T. Wiegelmann

Observatoire de Paris, Lutetia Parisorum, Île-de-France, France

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Publications (162)477.66 Total impact

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    ABSTRACT: We carry out a comprehensive investigation comparing the three-dimensional magnetic field restructuring, flare energy release, and the helioseismic response, of two homologous flares, the 2011 September 6 X2.1 (FL1) and September 7 X1.8 (FL2) flares in NOAA AR 11283. In our analysis, (1) a twisted flux rope (FR) collapses onto the surface at a speed of 1.5 km/s after a partial eruption in FL1. The FR then gradually grows to reach a higher altitude and collapses again at 3 km/s after a fuller eruption in FL2. Also, FL2 shows a larger decrease of the flux-weighted centroid separation of opposite magnetic polarities and a greater change of the horizontal field on the surface. These imply a more violent coronal implosion with corresponding more intense surface signatures in FL2. (2) The FR is inclined northward, and together with the ambient fields, it undergoes a southward turning after both events. This agrees with the asymmetric decay of the penumbra observed in the peripheral regions. (3) The amounts of free magnetic energy and nonthermal electron energy released during FL1 are comparable to those of FL2 within the uncertainties of the measurements. (4) No sunquake was detected in FL1; in contrast, FL2 produced two seismic emission sources S1 and S2 both lying in the penumbral regions. Interestingly, S1 and S2 are connected by magnetic loops, and the stronger source S2 has weaker vertical magnetic field. We discuss these results in relation to the implosion process in the low corona and the sunquake generation.
    The Astrophysical Journal 11/2014; 795(2). · 6.73 Impact Factor
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    Thomas Wiegelmann, Julia K. Thalmann, Sami K. Solanki
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    ABSTRACT: This publication provides an overview of magnetic fields in the solar atmosphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also responsible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the upper solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the magnetic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes.
    10/2014;
  • Tilaye Tadesse, Thomas Wiegelmann, Peter MacNeice
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    ABSTRACT: The solar coronal magnetic field produces solar activity, including extremely energetic solar flares and coronal mass ejections (CMEs). Knowledge of the structure and evolution of the magnetic field of the solar corona is important for investigating and understanding the origins of space weather. Although the coronal field remains difficult to measure directly, there is considerable interest in accurate modeling of magnetic fields in and around sunspot regions on the Sun using photospheric vector magnetograms as boundary data. In this work, we investigate effects of the size of the domain chosen for coronal magnetic field modeling on resulting model solution. We apply spherical Optimization procedure to vector magnetogram data of Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) with four Active Region observed on 09 March 2012 at 20:55UT. The results imply that quantities like magnetic flux density, electric current density and free magnetic energy density of ARs of interest are significantly different from the corresponding quantities obtained in the same region within the wider field of view. The difference is even more pronounced in the regions where there are connections to outside the domain.
    09/2014;
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    ABSTRACT: In this paper, we present a variety of well-observed dynamic behaviors for the flaring and peripheral magnetic loops of the M6.6 class extreme limb flare that occurred on 2011 February 24 (SOL2011-02-24T07:20) from EUV observations by the Atmospheric Imaging Assembly on the Solar Dynamics Observatory and X-ray observations by RHESSI. The flaring loop motion confirms the earlier contraction-expansion picture. We find that the U-shaped trajectory delineated by the X-ray corona source of the flare roughly follows the direction of a filament eruption associated with the flare. Different temperature structures of the coronal source during the contraction and expansion phases strongly suggest different kinds of magnetic reconnection processes. For some peripheral loops, we discover that their dynamics are closely correlated with the filament eruption. During the slow rising to abrupt, fast rising of the filament, overlying peripheral magnetic loops display different responses. Two magnetic loops on the elbow of the active region had a slow descending motion followed by an abrupt successive fast contraction, while magnetic loops on the top of the filament were pushed outward, slowly being inflated for a while and then erupting as a moving front. We show that the filament activation and eruption play a dominant role in determining the dynamics of the overlying peripheral coronal magnetic loops.
    The Astrophysical Journal 07/2014; 791(2):83. · 6.73 Impact Factor
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    ABSTRACT: Magnetic fields and flows in coronal structures, for example, in gradual phases in flares, can be described by 2D and 3D magnetohydrostatic (MHS) and steady magnetohydrodynamic (MHD) equilibria. Within a physically simplified, but exact mathematical model, we study the electric currents and corresponding electric fields generated by shear flows. Starting from exact and analytically calculated magnetic potential fields, we solveid the nonlinear MHD equations self-consistently. By applying a magnetic shear flow and assuming a nonideal MHD environment, we calculated an electric field via Faraday's law. The formal solution for the electromagnetic field allowed us to compute an expression of an effective resistivity similar to the collisionless Speiser resistivity. We find that the electric field can be highly spatially structured, or in other words, filamented. The electric field component parallel to the magnetic field is the dominant component and is high where the resistivity has a maximum. The electric field is a potential field, therefore, the highest energy gain of the particles can be directly derived from the corresponding voltage. In our example of a coronal post-flare scenario we obtain electron energies of tens of keV, which are on the same order of magnitude as found observationally. This energy serves as a source for heating and acceleration of particles.
    Astronomy and Astrophysics 07/2014; 569. · 5.08 Impact Factor
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    P. Vemareddy, T. Wiegelmann
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    ABSTRACT: We study the quasi-static evolution of coronal magnetic fields constructed from the Non Linear Force Free Field (NLFFF) approximation aiming to understand the relation between the magnetic field topology and ribbon emission during an X1.5 flare in active region (AR) NOAA 11166. The flare with a quasi-elliptical, and two remote ribbons occurred on March 9, 2011 at 23:13UT over a positive flux region surrounded by negative flux at the center of the bipolar AR. Our analysis of the coronal magnetic structure with potential and NLFFF solutions unveiled the existence of a single magnetic null point associated with a fan-spine topology and is co-spatial with the hard X-ray source. The footpoints of the fan separatrix surface agree with the inner edge of the quasi-elliptical ribbon and the outer spine is linked to one of the remote ribbons. During the evolution, the slow footpoint motions stressed the fieldlines along the polarity inversion line and caused electric current layers in the corona around the fan separatrix surface. These current layers trigger magnetic reconnection as a consequence of dissipating currents, which are visible as cusped shape structures at lower heights. The reconnection process reorganised the magnetic field topology whose signatures are observed at the separatrices/QSL structure both in the photosphere and corona during the pre-to-post flare evolution. In agreement with previous numerical studies, our results suggest that the line-tied footpoint motions perturb the fan-spine system and cause null point reconnection, which eventually causes the flare emission at the footpoints of the fieldlines.
    The Astrophysical Journal 06/2014; 792(1). · 6.73 Impact Factor
  • J. T. Su, J. Jing, S. Wang, T. Wiegelmann, H. M. Wang
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    ABSTRACT: Photospheric vector magnetograms from the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory are utilized as the boundary conditions to extrapolate both nonlinear force-free and potential magnetic fields in solar corona. Based on the extrapolations, we are able to determine the free magnetic energy (FME) stored in active regions (ARs). Over 3000 vector magnetograms in 61 ARs were analyzed. We compare FME with the ARs' flare index (FI) and find that there is a weak correlation (<60%) between FME and FI. FME shows slightly improved flare predictability relative to the total unsigned magnetic flux of ARs in the following two aspects: (1) the flare productivity predicted by FME is higher than that predicted by magnetic flux and (2) the correlation between FI and FME is higher than that between FI and magnetic flux. However, this improvement is not significant enough to make a substantial difference in time-accumulated FI, rather than individual flare, predictions.
    The Astrophysical Journal 06/2014; 788(2):150. · 6.73 Impact Factor
  • J. T. Su, J. Jing, S. Wang, T. Wiegelmann, H. M. Wang
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    ABSTRACT: Photospheric vector magnetograms from Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory are utilized as the boundary conditions to extrapolate both non-linear force-free and potential magnetic fields in solar corona. Based on the extrapolations, we are able to determine the free magnetic energy (FME) stored in active regions (ARs). Over 3000 vector magnetograms in 61 ARs were analyzed. We compare FME with ARs' flare index (FI) and find that there is a weak correlation ($<60\%$) between FME and FI. FME shows slightly improved flare predictability relative to total unsigned magnetic flux of ARs in the following two aspects: (1) the flare productivity predicted by FME is higher than that predicted by magnetic flux and (2) the correlation between FI and FME is higher than that between FI and magnetic flux. However, this improvement is not significant enough to make a substantial difference in time-accumulated FI, rather than individual flare, predictions.
    05/2014;
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    ABSTRACT: We studied the temporal evolution of the magnetic topology of the active region (AR) 11158 based on the reconstructed three-dimensional magnetic fields in the corona. The non-linear force-free field extrapolation method was applied to the 12 minute cadence data obtained with the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory during 5 days. By calculating the squashing degree factor Q in the volume, the derived quasi-separatrix layers (QSLs) show that this AR has an overall topology, resulting from a magnetic quadrupole, including a hyperbolic flux tube (HFT) configuration that is relatively stable at the timescale of the flare (~1-2 hr). A strong QSL, which corresponds to some highly sheared arcades that might be related to the formation of a flux rope, is prominent just before the M6.6 and X2.2 flares, respectively. These facts indicate the close relationship between the strong QSL and the high flare productivity of AR 11158. In addition, with a close inspection of the topology, we found a small-scale HFT that has an inverse tear-drop structure above the aforementioned QSL before the X2.2 flare. It indicates the existence of magnetic flux rope at this place. Even though a global configuration (HFT) is recognized in this AR, it turns out that the large-scale HFT only plays a secondary role during the eruption. In conclusion, we dismiss a trigger based on the breakout model and highlight the central role of the flux rope in the related eruption.
    The Astrophysical Journal 05/2014; 787(1):88. · 6.73 Impact Factor
  • J. T. Su, J. Jing, S. Wang, T. Wiegelmann, H. M. Wang
    [Show abstract] [Hide abstract]
    ABSTRACT: Photospheric vector magnetograms from Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory are utilized as the boundary conditions to extrapolate both non-linear force-free and potential magnetic fields in solar corona. Based on the extrapolations, we are able to determine the free magnetic energy (FME) stored in active regions (ARs). Over 3000 vector magnetograms in 61 ARs were analyzed. We compare FME with ARs' flare index (FI) and find that there is a weak correlation ($<60\%$) between FME and FI. FME shows slightly improved flare predictability relative to total unsigned magnetic flux of ARs in the following two aspects: (1) the flare productivity predicted by FME is higher than that predicted by magnetic flux and (2) the correlation between FI and FME is higher than that between FI and magnetic flux. However, this improvement is not significant enough to make a substantial difference in time-accumulated FI, rather than individual flare, predictions.
    04/2014;
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    ABSTRACT: We studied the temporal evolution of the magnetic topology of the active region (AR) 11158 based on the reconstructed three-dimensional magnetic fields in the corona. The \nlfff\ extrapolation method was applied to the 12 minutes cadence data obtained with the \hmi\ (HMI) onboard the \sdo\ (SDO) during five days. By calculating the squashing degree factor Q in the volume, the derived quasi-separatrix layers (QSLs) show that this AR has an overall topology, resulting from a magnetic quadrupole, including an hyperbolic flux tube (HFT) configuration which is relatively stable at the time scale of the flare ($\sim 1-2$ hours). A strong QSL, which corresponds to some highly sheared arcades that might be related to the formation of a flux rope, is prominent just before the M6.6 and X2.2 flares, respectively. These facts indicate the close relationship between the strong QSL and the high flare productivity of AR 11158. In addition, with a close inspection of the topology, we found a small-scale HFT which has an inverse tear-drop structure above the aforementioned QSL before the X2.2 flare. It indicates the existence of magnetic flux rope at this place. Even though a global configuration (HFT) is recognized in this AR, it turns out that the large-scale HFT only plays a secondary role during the eruption. In final, we dismiss a trigger based on the breakout model and highlight the central role of the flux rope in the related eruption.
    04/2014;
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    ABSTRACT: Dynamic phenomena indicative of slipping reconnection and magnetic implosion were found in a time series of nonlinear force-free field (NLFFF) extrapolations for the active region 11515, which underwent significant changes in the photospheric fields and produced five C-class flares and one M-class flare over five hours on 2012 July 2. NLFFF extrapolation was performed for the uninterrupted 5 hour period from the 12 minute cadence vector magnetograms of the Helioseismic and Magnetic Imager on board the Solar Dynamic Observatory. According to the time-dependent NLFFF model, there was an elongated, highly sheared magnetic flux rope structure that aligns well with an Hα filament. This long filament splits sideways into two shorter segments, which further separate from each other over time at a speed of 1-4 km s–1, much faster than that of the footpoint motion of the magnetic field. During the separation, the magnetic arcade arching over the initial flux rope significantly decreases in height from ~4.5 Mm to less than 0.5 Mm. We discuss the reality of this modeled magnetic restructuring by relating it to the observations of the magnetic cancellation, flares, a filament eruption, a penumbra formation, and magnetic flows around the magnetic polarity inversion line.
    The Astrophysical Journal Letters 03/2014; 784(1):L13. · 6.35 Impact Factor
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    ABSTRACT: With the cylindrical equal area (CEA) projection data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO), we reconstructed the three-dimensional (3D) magnetic fields in the corona, using a non-linear force-free field (NLFFF) extrapolation method every 12 minutes during five days, to calculate the squashing degree factor Q in the volume. The results show that this AR has an hyperbolic flux tube (HFT) configuration, a typical topology of quadrupole, which is stable even during the two large flares (M6.6 and X2.2 class flares).
    IAU Symposium; 01/2014
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    ABSTRACT: Magnetic reconnection is one of the primary mechanisms for triggering solar eruptive events, but direct observation of this rapid process has been a challenge. In this Letter, using a nonlinear force-free field (NLFFF) extrapolation technique, we present a visualization of field line connectivity changes resulting from tether-cutting reconnection over about 30 minutes during the 2011 February 13 M6.6 flare in NOAA AR 11158. Evidence for the tether-cutting reconnection was first collected through multiwavelength observations and then by analysis of the field lines traced from positions of four conspicuous flare 1700 Å footpoints observed at the event onset. Right before the flare, the four footpoints are located very close to the regions of local maxima of the magnetic twist index. In particular, the field lines from the inner two footpoints form two strongly twisted flux bundles (up to ~1.2 turns), which shear past each other and reach out close to the outer two footpoints, respectively. Immediately after the flare, the twist index of regions around the footpoints diminishes greatly and the above field lines become low-lying and less twisted (<=0.6 turns), overarched by loops linking the two flare ribbons formed later. About 10% of the flux (~3 × 10^19 Mx) from the inner footpoints undergoes a footpoint exchange. This portion of flux originates from the edge regions of the inner footpoints that are brightened first. These rapid changes of magnetic field connectivity inferred from the NLFFF extrapolation are consistent with the tether-cutting magnetic reconnection model.
    The Astrophysical Journal Letters 11/2013; 778(2):L36. · 6.35 Impact Factor
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    J. K. Thalmann, S. K. Tiwari, T. Wiegelmann
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    ABSTRACT: The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region corona, has been substantiated by high-resolution observations only recently. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al. 2013 (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on vector SDO/HMI magnetograms. We deliver estimates of the free magnetic energy associated to a braided coronal structure. Our model results suggest (~100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the active-region corona being heated by field line braiding. We were able to assess the coronal free energy appropriately by using vector field measurements and attribute the lower energy estimate of CG13 to the underestimated (by a factor of 10) azimuthal field strength. We also quantify the increase of the overall twist of a flare-related flux rope which had been claimed by CG13. From our models we find that the overall twist of the flux rope increased by about half a turn within twelve minutes. Unlike another method, to which we compare our results to, we evaluate the winding of the flux rope's constituent field lines around each other purely based on their modeled coronal 3D field line geometry -- to our knowledge for the first time.
    The Astrophysical Journal 11/2013; 780(1). · 6.73 Impact Factor
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    ABSTRACT: Solar eruptive phenomena, like flares and coronal mass ejections(CMEs) are governed by magnetic fields. To describe the structure of these phenomena one needs information on the magnetic flux density and the electric current density vector components in three dimensions throughout the atmosphere. However, current spectro-polarimetric measurements typically limit the determination of the vector magnetic field only to the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field for global solar atmosphere using a nonlinear force-free field(NLFFF) extrapolation codes implemented to a synoptic maps of photospheric vector magnetic field synthesized from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) as boundary condition. Using the resulting three dimensional magnetic field, we calculate the three dimensional electric current density and free magnetic energy throughout the solar atmosphere for Carrington rotation 2124. We found that spatially, the low-lying, current-carrying core field demonstrates strong concentration of free energy in the AR core, from the photosphere to the lower corona; the coronal field becomes slightly more sheared in the lowest layer and it relaxes to the potential field configuration with height. The free energy density appears largely co-spatial with the electric current distribution.
    Solar Physics 10/2013; 289(11). · 3.26 Impact Factor
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    ABSTRACT: The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently there are several modelling techniques being used to calculate three-dimension of the field lines into the solar atmosphere. For the first time, synoptic maps of photospheric vector magnetic field synthesized from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. 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. We solve the nonlinear force-free field equations using optimization principle in spherical geometry. The resulting three-dimensional magnetic fields are used to estimate the magnetic free energy content E_{free}=E_{nlfff}-E_{pot}, i.e., the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly on board SDO. For a single Carrington rotation 2121, we find that the global NLFFF magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions.
    09/2013;
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    P Vemareddy, A Ambastha, T Wiegelmann
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    ABSTRACT: Magnetic fields in the solar corona are responsible for a wide range of phenomena. However, any direct measurements of the coronal magnetic fields are very difficult due to lack of suitable spectral lines, weak magnetic fields, and high temperatures. Therefore, one extrapolates photospheric field measurements into the corona. Owing to low coronal plasma β, we can apply a force-free model in lowest order to study the slow evolution of active region (AR) magnetic fields. On applying these models to AR 11158 and compared with coronal plasma tracers, we found that (1) the approximation of potential field to coronal structures over large length scales is a reasonable one, 2) linear force-free (LFF) assumption to AR coronal fields may not be applicable model as it assumes uniform twist over the entire AR, and 3) for modeling fields at sheared, stressed locations where energy release in the form of flares are usually observed, non-linear force free fields (NLFFF) seem to provide a good approximation. The maximum available free-energy profile shows step-wise decrease that is sufficient to power an M-class flare as observed.
    Bulletin of the Astronomical Society of India 09/2013; 41:1-12. · 0.83 Impact Factor
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    ABSTRACT: We consider a magnetic configuration consisting of an arcade structure and a detached plasmoid, resulting from a magnetic reconnection process, as is typically found in connection with solar flares. We study spontaneous current fragmentation caused by shear and vortex plasma flows. An exact analytical transformation method was applied to calculate self-consistent solutions of the nonlinear stationary MHD equations. The assumption of incompressible field-aligned flows implies that both the Alfven Mach number and the mass density are constant on field lines. We first calculated nonlinear MHS equilibria with the help of the Liouville method, emulating the scenario of a solar eruptive flare configuration with plasmoids and flare arcade. Then a Mach number profile was constructed that describes the upflow along the open magnetic field lines and implements a vortex flow inside the plasmoid. This Mach number profile was used to map the MHS equilibrium to the stationary one. We find that current fragmentation takes place at different locations within our configuration. Steep gradients of the Alfven Mach number are required, implying the strong influence of shear flows on current amplification and filamentation of the MHS current sheets. Crescent- or ring-like structures appear along the outer separatrix, butterfly structures between the upper and lower plasmoids, and strong current peaks close the lower boundary. Impressing an intrinsic small-scale structure on the upper plasmoid results in strong fragmentation of the plasmoid. Hence fragmentation of current sheets and plasmoids is an inherent property of MHD theory. Transformations from MHS into MHD steady-states deliver fine-structures needed for plasma heating and acceleration of particles and bulk plasma flows in dissipative events that are typically connected to magnetic reconnection processes in flares and coronal mass ejections.
    Astronomy and Astrophysics 06/2013; · 5.08 Impact Factor
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    J K Thalmann, S K Tiwari, T Wiegelmann
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    ABSTRACT: Photospheric magnetic vector maps from two different instruments are used to model the nonlinear force-free coronal magnetic field above an active region. We use vector maps inferred from polarization measurements of the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (HMI) and the Solar Optical Telescope's Spectropolarimeter (SP) on board Hinode. Besides basing our model calculations on HMI data, we use both SP data of original resolution and scaled down to the resolution of HMI. This allows us to compare the model results based on data from different instruments and to investigate how a binning of high-resolution data affects the model outcome. The resulting three-dimensional magnetic fields are compared in terms of magnetic energy content and magnetic topology. We find stronger magnetic fields in the SP data, translating into a higher total magnetic energy of the SP models. The net Lorentz forces of the HMI and SP lower boundaries verify their force-free compatibility. We find substantial differences in the absolute estimates of the magnetic field energy but similar relative estimates, e.g., the fraction of excess energy and of the flux shared by distinct areas. The location and extension of neighboring connectivity domains differ and the SP model fields tend to be higher and more vertical. Hence, conclusions about the magnetic connectivity based on force-free field models are to be drawn with caution. We find that the deviations of the model solution when based on the lower-resolution SP data are small compared to the differences of the solutions based on data from different instruments.

Publication Stats

2k Citations
477.66 Total Impact Points

Institutions

  • 2014
    • Observatoire de Paris
      Lutetia Parisorum, Île-de-France, France
  • 2008–2014
    • New Jersey Institute of Technology
      • Space Weather Research Laboratory
      Newark, New Jersey, United States
    • National Astronomical Observatory of Japan
      Edo, Tōkyō, Japan
  • 2004–2014
    • Max Planck Institute for Solar System Research
      Göttingen, Lower Saxony, Germany
  • 2013
    • Chinese Academy of Sciences
      • Graduate School
      Peping, Beijing, China
  • 2012
    • Stanford University
      • Department of Physics
      Palo Alto, California, United States
    • Kyung Hee University
      • School of Space Research
      Sŏul, Seoul, South Korea
  • 2010
    • Paris Diderot University
      Lutetia Parisorum, Île-de-France, France
  • 2001–2008
    • University of St Andrews
      • School of Mathematics and Statistics
      Saint Andrews, Scotland, United Kingdom
  • 1995–2006
    • Ruhr-Universität Bochum
      • Institut für Theoretische Physik IV
      Bochum, North Rhine-Westphalia, Germany