Tidal evolution in close binary systems.
Abstract
The weak friction model for tidal interaction in a close binary system is investigated, in which the tides assume their equilibrium shape, but with a constant time lag, and the model is used to derive explicit equations of tidal evolution. An elementary derivation is presented of the perturbing tidal forces, and the perturbations are used to derive differential equations for the evolution of several orbital and rotational parameters of the binary system. Energy and angular momentum considerations are used directly instead of the general perturbation techniques of celestial mechanics. The tidal evolution equations are analyzed locally around equilibrium configurations. Time scales are derived for the rate of change of the semimajor axis, the rotational velocity, and for the eccentricity and inclination, which go to zero asymptotically. The global aspects of the tidal evolution equations are analyzed. For the case of small inclinations but arbitrary eccentricity, a complete classification is made of all types of tidal evolution possible in the model which is presented. Several relations are obtained analytically from the equations for tidal evolution in the weak friction model. The presented model is simple, but it is sufficiently general to be applicable to a wide class of binary stars
 Publication:

Astronomy and Astrophysics
 Pub Date:
 June 1981
 Bibcode:
 1981A&A....99..126H
 Keywords:

 Binary Stars;
 Celestial Mechanics;
 Stellar Evolution;
 Stellar Models;
 Tides;
 Two Body Problem;
 Angular Momentum;
 Companion Stars;
 Conservation Laws;
 Energy Dissipation;
 Equilibrium Equations;
 Gravitational Effects;
 Perturbation Theory;
 Stellar Rotation;
 Synchronism;
 X Ray Stars;
 Astrophysics