Authors: Oliver E. K. Rice (Durham University), Anthony R. Yeates (Durham University)

We investigate which scalar quantity or quantities can best predict the loss of equilibrium and subsequent eruption of magnetic flux ropes in the solar corona. Our models are initialised with a potential magnetic arcade, which is evolved by means of two effects on the lower boundary. The first is the gradual shearing of the arcade, modelling the differential rotation speed of the solar surface. The second is supergranular\ diffusion, representing the higher diffusion rates in the photosphere compared to the corona. This results in flux cancellation at the polarity inversion line and the formation of a twisted flux rope. We use three model setups – full magnetohydrodynamics (MHD) in cartesian coordinates and the magnetofrictional model in both cartesian and polar coordinates. The flux ropes are translationally-invariant, allowing for very fast computational times and thus a comprehensive parameter study, comprising hundreds of simulations and thousands of eruptions. Similar flux rope behaviour is observed using either magnetofriction or MHD, and there are several scalar criteria that could be used as proxies for eruptivity. The most consistent predictor of eruptions in either model is the squared current in the axial direction of the rope, normalised by the relative helicity, although a variation on the previously proposed ‘eruptivity index’ is also found to perform well in both the magnetofrictional and MHD simulations.