Breakout and Tether-Cutting Eruption Models Are Both Catastrophic (Sometimes)

We present a simplified analytic model of a quadrupolar magnetic field and flux rope to model coronal mass ejections. The model magnetic field is two-dimensional, force-free and has current only on the axis of the flux rope and within two current sheets. It is a generalization of previous models containing a single current sheet anchored to a bipolar flux distribution. Our new model can undergo quasi-static evolution either due to changes at the boundary or due to magnetic reconnection at either current sheet. We find that all three kinds of evolution can lead to a catastrophe, known as loss of equilibrium. Some equilibria can be driven to catastrophic instability either through reconnection at the lower current sheet, known as tether cutting, or through reconnection at the upper current sheet, known as breakout. Other equilibria can be destabilized through only one and not the other. Still others undergo no instability, but they evolve increasingly rapidly in response to slow steady driving (ideal or reconnective). One key feature of every case is a response to reconnection different from that found in simpler systems. In our two-current-sheet model a reconnection electric field in one current sheet causes the current in that sheet to increase rather than decrease. This suggests the possibility for the microscopic reconnection mechanism to run away.