On the Eruption of Coronal Flux Ropes

We present 3D MHD simulations of the evolution of the magnetic field in the corona where the emergence of a twisted magnetic flux tube is driven at the lower boundary into a pre-existing coronal potential arcade field. In all the simulations, a quasi-equilibrium of a coronal flux rope with an underlying sigmoid-shaped current sheet is formed after the emergence is stopped, and subsequently the flux rope under-goes a quasi-static rise due to reconnections in the current sheet. It is found that the onset of eruption of the coronal flux rope takes place when the flux rope reaches a critical height at which the corresponding potential field declines with height at a sufficiently steep rate, consistent with the onset of the torus instability of the flux rope. We find that the modeled magnetic field evolution in the corona during both the earlier quasi-static rise and the subsequent eruptive phase can explain several basic observed features associated with eruptive flares and CMEs originating from regions with pre-existing X-ray sigmoids. We also report progress on simulations of improved realism where the pre-existing coronal magnetic field and the lower boundary driving conditions are specified based on the observed magnetic field evolution on the solar surface.