Helioseismic observations have revealed many properties of the Sun: the depth and the helium abundance of the convection zone, the sound-speed and the density profiles in the solar interior. Those constraints have been used to judge the stellar evolution theory. With the old solar composition (e.g., GS98), the solar standard model is in reasonable agreement with the helioseismic constraints. However, a solar model with revised composition (e.g., AGSS09) with low abundance Z of heavy elements cannot be consistent with those constraints. This is the so-called "solar abundance problem", standing for more than ten years even with the recent upward revised Ne abundance. Many mechanisms have been proposed to mitigate the problem. However, there is still not a low-Z solar model satisfying all helioseismic constraints. In this paper, we report a possible solution to the solar abundance problem. With some extra physical processes that are not included in the standard model, solar models can be significantly improved. Our new solar models with convective overshoot, the solar wind, and an early mass accretion show consistency with helioseismic constraints, the solar Li abundance, and observations of solar neutrino fluxes.

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.

Turbulent convection models are thought to be good tools to deal with the convective overshooting in the stellar interior. However, they are too complex to be applied in calculations of stellar structure and evolution. In order to understand the physical processes of the convective overshooting and to simplify the application of turbulent convection models, a semi-analytic solution is necessary. We obtain the approximate solution and asymptotic solution of the turbulent convection model in the overshooting region, and find some important properties of the convective overshooting: I. The overshooting region can be partitioned into three parts: a thin region just outside the convective boundary with high efficiency of turbulent heat transfer, a power law dissipation region of turbulent kinetic energy in the middle, and a thermal dissipation area with rapidly decreasing turbulent kinetic energy. The decaying indices of the turbulent correlations k, u ′ r T ′ , and T ′ T ′ are only determined by the parameters of the TCM, and there is an equilibrium value of the anisotropic degree ω. II. The overshooting length of the turbulent heat flux u ′ r T ′ is about 1H k (H k = | dr dlnk |). III. The value of the turbulent kinetic energy at the convective boundary k C can be estimated by a method called the maximum of diffusion. Turbulent correlations in the overshooting region can be estimated by using k C and exponentially decreasing functions with the decaying indices.