Influence of turbulence on the shape of a spectral line: the analytical approach

We consider the propagation of spectral-line radiation in a correlated turbulent atmosphere. The ensembles of turbulent velocities u(r,t) and optical depths, τν, are assumed to be Gaussian. We investigate the explicit analytical solution of the stochastic radiative transfer equation for the intensity Iν of radiation. The scattering term is not taken into account. It is shown that, in addition to the usual Doppler broadening of the spectral line, correlated turbulent motions of atoms and molecules give rise to considerable changes in the shape of a spectral line. We find that the mean intensity I⁽⁰⁾ν (Iν=I⁽⁰⁾ν+I'ν, I'ν = 0) obeys the usual radiative transfer equation with renormalized extinction factor α^effν if the correlation length R0 of the turbulence is small as compared to a photon free path. A simple analytical expression for α^effν is given. This expression integrally depends on the two-point correlation function of the turbulent velocity field.