Percolation theory and the geometry of photospheric magnetic flux concentrations

Physics

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Magnetic Flux, Percolation, Photosphere, Solar Magnetic Field, Faculae, Magnetic Signatures

Scientific paper

A highly structured pattern without an apparent length scale is formed in the magnetic field of solar active regions. This pattern is studied in detail for a plage and its surroundings. The geometric properties of isolated patches of magnetic flux are analyzed. A fractal dimension of 1.54 +/- 0.05 for the relation between area and linear size is determined for patches with a linear size of 3 sec and which appear to be statistically self-similar. This value is very close to that found using percolation theory (1.56) for clusters of tracers placed randomly on a lattice with a tracer density below a critical threshold. The distribution of observed cluster areas and the distribution of clusters on such a lattice also agree. The similarity between observed clusters and clusters on randomly filled lattices implies that, following emergence, the sun's magnetic flux is randomly distributed up to sizes of at least 3 sec.

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