On the reliability of the fractal dimension measure of solar magnetic features and on its variation with solar activity

Context. Several studies have investigated the fractal and multifractal nature of magnetic features in the solar photosphere and its variation with the solar magnetic activity cycle. Aims. Here we extend those studies by examining the fractal geometry of bright magnetic features at higher atmospheric levels, specifically in the solar chromosphere. We analyze structures identified in CaIIK images obtained with the Precision Solar Photometric Telescopes (PSPTs) at Osservatorio Astronomico di Roma (OAR) and Mauna Loa Solar Observatory (MLSO). Methods. Fractal dimension estimates depend on the estimator employed, the quality of the images, and the structure identification techniques used. We examine both real and simulated data and employ two different perimeter-area estimators in order to understand the sensitivity of the deduced fractal properties to pixelization and image quality. Results. The fractal dimension of bright "magnetic" features in CaIIK images ranges between values of 1.2 and 1.7 for small and large structures respectively. This size dependency largely reflects the importance of image pixelization in the measurement of small objects. The fractal dimension of chromospheric features does not show any clear systematic variation with time over the period examined, the descending phase of solar cycle 23. Conclusions. These conclusions, and the analysis of both real and synthetic images on which they are based, are important in the interpretation of previously reported results.

[1]  A. Skumanich,et al.  On the statistical description of inhomogeneities in the quiet solar atmosphere. I - Linear regression analysis and absolute calibration of multichannel observations of the Ca/+/ emission network , 1975 .

[2]  Hartmut Jürgens,et al.  Fractals for the Classroom: Part One Introduction to Fractals and Chaos , 1991 .

[3]  E. Pérez,et al.  The Fractal Dimension of Projected Clouds , 2005, astro-ph/0501573.

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

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

[6]  Jack Ireland,et al.  Statistics of Active Region Complexity: A Large-Scale Fractal Dimension Survey , 2005 .

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

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

[9]  K. L. Harvey,et al.  Magnetic and Radiative Variability of Solar Surface Structures. I. Image Decomposition and Magnetic-Intensity Mapping , 1999 .

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

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

[12]  Philippe Baveye,et al.  Influence of image resolution and thresholding on the apparent mass fractal characteristics of preferential flow patterns in field soils , 1998 .

[13]  Martin Turner,et al.  Fractal geometry in digital imaging , 1998 .

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

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

[16]  S. Krantz.  Fractal geometry , 1989 .

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

[18]  F. Berrilli,et al.  On the Geometrical Properties of the Chromospheric Network , 1998 .