6.7 Application of nonlinear force-free codes

Despite the difficulties outlined in Section 6.6 NLFFF-codes have been used to study active regions in various situations. Several studies deal with the energy content of the coronal magnetic field in active regions. Bleybel et al. (2002Jump To The Next Citation Point) studied the energy budget of AR 7912 before and after a flare on 1995 October 14 with a Grad–Rubin method and found that the magnetic energy decreased during the flare. The magnetic field lines computed from the nonlinear force-free model seem to be in reasonable agreement with a soft X-ray image from Yohkoh, as shown in the top panel in Figure 11View Image. At least the nonlinear force-free model seems to agree better with the X-ray image than a linear force-free and a potential field model shown in the center and bottom panel, respectively. R egnier et al. (2002), also using the Grad–Rubin approach, studied the non-flaring active region AR 8151 in February 1998 and found that the available free magnetic energy was not high enough to power a flare. These results are consistent which the observation in the sense that nonlinear force-free field lines reasonably agree with coronal observations and a consistent flaring activity: The particular active regions flared (not flared) when the free magnetic energy computed with NLFFF-codes was high enough (too low). A decreasing free magnetic energy during flares has been confirmed in several studies. Thalmann and Wiegelmann (2008) and Thalmann et al. (2008), using the optimization approach, found that the force-free energy before a small C-class flare (observed in active region NOAA 10960 on 2007 June 7) was 5% higher than the potential field energy. Before a large M-class flare (observed in active region NOAA 10540 in January 2004) the force-free energy exceeded the potential field energy by 60%. In a statistic study, based on 75 samples extrapolate with the optimization approach, Jing et al. (2010) found a positive correlation between free magnetic energy and the X-ray flaring index. It seems that we can trust that there is a relation between computed free energy and flaring activity, whereas the results of Section 6.6 indicate that one might not fully trust in the exact numbers of magnetic energies computed with one NLFFF-code only. Recently, Gilchrist et al. (2012) pointed out that uncertainties in the vector magnetograms likely result in underestimating the computed magnetic energy. NLFFF-codes are, however, a strong tool to guide the investigation of coronal features. Régnier and Amari (2004), Valori et al. (2012), and Sun et al. (2012) applied the Grad–Rubin, MHD-relaxation and optimization approach, respectively and found at least qualitatively a good agreement of NLFFF-models with observed sigmoid or serpentine structures.
View Image

Figure 11: Yohkoh soft X-ray image overlaid with magnetic field lines from different models. Top: nonlinear force-free; center: linear force-free; bottom: potential fields. Image reproduced by permission from Figure 8 of Bleybel et al. (2002), copyright by ESO.

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