Plasma Motions and Turbulent Magnetic Diffusivity of Active Region AR 12158 Using a Minimum Energy Functional and Non-Force-Free Reconstructions of Vector Magnetograms

We present a generalization of the resistive minimum-energy fit (MEF-R: Tremblay and Vincent, Solar Phys.290, 437, 2015) for non-force-free (NFF) magnetic fields. In MEF-R, an extremum principle is used to infer two-dimensional maps of plasma motions [v(x, y) ] and magnetic eddy diffusivity [η_eddy(x, y) ] at the photosphere. These reconstructions could be used as boundary conditions in data-driven simulations or in data assimilation. The algorithm is validated using the analytical model of a resistive expanding spheromak by Rakowski, Laming, and Lyutikov (Astrophys. J.730, 30, 2011). We study the flaring Active Region AR 12158 using a series of magnetograms and Dopplergrams provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The results are discussed for a non-force-free magnetic-field reconstruction [B_NFF] (Hu and Dasgupta in Solar Phys.247, 87, 2008). We found that the vertical plasma velocities [v_z(x, y) ] inferred using MEF-R are very similar to the observed Doppler velocities [v_r(x, y) ]. Finally, we study the potential spatial correlation between microturbulent velocities and significant values of η_eddy(x, y).