Self-consistent Nonlinear Force-Free Field Reconstruction from Weighted Boundary Conditions

Photospheric vector magnetogram data are often used as boundary conditions for force-free coronal magnetic field extrapolations. In general, however, vector magnetogram data are not consistent with the force-free assumption. In this article, we demonstrate a way to deal with inconsistent boundary data, by generalizing the "self-consistency procedure" of Wheatland and Regnier (Astrophys. J. Lett. 700, L88, 2009). In that procedure, the inconsistency is resolved by an iterative process of constructing two solutions based on the values of the force-free parameter a on the two polarities of the field in the boundary (the P and N polarities), and taking uncertainty-weighted averages of the boundary a values in the P and N solutions. When the a values in the P and N regions are very different, the self-consistent solution may lose high a values from the boundary conditions. We show how, by altering the weighting of the uncertainties in the P or N boundary conditions, we can preserve high a values in the self-consistent solution. The weighted self-consistent extrapolation method is demonstrated on an analytic bipole field and applied to vector magnetogram data taken by the Helioseismic and Magnetic Imager (HMI) instrument on board the Solar Dynamics Observatory (SDO) spacecraft for NOAA active region AR 12017 on 2014 March 29.