Coronal Magnetic Field Extrapolation and Topological Analysis of Fine-Scale Structures during Solar Flare Precursors

Magnetic field plays an important role in various solar eruptions like flares, coronal mass ejections, etc. The formation and evolution of characteristic magnetic field topology in solar eruptions are critical problems that will ultimately help us understand the origination of these eruptions in the solar source regions. With the development of advanced techniques and instruments, observations with higher resolutions in different wavelengths and fields of view have provided more quantitative information for finer structures. So it is essential to improve our method to study the magnetic field topology in the solar source regions by taking advantage of high-resolution observations. In this study, we employ a nonlinear force-free field (NLFFF) extrapolation method based on a nonuniform grid setting for an M-class flare eruption event (SOL2015-06-22T17:39) with embedded magnetograms from the Solar Dynamics Observatory (SDO) and the Goode Solar Telescope (GST). The extrapolation results employing the embedded magnetogram for the bottom boundary are obtained by maintaining the native resolutions of the corresponding GST and SDO magnetograms. We compare the field line connectivity with the simultaneous GST/H$\alpha$ and SDO/AIA observations for fine-scale structures associated with precursor brightenings. Then we perform a topological analysis of the field line connectivity corresponding to fine-scale magnetic field structures based on the extrapolation results. The results indicate that by combining the high-resolution GST magnetogram with a larger HMI magnetogram, the derived magnetic field topology is consistent with a scenario of magnetic reconnection among sheared field lines across the main polarity inversion line during solar flare precursors.