The effect of data-driving and relaxation model on magnetic flux rope evolution and stability

Context. Understanding the flux rope eruptivity and e ects of data driving in modelling solar eruptions is crucial for correctly applying di erent models and interpreting their results. Aims. We investigate these by analysing fully data-driven modelled eruption of the active region (AR) 12473 and AR11176, as well as preforming relaxation runs for AR12473 (found to be eruptive) where the driving is switched o systematically at di erent time steps. We analyse the behaviour and evolution of fundamental quantities, essential for understanding the eruptivity of magnetic flux ropes (MFRs). Methods. The data-driven simulations are carried out with the time-dependent magnetofrictional model (TMFM) for AR12473 and AR11176. For the relaxation runs, we employ the magnetofrictional method (MFM) and a zero-beta magnetohydrodynamic (MHD) model to investigate how significant the di erences between the two relaxation procedures are when started from the same initial conditions. In total, 22 simulations are studied. To determine the eruptivity of the MFRs, we calculate and analyse characteristic geometric properties, such as the cross-section, MFR height along with physical stability parameters, such as MFR twist and the decay index. Furthermore, for the eruptive cases, we investigate the e ect of sustained driving beyond the point of eruptivity on the MFR properties and evolution. Results. We find that the fully-driven AR12473 MFR is eruptive while the AR11176 MFR is not. For the relaxation runs, we find that the MFM MFRs are eruptive when the driving is stopped around the flare time or later, while the MHD MFRs show eruptive behaviour even if the driving is switched o one and a half days before the flare occurs.We also find that characteristic MFR properties can vary greatly even for the eruptive cases of di erent relaxation simulations. Conclusions. The results suggest that data driving can significantly influence the evolution of the eruption, with di erences appearing even when the relaxation time is set to later stages of the simulation when the MFRs have already entered an eruptive phase. Moreover, the relaxation model a ects the results significantly, as highlighted by the di erences between the MFM and MHD MFRs, showing that eruptivity in MHD does not directly translate to eruptivity in MFM, despite the same initial conditions. Finally, if the exact critical values of instability parameters are unknown, tracking the evolution of typical MFR properties can be a pow