Statistics of Active Region Complexity: A Large-Scale Fractal Dimension Survey

A quantification of the magnetic complexity of active regions using a fractal dimension measure is presented. This fully automated approach uses full-disk MDI magnetograms of active regions from a large data set (2742 days of the SOHO mission, 9342 active region images) to compare the calculated fractal dimension of each region to both its Mount Wilson classification and flare rate. Each Mount Wilson class exhibits a similar fractal dimension frequency distribution, possibly suggesting a self-similar nature of all active regions. Solar flare productivity exhibits an increase in both the frequency and GOES X-ray magnitude of flares from regions with higher fractal dimension. Specifically, a lower threshold fractal dimension of 1.2 and 1.25 exists as a necessary, but not sufficient, requirement for an active region to produce M- and X-class flares, respectively, within 24 hr of the observation.

[1]  Craig E. Deforest,et al.  On Re-sampling of Solar Images , 2004 .

[2]  E. Lu.  The Statistical Physics of Solar Active Regions and the Fundamental Nature of Solar Flares , 1995 .

[3]  R. Muller,et al.  Structure of the solar granulation , 1986 .

[4]  Arnold Hanslmeier,et al.  Time Series of Solar Granulation Images. I. Differences between Small and Large Granules in Quiet Regions , 1997 .

[5]  Philip R. Goode,et al.  Scaling Behavior of Structure Functions of the Longitudinal Magnetic Field in Active Regions on the Sun , 2002 .

[6]  Philip R. Goode,et al.  Signature of an Avalanche in Solar Flares as Measured by Photospheric Magnetic Fields , 2003 .

[7]  F. Kneer,et al.  On the fractal dimension of small-scale magnetic structures in the Sun , 2003 .

[8]  Harold Zirin,et al.  The Dependence of Large Flare Occurrence on the Magnetic Structure of Sunspots , 2000 .

[9]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[10]  T. Berger,et al.  Weak-Field Magnetogram Calibration using Advanced Stokes Polarimeter Flux Density Maps – II. SOHO/MDI Full-Disk Mode Calibration , 2003 .

[11]  A. Ruzmaikin,et al.  On the Multifractal Distribution of Solar Magnetic Fields , 1996 .

[12]  C. Schrijver,et al.  Percolation theory and the geometry of photospheric magnetic flux concentrations , 1993 .

[13]  Jack Ireland,et al.  Automated Boundary-extraction And Region-growing Techniques Applied To Solar Magnetograms , 2005 .

[14]  N. Meunier.  Complexity of magnetic structures: Flares and cycle phase dependence , 2004 .

[15]  D. Hathaway,et al.  EVALUATION OF TWO FRACTAL METHODS FOR MAGNETOGRAM IMAGE ANALYSIS , 1997 .

[16]  C. J. Wolfson,et al.  The Solar Oscillations Investigation - Michelson Doppler Imager , 1995 .

[17]  P. McIntosh.  The classification of sunspot groups , 1990 .

[18]  Manolis K. Georgoulis,et al.  Statistics, Morphology, and Energetics of Ellerman Bombs , 2002 .

[19]  J. Lawrence.  Diffusion of magnetic flux elements on a fractal geometry , 1991 .

[20]  E. Wiehr,et al.  A New Algorithm for Pattern Recognition and its Application to Granulation and Limb Faculae , 2001 .

[21]  George E. Hale,et al.  The Magnetic Polarity of Sun-Spots , 1919 .

[22]  M. Wheatland.  A Bayesian Approach to Solar Flare Prediction , 2004, astro-ph/0403613.

[23]  A. Ruzmaikin,et al.  MULTIFRACTAL MODELS OF SMALL-SCALE SOLAR MAGNETIC FIELDS , 1994 .

[24]  N. Meunier.  Fractal Analysis of Michelson Doppler Imager Magnetograms: A Contribution to the Study of the Formation of Solar Active Regions , 1999 .

[25]  G. Barnes,et al.  Photospheric Magnetic Field Properties of Flaring versus Flare-quiet Active Regions. II. Discriminant Analysis , 2003 .

[26]  P. Démoulin,et al.  How are Emerging Flux, Flares and CMEs Related to Magnetic Polarity Imbalance in Midi Data? , 2003, astro-ph/0304092.

[27]  Robert C. Hilborn,et al.  Chaos and Nonlinear Dynamics , 2000 .

[28]  N. Meunier.  Statistical properties of magnetic structures: Their dependence on scale and solar activity , 2003 .

[29]  C. Schrijver,et al.  Anomalous Diffusion of Magnetic Elements across the Solar Surface , 1993 .

[30]  Alexander Ruzmaikin,et al.  Multifractal measure of the solar magnetic field , 1993 .

[31]  T. Fragos,et al.  On the distribution of magnetic energy storage in solar active regions , 2004 .