Insights into the rotation mechanism of erupting magnetic flux ropes from data-driven simulations

1 Introduction

Coronal mass ejections (CMEs) are violent, large-scale eruptive phenomena in the solar atmosphere. They can release a substantial amount of magnetic free energy within an extremely short period and eject large quantities of magnetized plasma into interplanetary space, thereby triggering geomagnetic storms and other geomagnetic effects, serving as a major source of hazardous space weather (Chen, 2011; Webb and Howard, 2012; Schmieder et al., 2015). Typically, the main body of the ejected magnetic structure is considered a magnetic configuration winding around a central axis, referred to as a magnetic flux rope (MFR or simply “flux rope”). When such a flux rope is filled with abundant plasma of diverse temperatures, it exhibits distinct radiative characteristics, including filaments, sigmoids and hot channels (Cheng et al., 2013; Cheng et al., 2014a; Cheng et al., 2014b; Li et al., 2025).

Previous observational studies have shown that flux ropes would undergo a rotation of varying angles during their ascent in the eruptive events, manifested as changes in the orientation of the filament spine or the twisting of Sigmoid structures (Green et al., 2007; Zhou et al., 2022). Notably, in some large-scale filament eruptions, the rotation angle of the filament spine can approach nearly 100°, forming an inverted-γ structure (Song et al., 2018; Zhou et al., 2023a). Such large-angle rotation can affect the magnetic field orientation of CMEs as they propagate through interplanetary space, thus having significant implications for space weather forecasting (Vourlidas et al., 2011). Furthermore, statistical results from Zhou et al. (2020) indicate a strong correlation between flux rope rotation and filament chirality where sinistral/dextral filaments (for MFR with positive/negative helicity) tend to rotate clockwise/counterclockwise (CW/CCW), respectively. It suggests that the rotation of flux ropes during eruptions is not incidental but is a key dynamic process associated with magnetic topology reconstruction and magnetic helicity transport, profoundly influencing the redistribution of magnetic energy and the final structure of interplanetary flux ropes.

Recently, multiple theoretical and numerical simulations focusing on flux rope rotation mechanisms have been performed, from which two plausible physical explanations corresponding to internal and external mechanisms are proposed (Zhou et al., 2022; 2023b; Zhang et al., 2024; 2025). The kink instability acts as a major internal driver for the torsional rotation of flux ropes (Török et al., 2004). Once the twist number of a flux rope surpasses the critical threshold, the magnetic configuration turns unstable. To release redundant magnetic helicity, the structure converts internal twist into axial writhe via rotational motion and gradually evolves toward mechanical equilibrium. Accordingly, the kink instability is widely recognized as a primary trigger of flux rope eruptions (Török and Kliem, 2005; Williams et al., 2005; Keppens et al., 2019; Filippov, 2024). Nevertheless, Zhou et al. (2019) demonstrated that filaments would fail to erupt even when their heights exceeded the critical height for tour instability onset (Kliem and Török, 2006), owing to the large-angle rotation of filament structures. This indicates that flux rope rotation exerts a vital modulating effect during filament eruptions (Jiang et al., 2023). On the other hand, rotation can also be driven by unbalanced torques applied to the two legs of the flux rope. Specifically, the external toroidal magnetic field interacts with the intrinsic poloidal current and generates a persistent net torque on the ascending flux rope, which further governs its rotation sense and evolutionary speed (Kliem et al., 2012; Jiang et al., 2021; Zhou et al., 2023b). Therefore, disclosing the physical origin of rotational motion during flux rope eruptions stands as a core scientific problem for unraveling the fine dynamics of solar eruptions and refining eruption physical models.

Although theoretical simulations have been devoted to exploring the rotation mechanisms of flux ropes, numerical simulations constrained by observational data remain largely inadequate. In this study, we perform an observationally data-constrained magnetohydrodynamic (MHD) simulation, with particular emphasis on elucidating the role of torques in modulating the flux rope rotation during its eruption. The numerical model and the complete scenario of the simulated eruption, including the onset mechanism and twist accumulation of the MFR, are presented in a companion paper by Guo J. et al. (2026). Here, we provide a brief introduction to the numerical simulation setup in Section 2. Section 3 presents a comprehensive description of the eruption and rotation process of the MFR. A systematic examination of the Lorentz force is carried out in Section 4. Section 5 contains the conclusions and discussion, and a brief summary is provided in Section 6.

2 Numerical setup

On 22 June 2015, a typical hot channel eruption took place in Active Region 12371, accompanied by an M5.6-class flare and a halo CME. Rotational motion of the hot channel was detected throughout the eruption, offering excellent observational conditions to explore the rotation mechanism of magnetic flux ropes. Furthermore, the active region resided close to the solar disk center and was relatively isolated, rendering it an excellent candidate for numerical simulations investigating the full eruption evolution.

Based on the SDO/HMI vector magnetogram, the pre-eruptive magnetic filed of this active region was reconstructed from a nonlinear force-free field (NLFFF) extrapolation using the magneto-frictional relaxation method (Guo et al., 2016a; b). To further construct the evolution of the magnetic field, we employed a zero-β MHD model consistent with the simulations presented in Guo J. et al. (2026), which can be described by the governing Equations 1–3 as follow.

∂ ρ ∂ t + ∇ ⋅ ρ v = 0 (1)

∂ ρ v ∂ t + ∇ ⋅ ρ v v − B B + ∇ B 2 2 = 0 (2)

∂ B ∂ t + ∇ ⋅ v B − B v = ∇ × η J (3)

where v , B , J , ρ and η represent the velocity, magnetic field, electric current, density and numerical resistivity, respectively. Detailed configurations of these parameters can be found in Guo J. et al. (2026). During the first 20 time units of the simulation, an ideal converging flow was applied to accelerate the magnetic flux cancellation and facilitate the eruption. The numerical calculations were performed using MPI-AMRVAC (Xia et al., 2018; Keppens et al., 2023), and the domain of the simulated region is [ X min , X max ] × [ Y min , Y max ] × [ Z min , Z max ] = [ − 173.4 , 173.4 ] × [ − 173.4 , 173.4 ] × [ 1,347.9 ] Mm 3, with the pixel size of uniform grid at 240 × 240 × 240.

3 MFR eruption and rotation

According to Guo J. et al. (2026), the eruption process of the MFR can be divided into a slow rise phase and an impulsive eruption phase. At the beginning, the average twist number of the magnetic field lines near the magnetic neutral line already exceeded one turn (T w = 1.19), which further increased to 1.27 before the CME initiation, indicating the core of the MFR has already formed prior to the eruption. At about t = 2τ 0, the MFR began to rise slowly. After the apex of the MFR reached a height of approximately 13 Mm, the MFR subsequently accelerated and entered into the impulsive phase at about t = 8τ 0. During this process, the twist number of the MFR steadily increased to 1.84, while its axis did not exhibit significant writhe. Guo J. et al. (2026) examined the temporal evolution of J / B, and found that the fast magnetic reconnection sets in after the eruption onset, as shown in their Figure 6, suggesting the increase of the twist is mainly due to the gentle magnetic reconnection before the eruption. This is different from models in which the twist number is built up through fast magnetic reconnection during the eruption. Following the eruption onset, the twist number rose further from 1.84 to 2.15 turns. As the MFR undergoes rotation, the twist number subsequently declined and settled at an approximately constant value of 1.9 turns, while a portion of the field line twist was converted into writhe. Moreover, the decay index of the potential field at 13 Mm is approximately 1.5, which is very close to the critical value for the torus instability (Kliem and Török, 2006). Therefore, it was suggested that the torus instability is likely the primary trigger for this eruption event. More details on the onset mechanism of the MFR eruption can be found in Guo J. et al. (2026).

After the MFR impulsive erupted, its main spine went through a significant rotating motion as shown in Figure 1, where panels (a) and (b) present the top view and side view observed from the MFR, respectively. From Figure 1 and attached movie, it was found that the northern leg of the MFR rapidly rose first as the impulsive phase started, and then the MFR was entirely expanded in an Ω shape. Subsequently, the MFR spine gradually changed its orientation from an east–west direction to north–south in a shape of reversed γ, indicating a large-angle counter-clockwise rotation with an angular change of approximately 90°. However, during this process, the twist number of the MFR remained stable at around 1.9 turns. This is inconsistent with the description of the kink instability (Török et al., 2004), in which the twist number is theoretical decreased and converted into writhe of the MFR spine. Therefore, we speculate that there should be an alternative mechanism, such as external force, is responsible for driving the rotation of the MFR during the eruption.

4 Force analysis

To further analyze the influence of the Lorentz force on the rotation of the MFR during its eruption, we decomposed the total magnetic field B in the simulation into external potential field ( B e ) and flux-rope field ( B F R ), as described in (Guo J. H. et al., 2026): B = B e + B F R. Since the potential field satisfies the current-free condition, the total current J can be considered to originate entirely from the flux-rope field: J = J F R = 1 μ 0 ∇ × B F R. So we can decompose the Lorentz force on the MFR into the external force and self force. Since the external force calculated from J F R × B e would include two components in x- and y-direction, respectively. Furthermore, we divided the transverse component of the external potential field into poloidal field ( B P ) and toroidal field ( B T ), where B P and B T were directly determined by the x- and y-components of the potential field, respectively. Hence, we can examine the effects of different components of the Lorentz force in x- and y-direction acting on the MFR, for the Lorentz force component J F R × B P lies in the y-z plane while force component J F R × B T lies in the x-z plane. In this way, the lateral Lorentz force on the MFR can be decomposed into contribution from the flux rope itself, the external toroidal and poloidal field.

To demonstrate the Lorentz forces acting on the MFR legs during the eruption, we take an x-y plane at a height of 42 Mm, where the MFR legs can be reliably intercepted at different simulation times and the field lines are relatively concentrated. Figures Figures 2, 3 present the transverse distribution of the Lorentz force in the x–y plane at a height of 42 Mm, which was divided into its x- (Figure 2) and y-direction (Figure 3), respectively. As shown in Figure 2, all Lorentz force components exhibit opposite directions (signs) at the two legs of the MFR, indicating the presence of a net torque that drives the rotation of the MFR. Furthermore, the self-force on the northern leg points to the right, while that on the southern leg points to the left, suggesting that the self-force alone would drive a clockwise rotation. This direction is opposite to the actual rotation of the MFR in the simulation, indicating that the self-force primarily hinders its rotation. In contrast, the external force acting on the MFR legs points in the opposite direction and thus plays a positive role in driving the observed counter-clockwise rotation. Comparing Figures Figures 2, 3, it was found that the Lorentz force in the y-direction is more significant than that in the x-direction. It implies that during the MFR eruption, the counter-clockwise rotation is most likely driven by the poloidal background field above the flux rope.

5 Conclusion

It has long been widely accepted that the rotation of an erupting flux rope reflects the conversion of magnetic twist into writhe based on the helicity conservation. Based on this picture, two implications are commonly inferred: (1) the rotation angle should increase with the twist number of the pre-eruptive flux rope; and (2) the lateral Lorentz force responsible for the rotation should primarily originate from the flux rope itself ( J F R × B F R ), rather than from interactions with the external magnetic field ( J F R × B e ).

The first implication suggests that eruptions exhibiting large-angle rotations are associated with strongly twisted pre-eruptive flux ropes. Furthermore, it has been argued that such large-angle rotations indicate that the eruption is triggered by kink instability, since a sufficiently high twist is required to exceed the kink-instability threshold. However, both our previous study and the present work lead to a different conclusion. Based on a parameter survey, Zhang et al. (2024) showed that large-angle rotation can occur in weakly twisted flux ropes when strong external toroidal magnetic fields are present. Therefore, the rotation angle during an eruption is not determined solely by the initial twist of the flux rope. In the present study, the decay index reaches the commonly adopted critical value of 1.5 at the onset of the eruption, suggesting that the eruption is more likely triggered by the torus instability rather than the kink instability. As illustrated in the Figure 6 in Guo J. et al. (2026), the twist number of the MFR continuously increases during the slow-rise and main-acceleration phases. This behaviour contradicts the standard picture of kink instability as an eruption trigger, where the twist number decreases as magnetic twist is converted into writhe of the MFR. Consequently, our results indicate that the large-angle rotation of filaments or hot channels observed during eruptions does not necessarily imply the presence of a highly twisted pre-eruptive flux rope, nor does it implies that the eruption is triggered by kink instability.

Regarding the second implication, our results show that the self Lorentz force of the flux rope ( J F R × B F R ) tends to produce a clockwise torque, opposite to the observed anticlockwise rotation. In contrast, the Lorentz force arising from the interaction between the flux-rope current and the external magnetic field ( J F R × B e ) drives the anticlockwise rotation, which is consistent with the dynamics of the observed flux rope. These findings suggest that the self-force of the flux rope actually suppresses its rotation, whereas the external magnetic field plays a dominant role in producing the observed rotational motion.

In summary, this work improves our understanding of the mechanism governing MFR rotation. Our simulations demonstrate that the rotation angle during an eruption is governed primarily by the external magnetic field rather than by the intrinsic properties of the flux rope itself. Moreover, a large rotation angle cannot be regarded as evidence that the eruption was initiated by kink instability.

6 Summary

In this paper, based on a data-driven MHD simulation, we reproduce the large-angle rotation ( ∼ 100 ° ) of an erupting flux rope. The eruption is initiated by the torus instability and eventually develops into a CME. Furthermore, through a decomposition analysis of the Lorentz force, we demonstrate that the lateral Lorentz force associated with the interaction between the flux-rope current and the external poloidal field ( J F R × B P ) is the primary driver of the flux-rope rotation, rather than the flux rope’s self-force ( J F R × B F R ) in the data-driven MHD simulation. These results suggest that the rotation of erupting flux ropes mainly reflects the magnetic configuration of the surrounding coronal field rather than the intrinsic properties of the flux rope itself, for both successful eruptions (Zhou et al., 2023b) and confined eruptions (Guo J. H. et al., 2026).

Generative AI statement

The author(s) declared that generative AI was used in the creation of this manuscript. For translation, spelling and grammar error checking.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fspas.2026.1919872/full#supplementary-material

Supplementary material Supplementary material at the source

Footnotes

Edited by: José Juan González-Avilés, National Autonomous University of Mexico, Mexico

Reviewed by: Keiji Hayashi, George Mason University, United States

Abril Sahade, NASA Goddard Space Flight Center, United States