Observational evidence in favor of scale free evolution of sunspot groups

Astronomy and Astrophysics. 2018. Vol. 618. P. A183-1–A183-13.

Shapoval S., Le Mouël J. -., Shnirman M. G., Courtillot V.

The hypothesis stating that the distribution of sunspot groups versus their size ($\varphi$) follows a power law in the domain of small groups was recently highlighted but rejected in favor of a Weibull distribution. In this paper we re-consider this question, and are led to the opposite conclusion. We suggest 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. With this new definition of ``size'', the width of the power-law part of the distribution increases from 1.5 to 2.5. The exponent of the power-law is close to 1. The width of the power-law part and its exponent are stable with respect to the different catalogues and computational procedures used to reduce errors in the data. The observed distribution is not fit adequately by a Weibull distribution. The existence of a wide power-law part of the distribution 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.

Keywords: magnetic field, анализ данных, data analysis, sunspots, солнечные пятна

Publication based on the results of: Construction of mathematical models designed for the analysis of data series, prediction of big systems’ evolution, and the control of the dynamics of these systems (2018)