Evolution of the Nonpotential Magnetic Field in the Solar Active Region 12673 Based on a Nonlinear Force-free Modeling

Active region (AR) 12673 has produced many M-class and several X-class flares, one of which being an X9.3 flare, which is recorded as the largest solar flare in solar cycle 24. We studied the evolution of the three-dimensional flare-productive magnetic field within AR 12673, using a time series of nonlinear force-free field extrapolations of every 12 hr from 2017 September 4 00:00 UT to 6 00:00 UT. Our analysis found that three magnetic flux ropes (MFRs) formed by September 4, one of which produced the X9.3 flare on September 6. One MFR has positive magnetic twist, which is a different sign from the other two MFRs. Since the temporal evolution of the magnetic flux of the MFR accumulating the positive twist is consistent with the profile of the GOES X-ray flux well observed from September 4 to 6, we suggest that the formation of the MFR having the positive twist is closely related to the occurrence of the M-class flares, including an M5.5 flare. We further found a magnetic null in the magnetic field surrounding the MFRs, in particular above the MFR having positive twist before the M5.5 flare, which is the largest M-flare observed during this period. By comparing with Atmospheric Imaging Assembly 1600 Å images, we found that the footpoints of the overlying field lines are anchored to the area where the brightening was initially observed. Therefore, we suggest that reconnection induced by the torus instability of the positively twisted MFR at the null possibly drove the M5.5 flare.