The evolution of twisting coronal magnetic flux tubes

Abstract

We simulate the twisting of an initially potential coronal flux tube by photospheric vortex motions, centred at two photospheric flux concentrations, using the compressible zero-beta ideal MHD equations. A twisted flux tube is formed, surrounded by much less twisted and sheared outer flux. Under the action of continuous slow driving, the flux tube starts to evolve quasi-statically along a sequence of force-free equilibria, which rise slowly with increasing twist and possess helical shape. The flux bundle that extends from the location of peak photospheric current density ( slightly displaced from the vortex centre) shows a sigmoidal shape in agreement with observations of sigmoidal soft X-ray loops. There exists a critical twist, above which no equilibrium can be found in the simulation and the flux tube ascends rapidly. Then either stable equilibrium ceases to exist or the character of the sequence changes such that neighbouring stable equilibria rise by enormous amounts for only modest additions of twist. A comparison with the scalings of the rise of flux in axisymmetric geometry by Sturrock et al. ( 1995) suggests the former. Both cases would be observed as an eruption. The critical end-to-end twist, for a particular set of parameters describing the initial potential field, is found to lie in the range 2.5pi < Phi(c) < 2.75pi. There are some indications for the growth of helical perturbations at supercritical twist. Depending on the radial profiles of the photospheric flux concentration and vortex velocity, the outer part or all of the twisted flux expands from the central field line of the flux tube. This effect is particularly efficient in the dynamic phase, provided the density is modeled realistically, falling off sufficiently rapidly with height. It is expected to lead to the formation of a cavity in which the twisted flux tube is embedded, analogous to the typical structure of coronal mass ejections.