Guiding Nonlinear Force-Free Modeling Using Coronal Observations: First Results Using a Quasi-Grad-Rubin Scheme

Abstract

At present, many models of the coronal magnetic field rely on photospheric vector magnetograms, but these data have been shown to be problematic as the sole boundary information for nonlinear force-free field extrapolations. Magnetic fields in the corona manifest themselves in high-energy images (X-rays and EUV) in the shapes of coronal loops, providing an additional constraint that is not at present used as constraints in the computational domain, directly influencing the evolution of the model. This is in part due to the mathematical complications of incorporating such input into numerical models. Projection effects, confusion due to overlapping loops (the coronal plasma is optically thin), and the limited number of usable loops further complicate the use of information from coronal images. We develop and test a new algorithm to use images of coronal loops in the modeling of the solar coronal magnetic field. We first fit projected field lines with those of constant-α force-free fields to approximate the three-dimensional distribution of currents in the corona along a sparse set of trajectories. We then apply a Grad-Rubin-like iterative technique, which uses these trajectories as volume constraints on the values of α, to obtain a volume-filling nonlinear force-free model of the magnetic field, modifying a code and method presented by Wheatland. We thoroughly test the technique on known analytical and solar-like model magnetic fields previously used for comparing different extrapolation techniques and compare the results with those obtained by currently available methods relying only on the photospheric data. We conclude that we have developed a functioning method of modeling the coronal magnetic field by combining the line-of-sight component of the photospheric magnetic field with information from coronal images. Whereas we focus on the use of coronal loop information in combination with line-of-sight magnetograms, the method is readily extended to incorporate vector-magnetic data over any part of the photospheric boundary.

Flux Emergence (Theory)

“…This requires knowledge of the footpoint mapping of field lines, which either requires the 3D magnetic field to be known throughout the coronal volume and/or inference of the footpoint mapping from imaging data of coronal loops. The 3D coronal field reconstruction method of Malanushenko et al (2012) may be well-suited for this method since the method uses fitted loops from imaging data to constrain the coronal field reconstruction.…”

Global Energetics of Solar Flares. I. Magnetic Energies

“…Instead, the simple (non-dissipative) magnetic potential field was calculated, and an ad hoc value of 30% was used to estimate the free magnetic energy. In the meantime, various nonlinear force-free field (NLFFF) codes have been developed that are able to calculate the free magnetic energy directly, either using information from vector magnetic field measurements (e.g., Metcalf et al 1995Metcalf et al , 2005Bobra et al 2008;Jiao et al 1997;Guo et al 2008;Schrijver et al 2008;Thalmann et al 2008Thalmann et al , 2013, or employing tools that take advantage of the geometry of coronal loops, which supposedly trace out the "true" coronal magnetic field (Aschwanden 2013a,b,c;Aschwanden and Malanushenko 2013;Malanushenko et al 2011Malanushenko et al , 2012Malanushenko et al , 2014. Thus, the new capabilities of calculating free magnetic energies as well as their decreases during flares with high-quality HMI/SDO data, represent one important justification to investigate the global energetics of solar flares now.…”

Nonlinear Force-free Coronal Magnetic Stereoscopy

“…the assumption that the boundary data are force-free consistent is not necessary, the method uses only the line-of-sight photospheric magnetic field and not the full vector field. Malanushenko et al (2012Malanushenko et al ( , 2014 proposed a NLFF field extrapolation method, called Quasi-Grad-Rubin, which uses the line-of-sight component of the surface magnetic field and the 2D shapes of the coronal loops from a single image as constraints for their extrapolation. They tested the method with a semi-analytic solution and also applied it on observational data.…”