Magnetic buoyancy and rotational instabilities in the tachocline

Perturbation solutions are found for the limit of large latitudinal wave number, a limit commonly used to maximize instability due to magnetic buoyancy. We find that at all middle and high latitudes vigorous rotational instability is induced by weak toroidal fields, particularly for high longitudinal wave number, even when the vertical rotation gradient is marginally stable without toroidal field.

We infer that this instability will prevent much storage of toroidal fields in the tachocline at these latitudes, but could be responsible for the appearance of ephemeral active regions there. By contrast, the low-latitude vertical rotation gradient, opposite in sign to that at high latitudes, is not only stable itself but also prevents magnetic buoyancy instability until the peak toroidal field is raised above a threshold of about 9 kG at the equator, declining to zero where the vertical rotation gradient changes sign, at 32 degrees.3 in our model.