The precession of gaseous stars

We discuss the precession of a gaseous star in a close binary system. We consider the case when the precessional amplitude is small and much less than the tidal distortion of the star justifying the treatment of the problem as one in linear oscillation theory. We find a close parallel with the problem of apsidal motion. The problem is complicated by the fact that the stellar oscillation spectrum is dense at frequencies of interest. Nevertheless we show that precession can still occur for time-scales of physical interest. Consideration of damping of the stellar modes enables us to estimate the decay rate of precessional motion. The analogy with apsidal motion allows us to show that precession is damped faster than, or on a comparable timescale to, the damping of eccentricity by tidal effects. Thus we expect to find no evidence of precession in the close binary systems, such as Her X-1, in which tidal circularization has already occurred.