Stability of toroidal magnetic fields in the solar tachocline

The stability of toroidal magnetic fields in the radiative interior of the Sun is studied in a three-dimensional environment. The underlying differential rotation in the tachocline depends on both latitude and radius. We found stability limits for toroidal fields of only 100 G even in the simplified, incompressible, but stably stratified case. Nonaxisymmetric modes are linearly unstable with a weak influence on the amplitude of the underlying differential rotation. We conclude that the tachocline is not a suitable location for the storage of magnetic fields as strong as 100 kG. Since the results are based on an extrapolation of the numerical computations to lower solar diffusivities, high-resolution calculations at higher magnetic Reynolds numbers are required