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

Abstract: Waiting time distributions of solar flares and {\sl coronal mass ejections (CMEs)} exhibit power law-like distribution functions with slopes in the range of $\alpha_{\tau} \approx 1.4-3.2$, as observed in annual data sets during 4 solar cycles (1974-2012). We find a close correlation between the waiting time power law slope $\alpha_\tau$ and the {\sl sunspot number (SN)}, i.e., $\alpha_\tau$ = 1.38 + 0.01 $\times$ SN. The waiting time distribution can be fitted with a Pareto-type function of the form $N(\tau) = N_0$ $(\tau_0 + \tau)^{-\alpha_{\tau}}$, where the offset $\tau_0$ depends on the instrumental sensitivity, the detection threshold of events, and pulse pile-up effects. The time-dependent power law slope $\alpha_{\tau}(t)$ of waiting time distributions depends only on the global solar magnetic flux (quantified by the sunspot number) or flaring rate, independent of other physical parameters of {\sl self-organized criticality (SOC)} or {\sl magneto-hydrodynamic (MHD)} turbulence models. Power law slopes of $\alpha_{\tau}\approx 1.2-1.6$ were also found in solar wind switchback events, as observed with the {\sl Parker Solar Probe (PSP)}. We conclude that the annual variability of switchback events in the heliospheric solar wind is modulated by flare and CME rates originating in the photosphere and lower corona.