The State of Self-Organized Criticality of the Sun During the Last 3 Solar Cycles. I. Observations

We analyze the occurrence frequency distributions of peak fluxes $P$, total fluxes $E$, and durations $T$ of solar flares over the last three solar cycles (during 1980–2010) from hard X-ray data of HXRBS/SMM, BATSE/CGRO, and RHESSI. From the synthesized data we find powerlaw slopes with mean values of ${\alpha }_P=1.72\pm 0.08$ for the peak flux, ${\alpha }_E=1.60\pm 0.14$ for the total flux, and ${\alpha }_T=1.98\pm 0.35$ for flare durations. We find a systematic anti-correlation of the powerlaw slope of peak fluxes as a function of the solar cycle, varying with an approximate sinusoidal variation ${\alpha }_P(t)={\alpha }_0+\mathrm{\Delta }\alpha \cos [2\pi (t-t_0)\mathrm{/}{T}_{cycle}]$, with a mean of ${\alpha }_0=1.73$, a variation of $\mathrm{\Delta }\alpha =0.14$, a solar cycle period $T_{cycle}=12.6$ yrs, and a cycle minimum time $t_0=1984.1$. The powerlaw slope is flattest during the maximum of a solar cycle, which indicates a higher magnetic complexity of the solar corona that leads to an overproportional rate of powerful flares.