The role of the external toroidal magnetic field on the large-angle rotation of magnetic flux ropes

Context. It is accepted that magnetic flux ropes might exhibit large-angle rotation in magnetic configurations, including strong external toroidal magnetic fields. The specific mechanisms leading to rotation still remain elusive, however. Aims. We examine the mechanisms by which the external toroidal magnetic field facilitates the flux-rope rotation, and we explore potential alternative rotation mechanisms beyond the effects of sheared fields and kink instability. Methods. We performed three-dimensional magnetohydrodynamic simulations to model the eruption of magnetic flux ropes in a magnetic configuration with and without external toroidal magnetic fields. We compared the morphology, the dynamics, the magnetic topology, and the Lorentz force acting on the flux rope. Results. The behavior of flux ropes in two simulations is significantly different. The flux rope that evolved without external toroidal fields successfully erupted was accompanied by minor rotation, and the flux rope that evolved with an external toroidal field was confined by large-angle rotation. The evolution of the magnetic topology, the Lorentz force, and the torque showed distinctive patterns in each scenario. Furthermore, the flux ropes in both simulations displayed observable signs of a drifting footpoint. Conclusions. We reveal that external toroidal magnetic fields facilitate the flux-rope rotation, which in turn releases initial twists and amplifies the lateral Lorentz force exerted on the flux rope. The slipping magnetic reconnection between the flux-rope field lines and sheared-arcade field lines can contribute to the rotation, as does the lateral Lorentz force and the kink instability, which is determined by the initial twist number. Moreover, our result suggests that the initial twist of the flux rope cannot determine the rotation angle. The rotation angle of the flux rope does not strictly increase with the initial twist. The rapid release of the twist number necessitates external toroidal magnetic fields.