The dynamical tide in a rotating 10 M ⊙ main sequence star a study of g - and r - mode resonances

We study the linear, but fully non-adiabatic tidal response of a uniformly rotating, somewhat evolved (X c = 0.4), 10 M ⊙ 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 M ⊙ star to be aligned perpendicular to the orbital plane and calculate the frequency ¯ σ 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 Ω s 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 rotation rates Ω s. 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.