Catastrophe of coronal magnetic flux ropes in partially open magnetic fields

Using a 2.5-D, time-dependent ideal MHD model in Cartesian coordinates, a numerical study is carried out to find equilibrium solutions associated with a magnetic flux rope in the corona. The ambient magnetic field is partially open, consisting of a closed arcade in the center and an open field at the flank. The coronal magnetic flux rope is characterized by its magnetic properties, including the axial and annular magnetic fluxes and the magnetic helicity, and its geometrical features, including the height of the rope axis, the halfwidth of the rope and the length of the vertical current sheet below the rope. It is shown that for a given partially open ambient magnetic field, the dependence of the geometrical features on the magnetic properties displays a catastrophic behavior, namely, there exists a certain critical point, across which an infinitesimal enhancement of the magnetic parameters causes a finite jump of the geometrical parameters for the rope. The amplitude of the jump depends on the extent to which the ambient magnetic field in open, and approaches to zero when the ambient magnetic field becomes completely closed. The implication of such a catastrophe in solar active phenomena is briefly discussed.