Abstract
Small-scale solar magnetic fields demonstrate features of fractal intermittent behavior, which requires quantification. For this purpose we investigate how the observational estimate of the solar magnetic flux density \(B\) depends on resolution \(D\) in order to obtain the scaling \(\ln B_{D} = - k \ln D +a\) in a reasonably wide range. The quantity \(k\) demonstrates cyclic variations typical of a solar activity cycle. In addition, \(k\) depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity \(a\) demonstrates some cyclic variation, but it is much weaker than in the case of \(k\). The scaling obtained generalizes previous scalings found for the particular cycle phases. The scaling is typical of fractal structures. In our opinion, the results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection.
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Notes
Solar and Heliospheric Observatory/Michelson Doppler Imager.
Following Landau and Lifshitz (1987) we note that this slope can be obtained from the standard \(5/3\)-slope in \(k\)-space: \(\int_{k}^{\infty}E(k)\,\mathrm{d}k \propto k^{-2/3} \propto l^{2/3} \propto v_{l}^{2}\), and we assume the same scaling for \(b_{l}\).
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Acknowledgements
The research is supported by RFBR under grants 14-02-00308 and 15-02-01407. We are grateful to the SOHO team for the data available on the Internet site http://sohowww.nascom.nasa.gov/cgi-bin/summary_query_form .
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Shibalova, A.S., Obridko, V.N. & Sokoloff, D.D. Intermittency of the Solar Magnetic Field and Solar Magnetic Activity Cycle. Sol Phys 292, 44 (2017). https://doi.org/10.1007/s11207-017-1069-4
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DOI: https://doi.org/10.1007/s11207-017-1069-4