A Double-decker Flux Rope Model for the Solar Eruption on 2012 March 10

We present a magnetic configuration of a compound solar eruption observed on 2012 March 10, from NOAA AR 11429 near the disk center, which displayed a soft X-ray sigmoid before the eruption. We constructed a series of magnetic field models, including double-decker flux rope configurations, using the flux rope insertion method. This produces three-dimensional coronal magnetic field models constrained by the photospheric magnetogram and observed EUV coronal structures. We used different combinations of flux rope paths. We found that two flux ropes sharing the same path at different heights quickly experience a partial merging in the initial iteration of the magnetofrictional relaxation process. Different paths with less than 30% overlap allowed us to construct stable double-decker structures. The high spatial and temporal resolution of the Solar Dynamics Observatory/Atmospheric Imaging Assembly facilitated the selection of a best-fit model that matches the observations best. Moreover, by varying fluxes in this validated nonlinear force-free field double-decker configuration, we successfully reproduce all three scenarios of eruptions of double-decker configurations: (i) eruption due to the instability of higher flux rope; (ii) eruption due to rising lower flux rope and merging with higher flux rope; and (iii) eruption due to the instability of both flux ropes. This demonstrates that magnetofrictional simulation can capture the large-scale magnetic structure of eruptions for a realistic field configuration at eruption onset.