Nonextensivity in the solar magnetic activity during the increasing phase of solar Cycle 23

TL;DR

This study investigates the statistical properties of solar activity data during solar Cycle 23, revealing scale-dependent behaviors and multifractality through nonextensive statistical mechanics, with implications for understanding solar dynamics.

Contribution

It introduces a comprehensive analysis of solar activity using the $q$-Triplet framework, highlighting scale-dependent distributions and multifractal characteristics in solar data.

Findings

Sunspot Number exhibits a persistent $q$-Gaussian distribution across scales.

Magnetic Field shows a transition from $q$-Gaussian to Gaussian at larger scales.

Total Solar Irradiance displays scale-dependent behavior consistent with equilibrium and non-equilibrium states.

Abstract

In this paper we analyze the behavior of the daily Sunspot Number from the Sunspot Index Data Center (SIDC), the mean Magnetic Field strength from the National Solar Observatory/Kitt Peak (NSO/KP) and Total Solar Irradiance means from Virgo/SoHO, in the context of the $q$--Triplet which emerges within nonextensive statistical mechanics. Distributions for the mean solar Magnetic Field show two different behaviors, with a $q$--Gaussian for scales of 1 to 16 days and a Gaussian for scales longer than 32 days. The latter corresponds to an equilibrium state. Distributions for Total Solar Irradiance also show two different behaviors (approximately Gaussian) for scales of 128 days and longer, consistent with statistical equilibrium and $q$--Gaussian for scales $<$ 128 days. Distributions for the Sunspot Number show a $q$--Gaussian independent of timescales, consistent with a nonequilibrium state. The values obtained ("$q$--Triplet"$\equiv$$\{$$q$$_{stat}$,$q$$_{sen}$,$q$$_{rel}$$\}$) demonstrate that the Gaussian or $q$--Gaussian behavior of the aforementioned data depends significantly on timescales. These results point to strong multifractal behavior of the dataset analyzed, with the multifractal level decreasing from Sunspot Number to Total Solar Irradiance. In addition, we found a numerically satisfied dual relation between $q_{stat}$ and $q_{sen}$.