The use of apriori information in the derivative of temperature structures from Xray spectra.
Abstract
The task of inferring the temperature structure of an astrophysical plasma from its Xray spectrum via inversion of the basic integral equation relating the source spectrum to the emissionmeasure function is discussed. The underlying Fredholm integral equation of the first kind is defined, and the bremsstrahlung problem associated with solar flare emission is outlined. The severity of the instability in typical spectral problems is examined by invoking the classical matrix quadrature method. It is shown explicitly that this method is likely to be unsuccessful even for 'perfect' data because of magnified discretization errors. Improvement of the inversion by application of the (classical) projection method of Miller and Guy (1966) is considered, but it is found that the derived solution is still highly unstable to small data perturbations. The possibilities of a nonclassical regularization method are then investigated. It is concluded that a soundly based attack on the spectral problem cannot be maintained without direct physical insight into the form of the solution.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 1977
 Bibcode:
 1977A&A....61..575C
 Keywords:

 Astronomical Models;
 Plasma Temperature;
 Solar XRays;
 X Ray Spectra;
 Bremsstrahlung;
 Integral Equations;
 Numerical Analysis;
 Plasma Radiation;
 Temperature Inversions;
 Astrophysics