The State of Self-organized Criticality of the Sun During the Last Three 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 -aEuro parts per thousand 2010) from SMM/HXRBS, CGRO/BATSE, and RHESSI hard X-ray data. From the synthesized data we find powerlaw slopes with mean values of alpha (P) =1.73 +/- 0.07 for the peak flux, alpha (E) =1.62 +/- 0.12 for the total flux, and alpha (T) =1.99 +/- 0.35 for flare durations. We find a tendency of an anti-correlation of the powerlaw slope of peak fluxes with the flare rate or sunspot number as a function of the solar cycle. The occurrence powerlaw slope is always steeper by Delta alpha a parts per thousand 0.1 during a solar-cycle minimum compared with the previous solar-cycle maximum, but the relative amplitude varies for each cycle or instrument. Since each solar cycle has been observed with a different instrument, part of the variation could be attributed to instrumental characteristics and different event selection criteria used in generating the event catalogs. The relatively flatter powerlaw slopes during solar maxima could indicate more energetic flares with harder electron-energy spectra, probably due to a higher magnetic complexity of the solar corona. This would imply a non-stationarity (or solar-cycle dependence) of the coronal state of self-organized criticality.