Global Energetics of Solar Flares. IX. Refined Magnetic Modeling

Abstract

A more accurate analytical solution of the {\sl vertical-current approximation nonlinear force-free field (VCA3-NLFFF)} model is presented that includes besides the radial $(B_r)$ and the azimuthal $(B_{\phi })$ magnetic field components a poloidal component $(B_{\theta }\ne 0)$ also. 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 re-analyze the sample of 173 GOES M- and X-class flares observed with the {\sl Atmospheric Imaging Assembly (AIA)} and {\sl Helioseismic and Magnetic Imager (HMI)} onboard the {\sl 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 $E_{VCA3}/E_W=0.99\pm 0.21$ with the Wiegelmann (W-NLFFF) code. The time evolution of the magnetic field reveals multiple, intermittent energy build-up and releases in most flares, contradicting both the Rosner-Vaiana model (with gradual energy storage in the corona) and the principle of time scale separation (${\tau }_{flare}\ll {\tau }_{storage}$) postulated in self-organized criticality models. The mean dissipated flare energy is found to amount to $7\%\pm 3\%$ of the potential energy, or $60\%\pm 26\%$ of the free energy, a result that can be used for predicting flare magnitudes based on the potential field of active regions.

arXiv comment40. p, 13 Figs

References in corpus (46)

• Torus instability
• Global Energetics of Thirty-Eight Large Solar Eruptive Events
• Ideal kink instability of a magnetic loop equilibrium
• Optimization code with weighting function for the reconstruction of coronal magnetic fields
• Preprocessing of vector magnetograph data for a non-linear force-free magnetic field reconstruction
• Evolution of Magnetic Field and Energy in A Major Eruptive Active Region Based on SDO/HMI Observation
• Solar Flare Prediction Using SDO/HMI Vector Magnetic Field Data with a Machine-Learning Algorithm
• A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953
• Toward Reliable Benchmarking of Solar Flare Forecasting Methods
• 25 Years of Self-Organized Criticality: Solar and Astrophysics
• A Comparison of Flare Forecasting Methods, I: Results from the "All-Clear" Workshop
• Solar Flare Prediction Model with Three Machine-Learning Algorithms Using Ultraviolet Brightening and Vector Magnetogram
• Global Energetics of Solar Flares: V. Energy Closure in Flares and Coronal Mass Ejections
• How to optimize nonlinear force-free coronal magnetic field extrapolations from SDO/HMI vector magnetograms?
• Predicting Coronal Mass Ejections Using Machine Learning Methods
• Catastrophe versus instability for the eruption of a toroidal solar magnetic flux rope
• A Statistical Fractal-Diffusive Avalanche Model of a Slowly-Driven Self-Organized Criticality System
• Flare Prediction Using Photospheric and Coronal Image Data
• Global Energetics of Solar Flares: II. Thermal Energies
• Global Energetics of Solar Flares: I. Magnetic Energies
• Investigating the Magnetic Imprints of Major Solar Eruptions with SDO/HMI High-Cadence Vector Magnetograms
• Global Energetics of Solar Flares: III. Non thermal Energies
• The Magnetic Field of Active Region 11158 During the 2011 February 12-17 Flares : Differences between Photospheric Extrapolation and Coronal Forward-Fitting Methods
• On the extrapolation of magneto-hydro-static equilibria on the sun
• Force-free field modeling of twist and braiding-induced magnetic energy in an active-region corona
• First 3D Reconstructions of Coronal Loops with the STEREO A+B Spacecraft: IV. Magnetic Modeling with Twisted Force-Free Fields
• Nonlinear Force-Free Magnetic Field Fitting to Coronal Loops with and without Stereoscopy
• The Vertical Current Approximation Nonlinear Force-Free Field Code - Description, Performance Tests, and Measurements of Magnetic Energies Dissipated in Solar Flares
• A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. I. Theory
• Global Energetics of Solar Flares: IV. Coronal Mass Ejection Energetics
• Bootstrapping the Coronal Magnetic Field with STEREO: I. Unipolar Potential Field Modeling
• Magneto-static modelling from SUNRISE/IMaX: Application to an active region observed with SUNRISE II
• On the reliability of magnetic energy and helicity computations based on nonlinear force-free coronal magnetic field models
• The nonpotentiality of coronae of solar active regions, the dynamics of the surface magnetic field, and the potential for large flares
• Predictive Capabilities of Avalanche Models for Solar Flares
• Predicting Solar Flares by Data Assimilation in Avalanche Models. I. Model Design and Validation
• Tracing the Chromospheric and Coronal Magnetic Field with AIA, IRIS, IBIS, and ROSA Data
• Global Energetics of Solar Flares: VIII. The Low-Energy Cutoff
• A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. II. Numeric Code and Tests
• A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy
• Magnetic Energy Dissipation during the 2014 March 29 Solar Flares
• Towards a Quantitative Comparison of Magnetic Field Extrapolations and Observed Coronal Loops
• Blind Stereoscopy of the Coronal Magnetic Field
• Time-energy correlations in solar flare occurrence
• Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops
• Global Energetics of Solar Flares: VII. Aerodynamic Drag in Coronal Mass Ejections

Cited by in corpus (9)

• Solar Force-free Magnetic Fields
• Is the High-Resolution Coronal Imager Resolving Coronal Strands? Results from AR 12712
• Torsional Alfvénic Oscillations Discovered in the Magnetic Free Energy During Solar Flares
• Global Energetics of Solar Flares. XII. Energy Scaling Laws
• Estimation of Key Sunquake Parameters through Hydrodynamic Modeling and Cross-Correlation Analysis
• Global Energetics of Solar Flares. XI. Flare Magnitude Predictions of the GOES-Class
• Non-Stationary Fast-Driven Self-Organized Criticality in Solar Flares
• Global Energetics of Solar Flares: X. Petschek Reconnection Rate and Alfven Mach Number of Magnetic Reconnection Outflows
• An exact analytical solution for the weakly magnetized flow around an axially symmetric paraboloid, with application to magnetosphere models