Nonlinear Force‐free Field Modeling of a Solar Active Region around the Time of a Major Flare and Coronal Mass Ejection

Abstract

Solar flares and coronal mass ejections are associated with rapid changes in field connectivity and are powered by the partial dissipation of electrical currents in the solar atmosphere. A critical unanswered question is whether the currents involved are induced by the motion of preexisting atmospheric magnetic flux subject to surface plasma flows or whether these currents are associated with the emergence of flux from within the solar convective zone. We address this problem by applying state-of-the-art nonlinear force-free field (NLFFF) modeling to the highest resolution and quality vector-magnetographic data observed by the recently launched Hinode satellite on NOAA AR 10930 around the time of a powerful X3.4 flare. We compute 14 NLFFF models with four different codes and a variety of boundary conditions. We find that the model fields differ markedly in geometry, energy content, and force-freeness. We discuss the relative merits of these models in a general critique of present abilities to model the coronal magnetic field based on surface vector field measurements. For our application in particular, we find a fair agreement of the best-fit model field with the observed coronal configuration, and argue (1) that strong electrical currents emerge together with magnetic flux preceding the flare, (2) that these currents are carried in an ensemble of thin strands, (3) that the global pattern of these currents and of field lines are compatible with a large-scale twisted flux rope topology, and (4) that the $10 32 erg change in energy associated with the coronal electrical currents suffices to power the flare and its associated coronal mass ejection.

Nonlinear force-free field extrapolation of the coronal magnetic field using the data obtained by the Hinode satellite

“…For the magnetograms that are not at the central area of the Sun's disk, the projection effect and the 180°ambiguity in the SP magnetic field data also need to be resolved more carefully and accurately [Georgoulis, 2005;Metcalf et al, 2006;Wiegelmann et al, 2008;Martin et al, 2008;Leka et al, 2009]. Besides the comparison between the extrapolated field lines and the coronal loop images, and the preliminary physical analyses used in this paper, topological techniques and more physical measures should be introduced to quantitatively analyze the topological and physical properties of the extrapolated fields [Longcope, 2005;Zhao et al, 2005;DeVore and Antiochos, 2000;Bleybel et al, 2002;Zhang and Low, 2005;Régnier and Canfield, 2006;Démoulin, 2007;Thalmann et al, 2008;Schrijver et al, 2008;DeRosa et al, 2009] and their relationships to the solar eruptive events.…”

“…[20] The active region NOAA 10930 is well known for the X3.4 class flare on 13 December 2006, which was captured by Hinode satellite soon after its launch, and has been carefully studied by many authors [e.g., Zhang et al, 2007;Moon et al, 2007;Kubo et al, 2007;Su et al, 2007;Yan et al, 2007;Schrijver et al, 2008;Jing et al, 2008;Guo et al, 2008;Su et al, 2008;Wang et al, 2008;Tan et al, 2009;Yan et al, 2009;Magara, 2009;Min and Chae, 2009;Li and Zhang, 2009;Jing et al, 2010]. Dozens of vector magneto-grams of NOAA 10930 were obtained by Hinode/SOT-SP when the active region crossed the Sun's disk during the first half of December 2006 [Matsuzaki et al, 2007].…”

“…Currently, several different numerical NLFFF extrapolation methods have been developed to calculate the 3-D coronal magnetic fields from the photospheric vector magnetic field measurements. Descriptions, comparisons, and reviews of these methods can be found in the papers by Schrijver et al [2006], Metcalf et al [2008], Schrijver et al [2008], DeRosa et al [2009], Régnier [2007], and Wiegelmann [2008] and in section 5.3 of the book by Aschwanden [2005, and references therein].…”

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy

“…In this Paper III of the series we are concerned with the calculation of the free energy, generally defined by the difference of the magnetic energies between the nonpotential field and the potential field (Equation (1)). We calculate free energies from simulated data (from Paper II), from the analytical NLFFF solution of Low and Lou (1990), from active region NOAA 10930 during an X3.4 flare modeled by Schrijver et al, (2008) and , and from stereoscopically triangulated loops observed with STEREO . Section 2 describes the analytical treatment, Section 3 the application to simulated datasets and observations, Section 4 contains a discussion, and Section 5 the conclusions.…”

Magnetic reconnection and energy release on the Sun and solar-like stars

“…Besides organised motion patterns random magnetic footpoint motions (shuffling) are considered important to entangle field lines leading to the formation of small-scale current sheets. Magnetic free energy is stored relatively low in an AR 20 Mm above the photosphere and may mainly be concentrated along the magnetic inversion line in the filament channel in form of current filaments ( Figure 1; Schrijver et al 2008). This is supported by a strong connection found between high-gradient, strong-field magnetic inversion lines and flaring in active regions by Schrijver (2007), who introduced a new metric, R, the summed unsigned magnetic flux of the overlap of positive and negative magnetic field areas, where B 150 Mx cm −2 with kernels of 6 × 6 .…”