Polytropes Applications in Astrophysics and Related Fields

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ASTROPHYSICS AND SPACE SCIENCE LIBRARY VOLUME 306

EDITORIAL BOARD Chairman W.B. BURTON, National Radio Astronomy Observatory, Charlottesville, Virginia, U.S.A. ([email protected]); University of Leiden, The Netherlands ([email protected]) Executive Committee J. M. E. KUIJPERS, Faculty of Science, Nijmegen, The Netherlands E. P. J. VAN DEN HEUVEL, Astronomical Institute, University of Amsterdam, The Netherlands H. VAN DER LAAN, Astronomical Institute, University of Utrecht, The Netherlands MEMBERS I. APPENZELLER, Landessternwarte Heidelberg-Königstuhl, Germany J. N. BAHCALL, The Institute for Advanced Study, Princeton, U.S.A. F. BERTOLA, Universitá di Padova, Italy J. P. CASSINELLI, University of Wisconsin, Madison, U.S.A. C. J. CESARSKY, Centre d'Etudes de Saclay, Gif-sur-Yvette Cedex, France O. ENGVOLD, Institute of Theoretical Astrophysics, University of Oslo, Norway R. McCRAY, University of Colorado, JILA, Boulder, U.S.A. P. G. MURDIN, Institute of Astronomy, Cambridge, U.K. F. PACINI, Istituto Astronomia Arcetri, Firenze, Italy V. RADHAKRISHNAN, Raman Research Institute, Bangalore, India K. SATO, School of Science, The University of Tokyo, Japan F. H. SHU, University of California, Berkeley, U.S.A. B. V. SOMOV, Astronomical Institute, Moscow State University, Russia R. A. SUNYAEV, Space Research Institute, Moscow, Russia Y. TANAKA, Institute of Space & Astronautical Science, Kanagawa, Japan S. TREMAINE, CITA, Princeton University, U.S.A. N. O. WEISS, University of Cambridge, U.K.

POLYTROPES Applications in Astrophysics and Related Fields

by G.P. HOREDT Deutsches Zentrum für Luft- und Raumfahrt DLR, Wessling, Germany

KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

eBook ISBN: Print ISBN:

1-4020-2351-0 1-4020-2350-2

©2004 Springer Science + Business Media, Inc. Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America

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TABLE OF CONTENTS

1

Polytropic and Adiabatic Processes 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

2

1

Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polytropic and Adiabatic Processes in a Perfect Gas . . . . . . . . . . . . . . . . . . . . Polytropic Processes for a General Equation of State . . . . . . . . . . . . . . . . . . . . Adiabatic Processes in a Mixture of Black Body Radiation and Perfect Gas . . . . . . . Adiabatic Processes in a Mixture of Electron-Positron Pairs and Black Body Radiation Adiabatic Processes in a Completely Degenerate Electron or Neutron Gas . . . . . . . . Numerical Survey of Equations of State, Adiabatic Exponents, and Polytropic Indices . Emden’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .