6.6 Comparison of methods and the NLFFF consortium

Since 2004, a group of scientists chaired by Karel Schrijver compare, evaluate, and improve methods for the nonlinear force-free computation of coronal magnetic fields and related topics. The test cases are available at External Linkhttp://www.lmsal.com/~derosa/for_nlfff/. So far, six workshops have been organized and the consortium published four joint publications:
  1. Schrijver et al. (2006) performed blind tests on analytical force-free field models with various boundary conditions to show that in general the NLFFF algorithms perform best where the magnetic field and the electrical currents are strongest, but they are also very sensitive to the specified boundary conditions. Nevertheless, it was shown that the optimization method as proposed by Wheatland et al. (2000) and as implemented by Wiegelmann (2004) was the fastest-converging and best-performing one for this analytical test case.
  2. Metcalf et al. (2008) tested the performance of the NLFFF algorithms applied to a solar-like reference model including realistic photospheric Lorentz forces and a complex magnetic field structure. All the codes were able to recover the presence of a weakly twisted, helical flux rope. Due to the sensitivity to the numerical details, however, they were less accurate in reproducing the field connectivity and magnetic energy when applied to the preprocessed, more force-free, chromospheric-like boundary conditions. When applied to the forced, not preprocessed photospheric data the codes did not perform successfully, indicating that the consistency of the used boundary conditions is crucial for the success of the magnetic field extrapolations. It also showed that the magnetic field connection between the photosphere, chromosphere, and lower corona needs to be additionally precisely modeled.
  3. Schrijver et al. (2008Jump To The Next Citation Point) used four different codes and a variety of boundary conditions to compute 14 NLFFF models based on Hinode/SOT-SP3 data of an active region around the time of a powerful flare. When applied to this real solar data, the models produced a wide variety of magnetic field geometries, energy contents, and force-freeness. Force-free consistency criteria, like the alignment of electric currents with magnetic field lines, have been best fulfilled for computations with the Grad–Rubin approach. It was concluded that strong electrical currents in the form of an ensemble of thin strands emerge together with magnetic flux preceding the flare. The global patterns of magnetic fields are compatible with a large-scale twisted flux rope topology, and they carry energy which is large enough to power the flare and its associated CME.
  4. DeRosa et al. (2009Jump To The Next Citation Point) found that various NLFFF models differ remarkably in the field line configuration and produce different estimates of the free magnetic energy when applied to Hinode/SOT-SP data. This problem was recognized already in the first application to Hinode data in Schrijver et al. (2008) and it has been worked out that a small field-of-view vector magnetogram, which does not contain an entire active region and its surroundings, does not provide the necessary magnetic connectivity for successful NLFFF extrapolations. As visible in Figure 10View Image the stereoscopically-reconstructed loops by Aschwanden et al. (2008bJump To The Next Citation Point) do not agree well with the NLFFF models. Unfortunately, the FOV of Hinode covered only a small fraction (about 10%) of area spanned by loops reconstructed from STEREO/SECCHI images. The quantitative comparison was unsatisfactory and NLFFF models have not been better as potential fields here. In other studies NLFFF methods have shown to be superior to potential and linear force-free extrapolations (Wiegelmann et al., 2005). NLFF field lines showed in particular excellent agreement with the observed loops, when both footpoints are within the FOV of the vector magnetogram and sufficiently far away from the boundaries.
View Image

Figure 10: A series of coaligned images of AR 10953. Blue lines are stereoscopically-reconstructed loops (Aschwanden et al., 2008b). Red lines are extrapolated nonlinear force-free field lines from Hinode/SOT with MDI data outside the Hinode FOV (the dotted line). Image reproduced by permission from Figure 1 of DeRosa et al. (2009Jump To The Next Citation Point), copyright by AAS.

When presented with complete and consistent boundary conditions, NLFFF algorithms generally succeed in reproducing the test fields. However, for a well-observed dataset (a Hinode/SOT-SP vector-magnetogram embedded in MDI data) the NLFFF algorithms did not yield consistent solutions. From this study we conclude that one should not rely on a model-field geometry or energy estimates unless they match coronal observations. It was concluded that successful application to real solar data likely requires at least:

  1. Large model volumes with high resolution that accommodate most of the field-line connectivity within a region and to its surroundings.
  2. Accommodation of measurement uncertainties (in particular in the transverse field component) in the lower boundary condition.
  3. ‘Preprocessing’ of the lower-boundary vector field that approximates the physics of the photosphere-to-chromosphere interface as it transforms the observed, forced, photospheric field to a realistic approximation of the chromospheric, nearly-force-free, field.
  4. The extrapolated coronal magnetic field lines should be compared and verified by coronal observations.

In the meantime, some work has been done in reply to these conclusions. New implementations of the Grad–Rubin and optimization methods do accommodate the measurement errors; see Sections 6.2 and 6.4 for an overview and Wheatland and Régnier (2009), Wiegelmann and Inhester (2010), and Amari and Aly (2010) for the corresponding original publications. On the instrumentation side SDO/HMI provides us with full-disk measurements of the photospheric magnetic field vector, which should allow us to find suitable large model volumes. The first vector magnetograms from SDO/HMI have been released at the end of 2011 and currently research on using them for force-free extrapolations is ongoing.

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