A New Method for Coronal Magnetic Field Reconstruction

A precise way of coronal magnetic field reconstruction (extrapolation) is an indispensable tool for understanding of various solar activities. A variety of reconstruction codes have been developed so far and are available to researchers nowadays, but they more or less bear this and that shortcoming. In this paper, a new efficient method for coronal magnetic field reconstruction is presented. The method imposes only the normal components of magnetic field and current density at the bottom boundary to avoid the overspecification of the reconstruction problem, and employs vector potentials to guarantee the divergence-freeness. In our method, the normal component of current density is imposed, not by adjusting the tangential components of A, but by adjusting its normal component. This allows us to avoid a possible numerical instability that on and off arises in codes using A. In real reconstruction problems, the information for the lateral and top boundaries is absent. The arbitrariness of the boundary conditions imposed there as well as various preprocessing brings about the diversity of resulting solutions. We impose the source surface condition at the top boundary to accommodate flux imbalance, which always shows up in magnetograms. To enhance the convergence rate, we equip our code with a gradient-method type accelerator. Our code is tested on two analytical force-free solutions. When the solution is given only at the bottom boundary, our result surpasses competitors in most figures of merits devised by Schrijver et al. (2006). We have also applied our code to a real active region NOAA 11974, in which two M-class flares and a halo CME took place. The EUV observation shows a sudden appearance of an erupting loop before the first flare. Our numerical solutions show that two entwining flux tubes exist before the flare and their shackling is released after the CME with one of them opened up. We suggest that the erupting loop is created by magnetic reconnection between two entwining flux tubes and later appears in the coronagraph as the major constituent of the observed CME.