CONVECTIVE OVERSHOOT MIXING IN MODELS OF THE STELLAR INTERIOR

Convective overshoot mixing plays an important role in stellar structure and evolution. However, overshoot mixing is also a long-standing problem; it is one of the most uncertain factors in stellar physics. As is well known, convective overshoot mixing is determined by the radial turbulent flux of the chemical component. In this paper, a local model of the radial turbulent flux of the chemical component is established based on hydrodynamic equations and some model assumptions and is tested in stellar models. The main conclusions are as follows. (1) The local model shows that convective overshoot mixing could be regarded as a diffusion process and the diffusion coefficient for different chemical elements is the same. However, if the non-local terms i.e., the gradient of the third-order moments, are taken into account, the diffusion coefficient for each chemical element should in general be different. (2) The diffusion coefficient of convective/overshoot mixing shows different behaviors in the convection zone and in the overshoot region because the characteristic length scale of the mixing is large in the convection zone and small in the overshoot region. Overshoot mixing should be regarded as a weak mixing process. (3) The diffusion coefficient of mixing is tested in stellar models, and 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 masses from 2 M to 10 M.