Sigmoidal active region on the sun: Comparison of a magnetohydrodynamical simulation and a nonlinear force-free field model

In this paper we show that when accurate nonlinear force-free field (NLFFF) models are analyzed together with high-resolution magnetohydrodynamic (MHD) simulations, we can determine the physical causes for the coronal mass ejection (CME) eruption on 2007 February 12. We compare the geometrical and topological properties of the three-dimensional magnetic fields given by both methods in their pre-eruptive phases. We arrive at a consistent picture for the evolution and eruption of the sigmoid. Both the MHD simulation and the observed magnetic field evolution show that flux cancellation plays an important role in building the flux rope. We compute the squashing factor, Q, in different horizontal maps in the domains. The main shape of the quasi-separatrix layers (QSLs) is very similar between the NLFFF and MHD models. The main QSLs lie on the edge of the flux rope. While the QSLs in the NLFFF model are more complex due to the intrinsic large complexity in the field, the QSLs in the MHD model are smooth and possess lower maximum value of Q. In addition, we demonstrate the existence of hyperbolic flux tubes (HFTs) in both models in vertical cross sections of Q. The main HFT, located under the twisted flux rope in both models, is identified as the most probable site for reconnection. We also show that there are electric current concentrations coinciding with the main QSLs. Finally, we perform torus instability analysis and show that a combination between reconnection at the HFT and the resulting expansion of the flux rope into the torus instability domain is the cause of the CME in both models.