Stability of Toroidal Magnetic Fields in Rotating Stellar Radiation Zones

Abstract

The questions of how strong magnetic fields can be stored in rotating stellar radiative zones without being subjected to pinch-type instabilities and how much radial mixing is produced if the fields are unstable are addressed. Linear equations are derived for weak disturbances of magnetic and velocity fields which are global in horizontal dimensions but short--scaled in radius. The equations are solved to evaluate the stability of toroidal field patterns with one or two latitudinal belts under the influence of a rigid basic rotation. Hydrodynamic stability of latitudinal differential rotation is also considered. The magnetic instability is essentially three--dimensional. It does not exist in a 2D formulation with strictly horizontal disturbances on decoupled spherical shells. Only stable (magnetically modified) r-modes are found in this case. The instability recovers in 3D. The most rapidly growing modes for the Sun have radial scales smaller than 1 Mm. The finite thermal conductivity makes a strong destabilizing effect. The marginal field strength for the onset of the instability in the upper part of the solar radiative zone is about 600 G. The toroidal field can only slightly exceed this critical value for otherwise the radial mixing produced by the instability would be too strong to be compatible with the observed lithium abundance. Also the threshold for hydrodynamic instability of differential rotation which exists in 2D is lowered in 3D. When radial displacements are included, the value of 28% for critical shear is reduced to 21%.

7 pages, 9 figures

References in corpus (3)

• Destabilisation of hydrodynamically stable rotation laws by azimuthal magnetic fields
• Magnetic field confinement by meridional flow and the solar tachocline
• Structure and stability of the magnetic solar tachocline

Cited by in corpus (8)

• On magnetic instabilities and dynamo action in stellar radiation zones
• Magnetic helicity effects in astrophysical and laboratory dynamos
• Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone
• Global simulations of Tayler instability in stellar interiors: The stabilizing effect of gravity
• Baroclinic Instability in Stellar Radiation Zones
• Global simulations of Tayler instability in stellar interiors: a long-time multi-stage evolution of the magnetic field
• Gravity's role in taming the Tayler instability in red giant cores
• Two-dimensional ideal magnetohydrodynamic waves on a rotating sphere under a non-Malkus field: I. Continuous spectrum and its ray-theoretical interpretation