Magnetic Buoyancy and Magnetorotational Instabilities in Stellar Tachoclines for Solar- and Antisolar-type Differential Rotation

We present results from an analytical model for magnetic buoyancy and rotational instabilities in full spherical shell stellar tachoclines that include rotation, differential rotation of either solar or antisolar type, and toroidal field. We find that in all cases, for latitudes where the tachocline vertical rotation gradient is positive, toroidal fields can be stored against magnetic buoyancy up to a limit that is proportional to the square root of the local vertical rotation gradient. For solar magnitude differential rotation, this limit is about 9 kG. For fixed percentage differential rotation, storage capacity varies linearly with the rotation rate. Faster rotators with the same percentage differential rotation can store larger fields, and slower rotators can store smaller fields. At latitudes where the vertical rotation gradient is negative, vigorous magnetorotational instability for even weak (≪1 kG) toroidal fields prevents such storage. We infer from these results that for stars with solar-type latitudinal differential rotation (fast equator, slow poles), any starspots present should be found in low latitudes, similar to the Sun. For antisolar differential rotation, any spots present should be found in mid- and high latitudes, perhaps with a peak of occurrence near 55°. These results hopefully provide some guidance for making and interpreting observations of stellar activity and differential rotation on stars with convection zones and tachoclines.