Radiative Magnetohydrodynamic Simulation of the Confined Eruption of a Magnetic Flux Rope: Unveiling the Driving and Constraining Forces

We analyze the forces that control the dynamic evolution of a flux rope eruption in a three-dimensional radiative magnetohydrodynamic simulation. The confined eruption of the flux rope gives rise to a C8.5 flare. The flux rope rises slowly with an almost constant velocity of a few kilometers per second in the early stage when the gravity and Lorentz force are nearly counterbalanced. After the flux rope rises to the height at which the decay index of the external poloidal field satisfies the torus instability criterion, the significantly enhanced Lorentz force breaks the force balance and drives the rapid acceleration of the flux rope. Fast magnetic reconnection is immediately induced within the current sheet under the erupting flux rope, which provides strong positive feedback to the eruption. The eruption is eventually confined due to the tension force from the strong external toroidal field. Our results suggest that the gravity of plasma plays an important role in sustaining the quasi-static evolution of the preeruptive flux rope. The Lorentz force, which is contributed from both the ideal magnetohydrodynamic instability and magnetic reconnection, dominates the dynamic evolution during the eruption process.