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\noften represented by a combination of thermal and power-law distributions.\nHowever, the estimates of the number and total energy of non-thermal electrons\nare sensitive to the determination of the power-law cutoff energy. Here we\nrevisit an `above-the-loop' coronal source observed by RHESSI on 2007 December\n31 and show that a kappa distribution model can also be used to fit its\nspectrum. Because the kappa distribution has a Maxwellian-like core in addition\nto the high-energy power-law tail, the emission measure and temperature of the\ninstantaneous electrons can be derived without assuming the cutoff energy.\nMoreover, the non-thermal fractions of electron number/energy densities can be\nuniquely estimated because they are functions of the power-law index only. With\nthe kappa distribution model, we estimated that the total electron density of\nthe coronal source region was ~2.4x10^10 cm^-3. We also estimated without\nassuming the source volume that a moderate fraction (~20%) of electrons in the\nsource region was non-thermal and carried ~52% of the total electron energy.\nThe temperature was 28 MK, and the power-law index d of the electron density\ndistribution was -4.3. These results are compared to the conventional power-law\nmodels with and without a thermal core component.\n