Magnetic Buoyancy and Rotational Instabilities in the Tachocline

Wednesday, January 17, 2018

Peter Gilman presents results from an analytical model for magnetic buoyancy and ro­tational instabilities in a full spherical shell tachocline that includes rotation. differential rotation close to that observed helioseismicly, and toroidal field. Per­turbation solutions are found for the limit of large latitudinal wave number, a limit commonly used to maximize instability due to magnetic buoyancy.

Instability domains in low and middle latitudes image
Instability domains in low and middle latitudes due to magnetic buoyancy and rotational instabilities, showing toroidal fields have a threshhod for instability in sunspot latitudes, but are unstable for all field strengths in middle and high latitudes, offering an explanation for why sunspots are only seen at low latitudes.

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 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 9kG at the equator, declining to zero where the vertical rotation gradient changes sign at 32.3°, in our model. Thus this rotation gradient provides a previously unnoticed mechanism for storage of toroidal fields until they amplify by dynamo action to of order 1OkG, whereupon they can overcome the rotation gradient to emerge as sunspots. These results provide a new explanation for why sunspots are seen only in low latitudes. The purely rotational instability at latitudes above 50° even without toroidal fields also suggests that the high latitude tachocline should be much thicker, due to MD turbulence, than has been inferred for lower latitudes from helioseismic measurements.

Link to article: Astrophysical Journal