Solar Interface Dynamos. II. Linear, Kinematic Models in Spherical Geometry

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Abstract
Numerical models of interface dynamos are constructed, and their properties discussed in some detail. These models are extensions in spherical geometry of the Cartesian interface models considered by Parker and in the first paper of this series. The models are cast in the framework of classical mean-field electrodynamics and make use of a realistic solar-like internal differential rotation profile. The magnetic diffusivity is assumed to vary discontinously by orders of magnitude across the core-envelope interface. This allows the buildup of very strong toroidal magnetic fields below the interface, as apparently required by recent models of erupting bipolar magnetic regions. Distinct dynamo modes powered either by the latitudinal or radial shear can coexist and, under certain conditions, interfere destructively with one another. Hybrid modes, relying on the latitudinal shear both in the envelope and below it, are most easily excited in some portions of parameter space, and represent a class of dynamo solutions distinct from the true interface modes previously investigated in Cartesian geometry. Which mode is preferentially excited depends primarily on the assumed ratio of magnetic diffusivities on either side of the core-envelope interface. For an α-effect having a simple cos θ latitudinal dependency, the interface mode associated with the radial shear below the polar regions of the interface is easier to excite than its equatorial counterpart. In analogy with more conventional dynamo models, interface modes propagate equatorward if the product of the radial shear (∂Ω/∂r) and α-effect coefficient (Cα) is negative, and poleward if that product is positive. Interface dynamo modes powered by the positive radial shear localized below the core-envelope interface in the equatorial regions can be produced by artificially restricting the α-effect to low latitudes. For negative dynamo number, those modes are globally dipolar, propagate toward the equator, and are characterized by a phase relationship between poloidal and toroidal magnetic field components that is in agreement with observations. While the models discussed in this paper are linear and kinematic, and consequently rather limited in their predictive power, results obtained so far certainly suggest that interface dynamos represent a very attractive alternative to conventional solar mean-field dynamo models.