Stability of latitudinal differential rotation in stars

¹ Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany e-mail: [lkitchatinov;gruediger]@aip.de
² Institute for Solar-Terrestrial Physics, PO Box 291, Irkutsk 664033, Russia e-mail: kit@iszf.irk.ru
³ Pulkovo Astronomical Observatory, St. Petersburg, 196140, Russia

Received: 13 February 2009
Accepted: 18 June 2009

Abstract

Aims. We investigate whether differentially rotating regions of stellar radiative zones (such as the solar tachocline) excite nonaxisymmetric r-modes that can be observed. We study the hydrodynamical stability of latitudinal differential rotation. The amount of rotational shear required for the instability is estimated to depend on the character of radial stratification, and the flow patterns excited by the instability are found.

Methods. 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.

Results. The critical magnitude of the latitudinal differential rotation for the onset of the instability is reduced considerably in the 3D theory compared to the 2D approximation. The instability requires a subadiabatic stratification. It does not exist in the bulk of the convection zone with almost adiabatic stratification but may switch on close to 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 to be the dominating instability mode. The vortices exhibit longitudinal drift rates retrograde to the basic rotation, which are close to that of the observed weak r-mode signatures at the solar surface.