The thermohaline, Richardson, Rayleigh-Taylor, Solberg-Hoiland, and GSF criteria in rotating stars

TL;DR

This paper analytically investigates the interactions of multiple stellar instabilities in rotating stars, considering effects like radiative losses and turbulence, revealing complex stability criteria and the importance of combined instability treatment.

Contribution

It introduces a unified analytical framework for multiple stellar instabilities in rotating stars, accounting for radiative losses, turbulence, and their interactions, which was not previously addressed.

Findings

Diffusion coefficient is derived from a general equation, not a sum of individual coefficients.

Thermohaline mixing in low-mass red giants requires weak horizontal turbulence.

Rotation laws with alpha > 1.6568 are unstable, refining classical criteria.

Abstract

Aims. We examine the interactions of various instabilities in rotating stars, which usually are considered as independent. Methods. An analytical study of the problem is performed, account is given to radiative losses, mu-gradients and horizontal turbulence. Results. The diffusion coefficient for an ensemble of instabilities is not given by the sum of the specific coefficients for each instability, but by the solution of a general equation. We find that thermohaline mixing is possible in low-mass red giants only if the horizontal turbulence is very weak. In rotating stars the Rayleigh-Taylor and the shear instabilities need simultaneous treating. This has for consequence that rotation laws of the form 1/r^(alpha) are predicted to be unstable for alpha > 1.6568, while the usual Rayleigh criterion predicts instability only for alpha > 2. Also, the shear instabilities are somehow reduced in Main Sequence stars by the effect of the Rayleigh-Taylor criterion. Various instability criteria should be expressed differently in rotating stars than in simplified geometries.