2021ApJ...923..166L

To explore overshoot mixing beyond the convective core in core helium-burning stars, we use the k-ω model, which is incorporated into the Modules of Experiments in Stellar Astrophysics to investigate overshoot mixing in the evolution of subdwarf B (sdB) stars. Our results show that the development of the convective core can be divided into three stages. The mass of the convective core increases monotonically when the radiative temperature gradient, ∇_rad, monotonically decreases outwardly, and overshoot mixing presents an exponential decay similar to Herwig. The splitting of the convective core occurs repeatedly when the minimum value of ∇_rad near the convective boundary is smaller than the adiabatic temperature gradient, ∇_ad. The mass at the outer boundary of the convective shell M_sc can exceed 0.2 M_☉ after the central helium abundance drops to about Y_c ≃ 0.45. It is close to the convective core masses derived by asteroseismology for younger models (0.22 to ∼0.28 M_☉). In the final stage, "core breathing pulses" occurred two or three times. Helium was injected into the convective core by overshoot mixing and increased the lifetime of sdB stars. The mass of the mixed region M_mixed can rise to 0.303 M_☉ by the end. The oxygen content in the central core of our g-mode sdB models is about 80% by mass. The high amounts of oxygen deduced from asteroseismology may be evidence supporting the existence of core breathing pulses.