An Improved Method to Derive the Lower Energy Cutoff of non-Thermal Electrons From Hard x-Rays of Solar Flares

By changing a dimensionless calculation to a dimensional one, introducing a more accurate bremsstrahlung cross section, and using a more reasonable fitting energy range, we have recalculated the hard X-ray bremsstrahlung produced by a beam of power-law electrons with a lower energy cutoff (E _c). The method to deduce E _c from the hard X-ray spectral observations has therefore been refined in comparison with our previous one. The universality of this method has been clarified and discussed. We have applied this improved method to the 54 BATSE/Compton Gamma Ray Observatory (CGRO) hard X-ray events. It was found that about 44% of sample hard X-ray spectra can be directly explained by a beam of power-law electrons with a lower energy cutoff. The value of E _c, varying from 45 keV to 97 keV, is on average 60 keV. Another 44% of sample hard X-ray spectra might be explained by a beam of power-law electrons with the energy cutoff lower than 45 keV, which is however beyond the availability of BATSE/CGRO. Still another 11% sample hard X-ray spectra cannot be explained by a beam of power-law electrons with a lower energy cutoff. These results, based on the lower energy resolution data, however, should be compared in the future with that based on a higher energy resolution data, like the data from HESSI.