A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953

Abstract

Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, forcefree vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this article, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate the three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems.

Three-Dimensional Nonlinear Force-Free Field Reconstruction of Solar Active Region 11158 by Direct Boundary Integral Equation

“…Figure 10 from bottom up. These values demonstrate the deviation from the force-freeness along these loops, which are quite good with a factor of about two smaller than those given by other NLFFF models yielding overall misalignment angles of 24 DeRosa et al 2009) and at the same order as a forward-fitting model using stereoscopically reconstructed loops as constraints (Sandman and Aschwanden 2011). G12, G13, and G14 consist of a series of large coronal loops which are open to the outside of the computing region (see Figure 11).…”

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

“…For the magnetograms that are not at the central area of the Sun's disk, the projection effect and the 180°ambiguity in the SP magnetic field data also need to be resolved more carefully and accurately [Georgoulis, 2005;Metcalf et al, 2006;Wiegelmann et al, 2008;Martin et al, 2008;Leka et al, 2009]. Besides the comparison between the extrapolated field lines and the coronal loop images, and the preliminary physical analyses used in this paper, topological techniques and more physical measures should be introduced to quantitatively analyze the topological and physical properties of the extrapolated fields [Longcope, 2005;Zhao et al, 2005;DeVore and Antiochos, 2000;Bleybel et al, 2002;Zhang and Low, 2005;Régnier and Canfield, 2006;Démoulin, 2007;Thalmann et al, 2008;Schrijver et al, 2008;DeRosa et al, 2009] and their relationships to the solar eruptive events.…”

“…[44] Another consistency test is to check to what extent the values of a match between positive polarity and negative polarity foot points of the reconstructed field lines [DeRosa et al, 2009]. By using the extrapolated 3-D magnetic fields, the value of a at a given field point in the modeling box can be computed through the following equation:…”

“…The current density values of the three extrapolated fields were calculated in the modeling box 168 × 88 × 30. Let L z represent the height of the modeling volume, by averaging the magnitude of the current density vertically [DeRosa et al, 2009],…”

“…The Hinode satellite, which was formerly called Solar-B and was launched in September 2006, can obtain high-quality photospheric vector magnetograms of solar active regions by SOT-SP instrument, and the simultaneous coronal loop images of the same active regions in soft X-ray band by the X-Ray Telescope (XRT) Kano et al, 2008] as well as in extreme ultraviolet band by the EUV Imaging Spectrometer (EIS) [Culhane et al, 2007]. These advantages makes the data of Hinode be valuable for NLFFF extrapolation studies DeRosa et al, 2009].…”