Models of the large-scale corona. I. Formation, evolution, and liftoff of magnetic flux ropes

The response of the large-scale coronal magnetic field to transport of magnetic flux in the photosphere is investigated. In order to follow the evolution on long timescales, the coronal plasma velocity is assumed to be proportional to the Lorentz force (magnetofriction), causing the coronal field to evolve through a series of nonlinear force-free states. Magnetofrictional simulations are used to study the formation and evolution of coronal flux ropes, highly sheared and/or twisted fields located above polarity inversion lines on the photosphere. As in our earlier studies, the three-dimensional numerical model includes the effects of the solar differential rotation and small-scale convective flows; the latter are described in terms of surface diffusion. The model is extended to include the effects of coronal magnetic diffusion, which limits the degree of twist of coronal flux ropes, and the solar wind, which opens up the field at large height. The interaction of two bipolar magnetic regions is considered. A key element in the formation of flux ropes is the reconnection of magnetic fields associated with photospheric flux cancellation at the polarity inversion lines. Flux ropes are shown to form both above the external inversion line between bipoles (representing type B filaments) and above the internal inversion line of each bipole in a sigmoid shape. It is found that once a flux rope has formed, the coronal field may diverge from equilibrium with the ejection of the flux rope. After the flux rope is ejected, the coronal field once again relaxes down to an equilibrium. This ability to follow the evolution of the coronal fields through eruptions is essential for future full-Sun simulations in which multiple bipoles are evolved for many months or years.