Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects

661 Pages·1983·25.25 MB·English

by  Stuart L. Shapiro

Black Holes,
White Dwarfs,
and Neutron Stars
The Physics of Compact Objects
Black Holes,
White Dwarfs,
and Neutron Stars
THE PHYSICS OF
COMPACT OBJECTS
Stuart L. Shapiro
Saul A. Teukolsky
Cornell University, Ithaca, New York
W IL EY-
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To Our Families
Preface
This textbook is the outgrowth of a course on the physics of compact objects,
which we have taught at Cornell University since 1975. As a class, compact stars
consist of white dwarfs, neutron stars, and black holes. As the endpoint states of
normal stellar evolution, they represent fundamental constituents of the physical
Universe.
This book, like the course itself, is a product of the burst of scientific activity
commencing in the 1960s which centered on compact objects. During this period,
pulsars and binary X-ray sources were discovered in our Galaxy. These dis-
coveries proved to be milestones in the development of the field. They furnished
definitive proof of the existence of neutron stars, which had previously existed
only in the minds of a few theorists. They made plausible the possibility of black
holes and even pointed to a few promising candidates in the night sky. More
important, perhaps, these discoveries triggered new theoretical studies and ob-
servational programs designed to explore the physical nature of compact stars. A
whole generation of experimental and theoretical physicists and astronomers has
been trained to participate in ths exciting, ongoing investigation.
An area of active current research and great popular interest, the study of
compact objects is far from complete. Not all-nor even most-of the basic
questions concerning their structure and evolution are fully resolved. Neverthe-
less, answers to these questions seem to be within our eventual reach. The field is
now firmly established both as an observational and as a rigorous theoretical
branch of physics. New information and new insights are generated constantly.
Moreover, as compact objects undergo interactions involving all four of the
fundamental forces of Nature, some of these insights should have an important
impact on other branches of physics. Who could foresee, for example, that the
question of whether or not nuclear matter makes a phase transition to a quark
state at high density might be settled by observations made from an X-ray
satellite!
Our book is intended for beginning graduate students or advanced under-
graduates in physics and astronomy. No prior knowledge of astrophysics or
general relativity is assumed. Instead, we introduce the necessary concepts and
vii
viii Preface
mathematical tools in these areas as they are required. We do assume that the
reader has familiarity with electromagnetism, statistical mechanics and thermody-
namics, classical and quantum mechanics, and special relativity at the advanced
undergraduate or first-year graduate level.
Since we develop only enough general relativity for our purposes, advanced
students may wish to consult one of the excellent recent texts on general relativity
for reference or further reading. We recommend Gravitation by C. W. Misner,
K. S. Thorne, and J. A. Wheeler or Gravitation and Cosmology by S. Weinberg.
Students wishing to explore the physics of “normal” nuclear-burning stars, prior
to their gravitational collapse to compact objects, are encouraged to read
Principles of Stellar Evolution by D. Clayton or Principles of Stellar Structure,
Vols. I and 11, by J. P. Cox and R. T. Giuli. We reemphasize, however, that we
have made a serious attempt to keep our book entirely self-contained.
We present the material in its natural order: For each type of compact object
(white dwarf, neutron star, or black hole) we first analyze the physical properties
of the star in its “ground” state. For example, we initially focus on spherically
symmetric, nonrotating, zero-temperature configurations. Next, we analyze the
stars when they are subjected to “perturbations,” for example, rotation, magnetic
fields, transient thermal effects, accretion, and so on. As in most physical systems,
the structure of compact stars is best revealed when they are perturbed in some
manner. (Indeed, unperturbed compact stars in deep space are unobservable!) We
invoke observations to motivate and elucidate the theoretical discussion whenever
possible.
We try to provide simple (e.g., “one-dimensional”) analytic model calculations
for very complicated results or somewhat inaccessible numerical calculations.
Such analytic models serve to highlight underlying physical principles, even
though they may not be terribly precise. When these back-of-envelope calcula-
tions are presented in Lieu of more exact computations, we are always careful to
clearly state the exact results-if they exist.
In order to keep the book to a manageable length, we have been forced to be
selective in our choice of topics. Some of our choices were arbitrary and based on
personal preference. In other cases, we have deliberately chosen to emphasize
certain topics over others so that the book will not become rapidly outdated. For
example, an understanding of polytropic stellar models or the equation of state of
an ideal Fermi gas is likely to be useful to the student forever. Similarly, while an
exact treatment of neutron star cooling lies still in the future, it is clear already
what the important physical principles are and how the calculation will be done.
We have accordingly included a detailed prototype” calculation; the numbers
“
may change, but the ideas will remain the same. On the other hand, we are still
ignorant of the detailed mechanism of pulsar emission. It is not even clear which
aspects of the physics underlying present models will survive. We have accord-
ingly given a briefer treatment to this topic. In 10 years or so, the reader will have
the pleasure of seeing which of our emphases were justified!
Preface ix
To make the book suitable for use as a course textbook, we have included over
250 exercises to be worked by the student. These exercises are sprinkled liberally
throughout the main text. Some involve the completion of derivations begun or
sketched in the text; others are of a more challenging variety. Answers to many
exercises are given. Because most of the results contained in the exercises form an
integral part of the discussion and are referred to frequently, we suggest that the
student at least stop to read those exercises he or she does not intend to solve. Of
course, as is true in all branches of physics, true mastery of the concepts only
emerges after one works in the field: in this case, work means the solving of
problems. To make this activity more interesting, we have included a number of
“computer exercises” in the book. These are somewhat longer, numerical exercises
that can be solved on a programmable hand calculator or on any small computer.
They serve not only to illustrate a physical point, but also to introduce the student
to numerical problem solving on the computer.
There exist a number of outstanding books and review articles that discuss
many aspects of the subject matter developed here. We have referred to them
frequently throughout the volume. In addition to the texts cited above, Relativistic
Astrophysics, Vol. 1, by Ya. 9. Zel’dovich and I. D. Novikov may serve as a
particularly useful reference volume for interested students.
Not surprisingly, a great many people at numerous institutions contributed to
the preparation of ths volume. Indeed, it is virtually impossible for us to recall all
of the occasions when students and colleagues gave us invaluable criticism,
suggestions, and instruction. However, we are particularly grateful to several
colleagues for carefully reading portions of an earlier draft of the book and
providing us with crucial feedback. For their enthusiasm, unselfish investment of
time, and numerous contributions we thank C. Alcock, J. Arons, J. N. Bahcall,
J. M. Bardeen, H. A. Bethe, R. D. Blandford, S. Chandrasekhar, J. M. Cordes,
T. Gold, K. Gottfried, P. C. Joss, D. Q. Lamb, F. K. Lamb, A. P. Lightman,
C. W. Misner, J. P. Ostriker, F. Pacini, D. Pines, S. A. Rappaport, E. E. Salpeter,
S. W. Stahler, J. H. Taylor, Y. Terzian, K. S. Thorne, H. M. Van Horn, R. V.
Wagoncr, and I. Wasserman. In addition, quite a few colleagues offered needed
encouragement and support during the preparation of this volume, Among others,
we are indebted to W. D. Arnett, G. A. Baym, G. W. Clark, D. M. Eardley, W. A.
Fowler, R. Giacconi, J. 9. Hartle, S. W. Hawking, M. Milgrom, C. J. Pethick,
W. H. Press, R. H. Price, M. J. Rees, M. A. Ruderman, D. N. Schramm, B. F.
Schutz, D. W. Sciama, P. R. Shapiro, L. L. Smarr, S. Weinberg, and J. A.
Wheeler. For meticulously scrutinizing a revised draft of the manuscript, includ-
ing the exercises, for errors, we acknowledge with gratitude R. C. Duncan, P. J.
Schinder, H. A. Scott, and J. Wang. Finally, we will be forever grateful to D. E.
Stewart and G. L. Whitacre for typing the manuscript and the countless revisions
that preceded the final draft.
For assistance in the research that went into this book we thank the National
Science Foundation for grants awarded to Cornell University; the Alfred P. Sloan
X Preface
Foundation for a fellowship awarded to one of us (S. L. S.), and the John Simon
Guggenheim Memorial Foundation for a fellowshlp awarded to the other
(S. A. T.).
STUARTL . SHAPIRO
SAULA . TEUKOLSKY
Ithucu, New York
Januuty 1983
Suggestions for
Using the Book
In our effort to be reasonably complete and self-contained, we have included
more material in the book than can be covered comfortably in a one-semester
survey course. Therefore, we have prepared the accompanying table to assist
instructors in choosing a manageable amount of “essential” subject matter for use
in such a course. General readers with similar time constraints may also wish to
use the table as a rough guide for independent study.
The basic prerequisites for each section in the table are listed by chapter in the
second column. Key chapter sections that can be adequately developed in lectures
are listed in the third column. Additional reading assignments for the students
may be chosen from the last column. In general, only those selections in the text
previously suggested for lectures or further reading constitute the prerequisite
material of a cited chapter.
The order of presentation of topics is somewhat flexible. However, we recom-
mend the order presented in the table to capture the faint threads of a “storyline”
running throughout the book.
Instructors may feel it necessary to cut their coverage of the text by an
additional 10 to 20% in order to develop the material in sufficient depth. On the
other hand, individual readers may wish to read those sections omitted from the
table which focus on their particular interests. For example, the omitted sections
of Chapters 3 and 4 may be of interest to students in solid-state physics; the
omitted sections of Chapters 8 and 11 may be of interest to students of nuclear
and particle physics, and so on. In such instances, a glance at the section heading
or a quick slumming of the introductory paragraphs will usually be sufficient to
surmise the content and personal relevance of a particular section.
The sections of the book omitted from the table, together with the appendixes,
can be more than adequately covered in a two-semester course. In this circum-
stance, the instructor may occasionally want to supplement the general discussion
in the text with additional, more advanced material contained in some of the
references.
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