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 AIA/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 $\approx 14$), but more comprehensive (multi-)thermal energy than an isothermal energy estimate from the same AIA data. We find a statistical energy ratio of $E_{th}/E_{diss} \approx 2\%-40\%$ 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, $EM_p=10^{47.3}-10^{50.3}$ 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 $E_{th,RTV} = 7.3 \times 10^{-10} \ T_p^3 L_p^2$, which predicts extremal values of $E_{th,max} \approx 1.5 \times 10^{33}$ erg for the largest flare and $E_{th,min} \approx 1 \times 10^{24}$ 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.