Origin of matter and evolution of galaxies 2000

Editors Taka Kajino "ihigeru Kubono

^en-ichi Nomoto

■ sao Tanihata

O r i g i n 0/ M a t t e r ^ E v o l u t i o n 0/ Galaxies 2

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O r i g i n 0/ M a t t e r ^ E v o l u t i o n 0/ Galaxies 2

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Editors Taka Kajino National Astronomical

Observatory, Japan

Shigeru Kubono Center for Nuclear Study, University of Tokyo, Japan

Ken-ichi Nomoto Department of Astronomy, University of Tokyo, Japan

Isao Tanihata Rl Beam Science Laboratory, RIKEN, Japan

O r i g i n of M a t t e : & . E v o l u t i o n of G a l a x i e s 2

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I© World Scientific ■

New Jersey • London • Singapore • Hong Kong

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Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: Suite 202, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

ORIGIN OF MATTER AND EVOLUTION OF GALAXIES 2000 Copyright © 2003 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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Printed in Singapore by World Scientific Printers (S) Pte Ltd

International Symposium on

Origin of Matter and Evolution of Galaxies 2000 Center for Nuclear Study, University of Tokyo Tanashi, Tokyo January 19 - 21, 2000

Organizing Committee of the Symposium: T. Kajino National Astronomical Observatory , co-chairman S. Kubono CNS, University of Tokyo, co-chairman T. Kifune ICRR, University of Tokyo K. Sato University of Tokyo Y. Suzuki ICRR, University of Tokyo I. Tanihata RIKEN H. Toki RCNP, Osaka University H. Miyatake KEK T. Motobayashi Rikkyo University Y. Nagai RCNP, Osaka University K. Nomoto University of Tokyo Hosted by:

Center for Nuclear Study, University of Tokyo Division of Theoretical Astrophysics, National Astronomical Observatory RI Beam Science Laboratory, RIKEN E-Group, KEK

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Preface This book is the proceedings of the International Symposium on Origin of Matter and Evolution of Galaxies which was held in Tokyo, Japan, during January 19 21 in 2000. We have organized a series of international meetings on this subject several times since 1992, and this meeting was held in a special occasion twofold. First, we are in the first year of new millenium that should bring us to a new stage of science, based on largely accumulated scientific knowledge and highly developed technology in the last century. Second, this symposium was the very last meeting held in Tanashi campus of the Center for Nuclear Studies, University of Tokyo, which has moved to Wako campus. The purpose of this symposium was to bringmany scientists together from vast science fields, i.e. nuclear physics, particle physics, cosmic-ray physics, cosmology, astronomy, geophysics, and others, in order to promote cooperative discussions and collaboration. We have made several scientific progress in recent years in this interdescipUnary field named Nuclear Cosmology and Astrophysics. Radioactive IonBeam Facilities at many institutes such as RTKEN, CNS, KEK, GSI, MSU, Oak Ridge, and others succeeded in producing (or planning to produce) new isotopes to study nuclear structure and reactions of exotic nuclei, and these new nuclei have quickly been used secondarily for the studies of nuclear astrophysics. Explosive nucleosynthesis in the Big-Bang Supernovae or Novae are now being deeply investigated both experimentally and theoretically, and the world biggest Telescopes SUBARU, KECK, and VLT will start operation to provide valuable and complemantary informatoion on understanding the origin and evolution of elements in the Universe. Kamiokande op ened anew frontier of neutrino astronomy, and Super-Kamiokande is expected to reveal the nature of neutrino. In addition to these terrestrial experimental projects, science has been done from celestial laboratories as well. X-ray satellite ASCA has revealed many interesting asp ects of activites of neutron star, black hole, extra-galaxies and cluster of galaxies. Radio-wave satellite HALCA was successfully launched and has started operation. All these are now being carried out in international collaborations. We actually live in an exciting epoch at the beginnig of the 21 s t century. It was really a great pleasure to organize this high quality international symposium in Japan. Taka Kajino, Co-Chairman National Astronomical Observatory Shigeru Kubono, Co-Chairman Center for Nuclear Study, University of Tokyo Ken-ichi Nomoto Department of Astronomy, University of Tokyo Isao Tanihata RI Beam Science Laboratory, RJKEN

VII

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Opening address

Dear Colleagues, good morning !

I would like to make a few words before starting the session. Today, we are very happy to have you all to this international symposium on Origin of Matter and Evolution of Galaxies 2000. We would like to thank all the participants, especially who came from outside of Japan for a long distance. In fact, this is the third meeting under the same title. Our primary interest is to get together the astronomers and physicists to discuss common problems of the Universe. Especially, here, we are emphasizing the importance of an axis of not only the elements but also the isotopes, namely the atomic nuclides, which should give us an important clue for understanding the phenomena of the Universe. This is a good occasion to make a scope of the field at the beginning of the new millennium. Our intention is to have, not only presentation of the completed works, but also to discuss the current problems and the possible future collaborations. We hope that you all enjoy the active and stimulating discussions in this symposium.

Thank you. S. Kubono Chairperson of the Organizing Committee

IX

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Contents

Preface Opening Address S. Kubono (Co-Chairperson,

vii ix CNS)

I. Early Universe and Chemo-Dynamic Evolution of Galaxies T. Kajino Prospects in Nuclear Cosmology: From the Big-Bang to Supernovae

3

T. Shigeyama Inhomogeneous Chemical Evolution in the Galactic Halo: Supernova-Induced Formation of Field Stars and Globular Clusters

14

T. Suzuki Light Elements in Inhomogeneous Early Galaxy and Their Astrophysical Interests

23

T. Kifune Prospects for Very High Energy 7-Ray Astronomy with Next Generation Imaging Cerenkov Telescope

31

H. Umeda Evolution and Explosion of Massive Pop III Stars and Their Nucleosynthesis

43

II. Observation of Elements S. Amari Presolar Grains as Probes of Nucleosynthesis in Stars and Evolution of the Galaxy

XI

55

XII

C. Iliadis Nucleosynthesis of Mg and Al in Globular Cluster Red Giant Stars

69

Y. Fukazawa X-Ray Measurements of Metal Abundances of Hot Gas in Clusters of Galaxies

77

H. Murakami X-Ray Diagnosis of the Galactic Center Abundance with an X-Ray Reflection Nebula

86

N. Hasebe Cosmic Ray Observation for Nuclear Astrophysics: CORONA Program

94

III. Stellar Evolution and the Nucleosynthesis: Hydrostatic Burning R.E. Tribble Direct Capture S-Factors from Asymptotic Normalization Coefficients

107

W.-P. Liu Solar Neutrino Problem Related Nuclear Physics Experiments

119

N. Iwasa Coulomb Dissociation of 8 B at 254 MeV/u for 7 Be(p, 7) 8 B

130

N. Kudomi Development for the Study of a Cross-Sectional Measurement of 3 He- 3 He Solar Reaction

138

IV. Nucleosynthesis in Explosive Burning and N e w Approach M.S. Smith Probing Stellar Explosions with Radioactive Beams at ORNL

149

J. D'Auria Measuring the Astrophysics Rate for Radiative Proton Capture on 21 Na

163

XIII

S. Kubono Nuclear Astrophysics Project with a New Low-Energy RIB Separator CRIB: Study of a Critical Stellar Reaction 15 0(a,7)19Ne

171

V. Explosion of Massive Stars S. Yamada Physics of Collapse-Driven Supernovae

181

M. Yasuhira Protoneutron Stars with Kaon Condensate and Possibility of Delayed Collapse

194

R.N. Boyd OMNIS, the Observatory for Multiflavor Neutrinos from Supernovae

201

Y. Fukuda Observation of Supernova Neutrino Burst at Super-Kamiokande

209

K. Homma Can the Negative Mass Square of the Electron Neutrinos Be an Indication of Interaction with Relic Neutrinos?

215

K. Nomoto Nucleosynthesis in Hypernovae

223

H. Tsunemi Overabundance of Calcium in the Young SNR RX J0852-0462: Evidence of Over-Production of 44 Ti

240

K. Koyama X-Ray Spectroscopy and Chemical Composition in the Universe

246

VI. Origin of Heavy Elements G.J. Mathews Neutron Star Mysteries

257

xiv H. Utsunomiya Photoneutron Cross Sections for 9 Be and the a-Process in Core-Collapse Supernovae

267

T. Suda RIKEN RI-Beam Factory (RIBF) Project and the Way to the r-Process Nuclei

276

M. Hashimoto Connection Between Crucial Nuclear Reaction Rates and the Modeling of Accreting Neutron Stars

283

VII. Neutron Stars and High Density Matter K. Sumiyoshi Unstable Nuclei and an EOS Table for Supernovae and the r-Process in a Relativistic Many-Body Approach

297

T. Takatsuka Baryon Superfluidity in Neutron Star Cores

305

T. Tatsumi Ferromagnetism of Quark Liquid and Magnetars

313

T. Kishimoto Kaonic Nuclei and Kaon Condensation in Neutron Stars

322

Poster Session A. Bamba Chemical Composition and Distribution of Heavy Elements in a Supernova Remnant G359.1-0.5

331

H. Ishiyama Tanashi Recoil Mass Separator for Nuclear Astrophysics

335

A. Iwazaki Collision Between Neutron Star and Axion Star as a Source of Gamma Ray Burst and Ultra-High Energy Cosmic Ray

339

XV

N. Kudomi Double Beta Decays of Observatory

100

Mo by ELEGANT V at Oto Cosmo 343

K. Maeda Nucleosynthesis in Aspherical Hypernova Explosions and Late Time Spectra of SN 1998BW

347

S. Nagataki Effects of Jet-Like Explosion in SN 1987A

354

N. Nakasato Formation and Chemical Dynamics of the Galaxy

358

J. Nakatsuru Explosive Nucleosynthesis in Pair-Instability Supernovae

362

M. Nishiuchi X-Ray Observations of SNRs and Hot ISM in the Large Magellanic Cloud: The Chemical Enrichment of the Galaxy

370

K. Otsuki r-Process Nucleosynthesis in Neutrino-Driven Wind: General Relativistic Effects and Short Dynamic Timescale Model

374

M. Terasawa The Critical Role of Light Neutron-Rich Nuclei in the r-Process Nucleosynthesis

378

G. Watanabe Thermodynamic Properties of Nuclear "Pasta" in Neutron Star Crusts

381

Symposium Program

385

List of Participants

391

Author Index

403

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I. Early Universe and Chemo-Dynamic Evolution of Galaxies

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Prospects in Nuclear Cosmology: From t h e Big-Bang to Supernovae Toshitaka Kajino National Astronomical Observatory Mitaka, Tokyo 181-8588 and Department of Astronomy, University of Tokyo Bunkyo-ku, Tokyo 113-0033

Abstract We study primordial nucleosynthesis in the presence of a net lept.on asymmetry. We explore a previously unnoted region of the parameter space in which very large baryon densities 0.1 < fit, < 1 can be accommodated within the light-element constraints. This parameter space consists of large v,, and uT degeneracies with a moderate ve degeneracy. Constraints on this parameter space from cosmic microwave background fluctuations are discussed [1]. We also study the r-process nucleosynthesis in neutrino-driven winds of gravitational core collapse SNell. Appropriate physical conditions are found for successful r-process nucleosynthesis, which meet, with several features of heavy elements discovered recently in metal-deficient, halo stars.

1

Big-Bang Cosmology

Recent progress in cosmological deep survey has clarified progressively the origin and distribution of matter and evolution of Galaxies in t.he Universe. The origin of the light elements among them has been a topic of broad interest, for its significance in constraining the dark matter component in the Universe and also in seeking for the cosmological model which best, fits the recent, data of cosmic microwave background (CMB) fluctuations. This paper is concerned with neutrinos during Big-Bang nucleosynthesis (BBN). In particular, we consider new insights into the possible role which degenerate neutrinos may have played in the early Universe. There have been many important contributions toward constrainig neutrino physics. Hence, a discussion of neutrinos and BBN is even essential in particle physics as well as cosmology. There is no observational reason to insist that the universal lept.on number is zero. It is possible, for example, for the individual lept.on numbers to be large

3

4

compared to the baryon number of the Universe, while the net total lepton number is small L ~ B. It has been proposed recently [2] that models based upon the Affleck-Dine scenario of baryogenesis might generate naturally lepton number asymmetry which is seven to ten orders of magnitude larger than the baryon number asymmetry. Neutrinos with large lepton asymmetry and masses ~ 0.07 eV might even explain the existence of cosmic rays with energies in excess of the Greisen-Zatsepin-Kuzmin cutoff [?>]. It. is, therefore, important for both particle physics and cosmology to carefully scrutinize the limits which cosmology places on the allowed range of both the lepton and baryon asymmetries.

1.1

Cosmological Neutrino and Primordial Nucleosynthe­ sis

Although lepton asymmetric BBN has been studied in many papers [4] (and references therein), there are several differences in the present, work: For one , we have included finite temperature corrections to the mass of the electron and photon [5]. Another is t h a t we have calculated the neutrino annihilation rate in the cosmic comoving frame, in which the M0ller velocity instead of the relative velocity is to be used for the integration of the collision term in the Boltzmann equations [6, 7]. Neutrinos and anti-neutrinos drop out of thermal equilibrium with the back­ ground thermal plasma when the weak reaction rate becomes slower than the universal expansion rate. If the neutrinos decouple early, they are not heated as the particle degrees of freedom change. Hence, the ratio of the neutrino to photon temperatures, Tu/Xy, is reduced. The biggest drop in temperature, for all three neutrino flavors occurs for £„ ~ 10. This corresponds to a decoupling temperature above the cosmic QCD phase transition. Non-zero lepton numbers affect, nucleosynthesis in two ways. First, neutrino degeneracy increases the expansion rate. This increases the ''He production. Secondly, the equilibrium n / p ratio is affected by the electron neutrino chemical potential, n / p = exp{ — (AM /Tnu ) — &,,.}, where AM is the neutron-proton mass difference and T„<+r is the freeze-out temperature for the relevant weak reactions. This effect either increases or decreases ''He production, depending upon the sign of £„ e . A third effect emphasized in this paper is t h a t T „ / T 7 can be reduced if the neutrinos decouple early. This lower temperature reduces the energy density of neutrinos during BBN, and slows the expansion of the universe. This decreases 4 He production. Figure 1 highlights the main result of this study, where we take ^ = — £ „ r . For low Qb/iJo models, only the usual low values for £,,c and £„ r are allowed. Between £lbh'(0 « 0.188 and 0.3, however, more than one allowed region emerges. For ftbh'io > 0.4 only the large degeneracy solution is allowed. Neutrino degen­ eracy can even allow baryonic densities up to Qbh^Q = 1.

5 1,4 T

n

,.''i=L0

1.2-

..--■'

..

"

.•■'

-i

]

mi- =o.3

o.8-

■;'

;/.'. ■

-.

]

«- k f 11.2 - :".

■S-iiJi:

=0.075

l),»r'. ■ . . ■ . . . . II

l . . . . III

\ i . . . .

i .. 20

I 3d

:

4ll

50

Figure 1: Allowed values of £,,c and £„, r for which the constraints from light. element abundances are satisfied for values of Ab^lo — 0-075, 0.1, 0.2, 0.3 and 1.0 as indicated.

1.2

Cosmic Microwave Background

Several recent works [8, 9, 10] have shown that neutrino degeneracy can dramat­ ically alter the power spectrum of the CMB. However, only small degeneracy parameters with the standard relic neutrino temperatures have been utilized. Here, we have calculated the CMB power spectrum to investigate effects of a diminished relic neutrino temperature. The solid line on Figure 2 shows a QA = 0.4 model for which ??. = 0.78. This fit is marginally consistent with the data, at a level of 5.2
1.3

Cosmic Age

There are several important, implications of the neutrino degenerate Universe models. One of them is on the cosmic age problem. Recent baloon experiments of detecting the CMB anisotropy has exhibited that the flat cosmology is more

6 '00,

80

r-r-^

-

ff\ ;jji \ u

f\

h

60

g.

i

iL

*~~^_jrt-

1 lV'. M

i

i ;

20

0 i

i

10

100

1000

/

Figure 2: CMB power spectrum from MAXIMA-1 [12] (circles) and BOOMERANG [11] (squares) binned data compared with calculated Q = 1 models. likely. C'ombining this with the result from high-redsliift supernova search, one may deduce a finite cosmological constant. QA ~ 0.6, leading to a cosmic age ~ 15 Gy. If this were the case, a potential difficulty that the cosmic age is likely to be shorter than the age of the Milky Way might be resolved. However, CMB anisofropy data provide with more details of sesveral cosmological parameters which may not necessarily accept this simplified interpretation. In our neutrino degenerate Universe models with Q. = 1, QA = 0.4, and fifc''go = 0.1, neutrino mass for vt,iT is constrained to be less than 0.3 eV as fas as Q.v < 0.5 [I, 13]. Even should the mass be 0.3 eV, our conclusion on the primordial nucleosynthesis does not change at all. Therefore, we assumed massless neutrino. With this possible choice of the parameters in cosmology and particle physics, we can estimate the cosmic expansion age « 12 ~ 13 Gy. Cosmic age problem seems still remained. Further careful studies of the age problem and also the nature of cosmological constant [14] are highly desirable.

7

2

Supernovae

We discuss in this section that the neutrino-driven winds from supernova explo­ sion of very massive stars could be a viable site for r-process nucleosynthesis. Stars with various masses provide a variety of production sites for intermediateto-heavy mass elements. Very massive stars > 10M,-., culminate their evolution by supernova (SN) explosions which are also presumed to be most, viable candi­ date for the still unknown astrophysical site of r-process nucleosynthesis. Even in the nucleosynthesis of heavy elements, initial entropy and density at (lie sur­ face of proto-neutron stars are so high that nuclear statistical equilibrium (NSE) favors production of abundant light nuclei. In such explosive circumstances of so called hot-bubble scenario, not only heavy neutron rich nuclei but light unstable nuclei play a significant role. The study of the origin of r-process elements is also critical in cosmology. It is a potentially serious problem that, the cosmic age of the expanding Universe derived from cosmological parameters may be shorter than the age of the oldest globular clusters. Since both age estimates are subject to (.he uncertain cosmo­ logical distance scale, an independent method has long been needed. Thorium, which is a typical r-process element and has half-life of 14 Gyr, has recently been detected along with other elements in very metal-deficient stars. If we model the r-process nucleosynthesis in these first-generation stars, thorium can be used as a cosmochronometer completely independent of the uncertain cosmological distance scale.

2.1

Neutrino-Driven Winds in Type-II Supernovae

Recent measurements using high-dispersion spec!rographs with large Telescopes or the Hubble Space Telescope have made it possible to detect minute amounts of heavy elements in faint metal-deficient ([Fe/H] < -2) stars [15]. The discovery of r-process elements in these stars has shown that (.he relative abundance pattern for the mass region 120 < A is surprisingly similar to the solar system r-process abundance independent of the metallicity of the star. Here metallicity is defined by [Fe/H] = log[N(Fe)/N(H)] - Iog[N(Fe)/N(H)] 0 . It obeys the approximate relation t/10 10 yr ~ \wFelH'. The observed similarity strongly suggests that the r-process occurs in a single environment which is independent of progenitor metallicity. Massive stars with 10M(:, < M have a short, life ~ 10' yr and eventually end up as violent supernova explosions, ejecting material into the intersteller medium early on quickly from the history of the Galaxy. However, the iron shell in SNe is excluded from being the r-process site because of the observed metallicity independence. Hot neutron stars just born in the gravitational core collapse SNell release most of their energy as neutrinos during the Kelvin-Hclmholtz cooling phase. An intense flux of neutrinos heat the material near the neutron star surface and drive matter outflow (neutrino-driven winds). The entropy in these winds is so high that the NSE favors a plasma which consists of mainly free nucleons and alpha particles rather than composite nuclei like iron. The equilibrium lepton

8

fraction, Ye, is determined by a delicate balance between ve + n —> p + 1 ~ and ve + p -4 n + e+, which overcomes the difference of chemical potential between n and p, to reach Ye ~ 0.45. R-process nucleosynthesis occurs because there are plenty of free neutrons at high temperature. This is possible only if seed elements are produced in the correct neutron-to-seed ratio before and during the r-process. Although VVoosley et al. [16] demonstrated a profound possibility that the r-process could occur in these winds, several difficulties were subsequently iden­ tified.- First, independent non relafivistic numerical supernova models [17] have difficulty producing the required entropy in the bubble S/k ~ 400. Relativistic effects may not be enough to increase the entropy dramatically [18, 19, 20]. Sec­ ond, even should the entropy be high enough, the effects of neutrino absorption IV + n -)• p + e~ and vt + A(Z, N) -»• A(Z + 1, A7 - 1) + e~ may decrease (.he neutron fraction during the nucleosynthesis process. As a result, a deficiency of free neutrons could prohibit the r-process [21]. Third, if neutrinos are massive and have appropriate mixing parameters, energetic vfl and ;/T are converted into ve due to flavor mixing. This activates the vt -f n —> p+ e~ process and results in a deficiency of free neutrons. In order to resolve these difficulties, we have studied [20, 22] neutrino-driven winds in a Schwarzschild geometry under the reasonable assumption of spherical steady-state flow. The parameters in the wind models are the mass of neutron star, M, and the neutrino luminosity, L„. The entropy per baryon, S/k, in the asymptotic regime and the expansion dynamic time scale, Tdyn > which is defined as the duration time of the a-process when the tempraftire drops from T « 0.5 MeV to 0.5/e MeV, are calculated from the solution of hydrodynamic equations. Then, we carried out r-process nucleosynthesis calculations in our wind model. We found [20] that the general relativistic effects make r,iyn much shorter, although the entropy increases by about 40 % from the Newtonian value of S/k ~ 90. By simulating many supernova explosions, we have found some interesting conditions which lead to successful r-process nucleosynthesis, as to be discussed in the following sections.

2.2

R-process Nucleosynthesis

Previous r-process calculations [16, 24] had complexity that the seed abun­ dance distribution was first calculated by using smaller network for light-toinfermediate mass elements, and then the result was connected further to an­ other r-process network in a different set of the computing run. For this reasaon it was less transparent to interpret the whole nucleosynthesis process. This inconvenience happened because it was numerically too heavy to run both aprocess and'r-process in a single network code for too huge number of reaction couplings among ~ 3000 isotopes. Our nucleosynthesis Calculation [20, 22] is completely free from this complexity because we exploited fully implicit single network code which is applied to a sequence of the whole processes of NSE a-process - r-process.

9

Solar system r-process abundances .1

>-

o

0

20

40

60

80

100

120

140

160

180

200

220

240

MASS NUMBER Figure 3: R-process abundance [20] (solid line) as a function of atomic mass number A compared with the solar system r-process abundance (filled circles) from Kappeler, Beer, k Wisshak [23]. The neutrino-driven wind model used is for L„ = 1052 ergs/s and M = 2M?,. The solar system r-process abundance is shown in arbitrary unit.

Let us remind the readers that, there were at least three difficulties in the previous theoretical studies of the r-process. The first difficulty among them is that an ideal, high entropy in the bubble S/k ~ 400 [16] is hard to be achieved in the other simulations [17, 18, 19, 20]. The key to resolve this difficulty is found with the short dynamic time scale Tdyn ~ 10 ms in our models of the neutrino-driven winds. As the initial nuclear composition of the relativisfic plasma consists of neutrons and protons, the oburning begins when the plasma temperature cools below T ~ 0.5 MeV. The 4 ]-le(aa,'))1-C reaction is too slow at this temperature, and alternative nuclear reaction path ' 1 He(an, -))f,Be(a, ?7)12C triggers explosive a-burning to produce seed elements with A ~ 100. Therefore, the time scale for nuclear reactions is regulated by the 4 He(a?i,7)''Be. It is given by T^ ~ (piY£Y„\(aan -¥w Be)) If the neutrino-driven winds fulfill the condition Tcly„ < 7w, then fewer seed nuclei are produced during the a-process with plenty of free neutrons left over when the r-process begins at T ~ 0.2 MeV. The high neufron-to-seed ratio, n/s ~ 100, leads to appreciable production of r-process elements, even for low entropy S/k ~ 130, producing both the 2nd (.4 ~ 130) and 3rd (.4 ~ 195) abundance peaks and the hill of rare-earth elements (.4 ~ 165) (Figure 3).

10

100

150

200

mass number

Figure A: The same as (hose in Figure 3, but for the neutrino-driven wind model of Lv — 5 x 1052 ergs/s. Solid line respresents the result, by using the Woosley fe Hoffman rate [25] of the 4He(an,7)''Be reaction, and long-dashed line for the rate multiplied by factor 2, as suggested by the recent experiment of Utsunomiya et al. [2(3]. The three body nuclear reaction cross section for *1He(o», 7)!'Be is one of the poorly determined nuclear data which may alter the r-process nucleosyn­ thesis yields. The inverse process has recently been studied experimentally by Utsunomiya et al. [2(3], and phofodisinfegration cross section of ;'Be has been measured with better precision than those of the previous experiments. Ap­ plying the principle of the detailed balance to this process, one can estimate the cross section for 4Ue(an,7)9Be. They found that the thermonuclear reac­ tion rate is almost, twice as big as that of Woosley and Hoffman [25] but in resonable agreement with recent compilation of Angulo et al. [27]. However, there still remain several questions on the consistency between their result and electron-scattering experiments, on the contribution from the narrow resonance J* = 5/2 _ (2.429 MeV), etc. It is also a theoretical challenge to understand the reaction mechanism and the resonance structure because two different channels, 8 Be + n and °He + a, contribute to this process. Therefore, we show two calculated results in Figure 4: The solid line displays the result, obtained by using the Woosley and Hoffman cross section [25], assum­ ing a 8 Be -f- n structure for !'Be. We also calculated the r-process by multiplying this cross section by factor of 2 (long-dashed line). This makes a drastic change in the r-process yields in the 3rd (A ~ 195) abundance peak. More theoretical and experimental studies of the '1He(o7i,7)!'Be reaction are highly desired.

11

2.3

Neutrino-nucleus interactions

Neutrino interactions with nucleons and nuclei take the key to resolve the second difficulty which was pointed out in sect. 1. The difficulty is that the effects of neutrino absorptions vt + n —> p + c~~ and ve + A(Z,N) —> A{Z + 1, N — 1) + e~ during the a-process may induce the deficiency of free neutrons and break down the r-process conditions [21]. These two types of neutrino interactions control most sensitively the electron fraction and the neutron fraction, as well, in a neutron-rich environment. In order to resolve this difficulty, we have updated the electron-type neutrino capture rates for all nuclei and electron-type antineutrino capture rate for free proton [28, 29]. The new r-process calculation proves to be almost invariant. One can un­ derstand this robustness of the succesful r-process in the following way: The specific collision time for neutrino-nucleus interactions is given by

^20lx [ ; i ,x(^)( T ^) 2 ( B M i ? )"',, > ,

„)

where Lj^i is the individual neutrino or antineufrino luminosity in unit.s of It)51 ergs/s, (j =< E'f > I < Ej > in MeV (/ = ve, />t, etc.), and (cr„) is the averaged cross section over neutrino energy spectrum. At the n-burning site of r « 100 km for L„i5i « 10,
,„„ = I" *

m

Jr. " where u is the fluid velocity of the wind. By setting the radius of neutron star surface 77 = 10 km and rj = 100 km, we get 7ilt.at. « 30 ms. The collision time r„ is given by Eq. (1) by setting L„ |5] « 10, c„ = (f„e + (,-,, )/2 = (12 + 22)/2 = 17 MeV, r «10 km, and {cr„) « 10~ 4 1 nn 2 . Let us compare riiea, and TV to one another: r„ K, 3.4ms
12

2.4

Neutrino oscillation

The third difficult}' discussed in sect. 1 is that the energetic massive i/,, and vT may change their flavors to emerge as ve due to the MSW effects. Although the luminosity of each type of neutrino Lj [i — v(y i>f, vfi, i>in vr, vT) is similar, average energies are different from one another; c„r = 12 MeV, r,,- = 22 MeV, and r„ — ([, = 34 MeV for the other flavors [18]. Because of this difference, if the flavor mixing happened, newly converted ue were more energetic so that the i/e + n —'t p + e~ reaction would decrease the neutron fraction. We have recently shown thai, the neutrino flavor oscillation destroy the rprocess condition only if the mixing parameters satisfy 0.3 eV" < Am2 [30]. Although recent experiments of the atmospheric neutrinos and the missing solar neutrinos have indicated much smaller Am1', the LSND experiment suggests remarkably larger Am~ which overlaps with our interesting parameter region. We should wait for more experiments.

References [I] M. Orifo, T. Kajino, (J. J. Mathews, ph/0005446, submitted to Ap.] (2000)

and R. N. Boyd,

asfro-

[2] A. Casas, W. Y. Cheng, fe G. Gelmini, Nucl. Phys. B., 538, 297, (1999) [3] G. Gelmini fc A. Kusenko Phys. Rev. Lett., 82, 5202, (1999) [4] H. Kang & G. Steigman Nucl. Phys. B., 372, 494, (1992) [5] N. Fornengo, C. W. Kim, fc J. Song, Phys. Rev. D., 5G, 5123, (1997) [6] P. Gondolo, fe G. Gelmini, Nucl. Phys. B., 3G0, 145, (1991) [7] K. Enqvist, K, K. Kainulainen, fe. V. Semikoz, Nucl. Phys. B., 374, 392, (1992) [8] W. K. Kinney fc A. Rioffo, Phys. Rev. Left., 83, 3366, (1999) [9] J. Lesgourgues fc S. Pastor, Phys. Rev. D., 60, 103521,, (1999)a.stroph/0004412 [10] S. Hannestad, Phys. Rev. Lett., submitted, (2000), asfro-ph/0005018 [II] P. Bernardls, et al. (Boomerang Collaboration) Nature., 404, 955, (2000) [12] S. Hanany, et al. (MAXIMA-1 Collaboration), ApJL submitted, astroph/0005123 [13] G. J. Mathews, M. Orit.o, T. Kajino, and Y. Wang, NAOJ-Th-Ap 2001 No.9, submitted to Phys. Rev. D. (2001)

13

[14] M. Yahiro, G. .]. Malhews, K. Ichiki, T. Kajino, and M. Orito, NAOJ-ThAp 2001 No.7, submitted to Phys. Rev. D. (2001) [15] Sneden, C , McWilliam, A., Preston, G. W., Cowan, J. J., Burris, D. L., k Armosky, B. J., Astrophys. J., 467 (1996), 819. [16] Woosley, S. E., Wilson, J. R., Mathews, G. J., Hoffman, R. D., k Meyer, B. S., Astrophys. .)., 433 (1994), 229. [17] Witti, .]., Janka, H.-Tli. k Takahashi, K., Astron. k Astrophys., 286 (1994), 842. [18] Qian, Y. Z. k Woosley, S. E., Astrophys. J., 471 (1996), 331. [19] Card all, C. Y. k Fuller, G. M., Astrophys. J., 486 (1997), L l l l . [20] Otsuki, K., Tagoshi, H., Kajino, T. fe Wanajo, S., Astrophys. .]., 533 (2000), 424. [21] Meyer, B. S., Astrophys. J., 449 (1995), L55. [22] Wanajo, S., Kajino, T., Mathews, G. J., k Otsuki, K., submitted to As­ trophys. J. (2000). [23] Kappeler, F., Beer, H., k Wisshak, K., Rep. Prog. Phys., 52 (1989), 945. [24] Meyer, B. S., Mathews, G. J., Howard, W. M., Woosley, S. E., k Hoffman, R. D., Astrophys. J., 399 (1992), 656. [25] Woosley, S. E. k Hoffman, R. D., Astrophys. J., 395 (1992), 202. [26] Utsunomiya, H., Yonezawa, Y., Akimune, H., Yamagata, T., Ohta, M., Fujishiro, M., Toyokawa, II., k Ohgaki, H., Phys. Rev., C63 (2001), 018801. [27] Angulo, C , et al. (NACRE collaboration), Nucl. Phys., A656 (1999), 3. [28] Qian, Y.-Z., Haxton, W. C., Langanke, K., k Vogel, P., Phys. Rev. C55 (1997), 1533. [29] Meyer, B. S., McLaughlin, G. C , k Fuller, G. M., Phys. Rev. C58 (1998), 3696. [30] Otsuki, K., Kajino, T., k Mathews, G. J., in preparation (2000).

I N H O M O G E N E O U S CHEMICAL EVOLUTION I N T H E GALACTIC HALO: S U P E R N O V A - I N D U C E D F O R M A T I O N OF FIELD STARS A N D G L O B U L A R CLUSTERS T. SHIGEYAMA Research

Center for the Early Universe, Graduate School of Science, Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan E-mail: [email protected]

University

of

T. T S U J I M O T O National

Astronomical Observatory, Mitaka-shi, Tokyo, E-mail: [email protected]

181-8588

Japan

A model describing the chemical evolution in each cloud of the Galactic halo is presented. The inhomgeneous nature introduced by supernova explosions is incor­ porated into this model. It is found that if field stars are formed from shells of individual supernova remnants and globular clusters are formed from cloud-cloud collisions the observed metallicity distribution functions of both objects can be reproduced.

1

Inhomogeneity in t h e Galactic Halo

Abundance measurements 6 n of the surfaces of extremely metal-poor field stars in the Galactic halo have shed light on the role of individual supernova (SN) events in the star formation (SF) processes * 12 . Tsujimoto et al. 17 have combined the supernova-induced SF with chemical evolution and constructed a scenario as follows: If chemical evolution proceeds by a successive sequence of supernova (SN) explosion, shell formation, and SF, the abundance pattern of each star will be composed not only of the heavy elements ejected from an SN of the preceding generation but also of those that have been already included in the interstellar gas swept up by the SN remnant (SNR). It follows that stellar abundance patterns are different from those of the gas at the time when stars form. It was shown 17 that the abundance ratios of low-metallicity stars can have a large scatter depending on the abundance patterns of SN ejecta with different progenitor masses and be reconciled with the observed abundance ratios of metal-poor stars. In next section, we will summarize our model for the chemical evolution of stellar abundances in the Galactic halo characterized by the inhomogeneous mixing of chemical compositions in dense SNR shells and ambient medium.

14

15

2

2.1

Chemical Evolution through Supernova-induced Star Formation Overview

An overview of our model is as follows: - (1) The metal-free Population III stars (Pop III) form by some (as yet unspecified) mechanism in primordialcomposition gas clouds of the Galactic halo. (2) The most massive stars among them explode as Pop III SNe II, which trigger a series of SF events. The SF rate (SFR) is assumed to be a function of the SN rate. (3) SF terminates when SNRs become unable to form dense shells. (4) Roughly 90 % of the cloud mass remains unused in SF, and may fall onto the still-forming Galactic disk. When the SF is induced by SNe as above, the SFR M*(t) at time t measured from the birth of Pop III stars can be expressed as a function of the SN rate or equivalently the SFR some time ago; M*(t) = F[ r"dm'M*(t

- r(m'))^P ),

\./max(m(,msN,i)

TO

(1)

y

where r(m) denotes the life time of a star with mass ofTO,and m t is the stellar mass for which T(m) = t. The initial mass function (IMF) 4>(m) used here is a Salpeter one with a slope irdex of —1.35. The upper mass limit of stars is assumed to be mu = 50 MQ, and the lower mass limitTO;= 0.05 MQ 15 . The lower mass limit of stars that explode as SNe is TOSN,; = 10MQ. Though the form of the function F introduced in equation (1) is not known, it can be expanded into a Taylor series around the point where no SN happens: Af,(<) = F(0) + F'(0) nUdm'Msh(m',t)^p-M*(t ■/max(mi,msN,l)

+ ^

- r(m'))

TO

M r'dm'M*{m',t)#^M.(t-T(m'))) 1

\Jmax(mt,msN,i)

m

.

(2)

)

In this scenario, stars cannot be formed without an SN. Thus F(0) — 0. The meaning of the next two terms in this equation will be discussed in the subsequent sections. Therefore one of the free parameters in our model is the mass fraction xm of metal-free Pop III stars initially formed in each cloud,

16

and the other parameters are related to equation (2). Following the argument of Tsujimoto et al. (2000) 18 , we use xm = 2.5 x 1 0 - 4 in this paper. 2.2

Formation of Field Stars \J\J

-I

I

I

I

I

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I

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+

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[Fe/H] Figure 1. T h e solid curve is the result of SN-induced star formation model described in TSY99 1 7 . The circles show the observed MDF of the field halo stars 1 0 .

Suppose that the first term in equation (2) expresses the formation rate of field stars. Then, as Tsujimoto et al. 17 have shown, -F'(O) = eMsh with e = 4.3 x 1 0 - 3 can reproduce the observed metallicity distribution function (MDF) of field halo stars (Fig. 1). Here the mass of the shell Msh(m,t) formed at time t from an SN with progenitor mass m is a sum of the mass of the SN ejecta M e j(m) and the mass of the swept up gas Msvl(m,t); Msh(m,t)

= M e j(m) +

Msvl(m,t),

(3)

with MSV!(m, t) = p6(t)R3sN (E (m),

pB(t)).

(4)

17

50

"i i i •

40

r

i

i i

i

r

i i i i i i i i i

r

L_J

I

NGC Nfwd

Nfie|d

30

N« field

20

10 —

i--l —I-

J

I

I

I

L_J

I

I

I

I

I

L

-4

[Fe/H] Figure 2. Filled circles show the observed M D F 4 of Galactic globular clusters. N denotes the differential number density with respect to the unit interval of [Fe/H]. Each curve is made up from the observed MDF 10 of field halo stars as indicated by labels. All the curves are normalized to give the same number of objects when integrated over [Fe/H].

where Pg(t) is the density of the interstellar gas and .RgN (E(m),pg(t)) is the maximum radius of the SNR shell. Msvl(m,t) is insensitive to time t because M sw is proportional to Pg(t)007 12 . The SN explosion energy is assumed to be E(m) — 1051 erg irrespective of stellar mass rn. Thus a constant value of Msvl{m,t) = 5.1 x 104 MQ has been used in constructing Fig. 1. 2.3

Formation of Globular Clusters

It has been shown in the preceeding section that the observed MDF has key information on the formation history of field halo stars. This might be the case also for the globular cluster formation. The observed MDF for globular clusters has steeper gradient than that for field stars. Actually, the square of the observed MDF for field stars reveals a shape quite similar to that

18 for globular clusters (Fig. 2). Thus the formation rate of globular clusters is expected to be proportional to the square of the SN rate. This indicates that a globular cluster forms as a result of SNR-SNR interactions. If the formation of a globular cluster is a consequence of cloud-cloud collision 8 9 in which each of the clouds includes some SNRs, the formation rate of clusters could be proportional to the square of the SN rate. An SNR-SNR interaction in a single cloud cannot form a cluster, because it involves only a mass of 2 x Msh that is too small to account for the mass of a massive globular cluster. Lee et al. (1995) 9 have shown that globular clusters formed from cloud-cloud collisions can reproduce the observed MDF, though it is not clear how their model increases the number of stars at early phases ([Fe/H]< —1.5). In this context, the globular cluster formation does not affect the forma­ tion of field halo stars. Since the elemental abundance of a globular cluster is a result of violent merging of two clouds, the diversity of abundances among member stars is expected to be small. 3

Site for iJ-process Nucleosynthesis

As recently discussed by Tsujimoto et al. (2000) 18 , both the current ob­ servational limitation in the abundance measurement and the limitation in the power of prediction by theoretical models for explosive nucleosynthesis led us to using [Ba/Mg] ratios observed on the surface of metal-poor stars as a probe to identify the site for r-process nucleosynthesis rather than using conventional [Eu/Fe] ratios. In Figure 3, which uses the data of McWilliam et al. (1995) 6 and McWilliam (1998) 7 , the [Ba/Mg] values for a sample of metal-poor stars are plotted against [Mg/H], together with four heavier r-process elements, La, Ce, Nd, and Eu. It is indeed remarkable that there appears a nearly vertical boundary at [Mg/H]~ —2.5, with [Ba/Mg] spanning the range from [Ba/Mg]= —2 to +0.6, whereas a horizontal line of [Ba/Mg]~ —1.4 emerges from [Mg/H]f» —2.5 down to —3.7. The data of Ryan, Norris, & Beers (1996) n for seven of their extremely metal-poor stars show a similar trend in the [Ba/Mg]-[Mg/H] plane. From figure 3, TSY00 18 have concluded that the metal-poor stars of the Galaxy populate two separate branches in the [Ba/Mg] —[Mg/H] plane. The first branch extends rightward of the vertical boundary which begins at ([Ba/Mg], [Mg/H])=(-2.0,-2.3) and ends at ([Ba/Mg], [Mg/H])=(+0.6,-2.7). The second branch is horizontal from [Mg/H] 2.5 to —3.7 at a constant value of [Ba/Mg]~ —1.4. Other r-process elements, such as La, Ce, Nd, and Eu, shown in Figure

19 2

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[Mg/H] Figure 3. The correlation of [Ba/Mg] with [Mg/H] for metal-poor stars. Filled circles show the d a t a of McWilliam (1998). Two stars (CS 22898-027, CS 22947-187) in his sample are excluded from the plots because their Ba abundances may be contaminated by s-process material accreted from binary companions 7 . Other r-process d a t a 6 are also shown by different symbols indicated in the figure.

3, populate the first branch identified from the behavior of [Ba/Mg], but we presently lack measurements of their abundances in the most metal-poor stars, which are required in order to confirm the presence of the second branch. The Eu yield was derived 16 as a function of SN II progenitor mass in the con­ text of supernova induced star formation, and it was shown that the average predicted value, weighted by the Salpeter initial mass function (IMF), suc­ cessfully reproduces a plateau value of [Eu/Fe] seen at —2 ,$ [Fe/H] ^ — 1. Thus, hereafter, we refer to the first branch as the y-branch, where the letter "y" stands for its origination in individual SNe II yields. As shown in the upper panel of Figure 3, the j/-branch is confined to stars with [Mg/H]> - 2 . 7 ; there is no star with [Mg/H] <, - 2 . 7 that belongs to the 2/-branch. On the other hand, it was shown 12 that the metallicity [Mg/H] of stars born from an SNR is well approximated by the average [Mg/H] inside the shell swept up by the SNR. This gives a relation between the metallicity [Mg/H] of stars and the mass M m s of SN II progenitor as shown in Shigeyama

20

Figure 4. (a) The color-coded frequency distribution of the long-lived stars in the [Ba/Mg] — [Mg/H] plane, convolved with a Gaussian having a=0.2dex for [Ba/Mg] and cr=0.1dex for [Mg/H]. The symbols represent the data taken from McWiUiam 1998 (filled squares), Ryan et al. 1996 (open circles), Burris et al. 1999 (filled triangles), Luck &; Bond 1985 (filled circles), Luck & Bond 1981 (open triangles), Magain 1989 (open squares), and Steenbock 1983 (crosses). For comparison, the result of the conventional one-zone chemical evolution model is shown by dashed line assuming the r-process site of 8 — 10 MQ supernovae, which is different from our proposed site of 20 — 25 MQ supemovae. (b) The same as (a) but for Eu. The dashed curve encloses the predicted region in which i-branch stars must exist.

k, Tsujimoto 12 . As a consequence, it is indicated that only SNe II with M m s ^ 20MQ produce Ba via the r-process. If we assume that the vertical boundary to the y-branch has a one-to-one correspondence to the Ba yield from individual SNe II, the progenitor mass range is confined to Mms = 20 — 25M 0 . It is straightforward to derive the Ba yield from the observed [Ba/Mg]-

21

value along the vertical boundary and the synthesized Mg mass, leading to M B a = 8.5 x 1O- 6 M 0 for M m s = 2OM 0 , and M B a = 4.5 x 1O~ 8 M 0 for M m s = 25M 0 . We now consider the origin of the second branch of [Ba/Mg], in the range of - 3 . 7 £ [Mg/H] £ - 2.7. This [Mg/H] range corresponds to M m s = 12 — 2OM 0 , for which SNe II, according to our present models, do not pro­ duce significant amounts of Ba. Therefore, our hypothesis is that the Ba abundances which are observed in the atmospheres of these stars come only from the interstellar matter (ISM) that was enriched in Ba by the preceding SNe II (with M m s = 20 — 25M 0 ), and that was swept up in the shells by later SNe II with Mms = 12 - 2OM 0 . Thus, in the following, we refer to this branch, as the «-branch, where the letter "i" stands for an ISM origin. We note that the [Ba/Mg] value in this branch should always be below its plateau value [Ba/Mg]~ —0.6 at higher metallicities. We also predict from the above argument that stars born from the shell swept up by SNe II with M m s > 25M 0 would form another i-branch at [Mg/H] it — 2.5, evidence for which is not seen in the sample of McWilliam et al. (1995) 6 .

Acknowledgments This work has been partially supported by COE research (07CE2002) and a Grant-in-Aid for Sceintific Research (11640229) of the Ministry of Education, Science, Culture, and Sports in Japan. References 1. Audouze, J., & Silk, J., ApJ 451, L49 (1995) 2. Beers, T. C , Preston, G. W., k Shectman, S. A., AJ 103, 1987 (1992) 3. Burris, D. L., Pilachowski, C. A., Armandroff, T. E., Sneden, C , Cowan, J. J., k Roe, EL, ApJ , in press (2000) 4. Harris, W. E., AJ 112, 1487 (1996) 5. Kappler, F., Beer, H., k Wisshak, K., Rep. Prog. Phys. 52, 945 (1989) 6. McWilliam, A., Preston, G. W., Sneden, C , k Searle, L., AJ 109, 2757 (1995) 7. McWilliam, A., AJ 115, 1640 (1998) 8. Murray, S. D., k Lin, D. N. C , ASP Conference Series 48, 738 (1993) 9. Lee, S., Schramm, D. N., k Mathews, G. J., ApJ 449, 616 (1995) 10. Ryan, S. G., k Norris, J. E., AJ 101, 1865 (1991)

22

11. 12. 13. 14. 15.

Ryan, S. G., Norris, J. E., k Beers, T. C , ApJ 471, 254 (1996) Shigeyama, T., k Tsujimoto, T., ApJ 507, L135 (1998) Smith, G. H., PASP 112, 12 (2000) Truran, J. W., A&A 97, 391 (1981) Tsujimoto, T., Yoshii, Y., Nomoto, K., Matteucci, F., Thielemann, F.-K., k Hashimoto, M. ApJ 483, 228 (1997) 16. Tsujimoto, T., k Shigeyama, T., ApJ 508, L151 (1998) 17. Tsujimoto, T., Shigeyama, T., k Yoshii, Y., ApJ 519, L64 (1999) 18. Tsujimoto, T., Shigeyama, T., k Yoshii, Y., ApJ 531, L33 (2000)

LIGHT ELEMENTS IN I N H O M O G E N E O U S EARLY G A L A X Y A N D THEIR ASTROPHYSICAL INTERESTS T.K.SUZUKI^-9, Y.YOSHIIc, T.KAJINO5, & T.C.BEERSD A

Department

Theoretical

c

of Astronomy,

Astrophysics

School of Science, University Tokyo, 113-0033, Japan Division, Tokyo,

National Astronomical 181-8588, Japan

of Tokyo,

Bunkyo-ku,

Observatory,

Mitaka,

Institute of Astronomy, School of Science, University of Tokyo, Mitaka, Tokyo, 181-8588 Japan; Research Center for the Early Universe, Faculty of Science, University of Tokyo, Bunkyo-ku, Tokyo, 113-0033 Japan

Department

of Physics

and Astronomy, Michigan MI 48824, USA

State

University,

East

Lansing,

The aim of this contribution is that presenting the interesting and important astrophysical aspects of light elements (LiBeB) in the early stages of Galaxy, based on a model of SN-induced chemical evolution ' , (l)Abundances of light elements observed in metal-poor stars can be used as their age indicators. (2)Our model determines the primordial 7 Li abundance precisely, and it gives an independent constraint on the baryon density of Universe. (3)We estimate the possibility of distinguishing the models of standard Big-Bang Nucleosynthesis and non-standard (inhomogeneous) Big-Bang Nucleosynthesis, by future observations of Be abun­ dances in metal-poor stars.

1

Introduction

Recent observation 3 ' 4 of elemental abundance of old metal-poor stars uncov­ ered evidence of inhomogeneous nature of the early Galactic halo. The abun­ dance pattern of heavy elements observed in these stars show that they were born from individual supernova (SN) remnant (SNR) shells because the gas was not well-mixed at that time. Based on these views, a model of SN-induced chemical evolution was constructed 1 , which explained very well the observed large scatters of abundance of europium (Eu) for the stars having the same metallicity or [Fe/H]. An important result of the model is that stellar metallicity has no one-to-one relation to their ages or the cosmic time. This model is extended 2 for the investigation of light elements (LiBeB), mainly produced by nuclear reactions involving Galactic Cosmic Rays (GCRs), and it is claimed that the abundnce of the light elements can be used as a cosmic clock because they are produced by GCRs which propagate globally without being easily

23

24

influenced by local enviromental effects.

2

Brief Description of the Model

Star-forming processes are assumed to be confined in separate clouds. The evolution of a cloud starts when a certain fraction of the cloud turns into metal-free Pop III stars according to the Salpeter initial mass function at time t = 0. Evolution of the cloud characterized by star formation processes is triggered by SN explosions, and all stars of subsequent generations are assumed to be born in the dense shells formed behind the radiative shock front of SNR. GCRs are accelerated from the shock of SNRs and produce the light elements both inside and outside of SNR shells through spallation and fusion reactions. General formulae1 of the SN-induced chemical evolution and specific formulae2,5 for the evolution of light elements are presented elsewhere.

3

Results

Using the SN-induced chemical evolution model, we show our results of cal­ culation in this section. The initial abundances of heavy elements are set to zero, but those of the light elements are taken as equal to the predicted pri­ mordial abundances, based on the standard BBN model 6 . The evolution of the cloud finishes at 0.6 Gyr from Pop III star formation when SNRs sweep up all the material of the cloud1. At that time, [Fe/H] of our cloud becomes -1.5.

3.1

Comparison with Observation

In Fig.l our results of predicted frequency distribution of long-lived stars (m< I M Q ) are compared with the recent observation. As a whole, our results have quite good concordance with the observed 6 Li, Be, and B abundances. In particular, the distribution of present observation of Be and B data appears to be consistent with the area of constant probability density of 10~ 3 . This implies that if the number of stars with measured Be and B is increased by a factor of 100, they fill in the area of the constant probability density of 10~ 5 . The observed linear trend of Be and B with Fe is well reproduced in a range of [Fe/H]> —3, because most of them are produced by the spallation of GCR CNO from SN-ejecta due to the lack of CNO in the ISM 5 .

25

Figure 1. Predicted frequency distributions of long-lived stars in the [Fe/H]-log(X/H) planes, convolved with Gaussian having a = 0.15 dex for Be, B, and Fe and a = 0.3 dex for 6 Li. Two contour lines, from the inside to the outside, correspond to those of constant probability density 1 0 - 3 , and 1 0 - 5 in unit area of A[Fe/H]-0.1XAlog(X/H)=0.1. The solid line shows the [Fe/H]-log(X/H) relation in the gas. The crosses represent the data with observational errors.

3.2

Stellar Age vs. Elemental Abundance Relation

Usually, abundance of heavy elements observed in a star is regarded as indicating the time at which the star was formed. Although this is expected from a simple one-zone model of chemical evolution, its basic assumption of well-mixed gas should be abandoned when considering the very early stage of evolving halo where the gas was poorly mixed. The abundances of heavy elements in metal-poor stars reflect those of synthesized elements by individual SNe that have just exploded near the site of formation of such stars. However, it was recently pointed 2 out that abundances of the light elements except for 7 Li in very metal-poor stars can still be used as age indicators because these elements are mainly produced by the reactions concerning with GCRs which propagate globally. Figure 2 shows the abundances of Fe, B, Be, and 6 Li as a function of time elapsed after the formation of Pop III star. The contours therein show the frequency distribution of long-lived stars with m < IMQ which born at time t, and the solid line represents the abundances in the ISM. Generally speaking, narrower distribution of stars along the solid line indicates a better correlation between stellar age and elemental abundance. In this respect, the predicted tFe correlation is considerably poor at earlier epochs, and a better correlation is achieved at [Fe/H]> —2, which indicates that Fe can be used as an age indicator only for stars with [Fe/H]> —2. The ideal element for a cosmic

26 -101

0.0

)

0.2

0.4

-11 [ ' ' ' '

0.0

0.2 0.4 time(Gyr)

0.6 i

0.6

-1F

0.0

0.2

0.4

0.6

0.2 0.4 time(Gyr)

0.6

-101

0.0

Figure 2. Predicted frequency distribution of long-lived stars in the i-log(X/H) planes as a function of time, convolved with Gaussian having a = 0.15 dex for X=Be, B, and Fe and cr = 0.3 dex for 6 Li. Time (t) is defined as that elapsed after the formation of metal-free Pop III stars. Two contour lines, from the inside to the outside, correspond to those of constant probability density 1 0 - 3 , and 10~ 5 in unit area of At = 10(Myr) X Alog(X/H)=0.1. Solid lines represent the evolution of abundances of the elements in the gas.

clock is 6Li for which a superior correlation is realized at all times from the beginning. This is because 6Li is mainly produced by the fusion of a-particles which are BBN products and are distributed globally in the entire halo. The t-Be correlation is marginally acceptable for use of Be as a cosmic clock, because it is produced by the spallation of CNO in GCRs which propagate globally. B may be used as a clock better than Fe but worse than Be, because a significant fraction of n B isotope is produced in the SNR shell by ^-process of SNe II, in addition to the spallation of CNO in GCRs. 3.3

Primordial7Li

and Baryon Density of Universe

Figure 3 presents a comparison of the recent accurate observations 11 of vl(Li) to the theoretical prediction of the frequency distribution of long-lived stars

27

in the j4(Li)-[Fe/H] plane. In this comparison we have used our best estimate of the primordial Li abundance >l(Li)p = 2.09(ref.l2), and we have used the data chosen for stars with Teff > 6000K and [Fe/H]< —1.5. The effects due to early Galactic chemical evolution of Li are seen already at [Fe/H]~ —3, which produces levels in excess of j4(Li)p; the predicted trend is quite consistent with the data. It should be emphasized that this increasing trend of Li abundance is naturally derived by use of the same model which fits the data of the other light elements in metal-poor halo stars. The average excess of total Li over the primordial 7Li value amounts to 0.09 dex at [Fe/H] = —2. We note that most of Li in our model of the early Galaxy is produced by GCR a + a reactions. 1

-

2.2 r

1

i

"H ~~-» 10

_ ?^-~ ^ — -

i

/-^""~~~"N

c

^^ y/ log(1kelihood]____^--^ ^/

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i

-

-3 [Fe/H]

Figure 3. Frequency distribution of long-lived stars in the A(Li)-[Fe/H] plane, convolved with a Gaussian having a = 0.03 dex for A(Li) and a = 0.15 dex for [Fe/H]. The primordial lithium abundance is chosen to be A(IA)V = 2.09, which is the best fit value in our model. The two contour lines, from inside out, correspond to those of constant probability density 1 0 - 4 a n d l O - 9 in unit area of A[Fe/H]=0.1X AA(Li)=0.002. The inset shows the likelihood as a function of yl(Li)p. The horizontal bar indicate the value of J 4(Li) p that gives the maximum likelihood, and the vertical bar shows a range of 95% confidence limits. The crosses with lozenge represent the data taken from RNB for stars with Teff > 6000K.

Since our model gives the correct amount of Li produced by post-BBN pro­ cesses, it can be used to predict the precise quantity of Li synthesized during the BBN era. We estimate the primordial Li abundance A(Li)p by construct­ ing likelihood plots as a function of A(Li)p (see ref.12 for more in detail). The inset of the top panel of Fig.3 shows the likelihood function established by using the data 1 1 . Based on our likelihood analysis, the 95% confidence region on the primordial Li abundance occurs for ,4(Li)p = 2.091°;°*

(1)

28

Following the previous works 13 , we now explicitly include estimates of system­ atic errors arising from various sources. The estimated value and confidence interval for A(Li)p then becomes

A(Li)p = 2.07±°;JI .

(2)

Figure 4. Primordial abundances of 4 He, 2 D and 7 Li as a function of ?jio(= r;/10 — 1 0 ). In the -4(Li) — 7j diagram (bottom panel), our determined Li value A(Li)p = 2 . 0 7 _ 0 0 4 is shown by horizontal line and the allowed region with errors by box. For the puipose of comparison, observational estimates of the primordial abundances of He and D are also shown. Their reference values of 'low 4 He', 'high 4 He', 'low 2 D ' , and 'high 2 D ' are taken from ref.15, ref.16, refs.l7&18, and ??19, respectively. The dashed box for "low 4 He"shows the result, derived from observations of HII regions in the Magellanic Clouds 2 0 . The dashed box for 'high 2 D ' shows the allowed region based on more conservative analysis of 2 D (ref.21).

Figure 4 shows our preferred value of A(Li)p = 2.07^° Q| with a horizontal line, and the allowed 95% confidence intervals by a box, along with the previous estimates of 4He and 2 D. The theoretical prediction of SBBN 6 ' 14 is superposed. Interestingly, our preferred value lies at the very bottom of the valley of the function of 7Li abundance against r], which means that we can assign a single value for rj, independent of the results from 4 He and 2 D. Our analysis indicates r)(Li) = (1.7 — 3.9) x 10~ 10 , which corresponds to a universal baryonic density

29 parameter fli,h2 = (0.64 — 1.4) x 10 /i = i 7 0 / 1 0 0 k m s - 1 M p c - 1 . 3.4

2

with the Hubble constant expressed as

Possibility of Distinguishing between SBBN and IBBN by Be-plateau

So far we have used the SBBN model to set our assumed initial abundances of light elements, although their abundances are strongly dependent on the BBN model which is chosen. For example, if the density distribution in the early universe is not uniform as in the inhomogeneous BBN (IBBN) model, more LiBeB are synthesized in neutron-rich regions22. In order to see how a non-standard BBN model changes the result, we calculate the frequency distribution of long-lived stars in the log(Be/H)-[Fe/H] plane using an optimal initial abundance of log(Be/H)= —14.3 taken from the IBBN model 23 , which is higher by more than 3 orders than the value, log(Be/H)= —17.9, predicted from the SBBN model 6 .

Figure 5. Frequency distribution of long-lived stars in the log(Be/H)-[Fe/H] plane for two different primordial Be abundances predicted in the SBBN and IBBN models. The contour lines, from the inside to the outside, correspond to those of constant probability density 1 0 - " and 1 0 - 5 in unit area of A[Fe/H]=0.1 X Alog(Be/H)=0.1 for the SBBN (solid lines) and for the IBBN (dashed lines). The crosses represent the data with observational errors 8 .

The resulting distribution for the IBBN model is compared with the SBBN model in Fig.5. Since the total probability integrated over the area between the inner and outer contours is less than 0.01, we need to measure BeB abun­ dances in several hundred halo stars in order to distinguish the IBBN from the SBBN on a statistical basis. A more direct way to distinguish these alter­ native hypotheses is to identify true Pop III stars, the atmospheres of which

30

consists of primeval gas. References 1. Tsujimoto, T., Shigeyama, T., k Yoshii, Y. 1999, ApJ, 519, L63 2. Suzuki, T. K., Yoshii, Y., k Kajino, T. 1999, ApJ, 522, L125 3. McWilliam, A., Preston, W., Sneden, C , k Searle, L. 1995, AJ, 109, 2757 4. Ryan, S. G., Norris, J. E., k Beers, T. C. 1996, ApJ, 471, 254 5. Suzuki, T. K. et al. 2000, in preparation 6. Thomas, D., Schramm, D. N., Olive, K. A., Mathews, G. J., Meyer, B. S., k Fields, B. D. 1994, ApJ, 430, 291 7. Smith, V. V., Lambert, D. L., k Nissen, P. E. 1998, ApJ, 506, 405 8. Boesgaard, A. M., Deliyannis, C. P., King, J. R., Ryan, S. G., Vogt, S. S., k Beers, T. C. 1999, AJ, 117, 1549 9. Duncan, D. K., Primas, F., Rebull, L. M., Boesgaard, A. M., Deliyannis, C. P., Hobbs, L. M , King, J. R , k Ryan, S. G. 1997, ApJ, 488, 338 10. Primas, F., Duncan, D. K., Peterson, R. C., k Thorburn, J. A. 1999, AkA, 343, 545 11. Ryan, S.G., Norris, J.E., k Beers, T.C. 1999, ApJ, 523, 654 12. Suzuki, T. K., Yoshii, Y., k Beers, T. C. 2000, submitted to ApJL 13. Ryan, S.G., Beers, T.C., Olive, K., Fields, B., k Norris, J.E. 2000, ApJL, in press 14. Fiorentini, G., Lisi, S., Sarkar, S., k Villante, F. L. 1998, phys.rev.D, 58, 063506 15. Olive, K.A., Skillman, E.D., k Steigman, G. 1997, ApJ, 483, 788 16. Izotov, Y.I., k Thuan, T.X. 1998, ApJ, 500, 188 17. Buries, S., k Tytler, D. 1998a, ApJ, 499, 699 18. Buries, S., k Tytler, D. 1998b, ApJ, 507, 732 19. Rugers, M., k Hogan, C.J. 1996, AJ, 111, 2135 20. Peimbert, M., k Peimbert, A. 2000, Proceedings of IAU Symp. 198 "Light Elements and Their Evolution," eds. L. da Silva, M. Spite, k J. R. de Medeiros, in press, astro-ph/0002120 21. Songaila, A., Wampler, E.J., k Cowie, L.L. 1997, nature, 385, 137 22. Kajino, T., k Boyd, R. N. 1990, ApJ, 359, 267 23. Orito, M., Kajino, T., Boyd, R. N., k Mathews, G. J. 1997, ApJ, 488, 515

P R O S P E C T S FOR V E R Y HIGH E N E R G Y 7-RAY ASTRONOMY WITH NEXT GENERATION IMAGING CERENKOV TELESCOPE T. KIFUNE Institute for Cosmic Ray Research, University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8582, JAPAN E-mail: [email protected] The ground-based technique has opened a way of detecting 7-rays at ~1 TeV energy by collecting the energetic photons with detection area ~ 104m2 and angular resolution ~ 0.1°. The next step of improving sensitivity is now going to be taken to exploit, to a larger extent, violent energetic phenomena in which the process of particle acceleration plays a dominant role. The basic concept of the currently going-on projects for the next generation 7-ray telescope is described in this paper, paying an attention on how and why the current status of very high energy 7-ray astronomy needs to be developed for improvements.

1

Introduction

Radiation beyond MeV has an energy spectrum described by power law. The emission is due to the progenitor particles which are not in the thermal equi­ librium with their environments. High energy 7-rays are a unique tool for understanding celestial, non-thermal processes, in particular, to uncover phe­ nomena in which acceleration of high energy particles plays a dominant role. However, any sources where protons accelerated to radiate 7-rays have not been discovered or confirmed yet, and instead the point-like sources of high energy 7-rays are explained by copious energetic electrons and positrons. X-ray stars, for instance, was disclosed more than thirty years ago. The temprature as high as ten milions Kelvins of the thermal X-rays is just well explained by the lib­ eration of gravitational potential energy of accreting matter on to a compact star, and provided evidence of neutron star in 5 years earlier than the discovery of pulsar. An 'archetype' source in such meaning still remains to be looked for in high energy 7-ray observation. The observation of 7-ray photons is suffered from poorer statistics at higher energies. However, the ground-based technique has opened, about a decade ago, a window of seeing the Universe through VHE (very high energy) 7rays in the energy band of ~lTeV (Weekes et al. 1997, references therein). The ground-based telescope detects VHE 7-rays by using air Cerenkov lights from a bundle of electrons and positrons which 7-rays produce in the upper atmosphere as a cascade shower process. The Cerenkov lights are emitted at angles of about 1° at about 10 km altitude and illuminate the ground uniformly.

31

32

The ground-based detection thus enjoys detection area of > 10 4 m 2 , almost five orders of magnitude larger than the satellite instrumentation at MeV to GeV energies. The imaging technique of Cerenkov lights is capable of rejecting about 99% of the overwhelming background of cosmic ray proton events. These conditions could bring about the "break-through" of detection technique; by firmly confirming the VHE 7-ray signal from the Crab nebula, thanks to the fact that the Crab flux of ~ 1 0 - 1 1 c m _ 2 s _ 1 (E 7 > 1 TeV) was just as intense as the sensitivity of the imaging Cerenkov telescope with observation time of tens of hours. The observation of the past 10 years has shown that further improvements are necessary to go beyond the limitation the current results have, for instance, in the number of discovered objects and in the distance to the sources that detection sensitivity allows. The world-wide efforts are thus attempting to construct the "next generation telescopes", which will reduce the detectable energy of 7-rays down to ~100 GeV. Observation will start in a few years to in more details uncover violent, energetic phenomena in which high energy acceleration of electrons and protons plays a dominant role. 2

High energy 7-ray sources

Considerable efforts in 7-ray observation have been spent in search for exotic phenomena, such as antimatter or primordial black holes, that could inform us of the debris of high energy particle interaction in earlier stages of the Universe. The searches have so far betrayed such speculative expectation. Instead, a wealth of non-thermal processes have been unexpectedly uncovered, as their typical energy spectra illustrated in Fig. 1, with a considerable number of high energy 7-ray sources as listed in Table 1 from the third catalogue (Hartman et al. 1999) of EGRET detection of CGRO (Compton Gamma Ray Observatory). The case of VHE 7-rays is also added in the bracket. VHE 7-rays are detected so far from AGN (active galactic nuclei), pulsar nebula, SNR (supernova remnant) and possibly from an X-ray close binary, Cen X-3 (Vestrand et al. 1997; Chadwick et al. 1998). We may indicate that there exist interesting dissimilarities between the two energy regions: There is no clear suggestion of stronger GeV sources likely to be a latent TeV source. Two distinct classes appear to exist in blazars, i.e. 7-ray emitting AGN, of GeV and TeV ones. The TeV blazars are not bright in GeV 7-rays and, rather, belong to less luminous sources of the EGRET catalogue (Ghisellini et al. 1998). Emission of GeV 7-rays is from the pulsar magnetosphere while VHE 7-rays are from pulsar nebulae. Conversely, pulsar nebulae are not detected as GeV source except for the Crab nebula. Such a transition of the features of 7-ray source appear to take place in the energy region of 10 -100 GeV, which remains

33

-7

i

GRB

_

-

% ° -9

Visible Star

^CrabNebula

e? o PL,

o

--1

-

f\^AGN

\

-11

—

-13

ys^

/ 1

\

SNR

s *' */ Galactic Disc " \ v Extra-galactic Diffuse" s

U

L

leV

1 keV

1 1 MeV

1 1 GeV

V

N 1 TeV

Photon Energy Figure 1: Schematic sketch of energy spectrum from 7-ray sources.

unexploited above the satellite and below the ground-based observation. The next generation of ground-based observation aims at this energy region, where a larger number of sources than in the TeV band are expected. The particle nature of photons becomes more prominent with increasing photon energy. Energetic 7-rays have inreraction of creating electron-positron pairs when they encounter photons of ambient softer radiation. The interacton sets limitation to the travelling distance to be no larger than ~ 100 Mpc for ~ 1 TeV 7-rays. The source must be optically thin for 7-rays to escape out of emission region. Weaker and remoter sources are likely to be disclosed by reducing the detectable energy of 7-rays. 3

Overview of the results in TeV energy region

The main part of VHE 7-ray astronomy remains still hidden below the current detection sensitivity. For instances, the emission from the Galactic disc is the most intense one in the GeV energy region and should extend to TeV energies, however, not yet detected at TeV energies because of the difficulty to detect extended emission with the current imaging Cerenkov technique. The imaging

34 Table 1: GeV (TeV) 7-ray sources

type of sources normal galaxy active galaxy

pulsar

unidenfified sources galactic latitude |6| < 1 0 ° galactic latitude |6| > 10°

number of GeV (TeV) sources 1 83 (2-4)

6(3)

note Large Magellanic Cloud quasar, BL Lac objects pulsed emission from pul­ sar magnetosphere in GeV energy (unpulsed from pulser nebula in TeV energy)

181 78

Violently time variable sources are included.

103

supernova remnant

?(2)

possibly sources

in

unidentified

X-ray binary

1(1?)

transient emission in GeV energy (Cen X-3)

Cerenkov telescope has a typical field of view of about 3°-5° diameter, and thus the survey over all the sky so far made is incomplete, particularly for time-variable, transient sources. 3.1 Extragalactic objects The active galaxies of GeV 7-ray emission distribute in red shift z as far as 2. However, the two firmly established ones of VHE 7-ray emission, Mrk 421 and Mrk 501 are of z~0.03. The distance that TeV 7-rays can travel through gets shorter with increasing 7-ray energy due to pair production of electron and positron in collision with softer photons with a greater spacial density of background radiation in extragalactic space. The maximum distance is estimated to be within about z~0.1 for 7-rays at ~1 TeV. The high energy activity of producing 7-rays are considered due to a mas­ sive black hole located in the central core of the active galaxies, i.e. AGN. The intense radiation field near the central engine of AGN was thought to prevent high energy 7-rays from escaping out. High energy 7-rays can come out against

35

such expectation thanks to the relativistic bulk motion of the AGN jet. The jet moving with a Lorentz factor T can enhance the energy and luminosity of 7-rays in the observer's frame than those in the rest frame of the jet by a factor T and T 4 ( r from each of the transformation of energy and time, and T2 from solid angle), respectively, thus reconciling the absorption effect due to electron-positron pair creation. Production of 7-rays is explained by energetic electrons scattering ambient soft photons up to 7-ray energies. By comparing this inverse Compton yield with synchrotron radiation into X-ray band, the 7-ray data could determine the parameters of the AGN jet such as magnetic filed B ~ 0.1G and T ~ 10. The data from VHE 7-rays are found useful to infer these values, but available objects are few to compare with those in the other bands. Another important question to be addressed and left for further efforts to answer is whether the energy of the jet is supplied by hadrons, i.e. due to acceleration of protons, or by non-hadronic process of electrons and positrons. In other words, there remains a question if AGN can be the source of extragalactic cosmic ray protons. 3.2

Galactic objects

CANGAROO (Collaboration between Australia and Nippon for a GAmma Ray Observatory in the Outback) has VHE 7-ray observation in Woomera, South Australia by using imaging Cerenkov telescope. The site has advantage of seeing the Galactic center near the zenith, and its main efforts were spent in surveying Galactic objects; mainly on pulsars and SNRs (e.g. Kifune 2000). The positive detections so far reported are from three pulsar nebulae of Crab, Vela, PSR1706-44 pulsars and from two SNRs of SN1006 and RXJ1713.7-3946 (Muraishi et al. 2000). In the case of Crab nebula, the observational data well cover wide energy bands to provide an "entire energy spectrum" of a two-peaked distribution which is interpreted as due to synchrotron and inverse Compton emissions and indicates that non-thermal electrons are the progenitor of the radiation. The spectra of the other sources also appear to be consistent with the view of electron progenitor. New results in observation generally stimulate new problems which re­ quire further efforts for advanced observation, in the case of VHE 7-rays from Galactic objects, for instances: (i) The two spectra of synchrotron and in­ verse Compton radiation may not be fully consistent with each other, or the entire spectrum needs to be known with better coverage over all the energy bands to enable the comparison with reasonably good accuracy, in order to confirm/clarify various kinds of different populations of progenitor particles; i.e. protons, fresh young or old aged electrons, (ii) Except for the case of

36

the Crab nebula, inverse Compton emission is considered to be from the col­ lision with 2.7K photons of cosmic microwave background, and the intensity ratio to synchrotron radiation suggests magnetic field as low as the value in the interstellar space ~ 3/uG. It is not clear what the low magnetic field im­ plies in relevance to particle acceleration mechanism, (iii) Emission region of VHE 7-rays from the Vela pulsar direction appears to be at the birth place of the pulsar which is displaced by about 0.3° from the present position. In order to have conclusive arguments about what these results may suggest, it is necesary to know the energy spectrum over broad, entire bands in more de­ tails for each source and on a greater number of Galactic VHE 7-ray sources than the current known ones; three pulsar nebulae, two SNRs and possibly one X-ray emitting close binary (Cen X-3). Electron progenitor is consistent with the data from pulsar nebulae and SNRs, but the currently known "entire" energy spectrum contain uncertainties which may allow, at least partially, the possibility of proton progenitor. 4

The next generation telescopes

As the next step of the ground-based telescope for VHE 7-rays, a system of multiple telescopes of 10m size is coming soon to provide a larger detection area added from many telescopes, better resolution of energy and arrival direction than single telescope. "Stereoscopic, simultaneous" operation of the multiple telescopes is intended to detect 7-rays in the energy region down to ~100 GeV. The concept is persued by the three projects. The CANGAROO group has started to construct four 10m telescopes, as a 5 years project, with a stereoscopic operation of two telescopes available in the 2001 year (Mori et al. 1999). The photograph of the first 10m telescope of the CANGAROO project is shown in Fig. 2. Two other projects, VERITAS collaboration in USA and H.E.S.S. of Euro­ pean collaboration lead by Max Planck Institute in Heidelberg, Germany, have proposed to construct 7 and 16 telescopes, respectively. The both projects ex­ pect to commence their first stage of constructing 4 telescopes in a few years almost at the same time with CANGAROO. The telescopes are installed with mutual distance of about 100 m which is less than the spread of the Cerenkov light pool to optimize detection area and rejection power of cosmic ray back­ ground. Slightly differently, another direction for the next generation of imag­ ing Cerenkov telescope is to achieve energy threshold of detectable 7-ray energy less than 50 GeV which overlaps the satellite detection, and the group lead by Max Planck Institute in Munich has started MAGIC project to construct a 17m aperture telescope.

37

Figure 2: The Cerenkov imaging telescope of 10m diameter of CANGAROO project.

The detectable energy of 7-rays is expected to be ~100 GeV by collect­ ing Cerenkov lights with the 10m aperture of reflection mirror. The largest telescope at present, the 10m telescope of Whipple group, has been, however, the threshold enegy of ~300 GeV, because Cerenkov lights emitted from single cosmic ray muon passing near the telescope produce a new kind of background events that resembles 7-ray signal of lower energies. A simple or easy way of distinguishing this background is to confirm no corresponding signal in the other telescopes of the stereoscopic operation, or improvements are necessary in the imaging camera of smaller pixel size as well as in the electronics circuit of better timing information. In addition to new sources that will be found in the energy region so far unexploited, the statistics of gathered number of 7-ray photons can be improved by going to lower 7-ray energies. The detection of energy flow at sensitivities better than 10 - 1 1 erg cm _ 2 s _ 1 is expected from observation duration time as short as 10 hrs for the sources that do not have very hard energy spectrum of VHE 7-rays. Comparison with the other energy bands of electromagnetic

38

radiation for the multi wavelength analysis will be made possible for a decent number of samples of VHE sources. The system of multiple telescopes will be operated in various ways. The opportunities of observing a number of targets are increased by setting each telescope to aim at each different objects. Alternatively, one same object is tracked simultaneously by multiple telescopes, and the effective duration time of observation or detection area is made larger. When multiple telescopes are within the area of the Cerenkov light pool of one event, "stereoscopic" image of 7-ray air shower event become available. Single imaging Cerenkov telescope has a power of identifying and rejecting about 99% of cosmic ray charged particles which is about 105 times more frequent than the intense flux from the Crab nebula. The rejection power can be increased in the stereoscopic observation as a product of the contributions from individual telescopes. The angular resolution of the single telescope depends on the direction relative to the elongation axis of Cerenkov light image. This drawback can be improved by using multiple telescopes and we will obtain angular resolution of ~ 0.1° for a single event. Thus, the stereoscopic observation makes it practically possible or easier to detect extended emission as well as weak sources so far hidden in cosmic ray background events. Search for more sources of AGN, pulsars and SNRs, is of prime importance in what will be done in the years to come. Our Galaxy can be surveyed for VHE sources brighter than the luminosity ~ 1032 erg s _ 1 within the distance as far as 10 kpc. A considerable number of 7-ray sources will be added to the multiwavelengths analysis. A systematic study of energy spectra from many AGN will determine the infrared intensity in extragalactic space and give estimate on the activities of galaxies, as well as extending our understandings about the high energy activity around the AGN jet in the Galaxy.

5

Prospects and problems

Existence of high energy, non-thermal electrons already came to our notice about a half century ago as a result of radio observation. The radiation from energetic protons emerges only in the 7-ray energy band, and those objects which are relevant to the origin of cosmic rays are naturally the ' archetype' 7-ray source. As one of such objects, SNR is generally accepted as the most likely object of accelerating cosmic rays up to ~ 1015 eV, however not beyond this energy. In addition to SNR, unknown site of the origin of cosmic rays must exist and remains to be seeked for. A new class of VHE 7-ray sources is to be found.

39 5.1

Origin of cosmic rays

Several unidentified EGRET 7-ray sources are accompanied by SNR, and such examples in the northern sky are studied by the Whipple, CAT and HEGRA groups to detect VHE 7-rays extrapolated from the GeV flux with a power index of ~2 as predicted from the shock acceleration model of cosmic ray pro­ tons. The efforts are so far negative in contrast with the result from SN 1006. The both SNRs of CANGAROO detection appear dissimilar to those SNRs in the unidentified EGRET sources; considerably dark in radio and GeV 7-rays but bright in non-thermal X-rays. The fact can be consistent with VHE 7-rays emitted from electrons and suggest that the component from proton progenitor is weak below the detection sensitivity. The shock acceleration of electrons in the shell of SNR is proved from the SN 1006 result. However, the path that will take us to understand the origin of cosmic rays is somewhat twisted from the standard expectation that detection of VHE 7-rays will directly provide evidence for acceleration of cosmic ray protons in SNR. The acceleration of cosmic ray protons and the subsequent 7ray emission depend on the complexity of various types of SNRs that may stem from environmental conditions. Emission of 7-rays may be modified from the earlier considerations (Drury et al. 1994; Naito and Takahara 1994) to allow for a variety of the characteristics which individual SNRs appear to show, as well as to refine the models of acceleration and radiation mechanism. It is argued that the confinement life time of cosmic rays in a cluster of galaxies is much longer than ~ 107 years, the time in our Galaxy, and even as long as the Hubble time (Volk et al. 1996). If so, cosmic ray interaction in a cluster of galaxies may give a VHE 7-ray flux which is detectable by using the system of Cerenkov telescopes. The star burst galaxies are likely to contain intense cosmic rays, and are also putative sources. The 7-ray observation of other galaxies would give new insights about the activities of high energy processes like supernova explosions during earlier periods and then their effects to the evolution of galaxies. 5.2

New population of sources?

The activities of AGN and pulsars which are the identified 7-ray sources in GeV and TeV energy region, are due to the compact object of black hole and neutron star. However, not all types of the compact objects are found to be 7-ray sources, as noted in Table 2. The emission from the compact objects appear violently time-variable sources, except for single pulsar, as observed in the other wave bands for instance X-rays. There is in any wave bands no evidence observed on single black holes (not in a binary system) and neutron

40 Table 2: Compact objects and 7-ray sources.

type

neutron star

Galactic candidates of black hole of M ~ 1QMQ

Black holes in the center of galaxies

single

^

no evidence

\J

in any wave band binary

^ (? ;Cen X-3)

(X-ray source)

(colliding galaxies !?)

The mark ^ indicates detection by 7-rays stars after its death as radio pulsar. The maximum energy of acceleration of electrons is likely determined by the radiation loss (Ghisellini et al. 1998), and the average energy density, for instance, of radiation field, in the vicinity of compact accreting objects de­ pends on the mass M of compact star (the spatial size and the brightness or the Eddington luminosity generally changes in scale to the mass M of com­ pact star, so that the energy density is generally proportional to the inverse of mass, oc M~l) as well as the amount of energy input supplied to the object. In the case of pulsars, accretion is the energy source for a pulsar in binary system. The size of radiation region is presumably no larger than the binary orbit, and less than 1 pc of the nebula size of single pulsars, giving the spatial density of radiation energy as higher in the case of binary system. For pro­ tons as the progenitor of 7-rays, the region where radiation and acceleration take place can be considerably separated from each other, because protons' radiation life time against ambient electromagnetic field is much longer than electrons' and the matter density required for 7r° production may be low in the acceleration region. The condition on the optical thickness against pair production is different from the electron. Latent sources of VHE 7-rays in a binary system, for instance Cen X3, have environmental conditions different from single pulsar and AGN, and thus likely with an emission mechanism dissimilar to the known 7-ray sources. However, investigation on such objects so far done is far from suffiient and complete. The unidentified EGRET sources of violent time-variability suggest a new population of 7-ray sources (Tavani et al. 1998). The time-variabile sources may include Galactic micro quasar which accompanies a relativistic jet to enhance high energy radiation like the case of AGN and 7-ray bursts.

41

Though these objects will be surveyed by using Cerenkov imaging telescope of the next generation, the field of view typically of 3° - 5° across is rather suited to pin-pointed deep study of selected objects. Cooperative informa­ tion from other bands are necessary for properly choosing observation targets such as violently time-variable sources as well as for simultaneous multi-bands observation and interpretation. Exotic interaction of particles generally has an energy threshold and can appear only at higher energies. A line emision from annihilating dark matters might exist in 100 GeV ~ 1 TeV region, and may be detectable with the energy resolution AE7/Ey ~20% which is expected for the system of mutiple telescopes. Increasing deviation of propagation speed of photons from the light velocity c might happen with increasing photon energies (Amelino-Camelia et al. 1998; Coleman and Glashow 1997), and the effect would modify the travelling distance of 7-rays (Kifune 1999). Extragalactic diffuse 7-rays have been measured up to about 50 GeV by EGRET. Extrapolation of the spectrum to higher energies and observation of VHE 7-ray emission from the halos of galaxies would provide a test for these exotic phnomena. 6

Conclusion

Observation of VHE 7-rays will extend into the energy region of ~ 100 GeV by using a system of ground-based multiple telescopes. A greater number of AGN at larger distances will be detected. Although investigation will be still limited to small values of redshifts in the order of ~ 0.1, the conversion effect itself of 7-rays to electron and positron pair provides us with the means of estimating the infrared intensity in extragalactic space. Efforts for understanding parti­ cle acceleration in AGN jet, pulsar wind and shock process will be continued by investigating more samples of AGN, pulsars and SNRs with more samples. Various types of objects are characterized by different values of, for instances, mass or luminosity which distrubutes in a wide range of the parameters. In unexploited values of these, a new population of 7-ray sources might emerge with different schemes of particle acceleration. The objects where proton ac­ celeration takes place still remain to be looked for. The study is linked to new populations of 7-ray sources, and extended to the case of extragalactic cosmic rays. As located in the highest energy band of electromagnetic radiation, tests for speculated exotic phenomena are a unique role to be done by VHE 7-ray astronomy. Cosmic rays are known to be the highest energy phenomenon in the present Universe, and VHE 7-rays are to extend the survey of such activity beyond our Galaxy.

42

References 1. G. Amelino-Camelia, J. Ellis, N.E. Mavromatos, D.V. Nanopoulos, and S. Sarkar, Nature 393, 763 (1998). 2. P.M. Chadwick et al, APJ 503, 391 (1998) 3. S. Coleman and S.L. Glashow, Phys L B405, 249 (1997) 4. L.O'C. Drury, F.A. Aharonian and H.J. Volk, AA 267, 959 (1994) 5. R.C. Hartrnan et al, APJS 123, 79 (1999) 6. G. Ghisellini et al, MNRAS 301, 451 (1998) 7. T. Kifune, APJ 518, L21 (1990) 8. T. Kifune, Adv,Space Res. 25, 641 (2000) 9. M. Mori, Proc. of TeV gamma-ray Workshop (Snowbird, Utah; August 1999) , (1999) 10. H. Muraishi et al, AA i, n (p)ress 2000 11. T. Naito and F. Takahara, J. Phys G 20, 477 (1994) 12. M. Tavani et al, APJ 497, L89 (1998) 13. W.T. Vestrand, P. Sreekumar and M. Mori, APJ 483, L49 (1997) 14. H.J. Volk, F.A. Aharonian and D. Breitschwerdt, Space Science Review 75, 279 (1996) 15. T.C. Weekes, F.A. Aharonian, D.J. Fegan and T. Kifune, Proc. of 4th CGRO Symposium (The American Institute of Physics, edited by C D . Dermer, M.S. Strickman and I.D. Kurfess; AIP Conference Proceedings 410) , 361 (1999)

Evolution and Explosion of Massive Pop III Stars and their Nucleosynthesis Hideyuki Umeda, Marii Shirouzu and Ken'ichi Nomoto Research

Center for the Early Universe and Department of Astronomy, of Tokyo, Hongo, Bunkyo-ku, 113-0033, Japan

University

We calculate stability, evolution and explosion of massive Pop III stars. We find the upper limit mass of the pulsationally stable Pop III ZAMS stars is about 13OM0, and the mass loss rate of unstable stars may be low. The nucleosynthesis results are compared with abundances of metal-poor halo stars to constrain the IMF of Pop III stars. The interesting trends of the observed ratios [Zn, Co, Mn, Cr/Fe] of the very metal-poor stars can be related to the mass ratio between the complete Si burning region and the incomplete Si burning region. We find that yields of Type II supernovae and Fe core collapse hypernovae can be consistent with the very low metal star abundances, if significant amount of complete Si-burning products are mixed out in the ejecta.

1

Introduction

Massive Pop III stars are important since they make the first metal enrichment of the universe, which affects significantly the following chemical and dynamical evolution of galaxies. There are several suggestions that the IMF of Pop III is different from Pop I and II, and the typical mass range of the first stars is likely to be 100 - 200M© (e.g., Nakamura & Umemura 1999, Ferrara 2000, Coppi 2000). If this is the case, the abundance pattern of the early galaxy should be similar to the yield of these stars. Recent observations have shown that the abundance pattern of halo stars are different for [Fe/H] < —2. Specifically, the Co/Fe and Zn/Fe ratios in­ crease significantly for smaller metallicity while Mn/Fe and Cr/Fe decreases (McWilliam et al. 1995, Ryan et al. 1996, Primas et al. 2000). These inter­ esting trends could be related to the IMF of Pop III stars. We have discussed that decreasing trend of Mn, Cr and increasing trend of Co can be explained simultaneously if the mass cut that divides the ejecta and the compact remnant tends to be deeper for massive core collapse supernovae (SNe) (Nakamura et al. 1999). This is because Mn and Cr are produced mainly in the incomplete Si burning region, while Co is produced in the deeper complete Si burning region. The mass cut is typically located somewhere close to the border of complete and incomplete Si burning. Therefore, if the mass cut is deeper, the abundance ratio of Co/Mn increases. Zn is also produced chiefly in the complete Si burning region, and our theory predicts increaseing trend of [Zn/Fe] below [Fe/H]~ —2.5, which matches with recent observations

43

44 Table 1: The results of the stability analysis for Pop III and Pop I stars. O a n d x represent that the star is stable and unstable, respectively. The e-folding time for the fundamental mode is shown after x in units of 10 4 yr. mass (M@) Pop III Pop I

80

100

o o

O

x (7.02)

120

o

x (2.35)

150 x (9.03) x (1.43)

180 x (4.83) x (1.21)

300 x (2.15) x (1.71)

(Primas et al. 2000, Ryan 2000). We study the nucleosynthesis pattern of massive Pop III stars with various masses to compare with abundances of metal-poor halo stars, and we try to constrain the typical mass range of Pop III stars that enriched the early galaxy. 2

Stability and Mass Loss of Massive Pop III stars

To determine the upper limit mass of the Zero Age Main Sequence (ZAMS), we analize a linear non-adiabatic stability of massive (SOMQ - 3OOM0) Pop III stars using a radial pulsation code (Shibahashi 2000). Stellar structures are calculated by the classical fitting method. We adopt e~ scattering and Kramers formula for the opacity, and the main nuclear reactions are pp-chain, hot-CNO cycle, and 3a reaction. Because the CNO elements are absent during the early stage of their evolution, the CNO cycle does not operate and the star contracts until temperature rises sufficiently high for the 3a reaction to produce 1 2 C. We calculate that these stars have X c n 0 ~ 1.6 — 4.0 x 10~ 10 , and the central temperature Tc ~ 1.4 x 108K on thier ZAMS. We also examine the models of Pop I stars for comparison. Table 1 shows the results for our analysis. The critical mass of ZAMS Pop III star is 128M 0 while that of Pop I star is 94M 0 . This difference comes from very compact structures (with high Tc) of Pop III stars. Stars more massive than the critical mass will undergo pulsation and mass loss. We note that the e-folding time of instability is much longer for Pop III stars than Pop I stars with the same mass, and thus the mass loss rate is much lower. These results are consistent with Ibrahim et al (1981) and BrafFe et al (2000). We thus assume that the mass loss is negligible in Pop III stars in the following calculations. 3

Stellar Evolution and Nucleosynthesis

We calculate the evolution of massive Pop III stars from ZAMS to SN explo­ sion. Stellar evolution is calculated with a Henyey type stellar evolution code

45

(Umeda et al. 2000 ; see also Nomoto & Hashimoto 1998) and SN explosion is simulated with a PPM code. The nucleosynthesis during the explosion is calculated by postprocessing (Nakamura et al. 2000). The stellar evolution and the mechanism of SNe explosion depend on the stellar mass. In the following, we classify these stars into four types, and describe the nucleosynthesis results for each one. 3.1

M ~ 10 - 25M 0 (Type II SNe)

Stars in the mass range M ~ 10 —25M 0 explode as ordinary Type II SNe (SNe II) with explosion energies jBexp ~ 10 51 erg. The abundance distributions after explosion for 13 and 25 MQ models are shown in Figures 1 and 2, respectively. In the ejecta, the mass fraction of complete Si burning products is larger if mass-cut is deeper (i.e., M c u t is smaller). In Figures 1 and 2 we show [Zn, Co, Mn/Fe] in the ejecta as a function of M c u t and the 56 Ni mass for the M c u t . We find that large [Zn, Co/Fe] and small [Mn/Fe] can be realized simulta­ neously with small M c u t . For example, in the 13M© model for M c u t ~ 1.55M 0 , [Zn/Fe] is large enough to explain the observed large ratio [Zn/Fe]~ 0.5. More massive stars also can realize large [Zn/Fe] if mass-cut is deeper. We should note that the ejected 56 Ni mass increases for deeper mass-cuts. Actually bright supernovae with larger 56 Ni mass ejection have been observed (Nomoto et al. 2000). However, the 56 Ni mass required to get [Zn/Fe]~ 0.5 appears to be too large in comparing with observations of [O/Fe]. However, as will be discussed in §4.2, the 56 Ni mass can be smaller without changing the [Zn/Fe] ratio if fall-back occurs after mixing. 3.2

M ~ 25 - 13OM0 (Ft Core Collapse Hypernovae)

Recently we had some evidences that at least some core collapse SNe explode with large explosion energy, which may be called "Hypernovae" (e.g., Nomoto et al. 2000). These SNe likely originate from relatively massive SNe (M > ~ 25M 0 ). In Figure 3 we show nucleosynthesis in the 25M 0 stars with the explosion energy 1052 erg to compare with the 10 51 erg model in Figure 2. We find that for larger explosion energy, boundaries of both complete and incomplete Si burning regions move outward in mass coordinate. We also find that for larger explosion energy incomplete Si burning region is thicker in mass. Therefore, hypernova explosions can eject a large amount of products from complete Si burning region only if more 56 Ni are ejected than ordinary SNe II. We also show [Zn, Co, Mn/Fe] and 56 Ni mass in the ejecta as a function of M c u t in Figure 3. Figure 3 indicates that if the ejected 56 Ni mass is fixed to

46 1

1

'

'

'

I

i

1


"0

™m

y*J

: zni

!rs i 4.1 i l l -1 :

i I

i

11

.:!.

i

i

i

-

^-'

~~

-1

\

\ \ . 1

j

'-" [Mn/Fe]

i

\

Cr

i

;"[Co7Fe)

..

\

i

0

.--:<

N\ V

;

i

1 ~ 13 M„, Z=0, EB,= 1 - [Zn/Fe]_^

13M 0 . Z - 0 . E s l - 1

. . ! . , . . .

-

a° > f »■

-2 0.1 O.OB 0.06 0.04 0.02 :

.--Vf 1 I

:

\

1.5

:

i i' ) i i i ■

- ^^^

0.07 M0

1.55

-_ -.

, 1 ?>-^—-J 1.8 1.85 M„,,/M0

M r (M 0 )

Figure 1: Left panel: Abundance distribution just after supernova explosion of the 13M@ Pop III star with £? e x p = 10 51 erg. The lines labeled by Cr, Mn, Co and Zn actually indi­ cate unstable 5 2 Fe, 5 5 Co, B 9 Cu, and 6 4 Zn, which eventually decay to the labeled elements. Right panel: Dependence of abundance ratios on the mass coordinate of the mass cut for the same model as the left panel.

1

' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I 2 5 M„. Z = 0 , E „ = l [Zn/Fe]

-2 0.6

[Co/Fe] I I I I | I I I I | I I I I | I I I I | I I I1!

Mr ( M „ )

Figure 2: Same as Figure 1, but for the explosion of 25MQ Pop III star with -EexP = 10 5 1 erg.

47

MP (M e )

Figure 3: Same as Figure 2, but for the case with Eexp

— 10 5 2 erg.

be O.O7M0, it is impossible to eject sufficient amount of Zn and Co, regardless of explosion energy. On the other hand, bright supernova models (i.e., larger 56 Ni mass) can eject relatively large amount of Zn. 3.3

M ~ 130 - 3OOM0 (Pair Instability

Supernovae)

Stars as massive as ~ 130 — 3OOM0 enters into the e ± pair instability re­ gion during the central oxygen burning stage. When these stars enter this region the core contracts rapidly and temperature rises quickly. This leads to explosive oxgen burning, and the thermal energy produced by this rapid oxy­ gen burning exceeds the gravitational binding energy. Hence the stars disrupt completely. These SNe are called Pair Instability SNe (Barkat et al. 1970). During the explosion, explosive burning takes place to produce 56 Ni and other heavy elements. The abundance ratios calculated in Nakatsuru et al. (2000) are qualitatively consistent with Heger et al. (2000). 3.4

300 < M < ~ 104M© (Very Massive Stars)

A star in this mass range also enters into the e± pair instability region during or before the central oxygen burning stage. If the star is not rotating sufficiently fast, it collapses into a black hole with no heavy element ejection. However, if the rotation is fast enough, an accretion disk would be formed around the central black hole. In this case, high energy jets along the rotational axis may

48

escape deep gravitational potential (e.g., Fryer et al. 2000). It is expected such jets induce heavy element synthesis, although no detailed calcations have been performed yet. 4

Comparison with Abundances of Metal Poor Halo Stars

Metal-poor halo stars may preserve abundance pattern of Pop III stars. By comparing the observations with nucleosynthesis theory, we may be able to constrain IMF of Pop III stars. The observed abundances show quite inter­ esting pattern. From [Fe/H]= —2.5 to [Fe/H]= —4.0, Mn and Cr decrease as —0.3 —> —1.3 and 0.0 -» —0.8 respectively, while Co increases as —0.1 —> 0.6 and Zn also increases from 0.0 to 0.5. In the followings, we discuss which mass range of Pop III SNe would better explain the observed trends. 4.1

SNe II

The interesting trends of the observed ratios in [Zn, Co, Mn, Cr/Fe] is related to the mass ratio between the complete Si burning region and the incomplete Si burning region. For SNe II that eject 0.07.M© 56 Ni, the fraction of complete Si burning products is larger for less massive stars, unless deep material is brought up by some mixing mechanisms. We find that yields of the lowest mass SNe II (M < 13M 0 ) can produce sufficiently large Zn/Fe ratio to be consistent with the abundances of very metal-poor stars. On the other hand, in order for more massive star to yield sufficiently large Zn, the mass-cuts needs to be deeper, or equivalently deep material from complete Si-burning region needs to be ejected by some mixing mechamism. 4-2

Fe Core Collapse Hypernovae

In these models, mass cuts may be deeper than ordinal SNe II and hence a larger amount of complete Si burning products can be ejected. Thus large [Zn, Co/Fe] and small [Mn, Cr/Fe] can be realized simultaneously. However, the ejected 56 Ni mass increases for deeper mass-cuts, and the 56 Ni mass required to get [Zn/Fe]~ 0.5 appears to be too large in comparing with [O/Fe] in metalpoor stars. Here we consider one possibility which realize effectively smaller mass-cuts without changing the 56 Ni mass. Two dimensional numerical simulations sug­ gest that mixing can take place between the complete and incomplete Si burn­ ing regions because of Rayleigh - Taylor instabilities (Kifonidis et al. 2000). Afterward substantial amount of matter could fall back onto the central rem­ nant. Suppose that the material is uniformly mixed between the "initial"

49 25M„, Z = 0, E„ = 10, 0'

'

51

'

5e

Ni = 0.19Mn, ©'

Figure 4: The abundance pattern for 25M@, Eexp dance.

M . =2.2Mn, fall = 79% mix

©'

= 10 52 erg normalized by the solar abun­

mass-cut (M cut (i)) and the top of the incomplete Si-burning region, and the matter below M cut (f) ( > Mcut(i)) falls back onto the compact remnants. Then the amount of ejected 56 Ni can be smaller without changing the mass ratio of (Zn, Co, Mn)/Fe from Figure 3. The overall abundance pattern normalized by the solar abundances for the massive energetic SNe II is shown in Figure 4. In obtaining this figure, the synthesized matter is mixed between Mcut(i) indicated in the figure and the top of the incomplete Si-burning region, which is defined by X( 5 6 Ni)=10 - 3 . Mcut(i) is chosen to realize [Zn/Fe] ~ 0.3 — 0.5. Some fractions of the mixing region is falled-back to the central remnant in order to make [O/Fe] not too large ([0/Fe]=l in these figure). Therefore observed abundance trends of very metal-poor stars are consistent with the idea that Pop III nucleosynthesis is dominated by the energetic massive SNe with large 56 Ni (hypernovae like).

4-3

Pair Instabillity SNe

These SNe produce heavy elements as well. The results, however, show that the Zn/Fe ratio is too small to fit the very low metal star abundance (Nakatsuru et al. 2000). This is because the maximum temperatures attained in these SNe are lower than SNe II, which makes the complete Si burning region relatively small. Furthermore, these SNe disrupt completely, so it is not possible to enhance the fraction of complete Si burning by mixing. Thus these stars might not be dominant in producing heavy elements in the early era of the Galaxy.

50

5

Discussion

So far we have not discussed how the stellar mass and [Fe/H] of metal-poor halo stars are related. In the early galactic epoch when the galaxy is not yet chemically well-mixed, the [Fe/H] is mostly determined by a single SN event. The formation of metal-poor stars is supposed to be driven by a supernova shock, so that the Fe/H is determined by the ejected Fe mass and the amount of circumstellar hydrogen swept by the shock wave. If M < 13M Q stars are making the observed trends of very metal-poor stars, it may be difficult to explain the observed trend [Zn, Co/Fe] ~ 0 for -2.5 < [Fe/H] < - 1 . This is because with Salpeter's IMF, 13M© stars sig­ nificantly contribute to the chemical evolution of these elements. If the 13M© star yield is [Zn, Co/Fe] ~ 0.5, it may be hard to make [Zn, Co/Fe] ~ 0 after averaging over IMF, though detailed chemical evolution models are necessary. When relatively massive stars (M > 25M Q ) are making the trends below [Fe/H] < —1, the following scenario can be considered as an example. Sup­ pose [Zn/Fe] is small (< 0) for M ~ 15 - 20M© and [Zn/Fe] ~ 0.1 - 0.2 for less massive stars, its averaged value over Salpeter's IMF could be [Zn/Fe]~ 0 as observed for [Fe/H] > —2. The abundance anomaly below [Fe/H] ~ —2 may be related to the peculiar IMF of Pop III stars. It is quite likely that the IMF of Pop III stars are different from Pop I and II, and more massive stars are abundant for Pop III. These stars can be more massive than the stars considered here. However, if they are Fe core collapse SNe with large explo­ sion energy, their nucleosynthesis would not be so different from the models considered here. If stars are more massive than ~ 150M©, these become pair instability SNe and their nucleosynthesis is different from the ones considred here. These SNe are difficult to produce sufficiently large Zn/Fe ratio. In this paper, we consider only a few elements to constrain the nucleosyn­ thesis of Pop III stars, because their trends are most clear. Data of other elements show less clear trends or currently have relatively large error bars. However, other information will be very useful. For example, [S/Fe] and [C/O] may be important to distinguish M < 13M 0 and M > 25M 0 models. Also mass-cut independent ratios [Ca, S, Si/Mg] will be important to constrain the explosion energies of SNe. We would like to thank C. Kobayashi, T. Nakamura, J. Nakatsuru, and S. Ryan, for discussion. This work has been supported in part by the grantin-Aid for COE Scientific Research (07CE2002, 12640233) of the Ministry of Education, Science, Culture, and Sports in Japan.

51

References 1. Baraffe, I., Heger, A., & Woosley, S. E. preprint, astro-ph/0009410. 2. Barkat, Z, Rakavy, G, & Sack, N. 1967, Phys.Rev.Lett, 18, 379 3. Coppi, P. 2000, in The Physics of Galaxy Formation, ed. M. Umemura, and H. Susa, in press 4. Ferrara, A. 2000, in The Physics of Galaxy Formation, ed. M. Umemura, and H. Susa, in press, astro-ph/0007179 5. Fryer, C. L., Woosley, S. E., & Heger, A. 2000, preprint, astroph/0007176 6. Heger, A., Woosley, S. E., & Waters, R. (2000), in The First Stars, ed. A. Weiss, T. Abel, & V. Hill (Berlin: Springer), 121 7. Ibrahim, A., Boury, A., & Noels A. 1981, A&A, 103, 390 8. Kifonidis, K., Plewa, T., Janka, H-Th, & Miiller, E. 2000, ApJ, 531, L123 9. McWilliam, A., Preston, G. W., Sneded, C., & Searle, L. 1995, AJ, 109, 2757 10. Nakamura, F. & Umemura, M. 1999, ApJ, 515, 239 11. Nakamura, T., Umeda, H., Nomoto, K., Thielemann, F.-K., & Burrows, A. 1999, ApJ, 517, 193 12. Nakamura, T., et al. 2000, ApJ, submitted, astro-ph/0011184 13. Nakaturu, J., Nakamura, T., Umeda, H., & Nomoto, K. 2000, in this volume 14. Nomoto, K. & Hashimoto, M. 1988, Phys. Rep., 256, 173 15. Nomoto, K., et al. 2000, in Supernovae and Gamma Ray Bursts, ed. M. Livio et al. (Cambridge University Press), in press, astro-ph/0003077 16. Primas, F. et al. 2000, in The First Stars, ed. A. Weiss, T. Abel, & V. Hill (Berlin: Springer), 51 17. Ryan, S. G., Norris, J. E., & Beers, T. C. 1996, ApJ, 471, 254 18. Ryan, S. G. 2000, in The Influence of Binaries on Stellar Populations Studies, ed. D. Vanbeveren (Kluwer), in press 19. Shibahashi,H. (2000) private communication 20. Umeda, H., Nomoto, & Nakamura, T. 2000, in The First Stars, ed. A. Weiss,'T. Abel, & V. Hill (Berlin: Springer), 150

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II. Observation of Elements

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PRESOLAR GRAINS AS PROBES OF NUCLEOSYNTHESIS IN STARS AND EVOLUTION OF THE GALAXY SACHIKO AMARI Laboratory

of Space Sciences and the Physics Department, Washington Brookings Dr., St. Louis MO 63130-4899 USA E-mail: [email protected]

University,

One

Presolar grains are Stardust extracted from meteorites. They remain intact after they formed in circumstellar envelopes or in supernova ejecta, keeping pristine information of their parent stars. The most commonly observed stellar sources are asymptotic giant branch (AGB) stars and supernovae (SNe). Mainstream SiC grains are believed to have formed in thermally pulsing AGB stars. Carbon, N, and 26A1 observed in the grains reflect core and shell H and He burning. The Si isotopic ratios of the grains reflect both neutron capture in the He-shell and initial isotopic compositions of the parent stars. The isotopic ratios of heavy elements show s-process signatures. Silicon carbide of type X, low-density graphite, and silicon nitride (Si,N,t) most likely formed in supernova ejecta. Their isotopic ratios can be explained if a jet of material from the innermost Si-rich zones is mixed with material of the outer He-rich zones. However, the SN models do not produce enough l5N and 2<,Si to account for the grain data.

1

Introduction

It has been more than 10 years since the first type of presolar grains were isolated from meteorites [1]. Presolar grains are defined as grains which formed in circumstellar envelopes or in supernova ejecta and were subsequently incorporated in meteorites. They exhibit huge isotopic anomalies that cannot be explained by processes occurring in the solar system, indicating that they remained intact during solar system formation and preserved information of their parent stars. The first hint that pristine Stardust might be hidden in meteorites came from isotopically anomalous noble gases found in meteorites [2, 3]. Some of the observed isotopic ratios deviated from the solar ratios by more than order of magnitude. Such huge isotopic anomalies can be best explained by nucleosynthesis occurring in stars. Edward Anders and Roy S. Lewis, and their coworkers at the University of Chicago [4] subjected these meteorites to a variety of chemical and physical treatments to isolate minerals which contained the anomalous noble gases. More than 99.9% of the meteorites were destroyed during the separation process. After 20 years of trial and error, presolar diamond was finally isolated and identified in the Allende meteorite [1], followed by SiC [5, 6] and graphite [7]. Since presolar corundum (A1203) and nitride (Si3N4) grains do not seem to contain anomalous noble gases [8], they were identified by Secondary Ion Mass Spectrometry (SIMS) [9-11]. Furthermore, refractory carbide grains have been found in presolar SiC and graphite grains [12, 13]. Presolar grains found in meteorites up to date are listed in Table 1.

55

56 Table 1. Presolar grains in meteorites

Grain Diamond Mainstream SiC Graphite SiC type X A1203 (Corundum) Si,N4

Abundance 5xl0' 4 6xl0' 6 lxlO"6 6xl0"8 3xl0' 8 2xl0"9

Size (urn) 0.0016 0.2 - 20 0.8 - 20 0.2 - 20 0.5-5 0.5 - 5

Inferred Stellar Sources SNe AGB stars SNe, AGB stars, Noave SNe RG stars, AGB stars SNe

There are two ways to study isotopic ratios of presolar grains. One is to measure isotopic ratios of aggregates of grains (defined as bulk). This method is applied for trace elements with low concentrations such as noble gases [14, 15], Sr [16], and Ba [17-19]. Another way is to measure isotopic ratios of individual grains. This is the ideal way of studying presolar grains, since each grain might have formed in a different star. Most data on individual grains have been obtained by SIMS. However, with present technology grains have to be relatively large (>0.5(im) to obtain data with reasonable errors. Isotopic studies of presolar grains provide us detailed information which cannot be obtained by any other method. In the following sections, several cases are discussed. 2

Mainstream SiC grains

Of various types of presolar grains, SiC has been extensively studied by several reasons. First, concentrations of SiC in meteorites are relatively high [20]. In the Murchison meteorite, the concentration of SiC is 6ppm, while that of graphite is about lppm [21]. Second, SiC grains have been observed in different types of meteorites, while presolar graphite has been observed only a handful of meteorites [20]. In addition, they have relatively high trace element concentrations, making it possible to obtain isotopic ratios of those elements [22].

2. /

Light element isotopes

Figure 1 shows C and N isotopic ratios of SiC grains analyzed by SIMS [23]. According to their C, N, and Si isotopic ratios, several populations can be distinguished. The mainstream grains comprise about 94% of SiC grains [24]. These, along with Y and Z grains, are believed to have formed in AGB stars [25, 26]. X grains are inferred to have a SN origin [10, 27]. The origin of A and B grains are not clear. It should be noted that the distribution of the grains in Fig. 1 does not

57

reflect their natural proportions, since rare types of grains were search by ion imaging techniques and are overrepresented.

Fig. 1 Carbon and N isotopic ratios measured in individual SiC grains from the Murchison meteorite. Five populations can be distinguished on the basis of the C, N, and Si isotopic ratios. Also indicated are the theoretically expected ranges resulting H and He burning and subsequent dredge-up and from extra mixing in low-to intermediate carbon stars.

It has been widely accepted that mainstream grains formed in thermally pulsing AGB stars [23, 28]. Bulk analyses have shown that isotopic ratios of trace elements, Kr [14, 15], Xe [14, 15], Sr [16], Ba [17-19], Nd, and Sm [18, 29] have s-process signatures, while AGB stars are considered to be a main s-process operating site. I2 13 C/ C ratios of mainstream SiC grains range from 30 to 100 and are in agreement with the observational values of C-rich AGB stars. Finally, 11.2(im feature which is characteristic of SiC has been observed in C-rich AGB stars [30]. Carbon and N isotopic ratios of most mainstream grains agree with models of AGB stars, if cool bottom processing (CBP) [31] or extra mixing [32, 33] is taken into account. However, low l4N/'5N ratios (<600) cannot be explained by a framework of the AGB star model and they have not been satisfactory explained yet. Most mainstream SiC grains have 26Mg excesses from the decay of 26A1 [23, 26 28]. A1 is produced by shell H burning and is mixed into the envelope by the third dredge-up [34], The inferred 26A1/27A1 ratios of the grains range from 3xl0"5

58

to 2xl0"2 and are in agreement with ratios of the envelope predicted in 1.5 and 3Msun AGB stars of solar metallicity [35]. Silicon in mainstream grains are enriched in neutron-rich isotopes. In the Si-3 isotope plot (Fig. 2), their isotopic ratios lie on the line of a slope 1.3 [23, 28]. (8 values are defined as follows: 8'Si/28Si (%0) = {(iSi/28Si)measured/(iSi/28Si)solar 1 JxlOOO). The expected shift of ratios due to neutron-capture in the He-shell, which are shown by the arrow in the figure, cannot explain the variation along the line. Instead, it is interpreted as the variation in the initial Si isotopic ratios: parent AGB stars of mainstream grains had a range of initial Si isotopic ratios (-20% in both M Si/28Si and 3<)Si/28Si). The variation of the initial compositions has been attributed to the Galactic chemical evolution [36, 37] or the heterogeneity of the interstellar medium (ISM) [38].

Fig. 2 Silicon isotopic ratios measured in individual mainstream SiC grains. The solid line is the slope 1.3 correlation line for mainstream SiC grains. The arrow is the predicted shift of Si isotopic ratios of the envelope of carbon-rich AGB stars.

2.2

Heavy element isotopes

Isotopes of heavy elements have been measured mostly in bulk samples. (Fig. 3). Isotopic ratios of Sr [16], Ba [17-19], Sm, and Nd [18, 29] show s-process

59

signatures. Recently, Mo and Zr isotopic ratios of individual SiC grains [39, 40] have been analyzed by Resonance Ionization Mass Spectrometry (RIMS). The measured isotopic ratios can be interpreted as a mixture of an s-process component in the He-shell and the envelope component which reflects an initial isotopic composition of the stars. The former component can be determined if a pure p- or rprocess isotope can be measured. If not, it is necessary to make an assumption of sprocess conditions in the He-shell. s-Process isotopes in the He-shell in AGB stars inferred from the grain data agree well with what is predicted in low-mass AGB star models of solar metallicity.

82

83

84 85

86

87 88

89

90

146 147 148 149 150 151 152 153 154

Mass (amu) Fig. 3 s-Process isotopic patterns of heavy elements inferred from bulk analyses of SiC from the Murchison meteorite. Different data points for the heaviest isotopes of Kr, Sr, and Ba are for different grain size fractions of SiC: the sizes of their grains increase from KJA to KJG.

Barium isotopic ratios in the He-shell in AGB stars inferred from the SiC bulk analyses show an s-process signature with excesses in ''14Ba and 116Ba [18, 19]. Gallino et al. [41] could successfully reproduce the pattern, only after adjusting neutron capture cross sections known at that time [42]. Later Ba neutron capture cross sections were remeasured [43-45] and the revised values for l35Ba and l36Ba were

60

surprisingly close to the predicted values by Gallino et al. [41]. However, a discrepancy remains for the 137Ba cross section. 3

Grains from supernovae

Among grains from supernovae (SN grains), low-density graphite [46, 47], SiC type X [27], and Si3N4 [10] have been extensively studied by SIMS [48]. Silicon carbide of type X is a minor population of SiC (-1%) [27]. They have common isotopic features which indicate their supernova origin [48]. For example, all the SiC X and Si,N4 grains have 28Si excesses up to 5x solar. Many graphite grains also have the excesses, while a few graphite grain have excesses in 29Si and 3"Si. Since 28Si is produced by hydrostatic and explosive O-burning region and neutronrich Si isotopes are produced in He and O rich zones in Type II supernovae, the Si isotopic ratios of the grains can be interpreted if they formed in supernovae. The strongest evidence of the SN origin of these grains come from the presence of 44Ti [49, 50], since it is produced only by explosive nucleosynthesis in supernovae, in Type II by a-rich freeze-out [51] and in Type la by explosive He burning [52]. Titanium-44 has a half life of 60 years, thus it is present as its decay product 44Ca in the presolar grains. A few SN grains have high ^Ca/^'Ca ratios up to 137x solar, while other Ca isotopic ratios remain close to solar [49]. This leaves little doubt that the huge excesses in '"Ca are due to the decay of 44Ti. Inferred " T i ^ T i ratios range from 10 3 to 0.4. [49, 50]. Recently, Clayton et al. [53] have proposed that SiC X grains might have formed Type la supernovae in a model with sub-Chandrasekhar mass. The advantage of this model is that isotopes which are necessary to explain the isotopic signature of X grains can be produced by a single nucleosynthetic process: explosive He burning. However, to reproduce the isotopic range of the grain data, it is required that the reaction product is mixed with the unprocessed material and that grains form under the condition C<0. Clayton et al. [54] have recently suggested that in radioactive environments the condition C>0 is not necessary to form carbonaceous grains, abundant electrons and H+ dissociate CO, making C available to the grain growth. It remains to be seen whether SiC X grains could form in Type la supernovae. Isotopic ratios of other elements have been also analyzed [48] (see Fig. 4). Many grains have isotopically light C and heavy N. About 60% of X grains and 10% of low-density graphite grains have 26A1/27A1 ratios on the order of 0.1. If the SN grains formed in Type II supernovae, the isotopic feature of SN grains should be explained by the framework of existing SN models. A Type II supernova consists of layers where different nucleosynthesic reactions take place (Fig. 5). Of them the He/N, He/C and C/O zones are the places where C/O ratios > 1, which is necessary to form carbonaceous grains. (Names of zones are coined according to

61

Meyer et al. [55], indicating the most abundant elements in the zones). In the He/N zone, l3C and l4N become highly enriched though CNO cycle and 26A1 by 25 Mg(p,y)2f'Al. In the He/C zone, l2C is produced by He-burning and 14N is rapidly destroyed and converted into 18 0. 15N becomes depleted in this zone during hydrostatic burning, but is produced at the bottom of the zone by explosive nucleosynthesis. The 26A1/27A1 ratio in the He/N zone is expected to be 0.2 and the l6 0/ l 8 0 ratio in the He/C zone to be 0.4 in a 15MSU„ model of solar metallicity [51].

-

l

I I mini

I I iiinll

io

,

too 8

' d/

13

I

IOOO

d

I I iniitl

IOOOO

\S\ I I I V I I I I I I I I I I I I I I

-500

o

500

1000

<53 0 Si/ 8 6 i3i

Fig. 4 Isotopic ratios of graphite grains (solid circles) are compared to ratios predicted to result from mixing of different zones of a SN type II by Woosley and Wewaver [51]. Various lines represent different ratios of M5/M2 (see Fig. 5) and M6/M2 to the resulting mix. Ranges which satisfy condition of C/0>1 and l2C/l3C ratios between 5 and 10" are shown. In (a), only 5% of the 14N in Ml has been used for the mix, indicating that l5N is underproduced in the SN models. (Travaglio et al. [47])

We note that these grains show features of both zones, high 26A1/27A1 ratios (Fig. 4c) reflecting contribution from the He/N zone, low 16 0/ 18 0 ratios in graphite grains and high l2C/'3C ratios (Fig. 4b) from the He/C zone. However, some of the

62

ratios in the zones are far too anomalous than what are observed in the grains, requiring mixing between the zones. For example, C in the He/C zone is essentially l2 C and the mixing with C in the He/N zone would be required to reproduce the observed range. It is also necessary to have material from innermost O-burning zones mixed into those of the C-rich zones to explain 28Si excesses and the presence of 44Ti of the grains, since 28Si is produced by hydrostatic and explosive nucleosynthesis and 44Ti by explosive nucleosynthesis in the O-burning zones. Between these zones are huge O-rich zones. To have isotopic characteristics of the grains, mixing during the explosion should be very extensive so that the outer He-rich zones and the innermost O-rich zones are involved. At the same time, it should be heterogeneous to avoid incorporating material from the huge O-rich zones in-between to fulfill a condition of C/O ratio > 1 for the mix to form carbonaceous grains. Travaglio et al. [47] have performed mixing calculations in order to quantitatively examine the mixing and to reproduce isotopic data of low-density graphite grains and other SN grains by using a Type II supernova model by Woosley and Weaver [51]. We will briefly summarize their results and discussions here.

Fig. 5 Travaglio et al. [47] divided a 15M supernova by Woosley and Weaver [51] into seven different zones. The zones Ml, M2, and M3 have C>6, zones M4 and M5 are dominated by 160 and zone M6 is dominated by 28Si, and zone M7 is dominated by 56Ni.

They divided a supernova into 7 zones, Ml, M2, M3 being He-rich, M4 and M5 being O-rich, M5 and M6 being Si-rich, and M7 being Ni-rich (Fig. 5). They mixed those zones so that the resulting mix should have the condition C/0>1 and

63 12

C/I3C ratios would be in the range of 5 to 104. The contribution from zone M4 is fixed and that of M5 and M6 are changed. Overall trend and the ranges of the isotopic data can be reproduced by the mixing (see Fig. 4). However, several isotopic features which cannot be explained by the model and the major problems are summarized below. 3.1

,5

N deficiency

If all the 14N in M1 (He/N) zone is incorporated in the mix, the N-isotopic ratios become much higher than those observed in the grains. Thus, they arbitrarily reduced the amount of 14N in the Ml zone by a factor of 20 (Fig. 4a). Their result strongly suggests that either 15N in the He/C zone is deficient in the model or most l4 N in the He/N zone does not go into the grains. The former is quite possible. Langer [56] examined rotational mixing in massive stars and found that by mixing proton into He-rich region, 15N production can be substantially higher than previously predicted. In addition, 15N production during explosive nucleosynthesis strongly depends on the strength of the shock. Thus, the l5N deficiency may be resolved once these effects are taken into account. 3.2

29

Si deficiency

As shown in Fig. 4d, the mix is short of 29Si to reproduce the grain data, most grains being plotted above the lines. It suggests that 29Si is underproduced in the model of Type II. This is strengthened by the fact that Timmes and Clayton [36] failed to explain the cosmic ratio of MSi/wSi (1.7) by using productions of different stellar sources including Type II supernovae. The deficiency of 29Si relative to MSi is also observed in another SN model by Thielemann et al. [57] and it may be a problem of fundamental parameters, such as reaction rates, in the models. Travaglio et al. [47] pointed out that 26Mg(a,n)29Si reaction rate can be higher by a factor of 2, possibly accounting for the 29Si deficiency. It remains to be seen whether this assumption can be justified. 4

Summary

As shown in the previous sections, isotopic analyses of presolar grains can provide the detailed information on nucleosynthesis inside stars and conditions of supernova explosion. Mainstream grains most likely formed in thermal-pulsing AGB stars. Overall isotopic ratios of the grains can be explained in the framework of the models of AGB stars. However, low l4N/lsN ratios of a few grains are difficult to explain by the models. The Si isotopic ratios reflect both initial isotopic compositions of the

64

parent stars and nucleosynthesis in the He-shell. Isotopic ratios of heavy elements of the grains are dominated by a component from the He-shell. s-Process isotopic ratios in the He-shell inferred from the grain data agree with what is predicted in low-mass AGG stars of solar metallicity. Silicon carbide type X, low-density graphite, and silicon nitride have a distinct isotopic feature which indicates that they formed in supernova ejecta. In order to quantitatively explain isotopic ratios of the grains, Travaglio et al. [47] calculated mixing between different zones of Type II supernova models by Woosley and Weaver [51]. The mixing model can explain general isotopic features if material from the Si-rich zones is assumed to penetrate the O-rich zones and is mixed with that of the C-rich zones. The major problems are that l5N is underproduced in the model and that 29Si/28Si ratios of the mixing are consistently lower than those in the grains. These problems can be overcome by multi-dimensional models and/or adjustment of cross sections. 5

Acknowledgements

I thank the organizing committee for inviting me to attend the OMEG2000 conference. I am grateful to Ernst Zinner for his continuous encouragement throughout the study of presolar grains. This work has been supported by NASA grant NAG5-8336. References 1. Lewis R. S., Tang M., Wacker J. F., Anders E. and Steel E., Interstellar diamonds in meteorites, Nature 326, (1987) pp. 160-162. 2. Black D. C. and Pepin R. O., Trapped neon in meteorites. II., Earth Planet. Sci. Lett. 6, (1969) pp. 395-405. 3. Black D. C , On the origins of trapped helium, neon and argon isotopic variations in meteorites II. Carbonaceous meteorites, Geochim. Cosmochim. Acta 36, (1972) pp. 377-394. 4. Anders E., Circumstellar material in meteorites: noble gases, carbon and nitrogen, In Meteorites and the Early Solar System, ed. by J. F. Kerridge and M. S. Matthews (University of Arizona Press, 1988) pp. 927-955. 5. Bernatowicz T., Fraundorf G., Tang M., Anders E., Wopenka B., Zinner E. and Fraundorf P., Evidence for interstellar SiC in the Murray carbonaceous meteorite, Nature 330, (1987) pp. 728-730. 6. Tang M. and Anders E., Isotopic anomalies of Ne, Xe, and C in meteorites. II. Interstellar diamond and SiC: carriers of exotic noble gases, Geochim. Cosmochim. Acta 52, (1988) pp. 1235-1244.

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7. Amari S., Anders E., Virag A. and Zinner E., Interstellar graphite in meteorites, Nature 345, (1990) pp. 238-240. 8. Lewis R. S. and Srinivasan B., A search for noble-gas evidence for presolar oxide grains, Lunar Planet. Sci. XXIV, (1993) pp. 873-874. 9. Nittler L. R., Alexander C. M. O'D., Gao X., Walker R. M. and Zinner E. K., Interstellar oxide grains from the Tieschitz ordinary chondrite, Nature 370, (1994) pp. 443-446. 10. Nittler L. R., Hoppe P., Alexander C. M. O'D., Amari S., Eberhardt P., Gao X., Lewis R. S., Strebel R., Walker R. M. and Zinner E., Silicon nitride from supernovae, Astrophys. J. 453, (1995) pp. L25-L28. 11. Nittler L. R., Alexander C. M. O'D., Gao X., Walker R. M. and Zinner E., Stellar sapphires: The properties and origins of presolar A120;, in meteorites, Astrophys. J. 483, (1997) pp. 475-495. 12. Bernatowicz T. J., Cowsik R., Gibbons P. C., Lodders K., Fegley B., Jr., Amari S. and Lewis R. S., Constraints on stellar grain formation from presolar graphite in the Murchison meteorite, Astrophys. J. 472, (1996) pp. 760-782. 13. Bernatowicz T. J., Amari S., Zinner E. and Lewis R. S., Interstellar grains within interstellar grains., Astrophys. J. 373, (1991) pp. L73-L76. 14. Lewis R. S., Amari S. and Anders E., Meteoritic silicon carbide: pristine material from carbon stars, Nature 348, (1990) pp. 293-298. 15. Lewis R. S., Amari S. and Anders E., Interstellar grains in meteorites: II. SiC and its noble gases, Geochim. Cosmochim. Acta 58, (1994) pp. 471494. 16. Podosek F. A., Prombo C. A., Amari S. and Lewis R. S., s-Process Sr isotopic compositions in presolar SiC from the Murchsion meteorite, Astrophys. J. (2000) in press. 17. Ott U. and Begemann F., Discovery of s-process barium in the Murchison meteorite, Astrophys. J. 353, (1990) pp. L57-L60. 18. Zinner E., Amari S. and Lewis R. S., s-Process Ba, Nd, and Sm in presolar SiC from the Murchison meteorite, Astrophys. J. 382, (1991) pp. L47-L50. 19. Prombo C. A., Podosek F. A., Amari S. and Lewis R. S., s-Process Ba isotopic compositions in presolar SiC from the Murchison meteorite, Astrophys. J. 410, (1993) pp. 393-399. 20. Huss G. R. and Lewis R. S., Presolar diamond, SiC, and graphite in primitive chondrites: Abundances as a function of meteorite class and petrologic type, Geochim.. Cosmochim. Acta 59, (1995) pp. 115-160. 21. Amari S., Lewis R. S. and Anders E., Interstellar grains in meteorites: I. Isolation of SiC, graphite, and diamond; size distributions of SiC and graphite, Geochim. Cosmochim. Acta 58, (1994) pp. 459-470.

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22. Amari S., Hoppe P., Zinner E. and Lewis R. S., Trace-element concentrations in single circumstellar silicon carbide grains from the Murchison meteorite, Meteoritics 30, (1995) pp. 679-693. 23. Hoppe P., Amari S., Zinner E., Ireland T. and Lewis R. S., Carbon, nitrogen, magnesium, silicon and titanium isotopic compositions of single interstellar silicon carbide grains from the Murchison carbonaceous chondrite., Astrophys. J. 430, (1994) pp. 870-890. 24. Hoppe P. and Ott U., Mainstream silicon carbide grains from meteorites, In Astrophysical Implications of the Laboratory Study of Presolar Materials, ed. by T. J. Bernatowicz and E. Zinner (AIP, New York, 1997) pp. 27-58. 25. Hoppe P., Annen P., Strebel R., Eberhardt P., Amari S. and Lewis R. S., Circumstellar SiC grains of Type Z: Evidence for extensive He shell dredge-up in low-metallicity low-mass AGB stars, Lunar Planet. Sci. XXVIII, (1997) pp. 599-600. 26. Amari S., Nittler L. R., Zinner E., Gallino R., Lugaro M. and Lewis R. S., Presolar SiC grains of Type Y: Origin from low-metallicity AGB stars, Astrophys. J. (2000) submitted. 27. Amari S., Hoppe P., Zinner E. and Lewis R. S., Interstellar SiC with unusual isotopic compositions: Grains from a supernova?, Astrophys. J. 394, (1992) pp. L43-L46. 28. Huss G. R., Hutcheon I. D. and Wasserburg G. J., Isotopic systematics of presolar silicon carbide from the Orgueil (CI) carbonaceous chondrite: Implications for solar system formation and stellar nucleosynthesis., Geochim. Cosmochim. Ada 61, (1997) pp. 5117-5148. 29. Richter S., Ott U. and Begemann F., S-process isotope abundance anomalies in meteoritic silicon carbide: new data, In Nuclei in the Cosmos, ed. by F. Kappeler and K. Wisshak (Institute of Physics Publishing, Bristol and Philadelphia, 1993) pp. 127-132. 30. Little-Marenin I. R., Carbon stars with silicate dust in their circumstellar shells, Astrophys. J. 307, (1986) pp. L15-L19. 31. Wasserburg G. J., Boothroyd A. I. and Sackmann I.-J., Deep circulation in red giant stars: A solution to the carbon and oxygen isotope puzzles?, Astrophys. J. 447, (1995) pp. L37-L40. 32. Charbonnel C , Clues for non-standard mixing on the red giant branch from 12 13 C/ C and l2C/14N ratios in evolved stars, Astron. Astrophys. 282, (1994) pp. 811-820. 33. Charbonnel C , A consistent explanation for 12C/13C, 7Li, and 3He anomalies in red giant stars, Astrophys. J. 453, (1995) pp. L41-L44. 34. Forestini M., Paulus G. and Arnould M., On the production of 26A1 in AGB stars, Astron. Astrophys. 252, (1991) pp. 597-604. 35. Gallino R., pers. comm. (2000)

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36. Timmes F. X. and Clayton D. D., Galactic evolution of silicon isotopes: Application to presolar SiC grains from meteorites, Astrophys. J. All, (1996) pp. 723-741. 37. Clayton D. D. and Timmes F. X., Placing the Sun in galactic chemical evolution: Mainstream SiC particles, Astrophys. J. 483, (1997) pp. 220227. 38. Lugaro M., Zinner E., Gallino R. and Amari S., Si isotopic ratios in mainstream presolar SiC grains revisited, Astrophys. J. 527, (1999) pp. 369-394. 39. Nicolussi G. K., Davis A. M , Pellin M. J., Lewis R. S., Clayton R. N. and Amari S., s-Process zirconium in presolar silicon carbide grains, Science 111, (1997) pp. 1281-1283. 40. Nicolussi G. K., Pellin M. J., Lewis R. S., Davis A. M., Amari S. and Clayton R. N., Molybdenum isotopic composition of individual presolar silicon carbide grains from the Murchison meteorite, Geochim. Cosmochim. Acta 62, (1998) pp. 1093-1104. 41. Gallino R., Raiteri C. M. and Busso M., Carbon stars and isotopic Ba anomalies in meteoritic SiC grains., Astrophys. J. 410, (1993) pp. 400-411. 42. Beer H., Voss F. and Winters R. R., On the calculation of Maxwellianaveraged capture cross sections, Astrophys. J. Suppl. 80, (1992) pp. 403424. 43. Voss F„ Wisshak K., Guber K., Kappeler F. and Reffo G., Stellar neutron capture cross sections of the Ba isotopes, Phys. Rev. C 50, (1994) pp. 25822601. 44. Koehler P. E., Spencer R. R., Winters R. R., Guber K. H., Harvey J. A., Hill N. W. and Smith M. S., Resonance neutron capture and transmission measurements and the stellar neutron capture cross sections of 134Ba and 136Ba, Phys. Rev. C 54, (1996) pp. 1463-1477. 45. Koehler P. E., Spencer R. R., Guber K. H., Winters R. R., Raman S., Harvey J. A., Hill N. W., Blackmon J. C , Bardayan D. W., Larson D. C , Lewis T. A., Pierce D. E. and Smith M. S., High resolution neutron capture and transmission measurement on 137Ba and their impact on the interpretation of meteoritic barium anomalies, Phys. Rev. C 57, (1998) pp. R1558-R1561. 46. Amari S., Zinner E. and Lewis R. S., Large 180 excesses in interstellar graphite grains from the Murchison meteorite indicate a massive star origin, Astrophys. J. 447, (1995) pp. L147-L150. 47. Travaglio C , Gallino R„ Amari S., Zinner E., Woosley S. and Lewis R. S., Low-density graphite grains and mixing in type II supernovae, Astrophys. J. 510, (1999) pp. 325-354. 48. Amari S. and Zinner E., Supernova grains from meteorites, In Astrophysical Implications of the Laboratory Study of Presolar Materials, ed. by T. J. Bernatowicz and E. Zinner (AIP, New York, 1997) pp. 287-305.

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49. Nittler L. R., Amari S., Zinner E., Woosley S. E. and Lewis R. S., Extinct 44 Ti in presolar graphite and SiC: Proof of a supernova origin, Astrophys. J. 462, (1996) pp. L31-L34. 50. Hoppe P., Strebel R., Eberhardt P., Amari S. and Lewis R. S., Type II supernova matter in a silicon carbide grain from the Murchison meteorite, Science 272, (1996) pp. 1314-1316. 51. Woosley S. E. and Weaver T. A., The evolution and explosion of massive stars, II. Explosive hydrodynamics and nucleosynthesis, Astrophys. J. Suppl. 101, (1995) pp. 181-235. 52. Woosley S. E. and Weaver T. A., Sub-chandrasekhar mass models for type la supernovae, Astrophys. J. 423, (1994) pp. 371-379. 53. Clayton D. D., Arnett W. D., Kane J. and Meyer B. S., Type X silicon carbide presolar grains: Type la supernova condensates?, Astrophys. J. 486, (1997) pp. 824-834. 54. Clayton D. D., Liu W. and Dalgarno A., Condensation of carbon in radioactive supernova gas, Science 283, (1999) pp. 1290-1292. 55. Meyer B. S., Weaver T. A. and Woosley S. E., Isotope source table for a 25 Msun supernova, Meteoritics 30, (1995) pp. 325-334. 56. Langer N., Heger A., Woosley S. E. and Herwig F., Nucleosynthesis in rotating stars, In Nuclei in the Cosmos V, ed. by N. Prantzos (Editions Frontieres, Paris, 1998) pp. 129-135. 57. Thielemann F.-K., Nomoto K. and Hashimoto M.-A., Core-collapse supernovae and their ejecta, Astrophys. J. 460, (1996) pp. 408-436.

NUCLEOSYNTHESIS OF M G A N D AL IN GLOBULAR CLUSTER R E D G I A N T STARS C. I L I A D I S Carolina, Chapel Hill, NC 27599, USA and Universities Nuclear Laboratory, Durham, NC 27708, USA E-mail: [email protected]

The University Triangle

of North

The proton-capture reaction on 2 4 M g has been investigated in the bombarding energy range of E p =0.2-1.7 MeV. Properties of low-energy resonances have been measured. From the experimental results, accurate proton partial widths, 7-ray partial widths and total widths have been deduced. The present experimental information establishes the 2 4 M g + p reaction rates over the temperature range T=0.02-2.0 GK with statistical uncertainties of less than 21%. Based on our results, we can rule out the recent suggestion that the total width of the E/j=223 keV resonance has a significant influence on the reaction rates. The astrophysical implications for hydrogen burning of 2 4 Mg at low stellar temperatures in globular cluster red giant stars are discussed.

1

Introduction

Standard stellar evolution theory predicts for low-mass stars in globular clus­ ters only minor changes in surface composition during the red giant branch phase. However, observations over the past two decades have shown a large variation in the abundances of C, N, O, Na, Mg and Al among globular cluster red giant stars l . These observations have been explained by hydrogen burning nucleosynthesis converting O to N, Ne to Na, and Mg to Al. However, the site in which the proton captures take place has not yet been identified. The observed surface abundance variations might result from internal nucleosyn­ thesis and deep, but yet unexplained, mixing in the red giants (evolutionary scenario), or could be caused by the nucleosynthesis in stars of a previous gen­ eration that contaminated the proto-stellar cluster gas (primordial scenario). For the globular cluster M13 there is increasing observational evidence in favour of the evolutionary scenario 1. For example, the observed abundance sum Mg+Al is approximately constant in M13 red giants that exhibit large variations in Al. The implication is that all stars had initially the same abun­ dance of Mg, but experienced different degrees of Al production and of deep mixing at the same evolutionary state. Theoretical model calculations 2 ' 3 that are based on the evolutionary scenario are in good qualitative agreement with most of the observed light-element abundance variations and correlations. The

69

70

calculations predict that 25 Mg and 26 Mg are converted to Al at temperatures of T=0.02-0.06 GK in the hydrogen-burning shell. However, recent observations of Mg isotopic abundances for a number of M13 red giants by Shetrone 4 have found, contrary to expectations, that the abundance of 24 Mg is anticorrelated with Al, and that the abundance sum 25 Mg+ 26 Mg is approximately constant for large variations in Al. This result is difficult to explain, since current esti­ mates of reaction rates for proton captures on Mg isotopes 5 ' 6 predict that the rates for 2 5 Mg+p and 2 6 Mg+p are much larger than for 2 4 Mg+p. However, it was recently pointed o u t 7 that the 2 4 Mg+p reaction rates might be much larger than previously assumed due to the uncertain contribution of the lowenergy wing of the ER=223 keV resonance. Accurate calculation of the wing contribution requires knowledge of the proton and 7-ray partial widths of this resonance. Here, we report on the measurement of the strength w-y and the branching ratio T 7 / r of the E#=223 keV resonance in 2 4 Mg+p. In addition, we have measured the mean lifetime r m of the E x =2485 keV state in 25A1 using the DSA method. The determination of the two unknown resonance parameters T p and T 7 from the three measured quantities T 7 / r , ivy and r m represents an important test of internal consistency. In the following we discuss the experi­ mental equipment, the experimental results and the astrophysical implications. For more details, the reader is referred to Ref. 8 . 2

Experimental Equipment

The experiments were carried out at the Triangle Universities Nuclear Lab­ oratory (TUNL). A 4 MV modified KN Van de Graaff accelerator provided proton beams up to 10 /uA on target at energies of E p =0.9-2.0 MeV. A 200 kV minitandem accelerator supplied proton beams in the energy range E p <480 keV. Targets for the 7-ray branching ratio measurements were prepared by evaporating 24 Mg onto Ta backings. For the lifetime measurements, a target was produced by implanting 24 Mg ions with an energy of 100 keV into a Ta backing. The total incident-ion dose was 450/uAxh over a target area of about 3.8 cm 2 . A stoichiometry of Nx a /NMs :: =0.3±0.1 was determined from the thick-target yield of the resonance at E;?=1654 keV in 2 4 Mg+p. Transmission targets were used for the resonance strength measurements. The targets were prepared by evaporating natural Mg metal onto carbon backing foils of 20 /xg/cm2 thickness. For the measurements of 7-ray branching ratios and mean lifetimes, the proton beam passed through a 3-mm-diameter collimator and was focused

71 into a profile of about 4 mm diameter on target. Typical beam intensities on target were « 7 fj.A. The target was directly water-cooled and mounted at an angle of either 45° or 90° with respect to the beam direction. For the resonance strength measurements the proton beam entered a scattering chamber through a 3-mm-diameter collimator, passed through the transmission target, and was stopped on the opposite side of the chamber. Proton beam intensities on target were typically 200-700 nA. Large—volume HPGe detectors were used to detect capture 7-rays. For the 7-ray branching ratio (resonance strength) measurements, a 140% HPGe detector was placed at 0 7 =55° (125°) with respect to the beam direction at a front-face-to-target distance of 5.9 (13.0 cm). For the lifetime measurements two 60% HPGe detectors were positioned at angles of 0° and 140° at distances of about 9.0 cm from the target. Relative 7-ray efficiencies for the energy range E 7 =0.7-11.0 MeV were determined by using a 56 Co source as well as resonant 7-rays from the reaction 27 Al(p,7) 28 Si ( E R = 9 9 2 keV). Accurate en­ ergy calibrations were obtained by using 7-ray lines from 56 Co. The overall uncertainty in 7-ray energy below E 7 =3.5 MeV was about 0.1-0.2 keV. For the resonance strength measurements, elastically scattered protons were detected with a 100-/txm-thick ion-implanted charged-particle detector. A 0.8-mmdiameter aperture was placed in front of the detector at a distance of 7.8 cm from the target. The energy calibration of the detector was obtained by mea­ suring protons elastically scattered from C, Mg and Al transmission targets. The detector angle was fixed at # p =155° with respect to the beam direction. 3 3.1

Results Branching Ratio

The branching ratio T 7 / r of the E f i =223 keV resonance (E x =2485 keV) in 24 Mg+p was measured by populating the broad resonance at E#=1616 keV (E x =3823 keV, T=36 keV). A primary 7-ray transition from the latter reso­ nance feeds the compound nuclear state at E-,,^2485 keV, which in turn decays via secondary transitions to the three lowest-lying 25A1 states. The branching ratio of interest is then given by the efficiency-corrected decay and feeding 7-ray intensities, F F

V* rdecay j-feeding

'

\ /

Note that the branching ratio in Eq. (1) does not depend on knowledge of absolute 7-ray detection efficiencies.

72

For the measurement of the branching ratio T 7 / r , a 7-ray spectrum was recorded at E p =1620 keV for an accumulated total charge of 1.0 C. By using Eq. (1), we obtain a value of r 7 /T=0.91±0.04. The quoted experimental error arises mainly from the uncertainties in the observed 7-ray intensities (±2 to ±9%) and the relative 7-ray efficiencies (±2%). 3.2

Resonance Strength

The strength UJJ of a proton-capture resonance in the 2 4 Mg+p reaction is denned by w 7 = ( J + l / 2 ) r p r 7 / r , with J the spin of the resonance. The absolute strength of the 2 4 Mg+p resonance at E#=223 keV has been measured in the present work by using the procedure described in Ref. 9 , to which the reader is referred for details. In brief, the resonance strength was derived by measuring simultaneously the number of resonant 7-rays, integrated over the thick-target yield curve, and the number of Rutherford scattered protons. The resonance strength in the center-of-mass system is then given by W7

= A^ B

^ ^

J NAE) """W

dE

>

<2>

with A the center-of-mass de Broglie wavelength of the incident proton, evalu­ ated at the resonance energy, Clcm the center-of-mass solid angle of the particle detector in steradians, GRUth the differential Rutherford cross section, Np< the number of observed elastically scattered protons, N 7 , B 7 , ry7 and W 7 , the number of observed 7-rays, the 7-ray branching ratio, the detection efficiency and the angular distribution, respectively, of the 7-ray transition under con­ sideration. The quantity Np/ in Eq. (2) has been corrected for the natural abundance of 24 Mg. It should be emphasized that the resonance strength in Eq. (2) is independent of the properties of the target (stoichiometry, stopping power, uniformity and stability) and the beam (current integration and strag­ gling) and depends on the observed numbers of resonant 7-rays and elastically scattered protons, and the 7-ray branching ratio. Also note that UJJ depends on the ratio Q,CmM-y and, consequently, is independent of the knowledge of absolute 7-ray and charged-particle detection efficiencies. The efficiency ra­ tio was directly measured with the 1 9 F(p,a27) 1 6 0 reaction (E#=340 keV) at E 7 =6129 keV. For the strength of the E#=223 keV resonance in 2 4 Mg+p we obtain a value of wy= (1.27±0.09)xl0- 2 eV. According to Eq. (2), the quoted exper­ imental error is determined mainly by uncertainties in the measured 7-ray and elastically scattered proton intensities (±2 to ±3%), the ratio of 7-ray and charged-particle detection efficiencies (±5%), the relative 7-ray efficien-

73

cies (±2%), and the primary 7-ray branching ratios (±4%). Our value for the resonance strength is 33% higher than the result W7=(0.95±0.20)xl0~ 2 eV, reported by Trautvetter 10 . The latter value was obtained relative to the strength of the E#=823 keV resonance in 2 4 Mg+p. In the present work the precision in ivy has been improved by a factor of three. 3.3

Lifetime

The mean lifetime r m of the E x =2485 keV state in 25A1 was measured using the Doppler shift attenuation (DSA) method. The experiment was performed by populating the broad 24 Mg(p,7) 25 Al resonance at E#=1616 keV (E x =3823 keV, T=36 keV, T m = V r ~ 2 x l 0 ~ 5 fs). This resonance feeds the E x =2485 keV state, which subsequently decays by emission of 7-radiation to the states at E x =452 and 945 keV. The latter 7-rays are emitted from a nucleus recoiling in the target, and their energy will be shifted by an amount depending on the instantaneous velocity of the nucleus by the time of emission. The attenuation factor F(r), defined as the ratio of the observed aver­ age Doppler shift A.E7 and the calculated maximum Doppler shift AE™ax, is given by F ( T ) = ( E ° 6 S - E 7 O ) / ( E 7 O A ) C O S # 7 ) , with E7o the unshifted 7-ray en­ ergy, fa the initial velocity of the 7-ray emitting nuclei and 91 the angle of the 7-ray detector with respect to the beam direction. Experimental values of F ( T ) = 0 . 9 1 ± 0 . 0 3 and 0.93±0.04 were obtained for the two transitions men­ tioned above, yielding a weighted average of F(r)=0.92±0.03. On the other hand, the attenuation factor can be calculated by using 1 F r

( ) = —W\ /

r°°

v^cosWy-^dt

,

(3)

TV{0) Jo with 4> the angle of divergence of the recoil nuclei from the original direction of motion. For the calculation of the mean scattering angle in Eq. (3), the method of Blaugrund 11 was adopted. Our measured attenuation factor corresponds to a mean lifetime of T m =5.3l^4 fs f° r the E x =2485 keV state. The quoted errors arise mainly from uncertainties in peak centroids, 7-ray energy calibrations, stopping powers, detector angles and target stoichiometry. 4

Discussion

For the E/j=223 keV resonance we find from our measured ivy and T 7 / r values, widths of r p =(1.40±0.12)xl0- 2 eV, r 7 =(1.41±0.63)xl0" 1 eV and r = ( 1 . 5 5 ± 0 . 6 3 ) x l 0 - 1 eV. Furthermore, from our measured lifetime TTO we ob­ tain a total width of r=(1.25^ 0 ' 4 4 ) x 10 _ 1 eV, consistent with the value quoted

74

above. These two independent results for the total resonance width yield a weighted mean of r=(1.55±0.48)xl0 _ 1 eV. Our recommended value of T is much smaller than the upper limit of T<32 eV 1 2 obtained from the front edge of a thick-target yield curve. In order to calculate the reaction rate contribution of the E#=223 keV resonance, we describe the cross section by using the one-level, single-channel approximation of R-matrix theory 1 3 ,

a(F) {

=

'

* 2

rp(E)r7(£) (Er - [S(E) - S(Er)}

2

7

- £)2 + I r ( £ ) 2 '

^'

with E r the center-of-mass resonance energy and S(E) the shift factor. The expression for the cross section given here implies the choice B c =+S(E r ) for the boundary condition parameter. The energy dependences of the proton and 7 ray partial widths have been taken explicitly into account. The reaction rates for a transition to a specific final state were calculated by numerical integra­ tion. The total reaction rates of the E#=223 keV resonance were obtained by summing the contributions of transitions to all final states. Total reaction rates (solid line) and individual contributions (dotted and dashed lines) are displayed in Fig. 1. Above T=1.0 GK the resonances at Eij=419 and 823 keV provide the largest contribution to INU <. The E#=223 keV resonance dominates the rates in the temperature region T=0.051.0 GK. The contribution of the direct capture process dominates the total 24 Mg+p reaction rates below T=0.05 GK. The maximum contribution of the E#=223 keV resonance wing to the total 2 4 Mg+p reaction rates amounts only to 18% at T=0.04 GK. All other resonances are negligible for the total 2 4 Mg+p reaction rates. Our values of N^ for temperatures T=0.02-2.0 GK are larger than the reaction rates of Ref. 5 ' 6 by 18-45%. The differences arise mainly from using the strength of the E#=223 keV resonance measured in the present work. Clearly, our results suggest that hydrogen burning of 24 Mg at temperatures below T=0.055 GK, corresponding to the maximum temperature achieved in the hydrogen-burning shells of low-mass stars according to standard stellar evolution theory, cannot account for the anticorrelation of 24 Mg with Al ob­ served in the envelopes of M13 red giants. Therefore, alternative explanations, such as thermal instabilities of the hydrogen-burning shell that cause episodes of elevated temperatures near T«0.07 GK 2 , or combinations of primordial and evolutionary scenarios 14 , appear more promising.

75

10'

'

' ;

: (a)

Total

10°

'o

x

'

■ /

/ I ' l l

:223 keV

/

•/' /

I |

D 1 0- 20 ; V . <

r /

* '

/ j i i i

/

// >{

:

/

■ l i t • ' I I I

■i '

A

/

' V / ;i/ /xi \

i DC / /

N

/

i

i

1 0"'

'

\ / ' / '/ \ / ' '"' / y / .'/ /

■

1 0"

^ - C ^ ? ^

\

i

l

/

823 keV

■

l

i

l

l

I

I

I

'■ :

ft /,' 1 :419 keV/ ■

'

i

/

'

/

/

E > 823 keV :

. . i . .. .ii i

10

R

i

10"

T(GK)

Figure 1: (a) Total reaction rate (solid line) and individual contributions of resonances (dashed lines) and direct capture (dotted line) for the reaction 2 4 Mg(p,7) 2 5 Al; (b) ratio of the present recommended total reaction rate to previous results of Ref. 5 .

76

Acknowledgments This work was supported in part by the U.S. Department of Energy under Contract No. DE-FG02-97ER41041. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

R.R Kraft et al, Astron. J. 115, 1500 (1998). G.E. Langer et al, Pub. Astron. Soc. Pac. 109, 244 (1997). R.M. Cavallo et al, Astrophys. J. 492, 575 (1998). M.D. Shetrone, Astron. J. 112, 2639 (1996). G.R. Caughlan and W.A. Fowler, At. Data Nucl. Data Tables 40, 283 (1988). C. Angulo et al, Nucl. Phys. A, in print (1999). C.S. Zaidins and G.E. Langer, Pub. Astron. Soc. Pac. 109, 252 (1997). D.C. Powell et al, Nucl. Phys. A, in print (2000). D.C. Powell et al, Nucl. Phys. A 644, 263 (1998). Trautvetter, H.-R, Nucl. Phys. A 243, 37 (1975). Blaugrund, A.E., Nucl. Phys. 88, 501 (1966). M. Uhrmacher et al, Nucl. Instr. Meth. B 9, 234 (1985). A.M. Lane and R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958). P.A. Denissenkov et al, Astron. Astrophys. 333, 926 (1998).

X-RAY M E A S U R E M E N T S OF METAL A B U N D A N C E S OF HOT GAS IN CLUSTERS OF GALAXIES YASUSHI FUKAZAWA Department

of Physics, E-mail:

University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, 113-0033, Japan [email protected]

Tokyo

Utilizing the imaging spectroscopic capabilities of the Japanease X-ray satellite ASCA, we measured Si and Fe abundances of 40 nearby clusters of galaxies. The spatially averaged Fe abundances of the intracluster medium (ICM) are 0.2-0.3 solar, with only weak dependence on the temperature of the intracluster medium, hence on the cluster richness. In contrast, the spatially averaged Si abundance is observed to increase from 0.3 to 0.6-0.7 solar from the poorer to richer clusters. These results suggest that the supernovae of both type-la and type-II significantly contribute to the metal enrichment of the intracluster medium, with the relative contribution of type-II supernovae increasing towards richer clusters. Many clusters exhibit a central increment in the Fe abundance, which is more pronounced in lower temperature clusters; +(0.1-0.2) solar at fcX > 5 keV, while +(0.2—0.3) solar at 1.5 < kT < 4 keV. These central excess metals are thought to be ejected from cD galaxies. Several low temperature cD type clusters also show significant Si abundance increase by +(0.1—0.2) solar at the central region. Compared with the Si-rich abundances observed in outer regions of rich clusters, the Si to Fe abundance ratio of central excess metals tends to be near the solar ratio, implying that type la products from cD galaxies are dominant in the central excess metals.

1

Introduction

Clusters of galaxies are quite popular objects, and contain 50-1000 member galaxies. Various optical observations indicate that clusters of galaxies are gravitationally bound systems. X-ray observations (e.g. Jones and Forman 1984) revealed that clusters of galaxies are filled with a large amount of X-ray emitting hot gas with the temperature of 10 7 ~ 8 K, which is called intracluster medium (ICM). The ICM mass is often 2-5 times massive than the total stellar mass in clusters of galaxies, and thus the ICM is an important constituent in clusters of galaxies and moreover in the universe. The ICM is thought to be gravitationally bound from various evidences obtained by X-ray observations (e.g. Jones and Forman 1984). The ICM contains a considerable amount of heavy elements, which is processed in the stellar interior, then ejected into interstellar/intergalactic space, and now accumulated in the ICM (Rothenflug and Arnaud 1985; Edge and Stewart 1991; Hatsukade 1989; Arnaud et al. 1992; Tsuru 1992). Therefore, significant fractions of heavy elements in the universe exist in clusters of galaxies, and the investigation of metal abundances

77

78

of the ICM is important to study the chemical evolution and star forming history in the universe. X-ray study of metal abundances of a cluster is in many respects more straightforward than the optical study of metal abundances of a galaxy. First, atomic lines observed in an X-ray spectrum from the ICM are emitted via physically much simpler processes than optical emission/absorption lines from stellar atmosphere. Second, the ICM is optically so thin that the X-ray lines are not affected by complex radiative transfer. Finaly, metal enrichment of the ICM is approximately "one-way" process wherein the feedback from the ICM to the member galaxies is negligible, whereas metals recycle in a very complicated manner within a galaxy between stars and interstellar gas. In fig­ ure 1, optically thin thermal bremsstrahlung spectra predicted by the plasma model (Raymond and Smith 1977) are shown. The Japanese fourth X-ray Observational satellite, ASCA (Tanaka et al. 1994), has an unprecedented energy resolution, a wide energy band 0.5-10 keV, and a moderate angular resolution 1-3', which are all essential for determining the temperature and metal abundances of extended hot gas. In particular, ASCA can resolve var­ ious atomic emission lines expected in the X-ray spectra of clusters. Before ASCA, only Fe abundance has been measured, and it is not spatially resoloved one.

Figure 1. Calculated X-ray spectra from optically thin hot plasmas with various temper­ atures. The Raymond-Smith plasma emission code (Raymond and Smith 1977) is used, assuming a metal abundance of 0.3 solar.

Utilizing ASCA, we can obtain metal abundances other than Fe. In this paper, in order to investigate the origin of metals in the ICM, we measured metal abundances of the ICM not only for Fe but also for Si as a function of the ICM temperature, together with their masses for a large sample clusters. Throughout this paper, we set the Hubble constant to be 50/iso km s _ 1 M p c - 1 . The detailed results are described in Fukazawa (1997), and main results are published in Fukazawa et al. (1998, 2000).

79

2

Observations and Data Reduction

We selected our sample clusters from the ASCA archival data, through the following rough criteria: the object must be extended enough to resolve spatially; it must be bright enough to constrain metal abundances; and it must not exhibit outstanding morphological asymmetry. The last criterion is necessary to avoid peculiar objects. In addition, we take attention so that clusters with various ICM temperatures can be included. Through these criteria, we have selected 40 clusters. Most objects are located at redshifts of z < 0.062. All the objects are brighter than 1 x 10~12erg s _ 1 c m - 2 in 0.5-10 keV which is enough to constrain metal abundances. Their ICM temperatures are distributed almost continuously from 1 to 10 keV. ASCA carries four indentical X-ray telescopes (XRT; Serlemitsos et al. 1995; Tsusaka et al. 1995) and two type focal plane imaging detectors with wide energy band 0.5-10 keV ; the GIS (Gas Imaging Spectrometer; Ohashi et al. 1996; Makishima et al. 1996) and the SIS (Solid-state Imaging Spectrometer), two detectors for both the GIS and SIS are onboard. The GIS has a moderate energy resolution 8% at 6 keV, and large field of view with the diameter 40', that covers the whole region of most clusters of galaxies. The SIS has a good energy resolution 120eV at 6 keV, good sensitivity in lower energy band, and smaller field of view 11' x 11' - 22' x 22'. The typical exposure time and count rate of each object are 20-80 ksec and 0.1-5 counts s e c - 1 per detector, respectively, and thus 10000-100000 photons were accumulated that is enough to mesaure the line strength. The background spectra were constructed from several blank-sky data, such as NEP, Draco, and QSF-3 fields for a total accumulation time of about 100 ksec, integrated in the same region as that of on-source spectra under the same data selection criteria. 3 3.1

Results Spatially Averaged Metal Abundances

Many clusters show a bright cool component and an abundance increase in the center (e.g. Fabian et al. 1994), which should be excluded from the present study of the average ICM properties. We therefore accumulated the GIS and SIS spectra for each cluster in a ring-shape region. The region typically has an inner radius of 0.1ftjj"0 Mpc and an outer radius of 0.4/ijT0 Mpc from the cluster center, respectively. In figure 2, we show an exmaple of ASCA spectra. Not only Fe-K lines but also Si, S, and Fe-L lines are detected.

80

■VV^/#/#^^ Energy (keV)

Energy

(keV)

Figure 2. The spatially averaged GIS/SIS spectra of A2199 cluster. The SIS data points exceed those of the GIS in lower energies; vise versa in higher energies. The solid line repre­ sents the best-fit single-temperature Raymond-Smith model assuming the solar abundance ratios, determined jointly by the two instruments. The model has been convolved through the XRT+SIS or XRT+GIS response to be compared with the SIS or GIS data. The left panel shows the whole band spectrum, and the right panel shows the spectrum around Si-K lines and solid lines represents the plasma model with the Si and S abundance to be 0 solar.

We perform combined fit to the GIS/SIS spectra with variable-abundance single temperature (IT) Raymond-Smith model (R-S model), that is typically utilized in X-ray astronomy. Solar abundances are taken from the solar photospheric values by Anders and Grevesse (1989), with (Fe/H) 0 = 4.68 x 10~ 5 and (Si/H)© = 3.55 x 10~ 5 . Free parameters of the fit are the interstellar absorption (A^H), temperature (kT), normalization, and the abundances of O, Mg, Si, S, and Fe. We asuume Ne abundances to be the same as O; Ca and Ar as S; and Ni as Fe, respectively, all in terms of the solar units. The abundances of He, C, and N are fixed at the solar values. For most clusters, the fit is acceptable with the reduced chi-square value of 1.4 or less with a typical degree of freedom 200. Thus, the spectra of most clusters can be represented fairly well by the IT R-S model with variable abundance ratios. In this way, we have determined spatially averaged metallicities of all clusters, with a typical accuracy of 10% or better for Fe and 40% for Si. Other elemental abundances are poorly constrained. We plot the derived Fe and Si abundances in figure 3a and 3b respectively, as a function of the ICM temperature. In figure 3a, the obtained Fe abundances distribute in a range of 0.2-0.4 solar, in rough agreement with the previous non-imaging results (e.g. Hatsukade 1989; Tsuru 1992). The Fe abundances of clusters with kT < 3 keV rely upon Fe-L lines. In order to evaluate the reliability of the Fe-L line results, we analyzed clusters with kT > 1.7 keV ignoring either Fe-K or FeL line regions of the spectrum, and obtained consistent results within 10%. This consistency is also reported by Mushotzky et al. (1996) and Hwang et

81

al. (1997) for several clusters. The ensemble-averaged Fe abundance is nearly independent of the temperature, at least over a range of 1.5 to 7 keV. This feature is common to different plasma codes utilized in the spectral fittings. The Fe abundance seems to decrease below kT ~ 1.5 keV. This trend is not convincing since the results depend on the plasma codes due to uncertainties in the Fe-L line modeling (Fabian et al. 1994; Fukazawa et al. 1996). As shown in figure 3b, Si abundance is 0.6-0.7 solar in rich clusters (kT > 4 keV), which is consistent with the previous ASCA measurements (e.g. Mushotzky et al. 1996). The present results thus extend their inference to a much larger sample. Moreover, in contrast with Fe, the Si abundance appears to correlate positively with the ICM temperature; it increases from 0.3 solar to 0.6-0.7 solar as the temperature increases, and it may saturate for kT > 4 keV.

1

2

5 10 1 2 5 10 kT (keV) kT (keV) Figure 3. Spatially averaged Fe and Si abundances excluding central regions, plotted as a function of the ICM temperature, (a) The Fe abundances of individual clusters obtained using the R-S code, (b) The same as panel (a), but for the Si abundance.

(D

Figure 4. Si to Fe abundance ratios aver­ aged over clusters with similar tempera­ tures, plotted as a function of the ICM tem­ perature. The different symbols denote dif­ ferent plasma codes.

o

S

kT (keV)

82

Finally, in figure 4, we present the sample-averaged Si to Fe abundance ratios in solar units, as a function of the ICM temperature. Figure 4 compares the R-S fitting results with those employing plasma emission codes by Masai (1984) and by Mewe-Kaastra-Liedahl (Mekal: Mewe et al. 1985; Liedahl et al. 1995): R-S, Masai, and Mekal codes are known to differ in the Fe-L line treatment (Fabian et al. 1994; Fukazawa et al. 1996). This ratio depends on the plasma code by 10-30%; the Mekal code gives the weakest correlation. Nevertheless, we can clearly see that the ratio positively correlates with the ICM temperature for all plasma code, increasing from ~ 1 at kT ~ 1 keV to ~2 at kT ~ 4 keV. This is the first detection of the variation of the abundance ratio in the ICM. Hwang et al. (1999) also reported that poor clusters exhibit lower Si to Fe abundance ratio than rich clusters. 3.2

Metal Abundances at the Central Cluster Region

We investigated the central 2' X-ray spectra to constrain metal abundances at the cluster central region. Here, we focus on clusters which contain a central dominant elliptical galaxy, since we are interested in the metal ejection from individual galaxies. It is found by ASCA that the averaged ICM temperature often decreases toward the cluster center (e.g. Fabian et al. 1994; Fukazawa et al. 2000). We thus try to fit the central spectra with two temperature R-S model (2T R-S model). In the 2T fitting, we fixed the temperature of the hot component to the spatially averaged cluster temperature. Metal abundances were assumed to be the same between the two components, since the data quality is usually not adequate to determine the abundances and normalization of the cool component independently. We plot the central Fe and Si abundances of clusters in figure 5 against the spatially averaged temperature. Many clusters, even hot ones, have higher Fe abundances than the spatially averaged values of 0.3 solar, and a clear negative correlation with the averaged ICM temperature is seen. This is in­ dependent of the plasma model. The Si abundance at the center also exhibits a noticeable difference from the outer-region values, instead of showing the positive correlation with the ICM temperature like in the outer region, the central Si abundance stays rather constant and high, 0.6-1.0 solar, except in the coolest objects. This is because cooler clusters exhibit stronger Si abun­ dance increases (by 0.2-0.3 solar) at the center, that is also seen by comparing figure 4 with figure 6 that plots the ensemble-avereged Si to Fe abundance ra­ tio. Finoguenov and Ponman (1999) also found the radial increase of Si to Fe abundance ratios of the ICM.

83 Fe Abundance in the center

Si Abundance in the center 1 1

I

I

t o

<

g0.5 a c

-

3 3 0.2 55 0.1

1

i

-<>-

i

,1

■XD «nXD-

II i-

11

: ■

1 ~ih ■ 1

10 5 kT (keV) kT (keV) Figure 5. Fe and Si abundances at the cluster central regions, plotted as a function of the ICM temperature, (a) The Fe abundances of individual clusters obtained using the R-S code, (b) The same as panel (a), but for the Si abundance.

2

Figure 6. Si to Fe abundance ratios at the cluster center averaged over clusters with similar temperatures, plotted as a function of the ICM temperature. The different symbols denote different plasma codes.

4

Discussions

2

<

kT (keV)

We have obtained spatially averaged Si and Fe abundances for 40 nearby clusters, excluding the central regions, and found that they depend on the ICM temperature in different ways. Our results on relatively rich (kT > 4 keV) clusters agree with those obtained by Mushotzky et al. (1996), in that the Si to Fe abundance ratio is high at 1.5-2 (in solar unit). Such abundance ratios are difficult to be explained by SNe la alone. This indicates that SNe II play a major role in hotter clusters (but see also Ishimaru, Arimoto 1997). Our results here are based on a large sample including clusters hotter than those analyzed by Mushotzky et al. (1996). The major finding in the present study is a significant decrease in the Si to Fe abundance ratio toward lower temperature clusters. What makes this change of abundance ratio? One possibility is that the chemical composition of the SNe II products depends on the cluster richness, due, e.g., to the difference in the initial mass function of stars. This is however inconsistent

84

with the fact t h a t there is no differences in color-magnitude ralation of ellipti­ cal galaxies between poorer and richer clusters (Visvanathan, Sandage 1977). Confinement of Si in dust in poor clusters is not likely, because the dust evap­ oration time scale is at most 10 8 yr in the ICM environment (Itoh 1989). On the other hand, we find that the cluster spectra are well described by a single t e m p e r a t u r e thermal model for b o t h poor and rich systems. Therefore, Si and Fe should be in thermal equilibrium with no indication of extra thermal energy in Si to cause its selective loss in poor clusters. As discussed above, our observational results are difficult to interpret as log as we assume that the origin of metals is exactly the same between richer and poorer clusters. Considering t h a t SNe l a produce Fe-rich metals compared with SNe II, it is n a t u r a l to think of a different mixing ratio of SNe la and SNe II products between richer and poorer clusters. The lower relative content of Si in poorer clusters suggests less contribution from SNe II. This in tern implies t h a t we need a significant contribution from SNe la in the metal production in poor clusters. Ishimaru and Arimoto (1997) discuss t h a t more t h a n half of Fe in the ICM can be produced by SNe la even in rich clusters. If this is correct, then most of the metals in poor clusters could have been produced by SNe la. Therefore, we conclude t h a t b o t h types of supernovae contribute significantly to the metal enrichment of the ICM, and their ratio of the metal supply varies as a function of the ICM t e m p e r a t u r e . This is the first evidence t h a t SNe la contribute significantly to the metal enrichment of the ICM. T h e SNe II products are thought to be supplied in the form of galactic wind in the early stage of galaxy formation, while the SNe la products are not. Therefore, we speculate t h a t more SNe II products have escaped from the system in the present poorer clusters, t h a t makes the observed reduction of Si to Fe abundance ratio toward the lower t e m p e r a t u r e clusters. On the other hand, we found t h a t the metal abundances increase at the central cluster region. Condensatation of metals is expected to take place on time scales much longer than the age of the universe (Sarazin 1988). Consid­ ering various observal features at the cluster center, we infer t h a t the excess metallicity around cD galaxies is due to metal-rich gas ejected from cD galax­ ies themselves. We have discovered t h a t the central excess metals around cD galaxies exhibit roughly solar-like chemical composition, compared with the Si-rich abundance in outer-region of rich clusters. In other words, the central regions of cD type clusters are probably more heavily contributed by SNe l a t h a n their outer regions. Although the central abundances could be subject to resonance line scattering, we do not find any such evidence. Since the SNe II should be rare in elliptical galaxies (e.g. van den Bergh and T a m m a n n

85

1991), the SNe la like chemical composition provides a strong support to our view t h a t the excess metals in the center of cD type clusters came from the cD elliptical galaxies. In 2000, three improved X-ray satellites begin more sensitive observations; Chandra, XMM, and the Japanease satellite Astro-E. C h a n d r a and XMM can measure metal abundances of distant clusters to constrain the evolution of metal abundances of the ICM. Astro-E with excellent energy resolution can measure Oxygen abundances t h a t strongly constrain the supernovae contri­ bution, and moreover might detect minor but important heavy elements such as Cr in the ICM. We hope to feed back observational abundance p a t t e r n s to the stellar nucleosynthesis theory. References 1. Anders, E. and Grevesse, N. 1989, Geochim. Cosmochim. Acta. 53, 197 2. Arnaud, M. et al. 1992, A&A 254, 49 3. Edge, A.C. and Stewart, G.C. 1991, MNRAS 252, 414 4. Fabian, A.C. et al. 1994, ApJ 436, L63 5. Finoguenov A. and Ponman T. J. 1999, MNRAS 305, 325 6. Fukazawa, Y. et al. 1996, PASJ 48, 395 7. Fukazawa, Y. 1997, Ph.D. Thesis, University of Tokyo 8. Fukazawa, Y. et al. 1998, PASJ, 50, 187 9. Fukazawa, Y. et al. 2000, MNRAS accepted 10. Hatsukade, I. 1989, Ph.D. Thesis, Osaka University 11. Hwang, U. et al. 1997, ApJ 476, 560 12. Hwang, U. et al. 1999, ApJ 516, 604 13. Ishimaru, Y. and Arimoto, N. 1997, PASJ 49, 1 14. Itoh, H. 1989, PASJ 41, 853 15. Jones, C. and Forman, W. 1984, ApJ 276, 38 16. Makishima, K. et al. 1996, PASJ 48, 171 17. Masai, K. 1984, Astrophys. Space Science 98, 367 18. Mewe, R. et al. 1986, A&AS 65, 511 19. Mushotzky, R.F. et al. 1996, ApJ 466, 686 20. Liedahl, D. et al. 1995, ApJ 438, L115 21. Ohashi, T. et al. 1996, PASJ 48, 157 22. Raymond, J.C. and Smith, B.W. 1977, ApJS 35, 419 23. Rothenflug, R. and Arnaud, M. 1985, AfcA 147, 337 24. Sarazin, C.L. 1988, X-ray emission from clusters of galaxies (Cambridge: Cam­ bridge university press.) 25. Serlemitsos, P.J. et al. 1995, PASJ 47, 105 26. Tanaka, Y., Inoue, H., and Holt, S.S. 1994, PASJ 46, L37 27. Tsuru, T. 1992, Ph.D. Thesis, University of Tokyo 28. van den Bergh S. and Tammann G.A. 1991, ARAA 29, 363 29. Visvanathan, N. and Sandage, A. 1977, ApJ 216, 214

X-RAY DIAGNOSIS OF T H E GALACTIC C E N T E R A B U N D A N C E WITH A N X-RAY REFLECTION N E B U L A H. M U R A K A M I , M. S A K A N O , M. T S U J I M O T O , K. K O Y A M A Department of Physics, Faculty of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan E-mail: [email protected]

Department

Y. M A E D A of Astronomy and Astrophysics, The Pennsylvania University Park, PA 16802-6305, U.S.A.

State

University,

We present the ASCA results of imaging spectroscopy of the giant molecular cloud Sgr B2 at the Galactic center region. The X-ray spectrum is found to be very peculiar; it exhibits a strong emission line at 6.4 keV, a low energy cutoff below about 4 keV and a pronounced edge-structure at 7.1 keV. The X-ray image is extended and its peak position is shifted from the core of the molecular cloud toward the Galactic center by about 1—2 arcminute. Since 6.4-keV line is a K-alpha line from neutral iron, these features indicate that the molecular cloud is irradiated by an external X-ray source, and emits fluorescent and scattered X-rays. Thus Sgr B2 may be called an "X-ray reflection nebula". This new category of X-ray source is similar to the X-ray diagnosis of the material. We can obtain the information about the abundance of the molecular cloud from the X-ray spectrum. The "X-ray reflection nebula" is a probe for revealing the Galactic center environment.

1

Introduction

Our Galactic center (GC) is a very peculiar region. There are many massive stars inside 50 pc a radius, which indicate an active star formation in the past. The chemical abundance in this region is very important to study about the past star formation history, an initial mass function under unusual conditions, and the chemical evolution of our Galaxy. However, the information on the abundance is lacking at the GC. From the observations of the SNRs, planetary nebulae or HII regions, the abundance gradually increases towards the GC (Shaver et a/.1; Ratag el al?; Binette et al3), while direct observations of the supergiant stars at the GC region indicate that the abundance is consistent with that of the solar. A new independent method is required to study further. Japanese X-ray astronomical satellite ASCA found diffuse emission from the 6.4-keV iron line; the brightest region is located over the giant molecular cloud Sgr B2, but its X-ray peak is shifted toward the GC from that of the a

l pc = 3 x l 0 1 8 c m

86

87

molecular gas (Koyama et a/.4). Because the 6.4-keV line is usually emitted as a fluorescent line from a neutral iron, Koyama et al. suspected that the cloud is irradiated from an external X-ray source, and emit fluorescent and scattered X-rays. Sgr B2 may be called an "X-ray reflection nebula" (XRN, hereafter). This mechanism resembles X-ray fluorescence analysis of a matter; we can obtain information about the kind and the amount of the elements by the X-ray emission lines. We may be able to study the chemical abundance at the Galactic center region by XRNs. The Sgr B2 cloud may thus become a new probe for studying the Galactic center region. However the previous report was based on limited data sets, their interpretations were rather preliminary and qualitative. We therefore have analyzed the X-ray spectrum and morphology of the Sgr B2 cloud in further detail combining all the available data. We verify the XRN hypothesis quantitatively, and try to apply the method of the ground X-ray fluorescence analysis to the Sgr B2 cloud. With the combined analysis of the CO molecular lines and the far-infrared dust emissions, the mass of Sgr B2 is estimated to be 6 xlO 6 M© within a region of ~ 45 pc in diameter (Lis & Goldsmith 5 ), hence it is one of the largest molecular clouds in the Galaxy. We assume the distance to Sgr B2 is ,the same as that to the GC (Sgr A*) or 8.5 kpc, which is within the error of estimated distance of 7.1 ± 1.5 kpc (Reid et a/.6). Then the distance between Sgr B2 and the Galactic nucleus Sgr A* is about 100 pc. 2

Observation

Two observations of Sgr B2 were made with ASCA on October 1, and on September 22-24. In both observations, all four detectors, two Solid-state Imaging Spectrometers (SISO, SISl) and two Gas Imaging Spectrometers (GIS2, GIS3) were operated in parallel, hence four independent data sets were pro­ vided. Details of the instruments, the telescopes and the detectors, are found in Tanaka, Inoue, & Holt', Serlemitsos et al?, Burke et al?, Ohashi et al}°, Makishima et al}1, and Gotthelf12. After standard filters were applied, the net observing times were 95 ksec for the GIS and 85 ksec for the SIS. 3 3.1

Results Iron Line Image of Sgr B2

Koyama et al* have already reported that the Sgr B2 cloud region is partic­ ularly bright in the 6.4-keV line. We therefore made X-ray images in narrow

88

Figure 1: (a) The 6.4-keV line intensity map around the Sgr B2 cloud obtained with the SIS, laid over the CH3CN line contours (Bally et al.). The 6.4-keV brightness distribution is shifted from the radio distribution by ~ 1'.2 to the Galactic center side (to the right in the figure), (b) The 6.4-keV line image with the GIS. The source and the background regions are shown by the solid circle and the dotted ellipse, respectively. The dotted circle encloses the other X-ray bright spot, which is excluded from the background region. The bright source at the boundary is a galactic binary X-ray source ( I E 1743.1—2843).

energy bands with a central energy of 6.4 keV and width of twice the energy resolution (FWHM): 5.8-7.0 keV for the GIS and 6.2-6.6 keV for the SIS. Figure 1 shows (a) the narrow band SIS image laid over the radio intensity contours of the CH3CN line (Bally et al}3) and (b) the GIS image. Since the SIS image is already found in Figure 3b in Koyama et al*, we present the combined image of the two observations. There is a clear peak at the Sgr B2 cloud, but the peak is shifted from the cloud core toward the Galactic center (to the right in the figure). The gap is about 1'.2, which is significantly larger than the X-ray position errors of about 40". 3.2

Spectrum of Sgr B2

For the X-ray spectrum, we used the GIS data, because, in the high energy band including the iron K-shell line, the GIS provides better statistics than the SIS. The GIS spectrum given in Figure 2 is obtained by summing the X-ray photons in 3'-radius circles around the X-ray peaks of the GIS images. For the background spectrum, we used an elliptical region with the major axis parallel to the Galactic plane, excluding the region of Sgr B2 (a 3'-radius circle) and the other X-ray bright spot (the other 3'-radius circle) at the west of Sgr B2.

89 GIS spectrum of Sgr B2

6

10

channel energy (keV)

Figure 2: The GIS (GIS2 + 3) spectrum of Sgr B2. The solid line shows the simulated spectrum of an XRN (see section 4.3), after the convolution of the response function.

The source and the background regions are shown in Figure lb with the solid circle and dotted ellipse, respectively. In order to derive quantitative feature of the Sgr B2 X-rays, we fit the spec­ trum to two phenomenological models, a thermal bremsstrahlung and a powerlaw model, each with a Gaussian line. We used the Morrison & McCammon14 cross section for the absorption. Due to large absorption at low energy, the available data to be fitted are in the 4.0-10.0 keV band. However the limited energy band and rather poor statistics do not allow us to constrain the model. Therefore we assumed a power-law of (fixed) photon index 2.0 (Koyama et al.f. The best-fit parameters are given in Table 1. The 6.4-keV line, as we expected, is very strong with an equivalent width of 2.9 keV. The hydrogen column density is Nu ~ 8 X 1023 H c m - 2 , and the luminosity is ~ 1035 erg s _ 1 (Here and elsewhere, all X-ray luminosities are corrected for absorption unless otherwise noted). The observed hydrogen column of 8 x 1023 H c m - 2 is at least 5 times larger than that of interstellar gas to the GC region (Sakano et a/.15). This means that the large absorption column is due to local gas near or at the Sgr B2 cloud. We found a deep iron edge in the spectrum. We fit the spectrum allowing the iron column density to be free. Then the iron column density is estimated to be 4 x l 0 1 9 Fe c m - 2 . This value is converted to a hydrogen column ./VH of 1.3 x 1024 H c m - 2 if the abundance is solar. The hydrogen column density

90 Table 1: Fitting Results of Sgr B2 to a Phenomenological Spectral Model Model Components Parameters Unit GIS Absorption NH (H c m " 2 ) S-St'to x 1Q23 Continuum Photon Index 2.0 (fixed) Flux (4-10 keV) (ph s " 1 c m " 2 ) 1.5 ± ° ' j X 1 0 " 4 Fe 6.4-keV Line Center Energy (keV) 6.38±o;03 Equivalent Width (keV) 2.9^'j (ph s 1 cm 2 ) Flux 9.7 +l{° X 10~ 5 Total Luminosity (erg s _ 1 ) l.ltSi'i x 1035 ■^4-lOkeV Reduced xl (d.o.f.) 0.91 (34)

determined from the low energy cutoff is NR ~ 8 x 1023 H cm 2 . Thus the absorption indicates that Sgr B2 is overabundant. 4

X-ray Reflection Nebula model

fn section 3, (1) we confirmed the presence of the very strong emission line at 6.4 keV, (2) we found a large low-energy cutoff and a deep absorption edge at 7.1 keV, both requiring an extremely large column near or at the Sgr B2 cloud, and (3) we found that the X-ray peak position has about 1-2 arcminute offset from the cloud center to the GC side. This peculiar X-ray spectrum and morphology are attributable to Thom­ son scattering (continuum emissions), photo-electric absorption of neutral iron atoms (low-energy cutoff and iron K-edge), and fluorescence (6.4-keV line), produced by an irradiation of an external X-ray source. We refer this sce­ nario as XRN model. This section is devoted to numerical simulations to see whether or not the XRN model reproduces the X-ray spectrum and morphol­ ogy of Sgr B2. 4-1

Numerical Simulations

We made numerical simulations of XRN model. The mass distribution of the cloud is taken from the result of 13 CO and the C 1 8 0 observations by Lis & Goldsmith5. For simplicity, we assumed that the reflection and fluorescence are isotropic, and a primary source is at the normal angle to the line of the sight. The spectrum of the primary source is a power-law with photon index of 2 (Koyama et a/.4). Since the Thomson scattering optical depth is much smaller than that of the photo-electric absorption in the relevant energy band below 10 keV, we neglect the multiple Thomson scattering. Then we simulated the image and the spectrum when the Sgr B2 cloud is irradiated from an external

91

Figure 3: The simulated XRN image of the 6.4-keV line. The brightest region is shifted from the cloud center to the side of the primary X-ray source.

X-ray source. 4-2

Simulated Image

Simulated XRN images of the 6.4-keV fluorescent line is shown in Figure 3. The X-ray peak is shifted from the cloud core about 1'.3, which is consistent with the observation. 4-3

Simulated Spectra

The simulated spectrum is convolved with the response function of instruments and compared with the observed spectrum. We first fit the observed spectrum to the simulated one with the XRN model of solar abundances, where a free parameter is only the normalization of the flux. This simulated spectrum, however, is rejected with a reduced x 2 of 2.35 (36 d.o.f.). Large residuals are found in the flux of the 6.4 keV line, depth of the K-edge and low-energy absorption. We accordingly vary the abundances collectively, fixing the relative ratio to be solar. We find an acceptable fit with the reduced-x 2 of 1.18 (35 d.o.f.), when the abundances are 2.2 solar. We further search for a better XRN model allowing the iron abundance to be an additional free parameter, and find a better fit with the reduced-^ 2 of 0.78 (34 d.o.f.). The best-fit XRN spectrum is given in Figure 2 by the solid line. The abundances of iron and the others are determined respectively to be 2.4 and 1.6. The allowable region is that iron is more than 2.0 solar and the others are more than 1.5 solar.

92

Figure 4: 5.8-7.0 kcV band image around the Sgr C cloud obtained with the GIS laid over the 1 3 CO line contours (Bally et al. . The solid circle shows the X-ray emitting region.

Thus the XRN model can reproduce the image and the spectrum of the Sgr B2 cloud, and the X-ray spectrum of Sgr B2 supports the overabundance at the GC region. 5

N e w Candidate of an X-ray Reflection Nebula

The XRN is a new category of X-ray source. There is no other XRN than Sgr B2. If the Sgr B2 cloud is an XRN, there is (was) a strong X-ray source near the cloud, and other molecular clouds also emit fluorescent and scattered X-rays. We analyzed ASCA data in detail, and found a new candidate of an XRN: the Sgr C cloud which is at the opposite side of the Galactic center to Sgr B2, and also a giant molecular cloud. Figure 4 shows the 6.4-keV line image of Sgr C laid over the radio intensity contours of the 13 CO line (Bally et a/.13). X-ray peak is shifted from the cloud core like Sgr B2. We can obtain a new information on the abundance of the GC region by combining two XRN. However, Sgr C is very faint source. More observations with a new generation X-ray satellites are required. 6

Summary 1. We propose a new category of X-ray source: "X-ray reflection nebula". 2. Numerical simulation of XRN model well describes the observed facts of Sgr B2.

93 3. The reflected spectrum of Sgr B2 indicates that the Galactic center is overabundant. 4. Another candidate of an "X-ray reflection nebula" is found, and they would be a new probe for studying the Galactic center region. Acknowledgments The authors express their thanks to all the members of the ASCA team. H.M, M.S. and Y.M. are financially supported by the Japan Society for the Promo­ tion of Science. The authors also thank Dr. T. Oka for his useful discussion. References 1. Shaver, P. A., McGee, R. X., Newton, L. M., Danks, A. C., k Pottasch S. R., Monthly Notices of the RAS 204, 53 (1983) 2. Ratag, M. A., Pottasch, S. R., Dennefeld, M., & Menzies, J. W., Astron­ omy and Astrophysics 255, 255 (1992) 3. Binette, L., Dopita, M. A., D'Odorico, S., & Benvenuti, P., Astronomy and Astrophysics 115, 315 (1982) 4. Koyama, K., Maeda, Y., Sonobe, T., Takeshima, T., Tanaka, Y., & Yamauchi, S., Publications of the ASJ 48, 249 (1996) 5. Lis, D. C , & Goldsmith, P. F., Astrophysical Journal 337, 704 (1989) 6. Reid, M. J., Schneps, M. H., Moran, J. M., Gwinn, C. R., Genzel, R., Downes, D., & Ronnang, B., Astrophysical Journal 330, 809 (1988) 7. Tanaka, Y., Inoue, H., & Holt S. S., Publications of the ASJ 46, L37 (1994) 8. Serlemitsos, P. J., et al., Publications of the ASJ 47, 105 (1995) 9. Burke, B. E., Mountain, R. W., Harrison, D. C., Bautz, M. W., Doty, J. P., Ricker, G. R., & Daniels, P. J., IEEE Trans., ED-38, 1069, (1991) 10. Ohashi, T., et al, Publications of the ASJ 48, 157 (1996) 11. Makishima, K., et al, Publications of the ASJ 48, 171 (1996) 12. Gotthelf, E. 1996, The ASCA news (Greenbelt: NASA GSFC), 4, 31 13. Bally, J., Stark, A. A., Wilson, R. W., & Henkel, C., Astrophysical Jour­ nal 324, 223 (1988) 14. Morrison, R & McCammon, D., Astrophysical Journal 270, 119 (1983) 15. Sakano, M., Nishiuchi, M., Maeda, Y., Koyama, K., & Yokogawa, J., IAU Symp. 184, The Central Regions of the Galaxy and Galaxies, ed. Y. Sofue (London: Kluwer Academic Publishers), 443 (1997)

COSMIC RAY OBSERVATION FOR NUCLEAR ASTROPHYSICS CORONAPROGRAM NOBUYUKI HASEBE AND M.N. KOBAYASHI Advanced Research Institute for Science and Engineering., Waseda 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555 Japan E-mail: [email protected]

University,

Cosmic Ray Observation for Nuclei Astrophysics (CORONA) program is a large-scaled spacecraft or space station approach for nuclear composition of relativistic cosmic rays 105S Z ^ 92 and of low-energy isotopes 1 S- Z S; 58 in space. A large area Spectrometer for Ultraheavy Nuclear Composition (SUNC) and a Large Isotope Telescope Array (LITA) are proposed in this program. CORONA program focuses on the composition of elements beyond the iron-peak nuclei (Z>60) and the isotopic composition of ultraheavy particles (Z>30)in galactic cosmic rays as well as solar and interplanetary particles. The observation of nuclear composition covers a wide range of scientific themes including studies of nucleosynthesis of cosmic ray sources, chemical evolution of galactic material, the characteristic time of cosmic rays, heating and acceleration mechanism of cosmic ray particles. Observation of solar particle events also make clear the physical process of transient solar events emitting wide range of radio, X-ray/gamma-ray, plasma and energetic particle radiation, and particle acceleration mechanism driven by CME.

1

Scientific Objectives

The Cosmic Ray Isotope Observation for Nuclei Astrophysics (CORONA) program aims to measure nuclear composition of energetic particles observed by large scaled spacecrafts including Space Station, covering comprehensive studies of solar, interplanetary, anomalous cosmic ray (ACR) and galactic cosmic ray (GCR) particles [1,2]. Scientific objectives covering a wide range of basic problems are summarized as : A. Nuclear Composition, the Origin and Evolution of Galactic Matter : - To search for evidence of special sources of CRs, such as supernovae and WR-stars. - To study nucleosynthesis and galactic evolution that distinguish solar system and galactic matter. - To determine and compare the composition of the solar corona, the local interstellar medium, and GCR sources. -To search for the existence of transuranic nuclei as the signature of fresh rprocess component in CRs indicating recent nucleosynthesis occurred nearby our solar system.

94

95

-2000X2000SFM1

100 SFM2 Si-stack (AEXE)

Si-stack (AEXE)

Si-stack (AEXE)

Si-stack (AEXE)

500

SUNC

T 300 j.

SFM3

(a) ^

^

u

^

tsll HI HI H I HP ■ iH HI iH H ^

■ HBP

■ ■ ■ ■ ■ (b)

(c)

Figure 1. Particle Instrument (LTTA & SUNC) in the CORONA Experiment

B. Injection, Acceleration and Transport Processes of Energetic Particles : - To study the injection mechanism and FlP-volatility problems. - To study particle acceleration and interaction processes in solar and interplanetary ion events. - To study the evolution of CME and the relation to the particle acceleration. - To determine the time for nucleosynthesis and the time of particle acceleration in the galaxy. - To search for evidence of continuous CR acceleration by supernova shock waves. - To study the confinement or propagation mechanism of CRs in the Galaxy. - To investigate acceleration mechanism of pickup ions at the solar wind termination shock.

96

The CORONA program is a large-scaled observation program of nuclear particles with high precision. Solar, interplanetary and galactic particle events would be continuously observed on satellites or the JEM of Space Station. In order to pursue the objectives described above, we propose an instrument consisting of two kinds of telescopes, SUNC and LITA (see Fig.l). We will observe elemental composition from Z=10 to 92 in atomic number with relativistic energy, and elemental and isotopic composition H (Z=l) - Ce (Z=58) of particles in the range from a 30 MeV/n to 400 MeV/n. We will also search the existence of trans-uranium atoms in relativistic cosmic rays. We will put stress on the measurement of elemental and isotopic abundance especially for heavy elements in the GCRs and solar and interplanetary ion events, especially UH particles in space.

2

Scientific Motivation and Significance

Elemental abundance in the cosmic radiation above Z=30 has been measured by experiments on the HEAO-3, ARIEL-6 and LDEF, with earlier exploration of the Z>50 region by using plastic track detectors at high altitude balloons [3-6]. The abundance of even-Z nuclei extending from Z=30 to 60 has been individually resolved. For Zs^60, observation data are still statistically poor and the charge resolution is broadened in the HEAO and ARIEL-6 data, making it necessary to group charges for meaningful abundance measurements. Isotopic abundance heavier than Se both in the solar and galactic cosmic rays has never been measured, while the abundance of lighter elements are clearly observed especially by CRIS and SIS experiments on ACE satellite. We still lack definitive data that could provide further understanding of the origin and history of galactic matter. Here we focus and discuss only on the nuclear composition of ultraheavy CRs and the necessity of the detailed measurements for them. [A] Neutron-Rich Cosmic Ray Nuclei and s-/r-Process Nucleosynthesis The study of elemental and isotopic composition in the UH cosmic rays is important step to understand the origin and history of CRs. Nuclei of Zs£30 include contributions not only from equilibrium (e-) process and proton (p-) capture process but also from the rapid (r-) and slow (s-) neutron capture processes. The study for heavier elements, Z ^ 3 4 , will give us much opportunity of the UH observations which should delineate the r-process and the s-process contributions to the CR7). Rprocess nucleosynthesis would be expected to dominate the production of As, Se, Br, Kr, Rb, Y and Te while s-process production would dominate in Ga, Ge, Sr, Zr, Mo, Ru, Pd, Ag, Cd, In, Sn, I, Ba and Ce. Some elements are dominated by a single significant nucleosynthesis, while others are mix contributions from r-, s-, pprocesses in the nucleosynthesis.

97 According to HEAO-3 and ARIEL-6 observations, the abundance of ultraheavy nuclei was best estimated by Binns et al. (1989) [3]. Abundance in the region 32^Z60, Pb-group (81-83) is substantially deficient. Elements of 62 ^SZ^S72, Pt-group (74-80) and actinides (Z>83) are substantially high, which suggests an enhanced r-process at the GCRS. The r-process enhancement Z>60 might indicate the admixture of some unusual r-process material (not the same as in the solar system). It seems evident that these physical conditions differ from those where the solar system material was produced. There are strong reasons for the precise abundance measurements of these nuclei with high charges. A high resolution study with good statistics would give important new information on the relative contributions of r- and s-process nucleosynthesis and on the evolution of galactic matter. An accurate measurement of the U/Th ratio will give a mean age of heavy cosmic rays from the time of nucleosynthesis, whose ratio may differ from the solar value [8]. The presence of transuranic nuclei would be the signature of a fresh r-process component in the cosmic rays, indicating recent nucleosynthesis occurred nearby our solar system. Higher precision measurements of the even Z nuclei would allow more detailed comparison with solar system, special source production of cosmic rays, and r- and s-process abundance. [B] Neutron-Rich Cosmic Ray Nuclei and Wolf Rayet-Stars The Wolf Rayet model predicts that a fraction of UH nuclei originate from the material emitted from Wolf-Rayet stars [7,9,10-12]. These massive stars are undergoing significant mass loss (~10-5 solar mass per year) by high-speed stellar winds (several thousand km/s). As a result, they have been stripped of their hydrogen envelopes, and He-burning products including 12C, 1 6 0, and 22Ne and are being expelled from their surface [9,11-13]. The high-speed winds make attractive sites for the acceleration of CRs to moderate energies. Material flowing from WCstars (carbon-rich WR stars) contains gas which has been processed through core-He burning, i.e. considerably enriched into 12C, 16 0 and 22Ne. This composition is making GCR source anomalies. If massive stars contribute significantly to the 12C, 16 0, arid 22Ne excesses at the CR sources, they should also enhance other neutronrich isotopes of UH CRs. The model also predicts that 67Zn, 69Ga, 71Ga, 70Ge, 80Kr, 82Kr, and 86Sr could be enhanced including enhanced abundance of light isotopes such as 12C, 1 6 0, and 22 Ne [14]. The charge region from Z=29 to 40 is relatively free of secondary production, because there are no abundant heavier nuclei and the HEAO-3 results indicate that CR nuclei with 31S=Z^S40 observed would be primary CRs in the observed flux of nucleil [5].

98 This charge region described above presents an opportunity to identify the contributions of several nucleosynthesis processes to GCRS material. In addition, problems of acceleration and propagation mechanism of CRs will be addressed from these measurements. [C] Elemental and Isotopic Composition in Solar and Interplanetary Energetic Particles Solar system abundance, especially isotopic ones, are actually based on the terrestrial material, while meteorites serve as the standard source for elemental abundance which is characterizing solar system material. Solar energetic particles present a direct sample of solar material that is used to study the most energetic acceleration processes that occur naturally in our solar system. Comprehensive survey of solar energetic particles (SEP) have shown that the elemental composition of solar corona differs from that of the photosphere in that the abundance of elements with first ionization potential (FIP) >10eV is depleted by a factor of about 4 relative to other elements. The difference apparently indicates that neutral species are less efficiently transported from the photosphere to the corona. The measurements of the SEP isotopic composition are presently available for only elements Z2S32. The uncertainties in the existing measurements for transiron elements are still large as results of statistical limits. With a greatly improved collecting power and excellent mass resolution, it will provide the systematic exploration of the rich storage bank of solar information. And we can make much progress in our knowledge of solar isotopic composition. Multi-satellite observation of particles with other missions and ground-based observations provide key diagnostics of coronal mass ejection (CME) source regions and initiation mechanisms. Multi-satellite observation and modeling activity are focused on the connection of interplanetary features to solar events, which leads to new insights to space weather application.

99 Table 1. Characteristics of Instrument for CORONA Experiment. Two compartments in the JEM-EF would be used CORONA experiment. CORONA experiment on the JEM-EF includes two large-area telescopes, SUNC and LTTA.

1

Spectrometer for Ultraheavy Nuclear Composition (SUNC) Charge identification Trajectory system + AE-detector + Velocity-detector Scintillating Fiber Matrix Trajectory system AE-detector Si- AE-detector Velocity-detector Aerogel Cerenkov detector Charge range Ne(10) - U(92) Charge resolution < 0.5 charge unit (fwhm) >3.0 GeV/n Energy range Geometric Factor 7.9 m2sr

2

Large Isotope Telescope Array (LITA) Isotope identification The well-established AE X E algorithm Multi-module array 16 (=4X4) modules 6.6-7.3m2sr Geometric Factor One telescope module 25( = 5 X5 Si-stacks) array 1 Stack Light isotopes from H through Mg 4 Stacks Heavy isotopes from Li through Kr 20 stacks Ultraheavy Isotopes from Mg through Ce Ultraheavy Isotopes from Mg Other 15 modules through Ce Each stack Two SFMs + 7 Si-AE detectors

Characteristics of LITA/module in the CORONA Telescope-1 Telescope-2 Telescope Units 1 stacks in 14-stacks in 1Module Module Charge range Mass range Charge resolution Mass resolution Energy range GF (cm2sr)

H(l)-Mg(12) M = 1 - 26 < 0.2q (fwhm) < 0.3 amu (fwhm) 10-200MeV/n 30.6 - 42.4

Li(3) - Kr(36) M = 6-86 < 0.3q (fwhm) < 0.4 amu (fwhm) 20 -400 MeV/n 122.4-169.4

Telescope-3 20-stacks in 1Module and 15 Modules Mg(12) - Ce(58) M = 24 -142 < 0.3q (fwhm) < 0.6 amu (fwhm) 20 -600 MeV/n 66408 - 72522

100

3

Instrumental Description

In order to achieve the scientific goal, CORONA program proposes two kinds of large area telescopes, called SUNC and LITA schematically shown in Fig.la-lc. SUNC is a large area spectrometer for ultraheavy composition in relativistic GCRs and LITA is a large isotope telescope array for solar and galactic particles from H to Ce with relatively low energies from 30 MeV/n to 400 MeV/n. [A] Spectrometer for Ultraheavy Nuclear Composition (SUNC) Telescope SUNC is a large area Si-Cerenkov detector telescope (Fig.la) which measure the elemental composition of heavy cosmic ray particles with relativistic velocity, especially elements beyond the iron-peak nuclei with high statistical precision. It has a total area of 4 (= 2 x 2) m2 to measure heavy nuclei, especially ultraheavy particles with Z2?60. The geometric factor is very large, 7.9 m2sr. With a long exposure of several years (2-3 years) in space, the SUNC will measure Pt/Pb elemental region, and even U and Th. SUNC will also search for trans-uranic nuclei such as Pu, Np, and Cm. The measurement could answer the question of whether cosmic rays are freshly synthesized material recently ejected from supernovae, or simply old local galactic interstellar material accelerated indirectly by passing supernova shock wave remnants. SUNC will be a sensitive detector for the measurements of the clocks in the actinide and trans-uranic nuclear region that would be a significant contribution of recent nuclear synthesis. SUNC shown schematically in Fig. la is a scintillation fiber matrix (SFM) combined with Cerenkov detectors. SFMs, which are also used for LITA, are placed on top two and bottom for the measurement of particle trajectory. And Si-detectors used as AE-detectors measure energy losses of relativistic nuclei in the Si medium and signals from Si-detectors coincident with SFM provide triggering signals. Aerogel Cerenkov detectors are used as a threshold detector for velocity determination. The characteristics of SUNC telescope is shown in Tablel. [B] Large Isotope Telescope Array (LITA) for Ultraheavy Cosmic Ray Observation The schematic configuration of the telescope (Large Isotope Telescope Array, LITA) is shown in Fig.la, Fig.lb and lc. LITA is a multi-module array (16 (= 4X4) modules : a module = 5X5 Si-stack array). It has a geometric factor of 6.65 - 7.27 m2sr in total which depends on the energy and incident species. In a telescope module, there are 25 Si-detector stack (see Fig.lb). One stack in one module is to measure light isotopes starting from H (Z=l) through Mg (Z=14). 4 stacks in the module measure isotopes from Li (Z=3) to Kr (Z=36), and other 20 stacks are for C (Z=6) - Ce (Z=56) isotopes. The remaining 15 modules measure heavy isotopes starting C (Z=6) through Ce (Z=58). Each stack consists of SFM and 7 AE detectors

101

in each unit (see Fig. lc). Measurements of particle trajectories are made by the use of SFM providing two-dimensional coordinates with an resolution (fwhm) of 0.5. SFM used for LITA are common to those for SUNC. Isotope identification can be made by the well-established AE X E algorithm. The characteristics of LITA telescope is shown in Tablel. [C] Electronics for CORONA Program The electronics box placed under bottom SFM in SUNC consists of digital processing circuits, CPU, low and high voltage supply and housekeeping monitor circuits. Analog electronics are installed nearby their detectors. The energy loss of particles entering the telescope is precisely measured by pulse height analyzers. The data produced by the SUNC/LITA contain pulse height and trajectory measurement for individual particles. CPU in each module categorizes the particle events to assign priority and optimize the mix of events. A small fraction of the data stream is used for housekeeping measurements. A valid particle event must penetrate at least top SFM and reach or penetrate the second SFM in the stack. For such events, the CPU reads a 14-bit pulse height from all of the Si-detectors including SFMs. To maximize the number of events sent to the ground, event data are compressed onboard. In addition to the data compression, diagnostic and calibration data will be sent back. The box is surrounded with by aluminum plate providing an RF shield around the module. CORONA instrument is covered with thermal blankets. CORONA's field of view is so wide that full FOV would be desired to be completely unobstructed. The structure should be designed to endure vibration and acoustic environment during launch.

4

Expected Performance

Species observed by CORONA experiment are ranging wide from H to U. The energy interval to be measured by the SUNC and LITA depends on elements. Some stacks used in the LITA experiment also measures hydrogen, helium and CNO flux which provide us the baseline in various particle events. Those fluxes are used as a baseline to examine the correlation with the fluxes of ultraheavy nuclei. The energy to be measured by SUNC and LITA is shown in Table 2 together with nuclear charge and mass resolutions expected. Clear separation of isotope masses for ultraheavy nuclei (Z2a50) in the GCRs is expected to be less than 0.20.25 amu (rms) by this Si-detector telescope array. And nuclear charge even for Pt and Pb groups will be clearly identified with about 0.2 charge unit (rms). SUNC has extremely large geometric factors. Total value of GF for SUNC becomes 7.9 m2 sr. It collects 2.0X108 Fe, 1100 Pt-group, 330 Pb with relativistic

102

energies for 3 years. A few year observation enables us to detect actinide elements and possibly to detect trans-uranium elements. Table 2 shows the number of ion events expected from SUNC for elements Fe to U [19]. LITA resolves isotopes starting from H isotopes up to at least M~110-120, and also abundant isotopes of heavier nuclei. The collecting power of such telescopes depends on the energy and species. The geometric factors GF for LITA are 30.6 - 42.4 cm2 sr for H -Mg isotopes, 122 -170 cm2 sr for Li - Kr isotopes and 6.6 -7.3 m2 sr for heavy isotopes which corresponds the geometric factor increased more than 300 times that for the GEOTAIL [16-18]. Approximate numbers for light nuclei of C with an integration four stacks for one year period of solar minimum to be collected by LITA will be >1.5 x 106. Approximate numbers for UH nuclei greater than Fe (Z=26) with an integration seven modules for 3 year period of solar minimum will be >2 x 106.

5

Necessity of Large-scaled Spacecraft Platform in Cosmic Ray Observation

The best location for performing this kind of measurements is outside the Earth magnetosphere to give the maximum number of particles. A polar orbiter of the nearEarth would be possible but the efficiency for collecting particles would become small. Because of the orbit of the Space Station which resides inside the Earth magnetosphere, rigidity cutoff effect decreases the intensity of low energy particles by about a few % compared to the outside of the Earth magnetosphere. Here we describe the necessity of cosmic ray observation using the polar orbiter or orbiter with high inclination. The intensity of heavy elements, especially trans-iron species in the cosmic ray, is extremely small so that the enlargement of the telescope and continuous observations for a long term are indispensable. Heavy element observations are not achieved on the ground. Only by using the large-scale satellites or the space station, meaningful results can be established. The advantages in the observation using the polar orbiter are: - Continuous observation over a few years - Small contamination of secondary cosmic rays from the atmosphere - Large and relatively heavy scientific payload acceptable - Large electric power available - High telemetry Particle telescope proposed in the CORONA program will accomplish a largescaled observation with high accuracy and high sensitivity that has never been realized before. The large-scale isotope observation has not been proposed elsewhere in the world. Relativistic particle observation up to the knee-energy

103

region is adopted as the ACCESS/KLEM-3 project using Space Station base, but the isotope observation is not included. The ENTICE program [20] is quite similar to the CORONA one except for the isotope measurement. ECCO would be dedicated to the observation of UH (Z>70) nuclei in GCR using the large-area glass detectors. ENTICE and ECCO would join together and a new experiment called HNX will start using space shuttle. Those projects have been proposed as a second-period observation plan of the Space Station experimental module. Therefore, it is important to execute the CORONA experiment in the same period or earlier than that the ACCESS/HNX and KLEM experiments. From this point of view, it is essential to achieve the CORONA program in the second-period observation time at least of the JEM-EF, or another choice is to collaborate a joint experiment with Russia and/or US using large satellite platform. International cooperative system with Russia/US and other countries will be a great help to promote researches and make a new progress in cosmic ray research. 6

Concluding Remark

A high quality and continuing series of observations of solar and galactic cosmic rays provide important exploratory data. Definitive measurements are now close to the availability of spacecraft capable of carrying very large scientific payloads for long extended period of years. Scientific objectives in such measurements are to determine the composition of rare ultraheavy nuclei up to uranium and trans-uranium at high energies and isotopic abundance above iron-peak elements. In these research fields, we have no date at all or still lack of decisive data that could characterize the origin of cosmic rays, the nucleosynthesis processes leading to cosmic ray matter and governing the chemical evolution of our galactic matter. And we are also short of definitive data that could further provide the understanding of the structure and properties of the interstellar medium, and the acceleration and transport mechanism of cosmic ray particles in the galaxy. In order to achieve the objectives, a large spacecraft platform and/or the International Space Station are best suited in the multilateral cooperation with Japan and other countries. The CORONA program is the large-scaled observation program of nuclear particles with high precision. Continuous observations of solar, interplanetary and galactic particle events would be observed on exposure facility in space like the JEM of International Space Station, Shuttle experiment and or Russian satellites with international collaboration with Russia and other countries. The development team for the CORONA Program is at present organized from core members in GEOTAIL HEP team and some other scientists from AoyamaGakuin Univ., Chiba Univ., and National Institute for Radiological Science, RIKEN, and SNI of Moscow State University as key institute as the Russian counterpart.

104

7

Acknowledgements

We appreciate the cooperative work with Dr. Shibata at Aoyama-Gakuin University, Dr. Uchihori at NIRS, Dr. Takashima at Nagoya University, Dr. Tanihata at RIKEN, and Dr. Kawai at Chiba University in the development of detectors. References 1. N. Hasebe, Cosmic Radiation, 1(1999)15-30 in Japanese. 2. N. Hasebe, Doke-Symposium. 3. W.R. Binns. et al., Proc. AIP Conf., Cosmic Abundance of Matter, 183(1989a)147. 4. W.R. Binns. et al., Astrophys. J., 297(1985)111. 5. W.R. Binns. et al., Astrophys. J., 346(1989)997. 6. P.H. Fowler, Astrophys. J., 314(1987)739. 7. J.P. Meyer, Proc. 17th Int. Cosmic Ray Conf. (Paris), 2(1981)3265. 8. A.J. Westphal et al., Proc. 24th Int. Cosmic Ray Conf. (Rome) 2(1995)581. 9. J.P. Meyer, L.O'C. Drury and D. Ellison, Astrophys. J., 487(1997)182. 10. M. Casse and J.A. Paul, Astrophys. J., 258(1982) 860. 11. A. Maeder, Astron. Astrophys., 120(1983)130. 12. N. Prantoz, M. Arnold and J.P. ArCoragi, Astrophy. J., 315(1987)209. 13. J.P. Meyer, Proc. 19th Int. Cosmic Ray Conf. (Calgary), 2(1985)141. 14. R.A. Mewaldt, Proc. AIP Conf., Particle Astrophysics, 203 (1990)268. 15. N. Prantoz et al., Proc.l9th Int. Cosmic Ray Conf. (Calgary), 3(1985)167. 16. T. Doke et al., J. Geomag. and Geophys., 46(1994)713. 17. N. Hasebe et al., Jpn. J. Appl. Phys., 31(1992)1191. 18. N. Hasebe et al., Nucl. Instrum. and Methods, Phys. Res.,A325(1993)335. 19. W.R. Binns. et al., Proc. AIP Conf., Particle Astrophysics, 203(1990)231. 20. W.R. Binns. et al., Proc. 25th Int. Cosmic Ray Conf. (Durham) 1(1997)65.

III. Stellar Evolution and the Nucleosynthesis - Hydrostatic Burning -

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Direct Capture S-factors from Asymptotic Normalization Coefficients R.E. Tribble, A. Azhari, H.L. Clark, C.A. Gagliardi, Y.-W. Lui, A.M. Mukhamedzhanov, A. Sattarov, X. Tang, L. Trache Cyclotron Institute, Texas A&M University, College Station, Texas 77843 V. Burjan, J. Cejpek, V. Kroha, S. Piskof, J. Vincour Institute for Nuclear Physics, Czech Academy of Sciences, Prague-Rez, Republic F. Carstoiu Institute for Atomic Physics, Bucharest,

Czech

Romania

Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANC). These coefficients, which provide the normalization of the tail of the overlap function, determine S-factors for direct capture reactions at astrophysical energies. A variety of proton transfer reactions have been used to measure ANC's. As a test of the technique, the 16 0( 3 He,d) 17 F reaction has been used to determine ANC's for transitions to the ground and first excited states of 1 7 F. The S-factors for le O(p,7) 17 F calculated from these 17 F -+ 1 6 0 + p ANC's are found to be in very good agreement with recent measurements. Following the same tech­ nique, the 10 B( 7 Be, 8 B) 9 Be and 14 N( 7 Be, 8 B) 13 C reactions have been used, along with optical model parameters for the radioactive beams that were obtained from a study of elastic scattering of loosely bound p-shell nuclei, to measure the ANC ap­ propriate for determining 7 Be(p,7) 8 B. The results from the two transfer reactions provide an indirect determination of S 17(0).

1

Introduction

Stellar evolution involves sequences of capture reactions and beta decays. Pre­ dicting the evolution of a star requires knowing reaction rates and half lives. Direct capture reactions of astrophysical interest usually involve systems where the binding energy of the captured proton is low. Hence at stellar energies, the capture proceeds through the tail of the nuclear overlap function. The shape of the overlap function in this tail region is completely determined by the Coulomb interaction, so the amplitude of the overlap function alone dic­ tates the rate of the capture reaction. The 7 Be(p,7) 8 B reaction is an excellent example of such a direct capture process. Indeed recent calculations of the nor­ malization constant have been used to predict the capture rate 1'2. But new measurements, both direct and indirect, are still needed as was underscored in a recent review of stellar reaction rates 3 which includes a detailed discussion of the uncertainties in our present knowledge of Si7(0) and its importance to

107

108

the solar neutrino problem. The asymptotic normalization coefficient (ANC) C for A+p ++ B specifies the amplitude of the tail of the overlap function for the system. In previous communications 1 ' 4 , we have pointed out that astrophysical S-factors for pe­ ripheral direct radiative capture reactions can be determined through measure­ ments of ANC's using traditional nuclear reactions such as peripheral nucleon transfer. Direct capture S-factors derived with this technique are most reliable at the lowest incident energies in the capture reaction, precisely where capture cross sections are smallest and most difficult to measure directly. Of course it is extremely important to test the reliability of the technique in order to know the precision with which it can be applied. Determining the S-factors for 1 6 0(p,7) 1 7 F from its ANC's has been recognized as a suitable test for this method 3 because the results can be compared to existing direct measurements of the cross sections 5,6 . Furthermore, the 1 6 0(p,7) 1 7 F reaction has substantial similarities to the 7 Be(p,7) 8 B reaction. As part of an ongoing program to mea­ sure ANC's, we have used the proton exchange reactions 9 Be( 10 B, 9 Be) 10 B and 13 C( 1 4 N, 1 3 C) 1 4 N to measure the ANC's for 10 B -> 9 Be + p and 14 N ->• 13 C + p. Below we briefly summarize these results. This is followed by a discus­ sion of a measurement of the another proton transfer reaction, 1 6 0( 3 He,d) 1 7 F, which is used to determine the ANC's for the ground and first excited states in 1 7 F . From these ANC's, we calculate S-factors for both 9 Be(p,7) 10 B and 16 0(p,7) 1 7 F and compare to experimental results. Finally we discuss our mea­ surement of the 10 B( 7 Be, 8 B) 9 Be and 14 N( 7 Be, 8 B) 13 C reactions, the extraction of the ANC's for 8 B -»• 7 Be + p and our determination of Si7(0).

2

A N C ' s from Proton Transfer Reactions

Traditionally spectroscopic factors have been obtained from proton transfer reactions by comparing experimental cross sections to DWBA predictions. For peripheral transfer, we show below that the ANC is better determined and is the more natural quantity to extract. Consider the proton transfer reaction a + A -» c + B, where a = c + p, B = A + p. As was previously shown 7 we can write the DWBA cross section in the form &1 _ V^ (CAplBjB) jBja

AplBJB

iCcpUjJ

~DW

m

Cplaja

where aP^f , „• is the reduced DWBA cross section and ji,U are the total and orbital angular momenta of the transferred proton in nucleus i. The factors bcpUja and bApiBjB a r e t n e ANC's of the bound state proton wave functions in

109

nuclei a and B. If the reaction under consideration is peripheral, the ratio frDW T>

_

iBJBlgja

AplBjB

(n\

°cplaja

is independent of the single particle ANC's bApiBjB a n ( i bcptaja. Thus for surface reactions the DWBA cross section is best parametrized in terms of the product of the square of the ANC's of the initial and final nuclei ( C B ) 2 ( C a ) 2 rather than spectroscopic factors. We have used this formulation to extract ANC's from the peripheral pro­ ton transfer reactions 9 Be( 10 B, 9 Be) 10 B, 13 C( 14 N, 13 C) 14 N and 1 6 0( 3 He,d) 1 7 F. The first two reaction studies were carried out with beams of 10 B and 14 N from the K500 superconducting cyclotron at Texas A&M University. Both elastic scattering and transfer reaction products were measured in the MDM spectrometer. Details of the experiments can be found in 7 ' 8 , including the re­ sults of DWBA fits using the code PTOLEMY 9 with optical model parameters obtained from an analysis of the elastic scattering and the extracted ANC's. The 1 6 0( 3 He,d) 1 7 F reaction was measured previously at a beam energy of 25 MeV 10 . We repeated the measurement at 29.75 MeV in order to obtain better angular coverage and to have a measurement at a second energy, both of which were necessary for extracting reliable ANC's. Data at laboratory scat­ tering angles between 6.5° and 25° were obtained using Si solid state detectors and a 3 He beam, incident on a 134 /zg/cm2 Mylar target, from the U-120M isochronous cyclotron of the Nuclear Physics Institute of the Czech Academy of Sciences. Additional data at laboratory angles between 1° and 11° were obtained using the MDM magnetic spectrometer and a molecular (3He—d)+ beam, incident on a 540 fig/cm2 Mylar target, from the Texas A&M University K500 superconducting cyclotron. Absolute cross sections were determined at the NPI using their detection system which has been well calibrated for (3He,d) reaction studies. The data obtained at TAMU were normalized to the data from the NPI measurement in the region where the two data sets overlapped. More details of the experiments can be found in 1 1 . In order to extract ANC's, DWBA calculations were carried out with the finite range code PTOLEMY, using the full transition operator. A check on the extracted ANC's versus Woods-Saxon well radial parameters indicated that the calculated DWBA cross sections are insensitive to assumptions about the 17 F wave functions in the nuclear interior. A range of optical model parameter sets was studied for both the entrance and exit channels, as detailed i n 1 1 . Normalizing the DWBA calculations to the data and dividing by the ANC's for the single particle orbitals yields the product of the ANC's for the 1 7 F -»■ 1 6 0 + p and 3 He -> d + p systems. Dividing this product by the known ANC for 3 He

110

-»• d 4- p 1 2 ' 1 3 provides C 2 for 1 7 F -»• 1 6 0 + p. The dominant contribution to the uncertainties is due to the variation in the extracted ANC's with different optical model parameter sets. Our final adopted ANC's are C 2 = 1.08(10) fm _ 1 and 6490(680) fin-1 for the ground and excited states, respectively. 3

Using A N C ' s to Predict Astrophysical S-Eactors: Test Cases

The ANC's found from the proton transfer reactions can be used to determine direct capture rates at astrophysical energies. Astrophysical S-factors have been determined for both 9 Be(p,7) 10 B and 1 6 0(p,7) 1 7 F as tests of the tech­ nique. The relation of the ANC's to the direct capture rate at low energies is straightforward to obtain. The cross section for the direct capture reaction A + p -> B + 7 can be written as a = A||2,

(3)

where A contains kinematical factors, I%p is the overlap function for B -> A+p, O is the electromagnetic transition operator, and ip\ ' is the scattering wave in the incident channel. If the dominant contribution to the matrix element comes from outside the nuclear radius, the overlap function may be replaced by W 2Kr)

lUr)*C ->»f

,

(4)

where C defines the amplitude of the tail of the radial overlap function I%p, W is the Whittaker function, r\ is the Coulomb parameter for the bound state B = A+p, and n is the bound state wave number. The required C's are just the ANC's found above from transfer reactions. Thus, the direct capture cross sections are directly proportional to the squares of these ANC's. Using the results outlined above, the S-factors describing the capture to both the ground and first excited states for 1 6 0(p,7) 1 7 F were calculated, with no additional normalization constants. The results are shown in Fig. 1 com­ pared to the two previous measurements of 1 6 0 ( p , 7 ) 1 7 F 5 ' 6 . Both E l and E2 contributions have been included in the calculations, but the E l components dominate the results. The theoretical uncertainty in the S-factors is less than 2% for energies below 1 MeV. Above 1 MeV the nuclear interaction begins to be important in the evaluation of the scattering wave function. The agreement between the measured S-factors and those calculated from our 1 7 F —> 1 6 0 + p ANC's is quite good, especially for energies below 1 MeV where the ap­ proximation of ignoring contributions from the nuclear interior should be very

111

Ep(MeV) Figure 1: A comparison of the experimental S-factors to those determined from the ANC's found in 1 6 0 ( 3 H e , d ) 1 7 F . The solid data points are from 5 , and the open boxes are f r o m 6 . The solid lines indicate our calculated S-factors, and the dashed lines indicate the ±1
reliable and the optical potential uncertainties are negligible. Overall, the re­ sults verify that the technique is valid for determining S-factors to accuracies of at least 9%. The S-factor for 9 Be(p,7) 10 B has contributions from both resonance and direct capture at stellar energies. Thus the connection between the ANC and the capture cross section is more complicated and is discussed in a separate publication 15 . Our measurement of the ANC's for 10 B —► 9 Be -I- p fixes the direct capture component. With this result, an R-matrix fit was made to the existing d a t a 1 6 using the known locations of the resonance states and their widths. The fit 15 , which is shown in Fig. 2, does an excellent job of reproducing the data. Prior to our determination of the direct capture contribution, similar attempts to fit the data required substantial changes in the known resonance positions and widths.

112 10 2

-Q

> in

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Ec.ra. (MeV) Figure 2: The result of an R-matrix fit to the direct plus resonance contributions to the S-factor for 9 Be(p,7) 10 B. Standard resonance widths and positions were used in the fit. The direct capture contribution to the S-factor is the dashed line.

4

A N C ' s for stellar processes

We have measured the ( 7 Be, 8 B) reaction on a 1.7 mg/cm 2 1 0 B target 1 7 and a 1.5 mg/cm 2 Melamine target 1 8 in order to extract the ANC for 8 B -> 7 Be + p. The radioactive 7 Be beam was produced at 12 MeV/u by filtering reaction products from the 1 H( 7 Li, 7 Be)n reaction in the recoil spectrometer MARS, starting with a primary 7 Li beam at 18.6 MeV/A from the TAMU K500 cy­ clotron. The beam was incident on an H 2 cryogenic gas target, cooled by LN 2 , which was kept at 1 atm. (absolute) pressure. Reaction products were mea­ sured by 5 cm x 5 cm Si detector telescopes consisting of a 100 fan AE strip detector, with 16 position sensitive strips, followed by a 1000 pim E counter. A single 1000 /xm Si strip detector was used for initial beam tuning. This detector, which was inserted at the target location, allowed us to optimize the beam shape and to normalize the 7 Be flux relative to a Faraday cup that measured the intensity of the primary 7 Li beam. Following optimization, the approximate 7 Be beam size was 6 mm x 3 mm (FWHM), the energy spread was « 1.5 MeV, the full angular spread was A# « 28 mrad and A 0 « 62 mrad, and the purity was >99.5% 7 Be for the experiment with the 1 0 B target. The beam size and angular spread were improved for the experiment with the

113 14

N target to 4 mm x 3 mm (FWHM), A0 « 28 mrad and A<j> » 49 mrad. Periodically during the data acquisition, the beam detector was inserted to check the stability of the secondary beam tune. The system was found to be quite stable over the course of the experiment with maximum changes in intensity observed to be less than 5%. The typical rate for 7 Be was « 1.5 kHz/pnA of primary beam on the production target. Primary beam intensities of up to 80 pnA were obtained on the gas cell target during the experiments. In order to extract ANC's from reactions involving radioactive-ion beams, it is necessary to have optical model parameters. Typically radioactive beam intensities are too small to measure elastic scattering and obtain good optical model parameters. Consequently we have carried out a series of elastic scat­ tering measurements with stable beam and target combinations that are close to those for our radioactive beam measurements. We used the folding model prescription to calculate the potential parameters and then renormalized the real and imaginary parts of the potentials to fit the data. Several different in­ teractions were tried but the most consistent results were found to be from the JLM interaction 19 . The renormalization coefficients were found to be 0.366 ± 0.014 for the real potential and 1.000 ± 0.087 for the imaginary potential. The uncertainties listed were from the dispersion in the renormalization coefficients that we found for the different reactions 20 . The large renormalization for the real part of the optical potential is mostly due to dynamic polarization effects which are not fully accounted for in the folding model. With these poten­ tial parameters, it is now possible to calculate elastic scattering and transfer reactions for loosely bound p-shell systems. Elastic scattering angular distributions for 7 Be on the 1 0 B and 14 N targets are shown in Fig. 3. For the 1 0 B target, the elastic scattering yield includes con­ tributions from three target components, 10 B(86%), 12 C(10%) and 1 6 0(4%), while the Melamine target includes 14 N(67%), 12C(28%) and ^ ( 5 % ) . A Monte Carlo simulation described below was used to generate the solid angle factor for each angular bin and the smoothing needed for the calculation to account for the finite angular resolution of the beam. The absolute cross section is then fixed by the target thickness, number of incident 7 Be, the yield in each bin, and the solid angle. The curves shown with the elastic scattering were found from the optical model, with the parameters discussed above, by adding together the cross section predictions for the target components in the labo­ ratory frame and then transforming the result to the center of mass assuming kinematics appropriate for either the 1 0 B or 14 N targets. In both cases, the optical model calculations are compared to the data without additional nor­ malization coefficients. The detector resolution is not sufficient to distinguish inelastic excitations from elastic scattering. This likely explains why the data

114

10

15

20

25

30

35

tfc.m. ( d e g )

Figure 3: Angular distributions for elastic scattering from the 10 B and 14N targets. The dashed curves are from optical model calculations of the target components and the solid curves are smoothed over the angular acceptance of each bin.

exceed the calculations in the minima. Overall, the agreement between the measured absolute cross sections and the optical model predictions is excellent thus providing confidence that our normalization procedure is correct. a

10

The 8 B Q-value spectra, shown in Fig. 4, were obtained by assuming either B( 7 Be, 8 B) 9 Be or 14 N( 7 Be, 8 B) 13 C reaction and correcting the 8 B reaction

115

-14

-12

-8

-10

-6

Q (MeV) 200

-14

-12

-10

Q (MeV) Figure 4: Q-value spectra for 8 B reaction products on the 10 B (top panel) and Melamine targets (bottom panel). The three peaks in the 10 B target spectrum correspond to the excitation of the ground state and second excited states of 9 Be and the ground state in 18 N from the l e O contamination in the target. Data for the Melamine target show a clear isolation of the ground state for 1 3 C.

products for kinematic energy shifts as a function of scattering angle. In the case of the 10 B target, the major contributions to the energy resolution are the beam energy spread, the target thickness and the nonuniformity of the target. The beam energy spread and differential energy loss in the target dominated the energy resolution for the Melamine target. Since the ground state of 9 Be is not cleanly separated from excited states, a Monte Carlo simulation of the experiment has been used to fix the line shape and determine cross sections.

116

The simulation, which is fine tuned to reproduce the measured beam properties and the resolution observed in elastic scattering, includes the geometry of the experimental setup, reaction kinematics, nonuniform energy loss in the target and the size, angular spread and energy spread of the beam. The beam location and angle at the target are determined by symmetry requirements on 7 Be elastic scattering data. The three peaks shown in Fig. 4 for the 1 0 B target correspond to the excitation of the ground and second excited states of 9 Be and the ground state of 15 N from the 1 6 0 contamination in the target. They were obtained by including the predicted angular distributions for the states in the Monte Carlo simulation and then extracting the associated Q-value spectrum. The normalization of the three peaks was done by a x2 minimization to the data. The cross section ratio for transitions to the ground and second excited states in 9 Be is in good agreement with theoretical expectations 21 . In the Melamine case, the ground state of 13 C is cleanly resolved from excited states making the normalization of the Q-value spectrum via the Monte Carlo simulation straight forward. The ANC for 8 B -> 7 Be + p was extracted based on the fit to the Q-value spectra and the ANC's 7 ' 8 for 1 0 B ->■ 9 Be + p and 14 N -> 13 C + p following the procedure outlined above in our test case. Two 8 B orbitals, lpi/2 and 1P3/2) contribute to the transfer reaction but the lp 3 /2 dominates in both cases. In calculating the angular distributions, we used the ratio for the two orbitals as given by a microscopic description of the 8 B ground s t a t e 4 . The optical model parameters were obtained from renormalized microscopic folding potentials using the JLM effective NN interaction 19 described above. The entrance channel parameters were the same as those used in calculating the elastic scattering angular distributions for 7 Be on 1 0 B and 14 N in Fig. 3. We have checked the sensitivity of the calculations by varying the normalization parameters. As in previous studies, the results are insensitive to bound state single particle well parameters in the DWBA calculations. Angular distributions for the ( 7 Be, 8 B) reactions populating the ground states of 9 Be and 13 C were extracted using the same procedure as for the elastic scattering. The results are compared to DWBA calculations in Fig. 5. The normalization factors between the data and calculations were obtained from the fits to the respective Q-value spectra. The astrophysical S-factor for 7 Be(p,7) 8 B has been determined from the ANC which includes an 8.1% uncertainty for optical model parameters, an uncertainty for experimental fits and normalization of the absolute cross section of 10.9% for the 10 B target and 8.1% for the 14 N target and the uncertainty in the ANC's for 1 0 B -> 9 Be + p and 14 N -» 13 C + p. The relative contribution of the two angular momentum couplings to the S-factor is straightforward to

117

10

15

20

25

30

tf=.m. ( d e g )

5

10

t5

20

^.m. ( d e g ) Figure 5: Angular distributions for 8 B populating the ground state of 9 Be from the 10 B target and I 3 C from the Melamine target. In the top figure, the dashed curve shows the result of a DWBA calculation for the dominant component that contributes to the cross section. Two components are shown in the bottom figure. In both cases, the solid curve is smoothed over the angular acceptance of each bin.

calculate and introduces a negligible additional uncertainty in our result 1>4 . The values that we find are Si7(0) = 18.4 ± 2.5 eV b for the 1 0 B target and 16.6 ± 1.9 eV b for the 14 N target, which are in good agreement with the recommended value 3 of 19J]4, eV b. One of the primary sources of uncertainty in the values quoted above for Si7(0) is the optical model parameters that are used to predict the angular

118

distribution. As indicated, we have developed a set of global optical model parameters for use with radioactive beams in this mass and energy region. Since the optical model parameters for the two different targets are derived by the same technique, this introduces correlations in the uncertainties between the two results. Accounting for this correlation, we find the S-factor from the combined measurements to be 17.2 ± 1.8 eV b. Recently we completed a measurement of the 1 4 N( 1 1 C, 1 2 N) 1 3 C reaction with a U C beam at about 110 MeV. Following the analysis of these data we will determine the direct capture rate for the 11 C(p,7) 12 N reaction which is important for stellar burning in low metallicity massive stars. This work was supported in part by the U.S. Department of Energy under Grant number DE-FG05-93ER40773 and by the Robert A. Welch Foundation. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

H.M. Xu et al, Phys. Rev. Lett.73, 2027 (1994). L.V.Grigorenko et al, Phys. Rev. C 57, R2099 (1998). E.G. Adelberger et al, Rev. Mod. Phys. Vol. 70(4), 1265 (1998). A.M. Mukhamedzhanov and N.K. Timofeyuk, J E T P Lett. 51, 282 (1990). R. Morlock et al, Phys. Rev. Lett. 79, 3837 (1997). H.C. Chow, G.M. Griffith and T.H. Hall, Can. J. Phys. 53,1672 (1975). A.M. Mukhamedzhanov et al., Phys. Rev. C 56, 1302 (1997). L. Trache et al, Phys. Rev. C 58, 2715 (1998). M. Rhoades-Brown, M. McFarlaneand S. Pieper, Phys. Rev. C 2 1 , 2417 (1980); Phys. Rev. C 2 1 , 2436 (1980). J. Vernotte et al, Nucl. Phys. A571, 1 (1994). C.A. Gagliardi et al, Phys. Rev. C 59, 1149 (1999). M. Kamimura and H. Kameyama, Nucl. Phys. A508, 17c (1990). A.M. Mukhamedzhanov, R.E. Tribble and N.K. Timofeyuk, Phys. Rev. C 51, 3472 (1995). R. Morlock, private communication. A. Sattarov et a/., Phys. Rev. C 60, 035801 (1999). D. Zhanow et al, Nucl. Phys. A589, 95 (1995). A. Azhari et al, Phys. Rev. Lett. 82, 3960 (1999). A. Azhari et al, Phys. Rev. C 60, 035801 (1999). J.P. Jeukenne, A. Lejeune and C. Mahaux, Phys.Rev. C 16, 80 (1977). L. Trache et al, Phys. Rev. C, in press. S. Cohen and D. Kurath, Nucl. Phys. 73, 1 (1965).

SOLAR NEUTRINO PROBLEM RELATED NUCLEAR PHYSICS EXPERIMENTS

WEIPING LIU'' 5 , XIXIANG BAI', SHUHUA ZHOU', ZHANWEN MA U - ZHICHANG LI 1 , YOUBAO W A N G ' 3 , ANLI LI', ZHONGYU MA', BAOQIU CHEN', XIAODONG TANG'- 4 , YINLU HAN', QINGBIAO SHEN' AND JINCHENG XU' 'China Institute of Atomic Energy, P.O. Box 275(46), Beijing 102413, P. R. China E-mail: wpliu@iris. ciae. ac. en 2

3

Department

Department

of Physics and Astronomy, 401 Nielsen Physics Building, The University of Tennessee, Knoxville, Tennessee 37996-1200, U.S.A

of Physics, University ofJyvaskyla,

P.O. Box 35 (Y5), 40351, Jyvaskyla,

Finland

4

Cyclotron Institute, Texas A&M University, College Station, Texas 77843, U.S.A

M. HELLSTROM 5 - 6 , R. COLLATZ 6 , J. BENLLIURE 6 , L. CHULKOV 7, D. CORTINA GIL 6 , F. FARGET 6 , H. GRAWE 6 , Z. HU 6 , N. IWASA 6 - 8 , M. PFUTZNER6-9, A. PIECHACZEK 1 0 , R. RAABE 1 0 ,1. REUSEN 10, E. ROECKL 6 , G. VANCRAEYNEST' 0 , A. WOHR 10 5

Lund University, Department of Physics, Division of Cosmic and Subatomic Physics, P.O. Box 118, S-22100 Lund, SWEDEN 6

Gesellschaftfur

Schwerionenforschung,

7

D-64291 Darmstadt,

Kurchatov Institute, 123182 Moscow, Russian

8

Germany

Federation

RIKEN, Institute of Physical and Chemical Research, Saitama 351-01,

9

Institute of Experimental

Japan

Physics, University of Warsaw, PL-00681 Warsaw,

'"Institut voor Kern-en Stralingsfysika,

Katholieke Universiteit, B-3030 Leuven,

Poland Belgium

The two measurements, performed in connection with the solar neutrino problem, are described. The 7Be(d,n)8B reaction was measured at E cm = 5.8 and 8.3 MeV for deducing the Sn(0) factor for the 7Be(p,y)8B reaction. The angular distribution data were analyzed by using a distorted-wave Born approximation. The S,7(0) factor for the 7Be(p,Y)8B reaction was derived to be 27.4±4.4 eV b through the asymptotic normalization constant extracted from the experimental data. The (3-decay of 4
119

120 40

Ti p-decay strength, the neutrino absorption cross-section was determined to be (14.3+ 0.3)xl0-4' cm2.

1

1.1

Introduction

The solar neutrino problem

The neutrinos that are produced by fusion reactions in the interior of sun provide most valuable information on our understanding of the physical processes inside the sun and of the electroweak interaction theory concerning the basic properties of neutrino [1], For more than 20 years, the comparison between experimental results (Homestake, Kamiokande, Gallex and Sage.) and the theoretical predictions have yielded the so-called solar neutrino problem [1]. It refers to the fact that the measured solar neutrino flux is significantly lower than that of the solar model predictions. Over the years, the large communities of astrophysics and of nuclear physics took enormous efforts in solving this problem. Based on all the information available experimentally and theoretically, it seems that a solution can only be found by introducing a new physics [1]. On the new physics explaining the missing solar neutrinos, especially the complete missing of 7Be neutrinos after evaluating the results of the available experiments, the most promising scenario is based on neutrino oscillation. Very recently, the Super-Kamiokande group announced the finding of neutrino oscillation - the first experimental observation of non-zero neutrino mass [2]. To confidentially reach such a conclusion, it is very important to carefully check the uncertainties in the terrestrial neutrino experiments and in the solar model calculations for neutrino production. For example, the different treatments of the diffusion effect in the different solar models resulted in neutrino fluxes that differed by 31 % [3]. Furthermore, the different selections of solar and nuclear physics parameters in these two models produced results differed by up to 62 % from each other [3]. Apparently, these differences were much larger than the uncertainties assigned to a single solar model [1]. Therefore, apart from a 'solar neutrino problem', there appears to be also a 'solar model problem'. Thus it is desirable to reach to agreement in treating the diffusion effects and in selecting the nuclear and astrophysical input parameters in solar model calculations. In this context, nuclear physics can make a significant contribution. In a solar model calculation, the uncertainties of nuclear reaction cross sections, such as those of 7Be(p,y)8B, contribute significantly to the uncertainties associated with the solar model prediction of neutrino fluxes [1]. However, in order to compare the prediction of a given solar model with the solar neutrino experiments, the neutrino fluxes predicted by this model have to be translated into reaction rates by using the nuclear absorption cross section of the detector material. Therefore, another

121

important nuclear physics contribution consists in an accurate determination of the absorption cross section in the relevant detector material. The Homestake experiment (neutrino detection via 37C1 inverse P-decay) and the proposed ICARUS experiment (neutrino detection using 40Ar inverse P-decay) may serve as examples. This argument is expressed in the following simple formula: Predicted reaction rates = Absorption cross section (nuclear physics input, e.g. 37Ca or 40Ti P-decay)x Solar neutrino flux (solar model + nuclear physics input, e.g. 7 Be(p,y)8B reaction) Moreover, the attempt to minimize the uncertainties of neutrino detection has lead to new generation detectors [4], which aim not only at measuring the neutrino flux of individual branches (pp, pep, 7Be and 8B) but also at detecting neutrino oscillation. The latter phenomenon is studied by measuring • the distortion of the neutrino energy spectra compared with solar model prediction (Super-Kamiokande), 7 • Be neutrino (Borexino), • the complete fluxes of neutrinos independent of their flavor (SNO), • the day-night difference of neutrino fluxes as predicted by MSW theory or seasonal difference as predicted by VO (Super-Kamiokande), • the ratio between the electron neutrino with neutrinos of all flavors (ICARUS). Apart from the observation of solar neutrinos, the long base line experiments such as K2k provide an alternative way for measuring the possible neutrino oscillations. Here ICARUS detector will serve as an neutrino detector. In the present paper, I shall give a detailed description of my contributions to two experiments which both yield to the nuclear physics data relevant to the solar neutrino problem. The first one is the determination of the 7Be(p,y)8B cross section [5], responsible for the 8B neutrino flux, the second one is the measurement of 40Ti P-decay [6], which is related to the 40Ar absorption cross section in the ICARUS detector. 1.2

7

Be(p,y)8B reaction

The high energy neutrinos from the p+ decay of 8B produced via the 7Be(p, y)8B reaction at solar energies play a very important role in the solar neutrino problem [1], as explained in Section 1.1. Therefore, the astrophysical Sl7(0) factor for the 7 Be(p, y)8B reaction has attracted an increasing attention for many years. There were a number of considerable efforts to study the SI7(0) factor through both direct radiative capture reaction [7, 8] and Coulomb dissociation reaction of 8B [9]. However, the obvious disagreement among the experimental results is still a challenging puzzle. Therefore further experiments were called for to reduce the uncertainties of the Sl7(0). Recently, the proton pickup reactions of 7Be were proposed as an indirect way to extract the S/7(0) factor by introducing a simple relation between the asymptotic normalization constant (ANC) and the S17(0) factor [10]. This approach was expected to yield the Sl7(0) factor with an accuracy at least

122

comparable to that of direct radiative capture or Coulomb dissociation reactions, and could thus provide a valuable cross examination as an independent method. We carried out a measurement of cross section and angular distribution of the protonpickup 7Be(d,n)8B reaction using a radioactive 7Be beam. /. 3

40

Ti P-decay and ICARUS detector

In the ICARUS detector [11], the energy and the direction of the electrons scattered by the incoming solar neutrinos, as well as of the electrons produced in the inverse P-decay 40Ar(ve,e")40K, can be measured in a large-volume liquid argon time-projection chamber. Since the inverse P-decay to the 40K ground state is forbidden, each neutrino-absorption event is accompanied by y-rays emitted from excited 40K levels, which produce Compton electrons. In this way the electron multiplicity distinguishes scattering and absorption events, making it possible to measure the ratio between these two types of events. This ratio is independent of the total neutrino flux impinging on a terrestrial detector whereas it depends significantly on possible neutrino oscillations. This is due to electrons being scattered by electron neutrinos as well as by \i and T neutrinos while the production of electrons via neutrino absorption is restricted to only electron neutrinos. Furthermore, quantitative information on the oscillation probability ue-H)^ T can be obtained from the experimental ratios. As indicated in Section 1.1, the cross sections for the different interaction processes must be known very well for a reliable evaluation of the ICARUS data. The scattering rates can be accurately calculated by using the standard electroweak theory [12], whereas the situation is more complicated for the case of neutrino absorption. While the value for the Fermi transition strength B(F) between the 40Ar ground state and the isobaric analog state (IAS) in 40K is given by the modelindependent sum-rule, it is more difficult to determine the transition strengths B(GT) for the individual contribution of allowed Gamow-Teller (GT) transitions to the neutrino-capture rate. In principle, the B(GT) values for the inverse P-decay can be deduced by using shell-model theory or from data measured for the zero-degree charge-exchange reaction 40Ar(p,n)40K. However, as has recently been shown, shellmodel calculations failed to reproduce the B(GT) distributions measured in the region around 40Ca [13]. Furthermore, the proportionality of P-decay transition strengths and zero-degree (p,n) reaction rates has been questioned, because a comparison of the p-decay of 37Ca with the 37Cl(p,n)37Ar mirror reaction showed that the differences were probably not entirely due to isospin-violating effects. Hence, a calibration of the neutrino absorption rate based on shell-model calculations or on (p,n)-reactions might jeopardize the quality of the ICARUS results. An alternative possibility of calibrating the 40Ar neutrino capture rate is to use, under the assumption of isospin symmetry, the B(GT) values of the mirror p-decay of 40Ti (see Appendix 2 for a general description of a P-decay process). In principle,

123

the large energy release of the 40Ti decay (QEC = 11680(160) keV [14]) enables one to extract all information that is relevant for the GT contributions to the rate of solar neutrinos absorbed by 40Ar, provided sufficiently accurate half-life and branchingratio data are available. It is interesting to note that the efficiency calibration for the 37 C1 experiment has recently been achieved in a similar way by using the B(GT) values measured in the P-decay of 37Ca. Prior to the work described here, the 40Ti P-decay had been investigated in only one measurement under severe experimental limitation [15]. The latter measurement yielded only singles data of P-delayed protons whereas in the experiment presented here proton-y coincidences were measured. This information is indispensable in order to clarify whether the P-delayed proton emission populates the ground state and/or excited states of 39Ca. Furthermore, the decay of 41Ti was studied in order to establish an energy calibration for the 40Ti proton data and to improve, by detecting p-delayed y-rays, the results of previous 4,Ti studies. 2

Angular Distribution for the 7Be(d, n)8B Reaction

The experiment was performed using a secondary beam line GIRAFFE [16] built at the HI-13 tandem accelerator of the China Institute of Atomic Energy. The 7Be beam with an energy of 26.0 MeV was produced via the 'H(7Li, 7Be)n reaction by bombarding a H2 gas cell at 1.2 ATM pressure with a 34 MeV 7Li ions. The 7 Be beam was collimated by a <|)4mm aperture and then directed onto a (b)(CH2)„ : secondary target placed on the focal plane. The resulting beam energy resolution was 1.2 MeV FWHM. A deuterated polyethylene ((CD2)n) foil of 0.97 mg/cm2 in thickness was used as the secondary target to study the reaction of interest, and a polyethylene((CH2)n) foil was used to the background. The 0 2 4 6 8 10 12 14 determine reaction products were detected and 1>» (deg) Figure 1. Particle identification of 8B. identified using the AE-E counter telescope. It consisted of an ionization chamber backed by a 45X45 mm2 two-dimensional position sensitive silicon detector (PSSD). The PSSD enabled us to determine both the energy and

124

emission angle of the outgoing particles. The inverse kinematics of the 'H(7Be, 8B)n reaction restricted the emerging angle of 8B to 9°, thus the full angular distribution could be covered. The overall angular resolution was 1.1° FWHM. The counter telescope simultaneously recorded the beam itself. In order to solve the pulse pileup problem, the beam intensity was kept at 200-400 cps. A pulse pileup rejection technique was used to reject the remaining pileup events. The beam time taken for the (CD2)n target was approximately 150 hours, during which about 300 8B events were accumulated. The background measurement with the (CH2)n target took about 50 hours. The contour plot of AE vs. E, was used to identify 8 B. A two-dimensional cut selected the 8B candidates from the 2H(7Be, 8B)n reaction. Fig. 1 displays the contour plot of E, vs. 0lab for the events within the cut, where the 6lah is the laboratory emission angle converted from the position data of PSSD. A parabola shaped window finally selects 8B events. It can be seen that the background mainly appears around 0° and obviously results from the remaining beam pulses piling up on each other. After background subtraction, the total cross section for 7Be(d, n)8B reaction at E cm = 5.8 MeV was then determined to be 58±8 mb. The resulting CM angular distribution is presented in Fig. 2. Since 8B has no excited states with detectable half-lives in the present experiment, the data include the ground state transition only. The distorted-wave Born 1 ' ■ ■ i ■' ■ i ' ■' i ' ■ ■ i ■ • ■ i ■ ■ • i approximation (DWBA) code [17] is to" ■i— Eiep, Data adopted in the analysis of the data. 0WBA1+CN c - - DWBA2+CN We used the following relation to CN extract the spectroscopic factor: 1

■ 111111

°"exp(#o) - ^CN(^)

= S,j(TDWBA{90)

(1) 10

W h e r e

°"exp(#o)

a n d

u

DWBA

are the values of the experimental and calculated differential cross sections,

&CN(@O)

^S

tne

compound nucleus contribution. The asymptotic normalization constant (ANC) of the overlap functions, Clj, is related to the spectroscopic factor by

1 -

0

and

il■■iI. ..I i ..I

■■■■■■ I . . . I i i
20 40 60 80 100 120 140 160 180

Figure 2. The angular distribution o f V S ' B reaction at Ecm. = 5.8 MeV and DWBA calculations,

^lj

=

where

^lj'Jnlj

b -U normalization

(2) is

the

of a

asymptotic single-particle

radial wave function u„,/r) with a certain geometry parameters r0, a of a Woods-Saxon potential,

125

K,j(r) « bnljW_nM(2KT)

Ir,

r > RN

(3)

here RN is the nuclear interaction radius between the proton and 7Be, W_

±

(2AT)

refers to the Whittaker function , and 77 stands for the Sommerfeld parameter. In our calculation the optical potential parameters for the deuteron and neutron are carefully chosen to fit experimental scattering data of the nearby nuclei at the closest energies. They are then extrapolated to the energies of the present study by reasonable energy dependence, which are listed as set 1 in Table 1. The depth of the Woods-Saxon potential for the proton bound state is chosen to fit the separation energy of the proton from 7Be, Bp=0.137 MeV for given geometry parameters. It can be seen from Table 1 that the choice of distorted-wave optical potential parameters makes about 10 % difference in ANC. The ANC C , for 8B -» 7Be+p was extracted to be 0.711±0.092 fm using Eqs. (l)-(3). From a microscopic calculation, it has been shown that the bnl /S17(0) is almost a constant^ 0.026) for different proton bound wave functions in 8B [10], where the spectroscopic factors are chosen the same as that given by Barker [18], satisfying Sl=] « 1.0. With this ratio, the S17(0) factor for 7Be(p, y)8B was derived to be 27.4+4.4 eV b. TABLE 1. The optical potential parameters used in DWBA calculation and the corresponding ANC and S17(0) values. Set Ch. 1

7

Be+d B+n 7 Be+d 8 B+n 8

2

C 2 (fm) '

V

r

a

4WD

r

D

aD

4VS0

r

so

a

-138.74 -48.19 -118.00 -42.36

1.02 1.13 1.00 1.35

0.86 0.72 0.94 0.55

65.36 45.32 27.48 37.76

1.31 1.43 1.98 1.35

0.76 0.66 0.59 0.75

-28.0 -24.8 -34.0 -20.0

1.64 1.13 1.00 1.35

0.81 0.77 0.711±0.092 27.4+3.6 0.94 0.55 0.796±0.103 15.2+1.5

so

SI7(0) (eVb)

For 7Be+d of set 1, the additional parameters are W—14.84, r,^\.64, a,y=0.29; V and W are in MeV, r and a are in fm.

3

Beta-decay of 40Ti

A 58Ni beam of 500-A MeV with an intensity of 1><109 ions/s from the heavy-ion synchrotron SIS at GSI in Darmstadt was used to produce 40Ti by fragmentation reactions in a 4 g/cm2 thick 9Be target. By using the projectile fragment separator FRS, an isotopically separated 40Ti beam was produced. The intensity of the 40Ti beam at the final focus of the FRS was measured to be about one atom per minute. During the experiment of 5 days, about 1.1 x 104 40Ti ions were produced. The 40Ti ions identified by energy-loss (AE) and mass-to-charge ratio (A/q), were slowed down to shift the implantation profile to the center of the silicon detector stack

126

. . .3

consisting of eight 300 um thick, 30 mm diameter silicon detectors. The three central counters were used to measure positrons and P-delayed protons, whereas the outer ones served as veto detectors to reject unwanted particles as described below. About 90 % of the 40Ti ions were implanted in the central three counters. An array of 14 large-volume Nal detectors were mounted close to the silicon detector stack to measure y-rays emitted in the 40Ti decay process. The photopeak efficiency was measured to be 15+2 % at a y-energy of 1.33 MeV. The proton energy calibration was based on the P-delayed proton spectrum of 4,Ti, measured in a separate FRS experiment. The delayed-coincidence technique, used in the off-line data analysis of the 4C Ti data, was based on a time window of 200 ms. This window was opened by a 40 Ti event, selected according to conditions with respect to AE and A/q, and closed by the subsequent decay event. In this way, decay events from positron and/or p-delayed proton 1 emitters (e.g. 38Ca) were rejected. The proton energy spectrum, shown in Figure 0 1000 2000 3000 4000 5000 6000 3, was generated by an anti-coincidence P r o t o n e n e r g y (keV) condition with the front and rear silicon 40 Figure 3. Ti p-delayed proton energy spectrum. counters in order to eliminate heavy ions, which were stopped in the first counter or penetrated through all of them. The proton events, which were not completely stopped in a single detector, were rejected by an anti-coincidence condition with adjacent counters. To get the proton branching ratios for individual proton transitions, the proton peak intensities were corrected for the full-energy detection efficiency, and were normalized to the total number of implanted 40Ti ions. The latter quantity was determined by selecting events recorded in coincidence between the adjacent counters. The proton-y coincidence data were used for identifying proton emission from 40Sc levels to excited states of 39Ca. This information was used for deducing the P-branching ratios from proton branching ratios. We used the revised 40Ti QEC value of 11466+13 keV [6,19], to calculate the transition strengths for 40Ti. The B(F) and B(GT) values from this work, are displayed in Figure 2 in comparison with results from the other recent P-decay measurement [20], a 40Ar(p,n)40K experiment [21], and a shell-model calculation [22]. The V assignment for 40Sc levels populated by p-decay of 40Ti is 1+, except for the 4365 keV level which was identified as the 0+, IAS. The latter interpretation is based on the observed p-strength of 4.01(31), which agrees with the theoretical value of |Z-N| = 4 for a pure Fermi transition. The integrated B(GT) value is

{

V^

:

127

5.84+0.39, which can be compared with the shell-model result of 5.62 [22] that was obtained by the free-nucleon GT operator quenched by a factor of 0.775. However, we note that the shell-model overestimates the excitation energies of the first two excited states of 40Sc by roughly one MeV. As can be seen from Figure 4, excellent agreement was found between the present results and those obtained by Trinder et al. [20] up to a 4f*j, rMf 40 Sc-excitation energy of 5 MeV. At T c i n d e c e t a 1. T i fl- dftc a y higher excitation energies, however, PLB415(97)211 the GT strength from this work is more 3 (GTJ * 5 . 9 ( 4 ! i^iUi fragmented than that obtained by ^ Trinder et al.. This discrepancy is not surprising, as the statistics of our data as well as of those obtained by Trinder *,^, ,M, - ,^.', A*, ^ t ! » , - i S et al. are too poor for proton energies Shell-Model above 5 MeV for an unambiguous decomposition into individual transitions. Our data agree with those c g y ! Mev ) of the (p,n) work [21]. From this Figure 4. Experimental Gamow-Teller strength comparison, we conclude that within distributions for the 40Ti p-decay and the the experimental uncertainties we did 4 40 "Ar(p,n) K reaction in comparison with a shellnot observe any isospin asymmetry in model prediction. the 40Ti-40Ar mirror pair. Following the procedure suggested by Ormand et al. [22], we calculated electron-neutrino absorption rates in 40Ar, based on the experimental 40Ti (3-decay strength from this work and the updated solar neutrino flux of 6.6^ \ x 106 cm'V [23]. In this calculation, we used the experimental 40K excitation energies whenever possible; otherwise the 40Sc excitation energies from this work were taken. Based on the 40Ti (3-decay measurement of the present work and that of Trinder et al. [20], we derived a recommended value of (14.3±0.3)xl0"43 cm2 for the electron-neutrino absorption cross-sections of 40Ar. This result, together with the solar neutrino flux according to [23], yields a recommended value of the electron-neutrino induced event rates for the ICARUS detector of 9.4±0.2(stat.)+_\36(syst.) SNU.

4

Summary

The angular distribution of 7Be(d, n)8B reaction has been measured for the first time, from which the S17(0) factor for the 7Be(p, y)8B reaction was derived to be 27.4±4.4 eV b. An independent analysis based on our data resulted a value of 23.5±6.7 eV b [24]. Recently, we preformed a separate measurement for 7Be(d, n)8B

128

reaction at Ecm = 8.3 MeV [25], aiming at checking the energy dependence of this ANC method, the resultant S17(0) factor was 25±5 eV b. Our S17(0) value supports the solar neutrino missing found in the Kamiokande and Homestake experiments. Similar experiments using one proton transfer, but with 10B [26] and 14N [27] targets, deduced the S17(0) factor of 17.8+2.9 and 16.6±1.9 eV b, respectively. Although the discrepancy is not inconsistent with the error bars, they do imply the uncertainty due to the selection of optical model parameter in DWBA calculation is underestimated. In any sense, this ANC method is of importance where the direct (p,y) measurement is not possible, as in the case of "C(p,y)12N reaction, the corresponding reaction of "C(d,n)l2N was measured by us recently by using the TOF analysis of "C secondary beam. The (3-decay of 40Ti was studied by measuring the [3-delayed proton- and yemission. Based on the experimental 40Ti p-decay strength, the neutrino absorption cross-section was determined to be (14.3±0.3)xl0 43 cm2. The results obtained in this work and in previous experiments imply that the 40Ar-absorption cross section is accurate enough. Accordingly, the solar model prediction for the 8B-neutrino flux represents the major source of the systematical uncertainty in the prediction of the reaction rate for the ICARUS detector. 5

Acknowledgment

The authors are grateful to the staff of tandem accelerator for smooth operation of the machine. This work was funded in part by National Science Foundation of China under Grant No. 19195007 and Nuclear Industry Science Foundation of China through Grant No. 92A01015. The research project in Germany was supported by European Union. One of them, Weiping Liu, thanks the Hong Kong Qiushi Science Foundation and German Academic Exchange Service for support. References 1. 2. 3. 4.

5. 6. 7. 8.

Bahcall J.N. and Pinsonneault M., Rev. Mod. Phys. 64,885 (1992). FukudaY. et al„ HEP-EX/9807003. Morrison D.R.O., 1994, IN 27th Int. Conf. on High Energy Physics. Oberauer L., 1998, in Procedings of the Interational Workshop XXVI on Gross Properties of Nuclei and Nuclear Excitaions, edited by M. Baballa et al. (GSI, Darmstadt), p. 262. W. Liu et al., Phys. Rev. Lett 77 (1996) 611. W. Liu et al, Phys. Rev. C58(1998)2677. Filippone B.W. et al, Phys. Rev. Lett. 50 (1983) 412. Hammache H. et al, Phys. Rev. Lett. 80 (1998) 929.

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9. Motobayashi T. etal,Phys. Rev. Lett. 73 (1994)2680. 10. Xu H.M. et al, Phys. Rev. Lett. 73, 2027 (1994). 11. ICARUS Collaboration, ICARUS II proposal, LNGS Report 995/99-1 (1993), see also http://www.aquila.infn.it:80/icarus/main.html. 12. Bahcall J.N. et al, Phys. Lett. B178 (1986) 324. 13. Trinder W. et al, Nucl. Phys. A620 (1997) 191. 14. Audi G. et al, Nucl. Phys. A624( 1997)1. 15. Detraz C. et al, Nucl. Phys. A519 (1990) 529. 16. Bai X. et al, Nucl. Phys. A588, 273c (1995). 17. Kunz P.D., computer code DWUCK4 (unpublished). 18. Barker F. C , Aust. J. Phys. 33, 177(1980). 19. LiuW., Ph.D. Thesis (1998). 20. Trinder W. et al, Phys. Lett. B415 (1997) 211. 21. Anderson B. D., private communication. 22. Ormand W. E. et al, Phys. Lett. B345 (1995) 343. 23. Bahcall J. N. et al, Rev. Mod. Phys. 67 (1995) 781. 24. Gagliardi C.A. et al, Phys. Rev. Lett. 80(1998)421. 25. Wang Y. et al, Chin. Phys. Lett. 16(1999)873. 26. Azari A. et al, Phys. Rev. Lett. 82(1999)3960. 27. Phys. Rev. C60(1999)55803.

Coulomb Dissociation of 8 B at 254 M e V / u for 7 Be(p,7) 8 B N. IWASA 1,2 , F . BOUE 1 ' 3 , G. SUROWKA 1,4 , K. SUMMERER1, T . BAUMANN1, B . B L A N K 3 , S. C Z A J K O W S K I 3 , A. M.

C. M A R C H A N D 4 , T . 1

E. S C H W A B , W .

3

1

1

8

5

S C H W A B , P . S E N G E R , J. S P E E R , C. S T U R M , A.

T. T E R A N I S H I , F .

2

K U L E S S A 4 , F.

M O T O B A Y A S H I 9 , H. O E S C H L E R 5 , A. O Z A W A 2 , M . S .

2

1

F O R S T E R 5 , M. G A I 6 , H. G E I S S E L 1 , E .

H E L L S T R O M 1 , P. K O C Z O N 1 , B . K O H L M E Y E R 8 , R.

5

5

U H L I G , A. W A G N E R , W .

4

W A L U S , and

C.A.

GROSSE7, LAUE5,

PRAVIKOFF3, SUROWIEC1,

BERTULANI10

Gesellschaft

fur Schwerionenforschung m.b.H. (GSI), D-64291 Darmstadt, Germany. RIKEN (Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan. Centre d'Etudes Nucleaires de Bordeaux-Gradignan, F-33175 Gradignan, France. 4 Jagellonian University, PL-30-059 Krakow, Poland. Technical University of Darmstadt, D-64289 Darmstadt, Germany. 6 University of Connecticut, Storrs, CT 06269-3046, U.S.A. 7 Forschungszentrum Rossendorf, D-01314 Dresden, Germany. Marburg University, D-35032 Marburg, Germany. Rikkyo University, Toshima, Tokyo 171, Japan. 10 Instituto de Fisica, Universidade Federal do Rio de Janeiro, 21945-970 RJ, Brazil. The Coulomb dissociation of 8 B into 7 B e and a proton was measured at £J( 8 B) = 254 MeV/u. The astrophysical Si7-factors for the 7 Be(p,7) 8 B reaction were ex­ tracted at ECm = 0.25 — 2.78MeV yielding the zero-energy Si7-factor relevant to the solar neutrino problem to be Si7(0) = 20.6 ± 1.2 ± 1.0 eV-b. Our results agree with the direct measurement results of Vaughn et al., Filippone et al., and Hammache et al. as well as the Coulomb dissociation results of Motobayashi et al. and Kikuchi et al. at E(SB) « 50 MeV/u.

1

Introduction

The precise knowledge of the astrophysical £17 factor for the 7 Be(p,7) 8 B re­ action at the Gamov-window energy « 20 keV is crucial for estimating the 8 B solar neutrino flux and the interpreting terrestrial neutrino measurements.1 The flux of the 8 B solar neutrinos is particularly important for the results of the Homestake, Super Kamiokande, and SNO experiments which measure high-energy solar neutrinos mainly or solely from the 8 B decay. Several direct measurements were reported for the 7 Be(p,7) 8 B reaction at low energies. 2,3,4,5,6 The £17 factor at zero energy was extracted from the measured cross sections at higher energies by an extrapolation based on the­ oretical calculations of the energy dependence of the cross section. However, such experiments have difficulty of the determination of the effective thickness

130

131

of radioactive Be targets. The difficulty reflects in the fact that the results of these experiments can be grouped into two distinct data sets which agree in their energy dependence but disagree in their absolute normalization by about 30%. In the point of view of this discrepancy, experimental studies with different methods are highly desirable. The Coulomb dissociation (CD) of 8 B was proposed as an alternative indi­ rect method for determining radiative capture cross sections.7 In this method, one measures the cross section of the dissociation process of 8 B into 7 Be and proton in the Coulomb field of the target nucleus 2 0 8 Pb, instead of measuring the 7 Be(p,7) 8 B cross section. Since the process can be regarded as absorp­ tion of a virtual photon, the dissociation cross section can be converted to the photo-absorption 8 B(7,p) 7 Be cross section which is directly related to the 7 Be(p,7) 8 B cross section. The CD yields are enhanced because a thicker target can be used and high detection efficiency was expected due to high-energy charged-particle measure­ ments. The radiative capture cross section of 1-1000 nb is enhanced to the CD cross section of 0.1-10 mb for 10 keV bin, because large phase space is available for the CD. Another advantage is that the method is free from the difficulty of determining the effective target thickness. Recently, Motobayashi et al. have performed a CD experiment at £'( 8 B) = 46.5 MeV/u and successfully extracted the 7 Be(p,7) 8 B cross section at Ecm = 0.6 — 1.7 MeV.8 The extracted (p,7) cross section is consistent with the results from the lower group of the direct reaction data. 4,5,6 Another measurement at E(8B) = 51.9 MeV/u by same group with improved accuracy led essentially to the same conclusion.9 In the other hand, CD measurements have different sensitivities to the multipole composition of the photon field from direct (p,7) measurements. The E2 amplitudes are enhanced in the CD due to the larger flux of E2 virtual photons than that of El virtual photons, whereas it can be neglected in the (p,7) reaction. Several experimental 10,11,12 and theoretical 13 studies on the E2 component of the CD were reported. In this article, we report an experiment of the CD of 8 B at i?( 8 B) = 254 MeV/u. This incident energy have several advantages: (i) because of strong forward focusing of reaction products, the magnetic spectrometer KaoS 1 4 was used for a kinematically complete measurement with high detection efficiency over a wide range of the p-7Be relative energy; (ii) a thicker target and tracking detectors (i.e. silicon micro strip detectors) can be used, because the influence of straggling on the experimental resolution is reduced at higher energies; (hi) effects that obscure the dominant contribution of El multipolarity to the CD, such as E2 admixtures and higher order contributions, are reduced; (iv) the

132

Figure 1: Schematic view of the experimental setup.

M l resonance peak at ETe\ = 0.63 MeV is excited stronger and therefore can be used to check the accuracy of t h e invariant mass calculation. 2

Experimental Setup

T h e experiment was performed at the radioactive beam facility at GSI. 1 5 A radioactive 8 B beam was produced by the fragmentation of a 350 M e V / u 12 C beam from the SIS synchrotron impinging on a beryllium target with a thickness of 8.01 g / c m 2 . T h e b e a m was isotopically separated in t h e frag­ ment separator (FRS) 1 5 and transported to the standard target position of the spectrometer KaoS 1 4 where an enriched 2 0 8 P b target with a thickness of 199.7(±0.2) m g / c m 2 and an effective target area of 22 x 20 m m 2 was placed. T h e averaged beam energy of 8 B at the center of the target was 254 M e V / u ; a typical intensity was 10 4 /spill with 7 s extraction time. Beam particles were identified event by event with the T O F - A £ " method by using a plastic scintillator with a thickness of 5 m m placed at 67 m upstream of the target and a large-area scintillator wall placed close to the focal plane of the KaoS. About 20% of the beam particles were 7 Be which could however unambigu­ ously discriminated from breakup 7 B e particles by their T O F . T h e b e a m size and spread-in angle at the target were measured without the target by using silicon micro-strip detectors described in the next paragraph to be crx = 2.9 mm, axi = 6.3 mrad,
133

of 56 x 56 mm 2 , and a strip pitch of 0.1 mm. Individual readout for each strip was performed by incorporating GASSIPLEX chips 16 for analog multiplexing of the energy-deposit signals, and CRAMS modules 17 for the digital readout of analog-multiplexed signals. This configuration enabled us to measure opening angles of two charged particles with an accuracy of 4.8 mrad mainly caused by angular straggling in the Pb target. The vertex at the target was reconstructed with an ler accuracy of 0.3 mm. The background events produced by the target frame or in the silicon detector could be largely eliminated with the vertex information. The remaining background events were measured under the same condition without the target to be less than 0.5% of the true events. The momenta of the reaction products were analyzed by trajectory re­ construction using position information of the micro-strip detectors and two two-dimensional multi-wire proportional chambers (MWPC) which detected 7 Be ions or protons placed at around the focal plane of KaoS. A large-area scintillator wall (TOF wall) with an active area of 180 x 40 cm 2 consisting of 30 plastic scintillator paddles with a thickness of 2 cm was placed behind of the MWPC. It served as a trigger detector for the data acquisition system and as a stop detector of the TOF measurement. The complete kinematics of the breakup products was determined and thus the p- 7 Be relative energy i?rei was reconstructed. 3

Results

The p- 7 Be coincidence yields were plotted in Fig. 2 (a) as a function of the p- 7 Be relative energy. Compared to the (p,7) reaction, the Ml resonance at Ecm = 0.63 MeV is not clearly visible. It is related to our energy resolution and relatively lower sensitivity of CD to the Ml transition than that to the El transition. Monte Carlo simulations were performed for evaluating the detection effi­ ciencies and resolutions. Events were generated with probabilities proportional to the CD cross section calculated by semi-classical formula.18 For the Ml res­ onance at Ecm = 0.63 MeV, the (p,7) cross section calculated from the total and gamma widths measured by Filippone et a/.5 was used. The non-resonant contribution was obtained by normalizing the El (p,7) cross section calculated by Bertulani 19 with a scale factor of 1.20. The simulation took into account of the beam spread in position, angle, and energy at the target, and finite size of the Si strip, MWPC, and TOF wall as well as our inability to discriminate proton and 7 Be for very small opening angles where both particle hit the same strips. The influence of angular and energy straggling and energy loss in the

134

>200 0)

(a)

= 150

4

0

iifioo ;o o ■§50 X

*1*"«

/

(b)

><0.8

c <1>

O °6 a> 0.4

i

i

Erel [MeV] Figure 2: (a) The p- 7 Be coincidence yields plotted as a function of relative energy. The solid and dashed histograms denote simulated E l + M l and E l yields, respectively, (b) the p- Be coincidence efficiency calculated by Monte Carlo simulations.

layers of matter was taken into account in the simulation. Further corrections in the simulation are due to the feeding of the excited state at 429 keV in 7 Be. We used the result by Kikuchi et al}1 who measured the 7-decay in coincidence with the CD of 8 B . The histograms in Fig. 2(a) show the simulated E l + M l yields (solid) and El yields (dashed). As seen in this figure, the shape and magnitude of the experimental energy dependence are fairly well reproduced. This indicates that the CD yield is well described by the combination of the Ml resonance and the pure El continuum. The total efficiency calculated by the simulations was shown in Fig. 2 (b) which is high over the entire Ere\ range covered in our study. The relative-energy resolution was estimated from the simulation to be e.g.
Discussion

The astrophysical Sn factors for the El multipolarity was extracted by com­ paring the experimental data to the simulated data in Fig.l (a). The resulting

135

0

1

2

3

Erel [MeV] Figure 3: The astrophysical Su factors deduced from the present experiment plotted as a function of the p- 7 Be relative energy (closed circles), in comparison with results from direct and other CD experiments (closed triangles by Kavanagh 3 , open boxes by V a u g h n 4 , open triangles by Filippone 5 , open crosses by H a m m a c h e 6 , and open circles by Kikuchi 9 ). The solid curve shows the prediction of Bertulani 1 9 fitted to our data, while the dashed curve shows a fit of the theoretical curve of Descouvemont et al?2 to the combined datasets of Refs. [4,5,6] The insert shows the low-energy part of the figure, where we have fitted the energy dependence of Jennings et al?6 to our data. Sn distribution was plotted in Fig. 3 as a function of the p- 7 Be relative energy, together with existing (p,7) and CD results. The (p,7) data were renormalized with the resonant cross section of the 7 Li(d,p) 8 Li reaction of 147 ± 11 mb.20 The binning of our data was chosen to be approximately equal to the FWHM of the ETe\ resolution. The errors shown in Fig. 3 result from sum­ ming in quadrature statistical errors and from uncertainty in the momentum calibration, in angular cutoff of pure Coulomb processes, and in feeding of the excited state in 7 Be. Since we are mostly interested in the El component, the simulated Ml component of the Ere\ = 0.63 MeV resonance was subtracted from the data. At low ETe\, our results agree well with the lower group of the (p,7) results 4,5 ' 6 and the CD result? We observed some discrepancies at higher Ere\. as shown in Fig. 3. We cannot explain the discrepancy with the result of Kikuchi et al? at higher Ere\ since all of the assumptions underlying their

136

and our analysis are identical. The discrepancy to the direct measurements may be due to our neglect of an E2 component which, in a proper theoretical treatment, might affect the high-.Erei data points while leaving the low Erei data virtually unchanged (see right-hand panel of Fig.11 in Ref. [13]). Several theoretical models for 8 B have been proposed to predict the shape and magnitude of the Sn energy dependence, such as one-body potential mod­ els 21,19 or more complex many-body (cluster) models. 22 ' 23,24 ' 25 Our data in Fig. 3 follow very closely the results obtained by Bertulani 1 9 over the entire range of energies as indicated by the solid curve which was normalized to our data points using a scaling factor of 1.20. The shape of the distribution pre­ dicted by the cluster model calculation,22 which was favored by the recent (p,7) experiment of Hammache et al. f does not agree equally well with our results at the higher energies (dashed line in Fig. 3). To obtain the zero-energy astrophysical Sn factor, we follow Jennings et al?6 in fitting the theoretical energy dependence only to data points below .EVel RS 0.45 MeV (see insert in Fig. 3) since this region should be largely free from uncertainties concerning nuclear excitations. From our two low ETei data points we extracted £17(0) = 20.6 ± 1.2 ± 1.0 eV-b where the first contribution results from fitting the data points of Fig. 3 and the second one is related to the uncertainty in extrapolating to zero i?rei- This result is compatible with the value of Si7(0) = 19.0 ± 1.0 ± 0.2 eV-b obtained by Jennings et al?6 when fitting the combined data points of Filippone et al? and Hammache,et al? and also with the adopted value of Sn(0) = 19+2 eV-b.20. We conclude that we have demonstrated that high-energy Coulomb dissoci­ ation is very useful for determining the astrophysical 5-factor of the 7 Be(p,7) 8 B reaction at low energies. However the information on E2 admixture and the influence of the interference between the El and E2 component is desirable for more accurate determination of the Sn factor. Further experimental studies are planed at GSI to obtain information on the E1-E2 interference by measur­ ing angular distributions with higher angular resolution. References 1. 2. 3. 4. 5. 6. 7.

J.N. Bahcall et al., Phys. Lett. B 433, 1 (1998). P.D. Parker et al., Astrophys. J. 153, L85 (1968). R.W. Kavanagh et al., Bull. Am. Phys. Soc. 14, 1209 (1969). F.J. Vaughn et al., Phys. Rev. C 2, 1657 (1970). B. W. Filippone et al, Phys. Rev. C 28, 2222 (1983). F. Hammache et al., Phys. Rev. Lett. 80, 928 (1998). G. Baur and H. Rebel, Annu. Rev. Nucl. Part. Sci. 46, 321 (1996).

137

8. T. Motobayashi et al, Phys. Rev. Lett. 70, 2680 (1994); N. Iwasa et al, J. Phys. Soc. Japan 65, 1256 (1996). 9. T. Kikuchi et al, Eur. Phys. J. A 3, 213 (1998). 10. J.v.Schwarzenberg et al, Phys. Rev. C 53, R2598 (1996). 11. T. Kikuchi et al, Phys. Lett. B 391, 261 (1997) 12. B. Davids et al, Phys. Rev. Lett. 8 1 , 2209 (1998). 13. H. Esbensen and G.F. Bertsch, Nucl. Phys. A 600, 37 (1997). 14. P. Senger et al, Nucl. Instr. Meth. A 327, 393 (1993). 15. H. Geissel et al, Nucl. Instr. Meth. B 70, 286 (1992). 16. J.C. Santiard, private communication. 17. Modules V-550 and V-551 manufactured by C.A.E.N., Viareggio, Italy. 18. C.A. Bertulani and G. Baur, Phys. Rep. 163 (1988) 300. 19. C.A. Bertulani, Z. Phys. A 356, 293 (1996). 20. E.G. Adelberger et al, Rev. Mod. Phys. 70, 1265 (1998). 21. S. Typel and G. Baur, Phys. Rev. C 50, 2104 (1994); S. Typel et al, Nucl. Phys. A 613, 147 (1997). 22. P. Descouvemont and D. Baye, Nucl. Phys. A 567, 341 (1994). 23. C.W. Johnson et al, Astrophys. J. 392, 320 (1992). 24. A. Csoto et al, Phys. Rev. C 52, 1130 (1995). 25. L.V. Grigorenko et al, Phys. Rev. C 57, R2099 (1998). 26. B.K. Jennings et al, Phys. Rev. C 58 (1998) 3711.

D e v e l o p m e n t for t h e s t u d y o f a C r o s s S e c t i o n a l M e a s u r e m e n t o f 3 H e - 3 H e Solar R e a c t i o n

N. Kudomi, T. Itahashi, K. Kume, K. Takahisa, S. Yoshida, H. Ejiri, H. Toki, and Y. Nagai Research Center for Nuclear Physics, Osaka Univ., Ibaraki, Osaka, Japan M. Komori Dept. of Phys. Facl. of Sci. Osaka Univ., Toyonaka, Japan H. Ohsumi Dept. of Culture and Education, Saga Univ., Saga, Japan The design and construction of a low-energy, high current accelerator for the study of fusion reactions are reported. The accelerator can produce an intense beam of 3 H e 1 + a n d 3He2"*" ions of more than 1mA. It enables us to provide extremely fine cross-section measurements of the 3 He( 3 He,2p)a at 40 to 50 keV. A detection efficiency for proposed detector assembly of AE-E counter telescope is simulated with GEANT program and it expects a detection efficiency about 10% for the two proton coincidence for 3 H e + He—>2p-fct:. Deuter contaminations in target chamber is estimated to be less than ppm by quadrupole mass spectrometer. To further develop the study of nuclear astrophysics, a plasma target as an experimental apparatus for electron screening effects is proposed. Some parts of such apparatus are assembled. A combination ECR plasma target with a high current ion generator is under construction. The facility will be installed in the underground laboratory, Oto Cosmo Observatory. The facility has just started to operate and, as explained here, it already has been used for the double beta decay measurement and dark matter search programs. The present status of the experimental apparatus and its development are described.

1

Introduction

A high brightness ion source and a precise low energy beam accelerator are indispensable tools in the study of fusion reactions in nuclear astrophysics. When a gas target is combined with a powerful ion source, such as a proton, deuteron, or helium isotope ion source, the necessary conditions appropriate for the measurement of extremely low cross-section events in this region can be fulfilled. Although the fusion reaction, p+p^d+e+is, is the operative reaction in the solar combustion of hydrogen, as well as the initial reaction in the chainreaction for producing photons and neutrinos, the rate of p + p ^ d + e + ^ is too slow ( ~ 1 0 _ 5 2 c m 2 ) to be measured experimentally at 6 keV, the energy range of the actual solar reaction. Of the reactions t h a t follows the basic fusion, such as d+p—> 3 He+7, 3 He+ 3 He—>2p+a, and 3 He-r-a—> 7 Be-|-7, we have focused on the cross-section measurement of the 3 H e + 3 H e reaction at the effective energy

138

139

Figure 1: Total system of a compact accelerator, beam transport and gas target for experiments in nuclear astrophysics.

E c m = 17-27 keV. The reaction manifests the so-called neutrino problem in the sun and can be used to verify the standard solar modef. Currently the LUNA group in the Laboratori Nationali del Gran Sasso (LNGS) has presented data down to 20.7 keV center of mass energy 2 . The present paper describes the construction of a compact ion accelerator facility in the underground laboratory of the OTO Cosmo Observatory, Oto, Nara, Japan (1270m below sea level) 3 . It reinforces the low-energy data obtained so far, and also provides the wider energy range of incident 3 He beam with more current than has been previously achieved. In addition, a preliminary test of the plasma target system for nuclear astrophysics is presented. In this report we describe the design of these facilities and the current status of their developments.

2

Experimental Apparatus

The accelerator consists of (1) a powerful ion source that provides an intense current of 3 He 1 + or 3 H e 2 + more than 1 mA at incident energies of 30-50 keV, (2) a low-energy beam transport with good transmission, (3) a windowless gas target and a circulation/purification system, (4) a reliable calorimeter, (5) detectors for reaction identification, and (6) an electronics and data acquisition system. The layout of this accelerator is shown in Fig. 1.

140

2.1

Ion source and extraction

electrodes

An intense ion source t h a t can produce 3 H e 1 + and 3 H e 2 + ions is essential for the present study. The N A N O G A N t r a p was obtained from P A N T E C H , it confines high-temperature electrons produced by the electron cyclotron reso­ nance (ECR) and in its complete assembled form becomes an E C R ion source at 50 kV potential with 10 GHz, 200 watt R F generator (CPI,VZX-6383G5). T h e design of multi-electrodes for ion extraction has been completed, as has a test model based on the design 4 , 5 , 6 . Recently, we obtained the analyzed current of 3 H e 1 + , with less than 10 w a t t s for R F power. T h e total current obtained so far was 3010/^A at the source extraction and 1203//A 3 H e 1 + at target position. We have further investigated the operational conditions in order to get a larger current of 3 H e 2 + ions. If we are able to obtain a larger current of 3 H e 2 + ions than ever achieved, we can study the present reaction via ionic states t h a t dif­ fer from those studied by other groups. It is also helpful to study the reaction in a wider energy range 7 . T h e required energy range of 3 H e ions should be between 30 to 50 keV, in which the astrophysical S-factor d a t a for 3 H e - f 3 H e fusion reaction can be deduced.

2.2

Low energy beam

transport

Despite the fluctuations of the beam, a nearly invariant b e a m form could be achieved at the exit using the multi-electrodes extraction system. In addition, from a source to a target b e a m t r a n s p o r t should be designed to maintain a high transport efficiency and other desirable b e a m qualities and thereby to allow precision measurement of the rare nuclear reaction 3 He+ 3 He—>2p+a. Generally, it is known that a strong space charge effect in the b e a m t r a n p o r t at ion current more than 1mA is present. It is essential t h a t this effect is accounted for when calculating the b e a m optics. A GIOS computer program by Wollnick et al. that incorporates such effects was used for the present calculation of our beam transport. Because it is easier to operate and has fewer elements we adopted the D(dipole 90 degree deflection a n g l e ) + Q + Q transport scheme. To maintain the m i n i m u m collimator aperture, we calculated the dimension of the beam at the target position by varying the parameters of elements and drift lengths to create smaller dx and dy. T h e beam transmission efficiency from the ion source through the target is about 30%(Table 1). 2.3

Window-less

gas target

T h e windowless gas target for a study of 3 H e + 3 H e reaction consists of differ­ ential pumping and gas recirculation and purification system (Fig. 2). For

141 Table 1: The achieved beam current at the ion source and the target.

H.V. 40kV 30kV

1+ 2+ 1+ 2+

Target(//A) 1208 103 1200 35

Ion source(^A) 3010 3000 3800 1900

3

H e gas target of less than the pressure of l m b a r in the chamber, the pumping system should be composed of the several stages between the target chamber and beam t r a n p o r t . T h u s we prepared a herical grooved vacuum p u m p as a main p u m p for evacuating the gas flow not only at the viscose region but also at the higher vacuum region. T h e recirculation system consists of pu­ rification via a cryopump without charcoal adsorbent, which is similar system as a cryo-trap technology without a consumption of liquid nytrogen. It also consists of helium tight pump, oil free diaphragm membranes compressor, resoivoir vessels, compounds gauges, ultra fine regulated valves and quadrupole mass spectrometer. T h e size of collimators were estimated by calculation in order to main­ tain the pressure at the target chamber about 0.3Torr. From the experimen­ tal study, we realized that the pressure at the target chamber was stayed 3.1(±0.1)Torr for about four days. As pointed out by Rolfs et al., the deuter contamination b o t h in target and in the b e a m resulting from the water vapour is a crucial problem for obtaining the low energy d a t a because d + 3 H e reaction-cross section is 10 6 times higher t h a n t h a t of 3 H e + 3 H e reaction. Therefore, we have measured the deuter contamination in commercial 3 H e gas by detecting H D + separately with Accelerator Mass Spectrometry(AMS). T h e experiment was carried out using the R C N P K = 1 4 0 AVF cyclotron. T h e cyclotron accelerator and the N E O M A F I O S ion source were operated only for the experiment on the b e a m injection line to the post accelerator ( R C N P Ring cyclotron). T h e performance of the N E O M A F I O S ion source has been detailed in a separate r e p o r t 8 . On the other hand, the deuter contamination in target was also estimated as follows. Total system was evacuated and the circulation and cryo-pump was operated. T h e n the pressure at target chamber was 1.2xlO~ 2 Torr, and at helical p u m p was 7 . 6 x l 0 _ 7 T o r r , respectively. T h e H2O component in the residual gas was measured by quadrupole mass spectrometer, and this exper­ iment indicates t h a t the H2O component was about 20%. Assuming that the amounts of H2O is same and abundance of deuterium is same sa natural abun-

142

n

| R.P

-. Cryo _ Magnetic > Pump ^ Floating

w

TMP

■VVXXXXVJLN

TMP1

-^h-

| R.P Figure 2: Total system of a window-less gas target evacuation and recirculation.

dance(0.014%), even in the pressure of 0.3Torr of 3 He gas, we can deduce the deuter contamination(D20) is about the order of ppm. This will satisfactory for this measurement as will discussed below. We also consider to additionaly install the liquid nitrogen trap and baking system. 2.4

Calorimeter

The beam current passing through a gas target, could be measured by using a calorimeter. The beam is stopped in the calorimeter, where the kinetic en­ ergy of the projectile is converted into heat. The converted heat is transfered through a heat flux sensor(OMEGA HFS-3) to a water cooled constant tem­ perature copper base. It is designed for the presize measurement of the heat transfer through any materials. In principle, since the heat transfer rate is di­ rectory proportional to the temperature difference across the thermal barrier. Total design is shown in Fig. 3 2.5

Detectors

In order to detect the reaction particles by 3 He+ 3 He reaction, where Q-value is 12.86 MeV, we should install the counter telescopes which surrounds the gas target. We are employing the Monte Carlo calculation with GEANT program

143

! permanent magnet —

target chamber

th

I

water cooling(constant te Tiperature)

glass

Ta aperture ion beam

th : thermister sensor hs : heat transfer sensor

50mm

Figure 3: Cross sectional view of the calorimeter.

to find the optimum detector set up for an efficient and background free mea­ surement. Dalitz plot and the energy correlations between emitted particles show that the maximum energy of the particles is about 4 MeV. On the other hand two protons share higher energy of 9 MeV to 12 MeV. The expected ultra rare reaction rate is around a few events per day or less, and the typical single background rate of the silicon detectors is one event per hour or more. To remove such accidental events, two proton coincedence is required for the identification of the present reaction. Four AE-E telescopes placed around the beam axis are planned for the two proton coincedence measurement. The AE and E detectors in each telescopes have an active area 2500mm2, the AE de­ tector has a thickness of 140pm and the E detector has a thickness of 1500//m. The estimated counting rates for true and fake signal are summurized in Table 2 3

Plasma target

In the astrophysical S-factor discussion concerning fusion reactions such as 3 He+ 3 He, 3 He+d and d+ 3 He, the electron screening effects have caused much confusion8'9. The best way to avoid such difficulties is to facilitate various atomic states for incident particles and targets. Several institutes have de­ veloped a technique using crossed ion beams to achieves sufficient luminosity

144 Table 2: The expected counting rates for 3 He( 3 He,2p)'*He and 3 He(D,p) 4 He reaction, ppcoin. indicates the two proton coinsidence is required in off-line analysis. 3

He+ 3 He pp-coin

Ecm lOOz/A 3 He a + 50 6.0x10* 40 6.0xl0 3 30 1.8xl0 2 lOOOz/A 3 He+ 25 1.4x10* 22 2.1X101 20 4.6X10" 1

3

He+D ppcoin

2.0x10* 2.0xl0 3 5.9X101

1.3x10^ 5-lxlO 1 1.3X101

1.3xl0~ 3 5.1xl0-4 1.3x10-*

4.5x10* 7.0 1.5X10- 1

4.8x10' 2.1X101 1.2X101

4.8x10-* 2.1x10-4 1.2x10-4

10

. We consider two alternatives for the target, one is ECR plasma and the other is EBIT (electron beam ion trapping). Here we discuss the applicability of this technique as a target for d+d fusion reactions. We also consider this apparatus useful for measuring the energy loss data of charged particles inside the plasma at a very low-incident energy. The prepared facility incorporates an ECR plasma powered by a 2.45 GHz RF source and a high current deuteron beam generator, as shown in Fig. 6. Recently we successfully transported H^ ions of a few hundreds nA through the ECR plasma target to a Faraday cup. 4

Project Status

The system was checked by the d+ 3 He reaction with bombarding the 3 He beam to deuterized-polyethylene. The obtained spectra(Fig. 4) for E and AE counter were consistent with the estimated energy deposite in Si-detector. By the end of March 2000, we will take the first data for a 3He+3He—>2p+a: reaction at the experimental area of RCNP Osaka, in the energy region from lOOkeV. ACKNOWLEDGEMENT This work was supported by the Grant-in-Aid of Scientific Research, Ministry of Education, Science, Culture and Sports.

1. J. N. Bahcall, W. F. Huebner, S. H. Lubow, P. D. Parker, and R. K. Ulrich Rev. Mod. Phys. 54, 767 (1982). 2. M. Junker, A. D'Alessandro, S. Zavatarelli, C. Arpesella et al , Phys. Rev. C57, 2700 (1998) and C. Arpesella et al Phys. Lett. B389, 452

145

2S0

500

750

1000

12S0

1500

1750

2000 2250 250O cnergy(channcl)

Figure 4: Energy spectra of d + 3 H e reaction for E-count(upper) and AE-counter(lower).

and U. Greife et al., Nucl. Instr. and Meth. A350, 327 (1994). 3. H. Ohsumi, H. Ejiri, M. Fujiwara, K. Fushimi, K. Hayashi, R. Hazamza, T. Kishimoyo, M. Komori, N. Kudomi, K. Kume, K. Matsuoka, H. Miyazaki, T. Nitta, N. Suzuki, and S. Tasaka, RCNP Annual Report, RCNP 1995, p. 175. 4. T. Itahashi, K. Takahisa, N Kudomi M. Komori, et.al., Rev. Sci. Instr. 69, 1032 (1998) ; T. Itahashi, T. Iki, M. Komori et. al., The 11th Symp. on Ace. Sci. and Tech., Harima, Hyogo, Japan, p. 45.; T. Itahashi, N Kudomi K. Kume, M. Komori, et.al., Rev. Sci. Instr. (2000) to be published. 5. P. Sortais, C. Bieth, P. Foury, et. al., Proc. of the 12th Intern. Workshop on ECR ion sources, RIKEN, Japan 1995 p. 45. 6. K. Takahisa et al, 24th INS Symposium on ECR Ion sources and their Applications, April 25-27, RIKEN 1995 p.115, and RCNP Annual Report, RCNP 1994 p.190. 7. G. Fiorentini, R. W. Kavanagh, C. Rolfs, Z. Phys. A350, 289 (1995). 8. K. Laganke, T.D. Shoppa, C. A. Barnes, C. Rolfs, Phys. Letts. B369, 211 (1996). 9. U. Greife, F. Gorris, M. Junker, C. Rolfs, and D. Zahnow, Z. Phys. A351, 107 (1995). 10. Proc. of the 19th INS Symp. Cooler Rings and Their Applications, Tokyo, Japan 1990

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IV. Nucleosynthesis in Explosive Burning and New Approach

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PROBING STELLAR EXPLOSIONS WITH RADIOACTIVE BEAMS AT ORNL

MICHAEL S. SMITH Physics Division, Oak Ridge National Laboratory, MS-6354, Bldg. 6010, P.O. Box 2008, Oak Ridge, TN 37831-6371, USA E-mail: [email protected]. ornl.gov Measurements of nuclear reactions on radioactive isotopes are necessary to understand stellar explosions such as novae and X-ray bursts. We have recently measured the l7F(p,p)"F, l7 F(p,a) l4 0 ; l8F(p,p)l8F, and '"F(p,a)150 excitation functions with beams of radioactive ions produced at the Holifield Radioactive Ion Beam Facility (HRIBF) at Oak Ridge National Laboratory. Our experimental setup includes a Silicon Detector Array and the Daresbury Recoil Separator coupled to a windowless, differentially-pumped hydrogen gas target system. We have also measured the l2C(p,y)L1N cross section to commission our recoil separator for proton capture reactions on radioactive isotopes. To support these measurements, we are making unique calculations of isotope synthesis in stellar explosions to determine the effect of nuclear physics uncertainties on explosion model predictions. We are also making detailed evaluations of some nuclear reactions rates that are important input for explosion models.

1

Physics Motivation

There are a number of important astrophysical events during which hydrogen serves as fuel for (i.e., is burned by) (p,y) fusion reactions under non-hydrostatic equilibrium conditions. These explosive hydrogen burning events, which include novae and X-ray bursts, are among the most energetic explosions (~1038 - 1045 ergs) known in the universe. Furthermore, these explosions affect the evolution of binary star systems and synthesize some of the elements comprising our bodies and the world around us. For these reasons, they have been the international focus of observational and theoretical efforts, as well as of laboratory measurements of the nuclear reactions that occur in (and sometimes drive) the explosions. Nova explosions are accretion-driven phenomena, caused by the transfer of mass from one star to a compact white dwarf companion. The mass transfer and subsequent rise in temperature and pressure can initiate a runaway thermonuclear explosion, resulting in the synthesis of heavy elements (to mass ~ 40) and subsequent ejection into space. These catastrophic stellar events are characterized by extremely high temperatures and densities - greater than 108 K and 103 g/cm3, respectively. Such conditions enable (p, y) and (oc,p) reactions to rapidly (on timescales of ns - min) produce unstable nuclei on the proton-rich side of the valley of stability. Any such nuclei (which decay via ^-emission) produced with half-lives longer than, or comparable to, the mean time between nuclear reactions will become targets for subsequent nuclear processing. Sequences of (p, y) and (cc,p) reactions on proton-rich radioactive nuclei therefore occur during these explosions [1,2] and

149

150

produce abundances which are very different than those from the hydrogen burning occurring in non-explosive environments. Indeed, observations of nova outbursts have revealed an elemental composition that differs markedly from solar [3,4]. Recent theoretical studies indicate that these differences are caused by the combination of convection with explosive hydrogen burning in the degenerate layer on the surface of a white dwarf star [5]. This results in a unique nucleosynthesis that is rich in odd numbered nuclei such as l3C, l5N, and l7 0 which are difficult to form in other astrophysical environments. Some of the radioactive nuclei (those with lifetimes longer than 100 s) synthesized in explosions may be carried by convection to the top of the envelope before they decay (and make a small contribution towards powering the expansion [6]). Observations of the y-ray lines (especially the 511-keV emission of l8F) resulting from such radioactive decays in the envelope may provide stringent tests of nova models [7,8,9]. These y-ray emissions depend sensitively on the amount of radionuclides synthesized by nuclear reactions in the explosion, which in turn depends on the rates of nuclear reactions driving the explosion [10,11]. Recently, it was shown that changes in the reaction rates used within a nova simulation had significant effects on both the production of individual isotopes (which can change by orders of magnitude in some cases) and on the peak luminosity and mass of ejected material [12]. Another study determined that the amount of observable 1SF surviving the nova thermonuclear runaway and transported into the envelope is severely constrained by the rates of nuclear reactions which destroy l8F [9]. Current nova models also have difficulty reproducing global observables. For example, predictions of the mass of ejected material are in some cases a factor of 10 smaller than observations [13], and improved reaction rates will help quantify this problem. Other accretion-driven phenomena important in astrophysics include X-ray bursts and X-ray pulsars. These can occur when material is accreted onto the surface of a neutron star, where temperatures and densities can reach over 109 K. and 106 g/cm3, respectively [14,15], The ensuing explosive hydrogen burning can synthesize isotopes with masses up to masses 80 - 100 or beyond [15,16,17]. Recent studies of nucleosynthesis in these violent explosions suggest that their X-ray luminosity is influenced by the nuclear reactions (most involving proton-rich radioactive isotopes) used in the model [18]. There are also other astrophysical sites [16] - e.g., the accretion disk around black holes [19] - where nuclear reactions on proton-rich radioactive isotopes may play an important role. Critical comparisons of models for any of these sites with observations require a knowledge of the rates of nuclear reactions on radioactive isotopes. Measurements of such reactions have been, until recently, impossible due to the lack of intense radioactive nuclear beams. Models therefore employ reaction rate estimates based on systematic properties of nuclear states, on information from analogue nuclei, on partial resonance information from stable beam transfer reaction studies, and on statistical model calculations. For rates dominated by resonances, these estimates can be incorrect by orders of magnitude [2], and therefore the model

151

predictions of isotope synthesis and energy generation are necessarily uncertain. The recent development of radioactive beams has initiated a new era in laboratory nuclear astrophysics - one in which previously unattainable cross sections of nuclear reactions of astrophysical importance can be measured and subsequently incorporated into an emerging generation of sophisticated, computationally intensive models of stellar explosions. Since numerous (p,y) and (ot,p) reactions on radioactive isotopes are thought to play an important role in stellar explosions, simulations have been used to determine which reactions are most important to measure. These simulations indicate that nuclear burning occurs through the Hot CNO cycles, including reaction sequences such as 12C(p,y),3N(p,y),40(e+ ve),4N(p,y)l50(e+ ve)'5N(p,cc)l2C and 16 0(p,y)17F(p,y)l8Ne(e+ve)18F(p,a)l50 [1,20]. Nuclei may be processed out of the Hot CNO cycles to isotopes with masses greater than 20 via reaction sequences such as 150(a,y)l9Ne(p,y)2()Na(p,y)2,Mg..., l8F(p,y)19Ne(p,y)20Na(p,y)2,Mg..., or 18 Ne(a,p)21Na(p,y)22Mg.... These can lead to hydrogen burning through the rapid proton capture process (rp-process) [1,20], involving (p, y) reactions near the proton drip line competing with e+ - decay and reaction cycles (e.g., the Ne-Na and Mg-Al cycles). At very high temperatures characteristic of X-ray bursts and X-ray pulsars (T9 ~ 1.5, where we define T9 as T(K)/10 9 K), the reaction sequence 12 C(p,y),3N(p,y)140(a,p),7F(p,y)18Ne(a,p)21Na(p,y)22Mg... is the trigger for the (cc,p)process, which transitions into the rp-process at approximately mass 40 [15, 19]. The viability of any of these sequences depends on the rates of the reactions involved, and those on proton-rich radioactive isotopes have the largest uncertainties. These sequences are important because they increase the energy generation rate compared to non-explosive burning while simultaneously altering the abundances (e.g., the ratio of nitrogen and oxygen isotopes) that are synthesized. The reactions ,4 0(a,p) 17 F, 17F(p,y)18Ne, l8F(p,y)19Ne, and 18F(p,a)150 play an important role in the sequences discussed above. For these reasons, we have studied these reactions via experiments with radioactive beams at ORNL's Holifield Radioactive Ion Beam Facility (HRIBF) to better determine their rates at temperatures corresponding to stellar explosions. 2

The Holifield Radioactive Ion Beam Facility (HRIBF)

The HRIBF [21] is the only U.S. user facility producing and accelerating beams of proton-rich radioactive heavy ions using the Isotope Separator On-Line (ISOL) technique. To date, radioactive beams of 17F, 18F, 6970As, and 66'67Ga have been produced at the HRIBF; intensities of the fluorine beams were as high as a few million per second on target. Beams of 56Ni and 7Be are under development, and tests are beginning with a uranium carbide target to produce beams of neutron-rich radioactive isotopes. Radioactive ions are produced when a high-temperature (1100 - 2200° C), thin, refractory target [22] is bombarded by a 0.5 kW light ion (p, d, 3He,

152 or 4He) beam from the K=105 Oak Ridge Isochronous Cyclotron (ORIC). For example, fibrous Hf203 targets [23] are being used to produce 17F via the 160(d,n)17F reaction at 45 MeV and to produce 18F via the 16 0(a,pn) ,7 F reaction at 85 MeV. This target material was chosen because of its high surface area to volume ratio and low density (enhancing diffusion of radioactive isotopes) and high melting point to withstand intense light-ion bombardment. A number of novel target configurations for high-efficiency release of radioactive isotopes are currently in use, and others are under design [22]. Once produced, the radioactive isotopes thermally diffuse out of the hot target material and effuse through a short (10 cm) transfer tube to an ion source for ionization and extraction. The particular ion source used is chosen to maximize the extracted radioactive species. An electron beam plasma ion source [23] has been used to produce positively-charged radioactive isotopes of F, As, and Ga, and a surface ionization source has been used to produce negatively-charged radioactive isotopes of F [24]. Once produced, the radioactive ions are then chargeexchanged (if they are positive ions) in a Cs vapor cell, then undergo two stages of mass separation (with the second having AM / M <0.5 - 1 • KT"). They are then injected into the 25-MV tandem accelerator, accelerated to the energies needed for experiments (typically 0.2 - 2 MeV/u for astrophysics studies), and delivered to the experimental areas. Radioactive ion beams produced at the HRIBF have a number of important characteristics which make them well suited for nuclear astrophysics studies: high isobaric purity, good energy resolution, low emittance, low energies, and relatively high intensities. 3

Experimental Equipment

Once the radioactive beams are produced, they are directed to an experimental station dedicated to nuclear astrophysics measurements. This station consists of a Silicon Detector Array (SIDAR) installed in a large target chamber, followed by the Daresbury Recoil Separator (DRS), a large mass separator optimized for measurements of capture reactions in inverse kinematics. 3.1

SIDAR

The SIDAR, located in a large (40 cm diameter) target chamber upstream of the DRS, consists of up to 3 annular arrays of highly-segmented transmission silicon detectors (similar to those in refs. [25,26]) coupled to high-density, low-noise electronics. It is optimized for use in coincidence measurements of excitation functions and angular distributions of scattering, transfer, and (p,a) reactions in inverse kinematics with radioactive ion beams. These measurements are being used to precisely determine the properties of resonances which dominate reactions of astrophysical interest at energies relevant to stellar explosions. For some experiments (e.g., (p,a) reactions), the annular arrays in the SIDAR are used to

153

detect both light-ion and heavy-ion products of these reactions. In other experiments (e.g., (p,p) reactions), the SIDAR is used to detect light-ion products of nuclear reactions while the heavy ions are detected by a gas ionization counter located directly behind the SIDAR. The ionization counter is also used to monitor the intensity of the radioactive ion beam - because Faraday cups are ineffective at these currents - as well as the beam purity.

Figure l.(a). Configuration of the Silicon Detector Array SIDAR used to measure l7 F(p,a) l4 0 (Section 4.2) with two stacked 128-strip detectors (for light ions) backed by a 64-strip detector (for heavy ions). (b) SIDAR configuration used for l8F(p,p)'*F and l8 F(p,a) 15 0 with an angled 96-strip followed by a gas ionization counter.

A variety of mounting configurations of these transmission silicon strip detectors (including normal to the beam axis, angled toward the beam axis, and stacked for particle identification) have been developed and used (Figure 1). The solid angle coverage differs for each configuration, but typically values of 25 % are achieved - corresponding to an even higher detection efficiency for some reactions because of the kinematic focussing of the light ions. Relatively low radioactive ion beam intensities (~10 4 - 106 s"1) can be utilized for many of these measurements, as

154

described in Section 4. The 170(p,p) and 17 0(p,a) cross sections have been measured to commission the S1DAR for radioactive ion beam measurements [27]. 3.2

Daresbury Recoil Separator

The Daresbury Recoil Separator (DRS) has been installed at the HRIBF and optimized for measuring capture reactions in inverse kinematics using a radioactive ion beam incident on a hydrogen or helium target. It is a large-acceptance (6.5 msr, ± 2.5 % in velocity), high-mass resolution (1 part in 300), 90-ton, 13-meter long device. It features two long (1.2 meter), crossed electric and magnetic field velocity filters, followed by a 50° dipole magnet that gives a mass/charge final focus [28]. Details of the installation of the DRS at ORNL can be found in refs. [29,30]. To determine the yield of a capture reaction, the DRS will be used to separate beam particles passing through the target from the products of the capture reaction. This approach, while challenging, has a number of advantages over more traditional capture y ray detection techniques [29,31]. The recoil detection technique for proton capture reactions was first proven viable with a measurement of the p(12C,13N)y reaction with a relatively small, non-optimized recoil separator at Caltech [31]. In that work, a suppression of scattered beam particles - defined by the ratio of beam particles reaching the focal plane to those incident on the target - of 10"'° was obtained. At the HRIBF, a measurement of the p(12C,,3N) y reaction was made with the DRS, using a 0.666 MeV/u 12C beam incident on a CH2 target. The DRS was tuned to focus the recoiling 13N particles on the focal plane detectors - a carbon-foil microchannel plate detector (providing timing and position signals) followed by a gas ionization counter (providing particle identification). The (non-optimized) suppression of the scattered beam particles was measured to be 3 • 10"", within the 10"10 to 10~12 range needed for capture reactions with cross sections o f - 1 ub. Furthermore, the gas ionization counter cleanly separated (i.e., with no overlap) the energy-loss (Bragg) curves of the low-mass, low-energy carbon and nitrogen particles above 0.4 MeV/u (Figure 2). In this first test, the combined projectile rejection of the DRS and the focal plane detector was well beyond that needed for capture reactions. Further commissioning tests are planned to optimize these results and to determine the transmission through the DRS. Current tests with the DRS have used polypropylene (CH2) foil targets. However, gas targets are preferred over foil targets because they have higher yields for the same target (energy loss) thickness, they have no background from carboninduced reactions, they have no physical degradation or hydrogen-depletion problems common to CH2 foils, and they enable measurements of alpha-induced reactions [(a, y) and (a, p)] when helium is used. Therefore, a windowless, differentially-pumped hydrogen and helium gas target system is under construction, similar to that used in ref. [32].

155

Figure 2. Identification of particles reaching the gas ionization counter at the DRS focal plane in a measurement of the 12C(p,y)13N reaction.

4

4.1

Recent Radioactive Beam Measurements

The NO(CC p)'7F Reaction

The rate of the ,4 0(a,p) 17 F reaction depends critically on properties of states in the compound nucleus 18Ne. In particular, a single J" = 1" state near Ex = 6 MeV and its interference with the direct reaction cross section may dominate the reaction rate at temperatures T9 < 1 [33, 34]. Despite recent studies of 18Ne using both stable beams [34] and a ,7F beam [35], the rate of the 140(a,p)17F reaction remains very uncertain due to the unknown total and alpha-partial widths of the V = 1" resonance, the nonresonant reaction component, and the sign of the interference between resonant and non-resonant contributions. We have studied the 'H(' 7 F,a) l4 0 reaction, the timeinverse of the l4 0(a,p)' 7 F gs reaction, using a radioactive l7F beam and a 100 ug/cm2 CH2 target at the HRIBF. Recoiling 140 ions were detected in coincidence with a

156

particles in the SIDAR: the heavy particles were detected at lab angles of 3.2° to 6.5° in a small, 64-segment annular detector while the alphas were detected at lab angles of 10° - 25° in two stacked rings of eight 16-segment annular detectors (Figure l.a).

Figure 3. Energy - Energy plot used to identify 140 - a coincidences in a measurement of the F(p,a) l4 0 reaction, and the gated angle - energy plot of the a particles.

l7

Stacking the detectors enabled AE - E particle identification which, along with gating on the energies of the 140 and a particles as well as the energy-angle relationship of the alphas (Figure 3), enabled us to distinguish the weak 'H(17F,a)140 channel from an intense background from 17F + 12C fusion evaporation. The beam current, up to 2 • 106 s"1 on target, was determined by measuring 17F + 12 C elastic scattering. An excitation function of the 'H(17F,a)140 reaction was determined by measuring the absolute cross section at 21 energies, covering for the first time the entire energy range of interest for 140(a,p)17F (Eacm = 1 . 0 - 2.6 MeV). The cross section varied by a factor of ~103 over this energy range, and the a - H 0 coincidence rate varied from ~1 min"' to 2 day"'. Properties of states in ,8Ne with excitation energies Ex = 6.0-7.7 MeV are currently being determined from our data, including the important J" = 1" state. The non-resonant reaction cross section and its interference with the 1" resonance were also measured. This will enable the 14 0(a,p)l7Fgs reaction rate to be determined with reasonable certainty for the first time covering temperatures important for novae and X-ray bursts.

157

4.2

The l7F(p,y) '"Ne Reaction

The 17F(p,y)'8Ne reaction rate was uncertain because of a 3+ state that was known in the analog nucleus lsO [36] but never conclusively observed in 18Ne. This missing 3+ state would provide a strong s-wave (1 = 0) resonance and, depending on its excitation energy, could dominate the l7F(p,y)18Ne reaction rate at temperatures corresponding to stellar explosions [37], Three calculations of the properties of this state differed by a factor of 8 in total width and by 314 keV in excitation energy [37-39]. Nine previous studies of this excitation energy range in 18Ne found no conclusive evidence for the existence of the 3+ state, including recent measurements of l60(3He,n)18Ne [38] and high precision measurements of 20Ne(p,t)l8Ne [40,41]. These efforts were hindered by using reactions that suppress the population of states with unnatural spin and parity (such as the 3+). The uncertainty in the l7F(p,y)18Ne reaction rate was as large as a factor of 100 based on theoretical estimates of properties of this resonance. To resolve this uncertainty, we measured the 'H(l7F,p)17F excitation function with a radioactive 17F beam at the HR1BF. This reaction is extremely sensitive to 2+and 3+ states in 18Ne, and our measurement provided the first unambigious evidence for the existence of the missing 3+ state [42]. A 17F beam with energies of 10 - 12 MeV, an average intensity of 8000 s"', and a typical ,7F to n O ratio of 1000 to 1, was used to bombard a 48 ug/cm2 polypropylene CH2 target. Scattered protons were detected in the S1DAR (at lab angles of 25 to 51 degrees) while recoil 17F ions were detected in coincidence (with more than 90 % coincidence efficiency) in our isobutane-filled ionization counter. The setup was similar to that in Figure 1 .b, but with the Si detectors normal to the beam axis. The beam current was determined by measuring 17F + 12C elastic scattering. A total of only 2 • 109 17F ions over the duration of the experiment were needed for this measurement. Proton yields were determined at 12 beam energies (Figure 4) by summing the coincident proton yields in all strips of the SIDAR and normalizing to the same incident beam current. The coincidence requirement was used to eliminate background from e+ particles arising from decay of scattered beam particles. A I7F + p resonance structure is clearly visible in Figure 4, and a fit to the data yields a resonance energy of Eres = 599.8 ± 1.5 (stat) ± 2.0 (sys) keV and a total width of T = 18 ± 2 keV. We conclude that we have observed the long sought 3+ state in ,8Ne for the following reasons: our measurement is sensitive to 3+ and 2+ states only; there are no 2+ states in lsO whose analogs have not been identified in l8 Ne; the observed width is consistent with the expected width of the 3+ state but is five times larger than what is expected for a 2+ state; and the angular distributions of the protons is consistent with a 3+ assignment.

158 Calculated Yield from Elastic Scattering Only (No Resonance) ORNL Data ORNL Fit (Resonant + Elastic Scattering)

900 T3

800

E

= 599.8 ± 2.5 keV r©s T = 18.0 ± 2.2 keV tot E = 4523.7 ± 2.9 keV X

C

o

700 600

-I—'

o © Nj

E o

500 Energy 400

10

17

F(MeV)

11

12

13

Figure 4. Excitation function for the l7F(p,p)!7F reaction showing the J" = 3 + resonance at EN = 4523.7 keV in Ne. The listed resonance properties were determined from a fit to the data.

Our discovery of the 3+ state resolves the greatest uncertainty in the 17F(p,y)l8Ne rate. This rate calculated with our new resonance parameters differs by up to a factor of 100 from some previous estimates. When inserted into a model of the synthesis of isotopes in an energetic nova explosion, the predicted production of some isotopes changed by more than a factor of 1000 when compared to predictions using the rate from [37]. However, the total l7F(p,y)18Ne rate is still somewhat uncertain because the direct capture cross section and partial gamma width of the 3+ state have not been measured. These problems could be solved with the direct measurement of ,7F(p,y)l8Ne planned at the HRIBF. 4.3

The IHF(p, afO and ,HF(p, y)'9Ne Reactions

Both the 18F(p,a)150 and l8F(p,y)"Ne reactions serve to destroy any 18F nuclei which could (via their radioactive decay) be observables in novae ejecta, and the former reaction is thought to be ~ 500 times faster than the latter [43]. Both reactions are possibly dominated at nova temperatures by a "Ne resonance near Ex = 7.07 MeV depending on its properties. Recent experimental results [26, 43-46] have differed by up to a factor of three in their adopted (p,a) resonance strength and by as much

159 as 21 keV in their excitation energy for this state. This results in up to a factor of three variation in the l8 F(p,a) l5 0 rate at stellar explosion temperatures. To resolve these discrepancies, we measured the 'H(l8F,p)18F and 'H( r8 F, a) l s O excitation functions with a thin (35 ug/cm2) CH2 target and a radioactive 18F beam at the HRIBF. Proton and alpha yields were measured in coincidence in the SIDAR with the heavy recoil nuclei at fifteen bombarding energies from 1 0 - 1 4 MeV. Six 16segment silicon strip detectors were configured to face towards the beam axis (Figure l.b) for a larger solid angle coverage than used in our 'H(,7F,p)l7F measurement [42]. In the 'H(18F, a) 1 5 0 measurement, the ls O particles were detected in the inner strips of the array (small angles from the beam axis), while the a particles were detected in coincidence in the outer strips (larger angles). Preliminary analysis suggests that we can extract the width of the Ex = 7.07-MeV resonance to 5 keV, the resonance energy to 1 keV, and the proton-width to a-width ratio to 5 %. 5

Other Astrophysics Research at ORNL

In addition to the measurements with radioactive beams described above, there are a number of other astrophysics research efforts at ORNL - in theoretical astrophysics, nuclear astrophysics data evaluation, heavy element nucleosynthesis measurements, theoretical atomic astrophysics, and atomic astrophysics data. The first two of these research programs are closely coupled to the HRIBF measurement program, and are briefly described in the following subsections. 5.1

Theoretical Astrophysics

A new program at ORNL in theoretical and computational astrophysics has as one of its foci the study of stellar explosions and explosive nucleosynthesis. One of the main areas of research is the core collapse supernova mechanism. Simulations in one-, two-, and three-dimensions focusing on issues of exact (Boltzmann) neutrino transport, convection, and their interplay in the explosion mechanism, are being carried out on supercomputers [47 - 49]. Another research effort is under way to model abundance yields in nova explosions, and to quantitatively determine the contributions of nuclear reaction rate uncertainties on the predictions of nova models. We are carrying out the first systematic analyses of the impact of all reaction rate uncertainties considered simultaneously on nova nucleosynthesis [50]. We are also determining the correlation between the uncertainties of individual rates with the production uncertainties of individual isotopes. This will enable us to make quantitative comparisons between theory and observations, as well as to determine the relative importance of changes in individual reaction rates and provide guidance in the selection of reactions for further experimental study. This work is closely

160 coupled to the HRIBF experimental measurement program and to the nuclear astrophysics data work described below. 5.2

Nuclear Astrophysics Data

Computer models of stellar explosions, as well as models of other astrophysical phenomena, require a very diverse set of nuclear physics information to determine the synthesis of isotopes and the energy released from nuclear reactions. There is a substantial need for more complete, precise, and timely evaluations of nuclear properties needed for astrophysical models [51]. A number of projects are underway to meet the nuclear astrophysics data needs of the ORNL experimental and theoretical nuclear astrophysics research programs. For example, to prepare for measurements of l4 0(a, p)17F and 17F(p, y)18Ne, we evaluated the rates of these reactions determined from indirect experimental measurements [52]. Similarly, evaluations 18F(p, y)18Ne and I8F(p, a) l s O are in progress, as are evaluations of ,7 0(p, y)18F and 170(p, a) l4 N - the latter two reactions to help understand the production of oxygen isotopes in Red Giant Stars. Rates for these reactions are being determined with uncertainties, in formats that can be readily input into reaction rate network codes, and will be posted on the WWW. Another project addressed the need to easily (i.e., electronically) incorporate the 160 thermonuclear reaction rates (and their inverses) in the Caughlan and Fowler 1988 reaction rate collection [53] into computer models. We prepared the first electronic dissemination of this extremely valuable rate collection in the form of a downloadable FORTRAN subroutine [54]. Tabular data for these rates and plots of rates versus temperature have been added, along with a graphical search engine based on the chart of the nuclides and the temperature derivatives of these rates - useful for coupling nucleosynthesis calculations to hydrodynamics. Another data project involved compiling a nuclear astrophysics data bibliography, with over 1200 references, that is posted on the WWW [54]. 6

Summary

Measurements of capture reactions on proton-rich radioactive isotopes are crucial to the understanding of explosive nucleosynthesis occurring in stellar explosions such as novae and X-ray bursts. We have recently measured the l7F(p,p), ,7 F(p,a) l4 0, l8 F(p,p), and l8F(p,a)lsO reactions at ORNL's Holifield Radioactive Ion Beam Facility with a Silicon Detector Array (SIDAR) to better understand these explosions. The Daresbury Recoil Separator (DRS) has also been installed at HRIBF and is being readied to study capture reactions in inverse kinematics. Initial tests with stable beams indicate that the DRS gives an excellent suppression of scattered beam particles in these reactions. Additionally, there are theoretical

161

astrophysics and nuclear astrophysics data evaluation work at ORNL which are closely coupled to the HRIBF experimental nuclear astrophysics work. 7

Acknowledgements

The author wishes to thank Co-chairpersons T. Kajino and S. Kubono for their hospitality during the Symposium. Thanks to D.W. Bardayan and D.C. Larson for helpful comments. RIBENS (Radioactive Ion Beams for Explosive Nucleosynthesis Studies) collaboration members D.W. Bardayan, J.C. Blackmon, W. BradfieldSmith, C. R. Brune, A.E. Champagne, A. Chen, T. Davinson, U. Greife, K.I. Hahn, V. Hansper, M. Hofstee, A.N. James, B.A. Johnson, P.E. Koehler, R.L. Kozub, C.S. Lee, R. Lewis, Z. Ma, P.D. Parker, D.E. Pierce, G. Rajbaidya, R.C. Runkle, CM. Rowland, A.C. Shorter, M.S. Smith, F. Strieder, K.B. Swartz, D.W. Visser, and P.J. Woods contributed to the HRIBF measurements, along with T.A. Lewis, J.W. McConnell, W.T. Milner, and D. Shapira. The theoretical collaborators were W.R. Hix, A. Mezzacappa, S. Starrfield, and D.L. Smith. ORNL is managed by UTBattelle, LLC for the U.S. Dept. of Energy under contract DE-AC05-00OR22725.

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19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

K. Arai, M. Hashimoto, Astron. Astrophys. 254 (1992) 191. M. Wiescher, J. Gorres, II. Schatz, J. Phys. G 25 (1999) R133. G.D. Alton and J.R. Beene, J. Phys. G 24 (1998) 1347. G.D. Alton, J.R. Beene, and Y. Liu, Nucl. Inst. Meth. A438 (1999) 190. R.F. Welton et al., Nucl. Inst. Meth. B159 (1999) 116. G.D. Alton, Y. Liu, C. Williams, and S.N. Murray, Proc. Eighth Int. Conf. Heavy Ion Accelerator Technology, ed. K.W. Shepard, (1999) p. 330. P.J. Sellin et al., Nucl. Inst. Meth. A311 (1992) 217. R. Cozach et al., Phys. Letts. B353 (1995) 184. D.W. Bardayan, Applications of Accelerators in Research and Industry, eds. J.L. Duggan, I.L. Morgan, AIP: New York, 1999, p. 326. A.N. James et al., Nucl. Inst. Meth. A267 (1988) 144. M.S. Smith et al., in Stellar Evolution, Stellar Explosions, and Galactic Chemical Evolution, ed. A. Mezzacappa, lOP: Bristol, 1998, p. 511. M.S. Smith, in Proc. Origin Matter Evolution Galaxies 97, eds. S. Kubono, T. Kajino, K.I. Nomoto, I. Tanihata, World Scientific: Singapore, 1998, p. 200. M.S. Smith, C. Rolfs, and C.A. Barnes, Nucl. Inst. Meth. A306 (1991) 233. L. Gialanella et al., Nucl. Inst. Meth . A376 (1996) 174. C. Funck and K. Langanke, Nucl. Phys. A480 (1988) 188. K. I. Hahn et al., Phys. Rev. C54 (1996) 1999. B. Harss et al., Phys. Rev. Lett. 82 (1999) 3964. D.R. Tilley, H.R. Weller, CM. Cheves, and R.M. Chasteler, Nucl. Phys. A595 (1995) 1. M. Wiescher, J. Gorres, R.-K. Thielemann, Ap. J. 326 (1988) 384. A. Garcia et al., Phys. Rev. C43 (1991) 2012. R. Sherr and H.T. Fortune, Phys. Rev. C58 (1998) 3292. K. I. Hahn et al., Phys. Rev. C54 (1996) 1999. S.H. Park et al., Phys. Rev. C59 (1999) 1182. D.W. Bardayan et al., Phys. Rev. Lett. 83 (1999) 45. S. Utku et al., Phys. Rev. C57 (1998) 2731. J.S. Graulich et al., Nucl. Phys. A626 (1997) 751. K.E. Rehm et al., Phys. Rev. C52 (1995) R460; C53 (1996) 1950; C55 (1997). J.S. Graulich, Ph.D. Thesis (in preparation). O.E.B. Messer et al., Ap. J. 507 (1998) 353. A. Mezzacappa et al., Ap. J. 493 (1998) 848. A. Mezzacappa et al., Ap. J. 495 (1998) 911. W.R. Hix, M.S. Smith, A. Mezzacappa, S. Starrfield, in Cosmic Explosions, a Conference Proceedings, ed. S.S. Holt, AIP: Melville (2000) in press.

5 1 . M . S . Smith et al., http://www.phy.ornl.gov/astrophysics/data/task/taskforce_report.html.

52. D.W. Bardayan and M.S. Smith, Phys. Rev. C56 (1997) 1647. 53. G.R. Caughlan, W.A. Fowler, At. Data Nucl. Data Tables 40, (1988) 283. 54. M.S. Smith et al., ORNL Nuclear Astrophysics Data Website: http://www.phy.ornl.gov/astrophysics/data/data.html.

MEASURING THE ASTROPHYSICS RATE FOR RADIATIVE PROTON CAPTURE ON 21 NA JOHN M. D'AURIA FOR THE DRAGON COLLABORATION Department of Chemistry, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 E-mail: [email protected] The 21Na(p,y)22Mg reaction is believed to play an important role determining the amount of the long-lived, radioisotope 22Na in the universe. This nuclide is important as a target of current and future generations of gamma ray telescopes, since its production is part of the pathway of a nova, and because its daughter, 22Ne, has been found in pre-solar grains in meteorites. Unfortunately the rate of this reaction has never been measured primarily due to the fact that 21Na is radioactive (T^ = 23 s). This report describes an experimental program aimed at measuring this rate using inverse kinematics at the new radioactive beams facility, ISAC. A new recoil mass separator, DRAGON, is being constructed to perform this and similar reaction rate studies; the status of this new facility is presented. New information on the levels of 22Mg, studied using a p,t reaction is also presented.

1

Introduction

1.1

Overview

Novae occur on the surfaces of white dwarf stars that accrete matter from a companion star. The accreted material gains a large amount of energy as it falls into the gravitational field of the white dwarf, arid this energy heats the surface layer. When the temperature is high enough to ignite thermonuclear reactions, an explosion occurs. Various reaction networks are believed to occur during the hydrogen burning of the outburst and the NeNa cycle could play a dominant role for certain class of novae. This consists of 20

Ne(p, y) 21Na((3+)21Ne(p,Y)22Na(p,Y)23Mg(P+)23Na(p,a)20Ne

(1)

Ne(p,- Y)21Na(p,Y)22Mg(p+)22Na(p,Y)23Mg(P+)23Na(p,a)20Ne

(2)

and 20

As the warm NeNa cycle (eq. 1) includes beta decay, the rate of the energy generation is limited by this (Ti/y=22 s) decay. By bypassing this decay, the hot NeNa cycle (eq. 2) can dramatically increase the energy generation of the explosion. As the rate of the 'Na(p,Y)22Mg determines when the transition between cycles takes place, knowledge of the actual rate of this reaction plays a key role in understanding this type of nova.

163

164

The radioactive nucleus, Na, is of interest because it decays with the emission 22

of a 1.28 MeV gamma ray, and because its daughter, Ne, has been found in meteorites. Ne-E was first found in carbonaceous meteorites (1). This gaseous component consists of neon, enriched in 22Ne by factors up to 103, or in other words, is nearly pure 22Ne. Ne-E is carried by grains of silicon carbide, probably pre-solar in nature. While the origin of the grains is unclear, clearly one production path for 22Ne is through decay of 22Na. There is speculation that understanding of how and why Ne-E exists could play an important role in expanding our understanding of nucleosynthesis in present day Galaxy and the Galaxy of 4.5 billion years ago. The production of 22Na in the universe is governed by the NeNa cycle and also the lNa(p,y)22Mg reaction which has not yet been measured. Another important role that the isotope Na plays is as a target of gamma ray astronomy. The emitted gamma ray of 1.28 MeV should be observable by gamma ray observatories and can be a useful probe of recent nova activity, the half-life is 2.6 years. Present estimates of the flux of ^Na (2) in a nova using estimates of the 21 Na(p,y)22Mg rate (3) indicate that it should be observable by the COMPTEL telescope on the NASA Gamma Ray Observatory. However, it has not yet been observed in several novae, and only upper limits have been set (4) for the novae Her 1991 and Cyg 1992. Again, better knowledge of the rate of the 21Na(p,y)22Mg reaction is needed to understand the lack of this observation in this complex, rapid explosion. 1.2

Current Knowledge of the 21Na(p, i)22Mg Reaction

It is believed that the rate of this reaction is dominated by narrow, isolated resonances and few of the key parameters are known to a reasonable degree of accuracy. The level scheme for Mg and its isobaric analogue, ^Ne are shown in Fig. 1.

165 (0,1)

6.980

3

6,904 /6,853

6,783

3'

(2,3) 1"

6.691 6.636

4"

6,345

0

6.237

2"

6.115

3'

5.909

6.585

4"

2

0"

5.966

<6

5.837

2~

5.714

5.502

2,

6.267

22

Na+p

,

22 Ne

Mg Figure 1. Levels of 22Ne and 22Mg

The key levels lie above 5.5 MeV and it is presently believed that only three resonances at 212.4, 336 and 464 keV are important at nova temperatures, although new information (5) may effect this as described below. The resonance strengths of these states have not been measured but using estimates (3), the expected thick target yields of a p, y reaction can be estimated (see Table 1). Given the uncertainty in both the strengths and the energy of the states, however, the availability of a' 'Na beam offers an excellent opportunity to study these. Table 1. Parameters for the 'H(21Na,22Mg)y Reaction

Er(AE) (MeV)

Ex (MeV)

J*

212.4(1.9) 336(5) 464(25)

5.714 5.84 5.97

2+ <6 0+

coy (MeV)

Yield* (xlO"12)

■^beam

l^recoil

(MeV/u)

(MeV/u)

2.2 11.3 2.5

6 20 3

0.22 0.35 0.486

0.20 0.33 0.46

Recoil Cone (mrad) 13.3 10.9 9.5

Assumes a gas target of 2 x 10 atoms/cm in a 10 cm long cylinder; P = 3 Torr. '* Assumes a 21Na beam intensity of 109 pps and a DRAGON transmission of 40%.

Count Rate** (cph) 10 33 5

166

2

Experimental

In order to perform this study will require a radioactive beam of Na, a windowless gas target of hydrogen gas, a high transmission and acceptance recoil mass separator in which all beam particles are eliminated, and a detection system of the recoiling reaction products. The study must be performed using inverse kinematics since the heavy reactant is radioactive. In addition preliminary studies must be performed to obtain more precise information on properties of Mg. These will be described below. 2.1

Production of the21 Na beam

The Na beam will be produced at the new accelerated radioactive beam facility, ISAC, located at the TRIUMF National Nuclear Laboratory in Vancouver, Canada. This facility started operations in 1998 and accelerated beams are expected by the end of 2000. The energy of the beam is variable from 0.15 to 1.5 MeV/u; table 1 shows the required beam energies for the 'Na study. Fig. 2 displays the plan view of the new experimental hall.

Figure 2. Plan View of ISAC Experimental Hall

The Na beam will be produced using 500 MeV protons from the TRIUMF cyclotron incident onto a thick target (probably either SiC or MgO), and the 21Na atoms extract through diffusion into a heated surface ion source. This source will only ionize alkali and alkaline elements, with ions extracted at a total energy of < 60

167

keV. Subsequent mass analysis of this ion beam will result in a pure beam of Na+ ions. These will be directed into the RFQ, a stripper, and then a DTL LiNAC acceleration system. Previous studies indicate that the final, accelerated beam incident onto the gas target should be of the order of 10 p/s. 2.2

Windowless Gas Target

A windowless gas target system for both He and H2 gas has been designed, built, and is now in the testing phase. It consists primarily of pumps (Roots Blowers, Turbos and Backing) in order to maintain a gas pressure of the order of 4 Torr and yet keep the pressure levels at both ends of the target -10" Torr. The inner target chamber is 10 cm in length with a circular opening of 6 mm. The target thickness is estimated to be 2 x 10 atoms/cm . Initially a flow-through system will be used but ultimately, a gas recirculation and cleaning system will be introduced. Initial tests of the assembled system indicated that the pressure prior to entry to the separator section is of the order of 2 x 10"6 torr for a central target pressure of 4 torr, He gas. 2.3

The Separator

Following the target will be a recoil mass separator with 100 % acceptance of all radiative proton and alpha capture reactions of interest. This separator consists of two separate sections with a momentum analyzer (magnetic dipole) and an energy analyzer (electric dipole) in each. The momentum analyzer will transmit one charge state of the beam and reaction products, and then the beam is rejected at the energy analyzer. With these two sections a beam rejection factor of >10 has been estimated assuming various beam scattering and beam charge exchange scenarios. This system also contains 10 quadrupoles, 4 steerers and 4 sextupoles and all are being constructed with high precision. All units have been designed, and in the construction phase. Installation commenced at the end of 1999 with commissioning with alpha sources to start by Sept. 2000. Fig. 3 displays a conceptual view of the DRAGON facility. 2.4

Detection Systems

At the end of the separator there will be several detectors. Initially the ions will pass through a carbon foil with the resulting electrons detected in a multichannel plate detector to generate a fast start signal. These ions may then pass into a gaseous detection chamber (ionization detector) through a thin polymer/grid supported window. At the front of the chamber, they pass through a PGAC (parallel gridded avalanche counter) positioned 0.5 m from the start detector, and this would provide a fast stop signal. The t-o-f would be the primary measure of mass when combined with the energy of the recoil. An alternate possibility is to use a second MCP detector system to provide a stop signal, without the PGAC. The total energy of the

168

ion would be provided by the multichamber ionization chamber. It may also be possible in some instances to provide some Z discrimination based upon the small AE in the sub-chambers. The ionization chamber has been built and tested but has only demonstrated an energy resolution of within a factor of 2 of the desired value of 1%. It should also be noted that a secondary t-o-f signal would also be generated using the pulsing structure of the accelerator as a start signal. A further beam rejection factor of at least a factor of 10 or optimistically, 102 is expected when using the recoil detection system.

Figure 3. Conceptual representation of the DRAGON facility

2.5

Gamma Array

It is also proposed to surround the gas target with a gamma array to provide an additional beam rejection trigger when the prompt gamma from the reaction is used in coincidence with the recoil detector. The design of the array however does face several challenges. The proton-rich ion beam itself is radioactive and upon passing through the target with its slits will deposit approximately .1% of its activity or about 10 cps. A highly segmented, fast scintillate system is under detailed review to detect with good energy resolution, the 1-8 MeV Gammas expected from the various reactions under consideration for study with DRAGON in the field of the

169

0.511 MeV annihilation gammas. Funding is being sought for an array which utilizes a BGO based, modular system with a total detection efficiency of about 65%. It is believed use of this system will provide a further beam rejection factor of >102. 2.6

Experimental Estimates

The last column in table 1 are estimates of the expected counting rates that would be observed for the different resonances given the assumptions indicated. These may have to be modified depending upon a final analysis of the study mentioned below on the key levels of "\Mg. 2.7 2.1 A

Related Studies Studies of the 22Mg levels

As indicated above additional information is needed on the energies of the levels in in order to perform this study. The resonance at 464 keV is only known to an accuracy of 25 keV, which is higher than the expected energy loss (10 keV) in the gas target. It is be very difficult to attempt to find narrow resonances with the relatively weak radioactive beams. Therefore studies were performed to measure this energy more accurately. Table 2 presents some of the preliminary data obtained in a (p,t) reactions performed at the CNS cyclotron in Tokyo, Japan. Also indicated are the accepted energies in the literature (6) for Mg. It is clear that additional levels have been observed in the energy range, which may play a role in the astrophysical rate of this reaction. A theoretical analysis is underway to understand the nuclear structure involved (5). Table 2. Preliminary Data from ^MgCp.t^Mg Reaction

E r (keV) (Endt) 4400.9 (1.4) 5037.0(1.4) 5292(3) 5317(5) 5464(5) 5713.9(1.2) 5837 (5) 5965(25) 6267(15) 6585(35) 6783 (19)

8° 5037.0 5089.5 (1.9) 5296.5(1.3)

16° 4399.0 (5.3) 5037.0 5090.9 (1.8) 5296.5(1.3)

20.5° 4400.5 (5.2) 5037.0 5089.1 (1.6) 5295.0(1.2)

5454.8(1.3) 5713.9

5454.3(1.3) 5713.9

5454.5(1.3) 5713.9

5961.1(2.4) 6044.6 (2.9) 6244.3(4.9) 6321.6(5.8) 6613.5(10.2) 6787 (14)

5964.4(2.6) 6048.6 (3.0) 6251.0(5.2) 6325.7(6.1) 6621.9(10.8)

6046.3 (3.0) 6246.2(5.0) 6322.7(5.9) 6604.7(10.3)

170

3

Summary

An experimental program is underway to measure the astrophysical rate of the 'H(21Na,y)22Mg reaction. This involves a new accelerated radioactive beams facility, IS AC, and a new detection facility, the DRAGON at the TRIUMF laboratory in Vancouver, Canada. It is expected that this study will be ready to receive beam by the end of 2000. New results have also been obtained concerning the levels of 'Mg and further analysis and possibly other indirect experiments will be performed. More details on many aspects of IS AC and DRAGON can be found at http://www.triumf.ca and http://www.sfu.ca/triumf. 4

Acknowledgements

Financial support of the Natural Sciences and Engineering Research Council of Canada and infrastructure support of TRIUMF are gratefully acknowledged. The efforts of all members of the DRAGON collaboration are also acknowledged. References 1. D.C. Black, Geochim. Cosmochim. Acta, 36, 377 (1972). 2. M. Politano, S. Starrfield, J.W. Truran, A. Weiss, W.M. Sparks, Ap. J. 448, 807 (1995). 3. M. Wiescher and K.-H. Langanke, Z. Phys. A, 325, 309 (1986). 4. A.F. Iyudin, et.al., A. & A., 300, 479(1995). 5. J. M. DAuria, et. al., private communication; paper to be submitted. 6. P.M. Endt, Nucl. Phys. A521, 1 (1990).

NUCLEAR ASTROPHYSICS PROJECT WITH A NEW LOWENERGY RIB SEPARATOR CRIB - Study of a Critical Stellar Reaction 150(<x,y)l9Ne S. KUBONO, S. MICHIMASA, T. TERANISHI, Y. YANAGISAWA, Z. FULOP, X. LIU, K. KUMAGAI, K. ABE, C. C. YUN, S. WATANABE, N. YAMAZAKI, Y. OHSHIRO Center for Nuclear Study, University of Tokyo (CNS), RIKEN Campus, Hirosawa 2-1, Wako, Saitama, 351-0198 Japan E-mail: [email protected]. u-tokyo.ac.jp M. KUROKAWA, P. STRASSER, K.I. HAHN, T. KISHIDA RIKEN, Hirosawa 2-1, Wako, Saitama, 351-0198 Japan N.IMAI Physics Department, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033 Japan S. KATO Physics Department, Yamagata University, Yamagata, 990-8560 Japan Y. FUCHI, AND M.H. TANAKA Institute of Nuclear and Particle Physics, High Energy Accelerator Organization (KEK), Tsukuba, Ibaraki, 305-0801 Japan

One of the critical stellar reactions for the onset of explosive hydrogen burning, 150(a,y)"Ne, is discussed with our recent experimental effort and a new possibility in our new RIB project. This reaction was investigated experimentally by indirect methods. Single particle nature of the threshold states was studied by the analog reactions, (d,t) and (d,3He) on 20Ne. The a-branching ratios for some states were also measured by a coincidence measurement of a triton and a from 19 3 F( He,t)''>Ne*(a)150(g.s.). Experimental plan for the problem was also discussed that uses a new low-energy RIB facility at CNS, called CRIB, which will come into operation soon.

1

Introduction

Proton-rich unstable nuclei play a crucial role in explosive hydrogen burning, which is called the rapid-proton capture process (rp-process) [1]. Nova is a typical site that involves the rp-process, where a chain of successive nuclear reactions together with beta decays lead to abundant production of variety of heavy elements such as Si, which is a stringent clue for understanding the rp-process [1,2]. Similarly, a recent x-ray observation gives us elemental distributions in the

171

172

expanding outburst of the supernovae, partly of which might come from the rpprocess. Line gamma-ray observations give us an interesting mapping of nuclides such as 26A1 in the galaxy [3], which also provides a very critical test of the models. The rp-process is discussed as a candidate for the production. In the rp-process under a condition of novae, the CNO material would be transmuted to heavier elements. The first step of the process is considered to be 15 0(a,y)19Ne in the scenario [1], and could be followed by a chain of the reactions; 19 Ne(p,T)20Na(p,7)21Mg(vp+)21Na(p,T)22Mg(vP+)22Na(p,Y)23Mg(p,y)24Al (p,y)2sSi ... [1,2,4]. Here, most of the nuclear reactions in the chain were studied previously by indirect methods, and many resonances near and above the proton thresholds were discovered [2]. Consequently, most of the reaction rates from 19Ne to 25Si are enhanced, resulting in reduction of the ignition temperature of the processes. From our estimates of the reaction rates, the limiting reaction of the chain is considered to be the first step, 150(oc,y)19Ne. However, the reaction rate of this process is not known well. We have studied the properties of the 19Ne excited states relevant to the 15 0(oc,y)19Ne reaction by the mirror reactions, (d,t) and (d,3He) on 20Ne, exciting the mirror states. The branching ratio measurement of the threshold states was also tried using the reaction 19F(3He,t)19Ne*(a)I50(g.s.). We discuss in sec. 2 on the spectroscopic nature of 19Ne threshold states, and in sec. 3 the measurement of ocbranching ratios of the states in !9Ne. A possibility of measurement of the a-widths, that provide the resonance strengths, using a new low-energy RIB separator which is under installation at Center for Nuclear Study, University of Tokyo (CNS), is also discussed in sec. 4. 2

Spectroscopic nature of the a-threshold states in 19Ne

The possible limiting reaction for ignition of the rp-process, 150(a,y)19Ne, was investigated first by studying the property of the threshold states in 19Ne with the charge symmetric reactions, 20Ne(d,t)19Ne and 20Ne(d,3He)19F [5]. If the reaction particles and. the residual states associated are all mirror states, the two reactions leading to the analog states would show similar angular distributions. This will be true because intermediate states which couple in the reactions would be also the mirror states and thus multi-step contributions could be roughly the same, resulting in angular distributions of similar shape. We may identify the mirror relation, and also get spectroscopic information on the states of interest. Figure 1 displays the level schemes of A = 19 nuclei, taken from ref. [6]. Since the peak temperature of novae is somewhere around T9 = 0.2 - 0.4, the nuclear levels relevant are those below 5 MeV in 19Ne. Especially, the main contribution of the 150(a,y)19Ne stellar reaction is considered to come from the 4.033 MeV 3/2+

173

4.014 15

N + a

5.107

5/2+

4.683

5/2-

4.648 4.556

13/2+ 3/2-

4.550

5/2+

4.378

7/2+

4.033

9/2-

3.999

7/2-

3.908

3/2+

5.092

5/2+

4.712

(5/2-)

4.635 4.600 4.549

13/2+

4.379

7/2+

4.197 4.140

(7/2-) (9/2-)

4.033

3/2+

(5/M

(1/2.3,

15

^ 0.0

0 + a

^ 1/2+

19p

0.0 l9

1/2+

Ne

Fig. 1 Nuclear level schemes of 19F and 19Ne [6]. state. However, the property of the level as well as of the nearby-levels are not known well yet. For instance, the spin assignment for the levels at 4.140 and 4.197 MeV is not determined yet. They would contribute to the synthesis to some extent if they are the analog states of the 3.999 MeV 7/2" state and the 4.033 MeV 9/2" state in I9 F. The experiment was made using a 30-MeV deuteron beam from the SF cyclotron at CNS. The reaction products tritons and 3 Hes' were momentum analyzed by a QDD spectrograph, and detected by a hybrid-type gas proportional counter and a plastic scintillator set behind on the focal plane. Figure 2 shows some spectra of the (d,t) and (d,3He) reactions on 20Ne at 30 MeV. The 4.033-MeV state

174 150

20

Ne(d.3He)"F 6^8=20° E(d)=30MeV

100

50

y "B 3(XXf 250 200

1L

JU„ Ne(d.I)"Nc 61^=20" E(d)=30MeV

20

150 100 50 100

400

200

JL 300

500

JL

400 500 600 700 Channel Number ( momentum )

600 700 Channel Number (momentum)

800

800

Fig. 2 Triton and 3He spectra from the (d,t) and (d,3He) reactions on 20 Ne, measured at 20 degrees with a 30-MeV deuteron beam. in l9Ne was very weakly excited by the (d,t) reaction. This suggests that there is very little d3/2 single particle component in this state. The doublet at 4.140 and 4.197 MeV, which could be weak-coupled a-cluster states, is excited with larger cross sections. The angular distributions were measured for these levels in 19Ne and the analog states in ' F.

175

A DWBA analysis explains well the angular distribution for the 4.033 MeV state in 19Ne with the angular momentum transfer 1 = 2, confirming the spin assignment of 3/2 for the state. The spectroscopic factor derived for the state is as small as S = 0.04. This state, however, was excited strongly by the 21Ne(p,t) 19Ne reaction [6]. These suggest that this state has a 5-particle 2-hole nature. The stellar reaction, 150(a,y)19Ne, would proceed only through a small component of 2p-3h in 15 0. This is very much consistent with the very small a width, 9.9+ 1.5 H-eV, estimated by an a-transfer reaction leading to the analog state in ' F [7]. 3

Measurement of a-branching ratios of the threshold states in 19Ne

If a radiative capture reaction of interest is dominated by a resonance, the reaction rate is roughly proportional to the resonance strength ory. Here, co is the spin factor and j is the particle-width of the resonance when the resonance sits close to the particle threshold and thus the total width of the resonance is dominated by the gamma width. The present 150(oc,y)I9Ne stellar reaction is just a typical case that the resonance is located close to the particle decay threshold. The critical state estimated is the 4.033 MeV 3/2+ state for the problem of novae, as mentioned earlier. This state is excited with a reasonable cross section by the (3He,t) reaction at 30 MeV. The experiment was performed at the SF cyclotron of CNS. The target was CaF2 of about 70 [ig/cm2, evaporated on C. The tritons from I9F(3He,t),9Ne*(oc)150 were momentum analyzed by the QDD magnetic spectrograph, and detected by the focal plane detector mentioned in sec. 2. The tritons were uniquely identified by AE, E, and Time-of-Flight. The decay a particles were measured at backward angles in coincidence with the tritons by four Si detectors of 60x60 mm" area that have 12 strips, which covers about 11 % of 4it. Figure 3 shows the energy spectra of the decay a particles from the excited states in 19Ne. The spectra for the states above 4.5 MeV show clearly the a decay peaks, but it is not clear among the background in the spectra for the states below 4.5 MeV. The angular correlation function of the a decays from the 5.35 MeV state shows an isotropic distribution because it has J*= l/2 + , where the energy spectra were deduced for 8 angles by summing some strips to get better counting statistics. This correlation function assures that the system is working properly. The branching ratios were deduced from the coincidence probabilities of the tritons relevant. Here, the total yields of a particles were derived by extrapolating the angular correlation functions to the unmeasured angles. The a-branching ratios were determined with a little better statistics in the present experiment than in the previous experiment [8], but are consistent with them for the high-lying states. However, the branching ratios of the critical levels at 4.033

176 E3 in coincidence with tritons £ 3 in accidental coincidence "with tritons

' ' ■ ' I '■ ■ ' ' I ' ' ■ ■ I ' ' ' ■ I E , » 6.09Z MeV

E . = 4.033 M«V

0.0

0.S

TzsssSsJkxzz&Dtsa-. 1.0

1.5

2.0

Energy (MeV)

Fig. 3 Energy spectra of decaying alpha particles from the states denoted in 19Ne, following the 19F(3He,t)19Ne reaction. and 4.379 MeV were not determined in the present experiment. Because of the very small a width, it is quite difficult to measure the branching ratio. It seems also quite difficult by the same reason to measure directly the cross section of the 4 He(150,y)19Ne reaction using an 1 5 0 beam at the stellar energies.

177

4

Study of lsO(a,y)19Ne with a new RIB separator CRIB

The direct measurement of 150(a,y)19Ne seems quite difficult because the yield rate expected would be very low, as discussed in the last section. An alternative way is to use a semi-direct method for the reaction, i.e., a direct oc-transfer reaction to deduce the a width. It could be investigated using the secondary beam of 15 0 from the new lowenergy RIB beam separator, CRIB, which is under construction at CNS in the RIKEN accelerator facility. As can be seen in Fig. 4, the system is composed of a gas target for the secondary beam production, a double achromatic separator with a degrader in between the two dipole magnets, and a Wien filter at end to get high purity secondary beams. Since the ion source technology has developed considerably in the recent years, one should be able to deduce the 15 0 beam of 108"9 aps on target. Since one may use (p,n) reaction at the energy just above the threshold energy in the inverse kinematics, the energy spread of the 1 5 0 beam should

Degrader

Fig. 4 A new low-energy RIB separator, CRIB, being installed at CNS, in the RIKEN accelerator facility.

178

be reasonably small, about 1 %, and the beam spot size of a few mm diameter at the focal plane. If one can use an 15 0 beam of 109 aps on target, one could measure the angular distribution for the 6Li(15O,19Ne*(4.033))d reaction either measuring deuterons at backward angles or 19Ne particles at forward angles from the reaction with a reasonable count rate, something like a few events per hour or more. Since the secondary beam has a certain energy spread, the energy resolution is the matter for the measurement of the direct a-transfer reaction, which should be taken care of in the experimental setups with the velocity filter at end. Since the CRIB is simply an in-flight beam separator, one does not need to develop ion source technology for RIB production. The production of nuclear spices is very much limited to the nuclei close to the line of stability, as we use an AVF cyclotron of K = 70 as the driver machine. However, the production rate is very high because of the inverse kinematics we adopt here and also the large cross sections for production, although the available target thickness is small. This weak point will be compensated with very high beam intensities from ECR ion sources. This method for low energy RIB production should be, thus, very useful in practice. The CRIB is the first extensive RIB facility constructed with this method at low energies. The beam energies of 5 -15 MeV/u is just a good energy region for nuclear spectroscopy for both in-beam gamma spectroscopy as well as charged particle spectroscopy. This work was partly supported by the Ministry of Education, Science, Sports, and Culture of Japan under contract No. 10440070. References 1. R. K. Wallace and S. E. Woosley, Astrophys. J. Suppl. 45 (1981) 389. 2. S. Kubono, Prog. Theor. Phys. 96 (1996) 275. 3. W. A. Mahoney, J. C. Ling, W. A. Wheaton, and A. S. Jacobson, Astrophys. J. 286 (1984) 578. 4. K. Langanke, M. Wiescher, W. A. Fowler, and I. Gorres, Astrophys. J. 301 (1986) 629. 5. K. Kumagai, MS thesis, Tohoku Unversity (1999). 6. D. R. Tilley, H. R. Weller, C. M. Cheves, and R. M. Chasteler, Nucl. Phys. A595(1995) 1. 7. Z. Q. Mao, H. T. Fortune, and A. G. Lacaze, Phys. Rev. Lett. 1A (1995) 3760. 8. P. V. Magnus, et al., Nucl. Phys. A 506 (1990) 332.

V. Explosion of Massive Stars

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PHYSICS OF COLLAPSE-DRIVEN

SUPERNOVAE

SHOICHI YAMADA Institute of Laser Engineering (ILE), Osaka University, 2-6, Yamadaoka, Suita, Osaka 565-0871, JAPAN E-mail: [email protected] In this paper I will review the physics involved in the collapse-driven Supernova, paying particular attention to some selected issues concerning both one- and multi­ dimensional aspects of the dynamics of supernova.

1

Introduction

The collapse-driven supernova is an explosive phenomenon which is supposed to occur at the end of the evolution of massive stars (>,8M 0 ). The highly en­ ergetic explosion with a typical explosion energy .Eexp ~ 1051erg is triggered by the gravitational collapse of a central core after it exceeds a certain critical density (~ 10 9 5 g/cm 3 ) or temperature (~ 10 9 7 K). The event is followed by the formation of a neutron star or a black hole. This type of supernova is essentially the same as the one formerly called Type II supernova, although the current classification is based on the mechanism of explosion rather than the spectroscopic feature. Hence some subclasses of type I supernova, namely, type Ib/Ic, are thought to belong to the collapse-driven supernova. The en­ ergy source of explosion is the gravitational binding energy liberated by the formation of a compact object, typically a neutron star. This enormous en­ ergy (ENS ~ 1053erg) which is about two orders of magnitude larger than the observed explosion energy is largely transported by neutrinos copiously emitted by a nascent neutron star. Therefore, it is reasonable to think that the neutrino transport plays an important role in producing a supernova. The main reason why the collapse-driven supernova is so fascinating is that it involves a rich variety of physics. As already mentioned above, microphysics such as the weak interaction and nuclear physics is supposed to dictate the macroscopic dynamics in a critical way. In particular, the under­ standing of the equation of state for the hot and dense nuclear matter and neutrino interactions therein are crucial. On the other hand, it has become a common sense that the collapse-drive supernova is in general not spherically symmetric. Various convections are expected to occur at different places and times, and some of them inside the supernova core might play a major role in producing an energetic explosion and some in the mantle and envelope mix up heavy elements synthesized explosively, which fact was supported observation-

181

182

ally in SN1987A. The stellar rotation is another ingredient which renders the explosion asymmetric and attracts much attention these days in connection with the rotational supernova (or better the hypernova) as a possible central engine of the gamma ray burst. It is, however, noted that SN1987A was glob­ ally asymmetric. The rotation may be important for the normal supernova as well. The interest in the magnetic field in the supernova will also be revived in the same context since the existence of highly magnetized neutron stars is now becoming realistic. All these microphysical as well as macrophysical is­ sues should be investigated to understand the collapse-driven supernova, that is definitely a major challenge. The collapse-driven supernova occupies an important position in astro­ physics. One of the reasons is that it is believed to be a major contributor for the chemical evolution of universe. The supernova distributes heavy el­ ements which are synthesized not only in the hydrostatic phase prior to the explosion but also during the explosion itself, thus increasing the metalicity of galaxies. The collapse-driven supernova is also expected to be a promising r-process site, since the matter is neutron rich due to the electron capture. As explained shortly, a strong shock wave is generated in the supernova, pass­ ing through the whole progenitor. It is, therefore, expected that high energy cosmic rays are generated around the supernova. As easily understood from the fact that the supernova is associated with the formation of a compact object, the supernova is a relativistic event. It is worth remembering that the supernova is a possible source of the gravitational radiation as massive stars are in general a rapid rotator. The expectation that the gamma ray burst is somehow associated with the collapse-driven supernova has been rising these days. The further observations of the gamma ray burst might turn out to reveal the new aspect of the supernova. Here I will briefly outline the temporal evolution of the collapse-driven supernova. It commences with the gravitational collapse of a white dwarf like core due to the reduction of pressure either by the electron capture or by the photodisintegration of irons. The collapse does not halt until the central density exceeds the nuclear saturation density and the matter recovers enough pressure to prevent further collapse. During this collapsing phase, neutrinos emitted by the electron capture are trapped inside the core after the density becomes larger than about 10 12 g/cm 3 and the matter becomes opaque even for the neutrino. As a result, the electron capture is ceased because of the fermi blocking for emitted neutrinos. At this point, the electron fraction is somewhat larger than 0.3. Since the entropy of the core remains low ~ kB and the electron fraction is this large, nuclei survive just up to the saturation density. Incidentally, the collapsing core is divided into two part; the inner

183

part shrinking subsonically and self-similarly referred to as the inner core, and the outer part falling supersonically called the outer core. Their masses are one of the important factor for the successful explosion. When the pressure gets sufficiently large due to the nuclear force, the inner core bounces and the shock wave is generated at the boundary of the inner and outer cores. The inner core serves as a piston to launch the shock wave out through the outer core. When the shock wave somehow reaches the surface of the core, we regard the explosion as successful, since the loosely bound outer envelope is hardly an obstacle for the shock wave. As mentioned above, heavy elements are synthesized explosively as the shock wave passes through the envelope, and when it breaks out the progenitor's surface, the familiar optical display of the supernova emerges. In the above sequence of events, what is most uncertain is how the shock wave manages to propagate the outer core up to the surface of the core. In fact, almost all elaborate simulations done so far showed that the initial shock energy is not large enough to push the shock beyond the core surface and the shock wave stalls somewhere inside the outer core, turning to be an accretion shock there. This failure of the so-called prompt explosion is understood by the following simple energetic consideration. According to numerical simula­ tions, the initial shock energy is about 5 x 1051erg. As the shock propagates through the outer core, it loses its energy due to the endothermic photodisintegration of nuclei which consumes about lO 5 1 erg/M 0 and to the neutrino emission. Hence, if the mass of the outer core is larger than about 0.5M@, then the shock will be stagnated by the dissociation of nuclei alone. The inner core mass is roughly equal to the Chandrasekhar mass corresponding to the electron fraction diminished by the electron captures (note that the Chandrasekhar mass is about 0.7M© for the electron fraction ~ 0.35, since the Chandrasekhar mass is proportional to the square of the electron frac­ tion). Thus, it is easy to understand that the prompt explosion is difficult for a massive iron core. It is, however, noted that the success of the prompt explosion is dependent not only on the initial core mass but also on the inner core mass which is determined by the electron fraction that in turn crucially relies on the'rates of electron captures on protons inside and outside nuclei. The initial shock energy is also an uncertain factor which is affected by the electron fraction again and by the nuclear equation of state as well. It is, therefore, impossible at present to rule out the prompt explosion. Despite these uncertainties, the theoretical research of the collapse-driven supernova has been done mainly in the context of the so-called delayed ex­ plosion, in which a stalled shock wave is reenergized by neutrinos copiously emitted out of the proto neutron star. As mentioned already, the gravita-

184

tional energy of the proto neutron star, E^s ~ 10 53 erg, that is liberated by the collapse of an iron core, is mainly transported by these neutrinos. This is so large an amount that it is not unexpected that many researchers have devoted themselves to this scenario. Again, however, the subtlety comes from microphysics. Since neutrinos interact with matter only through the weak interaction, it seemed that the deposition of their enormous amount of energy to matter is not large enough to revive the shock wave. The quantitative calculation of the efficiency of energy deposition, however, requires accurate estimates of the weak interaction rates as well as the sophisticated numerical treatment of neutrino transport. This has been the topics for the last couple of years. The multi-dimensional aspects of the dynamics of supernova has also been studied extensively. Among other things, the convection in various regions has attracted much attention. Since the microphysics in the hot and dense matter looks so complicated that it is justifiably expected that some robust hydrodynamical effect is responsible for the supernova explosion. Unfortunately, this has not been vindicated as yet. It is, however, no doubt that more effort will be dedicated to the multi-dimensional study for the next years to come, provided the possible link with the gamma ray burst. In the following sections, I will focus on some particular issues as briefly mentioned above and emphasized in the table on next page. The importance of these issues is, hopefully, well understood already from the above short introduction.

2

ID

In this section, I will discuss some issues which have been studied mainly by ID simulations. 2.1

Uncertainties in the prompt explosion

The difficulty in the prompt explosion lies mainly in the insufficient energy of the shock wave at the generation and the ensuing large energy loss. As men­ tioned in the introduction, the latter factor is determined by the proportion of the masses of the inner and outer cores as well as the total core mass. 1 The inner core mass is roughly equal to the Chandrasekhar mass corresponding to the electron fraction. The electron fraction is decreased due to the electron captures on free protons and nuclei, the latter of which is more important in the lower density regime (<,10 11 g/cm 3 . In this early phase of the core col-

P r o m p t Explosion systematics

c microphysics

convection

• energetically unlikely • only for very small cores 4k electron captures o n nuclei (A ~ GO­ TO) * nuclear EOS 4k free proton fractions

• convections just behind shock waves

Delayed Explosion • too small explosion energy • found by Wilson's group alone

4k nuclear many b o d y effects o n neu­ trino luminosity and energy 4k numerical treatment of neutrino transfer in supernova cores

• convections in hot bubbles due to neutrino heating 4k lepton-driven convections in proto neutron stars • many body effects on lepton-driven con­ vections in proto neutron stars

Q rotation

• effect of rotation on prompt shock energy 4k jets in the direction of a rotation axis

magnetic field

4k strong j e t s due t o t h e combination of magnetic field with rotation • magnetically induced convections

4k asymmetric neutrino radiation and heating of hot bubbles • effect of rotation on convections

• long term amplification of magnetic fields due to differential rotations

186 lapse, the neutron rich nuclei with the mass number of about 60 ~ 70 are most abundant and are responsible for the capture process. 2 However, the capture cross sections are highly uncertain, apart from crude numerical treat­ ments. Recent studies based on the large scale shell model calculations 3 show that the previous rates might have been systematically too large, leading to smaller electron fractions. If this is really the case, the inner core mass can be larger, which will be better for the successful prompt explosion. Incidentally, in the higher density regime where the electron capture on nuclei is effectively closed by the fermi blocking of the shell in the daughter nucleus, the electron fraction is further diminished by the capture on the free proton. However, this process is also difficult to handle, since the fraction of the free proton is very small (Xp ~ 10~ 3 - 10~ 2 ). 4 ' 5 ' 6 Further improvement on the theoretical esti­ mations of these rates is obviously required, not to mention their numerical implementations. Another nuclear physical uncertainty is a nuclear equation of state around the saturation density and higher. The shock wave is generated by bounce of the inner core, in which the compressibility of the nuclear matter is something like an elastic constant of a spring. As expected intuitively, a softer equation of state gives a larger shock energy, since a greater amount of gravitational energy is liberated. This in general leads to a higher chance of successful explosion, although the general relativity makes the argument a bit more complicated. 1 At the moment, only a few equations of state 4,5 ' e are available for elaborate simulations. Provided the complexity of nuclear physics, it is definitely important to have several different equations of state and study the dependence of results on their difference systematically. 2.2

Uncertainties in the delayed explosion

Despite the fact that there remain some uncertainties in the prompt explosion and that there is no denying the possibility of successful prompt explosion as discussed above, the current expectation of most researchers is that the de­ layed explosion is more promising. This is understandable if one considers the large amount of energy that neutrinos transport. Here the issue is the effi­ ciency of heating of matter behind the shock by neutrinos. It has been known from the early days that the heating rate does not seem to be so large as required for a vigorous explosion. 7 In fact, some additional convective trans­ port of energy has been claimed to be needed. 8 After eager numerical studies of the convective mixing in the outer envelope of SN1987A, the attention was directed to the convection inside the core which had been investigated in the former half of 80's by less sophisticated simulations. The results were not con-

187

elusive, though. For the convection just behind the stalled shock wave, SPH simulations tended to show more energetic explosions than finite-difference methods. 9 Putting aside the numerical complexities associated with the multi­ dimensional simulations, these studies made clear that the delayed explosion is a very delicate mechanism. Indeed, one numerical experiment which stud­ ied the dependence of the outcome on the neutrino luminosity by changing it by hand showed that some 10% of increase of the luminosity could turn an otherwise failed explosion into a successful one. 10 This observation stimu­ lated some researchers to find a way to enhance the luminosity or the energy of neutrinos other than the multi-dimensional hydrodynamics. Among other things is the neutrino reaction rates with nucleons in the hot and dense supernova core. 11.12>13,i4 p o r e x a m p i e , the scattering rates of neutrino on nucleons are conventionally calculated under the assumption that the nucleons are uncorrelated. This is, however, not true and the correlations might be important as the density exceeds ~ 10 13 g/cm 3 , where the mean separation of nucleons becomes comparable to or smaller than the neutrino wavelength. The correlations make a fraction of the scattered wave interfere destructively and lead to smaller reaction rates. This is true for the emission and absorption of neutrinos. If the opacity of the supernova core were smaller, the luminosity and energy of emerging neutrino would be higher, which could make the heating of the matter behind the shock wave more efficient. This was the basic idea behind some efforts to estimate the effects of the nuclear correlations on the weak interactions. The results are in general encouraging. However, it should be noted that the theoretical calculations have been done only approximately and the implementations for the numerical simulations are crude. Further improvement in both respects is obviously needed. It has also become clear that the numerical treatment of neutrino trans­ port is also a very important ingredient to study the delayed explosion sce­ nario quantitatively. As mentioned above, the inconclusiveness of the multi­ dimensional study of convection comes from the difficulty in the accurate treatment of the multi-dimensional neutrino transport. Hence, the sophis­ tication of one-dimensional neutrino transport has been attempted for the last couple of years. I5>i6,i7,i8,i9 j t j ^ s been made clear that the flux limited diffusion approximation that had been frequently employed in the literature tends to underestimate the neutrino number density, thus the heating rate of matter as well. 16 Some recent papers 18 ' 19 are giving conclusions not fully in accord. Follow-ups are definitely required here again.

188

3

Multi-D

In this section, I will wrap up some remaining issues concerning the multidimension aspects of the collapse-driven supernova. 3.1

Convection

Different kinds of convection occur at different places in the core and at dif­ ferent Times. Particularly important will be the lepton-driven convection around and inside the neutrino sphere, 20 ' 21 though the so-called Bethe con­ vection behind the shock wave has still some interest as mentioned above. 9 If the convection occurs near the neutrino sphere, it affects the luminosity and energy of neutrino and hence the heating rate of matter behind the shock. Although this issue is quite important, the numerical modeling is fairly com­ plicated. The fact that the convection occurs near the neutrino sphere means that the neutrino transport should be somehow taken into account. In fact, the lepton density distribution determined by the neutrino transport is a cru­ cial factor which governs the instability. As mentioned, the multi-dimensional treatment is extremely difficult. For example, the approximation that neu­ trinos flow only radially neglects the lateral transport between fluctuations, leading obviously to the overestimation of the growth of the instability. In­ cidentally, our preliminary simulations 22 showed that the reduction of the neutrino reaction rates due to the nuclear correlation tends to weaken this lepton-driven instability. This is simply because the neutrino can more easily smooth the lepton and entropy distribution which could drive the instability. Hence the convection and the correlation does not add up to enhance the neutrino luminosity and energy. Another complication for the convection in the core comes from the nu­ clear equation of state. The lepton-driven convection occurs simply because the lepton-rich matter is effectively lighter than the lepton-deficient one and the lepton stratification becomes unstable indeed near the neutrino sphere. As matter becomes more neutron-rich, this does not hold any longer since the nuclear symmetry energy kicks in. 23 For a given pressure, in this case, the electron-rich matter contains a larger amount of nucleons and hence is heav­ ier. This leads to a different criterion for the instability. It is sensitive to the equation of state employed where this change of criterion occurs. For exam­ ple, the Shen's equation of state 5 based on the relativistic mean field theory gives a larger electron fraction Ye that gives the above change of criterion for a give density than the Lattimer-Swesty's equation of state. 4 To what extent this uncertainty affects the convection should be studied systematically before

189

we can draw some conclusion on this convection. 3.2

Rotation

Another important factor that renders the dynamics asymmetric is selfevidently the stellar rotation. We know observationally that a massive star that can give a progenitor of collapse-driven supernova is in general a rapid rotator. 24 It is natural that we expect the iron core is also rotating prior to the onset of collapse. In fact, the observations of linear polarization of pho­ tons coming from supernovae suggest that the collapse-driven supernova is in general globally asymmetric. 25 The rotation of the iron core can affect the dynamics of supernova in several ways. First of all, the hydrostatic structure of the progenitor should be modified. 26 In general, the core mass tends to be increased, since the centrifugal force helps support a larger mass. This will do harm for the prompt explosion, since the shock wave should plow through a larger mass in the outer core. This is partly compensated by the fact that the inner core mass is also increased by the same centrifugal force. 27 It is also a generic tendency that the core bounce occurs at a lower density for the same reason. 2 r This has a profound implication for the prompt explosion. According to our numerical study, the shock energy is monotonically decreased as the angular momentum of the iron core is increased or as the core rotates more differentially. It seems very unlikely that we have a successful prompt explosion even with the smaller electron capture as long as the progenitor rotates rapidly. Incidentally, as a result of rotational collapse, the shock wave tends to become globally asymmetric and jet-like in the direction of the rotation axis. The rotation of progenitor can affect the dynamics of the delayed explo­ sion also. First of all, the neutrino will be emitted asymmetrically from a flattened core. It is intuitively natural that the direction of the rotation axis is favored. Shimizu et al. 28 showed by two dimensional simulations that this asymmetric neutrino emission leads to the anisotropic heating of matter be­ hind shock, stronger near the rotation axis, and triggers a globally asymmetric explosion which might accord with the observations of linear polarization of photons. They claimed that this is true even if the total luminosity is not sufficient for revival of the stagnated shock for the corresponding spherically symmetric model. Though the result is encouraging, the simulations were done with crude approximations for the neutrino transport. Again, further investigations remain to be done. The convection in the core is also affected by the rotation. Generally speaking, the rotation tends to stabilize the convection as long as the specific

190 angular momentum increases as the distance from the rotation axis becomes larger, which is usually the case. 24 This was actually shown by Keil et al. 20 In their two-dimensional simulations, the rapid rotation suppressed the convective motion near the rotation axis. If this is really true, the anisotropic neutrino heating discussed above might be also affected. Since the result is dependent on the distribution of the angular momentum, it is evidently nec­ essary to do consistent and systematic numerical experiments on this issue. 3.3

Magnetic field

I will pick up some miscellaneous issues here. In the past, supernova re­ searchers thought that magnetic fields would play no significant role for the dynamics of collapse. It is not that there is no magnetic field. There is some magnetic field, indeed, as suggested by pulsar. The point is that the magnitude is not just enough. It is easily seen that some 1016G of magnetic field is needed to be comparable in pressure to the matter. This value is far larger than the canonical number for the surface magnetic field of neutron star, that is, 10 12 G. This is the reason why there are only sporadic papers on the magnetic field in supernovae. 2 9 ' 3 0 This might be changing drastically. Since the discovery of 7-ray burst, it has been suspected that it might be associated somehow with the gravita­ tional collapse of a massive star. 31 As the expectation that the 7-ray burst, hypernova and magnetar might have the same origin rises, 2 5 I think that it is high time to study systematically the effect of the strong magnetic field on the supernova dynamics. According to the existing papers, 30 a couple of things should be expected. If the magnetic field is strong enough from the beginning, the combination with rapid rotation might lead to a strong jet-like prompt explosion in the direction of symmetry axis. The magnetic buoyancy may yield yet another kind of convection whose effect on the dynamics is unknown. Even if the magnetic field is not so large at the onset of collapse, it can be amplified in the delayed explosion scenario, 32 since there is a lot of time for winding up. The possible outcome has not been discussed so far. In any case, the explosion is expected to be jet-like and bipolar. If asym­ metry with respect to north and south is induced somehow, for example, by the asymmetric weak interactions of neutrinos in the magnetic field 33 or by the anisotropic neutrino oscillations, 34 then it will be a good candidate for the observed high proper motion of young pulsar. As I mentioned, the number of serious research of the magnetized supernova is very small. It will change in the very near future.

191

4

Conclusion

In this paper, I have discussed some issues which are remaining to be studied further. Instead of repeating them here, I put in the next page a similar table to the one I showed at the very beginning of this talk. Provided recent surprising discovery of hypernovae and magnetars, we have justifiable reason to expect much more to show up in the years to come and, hopefully, to help us deepen our understanding of the collapse-driven supernova. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

M. Takaharaand K. Sato, Prog. Theor. Phys. 68, 795 (1982). S.D. Bruenn, Astrophys. J. Suppl. 58, 771 (1985). K. Langanke and G. Martinez-Pinedo, Nucl. Phys. A673, 481 (2000). J.M. Lattimer and F.D. Swesty, Nucl. Phys. A535, 331 (1991). H. Shen, H. Toki, K. Oyamatsu and K. Sumiyoshi, Nucl. Phys. A637, 435 (1998). H. Shen, H. Toki, K. Oyamatsu and K. Sumiyoshi, Prog. Theor. Phys. 100, 1013 (1998). H.A. Bethe and J.R. Wilson, Astrophys. J. 295, 14 (1985). J.R. Wilson and R.W. Mayle, Phys. Rep. 163, 63 (1988). E. Miiller and H.-Th. Janka, Rev. Mod. Astron. 7, 103 (1994). H.-Th. Janka and E. Miiller, Astron. Astrophys. 306, 167 (1996). G. Raffelt, D. Seckel and G. Sigl, Phys. Rev. D 54, 2784 (1996). S. Reddy, M. Prakash, J.M. Lattimer and J.A. Pons, Phys. Rev. C 59, 2888 (1999). A. Burrows and R.F. Sawyer, Phys. Rev. C 59, 510 (1999). S. Yamada and H. Toki, Phys. Rev. C 61, 015803 (2000). A. Mezzacappa and S.W. Bruenn, Astrophys. J. 405, 637 (1993). S. Yamada, H.-Th. Janka and H. Suzuki, Astron. Astrophys. 344, 533 (1999). A. Burrows, T. Young, P.A. Pinto, R. Eastman and T. Thompson, As­ trophys. J. in press , (2000). M. Liebendorfer, A. Mezzacappa, F.-K. Thielemann, O.E.B. Messer, W.R. Hix and S.W. Bruenn, submitted to Phys. Rev. D , (2000). M. Rampp and H.-Th. Janka, Astrophys. J. Lett. 539, L33 (2000). W. Keil, H.-Th. Janka and E. Miiller, Astrophys. J. Lett. 473, LI 11 (1996). A. Mezzacappa, A.C. Calder, S.W. Bruenn, J.M. Blodin, M.W. Guidry, M.R. Strayer and A.S. Umar, Astrophys. J. 495, 911 (1998).

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22. H.-Th. Janka, W. Keil and S. Yamada, in preparation , (2000). 23. S.W. Bruenn and T.S. Dineva, Astrophys. J. Lett. 458, L71 (1996). 24. J.-L. Tassoul, Theory of Rotating Stars, (Princeton Univ. Press, Prince­ ton, 1978). 25. J.C. Wheeler, I. Yi, P. Hoflich and L. Wang, Astrophys. J. 537, 810 (2000). 26. A. Heger, N. Langer and S.E. Woosley, Astrophys. J. 528, 368 (2000). 27. S. Yamada and K. Sato, Astrophys. J. 434, 268 (1994). 28. T, Shimizu, S. Yamada and K. Sato, Astrophys. J. Lett. 432, L119 (1994). 29. J.M. LeBlanc and J.R. Wilson, Astrophys. J. 161, 541 (1970). 30. E. Symbalisty, Astrophys. J. 360, 242 (1984). 31. S.E. Woosley, Astrophys. J. 405, 273 (1993). 32. E. Miiller and W. Hillebrandt, Astron. Astrophys. 80, 147 (1979). 33. P. Arras and D. Lai, Phys. Rev. D 60, 043001 (1999). 34. A. Kusenko and G. Segre, Phys. Rev. Lett. 77, 4872 (1996).

P r o m p t Explosion systematics

Q microphysics

Delayed Explosion

• energetically unlikely • only for very small cores

• too small explosion energy • found by Wilson's group alone

• electron capture rates of nuclei are uncer­ tain, a larger trapped Ye is favorable for explosion

A nuclear many b o d y effects might en­ hance neutrino luminosities substan­ tially, leading to larger heating of hot bubble £ numerical improvement of neutrino transfer might increase neutrino heating in hot bubble

• nuclear EOS is also uncertain, softer EOS is generally favorable

convection

• prompt convections occur due to weaken­ ing shock, but unimportant for explosion

• Bethe convections occur in hot bubble due to neutrino heating and enhances heating rates, maybe, not sufficiently for explosion 4> lepton-driven convections occur in a proto neutron star and could raise neutrino energies and luminosities substantially • many body effects might reduce leptondriven convections in a proto neutron star

rotation

• prompt shock energy is reduced monotonically as rotation period becomes shorter

£ causes asymmetric neutrino radia­ tion and could enhance neutrino heating near rotation axis • centrifugal force weakens lepton-driven convections in a proto neutron star

magnetic field

£ strong jet might be induced by combina­ tion with rotation, but very strong mag­ netic fields are necessary • magnetically induced convection might occur

• magnetic field might be amplified in longer tme scales

Q 1 1

P R O T O N E U T R O N STARS WITH K A O N CONDENSATE A N D P O S S I B I L I T Y OF D E L A Y E D C O L L A P S E

Department

M. Y A S U H I R A and T . T A T S U M I of Physics, Kyoto University, Kyoto 606-8502, E-mail: [email protected], [email protected]

JAPAN

Equation of state with kaon condensate is derived in isentropic and neutrino-free or trapping matter. Both are important ingredients to study the possibility of the delayed collapse of a protoneutron star. Solving the TOV equation, we discuss the static properties of the protoneutron star and implications for its delayed collapse.

1

Introduction

After supernova explosion, a protoneutron star (PNS) is formed with hot, dense and neutrino-trapping matter. It usually evolves to cold (T ~ 0) neutron star through the deleptonization and the initial cooling eras. In the deleptonization era, trapped neutrinos are released in about ten seconds and the initial cooling means fast cooling by neutrino emissions in a few tens of seconds. But some of protoneutron stars may collapse to the low-mass black holes during these eras by softening the equation of state (EOS) due to the hadronic phase transitions 1 . This is called the delayed collapse; as a typical example neutri­ nos from SN1987A were observed at Kaomiokande, but no pulsar yet, which suggests the possibility of the delayed collapse in SN1987A. Kaon condensation, one of the candidates of the hadronic phase transi­ tions, is a kind of Bose-Einstein condensations. Fig. 1 shows the mechanism of the occurrence of kaon condensation. As density increases, single particle energy for K~ (e_) decreases due to the attractive KN interaction in medium, while electron chemical potential increases, which is equal to kaon chemical po­ tential in the beta-equilibrium and neutrino-free matter. When they become equal to each other, the Bose-Einstein condensation of kaons occurs. Kaon condensation has been studied by many authors mainly at zero tem­ perature since first suggested by Kaplan and Nelson2. We know that kaon condensation gives rise to a large softening of EOS. The phase transition is of first order and thereby the EOS includes thermodynamically unstable region ( see Fig. 2). We applied the Maxwell construction to obtain the equilibrium EOS for simplicity. Recently, there appear a few works about kaon condensation at finite tem­ perature using the meson exchange modeP' 4 , however, there was no consistent theory based on chiral symmetry. We have presented a new framework based

194

195

>

Figure 1: Mechanism of occurrence of kaon r-. „ „ „ . . . „„ s . Figure 2: Maxwell construction: c reprecondensation. Sobd bne represents single par. ... , j .. T^ , r i i iC sents critical density, Jt/qual pressure region t i d e energy for kaons e and dotted-bne, c o n t i n u e f r o m d e n s i t y "N" to density "K". electron chemical potential /i e .

on chiral symmetry to treat fluctuations around the condensate 5 ' 6 . We study here the properties of kaon condensed matter based on the framework and discuss the behavior of PNS, especially, the possibility of the delayed collapse. 2

Numerical Results and Discussions

With thermodynamic potential in the reference5,6, we, hereafter, use the heavybaryon limit for nucleons5. We show the phase diagram, the EOS and then discuss the properties of a PNS where thermal and neutrino-trapping effects are very important. 2.1

Kaon Condensed Matter: Phase Diagram and EOS

First, the phase diagram is shown in Fig.3. In the neutrino-trapping case, we set Yie = Ye + Y„e = 0.4 where Ye{Yv<.) is the electron(electron-neutrino) number per baryon, while Y„c = 0 in the neutrino-free case. Both of the thermal and neutrino-trapping effects largely suppress the occurrence of kaon condensation. The reason for the latter may be understood from the threshold condition: e_ = fix — Pe — ^i/ c : Hvc > 0 in the neutrino-trapping case while n„t = 0 in the neutrino-free case, which means that once neutrinos are trapped, kaons should wait to condense until its energy further decreases. Both effects stiffen the EOS (see Fig.4) and are remarkable around the critical

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Figure 3: Phase diagram: e-trapping(y; e = Figure 4: EOS in isothermal case: T = 0 0.4) [solid line] and i/-free cases [dashed line], [solid line] and X = 50MeV [dashed line].

density, mainly through the increase of the critical density, which would be very important when we discuss the possibility of the delayed collapse. In the realistic situation for protoneutron stars, the isentropic condition is more relevant than the isothermal one. Then we reconstruct the EOS by calculating the entropy as a function of temperature. 2.2

Protoneutron Stars

Solving the TOV equation with the isentropic EOS, we can study features of a PNS. Fig.5 shows the gravitational mass versus central density in the neutrino-trapping and -free cases with entropy per baryon S = 0,1 or 2. Both the thermal and neutrino-trapping effects make the gravitational mass larger for the almost all the central density. In the neutrino-free case, once kaon condensation occurs in the core of a star, gravitational mass is little changed as a result of the equal pressure region in the isothermal EOS, then gravitationally unstable region (negative gradient part) appears. Therefore the neutron-star branch is separated into two stable branches: one is for stars with kaon condensate in their cores (right hand side from gravitationally unstable region) and the other consisting of only normal matter (left hand side from gravitationally unstable region). Thermal effect to the gravitational mass is found to be very large around the critical density because the EOS changes largely there. However the maximum mass is hardly changed and even decreased by the thermal effect because of the strong gravitation resulting from the high central density. As temperature or entropy

197

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Figure 5: Gravitational mass versus central density for stars in s t r a p p i n g [ solid lines ] F l 6 u r e 6 : T o t a l b a r y ° n number versus mass for and ^-free cases [ dotted lines ]. gravitationally stable stars.

raises, the gravitational mass grows largely in the normal branch but not in the kaon condensed branch. In the neutrino-trapping case, the thermal effect is large around the crit­ ical density and small for high densities as well. However the situation is quantitatively different. In the S = 0 or 1 case we can see that the neutronstar branch is also separated by the gravitationally unstable region and the star with maximum mass exists in the kaon condensed branch. (Their central density is around lOpo) On the other hand, in the 5 = 2 case almost all of the stars including the kaon condensate are gravitationally unstable, and the maximum-mass star whose central density pc = 5.4po, still resides in the normal branch. For this reason the central density of the maximum-mass star is very different from that in the S = 0 or 1 case. 2.3

Possibility of the Delayed Collapse

To discuss the possibility of the delayed collapse of a PNS, the total baryon number NB should be fixed as a conserved quantity during the evolution7, under the assumption of no accretion. In Fig.6 we show the gravitational mass versus total baryon number for gravitationally stable stars. Each terminal point represents the maximum mass and the maximum total baryon number. If an initial mass of a new-born PNS exceeds the terminal point, the star should collapse into a black hole (It is not a delayed collapse but an usual formation of a black hole.). We have shown the neutrino-trapping and free cases; the

198

former case might be relevant for the deleptonization era, while the latter for the initial cooling era. It is interesting to see the difference between the neutrino-free and trapping cases: the curve is shortened as entropy increases in the former case, while elongated in the latter case, where the remarkable elongation in the 5 = 2 and neutrino-trapping case results from whether the maximum mass exists in the normal branch or the kaon condensed one. These features are essential for the following argument about the delayed collapse and the maximum mass of the cold neutron stars. The delayed collapse is possible if the initially stable star on a curve finds no corresponding poinl» on other curves during the evolution through delep­ tonization or initial cooling. Consider a typical scenario for example: A new born PNS initially consists of the 5 = 2 and neutrino-trapping (Yje = 0.4) matter after supernova explosion and evolves to the star with the S — 2 and neutrino-free matter during the deleptonization era. We can clearly see a PNS with large enough mass can exist as a stable star at the beginning but cannot find any point on the curve in 5 = 2 and neutrino-free case. Therefore it must collapse to the low-mass black hole by deleptonization. It is to be noted that because the stars on the curve in the 5 = 2 and Yje = 0.4 case hardly includes kaon condensate, its collapse is largely due to the appearance of kaon condensate in their cores. Thus we conclude that kaon condensation can cause the delayed collapse in the deleptonization era. On the other hand, during the initial cooling era after deleptonization the delayed collapse does not occur because neutron stars on the curve in the 5 = 2 and neutrino-free case seem to be able to find the corresponding stable points on the curve in the cold and neutrino-free case.

2.4

Maximum Mass of Neutron Stars

We can also determine the maximum mass of cold neutron stars by taking into account the evolution of stars during the initial cooling era. Usually we assign the maximum mass of the cold neutron stars from the solution of the TOV equation by the use of the EOS at T = 0 and it corresponds the terminal point of the curve in the 5 = 0 and neutrino-free case in Fig.6. However, it is not correct when we take into account the evolution, especially in the initial cooling era7. As already mentioned, the entropy dependence of the curve for the neutrino-free case is opposite to the neutrino-trapping case. Hence, once a PNS resides on the large-entropy curve, it necessarily evolves stably into the corresponding point with the same total baryon number on the smallerentropy curve during initial cooling era. As an example, consider the evolution of a PNS with 5 = 2. Because only the stars with NB < 2.14 x 1057 at the

199

beginning can evolve to the cold stars, the maximum mass of cold neutron stars can then be determined as 1.54M 0 . 3

Summary and Concluding Remarks

We have studied the kaon condensed matter at finite temperature based on chiral symmetry, and discussed the properties of protoneutron stars, especially the possibility of the delayed collapse. It is found that the delayed collapse is possible during the deleptonization era due to the appearance of kaon conden­ sate and impossible during the initial cooling era. In order to study the mechanism of the delayed collapse and mass re­ gion which should collapse in more detail, we had better study the dynamical evolution beyond the static argument?. There neutrino opacity is important to determine the duration of the deleptonization, and in the kaon condensed phase neutrino opacities may become larger than in normal phase9. As another remaining issue, it is also important to refine the EOS. We have adopted the chiral model for KN interaction, on the other hand, the effective potential formula for TV TV interaction in the non-relativistic limit. We are planning to incorporate the relativistic mean field theory besides the chiral model as an extension from the previous work at zero temperature 10 . We have applied the Maxwell construction to the thermodynamically unstable region in the EOS. However, restrictly speaking, we should impose the Gibbs conditions11 because there exist two chemical potentials: baryon and charge chemical potentials. Using the Gibbs conditions and neglecting the surface and Coulomb energy, the EOS should be smoothed due to the appearance of the mixed phase where the positively charged normal nuclear matter and the negatively charge kaon condensed matter coexist.

200

References 1. G. E. Brown and H. A. Bethe, ApJ. 423 (1994) 659. 2. D.B. Kaplan and A.E. Nelson, Phys. Lett. B175 (1986) 57; B179 (1986) 409(E). 3. M. Prakash, I. Bombaci, M. Prakash, P. J. Ellis, J. M. Lattimer and R. Knorren, Phys. Rep. 280 (1997) 1. 4. V. Thorsson and P.J. Ellis, Phys. Rev. D55 (1997) 5177. 5. T. Tatsumi and M. Yasuhira, Phys. Lett. B441 (1998) 9. 6. T. Tatsumi and M. Yasuhira, Nucl. Phys. A653 (1999) 133. 7. T. Takatsuka, Prog. Theor. Phys. 95 (1996) 901. 8. T.W. Baumgarte et al, ApJ. 443 (1996) 680. W. Keil and H.-Th. Janka, A&A. 296 (1995) 145. J A . Pons, S. Reddy, M. Prakash, J.M. Lattimer and J A . Miralles astroph/9807040. 9. T. Muto, T. Tatsumi and M. Yasuhira, in progress. 10. H. Fujii, T. Maruyama, T. Muto and T. Tatsumi, Nucl. Phys. A597 (1996) 645. 11. N.K. Glendenning and J. Schaffner-Bielich, Phys. Rev. Lett. 81 (1998) 4564; Phys. Rev. C60 (1999) 025803.

OMNIS, The Observatory for Multiflavor Neutrinos from Super novae R.N. Boyd Department of Physics Department of Astronomy Ohio State University, Columbus, Oh 43210 E-mail: [email protected]

USA

OMNIS, the Observatory for Multiflavor Neutrinos from Supernovae, is being planned for siting in the Center for Applied Repository and Underground Re­ search, CARUS, in New Mexico. OMNIS will consist of 14 kT of lead and iron which, when irradiated by neutrinos from a supernova, will produce secondary neutrons. Detection of the neutrons then will signal the arrival of the supernova neutrinos. A supernova at the center of the Galaxy, will produce about 2000 events in OMNIS, mostly from neutral current interactions. OMNIS' combination of lead and iron modules gives it particular sensitivity to neutrino oscillations of the type Vfj. -¥ ue or vT —>• i/e. Its intrinsic timing capability, better than 0.1 ms, gives it the (probably statistics limited) capability to measure neutrino mass from the time-of-flight shifts in the luminosity curves of the neutrinos of different flavors to a few e V / c 2 . OMNIS will also be able to detect differences in the luminosity cutoffs of the different flavors in the event of the fairly prompt collapse to a black hole, which might allow diagnostics on t h a t collapse process.

1

Introduction

The final state of evolution of a massive star results in a core collapse, or Type II, supernova, which will ultimately produce a few times 10 53 ergs of neutrinos (Burrows 1). The standard model of this process suggests that i>e's have a mean energy of around 11 MeV, L>e's around 16 MeV, and all others, f M 's, j/ M 's, vT's, and i/ T 's, around 25 MeV (Qian et al. 2 ) . This is a result of the fact that the z/e's and r/e's interact with matter through both the chargedand neutral-current interactions, whereas all the other neutrinos, at least at the energies at which they are produced in supernovae, interact only through the neutral-current interaction. Since the ve's and i?e's have more options for sharing their energy, they will emerge with a lower energy than will the neutrinos of the other flavors. However, the time distributions, or luminosities, of the neutrinos are also important. That for the electron neutrino should exhibit a sharp "neutronization spike" that would signal the beginning of the stellar collapse. These are produced by p + e~ -» n + ue.

201

(1)

202

Subsequent broad distributions, lasting at least several seconds, and possibly as long as a minute, would then be expected as a result of neutrinos being produced in the hot core of the star by e + + e~ ->■ v>i + i>i

(2)

where i = e, fi, or r. This is a process that occurs only about once in every 1019 e + e _ annihilations, but it can cool the core of the star in a few seconds. The luminosities may also exhibit interesting features, e.g., rapid (tens of ms) oscillations in the first second or so (Burrows 1 ) , apparently related to the success or failure of its attempt at a prompt explosion; or possibly a sharp termination, which would result from collapse to a black hole. Detection of the neutrinos from a supernova can provide diagnostics of the environment from which they are produced and by which they are trapped. Indeed, the observation of the i>e signal from SN 1987a produced a qualitative confirmation of the theoretical description of the trapping process, as the neu­ trinos are thought to be produced on a time scale of milliseconds (Burrows l ), but were observed over several seconds. However, much more can be learned both by observation of a much larger statistical sample of supernova neutrinos than were seen for SN 1987a (Hirata et al.3, Bionta et al.4) and by observation of the luminosities of neutrinos other than v>e's. 2

Technical Characteristics of OMNIS

With this in mind, we are designing OMNIS, the Observatory for Multifiavor Neutrinos from Supernovae. OMNIS involves collaborators from Ohio State University; the Universities of California at Los Angeles, San Diego, and Irvine; the University of Texas; the University of Wisconsin; Wittenburg University; and Lawrence Livermore, Los Alamos, and Oak Ridge National Laboratories. OMNIS was originally conceived (Cline et al.5, Cline et al.6) as utilizing the nuclei in the walls of an underground facility to convert the neutrinos into neutrons, which would then be detected in neutron detectors. However, the conversion efficiency of possible types of rock was found to be much less than that of iron or lead (Smith 7 ). Thus the present version of OMNIS consists of 4 kT of lead and 10 kT or iron. Slabs of each metal will be alternated with vertical racks of neutron detectors. The neutrinos will be detected when they interact with the iron or lead to emit secondary neutrons which, in turn, will be observed in the neutron detectors. Lead is a particularly efficient converter of the neutrinos to neutrons, as its threshold for neutron emission via neutral current interactions is only 7.37 MeV. In addition, ve's can interact with lead through the charged current

203

interaction to produce 208 Bi, a process which has a slightly higher threshold for neutron emission of 9.77 MeV, but a considerably larger cross section. Indeed, it has been calculated (Fuller, Haxton, and McLaughlin 8 ) that for a supernova occuring at a distance of 10 kpc, lead will produce about 880 neutron events per kT for the standard model supernova neutrino spectrum for all flavors, but primarily from neutral current interactions induced by v^s, z>M's, J/ T 'S and i>T's. Lead has an additional interesting feature: sufficiently high-energy neutrinos can produce events in which two neutrons are emitted. The threshold for that process is 14.98 MeV. OMNIS will have the capability to identify such events with fairly high efficiency. Although the yield of events from the charged current process is expected to be a small fraction of the total, ~55 events per kT in the lead, that yield is extremely dependent on the energy of the i/e's and ve's, a point discussed further below. Iron, by contrast, has a high threshold for neutron emission via neutral current interactions, 11.20 MeV, and a sufficiently high threshold for charged current processes that such production will be negligible. This is both a posi­ tive and a negative characteristic; it results in a lower efficiency, but calculation of its yield is simpler than for lead. Iron has been calculated (Woosley et al.9, Kolbe, Langanke, and Martinez-Pinedo 10) to produce around 100 events per kT for the standard model neutrino spectrum for a supernova at 8 kpc, with virtually all events coming from f^'s, v^s, uT's and DT's. Thus the two types of OMNIS converters will actually provide three time dependent spectra: one from the single-neutron events from lead, another from the two-neutron events from lead, and the third from the events from iron. The yields anticipated from a supernova at the galactic center, i.e., at 8 kpc from earth, are indicated in Table 1. Those yields assume a neutron detection efficiency determined (Zach et al.11) from Monte Carlo simulations performed by our group, and discussed in greater detail below. The yields anticipated for some other potential detectors capable of observing supernova neutrinos are also indicated. As can be seen, SuperKamiokande will produce most of the events observed, but they will almost all be ve induced. The main purpose of OMNIS is to provide, in addition, a statistically large sample of v^, v^, i/T, and vT induced events. We are planning to site OMNIS in the Center for Applied Repository and Underground Science, CARUS, in southeastern New Mexico. This facility is located 700 m underground, and has been observed to have a low natural neutron background (Balbes et al.12). The lead modules will occupy about 50 linear meters of the site, while the iron modules will occupy 150 meters. The height of the modules is restricted by the "back" (roof) of the "drifts" (tunnels) to be about 3.4 m, while the width of the drifts restricts the module width to

204

about 3.0 m. These dimensions will allow vertical access for construction and horizontal access for both construction and subsequent detector maintenance. The detectors will consist of alternating slabs of lead or iron and racks of scintillators with photomultiplier tubes at both ends. The ends of the lead or iron modules would also be covered by doors of lead or iron respectively, which will slide on rails so as to allow access to photomultiplier tubes or to the ends of the scintillators should maintenance be required. At present we are testing two types of detectors, one of plastic scintillator, (with the tests being conducted at the University of California at Los Angeles) and the other of liquid scintillator (with tests being conducted at Ohio State University). The individual detectors will either be 20 cm diameter by 2 m long cylindrical tubes of liquid scintillator, or plastic scintillators of comparable size. Either type of scintillator would be loaded with a small amount of Gd to produce the signatures of neutron induced events. 3

Sensitivity to Oscillations

The yield from the lead is particularly sensitive to some types of neutrino oscillations. Specifically, either v^ —» ve or uT —> ue oscillations would preserve the energy of the /z- or r-neutrinos while changing the flavor to that of eneutrinos, so would produce much more energetic i/e's than would be expected from the supernova. This would result in dramatic effects in the lead detector; if maximal mixing occurred the yield from the lead detector would be enhanced (Fuller, Haxton, and McLaughlin 8 ) by about a factor of four, and the twoneutron event yield would be enhanced by a factor of about 40. Thus the ratio of one- to two-neutron events from the lead would produce a clear signature of oscillations of this type. The effect of oscillations on the yields of the lead and iron modules is indicated in Table 1. 4

Fast Timing Capability of OMNIS

Another important feature of OMNIS is its fast timing capability. Once the neutrons are produced they lose little energy until they reach the scintillator used to detect them. There they lose most of their energy in their first few scatterings from the protons in the scintillator, which occur in a time (as indicated by extensive Monte-Carlo simulations (Zach et al. n ) of less than 200 ns. Their time since their production is essentially the same, since they lose very little energy in the lead or iron, so move rapidly during the time they spend therein. The subsequent thermalization of the neutrons requires roughly 30 /is, at which point they are captured by a Gd nucleus, a 0.1% additive to the scintillator. This capture produces four 7-rays with a total energy

205 Table 1: Yields of Supernova Observatories from an 8 kpc Distant Supernova

Detector SuperK SNO SNO OMNIS OMNIS no osc.

Target Material H20 H20 D20 Fe Pb

Mass (Ton) 32000 1600 1000 10000 4000

^M,r-^e

Target Element p, e, O p, e, O d, e, O Fe

Yield 180 16 190 20

ve Yield 8300 520 180 40

*/M + ^ + I / T + vr Yield 50 6 300 360

160 <4420

70 40

1400 640

Ve

of almost 8 MeV. The combination of these fast-slow signals provides both the signature for the neutron-induced events, and a remarkably fast timing capability for OMNIS. Note, though, that this signature requires that the possibility of an intervening background event be negligible; this necessitates sufficient modularity of OMNIS to reduce spurious events from /3-decays of impurities in the lead and iron in each submodule to an acceptable level.

4-1

Measuring Neutrino Mass

Because of OMNIS' intrinsic timing capability, the timing of the onset of any neutrino luminosity curve will actually be limited only by statistics. This limit will be much longer than the OMNIS intrinsic timing capability, but would be roughly a few ms for a supernova at the galactic center (Beacom 13 ) even so. This level of timing could produce a measurement of neutrino mass from the effect of the time-of-flight of the neutrinos on their distributions. If one neutrino is very light, the arrival time difference between those neutrinos and those of larger mass is At = 0.515(m/£) 2 £>,

(3)

where m is the mass of the heavier neutrino in units of eV/c 2 , E is its energy in MeV, and D is the distance to the supernova in units of 10 kpc. A supernova at the galactic center would be expected to determine the onset of the distri­ butions to a few ms, which in turn would determine the mass of the heavier neutrino to a few eV/c 2 (Beacom 13 ). This level of accuracy would be difficult to achieve in any other way.

206

4-2

Diagnosing Collapse to a Black Hole

Perhaps the most dramatic manifestation of such fast timing, though, would occur if the stellar collapse went fairly promptly to a black hole. If this did occur, the neutrino emission would be terminated by infalling matter near the black hole, after which both matter and neutrinos would be swallowed by the black hole. However, because the i',,'s and j?e's interact more strongly with the infalling matter (because they interact with both neutral- and charged-current interactions) than do neutrinos of other flavors, they would be trapped farther from the center of the star than would the v^'s and j/ T 's and their respective antineutrinos. This would suggest that the ve and ve luminosities would be terminated after those of the v^'s, z^'s, uT's and ur's, since the black hole would grow outward from the center of the star. Since this difference, estimated (Mezzacappa 14 , Baumgarte et al. 15 ) to be of the order of 10 ms, might be expected to depend on the details of collapse, e.g., angular momentum, the timing properties of OMNIS, together with the statistics associated with 2000 events (Beacom, Boyd, and Mezzacappa 1 6 ), might allow for diagnosis of the details of collapse to a black hole! 5

Frequency of Galactic Supernovae

Of course consideration of supernova observatories requires some consideration of the frequency of such events. The historical record suggests this is one or two per century. However, a more careful examination of those events shows that all the known supernovae are in the 10% of the galaxy inhabited by our solar system (Dragicevich, Blair, and B.urman 17 ; Hatano, Fisher, and Branch 1 8 ). This suggests that most galactic supernovae are obscured from observation in optical photons by intervening dust. Thus the actual rate may be closer to one every 10 to 20 years. 6

Results from a Close Supernova

It is conceivable that a supernova could occur much closer to earth than the galactic center; Betelgeuse, a 30 M0 red giant, is some 30 times closer to earth. Indeed, it would produce several million events in OMNIS if it became a supernova during OMNIS' lifetime. The amount of information that might be obtained from such a close supernova is tremendous. The fluctuations, discussed above, that might be observed in the first second of the neutrino lu­ minosities would require very good statistics to be seen; this might be possible with a close supernova. The determination of luminosity rise time improves with statistics, so a much more accurate time measurement could be made

207

using the signals from a close supernova. Note, though, that the time differ­ ence between neutrinos of different flavors would decrease, so the improvement for mass determination is more complicated than would result from just the improvement in the statistics. But, if the supernova went fairly promptly to a black hole, this would again allow for an unprecedented time determination, hence improved neutrino mass measurement, and an extraordinary diagnostic of the event itself. However, OMNIS (and other potential supernova neutrino detectors as well!) must be designed for a very high count rate if its high-event-rate capa­ bilities are to be realized. This is not particularly demanding, but OMNIS will be segmented, electronically at least, to insure that the signals from a close supernova will be kept at a low enough level so as not to saturate. While this might seem like a trivial concern, given the much more probable galactic-center supernovae, it would certainly be tragic if such a close supernova did occur and the high-event-rate capability were not planned for. We are, therefore, design­ ing sufficient modularity in OMNIS to accommodate the eventuality of a close supernova. 7

Conclusions

The unique physics and astrophysics that could be obtained from a statistically meaningful sample of neutrinos from the next Galactic supernova, including luminosities of all neutrino flavors, argue strongly for building an observatory to provide those data. We are planning OMNIS to fulfill that need. Furthermore, the fast timing characteristics of OMNIS give it the capability to measure neutrino masses at levels that would be difficult to achieve with any other technique, as well as possibly to diagnose the process of collapse to a black hole. Acknowledgements The support of the National Science Foundation through grant PHY9901241 is gratefully acknowledged. References 1. A. Burrows, Ann. Rev. Nucl. Part. Sci. 40, 181-212 (1990) 2. Y.-Z. Qian, G.M. Fuller, G.J. Mathews, R.W. Mayle, J.R. Wilson, and S.E. Woosley, Phys. Rev. Letters 71, 1965 (1993) 3. K.W. Hirata et a/., Phys. Rev. Letters 58, 1490 (1987) 4. R.M. Bionta et al, Phys. Rev. Letters 58, 1494 (1987)

208

5. 6. 7. 8. 9. 10. 11. 12.

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

D.B. Cline, et al, Astrophys. Lett. Commun. 27, 403-409 (1990) D.B. Cline, et al, Phys. Rev. D50, 720-729 (1994) P.F. Smith, Astropart. Phys. 8, 27-42 (1997) G.M. Fuller, W.C. Haxton, and G.C. McLaughlin, Phys. Rev. D59, 085005-1 - 085005-15 (1999) S.E. Woosley, D.H. Hartmann, R.D. Hoffman, and W.C. Haxton, Astro­ phys. J. 356, 272-301 (1990) E. Kolbe, K. Langanke, and G. Martinez-Pinedo, Phys.Rev. C60, 052801 (1999) J.J. Zach, A. St.J. Murphy, D. Marriott, and R.N. Boyd, private com­ munication (1999) M.J. Balbes, R.N. Boyd, J.D. Kalen, C.A. Mitchell, M. Hencheck, E.R. Sugarbaker, J.D. Vandegriff, D.A. Sanders, and S.D. Lieberwirth, Nucl. Instr. Methods in Phys. Research A399, 269 (1997) J. Beacom, private communication, 1999 A. Mezzacappa, private communication, 1999 T.W. Baumgarte, H.-Th. Janka, W. Kiel, S.L. Shapiro, and S.A. Teukolsky, Astrophys. J. 468, 823 (1996) J. Beacom, R.N. Boyd, and A. Mezzacappa, private communication, 1999 P.M. Dragicevich, D.G. Blair, and R.R. Burman, Mori. Not. R. Astron. Soc. 302, 693 (1999) K. Hatano, A. Fisher, and D. Branch, Mon. Not. R. Astron. Soc. 290, 360 (1997)

OBSERVATION OF S U P E R N O V A N E U T R I N O B U R S T AT SUPER-KAMIOKANDE Yoshiyuki F U K U D A Observatory, Institute for Cosmic Ray Research, University of Tokyo Higashi-Mozumi, Kamioka-cho, Yoshiki-gun, Gifu 506-1205, Japan E-mail: [email protected]

Kamioka

Super-Kamiokande has started since 1st of April, 1996. We are searching for the supernova neutrinos from not only our galaxy but also extra-galactic source within lOOkpc distance with a full detection efficiency. We present recent results from the observation of Super-Kamiokande. There is no evidence of supernovae explosion in obtained data. The 90%-confidence level upper limit to the rate of supernovae explosion is obtained by 0.58 yr~ x within lOOkpc distance, and also obtained by 0.28 y r - 1 within our galaxy, if we accumulate the Kamiokande 4.26 yr's result.

1

Introduction

On 23 February 1987, both Kamiokande x and 1MB 2 experiment observed the neutrino burst from SN1987A which locates in the Large Magellanic Clouds. This was the first time to detect neutrinos from supernova, and it introduced new method of investigation to the Astronomy. A type II (or lb) supernova explosion emits all flavors of neutrinos with energy of 3 x 10 53 erg in total. Temperature of each neutrinos obeys a Fermi distribution. Averaged energy of those neutrinos are calculated as < EVc > ~ 11 MeV, < E^ > ~ 16 MeV and < £vT,„M > ~ 25 MeV 3 . These energies are almost close to the energy of 8 B solar neutrinos so that not only the large volume scintillator experiments such as LVD, MACRO and KamLAND but also the experiments of solar neutrinos, which have a large volume of water like Super-Kamiokande, or have a large cross section for the neutral current interaction like SNO experiment are also sensitive to detect them. 2

Super-Kamiokande Detector

Super-Kamiokande is an imaging water Cherenkov detector with 50,000 tons of pure water in steal tank. The detector is located at 1000 meters underground (2700 meters of water equivalent) in Kamioka Zinc mine in the Gifu prefecture of Japan, at 36.4°N, 137.3°E and 25.8°N geomagnetic latitude. The experi­ ment has started since 1st of April, 1996. The raw trigger rate was changed

209

210

by 10Hz to 1.6kHz due to lower the trigger threshold. However, another trig­ ger level which is used for the real-time alert system, so called "SN-watch", which searches for supernova burst automatically, was not changed since the beginning of experiment, and it has full efficiency above 6.5 MeV. Most events from supernova neutrinos are expected with the reaction V^ + p— ► e + + n due to the largest cross section in water. Total expected number of events within 32.5 kton inner volume is calculated as about 4400 events for an explosion of supernova at the center of our galaxy. This higher statistics than the result from SN1987A in Kamiokande which observed only 11 events will make us to investigate not only the mechanism of gravitational core collapse but also the property of neutrinos as an elementary particle which is related to neutrino mass 4 ' 5 . Moreover, Super-Kamiokande detector has the ability to get 30,000 neutrino events without any electronics dead-time, even though those events happens in 1 second. This is very important for obtaining the direction of the Supernova as described later, and for investigating the stellar core collapse mechanism, in particular, obtaining the evidence of Black Hole formation 6 .

3

Criteria of searching for neutrino burst

From the theoretical calculation of supernova explosion, the time profile of all type neutrinos has a unique scheme. With initial 10 msec, electron neutrinos from the neutronization are released with the energy of order 1051 erg. After the neutronization, all flavors of neutrino are produced by electron-positron annihilation in the cooling process and are released with energy of order 10 53 erg with tens of seconds. From the Monte Carlo simulation, the expected number of events for each neutrino flavor can be obtained by Figure 1 (a) as a function of explosion time. Here, we used for delayed burst model 7 as energy spectrum of each neutrino flavor at several explosion step. Using this scheme, the SN-watch searches for the time clustering events in 22.5kton fiducial volume with the time window of 0.5, 2 and 10 seconds. The thresholds in each window are set by 7, 8 and 13 events, respectively. If one of the number of events exceeds the threshold, the SN-watch defines all events clustered within 20 seconds as a silent candidates. We called the number of events as multiplicity. Alarm threshold is defined by that the multiplicity should be greater than 16 and the average distance between each candidates should be greater than 9.5m. This is because of avoiding the spatial cluster due to spallation products. Figure 1 (b) shows the detection efficiency as a function of the distance from Earth for those two kinds of threshold. Full efficiency can keep up to ~ lOOkpc distant for a silent threshold.

211

Figure 1: (a)Expected number of events for each neutrino flavor assuming 12 Mg supernova explosion at center of our galaxy, (b)The detection efficiency of supernovae neutrino burst using Super-Kamiokande as a function of distance from Earth.

The obtained data by on-line DAQ are passed to the SN-watch for every 90 seconds, and usually the analysis completes after 1 minute. However, it will take about more 5 minutes if real supernova burst events exist in the data. If once the burst candidates are found, the SN-watch sends email to both on-site physicist and the supernova network server as described later. On-site physicist checks what kind of event happen just before possible candidates, and what kind of events exist in possible candidates. Most of fake candidates are caused by spallation products or flasher. In former case, the parent muon should be found just before the candidates, and the candidates itself are clustered along muon track. On the other hands, the clear flasher photo-multiplier should be found in later case. These fake alarms were found once a few months. If found candidate is possibly caused by real neutrinos, the data will be re-analyzed using off-line procedure immediately, and get a final result within a few hours. Another important feature is to measure the direction of supernova. Most of positrons generated by the reaction l^+p —> e + +n have a isotropic direction with respect to the supernova. However, the directions of electron generated by charged and neutral current have strong peak to induced neutrinos, so that the position of supernova can be measured with a detector angular resolution. The number of events is expected by about 250, if we assume that the super-

212

Figure 2: (a) Direction of recoiled electrons from Monte Carlo simulation in case of supernova explosion at center of our galaxy. Brightness corresponds to the number of events in each pixel on the celestial coordinate, (b) Case of the edge of our galaxy.

nova explodes at the center of our galaxy. Figure 2 shows the direction of recoil electrons on the celestial coordinate obtained by above Monte Carlo simula­ tion. Here we removed events with E > 15 MeV to see clear peak, because positron events likely have a larger energy than that of electrons. According to the numerical estimation of directional probability, 90 % confidence level corresponds to 18 degree at the center of our galaxy. 4

Results

The on-line SN-watch process has started since March 17, 1997. Figure 3 shows the live-time efficiency of Super-Kamiokande detector. Averaged livetime keeps about 95%, and remaining 5% of the dead-time is mainly due to calibrations. The efficiency for operation of real-time SN-watch is quite high (over 98%). In order to process for missing data, we re-analysis all data using off-line procedure. However, no candidate burst was found in both cases. Total detector live-time is obtained by 1441.5 days for the period of May 31st, 1996

213

Figure 3: Livetime efficiency as a function of time. It was almost 60 % at the beginning of experiment, however, it gradually went up and continued almost 95 %. Bigger dead-time seen around 1997 was caused by LINAC energy calibration.

to October 6th, 2000. The 90% confidence limits of Supernova explosion within lOOkpc distance is 0.58 SN per year. For the our Galaxy, we could also obtain the 90% confidence level upper limits as 0.28 SN per year including 4.26 year's operation of Kamiokande with period of December 1985 to August 1992 8 . 5

Network with other experiment

As mentioned in section 1, there are other possible detector to observe super­ nova neutrinos. Table 1 shows the summary of specific neutrino detectors. An international collaboration to establish global alert system, so called Supernova Early Warning System (SNEWS) 9 , was organized in 1998. Some experiments have already been connected by secure network via server computer to take a coincidence of signals. For Super-Kamiokande, we send information to the server in case of Alarm candidate. New experiments will join this project, then more confident alarm will be obtained. 6

Summary

We are searching for the neutrino burst from supernova explosion since 1996 using Super-Kamiokande detector. No candidate was found in obtained data.

214

Detector Super-Kamiokande MACRO LVD SNO AMANDA KamLAND Borexino OMNIS

Type water scintillator scintillator H20 D20 long string scintillator scintillator high Z

LAND

high Z

Mass (kton) 32 0.6 0.7 1.7 1.0 2/PMT 1.0 1.3 10 (Fe) 4 (Pb) 1

events (@10kpc) 4400 150 170 350 430 N/A 300 200 2000

status SNEWS SNEWS SNEWS SNEWS

450

2000+

running 2001 2001 2000+

Table 1: Summary of possible supernova experiments. Number of expected events are as­ sumed by lOkpc distance from Earth.

The 90%-confidence level upper limit of supernovae explosion rate is obtained by 0.58 y r - 1 within lOOkpc, and also obtained by 0.28 y r - 1 within our galaxy, if we accumulate the Kamiokande 4.26 yr's results. However, Super-Kamiokande will have a large statistics of anti electron neutrino events from supernovae, and it will make us to understand not only detailed mechanism of core collapse, but also the neutrino signature as an elementary particle. Pointing ability seems to be around 18 degree resolution on the celestial coordinate. We will give you most probable position within a few hours. This is very important for observing nuclear composition spectra using X-ray and gamma-ray by other astrophysical observatory and satellite at the beginning of explosion to understand more detailed mechanism of supernovae. References 1. 2. 3. 4. 5. 6. 7. 8. 9.

K.Hirata et al, Phys. Rev. Lett. 58, 1490 (1987). R.M.Bionta et al, Phys. Rev. Lett. 58, 1494 (1987). S.E.Woosley et al, Astrophys. J. 433, 229 (1994). Y.Fukuda et al., Phys. Rev. Lett. 81, 1158 (1998). J.F.Beacom and P.Vogel, Phys. Rev. D 58, 053010 (1998). J.F.Beacom, R.N.Boyd and A.Mezzacappa, hep-ph/0006015 R.Mayle, J.R.Wilson and D.Schramm, Astrophys. J. 318, 288 (1987). Y.Suzuki, Frontiers of Neutrino Astrophysics 61, (1993). http://hep.bu.edu/~snnet.html

C A N T H E NEGATIVE M A S S S Q U A R E OF T H E E L E C T R O N N E U T R I N O S B E A N I N D I C A T I O N OF I N T E R A C T I O N W I T H RELIC N E U T R I N O S ? KENSUKE HOMMA Hiroshima University, 1-3-1 Kagamiyama, Higashi-hiroshima 739-8526, Japan E-mail: [email protected] OSAMU JINNOUCHI University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan E-mail: [email protected] The unphysical result of the negative mass square of the electron neutrinos recently reported in several tritium /3-decay experiments, is one of the most attractive subjects. As a possible scenario to explain the anomaly, we have assumed a reaction with relic neutrinos which are predicted by the standard big bang cosmology. If such neutrinos could exist, the interaction of the relic neutrinos with the target tritium, i/e + 3H —> 3He + e~ could be laid under the large amount of the 0decay process, 3H —> 3He + e~ + ue, which would cause a peak-like structure beyond the end-point in the Kurie plot. Based on the assumption, we evaluated the cross section from the event rate found in the peak by re-fitting to the 1991 data published by Mainz Group. In this talk we will provide a scenario that could account for the evaluated cross section by assuming a coherent state of the neutrino sea, which would result much lower temperature than the prediction from the standard big bang cosmology.

1

Introduction

As an important consequence of the big-bang cosmology, there must exist relic neutrinos in the universe as well as relic photons which have been already discovered 1. In the standard cosmological thermal history 2 , the present temperature of the relic neutrino Tv, should satisfy T„ = (^■) 1 / 3 T 7 , where T 7 is the present temperature of the relic photon which is known as 2.73K by the observation. This corresponds to the mean thermal energy of neutrinos, ev ~ 10~ 4 eV, and the deduced number density for each flavor of neutrino from the observation of the relic photons is ~ 102 c m - 3 . This prediction is based upon the massless Fermi distribution in the radiation dominated epoch, where the neutrinos are enough relativistic and the effect of the mass can be neglected. Recently series of tritium /?-decay experiments 3>4'5-6'7 have reported re­ peatedly the negative mass square of the electron neutrino. As possible in­ terpretations to this anomaly, there are several considerations 8 ' 9 » 10 . In this

215

216

talk, we will report the result in the paper where we examined the as­ sumption that the relic neutrinos are interacting with neutrons in the tritium target via the process, ve + 3H —* 3He + e~ under the /?-decay process, 3 H —► 3He + e~ + i7e. In order to examine the assumption, we tried re-fitting to the 1991 data published by Mainz Group 3 . This possibility was originally pointed out by 12 , where the momentum of the electron in the final state might be increased by the chemical potential fiVe beyond the end-point in the Kurie plot, as far as fiUe > 0 is satisfied, that is, neutrinos dominate anti-neutrinos. Then it is followed by 13 , where the electron momentum in the final state would be increased by the incident electron neutrino mass which also induces a peak beyond the end-point. Although some papers 7 ' 9 conclude that the cross section of the process is too low to explain the anomaly based on the standard number density and temperature of the relic neutrinos, at present if massive neutrinos could be in a coherent state with much lower temperature, we might be able to expect much higher cross section than the calculation by the standard weak interaction. In this talk we will provide another scenario after the neutrino decoupling assuming the coherent state of the neutrino sea and give a hint how such state could be formed after the neutrino decoupling. 2 2.1

Derivation of Cross Sections The expected cross section from Mainz data

From the expected event rate found in the peak, it is possible to estimate the cross section using the equation, dN — = 2Nt nv a v e,

(1)

where the evaluated events rate dN/dt is 1.34 x 1 0 - 3 s _ 1 , the number of T% molecules -Nt is 2.8 x 1016 which was obtained from the T-i source geometry 3 used in the Mainz experiment, the number density of neutrino, nv and the relative velocity, v between n and ve, is pvc/mu cm/s, where we took into account only the thermal energy of neutrinos, but ignored the Fermi motion of neutrons in the tritium nuclei. The detection efficiency based on the solid angle from the tritium source to the spectrometer is e = 0.8/27T. Therefore the cross section becomes <7 = 6 . 3 x l ( r 3 0 - ^ - c m 2 .

(2)

217

2.2. The cross section for ve-\-n —> p + e The cross section for the elastic scattering of neutrinos with neutrons, ve+n —> ve + n , has been already calculated in reference 15 for both the non-relativistic and relativistic limit of background neutrinos. As suggested in 16 , the cross section for the inelastic scattering, ve + n —> p + e~ is much higher than the one for the elastic scattering. In the case where the momentum of the incident neutrino is in the relativistic limit, pv « 0.1 ~ 10 MeV, the cross section arei can be approximated as 1

/ < 2 2 N \ „2

2,

Orel = ^ ( J- j PZ COS2 0c,

(3)

where 6C is a cabbibo angle and G is a Fermi coupling constant. At the nonrelativistic limit, pv ss 10~ 4 ~ 10 _ 1 eV, the cross section anon r e ; can be approximated as

1 (G2\pe

O-non rel = T

T"

memv

,

COS 0C,

(4)

2 \4irJ pv where pe is the electron momentum in the final state, me and m„ are the rest masses of electron and neutrino respectively. The other conventions are same as above. 3

Scenario for Relic Neutrinos After Radiation Epoch

If the observed cross section in (1) coincides with the cross section in (4), the neutrino number density must satisfy the following value; , dN/dt -a = 1-3 x 10 17 (5) 2 Nt ■ (G /4n) -pe-rrie- cos 6c ec c m - 3 . Since nv is expected to be ~ 102 c m - 3 in the standard thermal history, the cross section in (4) is much smaller than the observed cross section in (1) by a factor of 1.3 x 10 15 . However, if it is assumed that the neutrino sea could be in a coherent state and the temperature could be much lower than the standard one, the cross section would be increased from the point of view of the quantum mechanics without introducing any new interactions. When the temperature is extremely low, the wave length of the neutrino becomes quite long that would cause the overlap of incident neutrino waves in a unit volume, even from neutrinos whose center positions are outside the unit volume. Since in a coherent state one can not distinguish with which neutrino a neutron interacts in a scattering, the amplitudes of incident neutrino waves which participate the unit volume must be summed up. This is the similar situation «, =

AT

(na/A

2

218

to the case of the coherent elastic scattering, although the summation of the amplitudes is taken over the targets in that case 15 . Whatever causes this coherency, based on the assumption we tried to evaluate the neutrino wave length naively, A„ which could raise the cross section using the following equation; f°°

n„ / J0

4

1

2

d r - T r ^ - p7rcr z - e - ^ = 1.3 x 10 17 , 3 V

(6)

where n„ is kept to be 102 c m - 3 and a corresponds to \„/2. From this wave length the temperature can be estimated as 5.8 x 10~ 10 eV. This situation is plotted in figure 1, where the cross sections are plotted with respect to the incident momentum and the wave length. The dashed line denotes the cross section without the summation over the incident waves, the solid line denotes the cross section with the summation, and the evaluated cross sections from the data are plotted as thicker lines. Since the cross section depends on the assumed electron neutrino mass, the cross sections for the mass of 0 eV, 1 eV, 0.1 eV and 0.01 eV are shown in the plot respectively. Of course this temperature contradicts with the assumed number density, nv of 102 c m - 3 , as long as the Fermi distribution of neutrinos is treated as the massless fermion in the radiation dominated epoch in the standard thermal history, where the number density is governed by the relation, nv oc T 3 . How­ ever, if an effective degeneration due to a spatially inhomogeneous neutrino distribution had occurred in time much later than the radiation dominated epoch, the Fermi distribution must follow the massive fermion case as far as neutrino has the finite mass, since the neutrinos would not be relativistic any more. The neutrino degeneration suggested by reference12 was originally the degeneration due to the lepton number asymmetry. However, the essence of the degeneration is in the imbalance between the number of neutrinos and anti-neutrinos, thus if the space around us is locally filled up with only neu­ trinos as an extreme case, such spatial inhomogeneity may cause the neutrino degeneration effectively. Then as long as the average number density is con­ served before and after the degeneration, it does not contradict with the obser­ vation of the relic photons, where neutrinos and anti-neutrinos were originally in the thermal equilibrium within a same volume during the radiation dom­ inated epoch, but at present it looks as if neutrinos are degenerated locally. Therefore this effective chemical potential may be different from the chemical potential inherited from the radiation dominated epoch by the lepton number asymmetry, for instance, as studied in reference17. Based on this scenario, we investigated whether we can find a region where the electron neutrino mass, mve and the effective chemical potential, fie/f can

219

-20 i^\\S. to

•^— Evaluated temperature

K— Temperature from the standard thermal history

Cross section evaluated ^**5J>^>W v^^O**^ from Mainz experiment V ^ >O , ^ v . i 111,= leV \\ O O S L rrY = 0. leV \\ ^ ^ ^ ^ m>0.01eV

o O

-30 -

•-;>... -:;;^

\ \ Cross section v \ with summation Yv\ m = leV \ \ rrY=0.1eV \V\nX=0.01eV

~~-- ~~- "~~ v \ \ [

-40 -

Cross section" ~ - - ~ N S \ . without summationKsN>^^

-

/

\S^>^

m = leV

^^0~<>----__^3^!^ ~mz===://

n\=0.1eV rn^,- O.Olev

-50 -

/

S

/mv=0eV i

-10

log 10 p v (eV) _i

i

i

i_

-5

-10

log10 X/27t (cm) Figure 1. Cross sections are plotted as a function of incident neutrino momentum pv and the wave length X/2n assuming that the neutrino number density is 102 c m - 3 . The dashed line denotes the cross section without the summation over the incident waves, the solid line denotes the cross section with the summation, and the evaluated cross sections from the data are plotted as the thicker lines. Since the cross section depends on the assumed electron neutrino mass, the cross sections for the mass of 0 eV, 1 eV, 0.1 eV and 0.01 eV are shown in the plot respectively.

be consistent with the position of the induced peak in our fitting using the

220

following massive Fermi distribution; . nv(mve,(j,eff)

A-K{2mvekTvf/2

. =

73 h

f°° /

Jo

Va dx

-.

l + exp \x-

^,

(7)

!$£)

where n„ = 102 c m - 3 and Tv = 5.8 x i O - 1 0 eV are used following the scenario. Solving the equation (7) numerically, the electron neutrino mass is plotted with respect to the absolute value of the effective chemical potential in figure 2. As seen from the figure, as long as the effective chemical potential is positive, there is a room which does not conflict with the position of the induced peak in our fitting. 4

Summary

We have attempted to explain the anomaly of the negative mass square of the electron neutrino observed in the tritium-/? experiments by the reaction with the relic neutrino. Introducing a 5-function as the induced peak by the relic neutrino into the fitting parameterization of the Mainz Group, we have found that our parameterization resulted better reduced-x 2 in the physical region of mu2 > 0 eV2.(See reference11.) Although the best value of the mass square was consistent with zero as the result of the fitting, if the finite energy resolution of the detector is taken into account, there is still a possibility for the electron neutrino to have the finite mass. We have evaluated the cross section from the event rate found in the induced peak based on the standard number density of the relic neutrinos, and also derived the cross section for the process ve + n —* p + e~ based on the weak interaction. Although the theoretically derived cross section is much smaller than the observed cross section, if the neutrino sea could be in a coherent state and the temperature could be 5.8 x 1 0 - 1 0 eV, the cross sec­ tion would be increased by the summation of amplitude of incident neutrino waves even with the standard neutrino number density. However, this tem­ perature contradicts with assumed number density, as far as neutrinos follow the massless Fermi distribution in the radiation dominated epoch. Therefore we attempted to introduce a scenario that an effective neutrino degeneration due to the spatially inhomogeneous distribution, had occurred later than the radiation dominated epoch, where the neutrino must follow the massive Fermi distribution as far as neutrino mass is finite. Based on this scenario we found that there is a allowed region where the electron neutrino mass is consistent with the position of the induced peak in our fitting, as far as the effective chemical potential is positive.

221

>

= Heff<°V

n=102cm"3

10

kT=5.8xl0"10eV

«s

& 10

10

M^eff > °

10 10

-3 b-

10

-4 b-

10

. 1 ilillll

J. 1J JU.nl

L.U.UI.ul

i|l

i,

I

i i i iiml

i i i inul

i

I

IOWIO-SO-'IO-SO-'IO^IO-'IO-2

iMul (cV) Figure 2. The electron neutrino mass is plotted with respect to the absolute value of the effective chemical potential solving the equation (7) numerically.

5

Discussion

The most obscure point is how such a coherent state of neutrino sea could be produced despite of the fact that neutrinos are fermions. As a known phenom­ ena which causes a coherency over a long distance even with fermions is the superconductivity in solid state materials with extremely low temperature. It

222

is understood that Cooper pairs of electrons form via phonon exchanges and they behave as bosons. In analogy to this phenomena, if Cooper pairs of the neutrinos could form in universe, they could be in a state of Bose-Einstein condensates which would cause a coherent state over wide ranges. In order to produce Cooper pairs, in general two critical conditions are necessary; the first one is that Fermi surface must form, and the second one is that there must be an attractive force between fermions. It is known that even if the attractive force is quite weak, as far as the first condition is satisfied, Cooper pairs would be produced. Therefore it is very exciting to study whether there are attractive channels between neutrinos. In particular, if attractive channels via lepton or quark exchanges could exist, spatially inhomogeneous neutrino condensates might be expected. References 1. A.A.Penzias and R.Wilson, Astrophys. J. 142, 419 (1965). 2. Edward W.Kolb,Michael S.Turner, The Early Universe, (Addison Wesley, 1990). 3. Ch.Weinheimer et al., Phys. Lett. B 300, 210 (1993). 4. A.I.Belsev et al., Phys. Lett. B 350, 381 (1992). 5. E.Holzschuh,M.Fritschi and W.Kiindig, Phys. Lett. B 287, 381 (1992). 6. H.Kawakami et al., Phys. Lett. B 256, 105 (1991). 7. R.G.H.Robertson et al., Phys. Rev. Lett. 67, 957 (1991). 8. Giani Simone, hep-ph/9712265. 9. Rabindra N.Mohapatra,Shmuel Nussinov, Phys. Lett. B 395, 63 (1997). 10. Francesco Vissani, Phys. Lett. B 413, 101 (1997). 11. O.Jinnouchi and K.Homma Phys. Lett. B 435, 381 (1998). 12. Steven Weinberg, Phys. Rev. 128, 1457 (1962). 13. J.M.Irvine and R.Humphreys, J.Phys.G 9, 847 (1983). 14. A.Picard et al., Nucl. Instrum. Methods B63, 345 (1992). 15. P.F.Smith, IL NUOVO CIMENTO 83A, 263 (1984). 16. P.F.Smith, RAL-91-017. 17. M.Kawasaki K.Kohri and K.Sato, Astrophys. J. 490, 72 (1997).

N U C L E O S Y N T H E S I S IN H Y P E R N O V A E K. N O M O T O 1 ' 2 , K. M A E D A 1 , T . N A K A M U R A 1 , K. I W A M O T O 3 , P.A. M A Z Z A L I 2 ' 4 , I.J. D A N Z I G E R 4 , F . P A T A T 5 1 Department of Astronomy, School of Science, University of Tokyo, Tokyo, Japan 2 Research Center for the Early Universe, School of Science, University of Tokyo, Tokyo, Japan 3 Department of Physics, College of Science and Technology, Nihon University, Tokyo, Japan 4 Osservatorio Astronomico di Trieste, via G. B. Tiepolo, Trieste, Italy ^European Southern Observatory, Garching, Germany We discuss the properties of the hyper-energetic Type Ic supernovae (SNe Ic) 1998bw and 1997ef. SNe Ic 1998bw and 1997ef are characterized by their large luminosity and the very broad spectral features. Their observed properties can be explained if they are very energetic SN explosions with the kinetic energy of .EK > 1 x 10 5 2 erg, originating probably from the core collapse of the bare C + O cores of massive stars (~ 30 — 4 0 M Q ) . At late times, both the light curves and the spectra suggest that the explosions may have been asymmetric; this may help us understand the claimed connection with GRB's. Because these kinetic energies of explosion are much larger than in normal core-collapse SNe, we call objects like these SNe "hypernovae". The mass of 5 6 Ni in SN 1998bw is estimated to be as large as 0.5 - 0.7 M Q from both the maximum brightness and late time emission spectra, which suggests that the asymmetry may not be extreme.

1

Introduction

Recently, there have been an increasing number of candidates for the gammaray burst (GRB)/supernova (SN) connection, which include GRB980425/SN Ic 1998bw, GRB971115/SN Ic 1997ef, GRB970514/SN Iln 1997cy, GRB980910/SN Iln 1999E, and GRB991002/SN Iln. The first example of such a candidate was provided by SN 1998bw. SN 1998bw was discovered in the error box of GRB980425 (Kulkarni et al. 1998), only 0.9 days after the date of the gammaray burst and was very possibly linked to it (Galama et al. 1998). Early spectra of SN 1998bw were rather blue and featureless, showing some similarities with the spectra of Type Ic SNe (SNe Ic), but with one major dif­ ference (Fig. 1): the absorption lines were so broad in SN 1998bw that they blended together, giving rise to broad absorption trough separated by appar­ ent 'emission peaks' (Patat et al. 2000). This supernova was immediately recognized to be very powerful and bright (Fig. 2). The SN was very bright for a SN Ic: the observed peak luminosity, L ~ 1.4 x 1043 erg s _ 1 , is almost ten times higher than that of previously known

223

224 SNe Ic near maximum

SN 1998 bw, 11 May, 1=16 days

5 Dec, t=1S days

6000 8000 Rest Wavelength (A)

Figure 1: Observed spectra of Type Ic supernovae 1998bw, 1997ef, and 19941. -i—i—i—I—i—i—i—i—i—i—i—i—i—i—i—i—i—i—|—r

'Co decay

C 0 1 3 8 & S N 1998bw

50

100

150

2W

Time since the explosion ( days)

Figure 2: Absolute magnitudes of Type Ic supernovae: the ordinary SN Ic 19941, and the hypernovae SN 1998bw (Galama et al. 1998) and SN 1997ef (Iwamoto et al. 2000) together with their models. The dashed line indicates the 5 6 Co decay rate.

225

SNe Ib/Ic. Models which described the SN as the energetic explosion of a C+O core of an initially massive star could successfully fit the first 60 days of the light curve (Iwamoto et al. 1998; hereafter IMN98). The very broad spectral features and the light curve shape have led to the conclusion that SN 1998bw had an extremely large kinetic energy of explosion, EK ~ 3 x 1052 ergs (IMN98; Woosley, Eastman, & Schmidt 1999). This is more than one order of magnitude larger than the energy of typical supernovae, thus SN 1998bw was termed a "hypernova" (IMN98). "Hypernova" is a term we use to describe the events of EK > 1052 erg without specifying whether the central engine is a collapsar or magnetar or pair-instability. SN 1997ef was also noticed for its unique light curve and spectra (Figs. 1, 2). The spectral similarities between SN 1997ef and SN 1998bw suggest that SN 1997ef may also be a hypernova (Iwamoto et al. 2000). In Figure 2 the visual light curve of SNe 1998bw (Galama et al. 1998) and 1997ef (Garnavich et al. 1997) are compared with the ordinary SN Ic 19941. Despite the spectral similarity, the light curve of SN 1997ef is quite different from those of SN 1998bw and SN 19941. Since the light curves are rather diverse, even in this limited number of samples, a range of energies and/or progenitor masses of SN Ic explosions may be implied. Here we summarize the photometric and spectroscopic properties of these hypernovae and the estimated explosion energies and ejecta mass using the hydrodynamical models. We also study nucleosynthesis in hypernovae. 2

Explosion Models for Supernovae and Hypernovae

We construct hydrodynamical models of an ordinary SN Ic and a hypernova as follows. Since the light curve of SN Ic 19941 was successfully reproduced by the collapse-induced explosion of C+O stars (Nomoto et al. 1994; Iwamoto et al. 1994), we adopted C+O stars as progenitor models for SNe 1997ef and 1998bw as well. We calculate the light curves and spectra for various C+O star models with different values of E^ and M e j. These parameters can be constrained by comparing the calculated light curves, the synthetic spectra, and the photospheric velocities with the data of SNe 1998bw and 1997ef. These model parameters are summarized in Table 1, together with model C021 for SN 19941. The position of the mass cut is chosen so that the ejected mass of 56 Ni is the value required to explain the observed peak brightness of SN 1997ef and SN 1998bw by radioactive decay heating. The compact remnant in CO60 is probably a neutron star because Mcut = 1.4 M Q , while it may be a black hole in CO100 and C0138 because M c u t may well exceed the maximum mass of a stable neutron star.

226

Table 1. Parameters of the C + 0 star models model C021 CO60 CO100 C0138H C0138L

3 3.1

(M0)

Mc+o

Mej

-15 -25 - 3 0 - 35 -40 -40

2.1 6.0 10.0 13.8 13.8

0.9 4.4 7.6 10 11

Mms

66

Ni mass

Mcut

0.07 0.15 0.15 0.5 0.5

1.2 1.4 2.4 4 3

EK(

10 5 1 erg)

1 1 8 60 30

SN 19941 1997ef 1998bw 1998bw

SN 1997ef Light Curve Models

In Figure 3 we compare the calculated V light curves for models CO60 and CO100 with the observed V light curve of SN1997ef. We adopt a distance of 52.3 Mpc. The light curve of SN 1997ef has a very broad maximum, which lasts for — 25 days. The light curve tail starts only — 40 days after maximum, much later than in other SNe Ic. The light curve of SN 1997ef can be reproduced basically with various explosion models with different energies and masses. In general, the properties of the light curve are characterized by the decline rate in the tail and the peak width, Tpeak- The peak width scales approximately as r p e a k oc K

^ M ^ E ^ ' \

(1)

where K denotes the optical opacity (Arnett 1996). This is the time-scale on which photon diffusion and hydrodynamical expansion become comparable. Since the model parameters of CO100 and CO60 give similar Tpeak, the light curves of the two models look similar: both have quite a broad peak and reproduce the light curve of SN1997ef reasonably well (Figure 3). The light curve of SN 1997ef enters the tail around day 40. The subsequent slow decline implies much more efficient 7-ray trapping in the ejecta of SN 1997ef than in SN 19941. The ejecta of both CO100 and CO60 are fairly massive and are able to trap a large fraction of the 7-rays, so that the calculated light curves have slower tails compared with C021. However, the light curves for both models decline somewhat faster in the tail than the observations. In §4.1, we will suggest that such a discrepancy between the early- and late-time light curves might be an indication of asphericity in the ejecta of SN 1997ef and that it might be the case in those SNe lb as well.

227

Time (days)

Time since Ihe explosion (days)

Figure 3: Left panel: Calculated Visual light curves of CO60 and CO100 compared with that of SN 1997ef. Right panel: Evolution of the calculated photospheric velocities of CO60 and CO100 (solid lines) compared with the observed velocities of the Si II 634.7, 637.1 nm line measured in the spectra at the absorption core.

3.2

Synthetic Spectra

To strengthen the arguments in §3.1, we compare the emergent spectra for the two explosion models. Using detailed spectrum synthesis, we can distinguish between different models more clearly, because the spectrum contains much more information than a single-band light curve. Around maximum light, the spectra of SN 1997ef show just a few very broad features, and are quite different from those of ordinary SNe Ib/c, but similar to SN 1998bw. However, at later epochs the spectra develop features that are easy to identify, such as the Ca II IR triplet at ~ 8200A, the 0 I absorption at 7500 A, several Fe II features in the blue, and they look very similar to the spectrum of the ordinary SN Ic 19941. We computed synthetic spectra with a Monte Carlo spectrum synthesis code using the density structure and composition of the hydrodynamic models CO60 and CO100. The lines in the synthetic spectra computed with the ordinary SN Ic model CO60 are always much narrower than the observations. This clearly indicates a lack of material at high velocity in model CO60, and suggests that the kinetic energy of this model is much too small. Synthetic spectra obtained with the hypernova model CO100 for the same

228

4000

6000 8000 Rest Wavelength (A)

10*

Figure 4: Observed spectra of SN 1997ef (bold lines) and synthetic spectra computed using model CO100 (fully drawn lines).

3 epochs are shown in Figure 4. The spectra show much broader lines, and are in good agreement with the observations. In particular, the blending of the Fe lines in the blue, giving rise to broad absorption troughs, is well reproduced, and so is the very broad Ca-0 feature in the red. The two 'emission peaks' observed at ~ 4400 and 5200A correspond to the only two regions in the blue that are relatively line-free. 4 4-1

S N 1998bw Model Ught curves

We calculate the light curve of SN 1998bw using progenitors of different masses and explosions of different energies. We find that the model that give the best agreement to both the light curve and the spectra is that of the explosion of a 13.8M© C+O star, ejecting 10 M 0 of material with EK = 6 x 1052 erg, including 0.5M® of 56 Ni (C0138H). In Figure 5 we compare the bolometric light curves of model C0138H (solid) with the V photometry of SN 1998bw. However, C0138H has difficulties reproducing the apparently exponential decline after day 60. On the other hand, C0138L (EK = 3 X 1052; dashed) is in better agreement after day 90, although the early light curve and photospheric velocities do not fit well.

229

0

100

200 300 400 time since the GRB (days)

500

600

Figure 5: The light curves of models C0138H (J5 K = 6 x 10 5 2 erg; solid) and C0138L ( B K = 3 X 10 5 2 erg; dashed) compared with the observations of SN1998bw (Galama et al. 1998; McKenzie & Schaefer 1999). A distance modulus of fi = 32.89 mag and Av = 0.0 are adopted. The dotted line indicates the energy deposited by positrons for C0138H.

After day ~ 200 the decline of the model light curve becomes slower, and it approaches the half-life of 56 Co decay around day 400. At t > 400 days most 7-rays escape from the ejecta, while positrons emitted from the 56 Co decay are mostly trapped and their energies are thermalized. Therefore, positron deposition determines the light curve at t > 400 days (dotted line in Fig. 5). If the observed tail should follow the positron-powered light curve, the 56 Co mass could be determined directly. The comparison between SN 1998bw and the model light curve of C0138H (which fits better at early phases) and C0138L (which is better for late phases) in Figure 5 suggests a departure from spherical symmetry. 4-2

Early Time Spectra

We have used model C0138H as a basis to compute synthetic spectra for the near-maximum phase of SN 1998bw. In Figure 6 we show the synthetic spectra obtained for 3 epochs. The synthetic spectra clearly improve over those of IMN98. In particular, those absorptions not due to broad blends, i.e. the Si II feature near 6000A, and the O I+Ca II feature between 7000 and 8000A are now much broader, in significantly better agreement with the data. Our fits at least demonstrate that a large E-& is necessary, and that a Type Ic SN O-dominated composition yields quite a reasonable reproduction of the observations.

230

4000

6000 Rest. Wavelength (A)

8000

Figure 6: Observed spectra of SN1998bw (full lines) and synthetic spectra calculated using model C0138H (EK = 6 x 10 B2 erg; dashed lines).

4-3

Late Time Evolution

In Fig. 7, a nebular spectrum of SN 1998bw on 12 Sept 1998 (rest frame epoch 139 days) is compared to synthetic spectra obtained with a NLTE nebular model based on the deposition of gamma-rays from 56 Co decay in a nebula of uniform density. Two models were computed. In one model (dotted line) we tried to reproduce the broad Fell] lines near 5300A. The 56 Ni mass is 0.65 M©, and the outer nebular velocity is 11,000km s" 1 , and the O mass is 3.5M Q . The average electron density in the nebula is log ne = 7.47 c m - 3 . In the other model (dashed line), we tried to reproduce only the narrow [01] 6300A emission line. The 56 Ni mass estimated from the broad-line fit is comparable to the value obtained from the light curve calculations. At early times, the fast-expanding lobes were much brighter than the rest, and so we observed the broad-lined spectra and the bright light curve. The fastmoving regions rapidly became thin, though, and soon emission lines appeared. Initially those were broad, dominated by the hyper-energetic lobes. Later, though, the 7-rays from the fast-moving 56 Co could escape that region more and more easily, and a significant fraction of them could penetrate down into the low-velocity region and excite the O and Mg there. Both the need for a high density region and the velocity inversion as well

231 15 SN 1998bw day 139

10

5

4000

6000

8000

10'

Figure 7: A nebular spectrum of SN 1998bw on 12 Sept 1998 (rest frame epoch 139 days) is compared to synthetic spectra obtained with a NLTE nebular model based on the deposition of gamma-rays from 6 6 C o decay in a nebula of uniform density (see text for details).

as polarization measurements (Patat et al. 2000) might indicate that the ex­ plosion is aspherical. If the outburst in SN 1998bw took the form of a prolate spheroid, for example, the explosive shock along the long axis was probably strong, ejecting material with large velocities and producing abundant 56 Ni. In directions away from the long axis, on the other hand, oxygen is not much burned and the density is high enough for 7-rays to be trapped even at ad­ vanced phases, thus giving rise to the slowly declining tail. We note that our estimate of the 56 Ni mass of ~ 0.6M© from the neb­ ula spectra in Figure 7 does not much depend on the asphericity. This is in good agreement with the spherical models C0138. Since Hoflich et al. (1999) suggested that the 56 Ni mass can be as small as 0.2 M 0 if aspherical effects are large, our results suggest that the aspherical effects might be modest in SN 1998bw.' 5

Possible Evolutionary Scenarios to Hypernovae

Here we classify possible evolutionary paths leading to C+O star progenitors. In particular, we explore the paths to the progenitors that have rapidly rotating cores with a special emphasis, because the explosion energy of hypernovae may be extracted from rapidly rotating black holes (Blandford & Znajek 1977). (1) Case of a single star: If the star is as massive as M m s > 40 M Q , it could lose its H and He envelopes in a strong stellar wind (e.g., Schaller et al.

232

1992). This would be a Wolf-Rayet star. (2) Case of a close binary system: Suppose we have a close binary system with a large mass ratio. In this case, the mass transfer from star 1 to star 2 inevitably takes place in a non-conservative way, and the system experiences a common envelope phase where star 2 is spiraling into the envelope of star 1. If the spiral-in releases enough energy to remove the common envelope, we are left with a bare He star (star 1) and a main-sequence star (star 2), with a reduced separation. If the orbital energy is too small to eject the common envelope, the two stars merge to form a single star (e.g., van den Heuvel 1994). (2-1) For the non-merging case, possible channels from the He stars to the C+O stars are as follows (Nomoto, Iwamoto, & Suzuki 1995). (a) Small-mass He stars tend to have large radii, so that they can fill their Roche lobes more easily and lose most of their He envelope via Roche lobe overflow. (b) On the other hand, larger-mass He stars have radii too small to fill their Roche lobes. However, such stars have large enough luminosities to drive strong winds to remove most of the He layer (e.g., Woosley, Langer, & Weaver 1995). Such a mass-losing He star would corresponds to a Wolf-Rayet star. Thus, from the non-merging scenario, we expect two different kinds of SNe Ic, fast and slow, depending on the mass of the progenitor. SNe Ic from smaller mass progenitors (channel 2-1-a) show faster light-curve and spectral evolu­ tions, because the ejecta become more quickly transparent to both gamma-ray and optical photons. The slow SNe Ic originate from the Wolf-Rayet progeni­ tors (channels 1 and 2-1-b). The presence of both slow and fast SNe Ib/Ic has been noted by Clocchiatti & Wheeler (1997). (2-2) For the merging case, the merged star has a large angular momentum, so that its collapsing core must be rotating rapidly. This would lead to the formation of a rapidly rotating black hole from which possibly a hyper-energetic jet could emerge. If the merging process is slow enough to eject the H/He envelope, the star would become a rapidly rotating C+O star. Such stars are the candidates for the progenitors of Type Ic hypernovae like SNe 1997ef and 1998bw. If .a significant amount of H-rich envelope remains after merging, the rapidly rotating core would lead to a hypernova of Type Iln possibly like SN 1997cy (or Type lb).

233

6 6.1

Nucleosynthesis in Hypernovae Explosive Nucleosynthesis

Since hypernovae explode with much higher explosion energies than usual su­ pernovae, explosive nucleosynthesis could have some special features. Also hypernovae have shown some aspherical signatures. We calculate explosive nucleosynthesis in hypernovae in the same way as has been done for normal supernovae; we use a detailed nuclear reaction network including 211 isotopes up to 71 Ge (Thielemann, Nomoto, & Hashimoto 1996; Hix & Thielemann 1996; Nakamura et al. 1999a) (Figure 8: top). Nucleosynthesis in normal supernovae (EK = 1 X 10 51 erg) is also shown in Figure 8 (bottom) for comparison. A similar comparison is made for CO60 and CO100. The total amount of nucleosynthesis products are summarized in Table 2. From this figure, we can see the following characteristics of nucleosynthesis with the very large explosion energy. (1) The complete Si-burning region is extended to the outer, lower density region. Whether this region is ejected or not depends on the mass cut. The large amount of 56 Ni observed in hypernovae (e.g., ~ 0.5M Q for SN1998bw and O.15M0 for SN1997ef) implies that the mass cut is rather deep, so that the elements synthesized in this region such as 59 Cu, 63 Zn, and 64 Ge (which decay into 59 Co, 63 Cu, and 64 Zn, respectively) are likely to be ejected more abundantly. In the complete Si-burning region of the hypernova, elements produced by a-rich freezeout are enhanced because nucleosynthesis proceeds under lower densities than in usual supernovae. Figure 8 clearly shows a trend that a larger amount of 4He is left in more energetic explosion. Hence, elements synthesized through a-captures such as 4 0 Ca (stable), 4 4 Ti and 48 Cr (decaying into 4 4 Ca and 4 8 Ti, respectively) become more abundant. (2) The more energetic explosion produces a broader incomplete Si-burning region. The elements produced mainly in this region such as 52 Fe, 55 Co, and 51 Mn (decaying into 52 Cr, 55 Mn, and 51 V, respectively) are synthesized more abundantly with the larger explosion energy. (3) Oxygen burning takes place in more extended, lower density region for the larger explosion energy, so that the abundances of elements like 0 , C, Al are smaller. On the other hand, a larger amount of ash products such as Si, S, Ar are synthesized by oxygen burning. Figure 9 shows the abundances of stable isotopes relative to the solar val­ ues for 3 x 1052 erg and 1 x 10 51 erg. The progenitor is the 16M Q He star and products from H-rich envelope are not included. The isotopic ratios relative to 16 0 with respect to the solar values are shown. As a whole, intermediate mass nuclei and heavy nuclei are more abundant for the more energetic explosion,

234

.001

.0001

.001

.0001

4.5 M,/Ma

5

5.5

6

6.5

Figure 8: The isotopic composition of ejecta of the hypernova (EK = 3 X 10 62 erg; top) and the normal supernova (En = 1 x 10 5 1 erg; bottom) for a 16M© He star. Only the dominant species are plotted. The explosive nucleosynthesis is calculated using a detailed nuclear reaction network including a total of 211 isotopes up to n G e .

235 Eexp = 3 0 f o e 1

I

10

o

I

I

I

I

I

I

I

i

i

i i i

i

20

I < i i ' l ' ' ' ' I

i

i

i

30

i i

i

i

i i i

40 m a s s number

50

60

0

Figure 9: Abundances of stable isotopes relative to the solar values for 3 xlO 5 2 ergs and 1 x l O 5 1 ergs. The progenitor is a 16M© He star (H-rich envelope is not included).

236

Table 2. Yields of hypernova and supernova models (M 0 ) model CO60 CO100 C0138H model CO60 CO100 C0138H

c

0.082 0.58 0.11 44Ti 2.1X10 - 4 4.5X10 - 5 2.2xl0~ 4

0

Mg

Si

S

Ca

Ti

Fe

Ni

3.0

0.10 0.42 0.95

0.037 0.19 0.52

0.006 0.025 0.088

0.0003 0.0003 0.0011

0.16 0.19 0.50

0.017 0.021

56Ni

0.24 0.22 0.29 57Nj

0.15 0.15 0.50

5.7xl0~ 3 5.7xl0"3 1.5xl0~ 2

5.6 6.6

0.028

except for the elements being consumed in oxygen burning like O, C, Al. Es­ pecially, the amounts of 4 4 Ca and 4 8 Ti are increased significantly because of the enhanced a-rich freezeout. 6.2

The Mass of Ejected

56

Ni

For the study of the chemical evolution of galaxies, it is important to know the mass of 56 Ni, M( 5 6 Ni), synthesized in core-collapse supernovae as a function of the main-sequence mass M m s of the progenitor star (e.g., Nakamura et al. 1999a). From our analysis of SNe 1998bw and 1997ef, we can add new points on this diagram. Figure 10 shows M( 56 Ni) against M m s obtained from fitting the optical light curves of SNe 1987A, 1993J, and 19941 (e.g., Shigeyama & Nomoto 1990; Nomoto et al. 1993, 1994; Shigeyama et al. 1994; Iwamoto et al. 1994; Woosley et al. 1994; Young, Baron, & Branch 1995). The amount of 56 Ni appears to increase with increasing M m s of the progenitor, except for SN II 1997D (Turatto et al. 1998). This trend might be explained as follows. Stars with M m s < 25 M Q form a neutron star, producing ~ 0.08 ± 0.03 M 0 56 Ni as in SN lib 1993J, SN Ic 19941, and SN 1987A (although SN 1987A may be a borderline case between neutron star and black hole formation). Stars with M m s > 25 M© form a black hole (e.g., Ergma & van den Heuvel 1998); whether they become hypernovae or ordinary SNe may depend on the angular momentum in the collapsing core. For SN 1997D, because of the large gravitational potential, the explosion energy was so small that most of 56 Ni fell back onto a compact star remnant; the fall-back might cause the collapse of the neutron star into a black hole. The core of SN II 1997D might not have a large angular momentum, because the

237 n—i—i—|—!—r"

I ' ' ' ' I

I8DWI 98bw(lc)

97ef(lc) 87A(llp)

93J(llb)

94l(lc)

97D(llp)

10

20

25 30 Main Sequence Mass (M 0 )

35

45

Figure 10: Ejected 5 6 Ni mass versus the main sequence mass of the progenitors of several bright supernovae obtained from light curve models.

progenitor had a massive H-rich envelope so that the angular momentum of the core might have been transported to the envelope possibly via a magneticfield effect. Hypernovae such as SNe 1998bw, 1997ef, and 1997cy might have rapidly rotating cores owing possibly to the spiraling-in of a companion star in a binary system. The outcome certainly depends also on mass-loss rate and binarity. 7

Concluding remarks

We have calculated the light curves and spectra for various C+O star models with different values of £ K and M ej and reached several striking conclusions. We have shown that the spectra of SNe 1998bw and 1997ef are much better reproduced with the hypernova models than with the ordinary SN Ic model. Therefore, we suggest that SNe 1997ef, 1998ey, and 1998bw form a new class of hyper-energetic Type Ic supernovae, which we may call "Type Ic" hyper­ novae. SN 1998bw produced ~ 0.5 - O.7M0 of 56 Ni, as much as a SN la, while SN 1997ef produced less, only ~ O.15M0, but still more than in ordinary SNe Ic. The progenitor must have been a massive star, which possibly un­ derwent spiral-in of the companion star in a close binary system. Continuing observations and theoretical modeling of this interesting class of objects are certainly necessary.

238

This work has been supported in part by the grant-in-Aid for Scientific Re­ search (07CE2002, 12640233, 12740122) of the Ministry of Education, Science, Culture and Sports in Japan.

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rows,A. 1999a, ApJ, 517, 193 25. Nomoto, K., & Hashimoto, M. 1988, Phys. Rep., 163, 13 26. Nomoto, K., Suzuki, T., Shigeyama, T., Kumagai, S., Yamaoka, H., & Saio, H. 1993, Nature, 364, 507 27. Nomoto, K., Yamaoka, H., Pols, 0 . R., van den Heuvel, E. P. J., Iwamoto, K., Kumagai, S., k Shigeyama, T. 1994, Nature, 371, 227 28. Nomoto, K., Iwamoto, K., & Suzuki, T. 1995, Phys. Rep., 256, 173 29. Patat, F. et al., 2000, ApJ, submitted 30. Schaller, G., Schaerer, D., Meynet, G., k Maeder, A. 1992, A&AS, 96, 269 31. Shigeyama, T., & Nomoto, K. 1990, ApJ, 360, 242 32. Shigeyama, T., Suzuki, T., Kumagai, S., Nomoto, K., Saio, H., Yamaoka,H. 1994, ApJ, 420, 341 33. Thielemann, F.-K., Nomoto, K., k Hashimoto, M. 1996, ApJ, 460, 408 34. Turatto, M., Mazzali, P. A., Young, T. R., Nomoto, K., Iwamoto, K., Benetti, S., Cappellaro, E., Danziger, I. J., de Mello, D. F., Phillips, M. M., SuntzefF, N. B., Clocchiatti, A., Piemonte, A., Leibundgut, B., Covarrubias, R., Maza, J., Sollerman, J., 1998, ApJ, 498, L129 35. van den Heuvel, E. P. J. 1994, in Interacting Binaries, ed. H. Nussbaumer k A.Orr (Berlin:Springer Verlag), 263 36. Wang, L., & Wheeler, J. C. 1998, ApJ, 504, L87 37. Woosley, S. E., Eastman, R. G., k Schmidt, B.P. 1999, ApJ, 516, 788 38. Woosley, S. E., Eastman, R. G., Weaver, T. A., k Pinto, P. A. 1994, ApJ, 429, 300 39. Woosley, S. E., Langer, N., k Weaver, T. A. 1995, ApJ, 448, 315 40. Young, T., Baron, E., & Branch, D, 1995, ApJ, 449, L51

Overabundance of Calcium in the young SNR. RX J0852-0462: evidence of over-production of

44

Ti

H. Tsunemi, E. Miyata, J. Hiraga Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043 JAPAN E-mail: [email protected] B. Aschenbach Max-Planck-Institut fur extraterrestrische Physik, D-85740, Garching, Germany E-mail: [email protected] Recently, COMPTEL has detected 7-rays of 1157keV from 44 Ti in the direction of the SNR RX J0852-0462 1. Since « T i is a product of explosive nucleosynthesis and its half-life, r, is about 60yrs, RX J0852—0462 must be a young supernova remnant and radiation is dominated by the ejecta rather than by interstellar matter. We have detected an X-ray emission line at 4.1 ± 0.2 keV which is thought to come from highly ionized Ca. The emission line is so far only seen in the northwest shell region of RX J0852—0462. The X-ray spectrum can be weli fitted with that of thin hot plasma of cosmic abundances except that of Ca, which is overabundant by a factor of about 7. Assuming that most of the Ca is 44 Ca, which originates from 44 Ti by radioactive decay, we estimate that there is about 8 x 10~4MQ of Ca. Combining the amount of 44 Ca and the observed flux of the 44 Ti 7-ray line, the age of RX J0852-0462 is around lOOOyrs.

1

Introduction

that from the interior was thin thermal emission. They claimed that the shell region in SN1006 was a site of cosmic ray shock acceleration with energies of up to 10 GeV. Accordingly, the shell-like structure does not al­ ways stand for a thermally radiating SNR. There are several 7-ray line emissions expected in the nucleothensesis in the supernova explosion as shown in table-!. If the life is short, it will be observed only in the Supernova explosion. If it is longer than the av­ erage life of the supernova remnant, like 2GAl, it will be observed from the interstellar matter as a diffuse emis­ sion. Among them, 7-ray lines from 44Ti has moderate life which makes it a strong connection with a relatively young supernova remnant. In other words, young SNRs will be good place to search for 7-ray line emission from 44 Ti. Cassiopeia-A, one of the young SNRs, is the first source from which 7-ray emission lines from 44 Ti have been reported 3 . 44 Ti is expected to be produced in the explosive nucleosynthesis inside the SN which also pro­ duces 56Ni. 44 Ti decays into 44Sc thereby emitting two hard X-ray lines of 68keV and 78keV with a mean life­ time of 4 hours. 44Sc decays further to 44 Ca emitting a 7-ray line at 1157keV with a half-life of 60yrs 4 that has been detected with COMPTEL. In this way, 44 Ti is con­ verted into 44 Ca. Taking into account the short lifetime of 44 Ti, its detection is a direct evidence of the source being a young SNR. The discovery of this second celestial source of 44 Ti has been reported by Iyudin l: it is located in the di­ rection of the south east part of the Vela SNR where Aschenbach 5 discovered a new independent SNR, RX

A supernova (SN) explosion is a source of heavy ele­ ments in the Galaxy. The nucleosynthesized material inside the star is dispersed into interstellar space at rela­ tively high temperatures. In young supernova remnants (SNR), there are many X-ray emission lines from highly ionized elements, which tend to be diluted when mixing with ambient interstellar matter. There are two types of young SNRs from a morpho­ logical point of view: shell-like structures and those of center filled morphology. There are also two types of young SNRs from the spectroscopic point of view: thin thermal emission and power law type spectra. The Crab nebula, a young SNR, shows a centerfilledstructure with a power law type spectrum. There is a neutron star, the Crab pulsar, in its center, which is the energy source of the SNR. There are more SNRs showing shell-like struc­ tures with spectra due to optically thin, thermal emis­ sion, e.g. Cassiopeia-A, Tycho and Kepler's SNRs. The shell structure is the result of the interaction of the shock waves and corresponding shock-heating of the associated plasma. This produces thin thermal emission including many emission lines. We note that the SNe of Tycho and Kepler have been witnessed and recorded in histori­ cal documents whereas there is no record of Cassiopeia-A which is estimated to be born late in the 17 th century. The remnant of the SN occurred in AD1006, SN1006, is another young SNR. It shows a pronounced shell-like structure as shown in figure-1. Koyama et al. 2 re­ vealed that the spectra from the north-east and south­ west regions of the shell followed a power law type while

240

241

Figure 1: X-ray image of SN1006 obtained with ASCA GIS. It clearly shows a shell like structure. The spectrum from the shell shows power law type while that from the interior shows thin thermal emission.

J0852—0462, which has a radius of 1° as shown in figure2. Based on the X-ray and 44 Ti data, RX J0852-0462 is expected to be born several hundred years ago in a sky region, which in principle could have been observed from China, and therefore some record in a historical docu­ ment is expected if the SN was of standard brightness. But if it were sub-luminous the event might have been missed by the contemporaries 6 . So far, no record has been found, which reminds us of some similarity with Cassiopeia-A. We note that quite recently a footprint of a historical SN has been found in terms of nitrate abun­ dance in Antarctic ice cores. The associated SN would have occurred around 1320 ± 30 yrs 7 . 2

Observation

We have observed RX J0852-0462 with ASCA on De­ cember 21-24, 1998 as a TOO target. This observation was performed with the two CCD camera (SIS)8 and the two imaging gas scintillation proportional counters (GIS) 9 which are placed at the focal plane of four thin-foil Xray mirrors 10 on board the ASCA satellite11. The observation was performed in 7 pointings so that we could cover the entire remnant with the GIS whereas we missed the south bright shell region as shown in figure3. The SIS, having 4 times better energy resolution than the GIS, can however cover only a very small fraction of the source. The GIS observation shows a shell-like structure similar to that obtained with ROSAT. Its X-

ray spectrum is almost uniform over the source, consist­ ing of two components: a power law component with a photon index of «■' 2.5 and thin thermal emission of (1.5 ± 0.1) x 107 K. The X-ray spectrum from the entire source is shown in figure-4 by the white square. RX J0852-0462 overlaps with the Vela SNR which emits a thin thermal emission with a temperature of about 2 x 106 K. Because of the similar temperatures it is likely that the low temperature component seen in RX J0852—0462 is basically background emission from the Vela SNR. Therefore we can expect that the emission from RX J0852-0462 is predominantly of the power law type originating from a shell-like region. The SIS can cover only the central region of each GIS observation. Among them, the spectrum in the bright north-west shell clearly shows features that differ from those observed elsewhere as shown in figure-4. We see a clear emission line structure at 4.1 ±0.2 keV. We only see this structure in the eastern part of bright shell region as shown in figure-3. The other regions covered with the SIS as well show feature-less spectra similar to that obtained with the GIS for the entire remnant. 3

Discussion and conclusion

What is the origin of this emission line ? There are some candidates from an astrophysical point of view. If it is a characteristic X-ray line, it must be either from neutral Sc-K or a helium-like Ca-K emission line. From the cos-

242

Figure 2: Low energy m a p (0.1-2 keV) for Vela SNR obtained with ROSAT (left). High energy m a p (1.5-2 keV) for the same region (right). In the high energy map, the Vela Pulsar and Puppis-A SNR (upper right) are clearly seen. Furthermore, a circular structure in the lower left becomes evident that is a supernova remnant, RXJ0852-4622.

Figure 3: The circular FOV of the GIS are superposed on the X-ray intensity map obtained with ROSAT. There are two bright shell regions: north and south. A small square shows the SIS FOV detected Ca emission line.

Table 1: Decay chain from nucleosynthesis in supernova. Decay chain M

Ni

-► >*Co - .

"Co-

i7

22

Na-

44

m

m

26

Fe

Fe

22

"Ti—

Fe-*

M

1.1

A'e

Sc—

Co-*

AI-* ™Mg

Mean life (year) 0.31

3.8 44

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m

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60

4.3 x 10 5

1.1 x 10 6

mic abundance point of view, it is very implausible that it comes from Sc. If it comes from shock-heated matter, it is plausible that it comes from Ca at high temperatures. If this is not the case, it can be either a red-shifted FeK line from an AGN or a cyclotron emission line from a strongly magnetized neutron star. Since the line emission region is quite extended judging from the ASCA image, neither one of the two hypotheses of a point-like source is very likely. We analyzed the data using a thin thermal model 12 in collisional ionization equilibrium (CIE) and we ob­ tained an acceptable fit. The temperature is (1.5 ±0.1) x 107 K. The metal abundances are similar to the cosmic abundances with the exception of Ca. The Ca abun­ dance, A, is 7 ± 4 times higher than the cosmic value. If we employ a thin thermal model with nonequilibrium collisional ionization (NEI)13, the temperature increases while the metal abundances do not change within the statistics. We cannot determine the abundances of the light elements from He to O, which produce emission lines outside our energy range. Whereas we can conclude that the relative metal abundances, from Ne to Fe, are con­ sistent with cosmic values with the exception of Ca. The overabundance of Ca can be a result of an over­ abundance of 44 Ti which is produced only in the SN ex­ plosive nucleosynthesis process. It is mainly produced deep in the interiQr of the star, both in a type la and type II SN. In the following we assume that the ejecta contain­ ing 44 Ti are uniformly expanding into ambient space. In the early phase of the SNR evolution, the major part of the emission does not come from the shock heating pro­

Energy (MeV) e+ 0.847 1.238 0.122 0.014 e+ 1.275 e+ 1.156 0.078 0.068 1.322 1.173 0.059 e+ 1.809

event/disintegration 0.2 1 0.7 0.88 0.88 0.9 1 0.94 1 1 1 1 1 1 0.85 1

cess but comes from accelerated and decelerating parti­ cles, which produce a power law type X-ray spectrum. In the north-west bright shell region, the ejecta might have recently collided with an interstellar cloud forming some shock-heated thermal plasma, which is the source of the Ca emission line. Assuming spherical symmetry for the plasma emitting region we find that the plasma density in this region is (1.4 ±0.1)(D/200 pc) -0 - 5 H cm3 where D is the distance to the source. The expanding ejecta happen to hit the interstellar cloud at the north-west shell. The ejecta expanding along other directions should also contain similar amounts of Ca but they are not yet shock-heated, so that just the power law type spectrum prevails with no emission lines. There is another bright shell region in the south, which we missed. Based on the emission line detected, we can estimate the total amount of Ca, Mc a , contained in RX J0852-0462 as 8 x l(r4M©(.D/200 pc) 25 (A/7). We as­ sume that all the 44Ca is in the shell region but only that fraction expanding towards the north-west shell is actually shock-heated and visible in the Ca line. The major isotope of Ca on the Earth is 40 Ca while the fraction of 44 Ca is about 2 x 10 - 2 14. If we assume that the other Ca isotopes are produced with terrestrial abundances 44 Ca, the product of 44 Ti, is heavily over­ produced, and we expect that almost all Ca detected must be 44Ca. Based on the theoretical model of Nomoto et al. 15 and Thieleman et al. 16, type II SN can produce Ca of 5 x 10~3 MQ depending on the progenitor star mass, whereas type I SN can produce 1.2 x 10~2 MQ. In both cases, the

244 .

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Figure 4: X-ray spectrum from the bright shell obtained with the SIS (crosses). It can be well fitted with a thin thermal emission model of (1.5 ± 0.1) x 10T K. Metal abundances are well fitted with cosmic values with the exception of Ca which is overabundant by about 7 ± 4. The X-ray spectrum from the entire remnant obtained with the GIS is also shown for comparison.

mass ratio between Si and Ca is less or similar to that of the cosmic value. These models cannot explain the overabundance of Ca. Whereas these models assume the point symmetric explosion. Asymmetric explosions can produce large metal abundance anomalies, which may explain the overabundance of Ca. If we assume that most of Ca comes from 44 Ti, we can estimate the age, t, of RX J0852-0462 using the observed flux of the 1157keV 7rays. We obtain t / r = 16 + log2 ((L/3x 10" 5 photon cm" 2 s"1) (D/200PC)1'2 (A / 7) ). This value results in an upper limit of the age of 960 yrs and the lowest limit for the expansion velocity of 2900 km s _ 1 . Since there occurs shock-heating associated with deceleration of the expansion the initial expansion velocity must be higher than this value. If we assume that Ca has an isotope population similar to that of the terrestrial value, the mass of 44 Ti is reduced by a factor of 50. Then we obtain a lower limit of the age of 630 yrs and an upper limit of the expansion velocity of 4600 km s _ 1 . Model calculations of SN show that the heavy ele­ ments are produced relatively deep inside the progenitor star. In type II SN, 44 Ti is produced very close to the mass-cut point, which is the critical boundary separating the ejecta and the mass forming a central compact rem­ nant. If the SN explosion occurs in a homologous fashion, 44 Ti and Ca are concentrated in a narrow layer. We can expect that the entire Ca is shock-heated simultaneously. Based on the SN model calculations the expanding ve­ locity of the Ca dominated layer is a few thousand km s" 1 1 7 . Therefore, the age of RX J0852-0462 is likely to be closer to 900 yrs rather than 570 yrs.

Astro-E, the fifth Japanese X-ray astronomy satellite to be launched in February 2000, will carry three instru­ ments, which are a hard X-ray detector (HXD), an X-ray CCD camera (XIS) and an X-ray calorimeter (XRS). 44 Ti emits 3 lines at 68 keV, 78 keV and 1157keV, one of which has been detected from RX J0852-0462 by COMPTEL. T^e HXD will have sufficient sensitivity to detect the other two lower energy lines. The XIS will be able to map the distribution of Ca across RX J0852-0462. The X-ray calorimeter XRS will test whether or not the emis­ sion line at 4.1 keV originates from highly ionized Ca. References 1. Iyudin, A.F., Schonfelder, V., Bennett, K., Bloemen, H., Diehl, R., Hennsen, W., Lichti, G.G., van der Meulen, R.D., Ryan, j \ , & Winkler, C.Nature 396, 142 (1998) 2. Koyama, K., Petre, R., Gotthelf, E.V., Hwang, U. Matsuura, M., Ozaki, M., Holt, S.S. Nature 378, 255 (1995) 3. Iyudin, A.F., Diehl, R., Bloemen, H., Hermsen, W., Lichti, G.G., Morris, D., Ryan, J., Schonfelder, V., Steinle, H., Varendorff, M., & Winkler, C. Astron. & Astrophys. 284, LI (1994) 4. Ahmad I., et al.,Phys. Rev. Lett. 80, 2550 (1998) 5. Aschenbach B. Nature 396, 141 (1998) 6. Aschenbach, B., Iyudin, Schonfelder, V., Astron. & Astrophys. 350, 997 (1999) 7. Burgess, C. P. & Zuber, K. 1999, astro-ph/9909010 8. Yamashita A., Dotani T., Bautz M., Crew G.,

9.

10. 11. 12. 13. 14. 15. 16. 17.

Ezuka H., Gendreau K., Kotani T., Mitsuda K. et al. IEEE Trans. Nuc. Sci. 44, 847 (1997) Makishima K., Tashiro M., Ebisawa K., Ezawa H., Fukazawa Y., Gunji S., Hirayama M., Idesawa E. et al. Publication of Astron. Soc. Japan 48, 171 (1996) Serlemitsos P.J., Jalota L., Soong Y., Kunieda H., Tawara Y., Tsusaka Y., Suzuki H., Sakima Y. et al. Publication of Astron. Soc. Japan 47, 105 (1995) Tanaka Y., Inoue H., Holt S.S. Publication of As­ tron. Soc. Japan 46, L37 (1994) Mewe, R., Gronenschild, E.H.B.M., k van den Oord, G.H.J., Astron. & Astrophys. 62,197(1985) Masai K., Astrophys. & Space Sci. 98, 267 (1984) Anders, E., k Grevesse, N. Geochim. Cosmochim. Acta 53, 197 (1989) Nomoto, K., Thielemann F.-K., Yokoi, K., Astro­ phys. Jounal 286, 644 (1984) Thielemann F.-K., Nomoto K., Hashimoto, M., Astrophys. Jounal 460, 408 (1996) Shigeyama, T., Nomoto, K., k Hashimoto, M. As­ tron. & Astrophys. 196, 141 (1988)

X-RAY SPECTROSCOPY A N D CHEMICAL COMPOSITION IN THE UNIVERSE

Department

K. K O Y A M A of Physics, Graduate School off Science, Kyoto Univesity, Kita-shirakawa, Sakyo-ku, Kyoto 606-8503, Japan. E-mail: [email protected]

This paper reviews the chemical evolution of massive stars and their remnants using the ASCA results of X-ray spectroscopy. We demonstrate that the ASCA spectrum of Eta-Carinae provides direct evidence for the CNO cycle reaction at the surface layer of the massive star. Then we present distinct difference of line emission features in the X-ray spectra of young supernova remnants (SNR) of two types of supernovae, type la and type II. We show that the chemical composition of a galaxy can be estimated by aged SNR samples. Finally we discuss related topics of SNRs, in particular of particle acceleration in the SNRs.

1

Introduction

Heavy elements such as C, N, 0 , Si, S and Fe are synthesized in massive stars and are distributed to the interstellar space by stellar wind or by supernova explosion. This scenario has been drawn, mainly thorough theoretical ap­ proaches. In this talk, I will review the sequence of chemical evolution using our ASCA data. Our technique for chemical composition study is X-ray spec­ troscopy. We use the cosmic high temperature plasma, in which most of the outer shell electrons of heavy elements are removed, hence the atoms should be in the form of very simple structure, namely He-like or hydrogen-like. In this simple structure, X-ray energy and intensity for the transition of excited level to the ground state are highly predictable. Furthermore, since the density of our cosmic plasma is ver low, any perturbation on the atomic transition by other particle is generally negligible. Thus from the observed X-ray spectra, we can acculately estimate the chemical composition in the plasmas. 2

Nuclear burning and the CNO cycle

Hydrogen-burning starts at the core of stars and move on toward the outer region. In the late stage of a massive star evolution, the H-burning due to the CNO cycle arrives at the surface of a star. Figure 1 shows the CNO reactioncycle. Moving one trun around the reaction-cycle, we get 4 protons and emit one He nucleus, while total number of C+N+O is conserved. Since the cross section of the 14 N 4- P reaction is the minimum among all the reactions in the CNO cycle, many 14 Ns are accumulated, like a traffic jam in a belt-way. In

246

247

other words, over-abundance of nitrogen relative to oxygen and carbon is key evidence for the presence of the CNO cycle.

He I .12,

16

/-y

F

,3

X

1 7

n^

L4TOF-#

N

*J?C

Figure 1. Diagram of the CNO cycle

Eta Carinae is the most massive star in our Galaxy, possiblly more than 100 of solar mass. In the last phase of evolution, massive stars exhibit occa­ sional eruptions of the surface layer of the star. The eruption makes a high temperature plasma by the collision to circumstellar gas, hence emits strong X-rays. The ASCA satellite obtained the best X-ray spectrum from this star (Tsuboi et al. 1999). Figure 2 is the observed X-ray spectrum together with the best-fit plasma model. Our surprise was a bump at 0.5 keV. We have never seen such structure in the X-ray spectrum of any other astronomical objects. The bump can be well explained by an Lyman alpha emission of enhanced abundance of nitrogen. In fact, the best-fit model requires number ratio of N/O = 3, about 30 times larger than that of solar abundance ratio of 0.1. Therefore this spectrum provides direct evidence of the CNO cycle reaction at the surface layer of a massive star.

248

1

2 Energy [keV]

5

10

Figure 2. X-ray sepctrum of Eta Carinae

In the surface hydrogen burning massive stars, inner core should be accu­ mulated by the final product of nuclear fusion, irons. When the iron mass exceeds the Chandrasekhar limiting mass, the iron core collapses to a neutron star or a black hole, converting the huge gravitational energy to the exlosion energy of the outer layer (type II supernovae). In the case of Eta Carinae, this dramatic explosion may occur in very near future. It may be tomorrow or 1 million years latter. I really hope to continue my study of the chemical composition after the supernova explosion of this massive star. However I have no time to wait for a spectacular supernova or even hypernova event of the most massive star Eta Carinae, hence I have to move on SNR samples of other massive pogenitor stars.

3

T y p i n g of Supernovae Using t h e X-ray S p e c t r a

Figure 3 shows the 2 typical X-ray spectra after about one thousand years of supernova explosions (Hayashi 1998). The over-all structure are similar with each other. However, in detail, we can find clear contrast in the line position and flux. From the line energy, we can identify the line emitting elements.

249

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-

/

/

U Ca

■f

1

\

F<

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... i 4 ( :--W^^M^^^^^ j j h V r t i # ^ E(k«v)

Figure 3. X-ray spectra of Type II (left) and Type la (right) SNRs

One supernova remnant (right) is dominated by lighter elements such as Oj Ne and Mg, while the other (left) is dominated by heavier elements such as Si, S, Ar, Ca and Fe. Theorists proposed two types of supernova explosions; one is Type II SN of very massive star induced by iron core collapse, and the other is a less mass star induced by explosive nuclear reaction from carbon and oxygen to iron nuclei, which is called Type la. Since Type II is an explosion of outer layer of a massive star, it releases a large amount of synthesized elements, namely O, Ne and Mg. On the other hand, Type la produce a lot of elements heavier than oxygen, typically iron. Thus figure 4 presents typical X-ray spectra of either type II or type la (Hughes et al. 1998). Inversely, X-ray spectrum is a good diagnostic tool to classify whether the remnant is due to a very massive star or due to a rather less mass star. 4

Chemical Composition of Interstellar Space and Old S N R s

Previous section demonstrates that X-rays from young SNRs are dominated by the gas ejected from the progenitor stars. As the age of SNR increases, swept-up interstellar gas increases. Therefore, X-rays from aged SNRs yield information on chemical composition of the interstellar gas. For this study, I pick up SNR samples in the Large Magellan Cloud, because the distance can be well-determined , which is essential for the accurate estimation of physical quantities. We have observed 3 young and 6 aged SNRs with ASCA (Hughes, Hayashi and Koyama 1998). Figure 4 shows the X-ray spectra for the young (top panel) and aged SNRs (middle and bottom panels). Compare with the young SNRs, all the aged SNRs have less prominent emission lines from various elements. This may be due to the dilution of metal-rich ejecta by metal-poor interstellar gas. For more detail discussion, we performed spectral analysis, and estimated chemical composition of each aged SNR.

250

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F i g u r e 4. X - r a y s p e c t r a for t h e y o u n g ( t o p p a n e l ) a n d a g e d S N R s ( m i d d l e a n d b o t t o m panels).

251

Figure 5 shows the mean abundance derived from the 6 aged remnants with object-to-object la scatters. The results by the optical data are also shown for comparison. We see X-ray determination of the interstellar chemical composition is more accurate than that determined with the optical data. Mean LMG Abundances

Figure 5. The mean abundance derived from the 6 aged remnants. The optical results are shown by the dotted line.

Our model-fit also predicts the age of the SNRs. The relation of abundance as a function of the SNR age is given in figure 6. The chemical compositions show slow decrease with the increasing SNR age, may be approaching to the true interstellar composition of this galaxy, possibly 0.2 of the solar value (see Nishiuch et al. in this Volume). 0.6

10

Age ( 1 0 3 y r s )

6. Chemical composition as a function of the SNR ages

252

5

R e l a t e d Topics

In this paper, I have demonstrated that the X-ray spectroscopy gives clear evidence for the current scenario of chemical evolution by the supernova ex­ plosions. Nice agreement of our data to the theory is rater surprising for me, because we have made rather simplified assumptions, such as spherical symme­ try, uniform interstellar density, and chemical composition. We also simplified that all the particles are thermalized to a typical energy of 103 eV. However, in some SNRs, we found that some fraction of particles get fur higher energy, up to 10 14_15 eV. An extreme case is SN1006. In the beginning of the last millennium, in AD1006, a bright SN explosion was recorded in the Oriental history, i.e. the Japanese famous diary Meigetuki written by Fujiwara Teika. The remnant of this SN is now X-ray bright. Exciting result is that the bright X-ray rims are dominated by non-thermal emission or synchrotron radiation by the electron of lO 1 4 " 1 5 eV (Koyama et al. 1996). 6

P r o s p e c t in the new Millennium

One may argue that the SNR physics become much more complicated due to the contamination of the non-thermal X-rays. Yes it is true. However I am rather excited by the fact that nature is more fantastic than we thought. In the new millennium, 8-th of Feb., we will launch the next X-ray satellite ASTRO-E. This satellite has about 10 times higher sensitivity than ASCA. The energy resolution is also 10 times better. Figure 10 shows our evolution of X-ray satellite in terms of the energy resolution. In 1987, the Ginga satellite obtained the spectrum of Cas A (top panel), in the next decade, in 1993, the ASCA satellite re-visited this SNR and got the spectrum given in the middle panel. The improvement of the energy resolution is about 10 times. Then in the new millennium, we can resolve fine structure of Kalpha- transition line (bottom panel). The flux ratio of these fine structure lines are key diagnos­ tic tool for the election temperature, election density and other fundamental physical parameters. Ion temperature would be directly determined for the first time by the line broadening of these fine structure. Thus the largely im­ proved energy resolution of ASTRO-E lead us to a more accurate and reliable estimation of chemical composition of many astronomical objects.

253 (TOTAL

7ia.r2B c m m n / s ^ |

Cas A

chonnaf energy (keV)

Figure 7. X-ray sepctrrum of Cas A obtained with Ginga(top) and /tSC7t(middle). The bottom panel is simulated spectrum of iorn K-shell line complex of Cas A with ASTRO-E

254

Acknowledgments I would like to express my thanks to Drs, J.P. Hughes, I. Hayashi, and Y. Tsuboi for fruituful collaborations on this work. References 1. J. P. Hughes et al, Astrophysical Journal 444, L81 (1995). 2. J. P. Hughes, I. Hayashi, and K. Koyama, Astrophysical Journal 505, 732 (1998). 3. K. Koyama et al, Nature 378, 255 (1995). 4. M. Nishiuchi This Volume. 5. Y. Tsuboi, K. Koayma, M. Sakano, and R. Petre, Publications of the Astronomical Society of Japan 49, 85 (1997).

VI. Origin of Heavy Elements

This page is intentionally left blank

NEUTRON STAR MYSTERIES

G. J . M A T H E W S , P. C. F R A G I L E , I. S U H , J . R . W I L S O N University of Notre Dame, Center for Astrophysics, Department of Physics, Notre Dame, IN 46556, USA E-mail: [email protected] Neutron stars provide a unique laboratory in which to explore the nuclear equa­ tion of state at high densities. Nevertheless, their interior structure and equation of state have remained a mystery. Recently, a number of advances have been made toward unraveling this mystery. T h e first direct optical images of a nearby neutron star have been obtained from HST. High quality d a t a for X-ray emission from low-mass X-ray binaries, including observations of nearly coherent oscilla­ tions (NCO's) and quasi-periodic oscillations (QPOs) now exist. The existence of a possible absorption feature as well as pulsar light curves and glitches, and studies of soft-gamma repeaters, have all led to significant new constraints on the massradius relation and maximum mass of neutron stars. We also discuss how models of supernova explosion dynamics and the associated r-process nucleosynthesis also constrain the nuclear equation of state, along with heavy-ion and monopole res­ onance data. Recent work on the search for the Friedman-Chandrasekhar-Schutz instability and the effects of internal magnetic fields are also discussed. The overall constraints on the neutron star equation of state are summarized.

1

Introduction

Neutrons stars are of much relevance to any discussion on the origin of matter and evolution of galaxies. They are formed as the end point in the evolution of massive stars. As such, they carry in their numbers a history of the past evolution of matter in the galaxy. However, there is still much that we do not understand about the structure, formation, and evolution of neutron stars. Even after over 60 years of research, these objects remain a mystery. This talk is an attempt to overview some current research into various aspects of the mystery surrounding neutron stars. 2

Maximum Neutron Star Mass and the Nuclear EOS

A key part of understanding the hydrodynamics and structure of neutron stars is the equation of state. The neutron star EOS must extend from normal iron nuclei on the surface to as much as 15 times nuclear matter density in the in­ terior. On the other hand, since neutron stars are in weak-interaction equilib­ rium they are highly isospin asymmetric. They may also carry net strangeness. Therefore, only pieces of the neutron-star equation of state, e.g. the nuclear compressibility, are accessible in laboratory experiments. One experimentally accessible quantity is the value for the nuclear compressibility Ks which can be

257

258 Table 1: Neutron star properties from various equations of state

Equation of State

Composition

Mean Nuclear Field

p,n,e~

Exotic P a r t i c l e s / Condensates

,n~

M a x i m u m Mass ( M Q )

R(km)

fti 2.0 ± 0 . 2

Rj 13 ± 3

tu 1.5 ± 0 . 2

fs9±l

A±,o.++i/f±,Oi7r±,Oi q u a r k S i e t c .

derived from the nuclear monopole resonance.1 The present value (Ks = 230 MeV) is consistent with a modestly soft nuclear equation of state. Heavy ion collision data can also be used to shed some insight, particularly for the super­ nova equation of state. McAbee & Wilson 2 studied heavy-ion collisions of 5 7 La on 57 La as a means to constrain the supernova EOS. The electron fraction for 57 La (Ye = 0.41) overlaps that of supernovae which range from Ye = 0.05 to 0.50. They showed that the pion contribution to the EOS could be constrained by the pion multiplicities from central collisions. The formation and evolution of pions was computed in the context of Landau-Migdal theory to determine the effective energy and momenta of the pions. A key aspect of hydrodynamic simulations of the heavy-ion data is the determination of the Landau parame­ ter g'. Their determination of the pion contribution to the equation of state, then implies a soft equation of state and a maximum neutron star mass of M < 1.64 M 0 . There have been dozens of nuclear equations of state introduced over the years. Summaries of some of them can be found for example in Schaab & Weigel3 and Arnett & Bowers4 As far as the maximum mass of a neutron star is concerned, theoretical equations of state fall into two groups, those which only describe the mean nuclear field even at high density and those which allow for various condensates, e.g. pions, kaons, hyperons, and even quarkgluon plasma. Table 1 sketches neutron-star properties according to most available nuclear equations of state. Equations of state which are based upon the mean nuclear field tend to be "stiff' at high density. Therefore, they reach lower interior densities for the same baryonic mass and tend to allow larger radii and a higher maximum neutron star mass mmax ~ 1.8 — 2.2 M Q . Such equations of state also tend to become acausal at the high densities associated with the maximum neutron star mass. On the other hand, the relativistic equations of state are generally causal at high density. They also tend to be somewhat "soft", therefore allowing a higher central density for a given baryon mass and generally implying smaller

259

radii and a lower maximum neutron star mass in the range mmax ~ 1.3 — 1.7 M0. For the most part, constraints on the neutron star equation of state must come from observations of neutron stars themselves. Over the years attempts have been made with limited success to constrain the equation of state based upon the maximum observed rotation frequency (e.g. Friedman et al.5) or the thermal response to neutron star glitches.6 In recent years, however, new observational constraints on the structure and properties of neutron stars are becoming available.7 Observations of quasi-periodic oscillations (QPOs 8 ' 9 ), pul­ sar light curves,10'11 and glitches,12 studies of soft-gamma repeaters, 13 ' 14 and even the identification of an isolated non-pulsing neutron star 1 5 ' 1 6 have all led to significant constraints on the mass-radius relation and maximum mass of neutron stars. 2.1

Pulsars

Two possible constraints come from measured pulsar systems. The most pre­ cisely measured property of any pulsar system is its spin frequency. The fre­ quencies of the fastest pulsars (PSR B1937+21 at 641.9 Hz and B1957+20 at 622.1 Hz) already constrain the equation of state under the assumption that these pulsars are near their maximum spin frequency.5 In particular, the equa­ tion of state cannot be too stiff, though maximum masses as large as 3 M Q are still allowed. A much more stringent constraint may come from the numerous deter­ minations of neutron star masses in pulsar binaries. There are now about 50 known pulsars in binary systems. Of these 50, approximately 15 of them have significantly constrained masses. These are summarized in Table 2. The measured masses are all consistent with low neutron star masses in the range m « 1.35 ± 0.10 M Q . n Even though these masses are low, this does not neces­ sarily mean that the maximum neutron star equation of state is in this range. If one adopts these masses as approaching the maximum neutron star mass, then the softer equations of state are preferred. However, this narrow mass range may be the result of the mechanism of neutron-star formation in supernovae and not an indication of the maximum neutron star mass. In a recent paper, Link et al.12 have proposed that glitches observed in the Vela pulsar and six other pulsars may place some constraint on the nuclear EOS. In particular, if the glitches originate from the liquid of the inner crust, and if the mass of the Vela pulsar is 1.35 consistent with Table 2, then the radius of the Vela pulsar must be _R>8.9 km. This result is consistent with either a soft or stiff equation of state. A better theoretical determination of the

260 Table 2: Summary of masses of observed pulsars in binaries. 1 1 Pulsar Double Neutron Star Systems J1518+4904 J1518+4904 B1534+12 B1534+12 B1913+16 B1913+16 B2127+11C B2127+11C B2303+46 B2303+46 Neutron Star/White-Dwarf Systems J1012+5307 J1713+0747 J1713+0747 B1802-07 B1855+09 Neutron Star/Main-Sequence Systems J0045-7319

Mass (M©) 1 'Sfi ° 1 3

os8:« 1.339 ±0.0003 1.339 ±0.0003 1.4411 ±0.00035 1.3874 ±0.00035 1.349 ±0.040 1.363 ±0.040 1 30

0 1 3

•3° 8:1? 1.7 ±0.5 1.45 ±0.31 1.34 ±0.20 1 ofi 0.08

1.41 ±0.10 1.58 ±0.34

pressure at the crust-core interface might lead to a more stringent constraint, however. 2.2

Luminosity Radii

A number of authors 17 ' 18 have attempted to obtain luminosity radii L = 4irR2aT4 from thermal neutron-star X-ray emission. These are all consistent with relatively compact ~ 10 km radii. Similarly, the luminosity radius from X-ray bursts 1 9 , 2 0 is consistent with a soft EOS and a compact star. A 4.1 KeV absorption line has been identified in some X-ray bursts. This line could arise from Ni, Fe, Cr, or Ti absorption. In any of these cases a massradius constraint can be deduced from from the implied gravitational redshift of this absorption line? 1 3/2

Ker2aT4 = cGM 1 - (2GM/c 2 r)

(1)

The implied radius for neutron star 1608-52 is <11 km and a mass less than 1.8 M 0 consistent with a soft EOS.

261

2.3

QPO's

The identification of kilohertz QPO's with the last stable orbit around a neu­ tron star also could significantly constrain the neutron-star equation of state (e.g. Schaab & Weigel 3 ) . For example, demanding that the 1.2 khz QPO from source KS 1731-260 be the last stable orbit requires a neutron-star mass of 1.8 M 0 . On the other hand, other interpretations are possible for the ori­ gin of QPO's. For example, they could be a harmonic of a lower frequency outer orbit, or they might result from effects closer to the neutron-star surface. Among proposals for the source of the QPO phenomenon are: boundary layer oscillations j 2 2 radial oscillations and diffusive propagation in the transition re­ gion between the neutron star and the last Keplerian orbit, 2 3 Lense-Thirring precession for fluid particles near the last stable orbit; 24 ' 25 and nonequitorial resonant oscillations of magnetic fluid blobs.26 2.4

NCO's

The association of nearly coherent oscillations (NCO's) with the rotation fre­ quencies of neutron stars in low-mass X-ray binaries (LMXB's) raises the possibility that these stars are spinning fast enough to become unstable to the development of gravitational-wave induced distortions of the neutron-star surface, the so-called Chandrasekhar-Friedman-Schutz instability.27 The most likely such oscillation is the polar /-mode. This instability probably requires that a neutron star be spinning at least ~ 0.6 times its limiting angular fre­ quency. Such rapidly rotating systems are not uncommon among LMXB's. Stars which exhibit ~kHz NCO's are probably rotating at close to their maximum frequency. In which case, if they are also undergoing an /-mode instability then they should exhibit a secondary peak less than the rotation frequency of the star in the range of 200-800 Hz. To look for such signals we have scanned the archived Type-I X-ray burst data from the Rossi X-ray Timing Explorer (RXTE). We have studied 8 bursts from 4U 1728-34 and Aql X-l. We divided each light curve into 1.5 s intervals and constructed the fast Fourier transform power spectrum of each interval. Ten of the intervals for 4U 1728-34 showed evidence of a secondary oscillation peak at 224 Hz. Six of the intervals for Aql X-l showed evidence for a peak at about 332 Hz. Figure 1 shows the total summed power spectrum for the six intervals from Aql X-l. The highest frequency peak is the previously identified 549 Hz NCO. The secondary peak at 332 Hz is at 60% of the NCO. Assum­ ing that the NCO is near the maximum frequency, the 332 peak could be a candidate for the CFS instability. The problem, however, is that if 549 Hz is

262

Aquila X-1

tw tWWW 0

200

400

600 800 Frequency (Hz)

1000

1200

Figure 1: Power spectrum for six 1.5 sec intervals from four different bursts from Aql X-1.

near the maximum, then the radius would have to be quite large, implying a very stiff EOS. 2.5

20 km,

Supernova constraints

The apparent lack of a radio pulsar in SN1987A (see however Middleditch et al.28), along with nucleosynthesis constraints on the observed change of helium abundance with metallicity has led to the suggestion by Bethe and Brown 30 ' 29 that the maximum neutron star mass must be ^1.56 M 0 . In their picture, the development of a kaon condensate tends to greatly soften the EOS after ~ 12 sec. Thus, even though neutrinos were emitted, the core subsequently collapses to a black hole. One constraint which is not widely appreciated comes from the neutrino signal itself observed to arise from supernova SN1987A. The fact that the neutrinos arrived over an interval of at least ten seconds implies a significant cooling and neutrino diffusion time from the core. This favors a soft equation of state in which the core is more compact and at higher temperature in the

263

supernova models. For example, the simulations of Wilson & Mayle 31 require an EOS with a maximum neutron star mass of ~ 1.6 M Q . There is also recent evidence 32 that the nucleosynthesis of heavy elements in the r-process probably requires a very compact neutron star. 2.6

An Isolated Neutron Star

A most promising constraint on the neutron-star EOS may come from the de­ termination of the radius for the isolated non-pulsing neutron star RX J1856353754, first detected by ROSAT (Walter et al.15) The inferred (red shifted) sur­ face temperature from the X-ray emission is about 35 eV. Atmospheric models of this emission then imply 7 ' 33 ' 34 that for a distance between 31 and 41 pc, a radius between 5.75 < R/km < 11.4 and a mass of 1.3 < M < 1.8, is most consistent with the observed emission. This is suggestive of a soft equation of state. However, this constraint requires that the distance be less than 41 pc. On the other hand, Wang et al.34 find that the cooling properties of the soft X-ray source RX J0720.4-3125 are most consistent with a moderately stiff or stiff EOS provided that the age of this star is less than 105 yr. Proper motion studies with HST are currently underway to determine a reliable distance to RX J185635-3754. Preliminary results indicate that the star is farther away implying a larger radius. The parallax is difficult to distinguish from proper motion, however, since distant background stars are obscured by a nearby starforming region. Eventually, these studies will provide a key constraint on the nuclear equation of state. 2.7

Magnetic Fields

Finally, we would like to mention our recent work 35 on possible changes in neutron-star structure due to the presence of interior magnetic fields. Recently, neutron stars with very strong surface magnetic fields have been suggested as the site for the origin of observed soft gamma repeaters (SGRs). We have investigated the influence of such strong magnetic fields on the properties and internal structure of these magnetized neutron stars (magnetars). We have examined properties of a degenerate equilibrium ideal neutron-proton-electron (npe) gas model both with and without effects of the nucleon anomalous mag­ netic moment in a strong magnetic field. The presence of a sufficiently strong magnetic field changes the ratio of protons to neutrons as well as the neutron drip density. We also studied the appearance of muons as well as pion conden­ sation in strong magnetic fields. We have also speculated upon the possibility that boson condensation in the interior of magnetars might be a source of SGRs.

264 T

'

r

0.9 - (log Ye =4)

0.8 -

A

0.7 -

-

npeuit

' 5

(logTe= )

0.6 0.5 I 15.1

■

' 15.3

■

' 15.5

'

' 15.7

■

' 15.9

■ 16.1

logp Figure 2: Adiabatic index T as a function of p (in g c m - 3 ) for a pion-condensate equation of state 3 5 for magnetic field strengths log(B/i?c) = 4 and 5. The thick and thin solid lines are for non-magnetic (B = 0) npefj. and npe/iir cases.

Perhaps, one of the most interesting aspect of this work is the possibility of a new oscillation instability. Figure 2 shows the equation-of-state index T as a function of the different interior field strengths (measured as log (B/Bc), where Bc = m2ecz/eh = 4.414 x 10 13 G is the critical magnetic field at which quantized electron cyclotron states begin to exist]. The rapid changes in this index occur as charged particles (mostly protons) beginning to occupy the next Landau level. We speculate that these rapid changes may lead to an interior vibrational instability. That is, a small compression could lead to a drastic softening of the pressure and therefore collapse, which would then halt and bounce. 3

Conclusions

In summary, we have seen that there still remain large uncertainties surround­ ing neutron-star structure, formation, and the nuclear equation of state at high density. The unknown role of magnetic fields is just beginning to be explored. The origin of X-ray and gamma-ray burst is still not quantitatively understood, and there is conflicting evidence regarding the correct equation of state. The

265

X-ray luminosities, binary pulsar masses, supernova neutrinos all would seem to argue for a soft EOS, while the Vela glitches, QPO's and RX J185635-3754 are perhaps arguing for larger radii and therefore a stiffer EOS. In the end, resolving this question will require a lot more work. Perhaps the best promise is that eventually a good parallax distance will be obtained for RX J1856353754. This could hopefully be combined with observations of absorption lines to determine the gravitational red shift and better model atmospheres. Then we would have clear evidence as to the correct neutron-star equation of state. Acknowledgments This work supported in part by DOE Nuclear Theory Grant DE-FG02-95ER40934. References 1. 2. 3. 4. 5. 6.

7.

8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

Blaizot, J.P. 1980, Phys. Rep. 64, 171. McAbee T. L. & Wilson, J. R. 1994, Nuclear Physics, 576A, 626 (1994). Schaab, C. & Weigel, M. K. 1999, MNRAS, 308, 717. Arnett, W. D. & Bowers, R. L. 1977, ApJ, 33,415. Friedman, J.L., Isper, J.R., & Parger, L. 1986, ApJ, 304, 115. Page, D. 1998 in Neutron Stars and Pulsars Thirty Years after the Dis­ covery), N. Shibazaki, etal., eds., (Universal Academy Press, Inc: Tokyo, Japan, pp. 183-190. Lattimer, J. M. 1998, in Neutron Stars and Pulsars Thirty Years after the Discovery, N. Shibazaki, et al., eds., (Universal Academy Press, Inc: Tokyo, Japan), pp. 103-110. Strohmayer, T. E., et al. 1996, ApJ, 469, L9. Van der Klis, et al. 1996, ApJ, 469, LI; 1997, ApJ, 481, L97. Yancopolos, S. Hamilton, T.T. & Helfand, D.J. 1994, ApJ, 429, 832. Thorsett, S.e. & Chakrabarty, D. 1999, ApJ, 512, 288. Link, B., Epstein, R.L. & Lattimer, J.M. 1999, Phys. Rev. Lett., in press. Kouveliotou, C , et al. 1998, Nature, 391, 235. Gotthelf, E. V., Vasisht, G., & Dotani, T. 1999, ApJ 522, L49. Walter, F. Wolk, S. & Neuhauser, R. 1996, Nature, 379, 233. Haberl, F. et al. 1997, A&A, 326, 662. Golden, A. & Shearer, A. 1999, Astron. & Astrophys., 342, L5. Shulz, N.S. 1000, ApJ, 511, 304. Titarchuk, L. 1994, ApJ, 429, 340. Rutledge, R. et al. 1999, ApJ, 514, 945.

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21. Inoue, H. 1992, in The Structure and Evolution of Neutron Stars, D. Pines, et al., eds, (Addison Wesley; Redwood City) p. 63. 22. Collins, T. J. B., Heifer, H. L., & Van Horn, H. M. 1998, ApJL, 508, L159. 23. Titarchuk, L. & Osherovich, V. 1999, ApJL, 518, L95. 24. Miller, M. C , Lamb, F. K. & Psaltis, D. 1998, ApJ, 508, 791. 25. Morsink, S. M. & Stella, L. 1999, ApJ, 513, 827. 26. Vietri, M. & Stella, L. 1998, 503, 350. 27. Wagoner, R.V. 1984, ApJ, 278, 345. 28. Middleditch, J. et al. 2000, New Astronomy, 5, 243. 29. Bethe, H. A. & Brown, G. E. 1995, ApJ, 445, L129. 30. Brown, G. E. & Bethe, H. A. 1994, ApJ, 423, 659. 31. Wilson, J. R. & Mayle, R. W. 1993, Phys. Rep., 227, 97. 32. Wanajo, S. et al., 2000, ApJ, submitted. 33. An, P., Lattimer, J.M., & Prakash, M., 1998, BAAS, 192, 8207. 34. Wang, J.C.L. et al. 1999, A&A, 345 869. 35. Suh, I. & Mathews, G. J. 2000, ApJ, in press.

P H O T O N E U T R O N CROSS SECTIONS FOR 9De A N D T H E a-PROCESS IN CORE-COLLAPSE SUPERNOVAE

H. U t s u n o m i y a , Y. Yonezawa, H. A k i m u n e , T . Y a m a g a t a , M. O h t a Department of Physics, Konan University, Kobe 658-0072, Japan E-mail: [email protected]

Osaka Prefecture

Quantum

Radistion

M. Fujishiro University, Sakai 599-8570,

H. Toyokawa, H. O h g a k i Lab., Electrotechnical Laboratory,

Japan

Tsukuba

305-8568,

Japan

Photoneutron cross sections were measured for Be in the energy range from 1.78 to 6.11 MeV with laser-induced Compton backscattered 7 rays. The data are compared with those from the Bremsstrahlung and the radioactive isotope mea­ surements. 7-decay widths for the 1/2"*" and 5/2~ states were deduced from the least-squares fit to the data as well as the energy-integrated cross section. Astrophysical implications are discussed.

In the neutrino-driven wind formed in core-collapse supernovae, n- and a-rich material is first processed into 9 Be through a ( a n, 7 ) 9 B e by bridging mass gaps A = 5 and 8 and then 9 B e ( a , n ) 1 2 C follows 1 . This sequence of 1 2 C production proceeds more efficiently t h a n the triple-a process. Seed nuclei for the r-process may be produced up to A ~ 100 by the recombination of a particles and neutrons, which is referred to as the a-process. 9 Be is a loosely-bound nuclear system consisting of two a ' s and a neutron. Non of any two constituents can form a bound system. Lifetimes of 5 H e and 8 B e are 1.1 x 1 0 - 2 1 and 0.97 x 10~ 1 6 s, respectively. Three adjacent thresholds exist at 1.573 MeV for a + a + n, at 1.665 MeV for 8 B e + n and at 2.467 MeV for 5 He + a. In view of the lifetime, the synthesis of 9 Be is considered to proceed more dominantly through 8 B e than through 5fTe. T h e ternary process is likely to play a minor role. Resonances near threshold govern the r a t e of the 9 Be synthesis. Resonance parameters of these states can be determined by photodisintegrating 9 Be. Previously, photoneutron cross sections near threshold were measured for Be using two kinds of real photon sources, Bremsstrahlung and radioactive isotopes. Bremsstrahlung measurements lacked great accuracy due to poor en­ ergy resolution 2 , 3 , while radioactive isotope measurements were limited mostly below 2.8 M e V 4 , 5 , 6 , 7 ' 8 ' 9 , 1 0 . Electron scattering was also used to study low-lying 9

267

268 2000

1500

a 3 y 1000

500

0 1000

1500 Channel

2000

Number

Figure 1: Energy distribution of LC photons measured with a Ge detector.

states in 9 Be. But the virtual photons excited the 1/2+ state only weakly 11,12 . Compton backscattering of laser photons incident on relativistic electrons in the storage ring TERAS of the Electrotechnical Laboratory (ETL) shortens the photon wave length by a multi-millionth, producing quasi-monochromatic 7 rays 13 . This new MeV photon source is energy-variable in the form of a pencil-like beam with a flux of ~ 104 photons/sec/mm 2 and energy spread of a few % below 9 MeV 14 . We report results of a photoneutron cross section measurement on 9 Be in the context of nuclear astrophysics. Nd:YLF laser photons with A = 1053 nm (1.2 eV) were led to a headon collision point of TERAS. The laser system which produced 100 % linearly polarized light in a normal mode was operated at 1 kHz. Unpolarized light was also produced by passing through a depolarizer quartz. Electron energy was varied from 316 to 587 MeV. The laser-induced Compton backscattered (LC) photons were collimated into 2 mm in diameter with a 20 cm thick Pb block at 5.5 m from the head-on collision point. The energy distribution of LC photons was measured with apure-Ge detector (120 % of 3" x 3" Nal(Tl)). Fig. 1 shows an energy spectrum of LC photons. The full energy peak characteristic of a low-energy wing 14 was calibrated with natural radioactivities 40 K and 208 T1 as well as a standard 60 Co source. As approaching to the 1.665 MeV threshold, LC photons in the low-energy wing increasingly lay below the threshold. The low-energy wing limited the present measurement at E 7 > 1.78 MeV. A 4 cm thick 9 Be rod of 99.5 % enrichment (2.5 cm in diameter) was irradi­ ated. Neutrons were measured with four 60 cmHg BF 3 counters (MITSUBISHI

269 10 8 w 6 e

8 "

4 2

0 0

200

400

600

800

1000

Channel Number Figure 2: Moderation time distribution of neutrons in the polyethylene cube.

ND8534-60: 2.5 cm in diameter x 24.1 cm in effective length) embedded in a 30 cm polyethylene cube. T h e BF3 counters were located, two each vertically and horizontally, in a concentric ring at 7.5 cm from the b e a m axis. Neutron moderation time in the polyethylene was measured in 1 ms time range with an O R T E C 566 TAG module. Fig. 2 shows a moderation time distribution. T h e moderation time constant was 144 yus. Background neutrons t h a t arrived at BF3 counters time-independently made a minor contribution to neutron counting. Neutron detection efficiency was measured at 265 keV with a 2 4 N a O H + D2O source and at the average energy of 2.35 MeV with a 2 5 2 Cf source. T h e production of the monoenergetic neutron source and its calibration followed Ref. 9 . Details were reported elsewhere 1 5 . T h e energy dependence of the efficiency was calculated with the Monte Carlo code M C N P 2 6 . Fig. 3 shows the neutron detection efficiency as a function of neutron energy. T h e 1 kHz LC photons were detected with a B G O detector (2" in diameter x 6" in length) placed at the end of t h e beam line. Pile-up spectra were obtained as typically shown in Fig. 4. T h e average number of photons per b e a m pulse was determined from the ratio in average channel number between the pile-up spectrum and a single photon spectrum. T h e single photon s p e c t r u m was separately taken with a DC beam. T h e total number of photons were obtained from the frequnecy and the d a t a acquisition time. Independent test measurements were carried out with a DC beam, in which foreground and background neutrons were measured before and after each measurement with

270 12 10 8

MCNP Monte Carlo Cal.

NaOH + D O 2

g6 4 'Cf

2 0 0

500

1000

1500

2000

2500

E (keV) n Figure 3: Neutron detection efficiency as a function of neutron energy.

the laser off. Results of the pulsed- and DC-beam measurements agreed to each other within 5 %. Photoneutron cross sections were obtained from Nn

Nyen(En)Ntf

(1)

where Nn is the number of neutrons detected, JV7 is the number of LC photons incident on the B G O detector, Nt is the number of target nuclei per cm 2 , and £n(En) is the neutron detection efficiency. A correction factor, / , was needed for a thick target measurement.

(2) fi is the total 7-attenuation coefficient in 9 Be 2 7 and t is the length (4 cm) of the target material. Photoneutron cross sections measured with polarized and unpolarized pho­ tons are shown by open and solid circles in Fig. 5, respectively. T h e decay channel was assumed to be n + 8 B e . Horizontal error bars stand for the skewed energy spread of LC photons in F W H M . As for vertical errors bars,

271 5000

4000 w C 3000 3 O O 2000

1000

0 0

1000

2000

3000

4000

channel n u m b e r Figure 4: Pile-up spectrum of LC photons measured with a BGO detector.

only statistical uncertainties are shown. The results of polarized and unpolarized photon measurements at 1.9, 2.7 and 3.3 MeV agreed to each other within statistics. It is noted t h a t the present cross sections for the narrow 2.44 MeV state formed a tail on the high-energy side. T h e tail arose from the low-energy wing of LC photons. T h e effect of the asymmetric photoneutron emission on en(En) was inves­ tigated with help of the M C N P code. For the asymmetries with a/b = 1.2 1 6 and 1.0 2 in a-\-bsin29 reported at 2.76 and 2.95 MeV, respectively, the associ­ ated uncertainty was found to be 9 - 12 %. This is regarded as the systematic uncertainty in the present measurement. For comparison, cross sections measured with other photon sources are also shown in Fig. 5. T h e horizontal error bars of the large crosses 3 as well as the dotted b u m p 2 corresponding to the 2.44 MeV state ( r < 1 keV) represent the energy resolution of Bremsstrahlung measurements. For l / 2 + , the result of not the Bremsstrahlung 2>3 but the radioactive-isotope measurement 9 is consistent with the present result. T h e least-squares fit to the d a t a was performed with the cross section of Breit-Wigner form. fjp

T

*,,„(£, .i^j)

T\

2J + I

he '

= -^7TTy(^)

ryrn {Ej

_ ERT

+ (r/a)»

7-decay widths for E l and M l are expressed 1 7 , respectively, by

(3)

272

JO

B

E (MeV) Figure 5: Photoneutron cross sections for 9 B e (solid circles for polarized LC photons and open circles for unpolarized LC photons). Data taken with Bremsstrahlung (dotted line [2], large crosses [3]) and radioactive isotopes (open squares [9,10], solid squares [8], solid triangles [7], open triangle [5], slashed-open square [4], diamonds [6]) are also shown. The best least-squares fit is shown by the solid lines (thick solid line for sum, thin solid lines for breakdown).

273

Ty(El)

= —a(hc)-2E*B(Ei)

(4)

and T 7 (M1) = — a(2Mcay2E*B(Mi),

(5)

where a is the fine-structure constant, M is the proton mass, and B(El) and B(Ml) are reduced transition probabilities given in units of e 2 / m 2 and (ek/2Mc)2. T„ for s-wave neutrons from 1/2+ was taken 1 8 as r „ = 2^eR(E7

- ET).

(6)

This form of neutron decay width leads to single-level approximation of Rmatrix theory 19 . T„ for other states was taken to be constant. The least-squares fit was performed to 49 data points up to 4.5 MeV with the Powell method 2 1 . The 49 data points excluded the data for the 2.44 MeV state and included those of Fujishiro et al. 9 . The El and Ml parametrizations were employed for the positive- and negative-parity states ( l / 2 + , 5/2 + , 1/2 - ), respectively. A straight-line background (a = 0.38i?7 - 1.21 mb) was assumed in the high-energy region. The least-squares fit resulted in the x2 minimum with B(M1) = 0 for 1/2". Thus, the presence of 1/2" was not confirmed as was the case in the electron scattering. The best fit (x 2 = 2.7 per degree of freedom) is shown by the thick solid line in Fig. 5. The best fit values for the l / 2 + state are the following. ER= 1.748 ±0MMeV B(E1) = 0.107 ±0.007e 2 /m 2 r ~ r „ = 283±42fceV Attached are the 1 a uncertainties from the error matrix. The B(E1 J.) value for l / 2 + is approximately twice those of electron scattering (0.050 ± 0.02011, 0.054 ± 0.004 12 , while it is close to that (0.106+Q oie) deduced from R-matrix fit to Fujishiro data alone 22 . It was pointed out 2 2 that the discrepancy for l / 2 + between the (7,n) 9 and the (e,e') n results may be due to background subtraction in the electron scattering. Tt was shown that, good agreement between the two was obtained by integrating the (7,n) cross section up to 2 MeV 2 2 . We used the energy-integrated cross section 20 to deduce T 7 for the narrow resonance state at 2.44 MeV.

274 f°°

J

,„

3jr 2 ,fic *


(7)

T h e 7-decay width for the 5 / 2 " state is 0.049 ± 0 . 0 1 2 e K . It is roughly half the (e,e') v a l u e 1 1 . Woosley and Hoffman put the first two resonance states into the rate equation for 9 B e 1. They took T 7 = 0.3 eV for 1/2+ and 0.089 eV for 5 / 2 " from the (e,e') scattering experiments. Since the l / 2 + state plays a dominant role in the reaction rate, the present result implies t h a t the rate be increased approximately by a factor of two. We would like to thank Mr. K. Okamoto (Research Reactor Institute of Kyoto University) for his assistance in the irradiation of a NaOH sample with thermal neutrons, Mr. Y. Ogawa (Kinki University) for his help in running the M C N P code, and Dr. K. Kudo (Electrotechnical lab.) for his cooperation in the detector calibration with the standard graphite pile. This work was supported by t h e J a p a n Private School Promotion Foundation. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

S.E. Woosley and R.D. Hoffman, Astrophys. J. 3 9 5 , 202 (1992). M.K. Jakobson, Phys. Rev. 1 2 3 , 229 (1961). R.J. Hughes et al, Nucl. Phys. A 2 3 8 , 189 (1975). B. Russel et. al, Phys. Rev. 7 3 , 545 (1948). B. Hamermesh and C. Kimball, Phys. Rev. 9 0 , 1063 (1953). R.D. Edge, Nucl. Phys. 2, 485 (1956/57). J.H. Gibbons et al, Phys. Rev. 114, 1319 (1959). W . John and J.M. Prosser, Phys. Rev. 1 6 3 , 958 (1967). M. Fujishiro et al, Can. J. Phys. 60, 1672 (1982). M. Fujishiro et al, Can. J. Phys. 6 1 , 1579 (1983). H.-G. Clerc et. al, Nucl. Phys. A 1 2 0 , 441 (1968). G. Kuechler et. al, Z. Phys. A 3 2 6 , 447 (1987). H. Toyokawa et al, Nucl. Instr. and Methods in Phys. Res. A 4 2 2 , 95 (1999). H. Ohgaki et al, I E E E Tran. Nucl. Sci. 38, 386 (1991). Y. Yonezawa and H. Utsunomiya, Mom. Konan Univ. Sci. Ser. 4 6 , 43 (1999). B. Hamermesh et al, Phys. Rev. 76, 611 (1953). J.M. Blatt and V.F. Weisskopf, Theoretical Nuclear Physics, (SpringerVerlag New York Inc. 1952) p . 583. F . C . Barker and B.M. Fitzpatrick, Aust. J. Phys. 2 1 , 415 (1968).

275

19. 20. 21. 22. 23. 24. 25. 26. 27.

28.

A.M. Lane and R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958). F.C. Barker, Nucl. Phys. 28, 96 (1961). M.J.D. Powell, Computer Journal 7, 155 (1964). F.C. Barker, Can. J. Phys. 61, 1371 (1983). C. Angulo et al, Nucl. Phys. A656, 3 (1999). K. Nomoto, F.-K. Thielemann and S. Miyaji, Astron. Astophys. 149, 239 (1985). F. Ajzenberg-Selove, Nucl. Phys. A413, 1 (1984). J.F. Briesiiieister, MCNP, A General Monte Carlo N-Particle Transport Code, Version 4B, Las Alamos National Laboratory, 1997. Engineering Compendium on Radiation Schielding, Vol. 1, edited by R.G. Jaeger, E.P. Blizard, A.B. Chilton, M. Grotenhuis, A. Honig, Th. A. Jaeger, and H.H. Eisenlohr (Springer-Verlag New York Inc. 1968) p. 173. G.R. Caughlan and W.A. Fowler, Atomic Data and Nuclear Data Tables 40, 283 (1988).

R I K E N R I - B E A M FACTORY (RIBF) P R O J E C T A N D T H E WAY TO T H E R-PROCESS NUCLEI

T. SUDA RI Beam Science, RIKEN, 2-1 Wako, Saitama, JAPAN E-mail:[email protected] RIKEN RI-Beam Factory (RIBF) is a next-generation heavy-ion accelerator facil­ ity, that aims at providing the most intense primary beam as high as lp/iA over a wide atomic range up to U. The maximum energy reaches 400 MeV/nucleon for light ions and 150 MeV/nucleon for Uranium. The intense primary beams and a large-acceptance fragment separator, Big-RIPS, allow efficient production of many unstable nuclei, and enable us to select them freely as a secondary RI beam over a wide range of proton and neutron numbers. RIBF will open a way to study the basic properties of very neutron rich nuclei, which are very important to describe the r-process.

1

Introduction

The astrophysical r-process is one of distinct nucleosynthetic mechanisms to produce heavy elements 1 , and the study of the process will offer valuable information for understanding the origin of heavy elements in our universe. Although the r-process path in the nuclear chart is defined by the locations of the measured abundance peaks, we know very little concerning on the basic properties of nuclei on the path, such as their masses, /3-decay properties and the internal structure. This is because they are so neutron rich that most of such nuclei have never been studied at the laboratories currently in operation. The basic nuclear properties mentioned above are essential to describe the r-process. They are important for calculations of the abundance distribution, and for constraints on parameters such as temperature and neutron flux of the r-process. For example, the mass differences between nearby nuclei determine their stability to (7,n) process, and their half-lives determine the abundance. Furthermore, their decay modes could produce shifts of the r-process peaks. Their nuclear structure may also play an important role to understand the process. The appearance of next-generation heavy-ion facilities, which provide high­ er intensity primary beams, will open a door to access the r-process nuclei whose production cross section is extremely small.

276

277

Figure 1: A plan view of the RIKEN RIBF project.

2

R I K E N R I B F Project

One of these facilities is RIKEN RI-Beam Factory (RIBF). It aims at supplying the most intense primary beam in the world over a wide range of nuclei up to Uranium. The intense primary beam will allow us to produce unstable nuclei far from the /^-stability line towards both neutron-rich and proton-rich side. Most of the proton drip-line nuclei will be covered and most of neutron-rich nuclei in the r-process path region will be able to be accessed. Figure 1 shows a plan view of the RIBF project, which is divided into two phases, namely Phase I and II. In the phase I, which is currently under construction, two cyclotrons will be newly constructed for further acceleration of primary beams extracted from the existing K540 RIKEN Ring Cyclotron (RRC). They are Intermediate Ring Cyclotron (IRC), and Superconducting Ring Cyclotron (SRC), whose K values are 930 and 2500, respectively. The cascade operation of these cyclotrons will provide the intense primary beams with the energy of several hundreds MeV/nucleon up to the U-beam. The expected beam current is as high as lp/xA, and the maximum beam energies are 400 MeV/u for light ions like Oxygen, and 300 MeV/u for Kr ions, 200 MeV/u for Xe ions and 150 MeV/u for U ions. Two fragment separators, called Big-RIPS, act as filters to select a specific isotope as a secondary RI beam for an experiment. The momentum accep­ tance of the separator will be ±3%, and the horizontal and vertical angular acceptance will be ±40 mrad and ±50 mrad to keep a large transmission even for isotopes produced by fission-in-flight of U-beam, which will be discussed later in detail.

278

Figure 2: Nuclear chart of accessible isotopes at RIBF.

The maximum rigidity of the separator is set to be 9.5 Tm. This value is chosen to produce very neutron-rich nuclei. A time-sharing system consisting of a pulse magnet will be installed in the beam transportation system from SRC to BigRIPS, which shares the primary beam to the two fragment separators simultaneously. This feature makes two independent experiments using two different RI beams at the same time possible. Figure 2 is the nuclear chart, in which the r-process path is indicated. In the figure, the production rate of 10~ 5 /sec at RIBF is indicated by a dashed line, which is roughly the yield limit for the mass and half-life measurements. One may find that the line for 10 _ 5 /sec production rate of RIBF is running well outside of the r-process path. Here the next phase of the RIBF project is briefly introduced. In the phase II, a new generation accelerator complex, MUlti-uSe Experimental Storage rings (MUSES) is proposed. The MUSES consists of several rings; an accumulator-cooler ring (ACR), a booster-synchrotron ring (BSR), doublestorage rings (DSR) and a 300-MeV electron linac. The ACR cools an RI beam by either an electron cooler or a stochastic cooler to reduce the beam emittance, and the BSR boosts up its energy, and the beam will be storaged in the DSR. One of typical experiments at the

279 T"

T"

10' U->Ni • (GSI exp.)

10° I

so '■a u

r

10

86

Kr->Ni m (EPAX2)

78

Ni

CO

\

t/3

!»

o

10 H

s-l

U 10

40

42

44

46

48

50

52

Neutron Number Figure 3: Production cross section for Ni isotope. Solid circle shows the production cross section in the fission-in-flight of U beam from GSI, and solid square the production cross section by the fragmentation of S6Kr beam calculated by EPAX2.

MUSES will be electron scattering from storaged RI beams using the DSR as an electron-nucleus collider. One can determine the electromagnetic form factor of many unstable nuclei for the first time. 3

Production of RI Beams

RI beams will be produced by either projectile fragmentation reaction or fission-in-flight reaction of U-beam. Projectile fragmentation has been already applied to produce secondary RI beams at various laboratories in the past, and the production cross sec­ tion and the kinematical behavior of fragments have been semi-quantitatively understood 2 . Fission-in-flight has been recently investigated at GSI 3>4>5, and it has been demonstrated to be quite powerful to produce very neutron-rich nuclei. As an example, the production cross section of Ni isotopes by the fragmentation and fission-in-flight reactions are compared in Fig. 3. The fission cross section are taken from GSI data 4 , and the cross section for fragmentation are calculat-

280

ed with a program EPAX2 6 . As one sees, the production cross sections of fission-in-flight are much larger (one to two order in magnitude) than those of fragmentation for producing all Ni isotopes. In the case of the fission reaction, fission fragments have much larger an­ gular and momentum spread than those by projectile fragmentation. For ex­ ample, the angular and momentum spread of fission fragments are typically about ±100mrad, and ±10% at the RIBF. This is why the separator, BigRIPS, has been designed to have large angular and momentum acceptances to keep reasonable transmission (about 8%) for fission fragments. Expected yields of Ni isotopes by fragmentation and fission were simulated using MOCADI 7 taking into account the BigRIPS acceptance. According to the simulation, the fission-in-flight method is found to give larger yields for all Ni isotopes than the projectile fragmentation, and the expected intensity of 78 Ni is about 1 Hz. Although one needs to check this by experiments, it is clear that fission-in-flight of the U-beam will play an important role especially for very neutron-rich r-process nuclei. 4

The Measurement of Half-Lives and Masses

The measurements of the half-lives of nuclei will be done by the stopping experiments. The half-lives of nuclei in the r-process region is expected to be an order of one second or less, and the production rate of such isotopes will be quite low. Isotopes, particle-identified by a usual Bp — AE — TOF method, will be implanted in, for example, a position-sensitive detector, and the observation of /3-decay at the same position in the detector as a function of time after the implantation will give the half-lives. A good position resolution is necessary to suppress background. A new detector system based on this method is under development at RIKEN 8 . Instead of using a position sensitive detector, a thin foil is used as an isotope catcher. Eleven thin foils are mounted on a rotating wheel, and one of foils is set on the beam line. In front of the foil, a position-sensitive plastic-fiber detector will be placed to mark the position of implantation on the foil. Just after implantation, the wheel rotates quickly to set the foil in front of a position-sensitive /3-ray detector for the half-life measurement, and simultaneously to place another foil on the beam line for further implantation. The detector system has five rotating wheels along the beam line, and allows the simultaneous half-life measurements of different isotopes which stop in different foils due to the range difference. This detector system is designed to determine the half-lives of nuclei, which are longer than 300 ms. The first

281

experiment using this new system at the present facility is scheduled in the beginning of year 2001. The same setup will be installed in the secondary beam line of RIBF, and the half-lives of nuclei along the r-process path will be determined. There will be several ways to determine the nuclear mass. One method em­ ployed in the first phase of RIBF will be the time-of-flight (TOF) measurement over a long flight path. The TOF measurements with good timing detectors of a few 10 ps resolution over 50 meter flight path will allow to determine the mass of the level of about a few 100 keV for A ~ 100 region, when the statistics is enough. The experimental hall is designed to provide such a long flight path with a momentum analyzing system. Another promising way to determine the nuclear mass is to use an accu­ mulator ring, such as ACR of MUSES. This method is quite powerful when the production rate is quite low. One is able to accumulate a nucleus of interest in the ACR until it decays, and to observe the circulating frequency. This method will allow very precise determination of the mass of a nucleus. As an example, let me introduce the mass measurements using a storage ring currently carried out at GSI. The experimental storage ring (ESR) has been used for this purpose. The ESR has been operated in isochronous mode. Two different techniques, namely non-destructive and destructive methods, have been employed for the precise mass measurement. The non-destructive method is to use the Schottky noise caused by the beam circulation in the storage ring 10 . In order to achieve high mass resolu­ tion, the RI beam must be cooled prior to the measurement. Therefore this method can be applied to nuclei whose half-lives are longer than a few seconds when one uses the electron cooler. It is reported that the mass resolving power of 350000 has been achieved. The other novel way (the destructive method) is to measure the flight time directly in a storage ring 1 1 . This new method has been recently applied at GSI 1 2 , and the nuclear mass, whose life time are shorter than a few ms, have been successfully measured with the mass resolution of 10~ 5 . A thin foil equipped with a MCP detector is set in the storage ring. When a circulating beam passes through the foil, secondary electrons are produced. The electrons provide the timing information, and one determines the circulating frequen­ cy. Since the time-of-flight is measured directly for each turn, no cooling is necessary. In the phase II of the RIBF project, the ACR operating in the isochronous mode will be a place to measure the masses of many unstable nuclei. The higher intensity of primary beams at RIBF will allow to determine the masses of more neutron-rich nuclei.

282

5

Conclusions

The determination of masses and half-lives of nuclei along the r-process path is one of the important subjects at the coming new-generation heavy-ion acceler­ ator facilities. Since they are so neutron rich, high-intensity heavy-ion beams are indispensable for their production. The RIKEN RIBF will be one of such facilities to study the r-process. High-energy and high-intensity primary beams and a large acceptance fragment separator, BigRIPS, allow us to select nuclei as secondary RI beam freely over a much wider range of proton and neutron numbers. The RIBF phase I will be completed in the year 2003. 1. E. Burbige et al, Rev. Mod. Phys. 29, 547 (1967). 2. J.A. Winger, B.M. Sherrill and D.J. Morrissey, Nucl. Instrum. Methods B 70, 380 (1992) 3. M. Bernas et al, Phys. Lett. B 331, 19 (1994). 4. M. Bernas, Proceedings of ENAM98 : Exotic Nuclei and Atomic mass­ es, edt by B.M. Sherrill, D.J. Morrissey and C.N. Davis, p.664, 1998, publisher 5. K.-H. Schmidt et al, GSI-Preprint-99-30, August 1999. 6. K. Suemmerer and B. Blank, GSI-Preprint-99-37, November 1999. 7. N. Iwasa et al, Nucl. Instrum. Methods B 126, 284 (1997). Nucl. Instrum. Methods B 70, 380 (1992). 8. S. Nishimura et al., A proposal for Nuclear Physics Experiment at RIKEN Ring Cyclotron (2000), 'Measurement of Properties of NeutronRich Nuclides Relevant to the Astrophysical r-process' 9. C D . Buchanan et al, Phys. Rev. D 45, 4088 (1992). 10. B.Schlitt et al, Nucl. Phys. A 626, 315c (1997). 11. H. Wollnik et al, Nucl. Phys. A 626, 327c (1997). 12. M. Hausmann et al., GSI report 1999, p.22.

CONNECTION B E T W E E N CRUCIAL NUCLEAR REACTION RATES A N D T H E M O D E L I N G OF A C C R E T I N G N E U T R O N STARS

M. H A S H I M O T O , O . K O I K E A N D R. K U R O M I Z U Department

of Physics,

Kyushu

E-mail:

University, Ropponmatsu, Fukuoka JAPAN [email protected]

810-8560,

M. F U J I M O T O Department

of Physics, Hokkaido University, Sapporo 060-0810, E-mail: [email protected]

JAPAN

K. A R A I Department

of Physics, Kumamoto University, Kumamoto 860-8555, E-mail: [email protected]

JAPAN

Effects of uncertainties of key nuclear reaction rates in the crucial nuclear processes on type I X-ray burst modeling have been reviewed/investigated. Special attention is devoted to the ignition condition of the thermonuclear flash. It is found that in the rapid proton capture process (rp-process), the ignition depends on the rates of 13 N ( p , 7 ) 1 4 0 , 1 4 0 ( a , p ) 1 7 F , and 1 5 0 ( a , 7) 1 9 Ne. On the other hand, for the pure helium flash suggested from a recent observation of X-ray bursts, we infer that the NCO-reaction plays a key role in triggering the flash.

1

Introduction

Type I X-ray bursts of low mass X-ray binaries (LMXBs) are considered to be thermonuclear runaways in accreted materials on the surface of neutron stars 1 ' 2 . Detailed evolutionary calculations have been performed taking into account the nuclear processes during the flash.3'4 In the mean while, many nuclear data have been revised and accumulated in these years, some of which may affect the modeling X-ray bursts. The nuclear process in the proton rich environments was investigated in detail by Wallace & Woosley5 who proposed the rapid proton capture process which has been initiated by the break out from the hot-CNO cycle. In a framework of the one zone model of constant pressure, explosive nucleosyntesis 6 and the rp-process 7 were investigated in detail using large nuclear networks. They showed clearly that not only the nucleosynthesis proceeds appreciably beyond 56 Ni but also appreciable amounts of the nuclear fuel of hydrogen and helium are left if the peak temperature exceeds 109 K

283

284 8.5 r—i

r

15

- 10

CO

O

bo 7.5

o - 5

_i 30

I 20

log P (Cgs) Figure 1. Structure of an accreting neutron star just before an ignition. Note that the temperature and the density are drawn against the pressure.

which corresponds to the case for the pressure of P > 3x10 dyn cm ; it was suggested that the fuel left unburnt may be responsible for the X-ray bursts at 10 minutes interval.8 Using the approximate network 7 , Fujimoto et al. 3 investigated X-ray bursts in detail with the full evolutionary calculations including the general relativity 9 for an accreting neutron star model. For example, Fig. 1 shows the temperature and density structure of an accreting neutron star after 2.63 x 104 s accretion; the total rest mass is 1.61067 M 0 and the radius 8.069 km; Then the luminosity is 29.6 L Q and the effective temperature is 3.95 x 106 K. In the present paper, we will investigate the thermonuclear flash with the use of an extended network up to " P d based on the network constructed by Koike et al. 10 which is coupled to the thermodynamical equation for the flash. On the other hand, in our stellar evolution calculation, we use the upto-date nuclear data and other physical inputs like screening factors. Previous approximate network which consists of 13 nuclei is updated changing the old nuclear data to new data. Then, it is shown that some crucial reactions govern

285 T

1

1

1

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3x10* -

2xl(f

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0 J

lxlOJ

50000

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t (sec) Figure 2. Model calculation of successive light curves of X-ray bursts during the accretion onto a neutron star with reaction rate compilations up to 1984.

the ignition timing of the shell flash as inferred from the temperature profile of Fig. 1. 2

General feature of the shell flash model connected with the rp-process

Stellar evolutionary code for an accreting neutron star has been developed n with the inclusion of the results of the nucleosynthesis calculations 6 , 7 ; Evolu­ tion code has been coupled to an approximate network code which simulates the rp-process results calculated using a large network. 12 Then radiative zero boundary condition is imposed for Mr/M ~ 1 p =

GMt(M - Mr) / 4TTR4

2GMt

Re2

-1/2

, L = Lph

(1)

where L*h means that it is the luminosity observed far from the star, the total mass Mt, the total rest mass M, the rest mass inside the radius Mr, and

286 i

,... 30000

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i

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1 1_L. J

1

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7150

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7200

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7250

t (sec) Figure 3. Profile of X-ray bursts for two cases of reaction rates; solid line: rates up to are included; dashed: all rates beyond 5 6 Ni are suppressed.

68

Se

the density of the rest mass p , respectively. The radiative luminosity L*h is considered to be the total luminosity in the present study. Model calculation of burst simulation is shown in Fig. 2 with dM/dt = 3 x 10~ 9 M©yr _1 , M = 1.6 MQ, and R = 8 km. It can be seen that the burst intervals are irregular between 3 h to 6 h and the magnitudes of the luminosity are different in each burst. It should be noted that regular/irregular profiles have been observed in 4U/MXB 1820-30 and 1636-536.1 Concerning the shell flash of combined hydrogen/helium burning on ac­ creting neutron stars, the rp-process proceeds beyond 56 Ni and reaches the production up to 68 Se. Since the nucleosynthesis beyond 56 Ni occurs after the flash peak, it supplies luminosity furthermore due to energy release from pro­ ton captures depending on the nuclear path. Effects of nuclear paths beyond 56 Ni on the light curves are designated in Fig. 3. It is clear that the tail of the light curve is lowered in luminosity significantly if reaction flows beyond 56 Ni are suppressed. For example, the rp-process on an accreting neutron star has been confirmed from the burst profile of GS 1826-238 by RXTE satellite. 2

287

Figure 4. Temperature variation against pressure through the ignition (between # 3 3 1 and 401) and the peak (#411) to the exhaustion of nuclear fuels (#421).

Table 1. Physical quantities in CGS units during the bursts. Radii of R and Rs are in km. STAGE

logP

logp

logT

R

Rs

#331 #401 #411 #421

22.94 23.09 23.09 23.09

6.31 6.40 6.22 6.36

8.30 8.52 9.09 8.88

8.06374 8.06337 8.06374 8.06374

8.06820 8.06958 8.08717 8.07285

Temperature variation before and after a shell flash is designated in Fig. 4 where stage numbers of stellar evolutionary calculation are attached with ' # ' . The peak of a shell flash corresponds to #411; The maximum temperature of 1.3 x 109 K is attained. Some physical quantities are shown in Table 1. It is found that the pressure is almost constant and the accreting layer is very thin: the depth to the burning layer R from the surface Rs is at most 24 m and the thickness of accreting layer is around 30 m (the bottom of the layer is 8.05688 km from the center).

288

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Figure 5. Mass fractions at the peak of a flash corresponding to the stage of # 411.

Composition profile of mass fractions at #411 is shown in Fig. 5. We can see that the nucleosynthesis has advanced beyond 56 Ni and up to 68 Se at the deep layers of the accreting surface region. 3

Nuclear ignition triggered by the break out from the hot-CNO cycle

Qualitative features of nuclear ignition are understood with the use of onezone model. 10 , since accreting layer can be well approximated by the plane parallel configuration. Then hydrostatic equation (1) is reduced to P = g.Jl,

= ^ V , E=. B? ' 4irR2 where V is the redshift factor as in Eq. (1). Burning layers prevail l o g P ~ 20 — 23 which are dominated by the partially degenerate electron gas. It is shown that the ignition epoch is affected significantly by the reaction rate of 1 5 0(a,7) 1 9 Ne. To demonstrate this effect we show two light curves in Fig. 6; left: the rate is taken from Wallance and Wooslley 5 ; right: the 9s

289

.

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.

.

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.

.

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t (S) Figure 6. Luminosities for two cases of reaction rates A's of

15

0 ( a , 7 ) 1 9 N e at # 61.

rate is reduced by a factor of 10; in the latter case, the flash delays about 50 sec and the luminosity peak is higher. On the other hand, to exaggerate the effects of 1 4 0 ( a , p) 1 7 F, we suppressed this rate artificially; The light curve is drastically changed in profile as shown in Fig. 7. Note that actually the ignition point is rather insensitive to the change of this rate. This can be seen as follows. Fig 8 shows the p — T tracks before and after the burst which are the deep layers of accumulated matter in connection with the ignition tracks of reaction rates. At #401 of burst ignition, T exceeds the ignition track for 14 0 ( a , p ) 1 7 F soon after the ignition track of 1 5 0 ( a , 7 ) 1 9 N e is reached. This means that the ignition points are generally controlled by the latter reaction. 4

Pure helium flash

Though the possibility of a pure helium flash has been proposed 2 ' 12 for MXB1636-53 and/or EXO 074-676 that the maximum of the peak luminos­ ity can be interpreted by the Eddington luminosity 2.3 x 10 38 erg s _ 1 , it is still unclear whether it occurs in X-ray bursts. Pure helium flash would be

290

30000 -

120000 -

3 10000 -

7100

7200

7300

7400

t (sec) Figure 7. Same as Fig. 6 except that the rate of

14

0 ( a , p ) 1 7 F is set to be 0 (dashed line).

judged to be occurred if the ratio a of the bolometric flux of the persistent emission to the bolometric fluence of the burst exceeds 100. Recent observa­ tion of X-ray burster SAX J1750.8-2900 and 4U 1812-12 suggests a pure He flash rather than a H-He flash due to the fast rise time of the burst (< 2 s) and/or the measured value of a. 13,14 as seen in Fig. 9. Though it is believed that this kind of helium flash is initiated by the 3a-reaction, concerning the hydrogen-exhausted layer and/or helium accreting compact stars, NCO re­ action, 1 4 N(e~,z/) 1 4 C(a,7) 1 8 0, can play a key role in triggering the helium flash. Since the threshold density for 1 4 N(e",i/) 1 4 C is ~ 106g cm" 3 , NCO reaction should be crucial in accreting neutron stars as in accreting white dwarfs 15 . Ignition epoch for a helium flash depends on the reaction rate of 1 4 C ( a , 7 ) 1 8 0 and/or the amount of 14 N in an accumulated layer. Since the reaction rate is very uncertain by a factor of ten around the relevarant ignition temperature, ignition timing depends on the rate crucially as shown in Fig. 10.

291

5

Concluding remarks

It is worthwhile to investigate X-ray bursts since so many observational data of not only type I X-ray bursts also type II bursts are now avairable. In some case, these different type bursts would be related each other through an accretion disk. Furthermore, many nuclear data relevant to type I burst such as nuclear cross section and weak interaction has been accumulated in these years 16 which prove an intimate connection between astrophysics and nuclear physics. These connections should also develop to clarify the mass-radius relation of neutron stars which have been still very uncertain. In addition, thermodynamical quantities like conductivity and opacity of neutron star will be studied keeping pace with the modeling of X-ray bursts. These research must be helpful also to solve the mechanism of supernova explosion and/or the evolution of proto-neutron stars like cooling mechanism.

Figure 8. Density and temperature tracks before and after the burst as Fig. 4 with ignition tracks of reactions which are denned by the proton/alpha capture lifetime equal to the /3decay time. The band for each ignition track originates from uncertainties of reaction rates.

292 10'

log P = 23 He flash

log gs = 14.75

10' -

•7 60 00

H/He burning

«? io -

5

10

time(s) Figure 9. Radiation losses of pure helium flash by the 3-a reaction and H/He combined burning with initial Hot CNO abundances. One zone model of the constant pressure is adopted.

References 1. R. E. Taam, Ann. Rev. Nucl. Part. Sci. 35, 1 (1985); W. H. G. Lewin, J. van Paradijs and R. E. Taam, Space Sci. Rev. 62, 233 (1993). 2. L Bildstern in Cosmic Explosions-.proc. 10th Annual Oct. Astrophysics Conference, ed. S.S. Holt and W.W. Zhang (astro-ph/0001135, 1999). 3. M. Fujimoto, M. Sztajno, W. H. G. Lewin and J. van Paradijs, Astrophys. J. 319, 902 (1987). 4. R. E. Taam, S. E. Woosley and D. Q. Lamb, Astrophys. J. 459, 271 (1996). 5. R. K. Wallance and S. E. Woosley, Astrophys. J. Suppl. 45, 389 (1981). 6. M. Hashimoto, T. Hanawa and D. Sugimoto, Publ. Astron. Soc. Japan 35, 1 (1983). 7. T. Hanawa, D. Sugimoto and M. Hashimoto, Publ Astron. Soc. Japan 35, 491 (1983). 8. T. Murakami et al., Publ. Astron. Soc. Japan 32, 543 (1980).

293

9. K. S. Thome, Astrophys. J. 212, 825 (1977). 10. O. Koike, M. Hashimoto, K. Arai and S. Wanajo, Astron. Astro­ phys. 342, 464 (1999). 11. M. Fujimoto, T. Hanawa, I.Jr., Iben, and M.B. Richardson, Astrophys. J. 278, 813 (1984). 12. T. Hanawa and M. Fujimoto, Publ. Astron. Soc. Japan 36, 199 (1984). 13. L. Natalucci et al., Astrophys. J. 523, L45 (1999). 14. M. Cocchi et al, astro-ph/0003151, 2000 15. M. Hashimoto, K. Nomoto, K. Arai and K. Kaminishi, Astrophys. J. 307, 687 (1986). 16. H. Schatz et al, Phys. Rep. 294, 167 (1998).

1

1

I

1

1

1

1

1

log P=24

1

Ti=9xl07 (K)

j

X(14N)=0.02 —

I

1 CF88 5

hHashimoto et al 1986 10" -

10°

no NCO

_

!

:

^___LJ J 1

1

1

- -1...

■

i

i

■

6.5

time (10' s) Figure 10. Helium flashes triggered by the NCO and/or 3-a reactions. One zone model of the constant pressure is adopted without a radiative loss. As the most effective case for the NCO reaction to occur, X(He) = 0.98 and the rest of 1 4 N are assumed.

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VII. Neutron Stars and High Density Matter

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U N S T A B L E NUCLEI A N D A N EOS TABLE FOR SUPERNOVAE A N D THE R-PROCESS IN A RELATIVISTIC M A N Y - B O D Y A P P R O A C H

K. The Institute of Physical Hirosawa, Wako, E-mail:

Sumiyoshia and Chemical Research (RIKEN), Saitama 351-0198, Japan [email protected]

We study supernova explosions and the associated r-process using a nuclear-matter equation of state (EOS) derived by a relativistic many-body approach. Recently, we have completed a relativistic EOS table which spans the wide range of density, composition and temperature relevant to supernova explosions. We apply this EOS table to numerical simulations of the gravitational core collapse, subsequent evolution of the proto-neutron star, and the r-process. To derive the requisite nuclear-physics ingredients for supernova, we have constructed a relativistic mean field (RMF) framework based upon relativistic Briickner-Hartree-Fock theory. We have successfully applied the constructed RMF framework to the ground state properties of many nuclei in the nuclear chart. We apply this same RMF framework to derive the supernova EOS table. As examples of astrophysical applications of the EOS table, hydrodynamical simulations of core collapse have been performed. We have also performed numerical simulations of the hydrodynamics of the i/-driven wind from the nascent proto-neutron star. We find that a successful r-process is indeed possible with a short expansion time scale in the ^-driven wind above the massive and compact proto-neutron star.

1

Introduction

The physics of supernovae is fascinating. It is the key to understanding many aspects of stellar evolution and the origin of heavy elements. The explosion mechanism of collapse-driven supernovae is still one of the big mysteries in astrophysics. Whether the r-process nucleosynthesis to create heavy elements happens in the supernovae is also an important question to be answered. To attack these problems, one has to perform careful numerical simulations with the reliable information of nuclear physics at extreme conditions. One of the essential ingredients from nuclear physics is the equation of state (EOS) of dense matter. The challenge is to describe both unstable nu­ clei and dense matter covering the wide range of densities, temperatures and neutron-rich composition during supernova explosions. Because of the lack of an EOS table to cover all conditions, it has been difficult to perform simu­ lations which follow the sequence of phenomena: gravitational collapse, core a

Present address: Numazu College of Technology, Ooka 3600, Numazu 410-8501, Japan E-mail: [email protected]

297

298 bounce, neutron-star birth, neutrino-driven wind which leads to the r-process, and explosion. Recently, we have completed a relativistic EOS table which spans the wide range of density, composition and temperature relevant to supernova explo­ sions 1 ' 2 . This relativistic EOS table enables us to perform the full simulations of supernova phenomena from the gravitational core collapse to the cooling of the newly formed neutron star. Here, we describe briefly the relativistic manybody framework to derive the EOS table as well as nuclear structure and show examples of the application of this EOS table to hydrodynamical simulations.

2

Relativistic EOS constrained by unstable nuclei

To provide the properties of unstable nuclei and dense matter in supernova conditions, we need to choose a reliable framework supported both by the­ oretical and experimental aspects. The recent success of relativistic nuclear many-body theories 3 , where the nuclear saturation is derived starting from a nucleon-nucleon interaction, motivates us to use extensively the relativistic many-body framework. At the same time, the increasing experimental data of unstable nuclei produced by radioactive nuclear beam facilities around the world, are helping to constrain the properties of matter in a neutron-rich en­ vironment 4 ' 5 . Having these two important trends in nuclear physics, we have constructed a relativistic mean field (RMF) framework as a reliable nuclear many-body framework. The RMF framework has been successful to describe the structure of unstable nuclei as well as stable ones 6 ' 7 ' 8 . We construct the effective Lagrangian with non-linear a and to terms based upon the relativistic BrucknerHartree-Fock theory. The parameters of the Lagrangian are constrained by fitting the experimental masses and charge radii of representative stable- and unstable nuclei. We have made the systematic calculation of nuclear structure for about 2000 even-even nuclei up to the drip lines in the RMF framework9. The global agreement with the experimental data of mass and charge radius is found to be extremely good. We have also seen the successful prediction of the neutron-skin thickness through the comparison with the systematic mea­ surements of matter radii for neutron-rich isotopes to constrain the matter properties in neutron-rich environment 6,10 . Having the RMF framework thus checked by experimental data, we apply this same RMF framework to a Thomas-Fermi calculation 1 ' 2 of an EOS table covering a wide region of conditions. We have made a numerical data table of the EOS. This provides all the desired physical quantities over the relevant

299

wide range of density, composition and temperature 6 . We then apply this relativistic EOS table to hydrodynamical calculations of core collapse, neutrino emission11, and the formation of a neutrino-driven wind from the proto-neutron star 12 . We present examples of such simulations in the following sections. 3

Core collapse and supernova explosions

The supernova explosion occurs at the end of the thermonuclear lifetime of massive stars. After the nuclear burning stages, the Fe core is formed at the center and starts collapsing due to the gravity. As a result of this collapse, the central density becomes high (up to or beyond nuclear matter density) and the inner part of the core bounces due to the nuclear repulsive force. A shock wave is launched as the proto-neutron star is born at the center. If the shock is strong enough to break through to the outer part of the core with sufficient energy left, the shock wave blows off the outer layers of the star. That is believed to be the scenario of a supernova explosion. However, whether this explosion is successful or not is a long-standing problem. To answer this question, one has to treat both the macrophysics (such as hy­ drodynamics and neutrino transport) together with the microphysics (such as neutrino physics and nuclear physics). Important ingredients in the microphysics are the properties of dense matter during the core collapse. The EOS determines crucially stellar structure, hydrodynamics and the reaction rates in the dense matter, and therefore, influences largely the supernova explosion. One has to provide the EOS for a wide range of the environments during the core collapse. However, the lack of such a complete table of EOS derived by the microscopic framework has been a hinderance for supernova studies. The relativistic EOS table, which we have completed recently, enables us to per­ form numerical simulations of the whole range of phenomena associated with supernova explosion. As a first example of the relativistic EOS table, we apply it to a hydrody­ namical simulation of core collapse. Here, we assume the adiabatic collapse, and drop the neutrino reactions to see hydrodynamical behavior using our EOS table. We cut out the Fe core from the 15M 0 progenitor model of Woosley13 and construct the initial configuration. Afterwards, we follow the general rela­ tivistic hydrodynamics 14 of the core, which is already gravitationally unstable. Figure 1 displays trajectories of mass elements in the supernova core during the simulation. Within 0.4 seconds, the inner core gravitationally collapses. It bounces back at high density, leaving a hot neutron star at the center. A shock wave is launched at the bounce and propagates outwards. The shock b

The relativistic EOS table is available for use upon request to K. Sumiyoshi

300

Figure 1: Positions of mass elements in the supernova core during the numerical simulation of core collapse are displayed as functions of time. The launched shock wave successfully propagates toward the surface, leading to a prompt explosion. wave goes through the outer core within 0.2 seconds and leads to a successful, prompt explosion in this calculation. Although this is only a test calculation treating hydrodynamics without the crucial neutrino transport, we have found that the EOS table works quite well even for dynamical situations. Moreover, the results suggest that prompt explosions might be possible for less massive progenitors if the electron capture is significantly suppressed by Pauli blocking. We are currently working on full simulations of hydrodynamics with neutrino transfer to clarify the mechanism of explosion, especially the delayed explosion for massive progenitors. 4

R-process in the neutrino-driven wind

The rapid neutron capture process (r-process) is believed to be the origin of about half of the abundance of heavy elements in the Universe. However, the neutron rich site of the r-process is one of the big mysteries in astrophysics. Supernova explosions are most likely the site, but where and how the r-process can occur in supernovae has not yet been clarified. We study the neutrinodriven wind from the proto-neutron star born shortly after the core bounce as an r-process site by hydrodynamical simulations 12 . Right after the core bounce, a hot, nascent neutron star is left, containing a high density of trapped neutrinos inside. At the surface of the proto-neutron star, the matter is heated up by escaping neutrinos from the core. Some

301

Figure 2: Schematic diagram of the neutrino-driven wind from the proto-neutron star just born in supernova explosion. surface material then escapes as a wind. This wind from the proto-neutron star surface is believed to be a site for r-process nucleosynthesis15 (See Fig. 2). However, the hydrodynamical conditions of the wind, such as the entropy, electron fraction and the dynamical time scale, have a large uncertainty 16 . We therefore performed numerical simulations of the hydrodynamics of the surface layers just above the proto-neutron star to better determine these conditions and to clarify whether the r-process occurs and how r-process products are. We have adopted a numerical code for general relativistic, implicit hy­ drodynamics in spherical symmetry 14 . The general relativistic treatment is essential to study the hydrodynamics around compact objects such as neutron stars. The heating and cooling processes due to neutrinos are added to the hydro code. The implicit time differencing is also essential to follow the hydro­ dynamics for a time, which is much longer than the sound crossing time in the dense matter of neutron stars. The hydro code uses a Lagrangian mesh, which is suitable to follow the thermal history for the nucleosynthesis. We adopt the relativistic EOS table, which was used for the supernova study mentioned above. Figure 3 demonstrates the hydrodynamical simulations of the neutrinodriven wind. The surface layers above the proto-neutron star are heated up due to neutrino interactions. Mass elements are ejected gradually escaping the gravitational potential. Matter is expanded and cools down as a result. From numerical results, we can examine the hydrodynamical nucleosynthesis condi-

302

0.0

0.2

0.4

0.6

0.8

1.0

time [sec] Figure 3: Positions of mass elements around the surface of the proto-neutron star during the hydrodynamical simulation of the neutrino-driven wind are displayed as functions of time. The surface layers heated by neutrinos are ejected one by one from the proto-neutron star surface.

tions to judge whether the r-process is possible. We found that the expansion time scale is shorter than those estimated in previous analytic studies 16 . A shorter expansion time scale is favorable for the r-process since it leads to a higher neutron-to-seed-nuclei ratio. Using the trajectory of the simulation, we performed nuclear reaction network calculations 12 ' 17 and found that the r-process occurs in the case of a short expansion time scale under certain con­ ditions for neutron star mass, radius and neutrino luminosity. Figure 4 shows the calculated abundances of r-process elements as a func­ tion of mass number. The peaks at A = 130 and A = 195 are produced successfully and the abundance pattern matches very well with the observa­ tional abundance of r-process elements in this case. This result implies strongly that the neutrino-driven wind is a promising site for the r-process. It is also interesting to remark that light neutron-rich nuclei play significant roles in the nuclear reaction network during nucleosynthesis in the neutrino-driven wind with a short expansion time scale 17 . Further numerical simulations of the neutrino-driven wind using the profiles and neutrino spectrum from the protoneutron star cooling simulations are being performed currently.

303

io-3

T

'

'

" ^

J

I

I

I

I

'

'

'

'

I

'

I

I

I

I

I

I

L

1

io-4 CO

I io 6 <

IO"7 IO"8

100

I

150 A

200

Figure 4: Abundance of the r-process elements as a function of mass number calculated by the nuclear reaction network using the trajectory of the neutrino-driven wind simulation. Observational abundance is shown by dots. 5

Summary

To derive reliable supernova EOS, we have constructed the RMF framework based on the relativistic Briickner-Hartree-Fock theory and we have checked the framework by the experimental data of unstable nuclei. We have used the relativistic mean field (RMF) framework to complete an EOS table that covers the wide range of density, composition and temperature relevant to supernova explosions. As an astrophysical application of the EOS table, we have demonstrated that our relativistic EOS table can be successfully applied to hydrodynamical simulations of supernova explosions. We have also shown by hydrodynamical simulations that the neutrino-driven wind in a supernova explosion is a promising site for the r-process to create heavy elements. Acknowledgments The author is grateful to H. Shen, K. Oyamatsu, D. Hirata, Y. Sugahara, M. Terasawa, K. Otsuki, H. Suzuki, S. Yamada, G. Mathews, T. Kajino, I. Tanihata, and H. Toki for continuous, fruitful collaborations. The author thanks also S. Wanajo for detailed discussions on the r-process nucleosynthesis and S. E. Woosley for providing the numerical data of the progenitor models. The numerical simulations have been performed on the supercomputers at RIKEN and KEK, Japan.

304

References 1. H. Shen, H. Toki, K. Oyamatsu and K. Sumiyoshi, Nucl. Phys. A 637, 435 (1998). 2. H. Shen, H. Toki, K. Oyamatsu and K. Sumiyoshi, Prog. Theor. Phys. 100, 1013 (1998). 3. R. Brockmann and R. Machleidt, Phys. Rev. C 42, 1965 (1990). 4. I. Tanihata et al, Phys. Rev. Lett. 55, 2676 (1985). 5. I. Tanihata et al, Phys. Lett. B 289, 261 (1992). 6. K. Sumiyoshi, D. Hirata, H. Toki and H. Sagawa, Nucl. Phys. A 552, 437 (1993). 7. Y. Sugahara and H. Toki, Nucl. Phys. A 579, 557 (1994). 8. K. Sumiyoshi, H. Kuwabara and H. Toki, Nucl. Phys. A 581, 725 (1995). 9. D. Hirata, K. Sumiyoshi, I. Tanihata, Y. Sugahara, T. Tachibana and H. Toki, Nucl. Phys. A 616, 438c (1997). 10. T. Suzuki et al., Nucl. Phys. A 658, 313 (1999). 11. K. Sumiyoshi, H. Suzuki and H. Toki, Astron. Astrophys. 303, 475 (1995). 12. K. Sumiyoshi, H. Suzuki, K. Otsuki, M. Terasawa and S. Yamada, Pub. Astron. Soc. Japan 52, 601 (2000). 13. S. E. Woosley and T. Weaver, Astrophys. J. Suppl. 101, 181 (1995). 14. S. Yamada, Astrophys. J. 475, 720 (1997). 15. S. E. Woosley, J. R. Wilson, G. J. Mathews, R. D. Hoffman and B. S. Meyer, Astrophys. J. 433, 229 (1994). 16. K. Otsuki, H. Tagoshi, T. Kajino and S. Wanajo, Astrophys. J. 533, 424 (2000). 17. M. Terasawa, K. Sumiyoshi, T. Kajino, I. Tanihata and G. Mathews, submitted to Astrophys. J., (2000); also M. Terasawa ibid.

B A R Y O N SUPERFLUIDITY I N N E U T R O N STAR CORES T. TAKATSUKA, S. NISHIZAKI Facility of Humanities and Social Sciences, Iwate University, Morioka 020-8550, JAPAN E-mail: [email protected], [email protected] Y. YAMAMOTO Physics Section, Tsuru University, Tsuru 402-005J, E-mail: yamamoto@tsuru. ac.jp

JAPAN

R. TAMAGAKI Kamitakano Maeda-Cho 26-5, Sakyo-ku, Kyoto 606-0097, JAPAN E-mail: [email protected] Whether hyperons admixed in neutron star cores couid be superfluid or not is inves­ tigated by a realistic approach to take account of the information on YY and YN interactions from hypernuclear data. It is found that the A-superfluid is surely realized, though in a restricted density region, and also the E _ - and S~-superfluids have a strong possibility to be realized. A comment is given to the influences of hyperon components on neutron superfluidity.

1

Introduction

Study on baryon matter composed of nucleons (N) and various hyperons (Y) is of great interest in relation to the physics of neutron stars and is a subject renewed by the recent advances in hypernuclear physics. In this paper, we address whether hyperons such as A, E~ and H~ admixed in dense core of neutron stars could be superfluid. The occurence of hyperon superfluidity plays a key role in a rapid cooling scenario of neutron stars, i.e., socalled "hyperon cooling" J as one of nonstandard cooling scenarios expected for some neutron s t a r s . 2 ' 3 In addition, we give a comment on the problem how the superfluidity of neutrons, primarily realized in neutron star cores, is affected by the increase of hyperon contamination. In the investigation, we pay particular attention to our present knowledge of YN and YY interactions based on hypernuclear data. The pairing interaction between hyperons is related directly to YY interaction and the effective mass mY of hyperons, an important parameter in the energy gap equation, is controlled by YN and YY interactions. First we concentrate on the A-superfluidity 4 ' 5 and then make an extended approach to E~ and E~ cases, since the AA interaction is taken reliable due to the check by the data from existing double A hypernuclei, whereas such a check is impossible for E ~ E ~ and H~2~ interactions due to the lack of double hypernuclei. We solve the 15'o gap equation for A by using realistic AA interactions and by taking account of the density (p)- and the hyperon fraction (yy)-dcpcndent rriy which is obtained from the G-matrix calculations for {n + Y} matter with yyThe E~ and H~ cases are discussed in reference to the A case, by using the 1So YY interactions of OBE-type based on the hypothesis of SU(3) invariance.

305

306 2

A-superfluidity

The problem of y-mixing as new constituents in neutron star cores has been dis­ cussed in several literatures 6 ~ 13 . The results show that it begins to occur at not so high-density but the population yY(p)(= PY/P) depends strongly on the manybody approach and the interactions assumed; for example, the threshold densi­ ties are estimated as pt(A) ~ Pt(E~) ~ ^Po and Pt(S~") ~ (3 — 4)po(po = 0.17 nucleons/fm 3 ~ 2.8 x 10 14 g/cc being the nuclear density) which are well below the central density pc ~ (5 — 10)po of typical neutron stars. Thus the effects of y-mixing is important for the superfluid properties of neutron stars as well as the equation of state. Since the hyperon fraction is not so large (t/y(p) ~ (10 — 20)%, a.t most), the Fermi energies of respective hyperons are rather low. Therefore, the pairing interaction responsible for the y-superfluidity should be the one in the 1SQ pair state which is most attractive at low scattering energies. Then the energy gap equation to be treated here is a well-known * So-type 1 4 :

q'2dq' < q> | VYY^SO) I 1 > ±WWW

A(?) = — / n

+ Ml')2,

(1)

Jo e{q) = e(q) - iF ~ (q2 - qF)/2MY, 2

(2)

r drj0(qr)VYY{r;

1

S0)j0(q'r),

(3)

where A(g) is the energy gap function, qp = {iir2 pyy-)1^ is the Fermi momen­ tum of y , and (F = h2q'F/2MY is the Fermi energy, with My being the hyperon mass. For convenience, the effective-rnass approximation, as in Eq.(2), is adopted for the single-particle energy e(q) with the effective-mass MY- The 1 5o-gap equa­ tion (1) with Eqs.(2) and (3) is solved numerically when the 1S'o-pairing interaction Vyy (r; 1 ^o), the y-fraction VY(P) and the effective-mass parameter mY = MY/MY are given. First we treat the A-case, by paying attention to the following points: (i) We choose two OBEP-type VAAOSO) which has been tested for reproducing the binding energy of AA pair in the double A hypernuclei ij^^Be,)^KB). One (abbreviated here to as ND-Soft) is a soft-core version of the Nijmegen-D hard-core potential (ND) l s and constructed so as to fit the i-matrix from the original ND potential. It is expressed as 3

VAA(lS0) = Y,{Vi + * • W } « r < r / w a

(4)

i=l

with Vf = {-21.337, -187.01,10853.3} MeV and Vfs = {0.19321,32.166,2035.1} MeV for A = {1.342,0.777,0.35} fm. The other (Ehime) 1 6 is the one from Ehime group, which is based on the framework of nonet mesons and SU(3) symmetry and has a soft repulsive core and the velocity-dependent short-range interaction. As shown in Fig.l, the ND-Soft potential has a stronger short-range repulsion and a deeper medium-range attraction as compared to the Ehime potential. The choice

307 of these two potentials is expected to cover the present uncertainties in the 1 5b A A interaction. Fig.l compares VAA^SO) with the 15'o NN interaction VNNCSO) from the Reid-Soft-Core potential l r , suggesting that the A- superfluidity is less favourable than that of protons so far investigated 18 .

100

ND-Soft(AA) Ehime (AA) RSC (NN)

V 50 (MeV)

1 i

(fm)

i

i

0

3 i

" 1

Ss

a 1

//

\

iV IV

-50

2

r

1

1

ii

ti 1\ l1 a

/

/

/

// /

1 ' / '

'

/' t

/ '

// '' /// ''' /' // /' / /

\ f '

-100 Figure 1: Comparison of 1So AA and NN potentials.

(ii) Generally, the resulting energy gap is sensitive to the effective mass. So it is important to take account of the p- and ^-dependences of m*A. Our m*A is taken from the G-matrix calculations performed for {n + A}-matter with the A-fraction 2/A and by using the ND potential. The reason to use the YN and YY interactions from ND potenial is that the ND gives a reasonable value of m A compatible with the A- hypernuclei d a t a 1 9 . The resulting m A (p,2M) is large, e.g., m*A ~ (0.80 —> 0.73) for J/A = 0.05 and ~ (0.84 —> 0.77) for J/A = 0.15, in contrast with those of protons; e.g., m A ~ (0.7 —> 0.5) for p = (1 —> 3)po 18- The larger m A suggests that the A-superfluidity is more likely than the p-superfiuidity as far as m A is concerned. (iii) As for the hyperon core model (i.e., ?/A(P))> we take the one from Pandharipande 7 , as a representative case, which increases with p, having a maximum value of about 11% at p ~ 6po and then decreasing gradually. In solving the gap equation at a given p, we use m*A(p) by combining the results of m*A(p, y A ) from (ii) and this

308

ND Soft

Figure 2: Critical temperature Tc of A-superfluidity as a function of density p, calculated for AA pairing interactions in Fig.l. po demotes the nuclear density.

UA(P)- Then the resulting energy gap versus density generates the density-region of neutron star cores where the A-superfluid exists. We show in Fig. 2, the results of critical temerature T c of A-superfluidity given by Tc ~ 0.66A(gi?) x 10 10 K with A in MeV. The superfluidity is realized when Tc exceeds the internal temperature (~ 10 8 K) of neutron stars. We see that the A-superfluidity is surely realized in the density region p ~ (2 — 3.7)p 0 for the NDSoft potential. For the Ehime potential, the aspect is similar but with higher Tc values and a wider density region p ~ (2 — 4.6)po- This comes mainly from the fact that the effect of short-range repulsion in the AA pairing interaction, growing with P A ( = VAP), is relatively small for the Ehime potential due to the weaker repulsive core in VAA(lS0) (Fig. 1). The restricted density region for the existence of A-superfluid, as above, means that for neutron stars with larger M (hence higher central density), a non-superfluid region takes part in their cores, lacking a mechanism necessary to supress "too rapid" hyperon cooling. This suggests that neutron stars compatible with "hyperon cooling" scenario should not be so massive, for example, M < 1.5M 0 , for the neutron star models from BJ-1H equation of state 2 0 . 3

S u p e r f l u i d i t y of E

and E

Now we discuss the possibility of E~ and S~ superfluids. For these cases, we treat the a 5o gap equation similarly to the A case. However, unfortunately our present knowledge of the E ~ E _ and H _ S ~ interactions is less certain than the A A one, due to the lack of experimental information, as mentioned in §1. So we are content to use, in the light of SU(3) symmetry, the 15'o YY interactions from the ND-Soft and the Ehime potentials for which the AA interaction has been tested by hypernuclear

-

i

i

i

i

|

i

(

.

r

21 id0 (K)

io 9 *

ND-Soft Ehime

m Y = i. yY = b°/o

F-G(A)

?'?a

1(f Figure 3: Critical temperature T c of E~ and S~ superfluids in comparison with that of A superfluid, by fixing parameters as mY = 1 and yy = 0.05, for three type of pairing interac­ tions (ND-soft, Ehime and F-G potentials).

data. The 1SQ E ~ E ~ and S~H~ pairing interactions corresponding to the NDSoft potential are constructed quite similarly to the AA case and are given in the form of Eq.(4), with parameters somewhat changed; Vi (7 = c, ss) —> CaV^ for i = l,2 and V^ -> C r K. (7) for i = 3 with Ca = 1.37(0.88) and Cr = 1.85(1.08) for E-E-(S-H-). Results for E~- and S~- superfluidities are shown in Fig.3 by focusing attention on a comparison with the A case for the same mY(= 1.0) and yy{= 5%) parameters. It is observed that for the Ehime potential (dashed lines) the Tc both of E~ and H~ are much larger than that of A. For the ND-Soft potential (solid lines), Tc(E~) is in a similar situation as the Ehime case (T C (E") > > TC(A)), but TC(H~) is somewhat smaller than TC(A). The latter situation, however, is changed as TC(E~) > Tc(A) when a, realistic my in medium is taken into account, since our G-matrix calculations with the ND potential suggests that m£,- and m„_ are remarkably larger than m*A; m^ > 1 and m~_ > 1 whereas m*A ~ 0.8. To summarize, we can expect that both of the E~- and H~- superfluids would be realized with the Tc comparable to or larger than that of A-superfluid. In Fig.3, we also add the results of T C (E~) and T C (S~) from another version of OBE YY potential (dotted lines) proposed very recently by Funabashi-Gifu group 2 1 , which confirms the results from the ND-Soft and Ehime potentials.

310 4

Effect of Y - m i x i n g o n s u p e r f l u i d i t y of n e u t r o n s

It has been shown that neutrons (n), a dominant component of neutron star cores (hence with high Fermi energy), become a superfluid of 3 P 2 -type (instead of x Sotype) at densities p > po due to the attractive effect of the 3 P 2 nn interaction which is most attractive at high scattering energies 14 . As the density goes higher (p > (3 — 4)po), however, this 3 P 2 n-superfiuidity becomes unlikely, because of the increasing short-mage effects in the 3 P 2 pairing interaction and the decreasing m*n. Here it is worth noting that this aspect has been obtained by neglecting the mixing of hyperons as new components. In this section, we give a comment as to the effect of y-mixing on the 3 P 2 n-superfluidity, that is, the effects coming from the decreasing yn (e.g. yn = 1 —> 0.7) with increasing yy in the dense core region (P 2 3po). The increase of the Y-population (hence the decrease of y„) has two effects. One is to lower the ep of neutrons at a given density and thereby to postpone the growth of a short-range repulsion in the pairing interaction, as compared with the case neglecting the Y-mixing. The other is to change m*n{p,yn) by a contribution from riY interaction and by a lowered qF- Clearly the former effect acts for the persistence of n-superfiuid at higher densities (p > (3 — 4)po). But the situation is defermind as a result of the combined two effects. For transparency, we simplify the problem as a comparison of Tc(n) between {n + A}-matter with yn = 0.7(J/A = 1 — yn = 0.3) and pure n-matter (yn = 1). We solve the 3 P 2 gap equation including the tensor coupling with the 3 F 2 state by adopting the OPEG sO — 1 potential 2 2 for a realistic nn interaction and by using the m*n(p,yn — 0.7) extracted from the G-matrix calculations with the ND potential. Results are shown in Fig.4. We see that the ep(n) is lowered as in Fig.4a but the m*n is made smaller as in Fig.4b, compared with those in pure nmatter. As a result of the combined effect of these, we have the Tc(n) in Fig.4c. By looking at the results at high densitites (p > 3po) where actually the Y(A)-mixing gets serious, we observe that the lowered ep(n) indeed acts for the increase of Tc(n) (a dotted line) but the inclusion of a reduced m*n compensates this advantage. It is remarked that a net effect of Y- mixing does not necessarily assist the realization of n-superfluidity at high densitites (p > 3po). If we use m* from NF (Nijmegen F) potential, the resulting Tc (n) gets still smaller, suggesting that the Y-mixing acts against the existence of n-superfluid at these high densities. 5

Concluding remarks

We have shown a strong possibility that hyperons such as A, E " and H~ in a hyperon-mixed core of neutron stars could be in a superfluid state, by paying at­ tention to the use of YY and YN interactions compatible with hypernuclear data. This result suggests that the idea of "hyperon cooling" scenario can be one of the candidates to account for an unusually low surface temperature observed for some neutron stars. The increase of hyperon components makes smaller the density (hence the Fermi energy) of neutrons, a dominant conponent, compared to the case without hyper-

311

150 100 (MeV) 50-

0.9h

0.7 _L

1

_L

-_L

2 p/o

3 (b)

n

m rn 0.8 0.7 0.6

2p,P

3

10

(k)

10°

J

2

I

9l?a

hl,.iii.iiii/lli\lii.,.,i.

3

Figure 4: (a) Comparison of neutron Fermi energy ep versus p between neutron fraction yn = 1 and 0.7 cases, (b) Neutron effective-mass m£ versus p compared between yn = 1 and 0.7 cases, calculated for Nijmegen D type (ND) and F type (NF) interactions, (c) Critical temperature Tc of neutron 3P2 superfluid for yn = 1 (a solid line) and yn = 0.7 (dashed lines). A dotted line illustrates the case where mjj for yn = 1 are used only to see the effect of lowered ep (yn = 1 —» 0.7).

312

ons, affecting the pairing attraction and the effective mass of neutrons. We have investigated this influence for a simplified system composed of n and A. It is found that the increase of A component does not necessarily work for raising the critical temperature of n-superfiuid at higher densities (p > 3po)-

Acknowledgement The authors wish to thank M. Wada for providing us with Funabashi-Gifu potential before publication. This work is indebted to a Grant-in-Aid for Scientific Research from Ministry of Education, Science, Sports and Culture (No. 11640245).

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Ferromagnetism of quark liquid and magnetars

Department

of Physics, E-mail:

Toshitaka Tatsumi Kyoto University, Kyoto 606-8502, [email protected]

Japan

Spontaneous magnetization of quark liquid is examined on the analogy with that in electron gas. It is pointed out that quark liquid has potential to be ferromagnetic at rather low densities, around nuclear saturation density. Some comments are given as for implications on magnetars.

1

Introduction

Recently a new type of neutron stars with extraordinary magnetic field, usually called magnetars, has attracted much attention in connection with pulsars associated with soft-gamma-ray repeaters (SGR) and anomalous X-ray pulsars (AXP). There have been known several magnetar candidates such as SGR 1806-20 and SGR 1900+14 1. Various analysis including the P - P curve have indicated an intense magnetic field of O(10 14-1,r> ) G, while ordinary radio pulsars have a magnetic field of O ( 1 0 1 2 _ u ) G . The origin of the strong magnetic field in compact stars, especially neutron stars, has been an open problem. Recent discoveiy of magnetars seems to renew this problem. Conservation of the magnetic flux during the collapse of a main sequence star has been a naive idea to understand the magnetic field in neutron stars 2 . Then the strength B should be proportional to R~2, where R is a radius of a star; for example, the sun, a typical main sequence star, has a magnetic field of O(10'j)G with the radius R ~ 10 1 0 - 1 1 cm. By decreasing the radius to 106cm for neutron stars B = O(10 12 )G, which is consistent with observations for radio pulsars. However, if this argument is extrapolated to explain the magnetic field for magnetars, we are lead to a contradiction: their radius should be O(104)cni to get an increase in B by a factor of ~ 10 12 , which is much less than the Schwartzschild radius of neutron stars with the canonical mass M = 1.4M 0 , RSc.h = IGM/c2 = 4 x 105cm. When we compare the energy scales for systems such as atomic system ( e - ) , nucleon system (p) and quark system (q), we can get a hint about the origin of the magnetic field. In Table 1. we list the interaction energy, Pint = ViB, of the magnetic field B = 1015G and each constituent with the Dirac magnetic moment, m = eiti/2miC. We also Ust a typical energy scale EtyP for each system. Then we can see that Etyp Eint for the nucleon and the quark systems; that is, the strength of O(10 l s )G is very large for the former system with the elec-

313

314

7(i;[MeV] Eint[UeV} Etyp

f Ol 5- 6 O(KeV)

p W 2.5 x l O " 3 > O(MeV)

q TTOO 2.5 x 10~ 2 - 2.5 > O(MeV)

Table 1.

tromagnetic: interaction, while it is not large for t h e latter systems with the strong interaction. Hence it m a y be conceivable t h a t the strong interaction should easily produce the magnetic field of the above magnitude. Since there is a bulk hadronic matter beyond nuclear saturation density (?io ~ 0.16fm~ 3 ) inside neutron stars, it should be interesting to consider the hadronic origin of the magnetic field; ferromagnetism or spin-polarization of hadronic m a t t e r may give such magnetic field. In 70's, j u s t after the first discovery of pulsars, there have been done many works about the possibility of the ferromagnetic transition in dense neutron matter, using G—matrix calculations or variations! calculations with the real­ istic nuclear forces. Through these works there seems to be a consensus t h a t ferromagnetic phase, if it exists, should be at very high densities, and there is no transition at rather low densities relevant to neutron stars i . We consider here the possibility of ferromagnetism of quark liquid interact­ ing with the one-gluon-exchange (OGE) i n t e r a c t i o n 4 . One believes t h a t there are deconfinement transition and chiral symmetry restoration at finite baryon density, while their critical densities have not been fixed yet. One interesting suggestion is t h a t three-flavor symmetric quark m a t t e r (strange m a t t e r ) may be the true ground state of QCD at finite baryon d e n s i t y 5 ' 6 . If this is the case, quark stars (strange quark stars), can exist in a different branch from the neutron-star branch in the mass-radius p l a n e 7 . Usually one implicitly assumes t h a t the ground state of quark m a t t e r is unpolarized. We examine here the possibility of polarization of quark m a t t e r . We shall see our results should give an origin of the strong magnetic field for magnetars in the context of strange quark-star scenario. 2 2.1

S p o n t a n e o u s m a g n e t i z a t i o n of q u a r k l i q u i d Rp.lativistic

formulation,

Quark liquid should be totally color singlet (neutral), which means t h a t only the exchange interaction between quarks is relevant there. This may remind us of electron system with the Coulomb force in a neutralizing positive charge

315

background. In 1929 Block first suggested a possibility of ferromagnetism of electron system 8 . He lias shown that there is a trade oif between the kinetic and the exchange energies as a function of a polarization parameter, the latter of which favors the spin alignment due to a quantum effect; electrons with the same spin orientation can effectively avoid the Coulomb repulsion due to the Pauli exclusion principle. When the energy gain clue to tke spin alignment dominate over the increase in the kinetic energy at some density, the unpolarized electron gas suddenly turns into the completely polarized state. In the following we discuss the possibility of ferromagnetism of quark liquid on the analogy with electron gas (Fig. 1).

k

Figure 1: Exchange interactions for electrons with the Coulomb force (left) and quarks with OGE interaction (right).

It is to be noted that there is one big difference between them; quarks should be treated in a relativistic way. The concept of the spin orientation is not well defined in relativistic theories, while each quark has two polarization degrees of freedom. Here we define the spin-up and -down states in tke rest frame of each quark. Then the projector onto states of definite polarization is given by P(«) = (1 + ^(f)/2 with the 4-pseudovector a, k(c ■ k)

a° =

c + mq(Ek+mqy

C-k

(1)

in a

for a quark moving with the momentum k = (Ek, k) 9 . Tke 4-pseudovector a is reduced into the axial vector £ (|£| = 1) in the rest frame, which is twice the mean spin vector in the rest frame. Hence a or £ can specify the polarized state. The exchange interaction between two quarks with momenta k and q (Fig. 1) is written as 2 „2 (f m„ / k C qc'-9mqEk

m„ [2m EVa "

k

q

m\a ■

1 b] (k - q)*

(2)

316

t t t t t Figure 2: Heisenberg ferromagnet in the coordinate space (left) and quark ferromegnet in the phase space (right).

where the 4-pseudovector b is given by the same form as in Eq. (1) for the momentum q. The exchange energy is then given by the integration of the interaction (2) over the two Fermi seas a for the spin-up and -down states; eventually, it consists of two contributions, ^x = e™ n _ / H p + 4!!p-

(3)

The first one arises from the interaction between quarks with the same po­ larization, while the second one with the opposite polarization. The non-flip contribution is the similar one as in electron gas, while the flip contribution is a genuine relativistic effect and absent in electron gas. We shall see that this relativistic effect leads to a novel mechanism of ferroiiiagnetism of quark liquid. 2.2

Symmetry consideration of ferromagnetic phase

Usual Heisenberg model describes the spin-spin interaction between adjacent spins localized at lattice points; that is, the Heisenberg ferromagnet is the spin alignment in coordinate space. On the other hand, the concept of spin alignment in quark liquid requires an extension to the phase space because of the coupling of spin with momentum. Since the spatial part of the quark wave functions take the plane wave, the spin orientation is obviously uniform in coordinate space, once £ is given. On the other hand, the spin does not necessarily take the same orientation in momentum space: generally £ should be momentum dependent (see Fig. 2). The most favorite configuration in momentum space may be determined by an energetic consideration, while it seems to be a difficult task. We consider here only a naive case, where the spin orientation is uniform even in the phase space. This is a direct analog of the nonrelativistic version. a

W e , here, don't consider any deformation of Fermi spheres for simplicity, while they may be deformed in a realistic case due to the momentum dependent interaction.

317

Anyway, the ferromagnetic phase is a spontaneously symmetry broken state with respect to the rotational symmetry in coordinate space: the order parameter is the mean value of £, {£), and symmetry is broken from G = 0(3) to H = 0(2) once (£) takes a special orientation. 3

Examples

We show some results about the total energy of quark liquid, etot — (kin + c?.x, by adding the kinetic term €*,,•„. Since gluons have not the flavor quantum numbers, we can consider one flavor quark matter without loss of generality. Then quark number density directly corresponds to baiyon number density, if we assume the three flavor symmetric quark matter as mentioned in §1. There are two QCD parameters in our theory: the quark mass mq and the quark-gluon coupling constant ac. These values are not well determined so far. In particular, the concept of quark mass involves subtle issues; it depends on the current or constituent quark picture and may be also related to the existence of chiral phase transition 10 . Here we allow some range for these parameters and take, for example, a set, mq = 300MeV for strange quark and ac = 2.2, given by the MIT bag model 11 . In Fig. 3 two results are presented as functions of the polarization parameter p defined by the difference of the number of the spin-up and -down quarks, nf. — n~ — pnq. The results clearly show the first order phase transition, while it is of second order in the Heisenberg model. The critical density is around nq ~ 0.16fm~'5 in this case, which corresponds to ?io f° r flavor symmetric quark matter. Note that there is a metastable ferromagnetic state (the local minimum) even above the critical density. Magnetic properties of quark liquid are characterized by three quantities, fie,x and »/; fie = etot{p = 1) — etot(jj — 0), which is a measure for ferromagnetism to appear in the ground state. For small p -C 1, etot - e,.ot(p = 0) = x " V + 0(p4).

(4)

X is proportional to the magnetic susceptibility. In our case it is less relevant since the phase transition is of first order. Finally, // = detot/dp | P =i, which is a measure for metastability to to exist. In Fig. 4 we present a phase diagram in the mq — ac plane for nq = 0.3fm - ! , which corresponds to about twice IIQ for flavor symmetric quark matter. The region above the solid line shows the ferromagnetic phase and that bounded by the dashed and dash-dotted lines indicates the existence of the matastable state. For heavy quarks, which may correspond to the current s quarks or the constituent quarks before chiral symmetry restoration, the ferromagnetic

318 n a =0.3fm J m.=300 MeV, ^.=2.2 242 240

n„=0.2 (fm'3

238

?
5

236

c" ^»-

234

vT

232

nq=0.1 (fm'3)

230

0

0

0.1 0.2 03 0.4 0.5 0.6 0.7 0.8 0.9 1

Figure 3: Total energy of quark liquid as a function of the polarization parameter for densities nq = 0.1,0.2fm - 3 .

50 100 150 200 250 300 350 400 450 500

mq (MeV)

P

Figure 4: Phase diagram in the mass (mq)- the coupling constant (o:(.) plane. Sf in the nonrel­ ativistic calculation is depicted for comparison (the dotted line) .

state is favored for small coupling constant due to the same mechanism as in electron gas. The ferromagnetic state is favored again for light quarks, which may correspond to the current u, d quarks, while the nonrelativistic calculation never show such tendency. Hence this is due to a genuine relativistic effect, where the spin-flip interaction plays an essential role. 4

S t r a n g e q u a r k star as m a g n e t a r

We have seen that quark matter has a potential to be ferromagnetic at rather low densities. Here we consider some implications on astrophysics. Since the idea that nucleons are made of quarks has been confirmed, one has expected the existence of quark stars as a third branch of compact stars next to the neutron-star branch; when pressure or density is increased enough, there should occur the deconnnement transition and matter consists of quarks rather than nucleons. This naive expectation has been shown to be wrong; if the deconfinement transition occurs and quarks are liberated beyond the maximum central density of neutron stars (several times of n0), they should behave like relativistic and almost free particles due to the asymptotic freedom of QCD. Thereby the adiabatic index (-fad) of quark matter becomes around 4/3. On the other hand, the criteria for the gravitationally stable stars reads lad > 4/3 + KGM/R, where the second term means the general relativistic

319

correction, ~ 0.4 for M ~ 1.4A/(., and R ~ IOK111. Hence, the quark-star branch subsequent to that of neutron stars is impossible. If quark matter exists, it might occupy only the small portion of the core of neutron stars. However, there is an alternative idea about quark matter and quark stars. As first indicated by Chin and Kerman 5 , a large contamination of strange quarks are favorable for quark matter at low baryon density around 0.26fm _! , which is about 1.5 /to- Their calculation shows that the energy per baryon of quark matter is larger than that of nucleon, while less than A particle. Subsequently, Witten and Farhi and Jaffe () have pointed out the possibility that the almost flavor symmetric quark matter (strange matter) is the ground state of QCD at finite density within the reasonable range of QCD parameters. Using the idea of strange matter some people suggested that quark stars with strange matter (strange quark stars) may be possible 7 . Since the EOS for strange matter shows the saturation property around ?IQ, strange quark stars can have any small radius and mass. Thereby, the quark-star branch can be clearly distinguished from that of neutron stars. If a ferromagnetic quark liquid exists stably or metastably around or above nuclear saturation density, it has some implications on the properties of strange quark stars and strange quark nuggets: they should be magnetized in a macro­ scopic scale. For quark stars with the quark core of rq, simply assuming the dipolar magnetic field, we can estimate its strength at the surface R ~ lOKm, _ Brnax

87T / 7 " „ \ 3 = y (^J /',;«,/,

(5)

with the quark magnetic moment \iq. It amounts to order of O(10 1 5 - 1 7 )G for '*,/ ~ O(R) and /t(/ = O(0.1)fm _i , which should be large enough for magnetars. A sketch of a strange quark star is presented in Fig 5. 5

Summary and Concluding remarks

We have seen that the ferromagnetic phase is realized at low densities and the metastable state is possible up to rather high densities for a reasonable range of the QCD parameters. We have found that ferromagnetic instability is feasible not only in the massive quark system but also in the light quark system: the spin-nonflip contribution is dominant in the nonrelativistic case as in electron gas, while a novel mechanism appears as a result of the large spin-flip contribution in the relativistic case. If a ferromagnetic quark liquid exists stably or metastably around or above nuclear saturation density, strange stars may have a strong magnetic field,

320

Figure 5: A model of strange quark star with M ~ IAM(.) and R ~ lOKiu. Almost all the portion is occupied by strange matter and a small vacuum gap may separate the quark core from the outer crust, which is composed of usual solid below the neutron-drip density.

which strength is estimated to be strong enough for magnetars. Thereby it might be interesting to model SGR or AXP using our idea. Our calculation is basically a perturbative one and the Fermi sea remains in a spherical shape. However, if we want to get more insight about the ferro­ magnetic phase, we must solve the Hartree-Fock equation and thereby derive a self-consistent mean-field for quark liquid. Moreover, we need to examine the long range correlation among quarks by looking into the ring diagrams, which has been known to be important in the calculation of the susceptibility of electron gas. Recently, there have been done many works about the color superconduc­ tivity of quark matter. The order of the energy gap amounts to O(100)MeV, while the energy gain per particle is rather small and several MeV around no , which should be the same order of magnitude as that for the ferromagnetism 12 . Hence it may be interesting to explore the phase diagram for ferromagnetic phase and superconducting phase. References 1. C. Kouveliotou et al., Nature 393, 235 (1998). K. Hurley et al., Astrophys. J. 510, L l l l (1999). 2. G. Chanmugam, Annu. Rev. Astron. Astrophys. 30, 143 (1992).

321

3. V.R. Pandharipande, V.K. Garde and J.K. Srivastava, Phys. Lett. B 38, 485 (1972). 4. T. Tatsumi, hep-ph/9910470 (RUNS 1611), nucl-th/0002014 (RUNS 1636). 5. S.A. Chin and A.K. Kerman, Phys. Rev. Lett. 43, 1292 (1979). E. Witten, Phys. Rev. D 30, 272 (1984). 6. E. Farhi and R.L. Jaffe, Phys. Rev. D 30, 2379 (1984). 7. for review articles, K.S. Cheng, Z.G. Dai and T. Lu, Int. J. Phys. 7, 139 (1998). J. Madsen, astro-ph/'9809032. 8. F. Bloch, Z. Phys. 57, 545 (1929). 9. V.B. Berestetsii, E.M. Lifshitz and L.P. Pitaevsii, Relativistic Quantum T7&eon/(Pergamoii Press, 1971). 10. A. Manohar and H. Georgi, Nucl. Phys.B 234, 189 (1984). 11. T. DeGrand et al., Phys. Rev. D 12, 2060 (1975). 12. D. Bailin and A. Love, Phys. Rep. 107, 325 (1984). J. Berges and K. Rajagopal, Nucl. Phys. B 538, 215 (1999).

Kaonic Nuclei and Kaon Condensation in Neutron Stars Tadafumi Kishimoto

a

"•Department, of Physics, Osaka University, Toyonaka, Osaka, 560-0043, Japan It is theoretically posulated that the kaon condensation is happening in dense nuclear matter, especially neutron stars. However, little evidence is obtained from experiments. Study of the kaonic nuclei can answer the question as to the existence of kaon condensation in neutron stars. We show that the kaonic nuclei can be produced by the (K~,p) and (K~,n) reactions with cross sections experimentally measurable. 1. Introduction The kaon-nucleon interaction at low energy region is particularly important nowadays because of the current interrest in the dense nuclear matter in neutron stars where the so-called kaon condensed state may be achieved by a strong attractive interaction [1,2]. The existence of the kaon condensed state softens the equation of state (EOS) of nuclear matter in the neutron stars and reduces their calculated maximum mass above which the neutron stars become black holes. The observed mass distribution of the neutron stars agrees with the calculation with this softening [3]. The introduction of strange hyperons in the EOS gives a similar softening. Strangeness is essential in both cases although quantitative understanding of the EOS requires a knowledge of both the kaon-nucleon and hyperon-nucleon interactions at high density [4]. The kaon-nucleon interaction, in particular, is known quite poorly experimentally. Recently, effective kaon mass in dense nuclear matter has been derived by the Chiral SU(3) effective Lagrangian including KN, 7rE, TTA systems[5]. Such a theoretical model reproduces well the A(1405) as a KN bound state due to the strong KN attractive interaction [5,6]. The KN interaction makes the K~ feel a strong attractive potential in nuclei which consequently leads to the existence of deeply bound kaonic nuclei. The A(1405), however, can also be interpreted as a three-quark state with £ = 1 excitation. In this case no attractive KN interaction is relevant and the deeply bound kaonic nuclei do not necessary exist. 2. KN Interaction Experimental data of K~ optical potential mostly come from kaonic atoms. The shifts and widths of atomic levels affected by the strong interaction were reproduced by intro­ ducing an appropriate optical potential in addition to the Coulomb interaction. Recent extensive analysis of kaonic X-ray data concludes that the potential is strongly attractive [7]. The derived depth is around -200 MeV which opens a possibility of kaon condensation

322

323 at around three times normal nuclear density. Derivation of the optical potential from the kaonic atom data is, however, subtle since the atomic state is sensitive only to the phase shift of K~ wave function at the nuclear surface. The phase shift alone cannot determine the depth of the potential since the K~ wave function has an ambiguity in number of nodes in the nucleus especially when the potential depth is quite deep. The strong imaginary part of the potential further obscures the nodes. Earlier studies with a different treatment of the nuclear surface gave much shallower potentials of —80 to —90 MeV [7] which tend to exclude the kaon condensation in the neutron stars. Heavy ion reactions have been studied to derive the K~ optical potential [8]. En­ hanced K~ production in the reactions suggests a strong attractive interaction although quantitative argument requires understanding of details of the reaction mechanism [10]. The KN interaction has been derived from kaon scattering experiments. However, the available low-energy data are insufficient for unique multichannel analysis and the existence of A(1405) makes the extrapolation of the amplitude below the threshold com­ plicated [9]. Recent theoretical calculations on the kaon interaction in nuclei predict an attractive interaction although they are still controversial quantitatively and existence of kaon condensation in neutron stars is as yet inconclusive [11,12]. 3. Kaon nucleus potential If .K'-nuclear potential is as attractive as derived from the kaonic atom stuides suggest [7], then deeply-bound kaonic nuclei should exist. The observation of kaonic nuclei gives directly the K~ optical potential and gives decisive information on the existence of kaon condensation in neutron stars. We show the general properties of the kaonic nuclei and that the [K~, N) reaction can excite them with cross section experimentally measurable. Energies and widths of kaonic nuclei are calculated with the potential given by the kaonic atom data. For the analysis of mesonic atoms the Klein-Gordon equation is usually used [7]. Here we use the Schrodinger equation with harmonic oscillator potential. It is a crude approximation although it is good enough for the present purpose. We are interested in gross structure of levels and an order-of-magnitude estimate of the cross section for the deeply bound state. For the moment we take the potential depth -200 MeV given by kaonic atom. It is roughly four times deeper than that for nucleon and the kaon mass is about half of that of a nucleon. Thus the major shell spacing (ftwjf) is %/E times the 40A""1/3 frequently used for nucleon. Since the kaon has no spin, no spin dependent splitting has to be considered. The huiK is roughly 40 MeV, for instance, for the kaonic ^Si nucleus. The Is state appears at around -140 {\TIUJK — 200) MeV bound, which is the deepest bound state ever observed in nuclear physics. If the potential shape is closer to the square-well it appears deeper. In order to observe the state its width has to be reasonably narrow. The width is given by the imaginary part of the potential, which decreases for the deeply bound state and is around 10 MeV [5,7], The narrow width is understandable since dominant conversion channels like KN —> 7rE or KN —> 7rA are energetically almost closed for such a deeply-bound state. Kaon absorption by two nucleons (KNN —> YN) gives little width since two nucleons have to participate to the reaction. Even though the width is twice wider the Is state should be seen well separated since the next excited state (lp) is

324 expected to appear 40 MeV higher. 4. (K~,N)

reaction to excite kaonic nuclei

The (K~,N) reaction where a nucleon (N) is either a proton or a neutron is shown schematically in figure 1. The nucleon is knocked out in the forward direction leaving a kaon scattered backward in the vertex where the K + N —>■ K + N takes place. This reaction can thus provide a virtual K~ or K° beam which excites kaonic nuclei. This feature is quite different from other strangeness transfer reactions like (K~,ir), (TT±, K+) and (7, K+) extensively used so far. They primarily produce hyperons and thus are sensitive to states mostly composed of a hyperon and a nucleus.

,A-1

Figure 1 Diagram for the formation of kaonic nuclei via the (K~,N) reaction. The kaon, the nu­ cleon, and the nucleus are denoted by the dashed, thin solid and multiple lines, re­ spectively. The kaonic nucleus is denoted by the multiple lines with the dashed line.

The momentum transfer, which characterizes the reaction, is shown in figure 2. It depends on the binding energy of a kaon. We are interested in states well bound in a nucleus (BE = 100 ~150 MeV). The momentum transfer for the states is fairly large (q = 0.3 ~ 0.4 GeV/c) and depends little on the incident kaon momentum for PK = 0.5 ~ 1.5 GeV/c, where intense kaon beams are available. Therefore one can choose the incident momentum for the convenience of an experiment. It is a little beyond the Fermi momentum and the reaction has characteristics similar to the (ir+, K+) reaction for hypernuclear production where so-called stretched states are preferentially excited [13]. Figure 2 The momentum transfer of the (K~,N) reaction at 0 degrees is shown for four reactions. Here binding energy of kaonic nucleus ^Mg is taken to be 150 MeV.

p(K,p)K- d(K\n)A(1405) "Si(K\p)"Al+K-"SidCpJ^g -

> £L 300

1000

PK (MeV/c)

1200

1400

1600

325 Recently deeply bound -K~ atoms were observed by the (d,3 He) reaction [14]. A small momentum transfer (~ 60MeV/c) was vital to excite the atomic states which were typi­ cally characterized by the size of the atomic orbits. If one wishes to excite kaonic atoms, a momentum transfer less than 100 MeV/c is desirable. It is achieved by kaon beams less than 0.4 GeV/c where available beam intensity is very small. The repulsive nature of the 7r-nucleus interaction allows no nuclear state although the strong attractive .RT-nucleus potential makes kaonic nuclei exist. The (K~,N) reaction can excite the deeply bound kaonic nuclei with large cross section in spite of the large momentum transfer of the reac­ tion. For the excitation of nuclear states the momentum transfer is typically characterized by the Fermi momentum. The (K~, N) reaction on deuteron is the simplest reaction by which one can study the KN component of excited hyperons. The d(K~,p) reaction excites K~n states which can only have 1 = 1. On the other hand d(K~,n) reaction excites a K~p state which can have either / = 1 or / = 0. Cross sections to the excited hyperons depend on their KN component. For instance, the well known A(1405 MeV) should be abundantly excited by the [K~,n) reaction if it is a KN bound state with I = 0 as usually believed. The d(K~,p) reaction, in particular, gives information on the K~n interaction below the threshold, which plays decisive role on the kaon condensation in the neutron stars. 5. Formalism We adopt here the distorted wave impulse approximation (DWIA) to evaluate the cross section. The DWIA calculation requires (a) distorted waves for entrance and exit channels, (b) two body transition amplitudes for the elementary (K~,N) process, and (c) a form factor given by initial nuclear and kaonic-nuclear wave functions. Relevant formulas for the calculation can be found elsewhere [13]. The differential cross section in the laboratory system for the formation of kaonic nu­ cleus is given by ,

da

/ ,

\K-N^NK-

Ida \

dn = {dn)Lfl.

_.

,„.

N

(1)

°"-

It is given by the two body laboratory cross section multiplied by the so-called effective nucleon number (Neff). We first use the plane wave approximation to evaluate N^. At 0 degrees, where only non-spin flip amplitude is relevant, N^Jf is given by NlJ} = (2 J + 1) (2jN + 1) (2EK + l)(£«

5

f ) F{q).

(2)

In this equation we assumed that a nucleon in a jn orbit is knocked out and a kaon enters in an £K orbit making transition from 0 + closed shell target to a spin J state. Here the form factor F(q) is given by the initial nucleon and final kaon wave functions as F(q) = (Jr2drRK(r)RN(r)jL(qr))

,

where L = J ± | is the transferred angular momentum.

(3)

326 For an oscillator potential of radius parameter b, the radial wave function is

Mr) = c<(r/6) V ' ^

(4) +2

3 /

1 2

for nodeless states, where Q = [2' /b y Tr(2l +1)!!] / . In the present case it is enough to consider natural parity stretched states with L = EN+£K since the transferred momentum q is larger than the Fermi momentum. The form factor (Eq. 4) is well known for the harmonic oscillator wave function [13] as (2Z)*e-» W

[T(L + 3 / 2 ) ] ' 2

[(2L + l ) ! ! ] F ( ^ + 3 / 2 ) r ( ^ + 3/2)

{

>

2

with Z = (bq) /2, where the radius parameter b = ~ has to be replaced by 2 _ 1

b^~^

1 +

(6;

bj

to account for the different radius parameters for the nucleon (&#) and the kaon (6^) where l/b2K = \/8/b2N. NlJf is further reduced by the distortion of incoming and outgoing waves as Neff = NlJfDetk

.

(7)

The distortion Deik is estimated by the eikonal absorption where the imaginary parts of the K~ and proton optical potentials are given by their total cross sections with nucleons. At PK= 1 GeV/c, total cross sections of if~-nucleon and p-nucleon are almost the same and we take both to be 40 mb. The small radius parameter b indicates larger cross sections through the high momentum component; we thus evaluated Neff for bx = &/v also as the smallest value. The cross section of the elementary reaction was given by the phase shift analysis of available data[15]. Here we need to consider only the non-spin flip amplitude (/) as explained above. Since the kaon and nucleon are isospin \ particles there are 1=0 (/°) and 1=1 (Z1) amplitudes. The amplitudes for elastic and charge exchange scattering are represented by appropriate linear combinations of the isospin amplitudes as //r-mx-n = / l

fK-V^K-V=\{f

)

+ f),

/*-,-#>„ = \UX - f°) ■

(8) (9) (io)

The cm. (center-of-mass) differential cross section of the three reactions at 180° are shown in figure 3 as a function of incident kaon momentum. The cross sections depend on the incident momentum. For instance, the K~p —> K~p reaction has a peak at around 1 GeV/c. We thus take 1 GeV/c for the incident kaon momentum. Since the target nucleon is moving in a nucleus, Fermi averaging has to be made for the two body cross section which smears the fine momentum dependence. The c m . cross section is reduced by 20 to 30 % depending on models for this averaging. We take ~1.3 mb/sr as the c m . cross section at 1 GeV/c.

327 Figure 3 The cm. differential cross sections of the three reac­ tions are shown as a func­ tion of incident kaon lab momentum.

200

800

1000

1200

1400

PK (MeV/c) Here we consider 1=0 symmetric nuclei as targets. The (K~,p) reaction produces only an 1=1 state; on the other hand the (K~,n) reaction can produce both 1=0 and 1 states. The KN system is strongly attractive in the 1=0 channel though not so much in the 1=1 channel. The kaon-nucleus potential is an average of both channels and thus depends little on the total isospin of kaonic nuclei. Consequently we expect that the 1=0 state produced by the (K~, n) reaction appears at nearly the same excitation energy. The elementary cross section for the (K~,n) reaction in eq (1) becomes the sum of the K~n —>■ K~n and K~p —> K°n cross sections. The incoherent sum of the two cross sections may not be inappropriate for the evaluation since the K~ and K° mass difference is considered to be large on a nuclear physics scale. 6. Cross section and feasibilty of t h e experiment The cross section for the kaonic nuclear Is states are shown in table 1. The (7r+, K+) reaction for the hypernuclear production shows distinct peaks corresponding to series of major shell orbits especially for target nuclei with j n = ln + 1/2 orbit closed. We thus take 12C and 28Si for the present study. Table 1 Calculated laboratory differential nucleus da/dQ jj,b/sT Deik cross sections of the Is states excited Ktf 12 Q 0.055~0.26 0.25 100~490 by the (K~,p) reactions at P # = l 28 35~180 GeV/c for the 12C and 28Si targets. Si 0.029~0.15 0.16 Range of values corresponds to the b parameter (see text) The calculated cross sections turn out to be quite large which can compensate for a low intensity kaon beam. The large cross section comes from the large cross section of the elastic K + N —> K + N reaction and from the transformation of cm. system to laboratory system. Feasibility of the experiment depends on backgrounds. Dominant backgrounds are nucleons from knock-out reactions, where kaons are scattered backward by the quasifree

328 process. Since the nucleons associated with the deeply-bound kaonic nuclei are much more energetic, the knock-out reactions will not be a problem. Kaon absorption by two nucleons in nuclei can generate energetic nucleons. The process has to involve another nucleon in addition to the (K~,N) reaction. Thus one expects the process gives smaller cross section than that of the (K~, N) reaction. The process can be interpreted as a spreading width of the kaonic nuclei. A A produced in the forward direction by the quasifree (K~,IT) reaction provides an energetic nucleon. It would not be a serious background since no peak structure is ex­ pected. It is shown that the (K~,p) and (K~,n) reactions can be used for the study of the kaonic nuclei. A study of the reaction requires intense low energy kaon beam for which the alternating-gradient synchrotron (AGS) of BNL and probably the proton synchrotron (PS) of KEK are particularly suitable. The beam momentum can be chosen by considering the cross section, beam intensity and momentum resolution of spectrometer. There are beam lines which provide K~ beam 0.5~2 GeV/c at BNL and KEK. The relatively broad width (~10 MeV) and simple structure of the state need spectrometers of only modest momentum resolution but wide momentum acceptance. We demonstrated that the (K~,p) and (K~,n) reaction can be used to obtain direct information on the KN interaction in nuclear matter. The calculation employed here is rather crude although it is based on well-known general concepts in nuclear physics. The anther is grateful to discussions with Professors A. Gal, Y. Akaishi, T. Tatsumi, and H. Toki. The anther thanks Dr. R. E. Chrien for careful reading of this manuscript. REFERENCES 1. D. B. Kaplan and A. E. Nelson, Phys. Lett., B175 (1986) 57 2. G. E. Brown, Nucl Phys A574 (1994)217, G. E. Brown, M. Rho, Phys. Rep. 269 (1996) 333, C. H. Lee, Phys. Rep. 275 (1996) 255 3. M. Prakash and J.M. Lattimer, Nucl.Phys. A639 (1998)433 4. P. J. Ellis, R. Knorren, M. Prakash. Phys.Lett.B349 (1995)11 5. T. Waas, N. Kaiser and W. Weise, Phys. Lett. B379 (1996) 34 6. P. B. Siegel and W. Weise, Phys. Rev. C, 38 (1998)221 7. C.J. Batty, E. Friedman, A. Gal. Physics Report 287 (1997) 385 8. R. Barth at al., Phys. Rev. Lett. 78 4027 (1997) 9. A. D. Martin, Nucl. Phys. B179 (1981) 33 10. G.Q. Li, C.H. Lee, and G.E. Brown, Phys.Rev.Lett.79 5214 (1997); G.Q. Li, G.E. Brown, C.H. Lee, Phys.Rev.Lett.81 2177 (1998) 11. A. Ramos and E. Oset, in Proceedings of XV Int. Conf. on Particles and Nuclei, Uppsala, Sweden, 1999 [Nucl. Phys. A (to be published)] 12. M. Lutz, Phys. Lett. B 426, 12 (1998) 13. C. B. Dover, L. Ludeking and G. E. Walker, Phys. Rev. C22 (1980) 2073 14. T. Yamazaki, et al., Z Phys. A 355, (1996) 219 15. Gopal et al., Nucl. Phys. B119 (1977) 362

Poster Session

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Chemical Composition and Distribution of Heavy Elements in a Supernova Remnant G359.1—0.5 A. Bamba, J. Yokogawa, M. Sakano, K. Koyama Department of Physics, Faculty of Science, Kyoto University Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan E-mail: [email protected] We present the result of the ASCA observation of a shell-like radio supernova remnant (SNR), G359.1—0.5. Unlike the radio morphology, X-rays from the SNR shows a center-filled structure. The spectrum of G359.1—0.5 has prominent K a lines of He-like silicon and H-like sulfur. The plasma requires at least two tem­ perature components: a lower temperature plasma (fcT ~ 0.6 keV — 7 X 10 K) and a sulfur-rich plasma with higher temperature (kT <~^ 4.4 keV = 5 X 10 K). The chemical composition of sulfur is found to be unusually high, larger than that of the solar vicinity by, at least, more than 10 times. We can estimate the total mass of silicon and sulfur to be O . I M Q and 0 . 3 M Q , respectively, where MQ is the mass of the sun of about 2 X 10 3 3 g. No current theory of nucleosynthesis in supernova explosions allows larger mass production of sulfur than that of silicon. This problem is solved with the assumption that the sulfur distribution is localized somewhere in SNR.

1

Introduction

How is chemical distribution in an supernova remnant (SNR)? It is said that an inner region of a progenitor star has an onion-like structure with layers of H, He, and heavy elements. However, nobody knows how these elements distribute in an SNR after supernova explosion, uniformly or non-uniformly with some blobs made with heavy elements. Recently, some evidence of nonuniform distribution is found, for example, Vela SNR (Aschenbach et al., 1995). X-ray spectroscopy of SNRs provides a powerful nucleosynthetic tool for heavy elements such as O, Ne, Mg, Si, S, and Fe, because K-shell emission lines of these elements come into the relevant X-ray band (0.5 keV < hv < 10 keV). ASCA is the first X-ray astronomical satellite which covers the full energy band, the resolution to separate the K-shell emission lines from these heavy elements. This paper reports the first detailed X-ray study of G359.1—0.5, a radio shell-like SNR near the center of our Milky Way Galaxy. G359.1—0.5 was first identified as a SNR with the 4.9 GHz observation by Dowens et al. (1979). Uchida et al.(1992) found a shell-like structure sur­ rounded by a 12 CO ring. Although Sun (1997) and Egger and Sun (1998) discovered X-rays from G359.1—0.5 with ROSAT, the spectral parameters, such as temperature and chemical composition are not well constramed, due to the poor statistics and limited energy resolution.

331

332

2

Observation and Data Reduction

During the observation of the most prominent radio filament (the Snake) made on March 20-22 in 1997, G359.1-0.5 was located in the GIS field. However, it was only partially covered with SIS field. GIS was always operated in the normal PH mode. We excluded high-background data and non-X-ray events with the standard method according to the user guide by NASA Goddard Space Flight Center. In total, the available exposure time of GIS is ~80ks for G359.1-0.5. 3

Analyses

Figure 1: GIS contour map in the 1.6-2.1 keV band with Galactic coordinates, superposed on the gray-scale radio map by Gray(1994). Contour levels are linearly spaced and are saturated at A1742-294 and 1E1740.7-2942. Source and background regions for spectral analyses are shown with solid and dotted lines, respectively.

Figure 2: The background-subtracted GIS spectrum of G359.1—0.5. Crosses are the data points. The solid line represents the best-fit twotemperature model, while the dotted lines are those of the individual components.

We found that X-rays are emitted from the central part within the shell of the SNR G359.1—0.5, although it exhibits a completely shell-like structure in the radio band. Figure 1 shows the GIS contour map in the energy of 1.62.1 keV, in which diffuse X-ray excess inside the radio shell is most clearly seen. We made the GIS spectrum of the SNR center, selecting the source and the background regions as shown by the solid and dotted lines in figure 1,

333

respectively. In the spectrum of G359.1—0.5 (figure 2), we can notice two emission lines at 1.86l0'g4 keV and 2 . 6 l l g 0 7 keV (here and after errors are at 90 % confidence level, unless otherwise mentioned). These line center energies are consistent with those of Ka emission from helium-like silicon (He-like Si; 1.86 keV) and hydrogen-like sulfur (H-like S; 2.63 keV), respectively. The presence of K-shell lines supports that X-rays from this SNR are due to a thin thermal plasma. However, these two lines can hardly coexist in a single temperature plasma because a higher temperature is required to ionize sulfur atoms than that to ionize silicon atoms. Therefore, we applied a twotemperature plasma model (a plasma code established by Mewe et al.(1985) and Kaastra (1994)) with an interstellar absorption. The abundances of Si and S in each plasma were treated to be free parameters, whereas those of the other elements were fixed to the solar values (Anders and Grevesse, 1989). This model is statistically accepted within 90 % confidence level. The best-fit model and parameters are given in figure 2 and table 1, respectively. A remarkable result is that the sulfur abundance in the higher temperature plasma (here component 2) is larger than tens of solar. Table 1: Best-fit parameters for G359.1—0.5 for the model of two thin thermal plasmas with an absorption.

kT

Flu^ (0.7-10 keV) component (keV) (10 2 2 H c m ~ 2 ) (ergs-1cm~2) 1 0.6(0.4-0.9) 2.5(1.2-8.4) <0.9 5.9(4.1-8.4) 7.8 x 1 0 " l a 2 4.4(2.2-13.2) not determined >38 * 6.1 X 1 0 ~ 1 3 Parentheses indicate 90 percent confidence regions for one relevant parameter. ' Abundance ratio relative to the solar value. * Common with component 1.

4

Si/fTf

S/Ht

JVH

Results and Discussion

G359.1—0.5 is found to exhibit a large absorption column of ~ 5.9xl0 22 Hcm~ 2 . Since Uchidaet al.(1992) reported that G359.1-0.5 is surrounded by the 12 CO ring of the total mass of about 2.5 x 10 6 M Q , local absorption due to the 12 CO ring may not be ignored. Assuming that the 12 CO ring is a homogeneous shell with nearly the same shape of the G359.1—0.5 radio shell, the absorption column due to the 12 CO ring is estimated to be ~ 3 x 10 22 Hcm~ 2 . Therefore, we infer that the column density of the foreground interstellar matter is about ~ 3 x 10 22 Hcm~ 2 . We can estimate the distance to the SNR from this value

334

to be ~ 8.5 kpc, (where 1 pc is about 3 x 10 18 cm). Then the diameter of the radio shell is estimated to be ~ 57 pc, while that of the X-ray emitting central sphere is ~ 28 pc. We found that G359.1—0.5 has at least two temperature plasmas; the cooler plasma (component 1) is abundant in Si, whereas the hotter one (com­ ponent 2) is extremely over-abundant in S. Assuming that about 10 % of ~ 28 pc-diameter of sphere is filled with a plasma, we estimate the total mass of Si and S to be about O.IMQ and 0.3M Q , respectively. However, no current theory of nucleosynthesis in supernova explosions predicts such large mass of S than Si (see e.g. Thielemann et al. 1990). Plausible scenario is that the sulfur distribution should be localized somewhere in the SNR, as is already found in the Vela SNR (Aschenbach et al. 1995) and called "shrapnel". We made a narrow band image including only the S-line (2.1-3.2 keV). However, it shows no spatial structure, mainly due to a lack of photon statistics. We expect to solve this problem with next generation satellites such as XMM or ASTRO-E, which will provide better photon statistics than ASCA. Acknowledgments We would like to thank Dr. Y. Maeda for useful comments and discussion. We also thank the members of the ASCA team. This work was supported by the Research Fellowship of the Japan Society for the Promotion of Science for Young Scientists. References 1. 2. 3. 4.

5. 6. 7. 8. 9. 10.

Anders, E., and Grevesse, N., 1989, Geochimiva et Cosmochimica Acta, 53, 197 Aschenbach, B. et al., 1995, Nature, 373, 587 Bamba, A. et al., 2000, PASJ, 52, printing Egger, R., and Sun, X., 1998, Lecture Notes in Physics, The Local Bubble and Be­ yond, Lyman-Spitzer Colloquium, Proceedings of the IAU Colloquium No,166, held in Garching, Germany, 21-25 April 1997, XXVII, (Springer-Verlag, Berlin), ed D. Breitschwerdt et al., 506, 417 Gray, A.D., 1994, MNRAS, 270, 835 Kaastra, J.S., 1992, An X-Ray Spectral Code for Optically Thin Plasmas, (Internal SRON-Leiden report, updated version 2.0) Mewe, R. et al., 1985, A&AS. 62, 197 Sun, X., 1997, Presented at International Astrornnomical Union Symposium No.184. The Central Regions of the Galaxy and Galaxies., Kyoto, Japan, 17-30 August Thielemann, F.-K. et al., 1990, in Supernovae, Les Houches Session LIV, ed S. Bludman et al., Zinn-Justin, p629 Uchida, K. et al., 1992, AJ, 104, 1533

TANASHI RECOIL MASS SEPARATOR FOR NUCLEAR ASTROPHYSICS H.1SHIYAMA, H.MIYATAKE, N.Y0SH1KAWA, S.C.JEONG, M.WADA, Y.ISHIDA, M.H.TANAKA, S.TAKAKU, Y.FUCHI, H.KAWASHIMA,K.NIKI,M.TOMIZAWA,M.OKADA,Y.TAKEDA,Y.ARAKAKI,S.ARAI, H.KAWAKAMI, I.KATAYAMA, T. NOMURA KEK-Tanashi,3-2-I Midoricho, Tanashi, Tokyo 188, Japn T.TERANISHI, M.MICHIMASA, I.IMAI, Y.YANAGISAWA, S.KUBONO Center for Nuclear Science, University of Tokyo,3-2-1 Midoricho, Tanashi, Tokyo 188, Japan P.STRASSER R1KEN.2-1 Hirosawa, Wako, Saitama 351, Japan S.KATO Department of Physics, Yamagata University, Yamagata 900, Japan A radioactive nuclear beam facilityfl] was constructed at KEK Tanashi branch and experiments using radioactive nuclear beams currently available have been carried out. This facility whose driving machine is SF cyclotron, is consisted of two target ion sources (an ECR ion source[2] and a surface ionized ion source), a high resolution isotope separator[3](ISOL), a 60m beam transport line, and a linac complex[4] by which radioactive nuclear ions of a charge to mass ratio of 1>30 are accelerated up to 1.04MeV/u. One of the major subjects using radioactive nuclear beams is an investigation of the nucleosynthesis in the universe. Especially we have tried to study rapid proton (rp) process in explosive hydrogen burning under astrophysical conditions of extreme temperature and density [5]. Along this theme, several experiments have been carried out recently. A recoil mass separator was constructed for' the investigation of nuclear astrophysics. There are two reasons why it is necessary for nuclear astrophysics experiments. 1. In the case where reaction rates of nuclear reactions, for examples, (p,y), (oc,y), are relatively small, the required beam intensity becomes 108- 10'° pps. For measurements of the reaction rates, recoil nuclei from the nuclear reactions have to be detected with little background. In order to avoid back ground caused by the radioactive nuclear beam itself, the recoil nuclei and the radioactive nuclear beam should be separated. Therefore, a recoil mass separator is necessary to suppress the radioactive nuclear beam at a focal plane detector.

335

336

2. In the case where reaction rates of nuclear reactions, for example, (p,p), (a,p), (a,n), are relatively large, the required beam intensity becomes 103-105 pps, and measurements of the reaction rates can be performed by directly driving the radioactive nuclear beam into a detector system. For carrying out these measurements, it is necessary to provide pure radioactive nuclear beams, which do not accompany with contaminant stable nuclei. A recoil mass separator plays an important role to suppress these contaminant stable nuclear beams. We have tested the performance of the Tanashi recoil mass separator for above two reasons. For the reason 1., several factors relating to the beam suppression was investigated. In practice, this investigation was done for ,9Ne(p,y) experiment. For the reason 2., stable nuclear beams could be suppressed by a charge state breeding with the recoil mass separator. In practice, this method was used for l8Ne(p,p) experiment. We introduce the results of the performance test of Tanashi recoil mass separator. The ion optical configuration from the linac to a target chamber is Q-Q-D-Q-D-QQ. At the downstream of the target chamber, there is a recoil mass separator(RMS), whose configuration is Q-Q-E-D-Q-Q, as shown in Fig.l, where Q,D and E stand for the quadrupole, dipole magnets, and electric dipole. As the first nuclear astrophysics experiment, we planned the measurement of the resonance strength at the 2.64MeV level in 20Na by the "Ne(p,y)20Na reaction[6]. The intensity of 19Ne beam was expected to become order of 108 pps at the target position. Therefore, required beam suppression factor of RMS itself had to be at least order of 10"4. But, at the first measurement using the 20Ne stable beam, its beam suppression factor was 10"3. In order to improve the beam suppression factor, the ray-trace simulation was carried out. From its results, two origins of this bad beam suppression were expected. One was that the 19Ne beam might collide with the vertical chamber wall in the dipole magnet. Another was that the beams with lower charge states might collide with the electric electrode plate in the electric dipole. To discuss these origins individually, 20Ne beams which had different charge states were provided. At the target chamber, a collimator whose size was 4mm<|> was set to realize an ideal beam spot. 20Ne ions were detected at the entrance of RMS by a silicon detector, and at the focal point of RMS by a position-sensitive silicon detector. For the determination of the contribution to the beam suppression factor by the first origin, the vertical position of 4mm<j> collimator was changed by 1mm steps, and 20Ne7+ ions yield was measured at the entrance and the focal point of RMS when the optical elements of RMS was tuned for AM=1 heavier ions than 20Ne ions. The result is shown in Fig.2. It shows that the ideal beam suppression factor becomes several x 10"5 and if the vertical beam position is 3mm lower than the center, it becomes near 10"3. For the determination of the contribution to the beam suppression factor by the second origin, the beam suppression factors were measured with 20Ne beams whose

337

D-mag

Target Chamber Electric Deflector

'%?

J^Fb-mag rin

Q

m

°0/'M

r

D_ma

^

C foil

9 -

^

Detector I H -Linac Chamber Fig. 1 The ion configuration from the linac to a detector system. At the downstream of a target chamber, There is a recoil mass separator.

beam suppression

olOl

•

u

factor

transprot

I

efficiency

no"

■

to

c o 0)

-4-

i

i

i

i

i

i

•

|

i

I

]

•

I

i

-1 •: 1 0

01 3 W TJ -t

O i—*

CD

—*

Q.

m

■

E

10'

CO* 3 O

CO CD

XI

cl . . . . . . . . i i . . . . i . . . . I . . . . j , , , , I , r , , i , , , ,

1 0 :

4

. 3 . 2 - 1 0 1 2 3 Collimator position [mm]

10

-3

Fig.2 The measured beam suppression factor with '"Ne7* beam. It was measured by changing vertical position of the collimator. RMS was tuned for AM=1 heavier ions than ones of the beam.

338

charge state were from 4+ to 8+. As the result, the beams whose charge state were lower than 4+ collided with the electric electrode, but their suppression factor were lower than 2x10"*. From the above mentioned fact, it was turned out that the main contribution to the bad beam suppression factor was that the beam collided with the vertical chamber wall in the dipole magnet. So, two new X-Y stairing magnets and more beam monitors were constructed and the vertical position of the ion optical elements were adjusted again. As the result, the beam suppression factor of RMS itself become 1 x 10-4. For the search of the resonance levels of l9Na by ,8Ne(p,p) reaction, required beam intensity would be 103pps. Because the 18Ne beam would be directly transported to a detector system including a gas target, consisting of a multiwire proportional counter and a position sensitive silicon detector. The l8Ne beam intensity had become 105 pps at the exit of ISOL, and contaminant ls O stable nuclear beam had become a few nA at the exit of ISOL. So, we had planned to separate ^Ne9* and 18 0 whose maximum charge state was 8+. The ions with A/q=18/2+ would be accelerated up to 1.04MeV/u. After passing through a thin carbon foil(10u.g/cm2) at the exit of the linac, the ions with A/q=18/9+ would be analyzed by available D-D-E-D. The measured beam suppression factor to , 8 0 became 1 X 10"8. As the final result, ,8 Ne beam intensity at the detector became 3 x 103pps and the maximum yield ratio of contaminant ,s O ions to 18Ne became 1.5%. In summary, a recoil mass separator was constructed for nuclear astrophysics and tested its performance. The measured beam suppression factor of RMS itself became 1 x 10"4 when it tuned for AM=1 heavier ions than the beam ions with A~20. It was the upper limit to carry out the 19Ne(p,y) experiment. By a charge state breeding, the suppression factor to contaminant stable nuclear beams became 1 x 10'8. This method is available to purify radioactive nuclear beams.

References 1. 2. 3. 4. 5. 6.

T.Nomura, Nucl. Instr. Meth. 870(1992)407. M.Oyaizu, et al., Rev. Sci. Inst. 69-2(1998)770. M.Wada, et al., Nucl. Inst. Meth. Res. A337(1993J11 M.Tomizawa, et al., Heavy ion Accelarator Technology: 8th International Conference, edited by Kenneth. W.Shepard (AIP, New York, 1999)451. A.E.Champagne, M.Wiescher., Annu. Rev. Nucl. Part. Sci. 42(1992)39. R.D.Pages, et. al., Phys. Rev. Lett. 73(1994)3066.

Collision between Neutron Star and Axion Star as a Source of Gamma Ray Burst and Ultra High Energy Cosmic Ray A. Iwazaki of Physics, Nishogakusha University, Chiba 277-8585, Japan E-mail: [email protected]

Department

We propose a model in which the ultra high energy cosmic rays and gamma ray bursts are produced by collisions between neutron stars and axion stars. An ac­ celeration of the cosmic ray is done by an electric field, ~ 10 15 eV c m " 1 , which is induced in the axion star by the strong magnetic field > 10 12 G of the neutron stars. On the other hand, gamma ray bursts are generated in the collisions between axion stars and neutron stars with relatively small magnetic field, e.g. ~ 10 10 G. In the former case the axion star evapolates emitting ultra high energy cosmic rays before colliding directly with the neutron stars, while in the latter case the axion star collides directly with the neutron star and dissipates rapidly its whole energy in an outercrust of the neutron star, which leads to a gamma ray burst. To explain both phenomena we need to assume the mass of the axion such as 1 0 - 9 eV. With this choice we can explain huge energies 10 s 4 erg of the gamma ray bursts as well as the ultra high energies ~ 10 2 0 eV of the cosmic rays. Additionally, it turns out that these axion stars are plausible candidates for MACHOs.

1

Introduction

The ultra high energy cosmic rays ( UHECRs ) is one of most mysterious phenomena in astrophysics*. We do not still have a reliable generation mech­ anism of the cosmic rays with extremely high energies > 1020 eV. Similarly, the gamma ray burst is one of most mysterious phenomena in astrophysics although some plausible generation mechanisms are proposed. The difficulty for explaining both phenomena is how huge energies are released; energies of the cosmic rays, > 1020 eV, and energies of gamma ray bursts, ~ 1052 erg. On the other hand, the dark matter in the Universe 2 is one of most mysterious puzzles in cosmology. Axion 3 ' 4 is one of the most plausible candidates for the dark matter although even its existence has not yet been confirmed. 'Proba­ bly, some of axions with mass ma may form boson stars ( axion stars ) in the present Universe by gravitational cooling 5 or gravitational collapse of axion clumps formed at the period of QCD phase transition 6 . Here we wish to sketch our results that collisions between axion stars and neutron stars generate UHECRs and GRBs. In our model the collision between the axion star and the neutron star with strong magnetic field > 1012 G produces both UHECRs and GRBs with very short durations ( less than

339

340

millisecond ) and very hard gamma rays. The collision between the axion star and the neutron star with relatively weak magnetic field ~ 1010 G produces only GRBs with both of short and long durations in this case; UHECRs can not be produced. In order to derive the results we need to assume that the mass of the axion is given by ~ 10~ 9 eV. Then, we have an additional bonus that the axion stars are plausible candidates for MACHOs 7 since their masses are given by ~ 1O _ 1 M 0 ; M© is solar mass. The essence in our mechanism 8 is that the axion star induces an electric field when it is exposed to the magnetic field of the neutron star. The strength of the field Ea is proportional to the strength of the magnetic field B, Ea ~ 1015 eV c m ' 1 B12mg, where B12 = B/1012 G and m 9 = m 0 / l ( r 9 eV with ma denoting the mass of the axion. This electric field can accelerate charged particles so that they can gain the energies 1020 eV when the strength of the magnetic field is given by ~ 1012 G. The strong electric field, however, is unstable 9 against electron-positron pair creations and hence the axion star decays producing UHECRs before colliding directly with the neutron star. It means that the axion star evaporates very rapidly around the neutron star with its surface magnetic field B > 1012 G. On the other hand, the electric field dissipates its energy in the conducting medium of the neutron star when its magnetic field is given by ~ 1010 G. It turns out that in such a case the electric field is stable so that the axion star can collide directly with the neutron star. Since its whole energy ~ 10 53 erg is dissipated only in an outercrust of the neutron star, the ejection leading to GRB is composed of particles in the crust. Thus, the baryonic contamination of the ejection is less than 1O~5M0 which is required observationally. 2

Axion Star

The axion star is a coherent object of the real scalar field a(x) describing the axion. An approximate form of the solution 10 representing axion star is given such that a(x) = fpQdo sin(m a i) exp(—r/Ra) where t ( r ) is time ( radial ) coordinate and JPQ is the decay constant of the axion. The value of JPQ is constrained 2 conventinally from cosmological and astrophysical considera­ tions 2 ' 4 such that 1010 GeV < fpQ < 1012 GeV (the axion mass ma is given in terms of JPQ such that ma ~ 107 GeV2/fpQ ). However, when we assume un­ conventionally entropy productons below the temperature 1 GeV of the early Universe, we may be released from the constraints 11 . In this paper we assume that fPQ ~ 1016 GeV or ma ~ 10" 9 eV. In the formula, Ra represents the radius of the axion star numerically given in terms of mass Ma of the axion star, Ra ~ 1.6 x i0 5 cmm^~ 2 10~1MQ/Ma.

341

Similarly, the amplitude ao in the solution is represented such that oo = 1.73 x 10 2 (10 5 cm/i? o ) 2 l ( r 9 e V / m a . Therefore, we find that the solution is parameterized by one free parameter, either one of the mass Ma or the radius Ra of the axion star. It is also important to note that the solution is not static but oscillating with the frequency of ma/2ir. The mass of the axion star may be typically given by the critical mass M c of the axionic boson star, Mc ~ 10 _ 1 M Q 10 _ 9 eV/m a ; axion stars with masses larger than the critical mass collapse gravitationally into black holes. Thus, the corresponding radius Ra for this critical mass is given such that Ra ~ 1.6 x H ^ m ^ c m . Let us explain how an electric field is induced in the axion star when it is under the magnetic field of a neutron star. Owing to the interaction between the axion and the electromagnetic field described by Lail = caaE • B/fpQ7r, where the value of c is of the order of unity, the Gauss law is modified such that dE = — cad ■ (aB)/fpQir + "matter" where the last term "matter" denotes contributions from ordinary matters. The first term in the right hand side represents the contribution from the axion. Thus, substituting the above solution into a(x) in the Gauss law, we find that the electric field induced in the axion star, Ea = —caa(x)B/fpQTr ~ 1015 eV c m - 1 Bumg with a ~ 1/137. This electric field is oscillating with the frequency, ma/2ir ~ 2.4x 105 ma Hz. Thus a charged particle with charge Ze can be accelerated in a direction within a half of the period, n/ma or in a distance ~ Ra ( ~ K/ma x light velocity ) by this field. Thus, the energy AE obtained by the particle is given such that AE = ZeEa x Tr/ma x light velocity ~ 10 2 0 ZeVSi 2 Therefore, the electric field of the axion stars can accelerate the charged particle so that its energy reaches ~ 10 20 Z eV of UHECRs. As we have mentioned, this strong electric field is unstable so that it decays very rapidly into electron-positron pairs, which are converted to baryons and photons after their production. These are UHECRs in our model. On the other hand, the electric field is stable when the magnetic field of the neutron star is not so strong, e.g. ~ 1010 G. Thus, the axion star collides directly with the neutron star and dissipate its whole energy ~ 10 53 erg in the conducting medium of the outercrust. The rate of the dissipation has been estimeted such as 10 46 erg/scm 3 , while the energy density of the axion star is given by 10 38 erg/cm 3 . Thus it turns out that the dissipation is very rapid; the axion star never enter a core of the neutron star. This rapid dissipation generates jets formed by particles of the neutron star, which leads to GRBs; the jets with small solid angles are produced since the ejections are accelerated by the strong electric field ~ 10 13 B i 0 e V c m _ 1 . In these ways UHECRs and GRBs are generated by the collisions between the axion stars and the neutron

342 stars. Acknowledgments This work is supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan No. 10640284 References 1. M.A. Lawrence et al. J. Phys. G. Nucl. Part. Phys. 17, 773 (1991), D.J. Bird et al. Phys. Rev. Lett. 71, 3401 (1993); ApJ 424, 491 (1994), N. Hayashida et al. Phys. Rev. Lett. 73, 3491 (1994), M. Takeda et al. Phys. Rev. Lett. 81, 1163 (1998); ApJ, 522, 225 (1999). 2. For a review, see, for example, E.W. Kolb and M.S. Turner, The Early Universe, Addison-Wesley, New York, (1990). 3. R.D. Peccei and H.R. Quinn, Phys. Rev. Lett. 38, 1440 (1977), S. Weinberg, Phys. Rev. Lett. 40, 223 (1978), F. Wilczeck, Phys. Rev. Lett. 40, 279 (1978). 4. J.E. Kim, Phys. Rep. 150, 1 (1987). 5. E. Seidel and W.M. Suen, Phys. Rev. Lett. 72, 2516 (1994). 6. E.W. Kolb and I.I. Tkachev, Phys. Rev. Lett. 71, 3051 (1993); Phys. Rev. D49, 5040 (1994). 7. C. Alcock et al. Astrophys. J. 449, 28 (1995), for a review, see C.S. Kochanek and J.N. Hewitt, eds, "Astrophysical Applications of Gravitational Lensing", IAU Symp. 173 (1996) (Kluwer, Dordrecht). 8. A. Iwazaki, Phys. Lett. B455, 192 (1999); Phys. Rev. D60 025001 (1999); Prog. Theor. Phys. 101, 1253 (1999). 9. J. Schwinger, Phys. Rev. 82, 664 (1951). 10. E. Seidel and W.M. Suen, Phys. Rev. Lett. 66, 1659 (1991), A, Iwazaki, Phys. Lett. B451, 123 (1999). 11. P.J. Steinhardt and M.S. Turner, Phys. Lett. B129 51, (1983).

Double B e t a Decays of

100

M o b y E L E G A N T V at O t o C o s m o Observatory

N. Kudomi a , H. Ejiri a , K. Fushimi b , K. Hayashi a , T. Kishimoto c , K. Kume a , H. Kuramoto a , H. Ohsumi c , K. Takahisa a , Y. Tsujimoto a , and S. Yoshidaa a)RCNP, Osaka Urtiv., Ibaraki, Osaka 567, Japan b)Facul. of Integ. Arts and Sci., The Univ. of Tokushima, Tokushima, 770, Japan c)Dept. of Phys., Osaka Univ., Toyonaka, Osaka 560, Japan Exclusive measurements of neutrino-less double beta decays(0^/3/3) of 1 0 0 M o were made by means of ELEGANT V. The present status of the double beta decay experiment with ELEGANT V is presented. The data at Oto lab., being combined with the data at Kamioka, gives stringent limits on half-lives for 0vf3j3 and (mv) < 1.8eV for the Majorana neutrino mass.

Double b e t a decays are of current interest from b o t h astroparticle and nuclear physics view p o i n t s 1 . T h e Ov/3/3, which violate t h e lepton number con­ servation law, provide one with very sensitive tests for t h e Majorana neutrino mass, t h e right handed weak currents and so on. 2i//3/3 gives directly the nuclear matrix element?. This is used t o verify nuclear structure calculations and t o se­ lect appropriate spin-isospin interactions HTa t o be used for evaluating t h e nu­ clear matrix element for Qvf3f3. Since /3/3 transition rates depend largely on t h e nuclear matrix elements, it is i m p o r t a n t t o study /?/? on several nuclei in order to extract universal values of physics quantities. T h e transition rate for lv/3/3 is simply written in terms of t h e M2v as [ T ^ ] - 1 = G2v\M2v\2, where T2J2 is t h e half-life and G2v is t h e phase space factor. T h u s M2v is derived experimentally from t h e observed 21/(3/3. T h e transition rate for Ov/3/3 associated with t h e neu­ trino exchange is written in t e r m s of the neutrino mass term (m„) and the R H C terms of (A) and (r,) a s 1 , [^(v)]'1 = G*v\M°v\2((mv) + C A (A) + Cn{r))f, 0v 0v where G and M are the phase space factor and t h e nuclear matrix element for t h e mass term. C,, with i being m, A and r), are t h e nuclear responses in units of M0v. These 01/(3/3 transition rates include both t h e nuclear matrix el­ ements (form factors) relevant to nuclear structures and t h e physics quantities relevant to particle physics. So far, Ov/3/3 decay rates have been studied on several nuclei, unique fea­ tures of this work of 1 0 0 Mo with E L E G A N T V4 are as follows. (1) Energy and angular correlations of two (3 and j are measured by E L E G A N T V. T h u s limits on the Ov/3/3 for individual terms can be obtained. (2) 1 0 0 M o has large phase space factors and the 2v/3/3 m a t r i x element is k n o w n 3 . (3) Origins of

343

344

/

00

\x —A< /

—^

|

Mo Source film Lead Shield Copper Shield

NQ

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Upper-Nal

3

a"T I

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.. i n m n n

«

Chamber - B

■« *

Chamber - A Lower-PL

innnn

Figure 1: Schematic view of ELEGANT V 4 .

the background are well investigated by the f3 and 7 correlation. Thus the correction for them is possible. The obtained limits on (mv) and others, depending somewhat on the ma­ trix elements used, are most stringent for 100 Mo. They are same orders of magnitudes as the values derived from other nuclei. Thus the present data with the unique points as given above, together with other data, may give stringent limits on the relevant values beyond the standard theory. ELEGANT V consists of drift chambers for /? trajectories, plastic scintillators(PL) for f3 ray energies and arrival times, and Nal scintillators(Nal) for 7 and X rays4(Fig. 1). The total weight of 100 Mo is 171gr. PL's and Nal's are calibrated by 7-rays of 511keV and 1275keV from the 22 Na 5 . The detection efficiencies of D C s are checked by the /?-ray from 90 Sr passing through DCs. At present, the j3/3 decays of 100 Mo are measured at Oto Cosmo Obser­ vatory with 1200m.w.e.. The sum energy spectrum is obtained by selecting events with several conditions with live time for the 6766hrs(Fig. 2). The major part of the spectrum is the 2z//?/? component. Background contribu­ tions from the natural radioactive contaminations were estimated as follows. The 214 Bi(Q^ = 3.28MeV) and 208 Tl(Q /3 = 4.99MeV) are two major isotopes, which may give background events in the 0^/?/? energy window. These isotopes are decay products of 238 U- and 232 Th-chain isotopes. 214 Bi is produced also from Rn contained in the air. As the first step, the total amounts of them were evaluated from the single electron//3-ray event rates in coincidence with 7-rays characteristic of the decays of each contents(Table 1). On the basis of the estimated 214 Bi and 208 T1 contents, Monte Carlo cal­ culations were carried out to evaluate the fake event rates by these isotopes, which may survive after the selections. The observed spectrum is reproduced

345

2

2.2

2.4

2.6

2.8

3 3.2 3.4 0 sum •n*rgy(M«V)

Figure 2: The sum energy spectrum.

by the sum of the estimated BG spectrum and the 2vj3j3 spectrum with the previously known half-life of 1.15 x 10 19 y 3 . There are no excess Of/?/? counts beyond the statistical fluctuations of the 2i>/?/?-|-BG events. In order to obtain upper limits on the number of the counts, the detection efficiencies for individ­ ual processes of the (m,), (A) and (77) terms were evaluated by Monte Carlo simulations, as shown in Table 2. The limits on the half-lives are obtained from the number of the observed counts and the number of the estimated 2z//?/?+BG counts. The standard method of the likelihood analysis was used 8 . The results at Oto together with those of the previous work at Kamioka are summarized in Table 2. Using the nuclear matrix elements 7 , the half-life limits leads to the upper limits of physics quantities. The present work measures the energy and angular correlations of two /? rays, which are important for the study of individual double beta processes. It is also important to study the double beta decay of several nuclei, because

Table 1: The

Origin * 14 Bi

Location Source DC-gas PL

214

Bi and

208

T 1 contents.

Amount (8.3 ± 1.7) x 10- 3 (2.2 ± 0.5) x 10-* (6.5 ±1.5) x 10-*

Bq/kg Bq/nr 5 Bq/m

346 Table 2: Limits with 68(90)%CL on the half-lives for the Oi//30 decay of and those obtained by combining with the Kamioka limits.

100

M o at Oto lab.,

(Oto(Preliminary), Live Time=:6766hrs) E window (MeV) 2.7-3.3 2.7-3.3 2.7-3.3 2.5-3.0

mode (mv) term (A) term {rj} term emission

0+ - * 0 +

Majoron

Yield (counts) 2 2 2 14

2v/3(5+BG (counts) 2.1 2.1 2.1 14.

e 0.18 0.11 0.16 0.029

Tl/2 (10 21 y) >46(25) >29(16) >40(22) >3.6(2.3)

(Combine) mode

0+^0+ Majoron

{mv) term (A) t e r m {rj) t e r m emission

T\/2 (10 2 1 y) 82(45) 50(27) 76(41) 6.9(4.0)

physics quantity (m„) <1.8(2.3)eV (A) < 2.9(3.9) x 1 0 - 6 (rj) < 1.7(2.3) < x l O - 8 (gB) < 6.5(8.5) x 1 0 " 5

the values of (m f ) and others depend somewhat on the matrix elements. The authors thank Oto and Nishi-Yoshino villages for their kind support and for the Oto lab. construction. This work is supported by the Grant-in-Aid of Sci. Res. and Ministry of Education, Sci. and Culture, Japan. K.F., N.K., K.K., K.N. and S.Y. were supported by JSPS Research Fellowships. References 1. W.C. Haxton and G.J. Stephenson, Jr. Prog, in Part. Nucl. Phys. 12, 409 (1984); M. Doi, T. Kotani and E. Takasugi, Prog. Theor. Phys. Suppl. 83, 1 (1985); H. Ejiri, Int. J. Mod. Phys. E 6, 1 (1997) 2. H. Ejiri and H. Toki, Joun. of Phys. Soc. of Japan, 65, 7 (1996) 3. H. Ejiri, et al., Phys. Lett. B258, 17 (1991); H. Ejiri, et al., J. Phys. G. Nucl. Part. Phys. 17, S155 (1991). 4. H. Ejiri, et al., Nucl. Instrum. Methods A302, 304 (1991). K. Nagata, et al. Nucl. Instrum. Methods A362, 261 (1995). 5. N. Kudomi, Nucl. Instrum. Methods A430, 96 (1999) 6. H. Ejiri, et al., Nucl. Phys. A611, 85 (1996). 7. T. Tomoda, Rep. Prog. Part. Phys. 54531991. 8. Particle Data Group, Phys. Rev. D50, 1173 (1994); O. Helene, Nucl. Instrum. Methods A390, 383 (1997)

N U C L E O S Y N T H E S I S IN A S P H E R I C A L H Y P E R N O V A EXPLOSIONS A N D LATE TIME S P E C T R A OF SN1998BW KEIICHI MAEDA, TAKAYOSHI NAKAMURA Department of Astronomy, School of Science, University of Tokyo KEN'ICHI NOMOTO Department of Astronomy & Research Center for the Early Universe, School of Science, University of Tokyo PAOLO A. MAZZALI Osservatorio Astronomico di Trieste, via G. B. Tiepolo, Trieste, Italy IZUMI HACHISU Department of Earth Science and Astronomy, Collage of Arts and Science, University of Tokyo Nucleosynthesis in aspherical hypernova explosions is calculated with a twodimensional hydrodynamical code and a detailed neclear reaction network. The results are compared with observations of SN1998bw, whose late time spectrum unusual features are shown to be explained by the aspherical explosion model.

1

Introduction

It was striking that SN 1998bw was discovered as an optical counterpart of GRB980425 2 . SN 1998bw was recognized as an unusually bright and energetic Type Ic supernova (SN Ic). The unusual light curve and spectra of SN 1998bw at early times have been successfully explained by a hyper-energetic explosion (kinetic energy of EK ~ 3 x 1052 ergs) of a massive C+O star 5 ' 1 4 . We use the term "hypernova" to refer to a SN explosion with E%_ more than ten times higher than normal core collapse surpernovae. Despite the success of the hypernova model in reproducing the observed features of SN 1998bw at early times, the observed light curve and spectra at late times show significant deviations from those predicted by spherically symmetric models. (1) The observed light curve tail declines slower than the model curve n . (2) Measurements of the velocities from the width of the nebular emission lines show that iron expands faster than oxygen 1. This is contrary to expectations from a spherical explosion model, where iron is produced in the deeper layers and thus has a lower velocity than oxygen. These discrepancies might be interpreted as signatures of an asymmetry of the ejecta.

347

348

These observational facts, together with the suggestion that gamma-ray bursts are intrinsically aspherical (jet-like) events 8,7 , encouraged us to exam­ ine aspherical explosion models for hypernovae. Here we study the effects of aspherical (jet-like) explosions on nucleosynthesis in core collapse supernovae. We compare the results with the observed late time spectra of SN1998bw and set a constraint on the degree of asymmetry. We also apply our nucleosynthesis results to the black hole binary GRO J1655-40, which has been suggested to be the relic of a hypernova. 2

Method

Our calculations are performed in two steps. The first step is a hydrodynamical simulation of the explosion with a two-dimensional Eulerian hydrodynamical code 3 . In this calculation we follow a number of test particles, keeping track of their density and temperature histories 9 . This history is used in the second step to calculate the change in the chemical composition with a reaction network including a total of 222 isotopes up to 7 1 Ge 1 3 . The progenitor model is the 16 M© He core of a 40 M Q star 10 . The explosion energy is set to E#_ = 1052 ergs to simulate a hypernova explosion. To start the hydrodynamical simulation, we deposit the energy 50% as thermal energy and 50% as kinetic energy below the mass cut that divides the ejecta from the collapsing core. We impose the initial velocity below the mass cut as follows. Vz —ax z and Vr = /3x r, where z,r denote cylindrical coordinates (z: jet direction). This means that at the mass cut the initial velocity (initial shock velocity) along the z-direction is set to be larger than along the r-direcion by a factor a/(3. The ratio of a/(3 is set at 8:1 for a strong aspherical case and at 2:1 for a weaker case. 3

Nucleosynthesis

Figure 1 shows the isotopic compositions of the ejecta of the strong aspher­ ical explosion (with the initial shock velocity ratio 8:1) in the direction of the jet (z:top) and perpendicular to the jet (nbottom). Larger amounts of heavy elements such as 56 Ni are produced along the z-direction than along the r-direction. In the z-direction the shock is stronger and post-shock tem­ peratures are higher, so that explosive nucleosynthesis takes place in a more extended, lower density region compared with the r-direction. Accordingly the expansion velocities of newly synthesized heavy elements are much higher in the z-direction. On the other hand, along the r-direction 56 Ni is produced only in the deep­ est layers, and the elements ejected in this direction are mostly the products

349

of hydrostatic nuclear burning stages (0) with some explosive oxygen-burning products (Si, S, etc) u . The expansion velocities are much lower compared with the z-direction. Our results are qualitatively consistent with previous 2D calculations for SN 1987A 9 .

4

The Late Time Spectra of SN 1998bw

We calculate the profiles of two nebular lines for several 2D models. One is the Fe-dominated blend near 5200A, the other 0 I] 6300.6363A. The profiles are calculated using the element distribution obtained from our 2D hydrodynamical models and line emissivities from a spherically symmetric NLTE calculation. Figure 2 shows the nebular line profiles of iron (left) and oxygen (right) for the strong aspherical case and different viewing angles (15°, 30° from the jet direction, respectively). Since 56 Ni (which decays into 56Fe) is produced mostly along the z (jet) direction, when the degree of asphericity is higher and the viewing angle is closer to the jet direction the component iron lines in the blend have a double-peaked shape. This makes the blend wider. In contrast, the oxygen line is narrower and has a sharper peak in this case, because 1 6 0 is produced mostly in the r-direction. Table 1 shows the half-width of the observed lines in SN1998bw and of our synthetic lines. The observed line profile is not explained by a simple spherical model. This is because in a spherical explosion oxygen is located at higher velocities than iron, resulting in a wider 0 line. In aspherical explosion models, however, the Fe line can become wider than the 0 line. If we view the strong aspherical explosion from near the jet direction, the widths of the 0 and Fe lines are consistent with the observations.

Table 1: Half Line Widths of Fe and O for SN1998bw ( "angle in degrees between the line of sight and the jet direction). Observation

Spherical

Fe[A]

300

O [A ]

200

Aspherical (2:1) 0 15 30

Aspherical (8:1) 0 15 30

230

290

280

260

350

330

300

400

390

390

390

130

200

250

Line of Sight"

350 15000 15500

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Figure 1: The isotopic composition of the ejecta of the strong aspherical explosion (£?K = 1.0 x 10 5 2 ergs, initial velocity ratio 8:1) in the direction of the jet (z:top) and perpendicular to the jet (r:bottom). The ordinate {Mr) indicates the initial spherical Lagrangian coordinate ( M r ) of the test particles. The expansion velocities of the particles are also shown.

351

b.'

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Figure 2: The line proHles of the Fe blend (left) and of O I] 6300, 6363A (right) viewed from 15° (solid) and 30° (dashed) to the jet direction in the strong aspherical explosion model. For comparison, the spherical model (dotted) is also plotted.

5

Black Hole Binary GRO J1655-40

Recently, Keck observations reported interesting abundance features in the atmosphere of the secondary star of the black hole binary GRO J1655-40 4 , which consists of a massive black hole and a low mass companion. In the secondary, the abundance ratios of O, Mg, Si, S and Ti relative to H are almost ten times the solar ratios, while the Fe/H ratio is almost solar. It has been suggested that these a-elements were ejected by the supernova explosion of the primary and captured by the secondary 4 . In order to eject a large amount of Ti, S and Si and yet to leave a massive black hole remnant (which implies a large mass cut), explosive nucleosynthesis should take place in outer layers with sufficiently large Mr and low densities, so that the explosion should be as energetic as hypernovae 4 ' 12 . The small Fe enhancement can be explained by appropriately placing the mass cut in the spherical model 12 . The enhancement of Ti (without ejecting much Fe) is difficult to explain (see below), but to explain the large [Ti/Fe] in metal-poor stars is a well-known problem for core collapse supernova models. An alternative explanation is that the explosion of the primary was as­ pherical and little Fe was ejected in the direction of the secondary. Then it is likely that the secondary star captured material ejected along the r-direction (i.e. on the orbital plane), which contains relatively little Fe compared with the z-direction (see Fig. 1). We compare our nucleosynthesis calculations with

352

the observed abundance pattern. Our main results are as follows. (1) The observed enhancement of O, Mg, Si and S can be explained with the r-direction ejecta abundances in the hypernova (1052 ergs) explosion of a 16 M Q He star. (2) A large amount of Ti and a small amount of Fe are difficult to reproduce concurrently by our models. Ti (Cr) is produced deep in the supernova, where Fe (Ni) is also produced. To get much Ti and little Fe, the mass cut should be located at the interface between complete and incomplete Si burning (see Fig. 1). Even in that case, though, the amount of Ti predicted by the model is smaller than the observed value by a factor of 2. (3) Aspherical models have one advantage compared with a spherical model. In a spherical model, to reproduce the small amount of Fe observed in the secondary, the total amount of ejected 56 Ni should be very small (about 1 0 - 2 M 0 or less). This is much smaller than in other observed hypernovae 5,6 . Also, this does not seem to follow the observational tendency that the ejected 56 Ni mass is larger for more massive progenitors u . In contrast, if the explo­ sion was aspherical, a lot (more than 0.1 MQ) of Fe was ejected along the jet direction, so that total amount of Fe is not so different from other hypernovae. Although the Ti/Fe problem is yet to be solved, we favour the scenario that the progenitor of GRO J1655-40 was a very massive C+O (or He) star which underwent an aspherical hyper-energetic explosion and produced a large amount of Fe. 6

Conclusions

We have calculated the nucleosynthesis in aspherical hypernova explosions to compare with observations. We have succeeded to explain the unusual widths of the 0 and Fe nebular lines in SN1998bw with the strongly aspherical explo­ sion model. We have also shown that an aspherical hypernova explosion can explain the abundance features of the secondary star of the black hole binary GRO J1655-40 better than the spherical explosion model. This is the first step quantitatively to examine the observed character­ istics of hypernovae/GRB candidates using aspherical explosion models. The inferred asphericity gives us clues to the GRB central engines and the explosion mechanism of very massive stars 8 ' 7 . This work has been supported in part by the grant-in-Aid for Scientific Research (07CE2002,12640233) of the Ministry of Education, Science, Culture, and Sports in Japan.

353

References 1. Danziger, I.J., et al. 1999, in The Largest Explosions Since the Big Bang: Supernovae and Gamma Ray Bursts, eds. M. Livio., et al. (Baltimore: STScI), 9 2. Galama, T.J. et al. 1998, Nature, 395, 670 3. Hachisu, I. et al. 1991, ApJ, 368, L27 4. Israelian, G. et al. 1999, Nature, 401, 142 5. Iwamoto, K. et al. 1998, Nature, 395, 672 6. Iwamoto, K., et al. 2000, ApJ 534, 660 7. Khokhlov, A.M., et al. 1999, ApJ, 524, L107 8. MacFadyen, A.I. & Woosley, S.E. 1999, ApJ 524, 262 9. Nagataki, S. et al. 1997, ApJ, 486, 1026 10. Nomoto, K. & Hashimoto, M. 1988, Phys. Rep., 256, 173 11. Nomoto, K. et al. 2000, in "Supernovae and Gamma Ray Bursts" eds. M. Livio., et al. (Cambridge University Press) 12. Podsiadlowski, Ph., Nomoto, K., Mazzali, P.A., & Schmidt, B.P. 2000, preprint 13. Thielemann, F.-K., Nomoto, K., & Hashimoto, M. 1996, ApJ, 460, 408 14. Woosley, S.E., Eastman, R.G., k Schmidt, B.P. 1999, ApJ, 516, 788

Effects o f J e t - l i k e E x p l o s i o n i n S N 1 9 8 7 A

S. N A G A T A K I Department

of Physics, School of Science, the University 7-3-1 Hongo, Bunkyoku, Tokyo 113, Japan E-mail: [email protected]

of

Tokyo,

We studied the effects of jet-like explosion in SN 1987A. Calculations of the explo­ sive nucleosynthesis and the matter mixing in a jet-like explosion are performed and their results were compared with the observations of SN 1987A. It was shown that the jet-like explosion model is favored because the radioactive nuclei 4 4 T i is produced in a sufficient amount to explain the observed luminosity at 3600 days after the explosion. This is because the active alpha-rich freezeout takes place be­ hind the strong shock wave in the polar region. It was also shown that the observed line profiles of Fe[II] are well reproduced by the jet-like explosion model. In partic­ ular, the fast moving component travelling at (3000-4000) k m / s is well reproduced, which has not been reproduced by the spherical explosion models. Moreover, we concluded that the favored degree of a jet-like explosion to explain the tail of the light curve is consistent with the one favored in the calculation of the matter mix­ ing. The concluded ratio of the velocity along to the polar axis relative to that in the equatorial plane at the Si/Fe interface is ~ 2 : 1. This conclusion will give good constraints on the calculations of the dynamics of the collapse-driven supernova. We also found that the required amplitude for the initial velocity fluctuations as a seed of the matter mixing is ~ 30%. This result supports that the origin of the fluctuations is the dynamics of the core collapse rather than the convection in the progenitor. The asymmetry of the observed line profiles of Fe[II] can be explained when the assumption of the equatorial symmetry of the system is removed, which can be caused by the asymmetry of the jet-like explosion with respect to the equa­ torial plane. In the case of SN 1987A, the jet on the north pole has to be stronger than that on the south pole in order to reproduce the observed asymmetric line profiles. Such an asymmetry may also be the origin of the pulsar kick. When we believe some theories that cause such an asymmetric explosion, the proto-neutron star born in SN 1987A will be moving in the southern part of the remnant.

1

Introduction

Supernova is the site where heavy nuclei are synthesized. There are two types of supernova explosion. One is the thermonuclear explosion and the other is the collapse-driven explosion. In this study, we discuss the collapse-driven supernova explosion. There is a problem with the collapse-driven supernova. In spite of many excellent studies, its mechanism has not been understood completely. In fact, almost all of the numerical simulations failed in exploding the progenitor. Al­ though Wilson (1985) proposed the promising mechanism of 'delayed explosion' in his one-dimensional calculation, its role seems controversial 2 .

354

355

To solve the problem, some researchers investigated the effect of rota­ tion of the progenitor 3 . They performed multi-dimensional hydrodynamical simulations and reported the dynamics becomes quite different from spherical explosion when the effect of rotation is included. For example, Yamada & Sato (1991) reported the possibility that a jet-like explosion could occur. So, rotation may be a key process of a collapsing star and jet-like explosion may be a common phenomenon among collapse-driven supernovae. If this is true, nucleosynthesis in a collapse-driven supernova has to be recalculated since it has been calculated assuming a spherical explosion. In this study, nucleosynthesis and matter mixing in an axisymmetrically deformed supernova are investigated and their results are compared with the observations of SN 1987A. As a result, we show in this study that the degree ~2:1 is favored for the axisymmetrically deformed shock wave in SN 1987A. 2 2.1

Explosive Nucleosynthesis Models

Since there is still uncertainty as to the mechanism of a collapse-driven super­ nova, precise explosive nucleosynthesis calculations have not been performed from the beginning of core collapse. Instead, explosion energy is deposited artificially at the innermost boundary 5 . In this study, this method is taken and the explosion energy of 1.0 x 1051erg is injected at the Fe/Si interface. The initial velocity of matter behind the shock wave is assumed to be radial and proportional to r x +a^?^—', where r, 9, and a are radius, the zenith angle, and the free parameter which determine the degree of the axisymmetric explosion. In the present study, we take a — 0 for a spherical explosion and a = | , | , and | (these values mean that the ratios of the velocity are 2:1, 4:1, and 8:1, respectively) for the axisymmetric ones. We name these models SI, Al, A2, and A3. We assumed that the distribution of thermal energy is same as the velocity distribution and that total thermal energy is equal to total kinetic energy. 2.2

Results

The required amount of 44 Ti in order to reproduce the tail of the light curve in SN 1987A 78 9 and calculated ones are shown in Figure 1. The required amount of 44 Ti from the observation depends on its half-life, which is not determined completely. Because of this reason, the required amount is drawn as a function of its half-life. However, in spite of the difficulty in determining the half-life of the long-lived nuclei, recent experiments give a converged value, r ~ 60

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Figure 1: Calculated masses of 44 Ti by the SI, Al, and A2 models. The synthesized mass of 44 Ti becomes larger along with the degree of the jet-like explosion. Required amounts of 44 Ti are also shown as a function of its half-life (Mochizuki & Kumagai 1998; Mochizuki et al. 1999a; Kozma 1999; Lundqvist et al. 1999). The most reliable value for its half-life is ~ 60 yrs (Ahmad et al. 1998).

yrs. Calculated masses of 4 4 Ti in the models Si, Al, and A2 are represented as horizontal lines. We can see the tendency that the synthesized mass of 44 Ti becomes larger along with the degree of axisymmetrically deformed shock wave. It is noted that the model Al is a good one to explain the amount of 44 Ti in SN 1987A. 3

Matter Mixing

Calculated velocity distributions of 56 Ni are shown in Figure 2. Velocity dis­ tributions are calculated assuming that the angle between the line of sight and the symmetry axis is 44°, which is inferred from the form of the ring around SN 1987A 10 . As can be seen from Figure 2, fast moving component can not be reproduced in the spherical explosion models, which is consistent with other works n 12 . On the other hand, fast moving component is reproduced in the jet-like explosion models when the amplitude of the initial fluctuations is set to be 30%. We conclude that the velocity distribution of the model Al with the initial fluctuation of 30% is most similar to the observed one among the all models.

357 I ' ' ' I

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Figure 2: Velocity distributions of 5 6 Ni seen from 9 = 44° at t = 5000 s after the explosion. Left: model SI; right: model A l . The initial amplitudes of the velocity fluctuations are 0% (short-dashed curve), 5% (dotted curve), and 30% (solid curve), respectively.

References 1. Wilson R.B. in Numerical Astrophysics, eds. J.M. Centrella, J.M. LeBlanc, R.L. Bowers (Jones & Bartlett, Boston, 1985) 2. Bethe H. A. ApJ 412, 192 (1993). 3. Yamada S. & Sato K. ApJ 434, 268 (1994). 4. Yamada S. & Sato K. ApJ 382, 594 (1991). 5. Hashimoto M. Prog. Theor. Phys. 94, 663 (1995). 6. Ahmad I., Bonino G., Cini Castagnoli G., Fischer, S.M. Kutschera W., Paull, M., Phys. Rev. Lett. 80, 2550 (1998) 7. Mochizuki Y.S., Kumagai S., Tanihata I. in Origin of Matter and Evo­ lution of Galaxies 97, eds. S. Kubono et al. (World Scientific, 1999) 8. Lundqvist P., Sollerman C., Kozma C., Larsson B., Spyromilio J., Crotts A.P.S., Danziger J., Kunze D. A&A 347, 500 (1999). 9. Kozma C. in Proc. Future Detections in Supernova Research: Progeni­ tors to Remnants, ed. S. Cassisi & P. Mazzali, to be published in Mem. Soc. Astr. Ital. (astro-ph/9903405). 10. Plait P., Lundqvist P., Chevalier R., Kirshner R. ApJ 439, 730 (1995). 11. Herant M., Benz W. ApJL 370 L81 (1991). 12. Herant M., Benz W. ApJ 387 294 (1992).

F O R M A T I O N A N D C H E M I C A L D Y N A M I C S OF T H E GALAXY

N. N A K A S A T O Department

of Astronomy,

School of Science, University Tokyo 113-0033

of Tokyo,

Bunkyo-ku,

The three-dimensional hydrodynamical N-body model of the formation of the Galaxy is presented. Since all previous numerical models of the Galaxy forma­ tion do not have a proper treatment of the chemical evolution and/or sufficient spatial resolutions, we have constructed the detailed model of the chemical and dynamical evolution of the Galaxy using our GRAPE-SPH code. Starting with the cosmologically motivated initial condition, we have obtained the qualitatively similar stellar system with the Galaxy.

1

Introduction

From the observational point of view, there were two distinct scenarios for the formation of the Galaxy. One is the "free-fall collapse" scenario proposed by Eggen, Lynden-Bell & Sandage (1962). By evaluating the orbital motions of stars near the sun, they found a strong correlation between the orbital motion of stars (eccentricity) and the ultraviolet excess (metallicity). From this facts, they have concluded that the collapse that produce the Galaxy was very rapid and occurred in nearly free-fall time scale. On the other hand, Searle & Zinn (1978) have proposed the "slow collapse" scenario. They analyzed the metallicity of the halo globular clusters and found no correlation between the metallicity of clusters and its position. From this fact, they have concluded that the formation of the Galaxy was not the ordered collapse as proposed by Eggen, Lynden-Bell &. Sandage (1962) but the processes in which small fragments continued to collapse for a longer time scale than the free-fall time scale. A recent theory predict that the galactic scale objects were formed by the structure formation in the cold dark matter (CDM). According to the CDM scenario, larger clumps increase their mass by the progressive merger of smaller clumps. During such evolutions, the angular momentum also increases due to the angular momentum transfer by a tidal force of surrounding clumps. At some epoch, the over-dense region is virialized to form a dark halo of a certain mass. Namely, the Galaxy formation occurred during the gradual formation of a dark halo in the CDM cosmology. Thus, the formation process of the Galaxy in the CDM cosmology was the midway of the "free-fall collapse" and "slow collapse" scenarios. In this paper, we investigate the formation process of the Galaxy using

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high resolution numerical simulations. The three-dimensional model for the formation of disk galaxies has been investigated by many authors (Katz 1992, Steinmetz & Muller 1995) and they have succeeded in many respects. We follow the methods and models by the previous authors but use much larger number of particles to study the detailed formation and evolution processes of the Galaxy. To properly model the dynamics of the merging history, we have to adopt the three-dimensional SPH method. Our SPH code uses the GRAPE (Sugimoto et al. 1990) and the Remote-GRAPE system (Nakasato, Mori, & Nomoto 1997) to compute the gravitational interaction between par­ ticles (GRAPE-SPH code). Our SPH code includes various physical processes, i.e., radiative cooling, star-formation, energy feedback from stars, and chem­ ical evolution. Using the chemical and dynamical SPH code, we simulate the evolution of the Galaxy starting from the plausible cosmological initial condition. 2

Model

To model the cosmological galaxy formation, we need to use the physically motivated initial conditions, which is described below. The initial model used in this paper is constructed by the following manner: First, we generate many number of a spherical top hat 3 a over-dense region as Katz (1992). Then we follow the evolution of dark matter particles of these spherical region with a usual N-body code from high redshift. At appropriate redshift, we examine the properties of each halo and select the desired halo for hydrodynamical simulations. After the selection of some halos, we restart the hydrodynamical N-body simulation from the beginning. The starting redshift is ~ 25. Initially, we use ~ 27,000 particles of both gas and dark matter particles, namely, the total number of particles is ~ 54,000 particles. 3

Results

At the beginning of the evolution, the spherical region is expanding due to the Hubble velocity while the small scale structures are growing. These small clumps gradually merge to produce the larger clumps. At t ~ 0.3 - 0.5 Gyr, the 3 clumps merge and the resulted clump become the primary halo that eventually becomes a spiral galaxy. At t ~ 1 Gyr, the dark matter is almost virialized and the evolution becomes a quasi-static state. The star formation rates (SFR) as a function of time is plotted in Figure 1. The first star for­ mation occurs at t ~ 0.015 Gyr. Within first 0.15 Gyr, the SFR remains low value. After t ~ 0.015 Gyr, the SFR increases with time and become

360

maximum at t ~ 0.4 Gyr. This time corresponds to the time of the largest merger event. After that time, the SFR gradually decreases and eventually become almost constant (~ 2 M© y r _ 1 ) after t ~ 3 Gyr. This constant star formation mainly occurs in the gas disk. After 5 Gyr of the evolution (up to Z ~ 1), over 80,000 star particles form and the number of gas particles decreases to ~ 13, 000. At this stage (Z ~ 1), we categorize the stars using the chemical properties and the formation epoch (tform) °f the star particles as seen in Figure 2. From the observational facts of the each components (halo, bulge, disk) of the Galaxy (Mihalas k Binney 1981), we categorize stars by the following conditions and present the results in Figure 2: • left panel : Metal-poor (Z/Z© < —3) stars • center panel : Old (tform < 1 Gyr) and metal-rich (Z/Z© > 0) stars • right panel : Young (tform > 4 Gyr) stars Here, Z is the metal fraction in stars. Metal-poor stars show the extended distribution since these stars formed at an early epoch and at high latitude. The old and metal-rich stars are concentrated in the galactic center. The young stars are located near the galactic plane, because the most recent star formation occurs in the disk. From these results, we conclude that we obtain the stellar system that is very similar to the Galaxy. The early evolution of our model have revealed that the star located near the center (bulge stars) formed during the sub-galactic merger. Because of the strong star burst induced by the mergers, the metallicity distribution function of the bulge stars becomes as wide as observed. Also the observed bi-modal metallicity distribution function is naturally explained with our chemical and dynamical model (Figure 3). From these results, we suggest that the Galactic bulge was formed through the sub-galactic clump merger in the proto-galaxy. References 1. 2. 3. 4. 5. 6. 7. 8.

Mihalas, D., k Binney, J., Galactic Astronomy (second edition) Eggen, O.J.; Lynden-Bell, D., k Sandage, A.R., 1962, ApJ, 136, 748 Searle, L., k Zinn, R., 1978, ApJ, 225, 357 Katz, N., 1992, ApJ, 391, 502 Nakasato, N., Mori, M., k Nomoto, K., 1997, ApJ, 484, 608 Steinmetz, M., k Miiller, E., 1994, AkA, 281, 97 Steinmetz, M., k Miiller, E., 1995, MNRAS, 276, 549 Sugimoto, D., Chikada, Y., Makino, J., et al., 1990, Nature, 345, 33

361

Figure 1. The total SFR as a function of time.

Figure 2. The projected particle positions at t = 5 Gyr for three components are shown. From the left panel, the metal-poor stars, the metal-rich and old stars, and the young stars (see text). The size of the panel is 20Kpc X 20Kpc.

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[Fe/H] Figure 3. The metallicity distribution function of the all stars located near the galactic center. The dashed and dotted lines correspond to the very old stars (t < 0.5 Gyr) and other stars, respectively

EXPLOSIVE NUCLEOSYNTHESIS IN PAIR-INSTABILITY SUPERNOVAE JUNKO NAKATSURU, TAKAYOSHI NAKAMURA, HIDEYUKI UMEDA, AND KEN'ICHI NOMOTO Department of Astronomy, and Research Center for the Early Universe, School of Science, University of Tokyo, Japan E-mail(Nakatsuru): [email protected] We calculate the final evolution of very massive population III stars in the mass range of 150 to 300 M Q and obtain detailed nucleosynthesis yields of their ex­ plosions. We perform hydrodynamic simulations of the collapse-explosion process caused by e + e""-pair creation instability during their oxygen burning phase and calculate explosive nucleosynthesis with an extended nuclear reaction network. We then obtain the following results: 1) Population III Stars of 150 — 2 0 0 M Q explode as pair-instability supernovae. The upper mass limit for the explosion is between 200 — 3 0 0 M Q . 2) In pair-instability supernovae, iron is produced more abundantly from more massive progenitors. 3) Pair-instability supernovae produce large amounts of Si, S, Ar and Ca relative to O. This is a similar characteristic as that of hypernovae [E > 10 5 2 erg), the progenitors of which have 30-40 MQ on their main-sequence. 4) We compare our yields with those of the observed metaldeficient stars. The abundance patterns are not in good accord and it implies that pair-instability supernovae were not dominant in the early Galaxy. 5) We also calculate theoretical light curves of a pair-instability supernova and find that they are very luminous (L ~ 10 4 3 erg s - 1 ) because of the large production of 5 6 Ni.

1

Introduction

Pair-instability supernovae originate from the stars which are more massive than ~ 100M Q (e.g., Fowler & Hoyle 1964). At the center of such massive stars, the temperature is so high when the oxygen-rich core forms that there exist many photons which have the energy greater than the rest-mass energy of two electrons. Besides, the effective adiabatic index T is close to 4/3 be­ cause of a large fraction of radiation pressure. Thus, copious electron-positron pairs are created and F drops below 4/3; then the star becomes dynamically unstable and begins to collapse. The central temperature gets higher and the contraction leads to the onset of explosive oxygen burning. Finally, oxygen burns explosively releasing a large amount of nuclear energy. After V becomes larger than 4/3 again, the infall is stopped and the cores start to re-expand. It is believed that a larger number of such massive stars existed, in the early Galaxy, than in the present epoch (e.g., Tohline 1980, Hutchins 1976). Both the initial absence of any metal and the influence of the background radiation would tend to make the stars considerably more massive. Therefore,

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very massive stars are likely to have affected the Galactic chemical evolution through pair-instability supernovae. Most of the previous studies for pair-instability supernovae were limited in a simple analysis with a small reaction network; therefore a detailed nucle­ osynthesis analysis has never been fully carried out. Thus, we are motivated to investigate the abundances of pair-instability supernova ejecta and their potential impact on the early Galactic chemical evolution. 2

Explosions & Nucleosynthesis

Presupernova models of 150 — 3OOM0 with no initial metal are used for our calculations (Umeda & Nomoto 2000; see also Umeda et al. 1999). They evolve through the hydrogen, helium and carbon burning stages, to the onset of the e + e"-pair creation instability. No mass loss is assumed because of no metals, near the surface. We use an equation of state which includes the effect of electron-positron pair creation to track the evolution correctly (Nomoto & Hashimoto 1988). Screening effects and Coulomb interaction (Slattery et al. 1982) are also taken into account. The effect of convection is neglected on the assumption that the evolution is too fast to allow for effective mixing (see Fraley 1968). Neutrino losses also have a minor influence in this fast evolution (Barkat et al. 1967), so their effect is included but negligible. The hydrodynamic evolutions are simulated using a one-dimensional PPM (piece-wise parabolic method) code (Colella & Woodward 1984). A small nuclear reaction network, which contains only 13 alpha-nuclei from 4 He to 56 Ni, is added to the hydrodynamics model to determine the rate of nuclear energy generation and the composition profiles. The detailed nuclear evolution is then calculated by a post-processing, using the thermodynamic trajectories from our hydrodynamic models and a large reaction network which contains 283 isotopes up to Br (Hix & Thielemann 1996). Models of 150, 170, 200 and 3OOM0 stars are calculated. Figure 1 shows the evolutionary paths of the central temperature and density. Table 1 sum­ marizes the physical quantities during the evolution and the amount of major elements in the ejected matter. The 170 M Q model becomes dynamically unstable at the central tempera­ ture Tc ~ 1.7 x 109 K and starts to collapse. In the early phase the dynamical evolution proceeds almost adiabatically with log T/logp ~ 1/3. The temper­ atures in the central region reach Tc ~ 3 x 109 K during the collapse and explosive oxygen burning sets in. The central temperature then rises above Tc = 3.5 x 109 K and heavy elements are synthesized. The inner region gradu-

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Figure 1: Schematic evolution of central density and temperature of a 170M© star. Two hatched areas show instability regions where T < 4 / 3 . The evolution of a 170M© star after the dynamical instability is presented.

ally exits the instability region and the nuclear energy release reverses the infall of the core into explosion. Finally the star undergoes complete disruption. Figure 2 displays the composition profile of the ejecta as functions of en­ closed mass and the expansion velocity (left) and the abundance ratios of stable isotopes relative to solar system values (right). Neutron-rich isotopes are less produced while the alpha-chain isotopes are more abundant than solar's. Also the intermediate nuclei from Si to Ca are synthesized very abundantly. In ad­ dition, odd-z isotopes, such as 23 Na, 27 A1, 3 1 P, 37C1 and 39 K, are less produced because of the use of metal-free stars as progenitors (see Umeda et al. 1999). The final explosion energy E = 1.5 x 1052 erg is much greater than that of a usual Type II supernova (for SN 1987A, E = (1.0 - 1.5) x 1051 erg; Shigeyama et al. 1990). The 200M Q star gives qualitatively the same result as that of the 170MQ star. However, the collapse proceeds to the higher central temperature, so iron is produced more abundantly and the explosion energy is greater than the 170MQ star. The calculation for the 3OOM0 star does not lead to the explosion. Most of the oxygen fuel is consumed and temperatures exceeds 7 x 109 K. Then

365 1600 2400

2700

2800

enclosed m a s s (M/MQ)

V (km/s)

Mass N u m b e r

Figure 2: Left: Final nucleosynthesis yields from a 17OJW0 Pop III pair-instability supernova. Only dominant abundances are presented. Right: Abundances of stable isotopes relative to the solar system values for a 170 M© star. The ratios are normalized to 1 6 0 . Isotopes of various elements are connected by solid lines.

the nuclei are photo-disintegrated into alpha-particles and nucleons, which consume more energy than previously released by oxygen and silicon burning. Thus, the star will collapse towards a black hole. Our lowest mass model of 150 M Q explodes as a pair-instability supernova. However, only 5 M© of oxygen is burned and the nuclear energy release from oxygen burning is relatively small. The final explosion energy E = 2.3 x 1051 erg is comparable with that of a usual Type II supernova (SN II). We also calculate theoretical light curves for pair-instability supernovae (Figure 3) with a one-dimensional spherically symmetric radiative transfer code (Iwamoto et al. 2000). We find that the light curve of a 170MQ pair-creation supernova is very bright (L ~ 10 43 erg s _ 1 ), about ten times that of usual SNe II, because of the large production of 56 Ni. The light curve keeps very luminous, even after it reaches the late tail phase around 300 days, in which the ejecta is thin against optical photons and the light curve is determined by the decay rate of 56 Co —> 56 Fe. It is interesting to compare with the brightest SN II 1997cy (Germany et al. 2000; Turatto et al. 2000), although the model curve declines faster than SN 1997cy. Our results are qualitatively consistent with previous studies (e.g., Herzig et al. 1990, Woosely k. Weaver 1982).

366 Table 1: Physical values of the pair-instability supernovae and their main nucleosynthesis products for all models.

Progenitor mass (MQ) He core mass (MQ) Tpeak (xlO 9 K) Ppeak ( X l O 6 g / c m 3 )

Explosion energy (xlO 51 erg) 4 He(M 0 ) 12 C(M 0 ) 16

24

44

Ti Cr 52 Fe 56 Ni 48

3

0(MQ)

Mg(M 0 ) 28 Si(M 0 ) 4O Ca(M 0 ) (decay into 44 Ca) (MQ) (decay into 48 Ti) (M©) (decay into 52 Cr) (M©) (decay into 56Fe) (M 0 ) Fe (MQ) Mg (MQ) [Fe/H] [Mg/H]

150 81 3.5 2.0 2.3 45 3.7 49 4.3 6.9 0.4 5.1 x 10" 5 1.7 x 10~4 1.8 x 10" 3 3.6 x 10" 2 5.8 x 10" 2 4.26 -3.58 -1.43

170 88 4.0 2.2 15 47 3.0 47 3.6 14 1.1 1.5 x 10" 4 2.5 x 10- 3 3.6 x 10" 2 0.69 0.74 3.6 -3.31 -2.33

200 102 4.5 3.5 17 66 2.7 53 4.1 16 1.3 1.8 x 10" 4 5.0 x 10" 3 1.0 x 10" 1 2.7 2.8 4.1 -2.80 -2.35

300 146 (collapsed)

Discussion Sz Conclusion

As we have seen in §2, pair-instability supernovae explode very energetically and produce large amounts of intermediate mass nuclei. Their abundance pat­ terns are quite different from those of usual Type II supernovae (Thielemann et al. 1996). However, models for the recently-discovered very energetic su­ pernovae, called hypernovae, such as SN1998bw and SN1997ef (Iwamoto et al. 1998, 2000; Nakamura et al. 2000), show similar abundance patterns as pairinstability supernovae. Both types of supernovae have large explosion energies and produce plenty of Si, S, Ar, Ca and Fe. The abundance data observed in metal-poor halo stars shows large starto-star variations and it suggests that the interstellar medium (ISM) of the halo was not well mixed and prior nucleosynthesis involved a single supernova or a few supernova (e.g., Audouze & Silk 1995; Shigeyama & Tsujimoto 1998). That is, the metal-deficient stars may have information on abundances of indi­ vidual supernovae which exploded at the early epochs of the Galactic evolution. We note that the observations of very metal-deficient stars (McWilliam et al.

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1995a,b; Ryan et al. 1996) have shown the interesting trends of the abun­ dances of iron-peak elements. The elements Mn and Cr become very underabundant in stars with lower metallicity ([Fe/H] < —2.5; [X/Y] ='logio(X/Y) — l°gio(X/Y)0), while Co becomes overabundant (Nakamura et al. 1999). Comparing with the observations, the abundances of a-elements in the 170 and 200 M Q pair-creation supernova ejecta are remarkably larger, especially the ratios [Si, S, Ar, and Ca/Fe]. On the other hand, [C/Fe] is smaller than the solar ratio. Theoretical abundances of iron-group nuclei are also different from those of metal-deficient stars and the above trend cannot be reproduced. [Cr/Fe] is larger than the observed abundance ratio while [Co/Fe] is much smaller (Note that too small [Co/Fe] is the common problem of SNe II yield; Nakamura et al. 1999). Although we have looked for the metal-deficient stars which have the same abundance patterns as our models, we have not found a good example yet. It suggests that pair-instability supernovae were not dominant in the early Galaxy. However, there still remains a possibility that a part of metal-poor stars was contaminated by the ejecta of pair-instability supernovae. The num­ ber of well-observed metal-poor stars is too small (~ 50) to conclude that no

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effect of pair-instability supernovae is seen in the early Galaxy, taking into account the theoretical occurrence ratio of this type of supernovae to all the types (~ 1/300). The characteristic abundance patterns of pair-instability supernovae presented in this paper, such as high [Si, Ca/Mg (or Fe)], might be a clear evidence. Future observations with a large telescope such as SUBARU might make it possible to find any metal-deficient stars which have the abundance pattern of pair-instability supernovae ejecta. It will provide us im­ portant information on the existence of pair-instability supernovae and their effect on the Galactic chemical evolution. This work has been supported by the grant-in-Aid for Scientific Research (12640233) and COE research (07CE2002) of the Japanese Ministry of Educa­ tion, Science, and Culture. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

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23. 24. 25. 26. 27.

from Astrophysical Plasmas, eds. P. Martens, S. Tsuruta, k M. Weber (PASP), p.347 Nomoto, K. k Hashimoto, M. 1988, Phys. Rev. Lett. 163, 13 Shigeyama, T., k Nomoto, K., 1990, ApJ, 360, 242 Shigeyama, T., k Tsujimoto, T. 1998, ApJ, 507, L135 Slattery, W. L., Doolen G. D., k De Witt H.E. 1982, Phys. Rev. A, 26,2255 Thielemann, F.-K., Nomoto, K., k Hashimoto, M. 1996, ApJ, 460, 408 Turatto, M., Suzuki, T., Mazzali, P.A., Benetti, S., Cappellaro, E., Nomoto, K., Nakamura, T., Young, T.R., Patat, F. 2000, ApJ, 534, 57 Ryan, S. G., Norris, J. E., k Beers, T. C. 1996, ApJ, 471, 254 Tohline, J. E. 1980, ApJ, 239, 417 Umeda, H., Nomoto, K., Nakamura, T. 2000, in The First Stars, eds.: Weiss, Abel, Hill, in press (astro-ph/9912248) Umeda, H., k Nomoto, K., 2000, in preparation Woosley, S. E.,& Weaver, T. A. 1982, in Supernovae: A Survey of Current Research, eds. M. J. Rees and R. J. Stoneham, Dordrecht: Reidel, p.79

X - r a y O b s e r v a t i o n s of S N R s a n d h o t I S M i n t h e Large M a g e l l a n i c Cloud —the c h e m i c a l e n r i c h m e n t of t h e g a l a x y

Mamiko Nishiuchi, Jun Yokogawa, Ichizo Hayashi, Katsuji Koyama Department of Physics, Faculty of Science, Kyoto University Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan E-mail: [email protected] John P. Hughes Department of Physics and Astronomy, Rutgers University 136 Frelinghuysen Road, Piscataway, NI 08854-8019 The great portion of the elements are thought to be produced in'the supernova (SN) explosions and gradually mixed into the interstellar matter (ISM) of the galaxies. We can trace the course of the chemical-pollution of the galaxies by observing the supernova remnants (SNRs) and ISM. We present the X-ray measurements of metal abundances of the Large Magellanic Cloud (LMC). All the archive data in the vicinity of the LMC taken with the Advanced Satellite for Cosmology and Astro­ physics (ASCA) were used. The X-ray spectroscopy of the diffuse X-ray emission spreading over a large portion of the LMC was carried out in order to measure the metal abundance of the ISM directly. With the good spectral resolution of ASCA the nature of this diffuse X-ray emission was first confirmed to be thermal in origin, likely to be emitted from hot ionized ISM in the galaxy, because ASCA detected line emissions from various elements, which was beyond the capability of previous X-ray satellites. The X-ray spectrum of diffuse X-ray emission was reproduced by the Non-Equilibrium Ionization (NEI) model with temperature of ~ 1.2 keV. The overall elemental abundances determined from X-ray spectroscopy of ISM is found to be also consistent with previous results determined through X-ray SNR spectroscopy derived by Hughes, Hayashi and Koyama (1998) and previous optical and UV analysis, except overabundance of sulfer.

1

Introduction

SNe and their remnants are the key to our understanding of the origin of the chemical elements in the universe. The nucleosynthesis process inside a star generates many elements and SN explosions blow t h e m out into the interstellar space. Finally blown out elements are thought to be gradually mixed into the ISM uniformly. In the hot plasmas (10 6 ~ 10 7 K) both of the SNRs and the ISM of the galaxies, most of the elements are ionized up to the H-like or He-like ion stages, emitting strong line emissions in the X-ray band. Therefore, the X-ray spectroscopy of the SNRs and the hot ISM in the galaxies can tell us much information, for example, what kind of and how much elements are ejected by

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the SN explosions (from the X-ray spectra of young aged SNRs), are contained in the ISM (from the X-ray spectrum of middle aged SNRs and ISM itself), and so on. This information leads us to the understanding of the chemical evolution of the galaxies. Because of the proximity, reasonable angular sizes (not too large) and the low interstellar absorption toward it, we selected the Large Magellanic Cloud (LMC), known as the satellite galaxy of our own, as a target to investigate this problem using the X-ray spectroscopy. Because the LMC is a younger galaxy than our own, investigating it means to probe the aspect of our Galaxy at early stage of its life. The LMC is known to have many X-ray emitting SNRs inside. From the systematic X-ray spectral analysis of middle aged SNRs (Hayashi PhD thesis 1997 and Hughes, Hayashi and Koyama 1998), the abundances of the elements in the ISM around SNRs are obtained. This method was completely independent of previous ones to get the abundances of elements, such as UV and optical observations. The derived overall abundance pattern was consistent with previous results. The LMC, at the same time, is known to have plenty of diffuse X-ray emis­ sion. Since satellites with imaging capability came into use, such as Einstein and ROSAT, many observations of this diffuse X-ray emission were carried out. However, the spectral resolution of both the Einstein and ROSAT was not good enough to know the nature of the diffuse X-ray emission, namely could not tell thermal from non-thermal in origin. In the following we present the abundance determination through the ASCA X-ray spectroscopy of the hot plasma in the LMC. In section 2, we briefly introduce the abundance determination using the X-ray spectroscopy of SNRs carried out by Hughes, Hayashi and Koyama (1998). Section 3 provides the description of the observations and results of the diffuse X-ray emission in the galaxy. Finally we discuss the abundance pattern derived from these two methods. 2

X-ray Spectroscopy of S N R s

Evolution of SNRs are considered to be classified into three phases; 1: The initial phase of evolution is so-called "free-expansion phase". Almost all the initial explosion energy transit into the kinetic energy of the ejected matter. The ejected matter is heated up at the shock front. In this phase the observed X-ray spectrum has strong line emissions of various elements contained in the ejecta of SN explosions. 2:The second phase is known to be "adiabatic phase" or "Sedov phase". In this phase the shell is decelerated and at the same

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time significant amount of ISM is swept up. So the X-ray spectrum traces the characteristics of heated up ambient ISM. 3: The final stage of the SNR evolution is called "radiative-cooling phase". In this stage, the radiative cooling begins in earnest. The cold and dense shell, which has no longer capability to emit X-ray emission, is left. Therefore, one can use the X-ray spectroscopy of SNRs in the adiabatic phase as a tool to determine the chemical composition of ISM. Hughes, Hayashi and Koyama (1998) made a systematic X-ray spectroscopy of intermediate age SNRs in the LMC, which are thought to be in the adia­ batic phase, using the ASCA data. Because of the poor angular resolution of ASCA, the SNRs at the distance of the LMC could not be spatial resolved. Therefore, in the spectral fitting analysis, they used the "Sedov self-similar solution model"; they divided the X-ray emitting region within the SNR into many shells in order to consider the radial distribution of density of the elec­ trons and ions and temperature of plasma inside. The entire spectrum of SNR is composed of those emitted by the series of shells. The derived abundances are shown in figure 1. The overall abundances are consistent with the previous results obtained by the optical data, but do not show anomalous overabundance of magnesium and silicon seen by the Russell & Dopita (1992). 3

X-ray Spectroscopy of ISM

ASCA had observed the LMC 53 times by the end of Sep. 1999. We used all those in the archive (49 pointing observations) and those taken in the LMC survey project during the ASCA Announce of Opportunity (AO) 7 phase (9 pointing observations), which are our own proposed observations. The total exposure time is 1920 ksec. All the archive data were obtained from NASA HEASARC (High Energy Astrophysics Science Archive Research Center) data system. Most of the optically bright position called optical bar and the region towards the northern part of the galaxy were covered with these data. After removing all the discrete sources which exceeded over 5 sigma signalto-noise level threshold, we accumulated the diffuse X-ray spectra from each pointing observation around optical bar and summed them up to obtain good statistics. In the spectral fitting, we tested the non-thermal model. However this model was completely rejected not only from the statistical point of view but also from the waving behavior of residuals from the best fit model, indicating the existence of the line emissions from various elements. On the contrary the thermal plasma models in which elemental abundances were treated as free pa-

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rameters were more appropriate for both of Collisional lonization Equilibrium (CIE) and Non-Equilibrium lonization (NEI) state conditions. The tempera­ ture was determined to be ~ 0.7 keV for CIE and ~ 1.2 keV for NEI model, respectively. This result shows, for the first time, that the diffuse X-ray emis­ sion in the LMC is thermal in origin, probably coming from the hot ISM of the LMC. At the same time, the NEI plasma model was more favorable than CIE one because the CIE plasma model required unreasonable high abundances of sulfur, argon and calcium, though the same kind of tendency was also seen, still less, in the NEI model. The derived abundances from NEI model fitting of hot ISM spectrum in the LMC are also shown in figure 1. The overall pattern of abundances derived from one temperature plasma model fitting are consis­ tent with the previous ones. However, the elements whose line energies are higher than sulfur take higher abundances and at the same time the elements whose line energies are lower than that of sulfur is in a little insufficient to the abundances obtained from the previous analysis. This condition maybe results from the artifact of the one temperature plasma model fitting and suggests us an implication of other higher temperature plasma component. Our future work will be devoted to the more detail abundance determination of the hot ISM with two temperature thermal plasma models.

Mean LMC Abundances

Figure 1: Mean LMC abundances derived from optical/UV observations (Russell &i Dopita 1992; RD92) and the X-ray spectroscopy of middle-aged SNRs (Hughes, Hayashi and Koyama 1998) and ISM (this work)

References 1. Russell, S.C., & Dopita, M.A., 1992, ApJ, 384, 508 2. Hayashi, I. PhD thesis, 1997, ISAS Research Note 620. 3. Hughes, J.P., Hayashi, I., and Koyama, K., 1998, ApJ, 505, 732

R-PROCESS NUCLEOSYNTHESIS IN NEUTRINO-DRIVEN W I N D : GENERAL RELATIVISTIC EFFECTS A N D SHORT DYNAMIC TIMESCALE MODEL

KAORI OTSUKI, TOSHITAKA KAJINO Division

of Theoretical

Astrophysics, National Astronomical Observatory Mitaka, Tokyol 81 -8588, Japan E-mail: [email protected], [email protected]

of

Japan,

SHIN-YA W A N A J O Department of Physics, Sophia University, 7-1 Kioi-cho Chiyoda-ku Tokyo 102-8554, Japan E-mail: [email protected] HIDEYUKI TAGOSHI Graduate

Department of Earth and Space Science, School of Science Osaka University, Toyonaka OSAKA E-mail: [email protected]

560-0043,

Japan

Neutrino-driven wind from young hot neutron star, which is formed by supernova explosion, is the most promising candidate site for r-process nucleosynthesis. We use spherical steady state flow model in general relativistic framework. Exploring wide parameter region which determines the expansion dynamics of the wind, we can find interesting physical conditions which lead to successful r-process nucle­ osynthesis.

1

Introduction

Neutrino-driven wind is one of the most promising candidates for r-process nucleosynthesis. It is generally believed that a neutron star is formed as a remnant of gravitational core collapse of Type II, lb or Ic supernovae. The hot protoneutron star releases most of its energy as neutrinos during KelvinHelmholtz cooling phase, and these neutrinos drive matter outflow from the surface. This outflow is called neutrino-driven wind. We briefly explain a r-process nucleosynthesis scenario in neutrino-driven wind. On the surface of a protoneutron star (the temperature T ~ 3-5 MeV), the ejected material consists of almost free neutron and proton. They are blown away from the surface and begin to cool down. When the temperature reaches T ~ 0.5 MeV, most protons are assembled into a-particles and acapture process begins. This is a process to produce seed nuclei. If the temperature subsequently reaches T ~ 0.3-0.2 MeV, charged particle reactions

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begin to freeze out and are followed by r-process nucleosynthesis. This scenario is consistent with observations which suggest that the r-process should be primary process 7 . Nevertheless, various numerical calculations of neutrino-driven winds do not agree on the entropy and show essentially different results of r-process nucleosynthesis calculation in the wind 2 6 8 9 10 . We use spherical steady state flow model in order to avoid uncertainty arising from numerical simulation methods, supernovae models, etc. We investigate suitable physical conditions for r-process nucleosynthesis in neutrino-driven wind. 2

Model

Since the wind blows near the surface of the neutron star, it is needed to study expansion dynamics of neutrino-driven wind in general relativity. Although there might be some conditions, such as rotation and convection, which break the spherical symmetry and steady states, we here assume the spherical sym­ metric and steady state cases in order to investigate the essential physical properties of neutrino-driven wind. The basic equations to describe the spherically symmetric and steady state winds in Schwarzschild geometry are given by M = 4Trr2pbu, du 1 dP ( , u— = — — 1+u2 dr ptot + P dr de dr

P dpb pi dr

(1) 2M\

M -—,

(2)

(3)

where M is the mass outflow rate, r is the distance from the center of the neutron star, pb is the baryon mass density, u is the radial component of the four velocity, ptot = Pb + Pb£ is the total energy density, e is the specific internal energy, P is the pressure, M is the mass of the neutron star, and q is the net heating rate due to weak interactions 5 6 . This heating rate depends on neutrino luminosity. We use the conventional units that the plank constant h, the speed of light c, Boltzmann constant fc, and gravitational constant G, are taken to be unity. We assume that the material in the wind consists of photons, relativistic electrons and positrons, and non-relativistic free nucleons. We fix T=0.1 Mev at 104 km to define the mass loss rate. In this calculation, we adopt the typical values of a protoneutron star: the radius r; = 10 km,and the baryon density at the surface pi = 10 10 g/cm 3 . Solving these differential

376

Figure 1. Relations of S and T^yn.

equations, we can obtain radial profiles of velocity, temperature, and density for various parameter sets of neutron star mass M and neutrino luminosity

3

Results

One of the most important hydrodynamic quantity, which characterizes the expansion dynamics of the neutrino-driven wind, is the duration time of the a-process; called dynamical timescale Tdyn. It is defined as a timescale that the temperature decreases one e-fold from 0.5MeV. Entropy per baryon, S, settles the fraction of free nucleon in NSE material. The electron fraction gives a ratio of neutron and proton in material. Since r-process nucleosynthesis is very sensitive to the electron fraction, it is regarded as free parameter in this work. Now we can calculate S - Tdyn relations for various neutron star masses and neutrino luminosities. We show the results in Fig. 1. Two hatched regions satisfy the approximate condition which produce A=200,130 nuclei 3 5 . We find that dynamical timescale as short as Tdyn — 6 ms with M = 2.0 M Q and Lv = 1052 ergs/s is preferable in this figure. Note that, in Newtonian framework, we can not find such a short dynamic timescale wind in 6 . Finally, we confirm that the second and third peaks are produced with these conditions by network calculations. Figure 2 shows final r-process abun­ dances in this calculation compared with these of the solar system 4 . The

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LogY

0

20

40

60

80

100

MASS

120

140

160

180

200

220

240

NUMBER

Figure 2. r-process abundance in our calculation and solar system.

r-process abundances in the solar system are adopted in arbitrary unit. For successful r-process nucleosynthesis, we can find interesting physical conditions, short dynamical timescale Tdyn ~ 6 ms and relatively low entropy S ~ 140. Unfortunately, we could not find such conditions on M = 1.4M0 case so far as spherical steady state flow. A continued effort in investigating various effects on neutrino-driven winds with detailed calculations would be required to reproduce r-process nucleosynthesis in the solar system. References 1. Burbidge, E.M., Burbidge, G.,R., Fowler, W.A., & Hoyle,F. Rev.Mod.Phys. 29, 547 (1957) 2. Cardall, C.Y. & Fuller, G. ApJL 486, L l l l (1997) 3. Hoffman, R. D., Woosley, S. E.,& Qian, Y.-Z. ApJ 482, 951 (1997) 4. Kappeler, F., Beer, H., & Wisshak, K. Rep.Prog.Phys. 52, 945 (1989) 5. Otsuki, K., Tagoshi, H., Kajino, T., & Wanajo, S. ApJ 533, 424 (2000) 6. Qian,Y.-Z., & Woosley, S., E. 1996 471, 331 (1996) 7. Sneden, C , McWilliam, A., Preston, G., Cowan, J.J.,Burris, D.L., & Armoski, B.J. ApJ 467, 819 (1996) 8. Takahashi, K., Witti, J., & Janka, H.-Th. A&A 286, 857 (1994) 9. Witti, J., Janka, H.-Th., & Takahashi, K. A&A 286, 842 (1994) 10. Woosley, S.E., Wilson,J.R., Mathews,G.J., Hoffman, R.D., & Meyer, B.S. ApJ 433, 229 (1994)

The Critical Role of Light Neutron-Rich Nuclei in the r-Process Nucleosynthesis Mariko Terasawaa, K. Sumiyoshib, T. Kajinoc, I. Tanihata d , G. J. Mathews6 and K. Langankef a

The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan

b

Numazu College of Technology (NCT), Numazu, Shizuoka 410-8501, Japan

c

National Astronomical Observatory (NAO), Mitaka, Tokyo 181-8588, Japan

d

The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198, Japan e

The University of Notre Dame, Notre Dame IN 46556

f

Institute of Physics and Astronomy, University of Aarhus, Denmark

We have extended the nuclear reaction network for 1 < Z < 10 in order to investigate the role of light neutron-rich nuclei in the r-process. We find that a new nuclear reaction flow path opens in the region of very light neutron-rich nuclei as the temperature decreases. This'new reaction flow can affect the final abundances by up to a few orders of magnitude, while still producing the characteristic three r-process peaks as well as the hill of the rareearth elements.

1. Introduction Most previous studies of r-process nucleosynthesis have been largely concerned with the reaction flow through heavy unstable nuclei. Typically, nuclear reaction networks have included a few thousand heavy nuclei, while only a limited number of the light-mass nuclei near the valley of stability were considered. However, if the r-process occurs in i/-driven winds material in the wind expands from a high-entropy hot plasma consisting initially of free neutrons, protons, and electron-positron pairs under an intense flux of neutrinos. In such conditions, neutron-rich light-mass nuclei as well as heavy nuclei can play an important role in the production of both seed nuclei and r-process elements. We therefore have extended the nuclear reaction network to include ~ 80 unstable nuclei up to the neutron-drip line for 1 < Z < 10. We compare the final r-process abundances in the i/-driven winds with and without this extension of the network.

378

379 2. Nuclear Reaction Network For 10 < Z < 94, we have used the network of Meyer et al. [1], which includes about 3000 nuclear species from the /^-stability line to the neutron drip line. However, for our purpose, their network is too narrow for light nuclei with Z < 10. It includes only ten nuclei n, p, 2H, 3H, a, 9Be, 12 C, 13C, 1 6 0, 1 7 0. We have extended this network to include 80 nuclei up to the neutron-drip line for Z < 10 (see dots in Fig. 1). Our network (hereafter called 'the full network') includes almost all charged-particle reactions for A< 28. For comparison, we have also used the narrower network ('the small network'). For the ^-interactions, we have included ve capture for all nuclei, as well as ve capture by free protons ([2]). For very neutron-rich nuclei, we have also included ^-induced neutron emission([3]) (see Terasawa et al. [4] for more details). 3. ^-driven winds We employ the ^-driven wind models of Sumiyoshi et al. [5]. We choose the case in which the expansion timescale is as short as Tdyn = 0.005 sec with M^ 2.0 M 0 , RNS = 10 km and, L„itotai = 6 x 1052 erg/sec. For illustration, we use one typical trajectory of the wind. We start the r-process network calculation from the time when the temperature drops to T 9 = 9.0. At this point, the initial nuclear statistical equilibrium consists of free neutrons and protons. The initial Ye 0.42 is taken from the hydrodynamical simulations. 3.1. Results

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Figure 2. Final abundances as a function of mass number.

It has often been noted in literature that the r-process path runs through nuclei with almost the same Sn-value. On the assumption of steady state flow, a typical neutron separation energy at freezeout is S n ~ 2 — 4MeV. In the present analysis using our

380 'full network', the corresponding Sn-value is nearly 1 MeV. This result indicates that the r-process path runs through a more neutron-rich region. The r-process path is displayed in Fig. 1 at a time of t=0.57 sec after core bounce. At this time T9 = 0.62, and p = 5.4 x 102g/cm3. Abundant nuclei are shown by open circles, whose diameters are proportional to the abundance yields. The main reaction path is indicated by arrows. Fig. 2 shows the final abundance distribution. The solid and dotted lines in this figure are the results obtained by using the 'full network' and 'small network', respectively . Data points are the solar-system r-process abundances from Kappeler et al. [6] in ar­ bitrary units. We get excellent agreement with the observed solar r-process abundance pattern in the 'full network' calculation, which includes the light neutron-rich nuclei. The nuclei for light-to-intermediate masses (A < 120) are more abundant and the height of the third r-process peak at A= 195 decreases slightly in the 'full network' calculation com­ pared to the calculation of the 'small network'. The main reason for this difference arises from the fact that a new nuclear reaction flow opens in the light neutron-rich nuclei. This results in a smaller contribution from the charged particle reactions to seed production

([4],[7]). Acknowledgments One of the authors (MT) wishes to acknowledge the fellowship of RIKEN Junior Re­ search Associate. One of the authors (GJM) also wishes to acknowledge the hospitality of the National Astronomical Observatory of Japan where much of this work was done.

REFERENCES 1. Meyer, B. S., Mathews, G. J.,Howard, W. M., Woosley, S. E., and Hoffman, R. D., ApJ, 399, 656 (1992) 2. Qian, Y.-Z., Haxton, W. C., Langanke, K., and Vogel, R, Phys. Rev. C55, 1533 (1997) 3. Meyer, B. S., McLaughlin, G. C., and Fuller, G. M., Phys. Rev. C58, 3696 (1998) 4. Terasawa, M., Sumiyoshi, K., Kajino, T., Tanihata, I., and Mathews, G., submitted to Astrophys. J. (2000). 5. Sumiyoshi, K., Suzuki, H., Otsuki, K., Terasawa, M., and Yamada, S., Pub. Astron, Soc. Japan 52, 601 (2000) 6. Kappeler, F., Beer, H., and Wisshak, K., Rep. Prog. Phys., 52, 945 (1989) 7. Terasawa, M., Kajino, T., Wanajo, S., Langanke, K., and Mathews, G., submitted to Astrophys. J. (2000).

T H E R M O D Y N A M I C PROPERTIES OF N U C L E A R "PASTA" IN N E U T R O N STAR CRUSTS G. WATANABE*, K. IIDA a ' b , K. SATO a ' c Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan h Department of Physics, University of Illinois at Urbana- Champaign, 1110 West Green Street, Urbana, IL 61801-3080, USA c Research Center for the Early Universe, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan a

Equilibrium phase diagrams for neutron star matter at subnuclear densities are obtained at zero temperature. Spherical, rod-like and slab-like nuclei as well as spherical and rod-like nuclear bubbles are taken into account by using a com­ pressible liquid-drop model. This model is designed to incorporate uncertainties in the nuclear surface tension and in the proton chemical potential in a gas of dripped neutrons. The resultant phase diagrams show that for typical values of these quantities, the phases with rod-like nuclei and with slab-like nuclei occur in the form of Coulomb lattice at densities below a point where the system becomes uniform. Thermal fluctuations leading to displacements of such nuclei from their equilibrium positions are considered through explicit evaluations of their elastic constants; these fluctuations can be effective at destroying the layered lattice of slab-like nuclei in the temperature region typical of matter in the neutron star crust.

1

Introduction

In the deepest region of the inner crust (p £ ft ~ 3 x 1014 g c m - 3 ; ft is the normal saturation density), not only nuclei are expected to have spherical shape, but also they are expected to have rod-like and slab-like shapes, and moreover, the system is expected to turn inside out in such a way that the constituents of the original nuclei form a liquid containing rod-like and roughly spherical bubbles of the dripped neutrons. These transformation in principle stem from a delicate competition between the nuclear surface and Coulomb energies 1,2 .. At what densities the phases with non-spherical nuclei and bubbles are energetically more favorable than the usual bcc phase and the phase of uni­ form nuclear matter depends on the properties of neutron-rich nuclei and of the surrounding pure neutron gas. The quantities that mainly describe such properties but are still uncertain are the nuclear surface tension jE7surf and the proton chemical potential in pure neutron matter fi\>'. However, previ­ ous works were performed by using specific nuclear models and values of these quantities are designated almost uniquely in each previous works (e.g. 3 ' 4 etc.).

381

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n„ (fm- ) Figure 1: Zero-temperature phase diagram on the n^ (baryon number density) versus C2 (its standard value is 1.0) plane, evaluated for C\ = 400 MeV fin2. (400 MeV fm2 is its standard value.)

2

Results

In the present work, by generalizing a compressible liquid-drop model devel­ oped by Baym et al.6 in such a way as to incorporate uncertainties in Esur( and (o) Here we set them as MP

/#> = -CxnT Esur{ = C 2 tanh I - ^ y

(1) (2)

where Ci, C2 and C 3 are the adjustable parameters being positive definite; fj,ii is the neutron chemical potential in the neutron gas; E^f is the surface tension used by BBP. Eq. (1) approximately reproduces the overall density dependence of the results obtained from the Hartree-Fock theory with Skyrme interactions and from the lowest-order Brueckner theory with the Reid soft-core potential. As for Eq. (2), if we set C2 = 1.0 and C3 = 3.5 MeV (hereafter, C 3 is fixed at 3.5 MeV), .Esurf agrees well with the RBP's Hartree-Fock calculation7. The resultant phase diagram (Fig. 1) show that while the phases with cylindrical holes and with spherical holes can exist only for unrealistically low •E'surf, the phases with cylindrical nuclei and with slab-like nuclei survive almost

383

cylinder

a

0.01 r

/iS-

Figure 2: The critical temperature Tc for the phases with planar and cylindrical nuclei as a function of baryon density rib- The thick curves lying between the two vertical lines are the results in the density region in which the phase with planar (or cylindrical) nuclei is energetically stable.

independently of J5surf and /J,\, '. For these two phases, as noted by Pethick and Potekhin5, elastic properties of the nuclear rods and slabs are characterized by elastic constants used for the corresponding liquid-crystal phases. We also estimate thermally induced displacements of these nuclei using their expressions. In Fig./ 2, we plot the critical temperature at which the relative displacements y/{\v\2)/(a/2 — TN), which mean the shortest distance between the surface of the nucleus in its equilibrium position and the boundary of the cell containing it, become unity. Focusing on the typical values of C\ = 400 MeV fm2 and C2 = 1.0, we can see that the layered lattice of slab-like nuclei will be melt at typical temperatures of the neutron star crusts (&BT ~ 0.1 MeV) by thermal fluctuations. The difference in T c between these two lattices, as can be observed from Fig. 2, suggests that if formation of these two lattices can occur dynamically in the star, the layered phase is formed later than the triangular phase during the star' s cooling. It is expected that latent heat is released when these phases are formed. We also estimated the amount of released latent heat Q, and found that it yields Q ~ 1046 erg. Its effect seems to be detectable if it occurs after the neutron star cools down enough.

384

3

Conclusion

We have examined the dependence on the surface tension ESUI{ and on the proton chemical potential fj,p in pure neutron matter, of the density region in which the presence of non-spherical nuclei and of bubbles is energetically favored at T = 0. We have found that as ESUT{ decreases or /xp ' increases, such a density region becomes larger. For the values of Eami and fj,p ' as adopted in recent literature, our results show that in the ground state, the phases with rod-like nuclei and with slab-like nuclei lie between the bcc lattice phase and the uniform nuclear matter phase. The fluctuational displacements of such non-spherical nuclei from their equilibrium positions have been estimated at finite temperature. It has been suggested that at temperatures typical of matter in the neutron star crust, such fluctuations may melt the layered lattice of slab-like nuclei. If the dynamical processes leading to the formation of the non-spherical nuclei, latent heat would be released when they occur. It is found that its effect is expected to be detectable if it occurs in old neutron stars. Acknowledgements We are grateful to Professor Takeo Izuyama for useful discussion and valuable comments. References 1. D.G. Ravenhall, C.J. Pethick and J.R. Wilson, Phys. Rev. Lett. 50 (1983) 2066. 2. M. Hashimoto, H. Seki and M. Yamada, Prog. Theor. Phys. 71 (1984) 320. 3. C.P. Lorenz, D.G. Ravenhall and C.J. Pethick, Phys. Rev. Lett. 70 (1993) 379. 4. K. Oyamatsu, Nucl. Phys. A561 (1993) 431. 5. C.J. Pethick and A.Y. Potekhin, Phys. Lett. B427 (1998) 7. 6. G. Baym, H A . Bethe, C.J. Pethick, Nucl. Phys. A175 (1971) 225 (BBP). 7. D.G. Ravenhall, C D . Bennett and C.J. Pethick, Phys. Rev. Lett. 28 (1972) 978 (RBP). 8. G. Watanabe, K. Iida and K. Sato, astro-ph/0001273.

Symposium Program

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Symposium Program

The Origin of Matter and Evolution of Galaxies 2000 January 19 (Wednesday) Open i ng M. Ishihara (Director of Center for Nuclear Study, U. Tokyo) S. Kubono (Co-Chairperson, CNS) Early Universe and Chemo-Dynamic Evolution of Galaxies I G. Mathews (U.Notre Dame) , Chair T. Kajino (NAO) Prospect of Nuclear Cosmology; From Big-Bang to Supernovae T. Shigeyama (U. Tokyo) Inhomogeneous Chemical Evolution in the Galactic Halo T. Suzuki (NAO) A New Model of Evolution of Light Elements in Inhomogeneous Galactic Halo Early Universe and Chemo-Dynamic Evolution of Galaxies II S. Kubono (CNS), Chair T. Kifune (ICRR, U. Tokyo) Prospect of Very High Energy Gamma Ray Astronomy with Next Generation Imaging Cerenkov Telescope S. Yanagita (Ibaraki U.) Some Evidence for Supernova Origin of Galactic Cosmic Rays Y. Ishimaru (U. Tokyo) The First Enrichment of the Galaxy Inferred from Neutron-Capture Elements H. Umeda (U. Tokyo) Nucleosynthesis in Massive Metal Free Stars Observation of Elements I T. Kajino (NAO), Chair S. Amari (Washington U.) Presolar Grains as Probe to Nucleosynthesis in Stars and Evolution of the Galaxy C. Iliadis (U. North Carolina) Nucleosynthesis in Globular Cluster Stars M.Y. Fujimoto (Hokkaido U.) Internal and External Process of Chemical-Pollution in Extremely Metal-Poor Stars Y. Fukazawa (U. Tokyo) X-Ray Measurements of Metal Abundances of Hot Gas in Clusters of Galaxies

387

388 Observation of Elements II M. Smith (ORNL), Chair H. Murakami (Kyoto U.) X-Ray Diagnosis of the Galactic Center Abundance with an "X-Ray Reflection Nebula" M. Teshima (ICRR) The Highest Energy Cosmic Rays N. Hasebe (Waseda U.) Cosmic Ray Observation for Nuclear Astrophysics; CORONA Program T. Kishimoto (Osaka U.) Kaonic Nuclei Excited by the (K~, N) Reaction Poster Session I (with 6 Minutes Presentation - No Question and Comment) M. Smith (ORNL), Chair A. Bamba (Kyoto U.) Chemical composition and Distribution of Heavy Elements in a Supernova Remnant H. Ishiyama (KEK) Tanashi Recoil Mass Separator for Nuclear Astrophysics A. Iwazaki (Nishogakusha U.) Col 1 ision between Neutron Star and Axion Star as a Possible Source of Gamma Ray Burst and Ultra High energy Cosmic Ray N. Kudomi (RCNP) Double Beta Decays of 100Mo by ELEGANT V at Oto Cosmo Observatory K. Maeda (U. Tokyo) Nucleosynthesis in Gamma-Ray Bursts and Abundances in Black Hole Binaries T. Minemura (Rikkyo U.) Coulomb Dissociation of 12N and 130 S. Nagataki (U. Tokyo) Effects of Jet-Like Explosion in SN 1987A N. Nakasato (U. Tokyo) Formation and Chemical Dynamics of the Galaxies January 19 (Thursday) Stellar Evolution and the Nucleosynthesis - Hydrostatic Burning J. D'Auria (TRIUMF), Chair R. Tribble (Texas A&M) Direct Capture S-factors from Asymptotic Normalization Coefficients N. Iwasa (RIKEN) Coulomb Dissociation of 8B for 7Be(p, y) N. Kudomi (RCNP) Beam Current Monitor and Gas Pressure Control Techniques of Development for 3He+3He Solar Reaction Nucleosynthesis in Explosive Burning and New Approach

389 R. Tribble (Texas M M ) , Chair M. Smith (ORNL) Probing Stellar Explosions with Radioactive Beams at ORNL J. D'Auria (TRIUMF) The DRAGON Facility for Nuclear Astrophysics Studies at the New ISAC Radioactive Beams Facility S. Kubono (CNS) New Radio-Isotope Beam Facility for Nuclear Astrophysics - Study of a Critical Stellar Reaction 150(a, y)19Ne T. Motobayashi (Rikkyo U.) Methods for Astrophysics Studies with Intermediate-Energy RI Beams Explosion of Massive Stars I R. Tribble, Chair S. Yamada (U. Tokyo) Physics of Collapse-Driven Supernovae M. Yasuhira (Kyoto U.) Protoneutron Stars with Kaon Condensate and Possibility of Delayed Collapse Explosion of Massive Stars II T. Motobayashi (Rikkyo U.), Chair R. Boyd (Ohio State U.) OMNIS, the Observatory for Multi-Flavor Neutrinos from Supernovae Y. Fukuda (ICRR, U. Tokyo) Observation of Supernova Neutrino at SuperKamiokande K. Homma (Hiroshima U.) Can the Negative Mass Square of the Electron Neutrino be an Indication of Interactions with Relic Neutrinos ? Poster Session II (with 6 Minutes Presentation - No Question and Comment) T. Motobayashi (Rikkyo U.), Chair J. Nakatsuru(U. Tokyo) Explosive Nucleosynthesis in Pair-Instability Supernovae M. Nishiuchi (Kyoto U.) X-Ray Observations of SNRs and Hot ISM in the Large Magellanic Cloud - The Chemical Enrichment of the Galaxy K. Otsuki (NAO) r-Process Nucleosynthesis in Neutrino-Driven Wind- General Relativistic Effects and Short Dynamic Timescale Model M. Serata (Rikkyo U.) Coulomb Dissociation of 13N and 140 M. Terasawa (NAO) New Nuclear React ion Flow towards r-Process Nucleosynthesis in Supernovae: A Critical Role of Light Neutron-Rich Nuclei 1 <= Z <= 10. G. Watanabe (U. Tokyo) hermodynamic Properties of Nuclear "Pasta'' in Neutron Star Crusts

390 Y. Yamamoto (CNS) The Role of 18Ne(2p, y)20Mg process in Nucleosynthesis K. Yamada (Rikkyo U.) Coulomb Excitation of 150 January 21 (Friday) Explosion of Massive Stars III T. Kifune (ICRR, U. Tokyo), Chair K. Nomoto (U. Tokyo) Nucleosynthesis in Hypernovae and Galactic Chemical Evolution H. Tsunemi (Osaka U.) Observation of RXJ0852-4622 with ASCA - A Line Gamma-Ray Emitter from 44Ti Y. Mochizuki (RIKEN) 44 Ti in Supernova Remnants K. Koyama (Kyoto U.) X-Ray Study for the Chemical Composition of Astrophysical Objects Origin of the Heavy Elements I K. Koyama (Kyoto U.), Chair G. Mathews (U. Notre Dame) Neutron-Star Mysteries, r-Process, .. S. Wanajo (NAO) The r-Process in Neutrino Winds of Core-Collapse Supernovae Origin of the Heavy Elements II R.N. Boyd (Ohio State U.), Chair H. Utsunomiya (Konan U.) Photoneutron Cross Sections for 9Be and the Alpha-Process in Core-Collapsed Supernovae T. Suda (RIKEN) RIKEN RI-Beam Facility Project and the Way to the r-Process Nuclei M. Hashimoto (Kyushu U.) Crucial Reactions for Accreting Neutron Star Models Neutron Star and High Density Matter H. Toki (Osaka U.), Chair K. Sumiyoshi (RIKEN) Unstable Nuclei and an EOS Table for Supernovae and the r-Process in a Relativistic Many-Body Approach T. Takatsuka (Iwate U.) Baryon Superfluidity in Neutron Star Cores T. Tatsumi (Kyoto U.) Ferromagnetism of Quark Liquid and Magnetars CI os i ng T. Kajino (Co-Chairperson, NAO)

List of Participants

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393

Dr. Minoru Adachi 3-30-10 Minami-nagasaki, Toshimaku, Tokyo, 171-0052 Japan

Dr. John D'Auria Department of Chemistry Simon Fraser University Burnaby, British Columbia V5A 1S6, Canada

Dr. Sachiko Amari Physics Department, Box 1105, Washington University, One Brookings Dr. St. Louis, 63130-4899, USA

Dr. Masayuki Fujimoto Department of Physics Hokkaido University Kita 10, Nishi 8, Sapporo, 060-0810 Japan

Dr. Nori Aoi Department of Physics, University of Tokyo 7-3-1, Hongo, Bunkyo, Tokyo, 113-0033, Japan

Dr. Yasuhi Fukazawa School of Science, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033 JAPAN

Dr. Aya Bamba Cosmic-Ray Group, Department of Physics, Faculty of Science, Kyoto University K i t ash irakawa-0 i wake-cho, Sakyo-ku, Kyoto, 606-8502, Japan

Dr. Tomokazu Fukuda E-Group, KEK 1-1 Oho, Tsukuba, Ibaraki, 305-0801 Japan

Dr. Richard Boyd Department of Physics Ohio State University Columbus, OH 43210 USA

Dr. Yoshiyuki Fukuda Kami oka Observatory, Institute for Cosmic Ray Research, University of Tokyo Higashi-Mozumi, Kamioka-cho, Yoshiki-gun, Gifu 506-1205, Japan

Dr. Eunjoo Choi Research Center for Nuclear Physics, Osaka University 10-1 Mihogaoka, Ibaraki, Osaka, 567-0047 Japan

Dr. Tomoko Gomi Department of Physics, Rikkyo, University 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo, 171-0021 Japan

394 Dr. Tomotsugu Goto Institute of Cosmic Ray Research, University of Tokyo 430-10 Iwami Miyake-cho Shiki-gun Nara-ken, Japan

Dr. Masaaki Hirai Deparment of Physics, University of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo, 113-0033 Japan

Dr. Nobuyuki Hasebe Advanced Research Institute for Science and Engineering, Waseda University 3-4-1, Okubo, Shinjuku, Tokyo, 169-8555, JAPAN

Dr. Haj ime Hiyogon Department of Earth Planet Physics, University of Tokyo 7-3-1, Hongo, Bunkyo, Tokyo, 113-0033, Japan

Dr. Masaaki Hashimoto Department of Physics Kyushu University 4-2-1 Ropponmatsu, Chuoh-ku Fukuoka, 810-0044 Japan

Dr. Kensuke Homma Hadron Physics Laboratory, Department of Physics, Hiroshima University 1-3-1 Kagamiyama, Higashi-hiroshima, Hiroshima 739-8526 Japan

Dr. Takashi Hashimoto Department of Physics, Faculty of Science and Technology, Science University of Tokyo 2641 yamazaki,Noda,Chiba, 278-8510 Japan

Dr. Christian Iliadis 176 Phillips Hall, Department of Physics and Astronomy, University of North Carolina Chapel Hill, NC 27599-3255 USA

Dr. Kin-ya Hibino Faculty of Enginnering, Kanagawa University Rokkakubashi 3-27-1, Kanagawa-ku, Yokohama 221-8686, Japan

Dr. Nobuaki Imai Department of Physics, University of Tokyo 7-3-1, Hongo, Bunkyo, Tokyo, 113-0033 Japan

Dr. Junko Hiraga Department of Physics, Osaka University 1-1 machikaneyama-cho Toyonaka Osaka 560-0043 Japan

Dr. Masayasu Ishihara Department of Physics, University of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo, 113-0033 Japan

395 Dr. Souichi Ishikawa Department of Physics Hosei University Fujimi 2-17-1, Chiyoda Tokyo 102-8160 Japan

Dr. Aiichi Iwazaki Department of Physics, Nishogakusha University Shonan, Ohi, Chiba 277-8585,

Dr. Yuhri Ishimaru Department of Astronomy, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

Dr. Atsuhi Iyono Okayama University of Science 1-1 Ridaichou Okayama 700-0005, Japan

Dr. Hironobu Ishiyama E-Group High Energy Accelarator Research Organization 1-1 Oho, Tsukuba, Ibaraki, 305-0801 Japan

Dr. Toshitaka Kajino Division of Theoretical Astrophysics, National Astronomical Observatory 2-21-1 Osawa, Mitaka, Tokyo, 181-8588 Japan

Dr. Chikako Ishizuka Nuclear Theory Group, Department of Physics, Hokkaido University Sapporo, Hokkaido 060-0810 Japan

Dr. Tsuneo Kamizato Department of Physics and Earth Sciences, Faculty of Science University of the Ryukyus 1 Senbaru, Nishihara, Okinawa, 903-0129 Japan

Dr. T. Itahashi Reserch Center for Nuclear Physics Osaka University 10-1 Mihogaoka, Ibaraki, Osaka, 567-0047 Japan

Dr. Tadashi Kifune Institute for Cosmic Ray Research University of Tokyo 3-2-1 Midori-cho, Tanashi, Tokyo, 188-8502 Japan

Dr. Naohito Iwasa Cycrotron Laboratory, RIKEN Hirosawa, Wako, Saitama, 351-0198 Japan

Dr. Tadafumi Kishimoto Department of Physics Osaka University Toyonaka, Osaka, 560, Japan

Japan

396 Dr. Kazunori Kohri Department of Physics, University of Tokyo 7-3-1, Hongo, Bunkyo, Tokyo, 188-0033, Japan

Dr. Xin Liu Center for Nuclear Study University of Tokyo 3-2-1 Midori-cho, Tanashi, Tokyo,188-0002 Japan

Dr. Osamu Koike Department of Physics, Kyushu University Ropponmatsu, Fukuoka, 810-8560, Japan

Dr. Keiichi Maeda Department of Astronomy, University of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo, 113-0033 Japan

Dr. Katsuji Koyama Department of Physics Kyoto University Kita-Shirakawa, Sakyo-ku, Kyoto, 606-8502 Japan

Dr. Grant Mathews Department of Physics University of Notre Dame Notre Dame, Indiana, 46556 USA

Dr. Shigeru Kubono Center for Nuclear Study University of Tokyo 3-2-1 Midori-cho, Tanashi, Tokyo, 188-0002 Japan

Dr. Shin-ichiro Michimasa Center for Nuclear Study, University of Tokyo 3-2-1 Midori-cho, Tanashi, Tokyo, 188-0002 Japan

Dr. Nobuyuki Kudomi Research Center for Nuclear Physics, Osaka University 10-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Dr. Toshiyuki Minemura Department of Physics, Rikkyo University 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo, 171-0021 Japan

Dr. Chie Kurokawa Nuclear Theory Group, Department of Physics, Hokkaido University Sapporo 060-0810 Japan

Dr. Hiroaki Miyatake E-Group, KEK 1-1 Oho, Tsukuba, Ibaraki, 305-0801 Japan

397 Dr. Yuko Mochizuki RI-Beam Science Laboratory RIKEN 2-1 Hirosawa, Wako, Saitama, 351-0198 Japan

Dr. Seitaro Nakamura 17-102, 4-1 Sakura-josui, Setakaya, Tokyo, 156-0045 Japan

Dr. Tohru Motobayashi Department of Physics Rikkyo University 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo, 171-0021 Japan

Dr. Naohito Nakasato Department of Astronomy, School of Science, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 Japan

Dr. Hiroshi Murakami Cosmic-Ray group, Department of Physics, Kyoto University Ki tashi rakawa-Oiwake-cho, Sakyo, Kyoto 606-8502 Japan

Dr. Junko Nakatsuru Department of Astronomy, School of Science, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

Dr. Kazuo Muto Department of Physics, Tokyo Institute of Technology Oh-okayama 2-12-1, Meguro-ku, Tokyo 152-8551 Japan

Dr. Kyoshi Nishijima Department of Physics, Tokai University 1117 Kita-Kaname, Hiratsuka, Kanagawa 259-1292 Japan

Dr. Shigehiro Nagataki Department of Physics University of Tokyo 7-3-1 Hongo Bunkyoku, Tokyo 113-0033, Japan

Dr. Mamiko Nichiuchi Cosmic Ray Group, Department of Physics, Kyoto University K i t ash i rakawa-0 i wake-Cho, Sakyo, Kyoto 606-8502, Japan

Dr. Hitoshi Nakada Department of Physics, Faculty of Science, Chiba University Yayoi-cho 1-33, Inage, Chiba 263-8522 Japan

Dr. Ken'ichi Nomoto Department of Astronomy, School of Science, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 Japan

398 Dr. Kengo Ogawa Department of Physics Chiba University 1-33 Yayoi-cho, Inage, Chiba, 263-0022 Japan

Dr. Katsuhiko Sato Department of Physics, School of Science, The University of Tokyo Hongo, Bunkyo-ku Tokyo, 113-0031, Japan

Dr. Makito Oi Center for Nuclear Study, University of Tokyo 3-2-1 Midori-cho, Tanashi, Tokyo, 188-0002 Japan

Dr. Mariko Segawa Research Center for Nuclear Physics, Osaka University 10-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Dr. Manabu Orito Division of Theoretical Astrophysics, National Astoronomical Observatory 2-21-1 Osawa, Mitaka, Tokyo, 181-8588 Japan

Dr. Masaki Serata Department of Physics, Rikkyo University 3-34-1, Nishi ikebukuro, Toshima-ku, Tokyo, 171-0021 Japan

Dr. Satoko Osone Institute for Cosmic Ray Research University of Tokyo 3-2-1 Midori-cho Tanashi, Tokyo 188-0002 Japan

Dr. Toshikazu Shigeyama Research Center for the Early Universe, Graduate School of Science, University of Tokyo Bunkyo-ku, Tokyo, 113-0033, Japan

Dr. Kaori Otsuki Division of Theoretical Astrophysics, National Astronomical Observatory 2-21-1 Osawa, Mitaka,Tokyo, 188-8588 Japan

Dr. Michael Smith Physics Division Oak Ridge National Laboratory MS-6354, Bldg. 6010, P.O. Box 2008, Oak Ridge, TN,37831-6354 USA

Dr. Keisuke Sakai Division of Theoretical Astrophysics, National Astronomical Observatory 2-21-1 Osawa, Mitaka, Tokyo, 18" Japan

Dr. Kazumi Suda RI-Beam Science Laboratory, RIKEN 2-1 Hirosawa, Wako, Saitama, 351-0198 Japan

399 Dr. Naoji Sugiura Department of Earth Planet Physics, University of Tokyo 7-3-1, Hongo, Bunkyo, Tokyo, 113-0033, Japan

Dr. Tatsuyuki Takatsuka Faculty of Humanities and Social Sciences, Iwate University 3-18-34 Ueda, Morioka, Iwate, 020-8550 Japan

Dr. Kosuke Sumiyoshi RI Beam Science Laboratory RIKEN 2-1 Hirosawa, wako, Saitama, 351-0198 Japan

Dr. Masahiko Tanaka E-Group, KEK 1-1 Oho, Tsukuba, Ibaraki, 305-0801 Japan

Dr. Hideyuki Suzuki IPNS, KEK Oho 1-1, Tsukuba, Ibaraki 305-0801, Japan

Dr. Toru Tanimori Department of Physics, Tokyo Institute of Technology Oh-okayama, Meguro, Tokyo, 152-8550 Japan

Dr. Takeru Suzuki Division of Theoretical Astrophysics, National Astronomical Observatory, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588 Japan

Dr. Toshitaka Tatsumi Department of Physics, Kyoto University Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan

Dr. Masatoshi Takano Advanced Research Institute for Science and Engineering, Waseda University 3-4-1 Okubo, Sinjuku-ku, Tokyo 169-8555 Japan

Dr. Mariko Terasawa Division of Theoretical Astrophysics, National Astronomical Observatory Oosawa, Mitaka, Tokyo 181-8588, Japan

Dr. Masaaki Takashina Department of Physics, Osaka City University 3-3-138 Sugimoto Sumiyoshi-ku Osaka, 558-8585 Japan

Dr. Masahiro Teshima Institute for Cosmic Ray Research, University of Tokyo 3-2-1 Midori-cho, Tanashi, Tokyo, 188-0002 Japan

400 Dr. Hiroshi Toki Research Center for Nuclear Physics, Osaka University 10-1 Mihogaoka, Ibaraki, Osaka, 567-0047 Japan

Dr. Shingo Ushida Department of Physics, Kyoto University Ki tashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan

Dr. Atsushi Tomyo Research Center for Nuclear Physics, Osaka University 10-1, Mihogaoka, Ibaraki-shi, Osaka 567-0047, Japan

Dr. Hiroaki Utsunomiya Department of Physics Konan University 8-9-1 Okamoto, Higashinada, Kobe, 658-0072 Japan

Dr. Robert Tribble Cyclotron Institute Texas A&M University College Station, TX 77843 USA

Dr. Shinya Wanajo Division of Theoretical Astrophysics, National Astronomical Observatory 2-21-1 Osawa, Mitaka, Tokyo, 181-8588 Japan

Dr. Hiroshi Tsunemi Department of Physics, Osaka University 1-1 Machikaneyama-cho, Toyonaka, Osaka, 560-0043 Japan

Dr. Gentaro Watanabe Department of Physics, University of Tokyo 7-3-1, Hongo, Bunkyo, Tokyo, 113-0033 Japan

Dr. Kouj i Ue Center for Nuclear Study, University of Tokyo 3-2-1, Midori-cho, Tanashi, Tokyo, 188-0002 Japan

Dr. Masanobu Yahiro Department of Physics and Earth Sciences University of the Ryukyus Nishihara-chou Okinawa 903-0213, Japan

Dr. Hideyuki Umeda Department of Astoronomy University of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo, 113-0033 Japan

Dr. Kazunari Yamada Department of Physics, Rikkyo University 3-34-1 Nishi-Ikebukuro, Toshima-ku, Tokyo 171-8501, Japan

401 Dr. Shoichi Yamada Research Center for the Early Universe Graduate School of Science, the University of Tokyo 7-3-1 Hongo, Bunkyo, Tokyo, 113-0033 Japan

Dr. Yasushi Yamamoto Center for Nuclear Study, University of Tokyo 3-2-1 Midori-cho, Tanashi, Tokyo, 188-0002 Japan

Dr. Yoshiyuki Yanagisawa Center for Nuclear Study, University of Tokyo 3-2-1 Midori-cho, Tanashi, Tokyo, 188-0002 Japan

Dr. Shohei Yanagita Faculty of Science, Ibaraki University 2-1-1, Bunkyo, Mi to, Ibaraki, 310-8512 Japan

Dr. Masatomi Yasuhira Department of Physics, Kyoto University Ki tashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, 606-8502 Japan

Dr. Jun Yokogawa Department of Physics, Faculty of Science, Kyoto University Kitashirakawa, Sakyo-ku, Kyoto, 606-8502, Japan

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Author Index Amari, S.

Tribble, R.E. 107 Tsunemi, H. 240

55

Bamba, A. Boyd, R.N. D'Auriaa, J.

331 201

Umeda, H. 43 Utsunomiya, H. Watanabe, G.

Fukazawa, Y. 77 Pukuda, Y. 209 Hashimoto, M. 283 Hasebe, N. 94 Homma, K. 215 Iliadis, C. 69 Ishiyama, H. 335 Iwasa, N. 130 Iwazaki, A. 339 Kajino, T. 3 Kifune, T. 31 Kishimoto, T. 322 Koyama, K. 246 Kubono, S. 171 Kudomi, N. 138, 343 Liu, W.-P.

119

Maeda, K. 347 Mathews, G.J. 257 Murakami, H. 86 Nagataki, S. 354 Nakatsuru, J. 362 Nakasato, N. 358 Nishiuchi, M. 370 Nomoto, K. 223 Otsuki, K.

267

163

374

Shigeyama, T. 14 Smith, M.S. 149 Suda, T. 276 Sumiyoshi, K. 297 Suzuki, T. 23 Takatsuka, T. 305 Tatsumi, T. 313 Terasawa, M. 378

381

Yamada, S. 181 Yasuhira, M. 194

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