The Goldreich-Schubert-Fricke instability in stellar radiative zones

TL;DR

This paper reevaluates the Goldreich-Schubert-Fricke instability in stellar radiative zones, demonstrating that it is less effective in angular momentum transport than previously thought, especially considering realistic viscosity and magnetic effects.

Contribution

The study provides a detailed analysis of the GSF instability with realistic viscosity and magnetic effects, challenging prior assumptions about its efficiency in stellar angular momentum transfer.

Findings

GSF instability occurs only in regions of strong shear.

Viscosity and magnetic fields have a stabilizing effect.

The instability may be absent or less effective in stars.

Abstract

The Goldreich-Schubert-Fricke (GSF) instability is a rotational instability that is thought to contribute to the transfer of angular momentum in differentially rotating stars. It has been included in recent codes of stellar evolution in a diffusion-like approximation, under the assumption that the kinematic viscosity $\nu$ is unimportant for the development of the instability. As noted previously by other authors, for most stellar applications this may not be a valid approximation. We discuss this issue in detail, solving the dispersion relation of the perturbed modes for realistic values of $\nu$ in the bulk of the radiative zone of the Sun and of three red giant stars at various evolutionary stages. We find that the GSF instability is triggered only in layers of extremely strong shear. In a simple case study, we also investigate the effect of a small deviation from axisymmetry or a small background magnetic field. We find that, like the viscosity, these have a stabilising effect. We conclude that this instability is probably far less efficient in transporting angular momentum than is often assumed, and may not even be present.