DYNAMICS OF STAR CLUSTERS

INTERNATIONAL ASTRONOMICAL UNION

UNION ASTRONOMIQUE INTERNA TIONALE

DYNAMICS OF STAR CLUSTERS

PROCEEDINGS OF THE 113th SYMPOSIUM OF THE INTERNA TIONAL ASTRONOMICAL UNION, HELD IN PRINCETON, NEW JERSEY, U.S.A,

29 MAY - 1 JUNE, 1984

EDITED BY

JEREMY GOODMAN California Institute of Technology,

Pasadena, California, U.S.A.

and

PIET HUT The Institute for Advanced Study,

Princeton, New Jersey, U.S.A.

D. REIDEL PUBLISHING COMPANY

A MEMBER OF THE KLUWER ACADEMIC PUBLISHERS GROUP

DORDRECHT/BOSTON/LANCASTER

Library of Congress Cataloging in Publication Data

International Astronomical Union. Symposium (1 13th: 1984: Princeton, N.J.) Dynamics of star clusters.

Includes index. 1. Stars-Clusters-Congresses. 2. Stars-Globular clusters-Congresses.

3. Stars-Open clusters-Congresses. I. Goodman, Jeremy, 1956-II. Hut, Piet, 1952- III. Title. QB853.I58 1984 523.8'5 85-1870

ISBN-13: 978-90-277-1965-2 e-ISBN-13: 978-94-009-5335-2 DOl: 10.1007/978-94-009-5335-2

Published on behalf of the International Astronomical Union

by D. Reidel Publishing Company, P. 0. Box 17, 3300 AA Dordrecht, Holland

All Rights Reserved © 1985 by the International Astronomical Union

Softcover reprint of the hardcover 1 st edition 1985

Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers,

190 Old Derby Street, Hingham, MA 02043, U.S.A.

In all other countries, sold and distributed by Kluwer Academic Publishers Group,

p. 0. Box 322, 3300 AH Dordrecht, Holland

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from

the publisher

TABLE OF CONTENTS

Preface Conference Photograph (Frontispiece) List of Participants

MAY 29 OBSERVATIONS OF GLOBULAR CLUSTERS

Ivan R. King OBSERVED SURFACE DENSITIES IN GLOBULAR CLUSTERS

Robert Lupton, James E. Gunn & Roger F. Griffin RADIAL VELOCITIES AND PROPER MOTIONS OF GLOBULAR CLUSTER STARS

Ie C. Freeman CHEMICAL GRADIENTS IN GLOBULAR CLUSTERS

Jonathan E. Grindlay X-RAYING THE DYNAMICS OF GLOBULAR CLUSTERS

M.. Auriere, J. P. Cordoni, O. Le Fevre, A. Terzan A HIGH SPATIAL RESOLUTION INVESTIGATION OF THE CORE OF SOME DYNfu~ICALLY EVOLVED GLOBULAR CLUSTERS

Kyle Cudworth, D.N.C. Lin&K.-S. Oh DYNAMICAL MODELING OF M13 PROPER MOTIONS

G.S. Da Costa & K.C. Freeman THE DYNAMICS OF 47 TUCANAE

S. Djorgovs'ki & H. Penner A SEARCH FOR POST-COLLAPSE CORES

P.J. Godwin CORE AND TIDAL RADI I OF THE CARINA mJAl-a·' SPHEROIDAL GALAXY FROM UK SCHMIDT TELESCOPE PLATES

William E. Harris & James E. Hesser A DEEP LUMINOSITY FUNCTION FOR 47 TUCANAE

E. Kontizas & M. Kontizas OBSERVED DYNAMICAL PARAMETERS OF STAR CLUSTERS IN THE SMC

xi xvi ixx

1

19

33

43

63

65

69

73

77

81

85

vi TABLE OF CONTENTS

P.M. Lugger, H. Cohn and J.E. Grindlay WHERE'S THE CUSP? (OR CCD PHOTOMETRY OF GLOBULAR CLUSTER CORES) 89

G. Meylan & M. Mayor ROTATIONAL FIELD AND VELOCITY DISPERSION IN GLOBULAR CLUSTERS: 93 w CEN AND 47 TUC

Charles J. Peterson BV CONCENTRIC APERTURE PHOTOMETRY OF GLOBULAR CLUSTERS 97

C.P. Pryor, David W. Latham & Martha L. Hazen-Liller AN EXTENSION OF THE SEARCH FOR SPECTROSCOPIC BINARIES IN M3 99

M.M. Shara, A.F.J. Moffat & D.A. Hanes A SEARCH FOR CATACLYSMIC BINARIES IN THE GLOBULAR CLUSTER M3 103

Graeme H. Smith POSSIBLE CHARACTERISTICS OF SUPERNOVA INDUCED ENRICHMENT OF 105 GLOBULAR CLUSTERS

DYNAMICAL EVOLUTION OF GLOBULAR CLUSTERS

Lyman Spitzer, Jr. PRE COLLAPSE EVOLUTION OF GLOBULAR CLUSTERS 109

Douglas C. Heggie DYNAMICAL EVOLUTION OF GLOBULAR CLUSTERS AFTER CORE COLLAPSE 139

MAY 30 MODEL SYSTEM IN THE POINT-MASS APPROXIMATION

Haldan Cohn DIRECT FOKKER-PLANCK CALCULATIONS

Jeremy Goodman CLOSE ENCOUNTERS

Shogo Inagaki DYNAMICAL EVOLUTION OF MULTI-COMPONENT CLUSTERS

Daiichiro Sugimoto GASEOUS MODELS

Erich Bettwieser GRAVOTHERMAL OSCILLATIONS

Piet Hut BINARY FORMATION AND INTERACTIONS WITH FIELD STARS

Sverre J. Aarseth DIRECT N-BODY CALCULATIONS

161

179

189

207

219

231

251

TABLE OF CONTENTS

Alan P. Lightman & Stephen L. W. McMillan A UNIFIED N-BODY AND STATISTICAL TREATMENT OF STELLAR DYNAMICS

J.G. Jernigan DIRECT N-BODY SIMULATIONS WITH A RECURSIVE CENTER OF MASS REDUCTION AND REGULARIZATION

S. Michael Fall & Carlos S. Frenk ROTATION AND FLATTENING OF GLOBULAR CLUSTERS

Joshua Barnes DYNAMICAL INSTABILITIES IN SPHERICAL STELLAR SYSTEMS

E. Bettwieser, K.J. Fricke, R. Spurzem WHY ARE STELLAR SYSTEMS ANISOTROPIC?

Stefano Casertano A STATISTICAL TREATMENT OF LOW-N SYSTEMS

Jacques Colin MINIMUM OF THE ECCENTRICITY OF THE GALACTIC GLOBULAR CLUSTER ORBITS

Eldad Dagan FUNCTIONAL INTEGRALS IN STELLAR DYNAMICS

Emmanuel Davoust MULTI-COMPONENT MODELS FOR THE STRUCTURE AND EVOLUTION OF SPHERICAL STELLAR SYSTEMS

G.Giannone & D. Molteni THE ROLE OF HARD BINARIES IN CLUSTER EVOLUTION

Henry E. Kandrup COLLISIONAL STELLAR DYNAMICS IN GENERAL RELATIVITY: AN OVERVIEW

Robert Lupton 3-INTEGRAL MODELS FOR GLOBULAR CLUSTERS

Stephen L.W. McMillan THE EARLY STAGES OF POST-COLLAPSE CLUSTER EVOLUTION

Seppo Mikkola NUMERICAL SIMULATIONS OF ENCOUNTERS OF HARD BINARIES

G. Severne & M. Luwel COLLISIONAL RELAXATION: A NEW APPROACH

vii

261

275

285

297

301

305

309

313

317

321

323

327

331

335

339

viii TABLE OF CONTENTS

.MAY 31 EXTERNAL FIELDS AND FINITE-STAR-SIZE EFFECTS

P. Seitzer TIDAL EFFECTS o.N GLo.BULAR CLUSTERS 343

Jeremiah P. o.striker PHYSICAL INTERACTIo.NS BETWEEN STARS 347

J.S. Stod6lkiewicz Mo.NTE-CARLo. CALCULATIo.NS 361

Stuart L. Shapiro Mo.NTE CARLO. SIMULATIo.NS o.F THE 2+1 DIMENSIo.NAL Fo.KKER-PLANCK 373 EQUATIo.N: SPHERICAL STAR CLUSTERS Co.NTAINING MASSIVE, CENTRAL BLACK Ho.LES

Martin J. Duncan CAN A Mo.DERATELY MASSIVE BLACK Ho.LE REVERSE Co.RE Co.LLAPSE? 415

M. Giersz TWO. Bo.DY CAPTURE IN LARGE N Bo.DY SYSTEMS 419

Richard B. Larson BLACK-Ho.LE REMNANTS IN GLo.BULAR CLUSTERS 421

T.S. van Albada & T.R. Bontekoe TIDAL STRIPPING AND DISRUPTIo.N o.F GLo.BULAR CLUSTERS 423

o.PEN CLUSTERS

Robert D. Mathieu THE STRUCTURE AND INTERNAL KINEMATICS o.F o.PEN CLUSTERS

Roland Wielen DYNAMICS o.F o.PEN STAR CLUSTERS

Michael Margulis, Charles J. Lada and David Dearborn THE DYNAMICAL EVo.LUTIo.N o.F yo.UNG o.PEN CLUSTERS

A.F.J. Moffat, W. Seggewiss and M.M. Shara THE DENSE STELLAR Co.RES o.F GIANT HII REGIo.NS

Elena Terlevich N-Bo.DY SIMULATIo.NS o.F REALISTIC o.PEN CLUSTERS

Floor van Leeuwen A PRo.PER Mo.TIo.N STUDY o.F THE PLEIADES CLUSTER

427

449

463

467

471

477

TABLE OF CONTENTS

JUNE 1 THE DYNAMICS OF STAR CLUSTERS: FUTURE PROSPECTS

John N. Baheall SPACE TELESCOPE OBSERVATIONS OF GLOBULAR CLUSTERS

Lyman Spitzer, Jr., Chairman of the PANEL DISCUSSION: WHAT NEXT? PRIORITIES IN THEORY AND OBSERVATIONS

Jeremiah P. Ostriker SOME SUMMARY REMARKS

Appendix I: V. A. Arnbartsumian

APPENDICES

ON THE DYNAMICS OF OPEN CLUSTERS

Appendix II: V. A. Antonov MOST PROBABLE PHASE DISTRIBUTION IN SPHERICAL STAR SYSTEMS AND CONDITIONS FOR ITS EXISTENCE

Appendix III: R. F. Webbink STRUCTURE PARAMETERS OF GALACTIC GLOBULAR CLUSTERS

Appendix IV: Floor van Leeuwen PROPER MOTION STUDIES OF STARS IN AND AROUND OPEN CLUSTERS

Index of Names

Index of Subjects

ix

481

499

511

521

525

541

579

607

615

PREFACE

The emphasis in these proceedings of lAD Symposium No. 113, Dynafrri-,'!s of Star Clusters. and·.~.Le. mab rPIHlon for orZ'lnizinp: thE" symposium in the spring of 1984, was the rapid increase during the preceeding year in our understanding of core collapse. The last I.A.D. Symposium to discuss the dynamics of star clusters at length was No.69, Dynamics of Stellar Systems~ held in Besan~on in 1974. For a few years afterwards, globular clusters receiveu much attention due to the discovery of X-ray bursters and the mounting evidence that X-ray sources in globular clusters were formed in completely different ways than those within our galaxy. Globular clusters, which until this time had a reputation for sedate old age, turned out to lead violent private lives at high energies.

However, in the early 80's globular clusters seemed to lose some of the glamor of the 70's. The grand speculations of heavy black holes lurking in their centers had to make way for a variety of observational evidence which indicated that the X-ray sources are low-mass close binaries instead. But, though dynamical fashion turned to heavy galac­tic halos and so on, some of the unsolved theoretical problems regard­ing the evolution of star clusters kept their fascination for a number of relatively isolated workers. After several years of inconspicuous labor, a number of preprints suddenly appeared in the spring of 1983 that studied the evolution of globular clusters after core collapse. This problem had been recognized clearly in the heyday of X-ray enthus­iasm, but with the notable exception of early work by Henon, all pre­vious attempts to model post-collapse evolution posited the existence of a massive central black hole.

With the appearance of detailed models of the post-collapse regime, a renaissance in globular cluster evolutionary calculations occurred, comparable to the rapid progress in stellar evolution in the late 50's. It was this development which led us to propose this symposium. The international scientific organizing committee decided to organize the symposium in a slightly unusual fashion. Recognizing the many devel­opments which had been taking place during the ten years since the pre­vious lAD symposium in Besancon, the committee expressed their inten­tion that the new symposium playa double role: to review those past developments; and to provide a forum for discussion of future direc­tions of research, both theoretical and observational. The feeling of the organizers was that these goals could best be reached by scheduling only a limited number of invited speakers, together with a larger num­ber of participants in poster sessions. In this way two objectives could be realized: the many new lines of research could be reviewed in a less hectic and more coherent way than would be possible if time were

xi

PREFACE

divided equally among all participants, and more time would be avail­able between the talks for informal discussion. We will leave it to the participants and to the readers of these proceedings to judge the success of this plan.

We regret that Dr. L. M. Ozernoy was not able to attend the sym­posium and deliver his invited lecture, due to circumstances beyond his control. Although he informed us that he intended to submit the in­vited paper for the proceedings, we unfortunately had not yet received his contribution by the time these proceedings went to press.

We editors do appreciate the many positive reactions we received at the end of the symposium; the enthusiasm of the participants was all the more gratifying because of the nearly incessant rain that they suffered and that obscured a near-total eclipse. (The group photograph included here gives an utterly false impression of the usual weather, as any participant will admit.)

Those of you who actually read prefaces, and especially those who work on open clusters, may have noticed a bias in favor of globular clusters. The main reason for this is that much recent progress has been made in understanding the latter objects, whereas the dynamics of open clusters have been less well explored, both theoretically and ob­servationally. In many ways the dynamics of open clusters are more difficult to study than those of globular clusters: theoretically, be­cause the combination of the lower number of stars and the younger age of open clusters make a statistical description much more difficult and its validity more questionable; and observationally, because the velo­city dispersion in'an open cluster is typically an order of magnitude lower than that in a globular cluster. These difficulties notwithstand­ing, significant progress has been made recently and is reported in these proceedings, and it is possible that in another ten years the study of open clusters may dominate a future star cluster symposium, in part because this study promises to increase our understanding of star formation in the galactic disk.

We express our hope that in the coming years the proceedings ,of this symposium will prove to be as valuable as those of its predecessor, I.A.D. Symposium 69, as a reference work for research on the dynamics of star clusters. To this end we urged all invited speakers to make a broad survey of their topics. In addition, on the final day of the symposium a discussion was held among a panel of six wise men to assess the scientific progress revealed by the conference and to identify the most promising directions for future research, a summary of which has been included here.

Four appendices have been added. The first contains an English translation of a classic paper by Arnbartsumian, in which he showed for the first time that the evolution of an isolated self-gravitating star cluster under the influence of two-body relaxation does not cease with the establishment of a maxwellian velocity distribution. The second appendix is a translation of that seminal paper by V.A. Antonov which led eventually to our present understanding of the gravothermal insta­bility. We would have liked to include a translation of Michel Henon's (1961) Ph.D. thesis, which has been much neglected but predicted many of

PREFACE xili

the essential phenomena of cluster evolution after core collapse; we felt, however, that the paper was too long to include in this already lengthy volume. To honor H~non's fundamental contributions, we have in­stead reproduced one of the illustrations which appeared in his thesis, side to side with a new calculation (reported in these proceedings by Stodolkiewicz) confirming many of the results obtained by Henon nearly a quarter century ago. We hope that his thesis will soon appear in translation elsewhere and thereby become accessible to a larger fraction of those working presently on the dynamics of star clusters.

The third appendix contains a list of observed parameters of globular clusters with the original references, compiled by Webbink, and a similar list for open clusters, by van Leeuwen, forms the fourth appendix. These appendices should increase the long-term value of this book sufficiently, even with the inevitable increase of the volume and thereby the price of the present proceedings. A detailed index of names and subjects follows. This index covers all papers and discus­sions included in these proceedings with the exception of the appendices which are already written in the form of compilations.

We must apologize to the reader for our failure to correct many small errors of grammar and spelling (sometimes even in the spelling of names) in the camera-ready manuscripts; we felt that since none of these errors is likely to cause confusion, our limited resources and the importance of publishing the proceedings quickly required that we let them pass. For errors in the organization of the book and in the indices we are, of course, wholly responsible.

We acknowledge the assistance which we received from many people, without whose help this symposium would not have been possible. We thank John Bahcall, Jeremiah Ostriker and Lyman Spitzer for their en­thusiastic support of our early plans to organize this symposium. We thank Harry Woolf and the Institute for Advanced Study for their hospi­tality. We thank Mary Wisnovsky, the conference coordinator, for her administrative expertise and enthusiastic support. We thank all the participants for their contributions, and especially the panel members who were rounded up at the last moment to give their impromptu comments. We thank Jens Verner Villumsen and Robert Lupton for their efficient and smooth organization of local affairs, scientifically and culturally. We thank Nels Anderson, Web Ewell, Steve Ratcliff and Tom Statler for their untiring operation of audiovisual aids. We thank Donald Lynden­Bell, Stuart Shapiro and Lyman Spitzer for supplying us with copies of originals and translations of the material in the first two appendices. The first appendix has been translated by Ludmilla Wightman, whose cheerful help we happily acknowledge. The second appendix is a revi­sion by Ludmilla Wightman of a translation by the British Admirality Translation Service. We thank Ron Webb ink and Floor van Leeuwen for delivering custom-made appendices, number three and four, respectively, on short notice. We thank Grace Rapp, Marge Barbosa and Barbara Pink­ham for their indefatigable assistance in the various stages of organi­zing the symposium and preparing these proceedings. Finally we express our thanks to the California Institute for Technology and especially to the Institute for Advanced Study, for bearing the expenses of both com-

xiv PREFACE

puter time and secretarial assistance needed for the preparation of these proceedings.

The members of the Scientific and Local Organizing Committees are listed below. We are grateful to them for their contribution to the success of this symposium.

Scientific Organizing Committee:

T.A. Agekian, K.C. Freeman, D.C. Heggie, P. Hut (Chairman), S. lnagaki, I.R. King, L.M. Ozernoy, L. Spitzer, J. Stodolkiewicz, R. Wielen.

Local Organizing Committee:

J.N. Bahcall, R. Lupton, J.V. Villumsen (Chairman), M. Wisnovsky.

The Editors,

Jeremy Goodman & Piet Hut

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LIST OF PARTICIPANTS

Aarseth, 3. J. Adler, D. S. Aguilar, 1. A. Anderson, N. Applegate, J.

Auriere, M. Bahcall, J. N. Bahcall, N. A. Barnes, J. Beichman, C.

Bettwieser, E. Casertano, S. Cohn, H. Colin, J. Cudworth, K.

Da Costa, G. S. Dagan, E. Davoust, E Des Forets, G. Djorgovski, S.

Dones, L. Duncan, M. J. Ewell, M. Fall, S. M. Freeman, K. C.

Frenk, C. S. Giannone, G. Gilden, D. Godwin, P. Goodman, J.

Grindlay, J. Gunn, J. E. Hanes, D.A. Harris, W. E. Heggie, D.C.

Cambridge, England, U.K. Charlottesville, VA, U.S.A. Berkeley, CA, U.S.A. Princeton, NJ, U.S.A. Pasadena, CA, U.S.A.

Observatorie du Pic du Midi, France Princeton, NJ, U.S.A. Baltimore, MD, U.S.A. Berkeley, CA, U.S.A. Pasadena, CA, U.S.A.

Gottingen, Germany Princeton, NJ, U.S.A. Bloomington, IN, U.S.A. Besancon, France Williams Bay, WI, U.S.A.

New Haven, CT, U.S.A. Jerusalem, Israel Besancon, France Paris: France Berkeley, CA, U.S.A.

Berkeley, CA, U.S.A. Scarborough, Ontario, Canada Princeton, NJ, U.S.A. Cambridge, England, U.K. Canberra, Australia

Santa Barbara, CA, U.S.A. Palermo, Italy Princeton, NJ, U.S.A. Edinburgh, Scotland, U.K. Pasadena, CA, U.S.A.

Cambridge, MA, U.S.A. Princeton, NJ, U.S.A. Kingston, Ontario, Canada Hamilton, Ontario, Canada Edinburgh, Scotland, U.K.

xx

Hut, P. Inagaki, S. Ipser, J. R. Jarvis, B. Jernigan, J. G.

Jog, C. J. Kandrup, H. E. King, 1. R. Kylafis, N. Lachieze-Rey, M.

Lake, G. R. Larson, R. B. Latham, D. Leonard, P. J. T. Lightman, A. P.

Lo Cascio, L. Lugger, P. Lupton, R. Luwel, M. Mamon, G.

Margulis, M. Mathieu, R. D. Mayor, M. McMillan, S. Meylan,G.

Mikkola, S. Moffat, A. Ostriker, J. P. Peterson, C. J. Phinney, E. S.

Pryor, C. P. Radhakrishnan, V.

Ratcliff, S. Ratnatunga, K. Schommer, R. A.

Seitzer, P. Semenzato, R. Severne, G. Shapiro, S. L. Shara, M.

LIST OF PARTICIPANTS

Princeton, NJ, U.S.A. Kyoto, Japan Gainesville, FL, U.S.A. La Serena, Chile Berkeley, CA, U.S.A.

Princeton, NJ, U.S.A. Austin, TX, U.S.A. Berkeley, CA, U.S.A. Princeton, NJ, U.S.A. Gif-sur-Yvette, France

Murray Hill, NJ, U.S.A. New Haven, CT, U.S.A. Cambridge, MA, U.S.A. Toronto, Ontario, Canada Cambridge, MA, U.S.A.

Palermo, Italy Columbia, MO, U.S.A. Princeton, NJ, U.S.A. Brussel, Belgium Princeton, NJ, U.S.A.

Tucson, AZ, U.S.A. Cambridge, MA, U.S.A. Sauverny, Switzerland Urbana, IL, U.S.A. Sauverny, Switzerland

Turku, Finland Montreal, Quebec, Canada Princeton, NJ, U.S.A. Columbia, MO, U.S.A. Princeton, NJ, U.S.A.

Victoria, BC, Canada Bangalore, India

Princeton, NJ, U.S.A. Princeton, NJ, U.S.A. New Brunswick, NJ, U.S.A.

Tucson, AZ, U.S.A. Padova, Italy Brussel, Belgium Ithaca, NY, U.S.A. Baltimore, MD, U.S.A.

LIST OF PARTICIPANTS

Smith, G. Smith, Jr., H. Spitzer, L. Statler, T. Stodolkiewicz, J.

Sugimoto, D. Sygnet, J. F. Terlevich, E. Toomre, A. Tremaine, S. D.

van Albada, T. van Leeuwen, F. Verter, F. Vi llums en , J. V. Wandel, A. Webb ink , R. F.

White, S. Wielen, R.

Cambridge, MA, U.S.A. Gainesville, FL, U.S.A. Princeton, NJ, U.S.A. Princeton, NJ, U.S.A. Warszawa, Poland

Tokyo, Japan Paris, France

xxi

Hailsham, East Sussex, England, U.K. Cambridge, MA, U.S.A. Cambridge, MA, U.S.A.

Groningen, The Netherlands Hailsham, East Sussex, England, U.K. Troy, NY, U.S.A. Princeton, NJ, U.S.A. Princeton, NJ, U.S.A. Urbana, 1L, U.S.A.

Santa Barbara, CA, U.S.A. Berlin, Germany