Solar Flare Geometries. I. The Area Fractal Dimension

Abstract

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 area fractal dimension D 2 , also called the Hausdorff dimension, with a box-counting method, which describes the fractal area as A(L) / L D 2. 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 f) varies from near zero at the beginning of the flare to a maximum of A(t)/A f ¼ 0:65 AE 0:12 after the peak time of the flare, which corresponds to an area fractal dimension in the range of 1:0 P D 2 (t) P 1:89 AE 0:05. We find that the total EUV flux F tot (t) is linearly correlated with the fractal area A(t). From the area fractal dimension D 2 , the volume fractal dimension D 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.