Evidence for departure from a power-law flare size distribution for a small solar active region

TL;DR

This study analyzes a small solar active region that produced only small flares, finding that its flare size distribution deviates from a pure power-law, likely due to finite energy constraints, with implications for flare models.

Contribution

It provides evidence that small active regions can exhibit departures from power-law flare size distributions, challenging existing models of solar flare statistics.

Findings

Flare size distribution shows a rollover above a certain flux level.

Flaring rate varies with time and correlates with magnetic complexity.

Waiting times are consistent with a piecewise-constant Poisson process.

Abstract

Active region 11029 was a small, highly flare-productive solar active region observed at a time of extremely low solar activity. The region produced only small flares: the largest of the $>70$ Geostationary Observational Environmental Satellite (GOES) events for the region has a peak 1--$8{\AA}$ flux of $2.2\times 10^{-6} {\rm W} {\rm m}^{-2}$ (GOES C2.2). The background-subtracted GOES peak-flux distribution suggests departure from power-law behavior above $10^{-6} {\rm W} {\rm m}^{-2}$, and a Bayesian model comparison strongly favors a power-law plus rollover model for the distribution over a simple power-law model. The departure from the power law is attributed to this small active region having a finite amount of energy. The rate of flaring in the region varies with time, becoming very high for two days coinciding with the onset of an increase in complexity of the photospheric magnetic field. The observed waiting-time distribution for events is consistent with a piecewise-constant Poisson model. These results present challenges for models of flare statistics and of energy balance in solar active regions.