Evidence for a Cutoff in the Frequency Distribution of Solar Flares from Small Active Regions

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Abstract
In this paper, we present evidence that active regions with small sunspot areas have an upper limit to the energy of the flares they produce. This result is consistent with predictions of the avalanche model of Lu et al. We used data from the Hard X-Ray Burst Spectrometer on the Solar Maximum Mission to study differences in the frequency distributions of solar flares as grouped by active region characteristics. The active region parameters considered were the total sunspot area, the longitudinal extent, the Mount Wilson class, and the McIntosh class. We find that there are significantly fewer high count rate flares (104 counts s-1 above 60 keV) from regions with small sunspot areas (0-500 microhemispheres) than would be expected from a power-law extrapolation from the frequency distribution of flares with peak rates greater than 50 counts s-1 above 60 keV. This is not found in the distribution of flares produced by regions with large sunspot areas (600-3600 microhemispheres). Using our analysis of the data and the predictions of the avalanche model, we calculated a limit to the energy of a flare that can be produced by an active region with given sunspot area. There are no statistically significant differences between the frequency distributions of flares with peak count rates 103 counts s-1 grouped according to the other region characteristics studied. We also find that, in all cases, large complex regions appear to produce a lower percentage of low-energy events than do smaller, simpler regions. It is possible that this effect is the result of biases against observations of low count rate flares and the determination of their locations.