Tests and Applications of Nonlinear Force-Free Field Extrapolations in the Spherical Geometry

Guo Yang, guoyang@nju.edu.cn, School of Astronomy and Space Science, Nanjing University, China
Ding Mingde, dmd@nju.edu.cn, School of Astronomy and Space Science, Nanjing University

Abstract
Nonlinear force-free field (NLFFF) extrapolations provide more information for the solar magnetic field, such as free magnetic energy and highly sheared magnetic field lines, compared to potential magnetic field models. In order to study large scale magnetic field connections between different active regions, the curvature of the solar surface cannot be ignored, which asks for magnetic field modeling in the spherical geometry. We test one version of the optimization method that aims to NLFFF in the spherical geometry with Low and Lou's analytical NLFFF solutions, and compare the NLFFF with the potential field source surface (PFSS) model. Next, we discuss the procedure and meaning of the preprocessing for the noisy bottom boundary data, and find that preprocessing is necessary for NLFFF extrapolations when we use the observed photospheric magnetic field as bottom boundaries. Finally, we apply the NLFFF modeling to a solar area where four active regions interacting with each other. An M8.7 flare occurred in one active region. NLFFF modeling in the spherical geometry seems to be necessary for simultaneously constructing the small and large scale magnetic field configurations in solar active regions.