  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.
