Double Stars

184 Pages·1978·4.321 MB·English

by  Wulff D. Heintz (auth.)

DOUBLE STARS
GEOPHYSICS AND
ASTROPHYSICS MONOGRAPHS
AN INTERNATIONAL SERIES OF FUNDAMENTAL TEXTBOOKS
Editor
B. M. MCCORMAC, Lockheed Palo Alto Research Laboratory, Palo Alto, Calif, U.S.A.
Editorial Board
R. GRANT ATHAY, High Altitude Observatory, Boulder, Colo., U.S.A.
W. S. BROECKER, Lamont-Doherty Geological Observatory, Palisades, New York, U.S.A.
P. J. COLEMAN, JR., University of California, Los Angeles, Calif, U.S.A.
G. T. CSANADY, Woods Hole Oceanographic Institution, Woods Hole, Mass., U.S.A.
D. M. HUNTEN, University of Arizona, Tucson, Ariz., U.S.A.
C. DE JAGER, The Astronomical Institute, Utrecht, The Netherlands
J. KLECZEK. Czechoslovak Academy of Sciences, Ondrejov, Czechoslovakia
R. LUST, President Max-Planck-Gesellschaft fur Forderung der Wissenschaften, Munchen, F.R.G.
R. E. MUNN, University of Toronto, Toronto, Ont., Canada
Z. SVESTKA, The Astronomical Institute, Utrecht, The Netherlands
G. WEILL, Institut d'Astrophysique, Paris, France
VOLUME 15
DOUBLE STARS
WULFF D. HEINTZ
Department of Astronomy, Swarthmore College, Swarthmore, U.S.A.
D. REIDEL PUBLISHING COMPANY
DORDRECHT: HOLLAND / BOSTON: U.S.A.
LONDON: ENGLAND
Library of Congress Cataloging in Publication Data
Heintz, Wulff Dieter.
Double stars.
(Geophysics and astrophysics monographs; v. 15)
Revised translation of Doppelsterne published in 1971.
Bibliography: p.
Includes index.
1. Stars, Double. I. Title. II. Series.
QB821.H413 1978 523.8'.41 78-9284
ISBN-13: 978-90-277-0886-1 e-ISBN-13: 978-94-009-9836-0
001: 10.1007/978-94-009-9836-0
Published by D. Reidel Publishing Company,
P.O. Box 17, Dordrecht, Holland
Sold and distributed in the U.S.A. Canada and Mexico
by D. Reidel Publishing Company, Inc.
Lincoln Building, 160 Old Derby Street, Hingham,
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All Rights Reserved
Copyright © 1978 by D. Reidel Publishing Company, Dordrecht, Holland
Sofl:cover reprint of the hardcover 1st edition 1978
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 informational storage and
retrieval system, without written permission from the copyright owner
TABLE OF CONTENTS
PREFACE vii
LIST OF MA THEMA TICAL SYMBOLS ix
I. Classes of Double Stars 1
2. When Double-Star Research Began 3
3. 19th-Century Achievements 5
4. Three Quarters of This Century 8
5. Catalogues and Data References 10
6. Selective Discovery and Abundance of Binaries 12
7. Optical and Temporary Double Stars 17
8. Relative Positions in Visual Double Stars 19
9. Micrometric Observation 21
10. Interferometric Observation 24
II. Photographic Positions 26
12. Magnitudes of Double-Star Components 28
13. The Orbital Elements of a Visual Binary 31
14. Ephemeris Formulae 34
15. Determination of Visual Binary Orbits 36
16. The Thiele-van den Bos Method 40
17. The Methods by Danjon and Rabe 42
18. The Edge-on Orbit 44
19. Correcting an Orbit 46
20. Formulae for Differential Corrections 47
21. The Parabolic Orbit 49
22. Absolute Orbits and Mass Ratios 49
23. Some Results from Visual Binary Orbits 53
24. Stellar Masses 55
25. The Mass-Luminosity Relationship (MLR) 59
26. Dynamical Parallaxes 62
27. Multiple Systems 64
28. Unresolved Systems 68
29. Some Systems of Special Interest 70
30. Radial Velocities 75
31. Spectroscopic Double Stars 78
32. The Elements of Spectroscopic Orbits 79
33. The Differential and the Sterne Formulae 85
34. The Combined Spectroscopic-Visual Orbit 86
35. Distortions of Radial-Velocity Curves 88
36. Photometric Double Stars and Light Curves 90
vi TABLE OF CONTENTS
37. Classes of Eclipsing Binaries and the Roche Lobe 92
38. Limb Darkening 97
39. Concepts of Photometric Orbit Determination 98
40. The Spherical Model 104
41. Rectification and Related Precepts 110
42. Eccentric Orbits 115
43. Mass Determinations from the MLR 116
44. On the Origin of Binary Stars 118
45. Mass Transfer After the Main-Sequence Phase 122
46. Binaries of the Type W UMa 127
47. Gas Streams and Hot Spots 132
48. Apsidal Rotation 137
49. Systemic Mass Loss 139
50. Atmospheric Eclipses 140
51. The Largest Stellar Masses 142
52. Binary Components of Wolf-Rayet Type 144
53. More Systems of Special Interest 145
54. Peculiar Prototypes: f3 Per and f3 Lyr 149
55. Cataclysmic Binary Components 153
56. X-Ray Binaries 159
REFERENCES 164
SUBJECT INDEX 171
INDEX OF STARS 173
PREFACE
Double and multiple stars are the rule in the stellar population, and single stars the
minority, as the abundance of binary systems in the space surrounding the sun shows
beyond doubt. Numerous stellar features, and methods of their exploration, ensue
specifically from the one but widespread property, the binary nature. Stellar masses
are basic quantities for the theory of stellar structure and evolution, and they are ob
tained from binary-star orbits where they depend on the cube of observed parameters;
this fact illustrates the significance of orbits as well as the accuracy requirements.
Useful in dating stellar history is the knowledge that components of a system, different
though they may appear, are of the same origin and age. Between star formation and
the genesis of binaries a direct connection can be traced.
The later stages of stellar life branch into a great variety as mutual influence between
the components of a close binary pair develops. Transfer and exchange of mass and
the presence of angular momentum in the orbit give rise to special tracks of evolution,
not found for single stars, and to peculiar spectral groups. This is not a new story but
it has a new ending: The patterns of evolution involving mass transfer appear to lead
ultimately to single objects. The ordinary pair of main-sequence provenience heads,
with intervening nova eruptions, toward the complete evaporation of the lesser body
as the dissipation of angular momentum forces it nearer to its degenerate mate; the
rare, very massive pairs disintegrate into two single compact bodies after a double
supernova event, and the W UMa stars - a less spectacular though apparently quite
non-conforming brand - merely may arrive at coalescence.
Close binaries have in recent years been an enormously active and increasingly com
plex field, as empirical data and their interpretation progressed rewardingly. The
knowledge of wider, lower moving pairs also grows as it benefits from the more ex
tended time span of observed records. The present book has been almost completely
rewritten since 1971 when its German edition appeared. Notwithstanding all revisions
and additions, the author hopes to have preserved its scope: namely to bridge over into
the topics of research and into the current technical literature - methods as well as
results - without requiring more astronomical background than what an introduc
tory textbook offers. The orbit analysis deserves at least an outline; although Kepler's
laws or the plane geometry describing eclipses of stellar disks do not change, the
superstructure of practised methods does so considerably. How much mathematical
detail actually is behind the curves of eclipsed light, beyond the fundamentals pre
sented here, may be found from Kopal's 1959 treatise 'Close Binary Systems' (quoted
as CBS), and even this basic theoretical work is being overgrown by many refinements.
The present text attempted to incorporate the literature up to late 1976. Needless to
say, the references quoted are a small fraction of the papers actually consulted, yet
they should help to backtrack other publications. Like on the previous edition with
the Wilhelm Goldmann Company, the author again enjoyed cooperation with a
vii
viii PREFACE
helpful and patient Series Editor, Dr. Billy McCormac, and with the efficient services
of the D. Reidel Publishing Company; their efforts are deeply appreciated.
June 1977
LIST OF MATHEMATICAL SYMBOLS
(Contains only the more frequently used symbols and those in duplicate use.)
a semiaxis major (apparent in arc sec; true in A. U. or km).
A angular momentum.
A, B, F, G (in combination) Thiele-Innes constants.
e orbital eccentricity
f fractional mass.
f(M) spectroscopic mass function.
G constant of gravity.
orbital inclination.
k ratio of radii.
kZ Gaussian constant of attraction.
K semi-amplitude of radial velocity (also KJ, Kz).
log logarithm to base 10.
L luminosity (p. 101 ff: light loss in eclipse).
m apparent magnitude.
M absolute magnitude.
M mass (unit = solar mass).
P period.
r, r radius vector between components.
T time of periastron passage.
u coefficient of limb darkening.
v true anomaly (polar angle in orbit).
V radial velocity.
x, y tangential coordinates in sky (p. 94: coordinates in orbital plane).
z radial coordinate (p. 111: ellipticity coefficient).
a right ascension (p. 98 ff: Russell's light-loss function).
f3 fractional luminosity.
r
radial velocity of center of mass.
o
declination (p. 105: normalized distance between star centers).
() position angle (p. 105: orbital phase).
A wavelength.
t-t mean orbital motion (in radians or degrees per specified time unit).
n parallax; inverse distance in parsecs. (For the number 3.14 the usual symbol n
is written only when unambiguous.)
p projected separation (in arc sec).
eft arc sin of eccentricity.
r/J frequency function.
w longitude of periastron.
() node (p. 94: gravity potential).
ix
1. Classes of Double Stars
Two or more stars held, by their mutual gravity attraction, in a long-term (usually
lifelong) association are termed a double star.
The gravitating force within the double star outpowers that from the general star
field and from stars randomly passing by, and it results in orbital motions. If the
average distance between independent stars is of the order of I parsec (pc), the self
gravity is already strongly dominant in double stars with component separations
around 0.1 pc.
The term 'double stars' usually means to include triple and multiple stars as well.
In most of the triple systems the component separations are very unequal, that is to
say, the separation between two components is much smaller than the distance to the
third body. The motion of the 'inner pair' is influenced very little by the distant com
panion, and vice versa. This also holds for higher-multiple stars, and is the result of
stability adjustments within the systems. The multiplicity thus becomes an array of
near-independent duplices, one inside the other, without much of further peculiarities
- except the fact that the observations ofthe parts will be impeded by the presence of
additional components.
This dynamical feature distinguishes double stars from members of star clusters.
The distances between cluster stars are large enough that long-lasting connections
between a few stars and stable orbital motions usually do not result. Borderline cases
are the so-called trapezium systems, i.e., small stellar groups with equal-order separa
tions between the components (p. 67). Though they are partly catalogued as mul
tiple stars, they actually form young stellar associations or part thereof.
The two English terms 'Double Stars' and 'Binary Stars' are used to mean much
the same. The term 'binary' is generally restricted to objects the physical relation and
orbital motion of which are established. Other languages rarely use this distinction.
Discovery and measurement of double stars fall into different realms of observation,
viz., the fields of astrometry (measures of positions, mostly visually and photographi
cally), of spectroscopy (measures of radial velocity), and of photometry (measures of
light intensity). This feature results in the conventional classification of double stars:
(a) Visual binaries are seen separated in the telescopes. They are by far the most
frequent kind with respect to the numbers of discovery, but in the majority of cases
the component separations are so large, and the orbital motions so slow (periods of
the order 105 and 106 yr) that the information obtainable is limited to the knowledge
of the physical relation and the common origin of the components. More detailed data
by way of orbit computation is obtained only for a small fraction, mostly for the
periods ranging from 20 to 300 yr. Toward the closer pairs the limited resolving power
of telescopes bounds the investigations although interferometric methods provide an
extension of the range of separation; few pairs with periods less than 10 yr are
observed. A few pairs are unresolved, an oscillation in the motion of a visible star
indicating the presence of an unseen companion. These objects are sometimes termed
'astrometric binaries' though they still are so few in number as not to require a
separate class name.
(b) Spectroscopic binaries are found from the Doppler effect (p. 7) of their orbital
motions, that is, by way of repeated radial-velocity measurements. Owing to the
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