Rossby waves on stellar equatorial beta-planes: uniformly rotating radiative stars

Rossby waves arise due to the conservation of total vorticity in rotating fluids and may govern the large-scale dynamics of stellar interiors. Recent space missions collected huge information about the light curves and activity of many stars, which triggered observations of Rossby waves in stellar surface and interiors. We aim to study the theoretical properties of Rossby waves in stratified interiors of uniformly rotating radiative stars with sub-adiabatic vertical temperature gradient. We use the equatorial beta-plane approximation and linear vertical gradient of temperature to study the linear dynamics of equatorially trapped Rossby and inertia-gravity waves in interiors of radiative stars. The governing equation is solved by the method of separation of variables in the vertical and latitudinal directions. Vertical and latitudinal solutions of the waves are found to be governed by Bessel functions and Hermite polynomials, respectively. Appropriate boundary conditions at stellar surface and poles define analytical dispersion relations for Rossby, Rossby-gravity and inertia-gravity waves. The waves are confined in surface layers of 30-50 $H_0$, where $H_0$ is surface density scale height, and trapped between the latitudes of $\pm 60^0$. Observable frequencies (normalized by the angular frequency of the stellar rotation) of Rossby waves with $m=1$ ($m=2$), where $m$ is the toroidal wavenumber, are in the interval of 0.65-1 (1.4-2), depending on stellar rotation, radius and surface temperature. Rossby-type waves can be systematically observed using light curves of Kepler and TESS stars. Observations and theory then can be used for the sounding of stellar interiors.