Tayler Instability Revisited

Abstract

Tayler instability of toroidal magnetic fields $B_{\varphi }$ 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 $B_{\varphi }$, 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.

Accepted in ApJ

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• Tayler-Spruit dynamo in stably stratified rotating fluids: Application to proto-magnetars
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• Magnetic Webs in Stellar Radiative Zones
• X-ray emission from helium star+black hole binaries as probes of tidally induced spin-up of second-born black holes
• Gravity's role in taming the Tayler instability in red giant cores