Modeling coexisting GSF and shear instabilities in rotating stars

TL;DR

This paper investigates the interaction of GSF and shear instabilities in rotating stars using simulations, revealing dominance patterns, the role of GSF as a primer, and proposing a new mixing model for stellar radiative zones.

Contribution

It demonstrates how GSF and shear instabilities coexist and influence each other in rotating stars, providing insights for stellar evolution models.

Findings

Either GSF or shear instability dominates depending on conditions.

Shear instability is subcritical and requires a finite-amplitude seed.

GSF can trigger shear instability, leading to relaxation oscillations.

Abstract

Zahn's widely-used model for turbulent mixing induced by rotational shear has recently been validated (with some caveats) in non-rotating shear flows. It is not clear, however, whether his model remains valid in the presence of rotation, even though this was its original purpose. Furthermore, new instabilities arise in rotating fluids, such as the Goldreich-Schubert-Fricke (GSF) instability. Which instability dominates when more than one can be excited, and how they influence each other, were open questions that this paper answers. To do so, we use direct numerical simulations of diffusive stratified shear flows in a rotating triply-periodic Cartesian domain located at the equator of a star. We find that either the GSF instability or the shear instability tends to take over the other in controlling the system, suggesting that stellar evolution models only need to have a mixing prescription for each individual instability, together with a criterion to determine which one dominates. However, we also find that it is not always easy to predict which instability "wins" for given input parameters, because the diffusive shear instability is subcritical, and only takes place if there is a finite-amplitude turbulence ``primer'' to seed it. Interestingly, we find that the GSF instability can in some cases play the role of this primer, thereby providing a pathway to excite the subcritical shear instability. This can also drive relaxation oscillations, that may be observable. We conclude by proposing a new model for mixing in the equatorial regions of stellar radiative zones due to differential rotation.