Kappa Distribution Model for Hard X-Ray Coronal Sources of Solar Flares

Abstract

Solar flares produce hard X-ray emission of which the photon spectrum 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 the 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 the power-law index only. With the kappa distribution model, we estimated that the total electron density of the coronal source region was ~2.4x10^10 cm^-3. We also estimated without assuming the source volume that a moderate fraction (~20%) of electrons in the source region was non-thermal and carried ~52% of the total electron energy. The temperature was 28 MK, and the power-law index d 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.