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

Context. Data-constrained models incorporate observed photospheric magnetic fields. However, due to the lack of magnetic field information 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. Aims. This study seeks to understand and reproduce a solar eruption SOL2014-12-18T21:41 that occurred in active region NOAA 12241, preceded by an M6.9 flare, and to investigate the impact of relaxing the initial force-free assumption. Methods. The resistive and compressible magnetohydrodynamic simulation is initiated using a non-force-free magnetic field extrapolated from a photospheric vector magnetogram taken minutes before the flare. The simulation includes a stratified atmosphere and non-ideal effects such as thermal conduction and radiative cooling. Results. A flux rope forms and rises in the simulation, carrying away dense material 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 toward regions of low magnetic pressure, escaping the domain at 350 km/s with approximately constant acceleration. Conclusions. A robust numerical framework for modelling flaring active regions was applied to the eruption of NOAA AR12241 as a case study, assuming a realistic non-force-free magnetic field near the flare onset. It exemplifies how an initial Lorentz force imbalance can successfully trigger a flux rope formation that later escapes the simulation domain. It also enables comparison with real observations through the addition of a stratified atmosphere spanning from the photosphere to the corona.