Variation of Magnetic Flux Ropes through Major Solar Flares

It remains unclear how solar flares are triggered and in what conditions they can be eruptive with coronal mass ejections. Magnetic flux ropes (MFRs) has been suggested as the central magnetic structure of solar eruptions, and their ideal instabilities, including the kink instability (KI) and torus instability (TI), are important candidates for triggering mechanisms. Here, using magnetic field extrapolations from observed photospheric magnetograms, we systematically studied the variation of coronal magnetic fields, focusing on MFRs, through major flares including 29 eruptive and 16 confined events. We found that nearly 90% of events possess MFRs before flares, and 70% have MFRs even after flares. We calculated the controlling parameters of KI and TI, including the MFR's maximum twist number and the decay index of its strapping field. Using the KI and TI thresholds empirically derived solely from the pre-flare MFRs, two distinctly different regimes are shown in the variation of the MFR controlling parameters through flares. For the events with both parameters below their thresholds before flares, we found no systematic change of the parameters after the flares, in either the eruptive or confined events. In contrast, for the events with any of the two parameters exceeding their threshold before flares (most of them are eruptive), there is systematic decrease in the parameters to below their thresholds after flares. These results provide a strong constraint for the values of the instability thresholds and also stress the necessity of exploring other eruption mechanisms in addition to the ideal instabilities.