On the tidal evolution of massive X-ray binaries: the tidal evolution time-scales for very long orbital periods

Abstract

In this paper we extend our previous calculations of tidal evolution rates for massive X-ray binaries to systems with very long orbital periods. We use a simple model in which internal gravity waves generated in the massive star by the time-dependent tidal potential propagate towards the surface layers where they are absorbed. The consequent energy dissipation and angular momentum transfer are responsible for the tidal evolution. The results presented in this paper agree reasonably with those we have obtained previously, by an exact method, at orbital frequencies for which a comparison can be made. We find that for moderately low orbital frequencies, due to the interference of waves generated at different locations, the tidal angular momentum transfer is an oscillating function of orbital frequency. In the limit of zero orbital frequency, provided the convective core is not too small, the angular momentum transfer rate becomes a smooth function of frequency. However, the frequencies at which this becomes valid are too low to be of practical interest.