Abstract

Many processes throughout the heliosphere such as flares, 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 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 at large enough waiting time, and we find that this power law is primarily controlled by the conditions when the driving is minimum. We find that the asymptotic behavior of the waiting time distributions of solar flares, coronal mass ejections, geomagnetic storms, and substorms exhibit power laws are in reasonable agreement with a sinusoidally driven nonstationary Poisson process.