Formation and rising phase of a flux rope through data-constrained simulations

Advances in data-constrained and data-driven simulations have shed light on the initiation of solar eruptions. These models incorporate observed photospheric magnetic fields. However, because we lack information about the magnetic field in the rest of the solar atmosphere, models rely on extrapolations that, in most cases, neglect the Lorentz force. Nevertheless, this force is present in the lower atmosphere and may play a key role in destabilising the equilibrium configuration and triggering eruptions. This study seeks to understand and reproduce solar eruption SOL2014-12-18T21:41, which occurred in active region NOAA 12241 and was preceded by an M6.9 flare. We also investigate the effect of relaxing the initial force-free assumption. The resistive and compressible magnetohydrodynamic simulation was initiated using a non-force-free magnetic field extrapolated from a photospheric vector magnetogram taken minutes before the flare. The simulation included a stratified atmosphere and non-ideal effects such as thermal conduction and radiative cooling. A flux rope forms and rises in the simulation and carries dense material away from the lower solar atmosphere. Its formation results from the non-zero Lorentz force acting on the initial sheared arcade, without assuming pre-existing flux ropes or photospheric driving motions. The flux rope is then deflected towards regions of low magnetic pressure, escaping from the domain at 350 km s -1 with approximately constant acceleration. A robust numerical framework for modelling flaring active regions was applied to the eruption of NOAA AR 12241 as a case study, assuming a realistic non-force-free magnetic field near the flare onset. It exemplifies how an initial imbalance in the Lorentz force can successfully trigger a flux rope formation that later escapes from the simulation domain. It also enables comparison with real observations through the addition of a stratified atmosphere spanning from the photosphere to the corona.