Observational Consequences of a Magnetic Flux Rope Emerging into the Corona

We show that a numerical simulation of a magnetic flux rope emerging into a coronal magnetic field predicts solar structures and dynamics consistent with observations. We first consider the structure, evolution, and relative location and orientation of S-shaped, or sigmoid, active regions and filaments. The basic assumptions are that (1) X-ray sigmoids appear at the regions of the flux rope known as "bald-patch-associated separatrix surfaces (BPSSs), where, under dynamic forcing, current sheets can form, leading to reconnection and localized heating, and that (2) filaments are regions of enhanced density contained within dips in the magnetic flux rope. We demonstrate that the shapes and relative orientations and locations of the BPSS and dipped field are consistent with observations of X-ray sigmoids and their associated filaments. Moreover, we show that current layers indeed form along the sigmoidal BPSS as the flux rope is driven by the kink instability. Finally, we consider how apparent horizontal motions of magnetic elements at the photosphere caused by the emerging flux rope might be interpreted. In particular, we show that local correlation tracking analysis of a time series of magnetograms for our simulation leads to an underestimate of the amount of magnetic helicity transported into the corona by the flux rope, largely because of undetectable twisting motions along the magnetic flux surfaces. Observations of rotating sunspots may provide better information about such rotational motions, and we show that if we consider the separated flux rope legs as proxies for fully formed sunspots, the amount of rotation that would be observed before the region becomes kink unstable would be in the range 40 degree -200 degree per leg/sunspot, consistent with observations.