GLOBAL ENERGETICS OF SOLAR FLARES. II. THERMAL ENERGIES

We present the second part of a project on the global energetics of solar flares and CMEs that includes about 400 M- and X-class flares observed with Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) during the first 3.5 years of its mission. In this Paper II we compute the differential emission measure (DEM) distribution functions and associated multi-thermal energies, using a spatially-synthesized Gaussian DEM forward-fitting method. The multi-thermal DEM function yields a significantly higher (by an average factor of approximate to 14), but more comprehensive (multi-)thermal energy than an isothermal energy estimate from the same AIA data. We find a statistical energy ratio of E-th/E-diss >> 2%-40% between the multi-thermal energy E-th and the magnetically dissipated energy E-diss, which is an order of magnitude higher than the estimates of Emslie et al.2012. For the analyzed set of M and X-class flares we find the following physical parameter ranges: L=10(8.2)-10 (9.7) cm for the length scale of the flare areas, T-p=10 (5.7)-10 (7.4) K for the DEM peak temperature, T-w=10 (6.8)-10 (7.6) K for the emission measure-weighted temperature, n(p)=10 (10.3)-10 (11.8) cm(-3) for the average electron density, EMp=10 (47.3)-10 (50.3) cm-3 for the DEM peak emission measure, and E-th=10 (26.8)-10 (32.0) erg for the multi-thermal energies. The deduced multi-thermal energies are consistent with the RTV scaling law E-th,E-RTV=7.3 x 10(-10) (TpLp2)-L-3, which predicts extremal values of E-th,E-max approximate to 1.5 x 10 (33) erg for the largest flare and E-th,E-min approximate to 1 x 10 (24) erg for the smallest coronal nanoflare. The size distributions of the spatial parameters exhibit powerlaw tails that are consistent with the predictions of the fractal-diffusive self-organized criticality model combined with the RTV scaling law.