Table Of ContentBINARY AND MULTIPLE
SYSTEMS OF STARS
BY
ALAN H. BATTEN
Dominion Astrophysical Observatory
Victoria, B.C., Canada
PERGAMON PRESS
OXFORD . NEW YORK · TORONTO
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Copyright © 1973 Pergamon Press Ltd.
First edition 1973
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To my parents
PREFACE
THE study of binary systems received a great stimulus a few years ago
when the first computations were made of the effects of exchange of
mass between the two components. Not long before this, there was
a revival of interest in the statistics of binary systems, especially their
distribution amongst different classes of stars. These two independent
lines of investigation have converged on one result: that membership
of binary systems may have had very important effects on the evolution
of many stars, and the origins of several different kinds of stars may
be connected with the disturbed evolution of binary components. As
a consequence of this, many astronomers, and even some scientists
in related fields, have become much more interested in the study of
binary stars than they formerly were. When Dr. ter Haar asked me to
contribute a volume on binary stars to this International Series of
Monographs in Natural Philosophy, it seemed to me that such a book
should most usefully be aimed at these people, who might well find
it useful to have a survey of the whole field of binary stars. I have
written, therefore, a series of connected review articles which certainly
do not exhaust the field, but do, I believe, cover most of its boundaries
with other fields in astronomy. The book is, by intention, not systemat
ic enough to be used as a course of instruction, but I hope that in
addition to its main purpose it will prove to be helpful to those who
have to prepare courses on binary stars, and at least to be useful as
background reading for graduate students.
Everyone has his own ideas of what should be put in to a book and
what should be left out. My own choices are unlikely to win general
agreement. Two principles have guided me. First, in view of the intend
ed readership, I have assumed a fairly good knowledge of modern
astrophysics, but have gone to some trouble to explain matters that
are specifically within the field of binary systems. This explains the
ix
X PREFACE
inclusion of quite elementary material in Chapter 1—a chapter that
many readers may choose to skip without great loss to their comprehen
sion of the book. The second principle was to attempt to strike a
balance between the desires to produce a self-contained book and to
avoid unnecessary duplication of previously published and readily
accessible work. Thus, I have not reprinted Popper's lists of reliable
masses, since these are available in recent publications that most
astronomical libraries possess. On the other hand, I have taken up
considerable space in a discussion of reliable determinations of the
apsidal-motion constant, because no other fully satisfactory discussion
seemed to me to be available. Similarly, I have repeated the frequently
cited, but seldom copied derivation by Tisserand of the effect of
apsidal motion on the times of minima of an eclipsing system, because
old volumes of Comptes Rendus are not readily available. The similar
derivation of the effect of light time in a long-period orbit on times of
minima is available in more recent publications, and is not repeated
here. In general, I have not given full derivations, even of important
formulae. This is partly because the emphasis of the book is on
observational results and their interpretation, and partly because it
seemed to me unnecessary to repeat the many derivations that can
be found in Kopal's Close Binary Systems. Judged by these principles,
I believe that neither my inclusions nor my omissions will appear
wholly capricious.
I have tried to emphasize what I believe to be the essential unity of
the study of binary systems, regardless of the method by which they
are observed. In the last chapter, in particular, it becomes evident
that the distinction between "close" and "wide" binary systems is not
necessarily the same as their division into eclipsing and visual binaries.
Nevertheless, much of the book is inevitably concerned with the
spectroscopic observations of binaries, since that is the part of the
field in which most of my experience lies.
The inclusion of multiple systems in the title may seem a little
presumptuous since only one chapter often is devoted to them. I believe
that this is the first book in which even that amount of space has been
allotted to multiple systems. It may also appear that while in other
PREFACE xi
chapters my problem has been to condense how much we know into a
reasonable number of pages, in Chapter 3 I succeed only in showing
how little we know. The justification for including multiple systems
in the title, however, is not found in Chapter 3 alone, but in the attitude
which, I hope, permeates the whole book, that it is essential to take
account of the known appreciable fraction of multiple systems if
observations of binary systems are to be correctly interpreted. Thus
there is scarcely a chapter in the book in which multiple systems are
not mentioned and the effects of a third body considered.
A book of this nature is bound to be out of date, in some respects,
before it appears in print. The first draft of this book was completed in
the early summer of 1970, although the final version was not sent to
the publishers until about a year later. Most papers published up to
about the end of 1969 were perused and considered before most of the
original draft was written. Papers published later than that were only
included if I received some advance intimation of their contents, or
they appeared to me to be important, or if for other reasons I had to
rewrite the section concerned. Anything published later than mid-1971
cannot be included in the text. Inevitably, elements of chance and
subjectivity have entered into these decisions, and to those who feel
I have ignored important new work of theirs, I can only apologize.
I am grateful to those who have made material available to me in
advance of publication especially Dr. H. A. Abt, and Dr. P. Broglia
whose light curve of U Cephei is used in Fig. 8.6.
Acknowledgements for permission to reproduce previously pub
lished material are due to the Astronomical Society of the Pacific
(Figs. 8.3 and 9.1 and much of Chapters 8 and 9), Royal Astronomical
Society of Canada (Fig. 1.4), Royal Astronomical Society (Figs. 5.1,
8.8), Società Astronomica d'Italia (Fig. 8.7), Annales d'Astrophysique
(published by Centre National des Recherches Scientifiques) (Fig. 2.2),
Specola Vaticana (Fig. 4.4), D. Reidei (Figs. 3.3 and 5.2) and Sky
and Telescope (Fig. 8.1). Several other diagrams have also appeared
in the Publications of the Dominion Astrophysical Observatory, and
the spectrograms reproduced in this book were all obtained at that
Observatory.
XÜ PREFACE
The first draft of the book was written during a very pleasant visit
to the Vatican Observatory at Castel Gandolfo. I am grateful to
Father D. J. K. O'Connell, S. J. (then the Director) and his staff for
the hospitality they extended to me and my family in the spring and
summer of 1970. I am also grateful to the Canadian Department of
Energy, Mines, and Resources for leave of absence and a travel grant.
The leave of absence was continued by the National Research Council
of Canada, after it took over administrative responsibility for the
Dominion Astrophysical Observatory in April 1970. I am especially
grateful to those who have read earlier drafts of this book and offered
their comments and criticisms, especially Drs. D. ter Haar, J. B.
Hutchings, M. Plavec, C. D. Scarfe, A. D. Thackeray, F. B. Wood
(and colleagues), and K. O. Wright. Finally it is a special pleasure to
thank those whose willing co-operation has enabled me to turn a
rough draft into a finished book. Dr. K. O. Wright, again, has helped
and encouraged me by placing the facilities of the Dominion Astro-
physical Observatory at my disposal. Miss H. D. Mann has efficiently
typed the final version. Mr. S. H. Draper has prepared the illustrations.
The staff and representatives of Pergamon Press, in particular Mrs.
J. A. Pope, Mr. D. Webb, and Dr. ter Haar, have performed the
final essential services. Drs. J. Andersen and B. Nordström have
kindly helped to check the proofs, and my son, Michael, has helped
me to compile the star index. To them all, I offer my thanks.
A. H. BATTEN
Dominion Astrophysical Observatory,
Victoria, B.C., Canada
CHAPTER 1
BASIC CONCEPTS AND TERMINOLOGY
DEFINITION AND CLASSIFICATION OF BINARY
SYSTEMS
A binary system can be simply defined as one containing two stars
that describe closed orbits around their common centre of gravity,
under the influence of their mutual gravitation. No restriction has
been placed in this definition on the separation of the two components.
They can be in contact, or separated by thousands of astronomical
units, or more. The definition would have to be stretched a little to
include common-proper-motion pairs, so many of which have been
discovered by Luyten (e.g. 1933), since it must for a long time remain
an open question whether such pairs are moving in very long-period
orbits, or simply travelling together. This book is almost exclusively
concerned with pairs that show a discernible orbital motion in about
a hundred years, at most. This effectively limits consideration to
pairs with separations of up to ten or a hundred astronomical units.
For the most part, the book is concerned with pairs of very much
smaller separation.
A class of objects in which one basic parameter is allowed to vary
over such a wide range will contain many dissimilar individuals, and
it is natural to look for some form of classification that will divide the
whole group into more nearly homogeneous sub-classes. An obvious
classification is provided by the methods of observation. Very wide
pairs can be resolved by the telescope and be recognized visually as
double stars, if they are near enough to us. These are the visual binary
systems. It is convenient to include in this class pairs that are not
actually resolved, but which are discovered' by careful measurements
of the position of a star relative to background stars in the same field.
These systems are usually termed astrometric binaries. Many binary
1
2 BINARY AND MULTIPLE SYSTEMS OF STARS
systems, however, contain stars that are so close together that they
can never be resolved in a telescope, or be discovered from their
transverse motions. They can be discovered spectroscopically from the
variations in their radial velocities, and are therefore called spectro-
scopic binaries. The orbital planes of some of these are oriented so
that the two components eclipse each other as seen from the Earth,
and these are called eclipsing binaries. There are two other groups of
objects whose binary nature is less directly inferred. The spectrum
binaries are stars that show composite spectra, but whose components
are too widely separated from each other to show observable velocity
changes; some of these might be visual binaries if they were nearer
to the Sun. Some, at least, of the ellipsoidal variables are binaries that
just fail to be eclipsing, but show periodic light variations because of
the distortion of their components.
The techniques used to observe these different kinds of binary are
very different, and a classification based on them is very useful for
distinguishing the astronomers who study binary systems. It has few
other merits, however. Recognition of a visual binary depends not
only on the true separation of its components, but also on its distance
from the Sun. Visual binaries, at least those for which orbits may be
determined, are relatively near neighbours. Spectroscopic binaries
can be recognized at much greater distances, since it is only necessary
for their discovery, that the system be bright enough for spectrograms
of a reasonably high dispersion to be obtained. Eclipsing variables
can be recognized at even greater distances if the eclipses are fairly
deep. Such binaries have been recognized in another galaxy (Baade
and Swope, 1965). Another objection to a classification based on
method of observation is that it is not unique. All eclipsing binaries
are at least potentially spectroscopic binaries. About a hundred visual
binaries can also be profitably observed spectroscopically. A few
(ε Aurigae and W Cephei for which astrometric orbits have been
published) can be observed in all three ways.
Schemes of classification have been proposed by Krat (1944),
Struve (1950), and Sahade (1960). All these depend on the position
of the component stars in the Hertzsprung-Russell diagram, and
BASIC CONCEPTS AND TERMINOLOGY 3
Sahade's scheme will be discussed as the type of this classification.
He recognizes five groups of binary systems: (i) those in which at least
one component is contracting towards the main sequence (Fig. 1.1);
(ii) those in which both components are on the main sequence, group
(ii) is subdivided into (iia) similar components and (iib) dissimilar
components; (iii) systems containing one component on the main
sequence, and one that is a giant or subgiant; (iv) systems in which
I I i i I
20,000 10,000 5,000 eK(Teff)
FIG. 1.1. Approximate evolutionary tracks in the Hertzsprung-Russell diagram
of stars of 1 wO and 5mQ .The straight line represents the theoretical main sequence.
Continuous lines show evolution towards the main sequence (contraction) and the
dashed lines evolution away from the main sequence (expansion). The ordinates
are absolute bolometric magnitude, and the abscissae are effective temperature.
The more massive star has a spectral type of about B3 when on the main sequence,
and about Kl at the extreme right-hand ends of its track. Its radius at this spectral
type must be about 30 times the radius it has on the main sequence, since its
luminosity is greater at the cooler spectral type.
