Determination of electron flux spectra in a solar flare with an augmented regularization method: application to RHESSI data

Kontar et al. (2004) have shown how to recover mean source electron spectra <div style="text-decoration: overline;">F</div>(<i>E</i>) in solar flares through a physical constraint regularization analysis of the bremsstrahlung photon spectra <i>I</i>(ε) that they produce. They emphasize the use of non-square inversion techniques, and preconditioning combined with physical properties of the spectra to achieve the most meaningful solution to the problem. Higher-order regularization techniques may be used to generate <div style="text-decoration: overline;">F</div> (<i>E</i>) forms with certain desirable properties (e.g., higher-order derivatives). They further note that such analysis may be used to infer properties of the electron energy spectra at energies well above the maximum photon energy observed. In this paper we apply these techniques to data from a solar flare observed by RHESSI on 26 February, 2002. Results using different orders of regularization are presented and compared for various time intervals. Clear evidence is presented for a change in the value of the high-energy cutoff in the mean source electron spectrum with time. We also show how the construction of the <i>injected</i> electron spectrum <i>F</i><sub>0</sub>(<i>E</i><sub>0</sub>) (assuming that Coulomb collisions in a cold target dominate the electron transport) is facilitated by the use of higher-order regularization methods