Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part one: Sunspot dynamics

TL;DR

This paper applies Tsallis non-extensive statistical theory to analyze sunspot dynamics, revealing phase transitions, intermittent turbulence, and multifractal behavior in solar plasma, with results aligning well with theoretical predictions.

Contribution

It introduces a nonlinear analysis of sunspot data within Tsallis statistics, identifying phase transitions and turbulence characteristics in solar plasma dynamics.

Findings

Detection of phase transition from high-dimensional SOC to low-dimensional chaos

Evidence of strong intermittent turbulence and multifractal diffusion

Agreement between Tsallis theory and experimental estimations of distributions and spectra

Abstract

In this study, the nonlinear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis. The triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum, the generalized Renyi dimension spectrum and the spectrum of the structure function exponents were estimated experimentally and theoretically by using the entropy principle included in Tsallis non extensive statistical theory, following Arimitsu and Arimitsu. Our analysis showed clearly the following: a) a phase transition process in the solar dynamics from high dimensional non Gaussian SOC state to a low dimensional non Gaussian chaotic state, b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov studies c) faithful agreement of Tsallis non equilibrium statistical theory with the experimental estimations of i) non-Gaussian probability distribution function, ii) multifractal scaling exponent spectrum and generalized Renyi dimension spectrum, iii) exponent spectrum of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.