An MHD Model of the December 13 2006 Eruptive Flare

We present a 3D MHD simulation that qualitatively models the coronal mag- netic field evolution associated with the eruptive flare that occurred on December 13, 2006 in the emerging {\delta}-sunspot region NOAA 10930 observed by the Hinode satellite. The simulation is set up where we drive the emergence of an east-west oriented magnetic flux rope at the lower boundary into a pre-existing coronal field constructed from the SOHO/MDI full-disk magnetogram at 20:51:01 UT on December 12, 2006. The resulting coronal flux rope embedded in the ambi- ent coronal magnetic field first settles into a stage of quasi-static rise, and then undergoes a dynamic eruption, with the leading edge of the flux rope cavity accel- erating to a steady speed of about 830 km/s. The pre-eruption coronal magnetic field shows morphology that is in qualitative agreement with that seen in the Hinode soft X-ray observation in both the magnetic connectivity as well as the development of an inverse-S shaped X-ray sigmoid. We examine the properties of the erupting flux rope and the morphology of the post-reconnection loops, and compare them with the observations.