The thermohaline, Richardson, Rayleigh-Taylor, Solberg–Høiland, and GSF criteria in rotating stars
Résumé
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 accounting for radiative losses, μ-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 leads to rotation laws of the form 1/rα being predicted to be unstable for α > 1.6568, while the usual Rayleigh criterion only predicts instability for α > 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.