The winding number of coronal flux ropes I. Data-driven time-dependent magnetofrictional modelling

Context. Magnetic flux ropes are key structures in solar and solar-terrestrial research. Their magnetic twist is an important quantity for understanding their eruptivity, their evolution in interplanetary space, and their consequences for planetary space environments. The magnetic twist is expressed in terms of a winding number that describes how many times a field line winds about the axis of the flux rope (FR). Due to the complexity of calculating the winding number, current methods rely largely on its approximation. Aims. We use a data-driven simulated FR to investigate the winding number T-g in comparison to the commonly used twist proxy T-w, which describes a winding of two infinitesimally close field lines. We also estimate the magnetic flux enclosed in the resultant FR(s). Methods. We use the magnetic field analysis tools (MAFIAT) software to compute T-g and T-w for data-driven time-dependent magnetofrictional modelling of AR12473. Results. We find that the FR boundaries can significantly differ depending on whether they are defined using the twist approximation T-w or the winding number T-g. This also significantly affects the FR structure and the estimates of the enclosed magnetic flux. For the event analysed here, T-g also reveals that the twisted flux system consists of two separate intertwined FRs. Conclusions. The results of this study suggest that the computation of the winding number (T-g) is important for investigations of solar FRs.