Multifractal Analysis Of Solar Magnetograms

As solar observational techniques improve, fine small-scale structures observed on the solar surface become more pronounced. Complex filigree structures of solar granulation, sunspots, photospheric magnetic and velocity fields cannot be described adequately by a single parameter (e.g., filling factor, fractal dimension, or power-law index). Methods which incorporate parameters that are a function of scale (multiscale methods) to describe the complexity of a field under study, should be involved. The multifractal approach offers such a possibility. In this paper the scaling of structure functions is proposed in order to analyze multifractality. Application of the approach to SOHO/MDI high-resolution magnetograms of active regions show that the structure functions differ for all active regions studied. For a given active region, the functions may maintain their shape during several hours; however, they can significantly change during a day. Flare-quiet active regions tend to possess a lower degree of multifractality than flaring active regions do. The increase in multifractality is a signal that a magnetic structure is driven to a critical state, thus gaining tangential discontinuities of various length scales.

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