The Roche Problem: And Its Significance for Double-Star Astronomy

ISBN-13: 9789401075282 / Angielski / Miękka / 2011 / 264 str.

Zdenek Kopal

Opis

The words of this preface were written when the book was ready to go to the press; and are limited to only a few points which are best made in this place. As is intimated by the sub-title, the whole volume was written with appli- cations in mind to double-star astronomy. The latter is, however, not the only branch of our science which could benefit from its contents. The same is true of certain aspects of the dynamics of stellar systems or galaxies (the stellar popula- tions of which are also characterized by the fact that the mean-free-path of their constituent stars are long in comparison with the dimensions of the respective systems); the central condensations of which are high enough to approximate the gravitational action of a "mass-point". This fact did not, to be sure, escape the attention of previous investigators (in the case of globular clusters, in particular, the Roche model was introduced in their studies under the guise of polytropic models characterized by the index n = 5); though no particular attention will be paid to these in this book. But possible applications of the Roche model are not limited to problems arising in stellar astrophysics. With Coulomb forces replacing gravitation, the equilibrium model finds a close analogy in the field of electrostatics-as was pointed out already at the beginning of this century by (then young) J. H. Jeans (cf.

Spis treści

List of Contents.- I. Introduction.- I.1 Bibliographical Notes.- II. The Roche Model.- II.1 Roche Model—A Definition.- II.2 Geometry of Roche Equipotentials.- A. Radius and Volume.- B. Roche Limit.- C. Geometry of the Eclipses.- D. External Envelopes.- II.3 Time-Dependent Roche Equipotentials.- A. Inclined Axes of Rotation.- B. Eccentric Orbits.- II.4 Bibliographical Notes.- III. Roche Coordinates.- III.1 Metric Transformations.- A. Integrability Conditions.- B. Rotational Problem.- C. Double-Star Problem.- III.2 Equations of Motion in Roche Coordinates.- A. Geometry of the Roche Coordinates.- B. Motion in the Equatorial Plane.- III.3 Bibliographical Notes.- IV. Continuous Mass Distribution: Clairaut’s Theory.- IV.1 Equipotential Surfaces.- IV.2 Rotational Distortion.- IV.3 Tidal Distortion.- IV.4 Interaction Between Rotation and Tides.- IV.5 Effects of Internal Structure.- IV.6 Bibliographical Notes.- V. Clairaut Coordinates.- V.1 Metric Transformation.- A. Differential Operators; Clairaut Harmonics.- V.2 Internal Structure.- A. Rotational Problem.- V.3 Vibrational Stability.- A. The Stability of Roche Equipotentials: Rotational Problem.- B. Stability of Roche Equipotentials: Double-Star Problem.- V.4 Bibliographical Notes.- VI. Generalized Rotation.- VI.1 Equations of Motion for Deformable Bodies.- A. Velocities and Accelerations.- B. Eulerian Equations.- C. Moments of Inertia.- D. Gyroscopic Terms.- VI.2 Dissipative Forces: Effects of Viscosity.- A. Tidal Friction.- B. Dissipation of Energy.- VI.3 Precession and Nutation of Deformable Bodies.- A. Secular and Long-Period Motion.- VI.4 Bibliographical Notes.- VII. Observable Effects of Distortion in Close Binary Systems.- VII.1 Radiative Transfer in Clairaut Coordinates.- A. Solution of the Equations.- VII.2 Light Variations in Close Binary Systems.- A. Light Changes of Distorted Stars Outside Eclipses.- B. Discussion of the Results.- VII.3 Light Changes of Distorted Systems Within Eclipses.- A. Geometry of the Eclipses: Special Functions.- VII.4 Radial Velocity Variations in Close Binary Systems.- A. Radial Motion of Rotating Stellar Discs.- B. Effects of Distortion on Radial Velocity.- C. Irradiation of the Components and its Effect on the Observed Radial Velocity.- VII.5 Bibliographical Notes.- References.