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
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.
Key words: line: formation / turbulence / masers
© ESO, 2006