Stability of toroidal magnetic fields in stellar interiors

摘要

Aims. Magnetic fields play an important role during the formation and evolution of stars. Of particular interest in stellar evolution is what effect they have on the transport angular momentum and mixing of chemical elements along the radial direction in radiative regions. Current theories suggest a dynamo loop as the mechanism responsible for maintaining the magnetic field in the radiative zone. This loop consists of differential rotation on one side and magnetohydrodynamic (MHD) instability ? the so-called Tayler instability ? on the other. However, how this might work quantitatively is still an unsettled question, largely because we do not yet understand all the properties of the instability in question. In this paper we explore some properties of the Tayler instability. Methods. We present 3D MHD simulations of purely toroidal and mixed poloidal-toroidal magnetic field configurations to study the behavior of the Tayler instability. For the first time the simultaneous action of rotation and magnetic diffusion are taken into account and the effects of a poloidal field on the dynamic evolution of unstable toroidal magnetic fields is included. Results. In the absence of diffusion, fast rotation (rotation rate, Ω∥, compared to Alfvén frequency, ωA,φ) is able to suppress the instability when the rotation and magnetic axes are aligned and when the radial field strength gradient p 1.5, rapid rotation does not suppress the instability but instead introduces a damping factor ωA/ 2Ω∥ to the growth rate, in agreement with the analytic predictions. For the mixed poloidal-toroidal fields we find an unstable axisymmetric mode, not predicted analytically, right at the stability threshold for the non-axisymmetric modes; it has been argued that an axisymmetric mode is necessary for the closure of the Tayler-Spruit dynamo loop.