Stability of latitudinal differential rotation in stars

TL;DR

This study investigates the stability of latitudinal differential rotation in stars, finding that 3D effects lower the threshold for instability and that certain modes may explain observed solar surface phenomena.

Contribution

The paper provides a 3D hydrodynamical stability analysis of stellar latitudinal differential rotation, highlighting the conditions for instability and the nature of excited modes.

Findings

3D theory reduces the critical differential rotation needed for instability.

Instability requires subadiabatic stratification, not present in the convection zone.

The dominant mode predicts vortices with drift rates matching observed solar r-modes.

Abstract

The question is addressed whether stellar differentially rotating radiative zones (like the solar tachocline) excite nonaxisymmetric r-modes which can be observed. To this end the hydrodynamical stability of latitudinal differential rotation is studied. The amount of rotational shear required for the instability is estimated in dependence of the character of radial stratification and the flow patterns excited by the instability are found. The eigenvalue equations for the nonaxisymmetric disturbances are formulated in 3D and then solved numerically. Radial displacements and entropy disturbances are included. The equations contain the 2D approximation of strictly horizontal displacements as a special limit. The critical magnitude of the latitudinal differential rotation for onset of the instability is considerably reduced in the 3D theory compared to the 2D approximation. The instability requires a subadiabatic stratification. It does not exist in the bulk of convection zone with almost adiabatic stratification but may switch on near its base in the region of penetrative convection. Growth rates and symmetry types of the modes are computed in dependence on the rotation law parameters. The S1 mode with its transequatorial toroidal vortices is predicted as the dominating instability mode. The vortices show longitudinal drift rates retrograde to the basic rotation which are close to that of the observed weak r-mode signatures at the solar surface.