Automated Solar Flare Statistics in Soft X-rays over 37 Years of GOES Observations - The Invariance of Self-Organized Criticality during Three Solar Cycles

TL;DR

This study analyzes 37 years of GOES soft X-ray data, revealing invariant powerlaw slopes consistent with the FD-SOC model, supporting self-organized criticality in solar flares and challenging nanoflare heating hypotheses.

Contribution

It provides the first extensive automated analysis of solar flare statistics over multiple solar cycles, confirming the invariance of powerlaw slopes predicted by the FD-SOC model.

Findings

Powerlaw slope of soft X-ray peak fluxes is approximately 2.0, invariant over three solar cycles.

Rise time powerlaw slope varies with solar cycle phase, indicating a pile-up bias effect.

Results support the FD-SOC model and suggest nanoflares are not the dominant heating mechanism.

Abstract

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.