Regularized Mean and Accelerated Electron Flux Spectra in Solar Flares
Eduard P. Kontar
A. Gordon Emslie, Michele Piana, Anna Maria Massone, John C. Brown
Hard X-ray spectra in solar flares permit, through knowledge of the bremsstrahlung cross-section, inference of the mean source electron spectrum that results from acceleration and propagation of electrons in the solar atmosphere. Here we develop and apply an enhanced regularization algorithm for this process which makes use of a variety of physical constraints on the possible form of the electron spectrum. The algorithm incorporates various features not heretofore employed in the solar flare context, such as the use of Generalized Singular Value Decomposition (GSVD), a rectangular representation of the discretized problem (so that the electron and photon energy ranges used are not necessarily the same), regularization using various operators. The use of non-square inversion techniques, with physical properties of the spectra to achieve the most meaningful solution to the problem. We apply these techniques to data from a few solar flares observed by RHESSI. Results using different regularization are presented and compared for various time intervals. We further note that such analyses may be used to infer properties of the electron energy spectrum that lie at energies well above the maximum photon energy observed. We also show how the construction of the accelerated (injected) electron spectrum (assuming that Coulomb collisions in a cold target dominate the electron energetics) is facilitated by the use of higher-order regularization methods. Clear evidence is presented for a change in the value of the high-energy cutoff in the mean source electron spectrum with time.