Tides in asynchronous binary systems

Abstract

Stellar oscillations are excited in non-synchronously rotating stars in binary systems due to the tidal forces. Tangential components of the tides can drive a shear flow which behaves as a differentially forced rotating structure in a stratified outer medium. In this paper we show that our single-layer approximation for the calculation of the forced oscillations yields results that are consistent with the predictions for the synchronization timescales in circular orbits. In addition, calibrating our model results to fit Zahn's relationship between synchronization timescales and orbital separation, we are able to constrain the value of the kinematical viscosity parameter. For the 4Mo+5Mo binary modeled in this paper, the kinematical viscosity is in the range 0.0015 -- 0.0043 Ro^2/d for orbital periods in the range 2.5 -- 25 d. Furthermore, the energy dissipation rate due to the shear flow is found to decrease by ~2 orders of magnitude as synchronization is approached, implying that binary systems may approach synchronization relatively quickly but that it takes a much longer timescale to actually attain this condition. Our model can be used to calculate the energy dissipation rates throughout the orbital cycle for arbitrary values of eccentricity and stellar rotational velocity. We suggest that the asymmetric distribution of energy dissipation over the stellar surface may lead to the appearance of localized regions of enhanced surface activity.