated nickel. The plating stress level necessary to distort the ﬁgure of electroformed shells is very small, about 5·105 Pa, and difﬁcult to measure. We have, instead, optimized the plating current density by using stress measurements to get us close and then plating a series of shells each at a slightly different current value. These were then measured to give the inside shell proﬁle and thus determine, through predictive software, which conditions gave the mirror shell with the best performance. To test this we have utilized a solid, thermally-conditioned mandrel, and plated a shell using the optimum plating conditions found above. To enable testing, but avoid spider-mountinduced errors, the shell was held at its intersection by gluing it to a support plate as shown in Figure 5 (left). The result of the x-ray test, shown in Figure 5 (right), is a half-power diameter of 11.5 arcsec at 40 keV. We can now ask, what are the factors contributing to this measured resolution ? The ﬁrst of these is gravity sag. Under 1 g, the optic, supported at each end, droops slightly. Using a ﬁnite element analysis program, we estimate the (small) effect of this sag and remove it from the measured resolution. This leaves us with 11 ± 0.5 arcsec. Next, we can remove the inherent mandrel ﬁgure. The conical mandrel used to electroform this shell has a predicted performance (derived from mandrel metrology) of 8.3 arcsec at this energy. This must be Springer

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Fig. 5 Test shell mounted at its intersection (left) and the resulting x-ray point-spread distribution (right)

subtracted in quadrature from the 11 arcsec to leave us with the inherent axial ﬁgure errors imparted by the electroforming process. This is 7 arcsec. We can now turn this around and ask, if we used a top-quality Wolter-1-ﬁgure mandrel what is the best (zero-g) shell that we could expect. The best mandrels available have ﬁgure accuracies of 4 arcsec (the Con-X program procured 0.5-m-diameter mandrels from Zeiss with this speciﬁcation). Applying our best electroformed-shell axial-ﬁgure quality to this, in quadrature, we could expect to fabricate mirror shells having a half-power-diameter of around 8.5 arcsec. It will be extremely challenging to improve electroformed optics much beyond this. The production of very thin shells necessitates an extremely low adherence of the plated deposit to the mandrel, otherwise large ﬁgure-distorting stresses will be imparted on the shell during separation, and this in turn necessitates a small amount of tensile stress in the plating bath to prevent the deposit from detaching from the mandrel surface during electroforming. Thus it can be expected that stress-induced ﬁgure distortions will always be present. One way to attempt to mitigate these effects is to stretch the shell material on the mandrel, to force it to more accurately conform, while simultaneously applying heat to anneal out residual stresses. We have investigated this effect with test samples and have found that both nickel and nickel/cobalt shell material can be strain hardened and take a permanent set at quite low temperatures. In practice this means simply heating the mandrel after electroforming the shell and before the shell is released. The mandrel, of course must maintain its ﬁgure at the elevated temperature. Figure 6 shows early results of this process on a small-diameter mandrel. In this ﬁgure a proﬁle of the mandrel is shown together with the internal proﬁle of a plated and released pure nickel shell, together with the proﬁle of a nickel shell that was heated to 75 ◦ C on the mandrel for 48 hr before release. It is evident from this ﬁgure that slightly stretching the shell, above its microyield point where parts-per-million permanent set takes place, has forced it to conform better to the mandrel’s shape. We are investigating this thermal setting phenomenon to derive optimum temperatures and strains to apply for both pure nickel and nickel/cobalt alloys. In parallel with this we are fabricating a high-stability 23-cm-diameter mandrel on which we hope to demonstrate sub-8-arcsec HPD shells using this stretching technique in the near future. Conclusion MSFC has an ongoing development program in electroformed-nickel replication for hardx-ray optics. Over 150 shells have been fabricated for the HERO balloon program and Springer

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Fig. 6 Comparison of “stretched” and “unstretched” shells (see text)

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for Constellation-X technology development. While ‘routine’ shells have 13–15 arcsec half-power diameters (HPD), optics at the 11 arcsec level have been demonstrated and ∼8–9 arscec-level optics should be possible with good stress control and stable high-quality mandrels. Techniques for improvements beyond this, by thermal setting/stretching, are currently under investigation.

References Ramsey, B.D., Alexander, C.D., Apple, J.A., Benson, C.M., Dietz, K.L., Elsner, R.F., Engelhaupt, D., Ghosh, K.K., Kolodziejczak, J.J., O’Dell, S.L., Speegle, C.O., Swartz, D.A., Weisskopf, M.C.: First images from HERO: A hard-x-ray focusing telescope. Astrophys. J. 568, 432–435 (2002) Ramsey, B.D., Elsner, R.F., Engelhaupt, D., Gubarev, M., Kolodziejczak, J.J., O’Dell, S.L., Speegle, C.O., Weisskopf, M.C.: The Development of Hard-X-ray Optics at MSFC. SPIE 5168, 129–135 (2003) Wolter, H.: Spiegelsysteme streifenden einfalls als abbildende optiken fur Rontgenstrahlen. Physik. Ann. 10, 94–114 (1952)

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Exp Astron (2005) 20:93–103 DOI 10.1007/s10686-006-9022-9 ORIGINAL ARTICLE

Small d-spacing WC/SiC multilayers for future hard X-ray telescope designs Carsten P. Jensen · Kristin K. Madsen · Finn E. Christensen

Received: 15 November 2005 / Accepted: 29 December 2005 C Springer Science + Business Media, B.V. 2006

Abstract Multilayer coatings for reﬂecting hard X-rays up to 80 keV, like W/Si and Pt/C, have been studied for several years. To go to higher energies, in the range of 100 keV to 250 keV, one needs coatings with smaller d-spacings than can currently be made with these material combinations, and a lower interfacial roughness. With the new material combinations of WC/SiC the interface roughness can be reduced down to between 0.23 nm and 0.25 nm enabling bi-layer thicknesses down to 1.0 nm to reﬂect efﬁciently. The production of thinner period coatings thus enables the possibility for focusing optic designs with reasonable focal lengths and throughput up to 250 keV. Keywords Hard X-ray telescopes . Multilayer . WC/SiC

1. Introduction Over the last 20 years several very successful satellites have been ﬂown with focusing optic for soft X-rays up to 10 keV, among these are Chandra, ROSAT, and XMM. These satellites have been using a conical approximation to a Wolter I design with total external reﬂection from Ir or Au, which prove inefﬁcient above 10 keV at the graze angles that were used. By going to depth graded multilayers in a conical approximation to a Wolter I design the regime of focusing X-ray is extended to energies above 10 keV, and two balloon payloads employing multilayers have been ﬂown to prove the concept. In 2004 the International Focusing Optics Collaboration (InFOCuS) (Ogasaka et al., 2003) ﬂew a single replicated mirror optic with a diameter of 400 mm, deposited with Pt/C multilayers and optimized for 20 keV to 40 keV. In 2005 the High Energy Focusing Telescope (HEFT) (Harrison et al., 2000) ﬂew three slumped glass optics each 240 mm in diameter, deposited with W/Si and optimized for 20 keV to 69 keV. Several satellite missions whose main goal is the energy band above 10 keV and below 100 keV are currently planned, and all intend to use multilayers such as NASA’s NuSTAR (Koglin

C. P. Jensen () · K. K. Madsen · F. E. Christensen Danish National Space Center, Copenhagen, Denmark e-mail: [email protected] Springer

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et al., 2004) and Constallation-X (White and Tananbaum, 2003), ESA’s XEUS (Parmar et al., 2003) and Japans NeXT (Furuzawa et al., 2003). Among proposed missions extending above 100 keV there is the High-Resolution Spectroscopic Imaging (HSI) mission (Harrison et al., 2003). The Danish National Space Center, DNSC, has for a long time been involved in the development of multilayers for hard X-ray optics, and besides having delivered all the coatings for the three HEFT optics, DNSC will also be coating the optics for NuSTAR, and are producing test coatings for XEUS and various other future high energy missions. Part of the development of multilayer coatings is the discovery and testing of new material combinations. Thus far W/Si has reigned supreme in the 20 keV to 69 keV range because of its relative low interfacial roughness and excellent stability over time, however, W has an absorption edge at 69 keV. The interface roughness of W/Si inﬂuence the limit by how small a dspacing it has been possible to produce, which inﬂuences the radius and energy of a telescope design. In this paper we will present results of a new type of multilayer coating, WC/SiC, which is both smoother than W/Si and allows for very small d-spacings. We will discuss the possibilities these properties open up in telescope design, and present a straw man design covering the energy band from 100 keV and up to 250 keV.

2. Multilayer designs Several types of thickness depth proﬁles are in use for multilayers; constant d-spacing, linear grading and power-law graded are among a few, each of which has their own particular area of application. In the case of a narrow band response or for multilayer coating development, the constant d-spacing thickness proﬁle is preferred. Such a proﬁle is described by its bilayer thickness, d = dspacer + dabsorber , the absorber thickness fraction, = dabsorber /d, and the number of bi-layers, N . For space application, a power-law graded thickness proﬁle of the multilayer is preferred, as the gradual grading of the layers shifts the position of the ﬁrst Bragg peak in such a way that a broad-band response is possible, which is needed for many astrophysical objects. The power-law thickness proﬁle used by HEFT and to be used by NuSTAR is deﬁned by Mao et al. (1999a), di =

a , (b + i)c

i = 1, . . . , N .

Here a, b and c are design constants, i the bi-layer number where N is next to the substrate, and thus the thickest bi-layer, dmax , is at the top of the stack and the thinnest, dmin , at the bottom. 3. Scattering theory Attenuation of the specular reﬂectivity as deﬁned by Fresnels equations (Born and Wolf), where the incidence angle is equal to the exit angle, is caused by interfacial roughness/interdiffusion, σ , which is the overall width of the interfacial density proﬁle. This can be divided into two main categories; inter-diffusion, which is the mixing of the two materials at the interface, and real roughness. The former causes absorption at the interface, while the latter is a sharp but jagged interface that causes the specular reﬂectivity to be reemitted at other Springer

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Fig. 1 A 2-dimentional scattering map of a sample with a constant d-spacing W/Si coating. The scatter angle, θscat , is the exit angle, θexit , minus the incidence angle, θinci , of the X-ray on the sample. The horizontal streak at θscat = 0 is the specular reﬂectivity and the angled streaks the transverse scans. The vertical shading strips are ﬁlter changes

angles than the incidence (Hol´y). At the Fresnel specular condition, these two roughnesses are indistinguishable. However, at non-specular angles it becomes possible to separate the two. There are several models describing the scattering off rough surfaces valid at different wavelength regimes. For X-rays two of the more well known are the Born Approximation and the Distorted Wave Born Approximation (DWBA) (Sinha et al., 1988). The Born Approximation is a kinematical theory and valid for graze angles much larger than the critical, and breaks down at small graze angles. Here the DWBA scalar theory works well, and treats the roughness as a perturbation of the reﬂectivity of an ideal surface. If the real roughness is perfectly replicated by each layer, correlated, the non-specular reﬂectivity will be concentrated into high intensity streaks intersecting the Bragg peaks as seen in Figure 1. If the roughness, on the other hand, is not correlated at all from layer to layer the scattered intensity will be redistributed into a uniform halo. Real stacks are a combination of both correlated, σcorr , and uncorrelated, σucorr , roughness but for W/Si there is a clear preference for correlated roughness (Madsen et al., 2004). This is also true for the other material combinations discussed in this paper W/SiC, WC/Si, and WC/SiC, and we have thus assumed the uncorrelated component to be negligible in all our modeling calculations, σucorr = 0. On this basis we deﬁne the interfacial roughness to be a combination of correlated jagged 2 1/2 roughness, σcorr , and a diffuse component, σd , such that, σtot = (σd2 + σcorr ) . Assuming that a surface is self-afﬁne, the surface can be described in the DWBA theory by a height-height correlation function (Sinha et al., 1988) 2/ h

2 [−(|R|/ξ ) h(r − R)h(r ) = σtot e

]

.

Here the fractal exponent h is connected to the fractal dimension D = 3 − h, 0 < h < 1, and describes the jaggedness of the surface, so that h → 0 means increasing jaggedness while h = 1 is a Gaussian distribution. The correlation length ξ is the in-plane correlation length Springer

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and is assumed to be equal for all layers. In the event that there is an uncorrelated component to the roughness, each layer is described by its own correlation length and additionally a depth dependent correlation length.

4. X-ray measurements If nothing else is mentioned, the X-ray measurements are made using an in house rotating anode, which operates at 8 keV (Cu K α ). The 40 keV measurements presented were made at beam line BM5 at the European Synchrotron Radiation Facility, ESRF, in Grenoble, France. To extract the non-specular information we have performed two types of scans, specular and transverse. To illustrate these two types of scans Figure 1 shows a 2-dimensional map of a constant d-spacing coated multilayer. The horizontal intensity streak at the scatter angle, α(scat) = 0 is the specular reﬂection with the higher intensity peaks on the streak corresponding to the Bragg peaks. The slated lines intersecting the Bragg peaks are the transverse scans. In the specular scan the incidence angle on the sample, αinci , is equal to the exit angle from the sample, αexit , so when the sample is rotated α the detector is rotated 2α. From this reﬂectivity curve we can derive the overall parameters, bi-layer thickness, d, absorber fraction, , and the total combined specular roughness/inter-diffusion σ spec . The transverse scans are made through a Bragg peak in the specular scan where the incidence angle αinci = αBragg . In the transverse scan the detector is held ﬁxed at 2 × αBragg with respect to the direct beam, while the incidence angle on the sample is scanned from αinci = 0 to αinci = 2 × αBragg . The shapes of the wings adjacent to the peak are then used to ﬁt the parameters, h, ξ , σd and σcorr . In an ideal world the roughness from the transverse scan, σtot , should be equal to the roughness/inter-diffusion derived from the specular scan, σspec .

5. Coating procedure All the coatings are made using the coating facility at DNSC. The coating chamber was, when the coatings for this work were made, equipped with two DC magnetron sputter cathodes. The cathodes are sputtering outwards and the samples are mounted facing inwards on a rotating ring. When all other parameters are set constant during a coating, like Ar pressure and applied power to the cathodes, the thickness of the coated layers are determined by the speed by which the substrate is rotated past the cathode. A full description of the coating facility is given in Jensen et al. (2003). The materials used for sputtering in this paper are W, WC, Si, and SiC and the purity of the materials are respectively 99.95%, 99.5%, 99.999%, and 99.5%. To make Si and SiC conducting they are both doped with B, Si with 32 ppm and SiC with 6900 ppm. All the coatings are made on commercial available Si wafers that have a surface roughness of 0.25 nm. After coating the samples are wrapped in a piece of lens paper and placed in a standard laboratory conditions.

6. WC/SiC coatings For years W/Si multilayer coatings have been heavily studied as coating for astrophysics missions. It is a good baseline material combination because it can coat relatively smooth multilayers and it maintains stability over time. It is very important to have a low interface Springer

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Table 1 Roughness parameters calculated for four different multilayers with approximate the same constant d-spacing and gamma. The roughness is calculated from both reﬂectivity scans and from 2 + σ 2 )1/2 transverse scans from the same samples. σtot = (σcorr d Reﬂectivity scan d-spacing (nm)

Transverse scan

σspec ξ h σcorr σd σtot (nm) (nm ± 10) (± 0.1) (nm ± 0.01) (nm ± 0.03) (nm ± 0.01)

W/Si

9.85

0.32 0.33

20

0.25

0.25

0.20

0.32

W/SiC

9.10

0.37 0.28

10

0.20

0.15

0.25

0.29

WC/Si

9.35

0.41 0.28

10

0.15

0.12

0.20 – 0.25

0.23 – 0.28

0.37 0.23

10

0.16

0.12

0.15

0.19

WC/SiC 10.05

roughness of the multilayer coating since that increases the reﬂectivity of the coating and decreases the scatter. In Table 1 are shown results from four constant d-spacing multilayer coated with W/Si, W/SiC, WC/Si, and WC/SiC. They are all 10 bi-layer coatings with d-spacings around 9.5 nm and gamma around 0.37. The roughness is calculated from the specular scans, and the diffuse and sharp interfacial roughness from the transverse scans. It can be seen from the reﬂectivity scans, that the specular roughness, σspec , of WC/SiC is much lower than for W/Si and that there is good agreement between the roughness calculated from the specular scan, σspec , and the total roughness calculated from the transverse scan, σtot . From the transverse scan there is an explanation for the decrease of the roughness. When introducing C in one of the layers we see an increasing diffusion, σd , compared to W/Si, probable caused by diffusion of C. When C is in both materials the diffusion decreases below that for W/Si. Now the C atoms can not defuse anywhere and the spaces between the W atoms is ﬁlled out with C so the Si atoms have a harder time to diffuse anywhere. The correlated roughness, σcorr , decreases when C is introduced in either W or Si and the fractal exponent parameter, h, also decreases. So the surface gets more jagged, but its height gets smaller than the height of the smoother more Gaussian surfaces. For the correlated roughness there is not a big effect to add C to both materials compared with adding it to just one of them. For all four coatings the correlation length, ξ , are the same since all the substrates are the same standard Si wafers. We have made the same experiment on 3 mm thick ﬂoat glass and here the correlation length was 900 nm independent of the multilayer material combination, indicating that the correlation length are dictated by the substrate. In order to have a good reﬂecting depth graded multilayer, it is important that all layers in the coating have a low roughness. The roughness as a function of the d-spacing is plotted in Figure 2 for some 30 bi-layer constant d-spacing WC/SiC coatings. It can be seen that the roughness calculated from the specular scans, σspec , are independent of the d-spacing and are between 0.23 nm and 0.25 nm. This is in good agreement with the roughness calculated from the transverse scans, σtot , except for the very thin coatings. The correlated roughness, σcorr , are independent of the d-spacing and in the range between 0.10 nm and 0.15 nm. From Figure 2 the diffusion seems to go up for coatings below 1.5 nm. When the d-spacing is about 1.0 nm the single layers are in the order of 0.5 nm and the assumption that the uncorrelated component of the roughness can be negligible is probably not correct. Unfortunately the transverse measurements of the very thin coatings so far have been background limited and a more precise analysis has not been possible. The increases in diffuse roughness for multilayer with a d-spacing below 1.5 nm are not a real effect and are also not seen in the roughness calculated from the specular scans. Springer

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Roughness (nm)

0,30 0,25 0,20 0,15 0,10 0,05 0,00 0

2

4

6

8

10

12

d Fig. 2 Roughness of WC/SiC multilayers with 30 bi-layers as function of d-spacing. The solid black line is the roughness from the specula scan, σspec , and the dotted black line is the roughness from the transverse scans, σtot . The dotted gray line is the correlated roughness, σcorr , and the solid gray line the diffuse roughness, 2 + σ 2 )1/2 , the dotted black line σd , where σtot = (σcorr d

1,E+00

Reflectivity

1,E-01 1,E-02 1,E-03 1,E-04 1,E-05 1,E-06 1,E-07 0,0

0,2

0,4

0,6

0,8

1,0

-1

q (Å ) Fig. 3 A WC/SiC sample with a d-spacing of 1.68 nm measured at 8 keV (dark gray) and 40 keV (light gray) both reﬂectivity scan and a transverse scan through ﬁrst Bragg peak. The black line is a ﬁt to the 8 keV data. ˚ −1 is a measuring The plot is in reciprocal space where q = 4π sin α/λ. The hump in the 40 keV data at 0.1 ( A) artifact

In Figure 3 are shown the reﬂectivity and transverse scans for a 1.68 nm thick 30 bi-layer WC/SiC coating measured with both 8 keV and 40 keV. To compare the measurements they are plotted in reciprocal space with reﬂectivity as function of q. Except for a measuring ˚ −1 for the 40 keV data, there is a really good agreement between artifact at around 0.1 ( A) the 8 keV and 40 keV reﬂectivity data and the ﬁtted curve. The ﬁt for both the specular scan and the transverse scan were ﬁrst made using the 8 keV data. Using the same parameters and only changing the energy to 40 keV the ﬁt to the specular scan done at 40 keV was perfect. To ﬁt the transverse scans one has to use an equipment function, which is different for the two experiments. Even though we took that into account there is a small difference in the ﬁt to the transverse scan when using the same parameters found at 8 keV and changing the energy to 40 keV. The correlated roughness was the same for the 8 keV and the 40 keV data, Springer

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1

2

3

4

5

6

7

Angle (degree)

(a)

8

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1

2

3

4

5

6

7

8

Angle (degree)

(b)

Fig. 4 Stability over time of two 30 bi-layer WC/SiC multilayer ﬁlm. The black lines are measured just after coating in November 2004 and the gray lines are measured in August 2005. (a) d-spacing is 0.8 nm. (b) d-spacing is 3.6 nm

but the diffuse roughness was a little lower at 40 keV than at 8 keV. In the plot only the ﬁtted curves to the 8 keV data are shown in order to make the plot a little easier to look at. Another important property of a multilayer is the stability over time. In Figure 4 are shown two different WC/SiC constant d-spacing multilayers measured with nine month gap in between. Both coatings, 0.8 nm d-spacing and 3.6 nm d-spacing, shows no degradation over the nine months. The transverse measurements made on WC/SiC with different d-spacings presented in this paper are all made nine month after the coatings were done.

7. Optical constants for SiC and WC To analyze the X-ray measurements of the multilayers and to model the properties at higher energies one needs to know the optical constants of the materials. It has been shown (Windt et al., 2003) that there is better agreement between theory and experiments when using measured optical constants instead of theoretical calculated for high energies. The telescope designs discussed in next section are up to 250 keV so this section will discuss the optical constants used in this paper for WC and SiC. The measured optical constants for SiC (Windt et al., 2003) are from 35 keV to180 keV and the values are by them extended to 200 keV. Figure 5 shows the measured optical constants, n and k, plotted as function of energy. At high energy both curves are very close to be ﬂat and the ﬁgure shows the extension that is used in this paper for energy up to 250 keV. For WC there are no measured optical constants and only calculated values up to 100 keV. For W we also have the calculated values up to 100 keV and measured values up to 180 keV. Figure 6 shows a good agreement between the calculated and measured optical constants for W in the range of 35 keV and up to 100 keV, with only a small shift in k and some disagreement around the W-absorption edge at 69 keV. When comparing the calculated optical constants for W and WC it is seen that for both n and k the difference is a shift caused by the smaller mass density of WC. With this in mind the optical constants for WC up to 250 keV used in this paper are designed by shifting the measured optical constants for W with the same amount as between the calculated optical constants for W and WC and then extrapolating the shifted curve for W to 250 keV. Springer

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8,E-09

0,9999999

6,E-09

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4,E-09

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n

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2,E-09

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50

25

75 100 125 150 175 200 225 250

50

75 100 125 150 175 200 225 250

Energy, E (keV)

Energy, E (keV) (a)

(b)

Fig. 5 (a, b) The gray lines are measured optical constants, n and k, for SiC from IMD (Windt, 1998). The black lines are an extension from 200 keV and up to 250 keV

1,0000000

5,E-08

4,E-08

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0,9999985 1,E-08

0,9999980

0,E+00

25

50

75

100

125

150 175

200

225

250

25

50

75

100

125

150

175

Energy, E (keV)

Energy, E (keV)

(a)

(b)

200

225

250

Fig. 6 (a, b) The thin black lines are measured optical constants, n and k, for W (Windt, 1998). The thin and thick gray lines are calculated optical constants for W and WC (Windt, 1998). The thick black lines are an extension from 100 keV and up to 250 keV for WC following the trend from the measured values (thin black line) of W. Inserted in (b), are the measured values for W and the extended values for WC multiplied by 10

8. Optimizations for a high energy telescope Telescopes using a Wolter I design employing W/Si multilayers have thus far been constrained by the smallest d-spacing it has been possible to coat, which is currently at 2.0 nm. This has placed limits on the largest radius one can reﬂect a given energy, and the highest possible energy that can be reﬂected at a ﬁxed radius. Figure 7 illustrates the dependence of the minimum bi-layer thickness, dmin , as a function of the energy for two ﬁxed grazing incidence angles. The energy and dmin are calculated using the refraction-corrected ﬁrst order Bragg law (Mao et al., 1999b). It can be seen that since the minimum bi-layer thickness can be decreased using WC/SiC the maximum energy it is possible to reﬂect at the given angle increases. This in turn means that by using WC/SiC coatings one can go to larger radii at a Springer

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6

dmin (nm)

5 4 3 2 1 0 100

150

200

250

Energy (keV) Fig. 7 The minimum d-spacing necessary for reﬂection of a maximum energy. The numbers are calculated using refraction-corrected ﬁrst order Bragg law. The black line is for a graze angle of 1.27 mrad, which with a focal length of 50 m corresponds to a radius of 0.25 m, and the gray line is for a graze angle of 1.82 mrad corresponding to a radius of 0.36 m

ﬁxed maximum energy than has been previously possible for a W/Si coated telescope, and thus in effect increase the effective area. The optimization procedure we have employed is based on Peter Mao’s Figure of Merit, FOM, optimization code (Mao et al., 1999a), and has been run on the parallel processing machines of CACR, Caltech’s Center for Advanced Computer Research. For the chosen energy range the minimum and maximum d-spacing can be determined using refractioncorrected Bragg’s law for the ﬁrst order peak, and from these the constants of the power-law proﬁle, a and b, are uniquely determined. For a power-law proﬁle, as described above, keeping the minimum and maximum d-spacing ﬁxed one optimizes over the number of bilayers, N, the power-law index, c, and the WC element thickness fraction, = dwc /d. The optimization runs over increasing N, and for each N ﬁnds the optimal combination of and c. Where the FOM tops the recipe is considered optimal. We have decided to optimize for an annulus, using WC/SiC as our multilayer. We have optimized for an annulus at graze angles, α = 1.27 mrad to α = 1.82 mrad, which for a focal length of 50 m corresponds to a radius of R = 0.25 m to R = 0.36 m. The energy range is 100 keV to 250 keV and the smallest bi-layer thickness we have used is 1.3 nm as can be seen in Table 2. The length of the two mirror sections in the Wolter I design are both 0.40 m and the mirror thickness is 0.2 mm. Table 2 shows the optimized design of the annulus broken down into 4 groups. Each group contains on average of 27 mirror shells, which are coated with the same recipe. The optimization has been stopped at 1000 bi-layers to keep the total thickness of the multilayer below 2.5 µm and the numbers of layers within a range so that the coating can be done in a day. The FOM is a very ﬂat function for such a high number of bi-layers and it is possible to decrease the numbers of bi-layers to 1000 without severely affecting the reﬂection. As discussed above, the optical constants of WC are currently unknown above 100 keV. To estimate the sensitivity of the design to a change in optical constants, we have calculated the optimized design for three different sets of optical constants: our estimated extrapolation and a small variation to each side. A “plus” variation with a small increase in n and a small decrease in k, and a “minus” variation with a small decrease in n and a small increase in k. Figure 8 shows the effective areas of the three designs, and illustrates the urgent need Springer

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Exp Astron (2005) 20:93–103 Table 2 Optimization results for an annulus of 0.25 m to 0.36 m coated with WC/SiC

Group

Material

R-range (m)

Dmin (nm)

Dmax (nm)

N

c

1

WC/SiC

0.25 – 0.27

1.78

6.96

1000

0.277

2

WC/SiC

0.27 – 0.30

1.63

6.36

1000

0.301

3

WC/SiC

0.30 – 0.33

1.49

5.81

1000

0.335

4

WC/SiC

0.33 – 0.36

1.36

5.31

1000

0.371

1000

2

Total effective areal (cm )

N is the number of bi-layers in the stack and c the optimized power-law index.

100

10

1 100

120

140

160

180

200

220

240

Energy (keV) Fig. 8 The black line shows the total effective area for the annulus described in Table 2 using the extrapolated optical constants for WC and SiC. A small “positive” variation of the optical constants causes the reﬂectivity to drop and thus the effective area. A “negative” variation has the opposite effect

for measurements of the optical constants. The “minus” variation causes the effective area to drop dramatically, while the “plus” variation increases it. In the best case there is about 100 cm2 effective area at 200 keV, and in the worst only a few cm2 . This is a factor of almost a hundred, and makes it difﬁcult to proceed beyond the point of conceptual designs.

9. Conclusions and what to do We have in this paper presented a new material combination, WC/SiC, which – because of the very low interface roughness compared to traditional coatings for hard X-ray telescopes – can coat multilayers with d-spacing below 1.0 nm, and with an interface roughness between 0.23 nm and 0.25 nm. By comparing WC/SiC with W/Si, W/SiC, and WC/Si we have understood the mechanism that makes WC/SiC coat much smoother than W/Si. The possibility to coat such thin bi-layer thickness gives the possibilities to make a telescope design, which will have a good throughput up to 250 keV and also have a reasonable effective area. To use WC/SiC as the material combination for future telescopes seems therefore very promising, but we also show that as there are no reliable optical constants for WC above 100 keV a large uncertainty exists. It is therefore very important to measure the optical constants up to several hundreds keV before a more realistic design using WC can be made. Springer

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Acknowledgements The authors would like to thank David Lumb from ESA and Eric Ziegler from ESRF for help and measuring time for the 40 keV data.

References Born, M., Wolf, E.: Principles of Optics, Cambridge, Seventh (expanded) Edition ed (1977) Furuzawa, A., Okajima, T., Ogasaka, Y., Tamura, K., Tawara, Y., Yamashita, K.: Proc. SPIE 4851, 708 (2003) Harrison, F.A., Boggs, S.E., Bolotnikov, A., Christensen, F.E., Cook, W.R., Craig, W.W., Hailey, C.J., JimenezGarate, M., Mao, P.H., Schindler, S.E., Windt, D.L.: Proc. SPIE 4012, 693 (2000) Harrison, F.A., Boggs, S.E., Christensen, F.E., Gehrels, N., Grindlay, J.E., Chen, C.M.H., Craig, W.W., Hailey, C.J., Pinto, P., Thorsett, S.E., Tueller, J., Windt, D., Woosley, S. E.: Proc. SPIE 4851, 345 (2003) Hol´y, T. B.: Phys. Rev. B 49, 10668 (1994) Jensen, C.P., Madsen, K.K., Chen, H.C., Christensen, F.E., Ziegler, E.: Proc. SPIE 4851, 724 (2003) Koglin, J.E., Chen, C.M.H., Chonko, J.C., Christensen, F.E., Craig, W.W., Decker, T.R., Hailey, C.J., Harrison, F.A., Jensen, C.P., Madsen, K.K., Pivovaroff, M.J., Stern, M., Windt, D.L., Ziegler, E.: Proc. SPIE 5488, 856 (2004) Madsen, K.K., Christensen, F.E., Jensen, C.P., Ziegler, E., Craig, W.W., Gunderson, K., Koglin, J.E., Pedersen, K.: Proc. SPIE 5168, 41 (2004) Mao, P.H., Harrison, F.A., Windt, D.L., Christensen, F.E.: Applied Optics 38, 4766 (1999a) Mao, P.H., Harrison, F.A., Windt, D.L., Christensen, F.E.: Applied Optics 38, 4766 (1999b) Ogasaka, Y., Tamura, K., Okajima, T., Tawara, Y., Yamashita, K., Furuzawa, A., Haga, K., Ichimaru, S., Takahashi, S., Fukuda, S., Kito, H., Goto, A., Kato, S., Satake, H., Nomoto, K., Hamada, N., Serlemitsos, P.J., Tueller, J., Soong, Y., Chan, K.W., Owens, S.M., Berendse, F.B., Krimm, H.A., Baumgartner, W., Barthelmy, S.D., Kunieda, H., Misaki, K., Shibata, R., Mori, H., Itoh, K., Namba, Y.: Proc. SPIE 4851, 619 (2003) Parmar, A.N., Hasinger, G., Arnaud, M., Barcons, X., Barret, D., Blanchard, A., Bb¨ohringer, H., Cappi, M., Comastri, A., Courvoisier, T., Fabian, A.C., Georgantopoulos, I., Grifﬁths, R., Kawai, N., Koyama, K., Makishima, K., Malaguti, P., Mason, K. O., Motch, C., Mendez, M., Ohashi, T., Paerels, F., Piro, L., Schmitt, J., van der Klis, M., Ward, M.: Proc. SPIE 4851, 304 (2003) Sinha, S.K., Sirota, E.B., Garoff, S., Stanley, H.P.: Phys. Rev. B 38, 2297 (1988) Windt, D.L.: Comput. Phys. 12, 360 (1998) White, N.E., Tananbaum, H.: Proc. SPIE 4851, 293 (2003) Windt, D.L., Donguy, S., Hailey, C.J., Koglin, J., Honkimaki, V., Ziegler, E., Christensen, F.E., Harrison, F.A.: Proc. SPIE 5168, 35 (2004)

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Exp Astron (2005) 20:105–113 DOI 10.1007/s10686-006-9029-2 ORIGINAL ARTICLE

Design aspects of grazing angle multilayer mirrors for soft γ -rays Ernst-Jan Buis · Marco Beijersbergen · Giuseppe Vacanti · Marcos Bavdaz · David Lumb

Received: 15 November 2005 / Accepted: 20 February 2006 C Springer Science + Business Media B.V. 2006

Abstract If sensitive enough, future missions for nuclear astrophysics will be a great help in understanding supernovae explosions. In contrast to coded-mask instruments, both crystal diffraction lenses and grazing angle mirrors offer a possibility to construct a sensitive instrument to detect γ -ray lines in supernovae. We report on possible implementations of grazing angle mirrors and simulations carried out to determine their performance. Keywords Nuclear astrophysics · Multilayers · Gamma-rays

1. Introduction An efﬁcient way to increase the sensitivity in future space-born γ -ray observatories is to use focusing optics. While the coded mask technique, such as applied on the Integral mission, is background limited, focusing optics offers the combination of a large collecting area with a small detector area. While focusing optics already have been realized using Laue lenses (Von Ballmoos et al., 2004), we discuss in this paper the design of a grazing angle multilayer optics. Grazing angle optics already have been realized for X-ray observatories, such as XMM-Newton and Chandra. With the use of multilayer coatings the reﬂectivity of the optics can be extended to the (soft) γ -ray regime. In particular, two nuclear lines are of interest in this regime. Firstly, the 158 keV γ -ray line is important for the study of Ni decay in supernovae. Secondly, observation of the line at 511 keV due to positron-electron annihilation is of interest for many subjects in (nuclear) astrophysics. For instance, the 511 keV line is found in supernovae and AGNs. Moreover there is an enigmatic strong source for this line in the center of our galaxy. E.-J. Buis () · M. Beijersbergen · G. Vacanti Cosine Science and Computing BV, Niels Bohrweg 11, 2333 CA Leiden, The Netherlands e-mail: [email protected] M. Bavdaz · D. Lumb Ofﬁce of Advanced Concepts and Science Payloads, ESA/ESTEC Postbus 299, 2200 AG Noordwijk, The Netherlands Springer

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In this paper, we show how a γ -ray telescope would look like and we present possible implementations for telescopes optimized for observing 158 keV and 511 keV respectively. We require an effective area of about 1 m2 to reach a sensitivity which is several orders better than Integral. The outline of this paper is as follows: the next section deals with the general design parameters of a γ -ray telescope. In Section 3 we review the scattering of γ -rays on multilayers and the implementation in our software. We also discuss the material selection for multilayer coatings. Then, in the following section we present a design procedure and illustrate the design with four explicit implementations.

2. Mirror design parameters and technology For the purpose of this paper we assume a hypothetical mission making use of the optics described here, would be devoted to a survey of point sources. Such a mission would not require any imaging capability, and the telescope optics can be reduced to that of a singlecone collimator. This means that γ -rays reaching the focal plane are only reﬂected once. This in contrast to X-ray optics, double reﬂection optics can be used for γ -rays to reduce the focal length and has been investigated in Buis et al. (2004). However, such a design requires a total mirror area of more than 5000 m2 , which is deemed to be unrealistic. A general layout of γ -ray optic telescope is depicted in Figure 1. At the energies of interest the reﬂection or diffraction angles are small, which results in a long focal length. Already at relatively soft γ -ray energies, the focal length is such that formation ﬂying of two spacecraft is required: one for the mirror and one for the focal-plane detector and associated electronics. Here, we only discuss the mirror spacecraft. Focusing mirrors for X-rays are produced using various technologies. An overview of the technologies is found in Beijersbergen et al. (2004). In order to get the maximum sensitivity any mirror design should aim for (i) the smallest plate scale and (ii) the smallest mirror spacing in combination with a minimum mirror thickness. The smallest plate scale is obtained with the smallest focal length. A small mirror spacing yields a small spot size on the focal plane detector and the focal plane detector should be as small as possible to reduce the number of background counts. The mirror thickness should be small to avoid aperture blocking. Hence an important parameter in the design of a γ -ray mirror is the so-called ‘aperture utility’,

Fig. 1 Schematic layout of a single-cone collimator. Various design parameters are indicated and discussed in the text.

nested mirrors

focal plane detector focal length

R0 mirror spacing mirror thickness

R1 L

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which is the fraction of the aperture which is not blocked by mechanical structure of the nests and the thickness of the mirrors. The technology to produce the γ -ray mirrors is assumed to be identical as the assembly of the XEUS mirror spacecraft. The so-called stacked mirror-plates Bavdaz et al. (2004) for the XEUS optics implies a mirror thickness of about 0.2 mm and a spacing of about 0.8 mm. According to these values for the thickness and spacing, an aperture utility of the order of 60–70% is anticipated.1 3. X-ray and γ -ray scattering on multilayers Starting point of the reﬂectivity calculations is the determination of the indices of refraction. The index of refraction n r for a given material is determined using the atomic form factors f 1 and f 2 using n r = 1 − ik − δ = 1 − nr0 λ2 ( f 1 + i f 2 )/(2π ),

(1)

where k and δ are the optical constants, r0 is the classical electron radius, λ is the wavelength and n the atom number density. The form factors f 1 and f 2 are obtained from photon interaction cross-sections taken from the Evaluated Photon Data Library (EPDL) Perkins and Cullen (1994) by adding the coherent effects to f 1 and the incoherent effects to f 2 . Once the atomic form factors have been determined, the reﬂectivity Ro can be calculated using the well-known Fresnel reﬂection formula. Reﬂection off a uniform medium, here called single-layer reﬂection in contrast to multilayer reﬂection, can be very efﬁcient, albeit at very small grazing angles (0.03 degree at 158 keV). The models for reﬂection off a medium, based on a complex index of refraction from the oscillator strength and the Fresnel laws of refraction and reﬂection, are not veriﬁed at higher energies as well as in the X-ray regime, but seem to work in principle up to a few hundred keV Windt et al. (2004). As in the X-ray regime the index of refraction is less than 1 in combination with absorption, resulting in total external reﬂection. Where singlelayer mirrors are limited to γ -rays with grazing angles below or close to the critical angle for that material, multilayer mirrors can reﬂect the photons at much larger grazing angles. Multilayers are a form of synthetic non-uniform crystals and consist of bilayers which consist of absorbers and spacers. Each bilayer in the coating has its individual thickness which contributes to the bandwidth in reﬂectivity. The choice of the absorber and spacer media in a multilayer depends in ﬁrst order on the optical constants. The index of refraction of the absorber medium is required to differ as much from unity as possible, whereas the index of refraction of the spacer should be close to unity. The index of refraction consists of a real and imaginary part. The imaginary part contributes to the absorption of the γ -rays, which should be small, but not too small since in principle a large imaginary part makes the index of refraction be further from unity. The X-ray reﬂection off uniform coating and the tracing of γ -rays through geometrical models has been included in an X-ray tracing software package, called “MSIM”. Originally the MSIM package is developed for simulation of X-ray reﬂections in XMM-Newton Erd et al. (1999). We have extended the energy range to γ -rays for design studies on γ -ray (imaging) missions by introducing the atomic form factors from Perkins and Cullen (1994) and reﬂection off a multilayer coating in the software. 1

The exact number depends on the number of nests and hence on the ﬁnal geometry of the mirror. Springer

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4. Design procedure and implementation 4.1. Parameter scan The design of mirrors for γ -ray collimator yields an optimization of the following variables: 1. 2. 3. 4. 5.

γ -ray energy; grazing angle and its bandwidth; absorber and spacer material; thickness of each bilayer; fractional thickness of the absorber in the bilayer.

For several materials and at different energies we have optimized the reﬂectivity and the number of layers to achieve this reﬂectivity following the method described in Kozhevnikov et al. (2001). Once the reﬂectivity is known, the spacecraft layout is straightforward. The layout of the conical mirrors is done as follows. The optic has an annular aperture and the grazing angles range between α0 and α1 , the aperture has an geometrical area of A = π f 2 [tan2 (2α1 ) − tan2 (2α0 )]

(2)

so that the effective collecting area is approximately Ae = U · R · A = U Rπ f 2 [tan2 (2α1 ) − tan2 (2α0 )]

(3)

where f is the focal length, U is the aperture utility and R the reﬂectivity. As mentioned in Section 1, we aim for a telescope with an effective area of at least Aeff = 1 m2 . From this requirement and the determination of the mean reﬂectivity between the angles α0 and α1 we calculate the focal length using Equation (3). In Figure 2 we show the focal length for various points in the design parameter space. According to Equation (3) the focal length is decreased when the reﬂectivity is large, i.e. when the number of layers layers ion the multilayer coating

Fig. 2 Scan of the design parameter space: showing the possible values for the focal length for a W-C and a Ni-C multilayer coating (left) and the relation between the number of layers in the coating and the focal length for the W-C coating. Springer

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Table 1 Four models and their design parameters

Model

Design energy [keV]

Material

Design angles [deg]

Fractional thickness

Number of layers

I II III IV

158 158 511 511

W, C Ni, C W, C Mo, C

0.13–0.15 0.02–0.15 0.01–0.07 0.02–0.03

0.42 0.47 0.45 0.48

541 4852 4798 1419

is large. In Figure 2 (right) this relation between the number of layers and the focal length becomes apparent. Note that in any case, the focal length would not be less than 150–200 m. We have scanned the parameter space for two different energies: 158 keV and 511 keV. A scan was carried out for W-C, Ni0.93 V0.07 -C and Mo-C coatings, where the grazing angles were varied between 0.02 and 0.2 degrees and the fractional thickness between 0.1 and 0.9. Notice that, in principle, many more absorber materials can be chosen at this stage, such as Pt, Ir etc. As a spacer material, we have taken carbon in all scans. However, carbon is in practice not the most ideal material to use in a multilayer coating, in view of the obtained surface roughness. Better coatings have been produced using a mixture of carbon and silicon (SiC) as a spacer material (Jensen). But, as we shall see later, the choice of spacer materials has less impact on the optical performance of the multilayer coating, so we expected similar results with SiC as spacer material. Out of the parameter scans we have chosen four points: two models for the 158 keV mirror and two conﬁgurations for the 511 keV lens. The choice for a particular point in the parameter is mainly driven by the state of the art in multilayer coating. In general, as discussed above, the number of layers should be as large as possible. Below we discuss the four models: two for each energy of which one conﬁguration has considerable less layers in the coating than the other. In Table 1 we list the four conﬁgurations with their design parameters. For two models, the number of layers is at least one order of magnitude higher than what have been produced to date an can be regarded as ideal case scenario. Models I and IV have multilayer coating, which are (nearly) within reach of the present technology. Figures 3 and 4 show the intensity reﬂectivity of the four conﬁgurations. In addition, the layer thickness distribution is shown. The plots show the relation between the number layers and the reﬂectivity of the coating: a

Fig. 3 Reﬂectivity (left) and layers thickness distribution (right). Springer

1 0.9

model III: W/C;

0.8

Edesign = 511 keV

model IV: Mo/C; E design = 511 keV

0.7 0.6

layer thickness [nm]

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reflectivity

110 5 4.5

model III: W/C; Edesign= 511 keV

4 model IV: Mo/C; Edesign= 511 keV

3.5 3 2.5

0.5 0.4

2

0.3

1.5

0.2

1

0.1

0.5

0

0.05

0.1

0.15 0.2 grazing angle [deg]

1000

2000

3000

4000 5000 layer number

Fig. 4 Reﬂectivity (left) and layers thickness distribution (right).

n = 1 - ik - δ change δ in W

1.2

change k in W change δ in C change k in C

1.1

1

relative change in reflectivity

relative change in reflectivity

n = 1 - ik - δ

change δ of Ni.93V.07

1.2

.93

change δ of C change k of C

1.1

1

0.9

0.9

0.8

0.8 0.8

0.9

1 1.1 1.2 change in optical constant

change k of Ni V.07

0.8

0.9

1 1.1 1.2 change in optical constant

Fig. 5 Relative change in the reﬂectivity as function of the relative change in the optical constants for model I (left) and model II (right).

high angular bandwidth is reach with a large number of layers. Moreover, a high reﬂectivity is found at lower grazing angles. In Figure 5 the relative change in the reﬂectivity as function of the relative change in the index of refraction is shown for model I and model II. The reﬂectivity in both models is mostly sensitive to the optical constant δ of the absorber material. The reﬂectivity in model II is in addition sensitive to δ in the spacer material, mainly due to the larger number of layers in this model. The ﬁgure shows the robustness of the results presented in this paper against the uncertainty of the optical constant at larger energies. For model I and IV in particular, the choice of the spacer material is not that crucial. 4.2. Mirror spacecraft layout To determine the on and off-axis response, we have constructed geometrical models in the MSIM package according the design parameters as listed in Table 2. A geometrical view is shown in Figure 6. Because the mirror space is ﬁxed, the lengths of all nest in the geometry Springer

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Table 2 Relevant parameters for various geometries for mirror spacecraft for a γ -ray observatory Model

Focal length [m]

Radii of annulus [m]

Number of nests

Mirror area [m2 ]

I II III IV

372.5 189.1 384.6 833.5

1.69–1.95 0.132–0.990 0.134–0.940 0.582–0.873

261 859 806 291

978 1633 3116 2438

Fig. 6 Three dimensional view of two mirror spacecraft models: model I for 158 keV (left) and model III for 511 keV (right). The geometry of model I is a ring structure with large radii of annulus. The optical axis of the system is perpendicular to the ring. For model III, the inner most nest has a much smaller radius than the outer most nest as in contrast to model I. Therefore the shape of this mirror system is much different than the shape from model I.

are different Moreover, the difference in length of the nests in the telescope is proportional to the difference in the radii of annulus2 : for model I the inner most nest is twice as long as the outer nest, while for model III the inner nest is about seven times longer. The total area mirror area is less than or in the order of 3000 m2 , which is the design value for the planned XEUS mission. 4.3. Effective area and vignetting The effective area curves for models I and II (158 keV) and for models III and IV (511 keV) are plotted in Figure 7. The effective area is close to the initial requirement of an effective area of 1 m2 . Note that the blocking of the mirror thickness is included, but the blocking due to the mechanical structure is not. This will reduce the effective area as shown in the ﬁgures by about 20%. The decrease of the effective area due to surface roughness is included in the calculations. The surface roughness is represented by a Debye-Waller factor and a target value for future ˚ Surface roughnesses as low a 2.3 A ˚ have already been missions should be around 2 A. achieved for WC/SiC coatings (Jensen). From the graphs it can be concluded that the bandwidth of the model is closely related to the number of layers. The design driver is therefore the number of layers in the coating. The vignetting curves show a quite large FOV for the optics spacecraft. However, in practice, 2

The radii of annulus are deﬁned as the radii of the inner most and outer most mirror nest. Springer

2

2

off-axis eff. area [m ]

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1.4

Edesign=158 keV Ni/C; σ = 0 Å

1.2

Ni/C; σ = 1 Å Ni/C; σ = 2 Å

1

W/C; σ = 0 Å

0.8

W/C; σ = 2 Å

W/C; σ = 1 Å

1.4

Ni/C; σ = 2 Å W/C; σ = 1 Å

0.4

0.2

0.2

300

400

500

W/C; σ = 0 Å W/C; σ = 2 Å

0.8

0.4

200

Ni/C; σ = 1 Å

1

0.6

100

Ni/C; σ = 0 Å

1.2

0.6

0

Edesign=158 keV

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 o incoming angle θ [ ]

600 700 Energy [keV]

(a)

(b)

Mo/C; σ = 2 Å W/C; σ = 0 Å

1.2

W/C; σ = 1 Å W/C; σ = 2 Å

2

Mo/C; σ = 1 Å

1.4

off-axis eff. area [m ]

Mo/C; σ = 0 Å

2

on-axis eff. area [m ]

Edesign=511 keV

1.4

Edesign=511 keV Mo/C; σ = 0 Å

1.2

Mo/C; σ = 1 Å Mo/C; σ = 2 Å

1

W/C; σ = 0 Å

0.8

0.8

W/C; σ = 2 Å

0.6

0.6

0.4

0.4

0.2

0.2

1

0

100

200

300

400

500

(c)

600 700 Energy [keV]

W/C; σ = 1 Å

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 o incoming angle θ [ ]

(d)

Fig. 7 Effective area (on-axis) as a function of the γ -ray energy (left) and the off-axis effective area at a ﬁxed energy (right). Note that the incoming angle is the deﬁned here as the angle of the gamma-ray w. r. t. the optical axis of the mirror system, and should not be confused with the grazing angle.

the FOV of the telescope will determine by the size of the focal plane detector: the optics suffers severe coma. To reconstruct the coma unpractical large focal plane detectors would be needed.

5. Summary and conclusions In this paper we have discussed the design of a multilayer coated γ -ray mirror for nuclear astrophysics. We have reviewed the reﬂectivity of γ -rays off multilayers. Using the reﬂectivity we have scanned a parameter space, consisting of the most relevant design parameters such as grazing angle and multilayer thickness distributions. For various materials we have constructed a geometrical model optimized to reﬂect 158 keV and 511 keV γ -rays. The initial requirement of a effective aperture of 1 m2 can be met and for γ -ray telescope optimized for the 158 keV line this is within the reach of current technologies. In comparison with the planned XEUS mission, the mirror area and the number of nests is not unrealistic. The main Springer

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challenge of a multilayer mirror is the number of layers in the coating. Preferably this number ˚ should be somewhere between 1000 and 5000, with a surface roughness of no more than 2 A.

References Buis, E.J. et al.: Proceedings of the SPIE 5488, 691–699 (2004) Beijersbergen, M., et al.: Proceedings of the SPIE 5488, 868–874 (2004) Bavdaz, M., et al.: Proceedings of the SPIE 5488, 829–836 (2004) Erd, C., et al.: in Mehringer D.M. (eds.), Astronomical Data Analysis Software and Systems VIII ASP Conference Series 172, 119–123 (1999) Jensen, C.: (2006), DOI: 10.1007/s10686-006-9022-9 Kozhevnikov, I.V., et al.: Nucl. Instr. Meth. A A 406, p. 424 (2001) Perkins, S.T., Cullen, D.E.: ‘ENDL type formats for the LLNL Evaluated Atomic Data Library, EADL, for the Evaluated Electron Data Library, EEDL, and for the Evaluated Photon Data Library, EPDL’ (1994) Von Ballmoos, P.V., et al.: New Astronomy Review 48, 243–249 (2004) Windt, D.L., et al.: Proceedings of the SPIE 5168, 35–40 (2004)

Springer

Exp Astron (2005) 20:115–120 DOI 10.1007/s10686-006-9032-7

Progress toward light weight high angular resolution multilayer coated optics M. P. Ulmer · M. E. Graham · S. Vaynman · J. Echt · M. Farber · S. Ehlert · S. Varlese

Received: 15 November 2005 / Accepted: 22 February 2006 C Springer Science + Business Media B.V. 2006

Abstract We have been working on 3 separate projects that together will give us the ability to make 1 arc second, light weight Wolter I optics that work above 40 keV. The three separate tasks are: (a) plasma spraying of metal-coated micro-balloons; (b) coating of the inside of Wolter I mirrors, (c) actuator designs for improving ﬁgure quality. We give a progress report on our work on all three areas. Keywords X- and gamma-ray Telescopes · X-ray · Gamma-ray 1. Introduction The community knows how to coat functional multilayers on surfaces to enhance the hard X-ray (10 keV) reﬂectivity, and the community knows how to make sub-arc second X-ray optics. There would be little difﬁculty in carrying out this approach if money were no object. For example, 10 m focal length Chandra-like mirrors (see Figure 1) could be made and over-coated with graded d-spacing multilayers (Jimenez-Garate et al., 2000; Ulmer et al., 2002). The difﬁculty comes in trying signiﬁcantly to reduce the cost of the X-ray mission. This involves reducing the cost of fabrication of the optics as well as reducing the mass of the optic and the optical bench. The mass of the optical bench and satellite can be reduced both by reducing the mass of the X-ray optics and by keeping the requirement of the focal

M. P. Ulmer () Department of Physics and Astronomy, Northwestern University, 2131 Tech Drive, Evanston, IL 60208-2900 e-mail: [email protected] M. E. Graham · S. Vaynman · J. Echt Department of Materials Science, Northwestern University M. Farber · S. Ehlert Department of Physics and Astronomy, Northwestern University S. Varlese Ball Aerospace and Technologies Corp Springer

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Fig. 1 The largest AXAF (now Chandra) hyperboloid undergoing ﬁnal inspection at Hughes Danbury Optical (now Goodrich).

length ﬂexible so as to meet the rocket fairing constraints. We have been addressing these new requirements by a three pronged approach: (a) making light weight optics by improving the value of the mirror material stiffness to mass ratio; (b) depositing multilayers on the inside of electroformed mirrors that are too small to have direct deposition on the inside; (3) actuator designs to modify the shape of the mirror after fabrication. The last point is key to achieve 1

or better angular resolution, as inherent stress in replicated optics has prevented better than approximately 10

half power diameter image quality (see Ref. Aschenbach (2002)). This paper is mostly a summary of previously reported work that touched on technology to reduce weight, to improve ﬁgure quality, and to coat the inside of electroformed Ni shells. We also give a summary of new work done at the Argonne National Laboratory Advanced Photon Source (ANL/APS). 2. Light weight optics We are using plasma spraying (Ulmer et al., 2002, 2003; Citterio et al., 2002; Hudec et al., 2003) to make light weight X-ray mirrors. Hollow micro-spheres made of glass or ceramic are precoated with Ni prior to being sprayed onto the backside of the initial electroformed nickel layer that replicates the mandrel surface. Thus, a low density layer is produced that, with the inclusion of another layer of Ni on top of the plasma sprayed surface, increases the stiffness and strength of the resulting shell. This lamination process is the unique feature of our approach compared to other published approaches. We have made some encouraging progress, as shown in Figure 2. The image on the left shows a ﬂat with negligible stress. Optical proﬁler measurements show that the deviation from ﬂat of 1/3 (λ, 600 nm) and smoothness as good as the master which was of 5.5 nm on the 10–100 µm length scale. The top Ni layer as seen in the ﬁgure is 140 µm thick and the total thickness is 400 µm, which translates into an areal density of 2 kg/m2 . This sample was dipped in liquid nitrogen with no discernible degradation in ﬁgure quality. The next step is to work a scale up to 10 cm diameter cylinders, and we have NASA Small Business Technology TRansfer (STTR) funding to extend this work. The requirement is to be able to make mirrors that are lighter weight than those that can be made out of pure Ni. This means that for about a 10 cm diameter mirror the net (the inner and outer layers combined) width of Ni width should be less than 80 µm. Preventing print through from the sprayed particle impact on the thin Ni replication layer as well as dealing with the potential stresses set up by the heat of the plasma spray (hot enough to melt Ni or ∼1,400 C) can be challenging. To alleviate the print through, we use Springer

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Fig. 2 Left, a laminate of Ni and microspheres; right a pipe shaped laminate on top of a ﬂat made from the same microspheres. The ﬂat has been made by a scintering process, and then treated by us to make smooth surface seen in reﬂection.

small mass (∼20–90 µm diameter) beads which have minimal momentum when sprayed. To minimize the stress, we keep the mandrel temperature below 100C during spraying. The payoff is the possibility of making optics with better ﬁgure quality than has been done to date with light weight glass segmented optics (Zhang et al., 2005). The plasma-sprayed laminates made by us have had about one half the coefﬁcient of thermal expansion of pure Ni, which helps in maintaining ﬁgure control when temperature ﬂuctuations or gradients can exist. 3. Multilayers There are several groups (e.g. Hudec et al., 2005; Jimenez-Garate et al., 2000; Pareschi et al., 2005; Romaine et al., 2005; Ulmer et al., 2003; Zhang et al., 2005) that are fabricating mirrors for hard X-ray astronomy. Our group is the only one that uses CNx to coat and smooth the mandrel (see Ulmer et al. (2003) and references therein), but the multilayer coating process we developed has been copied by at least one other group (i.e. Pareschi et al., 2005). This process is to coat a mandrel with multilayer, electroform over these layers, and then remove the electroformed multilayers with layers intact on the inside of the mirror. We used Cu as release layer that can then be removed without harming the multilayers as we have shown in Ulmer et al. (2003), and we repeat the main results from that work here. We show that the layers’ performance matches the same model for both 10 keV and 30 keV, which demonstrated the layers are intact both near the surface and signiﬁcantly below the surface. We rotated the mirror and were able to achieve the same performance which demonstrated the layers were uniform around the circumference of the mirror.

Fig. 3 The data are in bold white, the best ﬁts in dashed purple. The same model for the multilayers was used in all cases; we accumulated the two 10 keV data sets from a 90 before and after a 90 degree rotation of the mirror about its optical axis. Springer

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Fig. 4 Left image of a Ti-L line at 0.45 keV source 20 m from the mirror out of focus by 71 mm; pixel size 16 µm, 1.

47/pixel, image frame 512 × 576. Right, a 7 keV composite image from the APS slightly out of focus; see text.

4. Characterization of ﬁgure distortion and possible remediation A major drawback to all the current replication processes of making X-ray mirrors is that the best a replication process has achieved is ∼10

(see Aschenbach, 2002).This is not good enough for certain applications such as solar physics where approximately a factor of 10 improvement in angular resolution is needed (i.e., 1

). The major reason for the limitation to the angular resolution of replicated optics is that distorting stresses are built up in the mirror walls during the replication process. The application of restoring forces by judiciously designed actuators, however, may make it possible to reach an angular resolution of 1

or better. Therefore, our group has embarked upon a proof-of-concept study which, in “phase 1,” was simply to acquire data to model the deformations in the mirror and to carry out preliminary designs for the application of actuators. We present a small portion of our previous work (Ulmer et al., 2004) here along with new work. We show images in Figure 4 which we made to demonstrate simply that: (a) it is valuable to make out-of-focus images so the X-ray mirror azimuthal response can be examined; and, (b) we probably can use the ANL/APS within a 1 hour drive of the Northwestern University campus for X-ray measurements before using the much more extensive facilities used to calibrate the Chandra and XMM-Newton X-ray telescopes. The left image in Figure 4 was taken at the Lockheed Martin Advanced Technology Center Lockheed Martin Solar and Astrophysics Laboratory (LMATC/LMSAL) facility in Palo Alto. The later image was taken at the APS on the UNI-Cat 33 BM-C beam line. As the LMATC/LMSAL results have discussed in detail before (see Ulmer et al., 2004), we only discuss the ANL/APS measurements in this paper. The ANL/APS beam line we used was UNI-CAT 33BM-C beam line. The energy range we used was 7 keV. As the absorption is signiﬁcant in air over the path length of about 4 meters total, and the CCD/phosphor camera we used in not very efﬁcient (less than 1%), we placed He ﬁlled tubes in the air path of the X-ray beam. The beam was just wide enough in the horizontal direction (11.2 cm) to hit both sides of the front face of the mirror simultaneously. In the vertical direction, the beam was 1 mm wide. The beam emulates a nearly parallel beam with a divergence in the horizontal direction equivalent to a point source at 50 m. To produce the right hand image shown in Figure 4, we purposely tried to put the mirror out of focus to produce an image similar to that we obtained at the LMATC/LMSAL facility. The mirror we used was apparently deformed such that the initial out-of-focus image became nearly focused as we rotated the mirror about its optical axis. We estimate that the deformity corresponds to a change in graze angle slope of about 1 in both parts of the Wolter 1 mirror. Springer

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Such a slope deviation could be caused by a net deviation in radius of about 60 µm in each of the parabolic and hyperbolic 20 cm long sections of the Wolter I mirror. The effect of this deformation was that after we rotated the mirror and were committed to making a full 360 degree rotation about the optical axis, we found that most (all but 6 of 36) of the mirror orientations were actually nearly in focus at the separation distance (210 cm) between the parabola/hyperbola intersection portion of the mirror and the CCD camera. A lesson learned for further work is to allocate enough time to be sure we can take a set of measurements at more than one separation distance such as was done at the LMATC/LMSAL facility (see Ulmer et al. (2004)). The one drawback to working at the ANL/APS and at 7 keV versus 0.45 keV is that for mirrors that are not exceptionally smooth (e.g., <0.5 nm), the scattering can be more than 10 times worse at 7 keV than at 0.45 keV. However, once we progress to testing multilayers optimized for 40 keV and up, the access to higher energies available at the APS will be essential. A tantalizing possibility which we did not explore due to time limitations, but should be possible, is to use the very precise slit adjustment available at the ANL/APS to locate the beam so only a small portion of it (5 µm wide) hits the mirror. In this way, after we carry out our initial alignment and adjustment of the mirror relative to the beam, we can then cut down the beam to sample just a very tiny part or the mirror in order to understand how the mirror is affected by being reshaped with the actuators. We realize that actuators have potential pit falls such as the requirement of power and also being so thick as to prevent deep nesting. However, it may be possible to design thin (less than 1 mm thick) passive actuators that can be made to change the mirror shape and hold that improved shape. Until the basic concept is proved there is no need, however, to try to solve this second generation set of problems. 5. Summary and conclusion In summary, for future space missions it will be desirable for them to be affordable by reducing mass, keeping the focal length manageable, and yet having high ﬁgure quality. The avenues we have described above are straight forward paths to achieving this goal, but a great deal of work needs to be done to take us from the concept stage to a functional system. Acknowledgements We thank Yong Chu, Jenia Karapetrova, and Paul Zschack for APS support on the UNI-CAT Beam line plus Steve Wang and Alex Vaynman for help with the data taking. We thank Robert Stern and Lawrence Shing for help with the LMSAL experiment. The original work was supported in part by internal research grants at both the Lockheed Martin Advanced Technology Center Lockheed Martin Solar and Astrophysics Laboratory and Ball Aerospace and Technologies Corp., plus the Illinois Space Grant (97–319/04/NGT 5-40030; which also sponsored the latest APS work) and NASA STTR grant (NAS5-03069). References Aschenbach, B.: In-orbit performance of the XMM-Newton x-ray telescopes: images and spectra. In: Proc. SPIE, X-Ray Optics for Astronomy: Telescopes, Multilayers, Spectrometers, and Missions, Paul Gorenstein and Richard B. Hoover (eds.), 4496, 8–22 (2002) Springer

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Citterio, O., Ghigo, M., Mazzoleni, F., Pareschi, G., Parodi, G., Braeuninger, H.W., Burkert, W., Hartner, G.D.: Development of soft and hard x-ray optics for astronomy: progress report II and considerations on material properties for large-diameter segmented optics of future missions. In: Proc. SPIE 4496, 23–40, X-Ray Optics for Astronomy: Telescopes, Multilayers, Spectrometers, and Missions, Paul Gorenstein and Richard B. Hoover (eds.), 4496, 23–40 (2002) Hudec, R., Pina, L., Inneman, A., Sveda, L., Semencova, V., Skulinova, M., Brozek, V., Mika, M., Kacerovsky, R., Sik, J.: Novel technologies for x-ray multi-foil optics. In: Optics for EUV, X-Ray, and Gamma-Ray Astronomy II. O. Citterio and S.L. O’Dell (eds.), Proc. SPIE 5900, 276–287 (2005). DOI 10.1117/12.620425 Hudec, R., Pina, L., Inneman, A.V., Ticha, H., Brozek, V., Zentkova, M., Zentko, A., Chylek, T.: Lightweight x-ray optics for future space missions. In: X-Ray and Gamma-Ray Telescopes and Instruments for Astronomy. J.E. Truemper and H.D. Tananbaum (eds.), Proc. SPIE 4851, 656–665 (2003). DOI 10.1117/12.461590 Jimenez-Garate, M.A., Craig, W.W., Hailey, C.J., Christensen, F.E., Hussain, A.M.: Fabrication, performance, and ﬁgure metrology of epoxy-replicated aluminum foils for hard x-ray focusing multilayer-coated segmented conical optics. Optical Engineering 39, 2982–2994 (2000) Pareschi, G., Basso, S., Citterio, O., Ghigo, M., Mazzoleni, F., Spiga, D., Burkert, W., Freyberg, M., Hartner, G.D., Conti, G., Mattaini, E., Grisoni, G., Valsecchi, G., Negri, B., Parodi, G., Marzorati, A., dell’Acqua, P.: Development of grazing-incidence multilayer mirrors by direct Ni electroforming replication: a status report. In: Optics for EUV, X-Ray, and Gamma-Ray Astronomy II. O. Citterio and S.L. O’Dell (eds.), Proc. SPIE 5900, 47–58 (2005). DOI 10.1117/12.617362 Romaine, S., Basso, S., Bruni, R.J., Burkert, W., Citterio, O., Conti, G., Engelhaupt, D., Freyberg, M.J., Ghigo, M., Gorenstein, P., Gubarev, M., Hartner, G., Mazzoleni, F., O’Dell, S., Pareschi, G., Ramsey, B.D., Speegle, C., Spiga, D.: Development of a prototype nickel optic for the Constellation-X hard x-ray telescope: III. In: Optics for EUV, X-Ray, and Gamma-Ray Astronomy II. O. Citterio and S.L. O’Dell (eds.), Proc. SPIE 5900, 225–231 (2005). DOI 10.1117/12.620438 Ulmer, M.P., Altkorn, R., Graham, M.E., Madan, A., Chu, Y.S.: Production and performance of multilayercoated conical x-ray mirrors. Applied Optics 42, 6945–6952 (2003) Ulmer, M.P., Altkron, R.I., Graham, M.E., Madan, A., Chu, Y.S.: Production and performance of multilayer coated conic sections. In: Proc. SPIE, X-Ray Optics for Astronomy: Telescopes, Multilayers, Spectrometers, and Missions, Paul Gorenstein and Richard B. Hoover (eds.), 4496, 127–133 (2002) Ulmer, M.P., Stern, R.A., Shing, L., Farber, M., Smith, M.: Deformable x-ray optics for solar physics. In: Telescopes and Instrumentation for Solar Astrophysics. S. Fineschi and M.A. Gummin (eds.), Proc. SPIE 5171, 269–279 (2004) Zhang, W.W., Content, D.A., Lehan, J.P., Petre, R., Saha, T.T., Gubarev, M., Jones, W.D., O’Dell, S.L.: Development of lightweight x-ray mirrors for the Constellation-X mission. In: Optics for EUV, X-Ray, and Gamma-Ray Astronomy II. O. Citterio and S.L. O’Dell (eds.), Proc. SPIE 5900, 247–257 (2005). DOI 10.1117/12.614462

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Exp Astron (2005) 20:121–129 DOI 10.1007/s10686-006-9028-3 ORIGINAL ARTICLE

InFOCµS hard X-ray imaging telescope J. Tueller · H. A. Krimm · T. Okajima · S. D. Barthelmy · S. M. Owens · P. J. Serlemitsos · Y. Soong · K.-W. Chan · Y. Ogasaka · R. Shibata · K. Tamura · A. Furuzawa · Y. Tawara · H. Kunieda · K.Yamashita

Received: 15 January 2006 / Accepted: 14 February 2006 C Springer Science + Business Media B.V. 2006

Abstract InFOCµS is a new generation balloon-borne hard X-ray telescope with focusing optics and spectroscopy. We had a successful 22.5-hour ﬂight from Fort Sumner, NM on September 16,17, 2004. In this paper, we present the performance of the hard X-ray telescope, which consists of a depth-graded platinum/carbon multilayer mirror and a CdZnTe detector. The telescope has an effective area of 49 cm2 at 30 keV, an angular resolution of 2.4 arcmin (HPD), and a ﬁeld of view of 11 arcmin (FWHM) depending on energies. The CdZnTe detector is conﬁgured with a 12 × 12 segmented array of detector pixels. The pixels are 2 mm square, and are placed on 2.1 mm centers. An averaged energy resolution is 4.4 keV at 60 keV and its standard deviation is 0.36 keV over 128 pixels. The detector is surrounded by a 3-cm thick CsI anti coincidence shield to reduce background from particles and photons not incident along the mirror focal direction. The inﬂight background is 2.9 × 10−4 cts cm−2 sec−1 keV−1 in the 20–50 keV band. Keywords Hard X-rays · Multilayer mirror · CdZnTe pixellated detector · Balloon experiments · Background

1. Introduction The International Focusing Optics Collaboration for µCrab Sensitivity (InFOCµS) is a balloon-borne experiment with an X-ray imaging telescope in the hard X-ray band above 20 keV, where space-borne hard X-ray telescopes have not been available so far. Hard X-ray imaging observations, however, are very important to investigate strongly obscured objects,

J. Tueller · H. A. Krimm · T. Okajima () · S. D. Barthelmy · S. M. Owens · P. J. Serlemitsos · Y. Soong · K.-W. Chan NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA e-mail: [email protected] Y. Ogasaka · R. Shibata · K. Tamura · A. Furuzawa · Y. Tawara · H. Kunieda · K. Yamashita Nagoya University, Furo-cho, Chikusa, Nagoya, Aichi, 464-8602, Japan Springer

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study nuclear γ -ray lines from SNR, resolve hard X-ray emission from clusters of galaxies, understand acceleration mechanisms, discover new objects, and so on. InFOCµS intends to have multiple hard X-ray telescopes covering broad energy band from 20 keV up to 80 keV. The lower energy limit of 20 keV comes from atmospheric absorption, and the higher energy limit from the K absorption edge of a mirror material (platinum). In previous ﬁve years, InFOCµS ﬂew four times including a test ﬂight with the CZT detector only in 2000. Developments and improvements of the mirror and detector have been continuously done. In the most recent ﬂight from Fort Sumner, NM on September 16, 2004, we had a successful 22.5-hour ﬂight. We observed X-ray binaries, a galactic black hole candidate, a cluster of galaxies, and a Seyfert galaxy (Ogasaka et al., 2005). In this paper, we present performance of the multilayer mirror and CZT detector system for the 2004 ﬂight. The inﬂight detector background and sensitivity are also presented.

2. InFOCµS instruments overview The InFOCµS hard X-ray telescope consists of a depth-graded platinum/carbon multilayer mirror and a CdZnTe detector. The hard X-ray mirror is made of conical thin-foil mirrors (170 µm thick) which is similar to the Suzaku X-ray telescope (Kunieda et al., 2001), but with Pt/C multilayer mirror on the reﬂector surface and the longer focal length of 8 m. Its diameter is 40 cm and 255 mirror shells are nested in the mirror housing (Figure 1). The pixellated CdZnTe detector is conﬁgured with a 12 × 12 segmented array of detector pixels. The detector and pixel size are 1 inch and 2 × 2 mm2 , respectively. The detector is placed on the top of an aluminum cube with an ASIC (Figure 2). It is surrounded by a 3-cm thick CsI with 11 PMTs. They make an active shield utilizing anticoincidence of signals from the PMT and detector to reduce non X-ray background. The detector also has a tagged source system with 241 Am to monitor the energy gain of the detector during the ﬂight. Figure 3 shows the InFOCµS gondola. The mirror mounted on the left hand side of the truss structure. The detector is placed inside the pressure vessel on the other end of the truss. The gondola is an elevation-over-azimuth system. The truss is coupled to the center gondola platform at its center of gravity, and is attached into elevation direction by long-threaded screw driven by a DC motor mounted on the gondola platform. The whole gondola system is driven into azimuthal direction by a reaction wheel mounted on the gondola platform Fig. 1 Pt/C depth-graded multilayer hard X-ray mirror.

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Fig. 2 Pixallated CdZnTe hard X-ray detector.

Fig. 3 InFOCµS ﬂight gondola.

and also by a decoupler motor placed between the balloon and payload. Attitude sensors such as three-axis rate gyros, magnetometers, level sensors and differential GPS sensors are mounted on the gondola platform to determine its attitude. An elevation axis resolver determines relative elevation angle of the optical truss with respect to the gondola platform. Independent and absolute attitude sensors are mounted on the optical truss; a boresight star camera and differential GPS sensor. The speciﬁcation of the InFOCµS instruments are summarized in Table 1.

3. Depth-graded multilayer mirror The InFOCµS multilayer mirror was developed by Nagoya University and NASA/GSFC. Pt/C multilayer mirrors were deposited by a DC magnetron sputtering system. In order to control quality of mirrors during the production, their reﬂectivity for about 20% of all the mirrors was quickly measured using monochromatic W-Lα X-ray (8.4 keV). Measurement was performed by θ − 2θ angular scanning. Some of mirrors were also measured with continuum X-rays up to 50 keV at a ﬁxed incident angle. For example, we obtained reﬂectivity of more than 50% up to 35 keV at the incident angle of 0.187 deg. Quality of X-ray mirrors can be Springer

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Table 1 Summary of InFOCµS instruments for the 2004 ﬂight Pt/C multilayer mirror Energy Diameter/focal length Optics Incident angle Number of nesting Number of reﬂectors Reﬂector Reﬂector radius Reﬂector length Reﬂector thickness Reﬂector surface Periodic thickness Number of bi-layers Gondola system Dimensions/weight Attitude control Attitude determination

<50 keV 40 cm/8 m Conical Appr. of Wolter I 0.105–0.356 deg. 255 2040 Al-backed epoxy replica 59–200 mm 100 mm×2 170 µm Pt/C multilayer ˚ 29–130 A 25–65

CdZnTe detector assembly Detector size Pixel array Pixel spacing Pixel size/thickness Operating temperature Detection efﬁciency Active shield Collimator FOV

1 × 1 inch 12 × 12 (128 active pixels) 2.1 mm 2 × 2 mm2 /2mm 27 deg. C ∼100%(<50 keV) 3-cm thick CsI with PMTs 10 deg. (FWHM)

Tagged source

241 Am

(tagged by anti-coincidence)

9m-long × 5m-height/∼1600 kg Elevation-over-azimuth system+tilt-adjustment straps Star camera, gyroscopes, Magnetometors, Level sensors

Fig. 4 Measured effective area of the InFOCµS telescope (dots with errors) compared with Chandra (green), XMM-Newton (red) and Suzaku (blue).

also characterized by roughness of mirror surface and interface between layers. The roughness is represented by a Debye-Waller factor. Average roughness of our multilayer sample is 0.34 ± 0.05 nm and gradually increase toward larger radii of the mirror. Once we ﬁnished the production of all mirrors, we assemble them into the full hard X-ray mirror (Figure 1). Pre-ﬂight ground calibration of the hard X-ray mirror was performed at ISAS/JAXA and the synchrotron facility, SPring-8 in Japan. A soft X-ray characteristic, such as effective area, angular resolution, and ﬁeld of view (FOV), was measured at ISAS with Cu-Kα (8 keV) using a NaI scintillation detector and X-ray CCD. Hard X-ray measurement above 10 keV was done at SPring-8 using a position sensitive NaI+CCD detector. Detail of the measurement are described in Shibata et al. (2005). Figure 4 shows a measured on-axis effective area of the InFOCµS mirror compared with soft X-ray mirrors (Chandra, XMM-Newton,and Suzaku). The InFOCµS mirror has a signiﬁcant effective area above 10 keV. Measured effective area Springer

Exp Astron (2005) 20:121–129 Table 2 Summary of measured effective area and ﬁeld of view (FOV)

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Energy [keV]

Effective area [cm2 ]

FOV [arcmin]

20 30 40 50

68 49 23 11

12 11.5 11

Fig. 5 Vignetting functions of the mirror at various energy bands.

Fig. 6 3D image of InFOCµS telescope measured with 30 keV monochromatic X-rays (left). Encircled energy functions of 20–60 keV with 10 keV step (right).

is summarized in Table 2. Figure 5 shows vignetting functions at various energy bands. FOVs deﬁned by FWHM of the vignetting function are also listed in Table 2. A point spread function (PSF) and encircled energy function (EEF) were evaluated by using monochromatic parallel hard X-ray beam of 20–60 keV with 10 keV step. Figure 6 shows an on-axis image with monochromatic parallel X-ray beam of 30 keV and the EEFs with 20–60 keV. Half power diameter (HPD) of this mirror is 2.1–2.4 arcmin in the above energy band, and it has almost no energy dependence. Springer

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4. CdZnTe detector The InFOCµS CdZnTe detector was developed by NASA/GSFC. We performed a pre-ﬂight detector calibration in order to characterize the detector performance, such as energy-channel relations of individual pixels, distributions of energy gains and offsets over 128 pixels, and energy resolution. Tagged source spectra were obtained to monitor the energy gain during the ﬂight. The pre-ﬂight calibration data was taken under the ﬂight conditions. The detector temperature is 27 deg C, which is controlled by a thermal electric cooler. The bias voltage is 200 V. With this conﬁguration, the leakage current is 27 nA. The entire detector was illuminated with radioactive sources, 109 Cd, 133 Ba, 241 Am, and 57 Co, to get relations between raw PHA channel and energy for each pixel. The top panel of Figure 7 shows a distribution of PHA channels corresponding to the 60 keV peak of 241 Am. It distributes over 100 channels around 2400 ch for 128 pixels. Using multiple peaks from radioactive sources, we found the conversion (gain and offset) from the PHA channel to energy. We ﬁnd that the gain is about 0.22 keV/channel and channel-energy relation is linear up to 122 keV (57 Co). The FWHM of the 60 keV peak is 4.4 ± 0.36 keV. The bottom panel of Figure 7 shows the distribution of FWHM for the 60 keV peak. Once we convert PHA channel to energy, we can add all pixel spectra together to make a spectrum for the entire detector. Figure 8 shows spectra Fig. 7 The top panel shows the distribution of 60 keV peak position (241 Am) in PHA channel and the bottom panel FWHM of the 60 keV line (energy resolution).

Fig. 8 Calibration spectra. Peaks from left to right are 22 (109 Cd), 30 (133 Ba), 60 (241 Am), and 122(57 Co) keV, respectively.

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Exp Astron (2005) 20:121–129 Table 3 Measured energy resolution from the entire detector spectra

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Energy [keV] (109 Cd)

22 30 (133 Ba) 60 (241 Am)

Resolution (FWHM) [keV] 4.1 ± 0.047(18.6%) 3.8 ± 0.052(12.7%) 4.0 ± 0.059(6.7%)

Fig. 9 An example of tagged source spectrum (four hour accumulation) for pixel #32.

from different radio active sources for the entire detector. One can see large tail associated with peaks, especially for the 122 keV peak of 57 Co. This is due to loss of holes during the travel inside the CZT. Low energy photons are absorbed close to the top surface, while higher energy photons interact inside the detector. Holes have to travel longer paths to be collected. Measured energy resolutions of the entire detector spectra are summarized in Table 3. We extracted tagged source spectra by collecting only tagged events so that we were able to check not only the channel-energy relation but also the energy resolution during the ﬂight, compared with the ground calibration results. Figure 9 shows spectrum for pixel #32 with four hours accumulation as an example. The count rate of tagged events is 1.3 cts/sec for the entire detector (20–65 keV), so that rate for the 60 keV line is 0.005 cts/sec for one pixel. In the four hour accumulation, we can get 72 cts for the line. The peak position can be determined with 1 keV accuracy. Extracting the tagged source spectra every 30 minutes to check the gain stability, we found that the peak position was stable within ±2 ch, which corresponds to about 0.44 keV. And the energy resolution is consistent with that in the ground test.

5. Inﬂight background and sensitivity One of the important goals of the balloon ﬂights was to measure the background for the CZT detector in order to determine the InFOCµS sensitivity and to demonstrate the suitability of our active CsI shield. Figure 10 shows the InFOCµS detector background obtained in the 2004 ﬂight. The measured background from a 5.2-hour observation is rather ﬂat from 20–150 keV. This background spectrum was obtained by the following analysis. During our observation, the pointing direction ﬂuctuated by a few arcmin. First we reconstructed an X-ray image of a target according to the pointing information based on attitude sensors, such as a rate gyro and star camera onboard. A point source image was clearly seen in the reconstructed Springer

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Fig. 10 Detector background spectrum measured during the Sep. 2004 ﬂight at altitude of 35.2 km (residual atmosphere =5.4 g cm−2 ). Events vetoed by the anticoincidence shield have been removed.

X-ray image (Ogasaka et al., 2005). We were able to eliminate events from a source region, which is a circle centered at the image peak with a 5-arcmin radius. We take events outside the source region as background events. And noisy pixels are also masked so that we used only active pixels as the detector area. Note that according to the mirror PSF, the background events still may contain events from the target for about 8% of the source photons at largest. Finally the average background in 20–50 keV was obtained to be 2.9 × 10−4 cts cm−2 sec−1 keV−1 . We also ﬁnd that 97.3% of the background is rejected by the active CsI shield as vetoed events (Okajima et al., 2005). Passive shielding alone cannot reduce the background rate as it will be dominated by local particle interactions. This background is dominated by internal beta-decay as is usual for heavily shielded detectors. Our background is the lowest background ever achieved in balloon ﬂights. This measurement was taken at the ﬂoat altitude of 35.2 km (5.4g cm−2 ) without using any depth determination techniques to further reduce the background. This result is consistent with that in the previous InFOCµS ﬂights (Baumgartner et al., 2003). According to the measured background and effective area of the mirror, we can estimate the InFOCµS sensitivity as shown in Figure 11. We achieved the sensitivity as low as 5 × 10−6 cts cm−2 sec−1 keV−1 with 8-hour observations (in 20–50 keV and three sigma detection). This is more than one order of magnitude lower than that of non focusing instruments onboard previous experiments, such as HEAO and Ginga. And the INTEGRAL sensitivity (105 sec exposure) is comparable with the InFOCµS sensitivity with only 8-hour exposure, which is a typical long exposure for one target in balloon experiments. We plan a further improvement to achieve the sensitivity of better than the 100 µCrab level. The new hard X-ray mirror will have an angular resolution of 1 arcmin and effective area improved by 50%. This would be a factor of four improvement in the sensitivity. And also we will have two newly developed focal plane detector and shield units for both of the mirrors. The detectors have 1.5 mm pixels and a thinner CZT of 0.5 mm. This would be another factor of two improvement in the sensitivity. In total we would improve factor of 8 as shown in Figure 10. Springer

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Fig. 11 InFOCµS sensitivity plot. 2004 curve is as-ﬂown. 2006 curves are also shown. The sensitivity is for an 8-hour observation, E/E = 2, typical elevation proﬁle and atmospheric absorption. The IBIS curve is from the AO-2 observers manual, but IBIS is systematics-limited at this level.

6. Summary The InFOCµS hard X-ray imaging telescope was successfully ﬂown on September 16–17, 2004, from Fort Sumner, NM. The telescope consists of the depth-graded Pt/C multilayer hard X-ray mirror and CdZnTe pixellated detector. Its effective area is 49 cm2 at 30 keV, angular resolution 2.4 arcmin (HPD), and ﬁeld of view 11 arcmin (FWHM). The focal plane detector has the 12 × 12 segmented array of 2 mm square detector pixels. The averaged energy resolution is 4.4 keV at 60 keV. The detector is also surrounded by a 3-cm thick CsI anti coincidence shield to reduce background from particles and photons not incident along the mirror focal direction. The in-ﬂight background is 2.9 × 10−4 cts cm−2 sec−1 keV−1 in the 20–50 keV band, which is the lowest background in balloon experiments owing to the small detector volume and the active shield. Based on the in-ﬂight background, InFOCµS achieved the sensitivity as low as 5 × 10−6 cts cm−2 sec−1 keV−1 with 8-hour observations (in 20–50 keV and three sigma detection). We plan to ﬂy with the improvements on the mirror and detector. And we will be archiving 8 times greater sensitivity and exploring the hard X-ray universe.

References Baumgartner, W., et al.: Proc of SPIE 4851, 945 (2003) Kunieda, H., et al.: Applied Optics 40, 553 (2001) Ogasaka, Y., et al.: Proc of SPIE 5900, 217 (2005) Okajima, T., et al.: Proc of SPIE 5898, 452 (2005) Shibata, R., et al.: Proc of SPIE 5900, 205 (2005)

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Exp Astron (2005) 20:131–137 DOI 10.1007/s10686-006-9072-z ORIGINAL ARTICLE

Development of the HEFT and NuSTAR focusing telescopes Fiona A. Harrison · Finn E. Christensen · William Craig · Charles Hailey · Wayne Baumgartner · C. M. H. Chen · James Chonko · W. Rick Cook · Jason Koglin · Kristin-Kruse Madsen · Michael Pivavoroff · Steven Boggs · David Smith Received: 5 July 2006 / Accepted: 17 August 2006 C Springer Science + Business Media B.V. 2006

Abstract Hard X-ray/soft gamma-ray astrophysics is on the verge of a major advance with the practical realization of technologies capable of efﬁciently focusing X-rays above 10 keV. Hard X-ray focusing telescopes can achieve orders of magnitude improvements in sensitivity compared to the instruments based on coded apertures and collimated detectors that have traditionally been employed in this energy band. Compact focal planes enable high-performance detectors with good spectral resolution to be employed in efﬁcient, low-background conﬁgurations. We have developed multilayer coated grazing incidence optics and solid state Cadmium Zinc Telluride focal plane systems for the High Energy Focusing Telescope (HEFT) balloon-borne experiment, and for the Nuclear Spectroscopic Telescope Array (NuSTAR) Small Explorer satellite. In this paper we describe the technologies, telescope designs, and performance of both experiments.

Keywords X-ray telescopes . X-ray optics . X-ray detectors

F. A. Harrison () · W. Baumgartner · C. M. H. Chen · W. R. Cook Space Radiation Laboratory, California Institute of Technology F. E. Christensen · K.-K. Madsen Danish National Space Centre W. Craig · J. Chonko · M. Pivavoroff Lawrence Livermore National Laboratory C. Hailey · J. Koglin Columbia Astrophysics Laboratory, Columbia University S. Boggs University of California, Berkeley D. Smith University of California, Santa Cruz Springer

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1 Introduction The last decade has seen a major technological advance in hard X-ray/soft gamma-ray astronomy – the ability to focus efﬁciently – creating the potential for instruments that improve spatial and spectral resolution by more than two orders of magnitude at energies above 10 keV. Extending grazing incidence telescopes to operate efﬁciently in the hard X-ray band requires shallow graze-angle optics and position sensitive detectors with high quantum efﬁciency from 10–100 keV. Incorporating these technologies into astrophysical instruments results in greatly enhanced signal to background ratios compared to coded aperture imagers. Several research groups have developed focusing hard X-ray systems over the last ten years, and three balloon experiments have been constructed incorporating them. The InFOCuS experiment [4] extends the segmented aluminum foil mirror technology developed for Astro-E2 to 40 keV utilizing an optic coated with Pt/C depth graded multilayers. The InFOCuS focal plane consists of a CdZnTe detector with a 12 × 12 array of 2-mm pixels. The telescope achieves angular resolution of 2.2 (HPD) and spectral resolution of 4 keV at 32 keV, and has ﬂown twice, in 2001 and 2004. The HERO experiment [5] uses shallow graze-angle iridium-coated replicated nickel optics and xenon gas scintillation proportional counters to achieve 45

(HPD) angular resolution and 1.5 keV (FWHM) energy resultion at 30 keV. HERO ﬂew in 2001 with a small complement of shells, and in Spring 2005 with three telescope modules. In this paper, we describe the High Energy Focusing Telescope (HEFT) balloon payload, as well as the Nuclear Spectroscopic Telescope Array (NuSTAR) Small Explorer mission. Both of these experiments are based on multilayer-coated formed glass segmented optics and CdZnTe pixel detectors. HEFT ﬂew once in Spring 2005 with a complement of three telescopes, demonstrating angular resolution of 1.5 (HPD) and with spectral resolution of 1 keV (FWHM) at 60 keV. Results from the ﬂight are being published elsewhere. NuSTAR employs demonstrated improvements to the optics to achieve 40

(HPD) angular resolution in a high throughput three-module telescope array. In this paper we describe the optics and detector technologies, and the HEFT and NuSTAR experiment designs and performance.

2 Depth graded multilayer optics For HEFT and NuSTAR we developed depth-graded multilayer coated mirrors in a conical approximation to the Wolter I geometry. The optics are based on formed glass; each shell (full ﬁgure of revolution) is assembled from multiple segments [3]. Each segment is thermally formed from a glass sheet, and is coated using a planar magnetron sputtering system developed at the Danish National Space Centre for these programs [2]. The mirrors are assembled layer by layer using graphite spacers epoxied to the glass then machined to accomodate the next layer [1]. Figure 1 shows the assembled HEFT ﬂight optics. The angular resolution achieved using this method is currently dictated by the substrate quality, and depends on the segment size as well as the degree to which substrates are preselected based on ﬁgure. The HEFT optics achieved 1.5 HPD with no selection and 20 segments per shell. Several prototype optics have demonstrated that we can achieve 40

HPD with 32 segments/shell and 50% preselection on glass segments. Springer

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Fig. 1 Photo of the three HEFT ﬂight optics. Each unit is fabricated from formed, multilayer-coated glass

Fig. 2 Photo showing a HEFT focal plane detector system. Two CdZnTe/ASIC hybrid pixel sensors are mounted side-by-side

3 Cadmium zinc telluride pixel detectors We employ CdZnTe pixel detectors for the HEFT and NuSTAR focal planes. A focal plane is comprised of two hybrid sensors (see Figure 2). An individual sensor consists of a 1.2 × 2.4× cm, 2 mm thick CdZnTe crystal, with the anode contact segmented into pixels with 500 µm pitch. Gold stud/epoxy interconnects couple the sensor pixel contacts to a custom low-noise readout chip. The ASIC, designed at Caltech for HEFT, contains one circuit for each pixel, laid out on a grid exactly matching the detector pixel array. The state of the art design achieves excellent imaging and spectral performance, as well as the ability to measure the interaction depth of the event in the detector. Figure 3 shows an 241 Am spectrum from 100 pixels summed together (somewhat larger than, but not atypical of the number to be included in a point source reconstruction) taken at −5◦ C. The spectrum includes all detected X-ray events, including those where charge is shared among multiple Springer

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Fig. 3 Spectrum of an 241Am source illuminating 100 pixels of the HEFT detector. All events, including those where charge is split among multiple pixels, are included. For comparison, the blue line shows the same spectrum convolved through the response of an NaI detector

pixels. The FWHM of the 60 keV line is 900 eV, and of the 14 keV line is 800 eV (FWHM). The depth sensing ability, enabled by the ASIC design, allows events occuring in the back portion of the detector to be rejected as background, resulting in a factor 2–3 additional background rejection.

4 HEFT design and performance HEFT is a balloon payload developed by a collaboration among Caltech, Columbia, the Danish National Space Center (DNSC), Lawrence Livermore National Laboratories (LLNL) and Stanford University. Figure 4 shows a photo of the HEFT payload, indicating the major components. The telescope contains three co-aligned conical-approximation Wolter I mirror assemblies, each of which focuses hard X-rays/soft gamma-rays onto a shielded, solid-state Cadmium Zinc Telluride (CdZnTe) focal plane. The focal plane modules are housed inside a kevlar pressure vessel. The instrument focal length is 6 m. Table 1 provides an overview of the performance characteristics and instrument parameters. Each of the three optics has 70 shells, with shell radii ranging from 4–12 cm. The reﬂectors are coated with W/Si multilayers, which provide good reﬂectance up to the W K-edge at 69.5 keV. The lower energy limit is determined by atmospheric attenuation at balloon altitudes. The total instrument collecting area on-axis is 100 cm2 at 30 keV, not accounting for atmospheric attenuation. Each detector is surrounded by a Pb/Sn/Cu graded −Z passive well housed inside a 2-cm thick plastic scintillator. This arrangement attenuates cosmic and atmospheric backgrounds, and vetos charged particles that create local background in the passive shield. While not as effective as an alkali halide shield (NaI or CsI), this conﬁguration provides a cost-effective approach to reducing detector background. Springer

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Table 1 Instrument performance characteristics and conﬁguration. Sensitivity is listed for 3σ threshold, 20 ksec integration (corresponding to two source transits) Instrument performance characteristics Energy range Angular resolution (HPD) FOV (20 keV) Sensitivity (mCrab) Line sensitivity (γ /cm2 /s) Energy Resolution (fwhm) Effective area (3.5 g/cm−2 ) Aspect reconstruction (rms) Pointing stability (rms) Time resolution

20–70 keV 1.5 17 2 (20 - 60 keV) 2 ×10−5 (68 keV) 980 eV (68 keV) 50 cm2 (40 keV) 6

30

1 m sec

Instrument parameters Num. modules Focal Length Optics Mirror substrates Multilayer Detector Shielding Envelope Weight Power

3 6m Conical Wolter-I Formed glass W/Si 2 mm thick CdZnTe Graded-Z/plastic 6.5 m × 1.25 m diam. 1854 kg 400 Watts

Fig. 4 Photograph of the HEFT payload indicating the major components of the experiment

HEFT was launched on May 18, 2005 from Ft. Sumner, NM. During this ﬂight we used observations of three bright point sources; the Crab, Cygnus X-1, and GRS +1915 to verify the instrument pointing stability, imaging, and throughput. Results from this ﬂight are being published elsewhere.

5 NuSTAR design The NuSTAR Small Explorer satellite is based on the technologies developed for the HEFT experiment, combined with an extendible optical bench developed by ABLE Engineering and the Jet Propulsion Laboratory for the Shuttle Radar Topography Mission. NuSTAR was selected for a Phase A study in November, 2003 as one of four missions to compete for two launch opportunities. In January 2005 NuSTAR was selected for a launch date of February 2009, and was placed into an extended technical development phase. NuSTAR consists of three co-aligned telescope modules with a 10-m focal length. The optics and detectors are placed at either end of an extendible mast. For launch the mast is stowed inside a canister, and the entire payload ﬁts inside a Pegasus XL shroud. NuSTAR Springer

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Fig. 5 The NuSTAR payload, with each end shown separately

will be placed into an Equatorial circular 550 km orbit. Figure 5 shows a view of the two ends of the NuSTAR payload after deployment. The bench housing the three optics modules is extended outward from the spacecraft end, which houses the three focal plane modules. The optics consist of 130 shells each, with radii ranging from 5.5 to 16.9 cm. The shells are coated with a combination of W/SiC and Pt/SiC multilayers, with the coating dependent on the shell graze angle. This, combined with the relatively low graze angles, provides reﬂectance with a smooth response extending to 80 keV. NuSTAR will utilize smaller glass segments (32 per shell) compared to HEFT, and in addition the substrates will be preselected for ﬁgure quality. We have demonstrated through several prototypes that by accepting the best 50% of the glass segments, NuSTAR will achieve angular resolution (HPD) of 40

. The NuSTAR focal plane detectors have the same dimensions as the HEFT focal planes, but they are surrounded by an active CsI shield rather than the graded-Z/plastic shield used on HEFT. This, combined with the depth-sensing capability of the detectors, reduces the internal detector background to very low levels (<10−4 cts cm−1 , s−1 from 10–80 keV). In addition to the active well-shaped shield, an aperture stop consisting of rings of graded-Z material reduces diffuse cosmic background. The aperture stop deploys simultaneously with the mast after launch.

6 NuSTAR performance Table 2 summarizes the NuSTAR performance. Compared to coded aperture instruments that have operated in the same band, NuSTAR achieves more than two orders of magnitude improvement in continuum ﬂux sensitivity. The excellent energy resolution of the detectors will allow measurement of velocity shifts in the 44 Ti lines at 68 and 78 keV of ±1000 km s−1 . Using the combination of sensitivity, spectral and spatial resolution, NuSTAR will be able to undertake investigations not previously possible in the hard X-ray band. In extragalactic survey ﬁelds NuSTAR can resolve 50% of the hard X-ray background at 30 keV, and will Springer

Exp Astron (2005) 20:131–137 Table 2 NuSTAR instrument performance.

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Energy range Angular resolution (HPD) FOV Source positions Spectral resolution Timing resolution Line sensitivity (106 s, 68 keV) Continuum sensitivity (106 s, 3σ , E/E) = 0.5 Background in HPD/module (40 keV) Effective area (20 keV) ToO response

6–80 keV 40

8.4 × 8.4 5

900 eV 68 keV 0.1 ms 10−7 ph/cm2 /s 0.7 µCrab (20 keV) 6 µCrab (60 keV) 1.1 × 10−5 cts/s/keV 500 cm2 <24 h

detect several hundred obscured AGN in its 2 square degree survey ﬁelds. NuSTAR can also spatially resolve the 44 Ti line in Cas A, mapping the line doppler shifts with 1000 km s−1 resolution in 40

spatial bins. In surveys of the Galactic center region, NuSTAR can resolve the hard source populations discovered by Integral and XMM, and study the distribution in latitude of any truly diffuse component.

7 Summary The HEFT balloon experiment has demonstrated hard X-ray focusing optics and solid state pixel detectors by imaging cosmic sources in this band. These observations have fully veriﬁed the expected throughput, resolution, and sensitivity of the HEFT instrument. NuSTAR, which is based on the HEFT technologies, is ready to proceed to phase B, and will realize the potential of hard X-ray focusing in space.

References 1. Hailey, C.J., Abdali, S., Christensen, F.E., Craig, W.W., Decker, T.R., Harrison, F.A., Jimenez-Garate, M.: EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy VIII. In: Siegmund O.H., Gummin M.A. (eds.), Proc. SPIE 3114, pp. 535–543 (1997) 2. Jensen, C.P., Madsen, K.K., Chen, H.C., Christensen, F.E., Ziegler, E.: X-Ray and Gamma-Ray Telescopes and Instruments for Astronomy. In: Truemper J.E., Tananbaum H.D. (eds.), Proc. SPIE 4851, pp. 724–733 (2003) 3. Koglin, J.E. et al.: X-Ray and Gamma-Ray Telescopes and Instruments for Astronomy. In: Truemper J.E., Tananbaum H.D. (eds.), Proc. SPIE 4851, pp. 607–618 (2003) 4. Ogasaka, Y. et al.: X-Ray and Gamma-Ray Telescopes and Instruments for Astronomy. In: Truemper J. E., Tananbaum H.D. (eds.), Proc. SPIE 4851, pp. 619–630 (2003) 5. Ramsey, B.D. et al.: ApJ 568, 432 (2002)

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Exp Astron (2005) 20:139–149 DOI 10.1007/s10686-006-9062-1 ORIGINAL ARTICLE

The SIMBOL-X hard X-ray mission Giovanni Pareschi · Philippe Ferrando

Received: 13 June 2006 / Accepted: 19 July 2006 C Springer Science + Business Media B.V. 2006

Abstract SIMBOL-X is a hard X-ray mission based on a formation ﬂight architecture, operating in the 0.5–80 keV energy range, which has been selected for a comprehensive Phase A study, being jointly carried out by CNES and ASI. SIMBOL-X makes uses of a long (in the 25–30 m range) focal length multilayer-coated X-ray mirrors to focus for the ﬁrst time X-rays with energy above 10 keV, resulting in at least a two orders of magnitude improvement in angular resolution and sensitivity compared to non focusing techniques used so far. The SIMBOL-X revolutionary instrumental capabilities will allow us to elucidate outstanding questions in high energy astrophysics, related in particular to the physics and energetic of the accretion processes on-going in the Universe, also performing a census of black holes on all scales, achieved through deep, wide-ﬁeld surveys of extragalactic ﬁelds and of the Galactic center, and the to the acceleration of electrons and hadrons particles to the highest energies. In this paper, the mission science objectives, design, instrumentation and status are reviewed.

Keywords Hard X-ray telescopes . X-ray astronomical optics . Multilayer mirrors . X-ray detectors . Formation ﬂying PACS: 95.55 – Astronomical and space-research instrumentation 95.85 – Astronomical Observations 98.85.Nv – X-ray

G. Pareschi () INAF – Brera Astronomical Observatory, Via E. Bianchi 46, 23807 Merate (Lc), Italy e-mail: [email protected] P. Ferrando APC & DSM/DAPNIA/Service d’Astrophysique, CEA/Saclay, 91191 Gif-sur-Yvette, France Springer

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1. Introduction With the increase power of space observatories, high energy emission has been observed from objects of all scales in the Universe, from compact sources such as black holes to diffuse hot plasma pervading galaxies and clusters of galaxies, revealing violent processes which are thought to play a major role in the dynamics of these objects. These processes pertain to the two domains of accretion physics and particle acceleration mechanisms. In accretion physics, the accretion of matter onto Black Holes is a fundamental astrophysics topic. Identifying and understanding this phenomenon has indeed profound implications both on physics, since the Black Hole environment is the only place which allows tests of General Relativity beyond the weak-ﬁeld limit, and on cosmology since the accretion luminosity may dominate the radiant energy of the Universe emitted since the big-bang (this topic was particularly well addressed in the presentation of the scientiﬁc case for the HEXIT-SAT mission by Fiore et al. [1]). The second domain is also fundamental for astrophysics. One still lacks ﬁrm evidences of hadron acceleration in suspected astronomical sites (despite clearly seeing huge electron accelerations), and one still looks for the origin of the highest energy photons and cosmic rays which have been observed by ground experiments as e.g. the HESS and MAGIC Cherenkov telescopes [2, 3]. Identifying the processes at work in acceleration sites, as supernovae remnants or jets, and ﬁnding their limit is a key question in this issue. These processes are best revealed and characterized by their non thermal-emission in the low energy X-ray and hard X-ray domains, the latter probing the most energetic and violent environments. There is however a very large gap in angular resolution and sensitivity between these two domains. Below ∼10 keV, astrophysics missions are using X-ray mirrors based on grazing incidence reﬂection properties. This has allowed increasing by orders of magnitude the discovery space for compact accreting sources, for galaxies with an active nucleus and for high temperature thermal plasma sources. The use of collimated detectors on board the UHURU, Ariel-V, and HEAO1 satellites in the 1970 decade led to the discovery of <1000 X-ray sources in the whole sky, most of which with a redshift z < 0.5. Imaging detectors, ﬁrst on board Einstein and then ROSAT, produced the ﬁrst systematic observations of AGNs up to z = 2–3, and systematic mapping of galaxies, clusters of galaxies and supernova remnants. The superior image quality of Chandra and the high throughput of XMM-Newton have expanded the discovery space even further, resolving for example more than 80% of the cosmic X-ray Background below 5–6 keV, and starting to probe emission of star-forming galaxies, and to resolve jets lobes and hot spots in quasars and radio galaxies. Above 10 keV however, the situation contrasts strikingly with this picture. The most sensitive observations so far have been performed by a collimated instrument, the BeppoSAX PDS [4] and by coded mask instruments such as the INTEGRAL IBIS/ISGRI [5] and the Swift BAT [6]. Only a few hundred sources are known in the whole sky at E > 10 keV, a situation recalling the pre-Einstein era during the 1970s. More than two orders of magnitude are separating the sensitivity and angular resolution in hard X-rays compared to the one that is achieved in X-ray telescopes. This huge gap is entirely due to the fact that until recently there was no technology available to build a focusing instrument in hard X-rays. The ambition of the proposed hard X-ray pointed telescope, SIMBOL-X [7] is to utilize recent breakthroughs in the development of hard X-ray optics to assemble a large-area, high-resolution focusing telescope. To meet these objectives SIMBOL-X relies on the combination of the emerging “Formation Flying” technology, which allows the use of very long focal length optics, and of multilayer reﬂection mirror technology, providing the required sensitivity at high X-ray energies. These technological innovations offer a gain of roughly two orders of magnitude Springer

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Table 1 SIMBOL-X top-level scientiﬁc requirements Parameter

Requirement

Energy band Field of view – FWHM (at 30 keV) On-axis effective area

∼0.5–>80 keV 9 –13 (diameter) >1000 cm2 at < 2 keV∗∗ >600 cm2 at 8 keV ∼450 cm2 at 20–40 keV >100 cm2 at 70 keV <1 µCrab (3σ 1 Ms) at 20–40 keV Better than 10−3 cts/s/keV ∼15”, <20” E/ E 40–50 at 6–10 keV E/ E = 50 at 68 keV (goal) 100 µs (50 µs goal) ∼2 (radius, 90%,TBC) 3 yrs including commissioning and calibrations (at least 2 yrs of scientiﬁc program)

On-axis sensitivity Line sensitivity at 68 keV Angular resolution (HPD) Spectral resolution Absolute timing accuracy and Time resolution: Absolute pointing reconstruction Mission duration

in sensitivity and angular resolution compared to the current instruments above 10 keV. In addition to this fundamental breakthrough in hard X-rays, SIMBOL-X will have a low energy threshold around ∼0.5–1 keV, which will allow to fully cover the spectral transition from thermal to non-thermal emission as well as the Iron line spectral band, two important characteristics for the study of the highly variable accreting sources which are among the prime scientiﬁc goals of this mission. SIMBOL-X will offer an improvement of roughly two orders of magnitude in sensitivity and angular resolution compared to the instruments currently operating above 10 keV. This large gain in performance will allow SIMBOL-X to effectively address all the crucial scientiﬁc issues identiﬁed in a Top Level Requirements document jointly prepared by French and Italian scientists. The Top level scientiﬁc requirements are reported in Table 1. In particular, SIMBOL-X will be able to resolve up to the 65% of the cosmic X-ray background light into discrete sources in the spectral band where the cosmic power is maximum, ﬁnally solving the problem of the spectral paradox and revealing the exact nature of the sources that make the X-ray background. SIMBOL-X will operate in the time-frame 2013–2016 as a world-class X-ray facility providing a factor 2 better sensitivity and angular resolution combined with broader wavelength coverage even compared to similar efforts that may operate before the year 2010. As already mentioned, in addition to this fundamental breakthrough in hard X-rays, SIMBOL-X will have a low energy threshold around ∼0.5–1 keV, which will ensure full spectral coverage of the transition from thermal to non-thermal emission as well as the Iron line spectral band, two important characteristics for the study of the highly variable accreting sources which are prime scientiﬁc targets of this mission.

2. The mission concept The SIMBOL-X mission from system architecture point of view is the subject of another paper of these proceedings [8]. For sake of completeness, a few details are reported hereafter. The two satellites forming the SIMBOL-X space mission will be launched by a Soyuz rocket Springer

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Fig. 1 A sketch of the SIMBOL-X focusing telescope based on two different satellites (one hosting the optics module, the other the focal plane) in a “formation ﬂight” conﬁguration. It should be noted the presence of the two passive shielding systems, the “sombrero-like” and of the long collimator bafﬂes (surrounding the optics and on the top of the detector plane respectively), implemented to limit the opening angle to the sky of the focal plane (Credits: CNES)

with a Fregat upper stage. Both vehicles will be injected in a high elliptical orbit to minimize the particle background, being also the perigee outside the Val Allen belts. In the Phase 0 study carried out by CNES in 2005, the orbit has a perigee of 44,000 km and an apogee of 253,00 km at launch. In observation mode, the relatively heavy mirror satellite (master) maintains its orbit, while the detector satellite (slave) is positioned along the mirror axis, keeping the distance between the mirror and the focal plane assembly at the focal plane value. SIMBOL-X is basically built using a classical Wolter I optics focusing X-rays onto a focal plane detector system. The gain in maximum energy is achieved by having a long focal length, in the 20–25 m range, i.e. ∼3 times larger than the XMM–Newton mirrors. In this way it is possible to make use of a mirror module with the same external diameter as XMM, but with mirror reﬂecting angles much smaller (∼3 times less), able i.e. to efﬁciently reﬂect also in the hard X-ray domain. Since the a focal length of a few tens meters cannot ﬁt in a single spacecraft, the mirror and detectors will be ﬂown on two separate spacecrafts in a formation ﬂying conﬁguration, as sketched on Figure 1. SIMBOL-X is a pointed telescope, which is nominally required to be able perform very long uninterrupted observations (105 s or more) on the same target. The necessity to have a stable image quality, as well as to keep the full ﬁeld of view inside the detector area, dictates the requirements on the formation ﬂying stability. The constraint is that the distance between the two spacecrafts (along the telescope axis) must be kept at the focal length value within about ±10 cm, whereas the intersection of the telescope axis must be at the centre of the focal plane within about ±20 arcsec. It is also required that the arrival direction of each detected photon can be reconstructed to ±2 arcsec (radius, 90%), which imposes a knowledge (monitoring) of the relative positions of the two spacecrafts to that level of accuracy. Springer

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There are three main components in the SIMBOL-X payload. The ﬁrst one is the optics based on grazing incidence mirrors. It should be noted that in the initial design a Pt single layer coating was assumed, characterized a maximum threshold energy of ∼50 keV, and a Fieldof-View (FOW) at 30 keV of ∼6 arcmin Full-With-at-Half-Maximum (FWHM). However, in order to be fully compliant with the new Top Level Requirements reported in Table 1, which assumes a much larger energy operative range (up to 80 keV at least) and FOV (in the 9–13 arcmin FWHM range) with respect to the initial baseline, now the Pt coating has been replaced by a multi-layer Pt/C coating, while the focal length has been reduced in the 20–25 m range (the ﬁnal value will be deﬁned at the end of the on-going phase A study). The second component is the focal plane that, to cover a very broad energy operative range (0.5– 80 keV), will be based on two different solid-state detectors in stack conﬁguration, the ﬁrst one based on macropixel arrays made of Si (effective from 0.5 up to 10 keV), and the other on Cd(Zn)Te (effective from 10 keV up to 100 keV). It should be noted that Si is sufﬁciently transparent in the hard X-ray region to allow the hard X-ray photons to pass towards the ﬁrst detector without being absorbed. A third fundamental component of the payload is given by an efﬁcient active and passive detector background shielding, effective not only to prevent the particle background, but also to shield against the diffuse X-ray sky background component falling outside the ﬁeld of view of the X-ray telescope. These three components are shortly described in the Section 3.

3. The scientiﬁc payload 3.1. Optics design, technology and technical challenges The SIMBOL-X optics module will be based on pseudo-cylindrical monolithic Ni electroformed mirror shells with Wolter I proﬁle, adopting the technology already successfully used for making the gold coated soft X-ray mirrors of the Beppo-SAX [9], XMM-Newton [10] and Jet-X/Swift [11] missions. This approach, developed in the past two decades in Italy by the INAF/IASF-Milano and INAF-Osservatorio Astronomico di Brera in collaboration with the Media Lario Technonology company (www.media-lario.com), is well consolidated. The industrial readiness for production is very high, being a number of equipments (e.g. the lapping and metrology machines for mandrels, the electroforming baths, and the vacuum chambers for the gold coating deposition) already available from past projects, with particular regard to the XMM-Newton mission. The diameter of the outermost mirror shell will be 70 cm (as for the XMM project), which is the maximum size allowed with the present mandrel polishing technology. Just a few modiﬁcation of the process will be implemented:

r As already mentioned, the SIMBOL-X hard X-rays mirrors will rely on much smaller reﬂection angles than soft X-ray telescopes and, to maintain an external diameter as large as XMM, it is necessary to make use of a very large focal length (in the 20–30 m range), as allowed by the formation ﬂight architecture. The integration equipments based on optical/UV at present available at Media Lario Technologies can ﬁt a focal length ≤8 m; they therefore need to be refurbished for SIMBOL-X. r With respect to the baseline of the ﬁrst SIMBOL-X proposal, the reﬂecting coating is not longer a Pt single layer reﬂector, but instead a multilayer mirror coating will be applied. The use of broad-band multilayer reﬂecting ﬁlms [12] not only will make possible to rely on a much larger FOV (once provided a small decrease of the focal length from the initial value of 30 m to about 20 m), but also in this way the operative range is extended up to Springer

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Fig. 2 Scheme of the application procedure by a two-targets DC linear magnetron sputtering source of the multilayer Pt/reﬂecting coating onto the gold-coated Ni replicated mirror (XMM-like) shells

80 keV and beyond. The multilayer coating will be applied by adding an additional step to the usual process Ni replication process. Once that the gold-coated Ni mirror shell has been replicated from the mandrel, the multilayer mirror will be applied onto the internal surface of the shell by using a two-targets linear DC magnetron sputtering system (see Figure 2), following the approach e.g. developed at the Harvard-Smithsonian Center-forAstrophysics in the context of the Constellation-X Hard X-ray telescope related activities, that already obtained very promising results [13]. r Due to a need of maintaining the weight as low as possible (under 300 kg, including the two spiders and integration case), the Ni walls will be much thinner (∼a factor 2–3) than the XMM mirror shells. At this regard, a new integration procedure (already tested with success [14]) will be implemented with the scope of maintaining good imaging performances, compliant with the top level requirements, also with much thinner and ﬂoppy mirror shells. In particular, the new assembly approach is based on the use of two stiffening rings, to be applied at the top and bottom of each shell to restore an acceptable roundness proﬁle and to handle the shells during the integration in the spiders. The two rings will be removed once that the shell is ﬁxed by glue to the two spiders that, in order to maintain a sufﬁcient rigidity, will be based on a number of arms (24) larger than usual.

The ﬁnal conﬁguration of the SIMBOL-X optics is being addressed in the context of the on-going study Phase A study. The parameters of a particular attractive solution, based on a Focal Length of 20 m, are reported in Table 2. The corresponding expected on-axis effective area is shown in Figure 3. Springer

Exp Astron (2005) 20:139–149 Table 2 Main parameters of the SIMBOL-X mirror module assuming a focal length of 20 m

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Focal length Mirror conﬁguration Coating Outer and inner mirror diameter Mirror heigh (parabola + hyperbola) Shell material Wall thickness (max–min) Expected angular resolution (HPD) Field of view @ 30 keV (FWHM)

20 m Wolter I Pt/C multilayer 70–39 cm 60 cm Ni 0.4–0.2 mm 15–20 arcsec 12 arcmin

Fig. 3 Theoretical on-axis effective area for the SIMBOL-X optics conﬁguration based on a 20 m focal length whose parameters are reported in Table 2.

3.2. The SIMBOL-X focal plane The design of the detector assembly will be tightly tailored to the ﬁnal mission parameters that are being worked out and optimized during the phase A study [15]. At this stage, the present design takes into account the most important parameters for the mission assuming the 20 m focal length optics option. These are shown in Table 3. The above characteristics have led to the design of a two stages focal plane system, operating at a temperature between −30 and −40 ◦ C, which will be described in detail in the following. Basically, it is based on a silicon low energy detector on top of a Cd(Zn)Te high energy detector, both surrounded by an active and passive shielding (Figure 4). The low energy detector (LED) of SIMBOL-X is a Silicon Drift Detector (SDD) with DEPFET (DEPleted Field Effect Transistor) readout [16], also called “Macro Pixel Detector” or “Active Pixel Sensor” (APS). Prototypes of macro pixel detectors have already been developed, built and tested by the semiconductor laboratory of the MPE Institute (Garching, Germany). The LED consists of 128 × 128 pixels with a baseline size of 500 × 500 µm2 with ∼ 450 µm depletion depth. This thick depleted bulk in combination with a thin entrance window results in a high quantum efﬁciency of the bare detector of already >85% at 1.0 keV and 95% at 10 keV and still 45% at 20 keV. Springer

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Exp Astron (2005) 20:139–149 Table 3 The focal plane characteristics Parameter

Value (and origin)

Energy range Energy resolution

<0.5–80 keV ∼130 eV @ 6 keV (Fe line) ∼1 keV @ 68 keV (44 Ti line) 8 × 8 cm2 (coverage of 12 arcmin of FOV with 20 m focal length) ∼500 × 500 µm2 (oversampling of 15 arcsec HEW PSF) ∼10,000 c/s (observability of a ∼1 Crab ﬂux)

Overall size Pixel size Max count rate

Fig. 4 The SIMBOL-X focal plane, based on a stack of the low energy Si detector on top of the Cd(Zn)Te high energy detector; the whole system is surrounded by an active/passive shielding

The detector is logically and functionally divided into four quadrants of 64 × 64 pixels each. All four quadrants are read-out in parallel at a frame time of 256 µs. This short integration time allows the operation of the detector even at room temperatures with an expected energy resolution of about 500 eV (FWHM). In order to further reduce the noise contribution by leakage currents and to achieve an energy resolution of < 145 eV (FWHM) at 5.9 keV the wafer must be cooled down to only −30 ◦ C (assuming a leakage current of 0.26 nA/cm2 at room temperature). The high energy detector (HED) of SIMBOL-X is constructed from a mosaic of several identical cameras, each formed by individual 2 mm thick CdZnTe crystals. The whole detector surface will be ∼10 × 10 mm2 covered with 256 × 256 pixels. As an alternative 0.5 mm thick Schottky barrier CdTe crystal with the same number of pixels. Each crystal is connected to its own read-out electronics, the IDeF-X (Imaging Detector Front-end for Xrays) ASIC developed by CEA/Saclay, forming a complete individual X-ray camera which allows operating in the 5–100 keV range, partly overlapping the low-energy range of the silicon detector. In the current design eight individual X-ray cameras will be merged to form a 2-by-4 module having its own ﬂex for input and output signals. Reliable, radiation tolerant, low power consuming and low-noise read-out electronics in combination with high quality Cd(Zn)Te crystals covered with small pixels are therefore mandatory. The technology for the HED implementation is already pretty advanced and it will be consolidated during the Phase A study. Springer

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3.3. Passive and active shielding of the particle and X-ray diffuse background As there is no telescope tube between the mirror and the focal plane unit in a formation ﬂight conﬁguration, there is a need to protect the detectors from seeing X-rays coming from outside of the mirror, which would otherwise generate an unwanted background [17]. When integrated over even a modest solid angle, the Cosmic Diffuse X-ray Background outside the FOV of the mirror has indeed a level much larger than what is required to reach the desired sensitivity. As a matter of fact, in the case of a 2π opening angle of the detectors on the sky, the sensitivity would be reduced by two orders of magnitude, i.e. the gain in sensitivity brought by the focusing would be entirely lost. In order to stay on reasonable background level as 10−4 cts/cm2 /s/keV at 30 keV photon energy, a passive collimator system with an opening angle seen from the detector not larger than 3 deg FWHM should be used. In order to do that, we combine a “sky bafﬂe” placed on the mirror spacecraft around the mirror, and a collimator placed on top of the focal plane. Both the sky “sombrero-like” bafﬂe and the collimator will be graded shields to stop the highest X-ray background energies and to avoid unwanted ﬂuorescence lines. From the phase 0 mission study, we know that we for a complete shielding we should implement a 3 m diameter sky bafﬂe, so that a ∼1.5 m collimator is sufﬁcient. The collimator and the “sombrero-like” bafﬂe are both made of a layer of tantalum (with a transmission coefﬁcient of 10−4 up to 100 keV), followed by a series of layers of different materials, each able to stop the ﬂuorescence photons by the previous layer although emitting a lower energy X-rays. In the present conﬁguration this multilayer system is made of Ta, Sn, Cu, Al and C. The latter element emits photons of ∼0.4 keV, i.e. below the low energy threshold level of SIMBOL-X. Besides the X-rays entering the detector housing directly, we also need to take into account for the particle background due to the cosmic rays presence hitting the detector spacecraft isotropically. We will therefore make use of an active anticoincidence system in combination with a passive shield surrounding the two focal plane detectors. When charged particles crosses the detector payload, the anticoincidence system triggers simultaneously the detectors and the active shielding. The recorded events are tagged and can be easily removed from the science data. Presently, a very attractive solution to be consolidated during the Phase A study is based on plastic scintillators in combination with a passive shielding made of the same material as the collimator. A second “spare” solution is instead based on classic inorganic scintillators like BGO, NaI or CsI crystals. The former has the advantage that is not only mechanically and electronically easier to realize, with a more reduced weight, but also is not affected by unwanted activation induced background lines close the 30 keV region (which is of high scientiﬁc interest because it is where the CXB spectrum peaks), as are instead all the inorganic crystals above mentioned.

4. Performances In Figure 5 we show the SIMBOL-X ﬂux sensitivity for the optics design conﬁguration, reported in Table 2. The assumed integration time is 1 Ms. As can be seen, the mission will be characterized by an improvement in ﬂux sensitivity over INTEGRAL and SAXPDS by at least two orders of magnitude below ∼80 keV. In Table 4 we report the number of CXB sources resolved in the 20–40 keV energy interval (i.e. where there is the peak of the spectrum) for a single pointing and an observation time of 1 Msec for the SIMBOLX conﬁguration reported in the present paper, for the past SIMBOL-X design, and for the NUSTAR and NEXT missions. At this regards, this evaluation has performed by using the Springer

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Exp Astron (2005) 20:139–149 Table 4 Capability forpast and present SIMBOL-X conﬁgurations and other hard X-ray missions to resolve the Cosmic X-ray Background in the 20–40 energy region assuming 106 s of observing time Project

HPD

FOV

Flim µCrab

%CXB

Sources/FOVFWHM

• NuStar • NeXT • Simbol-X (old design) • Simbol-X ML

40

30

30

15

15

12

7 12

0.8 0.7 1.4 0.5–0.7

40% 50% 35% 65%

15 12 2 25

Fig. 5 Continuum on-axis sensitivity of SIMBOL-X for the options based on 20 m focal length and 70 cm external mirror (see parameters reported in Table 2). The sensitivity is calculated with the assumption of an internal background of 10−4 cts/s/cm2 /keV, 1 Ms of observation and E = E/2. For a better comparison the ﬂux sensitivities of INTEGRAL/IBIS, ROSSI/XTE/HXT and SAX-PDS also plotted in this ﬁgure. Finally also the expected NUSTAR performance is reported assuming the same integration time and background level as SIMBOL-X

logN/logS behaviour expected from the Comastri model for the Cosmic X-ray Background. As can be seen, with the new SIMBOL-X conﬁguration about the 65 % of the CXB will be resolved, with a performances better than the other missions used for comparison.

5. Conclusions We have presented the main characteristics of the SIMBOL-X mission, a formation ﬂight hard X ray telescope project being jointly studied by CNES and ASI, with a large participation of the French and Italian scientiﬁc communities (led by the CEA and INAF Institutions respectively). The MPE and IAAT German Institutes will also take part in the project. Thanks to the use of a long focal length, allowed by the formation ﬂight conﬁguration, and to the use of multilayer coated mirrors, it will be enabled the use of focusing optics in the hard X-ray region (10–100 keV), with an enormous gain in ﬂux sensitivity and angular resolution compared past unfocused missions. The use of a combined focal plane, formed by a stack of a Si-based and a Cd(Zn)Te-based soft and hard X-ray detectors will allow to cover a very Springer

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large X-ray band, ranging from 0.5 keV up to 100 keV. An active/passive shield system will be implemented to guarantee an instrumental background level as low as possible. The joint Phase A study will end in middle 2007, while the launch is foreseen by the 2013 year.

References 1. Fiore, F., Perola, G.C., Pareschi, G., Citterio, O., Anselmi, A., Comastri, A.: HEXIT-SAT: a mission concept for X-ray grazing incidence telescopes from 0.5 to 70 keV. SPIE Proc. 5488, 933 (2004) 2. Aharonian, F., et al.: The H.E.S.S. survey of the inner galaxy in very high energy gamma rays. Ap. J. 636, 777 (2006) 3. Lorenz, E., Martinez, M.: High energy astrophysics: The MAGIC telescope. Astron. Geophy. 46, 6.21 (2005) 4. Frontera, F., Costa, E., dal Fiume, D., Feroci, M., Nicastro, L., Orlandini, M., Palazzi, E., Zavattini, G.: The high energy instrument PDS on-board the BeppoSAX X-ray astronomy satellite. A & A Suppl. Ser. 122, 357 (1997) 5. Ubertini, P., et al.: IBIS: The Imager on-board INTEGRAL. Astron. Astrophys. 411, L131 (2003) 6. Barthelmy, S.D.: Burst Alert Telescope (BAT) on the Swift MIDEX mission. SPIE Proc. 5165, 175 (2004) 7. Ferrando, P., Goldwurm, A., Laurent, P., Limousin, O., Martignac, J., Pinsard, F., Rio, Y., Roques, J.P., Citterio, O., Pareschi, G., Tagliaferri, G., Fiore, F., Malaguti, G., Briel, U., Hasinger, G., Str¨uder, L.: SIMBOL-X: a formation ﬂying mission for hard-X-ray astrophysics. SPIE Proc. 5900, 195 (2005) 8. Cledassou, R.: SIMBOL-X: An hard X-ray formation ﬂying mission, Exp. Astron. DOI 10.1007/s10686006-9036-3 (2005) 9. Citterio, O., Bonelli, G., Conti, G., Mattaini, E., Santambrogio, E., Sacco, B., Lanzara, E., Brauninger, H., Burkert, W.: Optics for the X-ray imaging concentrators aboard the X-ray astronomy satellite SAX. Appl. Opt. 27, 1470 (1988) 10. Jansen, F.A.: XMM: advancing science with the high-throughput X-ray spectroscopic mission. ESA Bull. 100, 15 (1999) 11. Burrows, D.N., Hill, J.E., Nousek, J.A., Wells, A.A., Short, A.D., Willingale, R., Citterio, O., Chincarini, G., Tagliaferri, G.: Swift X-ray telescope. SPIE Proc. 4140, 64 (2000) 12. Joensen, K.D., Voutov, P., Szentgyorgyyi, A., Roll, J., Gorenstein, P., Høghøi, P., Christensen, F.E.: Design of grazing-incidence multilayer supermirrors for hard X-ray reﬂectors. Appl. Opt. 34, 7935 (1995) 13. Romaine, S., Basso, S., Bruni, R.J., Burkert, W., Citterio, O., Conti, G., Engelhaupt, D., Freyberg, M.J., Ghigo, M., Gorenstein, P., Gubarev, M., Hartner, G., Mazzoleni, F., O’Dell, S., Pareschi, G., Ramsey, B.D., Speegle, C., Spiga, D.: Development of a prototype nickel optic for the Constellation-X hard X-ray telescope: III. SPIE Proc. 5900, 225 (2005) 14. Pareschi, G., Citterio, O., Ghigo, M., Mazzoleni, F., Gorenstein, P., Romaine, S., Parodi, G.: Replication by Ni electroforming approach to produce the Con-X/HXT hard X-ray mirrors. SPIE Proc. 4851, 528 (2003) 15. Dirks, B., Limousin, O., Ferrando, P.R., Pareschi, G., Roques, J., Str¨uder, L.: The focal plane of the SIMBOL-X space mission. SPIE Proc. 6276, in press (2006) 16. Treis, J., Lechner, P.H., H¨alker, O., Herrmann, S., W¨olfel, S., Str¨uder, L., Lutz, G., Richter, R.H., Fischer, P., Peric, I., Harter, M., Porro, M.: Advancements in DEPMOSFET device developments for XEUS. SPIE Proc. 6276, in press (2006) 17. Malaguti, G., Pareschi, G., Ferrando, P., Caroli, E., Di Cocco, G., Foschini, L., Basso, S., Del Sordo, S., Fiore, F., Bonati, A., Lesci, G., Poulsen, J.M., Monzani, F., Stevoli, A., Negri, B.: Active and passive shielding design optimization and technical solutions for deep sensitivity hard X-ray focusing telescopes. SPIE Proc. 5900, 159 (2005) 18. Furuzawa, A., et al.: Design study of X-ray telescope onbard NeXT. SPIE Proc. 4851, (2002). 19. Koglin, J.E., Christensen, F.E., Craig, W.W., Decker, T.R., Hailey, C.J., Harrison, F.A., Hawthorn, C., Jensen, C.P., Madsen, K.K., Stern, M., Tajiri, G., Taylor, M.D.: NuSTAR hard X-ray optics. SPIE Proc. 5900, 266 (2005) 20. Comastri, A., Setti, G., Zamorani, G., Hasinger, G.: The contribution of AGNs to the X-ray background. Astron. Astrophys. 296, 1 (1995)

Springer

Exp Astron (2005) 20:151–170 DOI 10.1007/s10686-006-9064-z ORIGINAL ARTICLE

Laue diffraction lenses for astrophysics: Theoretical concepts Hubert Halloin · Pierre Bastie

Received: 13 June 2006 / Accepted: 19 July 2006 C Springer Science + Business Media B.V. 2006

Abstract Beyond the present technologies, Laue diffraction lenses are very promising tools in the ﬁeld of gamma-ray astrophysics. The theoretical concepts of this kind of instruments are based on the Laue diffraction in crystals, discovered almost 100 years ago. Though they are commonly used in crystallography, their application to γ -ray focusing in astrophysics requires some speciﬁc developments, e.g. in terms of energy and imaging responses. The present article describes the physics of X-ray diffraction in crystals. In the context of the Darwin model of mosaic crystals, some peculiar aspects, relevant to the astrophysical observation, are discussed. The evaluation and optimization of diffraction efﬁciency are discussed, especially with regards to the crystal’s mosaicity and thickness, its spatial extent and deviations to the “ideally imperfect” Darwin model. Keywords Focusing optics . Gamma-ray astrophysics . Crystal diffraction PACS 95.55.Ka . 61.50.Ah . 61.10.−i . 41.50.+h

1. Introduction Almost 100 years ago, Max von Laue discovered and demonstrated the diffraction of X-rays in crystals [1, 2]. The laws of the so-called Laue (or Bragg) diffraction in crystals are widely used in crystallography and solid states physics. Nevertheless, their application in astrophysics is much more recent and appears as one of the most promising way to perform the sensitivity leap needed in the hard X- and gamma-ray regimes.

H. Halloin () CESR, 9, avenue du Colonel Roche, 31028 Toulouse, France Present address: APC, 11, Place Marcelin Berthelot, 75231 Paris Cedex 05, France e-mail: [email protected] P. Bastie Laboratoire de Spectrom´etric Physique, BP 87 38402 st. Martin d’H`eres Cedex, France; ILL, BP 156, 38402 Grenoble Cedex 9, France Springer

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In the present paper, we will describe the bases of X-ray diffraction in crystals, from a “practical” point of view in the aim of lens design for astrophysics. The theoretical predictions presented here are used to design and study the instrumental response of a crystal diffraction lens, as described in an accompanying article ([3], this volume).

2. Diffraction lens geometry Since the wavelength of γ -ray photons is smaller than distances between atoms in solid matter, coherently deviating γ -rays has long been considered as impossible in nuclear astrophysics and only the corpuscular properties of these photons were used. Nevertheless, Friedrich, Knipping and Laue [1, 2], at the beginning of the 20th century demonstrated that γ -rays can interact coherently in a crystal lattice, provided that the angles of incident photons are very small and satisfy the Bragg relation: 2d sin θ = nλ,

(1)

where d is the crystal plane spacing, θ the incident angle with respect to the crystal planes, n is the reﬂection order and λ the wavelength of the photon. Thus, by mounting and tuning (i.e. orienting the crystal to get the correct scattering angle θ ) adequate crystals on concentric rings, a parallel beam can be focused on a single point. Historically, the idea of focusing X-rays through the use of crystal diffraction seems to have ﬁrst been proposed by Gouy in 1915 [4]. A few years later, Dardord in 1922 [5] and Fermi in 1923 [6] independently obtained images with monochromatic X-ray beams, following the method suggested by Gouy. The diffraction inside the crystal can either occur near the surface (Bragg geometry) or “in volume”, while the beam is propagating through the entire crystal (Laue geometry, see Figure 1). The Bragg geometry has been successfully used in multilayer optics in the X-ray regime. On the contrary, above a few hundreds of keV, the required incident angle (given by Equation (1)) is so small that the Bragg geometry appears out of question. As an example, a 1 × 1 cm2 beam at 511 keV, diffracted in a Ge[111] lattice, would require a 2.8 m long crystal. Beyond the difﬁculty of producing such big crystals, the complexity of the mounting and the mass of the tiles reject the Bragg geometry as a feasible option. Eventually, the mean free path of γ -rays in crystal is usually bigger than the optimal diffraction length, and the Laue geometry can be used in a γ -ray lens design. In the present article, we will describe the basics of the theory of X-ray diffraction in crystals, assuming a Laue geometry. The following concepts and equations are mainly taken from [7–10]. Please refer to these documents for further details as well as to other articles Fig. 1 Diffraction geometries

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in this volume for a good coverage of recent works on hard X-ray and gamma-ray focusing, both experimental and theoretical.

3. Diffraction by a single crystal Let us consider the reﬂection of an X-ray beam on a given plane of a crystal. k0 , resp. k1 , are the incident, resp. diffracted, wave vectors. With these deﬁnitions, and ∆k = k1 − k0 , it immediately follows:

k = |∆k| = 2k0 sin θi = 4π

sin θi , λ0

(2)

where λ0 is the wavelength of the incident beam, and θi is the angle of k0 w.r.t. the plane orthogonal to ∆k. The main property of a crystal is the periodicity of the elementary cell along the lattice axes a, b and c. Due to this periodicity, the intensity of the diffused, coherent emission is proportional to (sin N p k a/ sin k a)2 , where N p is the number of cells along axis a. Thus, 2 2 the intensity of the diffracted beam is essentially zero unless: ∆k · a = 2hπ,

h∈Z

and similarly, considering the axes b and c: ∆k · b = 2kπ,

∆k · c = 2lπ,

k, l ∈ Z

(3)

This set of equations forms the three Laue conditions that should be simultaneously satisﬁed [2]. From these equations k is then orthogonal to the crystal plane with Miller indexes (h, k, l). Thus, θi from Equation (2) is the incident angle of the beam on the (hkl) plane, and the Bragg relation follows: 2dhkl sin θi = λ0 ,

(4)

where dhkl is the planar spacing of planes (hkl). This relation is valid for an ideally perfect crystal. Actually, even for very good monocrystals, the reﬂection is not purely monochromatic and the angular range over which the crystal reﬂects the beam has a small width. Nevertheless, in practice and for monocrystals, this angular range is very small (a few arcseconds) and we will now consider that the measurements integrate over this angular range (and/or over the energy range). In that case, the integrated power P is given by: P = I0 QδV,

(5)

where I0 is the beam intensity, δV the diffracting volume and Q the diffraction efﬁciency [10]: Q=

re Vc

2 K2

|Fs (∆k)|2 λ30 sin 2θi

(6) Springer

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In this formula, the different terms correspond to: re : classical electron radius (≈2.81794 × 10−13 cm). Vc : volume of the elementary cell (=a 3 for a cubic cell of parameter a). Fs : structure factor (see below for its calculation). λ30 : Lorentz factor, due to the integration of the ﬂux in the diffracted peak. sin 2θi K 2 : polarization factor, between 1 − sin2 2θi and 1 (see below). For compactness, it is useful to deﬁne the so-called extinction length (whose meaning will be clariﬁed latter):

text

˚ 3) Vc E(Ke V)Vc ( A = ≈ 0.28622 µm re |Fs |λ0 |Fs |

(7)

One can then write the value of Q in the form: Q = K2

2 text

λ0 sin 2θi

(8)

Laue diffraction and polarization: Let us consider a linearly polarized incident beam with a polarization angle φ, deﬁned as the angle between the electromagnetic vector and the “scattering plane” (i.e the plane deﬁned by the incident and reﬂected beams). The polarization direction of the scattered beam (φ ) is then given by [11]: sin φ = sin φ/ 1 − sin2 2θi cos2 φ = sin φ 1 + 2θi2 cos2 φ + O θi4 So, strictly speaking, the polarization angle is unchanged (φ = φ) only for parallel (φ = 0) or normal (φ = π/2) polarization. Additionally, the intensity of the scattered beam depends on φ. More precisely, the polarization factor K 2 in Equation (6) is given by K 2 = 1 − sin2 2θi cos2 φ. The polarization modulation is then maximum for φ = π/2(K = 1) and minimum for a parallel polarization. In case of an unpolarized beam (e.g. an X-ray tube), K 2 should be averaged on the φ values: K 2 φ = 1 − sin2 2θi /2 = (1 + cos2 2θi )/2. For example, at 500 keV and considering a Cu111 plane, the relative polarization rotation and attenuation are of the order of 10−4 . Thus, except for low energy photons (E < 50 keV), the Laue lens is practically insensitive to polarization, though its direction is preserved and can be analyzed by the detector (e.g. through the Compton effect). Consequently, neglecting the polarization effect, Q can be simpliﬁed, using the Bragg relation (Equation (4)): Q≈

re Vc

2 |Fs ( k)|2 λ20 dhkl =

dhkl 2 text

(9)

Finally, the reﬂectivity is deﬁned as the diffracted integrated power (Equation (5)) divided by the incident integrated power (Pi = I0 x y cos θi , where x and y are the dimensions Springer

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of the crystal perpendicular to the propagation direction). Since δV = x yt0 , where t0 is the thickness of the crystal, one has: Rm =

P t0 =Q Pi cos θi

(10)

According to this formula, Q represents the reﬂectivity per unit of length and t0 / cos θi is the effective thickness, as seen by the incident beam. 3.1. Calculation of the structure factor The structure factor Fs ( k) is an imaginary coefﬁcient which quantiﬁes the scattering “efﬁciency” of an elementary cell, i.e considering the diffusion by each atom of the cell. Fs is composed of two terms: the scattering factor for a given atom and the geometrical factor, taking into account the interferences between atoms. The atomic scattering factor: The atomic scattering factor ( f ) represents the amplitude of the wave scattered by a single atom, expressed in unit of the contribution from a single electron. As a general rule f depends on sin θi /λ0 and approaches the electron number (Z) for small values of this ratio. The exact calculation of the atomic scattering factor for any sin θi /λ0 is usually difﬁcult since it requires to consider the coherent diffusion by each electron of an atom, taking into account screening factors and quantum physics. Theoretical results exist (e.g the Hartree and Thomas-Fermi methods) but it is much easier (and efﬁcient) to use the following formulas, valid for small incident angles (i.e less than ≈ 10 deg, so this condition is always satisﬁed in the X and gamma ray regimes): f =c+

4

ai e−bi (sin θi /λ0 ) , 2

(11)

i=1

that is, using the Bragg relation: f =c+

4

ai e−bi /4dhkl 2

(12)

i=1

˚ 2 ) coefﬁcients can be found in tables. As an example, Table 1 gives, The c, ai and bi (in A for a few elements, these values, as extracted from [12]. Table 1 Atomic scattering coefﬁcients

Element

Gold

Copper

Silicon

Germanium

a1 a2 a3 a4 c b1 b2 b3 b4

16.8819 18.5913 25.5582 5.8600 12.0658 0.4611 8.6216 1.4826 36.3956

13.3380 7.1676 5.6158 1.6735 1.1910 3.5828 0.2470 11.3966 64.8126

5.6627 3.0716 2.6245 1.3932 1.2471 2.6652 38.6634 0.9169 93.5458

16.0816 6.3747 3.7068 3.6830 2.1313 2.8509 0.2516 11.4468 54.7625 Springer

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Table 2 Coordinates of the atoms in a face centered cubic lattice

Origin Center face (100) Center face (010) Center face (001)

u

v

w

0 0 0.5 0.5

0 0.5 0 0.5

0 0.5 0.5 0

The structure factor: The atomic scattering factor gives the intensity of the beam, as diffused by a given atom. Since these atoms are in a crystal lattice, it is necessary to add the waves scattered by all the atoms of an elementary cell. This summation results in the structure factor (since it depends on the geometry of the lattice): Fs ( k) =

n

e−i k·(u m a+vm b+wm c) f m ,

(13)

m=1

and, using the Laue conditions relation (Equation (3)): Fs =

n

e−2iπ (hu m +kvm +lwm ) f m ,

(14)

m=1

where n is the number of atoms per elementary lattice, the mth atom being at the position (u m , vm , wm ) in the unit cell deﬁned by the lattice vectors ( a, b, c). f m is the atomic scattering factor of the mth atom. When all the atoms of the lattice are of the same kind (e.g copper, germanium, etc), the structure factor can be written as: Fs = f

n

e−2iπ(hu m +kvm +lwm )

(15)

m=1

= fG G is the geometrical factor, only depending on the positions of the atoms in the lattice and on the Miller indexes. The coordinates of the four atoms of a fcc lattice (e.g. copper) are given in Table 2. With these values, the geometrical factor is: G f cc = 1 + cos π(h + k) + cos π(h + l) + cos π (k + l) 4 if h, k, l, all odd or even = 0 otherwise

(16)

For a diamond lattice (e.g germanium) there are two fcc lattices with an offset of ( 14 , 14 , 14 ) : π G diam = G f cc 1 + e−i 2 (h+k+l) ⎧ π if h, k, l odd and h + k + l = 1 [4] 4 1 + e−i 2 ⎪ ⎪ ⎪ ⎨ 41 − e−i π2 if h, k, l odd and h + k + l = 3 [4] = ⎪ 8 if h, k, l even et h + k + l = 0 [4] ⎪ ⎪ ⎩ 0 otherwise Springer

(17)

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This geometrical factor shows that, due to destructive interferences, some crystal planes cannot reﬂect the beam. 3.2. Effect of thermal displacements on diffraction efﬁciency: The Debye factor Because of the thermal movements of the atoms in a solid, the effective emitted wave should be averaged over all the vibrational displacements. Compared to the ideal case of perfectly ﬁxed atoms, the structure factor should then be corrected: Fs =

n

e−2iπ (hu m +kvm +lwm ) f m e−Mm ,

(18)

m=1

where Mm is related to the mean amplitude of the atomic displacements ( X m ) [7, 9]: Mm = =

8π 2 sin2 θi X m2 = Bm 3λ20 Bm 2 4dhkl

sin θi λ0

2 ,

using the Bragg relation

(19) (20)

Equation (20) shows that the smaller the planar spacing (dhkl ), the bigger Mm and the smaller the intensity of the diffracted beam. Physically, this means that the thermal displacement “blurs” the effective distance between the planes, this effect being proportionally more important when dhkl is small.

X m may be different for different kinds of atoms and (hkl) planes. If there is only one kind of atom, the diffracted intensity should be multiplied by the Debye (or Debye-Waller) factor D = e−2M . Moreover, in the case of a cubic crystal containing only one kind of atom (e.g copper, germanium), X can be calculated using [7, 9]: 1 9h 2 Na T + ϕ 2 4π Ma k 4 T T y T ϕ dy = y T 0 e −1

X 2 =

where

(21) (22)

In this equation: h is the Planck constant, k is the Boltzman constant, Na is the Avogadro number, Ma is the atomic mass, T is the temperature of the crystal, is a characteristic temperature. Numerically, it follows: B= Additionally, 0.025, by:

1 4

+

T

1.149 × 104 g mol−1 K 1 T ˚2 + ϕ A Ma 4 T

(23)

ϕ ( ) can be roughly approximated, with an absolute error smaller than T 1 T T 1 T + ϕ ≈ + e−4 4 T 4

(24) Springer

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is not quite the same as the Debye temperature from the speciﬁc heat theory. Nevertheless, the difference is small and to a ﬁrst approximation the tabulated Debye temperature can be used.

4. Limitations and corrections to the kinematical model At this point, all the elements are deﬁned to calculate Q (in Equation (10)) in the ideal case of the kinematical theory which is based on a few assumptions: 1. The refraction index of the crystal is very close to the refraction index of the environment. This assumption is always valid for X and γ rays. 2. The absorption in a single crystal block is negligible, each atom receiving the same intensity from the source. This assumption is valid if the thickness of the crystal block is small compared to the mean free path of the material. 3. The interferences between direct and diffracted beams have been neglected in the crystal. This assumption, not always valid and difﬁcult to estimate, is discussed below. 4.1. The extinction effect The direct and diffracted beams interfere alternatively constructively and destructively, due to their phase difference, when propagating through the crystal. After a given thickness, the two effects are in equilibrium and increasing the size of the crystal does not result in a higher diffracted intensity (i.e an increase of Rm , as given in Equation (10)): this effect is called the extinction effect. For a thin crystal, the above equations (from the kinematical theory) are valid. For a thick crystal, one should use the dynamical theory which gives for the integrated reﬂectivity in Laue geometry [10]:

Rdyn

√ re 1 + | cos 2θi | D|Fs |λ20 t0 = Vc 2 2 sin 2θi cos θi

(25)

In practice, one has: Rkin > Rm > Rdyn ,

(26)

where Rkin is the integrated reﬂectivity from the kinematical theory, given by Equation (10), and Rm is the measured integrated reﬂectivity. One deﬁnes the parameter A = cosK θi ttext0 , where

2θi | K is the polarization factor: K = 1+| cos and K 2 = 1+cos2 2θi for an unpolarized beam, and 2 t0 is the thickness of the crystal block. With these deﬁnitions, the integrated reﬂectivity in Laue geometry can be written as [10]: 2

Rm =

K λ0 2 sin 2θi text

2A

J0 (ρ)dρ

(27)

0

In this formula, J0 is the 0-order Bessel function. Figure 2 shows the variations of I0 (2A) = 2A 0 J0 (ρ)dρ as a function of A. This curve increases until a maximum for A ≈ 1.202 is reached. It then oscillates around the value of 1, showing the saturation of the reﬂectivity Springer

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159 I0(2A)

1.4

I0(2A)/2A

1.2

1

0.8

0.6

0.4

0.2

0 0

2

4

6

8

10

12

14

A

Fig. 2 Relative variations of the integrated reﬂectivity with crystal thickness

(Pendell¨osung effect). In the two extreme cases, one has: 2A, if A 1 I0 (2A) = 1, if A 1

(28)

The transition from the kinematical to the dynamical theory is then driven by the extinction length (Equation (7)). When t0 text the crystal is thin and the kinematical theory applies. When t0 text the crystal is thick and one should use the dynamical theory. Numerically one can use the following approximation for I0 (x): ⎧ x N (x 2 ) ⎪ ⎪ , ⎨ D(x 2 ) 2 2 I0 (x) = 2 π x 8 8 8 ⎪ ⎪ ⎩1.0 + sin x − cos x − P − Q , πx x 4 x x 4

if x ≤8 if x>8

N (x) = 144725 + 15706.9297x − 73.034996x 2 − 33.49237x 3 + 1.30278x 4 − 0.0081205x 5 D(x) = 144725 + 27781.8340x + 1779.3622x 2 + 39.6246x 3 + 0.323458x 4 + 0.0087508x 5 P(x) = 1.0 − 0.015928x + 0.00334056x 2 − 0.00309143x 3 + 0.00172450x 4 Q(x) = 0.0781342 − 0.0050871x + 0.0010301x 2 − 0.0000876611x 3 + 0.0000806711x 4

(29) Springer

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Exp Astron (2005) 20:151–170 Table 3 Extinction length in µm at 293 K and 500 keV for various elements

Copper Silicon Germanium Gold

111

200

220

222

311

331

333

400

78.82 395.6 169.1 37.6

85

109.1 342.6 139.7 46.4

133.8

127.6 521.8 212.1 51.2

178.5 612.1 249.7 63.5

230.6 708.2 288.5 75.7

159.1 408.8 166.8 58.9

39.5

52.8

Finally, in the intermediate regime and considering an unpolarized beam, Equation (10) for the integrated reﬂectivity is always valid by replacing Q with Q deﬁned as follows (in Laue geometry) [10]: Q =

I0 (2A0 ) + | cos 2θi |I0 (2A0 | cos 2θi |) Q 2A0 (1 + cos2 2θi )

A0 =

A t0 = K cos θi text

(30)

Given the small incident angles of X and γ rays: Q ≈

I0 (2A0 ) I0 (2A0 ) dhkl Q≈ 2 2A0 2A0 text

≈ 3.4939

˚ I0 (2A0 ) dhkl ( A) |Fs |cm−1 2t0 (E(keV)Vc ( A ˚ 3 ))

(31)

These equations clearly show that the integrated reﬂectivity per unit of length decreases when the blocks’ thickness increases. Since the “mosaic” crystals are a conglomerate of such crystallites, one should keep their size t0 as small as possible. Unfortunately, the thickness of the crystallites depends on the growing process and this parameter appears difﬁcult to control. The extinction length is therefore the transition thickness from “thin” to “thick” crystals. For a given material and diffraction plane, the extinction length is proportional to the energy. Thus, a crystal which is “thick” at low energy may become “thin” (and so better) at higher energy. The Table 3 gives the extinction length for some materials and diffracting planes at 500 keV and 293 K (Debye factor). A simple proportional factor applies for any other energy.

5. Macroscopic crystals: The Darwin model According to the previous section, the integrated power of a “perfect” crystal saturates after a few tenth of mm, due to the extinction effect. Nevertheless, the measurements performed on “real” macroscopic crystals (of thickness T0 ) can be explained neither by the kinematical nor by the dynamical model of a “perfect” crystal. Actually, the angular (or energy) acceptance can be relatively large (up to a few degrees), and the integrated reﬂectivity is much higher than expected from a perfect crystal with a thickness T0 text . Darwin (see [10, 13–15]) proposed that a macroscopic crystal is actually an agglomerate of small, perfect crystals. The angular orientation of these small crystals is randomly distributed (see Figure 3). Thus, the diffracted beams from the individual crystals blocks do not interfere and the extinction effect Springer

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161

Fig. 3 Scheme of a mosaic crystal

(mostly) cancels out. This mosaic model is deﬁned through the angular distribution of the crystallites W (∆) (where ∆ is the orientation of the block) and their mean thickness (t0 ). Usually, the angular spread is projected on a given diffraction plane, and is assumed to be normally distributed: 2 1 − W ( ) = √ e 2η2 2πη

(32)

√ The mosaicity is then the FWHM of this distribution: m = 2 2 ln 2η. Another assumption of the mosaic model is that the mosaicity is much bigger than the angular reﬂectivity range of a single crystal. This assumption is usually valid for mosaicities above ≈ 10

. In this case, the reﬂectivity power of a layer of thickness t0 is given by R ≈ W (θ − θ B )Rm where θ is the incident angle of the beam, θ B is the Bragg angle corresponding to the beam energy and the mean orientation of the diffraction planes, Rm is from Equation (10). σ is then deﬁned as the integrated reﬂectivity per unit of length: σ = W (θ − θb )Rm /t0 . In case of crystallites of negligible size (i.e. smaller than the extinction length, t0 text ), the crystal is “ideally imperfect”, corresponding to the optimum reﬂectivity that can be obtained according to the Darwin model. Otherwise, the extinction effect (see Section 4.1) should be taken into account. So, using the appropriate expression for Q, depending on the mean thickness t0 (Equation (6) or (30)), one obtains: cos θ B σ ≈ σ ≈

W (θ B − θ)Q,

if t0 text

W (θ B − θ)Q ,

otherwise

(33)

When propagating through the crystal, the beam can be absorbed (linear absorption µ) or diffracted (σ ). Additionally, assuming the crystal to be homogeneous, the diffraction probability is the same from the incident to the diffracted direction, or vice versa. So, deﬁning P0 (T ), resp. P(T ), as the power (or intensity) of the beam in the incident, resp. diffracted, direction at the depth T , the following set of differential equations follows (in Laue geometry) [10]: µ + σ P0 dT + σ PdT cos θ µ + σ PdT + σ P0 dT dP = − cos θ P0 (T = 0) = P0 (0), P(T = 0) = 0 dP0 = −

(34a) (34b) (34c) Springer

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which leads to: T0 µ 1 P(T0 ) = sinh(σ T0 )e−( cos θ +σ )T0 = (1 − e−2σ T0 )e−µ cos θ P0 (0) 2

(35)

T0 µ 1 P0 (T0 ) = cosh(σ T0 )e−( cos θ +σ )T0 = (1 + e−2σ T0 )e−µ cos θ P0 (0) 2

(36)

Usually, the Bragg angle is small and so: P(T0 ) ≈ sinh(σ T0 )e−(µ+σ )T0 P0 (0) ≈

1 (1 − e−2σ T0 )e−µT0 2

(37)

Formula 37, along with Equation 33, is of constant use to estimate the diffraction efﬁciency of a mosaic crystal, and by extension, the efﬁciency of a Laue lens. There are usually two kinds of experiments performed in the laboratory to measure the reﬂectivity of a mosaic crystal: – The incident beam is monochromatic (θ B is constant) and we consider the variation of the reﬂectivity while changing the orientation (angle θ) of the crystal. This method, called a rocking curve, is adequate to precisely measure the reﬂectivity function, since the variation in θ doesn’t inﬂuence any other parameter. – The position of the crystal is ﬁxed (θ is constant), and the variation of reﬂectivity with the energy of the beam (variation of θ B ) is measured. In this case, the diffracted spectrum peaks at the energy E 0 that satisﬁes the Bragg relation for the mean plane orientation (λ0 = 2dhkl sin θ0 ). Besides, there are also 2nd order variations on µ and Q. These variations can be neglected if the diffracted energy bandwidth is small compared to the mean energy (i.e

E E 0 ) and the two experiments are then almost equivalent. 5.1. Some properties of the diffraction curve In this section, the orientation of the crystallites is assumed to be normally distributed: W ( θ ) = 2

ln(2) 1 − ln(2) e π m

θ m/2

2

,

(38)

Then, considering Equation (37), it is useful to deﬁne the following dimensionless parameters: α=4

ln(2) dhkl T0 , 2 π text m

u=

θ m/2

(39)

With these reduced parameters, the reﬂectivity curve has the form (see also Figure 4): 1 P(T0 ) − ln(2)u 2 e−µT0 , = 1 − e−αe P0 (0) 2

(40)

As previously mentioned, in the case of measurements with a constant incident angle but a variable wavelength, the variation of Q and µ in the diffracted energy bandwidth can usually Springer

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1

α = 0,1 α=1 α=5

0.8

0.6

0.4

0.2

0 0

1

2

3

4

5

2∆θ/m

Fig. 4 Normalized reﬂectivity curves for different values of α

be neglected. With this assumption, the FWHM and maximum of the diffraction curve are given by:

u FWHM = 2

P(T0 ) P0 (0)

= max

− ln −

P(T0 ) P0 (0)

1 α

ln 12 1 + e−α ln(2) =

u=0

1 (1 − e−α )e−µT0 2

(41a) (41b)

From these equations, one can demonstrate that u FWHM > 2 (i.e θFWHM > m) whatever the value of α. In other words, the FWHM of the rocking curve is always greater than the mosaicity. Additionally, it tends to the normal angular distribution of the crystallites for α → 0. More precisely, the Taylor series expansion around α = 0 of the diffraction curve and its FWHM gives: +∞ P(T0 ) 1 e−k ln(2)u k = (−1)k−1 α P0 (0) 2 k=1 k! α 1 α ≈ 2 1+ 1+ 1− 8 ln(2) 16 ln(2) 8 ln(2) 2

u FWHM

(42)

(43)

It is also often desirable to calculate the total ﬂux diffracted by a crystal, i.e the integration 0) of PP(T over θ (or λ). Unfortunately, this integration cannot be done analytically, but an 0 (T0 ) good approximation can be obtained by multiplying the FWHM of the diffraction curve with Springer

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its maximum amplitude. Mathematically, this means: Ru (α) = ≈ Rθ = ≈ ≈ Rλ = ≈

+∞

1 ln(2)u 2 1 − e−αe du −∞ 2 − ln − α1 ln 12 1 + e−α −α (1 − e ) ln(2) +∞ P(T0 ) d θ P 0 (T0 ) −∞ +∞ 1 m −µ − ln(2)u 2 e T0 1 − e−αe du 2 −∞ 2 m u ln(2) Ru (α) −µT0 R (α)e−µT0 = 2 QT0 e 2 π α +∞ P(T0 ) dλ ≈ 2dhkl Rθ −∞ P0 (T0 ) ln(2) Ru (α) −µT0 QT0 dhkl e dhklm Ru (α)e−µT0 = 4 , π α

(44)

where the upper indexes indicate the integration parameter (θ, λ or µ). Ru is dimensionless but this is not the case of Rθ and Rλ which are, respectively, the integrated ﬂux considering a rocking curve or a continuum energy emission, and are consequently expressed in photons(/s). So, m should be expressed in arcseconds in Rθ if the incident ﬂux is in photons/arcsec (we are only interested in the projection of the incident ﬂux in the meridian plane). In Rλ , m should be expressed in radians (since it indirectly comes from the linearization of the Bragg ˚ if the incident, polychromatic ﬂux is in (or converted to, using the relation) and dhkl in A 2 ˚ E 0 / hc factor) photons/ A. The validity of this approximation can be checked on Figure 5, where the numerical and approximated values of Ru (α) and Ru (α)/α are plotted. This approximation is also used and compared with a MC simulation of a broad band Laue lens in a accompanying article ([3], this volume). Alternatively, integrating the Taylor series of the diffraction curve (see Equation (42)) u − ln(2)u 2 gives the expansion of 0 21 (1 − e−αe ) dv :

u

Fα (u) = 0

=

1 4

1 − ln(2)u 2 dv 1 − e−αe 2

√ +∞ π erf( k ln(2)u) k α (−1)k−1 √ ln(2) k=1 kk!

(45)

From this equation, the Taylor series expansion of the integrated reﬂectivity (Ru (α) = 2Fα (∞)) follows: Ru (α) = Springer

1 2

+∞ π (−1)k−1 k α √ ln(2) k=1 kk!

(46a)

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2 Norm. integrated reflectivity Peak * Width α Peak * Width / α

Normalised integrated reflectivity

1.5

1

0.5

0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

α

Fig. 5 Normalized integrated reﬂectivity (without absorption) of a mosaic crystal. Crosses represent the numerical integration, the dot line is the approximated analytical model

The above equations (see also Figure 5) demonstrate that Ru (α)/α decreases with α and Ru (α)/α ≈ 1 if α 1. This means that the integrated reﬂectivity, for a given thickness T0 , asymptotically increases with the mosaicity, approaching a constant value if m 2dthkl2 T0 . ext This condition is not always satisﬁed though. Especially, the parameters optimization can 2 t . often lead to values for which Tm0 ≈ dext hkl 6. Crystal optimization strategies To get an idea of the “best” parameters of a mosaic crystal, let now try to “optimize” the reﬂectivity of a single crystal. In the context of the Darwin model, two parameters can eventually be optimized to non trivial values: the mosaicity and the thickness. The size of the crystallites (t0 ) should be much smaller than the extinction length (see Section4.1), so that the extinction effect is negligible. This latter condition is assumed to be satisﬁed in the following sections. 6.1. Maximum peak reﬂectivity for a given mosaicity The mosaicity of a crystal is often set by “external” constraints (e.g the growing process or the energy resolution of the detector in case of a line observation). In that case, optimizing the peak reﬂectivity (see Equation (41)) leads to the following thickness:

peak Tmax

dhkl ln 1 + 4 ln(2) 2 π mtext = , dhkl 4 ln(2) π mt 2

(47)

ext

Springer

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Since ln(1 + x)/x is always between 0 and 1 for x > 0, the optimal thickness is always peak smaller than the mean free path 1/µ, whatever the mosaicity m. Moreover, Tmax increases 2dhkl with m and tends to 1/µ if m t 2 µ . ext Since the width of the diffracted peak increases with the crystal thickness, the optimal signiﬁcance (taking into account the background noise in the diffracted bandwidth) could peak lead to a slightly different value of T0 (see below), smaller than Tmax . 6.2. Detection optimization for a broad band emission Here, we assume that both mosaicity and crystal thickness are free parameters. The optimization criterion is the detection signiﬁcance in the energy bandwidth of the crystal. According to the approximation of Equation (44), the signal is proportional to: PS ∝ m f (α) g(α)e−µT ,

(48)

where: 1 (1 − e−α ) 2 ln 12 (1 + e−α ) g(α) = − ln − α f (α) =

Besides, the background level can be estimated by integrating its ﬂux over the diffracted FWHM. Thus, the detection signiﬁcance (background dominated and assuming Poisson statistics) is proportional to: n σ ∝ f (α) m g(α)e−µT

(49)

The maximization of n σ , w.r.t the mosaicity m and to the thickness T0 can be performed analytically and leads to: σ Tmax =

1 2µ

m σmax = 0.57414

dhkl 1 ∝ 2 2 E µtext

(50)

In that case, it is worth noticing that the optimal thickness only depends on the material and diffracted energy, being half the mean free path, but not on the diffracting plane. Moreover, using this optimal mosaicity as an input for the peak reﬂectivity maximization procedure peak σ of the precedent section gives Tmax ≈ 1.18485.Tmax , which conﬁrms that the signiﬁcance optimization leads to thinner crystals than the peak efﬁciency optimization. The optimization criterion is nevertheless quite ﬂat around the optimum (in both cases) and, consequently, even signiﬁcant departure from optimal parameters (especially concerning the thickness) only slightly affects the “quality” of the crystal. In practice, other constraints affect the optimal parameters. First, experiments showed that the mean crystallites’ size is correlated with the mosaicity: the mosaicity is due to the dislocation density inside the crystal. Hence, the smaller the mosaicity, the bigger the mean Springer

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thickness of the perfect crystal blocks. Second, the ﬂatness of the optimum may lead to choose thinner crystal in order to save mass budget and/or increase the number of tiles.

7. Diffraction by an extended crystal Up to now, the radial extension of the crystal has been neglected. This is obviously not always valid in practice. Actually, if the source is at ﬁnite distance from the crystal, the incident angle, and hence the diffracted energy, depends on the impact radius. Since the mosaicity represents the angular width over which a crystal “line” reﬂects a monochromatic beam, the radial extension of the crystal is negligible only if the angular size of the crystal (as seen from the source) is small compared to the mosaicity. Given a radial crystal size of 1 cm and a mosaicity of 1 arcmin, this means a source distance greater than 34 m! This condition may be hard to achieve in laboratory experiments, unless a small slit is mounted in front of the crystal, which may then reduce too much the diffracted ﬂux. Nevertheless, some crystal properties can be derived from experiments with an extended crystal and a source at ﬁnite distance. Consider the experimental setup represented in Figure 6: a crystal with a radial extension of 2 r is mounted at a distance D of a source S. The detector is placed at the symmetrical point S , or at any other place so that the diffracted ﬂux is totally intercepted (but not the direct beam). Moreover the source is assumed to be isotropic, with an intensity I0 . Two different cases are discussed hereafter: a monochromatic or a continuum source. Besides, the angular distribution of the crystallites is assumed to be Gaussian. 7.1. Monochromatic source In that case, the incoming intensity, projected on the meridian plane is given by I0 in units of ph · s−1 · cm−1 . I0 is non-zero only for a given wavelength (λ0 ). If θm is the incident angle on the middle of the crystal, then the incident angle at the radius r (varying from − r to r ) is given by: θ = θm + θ , where θ ≈ r/D. Following the approach given in Section 5.1, let us deﬁne the reduced parameters:

um =

θ B − θm , m/2

ur =

θ r = , m/2 Dm /2

u r =

r , Dm /2

(51)

Fig. 6 Diffraction of an extended crystal and a source at ﬁnite distance Springer

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where θ B is the Bragg angle for the incident energy (λ0 ). With these notations and using the deﬁnition of Fα from Equation (45), the diffracted intensity is given by: Idiff = =

Dm 2

+ u r

− u r

1 − ln(2)(u r −u m )2 1 − e−αe du r e−µT0 I0 2

Dm (Fα ( u r − u m ) + Fα ( u r + u m ))e−µT0 I0 2

(52)

If the source is close enough and the crystal correctly oriented, then the crystal’s mosaicity is much smaller than its angular size and the reﬂectivity curve can be integrated over the full angular range. Mathematically, these conditions are: ⎧

r ⎪ ⎨ u r − u m 1 ⇔ − (θ B − θm ) D ⎪ ⎩ u r + u m 1 ⇔ r + (θ B − θm ) D

m 2 m 2

(53)

In that case, the diffracted intensity (in · ph s−1 ) is given by Idiff = D R θ I0 , where Rθ is from Equation (44). The diffraction efﬁciency is then: Mono =

Idiff D θ = R , 2I0 r 2 r

(54)

As expected, the diffraction efﬁciency increases with the source distance (the diffraction “volume” increases). 7.2. Polychromatic source In that case, the incoming, polychromatic intensity, projected on the meridian plane is given ˚ −1 . As usual, the energy bandwidth is assumed to be small so by I0 in units of ph s−1 cm−1 A that the crystal properties are almost constant. With this assumption, Equation (52) is still valid for a given wavelength, with I0 and u m depending on λ. Moreover if I0 is constant over the energy bandwidth, then integrating over λ leads to the total diffracted intensity (in ph · s−1 ): Idiff = 2 r Rλ I0 = 4 r dhkl Rθ I0 = (2 r )2

2dhkl Mono I0 D

(55)

where Rλ and Rθ are from Equation (44). The total diffracted intensity from a continuum emission is then independent of the source distance. One should nevertheless keep in mind that the energy bandwidth increases as the source comes closer to the crystal. Additionally and contrary to the monochromatic case, there is no obvious deﬁnition of a global efﬁciency in the polychromatic case, since the diffraction process transforms a continuum emission into a band-limited spectrum. Nevertheless, the mosaic energy spread (that is not due to the crystal angular size) is, according to the Bragg relation, λ ≈ 2dhkl m. So, deﬁning the averaged efﬁciency as the diffracted intensity divided by the incident ﬂux in Springer

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the mosaic bandwidth, one gets: poly =

Idiff Rθ 2 r = = Mono 2I0 r 2dhkl m m Dm

(56)

The conversion factor (2 r/Dm) corresponds to the angular size of the crystal in units of mosaicity (as expected. . . ). From the conditions expressed in Equation (53), it follows that the efﬁciency for a monochromatic beam is much lower than the “efﬁciency” for a polychromatic one, provided that the source is close to the crystal. This corresponds to the fact that only a small portion of the crystal diffracts in case of a line emission, whereas the whole volume is efﬁcient when using a continuum source. The above expressions are useful to estimate the expected diffracted intensity for a continuum emission knowing the efﬁciency measured with a monochromatic source, or vice versa. 7.3. Beam divergence of the diffracted beam Finally consider the effect of the mosaic spread on the divergence of the beam. The mosaic spread of a crystal increases its energy bandwidth and, consequently, the astrophysical interest of a Laue lens. However the mosaicity also induces a divergence of the diffracted beam in the meridian plane. So, since the deviation angle is twice the Bragg angle, the divergence of the beam is twice the angular width of the diffraction curve as given by Equation 40. In other words, due to the “reﬂection” effect on the crystal planes, the divergence of the diffracted beam is roughly twice the mosaic spread of the crystal. To ﬁrst order, the diffraction curve is proportional to the crystallites distribution (i.e. a Gaussian whose FWHM is the mosaicity m). Consequently, in case of an extended crystal and assuming a parallel incoming beam, the radial spot size is then roughly proportional to the convolution of the crystal footprint (2 r ) by a normal distribution, whose FWHM is 2Fdet m, Fdet being the distance from the lens to the detector. Mathematically, this means for the radial intensity on the detector plane: Idet (r ) ∝

1

r − r

r + r erf √ + erf √ , 2 2β 2β

(57)

√ where β = Fdet m/ 2 ln(2). When β 2 r (i.e if the detector is close to the crystal), Idet (r ) tends to a rectangular shape of width 2 r , i.e. the projected footprint of the crystal. On the contrary, if β 2 r , the radial distribution is close to a Gaussian with a FWHM of 2Fdet m. This effect of mosaic defocusing (as introduced by N. Lund in this conference) appears ﬁnally as the major limiting factor on the focal length and mosaicity.

8. Conclusion The precedent sections described the basics of X-ray diffraction and their application to Xray and gamma-ray focusing. Based on the Laue diffraction laws and the Darwin model of mosaic crystals, these theoretical developments demonstrated the interest of this technique for astrophysics. An accompanying article (Halloin, in this volume) describes more precisely the application of these concepts to Laue diffraction lenses, comparing experimental results and Monte-Carlo simulations based on the theory presented here. Springer

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From this model, the “best” crystal for a Laue lens appears as a trade-off between the different parameters: – The mosaicity enables the energy overlap from one ring to another but causes mosaic defocusing. – The crystallites’ mean size should be as small as possible but its effect is energy-dependent, hard to control in practice and correlated with the mosaicity. – The thickness of the crystal should be of the order of one half of the mean free path but the optimum is ﬂat enough to allow signiﬁcant deviation in beneﬁt of, e.g., the mass budget. – The radial extension of the tiles would ideally be very small so that the footprint be limited by mosaic defocusing. In practice, the consequently high number of tiles to be grown and the technical challenge of their cut and etching will temper this wish. One should nevertheless notice that the mosaic model, although well studied, understood . . . and realized, may not be the “best” for our purpose. Especially, the equilibrium between the diffracted and direct beams as well as the relatively large beam divergence (due to the wings of the crystallites’ angular distribution) limit the efﬁciency of the crystals. Further improvements in crystal growth or “synthesis” may potentially overcome these issues (e.g. see the article of R.K. Smither on gradient crystals in this volume [16]). To conclude, one should note that a computer program exists that can calculate many of the important crystal diffraction parameters, without the need of knowing the complicated mathematics behind the calculations. This program, called XOP (and available on many websites such as [17]) is extensively used in the synchrotron community and could now also be useful to the astrophysics community.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

Friedrich, P.K.W., Laue, M.: Annalen der Physik 41, 971 (1913) Laue, M.: Annalen der Physik 41, 989 (1913) Halloin, H.: Exp. Astron. 20, DOI 10.1007/s10686-006-9063-0 (2006) Gouy, M.: Ann. Phys. de Chimie 5, 241 (1916) Dardord, R.: J. Phys. Le Radium 3, 218 (1922) Fermi, E.: Nuovo Cimento 25, 63 (1923) Guinier, A.: Th´eorie et Technique de la Radiocristallographie. Dunod, Paris (1956) Halloin, H.: Ph.D. thesis, University Paul Sabatier, Toulouse (2003) Warren, B.E.: X-ray Diffraction. Addison-Wesley Publishing Company (1969) Zachariasen, W.H.: Theory of X-Ray Diffraction in Crystals. Dover Publications Inc., New York (1945) Zachariasen, W.H.: Acta Crystallogr. 16, 1139 (1963) Cromer, D.T., Waber, J.T.: International Tables for X-Ray Crystallography, vol. 4. Kynoch Press, Birmingham, pp. 71–147 (1974) Darwin, C.G.: Philos. Mag. 27, 315 (1914) Darwin, C.G.: Philos. Mag. 27, 675 (1914) Darwin, C.G.: Philos. Mag. 43, 800 (1922) Smither, R.K.: Exp. Astron. 20, DOI 10.1007/s10686-006-9019-9 (2006) Sanchez del Rio, M., Dejus, R.J.: Web page of the X-ray Oriented Programs (XOP), http://www.esrf.fr/computing/scientiﬁc/xop2.1/ (2003)

Springer

Exp Astron (2005) 20:171–184 DOI 10.1007/s10686-006-9063-0 ORIGINAL ARTICLE

Laue diffraction lenses for astrophysics: From theory to experiments Hubert Halloin

Received: 13 June 2006 / Accepted: 19 July 2006 C Springer Science + Business Media B.V. 2006

Abstract Based on the laws of X-ray diffraction in crystals, Laue lenses offer a promising way to achieve the sensitivity and angular resolution leap required for the next generation of hard X-ray and gamma-ray telescopes. The present paper describes the instrumental responses of Laue diffraction lenses designed for nuclear astrophysics. Different possible geometries are discussed, as well as the corresponding spectral and imaging capabilities. These theoretical predictions are then compared with Monte-Carlo simulations and experimental results (ground and stratospheric observations from the CLAIRE project). Keywords Focusing optics . Gamma-ray astrophysics . Crystal diffraction PACS 95.55.Ka, 61.50.Ah, 61.10.−i, 41.50.+h

1. Introduction Due to the very short wavelength of X and gamma rays, focusing instruments in high energy astrophysics has long been considered as impossible. Present telescopes in gamma-rays make use of direct shadowing (e.g. coded aperture telescopes such as INTEGRAL/SPI) or incoherent scattering (e.g. Compton telescopes such as CGRO/Comptel). Nevertheless, only a few years after the discovery of coherent scattering in crystal lattices by Friedrich, Knipping and Laue in 1912 [1], Gouy suggested an instrument focusing X-rays [2]. Following this method, Dardord in 1922 [3] and Fermi in 1923 [4] seem to have been the ﬁrst to obtain images by mean of X-ray focusing. Though commonly used in crystallography, the application of Laue diffraction to high energy astrophysics is much more recent. One can refer to the work of Lindquist and Weber in 1968 [5], Smither in 1982 [6] and Lund in 1992 [7]. Recently, the ﬁrst observation of an astrophysical source (the Crab nebula) has been performed during a stratospheric ﬂight (the CLAIRE project, see the article by P. von Ballmoos et al. [8] in this H. Halloin CESR, 9, avenue du Colonel Roche, 31028 Toulouse, France e-mail: [email protected] Present address: APC, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France Springer

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volume and [9, 10]). A spaceborne gamma-ray lens project, MAX, has also been proposed to the French Space Agency (see the corresponding article by N. Barriere [11] in this volume and [12, 13]). The theoretical basis of Laue diffraction lenses for astrophysics has already been given in another article in this volume ([14], hereafter cited as Paper 1). In the present article, the geometry and instrumental response of a Laue lens are more speciﬁcally studied. The expected instrumental response from X-ray diffraction theory is then compared with the results of ground and stratospheric observations.

2. Design of a gamma-ray lens As presented in Paper 1, it is possible to coherently deviate hard X-rays and gamma-rays in crystals, using the Bragg relation: 2d sin θ = nλ,

(1)

where d is the planar spacing of the crystal, θ the incident angle, λ the beam wavelength and n an integer. Moreover, the Darwin model of mosaic crystals predicts efﬁciencies that are suitable for astrophysical purposes. These properties can be used to design a Laue diffraction lens. Consider an X-ray beam impacting a crystal at Bragg angle θ B . After diffraction the beam direction is changed by 2θ B . With a ring of crystals, the diffracted beam can be focused on a single point. If appropriate d-spacing are used with different radii the same energy is diffracted from several rings. Alternatively, using the same diffracting plane at different radii allows the energy bandwidth of the lens to be increased. In this section, we will describe some properties and characteristics of a Laue lens. 2.1. Choosing the diffraction material The choice of the diffracting material is crucial in the design of a Laue lens. It is a trade-off between diffraction efﬁciency, absorption and practicability of crystal growth. As mentioned in Paper 1, Section 3.1, the atomic scattering factor tends to Z for small incident angles. So, as a ﬁrst approximation, the diffraction efﬁciency of a crystal is linked to its electronic density (see Figure 1). A more precise analysis would nevertheless require consideration of the lattice geometry of the crystal (via the geometrical factor) and the absorption (which increases with Z and decreases with energy). For our purpose here, the electronic density is a reasonably good indicator of the “quality” of the material. Among the “best” materials, at present only a few ones can be grown with the appropriate quality and mosaicity. Some of these candidates are indicated in Figure 1. Carbon (actually HOPG: Highly Oriented Pyrolitic Graphite) and silicon are widely used and their growth process is now well controlled thanks to the development of the semi-conductor industry (especially for silicon). The diffraction efﬁciency of these crystals is nevertheless quite low above a few tens of keV. Copper is a good diffraction material. While copper crystals with mosaicities at the level of a few arcminutes are “commonly” grown, until recently it has been quite difﬁcult to get homogeneous copper crystals with a mosaicity of the order of the arcminute, as required for a gamma-ray lens above about 100 keV. Recent improvements in the growth process of copper Springer

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80

173

Be N Ne Al S K Ti Mn Ni Ga Se Rb Zr Tc Pd In Te Cs Ce Pm Gd Ho Yb Ta Os Au Pb Ra Pa Pu Bk Li C F Mg P Ar Sc Cr Co Zn As Kr Y Mo Rh Cd Sb Xe La Nd Eu Dy Tm Hf Re Pt Tl Po Th Np Cm He B O Na Si Cl Ca V Fe Cu Ge Br Sr Nb Ru Ag Sn I Ba Pr Sm Tb Er Lu W Ir Hg Bi Rn Ac U Am

70

Electronic density [10

23

cm ]

Au

60 Ag

50 Cu

40

Ge

30 C

Si

20 10 0 0

10

20

30

40

50 60 Atomic number

70

80

90

100

Fig. 1 Electronic densities of pure materials. Materials that have been considered for Laue lenses are indicated

crystals achieve mosaicities of 1 arcmin or less (see the article of P. Courtois et al. [15], in this volume). Germanium (actually Ge1−x Six ) crystals were used to build the ﬁrst gamma-ray lens for astrophysics (the CLAIRE project, see [8] in this volume). Due to the amount crystals that had to be produced (≈1000), a good knowledge of the GeSi growing process and crystals parameters relevant for gamma-ray lenses now exists (see the article of N.V. Abrosimov in this volume [16] and [17]). Silver and gold are also promising candidates (especially at high energy) and have the same crystal structure as copper and similar melting temperature, although no attempt has yet been made to grow mosaic silver or gold crystals for a Laue lens.

2.2. Geometry of a Laue diffraction lens Let us now consider a crystal, located at a radius r from the optical axis of the lens, and a source at a distance D (see Figure 2). E ∞ , θ∞ and F∞ are the energy, Bragg angle and focal distance for a source on axis, at inﬁnity. Similarly, E, θ and F refer to a source at a distance D from the lens. In the hard X- and gamma-ray regimes, the Bragg angles are small and the linearization of the Bragg relation leads to: ˚ hc 100 keV 1A θ≈ ≈ 213.11 arcmin 2dhkl E dhkl E

(2) Springer

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Fig. 2 Scheme of a crystal diffraction on a Laue lens

Additionally, if D r , one has θ ≈ θ∞ +

r D

and so:

2dhkl r 1 1 + ≈ E E∞ hc D

100 keV dhkl 100 keV 10 m r ≈ + 0.16128 ˚ E E∞ 10 cm D 1A

(3)

This equation speciﬁes that it is equivalent (w.r.t the crystal planes orientation) to focus a beam of energy E ∞ from inﬁnity or one of energy E at distance D. This property is very useful when tuning a Laue lens in laboratory, where the distance of the X-ray source is limited. r In addition we have, F∞ ≈ 2θr∞ and F ≈ θ +θ and, consequently: ∞ r E ∞ dhkl hc ≈ 0.80644

F∞ ≈

E∞ 100 keV

r 10 cm

ddhkl ˚ 1A

m

(4)

and: 1 1 1 − ≈ F D F∞

(5)

The latter equation is very similar to the equation of thin lenses (but with an associated dependence of the beam energy). Equation (4) allows to deﬁne two kinds of Laue lenses: – lenses with a few keV energy bandpass and consequently a relatively “short” (few meters) focal length – those with a broad energy bandpass and therefore a long focal length (tens of meters). Monochromatic Laue lenses In order to focus a single energy (from inﬁnity) with crystals at different radii on the same focal point, the product r · dhkl should be constant (from Springer

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√ −1 Equation (4)). So, r (∝ dhkl ) can take only discrete values (e.g. r ∝ h 2 + k 2 + l 2 for cubic lattices). From the Bragg relation, any angular deviation θ (either the mosaicity or source’s depointing) leads to an energy offset E ≈ 2dhchkl E 02 θ . Since, in this conﬁguration, all the ring diffracts the same nominal energy, any depointing greater than (roughly) the mosaicity causes a noticeable change in the energy response of the lens. The diffraction efﬁciency −1 decreasing with dhkl , the contribution of the outer crystals rapidly becomes small and in practice the number of rings is limited. The demonstration lens built for the CLAIRE project had to be ﬂown on a stratospheric balloon and was consequently of this kind due to the requirement of a short focal length. This lens had a external diameter of about 40 cm, 8 rings of germanium crystals ((111) to (440) planes), a nominal diffracted energy of 170 keV at inﬁnity and a focal length of 2.7 m (see [8] in this volume and references therein). Broad band lenses In this case, the diffracted energy depends on the radius and the lens covers a wider energy bandpass. Actually, from one ring to another (with radii R and R + 2

r, r R), the diffracted energies differ by E ≈ dhkl E ∞ /(F∞ hc) r . On the other hand, the FWHM of the diffracted peak for a given ring is linked to the mosaicity m of the crystal: E ≈ 2mdhkl E 2 /(hc). Consequently, there is an energy overlap between two identical crystals at different radii only if r < 2F∞ m. Typically, the desired angular resolution of the lens leads to required mosaicities of the order of 1 arcmin, whereas, for the lens and detector to be on the same spacecraft, the focal length should not be greater than about 10 m. With these values (m = 1 arcmin and F∞ = 10 m), the smoothness of the energy response requires r 6 mm. In this case, concentric Laue rings would require small crystal tiles, with the accompanying difﬁculties in terms of cutting process and positioning. Nevertheless, following an idea proposed by Lund [7], the tiles can be mounted according to an Archimedes spiral, the crystal radius varying linearly with its azimuth angle. These geometry ensures a very smooth energy distribution and is foreseen for the HAXTEL project (see the article from F. Frontera in this volume [18] and [19]). For a longer focal length (∼100 m), requiring separated platforms, the mosaic energy spread is enough to realize a smooth energy response, even in case of concentric rings (which usually simpliﬁes the lens design). The MAX mission (see the article from N. Barriere in this volume [11] and [13]) is of this kind.

3. Spectral and imaging response of a Laue lens A Laue diffraction lens is similar to a “classical” optical lens as far as the capability of concentrating an on-axis source is concerned. Nevertheless, the observation of an off-axis source induces aberrations, i.e. a modiﬁcation of the diffracted spectrum, associated with a deformation of the point spread function (PSF). 3.1. On-axis point source In order to quantify the Laue lens response to a point source, consider a single ring of crystals. This ring is assumed to have a mean radius r , focusing an energy E ∞ from an on-axis point source at inﬁnity, on a detector located at the focal distance (F∞ ). The size of the focal Springer

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spot is due to the superposition of the tiles footprints, convolved by the radial divergence of the beam (see Paper 1, Section 7.3). Whereas the size of the crystals footprints does not depend on the detector distance, the “mosaic defocusing” (as introduced by N. Lund in this conference) increases with the focal length. This effect also induces a decrease of the instrument sensitivity, since the background level scales with the detection area. If the detector is close to the lens, or the mosaicity small, only the projection of the footprints has to be considered. In this case, the focal spot intensity distribution, diffracted by a full ring, is well approximated considering that the intensity at radius r on the detector is proportional to the mean value of the intensity diffracted by a single crystal at the same radius from its center (assuming a perfect alignment of all tiles). Mathematically, if 2L × 2l is the size of the tiles (with L > l), then the radial intensity is proportional to: ⎧ if r ≤ l ⎪ ⎪1 ⎪ ⎪ 2 1 ⎪ ⎪ ⎪ if l < r ≤ L ⎨ 1 − π arccos r I (r ) = √ ⎪ l L 2 ⎪ ⎪1 − arccos + arccos if L < r ≤ l 2 + L 2 ⎪ ⎪ π r r ⎪ ⎪ √ ⎩ 0 if r > l 2 + L 2

(6)

When the divergence of the beam cannot be neglected, the same procedure using the radial intensity from Paper 1, Equation (57) leads to:

I (r ) =

⎧ ⎪ 2 ⎪ ⎪ ⎨π

π/2

Idet (r sin θ)dθ

if r ≤ d⊥

0

⎪ ⎪ 2 ⎪ ⎩π

π/2

arccos(d⊥ /r )

(7) Idet (r sin θ)dθ

if r > d⊥ ,

where d⊥ is half the size of the crystal, perpendicular to the radius. As a consequence of this equation, I (r ) ∝ Idet (r )/r if r d⊥ . The effect of the mosaic defocusing has a major impact on the sensitivity. The area of the focal spot doesn’t depend on the focal distance F∞ , provided that the beam divergence (due to the mosaicity) is small w.r.t. the crystals’ footprint, i.e. if F∞ rc /m, where rc is the 2 half the radial size of a crystal. Conversely, it scales as F∞ if F∞ rc /m. Consequently, considering a position sensitive detector, the background noise variability is independent of F∞ for short focal length and increases as F∞ otherwise. 2 2 The collecting area being proportional to F∞ , the lens sensitivity scales as F∞ for short focal lengths and increases “only” linearly if F∞ rc /m (i.e. like a coded aperture telescope). This property is the main limiting factor, along with the mass constraint, to the increase of the focal length (and hence the effective area). 3.2. Off-axis point source Calculating the off-axis response of a Laue ring (with no radial extension) shows that the focal spot is no longer a circle but a ring with an azimuthal dependence of the energy. This effect is due to the “mirror effect” on the diffracting planes and the equivalence between angle and energy via the Bragg relation. Actually, considering a point source at inﬁnity with a small off-axis angle , the incident angle on the crystal located at the azimuth χ on the ring is ψ = cos(χ − φ), where φ is the azimuth of the source. Due to the reﬂection on the Springer

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crystal planes, the impact positions on the detector are located on a circle of radius F∞ , centered on the lens axis: x(χ) = F∞ cos(2χ − φ) (8) y(χ) = F∞ sin(2χ − φ) χ varying from 0 to 2π, the image on the detector is the superposition of 2 circles with the same radii and centers. In addition, the energy diffracted by the crystal at azimuth χ is shifted from the nominal “on-axis” energy E by: E ≈ − 2dhchkl E 2 cos(χ − φ). Finally, if the position on the impact circle is parametrized by α = 2χ − φ(α ∈ [0 : 4π ]), then:

E(α) ≈ −

2dhkl 2 E cos((α − φ)/2), hc

α ∈ [0 : 4π]

(9)

This formula demonstrates that for the same impact position (i.e. for α ∈ [0 : 2π] and α + 2π ), two energies are diffracted: E · (1 ± 2dhchkl E cos(α − φ)/2)). Moreover, for α = φ + π[2π ] the beam divergence is tangential to the impact circle, whereas its direction is along the radius for α = φ[2π]. Consequently, the impacts density and spread depends on the position on the impact circle. Actually, the maximum impact density is at the “geometrical” position (i.e at the intersection of the detector plane and the line of sight). According to Paper 1, Equation (57) and simplifying the rectangular footprint by a Gaussian distribution, the beam divergence induces a spatial dispersion whose FWHM is roughly given by (2 rc )2 + (2F∞ m)2 . So, two point sources (with one on-axis) can be separated by the lens provided that the diameter of the impact circle (from the off-axis source) is greater than the diameter of the “on-axis” spot size. This means 2F∞ (2 rc )2 + (2m F∞ )2 . The angular resolution of the lens is then approximately: min ≈

( rc /F∞ )2 + m 2

(10)

Consequently, the angular resolution of a Laue lens improves with the focal length, but is roughly equal to the mosaicity as soon as F∞ rc /m. The energy response to an off-axis point source can be considered as a convolution product: the response for a perfect pointing convolved by the “off-axis” broadening, whose width is roughly E ≈ 2 2dhchkl E 2 , as explained above. Thus, in case of a broad band Laue lens (i.e. with a long focal length), the energy response is only slightly affected, whereas the PSF is quite sensitive to the off-axis angle. On the contrary, the energy response of a narrow line lens (i.e. with a short focal length) is strongly dependent on , but not the impacts distribution. 3.3. Monte-Carlo simulations The instrumental response (spectral and imaging) has been simulated using a Monte-Carlo software, speciﬁcally developed for Laue lenses simulations. Two lens conﬁgurations have been simulated: – a broad band (0.2–2 MeV) lens with a focal length of 150 m – a narrow band (3 keV @170 keV) lens with a focal length of 2.77 m Springer

178 Table 1 Parameters of the broad band Laue lens used for Monte-Carlo simulations

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Parameter

Value

Focal length Number of crystals Crystals size Crystal material (radius range)

150 m 92488 2 × 2 cm2 Ge111 (0.31–0.39 m) Au111 (0.41–0.97 m) Cu111 (0.99–4.45 m) 30

2131 kg

Mosaicity Crystals mass

The broad band Laue lens is made of concentric rings of germanium, copper and gold crystals. The rings radii vary from 0.3 m to 4.45 m, corresponding to an energy range from 200 keV to 2 MeV. In order to limit the mass cost and foreseeing a deployable mechanism, the outer crystals are mounted on petals, as shown in Figure 3. In this case, diffraction orders from 1 to 3 have been considered. Additional information about the simulation is listed in Table 1. Comparisons are also made with a MC simulation of a narrow band Laue lens. For this simulation, the design of the CLAIRE lens has been used. It consists of 8 Ge rings, focusing the same energy at inﬁnity (170 keV) with a focal length of 2.763 m (see Table 2). The simulations have been performed for an on-axis source and for an off-axis angle of 3 arcminutes. The simulation results are illustrated on Figure 4 (broad band lens) and Figure 5 (narrow band lens). The simulated spectra are plotted in the upper part of the ﬁgures, above

Fig. 3 Implantation of crystals for the MC simulation of a broad band Laue lens. From inner to outer rings: Ge111 , Au111 and Cu111 Springer

Exp Astron (2005) 20:171–184 Table 2 Parameters of the narrow band Laue lens used for Monte-Carlo simulations

179

Parameter

Value

Focal length Number of crystals Crystals size

2.763 m 659 1 × 1 cm2 (except rings 5 and 7) 1 × 0.7 cm2 (rings 5 and 7) 61.7, 100.8, 118.2, 142.6, 156.18, 174.64, 188.15, 201.67 70 to 110

(depends on the ring) 111, 220, 311, 400 331, 422, 333, 440 2.1 kg

Rings radii in mm Mosaicity Diffracting planes Crystals mass

the density plot of the impacts on the detector, for the perfect pointing (right) and the off-axis source (left). Additionally, the spectral response of the broad band lens to an on-axis source has also been estimated using the analytical approximation of the total intensity diffracted by a crystal, as given in Paper 1, Equation (44). Compared to the MC simulation, this analytical approach reproduces quite well the spectral shape, though the “energy smoothing” due to the mosaicity is not taken into account. Using the analytical approximation has obviously the advantage of calculation time (a few seconds w.r.t. a few hours for the MC simulation) but, in the general case, it cannot easily reproduce the intensity map on the detector plane. These MC simulations, based on the basic principles and equations of the Darwin model of crystals, conﬁrm the spectral and imaging properties of a Laue lens, as described above. The energy response of a narrow band lens is very sensitive to the depointing, while the impact distribution is only slightly modiﬁed. On the contrary, the spectral shape of the broad band lens is almost unchanged between 200 keV and 2 MeV, apart from the “sharp” features at 850 and 1800 keV (which are smoothed). Conversely, the impact distribution becomes a ring, whose radius is about 13 cm (=150 m ×3 ). 4. Theory vs. experimental results The CLAIRE project [20–24] was intended to test the validity of the Laue lens concept on an astrophysical source. A narrow band Laue lens has been developed at the CESR (Toulouse, France) and tested on ground and during a stratospheric ﬂight (observation of the Crab Nebula). The characteristics (shape and ﬂux) of spectra recorded during the lens tuning allowed the determination of the parameters of the crystals (mosaicity and mean length of the crystallites). These parameters were then used for the development of realistic numerical models (Monte-Carlo simulations), which can be compared with experiments in various conditions of pointing, source spectrum and distance, etc. A detailed description of the CLAIRE project is given in P. von Ballmoos et al. ([8], this volume). Hereafter, we only quote the experimental results for comparison with theoretical expectations. In order to estimate the diffraction efﬁciency of the lens, as well as its angular response, two experiments have been conducted on ground. First, a radioactive source of 57 Co was observed with the lens. This source emits a line at 122.06 keV, corresponding to a distance of 14.07 m according to Equation (3). At this distance, the angular size of each crystal is ∼2.4 arcmin (crystal height of 1 cm) or 1.7 arcmin (0.7 cm). Since these values are larger than the mosaicity, only a small fraction of the crystal Springer

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Fig. 4 MC simulation of a broad band Laue lens. Upper graph: diffracted spectra for an on-axis source (analytical approximation and Monte-Carlo simulation) and a 3 arcmin off-axis source. Lower graphs: MonteCarlo simulations of impacts density on the focal plane (left: 3 off-axis source, right: on-axis)

is diffracting, leading to a diffraction efﬁciency (diffracted fraction of the incident radiation on the lens area) of 3.2±0.1 % (see Paper 1, Section 7.1). The numerical simulations can then be used to correct this efﬁciency of a monochromatic, divergent beam into a polychromatic, parallel beam. Finally, taking into account the estimated uncertainties on the crystals’ parameters, a semi-empirical value for the peak efﬁciency at 170 keV (considering a diffracted peak of 3 keV FWHM) can be set to 7.7±1 %. Additional ground measurements with a source at 205 m were performed on an aerodrome in Figure as, on the Spanish Mediterranean coast [25]. This experiment led to a peak efﬁciency of 8.5±1 %, taking into account an estimation of systematic effects. Figure 6 shows the energy response of the lens for various depointing angles (from 30 to 270 arcseconds). Springer

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181

Fig. 5 MC simulation of a narrow band Laue lens. See Figure 4 for a description of the ﬁgures

The curves are compared with the results of a Monte-Carlo simulation of these experiments. The shape and deformation of the energy response are well reproduced by the model. In that sense, this experiment validated the theoretical instrumental response of the lens. On June 14 2001, CLAIRE was launched on a stratospheric balloon by the French Space Agency (CNES) from its site at Gap in the French Alps and landed near the Atlantic coast 500 km west of the launch site. After data analysis, the spectrum exhibits a signiﬁcant excess of about 33 photons at 170 keV with an exposure time of 1h 12. This result leads to a peak +0 efﬁciency of 12.5±4−2 %, corrected for a perfect pointing and taking into account systematic effects. These experimental results are summarized and compared with numerical simulations in Table 3. Measurements and simulations are in good agreement and a value of 9±1 % of peak Springer

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Table 3 Comparison of experimental results and simulations Experiment

Measured eff.a,b

Simulated eff.a,c

Comments

Polychromatic source at inﬁnity Polychromatic source at 205 m 57 Co at 14 m

12.5±4−2 %

8.88±0.02 %

8.5±0.5±0.5 %

8.53±0.02 %

3.17±0.02±0.1 %

3.668±0.004 %

Measurement derived from the 2001 ﬂight analysis Long distance test (see text and [25]) Laboratory experiment with a radioactive sourced

+0

a

Peak efﬁciency assuming a peak FWHM of 3 keV for polychromatic sources, diffracted fraction of the incident ﬂux on the lens for monochromatic sources. b Error bars include the statistical uncertainty (ﬁrst ﬁgure) and an estimation of systematic effects (second ﬁgure). c Error bars are only statistical. d The low efﬁciency is due to the small diffracting volume for a monochromatic source at ﬁnite distance (see text). Rescaling gives a peak efﬁciency of about 7.7±1 % for a polychromatic source at inﬁnity.

efﬁciency for a polychromatic source at inﬁnity is compatible with both experimental and simulated data. Besides, the validity of the relationship between distance and diffracted energy (Equation 3) have been tested with various experiments using a continuum source: – tuning data (distance of 14.16 m) – source at 22.52 m with a partially tuned lens 6 Measurements MC simulations

5 4 3

Flux (cts/keV/s)

2 1 30 ’’ 0 60 ’’

90 ’’

210 ’’

270 ’’ 140

145

150

155

160

165

170

175

180

185

190

Energy (keV)

Fig. 6 Response of the CLAIRE lens during the long distance test, for various off-axis angles. The solid lines represent the measurements, the dashed lines are from an MC simulation. Successive plots have been shifted down for clarity Springer

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183

1000 Distance [m]

D=f(E) 100

10

Diffracted Intensity [arbitrary unit]

1 14.162 m 22.52 m 205 m infinity

0.8

0.6

0.4

0.2

0 110

120

130

140

150 Energy [keV]

160

170

180

190

Fig. 7 Recorded spectra for continuum sources at various distances. Upper graph: theoretical positions of the peaks. Lower graph: results of the experiments

– long distance test (205 m) – stratospheric ﬂight (inﬁnity. . .) Figure 7 represents the recorded spectra for these experiments (lower graph), compared with the theoretical relationship given by Equation (3) (upper graph). The position of the centroids are in very good agreement with theory, slight departures from theoretical values (less than 0.5 keV) being the consequence of the incident spectrum shape and/or the detector calibration drifts.

5. Conclusion In the ﬁeld of nuclear astrophysics, from a few tens of keV up to a few MeV, future spaceborne instruments will have to perform a signiﬁcant sensitivity and angular resolution leap. Present technologies, such as coded masks or Compton telescopes, have equivalent collecting and detecting area. Thus, their point source sensitivity seem to be “intrinsically” limited. Based on X-ray diffraction in crystals, discovered almost 100 years ago, a Laue diffraction lens offer a way to overcome the present sensitivity dead-end, with also a unprecedented angular resolution in this energy range (typ. 1 ). In the present paper, the main characteristics and design options of this kind of instruments have been described. Additionally, the expected instrumental responses are conﬁrmed by Monte-Carlo simulations, as well as by experimental results. Once the behavior, expectations and limitations of Laue lenses for astrophysics are correctly understood, the next step is to focus on the best design for a future spaceborne gamma-ray lens. . . Springer

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References 1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12.

13. 14. 15. 16. 17. 18. 19.

20. 21. 22. 23.

24. 25.

Friedrich, P.K.W., Laue, M.: Annalen der Physik 41, 971 (1913) Gouy, M.: Ann. Phys. de Chimie 5, 241 (1916) Dardord, R.: J. Phys. Le Radium 3, 218 (1922) Fermi, E.: Nuovo Cimento 25, 63 (1923) Lindquist, T., Webber, W.R.: Can. J. Phys. 46, S1103 (1968) Smither, R.K.: Rev. Sci. Instrum. 53, 131 (1982) Lund, N.: Exp. Astron. 2, 259 (1992) von Ballmoos, P., Halloin, H., Evrard, J., Skinner, G., Abrosimov, N., Alvarez, J.M., Hamelin, B., Hernanz, M., Jean, P., Kn¨odlseder, J., et al.: This volume (2006) Halloin, H., von Ballmoos, P., Evrard, J., Skinner, G.K., Hernanz, M., Abrosimov, N.V., Bastie, P., Hamelin, B., Lonjou, V., Alvarez, J.M., et al.: In: Citerrio, O., O’Dell, S.L. (eds) Optics for EUV, X-Ray, and Gamma-Ray Astronomy. Proceedings of the SPIE, vol. 5168. pp. 471–481 (2004) Halloin, H., von Ballmoos, P., Evrard, J., Skinner, G., Alvarez, J., Hernanz, M., Abrosimov, N., Bastie, P., Hamelin, B., Jean, P., et al.: ESA SP-552: 5th Integral Workshop on the Integral Universe. p. 739 (2004) Barriere, N., von Ballmoos, P., Halloin, H., Abrosimov, N., Alvarez, J., Andersen, K., Bastie, P., Boggs, S., Courtois, P., Courvoisier, T. et al.: This volume (2006) von Ballmoos, P., Halloin, H., Skinner, G.K., Smither, R.K., Paul, J., Abrosimov, N.V., Alvarez, J.M., Astier, P., Bastie, P., Barret, D., et al.: In: Citerrio, O., O’Dell, S.L. (eds) Optics for EUV, X-Ray, and Gamma-Ray Astronomy. Proceedings of the SPIE., vol. 5168. pp. 482–491 (2004) von Ballmoos, P., Halloin, H., Paul, J., Abrosimov, N., Andersen, K., Astier, P., Basa, S., Barret, D., Bastie, P., Bazzano, A., et al.: ESA SP-552: 5th Integral Workshop on the Integral Universe. pp. 747–753 (2004) Halloin, H., Bastie, P.: This volume (2006) Courtois, P., Andersen, K., Bastie, P.: This volume (2006) Abrosimov, N.: This volume (2006) Abrosimov, N., L¨udge, H.R. n. V.K.A., Borrissova, D., Halloin, H., von Ballmoos, P., Bastie, P., Hamelin, B., Smither, R.: J. Crystal Growth 275, e495 (2005) Frontera, F.: This volume (2006) Pisa, A., Frontera, F., De Chiara, P., Loffredo, G., Pellicciotta, D., Carassiti, V., Evangelisti, F., Andersen, K., Courtois, P., Hamelin, B., et al.: In: Citerio, O., O’Dell, S.L. (eds) Optics for EUV, X-Ray, and Gamma-Ray Astronomy II. Proceedings of the SPIE., vol. 5900. pp. 350–359 (2005) Naya, J.E., von Ballmoos, P., Smither, R.K., Faiz, M., Fernandez, P.B., Graber, T., Albernhe, F., Vedrenne, G.: Nucl. Instrum. Methods Phys. Res. Sect. A 373, 159 (1996) Kohnle, A., Smither, R., Graber, T., von Ballmoos, P., Laporte, P., Olive, J.-F.: Nucl. Instrum. Methods Phys. Res. Sect. A 408, 553 (1998) Laporte, P., Abrosimov, N.V., Bastie, P., Cordier, B., Di Cocco, G., Evrard, J., Laurent, P., Paltani, P., Skinner, G.K., Smither, R.K., et al.: Nucl. Instrum. Methods Phys. Res. Sect. A 442, 438 (2000) von Ballmoos, P., Evrard, J., Skinner, G.K., Abrosimov, N., Bastie, P., Di Cocco, G., George, M., Halloin, H., Hamelin, B., Jean, P., et al.: ESA SP-459: Proceedings of the 4th Integral Workshop ‘Exploring the Gamma-Ray Universe’. pp. 649–652 (2001) von Ballmoos, P.: Web page of the CLAIRE project, http://www.cesr. fr∼pvb/Claire/index.html (2003) Alvarez, J., Halloin, H., Hernanz, M., von Ballmoos, P., Jean, P., Skinner, G., Abrosimov, N., Smither, R.K., Vedrenne, G.: ESA SP-552: 5th INTEGRAL Workshop on the Integral Universe, pp. 757−+ (2004)

Springer

Exp Astron (2005) 20:185–194 DOI 10.1007/s10686-006-9025-6 ORIGINAL ARTICLE

Mosaic and gradient SiGe single crystals for gamma ray Laue lenses N. V. Abrosimov

Received: 9 January 2006 / Accepted: 30 January 2006 C Springer Science + Business Media, B.V. 2006

Abstract Both Ge1−x Six mosaic crystals and Si1−x Gex crystals with gradient of composition could be grown using the modiﬁed Czochralski technique to produce the diffracting elements for the MAX gamma ray telescope. Although many elements cut from the mosaic crystal and used before for CLAIRE gamma ray telescope had an efﬁciency up to 20%, the overall efﬁciency of the lens was about 8.1 ± 0.7 %, which is more than twice lower than the theoretically predicted efﬁciency. Some causes of this behaviour are discussed. In addition to mosaic crystals, the growth of Si1−x Gex crystals with a gradient of composition and their properties are analysed. Such composition-gradient crystals could be a promising way to improve the diffraction efﬁciency of Laue lens for MAX. Keywords X-ray diffraction . Mosaic crystal . Gradient crystal . Crystal growth . Czochralski method . Germanium silicon alloys

1. Introduction One of the possible solutions on the way to gamma ray detection is a crystal diffraction lens telescope. In this case because of the focusing effect one can increase the collection area of gamma rays without increasing the detection area that is very important for the observation of extraterrestrial objects like super nova with a weak ﬂux of radiation. There are some approaches to realize such telescope including Laue crystal lens as diffracting unit. But the question is: what crystals could be used to build the lens? Recently high quality Cu mosaic single crystals with a uniform and in this case very narrow intrinsic mosaicity between 30 arc sec and 5 arc min were grown by the Bridgman technique (Courtois et al. 2006). High homogeneity and high peak reﬂectivity make these crystals very promising for an application in crystal lens telescope. Other possible material candidates for the diffracting lens are bulk crystals of SiGe solid solutions in the form of N. V. Abrosimov () Institute for Crystal Growth, Max-Born-Str.2 D-12489 Berlin, Germany/Institute of Solid State Physics of Russian Academy of Sciences, 142432 Chernogolovka, Russia e-mail: [email protected] Springer

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both mosaic crystals and gradient crystals. In the last years, the growth of Si- and Ge-rich Ge1−x Six -single crystals with diameters of up to 50 mm using the Czochralski (Cz) technique opened new application areas like X-ray, gamma-ray and neutron optics (Abrosimov et al., 1996; Abrosimov et al., 1997). For example Si-rich crystals with an axial gradient of Ge are used as Bragg monochromators for synchrotron radiation to improve the spectral resolution and the spectral ﬂux density of the diffracted X-ray beam by compensating the incident beam divergence (Erko et al., 2002). R. Smither in his new experiments used crystals with curved crystalline planes including Si crystals and Si-rich SiGe gradient crystals for diffraction of the high energy X-ray beam from Advanced Photon Source and gamma rays from radioactive source (Smither et al., 2005). It was found that using this approach there is a potential of increasing both the diffraction efﬁciency and the bandwidth by a factor of 5 as compared to what can be done with mosaic crystals. Nevertheless, Ge-rich Ge1−x Six mosaic single crystals are also a promising material for gamma ray optics. Some years ago the two balloon-borne experiments CLAIRE using the high energy γ -ray telescope for pointing at the Crab Nebula were launched by the French Space Agency (CNES) (von Ballmoos et al., 2004 (1)). This was the ﬁrst astronomical observation with a gamma-ray lens telescope. Lately, the new concept of a space born crystal diffraction telescope MAX was presented by the MAX Scientiﬁc Advisory Group (von Ballmoos et al., 2004 (2)). The main feature of the telescope is based on the focusing γ -rays from the large collection area of a crystal diffraction lens onto a very small detector volume. As a consequence, the background noise is extremely low, making possible the unprecedented sensitivity. One of the main parts of the CLAIRE telescope was the γ -ray lens consisting of 556 Ge1−x Six diffracting elements, 1 × 1 cm2 cut from Ge1−x Six Cz grown mosaic crystals and mounted in concentric rings on a titanium frame. The mosaicity of the diffracting elements governs the ﬂux throughput, the angular resolution and the energy bandwidth of the crystal lens. A mosaicity between 25 and 50 arc sec was found to be optimal for the CLAIRE experiments. For the MAX crystal lens telescope, the optimal mosaicity of diffracting elements was calculated using Darwin’s model for mosaic crystals to be about 30 arc sec (von Ballmoos et al., 2004 (2)). In the Darwin model, the real defect structure of the crystal, which may be due to dislocations, inhomogeneous strain, etc., is described by an agglomerate of perfect crystal blocks that are slightly angle-shifted against each other. The block size taking part in the scattering process should be microscopic or sub-microscopic to reach higher diffraction efﬁciency, and the angular distribution of the blocks can be deﬁned as a continuous function. A FWHM of this Gaussian-like function is called the mosaic width, or here the mosaicity. This paper will describe the growth of both mosaic and gradient SiGe single crystals. 2. Crystal growth and characterization 2.1. Growth and characterization of mosaic crystals A reproducible growth of the Ge-rich SiGe mosaic crystals is different from the growth of perfect one. By the growth of the perfect crystals in two component systems one try to avoid the constitutional supercooling near the solid-liquid interface caused by the segregation of the second component, Si in this case. On the one hand constitutional supercooling leads to a morphological instability of the interface and to perturbations that can disrupt the single crystal growth. On the other hand one need such perturbations for the formation of cellular structure that gives the mosaicity of the grown crystals. The problem is to ﬁnd such growth conditions and to keep them during the whole growth process. Springer

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187

Fig. 1 Longitudinal distribution of Ge in two Si1−x Gex single crystals of diameters 33 and 38 mm grown from the melt with the same initial charge of M0 = 360 g and Ge concentration of 7 at% Ge

The Ge1−x Six mosaic crystals were grown by a modiﬁed Cz technique applying Si feeding rods to replenish the loss of Si in the melt during the growth because of kSi > 1 (Abrosimov et al., 1997). Pulling was generally performed under normal pressure of Ar + 2% H2 and constant gas ﬂow between 300 and 600 Nl·h−1 . The crystal growth begins with a Ge seed which is dipped in a pure Ge melt. When a neck is formed and the crystal begins to expand, the melt surface is contacted with the Si rods. The upward movement of the crucible with the melt gives the possibility to solve the Si rods continuously in the Ge melt. The rate of the crucible movement depends on the rods position in such a way that the silicon concentration gradient at the conical part of the crystal is maintained approximately constant. When the calculated concentration of Si in the crystal is achieved, the equilibrium between the solved Si and the crystallizing Si component is settled. It is supposed that the Si rods begin to solve immediately when they touch the surface of the Ge melt. Due to the relative movement between the rods and the melt, which is caused by the crucible rotation of about 10 rpm, the rods dissolve almost constantly. Using this technique it was possible to grow crystals of up to 35 mm diameter and 120 mm length with both constant and linear axial distribution of silicon (Figure 1). The mosaicity of the Ge1−x Six crystals was achieved by intentionally disturbing of the solid-liquid interface leading to a morphological instability and a cellular structure. Crystals of (100), (111), (211) and (130) orientations were grown with about 2 at%Si. The choice of the orientation was caused by the optimisation of the cutting process to fulﬁl the crystal preparation for 8 diffracting rings of the CLAIRE lens (von Ballmoos et al., 2004 (1)). The crystallisation rate during the growth was kept at about 6 mm·h−1 . The crystal structure and the shape of the solid-liquid interface of the grown crystals were studied by metallographic methods and the lateral photovoltage scanning (LPS) (Abrosimov et al., 2002) revealing the shape of impurity striations caused by segregation ﬂuctuations Springer

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during the growth. In case of Ge1−x Six crystals, the second component (here Si) and the doping elements (P) are segregated similarly as such striations. The HF:HNO3 :CH3 COOHetchant was used for etching the samples. The mosaicity of the grown crystals was investigated with the hard X-ray diffractometer at the Institute Laue-Langevin, Grenoble, using the continuous high-energy X-ray spectrum (100 keV and 400 keV) (Hamelin et al., 2004). The crystal diffraction efﬁciency was measured twice, during the tuning procedure of the lens at the energy of 122 keV (efﬁciency of individual diffracting elements) and by a long distance test at the energy of 165 keV simulating the telescope ﬂight experiment and showing the diffraction efﬁciency of the whole lens (Halloin et al., 2004). For the tuning procedure, the 122.06 keV photons from a 57 Co source situated 14.16 m in front of the lens on the optical axis were used. The diffracted photons were detected on the P01 INTEGRAL/SPI detector placed 2.33 m behind the lens on the optical axis. For the long distance test of the diffraction efﬁciency of the whole lens, an industrial X-ray generator with a 2.5 × 2.5 mm tungsten target (voltage 250 kV, current 1 mA) allowing a sufﬁcient X-ray ﬂux at 170 keV after absorption by 205 m on the air was used. 2.2. Growth of gradient crystals 2.2.1. Crystals with constant diameter Si-rich Si1−x Gex gradient single crystals were also grown by the Cz technique. The growth of gradient crystals is based on one of the peculiarities of a directional solidiﬁcation: the segregation of the second component with distribution coefﬁcient less than 1 leads to a nonuniform distribution of Ge along the crystal length. The Ge content increases with the rise of crystal length and solidiﬁed fraction g = Mcr /M0 , where Mcr – is the mass of the crystal s and M0 – the mass of the charge, 0 < g < 1. The Ge distribution in the crystal C Ge and the concentration changing in the melt C Ge are well described by the Scheil-Pfann expression: = C0,Ge (1 − g)k−1 , C Ge

s and C Ge = kC Ge

(1)

where C0,Ge - initial Ge concentration in the melt. In the range 0 < g < 0.6 the Ge concentration increases weakly with a quite constant gradient because of k = 0.35 and in the range g > 0.6 the gradient of the Ge concentration is increasing with increase of g. In the cylindrical part of the crystals g depends linearly on the crystal length according to the expression: g = Mcr /M0 = πρcr R 2 L/M0 ,

(2)

where ρcr , R and L are density, diameter and length of the crystal, respectively. Here, R and M0 are the parameters used for the choice of the required concentration gradient that will be obtained. In any case, if the initial mass of the charge is the same, the gradient is higher in the shorter crystals but in each crystal the gradient is rising from the begin to the end (Figure 1). 2.2.2. Crystals with variable diameter From the analyses of Equations (1) and (2) one can conclude that the crystals with the a constant gradient of doping impurity or the second component (Ge in our case) could be grown if the diameter of the crystal is gets smaller during the growth. Experimentally it is nearly impossible to grow such crystals with a constant gradient over the whole length, but Springer

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189

Fig. 2 Si1−x Gex single crystal grown from the melt with 7 at%Ge and the calculated proﬁle for attaining the gradient ∼ 0.8 at%cm−1 (see explanation in text). The vertical straight line corresponds to the beginning of the experimental curve of the longitudinal Ge distribution in Figure 3

for the main part of crystal it could be realized (Abrosimov et al., 2004). The equation for the shape of the crystals was found as the dependence of the crystal radius R from the length L (Abrosimov, 2004)

R(L) =

2−k k−1 B M0 B L +1 . πρcr (1 − k)C0,Ge kC0,Ge

(3)

Here, B is the impurity gradient (in at%·cm in the case of SiGe solid solution). The possibility to grow Si1−x Gex single crystals with a nearly constant gradient of Ge was proved by the growth from the melt with 7 at% Ge· Figure 2. shows one of the grown crystals and the calculated proﬁle of the crystal with constant gradient B = 0.8 at%·cm−1 . The dependence R(L) was calculated from Equation 3 for the following parameters: the initial charge M0 = 215 g, k = 0.32, and ρcr = 2.33 g · cm−3 . Here, we did not take into account that the crystal density changes with increasing Ge concentration. The calculated curve is given for the range 0.2 < g < 0.9; the crystal was grown upto g = 0.89. One can see from the comparison of the calculated proﬁle and the shape of the grown crystal that they coincide well in the middle part of the crystal. This fact is also conﬁrmed by Figure 3 that presents the Ge distribution measured along the crystal axis. In the middle part of the crystal, the Ge distribution is practically linear.

3. Results and discussion 3.1. Ge1−x Six mosaic crystals In general, the crystallographic defects like dislocations, cellular structures caused by dislocation rearrangement, low angle grain boundaries are undesired for the main applications of the crystals because the main task of the crystal grower is the growth of large perfect crystals (Rudolph). On the other hand such defects provide the mosaic structure being necessary for gamma-ray monochromators. Springer

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Fig. 3 Longitudinal distribution of Ge in Si1−x Gex crystal shown in Figure 2

It is difﬁcult to grow defect-free SiGe single crystals. The crystal structure of SiGe is extremely sensitive to perturbations near the solid-liquid interface like melt convection and thermal ﬂuctuations that are typical for the crystal growth from the melt. The main defects in these crystals are so-called rotational striations and dislocations. But the ﬁrst experiments with Ge1−x Six crystals showed that the striations (ﬂuctuations of Si concentration) and the grownin dislocations provide a mosaicity of less than 12

. Only the growth of Ge1−x Six crystals with a cellular structure gave us the possibility to achieve the mosaicity in the range of 30

and 60

. The density of the grown-in dislocations in such a crystal was in the range of 104 ÷ 105 cm−2 . The formation of a cellular structure in germanium crystals caused by constitutional supercooling near the solid-liquid interface was described in (Hurle et al., 1994). The crystals described were doped with Ga or In, both having distribution coefﬁcients in Ge of less than unity and a limited solubility. Due to microsegregation on the disturbed interface, the cell boundaries become enriched with doping elements and solute-rich droplets trapped within the germanium crystal. The advantage of Si as a doping element (second component) is based on the miscibility over the complete range of compositions of Si and Ge. Because the distribution coefﬁcient of Si in Ge is greater than unity, Si is preferentially segregated to the peaks of the cells, the cell boundaries become depleted, and no massive droplet formation is observed. Figure 4a shows the unstable microstructure detected by the LPS method and Figure 4b and Figure 4c show parts of detected region as etched pattern. During this growth stage the macroscopic growth parameters such as pulling rate, rotation rates of both crystal and crucible, and crucible translation rate were constant. The changes of morphology between stable and unstable state were caused by stochastic ﬂuctuations. At least, two features could be seen from Figure 4 which are important for optimising the crystal growth process: (1) the cell size, small just after appearing, increases during the growth and (2) the cellular structure occurs reversible (if only in some range). The ﬁrst point is important for controlling the cell size, which can be considered as diffracting element in the Darwin model of mosaic crystals. The latter shows that long crystals with a desired cellular structure can only be grown if the growth conditions are stable enough over a long time. Springer

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191

Fig. 4 Axial cut of a 112 -grown Ge1−x Six crystal, sample surface (220). Si concentration is 1.7 at%. (a) LPS measurement (38 mm × 10 mm), (b) and (c) micrographs showing the development of the cellular structure

As is known (Hurle et al., 1994), the morphology of the cellular structure depends on the crystal growth direction because, after initial perturbations, the micro-facets start to form on the solid-liquid interface and {111} plane faceting pyramids are developed. Figure 5 shows etched wafers of 100 , 112 and 130 orientated Ge1−x Six crystals with x = 0.02. All crystals have a convex (to the melt) solid–liquid interface. Size and form of the cells in the crystals with different orientation can be responsible for the different diffraction properties of the diffracting elements in CLAIRE’s lens. To fulﬁll the Bragg conditions in the 8 concentric rings, 8 diffraction planes – (111), (220), (311), (400), (331), (442), (333), Springer

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Exp Astron (2005) 20:185–194

Fig. 5 Morphology of the cellular structure after the growth in a) 100 , b) 112 , c) 130 directions. Micrographs of the etched wafers

(440) were chosen. To optimise the cutting procedure, crystals of (100), (111), (211) and (130) orientations were grown with the diffracting planes being parallel to the crystal axis. Nearly all diffracting elements were checked for mosaicity, and each element was tuned in the diffraction position and the diffracting efﬁciency was measured. A large variation of the diffraction efﬁciency from 3% to 15% was observed between different optical elements, Springer

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193

and the best crystals were selected for the installation into the lens. (The theoretical peak efﬁciency was estimated to range from 25% at the best ((111) diffracting plane) down to roughly 10% ((333) diffracting plane)). The diffraction efﬁciency of the whole lens deduced during the stratospheric ﬂight of the CLAIRE telescope was determined to be 6.7 ± 1.5% (von Ballmoos et al., 2004 (1)) which is in good agreement with the 8.1 ± 0.7% measured during the long distance experiment at the energy of 165.5 keV (Halloin et al., 2004). 3.2. Si1−x Gex gradient crystals The main feature of a gradient crystal, in which the component concetration varies monotonically over the crystal length, is that the lattice parameters vary also monotonically according to Vegard’s law. A lattice parameter gradient leads to the bending crystalline planes that can be used for diffraction of X-rays or gamma rays. The detailed analysis of the diffraction with such curved-plane crystals is given in detail by R. Smither (Smither et al., 2006). There are 3 different ways to produce diffracting elements with curved crystalline planes: through the temperature gradient, using the bending procedure and applaying two component gradient crystals like SiGe (Smither et al., 2006). The ﬁrst two ways are very effective in practice they are rather simple in the realization only on a laboratory scale because one should have in-situ control of the temperature or bending conditions. In the case of gradient crystals, a build-in gradient of lattice parameter is achived at the stage of crystal growth. It can simplify the construction of the MAX lens and decrease its weight. Figure 6. shows three possibilities to cut diffracting elements (monochromators) from the Si1−x Gex gradient crystals. The laterally graded crystals shown in Figure 6d. were used for the double crystal monochromator with symmetrical Bragg reﬂection by BESSY KMC-2 beam line. The spectral ﬂux density for such monochromator was found to be 4–6 times higher than others due to optimization of the Bragg conditions for a divergent beam using the lattice parameter gradient (Erko). For the MAX Laue lens application the diffracting elements can be cut along the crystals length as shown in Figure 6c. It should be taken into account that the different elements, in spite of the same gradient of the lattice parameter, have a different crystal composition that can inﬂuence the diffraction efﬁciency. The ﬁrst measurements of the diffraction efﬁcincy and FWHM of the rocking curve on the composition-gradient crystal are analysed in (Smither et al., 2005).

Fig. 6 The possibilities to cut the monochromators from the gradient crystal: (a) as-grown gradient crystal, (b) one non-banded monochromator, (c) banded monochromators, (d) two banded monochromators Springer

194

Exp Astron (2005) 20:185–194

There are some limits for the growth of Si1−x Gex gradient crystals. In general the higher gradient should be achieved, the shorter crystal could be grown. The maximal concentration gradient of 1.4 at% Ge per cm on 3 cm length with retantion of crystal quality was obtained by the growth from the melt with 7 at% Ge. The gradient of about 0.8 at% Ge per cm was achieved over a length of 8 cm. 4. Conclusion Both Ge1−x Six mosaic crystals and Si1−x Gex crystals with gradient of composition could be grown using the modiﬁed Czochralski technique to produce the diffracting elements for the MAX gamma ray telescope. To achieve a mosaicity of up to 60

, special growth conditions were needed which caused the interface perturbations and the development of the cellular structure. The morphology of the cellular structure depends on the growth direction and inﬂuences the mosaicity and the diffraction efﬁciency of the crystals. Although many elements have a diffraction efﬁciency of up to 20%, some elements show much lower diffraction efﬁciency. It was found that the overall efﬁciency of the lens is about 8.1 ± 0.7%, which is more than twice lower than the theoretically predicted efﬁciency. Further experiments are needed to improve the reproducibility of the growth process of Ge1−x Six mosaic crystals. In addition to mosaic crystals, the use of Si1−x Gex crystals with a gradient of composition could be a promising way to improve the diffraction efﬁciency of Laue lens for MAX. Further experiments are planned to study the inﬂuence of crystal quality and crystal composition on the diffracting properties of such composition-gradient crystals. References 1. Abrosimov, N.V., Rossolenko, S.N., Alex, V., Gerhardt, A., Schr¨oder, W.: J. Crystal Growth 166, 657–662 (1996) 2. Abrosimov, N.V., Rossolenko, S.N., Thieme, W., Gerhardt, A., Schr¨oder, W.: J. Crystal Growth 174, 182–186 (1997) 3. Abrosimov, N.V., L¨udge, A., Riemann, H., Schr¨oder, W.: J. Crystal Growth 237–239, 356–360 (2002) 4. Abrosimov, N.V., Erko, A., Kurlov, V.N., Rossolenko, S.N., Rasin, I.G., Riemann, H.: Bull. Russian Academy of Sciences: Physics 68, 955–959 (2004) 5. Courtois, P., Andersen, K., Bastie, P.: Experimental Astronomy (this issue) (2006) 6. Erko, A., Abrosimov, N.V., Alex, V.: Crystal Res. Technol. 37, 685–704 (2002) 7. Halloin, H., von Ballmoos, P., Evrard, J., Skinner, G.K., Hernanz, M., Abrosimov, N., Bastie, P., Hamelin, B., Lonjou, V., Alvarez, J.M., Jean, P., Kn¨odlseder, J., Smither, R.K., Verdenne, G.: Proc. SPIE 5168, 471–481 (2004) 8. Hamelin, B., Bastie, P.: Proc. SPIE, 4786, 29–39 (2002) 9. Hurle, D.T.J., Cockayne, B.: In: Handbook of Crystal Growth, Hurle, D.T.J. (ed.), (Elsevier Science B.V., 1994), pp. 99–211 (1994) 10. Rudolph, P.: Crystal Res. Technol. 40, 7–20 (2005) 11. Smither, R.K., Saleem, K.A., Roa, D.E., Beno, M., Kurtz, C., Khounsary, A., Abrosimov, N.: Rev. Sci. Instrum. 76, 123107 (2005) 12. Smither, R.K., Saleem, K.A., Roa, D.E., Beno, M., von Ballmoos, P., Skinner, G.: Experimental Astronomy (this issue) (2006) 13. von Ballmoos, P., Halloin, H., Evrard, J., Skinner, G., Abrosimov, N., Alvarez, J., Bastie, P., Hamelin, B., Hernanz, M., Jean, P., Kn¨odlseder, J., Lonjou, V., Smither, R.K., Verdenne, G.: New Astronomy Rev. 48, 243–249 (2004) 14. von Ballmoos, P., Halloin, H., Skinner, G.K., Smither, R.K., Paul, J., Abrosimov, N.V., Alvarez, J.M., Astier, P., Bastie, P., Barret, D., Bazzano, A., Blanchard, A., Boutonnet, A., Brousse, P.,. Gordier, B., Courvoisier, T., DiCocco, G., Giuliani, A., Hamelin, B., Hernanz, M., Jean, P., Isern, J., Kn¨odlseder, J., Laurent, P., Lebrun, F., Marcowith, A., Martinot, V., Natalucci, L., Olive, J.-F., Pain, R., Sadat, R., Sainct, H., Ubertini, P., Vedrenne, G.: Proc. SPIE 5168, 482–491 (2004) Springer

Exp Astron (2005) 20:195–200 DOI 10.1007/s10686-005-9018-x ORIGINAL ARTICLE

Copper mosaic crystals for Laue lenses P. Courtois · K. H. Andersen · P. Bastie

Received: 18 November 2005 / Accepted: 21 December 2005 C Springer Science + Business Media B.V. 2006

Abstract Large single crystals of copper with an uniform and very narrow mosaic spread between 25 seconds and 1 minute of arc are now available at I.L.L. This result is of great interest in the construction of a Laue lens for astrophysical applications for which such quality copper single crystals may be used. The X-ray diffraction properties of copper single crystals produced at I.L.L. were studied for x-ray energies ranging from 100 keV to 400 keV. Several monocrystalline plates with different thicknesses and mosaic distributions were then prepared from the as-grown crystals in order to measure their diffraction efﬁciency as a function of energy. As expected, the value of the peak reﬂectivity depends on the crystal thickness. Reﬂectivity measurements show the excellent properties of copper crystals for gamma-ray diffraction. A peak reﬂectivity of 24% was measured at 220 keV from a copper single crystal of 3.75 mm thickness having a mosaic spread of 1.5 minutes of arc. Some technical aspects on the preparation of copper single crystal plates are also discussed. Keywords Copper . Crystal growth . Mosaic crystal . Lens . X-ray diffraction . Reﬂectivity

1. Introduction A gamma-ray Laue lens for astrophysical applications based on mosaic copper single crystals requires crystals of high quality, with a homogeneous mosaic spread of less than 30 seconds of arc in order to achieve efﬁcient focusing of high-energy gamma-rays (100 keV – 1 MeV) onto a small detector volume [1]. The aim of the present work is to show the feasibility of making such a gamma Laue lens which is a real challenge. We present recent progress in the growth of high quality copper single crystals at I.L.L. and we brieﬂy discuss the difﬁculties P. Courtois () · K. H. Andersen Institut Laue Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble Cedex 9, France e-mail: [email protected] P. Bastie Laboratoire de Spectrom´etrie Physique de Grenoble, UMR 5588 du CNRS, Universit´e Joseph Fourier, GrenobleI, BP 87, 38402 Saint Martin d’H`eres cedex, France Springer

196 2.5

Copper Single Crystals Mo saic Spread (minutes of arc)

Fig. 1 X-ray mosaic spread distribution (fwhm) as a function of the vertical position on the as-grown copper single crystal, averaged over the horizontal cross-section

Exp Astron (2005) 20:195–200

2

1.5

june 2004

1

0.5 july 2005

0 0

5 10 15 20 relative position on the crystal (cm)

involved in the preparation of crystal pieces of small dimensions. We report hard X-ray scattering investigations of Cu200 in transmission geometry in the energy range from 100 to 350 keV showing the excellent quality of the crystals.

2. Crystal growth Faced with a growing demand for mosaic copper crystals for both neutron monochromators at I.L.L. [2] and Laue lenses for astrophysical applications [1;3], the I.L.L. has started a development program to optimize the crystal growth process in order to produce in-house high quality copper single crystals of large dimensions. This has been successful and detailed studies using hard X ray diffraction [4] have shown that it is now possible, since July 2005, to grow on a regular basis large ingots of 25 cm length and 8 cm diameter with a very narrow and uniform mosaic spread close to 30 seconds (Figure 1).

3. Crystal reﬂectivity The use of transmission geometry for the Laue Lens requires a careful optimization of the crystal thickness, with respect to both the (maximum) peak reﬂectivity and the integrated intensity. The optimum thickness also varies with x-ray energy. The peak reﬂectivity and the optimum thickness can be calculated using the model of the ideal imperfect mosaic crystal from Darwin’s theory [6]. However, because of primary and secondary extinction processes which are very difﬁcult to predict, the experimental peak reﬂectivity is generally smaller than the theoretical value and the optimum thickness may also be different from theory. It is interesting, although not entirely trivial, to test the diffraction efﬁciency of the copper crystals using the hard X-ray facility at the I.L.L., which provides a white beam with energies close to the energies of the X-ray and Gamma-Ray continuum spectra from celestial sources. 3.1. Sample preparation Monocrystalline plates having different thicknesses and mosaic spreads were then cut from the as-grown crystals using EDM machining. The direction of cutting was parallel to the Cu(022) crystal planes in order to obtain Cu pieces with the Cu(200) crystal planes Springer

Exp Astron (2005) 20:195–200

Cu(200)

Reflectivity (arb.units )

Fig. 2 Peak proﬁles obtained from a copper single crystal before (the as-grown crystal) and after cutting a crystal plate of 4 mm thickness. EDM machining induces surface damages

197

After cutting t = 4 mm As-grown crystal

fwhm = 3.5 '

fwhm = 1 '

angle position (arb. units)

before etching

Cu(200)

after etching

Reflectivity (arb. uni ts.)

Fig. 3 Peak proﬁles from copper crystals pieces of 8 mm thickness before and after chemical etching. At least, a thickness of 0.6 mm has to be removed in order to obtain crystal pieces of high quality

t = 7.4 mm fwhm = 1.1 min

t = 8 mm fwhm = 2 min

angle position (arb. units.)

perpendicular to the surface. Detailed studies using hard X-ray diffraction have shown that spark erosion induces damage at the surface of the copper single crystal [6]. Figure 2 shows hard X-ray diffraction patterns before and after cutting a crystal of 4 mm thickness. After cutting, we observe that the mosaic has a complex structure giving rise to large tails in the peak proﬁle and a larger width. The tails of the peak are weakened when cutting thicker crystals but defects are still present as indicated by the increase of the mosaic spread (Figure 3). The effect can be reduced by properly optimizing the machining conditions (minimum power and intensity) in order to minimize the electric discharge into the crystal but the problem of the formation of perturbed layers remains unsolved. Several methods were then tested with the aim of removing surface damage which are detrimental for X-ray diffraction applications. Since copper crystal is a very soft material, the use of classical mechanical machining or polishing is very difﬁcult, leading to other defects in the crystal structure such as plastic deformation. Although it is a rather slow process, chemical etching was found to be the best way in order to remove the perturbed layers. Figure 3 shows peak proﬁles before and after chemical etching from a crystal of 8 mm thickness. After the removal of 0.6 mm thickness (i.e. 0.3 mm on each side), the peak proﬁle is better, characterized by a Gaussian distribution and a mosaic spread very close to the original crystal, i.e.1 minute of arc. Springer

198 Fig. 4 Schematic representation of the quantities measured in hard X-ray diffractometry for reﬂectivity measurements. I0 = intensity of the direct beam, Id = intensity of the diffracted beam and It = intensity of the transmitted beam

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I0

θΒ <200>

t Id

It

Thus, Starting from an as-grown crystal with a mosaic spread of 1.5 minutes of arc, we cut several pieces having different thicknesses (2 to 13 mm). Each crystal was etched in order to remove a total thickness of 1 mm. In this way, we successfully prepared several crystals having a mosaic spread around 1.5 minutes of arc. 3.2. Experiments We used the hard X-ray facility at I.L.L. which provides a white beam of X-ray energies ranging from 100 keV to 400 keV [4], to measure the peak reﬂectivity from the Cu200 reﬂection in transmission geometry as a function of both thickness and energy. The X-ray beam was 0.5 mm wide and 2 mm high and X-ray beam intensities were recorded using a cooled germanium detector having a high energy resolution (0.5% at 200 keV). The orientation of the Cu200 planes (Bragg angle θ B ) with respect to the incident X-ray beam allows the selection of a given energy band of diffracted photons which depends on the mosaic structure of the crystal (Figure 4). Both, the intensity of the incident beam I0 and the Bragg diffracted intensity Id were measured. The intensity of the transmitted beam It was also recorded. The peak reﬂectivity r is given by the ratio Id /I0 after subtraction of the detector background. 3.3. Principal results and discussion Typical intensity curves obtained from a copper crystal of 3.75 mm thickness are illustrated in Figure 5. It can be seen that the depth of the dip in the transmitted beam intensity corresponds

Fig. 5 Intensities of the direct, diffracted and transmitted beams measured onto the Ge detector from a copper crystal of 3.75 mm of thickness

1500 Direct beam (I ) 0

Transmitted beam (It )

Counts / 600s

1000

Cu(200) t = 3.75 mm

500 Diffracted beam (Id )

0 210

215

220 Energy (keV)

Springer

225

230

Exp Astron (2005) 20:195–200 26 E = 300 keV - t E = 250 keV - t E = 200 keV - t

Peak reflectivity (%)

Fig. 6 Peak reﬂectivity as a function of the crystal thickness for three diffracted energies 200, 250 and 300 keV. The corresponding theoretical values of the optimum thickness tth are given for comparison

199

22

th th th

= 3.9 mm = 3 mm = 2.2 mm

18

14 Cu(200) fwhm = 1.5 ' 10

0

2

4

6

8

10

12

thickness (mm)

Fig. 7 Peak reﬂectivity as a function of the energy from copper single crystal of thickness 3.75 mm and 5.65 mm

30 Cu(200) fwhm = 1.5 '

Refl ectivity (%)

25

20

15 t = 0.565 cm

10

t = 0.375 cm 5 100

150

200

2 50

300

350

Energy (keV)

exactly to the diffracted intensities showing that no parasitic scattering occurs. This result conﬁrms the excellent quality of the crystals. In Figure 6, the peak reﬂectivity as a function of the crystal thickness is reported for three diffracted energies 200, 250 and 300 keV, as well as the theoretical optimum thickness tth calculated using the model of ideal imperfect mosaic crystal [6]. As expected from the theory, the peak reﬂectivity exhibits a maximum value and then decreases with increases thickness, because of absorption. The experimental optimum thickness is close to the theoretical value tth . Figure 7 shows the peak reﬂectivity as a function of the energy for crystals of thickness t = 3.75 mm and t = 5.65 mm. The peak reﬂectivity increases with energy up to a saturation value of 24% at 220 keV for t = 3.75 mm and 22% at 300 keV for t = 5.65 mm. The width of the plateau observed in the measured curves depends on the thickness indicating that absorption plays an important role in the limitation of the reﬂectivity. We note, however, that the value of reﬂectivity exceeds 20% for a wide range of energies close to 100 keV. Springer

200

Exp Astron (2005) 20:195–200

4. Conclusion and perspectives Copper single crystals with a mosaic spread of 30 seconds of arc are now available at I.L.L. This result is of great interest in the construction of a Laue lens for astrophysical applications for which such quality copper single crystals may be used. Chemical etching was found to be necessary in order to remove damage induced by EDM machining at the surface of the copper crystals. Reﬂectivity measurements using a white beam of x-ray energies ranging from 100 keV to 400 keV conﬁrm the excellent properties of copper single crystals and show the feasibility of making a Laue lens based on mosaic copper single crystals. The next step of this work will be the measurements of the absolute reﬂectivity of copper crystals for x-ray energies up to 900 keV at the European Synchrotron Radiation Facility (ESRF). In the future, we will also study the possibility of using bent copper single crystals which are interesting in order to improve the focusing properties of the lens.

References 1. Barri`ere, N. et al.: Experimental Astronomy 20, DOI:10.1007/s10686-006-9058-x 2. Courtois, P., Hamelin, B., Andersen, K.H.: Nuclear Instruments and Methods in Physics Research A529, 157–161 (2004) 3. Pisa, A.: SPIE Proc. 5536, 39 (2004) 4. Bastie, P., Hamelin, B., Courtois, P.: J.de Phys. IV France 10, 10–21 (2000) 5. Courtois, P.: ILL Annual Report, 100–101 (2002) 6. Schneider, J.R.: Nuclear Science Applications 1, 227–27 (1981)

Springer

Exp Astron (2005) 20:201–210 DOI 10.1007/s10686-005-9019-9 ORIGINAL ARTICLE

High diffraction efﬁciency, broadband, diffraction crystals for use in crystal diffraction lenses Robert K. Smither · Khaliefeh Abu Saleem · Dante E. Roa · Mark A. Beno · Peter Von Ballmoos · Gerry K. Skinner

Received: 9 November 2005 / Accepted: 21 December 2005 C Springer Science + Business Media B.V. 2006

Abstract A major goal of the MAX program is to detect and measure gamma rays produced following the nuclear reactions that take place in a supernova explosion. To detect a reasonable number of supernovae, sensitivities of the order of a few times 10-7 γ cm-2sec-1 are needed – much better than possible with current instruments. The approach in the MAX program is to use a crystal diffraction lens to collect photons over a large area and concentrate them on a small well-shielded detector, greatly improving the signal to noise ratio. The crystals need to have both high diffraction efﬁciency and a relatively broad energy bandwidth. With mosaic crystals there is a trade-off between bandwidth and diffraction efﬁciency – one can have either high efﬁciency or large bandwidth, but not both without losing too much intensity through atomic absorption. A recent breakthrough in our understanding of crystal diffraction for high-energy gamma rays has made it possible to develop crystals that have both high diffraction efﬁciency and a relatively broad energy bandwidth. These crystals have near perfect crystal structure, but the crystalline planes are slightly curved. Such curved planes can be obtained in 3 different ways, by using mixed crystals with a composition gradient, by applying a thermal gradient, and by mechanically bending a near perfect crystal. A series of experiments have been performed on all three types of crystals using high-energy x-ray beams from the Advanced Photon Source at the Argonne National Laboratory. Experiments performed at 3 energies, 93 keV, 123 keV and 153 keV, with both the thermal gradient Si crystals and with the mechanically bent Si crystals, demonstrated that one can achieve diffraction efﬁciencies approaching 100% with moderate energy bandwidths ( E/E = 1.4%) and low atomic absorption (transmission = 0.65), in excellent agreement with theory. The use of this type of diffraction crystal is expected to increase the sensitivity of gamma ray telescopes by a factor of 5 over that possible with normal mosaic crystals.

Keywords Gamma-ray astronomy · Crystal diffraction · Thermal gradient · Bent crystal

R. K. Smither · K. A. Saleem · D. E. Roa · M. A. Beno · P. V. Ballmoos · G. K. Skinner Argonne National laboratory Springer

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1. Introduction In 1981, a program was started at Argonne National Laboratory to investigate the feasibility of constructing a Laue type crystal diffraction lens to focus high energy x-rays and gamma rays in the energy range from 100 keV to 1 MeV. Several different approaches were considered theoretically and partially tested [1–4]. The most successful was a set of concentric rings of single crystals where the crystals in each ring used a different set of diffraction planes to focus the incident radiation. By adjusting the radius of each ring, their foci could be superimposed in single spot. The ﬁrst full-scale lens (55 cm dia.) was built at Argonne for the Department of Energy (DOE) Treaty Veriﬁcations Program. This lens used 8 crystal rings of Ge and made use of 8 different sets of crystalline planes to focus gamma-rays. The lens was tested with 8 different energies from 276.32 to 661.65 keV from 3 different radioactive isotopes. The lens demonstrated the feasibility of the concept and led to a collaboration between Argonne and CESR, Toulouse [5–8] This led to the demonstration of a lens for astrophysics in the CLAIRE program [8]. The Laue lenses built in these collaborations all used mosaic crystals, where one had to trade diffraction efﬁciency against energy bandwidth and visa versa. The success of Claire program has led to the proposal of the MAX space mission [7] As discussed by von Ballmoos et al. [7] the requirement to observe a reasonable number of supernovae per year places important requirements on the sensitivity. A factor of four improvement in diffraction efﬁciency allows one to see supernova in 8 times as many galaxies. Ideally, the crystals used in the lens should have both high diffraction efﬁciency and a relatively broad energy bandwidth. The later also implies a relatively broad acceptance angle for the incident gamma rays. With mosaic crystals there is a trade off between bandwidth and diffraction efﬁciency that limits the product of these two parameters. The maximum diffraction efﬁciency for a thick mosaic crystal is 0.50, but in order to achieve even a 0.30 diffraction efﬁciency with a modest energy bandwidth requires a thick crystal and a large loss of intensity by absorption. The product of the diffraction efﬁciency and the transmission through Laue crystals of Si and Ge, rarely exceeds 0.10 and is closer to 0.05 for higher energy gamma rays. One can do better with higher Z crystals, but it is very difﬁcult to grow the near perfect crystals of these high Z materials that is needed to apply the “bent-crystal” approach. A recent breakthrough in our understanding of crystal diffraction for high-energy gamma rays has made it possible to develop crystals that have both high diffraction efﬁciency and a relatively broad energy bandwidth [9–15]. These crystals have near perfect crystal structure, but the crystalline planes are slightly curved. The curvature has a dramatic effect on the diffraction efﬁciency of the crystal. A particular wavelength photon passes through a Laue crystal having curved planes until it ﬁnds a region where the Bragg condition (nλ = 2dsin θ ) is satisﬁed. At this point the photon is diffracted. After diffraction, the photon does not encounter another region where the Bragg condition is satisﬁed, so it exits the Laue crystal in the diffracted direction. A photon of a different wavelength will pass through the crystal until it reaches a different region where it’s Bragg condition is met, where it too is diffracted and becomes part of the diffracted beam. The difference between the curved plane crystal and a mosaic crystal is that after the ﬁrst diffraction, the diffracted beam in a curved plane crystal, will not see any crystalline planes that have the right Bragg angle to diffract them back into the undiffracted beam direction. This allows one to approach 100% diffraction efﬁciency.1 The net effect is a crystal that has both a high diffraction efﬁciency and a broad energy

1Note that efﬁciencies of diffraction quoted here do not include the effect of normal atomic absorption, which

must of course also be taken into account. Springer

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bandwidth, as well as a broad acceptance angle for a monochromatic beam. The crystal can also be thin enough that the transmission is high.

2. Crystals with curved crystalline planes This type of crystal can be produced in 3 different ways – (i) they can be grown as a twocomponent crystal where the relative concentration of two components is varied during growth [16–18], (ii) a thermal gradient can be applied to a near perfect crystal [19] and (iii) they can be produced by bending a near perfect crystal [20]. All three approaches have been explored in a series of experiments at Argonne National Laboratory with x-ray beams from the Advanced Photon Source. Figure 1(a) shows the curved crystalline planes in a two-component crystal of Si-Ge, where the higher concentration of Ge is at the top of the crystal. This is compared with the curved crystalline planes in a thermal gradient crystal where the hot surface is at the top of the crystal. In cross-section the crystal planes of a bent crystal will be appear similar to the latter but their form will be cylindrical, in contrast to the spherical shape found in the two-component and thermal gradient crystals. When an x-ray or gamma ray beam that is not monochromatic passes through a gradient crystal, the incident photons see a succession of crystalline planes at progressively changing incidence angle. Thus slightly different wavelengths are diffracted as a function of the distance the beam has traversed. This is illustrated in Figure 2. If a very small photon beam is incident on the convex side of the crystalline planes in a Laue crystal, it results in a divergent diffracted beam. Conversely, if it is incident on the concave side of the crystalline planes, a converging diffracted beam is produced. This effect can be used to focus the diffracted beam. A sharp focus will occur only for a beam with a small area. If one is diffracting 100 keV gamma rays from the [111] crystalline planes of silicon with a curvature of 5 arc sec per cm the focus will occur at a distance of 8 m. After that the diffracted beam will diverge. At 100 m from the diffraction crystal the gamma ray beam will have expanded to a width that is 2.5 mm larger than the original beam. A large area beam will show this increase in size at 100 m as well, as

Fig. 1 (a) The curved crystalline planes in a Si-Ge two-component crystal where the higher concentration of Ge is at the top of the crystal. (b) The curved crystalline planes in a thermal gradient crystal where the hot surface is the top surface. The planes of a bent crystal will be similar to (b) in cross-section Springer

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Fig. 2 (a) The diffraction of a gamma ray beam that is incident on the convex side of the curved crystalline planes. (b) The diffraction of a gamma ray beam that is incident on the concave side of the curved crystalline planes

will a beam incident on convex crystalline planes. This effect is small but it could become important for lenses with very long focal lengths.

2A. Measurements with thermal gradient crystals The major advantage of using thermal gradients to generate curved crystalline planes is that one can change the curvature by changing the thermal gradient. Thus one can measure the diffraction efﬁciency and FWHM of the rocking curve as a function of curvature for an individual crystal. If very perfect crystals such as Si are used, the curvature of the crystalline planes, which is spherical, can be very uniform. In the Argonne experiments the thermal gradient is applied by placing the silicon crystal between two large copper blocks that can either be heated or cooled. Thus the gradient applied to the crystal can be reversed without moving or changing diffraction system. This is illustrated in Figure 3 where a monochromatic x-ray beam from a monochromator enters from the right, is diffracted by the crystal, and detected by a photo diode. The undiffracted beam is monitored by a second photo diode. In these experiments, the thermal gradient is applied to a 1 cm cube of silicon. If the top of the crystal is cold and the bottom is hot, the x-ray beam is incident on the concave side of the crystalline planes, resulting in some focusing of the diffracted beam. Results from this Cold Top (CT) experiment with a 92.6 keV x-ray beam, are shown in Figure 4. The graphs are labeled with the temperature difference, T, applied to the crystal. The x-axis is the incidence angle of the diffraction process in arc sec and is deﬁned as zero at the center of

Fig. 3 The experimental set up use in the thermal gradient experiments Springer

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Fig. 4 Data taken with a pure silicon crystal using the [111] planes with the cold top geometry and a 92.6 keV x-ray beam. The thermal gradients, T, are in units of ◦ C/cm

the peak. Both the diffracted peak (solid circles) and the intensity of the undiffracted beam (hollow circles) are shown. Figure 4 shows a set of 12 rocking curves where a series of thermal gradients is applied. The diffraction efﬁciency, deﬁned as the ratio of the diffracted beam to the transmitted beam that exits the crystal when no diffraction occurs, is very small for zero thermal gradient but increases with increasing gradient to reach 95%. The FWHM increases almost linearly with thermal gradient. At the higher thermal gradients the rocking curve becomes ﬂat topped suggesting that the curvature is quite uniform. Springer

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3. Bent silicon crystals Although the thermal gradient crystals are very useful for exploring the use of diffraction crystals with curved crystal planes, they are impractical for use in astrophysics. The power requirements for a large lens would be many kilowatts. The use of elastically bent crystals is much more attractive. Bent crystals of silicon were tested in a recent synchrotron run at the Advanced Photon Source. The experimental set up is shown in Figure 5. The crystal plate is pressed against a curved surface. The pressure was applied to the crystal through a soft material, either rubber or cardboard. In some experiments a soft material was used between the crystal plate and the curved surface as well. A typical rocking curve for a bent silicon crystal using the [111] crystalline planes to diffract a 93 keV x-ray beam is shown on the left, in Figure 6. Both the diffracted (ﬁlled circles) and the undiffracted (open circles) counting rates are shown. The form of the rocking curve and its FWHM of 31.8 arc sec, are very similar to the one in Figure 4, for a thermal gradient of 77◦ C/cm (FWHM 33 arc sec), shown on the right. Both curves are ﬂat topped. The maximum diffraction efﬁciency of the bent crystal (0.997) diffraction is slightly higher than for the thermal gradient case (0.955). The dimensions of the bent silicon crystal were quite different from the 1 cm cube used in the thermal gradient experiments. The bent crystal was a single crystal 1 mm thick, 1 cm wide and 2 cm deep. The x-ray beam passed through the 2 cm dimension. The actual curvature per cm in the bent crystal (16 arc sec per cm) was one half of that in thermal gradient crystal (33 arc sec per cm). This lower curvature is better suited for the higher energy gamma rays. The x-ray beam from the monochromator used in the bent crystal experiments was 0.3 mm high and 2 mm wide. This is to be compared with the beam size of 1 mm high and 1 mm wide used Fig. 5 Is a schematic of the experimental set up

Fig. 6 Comparison of rocking curves using the [111] crystalline planes to diffract a 93 keV x-ray beam. Left: a bent crystal. Right; comparison measurements from Figure 4 for a thermal gradient crystal Springer

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Fig. 7 A plot of maximum diffraction efﬁciency verses the parameter α, deﬁned as the ratio of the extinction length x the curvature per unit length, divided by the Darwin width, for the bent crystal data. The solid circles are the Si [111] data and the open circles are the Si [220] data. The solid line is the theoretical limit for the reﬂectivity of a silicon [111] and [220] crystal

in the thermal gradient experiments. The smaller vertical height made it possible to work at lower curvatures without distorting the rocking curve. The slight asymmetric shape of the bent crystal rocking curve is caused by slightly different bend at the ends of the crystal. This reﬂects the difﬁculty in controlling curvature over the whole crystal. Figure 7 is a plot of the maximum diffraction efﬁciency as a function of a parameter α, deﬁned as the ratio of the extinction length in mm, times the curvature of the crystalline planes in arc sec per mm, divided by the Darwin width in arc sec. For Si, the extinction length for 93 keV x-rays is about 0.227 mm; the Darwin width is about 0.57 arc sec. Thus αis about 1.0 for a curvature of 2.5 arc sec per mm. The curvature needed for a given value of α decreases with the square of the energy, so the above value of 2.5 becomes 0.92 arc sec per mm at 153 keV. The theoretical limit [9–15] on the reﬂectivity as a function of α, is plotted as a solid line and given by I Re f = [1 − ex p(−2π/α)] The measured diffraction efﬁciency is always lower that the reﬂectivity because the diffraction efﬁciency includes the effect of the opening angle and energy spread of the synchrotron beam as well as any imperfections in the crystal and/or imperfection in the bending of the crystal. For very low values of curvature, the diffraction efﬁciency drops to ∼0.5, as is expected for a perfect, unbent crystal. The opening angle of the x-ray beam, about 2 arc sec, also plays a part in this decrease; if its effect is removed, the low curvature points move up and to the left. 4. Comparison of the different methods Apart from use of thermal gradients or mechanical bending, the third way to create curved crystalline planes in near perfect diffraction crystals is to grow a two-component crystal where the relative concentration of the two components changes as the crystal is grown. The Springer

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Fig. 8 The measured diffraction efﬁciency as a funtion of the curvature, θ/ L, times the extinction length divided by the Darwin Width for a perfect Si crystal. Circles show results for Si crystals in a thermal gradient experiment at 92.6 keV and the squares show the 153 keV data. Open and ﬁlled symbols are for the Cold Top and Hot Top thermal gradient data, respectively. The other sysmbols are data points from [9] for mixed Si-Ge crystals (+, ×.#,∗ correspond to 100; 120, 160 and 200 keV respectively)

best examples of the two-component type crystal have been grown at the Institute for Crystal Growth in Berlin [17–19]. They were Si-Ge crystals with starting concentrations of 3 to 7 percent germanium. Their properties were published in Keitel’s thesis [9] and in a series of articles [9–16]. The maximum diffraction efﬁciency obtained at Argonne in the thermal gradient experiments using pure Si crystals [20] are plotted in Figure 8 as a function of the parameter α deﬁned above. Data from Keitel’s thesis [9], for [111] diffraction of Si-Ge crystals are shown for comparison. The data in Figure 8 can be compared with those for the bent crystal data in Figure 7. The data points at low curvature in the bent crystal data are higher and do not drop much below the value of 0.5 expected in this limit. This better agreement with theory is believed to be due to the smaller vertical size of the incident x-ray beam, 0.25 mm as compared to 1.0 mm (and thus the smaller opening angle of the x-ray beam) for the thermal gradient experiments.

5. Gradient crystals for satellite telescopes The Claire balloon-based telescope [8] had a focal length limited to a few meters and was designed with rings of crystals using different lattice planes to concentrate photons within a single narrow energy band. Formation ﬂying satellite experiments now being planned, such as MAX [7] will have much larger focal lengths and larger lens radii. One of the favored designs uses only a few of the lowest diffraction orders in large diameter rings, each ring covering a slightly different energy band. When these overlapping responses are combined they cover one or more bands several hundred keV wide centered on energies of astrophysical interest. Springer

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Table 1 The optimized diffraction efﬁciency, transmission, their product and the effective area of a 200 cm radius by 2 cm wide ring. θ is the total curvature of the crystalline planes Energy keV

Thickness mm

θ arc sec

Diffraction efﬁciency (Diff. eff.)

Transmission (Trans.)

Diff. eff. × Trans

Effective Area cm2

80 100 150 200 400 600 800 1000 1200 1500 2000

5.5 6.5 10.0 11.5 18.5 24.0 30.0 35.0 39.0 46.0 56.0

50.9 40.7 27.2 20.4 10.18 6.79 5.09 4.07 3.40 2.72 2.04

0.899 0.885 0.942 0.852 0.786 0.736 0.713 0.688 0.661 0.640 0.606

0.747 0.759 0.706 0.703 0.650 0.628 0.598 0.584 0.577 0.562 0.545

0.672 0.672 0.665 0.599 0.511 0.462 0.427 0.402 0.381 0.360 0.330

1687 1686 1670 1504 1283 1160 1072 1009 956 904 828

A 200 cm-radius ring of Si crystals using the [111] planes to focus 400 keV gamma rays will have a focal length of 202.5 m. If the radial dimension of the crystals in the ring is 2 cm, than the area the ring will be 2514 cm2 . The 2 cm radial dimension will cover an energy range of 1 percent of the gamma ray energy, 4 keV, which corresponds to a Bragg angular change of 10.2 arc sec. Thus the angular bandwidth of the crystals should be at least 10.2 arc sec to cover the corresponding change in energy. The next ring would have a radius of 204 cm and cover the next 4 keV of the energy range, etc. The thickness, T, and curvature per unit length, θ/ L, of the crystals can be chosen to give the maximum product of the diffraction efﬁciency and transmission, the product of T × θ/ L being held at 10.2 arc sec. For a [111] Si crystal at 400 keV one ﬁnds optimum values of T = 18.5 mm and θ/ L = 0.550 arc sec/mm. This would result in a diffraction efﬁciency of 0.786 and a transmission of 0.650, giving for the product of these two terms = 0.511 and an effective area of this 200 cm radius ring with 2 cm × 2 cm × 1.85 cm crystals of 1285 cm2 . The gamma rays from a distant supernova could have an intensity of 2 to 4 photons per cm2 in 107 sec. Thus in 106 sec one could expect to focus 257 to 514 photons onto the detector from this ring. Larger rings and/or more rings would increase this number, but this performance is already attractive. Table 1 gives the results of similar optimization of a 200 cm radius ring with 2 cm by 2 cm area crystals for a range of gamma ray energies. Interestingly, one continues to get relativity high values for the product of the diffraction efﬁciency times the transmission even for energies as high as 2 MeV. The challenge is to demonstrate that this efﬁciency can be reached in practice. Acknowledgments The authors would like to thank Ruben Khachatryan of the Advanced Photon Source Optics Shop for orienting and cutting the silicon crystals used in the experiment and Peter Chupas for assisting in setting up the synchrotron experiment. This work was supported by the U.S. Department of Energy, Basic Energy Sciences, under contract no. W-31-109-Eng-38.

References 1. Smither, R.K.: Method for Focusing and Imaging X-Rays and Gamma-Rays with Diffraction Crystals, Sym. On Future X-Ray Experiments in the 80’s, GSFC, Oct. 1981, NASA Tech. Mem. No. 83848 (1981) Springer

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2. Smither, R.K.: New Method for Focusing X-Rays and Gamma-Rays, Rev. Sci. Instrum. 44, 131–141 (1982) 3. Smither, R.K.: Gamma Ray Telescope Using Variable-Metric Diffraction Crystals, 11th Texas Sym. On Relativistic Astrophysics, Austin Texas, Dec. 1982. Ann. of New York Acad. Sci. 44, 673 (1983) 4. Smither, R.K.: U.S. Patent No. 4,429,411, Instrument and Method for Focusing X-Rays, Gamma-Rays and Neutrons’ (1984) 5. Smither, R.K. et al.: Review of crystal diffraction and its application to focusing energetic gamma rays. Experimental Astronomy 6, 47–56 (1995) 6. Smither, R. K. et. al.: Crystal diffraction lens telescope for focusing nuclear gamma rays. Proc. SPIE, 2806, 509 (1996) 7. Ballmoos, P. von. et al.: MAX – a gamma-ray lens for nuclear astrophysics. Proc. SPIE 5168, 471 (2004) 8. Halloin, H. et al.: CLAIRE gamma-ray lens: ﬂight and long distance test results. Proc. SPIE 5168, 471 (2004) 9. Keitel, S.: Ph.D. Thesis, Untersuchung von Si(1−x) Ge(x) -Gradientenkristallen und in-situ getemperten Silizium-Einkristallen als Monochromatoren f¨ur hochenergetische Synchrotonstrahlung, Physics Department, University of Hamburg (1999) 10. Keitel, S. et al.: Si1−x Gex gradient crystals: a new monochromator materiaal for hard X-rays. Nucl. Instrum. Methods Phys. Res. A 414, 427 (1998) 11. Penning P., Polder, D.: Anomalous transmission of X-Rays in elastically deformed crystals. Philips Res. Repts. 16, 419 (1961) 12. Kato, N.: Pendell¨osung fringes in distorted crystals I. Fermat’s principle for bloch waves. J. Phys. Soc. Japan 18, 1785 (1963) 13. Kato, N.: Pendell¨osung fringes in distorted crystals II. Application to two-beam cases. J. Phys. Soc. Japan 19, 67 (1964) 14. Kato, N.: Pendell¨osung fringes in distorted crystals III. Application to homogeneously bent crystals, J. Phys. Soc. Japan 19, 971 (1964) 15. Balibar, F., Chukhovskii, F. N., Malgrange, C.: Dynamical X-Ray propagation: a theoretical approach to the creation of new wave ﬁelds. Acta Cryst. A 39, 387 (1983) 16. Malgrange, C.: X-Ray Propagation in distorted crystals: dynamical to kinematical theory. Cryst. Res. Technol. 37, 662 (2002) 17. Abrosimov, N.V., Rossolenko, S.N., Alex, V., Gerhardt, A., Schr¨oder, W.: Single crystal growth of Si(1−x) Ge(x) by the Czochralski technique. Journal of Crystal Growth. 166, 657–662 (1996) 18. Erko, A. et al.: On the feasibility of employing gradi¨ent kristal for high resolution synchrotron optics, Nucl. Instrum. Methods Phys. Res. A 375, 408–412 (1996) 19. Abrosimov, N.V., Rossolenko, S.N., Thieme, W., Gerhardt, A., Schroder, W.: Czochralski growth of Siand Ge-rich SiGe single crystals. Journal of Crystal Growth. 174, 182–186 (1997) 20. Smither, R., Abu Saleem, K., Beno, M., Kurtz, C., Khounsary, A., Abrosimov, N.: Diffraction efﬁciency and diffraction bandwidth of thermal gradient and composition gradient crystals, to be published in Rev. Sci. Instrum. 79, 1 (2005)

Springer

Exp Astron (2005) 20:211–217 DOI 10.1007/s10686-006-9026-5 ORIGINAL ARTICLE

An ‘‘ESA-affordable” Laue-lens Niels Lund

Received: 15 November 2005 / Accepted: 3 February 2006 C Springer Science + Business Media B.V. 2006

Abstract With ESA’s INTEGRAL mission gamma-ray astronomy has advanced to the point where major scientiﬁc advances must be expected from detailed studies of the many new point sources. The interest in developing focusing telescopes operating in the soft gamma-ray regime up to 1 MeV is therefore mounting rapidly. Telescopes based on Laue diffraction of gamma-rays from crystals appear as one promising route, although the practical difﬁculties of realizing a large scale Laue lens are certainly not small. In this paper I have attempted to develop an optimized lens design considering the size and mass constraints of a speciﬁc medium size launch vehicle. The introduction of the lens mass as a primary design driver has some surprising effects for the choice of material for the crystals and new tradeoff considerations are introduced. Keywords Instrumentation . Gamma-ray astronomy

1. Introduction Implicit in this study lies a number of assumptions and constraints: – The ﬁnancial boundary conditions for a ﬁrst space mission with a Laue lens. The validity of the Laue lens concept ought to be proven with a medium size mission. We accept here the mass and volume constraints of the Soyuz launcher [1]. – The INTEGRAL mission [9] has provided us with several hundred sources detected above the classical X-ray range. Most of these sources have been detected at the few mCrab level and requires an instrument with the same energy resolution as SPI [8] and about the same ﬂux collection power as IBIS/ISGRI [4, 7], but with much lower background for a deeper study of their spectra and time variability.

N. Lund Danish National Space Center, Juliane Maries Vej 30, DK-2100 Copenhagen Ø e-mail: [email protected] Springer

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– The large focal lengths of Laue lenses naturally lead us to a concept of formation ﬂying with a lens spacecraft and a detector spacecraft. Once the formation ﬂying concept is accepted we are conveniently free to choose the focal length based on the crystal properties. – The formation ﬂying conﬁguration can only be maintained at large distances from the Earth – near the Earth the station keeping is disturbed by the gravity gradient between the two spacecraft. A mission at the Lagrange point is conceptually appealing, but is expensive in terms of launch mass, communication constraints and a protracted launch phase. An elliptical orbit around the Earth with an orbital period of 7 days may offer an acceptable gravity gradient environment and be beneﬁcial regarding launch mass and communications [3]. – Rather than concentrating the lens response in a few energy bands which may appear particularly interesting today, I have chosen to optimize the lens for a continuous energy range between 200 and 1000 keV, with emphasis on the region around 511 keV. This choice may limit the sensitivity for certain spectral lines, but I am concerned about now designing a mission which is very speciﬁcally tailored to a limited range of astrophysical problems. – Given that the orbit must to go far away from the Earth the combined launch mass of the two spacecrafts (lens spacecraft and detector spacecraft) cannot be much higher than 2100 kg when basing the mission on the Soyuz ST launch vehicle. The dimensions at launch is limited to a diameter of 3.8 m and the height to 8 m. – In this study I have chosen not to consider imaging, but to go for the simplest possible focal plane design with just one (segmented) high-purity germanium detector. The dimension of this detector affects directly the lens design, I have assumed the diameter to be 60 mm. The detector thickness does not need to be speciﬁed at this stage.

2. A ﬁrst design The design calculations presented here are based on the formalism presented in [5]. Two key parameters are the diffraction efﬁciency and the absorbtion cross section for the crystal material, both of these are fundamental properties of the chemical element and both are functions of the photon energy. A third parameter, which can be modiﬁed and tailored by the crystal growth and preparation processes is the degree of disorder in the crystal. A certain, low level of disorder, mosaicity in the crystal structure is very beneﬁcial in order to maximize the integrated reﬂectivity of the crystals [2]. The mosaicity is usually characterized by the angular width of the reﬂectivity curve as the crystal is rotated past the Bragg angle. The response of a Laue lens to photons of a given energy peaks at a certain distance from the axis of the lens. We want our system to emphasize the response around 511 keV so for each crystal considered I have selected the focal length such that the ring diffracting 511 keV is placed at a radius of 180 cm, close to the maximum radius allowed by the launcher fairing. Higher energies, up to 1 MeV, will be diffracted by crystal rings lying at smaller radii (down to 92 cm), and lower energies, down to 200 keV will need crystals placed further out (out to 460 cm radius) – these latter ones will need to be placed on panels deployed after launch. When later comparing the qualities of various crystal candidates it is useful to recall that with these design choices the lenses all look exactly the same – the crystals diffracting any speciﬁc energy is lying in the same positions from lens to lens – only the focal length changes when switching from one crystal type to the other. To fulﬁll Braggs law for a lens of the above dimensions we will need a focal length of about 150 m – the precise value will depend on the d-spacing of the crystal material for the Springer

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213 Full lens area vs Energy. Fill factor: 0.85 Mosaic width 1’

4000

4000 Au (111) L: 174 m, M: 657 kg Ag (111) L: 174 m, M: 1098 kg Cu (111) L: 154 m, M: 1341 kg Ge (220) L: 148 m, M: 1855 kg Si (220) L: 142 m, M: 2442 kg

cm2

3500

3500

3000

3000

2500

2500

2000

2000

1500

1500

1000

1000

500

500

0

0 200

300

400

500

600

700

800

900

1000

Energy (keV)

Fig. 1 Effective area of full Laue lens, 1st order only, 85% crystal ﬁlling factor

lens. To achieve the highest throughput of the lens the mosaic width of the crystals should be chosen as large possible – keeping in mind that the mosaic width also leads to mosaic defocusing: the focal spot grows with increasing mosaic width. With our choice of detector diameter (60 mm) and focal length we can tolerate a mosaic width of one arcminute – at 150 m distance one arcminute corresponds to a displacement of 4 cm. This also means that we can use individual crystal elements of up to 4 cm diameter in the lens if we can reliably manufacture and handle this size of crystals. We can now calculate the response of a full, 9 m diameter, Laue lens covered 85 % with crystals of one arcminute mosaic width, and with the crystal thickness adjusted to maximize the peak reﬂectivity at each energy (see [5] for details). The result of this calculation is shown in Figure 1 for a number of candidate crystal materials. Only 1st order reﬂections are included in the calculations at this stage – higher orders will be included later. In the ﬁgures also the focal lengths and the total crystal mass for each lens is indicated. From Figure 1 one can draw some important conlusions: 1. 2. 3.

The ﬂux collection area of a full Laue lens is strongly emphasizing the lower energies. Looking only at the overall efﬁciency of ﬂux collection copper and silver appears as the best materials, while gold comes out best at energies above 400 keV. But surprisingly, considering also the crystal mass as a parameter, the advantages of gold as diffracting material for gamma rays suddenly becomes very apparent. The mass of crystals in the gold lens is only half of that in the copper lens and only a quarter of that of the silicon lens. Gold is light – silicon is heavy!! Measured in terms of diffraction cross section per gram, gold is way ahead of the other materials. The ordering of the materials is primarily decided by their atomic number, but the atomic packing density Springer

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4.

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also plays a role and there copper, silver and gold are close to peaks in the packing density distribution as function of the atomic number. Recalling that the maximum launch mass we have available using the Soyuz launcher is around 2100 kg we must conclude that we do not have the means to launch any of the lenses described in Figure 1. The mass allocation must ﬁrst be split between the detector and the lens spacecraft – maybe in the ratio 300 kg for the detector and 1800 kg for the lens, and then we must allow for all the systems and structure on the lens spacecraft. My guess is that we need to reduce the mass of the crystals to below 400 kg to have a chance to see the ends meet.

3. Weight saving In the ﬁrst calculations the thickness of the crystal was chosen to give the maximum intensity of the diffracted beam at each energy. This, however, is quite wasteful in terms of mass. Figure 2 shows a typical example of how the reﬂected power ﬁrst increases rapidly with increasing thickness, then reaches a ﬂat maximum and thereafter decreases slowly due to absorbtion in the crystal. One can note in Figure 2 that reducing the crystal thickness by a factor two from the peak reﬂectivity value only reduces the reﬂectivity by 15%. We shall accept this 15% loss in order to save a factor of two in the crystal weight. Another major weight saving can be achieved if we give up the idea that a Laue lens of necessity must be a nice complete disk. A full disk of the dimensions considered here would also need a very elaborate (and heavy) folding and deployment mechanism to ﬁt inside the Soyuz fairing. To save weight and make life easier for the mechanical engineers we will in the following consider a lens consisting of a hexagonal central part and six rectangular panels

Reflectivity as function of crystal thickness. Au(111), 511 keV, mosaic width 1 ’ 30

30

reflectivity (%)

1st order 1st order, half thickness 25

25

20

20

15

15

10

10

5

5

0

0 0

0.5

1

1.5 Thickness (mm)

Fig. 2 Reﬂectivity versus thickness for gold(111) at 511 keV Springer

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Taper lens: Crystal thickness and eff. lens area vs Energy. Fill factor 0.85. Mosaic 1 ’ 1400

7

1200

6

1000

5

800

4

600

3

400

2

200

1

0

Crystal thickness (mm)

Lens area (cm2)

Au (111) L: 174 m, M: 246 kg Ag (111) L: 174 m, M: 358 kg Cu (111) L: 154 m, M: 401 kg

0 200

300

400

500

600

700

800

900

1000

Energy (keV)

Fig. 3 Effective area of “ﬂower lens” with the crystal thickness tapered to save weight and maintain a constant effective area below 511 keV – only considering 1st order reﬂections. The crystal thickness as function of energy is also shown. It varies from a fraction of a mm at 200 keV to a few mm at 1 MeV Fig. 4 Sketch of “ﬂower lens” with the six crystal panels deployed

which can be folded up during launch. The hexagonal part is 3.7 m across corners and each panel measures 1.85 × 3.0 m. This ﬂower lens concept is illustrated in Figure 4. The effective area of this ﬂower shaped lens as function of energy is still increasing towards the lower energies and is still somewhat too heavy, at least if ﬁlled with copper or silver crystals. As a further weight saving measure I therefore reduced even further the crystal thickness for the crystal rings at large radii (low energies), now using the Springer

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Table 1 Characteristics of thickness tapered ‘ﬂower’ lenses Effective area per energy range Crystal material Mass (kg) Length (m) 200–400 keV (cm2 ) 400–511 keV (cm2 ) 1000 keV (cm2 ) Gold

246

174

987

1146

Silver

358

175

995

1141

605 549

Copper

401

155

964

1100

505

Germanium

526

148

740

838

368

Silicium

607

142

520

582

232

Taper lens area vs Energy. 2nd & 3rd order incl. Mosaic width 1 ’ 1200

1200 Au (111) L: 174 m, M: Ag (111) L: 174 m, M: Cu (111) L: 154 m, M: Ge (220) L: 148 m, M: Si (220) L: 142 m, M:

cm2

1000

246 kg 358 kg 401 kg 526 kg 607 kg

1000

800

800

600

600

400

400

200

200

0

0 200

300

400

500

600

700

800

900

1000

Energy (keV)

Fig. 5 Effective area for the lens conﬁguration of Figure 4, and including 2nd and 3rd order reﬂections. At the highest energies the effective area is increased by almost 50% by the higher order contributions

condition that the effective area should be constant below 511 keV. The resulting reﬂectivity curves are shown in Figure 3 together with the curves showing the crystal thicknesses as function of energy. The crystal weight now appear acceptable for copper, silver and gold crystals. In Figure 5 we show the reﬂectivity curves with 2nd and 3rd order reﬂections included.

4. Conclusions We have arrived at a lens design which we believe can be launched with a Soyuz. I have summarized the ﬁnal lens characteristics in Table 1. This table is worth some comments. In terms of effective ﬂux collection copper, silver and gold are almost equivalent except at the highest energies where gold is 10% better than silver and 20% better than copper. But the crystal mass required when using gold is 150 kg less than when relying on copper and 100 kg Springer

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less than when silver is used! This means that if 400 kg really is what Soyuz will allow us to use for the crystals then we may increase the area of the gold lens by 60% compared to the values shown in Table 1. Or we may use the extra kilos for extending the energy range to lower or higher energies. Although we can have misgivings about the security problems associated with building an instrument containing 250 kg of gold the price of the gold itself (∼ 3.5 MEuro in yesterdays prices) is not in itself preventive when we talk about a satellite project costing maybe 150 MEuro. But regardless of the crystal material chosen we have a number of difﬁcult technical problems to solve before we can launch our ﬁrst large scale Laue lens. The ﬁrst problem to address will be the production in quantity of crystals with the required low mosaicity. Together with the production of the raw crystal boules the machining, handling and mounting of thin disks of these very soft materials must be developed and mastered. All these techniques should be worked out ﬁrst for copper, where a large pool of experience already exist [1]. When we know how to deal with copper we may proceed to silver and gold. Most likely a support disk of a suitable material will be needed for each crystal. However, the very thin gold disks which appear to be required for the lowest energies (see Figure 3) can fortunately be replaced by silver or copper disks of more manageable thickness with only a marginal penalty in the total crystal mass. An important set of issues which must be addressed in some detail is whether an instrument offering “only” 1000 cm2 of collection area coupled with the energy resolution of SPI and a background rate lower than 5% of SPI is competitive as an ESA medium size mission? The limitation of this mission is that it strictly looks at one point source at a time. Are there sufﬁciently many targets which can provide enough photons in a short enough observation time? Is the probability of the bright transient high enough that this can be a signiﬁcant argument for this mission? We need to ﬁnd positive answers to this type of questions before we can hope to win a coming mission selection round.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

Courtois, P., Andersen, K., Bastie, P.: Exp. Astron. 20, DOI 10.1007/s10686-005-9018-x (2006) Halloin, H.: Exp. Astron. 20, DOI 10.1007/s10686-006-9063-0 (2006) Hinglais, E.: Exp. Astron. 20, DOI 10.1007/s10686-005-9020-3 (2006) Lebrun, F., Leray, J.-P., Lavocate, Ph., et al.: A&A 411, L141 (2003) Lund, N.: Exp. Astron. 2, 259 (1992) Starsem, Co., Soyuz Users Manual. http://www.starsem.com (2001) Ubertini, P., Lebrun, F., Di Cocco, G., et al.: A&A 411, L131 (2003) Vedrenne, G., Roques, J. P., Sch¨onfelder, V., et al.: A&A 411, L63 (2003) Winkler, C., Courvoisier, T. J.-L., Di Cocco, G., et al.: A&A 411, L1 (2003)

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Exp Astron (2005) 20:219–228 DOI 10.1007/s10686-006-9045-2 ORIGINAL ARTICLE

Optical properties of Laue lenses for hard X-rays (> 60 keV) Alessandro Pisa · Filippo Frontera · Gianluca Loffredo · Damiano Pellicciotta · Natalia Auricchio

Received: 31 January 2006 / Accepted: 24 April 2006 C Springer Science + Business Media B.V. 2006

Abstract We report on preliminary results obtained with a Monte Carlo (MC) code developed to study the optical properties of Laue lenses for astro-physical observations. The MC code is written in the Python programming language and uses open source libraries. Among the physical quantities which can be investigated with the MC code, we paid our attention mainly to the estimation of the effective area, ﬁeld of view (FOV) and point spread function (PSF) of the lens for observation of sources on-axis and off-axis. Keywords Laue lens . X-ray diffraction . X-ray telescope

1. Introduction A feasibility study of Laue lenses for the measurement of the continuum hard X-/γ -ray emission from celestial sources was already reported [9]. Here we summarize the main concepts and results. A Laue lens is a set of properly oriented crystals that focus X-ray photons via Bragg diffraction in the Laue geometry. X-ray diffraction can occur in perfect crystals because their lattice structure is periodic and its period is comparable with the wavelength λ of the X-rays: crystals are a natural diffraction grating for X-rays. Diffraction deviates photons from their incidence direction by an angle θ B (the Bragg angle) that depends on the wavelength λ and on the lattice interplanar distance dhkl , where hkl are the Miller indices of the planes. The Bragg angle can be obtained from the Bragg equation: 2dhkl sin θ B = nλ ,

(1)

A. Pisa () · F. Frontera · G. Loffredo · D. Pellicciotta · N. Auricchio Physics Department, University of Ferrara, Via Saragat 1, Ferrara, Italy e-mail: [email protected] F. Frontera IASF, CNR, Via Gobetti 101, Bologna, Italy Springer

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Fig. 1 Sketch of the cylindrical reference frame used for the Laue lens.

where n is the diffraction order. Taking a set of properly oriented crystals it is possible to build a lens capable of deviating photons from an X-ray source towards the focal point of the lens. However, perfect crystals are not suitable for building lenses for astro-physical investigations. Indeed they show a high reﬂection efﬁciency in a very narrow energy band (a small fraction of keV) and for a very narrow angular range (in the arcsecond range), while for studying the spectral properties of the continuum hard X-/γ -ray emission of celestial sources, a good reﬂection efﬁciency is required in a relatively broad energy band (tens to hundreds of keV, depending on the science goal), and a relatively large ﬁeld of view (in the arcminute range) is needed. For these kinds of lenses, special crystals, with appropriate lattice deformations, appear to be more useful. Some examples of crystals with controlled imperfections are mosaic crystals, bent crystals and crystals with non constant lattice parameter induced by doping materials or thermal gradient. This paper deals with Laue lenses made of Copper mosaic crystal tiles. We will consider crystal tiles with the (111) planes normal to the tile cross section, which is assumed to be a square with side l, and parallel to two of the four lateral tile surfaces as shown in Figure 1. The thickness of the tiles is t. As it was also conﬁrmed by our recent measurements results [2], the diffraction properties of the Copper mosaic crystals are consistent with the theoretical model proposed by Zachariasen [1]. To correctly focus photons, the direction of the lattice plane normal vector (which is parallel to the reciprocal lattice vector associated to the (111) planes, G111 ), has to intersect the focal axis and its inclination with respect to the focal plane should be equal to the Bragg angle θ B . The angle θ B depends on the tile center distance from the lens axis, ρ, and on the distance from the focal plane, focal length F (see Figure 1). The distances are measured with respect to the center of the upper surface of the tile. For a correct focusing, it is needed that: θB =

ρ 1 arctan . 2 F

(2)

Increasing the ratio ρ/F, the Bragg angle increases and thus also the wavelength of the focused photons. For a ﬁxed value of ρ/F, and hence of θ B , the diffracted wavelength can be obtained by the Bragg law (1). Springer

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In this paper we will show the dependence from several parameters (tile size, mosaic spread, ratio between lens radius and focal length) of fundamental optical and physical properties of Laue lenses. In particular we are interested to the behaviour of the effective area, the Point Spread Function (PSF), the angular resolution and the Field Of View (FOV). All the lens properties are the result of the cooperation of all the crystals in focusing photons from X-ray sources. The task of determining these properties can be faced by means of numerical calculation. To this end a dedicated software has been developed.

2. Monte Carlo code The software developed to calculate the physical properties of the lens has been coded in the Python programming language [3]. Python has been chosen because it is a high level object oriented programming language and because plenty of scientiﬁc libraries are available. By using these libraries it has been possible to minimize the effort for the code development, debugging and testing. This code imports the libraries Numerical Python [4], Scientiﬁc Python [5], xraylib [6] and the GNU scientiﬁc library [7, 8]. The code is modular and each module faces a particular task. The code includes four main blocks: (1) lens geometry, (2) photon source, (3) photons interaction with the lens crystals tiles in which the story of each photon is followed, (4) distribution of the photons in the focal plane and their analysis. The main free parameters of the lens are the tile properties (material, lattice orientation, size, mosaic spread), its geometry (the disposition of the crystal tiles in the lens), the lens focal length and its nominal energy passband. Available tile dispositions include the Archimedes’s spiral geometry [9, 10], the concentric rings as proposed by von Ballmoos and coworkers for the MAX mission [11], a single ring (see Section 3). The photon source, whose spectral parameter can be controlled by the user, is simulated using randomly generated numbers.

3. Case of a ring lens For sake of simplicity we derive the properties of a ring lens made of Cu (111) crystal tiles. The assumed number of tiles is N and the ring is at a distance F from the focal plane (focal length). The ring radius is ρ = R (see Figure 1) and N is assumed to be 100. The inclination of the tiles in the ring satisﬁes Eq. (2). Via the Bragg equation it is possible to get the energy of the diffracted photons. Viceversa, given the photon energy it is possible to calculate the ring radius and the Bragg angle needed for focusing these photons. The tile thickness can be properly chosen to optimize the diffraction efﬁciency [9, 10]. Using the cylindrical reference frame of Figure 1, the radial coordinate ρ and the polar angle θ are the same for each crystal, while the azimuthal angle difference between two contiguous tiles is 2 π/N . It is implicitly assumed that the ring radius is large enough for the tiles allocation to be possible. There are important scaling laws which apply to ring lenses. Varying F but keeping ﬁxed the ratio R/F, the Bragg angle does not change and so the lens focuses the same energy band (see Eq. 2). If the ratio l/F and the number of tiles, N, are kept ﬁxed, the focal spot size is proportional to F and the effective area is proportional to F 2 . Springer

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The focal spot size was discussed in a previous paper [9]. With the developed software we can study in detail the variation of the spot size as a function of energy, of the l/F ratio and of the mosaic spread β. r For this study we make use of the radial photon distribution φ(r ) and its integral (r ) = 0 φ(ρ)dρ, which gives the encircled photon fraction. r is the radius of a circle centered in the origin O of the reference adopted frame (see Figure 1). In addition we will investigate the distribution of the photon positions in the focal plane projected on the x and y axes ( f x (x) and f y (y)).

4. Monte Carlo results We have tested our code assuming a lens made of a Cu (111) crystal tile ring optimized for 150 keV photons. We have studied the effects on the lens effective area and on the focal spot caused by the variation of the lens conﬁguration parameters. 4.1. Reference conﬁguration We assume as a reference conﬁguration a lens made of a ring of Cu (111) crystals tiles with l = 10 mm, thickness of 2 mm and mosaic spread of 1 arcmin. The focal length of the reference lens is 50 m. The effective area of this conﬁguration is shown in Figure 2, while Figure 3 shows the radial distribution of the photons on the focal plane (left panel) and the encircled photon fraction as a function of r/F. 4.2. Effect of a different tile thickness The value of the thickness affects not only the diffraction efﬁciency, and thus the lens effective area and the lens gain, but also the lens weight. Figure 4 shows the dependence of the effective area on the photon energy for three different crystal thicknesses (1.5, 2.0, 2.5 mm). As can be seen from the left panel of Figure 4, variations of the thickness of the order of 25% with respect to the reference conﬁguration, result in small variations of the effective area for the ﬁrst order diffraction, unlike the weight of the lens which varies proportionally to the thickness. However a higher thickness signiﬁcantly increases the effective area due to the second order diffraction (right panel of Figure 4).

Fig. 2 Normalized effective area for the reference conﬁguration. The two diffraction orders are shown

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Fig. 3 Radial distribution and encircled photon fraction for the reference conﬁguration.

Fig. 4 Normalized effective area for different thickness values. (Left): First diffraction order; (Right): second diffraction order

4.3. Effects of different mosaic spread and tile size The increase of the mosaic spread leads to an increase of the energy passband of the lens, but also to a larger defocusing of the photons. Figure 5 shows the effective area vs energy for three different mosaic spreads (0.5, 1.0 and 2.0 arcmin) with an evident change of the energy passband and peak efﬁciency with the result that the number of focused photons increases with the mosaic spread. However the dispersion of the photons in the focal plane increases with the mosaic spread, with the result of a lower gain of the lens. This is shown in Figure 6, which exhibits the

Fig. 5 Normalized effective area for different mosaic spread values. (Left): First diffraction order; (Right): second diffraction order Springer

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Fig. 6 Encircled photon fraction for various values of the mosaic spread. In each ﬁgure are plotted the curves corresponding to different values of the ratio l/F

encircled photon fraction as a function of the circle radius for different values of the crystal mosaic spread and for different values of the l/F ratio. Thus a higher value mosaic spread implies higher spread of the focused photons, even though it also allows to use larger tiles with a reasonably negligible enlargement because the focal spot proﬁle and size is mainly dominated by the enlargement due to the mosaic spread. A useful quantity to describe the spot size is the half power radius (R50 ), the radius of the circle that contains the 50% of the focused photons. Figure 7 shows that R50 /(Fβ) as a function of l/(Fβ) do not strongly depend on the mosaic spread in our range of interest. Springer

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Fig. 7 Normalized half power radius for different mosaic spread as a function of the normalized tile size.

Fig. 8 Reference conﬁguration point spread function for a source on-axis (top) and for a source off-axis of 4 arcminutes (bottom).

5. Optical properties of the lens reference conﬁguration 5.1. On-axis and off-axis response We will now study how the Laue lens PSF changes for photons coming from a point-like source offset by an angle α with respect to the lens axis direction. For the reference conﬁguration, the on-axis PSF (α = 0) is shown in Figure 8 (top). Unlike the on-axis PSF, that obtained for an off-axis source (α = 4 arcmin) is no more symmetric. The photons are supposed to have a normalized wavevector that in Cartesian coordinate is (sin α, 0, cos α). Springer

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Fig. 9 Reference conﬁguration radial distribution of the photons at different offset angles.

Fig. 10 Reference conﬁguration photon distribution along the x axis.

Fig. 11 Reference conﬁguration photon distribution along the y axis.

The PSF has the shape of a ring with larger width for negative values of x. Even if the ring shape is not symmetric, it is found that the photon barycenter is still in the lens focus. It is also visible the effect of the single tiles on the image. Each of the stripes visible in the PSF of Figure 8 (bottom) is the contribution of two tiles placed symmetrically with respect to the y axis. The distribution of the photons is shown in Figures 9–11 for various offset angle values. Figure 9 shows the radial photon distribution, while Figures 10–11 show the distribution of Springer

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the photons projected, respectively, along the x and y axes. As can be seen the distribution along the y axis is symmetric, while that along the x axis is distorted for negative values of the coordinate. This distortion gives information on the direction of arrival of the photons. 5.2. Angular resolution Looking at the radial distribution function of the focal spot (see Figure 9) it is possible to see that the peak position increases with offset. We assume that two celestial sources separated by an angle α can be resolved when their radial distributions are separated by at least the sum of their half width at half maximum (HWHM). With this assumption the angular resolution of the reference conﬁguration lens is about 1.5 arcmin. 5.3. Field of view The numerical simulations show that the number of photons focused by the lens does not signiﬁcantly vary as a function of the offset angle for values of the angle that are in the arcminute range. Even if the source counts for on-axis and off-axis sources is similar, offaxis photons are spread on a much larger surface (see Figures 9–11) and therefore need larger detectors. Being the background rate proportional to the detector surface, off-axis sources are detected with a lower signal to noise ratio (SNR). The FOV of the lens is thus determined by the detector radius. Photons from sources offset by an angle greater than the FOV are automatically discarded, given that they produce a ring with radius larger than that of the focal plane detector.

6. Conclusions The main properties of a lens made of a single ring of Cu (111) mosaic crystals have been investigated. Starting from a reference conﬁguration of the lens, based on crystal tiles of 10 × 10 mm2 , 2 mm thickness, mosaic spread of 1 arcmin and a focal length of 50 m, we have investigated the effects of changing mosaic spread or thickness on the effective area and on the space distribution of the focused photons. The photon energy considered is 150 keV. As far as the crystal thickness on the effective area, its effect is relatively modest even for a signiﬁcant thickness range (25%). Thus, compatibly with its feasibility, thickness lower than that optimized for reﬂection efﬁciency, can be taken into consideration with a sensitive reduction of the lens weight. As far as the mosaic spread is concerned, it appears that a value of 1 arcmin is a good compromise for the optimization of both the effective area and the encircled photon fraction. With 1 arcmin mosaic spread we have investigated the PSF of the lens for on-axis and offaxis sources suggesting a possible criterion for deﬁning the lens resolution and we investigated the FOV, that for this kind of lens is basically limited by the detector size. The angular resolution is of the order of 2 arcmin. References Zachariasen, W.H.: Theory of X-Ray diffraction in crystals, Dover publications, Inc., New York, N.J. (1994) Pellicciotta, D. et al.: Laue lens development for hard X-rays (>60 keV), 2005 IEEE TNS, in press, (astroph/0511490). http://www.python.org http://www.numpy.org Springer

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http://www.scipy.org Brunetti, A. et al.: A library for X-ray-matter interaction cross sections for X-ray ﬂuorescence applications, Spectrochimica Acta Part B, 59, 1725–1731 (2004) http://www.gnu.org/software/gsl/ http://pygsl.sourceforge.net/ Pisa A. et al.: Feasibility study of a Laue lens for hard x rays for space astronomy, Proc. SPIE 5536, 39–48 (2004) Pisa, A. et al.: “Development status of a Laue lens for high-energy x rays (>60 keV), Proc. SPIE 5900, 350–359 (2005) von Ballmoos, P. et al.: MAX: A gamma-ray lens for nuclear astrophysics. Proc. SPIE 5168, 482-491 (2004) Frontera, F. et al.: Exploring the hard X-/soft gamma-ray continuum spectra with laue lenses, Proc. 39th ESLAB Symposium, in press, 2005 (astro-ph/0507175)

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Exp Astron (2005) 20:229–239 DOI 10.1007/s10686-005-9017-y ORIGINAL ARTICLE

Development of a new photon diffraction imaging system for diagnostic nuclear medicine D. E. Roa · R. K. Smither · X. Zhang · K. Nie · Y. Y. Shieh · N. S. Ramsinghani · N. Milne · J. V. Kuo · J. L. Redpath · M. S. A. L. Al-Ghazi · P. Caligiuri

Received: 7 November 2005 / Accepted: 22 December 2005 C Springer Science + Business Media, B.V. 2006

Abstract The objective of this project is to develop and construct an innovative imaging system for nuclear medicine and molecular imaging that uses photon diffraction and is capable of generating 1–2 mm spatial resolution images in two or three dimensions. The proposed imaging system would be capable of detecting radiopharmaceuticals that emit 100–200 keV gamma rays which are typically used in diagnostic nuclear medicine and in molecular imaging. The system is expected to be optimized for the 140.6 keV gamma ray from a Tc-99m source, which is frequently used in nuclear medicine. This new system will focus the incoming gamma rays in a manner analogous to a magnifying glass focusing sunlight into a small focal point on a detector’s sensitive area. Focusing gamma rays through photon diffraction has already been demonstrated with the construction of a diffraction lens telescope for astrophysics and a scaled-down lens for medical imaging, both developed at Argonne National Laboratory (ANL). In addition, spatial resolutions of 3 mm have been achieved with a prototype medical lens. The proposed imaging system would be comprised of an array of photon diffraction lenses tuned to diffract a speciﬁc gamma ray energy (within 100–200 keV) emitted by a common source. The properties of photon diffraction make it possible to diffract only one speciﬁc gamma ray energy at a time, which signiﬁcantly reduces scattering background. The system should be sufﬁciently sensitive to the detection of small concentrations of radioactivity that can reveal potential tumor sites at their initial stages of development. Moreover, the system’s sensitivity would eliminate the need for re-injecting a patient with more radiopharmaceutical if this patient underwent a prior nuclear imaging scan.

D.E. Roa · X. Zhang · K. Nie · N.S. Ramsinghani · J.V. Kuo · J.L. Redpath · M.S.A.L. Al-Ghazi University of California at Irvine – Medical Center, Department of Radiation Oncology Y.Y. Shieh · N. Milne University of California at Irvine – Medical Center, Department of Radiological Sciences R.K. Smither Argonne National Laboratory – Advanced Photon Source Division, Argonne, Illinois P. Caligiuri University of Chicago – Department of Radiology, Chicago, Illinois Springer

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Detection of a tumor site at its inception could allow for an earlier initiation of treatment and wider treatment options, which can potentially improve the chances for cure. Keywords Medical imaging . Lens . Photon diffraction . Radiopharmaceuticals . Nuclear medicine

1. Introduction The ﬁeld of medical imaging has at its disposal a variety of modalities that are used for anatomical imaging, brain mapping, and diagnosis of organ diseases, to name a few. In many respects, these imaging modalities complement each other. For instance, in nuclear medicine, diagnostic imaging provides to the physician a pathophysiological view of the patient’s body, while computed tomography (CT) and magnetic resonance imaging (MRI) provide high-resolution images of the patient’s anatomy. Moreover, multimodality systems such as positron-emission tomography (PET) combined with CT or PET-CT provides these two forms of information in a single unit1−9 . Nuclear medicine relies on radiopharmaceuticals – biological compounds containing a radioactive isotope – to locate physiological abnormalities in the body. These isotopes are typically gamma-ray emitters of ∼100–200 keV in energy and with half-lives on the order of a few hours (see Table 1). The basic process for nuclear imaging involves introducing a radiopharmaceutical into the patient (usually by intravenous injection) which subsequently accumulates in the target site or biological process of interest. Advances in radiopharmaceutical manufacturing have resulted in compounds that speciﬁcally target certain sites or processes in the body with relatively low up-take in the surrounding body tissues. Higher concentrations of the radiopharmaceutical yield a higher gamma-ray emission rate relative to surrounding tissues and background. These gamma rays are captured by large detector arrays (e.g., gamma cameras, single-photon emission tomography – SPECT cameras) that subsequently send the data to a computerized system that generates a two- or three-dimensional image4−11 (Figure 1). Currently, most nuclear medicine imaging systems have limited spatial resolution that ranges from 7 to 15 mm. PET, the latest diagnostic system in nuclear medicine, can achieve resolutions of 4–5 mm at best. Furthermore, because the radiopharmaceuticals needed for PET imaging have signiﬁcantly shorter half-lives (at most two hours), relatively large radiopharmaceutical doses must be prepared to leave enough activity to image the patient. In Table 1 Typical radiopharmaceuticals used in nuclear diagnostic medicine Nuclide

γ -Ray Energy (keV)

Purpose

320

Red cell volume

Cr-51

28 d

Ga-67

79.2 h

93, 185, 300, 393

Tumor location & inﬂammation

I-123

13.0 h

159

Imaging of thyroid

171, 245

Labeling white blood cells

140.5

Multi-purpose imaging Myocardial imaging

In-111 Tc-99m

67 h 6.02 h

Tl-201

73 h

135, 166

Xe-133

5.3 d

81

Ventilation imaging

1.83 h

511

Tumor imaging

F-18 Springer

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Fig. 1 Patient undergoing a scan using a gamma camera. Administration of a radiopharmaceutical (upper left display)

addition, most PET centers must be located in close proximity to a cyclotron facility, in order to minimize the transport time of the radiopharmaceutical from the preparation laboratory to the imaging room4−14 . The proposed imaging system uses an innovative approach based on photon diffraction for detecting gamma rays of a speciﬁc energy, within 100–200 keV, emitted by a radiopharmaceutical concentrated in a tumor site. Detection is carried out by focusing the incoming gamma rays into a small focal point on a detector’s sensitive area, analogous to a magnifying glass focusing visible light. Focusing gamma rays through photon diffraction has already been demonstrated with the construction of a gamma-ray diffraction lens telescope for astrophysics and a prototype lens for medical imaging15−20 . The application of this new system is envisioned to be for site speciﬁc scans of the patient’s body that can result in two- or three-dimensional images with a spatial resolution of ≤2 mm. If a patient has undergone a full-body scan and the data suggest the presence of a tumor or suspicious process (e.g., ischemia), a localized scan of that region could be performed with this imaging system without the need for injecting the patient with more radiopharmaceutical. This system may be better able to provide additional information to assess the size of the tumor or suspicious process and to more accurately deﬁne its location. 2. Materials and methods 2.1. Physics principles and conceptual view of a photon diffraction imaging system The proposed high spatial resolution imaging system relies on photon diffraction to redirect the trajectory of the gamma rays, emitted by a radiopharmaceutical concentrated in a tumor site, onto a detector. Photon diffraction is a three-dimensional process carried out by parallel planes of atoms within a crystal. This process is mathematically described by Bragg’s law21−26 , as: λ = 2d sin θ B

(1)

where “λ” is the photon’s wavelength, “d” is the spacing between atomic planes, and “θ B ”, known as the Bragg angle, is the angle subtended by the incoming gamma-ray trajectory and the lattice plane. The spacing between planes varies depending on the orientation of the lattice plane, which consequently varies the Bragg angle as well. Springer

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In the case of a cubic crystal, which is one of seven crystalline systems deﬁned in crystallography, the spacing between the lattice planes is a function of their Miller indices (h, k, l) and it is deﬁned as:

d= √

a h2 + k2 + l 2

(2)

where “a” is the crystal structure lattice constant. Subsequently, expressing the photon wavelength as:

λ=

hc Eγ

(3)

and incorporating equations 2 and 3 in equation 1 results in a re-deﬁned expression of Bragg’s law as a function of gamma-ray energy, crystal lattice constant and crystal lattice plane: θ B = sin

−1

√ hc h 2 + k 2 + l 2 . 2E γ a

(4)

Equation 4 can be used to construct a photon diffraction lens consisting of concentric rings of crystals of different crystalline planes. Speciﬁc crystalline planes for each ring, can be selected based on the gamma-ray energy from a nuclear imaging radiopharmaceutical and from the gamma-ray incident angle determined by the source-to-lens distance and the concentric ring radius (Figure 2). The proposed imaging system consists of an array of photon diffraction lenses aligned to focus the gamma rays emitted by a common radioactive source. Each lens is mounted equidistantly between the source and its corresponding detector which deﬁnes a symmetric diffraction conﬁguration. Gamma rays emitted within the boundaries of a lens’ solid angle are focused onto the sensitive area of the detector (Figure 3).

Fig. 2 Schematic diagram of the photon diffraction process carried out by a crystal diffraction lens Springer

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Fig. 3 (a) Conceptual view of the medical imaging system consisting of an array of 9 photon diffraction lenses. (b) Schematic diagram of a single lens with its corresponding detector and shield

This method of gamma-ray focusing and subsequent detection eliminates the need for high-spatial resolution collimators typically used in gamma cameras which causes signiﬁcant reduction in sensitivity6−8 . Moreover, this photon diffraction imaging system can be tuned to diffract a speciﬁc gamma-ray energy (within ∼100 – 200 keV) by simply adjusting the source-to-lens and lens-to-detector distance such that the lens remains equidistant between the source and detector. This adjustment changes the Bragg angle to match the gamma-ray energy in order for photon diffraction to occur. 2.2. Construction of a prototype photon diffraction lens A prototype photon diffraction lens was constructed at Argonne National Laboratory to demonstrate the viability of using photon diffraction for detecting small concentrations of radioactivity. The prototype lens consists of 828 copper crystals cut in small cubes of 4 × 4 mm2 in cross-sectional area and 3–4 mm in thickness. Copper crystals were chosen due to their high diffraction efﬁciency for gamma-ray energies of 100–200 keV17 . Prior to cutting smooth circular slabs of copper crystal into small cubes, a set of measurements in a photon diffraction enclosure were carried out to determine the orientation of the crystalline plane to be used. These were transmission measurements that consisted of ﬁnding the maximum diffraction signal from that crystalline plane (orthogonal to the crystal’s circular surface) by irradiating the crystal piece with a 122 keV gamma-ray beam from a Cobalt-57 source and determining the crystal’s rocking curve. The copper crystals were distributed in 13 concentric rings assembled in two separate low-Z material substrates for the odd and even ring numbers, respectively, which facilitated the assembly process. Together they comprise a sensitive area of 132 cm2 (Figure 4). These substrates were disks of ∼16 cm in diameter with a thickness of 1.5 mm and with a ﬂatness of approximately ±96 µradian. Although the substrates met this requirement around the central surface area, larger deviations were observed towards the edges. A dedicated lens assembly unit consisting of a Co-57 source, a 3-dimension translation stage, Pb collimators and a NaI detector was used to construct the prototype photon diffraction lens (Figure 5). Cobalt-57 with its 122 keV gamma-ray energy and 272 days half-life provided a suitable energy and time frame for assembly and determination of the diffraction response of the individual crystals in the lens. The diffraction response of a crystal was determined by isolating Springer

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Fig. 4 (a) Prototype crystal diffraction lens with its two substrates containing the concentric rings ﬁlled with crystals. (b) Mounting the two substrates for the actual lens conﬁguration

Fig. 5 (a) Photograph of the lens assembly. (b) Schematic diagram of the assembly

the photons diffracted by that crystal using a Pb disc with a slot of 4-mm in width suspended at ≤1 cm above the crystal. Each crystal cube was cemented in place after maximizing its diffraction response signal.

3. Preliminary results and discussion Phantom measurements were performed with the prototype lens using Co-57 and Tc-99m sources mounted inside a 15 × 15 × 15 cm3 Lucite block. For the experiments using the Co-57 source, the lens was positioned at a distance of 84 cm from the source in order to maximize the diffraction of the 122 keV gamma rays emitted by this cobalt isotope. Springer

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Table 2 Data collected with different amounts of Tc-99m inside a Lucite phantom

Volume (cc)

Activity (mCi)

Peak Rate (Bkg Subtracted) (1-Lens)

0.126 0.031 0.008

3.6 0.7 0.04

382.4 c/s 57.8 c/s 4.0 c/s

Peak Rate (Bkg Subtracted) (9-Lenses)

Normalized Peak Rate 9-Lenses (cpm/µCi/cc)

3441.2 c/s 519.8 c/s 35.6 c/s

455.2 1437.2 6675.0

Background (Bkg): 1-Lens = 0.04 c/s = 2.4 cpm; 9-Lenses = 0.36 c/s = 21.6 cpm

Fig. 6 (a) Diffraction response of the prototype lens for a 122 keV gamma ray energy from a Co-57 source, FWHM = 3 mm. (b) Depth scan also using a Co-57 source – FWHM = 17 mm

For the 140.6 keV gamma rays from Tc-99m, the lens was positioned at 100 cm from the source. These experiments consisted primarily of scans along the horizontal (XY) axes that depicted the lens diffraction response at different source positions and provided information regarding the spatial resolution, deﬁned as the full-width-at-half-maximum (FWHM) of the response signal. In addition, scans were performed to determine the lens’ sensitivity as a function of depth (Z-axis). Results from these scans using Co-57 yielded a diffraction response signal with a spatial resolution of FWHM = 3 mm for the horizontal scans and a depth sensitivity of FWHM = 17 cm (Figure 6). Measurements with Tc-99m were carried out using different amounts of this element in the form of sodium pertechnetate – a liquid substance. The Tc-99m was injected in 3 different cylindrical cavities of 0.126 cc, 0.031 cc and 0.008 cc, respectively. During a measurement, one of these cavities was mounted such that it was centrally located inside the Lucite phantom. The results are summarized in Table 2. As shown in Table 2, the data obtained for a single lens was extrapolated to the case of a 9-lens array like the one depicted in Figure 3a. Table 3 shows the estimated results expected Springer

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Exp Astron (2005) 20:229–239 Table 3 Estimated sensitivity data for a 9-lens array imaging system Volume (cc)

Diameter (mm)

cpm

√ S/N = Peak/ Bkg

1.0 0.5 0.01 0.005

12.4 9.8 2.7 2.1

2855.8 1427.9 28.6 14.3

614 307 6 3

Fig. 7 Calculated photon diffraction efﬁciency for a single lens

for a 9-lens system, assuming a tumor of spherical proportions with an activity of 1 µCi and using a normalized peak rate average of 2855.8 cpm/µCi/cc. However, it must be pointed out that in a clinical scan the tumor volume is not the only radioactive source. Surrounding organs adjacent to the tumor also absorb some of the radiopharmaceutical and the uptake is directly correlated to that organ’s volume. Consequently, these organs become a source of background during a clinical scan. Work in assessing the performance of the lens array system in a clinical scenario is currently in progress as described in the following section. In addition, efﬁciency calculations for a single lens based on photon diffraction theory resulted in a peak efﬁciency of 3% (Figure 7). This means that for a radioactive source emitting gamma rays isotropically, the overall efﬁciency -C1 for a single lens is:

- 1−Lens = (Diff. Eff.) × (132 cm2 /4π (100 cm)2 ) C - 1−Lens = 3.2 × 10−5 . C - 9−Lens = 2.9 × 10−4 , comparable For a 9-lens array, the overall efﬁciency becomes: C 8 with an overall efﬁciency for a gamma camera of Cγ −Camera = ∼3.0 × 10−4 . From the experimental data, the diffraction efﬁciency for the not fully optimized prototype lens was ∼1% which corresponds to an overall efﬁciency of 1.1 × 10−5 for a single lens and 1.0 × 10−4 for a 9-lens array. Springer

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4. Current status Monte Carlo calculations to assess the performance of the photon diffraction imaging system are currently in progress at the University of California at Irvine. These calculations are being performed using the Monte Carlo N-Particle (MCNP) computer code developed at Los Alamos National Laboratory27 . These calculations are aimed at determining the imaging system’s overall efﬁciency, sensitivity and speciﬁcity for detecting small tumors inside a patient’s body. This will be achieved systematically by:

r generating Monte Carlo calculations of the imaging system’s performance at different stages of development which will be used as benchmarks to assess the system’s experimental data, r assessing the overall efﬁciency of a fully assembled imaging system using Co-57 and Tc-99m radioactive sources inside a standard Lucite phantom, r assessing the imaging system’s overall efﬁciency using a Tc-99m radioactive source inside an anthropomorphic phantom, r assessing the imaging system’s overall efﬁciency using a Tc-99m radioactive source inside a small mammal. Also, measurements are currently in progress to determine the efﬁcacy of using solid state rather than scintillation detectors in the new imaging system. In particular, we are interested in the 10 × 10 × 5 mm3 Cadmium Zinc Telluride (CdZnTe) detector array, which is already available commercially28 . This detector array is comprised of independent pixel size detectors that have an overall average energy resolution of ∼6.4 keV at 140 keV, compared to a resolution of 14 keV from a NaI detector. Such an energy resolution would allow us to set a narrower electronic window for acceptance of a speciﬁc gamma ray energy. This detector array coupled to a diffraction lens in the imaging system array could provide images with increased contrast due to reduction in the scattering background. Further, using a detector array rather than a single detector can provide information regarding tumor location.

5. Conclusion Preliminary work on a prototype lens done at Argonne National Laboratory has demonstrated that it is feasible to use photon diffraction for producing a high spatial resolution image. Although, we were able to achieve a spatial resolution of 3 mm with a not fully optimized photon diffraction lens, this spatial resolution is already about a factor of 2 better than a gamma camera’s spatial resolution. Moreover, these measurements have demonstrated that the lens is capable of focusing speciﬁc gamma-ray energies (122 keV for Co-57 and 140.6 keV for Tc-99m) by adjusting the source-to-lens and lens-to-detector distances. The limitation in spatial resolution observed in these measurements was due to the quality of the copper crystals used for the prototype lens. These crystals were too imperfect (400 arc sec ≤ mosaic width) for this imaging application. In addition, the deviations in ﬂatness observed in the substrates also contributed to preventing us from achieving an optimal spatial resolution. However, we are conﬁdent that this technology can provide a signiﬁcant contribution to diagnostic imaging in nuclear medicine and, furthermore, to the ﬁeld of molecular imaging due to the high spatial resolution needed in this ﬁeld. Finally, a considerable amount of work remains to be done to achieve the realization of a photon diffraction imaging system. Assessing the capabilities of a fully assembled Springer

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diffraction imaging system using Monte Carlo simulations is only the ﬁrst step in the process towards realization. Measurements involving sophisticated anthropomorphic phantoms and subsequent, in-vivo measurements using small mammals will need to be carried out with this imaging system. Only upon successful results of these measurements could we move on towards a request for initiating testing of this system on patients. However, the beneﬁts that this imaging system can provide are sufﬁcient motivation to continue on this quest. Acknowledgements The authors would like to thank Edward J. Orlowski of the UCIMC Department of Radiation Oncology for some of the graphics work presented in this manuscript. Also special thanks goes to Algirdas Paugys for his work on making the lens setup and Lucite phantoms. This work was supported by a grant from the American Cancer Society – Institutional Research Grant #IRG-98-279-04 and the U.S. Department of Energy under contract W-31-109-Eng-38.

References 1. Beutel, J., Kundel, H.L., Van Metter, R.L.: Handbook of medical imaging, Vol. 1, SPIE Press, Bellingham, Washington (2000) 2. Curry, T.S., Dowdey, J.E., Murry, R.C., Jr.: Physics of diagnostic Radiology, Fourth Edition, Lea and Febiger Press, Philadelphia (1990) 3. Hall, E.J.: Radiobiology for the Radiologist. Fifth Edition, Lippincott Williams and Wilkins Press, New York (2000) 4. Adler, L.P., Weinberg, I.N., Bradbury, M.S., Levine, E.A., Lesko, N.M., Geisinger, K.R., Berg, W.A., Freimanis, R.I.: Method for combined FDG-PET and radiographic imaging of primary breast cancers. The Breast Journal 9(3), 163 (2003) 5. Carson, P.L., Giger, M., Welch, M.J., halpern, H., Kurdziel, K., Vannier, M., Evelhoch, J.L., Gazelle, G.S., Seltzer, S.E., Judy, P., Hendee, W.R., Bourland, J.D.: Biomedical imaging research opportunities workshop: report and recommendations. Radiology 229(2), 328 (2003) 6. Chandra, R.: Introductory physics of nuclear medicine. Third Edition, Lea and Febinger Press, Philadelphia (1987) 7. Wagner, R.H., Karesh, S.M., Halama, R.: Questions and answers in nuclear medicine. Mosby Press, Chicago (1999) 8. Palmer, E.L., Scott, J.A., Strauss, H.W.: Practical nuclear medicine. W.B. Saunders Company, Philadelphia (1992) 9. Khalkhali, I., Maublant, J.C., Goldsmith, S.J.: Nuclear oncology – diagnosis and therapy. Lippincott Williams and Wilkins Press, New York (2001) 10. Khalkhali, I., Villanueva-Meyer, J., Edell, S.L., Hanelin, L.G., Lugo, C.E., Taillefer, R., Freeman, L.M., Neal, C.E., Scheff, A.M., Connolly, J.L., Schnitt, S.J., Baum, J. K., Houlihan, M.J., Hale, C.A., Haber, S. B.: Diagnostic accuracy of Tc-99m SESTAMIBI breast imaging in breast cancer detection. J. Nucl. Med. 37, 74P (1996) 11. Boerman, O.C., Dams, E.Th.M., Oyen, W.J.G., Corstens, F.H.M., Storm, G.: Radiopharmaceuticals for scintigraphic imaging of infection and inﬂammations. Inﬂamm. Res. 50, 55 (2001) 12. Palmedo, H., Schomburg, A., Grunwald, F., Mallmann, P., Krebs, D., Biersack, H.: Technetium-99m-MIBI scintimammography for suspicious breast lesions. J. Nucl. Med. 37, 626 (1996) 13. Wagner, J.D., Schauwecker, D.S., Davidson, D., Wenck, S., Jung, S., Hutchins, G.: FDG-PET sensitivity for melanoma lymph node metastases is dependent on tumor volume. J. Surg. Onc. 77, 237 (2001) 14. Abella, H.: PET fails to match sentinel node biopsy for melanoma staging. Diagnostic Imaging Online, URL: www.diagnosticimaging.com/dinews/2003060201.shtml (2003) 15. Smither, R.K., Fernandez, P.B., Graber, T., von Ballmoos, P., Naya, J., Albernhe, F., Vedrenne, G., Faiz, M.: Review of crystal diffraction and its application to focusing energetic gamma rays. Exp. Astronomy 6, 47 (1995) 16. von Ballmoos, P., Smither, R.K., Naya, J.E., Albernhe, F., Faiz, M., Fernandez, P.B., Graber, T., Vendrenne, G.: A tunable crystal diffraction telescope for the energy range of nuclear transitions. Conf. Proc., Imaging in High Energy Astronomy, Anacapri, Italy (1994) 17. Kohnle, A.: A gamma-ray lens for nuclear astrophysics. Ph.D. Thesis, L’Universite Paul Sabatier, Toulouse, France (1998) Springer

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18. Smither, R.K., Roa, D.E.: Crystal diffraction lens for medical imaging. Proc. of SPIE: Medical Imaging 3977, 342 (2000) 19. Roa, D.E., Smither, R.K.: Copper crystal lens for medical imaging: ﬁrst results. Proc. of SPIE: Medical Imaging 4320, 435 (2001) 20. Smither, R.K., Roa, D.E.: The physics of medical imaging with crystal diffraction lenses. Proc. of SPIE: Medical Imaging 4320, 447 (2001) 21. Bragg, S.L.: The development of X-Ray analysis. In: Phillips, D.C., Lipson, H. (eds.), Dover Publications, New York (1992) 22. Blakemore, J.S.: Solid state physics. Second Edition, Cambridge University Press, New York (1985) 23. Ahscroft, N.W., Mermin, N.D.: Solid state physics. Saunders College Press, Philadelphia (1975) 24. Warren, B.E.: X-Ray Diffraction. Dover Publications, New York (1990) 25. Zachariasen, W.H.: Theory of X-Ray diffraction in crystals. Dover Publications, New York (1994) 26. Tipler, P.A.: Modern Physics. Worth Publishers, New York (1987) 27. X-5 Monte Carlo Team: MCNP – A general monte carlo n-particle transport code. Version 5, Los Alamos National Laboratory (2003) 28. Laboratoire d’Electronique de Technologie de l’Information, 17 rue des Martyrs
38 054 Grenoble CEDEX 9, URL: www-leti.cea.fr/uk/index-uk.htm (2003)

Springer

Exp Astron (2005) 20:241–251 DOI 10.1007/s10686-006-9050-5 ORIGINAL ARTICLE

HAXTEL: A Laue lens telescope development project for a deep exploration of the hard X-ray sky (>60 keV) F. Frontera · A. Pisa · G. Loffredo · D. Pellicciotta · V. Carassiti · F. Evangelisti · K. Andersen · P. Courtois · L. Amati · E. Caroli · T. Franceschini · G. Landini · S. Silvestri · J. Stephen

Received: 3 February 2006 / Accepted: 18 May 2006 C Springer Science + Business Media B.V. 2006

Abstract A review of the HAXTEL project devoted to the development of a Laue lens telescope for hard X-/gamma-ray observation of the continuum spectra of celestial sources is presented. Main design properties, open issues, the status of the project and an example of multi-lens conﬁguration with sensitivity expectations are discussed. Keywords Laue lenses · Gamma-ray instrumentation · Focusing telescopes · Gamma-ray source observations 1. Introduction The history of X-ray astronomy has shown that any advancement in our knowledge of the X-ray sky is strictly correlated with an increase in the instrument sensitivity. Above 10 keV, with respect to the traditional direct-viewing telescopes of the sky used till now, focusing optics appear the unavoidable solution to signiﬁcantly improve the sensitivity level achieved so far. Now, while up to 60 keV the X-ray optics based on multilayer coatings (ML) now under development or the use of grazing incidence mirrors with high focal lengths (>50 m) can signiﬁcantly improve the hard X-ray telescope sensitivity, above 100 keV, as we will see also in this paper, the best candidate technique appears the Bragg diffraction from mosaic crystals in transmission conﬁguration (Laue lenses). The intermediate band (60–100 keV) can be covered with lower efﬁciency by the ML mirrors but also, as we will demonstrate here, F. Frontera () · A. Pisa · G. Loffredo · D. Pellicciotta University of Ferrara, Department of Physics, Via Saragat 1, 44100 Ferrara, Italy e-mail: [email protected] V. Carassiti · F. Evangelisti INFN, Section of Ferrara, Via Saragat, 1, 44100 Ferrara, Italy K. Andersen · P. Courtois Institute Laue-Langevin, Grenoble, France L. Amati · E. Caroli · T. Franceschini · G. Landini · S. Silvestri · J. Stephen INAF/IASF-Bologna, Via Gobetti, 101, 40129 Bologna, Italy Springer

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by Laue lenses, with a great advantage in sensitivity also in this band and the possibility of an inter-calibration of ML telescopes and Laue lenses in the case of satellite missions which include both. A huge increase in sensitivity (by a factor 100 or more) above 100 keV would open a new window of investigation of the high energy astrophysics, with the concrete possibility of ﬁxing many open issues, apart from the prospect of unexpected discoveries. Among the open issues, we wish to mention (see also Frontera et al. [1]): – The properties of the high energy emission in presence of super-strong (>1013 G) magnetic ﬁelds (mass accreting X-ray pulsars, anomalous X-ray pulsars, Soft Gamma-Ray Repeaters); – The role of the Inverse Compton in compact mass accreting objects and in particular in Gamma Ray Bursts; – The role of non thermal mechanisms in extended objects (Supernova remnants, Galaxy clusters); – The role of the antimatter in the Universe from the study of the e+ − e− pair annihilation line and the effect on it of strong gravitational ﬁelds; – The study the star explosion mechanisms via the detection of the nuclear lines from synthesized elements (e.g., Co, Ni, Ti); – The high energy emission physics in AGNs from the study of the high energy cut-offs in their continuum spectra; – The origin of the high energy Cosmic X-/gamma-ray background (CXB). Synthesis models require a spectral roll-over with an e-folding energy of 100–400 keV in AGN. So far only a few spares measurements are available. Here we give an overview and the status of our HAXTEL (=HArd X-ray TELescope) project devoted to develop Laue lenses with a broad passband from 60 to 600 keV and beyond. This development is complementary to that which is being performed by other authors (e.g., von Ballmoos et al. 2004), devoted to the development of Laue lenses for the study of nuclear gamma-ray lines. 2. An overview of the results obtained thus far 2.1. Results of the feasibility study We summarize here the results of a theoretical feasibility study devoted to establish the best design of a Laue lens telescope along with its sensitivity expectations [3]. First of all the lens of our project is required to have a spherical shape with radius R and focal length f = R/2. If the crystals are available with ﬂat geometry, which was our assumption, in order to best approximate the spherical geometry of the lens, crystal tiles with small cross sections are required. Among the best candidate materials for their high reﬂectivity, Cu (111) with mosaic crystal structure appears the most attractive in the hard X-/gamma-ray range (see Figure 1), and it is one of the few materials for which the technology for growing it with mosaic structure has already been developed with good results (see below). Thus for our feasibility study we have assumed Cu (111). Once the material choice has been ﬁxed, crystal thickness and mosaic spread of the crystallites which make the mosaic crystal are the most crucial parameters to be ﬁxed to optimize the lens performance. However their best values depend on the nominal Springer

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Fig. 1 Peak reﬂectivity of three materials which show high Bragg reﬂectivity and for which technology has been developed for mosaic structure. Cu (111) shows the best reﬂectivity above 100 keV. Reprinted from [3]

lens passband (E min , E max ), where E min =

hc hc f ≈ 2d sin θmax drmax

E max =

hc hc f ≈ 2d sin θmin drmin

(1)

with d being the crystal lattice spacing, and θmax and θmin being the maximum and minimum diffraction angles, respectively, permitted by the lens geometry, and thus dependent on the outer and inner radii rmax and rmin of the spherical segment, respectively (see Figure 2). The effect of the crystal thickness on the lens effective area is exempliﬁed in Figure 3, in which a lens with 3 m focal length and a nominal passband from 60 to 200 keV are assumed. As can be seen, a single thickness is not the best solution for optimizing the lens effective area in its entire passband. While a thickness of 2 mm gives the highest effective area at low energies, a higher thickness (4 mm) optimizes the effective area at the highest energies. However the optimization of the lens effective area in a broad passband could imply a distribution of crystal thicknesses incompatible with lens weight constraints. We have investigated this issue elsewhere [5], ﬁnding that it is possible to ﬁnd a good compromize. Also the mosaic spread β (FWHM of the angular misalignment of the crystallites), which deﬁnes the energy bandwidth (FWHM) of the photons reﬂected by a single crystal when they impinge on it at a given Bragg angle θ B ( E = Eβ/ tan θ B ), affects the lens effective area: a higher spread gives a higher effective area [3]. However a higher spread also produces a higher defocusing of the reﬂected photons in the focal plane. The best parameter which takes into account of both the effective area and the size of the focal spot in the focal plane is the focusing factor G given by: G = f ph

Aeff Ad

(2)

in which Aeff is the effective area of the lens and Ad is the area of the focal spot on which a fraction f ph of photons reﬂected by the lens fall. Taking into account that the sensitivity of Springer

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Fig. 2 Geometry of the Laue lens. Reprinted from [4]

the lens is given by nσ Imin (E) = n d Aeff f ph

Bd Ad T E

(3)

where Imin (photons cm−2 s−1 keV−1 ) is the the minimum detectable intensity in the interval

E around E, n σ is the signiﬁcance level of the signal (typically n σ = 3–5), Bd is the instrumental background intensity (counts cm−2 s−1 keV−1 ), T is the exposure time to a celestial source, and n d is the focal plane detector efﬁciency at energy E, it can be seen that the lens sensitivity is inversely proportional to G. We have investigated the dependence of G on the focal length for three values of the mosaic spread (0.5, 1 and 2 arcmin) and for two different lens passbands: 90–110 keV (Low Energy, LE) and 450–550 keV (High Energy, HE). We ﬁnd, for f ph = 0.50 which gives the fraction of photons corresponding to the Half Power Radius (HPR), and for crystal tiles of 15 × 15 mm2 , the result shown in Figure 4. As can be seen, G is signiﬁcantly higher at low energies, it shows a saturation for high focal lengths, and, specially at high energies, a lower spread is more effective. This result has important consequences for the optimization the Laue lens design. It results that a lower spread is crucial to improve the lens sensitivity at high energies. However, compatibly with an acceptable G, a larger spread allows a higher effective area and thus Springer

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Fig. 3 Effect of the crystal thickness on the effective area. Reprinted from [3]

Fig. 4 Dependence of the focusing factor G on the focal length F for three different values of the mosaic spread in two different energy bands: 90– 110 keV (LE) and 450–550 keV (HE). See text

a better photon collection. A larger mosaic spread also requires a lower accuracy in the positioning of the crystals in the lens [3]. Another issue we have investigated is the disposition of the mosaic crystal tiles in the lens for a uniform coverage of the lens passband. The result is that the best crystal tile disposition is given by an Archimedes’ spiral (see Figure 5). As already discussed [3,4], this disposition, for low focal lengths, gives a smooth change of the lens effective area Aeff with energy, apart from jumps due to the contribution from higher diffraction orders (see, e.g., Figure 9). The advantage of the Laue lenses with respect to the direct-viewing telescopes, is better illustrated by the equivalent effective area S, deﬁned, in the case of a lens, as S = G 2 Ad , while, in the case of a direct-viewing telescope, S is the useful detector area. In both cases the sensitivity (see Equation (3)) is inversely proportional to S 0.5 , which, for the lenses, is proportional to G, which increases with the focal length as shown in Figure 4. Special care has to be taken in the accuracy of the crystal tile positioning in the lens. A deviation of the crystal orientation with respect to the nominal position degrades the focusing factor. The accuracy required in the crystal tile positioning to get a negligible degradation of the nominal focusing factor not only depends on the mosaic spread, as above mentioned, but also on the focal length. Higher focal lengths require higher positioning accuracies, which is Springer

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Fig. 5 Disposition of the mosaic crystal tiles in the lens. The lens size is that required for a 210 cm focal length and a 60–200 keV nominal bandpass

at the current stage of development one of the major problems to be faced for the realization of a Laue lens. 2.2. Reﬂectivity measurements of Cu (111) mosaic crystal samples To test the reliability of the our feasibility study, we have performed reﬂectivity measurements of mosaic crystal samples of Cu(111). Samples of this material were provided by the Institute Laue Langevin (ILL), that has developed the technology for growing large single crystals of Copper with a small mosaic structure. The crystal samples of Cu (111) with different thicknesses and mosaic spreads were supplied to us for being tested at the Ferrara X-ray facility [7, 8]. Reﬂectivity curves were derived in different positions of the crystal surface to study the uniformity of the mosaic properties. Results of these measurements have been reported and discussed by Pellicciotta et al. [4]. An example of the derived reﬂectivity is shown in Figure 6. The reﬂectivity curves were ﬁt with the theoretical model function derived by [9]. In most cases the results were found satisfactory. Figure 6 shows a typical result of the ﬁtting analysis. However evidence of crystal inhomogeneity was observed near the crystal boundaries, mainly due to the crystal cutting procedure which perturbs the mosaic structure. Given that, for our goals, the crystals should be as homogeneous as possible the cutting procedure requires further reﬁnement. In spite of that, the measurements results obtained substantially conﬁrm the expectations of our feasibility study.

3. Status of our lens development project We are now developing a Demonstration Model (DM) to establish the best crystal assembling technique of the lens. The DM is a sector of the lens shown in Figure 5 and will be composed of 30 mosaic crystals with 3 arcmin spread and 15 × 15 mm2 front surface. A ﬁrst mock-up of the DM, made of polycrystalline copper, has already been built for ﬁnding the best crystal assembly Springer

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Fig. 6 Example of measured reﬂectivity proﬁle. Also shown is the best ﬁt model and the residuals to the model (bottom panel). Reprinted from [4]

Fig. 7 Picture of the ﬁrst DM mock-up during its development phase

technique which gives the needed mechanical accuracy in the crystal tile positioning. A picture of the ﬁrst built mock-up during its development phase is shown in Figure 7. Once the DM has been developed and it is demonstrated to correctly work, a Prototype Model (PM) with the same focal length of the DM (210 cm) will be built, increasing the number of crystal tiles. The realization of the PM will be a good benchmark about our capabilities of scaling the assembling technology to larger lenses. Both DM and PM will be tested at the Ferrara X-ray facility which is now extended for this project [10]. Springer

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Fig. 8 Example of multi-lens conﬁguration for the study of the continuum emission in the 60–1000 keV passband. The focal length assumed is 50 m. Part of the front surface of the Low Energy Lens (LEL) is taken by the four High Energy Lenses (HELs). See text for details

In addition to the hardware development, also a Monte Carlo (MC) code devoted to understand the optical properties of the lenses (point spread function, off-axis response, angular resolution) has been developed. Preliminary results have already been reported [5].

4. Example of possible multi-lens conﬁguration for space astronomy As above discussed the gain of a Laue lens and thus its sensitivity approximately increase with the square of the focal length. We have already investigated different telescope conﬁgurations and focal lengths to efﬁciently cover the 60–1000 keV energy band. A multi-lens conﬁguration appear the most sound solution. We show here (see Figure 8) a possible conﬁguration with one large Low Energy Lens (LEL) with 60–600 keV energy passband and 4 High Energy Lenses (HELs) with 150–1000 keV nominal energy passband. All lenses have been assumed to have a focal length of 50 m and are designed according to the above discussed criteria, to study the continuum emission of celestial sources of gamma-rays. The main parameters of the lenses are summarized in Table 1. The advantage of this conﬁguration is the achieved compromize between large collection area (see Figure 9 for LEL and for one HEL unit), which guarantees a good statistics of the collected photons up to the highest energies. The 4 units also guarantee a redundancy in the case of a failure of a detector, as it occurred in the case of one of the 3 units of the BeppoSAX MECS telescopes [11]. A drawback of the LEL with an energy threshold at 60 keV is its large diameter, which could be decreased by adopting a petal conﬁguration to be launched folded and deployed in orbit. Also the lens weight is not negligible. The total weight of the crystals amounts to about 1600 Kg. A lighter solution can be obtained decreasing the number of HEL units. With 2 HELs the total crystal weight is 990 Kg. A possible further weight decrease could be obtained by decreasing the collection area of the LEL, e.g., adopting for the LEL a petal-like conﬁguration. Springer

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Table 1 Main features of the Low Energy (LEL) and High Energy Lenses (HEL)

Parameter

LEL

HEL

Focal length (m) Inner radius (cm) Outer radius (cm) Mosaic crystal material Crystal tile size (mm2 ) Number of crystal tiles Crystal weight (Kg) Mosaic spread (arcmin) Nominal energy passband (keV) Half power radius of the focused photons (mm)

50 50 496 Cu (111) 10 × 10 × 2 221347 395 1 60–600 10

50 30 198 Cu (111) 10 × 10 × 4 83409 298 1 150–1000 10

Even the single HEL and LEL lenses show an unprecedented spectrum determination sensitivity. Assuming 106 s of exposure time and an energy bandwidth E = E/2, the sensitivity (see Equation (3)) of the LEL and that of one of the HEL units is shown in Figure 10. We have assumed a detection efﬁciency ηd = 1, f ph = 0.5 and a background intensity level B = 5 × 10−5 counts cm−2 counts cm−2 s−1 keV−1 , which is approximately the mean value measured with the PDS instrument aboard BeppoSAX in the 60–300 keV band. As can be seen, a sensitivity of a few ×10−8 cm−2 s−1 keV−1 or better, is achieved

Fig. 9 Effective area of the lenses. Left panel: Low Energy Lens (LEL); right panel: High Energy Lens (HEL), 1 unit

Fig. 10 Expected 3σ sensitivity of the lenses for an exposure time of 106 s. Left panel: Low Energy Lens (LEL); right panel: High Energy Lens (HEL), 1 unit Springer

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in the entire energy band (60–1000 keV), combining the LEL and HEL sensitivities. The maximum lens throughput is obtained between 100 and 550 keV, where the sensitivity could achieve values of a few ×10−9 cm−2 s−1 keV−1 , corresponding, in energy, to a few ×10−16 erg cm−2 s−1 keV−1 . Also for a deep study of the high energy nuclear lines (>600 keV), Laue lenses appear to be the best solution, but they require a speciﬁc design to maximize the sensitivity in a band around the expected energy of the lines (see, e.g., [2]). The focal plane detector performance is crucial for achieving the best lens sensitivity. In addition to a spatial resolution of the order of 1 mm and an energy resolution (FWHM) better than 2 keV at 500 keV (for the study of the annihilation line), a high detection efﬁciency is mandatory (for achieving the above sensitivity we have assumed ηd ∼ 1). The extension of the energy passband to energies lower than 60 keV (possibly down to 1 keV) is highly desirable for an accurate broad band study of the known high energy sources and for the identiﬁcation of possible serendipitous sources we expect to discover with the unprecedented lens sensitivity. For spectral studies, a multilayer optics appears the best solution.

5. Conclusions The development of a Laue lens based on mosaic crystals for observing the hard X-ray sky in a broad continuum band has already successfully passed through a theoretical feasibility study to establish the best design of the lens and its expectations. Cu (111) has been suggested as a good candidate material. The experimental results obtained by the analysis of mosaic crystal specimens of Cu (111) produced at the ILL have encouraged our work and have demonstrated the correctness of our predictions. At the moment we are working on a Demonstration Model to establish the best assembling technique of the crystal tiles in the lens. After this phase a prototype model will be built and tested in our X-ray facility and, possibly, aboard a balloon ﬂight. The expected sensitivity of our designed Laue lenses is unprecedented and is expected to open a new window in the high energy astrophysics. Acknowledgements We acknowledge the ﬁnancial support by the Italian Space Agency ASI to the HAXTEL project. This research was possible also thanks to the received Descartes Prize 2002 of the European Committee.

References 1. Frontera, F. et al., Exploring the hard X-/gamma-ray continuum spectra with Laue lenses, Proc. 39th ESLAB Symposium, in press (2006) (astro-ph/0507175) 2. von Ballmoos, P. et al., MAX: a gamma-ray lens for nuclear astrophysics, Proc. SPIE 5168, 482 (2004) 3. Pisa, A. et al., Feasibility study of a Laue lens for hard X-rays for Space Astronomy, Proc. SPIE 5536, 39 (2004) (astro-ph/0411574) 4. Pelliciotta, D. et al., Laue lens development for hard X-rays (>60 keV), IEEE Trans. Nucl. Sci., in press (2006) (astro-ph/0511490) 5. Pisa, A. et al., Optical properties of Laue lenses for hard X-rays (>60 keV), Exp. Astron. 20, DOI 10.1007/s10686-006-9045-2 (2006) 6. Pisa, A. et al., Development status of a Laue lenses for hard X-rays (>60 keV), Proc. SPIE 5900, 350 (2005) 7. Loffredo, G. et al., X-ray facility for the ground calibration of the X-ray monitor JEM-X on board INTEGRAL, Astron. Astrophys. 411, L239 (2003) Springer

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8. Loffredo, G. et al., The X-ray facility of the Physics Department of the Ferrara University, Exp. Astr., in press (2006) 9. Zachariasen, W. H., Theory of X-rays Diffraction in Crystals, Wiley, New York (1945) 10. Loffredo, G. et al., The Ferrara hard X-ray facility for testing/calibrating hard X-ray focusing telescopes, Exp. Astron. 20, DOI 10.1007/s10686-006-9049-y (2006) 11. Boella, G. et al., The Medium-Energy Concentrator Spectrometer on board the BeppoSAX X-ray astronomy satellite, Astron. Astrophys. 122, 327 (1997)

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Exp Astron (2005) 20:253–267 DOI 10.1007/s10686-006-9071-0 ORIGINAL ARTICLE

CLAIRE: First light for a gamma-ray lens Peter von Ballmoos · Hubert Halloin · Jean Evrard · Gerry Skinner · Nikolai Abrosimov · Jose Alvarez · Pierre Bastie · Bernard Hamelin · Margarida Hernanz · Pierre Jean · Jurgen ¨ Kn¨odlseder · Bob Smither

Received: 15 May 2006 / Accepted: 16 August 2006 C Springer Science + Business Media B.V. 2006

Abstract The objective of the R&D project CLAIRE was to prove the principle of a gammaray lens for nuclear astrophysics. CLAIRE’s Laue diffraction lens has a diameter of 45 cm and a focal length of 277 cm; 556 germanium-silicon crystals are tuned to focus 170 keV photons onto a 1.5 cm diameter focal spot. Laboratory measurements of the individual crystals and the entire lens have been used to validate a numerical model that we use to estimate the lens performance for a source at inﬁnity. During a stratospheric balloon ﬂight on 2001 June 14, CLAIRE was directed at the Crab nebula by a pointing system able to stabilize the lens to within a few arcseconds of the target. In 72 min of valid pointing time, 33 photons from the Crab were detected in the 3 keV bandpass of the lens: CLAIRE’s ﬁrst light! The performance of CLAIRE’s gamma-ray lens, namely the peak reﬂectivity for a polychromatic source (9 ± 1%), has been conﬁrmed by ground data obtained on a 205 meter long test range. CLAIRE’s measured performance validates the principle of a Laue lens for nuclear astrophysics, opening the way for a space-borne gamma-ray lens telescope P. von Ballmoos () · H. Halloin · G. Skinner · P. Jean · J. Kn¨odlseder CESR, 9, av. du Colonel-Roche, 31028 Toulouse, France e-mail: [email protected] J. Evrard CNES, 18 Avenue Edouard Belin, 31401 Toulouse, France N. Abrosimov Institut f¨ur Kristallz¨uchtung, Max-Born-Str. 2, 12489 Berlin, Germany J. Alvarez · M. Hernanz IEEC, Edif. Nexus, 08034 Barcelona, Spain P. Bastie Laboratoire de Spectrom´etrie Physique, BP 87, 38402 St Martin d’H`eres, France B. Hamelin Institut Laue-Langevin, BP 156, 38042 Grenoble, France B. Smither Argonne Natl. Lab, 9700 South Cass Avenue, Argonne, Il 60439, USA Springer

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that will achieve one to two orders of magnitude improvement in sensitivity over present technologies.

Keywords Instrumentation . Nuclear Astrophysics . Gamma Ray Optics . Laue Crystals

Introduction Nuclear astrophysics presents an extraordinary scientiﬁc potential for the study of the most powerful sources and the most violent events in the Universe. Ranging from the life cycles of matter to the behaviour of matter under extreme conditions, the gamma-ray Universe is mostly non-thermal. Its principal science themes, cosmic explosions and cosmic accelerators, are discussed in Section 1 of this volume. Today, traditional telescope concepts for nuclear astrophysics are reaching the physical limits for space missions; disadvantages whose impact increases with detector size – mostly related to the high background in space borne gamma-ray detectors – have lead gamma-ray astronomy to an impasse where “bigger is not necessarily better”. Present telescope concepts for nuclear astrophysics are based on inelastic interaction processes making use of geometrical optics (shadowcasting in modulating aperture systems) or quantum optics (kinetics of Compton scattering). Improvements in the sensitivity of an instrument can usually be obtained by a larger collection area – in the case of “classic” gamma-ray telescopes this involves a larger detector surface. However, since the background noise is roughly proportional to the volume of a detector, a larger photon collection area is synonymous with higher instrumental background. For “classic” gammaray telescopes, the sensitivity is thus increases at best as the square root of the detector surface. A possible way out of this dilemma consists of taking advantage of the wave character of the photons. Gamma rays can interact coherently inside a crystal via Bragg diffraction, i.e. through the interference between the periodic nature of radiation and the periodic structure of matter in a crystal lattice. The principles of crystal diffraction are discussed by Halloin and Bastie [8]. In a Laue diffraction lens, a large number of crystals are oriented so as to deﬂect incident photons towards a common focal spot: γ -rays are focused from a large collecting area onto a small detector volume. As a consequence, the background noise – which scales with detector volume – is extremely low, making possible unprecedented sensitivities. With the R&D project CLAIRE we took up the challenge of proving the principle of a gamma-ray lens for nuclear astrophysics, namely by demonstrating a prototype Laue lens and measuring its actual performance when observing a celestial source. As a ﬁrst step, a ground-based Laue lens system had been set up and successfully tested by our collaboration [13]. The diffraction efﬁciencies of individual Ge crystals, were measured at the APS synchrotron at Argonne National Laboratories [11] and agreed with those expected from the Darwin model (efﬁciencies of 20 to 31% depending on energy and crystal planes). The next logical step towards a space-borne crystal lens telescope was to demonstrate a diffraction lens under space conditions and with an astrophysical target. This objective was realized between 1999 and 2003 with the CLAIRE project. Springer

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CLAIRE’s lens Concept and design Demonstrating the principle of a Laue diffraction lens during a short balloon ﬂight implied the observation of a dependable γ -ray point source. At declinations compatible with the latitude of the available launch site of CNES at Gap-Tallard (French Alps) the Crab nebula, one of the rare standard candles at γ -ray energies, was an obvious choice. Whereas the limited energy band of a Laue lens is not a handicap when nuclear lines are to be detected, observing the Crab nebula’s continuum spectrum with a narrow bandpass Laue lens is a challenge. However, for a strong continuum source such as the Crab, and within the mass and size constraints for an exploratory balloon ﬂight we found it advantageous to use all the crystal rings for a single, narrow energy band. To keep complexity and cost within the scope of a balloon project, it was clear that the energy to which the lens is tuned would be ﬁxed, even though a tunable lens prototype had been demonstrated [10]. The choice of the energy band to be diffracted was then guided by practical considerations : the structural rigidity of the telescope, the upper limit of 500 kg for balloon payloads ﬂying over France, and the severe pointing requirements for a balloon-borne lens made a short focal length preferable (see Equation 2 below). Since the focal length of a lens of a given diameter increases with energy, these arguments favoured energies below 200 keV for our 45 cm diameter lens frame. With the above constraints in mind, the energy to be diffracted was more or less arbitrarily chosen to be 170 keV for a source at inﬁnity (511 keV being the 3rd harmonic. . .), this energy is sufﬁciently far away from two strong lines that are known to appear in a GeD background spectra at 139.7 and 198.4 keV (Ge isomeric transitions) and which are useful for a precise energy calibration. Geometry In a Laue-type crystal diffraction lens, crystals are disposed on concentric rings such that they will diffract the incident radiation of a given energy onto a common focal spot (Figure 1). In order to be diffracted, an incoming gamma-ray must satisfy the Bragg-relation 2d sin θ B = nλ

(1)

where d is the crystal plane spacing, θ B – the incident angle of the photon (Bragg-angle), n – the reﬂection order, and λ – the wavelength of the gamma-ray. See Halloin [9] for a thorough discussion of the principles of diffraction optics. Fig. 1 The basic design of a crystal diffraction lens in Laue geometry

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Fig. 2 CLAIRE’s lens during tuning on the optical bench at CESR. In the centre of the lens is a small telescope and CCD camera mounted on precision ball bearings. The direction of a source whose image remains on the same pixel during rotation (the “invariant pixel”) deﬁnes the optical axis

In a narrow bandpass Laue lens such as CLAIRE, every ring of crystals uses a different set of crystalline planes [hkl] in order to focus photons in a single energy band (E 2 = E 1 = E i in Figure 1) onto a common focal spot. For a given focal distance f of the lens, ri is the radius of ring “i” is given by ri = f tan[2θ B,i ] ≈ f

λ , di

(2)

where di is the crystalline plane spacing of ring “i” and λ is the wavelength of the radiation to be focused. Table 1 lists the ring radii and dimensions of CLAIRE’s lens; the parameters are for ˚ concentrating 170 keV photons onto Germanium crystals (lattice parameter a = 5.65 A) a common focal spot at a distance of 277 cm. Since mosaic defocusing (see e.g. [8, 9]) is negligible for CLAIRE’s short focal length (beam broadening on the focal plane 0.4–1.5 mm), the size and shape of the focal spot is dominated by the size of the crystal tiles projected on Table 1 The eight rings of CLAIRE’s gamma-ray lens

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Ring

plane (Hkl)

d (hkl) ˚ A

Number of crystals

Crystal size (mm)

Mean radius (mm)

Scatter angle

0 1 2 3 4 5 6 7

111 220 311 400 331 422 333 440

3.27 2.00 1.71 1.41 1.30 1.15 1.09 1.00

28 52 56 72 80 88 96 104

10 × 10 10 × 10 10 × 10 10 × 10 10 × 7 10 × 10 10 × 7 10 × 10

61.7 100.8 118.2 142.6 156.2 174.7 188.2 201.7

0.64◦ 1.04◦ 1.22◦ 1.48◦ 1.61◦ 1.81◦ 1.92◦ 2.09◦

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the focal plane: in CLAIRE’s tuned lens, almost 100% of the diffracted photons are contained in a 1.5 cm diameter focal spot. Crystals CLAIRE’s crystals were produced by N. Abrosimov at the Institut f¨ur Kristallz¨uchtung (IKZ) in Berlin. The width of a crystals energy bandpass – and thus the lens efﬁciency – are governed by the mosaicity of the crystal [9]. In order to obtain homogeneous, constant quality crystals with the required optimal mosaicity (25–50 arcs), small amounts of Silicon are added to the Germanium melt during the growth process. The Germanium-rich Ge1−x Six crystals (x ≈ 0.02) were grown by a modiﬁed Czochralski technique using Silicon feeding rods to replenish the loss of Si in the melt during the growth [1]. The mosaicities of the Ge1−x Six crystals range between roughly 30 arcsec and 2 arcmin, leading to a ﬁeld of view of about 1.5 arcmin and a diffracted energy bandwidth of about 3 keV at 170 keV. A correlative study between crystal structure, mosaicity and diffraction efﬁciency of the CLAIRE crystals is presented in [2]. After cutting of the crystals ingots at IKZ Berlin, most of the crystal tiles were characterized (mosaicity) at the Hard X-Ray Diffractometer of ILL Grenoble. Lens assembly and tuning At CESR Toulouse, the individual crystal tiles were mounted on ﬂexible aluminium supports, which in turn are mounted on the lens frame. The reinforced 45 cm diameter titanium frame that holds up to 576 crystals on 8 rings (Table 1) was designed and manufactured at the Argonne National Laboratory, Argonne, USA. The tuning of the lens consists of tilting each crystal tile to the appropriate Bragg angle so that the diffracting energy is 170 keV for a source at inﬁnity. Instead of directly calibrating the lens for a parallel beam of 170 keV photons, crystal tuning on the 20 m optical bench at CESR uses a 150 kV X-ray generator situated on the lens optical axis at a distance of 14.16 m. At this distance, a crystal will be correctly tuned (170 keV at inﬁnity) if it diffracts 122.28 keV photons. A co-aligned mask (brass-lead sandwich) of the size of the entire lens, placed on the optical axis just in front of the lens, was used to select an individual crystal for tuning, while shielding already tuned crystals. The continuum spectrum of the X-ray generator allows us to quickly ﬁnd the diffraction peak as soon as it shows up at any energy (typically between 90–140 keV, corresponding to an angular tolerance of 0.4◦ to 1.4◦ depending on the ring). The crystal inclination is then manually ﬁne adjusted (by a screw pushing against the crystals aluminium support plate – 1% of a full turn corresponds to a shift of about 1 keV) so that the diffraction peak shifts until it reaches 122.28 keV. The CLAIRE crystals were tuned to within a precision of ± 0.3 keV, corresponding to a precision of ±8

(innermost ring) to ±25

(outermost ring), respectively. The conﬁguration of the CESR optical bench was chosen to allow for swift tuning/detuning veriﬁcation using the 122 keV line of a 57 Co source (see below). Pointing and alignment In order to be able to point the lens at a source (during tuning, ground tests, as well as in ﬂight), the lens optical axis has to be visualized. For this purpose, a small optical telescope equipped with a CCD camera is mounted in the centre of the lens frame on precision ball bearings; Springer

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the ball bearings allow the telescope to rotate around its optical axis. When observing a light source while this telescope is rotated, the image on the CCD describes a circle whose centre gives the direction of the rotating axis. This invariant pixel is then made the gamma-ray lens optical axis. The method provides an alignment accuracy better than 10 arcsec and was used throughout all operations of the lens – from crystal tuning to ﬂight alignment. Even when refocusing of the optical telescope becomes necessary (from the 14 m source to inﬁnity) or if the CCD camera is to be changed, the lens axis remains unchanged within the required precision. On the optical bench at CESR, the light source was a small lamp positioned on the optical axis as close as possible in front of the target of the X-ray generator tube. Performance of the individual crystals The spectra recorded during the tuning campaigns (2000, 2001, 2003) represent large databases with 400 to 600 individually measured crystals. The characteristics of the recorded spectra, mainly the integrated ﬂux, the width and the shape of the diffraction peak, permit the determination of the crystals’ parameters (mosaicity and mean size of the crystallites, see [6]). During the tuning campaign 2003, the integrated ﬂux in the diffraction peak was measured for 559 individual crystals. Figure 3 compares the statistics of these ﬂuxes in the eight rings. Two main lessons are conveyed by this graph: a. the innermost rings ([111] and [220] crystals) are roughly 4 times more efﬁcient than the outermost rings ([333] and [440] crystals). This behaviour is in agreement with theoretical peak efﬁciencies. Note that the largest part of the crystals is situated in the outer rings – where efﬁciencies are unfortunately lowest. b. the large spread of the measured ﬂuxes in a single ring means that the quality of the CLAIRE crystals is quite heterogeneous. The efﬁciency of the individual crystals within a ring varies by factors of 2 to 10, depending on the ring! The tuning data, however, also prove that real crystals can be as good as the Darwin model predicts: the best crystals of the lens have peak efﬁciencies above 20%.

1.5 111

2

diffracted photons [cm s µA]

Fig. 3 Diffracted ﬂuxes of 559 individual Ge1−x Six crystal from the 2003 tuning campaign. Boxes enclose 50% of the data set of each ring, the median value of the ﬂux is displayed as a line. The lines extending from the top and bottom of each box mark the minimum and maximum values within the crystal data set of each ring

220

311

400

331

422

333

440

CLAIRE 2003 tuning data of 559 Ge crystals 1

0.5

0 0

1

2

3

4

ring number

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5

6

7

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The parameters from the database were used for the development of a realistic numerical model of our lens (Monte-Carlo simulation). The lens model turned out to be essential for comparing and scaling the different experiments with their various conditions of pointing, source spectrum and distance. Ground tests In order to estimate the diffraction efﬁciency of the lens, as well as its angular response, several experiments have been conducted on the CESR optical bench, at the launch site in Gap-Tallard (French Alps) and during a “long distance” test near Figueras (Catalonia). The 57 Co standard The gamma-ray line at 122.06 keV from a small radioactive 57 Co source was observed at a distance of 14.07 m. This test was performed on the optical bench at CESR and on the launch site where an X-ray generator can not be operated. The resulting global reﬂectivity turned out to be merely 3.2 ± 0.1%; the reﬂectivity being deﬁned as the ratio of photons concentrated onto the focal spot over the number of photons incident on all the crystals of the lens. This low reﬂectivity is the consequence of two effects – the parallax of the crystals for a source at ﬁnite distance and the high absorption of the crystals whose thickness was optimized for 170 keV. At a distance of 14 m, the angular size of a 1 × 1 cm footprint crystal is ∼2.4 arcmin ∼1.7 arcmin for the crystals with 0.7 cm height). Since these values are typically 3–4 times larger than the mosaicity of the crystals, the Bragg condition is only satisﬁed in a fraction of the crystal volume, leading to an apparently low diffraction efﬁciency. We have used our numerical model to extrapolate the efﬁciency of the 57 Co tests (monochromatic, divergent beam at 122 keV) for an astrophysical target (polychromatic, parallel beam at 170 keV). Taking into account the estimated uncertainties on the crystals’ parameters and considering a diffracted peak width of 3 keV FWHM, the peak efﬁciency for parallel radiation at 170 keV estimated from the 57 Co data is 7.7 ± 1%. The 57 Co standard tests were performed before and after transferring the lens to the launch site, showing that the lens did not suffer signiﬁcant detuning during the 6 hour drive from CESR Toulouse to Gap-Tallard. X-ray beam tests on CESR optical bench In addition to crystal tuning, the optical bench at CESR also allowed measurements of the reﬂectivity in a polychromatic, though divergent, beam at energies below 150 keV. Although the continuum spectrum of the X-ray generator can “cover” the entire volume of each crystals with photons satisfying the Bragg condition, the peak reﬂectivities measured were too low (typically 3.5 ± 0.4%) for a reason very similar to the one that made the 57 Co standards look to low (see above): The total energy band “covered” by a single crystal is in fact determined by its angular width as seen from the source. However, at any one given energy within this band, only a slice of the crystal’s volume actually satisﬁes the Bragg condition and contributes to the diffracted ﬂux. The width of this energy slice is determined by the crystal’s mosaicity. As a consequence, the ratio of the total crystal volume to active volume is again the ratio of mosaicity to angular extent of the crystal. The semi-empirical value that is deduced from the laboratory X-ray generator data for the peak efﬁciency at 170 keV is 8.7 ± 1%. Springer

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1000 C preflight

normalized counts in focal spot

Fig. 4 The diffractions peak of CLAIRE’s lens for two “lens totals” performed on the CESR optical bench using the x-ray generator. Preﬂight data were taken in May 2001, post ﬂight data are from September 2002. The best ﬁts (Lorenzians) show widths of 3.0 and 3.4 keV FWHM, respectively

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data

postflight D

data

800

600

400

200

0 110

115

120

125

130

135

E [keV]

The overall diffraction efﬁciency of the lens was veriﬁed in this manner just before the 2001 balloon campaign, and again more than a year later, after the balloon ﬂight. The energy spectrum of the two diffraction peaks, normalized for equivalent experimental conditions (generator current, absorber thickness), are shown in Figure 4. In spite of a rough parachute landing (>50 g) and recovery, the two tests show virtually identical integrated reﬂectivities (roughly 2% reduction mostly due to crystals that detached during landing and recovery) and only a slight detuning. So although the CLAIRE lens had not been designed for this, its robustness has demonstrated that a gamma-ray lens can be made sturdy enough to withstand high-g shocks and vibrations. CLAIRE “TGD” In May 2003 the CLAIRE telescope was tested on a 205 m long optical bench, set up on a small airﬁeld near Figueras in northern Catalonia. At this “quasi inﬁnite” distance (TGD : Test a` Grande Distance) the diffracted energy is 165 keV. Three mobile cabins were installed on the airstrip : the gamma-ray lens and germanium detector were set up in a ﬁrst cabin, a second cabin about 200 meters away from the ﬁrst one was used to accommodate the X-ray source, a third cabin served as control room; its location, about 15 m from the lens/detector container, was chosen to be well out of the X-ray beam. The X-ray source consisted of an industrial X-ray generator with a 2.5 × 2.5 mm tungsten target. The voltage and current were set to 250 kV and 1 mA respectively, allowing for sufﬁcient X-ray ﬂux at 165 keV after absorption by 205 m of air. CLAIRE was pointed to the X-ray source with an alignment method similar to that used in the laboratory and in ﬂight: the X-ray tube was positioned such that a lamp mounted immediately in front of it coincided with the invariant pixel of the rotating CCD camera. The peak efﬁciency (205 m, diffracted energy 165 keV) was measured to be 8.5 ± 1%, in agreement with the lens simulations for this test, and compatible (considering the error bars) with the other ground tests. Springer

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Fig. 5 CLAIRE TGD energy response of the lens for various depointing angles

The different values for the lens efﬁciency measured on the ground (rescaled 57 Co standards, 7.7%; rescaled X-ray beam tests, 8.7%, and TGD, 8.5%) will be discussed below. Figure 5 shows the energy response of the lens for various off-axis angles of the source (from 30 to 270 arc seconds). The curves are compared with the results of a Monte-Carlo simulation of these experiments, using the crystal parameters as deduced from the tuning data. The shape and deformation of the energy response are well reproduced by the model, validating the theoretical instrumental response of the lens. For a detailed discussion of the CLAIRE TGD see [3].

The balloon instrument Gondola The lens module, detector package, and pointing systems are integrated into a telescope structure made of composite materials (Figure 6). The 3 m telescope structure, consisting of 18 carbon ﬁbre spars and 3 honeycomb platforms only weighed 100 kg. The structure was conceived, manufactured and tested by the University of Birmingham. The upper platform holds the lens and its ﬁne pointing system. The detecting system (detector matrix, Dewar, anticoincidence shield/collimator and electronics) are mounted on the lower platform. The entire payload weighs 500 kg. Detector Diffracted photons are collected on a small 3 × 3 array of high-purity germanium detectors, housed in a cylindrical aluminium cryostat. Each of the individual Ge bars is an n-type coaxial detector with dimensions of 1.5 cm × 1.5 cm and 4 cm long, with an internal electrode bore hole (35 mm depth, 5 mm diameter). Preampliﬁer electronics are located in a pressurized Springer

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Fig. 6 The CLAIRE telescope at Gap during the 2001 balloon campaign. On the ﬁrst platform, the gamma-ray lens in its two-axes gimbal

aluminum capsule directly behind the detector matrix. The detector is cooled by a liquid nitrogen dewar that was also pressurized during the ﬂight. The detector is actively shielded by a CsI(Tl) side shield and BGO collimators. The focal spot of the gamma-ray lens is visualized by the circle produced on the detector plane by a small laser mounted on the rotating alignment telescope. During ﬂight the spot may wander around on the Ge-detector matrix as the primary stabilization seeks its central position. The focal spot ideally is on the central detector of the Ge matrix. The surrounding detectors can be used either to enhance the detection efﬁciency of source photons having undergone a Compton scatter in the center detector, or alternatively they may be used for background rejection. Stabilization and pointing The CLAIRE stabilization and pointing system was developed by the balloon division of the French Space Agency CNES with the help of the Observatoire de Gen`eve, Switzerland. Two almost independent pointing stages allow the observation of a target located within a few degrees of the sun (on June 14 and 15 the Crab is within 1◦ of the sun). The primary pointing system stabilizes and points the entire telescope to within 10 arc minutes; azimuthal control is performed by a torque swivel (that also measures the torque between gondola and balloon), and by using azimuthal information from a magnetometer and a gyrometer. A screw jack in conjunction with an inclinometer is used for the elevation control. The system is completed by a device for passive damping of gondola motions. The ﬁne pointing system consists of a two-axes gimbal that stabilizes and points the gamma-ray lens only. Fast control of the gimbal is performed through two custom-made high precision actuators, the pointing is controlled by mechanical gyrometers and a sun sensor mounted on a two-axis turret for offset. The absolute offset is calibrated and controlled by the central CCD camera and a wide ﬁeld CCD camera. The stabilisation of the gamma-ray lens has been shown to be better than 3 arc seconds during the balloon ﬂights. Springer

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Table 2 The 2001 CLAIRE balloon ﬂight Launch Instrument weight Balloon Float altitude Targets Termination

6:29 UT, June 14, 2001, Aerodrˆome de Gap-Tallard 500 kg Zodiac, 600 000 m3 ≤3 hPa (41 km), attained at 9:02 UT Crab nebula, Sun – active region 9489 (9h45–9h52) 15:12 UT, landing close to Bergerac

Before pointing the Crab, the sun was simultaneously observed by the central telescope, by the wide ﬁeld CCD camera and by the sun-sensor. This operation allowed us to relate the invariant pixel and the zero point of the pointing system during the balloon ﬂight. A thorough description of the gondola and pointing system is given in Laporte et al. [12]. Balloon ﬂight On June 14 2001, CLAIRE was launched by the balloon division of the French Space Agency CNES from its base at Gap-Tallard in the French Alps (see Table 2). As for the technological maiden ﬂight a year earlier [14], the CNES crew succeeded again to launch in a narrow two day window (!) deﬁned by the sun’s angular proximity to the Crab nebula. The 500 kg payload was lifted from the Gap airﬁeld by a 600 000 m3 Zodiac balloon at 06:29 UT. Thanks to the auxiliary balloon technique routinely used by CNES the launch went very smoothly. The ﬂoat altitude of 2.8 hPa (corresponding to 41 km) was reached in about 2.5 h, termination took place after nearly 6 h at ﬂoat, close to Bergerac in southwestern France. Telemetry data indicated that the ﬁne pointing system performed very well with an error ≤0.01◦ elevation/cross-elevation for 89% of the time at ﬂoat, and that the primary pointing system stabilized the focal spot so that it stayed within the detector for 77% of the good ﬁne pointing spells. According to telemetry, we therefore expected roughly four hours of recorded Crab data. All nine germanium detectors showed nominal performance during the ﬂight, the energy resolution at 170 keV was about 2.5 keV FWHM. The anti-coincidence shield reduced background noise by a factor of 10, resulting in a rate of about 2.3 × 10−4 cts s−1 keV−1 cm−3 at 170 keV for single events (see top of Figure 7) – four background-lines dominate the spectrum: three Ge isomeric transitions (53.4, 139.7 and 198.4 keV) and the e− e+ annihilation line (511 keV). A thorough discussion of the detector and anticoincidence system is given by Halloin [6]. First light A comprehensive simulation of the observation (Crab spectrum, atmosphere, ﬂight – and pointing-data, lens reﬂectivity, detector efﬁciency) showed that a 4.5 σ detection was expected. Although both the ﬁne pointing quality of the lens, and the primary pointing of the gondola seemed to have worked satisfactory, an initial data analysis did not result in a positive detection of the Crab [7]. The key for ﬁnding a signal turned out to be the discovery of an offset of the lens axis, both in the ﬁne pointing system (the Crab pointing) and in the primary pointing system (position of the focal spot on the detector). The offset in the Crab pointing was due to an incomplete Springer

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Fig. 7 Top: Spectrum for single events at ﬂoat altitude (background noise spectrum); bottom : spectrum for single events recorded during time intervals with good Crab pointing: at 170 keV, an excess of 33 photons is detected

measurement of the prismatic effect in the CCD’s sun-ﬁlters. We were able to measure the direction and amount (70 arcsec) of the effect a posteriori in our laboratory. Reassembling and testing the telescope structure revealed that the focal point moves by 4.5 to 6 mm in elevation (Y-axis) when in the observing position, and that of its position in the X-axis is indeterminate to within a range of about −15 and 15 mm. These mechanical problems would have been taken care of by optical tracking of the alignment laser that materializes the focal spot during the observation. A detailed discussion of CLAIRE’s primary and ﬁne pointing is given by Halloin [6]. Crab detection The offset in the ﬁne pointing of the Crab led to a broadening of the peak of diffracted source photons to 8 keV FWHM – akin to the effect illustrated in Figure 5. This effect is readily taken into account in the data analysis. The corresponding broadening of the focal spot is negligible Springer

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since the size of the crystal tiles dominates the beam size in the case of CLAIRE’s short focal length. As a consequence of the remaining uncertainty in the focal spot position, we made 30 data-analysis trials in the mechanically possible range. The maximum signiﬁcance was found by assuming offsets of +5 mm in the vertical and +10 mm in the horizontal directions. With this detector offset and event discrimination the useful exposure time is reduced to 72 minutes, but now the spectrum (Figure 7 bottom) shows an excess of 33 photons at 170 keV, a 3.5 σ effect corresponding to a probability of 99.976%). For comparison, a spectrum of all single events for every detector at ﬂoat altitude (reference for background) is shown in the top part of Figure 7. To obtain the actual signiﬁcance of the detection, the number of trials has to be taken into account. The trial positions are strongly dependent since spectra from adjacent positions (1 mm apart) contain a large number of common events. A series of ﬂight simulations using background noise only (no Crab signal) showed that our 30 trials are equivalent to about 4.2 independent trials – the actual signiﬁcance of our detection is hence 3σ (0.999764.2 ≈ 0.99898). Flight performance For an off-axis source, the diffraction peak is broadened (i.e. 8 keV) but its integral remains roughly constant. Assuming a Crab ﬂux of (1.42 ± 0.02) × 10−4 ph s−1 cm−2 keV−1 at 170 keV [5], the detection of 33 photons implies a peak efﬁciency of ≈12.5 ± 4+0 −2 % (error bars: the ﬁrst ﬁgure is the statistical uncertainty, the second ﬁgure is an estimation of systematic effects), corresponding to an effective area of about 64 cm2 at 170 keV. The above efﬁciency is obtained using the following instrumental parameters: a mean detector efﬁciency of 45.5% (at 170 keV), a deadtime of 15%, a bandpass of 3 keV FWHM for the perfectly pointed lens, and a mean atmospheric transmission of 67% (at 170 keV, altitude of 41 km).

Conclusion Experiments with continuum sources at distances of 14.16 m, 22.52 m (CESR optical bench), 205 m (long distance test) and inﬁnity (Crab nebula) have demonstrated the performance of our Laue lens. Figure 8 represents the recorded spectra for these experiments (lower graph), compared with the theoretical energy-distance relationship for a diffracted source (upper graph). The energies of the centroids are in very good agreement with theory, slight departures from theoretical values (less than 0.5 keV) being the consequence of the incident spectral shape and/or the detector calibration drifts. Table 3 summarizes the measured peak efﬁciencies of these experiments, and compares them with equivalent simulations. Measurements and simulations are in fairly good agreement. Rescaling the measured efﬁciencies of the ground tests for a polychromatic source at inﬁnity (diffracted peak width of 3 keV FWHM), obtains values compatible with a peak efﬁciency of 9 ± 1%. CLAIRE’s stratospheric ﬂight has provided the ﬁrst observation of an astrophysical source with a gamma-ray lens. In combination with the long-distance test on the ground, these results validate the theoretical models and demonstrate the principle of Laue lens. Moreover, CLAIRE’s stratospheric ﬂight represents a ﬁrst demonstration of the Laue lens technology in space environment. In this article, we have described the performance of CLAIRE on the ground and in ﬂight. Springer

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Fig. 8 Recorded spectra for various source distances (lower graph). The upper graph represents the distance of the source as a function of diffracted energy. The vertical lines show the theoretical corresponding energies. 14.162 m corresponds to the tuning distance (E th = 122.29 keV). The measurement at 22.52 m (E th = 136.5 keV) was performed on the optical bench at CESR with a partially tuned lens. 205 m is the distance of the generator on the long distance test range (E th = 165.5 keV). The peak for an inﬁnite distance is taken from the stratospheric ﬂight of June 2001 (see above)

Extrapolating this performance to the case of a space-borne instrument [4], this volume) reveals an outstanding potential for nuclear astrophysics : a gamma-ray telescope using a Laue diffraction lens has the potential to combine narrow line sensitivities of a few 10−7 ph s−1 cm−2 , with high spectral and angular resolution, and the capability of measuring the polarization of the incident photons. The sensitive gamma-ray spectroscopy that Table 3 Comparison of experimental results and simulations

Experiment source

Dist. (m) Energy spectrum

Predicteda,b Measureda,c Rescaled eff.a efﬁciency (%) efﬁciency (%) at 170 keV, ∞ (%)

57

CESR optical bench Co isotope 14.1 CESR optical bench 150 kV X-ray generator 14.2 CLAIRE TGD 300 kV x-ray generator 205 CLAIRE balloon ﬂight Crab nebula a Peak

∞

122.1 keV narrow line 3.668±0.004

3.17±0.02±0.1 7.7±1

122.3 keV continuum

3.5±0.1±0.3

8.7±1

165.5 keV continuum 8.53±0.02

8.5±0.5±0.5

8.5±1

170 keV continuum

8.88±0.02

+0

12.5±4−2

12.5±4

efﬁciency assuming a energy bandpass of 3 keV FWHM for polychromatic sources, diffracted fraction of the incident ﬂux on the lens for monochromatic sources. bars are only statistical. c Error bars include the statistical uncertainty (ﬁrst ﬁgure) and an estimation of systematic effects (second ﬁgure) b Error

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can be performed by such an instrument addresses a wide range of fundamental astrophysical questions such as the life cycles of matter and the behaviour of matter under extreme conditions. Acknowledgments The authors wish to thank the balloon division of the French Space Agency (CNES), which built the pointing system and operated the CLAIRE ﬂights from the launch to the gondola recovery. This work was partly supported by the U.S. Department of Energy under contract W-31-109-Eng-38. The team at CESR is grateful for continuing support from the French Space Agency CNES. The authors of this article acknowledge valuable contributions of the two referees.

References 1. Abrosimov, N.V., Rossolenko, S.N., Thieme, W., Gerhardt, A., Schr¨oder, W.: J. Crystal Growth 174, 182 (1997) 2. Abrosimov, N.V., L¨udge, A., Riemann, H., Kurlov, V.N., Borissova, D., Klemm, V., Halloin, H., von Ballmoos, P., Bastie, P., Hamelin, B., Smither, R.K.: J. Crystal Growth 275, e495–e500 (2005) 3. Alvarez, J., Halloin, H., Hernanz, M., von Ballmoos, P., Jean, P., Skinner, G., Abrosimov, N., Smither, R., Vedrenne, G.: Proceedings of the 5th INTEGRAL Workshop, Munich 16–20 757, ESA SP-552 ( 2004) 4. Barri`ere, N. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9058-x (2005) 5. Bartlett, L.M.: High resolution gamma-ray spectroscopy of the Crab. PhD thesis, Univ. of Maryland (1994) 6. Halloin, H.: Premi`eres lumi`eres pour une lentille gamma, PhD, U. Paul Sabatier, Toulouse (2004) 7. Halloin, H., von Ballmoos, P., Evrard, J., Skinner, G.K., Abrosimov, N., Bastie, P., Di Cocco, G., George, M., Hamelin, B., Jean, P., Kn¨odlseder, J., Laporte, Ph., Badenes, C., Laurent, Ph., Laurens, A., Smither, R.K.: Proc. SPIE (Intl. Soc. for Optical Engineering), Vol. 4851, p. 895, 2003 8. Halloin, H., Bastie, P.: Exp. Astron. 20, DOI 10.1007/s10686-006-9064-z (2005) 9. Halloin, H.: Exp. Astron. 20, DOI 10.1007/s10686-006-9063-0 (2005) 10. Kohnle, A., Smither, R.K., Graber, T., Laporte, Ph., Olive, J.F., von Ballmoos, P.: Nuclear Instr. Meth. Phys. Res. Sect. A 408, 553–561 (1998a) 11. Kohnle, A., Smither, R.K., Graber, T., Fernandez, P., von Ballmoos, P.: Nuclear Instr. in Meth. in Phys. Res. Sect. A 416, 493 (1998b) 12. Laporte, Ph., Evrard, J., Laurens, A. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9067-9 (2005) 13. Naya, J., von Ballmoos, P., Smither, R.K., Faiz, M., Fernandez, P., Graber, T., Albernhe, F., Vedrenne, G.: Nuclear Instr. Meth. Phys. Res. Sect. A 373, 159 (1996) 14. von Ballmoos, P., Evrard, J., Skinner, G.K., Abrosimov, N., Bastie, P., Di Cocco, G., George, M., Halloin, H., Hamelin, B., Jean, P., Kn¨odlseder, J., Laporte, Ph., Laurent, Ph., Laurens, A., Smither, R.K.: ESA Symp. Proc., Exploring the Gamma-Ray Universe, SP-459, 649 ( 2001)

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Exp Astron (2005) 20:269–278 DOI 10.1007/s10686-006-9058-x O R I G I NA L A RT I C L E

MAX, a Laue diffraction lens for nuclear astrophysics N. Barri`ere · P. von Ballmoos · H. Halloin · N. Abrosimov · J. M. Alvarez · K. Andersen · P. Bastie · S. Boggs · P. Courtois · T. Courvoisier · M. Harris · M. Hernanz · J. Isern · P. Jean · J. Kn¨odlseder · G. Skinner · B. Smither · P. Ubertini · G. Vedrenne · G. Weidenspointner · C. Wunderer Received: 1 June 2006 / Accepted: 27 June 2006 C Springer Science + Business Media B.V. 2006

Abstract The next generation of instrumentation for nuclear astrophysics will have to achieve a factor of 10–100 improvement in sensitivity over present technologies. With the focusing gamma-ray telescope MAX we take up this challenge: combining unprecedented sensitivity with high spectral and angular resolution, and the capability of measuring the polarization of the incident photons. The feasibility of such a crystal diffraction gamma-ray lens has recently been demonstrated with the prototype lens CLAIRE. MAX is a proposed

N. Barri`ere () · P. von Ballmoos · M. Harris · P. Jean · J. Kn¨odlseder · G. Skinner · G. Vedrenne · G. Weidenspointner Centre d’Etude Spatiale des Rayonnements, 9, avenue du Colonel Roche, BP 4143 - 31028 Toulouse Cedex 4, France e-mail: [email protected] K. Andersen · P. Bastie · P. Courtois Institut Laue Langevin, 6, rue Jules Horowitz BP 156 – 38042 Grenoble Cedex 9, France N. Abrosimov Institut f¨ur Kristallz¨uchtung, Max-Born-Strasse 2, D-12489 Berlin, Germany H. Halloin APC, coll`ege de France, 11, place Marcelin Berthelot, 75231 Paris, France S. Boggs · C. Wunderer Space Sciences Laboratory #7450, University of California, Berkeley, CA 94720-7450, USA T. Courvoisier ISDC, Chemin d’Ecogia 16, 1290 Versoix, Switzerland J. M. Alvarez · M. Hernanz · J. Isern IEEC-CSIC, Campus UAB, 08193 Bellaterra (Barcelona), Spain B. Smither Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA P. Ubertini Istituto di Astroﬁsica Spaziale e Fisica Cosmica, Via del Fosso del Cavaliere 100, 00133 Roma, Italy Springer

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mission which will make use of satellite formation ﬂight to achieve 86 m focal length, with the Laue lens being carried by one satellite and the detector by the other. In the current design, the Laue diffraction lens of MAX will consist of 13740 copper and germanium (Ge1−x Six , x ∼ 0.02) crystal tiles arranged on 36 concentric rings. It simultaneously focuses in two energy bands, each centred on one of the main scientiﬁc objectives of the mission: the 800–900 keV band is dedicated to the study of nuclear gamma-ray lines from type Ia supernovae (e.g. 56 Co decay line at 847 keV) while the 450–530 keV band focuses on electron-positron annihilation (511 keV emission) from the Galactic centre region with the aim of resolving potential point sources. MAX promises a breakthrough in the study of point sources at gamma-ray energies by combining high narrow-line sensitivity (better than 10−6 cm−2 s−1 ) and high energy resolution (E/dE ∼ 500). The mission has successfully undergone a pre-phase A study with the French Space Agency CNES, and continues to evolve: new diffracting materials such as bent or composite crystals seem very promising. Keywords Instrumentation: Gamma-ray Laue lens . Gamma-ray astrophysics . Mosaic crystals PACS: 95.55.Ka, 29.30.Kv, 61.10.-i

1. Introduction Observing gamma-ray lines is ﬁrst and foremost a matter of extracting a weak signal swamped in an intense and complex instrumental background. This is partly due to the fact that all existing instruments are based on concepts where the collecting area is equal to the sensitive area. Since the instrumental background in a detector operating in space is roughly proportional to its volume, decoupling the instrument effective area from the detector volume would lead to a dramatic improvement of sensitivity. That is why focusing gamma rays appears today as the only way to study point sources with a sufﬁcient sensitivity to further our understanding of explosive nucleosynthesis and compact objects. MAX is a mission concept for a space-borne gamma-ray telescope using a Laue lens to focus nuclear gamma-ray lines from a large area onto a small detector. The lensing effect is based on Bragg diffraction in the volume of crystalline materials. CLAIRE, a prototype of such a Laue lens has already been realized in a CESR – CNES (the French space Agency) collaboration, and has demonstrated the feasibility of this concept [11, 23]. In this paper we ﬁrst provide an overview of the MAX mission: its principal scientiﬁc objectives, the characteristics of the current instrument design, sensitivity estimates for various crystal types and detector options. We then describe ongoing R&D on new diffracting materials, such as composite crystals or bent crystals.

2. Scientiﬁc motivations Gamma-ray astronomy presents an extraordinary scientiﬁc potential for the study of the most powerful sources and the most violent events in the Universe. While at lower wavebands the observed emission is generally dominated by thermal processes, the gamma-ray sky provides us with a view of the non-thermal Universe, where particles are accelerated by still poorly understood mechanisms to extremely relativistic energies and nuclear reactions and decays are creating the basic elements that constitute our world (see the ﬁrst section of this volume). Springer

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MAX aims to observe radioisotopes produced in Type Ia supernovae (SN) (see e.g. [19]) and around compact objects through their emitted nuclear lines. Type Ia supernovae (SN), with classical novae [12] and core collapse SN (Type Ib, Ic, II,. . .), are the main contributors to the production of heavy elements, playing a major role in the life cycle of matter in the Universe. The exceptional luminosity of SN Ia has made them a valuable tool for the measurement of extragalactic distances and for determining the metric of the Universe. The optical light produced in Type Ia SN is mostly powered by the decay chain 56 Ni → 56 Co → 56 Fe, which is directly observable mainly in two gamma-ray lines at 812 keV and 847 keV. Despite their great interest in many areas of astronomy, fundamental questions remain about all types of SN. Establishing the actual 56 Ni and 56 Co decay line intensities and shapes is a primary goal that will lead to a breakthrough for our understanding of the detailed physics at work in these explosions. A sensitivity of ∼10−6 cm−2 s−1 to broadened gamma-ray lines would allow at least one Type Ia SN per year closer than 20 Mpc to be observed with a detection signiﬁcance of 25σ , which would allow discrimination between various models [16]. Up to 5 y−1 could be detectable with a signiﬁcance of 3σ , in a radius of 50 Mpc. The search for potential sources of the positrons whose presence is implied by the 511 keV radiation observed with SPI/INTEGRAL constitutes the other main scientiﬁc theme of the MAX mission. Compact objects (microquasars, neutron stars and pulsars, X-ray binaries, . . .), active galactic nuclei, solar ﬂares and the high energy afterglow from gamma-ray bursts may release signiﬁcant numbers of positrons leading to 511 keV annihilation line emission. The shift and the shape of this line carry a lot of information about the region and conditions where positrons have annihilated [14]. Fine spectroscopy of the annihilation line combined with a good spatial resolution could elucidate the nature of these objects.

3. The MAX mission MAX was proposed in response to an announcement of opportunity issued by the CNES concerning a formation ﬂight demonstrator mission. It consists of a lens spacecraft and a detector spacecraft ﬂying in formation to form a gamma-ray telescope of 86 m focal length. The pre-phase A study led by the CNES/PASO group that ended in November 2005 conﬁrmed the feasibility of the mission, and indicated a mass margin of 400 kg. As a consequence we have updated the MAX design (which becomes MAX 3.0) with an increase of 72% in the focusing area (crystal tiles), resulting in dramatic increases in the effective areas of both bandpasses. MAX is still under development and so is continuously evolving. The version 3.0 presented here is based on crystals representing the current state of the art and which are relatively conservative compared to new diffracting materials that are highlighted by the current R&D program (see below). 3.1. Lens features In the current MAX design, the lens is made of 13740 crystal tiles of 1.5 cm × 1.5 cm including 90% copper crystals [8] and 10% germanium crystals [1]. The thicknesses, T0 , of crystal tiles are optimized for each ring according to the following formula which comes from the maximisation of a mosaic crystal peak diffraction efﬁciency for a given mosaicity: 1 2σ cos θ B T0 = ln 1 + . 2σ µ Springer

272 Table 1 MAX crystals masses and geometrical areas. LE: low energy band; HE: high energy band

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Focal length f Crystal mosaicity Geometrical area Mass of crystals Number of HE rings Mass of HE crystals Geometrical area of HE rings Number of LE rings Mass of LE crystals Geometrical area of LE rings

86 m 30 arcsec. 30915 cm2 235 kg 20 172 kg 15966 cm2 16 62 kg 14949 cm2

σ is the diffraction coefﬁcient for the crystalline material, µ is the absorption coefﬁcient (without coherent scattering which is precisely the origin of the Bragg diffraction), and θB is the angle of incidence of rays on the diffracting planes (called Bragg angle when diffraction occurs). The value of σ is calculated according to the dynamical theory of diffraction (see Halloin, Bastie [5, 6] for complete treatment). The crystal tiles are arranged on 36 concentric rings with radii ranging from 56.25 to 76.35 cm and from 93.05 to 129.05 cm. The resulting lens focuses simultaneously in two broad energy bands corresponding to the previously described scientiﬁc objectives (Figure 1): the lower energy band is centred on 500 keV. Its width permits the observation of red-shifted e− − e+ annihilation lines from compact objects (e.g. the supermassive black hole in the centre of our Galaxy), as well as the study of the 478 keV decay line from 7 Be. The bandpasses of the 14 Cu rings and 2 Ge rings combine to cover an energy band from 450 to 530 keV, with a total effective area of 1200 cm2 at 511 keV. The second energy bandpass is obtained with 18 Cu rings and 2 Ge rings whose responses superimpose to cover an energy band from 800 to 900 keV, with a total effective area of 660 cm2 at 847 keV. In addition, the second order diffraction of the crystals covering the lower energy bandpass extends this band up to 1050 keV. Details of masses and geometrical areas of both bandpasses are given in Table 1. 3.2. Detector features The baseline detector for MAX is a Compton camera consisting of a stack of planar germanium strip detectors (GeD). The stack is made of 5 GeD modules similar to the ones used in the balloon borne Nuclear Compton Telescope, which was successfully tested in 2005 (NCT, [4]). Each GeD is approximately 8 cm × 8 cm and 1.5 cm thick, and the strips are 2 mm pitch, which ensure a 1 mm3 3D-positionning. The design used to estimate sensitivities [24, 25] assumes a gap of 0.7 cm between two GeD. To reduce the background count rate, the detector is separated from the spacecraft by being placed on a 1 m “tower”. In addition, the Compton camera is encapsulated in a plastic veto shield, and a 5 cm thick active BGO crystal screens it from the emissions produced in the structure of the spacecraft. It has been established during the MAX pre-phase A study that cooling of the Compton camera can be achieved with a 1 m diameter radiator. Alternative solutions to the above baseline are being considered, including a high sensitivity Si/CdTe narrow ﬁeld of view Compton camera [17, 22], or Compton CdTe pixel detector [7]. The advantages of using a detector providing localization of the interactions are multiple: besides following any excursions of the focal spot across the detector plane, such a system allows the simultaneous measurement of signal and background. Most importantly, in a system with three-dimensional event localization, a signiﬁcant background reduction can be achieved by reconstructing the arrival direction of the photons using Compton Springer

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Fig. 1 Effective area of the lens for a perfect pointing on a point source. Each Gaussian curve is the contribution of a single ring. The second order diffraction of low energy (LE) rings extends the high energy (HE) bandpass up to 1050 keV. Various sets of Bragg planes in copper and germanium at different radii contribute to the two main energy bands: Cu(111), Cu(200) and Ge(111) are used for the LE band, whereas Cu(111), Cu(200), Cu(220), Cu(222) and Ge(311) diffract in the HE band. In this sense, this lens is a hybrid between a broad-band lens and a narrow-band lens

kinematics. This allows the rejection of photons not coming from the lens direction. In addition, a Compton camera is inherently sensitive to gamma-ray polarization. Lastly a ﬁne pixellated focal plane allows the limited imaging capabilities of the lens to be used. One drawback of a Compton camera is at present their low detection efﬁciency (ranging between 6–7% for a Ge- strip Compton stack). First steps in the optimisation for the particular case of a Laue lens have been performed [25] and this works will continue in the future. 3.3. Sensitivity estimates The modelled narrow line sensitivity of MAX in both energy bandpasses is shown in Figure 2. Lens efﬁciency estimates are derived from the diffraction efﬁciency given by the Darwin model, which are in agreement with the diffraction efﬁciencies measured for the lens prototype CLAIRE [11] and recent measurements made at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) [5, 6]. The upper curve (a) in Figure 2 shows the sensitivity with current technology, based on the lens MAX 3.0 and the baseline Compton camera described in Section 3.2. The lower curve in Figure 2b shows a sensitivity requiring advanced technology: a lens using bent crystals (see below) focusing onto an optimized Compton camera (the “LARGE” geometry in [25]). At this early stage, these estimates are rough but conservative. Numerous optimizations could still be done, as for example, improving the treatment of the Compton-rejected photons (93% of the signal), or the optimization of the detector geometry or the lens efﬁciency. 3.4. Lens PSF – imaging capabilities Although a crystal lens telescope is not a direct imaging system, the spatial response does depend on the source position in the ﬁeld of view. For an on-axis point source, the response is a Springer

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Fig. 2 The modelled narrow line sensitivity of MAX in both energy bands. Curve (a) is the sensitivity with current technology, using the baseline Compton camera (see above) and the current lens MAX 3.0. Curve (b) is the sensitivity reachable with a lens using bent crystals and an optimized Compton camera. The circle and the triangle are the sensitivities for a broad line (3%) at 847 keV

Fig. 3 MAX baseline detection plane (8 cm × 8 cm, 1 mm2 pixels) response for a point source. Flux is coded both by a grey square root scale and by square root contours. Left: image of an on-axis point source. Right: image of an off-axis point source when the lens is pointing 60 arcsec away from the source. The Monte-Carlo code used for these simulations was developed by Halloin [11] Springer

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Gaussian-like spot centred on the optical axis of the lens (Figure 3, right). For an off-axis point source, the focal spot becomes a donut shape (centred on the lens optical axis) presenting an azimuthal intensity modulation [18]. The average radius ra of the focal ring and the angular position of the maximum intensity ϕ m give the zenithal (off-axis) (θ s ) and the azimuthal (ϕ s ) angles of the source through the very simple relations: θ S = a tan ra/f , ϕ S = ϕm + π

where f is the focal distance of the lens for a source at inﬁnity. The minimum thickness of the focal ring (where the intensity is maximal) approaches the radial size of the crystals with increasing zenith angle of the source (individual square crystals are arranged on rings such that one side is tangential). Thus, mosaicity and crystal sizes dictate the angular resolution of the instrument. The ﬁeld of view of MAX is limited by two parameters: ﬁrstly, the size of the detection plane (8 cm × 8 cm) limits the radius of the recorded focal ring to 4 cm. Taking into account crystals radial size, the maximum radius of observable focal ring is 3.25 cm. The ﬁeld of view of MAX is therefore ±78 arcsec. The second limiting parameter is the decrease of the lens effective area when the zenithal angle of the source increases (Figure 4). For an angle of 60 arcsec, the effective area goes down by 45% and 40% at 511 keV and 847 keV respectively.

Fig. 4 Effective area as a function of position in the ﬁeld of view at 511 keV and 847 keV Springer

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4. The R&D towards a spaceborne Laue lens 4.1. Lens structure A ﬁrst design of the structure of the lens has been made in order to study its thermo-elastic deformations. The design is based on the ALCATEL structural concept [10, 13]: a main circular carrier structure supports 32 independent modules onto which the individual crystals are attached. The central carrier structure homogenizes the temperature and transmits mechanical forces to the satellite structure through four titanium links. Due to the penetrating nature of gamma rays it is possible to put the lens in a multilayers insulator (MLI) cocoon to ensure sufﬁcient thermal stability. Even with such a passive system the temperature would already be within ±3 K of the nominal temperature, whatever the orientation of the sun. For a 86 m focal distance, the diffracting planes of a crystal have to be oriented within ∼10 arcsec with respect to the lens line of sight to keep the position of the crystal footprint within ±1 cm of its nominal position. This value dictates the speciﬁcation for the lens out of plane deformation: modules have to keep their nominal orientation within ±10 arcsec. It has been shown in the MAX pre-phase A study that a ±2 K active thermal control around the nominal temperature (ambient) is sufﬁcient to satisfy this deformation speciﬁcation, a requirement that seems easily attainable [13]. 4.2. Diffracting materials 4.2.1. Lessons from the CLAIRE lens The CLAIRE lens was made of 556 crystals mounted on eight rings (see [11, 23] for an in-depth description of the CLAIRE project). These crystals, that are actually a solid solution of silicon in germanium (Ge1−x Six , x < 0.1), were grown using a modiﬁed Czochralski technique at the Institute of Kristalz¨uchtung (IKZ, Berlin, Germany) by [1]. CLAIRE was a narrow bandpass Laue lens, it focused radiation centered on 170 keV (for rays coming from inﬁnity) using a different family of crystalline planes for each ring. The overall diffraction efﬁciency of the lens was found to be about 10%, though some of the best crystals had a peak reﬂectivity of 25%. There are two reasons to explain the relatively low efﬁciency of the entire lens compared to that of the best crystals. Firstly, the theoretical diffraction efﬁciency decreases with increasing Miller index. For example, the eighth ring used the [440] reﬂection that has a theoretical integrated reﬂectivity 7.5 times lower than that of the (111) planes. Secondly, even on a given ring where all crystals are supposed to be identical, differences do exist. These differences that translate into differences in absolute reﬂectivity and energy bandpass, are due to mosaicity and crystallites length variation. Basically, the larger the crystallites, the worse is the reﬂectivity. A larger mosaicity offers a larger energy bandpass, but it, too, decreases the reﬂectivity. The CLAIRE project has emphasized the need to use preferentially sets of crystalline planes of lower Miller index, and to ensure that the quality of the crystals grown can be maintained consistently during the production of a large number of boules. 4.2.2. Existing crystals MAX lens would be mainly made with copper crystals, with 10% germanium-silicon crystals to provide enhanced collecting area in the energy bands of interest. Copper crystals combine high theoretical diffraction efﬁciency (higher than germanium) with inherent mosaic Springer

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structure. The challenge was to grow crystals with a mosaicity of about 30 arcsec, a value which is very small for this material. In 2005, this goal was achieved for the very ﬁrst time by [8] at ILL. Such a low mosaicity copper crystal have shown a peak reﬂectivity reaching 30%. Concerning germanium crystals, since the time when CLAIRE’s crystals were grown the quality of crystals obtained by the modiﬁed Czochralski technique has been improved. Using only the most efﬁcient reﬂections (low Miller index), we can count on peak diffraction efﬁciencies exceeding 25%. Nevertheless, the only way to completely avoid variation of the crystalline parameters, such as those noted in the CLAIRE lens, would be to characterize every crystal and to select only the best. 4.2.3. New generation of crystals Alternative crystalline materials are also being considered. One possibility is germanium ‘composite crystals’, made of perfect single-crystal germanium wafers that are stacked with a slight mis-oriention from one to the next (like the crystallites in a mosaic crystal). This kind of crystal presents potentially advantages with respect to mosaic crystals: single crystal wafers are easily reproducible and it is possible to optimize the wafer thickness according to the energy that the stack will have to diffract. Since wafers are perfect single crystals, the formulae given in subsection 3.1 do not apply any more, the optimal thickness of a wafer equals half of the Pendell¨osung period (the period of the oscillations of the diffracted intensity as a function of the thickness of the crystal; [3]). Of course the key point is to manage to build the stack properly. Indeed, a recent measurement run at the ESRF [5, 6] on a prototype composite crystal showed that the angular separation between wafers was greater than their angular bandpass1 , leading to an undesirable comb-like response. This still-evolving technique, especially the surface treatment of the wafers, has yet to be optimised. Bent crystals are another alternative that seem very promising. Smither [21] have already measured Si crystals with efﬁciency close to 100% (disregarding absorption2 ) in an angular bandpass of 30 arcsec. Bent diffracting planes can be obtained in 3 ways: by applying a thermal gradient to a crystal, by elastically bending a crystal, or by growing a composition-gradient crystal (Ge1−x Six ) [2]. In the latter case, a spherical curvature of atomic planes perpendicular to the gradient direction appears, due to the fact that Ge atoms are larger than Si atoms [21]. Bent crystals present two main advantages with respect to mosaic crystals: their peak diffraction efﬁciencies are not limited to 50% as is the case for mosaic crystals (see for instance Halloin, Bastie [5, 6]), and their rocking curves (curves representing the range of angles through which an incident beam can be diffracted) can have a square shape. As a comparison, mosaic crystals exhibit a Gaussian-like rocking curve, which is good for the lens ﬁeld of view, but degrades the focusing on the detector (since each crystal diffracts a diverging beam whose spatial distribution is Gaussian). Preliminary estimates of the sensitivity achievable with a lens made of bent crystals show a gain of a factor 2 with respect to the current version of MAX. 1 Even a perfect single crystal has an angular bandpass that is called the Darwin width. In addition, the cutting process induces deformations that increase the angular bandpass. 2 If we do not consider the absorption, when a beam goes through a crystal, it is shared in two complementary parts: the diffracted beam and the transmitted beam. In the case of a mosaic crystal, these two parts tend to be equal if the crystal is thick enough: the maximum diffraction efﬁciency without absorption is 50%.

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5. Summary With its Laue lens consisting of Cu and Ge crystals rings MAX promises a breakthrough for the study of point sources at gamma-ray energies by combining narrow line sensitivities better than 10−6 cm−2 s−1 and high energy resolution (E/dE ∼ 500). MAX features a Laue lens consisting of rings of Cu and Ge crystals, covering simultaneously two broad energy ranges: 800–900 keV and 450–540 keV. A small detector, maintained at a distance of 86 m by a second spacecraft ﬂying in formation, collects the focused radiation. A pre-phase A study of the French Space Agency CNES has established the feasibility of the mission with present technologies [10]. The performance of a future Laue lens depends mainly on the diffraction properties of its individual crystals. Despite the fact that mosaic crystals produce a focal spot not ideally concentrated on the detection plane, the copper crystals grown at ILL show peak reﬂectivities up to 30%. The growth of copper crystals can be fairly well controlled at present, with mosaicities ranging from a few minutes down to 30 arcsec. It is hence already possible to build an efﬁcient gamma-ray Laue lens using a combination of copper and germanium mosaic crystals. We have shown that Laue lenses can beneﬁt either from crystals having a composition gradient (causing curvature of the crystalline planes) or from “composite crystals” (having an “artiﬁcial mosaic structure” produced by assembling wafers with slightly different alignments). In either case, the efﬁciency-limitation, which prevents Laue mosaic crystals of having a reﬂectivity higher than 50%, can be exceeded. We also show the importance of improving the crystals point spread function to obtain a compact focal spot and thus a enhanced signal/noise ratio. Acknowledgements The authors acknowledge continuing support from the French Space Agency CNES.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

Abrosimov, N. et al.: J. Crystal Growth 275, e495–e500 (2005) Abrosimov, N.: Exp. Astron. 20, DOI 10.1007/s10686-006-9036-3 (2006) Authier, A.: Dynamical theory of X-ray diffraction. Oxford Science Publications (2001) Boggs, S.E. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9051-4 (2006) Bastie, P. et al.: ESRF User report, http://ftp.esrf.fr/pub/UserReports/32513 A.pdf (2006) Halloin, H., Bastie, P. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9064-z (2006) Caroli, E. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9048-z (2006) Courtois, P. et al.: Exp. Astron. 20, DOI 10.1007/s10686-005-9018-x (2006) Cosmic Vision, ESA, BR-247 Duchon, P. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9070-1 (2006) Halloin, H.: Phd Thesis, University Toulouse III, (2003) http://www.cesr.fr/∼pvb/MAX/publis/Diss Halloin 03.pdf Hernanz, M. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9036-3 (2006) Hinglais, E. et al.: Exp. Astron. 20, DOI 10.1007/s10686-005-9020-3 (2006) Jean, P. et al.: A&A 445, 579–589 (2006) Kn¨odlseder, J. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9031-8 (2006) Leising, M.: Exp. Astron. 20, DOI 10.1007/s10686-006-9052-3 (2006) Limousin, O. et al.: NIM A 504, 24–37 (2003) Lund, N.: Exp Astron 2, 259 (1992) Prantzos, N.: In Proc 5th INTEGRAL Science Workshop (ESA SP-552), 15 (2005) Smither, R. et al.: RSI 76, 123107 (2005) Smither, R. et al.: Exp. Astron. 20, DOI 10.1007/s10686-005-9019-9 (2006) Takahashi, T.: Exp. Astron. 20, DOI 10.1007/s10686-006-9059-9 (2006) von Ballmoos, P. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9071-0 (2006) Weidenspointner, G. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9035-4 (2006) Wunderer, C. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9034-5 (2006) Springer

Exp Astron (2005) 20:279–288 DOI 10.1007/s10686-006-9042-5 ORIGINAL ARTICLE

The gamma ray lens – an ESA technology reference study Craig Brown · Nicola Rando · Alexander Short · Aleksander Lyngvi · Tone Peacock

Received: 14 October 2005 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract The Science Payload and Advanced Concepts Ofﬁce (SCI-A) of the ESA Science Directorate conducts a number of Technology Reference Studies (TRS) on hypothetical scientiﬁc missions that are not part of the approved Science programme. Such TRS activities allow identifying, at an early stage, technology development needs as well as exploring future mission scenarios. As part of this effort, the Gamma Ray Lens (GRL) mission, a future generation gammaray observatory, has been the subject of a preliminary internal investigation. The present paper provides an overview of the science goals assumed for this study, the selection of the reference mission proﬁle, together with a preliminary description of the spacecraft design. The reference payload is also described, as well as the list of technology development activities derived from the study.

1. Introduction Technology Reference Studies (TRS) are conducted by the Science Payload and Advanced Concepts Ofﬁce (SCI-A) of the ESA Science Directorate, with the aim of establishing key technology development requirements necessary for the realisation of similar, future science missions [1]. A TRS consists of the investigation of a hypothetical future mission of scientiﬁc worth that is not currently part of the ESA science programme. Each study aims to highlight areas requiring technology development, as well as to establish mission drivers and areas of complexity. There are four primary areas for investigation within the TRS programme: planetary science, fundamental physics, solar physics and astrophysics missions. Increasing sensitivity of a gamma-ray mission is widely considered as the next important development in gamma-ray astronomy. The required leap in sensitivity implies the need of focussing optics that, in this high-energy range, is very difﬁcult to achieve. The Gamma Ray Lens (GRL) was an ideal candidate for an astrophysics TRS due to its challenging nature,

C. Brown () · N. Rando · A. Short · A. Lyngvi · T. Peacock Science Payload and Advanced Concepts Ofﬁce, European Space Agency, ESTEC, The Netherlands e-mail: [email protected] Springer

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and was studied in order to establish the technology development requirements needed to realise such a mission in the future. This paper will introduce the reference mission requirements used in this study, and will present the preliminary mission design for the Gamma Ray Lens.

2. Reference science requirements In order to conduct the Technology Reference Study, preliminary science requirements need to be assumed. There are two primary source types of interest that lead to three main energy bands for the GRL. Positron-electron annihilation, and the subsequent single, double and triple Compton backscattering processes, leads to two energy bands: 50–200 keV and 460– 522 keV. The band widths take potential red-shift into account, as well as intrinsic broadening of the spectral lines. The second source types of interest are sources of explosive nucleosynthesis and, in particular, type Ia Supernovae due to their use as cosmological candles. The primary energy of interest associated with these sources is the 847 keV 56 Co decay line, leading to an energy band of 825–910 keV. Table 1 shows a summary of the reference science requirements for the GRL mission. The requirements are compatible with those presented on behalf of the gamma-ray science community at the 2005 INTEGRAL Workshop at ESTEC [2].

3. Orbit selection The GRL mission has the following orbit requirements to best meet the mission goals.

r Long, stable observations for formation ﬂying between two spacecraft r Typical observation times of ∼2–3 weeks (80 days for SNe Ia) r Large portion of the sky visible at any one time r Stable thermal environment r Low number of eclipse periods r Minimal radiation damage to the detectors and other systems r Low v for orbit insertion and maintenance Table 2 outlines the orbit tradeoff that was performed in order to establish the most appropriate orbit for the Gamma Ray Lens. Note that a 5-point scale, ranging from –2 to +2, is used to demonstrate in detail the advantages and disadvantages between the differing orbit types. Table 1 Summary of preliminary assumed science requirements

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Attribute

Requirement

Energy band Effective area Angular resolution Energy resolution Line sensitivity Continuum sensitivity Typical integration time Sun restraint angle Nominal mission lifetime

425–522 keV, 825–910 keV, 50–200 keV 10000 cm2 @ 511 keV, 5000 cm2 @ 847 keV 1 Arcminute 2 keV @ 600 keV ∼5 × 10−7 ph.cm−2 s−1 ∼10−8 ph.cm−2 s−1 ∼106 sec. @ 511 keV, 2 × 105 sec. for SNeIa 30◦ , half cone ∼10 years (extendable to 15)

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Table 2 Outline of the trade-off between orbit types based on the GRL mission requirements Mission requirement

LEO

GEO

HEO

L2

Weighting

Stability and maintenance v Observation period Visibility of the sky Thermal environment stability Eclipse periods Radiation environment Communications and ground operations Launcher capacity Total Weighted total

−2 −2 −2 −1 −2 −1 0 2 −8 −5.75

0 −1 0 1 −1 1 2 −2 0 −2.25

−1 0 1 0 −1 −1 1 0 −1 −0.50

2 2 2 2 2 1 0 −1 10 7.25

1 1 1 0.5 0.5 0.25 0.25 1 – –

Table 3 Laue lens dimensions for the MAX [3], Soyuz Fregat and Ariane 5 conﬁgurations Conﬁguration

Focal length [m]

Rin Ge [cm]

Rout Ge [cm]

Rin Cu [cm]

Rout Cu [cm]

MAX Soyuz fregat Ariane 5

133 436 504

97 318 365

110 360 450

87 285 328

96 314 363

It is clear from this trade-off that an orbit at L2 is the most desirable. For the purpose of this study it has therefore been assumed that the GRL will utilise a Halo orbit at L2. 4. The gamma ray lens The energy bands of interest for the GRL mission (see Table 1) suggest two separate optic technologies: Multilayer Silicon Pore Optics, expected to perform well up to 200 keV, and Laue crystals which are suitable for the focusing of gamma rays from 200 keV to 2 MeV. Due to the focusing geometry of the Laue lens, a large (∼500 m) focal length is required. This implies the need for two separate spacecraft: A focusing optic spacecraft (OSC) housing the lens and a detector spacecraft (DSC) orbiting at the optic focal spot. Two mission proﬁles were investigated as part of the GRL TRS: a medium sized mission utilising two separate Soyuz Fregat launchers in a dual launch scenario and a single Ariane 5 launcher in a single launch scenario. The smaller Soyuz Fregat launcher capacity results in a limited payload capability. A silicon pore optic is not included in the Soyuz payload, meaning that only the two higher energies of interest are considered in this conﬁguration. The primary advantages of using the larger Ariane 5 conﬁguration are: (1) a larger payload capacity allowing observation of all energy bands of interest at increased effective areas; (2) the removal of any problems associated with a dual launch; (3) further potential for payload expansion. For comparison, the MAX mission has been considered in this study as a third, smaller mission concept. MAX is a gamma ray focusing mission based on Laue crystals, proposed by CESR (Centre d’Etude Spatiale des Rayonnements), Toulouse [3]. The mission is sized to ﬁt both detector and lens spacecraft into a single Soyuz Fregat launcher. The dimensions and speciﬁcations for MAX were input into the models developed for the Gamma Ray Lens TRS and are also presented in this paper in order to compare the GRL with MAX. Table 3 outlines the key dimensions of the Laue lens used for the MAX, Soyuz Fregat and Ariane 5 proﬁles. Springer

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Fig. 1 The modelled effective area for the Ariane 5, Soyuz Fregat and MAX Laue Lens conﬁgurations

An effective area and sensitivity model was created in order to analyse and compare the various Laue lenses proposed for different GRL conﬁgurations. Figures 1 and 2 show the effective area and sensitivity results, respectively, for the Soyuz Fregat and Ariane 5 conﬁgurations. The reported dimensions of the MAX lens were also input into the model, with the results shown here for comparison. Note that a real measured SPI INTEGRAL background [4], was used in the GRL sensitivity analyses presented in Figure 2. As such we have assumed a SPI INTEGRAL-style Ge spectrometer with a similar background rejection capability through anticoincidence shielding. It can be seen from Figures 1 and 2 that the Ariane 5 conﬁguration comfortably meets both effective area and sensitivity requirements outlined in Table 1. An improvement of ∼100 times better sensitivity than SPI INTEGRAL is achieved by the Ariane 5 conﬁguration.

5. Preliminary spacecraft design For the purpose of this section, only the Ariane 5 conﬁguration will be discussed. As noted, two separate spacecraft ﬂying in formation are required for the GRL mission: the OSC housing the Laue lens and Silicon Pore Optic, and the DSC supporting the SPI INTEGRALstyle germanium detector. Here, the preliminary spacecraft design is described. Figure 3 shows a diagram of the deployed OSC. The cylindrical bus was chosen due to the ring structure of the Laue lens and the ability to more easily stow the large structure during launch. In order to maintain a clear load path through the spacecraft during launch, the OSC bus was designed to match the diameter of the 2624 cm Ariane 5 launch adapter. Ensuring a clear load path will minimise the stress on the stacked conﬁguration during launch. Springer

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Fig. 2 The modelled sensitivity for the Ariane 5, Soyuz Fregat and MAX Laue Lens conﬁgurations, assuming a spectrometer based on an array of cooled Ge detectors

The ring-shaped bus was used due to the necessity of an unobstructed view for the multilayer silicon pore optic. Housing the silicon pore optic inside this ring provides a clear line of sight between the optic and the detector spacecraft. The silicon pore optic will be designed to have a focal spot that coincides with that of the Laue lens, thus enabling simultaneous observations in different energy ranges. The deployment mechanism is designed to ﬁt the lens within the Ariane 5 fairing during launch and then deploy the lens to the full 9 m diameter after spacecraft separation. It can be seen that the lens is composed of 30 separate petals. These are sized to simplify the construction, metrology and testing of the lens. When in stowed conﬁguration, the mass of the lens is concentrated towards the top of the OSC bus. The height of the bus is therefore determined by the need to secure the large crystal mass in the stowed conﬁguration, with stiffening rings used to re-enforce the structure. The thrusters are positioned to allow for full, three-axis stabilisation and transverse motion. Star trackers and sun sensors are placed around the craft providing attitude measurements, while the antennae provide omni-directional communication capability. Figure 4 shows the DSC spacecraft conﬁguration. The bus consists of two main parts: an outer octagonal wall and an internal cylindrical wall. The stacked conﬁguration is a primary driver in the design of the DSC, as this spacecraft has to be able to support the large mass of the OSC during launch. The cylindrical wall is designed to transfer the load path through the stacked conﬁguration (Figure 5), and has a 2624 cm diameter to match both the OSC diameter and the Ariane 5 adapter. The main detector payload, a cooled germanium spectrometer, is placed in the centre of the spacecraft. The spectrometer assumed in the GRL study consists of an array of 52 Springer

Fig. 3 (a) A 3D picture of a possible conﬁguration for the deployed OSC, (b) a face-on picture showing the dimensions of the OSC and (c) a side-on view

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Fig. 4 (a) A 3D picture of a possible DSC conﬁguration and (b) the DSC dimensions

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Fig. 5 (a) A 3D drawing of the GRL stack inside the Ariane 5 short 5660 SPELTRA fairing and (b) the dimensions of the stacked conﬁguration

hexagonal germanium detectors, covering an area of 405 cm2 . An anticoincidence vetoing shield surrounds the detector array at the focal plane. The spacecraft thrusters were positioned on the DSC to allow full three-axis stabilisation and transverse motion. Star trackers and sun sensors are placed around the craft to provide attitude measurements, while the antennae on the craft provide omni-directional communication capability. The formation-ﬂying package is assumed to be similar to the one baselined for the XEUS mission [5], modiﬁed to account for the large increase in focal length from 50 m to ∼500 m. The metrology system has three subsystems; (1) coarse radio metrology, (2) ﬁne radio metrology and (3) optical metrology. Radio metrology will bring the two spacecraft within 120 m of each other with an accuracy of a few centimetres. The optical metrology system for XEUS is very accurate at a focal length of 50 m (∼10’s µm laterally and 100’s µm longitudinally). The attitude requirements for the GRL are less stringent than that of XEUS, being ± 0.08 m laterally and ± 1 m longitudinally based on a 1 σ point spread function of 60 cm2 . It is therefore assumed that this system can be scaled for the GRL formation-ﬂying package. The larger, more active part of the metrology system will be located on the DSC. A laser will be located on the DSC and is reﬂected from the OSC in order to perform the optical metrology measurements and both ﬁne and coarse radio metrology can be performed by the same set of transmitters.

6. Conclusions The Gamma Ray Lens Technology Reference Study has highlighted a number of areas requiring further work if such a mission is to be viable in the future. Table 4 summarises the key GRL mission drivers and the associated areas of future activities required if the mission is to be realised. One of the key outcomes of the study is the fact that increasing the size of the mission eventually results in a limited sensitivity improvement due to the role of background. In order to become photon limited rather than background limited, vast improvements in background rejection should be a priority. Springer

• Need to strictly control mosaicity • Inter-crystal alignment • Deployment mechanism alignment accuracy • Thermal control to minimise spacecraft warping • Silicon Pore Optics development • Multilayer coating design for efﬁcient, broad energy coverage; 50–200 keV

PSF size

• Relatively long mission lifetime of 10–15 years. Poses potential difﬁculties for detector life since Ge isn’t radiation hard. • This has been noted as a desirable capability for a future gamma-ray mission

Mission lifetime

∗ Areas

envisaged to require major work or development

Gamma-ray polarisation∗

• ‘Better’ ACS detectors • Designing out intrinsic background lines from the spacecraft

Background rejection∗

Silicon Pore Optics∗

Petal Deployment

Laue Crystals∗

Metrology system

• AOCS design, constant formation control in order to maintain required accuracy • Scaling of current technology from missions such as XEUS, Darwin and LISA for a focal length of ∼500 m • Crystal growth • Crystal characterisation • Mounting on the lens–optimising packing factor • Crystal alignment, metrology and calibration • Deployment mechanism

Formation ﬂying and rendezvous

Key Mission Drivers

Table 4 Summary of key mission drivers and possible future activities required for the GRL mission

• Design of a detector capable of simultaneous spectroscopy and polarisation measurement, with possible balloon ﬂight test

• Development of ‘better’ ACS materials, e.g. LYSO, LuAP • Investigation of novel background rejection techniques e.g. Compton kinematic rejection • Possible development of other high-resolution, radiation hard focal plane detectors–LaI, LuI • Gamma-ray polarisation techniques

• Effective area and energy response modelling

• Design and characterisation of the SPO • Design of the multilayers

• Development of simple, accurate, large - scale deployment mechanism • Crystal mounting and alignment techniques • Full thermal analysis of the GRL spacecraft

• Design and testing of a metrology system capable of achieving the GRL requirements • Investigation of crystal growth and classiﬁcation techniques • Crystal mounting and alignment methods • Investigation of gradient crystals

• Establish a formation ﬂying package for the GRL

Future work

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The mission and spacecraft design presented here are the results of the preliminary science goals assumed at the start of the study. Nevertheless the suggested technology development activities would be still applicable if the science requirements would be changed. Acknowledgements The authors would like to acknowledge the work by Alan Owens, Alex Jeanes, Arvind Parmar, Christoph Winkler, Dave Lumb, Hubert Halloin, Peter von Ballmoos, Richard Grifﬁths and Thijs van der Laan.

References 1. Lyngvi, A. et al.: Technology reference studies, 55th international astronautical congress. Vancouver, Canada (2004) 2. Kn¨odlseder, J. et al: Prospects in space-based gamma-ray astronomy, 39th ESLAB symposium proceedings, Experimental Astronomy 20, DOI: 10.1007/s10686-006-9031-8 (2005) 3. Von Ballmoos, P. et al.: MAX: A gamma-ray lens for nuclear astrophysics, Proc. SPIE 5168, 482–491 (2004) 4. INTEGRAL special edition, Astronomy and Astrophysics 411, No. 1 (2003) 5. Bavdaz, M., Lumb, D., Peacock, A.: XEUS mission reference design, Proc. SPIE 5488, 530–538 (2004)

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Exp Astron (2005) 20:289–298 DOI 10.1007/s10686-006-9024-7 ORIGINAL ARTICLE

Gamma ray Fresnel lenses – why not? G. K. Skinner

Received: 17 November 2005 / Accepted: 30 January 2006 C Springer Science + Business Media B.V. 2006

Abstract Fresnel lenses offer the possibility of concentrating the ﬂux of X-rays or gammarays ﬂux falling on a geometric area of many square metres onto a focal point which need only be a millimetre or so in diameter (and which may even be very much smaller). They can do so with an efﬁciency that can approach 100%, and yet they are easily fabricated and have no special alignment requirements. Fresnel lenses can offer diffraction-limited angular resolution, even in a domain where that limit corresponds to less than a micro second of arc. Given all these highly desirable attributes, it is natural to ask why Fresnel gamma ray lenses are not already being used, or at least why there is not yet any mission that plans to use the technology. Possible reasons (apart from the obvious one that nobody thought of doing so) include the narrow bandwidth of simple Fresnel lenses, their very long focal length, and the problems of target ﬁnding. It is argued that none of these is a ‘show stopper’ and that this technique should be seriously considered for nuclear astrophysics. Keywords Gamma-ray . Astronomy . Optics

1. Introduction: Focusing as a phase control problem ‘Gamma-wave’ is a convenient term to employ when considering optics for high energy radiation (gamma-rays, or hard X-rays) in which the wave-like properties of the radiation need to be taken into account. We commence with a discussion of the general principles of focussing ‘gamma-waves.’ In its simplest form Fermat’s principle states that the path of radiation through an optical system is that which takes the least time. To be more precise, the time has a stationary value with respect to a small deviation in the path. In this form, Fermat’s principle does not take into account the wave aspect of the radiation – for example it does not work for diffraction gratings. However if restated in the form that the phase of the radiation at the destination

G. K. Skinner () Centre d’Etude Spatiale des Rayonnements, 9, avenue du Colonel Roche, 31028, Toulouse, France e-mail: [email protected] Springer

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Fig. 1 The phase at which radiation must be scattered to focus incoming radiation with plane horizontal wavefronts. At each position the intensity indicates the (relative) phases such that radiation will be focussed at the point indicated, with from 0–2π coded white to black. A cross-section is shown above the main ﬁgure. In three dimensions the iso-phase surfaces are paraboloids of revolution about the vertical axis

has a stationary value, then it is applicable quite generally. Thus the various paths through an optical system must result in the radiation arriving at the focal point with the same phase, modulo 2π . This is of course equally obvious if one considers Huygen’s principle and the fact that one wants all wavelets to interfere constructively. Suppose that we wish to bring parallel incoming radiation to a focus by scattering from elements within an optical system (‘scattering’ should here be thought of as generation of a Huygen’s wavelet; one could equally write ‘reﬂection’ or ‘diffraction’). Figure 1 shows the phase change necessary as a function of the position of the scattering element in the case of plane incoming wavefronts (source at inﬁnity). Often each scattering takes place with the same phase change (diffraction by identical atoms, reﬂection from surfaces . . . ). In this case the scatterers need to be distributed on isophase contours, which form a system of nested paraboloids. Figure 2 illustrates how grazing incidence mirrors, multilayer optics, and Laue diffraction ‘lenses’ use respectively reﬂecting surfaces, alternating layers, and planes of atoms to aim to populate parts of iso-phase surfaces. In each case only an approximation to the ideal is achieved. For Laue lenses, the planes of atoms are ﬂat and equispaced and so cannot perfectly follow the surfaces. In this case, and for grazing incidence or multilayer optic, practical tolerances are such that the scattering is coherent only very small regions. Lack of coherence means that on larger scales intensities are added, not amplitudes. 1.1. Changing the phase of a gamma-wave The requirements for focussing can be met exactly if the phase of the gamma-wave can be controlled. Figure 2(d) indicates how the phase change needs to vary across the surface of a planar focussing component in order to concentrate plane incoming wave onto a point. How does one change the phase of a gamma-wave? It turns out to be surprisingly easy (Skinner, 2002). It is well known that grazing incidence reﬂection relies on the fact that for X-rays and gamma-rays refractive indices are slightly less than unity. Conventionally one writes n = 1 − δ, where δ is small and positive. Thus the phase of X/γ -ray radiation will be changed Springer

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Fig. 2 The relationship of different focussing systems to isophase contours of Figure 1. (a) Nested grazing incidence mirrors should ideally follow a subset of the isophase surfaces of Figure 1. (b) The layers of multilayer mirrors follow also follow such surfaces. (c) In the case of a Laue lens, crystals planes approximate iosphase surfaces. (d) A cut along the line shown gives the phase change needed in a planar focussing device

by any material that it passes through. It is useful to deﬁne t2π = λ/δ, which is the thickness of material which leads to a phase change of 2π with respect to the phase in vacuo. This is of course the largest phase change ever needed. Table 1 gives an indication of orders of magnitude of t2π for some example materials and photon energies, as well as of the Springer

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Exp Astron (2005) 20:289–298 Table 1 Examples of the thickness of material necessary to change the phase of X/γ -ray radiation by 2π , and the corresponding absorption loss. Low atomic number materials show the least absorption. Gold is an example of a high density material which though having poor transmission at low energies minimises the lens thickness

Material

t2π µm

5 keV Absorption %

t2π µm

100 keV Absorption %

t2π mm

500 keV Absorption %

Polycarbonate Silicon Gold

23 13 2.1

6.3 51 93

470 260 39

0.9 0.9 32

2.4 1.3 0.19

2.6 2.7 5.2

transmission losses associated with this amount of material. Over a wide range of materials and energies, dimensions are convenient for manufacture and losses are very low. 1.2. An example Phase Fresnel lens for gamma-rays A consequence of the possibility of modulating the phase of a gamma-wave with a convenient thickness of material is that one can make a lens for focussing gamma-rays simply by giving a disk of material a thickness proﬁle with the form shown in Figure 2(d). This is essentially a Fresnel lens, but as the term is often applied to a simple lens whose thickness is stepped without consideration to maintaining phase, we term it a Phase Fresnel Lens, or PFL. As an example, such a lens for 500 keV gamma-rays might consist of a 5 m diameter disk of (say) aluminium with a thickness varying between tmin = 0.25 mm (to provide a substrate) and tmax = tmin + t2π = 1.4 mm. The absorption losses would be 1.6%. We shall consider below the example of such a lens in which the ﬁnest pitch, p, of the pattern (at the periphery) is ∼1 mm. 2. Advantages of Phase Fresnel lenses Phase Fresnel lenses seem to offer major advantages for gamma-ray astronomy. Angular resolution The diffraction-limited angular resolution of a PFL of diameter d at wavelength λ is given by the usual formula for a circular aperture, θ D = 1.22λ/d. In appropriate circumstances there is no reason why resolution close to this limit should not be achieved. For a 5 m diameter lens at 500 keV the diffraction limit is 0.12 micro seconds of arc (µas). Sub micro arc second resolution is exactly what is needed to image the space-time around a black hole – a speciﬁc objective of NASA’s ‘Beyond Einstein’ program. Simple manufacture Because the refractive index is very close to unity, the manufacturing tolerances necessary in the construction of a PFL are often relatively lax. For an aluminium lens working at 500 keV, λ/40 optical precision requires only 30 micron accuracy. In such circumstances Gamma-ray lens ‘polishing’ can be done with regular machine-shop tools! Collecting area Because of the low transmission losses and the large geometrical collecting area possible with PFLs, the effective area of a PFL-based telescope can be enormous. Even allowing for absorption, for reasonable detector efﬁciency (50%), and for rms wavefront Springer

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errors corresponding to λ/10, the effective area of the example 5 m diameter lens would be 65000 cm2 . Low aberrations and non-critical alignment With the typical dimensions which are being considered here, a PFL is an extreme example of a high aperture-ratio ( f -number), thin lens. Consequently geometrical aberrations are low (in fact entirely negligible for any conceivable size focal plane detector) and any tilt of the lens with respect to the viewing direction has little effect (tilts of ∼ 1◦ can be tolerated). In addition the depth of ﬁeld is relatively large.

3. The downside For a given lens diameter and λ the focal length of a Fresnel lens is given by f = pd/2λ. Table 2 gives some example values for a 5 m diameter lens. It can be seen that unless one reduces p to the atomic scale (as in Laue lenses), to the nanometric scale (as in multilayer mirrors), or at least to that entailing micromachining, then focal lengths are very long, particularly for high energies. Minimising the focal length of a PFL by adopting very small p is difﬁcult because the necessary thickness (depth) of the structure remains that discussed in Section 1.1 and the ‘aspect ratio’ (pitch/depth) of the required proﬁle becomes very high. Also, although it was argued in Section 2 that tolerances on the thickness are easily achieved, radial tolerances need to be p if diffraction limited focussing if not to be compromised. However, there are reasons for not trying to minimise f. The diffraction limited resolution will not be obtained if the detector does not have adequate spatial resolution or if chromatic aberration is too important. Combining the above expression for the focal length in terms of p with θD = 1.22λ/d shows that the physical dimension of the diffraction spot is simply 0.66 p, independent of λ. A detector with spatial resolution x which is of this order of magnitude or worse will cause blurring on an angular scale x/ f . Thus any PFL system with x > p, or equivalently f < x d/2λ, will be limited by detector resolution, not by diffraction. In the case of chromatic abberation, a spectral band of width λ leads to a blurring θC = 0.15(d/ f ) ( λ/λ). Thus both detector resolution problems and those of chromatic aberration ease with increasing f .

Table 2 Examples of the focal length f of a PFL having diameter, d = 5 m for various values of ﬁnest pitch p and photon energy. The aspect ratio is indicative (t2π / p) and supposes a moderately dense material (ρ ∼ 10).The ﬁrst two lines illustrate energy/pitch/focal-length combinations for which PFL aspect ratios are probably impracticable and for which Laue diffraction (Figure 1c) is more appropriate Pitch p

Energy (keV)

Aspect ratio

Focal length f

Notes

0.5 nm 0.5 nm 200 nm 25 microns 1.0 mm

100 1000 5 100 500

1.3 × 105 1.3 × 106 16 2.5 0.32

100 m 1 km 2 km 5000 km 106 km

Typical atomic spacing ” ” ” Note 1 Note 2 Example used here

Note. 1 Same pitch as the Chandra HEG grating [2]. Note. 2 Same aspect ratio as the Chandra HEG Diffraction grating. Springer

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Fig. 3 Continuous lines: the contributions to the angular resolution of a 5 m diameter PFL for 500 keV gammarays. That for chromatic abberation assumes a 2 keV band. Dashed lines show the corresponding values for a 2 m diameter PFL (the detector is of course unchanged). In each case the curves show the combination of the three components

Figure 3 shows the effect on the contributions to the angular resolution of changing the design focal length of an example Fresnel lens having d = 5 m and working at 500 keV. For the baseline design it is supposed that the detector resolution is limited by the track length of the electron receiving the energy of the incoming to x ∼ 0.5 mm. Similarly, the spectral band is assumed to be no narrower than the typical resolution of a Germanium detector,

E ∼ 2 keV at 500 keV. It can be seen that unless f > ∼ 106 km, then chromatic abberation will limit the angular resolution to no better than about one µas. Thus the two main problems which need to be addressed are chromatic aberration and long focal length. 3.1. Chromatic aberration The problems caused by chromatic aberration include both the loss of angular resolution due to blurring of the image and the decrease in sensitivity to which this blurring leads through the necessity of collecting the signal from a larger, and hence higher background, region of the detector. We have seen that the former effect is mimimised by using long focal lengths. The latter bears some discussion. Suppose one accepts that chromatic abberation is inevitable. Obviously for mono-energetic radiation there is not a problem. For broadband emission, one will properly focus only the radiation in a small fraction of the spectrum. With an energy resolving detector, radiation outside a band E can be ignored. One can then pose the question – how wide should E be for the best sensitivity? Suppose the sensitivity is limited by noise on the detector background, B, in a focal spot of diameter dd . We may take the detector background to be proportional to

E dd2 . If dd is dictated by chromatic aberration then it will be proportional to E. For a continuum source, so will the signal S. Consequently, assuming that the dominant source of noise is statistical background ﬂuctuations, the signal-to-noise ratio S/B 1/2 is proportional Springer

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Fig. 4 The efﬁciency of a 500 keV PFL if the detector distance is adjusted to match the focal length for each energy (note - the corresponding curve in reference Skinner (2002) is slightly incorrect)

to E −1/2 . One thus reaches the counter-intuitive conclusion that, in these circumstances, the best signal-to-noise ratio is obtained by using a band as narrow as the detector energy resolution will allow. This is of course also best for angular resolution. Using a narrow energy band, the sensitivity to a broadband signal will of course not be as good as if a wider bandpass had been possible without compromising the focusing, but given the large collecting area and the tiny background in a small focal spot and in a narrow energy range, it can be amazingly good. The narrow line sensitivity of our example 5 m, 500 keV lens could be <10−8 photons cm−2 s−1 . Of course, with an energy resolving detector one can use data from energies on either side of the design energy E of a PFL, but in general away from the optimum energy the sensitivity and angular resolution are not so supremely good. Diffraction limited focussing does occur also at harmonics of E, but the efﬁciency is low (ignoring differences in absorption, the response at 2E is 4.5% of that at E). In many circumstances it may be desirable to accept a lower sensitivity in order to gain information at other energies. The available surface area can then be divided into zones tuned to different energies, as is often proposed for Laue lenses. The zoning of the surface can be radial, azimuthal, or into separate lenses with independent focal spots. For many conﬁgurations the result will be that a broadband spectrum will be sampled at a limited number of relatively narrow bands – a situation which often has to be accepted in radio astronomy. Another possibility is to take advantage of the fact that a PFL works over a broad band of energies provided the instrument is refocused by moving the detector to the appropriate focal plane. Figure 4 shows that the E/E obtainable in this way is ∼1. The time available for each measure will of course be shorter, so in this case too the sensitivity at each energy will be poorer. Achromatic modiﬁcations of PFLs have been proposed (see Skinner, 2004, and references therein). These rely on combinations of diffractive and refractive components. In practical cases the refractive component has to be stepped to avoid excessive absorption. Such systems hold considerable promise, though because of the stepping the best performance is obtained only for a comb of energies and absorption losses tend to be signiﬁcant. It is worth noting that Laue lenses are just as subject to chromatic aberration as PFLs. Over a wide energy band, radiation falling on part of a PFL will be diffracted, though not in the ideal direction. This is directly analogous to Laue diffraction by a mosaic crystal – where again Springer

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all energies within a certain band are diffracted but with some dispersion in the diffracted direction. Assuming small angles, in each case one ﬁnds θ/θ ∼ − E/E. The differences are (i) crystal pass bands much narrower and (ii) Laue lenses have imaging properties which are much poorer. Consequently the chromaticity is often insigniﬁcant compared with other limitations. Interestingly, if the crystals could be composed of crystallites (or laminae) with the same orientation but having different crystal plane spacing it could be avoided. Such a system would be analogous to a graded spacing multilayer mirror but in Laue geometry in place of Bragg. 3.2. The focal length It has been argued above that to get the best performance, long focal lengths are inevitable. Given that formation ﬂying technology is necessary for any focal length above 10–20 m, what are the constraints? First it is worth noting that the idea of formation ﬂying satellites with a scale of 106 km is not unprecedented. The joint ESA-NASA Lisa gravitational wave mission will involve 3 spacecraft in a triangular formation with 5 × 106 km between each pair. The major difference between the formation ﬂying needed for LISA and that for a gamma-ray PFL mission is that the LISA formation rotates with respect to inertial space in such a way that each spacecraft follows the local gravity ﬁeld. Suppose that we have one spacecraft with a PFL and another carrying the corresponding detector. If the vector positions of the spacecraft are v1 and v2 , the direction of the separation vector f = v1 − v2 is the pointing direction of the instrument. For it to be constant we must have v¨ 1 = v¨ 2 . If the ﬁrst spacecraft is in a free orbit then its acceleration v¨ 1 is provided by the gravitational ﬁeld at v1 . In general the gravitational ﬁeld at v2 will be different and so cannot correspond to the acceleration v¨ 2 . To overcome the gravity gradient a station-keeping force must be supplied to one of the spacecraft by a constantly ﬁring thruster. Gravity gradients close to the earth are too large for a long focal length conﬁguration to be feasible. However a study by the NASA IMDC (Krizmanic et al., 2006) has shown that for a solar orbit, drifting away from the earth, the thrusts necessary are within the range of available ion engines and that the fuel requirements, although large, are not prohibitive. Other aspects of such a mission were found to present no overriding problems. The IMDC study set out only to establish feasibility and the orbit selected is not necessarily optimal. It may be that there that there are advantages in having one of the spacecraft relatively close to the earth-moon system, whose gravitational ﬁeld could, with judicious planning, be used to minimise fuel requirements. To repoint a million km long telescope at a new target will inevitably take an appreciable time. The IMDC study considered observations of several weeks, with a signiﬁcant part of the mission time, and the majority of the fuel, used for target changing. It was noted that the efﬁciency and fuel requirements could be much improved with two detector (or two lens) spacecraft. 3.3. Other considerations: Field of view and target ﬁnding The ﬁeld of view (fov) over which a gamma-ray PFL yields good imaging can be very large and geometric aberrations are never important. In practice the fov will be limited by detector size. Both pointing accuracy and knowledge of target positions must be good enough to ensure that the target image falls within the the part of the image plane recorded by the Springer

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detector. With a focal length of 106 km, a 1 m detector gives a fov of only 200 m.a.s. For comparison, the FGS points HST to an accuracy of 10 milli arc seconds (m.a.s.), 50 times worse. Existing astrometrical measurements do not provide target locations of the necessary precision. The Hipparchos catalog achieved ∼1 m.a.s. accuracy, though uncertainties in proper motion mean that it is no longer valid at this level. Successor missions DIVA and FAME will offer improvements for relatively bright stars. Other projected optical astrometry projects are expected to offer major progress in timescales shorter than any likely launch of a gamma-ray PFL mission. ESA’s Gaia (scheduled to be launched in 2010) will measure 300000 stars to 4 µas. Although further into the future and less certain, NASA’s OBSS and SIM PlanetQuest missions plans to push the precision down to close to 1 µas. Optical astrometry relies heavily on centroiding and care is necessary with AGN, in which the nucleus is generally embedded in surrounding emission. Radio measurements provide a surer means of astrometry for AGN and offer precisions which are as good as, and currently better than, those possible in other bands. At present the International Celestial Reference system is primarily realised by the International Celestial Reference Frame of 212 extragalactic radio sources with rms position uncertainties of 100 to 500 µas. As well as knowing the location of the source, the vector f above, deﬁning the separation and the orientation of the axis of the axis deﬁned by the two spacecraft must be measured and controlled. The problem has been studied in the context of the MAXIM mission, leading to proposals of solutions involving ‘super star trackers’ and/or super-conducting gyros (Phillips et al., 2004). Given the very long focal length required for a PFL, GPS-like surveying using radio delay/phase distance measurements can provide information on the positions of the spacecraft in 3-d space and hence constraints on the vector f, valuable in obtaining an attitude. A baseline limited by the size of the earth would probably not be adequate, so beacons or transponders on several further spacecraft would be desirable. The reference spacecraft need not necessarily be dedicated to the PFL mission – beacons on multiple, well distributed, spacecraft such as those of the LISA mission would be particularly valuable.1

4. Conclusions With their extremely good imaging properties, with the exceptionally large effective area possible from a simple device and with the very low background associated with their compact focus, PFLs would probably be the universal means of focussing gamma-rays were it not for the disadvantages discussed above. It has been argued above that in appropriate circumstances these disadvantages can all be overcome and that although an ambitious mission would be needed, there are no ‘showstoppers’. Particularly where the ultimate in angular resolution or in point source sensitivity in a relatively narrow energy band is required, PFLs hold enormous potential in the era of gamma-wave astronomy.

It is interesting to note that if a total of at least n ≥ 7 stations is involved, measurement of the distances and velocities between all pairs formally provides enough information to solve for the 6n coordinates locating them all in momentum space, using no reference other than the structure of the gravitation potential of the solar system. The formation itself becomes an inertial sensor!

1

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References 1. Skinner, G.K.: Diffractive/refractive optics for high energy astronomy -I : Gamma-ray Fresnel lenses. A&A 375, 691 (2001), “-II : Variations on the Theme”, A&A 383, 352 (2002) 2. Canizares, C.R. et al.: The Chandra high-energy transmission grating. PASP 117, 836 (2005) 3. Skinner, G.K.: Design and imaging performance of achromatic diffractive-refractive x-ray and gamma-ray lenses. Appl. Optics 43, 4845 (2004) 5. Gendreau, K.C. et al.: Requirements and options for a stable inertial reference frame for a 100-microarcsecond imaging telescope. Proc SPIE 4852, 685 (2002) 5. Phillips, J.D. et al.: Metrology and pointing for astronomical interferometers. Proc SPIE 5491, 320 (2004) 6. Krizmanic, J. et al.: Formation ﬂying for a Fresnel lens observatory mission. Experimental Astronomy 20, DOI: 10.1007/s10686-006-9038-1 (2005)

Springer

Exp Astron (2005) 20:299–306 DOI 10.1007/s10686-006-9030-9 ORIGINAL ARTICLE

Development of ground-testable phase fresnel lenses in silicon John Krizmanic · Brian Morgan · Robert Streitmatter · Neil Gehrels · Keith Gendreau · Zaven Arzoumanian · Reza Ghodssi · Gerry Skinner

Received: 16 November 2005 / Accepted: 22 February 2006 C Springer Science + Business Media B.V. 2006

Abstract Diffractive optics, such as Phase Fresnel Lenses (PFL’s), offer the potential to achieve excellent imaging performance in the x-ray and gamma-ray photon regimes. In principle, the angular resolution obtained with these devices can be diffraction limited. Furthermore, improvements in signal sensitivity can be achieved as virtually the entire ﬂux incident on a lens can be concentrated onto a small detector area. In order to verify experimentally the imaging performance, we have fabricated PFL’s in silicon using gray-scale lithography to produce the required Fresnel proﬁle. These devices are to be evaluated in the recently constructed 600-meter x-ray interferometry testbed at NASA/GSFC. Proﬁle measurements of the Fresnel structures in fabricated PFL’s have been performed and have been used to obtain initial characterization of the expected PFL imaging efﬁciencies. Keywords X-ray astronomy · Gamma-ray astronomy · Optics

1. Introduction The use of Phase Fresnel Lenses (PFL’s) offers a mechanism to achieve superb imaging of astrophysical objects in the hard X-ray and gamma-ray energy regimes (Skinner, 2001, 2002). In principle, PFL’s can concentrate nearly the entire incident photon ﬂux, modulo J. Krizmanic () · Z. Arzoumanian Universities Space Research Association e-mail: [email protected] J. Krizmanic · R. Streitmatter · N. Gehrels · K. Gendreau · Z. Arzoumanian NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA Brian Morgan · R. Ghodssi Dept. of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA G. Skinner CESR, 9, avenue du Colonel-Roche 31028 Toulouse, France Springer

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absorption effects, with diffraction-limited imaging performance. The impact of absorption is energy and material dependent, but can be almost negligible at higher photon energies. The performance of these diffraction optics is obtained via tailoring the Fresnel proﬁle of each zone to yield the appropriate phase at the primary focal point. However, PFL’s have long focal lengths and are chromatic; the excellent imaging is available over a narrow energy range. In order to demonstrate the imaging capabilities of these optics, we have fabricated ground-testable PFL’s in silicon.

2. Stepping to PFL’s

Phase Thickness (t/tπ)

PFL’s are a natural extension of Fresnel-diffractive optics. As opposed to Fresnel Zone Plates (FZP), where alternating half-period or Fresnel zones are completely blocked, and Phasereversal Zone Plates, where the blocked zone in a FZP is replaced by an amount of material to retard the phase by π , the entire proﬁle of each Fresnel zone in a PFL has the appropriate amount of material to achieve the proper phase shift at the primary focus. In practice, the exact proﬁle of a PFL can be approximated by a multiple-step structure as shown in Figure 1 which illustrates the ﬁrst four Fresnel zones (ridges) of a PFL with 4 steps per zone approximating √ the ideal PFL√proﬁle. The radial location of the step transitions is given by rk = R1 k/P where R1 (= 2 f λ) is the location of the ﬁrst Fresnel ridge ( f is the focal length and λ the photon wavelength) and P is the number of steps/Fresnel ridge with a step index of k. For the example given in Figure 1, k runs from k = 1 to k = 16. This choice leads to annuli, as deﬁned by each step, of constant area on the PFL. The step height tk is chosen via the prescription tk = (2 × MOD(k, P) − 1)π/P, where MOD is the modulo function. In Figure 1, the steps are represented in terms of phase thickness: ϕk = tk /tπ . Each step contributes equally, ignoring absorption, to the intensity at a given focal point. This conﬁguration of the stepped-phase proﬁle is denoted as a regular-stepped PFL. For an exact PFL proﬁle, all the irradiance appears in the ﬁrst order (n = 1) focus. In a stepped-proﬁle approximation, some energy appears in negative and higher order foci. Ignoring absorptive effects, the impact on the lens efﬁciency of approximating the exact PFL

2

1.5

1

0.5

0

0

0.5

1

1.5

2

Plate Radius (R/R1) Fig. 1 The ideal PFL proﬁle of the ﬁrst four Fresnel ridges compared to that for a stepped proﬁle with 4 steps/ridge Springer

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proﬁle by a step-wise function is given by Dammann (1970) Lrn =

sin(π/P) n(π/P)

2 for (n − 1)/P = m ∈ Integer

(1)

= 0 otherwise where Lrn is the relative intensity into the nth order focus for P steps in each Fresnel zone. As P increases, the indices with non-zero intensities of both the real and virtual higher order foci are pushed to higher n with the relative intensities into these higher orders decreasing. In the limiting case where P → ∞, the proﬁle is exact for the PFL with the relative intensity in the 1st order (n = 1) going to 100% (and the indices of the higher order foci being sent to ±∞). More practically, a stepped-PFL with P = 8 per Fresnel zone has 95% efﬁciency focussing into the 1st order focal point, sans absorption. The material needed in a PFL to retard the phase also will attenuate the ﬂux of incident photons. The index of refraction of matter can be expressed as n ∗ = 1 − δ − iβ and is related to atomic scattering factors (Henke et al., 1993). Thus for a photon of wavelength λ, a material of thickness t will retard the phase by ϕ = 2π tδ/λ while attenuating the intensity by e−t/τ where τ = (4πβ)−1 . The attenuating effects of the material in a Fresnel zone of a steppedPFL can be calculated by determining the amplitude of the waveform traversing each step of the PFL proﬁle. If tk is the material thickness of the kth step in a particular Fresnel zone, the phase will be retarded by ϕk . As shown in Figure 1, ψk represents the phase shift needed by the ideal PFL proﬁle at the radius of the kth step transition to make the amplitude to be in phase at primary focus, with deﬁning ψ0 ≡ 0. Thus the kth step retards the phase by ϕk between ψk−1 and ψk , and the amplitude can be expressed as (Kirz, 1974) Ak = =

C −tk /2τ e 2π

ψk

ei(ψ−ϕk ) dψ

(2)

ψk−1

C R α − iαkI 2π k

(3)

where C is a normalization constant and αkR = e−tk /2τ cos ϕk (sin ψk − sin ψk−1 ) − sin ϕk (cos ψk − cos ψk−1 ) αkI = e−tk /2τ cos ϕk (cos ψk − cos ψk−1 ) + sin ϕk (sin ψk − sin ψk−1 ) Summing over P steps leads to determining the intensity at the primary focus C2 I1 = |A| = A A = 4π 2 2

∗

P k=1

2 αkR

+

P

2 αkI

(4)

k=1

Note that circular symmetry is assumed for the PFL, and this calculation is for a single Fresnel zone. If a PFL contains a total of M individual Fresnel zones with identical, in phase, proﬁles, the irradiance at the focus would be increased by M 2 as each Fresnel zone has the same area on the PFL. This formulation holds for any step spacing, regular or irregular, as long as a sufﬁciently small scale exists where the phase thickness is effectively constant. Choosing an energy of 8 keV, the efﬁciency of a P = 8 regular-stepped PFL, including absorption, Springer

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is 82.3% in silicon. If absorption is ignored, the efﬁciency is 95% which is exactly that as determined from Equation (1) for n = 1. 3. Ground-test constraints and PFL fabrication For a PFL with diameter d, minimum Fresnel ridge spacing pmin , focusing at a photon wavelength λ, the focal length is given by pmin d 2λ pmin d E ≈4 µm cm keV

f =

(5) (6)

where f is in meters for pmin in µm, d in cm, and E in keV in Equation (6). Using the representative values of pmin = 25 µm, d = 1 cm, and E = 8 keV (Cu K-α), the focal length would be 800 meters which is rather long for a ground-test. At NASA Goddard Space Flight Center, a 600-meter Interferometry Testbed is available for testing of PFL optics. The nominal conﬁguration has an optics station 150 meters from an x-ray source and a detector station 450 meters from the optics station. Assuming the x-ray emission is isotropic within the ﬁeld-of-view of the optics, the effective focal length of an optic focussing at the detector station would be f Eff = f1f1+f2f2 = 112.5 meters, where f 1 is the distance from the source to the optics (150 m) and f 2 is the distance from the optics to the detector (450 m). This sets the value of the focal length of a PFL for incorporation into this test beam conﬁguration. Using f = 112.5 meters, d = 1 cm, and E = 8 keV, this leads to a minimum Fresnel ridge spacing of 3.5 µm which is the natural scale size for microfabrication in silicon. The Fresnel ridge height needed to retard the phase by 2π is given by t2π = λ/δ where λ is the photon wavelength and δ is the real part of the index of refraction. For silicon, t2π ≈ 2.57 [E γ /keV] µm or 20.5 µm at 8 keV. 3.1. PFL fabrication using gray-scale lithography The gray-scale lithographic fabrication process has been employed at the University of Maryland to create PFL structures in silicon wafers (Morgan et al., 2004). This implementation of the gray-scale process employs a lithographic mask that uses small, variable-transmission pixels (gray levels) that create, via projection photolithography, a designed, 3-dimensional structure in a photoresist spun on a silicon wafer. This pattern is then transferred into the silicon via deep-reactive ion etching (DRIE). The developed ground-test PFL’s have been fabricated using silicon-on-insulator (SOI) wafers in order to minimize the thickness of the required mechanical substrate under the PFL’s and thus maximize the x-ray photon transmission. The sandwiched oxide layer forms a natural etch stop to remove the silicon substrate directly under each PFL while leaving the surrounding material for mechanical stability. The unprocessed SOI wafer was 100 mm in diameter with 70 µm of silicon, 2 µm oxide, and 500 µm silicon forming the SOI wafer structure. A prototype silicon PFL fabricated using the gray-scale lithographic process is shown in Figure 2. Table 1 lists the four PFL designs that have been included in this ground-test fabrication. Note that this PFL fabrication incorporated a design to produce 4π , as opposed to 2π thick Fresnel optics. This was chosen for this initial fabrication to effectively double the minimum ridge spacing, pmin , for a set focal length, PFL diameter, and design energy. Although this Springer

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Table 1 Ground-test PFL design parameters. These devices are designed to have a Fresnel ridge height of approximately 40 µm corresponding to a 4π phase shift PFL designation

Diameter

pmin

# of Ridges

# Steps/Ridge

X3 X4 X5 X6

2.99 mm 2.99 mm 2.99 mm 4.72 mm

24 µm 24 µm 24 µm 15 µm

32 32 32 80

16 16 8 8

Fig. 2 A prototype PFL fabricated using the gray-scale lithographic process (Morgan et al., 2004). Copyright 2004 IEEE

will increase absorption losses, the relaxation of the pmin requirement eased the constraints on the device fabrication. The four PFL’s, along with several test structures, were grouped to form a die which is compact in spatial extent. Twelve of these dice in a 3 × 4 array were fabricated on the 100 mm SOI wafer via a step-and-repeat process. The goal of this fabrication was to produce a sample of PFL’s for testing in the 600 m beam line, and the process was not optimized for yield. In order to identify the optimal PFL’s for testing, an optical inspection rejected those with obvious defects. This rejected 15 out of the possible 48 PFL’s. The remaining PFL’s were scanned via an optical proﬁlometer (Veeco, WYKO NT1100) to determine the accuracy of the fabricated proﬁles. For the 3 mm diameter PFL’s, the ﬁrst and last 5 Fresnel ridges were scanned and compared to the design proﬁle. For the 5 mm PFL, the 5 ridges near the half radius were also scanned and compared. Using an analysis similar to that presented in Equation (4), albeit ignoring absorption and using a phasor formalism, the efﬁciency of each scanned PFL was estimated from the proﬁles obtained from the proﬁlometer measurements. Note that the proﬁles are measured along a chosen radial path and circular symmetry was assumed.Figure 3 illustrates the proﬁle measurements and a comparison to the design proﬁle for a 3 mm diameter PFL (X3) for the regions near the center of the device (leftmost plot) and near the edge (rightmost plot).

4. PFL anticipated performance Table 2 lists the maximum, minimum, and average efﬁciency for the different fabricated PFL’s based upon the proﬁle measurements. The values for the maxima and minima quoted for a PFL are that for a speciﬁc lens, i.e. the ensemble of measurements for a speciﬁc design Springer

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75.6% 77.2% 69.6%

59.0% 67.5% 48.0%

72.5% 80.9% 52.6%

54.8% 64.8% 41.1%

r = 1.5 mm

Center

r = 1.5 mm 68.5% 74.8% 59.1%

Center 55.3% 63.4% 36.5%

r = 1.5 mm

X5

61.6% 65.2% 35.8%

Center

The maximum and minimum designations are the efﬁciencies determined for a speciﬁc, fabricated PFL

Average Maximum Minimum

Center

X4

X3

55.1% 61.6% 54.8%

r = 1.5 mm

X6

Table 2 Fabricated PFL anticipated efﬁciencies obtained from proﬁle measurements and based upon PFL device type

32.4% 36.1% 21.1%

r = 2.5 mm

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305 Fresnel Ridge Height (µm)

Fresnel Ridge Height (µm)

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40

30

40

30

20

20

10

10

0

0

500

0

1400

PFL Radius (µm)

1500

PFL Radius (µm)

Fig. 3 The measured proﬁle (solid) of a fabricated, 3 mm diameter (X3) PFL as compared to the design proﬁle (dashed). The left plot shows the results at the center of the lens while the right plot illustrates the results near the outermost region of the lens. These measurements lead to anticipated efﬁciencies of 76% for the center region and 64% near the edge of the PFL

were used to determine the appropriate designation. The quoted efﬁciencies do not take into account absorptive losses due to either the Fresnel proﬁle or the ∼25 µm substrate. Assuming an 8 step/Fresnel ridge proﬁle and 8 keV, the reduction in collection efﬁciency is approximately 14%, i.e. 1 − 0.82 , due to the phase-retarding material in the stepped-Fresnel 0.95 proﬁle and 30%, i.e. 1 − e−25 µm/70 µm , due to the 25 µm silicon substrate. Note that the effects of attenuation can be signiﬁcantly reduced by fabricating PFL’s designed for higher photon energies. The data represented in Table 2 demonstrate that, as indicated from proﬁle measurements, stepped-proﬁle PFL’s micro-fabricated in silicon have efﬁciencies signiﬁcantly larger than that for the simpler zone plates and phase-reversal zone plates. The data also illustrate that efﬁciencies determined from the ﬁner pitch Fresnel zones are reduced as compared to the larger pitch center Fresnel zones. This is due to the fact that it is more difﬁcult to accurately fabricate zones with higher aspect ratios, deﬁned as the ratio of Fresnel ridge height to ridge pitch. A signiﬁcant contribution to this effect is due to the aspect-ratio dependence of the etching process; it is more difﬁcult to remove silicon from narrow ridge regions as shown in Figure 3. Work has progressed on designing appropriate compensation in the lithographic mask and this technique has been demonstrated in the fabrication of a second-generation of Fresnel Lens structures that exhibit a much reduced aspect-ratio dependence of the PFL proﬁles (Morgan et al., 2005). There are three components contributing to the angular resolution of a PFL: diffraction, detector spatial resolution, and chromatic aberration. For the 3 mm ground-test PFL imaging at 8 keV, the values of each of these terms is given by Diffraction Limit: ϑ D = 1.22λ/d = 8 milli−arcseconds (m

) Detector Spatial Limit: ϑs = x/F = 6 m

Chromatic Aberration Limit (Skinner, 2001): ϑ E = 0.2( E/E)(d/F) = 5 m

(7) Springer

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where a x = 13 µm detector pixel size is assumed with E = 140 eV FWHM and F = 450 meters. Note that the contribution to the angular resolution from the chromatic aberration term is reduced if one assumes the Cu K-α line width. Thus the anticipated angular resolution of these ground-test PFL’s are ∼10 milli-arcseconds (m

) which is a signiﬁcant improvement to that obtained from current astronomical missions, e.g. 500 m

for CHANDRA (Jerius et al., 2004), in this energy range.

5. Conclusions We have fabricated ground-test PFL’s in silicon using gray-scale lithography. We have determined the imaging performance of these devices via analysis of the measured proﬁles of the fabricated optics. These results indicate that the efﬁciencies, although less than ideal, are a signiﬁcant improvement over the theoretical maximum that can be obtained with zone plates and phase-reversal zone plates. We plan on introducing these devices into the 600 m test beam to demonstrate their imaging capability and verify the anticipated efﬁciency determination via in situ x-ray measurements. This material is based upon work supported by the National Aeronautics and Space Administration under Grant APRA04-0000-0087 issued through the Science Mission Directorate Ofﬁce and by Goddard Space Flight Center through the Director’s Discretionary Fund.

References Dammann, H.: Optik 31, 95 (1970) Henke, B.L., Gullikson, E.M., Davis, J.C.: At. Data Nucl. Data Tables 54, 181 (1993) Jerius, D., Gaetz, T.J., Karovska, M.: Proc. SPIE 5165, 433 (2004) Kirz, J.: J. Opt. Soc. Amer. 64, 301 (1974) Morgan, B., Waits, C.M., Krizmanic, J., Ghodssi, R.: J. Micro-Electro-Mechanical-Systems (JMEMS) 13, 113 (2004) Morgan, B., Waits, C.M., Ghodssi, R.: Microelect. Eng. 77, 850 (2005) Skinner, G.: Astron. Astrophys. 375, 691 (2001) Skinner, G.: Astron. Astrophys. 383, 352 (2002)

Springer

Exp Astron (2005) 20:307–315 DOI 10.1007/s10686-006-9046-1

Multiwavelength focusing with the Sun as gravitational lens Laurent Koechlin · Denis Serre · Gerald K. Skinner · Peter Von Ballmoos · Thomas Crouzil

Received: 10 January 2006 / Accepted: 18 May 2006 C Springer Science + Business Media B.V. 2006

Abstract The light deviation caused by the gravitational potential in the vicinity of the sun could be used as a means of focussing radiation that cannot be focussed easily otherwise. The gravitational lens formed by the sun is not stigmatic, but does have the advantage of being achromatic and acts identically on all types of mass-less radiations. For a source at inﬁnity, its geometrical characteristics present a “caustic” line starting at 550 astronomical units (UA) downstream from the sun. In a plane perpendicular to that caustic line, images of distant objects are formed. The perturbations by the solar corona plasma will signiﬁcantly blur electromagnetic radiation for wavelengths longer than those of the IR domain. At shorter wavelengths, for example the γ domain, the focussing process could lead to 108 ampliﬁcation factors. In order to reach the regions where images are formed, long distance space missions are necessary. Once launched, missions of this type would be dedicated to a single ﬁeld. Some possible targets are considered, such as Sagitarius A observed in X and γ rays. In this paper we study the point spread function (PSF) of the sun as a gravitational lens. Taking into account perturbations by the planets, the non sphericL. Koechlin · D. Serre · G. K. Skinner · P. V. Ballmoos · T. Crouzil Universite Paul Sabatier, Observatoire Midi Pyrenees, 14 Avenue Edouard Belin, 31400 Toulouse, France

ity of the sun and coronal plasma index, we derive limits within which such observations could be possible.

1. Introduction The deviation of electromagnetic radiation by the sun’s mass is a consequence of general relativity. It was observed as the ﬁrst experimental conﬁrmation of that theory: by Eddington (Dyson et al., 1919) in the visible, and later with more precision in the radio domain (Fomalont et al., 1975). Using the optical effects of General Relativity for astrophysical purposes is not a new idea: Einstein himself has published a paper entitled “Lenslike Action of a Star by the Deviation of Light in the Gravitational Field” (Einstein, 1936), and the idea of using the sun as a gravitational lens for detecting nebulae dates from 1937 (Zwicky, 1937). A lot of observational and theoretical work has since been done on gravitational lensing. It concerns principally the effect of lenses on distant ﬁelds when one or more lensing objects is present along the line of sight. From the resulting deformations, conclusions are drawn either about the gravitational potential of the lensing objects, or about the distant source objects (detected thanks to gravitational intensiﬁcation) or the environment of stellar objects through microlensing (Paczynski, 1996). In the case studied here, the situation is different: the distant ﬁeld is not imaged by a telescope. The sun Springer

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itself is the focussing telescope, acting as an optical lens. A detector placed at a large distance from the inner solar system scans a “focal plane” of that lens. The deformation of the far ﬁeld that is usually studied around a gravitational lens is not imaged here. What is recorded is an image plane, where a non-distorted and strongly intensiﬁed image of a narrow distant ﬁeld is formed. In this paper we will study the geometry of the problem, the scales involved, and the relatively “tough to deal with” Point Spread Function (PSF) of an imaging system involving a spherical mass as focussing objective. We will deﬁne upper limits for the aberrations caused by the gravitational perturbations from solar system objects and the non sphericity of the sun. Finally we will propose an observing scheme for a space mission dedicated to Sagitarius A in the 511 keV domain. 2. Geometry of the problem In the “thin lens” approximation, the deviation angle caused to a ray approaching at a closest distance r (impact parameter) from a mass M is θ = 4G M/r c2

(1)

where G = 6.676 × 10−11 m3 kg−1 s−2 is the gravitation constant, and c = 299792458 ms−1 the speed of light. In the case of light grazing the sun, where M = m 1.989 × 1030 kg and r ≥ r 6.96 × 108 m, the deviation angle is θ = 1.75 arc seconds. Using the small angles approximation, the shortest distance f at which originally parallel beams intersect when deﬂected by the sun is: f = r 2 c2 /4G M,

(2)

The rays intersection locus (a caustic) is a line starting at a distance f after the lens end extending to inﬁnity. For a one solar mass object and one solar radius impact parameter, the minimum “focal length” f is 548 astronomical units(AU) i.e. 8.2 × 1013 m. The impact parameter r may be smaller than a solar radius if one considers a transparent sun, as for neutrinos and gravitational waves (Macone, 1999), leading to shorter starting points of the optical caustic: f can be as small as Springer

40 AU : 5.98 × 1012 m. A non-zero neutrino mass will further shorten the focal length. In the case of X and γ rays, the impact parameter will be in the range of 1.1 to 1.5 solar radius, leading to focal distances of hundreds of AU.

3. Point Spread Function of a “perfect” gravitational lens From the strong dependence (eq. 2) of its “convergence length” f upon the impact parameter r, one can see that a gravitational lens is not stigmatic. However, although a gravitational lens has no optical axis, no pupil plane and no focal plane, one can deﬁne arbitrarily an optical axis as the line from a point source passing through the lens’s center of mass, a pupil plane (or lens plane) as a plane perpendicular to the optical axis and containing the center of mass, and ﬁnally a focal plane as a plane parallel to the pupil plane, at a distance from the center of mass corresponding to the convergence length f. As f varies according to r, a given focal plane is related to a given impact parameter for a source at inﬁnity. In the following, subscript “1 ” indicates variables in the lens plane, and subscript “2 ” variables in an arbitrarily chosen focal plane. We use polar coordinates (r, α) and consider an elemental area in each plane: d S1 = r1 dr1 dα1 and d S2 = r2 dr2 dα2 . The light from a point source is not actually focussed by a gravitational lens, but it is locally intensiﬁed in the vicinity of the caustic. One can deﬁne a Point Spread Function (PSF), from the expression of the intensiﬁcation as a function of the position in the focal plane: I (r2 , α2 )/I0 , I0 being the “unfocussed” light intensity from the distant source if the focussing mass were not present. The light collected by d S1 in the lens plane is sent into the conjugate area d S2 in the focal plane. I (r2 ) can be derived from the ratio d S1 /d S2 . High intensiﬁcation occurs as d S1 is much larger than d S2 . I (r1 , r2 , α1 , α2 ) = I0

r1 dr1 dα1 d S1 . = I0 r2 dr2 dα2 d S2

(3)

To express I as a function of (r2 , α2 ) only, we need relations between r1 , r2 , α1 and α2 . For the moment, we consider a centrosymetric mass distribution. This implies that α1 = α2 , yielding a centro-symmetric PSF, which only depends on the dis-

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Fig. 1 Position of the different planes and optical axis for the sun as a gravitational lens

tance r2 from the caustic. The relation between r2 and r1 is given by

dr2 dr1 = 2

r2 = r1 − f θ, which yields, after replacing f and θ by their expressions in eqs. (1) and (2): r2 = r1 − r02 /r1

r1 =

4r0 2 + r2 2 . 2

1±

r2

4r0 2 + r2 2

.

(6)

Placing r1 and dr1 into eq.(3) and adding the two contributions gives:

(4)

where r0 is the radius of the “Einstein ring”: the locus of points in the lens plane from which light intersects the caustic in that particular focal plane. r1 can be expressed as a function of r2 : r2 ±

Expressing dr1+ and dr1− as a function of dr2 yields:

(5)

There are two solutions: r1+ and r1− for a given r2 , this corresponds to contributions from two “gravitational arcs” in the lens plane which add up into an element area of the focal plane: one arc on each side of the lens.

2 r2 + 4r0 2 + r2 2 r1 dr1 = I (r ) = I0 r2 dr2 4r2 + 4r0 2 + r2 2 2 r2 + 4r0 2 + r2 2 + 4r2 + 4r0 2 + r2 2

(7)

which, when considering r2 r0 simpliﬁes to the approximation: I (r2 ) = I0

r0 . r2

(8)

Fig. 2 Images of two distant point sources represented as the intersection of their corresponding caustics and an image plane

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We can derive a normalized “geometrical” PSF, which can be expressed in Cartesian coordinates: x2 = r2 cos α, y2 = r2 sin α and vector x2 = (x2 , y2 ): P S Fgeom (x2 ) =

r0 |x2 |

(9)

This expression, being derived from geometrical hypotheses, tends to inﬁnity at x = 0. This divergence is suppressed by diffraction. What causes problems with such a PSF is the divergence of its surface integral for large x. It may impair the signal/noise ratio for small scale features on an extended background. The diffraction limited point spread function of a single ring aperture of radius r0 and focal f at wavelength λ would be P S Fring (x2 , λ) = J0

π|x2 |r0 λf

(10)

where J0 is the zero order Bessel function. As the light from collecting rings of different diameters travels optical paths which differ by much more than the coherence length, they contribute incoherently to the image. To estimate the order of magnitude of the effect of diffraction, one can consider r0 constant for the center part of the PSF and write: P S Fdiff (x2 , λ) J0

π|x|r0 λf

r0 ⊗ |x2 |

(11)

where ⊗ represents a 2D convolution operator and P S Fdiff is the point spread function of a gravitational lens with diffraction. The above approximation is only for the central and peaked part of P S Fdiff . A more precise expression should be built from the integration over the different contributing arcs in the pupil plane. For a distant object O(x, λ), the corresponding image I (x2 , λ) in the focal plane of a perfect sphere gravitational lens is: I (x2 , λ) = O(x, λ) ⊗ P S Fdiff (x2 , λ)

(12)

For the γ -ray domain, at 511 keV for example, the diffraction effects are small. The ﬁrst zero of J0 (Z ) at z = 2.405 corresponds to 1.3 × 10−7 m in the focal plane and 2.3 × 10−16 arc seconds angularly. In the next section we show that gravitational aberrations Springer

have larger effects than the diffraction at short wavelengths, the turnover being in the submillimetric domain. However, the path length aberrations due to the corona plasma are dominant at all wavelengths longer than the visible or close IR domain.

4. Aberrations The perturbations of the gravitational potential change the PSF. We will not give expressions for the aberrations, but derive from simple models some upper limits in angular resolution and radiation ampliﬁcation. The mass of planets perturb the deﬂection angles. Furthermore, the sun is not a perfect sphere, due to its rotation and seismic activity. 4.1. Effect of a planet To ﬁrst order, the mass of a planet causes a deviation of the caustic. In the focal plane related to impact parameter r0 , the image translation is: x2 = r o

m p ro rp m r p sin i r p

(13)

where vector r p corresponds to the heliocentric position of the planet, r p being its modulus, i the angle between r p and the line of sight. m p and m are respectively the mass of the planet and of the sun. In addition to translation, aberrations arise. Let’s consider two points on a ring of radius r0 in the pupil plane: the intersections of that ring with a plane containing the optical axis and the center of the planet. Due to the mass of the planet, the deviation angles at those two points differ:

θa =

4Gm p 4Gm p and θb = (r p + r0 )c2 (r p − r0 )c2

(14)

the resulting beams reach the focal plane at a distance

x from each other:

x2 =

m p rp 2r03 . (r p sin i)2 m r p

(15)

For two other beams in an axial plane perpendicular to the previous one, the deviation angles are equal

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and x2 = 0. When considering the whole “collecting ring”, the resulting aberration is of elongation x2 . Jupiter dominates the other planets for its effect on image displacement and aberration: respectively 1573 m and 6.5 m for a r0 = 1.15 solar radius impact parameter ( f = 724 AU). Venus causes the second largest displacement and aberration: respectively 29 and 0.8 m. For this upper limit of aberrations, we have considered the cases where the heliocentric angle between the planet and the target i = 30◦ . The best possible case (i = 90◦ ) would correspond to aberrations four times smaller. 4.2. Effect of the non sphericity of the sun The oblateness of the sun is r/r 1.0 10−5 (Stix, 2002) where r is the solar photosphere radius. To give an upper limit to the resulting aberrations, we consider the rotation axis of the sun perpendicular to the optical axis. We also consider the sun as having a uniform density. This yields a very crude upper limit, as the mass repartition in the sun is strongly offset towards the smaller values of r , and the oblateness r of an equipotential mass m of mean diameter r in rotation at ω is given by

r =

ω2r4 . 2Gm

(16)

We model the gravitational potential in a way similar to modeling the electric potential of a polarized atom: the sun’s oblate mass is approximated by two spheres of half the density, their centers being offset by 4 r . We then consider two perpendicular planes: the equatorial plane and a polar plane, both containing the optical axis. As r << r , the oblateness has a negligible effect , for beams in the polar plane and we get θpol 4Gm r0 c2 whereas in the equatorial plane we have: θeq =

2r0 4Gm . 2c2 r02 − 4 r 2

(17)

The corresponding size of the aberration in the focal plane is given by:

x = f (2θeq − 2θ pol ) = r0

8 r 2 /r02 1 − 4 r 2 /r0

(18)

which, when considering r << r0 simpliﬁes into:

x =

8 r 2 r0

(19)

This corresponds to an aberration of 0.37 m for a r0 = 1.15 solar radius impact parameter - comparable to, but smaller than, the planetary perturbations. The actual shape of the PSF due to planets positions and the oblateness of the sun is stable in time and can be modeled, so a matched deconvolution of the images in the focal plane could be performed, improving the resolution. However, other aberrations may arise from less predictable phenomena. 4.3. Other causes of gravitational aberrations The gravitational potential is affected by the density variations from helioseismic activity. To estimate these perturbations, we based our assumptions on data in “Astrophysical Quantities” (Cox and Allen, 1999) and “The Sun” (Stix, 2002). We ﬁnd an upper limit for the aberrations of 2.4 meters at the focal plane corresponding to r0 = 1.1 solar radius, considering the contribution from the whole spectrum of radial “p” modes. This upper limit is crudely overestimated. We have not been able to derive before the deadline for this paper a robust expression of these gravitational perturbations. This should be investigated by people more competent in solar physics. The perturbations of the gravitational ﬁeld are generally neglected in the literature for the equations that describe the pulsation modes of the sun. 4.4. Aberrations due to the corona plasma The refractive index of the solar corona plasma has been measured during several experiments made to test the validity of general relativity using the deﬂection of quasar sources angularly approaching the sun. The refraction effect has been probed in the radio domain, and its dependance over wavelength in λ2 has been published by Anderson et al. (2004) for solar distances from r0 = 1.2 to 5 solar radii in the X and K bands (8 and 32 GHz; respectively). The deviations deduced from these data at shorter wavelengths are given in the table in Fig. 3. This table is based on an averaged value of the coronal plasma index, considered isotropic around the sun Springer

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Fig. 3 Angular and linear deviations of electromagnetic radiations by the solar corona plasma at 1.2 solar radii for different wavelengths

and constant in time. Such a model causes a mere defocus, which should not affect the size nor the position of the caustic line, except for the distance of the closest focal plane. This would not induce aberrations. What causes aberrations is the non centro-symmetry of the solar corona index. In a conservative estimate of aberrations made here, we consider the upper limit of the index variations being as large as the average value. Considering this upper limit, the aberrations caused by corona index become smaller than those caused by planets (10 meters) at wavelengths shorter or equal to those of the visible domain. They should be negligible at high energies.

which has an extended image: 180 km in the focal plane. The sun at 500 AU from the focal plane is brighter in the visible (V = −13) and UV than the ampliﬁed targets, and exactly aligned with them, limiting observations to the γ domain. However, for the UV and softer domains the contribution from the sun can be ﬁltered out by a mask in the focal instrument, letting through the light from the imaged Einstein ring and blocking the central image of the sun. Such a coronographic device would reduce the apparent brightness of the sun by 5 magnitudes or more.

4.5. Contribution of the direct solar light 5. Deconvolution In the visible and at shorter wavelengths, the size of the aberration patch leads to ampliﬁcation factors of 6.1 × 107 (19.5 magnitudes) in the case of an unresolved stellar black hole accretion disk, and 5.6 × 105 (14.4 mag) in the case of the galaxy center accretion disk, Fig. 4 Point Spread Function in a focal plane at 724 astronomical units from the sun. The horizontal axis shows the offset from the center of the ﬁeld in micro arc seconds and the correspondence distance in meters. The vertical axis plots the light intensiﬁcation factor, limited to 4 × 108 as the aberrations caused by the planets spread the light over a 2 to 6 meter diameter patch

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In contrast to a standard optical instrument, the PSF of a gravitational lens does not converge when integrated over the image plane. For a given point, the contribution of an illuminated ﬁeld through this PSF integrates as:

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Fig. 5 Accretion disk around a black hole used as a test object for convolution by the PSF of a gravitational lens. From numerical simulations by J-P. Luminet (1998)

I (0) = r

θ

=

O(r2 , θ )

1 r2 dr2 dθ r2

O(r2 , θ )dr2 dθ

(20)

where O(r2 , θ ) is the ﬁeld illumination expressed in radial coordinates. Due to the convolution by that PSF, sources in the close vicinity (less than a few milli arc seconds) and extended objects will contribute

to a continuous background. We have simulated the convolution of a modeled extended object (an accretion disk around a black hole) by the PSF of a gravitational lens. Figures 5–7 show the model object, its convolution with the PSF (photon noise is added corresponding to 100 photons/pixel at the brightest point), and the result of a simple de-convolution regularized by a low-pass ﬁltering in spatial frequencies. In this simulation, the aberrations have been neglected, as the aberration size is smaller than the pixel size.

Fig. 6 Image obtained after convolution. Photon noise is added, corresponding to 100 photons per pixel

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Fig. 7 Deconvolved image using the gravitational PSF. Low-pass ﬁltering in spatial frequencies is applied

6. Prospective mission, object acquisition and image ﬁeld scanning One of the main challenges for this type of observation is to send a probe at more than 550 UA from the sun. This could be achievable by sling shots around inner planets and/or by ionic thrusters in the accelerated ﬁrst part of the trajectory, where solar energy is available at a sufﬁcient level. The probe will not have to slow down or stop at a given focal plane: it can travel along the caustic at unreduced speed, increasing its distance to the sun by 100 or 200 AU during the time of the observation mission. Fig. 8 Possible targets for a gravitational focussing X or γ mission

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In addition to this constant motion, several scans of a hundred lines each in a 100 × 100 km area in the focal plane can be performed by the use of slow motion thrusters, in order to sample a 0.1 mas ﬁeld, allowing a 100 × 10000 pixel image. One of the disadvantages of the PSF: its very extended wings, will turn out to be of some help for the acquisition of a target object as its coordinates will not be known with enough precision to locate it on the detector directly. There would be no possibility to change the target once the observation mission is started. Three possible targets are presented in the table in Figure 8:

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Sagitarius A∗ , a stellar gamma source as Cyg X 1, and an AGN.

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The advantages are very attractive: a perfectly achromatic instrument giving ampliﬁcations of 108 or more for radiations hard to focus otherwise, and nano arc second angular resolutions.

7. Conclusion Being independent of the type of radiation and thus perfectly achromatic for mass-less particles, the main interest of gravitational focussing is for radiations difﬁcult to focus otherwise, such as X and γ rays, and perhaps gravitational waves (Nemiroff 2005). Neutrinos will be also focussed, at shorter distances from the sun. We have investigated the possible causes of aberrations. This paper is a coarse approach of the problem, and there is room for a lot of improvement. For example, none of the authors of this paper are specialists in helioseismology and its consequences on focussing deserve more investigation. The main drawbacks of this technique are the large distances required for reaching the closest focal points, and the “single ﬁeld” nature of a space mission to any of those points. The image processing required to extract all the information from the foggy “raw images” will give work to image processing scientists, but these raw images seem usable, and the available deconvolution techniques should improve them signiﬁcantly.

References 1. John, D. Anderson, Eunice L. Lau, Giacomo Giampieri: Improved Test of General Relativity with Radio Doppler Data from the Cassini Spacecraft, 22nd Texas Symposium on Relativistic Astrophysics (2004). 2. Cox N. Allen C.: Astrophysical Quantities, 4th ed. p. 147, Springer (1999). 3. Dyson, F.W., Eddington, A.S., and Davidson C.R.: A determination of the deﬂection of light by the sun’s gravitational ﬁeld from observations made at the total eclipse of May 29, 1919, M.N.R.A.S. (1919). 4. Einstein A.: Lens-like Action of a Star by the Deviation of Light in the Gravitational Field, Science, 84, p.506. (1936). 5. Fomalont, E. B. and Sramek, R. A. Ap.J., 199 pp.749-755, (1975). 6. Luminet J.P.: “Black Holes: Theory and observation”, Black Holes: A General Introduction, Eds. F. Hehl, C. Kiefer, R. Metzler, Lecture Notes in Physics, pp. 3–36, Springer Verlag (1998). 7. Macone C. “The Sun as a Gravitational Lens: Proposed Space Missions”, (IPI Press: www.ipipress.com), (2002). 8. Nemiroff R.J.Ap.J., 628, part 1, pp.1081–1085, (2005). 9. Paczynski, B. An. Rev. Astro. Ap, 34 p. 419, (1996). 10. Michel Stix: The Sun. An introduction, A & A Library, Springer ISBN 0941 7834 Second edition (2002). 11. Zwicky, F. Phys. Rev, 51, p.290 & 679, (1937).

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Exp Astron (2005) 20:317–331 DOI 10.1007/s10686-006-9059-9 O R I G I NA L A RT I C L E

A Si/CdTe Compton Camera for gamma-ray lens experiment Tadayuki Takahashi

Received: 16 February 2006 / Accepted: 5 July 2006 C Springer Science + Business Media B.V. 2006

Abstract Cadmium telluride (CdTe) and cadmium zinc telluride (CdZnTe) have been regarded as promising semiconductor materials for hard X-ray and γ -ray detection. However, a considerable amount of charge loss in these detectors results in a reduced energy resolution. We have achieved a signiﬁcant improvement in the spectral properties by forming the Schottky junction on the Te side of the CdTe wafer. With the further reduction of leakage current by an adoption of guard ring structure, we have demonstrated a CdTe pixel detector with high energy resolution and full charge collection capabilty. The detector has a pixel size of a few mm and a thickness of 0.5 − 1 mm. We apply this high resolution detector to a new silicon and CdTe Compton Camera which features high angular resolution. We also describe a concept of the stack detector which consists of many thin CdTe layers and provides sufﬁcient efﬁciency for hard X-rays and gamma-rays up to several hundred keV maintaining good energy resolution. A narrow-FOV Compton telescope can be realized by installing a Si/CdTe Compton Camera inside the deep well of an active shield. This conﬁguration is very suitable as focal plane detector for future focusing gamma-ray missions. Keywords Gamma-ray astronomy . Compton telescope . CZT . CdTe . Narrow FOV Compton telescope . CdTe diode

1. Introduction The hard X-ray to γ -ray range is an important window for exploring the energetic universe. The Compton Gamma-ray Observatory (CGRO) satellite, which operated from 1991 to 2000, revealed that there are a variety of gamma-ray sources [1]. With its four onboard instruments, CGRO covered a wide energy range, from 20 keV to 30 GeV. This wide energy coverage, six decades in energy, played an important role in studying the realm of T. Takahashi The Institute of Space and Astronautical Science, JAXA, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan; University of Tokyo, 7-3-1, Hongo, Bunkyo, Tokyo 113-0033, Japan e-mail: [email protected] Springer

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non-thermal astrophysics. We can expect a further revolution brought by current operating missions such as INTEGRAL, Suzaku and other near-future missions (e.g. GLAST). However, when compared with X-ray astronomy, hard X-ray and γ -ray astronomy are still immature. While in the 10−100 keV band, current development of new concentrators such as multilayer mirrors could allow very soon high performance both on sensitivity and angular resolution. Above this energy band, it seems to be very difﬁcult to apply the technology such as a depth grated multi-layer mirror. The concept of a Laue lens are currently one of the most attractive candidate to realize the gamma-ray mission with great sensitivity and very high angular resolution in the sub-MeV region. The scientiﬁc output would be very signiﬁcant such technology becomes available. A Si/CdTe Compton Camera with a deep and active collimator, which we have been proposed for the NeXT mission in Japan, will provide high resolution spectroscopy with much higher sensitivity than present instruments [2, 3] Here, we report results of our prototype Si/CdTe Compton Camera in conjunction with the recent achievements of high-resolution CdTe detectors. 2. High resolution CdTe detector Among the range of semiconductor detectors available for γ -ray detection, CdTe and CdZnTe have a privileged position because of their high density and the high atomic number of their components, as well as a wide bandgap. In the 1990’s, the remarkable progress in the technology of producing a high quality single crystal of CdTe and the emergence of CdZnTe have dramatically changed the situations of high resolution room temperature detectors based on these materials. A review of the recent progress of CdTe and CdZnTe detectors is available in Takahashi and Watanabe [4]. The performance of CdTe for the IBIS instrument onboard the INTEGRAL mission and CdZnTe for the BAT instrument on the Swift mission are described in Limousing et al. [5] and Sato et al. [6], respectively. We have reported a signiﬁcant improvement in the spectral properties of CdTe detectors by means of a Schottky diode (CdTe diode) [4, 8–13]. The improvement of the energy resolution by adopting the Schottky junction is dramatic. For the detector with an area of 2 mm × 2 mm and a thickness of 0.5 mm, the leakage current of the CdTe diode is as low as 10 pA at 20 ◦ C at a bias voltage of 800 V. We have also found that the guard ring structure on Pt side further reduces the leakage current by one order of magnitude [14]. As demonstrated in Figure 1(a), an energy resolution of 1.1 keV (FWHM) for the 122 keV line from 57 Co is obtained [15]. When we cool the detector, the energy resolution is improved. From 137 Cs, an energy resolution of 2.1 keV (FWHM) for the 662 keV line is obtained with a 2 mm × 2 mm CdTe diode of thickness 0.5 mm at a bias voltage of 1400 V [7]. A CdTe diode with an area of 3 mm × 3 mm and a thickness of 1 mm installed in the system manufactured by Amptek (Amptek Inc.) has an energy resolution of 260 eV (FWHM) at 6.4 keV when operated at −40 ◦ C [17]. Another important reason for adopting thin devices is that the very low leakage current of the CdTe diode enables us to apply a high electric ﬁeld to ensure complete charge collection in devices with a thickness < 1 mm. When we increase the thickness of the CdTe/CdZnTe detector to improve the efﬁciency for high energy gamma-rays, the effects of incomplete charge collection, the low energy tail, become signiﬁcant. In some cases, the inactive region in the detector volume increases with the thickness, especially for the region close to the anode. The 0.5 mm thick CdTe diode becomes fully active, and even holes generated near the anode face can be completely collected. Springer

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Fig. 1 (a) 57 Co spectrum obtained with the CdTe diode operated at 20 ◦ C . The active area of the detector is 2 × 2 × 0.5 mm3 [15]. The applied voltage is 800 V. (b) High energy spectrum of 137 Cs above 620 keV with the same dimensions. The applied bias voltage is 1400 V and the operating temperature is −40 ◦ C . The energy resolution at 662 keV is 2.1 keV (FWHM) [7]

3. Stacked CdTe detector In order to extend the application of CdTe diodes to the detection of MeV gamma-rays, we proposed the idea of a stacked detector, in which several thin and large CdTe diodes are stacked together and operated as a single detector [4, 18, 19] This is only possible if charge careers generated in each layer volume are collected completely and there is no inactive region especially at the bottom region of each layer. Figure 2(a) shows a stacked detector consisting of 40 layers of large CdTe diodes each with an area of 21.5 mm × 21.5 mm and a thickness of 0.5 mm. A gap of only 0.7 mm has been achieved by utilizing 0.5 mm thick ceramic sheet for the detector housing. The total volume of the stacked detector amounts to 9.2 cm3 (a thickness of 2 cm), which provides a full peak efﬁciency of 20% at 500 keV and 7% at 1 MeV. In our stacked detector, the signal from each layer is processed independently using an individual analog chain. The gamma-ray spectrum from the detector is obtained by summing the spectra from all layers which record pulse heights above a certain threshold. With this approach, the energy resolution could be kept at the same level as that of a single layer. Although there is still room for improvement for the prototype detector, we obtain an energy resolution of 1.6– 1.7% (FWHM) for the two peaks of 1.17 MeV and 1.33 MeV in the energy spectrum of gamma-rays from 60 Co. The advantage over conventional scintllation counters is demonstrated in 2(b) in which gamma-ray lines up to 6 MeV from neutron captures in Na and Cl are shown. In addition to the increase of efﬁciency, the stack conﬁguration and individual readout provide informations of the interaction depth. This depth information is very useful to reduce the background in space applications, because we can expect that low energy gamma-rays interact in the upper layers and, therefore, we can reject low energy events detected in lower layers. Moreover, since the background rate is proportional to the detector volume, low energy events collected from the ﬁrst few layers in the stacked detector have a high signal to background ratio, in comparison with events obtained from a monolithic detector with a thickness equal to the sum of all layers. Springer

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Fig. 2 (a) The 40 layer CdTe stack detector and one of the layers from the stacked detector. (b) A spectrum of neutron capture gamma-rays obtained with the stacked detector. Neutrons from 252 Cf are slowed down by polyethylene and injected to NaCl. The peaks of 6.1 MeV, 5.6 MeV and 5.1 MeV correspond to gamma-rays from neutron captures in Cl nuclei, together with single and double 511 keV escapes. The peaks of 559 keV and 2.2 MeV correspond to gamma-rays produced by neutron captures of Cd and H, respectively [18, 19]

4. High resolution CdTe gamma-ray pixel module High energy resolution is very attractive for applications in astrophysics, where precise determination of the central energy and the proﬁle of X-ray and Gamma-ray lines are crucial. If we can form pixels on the electrode of the large area CdTe layer used in the stacked detector, the small capacitance of the pixel leads to the improvement of energy resolution. However, the number of channels to be handled in the system becomes very large and we need to have very low noise analog circuits implemented as multi-channel ASIC (ApplicationSpeciﬁc Integrated Circuit). The energy resolution around 1−2 keV is challenging if we have to rely on highly compact CMOS based ASICs. A new low noise front-end ASIC, VA32TA, has been developed to realize this goal in collaboration with Ideas ASA in Norway [20]. In order to demonstrate the performance of pixel detectors based on CdTe Schottky diode, we have developed 8 × 8 CdTe pixel detector modules with the pixel size of 2.0 × 2.0 mm2 and 1.4 × 1.4 mm2 with a thickness of 500 µm. The indium side is used as a common electrode and is biased with a voltage of 400 V. The platinum side is divided into 8 by 8 pixels surrounded by a guard ring with a width of 1 mm. Each pixel is connected to a fanout board by using In/Au stud bump bonding technology [7]. The signal from each pixel is fed into the VA32TAs on-board the FEC. Capacitance and leakage current of each pixel are 1 pF and a few pA at 0◦ C. Low leakage current is realized by employing a guard ring to absorb leakage current from the detector edge [14]. Figure 3(a) shows a photo of the CdTe pixel module. As shown in Figure 3(b), a large area can be obtained by buttering the modules. Energy resolution for the summed spectrum is 1.5 keV (FWHM) at 122 keV. Figure 4 shows summed spectra 57 Co taken at 30 min and 60 min after the bias voltage is turned on. No degradation due to possible charge accumulation Springer

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Fig. 3 (a) 8 × 8 CdTe pixel detector module. The detector has 8 × 8 = 64 pixels with a pixel size of 1.4 × 1.4 mm2 . The thickness of the detector is 0.5 mm. (b) large area CdTe detectors consists of four pixel moduless Fig. 4 Summed spectra 57 Co taken with the 8 × 8 CdTe pixel detector with the pixel size of 1.4 × 1.4 mm2 at 30 min and 60 min after the bias voltage is turned on. The operating temperature is 5 degree and the bias voltage is 600 V. Energy resolution from the summed spectrum is 1.5 keV (FWHM) at 122 keV

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is seen on this time scale. The energy resolution (FWHM) is 1.5 keV for gamma-rays of 122 keV. The energy threshold is measured to be as low as 7 keV.

5. Semiconductor Compton telescope By utilizing the technique of the Compton telescope, the COMPTEL instrument on-board the CGRO satellite has achieved pioneering results in this energy region. The energy band between 0.1 MeV and 10 MeV is poorly explored due to difﬁculties associated with the detection of such photons. The Compton telescope COMPTEL [3] on board CGRO demonstrated that a gamma-ray instrument based on the Compton scattering is useful for the detection of the gamma-rays in this energy band. Although COMPTEL performed very well as the ﬁrst orbit-based Compton telescope for MeV gamma-ray astrophysics, it suffered from large background, poor angular resolution, and complicated image decoding. Taking advantage of signiﬁcant progress in CdTe technology, we are developing a new generation of Compton telescope, the semiconductor Compton telescope [8, 22, 29–31]. In addition to the low background capability by utilizing the Compton kinematics, it features high spectral resolution (2 keV (FHWM) at 100 keV) and high angular resolution close Springer

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Fig. 5 Conceptual design of semiconductor Compton telescope consisting of layers thin silicon and CdTe imaging layers

to the theoretical limit deﬁned by the Doppler broadening. Capability to measure gammaray polarization from the directional information of scattered gamma-ray photons is also attractive feature of a Compton camera. The concept of the semiconductor Compton telescope, which we have been working on, is shown in Figure 6. The telescope is based on a hybrid semiconductor gamma-ray detector consisting of layers of thin Si and CdTe layers to detect photons in a wide energy band (0.05–1 MeV); the Si layers are required to improve the performance at a lower energy band (< 0.3 MeV). In the stack of Si and CdTe layers, we require each event to interact twice, once by Compton scattering and then by photo-absorption. Once the locations and energies of the two interactions are measured, the Compton kinematics allows us to calculate the energy and direction (as a cone in the sky) of the incident γ -ray following the Compton equation. The incident direction of a γ -ray is calculated from the position and the energy information of the interactions. Therefore, ﬁne energy resolution is the key requirement for the semiconductor Compton telescope to retain a low background level with Compton kinematics. The energy resolution around 1 keV is required for both Si and CdTe detectors to approach the physical limit of the angular resolution due to Doppler broadening.

Fig. 6 (a) The double-sided Si strip detector (DSSD). (b) A shadow picture obtained with the DSSD using 22 keV X-rays Springer

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Fig. 7 The six layered DSSDs. The pitch between DSSD layers is 5.4 mm

Regarding the uncertainty of the order of scattering in an event, we can use the relation that the energy deposition by Compton scattering is always smaller than that of the photoabsorption for energies below E γ = 255 keV (E γ = m e /2). This relation holds above this energy and there is only one solution, if the scattering angle θ is smaller than cos−1 (1 − 1 me 2 ( ) ) [3]. 2 Eγ The scattering part is very important in the Compton telescope. In order to cover a wide energy band and also to cover the wide scattering angle of the Compton interaction in the detector, the energy threshold of the detector must be low. Furthermore high Compton scattering probability is desirable to obtain a high efﬁciency as a Compton telescope. To this end, we have developed a new 0.3 mm thick double strip Si detector (DSSD) with Hamamatsu Photonics. For the ﬁrst step as a high resolution DSSD, we have chosen a strip length of 2.56 cm, a strip pitch of 0.4 mm and a strip gap of 0.1 mm. The Current-Voltage measurement indicates a depletion voltage of 65 V. The leakage current is 0.5 nA/strip at 20 ◦ C and 0.05 nA/strip at 0 ◦ C. The strip capacitance is measured to be 6.3 ± 0.2 pF. Intrinsic noise performance with a silicon strip detector is measured to be 1.0 keV (FWHM) at 0 ◦ C, which is in good agreement with the analytically calculated noise value of 0.9 keV [20]. Figure 6 shows a picture of the DSSD and its peripheral circuit. The signals from the strips are processed by front-end-cards (FECs) on which two low noise analog ASICs, VA32TAs are mounted. The strips on the p-side are connected directly to the input of the ASIC, while the strips of the n-side are connected via coupling capacitors. A shadow image by collecting 22 keV X-rays from a 109 Cd source is shown in Figure 6 [27]. The shadow mask is a bookmark made of brass covered with gold, whose thickness is 0.8 mm. Figure 8(a) shows the sum of the energy spectrum from 57 Co for all channels at −10 ◦ C. Fits yield energy resolutions of 1.1 keV (FWHM) for the 14 keV line and 1.3 keV for the 122 keV line. Figure 8(b) shows the energy spectrum from 241 Am at 0 ◦ C . A ﬁt yields an energy resolution of 1.3 keV at 60 keV [28]. By combining the stacked DSSDs and three CdTe pixel detectors, we constructed a prototype Si/CdTe semiconductor Compton telescope. A picture of the stacked DSSD in the prototype is shown in Figure 7. Two CdTe pixel detectors are placed underneath the DSSDs, and another detector is arranged on the side of the DSSDs [29]. Figure 9(a) shows the Compton reconstructed images a of 22 Na 511 keV gamma-ray source obtained with the prototype. The selected energy regions are 500–520 keV. From the calculated scattering angle and the two-hit positions, a Compton cone is drawn on the sky on an event by event basis. We project the cone onto the plane at the distance of 350 mm, Springer

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Fig. 8 (a) Energy spectrum of 57 Co for a DSSD measured at −10 ◦ C . (b) Energy spectrum of 241 Am measured at 0 ◦ C . The 122 keV peak and 60 keV peaks are magniﬁed in the vertical axis in inset plot for 57 Co and 241 Am, respectively 800

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Fig. 9 Compton reconstructed image (left) and spectrum (right) of the 511 keV gamma-ray obtained with a prototype Si/CdTe Compton telescope. The angular resolution is 3.9 degree. The energy resolution is 14 keV (FWHM) at 511 keV [29]. A circle with a radius of 5 degree is drawn as reference in the image

and obtain the image of the gamma-ray source. A circle with a radius of 5 degree is drawn together with each image as reference. We note that the images are asymmetric because the arrangement of CdTe absorbers is not symmetric. Figure 9(b) shows the reconstructed spectrum for 511 keV gamma-rays from the 22 Na gamma-ray source. The measured angular resolution is plotted in Figure 10, together with the estimated values ( θDB ) from the simulation. The scattering angle is determined with a resolution of 3.9 degree (FWHM) at 511 keV. The effect of the Doppler broadening becomes smaller as the incident energy becomes higher, because the binding energy and momentum of electrons in materials become relatively small for gamma-ray photons with higher energies. In the same ﬁgure, the effect of θposition , θenergy and θDopplerBroadening :

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Fig. 10 Relation between incident gamma-ray energy and angular resolution. Filled circles show the experimental data. Open triangles, squares and diamonds are estimated contributions of detector energy resolution, detector position resolution and Doppler broadening, respectively. The totals obtained by adding the three estimated values in quadrature are plotted by open circles [29]

by the effect of Doppler broadening, except that the contribution of position resolution is comparable to that of Doppler broadening in the higher energy region (>500 keV). According to the analysis based on Monte Calro detector simulation, we conﬁrmed the contribution of Doppler broadening is 2.6 degree, and the contributions from position resolution and energy resolution are 2.6 degree and 2.7 degree, respectively [29] Additionally, CdTe layers can also be used as scatterer if the energy of incident gamma-rays is high. According to our measurements, the obtained angular resolution is 35.9 degree at 122 keV, and 12.2 degree at 511 keV, which is mainly dominated by the effect of Doppler broadening [31]. When kinetic energy of an electron is above ∼ 250 keV, the range of electrons in silicomn exceeds the thickness of one layer of the DSSD (300 µm). In this case, the recoil electron deposits energy on the successive layers of the DSSDs and the direction of the electron could be tracked from the hit positions. Then, we can fully solve the Compton kinematics from the information obtained with the detectors. Although the information of the direction of electrons are smeared out by the effect of multiple scattering, we can limit the direction of incident gamma-rays as an arc, not a cone. In the calculation of Compton kinematics, the angles between the direction of recoil electrons and that of scattered gamma-rays can be used to reject background events, especially for those in which the scattered gamma-rays are not fully absorbed in CdTe. Figure 11 shows the reconstructed image of 662 keV gamma-rays from 137 Cs from events that satisfy the consistency of the angle between the electron and the scattered photon, which can be calculated either geometrically from hit positions or from the deposited energy [30]. In drawing the image, the width and the length of each arc are evaluated from the energy resolution and position resolution of the component detectors.

6. Narrow FOV Si/CdTe Compton telescope In the energy range above hundred keV (the sub-MeV region), the photon ﬂux is much smaller than that in X-ray region, therefore shielding against background photons becomes much more important. In this situation, the reduction of background becomes critical for performing “precise” experiments in this energy band. In the Hard X-ray Detector (HXD) onboard the Suzaku satellite, the well-type shield made of BGO scintillators, which surrounds the main detector part (Si PIN detector and GSO scintillator), is expected to reduce Springer

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Fig. 11 An image of 137 Cs obtained from the Compton reconstruction with electron tracking [30]

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the background to the limit achieved by the conﬁguration of active shield and collimator [23, 24]. In order to further reduce the background and thus to improve the sensitivity, we have proposed a new detector called the Soft Gamma-ray Detector (SGD) for the NeXT mission. The SGD is a Si/CdTe semiconductor Compton telescope mounted inside the bottom of a well-type active shield [3, 8, 17, 21, 25]. As shown schematically in Figure 12, the telescope consists of 24 layers of DSSDs (double-sided silicon strip detectors) surrounded by CdTe pixellated detectors. The opening angle provided by the BGO shield is 4 degrees at 500 keV. For the SGD, an additional copper collimator restricts the ﬁeld of view of the telescope to 30 for low energy photons (<100 keV) to minimize the ﬂux due to the Cosmic X-ray Background from within the FOV. These modules are then arrayed to provide the required area.

Fig. 12 Conceptual design of the SGD module [3]. A stack of 24 Si DSSDs and CdTe pixel detectors are assembled to form a semiconductor Compton telescope. The telescope is mounted inside the bottom of a well-type active shield. The opening angle provided by the BGO shield is 4 degrees at 500 keV. An additional copper collimator restricts the ﬁeld of view of the telescope to 30 for low energy photons (<100 keV). With this narrow FOV, events are rejected as background if the reconstructed Compton ring does not intercept the FOV

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The major advantage of employing a narrow FOV is that the direction of incident γ -rays is constrained to be inside the FOV. If the Compton ring does not intercept the FOV, we can reject the event as background. Most backgrounds can be rejected by requiring this condition (albeit with a corresponding reduction in instrument effective area). Background photons from the BGO and copper collimator for which the reconstructed Compton ring intersects the FOV cannot be eliminated if there is no signal detected in the active shield, however this source of background contributes only within a limited range of scattering angle. Combining background suppression techniques available in the SGD, we expect to achieve background levels of 5 × 10−7 counts/s/cm2 /keV at ∼100 keV and 2 × 10−7 counts/s/cm2 /keV at ∼500 keV. The effective area of the SGD in the Compton mode is 120 cm2 at 200 keV and 50 cm2 at 400 keV, if we use 25 units (total geometrical area of 625 cm2 ). The concept of a narrow FOV Compton telescope is expected to reduce dramatically the background from radio-activation of the detector materials, which is a dominant background in the case of the Suzaku HXD [24]. The 30 FOV of the ﬁne collimator is required to improve the sensitivity which is limited by source confusion below a few hundred keV. It should be noted that we can also measure polarization of incident gamma-rays from the azimuthal distribution of Compton scattered photons. The demonstration of the polarization measurement was performed by using a fully polarized synchrotron beam in the Spring 8 facility [9, 32].

7. A narrow FOV Si/CdTe Compton Camera for the gamma-ray lens mission Focusing instruments have two tremendous advantages: ﬁrst, the volume of the focal plane detector can be made much smaller than for non-focusing instruments, and second, the residual background, often time-variable, can be measured simultaneously with the source, and can be reliably subtracted. The MAX mission, which is based on the concept of Laue gamma-ray lens is very promising approach to extend the focusing capability above several hundred keV to reality. In order to achieve the ultimate sensitivity for the MAX mission, the focal plane detector should be designed very carefully. A Compton telescope is a good solution, because the direction of incident gamma-rays could be determined by the Compton reconstruction and therefore effective in discriminating gamma-rays coming from the lens. However, the angular resolution limited by the Doppler broadening is 2.5 degrees for 511 keV and also the ordering of interactions has to be solved before we determine the direction of incident gamma-rays. The concept of the narrow FOV Compton telescope realized with an active collimator made of BGO scintillator and a stack of Si/CdTe detector is a very attractive solution as the focal plane detector of the gamma-ray lens experiment. Figure 13 shows the conceptual design of the focal plane detector. The FOV of the active collimator is determined such that it only sees the gamma-ray lens. With this, all we can assume is that the signal gamma-rays come from the FOV of the collimator, and others can be rejected as background. Furthermore a thick BGO scintillator shields gamma-rays from other directions and also reduces the background due to activation in the BGO scintillator itself. This is quite important, because the 511 keV line from the β + decays becomes a major background source for the study of annihilation lines from the celestial objects. The fact that the Si/CdTe Compton telescope can be operated at moderate temperatures of 0 to −20 degrees makes the design of the shield easy for satellite applications. The compact design of a stack of Si and CdTe detectors also helps, because, if the volume of the shield becomes large, the dead time caused by the shield becomes signiﬁcant. Springer

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Fig. 13 Conceptual drawing for the focal plane detector for a gamma-ray lens mission

Fig. 14 Thickness of the detector which corresponds to τCompton = 1 for silicon and CdTe

The effective area of the scattering part could be a concern. As shown in Figure 14, a stack of Si detectors with a total thickness of ∼5 cm corresponds to τ = 1 for Compton scattering. This number is ∼2 cm for CdTe. Although CdTe detectors also act as the scatterer above 300 keV, the angular resolution is larger than 10 degrees. To have a sufﬁcient number of layers with DSSD would be preferable in terms of the angular resolution. Depending on the energy of interest, the number of Si and CdTe layers and their ratio should be chosen. Figure 15 shows the peak detection efﬁciency of events which undergo multi Compton scattering and Springer

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Fig. 15 Simulated peak detection efﬁciency for events which interact more than twice in the detector volume (more than one Compton scattering and ﬁnal photo-absorption). The detector consists of 80 layers of thin Si or CdTe detector. The results are shown for CdTe layers only (ﬁlled circles), Si layers only (ﬁlled triangls) and mixture (open circles). Dimensions of each layer are 25 × 25 cm2 with a thickness of 0.5 mm2 . Gamma-rays are injected at the center of the top layer

ﬁnal photo absorption in a 80 layer detector. The efﬁciency for the different numbers of Si and CdTe layers are shown as a function of photon energy. The dimensions of the detector are 25 cm × 25 cm and the thickness of each layer is 0.5 mm. Gamma-rays are injected to the center of the top layer. 8. Conclusion As gamma-ray energy increases to the MeV region, the detection of photons, the determination of the incident direction, and the rejection of background become very difﬁcult. Gamma-ray focusing technology should change this situation considerably. We have proposed a new detector called the Soft Gamma-ray Detector (SGD) for the NeXT mission, which utilizes the idea of a narrow FOV Si Compton telescope. In the SGD, we combine a stack of Si strip detectors and CdTe pixel detectors, to form a Compton telescope, which is mounted inside the bottom of a well-type active shield. We have demonstrated Compton reconstruction by using a prototype Si/CdTe Compton telescope, consisting of six-layered DSSDs and three 8 × 8 CdTe pixel detectors. By using this prototype, we have obtained Compton reconstructed images and spectra of gamma-rays from 122 keV to 662 keV. The achieved energy resolutions are 9.1 keV and 14 keV at 356 keV and 511 keV, respectively. The angular resolution is 3.9 degrees (FWHM) for 511 keV gamma-ray photons. The concept of the narrow FOV Compton telescope becomes a very attractive solution for the focal plane detector of the gamma-ray lens experiment. In order to obtain sufﬁcient efﬁciency for 511 keV lines for the future mission, we are now working on the larger scale model of the Si/CdTe Compton telescope with several tens of layers of DSSD and CdTe pixel detectors. Springer

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Acknowledgements This research was carried out in collaboration with K. Nakazawa, S. Watanabe, G. Sato, T. Mitani, T. Tanaka, K. Oonuki, K. Tamura, T. Kishishita, S. Takeda, M. Ushio, J. Katsuta (Institute of Space and Astronautical Science, JAXA), H. Tajima (Stanford Linear Accelerator Center), M. Nomachi (Osaka University) and Y. Fukazawa (Hiroshima University), and supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid in Japan (13304014, 14079207).

References 1. Amptek Inc.: http://www.amptek.com 2. Fukazawa, Y., Nakamoto, T., Sawamoto, N., Uno, S., Ohsugi, T., Tajima, H., Takahashi, T., Mitani, T., Tanaka, T., Nakazawa, K.: Low-noise double-sided silicon strip detector for soft gamma-ray Compton camera. Proc. SPIE 5501, 197–207 (2004) 3. Funaki, M., Ozaki, T., Satoh, K., Ohno, R.: Growth and characterization of CdTe single crystal for radiation detectors. Nucl. Instr. Meth. A436, 120–126 (2000) 4. Gehrels, N., Paul, J.: Phys. Today 51(2), 26 (1998) 5. Kamae, T. et al.: Astro-E hard X-ray detector. Proc. SPIE 2806, 314–328 (1996) 6. Kokubun, M. et al.: Improvements of the Astro-E2 hard X-ray detector (HXD-II). IEEE Trans. Nucl. Sci. 51, 1991 (2004) 7. Limousing, O., Blondel, C., Cretolle, J., Dzitko, H., Laurent, P., Lebrun, F., Leray, J.P. et al.: The ISGRI CdTe gamma-ray camera ﬁrst steps. Nucl. Instr. Meth. A442, 244–249 (2000) 8. Matsumoto, C., Takahashi, T., Takizawa, K., Ohno, R., Ozaki, T., Mori, K.: Performance of a new Schottky CdTe detector for hard x-ray spectroscopy. IEEE Trans. Nucl. Sci. 45, 428 (1998) 9. Mitani, T., Tanaka, T., Nakazawa, K., Takahashi, T., Takashima, T., Tajima, H., Nakamura, H., Nomachi, M., Nakamoto, T., Fukazawa, Y.: A prototype Si/CdTe compton camera and the polarization measurement. IEEE Trans. Nucl. Sci. 2432–2437 (2004) 10. Nakazawa, K., Oonuki, K., Tanaka, T., Kobayashi, Y., Tamura, K., Mitani, T., Sato, G., Watanabe, S., Takahashi, T., Ohno, R., Kitajima, A., Kuroda, Y., Onishi, M.: Improvement of the CdTe diode detectors using a guard-ring electrode. IEEE Trans. Nucl. Sci. 51(4), 1881–1885 (2004) 11. Oonuki, K., Tanaka, T., Watanabe, S., Takeda, S., Nakazawa, K., Mitani, T., Takahashi, T., Tajima, H., Fukazawa, Y., Nomachi, M.: Results of a Si/CdTe Compton telescope. Proc. SPIE 5922, 78–88 (2005) 12. Sato, G., Parsons, A., Hullinger, D., Suzuki, M., Takahashi, T., Tashiro, M., Nakazawa, K. et al.: Development of a spectral model based on charge transport for the Swift/BAT 32K CdZnTe detector array. Nucl. Instr. Meth. A541, 372–384 (2005) 13. Tajima, H., Kamae, T., Madejski, G., Mitani, T., Nakazawa, K., Tanaka, T., Takahashi, T., Watanabe, S., Fukazawa, Y., Ikagawa, T., Kataoka, J., Kokubun, M., Makishima, K., Terada, Y., Nomachi, M., Tashiro, M.: Design and performance of soft gamma-ray detector for NeXT mission. IEEE Trans. Nucl. Sci. in press (2005) 14. Tajima, H., Kamae, T., Uno, S., Nakamoto, T., Fukazawa, Y., Mitani, T., Takahashi, T., Nakazawa, K., Okada, Y., Nomachi, M.: Low noise double-sided silicon strip detector for multiple-Compton gammaray telescope. Proc. SPIE 4851, 875–884 (2002) 15. Tajima, H., Mitani, T., Tanaka, T., Nakamua, H., Nakamoto, T., Nakazawa, K., Takahashi, T., Fukazawa, Y., Kamae, T., Kokubun, M., Madejski, G., Marlow, D., Nomachi, M., do Couto e Silva, E.: Gamma-ray polarimetry with Compton telescope. Proc. SPIE 5488, 561–571 (2004a) 16. Tajima, H., Nakamoto, T., Tanaka, T., Uno, S., Mitani, T., do Couto e Silva, E., Fukazawa, Y., Kamae, T., Madejski, G., Marlow, D., Nakazawa, K., Nomachi, M., Oakada, Y., Takahashi, T.: Performance of a low noise front-end ASIC for Si/CdTe detectors in Compton gamma-ray telescope. IEEE Trans. Nucl. Sci. 51, 842–847 (2004b) 17. Takahashi, T. et al.: Wide band X-ray Imager (WXI) and Soft Gamma-ray Detector (SGD) for the NeXT mission. In: Proc. SPIE 5488, 549–560 (2004a) 18. Takahashi, T., Makishima, K., Fukazawa, F., Kokubun, M., Nakazawa, K., Nomachi, M., Tajima, H., Tashiro, M., Terada, Y.: Hard X-ray and gamma-ray detectors for the NeXT mission. New Astron. Rev. 48, 309–313 (2004b) 19. Takahashi, T., Watanabe, S., Sato, G., Okada, Y., Kubo, S., Kuroda, Y., Onishi, M., Ohno, R.: High resolution CdTe detector and applications to imaging devices. IEEE Trans. Nucl. Sci. 48(3), 287–291 (2001) 20. Takahashi, T., Hirose, K., Matsumoto, C., Takizawa, K., Ohno, R., Ozaki, T., Mori, K., Tomita, Y.: Performance of a new Schottky CdTe detector for hard X-ray spectroscopy. Proc. SPIE 3446, 29–37 (1998) Springer

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21. Takahashi, T., Mitani, T., Kobayashi, Y., Kouda, M., Sato, G., Watanabe, S., Nakazawa, K., Okada, Y., Funaki, M., Ohno, R.: High resolution Schottky CdTe diodes: IEEE Trans. Nucl. Sci. 49(3), 1297–1303 (2002a) 22. Takahashi, T., Nakazawa, K., Kamae, T., Tajima, H., Fukazawa, Y., Nomachi, M., Kokubun, M.: High resolution CdTe detectors for the NeXT generation multi-Compton gamma-ray telescope. Proc. SPIE 4851, 1228–1235 (2002b) 23. Takahashi, T., Mitsuda, K., Kunieda, H.: The NeXT mission. In: Proc. SPIE, in press (2006) 24. Takahashi, T., Nakazawa, K., Watanabe, S., Sato, G., Mitani, T., Tanaka, T., Oonuki, K., Tamura, K., Tajima, H., Kamae, T., Madejski, G., Nomachi, M., Fukazawa, Y., Makishima, K., Kokubun, M., Terada, Y., Kataoka, J., Tashiro, M.: Application of CdTe for the NeXT mission. Nucl. Instr. Meth. A541, 332–341 (2005) 25. Takahashi, T., Paul, B., Hirose, K., Matsumoto, C., Ohno, R., Ozaki, T., Mori, K., Tomita, Y.: Highresolution Schottky CdTe detectors for hard X-ray and Gamma-ray observations. Nucl. Instr. Meth. A436, 111–119 (2000) 26. Takahashi, T., Watanabe, S.: Recent progress on CdTe and CdZnTe detectors. IEEE Trans. Nucl. Sci. 48, 950–959 (2001) 27. Tanaka, T., Kobayashi, Y., Mitani, T., Nakazawa, K., Oonuki, K., Sato, G., Takahashi, T., Watanabe, S.: Recent achievements of the high resolution Schottky CdTe diode for gamma-ray detectors. New Astron. Rev. 48, 269–273 (2004a) 28. Tanaka, T., Mitani, T., Watanabe, S., Nakazawa, K., Oonuki, K., Sato, G., Takahashi, T., Tamura, K., Tajima, H., Nakamura, H., Nomachi, M., Nakamoto, T., Fukazawa, Y.: Development of a Si/CdTe semiconductor Compton telescope. Proc. SPIE 5501, 229–240 (2004b) 29. Tanaka, T., Watanabe, S., Takeda, S., Oonuki, K., Mitani, T., Nakazawa, K., Takashima, T., Takahashi, T., Tajima, H., Sawamoto, N., Fukazawa, Y., Nomachi, M.: Recent results from a Si/CdTe semiconductor Compton telescope. NIM A in press (2006) 30. Watanabe, S., Takahashi, T., Nakazawa, K., Kobayashi, Y., Kuroda, Y., Genba, K., Onishi, M., Otake, K.: A stacked CdTe gamma-ray detector and its application as a range ﬁnde. IEEE Trans. Nucl. Sci. 49(3), 1297–1303 (2002a) 31. Watanabe, S., Takahashi, T., Okada, Y., Sato, G., Kouda, M., Mitani, T., Kobayashi, Y., Nakazawa, K., Kuroda, Y., Onishi, M.: CdTe stacked detectors for Gamma-ray detection. IEEE Trans. Nucl. Sci. 49(3), 1292–1296 (2002b) 32. Watanabe, S., Tanaka, T., Nakazawa, K., Mitani, T., Oonuki, K., Takahashi, T., Takashima, T., Tajima, H., Fukazawa, Y., Nomachi, M., Kubo, S., Onishi, M., Kuroda, Y.: A Si/CdTe semiconductor Compton camera. IEEE Trans. Nucl. Sci. 52, 2045–2051 (2005)

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Exp Astron (2005) 20:333–339 DOI 10.1007/s10686-006-9027-4 ORIGINAL ARTICLE

New scintillators for focal plane detectors in gamma-ray missions Ernst-Jan Buis · Marco Beijersbergen · Stefan Kraft · Alan Owens · Francesco Quarati · Sytze Brandenburg · Reint Ostendorf

Received: 15 November 2005 / Accepted: 7 February 2006 C Springer Science + Business Media B.V. 2006

Abstract Recent developments of cerium-doped lanthanum-halide scintillators like LaBr3 : Ce show a remarkable performance in gamma-ray spectroscopy. When high energy resolution in combination with stopping power is required they provide excellent gamma-ray detector candidates for the use in space missions. Moreover, irradiation tests have shown that such detectors are radiation tolerant. In this paper we discuss a possible application of LaBr in nuclear astrophysics missions. We show results on recent proton irradiation tests at KVI in Groningen (NL) and discuss the damage and activation effects after irradiation. A possible implementation for a focal plane detector in a gamma-ray telescope and the expected performance is presented. Keywords Nuclear astrophysics · Scintillators · LaBr · Gamma-ray spectroscopy

1. Introduction One of the most prominent science objectives of future space-based gamma-ray telescopes is the direct detection of 56 Ni decay in supernovae. 56 Ni has a principle decay line at 158 keV with a peak ﬂux typically in the order of 10−6 cm−2 s−1 for supernovae at a distance of 10 Mpc (H¨oﬂich). (To compare, the 511 keV line from the Galactic center is about 10−3 cm−2 s−1 ). The E.-J. Buis () · M. Beijersbergen Cosine Science & Computing BV, Niels Bohrweg 11, 2333 CA Leiden, The Netherlands e-mail: [email protected] S. Kraft Cosine Research BV, Niels Bohrweg 11, 2333 CA Leiden, The Netherlands A. Owens · F. Quarati Ofﬁce of Advanced Concepts and Science Payloads, ESA/ESTEC Postbus 299, 2200 AG Noordwijk, The Netherlands S. Brandenburg · R. Ostendorf Kernfysische Versneller Instituut, Zernikelaan 25 9747 AA, Groningen, The Netherlands Springer

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observation of these gamma lines requires a sensitivity which is at least a factor 100 higher than what is achieved to date. One way to achieve the required sensitivity is to decouple the collecting area from the detection area through the use of focusing concentrators. A formation ﬂying concept of focusing gamma-ray mirrors or lenses and focal plane detectors has been subjected to many design studies. In evaluating the sensitivity of future gamma-ray telescopes, both the signal and background counts are equally important. One of the lessons learned from the Integral mission is that the activation of material in the spacecraft is an important source of background. As a rule of thumb the background scales with the volume of the active detector, so that in order to minimize the background, the detector should be as small as possible.

2. Instrument requirements The instrument requirements for a focal plane detector of a future γ -ray telescope can be summarized as follows: 1. Stopping power for gamma’s up to 500–600 keV. In addition, the photofraction of the material should be high, which means that the peak-to-compton ratio should be as high as possible. 2. Small detector to reduce the background. As mentioned above the background scales with volume. Note that all passive materials surrounding the detector (e.g. coolers, mechanical support structures, shielding), contribute to the (multiple scattered) background. Moreover, the smaller the detector, the smaller the shielding. Assuming an angular resolution

of 10 and a focal length of several hundred meters, the spot size and hence the desired detector radius could be as small as 3–5 cm. 3. Good energy resolution. Energy resolution is needed for the determination of blue shifts of the lines and for line separation. 4. Fast response, which leads to short integration times of the front-end electronics. Short integration times allow to minimize the chance of pile-up. 5. Radiation hardness. The detector should cope with a long mission lifetime, and preferably no observation time should be lost to detector recovery procedures (e.g. annealing), if possible at all. 6. Low activation. Activation is one of the largest contributions to the background. Moreover, activation lines may interfere with signal lines. Scintillators meet almost all the above listed requirements, but are outperformed by semiconductor materials on the energy resolution. However, the newly developed LaBr3 :Ce (van Loef, 2003) (called LaBr hereafter) has an energy resolution which is comparable to cadmium zinc telluride (CZT) detectors. Measurements using 241 Am, 137 Cs and 60 Co sources were carried out and showed an excellent energy resolution. In Figure 1 (a) we show the energy resolution in comparison to a CZT planar detector (Quarati, 2005). The energy resolution at the measured energies for both detectors is similar. The photofraction (as determined using Geant4 (Agostinelli, 2003)) of LaBr in comparison with CZT for various detector thicknesses is shown in Figure 1 (b). Although the photofraction for a detector of the same thickness is almost equal for CZT and LaBr, CZT detectors cannot be produced with a thickness such that a high photofraction is achieved in the energy range up to 500–600 keV. LaBr crystals, however, have been grown up to 1 inch, and it is expected that 2 inch crystals can be grown in the near future without loosing energy resolution. (LaCl3 crystals have been grown up to 3 inch.) Springer

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3. LaBr3 :Ce characterization 3.1. Experiment set up In order to characterize the performance of LaBr and to test its suitability for space applications several, LaBr assemblies were obtained from Saint Gobain Crystals. One such assembly is shown in Figure 2. A LaBr crystal (with a 5% Ce dopant concentration) with a diameter and length of 1 inch is mounted on a photomultiplier tube. Since LaBr is hygroscopic, the crystal was placed in an aluminum housing and optically coupled to the PMT through a glass window. The crystal could be detached from the PMT during irradiation. After characterization using radioactive sources (see Figure 1(a)) four crystals were irradiated. In addition to the crystal, other materials were irradiated such as a spare aluminum housing and a spare window. The purpose of the irradiation tests was to investigated the radiation hardness of LaBr and its activation properties. The irradiations were carried out at the Kernfysisch Versneller Institute (KVI) in Groningen, the Netherlands. Protons were accelerated with up to a maximum energy of 184 MeV and subsequently moderated with Cu and polystereen absorber plates to create an energy spectrum between 60 and 184 MeV. In this way a proton bundle was created that mimics a solar proton event. While the spectral shape of the proton beam was kept constant, the total integrated dose was varied (in four runs) between 109 and 1012 protons/cm2 . Note that these doses are rare in space at 1AU, but the primary purpose was to investigate the breakdown of the scintillator due to radiation damage. A typical solar proton event at 1AU has a total dose of 108 protons/cm2 and has about a 15% chance per year to occur. 3.2. Radiation hardness After being irradiated, the samples were characterized using radioactive sources. Shown in Figure 3(a) are the 137 Cs spectra before and after irradiation. As can be seen from the Springer

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Figure (b), the energy resolution for the various doses did not signiﬁcantly change after irradiation. However, a signiﬁcant deterioration of the energy resolution was found after the highest dose: 1012 protons/cm2 as shown in Figure 3(b). (For silicon this dose would correspond to 1 Mrad.) Indeed, the crystal seemed discolored after irradiation, but this was due to a decrease of the transmittance of the glass window. A reduced transmittance of the Springer

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Fig. 4 Example of external activation (a) measured using a germanium detector. In addition, the contribution of the aluminum housing is shown. In (b) the total external activation counts, integrated over the range of 50 keV–3 MeV, are plotted as a function of time. The plots are not corrected for the acceptance of the germanium detector (which is estimated to be in the order of 5%)

window implies a decrease of the light collection and hence the energy resolution. This was conﬁrmed by the transmittance measurement of the irradiated spare glass window and source measurements of the crystal after repackaging. We conclude that observed radiation effects are due to the non-radiation hardness of the BK-7 glass. This can be solved by using a more radiation tolerant glass such as quartz. 3.3. Activation The facilities at KVI included a lead castle, which consists of a well calibrated germanium detector inside a lead shield. This setup allowed the measurement of the external activation. This measurement is needed to identify the radioactively produced isotopes. It also allows the estimation of the background count rate once the detector is in space. In Figure 4(a) the activation of the crystal after irradiation is shown together with the contribution from the housing. The aluminum housing contributes 1–10% to the activation at the lower energies, which corresponds to the weight fraction of the housing to total weight of crystal and housing. In Figure 4(b) the activation, integrated over the range of 50 keV–3 MeV, is shown as a function of time. The count rate measured at the four samples is weighted according to the received dose to show the linearity of the activation with the integrated dose. Notice that the count rate is not corrected for the acceptance of the germanium detector, which is deﬁned as the fraction of the gammas that originate from the irradiated assembly and that deposit all of their energy in the germanium detector. An estimation of the acceptance is about 5%. 4. Scintillator focal plane detector 4.1. Implementation As pointed out in the introduction, the focal plane detector should be as small and as simple as possible. Since the scintillators can be produced in practically any shape, this allows a further Springer

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Fig. 5 Possible implementation of a LaBr in the focal plane in a scintisphere conﬁguration

optimization of the crystal. A spherical scintillator (a so-called scintisphere) as depicted in Figure 5 has an optimized detection volume, while the size of the photodiode – a potential source of noise – is kept to a minimum, thereby assuring a high light collection efﬁciency. The conﬁguration is simple and does not require large and heavy mechanical supports. A scintisphere would not allow imaging, but it is questionable whether imaging in this way is desirable at all. In contrast to missions such as XMM or the future Xeus mission which employs true Wolter optics, imaging in a single reﬂection telescope could be carried out only by determining the coma structure of off-axis objects on the focal plane. Such a measurement requires high line ﬂuxes from the observed object and a larger focal plane detector (which introduces more background). For a future gamma-ray telescope, however, most targets will be weak point sources. 4.2. Sensitivity It is illustrative to compare the measurement of the internal activation with a typical expected signal from a supernovae. We therefore have simulated the response of a 4 cm diameter scintisphere to a synthetic spectrum of a supernova and convoluted the resulting spectrum with the measured energy resolution as shown in Figure 1(b). In Figure 6(a) the synthetic

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spectrum of a supernovae type-Ia (model HeD6 from H¨oﬂich at a distance of 10 Mpc) is shown, seen by a telescope with an effective collection area (Ae ) of 1 m2 in the range of 0–500 keV and a focal plane detector as discussed above. In addition, the internal background due to activation after 4 days and 67 days is shown. The background count rate is scaled to the appropriated volume and a reasonable solar proton event of 108 protons/cm2 . As can be seen from the ﬁgure, the activation dose can indeed be a serious threat to the performance of the focal plane detector short after irradiation. The 270 keV line from 56 Ni decay will be obscured by the 240 keV line from 77 Br (decaytime 57 hrs). The 511 keV line is obscured as well. However, two months after irradiation the overall activation drops to a low level and interfering lines have mostly disappeared. Note in Figure 6 the changes of the shape of the background with time as the produced isotopes have different decay times. Finally, in Figure 6(b) we plot the sensitivity of the telescope as a function of the background count rate for two values of the photofraction which are expected at 159 and 511 keV. The sensitivity can be calculated through the commonly used expression (Diehl, 2001) shown in the ﬁgure (which is corrected here for the photofraction η). Although the activation does not represent the total background count rate, it is an important part of the total background. The sensitivities shown in this ﬁgure are therefore lower limits, albeit not far from the expected ones.

5. Summary and conclusion We have investigated the suitability of cerium doped LaBr3 scintillators in a focal plane detector of a focusing gamma-ray telescope. Characterization of LaBr before and after irradiation showed that the material is highly radiation tolerant and has a low activation potential. If the

optical performance of the mirror can be kept to 10 angular resolution, a small scintisphere with a diameter of 4 cm can be implemented as a focal plane detector. The activation measurements allowed us to confront the internal activation in the detector with the expected signal. We have identiﬁed possible lines that might interfere with the decay lines 56 Ni observed in supernovae. It is therefore desirable for future focal plane detectors that the activation is investigated a priori using beam facilities. It will help to understand and model the background once the instrument is brought into space, in particular when very weak objects such as supernovae are observed. Acknowledgements We acknowledge valuable contributions from R. Grifﬁths and G. Vacanti and thank P. H¨oﬂich for providing his Monte Carlo source code for the simulations of supernovae explosions.

References H¨oﬂich, P.: Hard X- and gamma rays from type I-a supernovae [arXiv:astro-ph/9709033] van Loef, E. V. D., et al.: IEEE trans. Nucl. Sci. 50, 1 (2003) Quarati, F., et al.: Evaluation of a CdZnTe pixel array for X-ray and gamma-ray spectroscopic imaging, ESSD proceedings, accepted for publication. In Nucl. Instr. Meth. A. (2005) Agostinelli, S., et al.: Nucl. Instr. Meth. A 506, 250 (2003) Diehl, R.: Nucleosynthesis in the Universe in gamma rays, V. Sch¨onfelder (ed.), A&A Library, Springer-Verlag Berlin (2001)

Springer

Exp Astron (2005) 20:341–351 DOI 10.1007/s10686-006-9047-0 ORIGINAL ARTICLE

A focal plane detector design for a wide-band Laue-lens telescope Ezio Caroli · Natalia Auricchio · Lorenzo Amati · Yuriy Bezsmolnyy · Carl Budtz-Jørgensen · Rui M. Curado da Silva · Filippo Frontera · Alessandro Pisa · Stefano Del Sordo · John B. Stephen · Giulio Ventura Received: 23 January 2006 / Accepted: 18 May 2006 C Springer Science + Business Media B.V. 2006

Abstract The energy range above 60 keV is important for the study of many open problems in high energy astrophysics such as the role of Inverse Compton with respect to synchrotron or thermal processes in GRBs, non thermal mechanisms in SNR, the study of the high energy cut-offs in AGN spectra, and the detection of nuclear and annihilation lines. Recently the development of high energy Laue lenses with broad energy bandpasses from 60 to 600 keV have been proposed for a Hard X ray focusing Telescope (HAXTEL) in order to study the X-ray continuum of celestial sources. The required focal plane detector should have high detection efﬁciency over the entire operative range, a spatial resolution of about 1 mm, an energy resolution of a few keV at 500 keV and a sensitivity to linear polarization. We describe a possible conﬁguration of the focal plane detector based on several CdTe/CZT pixelated layers stacked together to achieve the required detection efﬁciency at high energy. E. Caroli () . L. Amati . J. B. Stephen . G. Ventura INAF/IASF-Bologna, Italy N. Auricchio INAF/IASF-Bologna, Italy; Dipartimento di Fisica, Universit`a di Ferrara, Italy Y. Bezsmolnyy Semiconductor Materials and Instruments Laboratory Ltd, Ukraine C. Budtz-Jørgensen Danish National Space Centre, Copenhagen, Denmark R. M. Curado da Silva Departamento de Fisica, Universidade de Coimbra, Portugal F. Frontera Dipartimento di Fisica, Universit`a di Ferrara, Italy; INAF/IASF-Bologna, Italy A. Pisa Dipartimento di Fisica, Universit`a di Ferrara, Italy S. Del Sordo INAF/IASF-Palermo, Italy Springer

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Each layer can operate both as a separate position sensitive detector and polarimeter or work with other layers to increase the overall photopeak efﬁciency. Each layer has a hexagonal shape in order to minimize the detector surface required to cover the lens ﬁeld of view. The pixels would have the same geometry so as to provide the best coupling with the lens point spread function and to increase the symmetry for polarimetric studies. Keywords Laue lens . Hard X-ray . Focal plane . CZT 1. Laue lenses for high energy X-rays The energy band >60 keV is of key importance in the study the radiation emission mechanisms of the celestial sources, their nature, their evolution with time and their contribution to the Cosmic X-ray Background (CXB). The development of focusing optics at these energies is necessary to increase the statistical quality of the high energy spectra of weak celestial sources. Recently high energy Laue lenses (Von Ballmoos and Smither, 1994; Pisa et al. 2005) with broad energy band-passes from 60 to 600 keV have been proposed for use in a Hard X ray focusing Telescope (HAXTEL): a multi–lens conﬁguration appears the most efﬁcient and compact solution. To extend the telescope band-pass to lower energies, multilayer optics and/or coded mask telescopes, depending on the science goals, can complement the lenses. The nominal conﬁguration of the multi-lens telescope (Frontera et al. 2005) includes a Low Energy Lens (LEL) with a passband from 60 to 200 keV, containing 4 High Energy Lenses (HEL) with an operational energy range from 150 to 600 keV, in the hole left free from the LEL. The assumed focal length is 50 m and the expected Point Spread function (PSF) radius on axis is ≈ (2.63 ± 0.03) cm for LEL and ≈ (2.33 ± 0.03) cm for HEL at 90% collected photons (Fig. 1). 1.1. Focal plane detector requirements The characteristics of the HAXTEL telescope conﬁguration considered will require a focal plane detector able to fulﬁll the following requirements: 1. high stopping power: the detector has to be composed of a high-Z, high density material in order to provide signiﬁcant stopping power at energies up to 600 keV and, therefore, a high detection efﬁciency over the entire operating range of the lenses; 2. spatial resolution: a spatial resolution of the order of ∼1-2 mm in each direction is required; 3. energy resolution: the energy resolution is a critical scientiﬁc goal, a few keV at 500 keV; 4. small sensitive area: the area of the detector depends on the FOV. A trade off between low background and FOV should be implemented. A ﬁgure of 70 cm2 as detection area is compatible with the reference conﬁguration of the HAXTEL telescope. 5. sensitivity to the photon linear polarization (Lei et al. 1997): this is a crucial requirement because several of the astrophysical emission processes of hard X–/soft gamma–ray radiation are expected to produce polarized photons. This capability is strictly related to the pixel size, which represents the geometrical spatial resolution of the detector.

2. CZT focal plane detectors We have chosen CdTe/CZT as the starting material to design the focal plane detectors since it has emerged as a good material choice for the detection of hard X-rays and soft Springer

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Fig. 1 The Point Spread function (PSF) on axis (left) and 2’ off axis (right) at 120 keV for the LEL (top) and the HEL (bottom) of the HAXTEL telescope concept. The gray bars give the normalized counts levels

gamma-rays due to several characteristics: (a) the high detection efﬁciency [the high density of CZT (5.76 g/cm) and high average atomic number (50) result in a high stopping power], (b) good spectroscopic performances, (c) good time response, all without the need for cryogenic cooling. Unfortunately the low mobility of the charge carriers (particularly the holes) and trapping/detrapping phenomena degrade the CdTe/CdZnTe detectors’ response, depending on the distance between the charge formation position and the collecting electrodes. However the spectral properties can be improved by using either hardware or software techniques. Because of their characteristics the CdTe/CZT semiconductors are boosting the ﬁeld of hard X-ray astronomy. Currently there are two satellite that have onboard large CdTe/CZT detectors. The International Gamma-Ray Astrophysics Laboratory (INTEGRAL) launched in 2002 carries the Imager on Board the Integral Satellite (IBIS) that uses a CdTe array with a sensitive area of 2600 cm2 . The operating energy range is 15 keV–1 MeV. After 2 years of ﬂight operations, the 16384 CdTe crystals are very stable and only ∼2.5% have been disabled due to their noisy behaviour. Moreover a gain degradation of ∼2.6 % per year has been determined (Lebrun et al. 2005). The observed background level allows a expected sensitivity of ∼ 1milliCrab for a 10 6 s observation and of ∼ 1-2 10−8 erg s−1 cm−2 in the 15 keV to 150 keV energy range; The Swift MIDEX spacecraft, launched in November 2004, with onboard the Burst Alert Telescope (BAT) equipped with a large area detector array to detect gamma-ray bursts (GRBs) and also to perform an all-sky hard X-ray survey with a limit sensitivity of ∼ 2 mCrab. The detection area is of 5240 cm2 and the detector plane is composed of 32768 pieces of CZT having the same dimensions of ISGRI pixels (4 ×4 ×2 mm3 ). The BAT operates in the 15–150 keV energy range with 6.2 keV resolution at 122 keV, an expected sensitivity of Springer

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∼10−8 erg s−1 cm−2 and a 1.4 sr (halfcoded) FOV (Barthelmy et al. 2005; Sato et al. 2005). In twelve months of operation, BAT has detected and located onboard ∼96 bursts. 2.1. CdTe/CZT detectors: state of the art Various efforts have been made to overcome the hole-trapping drawback in CdTe/CZT detectors, particularly relevant for thick crystals, which are needed for detecting hard X and gamma rays: these include the application of a grid structure to improve the energy resolution (Luke, 1994), the use of hemispheric or coaxial detectors and the compensation of the deﬁcit of the pulse height based on the pulse rise time information (Lebrun et al. 1996; Verger et al. 2001). An example of the spectroscopic response obtained with typical detecting materials is shown in Fig. 2: (a) the detector tested is a Spectrometer Grade CZT single crystal (eVProducts, USA) of size 10 × 10 × 5 mm3 , with platinum contacts and grown by the High Pressure Bridgman technique. The 59.54 keV line of 241 Am has a width (FWHM) of 4.2 keV and the energy resolution (FWHM) of the peak at 122 keV of 57 Co is 4.8 keV; (b) the detector has size 10 × 10 × 2 mm3 (SMI-LAB, Ukraine). The energy resolution (FWHM) is 5.4 keV at 59.54 keV and 6.6 keV at 81 keV. 2.1.1. Spectroscopic performances Recently some improvement has been achieved in the spectroscopic performances utilizing indium as the anode electrode for p-type CdTe semiconductors (Tanaka et al. 2004). In this way a high Schottky barrier formed on the In/p-CdTe interface allows the detector to operate as a diode and not as an ohmic device (e.g. as in the standard conﬁguration with both Pt contacts). This leads to an improvement due to the very low leakage current achievable with the Schottky CdTe diode: at 400 V the leakage current of the In/CdTe/Pt detector with a thickness of 0.5 mm in the reversed biased condition is 2 orders of magnitude smaller than the leakage current of Pt/CdTe/Pt. As a consequence it is possible to apply a high electric ﬁeld to ensure a complete charge collection. In terms of energy resolution, the In/CdTe/Pt detectors show excellent performances with respect to devices realized with Pt electrodes, as can be seen in Fig. 3, where we presented some spectra acquired by us. However, at room temperature, they present time stability problems, since their original good spectroscopic Springer

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performance degrades after hours. Another drawback is that the thickness of the crystal is currently limited to 1 mm. A direct technique to improve the spectroscopic performances is represented by detector cooling (see Fig. 4a), while the method based on rise time discrimination has long been used to improve the spectral shape by using rise time information: all pulses with a rise time exceeding some threshold are rejected, in this way all pulses which would contribute to the trapping tail in the pulse height spectrum are rejected. This technique is effective in improving the resolution energy but the detector sensitivity, since many counts are discarded, is signiﬁcantly reduced. We have tested the XR-100T-CZT (Amptek, USA), that is a high performance X-ray and gamma ray detection system. It is based on a planar CZT detector, mounted on a thermoelectric cooler inside a small hybrid package. The plot in Fig. 4b shows the comparison between the spectra recorded with rise time discrimination turned off (FWTM = 5.5 keV) and turned on (FWTM = 1.9 keV). The methods based on measuring both risetime and induced charge are termed biparametric methods. We are developing a biparametric method based on a hybrid hardware and software technique utilizing a double pulse shaping active ﬁlter (one [fast] compatible with the electron transit time, and the other [slow] to allow for complete charge collection) in order to analyze the detector signals and to obtain an indirect measurement of the interaction depth 3500

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Fig. 5 Schematic design of the detector anode conﬁguration (not to scale). The size of each pixel is 2 ×2 ×3 mm3 (Kuvvetli and Budtz-Jørgensen, 2005)

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(direction z) between the electrodes of an incident photon in the detector material (Auricchio et al. 2004). The pixel number identiﬁes the interaction position in the x and y direction (Zhang et al. 2005). Alternatively, a group at the Danish National Space Centre has recently developed a device that consist of an array of anodes on one side of a CZT (eV-Products) slab with a contiguous single cathode on the other side of the slab. In order to achieve a 2D imaging capability, the drift strip electrode geometry (Van Pamelen et al. 2000) was applied for the pixels. This arrangement, consisting of 16 drift detector cells, is shown in Fig. 5. Each drift detector comprise 2 drift electrodes and one anode readout electrode. The pixel pitch is 2 mm while the crystal size is 10 mm × 10 mm × 3 mm. The anode readout electrode radius is 0.2 mm. The inner and outer radii for the ﬁrst surrounding drift electrode (G4) are 0.5 mm and 0.6 mm, respectively, while the rectangular common drift electrode (G3) is of 0.1 mm width. The ﬁrst drift electrodes (G4) are interconnected externally by the z-bonding technique. The typical spectroscopic response of a pixel is shown in Fig. 6: the results are quite good, being about a factor two better than that achievable with monoelectrode detectors of equivalent area. 2.1.2. Response uniformity An important characteristic of a detector, in particular for focal plane implementation, is the response uniformity (in terms of gain, efﬁciency and energy resolution). In this aspect, one of 400

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Table 1 Response uniformity results from the CZT pixel detectors mentioned in the text IMARAD (256 pixel)

eV Multipixel (16 pixel)

E FWHM /E (mean value) @ 122 keV 4.8% ± 0.64 (∼10 %) 2.82% ± 0.27 (∼10 %) Efﬁciency Dispersion from mean value (1 σ ) @ 122 keV

∼4.5%

∼8%

the most critical roles is played by the quality and homogeneity of the CZT/CdTe crystals over large volumes. In Table 1 we have considered the performances of a large area CZT detector (IMARAD), 40 × 40 mm2 , 5 mm thick, composed by 16 × 16 pixels of 2.5 × 2.5 mm2 area, and a 4 × 4 pixels CZT Multipixel (eV Products). The thickness of this detector is 5 mm, while the lateral dimensions are 10.6 × 10.6 mm2 with a pixel size of 2 × 2 mm2 . The non uniformity level shown by current devices can be easily corrected with an accurate calibration of each pixel, that involves the correction of the shift of photo-peak due to the charge transport properties and the readout chains gains equalization. 2.2. A Laue lens focal plane concept An adequate detection efﬁciency can be obtained using devices based on CdZnTe with a thickness of more than 5–7 mm as shown in Fig. 7. It is, however, difﬁcult to increase the thickness of the device while at the same time keeping good energy resolution throughout the energy range from 10 keV to a few hundred keV. This is because the effect of incomplete charge collection becomes more severe due to the low mobility and short lifetime of holes in CdZnTe. The inactive region in the detector volume degrades the energy resolution through a low energy tail in the spectral response. In order to achieve high efﬁciency over the entire range, we propose a stacked CdTe/CZT pixel detector. Taking as reference the HAXTEL concept, a possible conﬁguration of the focal plane detector for LEL is based on a CdTe/CZT pixellated layer, composed of 7 hexagonally shaped crystals (4 cm in diagonal) in order to minimize the detector surface required to cover the lens ﬁeld of view. The pixels of each detector unit have the same geometry so as to provide the best coupling with the lens point spread function and to increase the symmetry for polarimetric studies. One mosaic layer of CdTe/CZT crystals could be the focal plane Fig. 7 CZT efﬁciency calculated versus detector thickness

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Fig. 8 Conceptual drawing of our layer module (used as LEL focal plane). For HEL three (or more) of this CZT layers could be stacked to achieve the required efﬁciency

detector. The LEL focal plane (Fig. 8) can be considered as the basic layer with which to build the HEL focal plane stacked detector (Watanabe et al. 2005): e.g. a three layer detector can be considered to have ∼2 cm thickness and therefore to achieve a total detection efﬁciency above 60% up to 600 keV. Each layer can both operate as a separate position sensitive detector and polarimeter or work with other layers in order to enhance the total detection efﬁciency. The speciﬁcations of each single layer detector are reported in Table 2, while in Table 3 a tentative summary of the resources budget required both for LEL and HEL focal planes is given. As an alternative for the HEL instrument we can consider as the focal plane detector a single thick crystal used in the Planar Transverse Field conﬁguration (Auricchio et al. 1999), where the applied electric ﬁeld is orthogonal to the optical axis in order to obtain high detection efﬁciency, while maintaining small the charge collection distance so as to limit the trapping phenomena and to achieve a good energy resolution (Caroli et al. 2000).

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Exp Astron (2005) 20:341–351 Table 3 Resources budget for LEL and HEL Focal Plane

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3 CZT Stack 150 cm3 2 kg 10 W 12 cm × 5 cm

3. Alternative focal plane detectors CZT detectors satisfy the science requirements of a focal plane detector for LEL, promising excellent energy and spatial resolutions, and in addition the stacked detectors have high efﬁciency for HEL. Nevertheless it is convenient to consider alternative detector technologies, in relation to the cost and complexity associated with pixellated CZT detectors and particularly with their response uniformity. Progress is being made in the development of new inorganic scintillators that, when coupled with wavelength-shifting ﬁbers, photomultiplier tubes (PMTs) or photodiodes, could be successfully used to produce high performance hard-X ray detectors. Lanthanum bromide (LaBr3 ) is a new inorganic scintillator material, that provides an improved energy resolution (R = 3% FWHM at 662 keV) compared to CsI (R = 7% FWHM at the same energy). When doped with cerium it is an attractive and promising candidate for high energy photon detection due to its high light output, high stopping power, fast response, good linearity, and low cost. A valid alternative for focal plane detectors may be given by detection planes formed with LaBr3 scintillator coupled with a new generation of readout devices (McConnell et al. 2004). The plots of Fig. 9 compare the achievable efﬁciency considering conﬁgurations of focal plane detectors based on different materials and material combinations (reference thickness = 2 cm). As a reference these conﬁgurations are compared with a thick (8 cm) Ge detector such as that foreseen for a Laue Lens telescope proposed for Nuclear lines observation (Von Ballmoos et al. 2004). Germanium detectors are semiconductor diodes having a p-i-n structure in which the intrinsic (i) region is sensitive to incident radiation. Advances in manufacturing techniques have allowed to grown extremely pure Ge crystals. Depletion depths of several centimeters can be achieved using this High-Purity Germanium, that also has the advantage to be stored at room temperature. HPGe detectors are operated at temperatures of around 77 K, in order to reduce noise from charge carriers, which can be thermally excited at room temperature across the relatively low band gap (0.67 eV); this induced noise destroys the energy resolution of the detector. The characteristics of focal plane detectors based on different materials and/or material combinations are summarized in the Table 4. 4. Conclusion A detector suitable for space experiments should have high atomic number, high density and a band gap much larger than that of Ge to permit room temperature operation, without Springer

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Fig. 9 Total detection efﬁciency and photopeak efﬁciency of the different conﬁgurations calculated as a function of the energy

Table 4 Main characteristics of different focal plane detectors Energy resolution FWHM (%) Detector type

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Spatial Resolution (mm)

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an expensive cryogenic cooling. The development of high performance CZT/CdTe pixel detectors offer a very good answer to the requirements of new high sensitivity telescopes for hard X-/soft γ -ray astronomy because CdTe combines relatively high atomic numbers (48 and 52) with a large bandgap energy (1.47 eV) and a density (∼6 g/cm3 ) higher than that of NaI and CsI. In particular this kind of detector would allow high detection efﬁciency over a wide operative energy range (e.g 60–600 keV) with small material volume, enabling a compact and effective shielding. This is important in order to reduce the locally produced background, which above 100 keV becomes the most important noise contribution. A further advantage is the quite low difﬁculty to produce highly segmented detectors that could also be very useful to improve background rejection (i.e. through some Compton kinematics event selection) and to obtain high polarimetric capabilities together with spectroscopic imaging and timing without losing detection efﬁciency. In order to achieve high efﬁciency over the entire range 60–600 keV, we propose a stack of CZT pixel devices suitable as focal plane detector for Laue lens telescopes as the HAXTEL concepts, but before deﬁning optimum instrument conﬁguration we have planned a study of the instrumental background in different orbital radiation environment. Acknowledgements The authors wish to acknowledgment Alessandro Traci and Damiano Pellicciotta for their help on the preparation of focal plane drawings and laboratory measurements.

References Auricchio, N., et al.: IEEE Trans. Nucl. Sci. 46(4), 853–857 (1999) Auricchio, N., et al.: IEEE Trans. Nucl. Sci. 51(5), 2485–2491 (2004) Barthelmy, S.D., et al.: To be published in Space Science Reviews, (astro-ph/0507410) (2005) Caroli, E., et al.: IEEE Trans. Nucl. Sci. 47(6), 2055–2060 (2000) Frontera, F., et al.: In: Proceeding of 39th ESLAB Symposium, in press, (astro-ph/0507175) (2005) Kuvvetli, I. Budtz-Jørgensen, C.: IEEE Trans. Nucl. Sci. 52(5), 1975–1981 (2005) Lebrun, F., et al.: Nucl. Instrum. Methods in Phys. Res., A380, 414–418 (1996) Lebrun, F., et al.: IEEE Trans. Nucl. Sci. 52(6), 3119–3123 (2005) Lei, F., et al.: Space Sci. Rev. 82, 309–388 (1997) Luke, P.N.: Appl. Phys. Lett. 65(22), 2884–2886 (1994) McConnell, M.L., et al.: SPIE Proc. 5488, 944–955 (2004) Pisa, A., et al.: SPIE Proc. 5900, 350–359 (2005) Sato, G., et al.: Nucl. Instrum. Methods Phys. Res. A541, 372–384 (2005) Tanaka, T., et al.: New Astron. Rev. 48, 309–313 (2004) Van Pamelen, M.A.J., et al.: Nucl. Instrum. Methods Phys Res. A439, 625–633 (2000) Verger, L., et al.: Nucl. Instrum. Methods Phys. Res. A458, 297–309 (2001) Von Ballmoos, P., Smither, R.K.: Astrophys. J. Suppl. Series 92, 663–669 (1994) Von Ballmoos, P., et al.: SPIE Proc. 5168, 482–491 (2004) Watanabe, S., et al.: IEEE Trans. Nucl. Sci. 52(5), 2045–2051 (2005) Zhang, F., et al.: IEEE Trans. Nucl. Sci. 52(5), 2009–2016 (2005)

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Exp Astron (2005) 20:353–364 DOI 10.1007/s10686-006-9048-z ORIGINAL ARTICLE

Polarisation measurements with a CdTe pixel array detector for Laue hard X-ray focusing telescopes Ezio Caroli · Rui M. Curado da Silva · Alessandro Pisa · John B. Stephen · Filippo Frontera · Matilde T. D. Castanheira · Stefano del Sordo

Received: 23 January 2006 / Accepted: 18 May 2006 C Springer Science + Business Media B.V. 2006

Abstract Polarimetry is an area of high energy astrophysics which is still relatively unexplored, even though it is recognized that this type of measurement could drastically increase our knowledge of the physics and geometry of high energy sources. For this reason, in the context of the design of a Gamma-Ray Imager based on new hard-X and soft gamma ray focusing optics for the next ESA Cosmic Vision call for proposals (Cosmic Vision 2015-2025), it is important that this capability should be implemented in the principal on-board instrumentation. For the particular case of wide band-pass Laue optics we propose a focal plane based on a thick pixelated CdTe detector operating with high efﬁciency between 60–600 keV. The high segmentation of this type of detector (1–2 mm pixel size) and the good energy resolution (a few keV FWHM at 500 keV) will allow high sensitivity polarisation measurements (a few % for a 10 mCrab source in 106 s) to be performed. We have evaluated the modulation Q factors and minimum detectable polarisation through the use of Monte Carlo simulations (based on the GEANT 4 toolkit) for on and off-axis sources with power law emission spectra using the point spread function of a Laue lens in a feasible conﬁguration. Keywords CdTe · Pixel detector · Polarization · Hard X-ray · Laue lens

E. Caroli () · J. B. Stephen INAF/IASF-Bologna, Via Gobetti 101, 40129 Bologna, Italy e-mail: [email protected] R. M. Curado da Silva · M. T. D. Castanheira Departemento de Fisica da Universidade de Coimbra, 3000 Coimbra, Portugal A. Pisa Dip. di Fisica, Universit`a di Ferrara, Via Saragat 1, 44100, Ferrara, Italy F. Frontera Dip. di Fisica, Universit`a di Ferrara, Via Saragat 1, 44100, Ferrara, Italy; INAF/IASF-Bologna, Via Gobetti 101, 40129 Bologna, Italy S. del Sordo INAF/IASF-Palermo, Via Ugo La Malfa 153, 90146 Palermo, Italy Springer

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1. Introduction Polarimetry in astrophysics is still a quite unexplored domain in the X- and γ -ray energy band. By measuring the polarization degree and orientation of the radiation emitted by an astronomical source, a new, important observational parameter is obtained in addition to spectral and time variability information. Polarimetric observations offer novel information about constitution, physical processes and emissions of various sources, e.g. Pulsars, Solar Flares, Active Galactic Nuclei, Galactic Black Holes or Gamma-Ray Bursts (Lei et al., 1997). However, to date in the energy domain from hard X-rays up to soft γ -rays no dedicated polarimeters have ever been launched into space or on a balloon-borne experiment. Indeed for those few instruments which are capable of performing this type of measurement, polarimetry itself plays a secondary role in the mission objectives, the main purpose of these instruments being to perform spectral imaging and timing analysis of celestial sources. This is the case for COMPTEL (COMPton TELescope) (Sch¨onfelder et al., 1993) instrument on board CGRO (Compton Gamma-ray Observatory), RHESSI (Reuven Ramaty High Energy Solar Spectroscopic Imager) (McConnell et al., 2002) and IBIS (Imager on Board the INTEGRAL Satellite), that is part of the INTEGRAL (INTErnational Gamma-Ray Astrophysics Laboratory) mission (Ubertini et al., 2003). Several years ago, a collaboration between INAF/IASF – Bologna (Istituto di Astroﬁsica Spaziale e Fisica Cosmica), Italy and the Departamento de F´ısica da Universidade de Coimbra, Portugal started with the aim of studying the performance of solid state (in particular CdTe/CZT) detector arrays as high-energy (above 100 keV) Compton polarimeters. The main advantage of this kind of detector is that high-sensitivity polarimetric measurements can be performed simultaneously with spectral imaging and time variability observations. The collaboration has already proposed an instrument concept to measure the Crab pulsar polarization level in the range between 50–1000 keV: the CIPHER (Coded Imager and Polarimeter for High Energy Radiation) telescope (Curado et al., 2003): a Minimum Detectable Polarisation (MDP at 3σ ) level below 10% is expected for a typical balloon observation time (104 s). Because of the scientiﬁc importance of polarimetry measurements it is the right strategy to implement this capability in the principal on-board instrumentation in the design of a Gamma-Ray Imager based on new hard-X and soft gamma ray focusing optics for the next ESA Cosmic Vision call for proposals (Cosmic Vision 2015-2025), it is strategic to implement this capability in the principal on-board instrumentation. Herein we present a preliminary study of the achievable performance in high energy polarimetry for a Hard Xray focusing Telescope based on wide band-pass Laue optics (Pisa et al., 2005) with a focal plane based on a thick pixelated CdTe/CZT detector operating with high efﬁciency between 60–600 keV.

2. Scattering polarimetry: numerical model and experimental conﬁrmation The GEANT4 package is a very suitable and efﬁcient tool with which to implement a Monte Carlo code that simulates the response of a CdTe detection plane designed for polarimetric measurements. The code is logically split into two main tools: (a) the modules implementing the physics of the electromagnetic interactions of polarized photons in particular for the Compton scattering; (b) the detection system with the deﬁnition of the beam characteristics, the detection plane design (geometry and material) and the read-out logic. Springer

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2.1. Compton scattering polarimetry model Polarimetric measurements are based on the fundamental concepts associated with polarised Compton interactions. In the X- and γ -ray energy range, this electromagnetic interaction can be the cause of a non-uniformity in the spatial distribution of the detected photons. After undergoing Compton scattering, the polarised photons’ new direction depends on the orientation of its polarisation vector before the interaction. If photons interact at least twice inside the detector, the position of the ﬁrst and the second interaction (double event) allow us to infer the polarisation degree and direction of the radiation beam. The Klein-Nishina cross-section for linearly polarised photons gives an azimuthal dependency for the scattered photons: dσ r2 = 0 d 2

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E E 2 2 + − 2 sin θ cos ϕ , E E

(1)

where r0 is the classical electron radius, E and E are the energies of the incoming and outgoing photons respectively, θ is the angle of the scattered photon and ϕ is the angle between the scattering plane (deﬁned by the incoming and outgoing photon directions) and incident polarisation plane (deﬁned by the polarisation vector and the direction of the incoming photon). As can be seen from (1), ﬁxing all other parameters the scattering probability varies with the azimuthal angle ϕ. The maximum relative difference between the cross-section values arises for ϕ = 0◦ – where the cross-section reaches a minimum – and ϕ = 90◦ – where it reaches a maximum. This relative difference is maximised for a scatter angle θ M , which depends on the incident photon energy. For soft gamma and hard X-rays the θ M value is always around 90◦ (Lei et al., 1997). A planar detection plane conﬁguration is very suitable to polarimetric measurements since the planar conﬁguration ﬁts an essential condition: after a Compton interaction, outcoming photons with low and high θ values – when polarimetric asymmetries are less evident – take a direction away from the detection plane, while those emerging from interactions with θ close to 90◦ have a stronger probability of going through a second interaction inside the detector. Thus with a rather simple design, such as planar detector, it is possible to obtain a double events distribution that allow us to perform polarimetric studies of celestial bodies or phenomena. 2.2. Experimental veriﬁcation of the MC model The collaboration between the two research groups has already given rise to both extensive Monte Carlo (MC) studies (Curado et al., 2003) and experimental tests of pixel CdTe matrices used as polarimeters that have conﬁrmed the reliability of our MC codes. These Monte Carlo simulations allowed both the study of CdTe polarimeters (Q factor and detection efﬁciency) and the study of several problems and effects associated with the interaction of polarized radiation in planar pixel CdTe detectors, such as the inﬂuence on polarimetric performance of the X- and γ -ray incidence inclination with respect to the optical axis, full irradiated detector surface analysis techniques and the variation of modulation factor as a function of the angle between the polarisation direction and the detection plane axis. Experimental polarimetric studies were performed at the European Synchrotron Radiation Facility in Grenoble, France, where some 4 × 4 CZT pixelized matrices (with various thicknesses) were tested with a ∼100% polarized photon beam (Caroli et al., 2003) at different energies between 100 and 500 keV. These tests have shown a good agreement between the results obtained from our Springer

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Fig. 1 (a) a possible multi lens arrangement, where the LEL energy band-pass extends from 60 keV up to 200 keV and the HEL band-pass ranges from 150 keV up to 600 keV; (b) the focused photon percentage proﬁle integrated over the expected polychromatic PSF for an on-axis source in HE and LE lens with a focal length of 50 m.

MC simulation model with the geometry adapted to the experimental set-up and the beam measurements. The differences between the values of the Q factor obtained by MC simulation and by beam tests are small (5–10%) and within the statistical errors (Curado et al., 2004). These results have conﬁrmed the correctness of the numerical Compton scattering model that was developed by some of the authors and that was included in the GEANT4 code since the version 4.3. The conclusions obtained from these studies are very important in order to develop and to correct Laue lens CdTe/CZT focal plane polarimetric studies.

3. Laue lens telescope model geometry The development of focusing optics is necessary in order to increase the statistical quality of the X- and gamma-ray spectra of the celestial sources and to improve the study of the emission mechanisms of the celestial sources, their nature, their evolution with time and their contribution to the Cosmic X-ray Background. Recently the development of high energy Laue lenses with broad energy band-passes from 60 to 600 keV has been proposed for new high sensitivity hard X ray telescopes (Frontera et al., 2006) in multi-lens conﬁgurations. The conﬁguration of the multi-lens telescope (Figure 1a) includes a Low Energy Lens (LEL, light grey circle) with a nominal passband from 60 to 200 keV, 4 High Energy Lenses (HEL, dark grey circles) with a nominal pass-band from 150 to 600 keV and in the cavity left free from the LEL, a Wolter I Multi-Layer (ML) confocal optics covering the 10–80 keV energy band, that will not be considered in our studies. The focal length baseline is about 50 m. The focal plane conﬁguration proposed is based on a thick CdTe pixel detector in order to optimise the detection efﬁciency at high-energy (from 60 to 600 keV). A CdTe thickness of at least 3 mm (better 10 mm) is required, with pixel scales of the order of a few millimetres since the expected point spread function (PSF), for a 50 m focal length and for an on-axis source, has the integrated proﬁle of Figure 1b where 95% of the focussed photons lay inside a circular surface of 30 mm in diameter (Pisa, et al., 2006). To be compatible with this point spread function, a matrix composed of 32 × 32 CdTe pixels was simulated, where each pixel has a 2 × 2 mm2 surface area. Each pixel of the focal plane detector is labelled by an identiﬁcation number (x pixel ID, y pixel ID) along the x- and Springer

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y-axis parallel to the detector surface. The photon irradiation geometry implemented in the code allows the simulation of the near-uniform distribution of Laue focussed photons over an area as large as the expected PSF. Then a read out geometry identiﬁes the pixels where double and higher order events occur, counting the number of these events in each pixel pair, as well as the respective energy deposition. Since X-ray focusing with Laue lenses is based on low incidence angle diffraction, it has a negligible effect on the initial photons’ polarization state for high energy photons (at least above 10–20 keV). Therefore, throughout this study it was considered that Laue lenses had no affect on the polarization state of X- and gamma-ray celestial emissions (Frontera et al., 1994).

4. Focal plane polarimetric performance Both the modulation Q factor and the minimum detectable polarisation of the CdTe focal plane have been evaluated by GEANT4 based Monte Carlo simulations for a Crab pulsar type spectrum and using as expected background a value derived by a geometrical scaling (according to detector volume and FOV) from that given in (Curado da Silva, et al., 2006) for the LOBSTER CZT Gamma Ray Burst monitor and considering only the analytical response (PSF) of the Laue lens (Pisa et al., 2005). 4.1. Polarimetric Q factor and detection efﬁciencies The polarimetric performance of an instrument can be evaluated by analysing the distribution of double events through the modulation factor, Q. This is obtained by integrating the Compton differential cross section formula over the solid angles deﬁned by the physical geometry of the detection. For a pixel detector Q can be expressed as (Lei et al., 1997):

Q=

N// − N⊥ , N// + N⊥

(2)

where N// and N⊥ are the number of counts integrated in two orthogonal directions over the detection plane. In the simulations, a surface equivalent to the PSF area containing 95% of focused photons, was irradiated uniformly by a 100 % linearly polarised beam of 107 photons, with a Crab-like power law energy spectrum (∝ E−2 photons/cm2 ·s−1 · keV−1 ). The beams’ energy was divided into intervals corresponding to energy bands where the lenses have a nearly uniform response: 60–120 keV and 120–200 keV for LEL; 150–250 keV, 250–400 keV and 400–600 keV for HEL. Using the position of the two hits of each double (scattered) event, distribution maps (like those in Figures 2 and 3) are built where the pixel of one of the two hits is normalized to the centre and the other is added in the relative position in the map. At the end, each element of the double events distribution maps contains the number of second interactions from each scattering pixel of the detection plane and gives information on the angular distribution of Compton scattered events. As expected, an asymmetry arises in the double event distribution maps due to the polarization of the incoming beam. As can be seen, this asymmetry is perpendicular to the direction of the vector electric ﬁeld of the beam, as was also expected. As shown in Figure 2, the higher detection efﬁciency of the 10 mm thick detection plane Springer

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Fig. 2 Double event distribution maps (only second interactions) obtained by Monte Carlo simulations for a 3 mm and a 10 mm thick focal plane, when irradiating a detector central pixel by a Crab-type 100% polarized photon beam focused by the LEL in the energy band 120–200 keV.

results in a higher detection rate of Compton double events. The double events distribution maps represented in Figure 3 were obtained by photons focussed by one of the High Energy Lenses in two different energy bands: 150 keV to 250 keV and 250 keV to 400 keV. In the 250 to 400 keV energy range there is a higher probability that a Compton photon escapes the ﬁrst interaction pixel and produces a second interaction in a neighbor pixel, which explains the higher number of double events detected compared with 150 to 250 keV energy range. The double event distributions obtained for a combination of Laue lens type energy bandpass and the focal plane thicknesses of 3 mm (inferior limit) and 10 mm (superior limit) allowed us to calculate the corresponding Q factors from (2) and the respective double event

Fig. 3 Double event distribution maps obtained by Monte Carlo simulations in the 120–250 keV and 250– 400 keV energy bands, when irradiating a 3 mm thick focal plane by a Crab-type 100% polarized photon beam focused by the HEL. Springer

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Table 1 Q factors and double events absolute efﬁciencies obtained for HE and LE Laue lenses energy bands, considering a 3 mm (a) and a 10 mm (b) thicknesses focal plane Low Energy Lens

E (keV) Thickness (mm) Q factor Absolute Efﬁciency (%)

60–120 3 0.30 0.11

10 0.29 0.13

High Energy Lenses

120–200 3 0.35 1.43

10 0.32 2.86

150–250 3 0.36 2.35

10 0.33 5.63

250–400 3 0.37 3.57

10 0.33 12.3

400-600 3 0.36 2.82

10 0.31 13.0

absolute efﬁciencies (double events detected/total number of photons focussed by the lenses) integrated over each lens energy band-pass. Table 1 shows that for each Laue Lens type the Q factor is always higher for a 3 mm than a 10 mm thick focal plane, when the same energy range is considered. This is because for 3 mm thickness the fraction of double events detected that undergo Compton interactions whose θ is very close to 90◦ , is higher than the same fraction of double events detected for a 10 mm pixel thickness focal plane. For a larger pixel thickness the scattering acceptance angle is wider and therefore will decrease on average per-photon information about the polarization status of the scattered photons, which is optimal when this angle is close 90◦ . The decrease of the Q factor caused by Compton interactions whose θ diverge from 90◦ also occurs for photon energies higher than 400 keV, however in this case it is due to the Compton scattering physics. The mean Compton scattering angle decreases as the photon energy increases and therefore the number of double events occurring at polar angles around 90◦ is lower. As shown in previous Monte Carlo simulation studies performed over a 100 keV to 1 MeV energy range this effect becomes important for photon energies higher then 400 keV (Curado et al., 2003). From Table 1 it is evident that the double event absolute efﬁciency obtained is higher for thicker focal planes under the same simulation conditions and it increases with the photons’ energy, since the probability that the second interaction occurs outside the pixel where the ﬁrst interaction took place increases as well. Different methods can be applied to the original double event distribution to optimize the evaluation of the Q factor. A simple procedure is based on the fact that there is no a-priori restriction on the linear distance between the point of interaction inside the detector plane for valid events, thus allowing optimisation of Q by deﬁning the acceptance areas of events to be included in the sums of N⊥ and N|| depending as shown in Figure 4a. The Q evaluated with this event selection as a function of the acceptance angle is given in Figure 4b. A further improvement in the Q evaluation can be obtained by combining the event acceptance angular opening with different scattering distance intervals (Stephen et al., 2001). A proper evaluation (effective Q) should include the weighing of the calculated Q with its statistical signiﬁcance that depend on the fraction of double events (N( φ)/Ntot ) considered in the selection: Q effective = Q ( ϕ) ·

N ( ϕ) , Ntot

(3)

In fact the Q increases with linear separation between the two hits of a scattered event, while the efﬁciency decreases, leading to a maximum of the effective Q at some distance from the original interaction point, depending on the energy and on the geometrical characteristics of the detection plane (e.g. size of the pixel, thickness, etc.). In the case illustrated in Figure 4 Springer

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Fig. 4 The optimization of the Q factor: (a) a graphical representation of a method to improve the Q factor integrating over two angular sector with varying aperture ( ϕ) around the two orthogonal direction corresponding to the detector sides; (b) the modulation Q factor as a function of ϕ, showing that the best value is achievable considering 10–15 degree wide detector sector.

the Qeffective reach the maximum value of 0.44 for an integration angle of ∼30◦ . Greater integration angles do not further improve the polarimetric performance of the detector. The a priori knowledge of this limit could allow a reduction of background contributions (e.g. due to random coincidences). 4.2. Minimum detectable polarization In order to get a closer approximation to the in-ﬂight measurements, background noise was included in our model. The background noise level caused both by cosmic radiation and from secondary photons generated by particles interacting with the elements that compose the telescope can be critical to polarimetric measurements. The minimum detectable polarisation (MDP) of a polarimeter in the presence of background noise can be expressed as (Lei et al., 1997):

nσ MDP (100%) = A · ε · S F · Q 100

A · ε · SF + B , T

(4)

where nσ is the signiﬁcance, Q100 the modulation factor for a 100% polarized source, ε the double event detection efﬁciency, A the polarimeter detection area in cm2 , S f the source ﬂux (photons · s−1 · cm−2 ), B is the background ﬂux (counts/s) and T the observation time in seconds. For a 3σ detection signiﬁcance we calculated the MDP expected both for LEL and HEL telescopes when on the focal plane detector is focussed a source ﬂux with a Crablike spectrum and in the presence of a background level. The background used is derived by geometrical scaling from that expected for the LOBSTER GRBM, based on CZT array modules, planned onboard the ISS (low earth orbit at 340 km with ∼50◦ inclination), as described in (Amati et al., 2006). Due to the orbital characteristics of the ISS the background has the following average spectrum: 1.5 · E −1.4 photons/cm2 · s−1 · keV−1 . For a HAXTEL-like mission, which will operate in a very eccentric or L2 orbit, we have assumed a background normalisation of 0.3 (1/5 of the LOBSTER case) taking into account, the more efﬁcient shielding possible for a smaller focal plane detector, and the possibility to further reduce the effective background for polarimetry using Compton kinematics. The polarimeter Springer

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Table 2 The average effective area of the LEL and HEL instruments in the used energy band, with the background count rate in the same energy bands Low Energy Lens

High Energy Lens

E (keV)

60–120

120–200

150–250

250–400

400–600

Average Effective Area (cm2 ) Background (counts/s)

75 0.241

250 0.139

840 0.127

620 0.096

240 0.07

detection area (A) in equation (4) is determined from the Laue lens effective area, while the background (B) is integrated over an area equivalent to the PSF surface (∼7 cm2 ). Therefore for each lens energy band-pass, the MDP was calculated using the respective average lens effective area for the considered Cu Laue crystal lens arrangement and the background count rates, reported in Table 2. The Q100 factor and the absolute double event efﬁciency included in the MDP calculations for each of the considered energy range are those presented in Table 1. Figure 5 shows the calculated MDP, for a 3σ detection signiﬁcance, as a function of the observation time for the high and low energy Laue lens instruments respectively, for a source of 10 mCrab with a Crab-like energy spectrum. For the High Energy Laue Lens the MDP is shown for three energy ranges and considering a 10 mm focal plane, while for the Low energy Laue lens we report the MDP in the 120–200 keV band for two focal plane thicknesses (3 and 10 mm). Figure 4 (left) shows that it is potentially possible to measure degrees of polarization lower than 20% for 104 s observation times and lower than 2% for 106 s, in the energy range between 150 keV and 400 keV, and polarization degrees lower than 40% for 104 s observation times and lower than 4% for 106 s, in the energy range between 400 keV and 600 keV. In the higher energy band the Q factor is lower, which explains the higher MDP values. In the case of a 3 mm focal plane (not shown for simplicity), the MDP calculated was slightly higher than the 10 mm focal plane results due to the lower double event detection efﬁciency of the 3 mm pixels. The MDP obtained for 106 s observation times for a 3 mm CdTe focal plane was: ∼3% (150–400 keV) and 7.5 % (400–600 keV). Figure 4 shows that also the Low Energy Laue Lens instrument can achieve an MDP inferior than 40 % for 104 s observation

100

100

10mm 3mm

M D P (% )

MD P ( % )

150 to 250 keV 250 to 400 keV 400 to 600 keV

10

10

LE Laue Lens (120-200 keV) HE Laue Lens 10 mm thick CZT pixel detector

1 1,0E+03

1 1,0E+04

1,0E+05

Observation Time (s)

1,0E+06

1,0E+03

1,0E+04

1,0E+05

1,0E+06

Observation Time (s)

Fig. 5 (left plot) MDP in different energy bands for a 10 mm thick CdTe/CZT focal plane for the HE Laue lens telescope. (right plot) MDP in the 120–200 keV energy band for a 3 mm and a 10 mm CdTe/CZT focal plane for the LE Laue lens instrument. Both MDP were obtained for a 3σ detection signiﬁcance and considering a 10 mCrab emitting source. Springer

362 0,330

2,5

0,325

2

Qfactor

0,320 1,5 0,315 1

MDP (%)

Fig. 6 The Q factor (diamonds) and the MDP for a 106 s observation time (triangles) in function of pixel lateral size obtained for the LE Laue Lens and a 10 mm thickness CdTe focal plane in the 120 keV to 200 keV energy band.

Exp Astron (2005) 20:353–364

0,310 0,5

0,305

0,300

0 0,0

0,5

1,0

1,5

2,0

2,5

Lateral Pixel Size (mm)

times and inferior than 3 % for 106 s in the 120 to 200 keV band-pass. The MDP calculations for the LEL have also indicated that in the 60–120 keV band-pass polarization measurements are effective only for observation timescales above 105 s: e.g. for 106 s observations MDP at the level of ∼27 and ∼23% (for 3 mm and 10 mm thickness focal plane respectively) are achievable. This result is easily explained by the low double event efﬁciency (Table 1) in the lower energy band of the LEL instrument. In order to study the optimal pixel size of the Laue lens telescope focal plane, the MDP was calculated as a function of pixel lateral size dimensions under the same irradiation conditions as explained before. Since the expected point spread function is of about 30 mm, a pixel scale of a few mm (1–3) would be enough have a good sampling from the imaging and source detection point of view. A smaller pixel scale would allow a better sensitivity to the polarized emission, but it means an increase in the focal plane complexity (a large number of channels require more complex electronics and more resources). Therefore we limited our study to pixel lateral dimensions between 0.5 mm and 2 mm. Figure 6 shows the Q factor and the MDP (for 106 s observation time) obtained for the Low Energy Laue Lens in the 120 keV to 200 keV band-pass combined with a 10 mm thickness CdTe focal plane. Since it is constantly simulated a 32 × 32 CdTe matrix, for lateral pixel sizes smaller than 1.0 mm its volume is smaller and therefore a fraction of Compton photons escape from the detection plane before having a second interaction, which explains that Q decreases for lateral sizes smaller than 1.0 mm. From 1.0 mm on, this effect becomes residual and smaller lateral dimensions result in higher Q factors due to a higher rate of second interactions occurring inside pixels further from the central pixel, which contributes to an improvement in the double event distribution resolution. However, the net gain observed in the MDP for pixel dimensions lower than 1 mm does not compensate for the technical difﬁculties associated with its production. Therefore, focal plane pixel lateral dimensions of about 1 mm up to 2 mm provide a good trade off between focal plane complexity and polarimetric performance. Furthermore, we point out that the improvement in the MDP achievable with the smaller pixel scale might be obtained with less expensive background reduction techniques such as optimizing the shielding and/or applying event selection procedures based on Compton kinematics. 4.3. Sensitivity to polarized sources Using the polarimetric performance obtained for the multi Laue lens conﬁguration that we have considered we can also make a ﬁrst estimate of the sensitivity to the polarization level Springer

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Table 3 Evaluation of the sensitivity to the polarization level of a source Source Polarisation Level 50% (f = 0.5) 10% (f = 0.1) 2% (f = 0.05)

3σ Sensitivity for a polarized source [Ph/cm2/s/keV] For T = 106 s and E = 60–600 keV 1.7 × 10−7 8.5 × 10−7 4.3 × 10−6

(∼0.6 mCrab) (∼3 mCrab) (∼15 mCrab)

of a source. This ﬁgure will allow to know which is the minimum detectable ﬂux for a source with a given linear polarization level. The following equation represents, as a ﬁrst approximation, the polarization sensitivity (Lei, et al., 1997):

Fpol% =

Fmin ph/ s · cm 2 · keV , Q pol%

(5)

in which Qpol% is the Q factor for a source with a given polarized level of polarization in %. A rough estimate of this value can be obtained simply by multiplying the Q100 for the polarized fraction of the source (f). In this case we have used an average Q100 = 0.35 in the 60– 600 keV band. For the 3σ sensitivity (Fmin ) to non-polarized ﬂux we have adopted the value of 3 ×10−8 photons/keV/cm2 /s (60–600 keV energy band, 106 second observation time) as given in (Frontera et al., 2006), obtained using the HAXTEL effective area, a background level of 5 × 10−5 counts/s/keV/cm2 (i.e. the average of the BeppoSAX/PDS instrument between in the 60–300 keV energy range), and a unitary detection efﬁciency.

5. Conclusion The MC polarimetric results obtained for a wide band Laue lens instrument show that a pixellised CdTe focal plane is potentially well suited to the task of performing very sensitive polarimetric measurements. For typical satellite observation times (up to 106 s), polarization down to a level as low as 2% can be measured for X- and gamma-ray emissions from a 10 mCrab source. The Focal plane pixel dimensions study showed that a lateral pixel dimension of 1-2 milllimetres provides optimal polarimetric performance and that a thicker focal plane (10 mm) is a better choice. Acknowledgements This work was carried out in cooperation between the Departamento de F´ısica, Universidade de Coimbra, Portugal (Unit 217/94) and the IASF – Sezione di Bologna (Istituto di Astroﬁsica Spaziale e Fisica Cosmica), CNR, Italy and was supported in part by FEDER through project POCTI/FP/FNU/50228/2003 of Fundac¸a˜ o para a Ciˆencia e a Tecnologia, Portugal. The work of R.M. Curado da Silva was supported by the Funda¸ca˜ o para a Ciˆencia e Tecnologia, Portugal, through the research grant SFRH/BPD/11670/2002.

References Amati, L., et al.: Adv. Space Res. (2006, in press) (astro-ph/0605276) Caroli, E., et al.: Nucl. Instr. Meth. Phys. Res. A513, 350–356, (2003) Curado da Silva, R.M., et al.: Exp. Astron. 15, 45–65, (2003) Curado da Silva, R.M., et al.: IEEE Trans. Nucl. Sci. 51 (5), 2478–2484, (2004) Springer

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Curado da Silva, R.M., et al.: IEEE Trans. Nucl. Sci. 53 (1), 383–388, (2006) McConnell M.L., et al.: Solar Phys. 210, 125–142, (2002) Frontera, F., et al.: SPIE Proc. 2283, 85–93, (1994) Frontera, F., et al.: DOI: 10.1007/s10686-006-9050-5 (2006) Lei, F., Dean, A.J., Hills, G.L.: Space Sci. Rev. 82, 309–388, (1997) Pisa, A., et al.: SPIE Proc. 5900, 350–359, (2005) Pisa, A., et al.: DOI: 10.1007/s10686-006-9045-2 (2006) Sch¨onfelder, V., et al.: Astrophys. J. Suppl. 86, 657, (1993) Stephen, J.B., et al.: AIP Conf. Proc. 587, 816–820, (2001) Ubertini, P., et al.: Astron. Astrophys. 411 (1), L131, (2003)

Springer

Exp Astron (2005) 20:365–373 DOI 10.1007/s10686-006-9034-5 ORIGINAL ARTICLE

Simulated performance of dedicated Ge-strip Compton telescopes as γ -lens focal plane instrumentation C. B. Wunderer · P. von Ballmoos · N. Barri`ere · S. E. Boggs · G. Weidenspointner · A. Zoglauer

Received: 1 February 2006 / Accepted: 3 March 2006 C Springer Science + Business Media B.V. 2006

Abstract With focusing of gamma rays in the nuclear-line energy regime starting to establish itself as a feasible and very promising approach for high-sensitivity γ -ray (line) studies of individual sources, optimizing the focal plane instrumentation for γ -ray lens telescopes is a prime concern. Germanium detectors offer the best energy resolution available at ∼2 keV FWHM at 1 MeV and thus constitute the detector of choice for a spectroscopy mission in the MeV energy range. Using a Compton detector focal plane has three advantages over monolithic detectors: additional knowledge about (Compton) events enhances background rejection capabilities, the inherently ﬁnely pixellated detector naturally allows the selection of events according to the focal spot size and position, and Compton detectors are inherently sensitive to γ -ray polarization. We use the extensive simulation and analysis package assembled for the ACT vision mission study to explore achievable sensitivities for different Ge Compton focal plane conﬁgurations as a ﬁrst step towards determining an optimum conﬁguration.

Keywords X- and gamma-ray telescopes and instrumentation . Observation and data reduction techniques: computer modeling and simulation . Compton scattering . Nucleosynthesis

CBW thanks the Townes Fellowship at UCB and NASA Grant NNG05WC28G for Support. C. B. Wunderer () Space Sciences Laboratory, UC Berkeley, CA 94720, USA e-mail: [email protected] P. von Ballmoos · N. Barri`ere · G. Weidenspointner Centre d’Etude Spatiale des Rayonnements, Toulouse, France S. E. Boggs · A. Zoglauer Space Sciences Laboratory, UC Berkeley, CA 94720, USA Springer

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1. Introduction With Laue γ -ray lenses rapidly becoming a viable path to observing the MeV universe, the scope of their study must be broadened to include viable focal-plane instrumentation in addition to the lenses themselves. The detector of choice for any nuclear astrophysics mission allows to take maximum advantage of the information encoded in the astrophysical γ -ray lines, including any Doppler broadening or Doppler shifts of lines. Germanium detectors achieve the best energy resolutions in the energy regime of primary interest (∼100 keV to ∼2 MeV) in detectors of reasonably large volumes. While a companion paper (Weidenspointner et al.) compares the merits and demerits of similar-size monolithic, segmented, and Compton detectors at the focus of a Laue γ -ray lens, the work presented here constitutes a ﬁrst attempt at optimizing a Compton telescope focal plane. A Compton-detector focal plane would have several advantages: – It would have a much better capability for background rejection, since each individual photon’s origin can be determined to at least a circle on the sky. If this circle does not intersect the lens’ position, the photon is rejected. – A Compton detector is inherently ﬁnely pixellated. This would also enable on-the-ground selection of source events according to current focal spot size and position. Moreover, only a detector with many pixels could hope to utilize a Laue lens’ imaging (as opposed to merely concentrating) capability. – A Compton detector is inherently sensitive to γ -ray polarization. These advantages, of course, come at the cost of a signiﬁcant increase in the number of detector channels, with correspondingly higher demands on both instrument electronics and detector cooling. A Compton focal plane could also not be designed quite as compact as a single monolithic Ge detector, and would have to contend with a somewhat higher fraction of passive material inside the detector assembly itself to support the much higher number of channels and increased detector segmentation. Ge-strip Compton detectors are available today. The Nuclear Compton Telescope (NCT) balloon will ultimately be made up of twelve detectors; two such detectors have been tested extensively in the laboratory and ﬂew on a technology-demonstration balloon ﬂight in spring 2005 (Boggs et al.). In order to predict a Compton telescope’s performance, one ﬁrst must predict source and background interactions in the detectors, and then derive from these raw events the sensitivity achievable after Compton event analysis. The comparative performance evaluation of different Compton focal plane designs discussed here leverages heavily off the toolset assembled for the Advanced Compton Telescope (ACT) study (Boggs et al., 2005; Wunderer, et al., 2006 in press). 2. Compton telescope primer In Compton telescopes, each individual interaction of a photon in the detector volume is recorded separately; both interaction position and energy deposit are recorded for each hit (see Figure 1). Scatter angles and deposited energies are related via the Compton equation (Compton, 1923) cos ϕ = 1 − Springer

m e c2 m e c2 + Eγ E γ + E e

(1)

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Fig. 1 Schematic of photon interactions in a Compton focal plane. In the example, the photon incident from above with energy Eg undergoes two Compton scatters before photoabsorption. The photon origin can be reconstructed to a cone.

where m e c2 denotes the rest energy of the electron, E γ (E 2 + E 3 in Figure 1) the scattered photon’s energy and E e (E 1 in Figure 1) that of the scattered electron, and ϕ the angle between incident and scattered photon direction. Using this information, the incident photon’s energy and direction can be reconstructed. Measuring E e and E γ allows to calculate ϕ; together with the interaction positions this allows the restriction of the photon incident direction to a cone – a circle on the sky. In this manner, of course photons recorded in the detector can be rejected if they are not consistent with the direction of the source of interest (or in this case lens) – providing a powerful tool for background reduction in addition to detector-inherent imaging capability.

3. The models Figure 2 shows the three Compton detector designs considered. Each instrument was placed on the same generic spacecraft used for the comparison study of monolithic, segmented, and Compton stacks (Weidenspointner et al.). The detector is located at the top of a tower distancing it from the spacecraft bus and surrounded with plastic (top and sides) and BGO (bottom) anticoincidence shielding. To simulate photons from the Lens, a Laue-lens speciﬁc beam conﬁguration was implemented; the assumed beam FWHM is ∼2◦ . More detail about the spacecraft model and the lens-speciﬁc input photon beam is given in Weidenspointner et al..

Fig. 2 Detector models considered in the comparative study of different Ge Compton focal planes. From left: small, medium, and large Compton stack. For detailed descriptions of each stack see text. Springer

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Small Compton Stack. The small Compton stack is built from 5 Ge detectors identical to those ﬂown on the NCT balloon in Spring 2005 (Boggs et al.). The mass model faithfully represents all passive material in the existing detector assembly, as well as a cold ﬁnger and surrounding Aluminum for a cryostat. This mass model is identical to that used for the segmented and Compton stack models in the companion paper (Weidenspointner et al.). Medium Compton Stack. For the medium Compton stack, it is assumed that the guard ring width can be reduced, that the strip pitch is reduced by a factor of two, and that the top Ge layer has a hole to allow the photons from the lens to impinge on the surface of the second detector. Large Compton Stack. The large Compton stack makes similar assumptions as the medium one, but in addition two different thicknesses of Ge detectors are used, and the detectors are larger (available but more expensive). The aluminum bars and Ge protrusions used to mount the detectors are slimmed down within reasonable limits, resulting in a lower passive mass fraction. All the pieces required for detector mounting and operation remain part of the mass model. This stack is built from several tens of detectors. The intent was to design a photon bucket – however, the roughly circular shape of the assumed detectors leaves many “holes” through which photons can escape. Smaller, but truly rectangular detectors, together with a more careful stack design, should enable signiﬁcantly more efﬁcient assemblies than this one. Details of the different detector concepts are summarized in Table 1. The single-detector unit model in each case is based on the current NCT Ge detector design. Basing this entire study closely on existing balloon hardware – which of course was designed with cost and reliability paramount, and minimization of passive mass a secondary consideration – ensures that the mass models are if anything overly conservative. The single-detector mass models encorporate a high level of detail. Aluminum parts clamping the detector in place, passive Germanium “handles” the clamps attach to, and circuit boards protruding between detector active areas are faithfully represented at correct composition and mass – even screws are accounted for. There is only one spot where the mass models are too optimistic: for those detectors in the MED and LARGE concepts with a central hole, the hole is not surrounded by a guard Table 1 Details of the three Compton Detector conﬁgurations compared in the present study

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Small

Med

Large

Conﬁguration

5 layers

6 + 1 layer

Detector size Top hole (Diameter) Strip width Guard ring width # of 1.5 cm thick det # of 0.75 cm thick det Total mass active Ge Passive mass fraction in single det. assembly Spacecraft mass

8 × 8 cm2 no 2 mm 2.2 mm 5 0 2.5 kg

8 × 8 cm2 yes (1.9 cm) 1 mm 1.2 mm 7 0 3.4 kg

2 + 3 thin + 4 thick + sides 9.2 × 9.2 cm2 yes (1.5 cm) 1 mm 1.2 mm 17 21 19.4 kg

20% 313 kg

20% 315 kg

13% 363 kg

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Fig. 3 Overview over the Compton data analysis steps.

ring. A real detector would require ∼1 mm guard ring there. (Constraints of the simulation toolset used made the proper implementation of a guard ring in the simulations impossible within the scope of this work.)

4. Methods To properly assess the capabilities of any γ -ray instrument, in particular its sensitivity, an accurate evaluation of the system’s susceptibility to background radiation is required. A schematic overview of the necessary steps is given in Figure 3. 4.1. MGGPOD MGGPOD (Weidenspointner et al., 2005) is a suite of Monte Carlo codes built around the GEANT3.21 package CERN (1993) to simulate ab initio the physical processes relevant for the production of instrumental backgrounds at γ -ray energies. These include the build-up and delayed decay of radioactive isotopes as well as the prompt de-excitation of nuclei, both of which give rise to a plethora of instrumental γ -ray background lines in addition to continuum backgrounds. MGGPOD also comprises the GLECS (Kippen, 2004) and GLEPS (McConnell et al., 2006) packages for simulating the effects of atomic binding and polarization on photon scattering processes. Since a γ -ray lens mission would most likely require formation-ﬂying spacecraft and therefore probably reside in a high-earth orbit or at e.g. L2, Cosmic diffuse photon (Gruber et al., 1999) and Cosmic-Ray (CR) proton spectra (Moskalenko et al., 2002) in interplanetary space were used as input background spectra (spectra are those described in Weidenspointner et al. 2005). The contribution from CR electrons (Ferreira and Potgieter, 2002; Mizuno et al., 2004) (and positrons) turns out to be negligible. 4.2. MEGAlib The MEGAlib package (Zoglauer, 2005; Zoglauer et al., 2006 in press) was originally developed for the MEGA prototype, a tracking Compton and pair telescope consisting of a thin Si tracker and a CsI calorimeter (Kanbach et al., 2004). In the course of the ACT study, MEGAlib was enhanced to accomodate many more detector types and features, such as e.g. Springer

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Fig. 4 Schematic illustration of a 3+ interaction Compton sequence. E i denotes the deposited energy at interaction point i, gi is the ﬂight direction of the γ before the interaction, and ϕi is the Compton scatter angle.

vetoing using guard-ring readout. The package contains the complete data analysis chain for Compton telescopes, from discretizing simulation data and calibrating real measurements to the reconstruction and selection of events, up to high-level data analysis, i.e. image reconstruction, background estimation, and polarization analysis. Event Reconstruction. The raw instrument data only gives interaction positions and energies. For n interactions, in principle n! possibilities exist for the ordering of these hits – each corresponding to different possible photon incident directions. For events with two interactions (Compton scatter and – hopefully – subsequent photo absorption), it is very hard to discriminate between the two possible orderings except in cases for which only one order results in a valid cos φ. For this study, only two-site events were considered whose ordering could unambiguously be determined. For events with three or more interactions, redundant information is available that allows to determine the most likely sequence of events. The scatter angle ϕ2 in Figure 4 cannot only be determined from the energy deposits using Equation (1) but also from the interaction geometry (see ﬁgure for notations): →

cos ϕ2 =

→

g2 × g3

→

(2)

→

| g2 | · | g3 |

Consequently, in case of correct ordering the two evaluations of ϕ must agree, and the test statistics Tn =

geo 2

cos ϕiEn − cos ϕi

(3)

is smallest for the correct ordering. If none of the possible sequences results in a reasonably small value of Tn this is an indication that interactions are missing in the sequence – either because they happened in passive material or because the multiply-scattered photon escaped the detector. In either case the event should be rejected. Event Selection. After reconstruction of the events, those most likely originating from the direction of interest (the lens) must be selected. Criteria include the test statistic value Tn , the Compton scatter angle ϕ, the number of interactions, and the minimum angular distance of the Compton cone from the source direction, the so-called Angular Resolution Measure (ARM), in addition to the total deposited energy. The event selections, i.e. data cuts, resulting in the highest instrument sensitivity to the source are determined via calculation of sensitivities for a variety of setting combinations. The optimum settings of course vary from one detector geometry to the next, and also depend on photon energy, beam shape, and source intensity. Springer

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Fig. 5 Instrumental background recorded in the SMALL detector before and after event reconstruction and event selections – for comparison, a 847 keV 3% broadened source spectrum before and after the same analysis steps is also shown.

Optimum selections reject ∼75% of source counts compared to the raw detector spectrum – but well over 99% of the background events are rejected by the same selection criteria, resulting in a signiﬁcant overall improvement in sensitivity. Figure 5 provides an example. Springer

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Exp Astron (2005) 20:365–373 Table 2 Preliminary ﬁndings for sensitivities, efﬁciencies, and signal-tobackground ratios. Values are after application of all event selections for lens effective areas of 1200 cm2 at 511 keV and 660 cm2 at 847 keV

511 keV sensitivity [ph cm−2 s−1 ] 847 keV sensitivity [ph cm−2 s−1 ] 847 keV broad-line (3% FWHM) sensitivity [ph cm−2 s−1 ] Photopeak efﬁciency (@ 511 keV / @ 847 keV) signal-to-background ratio @ 511 keV

Small

Med

Large

1.3 × 10−6 1.3 × 10−6

1.2 × 10−6 1.1 × 10−6

9.4 × 10−7 9.2 × 10−7

3.5 × 10−6

2.7 × 10−6

2.0 × 10−6

6%/6%

7%/6%

7%/7%

10%

12%

13%

5. Results Our preliminary, conservative estimates indicate that sensitivities of 1·10−6 ph cm−2 s−1 for a narrow 511 keV line and 2·10−6 ph cm−2 s−1 for a 3%(FWHM) broadened 847 keV line are achievable with a Laue lens of 1200 cm2 effective area at 511 keV and 660 cm2 at 847 keV, respectively, using a Compton focal plane. (The lens effective areas are those predicted for one version of the MAX mission’s lens (Barri`ere et al., ).) To appreciate this result, and the fact that this constitutes a lower limit to the capabilities of a Compton focal plane rather than a ﬁnal or overly optimistic estimate, one must keep the following in mind: – The work presented here is based on ﬁrst guesses at good detector conﬁgurations, no optimization of designs has been performed yet. – To analyze the Compton telescope data, we have used ACT analysis methods as they stand, without any optimization for the different beam as well as detector geometries in a lens focal plane. – The detector geometries as modeled are certainly conservative, given that they reﬂect existing balloon hardware (NCT) rather than “what could reasonably be done”. This resulted in fairly massive Aluminum mounting structures for the Ge detectors, attaching to passive Ge “handles” protruding from the detectors themselves – rather than e.g. carbon ﬁber frames. – both the 511 keV electron-positron annihilation line and a broad-line region are especially demanding cases since background levels are higher than for many narrow lines at several hundred keV. Table 2 gives more detailed simulation results for the three different Compton detector focal plane designs.

6. Conclusions and outlook Our preliminary, conservative estimates indicate that sensitivities of 1·10−6 ph cm−2 s−1 for a narrow 511 keV line and 2·10−6 ph cm−2 s−1 for a 3%(FWHM) broadened 847 keV line are achievable with a Laue lens of 1200 cm2 effective area at 511 keV and 660 cm2 effective area at 847 keV respectively. Sensitivities achievable for narrow lines other than 511 keV should be signiﬁcantly better. Springer

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A Compton detector focal plane, in contrast to the simpler monolithic or segmented approaches discussed in Weidenspointner et al., will have secondary capabilities for survey science if it is not completely enclosed by a heavy scintillator shield. At least half the sky would be visible to the Compton detector at any time. Therefore, with a Compton-telescope focal plane, a Laue-Lens instrument might detect its own targets of opportunity, and over a mission lifetime could assemble sensitive all-sky surveys. Much remains to be done on the road to a good focal plane detector design for different mission concepts allowing different degrees of complexity for their focal planes: The compact and simplest SMALL design has little room for improvement – without changes to the individual detector’s conﬁguration, only the veto shields’ geometry and the detector distance can be further optimized. The slightly more complex MEDIUM detector requires tradeoff studies for both inter-detector distances and the size of the hole in the top Ge detector, in addition to the veto shields – overall, however, it performs reasonably well. The LARGE concept must undergo signiﬁcant redesign. The initial concept that is presented here has too many gaps between the side detectors that allow scattered photons to escape to even begin to justify the signiﬁcant increase in weight and complexity compared to the MEDIUM design. Data analysis methods can be improved as well, with a corresponding improvement in expected sensitivities: The initial study presented here relies on a simple and fast analytical, instrument-independent approach to reconstructing Compton events. The currently by far most promising approach, however, is based on an extensive, highly instrument-speciﬁc response matrix and Bayesian statistics. This very computing-time intensive method has yet to be applied to the lens focal plane designs discussed in this work.

References Barri`ere, N., et al.: MAX, a Laue Diffraction Lens for Nuclear Astrophysics, DOI:10.1007/s10686-006-9058-x, (2006) Boggs, S.E., et al.: Advanced Compton Telescope vision mission study Report (2005) Boggs, S.E., et al.: Performance of the Nuclear Compton Telescope, DOI:10.1007/s10686-006-9051-4, (2006) CERN: Geant – detector description and simulation tool. CERN Application Software Group; Computing and Networks Division version 3.21 (1993) Compton, A.H.: Phys. Rev. 21(5) (1923) Ferreira, S.E.S., Potgieter, M.S.: J. Geophys. Res. 107, 12–1 (2002) Gruber, D.E., et al.: Astrophys. J. 520, 124 (1999) Kanbach, G., et al.: New Astronomy Review 48, 275–280 (2004) Kippen, R.M.: New Astronomy Review 48, 221–225 (2004) McConnell, M., et al.: Astrophys. J. (2006) in prep. Mizuno, T., et al.: Astrophys. J. 614, 1113–1123 (2004) Moskalenko, I.V., et al.: Astrophys. J. 565, 280 (2002) Weidenspointner, G., et al.: Monte Carlo Study of Detector Concepts for the MAX Laue Lens Gamma-Ray Telescope, DOI:10.1007/s10686-006-9035-4, (2006) Weidenspointner G., et al.: Astrophys. J., Suppl. Ser. 156, 69 (2005) Wunderer, C.B., et al.: The ACT Vision Mission Study Simulation Effort. In: Proc. Astronomy with Radioactivities V. Elsevier (2006, in press) Zoglauer, A.: First Light for the Next Generation of Compton and Pair Telescopes. PhD thesis, Technical University Munich (2005) Zoglauer, A., et al.: MEGAlib – the Medium Energy Gamma-Ray Astronomy Software Library. In: Proc. Astronomy with Radioactivities V. Elsevier (2006, in press)

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Exp Astron (2005) 20:375–386 DOI 10.1007/s10686-006-9035-4 ORIGINAL ARTICLE

Monte Carlo study of detector concepts for the MAX Laue lens gamma-ray telescope G. Weidenspointner · C. B. Wunderer · N. Barri`ere · A. Zoglauer · P. von Ballmoos

Received: 18 January 2006 / Accepted: 3 March 2006 C Springer Science + Business Media B.V. 2006

Abstract MAX is a proposed Laue lens gamma-ray telescope taking advantage of Bragg diffraction in crystals to concentrate incident photons onto a distant detector. The Laue lens and the detector are carried by two separate satellites ﬂying in formation. Signiﬁcant effort is being devoted to studying different types of crystals that may be suitable for focusing gamma rays in two 100 keV wide energy bands centered on two lines which constitute the prime astrophysical interest of the MAX mission: the 511 keV positron annihilation line, and the broadened 847 keV line from the decay of 56 Co copiously produced in Type Ia supernovae. However, to optimize the performance of MAX, it is also necessary to optimize the detector used to collect the source photons concentrated by the lens. We address this need by applying proven Monte Carlo and event reconstruction packages to predict the performance of MAX for three different Ge detector concepts: a standard coaxial detector, a stack of segmented detectors, and a Compton camera consisting of a stack of strip detectors. Each of these exhibits distinct advantages and disadvantages regarding fundamental instrumental characteristics such as detection efﬁciency or background rejection, which ultimately determine achievable sensitivities. We conclude that the Compton camera is the most promising detector for MAX in particular, and for Laue lens gamma-ray telecopes in general. Keywords Gamma-rays . Laue lens . Germanium detectors . Compton telescopes . Nuclear lines . Positron annihilation

1. Introduction Gamma-ray lines carry unique information of prime importance for our understanding of fundamental astrophysical questions such as the origin of heavy elements or the G. Weidenspointner () · N. Barri`ere · P. von Ballmoos Centre d’Etude Spatiale des Rayonnements, 9 Avenue Colonel Roche, 31028 Toulouse Cedex 4, France e-mail: [email protected] C. B. Wunderer · A. Zoglauer Space Science Laboratory, UC Berkeley, Berkeley, USA Springer

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mechanisms behind the spectacular death of stars in supernovae (see e.g. reviews by Prantzos, 2005; Weidenspointner, 2006). Despite their paramount interest, observations of gamma-ray lines have historically been plagued by intense and complex instrumental backgrounds against which the much smaller signals from celestial sources need to be discerned (e.g. Weidenspointner et al., 2005). Recently, a novel experimental technique, promising to improve the sensitivity of existing gamma-ray telescopes by one to two orders of magnitude, has been demonstrated: the Laue lens (Halloin et al., 2004; von Ballmoos et al., 2004). A Laue lens takes advantage of Bragg diffraction in crystals to concentrate incident gamma rays onto a detector (Lund, 1992; Smither et al., 1995; Halloin et al., 2004; von Ballmoos et al., 2004). In this approach it is possible to employ a large photon collecting area together with a small detector volume, which results in a greatly increased signal-to-background ratio and hence a greatly improved sensitivity. MAX is a Laue lens telescope that has been proposed to the French Space Agency CNES in response to an announcement of opportunity for a formation ﬂight demonstration mission (Barri`ere et al., 2006; von Ballmoos et al., 2006). The MAX gamma-ray Laue lens consists of Ge and Cu crystals and has a focal length of about 86 m. MAX is designed to concentrate gamma rays in two 100 keV wide energy bands centered on the two lines which constitute the prime astrophysical interest of the mission: the 511 keV positron annihilation line, and the broadened 847 keV line from the decay of 56 Co copiously produced in Type Ia supernovae. Signiﬁcant effort is being devoted to studying different types of crystals that may be suitable for focusing gamma rays at nuclear line energies (e.g. Abrosimov et al., 2006; Courtois et al., 2006; Smither et al., 2006). However, to achieve the best possible performance of MAX, it is also necessary to optimize the detector used to collect the source photons concentrated by the lens. We address this need by applying proven Monte Carlo and event reconstruction packages to predict the performance of MAX for three different Ge detector concepts: a standard co-axial detector, a stack of segmented detectors, and a Compton camera consisting of a stack of strip detectors. We chose Ge as detector material since it provides the best energy resolution for line spectroscopy in the energy range of nuclear transitions. Each of these detector concepts exhibits distinct advantages and disadvantages regarding fundamental instrumental characteristics such as detection efﬁciency or background rejection, which ultimately determine achievable sensitivities. Our goal is to identify the most promising detector concept for a Laue lens. We consider the expected sensitivity to be the most important performance parameter, but also include capabilities for spectroscopy, imaging, and polarimetry in our ﬁnal decision. The most promising detector concept will be studied in more detail and optimized in the future. First advances in the design of a Compton detector are presented in a companion paper by Wunderer et al. (2006b). 2. Simulation of instrument performance This section provides a brief overview of the simulation and analysis techniques that we employed to estimate by ab initio Monte Carlo simulation the performance of three different detector concepts for MAX. Our study beneﬁted from experience gained from the modelling of the performance of past or existing gamma-ray missions such as TGRS on board Wind, the Ramaty High Energy Solar Spectroscopic Imager (RHESSI), or SPI onboard INTEGRAL by Monte Carlo simulation (see Weidenspointner et al., 2005; Wunderer et al., 2004; Weidenspointner et al., 2003, respectively) and the enhanced set of Monte Carlo and data analysis tools developed for predicting the performance of various instrumental concepts for a future Advanced Compton Telescope (Wunderer et al., 2006a; Boggs et al., 2006a). Springer

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Fig. 1 A side view of the MAX detector spacecraft model. The spacecraft body is cylindrical. The detector is situated on top of a 1 m tower. The circular radiator assumed to passively cool the detector is clearly visible. Details are given in the text

2.1. Instrument and spacecraft models Among other inputs, the simulation of the performance of a gamma-ray instrument requires a detailed computer description of the experimental set-up under study. This so-called mass model speciﬁes the geometrical structure of instrument and spacecraft, the atomic and/or isotopic composition of materials, and sets parameters that inﬂuence the transport of particles in different materials. The basic design of the MAX detector spacecraft and the mounting and cooling of the detector concepts assumed in this study emerged from the CNES pre phase A study of the MAX mission (Barri`ere et al., 2006; von Ballmoos et al., 2006). This basic design is identical for all three detector concepts, the only difference between the mass models is in the deﬁnition of the detectors. As can be seen in Figure 1, in each concept the detector is located on top of a 1 m tower; passive cooling is provided by a Be radiator of diameter 1 m. The dimensions of the cylindrical spacecraft body are radius 60 cm and height 192 cm. The spacecraft contains, among other components, tanks for hydrazine propellant and for cold gas, various electronics boxes, reaction wheels, and thrusters. The total mass of the spacecraft is about 260 kg. The tower separating the detector from the spacecraft body is intended to reduce possible instrumental background created in the satellite structure. In addition, a 5 cm thick BGO (bismuth germanate) crystal at the top of the tower and underneath the detector (see Figurs 2 and 3) serves as active (veto) and passive shield for the detector. The combined mass of the tower structure, the BGO veto shield, the radiator, and various detector electronics components is about 47 kg. To study the performance of a standard co-axial detector concept for MAX (hereafter: MAX-TGRS) we resorted to the TGRS Ge detector ﬂown on the Wind mission. The TGRS detector has been described by Owens et al. (1995); our mass model is a modiﬁed version of the TGRS mass model used by Weidenspointner et al. (2005) for their detailed instrumental background study. A section of the MAX-TGRS detector mass model, including the top of the Springer

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Fig. 2 A section of the MAX-TGRS detector mass model, including the top of the tower. The Ge crystal is surrounded by a plastic veto dome at the sides and at the top, and by a BGO crystal at the bottom

Fig. 3 A section of the MAX-NCTseg and MAX-NCTcompt detector mass models, including the top of the tower. The stack of Ge detectors is surrounded by a plastic veto dome at the sides and at the top, and by a BGO crystal at the bottom

tower, is depicted in Figure 2. Size, geometry, and material composition of Ge crystal, cathode, and Al housing remained unchanged. For MAX-TGRS, the radiative cooler of the original TGRS detector was removed. Instead, a cold ﬁnger leading to the radiator was introduced, and miscellaneous passive materials representing assumed detector support structure and electronics were positioned below the detector housing. The detector assembly is enclosed on the sides and at the top by a 0.5 cm thick plastic veto shield, which is viewed by two photomultipliers (PMTs). Also depicted in Figure 2 are the BGO veto shield beneath the detector assembly and the respective PMTs. Plastic dome and BGO crystal cover all lines of sight to the Ge crystal. The volume of the Ge crystal (height about 6.1 cm, radius about 3.4 cm) is about 216 cm3 , the total mass of the detector assembly including the plastic veto dome is about 3 kg. The performance of a stack of segmented detectors and of a Compton camera consisting of a stack of strip detectors was studied with the exact same mass model, but different analysis procedures for the simulated data (see Sec. 2.6). Both the segmented (hereafter: MAX-NCTseg) and the Compton detector (hereafter: MAX-NCTcompt) concepts consist of a stack of ﬁve detector modules modelled after the successfully tested Ge detectors of the balloon borne Nuclear Compton Telescope (NCT Boggs et al., 2006b). As can be seen in Figure 3, the basic layout of the instrument geometry (or mass model) for these two concepts Springer

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is the same as that of MAX-TGRS: the detector assembly is located inside a plastic veto dome, with the BGO veto shield below. Each of the ﬁve detector planes is roughly 8 × 8 cm2 in size, with a thickness of 1.5 cm, yielding a total detector volume of about 480 cm3 . The gap between adjacent detector planes was chosen to be 0.7 cm in our concepts. The total mass of the detector assembly including the plastic veto dome is about 6 kg. Each of these detector concepts exhibits distinct advantages and disadvantages. From a technical point of view, the MAX-TGRS concept is simplest and easiest to realize, while MAX-NCTcompt is the most complex and demanding. MAX-TGRS has only one detector channel, MAX-NCTseg a few, MAX-NCTcompt a few hundred; consequently cooling MAXNCTcompt is much more challenging than MAX-TGRS. MAX-NCTcompt offers superior background rejection capabilities, at the price of reduced photopeak efﬁciency, because much more information is available for each registered event than for the other two concepts. Finally, MAX-NCTcompt has the unique advantage of ﬁne spatial resolution, which is indispensable for realizing imaging and polarimetry. We would like to emphasize that all three detector concepts are conservative in the sense that we only used detector designs that have already been ﬂown and successfully operated in a space environment. However, the desgin of all three concepts can be improved, e.g. by minimizing the amount of passive materials, by carefully selecting the passive materials (e.g. elemental composition: carbon ﬁber instead of Al structure), or by optimizing the geometry and amount of detector material for the photon energies of interest to MAX. This is particularly pertinent for the NCT detectors, which currently are designed with emphasis on cost as well as reliability and robustness for use in a balloon demonstration ﬂight. We therefore expect our performance estimates to be conservative, and that improvements of the detector designs will result in improved performance. 2.2. Lens beam and effective area Estimating the performance of MAX detector concepts also requires a model for the focal spot distribution of photons concentrated by the Laue lens, and an estimate of its effective area (i.e. the geometrical area times the diffraction efﬁciency). For this study, both quantities were determined by Monte Carlo simulation. As described in more detail in Barri`ere et al. (2006), for this study the lens crystals were assumed to have a geometrical size of 1.5 cm × 1.5 cm and a mosaicity of 30

. The focal length was assumed to be 86 m, and the source was assumed to be located on the optical axis (i.e. the lens is pointed at the source). For these parameters, about 50% of the photons from an on-axis point source that are diffracted by the lens are concentrated within 1 cm from the center of the focal spot, as can be seen in Figure 4 depicting the simulated focal spot distribution. To actually perform the detector response simulations in our study, the Laue lens focal spot distribution was introduced as a new beam type named LRAD into the MGGPOD Monte Carlo suite described below in Sec. 2.4. Unlike the focal spot distribution of the Laue lens design considered here, the effective area of the lens is a function of energy: about 1191 cm2 and 661 cm2 at energies of 511 keV and 847 keV, respectively. 2.3. Radiation environment models In the CNES pre phase A study it was concluded that MAX would be best operated in either a high Earth orbit (HEO) or an L2 orbit (von Ballmoos et al., 2006). The instrumental background would then mainly be due to two radiation ﬁelds, namely diffuse cosmic gamma rays and Galactic cosmic rays. Both radiation ﬁelds were assumed to be isotropic in our Springer

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Fig. 4 The focal spot distribution of photons concentrated by the MAX Laue lens onto the detector plane. The three contour levels indicate, with increasing radius, the detector surface exposed to 50%, 75%, and 90% of all incident photons, respectively. More details are given in the text

simulations. The spectrum of the diffuse cosmic gamma-ray background was taken from the analytical description given by Gruber et al. (1999). The spectrum and intensity of Galactic cosmic-ray protons was modelled using the COSN default solar minimum spectrum of the MGGPOD package, which is based on the cosmic-ray propagation models of Moskalenko et al. (2002). Galactic cosmic rays not only produce prompt background due to hadronic interactions and de-excitations of excited nuclei, but also produce radioactive isotopes whose decay gives rise to delayed instrumental background. When simulating this delayed background, we assumed that the instrument and spacecraft materials had been irradiated for one year with the COSN cosmic-ray proton spectrum and intensity. 2.4. MGGPOD Monte Carlo suite We used the MGGPOD Monte Carlo package (Weidenspointner et al., 2005) to simulate the response and the instrumental background expected for each of the three different detector concepts for MAX. MGGPOD is a user-friendly suite of Monte Carlo codes that is available to the public from a site at CESR.1 MGGPOD is built around the widely used GEANT3.21 package (Brun, 1995) and allows simulation ab initio of the physical processes relevant for estimating the performance of gamma-ray instruments. Of particular importance is the production of instrumental backgrounds, which include the build-up and delayed decay of radioactive isotopes as well as the prompt de-excitation of excited nuclei, both of which give rise to a plethora of instrumental gamma-ray background lines in addition to continuum backgrounds. Among other packages, MGGPOD includes the GLECS (Kippen, 2004) and

1 http://sigma-2.cesr.fr/spi/MGGPOD/

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GLEPS (McConnell and Kippen, 2004) packages for simulating the effects of atomic electron binding and photon polarization for Rayleigh and Compton scattering. As mentioned in Section 2.2, for this study a new beam type named LRAD was introduced into the MGGPOD Monte Carlo suite. This beam allows the user to deﬁne an azimuthally symmetric incident photon ﬂux which is characterized by its radial proﬁle. The direction of incidence is assumed to be identical for all photons, rather than spread over the directions to the lens covering a few degrees in the ﬁeld-of-view, which is an approximation that should not signiﬁcantly affect our detector performance estimates at this early stage of the study. 2.5. MEGAlib analysis package The complex event analysis for the MAX-NCTcompt detector concept was performed with the MEGAlib package (Zoglauer et al., 2006). Originally, it had been developed for the MEGA Compton telescope prototype (Kanbach et al., 2004). The package provides the complete data analysis chain for Compton telescopes, including the crucial steps of event reconstruction and background rejection, which are described in more detail in Zoglauer (2005); Zoglauer et al. (2006); Wunderer et al. (2006b) and references therein. 2.6. Data analysis We compared the performance of the three MAX detector concepts under study for three different gamma-ray lines: narrow lines at 511 keV and 847 keV, and a broadened line (3% full width at half maximum, FWHM, deemed typical for Type Ia supernovae) at 847 keV. For each concept we simulated the instrumental response to these three lines for an on-axis point source. We also simulated the instrumental backgrounds due to diffuse cosmic gamma rays, to Galactic cosmic-ray protons at solar minimum, and to the decay of radioactive isotopes resulting from one year of cosmic-ray proton irradiation. For all three concepts radioactive decays in the detectors and diffuse cosmic gamma rays were found to be the dominant instrumental background components. In comparison, the prompt cosmic-ray induced background is small, and the background due to radioactive decays in the satellite structure is even smaller. Despite the fact that source photons are concentrated by the Laue lens onto the detector, MAX is still largely background dominated (the signal-to-noise ratio being on the order of several per cent), and we calculated its sensitivity to an on-axis gamma-ray line point source according to

fnσ =

nσ ·

nb

bi ( E) ·η √ Aeff · ( E) · ttot i=1

(1)

where f n σ is the sensitivity in [ph cm−2 s−1 ], n σ is the statistical signiﬁcance of the detection, nb −1 i=1 bi ( E) is the sum of all instrumental background components in [cts s ] in the analysis interval E centered on the line energy, Aeff is the effective area of the Laue lens in [cm2 ], ( E) is the photopeak efﬁciency, ttot is the total effective observation time in [s], and η is a factor in the range 1–2 whose value depends on how the instrumental background during an observation is determined. Ideally, the instrumental background is known, and η becomes 1. If the instrumental background is determined through an on-off observation strategy, i.e. one half of the total effective observation time is spent pointing at the source, and the other half pointing away from the source measuring the instrumental background, Springer

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η is 2. An intermediate case can be realized by operating two detectors simultaneously such √ that they alternately point at the source and away from it; η then assumes a value of 2. For MAX-TGRS data analysis is straight forward since the only event selections that can be applied in the case of a single detector crystal are the thresholds of the detector and of the veto shields and the width of the analysis energy interval. We assumed the same thresholds for all three concepts: 15 keV for the detector, and veto thresholds of 70 keV and 200 keV for the BGO and plastic dome shields, respectively. We assumed an energy resolution as measured for the SPI detectors (Lonjou et al., 2005) for the MAX-TGRS detector. In the MAX-TGRS concept it is impossible to separate source signal and instrumental background from a single observation; an on-off pointing strategy must be adopted, and η = 2 in Equation 1 when calculating the instrument sensitivity. At best, two MAX-TGRS √ detectors could be operated simultaneously; the minimum value of η therefore is 2 for this concept. For MAX-NCTseg, data analysis is slightly more complicated. As described in Section 2.2, for an on-axis point source the Laue lens concentrates source photons onto a relatively small focal spot. This can be exploited in the data analysis by including the criterion that a valid event must deposit energy in a cylindrical detector volume centered on the optical axis in a selected set of detector layers; events that do not deposit energy in these central detector volumes are most likely instrumental background that should be rejected. We implemented this simple scheme by assuming that each detector layer consists of two segments or pixels: a cylindrical, central segment, and a second segment comprising the remaining detector layer volume. Different values for the central radius were tried. In addition, we varied in the analysis the number of detector layers used to record source photons (source recording detector layers – SRDLs) in order to estimate the optimum number of detector layers for the MAX-NCTseg concept without performing a full simulation for each possibility. In doing so, we also had to choose how to treat remaining detector layers (background recording detector layers – BRDLs): these were either ignored or used as additional veto shields. A valid event was required to deposit more than 15 keV in at least one central pixel of the SRDLs without any veto trigger. We assumed an energy resolution as measured for the NCT detectors (S. Boggs,√priv. comm.). For the same reasons given for the MAX-TGRS concept, η lies in the range 2–2 for the MAX-NCTseg concept. Data analysis for MAX-NCTcompt was most complex and performed using MEGAlib. Many logical criteria can be applied to decide whether the energy deposits in the detector are consistent with an interaction sequence of a photon originating from the Laue lens, including the criterion that the ﬁrst interaction needs to occur in a cylindrical detector volume of a given radius centered on the optical axis in any one of a selected set of detector layers (see Wunderer et al., 2006b, for details). The spatial pitch of the Ge strip detectors was assumed to be 2 mm in the plane of the detectors, and 0.4 mm in depth (S. Boggs, priv. comm.). Again, we assumed an energy resolution as measured for the NCT detectors. The inherent imaging capabilities of the MAX-NCTcompt detector should permit both the source signal and the instrumental background to be measured in a single observation, as was the case for the imaging Compton telescope COMPTEL (Sch¨onfelder et al., 1993). Any need for off-source observations is therefore obviated, and the total effective observation time ttot can be spent pointing at the source. In this case the value of η approximates 1 in Equation 1. An exact determination of the value of η is difﬁcult and beyond the scope of this paper. We expect the number of data space bins free of source signal √ to exceed that of data space bins containing √ source signal, hence η should be smaller than 2. We conservatively adopt a range of 1– 2 for η for the Compton detector concept. Springer

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Table 1 The sensitivity of three detector concepts for MAX for three different gamma-ray lines. Sensitivities are for a statistical signiﬁcance of 3σ and a total effective observation time of 106 s. The effective area of the MAX Laue lens was assumed to be 1191 cm2 and 661 cm2 at 511 keV and 847 keV, respectively. The quoted values pertain to the energy interval E, centered on the line energy, that optimizes the sensitivity. The ranges in sensitivity reﬂect the possible values of η in Equation 1 as discussed in the text. The range in sensitivity for MAX-NCTseg in addition includes the two choices for treating energy deposits in background recording detector layers (see text for deﬁnition), which may be ignored or used as additional veto Sensitivity [10−6 ph/cm2 /s] Line Energy [keV]

MAX-TGRS

MAX-NCTseg

MAX-NCTcompt

511

4.2–6.0

2.5–4.6

1.3–1.8

847

4.9–6.9

2.6–3.8

1.3–1.8

847 (3% FWHM)

18–25

10–15

3.5–4.9

3. Results The sensitivities of the three different MAX detector concepts for an on-axis point source for three different gamma-ray lines are summarized in Table 1. Sensitivities are for a statistical signiﬁcance of 3σ and a total effective observation time of 106 s; the ranges reﬂect the possible values of η in Equation 1 as discussed above. The effective area of the MAX Laue lens was assumed to be 1191 cm2 and 661 cm2 at 511 keV and 847 keV, respectively. Sensitivity values are quoted for the best choices of both the radius of the central pixel and of the width of the energy interval E centered on the line energy. The range in sensitivity for MAX-NCTseg in addition includes the two choices for treating energy deposits in BRDLs, which may be ignored or used as additional veto, and are given for the optimal choice of SRDLs in each case. If energy deposits in BRDLs are ignored, for the 511 keV line it is best to use all ﬁve detector layers; for the 847 keV lines there is little difference between using three, four, or ﬁve layers (values are quoted for ﬁve layers). If BRDLs are used as additional veto the sensitivity can be slightly improved. It is then best to use only three detector layers in this case for both the 511 keV and the 847 keV lines. In either case the optimal central pixel radius is about 1.1 cm. For MAX-NCTcompt the best radial size of the detector region where the ﬁrst interaction needs to occur is slighty larger than for MAX-NCTseg; values range between 1.2 and 1.5 cm, depending on the details of the event selections. The achieved sensitivity depends only weakly on the choice of detector layers in which the ﬁrst interaction needs to occur. It seems that restricting the ﬁrst interaction to the top four layers is best. As can be seen from Table 1, the Compton detector concept MAX-NCTcompt offers the best sensitivity for each of the three lines. In order to illustrate fundamental performance characteristics such as detection efﬁciency or background rejection, Table 2 summarizes the photopeak efﬁciencies and the background count rates corresponding to the choices for energy band, detector layers, and event selections that optimize the sensitivity for each of the three detector concepts and all three lines under study. The ranges for the MAX-NCTseg concept reﬂect the two different treatments of energy deposits in BRDLs (the lower and upper bounds are obtained if BRDLs are treated as additional veto or ignored, respectively). The photopeak efﬁciencies for MAX-NCTseg do not fall far short of those obtained with MAXTGRS. Differences are due to the fact that photons can more easily escape MAX-NCTseg than MAX-TGRS, and that only a fraction of the incident photons interacts in one of the Springer

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Exp Astron (2005) 20:375–386 Table 2 The photopeak efﬁciencies and the background rates that went into the calculation of the line sensitivities in Table 1 Line energy [keV]

MAX-TGRS

MAX-NCTseg

MAX-NCTcompt

Photopeak efﬁciency [%] 511

38

22–28

6

847

24

16–22

6

847 (3% FWHM)

27

17–24

6

Background Rate [cts/s] 511

2.1 × 10−1

2.3 × 10−2 - 6.5 × 10−2

1.0 × 10−3

847

3.4 × 10−2

4.2 × 10−3

-

8.6 × 10−3

2.6 × 10−4

847 (3% FWHM)

5.2 × 10−1

8.0 × 10−2

-

1.6 × 10−1

2.1 × 10−3

central pixels of the segmented MAX-NCTseg detectors. In contrast, the MAX-NCTcompt photopeak efﬁciency is much smaller. For this concept the rather low photopeak efﬁciency is due to the severe event selections, which result in many source events being rejected. Nevertheless, the MAX-NCTcompt concept offers the best sensitivity because of its superior capabilities for rejecting instrumental background, as can be seen in Table 2.

4. Summary and conclusion We have used ab initio Monte Carlo simulations to compare the performance of three different Ge detector concepts for the MAX Laue lens gamma-ray telescope: a standard co-axial detector, a stack of segmented detectors, and a Compton camera consisting of a stack of strip detectors. The performance was assessed for an on-axis point source in three different gamma-ray lines: narrow lines at 511 keV and 847 keV, and a broadened (3% FWHM) line at 847 keV. We ﬁnd that the Compton detector concept MAX-NCTcompt offers the best sensitivity for each of the three lines. The Compton concept also offers other unique advantages over the other two concepts. Because of their ﬁne spatial resolution, the detectors of a Compton camera are ideally suited to follow the inevitable small excursions of the focal spot on the detector surface due to residual relative motions of the lens and detector spacecraft; with a Compton camera one could also adjust the size of the focal spot to the requirements of a given observation during data analysis. The ﬁne spatial resolution necessary for Compton detectors is also required if the limited imaging capabilites of a Laue lens are to be exploited, e.g. to separate close point sources or to study the morphology of slightly extended emission such as that from Galactic supernova remnants. Finally, the complementary characteristics of a Laue lens and of a Compton detector with respect to photon polarisation render their combination a powerful polarimeter. At nuclear line energies a Laue lens does not change the polarisation of the diffracted photons (Halloin and Bastie, 2006; Halloin 2006), while a Compton detector is intrinsically ideally suited for performing polarimetry because of the azimuthal variation of the scattering direction for linearly polarized photons (Lei et al., 1997). The combination of a Laue lens with a Compton detector will thus open a new observational window on many gamma-ray sources in which strong magnetic ﬁelds are present, such as pulsars, or on jets expelled by compact, accreting objects. We therefore conclude that a Compton camera is the most promising detector concept for MAX. We expect this conclusion to apply not only to Springer

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the three gamma-ray lines studied here, but to all Laue lens gamma-ray telescopes proposed for the nuclear line region, such as the Gamma-Ray Imager (GRI, Kn¨odlseder, 2006). Although not the primary focus of this study, it is still worth pointing out that even with a rather conservative design of the Compton camera that leaves still ample room for improvement, narrow line sensitivities of about 10−6 ph cm−2 s−1 are possible with a relatively small mission such as MAX – an improvement over the currently best gamma-ray spectrometer SPI onboard the INTEGRAL observatory of more than an order of magnitude. There are many aspects in which the Compton camera studied here can be improved. First steps towards optimizing the design of the MAX-NCTcompt detector are presented in a companion paper by Wunderer et al. (2006b) (there, MAX-NCTcompt is referred to as the SMALL design). Possible improvements include a revised design of the BGO veto shield to decrease the instrumental background contribution of cosmic diffuse photons, the reduction of passive materials around the Ge wafers (passive material is a source of instrumental background and in addition reduces the photopeak efﬁciency because some fraction of the source photon’s energy might be deposited there), the careful selection of passive materials used (e.g. elemental composition), the optimization of the geometry and the spatial and spectral resolution of the Ge detectors to increase the photopeak efﬁciency, or improvements of event reconstruction algorithms. Efforts to optimize the performance of a Compton detector for Laue gamma-ray lenses are ongoing (see e.g. the companion paper by Wunderer et al., 2006b) and will be reported in future publications.

References Abrosimov, N., et al.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9025-6 (2006) Barri`ere, N., et al.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9058-x (2006) Boggs, S.E., et al.: New Astron. Rev., in press (2006a) Boggs, S.E., et al.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9051-4 (2006b) Brun, R.: GEANT Detector Description and Simulation Tool, CERN Program Library Long Writeup W5013, http://wwwinfo.cern.ch/asd/geant/ (1995) Courtois, P., et al.: Exp. Astron. 20, DOI: 10.1007/s10686-005-9018-x (2006) Gruber, D.E., et al.: ApJ 520, 124 (1999) Halloin, H., et al.: In Proc. SPIE 5168, 471 (2004) Halloin, H.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9063-0 (2006) Halloin, H., Bastie, P.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9064-z (2006) Kanbach, G., et al.: New Astron. Rev. 48, 275 (2004) Kippen, M.: New Astron. Rev. 48, 221 (2004) Kn¨odlseder, J.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9031-8 (2006) Lei, F., et al.: Space Sci. Rev. 82, 309 (1997) Lonjou, V., et al.: NIM A 554, 320 (2005) Lund, N.: Exp. Astron. 2, 259 (1992) McConnell, M.L., Kippen, R.M.: AAS, HEAD Meeting #8, #41.01 (2004) Moskalenko, I., et al.: ApJ 565, 280 (2002) Owens, A., et al.: Space Sc. Rev. 71, 273 (1995) Prantzos, N.: In Proc. of 5th INTEGRAL Science Workshop (ESA SP-552), 15 (2005) Sch¨onfelder, V., et al.: ApJS 86, 657 (1993) Smither, R.K., et al.: Exp. Astron. 6, 47 (1995) Smither, R.K., et al.: Exp. Astron. 20, DOI: 10.1007/s10686-005-9019-9 (2006) von Ballmoos, P., et al.: New Astron. Rev. 48, 243 (2004) von Ballmoos, P., et al.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9071-0 (2006) Weidenspointner, G., et al.: A&A 411, L113 (2003) Weidenspointner, G., et al.: ApJS, 69 (156) (2005) Weidenspointner, G.: In Proc. of Population of High Energy Sources in Galaxies (230. IAU Symposium) (2006) Meurs, E.J.A., Fabbiano, A. (eds.), astro-ph/0601312 Springer

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Wunderer, C., et al.: In Proc. of 5th INTEGRAL Science Workshop (ESA SP-552), 913 (2004) Wunderer, C., et al.: New Astron. Rev., in press (2006a) Wunderer, C., et al.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9034-5 (2006b) Zoglauer, A.: First Light for the Next Generation of Compton and Pair Telescopes (dissertation), TU M¨unchen (2005) Zoglauer, A., et al.: New Astron. Rev., in press (2006)

Springer

Exp Astron (2005) 20:387–394 DOI 10.1007/s10686-006-9051-4 ORIGINAL ARTICLE

Performance of the Nuclear Compton Telescope Steven Boggs · Mark Bandstra · Jason Bowen · Wayne Coburn · Robert Lin · Cornelia Wunderer · Andreas Zoglauer · Mark Amman · Paul Luke · Pierre Jean · Peter von Ballmoos

Received: 24 February 2006 / Accepted: 18 May 2006 C Springer Science + Business Media B.V. 2006

Abstract On 1 June 2005, the prototype Nuclear Compton Telescope (NCT) ﬂew on a high altitude balloon from Fort Sumner, New Mexico. NCT is a balloon-borne soft γ -ray (0.2–10 MeV) telescope for studying astrophysical sources of nuclear line emission and γ ray polarization. Our program is designed to develop and test technologies and analysis techniques crucial for the Advanced Compton Telescope; however, our detector design and conﬁguration is also well matched to the focal plane requirements for focusing Laue lenses. The NCT prototype utilizes two, 3D imaging germanium detectors (GeDs) in a novel, ultracompact design optimized for nuclear line emission in the 0.5–2 MeV range. Our prototype ﬂight provides a critical test of the novel detector technologies, analysis techniques, and background rejection procedures developed for high resolution Compton telescopes. Keywords Compton telescopes · Gamma-ray spectroscopy · Gamma-ray astronomy · Balloon payloads

1. Introduction The Nuclear Compton Telescope (NCT) is a balloon-borne soft γ -ray (0.2–10 MeV) telescope designed to study astrophysical sources of nuclear line emission and γ -ray polarization (Boggs et al. 2003, 2004). It employs a novel Compton telescope design, utilizing twelve high spectral resolution germanium detectors (GeDs) with the ability to track the location of each photon interaction in three dimensions (Fig. 1). Tracking serves three purposes:

S. E. Boggs () · M. E. Bandstra · J. D. Bowen · W. Coburn · R. P. Lin · C. Wunderer · A. Zoglauer Space Science Laboratory, University of California, Berkeley, CA 94720 USA M. S. Amman · P. N. Luke Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA P. Jean · P. von Ballmoos Centre d’Etude Spatiale des Rayonnements, UPS-CNRS, Toulouse, France Springer

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Fig. 1 The NCT two-detector prototype GeD array, consisting of 15-mm thick cross strip detectors of active area 54 cm2 . Each detector has 37 × 37 2-mm pitch strips, resolving the active volume into over 4 × 104 individual elements of volume < 2 mm3 .

imaging the sky using Compton imaging techniques, measuring polarization, and very effectively reducing background. The entire set of detectors and their cryostat are enclosed inside an active BGO well (Fig. 2), giving an overall ﬁeld of view of >25% of the sky. The instrument is mounted in a pointed, autonomous balloon platform and is capable of long duration (>20 day) balloon ﬂights. NCT is designed to optimize sensitivity to nuclear line emission over the crucial 0.5– 2 MeV range, and sensitivity to polarization in the 0.2–0.5 MeV range. The guiding principle of NCT is that high efﬁciency and excellent background reduction are critical for advances in soft γ -ray sensitivity. NCT will explore a new phase space of nuclear γ -ray observations. Some of the long term goals of NCT include mapping both 26 Al and 60 Fe in the plane and bulge of our galaxy, measuring the amount of 44 Ti contained in recent core collapse supernova remnants, measuring with high resolution the spectra of AGN and searching for γ -ray polarization, looking for polarization in the emission from pulsars and associated plerions, and searching for redshifted deuterium lines from the surfaces of neutron stars. Fig. 2 NCT ﬂight cryostat during integration with the BGO shields into the instrument cradle. The cradle assembly, including shields and dewar, can pivot to allow pointing at an arbitrary positive elevation. The on-axis direction (perpendicular to the face of the detectors) is shown.

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Fig. 3 NCT ﬂight preamps in their shielded housing, with 10 compact preamps per board, four boards per GeD face. (The top cover has been removed and ﬂipped to show how each preamp is electrically shielded for low noise.)

The NCT prototype is a scaled down, two detector version of NCT. The NCT prototype ﬂew on a high altitude balloon from Fort Sumner, New Mexico on 1 June 2005. The duration of the ﬂight was approximately nine hours. The NCT prototype balloon ﬂight had two primary goals, to qualify the gondola for a future, Long Duration Balloon Flight (LDBF) from Alice Springs, Australia, and to measure our instrumental background at balloon altitudes. Our secondary goal was to obtain images and spectra of the Crab Nebula/Pulsar and possibly the transient X-ray pulsar A 0535 + 262. The analysis of the ﬂight data is ongoing, with results in preparation.

2. Instrumentation At the heart of the NCT prototype are two large volume, 3D positioning cross strip GeDs, fabricated at LBNL using their amorphous Ge contact technology (Luke et al. 1992). Each GeD is a 37 × 37 strip, 15 mm thick, p-type planar detector. Orthogonal strips were deposited on both faces of the GeD, with a strip pitch of 2 mm and a 0.2 mm gap between strips. A 2-mm thick guard ring surrounds this active area on both faces of the detector, with a 1 mm gap between the ring and the edge of the crystal. We instrumented the strips on both the ground (DC coupled, anode) and HV (AC coupled, cathode) sides with custom low power, low noise preampliﬁers. NCT uses custom GeD quality signal processing electronics (Coburn et al. 2004). Each detector strip has a compact, low power signal processing chain made predominantly of conventional surface mount components. Detector signal extraction is accomplished with a unique charge sensitive preampliﬁer (Fig. 3), in which excellent spectroscopic performance is achieved in a small footprint and at modest cost and low power, without sacriﬁcing signal bandwidth (Fabris et al. 2004). A much-simpliﬁed pulse-shaping ampliﬁer, with both a fast and a slow channel, follows each preampliﬁer. The slow channel, with a 3 µs peaking time, is followed by a peak detect and stretch function. The fast channel uses a small delay line constant fraction discriminator to time stamp each waveform at 50% of its maximum amplitude, generating a low time walk signal. Demonstrated resolutions for these large ﬂight detectors are 2.2 keV FWHM at 122 keV, and 0.4 mm FWHM depth determination for all interactions that deposit ≥40 keV. Spectroscopy signals uniquely match the fast-signal pairs for multiple interactions in the same GeD. One 16-channel signal-processing cluster resides on a single printed circuit card, with both the fast and slow analog signal processing electronics (Coburn et al. 2004). Five of Springer

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these “analog boards” are required for each GeD. Each set of ﬁve analog boards connects to a common back plane, which supplies bi-directional housekeeping communication, power, and event data channels. Low level input signals connect to the front panel, well away from the back plane, and are shielded for noise. Each analog board has two ACTEL Field Programmable Gate Arrays (FPGA). One ACTEL keeps track of the LLD, ULD and fast trigger rates in each strip, while the second coordinates the logic between the slow and fast channels, as well as the shield veto signals. A single Altera NIOS embedded processor board interfaces with each set of ﬁve analog boards, and communicates with the main ﬂight computer via an ethernet link. The total power per channel is currently 210 mW, although lower power options are currently being developed for the next ﬂight. 2.1. 3D Positioning There are two main keys to Compton imaging with this system. The ﬁrst is to accurately determine the energy deposited in the detector for each interaction. The second is successfully tracking, in all three dimensions, the γ -ray interactions within the detector. By segmenting the anode into strips, and the cathode into orthogonal strips, 2-D positioning is achieved directly through identiﬁcation of the active anode and cathode strips. Interactions are matched on the two faces of the detectors by performing spectroscopy on both anode and cathodes strips. Before matching interactions we must ﬁrst account for potential charge-sharing events on neighboring strips, or multiple interactions on the same strip. Optimization and performance of these event reconstruction techniques are still in progress. Measuring the “depth”, or “z position”, of the interaction in the detector (the distance between the γ -ray interaction and either the anode or cathode strip), is achieved by measuring the difference between electron and hole collection times on opposite faces of the detector. The Collection Time Difference (CTD) for an event is well deﬁned, and has been shown to be linear with depth to ﬁrst order (Amman & Luke 2000, Amrose et al. 2001). The drift time across a 15-mm thick GeD at our operating bias of −800 V is on the order of 200 ns and 250 ns for electrons and holes, respectively. To measure the time when the signal on each channel reaches 50% of its maximum amplitude, we use a simple analog constant fraction discriminator built into each channel’s electronics chain (Coburn et al. 2004). These “fast channels” give us an 0.4 mm FWHM spatial resolution at 60 keV. This is comparable to what get by digitizing the preamp signals, but with a much smaller, simpler, lower power system. The calibration of the interaction depth in terms of the CTD poses a unique problem since we cannot send in events of known depth. We can, however, send in events with a known depth distribution. Our technique of converting CTDs to depth, or z position, is discussed in detail in Amrose et al. (2003). 2.2. Spectral performance The spectral resolutions of each of the anode channels taken with the ﬂight electronics are quite good. On average, the resolutions obtained with the ﬂight electronics are identical to what we get using benchtop electronics. The variation of values obtained with the ﬂight electronics (±12%) is also similar to the range seen with lab equipment (±8%). Charge loss for events shared between strips remains minimal, and can be corrected (Coburn et al. 2002). Overall spectroscopy of multiple-site Compton events remains excellent (Fig. 4), though we are still in the process of optimizing the cross calibration of strips. Springer

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Fig. 4 Preliminary 60 Co (1173, 1333 keV) spectrum of all Compton-scatter events for the two-GeD prototype array. Resolutions of ∼4 keV FWHM are currently achieved, with ∼3 keV expected as cross-calibration between the strips improves. The low-energy tailing on these lines is partially due to our ﬁnite thresholds (∼ 15 keV), and partially due to charge loss between strips, which is largely correctable. Optimizing these spectra is work in progress.

2.3. Imaging With well calibrated positioning and spectroscopy, NCT can image wide γ -ray source ﬁelds with moderate angular resolution. In Fig. 5 we show the results of a calibration run of the NCT prototype with a 60 Co (1.173 MeV) source placed ∼60◦ above the instrument pointing axis. The source is obviously evident in the image and is well localized, demonstrating the wide FoV Compton imaging capabilities of NCT.

Fig. 5 “All-sky” 60 Co (1173-keV) image of a lab point source taken with the NCT balloon payload, processed using a simple event list, maximum entropy technique Wilderman et al. (1998). These are speciﬁcally two-site interaction which scatter between the detectors, more detailed analysis is still in progress. The source is ∼60◦ off axis, demonstrating the wide FoV capabilities of NCT. Springer

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Fig. 6 Flat ﬁelds of the the front detector (left) and rear detector (right) from ﬂoat during the 2005 balloon ﬂight. The data has been binned as pixels, meaning each event uniquely triggered a single crossed pair of strips. With the exception of strip 15 on the front detector, which was not functioning prior to the ﬂight, the ﬂat-ﬁeld detector response is very uniform. The curved corners of the detectors can also be seen in these images.

2.4. Detector uniformity Since our Compton imaging and background rejection techniques (Boggs & Jean 2000, 2001) rely on reconstructing multiple photon interactions across different strips and even detectors, the uniformity between strips and detectors of both the spectral and positioning resolutions is very important. The instrument response has to take into account all of the slight variations between strips, and that is part of our ongoing analysis of the calibration and ﬂight data from the last ﬂight, Fig. 6. Since the detectors are formed from a single germanium crystal, uniformity is high (Coburn et al. 2002).

3. Prototype ﬂight The NCT prototype payload was launched on a 39.5 Mft3 high altitude balloon from Fort Sumner, New Mexico on 1 June 2005 (Fig. 7). The balloon reached a ﬂoat altitude of ∼133 kft at approximately 20:30 GMT, and was at ﬂoat for approximately 5.5 h before termination. Details of the gondola systems and the ﬂight proﬁle are presented elsewhere Coburn et al. (2005). We had two main goals for this ﬂight. First, we wanted to qualify our gondola for a future LDBF. Second, we wanted to measure the instrumental background, telemetry rates, data vault needs, etc., at ﬂoat. For the 2005 ﬂight the instrument and associated electronics performed ﬂawlessly, and we achieved both of these goals. Detail analysis results are in preparation, currently focused on detailed calibration and detector backgrounds at ﬂoat. Our secondary goal was the observation of two science targets, the Crab Nebula/Pulsar and the transient accreting pulsar A 0535 + 262. Both pulsars are spatially close on the sky, separated by ∼4◦ , and therefore simultaneously fell with within the NCT ﬁeld of view. The Crab was chosen as a standard calibration source, as well as being an excellent candidate for polarization measurements. The pulsar A 0535 + 262 is transient, and we were fortunate enough that it was in a rare outburst state during our ﬂight. In addition to being able to image Springer

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Fig. 7 The NCT gondola on the ﬂight line, showing the relative positions of the instrument, electronics bay, SIP, and ballast hoppers.

two bright point sources, A 0535 + 262 provided the opportunity to search for hard X-ray cyclotron absorption features with unprecedented spectral resolution. The gondola pointing system was set up to keep the instrument at a ﬁxed elevation, but to actively point in azimuth to keep the Crab centered in the ﬁeld of view. Unfortunately, shortly after launch the azimuthal pointing system failed, seriously compromising our exposure to our sources and adding an extra level of complexity to the data analysis. The instrument aspect is known at all times, it just was not controllable during the ﬂight. Fortunately, with NCT’s wide FoV we hope to recover some of the source data. Our balloon gondola frame suffered some minor and mostly cosmetic damage during impact, but is otherwise ﬁne. The NSBF parachute termination package worked ﬂawlessly, releasing the parachute from the gondola right after landing. Since the ﬂight, the entire detector and data system has been powered up in the laboratory and is working ﬁne. Neither the detectors, cryostat, nor electronics suffered any damage during the ﬂight, landing, or recovery. The most important result of the ﬂight, however, was the fact that the instrument and associated electronics functioned ﬂawlessly for the duration. Overall the system logged more than 2.3 million events while at ﬂoat. The detectors and shields worked well, our detector electronics had no problems handing the incoming data, and all strips and channels performed as expected. So, although there was a failure in the pointing system and the data analysis is still ongoing, we are conﬁdent that this ﬂight will be a critical step in demonstrating the viability of the NCT concept for future space missions such as the Advanced Compton Telescope. 4. Future work Our next step is to prepare the instrument and gondola for a long duration balloon ﬂight from Alice Springs, Australia in December 2007. For the next ﬂight, we are currently fabricating four more GeDs for integration into our existing cryostat for two stacks of detectors, three Springer

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layers deep, bringing our total number of detectors to six. The gondola needs some minor mechanical work, but overall is in excellent shape. We are planning a redesign of our azimuthal pointing system, both to ﬁx the failure and to incorporate differential GPS for positioning. We are currently redesigning our entire electronics system for the LDBF, as well as in anticipation of future satellite applications. There are three primary goals for redesigning the electronics. First, we are redesigning the preampliﬁers for lower operating voltages, dropping their overall power requirements by factors of 5–6, low enough for direct application on satellite missions. Second, we are redesigning our analog readout electronics to be compatible with conversion to an ASIC design for future applications, which primarily requires a redesign of the fast (timing) circuit on each strip. Finally, we are redesigning the signal cabling to very low mass, ﬂexible coaxial ribbon cable, ideal for satellite requirement.

5. Focal plane technologies The Compton technologies and techniques developed for NCT are directly applicable to focusing Laue lens telescopes. The Compton tracking will allow identiﬁcation of the ﬁrst scatter site in the focal plane, with millimeter spatial resolutions consistent with the lens requirements. The Compton scatter information will allow superior background rejection and Compton continuum rejection, similar to those developed for the pure Compton telescope applications (Boggs & Jean 2000, 2001). Our current generation of GeDs provide excellent spectral resolution, high spatial resolution, and good stopping power to match the novel lens capabilities. Technologies we are developing for NCT that are directly applicable to satellite focal plane applications include the GeD design, detector mounting and fabrication, cryogenic design, low power preampliﬁers, and low mass cabling. Our redesigned analog electronics will be optimized for straight-forward conversion to ASICs. Finally, NCT background measurements should provide a direct check of focusing telescope backgrounds. Acknowledgements Thanks to C. Wunderer for presenting this work at Gamma Wave 2005.

References Amman, M. and Luke, P. N.: NIM A452, 155 (2000) Amrose, S. et al.: in Proc. IEEE, Nucl. Sci. Symp. Conf. Rec., N12–22 (1999) Amrose, S. et al.: NIM A505, 170 (2003) Boggs, S. E. et al.: Proc. SPIE 4851, 1221 (2003) Boggs, S. E. et al.: New Astr. Rev. 48, 251 (2004) Boggs, S. E. and Jean, P.: Astron. & Astrophys. Suppl. Ser. 145, 311 (2000) Boggs, S. E. and Jean, P.: Astron. & Astrophys. 376, 1126 (2001) Coburn, W. et al.: Proc. SPIE 784, 54 (2002) Coburn, W. et al.: Proc. SPIE 5165, 131 (2004) Coburn, W. et al.: Proc. SPIE 5898, 13 (2005) Fabris, L. et al.: NIM A424, 545 (1999) Luke, P. N. et al.: in Proc. IEEE, Nucl. Sci. Symp. Conf. 39, 590 (1992) Wilderman, S. J. et al.: IEEE TNS 45, 957 (1998)

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Exp Astron (2005) 20:395–403 DOI 10.1007/s10686-006-9040-7 ORIGINAL ARTICLE

The Compton and pair creation telescope MEGA Robert Andritschke · Andreas Zoglauer · Gottfried Kanbach · Peter F. Bloser · Florian Schopper

Received: 4 February 2006 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract MEGA, short for Medium Energy Gamma-ray Astronomy, is the development of a new technology telescope in the energy band 0.4–50 MeV. The wide energy range of MEGA, which spans nuclear γ -ray lines and energetic continuum spectra, the large ﬁeld of view, and the capacity for polarimetry enables unique investigations into cosmic nucleosynthesis, particle accelerators around compact objects, and explosive high-energy events. We describe the development and tests of a prototype detector. Results from laboratory tests using radioactive sources and from a beam test calibration are presented and an outlook of a potential space mission is sketched. Keywords Compton telescope · Pair telescope · Gamma-ray astronomy · Medium gamma-ray energies · MEGA 1. Introduction The photon interaction cross-sections in the MeV range go through a minimum in their transition from the photoelectric effect (≈100 keV) to pair creation (≈10 MeV). In this so-called “Compton range” gamma-ray astronomy is challenging. This is not only due to the low cross-sections but also to the unavoidable “radio-activation” of the spacecraft and instrument materials by energetic particles in space. This background of local origin needs to be effectively discriminated against to provide good sensitivity for astronomical targets. R. Andritschke () · F. Schopper Max-Planck-Institut f¨ur extraterrestrische Physik, Garching, Germany Present address: MPI Halbleiterlabor, Munich, Germany G. Kanbach Max-Planck-Institut f¨ur extraterrestrische Physik, Garching, Germany A. Zoglauer Space Sciences Laboratory, Univ. of California, Berkeley, CA, USA P. F. Bloser Space Science Center, Univ. of New Hampshire, Durham, NH, USA Springer

Fig. 1 Sensitivity levels for selected hard X- and γ -ray telescopes. The goal for a MEGA mission is shown with a dashed line

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A wide variety of astronomical sources have been discovered with COMPTEL [12] aboard the Compton Gamma-Ray Observatory (CGRO) which was in orbit from 1991 to 2000. COMPTEL showed that unique information can be gained in this difﬁcult energy range about cosmic high-energy accelerators, sites of active nucleosynthesis with γ -ray line emitting isotopes, and large-scale structures in the Galaxy and beyond. High energy processes around compact objects like galactic or stellar mass black holes and neutron stars lead to emission of γ radiation. Many objects are extremely dynamic like supernova explosions, gamma-ray bursts, accretion and jet phenomena. An instrument with large ﬁeld-of-view would deliver an all-sky-survey while simultaneously monitoring the sky for variable sources. Compton and pair-creation telescopes are well suited for this task. Figure 1 gives an overview of past, present, and near-future missions on the basis of their sensitivities. The gap between the instruments IBIS and SPI, both aboard the INGEGRAL spacecraft, and EGRET aboard CGRO is obvious. The GLAST mission, the successor of EGRET, is scheduled for launch in 2007. It will improve the sensitivity in the pair creation range by more than an order of magnitude. The visionary ACT concept aims at the same level of sensitivity in the Compton range. An intermediate step could cover the 1–10 MeV range between the coded mask instruments of INTEGRAL and the pair creation telescopes EGRET and GLAST as well as address the technical challenges on the way to an ACT mission. This task could be accomplished by the MEGA instrument which combines the working principles of COMPTEL and EGRET in one medium sized instrument. A schematic overview is shown in Figure 2, Compton scattering and pair creation takes place in the so-called tracker. Springer

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Fig. 3 The MEGA prototype with opened cover

Here the trajectories and energies of charged particles are recorded by double-sided strip detectors. Scattered photons and particles emanating from the tracker are measured in the calorimeter which surrounds the lower hemisphere of the tracker. The calorimeter is a ﬁnely pixellated scintillation detector with semiconductor read-out. In order to address the problems associated with a novel design we have developed a prototype (Figure 3 shows the prototype with opened cover). Its design and measured properties is described in this paper. Extensive simulations are used to extrapolate to a satellite geometry, four times the tracker area and three times the tracker depth compared to the prototype, later referenced as baseline satellite geometry.

2. Prototype development 2.1. The tracking detector The tracker consists of 99 double-sided silicon strip detectors. Design and test has been done by the MPI semiconductor lab, production by Eurisys Mesures (Lingolsheim, France). Each wafer measures 6 cm × 6 cm in area and is 500 µm thick. 128 strips with 470 µm pitch are manufactured (orthogonally) on both sides of the wafers. The decoupling capacitors are already implemented by silicon oxide/nitride layers directly on the wafers. A 3 × 3 array of wafers is mounted with the corresponding front-end electronics (FEE) on a plastic frame. The strips in a row (or column) are interconnected and read-out by one FEE channel. The ASICs (of type TA 1.1 by IDE AS, Oslo) have 128 read-out channels, each consisting of a charge sensitive ampliﬁer, a shaper, a sample-and-hold and a discriminator. The prototype houses a stack of 11 detector layers, one layer is shown in Figure 4. Energy resolutions averaged over the channels of one layer are typically 15–20 keV (FWHM) for the 122 keV line of 57 Co, but layers with high leakage currents show up to 30 keV. The position resolution is 290 µm derived from measurements of atmospheric muons. The time resolution is ≈1 µs [5]. 2.2. The calorimeter The calorimeter consists of CsI(Tl) scintillators (manufactured by Hilger Crystals, U.K.). It is divided into crystal bars with a cross-section of 5 mm × 5 mm facing towards the tracker. Springer

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Fig. 4 One layer of the tracking detector

Fig. 5 An opened calorimeter block, the shown version has 8 cm long crystals

The length of the crystals depends on their position relative to the tracker: Below the tracker the length is 8 cm, on the lower part of the side walls 4 cm and on the upper one 2 cm. An array of 10 × 12 bars is combined in a block (Figure 5) with the crystals separated by several layers of reﬂective Millipore paper. They are coupled to a monolithic silicon PIN-diode array (Hamamatsu, Japan) of the same lateral dimensions and 500 µm thickness. For the optical coupling an array of transparent silicone cushions (one for each corresponding crystal – diode pair) is fabricated directly onto the silicon diode array. A white, opaque grid of silicone separates the cushions and avoids cross talk of light into neighbouring pixels. Due to their aspect ratio the 8 cm crystals have read-out arrays on both ends. This allows the determination of the point of interaction in the dimension along the crystal axis. The same front-end ASIC (TA1.1) reads out the PIN diode array as used for the strip detectors of the tracker. There are 20 blocks in total, 4 below the tracker, 8 on the lower part of the sidewalls and the same amount on the upper part. The energy resolution depends only marginally on the crystal length and is on average 90 keV (FWHM) for the 662 keV line of 137 Cs. The position resolution of the 8 cm crystals along their axis depends on the surface quality of the crystal (good polishing results in a bad position resolution), the optical coupling and the deposited energy. It could be as good as 1 cm (FWHM) but the average is at 2.7 cm (for energy deposits ≥4 MeV). Springer

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2.3. Electronics, trigger processor, and data acquisition The problem of handling a large number of detector channels (8448 in the tracker, 2880 in the calorimeter) is solved in the prototype by using a highly multiplexed read-out method. Therefore the front-end chips already include an output multiplexer for its 128 channels and can be cascaded. The prototype has eight of these chains containing up to twelve chips. Each chain has its own power supply and is galvanically separated by optocouplers from the other chains and the further electronics due to technical and noise reasons (details can be found in Andritschke [2]). The actual data acquisition hardware consists of a VME rack holding a sequencer, ADC modules (one ADC channel for each chain of FEE chips), a coincidence electronics board, a digital in/out board and a single board computer. Except for the coincidence board, which is custom made, the VME modules are commercial hardware. The data acquisition is a multi step process. It begins with waiting for an interaction in the detector system. The front-end ASICs have discriminators implemented (one for each channel which are logically combined to one signal per chip) which notify the coincidence electronics about incoming signals (the trigger). The coincidence electronics has to decide from the pattern of triggering chips if this interaction should be recorded. A selection of events is stringent at this point since the large number of channels and the extreme multiplexing of signals leads to long read-out times (≈8 ms) limiting the read-out rate (selective read-out only of triggered chips is not possible with the existing hardware). The coincidence electronics has a look-up table implemented which holds a list of valid trigger patterns. This table is stored in a RAM chip and is loaded by the instrument CPU. Depending on the measurement situation an appropriate pattern can be loaded (for example we use an open pattern selecting events with at least one trigger in the tracker and at least one in the calorimeter for measurement of lab sources, at an accelerator measurement we used an pattern excluding events where the top layer had triggered in order to suppress pair creation interactions occuring in the passive material in front of the detector and we used an pattern selecting interactions with ﬁve or more triggers in adjacent tracker layers to select muons). After a valid trigger pattern is recognized the front-end chips are turned into the hold state, i.e. activating the sample-and-hold stages storing the current amplitude of the shaped pulses in the FEE ASICs. This ideally, but not always, happens at the maximum of the pulses, which leads to some amplitude-dependent errors (timewalk, for details see Schopper [13]). After the activation of the sample-and-holds the time critical phase is over and the (slow) digitalization phase is entered. The sequencer is started from the coincidence electronics generating the sequence in which one channel after another is multiplexed onto the line to the ADC and digitized (the eight read-out chains are working in parallel, so eight channels are digitized in one step – to be precise). The converted amplitudes are stored in memories on the ADC boards, so that no interaction of the instrument CPU is needed up to now. The end of the digitalization sequence is signaled to the instrument CPU starting the transfer of the sampled data in the ADC’s memories into the computer memory for further processing. After this the system is ready for acquiring the next interaction while the computer is still busy with reducing and storing the current data (the algorithms are described in Schopper [13]).

3. First level data processing, event reconstruction, and imaging The reduced data are stored as sets of interaction points (channel numbers and pulse height information), one for each read-out event in the detector. For further processing these values Springer

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have to be converted into physical units, i.e. positions and energies. Since each read-out channel has its own properties (gains, noise etc.) the channels have to be treated individually with their proper calibration factors. Therefore dedicated measurements of radioactive lab sources are performed where individual interactions in the detectors are recorded instead of coincident events. From these measurements the full-absorbtion peak is isolated and used as calibration. Besides the energy calibration the position determination is complicated in case of the third dimension in the 8 cm calorimeter crystals (see [1, 13] for details). Also reconstructing the positions in the double-sided strip detectors gets non-trivial if there is more than one interaction in one layer [17]. Once the interaction points are known by their physical properties the interaction itself can be reconstructed. Several possible processes could have triggered the read-out of a given event: a Compton scatter with an electron track; a Compton scatter without a track; a pair creation; a charged particle crossing the detector; a chance coincidence. Zoglauer [17] describes in detail the complex algorithms which are used to ﬁlter the Compton and pair events, sequence the interaction points and ﬁnally reconstruct the original photon. The code was developed and tested against extensive simulations. The pair recognition efﬁciency is as high as 73% at 10 MeV, increasing with energy to 98% at 100 MeV for a baseline satellite geometry; the radius which contains 68% of the reconstructed photons is 5.75◦ for 20 MeV on-axis incidenting photons. In the case of a Compton event where enough energy is transfered to the electron to leave the ﬁrst layer and generate a track, the electron’s path has to be traced and identifying the starting point from the two ends is of major importance. The information can be gained from the deposited energies and for long tracks from the increasing scatter angles along the track. The percentage of correctly reconstructed tracks is better than 70% (for tracks with four hits) and reaches 85–90% for tracks with seven or more hits (in a simulation of a ﬂat spectrum 0.5–5 MeV, isotropically incidenting on the baseline satellite geometry). In the ﬁnal step of Compton event reconstruction the combination of tracker and calorimeter hits is veriﬁed, if it complies with Compton kinematics. An overall reconstruction efﬁciency, i.e. untracked and tracked Compton interactions including the track reconstruction efﬁciency, is ≈90% with only a weak dependence on the energy. We emphasize that in a tracking gamma-ray telescope like MEGA, the track itself is one of the most valuable elements to identify the event type and the sequence of interactions. The track normally gives the starting point of an event and considerations of absorption probabilities etc. lead to a reduction of random coincidences as well as to the correct sequencing of good events. Moreover background is suppressed compared to the untracked case due to the restriction to arcs of cones instead of full cones and due to additional rejection criteria. From the reconstructed events the source distribution can be derived. Pair production events as well as three different types of Compton events need to be taken into account for image reconstruction: events without a track, events with a track, and high-energy events with a track but with incomplete absorbtion of the scattered photon. This is accomplished by the unbinned maximum-likelihood method called list-mode maximum-likelihood expectation maximization, which originally was developed for medical imaging with SPECT cameras [14]. It was later adapted for use in astrophysics [15, 16].

4. Calibration and tests From January to March 2003 the prototype was calibrated with laboratory sources (22 Na, 137 Cs, 88 Y) in the near-ﬁeld, and in April/May 2003 it was calibrated at the High Intensity Springer

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Fig. 6 A selection of reconstructed beam images from Zoglauer [17] The beam was incident on-axis for all images. Top row: 0.7–2 MeV untracked Compton, 5–8 MeV tracked (fully absorbed) Compton, 10◦ × 10◦ boxes. Bottom row: 12–49 MeV pairs, 20◦ × 20◦ boxes

Gamma-ray Source HIGS [9] at Duke University (Durham, North Carolina) in the far-ﬁeld. The latter calibration used monoenergetic ( E/E ≤ 2%) and 100% polarized pencil beams at different energies (0.7, 2, 5, 8, 10, 12, 17, 25, 37 and 49 MeV) and different angles of incidence (0◦ , 30◦ , 60◦ , 80◦ , 120◦ , 180◦ ) as described in Andritschke (2004a). Based on these data, the imaging properties, sensitivity to polarization and a preliminary effective area of the prototype telescope have been determined. In Zoglauer [17] beam images over the full measured energy range (Figure 6 shows a selection) and at angles of incidence up to 80◦ have been reconstructed (not shown). The increasing and decreasing widths reﬂect the varying angular resolutions with energy and can be explained as follows: From 0.7 to 8 MeV the angular resolution improves because the relative energy uncertainties in the calorimeter decrease with increasing energy. Additionally the Compton scatter angles get smaller thus on average larger portions of the incoming energy is deposited in the calorimeter intensifying the effect. The same effect can be seen when comparing Compton scatter events without and with electron track (at 2 MeV the image reconstructed from tracked Compton events is broader, image not shown). Here the tracked ones have a broader distribution because a large fraction of the total energy is transfered to the electron (otherwise the scattered electron would be stopped in the layer of the Compton interaction) leaving less energy for the scattered photon. The non-circular shape at 5 and 8 MeV results from a low number of photons (187 in case of the 8 MeV image) due to a strict ﬁltering of fully absorbed photons. Since the prototype’s calorimeter covers only about 30% of the lower hemisphere below the tracker and multiple scatterings in the calorimeter are very likely, only very few photons are fully absorbed above 5 MeV. In the pair regime the angular resolution is limited by the unknown recoil of the nucleus and Moli`ere scattering in the silicon layer of the pair creation. The inﬂuence of both effects reduces with increasing photon energy. Thus the angular resolution improves with higher energies. Besides point sources the applied imaging algorithm is able to reconstruct extended sources (as it must to image, for example, diffuse nuclear line emission in the galaxy). This is shown Springer

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Fig. 7 Reconstructed image of a radioactive ring taken from Zoglauer (2005) The circular source was produced by two rotating γ -ray sources (88 Y, only 0.9 MeV line used for imaging)

in a measurement of two 88 Y sources mounted on a propeller located 27 cm above the tracker (this corresponds to an angular diameter of 29◦ at inﬁnity). The image (Figure 7) contains 138 000 Compton events in the energy range from 0.8 to 1.0 MeV. The non-uniformities of the image are artifacts of the non-uniformities of the instrument response, an effect that should be correctable. The Compton cross section is polarization-dependent and has its strongest signature, a sinusoidal modulation in the azimuthal distribution, at large scatter angles. MEGA with its geometry is well suited to detect it. Since the HIGS facility delivers fully polarized photons the beam measurements are ideal to determine the polarization response of the prototype. It has been shown [17] that the measured polarization response is in good agreement with the values derived from simulations. During the beam measurement at the HIGS facility the beam intensity was monitored so that from the ﬂux of the beam and the number of measured events the effective area could be calculated. The (still preliminary) analysis delivers a range of 1 cm2 at 2 MeV to 2.5 cm2 at 50 MeV in agreement with the simulation.

5. A MEGA satellite mission The prototype has proven the feasibility of the concept. A wide ﬁeld-of-view, broad energy band, and sensitivity to polarization are the key features for a survey mission. Moreover, time variable and unexpected transient sources could be monitored all over the sky in a constantly zenith pointing mode. For a baseline satellite geometry as envisioned for a possible MEGA mission, simulations have been performed while extrapolating from the prototype and including background for an equatorial low-earth orbit (525 km) [17]. One example is a strong burst like GRB910814 measured from COMPTEL. Its polarization could be detected if the degree of polarization exceeds roughly 8%. Of course this number depends on the detector thresholds, trigger criteria and the ﬂux of the burst. The simulation indicate that this concept can achieve the desired sensitivity levels for the next step in low- to medium-energy gamma-ray astronomy. Springer

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6. Relation to a focussing telescope system If we consider placing a Compton telescope, either similar to the one described in this paper or a suitable variant, in the focus of a gamma-ray imaging system, we hope to achieve improvements in sensitivity of the imager and an extension of the scientiﬁc scope of such a mission. The extension derives mainly from the wide-angle ﬁeld of view of a Compton telescope that will ensure a monitoring function for a larger number of gamma-ray sources outside the proper ﬁeld of view of the focusing system and the chosen target. An extended energy range is a further aspect introduced by a Compton telescope. The supportive role of a Compton system in the focus of a concentrator can be seen in the ability to select photons coming from the lens system. This will greatly reduce background and enhance the sensitivity for the target source. Acknowledgements We thank V. N. Litvinenko (now at BNL) and his team for supporting the MEGA calibration. and J. R. Macri, R. S. Miller and S. D. Hunter from UNH and GSFC for their dedicated involvement and hardware support at the accelerator measurement. We acknowledge funding by the German Space Agency DLR for part of the hardware development under 50 TT 9738 9 and for a pre-phase A study under 50 OO 0002.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

Andritschke, R.: Diploma theses (in German), Technical University Munich (2000) Andritschke, R. et al.: in Proc. IEEE, Portland 2003, Nucl. Sci. Symp. Conf. Rec. IEEE(2004) Andritschke, R. et al.: New Astr. Rev. 48, 281 (2004) Bignami, G.F. et al.: Space Sci. Instr. 1, 245 (1975) Bloser, P.F. et al.: NIM A 512, 220 (2003) Deredeyn, S.M. et al.: Nucl. Instr. Meth. 98, 557 (1972) Kanbach, G. et al.: Space Sci. Rev. 49, 69 (1988) Kanbach, G. et al.: Proc. SPIE 4851, 1209 (2003) Litvinenko, V.N. et al.: SPIE 2521, 55 (1995) Michelson, P. et al.: AIP Conference Proceedings 587, 713 (2001) Ryan, J.M. et al.: Proc. SPIE, Glasgow, 2004, in press Sch¨onfelder, V. et al.: ApJ Suppl. 86, 657 (1993) Schopper, F.: PhD thesis (in German), Technical University Munich (2001) Wilderman, S.J. et al.: IEEE Trans. Nucl. Sci. 45, 957 (1998) Zoglauer, A.: Diploma thesis (in German), Technical University Munich (2000) Zoglauer, A. et al.: ESA SP-552, 917 Zoglauer, A.: PhD thesis, Technical University Munich (2005)

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Exp Astron (2005) 20:405–412 DOI 10.1007/s10686-006-9068-8 ORIGINAL ARTICLE

The MPE X-ray test facility PANTER: Calibration of hard X-ray (15–50 kev) optics M. J. Freyberg · H. Br¨auninger · W. Burkert · G. D. Hartner · O. Citterio · F. Mazzoleni · G. Pareschi · D. Spiga · S. Romaine · P. Gorenstein · B. D. Ramsey

Received: 13 February 2006 / Accepted: 26 July 2006 C Springer Science + Business Media B.V. 2006

Abstract The Max-Planck-Institut f¨ur extraterrestrische Physik (MPE) in Garching, Germany, uses its large X-ray beam line facility PANTER for testing X-ray astronomical instrumentation. A number of telescopes, gratings, ﬁlters, and detectors, e.g. for astronomical satellite missions like Exosat, ROSAT, Chandra (LETG), BeppoSAX, SOHO (CDS), XMMNewton, ABRIXAS, Swift (XRT), have been successfully calibrated in the soft X-ray energy range (<15keV). Moreover, measurements with mirror test samples for new missions like ROSITA and XEUS have been carried out at PANTER. Here we report on an extension of the energy range, enabling calibrations of hard X-ray optics over the energy range 15–50 keV. Several future X-ray astronomy missions (e.g., Simbol-X, Constellation-X, XEUS) have been proposed, which make use of hard X-ray optics based on multilayer coatings. Such optics are currently being developed by the Osservatorio Astronomico di Brera (OAB), Milano, Italy, and the Harvard-Smithsonian Center for Astrophysics (CfA), Cambridge, MA, USA. These optics have been tested at the PANTER facility with a broad energy band beam (up to 50 keV) using the XMM-Newton EPIC-pn ﬂight spare CCD camera with its good intrinsic energy resolution, and also with monochromatic X-rays between C-K (0.277 keV) and Cu-Kα (8.04 keV). Keywords X-ray astronomy . X-ray telescopes . X-ray optics . X-ray detectors . Multilayers . Calibration PACS: 95.55.Ka, 95.55.Aq, 41 50.+h, 07.85.Fv M. J. Freyberg () · H. Br¨auninger · W. Burkert · G. D. Hartner Max-Planck-Institut f¨ur extraterrestrische Physik, PANTER X-ray Test Facility, Gautinger Straße 45, 82061 Neuried, Germany e-mail: [email protected] O. Citterio · F. Mazzoleni · G. Pareschi · D. Spiga INAF–Osservatorio Astronomico di Brera, Via Bianchi 46, 23807 Merate (lc), Italy S. Romaine · P. Gorenstein Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA B. D. Ramsey Space Science Department, NASA/MSFC, Huntsville, AL 35812, USA Springer

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1 Introduction Until 1962 the Sun was the only known extraterrestrial X-ray source. A ballistic rocket ﬂight equipped with a Geiger-M¨uller counter revealed the existence of a distant bright X-ray source (Sco X-1) and of an unresolved apparently diffuse emission [1]. Then, X-ray astronomy was soon recognised as an important way to study the high energy universe. Enormous progress in instrumentation for X-ray astronomical satellite missions has been made since these early days. The ROSAT mission was a milestone with the ﬁrst imaging All-Sky Survey in the soft X-ray energy band (0.08–2.4 keV). This became possible by using a low-background position-sensitive detector combined with a high-throughput X-ray mirror system [2]. To develop and characterise the ROSAT optics the PANTER X-ray test facility was built (for reviews on X-ray telescopes and instrumentation see [3] and [4]). Wolter showed that a combination of paraboloid and hyperboloid surfaces under grazing incidence can be used as an imaging X-ray optics system [5, 6]. The reﬂectivity of X-rays decreases rapidly with increasing incidence angle. With nested confocal and coaxial mirrors the total reﬂecting area can be increased (Figure 1), the inner shells contribute most of the area at higher energies while at lower energies the outer shells (with larger incidence angles) are signiﬁcant. The so-called Wolter-I geometry is now a standard arrangement for astronomical X-ray telescopes. As an example: one XMM-Newton X-ray mirror module [7] is made of 58 gold-coated thin nickel (electroforming replication) shells with a maximum diameter of about 70 cm, focal length 7500 mm, and a total effective area of 1475 cm2 at 1 keV. Another example is the Chandra thick polished mirror shells with an excellent onaxis point spread function of ≤1”. A conic approximation to the paraboloid-hyperboloid geometry is realized by the Astro-E2 thin foil mirrors which are very light-weight, but at the price of reduced spatial resolution. Several future X-ray astronomy missions (e.g., Simbol-X and Constellation-X) have been proposed which carry hard X-ray optics based on multilayer

Fig. 1 Grazing incidence X-ray telescope principle in Wolter-I geometry (paraboloid and hyperboloid), illustration taken from [6]. For a parallel input beam the grazing incidence angles at paraboloid (αp ) and hyperboloid (αh ) are identical; for a ﬁnite source distance (divergent beam) αp increases while αh decreases, leading to an image distance greater than the focal length Springer

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coatings. With numerous stacks of alternating layers of low and high atomic number (e.g., W/Si, Pt/C) with different thicknesses (from about 1 nm to 10 nm) a signiﬁcant increase of reﬂectivity at high energies (10–80 keV) on the basis of Bragg reﬂection (constructive interference) can be achieved [8, 9]. 2 The MPE X-ray test facility PANTER

2.1 Overview The imaging performance of optics is ideally characterised by parallel illumination, both onand off-axis. On ground the realization of a wide aperture parallel X-ray beam is difﬁcult. The simplest approximation of a parallel beam is placing a point-like X-ray source at the largest possible distance, thereby minimising the divergence of the beam with respect to the aperture size of the optics to be tested. Another approach – giving up full illumination of the mirror system – is via pencil beams, where the aperture of the incident X-ray beam is very small and the beam can thus be assumed to be parallel. This, however, increases measurement times tremendously. In the case of the PANTER facility the distance from the X-ray sources (see Section 2.2) to the entrance of the instrument chamber is 123.6 m (Figure 2) [10]. The experiments (mirrors, gratings, ﬁlters, etc.) are placed in this 12.5 m long and 3.5 m diameter chamber. They can be moved and rotated by means of manipulators driven by stepper motors with a typical accuracy of <3 µm. The X-ray source, tube, and chamber are kept under high vacuum at a pressure of ≤10−6 mbar. Two cryo-pumps (with a pumping capacity of 160 m3 s−1 each) reduce the partial pressure of water vapour in the chamber by a factor of 10 or more, to avoid icing on the cooled CCD camera (see Section 2.3). Valves, pumps, manipulators, detectors, X-ray sources, etc., can be remotely controlled from the control room. All relevant parameters of the facility are logged and can be used in later analysis. The cleanliness of the facility is measured continuously; the chamber and the preparation room are temperature-stabilised clean areas of class 1000. 2.2 X-ray sources For calibration at the PANTER facility four different X-ray sources are available. These X-ray sources are mounted on a rail system and the exchange is done within a couple of hours. The main source is an open X-ray source using a target wheel with 16 different targets which provide characteristic X-ray lines of the target element between 0.28 keV (C-K) and 12 keV (Au-L). This source is accompanied by two ﬁlter wheels to suppress selected parts of the

Fig. 2 Overview of the X-ray Test Facility PANTER situated in Neuried in the southwest of Munich, with a 123 m vacuum tube connecting the X-ray sources (located to the right) and the instrument chamber (on the left of the image) Springer

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spectrum, e.g., the continuum or Kβ lines. A target change can be performed within minutes. Fluxes are of the order of 1–10 ×103 photons cm−2 s−1 , depending slightly on the material and ﬁlters chosen. For very high ﬂuxes and energies a commercial (sealed) X-ray source is available which provides a couple of X-ray lines in the 4.5–22 keV range and bremsstrahlung continuum up to 50 keV. Moreover, two tunable monochromators can be used to study the performance of X-ray optics in the vicinity of the relevant X-ray absorption edges. The reﬂection grating monochromator covers the softer energy band (0.25–1.0 keV, up to 2 keV using second order), while the double crystal monochromator provides photon energies between 1.5–25 keV (incl. second order). The energy resolution of each system is better than 4% (and much better in crossdispersion direction). 2.3 Focal plane instrumentation The ﬂight spare models of the ROSAT Position Sensitive Proportional Counter (PSPC) and the XMM-Newton EPIC-pn CCD camera serve as focal plane X-ray detectors for calibration measurements. The PSPC [11, 12] provides moderate spectral (40% at 0.93 keV) and spatial (280 µm) resolution, but it is well-suited for measuring effective areas as it is an exact photon counting device and not, for example, affected by pile-up (two photons hitting the same or neighbouring pixels in the same read-out cycle) present in CCD devices when exposed to high ﬂuxes. The PSPC wide ﬁeld-of-view of 80 mm diameter is useful for alignment procedures as well as for the analysis of mirror scattering. The EPIC-pn CCD camera [13] is used if higher spatial (150 µm pixels) or spectral (150 eV at 6 keV) resolution is required. It consists of 12 CCDs with 64 × 200 pixels on a monolithic silicon wafer with an area of about 6 × 6 cm2 . As a backside-illuminated device it is intrinsically radiation hard. It is operated at −90◦ C. The quantum efﬁciency (QE) is high throughout the energy band (Figure 3), even at 30 keV the QE exceeds 8%. The camera can be operated in various read-out modes, with the Full-Frame (FF) and Small-Window (SW) modes being the most relevant ones for our report. In FF mode the full CCD area is readout with a cycle time of 73.36 ms. In SW mode only an area of 64 × 64 pixels in one CCD is read out, allowing a shorter cycle time of only 5.67 ms which signiﬁcantly reduces pile-up effects. Moreover, the camera can be operated with two different gains, the high-gain mode with an energy range of 0.1–17 keV, and a low-gain mode with a factor of about 18 higher energies. It is planned to use the new frame-store CCD devices [14] developed for ROSITA [15] for a new camera at the PANTER facility. This camera will have smaller pixel size, better energy resolution, and increased thickness (and thus high-energy QE) and represents one aspect of a “growing facility”. The improved spatial resolution of the new camera will also be important for measurements of mirror test samples for missions like XEUS [16].

3 Multi-layer mirror calibration As already mentioned above, a ﬁnite source distance d changes the performance parameters such as the location of the image to z = f × d/(d − f ) instead of f , where f denotes the focal length, and also the incidence angles on the paraboloid and hyperboloid (Figure 1). An increased grazing incidence angle at the paraboloid means a reduction in reﬂectivity, which is not fully compensated by the decreased hyperboloid incidence angle. With the additional Springer

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Fig. 3 Quantum efﬁciency (QE) of the XMM-Newton EPIC-pn CCD camera as function of energy from 4–50 keV. The insert shows the range 0.2–2.8 keV and the effects of oxygen and silicon edges. Above 8 keV the efﬁciency is dominated by the absorption probability in the 300 µm bulk of silicon, at 30 keV the QE is about 8.7% (2.3% and 0.7% at 50 keV and 80 keV, respectively)

Fig. 4 Spider module holding one multilayer coated mirror shell (at the ring), the shutter door is seen at the right of the module, the hole in the centre is used for ﬂat-ﬁeld measurements (a shutter at the back of the module allows to open/close this central hole) [9] Springer

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Fig. 5 Reﬂectivity R(parabola) × R(hyperbola) as function of energy for a W/Si multilayer shell. The solid line represents a model ﬁt (with incidence angles of 0.218◦ and 0.111◦ , respectively), high-energy data points (E > 10 keV) with EPIC-pn CCD camera and continuum source, low-energy data points (E < 10 keV) using PSPC and target source at PANTER [9]

vignetting effects a net reduction in measured effective area is obtained [6]. With longer focal length and higher energy the effects of a divergent beam become more important. Moreover, the ﬁnite distance of the source from the mirror entrance causes also enhanced single reﬂections, i.e. photons are reﬂected at the paraboloid but do not hit the hyperboloid anymore and thus do not reach the focal point. These effects, however, can be calculated and taken into account when analysing the calibration data [8]. Figure 4 shows a NiCo replicated shell with W/Si multilayer coating (MSFC+SAO) mounted on a spider, just at the entry of the PANTER vacuum tube to the instrument chamber. The shell was 150 µm thick, 23 cm in diameter, and 42.6 cm long, with a focal length f = 10 m (which required this location for the measurements). The optics area (after subtraction of single reﬂections and spider rib obstruction) was 2.69 cm2 [9]. The half-energy width (HEW) of the point spread function was 26.5–30.5 arcsec for energies in the 0.27–8.04 keV range. At higher energies the HEW determination was affected by pile-up, because of the good performance of the mirror in terms of HEW and effective area. By de-focusing the beam the photons were spread out over a larger CCD area and pile-up effects could be reduced, and the total reﬂectivity could accurately be measured. This is shown in Figure 5. The solid line represents a model for incidence angles of 0.218◦ and 0.111◦ at parabola and hyperbola, respectively. Low-energy data have been taken with the ROSAT PSPC and the target source while the high-energy data points were obtained with the XMM-Newton EPIC-pn CCD camera and a continuum source (up to 50 keV). A different multilayer (Pt/C) coated Ni shell produced by INAF-OAB was calibrated at PANTER in a similar manner (the mirror shell was integrated and installed onto a jig which was put into the vacuum tube). The HEW was measured to be 39.4–53.8 arcsec in the 0.27–8.04 keV range, and 65.1 arcsec at 25 keV. The measured and modelled two-reﬂection reﬂectivities for this shell are displayed in Figure 6 [8].

4 Summary and conclusions We have shown that the PANTER X-ray Test Facility is not only well-suited for the calibration and characterisation of short focal length X-ray mirror performance parameters like effective Springer

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Fig. 6 Reﬂectivity R(parabola) × R(hyperbola) as function of energy for a Pt/C multilayer shell, with model (solid line) for incidence angles of 0.257◦ and 0.129◦ , respectively [8]

area and half-energy width in the “classical” soft X-ray range (up to 15 keV). It can very well also be used for longer focal lengths (here: 10 m) where the mirror sample will be put into the vacuum tube. Moreover, the XMM-Newton EPIC-pn CCD camera with the considerable quantum efﬁciency at energies as high as 50 keV combined with a high-ﬂux X-ray source allow the measurement of mirror shells at hard X-rays. Examples of such calibrations were multilayer coated nickel shells (W/Si, Pt/C). We are planning a further growth of the equipment at the PANTER facility and signiﬁcant improvements are projected in terms of spatial and spectral resolution of the focal plane instrumentation (as well as higher quantum efﬁciencies) up to 50 keV. Acknowledgements We would like to thank Bernd Aschenbach for critical reading and useful comments.

References 1. Giacconi, R., Gursky, H., Paolini, F.R., Rossi, B.B.: Evidence for X-rays from sources outside the solar system. Phys. Rev. Lett. 9, 439–443 (1962) 2. Aschenbach, B.: Design, construction, and performance of the Rosat high-resolution X-ray mirror assembly. Appl. Opt. 27, 1404–1413 (1988) 3. Aschenbach, B.: X-ray telescopes. Rep. Prog. Phys. 48, 579–629 (1985) 4. Ramsey, B.D., Austin, R.A., Decher, R.: Instrumentation for X-Ray Astronomy. Space Sci. Rev. 69, 139–204 (1994) 5. Wolter, H.: Spiegelsysteme streifenden Einfalls als abbildende Optiken f¨ur R¨ontgenstrahlen. Annalen der Physik, 10, 94–114 (1952) 6. VanSpeybroeck, L.P. Chase, R.C.: Design Parameters of Paraboloid-Hyperboloid Telescopes for X-ray Astronomy. Appl. Opt. 11, 440–445 (1972) 7. Aschenbach, B., Briel, U.G., Haberl, F., Br¨auninger, H., Burkert, W., Oppitz, A., Gondoin, P., Lumb, D.H.: Imaging performance of the XMM-Newton x-ray telescopes. Proc. SPIE, 4012, 731–739 (2000) 8. Pareschi, G., Basso, S., Citterio, O., Ghigo, M., Mazzoleni, F., Spiga, D., Burkert, W., Freyberg, M.J., Hartner, G.D., Conti, G., Mattaini, E., Grisoni, G., Valsecchi, G., Negri, B., Parodi, G., Marzorati, A., dell’Acqua, P.: Development of grazing-incidence multilayer mirrors by direct Ni electroforming replication: a status report. Proc. SPIE, 5900, 47–58 (2005) Springer

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9. Romaine, S.E., Pareschi, G., Gorenstein, P., Bruni, R.J., Basso, S., Citterio, O., Ghigo, M., Mazzoleni, F., Conti, G., Ramsey, B.D., Speegle, C., O’Dell, S.L., Gubarev, M.V., Engelhaupt, D.E., Burkert, W., Hartner, G.D., Freyberg, M.J.: Development of a prototype nickel optic for the Constellation-X hard-x-ray telescope: part III. Proc. SPIE, 5900, 225–231 (2005) 10. Br¨auninger, H., Burkert, W., Hartner, G.D., Citterio, O., Ghigo, M., Mazzoleni, F., Pareschi, G., Spiga, D.: Calibration of hard X-ray (15–50 keV) optics at the MPE test facility PANTER. Proc. SPIE, 5168, 283–293 (2004) 11. Pfeffermann, E., Briel, U.G., Hippmann, H., Kettenring, G., Metzner, G., Predehl, P., Reger, G., Stephan, K.H., Zombeck, M., Chappell, J., Murray, S.S.: The focal plane instrumentation of the ROSAT Telescope. Proc. SPIE, 733, 519–532 (1986) 12. Pfeffermann, E., Briel, U.G., Freyberg, M.J.: Design and in-orbit-performance of the position sensitive proportional counter onboard the X-ray astronomy satellite ROSAT. Nucl. Inst. Meth. Phys. Res. A, 515, 65–69 (2003) 13. Str¨uder, L., Briel, U.G., Dennerl, K., Hartmann, R., Kendziorra, E., Meidinger, N., Pfeffermann, E., Reppin, C., Aschenbach, B., Bornemann, W., Br¨auninger, H., Burkert, W., Elender, M., Freyberg, M.J., Haberl, F., Hartner, G.D., Heuschmann, F., Hippmann, H., Kastelic, E., Kemmer, S., Kettenring, G., Kink, W., Krause, N., M¨uller, S., Oppitz, A., Pietsch, W., Popp, M., Predehl, P., Read, A., Stephan, K.-H., St¨otter, D., Tr¨umper, J., Holl, P., Kemmer, J., Soltau, H., St¨otter, R., Weber, U., Weichert, U., von Zanthier, C., Carathanassis, D., Lutz, G., Richter, R.H., Solc, P., B¨ottcher, H., Kuster, M., Staubert, R., Abbey, A., Holland, A., Turner, M., Balasini, M., Bignami, G.F., La Palombara, N., Villa, G., Buttler, W., Gianini, F., Lain´e, D., Lumb, R., Dhez, P.: The European Photon Imaging Camera on XMM-Newton: The pn-CCD camera. Astron. Astroph. 365, L18–L26 (2001) 14. Meidinger, N., Bonerz, S., Eckhardt, R., Englhauser, J., Hartmann, R., Hasinger, G., Holl, P., Krause, N., Lutz, G., Richter, R., Soltau, H., Str¨uder, L., Tr¨umper, J.: First measurements with a frame store PN-CCD X-ray detector. Nucl. Inst. Meth. Phys. Res. A, 512, 341–349 (2003) 15. Predehl, P., Friedrich, P., Hasinger, G., Pietsch, W.: ROSITA. Astron. Nachr. 324, 128–131 (2003) 16. Parmar, A.N., Arnaud, M., Barcons, X., Bleeker, J.M., Hasinger, G., Inoue, H., Palumbo, G., Turner, M.J.L.: Science with XEUS: the X-Ray Evolving Universe Spectroscopy mission. Proc. SPIE, 5488, 388–393 (2004)

Springer

Exp Astron (2005) 20:413–420 DOI 10.1007/s10686-006-9049-y ORIGINAL ARTICLE

The Ferrara hard X-ray facility for testing/calibrating hard X-ray focusing telescopes Gianluca Loffredo · Filippo Frontera · Damiano Pellicciotta · Alessandro Pisa · Vito Carassiti · Stefano Chiozzi · Federico Evangelisti · Luca Landi · Michele Melchiorri · Stefano Squerzanti

Received: 31 January 2006 / Accepted: 18 May 2006 C Springer Science + Business Media B.V. 2006

Abstract We will report on the current conﬁguration of the X-ray facility of the University of Ferrara recently used to perform reﬂectivity tests of mosaic crystals and to calibrate the experiment JEM–X aboard Integral. The facility is now located in the technological campus of the University of Ferrara in a new building (named LARIX laboratory = LARge Italian X-ray facility) that includes a tunnel 100 m long with, on the sides, two large experimental rooms. The facility is being improved for determining the optical axis of mosaic crystals in Laue conﬁguration, for calibrating Laue lenses and hard X-ray mirror prototypes. Keywords Astronomy · Diffractometer · Instrumentation · X-ray

1. Introduction There is a general consensus that the next generation of hard X-ray (>10 keV) telescopes will include focusing optics. Only with these optics it is possible to improve, by orders of magnitude, the sensitivity of the direct-viewing instruments. The focusing techniques, with multilayers (E < 70 keV) or with mosaic crystals (E > 70 keV), are in an advanced stage of development [1–3]. Accurate test and calibration of these focusing telescopes are crucial in order to correctly derive their response function and thus to avoid systematic errors in the determination of spectral, temporal and energetic properties of the X-ray celestial sources. In order to perform these calibrations, monochromatic and parallel hard X-ray beams are desired. The beam

G. Loffredo () · D. Pellicciotta · A. Pisa Physics Department, University of Ferrara, via Saragat 1, I-44100, Ferrara, Italy V. Carassiti · S. Chiozzi · F. Evangelisti · L. Landi · M. Melchiorri · S. Squerzanti Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Ferrara, Italy F. Frontera IASF, CNR, Via Gobetti 101, Bologna, Italy Springer

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Fig. 1 Sketch (not to scale) of the recent conﬁguration of the Ferrara X-ray facility. From the left: the X-ray tube, the monochromator system, the sample holder and the detector holder. The X-ray beam travels partially within an evacuated tube and partially in a helium atmosphere.

energies have to cover the energy passband of these new telescopes (up to several hundreds of keV). Either for testing or calibrating these new telescopes, suitable hard X-ray facilities are needed. The Ferrara X-ray facility has already been used to, e.g., perform the ground calibration of the JEM-X (Joint European Monitor for X-rays) detectors on board the INTEGRAL satellite [4], reﬂectivity measurements of mosaic crystals (graphite [7], Cu (111) [5]) and non linearity tests of hard X-ray detectors ([8]). Here we summarize the past conﬁguration of the Ferrara X-ray facility and the current extention.

2. The X-ray facility and its applications The X-ray facility of the Ferrara University was initially motivated to test the PDS aboard BeppoSAX [6] in the range from 15 to 140 keV. The conﬁguration of the X-ray facility used for the most recent measurements/calibrations is shown, not to scale, in Fig. 1. The main components include two alternative X-ray tubes as sources of polychromatic X-ray beam (one working at lower energies (6–60 keV) and the other at higher energies (15–140 keV)), a hybrid vacuum-helium system with vacuum tubes and an helium box where a ﬁxed–exit double-crystal monochromator is installed, a system of collimators plus a Pb shield to stop the scattered radiation in the testing room, a six-axis table used as sample holder, and a four-axis table as detector holder. Currently the facility is being extended in the LARge Italian X-ray facility (LARIX), see Fig. 2. As the ﬁgure shows, LARIX includes two large experimental rooms and a 100 m long tunnel linking these rooms. The X-ray facility described in Fig. 1 is now positioned in the large experimental room. The sample holder, the detector holder and the holder which measures the position of the sample holder, can be movedon 10 m long rails as Figs. 3 and 4 Springer

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Fig. 2 Plan of LARIX. From the left: large experimental room where the facility is actually positioned, the tunnel and the second experimental room.

Fig. 3 Plan of the facility installed in the large experimental room of LARIX. The wall around the facility are Pb shield in order to devide the X-ray environment and the console room. On the optical table are positioned the X-ray tubes, the monochromator system, the collimation system. The sample holder and the detector holder can be moved on the rails.

show. The sample holder has 6 degrees of freedom, three translations and three rotations, the detector holder is improved with a rotation in addition to the three linear stages. We see in Fig. 4 the walls 2 meter high, made of Al + Pb which separate the X-ray equipment from the console room. This is equipped with three computers which manage the X-ray facility instrumentation. The X-ray tubes are shielded by a box made of a Pb layer 5 mm thick. An overhead travelling crane (1000 kg weight–bearing, 20 m long) is installed parallel to the 10 m long rails. The facility in the current conﬁguration can be used for calibrating position sensitive detectors, for a detailed study of the response function of hard X-ray detectors, e.g. the study of linearity discontinuities in X-ray detectors (e.g. [8], for hard X-ray reﬂectivity measurements (mosaic crystals, multilayers, etc) and calibration of hard X-ray optics and other applications, such as transparency measurements of complex materials. Springer

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Fig. 4 Picture of a part of the X-ray facility in the present conﬁguration. It shows the 10 m long rails hosting the sample holder, the detector holder and the other holder which read the position of the sample putted on the sample holder. We see also the Pb walls which divides the X-ray environment from the console room.

3. Main components of the X-ray facility A detailed description of the Ferrara X-ray facility has already been recently reported [9]. Here we summarize the main components. 3.1. X-ray sources Two X-ray tubes, with different operational voltage, are mounted onto an optical table and powered by independent high voltage supplies. One of the tubes, supplied by Philips (2001), is equipped with a Molybdenum anode, with its voltage which can be varied from 20 to 60 kV and the circulating current from 10 to 60 mA. The spot size is 5 × 5 mm2 . The other tube, supplied by Siemens (1990), is equipped with a Tungsten anode, with its voltage which can be set in the range from 40 to 140 kV and its current from 0.1 to 5 mA. The spot size is 5 × 5 mm2 . The X-ray output window of the ﬁrst tube is equivalent to a 0.3 mm thick Beryllium foil, while that of the second tube is equivalent to a 1.5 mm thick aluminium foil. The window thickness ﬁxes the low energy threshold of the X-ray beam: about 6 keV with the ﬁrst tube, 15 keV with the second. By means of manipulators both tubes can be moved up and down and translated along a direction perpendicular to the X-ray beam. Every movement is directed by remote control. 3.2. Monochromator The continuum spectrum provided by either X-ray tube is monochromatized with a double crystal diffractometer [10]. Its main feature is that it provides a ﬁxed-exit beam independently of the photon energy selected. Figure 5 shows the diffractometer scheme: the ﬁrst crystal (B) has the role of selecting the desired wavelength from the incident continuum beam, while the second crystal (D) re-directs the monochromatized radiation along a direction parallel to the incident beam [4]. Springer

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Fig. 5 Top of view of the Bragg-Bragg ﬁxed exit conﬁguration: A is the rotation axis, θin is the Bragg angle and h = 2 × p.

Fig. 6 Three dimensional view of the X-ray facility.

3.3. X-ray beam path environment The monochromator system is inside a sealed plexiglass box, where helium is pumped. The X-ray entrance and exit window of the helium box are made of polyethylene terephthalate (PET) 75 µm thick with a very high transparency at the operation energies. Outside the helium box, the X-ray beam travels in evacuated tubes (10−3 mbar) up to the position of the sample to be tested. 3.4. Sample and detector holders The sample holder can be accurately moved in three perpendicular directions (X, Y, Z) and rotated around vertical and the horizontal axes. An angular position accuracy of 3

can be achieved with a repeatability of 1

. The above movements are monitored with an external system of optical encoders. In this way the true position of the sample and the performances of the XYZ table can be accurately measured. The detector holder can be also accurately moved in three perpendicular directions (X, Y, Z) and is equipped with a rotation stage around the vertical. The resolution of this stage is 3.6

. Both the sample and the detector holders can translate on the 10 m long rails. Figure 6 shows a three dimensional view of the X-ray facility in the extended conﬁguration. 3.5. Collimation of X-ray beam A set of collimators (see Fig. 6) limits the divergence of the X-ray beam. The divergence of the beam inﬂuences the energy width of the monochromatized beam. Generally the aperture Springer

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55 50

Energy (keV)

45 40 35 30 25 20 15 10 2

3

4

5 6 7 Bragg angle (deg)

8

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Fig. 7 Energy measured of the X-ray beam as a function of the Bragg angle of the crystal No. 1 of the double–crystal monochromator. The expected energy, derived from the Bragg law, is also shown (reprinted from [4]).

of the collimators depends on the kind of experiment to be performed. For example, to radiate the entire cross section of our CZT detector, see below, which has an X-ray entrance window of 5 × 5 mm2 , when it is positioned to the end of long rails, the pinhole size of the second collimator needs to be at least 0.3 × 0.3 mm2 , otherwise the cross section of the beam is lower than the detector’s window. The ﬁrst collimator does not signiﬁcantly inﬂuence the size of the beam but inﬂuences the beam intensity. The second collimator is crucial to get the size of the spot needed for the speciﬁc applications. 3.6. Detectors A set of detectors is available for the X-ray facility. They include three NaI(Tl) scintillators, one of which is an imager, a Cadmium Zinc Telluride (CZT) detector, a high purity germanium detector (HPGe), and a large area imaging detector. The NaI(Tl) imager has a square shape with a side of 42 mm and a thickness of 3 mm. The crystal is viewed by a position sensitive PMT. An PC-based interface running LabView provides a user-friendly environment for using this X-ray imager for locating the X-ray beam and other user applications. Details on the detector conﬁguration can be found elsewhere ([11], [5]). The CZT X-ray detector, Peltier–cooled to 250 K, is used to monitor the intensity and the spectrum of the pencil beam incident on the sample to be tested. It shows a very good energy resolution (0.94 keV at 60 keV). Its cross section is 5 × 5 mm2 , its thickness 2 mm, while its X-ray entrance window is made of a 0.25 mm thickness beryllium layer. The high purity germanium detector (HPGe), cooled with liquid nitrogen, has a surface area of about 78.5 cm2 , a thickness of 13 mm and an X-ray entrance window of 0.254 mm Beryllium thickness. This conﬁguration gives an high detection efﬁciency to the X-rays provided by the facility. The energy resolution is about 0.44% at 122 keV. The large area imaging detector is an X-ray Image Intensiﬁer equipped with a CCD camera with 1000 × 1000 pixels and a digital video output. The X-ray entrance window has a 215 mm diameter. The X-ray detection efﬁciency is about 65% at 59.5 keV and the position resolution is 0.2 mm. In the present conﬁguration the X-ray Image Intensiﬁer and the high Springer

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Fig. 8 Reﬂectivity curve of a Cu (111) mosaic crystal sample in transmission conﬁguration (Laue geometry) at about 90 keV. The best ﬁt curve and parameters of the model function to the data are also shown: θ0 is the Bragg angle, FWHM is the full width half maximum of the reﬂectivity curve and t0 is the average thickness of the microcrystals of the mosaic crystal (reprinted from [4]).

Fig. 9 Experimental setup in determining the optical axis of the copper tiles. In (a) the incident beam is diffracted with the angle α1 = θ + δ rispect to the normal n. By rotating of π the crystal around n, (b), the angle becames α2 = θ − δ.

purity germanium detector (HPGe) are positioned on the detector holder and can be translated and rotated simultaneously. An example of facility calibration with the CZT detector is shown in Fig. 7.

4. Some example of recent applications of the X-ray facility After the ground calibration of the JEM-X detectors, as mentioned before [4], the facility in the current conﬁguration has been used for reﬂectivity measurements of crystal samples of Cu (111) in Laue conﬁguration within the development project of a hard X-ray focusing optics [5]. The centroid energy of the monochromatized photons measured with the CZT detector is compared with the energy expected from the Bragg law (see Fig. 7). An example of reﬂectivity measurement of a mosaic crystal sample of Cu (111) expected to be used as reﬂecting material in a Laue lens [5] under development is shown in Fig. 8. In the context of the development project of a Laue lens, a key task is the measurement of the optical axis of mosaic crystals tiles of Cu (111) used for the lens and provided by Springer

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Fig. 10 Set up for the crystal axis determination. The X-ray Imager Intensiﬁer is able to resolve the distance x which is quite 2δL

the Institute Laue Langevin of Grenoble. The optical axis of the Cu (111) tiles is required to be determined with an accuracy better than 10 arcsec. As ﬁgs. 9 show the angle between the normal to the crystal’s surface, n, to the average orientation of the crystal’s plane is δ and the angle between the diffracted beam to n is α. If δ = 0 then α = θ where θ is the angle between n and the incident beam. By rotating of π the crystal around n, the geometry shows two angles between n and the diffracted beam: α1 = θ + δ, Fig. 9(a), and α2 = θ − δ, Fig. 9(b). As Fig. 10 shows, if the distance from the crystal to the X-ray Image Intensiﬁer is L, we can measure the distance x between the focal spot of the beam diffracted with the angle α1 from that diffracted with the angle α2 . Immediately we can see: x ≈ δ. 2L

(1)

The X-ray Image Intensiﬁer permit us to achieve 0.2 mm of spatial resolution and the rails to change the distance from the cryslal up to the X-ray detector. The maximum distance L from the crystal up to the X-ray Image Intensiﬁer is 6 m and it permit us to achieve δ ≈ 4 arcsec. References 1. Pareschi, G., et al.: Astronomical soft X-ray mirrors reﬂectivity enhancement by multilayer coatings with carbon overcoating, SPIE, 5488 (2004) 2. Pisa, A., et al.: Development status of a Laue lens for high energy X-rays (≥ 60 keV), Proc. SPIE 5900, 350–359 (2005) 3. von Ballmoos, P., et al.: The MAX mission: focusing on high sensitivity gamma-ray spectroscopy, Proceedings of the 5th INTEGRAL Workshop, Munich 16–20 February 2004, ESA SP-552 (2004) 4. Loffredo, G., et al.: X-ray facility for the ground calibration of the X-ray monitor JEM-X on board INTEGRAL, A&A 411, L239 (2003) 5. Pellicciotta, D., et al.: Laue Lens Development for Hard X-rays (>60 keV), IEEE Trans. on Nucl. Sci., (2006) (in press) 6. Frontera, F., et al.: Hard x-ray (>15 keV) facility for calibration of Space Astronomy Experiments, IEEE TNS 40, 874 (1993) 7. Frontera, F., et al.: Hard X-ray imaging via crystal diffraction: ﬁrst results of reﬂectivity measurements, Proc. SPIE 1549, 113–119 (1991) 8. Zavattini, G., et al.: Linearity discontinuities in Xe–ﬁlled X-ray microstrip detectors, Nucl. Instr. & Meth. A401, 206 (1997) 9. Loffredo, G., et al.: The X-ray facility of the Physics Department of the Ferrara University, Experimental Astronomy 18, 1–11 (2004) 10. Mills, D.M. & King, M.T. A tunable, ﬁxed–exit, monolithic X-ray monochromator for synchrotron radiation sources, Nucl. Inst. and Meth. 208, 341 (1983) 11. Poulsen, J.M., Verbeni, R., and Frontera, F. Position–sensitive scintillator detector for hard X-rays, Nucl Instr. & Meth. A310, 398–402 (1991) Springer

Exp Astron (2005) 20:421–434 DOI 10.1007/s10686-006-9060-3 ORIGINAL ARTICLE

SIMBOL-X: An hard X-ray formation ﬂying mission Rodolphe Cl´edassou · Philippe Ferrando

Received: 20 January 2006 / Accepted: 13 July 2006 C Springer Science + Business Media B.V. 2006

Abstract In 2004 and 2005 CNES decided to perform phase 0 studies on 4 scientiﬁc missions: ASPICS (Solar physics), MAX (γ -rays Laue lens), PEGASE (hot Jupiter study by an interferometer in the 2 µm to 4.5 µm range) and SIMBOL-X (hard X-rays telescope). This last mission had already undergone a feasibility study in 2003 (ref. [4]), however a complementary study was necessary to take into account the possibilities of increasing the payload mass allowance, as well as the developments in the payload design and science goals (see ref. [1]). The output of this new detailed study is described hereafter.

1. SIMBOL-X scientiﬁc mission The SIMBOL-X project is a high energy new generation telescope covering by a single instrument a continuous energy range starting at classical X-rays and extending to hard X-rays ie from 0.5 to 80 keV. It is using in this ﬁeld a focalizing payload which until now was only used at energy below 10 keV, via the construction of a telescope distributed on two satellites ﬂying in formation. SIMBOL-X permits a gain of two orders of magnitude in sensibility and spatial resolution in comparison to state of the art hard X-rays instruments. The energy range targeted by SIMBOL-X is the one where thermal emissions leave place to harder emissions which are due to particles acceleration or which are due to accretion phenomena on a massive central object. The study of these phenomena is the heart of SIMBOL-X scientiﬁc objectives.

R. Cl´edassou () Centre National d’Etudes Spatiales, 18 Avenue Edouard Belin, 31041 Toulouse Cedex, France P. Ferrando UMR 7164, APC & DSM/DAPNIA/Service d’Astrophysique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France Springer

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1.1. Why hard-X rays? Non thermal emissions in X and γ rays are unique signatures needed to answer fundamental questions in modem astrophysics: – How works the dynamics of the universe at all scales? From star formation to cosmological large structure formation, this is driven by accretion power, particularly on Black Holes, and violent non thermal phenomena (as jets) – How good are our physics laws in extreme conditions, of gravity, pressure, magnetic ﬁeld? Do we need new physics? – How and where are accelerated the cosmic rays at the highest energies?

2. SIMBOL-X mission SIMBOL-X orbit has been revisited during the 2005 study. It has permitted to deﬁne an orbit giving more mass allowance at launch, as well as a very good ﬂexibility in the mission scheduling. In particular the mass impact linked to the major drivers (redundancy, collimator) revisit have been absorbed and left intact a comfortable system margin (>30%). This mission should allow for observations during 2 years (cumulated observations). It means that the total space system life duration would be about 3 years (taking into account some months for “In ﬂight formation acquisition, reacquisition and checking” and a provision for servicing operations and accidental safe mode). Scientiﬁc observations have to be performed outside the Van Allen belts (no instrument background noise): that is to say an altitude greater than 73 000 km. Nevertheless it has been accepted to pass very high in these belts once every week. The telescope is implemented with a “mirror spacecraft” and “detector spacecraft” in formation ﬂying. Optimizing the global resources of both spacecrafts led then to select a scientiﬁc orbit with a 44 000 km perigee altitude/a 253 000 km apogee altitude/a 7 sidereal days period /Low initial inclination. This orbit is subject to signiﬁcant luni solar effect. It has been chosen to give 90% time above 73 000 km which maximizes the science return. The satellites V is around 500 m/s and can be achieved with a classical and robust hydrazine system. The daily visibility are ∼12 hours per station with a maximum of 2 hours gap. At perigee the visibility is permanent (24 hours) for the chosen station. Springer

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During mission there is no need to maintain exactly the orbit parameters. The important point is to keep the correct orbit period and the phasing with the ground segment to facilitate the operations with the Ground at perigee pass (maximization of telemetry rate). In that perspective roughly one manoeuvre per month is expected to maintain the semi-major axis. The result is that orbit parameters evolution are constrained by luni-solar effects and the perigee will increase to ∼70 000 km after 2 years due to lunar effects combined to semi major axis conservation (see below).

Typical operations on such an orbit consists in performing science during 6 days (out of perigee) and to use permanent perigee visibility to download the bigger part of the telemetry. Outside perigee a daily contact of one to two hours is sufﬁcient for Status of Health and/or monitoring of the formation repointing to a new target.

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The distributed instrument (“mirror spacecraft” and “detector spacecraft”) would be able to observe a great variety of astrophysical sources. Depending on them the observation time varies a lot. As an example a bright source like the “Crab” one needs an observation time in the range of an hour, on the contrary a faint source or a deep ﬁeld observation could need several days of continuous observation. In the satellite design 500 observations per year have been taken into account. The following schemes are giving examples of operation for different sources.

Example 1. Several bright sources on one day (22 ks each; >1m Crab)

Example 2. One weak source (79 ks; <50µ Crab)

Example 3. Deep field (∼1 Ms) Springer

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3. GNC & formation ﬂying constraints On the pre-selected orbit the conditions are very favourable for the formation ﬂying as it can be seen on the following scheme:

Variation of the gravity gradient on an orbit period along the different axis The solar pressure is the main contributor to the perturbations except around the perigee. Nevertheless, gravity gradient perturbations being low, the system will be designed to keep formation around perigee and thus avoid to break/reconstruct itself once per orbit. The instrument ﬁeld of view is equal to 6 arc min in the design studied in phase 0. The angular resolution must be better than 20 arc sec and the telescope line of sight measurement accuracy better than 3 arc sec. This last requirement is rather demanding. The mirror attitude control accuracy shall be better than 10 arc sec during scientiﬁc observation. The following summarizes the main constraints due to formation ﬂying: Relative positioning: – lateral/L.O.S.:+/− 1 cm – longitudinal: +/− 10 cm – lateral position knowledge: 0.5 mm (or 3

LOS) Constraint on inertial and relative metrology lateral sensor + star tracker with 1 arc sec accuracy range Springer

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Mirror attitude control: – Pointing: 10 arc sec – Stability: no constraint Detector attitude control: – Pointing: 5 arc min – Stability: 5 arc min In the following paragraph, we summarize the main choice relative to the GNC functions. – G.N.C. concept: The selected philosophy for Formation Guidance Navigation and Control consists in having all the functions on one spacecraft (the detector satellite). Then, the “detector spacecraft” is position controlled with respect to the “mirror spacecraft”. This last one stands on its natural orbit and performs the ﬁne pointing. The relative position is measured with respect to the “mirror spacecraft” reference frame. This ensures good performances by decoupling position and ﬁne attitude control. Moreover, this concept simpliﬁes in ﬂight operations and improves system safety. – Metrology system: For the deployment and saﬁng phases, a RF localization system based on GPS metrology constitutes the baseline. Each spacecraft is equipped with a Rx/Tx terminal (Receiver/Transmitter) plus a set of antennae and the 3D position is reconstructed from the range and line of sight measurements. This system permits moreover to fulﬁl the observation phases requirements for the relative longitudinal position knowledge. For observation phases, the requirement of relative position knowledge is driving the use of a lateral sensor, including a laser source, which measures the line of sight of the beam reﬂected by a corner cube with a 1

precision. This sensor is installed on the “detector spacecraft”.

Formation guidance is located by choice on the detector spacecraft which directly communicates with the Ground Station. This strategy is still to be conﬁrmed but by this way during routine science phases the formation could be seen by the Ground Segment as a Springer

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“single satellite”. For non nominal phases or for commissioning or positioning, each satellite is independent and communicates directly with the Ground (see ﬁgure below):

Then to summarize, 2 communications modes are foreseen:

r Housekeeping mode (TC + HKTM + ranging) r TMCU download (TC + TM high rate, detector only). The access to the mirror will be done through the inter satellite link (ISL) in nominal phase. There will be direct access to the mirror (parallel communications) for:

r Cruise & positioning r Commissioning r Emergency Considering all this a list of equipment set can be given for each satellite:

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There seems to be no critical technology in metrology (currently in development or R&D studies) and propulsion (already available).

4. Satellites conﬁguration Two main topics are sizing for the satellites conﬁgurations:

– The observations constraints (as described below), – The payload protection against the X-ray background thanks to a collimator. The “distributed telescope” L.O.S. (X-axis on Figure 5) shall be “quasiorthogonal”(+/−20◦ ) to the Sun direction. This quasi-inertial pointing allows to have ﬁxed solar generators and then simpliﬁes “mirror spacecraft” and “detector spacecraft” architecture. This hypothesis allows access to ∼35% of the entire sky at any given time (excluding short eclipses by the Earth). Thus, the entire sky coverage could be performed within 4, 5 months:

As described in the here after scheme, the detector satellite focal plane shall be protected against the satellite nuclear noise and the deep sky X-ray background, in such a way that it sees only the targeted object signal focalized by the mirror module. Springer

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The satellite nuclear noise will be measured and taken into account thanks to an active anticoincidence system which surrounds the detection payload.

For the deep sky X-ray background a shielded collimator is foreseen. A sharing was to be done on the protections between both satellites. The “mirror satellite” can use a shielded sky screen which blocks the X-rays and the “detector satellite” uses a collimator. In the hypothesis where no sky screen equips the “mirror satellite”, the collimator is very long and heavy (several meters). The sky screen permits to reduce the collimator lengths and a good balance was found with a collimator of roughly 1,5 meter and a sky screen of about 3 meters diameter. The following scheme shows that an optimum in mass exists for the sharing of both equipment among the two satellites.

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Given that several options can be pursued to implement the detector payload (as shown below)

Depending on the one chosen, several reference planes are needed to mount the sensors needed to perform the formation ﬂying and relatively to the payload. To optimize the global pointing accuracy management, GNC sensors and detection plan must be nearby one to each other as much as possible to avoid all possible structural deformations. This is why the solution with 3 planes has been rejected and only two options remained opened. The following ﬁgures present the “detector satellite” for a payload mounted on top of it. In that case the interfaces between the payload and the platform seems less intricate. On another point, the satellite is higher and ISL antennas need to be mounted on top of the collimator. Springer

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On the following scheme showing details of the propulsion system, the collimator crosses the whole platform.

The “mirror satellite” is carrying the mirror module. As it is already naturally quite large, the implementation of the sky screen can be done with a small mass impact (see ﬁgure below). Springer

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The mirror module itself consists in a set of roughly 100 Wolter-I mirror shells which are embedded and structurally maintained thanks to two spiders one at entrance and one at exit. For this two apertures a very thin kapton ﬁlm is foreseen to regulate homogeneously the shells thermally and reduces dramatically the power needs. Such ﬁlms obviously reduce the X-ray transmission on the low energy side, but it is anticipated that transmissions of at least 20% around 1 keV can be achieved, resulting in negligible impact of the performances for the science objectives of Simbol-X. An X-bafﬂes at entrance completes the module.

Launch conﬁguration: There are several possibilities for this, the two extremes are: – 2 independent satellites with their own interface and separated by the new Soyouz SYLDA. Then each of them performs individually the positioning on the scientiﬁc orbit. – Two satellites attached during launch, cruise and positioning maneuvers (some weeks). The 1st solution is the most mass constrained. It has also the advantage to maximize the uncoupling of the satellites development. In addition the interfaces are simpler. The 2nd solution is the best for mass and permits to minimize the propulsion on the carried satellite thus allowing the reuse of existing platform (mostly structure, thermal & propulsion subsystem). Even if it has mass penalty and if the launch cost would be slightly greater. (we have to note that the dispenser is currently under study by STARSEM for development, independent from the project). On another hand the carrying satellite structural design is importantly impacted (composite would be 5 meters high !) and the satellite development & interfaces are intricate (which should be the source of over cost). Finally, we have to consider that the composite will be really a third satellite with its own modes during quite a long time (positioning phase) and this is another complexity increase of the mission. Springer

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Due to those considerations the most favoured option is the “independent satellites” one. An intermediate solution (if mass were to be a problem), would be to couple the satellites during launch (to avoid the SYLDA) and to separate them at injection by Soyouz. Springer

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5. Conclusions SIMBOL-X is a “permanent observatory” which propose a great number of observations (∼500 per year) and a great variety of these sources. The short duration of the observation times (less than a day in general) authorizes a great scheduling ﬂexibility or a short term redeﬁnition of the objectives. The substantial spacecraft mass margins allows to envisage several mirror options (with adapted focal between 20 m and 30 m): – Mirror thickness similar to XMM mirror, – Thinner mirrors with Platinum coating, – Mirrors with multilayer These options shall have to be studied during phase A and the choice conﬁrmed at the end of this one. The decrease of the transmission at low energy (20% at 1,5 keV) should permit to decrease the necessary resources for the mirror module thermal control (addition of insulating layers at the entrance & exit), it is an important simpliﬁcation with respect to XMM constraints. The necessity of including a collimator in front of the detector (perturbations due to diffuse X-ray emission), led to deep modiﬁcations of the detector satellite conﬁguration and at a lower level of the mirror satellite one. Nevertheless, a broad space for optimization of the satellite conﬁgurations exists. In addition, a fairly detailed deﬁnition of the detector payload and a strong technical support by CEA allowed to identify suitably the constraints imposed by this one on the space segment. The result of this is that the mission and space system are, then, strong & robust (detection function). Acknowledgments We would particularly like to thank Mrs. Paul Duchon & Emmanuel Hinglais (CNES Toulouse) and all the team in CNES and CEA and of the Observatory of Brera which participated to the 2005 phase 0 study for SIMBOL-X.

References 1. SIMBOL-X.: A formation ﬂying mission for hard X-rays astrophysics. P. Ferrando, et al., SPIE (2005) 2. Ferrando, P. et al.: SIMBOL-X, a new generation X-ray telescope in the 0.5–50 keV range. 1st Formation Flying International Symposium. Toulouse, 29–31 October 2002 and SIMBOL-X.: A new generation hard X-ray telescope. Proceeding SPIE 5168, 65–76 (2004) 3. Delpech, M., Fourcade, J.: GNC system design for a new concept of X-Ray distributed telescope. 2nd Formation Flying International Symposium. Washington-DC 14–16 September (2004) 4. Duchon, P., Mercier, K. et al.: SIMBOL-X, a formation ﬂying for high energy astrophysics mission. 2nd Formation Flying International Symposium. Washington-DC 14–16 September (2004)

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Exp Astron (2005) 20:435–445 DOI 10.1007/s10686-005-9020-3

Distributed space segment for high energy astrophysics: Similarities and specificites Emmanuel Hinglais (CNES)

Received: 10 November 2005 / Accepted: 21 December 2005 C Springer Science + Business Media B.V. 2006

Abstract This paper analyses two height energy astrophysics missions, MAX and SIMBOLX, which have been studied in CNES in the frame of a large formation ﬂying study program. It is particularly interesting to notice that the scientiﬁc speciﬁcations of two different missions lead to the same engineering solutions for the whole mission aspects and then advocate for a similar space segment architecture and re-use of common elements, thus allowing potential cost reductions for a second mission. In deed, the same level of data to download and a similar signal-to-noise ratio requirements leads to the same orbit and communications system, the same level of pointing precision and distance inter satellites lead to the same formation ﬂying Guidance Navigation and Command (GNC) architecture. At the end, the same level of mass and thermal constraints leads to the same range of platform and the same propulsion systems and ﬁnally to the same launcher. Keywords Formation ﬂying: Height energy astrophysics missions · MAX · SIMBOL-X

1. Introduction During the last two years, the CNES pre projects structure, called PASO, studied 4 formationﬂying missions for astrophysics including two of them for High-energy astrophysics, MAX and SIMBOL-X. They act as telescopes for high-energy observations distributed on two satellites in formation ﬂying. One satellite is a collector focusing photons on the detector plan of the second satellite. From a cost point of view, these two missions are considered as medium class missions and the cost must remained a major driver. Based on this background and seen from a pure technical point of view coming out an analysis of the scientiﬁc need, this paper aims to demonstrate that these two last present a lot of similarities which could lead to a common space segment architecture.

E. Hinglais (CNES) CNES Centre National d’ Etudes Spatiales, 18 Avenue Edouard Belin, 31401 Toulouse Cedex 9, France e-mail: [email protected] Springer

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For this class of mission, the number of targets and the exposures lead to two years of observation time which means 2.5 years of mission that takes into account the commissioning phase which can be quite long for a ﬁrst formation ﬂying mission. Another characteristic of this mission class is the amount of scientiﬁc data to download. The data volume is about 600 kbit/day on average during the mission including the house keeping data for both satellites. Due to these commonalities and because an interesting orbit was found for both missions, the operability of the system can be the same in both cases. For the formation ﬂying aspect, the same level of technology is mandatory because the relative and absolute pointing and knowledge precision is very similar. In these types of missions, the values are in a medium range of difﬁculties. 1 cm in lateral and 10 cm in longitudinal for the relative pointing. 10 arc sec for the Focuser satellite and 1◦ for the Detector satellite for the absolute pointing. Even if the payloads are very speciﬁc, they operate by following a similar method which uses a focusing principle in quite high energy bands. In both cases, the focusing system requests a very good dimensional stability over mounting quality. Particularly, thermo elastic effects have to be very well mastered and it appears that, in both cases, the thermal stability remains in the same range. The detection system temperature levels are not in the same range, but despite the speciﬁcity of each one, the technical solutions are very similar. At the end both payloads lead to the same engineering solution.

2. Orbit Because in these ranges of energy the number of photons is quite low, the detection systems must be very sensitive and very well protected from noise. In that high energy domain, an important condition to have a low level of noise on the detection plan is to be very high above the Earth radiation belts. A good inferior limit is 70 000 Km in altitude. In any cases, it covers the Gamma band need and is very comfortable for the X band. Moreover a good thermal stability is needed which advocates too for a high orbit far from the Earth albedo thermal perturbations. At the end, a need to limit as much as possible the gravity gradient is important for the formation ﬂying control propellant budget. All these points could make it evident to choose a Lagrange second point orbit. With a Soyuz launcher, this last is reachable and then seems very attractive for all the above mentioned reasons. From a practical point of view, this scenario presents complexity aspects which lead to a very expensive implementation compared to other possible options. This orbit demands a long cruise phase of about four months and an additional positioning phase of about 2 months on a Lissajous orbit. During these phases, different solutions can be chosen to manage the formation of the two satellites. The ﬁrst one consists in an independent ﬂying which implies a speciﬁc management up to 1.5 million Km of the two very close satellites and a ﬁrst setting formation manoeuvre at this distance. The second one, at the opposite, consists in a setting formation just after launch and before the launcher injection corrections which must be operated very early. After this last, the formation ﬂying management has to be guaranteed up to the ﬁnal orbit. Because this orbit is unstable, a very precise control is needed all along the mission duration. At the end, even if the Lagrange point begins to be well known and used, the operational conditions for the ﬁrst formation ﬂying missions bring additional complications which remain risky. On top of that, the large distance implies a complete X band communications Springer

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system with at least a mean gain antenna which demands an Earth pointing to download the scientiﬁc data.

Another orbit solution could be a circular one above 70 000 Km with an altitude which allows a good phasing with a ground station. Unfortunately, this last has the disadvantage of being very energetic and then of requiring a bigger launcher or an important additional boost stage. In the end the solution which was found as a good compromise for all these sort of missions is a High Elliptical Orbit (HEO).

This last was chosen for the following reasons. First of all, 90% of the time is spent over 70 000 Km which is sufﬁcient for the scientiﬁc observation need. Next because it is a low energetic orbit compared to the circular one. Moreover, it is easy to ﬁnd a phasing with ground station, and it is easy to operate. Then at last, the orbit presented on the above ﬁgure presents a lot of advantages allowing a launch with Soyuz from Kourou. It can be noticed that the launcher performance, in term of launched mass, is the same for a Lagrange orbit as for an inclination of 45◦ for the 7 days HEO.

3. Communications This last orbit does not request X band transponder as already presented for a L2 orbit and an S band system, much cheaper, is sufﬁcient. The orbit control is limited to the management of the perigee above the ground station which demands some few m/s of V on the two and a half years of the mission. under these conditions, the spacecraft doesn’t need any speciﬁc Springer

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pointing for communications because the budget link allows omni directional antennas on board and a standard 15 m antenna ground station. Geometrically speaking, the station visibility is 24 h every seven days at perigee above the station with a high rate of communication capability and about 12 h every day with a quite low rate of communication. For both missions, thanks to the focusing concept, the detector of the scientiﬁc payload is quite small. An important consequence is that the amount of data to download is reasonable and requests only a small window in the station visibility capability, about the ﬁfth in average. So the communications don’t imply an important budget. Another advantage can be pointed out. On one hand, only the Detector satellite has scientiﬁc data to download. On the other hand, the two satellites can exchange house keeping data through a speciﬁc Inter Satellite Link, used at the base for the relative metrology. At last, only one satellite-ground link can be used in nominal operational mode for all sorts of data coming from both satellites. Of course, the remote controls reach up each satellite through the same system. This capability is an important simpliﬁcation factor for the ground station management. Of course again, for the in orbit setting, the coast phase and the survival modes, it is possible to communicate independently on each satellite.

4. Propulsion Different manoeuvres request a propulsion system on each satellite. It concerns the satellites positioning and the orbit maintenance, mainly for the ground station phasing. It also concerns the setting formation and the anti-collisions manoeuvres. All these operations need abound 500 m/s of V and then a reasonable Isp to avoid too much propellant mass on board. Finally, each satellite must have a Hydrazine propulsion system at least. On the other hand, the formation ﬂying control requests a very small Minimum Impulse Bit (MIB) in the range 0.5 to 1 mNs. Except for the Field Emission Electric Propulsion (Feep) technology which is still under development and which is complicated and expensive, only a cold Nitrogen micro thrust propulsion system allows this performance. In the chosen formation ﬂying concept as presented farther, only the detector satellite needs this low MIB. Then only this last one needs such a propulsion system in addition to the Hydrazine one. It can be noticed than a Hydrazine propulsion system has an Isp of 220s when a Nitrogen one is only 60s, but for this last only a few tens of m/s of V are needed. The propulsion system architecture is quite simple and standard for the Focuser satellite as presented on the following ﬁgure: Springer

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Here, a pressurized system is presented to save room on board but not mandatory and a blow down system could work for this application too. Concerning the detector satellite for which 2 different systems must be implemented, a combined one as presented on the following ﬁgure allows saving room and mass.

In the ﬁgure above, the Nitrogen is used to pressurize the Hydrazine system to save room and it is used too as cold gas for the low thrust propulsion system. Springer

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5. Guidance Navigation and Control for formation ﬂying Here the Formation Flying means autonomous relative ﬂying. The chosen concept is basically to leave the Focuser satellite in a free ﬂying conﬁguration on its natural orbit. Its only job is to point with 10 arc second of precision the target to be observed. The Detector satellite is then on a forced orbit and has in charge the relative positioning between both satellites in a range of 1cm in lateral in relation to the line of sight and 10cm in longitudinal. The pointing attitude itself requests only 1◦ of precision. Typically for these sorts of missions, these levels are needed for a distance in a range of 100m between satellites. To achieve these values, the GNC algorithm on board needs sensors and actuators as deﬁned below. Sensors are split into two different stages acting in series depending on the precision range. A ﬁrst one, based on a radio electric local GPS principle called RF metrology system, allows a precision level close to 1cm and 1◦ of relative precision between both satellites for 3 antennas on a 1m base on the ﬁrst satellite and the second satellite at 100 m far away. The second stage, uses lateral and longitudinal optical sensors, starts from that location precision level and allows gaining more than one order of magnitude in precision. The longitudinal sensor, based on a laser beam, once reﬂected on the second satellite, allows a very high precision depending of the wavelength. The lateral sensor acts as a star tracker watching three diodes mounted on the other satellite. A ﬁlter allows discriminating these diodes from stars which could appear in the ﬁeld of view. These metrology optical systems allow performances in the range of the tenth of millimetre and the arc second, which is largely in the need of astrophysics accuracy range. In the MAX and SIMBOL-X cases, the longitudinal requested precision do not implies an optical sensor. Over the relative positioning, a 1 arc second precision range star tracker is needed to master the last degrees of freedom. It can be noticed that the radio frequency system, depending on the antenna net on board of the two satellites, allows having distance information, and attitude information in restrictive cases, with a low precision up to 10 km at least. Moreover, this system acts as a real Inter Satellite Link (ISL) allowing a data output of about 10 Kbit/s at 10 km and then is used for general communications as explained in the communications paragraph. The actuators are only reaction wheels on the Focuser satellite as only an attitude control is requested. On the Detector satellite, the low thrust propulsion system, using a set of 8 or 12 thrusters, is able to control independently the 6 degrees of freedom and then, is the only one requested system. The following ﬁgures summarize the principle:

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It can be noticed that all the equipments described above are the ones requested for the formation ﬂying control. For the general manoeuvres, classical equipments are used and not deﬁned in this paper. 6. Speciﬁcity of the payloads for both missions Even if the payloads of MAX and SIMBOL-X are of course very different in the concept as they are for the speciﬁcations, it is however remarkable to notice that the engineering technical solutions and their implementing are the same. Concerning the detection systems, even if the operational temperature is really not the same between both missions, it was shown that it is possible to design a passive thermal cooling down system guaranteeing the requested level of cold and thermal stability. For that, it is taken advantage of the light mass, light volume and light dissipation of the cold part of the detection chain. It is also taken advantage of the capability of the satellite to keep a face positioned towards deep space at any time.

Of course, the level of complexity is much higher for the MAX cryogenic system and it is treated with a more complex multi stages cryostat.

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Concerning the focusing system on both satellites, here particularly, the principle is radically different between them, but the basic question is the same. How to guarantee the requested dimensional stability during long exposures. In both cases it was shown that, once the mounting defects are managed, the major contributor is the in orbit thermo elastic effect. The XMM background experience allows to consider that the internal thermal gradients in the mirror module have to stay in a range of 2◦ at a level of 20 ◦ C. For the SIMBOL-X mirror module, the same values are kept in the present study.

Compared to XMM, the thermal control presents two speciﬁcities. On one hand the module is open toward the deep space on its both sides and then much more demanding in energy to reach the thermal balance. But on the other hand, it is possible to mask the apertures with a thin kapton layer because the observed energy band is signiﬁcantly higher than for XMM and then very little degraded by this obstacle: 20% less sensitivity at 1 KeV when it is considered as the early beginning of the interesting band. In a general way, except for the apertures and the mechanical interface, the whole system has to be thermally insulated to be controllable. The mechanical interface has to be speciﬁcally thermalized to avoid ﬂuxes which generate gradients. Over the thin layer already mentioned, the external radiative ﬂuxes must be controlled with particular bafﬂes which are themselves thermalized. In the end, a design as presented on the following ﬁgure seems to be acceptable.

Because the Laue Lens concept of MAX is new, it was necessary to look at its dimensional sensitivity to internal thermal gradients. On the other hand, a cocooning with Multi Layer Insulators (MLI), which can guarantee passively a natural internal balance, is much easier to implement in this case because the gamma energy band does not interact with these blankets. Moreover, the mechanical interface is here realised by using structural and isolator points which are easy to thermalize. Despite the fact that the Sun can be seen in any direction, this basic thermal protection guarantees natural internal gradients in the range of 3◦ maximum. Springer

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In parallel, scientists have deﬁned the precision requested for the crystals alignment. Basically it is deﬁned as 10 arc seconds of depointing limit for each crystal from the line of sight. From this primitive value, deformation limits are deﬁned for the global lens as 2 mm in plan and 0.1 mm out of plan. In order to assess the importance of this requirement, different temperature gradients were imposed directly to the CeSic lens structure inside the cocoon to look for the acceptable limits behind the speciﬁcations. These gradients were applied by taking into account different Sun attitudes and different mechanical interface points behaviour.

The results show that, with regard to the global deformations, the speciﬁcation limits can’t be reached because the passive system is sufﬁcient to limit the gradient under the computed values. On the other hand, a gradient of 2◦ is sufﬁcient to reach the individual alignment limit. Because this value is smaller than the value guaranteed by the simple cocoon, it will be necessary to install an additional system directly on the structure. But this additional thermal system is very simple because it’s composed of a few heaters and thermistors at any places because there is no restriction unlike what there is on the SIMBOL-X mirrors. At last, the level of temperature at 20◦ C is not far from a natural body temperature under MLI in space and seeing the Sun. This level of temperature is the same as on ground during integration and in the same range as the platform temperature which allows to naturally limit the thermal ﬂuxes at the interface points. Moreover, it can be noticed that the level of mass and energy are in the same range for both payloads.

7. Architecture considerations All sub-systems have not been reviewing here. In deed, if all ones seen above can be identical, automatically the other one as power and avionics for instance will be the same too.When the Springer

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different sub-systems and the payloads are deﬁned, some architectural considerations can be highlighted. First of all, the degree of reliability of the global system must be in accordance with the global cost of the mission. Such a system is quite signiﬁcant and complex because it is composed of two satellites, a formation ﬂying package and the associated operations, and an important and innovative scientiﬁc payload. At the end the global cost is high and the level of reliability must be high too. With this consideration, the base to be considered is “no single point failure”. It means a complete level of redundancy for all equipment which is quite heavy. Even then, some electronics equipment can have internal redundant boards as for the On Board Computer for instance. Typically for the GNC sub-system, four reaction wheels are installed when three are nominally needed. On the propulsion system, the tanks are not doubled of course. The command-control aspect is new for this sort of mission and was analysed carefully. Some speciﬁcities can be pointed out as the sharing control between autonomy and ground control for the two satellites management or the internal hierarchical organization to secure the failure mode and the collision avoidance management. Once established, the principles can be generalized for all these sorts of missions. The external geometry of the satellites is important too because it is important to optimise the gas consumption for the formation ﬂying maintenance. The main troublemakers are the solar ﬂux pressure and the gravity gradient.

The gravity gradient decreases with altitude of course and, on this orbit, the ﬁgure shows that the solar pressure becomes the main contributor. That is the reason why it is important to minimize its impact on the satellites. The ﬁrst way is managing to have a similar ballistic coefﬁcient on both satellites as much as possible to minimize the relative translation effect between them. This coefﬁcient represents the surface area facing the Sun on the mass. The second way consists in having an axisymetrical geometry to limit the disruptive torque. That is the reason why the solar array is shared into two symmetrical wings. At last, a modular architecture was looked for to make the integration process easier and, above all, to be ﬂexible to different payloads, amount of propellant and launcher accommodations. Springer

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At the end, the wet mass budget presented in the following board shows: – the full compatibility with the Soyuz launcher, – the important mass margin of the MAX lens which could be used to drastically improve its sensibility.

Focuser Sat Detector Sat

MAX

SIMBOL-X

850 Kg 550 Kg

1255 Kg 553 Kg

8. Conclusion This paper mainly aims at demonstrating that both missions MAX and SIMBOL-X are very similar because the different scientiﬁc needs can be translated into the same technical solutions for many aspects including the payload accommodation engineering constraints. A same orbit, a similar amount of data, same pointing precisions and a same time life lead to have the same space and ground segments and the same operations. This fact could allow to develop a common platform architecture for these sorts of missions as it was the case for XMM and INTEGRAL in the past. Further activities ought to take this possibility into account. Moreover, MAX and SIMBOL-X present the same degree of complexity, which is not extremely high except that the formation ﬂying concept is new. Finally, a cost evaluation that takes into account a recurrent effect leads to the conclusion that the global cost of both missions could be the third of the previous generation one. References Rapport De Phase 0 Max, CNES/PASO study report, November 05 Rapport De Phase 0 Simbol-X, CNES/PASO study report, November 05 Related articles in the Gamma Wave 1st Int. Symposium on focusing telescopes in nuclear astrophysics, Bonifacio, France, September 12–15, (2005) Formation Flying for Astrophysics, SIMBOL-X: An X Ray Mission, Rodolphe Cl´edassou (CNES) MAX: Formation Flying For Nuclear Astrophysics, Paul Duchon (CNES) Springer

Exp Astron (2005) 20:447–454 DOI 10.1007/s10686-006-9067-9 ORIGINAL ARTICLE

The CLAIRE gondola: Testing the ﬁrst gamma-ray lens on a stratospheric balloon Ph. Laporte · J. Evrard · A. Laurens

Received: 2 February 2006 / Accepted: 27 July 2006 C Springer Science + Business Media B.V. 2006

Abstract For more than 40 years CNES has ﬂown scientiﬁc balloon ﬂights to perform measurements in a near space environment. The CNES balloon team provides the scientiﬁc teams with expertise in the construction of the gondola, the link between the instrument and the balloon. This gondola provides to the scientiﬁc instrument power supply, thermal and landing protection, attitude measurement and also pointing capability where needed. The project CLAIRE provides a good illustration of the CNES expertise in this domain. The goal of this project was to demonstrate that it is possible to focus a gamma-ray beam intercepted by a large area onto a small focal point. The concept has been demonstrated on ground in the 90s, but a validation under space conditions was necessary to measure the performance of such a telescope for a source at inﬁnity. Keywords Gamma-ray . Balloon ﬂight 1. Introduction Since its beginning in the 1960s, gamma-ray astronomy has struggled with low signal to noise ratios. The “impossibility” of concentrating energetic gamma-ray photons led to a requirement for large detector areas and, consequently, high background noise. Moreover, the low gamma-ray source ﬂuxes necessitate long observation periods – up to many weeks. A possible way out of this dilemma consists of focusing gamma-rays by taking advantage of Bragg diffraction in crystals. The principles of crystal diffraction are discussed by [1]. In a Laue diffraction lens, a large number of crystals are oriented so as to direct incident photons towards a common focal spot. Gamma-rays are focused from a large collecting area onto a small detector volume. As a consequence, the background noise is extremely low, making possible unprecedented sensitivities. Ph. Laporte () GEPI, 5 Place Janssen, 92195 Meudon, France J. Evrard · A. Laurens CNES, Balloon borne Stabilized Gondolas, CNES, 18, Avenue Edouard Belin, 31401 Toulouse cedex 9, France Springer

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The objective of the research and development program CLAIRE was to demonstrate, for the ﬁrst time, a gamma-ray lens for astrophysical observation. The ﬁrst ﬂight of CLAIRE occurred on June, 15th 2000 in France and the second one year later. After a brief presentation of the CNES stabilized gondolas and the CLAIRE payload, we describe the different parts of the CLAIRE gondola: power supply, thermal coating, communication and pointing system. The last section is dedicated to the ﬂight and to its monitoring and a conclusion follows.

2. The CNES stabilized gondola Balloon systems have long been used to ﬂy science instruments and technology experiments in the stratosphere. They permit the study of the upper atmosphere itself, in particular the stratosphere, which is too low for access by satellites and which sounding rockets often traverse too quickly to obtain sufﬁcient data. But with the capability of staying aloft for extended periods at altitudes from 12 to 45 km they also address scientiﬁc topics in astronomy, and allow R&D of space technology. CNES has developed its balloon activity in the last 40 years and has extensive expertise in the design, construction, launch and operation of lighter-than-air vehicles. To fulﬁl the requirements of a large variety of science payloads (stabilisation and pointing capabilities, analogous to satellite attitude control subsystems), the balloon division of CNES provides a range of versatile stabilized gondolas. Since gondolas have to host various kinds of payloads, they have to meet widely varying requirements along with constraints of low-cost and short delays. They are therefore designed as generic platforms, with the design adapted in order to ﬁt new missions and comply with instrument evolution. The advantages of balloon ﬂights over satellites are multiple. Balloon instrument are less demanding in terms of thermal and mechanical requirements, the rules for their design are less restricting and the cost is far smaller. Despite this, balloons offer an access to the space environment for several hours or days.

3. Features of the CLAIRE lens In brief, CLAIRE’s gamma-ray lens consists of a series of concentric rings, machined from a titanium frame, on which are mounted crystals that are tuned to redirect the desired wavelength onto a common focal spot (see Figure 1). By construction, the CLAIRE lens is monochromatic, its focal distance being determined by the energy (i.e. the Bragg angle) and the radius of the rings. A detailed description of the mission is given in [2]. The ﬁeld of view (FoV) of the lens is determined by the mosaic structure of the crystal used. The mosaic structure can be compared to the disorder in the crystal structure. This disorder means that the Bragg relation is fulﬁlled over a range of incident angles. The mosaic width of 30–60 arc seconds of the CLAIRE crystals results in a ﬁeld of view of roughly 60 arc seconds and constrains the pointing system accuracy.

4. The gondola A gondola is not only a structure that links the scientiﬁc instrument to the balloon, t has also to provide energy, communication with the ground, pointing, landing protection and all Springer

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Fig. 1 CLAIRE’s lens before its ﬁrst ﬂight with its 376 crystals arranged in six rings. The outer dimension of the frame is 450 mm for a thickness of 25.4 mm. In black, the inner gimbal.

the other speciﬁc requirements of the instrument. We will address each of these topics in the following paragraphs. In this section, the term instrument refers to the telescope, which consists of the lens and, 2.77 m behind it, the detector with its cryostat 4.1. Power supply and thermal insulation On CNES gondolas the power supply for the instrument and the gondola operations is provided by battery units of about 1 kg that are distributed over the gondola so as to ﬁne tune the centre of gravity. This adjustment is very important in the case of CLAIRE because of the solution adopted for the elevation pointing (see Section 4.5.). The number of batteries is determined by the total power required plus a margin to ensure that even in the case of unexpected problems the control can be kept during the entire ﬂight. We will see in Section 5 that the altitude of the ﬂight was about 40 km for both the ﬁrst and the second ﬂight. At this altitude the ambient the temperature is about −40◦ C. This temperature is not problematic for the actuators, detectors, lubricants and electronic, but it is not acceptable for the CLAIRE instrumentation. The crystals were tuned with an accuracy of a few arc seconds and with temperature changes differential thermal expansion could detune the crystal angle. Moreover, the mass budget was tight so that the number of batteries had to be minimized, precluding the general use of heaters. The solution was to cover the whole telescope and gondola with a thermal cover to prevent thermal loss by radiation (convection being negligible at 40 km in altitude, where the pressure is about 4 mb). This cover was white to reﬂect the suns radiation and consisted of expanded polystyrene or MLI (Multi Layer Insulator), tailored to the complicated shapes to be protected. The insulation was ﬁtted when the whole gondola and instrument was ready for launch. 4.2. Telecommunications Each gondola has a telecommunication package that allows a bi-directional data stream, both sending and receiving data. ETNA is a CNES proprietary L-band (1.5 Ghz) telecom system, giving a user-side total data rate of 800 Kb/s. ETNA is used to send commands to the gondola and to the scientiﬁc instrument and to receive from them scientiﬁc raw data and technical data. Commands include everything from, example, simple instrument ON/OFF commands, Springer

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through new commands for pointing and changed instrument parameters, to the ﬁnal balloonpayload separation command. The downlinked data stream contains acceleration values, inclinometer measures, pointing measurements and all other information that could be useful in extracting scientiﬁc results from the raw data. The TM/TC software is modiﬁable. All the data are available on the CNES web site a few weeks after the end of the mission. 4.3. The gondola’s structure For ﬂights over France, a balloon gondola is limited in weight to 500 kg. This was a strong constraint for the CLAIRE gondola because the instrument itself weighted about 150 kg. Allowing for the telecommunication package, the batteries and the pointing system, cables and connectors, the mass budget for both the gondola and the telescope was limited to 100 kg. At the same time, stiffness was an important issue because of the need to keep the focal spot produced by the lens on the detector. Some ﬂexure of the structure due to the weight is inevitable and this deformation will not be constant because the elevation angle of the gamma-ray source changes during the ﬂight. The maximum permitted deformation was only a few mm over the 2.77 m of the focal length. Finally, for control loop command reasons, the lowest eigen-frequency of the assembly (gondola and telescope) was requited to be at least 10 Hz and the structure had to be capable of supporting an acceleration of 5 to 10 g at the time of parachute opening. To fulﬁl these requirements, the gondola and the telescope were built with an assembly of carbon ﬁbre rods and platforms (see Figure 2). The gondola is the upper part of the structure and the telescope is the inclined structure. The ﬁrst platform (#3, at the top end

Fig. 2 CLAIRE gondola and telescope structure. The vertical assembly is the gondola and the tilted assembly is the telescope structure. They are linked by the red elevation axis bearings. One can see the particularity of this gondola: it is smaller and lighter than the telescope it has to point Springer

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in the ﬁgure) accommodated the ﬁne pointing system (Section 4.5) and the lens. The last platform (#1, bottom end) housed the detector and its cryostat. The intermediate platform links the telescope and the gondola. The whole structure was designed, realized and tested by the University of Birmingham (UK). The result was a structure of 90 kg for the ﬁrst ﬂight and was further optimised for the second ﬂight where it weighted only 60 kg. 4.4. Coarse pointing system Winds are a major concern during the launch of a balloon as discussed below, but even at altitude the fact that winds are neither constant nor uniform means that pointing an instrument beneath a stratospheric balloon (surface, ∼25,000 m2 ) to within a few arc seconds is a nontrivial task. The gondola has always a pendulum motion with a period of about 30 s. Often there are other movements such as roll, pitch and yaw. Even though the pendulum movement decreases with time, some disturbances produced by the wind or excited by the pointing system itself are always present. Because of the inertia involved, all these disturbing motions occur at low frequencies. Thus, a pointing system has to cope with large but slow movements. For CLAIRE, a coarse pointing system, with the azimuthal and elevation controls was needed to ensure that the focal spot remained on the detector. The azimuthal control consisted of three systems. The ﬁrst one was a swivel motor placed above the gondola to rotate it. The second comprised several measurement devices such as magnetometers and gyros to get information on the real azimuthal orientation of the gondola and its velocity, together with a torque motor driven swivel. The third system was the computing electronics. The system relies on the fact that the moment of inertia of the balloon is very much greater than that of the gondola (see Section 5.1. for the balloon details). The elevation control is also divided in three systems and consisted of a screw jack, about 2 m in length, for the actuator, an inclinometer for the measurement and the same computing electronics as the azimuth control. As the gondola weighed less than the telescope (see Figure 2) it was important that the centre of gravity of the telescope was coincident with the azimuth axis, so that as the telescope was moved by the screw jack linked to the gondola, the perturbation of the gondola was minimised. The coarse pointing system was necessary to keep the lens-detector axis of the telescope such that the image fell on the detector, but also because ﬁne pointing system has a limited range. The ﬁnal accuracy of the coarse pointing was limited to about 8 arc minutes because of variations and uncertainties in the terrestrial magnetic ﬁeld, which varies with parameters such as the altitude and the latitude, and because high frequency disturbances are not controlled. The 8 arc minute accuracy corresponds to a shift of 6 mm on the detector, compared with its size of 45 × 45 mm. 4.5. Fine pointing system For many years, the Geneva Observatory (GO) has built and ﬂown stabilized gondolas as a service to the European science community. CNES took over this activity in 1998 when the GO decided to discontinue it. CNES gondolas are still based on the GO design and some elements (such as the generic structure, azimuth swivel, various sensors and actuators, ﬁne pointing analogue control) are reused. Nevertheless, some improvements have been introduced, mainly in on-board computers, numeric control and the telecommunications systems. In a precision pointing system, a guide-star is usually required. For CLAIRE, which has the Crab nebula as astrophysical target, the guide-star was the sun. Hence, a solar sensor was Springer

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pointed at the sun while the lens had to be pointed at the Crab. Provided that the balloon is launched on June 14 or 15, the Sun and Crab are at an angular distance of only about one degree. At such a small angular distance “ﬁeld rotation” (rotation of the instrument around the sun trackers axis) becomes a secondary effect. The sun tracker was mounted on a twoaxis turret with a precise encoder ensuring an accuracy of one arc second. One of the major challenges was to precisely calibrate the alignment between the sensor and the telescope before the ﬂight and to maintain it at the correct (time variable) value during the ﬂight. The overall accuracy of the Crab pointing was 20 arc seconds. As the FoV of the lens was about one arc minute and as the Crab nebula’s size at 170 keV is less than one arc minutes, the scientiﬁc target had to remain in the FoV most of the time. The unprecedented pointing requirements of CLAIRE presented the adaptability of the CNES Stabilized Gondola team with a major challenge. For the CLAIRE it was necessary to develop software that calculates precisely the coordinates of the sun and of the Crab nebula and include it in the calculator loop. Calculating the coordinates on ground and sending them to the gondola would have been possible – and simpler – but the response time necessary to obtain arc second accuracy did not permit this kind of philosophy: the calculation had to be done on board to the avoid time delay due to the communication. The CNES software takes into account a large number of effects and provides an overall accuracy of about one arc second.

5. The ﬂight 5.1. The balloon and its ﬂight train The CNES provides three kinds of balloons. The smallest balloons (less than 12 m diameter, payload of a few tens of kgs) are designed to ﬂy three or four weeks. These balloons are sealed and their envelop is not elastic, so the volume remains constant whatever the atmospheric conditions. Usually, these balloons are used for atmospheric study. Another kind of balloon is the infrared hot-air balloon. The principle is identical to the classical hot-air balloon except that the heating is provided by the infrared radiation of the sun – during the day – or by the earth, during the night. They can reach an altitude that oscillates between 20 and 30 km according to the day-night cycle. The ﬂight lasts two or three weeks and the payload weight can reach 360 kg. The third kind of balloon, named OSB for Open Stratospheric Balloon, is the largest on, their volume ranging from 400,000 to 1,200,000 m3 . They are well suited for ﬂights lasting several days or even weeks. Inﬂated with helium, these balloons can reach an altitude ranging from 17 to 43 km, depending on the quantity of helium. The payload can weigh up to 3000 kg (500 kg in France). Based on the CLAIRE mass and altitude requirement, the OSB was the natural transportation. The ﬂight train is the link between the balloon and the gondola. It includes several devices, visible in the Figure 3: – an altitude coder and an ARGOS beacon, – a ﬂashing lamp, like those used on aeroplanes, – a radar reﬂector and a beacon to make the balloon visible when it crosses through aircraft altitudes (5000 meters to 12 000 meters), – a ballast hopper containing lead balls (NSO) to lengthen the ﬂight by lightening the total ﬂying mass, Springer

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c Fig. 3 Left: a schematic of the ﬂight chain with its devices. CNES. Right: CLAIRE taking off at Gap Tallard in June 2001. The auxiliary balloon above the CLAIRE payload is used to lift the gondola during launch only. c The main balloon is visible on the right. CNES

– three parachutes for landing, – a separation device to separate the balloon and the ﬂying train at the end of the ﬂight. All these devices and the launch team are provided by CNES whatever the launch base. 5.2. The choice of the launch base Pressurized balloon can be launched from anywhere over the world because their small size, but huge balloons like OSB need a dedicated launch pad. CNES has its own bases but can also rent a base (such as Kiruna in Lapland), leading to six possibilities all over the world. – in France: Aire-sur-l’Adour and Gap Tallard (Alps), – in Europe: Kiruna, Trapani, – rest of the world: Brasil, Africa. This range of possibilities is essential in order to be able to provide the best possible match to scientiﬁc objectives. As explained above, the scientiﬁc target for CLAIRE was the Crab nebula for its intense and constant gamma-ray ﬂux at 170 keV. The elevation of a source depends on its declination and on the latitude of the launch base. To avoid the balloon obscuring the optical line of sight, the maximal elevation of the source should be no more than 70◦ (see Figure 4) leading to an optimum latitude of 42◦ for the declination of the Crab (close to 22◦ ). The launch base chosen for CLAIRE was Gap-Tallard, at a latitude of 44◦ north. 5.3. The ﬂights In June, stratospheric winds above France are well established in a westerly direction. After a take off from Gap Tallard the balloon ﬂew from the south east of France to the south west Springer

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Fig. 4 Scheme of the balloon its ﬂight chain and the gondola. Due to the balloon’s size, an instrument requiring a visible line of sight to the source cannot point at targets having an elevation above 70◦

in 6 h15 for the ﬁrst ﬂight (15.6.2000) and 5 h20 for the second (14.6.2001). Float altitudes were above 40 km. Longer ﬂights are possible, however the required launch window for CLAIRE did not correspond to the best period when the winds are less strong. to. Thus, the goal was simply to reach the highest altitude to minimise the atmospheric absorption during the limited ﬂight time. The landing area is selected at the ﬂight control centre with the help of very detailed map displaying towns, power lines, relief, etc and also displaying the actual balloon position. The most probable landing trajectory is also displayed in real time thanks to CNES metrological weather forecasting. Thus, at the end of the ﬂight, when the projected landing spot is in a non-habited area, the gondola is separated from the balloon and the parachutes are opened. 6. Conclusion The “BA/NA” team of the balloon division of the French Space agency CNES has provided an efﬁcient pointing and stabilisation system for the ﬁrst gamma-ray lens telescope CLAIRE. The unusual conﬁguration of the gondola and telescope required a ﬁrst, purely technological, ﬂight in June 2000. After improving parts of the pointing system, CLAIRE’s lens observed the Crab nebula in June 2001 with a pointing stability of 3 arcsec. For the CNES team, CLAIRE was a challenge in term of delay, pointing loop control and accuracy control over the whole chain of devices. CLAIRE perfectly illustrates the interest of balloon ﬂights to validate an instrumental concept. After only two ﬂights, CLAIRE has demonstrated the principle of a gamma-ray lens for nuclear astrophysics. The knowledge obtained with this balloon project has largely contributed to the deﬁnition and optimisation of the future space borne gamma-ray lens.

References 1. Halloin, H., Bastie, P.: Exp. Astron. 20, DOI 10.1007/s10686-006-9064-z (2006) 2. von Ballmoos, P. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9071-0 (2006) Springer

Exp Astron (2005) 20:455–464 DOI 10.1007/s10686-006-9044-3 ORIGINAL ARTICLE

Recent advances and low cost concept for the gamma-ray lens project MAX Xavier Leyre · Michel Sghedoni · Francis Arbusti · Primo Attina · Peter von Ballmoos

Received: 7 February 2006 / Accepted: 14 April 2006 C Springer Science + Business Media B.V. 2006

Abstract Until recently, focusing of gamma-radiation was regarded as an impracticable task. Today, gamma-ray lenses have become feasible and present promising perspectives for future instrumentation. For the ﬁrst time in high energy astronomy the signal/noise ratio will be dramatically improved as gamma-rays are collected on the large area of a lens from where they are focused onto a small detector. Besides an unprecedented sensitivity, MAX will feature very high angular and energy resolution. The conjunction of this new technique of Gamma Ray focusing and the new possibilities brought by the developping formation ﬂying technology will allow a great step for Gamma Astronomy. This paper will describe after a short recall of the scientiﬁc objectives of MAX, the design of the MAX formation ﬂying concept and the associated main design drivers and constraint. Keywords Gamma ray . Formation ﬂying . Lagrange point L2 . Metrology

Introduction The next generation of instrumentation for the domain of nuclear astrophysics will have to achieve a factor of 10–100 improvement in sensitivity over present technologies. Combining a sensitivity of a few 10−7 ph s−1 cm−2 with high spectral and angular resolution, and the capability of measuring the polarization of the incident photons, the focusing gamma-ray telescope MAX takes up this challenge. Focusing gamma-rays from a large collecting area of a crystal diffraction lens onto a very small detector volume results in extremely low background, making possible unprecedented sensitivities. X. Leyre · M. Sghedoni () · F. Arbusti Alcatel Alenia Space Cannes, 100 Bd du Midi 06400 Cannes, France P. Attina Alcatel Alenia Space Torino, Strada Antica di Collegno, 253, 10146 Torino, Italy P. von Ballmoos CESR – Centre d’Etude Spatiale des Rayonnements 9, av. du Colonel-Roche, 31028 Toulouse Cedex 4, France Springer

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The MAX mission addresses a wide range of fundamental astrophysical questions such as the life cycles of matter and the behaviour of matter under extreme conditions. The primary scientiﬁc objective of MAX is the study of supernovae of type Ia (SN Ia) by measuring intensities, shifts and shapes of their nuclear gamma-ray lines. Moreover, the sensitive gamma-ray line spectroscopy performed with MAX is expected to clarify the nature of galactic microquasars (e− e+ annihilation radiation from the jets), neutron stars and pulsars, X-ray Binaries, AGN, solar ﬂares and gamma-ray afterglow from gamma-burst counterparts. In the following it is shown that the formation ﬂying concept we propose for MAX can become reality with present day technology in a very reasonable timeframe, minimizing the risks and allowing for a demonstration of advanced formation ﬂying. The formation ﬂying concept Today, scientiﬁc missions in space are limited by the size of the instrument: while scientiﬁc performances are directly proportional to the size of optics, focal length or base-line, instrument sizes are restricted by platform and launchers capabilities. To circumvent these limitations, the key idea is to distribute the instrument functions over several spacecrafts. This association of satellites composes a Formation Flying (FF) space system. There is no longer individual satellites, but formation function and performance. Then the major constraint for the formation is to keep the inter-satellite geometric stiffness:

r the formation shall hold a unique kinematics, r the relative dynamics between S/C shall be minimized (position & attitude). This concept of spacecraft formation leads to developing new technologies and engineering activities:

r dedicated position and attitude sensors: the Formation Flying metrology, r dedicated actuators: FEEPS, gold gas, r new command/control concepts: collision avoidance, centralized/non-centralized/hybrid, r new orbit maintenance and deployment strategies, r dedicated guidance navigation control (GNC) architecture and control laws, r new dedicated test-bench and validation approach. Alcatel Alenia Space has been studying Formation Flying based missions since 1999 with the highly challenging DARWIN mission. Alcatel Alenia Space has since contributed to identify several science mission with high science return increase thanks to formation ﬂying: preliminary assessment of these missions has been performed internally to assess feasibility, technical challenges and formation ﬂying performance classes. Based on the identiﬁed technical challenges, key technologies have been the object of internal and institutional (ESA and CNES) R&T:

r Formation Control Techniques, r Optical and RF Metrology, r Command / Control and Avionics architecture, r Validation test bench, r System architecture, Springer

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Fig. 1 The FF European missions and the technology steps

Alcatel is involved in all the ﬁelds of activities relevant of the Formation Flying. As a function of all the potential FF missions in Europe. Figure 1 shows the technological developments an the different steps to achieve. As the ﬁrst step of technology acquisition, Alcatel Alenia Space is involved in the PRISMA FF ﬂight demonstrator in a frame of a collaboration between Swedish Space Corporation (SSC) and CNES. This Swedish ﬂying test-bed mission for RdV & FF sensors and technologies is led by SSC who has invited main space actors to validate their technologies. Alcatel Alenia Space will deliver the RF sensor and some GNC control laws based on RF sensor, embedded in ﬂight software. MAX spacecrafts design as presented in this paper was based on a cost effective approach reusing CNES/Alcatel Alenia Space platforms. Max could be one of the ﬁrst FFs missions mixing ﬂight proven platform and technologies associated to high performances equipments as metrology sensors and new GNC techniques.

System design and speciﬁcation The mission is composed of two satellites in formation ﬂying . One is dedicated to the detector while the second is dedicated to the lens. The master (detector satellite) of the formation includes all the subsystems necessary for the mission, while the second (the lens) is a complete slave. Formation is presented in Figure 2. The main system speciﬁcation are driven by the scientiﬁc goals as described hereabove applied to a formation ﬂying system based on the two satellites system : the lens and the detector satellites. The Main Scientiﬁc Requirements for MAX mission are summarized in the Table 1. The both spacecrafts mains characteristics are presented in Table 2. Figure 3 is a schematic view of the scientiﬁc payload on the lens spacecraft. Springer

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Exp Astron (2005) 20:455–464 Table 1 Main scientiﬁc requirements for MAX mission

Main bands Band pass Sensitivity Spectral resolution E/ E Angular resolution Temporal resolution Polarisation, amplitude modulation

Band 1

Band 2

annihilation e− e+ (511 keV) 7 Li∗ (478 keV) 450–550 (keV)

56 Co

=40%

(847 keV) (812 keV) 800–900 (keV) =10−6 (photons cm−2 s−1 ) ∼500 <1 (arcmin) ∼100 (microsec) =20% 56 Ni

Reduced cost approach is the evolution of high-performance Alcatel Alenia Space/CNES platforms The key constraint of the space programs of the new century is to lead spacecraft development for high interest scientiﬁc missions in a context of limited funding and reduced budget. Today, CNES and Alcatel Alenia Space have developed two platforms covering the payload demand in the range [100 Kg, 600 Kg]:

r Proteus : 600 Kg, 600 W, 1 m cube for service module, gyro-stellar AOCS and 3 axes stabilization, magnetic wheel unloading using magneto-torquer bars (see [1]).

r Myriade: 100 Kg, 140 W, 0.5 m cube, star tracker based AOCS and 3 axes stabilization (see [2]). The ﬁrst ﬂight of the Proteus plat-form was in the framework of a the NASA/CNES mission Jason 1, end of 2001, dedicated to observation of Ocean. The spacecraft Demeter, launched mid 2004, is the ﬁrst of the low cost CNES missions. Its goal is the Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions. Figure 4 shows the spacecrafts Jason 1 and Demeter.

Fig. 2 The two spacecrafts on formation ﬂying of MAX mission Springer

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Table 2 Lens and detector satellites main characteristics Lens satellite requirements Absolute pointing Crystals mass Inner radius Outer radius Mask

<15 arcsec

Detector satellite requirements Detector

150 kg Absolute pointing 56 cm Mass 223 cm Size 16 cm × 16 cm Power (efﬁcient <100 keV) <15 arcsec (∼0.7 micron/cm) Data rate

Crystal mounting Power 50 W Data rate Option: optical monitor Distance between Satellites (focus) Position accuracy

Thermal control

Segment Ge <1 degree 60 kg ∼25 cm × 25 cm × 40 cm <40 W 5 kbit s−1 85 K, passive

86 m ±0.1 cm lateral, ±0.1 m axial

requirements

Fig. 3 Max instrument of the lens spacecraft

Fig. 4 Jason 1 (Proteus) and Demeter (Myriade)

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Fig. 5 The two spacecraft assembly inside Soyuz fairing

The approach we propose, is to lead an evolution of these two platforms, mainly in the GNC and Command Control ﬁeld, to answer to the speciﬁc demands of the formation ﬂying concept: – the Lens satellite is an adaptation of Myriade platform, – the Detector satellite is based on Proteus platform. The science beam is directly focused by the Lens hold and controlled by the Myriade platform, toward the master spacecraft including all the Detector payload, using the Proteus platform. This latest includes systems for the ﬁne pointing and the control of the formation.

Mission and satellite concept Going to L2 Lagrange point Due to the constraints of formation ﬂying and the derived stability requirements both in attitude and position, ﬁne formation ﬂying led to the selection of the most appropriate orbit in order to minimize the disturbance forces and torques and to increase the thermal stability required. In addition to these mission requirements, the launcher constraints and capabilities lead to the selection of L2 type orbit with respect to Geo like orbit. Launcher like Soyuz Fregat are able to send to L2 points up to 2 tons whereas the GEO target is reduced to approximately 450 kg. All these arguments leads to the selection of the L2 type orbit both from technical and programmatic reason. As we will see later the data transmission will not be a problem at this point. In order to comply with the ﬁnal orbit selection together with the ﬁne formation ﬂying requirements, a major trade off has been conducted for the propulsion selection. The classical hydrazine propulsion subsystem has been kept as is (28 kg of hydrazine) allowing to ensure the necessary V after the Soyuz Fregat separation up to the L2 injection, covered by the 28 kg of hydrazine included in baseline of the Proteus platform. A composite with the Detector satellite holding the lens satellite is driven to L2 using the Detector satellite Guidance Navigation Control system. The global mass of the composite is estimated at 650 kg maximum.The composite is shown in Figure 5. Springer

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Once in orbit (Lissajous type around L2 point), tanks are purged in order to avoid any sloshing and the ﬁnal propulsion is performed thanks to the second propulsion subsystem based on cold gas (Nitrogen). Liquid option (although with a much better Isp) have been eliminated also in order to eliminate any sloshing. A global V budget has been estimated for the Lens satellite as for the Detector satellite with the manoeuvres, together with the attitude control. The total mission lifetime is covered by 4 tanks of 3 kg nitrogen each both for the two spacecrafts. The budget is globally equivalent for both spacecrafts although the perturbations and manoeuvres are different. Taking into account the delay manoeuvre and the availability of the ground station (worst case 6 h per day), the downloading philosophy of the data is to rotate the Proteus satellite and its high gain antenna towards the Earth once after each target has been acquired. High data allows to downlink the 2 Gbits stored on board in the standard mass memory of the Proteus DHU. This covered easily the data stored for each target with respect to the quite limited data rate needed. Standard Proteus design is reused except wheels and torquer bar which will be replaced by ﬁne propulsion on cold gas and the 4 Nitrogen tanks. The Myriade design is also globally kept, except the four additional Nitrogen tanks being added. The mass and power budgets are compatible with the Proteus ones and the Myriad’s ones. The power budget and energy budget is compatible with ﬁxed solar array at L2 point. All mobile parts have been deleted together with all potential sources of sloshing, allowing to cancel any internal disturbance torque sources. A passive thermal control concept with radiator and service module allows to keep the detectors at the operational temperature. The RF link used for the deployment, collision avoidance and raw positioning is also used for intercommunication between the lens satellite and the Proteus Detector. Associated data budget and link budget are fully compatible.

Formation reconﬁguration The formation reconﬁgurations (spacecraft attitude reorientation, intra-distance satellite resizing), allowing to fulﬁl the scientiﬁc objectives is one a the major innovations to realize with the collision avoidance, at spacecraft dynamics level. During the reconﬁguration manoeuvres, although the mission does not require to maintain the accuracy of the formation, it can be envisaged to do so as a demonstration for more demanding mission; then the accuracy of the ﬂeet while performing all the manoeuvres (translations and rotations) will be monitored.

Metrology concept The metrology concept used in order to ensure an accuracy compatible with the scientiﬁc requirement is split into two different subassemblies: – First the RF subsystem from GPS type allows a raw positioning for the deployment phase and after the deployment phase and is also used for collision avoidance and safe mode. It is based on triangular antenna pods and emitter/receivers based from Alcatel Alenia Space Topstar 3000 GPS receiver. The accuracies in distance measurement is in the range of 1 cm and for the direction close to 1 degree. Figure 6 shows the scheme of principle and a view of hardware of RF sensor. Springer

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Fig. 6 RF sensor principle and bread-board developed in frame of ESA and CNES contracts

Fig. 7 Several possible concepts for lateral metrology

Fig. 8 The lens satellite using Myriade platform

– Second, a classical optical metrology (Figure 7) based on retroreﬂectors placed on the Lens and simple laser and CCD receiver based on the Detector, will allow to reach a lateral positioning better than 100 microns. The ﬁnal pointing, is performed thanks to standard Star trackers present both on the Lens and Detector satellites. The lens satellite As shown in Figure 8, the lens satellite is based on the lens which support the antenna of the RF positioning system. These antennas are located on a equilateral triangle on both sides of the lens allowing a complete coverage and an optimal resolution starting from the diameter of the lens. Springer

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Fig. 9 The detector satellite using Proteus platform

The three optical retroreﬂectors are located only on one side of the lens as the lens satellite will be positioned at centimetre level and arcminute level before entering into the optical metrology loop. The core part derived from Myriade type satellite has the electronics reduced to a centralized computer able to interface the cold gas propulsion subsystem, AOCS sensors and RF subsystem. The RF subsystem is used both for raw metrology purpose and for communication between the lens satellite and the master satellite. The scientiﬁc payload is made of the purely passive lens design on a torus like shape made of CeSiC material allowing the required stability. The detector satellite The detector satellite presented Figure 9 includes all the standard subsystem and is in charge of conditioning, storing, processing and transmission to ground of all the housekeeping data both from the Lens satellite and from the Detector satellite. In addition the active part of the detector instrument is included and processed aboard. The detector is located on a mast in order to minimize the inﬂuence of the global mass of the satellite. A shield is nevertheless foreseen. The detector is passively regulated. Conclusion The design proposed for the MAX mission is based on the heritage and knowledge of Alcatel Alenia Space scientiﬁc programs and standard and ﬂight proven Proteus and Myriade Platforms. This approach will allow to develop in a cost effective and programmatic effective manner, this ambitious Gamma Ray Astronomy mission while reducing the development risks to a minimum. It will allow focusing on the payload developments and challenges while demonstrating all the potentialities of the formation ﬂying technologies. A close cooperation between Alcatel Alenia Space and the CESR scientiﬁc community has allowed to imagine and consolidate this approach. By taking into account, from the very beginning, the scientiﬁc requirements and the industrial constraints, this approach allows to reduce development risks and to optimize the ﬁnal concept. Springer

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References 1. Overview on PROTEUS smallsats family: Jason 1 ﬂight results and further applications. Ph. Landiech, F. Douillet. IAF 2002, IAC-02-U.4.05 2. MYRIADE, Technological step versus performances for the next 10 years, B. Deligny and all. Small Satellite and Small Service Symposium, La rochelle, France, September 2004

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Exp Astron (2005) 20:465–482 DOI 10.1007/s10686-006-9069-7 ORIGINAL ARTICLE

Small-sat platforms and formation ﬂying: An opportunity for the gamma ray telescope MAX J. Borde · P. von Ballmoos · R. Soumagne

Received: 2 February 2006 / Accepted: 2 August 2006 C Springer Science + Business Media B.V. 2006

Abstract This paper presents the results of a study performed by EADS Astrium in support to the Centre d’Etude Spatiale des Rayonnements (CESR, Toulouse) for the preliminary deﬁnition of the MAX space segment, based on a small-sat platform in the 200 kg range. MAX is an innovative gamma ray telescope with as prime objective the study of type Ia supernovae. The concept of MAX is radically different from the traditional gamma ray telescopes: gamma rays are focused from the large collecting area of a crystal diffraction lens on a very small detector volume. This paper discusses the implementation of the MAX space mission as lens-detector duo satellites in an active Formation Flying geometry. First, the 3-year mission objectives, science payload and system requirements are presented. Then, the MAX mission is described with an overview of the different mission phases, the selection of the orbit and launcher, the operational concept and some ground segment aspects. The space segment is then detailed. The satellites external conﬁguration and accommodation under the launcher fairing is shown, followed by the description of the 200 kg platform and completed by the review of the Formation Flying sensors and actuators required to fulﬁl the mission objectives. Some programmatic aspects are also provided. Keywords Formation ﬂying . Gamma-ray science . MAX mission . Small-sat platforms

J. Borde EADS Astrium, 31 avenue des Cosmonautes, ZI du Palays, 31402 Toulouse Cedex 4, France e-mail: [email protected] P. von Ballmoos Centre d’Etudes Spatiales des Rayonnements, 9 avenue du Colonel Roche, 31028 Toulouse Cedex 4, France e-mail: [email protected] R. Soumagne Centre National d’Etudes Spatiales, 18 avenue Edouard Belin, 31401 Toulouse Cedex 4, France e-mail: [email protected] Springer

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Exp Astron (2005) 20:465–482 Table 1 MAX scientiﬁc requirements Bandwidth Sensitivity Spectral resolution (E/ E) Angular resolution Time resolution

Table 2 MAX position control and measurement requirements

Band 1: 800–900 keV Band 2: 450–540 keV Few 10−7 photons/cm2 /sec (10−6 at 511 keV) About 500 1 arcmin <1 micro sec

Focal length (ISD) Lateral position measurement Lateral position control Longitudinal position measurement Longitudinal position control Lens absolute pointing error Detector absolute pointing error

86 m 1 mm 1 cm 10 cm 10 cm 15 arcsec 1◦

1 MAX mission objectives and system requirements 1.1 Mission objectives MAX is a new concept of gamma ray telescope with as prime objective the study of type Ia supernovae by measuring intensities, shifts and shapes of their nuclear gamma-ray lines [7]. Moreover, the sensitive gamma-ray line spectroscopy performed with MAX is expected to clarify the nature of galactic microquasars (e− e+ annihilation radiation from the jets), neutron stars and pulsars, X-ray Binaries, AGN, solar ﬂares and gamma-ray afterglow from gamma-burst counterparts (see [6], and the articles in the ﬁrst section of this volume). The concept of MAX is radically different from the traditional gamma ray telescopes: gamma rays are focused from the large collecting area of a crystal diffraction lens on a very small detector volume. During its three year mission, MAX shall be able to observe gamma ray sources from any inertial direction, the Sun direction being a secondary objective. Beyond its scientiﬁc objectives, the MAX mission can be used as a demonstration programme to test and validate in-ﬂight Formation Flying (FF) concepts and techniques. In that case, the requirements can be more stringent than those required by the scientiﬁc MAX mission (Tables 1 and 2). 1.2 Overview of the lens The MAX lens [2] is composed of 8625 Ge and Cu crystals with a total weight of 180 kg (with 20% margin, w/o supporting frame) accommodated on 23 concentric rings mounted on a torus frame. The working principle of the lens is based on Bragg diffraction in Laue geometry: photons traverse the crystal using its entire volume for diffraction. The crystals mounted on one of the 23 concentric rings are oriented such that they all diffract the incident radiation of a same energy band onto a focal spot common to all of the rings (Figure 1). The different Bragg-angles of the various rings allow the MAX lens to cover two broad energy bands simultaneously. Springer

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Fig. 1 Diffraction principle of the Laue lens

Fig. 2 Principle of MAX detector

1.3 Overview of the detector A small gamma camera, maintained at a distance of 86 m by the station keeping detector spacecraft, collects the focused radiation (Figure 2). The detector will have to provide localisation of the interactions to within typically a millimetre. This permits to follow the excursions of the focal spot across the detector plane. Also, event localisation provides the scatter direction of the predominantly Compton scattering photons allowing for dramatic background reduction, and for measuring the polarization of the incident photons. The baseline detector for MAX is a stack of planar Ge detectors using orthogonal strips, representing a volume of about 8 × 8 × 8 cm3 [9, 10]. Alternative solutions include (i) a single high purity germanium detector (INTEGRAL/SPI type); (ii) an efﬁciency optimised narrow Field of View Compton Camera featuring Si strips and CdTe pixels [1, 4, 8]; and (iii) an array of low temperature calorimeters [5]. 1.4 Requirements for the lens and detector satellites design The scientiﬁc functions required for the lens satellite are (i) to point towards the gamma ray source with 15 arcsec accuracy and (ii) diffract the gamma rays towards the detector satellite located 86 m away from the lens satellite (Table 3). The torus shaped lens shall keep a wide-open Field Of View (FOV) relative to both the observed source and the detector satellite. The detector shall be cooled down to 85 K, meaning that the detector satellite shall implement a cold face (a face which never sees the Sun) and an active or passive cooling technology (Table 4). While a small cryocooler impose less constraints on the observation startegy, a passive radiator (no moveable parts) is less complex and has no power consumption. The detector shall be distant from the platform to minimise the background noise. Springer

468 Table 3 Lens characteristics for satellite design

Table 4 Detector characteristics for satellite design

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Total mass External diameter Internal diameter Pointing requirement Required power

Detector + structure mass Detector + structure dimensions Pointing requirement Required power Data rate Operating temperature

180 kg 222 cm 112 cm 15 arcsec 20 W

30 kg 25 × 25 × 40 cm3 1◦ 40 W 5 kbps 85 K

1.5 Observation requirements During its mission, MAX shall be able to observe gamma ray sources from any inertial direction, the Sun direction being a secondary objective. Due to low gamma-ray source ﬂuxes, targets shall be observed for periods of up to 15 days (including margin). A part of the observations cannot be planned prior to launch : the occurrence of novae and supernovae can not be predicted. The satellites will be requested to acquire this new source within 12 hours typically. Both the lens and the detector satellites offer a degree of freedom (DoF) in rotation around the observation Line Of Sight (LOS). To be able to acquire and maintain for several days any inertial attitude, the satellites shall implement a rotating solar array. The combined effect of these two DoF allows pointing at the same time the observation LOS to any inertial direction and the solar array to the Sun. With a rotating solar array, spacecraft manoeuvring capability and a degree of freedom around the antenna axis, there is no need for an articulated antenna. During Earth communication sessions, the antenna can be Earth pointed with the solar array pointed to the Sun. 2 MAX mission deﬁnition The implementation of the MAX space mission consists in ﬂying a lens-detector duo satellites in an active Formation Flying geometry. The lens satellite is kept inertial and pointing to the gamma ray source with an accuracy of 15 arcsec, while the detector satellite is controlled in attitude and position with respect to the lens at a constant distance of 86 m (focal length of the system), within an accuracy of 1 cm in lateral and 10 cm in longitudinal. The lens and detector satellites will operate on the free-insertion halo orbit around the second Lagrange point L2. They will be transferred to this operational orbit by a Soyuz ST/Fregat dual launch foreseen to take place mid-2011. The mission duration is 3 years including cruise. 2.1 Orbit and launcher selection The MAX operational orbit requires a quiet radiation environment for science (i.e. far from the Earth radiation belts) and a ﬂat gravitational ﬁeld for the Formation Flying. Among the candidate orbits (high elliptical orbits, 3-day period circular orbits, Earth trailing orbit, Lissajous/halo orbit around the Earth-Sun Lagrange points L1 or L2), the Springer

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Launcher separation

Deployment

Operational phases Lens and Detector inertially pointing Attitude slew for Lens and Detector. to the Earth. Coarse manoeuvre for the Detector. TM/TC communication.

Cruise

Re-targetting

Orbit insertion

Observation

Injection to natural Lissajous orbit Rendez-vous Lens-detector initialisation

Lens and Detector inertially pointing to the gamma ray source. Attitude and position control.

Communication

Attitude slew Attitude slew for Lens and Detector. No manoeuvre

Fig. 3 Overview of the mission phases

free-insertion halo orbit around L2 is selected as operational orbit for the MAX mission. The Lagrange point L2 is located along the Sun-to-Earth line, behind the Earth as seen from the Sun, and at a distance of 0.01 AU (1 astronomical unit = 150 million km) from the Earth. The “diameter” of the free insertion halo orbit is about 0.01 AU. In addition to the compliance to the requirements mentioned above, this eclipse-free orbit offers a full Earth and Sun visibility and does not require propellant for capture. The ∼2000 kg injection capacity to L2 of the Soyuz ST/Fregat launcher is compatible with the MAX mission, as the mass of the two satellites is estimated to be around 1000 kg. Therefore, a dual launch with Soyuz ST/Fregat is baselined. For a mission in 2011, a launch from Kourou is the most likely possibility. 2.2 Mission phases The mission is split in several phases (Figure 3). The Deployment phase starts after launcher separation and ends when the satellites are in a safe attitude with the inter-satellite distance controlled to a few tens of km. The satellites are separated just after the end of the Fregat ﬂight; the separation will be managed by the launcher. This solution is preferred to a separation at L2 mainly for cost and risks reasons. As major consequences, the two satellites will be operated separately from launch, and each satellite will be autonomous with respect to the other one and to the ground. During the Cruise phase, each satellite is kept in a safe attitude relative to power (the solar arrays are Sun pointed) and Earth communications (the Medium Gain Antenna – MGA – is Earth pointed); the inter-satellite distance (ISD) is kept equal to a few tens of km to avoid collision. Each satellite is operated separately from the ground. The two satellites arrive at L2 separately for the Insertion phase. By deﬁnition, no V is needed for insertion on the selected operational orbit. After a rendezvous between the lens and the detector satellites, the ISD is reduced from several tens of km down to the 100 m range using the chemical propulsion, and the formation geometry is initialised. The operational phases start when the satellites have reached the ﬁnal orbit. Distinction is made between (i) the Observation phase where the lens and detector are inertially pointed Springer

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Detector

Lens

current source

Initial FF geometry, inertial pointing Detector

Lens

4-step approach to re-initialise the FF to new target

new source

Fig. 4 Target to target manoeuvre and slews

to the gamma ray source with the 3D position of the detector controlled with respect to the lens within the required accuracy; (ii) the retargeting manoeuvre where the lens is slewed to point towards the new source and the detector is slewed to get the same attitude and manoeuvred to align its LOS with the LOS of the lens and the gamma ray source direction; (iii) the communication phase where both the lens and the detector are Earth pointed for data down-load and mission planning up-load; and (iv) attitude slews where both the lens and detector are slewed from an observation attitude to an Earth pointed attitude. 2.3 Science operational concept The selected gamma ray source is observed for 15 days without interruption. During observation, the solar arrays of the lens and the detector satellites remain ﬁxed and pointing to the Sun, in order not to alter the pointing stability (in 15 days, the available power remains quasi constant and above 99% of its maximum). Continuous housekeeping telemetry is down loaded to the Earth through the Low Gain Antenna (LGA) in X-band. The lens satellite is controlled in attitude within 15 arcsec accuracy thanks to a gyro-stellar attitude estimation and a control with the reaction wheels. The lens satellite remains “free ﬂying” and is not controlled in position. The detector satellite is controlled in attitude using the same mode as the lens for optimising the design, validation and operations. Its 3D position relative to the lens is sensed by the optical metrology (initialised by the RF metrology) and controlled by the cold gas thrusters. At the end of an observation phase, the lens and the detector satellites are slewed to an Earth pointing attitude using the reaction wheels for data down load. At the end of the communication session, the lens and the detector are slewed to point to the new target and a manoeuvre is performed on the detector with the chemical propulsion to align the lens and detector LOS with the new gamma ray source (Figure 4). The slews and the manoeuvre can be done simultaneously or in sequence, as there is no strong timing constraint for acquiring a new target. During re-targeting, the optical metrology is switched off and replaced by the RF metrology for position control. Springer

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2.4 Ground segment coverage On the free-insertion halo orbit around L2, the maximum angle between the spacecraft-toEarth direction and the equator plane is about 60◦ . Therefore, the MAX satellites are always under visibility of ground stations with latitude below 30◦ (assuming a station minimum elevation angle of 10◦ ). This means that Kourou (5◦ North latitude) can be used during the whole mission with comfortable margin (as far as its geographical location is concerned). Perth and New Norcia (31◦ South latitude) can also be used most of the time. For larger latitude ground station locations, the ground station coverage suffers from a seasonal effect so that one station in the southern hemisphere and one station in the northern hemisphere shall be alternatively used. 3 Preliminary design of the MAX space segment 3.1 Space segment overview The proposed MAX space segment design is driven by science objectives. It relies on emergent Formation Flying concepts and techniques and new-generation small-size platform products [3]. The MAX space segment is composed of 2 different autonomous satellites, the lens satellite and the detector satellite. Both spacecraft are fully autonomous with respect to ground operations, and each satellite is independent from the other one. The two satellites differ because of the accommodation of a different science payload, and the FF concept, which considers an active detector satellite and a passive lens satellite. A passive lens and active detector concept implies that (i) the volume of the chemical propulsion tank is larger on the detector, as the detector will perform large manoeuvres for gamma ray source retargeting; (ii) the size of the Mass Memory is larger for the detector as more data storage is required; (iii) the active optical metrology is embarked on the detector, while the lens only implements a set of reﬂecting corner cubes; (iv) cold gas propulsion, required for the accurate control of the formation, is implemented only on the detector, as the lens is free-ﬂying. On another hand, Electrical and Power, space to ground RF communication, Data Management (except the external Mass Memory size, see above), Attitude and Orbit Control System (AOCS), chemical propulsion (except the size of the tank, see above) and inter-satellites RF link are identical on the lens and detector satellites. 3.2 Satellites conﬁguration 3.2.1 Accommodation of the satellites under the Soyuz fairing The satellites mechanical conﬁguration is compatible with a launch with Soyuz ST/Fregat thanks to standard adaptor between Fregat and the bottom satellite (the lens) and a speciﬁc adaptor sustaining the detector above the lens (Figure 5). 3.2.2 Satellites external conﬁguration The external conﬁguration of the satellites is driven by the following considerations: Springer

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Fig. 5 Lens - detector launcher accommodation

• rotating solar array and one degree of freedom around the observation LOS to safely point any inertial attitude for several days, • face-to-face RF and optical metrology Field Of View: RF antennas, laser beam, reﬂecting corner cubes, • reﬂecting corner cubes mounted on the lens supporting structure to minimise the misalignment effects for an accurate 3D position control, • Star Tracker (STR) LOS aligned with the observation LOS and accommodated so as to minimise the misalignment between the STR LOS and the lens reference frame, • detector distant from the platform to minimise the background noise, • lens platform embedded inside the lens supporting torus to keep a wide open FOV with respect to both the gamma ray source and the detector, • cold face for the detector satellite so as to implement a radiator with maximum FOV towards the deep space. 3.3 Satellite architecture and platform conﬁguration 3.3.1 Functional architecture The MAX satellites functional architecture, the Avionics concept (command/control, data management, AOCS), the power distribution and the space to ground interfaces are depicted in Figure 8 for the detector satellite (refer to the text for the differences between the satellites). The MAX platform is based on a new generation platform product in the 200 kg range. This new platform, under design at EADS Astrium, is inherited from the Pleiades and Rocsat 2 platforms. It is adapted to account for the speciﬁcities of the interplanetary MAX mission, Springer

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Fig. 6 Functional external conﬁgration of the lens satellite

to detector satellite gamma ray source

gamma ray source

Fig. 7 Functional external conﬁguration of the detector satellite

with a dedicated chemical propulsion system to go to L2 and a customised structure to support the lens or the detector. 3.3.2 Thermal control The detector satellite requires a cooling system to operate at 85 K. Both a passive and an active cooling are feasible. As the detector spacecraft embarks a rotating solar array and has a degree of freedom around the observation LOS, the face normal to the solar array axis and observation LOS can always be anti-Sun pointed. This means that a radiator can be implemented on that face. Preliminary computation shows that a 0.7 m2 area is required (assuming a 1W dissipation of the detector).

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Fig. 8 Functional architecture of the detector satellite (refer to the text for the differences with the lens satellite)

On another hand, a cryo-cooler or Pulse Tube Cooler can be implemented. The required 20 000 h lifetime is not a killer and no µ-vibration problem is expected for a 1 mm position accuracy. 3.3.3 Data management The Data Management System (DMS) is organised around a new generation On-Board Management Unit (OBMU) running the on-board software and managing the platform, the FF units and the science payload. The fully redundant OBMU includes an ERC 32 processor module, an internal 2 Gbits system Mass Memory, TM encoders and TC decoders. The OBMU is directly connected to the platform units and FF units through a standard MIL-STD-1553B bus and to the science payload thanks to a SpaceWire. The 2 Gbits Mass Memory internal to the OBMU is used for the day-to-day operations (storage of the Mission Timeline, commands ﬁles, on-board command procedures), platform housekeeping, events and acknowledgement data storage. Each satellite embarks its autonomous science data storage so that there is no need for data exchange between the spacecraft prior to down-link. The needs in term of data acquisition and storage are different for the lens and the detector: a 20 Gbits Mass Memory is baselined on the lens satellite and a 40 Gbits unit is embarked on the detector satellite. 3.3.4 Electrical and power The electrical power generation and distribution system of each satellite is composed of one rotating solar array with GaAs triple junction solar cells, one Li-Ion battery, one Power Conditioning and Distribution Unit (PCDU), one Solar Array Drive Mechanism (SADM) and one pyro-module for the deployment of the solar arrays. Springer

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The required solar array areas are different on the lens and the detector: a 1.5 m2 area shall be considered for the lens satellite while 2.5 m2 are needed for the detector satellite. The battery need is quite small as the satellites are always Sun pointed during observation and Earth communication sessions. Almost 100% of power is available during the 15-day observations and power only decreases during attitude slews from inertial to inertial or inertial to Earth pointed attitudes. A battery capacity of 180 and 320 Wh is embarked on the lens and detector satellites respectively. 3.3.5 Space to ground RF communications The space to ground RF communication system relies on X-band for up-link and down-link. It is composed of two X-band transponders including one X-band transmitter (X-TX) and one X-band receiver (X-RX), two High Power Ampliﬁers, one ﬁxed MGA, two LGAs and one RFDU (RF Distribution Unit). The MGA is used for nominal operations during Cruise and science observation. Each LGA has an hemispherical coverage for a complete 4π sr RF coverage during LEOP (Launch and Early Operations Phase), critical operations and backup. The X-band transponders are cross-strapped with the OBMU; the X-RX are used in hot redundancy (always on) and the X-TX are used in cold redundancy. The High Power Ampliﬁers connected to the X-TX provide a 22 W RF signal (end-of-life). The RFDU, including diplexers and switches, provides a full cross-strapping between antennas, transponders and ampliﬁers. 3.3.6 Inter-satellites RF link Even if (i) a decentralised Guidance Navigation and Control (GNC) considering separate attitude/position control for the detector and the lens can be designed, and (ii) a Failure Detection Isolation and Recovery (FDIR) based on metrology data only can be established, a two-way inter-satellites link would permit the design of a centralised and more accurate GNC together with a more robust FDIR (e.g. for exchanging health statuses). Also, this link would allow the ground operating the formation through a single satellite, resulting in simpliﬁed operations. In case of a centralised GNC, the cold gas propulsion can be distributed on the detector and the lens satellites. The hardware supporting the inter-satellites link function can be either the hardware supporting the RF metrology, or a dedicated hardware such as an S-band transponder with omni-directional antennas. 3.3.7 Dynamics, AOCS and GNC Attitude control. The AOCS is in charge through the OBMU of the management of the AOCS equipment, AOCS modes and transitions, attitude estimation, control laws algorithms and commands generation to the actuators. The AOCS is also in charge of the management of the mono-propellant and cold gas propulsion systems, and of the data acquisition from RF and optical metrology units. Gyro-stellar attitude estimation and reaction wheels control are baselined for science observation, Earth communication sessions and attitude slews. The STR is aligned with the observation LOS. The Safe Mode and attitude acquisition rely on the same mode and Springer

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Table 5 Equipment used by the AOCS/GNC for attitude and position control

Fig. 9 AOCS/GNC modes transition logic

Star Tracker Gyros Coarse Sun Sensor RF metrology Optical metrology Reaction Wheel Chemical propulsion Cold gas propulsion

Lens

Detector

1+1 2 × 3 axis 3 1+1 None 3+1 4+4 None

1+1 2 × 3 axis 3 1+1 1 3+1 4+4 8+8

Stand-by Mode

Sun Acquisition Mode

from any mode upon failure

Coarse Transition Mode

Normal Mode

Orbit Control Mode

are based on Coarse Sun Sensors, gyros and chemical propulsion. Wheels-off-loading are performed with the chemical propulsion. Position control. The 3D position of the lens relative to the detector is sensed by the RF and optical metrology. The inter-satellite distance is controlled in the lateral plane and along the longitudinal axis with a 8 cold gas thrusters conﬁguration providing a pure force actuation capacity without disturbance due to thrusters misalignment (Table 5). AOCS/GNC modes. Four AOCS/GNC modes are designed to fulﬁl the mission requirements (Figure 9): • Sun Acquisition Mode (SAM): starting from any mode, this mode is entered to acquire and maintain a Sun pointing attitude using gyros, Coarse Sun Sensors and chemical thrusters; this mode is also used for attitude re-acquisition in case of Safe Mode. • Coarse Transition Mode (CTM): starting from the SAM, this mode is used for the STR initialisation and stars acquisition; the attitude is estimated from the STR and gyros measurements and controlled with the thrusters. • Normal Mode (NM): this mode includes 3 sub-modes for the control of the spacecraft attitude during inertial pointing phases (Earth or gamma ray source before activation of the FF units), attitude slews and science observation sessions, where the 3D position of the detector relative to the lens is also controlled.

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Table 6 Formation ﬂying package units Lens

Detector

Optical metrology

2 transceivers Emit/receive antennas Reﬂecting corner cubes

Cold gas propulsion

None

2 transceivers Emit/receive antennas Coarse lateral metrology Fine longitudinal metrology Cold gas tank 2 × 8 thrusters

RF metrology

• Orbit Control Mode (OCM): this mode is used for trajectory correction manoeuvres during cruise and source re-targeting on the operational orbit. When the system is switched on, the AOCS is ﬁrst set in a Stand-by Mode where no control is active and all AOCS units are off. A priori, this mode is not used later on during the mission. 3.3.8 Chemical propulsion Chemical propulsion is used on both satellites for the trajectory correction manoeuvres from LEOP up to the ﬁnal orbit acquisition at L2, and also on the detector satellite for the gamma ray source retargeting manoeuvres. Therefore, the volume of propellant tank required on the detector satellite is larger than the one required on the lens satellite: a 50 l tank is embarked on the lens and a 70 l tank is required on the detector. A nominal and redundant set of four 1N thrusters are mounted on the spacecraft. They are located on the same side. Therefore, each thruster activation will have to be preceded by an attitude slew (with the reaction wheels) to get the correct attitude before the thrust. 3.4 The formation ﬂying package FF units are functionally decentralised in a dedicated Formation Flying Package (FFP), different on the lens and the detector due to the selected FF concept (Table 6). The FFP includes the RF metrology, the optical metrology and the cold gas propulsion, used for the ﬁne position and attitude control of the detector relative to the lens. All units of the FFP are directly connected to the OBMU for command control and to the PCDU for power distribution. Data acquired by the FFP units are transferred to the OBMU and stored in the large size Mass Memory. 3.4.1 RF metrology The same RF metrology is embarked on both satellites. It consists of a pair of redundant transceivers (emitter/receiver) and a set of emit/receive antennas. Each antenna has a 2π sr coverage and is used both in emission and reception. It is assumed that the RF metrology system can also be used for data exchange between the satellites if required, so that there is no need for other inter-satellite link facility.

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Exp Astron (2005) 20:465–482 Table 7 Expected measurement performances of the ﬁne RF metrology Operational range

Required measurement accuracy

Longitudinal axis

250 m

Lateral plane

5◦ half cone

Position bias: 3 cm Position noise: 0.4 mm (1-σ ) Stability noise: 0.5 mm/s (1-σ ) Position bias: 0.2◦ Position noise: 0.07◦ (1-σ ) Stability noise: 0.5 mm/s (1-σ )

The RF metrology is used to determine the lateral and longitudinal position of the detector relative to the lens. The STR is used to point the satellites to the same inertial direction, with the detector and lens LOS aligned with the gamma ray source direction. Antennas are mounted on face-to-face sides. With a minimum set of 1 antenna on the detector and 3 antennas on the lens, the detector will know the 3D position of the lens, and the lens will know at which distance is the detector. For safety reason and/or to get a symmetrical conﬁguration, the number of antennas can be enlarged. The antennas are placed on the same sides as the optical metrology to get simultaneous RF and optics measurement in the same attitude (for RF-optical metrology transition or comparison). For functional aspects, distinction is made between a coarse RF metrology and a ﬁne RF metrology (even if both can rely on the same equipment). The operational range of the coarse RF metrology is assumed to be 30 km longitudinal and 2π sr lateral. It is used at the beginning of the mission. Its typical measurement accuracy is 10 cm in longitudinal and 5◦ in lateral. The operational range of the ﬁne RF metrology is 250 m longitudinal and 5◦ half cone lateral. It is used to acquire the optical metrology and as backup position sensing. Its typical performances are reported in Table 7. 3.4.2 Optical metrology The optical metrology embarked on MAX (Figure 10) includes a coarse lateral optical metrology for the measurement of the position in the lateral plane (normal to the lens to detector direction), and a ﬁne longitudinal optical metrology for the measurement of the position along the longitudinal axis (focal length, along the detector-lens LOS). The active metrology (laser source, optics, detector, Fabry-Perot) is implemented on the detector satellite only. The lens detector, fully passive, only embarks a series of reﬂecting corner cubes. The ﬁne longitudinal optical metrology is not strictly required for MAX science, but is baselined as MAX is likely to be also an FF demonstration mission. It is based on a Frequency Shift Interferometer (FSI) with a large or ﬁne beam. The source is a tuneable ECDL (External Cavity Diode Laser) with a 25 GHz frequency sweep. The Fabry-Perot used for calibration of the frequency sweep has a free spectral range of 0.5 GHz and a thermal stability of 0.01 K. The sweep range uncertainty is 6 kHz, the fractional fringe counting uncertainty is 1/165 (Table 8). 3.4.3 Cold gas propulsion Cold gas is used during science observation sessions for controlling the 3D position of the detector relative to the lens. Ten kg of cold gas (N2 ) are embarked in a 30 l tank pressurised at Springer

Exp Astron (2005) 20:465–482 Table 8 Measurement range and performances of the optical metrology

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Fine Longitudinal

Coarse Lateral

Operational range

Measurement accuracy

1 km 0.25◦ half cone <1 mm/s 1 km 0.25◦ half cone

0.01 mm

0.1–1 mm

300 bar. As pure force is required for an accurate position control, a nominal and redundant set of 8 thrusters are implemented. 4 Preliminary system budgets The mass budget of the MAX detector and lens spacecraft is compatible with a launch with Soyuz ST/Fregat with comfortable margin (Table 9). The overall mass of both satellites is smaller than 1000 kg including a contingency of 20%. With a preliminary worst case mass estimate of 300 kg for the complete launch adaptor (i.e. launcher to satellite and inter-satellites adaptors), the mass margin with respect to the 2000 kg Soyuz capacity to Lagrange point is acceptable at this stage of the programme. The power budget of the lens and the detector satellites have been computed for the observation, communication and re-targeting phases (Tables 10 and 11). The power demand is about 200 W for the lens and 340 W for the detector (the difference being mainly due to the payload). Table 12 provides the chemical and cold gas mass required to fulﬁl the mission needs. As the retargeting manoeuvres (30 kg with 50% margin) are performed by the detector, the need is to embark 70 kg of mono-propellant on the detector and 40 kg on the lens. Ten kg of cold gas are embarked on the detector satellite for ﬁne manoeuvres. Table 13 shows that during a 15-day observation session, less than 20 Gbits of data are generated on-board the detector, and less that 10 Gbits for the lens. These ﬁgures have been used to baseline with 100% margin a 40 Gbits and 20 Gbits Mass Memory for the detector and the lens respectively.

Fig. 10 Coarse lateral metrology (in red) and ﬁne longitudinal metrology (in bule). The lens satellite is on the left

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5 Programmatics The launch of MAX can be envisaged mid-2011 providing a phase A study is initiated at the beginning of 2006. The development of the FF package and the science payloads are on the critical path. To secure the programme, the development of the optical metrology has to start shortly after Phase B kick-off, and the deﬁnition and development of the science payload has to run in parallel with the development of the platform and FF units (Table 14).

Table 9 Preliminary mass budget including 20% margin Platform Structure AOCS/GNC Chemical propulsion Thermal Data handling Power RF Communication FF payload RF metrology Optical metrology Cold gas propulsion FF Interface Unit Science payload Crystals set Supporting frame Passive radiator Detection plane Electronics Total

Lens satellite

Detector satellite

266 78 14 50 10 24 58 33 30 24 2 0 4 252 180 72

283 78 14 67 10 24 58 33 70 24 19 23 4 72

548 kg

Table 10 Preliminary power budget for the lens satellite including 20% margin

Platform AOCS/GNC Chemical propulsion Thermal Data handling Power PF Communications Formation ﬂying Science Payload Total (W)

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Observation

Earth comms

Re-targetting

136 25

136 25

36 20 18 36 24 24 184

36 20 18 36 24 24 184

160 25 24 36 20 18 36 24 24 208

24 36 12 425 kg

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Table 11 Preliminary power budget for the detector satellite including 20% margin

Platform AOCS/GNC Chemical propulsion Thermal Data handling Power RF Communications Formation ﬂying Science payload Total (W)

Observation

Earth comms

Re-targetting

136 25

136 25

36 20 18 36 48 156 340

36 20 18 36 24 156 316

160 25 24 36 20 18 36 24 156 340

Table 12 Mono-propellant and cold gas preliminary budgets Chemical (kg) Compensation for perigee velocity variation Removal of launcher dispersion Mancruvres during Cruise Transfer to operational orbit Correction after injection Rendez-vous at L2, ISD initialisation Constant lens-detector ISD control Gamma ray source re-targetting FDIR, anti-collision Total With 50% margin (kg)

Gold gas (kg)

2.4 6.0 1.2 0.0 0.5 12.0 6.0 20.0 2.4 45 67

6 9

Table 13 Preliminary data generation budget P/F housekeeping (kbps) FF housekeeping (kbps) Science (kbps) Total (kbps) Observation duration (days) Data volume (Gbits)

Lens

Detector

5 2 0 7 15 8.7

5 5 5 15 15 18.5

Table 14 MAX development planning Phase A Phase B Phase C/D AIT Margin Launch campaign Launch

12 months, starting Jan 06 12 months, starting Jan 07, with a P/F Suitability Review in Sep 07 and the PDR in Dec 07 36 months, starting Jan 08, with the CDR in Jun 09 15 months for the detector, 12 months for the lens 4 months 2 months June 2011

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The development of both satellites relies on a Structural Model (SM), a Proto-Flight Model (PFM), and a System Validation Bench (SVB) including ﬂight representative models of the OBMU, RF metrology, optical metrology and science payloads. No Engineering Qualiﬁcation Model is foreseen. Risks have been identiﬁed at system level with the development and validation of new closed loop GNC algorithms with dedicated sensors and actuators, resulting in a complex GNC on-board software.

6 Conclusion Beyond its scientiﬁc interest for nuclear astrophysics, MAX is a good opportunity for demonstrating Formation Flying concepts and technologies in space. EADS Astrium propose a space implementation of the MAX gamma ray telescope as a pair of satellites in active Formation Flying, one satellite supporting the lens, one satellite embarking the detector. The lens satellite is kept inertial and pointing to the gamma ray source with an accuracy of 15 arcsec, while the detector satellite is controlled in position and attitude with respect to the lens at a constant distance of 86 m, within an accuracy of 1 cm in lateral and 10 cm in longitudinal. The proposed satellites are fully autonomous with respect to each other and with respect to the ground. They include all the redundancy required by an interplanetary space science mission. The satellites operate on the free-insertion halo orbit around the Earth-Sun Lagrange point L2. The proposed mission considers the observation of 50 gamma ray sources, each one with a continuous duration of 15 days. The platform is based on a new generation platform in the 200 kg range. The large experience gained by EADS Astrium in Formation Flying through numerous ESA and CNES studies and internal funding, allows the deﬁnition of the Formation Flying package that fulﬁls the requirements of the MAX science mission with margins. Mock-ups of GNC and optical metrology benches are already under development at EADS Astrium. With a phase B kick-off in early 2007, the satellites would be ready to be launched midJune 2011 by a Soyuz ST/Fregat from Kourou.

References 1. Andritschke, R. et al.: this volume (2006) 2. Barri`ere, N. et al.: this volume (2006) 3. Borde, J., von Ballmoos, P.: Proceedings of the 6th Small Satellites Systems and Services Symposium, September 2004, La Rochelle (2004) 4. Caroli, E. et al.: this volume (2006) 5. Giuliani, A.: Proc. SPIE 4507, 203 (2001) 6. Kn¨odlseder, J.: this volume (2006) 7. Leising, M.: this volume (2006) 8. Takahashi, T.: this volume (2006) 9. Weidenspointner, G. et al.: this volume (2006) 10. Wunderer, C. et al.: this volume (2006)

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Exp Astron (2005) 20:483–495 DOI 10.1007/s10686-006-9070-1 ORIGINAL ARTICLE

MAX: Formation ﬂying for nuclear astrophysics Paul Duchon

Received: 2 December 2005 / Accepted: 10 August 2006 C Springer Science + Business Media B.V. 2006

Abstract In 2004 CNES decided to perform 4 phase 0 studies dedicated to Astrophysics and achieved thanks to Formation Flying space systems: ASPICS (A Solar Physics Mission to observe in UV and Visible the Solar Corona between 1.01 and 3.2 Solar Radius), PEGASE (an IR interferometry mission to observe Hot Jupiter, Brown Dwarfs and Proto planetary disks), SIMBOL-X (hard X-rays telescope to observe: Accretion onto compact objects, Black Holes, obscured Galactic Nuclei, . . . .) and MAX (a Nuclear Astrophysics Mission to observe: Supernovae, Neutron Stars,. . .). For this last mission, presented here, two spectral bands around important gamma-ray lines have been selected (450–530 and 800–900 keV). The formation ﬂight allows to realise a long focal length of 80–90 m which is necessary to build a reasonably sized gamma-ray telescope based on a Laue crystal lens. The Space System design allows to have a good spacecrafts mass margin in High Elliptical Orbit with a Soyuz launch (Initial Orbit: Perigee altitude ∼44,000 km and Apogee altitude ∼253,000 km). Keywords Space system . Astrophysics . Gamma ray imaging . Pre-project study 1 Introduction The MAX concept telescope is based on 2 main parts: A “gamma-ray Lens” and a “Detector”. The Lens is fully formed of diffractive crystals (Cu and Ge) disposed on concentric rings. In order to be diffracted, an incoming gamma-ray must satisfy the Bragg-formula (2d sin[θB ] = nλ) where d is the crystal plane spacing, θB is the Bragg angle, n the reﬂection order, and λ the wavelength of the gamma-ray. A crystal at a distance r from the revolution axis of the ring, which represents the optical axis of the lens, is oriented so that the angle between the incident beam and the crystal planes is the Bragg angle θB . The focal length of the system, f, is then given by the equation f = (r × d)/(n × λ) (see [6]). Thus, the “Detector” is located at a distance f of the “Lens” with f ∼ 86 m for this MAX study. P. Duchon Centre National d’Etudes Spatiales, 18 Avenue Edouard Belin, 31041 Toulouse Cedex, France Springer

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In the following we will call “lens spacecraft” the satellite which carries the gamma-ray lens and “detector spacecraft” the satellite that carries the detector, situated at the focal spot.

2 Max scientiﬁc mission The two spectral bands of MAX correspond to the two main objectives of the mission. The 800–900 keV band covers the 847 keV gamma-ray line that is expected from explosive nucleosynthesis in Type Ia supernovae, following the radioactive decay of 56 Ni → 56 Co → 5 6Fe. The sensitivity that is required in this line to discriminate between various explosion models amounts to a few 10−7 ph cm−2 s−1 . The 450–530 keV band covers the 511 keV electron-positron annihilation line, which eventually could be detected from micro-quasars (see below), active galactic nuclei (AGN, see below) or in pulsars (see below). In addition, the 478 keV desexcitation line of 7 Li falls also in this band, allowing studies of cosmic-ray interactions in the universe.

3 Max space system 3.1 The Laue lens payload The MAX “Lens Spacecraft” embarks a Laue diffraction lens containing more than 7800 germanium and copper crystal tiles disposed on 24 concentric rings [1]. It allows to focus simultaneously in the two spectral energy bands described previously (Figure 1). 3.2 The detection payload The MAX detection plane makes use of “Compton germanium detectors” yielding a spectral resolution of 2 keV (see Figure 2 and the presentations in the detector section of this volume). The baseline cross strip Ge detector has a size of 80 mm × 80 mm × 15 mm, and consists of four layers (37 × 37 strips). The 300 channels of the Ge stack will consume 31 W, the detectors system weighs 15 kg. The detectors operate at a temperature 75 to 95◦ K (Figure 3).

Fig. 1 The effective area of the lens as a function of energy (the total geometric area is 18,000 cm2 , the mass of the crystal tiles is 140 kg) Springer

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Fig. 2 Example of a cross Strip 3-D Ge Detector [2]

Fig. 3 Layout of the detector electronics

3.3 Space system study & scenarios During MAX phase 0 at CNES/PASO we studied several Space System scenarios [3]. We present here only the main option that has been identiﬁed (Figures 4 and 5). 3.4 Orbit & mission operation Scientiﬁc observations have to be performed outside the Van Allen belts (to reduce the instrumental background), that is to say an altitude greater than 73,000 km. Nevertheless it has been accepted to intersect the belts partially at a very high altitude once per week. L2 (Sun/Earth) orbit would be the best choice from this point of view and for gravity gradient perturbation for the Guidance Navigation & Control (GNC) of the formation but an High Springer

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Fig. 4 Scientiﬁc mission and main orbit options. The minimal mission lifetime is 2.5 years with 2 years for science operations

Fig. 5 The space segment. The main option is a Soyuz launch from Kourou

Elliptical Orbit (HEO) is preferred and sufﬁcient taking into account the main decisive parameters (cost, mass margin for given Launcher, . . . . .). Optimizing the global resources of both spacecraft (S/C) led then to select a scientiﬁc Orbit with 44,000 km perigee altitude/253,000 km apogee altitude/7 sidereal days period/Low initial inclination. It has been chosen to give more than 90% time above 73,000 km which maximizes astrophysics observations (Figure 6). The satellites V is around 500 m/s and can be achieved with a classical and robust hydrazine system. The daily visibility are ∼12 h per station with a maximum visibility gap of 2 h. At perigee the visibility is permanent (24 h) for the chosen station. During mission there is no need to maintain exactly the orbit parameters. The importance is to keep the correct orbit period and the phasing with the ground segment to facilitate the operations. In that perspective roughly one manoeuvre per month is Springer

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Fig. 6 Three to four eclipses of 87 –105 min occur in spring and autumn in MAX’s High Elliptical Orbit (HEO) Fig. 7 Evolution of the orbits inclination (increase of perigee, decrease of apogee)

Fig. 8 Operation activities during on orbit: the ﬁrst day (J1, during perigee is generally reserved for housekeeping tasks, during J2–J7 science operations dominate)

expected to maintain the semi-major axis of the orbit. The result is that the orbit parameters evolution is constrained by Luni-solar effects and the perigee will increase to ∼70,000 km after 2 years due to lunar effects combined to semi major axis conservation (Figure 7). Typical operations on such an orbit consists to perform science during 6 days (out of perigee) and to use permanent perigee visibility to download the bigger part of the telemetry. Outside perigee a daily contact of one to two hours is sufﬁcient for scientiﬁc observations programming and/or monitoring of the formation repointing to a new target (Figure 8). The typical observation time could need 1 Ms (106 s) of continuous observation (∼12 days). In the space system design 60 targets per 2 years have been taken into account. The following scheme is giving an example of operation (Figure 9). Springer

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Fig. 9 Example of in-orbit operation

3.5 Guidance Navigation and Control (GNC) of the formation On the pre-selected orbit the conditions are very favourable for the formation ﬂying as it can be seen in Figure 10 [3]. The solar pressure is the main contributor to the perturbations except around the perigee. At perigee, gravity gradient perturbations become dominant. However, these perturbations are still rather low on an absolute level, and it has been decided to actively keep the formation around perigee in order to avoid its break-up and reconstruction after perigee passage. The instruments ﬁeld of view amounts to about 1 arcmin; the requested pointing accuracy is hence 15 arcsec. Since a pointing accuracy of 15 arcsec is required there is no need of having a line of sight measurement accuracy of better than 2 arcsec. 15 arcsec would be perfectly ﬁne. The lens attitude control accuracy shall be better than 10 arcsec during scientiﬁc observation. In the following we summarise the main requirements for the formation ﬂight: Relative positioning: – lateral control accuracy (Formation LOS.): ±1 cm (±24 arcsec) – longitudinal control: ±10 cm – lateral position knowledge: 1 mm (or 2 arcsec LOS) Constraint on inertial and relative metrology lateral sensor + star tracker with 1 arcsec accuracy range Fig. 10 Variation of the gravity gradient during an orbit

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Lens Spacecraft attitude control: – Pointing: 15 arcsec – Stability: no constraint Detector Spacecraft attitude control: – Pointing: 1 deg – Stability: no constraint – low constraints on attitude control We now summarise the main choice that has been taken considering the Guidance Navigation and Control (GNC) functions: – G.N.C. concept: The selected philosophy for MAX Formation Guidance Navigation and Control consists in having all the relative position control function in only one spacecraft (the detector satellite). Then, the Detector Spacecraft is position controlled with respect to the Lens Spacecraft. This last one stands on its natural orbit and performs its ﬁne pointing. The relative position is measured with respect to the Lens Spacecraft reference frame. This ensures good performances by decoupling position and ﬁne attitude control. Moreover, this concept simpliﬁes in ﬂight operations and improves system safety. – Metrology system: For the deployment and safe mode phases, a RF localization system based on GPS metrology constitutes the baseline. Each spacecraft is equipped with a Rx/Tx terminal (Receiver/Transmitter) plus a set of antennae and the 3D position is reconstructed from the range and line of sight measurements. This system permits moreover to fulﬁl the observation phases requirements for the relative longitudinal position knowledge. For observation phases, the requirement of relative position knowledge is driving the use of a lateral sensor, including a laser source, (installed on the Detector Spacecraft) which measures the line of sight of the beam reﬂected by a set of corner cubes (on the Lens Spacecraft) with a 1 arcsec precision. Formation GNC is located by choice on the detector spacecraft which directly communicates with the Ground Station. This strategy is still to be conﬁrmed but by this way during routine science phases the formation could be seen by the Ground Segment as a “single satellite”. For non nominal phases or for commissioning or positioning, each satellite is independent and communicates directly with the Ground (see Figures 11 and 12): Then to summarize, 2 communications modes are foreseen:

r Housekeeping mode (telecommand (TC), housekeeping telemetry (HKTM), and ranging) r Sapcecraft telemetry (TMCU) download (TC and telemetry(tm) high rate from the detector only). The access to the Lens S/C will be done through the ISL (intersatellite link) in nominal phase. There will be direct access to the Lens S/C (parallel communications) for:

r Cruise & positioning r Commissioning r Emergency Springer

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Fig. 11 Formation ﬂying and GNC

Fig. 12 Formation ﬂying and communications

These considerations leads us to the following proposal of equipments needed for each of the satellites: There seems to be no critical technology in metrology (currently in development or R&D studies) and propulsion (already available) (Figure 13). 3.6 Spacecrafts conﬁguration There are two issues that have important impact of the conﬁguration of the MAX mission: (A) observational constraints, and (B) the quality of the lens shape, and in particular its thermoelastic behaviour [3]. (A) Observational constraints: The limited number of targets accessible on the celestial sphere, for this mission (Supernovae, Active Galaxy Nuclei, pulsar, . . . .), forces to maximize the celestial zone accessible by the “distributed telescope” L.O.S. (Line Of Sight: X-axis in Springer

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Fig. 13 Required technology for metrology and actuation

Fig. 14 The MAX pointing strategy

Figure 14). If a quasi allsky access is desired, a thermal enclosure of the Laue lens with MLI (Multi Layer Insulator) layers has to be foreseen, which can guarantee a passive thermal internal balance irrespectively of the Sun aspect angle (the interaction of gamma-rays with the MLI material can be considered as negligible). In addition to this, both spacecraft (Lens S/C and, particularly, Detector S/C) .. need a cold face that has to be situated opposite to the Sun direction. To solve this problem, we study a pointing strategy described (Figure 14, illustrated with the Detector S/C). Springer

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Fig. 15 The conﬁguration of the solar panels, the passive radiator and the telescopes LOS permits the sun as possible target

Fig. 16 The multi stage passive radiator cooling the detector cryostat

If +X is the LOS (Line Of Sight) direction (Detector S/C to Lens S/C), we propose to maintain the −z direction within the hemisphere that is located opposite to the Sun direction. For this purpose two rotations are performed: a ﬁrst around the z axis (which is directed towards the Sun) and a second around the y axis. The second rotation may cover the angle range +/− pi/2; the solar panels must not follow this second rotation (i.e. they should Tank counter-rotate). In Figure 15, we see that it is possible to have the sun as target (putting a tilt of 5◦ between the “detector cold face” and LOS at detector structure level). This observation strategy will be possible with this Detector Spacecraft conﬁguration (see Figure 17). Concerning the detection assembly, the thermal constraint is mainly given by the detection chamber temperature (75◦ K < TGe stacks < 95◦ K; See § 3.2 and Figure 16. This level of temperature justiﬁes a multi stages cryostat with stiffener and thermal dispenser to carry the detection chamber. In addition to that, we decided, during the MAX phase 0 study to have a strong commonality between both platforms; in particular, to have a Lens S/C diameter (950 mm) smaller than the lens minimum diameter (1100 mm). Thus, Detector and Lens platform are similar and “thin”! The detector S/C height is, approximately, 2.8 m or 3.3 m according to the option chooses during transfer phase (Spacecrafts respectively attached or separated during transfer orbit) (Figures 17 and 19). Springer

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Fig. 17 The MAX detector spacecraft

Fig. 18 The CNES/ALCATEL concept for the lens support structure

Fig. 19 The MAX lens spacecraft

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Fig. 20 (a) Option 1, Soyuz–Sylda fairing conﬁguration. (b) Option 2, Soyuz fairing conﬁguration

(B) Lens quality shape (see [5]): The main requirement is the maximum angular orientation uncertainty for each crystal with respect to the nominal LOS. The value of this requirement is 10 arcsec. A detail study of the lens behaviour has shown that the lens thermal enclosure with an additional thermal system composed of a few heaters and thermistors will be enough to satisfy the “10 arcsec” speciﬁcation. The lens structural concept [4, 5] is represented in Figure 18. Springer

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We saw that Detector and Lens Platforms have the same diameter D = 950 mm (see previously: Section 3.6.A). The height of the Lens S/C height is, approximately, 2 m or 1.8 m according to the option chooses during transfer phase (Spacecrafts respectively attached or separated during transfer orbit) (Figures 17, 19 and 20). The total mass is, about, 850 kg for the Lens Spacecraft and 570 kg for the Detector Spacecraft (with 30% system margin and in the option “separated during transfer orbit”). 3.7 Launch conﬁguration Soyuz-fregat is the optimal Launcher for this class of mission (total mass ∼1500–2000 kg in high elliptical orbit between ∼44,000 and ∼250,000 km). Two launch options were considered during this study with this launcher: – 1st Launch option, see Figure 20(a): Use of the “Soyuz-Sylda fairing” where each spacecraft is carried by the launcher or the Sylda structure (Additional mass: 300 kg). – 2nd Launch option, see Figure 20(b): The Detector spacecraft is carried by the Lens spacecraft on the launcher. The 1st launch option “Soyuz-Sylda fairing” joint with the transfer orbit option “separated during transfer orbit” is the favoured solution. An intermediate solution (if mass were to be a problem), would be to couple the satellites during launch (to avoid the Sylda: 2nd launch option) and to separate them at injection by the launcher (Transfer orbit option “separated during transfer orbit”). 4 Conclusion During this phase 0 study with CESR we have shown that the accessible ﬁeld of view reached by the MAX distributed instrument L.O.S. (close to 4π strd) allows to maximize nuclear astrophysics observation (∼30 targets/year; Each during 1 Ms). In this condition, passive cryogenics thermal subsystem satisﬁes and simpliﬁes the space segment needs (on the Detector spacecraft as well as on the Lens spacecraft). Special attention must be paid to the quality of the lens shape. In fact, the focal length of ∼86 m requires a mounting accuracy of the lens crystals to better than 10 arcsec. The MAX Formation Flying performances are moderate and accessible in ﬂight in the near future (2011–2013 launch). Both orbit options (L2 & HEO) allow to release substantial mass margins (mainly for Soyuz launch from Kourou in HEO: 400 kg margin with 30% system margin). In addition to that MAX in HEO is less risky, easier and cheaper. Acknowledgements We would particularly like to thank Mrs. Peter von Ballmoos, Nicolas Barri`ere, Gerry Skinner (CESR-Toulouse), Emmanuel Hinglais, Rodolphe Cl´edassou, (CNES Toulouse) and all the team at CNES and CESR which participated in the 2005 phase 0 study for MAX.

References 1. 2. 3. 4. 5. 6.

Barri`ere, N. et al.: Exp. Astron. DOI 10.1007/s10686-006-9058-x (2005) Boggs, S. et al.: Exp. Astron. DOI 10.1007/s10686-006-9051-4 (2005) Duchon, P. et al.: Rapport de phase 0 MAX, CNES/PASO study report, November 05 (2005) Leyre, X. et al.: Exp. Astron. DOI 10.1007/s10686-006-9044-3 (2005) Hinglais, E. et al.: Exp. Astron. DOI 10.1007/s10686-005-9020-3 (2005) von Ballmoos, P. et al.: Proceedings of the 5th INTEGRAL Workshop, Munich 16–20 February 2004, ESA SP–552 (2004) Springer

Exp Astron (2005) 20:497–503 DOI 10.1007/s10686-006-9038-1 O R I G I NA L A RT I C L E

Formation ﬂying for a Fresnel lens observatory mission John Krizmanic · Gerry Skinner · Neil Gehrels

Received: 18 November 2005 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract The employment of a large area Phase Fresnel Lens (PFL) in a gamma-ray telescope offers the potential to image astrophysical phenomena with micro-arcsecond (µ

) angular resolution [1]. In order to assess the feasibility of this concept, two detailed studies have been conducted of formation ﬂying missions in which a Fresnel lens capable of focussing gamma-rays and the associated detector are carried on two spacecraft separated by up to 106 km. These studies were performed at the NASA Goddard Space Flight Center Integrated Mission Design Center (IMDC) which developed spacecraft, orbital dynamics, and mission proﬁles. The results of the studies indicated that the missions are challenging but could be accomplished with technologies available currently or in the near term. The ﬁndings of the original studies have been updated taking account of recent advances in ion thruster propulsion technology. Keywords Gamma-ray astronomy · Optics · Formation ﬂying 1. Introduction A unique feature of missions using Fresnel lenses for gamma-ray astronomy is the large distances over which precise station-keeping of two spacecraft is required. The concept of a mission using a Fresnel lens for ultra-high angular resolution gamma-ray astronomy has been studied by the NASA GSFC Integrated Mission Design Center (IMDC) [2]. The IMDC is a resource dedicated to developing space mission concepts into advanced mission designs by J. Krizmanic () Universities Space Research Association, NASA, Goddard Space Flight Center, Greenbelt, Maryland 20771, USA e-mail: [email protected] N. Gehrels NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA G. Skinner CESR, 9, avenue du Colonel-Roche 31028, Toulouse, France Springer

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providing system engineering analysis of all the ﬂight systems and subsystems. The IMDC process involves the mission scientists working with engineers of all the major engineering disciplines, e.g. mechanical, electrical, propulsion, ﬂight dynamics, communications, mission operations, etc., in a highly interactive environment which naturally allows for inter-discipline communications and trade studies. For the Fresnel mission studies, an additional formationﬂying ﬂight dynamics group also participated. Two conﬁgurations of the mission were studied, a deﬁnitive Fresnel mission with a 106 km spacecraft separation and a smaller, pathﬁnder mission with a 105 km focal length. The choice of Fresnel conﬁgurations assumed for the IMDC study was driven by the desire to bound the formation-ﬂying problem via a fairly ambitious mission and to determine how the study-developed parameters varied for a more relaxed conﬁguration. Thus, the designation of ‘pathﬁnder’ should be viewed in this context and is not meant to preclude an initial Fresnel mission with a more modest mission proﬁle, e.g. achieving milli-arcsecond angular resolution with a much shorter satellite separation. Each mission conﬁguration completed a dedicated, one week IMDC study. After discussing the requirements and assumptions used as input for the IMDC studies, the mission proﬁles and key ﬁndings are summarized along with a re-analysis of the propulsion requirement to include the implications of recent advances in ion thruster technology.

2. Mission requirements and assumptions The overarching philosophy inherent in both of these IMDC studies was that only technologies already existing or anticipated in the near future were considered as available resources for the spacecraft and mission development. Thus the results indicate if the missions are feasible in the near term, while identifying areas that need to be improved or developed. Table 1 details the parameters that were used to deﬁne the science payloads. Starting with the full Fresnel mission, two 4.5 meter diameter aluminum Fresnel lenses in an orthogonal arrangement were incorporated into the lens-craft. The lenses would be designed for different photon energies and require a simple, 90◦ rotation to exchange one lens for the other. The size of the Fresnel lenses were reduced to 1 meter in diameter for the pathﬁnder conﬁguration. Table 1 The parameters for the science payloads for the Full and Pathﬁnder Fresnel missions

Focal length Angular resolution Fresnel lens diameter Fresnel lens mass CZT detector size Detector mass Detector powera CZT pixel size Pixel angular resolution Telescope ﬁeld-of-view Time on target Mean repointing time

Pathﬁnder

Full

105 ∼10 1 30 1 200 200 2×2 4 2000 21 minimize

106 ∼1 4.5 600 1 200 200 2×2 0.4 200 21 minimize

km µ

meter kg meter2 kg watts mm2 µ

µ

days

a The power available for detector operation will be much larger due to that needed by the ion propulsion for target re-orientation

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The detector, located on a separate detector-craft, was chosen to be a 1 meter2 CZT array, segmented into 2 × 2 mm2 pixels. This allowed for the experience with the SWIFT mission [3] to easily deﬁne the detector system parameters, e.g. mass and power. A single lens-craft and a single detector-craft were initially chosen for each mission conﬁguration along with the desire to accommodate these in a single launch vehicle with an existing deﬁned dual-manifest capability. 2.1. Flight dynamic parameters The choices of orbits and and spacecraft alignment orientations are dictated by the objective of minimizing the propulsion requirements while allowing for the potential viewing of astrophysical objects in any direction, albeit at different times of the orbit cycle. The on-target time was chosen a priori to be 3 weeks with the goal of minimizing re-orientation times between observational targets. A representative list of potential astronomical sources of gamma-rays determined the average re-orientation to be 20◦ . The spacecraft control and alignment requirements are determined by the performance of the telescope. The gamma-ray source measurements are insensitive to modest (∼1◦ ) tilts of either the lens or detector and to mild changes in the separation of the two spacecraft (a 1000 km displacement leads to a E = 0.1% for a 106 km baseline). However, position control and knowledge are essential in the lateral direction, especially in a narrow ﬁeldof-view system. Attitude control must ensure that the image produced by the optics falls onto the detector, and the knowledge of this positioning must be at the level of the size of a detector pixel. Using a meter size scale for the detector with 2 mm size pixels, the control of the spacecraft needs to be accomplished at the ∼10 cm level with knowledge of ∼1 mm. 3. IMDC mission proﬁle The challenging aspects of the Fresnel mission are the ﬂight dynamics and satisfying the propulsion requirements. Flight dynamic analysis led to the selection of an Earth-trailing heliocentric orbit at 1 AU for both missions. The lens-craft would be in a true orbit while the detector-craft would be in an appropriately offset pseudo-orbit and thus require stationkeeping propulsion. The pseudo-orbit can be within or outside the ecliptic plane depending on the direction of the gamma-ray source. Other orbits, such as those around Lagrange points, were considered but the analysis was determined to be too complex for these studies. Table 2 details the spacecraft and ﬂight dynamic parameters developed from the IMDC studies. For the full mission, a Delta-IV-Heavy was identiﬁed as the launch vehicle. The availability of a 19.2 m tall, 5 meter diameter dual-manifest fairing naturally ﬁts the full Fresnel mission proﬁle. The Delta-IV-H can also throw ∼9300 kg outside the Earth’s gravitational potential. For the pathﬁnder mission, a smaller Delta-IV-M has sufﬁcient capabilities to achieve the launch although a mission speciﬁc dual-payload-attachment-fairing (DPAF) would have to be developed. 3.1. Propulsion requirements Ion thrusters were identiﬁed as the propulsion technology to accomplish both the stationkeeping and the re-pointing between observational targets. The ion thrusters would be Springer

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Exp Astron (2005) 20:497–503 Table 2 The parameters developed from the IMDC analysis for the Full and Pathﬁnder Fresnel missions

Lens-craft dry mass Lens-craft power Detector-craft dry mass Detector-craft power Station-keeping v On-target time Station keeping thruster ISP Station keeping trusta Mean repointing time Mean repointing v Repointing thruster ISP Repointing thrusta Total propellant mass # of targets in 5 yearsb

Pathﬁnder

Full

370 260 1115 4.65 4.2 21 3000 7.8–10 7 120 3000 110–145 320 52

940 260 1285 22 42 21 6000 90–185 21 830 6000 580–1200 1320 43

kg watts kg kwatts m/s/week days s mN days m/s s mN kg

a

The thrust range is deﬁned by the end-of-life (dry) mass versus the initial (wet) spacecraft mass. If the number of detector-craft is increased to 2, the number of targeted observations could be increased up to a factor of 2 b

incorporated into the detector-craft while both spacecraft would have cold-gas propulsion for ﬁne attitude control. Solar sail propulsion was considered but dismissed due to the large (∼1 km2 ) sail size required and the mission constraints imposed by the inherent directional asymmetry in using the solar ﬂux. The propulsion requirements were developed from the analysis of the mission ﬂight dynamics. The results are summarized by detailing the accelerations, v, and thrust requirements, which were evaluated in the context of the available ion thruster performance data, to form each mission proﬁle. As there is some freedom in the propulsion parameterization, the pathﬁnder mission will be described using the propulsion performance assumed for the IMDC study while the full Fresnel mission will be considered taking into account recent improvements in ion thruster performance. The power available for the propulsion is limited to that which can be delivered by the nearly 50 m2 solar arrays assumed in the IMDC design of the detector-craft and corresponds to 19.8 kwatts peak power. The ﬂight dynamic analysis for the Fresnel pathﬁnder mission determined that the accelerations needed for station keeping in an Earth-trailing heliocentric pseudo-orbit varied between 4 − 8 × 10−6 m/s2 over the orbit cycle. Conservatively assuming a mean acceleration of 7 × 10−6 m/s2 translates into a v S K = 4.2 m/s/week and an 8.4 mNewton thrust requirement for a 1200 kg detector-craft. Assuming a two week time to repoint 20◦ between targets, an acceleration of 10−4 m/s2 and a v R P = 120 m/s are needed. The value of v R P includes the effects of having to start and stop the detector-craft and using continuous versus impulsive repointing maneuvers. The full Fresnel mission requires the spacecraft separation distance to be increased by a factor of 10 to a focal length of 106 km. Thus the required station-keeping acceleration and

v S K also increases by 10 over that needed for the pathﬁnder mission. Assuming a 3 week repoint time and 20◦ between targets, an acceleration of 4.5 × 10−4 m/s2 and a v R P = 830 m/s are required. An interesting result from the ﬂight dynamics analysis is that the effects of solar gravity do not signiﬁcantly increase the repointing acceleration requirement for times less than ∼3 weeks. Springer

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Table 2 details the ﬂight dynamical requirements and the propulsion parameters for speciﬁc conﬁgurations of the pathﬁnder and full Fresnel missions. For the pathﬁnder mission, the propulsion parameters for the ion thrusters assumed in the IMDC study are used. The stationkeeping is performed via a single RIT-10 thruster [4] while the repointing maneuvers require the addition of an NSTAR ion thruster [5]. Both of these thrusters have ﬂight heritage and have demonstrated >20, 000 hours of operation with speciﬁc impulses (ISP’s) >3000 s. The propulsion power requirements assumed 650 watts for the RIT-10 and 4 kwatts for the NSTAR thruster. It was noted by the IMDC that this conﬁguration allows for the size of the solar arrays to be reduced to 16 meter2 . For the full Fresnel mission, a re-analysis of the propulsion has been performed, and veriﬁed by the IMDC, incorporating recent advances in ion thruster technology. The RIT-22 thruster [6] has demonstrated an ISP > 6000 s with thrusts up to 250 mN in the laboratory. From the data in Table 2, the station keeping can be accommodated with a single RIT-22 while the repointing could be accomplished with 4 RIT-22, assuming the thrust could be increased to 300 mN per thruster. The power requirement assumed 5.5 kwatts per thruster which would require increasing the solar array size by ∼10% from the 50 m2 assumed in the original IMDC detector-craft deﬁnition. Although not presented in Table 2, employing RIT-22 thrusters in the pathﬁnder conﬁguration would allow the repointing to be accomplished on a week timescale. Thus 60 targets could be viewed in a 5 year mission using 335 kg of fuel with a power requirement of 16.5 kwatts. A single RIT-10 thruster would still be employed for station-keeping propulsion. The availability of the improved ion thruster performance allows mass savings such that one could consider including a second detector craft in the full Fresnel mission proﬁle. The addition of a third spacecraft would allow observations with one detector-craft while the other is maneuvering for the following observation. Using the data presented in Table 2, the total mass for a single lens-craft and two detector-craft leads to a total of 6150 kg, which is well below the capability of a Delta-IV-H to launch a payload outside the Earth’s gravitational potential, even with the customary 20% contingency. However, the feasibility of integrating the three spacecraft with a custom payload attachment structure needs to be assessed. 3.2. Attitude control The orientation of the lens spacecraft is not critical (60

control and 10

knowledge were assumed, though even though these requirements could be further relaxed). Commercially available laser gyro, star-tracker and reaction wheel units having the necessary capabilities were identiﬁed in the IMDC studies. The intrinsic requirements for the detector-and lens-craft alignment in the two Fresnel conﬁgurations are similar. The formation ﬂying alignment could be accomplished by employing a laser beacon on the lens-craft, which then would be observed by a sensor on the detector-craft. This would require a sensor working at the micro- arcsecond level for the full Fresnel mission, with perhaps a 100 micro-arcsecond ﬁeld-of-view. One of the options considered was to place the sensor on a gimbal to allow ﬁne pointing without placing undue constraints on the spacecraft orientation. A key ﬁnding of the IMDC study was the need for further development of a metrology system to determine the absolute position of the gamma-ray sources in the narrow ﬁeld-ofview of the telescope. The employment of a micro-arcsecond star tracker was determined to be problematic as it required meter-sized apertures and excessive integration times or a star of sufﬁciently large magnitude in the ﬁeld-of-view. A gimbaled micro-arcsecond star Springer

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tracker of more modest size viewing bright, off-axis stars operating with precise gyros was identiﬁed as a possible solution. However, this technology needs to be further developed. Other missions, such as MAXIM, have similar metrology requirements and could offer a solution to this problem [7]. Another intriguing possibility considered by the IMDC was to include the deployment of another detector-craft at a much shorter separation, from the lenscraft, to act as a ﬁnder-craft. The widened ﬁeld-of-view of this telescopic conﬁguration relaxes the source-ﬁnding problem. The alignment of the three spacecraft places the astrophysical source in the ﬁeld-of-view of the longer, baseline conﬁguration, once the ﬁnder-craft drifts out of the ﬁeld-of-view. However, this bootstrapping technique requires the addition of a third, maneuverable spacecraft, albeit with modest propulsion requirements. The strict metrology requirements of a micro-acrsecond mission may be loosened if a Fresnel mission with a milli-arcsecond performance is considered. Although a milli-arcsecond Fresnel mission was not studied in the IMDC mission development, understanding its impact on the metrology is straightforward. A 100 km focal length (satellite separation) with a detector array of a square meter in size yields a ﬁeld-of-view for the telescope that is larger than an arcsecond. This larger viewing aperture signiﬁcantly improves the ability to place the astronomical targets in the ﬁeld-of-view, and the satellites need to be aligned to ‘only’ the milli-arcsecond level. However, the satellite alignment spatial tolerances can be more strict for shorter focal length conﬁgurations. The component of the angular resolution due to the ﬁnite pixel size is δθPixel = x/F where x is the linear pixel dimension and F is the focal length. If the value of this term is set to the desired angular resolution, x ≈ 5 mm for δθPixel = µ

and F = 106 km, while x ≈ 0.5 mm for δθPixel = m

and F = 100 km. Thus, the knowledge of the absolute positioning needs to be 10 times more precise for such a milli-arcsecond conﬁguration while the spatial control is the same for both missions assuming a same-sized detector array. For a set angular resolution and detector size, the spatial alignment constraint eases as the focal length is increased but at the expense of reducing the ﬁeld-of-view. 3.3. Spacecraft, thermal control, telemetry Other aspects of the IMDC study, such as spacecraft mechanical and electrical design, thermal control and management, telemetry, etc., were found by the IMDC studies to be straightforward. Communications could be handled as an S-band link between the two spacecraft for ranging, with the data from the lens-craft being relayed through the detector-craft. A 1.5 m gimbaled antenna then would allow all data from both spacecraft to be sent to the ground during a single daily 15 minute DSN contact. It was noted that halting the Earth-drift-away orbit at ∼0.1 AU would preclude any obscuring of the spacecraft by the sun.

4. Conclusions Two gamma-ray astronomy missions employing Fresnel lenses were developed at the NASA GSFC Integrated Mission Design Center: a pathﬁnder mission with a 105 km spacecraft separation and 10 micro-arcsecond (µ

) imaging ability and a deﬁnitive mission with a 106 km separation and with a 1 µ

angular resolution. The development of the spacecraft was determined to be straightforward. While the studies determined that the ﬂight dynamics and propulsion requirements are challenging, they can be accomplished with current ion propulsion technology if a re-pointing time scale of a week is used. Furthermore, recent advances in ion thrusters have relaxed the propulsion requirements potentially allowing the Springer

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incorporation of an additional detector-craft into a mission proﬁle, thus doubling the number of viewed gamma-ray sources in a 5 year mission lifetime. Acknowledgements This work was supported by a grant from the NASA Revolutionary Aerospace Systems Concepts (RASC) program.

References 1. 2. 3. 4. 5. 6. 7.

Skinner, G.: Astronomy and Astrophysics 375, 691 (2001) For information on the IMDC see http://imdc.nasa.gov/ Barthelmy, S.D.: Proc. SPIE 4140, 50 (2000) http://cs.space.eads.net/sp/SpacecraftPropulsion/Rita/RIT-10.html http://www.inspacepropulsion.com/tech/next gen.html http://cs.space.eads.net/sp/SpacecraftPropulsion/Rita/RIT-22.html Gendreau, K.C. et. al.: Proc. SPIE 4852, 685 (2003)

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