Stability of toroidal magnetic fields in stellar interiors

¹ Universität Bonn, Argelander Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
² Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
³ American Museum of Natural History, Department of Astrophysics, 79th Street at Central Park West, New York, NY 10024, USA
e-mail: jibanezmejia@amnh.org

Received: 25 June 2014
Accepted: 22 February 2015

Abstract

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, ω_A,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 (where p ≡ ∂lnB/∂lnϖ and ϖ is the cylindrical radius coordinate). When diffusion is included, this system turns unstable for diffusion dominated and marginally diffusive dominated regions. If the magnetic and rotation axes are perpendicular to each other, Ω_⊥, the stabilizing effect induced by the Coriolis force is scale dependent and decreases with increasing wavenumber. In toroidal fields with radial field gradients bigger than p> 1.5, rapid rotation does not suppress the instability but instead introduces a damping factor ω_A/ 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.