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

## TL;DR

This study models tidally driven mean flows in rotating massive stars within binary systems, revealing how these flows depend on tidal frequency, resonance, and stellar parameters, with significant surface and equatorial effects.

## Contribution

It introduces a linear oscillation-based method to compute tidally driven mean flows in rotating stars, highlighting the surface and equatorial localization of these flows.

## Key findings

- Mean flows are dominated by the azimuthal component.
- Flow amplitudes are significant near the surface where non-adiabatic effects matter.
- Flow amplitudes depend on the mass ratio and orbital separation.

## 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.