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Convective overshoot mixing in stellar interior models

The convective overshoot mixing plays an important role in stellar structure and evolution. However, the overshoot mixing is a long standing problem. The uncertainty of the overshoot mixing is one of the most uncertain factors in stellar physics. As it is well known, the convective and overshoot mixing is determined by the radial chemical component flux. In this paper, a local model of the radial chemical component flux is established based on the hydrodynamic equations and some model assumptions. The model is tested in stellar models. The main conclusions are as follows. (i) The local model shows that the convective and overshoot mixing could be regarded as a diffusion process, and the diffusion coefficient for different chemical element is the same. However, if the non-local terms, i.e., the turbulent convective transport of radial chemical component flux, are taken into account, the diffusion coefficient for each chemical element should be in general different. (ii) The diffusion coefficient of convective / overshoot mixing shows different behaviors in convection zone and in overshoot region because the characteristic length scale of the mixing is large in the convection zone and small in the overshoot region. The overshoot mixing should be regarded as a weak mixing process. (iii) The result of the diffusion coefficient of mixing is tested in stellar models. It is found that a single choice of our central mixing parameter leads to consistent results for a solar convective envelope model as well as for core convection models of stars with mass from 2M to 10M.