Correlation of the Sunspot Number and the Waiting-time Distribution of Solar Flares, Coronal Mass Ejections, and Solar Wind Switchback Events Observed with the Parker Solar Probe

Waiting-time distributions of solar flares and coronal mass ejections (CMEs) exhibit power-law-like distribution functions with slopes in the range of α _τ ≈ 1.4–3.2, as observed in annual data sets during four solar cycles (1974–2012). We find a close correlation between the waiting-time power-law slope α _τ and the sunspot number (SN), i.e., α _τ = 1.38 + 0.01 × SN. The waiting-time distribution can be fitted with a Pareto-type function of the form N(τ) = N ₀ ${({\tau }_0+\tau )}^{-{\alpha }_{\tau }}$, where the offset τ ₀ depends on the instrumental sensitivity, the detection threshold of events, and pulse pileup effects. The time-dependent power-law slope α _τ(t) of waiting-time distributions depends only on the global solar magnetic flux (quantified by the sunspot number) or flaring rate, which is not predicted by self-organized criticality or magnetohydrodynamic turbulence models. Power-law slopes of α _τ ≈ 1.2–1.6 were also found in solar wind switchback events, as observed with the Parker Solar Probe during the solar minimum, while steeper slopes are predicted during the solar maximum. We find that the annual variability of switchback events in the heliospheric solar wind and solar flare and CME rates (originating in the photosphere and lower corona) are highly correlated.