Modeling the initiation of the 2006 December 13 coronal mass ejection in AR 10930: the structure and dynamics of the erupting flux rope

We carry out a three-dimensional magneto-hydrodynamic (MHD) simulation to model the initiation of the coronal mass ejection (CME) on 13 December 2006 in the emerging {\delta}-sunspot active region NOAA 10930. The setup of the simulation is similar to a previous simulation by Fan (2011), but with a significantly widened simulation domain to accommodate the wide CME. The simulation shows that the CME can result from the emergence of a east-west oriented twisted flux rope whose positive, following emerging pole corresponds to the observed positive rotating sunspot emerging against the southern edge of the dominant pre-existing negative sunspot. The erupting flux rope in the simulation accelerates to a terminal speed that exceeds 1500 km/s and undergoes a counter-clockwise rotation of nearly 180 degrees such that its front and flanks all exhibit southward directed magnetic fields, explaining the observed southward magnetic field in the magnetic cloud impacting the Earth. With continued driving of flux emergence, the source region coronal magnetic field also shows the reformation of a coronal flux rope underlying the flare current sheet of the erupting flux rope, ready for a second eruption. This may explain the build up for another X-class eruptive flare that occurred the following day from the same region.