A magnetohydrodynamic model of the 2006 December 13 eruptive flare

We present a three-dimensional magnetohydrodynamic simulation that qualitatively models the coronal magnetic field evolution associated with the eruptive flare that occurred on 2006 December 13 in the emerging δ-sunspot region NOAA 10930 observed by the Hinode satellite. The simulation is set up to drive the emergence of an east-west-oriented magnetic flux rope at the lower boundary into a preexisting coronal field constructed from the Solar and Heliospheric Observatory/Michelson Doppler Imager full-disk magnetogram at 20:51:01 UT on 2006 December 12. The resulting coronal flux rope embedded in the ambient 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 accelerating to a steady speed of about 830kms^-1. 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.