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

¹ Department of Physics, University of Helsinki, PO Box 64 FI-00014 Helsinki, Finland
² CmPA/Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
³ Instituto de Astrofísica e Ciências do Espaço, Department of Physics, University of Coimbra, Coimbra, Portugal
⁴ School of Mathematics and Statistics, University of Sheffield, Solar Physics and Space Plasma Research Centre (SP2RC), Sheffield, United Kingdom
⁵ Udaipur Solar Observatory, Physical Research Laboratory, Dewali, Badi Road, Udaipur 313001, India
⁶ Institute of Physics, University of Maria Curie-Skłodowska, ul. Radziszewskiego 10, 20-031 Lublin, Poland
⁷ Instituto de Astrofísica e Ciências do Espaço, Department of Earth Sciences, University of Coimbra, Coimbra, Portugal
⁸ Department of Astronomy, Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
⁹ Gyula Bay Zoltan Solar Observatory (GSO), Hungarian Solar Physics Foundation (HSPF), Petőfi tér 3, H-5700 Gyula, Hungary

^⋆ Corresponding author; andreas.wagner@helsinki.fi

Received: 1 May 2024
Accepted: 22 October 2024

Abstract

Context. Understanding the flux rope eruptivity and effects of data driving in modelling solar eruptions is crucial for correctly applying different models and interpreting their results.

Aims. We aim to investigate these by analysing the fully data-driven modelled eruption of the active regions (ARs) 12473 and AR11176, as well as preforming relaxation runs for AR12473 (found to be eruptive) where the driving is switched off systematically at different time steps. We intend to analyse the behaviour and evolution of fundamental quantities that are essential for understanding the eruptivity of magnetic flux ropes (MFRs).

Methods. The data-driven simulations were carried out with the time-dependent magnetofrictional model (TMFM) for AR12473 and AR11176. For the relaxation runs, we employed the magnetofrictional method (MFM) and a zero-beta magnetohydrodynamic (MHD) model to investigate how significant the differences between the two relaxation procedures are when started from the same initial conditions. In total, 22 simulations were studied. To determine the eruptivity of the MFRs, we calculated and analysed characteristic geometric properties such as the cross-section, MFR height, and physical stability parameters such as MFR twist and the decay index. Furthermore, for the eruptive cases, we investigated the effect 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 off 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 different relaxation simulations.

Conclusions. The results suggest that data driving can significantly influence the evolution of the eruption, with differences 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 affects the results significantly, as highlighted by the differences between the MFM and MHD MFRs, showing that eruptivity in MHD does not directly translate to eruptivity in the 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 powerful tool for determining MFR eruptivity.