Regularized Reconstruction of the Differential Emission Measure from Solar Flare Hard X-Ray Spectra

Details Regularized Reconstruction of the Differential Emission Measure from Solar Flare Hard X-Ray Spectra Regularized Reconstruction of the Differential Emission Measure from Solar Flare Hard X-Ray Spectra

Aug 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006soph..237...61p&link_type=abstract

Solar Physics, Volume 237, Issue 1, pp.61-83

Physics

10

Scientific paper

We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectrum ( I(ɛ)) is consistent with a purely thermal (locally Maxwellian) distribution of source electrons, and, if so, how to reconstruct the corresponding differential emission measure (ξ( T)). Unlike previous analysis based on the Kramers and Bethe-Heitler approximations to the bremsstrahlung cross-section, here we use an exact (solid-angle-averaged) cross-section. We show that the problem of determining ξ( T) from measurements of I(ɛ) invOlves two successive inverse problems: the first, to recover the mean source-electron flux spectrum (overline{F}( E)) from I(ɛ) and the second, to recover ξ( T) from overline{F}( E). We discuss the highly pathological numerical properties of this second problem within the framework of the regularization theory for linear inverse problems. In particular, we show that an iterative scheme with a positivity constraint is effective in recovering δ-like forms of ξ( T) while first-order Tikhonov regularization with boundary conditions works well in the case of power-law-like forms. Therefore, we introduce a restoration approach whereby the low-energy part of overline{F} ( E), dominated by the thermal component, is inverted by using the iterative algorithm with positivity, while the high-energy part, dominated by the power-law component, is inverted by using first-order regularization. This approach is first tested by using simulated overline{F}( E) derived from a priori known forms of ξ( T) and then applied to hard X-ray spectral data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI).

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