Overstable Convective Modes in Rotating Early Type Stars

We calculate overstable convective (OsC) modes of $2M_\odot$, $4M_\odot$, and $20M_\odot$ main sequence stars. To compute non-adiabatic OsC modes in the core, we assume $(\nabla\cdot\vec{F}_C)^\prime=0$ as a prescription for the approximation called frozen-in convection in pulsating stars where $\vec{F}_C$ is the convective energy flux and the prime $^\prime$ indicates Eulerian perturbation. We find that the general properties of the OsC modes are roughly the same as those obtained by Lee \& Saio (2020) who assumed $\delta (\nabla\cdot\vec{F}_C)=0$, except that no OsC modes behave like inertial modes when they tend toward complete stabilization with increasing rotation frequency where $\delta$ indicates the Lagrangian perturbation. As the rotation frequency of the stars increases, the OsC modes are stabilized to resonantly excite $g$-modes in the envelope when the core rotates slightly faster than the envelope. The frequency of the OsC modes that excite envelope $g$-modes is approximately given by $\sigma\sim |m\Omega_c|$ in the inertial frame and hence $\sigma_{m=-2}\approx2\sigma_{m=-1}$ where $m$ is the azimuthal wavenumber of the modes and $\Omega_c$ is the rotation frequency of the core. We find that the modal properties of OsC modes do not strongly depend on the mass of the stars. We discuss angular momentum transport by OsC modes in resonance with envelope $g$-modes in the main sequence stars. We suggest that angular momentum transfer takes place from the core to the envelope and that the OsC modes may help the stars rotate uniformly and keep the rotation frequency of the core low during their evolution as main sequence stars.