Catastrophe of coronal flux rope in unsheared and sheared bipolar magnetic fields

This article investigates the catastrophic behavior of a preexisting coronal magnetic flux rope embedded in a dipolar or partially open bipolar background field, which is either unsheared or sheared with a given footpoint displacement of magnetic field lines. It is found that in the unsheared background field the catastrophic energy threshold decreases slightly with increasing extent of opening of the background field and increasing annular flux or decreasing axial flux of the flux rope, varying in the range between 1.08 and 1.1 times the magnetic energy of the corresponding fully open field. As the background field is sheared, on the other hand, catastrophe may be triggered by shear provided that the presheared magnetic energy of the system is high enough. The catastrophic energy threshold is almost invariant but then increases monotonically with the increase of the presheared magnetic energy of the system, and it is bounded above by the energy of the corresponding flux rope system associated with an unsheared background field.