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 before a flare correlates with its magnitude, the "saturation" relationship results in the time 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.

Solar Flare Build-Up and Release

“…The new search of GOES flare statistics for the largest sunspot groups of Cycle 24 has not revealed the existence of a correlation between flare magnitude and the waiting time until the next flare, thought to reveal a mechanism in which a reservoir (containing free magnetic energy, for example) releases random amounts of its content at a prescribed threshold level. This contradicts the earlier finding (Hudson, 2020) of such a correlation, apparently present in two isolated regions. The weakness and intermittency of any such correlation means that it has no application to the prediction of flare properties, unlike the case of the pulsar PSR J0537-6910, for which Middleditch et al (2006) found a precise predictive capability.…”

“…The behavior here differs from that found by Hudson (2020) in at least two ways. First, NOAA 12673 was distinctly not an isolated group, suggesting that the coronal environment of this region has not masked its BUR behavior.…”

“…This sampling typically yielded about 10 flares per one-day interval. In these checks no systematic pattern occurred, in disagreement with the earlier results on two isolated regions studied previously in this way (Hudson, 2020).…”

“…The lower panels show the different interval-size correlations for these before and after cases. From Hudson (2020).…”

“…Recently Hudson (2020) presented evidence for a solar BUR relationship, but based only on the examination of two unusual active regions (ARs): NOAA 7978 in 1997 and NOAA 10930 in 2006, the "last best" major active regions of Solar Cycles 22 and 23, respectively. That search relied upon GOES soft X-ray peak fluxes in the standard 1-8 Å band, and this study continues that approach.…”