Fundamental limitations of Xray spectra as diagnostics of plasma temperature structure.
Abstract
The problem of deriving the temperature distribution in hot optically thin plasmas from their Xray spectra is discussed, and it is argued that Xray spectral data are fundamentally insensitive to the thermal structure of the source, regardless of the spectral resolution of the observations. The problem is formulated in terms of the integral equation which relates both line and continuous spectra to the differential emission measure of the source. The mathematical difficulties underlying the solution of such integral equations are outlined, emphasizing the key role of the kernel function. Continuous bremsstrahlung spectra are considered, and it is shown that the kernel involved (the Laplace transform) is highly unstable to small perturbations in the spectrum due to the flatness of the kernel function. The linespectrum problem is examined, and gross errors in the solution are shown to result from very small observational errors. A specific example for solar active regions demonstrates that most existing models for the differential emission measure are likely to be spurious. Suggestions are made for the most realistic and economic approach to analysis of existing spectra as well as for designs of future spectrometers.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 June 1976
 Bibcode:
 1976A&A....49..239C
 Keywords:

 High Temperature Plasmas;
 Plasma Diagnostics;
 Plasma Temperature;
 Solar Physics;
 Temperature Distribution;
 X Ray Spectra;
 Bremsstrahlung;
 Continuous Spectra;
 Fredholm Equations;
 Kernel Functions;
 Line Spectra;
 Numerical Stability;
 Solar Flares;
 Astrophysics