The deduction of energy spectra of non-thermal electrons in flares from the observed dynamic spectra of hard X-ray bursts

The derivation of dynamic spectra of high energy electrons in flares from high resolution hard X-ray observations is considered. It is shown that the Bethe-Heitler formula for the electronproton bremsstrahlung cross-section over the 20–100 keV range of energies admits of a general analytic solution for the electron spectrum in terms of the X-ray spectrum, in a form convenient for computation. The bearing of this analysis on different models of flare conditions is considered. In examining the hypothesis that the X-rays are produced in regions of high ambient density, the duration of the burst being governed by modulation of the electron source rather than by the decay of trapped electrons injected impulsively, it is emphasised that the energy spectrum of the electrons at their source is different from their effective spectrum in the X-ray emitting region. This spectrum, at the source, is found to be much steeper than that in the X-ray region which means that the entire energy of the flare could reside in the injected electrons.