The dynamical tide in a rotating $10M_{\odot}$ main sequence star: a study of g- and r-mode resonance

We study the linear, but fully non-adiabatic tidal response of a uniformly rotating, somewhat evolved X_c=0.4, 10 Msun main sequence star to the dominant l=2 components of its binary companion's tidal potential. This is done numerically with a 2D implicit finite difference scheme. We assume the spin vector of the 10 Msun star to be aligned perpendicular to the orbital plane and calculate the frequency and width of the resonances with the prograde and retrograde gravity (g) modes as well as the resonances with quasi-toroidal rotational (r) modes for varying rotation rates of the main sequence star. For all applied forcing frequencies we determine the rate of tidal energy and angular momentum exchange with the companion. In a rotating star tidal energy is transferred from l=2 g-modes to g-modes of higher spherical degree (l=4,6,8,...) by the Coriolis force. These latter modes have shorter wavelength and are damped more heavily, so that the l=2 resonant tidal interaction tends to be reduced for large stellar rotation rates. On the other hand, the density of potential resonances (a broad l spectrum) increases. We find several inertially excited unstable l>4 g-modes, but not more than one (retrograde) unstable l=2 g-mode and that only for rapid rotation. Our numerical results can be applied to study the tidal evolution of eccentric binaries containing early type B-star components