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Title: Nonlinear Force-free Coronal Magnetic Stereoscopy

Abstract

Insights into the 3D structure of the solar coronal magnetic field have been obtained in the past by two completely different approaches. The first approach are nonlinear force-free field (NLFFF) extrapolations, which use photospheric vector magnetograms as boundary condition. The second approach uses stereoscopy of coronal magnetic loops observed in EUV coronal images from different vantage points. Both approaches have their strengths and weaknesses. Extrapolation methods are sensitive to noise and inconsistencies in the boundary data, and the accuracy of stereoscopy is affected by the ability of identifying the same structure in different images and by the separation angle between the view directions. As a consequence, for the same observational data, the 3D coronal magnetic fields computed with the two methods do not necessarily coincide. In an earlier work (Paper I) we extended our NLFFF optimization code by including stereoscopic constrains. The method was successfully tested with synthetic data, and within this work, we apply the newly developed code to a combined data set from SDO /HMI, SDO /AIA, and the two STEREO spacecraft. The extended method (called S-NLFFF) contains an additional term that monitors and minimizes the angle between the local magnetic field direction and the orientation of themore » 3D coronal loops reconstructed by stereoscopy. We find that when we prescribe the shape of the 3D stereoscopically reconstructed loops, the S-NLFFF method leads to a much better agreement between the modeled field and the stereoscopically reconstructed loops. We also find an appreciable decrease by a factor of two in the angle between the current and the magnetic field. This indicates the improved quality of the force-free solution obtained by S-NLFFF.« less

Authors:
; ;  [1]
  1. Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany)
Publication Date:
OSTI Identifier:
22661342
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 837; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCURACY; BOUNDARY CONDITIONS; EXTRAPOLATION; MAGNETIC FIELDS; NOISE; NONLINEAR PROBLEMS; OPTIMIZATION; SOLAR CORONA; SPACE VEHICLES; STELLAR CORONAE; SUN

Citation Formats

Chifu, Iulia, Wiegelmann, Thomas, and Inhester, Bernd, E-mail: chifu@mps.mpg.de. Nonlinear Force-free Coronal Magnetic Stereoscopy. United States: N. p., 2017. Web. doi:10.3847/1538-4357/AA5B9A.
Chifu, Iulia, Wiegelmann, Thomas, & Inhester, Bernd, E-mail: chifu@mps.mpg.de. Nonlinear Force-free Coronal Magnetic Stereoscopy. United States. doi:10.3847/1538-4357/AA5B9A.
Chifu, Iulia, Wiegelmann, Thomas, and Inhester, Bernd, E-mail: chifu@mps.mpg.de. Wed . "Nonlinear Force-free Coronal Magnetic Stereoscopy". United States. doi:10.3847/1538-4357/AA5B9A.
@article{osti_22661342,
title = {Nonlinear Force-free Coronal Magnetic Stereoscopy},
author = {Chifu, Iulia and Wiegelmann, Thomas and Inhester, Bernd, E-mail: chifu@mps.mpg.de},
abstractNote = {Insights into the 3D structure of the solar coronal magnetic field have been obtained in the past by two completely different approaches. The first approach are nonlinear force-free field (NLFFF) extrapolations, which use photospheric vector magnetograms as boundary condition. The second approach uses stereoscopy of coronal magnetic loops observed in EUV coronal images from different vantage points. Both approaches have their strengths and weaknesses. Extrapolation methods are sensitive to noise and inconsistencies in the boundary data, and the accuracy of stereoscopy is affected by the ability of identifying the same structure in different images and by the separation angle between the view directions. As a consequence, for the same observational data, the 3D coronal magnetic fields computed with the two methods do not necessarily coincide. In an earlier work (Paper I) we extended our NLFFF optimization code by including stereoscopic constrains. The method was successfully tested with synthetic data, and within this work, we apply the newly developed code to a combined data set from SDO /HMI, SDO /AIA, and the two STEREO spacecraft. The extended method (called S-NLFFF) contains an additional term that monitors and minimizes the angle between the local magnetic field direction and the orientation of the 3D coronal loops reconstructed by stereoscopy. We find that when we prescribe the shape of the 3D stereoscopically reconstructed loops, the S-NLFFF method leads to a much better agreement between the modeled field and the stereoscopically reconstructed loops. We also find an appreciable decrease by a factor of two in the angle between the current and the magnetic field. This indicates the improved quality of the force-free solution obtained by S-NLFFF.},
doi = {10.3847/1538-4357/AA5B9A},
journal = {Astrophysical Journal},
number = 1,
volume = 837,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}
  • We developed a new nonlinear force-free magnetic field (NLFFF) forward-fitting algorithm based on an analytical approximation of force-free and divergence-free NLFFF solutions, which requires as input a line-of-sight magnetogram and traced two-dimensional (2D) loop coordinates of coronal loops only, in contrast to stereoscopically triangulated three-dimensional loop coordinates used in previous studies. Test results of simulated magnetic configurations and from four active regions observed with STEREO demonstrate that NLFFF solutions can be fitted with equal accuracy with or without stereoscopy, which relinquishes the necessity of STEREO data for magnetic modeling of active regions (on the solar disk). The 2D loop tracingmore » method achieves a 2D misalignment of {mu}{sub 2} = 2. Degree-Sign 7 {+-} 1. Degree-Sign 3 between the model field lines and observed loops, and an accuracy of Almost-Equal-To 1.0% for the magnetic energy or free magnetic energy ratio. The three times higher spatial resolution of TRACE or SDO/AIA (compared with STEREO) also yields a proportionally smaller misalignment angle between model fit and observations. Visual/manual loop tracings are found to produce more accurate magnetic model fits than automated tracing algorithms. The computation time of the new forward-fitting code amounts to a few minutes per active region.« less
  • We develop a nonlinear force-free field (NLFFF) extrapolation code based on the magnetohydrodynamic (MHD) relaxation method. We extend the classical MHD relaxation method in two important ways. First, we introduce an algorithm initially proposed by Dedner et al. to effectively clean the numerical errors associated with ∇ · B . Second, the multigrid type method is implemented in our NLFFF to perform direct analysis of the high-resolution magnetogram data. As a result of these two implementations, we successfully extrapolated the high resolution force-free field introduced by Low and Lou with better accuracy in a drastically shorter time. We also appliedmore » our extrapolation method to the MHD solution obtained from the flux-emergence simulation by Magara. We found that NLFFF extrapolation may be less effective for reproducing areas higher than a half-domain, where some magnetic loops are found in a state of continuous upward expansion. However, an inverse S-shaped structure consisting of the sheared and twisted loops formed in the lower region can be captured well through our NLFFF extrapolation method. We further discuss how well these sheared and twisted fields are reconstructed by estimating the magnetic topology and twist quantitatively.« less
  • Solar filaments are commonly thought to be supported in magnetic dips, in particular, in those of magnetic flux ropes (FRs). In this Letter, based on the observed photospheric vector magnetogram, we implement a nonlinear force-free field (NLFFF) extrapolation of a coronal magnetic FR that supports a large-scale intermediate filament between an active region and a weak polarity region. This result is a first, in the sense that current NLFFF extrapolations including the presence of FRs are limited to relatively small-scale filaments that are close to sunspots and along main polarity inversion lines (PILs) with strong transverse field and magnetic shear,more » and the existence of an FR is usually predictable. In contrast, the present filament lies along the weak-field region (photospheric field strength ≲ 100 G), where the PIL is very fragmented due to small parasitic polarities on both sides of the PIL and the transverse field has a low signal-to-noise ratio. Thus, extrapolating a large-scale FR in such a case represents a far more difficult challenge. We demonstrate that our CESE-MHD-NLFFF code is sufficient for the challenge. The numerically reproduced magnetic dips of the extrapolated FR match observations of the filament and its barbs very well, which strongly supports the FR-dip model for filaments. The filament is stably sustained because the FR is weakly twisted and strongly confined by the overlying closed arcades.« less
  • A study of the magnetic configuration and evolution of a long-lasting quiescent coronal sigmoid is presented. The sigmoid was observed by Hinode/XRT and Transition Region and Coronal Explorer (TRACE) between 2007 February 6 and 12 when it finally erupted. We construct nonlinear force-free field models for several observations during this period, using the flux-rope insertion method. The high spatial and temporal resolution of the X-Ray Telescope (XRT) allows us to finely select best-fit models that match the observations. The modeling shows that a highly sheared field, consisting of a weakly twisted flux rope embedded in a potential field, very wellmore » describes the structure of the X-ray sigmoid. The flux rope reaches a stable equilibrium, but its axial flux is close to the stability limit of about 5 x 10{sup 20} Mx. The relative magnetic helicity increases with time from February 8 until just prior to the eruption on February 12. We study the spatial distribution of the torsion parameter alpha in the vicinity of the flux rope, and find that it has a hollow-core distribution, i.e., electric currents are concentrated in a current layer at the boundary between the flux rope and its surroundings. The current layer is located near the bald patch separatrix surface (BPSS) of the magnetic configuration, and the X-ray emission appears to come from this current layer/BPSS, consistent with the Titov and Demoulin model. We find that the twist angle PHI of the magnetic field increases with time to about 2pi just prior to the eruption, but never reaches the value necessary for the kink instability.« less
  • At present, many models of the coronal magnetic field rely on photospheric vector magnetograms, but these data have been shown to be problematic as the sole boundary information for nonlinear force-free field extrapolations. Magnetic fields in the corona manifest themselves in high-energy images (X-rays and EUV) in the shapes of coronal loops, providing an additional constraint that is not at present used as constraints in the computational domain, directly influencing the evolution of the model. This is in part due to the mathematical complications of incorporating such input into numerical models. Projection effects, confusion due to overlapping loops (the coronalmore » plasma is optically thin), and the limited number of usable loops further complicate the use of information from coronal images. We develop and test a new algorithm to use images of coronal loops in the modeling of the solar coronal magnetic field. We first fit projected field lines with those of constant-{alpha} force-free fields to approximate the three-dimensional distribution of currents in the corona along a sparse set of trajectories. We then apply a Grad-Rubin-like iterative technique, which uses these trajectories as volume constraints on the values of {alpha}, to obtain a volume-filling nonlinear force-free model of the magnetic field, modifying a code and method presented by Wheatland. We thoroughly test the technique on known analytical and solar-like model magnetic fields previously used for comparing different extrapolation techniques and compare the results with those obtained by currently available methods relying only on the photospheric data. We conclude that we have developed a functioning method of modeling the coronal magnetic field by combining the line-of-sight component of the photospheric magnetic field with information from coronal images. Whereas we focus on the use of coronal loop information in combination with line-of-sight magnetograms, the method is readily extended to incorporate vector-magnetic data over any part of the photospheric boundary.« less