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We analyze a three-dimensional (3D) magnetic structure and its stability inlarge solar active region(AR) 12192, using the 3D coronal magnetic fieldconstructed under a nonlinear force-free field (NLFFF) approximation. Inparticular, we focus on the magnetic structure that produced an X3.1-classflare which is one of the X-class flares observed in AR 12192. According to ouranalysis, the AR contains multiple-flux-tube system, {\it e.g.}, a large fluxtube, both of whose footpoints are anchored to the large bipole field, underwhich other tubes exist close to a polarity inversion line (PIL). These variousflux tubes of different sizes and shapes coexist there. In particular, thelater are embedded along the PIL, which produces a favorable shape for thetether-cutting reconnection and is related to the X-class solar flare. Wefurther found that most of magnetic twists are not released even after theflare, which is consistent with the fact that no observational evidence formajor eruptions was found. On the other hand, the upper part of the flux tubeis beyond a critical decay index, essential for the excitation of torusinstability before the flare, even though no coronal mass ejections (CMEs) wereobserved. We discuss the stability of the complicated flux tube system andsuggest the reason for the existence of the stable flux tube. In addition, wefurther point out a possibility for tracing the shape of flare ribbons, on thebasis of a detailed structural analysis of the NLFFF before a flare.

Structure and Stability of Magnetic Fields in Solar Active Region12192 Based on Nonlinear Force-Free Field Modeling