Energy shortage of nonthermal electrons in powering a solar flare

Within a deka-keV energy range, the power-law electron beams interacting wi th the solar atmosphere also result in the power-law bremsstrahlung of hard X-rays. The energy spectrum of electrons can thus be deduced from the obse rved hard X-ray spectrum, and the total energy carried by accelerated elect rons can then be estimated. For quite a long time, one has always assumed t he lower energy cutoff (E-c) of the power-law electron beams to be around 2 0 keV, an assumption that constitutes a main ingredient of the so-called st andard picture of a solar flare, since the nonthermal electrons are substan tial in powering a solar flare. However, there is in fact no solid observat ional basis for E-c = 20 keV. Here we present a quantitative method to dete rmine E-c and its application to 14 BATSE/Compton Gamma Ray Observatory har d X-ray events. We find that E-c, varying from 47 to 141 keV in our samples , is on average 76.4 keV. The total energy carried by nonthermal electrons is therefore shown to be at least 1 order of magnitude lower than that deri ved by taking E-c = 20 keV. This energy shortage of nonthermal electrons in our sample hard X-ray events conflicts with the widely accepted scenario o f a solar flare.