JOINT INSTABILITY OF LATITUDINAL DIFFERENTIAL ROTATION AND TOROIDAL MAGNETIC-FIELDS BELOW THE SOLAR CONVECTION ZONE

Below the convection zone, where the stratification is radiatively con trolled, large-scale motions should be mainly horizontal, i.e., in sph erical shells due to the stabilizing effect of negative buoyancy on ra dial displacements. Watson showed that the observed surface solar diff erential rotation is at the threshold for instability to horizontal di sturbances. Therefore, since helioseismology tells us the latitudinal differential rotation below the convection zone is less than the surfa ce value, the profile should be stable too. We show that in the presen ce of a broad, nonuniform toroidal held the solar differential rotatio n is unstable. This is true for a wide range of kinetic and magnetic e nergies of the unperturbed state, from well below equipartition to wel l above it. We find instability for essentially all values of differen tial rotation and toroidal fields for which we are able to find conver ged solutions. The instability appears to occur only for longitudinal wave number 1. Disturbance symmetries about the equator and profiles i n latitude depend on the amplitude of the toridal held. Peak e-folding times are a few months. The primary energy source for the instability is differential rotation for low field strengths and the toroidal fie ld for high field strengths. The mechanism of energy release from the differential rotation is the poleward transport of angular momentum, b y the Maxwell stress rather than the Reynolds stress. For the profiles studied, the Reynolds stress is almost always trying to rebuild diffe rential rotation, the exact opposite of the nonmagnetic case. Second-o rder perturbation theory predicts that the unstable modes produce zona l jets and fine structure in the toroidal field, the latitude of which migrates toward the equator with increasing magnetic field strength. The instability we have found may play a role in the solar dynamo, alt hough being two-dimensional, it cannot produce a dynamo by itself. Mix ing of angular momentum caused by the instability could allow achievem ent of equilibrium of the solar tachocline hypothesized by Spiegel & Z ahn.