NONADIABATIC TIDAL FORCING OF A MASSIVE, UNIFORMLY ROTATING STAR

We study the fully non-adiabatic tidal response of a uniformly rotatin g 20-M. ZAMS star to the dominant I = m = 2 component of the companion 's perturbing potential. This is done numerically with a 2D implicit f inite difference scheme. We assume the star is rotating slowly with an gular speed Omega(s) much less than Omega(c), so that the centrifugal force can be neglected, but we take the Coriolis force fully into acco unt. It is found that the l = m = 2 forcing can be resonant not only w ith predominantly l = 2 gravity modes but, as expected, also with grav ity modes with predominantly I = 4, 2 = 6, etc. because of the rotatio nal coupling between different I-components. We have used our results for the non-adiabatic response to calculate the tidal spin-up rate of the slowly rotating massive star. Because of the additional resonances the tidal spin-up rate of a rotating star is a considerably more erra tic function of orbital frequency than that of a non-rotating star. We compare the rotational frequency shift of resonances with m = 2 modif ied g-modes with the values obtained from first-order perturbation the ory. By extrapolating our numerical results to low rotation speeds we obtain frequency shifts consistent with the first-order approximation. However, even for the moderately small rotation speeds considered in this paper, the calculated frequency shifts deviate substantially from the values predicted by first-order perturbation theory. In the inert ial regime, in which the relative forcing frequency is less than 2 Ome ga(s), it is found that the response contains large-amplitude, very sh ort-wavelength components which cannot be resolved on the numerical gr id (effectively 400 x 256 for the full meridional cross-section), unle ss the so-called 'traditional approximation' is used, in which the the ta-component of the rotational angular velocity is ignored. Then tidal resonances with rotationally modified gravity modes continue into the inertial regime. Outside the inertial regime the traditional approxim ation gives results similar to the full code calculations. Inside the inertial regime this is only true for the strongly stratified layers w here the Brunt-Vaisalla frequency is larger than about three times the stellar break-up speed Omega(c). We find evidence that the singular r esponse in the inertial regime, obtained with the full code, may be re al and due to resonant excitation of rotationally controlled inertial modes in the convective core and the adjacent, weakly stratified, radi ative layers. Because the spectrum of the rotationally controlled iner tial modes is dense, resonant excitation of these modes may give rise to significant tidal effects. Further progress requires higher resolut ion calculations incorporating viscosity to deal with the very short-w avelength components in the inertial regime.