Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007ap.....50..175n&link_type=abstract
Astrophysics, Volume 50, Issue 2, pp.175-186
Astronomy and Astrophysics
Astrophysics
Stars, Atmospheres, Spectral Lines
Scientific paper
The formation of spectral lines in a turbulent atmosphere with a spatially correlated velocity field is examined. A new approach for solving this problem is proposed which is not based on the Fokker-Planck formalism. The invariant imbedding method makes it possible to reduce the problem of finding the mean radiant intensity observed in a line to solving a system of differential equations. This possibility is based on determining the mean intensity of the radiation emerging from the medium for a fixed value of the turbulent velocity at its boundary. A separate integral equation is derived for this quantity. The dependence of the line profile, integrated intensity, and width on the mean correlation length and the average value of the hydrodynamic velocity is studied. It is shown that the transition from a microturbulent regime to a macroturbulent regime occurs within a comparatively narrow range of variation in the correlation length. The proposed method yields a solution to the problem for a family of inhomogeneous atmospheres with different optical thicknesses, which makes it easy to determine the radiation field inside the turbulent medium. This approach can be generalized in various ways, in particular, it can be applied without significant changes to the case where the correlation length depends on position within the atmosphere.
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