The Restless Universe Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems PDF
Preview The Restless Universe Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems
THE RESTLESS UNIVERSE APPLICATIONS OF GRAVITATIONAL N-BODY DYNAMICS TO PLANETARY, STELLAR AND GALACTIC SYSTEMS Proceedings of the Fifty Fourth Scottish Universities Summer School in Physics, Blair Atholl, 23 July 5 August 2000. - A NATO Advanced Study Institute Edited by B A Steves - Glasgow Caledonian University A J Maciejewski - Nicolaus Copernicus University Series Editor P Osborne - University of Edinburgh Copublished by Scottish Universities Summer School in Physics & Institute of Physics Publishing, Bristol and Philadelphia Copyright © 2001 The Scottish Universities Summer School in Physics Copyright @ 2001 The Scottish Universities Summer School in Physics No Part of this book may be reproduced in any form by photostat, microfilm or any other means without written permission from the publishers. British Library cataloguing-in-Publication Data: A catalogue record for this book is available from the British Library ISBN 0- 7503-0822-2 Library of Congress Cataloging-in-Publication Data are available. Copublished by SUSSP Publications The Department of Physics, Edinburgh University, The King’s Buildings, Mayfield Road, Edinburgh EH9 352, Scotland. and Institute of Physics Publishing, wholly owned by The Institute of Physics, London. Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. US Editorial Office: Institute of Physics Publishing, The Public Ledger Building, Suite 1035, 150 Independence Mall West, Philadelphia, PA 19106, USA. Printed in Great Britain by J W Arrowsmith Ltd, Bristol. Copyright © 2001 The Scottish Universities Summer School in Physics SUSSP Proceedings 1 1960 Dispersion Relations 2 1961 Fluctuation, Relaxation and Resonance in Magnetic Systems 3 1962 Polarons and Excitons 4 1963 Strong Interactions and High Energy Physics 5 1964 Nuclear Structure and Electromagnetic Interactions 6 1965 Phonons in Perfect and Imperfect Lattices 7 1966 Particle Interactions at High Energy 8 1967 Methods in Solid State and Superfluid Theory 9 1968 Physics of Hot Plasmas 10 1969 Quantum Optics 11 1970 Hadronic Interactions of Photons and Electrons 12 1971 Atoms and Molecules in Astrophysics 13 1972 Properties of Amorphous Semiconductors 14 1973 Phenomenology of Particles at High Energy 15 1974 The Helium Liquids 16 1975 Non-linear Optics 17 1976 Fundamentals of Quark Models 18 1977 Nuclear Structure Physics 19 1978 Metal Non-metal Transitions in Disordered Solids 20 1979 Laser-Plasma Interactions: 1 21 1980 Gauge Theories and Experiments at High Energy 22 1981 Magnetism in Solids 23 1982 Lasers: Physics, Systems and Techniques 24 1982 Laser-Plasma Interactions: 2 25 1983 Quantitative Electron Microscopy 26 1983 Statistical and Particle Physics 27 1984 Fundamental Forces 28 1985 Superstrings and Supergravity 29 1985 Laser-Plasma Interactions: 3 30 1985 Synchrotron Radiation Sources and their Applications 31 1986 Localisation and Interaction 32 1987 Computational Physics 33 1987 Astrophysical and Laboratory Spectroscopy 34 1988 Optical Computing 35 1988 Laser-Plasma Interactions: 4 /continued V Copyright © 2001 The Scottish Universities Summer School in Physics sus SP Proceedings (continued) 36 1989 Physics of the Early Universe 37 1990 Pattern Recognition and Image Processing in Physics 38 1991 Physics of Nanostructures 39 1991 High Temperature Superconductivity 40 1992 Quantitative Microbeam Analysis 41 1992 Nonlinear Dynamics and Spatial Complexity in Optical Systems 42 1993 High Energy Phenomenology 43 1994 Determination of Geophysical Parameters from Space 44 1994 Quantum Dynamics of Simple Systems 45 1994 Laser-Plasma Interactions 5: Inertial Confinement Fusion 46 1995 General Relativity 47 1995 Laser Sources and Applications 48 1996 Generation and Application of High Power Microwaves 49 1997 Physical Processes in the Coastal Zone 50 1998 Semiconductor Quantum Optoelectronics 51 1998 Muon Science 52 1998 Advances in Lasers and Applications 53 1999 Soft and J?ragile Matter 54 2000 The Restless Universe 55 2001 Heavy Flavour Physics vi Copyright © 2001 The Scottish Universities Summer School in Physics Lecturers Sverre Aarseth Institute of Astronomy, Cambridge, UK Alessandra Celletti Universith di Roma Tor Vergata Hugh Couchman McMaster University, Ontario Rudolf Dvorak University of Vienna, Austria Claude Froeschlh Observatoire de la Cote d'Azur Douglas Heggie University of Edinburgh Martin Hendry University of Glasgow Andrzej J Maciejewski Nicolaus Copernicus University, Torun Christian Marchal D.E.S. ONERA, Chatillon, France Michael Merrifield University of Nottingham David Merritt Rutgers University, New Jersey Philip James Message University of Liverpool Andrea Milani Universita di Pisa Tom Quinn University of Washington, Seattle Carles Sim6 Universitat de Barcelona Bonnie A Steves Glasgow Caledonian University David Vokroulickj, Charles University, Prague Joerg Waldvogel ETH-Zentrum, Zurich Martin Weinberg University of Massachusetts Gustavo Yepes Universidad Aut6noma de Madrid Postal and e-mail addresses for lecturers, students and committee members can be found at . http://www.astro.gla,ac.uk/users/martin/nato/natoconf.html vii Copyright © 2001 The Scottish Universities Summer School in Physics Executive Committee Dr B A Steves Glasgow Caledonian Univ. Co-Director and Co-Editor Prof. A E Roy University of Glasgow Treasurer Dr M Hendry University of Glasgow Secretay International Advisory Committee Dr B A Steves Glasgow Caledonian Univ. Co-Director and Co-Editor Prof. A J Maciejewski Nicolaus Copernicus Univ. Co-Director and Co-Editor Prof. C1 Froeschlk Observatoire de Nice, France Prof. D Heggie University of Edinburgh, Scotland Dr M Hendry University of Glasgow, Scotland Prof. A Milani Universita di Pisa, Italy viii Copyright © 2001 The Scottish Universities Summer School in Physics Preface The gravitational N-body problem dominates much of theoretical astrophysics. It arises in problems ranging from the motion of artificial and natural satellites to the behaviour of stars in star clusters and galaxies and the formation of large-scale structure in the universe. Since the early years of the twentieth century, the techniques and scientific issues involved in gravitational dynamics have diversified widely. Recently, however, there have been signs for the need to exchange ideas and techniques between the disciplines of celestial mechanics, stellar dynamics and galactic dynamics as many of the established techniques in one field are being rediscovered or reinvented for use in another field. This especially concerns theoretical achievements allowing better understanding of dynamics in multidimensional phase space and global properties of investigated systems. This state of the art textbook provides an invaluable reference volume for all students and researchers in these subjects. Based on the recent joint NATO Advanced Study Insti- tute and Scottish Universities Summer School in Physics entitled ‘The Restless Universe: Applications of Gravitational N-Body Dynamics to Planetary, Stellar and Galactic Sys- tems’, the book, written by the lecturers at the School, is aimed at young scientists at PhD level who wish to learn of recent developments in their fields. By the nature of the different themes involved in N-body gravitational dynamics, the book is also relevant to research specialists in each field providing them with an up-to-date synoptic view of their own discipline, while enabling them to obtain a review of gravitational N-body dynamics from the viewpoint of the other disciplines. A major aim of the volume, like that of the School, is to lead the reader from a strong element of review in tutorial form to a clear picture of the state-of-the-art of research being conducted in the application of gravitational N-body dynamics in the following fields. Within the Solar System (the traditional realm of celestial mechanics), studies of the three, four or few body problems come into their own. Recent numerical and analytical methods such as the use of fast Lyapunov indicators are being used to study chaos and resonance in the three body problem. While exciting applications of these new analyses are found in such studies as the distribution and impact probabilities of Near Earth Asteroids, the formation and evolution of planetary systems and more particularly in the dynamics of small bodies in the solar system, in recent years it has become apparent that the developing theory of chaotic motion in celestial mechanics has also serious application in the relaxation of galactic structures. Stellar dynamics is the application of the N-body problem to the formation, evolution and dynamics of galaxies, star clusters, and multiple star systems of few bodies. It therefore finds common ground with both cosmology and celestial mechanics. Specially tailored algorithms and specially designed computer hardware are developed to handle the N- body problem to high accuracy and high speed. Such techniques, for example, are becoming increasingly important in the study of galaxy formation where direct numerical ix Copyright © 2001 The Scottish Universities Summer School in Physics simulations of galaxy formation are fast approaching the resolution required to model galaxy morphology. Cosmology studies the formation and evolution of galaxies in the context of the stan- dard Big Bang model, and so draws together several other strands of cosmology, including the analysis of large scale structure and the physics of the early Universe. Numerical sim- ulations of large-scale structure we raising important questions about the relationship between galaxy evolution and the background cosmological model. Dynamical studies of the matter distribution in galaxy clusters, and their large scale streaming motions, are also being used to constrain the mean mass density of the universe and determine its eventual fate. Many of the well-established techniques of celestial mechanics and stellar dynamics are being rediscovered or reinvented to help study these problems. The SUSSP54/NATO AS1 was held in the Atholl Arms Hotel, Blair Atholl, Scotland. The two week long AS1 brought together 80 scientists from more than 30 countries. Blair Atholl in Perthshire was an ideal location for the School. It fitted the NATO criteria of being comparatively secluded and quiet, yet major towns were only one hour’s train journey away. The Atholl Arms Hotel, built in 1832, is completely refurbished in the style of a traditional highland hotel. Located in the heart of the Scottish highlands it enabled us to provide a variety of outdoor pursuits and cultural interests amidst spectacular mountain scenery. We would like to thank Professor Archie Roy, Dr Martin Hendry and Ms. Gail Penny (University of Glasgow), Dr Winston Sweatman (Napier University) and Mr Peter Duncan (Glasgow Caledonian University) for their unstinting help which contributed so much to the success of the School. The proprietor and hotel staff of the Atholl Arms Hotel are also in our debt for the high standard of service they provided. We are also indebted to the NATO Scientific Affairs Division and the SUSSP Committee for their valuable help and sponsorship. Further information on the School, including addresses of all participants, can be found at the web address: http://www.astro.gla.ac.uk/users/martin/nato/natoconf.htm.l Bonnie A Steves and Andrzej J Maciejewski CO-Directors, March 2001 X Copyright © 2001 The Scottish Universities Summer School in Physics Contents Solar system dynamics N-body simulations of the Solar System, planet formation, and galaxy clusters.. ............................................................. .l Thomas Quinn On the Trojan problem.. ....................................................... .21 Rudolf Dvorak and Elke Pilat-Lohinger Ideal resonance and Melnikov’s theorem. ..................................... .43 Philip J Message The Yarkovsky effect in the dynamics of the Solar System... .............. .53 David Vokrouhlicky’ Are science and celestial mechanics deterministic? Henri PoincarB, philosopher and scientist ..................................... 79 Christian Marchal Stellar kinematics and dynamics Regularization methods for the N-body problem ........................... .93 Sverre J Aarseth Escape in Hill’s problem.. ..................................................... .lo9 Douglas C Heggie Galactic dynamics Galaxies: from kinematics to dynamics., .................................... .129 Michael R Merrifield Non-integrable galactic dynamics. ............................................ .145 David Merritt Evolution of galaxies due to self-excitation. ................................. ,167 Martin D Weinberg f cont xi Copyright © 2001 The Scottish Universities Summer School in Physics - Cosmology Large scale structure dynamics Dynamical methods for reconstructing the large scale galaxy density and velocity fields.. ............................................................ ,191 Martin Hendy Cosmological numerical simulations: past, present and future .............2 17 Gustavo Yepes Gravitational N-body simulation of large-scale cosmic structure. .........,2 39 H M P Couchman General dynamics Periodic orbits of the planar N-body problem with equal masses and all bodies on the same path... ........................................... ,265 Carles Simd Central configurations revisited ......................... 285 Jorg Waldvogel Surfaces of separation in the Caledonian Symmetrical Double Binary Four Body Problem.,. .................. 301 Bonnie A Steves and Archie E Roy The Fast Lyapunov Indicator ................................................. ,327 Claude Froeschle', Massimiliano Guzzo and Elena Lega Determination of chaotic attractors in short discrete time series ..........3 39 Alessandra Celletti, Claude Froeschle', Igor V Tetko and Alessandro E P Villa Non-integrability in gravitational and cosmological models. ................3 61 Andrzej J Maciejewski Index... ......................................................................... ,387 xii Copyright © 2001 The Scottish Universities Summer School in Physics
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