On a Babcock‐Leighton Solar Dynamo Model with a Deep‐seated Generating Layer for the Toroidal Magnetic Field. IV.

Abstract

In a previous paper (Paper I), we studied a dynamo model of the Babcock-Leighton type (i.e., the surface eruptions of toroidal magnetic field are the source for the poloidal field) that included a thin, deep seated, generating layer (GL) for the toroidal field, Bφ. Meridional motions (of the order of 12 m s-1 at the surface), rising at the equator and sinking at the poles were essential for the dynamo action. The induction equation was solved by approximating the latitudinal dependence of the fields by Legendre polynomials. No solutions were found with Φp = -Φf where Φp and Φf are the fluxes for the preceding and following spot, respectively. The solutions presented in Paper I, had Φp = -0.5 Φf, were oscillatory in time, and large radial fields, Br, were present at the surface. Here, we resume the study of Paper I with a different numerical approach allowing for a much higher resolution in θ, the polar angle. The time dependent partial differential equations for the toroidal and poloidal field are solved with the help of a second order, time and space centered, finite difference scheme. Oscillatory solutions with Φp = Φf are found for various values of the meridional motions and diffusivity coefficients. The surface values of Br, while considerably smaller than those of Paper I, are still unacceptably large, specially at the poles. The reason can be traced to the eruption of toroidal field at high latitudes. It appears that in order to obtain small values for the radial field in the polar regions, high latitude sources (θ smaller than π/4, say), must reach their maximum below the surface. Weaker meridional motions near the poles than in the equatorial region are also suggested. © 1996 Kluwer Academic Publishers.