We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Regularized Reconstruction of the Differential Emission Measure from Solar Flare Hard X-Ray Spectra.
- Authors
Prato, M.; Piana, M.; Brown, J. C.; Emslie, A. G.; Kontar, E. P.; Massone, A. M.
- Abstract
We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectrum ( I(∊)) 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(∊) invOlves two successive inverse problems: the first, to recover the mean source-electron flux spectrum ( $$\overline{F}$$ ( E)) from I(∊) 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).
- Subjects
SOLAR flares; X-ray astronomy; SPACE astronomy; PHOTON emission; ELECTROMAGNETIC waves; SPECTROSCOPIC imaging
- Publication
Solar Physics, 2006, Vol 237, Issue 1, p61
- ISSN
0038-0938
- Publication type
Article
- DOI
10.1007/s11207-006-0029-1