Preprocessing of Vector Magnetograph Data for a Nonlinear Force-Free Magnetic Field Reconstruction

Wiegelmann, T.; Inhester, B.; Sakurai, Takashi

doi:10.1007/s11207-006-2092-z

Cited by 408 publications

(384 citation statements)

References 28 publications

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“…The 180 • ambiguity is removed by the minimum energy method (Leka et al 2009). We first pre-process the vector magnetic field data to remove the magnetic force and torque (Wiegelmann et al 2006). We then correct for projection effects and transform the line-of-sight and transverse components of the vector magnetic field to the heliographic components as described in Gary & Hagyard (1990).…”

Section: Data Analysis and Resultsmentioning

confidence: 99%

Understanding the white-light flare on 2012 March 9: evidence of a two-step magnetic reconnection

Hao¹,

Guo²,

Dai³

et al. 2012

A&A

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Aims. We attempt to understand the white-light flare (WLF) that was observed on 2012 March 9 with a newly constructed multiwavelength solar telescope called the Optical and Near-infrared Solar Eruption Tracer (ONSET). Methods. We analyzed WLF observations in radio, Hα, white-light, ultraviolet, and X-ray bands. We also studied the magnetic configuration of the flare via the nonlinear force-free field (NLFFF) extrapolation and the vector magnetic field observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). Results. Continuum emission enhancement clearly appeared at the 3600 Å and 4250 Å bands, with peak contrasts of 25% and 12%, respectively. The continuum emission enhancement closely coincided with the impulsive increase in the hard X-ray emission and a microwave type III burst at 03:40 UT. We find that the WLF appeared at one end of either the sheared or twisted field lines or both. There was also a long-lasting phase in the Hα and soft X-ray bands after the white-light emission peak. In particular, a second, yet stronger, peak appeared at 03:56 UT in the microwave band. Conclusions. This event shows clear evidence that the white-light emission was caused by energetic particles bombarding the lower solar atmosphere. A two-step magnetic reconnection scenario is proposed to explain the entire process of flare evolution, i.e., the firststep magnetic reconnection between the field lines that are highly sheared or twisted or both, and the second-step one in the current sheet, which is stretched by the erupting flux rope. The WLF is supposed to be triggered in the first-step magnetic reconnection at a relatively low altitude.

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Section: Data Analysis and Resultsmentioning

confidence: 99%

Understanding the white-light flare on 2012 March 9: evidence of a two-step magnetic reconnection

Hao¹,

Guo²,

Dai³

et al. 2012

A&A

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“…The energy values and their relative errors therefore vary continuously as a function of the preprocessing parameters, quite independently of the particular extrapolation method that is employed (see, e.g., Metcalf et al 2008). No unequivocal method is available in order for determining the best parameters to use (see, e.g., Wiegelmann et al 2006Wiegelmann et al , 2012Fuhrmann et al 2011), which leaves energy estimations subjected to uncomfortable arbitrariness.…”

Section: Role Of Small Scales and Preprocessingmentioning

confidence: 99%

Accuracy of magnetic energy computations

Valori

Démoulin

Pariat

et al. 2013

A&A

118

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Context. For magnetically driven events, the magnetic energy of the system is the prime energy reservoir that fuels the dynamical evolution. In the solar context, the free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. A trustworthy estimation of the magnetic energy is therefore needed in three-dimensional (3D) models of the solar atmosphere, e.g., in coronal fields reconstructions or numerical simulations. Aims. The expression of the energy of a system as the sum of its potential energy and its free energy (Thomson's theorem) is strictly valid when the magnetic field is exactly solenoidal. For numerical realizations on a discrete grid, this property may be only approximately fulfilled. We show that the imperfect solenoidality induces terms in the energy that can lead to misinterpreting the amount of free energy present in a magnetic configuration. Methods. We consider a decomposition of the energy in solenoidal and nonsolenoidal parts which allows the unambiguous estimation of the nonsolenoidal contribution to the energy. We apply this decomposition to six typical cases broadly used in solar physics. We quantify to what extent the Thomson theorem is not satisfied when approximately solenoidal fields are used. Results. The quantified errors on energy vary from negligible to significant errors, depending on the extent of the nonsolenoidal component of the field. We identify the main source of errors and analyze the implications of adding a variable amount of divergence to various solenoidal fields. Finally, we present pathological unphysical situations where the estimated free energy would appear to be negative, as found in some previous works, and we identify the source of this error to be the presence of a finite divergence. Conclusions. We provide a method of quantifying the effect of a finite divergence in numerical fields, together with detailed diagnostics of its sources. We also compare the efficiency of two divergence-cleaning techniques. These results are applicable to a broad range of numerical realizations of magnetic fields.

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“…(1) only to the accuracy of the finite-difference scheme used in the relaxation, it is necessary to quantify the compatibility of their magnetograms with the force-free hypothesis implicit in the extrapolation method. For this purpose, we use normalized integral averages of flux, force, and torque in the lower boundary as defined in Wiegelmann et al (2006b), which vanish for perfect compatibility. These metrics, reported in Table 2, show that the flux imbalance is negligible and that the residual force and torque values remain small, even for the unstable case.…”

Section: Test Equilibriamentioning

confidence: 99%

“…Therefore, in the following we do not need to consider deviations from force-freeness in the photosphere, the ambiguity of the transverse field direction, noise, and insufficient resolution, all of which are associated with measured magnetograms. Attempts to deal with some of these problems are discussed, e.g., in McClymont et al (1997), Amari et al (1997), Wiegelmann et al (2006b), Fuhrmann et al (2007), Metcalf et al (2008), Wiegelmann et al (2008), Schrijver et al (2008a), andDeRosa et al (2009).…”

Section: Introductionmentioning

confidence: 99%

Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions

Valori¹,

Kliem

Török³

et al. 2010

A&A

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We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and Démoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version with a parabolic current density profile is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade -"hyperbolic flux tube" and "bald patch separatrix surface" -are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy of reconstruction is also addressed, confirming that the initial field that best matches the external potential field of the model quite naturally leads to the best reconstruction. Extrapolating the magnetogram of a Titov-Démoulin equilibrium in the unstable range of parameter space yields a sequence of two opposing evolutionary phases, which clearly indicate the unstable nature of the configuration: a partial buildup of the flux rope with rising free energy is followed by destruction of the rope, losing most of the free energy.

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Preprocessing of Vector Magnetograph Data for a Nonlinear Force-Free Magnetic Field Reconstruction

Cited by 408 publications

References 28 publications

Understanding the white-light flare on 2012 March 9: evidence of a two-step magnetic reconnection

Understanding the white-light flare on 2012 March 9: evidence of a two-step magnetic reconnection

Accuracy of magnetic energy computations

Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions

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