Reversal of Current Helicity Trend During Solar Eruptions

Zheng Sun^1,2, Ting Li^3,4, Xinkai Bian⁵, Yijun Hou^3,4, Ioannis Kontogiannis^6,7, and Ziqi Wu^1,8

1 School of Earth and Space Sciences, Peking University, Beijing 100871, People’s Republic of China
2 Leibniz Institute for Astrophysics Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
3 State Key Laboratory of Solar Activity and Space Weather, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, People’s Republic of China
4 School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
5 Shenzhen Key Laboratory of Numerical Prediction for Space Storm, School of Aerospace, Harbin Institute of Technology, Shenzhen 518055, People’s Republic of China
6 Institute for Particle Physics and Astrophysics, ETH Zürich, Otto-Stern-Weg 5, 8093 Zürich, Switzerland
7 Istituto ricerche solari Aldo e Cele Daccò (IRSOL), Faculty of Informatics, Universitá della Svizzera italiana, CH-6605 Locarno, Switzerland
8 Centre for Mathematical Plasma Astrophysics, KU Leuven, Celestijnenlaan 200B bus 2400, B-3001 Leuven, Belgium

How to calculate current helicity?
To calculate the current helicity, we first obtain the three-dimensional photospheric magnetic field, which includes the vertical component $B_z$ and the horizontal components $B_x$ and $B_y$ . The vertical current density $j_z$ can then be derived from the horizontal magnetic field as $j_z = \frac{\partial B_y}{\partial x} - \frac{\partial B_x}{\partial y}$ . The photospheric current helicity density is defined as $h_c = j_z B_z$ . By integrating over the entire region of interest, we can further obtain the total magnetic flux $\Phi = \int B_z \, dS$ , the total vertical current $J_z = \int j_z \, dS$ , and the total current helicity $H_c = \int h_c \, dS$ .

Parameter evolution from Simulations
We performed 3D magnetohydrodynamic (MHD) flux rope eruption simulations based on the tether-cutting eruption scenario^[1,2]. The bottom boundary of the simulation domain is treated as the photosphere, allowing us to compute the photospheric parameters mentioned above.

Video 1: Time evolution of the two-dimensional distributions of $B_z, j_z, \& h_c$ , and the temporal variations of $\Phi_z, J_z, \& H_c$ . The time t=0 denotes the eruption onset.

Our analysis reveals a clear reversal in the evolution trend of current helicity associated with the eruption: a decrease before the eruption and an increase after the eruption (see the online animation). Interestingly, while $H_c$ exhibits a distinct reversal, neither $\Phi_z$ nor $J_z$ shows such behavior individually, suggesting that the variation originates not from the magnitude of these quantities but from their spatial redistribution during the eruption.

What is the mechanism of the reversal?
Since $h_c$ is defined as the product of $B_z$ and $j_z$ , regions with weak $B_z$ contribute little to $h_c$ . Therefore, we focus on the strong- $B_z$ regions, which dominate the helicity contribution. These regions (the magnetic poles) are enclosed by the orange contours in Figure 1. We then analyze the current variation within these areas.

Figure 1. Evolution of the current density in the model. Panel (a) shows the pre-eruption distribution of $j_z$ . Panels (b) and (c) exhibit the pre-eruption and post-eruption variations of $j_z$ . Panel (d) shows the average $j_z$ variations of the magnetic poles (orange) and PIL (cyan).

According to the difference maps of the current, we find that before the eruption (panel b), the current within the strong- $B_z$ regions decreases. However, it increases near the polarity inversion line (PIL), where $B_z$ is weak. This behavior is consistent with the energy accumulation scenario in the tether-cutting eruption model, where shear motions drive magnetic energy and electric current to concentrate along the PIL. As a result, the current in the strong- $B_z$ regions decreases, leading to a corresponding decrease in $H_c$ .

After the eruption (panel c), the current ribbons separate from each other, consistent with the flare ribbon separation process. In this phase, currents move away from the PIL, causing an increase of current in the strong- $B_z$ regions and consequently an increase in $H_c$ .

Panel (d) further quantifies this behavior: before the eruption, current moves from the strong- $B_z$ regions toward the PIL, whereas after the eruption, it moves from the PIL back to the strong- $B_z$ regions. This opposite motion of current before and after the eruption naturally results in the reversal trend of current helicity.

Can we find the reversal from observations?
We conducted a statistical analysis involving 50 > M5.0 solar flares. The data cover a time range of six hours before and four hours after each eruption. We found that 58% (29/50) of the cases exhibit a similar current helicity reversal trend (Figure 2a), whereas 42% show only a post-eruption increase without a pre-eruption decrease (Figure 2b).

Figure 2. Current helicity evolution in the observations. The samples can be divided into cases with pre-eruption decrease (a) and cases without pre-eruption decrease (b).

A detailed analysis of two representative reversal cases reveals that the underlying mechanism is consistent with our simulation results: before the eruption, the electric current tends to converge toward the PIL, whereas after the eruption, the current moves away from the PIL.

For the 42% of cases without a pre-eruption helicity decrease, we suggest that this may occur when the accumulation of current and magnetic energy does not take place immediately before the eruption, but rather at an earlier stage. For instance, a coherent flux rope may already exist in a stable state without further energy build-up^[3]. Therefore, we propose that the helicity decrease can serve as an indicator of the timing of energy accumulation in the active region.

Furthermore, by extending the pre-eruption time window for several cases, we found that the helicity decrease can be observed clearly even in the two-day evolution of the helicity curve, suggesting that this signature has potential predictive value for solar eruptions.

For details of this work, please refer to our full publication^[4].

References

[1] Moore, R. L., Sterling, A. C., Hudson, H. S., & Lemen, J. R. 2001, ApJ, 552, 833
[2] Jiang, C., Feng, X., Liu, R., et al. 2021, NatAs, 5, 1126
[3] Patsourakos, S., Vourlidas, A., & Stenborg, G. 2013, ApJ, 764, 125
[4] Sun, Z., Li, T., Bian, X., et al. 2025, ApJ, 990, 45

HMI Science Nuggets

218. Reversal of Current Helicity Trend During Solar Eruptions

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