Astronomy and Astrophysics – Astronomy
Scientific paper
Nov 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976natur.264..340c&link_type=abstract
Nature, vol. 264, Nov. 25, 1976, p. 340-342. Research supported by the Science Research Council.
Astronomy and Astrophysics
Astronomy
52
Astronomical Spectroscopy, Cosmic X Rays, High Resolution, X Ray Astronomy, X Ray Spectra, Energy Distribution, Fredholm Equations, Particle Energy, Radiant Flux Density, Temperature Distribution, X Ray Sources
Scientific paper
The author points out the mathematical difficulties involved in inferring source structure in terms of temperature distribution of thermal particles or energy distribution of nonthermal particles from high-resolution X-ray spectra. Basically, the thermal problem of emission from an optically thin nonisothermal atmosphere is reduced to a Fredholm integral equation of the first kind, where the emission measure of the source as function of temperature must be found, given the emission function (the kernel) and the X-ray flux as a function of energy. This problem is ill-posed, and it can be shown that in solving the equation by inversion for some discrete approximation of the emission measure, given a data vector for the X-ray flux spectrum and a suitable temperature grid, a variety of source temperature structures can be found which reproduce the X-ray spectrum up to 5%. This means that the emitted spectrum has a very low sensitivity to any features of source temperature structure other than its crudest nature.
Brown John C.
Craig Donald I. Jr.
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