Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO: II. Hydrodynamic Scaling Laws and Thermal Energies Markus J. Aschwanden Lockheed Martin Advanced Technology Center, Org. ADBS, Bldg.252, 3251 Hanover St., Palo Alto, CA 94304, USA; e-mail:
[email protected] and Toshifumi Shimizu Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan; e-mail:
[email protected] ABSTRACT 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 differential emission measure (DEM) analysis to determine the flare peak emission measure EMp, 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(EMp)= 47.0 50.5, T =5.0 17.8 MK, n =4 109 9 1011 cm−3, and thermal energies of E = − p − p × − × th 1.6 1028 1.1 1032 erg. We find that these parameters obey the Rosner-Tucker-Vaiana (RTV) × − × scaling law T 2 n L and H T 7/2L−2 during the peak time t of the flare density n , when p ∝ p ∝ p p 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.