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 th e 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 encircle s the Sun. Initially, the flux rope is suspended in the corona by a balance between magnetic tension, compression, and curvature forces, but this bala nce is lost if the photospheric sources of the coronal field slowly decay w ith time. The evolution of the system shows catastrophic behavior as occurr ed in previous models, but, unlike the previous models, flux ropes with lar ge radii are more likely to erupt than ones with small radii. The maximum t otal 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 li miting value of 1.662 for the fully opened field. As a consequence, the los s of ideal MHD equilibrium that occurs in the model cannot completely open the magnetic held. However, the loss of equilibrium does lead to the sudden formation of a current sheet, and if rapid reconnection occurs in this she et, 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 th e photospheric field strength falls below a critical value. This behavior i s analogous to the opening of a spherically symmetric arcade in response to a finite amount of shear.