Stability of toroidal magnetic fields in the solar tachocline and beneath

TL;DR

This paper analyzes the stability of toroidal magnetic fields in the solar tachocline, finding that fields slightly above 600 G are marginally stable and that the tachocline's stability depends on rotation and magnetic field strength.

Contribution

It provides a detailed stability analysis of toroidal magnetic fields in the solar tachocline, considering both uniform and differential rotation, and assesses implications for stellar magnetic fields.

Findings

Critical magnetic field for instability is about 600 G.

Unstable disturbances have short radial scales (~1 Mm).

Internal solar magnetic fields can marginally exceed 600 G without conflicting with lithium observations.

Abstract

Stability of toroidal magnetic field in a stellar radiation zone is considered for the cases of uniform and differential rotation. In the rigidly rotating radiative core shortly below the tachocline, the critical magnetic field for instability is about 600 G. The unstable disturbances for slightly supercritical fields have short radial scales ~1 Mm. Radial mixing produced by the instability is estimated to conclude that the internal field of the sun can exceed the critical value of 600 G only marginally. Otherwise, the mixing is too strong and not compatible with the observed lithium abundance. Analysis of joint instability of differential rotation and toroidal field leads to the conclusion that axisymmetric models of the laminar solar tachocline are stable to nonaxisymmetric disturbances. The question of whether sun-like stars can posses tachoclines is addressed with positive answer for stars with rotation periods shorter than about two months.