MULTI-WAVELENGTH OBSERVATIONS OF THE SPATIO-TEMPORAL EVOLUTION OF SOLAR FLARES WITH AIA/SDO. II. HYDRODYNAMIC SCALING LAWS AND THERMAL ENERGIES

In this study we measure physical parameters of the same set of 155 M- and X-class solar flares observed with AIA/SDO as analyzed in Paper I, by performing a differential emission measure analysis to determine the flare peak emission measure EMp, peak temperature T-p, electron density n(p), and thermal energy E-th, in addition to the spatial scales L, areas A, and volumes V measured in Paper I. The parameter ranges for M- and X-class flares are log(EMp) = 47.0-50.5, T-p = 5.0-17.8 MK, n(p) = 4 x 10(9)-9 x 10(11) cm(-3), and thermal energies of E-th = 1.6x10(28)-1.1x10(32) erg. We find that these parameters obey the Rosner-Tucker-Vaiana (RTV) scaling law T-p(2) proportional to n(p)L and H proportional to (TL-2)-L-7/2 during the peak time t(p) of the flare density n(p), when energy balance between the heating rate H and the conductive and radiative loss rates is achieved for a short instant and thus enables the applicability of the RTV scaling law. The application of the RTV scaling law predicts power-law distributions for all physical parameters, which we demonstrate with numerical Monte Carlo simulations as well as with analytical calculations. A consequence of the RTV law is also that we can retrieve the size distribution of heating rates, for which we find N(H) proportional to H-1.8, which is consistent with the magnetic flux distribution N(Phi) proportional to Phi(-1.85) observed by Parnell et al. and the heating flux scaling law F-H proportional to HL proportional to B/L of Schrijver et al.. The fractal-diffusive self-organized criticality model in conjunction with the RTV scaling law reproduces the observed power-law distributions and their slopes for all geometrical and physical parameters and can be used to predict the size distributions for other flare data sets, instruments, and detection algorithms.