Data-constrained MHD Simulation of a Multi-ribbon Flare Corresponding to a Successful and a Confined Eruption

The formation and eruption mechanisms of multi-ribbon flares are extremely complicated, especially when the flare is associated with homologous eruptions in the same region. In this paper, we investigate such an event, corresponding to a successful eruption and a confined eruption. This is an M7.1 flare, starting at 12:33 UT on 2011 September 24 in active region NOAA 11302. We obtain the coronal magnetic configuration for this region, using a nonlinear force-free field extrapolation based on the photospheric magnetogram at 12:00 UT. Taking this as the initial condition, we perform a data-constrained MHD simulation to study the evolution of the magnetic topology for this region. We analyze the magnetic null points and the 3D squashing degree for this region, indicating the existence of three flux ropes and two spine–fan structures. The model reproduces the rising processes of the two flux ropes, which form two homologous eruptions consistent with the observations as shown in 94 Å: a large-scale successful eruption that is followed by a small-scale confined eruption. By analyzing the magnetic configuration, the Lorentz force, and the decay index, we find that the torus instability plays an important role in driving the successful eruption of the large flux rope. The magnetic reconnection above the medium flux rope changes the direction of the overlying magnetic field, which provides a downward component of the Lorentz force to confine the eruption of the medium flux rope.