E. Liokati^{1}, A. Nindos^{1}, & Y. Liu^{2}

1 Section of Astrogeophysics, Department of Physics, University of Ioannina, 45110, Greece

2 W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305-4085, USA

Magnetic helicity (a conserved quantity describing the complexity and twist of magnetic field, e.g., see the review Ref. [1]) and magnetic energy in solar active regions (ARs) are two important physical quantities for the study of magnetic origin of solar eruptions, such as coronal mass ejections (CMEs) and flares (e.g., see the review Ref. [2]). However, little is known about their role in the initiation of CMEs from emerging ARs. To remedy this situation, we use vector magnetic field data obtained by the SDO/HMI and calculate the magnetic helicity and energy injection rates across the photosphere, as well as the resulting accumulated budgets in 52 emerging ARs from the start time of magnetic flux emergence until it reached a heliographic longitude of 45° West (W45). The results are checked against the eruptive potential of the ARs: 7 of them produced CMEs, but 45 did not. An indicative example of the evolution of the magnetic configuration of one of our eruptive ARs is presented in Figure 1, where we show snapshots of the normal component (B_{z}) of the AR’s magnetic field.

Figure 1| Selected HMI images of the normal component, B

_{z}, of the photospheric field of eruptive AR 11422 taken during the study interval. All images are saturated at ±1900 G. The horizontal white line corresponds to 150″.

From our magnetic energy and helicity computations we construct scatter plots of the accumulated amount of magnetic helicity and energy. We find that, in a statistical sense, the eruptive ARs accumulate larger budgets of magnetic helicity and energy than the noneruptive ARs over intervals that start from the flux emergence start time and end (i) at the end of the flux emergence phase (Figure 2, left) and (ii) when the AR produces its first CME or crosses W45, whichever occurs first (Figure 2, right).

The most important feature of the scatter plots of Figure 2 is that the eruptive ARs tend to appear in the top right part of this plots. This indicates that if magnetic helicity and energy thresholds of 9×10^{41} Mx^{2} and 2×10^{32} erg are crossed, ARs are likely to erupt. In terms of accumulated magnetic helicity and energy budget, the segregation of the eruptive from the noneruptive ARs is violated in one case (region (iii), Figure 2 right) when an AR erupts early in its emergence phase, and in six cases (region (i), Figure 2 right) in which noneruptive ARs exhibit large magnetic helicity and energy budgets.

Figure 2| Scatter plots of the accumulated amount of magnetic energy vs absolute helicity during the flux emergence intervals of the ARs (left panel) and during the intervals from emergence start time until the ARs cross W45 or produce their first CME, whichever occurs first (right panel). The red boxes and black crosses correspond to eruptive and noneruptive ARs, respectively. The blue dashed lines define the thresholds for magnetic helicity and energy above which ARs show a high probability to erupt. The green lines show least-squares best logarithmic fits.

For these six ARs we investigate whether the overlying background magnetic field inhibited eruptions. In Figure 3 we show scatter plots of accumulated budgets of magnetic helicity and energy, which were registered in the right panel of Figure 2, versus the height at which the decay index reached the critical value of n_{c}=1.5. Both the magnetic helicity and energy budgets spread all over the n_{c} heights. However, the six outlier ARs tend to acquire n_{c}=1.5 at larger heights (>60 Mm) than most eruptive ARs (compare the locations of the red boxes and the green diamonds). Therefore, although these ARs possess significant helicity and energy budgets, they did not erupt because the overlying magnetic field tended to provide stronger or more extended confinement than in eruptive ARs.

Figure 3| Top: Accumulated magnetic energy from emergence starting times until the ARs produce their first CME or cross W45, whichever occurs first, vs height at which the decay index that has been calculated at the end of the intervals that were used to determine the magnetic energy budgets, reaches a value of 1.5. Red boxes denote eruptive ARs, and green diamonds denote the noneruptive ARs that appear in region (i) in the right panel of Figure 2. All other ARs are marked by crosses. Bottom panel: Same as the top panel, but for magnetic helicity instead of magnetic energy.

Our results indicate that emerging ARs tend to produce CMEs when they accumulate significant budgets of both magnetic helicity and energy. Any study of their eruptive potentials should consider magnetic helicity together with magnetic energy.

This work is based on a paper that has been accepted for publication in A&A (Ref. [3]).

### References

[1] Pevtsov, A.A., Berger, M. A., Nindos, A., Norton, A. A., & van Driel-Gesztelyi, L, 2014, *Space Sci Rev*, **186**, 285

[2] Georgoulis, M. K., Nindos, A., & Zhang, H. 2019, *Phil. Trans. Royal Soc. London Ser. A*, **377**, 20180094

[3] Liokati, E. Nindos, A. & Liu, Y, 2022, *A&A*, in press, http://arxiv.org/abs/2202.04353