A Rapid, Manual Method to Map Coronal-Loop Structures of an Active Region Using Cubic Bezier Curves and Its Applications to Misalignment Angle Analysis

A rapid and flexible manual method is described that maps individual coronal loops of a 2D EUV image as Bezier curves using only four points per loop. Using the coronal loops as surrogates of magnetic-field lines, the mapping results restrict the magnetic-field models derived from extrapolations of magnetograms to those admissible and inadmissible via a fitness parameter. We outline explicitly how the coronal loops can be employed in constraining competing magnetic-field models by transforming 2D coronal-loop images into 3D field lines. The magnetic-field extrapolations must satisfy not only the lower boundary conditions of the vector field (the vector magnetogram) but also must have a set of field lines that satisfies the mapped coronal loops in the volume, analogous to an upper boundary condition. This method uses the minimization of the misalignment angles between the magnetic-field model and the best set of 3D field lines that match a set of closed coronal loops. The presented method is an important tool in determining the fitness of magnetic-field models for the solar atmosphere. The magnetic-field structure is crucial in determining the overall dynamics of the solar atmosphere.