Spatial spectroscopic diagnostics of planetary nebulae. V - Regularization of Abel's equation

Details Spatial spectroscopic diagnostics of planetary nebulae. V - Regularization of Abel's equation Spatial spectroscopic diagnostics of planetary nebulae. V - Regularization of Abel's equation

Sep 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985baicz..36..305h&link_type=abstract

Astronomical Institutes of Czechoslovakia, Bulletin (ISSN 0004-6248), vol. 36, Sept. 1985, p. 305-311.

Astronomy and Astrophysics

Astronomy

1

Astronomical Spectroscopy, Planetary Nebulae, Abel Function, Integral Equations

Scientific paper

The three-dimensional determination of an upper level population of an optically thin line of a spherically symmetric planetary nebula is derived. The problem is based on the suitable inversion of Abel's integral equation. It is demonstrated that the inversion of Abel's equation is an ill-conditioned problem. Regularization by the method of best determined terms is suggested and numerically examined. Inherent limitations of the method of Abel's integral equation are shown and briefly discussed.

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