Tayler Instability Revisited

TL;DR

This paper revises the linear stability analysis of Tayler instability in stars, revealing how diffusive processes trigger wave overstability and highlighting differences based on magnetic Prandtl number, impacting dynamo theories.

Contribution

It provides a systematic analysis of diffusive effects on Tayler instability, introducing a new physical picture of wave overstability in rotating stars with implications for stellar dynamos.

Findings

Instability requires diffusive processes like viscosity or magnetic diffusion.

Different diffusive effects trigger overstability of magnetostrophic and inertial waves.

Unstable modes show non-universal scaling depending on magnetic Prandtl number.

Abstract

Tayler instability of toroidal magnetic fields $B_\phi$ is broadly invoked as a trigger for turbulence and angular momentum transport in stars. This paper presents a systematic revision of the linear stability analysis for a rotating, magnetized, and stably stratified star. For plausible configurations of $B_\phi$, instability requires diffusive processes: viscosity, magnetic diffusivity, or thermal/compositional diffusion. Our results reveal a new physical picture, demonstrating how different diffusive effects independently trigger instability of two types of waves in the rotating star: magnetostrophic waves and inertial waves. It develops via overstability of the waves, whose growth rate sharply peaks at some characteristic wavenumbers. We determine instability conditions for each wave branch and find the characteristic wavenumbers. The results are qualitatively different for stars with magnetic Prandtl number $Pm\ll 1$ (e.g. the Sun) and $Pm\gg 1$ (e.g. protoneutron stars). The parameter dependence of unstable modes suggests a non-universal scaling of the possible Tayler-Spruit dynamo.