Magnetohydrodynamic Simulations for Solar Active Regions using Time-series Data of Surface Plasma Flow and Electric Field Inferred from Helioseismic Magnetic Imager Vector Magnetic Field Measurements

Temporal evolution of magnetic structures of the solar active region (AR) NOAA AR 11158, is simulated with our magnetohydrodynamic (MHD) simulation models using time-dependent solar-surface electric field or plasma flow data. Using the Solar Dynamics Observatory/Helioseismic Magnetic Imager vector magnetogram data, the solar-surface boundary electric field maps are derived with our recently developed algorithm to reproduce the temporal evolution of solar-surface vector magnetic field as observed. The plasma motion velocity maps are calculated through the Differential Affine Velocity Estimator for Vector Magnetograms. In both data-driven models, the simulated evolutionary magnetic field structures at strong-field low-beta regions appear near force-free state, as the current helicity density (${\boldsymbol{J}}\cdot {\boldsymbol{B}}/{B}^{2}$) are roughly constant along each field line. Although the magnetic energy simulated with the newly developed plasma-velocity-driven model is about 10% of that by the electric-field driven model, the plasma-velocity-driven model can maintain the frozen-in condition, and evolution of current and free energy generated by the solar-surface plasma motions can be spatially and temporally traced. The present MHD simulation models for AR system can be a step toward better, more realistic data-driven evolutionary modeling, in particular, establishing boundary treatments for introducing the time-dependent observation data in a physically and mathematically consistent manner.