Tides in asynchronous binary systems

¹ Instituto de Ciencias Físicas, Universidad Nacional Autonoma de México, Apdo. Postal 48-3, Cuernavaca, Mor. 62251, Mexico e-mail: [oswaldo;gloria]@ce.fis.unam.mx
² Instituto de Astronomía, Universidad Nacional Autonoma de México, Apdo. Postal 70-264, D.F. 04510, Mexico e-mail: edmundo@astroscu.unam.mx
³ Sterrenkundig Instituut, Universiteit Utrecht, Postbus 80.000, Utrecht, The Netherlands e-mail: [R.G.Detmers;N.Langer]@astro.uu.nl

Received: 8 June 2006
Accepted: 8 October 2006

Abstract

Context.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.

Aims.The aims of this paper are to 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,  ~ a⁶, thus providing a simplified means of computing the energy dissipation rates, . Furthermore, by calibrating our model results to fit the relationship between synchronization timescales and orbital separation, we are able to constrain the value of the kinematical viscosity parameter, ν.

Methods.We compute the values of for a set of 5  model binary systems with different orbital separations, a, and use these to estimate the synchronization timescales.

Results.The resulting  vs. a relation is comparable to that of Zahn (1977, A&A, 57, 383) for convective envelopes, providing a calibration method for the values of ν. For the binary modeled in this paper, ν is in the range 0.0015–0.0043  /day for orbital periods in the range 2.5–25 d. In addition,  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.

Conclusions.The relevance of these results is threefold: 1) our model allows an estimate for the numerical value of ν under arbitrary conditions in the binary system; 2) it can be used to calculate the energy dissipation rates throughout the orbital cycle for any value of eccentricity and stellar rotational velocity; and 3) it provides values of the tangential component of the velocity perturbation at any time throughout the orbit and predicts the location on the stellar surface where the largest shear instabilities may be occurring. We suggest that one of the possible implication of the asymmetric distribution of  over the stellar surface is the generation of localized regions of enhanced surface activity.