Linear and nonlinear evolution of the Parker instability of magnetic-flux sheets in co-rotating coordinates

We present a study of the magnetic buoyancy instability (or Parker instability) of stellar, atmospheres, in particular that of the effect of the Coriolis force, via a linear stability analysis and nonlinear 3-D MHD simulations. We find that fast rotation stabilizes this mode for a toroidal flux sheet located near to the equator: magnetic flux sheets in low-latitude regions are locally stable, while the growth rate of the flux sheet near to the polar zone is not much reduced by the Coriolis effect. This may explain the observational result that stellar spots of fast rotating stars appear toward the polar region. Another effect of the Coriolis force is that there is a cut-off rotational angular velocity above which the long-wavelength transverse perturbations are more unstable than the short wavelength ones. This may explain why large stellar patches are observed in fast rotating stars. 3-D simulations of magnetic flux sheets under buoyancy instability have also been carried out in co-rotating Cartesian coordinates. The simulation results show that the combination of the buoyancy instability and the Coriolis effect gives rise to a mechanism to twist the magnetic-flux sheet embedded in the solar (or stellar) atmosphere of a slowly rotating star (such as the Sun), emerging to the surface with a helical structure. We suggest that this can be a model to explain the S-shaped active regions in the low latitudes of the Sun shown in the soft X-ray picture taken by the Yohkoh satellite.