2019ApJ...870...77L

Overshooting and semiconvection are among the most noteworthy uncertainties in the evolution of massive stars. Complete mixing over a certain distance beyond the convective boundary and an exponentially decaying diffusion outside the convection zone are commonly adopted for the overshoot mixing. Recently, Li developed the k-ω model, which can be used in both convection zones and overshooting regions. We incorporated it in calculations of 30 M_☉ stellar models. We find that in the main-sequence stage, models with the k-ω model are almost identical to models with complete mixing in the overshooting region beyond the convective core, and the overshooting in the k-ω model is equivalent to an overshooting distance of about 0.15 H_P. In the post -main-sequence stage, we find that the overshooting below the bottom of the intermediate convection zone beyond the hydrogen-burning shell can significantly restrict the size of the hydrogen-depleted core, and can penetrate effectively into the hydrogen-burning shell. These two effects are crucial for the evolution of the core helium-burning stage. During the core helium-burning stage, we find that the overshooting model based on the k-ω model results in a similar complete mixing region but a much wider partial mixing region than the overshooting model based on Herwig. In particular, the overshooting distance in the core helium-burning stage may be significantly smaller than that in the main-sequence phase for massive stars.