A matter of class and flare Flare productivity in solar active regions and power-law constraints on the flare frequency distribution

Abstract

Solar active regions are the source of virtually all significant space weather events, therefore the relationship between their observable properties and flare production is important to characterize. The flare productivity of solar active regions is analyzed across solar cycles 23--25 as a function of magnetic complexity, sunspot area, and solar-cycle phase. Additionally, the power-law index of the peak flux frequency distribution is estimated. The GOES soft X-ray event reports matched with daily Solar Region Summaries (SRS) are used to create a robust active region catalog. This catalog is supplemented with the 50-year HEK flare catalog and the newly released STIX flare catalog from Solar Orbiter to estimate the power-law index. Magnetically complex active regions ($βγ$, $βδ$, $βγδ$) produce the majority of M- and X-class flares while comprising only $\sim$13\% of all daily active-region observations, showing that larger flares disproportionately occur in larger area sunspots. All three catalogs can be represented with a consistent power-law index of $α= 2.02 \pm 0.01$ for the peak flux frequency distribution. However, a class-by-class analysis of the C/X and M/X flare ratios reveals that the distribution steepens significantly towards higher energies. Fitting this steepening as a lognormal tail and extrapolating two decades beyond the X-class threshold predicts a recurrence time of $370^{+292}_{-159}$~yr for an X100-class (`Carrington-type') superflare, compared to only $\sim$26~yr from a naive single power-law extrapolation. While $α\approx 2$ provides a useful global description of the flare frequency distribution, the steepening area-productivity relation and the divergence between C/X and M/X derived slopes both point to a deficit of the most energetic flares ...