Abstract
Multiple recent investigations of solar magnetic-field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17 733 magnetograms in total) observed by SOHO’s Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i) a widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii) a lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately, for major solar-flare prediction.
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Abramenko, V.I.: 2005, Relationship between magnetic power spectrum and flare productivity in solar active regions. Astrophys. J. 629, 1141 – 1149. doi: 10.1086/431732 .
Abramenko, V., Yurchyshyn, V.: 2010, Intermittency and multifractality spectra of the magnetic field in solar active regions. Astrophys. J. 722, 122 – 130. doi: 10.1088/0004-637X/722/1/122 .
Abramenko, V., Yurchyshyn, V., Wang, H.: 2008, Intermittency in the photosphere and corona above an active region. Astrophys. J. 681, 1669 – 1676. doi: 10.1086/588426 .
Abramenko, V.I., Yurchyshyn, V.B., Wang, H., Spirock, T.J., Goode, P.R.: 2002, Scaling behavior of structure functions of the longitudinal magnetic field in active regions on the Sun. Astrophys. J. 577, 487 – 495. doi: 10.1086/342169 .
Abramenko, V.I., Yurchyshyn, V.B., Wang, H., Spirock, T.J., Goode, P.R.: 2003, Signature of an avalanche in solar flares as measured by photospheric magnetic fields. Astrophys. J. 597, 1135 – 1144. doi: 10.1086/378492 .
Aschwanden, M.J., Aschwanden, P.D.: 2008a, Solar flare geometries. I. The area fractal dimension. Astrophys. J. 674, 530 – 543. doi: 10.1086/524371 .
Aschwanden, M.J., Aschwanden, P.D.: 2008b, Solar flare geometries. II. The volume fractal dimension. Astrophys. J. 674, 544 – 553. doi: 10.1086/524370 .
Aschwanden, M.J., Parnell, C.E.: 2002, Nanoflare statistics from first principles: fractal geometry and temperature synthesis. Astrophys. J. 572, 1048 – 1071. doi: 10.1086/340385 .
Bak, P.: 1996, How Nature Works: The Science of Self-Organized Criticality, Copernicus Press, New York.
Bak, P., Tang, C., Wiesenfeld, K.: 1987, Self-organized criticality – An explanation of 1/f noise. Phys. Rev. Lett. 59, 381 – 384. doi: 10.1103/PhysRevLett.59.381 .
Berger, T.E., Lites, B.W.: 2003, Weak-field magnetogram calibration using Advanced Stokes Polarimeter flux density maps – II. SOHO/MDI full-disk mode calibration. Solar Phys. 213, 213 – 229.
Biskamp, D., Welter, H.: 1989, Dynamics of decaying two-dimensional magnetohydrodynamic turbulence. Phys. Fluids, B Plasma Phys. 1, 1964 – 1979. doi: 10.1063/1.859060 .
Brandenburg, A., Tuominen, I., Nordlund, A., Pulkkinen, P., Stein, R.F.: 1990, 3-D simulation of turbulent cyclonic magneto-convection. Astron. Astrophys. 232, 277 – 291.
Cadavid, A.C., Lawrence, J.K., Ruzmaikin, A.A., Kayleng-Knight, A.: 1994, Multifractal models of small-scale solar magnetic fields. Astrophys. J. 429, 391 – 399. doi: 10.1086/174329 .
Cattaneo, F., Emonet, T., Weiss, N.: 2003, On the Interaction between convection and magnetic fields. Astrophys. J. 588, 1183 – 1198. doi: 10.1086/374313 .
Conlon, P.A., Gallagher, P.T., McAteer, R.T.J., Ireland, J., Young, C.A., Kestener, P., Hewett, R.J., Maguire, K.: 2008, Multifractal properties of evolving active regions. Solar Phys. 248, 297 – 309. doi: 10.1007/s11207-007-9074-7 .
Conlon, P.A., McAteer, R.T.J., Gallagher, P.T., Fennell, L.: 2010, Quantifying the evolving magnetic structure of active regions. Astrophys. J. 722, 577 – 585. doi: 10.1088/0004-637X/722/1/577 .
Dimitropoulou, M., Georgoulis, M., Isliker, H., Vlahos, L., Anastasiadis, A., Strintzi, D., Moussas, X.: 2009, The correlation of fractal structures in the photospheric and the coronal magnetic field. Astron. Astrophys. 505, 1245 – 1253. doi: 10.1051/0004-6361/200911852 .
Evertsz, C.J.G., Mandelbrot, B.B.: 1992, Self-similarity of harmonic measure on DLA. Physica A 185, 77 – 86. doi: 10.1016/0378-4371(92)90440-2 .
Falconer, D.A., Moore, R.L., Gary, G.A.: 2006, Magnetic causes of solar coronal mass ejections: Dominance of the free magnetic energy over the magnetic twist alone. Astrophys. J. 644, 1258 – 1272. doi: 10.1086/503699 .
Fragos, T., Rantsiou, E., Vlahos, L.: 2004, On the distribution of magnetic energy storage in solar active regions. Astron. Astrophys. 420, 719 – 728. doi: 10.1051/0004-6361:20034570 .
Frisch, U.: 1995, Turbulence. The Legacy of A.N. Kolmogorov, Cambridge University Press, Cambridge.
Gallagher, P.T., Phillips, K.J.H., Harra-Murnion, L.K., Keenan, F.P.: 1998, Properties of the quiet Sun EUV network. Astron. Astrophys. 335, 733 – 745.
Georgoulis, M.K.: 2005, Turbulence in the solar atmosphere: Manifestations and diagnostics via solar image processing. Solar Phys. 228, 5 – 27. doi: 10.1007/s11207-005-2513-4 .
Georgoulis, M.K., Rust, D.M.: 2007, Quantitative forecasting of major solar flares. Astrophys. J. Lett. 661, L109 – L112. doi: 10.1086/518718 .
Georgoulis, M., Kluiving, R., Vlahos, L.: 1995, Extended instability criteria in isotropic and anisotropic energy avalanches. Physica A 218, 191 – 213.
Georgoulis, M.K., Raouafi, N.E., Henney, C.J.: 2008, Automatic active-region identification and azimuth disambiguation of the SOLIS/VSM full-disk vector magnetograms. In: Howe, R., Komm, R.W., Balasubramaniam, K.S., Petrie, G.J.D. (eds.) Subsurface and Atmospheric Influences on Solar Activity CS-383, Astron. Soc. Pac., San Francisco, 107 – 114.
Georgoulis, M.K., Rust, D.M., Bernasconi, P.N., Schmieder, B.: 2002, Statistics, morphology, and energetics of Ellerman bombs. Astrophys. J. 575, 506 – 528. doi: 10.1086/341195 .
Hewett, R.J., Gallagher, P.T., McAteer, R.T.J., Young, C.A., Ireland, J., Conlon, P.A., Maguire, K.: 2008, Multiscale analysis of active region evolution. Solar Phys. 248, 311 – 322. doi: 10.1007/s11207-007-9028-0 .
Hirzberger, J., Vazquez, M., Bonet, J.A., Hanslmeier, A., Sobotka, M.: 1997, Time series of solar granulation images. I. Differences between small and large granules in quiet regions. Astrophys. J. 480, 406. doi: 10.1086/303951 .
Hurlburt, N.E., Brummel, N.H., Toomre, J.: 1995, Local-area simulations of rotating compressible convection and associated mean flows. In: Hoeksema, J.T., Domingo, V., Fleck, B., Battrick, B. (eds.) Helioseismology SP-376, ESA, Noordwijk, 245 – 248.
Janßen, K., Vögler, A., Kneer, F.: 2003, On the fractal dimension of small-scale magnetic structures in the Sun. Astron. Astrophys. 409, 1127 – 1134. doi: 10.1051/0004-6361:20031168 .
Jaynes, E.T.: 2003, Probability Theory: The Logic of Science, Cambridge University Press, Cambridge.
Kluiving, R., Pasmanter, R.A.: 1996, Stochastic selfsimilar branching and turbulence. Physica A 228, 273 – 294.
Kolmogorov, A.: 1941, The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers. Dokl. Akad. Nauk SSSR 30, 301 – 305.
Kraichnan, R.H.: 1965, Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8, 1385 – 1387. doi: 10.1063/1.1761412 .
LaBonte, B.J., Georgoulis, M.K., Rust, D.M.: 2007, Survey of magnetic helicity injection in regions producing X-class flares. Astrophys. J. 671, 955 – 963. doi: 10.1086/522682 .
Lawrence, J.K., Ruzmaikin, A.A., Cadavid, A.C.: 1993, Multifractal measure of the solar magnetic field. Astrophys. J. 417, 805. doi: 10.1086/173360 .
Leka, K.D., Barnes, G.: 2003, Photospheric magnetic field properties of flaring versus flare-quiet active regions. II. Discriminant analysis. Astrophys. J. 595, 1296 – 1306. doi: 10.1086/377512 .
Leka, K.D., Barnes, G.: 2007, Photospheric magnetic field properties of flaring versus flare-quiet active regions. IV. A statistically significant sample. Astrophys. J. 656, 1173 – 1186. doi: 10.1086/510282 .
Lites, B.W., Elmore, D.F., Streander, K.V.: 2001, The Solar-B Spectro-Polarimeter. In: Sigwarth, M. (ed.) Advanced Solar Polarimetry – Theory, Observation, and Instrumentation CS-236, Astron. Soc. Pac., San Francisco, 33 – 40.
Longcope, D.W., Fisher, G.H., Pevtsov, A.A.: 1998, Flux-tube twist resulting from helical turbulence: The sigma-effect. Astrophys. J. 507, 417 – 432. doi: 10.1086/306312 .
Mandelbrot, B.B.: 1983, The Fractal Geometry of Nature, Revised and enlarged edition, Freeman, New York.
Mason, J.P., Hoeksema, J.T.: 2010, Testing automated solar flare forecasting with 13 years of Michelson Doppler Imager magnetograms. Astrophys. J. 723, 634 – 640. doi: 10.1088/0004-637X/723/1/634 .
McAteer, R.T.J., Gallagher, P.T., Ireland, J.: 2005, Statistics of active region complexity: A large-scale fractal dimension survey. Astrophys. J. 631, 628 – 635. doi: 10.1086/432412 .
McAteer, R.T.J., Gallagher, P.T., Conlon, P.A.: 2010, Turbulence, complexity, and solar flares. Adv. Space Res. 45, 1067 – 1074. doi: 10.1016/j.asr.2009.08.026 .
Metcalf, T.R., Canfield, R.C., Hudson, H.S., Mickey, D.L., Wulser, J.P., Martens, P.C.H., Tsuneta, S.: 1994, Electric currents and coronal heating in NOAA active region 6952. Astrophys. J. 428, 860 – 866. doi: 10.1086/174295 .
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 – 811. doi: 10.1086/307050 .
Nicolis, G., Prigogine, I.: 1989, Exploring Complexity. An Introduction, Freeman, New York.
Reinard, A.A., Henthorn, J., Komm, R., Hill, F.: 2010, Evidence that temporal changes in solar subsurface helicity precede active region flaring. Astrophys. J. Lett. 710, L121 – L125. doi: 10.1088/2041-8205/710/2/L121 .
Roudier, T., Muller, R.: 1987, Structure of the solar granulation. Solar Phys. 107, 11 – 26.
Scherrer, P.H., Bogart, R.S., Bush, R.I., Hoeksema, J.T., Kosovichev, A.G., Schou, J., Rosenberg, W., Springer, L., Tarbell, T.D., Title, A., Wolfson, C.J., Zayer, I., MDI Engineering Team: 1995, The solar oscillations investigation – Michelson Doppler Imager. Solar Phys. 162, 129 – 188. doi: 10.1007/BF00733429 .
Schrijver, C.J.: 2007, A characteristic magnetic field pattern associated with all major solar flares and its use in flare forecasting. Astrophys. J. Lett. 655, L117 – L120. doi: 10.1086/511857 .
Schrijver, C.J., Zwaan, C., Balke, A.C., Tarbell, T.D., Lawrence, J.K.: 1992, Patterns in the photospheric magnetic field and percolation theory. Astron. Astrophys. 253, L1 – L4.
Schroeder, M.: 1991, Fractals, Chaos, Power Laws. Minutes from an Infinite Paradise, Freeman, New York.
Seiden, P.E., Wentzel, D.G.: 1996, Solar active regions as a percolation phenomenon. II. Astrophys. J. 460, 522. doi: 10.1086/176989 .
Vlahos, L., Georgoulis, M.K.: 2004, On the self-similarity of unstable magnetic discontinuities in solar active regions. Astrophys. J. Lett. 603, L61 – L64. doi: 10.1086/383032 .
Vlahos, L., Fragos, T., Isliker, H., Georgoulis, M.: 2002, Statistical properties of the energy release in emerging and evolving active regions. Astrophys. J. Lett. 575, L87 – L90. doi: 10.1086/342826 .
Wentzel, D.G., Seiden, P.E.: 1992, Solar active regions as a percolation phenomenon. Astrophys. J. 390, 280 – 289. doi: 10.1086/171278 .
Wheatland, M.S.: 2005, Initial test of a Bayesian approach to solar flare prediction. Publ. Astron. Soc. Aust. 22, 153 – 156. doi: 10.1071/AS04062 .
Zhou, G., Wang, J., Wang, Y., Zhang, Y.: 2007, Quasi-simultaneous flux emergence in the events of October November 2003. Solar Phys. 244, 13 – 24. doi: 10.1007/s11207-007-9032-4 .
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Solar Image Processing and Analysis
Guest Editors: J. Ireland and C.A. Young.
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Georgoulis, M.K. Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent Than Others?. Sol Phys 276, 161–181 (2012). https://doi.org/10.1007/s11207-010-9705-2
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DOI: https://doi.org/10.1007/s11207-010-9705-2