Force balance analysis of a coronal magnetic flux rope in equilibrium or eruption

Based on a flux rope catastrophe model for coronal mass ejections (CMEs), we calculate the Lorentz forces acting on the rope in equilibrium or eruption in the background field, which is taken to be either a partially open bipolar field or a closed quadrupolar field. The forces, including upward lifting and downward pulling ones, are exerted by the coronal currents inside and outside the rope, as well as the potential field, which has the same normal component distribution on the photosphere as the background field. The resultant of forces vanishes for a rope in equilibrium. For both cases with different background fields, the primary lifting force is provided by the azimuthal current inside the rope and its image below the photosphere. It is mainly balanced by the pulling force produced by the background potential field when the rope is in equilibrium. During an eruption of the rope caused by catastrophe, the two predominant forces mentioned above decrease rapidly with the ascent of the rope. In the meantime, the vertical and/or transverse current sheets and their images, which form and develop along with the rope eruption, contribute additional and significant pulling ( or restoring) forces that decelerate the rope. When fast magnetic reconnection takes place across these current sheets, the restoring force provided by the sheets will be greatly reduced, which may play an important role in the dynamics of the rope. The implication of such a conclusion in the acceleration of CMEs is briefly discussed.