On the bremsstrahlung efficiency of nonthermal hard X-ray source models

Abstract

It has often been stated, but never rigorously proven, that interpreting observed hard X-ray emission in terms of a thick-target source gives a lower limit to the flux of electrons which have to be injected into the source. The truth of this statement, for theburst-integrated emission, is rigorously established here. Also an explicit inversion for the injected electron flux in terms of the photon spectrum is given, for the case where all electrons traverse a single value of column density. This generalises the previous results for the thick- and thin-target limits. The use of the standard thick-target formalism for the interpretation of instantaneous (as opposed to burst-integrated) photon fluxes is also discussed. By considering the specific case of the thick-target trap model, it is shown that use of this formalism can either under-estimate or over-estimate the injected electron flux, at different times in the same event, but that integration of the inferred electron fluxes over the event nevertheless yields the true, burst-integrated electron flux.