Global shallow water magnetohydrodynamic waves in the solar tachocline

TL;DR

This paper derives analytical solutions for global shallow water magnetohydrodynamic waves in the solar tachocline, revealing how stratification and magnetic fields influence wave behavior and trapping locations.

Contribution

It provides the first analytical dispersion relations for magnetic Poincaré and Rossby waves in the solar tachocline, considering different stratification regimes and magnetic field effects.

Findings

Magnetic Rossby waves split into fast and slow modes.

Waves are concentrated near equator or poles depending on stratification.

Wave frequencies are lower in weakly stratified regions.

Abstract

We derive analytical solutions and dispersion relations of global magnetic Poincar\'e (magneto-gravity) and magnetic Rossby waves in the approximation of shallow water magnetohydrodynamics. The solutions are obtained in a rotating spherical coordinate system for strongly and weakly stable stratification separately in the presence of toroidal magnetic field. In both cases magnetic Rossby waves split into fast and slow magnetic Rossby modes. In the case of strongly stable stratification (valid in the radiative part of the tachocline) all waves are slightly affected by the layer thickness and the toroidal magnetic field, while in the case of weakly stable stratification (valid in the upper overshoot layer of the tachocline) magnetic Poincar\'e and fast magnetic Rossby waves are found to be concentrated near the solar equator, leading to equatorially trapped waves. However, slow magnetic Rossby waves tend to concentrate near the poles, leading to polar trapped waves. The frequencies of all waves are smaller in the upper weakly stable stratification region than in the lower strongly stable stratification one.