Non-Linear Force-Free Modeling With The Aid of Coronal Observations

Currently many models of coronal magnetic field rely on vector magnetograms and other kinds of information drawn from the photosphere. Magnetic fields in the corona, however, manifest themselves in the shapes of coronal loops, providing a constraint that at the present stage receives little use due to mathematical complications of incorporating such input into the numeric models. Projection effects and the limited number of usable loops further complicate their use. We present a possible way to account for coronal loops in the models of magnetic field. We first fit the observed loops with lines of constant-alpha fields and thus approximate three-dimensional distribution of currents in the corona along a sparse set of trajectories. We then apply a Grad-Rubin-like averaging technique to obtain a volume-filling non-linear force-free model of magnetic field, modified from the method presented in Wheatland & Regnier (2009). We present thorough tests of this technique on several known magnetic fields that were previously used for comparing different extrapolation techniques (Schrijver et. al., 2006; Metcalf et. al., 2008; Schrijver et. al., 2008; DeRosa et. al., 2009), as well as on solar data and compare the results with those obtained by the currently developed methods that rely completely on the photospheric data.