A Comparison of the Minimum Current Corona to a Magnetohydrodynamic Simulation of Quasi‐Static Coronal Evolution

Abstract

We use two different models to study the evolution of the coronal magnetic field that results from a simple photospheric field evolution. The first, the minimum current corona (MCC), is a self-consistent model for quasistatic evolution that yields an analytic expression approximating the net coronal currents and the free magnetic energy stored by them. For the second model calculation, the nonlinear, time-dependent equations of ideal magnetohydrodynamics are solved numerically subject to line-tied photospheric boundary conditions. In both models high current density concentrations form vertical sheets along the magnetic separator. The time history of the net current carried by these concentrations is quantitatively similar in each of the models. The magnetic energy of the line-tied simulation is significantly greater than that of the MCC, in accordance with the fact that the MCC is a lower bound on energies of all ideal models. The difference in energies can be partially explained from the different magnetic helicity injection in the two models. This study demonstrates that the analytic MCC model accurately predicts the locations of significant equilibrium current accumulations. The study also provides one example in which the energetic contributions of two different MHD constraints, line-tying constraints and flux constraints, may be quantitatively compared. In this example line-tying constraints store at least an order of magnitude more energy than do flux constraints.