Indian Institute of Astrophysics, II Block, Koramangala, Bengaluru-560 034, India
Magnetic helicity is believed to play a fundamental role in generating large-scale activity on the Sun. Magnetic helicity describes the magnetic field complexity, including twist, writhe, knot, and linkages of magnetic field. When coronal magnetic field is being pumped with helicity and energy, the magnetic complexity and non-potentiality increases. Using simultaneous magnetic field and coronal observations, several studies focused on the magnetic non-potential parameters to understand their roles in CMEs and flares. From those studies, it is now believed that the magnetic flux rope is built up by line-tied photospheric flux motions, such as magnetic flux emergence or horizontal flows. These processes inject magnetic helicity into the higher solar atmosphere, increasing the twist and kink of a flux rope (self-helicity) and the linkage between different flux ropes (mutual helicity). Magnetic helicity is conserved in an ideal MHD process and changes very slowly in a resistive process. Thus, a flux rope with continuous injection of magnetic helicity inevitably erupts to remove the accumulated helicity, manifested as a CME.
Figure 1| Magnetic evolution in AR 12673: a) net flux in positive (north) and negative (south) magnetic polarities. Disk integrated GOES X-ray (1.0–8.0Å passband) flux is also shown with y-axis scale on the right. b) Systematic evolution of net vertical current from north and south polarities. c) Neutralization of net current in individual polarities. Horizontal dashed line marks the neutralization level of unity. Total length of all SPIL segments are also plotted with y-axis scale on right. d)time-rate of helicity flux normalized by averaged net flux of positive and negative polarities. Normalized accumulated helicity () is also plotted with y-scale on right. The normalized helicity flux reaches to 0.09 turns indicating the moderately twisted flux system. e) Energy flux injection and its accumulative quantity. Rapid flux emergence phase is marked with grey shade and the two major flaring phases are indicated with orange shade.
The above scenario of helicity role in the AR eruptivity is well portrayed in a recent study. Using the uninterrupted observations of space-borne Solar Dynamics Observatory, we studied the most violent AR 12673 that produced strongest flares in Solar Cycle 24. The AR emerged with two bipolar regions on September 2, 2017 in a pre-existing positive-polarity sunspot. The velocity field derived from tracked vector-magnetograms indicates persistent shear and converging motions of flux regions about the polarity inversion line (PIL). In Figure 1, the time evolution of the X-ray flux, net-electric current, helicity, energy flux injection are shown. A major helicity injection occurs during rapid flux emergence, consistent with the very fast flux emergence phase. While this helicity flux builds up the sigmoid by September 4, the helicity injection by the continued shear and converging motions in the later evolution contributes to the sigmoid sustenance and its core field twist, as a manifestation of the flux rope that erupts after exceeding critical value of twist. Moreover, the total length of the sheared PIL segments correlates with the non-neutralized currents and maintains a higher value in both polarity regions as a signature of eruptive capability of the AR, according to flux rope models. This result also implies that the non-neutralized currents arise in the vicinity of the sheared PIL. In Figure 2, an example of force-free extrapolation to the AR 12673 is displayed. The modeled magnetic structure well resembles the coronal observation of AIA 94Å, capturing major features like twisted core flux as flux rope, and hook-shaped sections connecting in the middle of the PIL. The emission in 304Å is also reproduced in vertical integration of volume electric current. The study of quasi-separatrix-layers reveals that the sheared arcade, enclosing the flux rope, is stressed to a critically stable state and its coronal height becomes doubled from September 4-6.
Figure 2| Magnetic field extrapolation by force-free field approximation to the corona. a) Field lines showing the magnetic structure of AR 12673 on September 4, 2017 at 18:00UT. Background is radial magnetic field map. b) Magnetic structure on coronal 94Å image. c) Map of vertically integrated electric current. d) Coronal image of 304Å from AIA.
In order to have more insight on the helicity flux input, we compare normalized helicity flux injection () from different ARs (Figure 3). This value is a measure of non-potentiality per unit flux per unit time and indicates how fast the AR accumulates energy and helicity in the corona. As is clear from the plot, this parameter evolves at a higher rate by a factor of 3 in AR 12673 compared to other ARs. The AR 12192 is a flare-prolific region without CMEs in contrast to the rest of the ARs, and has small injection value per flux tube. Interestingly, this value in the AR 12673 is quite stronger by a factor of 2 than the strong CME-prolific ARs 12371 and AR11429. This suggests that the normalized helicity flux is a key parameter to distinguish eruptive and non-eruptive ARs and also predicts the severe space-weather events.
Figure 3| Comparison of normalized helicity flux injection in 4 flare/CME producing ARs. Starting times are 2017-08-31T19:12 UT, 2015-06-19T00:00 UT, 2014-10-21T00:00 UT, 2012-03-06T00:00 UT , for AR 12673, 12371, 12192, 11429 respectively. Normalized helicity flux injection in AR12673 is comparatively high with major injection phase co-temporal with rapid flux emergence.
 Taylor, J. B. 1974, Phys. Rev. Lett., 33, 1139
 Vemareddy, P., 2019, ApJ, 872, 182
 Sun, X., Bobra, M. G., Hoeksema, J. T., & et al. 2015, ApJ, 804, L28
 Vemareddy, P., 2017, ApJ, 845, 59