Instability by magnetic buoyancy

Abstract

Recent developments in the theory of instability by magnetic buoyancy are discussed in an astrophysical context and, where appropriate, extended to provide a more unified picture. Emphasis is placed on the effects of density stratification and rotation, which are usually stabilizing. In one strongly-stratified and rapidly-rotating parameter régime, however, it is possible to render a magnetic field configuration unstable by increasing the ‘statically-stable’ stratification, although increasing it beyond a certain limit eventually stabilizes the system, as one would intuitively expect.

We find that stratification exerts a strongly stabilizing influence in the solar radiative interior, despite the high thermal diffusivity κ. Rotation plays a rather minor role. We emphasize the importance of a ‘doubly-diffusive’ parameter D _* involving the ratio of κ to η, the magnetic diffusivity, and find that magnetic buoyancy instability typically requires field strengths in excess of about 50 000 G. The development time ties in with the rise-time of buoyant flux tubes in a stably-stratified environment calculated by Parker (1974, 1975). A reasonable gradient of molecular weight in the central core could only stabilize a (mainly) toroidal field strong enough to affect the neutrino flux if the magnetic diffusivity η were rather smaller than is usually supposed, for otherwise such a field would be subject to either a doubly-diffusive magnetic instability, which would initially take the form of overstable buoyancy oscillations, or rapid ohmic decay.

In the solar convection zone we find that the rotation of the Sun has an extremely strong and suppressing influence on magnetic buoyancy instability, and that this is only likely to occur for large field strengths of about 1000 G in the top half of the zone.