Global Energetics of Solar Flares. IX. Refined Magnetic Modeling
Abstract
A more accurate analytical solution of the vertical-current approximation nonlinear force-free field (VCA3-NLFFF) model is presented that includes, besides the radial (B r ) and azimuthal (B φ ) magnetic field components, a poloidal component ({B}θ \ne 0) as well. This new analytical solution is of second-order accuracy in the divergence-freeness condition and of third-order accuracy in the force-freeness condition. We reanalyze the sample of 173 GOES M- and X-class flares observed with the Atmospheric Imaging Assembly and Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory (SDO). The new code reproduces helically twisted loops with a low winding number below the kink instability consistently, avoiding unstable, highly twisted structures of the Gold-Hoyle flux rope type. The magnetic energies agree within {E}VCA3}/{E}W=0.99+/- 0.21 with the Wiegelmann (W-NLFFF) code. The time evolution of the magnetic field reveals multiple, intermittent energy buildup and releases in most flares, contradicting both the Rosner-Vaiana model (with gradual energy storage in the corona) and the principle of timescale separation (τ flare ≪ τ storage) postulated in self-organized criticality models. The mean dissipated flare energy is found to amount to 7% ± 3% of the potential energy, or 60% ± 26% of the free energy, a result that can be used for predicting flare magnitudes based on the potential field of active regions.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- November 2019
- DOI:
- 10.3847/1538-4357/ab46c1
- arXiv:
- arXiv:1909.08672
- Bibcode:
- 2019ApJ...885...49A
- Keywords:
-
- Solar flares;
- Magnetic fields;
- Astrophysics - Solar and Stellar Astrophysics
- E-Print:
- 40. p, 13 Figs