Tidal interaction of a rotating 1 M ⊙ star with a binary companion

We calculate the tidal interaction of a uniformly rotating 1 M⊙ star with an orbiting companion at various phases of core hydrogen burning from the ZAMS to core hydrogen exhaustion. By using the traditional approximation we reduce the solution of the non-adiabatic oscillation equations for the tidal forcing of a rotating star to a one dimensional problem by solving a separate eigenvalue problem for the angular dependence of the tidal perturbations. The radial oscillation equations are then solved by using finite differencing on a fine grid with an implicit matrix inversion method like for stellar evolution calculations. We are able to identify resonances with gravity (g-)modes and quasi-toroidal (q-)modes with up to ≃ 1000 radial nodes in the more evolved stellar models. The resulting tidal torque is calculated down to low forcing frequencies close to corotation. For low tidal frequencies we find significant response due to inertial (i-)modes in the convective envelope. The inertial modes are damped by turbulent dissipation in the envelope and generate a relatively high torque-level in the low frequency region where the (retrograde) high radial order g-mode resonances become tidally inefficient due to their rotational confinement to the stellar equator and strong damping by radiative losses. For still lower retrograde forcing frequencies we find a large number of closely spaced weakly damped quasi-toroidal q-mode resonances. Our results indicate that effects related to stellar rotation can considerably enhance the speed of tidal evolution in low-mass binary systems.