Nonstationary Radiative Transfer: Evolution of a Spectrum by Multiple Compton Scattering

A new method is used for numerical solution of the nonlinear integro-differential radiative transfer equation for the evolution of a homogeneous emission spectrum owing to Compton scattering on equilibrium free electrons in an infinite uniform space. The temperature of the electron gas is assumed constant with no limits placed on it: the electrons can be both nonrelativistic and relativistic. The evolution of the spectrum is found to depend substantially on the initial dimensionless photon density. There is a bounday value for this density such that at lower values, there is a limiting equilibrium Bose-Einstein photon distribution, but not at higher values. In the latter case a quasi-line develops which shifts to shorter wavelengths with time while its width decreases and its maximum intensity increases. Calculations are carried out using two frequency redistribution functions of the photons, exact and simplified (assuming an isotropic distribution in the laboratory coordinate system). The results are compared with solutions of the Kompaneets equation.