Role of Solar Minimum on Waiting Time Distributions Throughout the Heliosphere

Abstract:

The solar activity cycle impacts processes ranging from the sun throughout the heliosphere. Many processes can be identified as "events" such as solar flares, geomagnetic storms, and geomagnetic substorms. The waiting times between these events are governed by a combination of external driving by the activity cycle and internal dynamics. If the events occur randomly, the process can be described as a Poisson process. However, because the magnetic activity cycle generally modulates the rate of the events, the process is better described as a nonstationary Poisson process. For longer waiting times, Aschwanden [2010] showed that nonstationary Poisson processes with piecewise continuous exponential occurrence rate functions generate waiting time distributions that are power-law-like. Such tails are characteristic of many processes throughout the heliosphere including solar flares, geomagnetic storms, and substorms. In our study, we explore the tail of various waiting times datasets with nonstationary Poisson distribution with a sinusoidal dependence. Analytically, we find that the distribution of large waiting times of such processes can be described using a power law slope of -2.5. We show that this result applies more broadly to any nonstationary Poisson process driven periodically such as solar/stellar flares, geomagnetic storms, and substorms. We also discuss how the power law specifically relates to the behavior of driver near its minima.