Mathematics
Scientific paper
Jun 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995azh....72..353b&link_type=abstract
Astronomicheskij Zhurnal, vol. 72, p. 353
Mathematics
1
Stellar Envelopes, Ill-Posed Problems (Mathematics), Fredholm Equations, Integral Equations, Absorptivity, Emission Spectra, Angular Resolution
Scientific paper
The reconstruction of the source function for a spherically symmetric circumstellar shell is treated in terms of the analysis of its intensity distribution. It is shown that this problem reduces to solving an ill-defined inverse problem for Fredholm's integral equation of the first kind. In the case of an optically thick shell, the depth dependence of the volume absorption coefficient must be known for the kernel of this equation to be calculated. For an optically thin shell, the law of variations in the volume emission coefficient with depth can be restored from high angular resolution observations; if the intensity distribution across the stellar disk is known, then it is, in principle, possible to obtain information about the volume absorption coefficient from the analysis of different regions of the intensity profile. The solution to the integral equation is sought on a compact set of convex nonnegative functions. Numerical experiments show high stability of the solution to random noise.
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