First insights into the applicability and importance of different 3D magnetic field extrapolation approaches for studying the preeruptive conditions of solar active regions

The three-dimensional (3D) coronal magnetic field has not yet been directly observed. However, for a better understanding and prediction of magnetically driven solar eruptions, 3D models of solar active regions are required. This work aims to provide insight into the significance of different extrapolation models for analyzing the preeruptive conditions of active regions with morphological parameters in 3D. Here, we employed potential field (PF), linear force-free field (LFFF), and nonlinear force-free field (NLFFF) models and a neural network-based method integrating observational data and NLFFF physics (NF2). The 3D coronal magnetic field structure of a "flaring" (AR11166) and "flare-quiet" (AR12645) active region, in terms of their flare productivity, is constructed via the four extrapolation methods. To analyze the evolution of the field, six prediction parameters were employed throughout, from the photosphere up to the base of the lower corona. First, we find that the evolution of the adopted morphological parameters exhibits similarity across the investigated time period when considering the four types of extrapolations. Second, all the parameters exhibited preeruptive conditions not only at the photosphere but also at higher altitudes in the case of active region (AR) 11166, while three out of the six proxies also exhibited preeruptive conditions in the case of AR12645. We conclude that: (i) the combined application of several different precursor parameters is important in the lower solar atmosphere to improve eruption predictions, and (ii) to gain a quick yet reliable insight into the preflare evolution of active regions in 3D, the PF and LFFF are acceptable; however, the NF2 method is likely the more suitable option.