KAPPA DISTRIBUTION MODEL FOR HARD X-RAY CORONAL SOURCES OF SOLAR FLARES

Solar flares produce hard X-ray emission, the photon spectrum of which is often represented by a combination of thermal and power-law distributions. However, the estimates of the number and total energy of non-thermal electrons are sensitive to the determination of the power-law cutoff energy. Here, we revisit an above-the-loop coronal source observed by RHESSI on 2007 December 31 and show that a kappa distribution model can also be used to fit its spectrum. Because the kappa distribution has a Maxwellian-like core in addition to a high-energy power-law tail, the emission measure and temperature of the instantaneous electrons can be derived without assuming the cutoff energy. Moreover, the non-thermal fractions of electron number/energy densities can be uniquely estimated because they are functions of only the power-law index. With the kappa distribution model, we estimated that the total electron density of the coronal source region was similar to 2.4 x 10(10) cm(-3). We also estimated without assuming the source volume that a moderate fraction (similar to 20%) of electrons in the source region was non-thermal and carried similar to 52% of the total electron energy. The temperature was 28 MK, and the power-law index delta of the electron density distribution was -4.3. These results are compared to the conventional power-law models with and without a thermal core component.