Scale-Free Magnetic Networks: Comparing Observational Data with a Self-Organizing Model of the Coronal Field

TL;DR

This paper models the solar coronal magnetic field as a scale-free network arising from self-organized critical dynamics, supported by observational data and numerical simulations, revealing scale-invariance across various magnetic structures.

Contribution

It introduces a self-organized critical model of the coronal magnetic field that matches observed power-law distributions and predicts new scale-free statistical properties of magnetic flux connections.

Findings

Magnetic concentration strengths follow a power-law distribution with index 1.7.

Numerical simulations reproduce the observed flux distribution index.

Calibrated model estimates the flux turnover time as about 10 hours.

Abstract

We propose that the coronal magnetic field, linking concentrations on the photosphere through an interwoven web of flux, embodies a scale-free network. It arises from a self-organized critical dynamics including flux emergence, the diffusion and merging of magnetic concentrations, as well as avalanches of reconnecting flux tubes. Magnetic concentrations such as fragments, pores and sunspots, are `nodes' joined by flux tubes or `links'. The number of links emanating from a node is scale-free. We reanalyze the quiet-Sun data of Close et al and show that the distribution of magnetic concentration strengths is a power law with an index $\gamma= 1.7 \pm 0.3$, over the entire range of the measurement, about $(2-500)\times 10^{17}$ Mx. This distribution is compatible with that for the sizes of active regions reported by Harvey and Schwaan. Thus magnetic concentrations may be scale-free from the smallest measurable fragments to the large active regions. Numerical simulations of a self-organized critical model give the same index $\gamma$, within statistical uncertainty. The exponential distribution of flux tube lengths also agrees quantitatively with results from the model. Calibration with the measured diffusion constant of magnetic concentrations allows us to calculate a flux turnover time in the model to be of order 10 hours and the total solar flux to be of order $10^{23}$Mx, agreeing with observations. We introduce two other statistical quantities to characterize scale-free networks. The probability distribution for the amount of flux connecting a pair of concentrations, and the number of distinct concentrations linked to a given one are predicted to be scale-free, with different indices. Our approach unifies the observation of scale free flare energies with the coronal magnetic field structure.