Double catastrophe of coronal flux rope in quadrupolar magnetic field

Using a relaxation method based on time-dependent ideal magnetohydrodynamic simulations, we find 2.5-dimensional force-free field solutions in spherical geometry, which are associated with an isolated flux rope embedded in a quadrupolar background magnetic field. The background field is of Antiochos type, consisting of a dipolar and an octopolar component with a neutral point somewhere in the equatorial plane. The flux rope is characterized by its magnetic fluxes, including the annular flux Phi(p) and the axial magnetic flux Phi(phi), and its geometric features described by the height of the rope axis and the length of the vertical current sheet below the rope. It is found that for a given Phi(p), the force-free field exhibits a complex catastrophic behavior with respect to increasing Phi(phi). There exist two catastrophic points, and the catastrophic amplitude, measured by the jump in the height of the rope axis, is finite for both catastrophes. As a result, the flux rope may levitate stably in the corona after catastrophe, with a transverse current sheet above and a vertical current sheet below. The magnetic energy threshold for the two successive catastrophes are found to be larger than the corresponding partly open field energy. We argue that it is the transverse current sheet formed above the flux rope that provides a downward Lorentz force on the flux rope and thus keeps the rope levitating stably in the corona.