We test a nonlinear force-free field (NLFFF) optimization code in sphericalgeometry using an analytical solution from Low and Lou. Several tests are run,ranging from idealized cases where exact vector field data are provided on allboundaries, to cases where noisy vector data are provided on only the lowerboundary (approximating the solar problem). Analytical tests also show that theNLFFF code in the spherical geometry performs better than that in the Cartesianone when the field of view of the bottom boundary is large, say, $20^\circ\times 20^\circ$. Additionally, We apply the NLFFF model to an active regionobserved by the Helioseismic and Magnetic Imager (HMI) on board the SolarDynamics Observatory (SDO) both before and after an M8.7 flare. For eachobservation time, we initialize the models using potential field source surface(PFSS) extrapolations based on either a synoptic chart or a flux-dispersalmodel, and compare the resulting NLFFF models. The results show that NLFFFextrapolations using the flux-dispersal model as the boundary condition haveslightly lower, therefore better, force-free and divergence-free metrics, andcontain larger free magnetic energy. By comparing the extrapolated magneticfield lines with the extreme ultraviolet (EUV) observations by the AtmosphericImaging Assembly (AIA) on board SDO, we find that the NLFFF performs betterthan the PFSS not only for the core field of the flare productive region, butalso for large EUV loops higher than 50 Mm.
展开▼
