Stability of toroidal magnetic fields in the radiation zone of a star

The stability of a toroidal magnetic field in the rotating radiation zone of a star is analyzed to estimate the maximum possible magnitude of relic fields. Equations for small perturbations are obtained taking into account the finite diffusivity and the stabilizing effect of the subadiabatic stratification. The numerical solution of the eigenvalue problem indicates that the threshold field strength for the onset of instability in the radiation zone of the Sun is about 600 G. This figure sets an upper bound for the strength of the relic field. The assumption that magnetic instabilities are present in the solar radiation zone disagrees with the observed abundance of lithium. Our analysis of joint stability of toroidal field and nonuniform rotation shows that two-dimensional MHD solutions for the solar tachocline are stable against three-dimensional perturbations.