Relativistic Milne-Eddington-type solutions with a variable Eddington factor for relativistic plane-parallel flows

Relativistic radiative transfer in a relativistic plane-parallel flow is examined in a fully special relativistic treatment. Under the assumption of a constant flow speed and using a variable Eddington factor, we analytically solve the relativistic moment equations in the comoving frame for several cases, such as the radiative equilibrium or local thermodynamical equilibrium, and obtain relativistic Milne-Eddington-type solutions. In all the cases, the solutions exhibit an exponential behavior on the optical depth; the solutions are expressed by the linear combination of the exponential terms. In addition, the optical depth τ in the exponential term is replaced by the apparent optical depth Γτ, where Γ is a function of the flow speed v. This is the essential properties of the relativistic regime of the radiative transfer. In the case of the radiative equilibrium, the radiation energy density in the comoving frame approaches a constant value, while the radiative flux becomes zero as the optical depth increases. In addition, with uniform heating, the radiative quantity in the comoving frame generally decreases compared with that in the case without heating, whereas, if there is advection cooling, the radiative quantity generally increases. In the case of the local thermodynamic equilibrium, the radiative quantity approaches the LTE values as the optical depth increases.