Clustering Behavior in Solar Flare Dynamics

The solar magnetic activity cycle provides energy input that is released in intense bursts of radiation known as solar flares. As such, the dynamics of the activity cycle is embedded in the sequence of times between the flare events. Recent analysis shows that solar flares exhibit memory on different timescales. These previous studies showed that the time ordering of flare events is not random, but rather there is dependence between successive flares. In the present work, the clustering of flares is demonstrated through a straightforward nonparametric method where the cumulative distribution function of successive flares is compared with the cumulative distribution function of surrogate sequences of flares obtained by random permutation of flares. The random permutation is performed within rate-variable Bayesian blocks during which the flare rate is assumed to be constant. Differences between the cumulative distribution functions are substantial on a timescale around 3 hr, suggesting that flare recurrence on that timescale is more likely than would be expected if the waiting time were drawn from a nonstationary Poisson process.