Rossby waves on stellar equatorial β planes: Uniformly rotating radiative stars

¹ Georg-August-Universität, Institut für Astrophysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
e-mail: mariam.albekioni.1@iliauni.edu.ge
² Department of Astronomy and Astrophysics at Space Research Center, School of Natural Sciences and Medicine, Ilia State University, Kakutsa Cholokashvili Ave. 3/5, Tbilisi 0162, Georgia
³ Evgeni Kharadze Georgian National Observatory, Abastumani, Adigeni 0301, Georgia
⁴ Institut of Physics, IGAM, University of Graz, Universitätsplatz 5, 8010 Graz, Austria

Received: 9 May 2022
Accepted: 2 January 2023

Abstract

Context. 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 have collected a lot of information about the light curves and activity of many stars, which triggered observations of Rossby waves in the stellar surface and interiors.

Aims. We aim to study the theoretical properties of Rossby waves in stratified interiors of uniformly rotating radiative stars with a sub-adiabatic vertical temperature gradient.

Methods. We used the equatorial β 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 was solved by the method of separation of variables in the vertical and latitudinal directions.

Results. Vertical and latitudinal solutions of the waves are found to be governed by Bessel functions and Hermite polynomials, respectively. Appropriate boundary conditions at the 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 H₀, where H₀ is the surface density scale height, and they are trapped between the latitudes of ±60⁰. Observable frequencies (normalised 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 the stellar rotation, radius, and surface temperature.

Conclusions. Rossby-type waves can be systematically observed using light curves of Kepler and TESS (Transiting Exoplanet Survey Satellite) stars. Observations and theory then can be used for the sounding of stellar interiors.