Numerical Simulations of Three‐dimensional Coronal Magnetic Fields Resulting from the Emergence of Twisted Magnetic Flux Tubes

We present the results of MHD simulations in the low-β regime of the evolution of the three-dimensional coronal magnetic field as an arched, twisted magnetic flux tube emerges into a preexisting coronal potential magnetic arcade. We find that the line-tied emerging flux tube becomes kink-unstable when a sufficient amount of twist is transported into the corona. For an emerging flux tube with a left-handed twist (which is the preferred sense of twist for active region flux tubes in the northern hemisphere), the kink motion of the tube and its interaction with the ambient coronal magnetic field lead to the formation of an intense current layer that displays an inverse-S shape, consistent with the X-ray sigmoid morphology preferentially seen in the northern hemisphere. The position of the current layer in relation to the lower boundary magnetic field of the emerging flux tube is also in good agreement with the observed spatial relations between the X-ray sigmoids and their associated photospheric bipolar magnetic regions. We argue that the inverse-S-shaped current layer formed is consistent with being a magnetic tangential discontinuity limited by numerical resolution and thus may result in the magnetic reconnection and significant heating that causes X-ray sigmoid brightenings.