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Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO: II. Hydrodynamic Scaling Laws and Thermal Energies View all abstracts by submitter

Markus J. Aschwanden   Submitted: 2013-08-23 12:16

In this study we measure physical parameters of the same set of 155 M and X-class solar flares observed with AIA/SDO as analyzed in Paper I, by performing a {sl differential emission measure (DEM)} analysis to determine the flare peak emission measure EM_p, peak temperature Tp, electron density np, and thermal energy Eth, in addition to the spatial scales L, areas A, and volumes V measured in Paper I. The parameter ranges for M and X-class flares are: log(EM_p)=47.0-50.5, T_p=5.0-17.8 MK, n_p=4 imes 109-9 imes 1011 cm-3, and thermal energies of Eth=1.6 imes 1028-1.1 imes 1032 erg. We find that these parameters obey the Rosner-Tucker-Vaiana (RTV) scaling law T_p^2 propto n_p L and H propto T7/2 L-2 during the peak time tp of the flare density np, when energy balance between the heating rate H and the conductive and radiative loss rates is achieved for a short instant, and thus enables the applicability of the RTV scaling law. The application of the RTV scaling law predicts powerlaw distributions for all physical parameters, which we demonstrate with numerical Monte-Carlo simulations as well as with analytical calculations. A consequence of the RTV law is also that we can retrieve the size distribution of heating rates, for which we find N(H) propto H-1.8, which is consistent with the magnetic flux distribution N(Phi) propto Phi-1.85 observed by Parnell et al. (2009) and the heating flux scaling law F_H propto H L propto B/L of Schrijver et al. (2004). The fractal-diffusive self-organized criticality model in conjunction with the RTV scaling law reproduces the observed powerlaw distributions and their slopes for all geometrical and physical parameters and can be used to predict the size distributions for other flare datasets, instruments, and detection algorithms.

Authors: Markus J. Aschwanden and Toshifumi Shimizu

Publication Status: The Astrophysical Journal 776, 132
Last Modified: 2014-03-25 16:25
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