Tidally driven mean flows in slowly and uniformly rotating massive main-sequence stars

Abstract

We calculate tidally driven mean flows in a slowly and uniformly rotating massive main sequence star in a binary system. We treat the tidal potential due to the companion as a small perturbation to the primary star. We compute tidal responses of the primary as forced linear oscillations, as a function of the tidal forcing frequency $\omega_{\rm tide}=2(\Omega_{\rm orb}-\Omega)$, where $\Omega_{\rm orb}$ is the mean orbital angular velocity and $\Omega$ is the angular velocity of rotation of the primary star. The amplitude of the tidal responses is proportional to the parameter $f_0\propto (M_2/M)(a_{\rm orb}/R)^{-3}$, where $M$ and $M_2$ are the masses of the primary and companion stars, $R$ is the radius of the primary and $a_{\rm orb}$ is the mean orbital separation between the stars. For a given $f_0$, the amplitudes depend on $\omega_{\rm tide}$ and become large when $\omega_{\rm tide}$ is in resonance with natural frequencies of the star. Using the tidal responses, we calculate axisymmetric mean flows, assuming that the mean flows are non-oscillatory flows driven via non-linear effects of linear tidal responses. We find that the $\phi$-component of the mean flow velocity dominates. We also find that the amplitudes of the mean flows are large only in the surface layers where non-adiabatic effects are significant and that the amplitudes are confined to the equatorial regions of the star. Depending on $M_2/M$ and $a_{\rm orb}/R$, the amplitudes of mean flows at the surface become significant.