Three-dimensional Simulation Study of Flux Rope Dynamics in the Solar Corona

The three-dimensional stability and the nonlinear dynamics of a flux rope embedded in a magnetic arcade are investigated using magnetohydrodynamic (MHD) simulations, with the goal of understanding the mechanism of filament eruption in the solar corona. The flux rope equilibrium proposed by Forbes in 1990 is adopted as the initial state of the three-dimensional simulation, and we find that the equilibrium is linearly unstable to the kink mode instability, when the system approaches the loss-of-equilibrium state. The three-dimensional simulation demonstrates that when the flux rope is long enough, it can escape from the arcade at an almost constant speed after the accelerated launching phase due to the kink instability. The continuous ascending of the flux rope is driven by the nonlinear growth of several kink modes. In the case of a short flux rope, however, the flux rope ascension fails at some height. This suggests that the flux rope eruption must proceed through the multiple stages, which are driven by the loss of stability in the launching phase and by the loss of equilibrium in the late ascending phase. Since the short rope could not come up to the critical height for the transition from the first to the second stage, the ascending must stop. The role of magnetic reconnection in the late ascending phase and the formation mechanism of density cavity, which corresponds to dimming region observed in CMEs, is also discussed using the simulation results.

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