On the tidal evolution of massive X-ray binaries: the spin-up and circularization rates for systems with evolved stars and the effects of resonances

Abstract

We calculate the response of a non-rotating 20M⊙ star to a periodic perturbing tidal potential. The fully non-adiabatic, but linearized equations are solved numerically for a wide range of orbital frequencies for various stages of the core hydrogen burning phase of the star. We give results from which the tidal spin-up and orbital circularization rates can be determined at any stage of the core hydrogen burning phase. We then present some calculations of the orbital evolution starting from periods of four and six days and eccentricity of 0.25. In each case we find that the effectiveness of tidal evolution increases substantially during the late phases of core hydrogen burning, resulting in circularization of the orbit and a sharp decrease of the orbital period. The relationship of our results to previous results obtained from asymptotic theory for low frequencies is also discussed.