Multi-wavelength observations of the spatio-temporal evolution of solar flares with AIA/SDO. II. Hydrodynamic scaling laws and thermal energies

Abstract

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 EM p , peak temperature Tp , electron density np , 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, Tp = 5.0-17.8 MK, np = 4 × 109-9 × 1011 cm-3, and thermal energies of E th = 1.6 × 10 28-1.1 × 1032 erg. We find that these parameters obey the Rosner-Tucker-Vaiana (RTV) scaling law and H∝T 7/2 L -2 during the peak time tp 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)∝H -1.8, which is consistent with the magnetic flux distribution N(Φ) ∝Φ-1.85 observed by Parnell et al. and the heating flux scaling law FH ∝HL∝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. © 2013. The American Astronomical Society. All rights reserved..