THE EFFECT OF TIDAL FRICTION ON THE STABILITY OF TRIPLE-SYSTEMS

The dynamical evolution of hierarchical triple systems containing clos e binary systems is considered. The effects of tides on the stability of triple systems are studied, and plane triple systems with initially circular orbits for both the inner and outer binaries are investigate d. The directions of revolution of both binaries are coincident; the a xes of stellar rotation and the vector of the orbital angular momentum of the triple system are co-linear. Four choices for the initial rota tional velocities are considered: zero velocities; synchronization of the stellar rotation with the orbital motion; average velocities for m ain-sequence stars of a given mass; and critical velocities correspond ing to equality of the gravitational and centrifugal forces at the equ ators of the stars. Stars with convective envelopes are considered. It is shown that, in the case of rotational velocities that are less tha n the synchronized values, there is an increase in the stability of th e triple system. The opposite trend is found for stars with rotational velocities that are larger than the synchronized values. The effects of tidal interactions on the stability of hierarchical triple stars co uld be estimated analytically using the theory of close binary systems , apart from the case of strong perturbations from the heavy distant b ody, and the case of small tidal effects (small eccentricities and syn chronization). The equilibrium state of circularization and synchroniz ation is not achieved in close binaries because the third body perturb s the orbit of the binary and the state of zero eccentricity is unatta inable. Therefore the energy of orbital motion is continuously convert ed into the energies of the components.