Solar Flare Geometries. I. The Area Fractal Dimension

• Published in: The Astrophysical journal 2008-02, Vol.674 (1), p.530-543
• Main Authors: Aschwanden, Markus J, Aschwanden, Pascal D
• Format: Article
• Language: English
• Subjects: Astronomy; Earth, ocean, space; Exact sciences and technology
• ISSN: 0004-637X; 1538-4357
• DOI: 10.1086/524371

In this study we investigate for the first time the fractal dimension of solar flares and findthat the flare area observed in EUV wavelengths exhibits a fractal scaling. We measure the area fractal dimension D sub(2), also called the Hausdorff dimension, with a box-counting method, which describes the fractal area as A(L) proportional to L super(D1). We apply the fractal analysis to a statistical sample of 20 GOES X- and M-class flares, Including the Bastille Day 2000 July 14 flare, one of the largest flares ever recorded. We find that the fractal area (normalized by the time-integrated flare area A integral of ) varies from near zero at the beginning of the flare to a maximum of A(l)/A integral of = o.65 plus or minus 0.12 after the peak time of the fiare, which corresponds to an area fractal dimension in the range of 1.0 [unk] D sub(2)(l) [unk] 1.89 plus or minus 0.05, we find that the total EUV flux F [unk] (l) is linearly correlated with the fractal area A(l). From the area fractal dimension D sub(2), the volume fractal dimension D sub(3) can be inferred (subject of Paper II), which is crucial to inferring a realistic volume filling factor, which affects the derived electron densities, thermal energies, and cooling times of solar and stellar flares.