Global energetics of solar flares. I. Magnetic energies

Markus J. Aschwanden, Yan Xu, Ju Jing

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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 (Ep ), the nonpotential (Enp) or free energies (Efree = Enp-Ep ), and the flare-dissipated magnetic energies (Ediss). We calculate these magnetic parameters using two different NLFFF codes: the COR-NLFFF code uses the line-of-sight magnetic field component Ezfrom 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 Ep = 1 × 1031-4 × 1033 erg, while the free energy has a ratio of E Ep 1%-25%. The Poynting flux amounts to Fflare 5 × 108-1010 erg cm-2 s-1 during flares, which averages to FAR 6 × 106 erg cm-2 s-1 during the entire observation period and is comparable with the coronal heating rate requirement in active regions.

Original languageEnglish (US)
Article number50
JournalAstrophysical Journal
Issue number1
StatePublished - Dec 10 2014

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Sun: UV radiation
  • Sun: flares
  • magnetic fields


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