Statistical Analysis of Torus and Kink Instabilities in Solar Eruptions

A recent laboratory experiment of ideal magnetohydrodynamic instabilities revealed four distinct eruption regimes readily distinguished by the torus instability (TI) and helical kink instability (KI) parameters. To establish its observational counterpart, we collected 38 solar flares (stronger than GOES-class M5 in general) that took place within 45 degrees of disk center during 2011-2017, 26 of which are associated with a halo or partial halo coronal mass ejection (CME; i.e., ejective events), while the others are CME-less (i.e., confined events). This is a complete sample of solar events satisfying our selection criteria detailed in the paper. For each event, we calculate a decay index n of the potential strapping field above the magnetic flux rope (MFR) in and around the flaring magnetic polarity inversion line (a TI parameter) and the unsigned twist number T-w of the nonlinear force-free field lines forming the same MFR (a KI parameter). We then construct an n-T-w diagram to investigate how the eruptiveness depends on these parameters. We find that (1) Tw appears to play little role in discriminating between confined and ejective events; (2) the events with n greater than or similar to 0.8 are all ejective, and all confined events have n less than or similar to 0.8. However, n greater than or similar to 0.8 is not a necessary condition for eruption because some events with n less than or similar to 0.8 also erupted. In addition, we investigate the MFR's geometrical parameters, apex height, and distance between footpoints, as a possible factors for the eruptiveness. We briefly discuss the difference of the present result for solar eruptions with that of the laboratory result in terms of the role played by magnetic reconnection.