Simulating the Formation and Eruption of Flux Rope by Magneto-friction Model Driven by Time-dependent Electric Fields

Aiming to capture the formation and eruption of flux ropes (FRs) in the source active regions (ARs), we simulate the coronal magnetic field evolution of the AR 11429 employing the time-dependent magneto-friction model (TMF). The initial field is driven by electric fields that are derived from time-sequence photospheric vector magnetic field observations by invoking ad hoc assumptions. The simulated magnetic structure evolves from potential to twisted fields over the course of two days, followed by rise motion in the later evolution, depicting the formation of an FR and its slow eruption later. The magnetic configuration resembles an inverse S-sigmoidal structure, composed of the potential field enveloping the inverse J-shaped fields that are sheared past one another and a low-lying twisted field along the major polarity inversion line. To compare with observations, proxy emission maps based on averaged current density along the field lines are generated from the simulated field. These emission maps exhibit a remarkable one-to-one correspondence with the spatial characteristics in coronal extreme ultraviolet images, especially the filament trace supported by the twisted magnetic field in the southwest subregion. Further, the topological analysis of the simulated field reveals the cospatial flare ribbons with the quasi-separatrix layers, which is consistent with the standard flare models; therefore, the extent of the twist and orientation of the erupting FR is indicated to be the real scenario in this case. The TMF model simulates the coronal field evolution, correctly capturing the formation of the FR in the observed timescale and the twisted field generated from these simulations serves as the initial condition for the full MHD simulations.