Modeling Magnetic Field Structure of a Solar Active Region Corona using Nonlinear Force-Free Fields in Spherical Geometry

TL;DR

This study evaluates a nonlinear force-free field (NLFFF) modeling code in spherical geometry, tests its accuracy with analytical solutions, and applies it to solar active region data, demonstrating improved magnetic field extrapolation over traditional methods.

Contribution

The paper introduces an NLFFF code in spherical geometry, showing it outperforms Cartesian approaches and effectively models solar active regions before and after flares.

Findings

Spherical NLFFF performs better than Cartesian for large fields of view.

NLFFF models with flux-dispersal boundary conditions have higher free magnetic energy.

NLFFF extrapolations align more closely with EUV observations than PFSS models.

Abstract

We test a nonlinear force-free field (NLFFF) optimization code in spherical geometry using an analytical solution from Low and Lou. Several tests are run, ranging from idealized cases where exact vector field data are provided on all boundaries, to cases where noisy vector data are provided on only the lower boundary (approximating the solar problem). Analytical tests also show that the NLFFF code in the spherical geometry performs better than that in the Cartesian one 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 region observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) both before and after an M8.7 flare. For each observation time, we initialize the models using potential field source surface (PFSS) extrapolations based on either a synoptic chart or a flux-dispersal model, and compare the resulting NLFFF models. The results show that NLFFF extrapolations using the flux-dispersal model as the boundary condition have slightly lower, therefore better, force-free and divergence-free metrics, and contain larger free magnetic energy. By comparing the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly (AIA) on board SDO, we find that the NLFFF performs better than the PFSS not only for the core field of the flare productive region, but also for large EUV loops higher than 50 Mm.