Amended results for hard X-ray emission by non-thermal thick target recombination in solar flares

Brown & Mallik 2008 and the Brown et al. 2010 corrigendum of it presented expressions for non-thermal recombination (NTR) in the collisionally thin- and thick-target regimes, claiming that the process could account for a substantial part of hard X-ray continuum in solar flares usually attributed entirely to thermal and non-thermal bremsstrahlung (NTB). However, we have found the thick-target expression to become unphysical for low cut-offs in the injected electron energy spectrum. We trace this to an error in the derivation, derive a corrected version which is real-valued and continuous for all photon energies and cut-offs, and show that, for thick targets, Brown et al. over-estimated NTR emission at small photon energies. The regime of small cut-offs and large spectral indices involve large (reducing) correction factors but in some other thick-target parameter regimes NTR/NTB can still be of order unity. We comment on the importance of these results to flare and to microflare modeling and spectral fitting. An empirical fit to our results shows that the peak NTR contribution comprises over half the hard X-ray signal if delta > 6 (E_0c/4 keV)^(0.4).