Dynamics of Close Binary Systems

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Springer Science & Business Media, Aug 31, 1978 - Science - 513 pages
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The aim of the present book will be to provide a comprehensive account of our present knowledge of the theory of dynamical phenomena exhibited by elose binary systems; and on the basis of such phenomena as have been attested by available observations to outline probable evolutionary trends of such systems in the course of time. The evolution of the stars - motivated by nuelear as weIl as gravitation al energy sources - constitutes nowadays a well-established branch of stellar astronomy. No theo ries of such an evolution are as yet sufficently specific - let alone infallible - not to require continual tests by a confrontation of their consequences with the observed prop erties of actual stars at different stages of their evolution. The discriminating power of such tests depends, of course, on the range of information offered by the test objects. Single stars which move alone in space are now known to represent only a minority of objects constituting our Galaxy (cf. Chapter 1-2); and are, moreover, not very revealing of their basic physical characteristics - such as their masses or absolute dimensions. If there were no binary systems in the sky, the only star whose vital statistics would be fully known to us would be our Sun.
 

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Contents

BINARY STARS IN THE SKY
1
11 BinaryStar Population in our Galaxy
10
BIBLIOGRAPHICAL NOTES
16
FIGURES OF EQUILIBRIUM
18
II2 Rotational Distortion
26
II3 Tidal Distortion
36
II4 Interaction between Rotation and Tides
46
II5 Effects of Internal Structure
58
A DEFINITION
253
C RELATION BETWEEN ORBITAL PERIOD AND TIMES OF THE MINIMA
261
V5 Effects of Variable Mass
264
A GENERALIZED EQUATIONS OF MOTION
265
B ISOTROPIC MASS LOSS
268
C NONISOTROPIC MASS LOSS
272
V6 Perturbations by a Third Body
276
A EQUATIONS OF THE PROBLEM
277

II6 Gravity Density Distribution and Moments of Inertia
68
BIBLIOGRAPHICAL NOTES
77
DYNAMICAL TIDES
80
III1 Equations of the Problem
81
B RADIATING SYSTEMS
87
III2 Linearized Equations
93
A VISCOUS SPHEROIDAL DEFORMATIONS
95
B BOUNDARY CONDITIONS
101
C HOMOGENEOUS MODEL
103
Dynamical Tides
110
A MASSPOINT MODEL
111
B CENTRALLYCONDENSED MODEL
116
C DISTURBING POTENTIAL
117
III4 Dissipation of Energy by Dynamical Tides
126
A VISCOUS FRICTION
130
B APPLICATION TO BINARY SYSTEMS
132
BIBLIOGRAPHICAL NOTES
136
GENERALIZED ROTATION
138
IV1 Equations of Motion for Deformable Bodies
140
A EULERIAN EQUATIONS
147
IV2 Rotation of Deformable Bodies
154
A EFFECTS OF DEFORMATION
156
B MOMENTS AND PRODUCTS OF INERTIA
161
C COEFFICIENTS OF DEFORMATION
165
IV3 Effects of Viscosity
170
SPHERICAL CONFIGURATIONS
178
SPHEROIDAL CONFIGURATIONS
183
D DISSIPATION OF ENERGY BY TIDAL FRICTION
187
IV4 Nonuniform Rotation
191
B NONSTEADY ROTATION
197
BIBLIOGRAPHICAL NOTES
200
DYNAMICS OF CLOSE BINARIES
201
V1 Equations of the Problem
202
A PERTURBATION EQUATIONS
203
TIDAL LAG
209
V2 Perturbations of the Orbital Plane Precession and Nutation
211
A EFFECTS OF VISCOSITY
212
B LINEARIZED CASE
215
C SECULAR AND LONGPERIODIC MOTION
222
D SOLUTION OF EQUATIONS
225
V3 Perturbations in the Orbital Plane
232
TIDAL DISTORTION
236
COMPARISON WITH OBSERVATIONS
243
V4 Period Changes in Eclipsing Binary Systems
249
A GENERALIZED LAW OF AREAS
250
B SHORTRANGE PERTURBATIONS
279
C LONGRANGE PERTURBATIONS
293
D EFFECTS OF THE LIGHT EQUATION
304
BIBLIOGRAPHICAL NOTES
309
THE ROCHE MODEL
312
VI1 Roche Equipotentials
313
A SURFACES OF ZERO VELOCITY
318
VI2 Geometry of Roche Surfaces
322
B ROCHE LIMIT
325
C GEOMETRY OF THE ECLIPSES
331
D EXTERNAL ENVELOPES
336
VI3 The Roche Coordinates
339
A ROTATIONAL PROBLEM
340
B TIDAL PROBLEM
343
C DOUBLESTAR PROBLEM
346
BIBLIOGRAPHICAL NOTES
360
STABILITY OF THE COMPONENTS OF CLOSE BINARY SYSTEMS
361
VIII Criteria of Stability
362
A ROTATIONAL PROBLEM
369
B DOUBLESTAR PROBLEM
374
VII3 Dynamical StabUity
380
A VIBRATIONS OF THE ROCHE MODEL
383
V1I4 Concluding Remarks
387
BIBLIOGRAPHICAL NOTES
389
ORIGIN AND EVOLUTION OF BINARY SYSTEMS
390
VIII1 Evolution of the Star
391
VIII2 Classification of Close Binary Systems
400
A CHARACTERISTIC PARAMETERS
402
VIII3 Nuclear Evolution of Close Binary Systems
405
A DETACHED SYSTEMS
406
B SEMIDETACHED SYSTEMS
413
CCONTACT SYSTEMS
430
VIII4 Tidal Evolution of Close Binary Systems
437
A ENERGY AND MOMENTUM
441
B EVOLUTION WITH CONSTANT MOMENTUM
446
C COMPARISON WITH OBSERVATIONS
451
D TIDAL EVOLUTION
458
VIII5 Beginnings and Ends
464
SUBDWARF BINARIES
467
C XRAY BINARIES AND BLACK HOLES
475
BIBLIOGRAPHICAL NOTES
487
REFERENCES
491
INDEX OF NAMES
502
INDEX OF SUBJECTS
507
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