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Self-similar and self-affine structures in the observational data on solar activity

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Abstract:

Stochastic self-similarity and self-affinity in the data on the solar activity phenomena is discussed in this paper. The following results are given and discussed. Firstly, the area–perimeter method was applied to obtain the fractal dimension values of solar spot umbras and of equal-intensity field lines in solar active regions (ARs). The fractal dimension value D 0 =1.35±0.03 has been obtained for sunspot umbras. Field lines of equal intensity have different values of fractal dimensions for north and south polarities. Secondly, it is shown that the fractal dimension extracted from correlation between the magnetic flux and its cross-sectional area ( i.e . a photosphere) is temporally invariant for an AR, but the fractal dimensions can be considerably different for various ARs. Thirdly, the multifractal nature of ARs magnetic fields was confirmed by a study of the scaling properties of their Renyi entropy. Fourthly, the R / S analysis was used for the Wolf series with purpose of estimating the long-time ‘memory' structure of this series. Time periods with different frequency bands were found in the series. Fifthly, the Renyi entropy and the Higuchi method were used for the study of solar X-ray flux variations. It is shown that the fractal dimensions obtained with this algorithm can be used as a good X-ray index.

Keywords: Entropies; Fractals; Solar activity

Document Type: Research Article

DOI: https://doi.org/10.1080/10556790500126472

Affiliations: Sternberg Astronomical Institute, Universitetskij Prospekt 13, Moscow, 119899, Russia

Publication date: 2005-04-01

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