The effect of curvature on flux-rope models of coronal mass ejections

The large-scale curvature of a flux rope can help propel it outward from the Sun. Here we extend previous two-dimensional flux-rope models of coronal mass ejections to include the curvature force. To obtain analytical results, we assume axial symmetry and model the flux rope as a torus that encircles the Sun. Initially, the flux rope is suspended in the corona by a balance between magnetic tension, compression, and curvature forces, but this balance is lost if the photospheric sources of the coronal field slowly decay with time. The evolution of the system shows catastrophic behavior as occurred in previous models, but, unlike the previous models, flux ropes with large radii are more likely to erupt than ones with small radii. The maximum total magnetic energy that can be stored before equilibrium is lost is 1.53 times the energy of the potential field, and this value is less than the limiting value of 1.662 for the fully opened field. As a consequence, the loss of ideal MHD equilibrium that occurs in the model cannot completely open the magnetic field. However, the loss of equilibrium does lead to the sudden formation of a current sheet, and if rapid reconnection occurs in this sheet, then the flux rope can escape from the Sun. We also find that the held can gradually become opened without suffering any loss of equilibrium if the photospheric field strength falls below a critical value. This behavior is analogous to the opening of a spherically symmetric arcade in response to a finite amount of shear.