The catastrophe of coronal magnetic flux ropes in CMEs

A brief review is given on the progress made in the study of the catastrophe of coronal magnetic flux ropes with implication in coronal mass ejections (CMEs). Relevant studies have been so far limited to 2.5-D cases, with a flux rope levitating in the corona, either parallel to the photosphere in Cartesian geometry or encircling the Sun like a torus in spherical geometry. The equilibrium properties of the system depend on the features of the flux rope and the surrounding background state. Under certain circumstances, the flux rope exhibits a catastrophic behavior, namely, the rope loses equilibrium and erupts upward upon an infinitesimal variation of any control parameter associated with the background state or the flux rope. The magnetic energy of the system right at the catastrophic point may exceed the corresponding open field energy so that after the background field is opened tip by the erupting flux rope, a certain amount of magnetic free energy is left for the heating and acceleration of coronal plasma against gravity. The flux rope model has been used to reveal the common features of CMEs and to simulate typical CME events, proving to be a promising mechanism for the initiation of CMEs. Incidentally, the Aly conjecture on the maximum magnetic energy of force-free fields places a serious constraint on 2.5-D flux models. Nevertheless, current sheets must form during a catastrophe on the Alfven timescale, and magnetic reconnection across the newly formed current sheets may contribute to circumventing such a constraint. In this sense, the catastrophe simply plays a role of driver for the fast magnetic reconnection, and a combination of them is thus responsible for the initiation of CMEs.