Criteria for flux rope eruption: Non-equilibrium versus torus instability

Abstract

The coronal magnetic configuration of an active region typically evolves quietly for a few days before becoming suddenly eruptive and launching a coronal mass ejection (CME). The precise origin of the eruption is still under debate. The loss of equilibrium, or an ideal magnetohydrodynamic (MHD) instability such as torus instability are among the several mechanisms that have proposed to be responsible for the sudden eruptions. Distinct approaches have also been formulated for limited cases having circular or translation symmetry. We revisit the previous theoretical approaches setting them in the same analytical framework. The coronal field results from the contribution of a non-neutralized current channel added to a background magnetic field, which in our model is the potential field generated by two photospheric flux concentrations. The evolution on short Alfvénic timescale is governed by ideal MHD. We first show analytically that the loss of equilibrium and the stability analysis are two different views of the same physical mechanism. Second, we identify that the same physics is involved in the instabilities of circular and straight current channels. Indeed, they are just two particular limiting cases of more general current paths. A global instability of the magnetic configuration is present when the current channel is located at a coronal height, h, large enough so that the decay index of the potential field, ∂ ln |Bp|/∂ ln h, is larger than a critical value. At the limit of very thin current channels, previous analysis has found critical decay indices of 1.5 and 1 for circular and straight current channels, respectively. However, with current channels being deformable and as thick as that expected in the corona, we show that this critical index has similar values for circular and straight current channels, and is typically in the range [1.1,1.3]. © 2010. The American Astronomical Society. All rights reserved.