Johan Muhamad¹ & Kanya Kusano²
1 Research Center for Space, National Research and Innovation Agency (BRIN), Indonesia
2 Institute for Space-Earth Environment Research, Nagoya University, Japan

Coronal mass ejections (CMEs) often accompany solar flares, which can cause geomagnetic disturbances on Earth. However, many flares occur without associated CMEs. The underlying mechanisms driving flare-CME associations remain unclear. Recognizing the more significant threat posed by eruptive flares, it is essential to improve our understanding of active regions (ARs) that have the capacity to produce both phenomena. To better understand this relationship, we analyzed ARs that produced solar flares with and without CMEs during solar cycle 24.

Current neutralization, defined as the ratio between electric direct-current and return-current (DC/RC), often correlates with magnetic shear along the polarity inversion line (PIL)^[1,2]. While large flares show different current neutralization levels between eruptive and confined events, a clear distinction remains elusive. Despite the known link between torus instability and eruptions, its relationship with current neutralization is unexplored. This study investigates current neutralization ratios and decay index critical heights in active regions (ARs) with and without coronal mass ejections (CMEs)^[3].

Figure 1| (a) Bz of the vector magnetic field for AR 11158. (b) Red (yellow) rectangle indicates the boundary of the region of interest (ROI) from which field lines were traced from positive (negative) polarity regions. (c) Jz, derived from the vector magnetogram data, with red and blue contours outlining values of 20 and −20 mA m⁻² respectively. (d) Contours of the magnetic flux used in the analysis, for positive (red) and negative (blue) polarities. The red cross in (d) marks the location of the maximum free-energy density.

We selected 45 flare events from solar cycle 24 with confidently assigned classifications (31 eruptive and 14 confined) based on the event lists compiled by Ref. [4]. These flares were chosen from events with a GOES SXR class exceeding M5.0 and located within 45° of the solar disk center between May 2010 and April 2016. Additionally, we utilized Spaceweather Helioseismic and Magnetic Imager Active Region Patch (SHARP) data, including Bp, Br, Bt, their associated errors, and disambiguation confidence levels. To analyze the magnetic field line connectivities, we employed nonlinear force-free field (NLFFF) models of the 45 selected ARs obtained from the ISEE NLFFF database at Nagoya University^[5].

Using vector magnetogram data (Figure 1a), we computed vertical electric current (Figure 1c). Subsequently, we estimated the current neutralization in the positive and negative polarities of the selected regions by considering magnetic field line connectivities derived from the NLFFF model (Figure 1b), then averaged these for each AR to get the total degree of current neutralization. After calculating the decay index (n) above each AR, we defined the critical height for torus instability as the altitude where n=1.5 above the location of maximum free-energy density.

Figure 2| Distribution of |DC/RC| (a) and critical heights (b) for eruptive and noneruptive flares. (c) Plot of critical heights of decay index and degrees of current neutralization for eruptive and noneruptive flares, normalized by the mean value of all critical heights in the data set. (d) The distribution of S parameter for eruptive and noneruptive flares. Dashed vertical lines mark the mean value of each population.

Figure 2a and Figure 2b show that eruptive events tend to originate from active regions exhibiting non-neutralized current or have low critical heights. On the other hand, confined flares are typically characterized by neutralized current conditions and high critical heights. Figure 2c highlights the value of combining information on both the degree of current neutralization and critical height for discriminating between eruptive and non-eruptive events.

Furthermore, we introduce a novel non-dimensional parameter, S, defined as the ratio of the degree of current neutralization to the normalized critical height. In contrast to the individual distributions of current neutralization and critical height, the distribution of S shows minimal overlap between eruptive and non-eruptive events (Figure 2d). This suggests that the S-parameter is potential as a reliable discriminator between these two types of eruptive ability. These findings imply that eruptive flares are more likely in active regions where flux ropes possess strong outward hoop forces and are situated at low critical heights, making them prone to the torus instability. On the other hand, non-eruptive flares may result from active regions with weaker outward forces, insufficient to initiate this instability.

References

[1] Liu, Y., Sun, X., Török, et al. 2017, ApJL, 846, L6
[2] Avallone, E. A., & Sun, X. 2020, ApJ, 893, 123
[3] Muhamad, J. & Kusano, K. 2025, ApJL, 983, L28
[4] Toriumi, S., Schrijver, C. J., Harra, L. K., et al. 2017, ApJ, 834, 56
[5] Kusano, K., Iijima, H., Kaneko, T., et al. 2021, Nagoya Univ. doi:10.34515/DATA.HSC-0000