The aim of this study is to describe the physical processes taking place in the solar photosphere. Based on 3D hydrodynamic simulations including a detailed radiation transfer scheme, we investigate thermodynamic structures and radiation fields in solar surface convection. As a starting model, the initial stratification in the outer envelope calculated using the solar calibrations in the context of the standard stellar theory. When the numerical fluid becomes thermally relaxed, the thermodynamic structure of the steady-state turbulent flow was explicitly collected. Particularly, a non-grey radiative transfer incorporating the opacity distribution function was considered in our calculations. In addition, we evaluate the classical approximations that are usually adopted in the onedimensional stellar structure models. We numerically reconfirm that radiation fields are well represented by the asymptotic characteristics of the Eddington approximation (the diffusion limit and the streaming limit). However, this classical approximation underestimates radiation energy in the shallow layers near the surface, which implies that a reliable treatment of the non-grey line opacities is crucial for the accurate description of the photospheric convection phenomenon.

Abstract
1. INTRODUCTION
2. HYDRODYNAMICS
3. RADIATIVE TRANSFER
    3.1. Non-Grey Atmospheres
    3.2. The generalized Eddington Approximation
4. SIMULATIONS
    4.1. Initial Configurations
    4.2. Numerical Simulations
5. THE VALIDITY TEST OF THE CLASSICALAPPROXIMATIONS
6. SUMMARY
REFERENCES

• Kiehunn Bach(Department of Astronomy, Yonsei University) Corresponding author