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Solar Flare Geometries. II. The Volume Fractal Dimension View all abstracts by submitter

Markus J. Aschwanden   Submitted: 2007-06-06 15:50

Based on the area fractal dimension D2 of solar flares measured in Paper I, we carry out modeling of the 3D flare volume here and derive an analytical relation between the volume fractal scaling V(L) propto LD_3 and the area fractal scaling A(L) propto LD_2. The 3D volume model captures a flare arcade with a variable number of flare loops and its fractal structure is not isotropic, but consists of aligned 1D substructures. The analytical model predicts the scaling of the area filling factor q_A(nloop) and volumetric filling factor q_V(nloop) as a function of the number of loops nloop, and allows to predict the volume filling factor q_V(q_A) and volume fractal dimension D_3(D_2) from the observationally measured parameters qA and D2. We corroborate the analytical model also with numerical simulations. We apply this fractal model to the 20 flares analyzed in Paper I and find maximum volume filling factors with a median range of q_Vapprox 0.03-0.09 (assuming solid filling for loop widths of lapprox 1 Mm). The fractal nature of the flare volume has important consequences for correcting electron densities determined from flare volume emission measures and density-dependent physical quantities, such as the thermal energy or radiative cooling time. The fractal scaling has also far-reaching consequences for frequency distributions and scaling laws of solar and stellar flares.

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

Publication Status: Subm. to ApJ, (June 6, 2007)
Last Modified: 2007-06-07 12:37
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