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A Fractal Analysis of Magnetograms Within Active Regions

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Abstract

The magnetograms of 16 active regions, observed during June–November 2015, were obtained from the Joint Science Operations Center (JSOC) from the Solar Dynamics Observatory (SDO) using the Helioseismic and Magnetic Imager (HMI) and used to determine the fractal dimensions of various magnetic field groups. The fields were divided into strong (positive and negative) and weak (positive and negative) groupings. The area-perimeter method was used to determine the fractal dimensions for the umbral and penumbral regions of the magnetograms. The fractal dimensions were found to be \(1.79 \pm 0.49\) and \(1.96 \pm 0.29\) for strong and weak magnetic fields, respectively. When compared to the umbral and penumbral fractal dimensions determined by Rajkumar, Haque and Hrudey (Sol. Phys.292, 170, 2017) using white light images, an inverse relationship was found, with the umbra showing lower fractal dimensions than the penumbra for the magnetic field groups compared to the intensity images. This directly implies that there is greater complexity in the penumbral magnetic field groupings than the umbral region. This has implications for models that constrain how the magnetic field groups are contained in the cooler umbral regions.

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References

  • Abramenko, V.I.: 2005, Multifractal analysis of solar magnetograms. Solar Phys.228, 29. DOI .

    Article  ADS  Google Scholar 

  • Baish, J.W., Jain, R.K.: 2000, Fractals and cancer. Cancer Res.60, 3683.

    Google Scholar 

  • Balke, A., Schrijver, C., Zwaan, C., Tarbell, T.: 1993, Percolation theory and the geometry of photospheric magnetic flux concentrations. Solar Phys.143, 215. DOI .

    Article  ADS  Google Scholar 

  • Bershadskii, A.G.: 1990, Large-scale fractal structure in laboratory turbulence, astrophysics, and the ocean. Sov. Phys. Usp.33, 1073. DOI .

    Article  ADS  Google Scholar 

  • Bunde, A., Havlin, S.: 2013, Fractals in Science, Springer, Berlin.

    MATH  Google Scholar 

  • Chumak, O.: 2005, Self-similar and self-affine structures in the observational data on solar activity. Astron. Astrophys. Trans.24, 93. DOI .

    Article  ADS  Google Scholar 

  • Chumak, O., Chumak, Z.: 1996, Sunspots. The model of “elastic sceletons”. Estimation of sunspot umbra fractal dimension. Astron. Astrophys. Trans.10, 329.

    Article  ADS  Google Scholar 

  • Deng, L.: 2016, Multi-fractal property and long-range correlation of chaotic time series. In: 2016 3rd International Conference on Information Science and Control Engineering (ICISCE), IEEE Press, New York, 1361. DOI .

    Chapter  Google Scholar 

  • Feder, J.: 2013, Fractals, Springer, Berlin. DOI .

    Book  MATH  Google Scholar 

  • Georgoulis, M.K.: 2012, Are solar active regions with major flares more fractal, multifractal, or turbulent than others? Solar Phys.276, 161. DOI .

    Article  ADS  Google Scholar 

  • Golovko, A., Salakhutdinova, I.: 2012, Fractal properties of active regions. Astron. Rep.56, 410. DOI .

    Article  ADS  Google Scholar 

  • Harvey, K.L., Zwaan, C.: 1993, Properties and emergence patterns of bipolar active regions. Solar Phys.148, 85. DOI .

    Article  ADS  Google Scholar 

  • Hathaway, D.H., Upton, L.: 2014, The solar meridional circulation and sunspot cycle variability. J. Geophys. Res.119, 3316. DOI .

    Article  Google Scholar 

  • Hoeksema, T.: 2014. In: HMI_M.ColorTable (ed.), pdf. http://jsoc.stanford.edu . http://jsoc.stanford.edu/jsocwiki/MagneticField .

  • Ioshpa, B., Obridko, V., Rudenchik, E.: 2008, Fractal properties of solar magnetic fields. Astron. Lett.34, 210. DOI .

    Article  ADS  Google Scholar 

  • Ioshpa, B., Mogilevskii, E., Obridko, V., Rudenchik, E.: 2005, Some fractal properties of solar magnetic fields. In: Proceedings of the International Scientific Conference on Chromospheric and Coronal Magnetic Fields, ESA SP-596.

    Google Scholar 

  • Jaeggli, S.: 2011, An observational study of the formation and evolution of sunspots. PhD thesis, University of Hawaii. DOI .

  • Jaeggli, S.A., Lin, H., Uitenbroek, H.: 2012, On molecular hydrogen formation and the magnetohydrostatic equilibrium of sunspots. Astrophys. J.745, 133. DOI .

    Article  ADS  Google Scholar 

  • Jurčák, J., Rezaei, R., González, N.B., Schlichenmaier, R., Vomlel, J.: 2018, The magnetic nature of umbra–penumbra boundary in sunspots. Astron. Astrophys.611, L4. DOI .

    Article  ADS  Google Scholar 

  • Loughhead, R., Bray, R.: 1958, The Wilson effect in sunspots. Aust. J. Phys.11, 177. DOI .

    Article  ADS  Google Scholar 

  • Mandelbrot, B.B.: 1983, The Fractal Geometry of Nature, W.H. Freeman and Company, New York.

    Book  Google Scholar 

  • McAteer, R.J., Gallagher, P.T., Ireland, J.: 2005, Statistics of active region complexity: a large-scale fractal dimension survey. Astrophys. J.631, 628. DOI .

    Article  ADS  Google Scholar 

  • Meunier, N.: 1999, Fractal analysis of Michelson Doppler Imager magnetograms: a contribution to the study of the formation of solar active regions. Astrophys. J.515, 801. DOI .

    Article  ADS  Google Scholar 

  • Nesme-Ribes, E., Meunier, N., Collin, B.: 1996, Fractal analysis of magnetic patterns from Meudon spectroheliograms. Astron. Astrophys.308, 213.

    ADS  Google Scholar 

  • Rajkumar, B., Haque, S., Hrudey, W.: 2017, Fractal dimensions of umbral and penumbral regions of sunspots. Solar Phys.292, 170. DOI .

    Article  ADS  Google Scholar 

  • Régnier, S., Canfield, R.C.: 2006, Evolution of magnetic fields and energetics of flares in active region 8210. Astron. Astrophys.451, 319. DOI .

    Article  ADS  Google Scholar 

  • Ruzmaikin, A., Sokoloff, D., Tarbell, T.: 1991, Fractal flux tubes of the solar magnetic field. In: International Astronomical Union Colloquium130, Cambridge University Press, Cambridge, 140. DOI .

    Chapter  Google Scholar 

  • Schroeder, M.: 2009, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise, Courier Corporation.

    MATH  Google Scholar 

  • Solanki, S.K.: 2003, Sunspots: an overview. Astron. Astrophys. Rev.11, 153. DOI .

    Article  ADS  Google Scholar 

  • Takayasu, H.: 1990, Fractals in the Physical Sciences, Manchester University Press, Manchester.

    MATH  Google Scholar 

  • Voss, R.F.: 1988, The Science of Fractal Images, Springer, New York, 21. DOI .

    Book  Google Scholar 

  • Weitz, D., Huang, J., Lin, M., Sung, J.: 1985, Limits of the fractal dimension for irreversible kinetic aggregation of gold colloids. Phys. Rev. Lett.54, 1416. DOI .

    Article  ADS  Google Scholar 

  • Zelenyi, L., Milovanov, A.: 1991, Fractal properties of sunspots. Sov. Astron. Lett.17, 425.

    ADS  Google Scholar 

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Acknowledgment

The authors thank the referees whose comments were very valuable in improving the manuscript.

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  1. Department of Physics, University of the West Indies, St. Augustine, Trinidad, W.I., Trinidad and Tobago

    B. Rajkumar & S. Haque

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  1. B. Rajkumar
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  2. S. Haque
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Correspondence to S. Haque.

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Rajkumar, B., Haque, S. A Fractal Analysis of Magnetograms Within Active Regions. Sol Phys 295, 10 (2020). https://doi.org/10.1007/s11207-019-1578-4

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