The Apparent Critical Decay Index at the Onset of Solar Prominence Eruptions

A magnetic flux rope (MFR) embedded in a line-tied external magnetic field that decreases with height as z^-n is unstable to perturbations if the decay index of the field n is larger than a critical value. The onset of this instability, called torus instability, is one of the main mechanisms that can initiate coronal mass ejections. Since flux ropes often possess magnetic dips that can support prominence plasma, this is also a valuable mechanism to trigger prominence eruptions. Magnetohydrodynamic (MHD) simulations of the formation and/or emergence of MFRs suggest a critical value for the onset of the instability in the range [1.4-2]. However, detailed observations of prominences suggest a value in the range [0.9-1.1]. In this Letter, by using a set of MHD simulations, we show why the large discrepancy between models and observations is only apparent. Our simulations indeed show that the critical decay index at the onset of the eruption is n = 1.4 ± 0.1 when computed at the apex of the flux rope axis, while it is n = 1.1 ± 0.1 when it is computed at the altitude of the topmost part of the distribution of magnetic dips. The discrepancy only arises because weakly twisted curved flux ropes do not have dips up to the altitude of their axis.