Overshoot at the base of the solar convection zone: A semianalytical approach

Despite the importance of overshoot at the base of the solar convection zone for the storage of strong toroidal magnetic field produced there by the solar dynamo, uncertainties concerning the depth and mean subadiabatic stratification remain large. Overshoot models based on the nonlocal mixing-length theory generally produce a shallow, weakly subadiabatic region with a sharp transition to the radiative interior, whereas several numerical simulations lead to significantly subadiabatic overshoot with penetration depth of more than a pressure scale height. We present a semianalytical convection zone/overshoot region model based on the assumption that the convective energy flux is governed by coherent downflow structures starting at the top of the domain and continuing all the way down into the overshoot region, which allows for modeling both the parameter regime addressed by nonlocal mixing-length approach and the regime addressed by numerical simulations. It turns out that the main differences between the nonlocal mixing-length approach and numerical simulations (nearly adiabatic vs. strongly subadiabatic overshoot) are caused by the much larger energy flux used in numerical simulations as a consequence of larger thermal diffusivities required by numerical constraints. The depth of the overshoot region is determined predominantly by the mixing between downflows and upflows in the convection zone. Furthermore, our model shows that the sharp transition between the nearly adiabatic overshoot and radiative interior, a typical result of the nonlocal mixing-length approach, can be avoided by assuming an ensemble of downflows with different strength.