Relativistic Milne-Eddington Type Solutions with a Variable Eddington Factor for Relativistic Spherical Winds

Relativistic radiative transfer in a relativistic spherical flow is examined in the fully special relativistic treatment. Under the assumption of a constant flow speed and using a variable (prescribed) Eddington factor, we analytically solve the relativistic moment equations in the comoving frame for several restricted cases, and obtain relativistic Milne-Eddington type solutions. In contrast to the plane-parallel case where the solutions exhibit the exponential behavior on the optical depth, the solutions have power-law forms. In the case of the radiative equilibrium, for example, the radiative flux has a power-law term multiplied by the exponential term. In the case of the local thermodynamic equilibrium with a uniform source function in the comoving frame, the radiative flux has a power-law form on the optical depth. This is because there is an expansion effect (curvature effect) in the spherical wind and the background density decreases as the radius increases.