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

Previous calculations of tidal evolution rates for massive X-ray binaries are extended to systems with very long orbital periods. A simple model is used 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 obtained previously, by an exact method, at orbital frequencies for which a comparison can be made. It is found 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. (author)