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.