The triggering process of an X-class solar flare on a small quadrupolar active region

Solar flares are one of the most explosive phenomena in the Sun’s atmosphere and may impact the space weather (Schwenn, 2021). Therefore, the triggering mechanism of major flares ($\geqslant$ M1.0) has been the focus of solar physics researches and the space weather forecasting. Its enormous energy of up to 10³² erg comes from the solar magnetic field. The previous studies (Sammis et al., 2000; Teh, 2019) have shown that major flares usually tend to erupt from large active regions (ARs), where the total unsigned magnetic flux is generally large too. Other parameters of the magnetic field, such as the magnetic shear and the magnetic free energy of ARs, are also important tools to analyze major flares (Wang et al., 1996; Titov & Démoulin, 1999; Leka & Barnes, 2007).

The magnetic field continuously emerges from the convective zone to the photosphere of the Sun, and emerging flux regions (EFRs) carry a considerable amount of magnetic flux and magnetic shear, which may effectively enhance the non-potentiality and the occurrence of major flares (Song et al., 2013). Recent research has revealed that collisional shearing of opposite polarities from different EFRs may lead to major flares (Chintzoglou et al., 2019). The magnetic flux cancellation (Aulanier et al., 2010; Green et al., 2011) and fast rotating sunspots (Zhang et al., 2007) are closely related to the eruptions of flares and coronal mass ejections (CMEs). Sometimes, the various magnetic field characteristics mentioned above are concentrated around the polarity inversion line (PIL) of a $\delta$ sunspot, where the umbrae of opposite polarities in a single penumbra, resulting in the great activity of ARs (Zirin & Liggett, 1987; Liu et al., 2005; Yang et al., 2017b; Toriumi et al., 2017; Liu et al., 2021).

Previous studies have shown that the tether-cutting reconnection, kink instability, and torus instability may be responsible for the onset of solar magnetic explosions (Moore et al., 2001; Chen et al., 2014, 2018, 2019). The interaction of two filaments supported by two magnetic flux ropes (MFRs) can also lead to an eruption (Linton et al., 2001; Yang et al., 2017a), and some of the observed cases were the interaction or even merging of two filaments with the same chirality (Jiang et al., 2014; Zheng et al., 2017), and some were with opposite chiralities (Joshi et al., 2016).

Generally, the CSHKP standard flare model (Carmichael, 1964; Sturrock, 1966; Hirayama, 1974; Kopp & Pneuman, 1976) is used to explain the magnetic reconnection and the flare process in a two-dimensional (2D) scenario. In the CSHKP model, the core magnetic structure of the eruption (for example, MFRs) located near the PIL rises for some reasons, resulting in a vertical current sheet and the magnetic reconnection below it in the corona (Forbes & Isenberg, 1991). Particles accelerated by the energy released by the magnetic reconnection will then move downward along the reconnecting magnetic loops to the chromosphere and even to the photosphere, where two gradually separated flare ribbons are formed at the foot points of the magnetic field lines. As a result, these flares are called two-ribbon flares (Yokoyama & Shibata, 1997; Fletcher et al., 2011).

However, recent studies on X-shaped flares highlighted the limitations of the CSHKP model as a 2D model and explored the three-dimensional (3D) nature of the flare process (Liu et al., 2016a; Jiang et al., 2017; Kawabata et al., 2017). As the term suggests, X-shaped flares display a relatively rare, complex flare ribbon that resembles the letter ‘X’. The source region for an X-shaped flare is usually a 3D quadrupolar magnetic field, which consists of two oppositely directed dipoles that are not in the same line. It forms magnetic topologies like null points and quasi-separatrix layers (QSLs), where the currents are accumulated and finally lead to magnetic reconnections (Li et al., 2021). Quadrupolar fields of different scales may exist at various locations on the Sun. Some quadrupolar magnetic fields were composed of two ARs that were respectively located in the northern and southern hemispheres of the Sun (Sun et al., 2014), and someones were composed of large-scale magnetic structures among multiple ARs in the same hemisphere (Hou et al., 2020). Occasionally, the quadrupolar magnetic configuration was located in a limited part of an AR (Sun et al., 2012; Li et al., 2016; Mitra et al., 2022) or at the outskirts of an AR (Liu et al., 2016a). The quadrupolar magnetic field may constitute the main part of an AR, but it has not been reported yet.

This paper reports a small AR (NOAA AR 12887) mainly constituted by a 3D quadrupolar magnetic field, in which the second X-class flare of the current Solar Cycle 25 erupted. The observations and data related to the X-class flare will be briefed in Section 2. Section 3 focuses on an interesting question: how a powerful flare was triggered in the small AR? The discussion and conclusions are given in Section 4.

This study used the ultraviolet and extreme ultraviolet (UV/EUV) multi-wavelength images of Atmospheric Imaging Assembly (AIA, Lemen et al. 2012) onboard the Solar Dynamics Observatory (SDO, Pesnell et al. 2012), with a cadence of 12 seconds and a spatial resolution of 0.6″ pixel^-1, as well as 195 Å images of the Solar X-ray and Extreme Ultraviolet Imager (X-EUVI, Chen et al. 2022; Song et al. 2022) onboard the FengYun-3E (FY-3E, Zhang et al. 2022) satellite, with a cadence of $\sim$7 seconds and a spatial resolution of $\sim$2.5″ pixel^-1. FY-3E, successfully launched at 23:28 UT on 4 July 2021, is the world’s first early-morning-orbit civil meteorological satellite, and X-EUVI is the first solar X-ray and EUV imager of China in orbit. We analyzed the evolution of sunspots and the magnetic field of AR 12887 by combining the intensitygrams and magnetograms observed by the Helioseismic and Magnetic Imager (HMI, Scherrer et al. 2012) onboard the SDO. All the SDO data used in this study were processed by the SolarSoftWare (SSW) standard procedures¹¹1https://www.mssl.ucl.ac.uk/surf/sswdoc/.

To investigate the quadrupolar magnetic configuration of AR 12887, the photospheric vector magnetograms were also used to extrapolate the coronal magnetic fields in this work. The photospheric vector magnetic fields were computed by the Very Fast Inversion of the Stokes Vector code (Borrero et al., 2011), and the remaining 180° azimuth ambiguity was resolved by the Minimum Energy method (Metcalf, 1994; Leka et al., 2009). We used the vector magnetograms provided by the Space-weather HMI Active Region Patches (SHARP, Bobra et al. 2014) with a cadence of 12 minutes from 00:00 UT to 19:48 UT on October 28, 2021, for extrapolations and free energy calculations of AR 12887. At first, all vector magnetograms from photospheric measurements were preprocessed to meet the force-free assumption (Wiegelmann et al., 2006). The nonlinear force-free magnetic field (NLFFF) with the “weighted optimization” method of Wheatland et al. (2000) and Wiegelmann (2004) then was used to obtain the 3D coronal magnetic fields. The calculation was conducted within a box of $232\times 208\times 232$ uniform grid points with $\Delta x=\Delta y=\Delta z=1$″, which was downscaled from the original resolution of 0.5″pixel^-1. As a result, we obtained a series of extrapolations over every 12 minutes. Based on the NLFFF extrapolation of the coronal magnetic field, the distributions of the twist number $T_{w}$ (Berger & Prior, 2006) and the squashing factor $Q$ (Demoulin et al., 1996; Titov et al., 2002) were calculated by the code developed by Liu et al. (2016b).

This work also used solar region summary and events documents²²2ftp://ftp.swpc.noaa.gov/pub/warehouse/ of the National Oceanic and Atmospheric Administration (NOAA) Space Weather Prediction Center to statistically analyze the area of the ARs that produced M- and X-class flares from August 1996 to November 2021. Although some omissions and inaccuracies were found in the NOAA documents, it would not affect the overall results of this study due to the large number of statistical samples. Geostationary Operational Environmental Satellites (GOES) soft X-ray (1-8 Å) flux³³3http://www.ngdc.noaa.gov/stp/satellite/goes/index.html is employed to determine the class of the X-ray flares.

On October 28, 2021, the Sun produced a GOES X1.0 flare, the second X-class flare of Solar Cycle 25, from a small AR NOAA 12887. According to the NOAA-reported AR areas (in millionths of a solar hemisphere or $\mu h$) and flare events, the average area of AR 12887 (313 $\mu h$) is much smaller than the average area of the X-class flare-productive ARs over the past 25 years (781 $\mu h$) and even smaller than that of the M-class flare-productive ARs (504 $\mu h$). If an X-class flare occurs in a small AR, it may indicate that there is a large amount of magnetic free energy that can be released and converted into the radiation and other forms of energy. Fortunately, unlike the first X-flare of Solar Cycle 25 that exploded on the solar west limb, AR 12887 appeared near the center of the solar disk at location S26W07 on October 28 (Figure 1(b1)-(b2)), which provided an opportunity to study the evolution of the magnetic field configuration of the AR.

The above results converge to a clear and concise scenario shown in Figure 7. In the beginning, the AR has a magnetic field configuration composed of a quadrupolar field and large-scale arcades overlying filament (Figure 7(a)). Several EFRs appeared in the AR, while a large sunspot (N2) disintegrated. The magnetic configuration of a 3D quadrupolar field may be favorable for the formation of multiple filaments, but an appropriate mechanism is still needed to trigger a major eruption. One small sunspot (Nc) and one end of a filament (MFR1) fast move toward the center of the quadrupolar field (Figure 7(b)). The sunspot Nc collides with a nonconjugated opposite magnetic polarity Pc (i.e., the collision of polarities), and another filament (MFR2) meets MFR1 at the same area. Then the tether-cutting-like reconnection occurs above the area, resulting in the merging of these two MFRs, and the rising of the newly-formed large filament (MFR3) finally triggers an energetic X-class flare (Figure 7(c)). A two-ribbon flaring loop first appears below the rising large filament, and then the rising filament pushes the overlying magnetic fields westward and forms some flaring loops around the core of the AR (i.e., the null point) during the impulsive phase of the X-class flare. Similar scenario has also been reported in Hou et al. 2020, where an erupting filament pushed its overlying fields toward the fields above another stable filament around and caused successive external reconnection between their overlying fields, resulting in simultaneous brightenings on both sides of the stable filament. Eventually, the flaring loops of the X1.0 flare in AR 12887 display a mixed morphology of the two-ribbon flare and the X-shaped flare (Figure 7(d)), and accompanied by a halo CME, a major solar energetic particle event, and a global EUV wave event (Hou et al., 2022).

Quadrupolar-field ARs are found to a desire birth place of solar flares (e.g., AR 11967 and AR 12887), but appropriate conditions are need for a major flare (Nishizuka et al., 2017). Previous studies tended to attribute the occurrence of major flares in quadrupolar ARs to magnetic reconnection at a null point or QSLs. In quadrupolar ARs, magnetic reconnection in these unique magnetic topologies theoretically can lead to more complex flare ribbons than bipolar ARs. Indeed, several previous studies have reported the occurrence of X-shaped major flares in quadrupolar ARs, such as NOAA 11967 (Li et al., 2016; Jiang et al., 2017; Kawabata et al., 2017). In our current study, the X-class flare in the quadrupolar AR 12887 is found to associate with quasi-X-shaped flare ribbons, and it displayed three distinct observational features: (1) the NOAA-reported area of AR 12887 (250 $\mu h$ on the day of the X-class flare) is much smaller than that of AR 11967 (1410 $\mu h$ on the day of three X-shaped M-class flares), but AR 12887 unexpectedly erupted an X-class flare and AR 11967 only erupted M-class flares. (2) In our case, the flare ribbons swept the whole AR, but those flare ribbons reported in other ARs only located at the outskirts or a limited part of their corresponding AR. (3) The X-class flare in our case indeed included an ensuing null-point reconnection, but it appeared to be a byproduct at the overlying null point due to the merging and ensuing eruption of two MFRs. Based on these features, we suggest that the collision of Nc and Pc facilitated the interaction and merging of two adjacent MFRs, triggering an eruption in the quadrupolar magnetic configuration. As a result, due to the merging eruption process, additional reconnection was induced at the overlying null-point topology. Therefore, the entire AR 12887 participated in the eruption and released more amount of magnetic free energy, leading to the unexpected X-class flare.

Moreover, the collisional polarities (Nc and Pc) in AR 12887 come from different EFRs (i.e., nonconjugated polarities), which is consistent with AR 11158 and AR 12017 in a previous study (Chintzoglou et al., 2019). They have collisional shearing at the center of the quadrupolar field in AR 12887, accompanied by the magnetic cancellation, magnetic emergence, and sunspot rotation. The collisional polarities of AR 12887 is somewhat similar but not strictly a $\delta$ sunspot because the umbrae of opposite polarities are only partially surrounded by the penumbra. It is also small ($\sim$10 Mm) with a short main PIL. Compared with large $\delta$ spots in other ARs (Liu et al., 2005; Yang et al., 2017b) which may store more magnetic free energy, the main function of the collisional polarities in AR 12887 may be to act as a trigger of the flare process. It has indeed played a similar role to large $\delta$ spots, providing a common PIL for the two filaments (F1 and F2), so that the magnetic axes of the originally approximately perpendicular filaments are parallel in the PIL, and eventually lead to the merging of two filaments with the same chirality. In addition, the three X-shaped flares of AR 11967 were all confined (i.e., without CME), but the X1.0 flare of AR 12887 was accompanied by a CME due to the existence and eruption of the filaments in its 3D quadrupolar configuration.

Traditional flare forecasting methods usually use the area and the magnetic classification of an AR to quickly estimate the probability of the occurrence of a major flare. However, AR 12887 is not only small in area but also has a relatively simple magnetic classification ($\beta\gamma$ on October 28, 2021). It may lead to underprediction and confirms the importance of magnetic parameter calculations in flare forecasting.

This study focused on the X1.0 flare that occurs in the complicated magnetic configuration of AR 12887, which is a large-scale quadrupolar field accompanied by the pre-existing filament magnetic system. We found that: 1) although the area of AR 12887 is smaller than the average area of the major flare-productive ARs over the past 25 years and also smaller than those of previously reported X-shaped flare ARs, the magnetic emergence, magnetic shear, and other magnetic field evolution processes in the AR accumulate enough magnetic free energy to produce an X-class flare; 2) the main function of the collision of polarities is triggering the coupled eruption of the magnetic configuration with the pre-existing filament magnetic system and the quadrupolar field, i.e., the fast convergence and collision of nonconjugated polarities lead to two filaments (MFRs) interacting and subsequent merging into a larger filament due to the tether-cutting-like reconnection process with their opposite-polarity footpoints located on the different polarities, and then the newly-formed large filament loses its equilibrium, rises and erupts, involving the entire AR, and finally produce the mighty eruption of the X-class flare with a quasi-X-shaped flare ribbon and a CME. Therefore, this work provides a unique observational ingredient for understanding major flares in multipolar ARs and also has a practical significance for the forecasting operation of space weather.