Study of Three-dimensional Magnetic Structure and the Successive Eruptive Nature of Active Region 12371

We study the magnetic structure of successively erupting sigmoid in active region 12371 by modeling the quasi-static coronal field evolution with non-linear force-free field (NLFFF) equilibria. HMI/SDO vector magnetograms are used as input to the NLFFF model. In all eruption events, the modeled structure resembles the observed pre-eruptive coronal sigmoid and the NLFFF core-field is a combination of double inverse J-shaped and inverse-S field-lines with dips touching the photosphere. Such field-lines are formed by flux-cancellation reconnection of opposite-J field-lines at bald-patch locations. It implies the formation of a weakly twisted flux-rope from large scale sheared arcade field lines. Later on, this flux-rope undergo coronal tether-cutting reconnection until a CME is triggered. The modeled structure captured these major features of sigmoid-to-arcade-to-sigmoid transformation, that is being recurrent under continuous photospheric flux motions. Calculations of the field-line twist reveal a fractional increase followed by a decrease of the number of pixels having a range of twist. This traces the buildup process of a twisted core-field by slow photospheric motions and the relaxation after eruption, respectively. Our study infers that the large eruptivity of this AR is due to a steep decrease of the background coronal field meeting the torus instability criteria at low height ($\approx 40$ Mm) in contrast to non-eruptive ARs.