Two-dimensional stellar radiative transfer resulting from a core eccentricity

In this paper we derive a two-dimensional analytical solution for the radiative transfer in a homogeneous static medium. An energy source is placed inside a diffusive spherical medium. The position of the source is not the symmetry centre of the configuration. In this study, we give the analytical distribution of temperature, T, inside the configuration, as a function of the eccentricity (departure from the symmetry centre) of the source. A large anisotropy of temperature may result from this eccentricity. The influence on the energy flux is more important because the flux varies as T⁴. Moreover we examine the dependence on the opacity or the Rosseland mean-free-path, λ. Although the surface temperature T_S is formally dependent on λ, it appears that T_S is nearly insensitive to variations of the opacity. On the other hand the inner distribution is strongly dependent on λ.