Reconstructing the local twist of coronal magnetic fields and the three-dimensional shape of the field lines from coronal loops in extreme-ultraviolet and X-ray images

Nonlinear force-free fields are the most general case of force-free fields, but the hardest to model as well. There are numerous methods of computing such fields by extrapolating vector magnetograms from the photosphere, but very few attempts have so far made quantitative use of coronal morphology. We present a method to make such quantitative use of X-ray and EUV images of coronal loops. Each individual loop is fit to a field line of a linear force-free field, allowing the estimation of the field line's twist, three-dimensional geometry, and the field strength along it. We assess the validity of such a reconstruction since the actual corona is probably not a linear force-free field, and that the superposition of linear force-free fields is generally not itself a force-free field. To do so, we perform a series of tests on nonlinear force-free fields, described in Low & Lou. For model loops we project field lines onto the photosphere. We compare several results of the method with the original field, in particular the three-dimensional loop shapes, local twist (coronal α), distribution of twist in the model photosphere, and strength of the magnetic field. We find that (1) for these trial fields, the method reconstructs twist with a mean absolute deviation of at most 15% of the range of photospheric twist, (2) heights of the loops are reconstructed with a mean absolute deviation of at most 5% of the range of trial heights, and (3) the magnitude of non-potential contribution to a photospheric field is reconstructed with a mean absolute deviation of at most 10% of the maximal value.