Equatorially trapped Rossby waves in radiative stars

TL;DR

This paper develops a theoretical model for equatorially trapped Rossby waves in radiative stars, linking wave properties to stellar parameters and suggesting their use in asteroseismology.

Contribution

It provides an analytical framework for understanding Rossby wave dynamics in radiative stars and connects wave frequencies to stellar temperature gradients and rotation.

Findings

Vertical modes are concentrated near the stellar surface.

Wave frequency depends on temperature gradient and rotation.

Rossby waves can serve as a new asteroseismic diagnostic.

Abstract

Observations by recent space missions reported the detection of Rossby waves (r-modes) in light curves of many stars (mostly A, B, and F spectral types) with outer radiative envelope. This paper aims to study the theoretical dynamics of Rossby-type waves in such stars. Hydrodynamic equations in a rotating frame were split into horizontal and vertical parts connected by a separation constant (or an equivalent depth). Vertical equations were solved analytically for a linear temperature profile and the equivalent depth was derived through free surface boundary condition. It is found that the vertical modes are concentrated in the near-surface layer with a thickness of several tens of surface density scale height. Then with the equivalent width, horizontal structure equations were solved, and the corresponding dispersion relation for Rossby, Rossby-gravity, and inertia-gravity waves was obtained. The solutions were found to be confined around the equator leading to the equatorially trapped waves. It was shown that the wave frequency depends on the vertical temperature gradient as well as on stellar rotation. Therefore, observations of wave frequency in light curves of stars with known parameters (radius, surface gravity, rotation period) could be used to estimate the temperature gradient in stellar outer layers. Consequently, the Rossby mode may be considered as an additional tool in asteroseismology apart from acoustic and gravity modes.