Small-Scale and Global Dynamos and the Area and Flux Distributions of Active Regions, Sunspot Groups, and Sunspots: A Multi-Database Study

TL;DR

This study analyzes multiple sunspot and active region databases to reveal that their area and flux distributions are best described by a composite of Weibull and log-normal distributions, indicating two distinct magnetic structure formation mechanisms.

Contribution

It introduces a unified model combining Weibull and log-normal distributions to explain the flux distributions across diverse datasets, linking them to different dynamo processes.

Findings

Distributions are reconcilable via a proportionality constant.

The composite distribution indicates two separate formation mechanisms.

Weibull distribution aligns with power-law behavior at small fluxes.

Abstract

In this work we take advantage of eleven different sunspot group, sunspot, and active region databases to characterize the area and flux distributions of photospheric magnetic structures. We find that, when taken separately, different databases are better fitted by different distributions (as has been reported previously in the literature). However, we find that all our databases can be reconciled by the simple application of a proportionality constant, and that, in reality, different databases are sampling different parts of a composite distribution. This composite distribution is made up by linear combination of Weibull and log-normal distributions -- where a pure Weibull (log-normal) characterizes the distribution of structures with fluxes below (above) $10^{21}$Mx ($10^{22}$Mx). We propose that this is evidence of two separate mechanisms giving rise to visible structures on the photosphere: one directly connected to the global component of the dynamo (and the generation of bipolar active regions), and the other with the small-scale component of the dynamo (and the fragmentation of magnetic structures due to their interaction with turbulent convection). Additionally, we demonstrate that the Weibull distribution shows the expected linear behavior of a power-law distribution (when extended into smaller fluxes), making our results compatible with the results of Parnell et al. (2009).