Hydrodynamic Scaling Laws and Solar Flare Statistics from AIA
Abstract
We present a statistical solar flare study of 155 GOES M- and X-class flares observed with AIA/SDO in all 7 coronal wavelengths (94, 131, 171, 193, 211, 304, 335 A) and investigate the wavelength-dependence of scaling laws and statistical distributions. Except for the 171 and 193 A wavelengths, which are affected by EUV dimming caused by coronal mass ejections (CMEs), we find near-identical size distributions of geometric (flare size L, area A, volume V, fractal dimension D2), temporal (flare duration D), and spatio-temporal parameters (diffusion coefficient, spreading exponent, and maximum expansion velocity) in different wavelengths, which are consistent with the universal predictions of the fractal-diffusive avalanche model of a slowly-driven self-organized criticality (FD-SOC) system, i.e., N(L) L^(-3), N(A) A^(-2), N(V) V^(-5/3), N(D) D^(-2), D2=3/2, for a Euclidean dimension d=3. We perfom also a differential emission measure (DEM) analysis in all flares to determine the flare peak emission measure EM_p, peak temperature T_p, electron density n_p, and thermal energy E_th. We find that these parameters obey the Rosner-Tucker-Vaiana (RTV) scaling law T_p^2 n_p L and H T^(7/2) L^(-2) during the flare peak time t_p of maximum 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 powerlaw 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(Phi) Phi^(-1.85) observed by Parnell et al. (2009) and the heating flux scaling law F_H H L B/L of Schrijver et al. (2004). The fractal-diffusive self-organized criticality model in conjunction with the RTV scaling law reproduces the observed powerlaw distributions and their slopes for all geometrical and physical parameters and can be used to predict the size distributions for other flare datasets, instruments, and detection algorithms.
- Publication:
-
SDO-3: Exploring the Network of SDO Science
- Pub Date:
- March 2013
- Bibcode:
- 2013enss.confE..75A
- Keywords:
-
- SDO;
- SDO-7;
- SDO 7;
- SDO Workshop;
- 2013 LWS/SDO Science Workshop;
- Solar Dynamic Observatory