The slender solar tachocline: a magnetic model

A model for the sharp transition from differential rotation in the solar convection zone to rigid rotation in the radiative interior is presented. Differential rotation in the radiative zone is shown to be quenched efficiently by an internal magnetic field. The poloidal field amplitude, B-0 is the input parameter for our model which determines the transition layer thickness and the toroidal field strength. It is illustrated analytically and confirmed numerically that a rather small field, B-0 = 10(-4) Gauss, suffices to satisfy the helioseismological restrictions on the depth of the differential rotation penetration below the convection zone. The transition layer thickness decreases further with increasing B-0. The toroidal field amplitude B similar or equal to 200 Gauss is almost independent of B-0.