Asymptotic scaling in transfer problems for resonance radiation in linearly expanding media. I. Kernels of the integral equations and photon escape probabilities

Abstract

A study is made of the transfer of resonance radiation in media expanding isotropically or in a plane-parallel manner with dimensionless velocity gradient ..gamma.. constant over the depth. Both three- and one-dimensional media are considered. It is assumed that when scattering takes place there is complete frequency redistribution in the comoving coordinate system. It is shown that for small ..gamma.. the kernels of the integral equations, the photon escape probabilities, and their Laplace transforms can be expressed in terms of functions containing one less argument, the new arguments being combinations of the previous arguments (which include the parameter ..gamma..). These functions are found for the cases of Doppler and power-law profiles of the absorption coefficient. In the case of a Doppler absorption coefficient in a one-dimensional medium, and also a power-law profile with Lorentzian wings, they are expressed in terms of elementary or well-known special functions.