Orbital Evolution in Binary and Triple Stars, with an Application to SS Lacertae

Abstract

We present equations governing the way in which both the orbit and the intrinsic spins of stars in a close binary should evolve subject to a number of perturbing forces, including the effect of a third body in a possibly inclined wider orbit. We illustrate the solutions in some binary star and triple star situations: tidal friction in a wide but eccentric orbit of a radio pulsar about a B star (0045-7319), the Darwin and eccentricity instabilities in a more massive but shorter period massive X-ray binary, and the interaction of tidal friction with Kozai cycles in a triple star, such as β Per at an early stage in that star's life, when all three components were zero-age main sequence stars. We also attempt to model in some detail the interesting triple system SS Lac, which stopped eclipsing in about 1950. We find that our model of SS Lac is quite constrained by the relatively good observational data of this system and leads to a specific inclination (29°) of the outer orbit relative to the inner orbit at epoch zero (1912). We make some predictions about changes to system parameters in the short term (20-40 yr) and also in the medium term (up to ~3000 yr). Although the intrinsic spins of the stars have little effect on the orbit, the converse is not true: the spin axes can vary their orientation relative to the close binary by up to 120° on a timescale of about a century.