Reconciliation of Waiting Time Statistics of Solar Flares Observed in Hard X-Rays

We study the waiting time distributions of solar flares observed in hard X-rays with ISEE-3 / ICE , HXRBS/ SMM , WATCH/GRANAT, BATSE/ CGRO , and RHESSI . Although discordant results and interpretations have been published earlier, based on relatively small ranges (<2 decades) of waiting times, we find that all observed distributions, spanning over 6 decades of waiting times (Δ t ≈ 10 −3 –10 3 hr), can be reconciled with a single distribution function, N (Δ t ) ∝ λ 0 (1 + λ 0 Δ t ) −2 , which has a power-law slope of p ≈ 2.0 at large waiting times (Δ t ≈ 1–1000 hr) and flattens out at short waiting times Δ t ≲ Δ t 0 = 1/λ 0 . We find a consistent breakpoint at Δ t 0 = 1/λ 0 = 0.80 ± 0.14 hr from the WATCH, HXRBS, BATSE, and RHESSI data. The distribution of waiting times is invariant for sampling with different flux thresholds, while the mean waiting time scales reciprocically with the number of detected events, Δ t 0 ∝ 1/ n det . This waiting time distribution can be modeled with a nonstationary Poisson process with a flare rate λ = 1/Δ t that varies as f (λ) ∝ λ −1 exp − (λ/λ 0 ). This flare rate distribution requires a highly intermittent flare productivity in short clusters with high rates, separated by relatively long quiescent intervals with very low flare rates.