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.

We investigate physical properties of the nearby (∼ 7.5 pc) astrometric binary μ Cas in the context of standard evolutionary theory. Based on the spectroscopically determined relative abundances ([/Fe] & +0.4 dex, [Fe/H] ∼ −0.7 dex), all physical inputs such as opacities and equation of state are consistently generated. By combining recent spectroscopic analyses with the astrometric observations from the HIPPARCOS parallaxes and the CHARA array, the evolutionary model grids have been constructed. Through the statistical evaluation of the 2-minimization among alternative models, we find a reliable evolutionary solution (MA, MB, tage) = (0.74 M⊙, 0.19 M⊙, 11 Gyr) which excellently satisfies observational constraints. In particular, we find that the helium abundance of μ Cas is comparable with the primordial helium contents (Yp ∼ 0.245). On the basis of the well-defined stellar parameters of the primary star, the internal structure and the p-mode frequencies have been estimated. From our seismic computation, μ Cas is expected to have a first order spacing
 ∼ 169 μHz. The ultimate goal of this study is to describe physical processes inside a low-mass star through a complete modelling from the spectroscopic observation to the evolutionary computation.

Recent cosmological observations indicate that the reionized universe may have started at around z = 6, where a significant suppression around Lyα has been observed from the neutral intergalactic medium. The associated neutral hydrogen column density is expected to exceed 1021 cm−2, where it is very important to use the accurate scattering cross section known as the Kramers-Heisenberg formula that is obtained from the fully quantum mechanical time-dependent second order perturbation theory. We present the Kramers-Heisenberg formula and compare it with the formula introduced in a heuristic way by Peebles (1993) considering the hydrogen atom as a two-level atom, from which we find a deviation by a factor of two in the red wing region far from the line center. Adopting a representative set of cosmological parameters, we compute the Gunn-Peterson optical depths and absorption profiles. Our results are quantitatively compared with previous work by Madau & Rees (2000), who adopted the Peebles approximation in their radiative transfer problems. We find deviations up to 5 per cent in the Gunn-Peterson transmission coefficient for an accelerated expanding universe in the red off-resonance wing part with the rest wavelength Δλ ∼ 10 °A.