Electron flux spectral imaging of solar flares through regularized analysis of hard X-ray source visibilities

We introduce a new method for imaging spectroscopy analysis of hard X-ray emission during solar flares. The method avoids the ‘‘traditional’’ noise-sensitive step of stacking independent images made in different count-based energy intervals. Rather, it involves regularized inversion of the count visibility spectra (i.e., the two-dimensional spatial Fourier transforms of the spectral image) to obtain smoothed (regularized) forms of the corresponding electron visibility spectra. Application of conventional visibility-based imaging algorithms then yields images of the elec- tron flux that vary smoothly with energy. We apply the method to a solar flare observed on 2002 February 20 by the RHESSI instrument. The event is characterized by two bright footpoints with a more diffuse emission between them. Analysis of the regularized electron flux images reveals that the electron flux spectra at the footpoints are systemat- ically harder than those in the region between the footpoints and that the observed degree of hardening is consistent with that produced by Coulomb collisions between an acceleration site high in the corona and the dense chromo- spheric footpoint regions.