2003/09/08 by David Hughes, David W. Hughes, Hughes, David +2 · 1 citation
Physics and Astronomy · #Astrophysics (astro-ph) #Condensed Matter (cond-mat) #FOS: Physical sciences #Plasma Physics (physics.plasm-ph) #Solar and Space Plasma Dynamics #astro-ph #cond-mat #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0309230
16 pages, 11 figures
arxiv created 2003/09/08 · openalex publication_date 2003/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 γ= 1.7 ± 0.3, over the entire range of the measurement, about (2-500)× 1017 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 γ, 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 1023Mx, 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.