Origin and Use of the Laplace Distribution in Daily Sunspot Numbers

TL;DR

This paper explains the physical origin of the Laplace distribution in daily sunspot number changes and introduces a simulation method that reproduces observed sunspot variability over solar cycles.

Contribution

It reveals the physical basis for the Laplace distribution in sunspot changes and presents a new simulation approach for daily sunspot numbers across solar cycles.

Findings

Laplace distribution arises from sunspot formation, evolution, and decay.

The simulation method accurately reproduces observed daily change distributions.

The approach works across multiple recent solar cycles.

Abstract

Recently Pop ({\it Solar Phys.} {\bf 276}, 351, 2012) identified a Laplace (or double exponential) distribution in the number of days with a given absolute value in the change over a day, in sunspot number, for days on which the sunspot number does change. We show this phenomenological rule has a physical origin attributable to sunspot formation, evolution, and decay, rather than being due to the changes in sunspot number caused by groups rotating onto and off the visible disc. We also demonstrate a simple method to simulate daily sunspot numbers over a solar cycle using the \cite{2012SoPh..276..351P} result, together with a model for the cycle variation in the mean sunspot number. The procedure is applied to three recent solar cycles. We check that the simulated sunspot numbers reproduce the observed distribution of daily changes over those cycles.