Local heating due to convective overshooting and the solar modelling problem

Abstract : Recent hydrodynamical simulations of convection in a solar-like model suggest that penetrative convective flows at the boundary of the convective envelope modify the thermal background in the overshooting layer. Based on these results, we implement in one-dimensional stellar evolution codes a simple prescription to modify the temperature gradient below the convective boundary of a solar model. This simple prescription qualitatively reproduces the behaviour found in the hydrodynamical simulations, namely a local heating and smoothing of the temperature gradient below the convective boundary. We show that introducing local heating in the overshooting layer can reduce the sound-speed discrepancy usually reported between solar models and the structure of the Sun inferred from helioseismology. It also affects key quantities in the convective envelope, such as the density, the entropy, and the speed of sound. These effects could help reduce the discrepancies between solar models and observed constraints based on seismic inversions of the Ledoux discriminant. Since mixing due to overshooting and local heating are the result of the same convective penetration process, the goal of this work is to invite solar modellers to consider both processes for a more consistent approach.