Rui Wang1, Ying D. Liu1, 2, Shangbin Yang3, 2, Huidong Hu1
1 State Key Laboratory of Space Weather, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China
2 University of Chinese Academy of Sciences, Beijing 100049, China
3 Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
Homologous coronal mass ejections (CMEs) are an interesting phenomenon, and it is possible to investigate the formation of CMEs by comparing multi-CMEs under a homologous physical condition. AR 11283 had been present on the solar surface for several days when a bipole emerged on 2011 September 4 (Figure 1a). Four successive major eruptions happened from September 6 (two Mclass flares and two X-class flares, all with CME eruption; the four eruptions are named as E1, E2, E3, and E4). Its positive polarity collided with the pre-existing negative polarity belonging to a different bipole, producing recurrent solar activities along the polarity inversion line (PIL) between the colliding polarities (shown by the green dots in Figure 1b), namely the so-called collisional PIL (cPIL). Our results show that a large amount of energy and helicity were built up in the form of magnetic flux ropes (MFRs), with recurrent release and accumulation processes (see Figure 2).
Figure 1| SHARP vector magnetogram for the AR 11283. The vertical field (Bz) is plotted in the background with isocontours at 350 G (−350 G) in black (white); blue (red) arrows indicate the transverse field (Bt; |Bt| > 200 G) with a positive (negative) vertical component. The yellow and green rectangles indicate the regions for calculating the average decay index and the shear angle along the collisional PIL, respectively. The yellow arrows present the moving directions of P2-N2. The white rectangle and the black polygon show the masks for calculating the magnetic fluxes of P2 and N2, respectively. (b) 3D spacetime representation of the emerging bipoles using isosurfaces of |B| = 1000 G as viewed from the north. The green dots show the times of the four eruptions.
Figure 1a shows that AR 11283 was in a decay phase and that the pre-existing polarity pair P1-N1 was also decaying, but near the major polarity N1 in the south (N1S), a pair of emerging polarities P2-N2 was tracked from the beginning of 2011 September 4 to the end of September 8. The dynamic evolution of the emerging bipole also can be expressed in a 3D representation by means of an image stacking method. The 3D space-time representation of the magnetic flux tube structures in Figure 1b indicates the connectivity of the pairs of magnetic polarities. A flux deficit method is adopted and shows that magnetic cancellation happens along the cPIL due to the collisional shearing scenario proposed by Chintzoglou et al.
Figure 2| Evolution of magnetic free energy and helicities of AR 11283 over five days. (a) Magnetic energy (blue) derived from the NLFFF and PF extrapolation with an 1 hr cadence (green dotted line). (b) Magnetic helicity calculated by the finite volume method. GOES soft X-ray flux (1–8 Å channel, black) is overplotted
in (a) and (b). (c) Accumulated helicities from the shear term, the emergence term, and the total are colored in red, blue, and black, respectively. (d) Helicity fluxes across the photosphere from shear and emergence terms are colored in red and blue, respectively. The results are smoothed using central moving averages of 2 hr time series. The 1σ error is presented by the light-colored error bars. The sun-center angle of the emerging region is presented on the top x-axes. The vertical lines represent the onset times of the successive eruptions.
To implement the flux deficit method, we have to calculate each of the conjugated polarities individually. A mask is needed first to separate the like-signed polarities from different bipoles. There are some rules to define the mask (Chintzoglou 2021, private communication). (1) We must properly isolate the individual polarities from other like-signed polarities, and (2) we must contain as much surface area as necessary to account for the dispersion of flux from the polarity concentrations to the quiet Sun areas. We assume that the flux decay rate is similar for each polarity in our study, and therefore the rate of escape of flux from each mask is assumed to be the same. (3) We allow masks for conjugated polarities (opposite polarities can be distinguished by setting thresholds) to overlap, but no overlap of masks for like-signed polarities from different bipoles is allowed. (4) When measuring the flux of a conjugate bipole, i.e., P2-N2, the masks for positive and negative polarities should have equal pixel areas, to mitigate the errors coming from summing different amounts of quiet sun areas around the polarities to ensure a flux balance. For our case, P2 and N2 do not move too fast, and as a result it is easy to define a large area in which the negative and positive fragments can be counted in the P2 and N2 fluxes within the selected areas, respectively (see Figure 1a).
Figure 3| Time evolution of the magnetic flux for the conjugated polarities P2 (red) and N2 (blue). The green curve represents the flux deficit of N2-P2. The sun-center angle of the emerging region is presented on the top x-axis. The black arrows indicate the onset time of each flux emergence episode. The red arrow shows the onset of collision. Error bars for the deficit are plotted every 6 hr from the onset of collision. The vertical lines mark the onset times of the four eruptions.
Figure 3 shows that the total amount of canceled flux was ∼0.7×1021 Mx with an uncertainty of ∼13.2% within the confidence region of the 30° sun-center distance. The canceled flux amounts to 24% of the total unsigned flux of the bipolar magnetic region.
The results show that the magnetic fields beside the cPIL are very sheared, and the average shear angle is above 70° after the collision. The fast expansion of the twist kernels of the MFRs and the continuous eruptive activities are both driven by the collisional shearing process. These results are important for better understanding the buildup process of the MFRs associated with homologous solar eruptions.
For details of this work, please refer to our full publication Ref. .
 Chintzoglou, G., & Zhang, J. 2013, ApJL, 764, L3
 Chintzoglou, G., Zhang, J., Cheung, M. C. M., & Kazachenko, M. 2019, ApJ, 871, 67
 Wang, R., Liu, Y. D., Yang, S., & Hu, H. 2022, ApJ, 925, 202