Observational evidence in favor of scale-free evolution of sunspot groups

¹ National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, 101000 Moscow, Russia
e-mail: abshapoval@gmail.com
² Institut de Physique du Globe, Sorbonne Paris Cité, Paris, France
³ Institute of Earthquake Prediction Theory and Mathematical Geophysics, RAS, Profsoyuznaya 84/32, 117997 Moscow, Russia

Received: 9 February 2018
Accepted: 13 August 2018

Abstract

Context. The hypothesis stating that the distribution of sunspot groups versus their size (φ) follows a power law in the domain of small groups was recently highlighted but rejected in favor of a Weibull distribution.

Aims. In this paper we reconsider this question, and are led to the opposite conclusion.

Methods. We have suggested a new definition of group size, namely the spatio-temporal “volume” (V) obtained as the sum of the observed daily areas instead of a single area associated with each group.

Results. With this new definition of “size”, the width of the power-law part of the distribution φ ∼ 1/V^β increases from 1.5 to 2.5 orders of magnitude. The exponent β is close to 1. The width of the power-law part and its exponent are stable with respect to the different catalogs and computational procedures used to reduce errors in the data. The observed distribution is not fit adequately by a Weibull distribution.

Conclusions. The existence of a wide 1/V part of the distribution φ suggests that self-organized criticality underlies the generation and evolution of sunspot groups and that the mechanism responsible for it is scale-free over a large range of sizes.