We analyzed the soft X-ray light curves from the 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 \pm 0.11 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 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 \pm 0.04 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 .