Quantitative analysis of nonthermal electrons in impulsive hard X-ray flares

We present a quantitative study of nonthermal electrons in solar hard X-ray flares. In this study, we focus on the lower energy cutoff (E.) in the spectrum of nonthermal electrons. Instead of adopting the usual assumption of E, to be a fixed value (20 keV or 30 keV), we derive it by assuming that the total energy of nonthermal electrons released during the impulsive phase balances with the increase in the thermal energy of the soft X-ray emitting flare plasma during the impulsive phase. We apply this method to the six hard X-ray flares observed with Yohkoh and successfully estimate several physical variables of nonthermal electrons in the impulsive phase of the flares. What we find are as follows: (1) The values of the derived E, are ranging in 20-45 keV. (2) There is a positive correlation between the nonthermal electron rate in the impulsive phase and the number density of the soft X-ray emitting Rare plasma in the pre-impulsive phase. (3) There is a positive correlation between the derived lower energy cutoff and the hard X-ray sources separation distance.