Automated Solar Flare Statistics in Soft X-rays over 37 Years of GOES   Observations - The Invariance of Self-Organized Criticality during Three   Solar Cycles
  We analyzed the soft X-ray light curves from the {\sl Geostationary Operational Environmental Satellites (GOES)} over the last 37 years (1975-2011) and measured with an automated flare detection algorithm over 300,000 solar flare events (amounting to $\approx 5$ times higher sensitivity than the NOAA flare catalog). We find a powerlaw slope of $\alpha_F=1.98\pm0.11$ for the (background-subtracted) soft X-ray peak fluxes that is invariant through three solar cycles and agrees with the theoretical prediction $\alpha_F=2.0$ of the {\sl fractal-diffusive self-organized criticality (FD-SOC)} model. For the soft X-ray flare rise times we find a powerlaw slope of $\alpha_T =2.02\pm0.04$ during solar cycle minima years, which is also consistent with the prediction $\alpha_T=2.0$ of the FD-SOC model. During solar cycle maxima years, the powerlaw slope is steeper in the range of $\alpha_T \approx 2.0-5.0$, which can be modeled by a solar cycle-dependent flare pile-up bias effect. These results corroborate the FD-SOC model, which predicts a powerlaw slope of $\alpha_E=1.5$ for flare energies and thus rules out significant nanoflare heating. While the FD-SOC model predicts the probability distribution functions of spatio-temporal scaling laws of nonlinear energy dissipation processes, additional physical models are needed to derive the scaling laws between the geometric SOC parameters and the observed emissivity in different wavelength regimes, as we derive here for soft X-ray emission. The FD-SOC model yields also statistical probabilities for solar flare forecasting. 
Markus J. Aschwanden and Samuel L. Freeland
astro-ph.SR