A numerical MHD model for the solar tachocline

There are successful approaches to explain the formation of the tachocline by a poloidal magnetic field in the solar core. We present here the first MHD simulations of the solar tachocline which self-consistently include the meridional circulation. We show that the meridional flow significantly changes the shape and the characteristics of the tachocline. We find that after the inclusion of the meridional circulation, a tachocline can be formed even when the poloidal field lines are crossing the boundary between the radiative zone and the convection zone. We also discuss the effects of the magnetic Prandtl number as well as of the magnetic Reynolds number on the properties of the tachocline. The tachocline is much thinner for higher magnetic Reynolds numbers and/or lower magnetic Prandtl numbers. We expect that a poloidal magnetic seed field of around 1 G will be sufficient to produce the tachocline of the Sun. However, the model requires the initial magnetic field to be in a narrow range for satisfying tachocline solutions. The simulations including a stable temperature gradient produce a shallower as well as slower meridional circulation than the ones without it, as desired from the Lithium abundance at the solar surface.