The Astrophysical Journal: We present first results of the hybrid data–driven magnetofrictional (MF) and data–constrained magnetohydrodynamic (MHD) simulations of solar active region NOAA 11158, which produced an X-class flare and coronal mass ejection on 2011 February 15. First, we apply the MF approach to build the coronal magnetic configuration corresponding to the SDO/HMI photospheric magnetograms by using the JSOC PDFI SS electric field inversions at the bottom boundary of the simulation domain. We then use the pre-eruptive MF state at about 1.5 hour before the observed X-class flare as the initial state for the MHD simulation, assuming a stratified polytropic solar corona. The MHD run shows that the initial magnetic configuration containing twisted magnetic fluxes and a 3D magnetic null point is out of equilibrium. We find the eruption of a complex magnetic structure consisting of two magnetic flux ropes, as well as the development of flare ribbons, with their morphology being in good agreement with observations. We conclude that the combination of the data–driven MF and data–constrained MHD simulations is a useful practical tool for understanding the 3D magnetic structures of real solar ARs that are unobservable otherwise.
(left panel) Evolution of the plasma temperature enhancement near the bottom boundary of the simulation as a flare ribbon proxy, compared with (right panel) the EUV SDO/AIA 1600 A observation of flare ribbons. In the left panel, the light(dark)-grey contours represent positive (negative) radial magnetic field values of 300 G (dotted lines) and 30 G (solid lines), and the magnetic polarities are marked with the letters. The middle panel shows the reconnection flux derived from the simulated and the observed flare ribbon evolutions.