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

AbstractWe review nonlinear force-free field (NLFFF) modeling of magnetic fields in active regions. The NLFFF model (in which the electric current density is parallel to the magnetic field) is often adopted to describe the coronal magnetic field, and numerical solutions to the model are constructed based on photospheric vector magnetogram boundary data. Comparative tests of NLFFF codes on sets of boundary data have revealed significant problems, in particular associated with the inconsistency of the model and the data. Nevertheless NLFFF modeling is often applied, in particular to flare-productive active regions. We examine the results, and discuss their reliability.

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Simulating the Coronal Evolution of Bipolar Active Regions to Investigate the Formation of Flux Ropes

Solar Physics ◽

10.1007/s11207-020-01749-2 ◽

2021 ◽

Vol 296 (1) ◽

Author(s):

S. L. Yardley ◽

D. H. Mackay ◽

L. M. Green

Keyword(s):

Magnetic Field ◽

Large Scale ◽

Initial Conditions ◽

Free Field ◽

Active Regions ◽

Coronal Magnetic Field ◽

Solar Dynamics Observatory ◽

Horizontal Magnetic Field ◽

Nonlinear Force ◽

Force Free Field

AbstractThe coronal magnetic field evolution of 20 bipolar active regions (ARs) is simulated from their emergence to decay using the time-dependent nonlinear force-free field method of Mackay, Green, and van Ballegooijen (Astrophys. J. 729, 97, 2011). A time sequence of cleaned photospheric line-of-sight magnetograms, which covers the entire evolution of each AR, is used to drive the simulation. A comparison of the simulated coronal magnetic field with the 171 and 193 Å observations obtained by the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA), is made for each AR by manual inspection. The results show that it is possible to reproduce the evolution of the main coronal features such as small- and large-scale coronal loops, filaments and sheared structures for 80% of the ARs. Varying the boundary and initial conditions, along with the addition of physical effects such as Ohmic diffusion, hyperdiffusion and a horizontal magnetic field injection at the photosphere, improves the match between the observations and simulated coronal evolution by 20%. The simulations were able to reproduce the build-up to eruption for 50% of the observed eruptions associated with the ARs. The mean unsigned time difference between the eruptions occurring in the observations compared to the time of eruption onset in the simulations was found to be ≈5 hrs. The simulations were particularly successful in capturing the build-up to eruption for all four eruptions that originated from the internal polarity inversion line of the ARs. The technique was less successful in reproducing the onset of eruptions that originated from the periphery of ARs and large-scale coronal structures. For these cases global, rather than local, nonlinear force-free field models must be used. While the technique has shown some success, eruptions that occur in quick succession are difficult to reproduce by this method and future iterations of the model need to address this.

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Studying Magnetic Field Variations Accompanying the 2011 June 7 Eruptive Event, by Using Nonlinear Force-Free Field Modeling

Solar Physics ◽

10.1007/s11207-020-01613-3 ◽

2020 ◽

Vol 295 (4) ◽

Author(s):

Y. I. Egorov ◽

V. G. Fainshtein ◽

I. I. Myshyakov ◽

S. A. Anfinogentov ◽

G. V. Rudenko

Keyword(s):

Magnetic Field ◽

Free Field ◽

Eruptive Event ◽

Field Modeling ◽

Nonlinear Force ◽

Magnetic Field Variations ◽

Force Free Field

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Study of magnetic field topology of active region 12192 using an extrapolated non-force-free magnetic field

Proceedings of the International Astronomical Union ◽

10.1017/s1743921318001151 ◽

2018 ◽

Vol 13 (S340) ◽

pp. 81-82

Author(s):

A. Prasad ◽

R. Bhattacharyya ◽

Q. Hu ◽

S. S. Nayak ◽

Sanjay Kumar

Keyword(s):

Magnetic Field ◽

Active Region ◽

Free Field ◽

Coronal Magnetic Field ◽

Solar Photosphere ◽

Magnetic Field Topology ◽

Cycle 24 ◽

Magnetic Null ◽

The Magnetic Field ◽

Force Free Field

AbstractThe solar active region (AR) 12192 was one of the most flare productive region of solar cycle 24, which produced many X-class flares; the most energetic being an X3.1 flare on October 24, 2014 at 21:10 UT. Customarily, such events are believed to be triggered by magnetic reconnection in coronal magnetic fields. Here we use the vector magnetograms from solar photosphere, obtained from Heliospheric Magnetic Imager (HMI) to investigate the magnetic field topology prior to the X3.1 event, and ascertain the conditions that might have caused the flare. To infer the coronal magnetic field, a novel non-force-free field (NFFF) extrapolation technique of the photospheric field is used, which suitably mimics the Lorentz forces present in the photospheric plasma. We also highlight the presence of magnetic null points and quasi-separatrix layers (QSLs) in the magnetic field topology, which are preferred sites for magnetic reconnections and discuss the probable reconnection scenarios.

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Solar Flares and Related Coronal Magnetic Field Structures in NOAA 8100

Symposium - International Astronomical Union ◽

10.1017/s0074180900219487 ◽

2001 ◽

Vol 203 ◽

pp. 341-343

Author(s):

Y. Yan

Keyword(s):

Magnetic Field ◽

Solar Flares ◽

Free Field ◽

Coronal Magnetic Field ◽

New Technique ◽

Field Reconstruction ◽

Flare Process ◽

A New Technique ◽

Force Free Field

In this paper we describe the available methods for the non-constant-α force-free field reconstruction and study the associations between reconstructed 3-d coronal fields by a new technique and the 2B/X2 flare process from observations in AR 8100 on 4 November 1997.

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Hinode magnetic-field observations of solar flares for exploring the energy storage and trigger mechanisms

Proceedings of the International Astronomical Union ◽

10.1017/s1743921316000521 ◽

2015 ◽

Vol 11 (S320) ◽

pp. 175-178

Author(s):

Toshifumi Shimizu ◽

Satoshi Inoue ◽

Yusuke Kawabata

Keyword(s):

Magnetic Field ◽

Free Field ◽

Coronal Magnetic Field ◽

Field Configuration ◽

Optical Telescope ◽

Magnetic Field Data ◽

Trigger Mechanisms ◽

The Magnetic Field ◽

Force Free Field ◽

Chromospheric Flare

AbstractThe spectro-polarimeter in the Hinode Solar Optical Telescope (SOT) is one of the powerful instruments for the most accurate measurements of vector magnetic fields on the solar surface. The magnetic field configuration and possible candidates for flare trigger are briefly discussed with some SOT observations of solar flare events, which include X5.4/X1.3 flares on 7 March 2012, X1.2 flare on 7 January 2014 and two M-class flares on 2 February 2014. Especially, using an unique set of the Hinode and SDO data for the X5.4/X1.3 flares on 7 March 2012, we briefly reviewed remarkable properties observed in the spatial distribution of the photospheric magnetic flux, chromospheric flare ribbons, and the 3D coronal magnetic field structure inferred by non-linear force-free field modeling with the Hinode photospheric magnetic field data.

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Solar force-free magnetic fields

Living Reviews in Solar Physics ◽

10.1007/s41116-020-00027-4 ◽

2021 ◽

Vol 18 (1) ◽

Author(s):

Thomas Wiegelmann ◽

Takashi Sakurai

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Free Field ◽

Coronal Magnetic Field ◽

Electric Currents ◽

Magnetic Forces ◽

Special Cases ◽

Field Lines ◽

The Magnetic Field ◽

Force Free Field

AbstractThe structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces such as plasma pressure gradients and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relationship between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently a large area of research, as accurate measurements of the photospheric field are available from ground-based observatories such as the Synoptic Optical Long-term Investigations of the Sun and the Daniel K. Inouye Solar Telescope (DKIST) and space-born, e.g., from Hinode and the Solar Dynamics Observatory. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma.

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Chromospheric Magnetic Field: A Comparison of He i 10830 Å Observations with Nonlinear Force-free Field Extrapolation

The Astrophysical Journal ◽

10.3847/1538-4357/ab9816 ◽

2020 ◽

Vol 898 (1) ◽

pp. 32 ◽

Cited By ~ 1

Author(s):

Yusuke Kawabata ◽

Andrés Asensio Ramos ◽

Satoshi Inoue ◽

Toshifumi Shimizu

Keyword(s):

Magnetic Field ◽

Free Field ◽

Nonlinear Force ◽

Force Free Field

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An Optimization Principle for Computing Stationary MHD Equilibria with Solar Wind Flow

Solar Physics ◽

10.1007/s11207-020-01719-8 ◽

2020 ◽

Vol 295 (10) ◽

Author(s):

Thomas Wiegelmann ◽

Thomas Neukirch ◽

Dieter H. Nickeler ◽

Iulia Chifu

Keyword(s):

Magnetic Field ◽

Free Field ◽

Coronal Magnetic Field ◽

Optimization Method ◽

Field Configuration ◽

Optimization Principle ◽

Mhd Equilibria ◽

Solar Wind Flow ◽

Nonlinear Force ◽

Flow Effects

Abstract In this work we describe a numerical optimization method for computing stationary MHD equilibria. The newly developed code is based on a nonlinear force-free optimization principle. We apply our code to model the solar corona using synoptic vector magnetograms as boundary condition. Below about two solar radii the plasma $\beta $ β and Alfvén Mach number $M_{A}$ M A are small and the magnetic field configuration of stationary MHD is basically identical to a nonlinear force-free field, whereas higher up in the corona (where $\beta $ β and $M_{A}$ M A are above unity) plasma and flow effects become important and stationary MHD and force-free configuration deviate significantly. The new method allows for the reconstruction of the coronal magnetic field further outwards than with potential field, nonlinear force-free or magnetostatic models. This way the model might help to provide the magnetic connectivity for joint observations of remote sensing and in-situ instruments on Solar Orbiter and Parker Solar Probe.

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Tests and applications of nonlinear force-free field extrapolations in spherical geometry

Proceedings of the International Astronomical Union ◽

10.1017/s1743921313003190 ◽

2012 ◽

Vol 8 (S294) ◽

pp. 553-554

Author(s):

Y. Guo ◽

M. D. Ding

Keyword(s):

Magnetic Field ◽

Analytical Solution ◽

Large Scale ◽

Initial Conditions ◽

Free Field ◽

Spherical Geometry ◽

Source Surface ◽

Field Source ◽

Nonlinear Force ◽

Force Free Field

AbstractWe test a nonlinear force-free field (NLFFF) optimization code in spherical geometry with an analytical solution from Low and Lou. The potential field source surface (PFSS) model is served as the initial and boundary conditions where observed data are not available. The analytical solution can be well recovered if the boundary and initial conditions are properly handled. Next, we discuss the preprocessing procedure for the noisy bottom boundary data, and find that preprocessing is necessary for NLFFF extrapolations when we use the observed photospheric magnetic field as bottom boundaries. Finally, we apply the NLFFF model to a solar area where four active regions interacting with each other. An M8.7 flare occurred in one active region. NLFFF modeling in spherical geometry simultaneously constructs the small and large scale magnetic field configurations better than the PFSS model does.

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