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. Plain Language Summary: Many events in the solar system are driven by the magnetic activity cycle of the sun. In this study, we show that for cyclical driving of a Poisson process, the probability of the time between events satisfies a power law of −2.5 when the time between events is large. We show that this power law reasonably describes the distribution of waiting times for solar flares, CMEs, and storms at long waiting time. Additionally, we show that the distribution of long waiting times is primarily determined by the minimum of the driving process. Key Points: Many heliospheric waiting time distributions are consistent with sinusoidal driving of a random processMinima in the driving process determine the tail of the waiting time distributionThe power law of the waiting time distribution is asymptotic to −2.5 for sinusoidal driving [ABSTRACT FROM AUTHOR]