Angular momentum and overshooting: two as yet unsolved problems in stellar mixing

Abstract

AbstractHelioseismological data have given us two interesting results: the differential-to-uniform solar rotation curve and the extent of the overshooting region (OV). As of today, no model (including numerical simulations) has been able to reproduce these findings. Here, we first present a new model for the angular momentum. It contains new terms representing vorticity and buoyancy that were left out in all previous formulations without a clear justification. It is shown that they extract angular momentum from the stellar core, a welcome feature since the standard angular momentum equation leads to a rotation curve that is considerably higher than what is observed. As for the overshooting extent, all models yield values that are an order of magnitude larger than the helio data of 0.07Hp. We propose a criterion whose main ingredient is a new flux conservation law that includes new terms, one of which increases the dissipation in the radiative zone and thus lowers the OV extent, a tendency in the desired direction. Since we have not coupled the new models to a solar structure-evolution code, we cannot at this stage carry out a comparison with the helio data. The purpose is to exhibit the fact that in both cases the missing ingredients are of such nature as to improve the previous model predictions. A proper quantification remains to be done.