Role of the Solar Minimum in the Waiting Time Distribution Throughout the Heliosphere

Many processes throughout the heliosphere such as flares, coronal mass ejections (CMEs), storms and substorms have abrupt onsets. The waiting time between these onsets provides key insights as to the underlying dynamical processes. We explore the tail of these waiting time distributions (WTDs) in the context of random processes driven by the solar magnetic activity cycle, which we approximate by a sinusoidal driver. Analytically, we find that the distribution of large waiting times of such a process approaches a power law slope of −2.5, which is primarily controlled by the conditions when the driving is minimum. We find that the asymptotic behavior of WTDs of solar flares, CMEs, geomagnetic storms, and substorms exhibit power laws that are in reasonable agreement with a sinusoidally driven nonstationary Poisson process. However, the WTD of substorms during solar minimum may be more consistent with prolonged periods of weak driving followed by abrupt increase in the rate.