The effects of the shape and width of the tachocline on the butterfly diagram of the solar cycle

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Flux-dominated kinematic solar dynamo models, which have demonstrated to be quite successful in reproducing most of the observed features of the 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, we here explore the contribution of both the radial and the latitudinal shear in the generation of the toroidal magnetic fields by varying the shape and the width of the solar tachocline. We find that a prolate tachocline (as suggested by recent observations) is unable to resolve the aforementioned problem. On the other hand, we find that the latitudinal component of the shear term of the dynamo equation is always dominant over the radial component for producing toroidal field amplification, and that this field is suppressed at high latitudes if the tachocline has a width d ≤ 0.03 solar radius or d ≥ 0.1 solar radius. The best fit to the observed butterfly diagram is found for a tachocline with width smaller than 3% of the solar radius. We should note, however, that this result is somewhat sensitive to the adopted magnetic diffusivity. In the present work, we have adopted a diffusion profile for which the tachocline is approximately half subadiabatic and half turbulent. If we had taken, for instance, a tachocline with a smaller turbulent portion, then its width could be a slightly larger than the value above.

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