Onset of coronal mass ejections due to loss of confinement of coronal flux ropes

Using MHD numerical simulations in a three-dimensional spherical geometry, we model the loss of confinement and eruption of a flux rope emerging quasi-statically into a preexisting coronal arcade field. Our numerical experiments investigated two distinct mechanisms that led to the eruption of the flux rope. In one case, the overlying arcade field declines with height slowly such that the emerging flux rope remains confined until its self-relative magnetic helicity normalized by the square of the rope's flux reaches -1.4 and the flux rope becomes significantly kinked. The kinking motion causes rotation of the tube to an orientation that makes it easier for it to rupture through the arcade field, leading to an eruption. In the second case, the overlying field declines more rapidly with height, and the emerging flux rope is found to lose equilibrium and erupt via the torus instability when its self-relative magnetic helicity normalized by the square of its flux is only approximately -0.63, before it becomes kinked. The values of the total relative magnetic helicity of the entire coronal magnetic field (including both the flux rope and the arcade field) normalized by the square of the total magnetic flux are, on the other hand, of similar magnitudes for the two cases when the eruption takes place. We compare and contrast the eruptive properties and the posteruption states resulting from the two cases.