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

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, (Bp · ∇)Ω = Br∂Ω./∂r + Bθ/r ∂Ω/∂θ 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 ηc and the radius rc of transition between a weak and a strong turbulent region). A diagram of the toroidal field at a latitude of 60° 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 d1 ≳ 0.08 R⊙ (for ηc ≃ 2 × 109 -1 × 1010 cm2 s -1 and rc = 0.715 R⊙), or for d 1 ≲ 0.02 R⊙ and almost any value of ηc in the appropriate solar range. For intermediate values of d1 ≃ 0.04 R⊙-0.06 R⊙, 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. © ESO 2007.