How does the shape and thickness of the tachocline affect the distribution of the toroidal magnetic fields in the solar dynamo?

Astronomy Department, Instituto de Astronomia, Geofísica e Ciências Atmosfêricas, Universidade de São Paulo, Rua do Matão 1226, São Paulo, Brazil e-mail: guerrero,dalpino@astro.iag.usp.br

Received: 15 June 2006
Accepted: 27 October 2006

Abstract

Flux-dominated solar dynamo models, which have been demonstrated to be quite successful in reproducing most of the observed features of the large-scale solar magnetic cycle, generally produce an inappropriate latitudinal distribution of the toroidal magnetic fields, showing fields of large magnitude in polar regions where the radial shear has a maximum amplitude. Employing a kinematic solar dynamo model, here we explore the contributions of both the radial and the latitudinal shear in the generation of the toroidal magnetic fields by varying the shape and the thickness of the solar tachocline. We also explore the effects of the diffusivity profile of the convective zone. Considering the shear term of the dynamo equation, , we find that the latitudinal component is always dominant over the radial component at producing toroidal field amplification. These results are very sensitive to the adopted diffusivity profile, specially in the inner convection zone (which is characterized by the diffusivity and the radius r_c of transition between a weak and a strong turbulent region). A diagram of the toroidal field at a latitude of  versus the diffusivity at the convection layer for different values of the tachocline width has revealed that these fields are mainly eliminated for tachoclines with width (for  cm² s^-1 and ), or for and almost any value of in the appropriate solar range. For intermediate values of -, strong toroidal fields should survive at high latitudes in the butterfly diagram and those values are therefore not suitable. We have built butterfly diagrams for both a thin and a thick tachocline that best match the observations. We have also found that a prolate tachocline is able to reproduce solar-like butterfly diagrams depending on the choice of appropriate diffusivity profiles and tachocline width range.