Statistical Analysis of Torus and Kink Instabilities in Solar Eruptions

A recent laboratory experiment of ideal magnetohydrodynamic (MHD) instabilities reveals four distinct eruption regimes readily distinguished by the torus instability (TI) and helical kink instability (KI) parameters \citep{Myers2015}. To establish its observational counterpart, we collect 38 solar flares (stronger than GOES class M5 in general) that took place within 45$^{\circ}$ 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 CMEless (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 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 non-linear force-free (NLFF) field lines forming the same MFR (a KI parameter). We then construct a $n-T_w$ diagram to investigate how the eruptiveness depends on these parameters. We find: (1) $T_w$ appears to play little role in discriminating between confined and ejective events; (2) the events with $n\gtrsim0.8$ are all ejective and all confined events have $n\lesssim0.8$. However, $n\gtrsim0.8$ is not a necessary condition for eruption, because some events with $n\lesssim0.8$ also erupted. In addition, we investigate the MFR's geometrical parameters, apex height and distance between footpoints, as a possible factor 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.