Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO: I. Universal Scaling Laws of Space and Time Parameters

We extend a previous statistical solar flare study of 155 GOES M- and X-class flares observed with AIA/SDO (Aschwanden 2012) to all 7 coronal wavelengths (94, 131, 171, 193, 211, 304, 335 \ang) to test the wavelength-dependence of scaling laws and statistical distributions. Except for the 171 and 193 \ang\ wavelengths, which are affected by EUV dimming caused by coronal mass ejections (CMEs), we find near-identical size distributions of geometric (lengths $L$, flare areas $A$, volumes $V$, fractal dimension $D_2$), temporal (flare durations $T$), and spatio-temporal parameters (diffusion coefficient $\kappa$, spreading exponent $\beta$, and maximum expansion velocities $v_{max}$) 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., $N(L) \propto L^{-3}$, $N(A) \propto A^{-2}$, $N(V) \propto V^{-5/3}$, $N(T) \propto T^{-2}$, $D_2=3/2$, for a Euclidean dimension $d=3$. Empirically we find also a new strong correlation $\kappa \propto L^{0.94\pm0.01}$ and the 3-parameter scaling law $L \propto \kappa\ T^{0.1}$, which is more consistent with the logistic-growth model than with classical diffusion. The findings suggest long-range correlation lengths in the FD-SOC system that operate in the vicinity of a critical state, which could be used for predictions of individual extreme events. We find also that eruptive flares (with accompanying CMEs), have larger volumes $V$, longer flare durations $T$, higher EUV and soft X-ray fluxes, and somewhat larger diffusion coefficients $\kappa$ than confined flares (without CMEs).