Talk abstract details

The stability of toroidal magnetic fields in rotating stellar tachoclines is studied for realistic values of the Prandtl numbers. The resulting complex eigenfrequencies including growth rate and drift velocity are calculated in Boussinesq approximation for a given radial wavenumber of a nonaxisymmetric perturbation. The ratio of the Alfv\'en frequency to the rate of the stellar rotation controls the solutions. For strong fields they do not feel the thermal diffusion and the growth rates are very high. For weaker fields the growth rate depends on the thermal conductivity. For fields with dipolar parity and for typical values of the heat conductivity the resulting very long growth times (many years) are almost identical with those for vanishing gravity. The rotation law in the tachoclines is shown as basically stabilizing the instability independent of the sign of the shear. Already very small shear values lead to an increase of the critical magnetic field by one order of magnitude. For the solar tachocline we find a maximum magnetic field amplitude of about 1 kGauss as stable.