Influence of turbulence on the shape of a spectral line: the analytical approach
Abstract
We consider the propagation of spectralline 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^{eff}ν if the correlation length R0 of the turbulence is small as compared to a photon free path. A simple analytical expression for α^{eff}ν is given. This expression integrally depends on the twopoint correlation function of the turbulent velocity field.
 Publication:

Astrophysical Masers and their Environments
 Pub Date:
 March 2007
 DOI:
 10.1017/S1743921307012525
 Bibcode:
 2007IAUS..242...32S
 Keywords:

 turbulence;
 molecular processes;
 radio lines: ISM;
 radio lines: stars;
 masers: circumstellar matter