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Solar Flare Geometries. I. The Area Fractal Dimension View all abstracts by submitter

Markus J. Aschwanden   Submitted: 2006-11-27 16:33

In this study we investigate for the first time the fractal dimension of solar flares and find that the flare area observed in EUV wavelengths exhibits a fractal scaling. We measure the {sl area fractal dimension} D2, also called {sl Hausdorff dimension}, with a box-counting method, which describes the fractal area as A(L) propto LD_2. We apply the fractal analysis to a statistical sample of 20 GOES X- and M-class flares, including the Bastille-Day 2000-Jul-14 flare, one of the largest flares recorded in history. We find that the fractal area (normalized by the time-integrated flare area Af) varies from near zero at the beginning of the flare to a maximum of A(t)/A_f = 0.65 pm 0.12 after the peak time of the flare, which corresponds to an area fractal dimension in the range of 1.0 lapprox D_2(t) lapprox 1.89pm0.05. We find that the total EUV flux Ftot(t) is linearly correlated with the fractal area A(t). From the area fractal dimension D2, the volume fractal dimension D3 can be inferred (subject of Paper II), which is crucial to infer a realistic volume filling factor, which affects the derived electron densities, thermal energies, and cooling times of solar and stellar flares.

Authors: Markus J. Aschwanden and Pascal D. Aschwanden
Projects: TRACE

Publication Status: ApJ, subm. May 2007
Last Modified: 2007-06-06 15:47
Go to main E-Print page  Observations and Models of the Dynamical Evolution of Solar Flares  Modeling and measuring the flux reconnected and ejected by the two-ribbon flare/CME event on 7 November 2004  Edit Entry  Download Preprint  Submitter's Homepage Delete Entry 

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