Comparison of Two Coronal Magnetic Field Models to Reconstruct a Sigmoidal Solar Active Region with Coronal Loops

Abstract

Magnetic field extrapolation is an important tool to study the three-dimensional (3D) solar coronal magnetic field which is difficult to directly measure. Various analytic models and numerical codes exist but their results often drastically differ. Thus a critical comparison of the modeled magnetic field lines with the observed coronal loops is strongly required to establish the credibility of the model. Here we compare two different non-potential extrapolation codes, a non-linear force-free field code (CESE-MHD-NLFFF) and a non-forcefree field (NFFF) code in modeling a solar active region (AR) that has a sigmoidal configuration just before a major flare erupted from the region. A 2D coronal-loop tracing and fitting method is employed to study the 3D misalignment angles between the extrapolated magnetic field lines and the EUV loops as imaged by SDO/AIA. It is found that the CESE-MHD-NLFFF code with preprocessed magnetogram performs the best, outputting a field which matches the coronal loops in the AR core imaged in AIA 94 Å with a misalignment angle of ∼ 10 • . This suggests that the CESE-MHD-NLFFF code, even without using the information of coronal loops in constraining the magnetic field, performs as good as some coronal-loop forward-fitting models. For the loops as imaged by AIA 171 Å in the outskirts of the AR, all the codes including the potential-field give comparable results of mean misalignment angle (∼ 30 • ). Thus further improvement of the codes is needed for a better reconstruction of the long loops enveloping the core region. . Three magnetic field models often used include the potential field, linear force-free field (LFFF), and nonlinear force-free field (NLFFF). All these models are derived from a basic assumption that the Lorentz force in the corona vanishes in the case of extremely low plasma β (β is the ratio of the plasma pressure to the magnetic pressure) and quasi-static equilibrium of the coronal field. Consequently the electric current J = ∇ × B must be parallel to the magnetic field, i.e., J = αB where α is called the force-free parameter. In the potential field model, α = 0; in the LFFF, α is a constant; and in the NLFFF, α is variable in space. The earliest models were based on potential field (Altschuler & Newkirk 1969;Sakurai 1982) and LFFF (Seehafer 1978) that are extrapolated from only the data of line-of-sight (LoS) component of the photospheric field since the transverse components were not measured. Now both the LoS and transverse components of the photospheric magnetic field can be measured (e.g., Hoeksema et al. 2014) and information of the electric current passing through the photosphere can derived. Nonlinear force-free field (NLFFF) reconstructions, which are based on the vector magnetograms, are more robust than those earlier models, and employ several numerical schemes

A Study of Pre-flare Solar Coronal Magnetic Fields: Magnetic Flux Ropes

“…Such difference of our results from Jing et al (2018)'s can be attributed to many factors, and we suspect that the leading one is that different coronal field reconstruction methods were used (the Wiegelmann's code was used in Jing et al (2018)). The inconsistence between different reconstruction codes applied to the real data has been extensively reported (e.g., DeRosa et al 2009;Régnier 2013;Aschwanden et al 2014;Duan et al 2017;Wiegelmann et al 2017), even though they can provide rather consistent results in some benchmark tests using idealized or artificial magnetograms. Furthermore, the computational method of decay index at the MFR's axis and the using of the maximum |T w | in the MFR as the KI parameter are also different from the analysis method in Jing et al (2018).…”

“…However, as also pointed out by the authors, such results might strongly depends on the quality or reliability of the coronal magnetic field reconstructions. Currently there are many methods available for NLFFF extrapolations from the vector magnetograms, but different methods seem to produce rather inconsistence results between each other (e.g., DeRosa et al 2009;Régnier 2013;Aschwanden et al 2014;Duan et al 2017;Wiegelmann et al 2017). Thus any results based on any single NLFFF code must be taken with cautions, and independent studies with different codes are required for a better inspection.…”

A Magnetohydrodynamic Simulation of Magnetic Null-point Reconnections in NOAA AR 12192, Initiated with an Extrapolated Non-force-free Field

“…The NLFFF can be solved analytically (in spherical polar coordinates) under the assumption of axisymmetry (Low & Lou 1990;Prasad et al 2014) but the analytical solution fails to effectively capture the complexity of an active region magnetogram, which is often non-axisymmetric. Such complexities are well replicated in NLFFF extrapolations (Duan et al 2017). Recent MHD simulations based on NLFFF extrapolations were successful in simulating the coronal dynamics leading to eruptions (Jiang et al 2013;Kliem et al 2013;Amari et al 2014;Inoue et al 2014Inoue et al , 2015Savcheva et al 2015Savcheva et al , 2016Inoue 2016).…”

Estimating the Magnetic Structure of an Erupting CME Flux Rope From AR12158 Using Data-Driven Modeling

“…In this paper we investigate the eruptive flux rope on September 12, 2014. This event has been analyzed in previous studies by Vemareddy et al (2016), Zhao et al (2016), and Duan et al (2017) by performing NLFFF extrapolation of the photospheric magnetic field. We instead apply TMFM (Pomoell et al, 2019), i.e., our simulation is fully data-driven and timedependent allowing it to model the formation and early evolution of the flux rope using photospheric vector magnetograms as its sole boundary conditions.…”