Abstract
Several studies indicate that fractal and multifractal parameters inferred from solar photospheric magnetic field measurements may help assessing the eruptive potential of Active Regions (ARs) and also predicting their flare activity. We further investigate this topic, by exploring the sensitivity of some parameters already used in the literature on data and methods employed for their estimation. In particular, we measured the generalized fractal dimensions D 0 and D 8, and the multifractal parameters C div and D div, on the time series of photospheric magnetograms of the flaring AR NOAA 11158 obtained with the SOHO/MDI and SDO/HMI. The observations by the latter instrument are characterized by a higher spatial and temporal resolution, as well as higher flux sensitivity, than the ones obtained from SOHO/MDI, which were widely employed in earlier studies. We found that the average and peak values of complexity parameters measured on the two data sets agree within measurement uncertainties. The temporal evolution of the parameters measured on the two data sets show rather similar trends, but the ones derived from the SOHO/MDI observations show larger and spurious variations over time than those deduced from analysis of the corresponding SDO/HMI data. We also found a larger sensitivity of these measurements to characteristics of the data analyzed than reported by earlier studies. In particular, analysis of the higher resolution and higher cadence SDO/HMI data allows us also to detect slight variations of the complexity indicators that cannot be derived from the analysis of the SOHO/MDI data. These variations occur right after the major events in the analyzed AR. They may be the signature of photospheric effects of coronal magnetic field re-arrangement.
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References
Abramenko, V.I.: 2005, Multifractal analysis of solar magnetograms. Solar Phys. 228, 29 – 42. 10.1007/s11207-005-3525-9 .
Abramenko, V., Yurchyshyn, V.: 2010, Intermittency and multifractality spectra of the magnetic field in solar active regions. Astrophys. J. 722, 122 – 130. 10.1088/0004-637X/722/1/122 .
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. 10.1086/378492 .
Baveye, P., Boast, C.W., Ogawa, S., Parlange, J.Y., Steenhuis, T.: 1998, Influence of image resolution and thresholding on the apparent mass fractal characteristics of preferential flow patterns in field soils. Water Resour. Res. 34, 2783 – 2796. 10.1029/98WR01209 .
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. 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. 10.1088/0004-637X/722/1/577 .
Couvidat, S., Rajaguru, S.P., Wachter, R., Sankarasubramanian, K., Schou, J., Scherrer, P.H.: 2012, Line-of-sight observables algorithms for the helioseismic and magnetic imager (HMI) instrument tested with interferometric bidimensional spectrometer (IBIS) observations. Solar Phys. 278, 217 – 240. 10.1007/s11207-011-9927-y .
Criscuoli, S., Rast, M.P., Ermolli, I., Centrone, M.: 2007, On the reliability of the fractal dimension measure of solar magnetic features and on its variation with solar activity. Astron. Astrophys. 461, 331 – 338. 10.1051/0004-6361:20065951 .
Criscuoli, S., Romano, P., Giorgi, F., Zuccarello, F.: 2009, Magnetic evolution of superactive regions. Complexity and potentially unstable magnetic discontinuities. Astron. Astrophys. 506, 1429 – 1436. 10.1051/0004-6361/200912044 .
Evertsz, C.J.G., Mandelbrot, B.B.: 1992, Harmonic measure around a linearly self-similar tree. J. Phys. A, Math. Gen. 25, 1781 – 1797. 10.1088/0305-4470/25/7/020 .
Georgoulis, M.K.: 2005, Turbulence in the solar atmosphere: manifestations and diagnostics via solar image processing. Solar Phys. 228, 5 – 27. 10.1007/s11207-005-2513-4 .
Georgoulis, M.K.: 2012, Are solar active regions with major flares more fractal, multifractal, or turbulent than others? Solar Phys. 276, 161 – 181. 10.1007/s11207-010-9705-2 .
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. 10.1007/s11207-007-9028-0 .
Janßen, K., Vögler, A., Kneer, F.: 2003, On the fractal dimension of small-scale magnetic structures in the Sun. Astron. Astrophys. 409, 1127 – 1134. 10.1051/0004-6361:20031168 .
Kestener, P., Conlon, P.A., Khalil, A., Fennell, L., McAteer, R.T.J., Gallagher, P.T., Arneodo, A.: 2010, Characterizing complexity in solar magnetogram data using a wavelet-based segmentation method. Astrophys. J. 717, 995 – 1005. 10.1088/0004-637X/717/2/995 .
Lawrence, J.K., Cadavid, A.C., Ruzmaikin, A.A.: 1996, On the multifractal distribution of solar magnetic fields. Astrophys. J. 465, 425. 10.1086/177430 .
Li, Y., Luhmann, J., Fisher, G., Welsch, B.: 2004, Observational evidence for velocity convergence toward magnetic neutral lines as a factor in CME initiation. J. Atmos. Solar-Terr. Phys. 66, 1271 – 1282. 10.1016/j.jastp.2004.03.017 .
Liu, Y., Hoeksema, J.T., Scherrer, P.H., Schou, J., Couvidat, S., Bush, R.I., Duvall, T.L., Hayashi, K., Sun, X., Zhao, X.: 2012, Comparison of line-of-sight magnetograms taken by the solar dynamics observatory/helioseismic and magnetic imager and solar and heliospheric observatory/Michelson doppler imager. Solar Phys. 279, 295 – 316.
Mandelbrot, B.B.: 1983, The Fractal Geometry of Nature. Freeman, New York. Revised and enlarged edition.
McAteer, R.T.J., Gallagher, P.T., Conlon, P.A.: 2010, Turbulence, complexity, and solar flares. Adv. Space Res. 45, 1067 – 1074. 10.1016/j.asr.2009.08.026 .
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. 10.1086/432412 .
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. 10.1086/307050 .
Meunier, N.: 2004, Complexity of magnetic structures: flares and cycle phase dependence. Astron. Astrophys. 420, 333 – 342. 10.1051/0004-6361:20034044 .
Norton, A.A., Graham, J.P., Ulrich, R.K., Schou, J., Tomczyk, S., Liu, Y., Lites, B.W., López Ariste, A., Bush, R.I., Socas-Navarro, H., Scherrer, P.H.: 2006, Spectral line selection for HMI: a comparison of Fe i 6173 Å and Ni i 6768 Å. Solar Phys. 239, 69 – 91. 10.1007/s11207-006-0279-y .
Romano, P., Pariat, E., Sicari, M., Zuccarello, F.: 2011, A solar eruption triggered by the interaction between two magnetic flux systems with opposite magnetic helicity. Astron. Astrophys. 525, A13. 10.1051/0004-6361/201014437 .
Sánchez, N., Alfaro, E.J., Pérez, E.: 2005, The fractal dimension of projected clouds. Astrophys. J. 625, 849 – 856. 10.1086/429553 .
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.: 1995, MDI engineering team, the solar oscillations investigation – Michelson doppler imager. Solar Phys. 162, 129 – 188. 10.1007/BF00733429 .
Scherrer, P.H., Schou, J., Bush, R.I., Kosovichev, A.G., Bogart, R.S., Hoeksema, J.T., Liu, Y., Duvall, T.L., Zhao, J., Title, A.M., Schrijver, C.J., Tarbell, T.D., Tomczyk, S.: 2012, The helioseismic and magnetic imager (HMI) investigation for the solar dynamics observatory (SDO). Solar Phys. 275, 207 – 227. 10.1007/s11207-011-9834-2 .
Schou, J., Scherrer, P.H., Bush, R.I., Wachter, R., Couvidat, S., Rabello-Soares, M.C., Bogart, R.S., Hoeksema, J.T., Liu, Y., Duvall, T.L., Akin, D.J., Allard, B.A., Miles, J.W., Rairden, R., Shine, R.A., Tarbell, T.D., Title, A.M., Wolfson, C.J., Elmore, D.F., Norton, A.A., Tomczyk, S.: 2012, Design and ground calibration of the helioseismic and magnetic imager (HMI) instrument on the solar dynamics observatory (SDO). Solar Phys. 275, 229 – 259. 10.1007/s11207-011-9842-2 .
Shibata, K., Magara, T.: 2011, Solar flares: magnetohydrodynamic processes. Living Rev. Solar Phys. 8, 6. 10.12942/lrsp-2011-6 .
Turner, M.J., Blackledge, J.M., Andrews, P.R.: 1998, Fractal Geometry in Digital Imaging. Academic Press, San Diego.
Vogelaar, M.G.R., Wakker, B.P.: 1994, Measuring the fractal structure of interstellar clouds. Astron. Astrophys. 291, 557 – 568.
Wachter, R., Schou, J., Rabello-Soares, M.C., Miles, J.W., Duvall, T.L., Bush, R.I.: 2012, Image quality of the helioseismic and magnetic imager (HMI) onboard the solar dynamics observatory (SDO). Solar Phys. 275, 261 – 284. 10.1007/s11207-011-9709-6 .
Acknowledgements
The research leading to these results has received funding from the European Union’s Seventh Programme for Research, Technological Development and Demonstration under the grant agreements eHeroes (project n 284461, www.eheroes.eu ) and SOLARNET (n 312495, www.solarnet-east.eu ). This work was also supported by the Istituto Nazionale di Astrofisica (PRIN-INAF-2010). The authors acknowledge useful discussions from Giuseppe Consolini, Aimee Norton, and the Team on Flux Emergence at ISSI, Bern.
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Ermolli, I., Giorgi, F., Romano, P. et al. Fractal and Multifractal Properties of Active Regions as Flare Precursors: A Case Study Based on SOHO/MDI and SDO/HMI Observations. Sol Phys 289, 2525–2545 (2014). https://doi.org/10.1007/s11207-014-0500-3
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DOI: https://doi.org/10.1007/s11207-014-0500-3