Geomagnetism and Aeronomy

, Volume 54, Issue 7, pp 892–898 | Cite as

The multifractal nature of solar magnetism and the solar dynamo problem

  • V. I. Abramenko


Based on observation data with a high spatial resolution, the multifractal properties of turbulent magnetized plasma in a nonperturbed solar atmosphere are revealed. It is shown that magnetic fluxes in elements of the magnetic field, as well as the size of elements, are distributed lognormally, which is indicative of multifractality. In coronal holes (CHs), the multifractality of magnetic fields is observed on scales of 10000-400 km; at the same time, it is observed on smaller scales as the resolution improves, and its degree increases. It is shown that two subsets of granules exist: the usual granules, with a characteristic size of 1000–1300 km and Gaussian size distribution, and mini-granules, which do not have a well-pronounced characteristic size and are mostly less than 600 km in diameter. The size distribution function of the mini-granules obeys lognormal law and their multifractal character is seen on small scales down to 50 km, which allows one to make a conclusion about the presence of multifractality of photospheric plasma flows in CHs and in a nonperturbed photosphere. A conclusion is made that multifractality takes place for small-scale magnetic fields of quiet regions, as well as for large-scale fields of active regions. This makes it possible to suppose that solar magnetic fields are generated by a common nonlinear dynamical process.


Solar Magnetic Field Multifractality Spectrum Quiet Region Solar Magnetism Thick Gray Line 
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  1. Abramenko, V.I., Multifractal analysis of solar magnetograms, Sol. Phys., 2005, vol. 228, pp. 29–42.CrossRefGoogle Scholar
  2. Abramenko, V.I. and Longcope, D.W., Distribution of the magnetic flux in elements of the magnetic field in active regions, Astrophys. J., 2005, vol. 619, no. 2, pp. 1160–1166.CrossRefGoogle Scholar
  3. Abramenko, V.I., and Yurchyshyn, V.B. Intermittency and multifractality spectra of the magnetic field in solar active regions, Astrophys. J., 2010, vol. 722, no. 1, pp. 122–130.CrossRefGoogle Scholar
  4. Abramenko, V.I., Yurchyshyn, V.B., Goode, P.R., Kitiashvili, I.N., and Kosovichev, A.G., Detection of smallscale granular structures in the quiet Sun with the new solar telescope, Astrophys. J., Lett., 2012, vol. 756, no. 2, pp. L27–L32.CrossRefGoogle Scholar
  5. Abramenko, V.I., Yurchyshyn, V.B., Wang, H., Spirock, T.J., and Goode, P.R., Scaling behavior of structure functions of the longitudinal magnetic field in active regions on the sun, Astrophys. J., 2002, vol. 577, no. 1, pp. 487–495.CrossRefGoogle Scholar
  6. Biskamp, D., Nonlinear Magnetohydrodynamics, Cambridge UK: Cambridge Univ. Press, 1993.CrossRefGoogle Scholar
  7. Brandenburg, A., Sokoloff, D., and Subramanian, K., Current status of turbulent dynamo theory. From largescale to small-scale dynamos, Space Sci. Rev., 2012, vol. 169, nos. 1–4, pp. 123–157.CrossRefGoogle Scholar
  8. Cao, W., Gorceix, N., Coulter, R., Ahn, K., Rimmele, T.R., and Goode, P.R., Scientific instrumentation for the 1.6 m New Solar Telescope in Big Bear, Astron. Nachr., 2010, vol. 331, no. 6, pp. 636–641.CrossRefGoogle Scholar
  9. Feder, J., Fractals, New York: Plenum, 1988.CrossRefGoogle Scholar
  10. Frisch, U., Turbulence-The legacy of A.N. Kolmogorov, Cambridge UK: Cambridge Univ. Press, 1995.Google Scholar
  11. Makarenko, N.G., Karimova, L.M., Kozelov, B.V., and Novak, M.M., Multifractal analysis based on the Choquet capacity: Application to solar magnetograms, Phys. A (Amsterdam, Neth.), 2012, vol. 391, no. 18, pp. 4290–4301.CrossRefGoogle Scholar
  12. McAteer, R.T.J., Young, C.A., Ireland, J., and Gallagher, P.T., The bursty nature of solar flare X-ray emission, Astrophys. J., 2007, vol. 662, no. 1, pp. 691–700.CrossRefGoogle Scholar
  13. Miesch, M.S., The solar dynamo, Philos. Trans. R. Soc., A, 2012, vol. 370, no. 1970, pp. 3049–3069.CrossRefGoogle Scholar
  14. Moss, D., Pipin, V.V., Sokoloff, D.D., and Hoeksema, J.T., Reversals of the solar magnetic dipole in the light of observational data and simple dynamo models, arXiv:1312.6379.2013.Google Scholar
  15. Nagovitsyn, Yu.A. and Kuleshova, A.I., Recurrence of flare energy releases in solar active regions (Cycle 23), Geomagn. Aeron. (Engl. Transl.), 2013, vol. 53, no. 8, pp. 985–988.CrossRefGoogle Scholar
  16. Zel’dovich, Ya.B., Molchanov, S.A., Ruzmaikin, A.A., and Sokolov, D.D., Intermittency in random media, Phys.-Usp., 1987, vol. 30, pp. 353–369.Google Scholar

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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Big Bear Solar ObservatoryBig BearUSA

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