Nonuniform target ionization and fitting thick target electron injection spectra to RHESSI data

Past analyses of flare hard X-ray (HXR) spectra have largely ignored the effect of nonuniform ionization along the electron paths in the thick-target model, though it is very significant for well-resolved spectra. The inverse problem (photon spectrum to electron injection spectrum F-o(E-o)) is disturbingly non-unique. However, we show that it is relatively simple to allow for the effect in forward fitting of parametric models of F-o (E-0) and provide an expression to evaluate it for the usual single power-law form of F-o(E-o). The expression involves the column depth N* of the transition region in the flare loop as one of the parameters so data fitting can enable derivation of N* (and its evaporative evolution) as part of the fitting procedure. The fit to RHESSI data on four flares for a single power law F-o(E-o) is much improved when ionization structure is included compared to when the usual fully ionized approximation is used. This removes the need, in these events at least, to invoke broken power laws, or other forms, of the acceleration spectrum F-o(E-o) to explain the observed photon spectrum.