2018ApJ...863...12L

Mixing in the convective core is quite uncertain in core helium-burning stars. To explore the overshooting mixing beyond the convective core, we incorporated the k-ω proposed by Li into the Modules of Experiments in Stellar Astrophysics (MESA), and investigated the overshooting mixing in evolution of subdwarf B (sdB) models. We found that the development of the convective core can be divided into three stages. When the radiative temperature gradient, ∇_rad, monotonically decreases outwardly, the overshooting mixing presents exponential decay similar with Herwig, and the overshooting distance is to make ∇_rad≃∇_ad at the boundary of the convective core, in agreement with the prediction of the self-driving mechanism Castellani et al. When the radiative temperature gradient, ∇_rad, shows a minimum value near the convective boundary, the convective core may be divided into two if the minimum value of ∇_rad is smaller than the adiabatic temperature gradient ∇_ad. For the single-zone case, the overshooting mixing shows exponential decay, but the overshooting distance is much smaller than in the initial stage. For the double-zone case, the overshooting mixing is similar to that of the single case beyond the convective core, while it almost stops on both sides of the above convective shell. Our overshooting mixing scheme is similar to the maximal overshoot scheme of Constantino et al. In the final stage, helium injections into the convective core by the overshooting mixing happens, similar to the "core breathing pulses."