  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 wavenumber of a nonaxisymmetric perturbation with
m=1. The ratio of the Alfven frequency, \Omega_A, to the rate of the basic
rotation, \Omega, controls the eigenfrequency of the solution. For strong
fields with \Omega_A > \Omega the solutions do not feel the thermal diffusion.
The growth rate runs with \Omega_A and the drift rate is close to -\Omega so
that the magnetic pattern will rest in the laboratory system. For weaker fields
with \Omega_A < \Omega 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.
