Stability and Dynamic Evolution of Three-dimensional Flux Ropes

A crucial problem in the study of coronal mass ejections (CMEs) and solar flares is the identification of initial configurations and boundary conditions that can produce an eruption of the field configuration. In this paper we use (ideal) magnetohydrodynamic (MHD) simulations to investigate the stability and dynamic evolution of two (approximate) equilibrium configurations. The initial models investigated are derived within a general framework for the construction of series of suitable coronal states. They consist of twisted flux ropes, connected to the photosphere and anchored in the corona by an overlying arcade, embedded in a helmet streamer type configuration. The two models studied differ by the magnitude of the toroidal field and, correspondingly, the degree of twist and the amount of plasma pressure. The model with the least twist remains stable and settles into an equilibrium that differs only slightly from the initial state. In contrast, the more strongly twisted flux rope becomes unstable. Some portion of it breaks out in a kinklike fashion and moves rapidly outward, while another portion remains below. The evolved stage is characterized by the formation of a thin current sheet below an outward-moving rope.