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Onset Mechanism of M6.5 Solar Flare Observed in Active Region 12371

We studied a flare onset process in terms of stability of a three-dimensional (3D) magnetic field in active region 12371 producing an eruptive M6.5 flare in 2015 June 22. In order to reveal the 3D magnetic structure, we first extrapolated the 3D coronal magnetic fields based on time series of the photospheric vector magnetic fields under a nonlinear force-free field (NLFFF) approximation. The NLFFFs nicely reproduced the observed sigmoidal structure which is widely considered to be preeruptive magnetic configuration. In particular, we found that the sigmoid is composed of two branches of sheared arcade loops. On the basis of the NLFFFs, we investigated the sheared arcade loops to explore the onset process of the eruptive flare using three representative magnetohydrodynamic instabilities: the kink, torus, and double arc instabilities (DAI). The DAI, recently proposed by Ishiguro & Kusano, is a double arc loop that can be more easily destabilized than a torus loop. Consequently, the NLFFFs are found to be quite stable against the kink and torus instabilities. However, the sheared arcade loops formed prior to the flare possibly become unstable against the DAI. As a possible scenario for the onset process of the M6.5 flare, we suggest a three-step process: (1) double arc loops are formed by the sheared arcade loops through the tether-cutting reconnection during an early phase of the flare, (2) the DAI contributes to the expansion of destabilized double arc loops, and (3) finally, the torus instability makes the full eruption.