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Stability of Toroidal Magnetic Fields in Rotating Stellar Radiation Zones

Aims. Two questions are addressed as to how strong magnetic fields can be stored in rotating stellar radiation zones without being subjected to pinch-type instabilities and how much radial mixing is produced if the fields are unstable. Methods. Linear equations are derived for weak disturbances of magnetic and velocity fields, which are global in horizontal dimensions but short–scaled in radius. The linear formulation includes the 2D theory of stability to strictly horizontal disturbances as a special limit. The eigenvalue problem for the derived equations is solved numerically to evaluate the stability of toroidal field patterns with one or two latitudinal belts under the influence of rigid rotation. Results. Radial displacements are essential for magnetic instability. It does not exist in the 2D case of strictly horizontal disturbances. Only stable (magnetically modified) r-modes are found in this case. The instability recovers in 3D. The minimum field strength Bmin for onset of the instability and radial scales of the most rapidly growing modes are strongly influenced by finite diffusion, the scales are indefinitely short if diffusion is neglected. The most rapidly growing modes for the Sun have radial scales of about 1 Mm. In the upper part of the solar radiation zone, Bmin � 600 G. The toroidal field can exceed this value only marginally, for otherwise the radial mixing produced by the instability would be too strong to be compatible with the observed lithium abundance.