Maximum Entropy Limit of Small-scale Magnetic Field Fluctuations in the Quiet Sun

TL;DR

This study models small-scale magnetic field fluctuations in the quiet Sun as a maximum entropy Markov process, revealing how data resolution and polarity mixing influence the convergence to equilibrium.

Contribution

It introduces a novel data analysis method that quantifies magnetic field fluctuations without subjective feature identification, using a maximum entropy Markov process approach.

Findings

Different convergence rates depend on data resolution and polarity fluctuations.

Magnetic field fluctuations can be modeled as a stationary Markov process.

The method provides an objective way to analyze solar magnetic field dynamics.

Abstract

The observed magnetic field on the solar surface is characterized by a very complex spatial and temporal behavior. Although feature-tracking algorithms have allowed us to deepen our understanding of this behavior, subjectivity plays an important role in the identification and tracking of such features. In this paper, we continue studies Gorobets, A. Y., Borrero, J. M., & Berdyugina, S. 2016, ApJL, 825, L18 of the temporal stochasticity of the magnetic field on the solar surface without relying either on the concept of magnetic features or on subjective assumptions about their identification and interaction. We propose a data analysis method to quantify fluctuations of the line-of-sight magnetic field by means of reducing the temporal field's evolution to the regular Markov process. We build a representative model of fluctuations converging to the unique stationary (equilibrium) distribution in the long time limit with maximum entropy. We obtained different rates of convergence to the equilibrium at fixed noise cutoff for two sets of data. This indicates a strong influence of the data spatial resolution and mixing-polarity fluctuations on the relaxation process. The analysis is applied to observations of magnetic fields of the relatively quiet areas around an active region carried out during the second flight of the Sunrise/IMaX and quiet Sun areas at the disk center from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory satellite.