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 mainly the kink instability (KI) and torus instability (TI) provide 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% events possess MFR before flare and 70% have MFR even after flare. We calculated the controlling parameters of KI and TI, including the MFRs maximum twist number and the decay index of its strapping field. Using the KI and TI thresholds empirically derived from solely the pre-flare MFRs, two distinct different regimes are shown in the variation of the MFR controlling parameters through flares. For the events with both parameters below their thresholds before flare, 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 flare (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.
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