The kink-type instability of toroidal stellar magnetic fields with thermal diffusion∗

The stability of toroidal magnetic fields in rotating radiative stellar zones is studied for realistic values of both the Prandtl numbers. The two considered models for the magnetic geometry represent fields with odd and even symmetry with respect to the equator. In the linear theory in Boussinesq approximation the resulting complex eigenfrequency (including growth rate and drift rate) are calculated for a given radial wave number of a nonaxisymmetric perturbation with m = 1. The ratio of the Alfvén frequency, ΩA, to the rate of the basic rotation, Ω, controls the eigenfrequency of the solution. For strong fields with ΩA> Ω the solutions do not feel the thermal diffusion. The growth rate runs with ΩA and the drift rate is close to −Ω so that the magnetic pattern will rest in the laboratory system. For weaker fields with ΩA < Ω the growth rate strongly depends on the thermal conductivity. For fields with dipolar parity and for typical values of the heat conductivity the resulting very small growth rates are almost identical with those for vanishing gravity. For fields with dipolar symmetry the differential rotation of any stellar radiative zone (like the solar tachocline) is shown as basically stabilizing the instability independent of the sign of the shear. Finally, the current-driven kink-type instability of a toroidal background field is proposed as a model for the magnetism of Ap stars. The recent observation of a lower magnetic field treshold of about 300 Gauss for Ap stars is understood as corresponding to the minimum magnetic field producing the instability