On a Babcock-Leighton dynamo model with a deep-seated generating layer for the toroidal magnetic field

A dynamo model of the Babcock-Leighton type having the following features is studied. The toroidal fieldB is generated in a thin layer (the GL), located at the lower solar convection zone, by a shear in the angular velocity acting on the poloidal fieldB _p (= × 0, 0,A ].) If, in this layer, and for a certain value of the polar angle,, |B _Ø | exceeds a critical field,B _cr , then the eruption of a flux tube occurs. This flux tube, which is assumed to rise radially, generates, when reaching the surface, a bipolar magnetic region (BMR) with fluxes _p and _f for the preceding and following spot respectively. For the purpose of the numerical calculations this BMR is replaced by its equivalent axisymmetrical magnetic ring doublet. The ensemble of these eruptions acts as the source term for the poloidal field. This field, generated in the surface layers, reaches the lower solar convection by transport due to meridional motions and by diffusion. The meridional motions are the superpositions of a one-cell velocity field that rises at the equator and sinks at the poles and of a two-cell circulation that rises at the equator and poles and sinks at mid latitudes. The toroidal field andA _Ø were expanded in Legendre polynomials, and the coupled partial differential equations (int andr; time and radial coordinate) satisfied by the coefficients in these expansions were solved by a finite difference method. In the expansions, Legendre polynomials up to order thirty were included.In spite of an exhaustive search no solutions were found with _p = – _f . The solutions presented in this paper were obtained with _p = –0.5 _f . In this case, the northern and southern hemisphere are not entirely decoupled since lines of force join both hemispheres. Most of the solutions found were periodic. For the one-cell meridional flow described above and for a purely radial shear in the GL (the angular velocity increasing inwards) the dynamo wave propagates from the pole towards the equator. The new cycle starts at the poles while the old cycle is still present in the equatorial regions.