Solar interface dynamo models with a realistic rotation profile

Extensions of the interface dynamo model of Parker are considered through two-dimensional numerical simulations in spherical geometry. In the interface model, the production of the poloidal and toroidal components of the magnetic field occur in two separate regions coupled by diffusion. A large discontinuous jump in the diffusivity at the interface allows the production of a sufficiently strong toroidal magnetic field in the lower region while avoiding the difficulty of alpha quenching. When the rotation rate is assumed to vary only radially, dynamo waves that closely resemble the analytical solutions in Cartesian geometry found by Parker are found propagating along the interface. However, when a fit to the solar rotation profile-as determined from helioseismology, with both latitudinal and radial dependence-is included, no fully satisfactory solar-like oscillatory solutions are found. For an appropriately large diffusivity contrast, only steady modes are found for negative dynamo number, and only purely decaying solutions are found for positive dynamo number. Here the effect of the latitudinal variation of rotation is to suppress the oscillatory interface modes driven by the radial shear. Oscillatory solutions can be found for a small diffusivity contrast, but these solutions have field strengths that are too low for the solar case. The hybrid mode of Charbonneau & MacGregor found from similar calculations is shown to result from an incorrect boundary condition imposed at the interface and thus is not a valid solution.