Comparison of Non-Linear Force-Free Field Extrapolation with Magnetohydrodynamics Simulations

We investigate how well non-linear force-free (NLFF) fields are able to match the coronal component of a more complex magnetohydrodynamic (MHD) simulation of flux emergence. To this end, we use the photospheric vector magnetic field obtained from an MHD simulation of flux emergence in order to specify the lower bound for a NLFF field extrapolation. We then compare the resulting NLFF field with the field given by the MHD simulation, in order to address the important question of how well NLFF fields can reproduce the coronal fields associated with solar active regions. We examine how even small departures from a force-free state in an active region field cause discrepancies with a NLFF reconstruction, and we examine how these discrepancies evolve with time. We discuss possible explanations for the interesting and perhaps very significant differences between the MHD results and the NLFF results that occur at times when the MHD results are expected to be force-free.