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

TL;DR

This study analyzes solar flare data across seven wavelengths, revealing universal scaling laws and correlations consistent with a fractal-diffusive avalanche model, and distinguishes properties of eruptive versus confined flares.

Contribution

It extends previous solar flare statistical analysis to all seven coronal wavelengths, confirming wavelength-independent scaling laws and identifying new correlations in flare parameters.

Findings

Size distributions follow universal power laws.

Eruptive flares have larger volumes and longer durations.

Strong correlation between diffusion coefficient and length.

Abstract

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).