Global Energetics of Solar Flares: I. Magnetic Energies

Abstract

We present the first part of a project on the global energetics of solar flares and coronal mass ejections (CMEs) that includes about 400 M- and X-class flares observed with AIA and HMI onboard SDO. We calculate the potential energy, free energy, and the flare-dissipated magnetic energy. We calculate these magnetic parameters using two different NLFFF codes: The COR-NLFFF code uses the line-of-sight magnetic field component $B_z$ from HMI to define the potential field, and the 2D coordinates of automatically detected coronal loops in 6 coronal wavelengths from AIA to measure the helical twist of coronal loops caused by vertical currents, while the PHOT-NLFFF code extrapolates the photospheric 3D vector fields. We find agreement between the two codes in the measurement of free energies and dissipated energies within a factor of $\approx 3$. The size distributions of magnetic parameters exhibit powerlaw slopes that are approximately consistent with the fractal-diffusive self-organized criticality model. The magnetic parameters exhibit scaling laws for the nonpotential energy, $E_{np}\propto E_p^{1.02}$, for the free energy, $E_{free}\propto E_p^{1.7}$ and $E_{free}\propto B_{\phi }^{1.0}{L}^{1.5}$, for the dissipated energy, $E_{diss}\propto E_p^{1.6}$ and $E_{diss}\propto E_{free}^{0.9}$, and the energy dissipation volume, $V\propto E_{diss}^{1.2}$. The potential energies vary in the range of $E_p=1\times 10^{31}-4\times 10^{33}$ erg, while the free energy has a ratio of $E_{free}/E_p\approx 1$. The Poynting flux amounts to $F_{flare}\approx 5\times 10^8-10^{10}$ erg cm${}^{-2}$ s${}^{-1}$ during flares, which averages to $F_{AR}\approx 6\times 10^6$ erg cm${}^{-2}$ s${}^{-1}$ during the entire observation period and is comparable with the coronal heating rate requirement in active regions.

arXiv comment63 pages, 22 Figures, 4 Tables, Paper I of series on "Global Energetics of Solar Flares"

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