Global energetics of solar flares. I. Magnetic energies

We present the first part of a project on the global energetics of solar flares and coronal mass ejections that includes about 400 M- and X-class flares observed with Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). We calculate the potential (E_p ), the nonpotential (E_np) or free energies (Efree = E_np-E_p ), and the flare-dissipated magnetic energies (E_diss). We calculate these magnetic parameters using two different NLFFF codes: the COR-NLFFF code uses the line-of-sight magnetic field component E_zfrom HMI to define the potential field, and the two-dimensional (2D) coordinates of automatically detected coronal loops in six coronal wavelengths from AIA to measure the helical twist of coronal loops caused by vertical currents, while the PHOT-NLFFF code extrapolates the photospheric three-dimensional (3D) vector fields. We find agreement between the two codes in the measurement of free energies and dissipated energies within a factor of ≲ 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, , for the free energy, and , for the dissipated energy, and , and the energy dissipation volume, . The potential energies vary in the range of E_p = 1 × 10³¹-4 × 10³³ erg, while the free energy has a ratio of E E_p 1%-25%. The Poynting flux amounts to F_flare 5 × 10⁸-10¹⁰ erg cm^-2 s^-1 during flares, which averages to F_AR 6 × 10⁶ erg cm^-2 s^-1 during the entire observation period and is comparable with the coronal heating rate requirement in active regions.