The Outer Heliosphere: The Next Frontiers, Volume 11

COSPAR COLLOQUIA SERIES VOLUME 11

THE O U T E R HELIOSPHERE: THE NEXT F R O N T I E R S

PERGAMON

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THE OUTER HELIOSPHERE: THE N E X T FRONTIERS Proceedings of COSPAR Colloquium held in Potsdam, Germany 24-28 July 2000

Edited by

Klaus Scherer dat-hex, Katlenburg-Lindau, Germany

Horst Fichtner Institutfiir Theoretische Physik IV, Ruhr-Universiti~tBochum, Bochum, Germany

Hans J0rg Fahr Institut Ff~rAstrophysik und extraterrstrische Forschung, Universittit Bonn, Bonn, Germany

Eckart Marsch Max-Planck-Institutfiir A eronomie, Katlenburg-Lindau, Germany

2001

) PERGAMON An Imprint of Elsevier Science Amsterdam

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Preface The 11th COSPAR Colloquium "The Outer Heliosphere: The Next Frontiers" was held in Potsdam, Germany, from July 24 to 28, 2000, and is the second dedicated to this subject after the first one held in Warsaw, Poland in 1989. Roughly a century has passed after the first ideas by Oliver Lodge, George Francis FitzGerald and Kristian Birkeland about particle clouds emanating from the Sun and interacting with the Earth environment. Only a few decades after the formulation of the concepts of a continuous solar corpuscular radiation by Ludwig Biermann and a solar wind by Eugene Parker, heliospheric physics has evolved into an important branch of astrophysical research. Numerous spacecraft missions have increased the knowledge about the heliosphere tremendously. Now, at the beginning of a new millennium it seems possible, by newly developed propulsion technologies to send a spacecraft beyond the boundaries of the heliosphere. Such an Interstellar Probe will start the in-situ exploration of interstellar space and, thus, can be considered as the first true astrophysical spacecraft. The year 2000 appeared to be a highly welcome occasion to review the achievements since the last COSPAR Colloquia 11 years ago, to summarize the present developments and to give new impulses for future activities in heliospheric research.

The conference drew not only scientific but also public interest, which became evident from a variety of related TV and radio presentations as well as a couple of articles in the local press. To cover all aspects of outer heliospheric research and future exploration the conference programme was structured into eleven major sessions, namely: the Large-scale Structure of the Heliosphere, Heliospheric and Interstellar Connections, Messengers from the Outside, Echoes from the Heliopause, the Heliosphere and the Galaxy, Views of Space Agencies and Companies, At the Edge of the Solar System, New Kinetic Aspects of Heliospheric Physics, Modern Heliospheric Spacecraft and Missions, Modern Heliospheric Technologies, and Connections to Earth.

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Preface We thank all the participants who have submitted a written version of their presentations and also all referees who helped to improve these manuscripts, and, thus, enabled us to compile this volume of high-quality articles. The remaining presentations are included with their abstracts, and, if published elsewhere, a reference is given. A special thanks go to the conveners for putting together the invited talks. Finally, we are grateful that the Colloquium was held under the auspices of COSPAR.

Klaus Scherer Horst Fichtner Eckart Marsch Hans J. Fahr

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Acknowledgements

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Prologue Following the example of the first COSPAR Colloquium of the Outer Heliosphere, also during the second COSPAR Colloquium on the same topic a poll about the distance of the heliospheric termination shock has been taken from the participants. The results of both polls are shown in the figure. On the basis of these "data" we are now able to perform a "non-standard" analysis of the shock dynamics.

Mean S h o c k D i s t a n c e 96.96 [AU]

20.0.

COSPAR

g

~

i0(~

90.0 H e l i o s p h e r i c t e r m i n a t i o n s h o c k d i s t a n c e [AU]

Figure 1. The polls taken at the two COSPAR Colloquia on the Outer Heliosphere in New Hampshire (left panel) and in Potsdam (right panel).

Vshock ~

~ 3.27AU yr -1 11 yrs which is, interestingly enough, about the speeds of the Voyager 1 and 2 spacecraft, of 3.5 and 3.1 AU yr -1. We included an additional question in the Potsdam poll: Will the Voyagers reach the shock at all ? The result was, that 83% of the participants of the poll expected this to happen, 11% did not, and 6% made no guess. From our high-quality data set and the fact that Voyager 1 was at 76 AU at the time of the Colloquium, we can estimate the shock encounter to happen in the year 2091 at a distance of about 395 AU under the (probably wrong) assumption that the shock is continuously moving outward. To check these and other (more serious) predictions made during this second Colloquium on the Outer Heliosphere, we suggest to organize a third one in the year 2011, i.e. again another solar activity cycle later.

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Opening Remarks by the COSPAR President

Dear Organizers, Dear Participants, Ladies and Gentlemen,

It is a pleasure for me to convey the best wishes of COSPAR Bureau and Secretariat for a successful Colloquium and at the same time our sincere thanks to the organizers and editors for having undertaken the task to organize this event and publish its proceedings. The great number of attendees tells me that it was timely and worth while to do so. Let me formulate a few thoughts which were stimulated by the theme of your meeting, the outer heliosphere. The scales of the universe are incomprehensible. We, who deal every day with them, have of course developed a way to work with these scales by introducing the parsec as unit and thus shrink the universe into something that can be handled and visualized. We can easily feel at home in this vast space and forget how small the part is that we are occupying. The heliosphere, although small by comparison, is well suited to teach us modesty in two respects. We realize the true size of cosmic distances much better when we think that it takes one day for light to cross the heliosphere, with the nearest star being at a distance of four light years. But it makes us even more humble when we reflect about the completely accidental and by no means distinguished location of the heliospere inside some odd filament of a supernova remnant. If we truely tried to absorb these facts, should we not be equallly shaken as the Portuguese were in 1755 after the earthquake of Lisbon? Under the impression that it struck good and evil people, pious ones and heretics without differentiation, they began to ask questions like: is god not good? does god really exist? Should our questions not be: is our life, are we really the culmination of the universe? are we unique? For you who have assembled here during this week the heliosphere is a place of action, of the solar wind colliding with the interstellar medium, of the interplanetary magnetic field winding up and forming shocks, of interstellar ions being picked up to be accelerated to very high energies, of radio waves bringing back messages from the boundaries, of dust particles telling stories about the chemistry in the expanding clouds of exploding stars, and of many other cosmic processes which you can study here in situ in an exemplary fashion. The communication of your latest insights will keep you away from unhealthy thoughts like the above. You might also consider more practical matters like advancements of the propulsion techniques or the technology of large extended surfaces enabling farther and more efficient space travel. You may wonder whether Europe is going to confine itself for ever to "- iX--

Opening remarks by the COSPAR President

the innermost part of the solar system because of its reluctance to fly RTG's. I think that a meeting like this could also serve as a platform from which messages can go to the agencies and the public about the long-range needs of your science and its benefits in understanding our position in the universe. There is also a task in education. I do not think that scientists have to convey to the public all the deep lying discoveries of their respective disciplines. But teaching them respect for the basic laws of nature and making them aware of the reality of our place in the universe is a duty that we should accept again and again. The imagination of our children is so full of aliens, of UFO's and supermen that they may think that everything is possible and never realize how confined we are to our vulnerable planet. Telling stories about the solar system, the true extent and emptiness of the heliosphere, the efforts and times needed to conquer its distances will not only correct some of the light-heartedly accepted illusions, but also raise curiosity about the wider environment and origin of our Earth. Heliospheric physics is eminently suited to fulfill such an educational role. Finally, I have a few words about the publication of your contributions within the COSPAR Colloquium Series. You and also COSPAR want the book to be purchased and read by a community much wider than what is assembled in this room. Therefore, quality of the papers and reasonably wide interest of the topics are of great importance. Not all of the preceding volumes fulfill these conditions. To achieve the goal implies careful refereeing and editorial judgement. One may also want to fill some gaps by accepting additional papers. You who are involved in this process do a great service to your and the wider space science community. Let me express once more my sincere thanks and wish you an exciting week in Potsdam.

Gerhard Haerendel

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Contents S e s s i o n 1: L a r g e S c a l e S t r u c t u r e

Physics of the solar wind interaction with the local interstellar medium G.P. Zank and H.-R. Mfiller Relating models of the heliosphere to Lyman-a absorption observed in Hubble spectra H.-R. Miiller and B.E. Wood

13

Interstellar atoms in the heliospheric interface V. Izmodenov

23

MHD modeling of the outer heliosphere: Numerical aspects N.V. Pogorelov

33

Interaction of the local interstellar medium with the heliosphere: Role of the interior and exterior magnetic field A. Barnes

43

Modeling stellar wind interaction with the ISM: Exploring astrospheres and their Lyman-a absorption H.-R. Mfiller, G.P. Zank, and B.E. Wood

53

Stationary MHD-equilibria of the heliotail flow D. Nickeler and H.J. Fahr

57

Non-stationary magnetic field geometry in the heliosphere I.S. Veselowsky

61

Solar cycle heliospheric interface variations: Influence of neutralized solar wind N.A. Zaitsev and V.V. Izmodenov

65

Time dependent radiation pressure and time dependent, 2D ionisation rate for heliospheric modeling M. Bzowski

69

*Magnetic fields in the heliosphere: Introductory remarks W.I. Axford

73

*Temporal variations of Lyman-alpha-intensities, backscattered from the interstellar hydrogen atoms upstream of the Sun" The ULYSSES-Gas observations M. Witte

73

General Discussion

75

S e s s i o n 2: H e l i o s p h e r i c

and Interstellar Connections

Radiative transfer at Lyman-a in the outer heliosphere E. Quemerais

79

A fluid approach to the heliosphere/VLISM problem R.L. McNutt Jr, M. Wiltberger, J. Lyon, and C.C. Goodrich

89

Possible effects of the interstellar magnetic field on the heliospheric structure and H-atom penetration to the solar system V.B. Baranov

99

*Oral papers and posters which were given at the conference, but for which no manuscripts were submitted - - xi - -

Contents

Interstellar gas flow into the heliosphere E. M5bius, Y. Litvinenko, L. Saul, M. Bzowski, and D. Rucinski

109

Non-stationary transport of neutral atoms in the heliosphere A.I. Khisamutdinov, M.A. Phedorin, and S.A. Ukhinov

121

Pickup ion turbulence: A stochastic growth model G.P. Zank and I.H. Cairns

125

A time-dependent, 3D model of interstellar hydrogen distribution in the inner heliosphere M. Bzowski, T. Summanen, D. Rucinski, and E. Kyr51~i

129

Charge exchange ionization rate of interplanetary hydrogen atoms and Lyman-a intensity pattern in the inflow direction of the interstellar gas T. Summanen, T. M~ikinen, E. Kyr51~i, and W. Schmidt

133

New results derived from Pioneer 10/11 UV data H. Scherer and K. Scherer

137

*Composition and characteristics of the local interstellar cloud and the inner source obtained from pickup ions G. Gloeckler

141

*H atom velocity distribution in the heliospheric interface V.V. Izmodenov, Y.G. Malama, M. Gruntman, and R. Lallement

141

*Estimation of interplanetary hydrogen flow parameters from SWAN Lymanalpha observations E. KyrSl~i, J. Jaatinen, T. Summanen, W. Schmidt, T. M~ikinen, R. Lallement, E. Quemerais, J. Costa, and J.L. Bertaux

142

*The influence of a time variable solar H-Lyman-alpha line profile on LISMparameter deductions from interplanetary glow spectra H. Scherer, H.J. Fahr, M. Bzowski, and D. Rucinski

142

General Discussion

143

Session 3: M e s s e n g e r s from Outside The discovery and early development of the field of anomalous cosmic rays H. Moraal

147

Anomalous cosmic rays: Current and future theoretical developments J.A. le Roux

163

Anomalous cosmic ray observations in the inner and outer heliosphere B. Heber and A. Cummings

173

Cosmic rays as messengers from outside the inner heliosphere M.A. Lee and H. Fichtner

183

Modulation region of galactic cosmic rays in the heliosphere: Estimation of dimension, radial diffusion coefficient, intensity out of region L.I. Dorman

187

Latitudinal gradients and charge sign dependent modulation of galactic cosmic

191

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Contents

Antiprotons below 200 MeV in the interstellar medium: Perspectives for observing exotic matter signatures I.V. Moskalenko, E.R. Christian, A.A. Moiseev, J.F. Ormes, A.W. Strong

195

Anomalous cosmic rays outside of the termination shock A. Czechowski, S. Grzedzielski, H. Fichtner, M. Hilchenbach, and K.C. Hsieh

199

Ionizing media and the observed charge states of anomalous cosmic rays A.F. Barghouty, J.R. Jokipii, and R.A. Mewaldt

203

ACR modulation inside a non-spherical modulation boundary S.R. Sreenivasan and H. Fichtner

207

The injection problem for anomalous cosmic rays G.P. Zank, W.K.M. Rice, J.A. le Roux, and W.H. Matthaeus

211

Self-consistent acceleration of pickup ions at the termination shock J.A. le Roux, H. Fichtner, G.P. Zank, and V.S. Ptuskin

215

Energetic neutral helium of heliospheric origin at 1 AU A. Shaw, K.C. Hsieh, M. Hilchenbach, A. Czechowski, D. Hovestadt, B. Klecker, R. Kallenbach, E. M5bius, and P. Bochsler

219

Effects of the heliospheric termination shock on possible local interstellar spectra for cosmic ray electrons and the associated heliospheric modulation S.E.S. Ferreira, M.S. Potgieter, and U.W. Langner

223

*Galactic cosmic rays: Overview M. Forman

227

*Galactic cosmic rays: the outer heliosphere (late paper: see page 513) J.R. Jokipii

227

*Modulation of galactic and anomalous cosmic rays E. Christian, W. Binn, C. Cohen, A. Cummings, J. George, P. Hink, R. Leske, R. Mewaldt, E. Stone, T. von Rosenvinge, M. Wiedenbeck, and N. Yanaska

228

*The spectrum of ACR oxygen and its variations in the outer heliosphere from 1992 to 2000 D.C. Hamilton, M.E. Hill, N.P. Cramer, R.B. Decker, and S.M. Krimigis

228

*On the variability of suprathermal pickup He + at 1 AU B. Klecker, A.T. Bogdanov, M. Hilchenbach, A.B. Galvin, E. M5bius, F.M. Ipavich, and P. Bochsler

229

*Observations of pickup ions in the outer heliosphere by Voyager 1 and 2 and implications on pressure balance S.M. Krimigis and T.B. Decker

229

*Consequences of recently observed galactic synchrotron radio emissions on the local interstellar spectrum for cosmic ray electrons U.W. Langner, O.C. De Jager, and M.S. Potgieter

230

*Variation of the fluxes of energetic He + and He 2+ during the passage of corotating interaction regions D. Morris, E. M5bius, M.A. Popecki, L.M. Kistler, A.B. Galvin, B. Klecker, and A. Bogdanov

230

*The cosmic ray electron to positron ratio in the heliosphere M.S. Potgieter and U.W. Langner

231

General Discussion

233

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Contents

Session 4: Echoes from t h e H e l i o p a u s e Energetic neutral atom imaging of the outer heliosphere- LISM interaction H.O. Funsten, D.J. McComas, and M. Gruntman

237

Dual spacecraft measurements as a tool for determining the source of low frequency heliospheric radio emissions W. S. Kurth and D. A. Gurnett

245

Theories for radio emissions from the outer heliosphere I.H. Cairns and G.P. Zank

253

Mapping the heliopause in EUV M. Gruntman

263

Energetic neutral hydrogen of heliospheric origin observed with SOHO/CELIAS at 1 AU M. Hilchenbach, K.C. Hsieh, D. Hovestadt, R. Kallenbach, A. Czechowski, E. MSbius, and P. Bochsler

273

Acceleration of pickup ions at the termination shock in the limit of weak scattering S.V. Chalov and H.J. Fahr

277

Doppler shifted photon emission expected due to reactions of energetic protons with the LISM atoms in the heliosphere M. Hilchenbach, K. C. Hsieh, and A. Czechowski

281

A new diagnosis tool to map the outer heliosphere regions R. Ratkiewicz and L. Ben-Jaffel

285

The Lyman-a echo from the heliospheric bow shock region and its observability from earth H.-J. Fahr, H. Scherer, G. Lay, and M. Bzowski

289

*Energetic neutral atoms in the heliosphere M.A. Gruntman

295

*Radio emission from the outer heliosphere D. Gurnett and W.S. Kurth

295

*Energetic neutral atoms as tracers of the ionization state of the local interstellar medium V.V. Izmodenov and M. Gruntman

296

*Simulation of ENA images of the heliospheric termination shock and interface region E.C. Roelof

296

General Discussion

297

Session 5: T h e H e l i o s p h e r e a n d G a l a x y The solar wind: Probing the heliosphere with multiple spacecraft J.D. Richardson

301

Propagation of the solar wind from the inner to outer heliosphere: Three-fluid model C. Wang and J.D. Richardson

311

Relationships of corotating rarefaction regions outside 40 AU with solar observations: Heliospheric mass loading A. Posner, N.A. Schwadron, and T.H. Zurbuchen

315

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Contents

Recurrent ion events and plasma disturbances at Voyager 2" 5 to 50 AU R.B. Decker, C. Paranicas, S.M. Krimigis, K.I. Paularena, and J.D. Richardson

321

Mapping the detailed structure of the local interstellar medium S. Redfield and J.L. Linsky

325

Effect of different possible interstellar environments on the heliosphere: A numerical study H.-R. Mfiller, G.P. Zank, and P.C. Frisch

329

General Discussion

333

Session 6: View of Space Agencies and Companies Solar sail technology development and application to solar system exploration M. Leipold

337

*Contributions to the Outer Heliospheric Missions in frame of the German Space Program O. RShrig

345

*Deep space missions and technological challenges C. Schalinski and K. Eckardt (Astrium Consortium)

345

General Discussion

347

Session 7: At the E d g e of the Solar System The probable chemical nature of interstellar dust particles detected by CIDA on Stardust J. Kissel, F.R. Kriiger, J. Sil@n, and G. Haerendel

351

In-situ studies of interstellar dust from spacecraft I. Mann and H. Kimura

361

Dynamics of interstellar dust at the heliopause A. Czechowski and I. Mann

365

*Kuiper Belt Objects S.F. Green

369

*Dust in the Outer Heliosphere and Interstellar Dust E. Griin

369

*Comets as a source of heliospheric ions J. Geiss, G. Gloeckler, and K. Altwegg

370

*A Cometary and Interstellar Dust Analyzer for the STARDUST Mission J. Kissel, A. Glasmachers, H. von Hoerner, and H. Henkel

370

*Orbital Evolution of Dust in the Outer Heliosphere under the dust-gas drag force K. Scherer

371

General Discussion

373

Session 8: New Kinetic Aspects of Heliospheric Physics The injection problem J. Giacalone

377

A hydrokinetic description of solar wind electrons using hemispheric distribution functions I.V. Chashei, H.J. Fahr, and G. Lay

387

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Contents

*The solar wind electron velocity distribution O. Lie-Svendson

393

*General aspects of Boltzmann H-theorem for generalized collisions R.A. Treumann

393

*Heating and acceleration of ions by cyclotron- and Landau-resonances E. Marsch and C.-Y. Tu

394

General Discussion

395

S e s s i o n 9: M o d e r n H e l i o s p h e r i c Spacecraft and M i s s i o n s

In-space nuclear power as an enabling technology for exploration of the outer heliopause R. Sackheim, M. Van Dyke, M. Houts, D. Poston, R. Lipinski, J. Polk, and R. Frisbee

399

Interstellar probe using a solar sail: Conceptual design and technological challenges P.C. Liewer, R.A. Mewaldt, J.A. Ayon, C. Garner, S. Gavit, and R.A. Wallace

411

Propulsion for interstellar space exploration G. Genta

421

A realistic interstellar probe R.L. McNutt Jr, G.B. Andrews, J.V. McAdams, R.E. Gold, A.G. Santo, D.A. Ousler, K.J. Heeres, M.E. Fraeman, and B.D. Williams

431

Artificial intelligence techniques for the onboard analysis of space science data P.R. Gazis

435

Sunlensing the cosmic microwave background from 763 AU C. Maccone

439

*Propulsion options for the interstellar probe mission L. Johnson

445

*Solar Orbiter- A high resolution mission to the Sun and the inner heliosphere E. Marsch, B. Fleck, and R. Schwenn

445

General Discussion

447

S e s s i o n 10: M o d e r n H e l i o s p h e r i c T e c h n o l o g i e s

Scientific Payload for an interstellar probe mission R.A. Mewaldt and P.C. Liewer

451

Using multilayer mirrors to detect photons from the heliopause B.R. Sandel

465

A cosmic ray detector for an interstellar probe W. DrSge, B. Heber, M.S. Potgieter, G.P. Zank, and R.A. Mewaldt

471

*Future observations of the outer heliosphere M. Hilchenbach and H. Rosenbauer

475

*State-of-the-art solid state arrays and advanced analog microelectronics for heliospheric physics H.D. Voss

475

General Discussion

477

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Contents

Session 11: C o n n e c t i o n s to E a r t h

The heliosphere as viewed from Earth E.N. Parker

481

The heliosphere, cosmic rays, climate K. Scherer, H. Fichtner, and O. Stawicki

493

*Heliospheric changes in the past: Evidence from cosmogenic isotopes in the polar ice J. Beer

497

*The UV radiation climate on Earth and its impact on the biosphere: past, present and future trends G. Horneck

498

General Discussion

499

S e s s i o n 12: M i s c e l l a n e o u s

Aurora vortex structures as a result of disturbed geomagnetic conditions M.A. Danielides and A. Kozlovsky

503

A non-solar origin of the "SEP" component in lunar soils R.F. Wimmer-Schweingruber and P. Bochsler

507

*Disconnection events in P/Halley's plasma tail M.R. Voelzke and H.J. Fahr

511

Late paper:

Cosmic rays in the outer heliosphere and nearby interstellar medium J.R. Jokipii

513

List of participants

521

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Session 1: Large Scale S t r u c t u r e

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Physics of the Solar Wind Interaction with the Local Interstellar Medium G.P. Zank and H.-R. Mtfller Bartol Research Institute, University of Delaware, Newark, DE 19716, USA Plasmas in interstellar and interplanetary space are frequently partially ionized. Thus, the solar wind and stellar winds often interact with an interplanetary medium that is an admixture of protons, electrons, other charged ions, and neutral atoms. For example, the very local interstellar medium surrounding our heliosphere may be less than 50% ionized, with the dominant constituent being neutral hydrogen (H). As a result, the composition of the solar wind in the outer heliosphere beyond some 10 - 15 AU is dominated by neutral interstellar H. Our understanding of the complex physics describing the interaction of the solar wind with the partially ionized local interstellar medium has advanced significantly in the last 5 years with the development of very sophisticated models which treat the coupling of neutral atoms and plasma self-consistently. A number of major predictions have emerged from these models, such as the existence of a large wall of heated neutral hydrogen upstream of the heliosphere. Remarkably, in the ensuing years, this prediction has been confirmed by high resolution Hubble Space Telescope Lyman-~ spectroscopic data. An introductory review of the physics, and associated observations, of the interaction of the solar wind with the interstellar medium is presented for this exciting, rapidly developing field. 1. INTRODUCTION The solar wind forms a bubble, called the heliosphere, in the local interstellar medium (LISM), within which the solar system resides and whose size and properties are determined by the manner in which the solar wind plasma and the partially ionized LISM are coupled. In the last decade, great progress has been made in our understanding of the physical processes thought to describe the outer heliosphere. Fundamental to these advances has been the recognition that the interstellar medium is coupled intimately to the heliosphere itself and that much of outer heliospherie physics cannot be understood independently of the local interstellar medium. With the possibility that the aging spaeeerat~ Voyager 1,2 and Pioneer 10,11 might encounter the heliospherie boundaries in the not too distant future, interest in the far outer reaches of our solar system and the LISM has been rekindled. A convenient, if slightly vague, definition of the outer heliosphere, and one that is adopted here, is that it is that region of the solar wind influenced dynamically by physical processes associated with the LISM. Thus, for example, neutral interstellar hydrogen is the dominant (by mass) constituent of the solar wind beyond an ionization cavity of-~6 - 10 astronomical units (AU) in the upstream direction (the direction anti-parallel to the incident interstellar wind). The neutral hydrogen is coupled weakly to the solar wind plasma via resonant charge exchange - a coupling which leads to the production of pickup ions that come to dominate the internal energy of the solar wind. The solar wind changes then from a small plasma beta ]3sw (the ratio of plasma pressure to magnetic field pressure) environment to one in which [3sw > 3. Figure 1 shows the complex interaction between solar wind plasma and the LISM. While clearly simplistic, it serves to illustrate the primary physical processes. The interstellar plasma may or may not impinge supersonically on the heliosphere. The LISM flow is diverted about the heliospherie obstacle either adiabatically or by a bow shock (BS). The LISM plasma is coupled to the neutral interstellar hydrogen (H) primarily through charge exchange. Charge exchange corresponds to a neutral atom surrendering an electron to a passing ion (typically a proton), so creating a new charged particle and (a hydrogen) atom. Thus, when neutral H charge exchanges with LISM plasma that has been decelerated,

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G.P. Zank and H.-R. Miiller heated and diverted about the heliosphere, the neutral H acquires a subpopulation that too is heated, decelerated and diverted. This neutral hydrogen, together with the LISM H, is called component 1 and is created in region 1 of Figure 1. If the charge exchange mean free path is sufficiently small in the region of decelerated LISM flow, a "wall" of neutral hydrogen will form in the upstream direction (the hydrogen wall). Resonant charge exchange is essentially a scattering rather than an extinction process. A boundary, called the heliopause (HP), separates the heliosphere and the LISM plasma, and is either a contact or a tangential discontinuity. The supersonic solar wind is decelerated, diverted and heated by a reverse shock called the termination shock (TS). The location of the TS is determined by the steady and temporal solar wind pressure exerted on the LISM.

H3-Xk'",, /

HAcR I

+ \

\ d ; . X ~ 2,. I

Figure 1. Schematic of the solar wind - LISM boundary regions which act as neutral H sources whose characteristics are identifiably distinct. The solar wind is enclosed by the termination shock (the curve labeled TS) and is identified as region 3. The shocked solar wind, the heliosheath, is bounded by the termination shock (TS) and the heliopause (HP) and is identified as region 2, while the interstellar medium is found beyond the heliopause. The LISM may or may not form a bow shock (BS) depending on whether the interstellar flow velocity is supersonic. Some sample plasma (H§ and pickup ion (H§ trajectories (dashed) are shown, as well as trajectories of neutral H (solid) which comes into the region from the LISM (Husu) and experiences charge exchange (solid arrow heads) outside the HP (component 1 neutrals, HI), between TS and HP (component 2, H2), and in region 3 (fast component 3, H3).

Neutral interstellar hydrogen that crosses the heliopause into the heliosphere can also experience charge exchange. Neutral H atoms that are created by charge exchange with the very hot subsonic plasma downstream of the heliospheric termination shock possess thermodynamic attributes that correspond to their origin, i.e., very hot (--10 6 K) with a large random velocity and an approximately outwardly directed velocity component. This population of neutral atoms, called component 2, is created in region 2 (Figure 1), and it streams away from the heliosphere and is quite distinguishable from component 1. By means of secondary charge exchange with the LISM plasma, component 2 acts to transport heat from the heliosheath (the region located between the heliospheric termination shock and the heliopause) into the LISM and this leads to an increase in the LISM temperature in the immediate vicinity of the heliopause. The final neutral component, component 3, possesses characteristics quite distinct from the other two components and has its origin in the supersonic solar wind (region 3, Figure 1). Component 3 has large outward radial velocities and relatively low temperatures but is dynamically unimportant owing to its very low energy density. The ions born of charge exchange in the supersonic solar wind, the pickup ions, are, however, of considerable dynamical importance since they remove both momentum and energy from the bulk solar wind flow. The solar wind is decelerated, so reducing the ram pressure and hence the expected size of the heliospheric cavity, and the solar wind acquires a tenuous non-thermalized population of suprathermal ions (typical energies-1 keV). The initial pickup ion population is unstable, generating low frequency magnetic turbulence which can scatter both pickup ions and cosmic rays. Some fraction of the pickup ions is further energized, possibly by shock acceleration, to form the anomalous cosmic ray component, although the precise injection mechanism awaits clarification.

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Physics of the solar wind interaction with the local interstellar medium It should be noted that, historically, LISM conditions were very different in the past than they are presently (and indeed will be in the future) and thus the structure of the heliosphere may have been very different from the models discussed here. 1 Furthermore, since the interstellar medium is frequently partially ionized, we can expect that the interaction of winds of stars whose luminosity is relatively low (comparable to the sun, for example) with their LISM will be similar to that of the heliosphere. Thus, we may expect hydrogen walls to form ahead of the astrospheres of, for example, G-type stars. 2 The material presented here has been reviewed extensively by Holzer and Zank 3 and the reader is referred to these works for more detail and an extended bibliography. 2. THE LOCAL I N T E R S T E L L A R MEDIUM Many of the pertinent physical parameters of the LISM are poorly constrained and so, by implication, the detailed solar w i n d - LISM interaction is not yet well understood. Our best inferences about the LISM flow velocity and temperature have been made from observations of neutral interstellar hydrogen (H) and helium (He) within the heliosphere, using either resonantly scattered solar UV light techniques 4 (since H atoms in the heliosphere are illuminated by the Sun in the HI resonance line i.e., the Lyman-~ line) or in situ spacecraft measurements of the He distribution: The bulk velocity of the LISM flow is-~26 km/s and the plasma temperature is-~8000 K. The H and H + number densities are not well determined, although approximate limits can be derived. For HI (i.e., neutral H only), number densities lie in the range of --4).15 - 0.34 cm -3, while for HII (ionized H), the range is -4).03 - 0.14 cm3, depending on whether the EUV radiation field is included or not. 6 This leads to a limit on the total number density of both neutral and ionized interstellar hydrogen in the range --0.15 - 0 . 3 4 cm 3. Although most models assume that the relative motion of the heliosphere through the interstellar medium is supersonic, it is by no means clear that such an assumption is completely warranted. Our knowledge of both the local interstellar magnetic field strength and orientation and the energy density in interstellar cosmic rays is somewhat rudimentary. Cosmic rays with energies of 300 MeV/nucleon and less may contribute -~ (3 + 2) x 10 -13 dynes cm -2, which can yield an interstellar flow that is either sub-magnetosonic or subsonic. 7 The magnetic field orientation appears to be perpendicular to the interstellar flow velocity vector and estimates for the magnetic field strength range from---1.3 to 2 ktG.S Evidently, our knowledge about important LISM plasma and neutral H parameters is rather poor and this must therefore be taken into account when evaluating models of the global heliosphere. Nonetheless, the basic underlying physical processes appear to be reasonably well understood. 3. GLOBAL H E L I O S P H E R I C STRUCTURE The dynamical or ram pressure (given by p U 2 , 13 the fluid mass density and u the flow speed) and thermal pressure p of the solar wind decrease with increasing heliocentric distance and must reach a value which eventually balances the pressure exerted by the LISM. The relaxation towards pressure equilibrium between the solar and interstellar plasmas is characterized by (i) a transition of the supersonic solar wind flow to a subsonic state, and (ii) a divergence of the interstellar flow about the heliospheric obstacle. The transition of the supersonic solar wind is most likely accomplished by means of a termination shock (TS), and it is anticipated that at least the Voyager spacecraft will encounter this boundary in the early 21 st century. The divergence of the LISM flow about the heliosphere may be accomplished either adiabatically (if the relative motion between the sun and the LISM is subsonic) or by means of a bow shock in the case of supersonic relative motion. If we neglect both the deceleration of the solar wind by resonant charge exchange and temporal variations in the

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G.P. Zank and H..R. Mfiller

solar wind ram pressure, the minimum radius Rrs of the solar wind shock transition can be estimated from 9 Rrs=

~/+3

P0u02

(1)

R0 2(~/+ 1) Po0 ' 2 where PoUo is the solar wind ram pressure at R o = 1AU, y the solar wind adiabatic index, and p~ the total LISM pressure. The LISM pressure term can include the thermal gas, cosmic rays, the interstellar ram pressure, the magnetic field pressure, MHD turbulence, and may be expressed as Poo = pu 2 + Pth + 1"1 + PcR + Paust + P~B2 , where the terms are all evaluated in the LISM and the factor r I is an attempt to include the effects of interstellar magnetic field obliquity. 3' 10.18 Although one can estimate the location of the TS and the heliopause (HP) using simple pressure balance arguments, the interaction of the solar wind with the LISM is fundamentally multidimensional. Thus, the main advances in our understanding of global heliospheric structure since the original analytic models have been more recent and based largely on computer simulations. The initial simulations were of one-fluid gas dynamic models and only now has the inclusion of neutral interstellar hydrogen been considered self-consistently, with the prediction of a hydrogen wall. 11 To model the interaction of the solar wind with a partially ionized LISM, the usual set of 3D MHD equations must be solved. The collisional processes coupling plasma and neutral atoms depend on their relative energies and their relative importance can vary from region to region of a complex plasma system such as the solar wind/LISM interface. The Knudsen number Kn = ~,/L (~, the mean free path of neutral atoms and L a characteristic macroscopic length scale, such as the size of the solar heliosphere,-100 AU), which is a measure of the neutral distribution relaxation distance, is >> 1 inside the heliosphere and-1 in the very local ISM. The introduction of neutral atoms into the magnetized heliospheric plasma with a large Knudsen number implies that the neutral and plasma distributions cannot equilibrate and may possess quite distinct bulk flow speeds and temperatures. Charge exchange between the coupled, non-equilibrated neutral and charged particle populations can therefore introduce distinct new populations of neutral atoms and plasma whose characteristics reflect their parent population. The subsequent interaction and assimilation of the newly created plasma and neutral populations into the existing plasma and neutral distributions may then lead to the substantial modification of the overall partially ionized plasma system. Thus, the total neutral distribution cannot relax to a single Maxwellian distribution, and one must therefore use a multi-component transport or kinetic description for the neutral populations. To work directly with the kinetic description of interstellar and heliospheric neutral hydrogen, one must solve the Boltzmann equation 12 -~t + v . V f +

.V v f=

P-L,

(2)

for neutral H directly. Here, jr(x, v, t) is the neutral hydrogen distribution function expressed in terms of position x, v, and time t. F is the force acting on a particle of mass m, typically gravity and radiation pressure. The terms P and L describe the production and loss of neutral particles at (x, v, t) and both terms are functions of the plasma and neutral distributions. An alternative approach, and one that is much less prohibitive computationally, is to recognize that the heliosphere-LISM environment comprises three thermodynamically distinct regions; the supersonic solar wind (region 3), the very hot subsonic solar wind (region 2), and the LISM itself (region 1 ) Figure 1. Each region acts as a source of neutral H atoms whose distribution reflects that of the plasma

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Physics of the solar wind interaction with the local interstellar medium

distribution in the region. One may identify neutral components 1, 2, and 3 with neutral atoms originating from regions 1, 2, and 3. Each of these three neutral components is approximated by a distinct Maxwellian distribution function appropriate to the characteristics of the source distribution. This observation allows the use of simpler production and loss terms for each neutral component. The complete highly non-Maxwellian H distribution function is then the sum over the three components, i.e., 3

f ( x , v , t ) = ~--'f ( x , v , t ) . i=1

Under the assumption that each of the neutral component distributions is approximated adequately by a Maxwellian, one obtains an isotropic hydrodynamic description for each neutral component, and thus a closed multi-fluid transport model describing selfconsistently the interaction of the solar wind with the partially ionized LISM. ~3

Figure 2. (a) A 2D plot of the global plasma structure for the two-shock model when neutral H is included self-consistently. The contouring refers to Logl0[temperature]. (b) A 2D plot of the corresponding component 1 neutral distribution, where the shading refers to the number density. The hydrogen wall is clearly visible between the bow shock and the heliopause.

Models of the heliosphere that do not include neither interstellar neutrals, interplanetary nor interstellar magnetic fields TM show the basic structure of terminations shock and heliopause. The TS possesses a characteristic bullet-shape, quite unlike the approximately spherically symmetric heliosphere that is assumed typically. The supersonic solar wind velocity is constant until the very strong TS (Mach number-~170). The solar wind temperature decays adiabatically with increasing heliocentric distance. An extended and very hot tail of subsonic solar wind is formed (called the heliotail) in the downstream direction. When neutral H is included, a major effect of charge exchange on the heliospheric interfaces is to decrease the distances to the TS, HP and BS. 15The decrease in distance results primarily from the reduction in solar wind ram pressure, this due to the mediation of the wind by charge exchange. Besides the distance to the various heliospheric boundaries, illustrated in Figure 2a, charge exchange affects the shape of the termination shock, making it more spherical compared to the purely ionized gas dynamic description. This is a consequence of charge exchange in the heliosheath ensuring that the sheath plasma remains subsonic in this region.

Owing to the deposit of interstellar protons in the solar wind when charge exchange is included, the solar wind flow now departs slightly from simple spherical symmetry, and the contribution to the internal energy of the supersonic solar wind by pickup ions is substantial. The tail region is also cooler when the proton fluid and neutral fluid are coupled compared to no-charge exchange models. The very hot heliotail is cooled by charge exchange with cooler component 1 neutrals. To enter the heliosphere, a hydrogen atom has to cross three thermodynamically distinct regions. Through resonant charge exchange, the diverging LISM flow and the shocked solar wind flow act to

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G.P. Zank and H.-R. Mfdler

divert some fraction of the incident interstellar neutral H flux away from the heliosphere. Figure 2b, a 2D plot of the component 1 neutral H density distribution, shows that inflowing component 1 neutrals are decelerated substantially and filtered by charge exchange with the interstellar plasma between the BS and HP in the upstream direction. This leads to the formation of a hydrogen wall with maximum densities-~0.2-0.3 cm -3, column densities .--10TM cm 2, and temperatures ranging from 18 000K to 28 000K (depending on the assumed LISM parameters). The pile-up in the neutral gas results from the deceleration and deflection of the neutral flow by charge exchange with the interstellar plasma, which is itself decelerated and diverted due to the presence of the heliosphere. Note that the charge exchange mean-flee-path is typically less than the separation distance between the HP and BS and so a large part of the incident interstellar neutrals experience charge exchange. Component 2, produced via charge exchange between component 1 and hot shocked solar wind plasma between the TS and HP, streams across the HP into the cooler shocked interstellar gas and heats the plasma through a second charge exchange. This leads to an extended thermal foot abutting the outside edge of the HP. This heating of the plasma by component 2 serves to broaden the region between the BS and HP, as well as to (indirectly) further heat the component 1 interstellar neutrals after subsequent charge exchanges. Some heating of the unshocked LISM also occurs upstream of the BS, thereby marginally reducing the Mach number of the incident interstellar wind. The temperature of component 1 neutrals once inside the heliosphere remains fairly constant in the upstream region, and represents a substantial increase over the assumed LISM temperature. A further increase in the component 1 temperature occurs in the downstream region.

Figure 3a. An example of a kinetic simulation described by Mailer et al. 16for a 2-shock model. One-dimensional profiles of plasma density np and plasma temperature Tp are shown as dashed lines over radial distance R from the sun, and neutral density nH and (averaged) temperature THas solid lines. The profiles are obtained in the upstream direction, antiparallel to the LISM flow. The middle row depicts two-dimensional neutral velocity distribution functions (logarithmic density scale) at various locations on that axis, with prominent HLISM and H~ 26km/s neutrals, and evidence of 100-300 km/s H2 and 400 km/s H3 neutrals.

Figure 3b: Normalized H I radial velocity distribution at a point in the hydrogen wall located 160 AU from the Sun in the upwind direction of the interstellar flow into the heliosphere. The jagged line is the distribution given by the Boltzmann code, and the smooth curve is the distribution resolved by the multifluid code through three-component MaxwellianslS. The total distribution is clearly non-Maxwellian.

The number density of component 1 crossing the TS is approximately half the assumed incident LISM number density ("filtration"). The density varies only weakly between the TS a n d - 1 0 AU from the Sun in the upstream region. In the downstream direction, component 1 densities are lower within the heliosphere. The 1D component 1 density and temperature profiles are plotted in Figure 3a, and the heated hydrogen wall is exhibited clearly. A further effect of filtration is to decelerate the upstream neutral gas from 26 krn/s in the LISM to -~19 km/s at the TS in the region of the nose. Deflection of the

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Physics of the solar wind interaction with the local interstellar medium

flow also reduces the radial velocity component at angles away from the nose (a deceleration which is in accord with observations of the Lycx resonance line scattered by neutral H in the heliosphere). Also plotted in Figure 3 (taken from a kinetic simulation ~6) is the evolution of the neutral H distribution from the interstellar medium into the heliosphere. Components 1 and 2 are not always easily distinguished in 1D omnidirectional plots (Figure 3b) but the departure from a Maxwellian distribution is pronounced. The smoothed curve shows the distribution predicted by a multi-fluid model, which assumes a superposition of Maxwellian distributions corresponding to components 1, 2, and 3. While clearly distinct in detail, the basic aspects of the neutral distribution predicted by kinetic and multifluid models are surprisingly similar. Models which assume a subsonic LISM flow do not have a bow shock. Instead, upstream of the heliopause, the LISM flow is compressed adiabatically. This more gradual compression leads to the formation of a lower amplitude hydrogen wall that is more extended in the radial direction. It is also less extended in the transverse direction because of the localized nature of the adiabatic compression. The maximum density of the wall in the upstream direction is smaller than that of the two-shock counterpart (though still larger than the incident LISM number density). However, because it is wider, the column density is comparable with the two-shock case. The heliosphere is smaller due to the higher assumed LISM pressure. Three dimensional models of the solar wind during solar minimum introduce some interesting differences from the 2D models discussed above. The presence of an anisotropic solar wind with a high velocity, low density, high temperature polar steam acts to divert both the subsonic solar wind and the LISM plasma flow into the ecliptic region of the heliosphere. ~7The presence of a high density band of plasma about the ecliptic plane increases the filtration of neutrals compared to the higher polar regions. With an increased neutral flux of H over the poles, the polar solar wind experiences comparatively greater deceleration than the ecliptic wind, so reducing the degree of anisotropy seen in 3D gas dynamic simulations. In addition, the global distribution of neutral H is anisotropic in heliolatitude. Structurally, the heliosphere at low latitudes can revert to a "bullet" shape, typically seen only in models which neglect to include interstellar neutral hydrogen. It should be borne in mind that these remarks pertain primarily to the period of solar minimum observed by the Ulysses spacecraft. Very few simulations include either the interplanetary or interstellar magnetic fields dynamically and those that do neglect neutral H completely or use an extremely simplified description. TM Nonetheless, it appears that the magnetic field in the heliosheath can acquire a very interesting structure. Along the stagnation line in the heliosheath, the flow velocity decreases approximately as r -2 (r the heliocentric radial distance), leading to an amplification in the azimuthal magnetic field in the region. This, together with the J x B force causes the equatorial current sheet to bend either upward or downward (depending on solar cycle) away from the equatorial plane. This leads to the formation of an asynmaetric 3D magnetic shell or wall in the outer region of the upstream heliosheath with a gap in the neighborhood of the displaced current sheet. The region between the termination shock and the magnetic wall is occupied by solar wind originating from the middle and high latitudes whereas, thanks to the gap in the magnetic wall, the solar wind in the region between the magnetic wall and heliopause originates from the low latitude equatorial neutral sheet region. The ram pressure pu2of the solar wind varies by a factor o f - 2 with solar cycle. Since the location of the termination shock and heliopause is determined by a balance of the ram pressure and the interstellar pressure, temporal variation in the solar wind ram pressure must therefore play an important role in determining the global structure of the heliosphere. The time dependent multi-fluid model 15has been used to extend earlier studies of the effect of solar cycle variability on the global structure of the heliosphere. 19The varying ram pressure of the solar wind leads to large arrhythmic

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G.P. Zank and H.-R. Miiller

excursions of the TS and smaller excursions of the HP. The motion of the TS drives pressure waves into the inner heliosheath which steepen into shocks which propagate into the LISM. For a two-shock model, the dynamical train of shocks propagating into the LISM acts to increase the separation distance between the HP and BS, whereas in the one-shock case, the emitted shocks act as a surrogate bow shock(s) for the heliosphere. In both cases, the emitted shocks in the LISM introduce some variability into the neutral H entering the heliosphere on long time scales. Finally, it has been found that ion-neutral friction can destabilize the HP. 19 4. HELIOSPHERIC STRUCTURE INFERRED FROM L Y - ~ MEASUREMENTS

Until Voyager 2 encounters the termination shock and heliopause, we are forced to rely on remote observations to infer the structure of the heliosphere. The most promising approach presently is to use the Lytz absorption line in the direction of nearby stars) ~ A neutral hydrogen pileup or wall may be detectable in directions where the decelerated H is red-shifted out of the shadow of the interstellar absorption if the interstellar column density is sufficiently low. Red-shifted excess absorption in Hubble Space Telescope GHRS Lyo~ observations towards o~-Cen (seen previously by Copernicus and IUE) have been interpreted as evidence for the existence of the solar hydrogen wall) 1 Shown in Figure 4 are observations towards o~ Cen A (the jagged solid curves), and the wavelength scale is relative to the Lyman-o~ line center in the heliocentric rest frame. The upper solid curve is the assumed intrinsic stellar Lyo~ emission profile. The accurate representation of the intrinsic stellar profile is unimportant since the absorption features of interest vary sharply. The remaining smooth solid curve (the saturated absorption curve) of Figure 4 gives the attenuation of the stellar Lyo: emission by interstellar H. The column density for H was fixed by scaling to the Deuterium column density, assuming the commonly accepted value of D/H = 1.6 x 10 -5 for the local interstellar medium) 2 Figure 5 shows very clearly that additional absorption is required both redward and blueward of the interstellar feature if the fit is to be completed. Furthermore, the fit must be applied preferentially to the redward side, so arbitrarily changing the D/H ratio is unacceptable. The additional redward absorption has been interpreted as evidence for the detection of the hydrogen wall. The blueward absorption suggests the possibility of a hydrogen wall about o~ Cen A and B. Figure 4. The solid jagged curves are GHRS Lyman-O~absorption profiles Since the column depth of the hydrogen wall is three orders of towards O~ Cen A. The uppermost magnitude smaller than the column depth in the LISM toward t~ solid curve is the assumed intrinsic Cen, it may be surprising at first glance that the heliospheric optical stellar Lyman-~ emission profile. depth at +0.1 A is of the same order as the LISM optical depth at The smoothed solid line, which exthat wavelength. The key difference is that the hydrogen wall is hibits saturated absorption, corresponds to the intrinsic stellar emisheated and decelerated, which both broadens and redshifts the sion line after absorption from the heliospheric component away from the -0.07 A centroid of the LISM only. Corresponding theoreLISM absorption and toward the +0.1 A wavelength of interest. tical absorption profiles are plotted22 Figure 4 also shows the Lyo~ absorption at the red edge of the LISM feature computed from models for three assumed LISM Mach numbers (supersonic, subsonic and ~sonic) 22. These synthetic data are compared with the observed heliospheric absorption. The primary and very important conclusion to emerge from such modeling is that the synthetic Lyo~ profiles support the interpretation of the observed additional redward Lyo~ absorption towards o~-Cen as evidence for the remote detection of the hydrogen wall. Thus, it appears that the hydrogen wall has indeed been observed! The unprecedented accuracy of the Hubble GHRS observations suggests further that, with the refinement of solar wind - LISM interaction models, the question of whether the heliosphere has a one- or a two-

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Physics of the solar wind interaction with the local interstellar medium

shock structure may be answered in the foreseeable future by a combination of modeling and observations as discussed further elsewhere 23' 24. 5. CONCLUDING R E M A R K S Evidently, many more physical processes remain to be incorporated in models describing the interaction of the solar wind with the LISM. This will undoubtedly be accomplished in the next decade as computational power increases and the underlying physics is better understood. However, the most important limitation that the field currently faces concerns the paucity of information about the state of the local interstellar environment. Until LISM parameters are better constrained, all modeling efforts describing the solar w i n d - LISM interaction must be viewed as somewhat hypothetical. Nonetheless, with new observational techniques emerging, new missions planned, and the increasing sophistication of theoretical modeling efforts, the outlook for understanding the physics of the outer heliosphere is bright indeed. Furthermore, with the detection and modeling of hydrogen walls about nearby low luminosity stars 24' 25, n e w opportunities for investigating the physics of hitherto undetectable stellar winds and their LISM now exist. Acknowledgements. This work is supported in part by an NSF-DOE grant ATM-0078650, a NASA grant NAGS-6469, a Jet Propulsion Laboratory contract 959167, and a NASA Space College Grant award. REFERENCES

1 G.P. Zank and P.C. Frisch, Astrophys. J. 518, 965 (1999); H.-R. Mtiller, G.P. Zank, and P.C. Frisch, "Effect of different possible interstellar environments on the heliosphere: A numerical study", submitted to the proceeding of the Cospar colloquium "Outer Heliosphere", Potsdam, 2000, edited by K. Scherer (Elsevier, Amsterdam, 2001). 2 P.C. Frisch, Astrophys. J. 407, 198 (1993). 3 T.E. Holzer, in Solar System Plasma Physics, edited by E.N. Parker, C.F. Kennel, and L.J. Lanzerotti (NorthHolland, New York, 1979), p. 101; G.P. Zank, Space Sci. Rev. 89 3-4, 413 (1999). 4 J.-L. Bertaux, R. Lallement, V.G. Kurt, and E. Mironova, Astron. Astrophys. 150, 1 (1985); E. Qu6merais, B.R. Sandel, R. Lallement, and J.-L. Bertaux, Astron. Astrophys. 299, 249 (1995); R. Lallement, Space Sci. Rev. 78, 301 (1996). 5 M. Witte, M. Banaszkiewicz, and H. Rosenbauer, Space Sci. Rev. 78, 289 (1996). 6 j. Vallerga, Space Sci. Rev. 78, 277 (1996); G. Gloeckler, ibid, 335. 7 W._H" Ip and W.I. Axford, Astron. Astrophys. 149, 7 (1985). s j. Tinbergen, Astron. Astrophys. 105, 53 (1982); P.C. Frisch, Science 265, 1423 (1994); Space Sci. Rev. 72, 499 (1995). 9 L.E. Davis, Phys. Rev. 100, 1440 (1955); E.N. Parker, Interplanetary Dynamical Processes (Interscience, New York, 1963). ~0R. Ratldewicz, A. Barnes, and J.R. Spreiter, S.S. Stahara, M. Vinokur, and S. Venkateswaran, Astron. Astrophys. 335, 363 (1998); R. Ratldewicz, A. Barnes, and J.R. Spreiter, "Local interstellar medium and modeling the heliosphere", submitted to J. Geophys. Res. ~ V.B. Baranov, M.G. Lebedev, and Y.G. Malama, Astrophys. J., 375, 347 (1991). 12V.B. Baranov and Y.G. Malama, J. Geophys. Res. 98, 15157 (1993); V.B. Baranov and Y.G. Malama, J. Geophys. Res. 100, 14755 (1995); H.-R. Mtiller, G.P. Zank, and A.S. Lipatov, Proceedings, Solar Wind 9, Nantucket, 1998, edited by S.R. Habal et al. (AIP Conf. Proceed., 1999), Vol. 471, p. 819; J. Geophys. Res. 105, 27,419 (2000); V.V. Izmodenov, J. Geiss, R. Lallement, G. Gloeckler, V.B. Baranov, and Y.G. Malama, J. Geophys. Res. 104, 4731 (1999). 13H.L. Pauls, G.P. Zank, L.L. Williams, and D.T. Hall, Proceedings, Solar Wind 8, edited by D. Winterhalter et al. (AIP Conf. Proceed., New York, 1996), Vol. 382, p. 605; Zank et al.15; L.L. Williams, D.T. Hall, H.L. Pauls, and G.P.Zank, Astrophys. J. 476, 366 (1997); Liewer (1997). 14T. Matsuda, Y. Fujimoto, E. Shima, and T. Inaguchi, Prog. Theor. Phys. 81, 810 (1989); V.B. Baranov and Y.G. Malama, J. Geophys. Res. 98, 15157 (1993); R.S. Steinolfson, J. Geophys. Res. 99, 13307 (1994); R.S.

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Steinolfson, V.J. Pizzo, and T. Holzer, Geophys. Res. Lett. 21,245 (1994); S.R. Karmesin. P.C. Liewer, and J.U. Brackbill, Geophys. Res. Lett 22, 1153 (1995); H.L. Pauls, G.P. Zank, and L.L. Williams, J. Geophys. Res. 100, 21595 (1995); C. Wang and J.W. Belcher, J. Geophys. Res. 103, 247 (1998). 15G.P. Zank, H.L. Pauls, L.L. Williams, and D.T. Hall, J. Geophys. Res. 101, 21639 (1996). 16H.-R. MUller, G.P. Zank, and A.S. Lipatov, J. Geophys. Res. 105, 27,419 (2000). 17H.L. Pauls and G.P. Zank, J. Geophys. Res. 101, 17081 (1996); H.L. Pauls and G.P. Zank, J. Geophys. Res. 102, 19779 (1997);A. Barnes, J. Geophys. Res. 103, 2015 (1998); T. Tanaka and H. Washimi, J. Geophys. Res. 104, 12,605 (1999). 18H. Washimi and T. Tanaka, Space Sci. Rev. 78, 85 (1996); Ratkiewicz et al.l~ T. Linde, T.I. Gombosi, P.L. Roe, K.G. Powell, D.L. DeZeeuw, J. Geophys. Res. 103, 1889 (1998); N.V. Pogorelov and T. Matsuda, ibid, 237. 19G.P. Zank, Proceedings, Solar Wind 9, Nantucket, 1998, edited by S.R. Habal et al. (AIP Conf. Proceed., 1999), Vol. 471, p. 783. 20B.E. Wood, H.-R. Mtiller, and G.P. Zank, Astrophys. J. 542, 493 (2000). 21 J.L. Linsky and B.E. Wood, Astrophys. J. 463, 254 (1996); Gayley et al.22 22K. Gayley, G.P. Zank, H.L. Pauls, P.C. Frisch, and D.E.Welty, Ap.J. 487, 259 (1997). 23 Gayley et a1.22;B.E. Wood and J.L. Linsky, Astrophys. J, 492, 788 (1998); B.E. Wood, J.L. Linsky, and G.P. Zank, Astrophys. J. 537, 304 (2000). 24B.E. Wood, J.L. Linsky, H.-R. Miiller, and G.P. Zank, "Observational estimates for the mass-loss rates of ct Cen and Proxima Cen using HST Lyman-ct spectra", Ap J. Lett., 547, 49 (2001). 25H.-R. Miiller, G.P. Zank, and B.E. Wood, Ap.J. 551,495 (2001).

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Relating Models of the Heliosphere to Lyman-c~ Absorption Observed in Hubble Spectra H.-R. Mfiller ~ and B. E. W o o d b* ~Bartol Research Institute, University of Delaware, Newark, DE 19716 bjILA, University of Colorado and NIST, Boulder, CO 80309-0440 We model the interaction of the solar wind with the partially ionized local ISM using a self-consistent hybrid model in which the Boltzmann equation for neutral hydrogen is solved with a kinetic particle code. The degree of external contribution to the ISM plasma pressure (e.g. due to cosmic rays or to magnetic pressure) is varied as a model parameter, resulting in a family of heliospheric models ranging from two-shock models to one-shock heliospheres (subsonic ISM). We give an overview of the neutral hydrogen distributions in these models. The column density and temperature of the heliospheric neutral hydrogen have been observed to be large enough to produce detectable absorption signatures in Lyc~ spectra of nearby stars. The heliospheric models can be used to predict the amount of absorption for various lines of sight, and we compare these predictions with Lyc~ observations of six nearby stars obtained by the Hubble Space Telescope, sampling lines of sight ranging from nearly upwind to nearly downwind. We find that the Boltzmann models tend to predict too much absorption in sidewind and downwind directions, especially when we assume high Mach numbers for the interstellar wind. 1. I N T R O D U C T I O N The basic heliospheric structure created by the interaction between the fully ionized solar wind and the partially ionized local interstellar medium (LISM) can to first order be modeled by considering plasma interactions alone [1-3]. However, charge exchange, whereby an interstellar neutral loses its electron to a proton, allows the neutrals to take part in the solar-wind/LISM interaction in important ways (see review by Zank [4]). Heliospheric models that treat the neutral gas and plasma in a self-consistent manner predict somewhat different properties than plasma-only models, such as shorter distances to the termination shock, heliopause, and bow shock [5-9]. These models also suggest that neutral hydrogen in the heliosphere should be very hot, with temperatures of order 20,00040,000 K. The importance of this prediction is that this high temperature gas should *This research was supported by NASA grant NAG5-9041 to the University of Colorado, by an NSF travel grant administered by the American Astronomical Society, and by NASA grant NAG5-6469, NSF-DOE award ATM-0078650,JPL contract 959167, and NASA Delaware Space Grant College award NGT5-40024 to the Bartol Research Institute.

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H.-R. Miiller and B.E. Wood

produce H I Lya absorption broad enough to be separable from the interstellar absorption observed toward nearby stars, meaning hydrogen in the outer heliosphere can potentially be directly detectable. This absorption has in fact been observed using observations by the Hubble Space Telescope (HST). Excess Lya absorption is evident in high-resolution HST spectra of the nearby stars a Cen A and B, and this absorption has been demonstrated to be consistent with a heliospheric origin [10,11]. Models that self-consistently treat the neutrals and plasma are essential to help interpret these observations, but such models are a complex theoretical and computational problem. The fundamental difficulty is that neutrals in the heliosphere are far from equilibrium, and their velocity distribution at a given location can be highly non-Maxwellian. Lipatov et al. [12] adopted a particle-mesh method for solving the neutral Boltzmann equation, which should yield accurate particle distribution functions (see also [13,14]). This creates the opportunity to use heliospheric models created by this Boltzmann code to predict heliospheric Lya absorption profiles that can be compared with the HST observations. In this paper, we create models assuming different Mach numbers for the inflowing LISM to see which best matches the observed amount of absorption. For the a Cen line of sight, a similar analysis has previously been carried out using four-fluid rather than Boltzmann models [11], and assuming different LISM parameters. We compare the absorption predicted by the models with lines of sight observed by HST, including a Cen, 36 Oph, and Sirius lines of sight, which all show evidence for heliospheric absorption [15,16]. 2. M O D E L

DESCRIPTION

AND

RESULTS

We compare the HST observations of absorption of stellar Lya to absorption profiles synthesized from models of neutral hydrogen (H) in the global heliosphere. We use the fully time-dependent hybrid code described by [14] that includes neutral H and its charge exchange interaction with plasma in a self-consistent way. It consists of a 2D gas-dynamical description of the plasma of both solar and interstellar origin coupled to a 2.5D particle description of neutral hydrogen. The plasma code uses the Euler equations of fluid dynamics to solve for the bulk plasma variables of number density np, temperature Tp, and velocity u. This treatment is justified because the mean free path of the protons of the plasma is small in comparison to heliospheric length scales, and the proton distribution function is Maxwellian. The Boltzmann code for neutral H does not restrict the neutral distribution function to a Maxwellian, but admits arbitrary distributions. Transporting and influencing the particles in phase space, the particle code indirectly solves the Boltzmann equation for the time evolution of the neutral hydrogen distribution function. The Boltzmann code thus treats even those neutral components correctly whose mean free path is no longer smaller than typical heliospheric scales (component 2 neutrals and splash component, see below). For the sake of comparing the spatial distributions of the neutral and the ionized species, it is customary to take moments of the neutral distribution functions to arrive at the neutral H number density nil, effective temperature TH, and bulk neutral velocity u s . The effective neutral temperature is misleading in the sense that one often associates it with a single Maxwellian, which is an oversimplification of the intricate shapes of the neutral distribution functions that are encountered in the heliosphere.

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Relating models o f the heliosphere to Lyman-a absorption...

To first order, the dominant interaction between neutral H and plasma is resonant charge exchange. It is incorporated in each piece of the hybrid code through source terms. The source terms of the Euler gasdynamic equations make use of n i l , TH, and UH. Within the particle code, charge exchange is accounted for by loss and production terms in the neutral Boltzmann equation. These terms invoke the bulk plasma parameters as well as an approximation for the Maxwellian plasma distribution function. For the charge exchange cross section, we use an empirical fit [17]. Charge exchange deletes one neutral particle from the neutral distribution, and adds a new neutral that bears the characteristics of the plasma at the site where the exchange took place. The deleted neutral is most likely from the dominant neutral category, i.e., a "component 1 neutral" originally from the LISM neutral population, and its deletion therefore does not significantly change the neutral distribution. The newly born neutral can have very different characteristics, in particular when exchange takes place in the heliosheath or in the heliotail ("region 2") where the plasma is hot and has a low bulk speed, due to the shock heating and deceleration of solar wind plasma at the termination shock. These so-called component 2 neutrals have thermal speeds on the order of 100 km/s, corresponding to 106 K, and travel in essentially random directions. Some of them have trajectories directed towards the inner solar system where they can be detected as energetic neutral (hydrogen) atoms (ENA) in the low energy range below 1 keV [14]. So-called splash neutrals form another distinct component of neutrals, born inside the termination shock ("region 3") through charge exchange with the solar wind plasma that is still supersonic and cold, except close to the Sun. Charge exchange inside the termination shock heats the plasma through the generation of pickup ions, whereas the plasma in the heliosheath between ter~nination shock and heliopause (also in the heliotail) is cooled by charge exchange. In the heliotail, this mechanism works to equilibrate neutral H with the plasma, thereby heating and accelerating neutral H. Some of the hot component 2 neutrals created in the heliosheath deposit their energy upstream of the heliopause through secondary charge exchange, creating an anomalous heat transfer into the oncoming LISM. The resulting plasma temperature gradient in the LISM upstream of the heliopause is communicated to neutral H through charge exchange, creating a neutral temperature gradient as well. This gradient is even more pronounced when the incoming LISM plasma is supersonic. In this case, a bow shock exists where the plasma becomes subsonic, and the associated shock heating of the plasma steepens the plasma temperature gradient and consequently further heats the neutral H between the heliopause and bow shock. The deceleration of neutral H through charge exchange with the decelerated (stagnating) plasma creates what has been termed a hydrogen wall, a density enhanced region of neutral H upstream and sidestream of the heliopause (and bounded on the other side by the bow shock in two-shock models). The filtration of neutral H by the hydrogen wall creates a depletion of neutral H in the heliosphere. For the LISM boundary conditions we choose TH -- Tp - 8000 K, nH -- 0.14 cm -3, np -- 0.10 cm -3, and v - 26 km/s, which are consistent with observations [18-22]. The inner boundary is an inflow of solar wind plasma at 1 AU with T - 105 K, np - 5.0 cm -3, and v - 26 km/s. 7 is set to 5/3 throughout. Figure 1 serves as an illustration of the spatial distribution of neutral density and temperature of a typical model. The Sun is at the origin and the LISM enters from the right. The stagnation axis, which

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H.-R. Miiller and B.E. Wood

cb)t..

+~ -

-

-

b.16,o ~ii.3~I:~ ,~,.c~-o~

9

-,S.; Oo I))} --

~

~..

~0

-,so-j,.,,_.. -soo-

J

."

9 9 0

+

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9

Figure 1. Contour plots of (a) neutral H density and (b) effective neutral temperature (for model 5 of Table 1). The Sun is at the origin; the neutral flow field is illustrated by the streamlines in (b). The five density contour levels (in cm -3) and the temperature levels 20,000, 50,000, and 115,000 K are marked in the plots. The small lower panels show 1D profiles along the stagnation axis. Both value axes have a logarithmic scale.

runs parallel to the LISM flow and through the Sun, is a symmetry axis. One can clearly see the density enhancement above the interstellar value of 0.14 cm -3. The 0.16 cm -3 contour approximately follows the hydrogen wall, whose sunward side coincides with the heliopause. The region of maximum density is enclosed by the 0.20 cm -3 contour. The tailward termination shock intersects the stagnation axis at ~100 AU. Downwind of that we see a density depletion and a temperature increase. The neutral temperature also experiences an increase at the wall and in sidestream regions where the plasma has also an increased temperature. Whether or not a bow shock exists upstream of the heliosphere is currently an open question. The LISM plasma temperature and velocity alone would point to the existence of a bow shock (a "two-shock heliosphere") because the Mach number is M - 1.7. However, there is the possibility that mechanisms such as the pressure due to galactic cosmic rays or the pressure of an interstellar magnetic field contribute to the plasma energy, lowering the Mach number of LISM protons to subsonic values and resulting in a one-shock heliosphere. We model such a pressure contribution using a generic factor a to indicate that only a fraction of the total pressure outside of the heliopause is due to LISM protons. The equation of state then reads P - a n v k B T p , where P is the total pressure. The minimal a is 2, expressing the usual assumption that the LISM electrons have the same density and temperature (and therefore the same contribution to the total pressure) as the proton plasma.

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Relating models of the heliosphere to Lyman-a absorption... Table 1 Model parameters. Model # 1 c~ 2.0 Mach# 1.75 Tpl[K] 8,000

2 3.5 1.32 14,000

3 5.0 1.11 20,000

4 7.5 0.90 30,000

5 9.6 0.80 38,000

6 12.5 0.70 50,000

7 18.4 0.58 74,000

We have run seven simulations with differing values for the parameter c~. The values and the corresponding LISM plasma Mach numbers are listed in Table 1. The models range from supersonic without any additional pressure contribution (model 1) to subsonic oneshock models (4-7). The effective plasma temperature Tpl in Table 1 gives an indication what the plasma temperature would be if only LISM protons and electrons accounted for the total pressure. The real temperature for protons, electrons, and neutral H in the LISM is assumed to be 8000 K at the outer boundary in our models.

Table 2 Hydrogen wall results, and c~ M TH,wall [K] 1 2.0 1.75 89,000 2 3.5 1.32 58,000 3 5.0 1 . 1 1 73,000 4 7.5 0.90 78,000 5 9.6 0.80 70,000 6 12.5 0.70 100,000 7 18.4 0.58 80,000

comparison to Lya observations. rtpeak HP Extent Consistency with [cm -3] [ A U ] [AU] 12~ 52 ~ 73 ~ 112 ~ 0.219 104 210 Y N N N 0.229 99 210 Y N N N 0.228 95 210 N Y Y N 0.228 92 250 N Y Y N 0.221 91 260 N Y N N 0.196 88 150 N Y Y Y 0.181 87 180 N Y Y Y

data 139 ~ N N N N N Y Y

148 ~ N N N N N N Y

In Figure 2, we plot one-dimensional profiles of the neutral H density along the stagnation axis for all seven models. The prominent feature in all models is the hydrogen wall, where the densities reach above the 0.14 cm -3 LISM value. The peak density in all the hydrogen walls is the same, rtpeak = 0.22 cm -3 (Table 2), with the exception of models 6 and 7 where it is ,-15% lower. Table 2 contains the locations where the heliopause (HP) intersects the upstream stagnation axis, showing the effect of the increasing interstellar ram pressure for increasing c~. The table also contains estimates for the extent of the hydrogen walls, defined here as the length of the region of the stagnation axis where the neutral density is distinctly larger than the LISM value. This wall extent, too, is constant (~200 AU) for models 1-5 and somewhat thinner for models 6 and 7. The typical effective temperatures of neutral H inside the wall listed in Table 2 don't seem to follow a particular pattern and range from 60,000 K to 100,000 K. Downwind of the hydrogen wall, neutral hydrogen is depleted but hot (~ 105 K, see Fig. l b). In the tail region, the subsonic models have generally lower densities than the two-shock models (see left panel of Figure 2), with the difference between model 1 and model 7 being 20% at 100 AU and

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H.-R. Miiller and B.E. Wood 0.10

I, t~,

Figure 2. 1D density profiles of neutral H upstream (right) and downstream (left) of the Sun, for all models. Note the different scales of the left and right hand panels.

growing to 40% at 1000 AU. In general, higher heliospheric hydrogen temperatures and densities are observed for models with lower values of c~, which is expected since a lower c~ corresponds with a higher LISM Mach number and therefore more heating. Because higher temperatures and column densities will produce broader Lyc~ absorption profiles, models with higher Mach numbers will also generally produce more absorption. The particle Boltzmann code returns the complete phase space information of neutral H. In particular, we obtain the velocity distribution function throughout the heliosphere that we can use to compute the absorption profiles. In Figure 3, radial velocity distributions are displayed for neutral hydrogen particles in the upwind and downwind directions for Model 1. In order to create these distributions, particles are summed within a certain area centered on the locations indicated in the figure. The area measures 104 AU 2 for Figure 3 and 3000 AU 2 for the Lyc~ absorption calculations in Section 3. Poissonian error bars (N ~ are displayed for each velocity bin. The bin size of the histogram is 6 km s -1. Gaussians have been fitted to the distributions (dashed lines), and the poor fits illustrate the non-Maxwellian character of the distributions. Looking upstream, the distribution functions have a broad core at -17 km s -1 which corresponds to moderately heated, decelerated neutral H of LISM origin coming toward the Sun. In the downstream direction, neutral H is moving away from the Sun, with the peak in the distribution at 28 km s -1. In both directions, there is a peak at 400 km s -1 which is the signature of splash component neutrals born through charge exchange in the solar wind. Neutrals with velocities between 100 and 300 km s -1 are component 2 neutrals produced in both the hot heliosheath and the heliotail. 3. C O M P A R I S O N

TO HST DATA

In upwind directions, the heliospheric H I column density is dominated by compressed, heated, and decelerated material just outside the heliopause (the hydrogen wall). For an observer at Earth, the absorption due to LISM H I in the upwind direction is blueshifted relative to the Ly~ rest wavelength. The decelerated heliospheric H I absorption is also blueshifted, but less than that of the LISM. Therefore, the hydrogen wall material accounts

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Relating models of the heliosphere to Lyman-a absorption...

1000.0

-

100.0

10.0

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o

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0.1 150 0 -150 1000.0

100.0

o

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-

-100 -200

- 100

0

100

200

300

400

500

( k m s -1) Figure 3. Neutral H radial velocity distributions for two different heliospheric locations based on Model 1, where 0 is the angle relative to the upwind direction of the interstellar flow, and R is the distance from the Sun. The dashed lines are Gaussian fits to the distributions, and residuals of the fits are shown below each panel. From [24].

for most of the non-LISM absorption observed on the red side of the s~turated core of the Lya absorption profile. Component 1 neutral hydrogen develops only small perpendicular velocity components in the hydrogen wall, such that the above holds for all sightlines through the hydrogen wall less than 90 ~ from the upwind direction. At hydrogen walls around other stars, where an observer looks from the outside rather than the inside, this scenario is reversed, meaning that the decelerated material of the stellar hydrogen wall is in fact more blueshifted than the LISM, and the additional absorption shows up at the blue wing of the main (interstellar) absorption feature. Figure 4 shows the observed Lya profile of a Cen B [10], which is 52 ~ from the upwind direction. Excess H I absorption is present on both the blue and red sides of the LISM absorption. The red side excess is due to the heliospheric absorption, while the blue side excess is due to absorption from analogous "astrospheric" material [11]. An additional detection of heliospheric H I absorption only 12~ from the upwind direction was provided by HST observations of 36 Oph [15]. For downwind lines of sight the H I density is much lower than in the hydrogen wall, but the sightline through the heated heliospheric H I is longer, potentially allowing heliospheric Lya absorption to be observed downwind as well [23], again on the red side because neutrals in the tail are accelerated by charge exchange to speeds higher than the LISM speed. A detection of heliospheric absorption along a downwind line of sight toward Sirius has been reported [16].

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H.-R. Miiller and B.E. Wood

2.5 T 2.0

7 O

1.5

~0

o

1.0

" ~ 0.5 N 0.0 1215.0

1215.2

1215.4 1215.6 1215.8 Wavelength

1216.0

1216.2

Figure 4. HST/GHRS Lye spectrum of c~ Cen B, showing broad H I absorption at 1215.6 ~ and D I absorption at 1215.25 ~. The upper solid line is the assumed stellar emission profile and the dashed line is the ISM absorption alone. The excess absorption is due to heliospheric H I (vertical lines) and astrospheric H I (horizontal lines).

We can use the models listed in Table 1 to predict the amount of Lyc~ absorption we expect to see for various lines of sight through the heliosphere [24]. We compare these predictions with the observations of c~ Cen, 36 Oph, and Sirius, which we have already mentioned above as having excess Lyc~ absorption that is presumably heliospheric. In addition to those lines of sight, we also consider three additional lines of sight toward 31 Com, /3 Cas, and c Eri. The HST Lyc~ spectra of these stars show no evidence for excess absorption on the red side of the line that could be heliospheric [25], but these data still provide useful upper limits for the amount of absorption that could be present and they sample different directions through the heliosphere. In Figure 5, the absorption predicted by the seven models in Table 1 is compared with the Lyc~ absorption profiles observed toward the six stars. The 0 values shown in the figure are the angles from the upwind direction, which range from the nearly upwind line of sight toward 36 Oph (0 = 12~ to the nearly downwind line of sight toward c Eri (0 = 148 ~ The predicted Lyc~ absorption is shown after combination with the LISM absorption toward these stars, as determined from previous empirical analyses [10,15,16,25]. An attempt has been made to maximize the agreement between the data and the models by tweaking the assumed stellar emission profiles, as described by [24]. Significant disagreement remains in most cases despite these efforts. Based on Figure 5, we provide in the last six columns of Table 2 our evaluation of which observed stellar lines of sight (labeled by their 0 angles) are inconsistent with which models. None of the models are consistent with every line of sight. The low c~ models do better upwind and the high c~ models do better downwind. In general, the models predict too much absorption, the exception being the 36 Oph line of sight for which most of the models predict too little absorption. Model 7 is the only model that does not predict too much absorption along the downwind line of sight to e Eri.

-20-

Relating models of the heliosphere to Lyman-a absorption...

Cen

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40

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Figure 5. The red side of the Lya absorption profiles observed toward six stars, sampling different angles 0 relative to the upwind direction of the interstellar flow into the heliosphere. These data are compared with the heliospheric absorption predicted by the seven models listed in Table 1, which assume different values for a. From [24].

4. C O N C L U S I O N S We have presented models of the heliosphere constructed using a hybrid code combining a fluid treatment for the plasma and a kinetic treatment for the neutral particles. These models are potentially very useful for analyzing the heliospheric H I Lya absorption that has been detected toward a number of stars using HST observations. The models provide detailed information on the spatially-dependent, highly non-Maxwellian neutral H velocity distributions within the heliosphere. In principle, these distributions should allow accurate Lya absorption profiles to be computed for comparison with the HST data. However, we were unable to find a model which successfully reproduced the observed absorption. There are many possible reasons for this lack of success. One is that we simply have not experimented with a large enough range of input parameters. It is only the a parameter that is varied in the set of models in Table 1. It is possible that assuming somewhat different LISM or solar wind parameters, while still forcing them to be within available observational constraints, would improve agreement with the data. Another possibility is that we have neglected one or more physical processes in the models which could be

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H.-R. Miiller and B.E. Wood

important and affect our results, such as processes involving magnetic fields. One particular physical process that might be a factor is non-charge exchange interactions between the neutrals and the plasma, which are not considered in the current models. Perhaps there are enough neutral-proton collisions to remove a significant number of particles from the far wings of the velocity distributions (see Figure 3), thereby reducing the amount of predicted Lya absorption. This could be especially important for downwind directions where neutrals have traveled longer pathlengths through the heliosphere and have therefore had more opportunity for collisions with protons. And it is particularly in downwind directions where the current models predict way too much absorption. In future analyses, we hope to explore this possible explanation, and others. REFERENCES o

2. 3. 4. 5. 6. 7. o

9. 10. 11. 12. 13. 14. 15. 16. 17.

20. 21. 22. 23. 24. 25.

T. E. Holzer, Ann. Rev. Astr. & Astrophys., 27 (1989) 199. R. S. Steinolfson, V. J. Pizzo, and T. E. Holzer, Geophys. Res. Left., 21 (1994) 245. C. Wang and J. W. Belcher, J. Geophys. Res., 103 (1998) 247. G. P. Zank, Space Sci. Rev., 89 (1999) 413. V. B. Baranov and Y. G. Malama, J. Geophys. Res., 98 (1993) 15157. V. B. Baranov and Y. G. Malama, J. Geophys. Res., 100 (1995) 14755. P. C. Liewer, S. R. Karmesin, and J. U. Brackbill, in Solar Wind 8, ed. D. Winterhalter et al. (New York: AIP, 1996) 613. H. L. Pauls, G. P. Zank, and L. L. Williams, J. Geophys. Res., 100 (1995) 21595. G.P. Zank, H.L. Pauls, L.L. Williams, & D. Hall, J. Geophys. Res., 101 (1996) 21639. J. L. Linsky and B. E. Wood, Astrophys. J., 463 (1996) 254. K. G. Gayley, G. P. Zank, H. L. Pauls, P. C. Frisch, and D. E. Welty, Astrophys. J., 487 (1997)259. A. S. Lipatov, G. P. Zank, and H. L. Pauls, J. Geophys. Res., 103 (1998) 20631. H.-R. Mfiller and G. P. Zank, in Solar Wind 9, ed. S. R. Habbal et al. (New York: AIP, 1999) 819. H.-R. Mfiller, G. P. Zank, and A.S. Lipatov, J. Geophys. Res., 105 (2000) 27419. B. E. Wood, J. L. Linsky, and G. P. Zank, Astrophys. J., 537 (2000) 304. V. V. Izmodenov, R. Lallement, and Y. Malama, Astron. Astrophys., 342 (1999) L13. W. L. Fite, A.C.H. Smith, and R.F. Stebbings, Proc. R. Soc. London Ser. A, 268 (1962) 527. J. L. Linsky, S. Redfield, B. E. Wood, & N. Piskunov, Astrophys. J., 528 (2000) 756. R. Lallement, R. Ferlet, A. M. Lagrange, M. Lemoine, and A. Vidal-Madjar, Astron. Astrophys., 304 (1995) 461. E. Qu~merais, J.-L. Bertaux, B. R. Sandel, and R. Lallement, Astron. Astrophys., 290 (1994) 941. G. Gloeckler, et al., Science, 261 (1993) 70. B. E. Wood and J. L. Linsky, Astrophys. J., 474 (1997) L39. L.L. Williams, D. T. Hall, H. L. Pauls, and G. P. Zank, Astrophys. J., 476 (1997) 366. B. E. Wood, H.-R. Mfiller, and G. P. Zank, Astrophys. J., 542 (2000) 493. A. R. Dring, J. L. Linsky, J. Murthy, R. C. Henry, W. Moos, A. Vidal-Madjar, J. Audouze, and W. Landsman, Astrophys. J., 488 (1997) 760.

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Interstellar atoms in the heliospheric interface V. V. Izmodenov a, aDepartment of Aeromechanics and Gas Dynamics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Vorob'evy Gory, Glavnoe zdanie MGU, Moscow 119899, Russia ([email protected]) In order to enter the heliosphere the interstellar atoms pass through the heliospheric interface - the region of the solar wind and interstellar plasma interaction. In the interface, the interstellar hydrogen atoms strongly interact with the LISM plasma component by charge exchange. This interaction results in the modification of both plasma and interstellar atom flows. Thus, the atoms penetrate into the heliosphere disturbed. This opens a possibility to use interstellar atoms and their derivatives - pickup ions and anomalous cosmic rays - for remote diagnostics of the heliospheric interface plasma structure. However, the interpretations of remote experiments are critical to accurate theoretical models. In this paper advanced self-consistent models of the heliospheric interface are reviewed. Evolution of the atom velocity distribution in the heliospheric interface is discussed with the emphasis on interpretation of present and future space experiments. 1. I n t r o d u c t i o n At the present time there is no doubt that local interstellar medium (LISM) is partly ionized plasma. Interstellar plasma component interacts with the solar wind (SW) plasma and forms the heliospheric interface (Figure 1). The heliospheric interface is a complex structure, where the solar wind and interstellar plasma, interplanetary and interstellar magnetic fields, interstellar atoms, galactic and anomalous cosmic rays (GCRs and ACRs) and pickup ions play prominent roles. In this paper I will review physical processes connected with interstellar atoms. Interstellar atoms of hydrogen are the most abundant component in the circumsolar local interstellar medium. These atoms penetrate deep into the heliosphere and interact with interstellar and solar wind plasma protons by charge exchange. This interaction influences the structure of the heliospheric plasma interface significantly. Being disturbed in the interface, interstellar H atoms and their derivatives such as pickups and ACRs can serve as remote diagnostics of the heliospheric interface. To make constructive conclusions from space experiments one must use an adequate theoretical model. The main difficulty in the modelling of the heliospheric interface is a kinetic character of the interstellar H *The research described in this publication was made possible in part by Award No.RP1-2248 of the U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF), INTAS projects # 97-0512 and #YSF 00-163, RFBR grants # 01-02-17551, 99-02-04025, and International Space Science Institute in Bern.

-23 -

K Izmodenov

Figure 1. Structure of the heliospheric interface. The termination shock (TS), the heliopause (HP), the bow shock (BS) separates the heliospheric interface in four regions. Region 1 is the supersonic solar wind. Region 2 is the heliosheath with compressed solar wind plasma. Region 3 is the region of disturbed interstellar medium. The region is extended upstream BS (see, section 3). Region 4 is undisturbed interstellar medium.

atom flow in the heliospheric interface. Since the effects of elastic H-H, H-p collisions are negligibly small as compared with charge exchange, the latter process determines the character of the H atom flow in the interface (see, e.g., [10] and section 3 of this paper). Atoms newly created by charge exchange have local plasma properties. Since plasma properties are different in four regions shown in figure 1, there are four populations of interstellar atoms in the heliospheric interface. Population 1 is the atoms created in the supersonic solar wind. Population 2 is the atoms created in the heliosheath. Population 3 is the atoms created in the region of disturbed interstellar plasma (region 3 in Figure 1). Population 4 is the original interstellar atoms. The strength of H atom-proton coupling can be estimated through the calculation of mean free paths of H atoms in plasma. Generally, the mean free path of s-particle in t-gas can be calculated by the formulae: L - 5 M s~t / S t " Here w~ is the individual velocity of s-particle, S M u t ~ S t is individual Sparticle momentum transfer rate in t-gas, which is a function of local plasma parameters. Table 1 shows the mean free paths of H atoms with respect of charge exchange with protons. The mean free paths are calculated for typical atoms of different populations at different regions of the interface in the upwind direction. For every population of H atoms there is at least one region in the interface where Knudsen number K n N~ 0 . 5 - 1"0. Therefore kinetic Boltzmann approach must be used to MeanFreePath CharacteristicLength

-24-

Interstellar atoms in the heliospheric interface describe interstellar atoms in the heliospheric interface.

Table 1 Meanfree paths of H-atoms in the heliospheric interface with respect to charge exchange with protons, in AU Population At TS At HP Between HP and BS LISM 110 870 4 (primary interstellar) 150 100 58 190 3 (secondary interstellar) 66 40 110 200 2 (atoms originated in the heliosheath 830 200 240 490 1 (neutralized solar wind) 16000 5!0 , ,

.....

....

2. Heliospheric Interface M o d e l Baranov et al. [1] and Baranov and Malama [2] considered a two-dimensional (2D) axisymmetric model of the SW/LISM interaction. The interstellar and solar wind plasma components were treated as fluids. To describe the flow of interstellar atoms the Boltzmann equation was solved: HPf.(r. wp)dwp 0/H(r , WH) ~ F O/H (r, WH) = --fH(r. WH) If IWH -- Wpla.z WH" 0r mH 0WH -+-fp(r, W H ) [fW ~ i

WH [ HP fH(r, WH)dWH 9 9

(~ §

(1)

r, WH).

Here fH(r, WH) is the distribution function of H atoms; fp(r, wp) is the local distribution function of protons, assumed to be Maxwellian; wp and wH are the individual proton and H atom velocities, respectively; a HP is the charge exchange cross section of a H atom with a proton; fli is the photoionization rate; mH is the atomic mass; ~imp~t is the electron impact ionization rate; and F is the sum of the solar gravitational force and the solar radiation pressure force. The plasma and neutral components interact mainly by charge exchange. However, photoionization, electron impact ionization, solar gravitation, and radiation pressure are also taken into account in equation (1). The interaction of the plasma and neutral components leads to the mutual exchange of mass, momentum and energy. The effect of this interaction can be represented by adding source terms Q -- {ql, q2,z, q2,r, q3, O)T to the right-hand side of the plasma equations. The terms ql, q2 = {q2,~,q2,~}, q3 describe the mass, momentum, and energy sources in the thermal plasma component due to interaction with neutrals. These source terms can be expressed through the integrals of the atom distribution function fH:

q~ - n i l " (~i + ~imp~t), nH = f fH(WH)dWH,

wp) f~ (WH)fp (wp)dw~dwp,

-25-

K Izmodenov 1

Here f l r f uaHP(u)fv(wp)dw v is the charge exchange rate, and u is the relative atomproton velocity. Supersonic boundary conditions are used for the unperturbed interstellar plasma and for the solar wind plasma at the Earth's orbit. The velocity distribution of interstellar atoms is assumed to be Maxwellian in unperturbed interstellar medium. 3. On t h e effect of H-H, H-p elastic collisions Recently Williams et al. [3] have suggested that a population of hot hydrogen atoms is created in the heliosphere through elastic H-H collisions between atoms of population 1 and interstellar atoms of populations 3 and 4. Izmodenov et al. [5] examined the approach used by Williams and argued that two assumptions used by Williams et al. result in significant overestimation of the H-H collision effect. 1. Williams et al. [3] applied the momentum transfer cross-section calculated by Dalgarno [4] for quantum mechanically indistinguishable particles in H-H collisions. Treating the colliding particles as quantum mechanically indistinguishable or classically distinguishable could lead to significant differences in the meaning and values of the cross-sections. Dalgarno's approximation is appropriate for a quantum particle ensemble when velocities of distinct particles are correlated with each other. However Williams et al. applied this like-particles H-H collision momentum transfer cross-section to the description of the collisions between different populations of H atoms that are classically distinguishable. Classical statistics should be used under such conditions. Izmodenov et al. [5] calculated the momentum transfer cross-section for H-H collisions in the 0.01-1000 eV energy range treating colliding particles as classically distinguishable. Figure 2A compares the calculated momentum transfer, Dalgarno, and charge exchange cross sections as functions of relative velocity of the colliding particles. It is seen that the cross-section calculated in [5] is significantly smaller than the Dalgarno cross-section when V > 10 km/s. 2. Williams et al. [3] used a Bhatnagar-Gross-Krook (BGK)-like approximation for the Boltzman's equation collision term. This approximation is based upon on an assumption of a complete randomization of particle velocities in the collisions, without making a distinction between 'strong' and 'weak' collisions. If one calculates momentum transfer term for different H-atom populations using the BGK-like approximation, one would obtain the values that 1-2 order of magnitude larger than for our approximation. For calculations with the Dalgarno's cross section, the overestimation introduced by the BGKlike approximation is much smaller, but still significant. This effect can be explained by different functional dependencies of the cross sections and by the BGK-like collision term. Izmodenov et al. [5] concluded that the influence of elastic H-H, H-p collisions is negligible in the heliospheric interface since the dynamic influence of charge exchange is stronger by several orders of magnitude. 4. Basic results of t h e model: H a t o m s Since the elastic H-H, H-p collisions are not important dynamically, Baranov-Malama model [2] describes the main physical processes correctly. In this section main results of

-26-

Interstellar atoms in the heliospheric interface

~ 10- 6

f

l.qarno [1960i -

~

: E

Figure 2. A. Momentum transfer cross section (in cm 2) as functions of relative velocity (in cm sec-~; B. Comparison of momentum transfer of population 2 due to elastic collisions with other H atom populations (in (cm sec) -2) in the upwind direction.

the model are briefly reviewed. Detailed results of the model reported in Baranov and Malama ([2], [6], [7]), Baranov et al. [8], Izmodenov et al. [9], Izmodenov [10]. One of the main and the most spectacular results of the model is prediction of the hydrogen wall, a density increase at the heliopause (figure 3A). The hydrogen wall is made up by secondary interstellar atoms of population 3. The hydrogen wall was predicted by Baranov et al. [1]. Linsky and Wood [11] were first to demonstrate that observed by HST Ly-a spectra toward Sirius can not be understood without taking into account the absorption produced by heliospheric hydrogen wall. Figure 3C shows the heliospheric absorption toward a-Cen calculated on the basis of Baranov-Malama model. There is still a missing absorption on the blue side. This is probably absorption produced by heated neutral gas around the target star (" astrosphere"), as suggested first by Wood and Linsky. Interpretation of stellar spectra can provide us constraints on both the heliospheric interface and astrospheres. The first attempt to constrain the interface with to help of stellar spectra was done by Gayley et al. [12]. Later, Izmodenov et al. [13] interpreted Ly-c~ spectra toward star Sirius-A (Figure 3D) on the basis of the heliospheric interface model. It has been shown that in this direction (41 ~ from downwind) two populations (populations 3 and 2) of neutral H atoms produce a non-negligible absorption. Figure 3B shows number density of population 2 toward Sirius direction. Despite small number density this population produces non-negligible absorptions due to high temperature. During this COSPAR Colloqium Wood, Muller and Zank reported the study of Ly-a spectra toward six nearby stars observed by HST. Comparing their model calculations with data the authors concluded that their model predict too much absorption in sidewind and downwind directions. More theoretical work has to be done to understand these discrepancies between theory and observations.

-27-

K Izmodenov

Figure 3. A. The hydrogen wall is an increase of number density of population 3 at the heliopause. The distribution is shown for direction toward c~Cen. B.The distribution of population 2 toward Sirius. C. HST spectrum of a Cen-A near Ly-a line center. Also shown is simulated stellar profile prior to interstellar absorption, the same profile after interstellar absorption and the expected profile after the cloud plus the calculated heliospheric H absorption. A missing absorption on the blue side is probably "astrospheric". D. HST spectrum of Sirius-A near Ly-a line center. Simulated profiles are similar of profiles on plot C.

5. Basic results of t h e model: influence on p l a s m a flows Interstellar atoms strongly influence the heliospheric interface structure. In the presence of interstellar neutrals, the heliospheric interface is much closer to the Sun than it would be in a pure gas dynamical case (see, e.g., figure 2 in Izmodenov, 2000 [10]). The termination shock becomes more spherical. The Mach disk and the complicated shock structure in the tail disappear. Interstellar neutral atoms also affect the flow of supersonic interstellar plasma upstream of the bow shock, the flow of the supersonic solar wind upstream of the termination shock, and plasma structure in the heliosheath. The flow of the supersonic solar wind upstream of the termination shock is disturbed by charge exchange with the interstellar neutrals. The new created by charge exchange ions are picked up by the solar wind magnetic field. The Baranov-Malama model assumes immediate assimilation of pickup ions into the solar wind plasma. The effect of charge exchange on the solar wind is significant. By the time the solar wind flow reaches the termination shock it is decelerated (15-30 %), strongly heated (in 5-8 times) and mass

-28-

Interstellar atoms in the heliospheric interface

loaded (20-50 %) by the pickup ion component. The interstellar plasma flow is disturbed upstream of the bow shock by charge exchange with the secondary atoms originated in the solar wind and compressed interstellar plasma. Charge exchange results in the heating (40-70 %) and deceleration (15-30 %) of the interstellar plasma before it reaches the bow shock. The Mach number decreases and for a certain set of interstellar parameters (nH,LISM > > ?~p,LISM)the bow shock may disappear. The plasma structure in the heliosheath is also modified by the interstellar neutrals. In a pure gasdynamic case (without neutrals) the density and temperature of the postshock plasma is nearly constant. However, the charge exchange process leads to a strong increase of the plasma number density and decrease of its temperature. Baranov and Malama (1996) [7] pointed out that the electron impact ionization process may influence the heliosheath plasma flow by increasing the gradient of the plasma density from the termination shock to the heliopause. The effects of interstellar atom influence on the heliosheath plasma flow may be important, in particular, for the interpretations of (1) kHz radio emission detected by Voyager (see, [15], [16]) and (2) possible future heliospheric imaging in energetic neutral atom (ENA) fluxes [17].

6. Interpretations of spacecraft experiments on the basis of the BaranovMalama model The Sun/LISM relative velocity and the LISM temperature are now well constrained. Using the new SWICS pickup ion results and an interstellar HI/HeI ratio of 13 i 1 (the average value of the ratio toward the nearby white dwarfs), Gloeckler et al. (1997) [18] concluded that n L r s M ( H I ) -- 0.2 • 0.03 am -3. However there are no direct ways to measure the circumsolar interstellar electron (or proton) density. Therefore, there is a need for indirect observations (inside the heliosphere) which can bring stringent constraints on the interstellar plasma density and on the shape and size of the interface. Such constraints can been done on the basis of theoretical models of the interface. Izmodenov et al. [9] used the Baranov-Malama model to study the sensitivity of the various types of indirect diagnostics of local interstellar plasma density. The diagnostics are the degree of filtration, the temperature and the velocity of the interstellar H atoms in the outer heliosphere (at the termination shock), the distances to the termination shock, the heliopause, and the bow shock, and the plasma frequencies in the LISM, at the bow shock and in the maximum compression region around the heliopause which constitutes the "barrier" for radio waves formed in the interstellar medium. Izmodenov at al. [9] searched also for a number density of interstellar protons compatible with SWICS/Ulysses pickup ion and Voyager, HST, SOHO observations of backscattered solar Ly c~ and kHz radiations observed on Voyager. Table 2 presents estimates of np,niSM obtained from different types of observations using the Baranov-Malama model. Izmodenov et al. [9] concluded that it is difficult to reconcile these estimates without some modification to the model. Two mutually exclusive solutions have been suggested: (1) It is possible to reconcile the pick-up ions and Ly a measurements with the radio emission time delays if a small additional interstellar (magnetic or low energy cosmic ray) pressure is added to the main plasma pressure. In this case, n p , L I S M - 0.07 cm -3 and n H , L I S M - - 0.23 cm -3 is the favored pair of interstellar densities. However, in

-29-

V. Izmodenov

this case, the low frequency cutoff at 1.8 kHz doesn't correspond to the interstellar plasma density, and one has to search for another explanation. (2) The low frequency cutoff at 1.8 kHz constrains to the interstellar plasma density, i.e., rtp,LISM - - 0 . 0 4 a m - 3 . In this case, the bulk velocity deduced from the Ly a spectral measurement is underestimated by about 30-50% (the deceleration is by 3 km s -1 instead of 5-6 km s-~). Model limitations (e.g. stationary hot model to derive the bulk velocity) or the influence of a strong solar Ly a radiation pressure may play a role. In this case, there would be a need for a significant additional interstellar (magnetic or cosmic ray) pressure as compared with case (1).

Table 2 Intervals of Possible Interstellar Proton Number Densities Type of Heliospheric Interface Diagnostics Range of Interstellar Proton Number Density SWICS/Ulysses pick-up ion 0.02 c m - 3 < rtp,LISM < 0.1 c m - 3 0.09 cm -3 < nH,TS < 0 . 1 4 cm -3 Gloeckler et al., [1997] Ly- a, intensity 0.11 cm -3 < nH,TS < 0.17 cm -3 Qugmerais et al., [1994]

np,LISM '( 0.04 cm -3 or

Ly-a, Doppler shift 18 km s -1 < VH,TS < 21 km s -1 Bertaux et al. [1985], Lallement et al. ,

0 . 0 7 c m - 3 < np,LISM <

0.2 cm -3

0 . 0 8 c m - 3 < rtp,LISM <

0.22

[1996], Cl.rk

np,LISM < 0.07 cm -3 (for nH,LISM - - 0.23 cm -3)

el. [199S]

Voyager kHz emission (events) 110 AU < RAU < 160 AU Gurnett and Kurth [1996] Voyager kHz emission (cutoff) 1.8 kHz Gurnett et al. [1993], Grzedzielski and Lallement [1996]

cm -3

np,LISM - - 0 . 0 4 c m - 3

7. N e x t F r o n t i e r s Several important physical effects are not taken into account in the model. These effects may be: 1) interstellar and heliospheric magnetic fields; 2) heliolatititudional and solar cycle variations of the solar wind; 3) galactic and anomalous cosmic rays; 4) essentially multi-fluid character of the solar wind, when the solar wind protons, pickup protons and electrons must be considered as different fluids. During the last years a big theoretical effort of several groups has been focused on understanding the influence of these (and other) effects on the heliospheric interface. For a recent review of of the theoretical models of the heliospheric interface see Zank (1999)

[19].

-30-

Interstellar atoms in the heliospheric interface

In spite of many interesting and important physical effects studied, many models don't take into account the interstellar neutrals or take them into account in oversimplified approximations. Since the H atoms are probably the most dominant component of LISM, one must be very careful when applying these models in the interpretations of the heliospheric interface observations. The use of inadequate theoretical models can result in incorrect interpretations of spacecraft experiments. This, in turn, may results in wrong conclusions on the interstellar parameters. From our point of view, the future theoretical models of the heliospheric interface must preserve the main advantage of the Baranov-Malama model - the kinetic description of nterstellar atoms- and introduce the new effects one by one. An example of a such study has been done in [21], [20]. These authors considered the effect of the galactic cosmic rays (GCRs) on the heliospheric interface structure. Firstly, the influence of GCRs on the heliospheric interface plasma structure has been studied in the absence of the interstellar neutrals ([21], [20]). Then the interstellar atoms have been added to the model. The results were compared with the results of Baranov-Malama model. In spite of the significant influence of the GCRs on the heliospheric plasma structure in the two component (plasma+ GCRs) model, most of the effects reduce or disappear in case of the three-component model. The influence of GCRs on the plasma flow pattern is negligible as compared to the influence of H atoms everywhere in the heliospheric interface, except near the bow shock, the structure of which can be strongly modified by GCRs. Another example of such study were presented by Vladimir Baranov during this COSPAR Colloquim. He and his co-workers made self-consistent study of the interstellar magnetic field (IMF). It has been shown that in the presence of interstellar atoms the effect of IMF signicantly reduces. Similar studies are needed to account for other physical effects that that have been found to influence the structure of the heliospheric interface in the models without neutrals. Such studies can bring new constraints on the local interstellar parameters and on the structure of the heliospheric interace. Significant progress can be reached if such new theoretical models will be tested by the old and new measurements. One of the promising methods of the heliospheric interface diagnostics is interpretation of absorption spectra measured toward nearby stars. It was briefly discussed in section 4. Another possible heliospheric interface diagnostics is the study of the interstellar minor elements as O, N, Ne, C. The interest in minor species is now growing due to the recent successful detection of pickup and ACR ions, by the Ulysses and Voyager spacecraft, respectively. Oxygen is of particular interest, because it is one of the most perturbed elements due to its large charge exchange cross section with protons. Izmodenov et al. [22] [23] compared OI/HI heliospheric and interstellar ratios. The heliospheric interface filtrations of both hydrogen and oxygen have been computed on the basis of the Baranov-Malama model. A rather good agreement has been found between data and theory. More detail study of the interstellar oxygen (and other elements) in the interface and how their density inside the heliosphere sensive to interstellar parameters is required. Such study can give us additional constraints on the heliospheric interface parameters. The interest to interstellar oxygen in the heliospheric interface increases also, because Gruntman and Fahr ([24], [25]) proposed a mapping of the heliopause in the oxygen ion O + resonance line (83.4 nm).

-31 -

V. Izmodenov A very promising and powerful tool to study the solar wind interaction with the surrounding local interstellar medium is global imaging of the heliosphere in the fluxes of energetic neutral atoms (ENA) ([17]). The ENAs that are produced in charge exchange of the heated plasma and background neutral gas can be readily detected at 1 AU. Global ENA images, the angular and energy dependences of ENA fluxes, are dependent on the solar plasma density, temperature, and velocity in the heliosheath. The size and structure of the heliospheric interface region depend on the parameters of the interstellar plasma and gas. Hence the ENA images should also depend on the LISM parameters (Izmodenov and Gruntman, this conference). Finally, we can conclude, that in spite of our general understanding of the physical processes in the heliospheric interface, a major theoretical and experimential effort is needed to obtain the detailed structure of the heliospheric interface and local interstellar parameters. Acknowledgement. I thank to the referee of this paper for very helpful comments and suggestions. I thank to Baranov, Malama, Lallement, Geiss, Fahr and Gruntman for useful discussions. I also thank to Rosine Lallement for Figures 3C and 3D. REFERENCES

Baranov V.B., Lebedev M.G., Malama Yu.G., Astrophys. J. 375, 347-351, 1991. Baranov V.B., Malama Yu.G., J. Geophys. Res.,98, 15157-15163, 1993. Williams L.L., D.T. Hall, L. Pauls, G. Zank, Astrophys. J., 476, 366 1997. Dalgarno A., Proc. Phys. Soc., 75, 374-377, 1960. Izmodenov V. V., Yu.G. Malama, et al., Astrophys. Space Sci. 274, 71-76, 2000. Baranov V.B., Malama Yu.G., J. Geophys. Res.,100, 14755-14761, 1995. Baranov V.B., Malama Yu.G., Space Sci. Rev., 78, 305-316, 1996. 8. Baranov V.B., Izmodenov V.V., Malama Yu.G., J. Geophys. Res. 103, 9575, 1998. 9. Izmodenov V. V., J. Geiss, R. Lallement, et al., J. Geophys. Res. 104, 4731,1999a. 10. Izmodenov V. V., Astrophys. Space Sci., 274, 55-69, 2000. 11. Linsky, J. and B.Wood, Astrophys. J., 463, 254L, 1996. 12. Gayley, K.G., Zank, G.P., Pauls, H.L., Frisch P.C., Welty D.E., ApJ, 487, 259, 1997. 13. Izmodenov V.V., R. Lallement, Yu. G. Malama, A & A 342, L13-L16, 1999b. 14. Wood B., H. Muller, G. Zank, this issue. 15. Gurnett D. and W. S, Kurth, Space Sci. Rev., 78, 53-66, 1996. 16. Treumann,R. A., Macek, W.M. and V.V. Izmodenov, A & A 336, L45, 1998. 17. Gruntman M., Rev. Space Instr. 68, 3617-3656, 1997. 18. Gloeckler, G., L. Fisk, J. Geiss, Nature, 386, 374-377, 1997. 19. Zank, G., Space Sci. Rev., 89, 413, 1999. 20. Myasnikov, A. V., D.B. Alexashov, et al., J. Geophys. Res. 105, 5167, 2000. 21. Myasnikov, A. V., V.V. Izmodenov, et al., J. Geophys. Res. 105, 5179, 2000.. 22. Izmodenov V.,Lallement R.,Malama Yu.G., Astron. Astrophys., 317, 193-202, 1997. 23. Izmodenov V. V., R. Lallement, J. Geiss, Astron. Astrophys. 344, 317- 321, 1999c. 24. Gruntman M., H. Fahr, GRL 25, 1261-1264, 1998. 25. Gruntman M., H. Fahr, JGR 105, 2000. 26. Izmodenov V. and M. Gruntman, this conference, 2000. .

2. 3. 4. 5. 6. 7.

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MHD modeling of the outer heliosphere: Numerical Aspects Nikolai V. Pogorelov

a,

aInstitute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Vernadskii Avenue, Moscow 117526, Russia

Current achievements and future prospects are discussed in the modeling of the solar wind interaction with the local interstellar medium in magnetohydrodynamic approximation. Farfield boundary conditions are described that make it possible to attain a substantial improvement in the resolution of the complicated flow structure. Special attention is paid to structurally unstable, nonevolutionary MHD shocks which can occur even in three-dimensional cases due to the presence of the symmetry plane.

1. I N T R O D U C T I O N Modern non-linear high-resolution numerical methods have recently become an efficient tool for solving complex multi-shocked gas dynamic flows. This is due to their robustness for strong shock wave computations. Application of linear numerical schemes of an order of accuracy higher than one results in spurious oscillations of distributions in the vicinity of discontinuities [18]. First order of accuracy, however, is insufficient for sharp resolution of discontinuities. For this reason linear schemes of higher order of approximation involve various additional terms called artificial dissipation. Extension of non-linear characteristicallyconsistent numerical methods to magnetohydrodynamics is not straightforward. These methods (Godunov schemes) in one or another way use the solution of the hyperbolic Riemann problem to determine numerical fluxes through the computational cell interfaces [43]. Although the exact solution of the MHD Riemann problem exists [ 19], it is too complicated and multivariant to be used in regular calculations. For this reason different approximate solutions or solutions of the linearized problem are widely applied. Written for the components of the state vector U, the conservative system of ideal MHD has the form (the notation is conventional [22])

0U 0E OF 0G o t + -g-Tx + --~y + Oz

(1)

~ a~

*The work was partially supported by the Russian Foundation of Basic Research under grant No. 98-01-00352.

-33-

N. K Pogorelov

where pv

pu Pu2 + PO

p

pu pv pw e Bx By Bz

U

puv -

,

4re

BxBy

47r BxBz puw 47r (e + po)u - -Bx ~ (v. B)

E-

puw pvw w

F

0 u B y - vBx uBz - wBx

v B x - uBy

0 vBz

pw

G

BxBy 47r By2 Pv2 + PO 47r ByBz pvw 47r By (e + po)v - - ~ (V" B) puv

-

wBy

0

BxBz 47r ByBz 4zc

Pw2 + PO

n

~

m

Bz

47r

x div B.

8Z(v.B)

(e + po)w - - ~

bl V W

w B ~ - uBz wBy - vBz 0

Here we intentionally preserved the source term H which is identically zero, since magnetic charge does not exist and magnetic field is therefore divergence-free. One can omit this term and solve the resulting system. In this case, however, special care must be taken in order to preserve the condition div B = 0 numerically [7]. Different approaches which are frequently used for this purpose include the application of the magnetic field vector potential [17,25], artificial scalar potential [39,41], and staggered grid methods [12,40]. A new method has recently been developed [24] which, in an efficient way, combines the vector potential and staggered grid approaches. Otherwise, one can solve the modified nonhomogeneous system (1) as suggested in [2] and [33]. It seems to allow the numerical magnetic charge to convect away from the computational region. Although this approach became rather popular (see [23,27,36]), it is questionable whether it can be used near stagnation points, in vortex regions, and in genuinely unsteady problems. It is possible to discretize system (1) on the numerical mesh and take advantage of the finite-volume approximation, in which equations are solved expressing the conservation of fundamental properties of the medium in an individual computational cell. To determine the fluxes through the computational cell interfaces, solutions of the MHD Riemann problem are used. The schemes actually differ from each other by the choice of the Riemann problem solver applied. For example, the scheme used in [47,48] is based on the solutions in the form of simple waves (even shocks are approximated by compression waves). This approach represents the extension to MHD of the numerical scheme [6], which is a version of the Osher scheme [22]. In [11] an MHD extension of the PPM (piecewise-parabolic method [9]) was suggested. It is

-34-

MHD modeling of the outer heliosphere: Numerical aspects based on the iterative nonlinear Riemann problem solver in which the relations on discontinuities are exactly satisfied. This method, however, treats expansion waves as expansion shocks. This is a dangerous procedure, since such nonphysical shocks can truly arise in the process of calculation. One of the advantages of this method is that it includes Alfv6n waves in the possible configurations of shocks connecting the states on the opposite sides of a computational cell even in coplanar problems. As will be shown later, this may help to get rid of structurally unstable, nonevolutionary MHD shocks and combination of shocks. The Roe-type method [38] can formally be written out for a MHD system [8,20,32]. This method is based on the solution of the linearized Riemann problem which exactly satisfies, however, the conservation relations on discontinuities. This solution was shown to be nonunique [29,30]. On the other hand, the procedure ensures an exact satisfaction of the Hugoniot relations only in one-dimensional problems. This is also true for pure gas dynamics, but the error in MHD case can be much greater. The main reason lies in the fact that the magnetic field component Bx normal to the cell surface must be continuous in the one-dimensional statement, which is not true as far as multidimensional problems are concerned. The attempts to formulate a Roe-type solver for the one-dimensional version of the nonhomogeneous system (1) turned out to be unsuccessful [34] and this method is now frequently substituted by the Courant-IsaacsonRees type method. In the latter, the numerical flux at the cell interfaces is calculated using the arithmetic mean of the quantities on the both sides of the individual interface [35]. One more possibility is to use an extremely robust TVD Lax-Friedrichs scheme [5].

2. MHD MODELING OF THE SW-LISM INTERACTION 2.1. Current achievements The presence of the solar and interstellar magnetic fields necessitates solving the MHD equations to model the solar wind (SW) interaction with the local interstellar medium (LISM). The influence of magnetic field is important if the magnetic pressure becomes comparable with the dynamic pressure of the flow. The magnitude and direction of the interstellar magnetic field is uknown. We can only say that a strength of about 1.6 #G is consistent with observations of polarization and pulsar dispersion measurements [ 15]. Estimates of the heliosphere confinement pressure give an upper limit of 3-5 #G (see [10]). Concerning the direction of the magnetic field in the local interstellar cloud, we can only refer to [ 16] which states that if the cloud surface is perpendicular to the direction of the gas flow, the direction of the magnetic field is approximately parallel to the cloud surface. These estimates lead us to the conclusion of the importance of MHD modeling. The first numerical study of the stellar wind interaction with the magnetized LISM was performed in [17,25] by a rather viscous flux-splitting method for the case of B~ II V~, where the subscript oc refers to the LISM parameters. The authors, actually, performed parametric calculations for various ratios of dynamic pressures and stagnation temperatures and some of them were very far from the SW-LISM interaction case. In [3] very accurate shock-fitting calculations of the upwind region of the interaction were performed and some of the results obtained in [17] were criticized. As later turned out [28], this mainly concerned the case of an irregular interaction in which parallel fast MHD shocks were nonevolutionary (structurally unstable), while singular (switch-on) shocks could not exist due to the symmetry restrictions. It was noticed in [45] that the toroidal component of the interplanetary magnetic field (IMF)

-35-

N. V. Pogorelov

Figure 1. General configuration of the heliosphere: density (below the symmetry axis) and total pressure logarithm isolines [28]. The LISM flow is directed from right to left. The Sun is at the origin. can be important. Three-dimensional calculations with the presence of IMF for B ~ ]1 V~ were reported in [46]. Systematic shock-capturing MHD calculations of axisymmetric problems for various magnitudes of the interstellar magnetic field (ISMF) were made in [28,31]. Both regular interaction with a single bow shock and irregular interaction with additional discontinuities were discovered. The general configuration of the flow pattern corresponding to the two-shock model [4] is shown in Fig. 1 for the following SW and LISM parameters: ne = 7 cm -3, Ve = 450 km s -~ , Me = 10, no~ - 0.07 cm -3, Voo = 25 km S-1, and Moo = 2. Here the subscript e refers to the SW parameters at Earth's distance from the Sun. M stands for the Mach number. The dimensionless value of the magnetic field is specified via the Alfv6n number A ~ - V~/~/B2/47rp~. In the presented case A~ = x/~ (see [28]). The abbreviations BS, TS, and HP correspond to the bow shock, the heliospheric termination shock, and the heliopause, respectively. The influence of the ISMF direction on the shape of the global heliopause was studied in [27], [36]. The results turned out to be consistent with the MHD modeling of the three-dimensional heliopause on the basis of the Newtonian approximation [ 14]. The distribution of the streamlines and magnetic field lines in the symmetry plane for the cases with Ao~ = 2 for two different angles between ISMF and LISM velocity are shown in Fig. 2 (see [27]). All previously cited calculations disregarded the charge exchange processes occurring among neutral and charged particles which are extremely important in the SW-LISM interaction. The IMF was also neglected. Three-dimensional calculations for various direction of ISMF, with IMF in the form of the Parker nominal spiral and with the simplified treatment of the charge-exchange processes were performed in [23]. McNutt at al. [26] investigated three-dimensional, both purely hydrodynamic and MHD flows, taking into account the latitudinal variation of the SW velocity and density in accordance with the Ulysses data. The solar cycle dependence of the heliospheric shape was studied in [42] on the basis of

-36-

MItD modeling of the outer heliosphere: Numerical aspects

Figure 2. Streamlines and magnetic field lines for A~ - 2 in the symmetry plane. The angle between B~ and V~ is equal to 90 ~ (left) and 45 ~ (right). a global MHD simulation of the time-dependent SW interaction with the magnetized LISM. Charge exchange processes were, however, neglected. This is not very reasonable, since the one-dimensional results [37] and [44] show that even if magnetic field is added, pick-up ions still remain a dominant factor of the interaction. This is in agreement with the recent results [ 1] where self-consistent axisymmetric MHD calculation were performed with Monte Carlo modeling of the neutral particle motion. The accuracy of numerical calculations can be substantially increased if we reduce the size of the computational region. Otherwise, the resolution of discontinuities will be rather poor [36]. To do this, we must shift the boundary conditions from infinity to the finite distance from the Sun and state nonreflecting boundary conditions at it. Below we consider an efficient approximate procedure created for this purpose.

2.2. Far-field boundary conditions Let us consider a local one-dimensional system 0U 0U 0--7 + a ~ x - 0.

(2)

The x-axis is directed perpendicular to the computational cell interface F. Let us choose the following form of the unknown vector in Eq. (2):

u-

[ p . . . v. w. Ca. 8x. By.

where, in addition to the purely gas dynamic case, the components of the magnetic field strength vector occur as normal (Bx) and tangential (By and Bz) to F (Ca is the acoustic speed of sound). We consider the exit boundary with u > 0. The minimum eigenvalue in this case is ,~ = u - af, where af is the largest of the two magnetosonic speeds af and a~ (af > Ca _> as): af,~- ~-

~

+ x/~

+

c~q 4 ~ r p

-37-

x/~

'

(4)

N. K Pogorelov

IBI 2 - n2x + By2 "-t-"n z2 . Let us fill the artificial cell outside the boundary by the parameters at infinity. If the outflow velocity in the center of the cell adjacent to the boundary is superfast magnetosonic, u0 > af0, we need no boundary conditions. If u0 < af0 but u~ > a f t , we introduce a rarefaction wave accelerating the flow to fast magnetosonic speed at the boundary. If u0 < af0 and uo~ < afo~, we can simply solve the Riemann problem between U0 and U~. The eigenvector corresponding to the chosen eigenvalue is (7 is a specific heat ratio)

r-

[1

1)Ca 0, t~By, ~ B z

af aBy, ceBz, ( 7 '

p'

2p

Caas

vf~

c~ - 2 P v ' T - ~ ( d a - a~) -

'

lT ,

a~(a~ - C2a)sgnBx --ca(By2 ~ nz )-BSS ,

(5)

c 2a 47r(a 2 -- c 2) fl - p(C2a - a~) = By2 + B2z "

If we seek the solution to (2) in the form of a simple wave U(x, t) = U(() with ~ = x / t , we obtain ( A - AI)Ur = 0,

A=(,

where I is the identity matrix. Thus, Ur is proportional to the right eigenvector of A corresponding to A = ~. If we denote the proportionality factor as d, we can rewrite system (2) in the form

afd ur = - - ~ , v( -- ceByd, - c~Bzd, p (Bx)r - O , (By)r - /3Byd, (Bz)r - /3Bzd, u-af- d,

(Ca) r =

('7 - 1)cad , 2p

(6)

~.

In system (6) we now substitute the equation for Ca by the equation for af, which can be easily obtained from Eq. (4) by direct differentiation with respect to ~ and by using Eqs. (6), yielding

tgd (af)( = 7 '

tg-

Oaf

r.

One can easily notice that the eigenvector (5) degenerates for C a - - a~. This happens if 0 and Ca < aA. It is apparent from Eqs. (6) that the derivatives ( B y ) ( and (Bz)r become infinite at degeneration points. One can easily obtain, however, that

By2 + B z2 -

-- ca)by,zpr

,

where by,z - By,z/(B2y + B~) 1/2. The right-hand side of this relation never degenerates if we assume by - bz - 1/x/2 for By2 + B z2 - 0 (see, e. g., [22]). If we take into account the relation

18xl a~af-

Ca2v/_~ ,

the equations for the derivatives of the transverse components of the velocity vector can also be transformed to the form suitable for further application,

vr

Bx ~47rpa~(BY)~'

we-

Bx ~(Bz)r

-38-

M H D modeling of the outer heliosphere: Numerical aspects

Thus, by passing from d to PC, we obtain the reduced system of equations that can be approximated, for example, by finite differencing 0er = (fr -f0)/A~). The system becomes:

(af)r

-

(

u0 + a~

O+af

(Ca)F--(Ca)0+(q/--1)

)

,

0

Pr

-

af)

P0 1 -~ 0 + af 0

vr - vo +

()

Bx 47rpaf

o (Byr - Byo),

(8)

i xl -i xlo,

\~p/

0 (B2)r _ B~~ + 87r[(a 2 _ Ca)by]O(DF2 2 Do),

,

(B2)F --

Wr - Wo +

2 + Srr[(a2 nzo 47rpaf

-

2 ca)b2]o(fiF -- rio),

o

3. NONEVOLUTIONARY MHD SHOCKS 3.1. Concept of evolutionarity The important subject of discussion is related to the fact that certain initial- and boundary-value problems can be solved nonuniquely using different shocks or different combinations of shocks, whereas physically one would expect only unique solutions. The situation in MHD differs from that in pure gas dynamics of perfect gas, where all entropy-increasing solutions are evolutionary and physically admissible. The term "evolutionary" means that the necessary conditions of well-posedness for the linearized problem of the shock interaction with small disturbances are satisfied. In MHD, the condition of entropy increase is necessary, but not sufficient for the shock to be admissible. Only slow and fast MHD shocks were found to be evolutionary, while intermediate (or improper slow) shocks were not and therefore must be excluded in ideal MHD. All MHD shocks are plane-polarized, that is, the magnetic field and the shock normal vectors lie in the same plane both ahead and behind the shock. In contrast to evolutionary shocks, the tangential component of the magnetic field behind a nonevolutionary shock acquires the direction opposite to what it had ahead of the shock. Thus, rotations of the magnetic field vector are possible only on two types of discontinuities" Alfv6n ones and nonevolutionary shocks. If the statement of the problem rules out Alfv6n discontinuities, nonevolutionary shocks can fairly easily occur in the numerical solution [5]. There is a simple rule to determine whether the shock is evolutionary. Fast MHD shocks are always super-Alfv6nic, that is, the magnitude of the velocity component normal to the shock is larger than the Alfv6n velocity a A - - [B~l/2x/-~ both ahead of the shock and behind it. Slow shocks are sub-Alfv6nic. Nonevolutionary shocks are trans-Alfv6nic. 3.2. Nonevolutionary shocks in the SW-LISM interaction If the magnetic field vector is parallel to the shock normal, we have a parallel shock. The behaviour of parallel shocks depends on whether the Alfv6n velocity ahead of them is smaller or larger than the acoustic speed of sound. In the former case, slow MHD shocks do not exist, while fast shocks are evolutionary and admissible for all their intensities. In the latter case, on the contrary, slow shocks are admissible for all their intensities, while fast shocks are admissible only in a certain range of parameters ahead of the shock, even if they correspond to a superAlfv6nic flow. Singular shocks are those for which the tangential component of magnetic field is equal to zero ahead of (behind) the shock and not zero behind (ahead of) it. Such shocks are called switch-on (switch-off), as the tangential component of the magnetic field vector is

-39-

N. V. Pogorelov

switched on (off) at them. Switch-on shocks are always fast while switch-off shocks are always slow, since the tangential component of the magnetic field always increases across fast and decreases across slow MHD shocks. Let us consider what happens if we increase the value of the LISM magnetic field Boo with the rest of the LISM quantities being fixed. We have two dimensionless parameters relating the quantities ahead of the shock, namely, the Mach number M ~ = V~/Caoo and the Alfv6n number A ~ = Voo/aaoo. If C~o~ > aao~ for Mo~ > 1, the forward point of the bow shock corresponds to a fast parallel shock which is always realizable. If we further increase Bo~, sooner or later a a ~ will become larger than Caoo with A~ > 1. In this case the parallel shock, though remaining fast, will be still evolutionary until Boo acquires the value corresponding to the interval

( 7 + 1)M 2

1
(9)

2 + ( 7 - 1 ) M 2"

For A~ from the interval (9), the Alfv6n number behind the shock is smaller than 1, thus resulting in a trans-Alfv6nic shock which is not evolutionary. Occasionally, a singular (fast switch-on) shock becomes admissible exactly in this range of A~. On switch-on shocks B [I n ahead of the shock but B ~/n behind it. That is, a tangential component of the magnetic field must appear at the forward point of the bow shock. On the other hand, this cannot occur due to geometrical reasons, such as the axial symmetry of the flow due to the condition Boo [[ V~. It could be fairly easily expected that the structure of the flow for the mentioned values of Boo must be different from that in the regular case. Let us choose such a strength of the magnetic field Boo for which A~ - x/2, that is, we are within the interval (9). This corresponds to B~ ~ 2.3 #G. The heliosphere pattern is shown in Figs. 1 and 3. In order to see a fine structure of the flow in Fig. 3b we show only the density lines between 1 and 2.6 with the increment 0.04. We see the origin of an additional shock and a high-density layer near the surface of the heliopause. Addition of rotational perturbations makes almost all shocks evolutionary [28], except for the vicinity of the axis, where the obtained configuration of the bow shock can be interpreted as merged switch-on and switch-off shocks. This combination, however, is also known to be structurally unstable [21 ]. As noted on another occasion in [ 13], the obtained solution will be metastable if we introduce a small angle between Voo and B~. The whole pattern rotates under this condition, as shown in Fig. 2. In this case nonevolutionary shocks are expected to appear in the vicinity of the point where the bow shock normal is parallel to the ISMF vector. Due to the absence of axial symmetry, an irregular interaction pattern with the presence of an additional shock can be realized only on one side of this point. This is now due to the presence of the symmetry plane (the mutual plane of Boo and V~). If we introduce a perturbation of the LISM flow which takes the ISMF vector out of this plane, the initial nonevolutionary pattern will be destroyed. It may appear, however, later on in the new symmetry plane. Since various perturbations can be found in the LISM, the resulting solution will be highly unsteady and, due to perturbations of the symmetry plane, nonevolutionary shocks will exist only as time-dependent shock-like structures.

-40-

MHD modeling of the outer heliosphere: Numerical aspects

Figure 3. (a) Streamlines (below the symmetry axis) and magnetic field lines and (b) density (below the symmetry axis) and thermal pressure isolines. 4. CONCLUSIONS AND DISCUSSION Let us try to understand what we might expect if the ISMF magnitude increases. First, assume that ISMF is parallel to the LISM velocity and that parameters for the solar and interstellar winds are adopted as denoted in Section 2.1. Since the Mach number of the LISM flow is greater than 1, the bow shock, if exists, is always fast. If we increase Br soon we obtain a magnetic field dominated flow in which the Alfv6n velocity is greater than the acoustic speed of sound. If Bo~ > 2.152 #G, we reach the irregular region of interaction, and structurally unstable patterns are to be expected. If B~ > 3.253 #G, the Alfv6n number becomes less than 1 and the bow shock disappears. If ISMF is perpendicular to the LISM velocity, from Eq. (4) it is easy to determine that the bow shock disappears for B~ > 2.4 #G. Numerical simulation of hyperbolic problems characterized by the presence of the bow shock can be performed on the basis of the described numerical methods. Otherwise, the stationary problem becomes elliptic and other numerical methods must be developed for its solution. It is clear that the most up-to-date task is to perform regular MHD calculations accompanied by the Monte Carlo treatment of neutrals. In three space dimensions this will require tremendous computer resources. For this reason the application of simple and robust MHD codes is highly favourable.

REFERENCES 1. D.B. Aleksashov, V. B. Baranov, E. V. Barsky, and A. V. Myasnikov, Astron. Lett. 26 (2000) 743. 2. N. Aslan, Computational Investigations of Ideal MHD Plasmas with Discontinuities, Ph.D. Thesis, Nuclear Eng. Dept., University of Michigan, 1993. 3. V.B. Baranov and N.A. Zaitsev, Astron. Astrophys. 304 (1995) 631. 4. V.B. Baranov, K.V. Krasnobaev, A.G. Kulikovskii, Soviet Physics Doklady 15 (1971) 791. 5. A.A. Barmin, A.G. Kulikovskii and N.V. Pogorelov, J. Comput. Phys. 126 (1996) 77. 6. J.B. Bell, P. Colella and J.A. Trangenstein, J. Comput. Phys. 82 (1989) 362.

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N. V. Pogorelov

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 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.

J.U. Brackbill and D.C. Barnes, J. Comput. Phys. 35 (1980) 426. P. Cargo and G. Gallice, C.R. Acad. Sci. Paris 320 (1995), Serie 1, 1269. P. Colella and P. R. Woodward, J. Comput. Phys. 54 (1984), 174. G. Gloeker, L.A. Fisk and J. Geiss, Nature 386 (1997) 374. W. Dai and P.R. Woodward, J. Comput. Phys. 115 (1994) 485. W. Dai and P.R. Woodward, Astrophys. J. 494 (1998) 317. H. De Sterk and S.Poedts, Astron. Astrophys. 343 (1999) 641. H.J. Fahr, S. Grzedzielski and R. Ratkiewicz, Annales Geophysicae 6 (1988) 337. P.C. Frisch, in Physics of the Outer Heliosphere, COSPAR Colloquia Ser. 1 (1991) 19. P.C. Frisch, Space Sci. Rev. 78 (1996) 213. Y. Fujimoto and T. Matsuda, Preprint KUGD91-2, Dept. Eng., Kyoto University, 1991. S.K. Godunov, Math. Sbomik 47 (1959) 271. V.V. Gogosov, J. Appl. Math. Mech. 25 (1961) 148. T. Hanawa, Y. Nakajima and K. Kobuta, Preprint DPNU-94-34, Dept. of Physics, Nagoya University, 1994. A. Jeffrey and T. Taniuti, Nonlinear Wave Propagation, Academic Press, New York, 1964. A.G. Kulikovskii, N.V. Pogorelov, A.Y. Semenov, Mathematical Aspects of Numerical Solution of Hyperbolic Systems, Chapman & Hall/CRC Press, London, Boca Raton, 2001. T. Linde et al., J. Geophys. Res. 103 (1998) A1889. P. Londrillo and L. Del Zanna, Astrophys. J. 530 (2000) 508. T. Matsuda and Y. Fujimoto, Proc. 5th Int. Symp. on Comput. Fluid. Dyn., Sendai, 2 (1993) 186. R.L. McNutt, Jr., et al. Solar Wind Nine, CP471, The American Institute of Physics, 823, 1999. N.V. Pogorelov and T. Matsuda, J. Geophys. Res. 103 (1998) A237. N.V. Pogorelov and T. Matsuda, Astron. Astrophys. 354 (2000) 697. N.V. Pogorelov and A.Yu. Semenov, Numerical Methods in Engineering 96, 1022, John Wiley, Chichester, 1996. N.V. Pogorelov and A.Yu. Semenov, J. Russian Acad. Sci. Physics-Doklady 42 (1997) 37. N.V. Pogorelov and A.Yu. Semenov, Astron. Astrophys. 321 (1997) 330. N.V. Pogorelov et al. Papers 6th Int. Symp. on Comput. Fluid Dyn., Lake Tahoe, 2 (1995) 952. K.G. Powell, ICASE Rept. No. 94-24, ICASE NASA Langley Research Center, Hampton, VA, 1994. K.G. Powell et al., AIAA 12th Comput. Fluid Dyn Conf., San Diego, CA, June 19-22 (1995) 661. K.G. Powell et al., J. Comput. Phys. 154 (1999) 284. R. Ratkiewicz et al., Astron. Astrophys. 335 (1998) 363. W.K. Rice and G.P. Zank, J. Geophys. Res. 104 (1999) A12563. P.L. Roe, J. Comput. Phys. 43 (1981) 357. D. Ryu, T.W. Jones and A. Frank, Astrophys. J. 452 (1995) 785. D. Ryu, E Miniati, T.W. Jones and A. Frank, Astrophys. J. 509 (1998) 244. T. Tanaka, J. Comput. Phys. 111 (1994) 381. T. Tanaka and H. Washimi, J. Geophys. Res. 104 (1999) A12605. E.E Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, Berlin, 1997. C. Wang, J.D. Richardson and J.T. Gosling, J. Geophys. Res. 105 (2000) A2337. H. Washimi, Adv. Space Res. 13(6) (1993) 227. H. Washimi and T. Tanaka, Space Sci. Rev. 78 (1996) 85. A. Zachari and P. Colella, J. Comput. Phys. 99 (1992) 341. A. Zachari, A. Malagoli and P. Colella, SIAM J. Sci. Comput. 15 (1994) 263.

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Interaction of the local interstellar m e d i u m with the heliosphere: role of the interior and exterior magnetic fields Aaron Barnes Space Sciences Division, NASA Ames Research Center, 245-3, Moffett Field, CA 94035-1000, USA

This paper reviews the role that the exterior magnetic field (of interstellar origin) and the interior magnetic field (of solar origin) may play in the heliosphere-LISM interaction.

1. INTRODUCTION When the solar wind reaches some distance where the dynamical pressure of the flow is comparable to pressure that is characteristic of the local interstellar medium (LISM), the flow must adjust to the exterior obstacle and pass through a termination shock. The post-shock heliospheric flow is subsonic, and forms a region known as the heliosheath. The heliosheath is confined by the LISM, and swept back by the exterior flow to form a long tail-like region; the boundary between the heliosheath and LISM is called the heliopause. The LISM itself is flowing past the solar region at a speed of about 26 km/s (probably supersonic), so that most likely the ionized component of the LISM passes through a bow shock as it is deflected around the heliosphere. For a valuable general review of conditions in the local interstellar medium, the reader is referred to Frisch/1/. Table 1 summarizes our current best estimates of interstellar conditions very near the Sun. The neutral and ionized hydrogen densities (Nn)is and (Nn+)~s, the temperature (T)~s, and the flow velocity (V)is (including the direction) are fairly well constrained by observations./2,3,4,5,6,7/. Although there is some observational information about the magnitude and direction large-scale galactic magnetic field in the Sun's neighborhood/8,9/, the local environment may be extremely inhomogeneous and we can say nothing with certainty about the magnitude or direction of the field just outside the heliosphere. Based on what is known about the general galactic field, (B)is--1-3 #G is a plausible guess for the magnitude, and the direction could be anything. Table 1 also shows the external pressures that follow from the values of the observed (or, in the case of the magnetic field, guessed) parameters for the LISM. Taken at face value, these pressures suggest that the location of the termination shock is somewhere in the range 70-150 AU from the Sun, and that the neutral hydrogen component of the LISM has the greatest ef-

-43 -

A. Barnes

Table 1 Parameters for local LISM Observed Parameters

Derived Pressures

(NH)IS

0.10-0.24 cm -3

(PHV2)IS

--1.2-2.8x10 -12 dyne cm -2

(Nn+)is

0.04-0.15 cm -3

(Pn+W2)is

--0.5-1.7•

(T)xs

~7x10 3 K

(NHkT)I S

-~1-2.3x 10-13 dyne

(V)~s

26 km/s

(2NH+kT)Is

-~0.8-2.9•

-13 dyne cm -2

(B)is*

--1-3 #G

(B2[8 ~)is

--0.4-3.6•

-13 dyne cm -2

-12 dyne cm -2 c m -2

*The field direction is unknown. fect in confining the heliosphere. However, the contribution of the ionized component may be appreciable, and other pressures, especially the magnetic pressure, may not be entirely negligible. Moreover, even if the confining pressure of the interstellar magnetic field is modest, its direction can substantially affect the configuration of the heliosphere, especially the location and orientation of the heliospheric discontinuities, as will be discussed later. The densities given in Table 1 correspond to mean free paths of order 100-1000 AU for neutral-neutral and neutral-ion collisions; this may be compared to a mean free path of order 1 AU for ion-ion collisions and an ion gyroradius of order 103 km for any plausible value of the interstellar magnetic field. It may be argued that over regions large in comparison with the heliosphere, to a reasonable approximation, the ionized interstellar medium moves with the neutral component and is in temperature equilibrium with it. On the other hand, although the two components may be strongly coupled for length scales larger than --1000 AU, on the scale of the heliospheric interaction it is probably a fair approximation to regard the interstellar magnetic field as frozen into the ionized interstellar material, which in turn can flow unimpeded through the neutral component. Nevertheless, the neutral component is expected to interact strongly with ionized material inside the heliosphere/10,11,12,13,14,15,16,17/.

2. EFFECTS OF THE INTERIOR HELIOSPHERIC MAGNETIC FIELD As the solar wind flows outward it carries with it magnetic field lines whose footpoints are rooted in the Sun. This field is generally relatively weak.; for heliocentric distances beyond 23 AU the ratio of magnetic to dynamic pressure is typically -- a few times 10-3, so that the field has negligible effect on the unshocked solar wind. During most of the sunspot cycle the geometry of the heliospheric field is fairly simple, comprising two quasi-hemispheres of op-

-44 -

Interaction of the local interstellar medium with the heliosphere:...

positely directed magnetic polarity. The separatrix of polarity is generally tilted with respect to the solar equator; due to the Sun's rotation a periodic alteration of polarity is seen by a stationary observer at low heliographic latitude. As the solar wind crosses the termination shock, the magnetic field will be compressed in direct proportion to the density, because the field is 'frozen in' to the plasma, If the termination shock is a magnetohydrodynamic (or gasdynamic) shock the maximum possible compression is a factor 4. Thus the ratio of magnetic to dynamic pressure in the shocked plasma is at most of order --10%, too small to be of dynamical importance in the immediate post-shock flow. However, it should be noted that the compression ratio may be substantially larger if the shock is non-magnetohydrodynamic (e.g., if it gives up a substantial fraction of the upstream energy into acceleration of the anomalous cosmic rays), and the consequent amplified magnetic field could be dynamically significant/18,19/. Even if the termination shock is magnetohydrodynamic, and therefore the magnetic field is only a minor participant in the immediate post-shock flow, the magnitude of the field farther downstream can be amplified as a natural consequence of the flow process (the CranfillAxford effect/20/). Kinematic models/21,22/predicted that this mechanism would lead to the formation of a "ridge" of magnetic pressure strong enough to be dynamically important in the heliosheath. Fully self-consistent MHD models/23,24,25/seem to confirm this prediction. In particular, in the flow on the heliospheric flanks, the magnetic ridge appears as a separator between materials originating at polar and equatorial solar latitudes/21,22/. In steady MHD models the interior magnetic field introduces a formal asymmetry to the problem, owing to the fact that the solar magnetic field is oppositely directed in the northern and southern hemispheres. It can happen that the interior and external fields near the heliopause are nearly parallel in one hemisphere, and nearly antiparallel in the opposite hemisphere. The resulting asymmetry of the flow patterns is demonstrated clearly in Plates 5 through 10 of the paper of Linde et al./24/. However, this asymmetry requires precise alignment of the heliospheric current sheet with the solar equator, a condition unlikely to arise in practice. In fact, the heliospheric current sheet is generally tilted relative to the equator, and, as Suess and coworkers have pointed out/21,22/, field lines near the heliopause are expected to originate at low heliographic latitudes. Thus, at any given point near the heliopause the field will exhibit alternating polarity due to solar rotation. The solar rotation period is short in comparison with time scales required for establishment of a steady state for the heliosphere, so that the global asymmetry due to the heliospheric field, as found in the models of Linde et al/24/, will not occur in the real heliosphere. Rather, the heliospheric magnetic field near the heliopause will exhibit complex time variability, possibly associated with reconnection and a leaky, diffuse heliopause. Altogether, the interior heliospheric magnetic field may play a role in organizing heliosheath flow, especially near the nose region, and possibly lead to magnetic reconnection and a locally leaky, diffuse heliopause. Apart from these features, however, the interior field probably does not affect the global structure of the heliosphere in a major way.

-45 -

A. Barnes

Table 2 3-D MHD Models of the Outer Heliosphere Model Neutral gas? Ionized gas? Heliospheric B?

Interstellar B?

(B)is oblique?

/23/

No

Yes

Yes

Yes

No

/24/

Yes

Yes

Yes

Yes

No

/39/

No

Yes

No

Yes

Yes

/40/

No

Yes

No

Yes

Yes

/25/

Yes

Yes

Yes

Yes

Yes

/41/

No

Yes

No

Yes

Yes

3. E F F E C T S OF T H E L O C A L I N T E R S T E L L A R M A G N E T I C F I E L D A substantial number of theoretical investigations have focused on various aspects of the interaction between the heliosphere and LISM related to the global magnetic fields, at differing levels of approximation/21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39, 40,41/. All of these, of course, build upon earlier analyses starting with the work of Parker /42/. An excellent thorough review of the subject has recently been given by Zank/17/; valuable earlier reviews have been given by Axford/20/and Holzer/43/. Fully self-consistent three-dimensional steady-state MHD simulations of the global heliosphere have been published by Washimi and Tanaka/23/, Linde et al./24/, Pogorelov and Matsuda /3 9/, Ratkiewicz et al./40/, McNutt et al./25/, and Ratkiewicz et al./41/. Some of these models allow for the neutral LISM and/or internal heliospheric magnetic field, others do not (see Table 2); however, all take account of the interstellar plasma and magnetic field as characterized by parameters consistent with Table 1. Intercomparison of the models shows an overall qualitative consistency, although, because of their differing assumptions, it is not useful in most cases to make detailed quantitative comparisons. In all cases deflection of the interstellar plasma and field involves an interstellar bow shock (the flow is super-Alfv6nic for all models); magnetic field lines in the shocked interstellar plasma are draped around the heliopause. The combined effects of dynamic and magnetic field pressures compress the heliosphere, as well. However, the neutral component of the LISM may be more important for determining the scale of the heliosphere. For example, of all the self-consistent MHD models, that of Linde et a l . / 2 4 / h a s by far the largest external pressure, due primarily to the flow of the interstellar medium (2/3 neutral, 1/3 ionized). The heliosphere is smaller in this model than in the others (this difference is probably due mostly to the large total external pressure rather than to the

-46-

Interaction of the local interstellar medium with the heliosphere:...

Figure 1. Stream lines comparing (a) aligned

(B~sllVis) and (b) transverse (BIs.J_VIs) flow from/41/.

The

models are based on interstellar and solar wind parameters that are identical except for the direction of the interstellar magnetic field: (nH,)XS=0.04 cm 3, (V)~s=26 km/s, (T)~s=7000 K, (B)is = 2 ~tG, (nH§

cm -3 at 1 AU, (V)sw=400 km/s. The two panels are plotted to the same spatial scale; the

interstellar wind flows from-x, and the interstellar magnetic field lies in the x-y plane.

-47-

A. Barnes

inclusion of neutrals per se). Another distinctive feature of this model is that its termination shock is approximately spheroidal in shape, with its center displaced downwind relative to the interstellar flow. This feature is most probably a signature of the interaction of neutral gas with the solar wind, because models without neutral gas give a more 'bullet-shaped' figure for the termination shock. The direction of the interstellar field can have an appreciable effect on the configuration of the solar wind-LISM interaction. First of all, the morphology of the heliosphere-LISM interaction depends sensitively on whether the magnetic field in the interstellar flow is quasialigned (a-Z(V~s,B~s)-0) or quasi-transverse (a-re/2). Figure 1 shows a comparison of the heliospheric configurations for exactly aligned and exactly transverse flows (from/41/), all other solar wind and interstellar parameters being identical (see the figure caption for details). The two panels are drawn to the same spatial scale. The heliopause and termination shock are substantially smaller in the transverse case, owing to the compression of the magnetic field in the nose region (cf. plates 2 and 3 of/41/). Figure 1 shows only streamlines in the plane containing Bis and VIs; for the transverse case there is an asymmetry, i.e., the heliosphere is flattened toward the Bis-Vis plane (e.g., see figure 4 of Ratkiewicz et al./41/). In the example given here the interstellar field provides a substantial fraction of the external confining pressure (Alfv6nic Mach number = 1.2). A reviewer of this paper has pointed out that this choice of parameters, for the field-aligned case, corresponds to the irregular interaction regime described by Pogorelov and Matsuda/441, so that the detailed fine structure of the nose region given in figure la may not be completely resolved. However, the overall morphology is correct, and figure 1 properly illustrates the contrast between quasi-aligned vs. quasi-transverse flow. In fact, the question of quasi-aligned vs. quasi-transverse flow is important even when the magnetic energy is relatively small. For example, the calculations of Linde et al./24/ showed that variation of the interstellar field direction could shift the position of the termination shock by over 10%. Additional asymmetry is introduced if the interstellar field is oblique, i.e., if the angle a=Z(Vis,BIs ) is different from 0 or rt/2. This situation has been investigated in detail by Pogorelov and Matsuda /39/ and Ratkiewicz et al./40,41/. These models exclude the effects of the LISM neutral component, and therefore leave out a process of substantial importance, but do have the advantage of exhibiting magnetic effects in isolation. Also, by good fortune, the independently calculated models can be compared in substantial detail, because they use quite similar parameters to characterize the solar wind and LISM (Table 3). In both models, the shape and structure of the heliospheric boundary region were calculated for various inclination angles a, ranging from 0 to rt/2. The results are in good agreement and show an asymmetry of the interface region. The noses of the heliopause and solar-wind termination shock are shifted away from the upwind direction, so that the direction toward the nose is roughly transverse to the direction of the interstellar magnetic field. The nose of the interstellar bow shock is shifted in the opposite sense. This asymmetry increases with increasing inclination

-48-

Interaction of the local interstellar medium with the heliosphere:...

Table 3 Interior and exterior parameters for two independent, comparable pure MHD models Pogorelov & Matsuda/39/

Ratkiewicz et al./40/

(nn+)~s, c m -3

0.07

0.1

B is, laG

1.5

0.8 to 2.5

V is, km/s T is, K

25 5.7•

26 9.6•

(nn+)sw, c m -3 (1 AU)

7

10

V~w, km/s

450

400

angle a, until it reaches a maximum for some value of a (which depends on the interstellar field strength), and then declines for larger c~, achieving symmetry for a =rt/2. A detailed discussion of the physics associated with this asymmetry, including extensive graphics, is presented in/41/. One final remark is that, at least for situations in which the contribution of the interstellar field to the exterior confining pressure is non-negligible, for most values of a. the heliospheric configuration is more nearly like the case of transverse flow than aligned flow. As an illustration of the point, we may note that figure 2 of/41/shows a quasi-transverse configuration even for a=zr/6. Given that the actual direction of Bis is unknown, the a priori probability that a
4. I M P O R T A N C E OF TIME VARIATIONS Disturbances in the heliosphere will propagate at some characteristic speed Vcharwhose order of magnitude may be estimated as either the flow speed of the unshocked solar wind, or the heliosheath sound speed; Vchar"100 AU/year-480 km/s is a reasonable estimate. Because the characteristic dimensions of heliospheric structures (apart from sharp boundaries) lie in the range from tens to many hundreds of AU, the time scale for readjustments of the heliosphere ranges from months, for the nose region, say, to many years for the entire heliosphere. On the other hand, the solar wind and heliospheric magnetic field exhibit temporal variations on scales ranging from less than the solar rotation time to the time scale of the sunspot cycle, so that the global heliosphere can never be in a truly steady state. In particular, the concept of

-49-

A. Barnes

a quasi-steady heliosphere that expands and contracts with the course of the sunspot cycle is

invalid. The termination shock is unlikely ever to be in equilibrium, and will move inward and outward in response to solar wind variations/18,19,32,45,46,47,48,49,50,51,52,53,54,55,56, 57,58/, and, perhaps, in response to variations in the local interstellar medium/59,60/. Solar wind disturbances generally affect limited ranges of heliographic latitude and longitude, so that at a given moment some portions of the termination shock will move outward while others simultaneously move inward/61/. Abrupt solar wind disturbances will reach the termination shock, propagate outward to the heliopause where they will be reflected, then propagate backward to the termination shock to be reflected again, etc., possibly resulting in a quasiresonant "ringing" of the outer heliospheric boundaries/55/. Considerations of this kind serve as a warning to use care in drawing inferences from the results of steady-state models such as those discussed in this paper. A case in point arises in studies of the role of the (interior) heliospheric magnetic field. As discussed above, field lines near the heliopause are expected to originate at low heliographic latitudes, and will alternate polarity as the Sun rotates/21,22/. Therefore the heliospheric magnetic field near the heliopause will exhibit complex time variability, possibly associated with reconnection and a leaky, diffuse heliopause.

5. SUMMARY This review has focused on the possible roles that the heliospheric and interstellar magnetic fields may play in the heliosphere-LISM interaction. The field in the unshocked solar wind is weak and does not strongly influence the size or shape of the heliosphere. However, the heliosheath field may be of local dynamic importance near the nose of the heliosphere. Near the heliopause the heliospheric field will exhibit alternation of polarity, due to solar rotation, possibly producing intermittent reconnection events. The dominant external pressures of the heliosphere are probably due to the ram pressure of the neutral and ionized components of the LISM. The magnitude and direction of the interstellar field are not known, and therefore we are uncertain about the relative importance of the magnetic field. However, the direction of the interstellar field can exert substantial influence on the structure of the heliosphere, even if the magnetic pressure is somewhat smaller than the ram pressures. For quasi-aligned flow the shock near the nose is essentially a gasdynamic shock, and the exterior magnetic field is convected passively around the heliosphere. In contrast, for quasi-transverse flow the field is highly compressed at the nose of the shock, and actively compresses the heliosphere. Other things being equal, quasi-transverse flow leads to (1) a substantially smaller heliosheath, (2) a termination shock that is smaller and more "bulletshaped" and (3) a weaker, more distant interstellar bow shock. Even for small values of

-50-

Interaction of the local interstellar medium with the heliosphere:... c~-Z(VIs,B~s), the configuration of the heliosphere is much closer to the quasi-transverse than quasi-aligned shape. Oblique alignment of the interstellar field ( a r 0, 7r/2) leads to asymmetries of the heliosphere and shocked interstellar medium. The noses of the heliopause and termination shock are shifted away from the (interstellar) upwind direction, so that the direction to the nose is roughly transverse to the interstellar magnetic field direction. The nose of the interstellar bow shock is shifted in the opposite sense. Finally, it should be kept in mind that time variations in the solar wind plasma and in the heliospheric magnetic field polarity are of essential importance in the global heliosphericLISM interaction.

ACKNOWLEDGMENTS The perspective that I have presented here has evolved and been nurtured in the context of collaborations with R. Ratkiewicz and the late J.R. Spreiter. I also wish to acknowledge helpful discussions and insights from W.I. Axford, V.B. Baranov, H.J. Fahr, R.L. McNutt, E.N. Parker, N.V. Pogorelov, S.T. Suess, and G.P. Zank.

REFERENCES 1. P.C. Frisch, Space Sci. Rev., 72 (1995) 499. 2. M. Witte, H. Rosenbauer, M. Banaszkiewicz, and H.-J. Fahr, Adv. Space Res., 13(6) (1993) 121. 3. G. Gloeckler, Space Sci. Rev., 78 (1996) 335. 4. E. Moebius, Space Sci. Rev., 78 (1996) 375. 5 M. Witte, M. Banaszkiewicz, and H. Rosenbauer, Space Sci. Rev., 78 (1996) 289. 6. R. Lallement, in The Local Bubble and Beyond, D. Breitschwerdt, M.J. Freyberg and J. Truemper (eds.), p. 19, Springer-Verlag. New York, 1998. 7, O. Puyoo, and L. Ben Jaffel, in The Local Bubble and Beyond, D. Breitschwerdt, M.J. Freyberg and J. Truemper (eds.), p. 29, Springer-Verlag. New York, 1998. 8. J. Tinbergen, Astron. Astrophys., 105 (1982) 53. 9. C. Heiles, in The Local Bubble and Beyond, D. Breitschwerdt, M.J. Freyberg and J. Truemper (eds.), p. 229, Springer-Verlag. New York, 1998. 10. V.B. Baranov and Y.G. Malama, J. Geophys. Res., 98 (1993) 15,157. 11. V.B. Baranov and Y.G. Malama, J. Geophys. Res., 100 (1995) 14,755. 12. G. P. Zank, H.L. Pauls, L.L. Williams, and D.T. Hall, J. Geophys. Res., 101 (1996) 21,639. 13. V.B. Baranov, V.V. Izmodenov, and Y.G. Malama, J. Geophys. Res., 103 (1998) 9575. 14. R.L. McNutt, Jr., J. Lyon, and C.C. Goodrich, Simulation of the heliosphere: Model, J. Geophys. Res., 103 (1998) 1905. 15. V.V. Izmodenov, J. Geiss, R. Lallement, G. Gloeckler, V.B. Baranov, and Y.G. Malama, J. Geophys. Res., 104 (1999) 4731. 16. R.L. McNutt, Jr., J. Lyon, and C.C. Goodrich, J. Geophys. Res., 104 (1999) 14,803. 17. G. P. Zank, Space Sci. Rev., 89 (1999) 413. 18. A. Barnes, J. Geophys. Res., 98 (1993) 15,137. 19. A. Barnes, J. Geophys. Res., 99 (1994) 6553. 20. W.I. Axford, The interaction of the solar wind with the interstellar medium, Solar Wind, NASA SP-308, p. 609, 1972.

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21. S.T. Suess, and S.F. Nerney, Geophys. Res. Lett., 20 (1993) 329. 22. S. Nerney, S.T. Suess, and E.J. Schmahl, J. Geophys. Res., 98 (1993) 15169. 23. H. Washimi, and T. Tanaka, Space Sci. Rev., 78 (1996) 85. 24. T.J. Linde, T.I. Gombosi, P.L. Roe, K.G. Powell, and D.L. DeZeeuw, J. Geophys. Res., 103 (1998) 1889. 25. R.L. McNutt, J. Lyon, C.C. Goodrich, and M. Wiltberger, in Solar Wind Nine, S.R. Habbal, R. Esser, J.V. Hollweg, and P.A. Isenberg (eds.), p. 823, AIP Press, Woodbury, N.Y., 1999. 26. H.J. Fahr, R. Ratkiewicz and S. Grzedzielski, Adv. Space Res., 6(1) (1986) 389. 27. H.J. Fahr, W.J. Neutsch, S. Grzedzielski, W. Macek, and R. Ratkiewicz-Landowska, Space Sci. Rev., 43 (1986) 329. 28. S.T. Suess, and S.F. Nerney, J. Geophys. Res., 95 (1990) 6403. 29. S.T. Suess, and S.F. Nerney, J. Geophys. Res., 96 (1991) 1883. 30. Y. Fujimoto, and T. Matsuda, KUGD91-2, Dep. of Aeronaut. Eng., Kyoto Univ., Kyoto, Japan, 1991. 31. H. Washimi, Adv. Space Res., 13(6) (1993) 227. 32. K. Naidu and A. Barnes, J. Geophys. Res., 99 (1994) 17,673. 33. V.B. Baranov and N.A. Zaitsev, Astron. Astrophys., 304 (1995) 631. 34. J.U. Brackbill and P.C. Liewer, EOS Trans. AGU, 77(46) Fall Meet. Suppl., SH31A-24, 1996. 35. S.T. Suess, and E.J. Smith, Geophys. Res. Lett., 23 (1996) 3267. 36. V.B. Baranov, A.A. Barmin, and E.A. Pushkar', J. Geophys. Res., 101 (1996) 27,465. 37. S.T. Suess, E.J. Smith, J. Phillips, B.E. Goldstein, and S.F. Nerney, Astron. Astrophys., 316 (1996) 304. 38. N.V. Pogorelov, and A.Yu. Semenov, Astron. Astrophys., 321 (1997) 330. 39. N.V. Pogorelov, and T. Matsuda, J. Geophys. Res. 103 (1998) 237. 40. R. Ratkiewicz, A. Barnes, G.A. Molvik, J.R. Spreiter, S.S. Stahara, M. Vinokur, and S. Venkateswaran, Astron. Astrophys., 335 (1998) 363. 41. R. Ratkiewicz, A. Barnes, and J.R. Spreiter, J. Geophys Res., 105 (2000) 25031. 42. E. N. Parker, Interplanetary Dynamical Processes, Interscience, New York, 1963. 43. T.E. Holzer, Ann. Rev. Astron. Astrophys., 27 (1989) 199. 44. N.V. Pogorelov and T. Matsuda, Astron. Astrophys., 354 (2000) 697. 45. J.W. Belcher, A.J. Lazarus, R.L. McNutt, Jr., and G.S. Gordon, Jr., J. Geophys. Res., 98 (1993) 15,177. 46. S. Grzedzielski and A.J. Lazarus, J. Geophys. Res., 98 (1993) 5551. 47. S.T. Suess, J. Geophys. Res., 98 (1993) 15,147. 48. Y.C. Whang and L.F. Burlaga, J. Geophys. Res., 98 (1993) 15,221. 49. K. Naidu and A. Barnes, J. Geophys. Res., 99 (1994) 11,553. 50. R.S. Steinolfson, J. Geophys. Res., 99 (1994) 13,307. 51. S.R. Karmesin, P.C. Liewer, and J.U. Brackbill, Geophys. Res. Lett., 22 (1995) 1153. 52. T.R. Story and G.P. Zank, J. Geophys. Res., 100 (1995) 9489. 53. T.R. Story and G.P. Zank, J. Geophys. Res., 102 (1997) 17,381. 54. R. Ratkiewicz, A. Barnes, and G.A. Molvik, in Solar Wind Eight, D. Winterhalter, J.T. Gosling, S.R. Habbal, W.S. Kurth, and M Neugebauer (eds.), p. 646, AIP Press, 1996. 55. R. Ratkiewicz, A. Barnes, G.A. Molvik, J.R. Spreiter and S.S. Stahara, J. Geophys. Res., 101 (1996) 27,483. 56. V.B. Baranov and N.A. Zaitsev, Geophys. Res. Lett., 25 (1998) 4051. 57. T. Tanaka and H. Washimi, J. Geophys. Res., (1999) (104) 12,605. 58. N.V. Pogorelov, Astrophys. Space Sci., 274 (2000) 115. 59. R. Ratkiewicz, A. Barnes, and J.R. Spreiter, Geophys. Res. Lett., 24 (1997) 1659. 60. G.P. Zank and P.C. Frisch, Astrophys. J., 518 (1999) 965. 61. A. Barnes, Motion of the heliospheric termination shock at high heliographic latitude, The HighLatitude Heliosphere (R.G. Marsden, ed), p. 233, Kluwer, Dordrecht, 1995.

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Modeling stellar wind interaction with the ISM" Exploring astrospheres and their Lyman-c~ absorption H.-R. Mfiller ~, G. P. Zank ~, and B. E. Wood b* ~Bartol Research Institute, University of Delaware, Newark, DE 19716 bjILA, University of Colorado and NIST, Boulder, CO 80309-0440 A numerical study of the interaction of a partially ionized interstellar medium with a stellar wind is presented. Of particular interest are the distributions of neutral hydrogen in the resulting astrospheres. We study e Ind which has a higher relative velocity with respect to its local ISM than the Sun, and a solar-like stellar wind. A second study considers the astrosphere of a star with a mass-loss rate that is different from that of the Sun (~ And). We calculate the additional absorption of the Ly-c~ lines of c Ind and ,~ And due to their respective astrospheric hydrogen walls and compare it with high-resolution UV spectra obtained by the Hubble Space Telescope (HST). Optimizing the fit between data and models leads to estimates of the otherwise elusive stellar wind parameters. 1. I N T R O D U C T I O N The solar wind plasma and the ionized component of the local interstellar medium (LISM) interact with interstellar neutral hydrogen (H I) to create a neutral density enhancement upstream of the heliosphere, the hydrogen wall. This coupling of H I to the plasma through charge exchange heats and decelerates the neutral H, including the population in the hydrogen wall [1]. Since HST high-resolution UV spectra of nearby stars have become available, it has been recognized that, besides the absorption afforded by the column density of H I in the ISM along the line of sight, the H I population of the hydrogen wall contributes to the absorption of stellar Ly-c~ line profiles in upwind directions, such as those toward c~ Cen [2] and 36 Oph [3]. For downwind lines of sight the H I density is much lower than in the hydrogen wall, but the sightline through the heated heliospheric H I is longer, allowing heliospheric Ly-c~ absorption to be observed downwind as well as upwind [4,5]. As was noted subsequently [4,6,7], the analogous creation of an "astrosphere" and a stellar hydrogen wall stemming from the interaction of a stellar wind with its surrounding ISM is possible for other stars as well. While the heliospheric absorption occurs on the red side of the Ly-c~ profile, the astrospheric H I populations give rise to an additional *This research was supported by NASA grant NAGh-9041 to the University of Colorado, by an NSF travel grant administered by the American Astronomical Society, and by NASA grant NAG5-6469, NSF-DOE award ATM-0078650, JPL contract 959167, and NASA Delaware Space Grant College award NGT5-40024 to the Bartol Research Institute.

-53-

H.-R. Miiller, G.P. Zank and B.E. Wood

Table 1 Model parameters. M/Mo

/~ AND 1 AU 5, 10, 40 LISM e INS 1 AU 0.5, 0.8, 1 LISM

nH [cm -3]

0.14 0.14

np [cm -3] 25, 50, 200 0.10 2.5, 5 0.10

v [km/s] 400 53 400 68

T [K] 105 8000 105 8000

Mach 7.6 3.6 7.6 4.6

0E 89 ~ 64 ~

absorption component to stellar Ly-c~ on the blue side [8]. In view of this, we present a numerical study of the interaction between the stellar winds of two stars and their respective local interstellar media, applying a multifluid model [9]. We choose the G8 IVIII star ,~ AND (d - 26 pc) and the K5 V star e IND (d - 3.63 pc) because of the thorough analysis of high-resolution spectral observations of Ly-c~ presented by [7], which suggests the presence of astrospheric absorption toward both stars. 2. M O D E L P A R A M E T E R S

AND RESULTS

Our numerical study [10] assumes boundary parameters for the ISM environment that are similar to those estimated for the vicinity of the heliosphere (the local interstellar cloud). This explicit assumption will be relaxed in future studies which will vary these parameters as well. Here, we only vary stellar wind parameters since they are even less accessible than the LISM values. The LISM parameters are listed in Table 1 (LISM rows), and include the H I density nil, the plasma density np, the temperature T, and the computed bulk velocities v in the astrocentric frame of reference, which are quite large compared to the LIC value for the Sun (26 km/s). Table 1 also shows the effective plasma Mach number and the direction 0E to Earth in the astrocentric frame. The inner radial boundary condition of the model is a prescribed stellar wind plasma; the values at a reference distance of 1 AU are listed in Table 1. Temperature and velocity are assumed to be identical to those of the average solar wind measured at 1 AU. For the star ,~ AND, we assume a mass-loss rate larger than that of the Sun since ,~ AND is classified as being between a subgiant and giant star. We probe parameter space by assuming three different mass loss rates for both ,~ AND and e IND. The stellar wind expands into the ISM until pressure balance prevents further expansion. The supersonic stellar wind terminates at a termination shock (TS), beyond which the decelerated wind flow, now subsonic and very hot, is diverted towards the astrotail. In both stellar systems, this flow becomes supersonic and is shocked again close to a triple point in the tailward TS that defines a bullet shaped astrosphere. The supersonic LISM plasma shocks at a bow shock (BS). A tangential discontinuity (the astropause AP) between the TS and the BS separates the stellar wind and the ISM plasma. As compared to the heliosphere, both the stellar wind ram pressure and the LISM ram pressure are higher for ~ AND. The stationary ~ AND system with 40/1;/| has roughly the same aspect ratio as the heliosphere [10], with distances scaling by a factor of about 1.5 except for the BS. The TS is found at 145 AU upstream (475 AU downstream), the AP at 195 AU, and the BS at 320 AU upstream. Comparable numbers for models of the heliosphere are 95 AU,

-54-

Modeling stellar wind interaction with the ISM: ...

~,~

~. . . . . . . .

10 s

#

. . . . . . . . .

, . . . . . . . .

~

.

.

.

.

.

.

.

.

.

,

-

,,,i

.

.

.

.

.

.

.

.

.

.

.

.

i

.......

IS,....

, .

.

.

,

10 s

7" ~ 1 r 0+

Figure 1. Log-log profiles along the e IND stagnation axis, showing density n (left) and temperature T (right), both for H I (solid) and H II (dashed). Both plots have two panels, the first covering distances from the tail region to the Sun at 0, the second containing the upstream region from the Sun to the LISM flowing in at 1000 AU.

140 AU, and 310 AU, respectively [9]. At e IND with a solar mass loss rate, the TS is found at 32 AU upstream (140 AU downstream), the AP at 41 AU, and the BS at 63 AU upstream (Figure 1). The astrosphere of e IND has an elongated shape in comparison to the heliosphere, owing to the high LISM velocity of 68 km/s. The associated LISM ram pressure dominates the pressure balance, shifting the boundaries closer to the star, and "wrapping" the bow shock and the hydrogen wall around the astropause. The mean free path of H I inside this small astrosphere is long compared to the size of the astrosphere, which calls for a kinetic treatment of the neutrals. We have employed here a multifluid representation of the neutrals [9], which is computationally less demanding yet captures the overall neutral distribution reasonably well. A hydrogen wall of peak density 0.5 cm -3 forms in the ,~ AND case between BS and AP. In the wall, neutral H is decelerated (,,~15 km/s) and heated (from 50,000 K at the BS to 105 K at the AP) through secondary charge exchange. The e IND system has a hydrogen wall with a peak density of 0.58 cm -3 (more than a fourfold enhancement over the LISM value, Fig. 1). The structure of the astrospheres in the direction towards Earth is quite similar to the upstream direction. The hydrogen wall of e INS has a peak density of 0.45 cm -3 and a temperature of ~70,000 K in this direction (,~ AND: 0.38 cm-3; ~60,000 K). 3.

ABSORPTION

RESULTS

In Figure 2, we present a calculation of the Ly-c~ absorption that includes the ISM and the modeled astrospheric component. The histograms are the blue-side wings of highresolution HST/GHRS spectra of the Ly-a line analyzed by [7]. The absorption feature centered at 1215.37 A (for A AND) is due to interstellar deuterium. The dotted line shows the ISM absorption along the line of sight, as determined by [7]. Clearly, there is excess absorption in the spectrum between 1215.4 ~ and 1215.5 .~ where absorption by the ISM alone is less than observed by HST. In principle, the modeling outlined above allows us to constrain the stellar wind parameters of A AND and c IND by varying the stellar wind plasma density, velocity, and temperature, and identifying which model best fits the HST spectra of Fig. 2. Here, we only vary the density (mass loss rate). The dashed and dot-dashed lines in Fig. 2a represent the line profile after both ISM and astrospheric absorption from three ,~ AND models with mass loss rates 5, 10, and 40 times that of the Sun have been included. The calculation of the line profile with both ISM and 40.g/| ~ AND astrospheric absorption included (triple dot-dashed) results in far too much absorption, especially near 1215.45 .t. The increased opacity in this model compared to

-55-

H.-R. Miiller, G.P. Zank and B.E. Wood . . . . . . . . .

i . . . . . . . . .

i . . . . . . . . .

i . . . . . . . . .

~, A n d ..................

-,

2

-

~,~.

ISM

.................. ISM A b s o r p t i o n

Absorption

i ,,u .......... ............

. . . . . . . . . . . I~I=40 l~Ie

'.,, ,~.

?

~ = 1.0 ~

:~

o

~9

1. i1)

,:"

"...

..'

....

"...

;:

...........

/,,"',,,

~}.

,'

",,, ,

-

.

I

1215.2

. . . . . . . . . 1215.3

1215.4 Wavelength

1215.5

12

-

5.6

1215.20

1215.30

1215.40

1215.50

Wavelength

Figure 2. Blue side of the HST spectrum of c IND (a, le•hand panel) and ,~ AND (b, righthand panel) as histograms, together with modeled Ly-c~ profiles at Earth after accounting for ISM absorption alone (dotted), and ISM + astrospheric absorption derived from the models discussed in the text. From [10].

the 5/~omodel lies in the greatly increased extent of the hydrogen wall between the AP and BS while densities remain comparable. The neutral temperature in the 40/1)/r ,~ AND wall is also higher. The ~ AND mass loss rate model of M - 5/1//o fits the data very well. For the c IND absorption (Fig. 2b), we employ three models with mass loss rates 0.5, 0.8, and 1. Two profiles "bracket" the data on the high and on the low side between 1215.4 ~ and 1215.5.1. leading us to the conclusion that the stellar wind of ~ IND has a mass loss rate between 0.5 and 0.8 solar mass loss rates. The results underscore the importance of the astrospheric neutral H distribution for Lyc~ absorption calculations. They also strongly suggest that our model has captured the basic distribution of neutral densities and velocities as well as the basic, effective neutral temperatures that arise at the investigated stars due to the interaction of the LISM with its stellar wind. The reasonably good fit, in turn, supports the principal results, namely the above described morphology of the astrosphere and the estimate of sensible stellar wind parameters. This is the currently most promising method, albeit indirect, to investigate the morphological structure and characteristics of remote astrospheres [10,11]. REFERENCES .

2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

G. P. Zank, Space Sci. Rev. 89 (1999) 413. J. L. Linsky & B. E. Wood, ApJ 463 (1996) 254. B. E. Wood, J. L. Linsky, & G. P. Zank, ApJ 537 (2000) 304. V. V. Izmodenov, R. Lallement, & Y. G. Malama, A&A 342 (1999) L13. L. L. Williams, D. T. Hall, H. L. Pauls, & G. P. Zank, ApJ 476 (1997) 366. K. G. Gayley, G. P. Zank, H. L. Pauls, P. C. Frisch, & D. E. Welty, ApJ 487 (1997) 259. B. E. Wood, W. R. Alexander, & J. L. Linsky, ApJ 470 (1996) 1157. H.-R. Miiller & B. E. Wood, this volume (2001). G. P. Zank, H. L. Pauls, L. L. Williams, &: D. T. Hall, J. Geophys. Res. 101 (1996) 21639. H.-R. Miiller, G. P. Zank, ~ B. E. Wood, ApJ 551 (2001) 495. B. E. Wood, J. L. Linsky, H.-R. Miiller, & G. P. Zank, ApJ 547 (2001) L49.

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Stationary MHD-equilibria of the heliotail flow Dieter Nickeler & Hans Fahr ~ ~Institut fiir Astrophysik und extraterrestrische Forschung Auf dem Hiigel 71, 53121 Bonn, Germany

The solar wind, passing through the termination shock, is declined into the heliospheric tail and leaves the solar system as a subalfv~nic tail flow. In this article we present an analytical method to calculate nonlinear and selfconsistent stationary ideal MHD-equilibria with incompressible, field aligned magnetized plasma flow in the heliotail. In this case within the framework of a one fluid approximation it is possible to reduce the governing MHD-equations of the problem for stationary flow states to static MHDequilibria. In magnetohydrostatics (MHS), assuming quasi-independence with respect to one coordinate (-direction) in the plane perpendicular to the tail axis, the equations reduce then to one single nonlinear, elliptic partial differential equation, the Grad-Shafranovequation (GSE) (see e.g. Grad & Rubin [1]). First we calculate static equilibria to determine the geometry and topology of permitted field configurations and map this onto corresponding stationary equilibria with plasma flow to obtain the structure of the electric currents and the magnetic field.

1. I N T R O D U C T I O N Beyond the solar wind termination shock (TS) the plasma of the solar wind is decelerated and the magnetic field is amplified, so that there exists a subalfv~nic plasma flow in the downstream direction. Scherer et al. [2] showed that for small Mach numbers the bulk flow can be assumed to behave incompressible, which even more holds for field aligned flows, where the field lines are acting as quasi-isothermals. As the decelerated solar wind has to adapt to the outer magnetized VLISM (Very Local InterStellar Medium) conditions (e.g. thermal, ram and magnetic pressure) a contact or tangential discontinuity forms, the heliopause (HP), which is stretched into downwind direction. Between the TS and the HP there exists an inner heliosheath extending into the heliotail, similar to the Earth's magnetotail. In the magnetotail the MHD quantities mainly depend on one direction perpendicular to the tail axis, connected with the theta-shaped current system (e.g. Birn [3]). In view of evident similarities we here apply a similar description to the heliotail.

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D. Nickeler and H.J. Fahr 2. S T A T I O N A R Y S T A T E S I N I D E A L M H D The equations for ideal MHD are the conservation of mass, conservation of momentum with isotropic pressure P, Amp~re's law, and the induction equation reading -

•

o

.o5'

- 5" •

- p

e)

(1)

e •

(2) --+

..+

where p is the mass density, B is the magnetic field, g the velocity field, and j the electric current density vector. For incompressible flows with V. g - 0 we can define a flow vector ~ "- v ~ g" These two conditions imply g. V p - 0 and V . ~ - 0. We also introduce the 1--,2 Bernoulli-pressure II "- P + gw . .-+

2.1. Field aligned flows These stationary equilibria should later be tested with respect to their stability and be used to derive dynamical time scales, which may be important with respect to the VLISM-solar wind interaction. In the inconsistent picture given by Suess & Nerney ([4] and references therein) only a kinematic treatment (frozen-in test field approximation) is used. These authors find strong amplification of convected magnetic fields. In addition they identify a cone of 30 degrees, in which their kinematical approach is invalidated. Such orthogonal velocity fields (with respect to components of the magnetic field) have a saddle point structure in linear stability analyses (see Hameiri [5]) and are therefore not suitable to test stability. From this point of view it may be motivated to make the simplifying assumption of a field aligned flow, i.e 9 g - P xMA /~ ' with automatic fulfillment /-fi~ of the induction equation. With all these assumptions, made in section 2., the Euler equation reads VII-

1 (1- M~)(Vx/3)x/3#o

1 / 3 2 V ( 1 - M A 2)

(3)

2/-to

allowing to conclude, that the density p and the Alfv~n Mach number MA on field lines, however, varying perpendicular to them.

are

constant

2.2. Representation by Euler potentials In 1984 Zwingmann [6] had shown the similarity between MHS-equilibria and stationary MHD-equilibria with incompressible, field aligned flows. Later the theory was improved by Gebhardt & Kiessling [7], and used for modelling sunspot magnetic fields with plasma flow by Petrie & Neukirch [8]. In general, magnetic fields can be represented by using Euler potentials. The magnetic fields of MHS-equilibria used in this case are written as BMHS -- V f • Vg, where f and g are scalar functions (Euler potentials) of x, y, z. The equations below show how the magnetohydrostatic fields are mapped to the stationary fields, by performing the noncanonical transformation f = f(a,/5) and g = g(a, ~) with the Poisson bracket 0 < ([f, g],,Z)2 ._ 1 - M~ (valid for subalfv~nic flows).

BMUS

-58-

(4)

Stationary MHD-equilibria of the heliotailflow PMHS - PMHS(f, g)

~

1

P - PMHS- _~pg2

(5)

with the velocity field g - MA BMHS/V/#op (1 -- M~). In these equations f and g are the static potentials, while c~ and/5 are the stationary potentials. Since the post-shock plasma is very hot (see Jgger & Fahr [9]), we have high values of ~-~2, i.e. of the plasma/5, and of the sound velocity c~2 > v~ > V 2 , therefore we are allowed to use these transformations.

2.3. Two-dimensional equilibria Let f = A(x, y); g = z and the transformation c~ = ~(A);/3 = g, where the GSE is written as AA = - # 0 dPMHs/dA , valid under the assumptions adapted here, then the electric current of the stationary equilibrium is calculated by A a - d--~ + ~-~ -#o jz. In the first step we assume, that AA = 0 (potential field), which means that we can find suitable solutions by using a two-dimensional multipole representation. This enables us to find equilibria, e.g. with magnetic neutral points, to get stagnation points in front of the heliosphere, which can be used to receive a Parker-like configuration of flow trajectories/magnetic field lines. We use an extended form of a Laurent series (more in a forthcoming paper). For this general kind of a conformal mapping we exclude the domain around the singularity at (x, y) = (0, 0 ) , representing the inner region of the heliosphere. Symmetric systems have two kinds of boundaries: the axis of symmetry, here the x axis, for which we assume A = 0 and the other three boundaries for which we assume asymptotic boundary conditions, namely lime_~ A = B~ y, where ~ = ~/x2+ y2 and B ~ e~ is the asymptotic VLISM magnetic field, representing the influence of the VLISM. This ensures the homogeneity of the unperturbed VLISM magnetic field and the VLISM plasma flow. Therefore within a second step we have to use suitable transformations. To get three expected current sheets we use the mapping x

oz(A) - 6' A + ~ ak In cosh k=~

/

(6)

dk

where Yk are the locations of the current sheets, i.e. y~ and ya are the heliopause current sheets, and Y2 could be the continuation of the heliospheric or heliotail current sheet (with finite thickness). The other values are normalization constants (dk = thickness of current sheets, C ensures that doz/dA > 1, guaranteeing that the flow is subalfv~nic). 3. D I S C U S S I O N

AND CONCLUSIONS

In the following figures there are shown some representative MHD-values. In MHS, isocontours of the thermal pressure and of the current density are field lines. In Figs. 1 and 2 we can see that this is violated in the case of MA ~ O. If we calculate symmetric potential fields it is also possible to choose transformations to get equilibria with asymmetric field strengths, although the trajectories are symmetric. It is also possible to model a global heliosplaere with asymmetric trajectories, so the stagnation point can lie off the x-axis. The coefficients in equation (6) could be chosen in this way that different current directions are possible for the different current sheets. Therefore this technique permits a great flexibility to construct MHD-flows for stellar magnetospheres far away from the central star, moving through the VLISM.

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D. Nickeler and H.J. Fahr

Figure 1. Symmetrical field/stream lines. The length scale is 100 AU, so the standoff distance of the heliopause is -1.5 (= 150AU).

Figure 2. Isocontours of the current density for a certain transformation, which corresponds to the symmetric field lines of the mapped MHS-equilibrium. The tail field lines are open, while the isocontours are closed. The sun is located in (x, y) = (0, 0).

A c k n o w l e d g e m e n t : We are grateful for financial support granted by the Deutsche Forschungsgemeinschaft within the project Fa 97/23-2. REFERENCES

1. H. Grad, H. Rubin, Proceedings of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy, Geneva 1958, Vol. 31, p.190 ft. 2. K. Scherer, H. Fahr, R. Ratkiewicz, A&A, 287 (1994), p. 219 3. J. Birn, JGR Vol. 92 (1987), p. 11101 4. S.T. Suess, S. Nerney, JGR, Vol. 100 (1995), p. 3463 5. E. Hameiri, Physics of Plasmas, Vol. 5 (1998), p. 3270 6. W. Zwingmann, PhD-thesis, Ruhr-Universit/it-Bochum (1984), Germany, p. 53 ft. 7. U. Gebhardt, M. Kiessling, Physics of Fluids, B 4(7) (1992), p. 1689 8. G. Petrie, T. Neukirch, Geophys. Astrophys. Fluid Dynamics, Vol. 91 (1999), p. 269 9. S. J/iger, H. Fahr, Solar Physics, Vol. 178 (1998), p. 631

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Non-stationary magnetic field geometry in the heliosphere I.S.Veselovsky a ~Institute of Nuclear Physics, Moscow State University, Moscow 119899, Russia Model examples of the 3D time-dependent magnetic fields with the open, semi-open and closed configurations in the heliosphere are presented. 1.

INTRODUCTION

The magnetic field in the heliosphere is dependent on space and time because of the imposed boundary conditions and internal dynamical processes (see, e.g., reviews by Mariani and Neubauer, 1990; Burlaga, 1991). Quasistationary and transient structures coexist in proportions varying with the solar cycle. The purpose of this paper is to present model examples showing magnetic field lines with different geometric properties in the heliosphere. 2.

MODEL ASSUMPTIONS

Let us consider magnetic fields under the ideal conductivity approximation neglecting displacement currents. In this case, the governing Maxwell equations read as follows

-

o.

(2)

If the velocity field g(~', t) is given (kinematic approximation), we have four scalar equations (1,2) for three magnetic field vector components. This means that the system (1,2) is overdetermined as a rule, and nontrivial solutions for B are possible only under specific additional restrictions. Boundary conditions for the magnetic fields can be not prescribed arbitrary, but they are adjusted to the given velocity field. The remaining Maxwell equations can be used for explicit calculations of the electric charges and currents via (V. E ) a n d (V x B ) . Hence, the set (1,2) with some boundary conditions totally determines the magnetic field structure in space and time when g(~', t) is given. This approach is well known in applications to the heliosphere when using the method of characteristics. -+

-+

-61

-

LS. Veselowsky

3.

EXAMPLES

1) In the case when g(~', t) - const and the velocity has only the radial component v, the solution of equation (1) can be written as follows -

--

Bo~

T

Bo -

--

Boo

r

(?)

B~ -

Boo

( (

0,7),t

,

(3)

V

O, ~, t

,

(4)

.

(5)

v

O, ~ , t v

The magnetic field vector at the initial sphere is not an arbitrary function of its arguments, but obeys the additional condition J~0r

0 (sin OBoo) + r0 sin 0 gO

--

OBoe]

o~

(6)

- O.

This restriction is very important. In particular, for the stationary axially symmetric boundary conditions this means Boo - 0 and Bo - O. The field line equation dr rdT)

Br

:

(7)

B~

can be integrated in a straightforward manner with the result showing a family of integral curves starting at the sphere with radius r0. Each field line belongs to the cone defined by 0 = 00 and goes from r0 to infinity along the conical spiral when Bo~ -r 0 or along the radial direction when B0~ =0. The overall geometry of the field lines could be termed as semi-open. 2) For the boundary ..+ conditions which are stationary in the reference frame rotating with the Sun, one has B0 (0, 7)- f~t) at the initial sphere r0. Here ft is the angular velocity of the rotation. In the case when Boo = 0 one obtains from (6) the relation v

f~Bo~ +

r sin 0

Bo~ - 0

(8)

and the solution (3-5) looks as follows

Br

-

(~0) -- ~ Bo~(O,~-f~t'),

(9)

7"

(10)

Bo - 0 , B~-(t--~

B o ~ ( 0 , 7 ) - F i t ' ) sin--------~0v f~r~ '

(11)

where t' - t - ~-r0. Field lines are represented in this case by Archimedian spirals v r sin 0 + a7) - const on the cone, 0 - const, where a - v/f~(O) (Parker, 1958). The spirals

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-

Non-stationary magneticfieM geometry in the heliosphere are tighter near the equatorial plane because of the differential rotation f~(0). The real heliospheric magnetic fields follow the model (9-11) rather well in a broad range of heliospheric distances only under the appropriate time averaging because of the non-stationary boundary conditions on the Sun (Mariani and Neubauer, 1990). The strong violation of the assumption Bo = 0 takes place for instantaneous magnetic fields. The measurements show that Bo :/= 0, and that Bo is comparable to Be as a rule for instantaneous fields, and the more general relations (3-5) are better applicable. 3) Let us consider solution (3-6) near the stationary "neutral points", where B~ = 0 in the rotating reference frame. This situation corresponds to the long-living "neutral point" B0~ = 0 in the solar wind source region at r = r0. In this case, the "neutral point" is "projected" from the sphere r0 along the Archimedian spiral into the heliosphere and forms the "neutral line" there. Hence, isolated stationary neutral points cannot exist in the heliosphere and the manifold of neutral points is organized in neutral lines of a spiral shape. The field B(0, Bo, B~) is tangential to the heliocentric spheres at the mentioned neutral lines. In the simplest case when B0~ = B~ - 0 one obtains a'family of similar open or closed field lines on concentric spherical surfaces disconnected from the Sun and from the infinity with two components Bo ~ r -~, B~ ~ r -~, obeying the condition of a vanishing divergence. 4) The potential part of the solar magnetic field can be represented by the multipols varying with the Hale cycle (Hoeksema et al., 1983). The dominat poloidal (r, 0) contributions on the source surface are produced by the lowest harmonics. In addition to this, non-potential fields are present and the toroidal (~) component is not negligible. The magnetic field on the Sun and in the heliosphere is more structured during years of higher solar activity. Higher poloidal and toroidal harmonics are stronger at this time. The number of non-stationary zero points and lines increases at the source surface and in the heliosphere. Accordingly, closed and loop-like structures are more common at the high solar activity years on the Sun and in the heliosphere. 5) A full set of the nonlinear MHD equations should be used instead of Eqs. (1,2) if the velocity field g(~', t) is not given. The structures with laminar and turbulent states of the magnetic field are known when the overall geometry is open, closed or intermittent one. More observations, especially multi-point and tomographic ones, are needeed for a better understanding of the heliospheric structure. Sometimes, the linear analysis is applicable. In this case, "perturbations" are small and a background state is well defined. It could be given by the stationary or evolving solution. The "eigen mode problem" arises for small perturbations. This can be solved only in the simplest cases exemplified by discrete and/or continuous spectra of "waves" and "convective branches". Practically, explicit solutions for the background state and perturbations are not easy to find. Partially because of these difficulties, we do not have as yet even a "common language" to describe observations. A dimensionless scaling approach is pomising in this respect. 6) The degree of openness of the heliospheric field increases with the distance from the Sun in the simplest model, when the solar formation region geometry is represented by a superposition of a dipole and a current sheet. The ratio of the closed field line areas at a given distance r from the Sun decreases with this distance approximately as

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I.S. Veselowsky \

-

1 + ar ) 1 where a is proportional to the length scale #/(~. Here # is the magnetic dipole of the "su n, (I) is the magnetic flux of the polar coronal holes, which is proportional to the heliospheric current sheet strength. This model is semi-quantitatively correct for the solar minimum years. The solar magnetic dipole strength decreases with the activity cycle, when the current sheet strength increases and the number of open field lines should increase because of this. As a consequence, the outer corona looks more radially stretched during the maxima. An opposite tendency is imposed by other, time dependent factors. The corona is more structured and dynamical at maxima. Coronal mass ejections are more numerous. Radially expanding non-stationary elements bring their local fields which could be both open and closed, as well as intermittent. As a result, the overall heliospheric field topology needs additional investigations especially during the high solar activity. 4. C O N C L U S I O N S Non-stationary magnetic fields in the heliosphere are partially open, semi-open or closed in different proportions dependent on time and location. The instantaneous magnetic field lines at distances about 1 AU on average strongly deviate from conical Archimedian spirals and provide the non-stationary magnetic coupling between different latitudes, longitudes and distances inside the corresponding correlation lengths, which are determined mainly by variable boundary conditions near the Sun for B and g as well as by non-local dynamical processes in the heliosphere. Because of the heliospheric curent sheets, the degree of openness of the field in general increases with the distance from the Sun. The heliospheric magnetic field is more fragmented, dynamical and has a larger number of neutral lines, separators and closed elements connected and disconnected from the Sun during the years of high activity, but the overall topology remains to be investigated. 5. A c k n o w l e d g m e n t s This work was supportedd by the RFBR grant 98-02-17660, the Federal Program "Astronomy" project 1.5.6.2, the Federal Program "Universities of Russia" project 990600 and the INTAS/ESA grant 99-00727. The author is grateful to the Organizing Committee of the COSPAR Colloquium in Potsdam for the financial support facilitating the attendance at the meeting and for the help in preparation of the final manuscript.

1. Mariani, F., and F.M. Neubauer. The Interplanetary Magnetic Field, in Physics of the Inner Heliosphere I, eds. R.Schwenn and E.Marsch, pp.183-206, Springer Verlag, Berlin, 1990. 2. Burlaga, L.F.E., Magnetic Clouds, in Physics of the Inner Heliosphere II, eds. R.Schwenn and E.Marsch, pp.1-22, Springer Verlag, Berlin, 1991. 3. Parker, E.N. Dynamics of the Interplanetary Gas and Magnetic Fields, Astrophys. J., 328, 848-855, 1958. 4. Hoeksema, J.T., J.M.Wilcox, and P.H.Scherrer, The Structure of the Heliospheric Current Sheet: 1978-1982, J. Geophys. Res., 88, 9910-9918, 1983.

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64

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Solar cycle heliospheric interface variations" influence of neutralized solar wind N. A. Zaitsev a and V. V. Izmodenov b* aKeldysh Institute of Applied Mathematics, Russian Academy of Sciences, [email protected] bDepartment of Aeromechanics and Gas Dynamics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, [email protected] New non-stationary self-consistent model of the solar wind interaction with a twocomponent (atoms and plasma) local interstellar cloud is proposed. In this model the primary and secondary interstellar atoms are treated as quasi-stationary kinetic gas. Population of H atoms originated in the supersonic solar wind is considered as zero-pressure fluid. Specific non-stationary effects introduced by the solar cycle fluctuations of the neutralized solar wind are explored. 1. I n t r o d u c t i o n The solar wind (SW) interacts with the local interstellar cloud (LIC). The heliospheric interface is formed in this interaction. The structure of the interface and the interface plasma flow depend on the parameters of the SW and LIC and their variations with time. The LIC velocity with respect to the Sun ( VLIC ~ 26 km s -1) and the LIC temperature (TLIC ~ 7000 K) are reliably established. The sonic velocity, aLIC, corresponding to TLIC, is smaller than VLIC. Therefore, the interstellar flow is supersonic and the LIC Mach number, MLIC = VLIC//aLIC, is larger than unity. Therefore, the interstellar plasma flow is supersonic and two-shock plasma structure is formed in the LIC/SW interaction. Interstellar atoms, galactic and anomalous cosmic rays, interstellar and interplanetary magnetic fields may affect the interface. However, the basic features of the heliospheric plasma interface are the same: 1) the heliopause (HP) separates the SW plasma from interstellar plasma, 2) the termination shock (TS) decelerates, heats and compresses the solar wind plasma and 3) there is the pile-up plasma region - plasma wall- between the heliopause and the bow shock. Interstellar H atom charge exchange with protons and significantly influence the heliospheric interface structure. The mean free path of H-atoms is compatible with the characteristic length of the problem considered. Therefore it is not correct to describe the * T h e research described in this publication was made possible in part by Award No.RP1-2248 of the U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF), INTAS projects # 97-0512 and #YSF 00-163, RFBR grants # 01-02-17551, 99-02-04025, and International Space Science Institute in Bern.

-65

-

N.A. Zaitsev and K V. Izmodenov

H atom motion hydrodynamically ([1], [3]). The self-consistent axisymmetric model of the SW interaction with two-component (plasma and H atoms) LIC has been developed by Baranov and Malama [2]. A kinetic approach was used to describe H atoms in the model. However, the model does not take into account non-stationary processes in the SW. Steinolfson [4] has numerically investigated the problem of the heliospheric interface response to 180 day period fluctuations in the solar wind ram pressure in the case of subsonic fully ionized interstellar gas. He found that the variation in the distance to the termination shock is only about 1 AU. Karmesin et al. [5] and Baranov and Zaitsev [6] studied the influence of the 11 year variation of the solar wind pressure onto the heliospheric interface with 2D hydrodynamic models. These authors concluded that the response of the position of the termination shock to the changes of the solar wind parameters is within 8 - 12% (or about 10 AU). The response of the heliopause is smaller and the response of the bow shock is negligible. Baranov and Zaitsev also pointed out that in the supersonic solar wind as well as in the heliosheath the plasma flow has a quasi-stationary behaviour, while in the pile-up region between the bow shock and the heliopause there is a sequence of shocks and rarefaction waves. However, the mean plasma distribution is close to the stationary plasma distribution. In this work we investigate the effect of the solar cycle fluctuations of the fast solar neutrals flux onto the heliospheric interface. These energetic neutrals are created by charge exchange inside the heliopause and have significant influence on the compressed interstellar plasma (see, e.g., [3]). 2. F o r m u l a t i o n of t h e P r o b l e m The model [2] clearly shows, that there are four different types of H atoms in the heliospheric interface: i) the unperturbed interstellar neutral H atoms called Primary Interstellar Atoms or PIAs; ii) the compressed, decelerated, and Heated Interstellar Atoms (HIAs) formed by charge exchange with heated interstellar protons outside the heliopause; iii) the neutralized, decelerated, and Heated Solar Wind Atoms (HSWAs) formed in the heliosheath by charge exchange between the neutral interstellar gas and the hot protons of the decelerated and compressed solar wind, and iv) the neutralized Supersonic Solar Wind Atoms (SSWAs). These types of neutrals have different energy and spatial distributions in the interface. In Baranov-Malama model the influence of neutrals on plasma flow were taken into account as source terms Q in the right parts of ithe Euler equations for plasma component. To study properly the solar cycle influence on the heliospheric interface one should solve simultaneously the time-dependent Euler and Boltzmann equations. While the development of the corresponding Monte-Carlo algorithm is still in progress we would like to understand the basic physical effects of the solar cycle on the time-dependent interface from a simplified model. To study the influence of interstellar atoms we made the following assumptions: 1. Since the positions of the BS and the HP do not change significantly and fluctuations of plasma in this region are around stationary distributions, we assume that there is no influence of the solar cycle on the PIA's and HIA's. Hence the source terms QPIA and

-

66-

Solar cycle heliospheric interface variations: Influence of neutralized solar wind

QHIA into the plasma equations do not depend on the solar cycle and can be taken from the stationary solution. 2. We neglect the changes of HSWA's over the solar cycle. 3. For the number densities npIA and nHIA we assume that nH -- exp

7~H,TS~

T VH,TS

where a~z is the charge exchange cross section; rtE, VE a r e the solar wind proton number density and temperature, respectively; nH,TS VH,TS the number densitrnd velocity of interstellar atoms at the termination shock, r is the heliocentric distance, rE--1 AU is the distance to the Earth. This formula is the zero order approximation of interstellar neutral distributions in the interface, but for our objectives it is sufficient. 4. We assume that SSWA's can be treated as a zero-pressure fluid. The governing equations for this fluid are mass and momentum conservation lawis under the condition that the pressure PSSWA = O. The mutual influence of H-atoms and the plasma flow is modelled by the corresponding source terms in the mass conservation law and the momentum conservation law. In the stationary case this model gives the distribution of the SSWA's number density close to that obtained with the Monte-Carlo simulation. In order to simulate the ll-year solar cycle we changed the plasma velocity at the Earth orbit according to a sinusoidal law so that the ram pressure was varied by a factor of two. The sinusoidal variation of VE is the first harmonic of the real time dependence of the SW parameters. 3. N u m e r i c a l r e s u l t s Numerical results discussed below were obtained on the basis of a statinary solution computed for the following parameters [7]" np~ - 0.07 cm -3, n H ~ -- 0.2 cm -3, V~ = 25 kin~s, T~ = 5672K, nEo = 7 cm -3, VEO = 450 kin~s, TEO = 73507K. Our calculations show that the qualitative features of the non-stationary LIC - SW interaction established in [6] take place in the presence of neutral H-atoms as well. But the effect of the solar activity cycle is quantitatively stronger because the interface is closer to the Sun. For example, the TS excursion during the solar cycle on the axis of symmetry is about 30 AU, i.e. about 30% of its mean solar distance. Figure 1 shows the farthest and the nearest discontinuities positions in the upwind hemisphere parameters (solid lines). In the same figure the steady state positions of the BS, HP and TS are shown (by circles). One can see that the region between the BS and HP becomes wider: the mean location of the BS is farther from the Sun and the mean location of the HP is closer to the Sun than the corresponding steady state positions. The mean distributions of the plasma number density on the axis of symmetry in the region between the BS and HP is shown in Figure 2. The stationary distribution of the plasma number density in the same region is also shown. One can see that the mean density in the non-stationary cases is much less than in the stationary solution. This phenomenon can significantly influence the penetration of neutral H-atoms into the solar system. Figure 2 also shows the presense of a sequence of shocks and rarefaction waves moving from the HP to the BS similar to the one obtained in [6].

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N.A. Zaitsev and V. V. Izmodenov

Figure 1. The geometrical pattern of the discontinuities: solid lines minimum and maximum heliocentric distances, circles the stationary position of the TS.

Figure 2. The interstellar plasma density: stationary solution (solid line), nonstationary solution (diamonds) and the mean density distribution (dashed line).

4. Conclusions The conclusions of presented study can be summarized as following: 1. The solar cycle influence on the variation of the termination shock is stronger in the case with H atoms than it would be in the case without H atom component. 2 Due to the solar cycle variations of the neutralized solar wind, i.e. atoms created in the supersonic solar wind by charge exchange with solar wind protons, the region between the heliopause and the bow shock become wider and mean plasma density in the region become smaller than for the stationary problem. This can be important for interpretations of heliospheric absorption in Ly-c~. REFERENCES

1. Baranov, V. B., V. V. Izmodenov, and Y. G. Malama, J. Geophys. Res., IDS, 95759585, 1998. 2. Baranov, V. B., and Y. G. Malama, J. Geophys. Res., 98, 15157-15163, 1993. 3. Izmodenov, V. V., this issue. 4. Steinolfson, R. S., J. Geophys. Res., 99, no. 7, pp. 13307-13314, 1994. 5. Karmesin, S. R., Liewer, P. C. and Brackbill, J. U. Geophys. Res. Lett., vol. 22, no. 9, pp. 1153- 1156, 1995. 6. Baranov, V. B. and Zaitsev, N. A. Geophys. Res. Lett., Vol. 25, No. 21, pp. 40514054, 1998. 7. Izmodenov V. V., J. Geiss, R. Lallement, et al., J. Geophys. Res. 104, 4731,1999a.

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Time dependent radiation pressure and time dependent, 2D ionisation rate for heliospheric modelling M. Bzowski ~ * ~Space Research Centre PAS, Bartycka 18A, 00-716 Warsaw, Poland

1. M O T I V A T I O N The objective of this research was to develop time dependent, 3D models of the 3 solar parameters affecting the distribution of neutral interstellar hydrogen in the inner heliosphere: Lyman-c~ radiation pressure, charge exchange rate of H-atoms on solar wind protons, and photoionisation rate. The models are intended to be used in a program calculating the hydrogen density (see Bzowski et al., this volume) and while they are based on actual measurements, some simplifying assumptions were a priori made: the modelled quantities depend as 1/r 2 on the heliocentric distance, the periodicities allowed are longer than ~ 1 year, temporal variations of the solar wind occur immediately throughout the heliosphere; furthermore the functional form of the models was chosen to facilitate their use in numerical calculations. 2. R A D I A T I O N

PRESSURE

In lack of reliable data available it was assumed that the solar Lyman-a radiation pressure is spherically symmetric. The time series of the net solar Lyman-a flux from several spacecraft, recalibrated by Tobiska et al. (1997) and covering a time interval from 1977 till 1997.5, was expressed in the units of solar gravity assuming that the flux at the line centre is by number equal to the net flux. Next a periodogram analysis was performed (Press & Rybicki 1986) and based on the periodicities Pj found, a formula J, # (t) - #o + E (PJ cos cejt + qj sin wit), where wj - 2~r/Pj,

(1)

j=l

was fitted. The time series and the fitted model are presented in Fig.1 (left-hand panel) and the numerical values of the parameters in Table 1. 3. I O N I S A T I O N R A T E The net ionisation rate is an arithmetic sum of photoionisation and charge exchange rates, calculated as follows. *M.B. was supported by Polish SCSR grants 2P03C 004 14 and 2P03C 005 19.

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M. Bzowski Table 1 Fitted parameters of radiation pressure and ionisation rates j Radiation pressure Photoionisation Charge exchange #0 = 1.27864 ~ph0 = 11.1862. 10-8s -1 ~chx0 = 55.5692- 10-Ss -1 qj Pj [y] pj 10 .8 qj 10 .8 Pj [y] pj 10 -8 qj 10 -8 Pj[Y] Pj 1 10.653 0.26043 -3.31286 30.007 1.3110 0.4609 27.261 5.1296 -7.5059 26.1185 -0.45974 0.46164 15.125 -0.0292 0.0046 7.5450 1.8444 2.2619 34.8206 -0.04823 0.12659 10.761 5.1934 0.9897 5.2490 -2.5727 -4.6350 43.1192 -0.17331 -0.26181 8.2470 -0.0822 1.3457 B0 = 25.3629 9 10 -s s-1 , b = 3 . 3 5 9 1 9 f o r n = 2 , B 0 = 2 6 . 0 1 9 3 - 1 0 - a s -1, b = 1 7 4 1 . 7 9 f o r n = 8 .....

Lyman-a radiation pressure 2.5 . . . . . . . . . . . . . . . . . . . . . . . .

1.5 1 0.5~

Solar photoionisation rate

'~J : .

1975

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1980 1985 1990 1995 2000 time [y]

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1975

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1980 1985 1990 1995 2000 time [y]

Figure 1. Solar radiation pressure (left-hand panel) and photoionisation rate (right-hand panel): models defined in Eq.1 vs data.

3.1. Photoionisation In absence of sufficiently long time series of actual data, the rate of photoionisation of hydrogen at 1 AU was calculated from a proxy based on the linear correlation between the solar 10.7 cm radio flux and the solar EUV flux, indicated by Hodges & Tinsley (1981). The formula to convert the 10.7 cm radio flux to the hydrogen photoionisation rate at 1 AU from the Sun was developed following a suggestion by Cummings (private communication), who derived this quantity from the solar EUV flux reported by Torr et al. (1979) for the day 113 of 1974 (solar minimum) and day 50 of 1979 (solar maximum). The photoionisation rates for these dates were equal, correspondingly, to 0 . 5 3 2 . 1 0 -7 s -1 and 1.87.10 -7 s -1 and the 10.7 cm adjusted flux to 66.5 and 214.10-22 W cm -2 s -1. Based on these data, a system of two equations with two variables was solved, yielding the following conversion formula: 9ph --

8.7661.1012 F10.7[W m -2 s -1] - 5.84576.10 -1~

(2)

With the use of this formula, daily averages of the 10.7 cm flux, covering the interval from 1948 till 1998 and publicly available in the Internet ( h t t p : / / w w w . d r a o . n r c . c a / i c a r u s / sol_home.shtml), were converted to a photoionisation rate time series and subjected to a similar analysis as in the case of radiation pressure. The periodicities and model parameters found are presented in Table 1 and a plot of the data and the model curve can be seen in Fig.1 (right-hand panel). Good correlation between the solar Lyman-c~ radiation

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Time dependent radiation pressure and time dependent, 2D ionisation rate for heliospheric modeling pressure and the hydrogen photoionisation rate is striking but the model does not fit perfectly to the data; in particular, a 30% discrepancy about 1996 is visible. While it was possible to reduce this discrepancy by clipping the dataset to the recent solar cycle, this solution was rejected because it was giving unrealistic forward extrapolation and wrong timing of minima and maxima of the earlier solar cycles. Since photoionisation is not the dominant sink of hydrogen in the heliosphere, the 1996 underestimate should not be important for hydrogen distribution modelling.

3.2. Charge exchange Details of derivation of the charge exchange model will be published elsewhere because of the lack of space. In this paper results only will be presented.

Figure 2. Charge exchange rate adjusted to 1 AU in ecliptic (left-hand panel) and from the Ulysses Fast Latitude Scan (right-hand panel).

The rate of charge exchange between hydrogen atoms of the neutral interstellar wind and protons of the supersonic solar wind is calculated from the formula ~ch-x (t, (~) -- O'ch_ x (Vrel) ~tSW (t, r

Vrel

(t, r

/r 2, where Vre 1 -- VSW

(3)

and r is the heliocentric distance in AU, r the heliographic latitude, t time, V~el the relative velocity between the colliding particles, Gch-x the reaction cross section, nsw the solar wind density at 1 AU, and Vsw the solar wind speed, assumed independent on r. The charge exchange cross section used to be calculated from a formula by Fite et al. (1962) or by Maher & Tinsley (1977). But in comparison with experimental data compiled by Barnett et al. (1990), Fite's formula is 30 40% too high and Maher & Tinsley's is good from 120 to 450 km/s. Since the velocity range relevant for heliospheric modelling is from just a few to about 800 km/s, a new formula, spanning the whole range and accurate to at least 2.5%, was fitted to Barnett's data (velocity is expressed in cm/s)" a~h-x (v) - -2.01848.10 -17 In 3 v+1.00136.10 -15 In 2 v-1.71725.10 -~4 In v+1.03807.10-~3(4) Based on the data from Ulysses (Marsden 1996) it was assumed that the solar wind is steady in the polar regions and its variability is limited to an equatorial band. Hence a

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M. Bzowski functional form of the charge exchange rate model was adopted as r 2/Sch_ x ( r

/~o - Bo + ~ (pj cos wjt + qj sin wit)

t) -- B 0 -t-

exp [-b r

(5)

j=l

To find parameters of this formula, time series of daily averages of charge exchange rate were calculated using Equ.(3) from multispacecraft in-ecliptic solar wind data (time span from 1972 till 1998) and from Ulysses Fast Latitude Scan. The first time series was then converted to monthly averages and subjected to an analysis as for the photioinisation rate and yielded parameters COj - - 27c/Pj, pj, qj, and/50 (Table 1, Fig.2, left-hand panel). The latitudinal profiles were fitted to the second time series and yielded B0 and b for the two models assumed (n = 2, referred to as the gaussian bulge, and n = 8, referred to as the rectangular bulge, see Fig.2, right-hand panel). ,--, 10
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1991 1992 1993 1994 1995 1996 1997 time [y]

Figure 3. Charge exchange rate adjusted to 1 AU calculated from the whole Ulysses data set from launch till 1997.5 compared with the rectangular bulge model (broken line) and the preferred gaussian bulge model (solid line).

While the rectangular bulge model reproduces better the UFLS data, the gaussian bulge model reproduces better the whole Ulysses data set available (see Fig.3). The model seems to be accurate enough for solar minimum but it needs to be improved to better reproduce the latitudinal behaviour of charge exchange rate during solar maximum. REFERENCES

Barnett, C. F., Hunter, H. T., Kirkpatrick, M. I., Alvarez, I., Cisneros, C., & Phaneuf, R. A. 1990, Atomic data for fusion. Collisions of H, H2, He and Li atoms and ions with atoms and molecules, Vol. ORNL-60S6/V1 (Oak Ridge, Tenn.: Oak Ridge National Laboratories) Fite, W. L., Smith, A. C. S., & Stebbins, R. F. 1962, Proc. R. Soc. London Ser. A, 268, 527 Hodges, R. R. & Tinsley, B. A. 1981, J. Geophys. Res., 86, 7649 Maher, L. J. ~z Tinsley, B. A. 1977, J. Geophys. Res., 82, 689 Marsden, R. 1996, Space Sci. Rev., 78, 67 Press, W. H. & Rybicki, G. B. 1986, Astrophys. J., 338, 277 Tobiska, W. K., Pryor, W. R., & Ajello, J. M. 1997, Geophys. Res. Lett., 24, 1123 Torr, M. R., Torr, D. G., R.A, Ong, & Hinteregger, H. E. 1979, Geophys. Res. Lett., 6, 771

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Oral p a p e r s a n d p o s t e r s

MAGNETIC FIELDS IN THE HELIOSPHERE: INTRODUCTORY REMARKS

W.I. Axford Max-Planck-Institut fiir Aeronomie, Katlenburg-Lindau [email protected]/Fax: +49-5556-979410 In general the heliospheric magnetic field is rather weak and should not have significant effects apart from the region near the stagnation point where it may grow substantially. Nevertheless its topology is interesting and this in turn may have an effect on the entry and escape of low energy cosmic rays and other energetic particles. Reconnection between the internal (solar) magnetic field and the external (interstellar) magnetic field may also be important in this regard. It is also of significance to consider deviations of the field from a simple spiral form either as a result of the random motion of foot-points at the base of the corona or of the differential rotation of the sun.

TEMPORAL VARIATIONS OF LY-c~-INTENSITIES, BACKSCATTERED FROM THE INTERSTELLAR HYDROGEN ATOMS UPSTREAM OF THE SUN: ULYSSES-GAS OBSERVATIONS Manfred Witte Max-Planck-Institut fiir Aeronomie, D-37191 Katlenburg-Lindau, Germany.

While the flow of interstellar neutral hydrogen particles approaches the sun, it becomes increasingly depleted closer to the sun due to charge exchange with the solar wind. The Ly-a intensities emitted by the sun decrease with larger distances, so that the Ly-a intensity/8, scattered from the H-distribution (Is ,'~ nn x/solar) has a maximum at a distance of 1 to 3 AU upstream of the sun (so called maximum emission region, MER). In 1999, this region has been monitored over several solar rotations by the GAS-instrument on ULYSSES, positioned about 5 AU from the sun in crosswind direction, with a time resolution of about 4 days. The observed intensities reveal pronounced temporal and latitudinal (!) variations: 9 there is a longterm trend, lasting several solar rotations 9 there is a pronounced periodic (~ 25 days) variation (solar rotation) 9 and, most noticable, this latter variation is small at equatorial latitudes, but already significant at latitudes of + 20 degrees. The interpretation of these variations will give insight into the variability of a) the solar Ly-c~ radiation, b) the efficiency of the charge exchange process, modifying the H-atom densities in the inner heliosphere. Details of the observations and first interpretations will be presented.

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General D i s c u s s i o n Jokipii to Zank: What is the compression ratio of travelling shocks just immediately upstream of where the heliospheric bow shock is? Zank: Those tend to be fairly weak - compression ratios of no more than 1.8 to 2 at most. Dorman to Zank: Did you take into account the non-spherical solar wind? And how did you take into account the nonlinear effect of cosmic rays (CRs)? Zank: In answer to your first question: that was part of the point about the 3-D simulations. There we assumed Ulysses parameters that have been measured, so the velocity of the solar wind over the poles was about 800 km/s and in the ecliptic about 400 km/s. The question about the CRs: we just assume that they contribute to the interstellar pressure. So, we keep galactic CRs in the models but only in a very simple way. We don't actually solve a CR transport equation at this point. Baranov to Mfiller: What parameters do you take into account in your Boltzmann equation? For example for the gravitational and radiation forces? And what is the assumption about the distribution function of protons? Miiller: The last question first: tile protons come out of a gasdynamic simulation, so we assume Maxwellian proton distribution functions. We are further assuming that the radiation pressure is balanced by gravity or vice versa, and we have not included photo ionization yet. Sreenivasan to Izmodenov: How do you treat the right-hand side of your Boltzmann equation? Izmodenov: We use the Monte-Carlo scheme and we just model the effect of charge exchange. We compute the probability of charge exchange and we use the method of splitting of trajectories. The Monte-Carlo code allows us to calculate the distribution functions directly. Baranov to Izmodenov: Could you compare the distribution functions obtained in your model with those obtained with the model by Miiller et al.? Izmodenov: One can probably compare but our calculations are computed in much smaller cells in all regions. Veselovsky to Izmodenov: What can be said about the accuracy of the current cross sections for atomic collisions from experiment and theory? Izmodenov: The cross section that I have shown have been calculated theoretically - experimental data are not available at such low energies, as far as I understand. Jokipii to Nickeler: You use the assumption of field-aligned flows. That seems to be violated rather seriously. Could you tell me the effect of that assumption? Nickeler: It is a simplification, of course. The interesting thing is that, because of the non-linearity of the magnetohydrostatic equations, it is difficult to find analytical solutions. However, we also try to find methods in the same way with a transformation with components of the flow orthogonal to the field lines.

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General Discussion

Fahr to Witte: Is there anything left in your fits for electron impact ionization? Witte: I think to answer that needs more modelling to get the actual shape of the maximum emission region. So far, we are not talking about any values of ionization rates here. Baranov to Axford: Two years ago Linde et al. published a model taking into account the heliospheric as well as the interstellar magnetic field. Are your interesting ideas supported by their results regarding reconnection or the effect of the heliospheric magnetic field near the heliopause? Axford: Reconnection is essentially impossible to stop in these circumstances, it's going to happen all over the place. It means that field is even more complex, and it may be important for low energy electrons to come in. Sreenivasan to Barnes: Astrophysicists generally believe the interstellar magnetic field is of the order of 5-6#G and its direction is supposed to be along the spiral arms with some fluctuating component. Your values are quite different. Do these things make a substantial difference for the direction as well as magnitude of the external field? Barnes: On a scale of things small compared with the Local Bubble, like the heliosphere, any relation between the magnitude and direction of the magnetic field to what it maybe in the general galactic neighbourhood is not at all clearcut. Richardson to Bzowski: The charge exchange ionization rate depends on the solar cycle. Have you modelled that? Bzowski: We have modelled this by a~ssuming that tile rate at the poles is fixed and the ration in the ecliptic is going up and down.

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Session 2: Heliospheric and I n t e r s t e l l a r Connections

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Radiative Transfer at Lyman cu in the Outer Heliosphere Eric Qu~merais ~ ~Service d'A(~ronomie du CNRS B.P. 3, 91371, Verrihres le Buisson, France eric. quemerais~aerov.j ussieu.fr We present here the results of a model of multiple scattering at Lyman c~ in the interplanetary medium. It uses the formalism of Angle Dependent Partial Frequency Redistribution which allows a computation of the actual line profile for a given hydrogen velocity distribution taking into account actual local velocities and temperatures. This model is applied to prove that multiple scattering effects cannot be neglected anywhere in the heliosphere. We also give results for intensity, apparent velocity and apparent temperature with increasing solar distance. 1. I n t r o d u c t i o n The existence of a strong Lyman c~ background observed in the interplanetary medium has shown the presence of neutral hydrogen atoms backscattering the solar photons. In the outer heliosphere, say outside 40 AU, the hydrogen distribution is not affected by solar EUV photo-ionization or charge exchange with solar wind protons. There, the H atoms are mainly influenced by the interface structure between the expanding solar wind and the ionized component of the interstellar medium. This interface is the object of many speculations concerning its nature, stability and actual position. For a review concerning this problem, see e.g. Baranov [1990]. The neutral H atoms are coupled to the plasma components of the solar wind and of the interstellar medium through charge exchange processes. As a result, the outer heliosphere hydrogen distribution is substantially different from the case of the hot model where the H atom distribution is a simple gaussian distribution with constant number density far away from the sun [Thomas, 1978]. One striking feature of the outer hydrogen atom distribution obtained by theoretical models including the effects of the heliospheric interface is the so-called hydrogen wall. This wall is due to a pile-up of neutral H atoms in the region where the interstellar plasma is strongly heated and decelerated. Charge exchange between slowed down interstellar protons and neutral hydrogen atoms leads to a new neutral hydrogen component. It is characterized by a large temperature and a small bulk velocity in the solar frame [Baranov and Malama, 1993; Zank et al., 1996; Baranov et al., 1998]. Since 1993, a series of observations have been performed by the UV Spectrometers on board the Voyager 1 and Voyager 2 spacecraft to try to observe the signature of the hydrogen wall in the Lyman a pattern [Qu6merais et al., 1995]. Hall et al. [1993] reported that the Lyman c~ intensity measured away from the sun was falling off with distance less quickly

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E. Quemerais than expected from a standard hot model. This result suggested that there was a positive gradient of neutral hydrogen at large distance from the sun and could be explained by the existence of an interface region. However, the actual gradient observed by Hall et al. [1993] was not confirmed by later dedicated observations [Qu~merais et al., 1995]. An alternate explanation is now considered, i.e. that the increase of Lyman c~ intensity in the upwind direction could be partially due to a constant emission from HII regions in the galactic plane [Qu~merais et al., 1995]. This question is still unresolved and the latest data will need to be compared to the best modeling available. In the previous literature, radiative transfer effects have not often been considered very precisely. The main reason is that in the inner heliosphere, the interplanetary medium is supposed to be optically thin at Lyman c~. In such a case, one needs only to integrate the first scattering order over the line of sight to compute the scattered intensity. Unfortunately, this is not quite correct as shown by Keller et al. [1981] and confirmed by Hall et al. [1992] and Qu~merais and Bertaux [1993]. Those three previous models were obtained from Complete Frequency Redistribution hypothesis. A more correct representation of the scattering process was used by Scherer and Fahr [1996] and Qu~merais [2000]. This is called Angle Dependent Partial Frequency Redistribution (A.D.P.F.R.) and was extensively described by Mihalas [1970]. Although, the physical basis used for the computation is very similar, the results obtained by these two groups were different. Scherer and Fahr [1996] estimate that all higher orders of scattering are negligible and that the computation can be stopped at the first scattering in the inner heliosphere. On the contrary, Qu~merais [2000] finds that total intensity computations obtained from ADPFR is very similar to CFR results and confirms the results of Keller et al. [1981], Hall [1992] and Qu~merais and Bertaux [1993], i.e. even in the inner heliosphere, it is necessary to include higher orders of scattering in the computation of ther backscattered intensity. This is even more necessary in the outer heliosphere. The first section tries to give quantitative results on this problem. The second section gives a presentation of the main results obtained for intensity, apparent velocity and apparent temperature derived from line profiles in the outer heliosphere.

2. A r e R a d i a t i v e

Transfer Models

Necessary?

The optical thickness at Lyman c~ in the interplanetary medium varies by 1 for 10 AU. This very rough estimate shows that the medium is optically thick in the outer heliosphere. To illustrate that, we show in figure 1 the profile of the local emissivity corresponding to the first order of scattering for a point in the outer heliosphere. More details are given in Qu~merais [2000]. Keller et al. [1981] were the first authors who carefully computed the effects of multiple scattering for an observer at various distances from the sun and looking radially away from the sun. Their computations were based on a Monte-Carlo approach and used the assumption of Complete Frequency Redistribution. Their conclusions were very important for the study of the interplanetary Lyman c~ background. Indeed, they showed that even at 1 AU from the sun, where the H number density is very small, the optically thin approach does not apply. In the downwind cavity, they found an intensity ratio for multiple scattering over optically thin assumption equal to 1.35. These results were later

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Radiative transfer at Lymanla in the outer heliosphere

--

/

-

\

t;

a

/

-

/

_

f'

\ ,

/\

_

L

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l I~] 17~I l~l~l I~l 17~I l~

~~ ~ ~ I~

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Figure 1. Line profile of primary emissivity for a scattering point at 54.2 AU from the sun in the crosswind direction. The dash line shows the radial profile and the dashdot line shows the perpendicular profile. The Monte Carlo results are shown by squares (radial) and diamonds (perpendicular). The hot model parameters in this simulation are NH = 0.15 cm -a, VH = 20 km s -1 and TH = 8000 K.

confirmed independently by Hall [1992] and Qu~merais and Bertaux [1993]. Following this result, various approaches have been adopted. The first one includes a correction to the optically thin computation derived from a comparison with a radiative transfer computation. This was done by Ajello et al. [1987] or Pryor et al. [1992]. Usually this correction is computed for one set of parameters defining the hydrogen distribution assuming that the ratio of intensity from radiative transfer to intensity from optically thin approximation will not change too much with different hydrogen distributions. A second approach used by Bertaux et al. [1985] is based on the following remark. The total intensity can be divided between first order scattering photons and higher orders. It is rather easy to compute the first term which includes extinction between the sun, the scattering point and the observer. However by neglecting extinction between the sun and the scattering point, one will somewhat over estimate the first term thus compensating for the lack of the second term. The main problem with this assumption is that it is not

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E. Quemerais based on any actual computation. 2.1. C a n M u l t i p l e S c a t t e r i n g be N e g l e c t e d at 1 A U ? The aim of this section is to prove q u a n t i t a t i v e l y that multiple scattering effects cannot be neglected anywhere in the heliosphere, even at 1 AU from the sun, even for low hydrogen number ~t infinity as stated in Scherer and Fahr [1996]. The model used here is a so-called hot model with no interface. The interstellar hydrogen distribution is defined by a bulk velocity of 20 km s -1 and a temperature of 8000 K. We have taken a value for the hydrogen number density equal to 0.05 cm -3 which corresponds to a lower limit of what is currently believed. Higher values of NH will increase the relative importance of multiple scattering. Radiative transfer effects have been computed as described in Qu6merais [2000]. The hydrogen distribution is described locally by its mean velocity in the solar rest frame and temperatures along 3 perpendicular axes. This distribution is used for all scatterings without any simplification.

Table 1 Characteristic Values in the Inner Heliosphere Nu = 0.05 cm -3 UPWIND r in AU 1.00 2.00 5.00 7 2.73 x 10 .3 0.0107 0.0638 T(T) 0.998 0.992 0.956 el/cO 0.0156 0.0361 0.123 0.00 0.00148 0.0480 CROSSWIND r in AU 1.00 2.00 5.00 T 7.12 • 10 - 4 3.66 x 10 .3 0.0314 T(7-) 0.999 0.997 0.978 el/e0 0.0115 0.0265 0.0954 e2/e0 0.00 9.97 10 - 3 0.0456 DOWNWIND r in AU 1.00 2.00 5.00 w 4.17 • 10 .6 5.92 • 10 .5 1.81 • 10 .3 T(~-) 0.999997 0.999958 0.9987 el/C0 0.00640 0.0139 0.0495 e2/eo 0.00 0.00 0.00

10.00 0.207 0.865 0.284 0.178

20.00 0.558 0.682 0.545 0.809

50.00 1.82 0.319 0.785 4.34

10.00 0.128 0.914 0.237 0.183

20.00 0.403 0.757 0.488 0.719

50.00 1.50 0.380 0.818 4.10

10.00 0.0165 0.988 0.134 0.187

20.00 0.0945 0.936 0.321 0.523

50.00 0.629 0.651 0.745 2.83

Table 1 gives the characteristic values of interest here in the case where the interstellar hydrogen number density is equal to 0.05 cm -3 for points at 6 distances from the sun along three directions, upwind, crosswind and downwind. For each point we give the distance from the sun, the optical thickness at line center, the equivalent transmission computed from the Holstein function [Holstein, 1947], and the ratio over the primary term of the emissivity of the two first scattering orders cl and c2.

-82-

Radiative transfer at Lyman-a in the outer heliosphere From this table, we note that for a point at 1 AU from the sun, the secondary emissivity corresponds to roughly less than 2% of the primary term. This would lead us to neglect multiple scattering effects. H o w e v e r this r e a s o n i n g is w r o n g because, in that way one forgets the fact that t h e i n t e n s i t y is o b t a i n e d by i n t e g r a t i o n over t h e line of sight. This line of sight extends over more 10 AU. At 5 AU from the sun in the upwind direction, the secondary term corresponds to more than 25% of the primary term. At 10 AU, it is more than 75%. Although at 1 AU the interplanetary medium is optically thin at Lyman c~, the contribution of the medium beyond 10 AU is still important and at that distance from the sun the interplanetary medium is optically thick at Lyman c~ . Table 2 gives quantitative values for the various components contributing to the total intensity as seen at 1 AU looking radially. The computation has been made for 3 different values of the interstellar hydrogen number density. In the best case, i.e. upwind for 0.05 cm -3, the primary term corresponds to 73% of the total intensity. Photons with order of scattering equal to 2 or higher still represent 15% of the total intensity.

Table 2 Estimates of Various Components of Intensity at 1 AU NH Line of Sight Itot~t Io/[total 0.05 0.05 0.05

I1/Itot~l

I<2/Itotat

UPWIND CROSSWIND DOWNWIND

236 R 164 R 53 R

73% 73% 44%

12% 13% 14%

15% 14% 42%

0.10 cm -3 0.10 cm -3 0.10 cm -3

UPWIND CROSSWIND DOWNWIND

464 R 330 R 118 R

65% 57% 34%

13% 14% 13%

22% 29% 53%

0.15 cm -3 0.15 cm -3 0.15 cm -3

UPWIND CROSSWIND DOWNWIND

684 R 493 R 184 R

60% 52% 29%

14% 14% 12%

26% 34% 59%

cm -3 cm -3 cm -3

3. L y m a n a B a c k g r o u n d in t h e H e l i o s p h e r e This section will detail the results of our Angle Dependent Partial Frequency Redistribution computations for a hot model. This study does not take the interface into account, so the results in the outer heliosphere will be very different from what would be obtained from interface models. In what follows, the observer is looking radially away from the sun. All the computations include the classical phase function established by Bran& and Chamberlain [1959]. The solar parameters are r the ratio of radiation pressure over solar gravitation equal to 1 and the hydrogen lifetime against ionization at 1 AU equal to 1.2 x 106 seconds. These are standard values for an isotropic hot model. The hydrogen distribution depends also on the interstellar parameters. The hydrogen number density distribution is proportional

-83

-

E. Quemerais

~ .

...... 0..

,,'\ -

'\

""-.

X

\

',,\

\,\, ':'\,

B

: -

'\

""-.

~

.......

",,\

, \

.........

..............

", ~ ~ \ X

9

,

\

\ ,

"\,

"\,

"- -..

'\,

\ 9

~ .

-

-~

9

0

_

9

9

_

........

~..

20

40

60

Figure 2. Upwind radial intensity as a function of solar distance between 1 and 60 AU. After 30 AU, the optically thin approximation falls off like 1/r. The radiative transfer computation follows 1/r ~ where 1 _< c~ _< 2, depending on the optical thickness of the medium. The other computations decrease very quickly with solar distance.

to NH, the value of the hydrogen number density at large distance from the sun. In this study, we have used 0.12 cm -3 . 3.1.

Lyman

a Background

in t h e O u t e r H e l i o s p h e r e

No approximation can be used to describe the intensity away from the inner heliosphere. Figure 2 is an illustration of this statement. This shows a computation of the intensity for an observer upwind at different distances from the sun and looking radially away from the sun. All approximations, except optically thin, fall down much faster than the multiple scattering value. Since there is no extinction, the optically thin approximation overestimates the correct decrease of intensity. It must be noted that for our model here, the density distribution outside 30 AU is more or less constant. In that case, the optically thin approximation falls off like 1/r and the radiative transfer case falls off like 1/r ~, where a is a coefficient between 1 and 2 [Hall, 1992]. The coefficient a depends on the optical thickness of the medium, i.e. on the value of NH and distance from the sun. When an interface is included the upwind hydrogen number density shows a positive gradient in

- 84-

Radiative transfer at Lyman-a in the outer heliosphere

the outer heliosphere [Baranov and Malama, 1993]. In that case, c~ can be smaller than 1. This is why measuring the fMl-off of the upwind intensity from the Voyager UVS data is important [Hall et al., 1993; Qufimerais et al., 1995].

-- .

~

"'~

.........

_ _2

.

~

2 _

Figure 3. Downwind radial intensity as a function of solar distance between 1 and 60 AU. Here the situation is much more complex than in the upwind direction because even at 60 AU the H number density is not constant. We see also that multiple scattering effects are predominent.

In the downwind direction (Figure 3), the situation is more complex. The hydrogen cavity extends much farther from the sun and even at 60 AU the hydrogen number density has not reached a constant value. The size of the cavity is affected by the solar parameters and its filling by the mean velocity and temperature of the interstellar gas. Study of the downwind interplanetary background as a function of solar distance is then more dependent on the solar and interstellar parameters. It is also strongly affected by the variability of the solar parameters [Rucitlski and Bzowski, 1995]. Figure 4 shows how the upwind profile mean shift (apparent velocity) changes with solar distance. This has been computed for three different values of V/-/, namely 20, 22 and 26 km s -1. We see that the apparent velocity of the line seems to increase by

-85-

E. Quemerais

-18

V_H =

-20

_.. .

.

.

_ . _

E

EL

20 . . . . . . .

km/s,

T_H . . . . .

=

8000

K

9 . . . . . . . . . . . . . . . . . . . . .

_ i

V_H = 22 kin/s, T_H = 10000 K . . . . . . .

- . . . . .

--"

_2.

. . . .

C . _

F--

. . . .

_

,/ ,'/

. . . . . . . . . . .

.

_

-24

I c/')

_

_

z < W

-26

-28

-50

Figure 4. Mean shift of the line profile obtained for an observer looking radially away from the sun in the upwind direction. In the case of the hot model, at large distance from the sun, the shift is equal to the velocity of the interstellar gas. The shifts have been computed for three types of models with VH -20, 22 and 26 km s -1. At one AU in the upwind direction, the apparent velocities found for each model are-22.8 km s -I, -25.1km s -1 and-27.9 km s -1, respectively.

roughly 3 km 8 - 1 in the inner heliosphere. This is caused by the apparent acceleration of the hydrogen atoms due to selection effects (here # = 1, so there is no gravitational acceleration). Slower atoms are more easily ionized because they spend more time near the sun. This results in a selection of faster atoms and an increase of the local mean velocity, i.e. an apparent acceleration. Figure 5 shows the apparent temperature in both the upwind and downwind directions as a function of distance from the sun. On this figure, we show the results for the optically thin approximation (dotted line), the A D P F R radiative transfer (solid line) and the selfabsorbed computation (dashed line). The primary term is not shown here because the extinction near line center makes the estimation of the apparent temperature completely unrealistic. First, we note that the optically thin approximation strongly underestimates the apparent temperature. It goes asymptotically back to the value of the gas in the

-86-

Radiative transfer at Lyman-a in the outer heliosphere

-

"~

~

-.~ _

~.

/

04

11//

/ J

. . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

-..-

o

Figure 5. Apparent temperature of line profiles obtained for an observer looking radially away from the sun. The values are shown in both the upwind and downwind directions. The dotted line gives the result of the optically thin approximation, the solid line the ADPFR result and the dashed line corresponds to the computation of the self-absorbed c&se.

interplanetary medium. Self-absorption gives the value closest to the actual result of ADPFR although the results are systematically underestimated by roughly 1000 Is At very large distance from the sun, the apparent temperature is a complex mixture of coherent and perpendicular scatterings. We know that perpendicular scatterings have an apparent temperature equal to the temperature of the medium. On the other hand, after many scatterings the profile of the photons which are scattered is not white anymore. In an extreme case, let us assume that after n scatterings the source profile for the n + 1 scattering is a doppler profile at the temperature of the gas. Then because we assume a doppler scattering cross section, the coherently scattered profile has an apparent temperature which is half the actual temperature of the gas. The total emissivity will be a complex mixture of these various profiles. The widening of the line is mainly driven by extinction when integrating over the line of sight. A gaussian profile at temperature T attenuated following a gaussian at the same temperature yields an apparent temperature

-87-

E. Quemerais

which is larger than the original one. All these antagonist effects are taken into account in our computation. Finally, the variation of the Lyman a line profile with distance depends strongly on the optical thickness in the interplanetary medium, hence of the parameter

NH. 4. D i s c u s s i o n

The first result we wish to point out here is that our code shows that multiple scattering effects cannot be neglected even in the close vicinity of the sun. This is in contradiction with the results of Scherer and Fahr [1996] and we have given quantitative results to justify this. We have compared systematically the results of our ADPFR multiple scattering code with the different approximations used by various authors. Finally, we have shown typical results for intensity, apparent velocity and apparent temperature both in the inner and the outer heliosphere. We expect that the inclusion of effects of the heliospheric interface on the hydrogen distribution, as obtained by Baranov and Malama [1993] for instance, will modify the line shapes in a dramatic fashion, especially in the outer heliosphere. In that respect, the previous section on outer heliosphere Lyman a background must be taken as a study case. Hall et al. [1993] or Qu~mer~is et al. [1995] have shown that the UVS data in the outer heliosphere do not agree with the results of hot model type computations. REFERENCES o

2. 3. 4. 5. 6. 7. .

9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Ajello J. M., Stewart A. I. F., Thomas G. E., & Graps A., 1987, A p J , 317, 964 Baranov V. B., 1990, Space Science Reviews, 52, 89. Baranov V. B. & Malama Y. G., 1993, J. G e o p h y s . Res. , 98, 15157 Bertaux J. L., Lallement R., Kurt V. G., & Mironova E. N., 1985, A & A , 150, 1. Bran& J.C. and Chamberlain J.W., 1959, A p J , 130, 670. Hall D. T., 1992, Ph. D. Thesis, University of Arizona, Tucson. Hall D. T., Shemansky D. E., Judge D. L., Gangopadhyay P., & Gruntman M. A., 1993, J. G e o p h y s . R e s . , 98, 15185. Holstein T., 1947, Physical Review, 72, 1212. Keller H. U., Richter K., & Thomas G., 1981, A & A , 102, 415. Mihalas D., 1970, in Stellar Atmospheres, W.H. Freeman & Co, San Francisco. Pryor W. R. et al., 1992, A p J , 394, 363 Qu(~merais E. & Bertaux J. L., 1993, A & A , 277, 283 Qu~merais E., Sandel B. R., Lallement R., & Bertaux J. L., 1995, A & A , 299, 249 Qu~merais E., 2000, A & A , 358, 353-367 Rucifiski D. and Bzowsli M., 1995, A & A , 296, 248. Scherer and Fahr, 1996, A & A , 309, 957. Thomas G. E., 1978, Ann. Rev. E a r t h P l a n e t . Sci., 6, 173 Zank et al., 1996, J. Geophys. R e s . , 101, 21.

-88-

A Fluid A p p r o a c h to the H e l i o s p h e r e / V L I S M P r o b l e m R. L. McNutt, Jr. a, M. Wiltberger b, J. Lyon b, and C. C. Goodrich c aThe Johns Hopkins University Applied Physics Laboratory Laurel, MD 20723-6099, U.S.A. bDartmouth College, Hanover, NH 03755, U.S.A. cUniversity of Maryland, College Park, MD 20742, U. S. A. The interaction of the solar wind with the very local interstellar medium (VLISM) depends strongly upon charge exchange between the neutral and ionized hydrogen outside of the heliopause. The resulting structure is of the order of only one mean free path for such collisions, so strictly a kinetic approach is required. However, such an approach is very computationally intensive, while a fluid approach is less so. We consider how far the fluid approach can be pushed in this problem and compare some results with those obtained from kinetic approaches. 1. INTRODUCTION Accurate modeling of the heliosphere-solar-wind system is required to plan for a probe to near-interstellar space. A probe toward the "nose" of the heliosphere minimizes the distance, and hence, flight time into the interstellar medium [ 1-6]. The heliospheric structure has a characteristic scale size of--100 AU; a 10% change in the spatial scale translates into years of probe travel. To plan such a mission, there are both scientific and engineering needs to "get the numbers right." Our approach is to (1) compare fluid and kinetic models using the same sets of parameters to identify similarities and differences, (2) run multiple simulations varying one parameter at a time to test sensitivity to the various input parameters, (3) compare density profiles along the upstream stagnation line as a means of getting a quick look at model differences, and (4) explore fluid models with T e - Tprotonfor comparison with a broad number of kinetic model results. 2. T H E

PROBLEM

The charge-exchange process that diverts the neutral interstellar flow around the heliosphere has a mean free path comparable to the interaction region size. Large mean free paths strictly require a kinetic treatment [7], but a fully time-dependent, six-dimensional kinetic treatment is computationally intensive. Fluid models offer a less computationally-complex approach, but with limitations [8-11 ]. Other approaches, including those with hybrid codes have limitations as well [for a review, see 12].We compare results from the limiting case of no magnetic field and a cylindrically symmetric geometry with results obtained using a kinetic/hydrodynamic approach. We also consider the next order corrections to the hydrodynamic (HD) equations for the neutral component and estimate the size of the errors made in not including these further refinements to the HD approach.

- 89-

R.L. M c N u t t Jr. et al.

2.1. Solution Space The numerical simulation is run in a region between a spherical shell of 20 AU radius out to a cylindrical region stretching from - 6 0 0 AU in the upwind (-x) direction to ~ 1000 AU in the downwind (+x) direction. The cylindrical region is - 8 0 0 AU in radius. The simulations cover roughly 2.72 years every 1000 time steps (-1 day per step). The time steps are adjusted by the code as required: steps are sufficiently small that signals propagate at most across -1/3 cell. The simulations begin at t= 0 with a uniform neutral and plasma interstellar flow pervading the solution space and the solar wind outflow commencing radially outward at the 20 AU inner boundary. Simulations are run to an asymptotic state (--1500 years), and then grid resolution is increased by a factor o f - 2 . The simulation is then run until transients from the regridding damp out (another -- 100 years) [9]. 2.2. Charge Exchange Formulation For a large range of values, the charge-exchange cross section is very accurately represented by a power law. CYcx( g ) - cY0g ~

(1)

where g is the relative speed of two colliding particles. The charge-exchange operators can be determined e x a c t l y for this case. For comparisons with Izmodenov et al. [7] we use the cross section [ 13] CYcx,MT ( g ) - 10 -14 ( 1.64 - 0.0695 In g [cm s -1 ]

)2

[ cm 2]

(2)

A least squares fit in the range from 1 to 1000 km s-~ yields [ 10] Crcx,m = rt(6.6504 a 0 )2

g-0.2398

(3)

corresponding to a repulsive force law -- r -~8(here a 0 is the Bohr radius). Special cases results from taking or, -- cy0 g-1 o r CYcx-- cy0 corresponding to the "hard-sphere model" for purposes of evaluating the momentum-and-energy-exchange terms [8]. We use this latter formulation (v=0) for comparison with [7].

2.3. Analytic Approximations From [ 10] we make use of the approximation

r(2 + n + 89v) y.,,,(a) -

M(_I

_ 1 v , n + ~ , - a 2) = [(88+ n + x1 v) + a 2]89

(4)

r(n+3)

For values of v from -1 to 0, the maximum error occurs for Y0,0 and is less than 2.0%. With a force law F - ~c r -s, we have s = 1 - 4/v so these cases correspond to hard spheres ( s ---> oo ) to Maxwell molecules (s = 5) [14]. This approximation remains fairly good through v - -2 (corresponding to s = 3) with an error of less than -15%.

- 90-

A fluid approach to the heliosphere/VLISMproblem From these results, we define corresponding characteristic speeds *

(5)

2

--

+

(6)

2.4. S i m u l a t i o n E q u a t i o n s

The ion equations are[10]"

a(pu)

Ot

1

+ V 9 (puu) + V P - 7 J x B - QM, H+_~H --

-u)

m proton

OEPl- V* [(Ep + P ) u ] -

J * E - Qe.., .+-~n oa

_U ac~(U~)(2+Tv)(pp, m

a~x(V[.) pp.v;

*

1

,

(7)

puP)+U~u ~cx(U~,M) lpp.(u2-u2) ' m proton 2

m

*

m proton

m

The same methodology can be used analogously to write out explicitly equations for the neutral component. Note that CYcx- const corresponds to v - 0 . 2.5. N e u t r a l C o m p o n e n t E q u a t i o n s to Next O r d e r

The neutral equations become [ 10, 15, 16]" O(PnUn)

Ot

pp.v;

+ V * (puunun + P n ) - - Q M , n+_~u

-u)

m proton

Ep,H

~ +

V - [(Ep,. + Pn)un + q n ] - - Q e

0t

(8)

- -U~ ac~ (U~) (2 + ~ v)(pPn m

....,.n+-~"

*

1

mproton

m

pnP)- U,,M ac~(U~,M) 1 *

mproton

2 ppH(u2H-u2)

where Pn is the pressure tensor and qn the heat flux vector for the neutral component. In the model as implemented qn - 0 and the off-diagonal elements of PH are zero and the diagonal elements of Pn are all equal. Examples of the proton and neutral hydrogen densities using this model and the same parameters as in [9] are shown in Figure 1. The effect of different chargeexchange power laws in shown in Figure 2. 3. C O M P A R I S O N S

Comparisons of the MHD/HD approach with the HD/kinetic approach can be carried out by making the following simplifications to our simulation model: (1) Set B - 0 (2) Use a radially symmetric solar wind (3) Align the interstellar flow with the -X axis of the simulation coordinates.

-91 -

R.L. McNutt Jr. et al.

Figure 1. Logarithm of the proton density (top) and of the neutral hydrogen density (bottom). The case presented here uses the parameters of [9], viz. electron temperature of zero, upstream ion density of 0.30 cm -3, upstream neutral density of 0.10 cm -3, ion and neutral upstream temperatures of 7000K, VLISM velocity of 25.7 km s-1 toward ecliptic longitude 74.9 ~ and latitude of -7.8 ~ A local interstellar magnetic field of 0.14 nT toward galactic longitude 70 ~ and latitude 0 ~ is included in the model. Solar wind parameters are taken from IMP 8 and Ulysses data (details in [9]). Density profiles in the plane of the solar rotational equator are shown.

-

92-

A fluid approach to the heliosphere/VLISMproblem

Figure 2. Differences of the densities of protons (top) and neutral hydrogen atoms (bottom) from using the same run parameters as used in Figure 1 using power-law indices (here labeled as "n" and "nu", cf. Equation 1 of the text) of-1 (Maxwell molecules) and -0.2654; the runs in Figure 1 used indices of 0. Maximum differences are --5% for the proton density and ~ 15% for the neutral density. The index of-0.2654 is slightly different from the best fit to the power law of [7].

-93 -

R.L. McNutt Jr. et al.

These simplifications lead to an axisymmetric model with both the plasma and neutral fluids described by the hydrodynamic equations. 3.1. C o m p a r i s o n P a r a m e t e r s Izmodenov et al. [7] have used a symmetric model with an HD/kinetic implementation. They have included photoionization, electron impact, and radiation pressure on the neutral hydrogen, as well as the effects of gravity. These effects should primarily be noticeable in the inner heliosphere, so we can compare our approach with their runs on a fairly equal basis, even though we have not implemented these effects in our code. The parameters they use are:

7 cm -3 (differs from [17])

nE=

V E "- 450 km S-1

10 (w = 45 km s -1 where 1/2row 2 = kT; differs from [17]) noo ( H ) - 0.2 cm -3 (differs from [17]) noo ( H § ) - 0.3, 0.2, 0.1, 0.07, 0.04 cm -3 (includes case of 0.07 in [ 17]) Vo~ - 25 km s -~ (differs from [17]) Too ( H ) - Too ( H § ) - 5600K (differs from [17]), so that Moo- 2 (woo- 9.615 km s -~ and coo = 12.4 km s-~ for Tio n "- Telectron and y = 5/3. These are lower than currently accepted values but more realistic than the Baranov et al. [17] case) with ~cx - 10 -~4 ( 1.64 - 0.0695 In v )2 (v in cm s-l). We have set both Tio n > > T electronas well a s Tio n -- Telectronas in [7] and compare both cases with the kinetic approach. These are shown in Figure 3. M E -

4. C H A P M A N - E N S K O G E X P A N S I O N To find next-order corrections in collisional hydrodynamics, the Chapman-Enskog approach [15] is used yielding the following q(1) _ _)hV T (9) e/(1)--]-~1

o~j "[- oqxi

- 3

'~

where ( P)~j = P 8..,j+ P..(~,j~and Tr P..,j(~) = 0 by construction. In addition, to carry out fully the nextorder expansion we would need to include the next-order correction terms to the momentumand energy-exchange operators, e.g. _ O(q(1).AU) a n d - O ( AUop~I).AU ). 4.1. R e p u l s i v e P o w e r - L a w Potentials We evaluate the first-order coefficient of viscosity B~ and first-order thermal conductivity ~ using the results of [ 15] for power-law repulsive forces between atoms of monatomic gases, viz. /~'1 ~

q(1)_

15

k

-4-~'/1 u

(10)

2m5/11 V ( 3 k T )

- 94-

A fluid approach to the heliosphere/VLISMproblem

Figure 3. Comparisons of boundary locations using the fluid model described here and the kinetic model of [7]. The top panel shows the comparison for equal proton and electron temperatures and the bottom panel for a negligible electron temperature. The bottom panel also shows one case with a strong magnetic field. The boundary locations are plotted as a function of distance from the Sun along the stagnation line in the flow, i.e., opposite the direction from which the interstellar wind is blowing. Agreement is better for larger values of the interstellar proton density. Note that assumptions on electron temperature have marginal effect on the boundary locations.

-95-

R.L. McNutt Jr. et al.

and (see Chapter 8 of[18])

5~ ]"11-- -8

mw

Al(S)

1 (11)

acx('~W ) A2(s ) F(4 + })

For the hard-sphere model v = 0 and so we use

[.l 1 "-- 0 , 1 9 5 8 3

mw

Oc ( w) kw

'~'1 -" 0 . 7 3 4 3 6

(12)

Oc ( w)

4.2. Steady State Comparison of Terms

In steady state, the equations of motion for the neutral hydrogen are

v.(p.u.)=o V 9 (pnunun) + V P z - - V

*

p~l)_ QM, II+-->H

(13) V * [ ( E z + P.)un ] - - V , (q~' +

u*

p(HI')--QE,o,,t,H+_.>H

and we use these equations to find the fractional corrections introduced by the Chapman-Enskog terms. Note that since the mean free path )~fp~ (ncy)-1 we have P-- pw -- (/fpV) u

(14)

q - nw ~ (lfpV) kT

(15)

To estimate the magnitude of the corrections to the runs as made we can use Equations (9) and (13) to estimate the magnitude of the viscosity term along the stagnation line. This correction term is

xx "-- 3 0 ~

(16)

jUl

For the high-density case the contribution is substantial indicating a lack of self-consistency in the solution. In Figure 4 we show this correction term as well as the other pressure terms. It should be kept in mind that the physically relevant quantities are the gradients of each term as the gradients balance the momentum exchange in Equation (13).

- 96-

A fluid approach to the heliosphere/VLISMproblem Figure 4. Comparison of pressure terms along the upstream stagnation line for the high-density symmetric fluid model. The black line indicates the m a g n i t u d e of the viscosity correction in Equation (16). The solid line indicates the contribution in positive and the dashed line, negative. The lowest-density case has the same qualitative features but at a lower magnitude (by a factor-4).

5. NEED FOR M O D E L S W I T H TIME VARIATION

The recent large solar events once again may produce a global merged interaction region (GMIR) in the outer heliosphere. The speed at 1 AU on 15 July 2000 was -1050 km s-~ (from IMP 8, A. J. Lazarus, private comm.). This suggests that the heliospheric VLF radio noise [ 19] may well again appear in just over a year, if large particle events are seen by both the Voyagers first (signaling a truly "global" event). One can make rough timing predictions [20-22] of the noise onset time, but quantitative models can potentially give us another experimental location for the heliopause interface region [23]. Quasi-similarity models [22] suggest a shock may appear near Voyager 1 in early 2001 with another episode of radio emission --September 2001. It remains to be seen whether this will occur. In any case, in addition to future direct exploration of the VLISM by an interstellar precursor mission, this phenomenon is another reason for the continued investigation of quantitative models of the heliospheric cavity and its dynamics. 6. CONCLUSIONS The MHD/HD simulation run with a no magnetic field compares favorably with the HD/ kinetic approach in a qualitative sense. Quantitatively, the hydrodynamic simulation predicts a higher hydrogen wall in the upstream direction. Furthermore, the wall thickness and height are not as sensitive to the upstream proton density as in the HD/kinetic simulation. The MHD/HD simulation consistently predicts a closer external shock and further heliopause and termination shock than the kinetic approach. The two approaches tend to converge at sufficiently high upstream proton density -0.30 cm-3). Corrections to the lowest order HD equations still need to be explored quantitatively (ChapmanEnskog terms) to see if these may yet yield a moment approach that gives results consistent with the kinetic/HD approach. The variation of the charge-exchange cross section with collision speed can be accurately approximated as a power law and incorporated into the momentum- and energy-exchange operators. To the extent that we can assume the atoms behave as "Maxwell molecules" in the collision process, all moments of the Boltzmann collision operator are independent of the form of the distribution function. Hence, there is justification that an MHD/HD approach may allow a fast, yet accurate, computational treatment and allow for cross checks with kinetic computations.

-97-

R.L. McNutt Jr. et al.

To continue with exploring the possibilities of a fluid approach, the next step is to retain the isotropic-Maxwellian representation for the ions, but adopt the Chapman-Enskog approximation for the neutral distribution. In this case the distribution function has a first-order correction parameterized by the full pressure tensor and the heat flux vector. This distribution can then be used to calculate self-consistently the collision operator for transferring momentum and energy between the two populations. The modified energy and momentum equations can then be used to provide a next-order comparison with the kinetic approach. This is about as far as one can go with such fluid approximations. Further expansion of the fluid equations to next-order terms is possible [24], but typically this yields less-satisfactory results [15]. ACKNOWLEDGMENTS

Support was provided by the Voyager Interstellar Mission under NASA Contract NAG5-4365. REFERENCES

1. 2. 3. 4. 5.

T. E .Holzer, et al. The Interstellar Probe, NASA Publication, 1990. L.D. Jaffe and C. V. Ivie, Icarus 39 (1979) 486. E C. Liewer, R. A. Mewaldt, J. A. Ayon, and R. A. Wallace, STAIF-2000 Proc., 2000. R.A. Mewaldt, J. Kangas, S. J. Kerridge, and M. Neugebauer, Acta Astron., 35 (1995) 267. R.L. McNutt, Jr., R. E. Gold, E. C. Roelof, L. J. Zanetti, E. L. Reynolds, R. W. Farquhar, D. A. Gurnett, and W. S. Kurth, J. Brit. Inter. Soc., 50 (1997) 463. 6. R.L. McNutt, Jr., G. B. Andrews, J. McAdams, R. E. Gold, A. Santo, D. Oursler, K. Heeres, M. Fraeman, and B. Williams, STAIF-2000 Proc., 2000. 7. V.V. Izmodenov, J. Geiss, R. Lallement, G. Gloeckler, V. B. Baranov, and Y. G. Malama, J. Geophys. Res., 104 (1999) 4731. 8. R.L. McNutt, Jr., J. Lyon, and C. C. Goodrich, J. Geophys. Res., 103 (1998) 1905. 9. R.L. McNutt, Jr., J. Lyon, C. C. Goodrich, and M. Wiltberger, AIP Conference Proceedings, CP47 (1999) 823. 10. R. L. McNutt, Jr., J. Lyon, and C. C. Goodrich, J. Geophys. Res., 104 (1999)14,803. 11. G. E Zank, H. L. Pauls, L. L. Williams, and D. T. Hall, J. Geophys. Res., 101 (1996) 21,639. 12. G. E Zank, Space Sci. Rev., 89 (1999) 413. 13. L. J. Maher and B. A. Tinsley, J. Geophys. Res., 82(1977) 689. 14. J. C. Maxwell, Phil. Trans. R. Soc., 157 (1867) 49. 15. S. Chapman, and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, Third Edition, Cambridge University Press, New York, 1998. 16. S. Harris, An Introduction to the Theory of the Boltzmann Equation, Holt, Rinehart, and Winston, Inc., New York, 1971. 17. V. B. Baranov, V. V. Izmodenov, and Y. G. Malama, J. Geophys. Res., 103 (1998) 9575. 18. J. M. Burgers, Flow Equations for Composite Gases, Academic Press, New York, 1969. 19. W. S. Kurth, D. A. Gurnett, E L. Scarf, and R. L. Poynter, Nature, 312 (1984) 27. 20. R. L. McNutt, Jr., Geophys. Res. Lett., 15 (1988) 1307. 21. R. L. McNutt, Jr., Adv.Sp.Res., 9 (1989) 235. 22. R. L. McNutt, Jr., A. J. Lazarus, J. W. Belcher, J. Lyon, C. C. Goodrich, and R. Kulkarni, Adv. Space Res., 16 (1995) 303. 23. D. A. Gurnett, W. S. Kurth, S. C. Allendorf, and R. L. Poynter, Science, 262 (1993) 199. 23. D. Burnett, Proc. Lond. Math. Soc., 40 (1935) 382

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Possible effects of the interstellar magnetic field on the heliospheric structure and H-atom penetration to the solar system V.B. Baranov a* ~Institute for Problems in Mechanics of the Russian Academy of Sciences, Prospect Vernadskogo 101-1, 117526 Moscow, Russia At present neither direction nor magnitude of the interstellar magnetic field in the vicinity of the solar system are experimentally known. However, there are many papers concerning theoretical problems of its effect on the solar wind interaction with the local interstellar medium (LISM). Critical review of such papers are presented here. Possible effects of the interstellar magnetic field on H-atom penetration to the solar system are discussed. The first results of self-consistent model solution taking into account mutual effect of plasma component, H-atoms and interstellar magnetic field are given in an axisymmetric approximation which is correct in the case when the vector of the LISM velocity is parallel to the vector of the LISM magnetic field intensity. 1. I N T R O D U C T I O N Constructing a quantitative theoretical model for the prediction and explanation of the experimental data is an important goal in various branches of scientific knowledge. However, such a model is useful if it has a reliable, physically correct theoretical basis; otherwise, an interpretation of experiments could be wrong. Let us consider, for example, a problem of the solar wind interaction with the supersonic interstellar gas flow. As it is known [1], four regions of the flow are formed in this case (Figure 1) for the plasma component (electrons and protons) due to the formation of the bow shock (BS), heliopause (HP) and termination shock (TS). Hydrogen atoms of the local interstellar medium (LISM) penetrate the solar system interacting with the plasma component due to processes of the resonance charge exchange. Their parameters are measured on the basis of the interpretation of the scattered solar Lyman-alpha radiation. The results of the interpretation depend critically on a theoretical model considered. Up to the beginning of 80-th the "hot" model was used to interpret experimental data (see, for instance, [2]). A "filter" effect of the interface between the solar wind and the plasma component of the LISM (regions 2 and 3 in Figure 1) is not taken into account in the framework of this model. The first theoretical papers ([3-6]) showed that this effect, predicted first qualitatively in [7], is very important. That is why invalid magnitudes of the LISM hydrogen number density, temperature and bulk velocity were predicted by the "hot" model. *This work was partially supported by CRDF Grant 6096, RFBR Grants 98-01-00955, 99-02-04025.

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V.B. Baranov

f

H sw (population 2) Moo>

1

H+ e

(4)

H

sw

(population 1 )

Figure 1. Qualitative picture of the solar wind interaction with the LISM without magnetic field. Regions 1 - 4 are the supersonic solar wind (preshock of the TS), the thermalized (in the TS) solar wind, the thermalized (in the BS) LISM plasma and the LISM plasma respectively. Dotted lines are trajectories of different H-atom populations.

The mutual effect of the plasma and hydrogen components was self-consistently taken into account in [4]. These authors used the simplest possible hydrodynamic scenario, where it was assumed that the velocity VH and the temperature TH of neutral hydrogen remain constant throughout the whole computational domain and that the LISM H-atoms are lost only in the regions 1, 2 and 3 (Figure 1) due to resonance charge exchange. This means that they solved only the continuity equation for neutrals. It was impossible to interpret experiments connected with the Lyman-alpha glow on the basis of this simplest scenario. The model suggested in [4] was criticized in [8] where the correct kineticgasdynamic model was suggested. H-atoms are kinetically described by the Monte Carlo method in this model, because the mean free path of the H-atoms is comparable with the characteristic length of the problem (for example, with the size of the heliopause) and the hydrodynamic approximation is not correct all over for the H-atom component. Recently, authors of [9,10] and [11] revisited the hydrodynamic description of H-atom motion in the problem of the solar wind interaction with the LISM although this description is not correct as we have seen above. It was shown in [12] and [13] that the distribution function of the all H-atom populations is not Maxwellian and, therefore, the multi-fluid model in [10] cannot be used to interpret experimental data. The same result is obtained in [29] for subsonic plasma-plasma interface. In Figure 2 (Figures 5c and 7b from [12]) some results of the kinetic-gasdynamic model in [8] and the multi-fluid model in [10] are compared. From Figure 2a we see that the bulk velocity (along the axis of symmetry) of the LISM hydrogen atoms (primary and secondary), which are responsible

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Possible effects of the interstellar magnetic field...

Figure 2. Comparison of some results obtained on the basis of the kinetic-gasdynamic model by Baranov and Malama (1993) and the multi-fluid model by Zank et al. (1996): (a) the component (along the axis of symmetry) of the H-atom (born in region 1) velocity and (b) the H-atom (born in region 1) temperature as functions on the heliocentric distance.

for the interpretation of the scattered solar Lyman-alpha radiation, changes its sign in the downwind direction for the model in [10]. In this case the continuity equation is not satisfied in the stationary approximation [10] and, therefore, the results of these authors are not physically real. Figure 2b demonstrates another physically unrealistic result obtained in [10]. Namely, the temperature of the energetic solar wind H-atoms, which are born due to the charge exchange between the LISM H-atoms and the solar wind protons (in the region 1), is two orders of magnitude larger (10 ~ K) than the solar wind proton temperature although there are no reasons for their heating. It follows that the model in [10] can also not be used to interpret results of planned experiments connected with the detection of energetic neutral atom (ENA) fluxes with 1 AU [14]. In the last few years several numerical magnetohydrodynamic (MHD) models of the solar wind interaction with the magnetized LISM were published although at present neither direction nor magnitude of the interstellar magnetic field in the vicinity of the solar system are experimentally known. The example of multi-fluid model results mentioned above (Figure 2) shows that caution must be exercised by observers to interpret experimental results on the basis of theoretical models. That is why the part of this presentation will be devoted to the critical review of MHD models of the solar wind interaction with the magnetized LISM (Section 2). In the Section 3 some problems of the interstellar magnetic field effect on H-atom penetration from the LISM to the solar system will be considered.

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V.B. Baranov

(a)

Hyperbolicregion

(b) Ellipticregion

(c)

Quasihyperbolic region

BS HI'

I-IP

Figure 3. Possible geometrical patterns of the MHD flow in the case when the interstellar magnetic field Boo and the bulk velocity V ~ are parallel. Hyperbolic, elliptic and quasihyperbolic regions are (a),(b) and (c) respectively.

2. A B O U T T H E F U N D A M E N T A L M H D P R O B L E M C O N N E C T E D W I T H THE INTERACTION BETWEEN THE SOLAR WIND AND MAGNETIZED LISM'S PLASMA It is known that a supersonic flow near hard bodies is characterized by a bow shock formation. The wings of the bow shock are weak discontinuities where parameters are continuous but their gradients are not. In doing so the weak discontinuities coincide with characteristics which are lines of small perturbation propagation. Their direction always coincides with a downwind direction in the classic gas dynamics. We have a more complicated situation in the magnetohydrodynamics (MHD) because there are four velocities of small perturbations (entropic, slow and fast magnetosonic and alfvenic) in the presence of the magnetic field. In particular, characteristics can be directed in the upwind direction as well as in the downwind one (see, for example, in [15]). The heliopause HP plays the role of the hard body in the problem of the solar wind interaction with the magnetized interstellar plasma. Possible geometrical patterns of the flow considered are qualitatively shown in Figure 3 in the most simple case when the magnetic field B~ and the bulk velocity V~ of the interstellar gas are parallel (see [16]). Figure 3a demonstrates a possible shape of the bow shock at V~ > max(a0, aA), where a0 and a A - are the sonic and alfvenic velocities of the interstellar plasma respectively, i.e. at the weak interstellar magnetic field. It is the hyperbolic region and analytical results give rise to real characteristics directed to the downwind direction (see wings of the bow shock in Figure 3a). To investigate the shape of the bow shock in the vicinity of the nose region numerical calculations must be used. All published numerical results (see,

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Possible effects of the interstellar magnetic field...

for example, [16-21]) are obtained in the case presented in Figure 3a (in the hyperbolic region). The geometrical pattern of the flow considered can be significantly changed at an increase of the magnetic field intensity. For example, the bow shock must be absent in the elliptical region which is characterized by inequalities Vo~ < aoaA/(a 2 + a~) -1/2

and

min(a0, aA) < Vo~ < max(a0, aA)

Real characteristics are absent in this region (see Figure 3b). Characteristics are directed in the upwind direction (see Figure 3c) if inequalities

a0a /(a +

<

< min(a0, aA)

are satisfied. It is a quasi-hyperpolic region [15]. There are no published calculations of the flow in the regions presented in Figure 3b and 3c, i.e. at large magnetic field intensities. Let us compare now the numerical results published in [19,21] and [20] for the case presented in Figure 3a. These results are not realistic for real heliospheric structure because they are obtained at n i -- 0 (nil is the number density of hydrogen atoms). However, they are interesting for fundamental problems of MHD. For comparisons we used only the results M ~ = 2 and Alfven Mach number A~ = 1.4 in the interstellar plasma ( M - V/ao, A - V / a A ) . In the Figure 4 the lines p - const are presented, where p is the static pressure. As we see from Figure 4, numerical results of different authors give rise to the different structures of the MHD flow between the bow shock and heliopause (in the nose region of the heliosphere). For example, the bow shock splitting (A-like structure) is observed (Figure 4a) in [19] as well as in [17]. We see a different feature of the bow shock splitting in Figure 4b obtained in [21]. We can not interpret a character of the flow from Figure 4c obtained in [20] due to a not well resolution of these authors numerical method. The pictures presented in Figure 4 are obtained at the use of different versions of the shock capture numerical method. In [16] the shock fitting method was used where relations on the discontinuities (BS, HP and TS) were exactly satisfied. Authors of [16] did not obtain the bow shock splittings, presented in Figure 4a and 4b, and criticized the numerical method used in [17]. However, their calculations were made at A~ - 1.5. From Figure 4 we also see that the complicated structure of the flow in the downwind direction connected with a formation of the Mach disc disappears in the presence of the magnetic field. We interpret different results of different authors, presented in Figure 4, with numerical problems rather than as physical ones. Unfortunately, one can notice that the unpleasant tendency to skip the results of other authors have been formed last time in the heliospheric theoretical community. We tried to correct this tendency. We considered here only the axisymmetric MHD problem to underline difficulties of this flow calculations and their interpretations even for the most simple situation although 3D MHD problems are already considered in literature (see, for example, [20,22]). However, H-atom component and, in particular, a important effect of the resonance charge exchange is not taken into account in these publications. That is why their applications to the problem of the solar wind interaction with the LISM are not physically realistic. Below

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V.B. Baranov

Ratkiewicz

et al. (1998)

Figure 4. Comparison of the MHD geometrical patterns obtained by different authors in the case when the interstellar magnetic field Boo and the bulk velocity V ~ are parallel (the hyperbolic region)" (a) static pressure (below the symmetry axis) and logarithm density isolines, (b) static pressure (upper half) and density isolines, (c) static pressure isolines.

we will consider some results of the kinetic-MHD model obtained in [23] where H-atom component was self-consistently taken into account for axisymmetric problem. 3. P O S S I B L E E F F E C T OF T H E I N T E R S T E L L A R M A G N E T I C F I E L D ON H - A T O M P E N E T R A T I O N F R O M T H E LISM T O T H E S O L A R S Y S T E M The first 3D MHD numerical model taking self-consistently into account the LISM hydrogen atoms and solar and interstellar magnetic fields was constructed in [24]. Accurate results were obtained due to excellent numerical scheme. However, to simulate the interaction of the H-atom and plasma components via charge exchange processes authors of [24] used the simplest possible scenario that was originally suggested in [4] (see Section 1). Therefore, the model in [24] can not be used for the interpretation of H-atom observations (see below). In particular, the "hydrogen wall" predicted in [25] and first observed in [26] cannot be obtained in the framework of the model in [24] neglecting the secondary LISM

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Possible effects of the interstellar magnetic fieM...

-

A

oo

=o~

9

..............

6oo

-

A ~

=

1.18

Ao0

=

0.9

t

- -

-I

-

. m

Z,

a.u.

Figure 5. Effect of the interstellar magnetic field on the geometrical pattern of the MHD flow at nH~ --0.2cm -3 in the axisymmetric problem.

H-atoms. Let us consider now the self-consistent axisymmetric MHD model of the solar wind interaction with the magnetized two-component (H-atom and plasma components) LISM's gas calculated in [23]. The model constructed in [8] is extended by these authors to include the interstellar magnetic field. The plasma component is described by MHD equations with source terms taking into account its interaction with H-atoms. Trajectories of Hatoms are calculated by Monte Carlo method suggested in [27] to calculate the source terms in MHD equations. To solve the self-consistent problem as a whole the numerical method suggested in [19] for solving MHD equations and the method of global iterations are applicated. This model and the model in [8] differ by the presence of the interstellar magnetic field, which is parallel to the LISM plasma bulk velocity. The some results of the model in [23] are presented in Figure 5 - 7. The change of the geometrical pattern with increasing the interstellar magnetic field intensity (with decreasing the Alfven Mach number Ao~) in Figure 5 is shown. Comparisons with the MHD results obtained in [16], where the neutral component (nil = 0) was not taken into account, show that the character of the geometrical pattern change is qualitatively retained at n H ~ 0 although a presence of the bow shock at sub-alfvenic interstellar gas velocity (A < 1) is a surprise which authors could not explain physically. It is interesting to note here that the problem of the bow shock splitting (see Section 2) is absent in the presence of the neutral component due to the effect of resonance charge exchange processes. There are 4 populations of H-atoms in the problem considered. Populations 1-4 in the regions 1-4 (Figure 1) are formed respectively. Effect of the interstellar magnetic field on the "hydrogen wall" formed by Populations 3+4 is presented in Figure 6. We see that

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KB. Baranov

(a) 0.3

0=0

o,

,

. . . . .

A = = 1.18

.......

A ~ = 1.18

Ao~= 0.9

. . . . .

A ~ = 0.9

A

R,

R,

a.u.

a.u.

Figure 6. Effect of the interstellar magnetic field on the "hydrogen wall"" (a) in the upwind direction and (b) in sidestream direction.

this effect is small although it is any lager in the sidestream direction than in the upwind one. Magnitudes of the interstellar magnetic field considered here (from 0 till 3.5.10 -6 G) cannot change an interpretation of the hydrogen wall in [26]. The effect of the interstellar magnetic field on the distribution of the Population 2 number density is presented in Figure 7. We see that this effect is important. Therefore, it can influence the interpretation of the Lyman-alpha absorption spectrum of stars in the downwind direction [28] and the interpretation of the heliosphere ENA image with 1 AU

[14]. 4. C O N C L U S I O N On the basis of the results presented above we can make following conclusions: 1. Examples presented in this paper show that a caution must be exercised by observers at the interpretation of their experimental data on the basis of numerical models. 2. The most published MHD numerical models do not take into account H-atom component. Therefore, they are physically not applicable to the problem of the solar wind interaction with the LISM. In addition, their results are only obtained for weak interstellar magnetic fields (in the hyperbolic region). 3. First results of the self-consistent MHD problem solution (H-atoms, plasma component and the interstellar magnetic field) in axisymmetric approximation show that the effect of the magnetic field on the "hydrogen wall" is not important as the magnetic field is changing from 0 till 3.5-10 -6 gauss. However, this effect can be important for the interpretation of the ENA-fluxes from 1 AU (see [14]).

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Possible effects of the interstellar magnetic field...

'

o5) O = O

~

i

. . . . . . . .

Ao==

l:.

t

. . . . .

A=o = O.9

'

t.'

'

i!

~

i "1,

1.18

O

=

7"1;/2

i .: [

'

........

Ao== Aoo=

oo 1.18

. . . . .

Aoo=

0.9

i'! i- !

!'i l:i

/ii ~"~r~

-

,~ t _,r."

, ;:

" i - i -

i

;J

-".i t .

S'o.

.-:.- .......

o

i

|

R,

~ ' ~ ' ~ " :

-'1" -" "=" "

:~

|

o

|

a.u.

(o O.O06

""~" " ~ ""

-

O

=

.-""

n

..--

0.005

ooo~ ~ ...... o.ool

o

i

i

. . . . . . . .

A==

1.18

. . . . .

A~

0.9

i

R,

i

i

a.u.

Figure 7. Effect of the interstellar magnetic field on the number density distribution of the Population 2 hydrogen atoms: (a) in the upwind direction, (b) in the sidestream direction and (c) in the downwind direction.

REFERENCES 1. V.B. Baranov, K.V. Krasnobaev, and A.G. Kulikovsky, Sov. Phys. Dokl. 15 (1971) 791. 2. J.-L. Bertaux, R. Lallement, V.G. Kurt, and E.N. Mironova, Astron. Astrophys. 150

(1985) 3. V.B. Baranov, M.G. Lebedev, and M.S. Ruderman, Astrophys. Space Sci. 66 (1979) 441. 4. V.B. Baranov, M.K. Ermakov, and M.G. Lebedev, Sov. Astron Lett. 7 (1981) 206. 5. H. Ripken and H.J. Fahr, Astron. Astrophys. 122 (1983) 183. 6. H.J. Fahr and H.Ripken, Astron. Astrophys. 139 (1984) 551. 7. M. Wallis, Nature, 254 (1975) 207. 8. V.B. Baranov and Yu.G. Malama, J. Geophys. Res. 98 (1993) 15,157. 9. H.L. Pauls, G.P. Zank, and L.L. Williams, J. Geophys. Res. 100 (1995) 21,595. 10. G.P. Zank, H.L. Pauls, L.L. Williams, and D.T. Hall, J. Geophys. Res. 101 (1996) 21,639.

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11. G . P . Zank and H.L. Pauls, Space Sci. Rev. 78 (1996) 95. 12. V.B. Baranov, V.V. Izmodenov, and Yu.G. Malama, J. Geophys. Res. 103 (1998) 9575. 13. V.V. Izmodenov, M.A. Gruntman and Yu.G. Malama, J. Geophys. Res. (2001) in press. 14. M.A. Gruntman, COSPAR Coll. on: The Outer Heliosphere: The Next Frontiers (Potsdam, Germany, 24- 28 July, 2000), Abstracts (2000) p.16. 15. A.G. Kulikovsky and G.A. Lyubimov, Magnetohydrodynamics (1965), AddisonWesley, Reading. 16. V.B. Baranov and N.A. Zaitsev, Astron. Astrophys. 304 (1995) 631. 17. Y. Fujimoto and T. Matsuda, KUGD91 - 2 (1991). 18. N.V. Pogorelov and A.Y. Semenov, Astron. Astrophys. 321 (1997) 330. 19. A.V. Myasnikov, Preprint IPM RAS (1997) No. 585. 20. R. Ratkiewicz, A. Barnes, G.A. Molvik et al., Astron. Astrophys. 335 (1998) 363. 21. N.V. Pogorelov and T. Matsuda, Astron. Astrophys. 313 (2000) 697. 22. N.V. Pogorelov and T. Matsuda, J. Geophys. Res. 103 (1998) 237. 23. D.B Alexashov, V.B. Baranov, E.V. Barsky, and A.V. Myasnikov A.V., Pis'ma v Astron. Zh. (2000) No. 11 (Astronomy Letters, English translation). 24. T.J. Linde, T.I. Gombosi, P.L. Roe et al., J. Geophys. Res. 103 (1998) 1889. 25. V.B. Baranov, M.G. Lebedev, and Yu.G. Malama, Astrophys. J. 375 (1991) 347. 26. J.L. Linsky and B.E. Wood, Astrophys. J. 463 (1996) 254. 27. Yu.G. Malama, Astrophys. Space Sci. 176 (1991) 21. 28. V.V. Izmodenov, R. Lallement, and Yu.G. Malama, Astron. Astrophys. 342 (1999) L13. 29. R. Osterbart and H.J. Fahr, Astron. Astrophys. 264 (1992) 260.

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Interstellar Gas F l o w Into the Heliosphere E. M6bius a, Y. Litvinenko a, L. Saul a, M. Bzowski b, D. Rucinski b aDept, of Physics and Space Science Center, University of New Hampshire, Durham, NH03824, USA bSpace Research Centre, Polish Academy of Sciences, Warsaw, Poland Flow speed, temperature, composition of the local interstellar medium and its interaction with the heliosphere, leave their imprint on the gas flow pattern through the inner solar system. Through diagnosing resonant scattering of light by the neutral gas, measuring the distribution function of pickup ions, and imaging directly the gas flow we can tap this information. Recently, even a direct signature of the neutral gas flow has been identified in the pickup ion cutoff that can be used to derive the flow velocity. In particular for helium all these methods complement each other, their consistency can be tested and a firm parameter be derived. All of these methods carry information not only about the spatial distribution of the gas, but also about its original velocity distribution. Helium is not significantly affected by the heliospheric interface and thus provides an almost unbiased view of the nearby interstellar medium. Conversely, hydrogen and oxygen are slowed down and heated by charge exchange in the interface region, thereby producing an altered flow pattern, which allows us to unravel these interaction effects. We will review current attempts to combine different in-situ observations of pickup ions and neutral gas distributions and outline applications to derive the physical processes in the heliospheric interface region. 1. MOTIVATION TO STUDY THE LOCAL INTERSTELLAR GAS The local interstellar medium (LISM) has received increasing attention over the past decade for a variety of reasons. Firstly, the interstellar gas constitutes the raw material of stars, planets and ourselves. This causal connection has sparked our interest in the very nature and composition of interstellar material, which also holds the key to its origin and evolution, generally referred to as nucleosynthesis. All chemical elements and their isotopes were or still are synthesized in three principal environments: 1) Light nuclei, such as H, He, their isotopes, and some 7Li (e.g. [1]), were produced in the Big Bang. 2) Stars synthesize C and all the heavier elements [2], but destroy D [3]. 3) Through spallation, galactic cosmic rays produce very rare elements, e.g. Be and B, in the interstellar medium [4]. The natural sequence of this still ongoing element and isotope formation leads to a continuous increase of the species formed under 2) and 3), which can be traced in the history of the galactic material. In fact, all material that belongs to the solar system has frozen in the state at the sun's birth about 4.5 billion years ago, while a sample of the LISM represents today's galactic material. A detailed comparison of the elemental and isotopic composition of these two disparate samples will provide much needed constraints for the models of galactic matter evolution. Secondly, the LISM is our immediate neighborhood in the galaxy. It imposes the outer boundary conditions on the heliosphere, a region, which is carved out of the interstellar me-

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E. MObius et al.

dium by the solar wind and its imprinted interplanetary magnetic field (IMF). A balance between the solar wind and the pressure of the LISM determines the size of the heliosphere. Currently, the space environment of the Earth is controlled entirely by the solar wind. The large size of the heliospheric bubble keeps the overwhelming majority of energetic cosmic radiation outside our planetary system and only a small fraction of the most energetic particles reach the Earth. If we consider the relative motion of the Sun and the various local components of the LISM an interesting scenario emerges. Our heliosphere was probably even larger several hundred thousand years ago when the sun was in a very dilute and hot environment, but may shrink substantially a few hundred thousand years from now, when it encounters interstellar clouds of much higher density [5, 6, 7]. Turning our view to our galactic neighborhood, the heliosphere also impacts the surrounding medium by diverting the flow and by filling the vicinity with additional energetic particle populations, generated at its boundaries. In essence our heliosphere is an example - in fact the only example that can be closely examined - o f the more general phenomenon of astrospheres. As an indication for an astrosphere, the diversion and deceleration of the interstellar gas flow appears as an additional Doppler-shifted component in absorption lines of interstellar H in the light of the respective star. Observations of astrospheres in our neighborhood have recently been reported by Linsky [8] and Wood et al. [9]. In order to tackle these important questions, the elemental and isotopic composition as well as the physical parameters, density, temperature, bulk flow and ionization, of key species in the LISM must be determined. To date we have only direct access to local interstellar material that penetrates the boundaries of our system or to line-of-sight integrals that provide an average over several light years. Given these constraints, it is obvious that our current knowledge of the LISM immediately outside the heliosphere is limited and efforts in various directions are needed to improve this situation. Since the heliosphere is impenetrable to interstellar plasma, only the neutral component of the LISM is currently accessible. Even this access is substantially biased by filtering of several species, such as H and O, in the heliospheric interface through charge exchange with the interstellar plasma flow [10, 11, 12, 13]. However, the amount of filtering, a related deceleration and heating of the interstellar material during the passage of the interface, and the degree of ionization of H are causally connected. Therefore, a careful comparison of the observed flow characteristics of species affected by resonant charge exchange (e.g., H and O) with those that are not (e.g., He and Ne) will provide the necessary information. In addition, the comparison of the physical parameters obtained for several species will provide insight whether the LISM is isothermal or non-thermal effects are important. Finally, the LISM may be inhomogeneous on much smaller scales than indicated above. Such inhomogeneities can only be identified by long term observations of the physical parameters. This can be achieved by extension of our data sets into the future and by providing the tools to interpret earlier data sets quantitatively so that a comparison with current results is possible. In this paper we will first summarize the current status of LISM observations and compare different observation methods. We will then describe briefly a coordinated observation campaign aimed at the physical parameters of interstellar He. Finally, we will concentrate on the determination of the LISM flow from pickup ion and neutral gas observations and how this can help to identify interface effects. 2. STATUS OF LISM OBSERVATIONS Of the LISM components, helium is the species for which the neutral parameters can be determined from inside the heliosphere without modification [14, 15]. Helium is also very intriguing because of recent results that it appears to be more highly ionized than hydrogen, in

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Interstellar gas flow into the heliosphere spite of its higher ionization potential. Currently, this has not been reconciled yet with the local radiation environment in the LISM [16]. Over the last fifteen years the tools for the determination of the LISM parameters, density, temperature and bulk flow vector, have been dramatically improved and diversified. The traditional method to observe interstellar neutral He inside the heliosphere by means of resonant scattering of solar UV, first reported by Weller and Meier [ 17], has been augmented by direct particle measurements, using pickup ion distributions [18, 19] and neutral atom imaging [20]. Yet the derivation of the interstellar parameters with all these methods relies on a detailed modeling of the gas flow through the heliosphere and ionization losses on its way. Because of the modeling steps involved in each of the methods and the need for additional information on the sun's radiation and solar wind environment, results of these methods have differed to varying degrees in the past. In addition, the influence of the sun and the heliosphere on the gas distribution changes with the solar cycle, a subject of great interest in itself. A compilation of the physical parameters of He as obtained with the different methods can be found in Table 1. Observationally, these methods can be subdivided into two groups: in-situ methods, i.e. direct detection of the neutral atoms or their pick-up ions in the solar wind, and remote sensing methods, i.e. resonant scattering of solar UV at gas inside the heliosphere or line absorption of stellar UV. Each of these methods provides different raw observations that require substantial physical interpretation and extensive modeling in order to derive the physical parameters. Among these, the use of interstellar UV absorption lines in the spectrum of nearby stars is distinctly different from the other methods. It provides an average temperature and bulk flow velocity along the line-of-sight from the observed line profile over several light years and may be used to assess the homogeneity our neighborhood. From the observations inside the heliosphere one can either use directly the flow velocity information, when available, or the spatial distribution of the neutral gas to derive flow speed and temperature in the LISM. The observed flow velocity distribution in the inner heliosphere allows a direct extrapolation to the flow parameters at the boundary by invoking Keplerian trajectories of the neutral gas in the sun's gravitational field. The flow speed can be obtained by measuring the deflection of the neutral atoms in the sun's gravity [20], from the Doppler shift of scattered UV (e.g. [21 ]), and from the shift of the pickup ion cut-off compared with its nominal value of two times the solar wind speed [22]. So far the particle observations were made for He, while the UV observation has been obtained for H. Similarly, the spatial Table 1" Observations of interstellar helium parameters structure of the He Pick-up Ions Neutral Atoms ln-Situ Pick-up Ions distribution in the ( A M P T E SULEICA) (SWICS) (Ulysses G AS) Methods inner heliosphere r/He (cm -3) 0.009 - 0.012 0.0153+0.002 0.015-0.017 that is formed by the (Ulysses) combined action of 7850+550; 9900+500 5800- 7600 4800- 7200 THe (K) (corrected for diffusion) the sun's gravita25.3 + 0.4 23 - 30.5 VreI (km/s) tional field and ioni(corrected for diffusion) zation by solar UV [25], [38] [20] Reference [39], [42] and solar wind conRemote SensUV Absorption UV Scattering UV Scattering tains the imprint of ing Methods (non-local) the bulk flow and 0.015 0.02 0.0055 0.0145 nile (cm-3) temperature at the 16000 8OO0 7000 • 200 THe(K) boundary. Most pro(shifted UV line) minently, a gravita24 - 30 19-24 25.7 • 1 V~-el(km/s) tional tbcusing cone (shifted UV line) of enhanced He denReference [54] [521 [531

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sity is formed on the downwind side of the sun with respect to the flow. From a deconvolution of the UV scattering intensities (e.g. [23]) and from the spatial distribution of pickup ions along the Earth's orbit (e.g. [24]) the density, temperature and bulk flow velocity are derived. Surprisingly, the temperature and bulk flow speed, as derived from direct neutral gas flow observations inside the heliosphere and from absorption line profiles, seem to agree within their respective uncertainties. This might indicate that the conditions at the location of the solar system are well represented by the average in our neighborhood. However, there are still noticeable differences between different methods and even individual observations within a method, if the shape of the gravitational focusing cone is used. These differences call for a careful assessment of observational and modeling uncertainties. Each of these observations and methods has their own strengths and weaknesses. Ideally they could complement each other in the attempt to determine a benchmark set of parameters. Direct observation of neutrals promises the most accurate account of the LISM parameters, but is currently limited in its application to He. Conversely, pickup ions and UV scattering show greater potential towards widespread use among different species and long term observations. Therefore, a successful cross-calibration of all methods will substantially enhance our capabilities. Pickup ions can be observed from a variety of species. In addition to He, the density of H has been derived from pickup H + [19], and the abundance of N, O and Ne in the LISM has been inferred from N +, O +, and Ne + [25, 26]. These results make pickup ions a very versatile tool for the detailed study of the interstellar gas bulk parameters as well as the elemental and isotopic composition, provided the transfer and transport processes from the original interstellar neutral gas population to the measured pickup ion distributions are fully understood. Likewise density, bulk velocity and temperature of H have been derived from observations of scattered Lycz radiation (e.g., [21], [23]). It should be noted here that UV scattering observations are available for H and He since the early 1970' s, i.e. have the longest history. However, there are substantial differences in the results obtained from different data sets. Some of the differences may be due to the quality of the data, which certainly improved over time, but some of them may Table 2: Comparison of LISM observation methods also be connected to intrinsic difficulties of the methods. Strengths Weaknesses The respective strengths and Pickup Ions weaknesses of each method 9Many species (H, He, N, O, Ne, ) ~ Requires knowledge of have been compiled in Table 9 Spatial distributions, Vion "-) Ionization rates 2. As pointed out above, 9 Benchmark He density: He2+ ~ Transport effects pickup ions show the promise 9Long history:1984 - today ~ Unknown variations of fluxes 9 Connection to energetic ions of the most versatile data set in terms of LISM species. Imaging of the Neutral Gas Flow Instruments with large col9 So far only He 9Most precise observations may be extended to O, H, -) Bulk Speed lecting power are possible, and possibly others -') Direction and observations are available 9Minimum S/C- Neutral Temperature that go back to 1984. From velocity 9 Density (good calibration) the pickup ion energy spec~Vionfrom indirect trajectories trum information on the local UV Scattering ionization rate and the spatial 9 Long history: 1970- today ~Very sensitive to solar line distributions can be extracted. ~ Relatively small instruments profiles and variations In addition, a b e n c h m a r k 9 3-D view of spatial distribution 9Only 2 species (H, He) value for the He density has UV A bsorption been derived from He 2+ 9Variety of ISM species 9No Local ISM values pickup ions, because their 9 Connection with Astrophysics

Interstellar gas flow into the heliosphere production by solar wind He 2+ allows observation of both constituents with the same instrument and thus eliminates most calibration uncertainties [27]. However, this method requires independent knowledge of production rates for most species and is subject to a variety of transport effects. Also pickup ion fluxes still show a substantial variation on a wide range of time scales that is not fully understood and is usually taken out by long integration times. The most detailed and direct information on bulk speed, direction and temperature can be deduced from observations of the angular distribution of the interstellar gas flow on the downwind side of the sun. The method makes use of the dependence of the gravitational deflection of the neutrals on their original velocity [20]. In addition, the separation of direct and indirect Keplerian trajectories allows an independent determination of the total ionization rate. However, density determination requires elaborate absolute calibration. The minimum detection energy for atoms limits the application to parts of spacecraft orbits, where the interstellar gas and spacecraft velocities add up favorably. In addition, the method has only been applied to He so far. An extension to O and H appears possible with some development [28, 29]. Yet species, which cannot be easily converted into a negative ion, such as N or Ne, may not be accessible at all. The resonant UV scattering methods have the longest history, rely on relatively small instruments and provide a 3-dimensional view of the spatial distribution [30]. However, the results are very sensitive to the original solar line profiles and their variation. The radiation transport problem for Lycz has recently been treated by Scherer et al. [31]. This also requires a complex deconvolution, including among others careful modeling temporal variations of neutral gas density and velocity within a few AU from the sun [32, 33]. Direct velocity determination via the Doppler effect is only possible for H so far. In addition, only the two main species of the LISM seem to provide enough sensitivity for the method. An extension of this method, i.e. imaging the heliopause in the light of ionized O has been proposed by Gruntman and Fahr [34]. It will become possible with a sensitivity improvement by two orders of magnitude [35]. 3. COORDINATED OBSERVATION CAMPAIGN FOR INTERSTELLAR HELIUM With a unique combination of heliospheric and astronomical spacecraft it has become possible for the first time to employ all methods simultaneously, with the great advantage that they can complement each other with their capabilities. Each year in early December the Earth, and with it all earthbound spacecraft, pass through the interstellar focusing cone, whose structure depends critically on the interstellar parameters and the ionization in the heliosphere. However, the passage in December 2000 provides the opportunity for the most complete coverage. It is also close to maximum solar activity. The combination of UV observations is depicted in Fig. 1. EUVE, still in operation, provides a 3-D view of the cone in the anti-sunward direction [36, 37], while SOHO UVCS scans the cone very close to the sun, where it is most sensitive to the ionization (Raymond, private communication, 2000). Because the LISM flow is inclined by ~ 7 ~ w.r.t, the ecliptic plane the maxima of the scattered light appear below the ecliptic and below the sun, respectively. At the same time ACE, Wind, and Geotail provide a complete and contiguous spatial profile of the pickup ions at 1 AU. SOHO CELIAS SEM observes directly the UV ionization rate [38] and SOHO EIT provides a full disk image of the He II 304 A line, which contributes substantially to the He ionization rate. SOHO CDS and SUMER obtain the disk image and line profile of the He I 584 A line that controls the intensity of the scattered light. In addition, the relative speed of the LISM flow and Ulysses exceeds the observation threshold for the GAS sensor again, and direct neutral observations can be obtained. This combination lends itself to a comprehensive 3-dimensional imaging of the cone from close to the sun to beyond 1 AU with simultaneous in-situ observation of the velocity distribution of the neutrals. The coordinated effort is supported through a Scientific

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E. MObius et al. Team at the International Space Science Institute (ISSI) with contributions by: J.-L. Bertaux, S. Chalov, H. Fahr, G. Gloeckler, R. Kallenbach, R. Lallement, E. MObius (Chair), D. McMullin, H. Noda, J. Raymond, D. Rucinski, W. Thompson, 7". Terasawa, J. Vallerga, R. yon Steiger, M. Witte. How the different data sets complement each other in the comparison with the modeled interstellar gas distribution to deduce the interstellar parameters is shown in Fig. 2. The combination of the neutral gas and pickup ion observations will provide the most accurate results on the He density and flow vector. On the other hand UV observations will add the most accurate account of the ionization processes, because they reach closest to the sun. In particular, with SOHO SEM and EIT the photoionization rate is measured directly and simultaneously, so that the still largely unFig 1: In-ecliptic (top) view and anti-sunward known electron impact ionization can be deview (lower left) of the EUVE pointing, rerived. A main weakness of the UV scattering spectively sunward view (lower right) of the technique has been its strong sensitivity to the UVCS pointing for the coordinated UV scatintensity, location and profile of the relevant tering observations of the gravitational focusing solar line, in this case the He I 584 A line. cone of interstellar He. The extent and location Observations of SOHO CDS and SUMER of the cone is shown schematically by gray will provide the information to remove these shading. uncertainties. Recent observations of the He cone with ACE SWICS [39] provide a substantially improved basis for the derivation of the He flow parameters than the widely spaced observations with AMPTE IRM [24]. Yet transport effects that lead to notably anisotropic pickup ion distributions [40, 41], in particular during times of radial IMF orientation, are likely to modify the spatial distribution of pickup ions in comparison with the original neutral distribution [42]. Because of incomplete pitch angle scattering pickup ions are not immediately convected with the solar wind, leading to a non-radial transport of the interstellar ions. This results in a redistribution of the pickup ions with respect to the neutral profile and thus effectively to an apparent widening of the focusing cone. In addition, substantial variations of the pickup ion fluxes have been observed on a variety of time scales [43], whose origin is not fully understood yet. Therefore, long term averaging has been applied to the data before they are used to derive LISM parameters. While this appears to have a minimal effect in the determination of the LISM density, a systematic effect on the apparent cone width and thus the derived temperature and bulk velocity can be expected. A careful modeling of the pickup ion transport [44, 45, 46] will bridge this gap in understanding, and the comparison of the pickup ion results with the other methods will provide a handle on the transport effects themselves. The neutral gas and He 2+ pickup ion observations with Ulysses provide an independent test for the flow characteristics and absolute density of He, respectively. Reconciliation between the complementary measurement methods raises the expectation that an extended database can be used to study temporal variations of the heliosphere - LISM interaction due to the solar cycle and potential LISM variations. UV scattering observations go

Interstellar gas flow into the heliosphere

Fig 2: Interrelationship of the different complementary observations of the interstellar He parameters together with required auxiliary observations and modeling efforts. back to the 1970's, and those of pickup ions to 1984. It was pointed out recently that also electrostatic analyzers without mass resolution have the capability to distinguish pickup ion distributions (Noda and Terasawa, private communication, 2000) as another welcome addition to the database. 4. OBSERVATION OF THE ISM NEUTRAL SPEED FROM PICKUP IONS

Recently, direct evidence for the influence of the neutral gas flow on the pickup ion distribution has been presented [22]. In contrast to a model in which pickup ions start from neutrals at rest, the cut-off speed is shifted beyond the canonical value of 2V~w in the upwind direction of the LISM flow, most notably for slow solar wind. The reason for this shift is that in the rest frame of the solar wind the injection velocity of pickup ions is the vector sum of the solar wind and the local gas flow. In the upwind direction of the flow these two velocities add, forming a sphere in velocity space whose diameter is increased by the ratio of the neutral and solar wind speeds. Conversely, the sphere is smaller on the downwind side with a cut-off at values lower than 2V~w. Therefore, the cut-off shift varies distinctly along the Earth's orbit. It should be noted that the neutral speed at 1 AU is defined by the original flow speed VBulkin the LISM and the gravitational acceleration to 1 AU. Fig. 3 shows the relative shift of the pickup ion cut-off Av/Vsw as a function of the day of the year (DOY), as obtained with SOHO CELIAS in partially overlapping 30-day intervals. For the analysis all time periods with 300 < Vsw < 350 km/s and an angle between solar wind and IMF of >60 ~ were accumulated. Av/V~w was derived for each interval by modeling the pickup ion spectrum with the appropriate shift to match by eyeball fit the observed cut-off. A suprathermal tail of the pickup ions [22] was ignored, but it was assumed that the steepest part of the cut-off is unaffected by the tail. The lines show the expected cut-off shift of the correct radial flow component at 1 AU for VBulk= 38 km/s at the heliospheric boundary and solar wind speeds of 300, 325 and 350 km/s, with the center line representing the best fit to the current data set. Translating the width of the chosen solar wind

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speed interval into an estimated uncertainty of the bulk flow, our result is equivalent to VBulk= 38+7 km/s. The observation agrees qualitatively with the expected variation along the Earth's orbit. However, the value is significantly higher than the reported LISM flow speed of ~25 km/s and contains a relatively large error. A potential reason for the relatively large value of VBulk may be the following. We have ignored any effect of suprathermal ions on the cut-off, and no energy diffusion of pickup ions is included in our model. Both effects would lead to higher cut-off values. In a data set that contains observations on the upstream and the downstream side of the flow these effects can be separated from the bulk flow effect, because the latter switches sign. Therefore, better coverage along the Earth's orbit and a more detailed analysis that includes all transport effects of the pickup ion distribution [46] will probably improve this method significantly over this crude analysis. However, the determination of the flow speed from pickup ions will likely be much less accurate than from direct neutral gas observations.

Fig. 3: Relative cut-off shift Av/Vsw of the pickup ion distribution along the Earth's orbit with SOHO CELIAS in 1996. The horizontal bars indicate the accumulation of intervals. The data points have been obtained as the best fit of the measured distribution at the cut-off with a model distribution that was shifted accordingly ([22]). The lines give the predicted shift for different Vsw with a heliospheric longitude of the flow vector of 75 ~

5. PERSPECTIVES FOR NEUTRAL GAS OBSERVATIONS As pointed out before, the most detailed information about the interstellar flow can be obtained from observations of the velocity distribution of the neutral gas under investigation, in the inner heliosphere. Keplerian trajectories provide a unique transformation for the original velocity distribution after the passage through the interface. Therefore, the distribution at the interface can be constructed from these observations. Current observation methods for neutral atoms can provide precise angular images of the flow, but do not retain adequate energy resolution. This is true for the observation of interstellar helium through sputtering off a LiF surface as used in the Ulysses GAS instrument [20] and for the proposed negative ion conversion instruments for species, such as O and H (e.g. [47], [27]). Therefore, the differential deflection of the interstellar neutral gas flow in the gravitational field of the sun is utilized to convert speed differentials into an angular image. The basic idea is illustrated in Fig. 4. As observed from a specific location, slower gas is deflected stronger, which turns a velocity distribution into an image. The analysis of such images through a deconvolution technique has been described in detail by Banaszkiewicz et al. [48]. The very precise temperature and bulk flow values for LISM He have been derived in this way. If the velocity distribution of H and O were studied with the same scrutiny, this would return decisive information about the filtration of these LISM components, which is needed to derive exact neutral densities and the ionization-state of the LISM. The velocity distribution contains unique information about the related processes, because filtration is accompanied by an effec-

Interstellar gas flow into the heliosphere

tive slowdown and heating of the gases compared with their original state [12]. In detail, neutrals are first lost to the plasma flow by charge exchange and now contribute to a rather hot plasma distribution that is diverted around the heliosphere. In turn ions of this hot flow are converted to neutrals, of which a good fraction are directed towards the inner heliosphere. These neutrals constitute an additional secondary and rather hot gas distribution that is added to the original depleted flow. Because the fraction of these secondaries and their distribution scale with the column density of the heliospheric interface, their observation holds a key to understanding the processes and to constraining the overall effect.

Fig. 4: Schematic view of interstellar neutral trajectories in the inner solar system for different inflow speeds at the heliospheric boundary observed from a spacecraft at 135 ~ from the ISM apex on a 1 x 3 AU orbit. Lower speed leads to stronger deflection in the sun's ~ravitational field.

In order to estimate the observable effect and to define the parameters of the needed instrumentation we have simulated the neutral O distribution in the inner heliosphere and the respective observations at various positions of a spacecraft. We have chosen a 1 x 3 AU orbit with its major axis at 90 ~ w.r.t, the LISM flow, as shown in Fig. 4 and recently proposed for an Interstellar Pathfinder Mission [49]. It was assumed that the original O distribution in the LISM resembles that of He with VBulk= 25 km/s and T = 7000 K as obtained by Witte et al. [20]. According to Izmodenov et al. [ 12], the filtration was adjusted so that the resulting neutral gas flow contains 50% of the primary distribution. 20% of a secondary distribution with a reduced speed of VSec = 21 km/s and T s e c = 10000 K were added. Now the sun's gravitational field is employed to derive flow velocities, from the observed image of the flow in the sky, at locations downstream of the sun. Figure 5 shows simulated data (diamonds) as obtained by a neutral gas imaging instrument with an effective collection area of 1 cm 2 and an angular resolution of 40 in the direction of the scan, utilizing the spacecraft spin. The 1~ spacing of the data points is achieved by oversampling. Such an instrument will achieve the angular resolution by means of a collimator. The neutrals are then converted into negative ions on a conversion surface, which are accelerated into a time-of-flight spectrometer and analyzed for their mass. Overall conversion efficiencies of several % have been reported for O in the expected energy range [28]. The counting statistics of the simulated data reflects the assumption of a conservative overall detection efficiency of 1% and accumulation over 10 days, including the duty cycle due to the spinning spacecraft. The simulated data (diamonds) are compared with an O distribution with the original He parameters (line). The distribution has been normalized such that no negative values are computed after subtracting this distribution from the simulated data up to 10% of the peak value. The squares represent the resulting secondary distribution and its statistical error after this subtraction. The presence of a secondary distribution and its total relative contribution can be determined with ~10% accuracy in the current example. Also its position in angle space and thus its bulk velocity can be determined along with the temperature. This simulated observation applies to a position 135 ~ from the flow direction (c.f. Fig. 4). At a position 225 o from the flow (not shown here) we find a much weaker deviation from the original distribution, because of the

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high relative velocity when the spacecraft is moving into the flow. In addition, the absolute flux is much lower, because the O density decreases rapidly towards the sun. Generally, the gravitational deflection is stronger closer to the sun, but the total flux of neutral atoms is greatly reduced. A l x3 AU orbit appears to be an ideal compromise for the attempted neutral gas imaging. With contiguous data along the downwind portion of the orbit, even much smaller secondary O contributions with velocities closer to that of the original LISM flow can be detected and evaluated. Currently, instrumental efforts are unFig. 5: Simulated angular distribution of the interstellar derway to extend the sensitivity of the O flow as observed with an instrument with 5~ resoluneutral to negative ion conversion to tion. In addition to the original primary O component low energy ( 1 0 - 4 0 eV) H atoms, with velocity and temperature as obtained for LISM He a secondary component of 25% is assumed, which is which will then also allow to image produced by charge exchange in the heliospheric interthe H flow of the LISM. As can be seen from this preliminary analysis, a face according to Izmodenov et al. [12]. The error bars indicate the statistical error of the observed distribution comparison of the He, O and H flow (diamonds) and for the derived secondary distribution characteristics in the inner heliosphere (squares) after subtraction of a normalized primary diswill provide powerful tool to deduce tribution. the amount of filtration and its related processes quantitatively from observations in the inner heliosphere. This will be an important task in the near future in order to allow an accurate deduction of the composition of the LISM and its ionization state from observations inside the heliosphere. Any deviation of the flow vector of interface affected species from that of He will also provide constraints on the interstellar magnetic field direction in our neighborhood. The flow pattern of H in the inner heliosphere is also affected by radiation pressure. Imaging neutral H from various locations will provide the most accurate account of this effect and will allow unambiguous separation of interface and radiation pressure related effects. In addition, radiation pressure may also serve as a discriminator between H and D, because the strength of the effect depends on the particle mass. As a result the D image will be separated from the H image in angle, thus giving a neutral imaging mass spectrograph an advantage in the observation of D in the LISM. The D/H ratio in the interstellar medium has been considered an important data point for the evolution of matter [50, 3, 2], because D is the only isotope that is clearly being depleted by reactions inside stars over the primordial amount. Whereas local observations of 3He have been obtained, this task appears to be much more difficult for D [51 ]. 6. CONCLUSIONS AND OUTLOOK Over the past 15 years in-situ observations of interstellar material inside the heliosphere have been established as an important tool to determine the physical parameters and the composition of the LISM just outside the heliosphere. Having a full complement of pickup ion, neutral gas and UV instruments on operating spacecraft provides the unique opportunity to analyze the LISM simultaneously with all complementary in-situ and remote sensing techniques.

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Interstellar gas flow into the heliosphere Therefore, benchmark values of the He component in the LISM can be expected in the near future. From here pickup ion instrumentation and constant monitoring in UV will provide a broad database on LISM composition and the long term response of the heliosphere to variations of the sun and the LISM as drivers. The role of the heliospheric interface in the translation between the data obtained inside and the values in the LISM is on one hand a challenge. It must be overcome on the road towards high accuracy benchmark values for our neighborhood sample of the interstellar medium. On the other hand the variety of observations hold clues themselves about the related interactions in the interface. Future progress in the direct observation of interstellar neutrals beyond He will play a key role in this effort. The effort to extend the composition information to key isotope ratios that provide insight into the various nucleosynthetic processes and the study of the heliospheric interface interactions will require a spacecraft mission, dedicated to the study of the LISM. It requires high collecting power pickup ion instrumentation and an advanced neutral gas imager. Both instrument families are extensions of currently available hardware. These goals can be achieved on broad footing with a Discovery class mission or with some reductions in scope under the NASA Explorer program with a spacecraft on a 1 x 3 AU orbit. A similar mission has been proposed already as Interstellar Pathfinder [49]. Such a mission will be the ideal predecessor for an Interstellar Probe that would explore the interstellar medium itself. ACKNOWLEDGMENTS We wish to thank the International Space Science Institute (ISSI) for its hospitality and all members of the ISSI Team on the interstellar He cone for their efforts. The work benefitted from helpful discussions with P.A. Isenberg and M.A. Lee. This work was supported under NASA Grants NAG 5-2754, NAG5-8733, NAG 5-6912 and 5-4818, NSF Grant ATM9800781, and Polish Committee for Space Research Grant 2P 03C 005 19. REFERENCES: 1. Schramm, D.N., Space Sci. Rev, 84 (1998) 3. 2. Prantzos, N., Space Sci. Rev, 84 (1998) 225. 3. Mullan, D.J., and J.L. Linsky, Astrophys. J., fill (1998) 502. 4. Primas, F., Space Sci. Rev., 84 (1998) 161. 5. Frisch, P.C., Space Sci. Rev., 86 (1998) 107. 6. Frisch, P.C., Am. Scientist, 86 (2000) 52. 7. Zank, G.P., and P.C. Frisch, Astrophys. J., 518 (1999) 965. 8. Linsky, J.L., Space Sci. Rev., 78 (1996) 157. 9. Wood, B.E., J.L. Linsky, and G.P. Zank, Astrophys. J., 537 (2000) 304. 10. Baranov, V.B., Space Sci. Rev., 52, (1990) 89. 11. Fahr, H.J., Space Sci. Rev., 78 (1996) 199. 12. Izmodenov, V., Yu. Malama, and R. Lallement, Astron. Astrophys., 317 (1996) 193. 13. Zank, G.P., and H.L. Pauls, Space Sci. Rev., 78 (1996) 95. 14. Lallement, R., Space Sci. Rev., 78 (1996) 361. l 5. Lallement, R., J.L. Linsky, J. Lequeux, and V.B. Baranov, Space Sci. Rev., 78 (1996) 299. 16. Frisch, P.C., and J.D. Slavin, Space Sci. Rev., 78 (1996) 223. 17. Weller, C.S., and R.R. Meier, Astrophys. J., 193 (1974) 471. 18. M6bius, E., et al.,Nature, 318 (1985) 426. 19. Gloeckler, G., et al., Science, 261 (1993) 70.

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E. MObius et al. Witte, M., M. Banskiewicz, and H. Rosenbauer, Space Sci. Rev., 78 (1996) 289. Quemarais, E., et al., J. Geophys. Res., 104 (1999) 12585. MObius, E., et al., Geophys. Res. Lett, 26 (1999) 3181. Chassefiare, E., J. L. Bertaux, R. Lallement, and V. G. Kurt, Astron. Astrophys., 160 (1986) 229. MObius, E., D. Rucinski, D. Hovestadt, and B. Klecker. Astron. Astrophys., 304 (1995) 505. Geiss, J., et al., Astron. Astrophys., 282 (1994) 924. Gloeckler, G. and J. Geiss, Space Sci. Rev., 86 (1998) 127. Gloeckler, G., L.A. Fisk, and J. Geiss, Nature, 386 (1997) 374. Wurz, P., et al., Opt. Eng., 34 (1995) 2365. Wurz, P., R. Schletti, and M.R. Aellig, Surf Sci., 373 (1997) 56. Lallement, R., Scattering of solar UV on local neutral gases, in: Physics of the Outer Heliosphere, S. Grzedzielski and D.E. Page ed.s., COSPAR Coll. Ser., 1 (1991) 49. 31. Scherer, H., H.-J. Fahr, M. Bzowski and D. Rucinski, Astrophys. Space. Sci., 274 (2000) 133. 32. Bzowski, M., and D. Rucinski, Astron.. Astrophys., 296 (1995) 248. 33. Bzowski, M., H. Fahr, D. Rucinski, and K. Scherer, Astron.. Astrophys., 326 (1997) 396. 34. Gruntman, M., and H.J. Fahr, Geophys. Res. Lett, 25 (1998) 1261. 35. Gruntman, M., and H.J. Fahr J. Geophys. Res., 105 (2000) 5189. 36. Vallerga, J., Space Sci. Rev., 78 (1996) 277. 37. Flynn, B., J. Vallerga, F. Dalaudier, and G.R. Gladstone, J. Geophys. Res., 103 (1998) 6483. 38. Judge, D., et al., Solar Phys., 177 (1997) 161. 39. Gloeckler, G., and J. Geiss, Space Sci. Rev., in press (2001). 40. Gloeckler, G., L.A. Fisk, and N. Schwadron., Geophys. Res. Lett., 24 (1995) 93. 41. MObius, E., D. Rucinski, M.A. Lee, and P.A. Isenberg., J. Geophys. Res., 103 (1998) 257. 42. MObius, E., D. Rucinski, P.A. Isenberg, and M.A. Lee. Ann Geophys., 14 (1996)492. 43. Gloeckler, G., J.R. Jokipii, J. Giacalone, and J. Geiss, Geophys. Res. Lett., 21 (1994) 1565. 44. Isenberg, P.A., J. Geophys. Res., 102 (1997) 4719. 45. Schwadron, N.A., J. Geophys. Res., 103 (1998) 20643. 46. Chalov, S., and H.-J. Fahr, Astrophys. Space Sci., 363 (2000) L21. 47. Ghielmetti, A., et al., Optical Eng., 33 (1994) 362. 48. Banaszkewiecz, M., M. Witte, and H. Rosenbauer, Astron. Astrophys. Suppl. Set., 120 (1996) 587. 49. Gloeckler, G., et al., LOS, Trans. Am. Geophys. Union, 80 (1999) $237. 50. Linsky, J.L., Space Sci. Rev., 84 (1998) 285. 51. Gloeckler, G., and J. Geiss, Nature, 381 (1996) 210. 52. Dalaudier, F., J. L. Bertaux, V. G. Kurt, E. N. Mironova, Astron. Astrophys., 134 (1984) 171. 53. Chassefiare, E., J. L. Bertaux, R. Lallement, B. R. Sandel, and L. Broadfoot, Astron. Astrophys., 199 (1988) 304. 54. Bertin, P., R. Lallement, R. Ferlet, A. Vidal-Madjar, and J.L. Bertaux, J. Geophys. Res., 98 (1993) 15193.

20. 21. 22. 23. 24. 25. 26. 27. 28. 29 30.

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N o n - s t a t i o n a r y transport of neutral atoms in the H e l i o s p h e r e A.I. Khisamutdinov a M.A. Phedorin b and S.A. Ukhinov b Sobolev Institute of Mathematics of the Siberian branch of Russian Academy of Science, Acad. Koptyug prospect 4, Novosibirsk, 630090, Russia b Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russia

a

A problem on non-stationary transport of neutral H-atoms in the two-shocks Heliospheric plasma is considered. A point impulse source of H-atoms is situated on the outer boundary of Heliosphere. Some time-spatial-velocity distributions of the atoms are computed by a Monte Carlo methods specially developed. 1. I n t r o d u c t i o n

Interaction between the Local Interstellar Medium (LISM) and the Heliosphere is an object of the scientific interest and research, and this fact is reflected in a lot of publications. One of the problems deals with propagation of neutral particles (arising from LISM) in the Outer Heliosphere (including domains both before and behind the Heliopause) whose parameters are assumed to be independent of the particles. A mathematical model of this physical phenomenon is some Markov jump process, and the linear kinetic transport equation is the "master" equation of this process, in fact. This all makes natural applications of Monte Carlo methods for investigation of neutral atoms' distributions. A few stationary problems on the propagation of H and O atoms were considered in [2-4] with use of the Monte Carlo methods, and interesting results were obtained. Non-stationary problems of the neutral particles transport are more complex for the computation than the stationary ones. As to the most important non-stationary problems, it should be pointed a problem on propagation of the neutral atoms in Heliosphere interface whose parameters are periodic functions (with period of the Solar cycle). In other important problem, parameters of the medium (Heliosphere) are assumed to be stationary but the flux of the neutral atoms from the LISM varies in time. In the present paper we consider a problem of above indicated second type on propagation of H-atoms; the source of H-atoms is impulse point, and its velocity distribution density q~(v) corresponds to the Maxwell distribution in LISM We carry out numerical solving employing Monte Carlo methods, and then analyze some properties of the phenomenon considered. 2. M o d e l of m e d i u m , T r a n s p o r t e q u a t i o n , and functionals c o m p u t e d

Axially symmetric model of the Heliospere is considered, which is chosen according to twoshocks gasdynamical model (see [1, 3]). Heliosphere is assumed to be confined in a bounded spatial domain Va with piecewise smooth boundary c3V~. The scheme of the Heliosphere model is shown in Fig. 1. The origin of the Cartesian coordinate system coincides with Sun center, OZ (axis) is the symmetry axis of the system and is directed towards the flow of interstellar gas. Only the "upwind direction" region is considered in our problem, 0 <_z _<400 au. In order to simplify the assignment of the medium model data, the whole domain V~ was divided into 8 sub-domains (zones): each of four layers between natural boundaries LISM, BS, HP, TS, and the sphere of 1 au radius were cut by the cone of n / 4 angle (see Fig. 1). In Fig. 1 the zones are indicated by numbers from 1 to 8. The distribution of velocities for the plasma protons in Heliosphere is assumed to be Maxwellian with corresponding values of mean velocities and temperatures. The values of plasma parameters in indicated 8 zones were taken according to the Ref. [3] at the points shown in Fig. 1 as "D2 ~ and "D3". It is assumed that the atoms interact with the medium by means of two well-known types of interactions: a charge-exchange scattering and a photoionization (absorption). To express boundary conditions also it is assumed that outside the surface c3V~ an "absolutely absorbing" medium is situated. We introduce the following denotations and assumptions: X=R 6 is a phase space of coordinates r and velocities v; x=(r, v ), x ~ X, V~ -(Vc, ~c?VG) G-Va|

3 GcX

q(t,x) = 6 ( t ) 6 ( r - r0). qv(v ) is the density of H-atoms source, r0 ~ c3V~, r0 = (0,0,z0) , z0=400 au; II q(t, x). dtdx - 1

,/d

- 121 -

A.L Kishamutdinov, M.A. Phedorin and S.A. Ukhinov np(r) is a number density of plasma protons at a point r, Vp is a velocity of a plasma proton, V p E R 3", V(r) is the mean value of velocities of plasma protons at a point r; P m(u[r) , U=Vp-V, is

the density of Maxwellian distribution of protons velocities at r with given mean velocity V(r) and the corresponding temperature T, T=T(r); g=[V-Vp[is the modulus of relative velocity of atom and proton;

Fig. 2. Probability of Remaining in the Heliosphere and Fig. 1. Scheme of the model of the Probability density of the Escaping through its Heliosphere accepted for the current boundaries vs. time for the H-atoms in Heliosphere investigation, resulted from the point 8(0 source situated on the system's axis. croh~(g ) is microscopic cross-section of the "charge exchange" interaction between the atom and proton; wl(g ) - g . Crch.ex ( g ) ; Wohex(g,r) -- n p ( r ) ' w l ( g ) , Vr ~ VG, Vg >_0; C(v -+ v'[Vp) is an indicatrix of charge-exchange scattering of the atom with the velocity v by the proton with the velocity Vp; P0 - {Xt }t~0 is a jump Markov process of the atoms propagation, which is determined by the above given elements; its states are in X ~ {-a , where {a is an absorption state; m t ( x ) - m(t, x), x ~ X w {a , is a phase density of atoms in P0 ; Everywhere above and below the integration domain is not indicated if it coincides with the whole domain (of integration). The phase density m t (x) being considered as some generalized solution satisfies on X to the kinetic transport equation, whose terms of the source and the scattering are q(t,x) and S § respectively, A

S +m(t, x) - II m(t, r, v'). Wch~• ([ V'--Vp I, r)C(v'---~ v [Vp). Pm (U I r)" a v e 9d v ' ,

Vx E a.

In this study we used the values of O'ch.ex ( g ) , C ( v --~ v ' l V p ) and the frequency of photoionization, which are given in [5, 2, 4]. The values of interstellar gas temperature and mean velocity, accepted at assignment of the source, were set as the following: 6700 K and (0, 0 , - 5 . 4 7 7 ) au/year, respectively. To obtain and study the solution m(t,x) different functionals on it are computed: (1) mean densities (including concentrations) and mean fluxes of atoms over given surfaces in V G and over given time intervals for different velocity subsets; (2) mean densities (concentrations) of atoms in given volumes in V~ for given time moments; (3) mean velocities as the ratio of mean fluxes and the corresponding mean densities of atoms. First two types of the means are the linear functionals on m(t,x) of the following form

Is - l d t l d v l d S ' [ ( V , ns)lm(t,x)'Oes(t,x), It,.v- Idx'mt,(x)'oC'v(t*,x), (s)

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Non-stationa~ transport of neutral atoms in the heliosphere

where (S) is the surface with the normal ns(r) at the point (r), t* is the time moment (t*>0), (V) is the volume, OCs(t,x) and OCv(t*,x ) are the corresponding weight functions. In particular, we have for the mean concentration of atoms over (S) and over the time interval (tl, t2): t2

i d t l d S i d v , l(v, ns)lm(t,r,v)" ~ <s~

1

I(v,n )l-(t2

- t )-II S I1' where IISII is the area size of (S); on the Fig. 3 these functionals are denoted as n. Total numbers of computed functionals were 12"15 of type Is and 1"8 of type It,,v. As volumes (V) the volumes of zones 1 to 8 were used. As a surfaces (S) a flat, perpendicular to OZ axis rings were used; the "thickness" of each ring, i.e. (emax-Rmin), was about 40 au, where Rmax and emin are the maximal and minimal radius of a ring, respectively. Three levels of positions of the surfaces (S) are shown in Fig. 1 as "D 1", "D2", and "D3 ", where markers indicate the positions of the central radius of the rings

(i.e. (Rmax-emin)/2). 3. M o n t e Carlo m e t h o d used

In order to compute all functionals Is and It,,v, trajectories of a random process close to P0 were simulated and corresponding "imitation" estimators were used. When saying about the close process, we mean the fact that the photoionization absorption was taken into account by the known technique "analytical averaging of absorption". It is the important feature that a new method of simulation for joint distribution of random time instant and spatial coordinates of atom's collision and of random velocity of colliding proton under the charge exchange was constructed. In the new method a rejection technique is used, the "rejected" values are treated as the collisions of some complementary type, not changing the phase density. The mean numbers of physical and "fictitious" (complementary type) collisions are given in Table 1. One can see that the method constructed is sufficiently effective. 4. Results and Discussion

For computation a new code was generated. Here are some data about the computational cost and the relative standard errors. The computation time for 50,000,000 trajectories was equal to 9,800 s for the Intel Celeron 500 MHz processor. The errors of all computed functionals were within ( 1-10 %). At first we discuss some common patterns of time behavior, connected with V6 and c3Vc;. These are the probability for atom to stay in V6, the probability density to escape through the "upwind" and "downwind" parts of c3V~, the mean free path, and the mean free flight time between collisions, and .others, that are given in Fig. 2 and Table 1. It is interesting to notice the presence of two maxima on one of the curves on the Fig. 2. The characteristic phenomenon that was established for the stationary problems of H-atoms transport in Heliosphere is the effect of the "hydrogen wall" (see Ref. [3]). This phenomenon is also appearing in the obtained solution of non-stationary problem. As a basic form for presentation of the results obtained we have chosen the time distributions (histograms) of Is. It is adequate for the data analysis to present the phase density of H-atoms as sum of two densities: the scattered and non-scattered atoms; two corresponding summands for any Is turned out to be the functions with the single maximum and vanishing when t -+ 0 and t --~ oo Table 4. Basic parameters characterizing the non-stationary transport of H-atoms in the Heliosphere Time, after which the half (V2) of the H-atoms that initially come into 105 years Heliosphere, abandon it Mean life-time of the H-atom in the Heliosphere 110 years Mean number of the "charge-exchange" collisions 4.8 Mean trajectory length in the Heliosphere 573 au Mean time / mean path among two subsequent collisions 22.9 years / 119.3 au Mean number of the fictitious collisions in the Heliosphere 1.94 Probability of escaping through the plane Z=0 0.96 Probability of absorbing in the Heliosphere _ 0.01 - 123-

A,L Kishamutdinov, M.A. Phedorin and S.A. Ukhinov

One can treat this fact as superposition of some two waves. Naturally, the peaks of non-scattered densities are situated not later the peaks of scattered ones. Everywhere in Fig. 3 and Fig. 4 these two summands are given. It is also important to note that the mean velocities vz(t) of scattered particles for the zones 4,7, and 8 change their sign (see, e.g., zone 4 in Fig. 4).

Fig. 3. Histograms of H-atoms density (a) and velocity module ~) distributions in zone 2 of the accepted model of the Heliosphere.

Fig. 4. Histograms of vz component of the velocity distribution of H-atoms in zones 2 (a) and 4 (b) of the accepted model of the Heliosphere. The characteristic property of all histograms of all different mean velocities for scattered particles is their identical asymptotical behavior under t ~ oo, i.e. the fact that all curves tend to some constants. It should be noticed that absolute values of the corresponding densities and fluxes decrease and vanish under t -4 oo. The reason of this phenomenon as we suppose is the following the phase density of scattered particles mso(t,x) is represented under t - ~ oo as the product of two factors, mso (t, x) => m 1 (t, r). m 2 (v ] r), t-+oo

where the density of conditional distribution of velocity m2(vlr) is time-independent already. 5. A c k n o w l e d g e m e n t s

This work has been supported by INTAS-CNES cooperation project # 97-00512 and International Space Science Institute in Bern. We are also grateful to all participants of the project and especially to R. Lallement, V.B. Baranov, V. Izmodenov, and Yu.G. Malama for useful discussions and for the data presented. References

[1] [2] [3] [4] [5]

Baranov V.B., Space Sci. Rev., 52, 1990, p. 89-120 Malama Yu.G., Astrophys. Space Sci., 176, 1991, 21-46 Baranov V.B. and Malama Yu.G., Space Sci. Rev., 78, 1996, p. 305-316 Izmodenov V., Malama Yu. G., and Lallement R., Astron. Astrophys. 317, 1997, p. 193-202 Maher L. and Tinsley B., J. Geophys. Res., 82, 1977, p. 689-695 - 124-

Pickup Ion Turbulence: A Stochastic Growth Model I

G.P. Zank I and Iver H. Cairns 2 ~Bartol Research Institute, University of Delaware, Newark, DE 19716, USA 2School of Physics, University of Sydney, Sydney, NSW 2006, Australia A new characterization of interplanetary MHD turbulence over the polar regions of the sun, based on a stochastic growth model for waves driven by pickup ion instabilities, is presented. By considering temporal and spatial variations in the local interplanetary magnetic field (IMF), we find that the mean wave growth rate can be very small (and even negative), but the variance can be large, indicating that localized regions experience significant wave growth in a stochastic fashion. This suggests that pickup ion driven turbulence in the outer polar heliosphere has a bursty or intermittent character, occurring in clumps. Thus, individual wave growth events are rarely detected, and persistent beamlike anisotropies in observed pickup ion distributions are expected. 1. INTRODUCTION Virtually all theoretical work addressing interstellar pickup ions in the solar wind over the last ~25 years has assumed that pickup ions generate significant levels of magnetic field fluctuations. The fluctuations were then assumed to scatter the pickup ions rapidly, so ensuring that the pickup ion distribution was essentially isotropic in the solar wind frame and co-moving with the solar wind (see [ 1] for a review). However, concerns about this picture for the pick-up of interstellar ions, wave generation and scattering appeared when a concerted effort by several groups failed to find definitive observational evidence for wave generation by pickup ions in the outer heliosphere. The few events identified as enhancements of magnetic fluctuation spectra near the ion cyclotron frequency and interpreted in terms of pickup ion-driven waves, all occurred during periods when the large scale interplanetary magnetic field IMF was quasi-radial [2,3,4]. During periods when pickup ions were observed, it was difficult to consistently identify enhancements in local IMF spectra that might be associated with pickup ion generated waves, suggesting that the observed wave growth rate Fob s "~ 0 much of the time. Such low wave growth rates would be consistent with the observed anisotropic pickup ion spectra. However, long-time averages of magnetic fluctuations in the outer heliosphere [5] suggest that pickup ions are driving turbulence in the outer heliosphere and at a rate that is consistent with simple scaling estimates [ 1]. The observations are in contrast to the predictions of quasi-linear theory. Here, we describe a newly developed model [6], based on stochastic growth theory (SGT) [7], for the growth of waves driven by the pickup process in the polar solar wind, and offer a resolution to the paradoxical observations of anisotropic pickup ion distributions, the frequent absence of local wave enhancements in magnetic fluctuation spectra, and the significant energy density in pickup ion-generated waves in the outer heliosphere. This work supported in part by NASA grants NAG5-6469, NAG5-7796, an NSF-DOE award ATM0078650, and an NSF award ATM-0072810.

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G.P. Zank and 1.11. Cairns

Although the large-scale polar IMF is radial, significant small-scale variation is present. We show that variation in field direction engenders spatial and temporal variations of pickup ion distributions that can lead to the wave growth varying in a stochastic manner. 1.1 S u m m a r y of pickup ion bean instabilities

Let 0 denote the angle between the magnetic field B and the radial solar wind flow. For 0 ~ < 0 < 45 ~ the ion-ion right-hand resonant instability dominates, whereas for 0 > 70 ~, the left-hand polarized ion cyclotron instability begins to dominate. The ion-ion righthand resonant instability growth rate is greatest for waves parallel to B and decreases monotonically with increasing obliquity. Simulations show a decreasing level of fluctuations as 0 increases; a result which is consistent with observations made at comet Giacobini-Zinner, which show the absence of large amplitude magnetic fluctuations near the water group ion cyclotron frequency when 0 = 90 ~. See [8] for a review. The basic conclusion that emerges from the above summary is that pickup of interstellar atoms when the IMF is almost radially aligned with the solar wind flow drives the fastest growing waves with the highest saturation level. In contrast, the waves should saturate at a low level in regions where 0 ~ 90 ~. 2. STOCHASTIC G R O W T H OF MHD FLUCTUATIONS At some instant, suppose that the polar interplanetary magnetic field, although radial on a sufficiently large time and spatial scale, has the form depicted in Figure 1. Consider an arbitrary region C with a scale length L and assume that any excited modes are Alfvrnic. Below, we shall use a value of L corresponding to the correlation length for the IMF fluctuations. In choosing a value for L, one should recognize that, in the region of ionization, the magnetic field should be "local." A characteristic interaction time tg of excited Alfvrn waves with C is then tg =- L / VA . C will experience perturbations in the wave growth rate during the time tg as ring-beams created in regions of different magnetic field orientations interact with C. The most important ring-beams, since they have the largest growth rate and highest saturation levels, are the almost pure beam distributions created in nearly radial magnetic fields. Moreover, outside growth sites, the beams tend to reform due to fast particles outrunning slow particles. Physically, we may expect a net balance between particle streaming, which generates waves, and particle scattering caused by wave growth, which attempts to drive the beam towards isotropy. This in turn reduces the wave growth and hence diminishes the scattering and so allows the beam to reform partially. Like all physical systems with instabilities, we expect the waves and particles to relax towards marginal stability [7]. To summarize, if beam-driven waves are most important, then since the driven waves have wave vectors close to parallel to the local field, changes in the background field direction will cause the growth region of wave vector space to move, thereby causing the growth/damping rate of waves with a given wave vector to vary with time and location. (Note that the beam particles remain in the same place in (v H,v;) space, but not in (v x, Vy, Vz) space.) There are thus two reasons for stochastic variations in the growth rate of waves: (i) the "direct" SGT reason of competition between rebuilding and destruction of the beam source of wave growth,

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Pickup ion turbulence." A stochastic growth model and (ii) changes in the location in wave vector space of locally driven waves due to changes in magnetic field direction. The mean growth rate and its standard deviation, for pickup ion driven turbulence in the outer polar hemisphere, are then [6] ( F ) ~ (Z) and

(Z)(vb)L Z • = u + b / ~

(e}'e

'

- - where F - F - 7

and F / 7 are the wave growth and

'

damping rates, u and b denote fluctuations in velocity and magnetic field (p denotes density), (e) denotes the magnetic fluctuation correlation length, (v~) is a mean beam speed, and P is the probability that a particular section of length (g) is quasi-radial. 3. DISCUSSION, I M P L I C A T I O N S AND CONCLUSIONS Consider the region C for which L ~ (g) and use values Z 2 ~ 2.5 x 10 s m 2 s -2 (g) ~ 2 x 10 9 m, (vb)~ 6 x 10 s m s

-1 .

Then c (F) ~ 5 x 10-' P .... s "1, and (F) = -4 • 10-~ s 1 for the polar regions. The characteristic interaction time for waves in a region with size (g) is tg = 5 x 10 4 s = 14 hours, during which time a number ng((g)) = P ( V b ) / V A ~ 30P of beam

+m

inhomogeneities with characteristic time scale t i = P(e)/(Yb) ~ 1667P s 0.46P hours should pass through. It is important that 1; this

n~((e))>>

o

o

Figure 1. Snapshot of the interplanetary magnetic field, illustrating local departures from the mean IMF (B) and the different newborn pickup ion distributions from region to region. Local newborn velocity space distributions are shown below the magnetic field sketch for regions 1 - 5 and C, showing how distributions range from beam to ring. The horizontal axis in each phase space plot is v, (i.e., particle speed parallel to the local

indicates that the system should indeed evolve to an SGT state close to marginal stability and suggests that the SGT model developed above is self-consistent. The SGT model also predicts the degree ofburstyness of the waves, the characteristic time scale for the SGT inhomogeneities in the pickup ion distributions, and the characteristic size of regions where pickup ion-driven waves might be observable.

The growth rate of the unstable low frequency waves may be estimated [ 1] using F << co ~ (V~/Usw)f~, where f2 is the pickup ion gyrofrequency and co the solar wind frame frequency. At ~3 AU, co r ~ 7 X 10 -4 S-~ , r

-

127-

G.P. Zank and I.H. Cairns

from which F _<10 - 4 S -1 is a reasonable estimate. We use F = 5 x 10 -5s -~ below. Note that o(F) = 5 • 10-~s-' = F, so that this value of F is quite reasonable, as is the value for o(F). Suppose the magnetic field within C is oriented randomly, and, for example, the normalized standard deviation from the mean magnetic field is 30 ~ In this case, P ~ 0.68 and ~ ( F ) / ( F ) ~ 14.5. The number of beam inhomogeneities interacting with C is ng((g)) ~ 20.4, each of which has a characteristic time scale tg ~ 1134s = 0.32 hours. If,

fortuitously, the beams arrive almost successively to interact with C, so giving a total interaction time -~ 2 x 104 s, we can expect large wave amplification within C (since Ft i ~ 1). However, since o ( F ) / ( F ) i s large, substantial wave amplification will be infrequent and wave enhancements will have a bursty character. The conclusions for the I"1= 30 ~ case continue to hold for an IMF with a smaller variance in local departures from the radial mean field direction. However, if the mean IMF is close to radial but the variance is large e.g., 11 = 60 ~ we find that the number of beams ng((g)) is reduced (~11.5) and ti is correspondingly smaller (~637s), so making effective wave amplification more bursty and less likely to be observable (since ~ ( F ) / ( F ) ~ 19.4). In summary, our results support an SGT description of pickup ions and associated MHD waves. The consequent closeness of the system to marginal stability (averaged over time and volume) and the associated arguments for the preservation of beam-like distributions of pickup ions immediately provides a qualitative explanation for the observed pickup ion anisotropies. The primary conclusion to emerge from this study is that the dynamical character of the quasi-radial polar IMF prevents the formation of statistically steady-state pickup ion driven wave enhancements in the magnetic fluctuation spectra. The parameter controlling the frequency of wave enhancements is the variance in the orientation of the fluctuating IMF about the mean radial field. We find that even were the mean field radial, a large standard deviation from the radial direction in the local IMF fluctuations on the length scale of the correlation length would lead to very little effective wave growth. Thus, the SGT model predicts bursty wave growth in polar regions with, first, quasiradial IMF direction and, second, magnetic fluctuations that possess only a small variance in direction from the mean field direction. Such an intermittent and bursty character for pickup ion driven turbulence in the polar solar wind must therefore make the detection of individual wave events difficult. Additionally, the model predicts a bursty, intermittent character for the pickup ion distribution, with preservation of beam-like features and anisotropies in particular. Further details can be found in [6]. REFERENCES 1.

2. 3. 4. 5. 6. 7. 8.

Zank, G.P., Space Sci. Rev., 89 (1999), 413. Smith, E.J., et al., EOS Trans. AGU, 75(16), Spring Meeting Suppl. (1994), $297. Murphy, N., et al., Space Sci. Rev., 72 (1995) 447. Intriligator, D.S., G.L. Siscoe, and W.D. Miller, Geophys. Res. Lett., 23 (1996) 2181. Zank, G.P., Matthaeus, W.H., & Smith, C.W., J. Geophys. Res., 101, (1996) 17 081. Zank, G.P. and I.H. Cairns, Ap.J., 541, (2000), 489. Cairns, I.H., and P.A. Robinson, Phys. Rev. Lett., 82, (1999) 3066. Gary, S.P., Theory of Space Plasma Microinstabilities, Cambridge, 1993.

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A time-dependent, 3D model of interstellar hydrogen distribution in the inner heliosphere M. Bzowski ~ *, T. Summanen b, D. Rucifiski ~, and E. KyrSls b ~Space Research Centre PAS, Bartycka 18A, 00-716 Warsaw, Poland bFinnish Meteorological Institute, Vuorikatu 15A, 00101 Helsinki, Finland

1. M O D E L The density of interstellar hydrogen in a local point in the inner heliosphere is calculated as a 3D numerical integral of the distribution function composed of a Maxwellian shifted by the bulk velocity vector at infinity, multiplied by the probability of survival of a test atom against 2D, time dependent ionisation during the travel from "infinity" to a local point. The link between the distribution function in the local point and in "infinity" and the probability of survival of the test atom against ionisation are calculated by numerical tracking of the atom travelling in a time- and latitude-dependent ionization field under dynamic influence of the solar gravity and spherically symmetric, time dependent radiation pressure. The concept of the numerical method used was presented by Rucifiski & Bzowski (1995). The models of temporal evolution of the solar Lyman-a radiation pressure and of the time- and latitude dependence of the photoionisation efficiency and of the rate of charge exchange of the hydrogen atoms with the solar wind protons are discussed in the companion paper (Bzowski, this volume). 2. C A L C U L A T I O N S Throughout the paper we used two latitudinal profiles of the ionization rate discussed in the companion paper and two sets of bulk velocity and temperature of the interstellar warm and slow gas) and (VB = 25 km/s, gas at infinity: (VB = 20 km/s, T~ = 12000 K T~ = 7500 K); the ecliptic coordinates of the inflow direction were assumed (AB,/~B) = (252.4~ 7.5~ The calculations were performed in the following three planes: (i) the ecliptic plane; (ii) the polar plane, i.e. the plane perpendicular to the ecliptic and including the inflow direction the scan starts upwind and goes through the north ecliptic pole, downwind direction and the south pole back to the upwind direction; and (iii) the crosswind plane, i.e. the plane perpendicular to the inflow direction and containing the Sun. None of the latter two planes goes through the heliographic poles, the minimum distance is ~ 8~ *M.B.

and D.R. were supported by a Polish State Committee for Scientific Research grant 2P03C 004 14

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3. H Y D R O G E N

DENSITY DISTRIBUTION

The asymmetry of the ionisation rate eliminates the axial symmetry of hydrogen density distribution (see e.g. Summanen 1996). Indeed, a considerable pole-to-ecliptic asymmetry in density extends to about 25 AU from the Sun, where it is still equal to ~ 1.05. Closer to the Sun, the ratio varies from ~ 1.2 to ~ 1.3 at 10 AU and from ~ 1.5 to ~ 2 at 2.5 AU, depending on the phase of solar cycle. Hence also the hydrogen cavity, defined as the region where the gas density is lower than 1/e of density at infinity, is asymmetric. This asymmetry changes with time. The size of the cavity from upwind to downwind, from pole to pole and in-ecliptic varies by ~ 30% during the solar cycle, as shown in Fig.1. and it depends quite strongly on the gas parameters at infinity.

Figure 1. Mean hydrogen cavity (thick ovals) in the three scan planes, superimposed on isocontours of 10% (light), 25% (medium), and 50% (dark) variability amplitude. In the lower-right panel: evolution of the cavity size in time for the warm and slow gas (solid lines) and cool and fast gas (broken lines).

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A time-dependent, 3D model of interstellar hydrogen distribution...

Crosswind scan, relative intensity profiles

Polar scan, relative intensityprofiles 1.1

1.25

1.05 "~

1.3 rectangular bulge

.~ 1.2

1

"~ 0.95

~ 1.15

~

o.9

~. 1.1

0.85

1.05

0.8 -75 -50 -25 0 25 50 ecliptic latitude/3

-75 -50 -25 0 25 50 ecliptic latitude/3

75

75

Figure 2. Profiles of backscattered intensity in the polar scan (upwind hemisphere) and crosswind scan, normalised to the intensity at solar minimum respectively in the upwind and crosswind in-ecliptic directions, for the warm and slow gas and two different profiles of the ionization rate.

The amplitude of density variations, defined as maximum deviation of the local density from the local density averaged over time, is also presented in Fig.1. In the upwind hemisphere, the mean cavity almost coincides with the region where the amplitude of density variations exceeds 25%. The 50% amplitude region coincides roughly with the positions of peaks of the emissivity function along heliocentric lines of sight and it contains the orbit of Ulysses. 4. E F F E C T S I N I N T E N S I T Y

OF BACKSCATTERED

RADIATION

The intensities of the solar Lyman-a radiation backscattered by the neutral interstellar hydrogen were calculated with the use of the optically thin approximation along hellocentric lines of sight from 1 AU. The calculated intensity patterns vary in time and reproduce qualitatively the groove patterns observed by SWAN on SOHO during the solar minimum (KyrS1/i et al. 1998; Bertaux et al. 1999) (see Fig.2, left-hand panel). The shape of the profile is sensitive to the adopted latitudinal profile of the ionisation rate (Fig.2, right-hand panel). However, during the solar miaxnimum the groove seems to have disappeared from SWAN images, which suggests that contrary to the ionization model adopted, the solar wind is symmetric during that phase. The profiles of the ratio of backscattered intensity at various latitudes to the intensity at crosswind in ecliptic show correlation with the ionisation model. The intensity distribution has some north-to-south asymmetry (see particularly Fig.2, right-hand panel) although the ionisation model used is symmetric about the solar equator. This is caused by the tilt of the gas inflow direction to the solar equator.

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M. Bzowski et aL Pole-to-ecliptic intensityratio

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~ 1.4 o

9

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.

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,

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.

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.

Intensity at pole and ecliptic 1.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I_pol/ 1.3 1.2 A 1.1

.

/3_ratio

i

"~ 1.2

9 ,...i

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.

.

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.

,

,

i

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,

i

1986 1988 1990 1992 1994 1996 1998 2000 time [y]

0.9 0.8 0.7 1986 1988 1990 1992 1994 1996 1998 2000 time [y]

Figure 3. Correlation of Irati o intensity ratios for warm and slow gas, gaussian bulge model with the/~ratio ionisation efficiency ratio is clearly visible in the left-hand panel (see Equ.(1) for definitions). Ipole/{/pole} and Ie~l/(Iec]) values for 90 ~ off the upwind direction are presented in the right-hand panel. The quantities practically do not depend on the gas parameters at infinity.

The ratio of intensities above the poles to intensities in ecliptic in the crosswind plane is strongly correlated with the ratio of hydrogen ionisation rate in ecliptic to the rate at the pole. In Fig.3 the evolution of quantities Ir~tio and/~ratio is presented, where

/ratio -- /pole (t) / (/pole} and /~ratio -- /~ecl (t) / (/~ecl) /eel (t) / (Iecl} ~pole (t) / (/~pole)

(1)

and (/pole}, (/ecl)and (/3pole),
Bertaux, J.-L., KyrS1/i, E., Qu~merais, E., Lallement, R., Schmidt, W., Summanen, T., Costa, J., & MS&inen, T. 1999, Space Sci. Rev., 87, 129 KyrS1/i, E., Summanen, T., Schmidt, W., Mgkinen, T., Bertaux, J. L., Lallement, R., Qu~merais, E., & Costa, J. 1998, J. Geophys. Res., 103, 14523 Rucifiski, D. & Bzowski, M. 1995, Astron. Astrophys., 296, 248 Summanen, T. 1996, Astron. Astrophys., 314, 663

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L y m a n ct i n t e n s i t y p a t t e r n in t h e inflow d i r e c t i o n of t h e i n t e r s t e l l a r g a s T. Summanen a , T. M~ikinen, E. Kyrhl~i and W. Schmidt aFinnish Meteorological Institute, P.O. Box 503, 00101 Helsinki, Finland Theoretical results by Summanen[1] showed that the local minimum of the interplanetary Lyman ce intensity in the inflow direction of the interstellar gas (wind direction), while observed in the sidewind direction at 1 AU and when high ionization rate is assumed near the heliomagnetic equator, disappears when the tilt angle of the heliomagnetic equator with respect to the heliographic equator is approximately 20 ~ Interplanetary Lyman c~ data measured by SWAN shows that the minimum in the interplanetary Lyman c~ intensities in the inflow direction disappeared in 1998. The maximum extent of the heliosperic current sheet, calculated using the radial and the classic potential field models from the photospheric field observations ([2], [3]) grew from 20 ~ to 60 ~ and from 40 ~ to 75 ~, respectively, in 1998. Thus, results show that the ionization rate which varies according to the heliomagnetic equator is sufficient to explain the disappearance of the local minimum in the interplanetary Lyman ce intensity data measured by SWAN around 1998. 1. I N T R O D U C T I O N The presence of the "groove", the local minimum in the interplanetary Lyman ce intensities near the inflow direction of the interstellar gas during the solar minimum in Prognoz-5 observations, was pointed out by Bertaux et al.[4]. They proposed that the depth of the groove depends on the configuration of the heliospheric current sheet around the heliographic equator. In the observations of OGO 5 there was seen one Lyman c~ intensity maximum in the inflow direction in 1969 and 1970 ([5], [6]). Thus, it was plausible, that a change from the groove to one maximum pattern would be seen also during this solar cycle. In this work we have compared theoretical results by Summanen [1], concerning the Lyman ce intensities in the inflow direction when the ionization rate varies as a function of the heliomagnetic latitude, to the observations of the SWAN (Solar Wind ANisotropies) instrument. 2. O B S E R V A T I O N S O F S W A N SWAN instrument [7] onboard the SOHO satellite has measured interplanetary Lyman c~ intensities in all directions of the sky since January 1996. Figure 1 shows SWAN data in the directions where the ecliptic longitude is 253 ~. The data is shown in two

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T. Summanen et al.

Figure 1. SWAN observations in the directions of the ecliptic longitude 253 ~.

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Charge exchange ionization rate of interplanetary hydrogen atoms... parts, the first is measured during Jan 21, 1996- Jun 24, 1998. The second part is measured after the failure and recovery of SOHO during Nov 20, 1998 - Nov 27, 1999. Note that, the sensitivity level of SWAN sensors changed during the data gap. The actual intensity levels of the recent measurements as compared to the earlier measurements are not known, because the Lyman ~ intensity of the Sun also changed during the failure. We have adjusted the level of the intensity to reflect the solar activity increase. In the first part of Figure 1 there is the local minimum present near the ecliptic plane almost all the time shown blue and magenta. In the second part of the figure this minimum is no longer present. It is difficult to say when exactly the local minimum disappears, because the observation direction is obscured by the satellite near the edge of the first part and by the Sun at the beginning of the measurements in the second part. There is also a large data gap in the second part. However, we can say that the local minimum is not visible in the data any more in 1999.

~

9

~

1200

60

:t

" ~,, 'l,J

400 N

0

Figure 2. Theoretically calculated interplanetary Lyman c~ intensities in the inflow direction of the interstellar wind (ecliptic longitude 254.5~ The distance of the observation point from the Sun is 1 AU, its ecliptic longitude is 164.5 ~ and ecliptic latitude is 0 ~

Figure 3. Maximum extents of the heliospheric current sheet calculated using T. Hoeksema's [2], [3] radial (solid line) and classic (dashed line) potential field model.

3. D I S C U S S I O N Summanen [1] calculated the interplanetary Lyman ~ intensities near the inflow direction of the interstellar gas using the hot model for the calculation of the interplanetary hydrogen density and an optically thin model for the calculation of the interplanetary Lyman c~ intensity. In the optically thin model the intensity is calculated as a line-of-sight integral over the density along the line, the phase function and a g-factor corresponding

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a flat solar Lyman ~ line profile. Details are presented for example in [8]. The calculation of the ionisation factor of the interplanetary hydrogen atoms was modified to take into account the changing ionisation probability of an atom on its path through the solar system, when the ionisation rate of the interplanetary hydrogen atoms is assumed to vary as a function of the heliomagnetic latitude. In the calculations the ionization rate of the interplanetary hydrogen was assumed to vary from 3.05x10 -~ s -1 (approximately from +90 ~ to -4-30~ of heliomagnetic latitude) to 7.0x10 -7 s -1 (at the heliomagnetic equator). The distance of the observation point from the Sun was 1 AU and its ecliptic longitude was 164.5~ and ecliptic latitude was 0 ~ Other parameters used in the calculations are given in [1]. Figure 2 shows (keeping in mind the assumptions of the hot model, the optically thin model and the used ionisation rate) that the local minimum in the interstellar wind direction disappears when the tilt angle of the heliomagnetic equator with respect to the heliographic equator is around 20 ~ Figure 3 shows the maximum extent of the heliospheric current sheet using data from [2]. It shows that the maximum extent of heliospheric current sheet increased from 20 ~ to 60 ~ according to the radial model and from 40 ~ to 75 ~ classic potential field model calculated using photospheric field observations [3] in 1998. The comparison of the results presented in Figures 1, 2 and 3 show that the assumption of the ionisation rate which varies according to the heliomagnetic equator is sufficient to explain the disappearence of the local minimum in the interplanetary Lyman c~ intensity data measured by SWAN around 1998. However, a full analysis of the disappearance of the groove would require a model which take into account the change of the tilt angle as a function of the solar cycle. 4. A C K N O W L E D G E M E N T S The authors thank Todd Hoeksema for the data used in the Figure 3 and Academy of Finland for supporting this work. REFERENCES 1. T. Summanen, Astrophys. and Space Sci. 274, 2000, 143. 2. J. T. Hoeksema, The Wilcox Solar Observatory www-pages, http://quake.stanford.edu/-wso/Tilts.html, visited July, 2000. 3. J . T . Hoeksema, Solar Wind Seven, COSPAR Colloquia Series Vol. 3, eds. E. Marsch and R. Schwenn, Pergamon Press, 191, 1992. 4. J.L. Bertaux, E. Qu~merais and R. Lallement, Geophys. Res. Lett. 23, 1996, 3675. 5. J.L. Bertaux and J. E. Blamont, Astron. Astrophys. 11, 1971, 200. 6. G.E. Thomas and R. F. Krassa, Astron. Astrophys. 11, 1971, 218. 7. J . L . Bertaux, E. KyrSl~i, E. Qu(~merais, R. Pellinen, R. Lallement, W. Schmidt, M. Berth~, E. Dimarellis, J. P. Goutail, C. Taulemesse, C. Bernard, G. Leppelmeier, T. Summanen, H. Hannula, H. Huomo, V. Kelh~i, S. Korpela, K. Lepp~il~i, E. StrSmmer, J. Torsti, K. Viherkanto, J. F. Hochedez, G. Chretiennot, R. Peyroux and T. Holzer, Solar Phys. 162, 1995, 403. 8. T. Summanen, R. Lallement and J.-L. Bertaux, J. Geophys. Res. 98, 1993, 13 215.

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N e w R e s u l t s d e r i v e d from P i o n e e r 10/11 U V d a t a Horst Scherer ~ and Klaus Scherer b ~Institut ffir Astrophysik und Extraterrestrische Forschung der Universitgt Bonn, Auf dem Hiigel 71, 53121 Bonn, Germany bdat-hex, Torstrafie 3, 37191 Katlenburg-Lindau, Germany In earlier endeavors the Pioneer 10/11 resonantly backscattered hydrogen (1215 /~) and helium (584 ~) UV glow data from the interplanetary medium had been studied in low spatial and time resolution (except at and during planetary encounters). We have now completely reanalyzed the Pioneer 10/11 UV-data from launch towards 1990, which enabled us to study highly resolved data in up to now unknown details. From the combined hydrogen and helium data over the entire period we can show that the optical thin models are good approximations also for the hydrogen. As example for the highly resolved spatial data we show the region of the highest intensities of resonant hydrogen and helium glow close to the direction of the inflowing interstellar medium. 1. T h e d a t a analysis The Pioneer 10/11 UV instruments are mounted with an angular offset onto the spinning spacecraft. It described in detail in Carlson and Judge 1994 [1]. Every two spin periods the data collection switches between the hydrogen and helium channels, which is difficult to handle when the synchronization is lost. We reanalyzed raw data with an improved algorithm, including corrections for the dead currents, and especially, the handling of the data at the boundary between the collection of the hydrogen and helium data. The results are presented in the following figures. 2. T h e i n t e r p l a n e t a r y glow Before 1974 the events in both panels are most probably connected with planetary objects, while the events after 1974 are caused by stars. The helium channel shows an optically thin behavior weakly modulated by the solar cycle. Beyond 1984 the helium channel is contamined by cosmic rays and shows therefore an unusual strong increase [3]. In the hydrogen channel the solar cycle modulation is more prominent. The ratio between the helium and hydrogen intensities are constant until 1984 when the cosmic ray contamination of the helium channel begins. Beside this contamination, it follows from the constant ratio between the hydrogen and helium data that also hydrogen can be fairly well modeled by an optical thin approxi-

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H. Scherer and K. Scherer

distance (~ 30 AU) over the period 1972 to 1984. In the left panel the glow intensities observed by Pioneer 11 are shown. As it can be seen the hydrogen chanel deviates from all known models (e.g. [2]). This may be caused by a degradation of the instrument beginning at 1977. Nevertheless, the helium data show the same behavior as for the Pioneer 10 data, except that there is no modulation caused by the cosmic rays, because Pioneer 11 has not reached large heliocentric distances during solar minium. Hence, the low energetic cosmic rays could not reach the spacecraft and contamine the data. 3. P l a n e t a r y and i n t e r p l a n e t a r y f e a t u r e s

In left panel of Fig. 2 an one minute clock angle average for the one year period 1972 is shown. It can be seen in the left panel of Fig 2, that there are some objects in the field of view. A precise identification of the objects is at the moment not possible because of problems with the old position data. Nevertheless, a preliminary identification can be made: day

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New results derived from Pioneer 10/11 UV data

136-138 (see right panel of Fig: 2) is most probably connected with the most emission region, expected in the direction of the inflowing interstellar medium, while during day 152-153 and day 218-225 the Jovian system comes into the field of view. For the days 219-221 in 1972 this is further resolved in Fig 3, where the 5 m i n time averaged spatially resolved H-Lyman-a (left panel) and helium (right panel) data are shown. The x- and y-axes show the heliocentric longitude and latitude in degrees, respectively. The intensity given in Rayleigh is color-coded. The start points of the 5 min. intervals are given by the numbers inside the circles. Gaps are caused by missing data. The intensity increase of the H-Lyman-a glow begins later than the intensity increase in the short-wave channel. This is caused by the fact that the Io-torus is in the ecliptic by a factor 5 more extended than Jupiter. Moreover, Jupiter is more or less a point source, which is indicated by the 'hot spot' in the left figure between 18:55 to 21:55. The short-wave channel does not show such features, but the intensity is completely smeared out through the entire circles, caused by the enlarged structure of the Io-torus. 4. S u m m a r y

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H. Scherer and K. Scherer

backscattered interplanetary glow can be modeled by a optical thin approximation. Additionally, we have presented highly spatial and time resolved observations of the Jovian system. We found that the intensity of the hydrogen channel is most probably caused by Jupiters glow, while the short-wave channel is dominated by the emission lines of different elements in the Io-torus-plasma. To our knowledge, this is the first time that simultaneous observations in the hydrogen and helium glow were presented, except during planetary encounters. Acknowledgment

We are gratefully to Prof. Dr. Darrell L. Judge, who provided us with the raw data of Pioneer 10/11 UV-instruments. REFERENCES 1. Carlson, R.W., Judge, D.L., J.Geophys. Res. 79, (1974), 3623 2. Scherer, H., in: The Outer Heliosphere: Beyond the Planets (Eds. Scherer,K., Fichtner, H., Marsch, E., Copernicus Gesellschaft, (2000), 91-138 3. Scherer, K., Scherer, H., private communication, 2000

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Oral papers and posters

C O M P O S I T I O N A N D C H A R A C T E R I S T I C S OF T H E L O C A L INTERSTELLAR CLOUD AND THE INNER SOURCE OBTAINED F R O M P I C K U P IONS G. Gloeckler Department of Physics and IPST, University of Maryland, Department of Oceanic, Atmospheric and Space Sciences, University of Michigan.

Local Interstellar Cloud (LIC) and of the newly discovered "Inner Source". Knowledge gained from this work will be reviewed with an emphasis on LIC characteristics, such as the isotopic and elemental composition of the LIC gas, its density, temperature and ionization state, and limits on the strength of the LIC magnetic field. Future directions for further dramatic advances in pickup ion observations will also be discussed. published in: Space Sci. Rev., in press, 2001

H A T O M V E L O C I T Y D I S T R I B U T I O N S IN H E L I O S P H E R I C INTERFACE V. V. I z m o d e n o v (1), Yu. G. Malama (2), M. Gruntman (3) and R. Lallement (4) (1) Department of Aeromechanics and Gas Dynamics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Vorob'evy Gory, Moscow, 119899, Russia, (2) Institute for Problems in Mechanics, Moscow, Russia, (3) University of Southern California, Los Angeles, California, (4) Service d'A6ronomie, Verrieres-le-Buisson, France. We study evolution of the velocity distribution function of interstellar neutral gas in the heliospheric interface, the region of the solar and interstellar wind interaction. We numerically solve the kinetic equation for neutral gas selfconsistently with hydrodynamical equations for plasma. Neutral and plasma components interact by charge-exchange. This interaction disturbs of atom velocity distribution, which is assumed Maxwellian in the circumsolar interstellar medium. To describe a complex of velocity distribution of interstellar atoms in the heliospheric interface we introduce three atom populations in addition to the primary interstellar neutrals. We present velocity distributions of these populations and discuss their kinetic properties.

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E S T I M A T I O N OF I N T E R P L A N E T A R Y H Y D R O G E N F L O W PAR A M E T E R S F R O M S W A N L Y M A N c~ O B S E R V A T I O N S E. KyrSl~i (1), J. Jaatinen (1), T. Summanen (1), W. Schmidt (1), T. M~kinen (1), R. Lallement (2), E. Quemerais (2), J. Costa (2) and J . L . Bertaux (2) (1) Finnish Meteorological Institute, Geophysical Research Division, P.O. Box 503, FIN-00101 Helsinki, Finland, (2) Service d'Aeronomie du CNRS, BP. 3, 91371 Verrieres-le-Buisson, France. The SWAN instrument on board SOHO has measured the full sky distribution of Lyman ~ radiation since the beginning of 1996. The full sky coverage and the possibility to obtain spectral measurements by using the hydrogen cells of SWAN make it possible to investigate parameters controlling the flow of interstellar hydrogen through the heliosphere. Here we present results from the fitting of a single-scattering model of the interplanetary Lyman alpha radiation to SWAN spectral data. The new results, that still have considerable uncertainties, show that the inflow direction is 253 deg (longitude) and 11 deg (latitude) that differ only slightly from the earlier results. The same is true for the average inflow velocity, 21 km/s. The unperturbed temperature of the gas, 12000 K, is, however, much larger than previously estimated. The ratio between the radiation pressure and the gravitational attraction was estimated to be 0.99 indicating nearly force-free propagation of H-atoms in the interplanetary space. The data used in this analysis are from measurements obtained during the solar minimum in 1996 and measurement directions are toward areas in the sky that are void of stars.

I N F L U E N C E OF A T I M E V A R I A B L E S O L A R H - L Y M A N ALPHA LINE PROFILE ON LISM-PARAMETER DEDUCTIONS FROM INTERPLANETARY GLOW SPECTRA

THE

H. Scherer (1), H.J. Fahr (1), M. Bzowski (2) and D. Rucifiski (2) (1) Auf dem Hiigel 71, 53121 Bonn, Germany, (2) Space Research Centre of the Polish Academy of Sciences, Bartycka 18 A, PL-00-716 Warsaw, Poland. During a period of 18 months 5 Hubble-Space-Telescope-GHRS interplanetary HLyc~ glow spectra were obtained with different lines of sight from different positions of the earth in its orbit. No common parameter set for density, temperature and velocity of the interstellar hydrogen could be decuced from these Hubble-space-Telescope data. Despite application of a radiation transport model with angle-dependent partial frequency redistribution, selfabsorption by interplanetary hydrogen, realistic solar HLya emission profile, and a time-dependent hydrogen model there still remain some distinct discrepancies between data and the theoretical description, mainly manifest over time scales of the order of a year. These residuals could be explained by possible variations in time of the spectral shape of the solar HLy~ line profile, adopted in earlier attempts of data-interpretation as constant when modeling the radiation pressure and the resonance intensities. The influence of such a variation in time of the solar HLya line profile on the spectral shift of the peak of modeled intensity spectra is tested. Also, the influence on frequency integrated line of sight intensities is checked. Thereby, the possibility to see the effect of such a variation in time of the solar HLya line profile in older data sets (e.g. Pioneer 10/ 11 glow data) is proven.

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General Discussion Judge to Quemerais: Isn't your measurement depending on the direction of the scan? Quemerais: Yes. So, one thing will be to try directions different from those we had before. Zank to Quemerais: Can you actually look in all directions? Quemerais: No, we don't have the time to make full coverage of the sky. Sreenivasan to McNutt: Have you tried Lattice-Boltzmann techniques? McNutt: No, we haven't used the Lattice-Boltzmann approach. Jokipii to McNutt: I think you are really optimistic on this going to the next order in kinetic theory. There is a magnetic field threading through all of this, you got to have 81 viscosity coefficients to worry about, and there is anisotropic transport. McNutt: I won't argue that point with you. But right now I have just been talking about going to the next order just in the neutral component, so you are not worried about the magnetic field. Jokipii to McNutt: If you are talking about the neutral gas, your mean-free-path is of the size of the system. McNutt: It's interesting to look into the problems of radiation transfer in stellar atmospheres that were solved back a few decades ago. If you look at that treatment of kinetic t h e o r y - it also comes up in neutron kinetic t h e o r y - it turns out that one can actually get rigorous solutions to the kinetic equations that are good down to 1/10 of the meanfree-path. Fahr to Baranov: There is something which you did not take into account, namely the fact that - by producing new ions - you produce a new proton population which doesn't go the way the other protons go. So, you have more or less a two-stream instability situation and you can drive instabilities as well as have a change in the electrical conductivity of the plasma. That may mean you have to apply non-ideal MHD by including an anonalous resistivity. Baranov: Thank you very much for this recommendation. Bzowski to Kyr61g: The radiation pressure value you derived agrees perfectly with the value I derived in my radiation pressure model based on totally independent measurements. What concerns the ionization rate, in the ecliptic I have a slightly higher value in my model, namely 5 x 10 -7 rather than your 4 to 4.5. KyrSlg: Ours was not in the e c l i p t i c - it was at high latitudes. We avoided the ecliptic because of the solar wind anisotropy which poses a more complicated problem. Zank to Gloeckler: You began by showing interstellar pick-up ions as tails of the distributions. Do you see those same tails on the distribution of the inner source ions during quiet periods and do you see similar anisotropies of the inner source? Gloeckler: The inner source is getting pretty weak in the tail, and we are too far away from the inner source. Solar Probe would be good for studying this.

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General Discussion

Gruntman to M5bius: A lot of pick-up ions are born within 1 AU [and, therefore, are not interstellar]. What about them? MSbius: Yes, this is a good point. We haven't modelled that yet. Lee to Gloeckler: I was trying to think about the really outstanding problems in the transport of interstellar pick-up ions and two came to my mind. One is these very large time variations in the intensities of, in particular, h e l i u m - larger than you would expect from the changes of the UV radiation. The other is these very high energy tails and the puzzling fact that they are not observed in the high-speed streams but in the in-ecliptic low-speed streams. What is the acceleration mechanisms? I know that Len Fisk has suggested transit-time damping but why doesn't it really occur in the high-speed streams? Gloeckler: Regarding the tails, after all, the fast wind is very smooth - the density, temperature and other solar wind parameters, like the ratio of protons and alphas, are very constant with a least amount of fluctuations. So, Len Fisk would probably a~'ee that there is also a different level of turbulence. As to the first p r o b l e m - these puzzling large variations in the pick-up ion fluxes- I don't know the answer to that. Question to Khisamutdinov: Which term is used in your model for charge exchange cross section? Khisamutdinov: In our new method of modelling the general property of a monotonic non-decreasing function was used.

Session 3: Messengers from Outside

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The d i s c o v e r y a n d early d e v e l o p m e n t of the field of a n o m a l o u s c o s m i c rays H. Moraal School of Physics, Potchefstroom University for CHE, Potchefstroom 2520, South Africa, fskhmC~uknet, puk.ac.za This contribution is the first of three that review the discipline of anomalous cosmic rays. This paper concentrates on the discovery of anomalous cosmic rays in 1973 and the first 20 years of observation, modelling, and the early theoretical understanding of the subject, with the emphasis on the latter. The papers of Heber and Cummings (2001) and le Roux (2001) that follow after this one, respectively review the subsequent experimental and theoretical developments. 1.

DISCOVERY

Anomalous cosmic rays were discovered by Garcia-Munoz et al. (1973), who announced that four points on the Helium spectrum, between 20 and 50 MeWnucleon, observed on the IMP5 satellite during 1972, lay much higher than expected. In Figure 1 these points are marked by the letters A, B, C, and D, and it shows that the He intensity is so high that it exceeds even that of protons. It also deviates strongly from the form proportional to kinetic energy, which is the expected shape in the adiabatic limit of cosmic ray transport.

Figure 1. Proton and helium spectra observed by Garcia-Munoz et al. (1973), in which the data points marked A, B, C, and D show the anomalous character of the Helium spectrum.

:* 9 10

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The authors drew attention to the tact that this behaviour had not been seen during the previous solar minimum in 1965, and noted that it could not be explained with "previously successful boundary conditions" for the cosmic ray transport equation. In a subsequent paper, Hovestadt et al. (1973) observed a high Oxygen intensity between 1 and 6 MeWnucleon, higher than expected from inferences from 1965 and 1969 measurements, and from the steep spectra of solar energetic particles below this energy range. These points are marked A, B, C in Figure 2 (left). It was uncertain whether the two Carbon measurements, D and E, were also enhanced, because they were upper limits. In this paper, little inference could be drawn about the origin of these particles.

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H. Moraal

The first definite combined m e a s u r e m e n t and interpretation of this new feature in cosmic ray spectra came from McDonald et al. (1974), who observed that O (and N) spectra were strongly enhanced relative to C and He at 3 to 30 MeV/nucleon. This is shown in Figure 2 (right), with the enhanced O points marked as A, B, C, D, and E. This paper seems to be the first one to use the term "anomalous" for these cosmic rays, a name by which they are still known. This term "anomalous" refers to the unexpected composition rather than to the spectral shape. This is an important distinction, namely that the O and N abundances are anomalously high relative to that of C (and even He). If all species had spectra that strongly deviated from the then well-known ':] ~ T " adiabatic limit, there would have been no story to tell, because one simply would have to search for a different rigidity dependence of the modulation. The true anomaly of these observations was that species like O and N, and to some extent He, showed abnormal abundances, but that others, notably, C and H did not. McDonald et al. (1974) also used observations from Pioneer 10, which was at a radial distance of a few AU, to infer that the radial gradient of these anomalous components was slightly positive. This excluded a solar origin, because then the gradient would have been strongly negative. On the basis of this evidence the authors concluded that "....this is most likely a new extrasolar component of cosmic rays". Figure 2. Spectra observed by Hovestadt et (1973) (left panel) al. which shows high Oxygen intensities marked by A, B, and C, and possibly high Carbon intensities, marked by D and E. The right panel by McDonald et al. (1974) definitely shows anomalously high Oxygen intensities (points A to E), but no high Carbon intensities.

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........

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2.

I N T E R P R E T A T I O N AND T H E D E V E L O P M E N T OF A D I S C I P L I N E

Fisk et al. (1974) almost immediately came forward with an interpretation for the anomalous species, namely that they originated as interstellar neutral atoms, of species with high first ionisation potentials, which became singly ionised in the inner heliosphere, picked up by the heliospheric magnetic field and solar wind, and subsequently accelerated to cosmic ray energies. The acceleration mechanism itself was not specified in this first paper. This proposal of Fisk et al. connected three independent fields of study, which were only weakly developed at the time, namely (a) the properties and transport of neutral particles in the heliosphere, (b) the acceleration of low energy particles to cosmic ray energies, and (c) cosmic ray transport. Of these three, cosmic ray transport was perhaps the best understood, and it took a surprisingly long time to unify these fields to establish the anomalous cosmic ray paradigm. Figure 3 is a timeline of discovery that shows how the fields of anomalous cosmic rays, pick-up ions in the solar wind, shock drift acceleration, and cosmic ray transport theory

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The discovery and early development of the field of anomalous cosmic rays

ACR

Titneline

Figure 3. Timeline of discoveries in the field of anomalous cosmic rays were integrated over a period of 20 years into this single discipline. This paper is organised according to this diagram. Each of the discoveries marked on it will be discussed. Four of them are highlighted in heavy boxes, because I regard them as landmarks. They are (i) the ACR discovery itself (described in Section 1 above), (ii) the discovery of first order Fermi acceleration, also known as compressive shock acceleration, in 1977, (iii) the first unambiguous observation of pick-up ions, which are the seed particles of ACR's, in the solar wind, in 1985, and (iv) the determination of the charge state in the early 1990's 3.

PICKUP

IONS IN THE SOLAR WIND

The Fisk et al. (1974) hypothesis implies that the ultimate source of anomalous cosmic rays is neutral interstellar gas that is ionised in the inner heliosphere. This gas sweeps relatively freely through the heliosphere, due to the 25 km/s motion of the heliosphere

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H. Moraal

relative to its interstellar environment. When these particles get near enough to the sun they become singly ionised, mainly due to charge exchange with particles of the solar wind, the density of which falls off as 1/r ~ with radial distance r, as well as through photo-ionisation. In the early 1970's the properties of this singly charged component was studied by authors such as Axford (1972), Bertaux and Blamont (1972), Fahr (1968, 1972), and Thomas (1972). The main motivation for these studies was the effect that this freshly ionised interstellar component might have on the solar wind flow beyond several AU - the so-called mass loading effect. Calculations such as those by Axford (1972) showed that typical mean penetrating distances before ionisation should be 3 to 4 AU for H, O, and N (with first ionisation potentials of the order of 14 eV), while He (24,6 eV) easily penetrates to 0,5 AU, where the probability for photo-ionisation also becomes large. The presence of these pick-up ions could be indirectly inferred from the UV backscatter of radiation from the interstellar neutrals. Vasyliunas and Siscoe (1976), however, calculated the spatial distribution and energy spectrum of these ions, with the view to see whether they could be detected directly. The principle behind the development of the energy spectrum is illustrated in Figure 4. The top left panel shows that when the interstellar neutrals are ionised, they start to spiral about the heliospheric magnetic field with a speed almost equal to the solar wind speed of about 400 km/s (because the interstellar neutral speed is much smaller than this value). According to the top right panel, these particles then lie in a ring distribution relative to the magnetic field, all with the same pitch angle. The irregular component of the field causes pitch angle scattering, therefore the bottom left panel shows that the distribution develops into a shell. Finally, adiabatic and/or other losses will let the distribution develop into a sphere. If this sphere becomes equally filled, the speed distribution is flat, with a cutoff determined by the solar wind speed. For a typical value of = 450 km/s, the kinetic energy cutoff occurs at - 1 keV. This very high energy, compared to typical solar wind energy of a few eV, sets the two populations apart as far as acceleration mechanisms are concerned.

Figure 4b. The first direct observation of He pickup ions by M6bius et al. (1985).

Figure 4a. The evolution of the pickup ion distribution function, described in the text 4.

EARLY P R O P A G A T I O N AND A C C E L E R A T I O N MODELS

The first source mechanism for ACR's, due to Fisk (1976a), is not actually an acceleration mechanism, but rather an investigation of diffusion and trapping of singly ionised particles. If the particles are singly charged, then for Oxygen with energies of the order of 10 MeV/nucleon, the particles should have a very high rigidity, of several GV. Normally, a diffusion coefficient is the product of particle speed with an increasing function of rigidity. Fisk then looked at scattering and trapping situations where there is

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The discovery and early development of the field of anomalous cosmic rays no (or weak) speed dependence. In such cases, the diffusion coefficient is just as large as that for electrons of a few GV, and this then explains why the modulation may be very weak relative to that of galactic cosmic rays of the same kinetic energy per nucleon. Next, Fisk (1976b) described the process of transit time damping of fluctuations in the heliospheric magnetic field by the particles, as a specific acceleration mechanism. He apparently did this for two reasons, namely to interpret intensity increases in co-rotating interaction regions, as observed by McDonald et al. (1976), as well as to derive an acceleration rate for pick-up ions to anomalous cosmic ray energies. The appropriate momentum diffusion coefficient was derived in this paper, but it was not actually applied to a model calculation on ACR's. This was left for the paper of Keckler (1977) who calculated accelerated (and subsequently modulated) ACR spectra in the heliosphere. His results are shown in Figure 5. Curves I and 2 are calculated spectra for galactic and anomalous species respectively. The solutions contain free parameters and they are approximate in the sense that spectra of the anomalous species are first calculated at a large radial distance by assuming that the spatial diffusion term in the transport equation can be neglected at these high rigidities. Then, standard one-dimensional modulation theory (including the spatial diffusion term) is used to modulate these spectra. Despite these approximations, this very first attempt to fit model ACR spectra, together with galactic ones, obviously produced quite remarkable results.

Figure 5. Model fits by Keckler (1977) to observed anomalous spectra. 5.

THE COSMIC RAY T R A N S P O R T E Q U A T I O N

The acceleration and transport models discussed in the previous section were more or less developed specifically as source mechanisms for ACR's because, at the time of their discovery, there were no obvious acceleration mechanisms available for this species. An exception is, perhaps, the process of shock drift acceleration in quasi-perpendicular shocks (to be described in the next section). The problem with this mechanism, however, was that it only gives a factor of-- 3 acceleration per shock crossing, which is not nearly enough to accelerate pick-up ions form -- 1 keV to several 10's of MeV. Furthermore, the notion of a quasi-perpendicular solar wind termination shock (SWTS), which could produce this acceleration, was almost non-existent at the time, although Jokipii (1968) drew attention to the possibility of acceleration in the termination shock of a stellar wind. This lack of a universal acceleration mechanism changed drastically in 1977 with the discovery of so-called first-order Fermi, or compressive, acceleration. This key discovery eventually led to an integrated understanding of first-order Fermi and shock drift acceleration in the solar wind termination shock as the source of ACR's. This development, however, took surprisingly l o n g - almost 10 years before all the key physical effects were properly understood, and another five years or so before extensive modelling of these effects was being done. The reason for this slow progress is probably the incremental increase in our understanding of the content of the cosmic ray transport equation, which was first

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H. Moraal derived by Parker (1965) and subsequently by Gleeson and Axford (1967). All the relevant acceleration and transport effects (even stochastic or 2 ~d order Fermi acceleration in principle) are contained in this robust and very general equation which has not been augmented in any way during its 36 years of existence. Its significance was extensively reviewed by Fisk (1999), and because of its central importance I write down the equation in full. It has the form of a continuity equation in configuration and momentum space" ~f / ~t + V.S + p-2 (< p > pZf) _ Q, where f is the directionally averaged cosmic ray distribution function. Its relationship with the differential particle density, U z,, expressed as particles/volume/momentum, is U p - 4 z p Z f . Webb (1976) discussed this form of the equation in detail and showed that the rate of momentum change, , for adiabatic compression/expansion is given by / p - 1 / 3 V . V f / f , (instead of the more generally perceived value of -1/3 V. V ), where V is the plasma flow (solar wind) velocity. The source function on the right hand side is such that Q / 4 z p 2 is the number of injected particles/volume/momentum/time. The differential streaming, or flux density is given by S / 4zp: in particles/area/ momentum/time, where

S - C V f - K . V f - C V f - K S . Vf +S~rir~, and Sdri]t - K r ( B / B ) x V f . Here C - -1/3 (Olnf/Olnp) is the so-called Compton-Getting coefficient, ~r - ~P/3B, where P is particle rigidity, and the diffusion tensor is separated into symmetrical and antisymmetrical parts as K-,,

0

0

0

0

0

;c

0

0

0

I -ll 1 0

where K ~'describes scattering in the field irregularities parallel and perpendicular to the background field, and K T describes gradient and curvature drifts. The flux was first written down by Gleeson and Axford (1968). When these quantities are inserted into the continuity equation, they produce the cosmic ray the transport equation in the two equivalent forms

~f / ~ t - V . ( K S . V f + K r . V f ) + V . V f --1/3(V.V)~f / ~ l n p - Q O f / ~ t - V . ( K S . V f ) + ( V + Vdrilt).Vf - 1/3 ( V . V ) ~ f / O l n p - Q,

and

(la) (lb)

where Vdr;/, - V x K T B / B is the average gradient and curvature drift velocity of the distribution function in the inhomogeneous background field. The form (la) is nearest to the original form of Parker (1965). Jokipii et al. (1977) emphasized the equivalence of the two forms, as well as the subtlety that while the distribution drifts with the velocity, the drift flux of particles is given by the term S drit, above. This means that bulk drift motion of the particles is due to gradients in the field, but the (measurable) drift flux is caused by gradients in the density. The two quantities are related by V. Sdr;/t --Vdrtp. Vf 9 Isenberg and Jokipii (1979), Burger et al. (1985), and Burger (1987) showed that the drift velocity Vj,it, is complete, i.e., that gradient and curvature drift effects are included in this simple expression without any approximation, provided only that the distribution can be expanded in a 0th and 1st order moment only. This near-isotropic approximation is an excellent one for cosmic rays in almost all situations. This comprehensive description of gradient and curvature drift is shown as a separate box in the line of

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The discovery and early development of the fieM of anomalous cosmic rays discovery on the right h a n d side of Figure 3, because it has played a crucial role in our u n d e r s t a n d i n g of ACR t r a n s p o r t and acceleration. F o r m a n and Gleeson (1975) emphasized t h a t electric field drift is implicitly contained in the convective t e r m of the equation, because the induced electric field in the highly conducting p l a s m a is E = - V x B , so t h a t electric field drift velocity is given by V E - (E x B ) / B 2 - - ( V x B) x B / B 2 - [ B 2 V - ( V . B ) B ] / B 2 -V-V,~-Vs. Thus, the component of the convection velocity perpendicular to the background field is the electric field drift velocity, and this drift should not be added post-hoe. An i m p o r t a n t feature of the t r a n s p o r t equation is t h a t its validity is not limited to gradually varying plasmas, i.e. those with small spatial gradients. Isenberg and Jokipii (1979, 1981) showed t h a t as long as the cosmic ray distribution r e m a i n s nearly isotropic, the equation can be applied to discontinuous changes in plasma flow. This has led to the successful description of cosmic ray modulation in and around the heliospheric neutral sheet, first described by Jokipii et al. (1977), as well as of the process of first order Fermi acceleration in eollisionless astrophysical shocks. 6.

FIRST ORDER FERMI OR COMPRESSIVE

SHOCK ACCELERATION

The discontinuous compression and reduction in flow speed in a shock causes the term 1/3(V.V)Of/Olnp in the t r a n s p o r t equation to represent adiabatic heating, or acceleration. As long as the distribution function remains quasi-isotropic, the t r a n s p o r t equation can be applied to such a situation. Krymski (1977), Axford et al. (1977) and Blandford and Ostriker (1978) therefore showed t h a t in a plane, steady shock, where the field lines are parallel to the normal on the shock front, the solution of the transport equation is t h a t a mono-energetic distribution function in the u p s t r e a m medium is accelerated to a power law of the form f ~ p-3.,/~.,-~, where s - V 2/V~ is the compression ratio of the shock. For a strong shock, this value is s = 4, leading to a distribution function of the form f ~ p-4 or, equivalently, to an intensity spectrum ~ p-2. This solution is the result of matching the intensities on both sides of the shock, and integrating the t r a n s p o r t equation across it, which produces the result [S.n]~ - Q ,

(2)

i.e. t h a t the difference in the s t r e a m i n g vector across the shock equals the source strength. Since this m e c h a n i s m holds for a parallel shock, in which the background magnetic field goes t h r o u g h it continuously, this field has no effect on the solution. The accelerated spectral shape is independent of s:, although the acceleration is caused by the process of pitch angle scattering off the irregularities in the field on both sides of the shock t h a t cycles the particles back across the shock m a n y times before they eventually escape downstream. The reason why ~ is absent from the solution is t h a t the strength of the scattering only determines the rate of acceleration, which can not be derived from the steady state solution. The process is better illustrated by the alternative single-particle, microscopic description by Bell (1978a,b). This explicitly highlights the fact t h a t field irregularities move s times faster from the u p s t r e a m medium into the shock t h a n away from it into the downstream medium. Thus, when viewed from either u p s t r e a m or downstream, the particle sees the irregularities in the other medium always approaching it, i.e., it always makes a head-on collision. Bell showed t h a t (i) this leads to an energy gain per shock crossing of O(V/v), where V and v are flow speed and particle speed, typically with V <<

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v, and (ii) repetitive crossings with this energy gain lead to the same power law spectrum as was found from the solution of the transport equation mentioned above. The value of ~; or the strength of scattering, determines the rate of the acceleration. In Drury (1983), and references therein, it is shown that the time scale to establish the above-mentioned power law up to momentum p is given by P

The process is called first order Fermi acceleration to distinguish it form the classical second order Fermi acceleration in randomly moving irregularities, where the acceleration rate is only O ( V / v ) ~, i.e., of second order in small numbers. Because it is a stochastic process that depends on the compression of field irregularities, appropriate alternative names are also compressive or diffusive shock acceleration. First order Fermi acceleration was immediately applied to the blast waves of supernova remnants to demonstrate that they could be the source of cosmic rays up to at least 1015 eV, providing a compelling explanation for the observed power law spectra with spectral index just somewhat softer than o~ p-2 (e.g. Bogdan and V61k, 1983, Moraal and Axford, 1983, Lagage and Cesarsky, 1983). It took a long time, however, to apply this mechanism to the origin of ACR's in the heliosphere. In hindsight, it seems that the main reasons for this delay were that (i) the notion of a permanent, steady solar wind termination shock in the outer heliosphere was only weakly developed at the time, and (ii) even when one thought about such a shock, it was realised that it had a perpendicular magnetic geometry (with the azimuthally directed field lines perpendicular to the normal on the shock, except near the poles), instead of a parallel one. Pitch angle scattering in such a perpendicular shock does not cycle particles back across the shock front repetitively, and it was, therefore, difficult to see how shocks in the outer heliosphere could cause the acceleration. Despite these conceptual problems, Webb et al. (1985) applied the process to the termination shock of a stellar wind, disregarding its magnetic field structure. The analytical solution of the spherically symmetric transport equation produced spectra, but only for a diffusion coefficient that was independent of momentum, which is not realistic. Spherical (or any non-planar) shocks introduce an additional upper limit for the acceleration, namely that the power laws can only be established for energies where ~: /V < r,.,

(4)

i.e., where the diffusive length scale is less than the shock radius. Otherwise, the upstream medium becomes too small to contain the particles that are scattered back into it. It is instructive to note that for an effective radial diffusion mean free path = 1.0P(GV) AU, bearing in mind that ~: =/~v / 3, and for a SWTS with a radius q. - 90 AU, this cutoff in the spectrum occurs at -- 200 MeV for protons, and at 95 and 23 MeV/nucleon, respectively, for singly charged Helium and Oxygen. Before a full and comprehensive application of acceleration models to ACR's developed, however, much more thought had to be applied to the role of the background magnetic and electric fields. These fields produce shock drift and shock drift acceleration, which were known long before first order Fermi acceleration, with the work of, e.g., de Hoffman and Teller (1950), Hudson (1965), and Chen and Armstrong (1975). This acceleration process seemed to be entirely different to that of first order Fermi acceleration. A series of four papers by J.R. Jokipii and his co-workers, however, developed a fully integrated approach to the two mechanisms. The first paper in this series, by Pesses et al. (1981) was exploratory in nature. It discussed (some of the) physical mechanisms without giving

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The discovery and early development of the field of anomalous cosmic rays detailed results. On the timeline of Figure 3 I show that the second paper of Jokipii (1982) did not apply shock drift acceleration to the SWTS as such, but it emphasized the complementary nature of the two mechanisms. Jokipii (1986) presented the first numerical solutions of the transport equation that included this integrated mechanism, while Jokipii (1987) highlighted that perpendicular shocks may indeed be more efficient accelerators than parallel ones, contrary to belief at the time. I will discuss the developments contained in these four papers in the next two sections, not necessarily in chronological order. 7.

SHOCK DRIFT AND SHOCK DRIFT ACCELERATION

The fundamental point in this mechanism is that the more perpendicular the geometry of a shock, the more acceleration it produces. In what follows I will only refer to the limits of purely parallel and perpendicular shocks. The acceleration does, however, occur for any angle between the shock normal and the magnetic field, and these more general results are written up in the Jokipii papers. Figure 6 summarises the relevant aspects of the problem. The top left panel shows that in a parallel, collisionless shock in a smooth field, a charged particle spirals through a shock without being aware of its presence. The same parallel geometry is drawn in the top right panel, but here the field has irregularities. These irregularities scatter the pitch angle of the particle, so that it can cycle back across the shock many times before it eventually escapes downstream, leading to the process of first order Fermi acceleration, described in the previous section. The bottom left diagram depicts a perpendicular shock. Here the outward pointing, frozen-in field moves through the shock with the flow velocity. Thus, the field in the downstream medium is compressed by a factor s, the shock compression ratio. The moving B field causes an induced electric field, E = - V x B , pointing upwards, and having the same value on both sides of the shock, because the field and flow velocity change by a factor of s and 1/s across the shock, respectively. In this case the particle does not spiral through the shock, but it E-cross-B drifts with the velocity given in section 5. As the particle moves through the shock, it experiences an upward directed gradient drift. The geometric reason for this drift is that the upstream gyroradius is s times larger than the downstream one. It is readily seen that the drift direction is given by Vj,.ii, in Section 5, because in this situation V x B / B = ( V x B ) / B + V ( 1 / B ) x B = V ( 1 / B ) x B , which is, indeed, upward. The magnitude in this case is a Dirac delta, written down by Jokipii (1987), but the virtue of the transport theory is that, as was mentioned in Section 5, this produces a finite drift flux, represented by the term Sjritt. Finally, while the shock drift is due to the gradient in the magnetic field, the particle gains its energy from the electric field, because this field obviously does more "upward directed" work while the particles is in the upstream medium than "downward directed" when it is downstream. A classical result, summarised in, e.g., McLoud and Moraal (1990), is that this process produces an energy gain of-- 3 for a strong shock (compression ratio s = 4). This gain is much larger than the (typically) small gain in the top right hand panel, but it only occurs once, because in this perpendicular geometry, pitch angle scattering seemingly does not cycle the particle back across the shock. It merely transports the particle forwards and backwards along the shock surface, while it E-cross-B drifts away into the downstream medium. Thus, the question mark in the bottom right panel means that it is uncertain how a quasi-perpendicular shock such as the SWTS acts as the source of ACR's.

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H. Moraal

In view of this problem, Pesses et al. (1981) were first to point out that the combined mechanisms of first order Fermi and shock drift acceleration in the SWTS provided a logical source mechanism for ACR's, and they gave the first steps in the development of a full model. Figure 7 shows a meridian cut of the northern half of the heliosphere, with the magnetic field directions drawn in. In this so-called qA>0 state of the heliosphere, the Parker spiral field in the northern hemisphere points outward in the inner heliosphere, and curves out of the paper with increasing radial distance. The field is oppositely directed south of the neutral sheet, which lies in (or near) the ecliptic plane. The field's spiral angle is given by tan~ = ~ ( r - r , . u , ) s i n 0 / V , with 0 the polar angle and g~ the angular velocity of the sun. For typical values of ~ and V, this angle is > 45 ~ if r sin 0 > 1 AU. Thus, in the outer heliosphere this field is quasi-perpendicular, except in a cylinder with a radius of 1 AU over the poles. This means that the shock is quasi-perpendicular almost everywhere, and the physical process of particle transport and acceleration is best described by the bottom left panel of Figure 6. The almost azimuthal magnetic field produces a poleward directed electric field in both hemispheres. When some of these particles reach the poles, the first order Fermi process operates on them in the quasiparallel cylinder. While these particles are accelerated, they penetrate deeper into the heliosphere, and they then drift toward the neutral sheet in (or near) the ecliptic plane, to be observed as anomalous cosmic rays. The cycle may also repeat itself, because the particles E-cross-B drift, or convect outwards again, aided by the so-called neutral sheet drift. From there they land on the shock, drift poleward and gain energy once more.

Figure 7. Half meridian cut of the heliosphere showing drifts in the so-called qA>0 magnetic configuration.

Figure 6. Shock drift (left) and 1 st order Fermi acceleration (right) in parallel (top) and perpendicular (bottom) shocks.

This cycle will only operate if the particles do not escape downstream before they reach the poles. This requirement can be realised through a more refined application of the process of perpendicular diffusion: every time that a particle scatters its pitch angle along the mean field direction, its phase angle also changes abruptly, displacing it approximately one gyroradius perpendicular to the field. This effect scatters a fraction of the particles back across the shock, so that they can repeat the shock drift acceleration of the bottom left panel of Figure 6. This process will, however, only be efficient for particles

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The discovery and early development of the fieM of anomalous cosmic rays that have already gained a substantial amount of energy relative to the background plasma, because such high energy particles only drift a small fraction of one gyroradius downstream per gyro-orbit. Thus, when they are scattered in pitch and phase angle, they have a high probability to scatter back across the shock. Low energy particles, on the other hand, drift a large fraction of a gyroradius, or even multiple gyroradii per gyroperiod. Consequently, a scattering in phase angle will not be sufficient to cycle them back across the shock. This is the origin of the well-known injection problem for quasiperpendicular shocks, referred to again later. This shock drift mechanism, aided by perpendicular diffusion, enables one to estimate an upper limit for the energy gain in such a perpendicular shock. Jokipii (1982, 1990) pointed out that the electric field causes a potential difference between the ecliptic plane and the poles given by rt/2

rt/2

ArP - ~ Eds = f VB~.dO~ (VB~r~/~f2) f sinOdO ~ 200 MV, 0

(5)

0

which is independent of shock radius, r,., as long as r,. >> re, and where B has been expressed in terms of its value at earth as B - Be(r~ / r) 2 / (~/2cos~), using the numerical values Be = 5 nT, and V =400 km/s. Thus, if the particle manages to stay on the shock from ecliptic to pole, assisted in this by perpendicular scattering, it can gain an energy ZeAO or -- 200 MeV per charge. This number happens to be in the same order of magnitude as the curvature limit Vrs / ~ > 1 of the first order Fermi process in (4) above, and this is no coincidence: Jokipii (1982) showed that the energy gain of the shock drift mechanism in (5) formally has the same structure as that derived form the diffusive matching condition (2). In the shock drift picture dT= ZeEds= ZeVBds, with the important point being that the gain is strictly proportional to the distance travelled along the shock. Jokipii showed that the diffusive matching condition can be put in the same form. In that mechanism, however, the distance that the particle manages to stay on the shock is not only determined by the geometry of the shock, but also by the amount of perpendicular scattering. This equivalence establishes that all the shock drift considerations are properly contained in the diffusive matching condition (2), and that the transport equation contains all the relevant physics to describe shock acceleration. The paper of Jokipii (1986) was the first one to take all of these physical effects into account in a numerical solution of the cosmic transport equation, with the matching condition (2) across the SWTS, to calculate ACR spectra. Subsequently, a similar model was developed by Steenkamp (1995), and since then the numerical modelling of ACR spectra by several groups has become routine. There is one remaining point, namely that Jokipii (1987) showed that the rate of acceleration, calculated from (3), is much faster for a perpendicular shock than a parallel one. I f / ~ = r / r , and if ~• is calculated from the so-called hard sphere scattering model, then ~• / ~,~ = 1 / (1 + r/2) , and the acceleration rate in a perpendicular shock is 1+ 7/2 times as fast as in a parallel one. This scattering model may be oversimplified, but it serves to demonstrate the point. Values of 7/__ 10 are realistic, but there is an upper limit to this parameter. This is set by the requirement that the transport must remain diffusive to keep the anisotropies small, and it is given by 71< v / V , leading to r < ~;• which becomes a stringent condition for low energy particles. In fact, combining this with the curvature limit of (4), establishes that a quasi-perpendicular shock is an efficient accelerator when the diffusive length scale ~ • falls in the range

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H. Moraal

re < t r 1 7 7 <1",..

(6)

If the lower limit is violated it leads to the well-known, non-diffusive preacceleration/injection problem which remains one of the main research problems in this field, and which is further mentioned in Section 10. Basically, for typical parameters the pick up ions must be accelerated by a factor of = 100 before the perpendicular shock becomes efficient. If the upper limit is exceeded the system becomes too small to contain the particles. Steenberg and Moraal (1999) have pointed out that there is a danger to interpret the order-of-magnitude nature of the upper limits (4) and (5) too quantitatively. Numerical solutions of the transport equation indicate that this cutoff already becomes appreciable at energies at least 5 times lower than this limit. A parallel shock does, of course, not suffer from the lower limit in (6) and can accelerate particles directly from the pickup ion pool. One must also keep in mind that for strong scattering 77--1, ~,l--~• and drift effects in the background field become much less important. In this case the curvature cutoff (4) is just as much determined by ~,~. In fact, from the matching condition (2) it follows that it is always the effective radial value of ~: that determines this cutoff. In the case of weak scattering it is modified strongly by drifts. For strong scattering these drifts have little effect on the acceleration. In this sense the spherically symmetric no-drift solution of Webb et al. (1985) can be interpreted as a strong scattering approximation. The numerical solutions of Steenberg and Moraal (1999) are of the same character. Apart from the kinematics of particle transport discussed above, there are two other equally important theoretical developments, namely that of the back reaction of accelerated particles on the shock structure and on the wave fields that scatter them. These topics formed part of the theoretical development right from the beginning, e.g., in Axford et al. (1977), but they are still actively investigated, and extensively dealt with in the companion paper of le Roux (2001). 8.

DIRECT OBSERVATION

OF PICKUP IONS IN THE SOLAR WIND

The third heavily marked discovery in Figure 3 is the first direct observation of pickup ions. M6bius et al. (1985) observed He + ions of interstellar origin in the solar wind, by measuring their velocity distribution function. Their measurement is shown in Figure 4b, which shows the bump on the mass/charge = 4 channel around 10 keV, cutting off sharply at 4 times the solar wind energy. These measurements were done on the earthbound AMPTE satellite, and for this reason only the He + species could be detected, because its ionisation potential is sufficiently high to become ionised within 1 AU. The connection of this measurement with ACR's in Figure 3 is shown in a dashed line, because the authors did not mention ACR's explicitly, although the implications were certainly quite clear. Detection of the other species, which typically ionise at several AU already, had to await the launch of Ulysses. These first detections are described by Geiss et al. (1994a, 1994b) and Gloeckler et al. (1993, 1994). This detection has been such a success that, as described in Gloeckler et al. (2000), instruments on Ulysses and ACE now provide us with comprehensive elemental and charge state composition measurements in the range from typical solar wind energies (1 keV) to tens of MeV/amu. 9.

THE CHARGE STATE OF ANOMALOUS COSMIC RAYS

The final piece in the ACR puzzle was to unambiguously establish their charge state. The only method available to directly determine this charge state at ACR energies - 158-

The discovery and early development of the field of anomalous cosmic rays

requires the use of the earth's magnetic field as a particle rigidity filter. The basic principle is t h a t for a given energy, the rigidity of a particle decreases with increasing charge state. Thus, when singly charged ions penetrate into the magnetosphere and lose an additional electron through interaction with the upper layers of the atmosphere, their rigidity suddenly drops, trapping them in L-shells of the geomagnetic field to which they would not have had access if they had come in with the higher charge state. The presence of these particles can then be measured by low-orbiting polar satellites. This technique was pioneered on the COSMOS series of satellites in the mid- and late 1980's. With the planned launch of Sampex in 1992, a Russian/American study group on this topic was formed in about 1990. Their joint results were then presented in a highlight session of the 23 rd International Cosmic Ray Conference by Cummings et al. (1994), Panasyuk (1994), and Tylka (1994). Since then, the procedure has become routine, and the results are briefly discussed in the companion paper of Heber and Cummings (2001), and reviewed more extensively by Leske et al. (2000). 10.

FURTHER

DEVELOPMENTS

The experimental and theoretical developments described above established the field of anomalous cosmic rays as a mature discipline in the early 1990's, about 20 years after their discovery. I emphasised the development of the early theory, because without it, one would hardly be able to talk of a true discipline. After this paradigm was established, studies have actively continued during the last decade. These newer developments are described in the companion papers of Heber and Cummings (2001) and le Roux (2001), as well as in two recent, comprehensive reviews by Zank (1999) and Fichtner (2001). These newer developments are mainly about the problems of injection/pre-acceleration, mass composition, and the back reaction of the accelerated particles onto the plasma. All these effects determine the overall efficiency of the process. Parallel to this, numerical solutions of the cosmic ray transport equation continue to be applied to observed ACR spectra to verify to what extent the developing theories fit the newer observations, e.g., Moraal et al. (1999). The detection of multiple charges by Mewaldt et al. (1996) and their explanation, as reviewed by, e.g., Leske et al. (2000) and Jokipii (2000), poses interesting further challenges to this modelling. Modelling of transport and modulation effects in the downstream region of the SWTS is also becoming feasible and important. The SWTS itself has not yet been detected, but Adams and Leising (1991) already concluded that there is no other viable option as an accelerator, because if ACR O*, at a few MeV/nucleon for example, was accelerated outside the heliosphere and had thus travelled more than 0.2 pc, it would have become multiply charged at much lower energies than was subsequently seen. If the source is heliospheric, the SWTS seems to be the only option, because when the realistic numbers ~ = 1.0P(GV) AU and r,. = 90 AU are used in (3), the acceleration time scale is of the order of 5 years. This time scale was directly confirmed by numerical solutions of Steenberg (1998). It is fast enough to avoid excessive multiple ionisation. Energetic Neutral Atoms (ENA's), with energies up to at least 100 keV have been observed and modelled by, respectively, Hshieh and G r u n t m a n n (1993) and Czechowksi et al. (1999), and references therein. These particles originate form the charge exchange of ACR's and pre-accelerated pickup ions with plasma outside the SWTS. This new component implies that there are now at least five distinguishable particle populations in the entire discipline: (i) interstellar neutrals, (ii) pickup ions, (iii) anomalous cosmic rays,

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H. Moraal (iv) geomagnetically trapped radiation, and (v) energetic neutral atoms. This makes the discipline much richer and much more diverse than that of galactic cosmic rays. In addition, the number and energy density of anomalous cosmic rays inside the heliosphere (or, indeed, in the astrosphere of any star) may exceed that of galactic cosmic rays. These numbers can easily be calculated by integrating under the respective spectra. Integrating from the cutoff point, Vr,./~= 1, upwards in energy (which favours the galactic component) shows that the number density in ACR's is -- 3 times that of GCR's. Similarly, the ACR energy density is -- 1/3 of that of the GCR's. These values are calculated for the outer heliospheric dominate the average over the entire heliosphere due to the volume factor. Thus, anomalous cosmic rays are at least as important and abundant as galactic ones, and it has become anomalous to call them by that name. "Heliospheric cosmic rays" is more appropriate. REFERENCES

Adams, J.H. and Leising, M.D., Proc. 22 nd ICRC., Dublin, 3, 304-306, 1991. Axford, W.I., ed. C.P. Sonnet, et al. NASA Spec. Publ., 308, 609, 1972. Axford, W.I., Leer, E. and Skadron, G., Proc. 15th ICRC., Plovdiv, 11,132-137, 1977. Bertaux, J-L., and Blamont, J.E., Solar Wind, NASA Spec. Publ., 308, 661, 1972. Bell, A., MNRAS, 182, 147, 1978a. Bell, A., MNRAS, 182, 443, 1978b. Blandford, R.D. and Ostriker, J.P., Astrophys. J., 221, L29-L32, 1978. Bogdan, T., and V61k, H.J., Astron. Astrophys., 112, 129, 1983. Burger, R.A., Ph.D. Thesis, Potchefstroom University, 1987. Burger, R.A., Moraal, H., & Webb, G.M., Astrophys. Space Sci., 116, 107-129, 1985. Chen, G, and Armstrong, T.P., Proc. 1 5 th ICRC. 5, 1814, 1975. Cummings. J.R., Cummings, A.C., Mewaldt, R.A.., Selesnick, R.S., Stone, E.C., von Rosenvinge, T.T., Proc. 23 rd ICRC., Invited, Rapporteur, Highlight Vol., 475-482, 1994. Czechowski, A., Fahr, H.J., Fichtner, H., Kausch, T., Proc. 26 th ICRC, 7, 464-467, 1999. De Hoffman, F., and Teller, E., Phys. Rev., 80, 692-703, 1950. Drury, L.O'C., Rep. Prog. Phys., 46, 973, 1983. Fahr, H.J., Astrophys. Space Sci., 2, 496, 1968. Fahr H.J., Report 72-10, Forschungsber. der Astron. Inst. Bonn, 1972. Fichtner, H., Accepted for publication in Space Sci. Rev., 2001. Fisk, L.A., Astrophys. J., 206, 333-341, 1976a. Fisk, L.A., Adv. Space Res., 23, 415-423, 1999. Fisk, L.A., J. Geophys. Res., 81, 4633-4640, 1976b. Fisk, L.A., Gloeckler, G., Zurbuchen, T.H., and Schwadron, N.A., ACE2000 Symposium, ed. R.A. Mewaldt et al, 229-233, 2000 Fisk, L.A., Kozlovsky, B., Ramaty, R., Astrophys. J., 190, L35, 1974. Forman, M.A., and Gleeson, L.J., Astrophys. Space Sci,. 32, 77, 1975. Garcia-Munoz, M., Mason, G.M., Simpson, J.A., Astrophys. J., 184, 967, 1973. Gleeson, L.J., Axford, W.I., Astrophys. J. Lett., 149, Ll15, 1967. Gleeson, L.J., and Axford, W.I., Astrophys. Space Sci., 2, 431-437, 1968. Geiss, J., Gloeckler, G., Mall, U, von Steiger, R., Galvin, A.B., and Ogivlie, K.W., Astron. Astrophys., 282, 924, 1994a. Geiss, J., Gloeckler, G. and Mall, U., Astron. Astrophys. 289, 933, 1994b. Gloeckler, G., Geiss, J., Balsiger, H., Fisk, L.A., Galvin, A.B., Ipavich, F.M., Ogilvie, K.W., von Steiger, R., and Wilken, B., Science, 261, 70-73, 1993.

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Gloeckler, G., Geiss, J., Roelof, E.C., Fisk, L.A., Ipavich, F.M., Ogilvie, K.W., Lanzerotti, L.J., von Steiger, R., Wilken, B., J. Geophys. Res. 99, 17637-17643, 1994 Gloeckler, G., Fisk, L.A., Zurbuchen, H., and Schwadron, N.A. ACE2000 Symposium, ed. R.A. Mewaldt et al, 221-228, 2000. Heber, B, and Cummings, A., this volume, 2001. Hovestadt, D.O., Vollmer, O., Gloeckler, G., Fan, C.Y., Phys Rev.Lett., 31,650, 1973 Hsieh, K.C., and Gruntmann, M.A., Adv. Space Res., 13, 131-139, 1993. Hudson, P.D., M.N.R.A.S., 131, 23, 1965. Isenberg, P.A. and Jokipii, J.R., Astrophys. J., 234, 746, 1979. Isenberg, P.A. and Jokipii, J.R., Astrophys. J., 248, 845, 1981. Jokipii, J.R., Astrophys. J., 152, 799-808, 1968. Jokipii, J.R., Astrophys. J., 255, 716, 1982. Jokipii, J.R., J. Geophys. Res., 91, 2929, 1986. Jokipii, J.R., Astrophys. J., 313, 842, 1987. Jokipii, J.R. COSPAR Colloquia Series, 1, 169-178, 1990. Jokipii, J.R., ACE2000 Symposium, ed. R.A. Mewaldt et al, 309-316, 2000. Jokipii, J.R., Levy, H. and Hubbard, W.B., Astrophys. J., 213, 861, 1977. Kecker, B., J. Geophys. Res., 82, 5287-5291, 1977. Krymsky, G.F., Dokl. Akad. Nauk. SSR, 234, 1306, 1977. Lagage, P.O., and Cesarsky, C.J., Astron. Astrophys, 118, 223-228, 1983. Le Roux, J.A., this volume, 2001. Leske, R.A., Mewaldt, R.A., Christian, E.C., Cohen, C.M.S., Cummings, A.C., Slocum, P.L., Stone, E.C., von Rosenvinge, T.T., and Wiedenbeck, M.E. ACE2000 Symposium, ed. R.A. Mewaldt et al, 293-300, 2000. McDonald, F.B., Teegarden, B.J., Trainor, J.H. Webber, W.R., Astrophys. J., 187, L105 L108, 1974. McDonald, F.B., Teegarden, B.J., Trainor, J.H., and Webber, W.R., Astrophys. J., 203, L149, 1976. McLoud, W., and Moraal, H., J. Plasma Phys., 44, 123-136, 1990. Mewaldt, R.A., Selesnick, R.S., Cummings, J.R., Stone, E.C., von Rosenvinge, T.T., Astrophys. J., 466, L43, 1996. MSbius, E., Hovestadt, D., Kecker, B., Scholer, M., Gloeckler, G. and Ipavich, F.M., Nature 318, 426-429, 1985. Moraal, H., and Axford, W.I., Astron. Astrophys., 125, 204-216,1983. Moraal, H., Steenberg, C.D., and Zank, G.P., Adv. Space res., 23, 425-436, 1999. Panasyuk, M.I. Proc. 23 r~ ICRC., Invited, Rapporteur, Highlight Vol., 455-463, 1994. Parker, E.N., Planet. Space Sci., 13, 9, 1965. Pesses, M.E., Jokipii, J.R. and Eichler, D., Astrophys. J., 246, L85, 1981. Steenberg, C.D., Ph.D. thesis, University of Potchefstroom, South Africa, 1998. Steenberg C.D., and Moraal, H., J. Geophys. Res., 104, 24879 - 24884, 1999. Steenkamp, R., Ph.D. thesis, Potchefstroom University, 1995. Thomas, G.E., Solar Wind, NASA Spec. Publ. 308, 668, 1972. Tylka, A. Proc. 23 rd ICRC, Invited, Rapporteur, Highlight Vol., 465-474, 1994. Vasyliunas, V.M. and Siscoe, G.L., J. Geophys. Res., 81, 1247, 1976. Webb, G.M. PhD Thesis, University of Tasmania, Hobart, Tasmania, 1976. Webb, G.M., Forman, M.A., and Axford, W.I. Astrophys. J. 298, 684-709, 1985. Zank, G.P., Space Sci. Rev., 89, 413-688, 1999. Zank, G.O., Rice, W.K.M., le Roux, J.A., Lu, J.Y., and Mfiller, H.R., ACE2000 Symposium, ed. R.A. Mewaldt et al, 317-324, 2000.

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A n o m a l o u s c o s m i c rays: C u r r e n t and future theoretical d e v e l o p m e n t s J. A. le Roux Bartol Research Institute, University of Delaware, Newark, DE 19716, USA

Since the discovery of anomalous cosmic rays during the 1970s much progress has been made in clarifying the origin of these particles. However, the formation and transport of the anomalous component involve a complex chain of events cutting across different disciplines in space physics so that many of the details still need unraveling. A brief review of some of the current and future theoretical efforts in this regard is presented.

1. INTRODUCTION It is currently firmly believed on the basis of theory, simulations and observations that anomalous cosmic rays (ACRs) are formed when mostly interstellar pickup ions (PUIs) experience diffusive shock acceleration at the solar wind termination shock (TS). However, a lot of the complex details of PUI and ACR transport in the solar wind still have to be worked out. For example, it is not well understood (i) how PUIs are pre-accelerated while being transported to the TS by the solar wind, (ii) how PUIs are injected into the process of diffusive shock acceleration at the TS to become ACRs, (iii) how PUIs and ACRs modify the TS, and (iv) how the upstream transport of these particles should be described. A more detailed understanding of the above is essential for explaining why the ACR composition reveals an underabundance of the lighter elements such as hydrogen especially compared to the composition of PUIs [1]. A brief review of the current status and future direction of theoretical work and simulations in these research areas is presented.

2. PICKUP ION TRANSPORT TO THE TERMINATION SHOCK According to current wisdom it is only at a nearly perpendicular TS that the rate of standard diffusive shock acceleration is fast enough to explain the formation of the ACR component as observed [2]. Standard diffusive shock acceleration at a nearly perpendicular TS should be thought of in the context of ACRs undergoing repeatedly shock drift acceleration because scattering by magnetic field fluctuations keep the ACRs close to the TS. This mechanism is described by standard ACR transport theory in the limit of near isotropic ACR distributions [3]. The diffusive acceleration mechanism only works if the ACRs downstream move across magnetic field lines back to the TS which is more difficult than for a parallel TS where the path back to the TS is along field lines. This suggests the existence of an "injection" problem in that unaccelerated PUIs need to be pre-accelerated before crossing the threshold of

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J.A. le Roux

standard diffusive shock acceleration at a nearly perpendicular TS whereby the formation of the ACR component could be viewed as a two-stage acceleration process. An issue that needs to be resolved in this regard is whether more energetic PUIs are injected directly into diffusive shock acceleration at the TS after pre-acceleration in the upstream solar wind by interplanetary shocks and MHD turbulence, or whether low-energy PUIs injected indirectly into diffusive shock acceleration after local pre-acceleration at the TS itself contribute the most to the formation of ACRs. To resolve this issue a better understanding of PUI preacceleration in the upstream solar wind must be achieved.

2.1 Pickup pre-acceleration by MHD turbulence PUI pre-acceleration in the upstream solar wind itself is currently believed to be a twostage acceleration process with standard diffusive shock acceleration as the second stage occurring at quasi-perpendicular corotating shocks. No consensus exists currently on the dominant first stage acceleration mechanism~ On the one hand, it has been considered that the stochastic acceleration of PUIs by the cyclotron resonant interaction with Alfv6nic turbulence (2nd-order Fermi acceleration) [4] and by the magnetic Landau resonance (transit time damping) with fast mode magnetosonic turbulence [5] are responsible for the initial PUI preacceleration. These mechanisms are believed to be important between the forward and reverse corotating shock pair where there is enhanced turbulence. In contrast, mechanisms that operate at the shock itself, such as stochastic magnetic mirroring acceleration [6], and multiply reflected ion (MRI) acceleration [7] also known as shock surfing acceleration [8], are invoked. Recent observations of PUI spectra close to the Sun suggest that PUIs have accelerated "tails" all the time in the equatorial regions, leading to the speculation that PUIs are accelerated by shocks, but also by MHD turbulence in between and near shocks [9]. It is clear that this issue will continue to receive attention in the future. Regarding the stochastic pre-acceleration of PUIs by MHD turbulence, it was pointed out that fast mode magnetosonic turbulence is more important than Alfv~nic turbulence close to the Sun [5]. This makes sense because close to the Sun Alfv~nic turbulence in the solar wind frame is mainly directed away from the Sun whereby 2nd-order Fermi acceleration is ineffective. However, simulations valid for the quiet background solar wind suggest that Alfv6nic turbulence is more important for PUI pre-acceleration beyond a few AU from the Sun [10], where the amount of inward and outward propagating Alfv~nic fluctuations balances. Another interesting aspect about PUI pre-acceleration in the upstream solar wind is that this may have consequences for the ACR composition. Studies of self-consistent 2nd-order Fermi pre-acceleration of PUIs in the quiet solar wind [11, 12] predict that PUIs damp Alfv6nic turbulence according to an inverse mass dependence at large heliocentric distances so that H + has the largest effect in damping this turbulence. Consequently, because waves that resonantly scatter H + are damped, the efficiency of 2nd-order Fermi acceleration mechanism is biased in favor of the heavier PUI elements so that the pre-accelerated PUI tails represent a potential source for diffusive shock acceleration at the TS with a composition more resembling ACRs than unaccelerated PUIs. A similar trend was also noticed in simulations involving the stochastic pre-acceleration of PUIs due to interaction with large-scale fluctuations in the solar wind speed associated with corotating interaction regions [13]. Observations [14], theory [15] and simulations [16] suggest that MHD turbulence in the solar wind may consist predominantly of two-dimensional (2-D) turbulence with a minor component of Alfv6nic turbulence. However, the effect of 2-D turbulence on the stochastic

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Anomalous cosmic rays: Current and future theoretical developments

pre-acceleration of PUIs still awaits investigation. 2-D incompressible MHD simulations suggest that strong stochastic turbulent electric fields associated with turbulent reconnection processes for a high Reynolds number appropriate for the solar wind can accelerate particles efficiently so that power law spectra result over a certain energy range [17]. This indicates that PUI pre-acceleration by 2-D turbulence in the outer heliosphere might be more significant than provided by Alfv6nic turbulence that typically results in softer exponential spectra.. 2.2 Pickup ion pre-acceleration by corotating shocks The idea to study particle acceleration at quasi-perpendicular interplanetary shocks using the gyrophase-averaged conservation of the magnetic moment across a shock whereby some particles are reflected (magnetic mirroring acceleration) and some are transmitted (shock drift acceleration) is well established [6]. Without scattering to return particles to the shock, however, this approach to first stage acceleration may have difficulty in accelerating particles across the threshold for standard diffusive shock acceleration. Models that combine magnetic moment conservation with allowing particles leaving the shock along magnetic field lines to return to the shock through scattering by magnetic field fluctuations, show substantial additional acceleration [ 18, 19] that might be sufficient for injection. It is only recently that the idea of MRI/shock surfing acceleration has been considered for 1st stage PUI pre-acceleration at quasi-perpendicular interplanetary shocks [7, 8]. According to this approach PUIs with a sufficiently small velocity component along the shock normal are reflected by the cross-shock electric field and energized by the motional electric field in a skimming motion along the shock front with maximum energies reached when their Lorentz force overcomes the cross-shock electric field. Test particle simulations predict that this mechanism should be able to accelerate PUIs up to energies of--1 MeV which should be sufficient to cross the threshold for standard diffusive shock acceleration. Such efficient acceleration requires a narrow shock ramp of the order an electron inertial length. Observations of quasi-perpendicular Earth Bow shock events indicate that the shock ramp width is typically of the order of an ion inertial length, but that there exist strong fluctuations inside the ramp which are much narrower [20]. Simulations including fine structure of the shock ramp show that MRI acceleration is effective [21]. The challenge for continuing research is to study the role and relative importance of the MRI mechanism as a first stage mechanism in comparison with the conservation of magnetic moment approach. Time-dependent MHD simulations of the solar wind show that corotating shocks weaken substantially with increasing distance from the Sun. The inclusion of PUIs in the solar wind MHD simulations raises the fast mode magnetosonic speed somewhat, causing a slightly further reduction in the compression ratio of corotating shocks [22]. This implies that corotating shocks beyond some distance from the Sun may become too weak to reflect and preaccelerate PUIs efficiently in the case of the MRI and the mirroring acceleration mechanisms so that injection into second stage diffusive shock acceleration might cease. The results from recent simulations [23] include an estimate at which heliocentric distance PUI injection into diffusive shock acceleration at corotating shocks ceases. It was found that in order to explain the observed delay between the arrival of interplanetary shocks and the peaks in the ~1 MeV energetic particle fluxes at -47 AU [24], the shock should lose its ability to inject particles into diffusive shock acceleration at --34 AU from the Sun where the corotating shock compression ratio falls below 1.5. This suggests that beyond ~34 AU the preaccelerated PUI spectra will decay due to the dominating effect of solar wind convection and

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J.A. le Roux adiabatic cooling. A recent interpretation of Voyager observations [25] at large heliocentric distances suggests that this is indeed the case, as the energetic particle fluxes associated with merged corotating interaction regions have a r -3 dependence instead of r -2 associated with convection but no cooling. This raises the question whether enough pre-accelerated PUIs will be injected directly into diffusive shock acceleration at the TS [26] to explain the observed modulated ACR spectra as suggested by ACR drift transport calculations based on preaccelerated source PUI spectra inferred from Voyager observations [27].

3. PICKUP ION INJECTION AT ANOMALOUS C O M P O N E N T

THE

TERMINATION

SHOCK

AND

THE

As mentioned above, it is only at a nearly perpendicular TS that the rate of standard diffusive shock acceleration is deemed fast enough to explain the observed ACR component. Unfortunately, it is at a perpendicular TS that PUIs will face the largest energy threshold for injection into this acceleration process. The pre-acceleration of PUIs in the upstream solar wind might be the solution, but it is not clear whether enough of them will arrive at the TS with sufficiently high energies. Recent work indicates that if the pre-accelerated PUIs observed at ---40 AU are extrapolated to the TS with a r -3 radial dependence [25] and injected into diffusive shock acceleration at the TS with a minimum injection energy of 50 keV, then there would not be enough PUIs to reproduce the observed ACR component [26]. Therefore, a point of considerable debate is whether low-energy PUIs can be pre-accelerated locally at the TS across the threshold for standard diffusive shock acceleration if the TS is nearly perpendicular. 3.1 The injection of low-energy pickup ions PUI magnetic mirroring at a nearly perpendicular TS is not an option for 1 st stage acceleration because only very high energy particles will be reflected [18], and simulations show that shock drift acceleration is only effective in the presence of high amplitude turbulence [28]. However, then shock drift can be interpreted as standard diffusive shock acceleration operating above a low energy threshold [29]. Such high levels of turbulence seem unlikely for the TS [30]. The MRI mechanism, on the other hand, is ideally suited for the pre-acceleration of low energy PUIs at the TS because of the preferential reflection and acceleration of PUIs with a small velocity component along the shock normal [7]. Test particle simulations show that unaccelerated PUIs can be efficiently pre-accelerated at a perpendicular shock to energies of --1 MeV which should be sufficient for injection [7]. This and other work also suggest that hard MRI spectra with an omnidirectional distribution function fMRI (P) ~ p-4 result for uncooled --1 keV PUIs. The implication of these MRI spectra are an associated large MRI pressure of the order of the upstream solar wind ram pressure given that a significant fraction of PUIs are MRI-accelerated as predicted by theory [7]. This suggests that self-consistent calculations need to be done to investigate whether TS mediation by the MRI particles and the ACR source that develops from these particles after injection will not weaken the TS to such a degree that MRI acceleration and injection becomes inefficient. This will be discussed in 3.2. It might be argued that the MRI acceleration mechanism is not the answer for local PUI pre-acceleration at the TS because it predicts the preferential pre-acceleration of the lighter

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Anomalous cosmic rays: Current and future theoretical developments

PUI elements [7] while the opposite has been concluded from the observed composition of the ACR component [1]. Based on two models for perpendicular diffusion, namely, either a resonant diffusion model using a classical scattering approach, or a postulated model determined by field line random walk, a recent calculation shows that a threshold velocity for injection into standard diffusive shock acceleration can be derived which, when applied to the locally MRI pre-accelerated PUIs at the TS, results in ACRs with a similar composition as observed [31 ]. The possibility also exists that the TS is not nearly perpendicular but somewhat more oblique on average. In this case stochastic magnetic mirroring acceleration becomes a candidate for low-energy PUI pre-acceleration because it operates at much lower energies than for a nearly perpendicular TS. Unaccelerated PUIs, however, do not have enough energy to undergo magnetic mirroring at the TS so that pre-acceleration upstream is needed [ 18, 19]. However, recent simulations show that unaccelerated PUIs can be injected into the magnetic mirroring mechanism at a more oblique TS with the aid of MRI acceleration [19]. This implies that at a more oblique TS low-energy PUIs might locally be pre-accelerated in two stages followed by standard diffusive shock acceleration as the third stage. Another argument is that the TS will only be nearly perpendicular on average, but some part of the time quasi-parallel when the threshold is lower. Diffusive shock acceleration of PUIs during times when the TS is quasi-parallel can then serve to bring PUIs across the threshold. Alternatively, PUIs might be pre-accelerated where the TS is most of the time quasi-parallel as expected at high heliolatitudes and then be transported down toward the equatorial plane along the TS front where the TS is expected to be nearly perpendicular. This would be effective when the polarity of the IMF was directed inward above, and outward below, the HCS, in which case particles would drift from high to low latitudes along the TS in both the northern and southern hemispheres. On the basis of work referenced it seems plausible that both low-energy PUIs locally preaccelerated at the TS as well those pre-accelerated upstream will contribute to the formation of the ACR component. The challenge for current and future research is to find which part of the PUI spectrum makes the dominant contribution. 3.2 How pre-accelerated pickup ions and anomalous cosmic rays affect the termination shock structure

One of the exciting discoveries to be made by the Voyager spacecraft is the solar wind TS structure and position, which will be the first in situ observation of such a structure. In this regard it will be interesting to know whether and to what degree pre-accelerated PUIs and ACRs can mediate the TS. If enough PUIs are injected into diffusive shock acceleration at the TS, simulations show that ACRs have the potential to modify the TS significantly [32]. This follows because ACRs are more or less non-relativistic particles with short enough mean free paths so that a large pressure gradient might develop at the TS. Unfortunately, the injection efficiency is at this stage a poorly constrained parameter due to uncertainties about how PUI injection occurs as discussed above. In recent work [33, 34], further progress was made by going beyond the ad-hoc approaches used to inject PUIs into diffusive shock acceleration at the TS in ACR transport models. This was achieved by using the main features of the theory for MRI acceleration of PUIs [7] to model the physics of injection for a nearly perpe