A Correlation in the Waiting-time Distributions of Solar Flares

Abstract: In isolated solar active regions, we find that the waiting times between flares correlate with flare magnitudes as determined by the GOES soft X-ray fluxes. A "build-up and release" scenario (BUR) for magnetic energy storage in the solar corona suggests the existence of such a relationship, relating the slowly varying subphotospheric energy sources to the sudden coronal energy releases of flares and CMEs. Substantial amounts of research effort had not previously found any obvious observational evidence for such a BUR process. This has posed a puzzle since coronal magnetic energy storage represents the consensus view of the basic flare mechanism. We have revisited the GOES soft X-ray flare statistics for any evidence of correlations, using two isolated active regions, and have found significant evidence for a "saturation" correlation. Rather than a "reset" form of this relaxation, in which the time \textit{before} a flare correlates with its magnitude, the "saturation" relationship results in the time \textit{after} the flare showing the correlation. The observed correlation competes with the effect of reduced GOES sensitivity, in which weaker events can be under-reported systematically. This complicates the observed correlation, and we discuss several approaches to remedy this.