Influence of turbulence on the shape of a spectral line

The analytical approach

¹ Instituto Nacional de Astrofísica, Óptica y Electrónica, Apartado Postal 51 y 216, Z.P. 72000 Pue., México e-mail: silant@inaoep.mx
² Main Astronomical Observatory of Russian Academy of Sciences, Pulkovo, 196140 St. Petersburg, Russia
³ Sternberg Astronomical Institute, 13 Universitetskij prospect, 119992 Moscow, Russia

Received: 15 March 2005
Accepted: 24 March 2006

Abstract

We consider the propagation of a spectral-line radiation in a correlated turbulent atmosphere. The ensembles of realizations of turbulent velocities and optical depth  are assumed to be Gaussian. We investigate the explicit analytical solution of the stochastic radiative transfer equation for the intensity 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. It was found for the first time that the mean intensity () obeys the usual radiative transfer equation with renormalized extinction factor if the correlation length R₀ of the turbulence is small as compared to a photon free path. A simple analytical expression for is given. This expression integrally depends on the two-point correlation function of the turbulent velocity field. We also discuss the problem how to obtain the main turbulence parameters from the analysis of the shape of a spectral line.