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

TL;DR

This paper analyzes how the solar minimum influences the distribution of long waiting times between solar and geomagnetic events, revealing a power law behavior with a slope of -2.5 in nonstationary Poisson processes driven periodically.

Contribution

It provides an analytical description of the tail behavior of waiting time distributions in nonstationary Poisson processes with sinusoidal drivers, applicable to solar phenomena.

Findings

Large waiting times follow a power law with slope -2.5.

The power law relates to the driver near its minima.

Results apply broadly to periodically driven nonstationary Poisson processes.

Abstract

We explore the tail of various waiting time datasets of processes that follow a nonstationary Poisson distribution with a sinusoidal driver. 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. Examples of such processes include solar flares, coronal mass ejections, geomagnetic storms, and substorms. We also discuss how the power law specifically relates to the behavior of driver near its minima.