Unstable Coronal Loops: Numerical Simulations with Predicted Observational Signatures

We present numerical studies of the nonlinear, resistive magnetohydrodynamic (MHD) evolution of coronal loops. For these simulations we assume that the loops carry no net current, as might be expected if the loop had evolved because of vortex flows. Furthermore, the initial equilibrium is taken to be a cylindrical flux tube with line-tied ends. For a given amount of twist in the magnetic field, it is well known that once such a loop exceeds a critical length it becomes unstable to ideal MHD instabilities. The early evolution of these instabilities generates large current concentrations. First we show that these current concentrations are consistent with the formation of a current sheet. Magnetic reconnection can only occur in the vicinity of these current concentrations, and we therefore couple the resistivity to the local current density. This has the advantage of avoiding resistive diffusion in regions where it should be negligible. We demonstrate the importance of this procedure by comparison with simulations based on a uniform resistivity. From our numerical experiments we are able to estimate some observational signatures for unstable coronal loops. These signatures include the timescale of the loop brightening, the temperature increase, and the energy released and the predicted observable flow speeds. Finally, we discuss to what extent these observational signatures are consistent with the properties of transient brightening loops.