Waiting Time Distribution and Multifractality Analysis of Solar Flares.

The statistical properties of solar flare occurrence are critical for understanding coronal energy release, yet the nature of their underlying dynamics remains heavily debated. Analyzing over two decades of soft x-ray observations from a comprehensive geostationary operational environmental satellite (GOES) dataset, we demonstrate that flare waiting time distributions exhibit a previously unreported scale invariance under coarse graining by flare size. This self-similarity proves the existence of long-range temporal correlations between events. This finding is supported by a complementary multifractal analysis of the x-ray flux, which confirms the presence of intermittency and turbulentlike scaling. By ruling out independent event occurrence, these results establish new statistical constraints on solar flare dynamics and link their intermittent behavior to shared multiscale avalanche phenomena in complex systems.