Recurring Homologous Solar Eruptions in NOAA AR 11429

Solar eruptions, manifested as flares and Coronal mass ejections (CMEs), are the most spectacular phenomena happening on the solar corona. Besides being magnificent, these are the main sources of the disturbances in the interplanetary space and also the space weather effects near the Earth. Flares and CMEs (often occur together) are probably the manifestation of a single energy release process, during which a tremendous amount of stored magnetic energy is released from the solar atmosphere (see, Forbes 2000; Zhang et al. 2001). The general model of solar eruptions, also known as CSHKP model (initially developed by Carmichael 1964; Sturrock 1966; Hirayama 1974; Kopp & Pneuman 1976), describes the process as the eruption of magnetic flux rope (MFR) through magnetic reconnection. An MFR is a highly sheared and twisted magnetic field structure and carries a large amount of free magnetic energy. It is kept under equilibrium by the magnetic pressure of the overlying magnetic fields and its instability makes it to rise. While rising it drags the overlying magnetic field lines, making them to come close to each other in an anti-parallel manner below it and form a current sheet. The magnetic reconnection at current sheet results in flares and the new connection removes the overlying constrain over MFR and accelerate it (see, Forbes 2000; Chen 2011 for review). As long as there is an erupting MFR, the general theory describes the evolution of solar eruptions very well. However, it does not address the initial formation of MFRs and onset of solar eruptions.

Many agree with the notion that the MFR is an essential feature for solar eruption. However, there is a debate regarding when, how and where it is formed. It can exist before (e.g., Kliem & Török 2006; Zhang et al. 2012) or form during solar eruption (e.g., Antiochos et al. 1999; Cheng et al. 2011). Its detection before the eruption is a difficult task, due to low plasma density and technological insufficiency to measure magnetic field directly in the corona. Nevertheless, its existence is suggested through sigmoidal bright loops in X-rays (Rust & Kumar 1996; Green et al. 2007), AIA/SDO hot-channel structures (Cheng et al. 2011; Zhang et al. 2012), dips or bald patches in filament channels (Lites 2005; López Ariste et al. 2006), and nonlinear force-free field (NLFFF) extrapolation results (e.g., Chintzoglou et al. 2015). Several mechanisms are associated with its formation, such as flux emergence (e.g. Fan & Gibson 2003; Leake et al. 2013), shearing motion between opposite magnetic fluxes (e.g., Amari et al. 2000, 2003; Jacobs et al. 2009), magnetic flux cancellation along the polarity inversion lines (PILs) (e.g., van Ballegooijen & Martens 1989; Aulanier et al. 2010; Green et al. 2011), and confined flaring (e.g., Patsourakos et al. 2013, Chintzoglou et al. 2015).

A typical solar eruption has three phases: (1) the precursor phase (PP), (2) the impulsive phase (IP), and (3) the gradual phase (GP; see, Zhou et al. 2016 for discussion); these are associated with three distinct acceleration phases of CMEs (Zhang et al. 2001). PP is important to understand the initiation and validating different models of solar eruptions. In the past, different observational signatures have been identified in precursor phase for certain individual events, such as: soft X-rays (SXR) emission (Fárník et al. 1996; Fárník & Savy 1998), hard X-rays burst (Harra et al. 2001), UV/EUV brightenings (e.g., Joshi et al. 2011; Awasthi et al. 2014), type II radio bursts (e.g., Klassen et al. 2003; Liu et al. 2007), prominence oscillation (Chen et al. 2008) and MFR oscillation (Zhou et al. 2016). However, due to weak or entirely absent observational activities during precursor phase its current understanding is very poor compared to IP and GP (Hudson 2011).

Most of the time, single and independent solar eruption happens on the Sun. However, there are cases where multiple eruptions occur in a short time-span. Such eruptions are known as sympathetic eruptions. These could occur in different active regions (ARs) or at different locations within the same complex AR. Although interrelation among these is a debatable issue (see, Biesecker & Thompson 2000), but causal relationship have been identified in many cases (e.g., Schrijver & Title 2011; Török et al. 2011; Liu et al. 2009).

Besides sympathetic eruptions, multiple eruptions could happen from the same local region consecutively. Consecutive CMEs originating from the same region, associated with homologous flares, having similar coronographic appearance and similar dimming in extreme ultraviolet imaging are known as homologous CMEs (Zhang & Wang, 2002). Homologous eruptions are possible only if there are mechanisms that continuously store magnetic energy in the same local region. Therefore, their studies are important to understand the long-term magnetic energy build-up in the corona. In the past, they have been studied either during magnetic flux emergence phase and were considered due to flux emergence (e.g. Nitta & Hudson 2001; Chatterjee & Fan 2013) or flux decaying phase and were considered due to shearing motion and magnetic flux cancellation (e.g., Li et al. 2010; Vemareddy 2017a). The persistent photospheric horizontal motion of magnetic structure along the PIL was also considered to produce homologous eruptions (e.g., Romano et al. 2015; Romano et al. 2018). Past studies also suggest that homologous eruptions can be triggered by similar mechanisms, such as moving magnetic features (Zhang & Wang 2002), coronal null point magnetic configuration (e.g., DeVore & Antiochos 2008) and shearing motion and magnetic reconnection (e.g., Vemareddy 2017a)

In this paper, we analyze three homologous eruptions, viz., SOL2012-03-07T01:05, SOL2012-03-09T03:22, and SOL2012-03-10T16:50. These eruptions originated from the same location in the complex AR 11429, but at different magnetic flux evolutionary phase. An MFR of similar morphology was formed, along the same PIL, before each of the three eruptions. Magnetic flux cancellation led by the shearing and converging motion and new connectivity in the corona were responsible for its formation. A confined flare was observed during the PP of each eruption, which helped in the eruption by weakening the constraint of overlying magnetic fields. The paper is structured as follows. Instrument and data are described in Section 2. The precursor phase and each eruption are described in Section 3. Evolution of the AR before each eruption and pre-eruptive coronal magnetic structures are described in Section 4, and the discussion and conclusion are presented in Section 5.

This study mainly used the data from the Atmospheric Imaging Assembly (AIA; Lemen et al. 2012) and Helioseismic and Magnetic Imager (HMI; Schou et al. 2012), onboard the Solar Dynamics Observatory (SDO ; Pesnell et al. 2012). The AIA provides full-disk images of the Sun with unprecedented temporal cadence (12 s) and spatial resolution ($1\farcs 2$). The different spectral bands of AIA observe the Sun from the photosphere, chromosphere, and corona up to 0.5 $R_{\sun}$ above the solar limb. The HMI provides the photospheic line-of-sight and vector magnetic field observations at a cadence of 45 s and 720 s respectively. The SDO has an inclined geosynchronous orbit around the Earth. During two seasons of each year, the view of the SDO gets obscured by the Earth temporarily each day for two-three weeks (SDO eclipse; Pesnell et al. 2012). In this study, we focused on the SDO observation during the solar front disk passage of the NOAA AR 11429 from 2012 March 6, 00:00 UT to 2012 March 10, 19:00 UT. There were some data-gaps during the observational period due to SDO eclipse. In addition, we used observations from the Large Angle Spectrometric Coronagraph (LASCO; Brueckner et al. 1995) on board the Solar and Heliospheric Observatory (SOHO), white light images of the Sun-Earth Connection Coronal and Heliospheric Investigation (SECCHI; Howard et al. 2008) onboard Solar Terrestrial Relations Observatory (STEREO; Kaiser et al. 2008), H$\alpha$ image from Big Bear Solar Observatory (BBSO; Denker et al. 1999), X-ray Telescope (XRT; Golub et al. 2007) onboard the Hinode (Kosugi et al. 2007), and the Solar X-ray Imager (SXI; Hill et al. 2005 and Pizzo et al. 2005) on board the Geostationary Operational Environmental Satellite (GOES).

The NOAA AR 11429 was initially emerged on the backside and appeared on the eastern limb of the Sun on 2012 March 4. During its front disk transition, the AR acquired very complex magnetic-configuration ($\beta/\gamma/\delta$), with many small magnetic polarities (see Elmhamdi et al. 2014 for more details about the evolution of magnetic configuration). However, as discussed in Chintzoglou et al. 2015 and Dhakal et al. 2018, it could be divided into two relatively simpler sub-regions namely: northeast (NE) and southwest (SW) sub-regions, more discussed in the section 4.1. Also, it had an anti-hale magnetic configuration i.e., the leading magnetic polarity (positive) was opposite of the normal hemispheric trend (negative). Both $\delta$ and anti-hale magnetic configuration are identifiable with severe flaring activity (e.g., Zirin 1970; Tanaka 1991; Sammis et al. 2000). Indeed, it was super-flare productive. Most of the flares were observed before it crossed the central meridian on March 9. By the end of March 9, it had produced 3 X-class, 11 M-class, and 30 C-class flares. Afterward, there were only 2 M-class flares and 7 C-class flares. The events under study occurred in the SW sub-region in the interval of $\sim$4 days. These homologous eruptions are summarized in Table 1.

The first solar eruption occurred on 2012 March 7 at $\sim$01:05 UT when the AR was in the north-east quadrant of the solar disk. On March 7, within one hour, there were two solar eruptions viz., SOL2012-03-07T00:02 (shown in red dotted line in Figure 1(a)) and SOL2012-03-07T01:05 (shown in black line in Figure 1(a)) from the NE and SW sub-regions respectively (see Chintzoglou et al. 2015). Here, we study the eruption from the SW sub-region. It was associated with X1.3 class flare and its location was $\sim$N15E26. Associated flare ribbons were concentrated mainly on the positive and negative fluxes of the SW sub-region (see Figure 1(d) for observed flare ribbon in AIA 1600 Å) and were observed to move away on either side of the PIL during the MFR eruption. The position and separation of the flare ribbons indicated that the MFR erupted from the SW-PIL. The eruption led to the coronal mass depletion in the region and observed as coronal dimming in different AIA passbands (e.g. Tian et al. 2012; see Figure 1(g) for observed dimming in AIA 193 Å). Later it was observed as halo CME, moving with 1825 km/s (CDAW CME catalog), in LASCO white light observation at 01:30 UT. The morphology of the CME at a single time snapshot is not clear due to contamination from the earlier CME. However, its morphology was clear in STEREO-A FOV as eastward-moving CME and in STEREO-B FOV as westward-moving CME (see upper panels of the Figure 2).

The second solar eruption started on 2012 March 9, at $\sim$03:22 UT when the AR was located around the central meridian of the solar disk. It was associated with an M6.3 class flare (see Figure 1(b)) at $\sim$N15W03. The flare ribbons, similar to the ribbons of the previous eruption, evolved and concentrated on the opposite magnetic flux in the SW sub-region (see Figure1(e)). This again indicated that the MFR had erupted from the SW-PIL. A dimming similar to the previous eruption was observed in EUV observation (see Figure 1(h)) and eventually observed as halo CME in LASCO C2 at 04:26 UT. In the LASCO FOV CME moved with a linear velocity of 950 km/s. STEREO-A data was not available during that period, but like the earlier eruption it appeared as westward-moving CME in STEREO-B FOV (see middle panels of the Figure 2).

The third solar eruption started on 2012 March 10, at $\sim$ 16:50 UT when the AR was at the north-west quadrant. It was associated with an M8.4 class flare (see Figure 1(c)) at $\sim$N17W24. The evolution and separation of flare ribbons were similar to the previous two eruptions and they were primarily concentrated on the opposite magnetic flux of the SW sub-region (see Figure1(f)). Therefore, the third MFR also erupted from the SW-PIL. Observed EUV dimming was also similar to the previous two eruptions (see Figure 1(i)). It appeared as halo CME in LASCO C2 at 18:00 UT, moving with a linear velocity of 1296 km/s. Like earlier eruptions, it was observed as eastward-moving CME in STEREO-A, and westward-moving CME in STEREO-B (see the lower panels of Figure 2) with a similar CME morphology.

All three solar eruptions were originated from the SW-PIL of the AR 11429. The direction of successive CMEs seemed to move towards north-side in STEREO FOV and this could be due to the change in magnetic flux distribution with evolution. Nevertheless, the overall morphology of the CMEs appeared similar in each recurring eruptions. Also, the X-ray profile, evolution of flare ribbons, and EUV dimming associated with these eruptions were nearly identical to be homologous eruptions. The time difference between the first and the second eruption was $\sim$50 hours, and the time difference between the second and the third eruption was $\sim$37 hours. The next section discusses the evolution of the AR that led to identical solar eruptions.

We used the preprocessed cutouts of SHARP data products (hmi.sharp_cea_720s) to study the photospheric evolution of the magnetic flux distribution in the AR. Preprocessing resolves the 180^∘ azimuthal uncertainty and remaps helioprojective images into a cylindrical equal-area (CEA) projection, where each pixel has the same surface area (Hoeksema et al. 2014). Although there were several episodes of new magnetic flux emergence in the early evolutionary period, no major emergence was observed after March 8, as is evident from the time-profile of magnetic flux of the AR shown in the Figure 3 (also, see the movie accompanying Figure 4). Here, we used the CEA maps of HMI LOS-magnetogram to analyze the magnetic flux. The apparent 12-hour periodicity in the plots of magnetic flux (in Figure 3) is due to instrumental effect and related to spacecraft orbital velocity, also there is a variation of the number of pixels contributing to the low-to-moderate magnetic field values as AR moves from central meridian to the limb (see, Hoeksema et al. 2014). Solar eruptions under consideration had occurred at the different evolutionary phases of the AR (eruptions are shown by dashed-vertical lines in Figure 3). The first eruption had occurred when the total magnetic flux was increasing i.e. during the magnetic flux emergence phase. The second eruption happened at the end of the flux emergence phase, and the third eruption happened during the flux decay phase of the AR. In the following, we describe the evolution of the AR, focusing on SW sub-region, in the period of 2012 March 6 to March 11.

Our primary goal of the present study is to understand the recurrent homologous solar eruptions from the AR 11429. There were three homologous eruptions from the southwest (SW) sub-region within 87 hours. The first eruption was associated with X-class flare and the other two eruptions were associated with M-class flares. Nevertheless, the shape of X-ray profiles of the three flares was very similar. The same photospheric location, similar evolution and location of flare ribbons, EUV dimmings, and identical coronographic morphology of the CME invoked them as homologous eruptions.

Our main result of the study is that the continuous flux cancellation due to shearing motions and the convergence of opposite magnetic bipoles along the PILs was the primary factor for the homologous solar eruptions. Flux emergence was observed only in the initial evolutionary period of the AR, flux cancellation was observed throughout the evolution that span all three events, including prior to the first event. While flux emergence was important and relevant in AR 11429, our study suggests that long-term flux cancellation and shearing motions were the most probable mechanisms that produced homologous eruptions. The photospheric motions of magnetic flux injected magnetic helicity and magnetic energy in the corona gradually. Stored helicity and energy released intermittently during solar eruptions. We believe that due to continuous shearing and converging motions of the magnetic flux, there was a cycle of storage and release of magnetic helicity and magnetic energy from the AR. In general, opposite magnetic poles of an emerging bipoles (conjugate pair) move away from each other, the separation distance depends on the flux content of the emerged bipoles (Wang & Sheeley 1989). In the present case, we did not observe the separation between opposite poles in SW sub-region, instead they were converging towards each other throughout the observational period. Therefore, we believe that these were non-conjugate pair. It was accompanied by the persistent shearing motion and magnetic flux cancellation. Chintzoglou et al. (2019) suggests that the convergence of opposite magnetic poles of non-conjugated pair leads to the magnetic flux cancellation and shearing motions, which could produce solar eruptions.

A filament was lying along the SW-PIL throughout the observational period and was observed soon after the eruptions. A filament survives and would be visible after a partial eruption. Partial eruption could happen either by the splitting of a single flux rope during the eruption(e.g., Gibson & Fan 2006; Zhang et al. 2015) or by the eruption of upper part of double-decker system (e.g., Liu et al. 2012; Kliem et al. 2014). Though a double-decker system was observed along the SW-PIL before the eruption on March 10 (see Dhakal et al. 2018), it is hard to say whether a single flux rope split or a double-decker system was present before the eruption on March 7 and March 9. Nevertheless, we believe that there was a partial eruption of the magnetic system from the SW-PIL.

A magnetic structure was formed along the SW-PIL before each eruption. It was observed as a coherent hot-channel structure in AIA EUV and sigmoid in X-ray images. Reforming HCS/sigmoid was almost identical in appearance. HCS and sigmoid are considered as an observational proxy of magnetic flux rope (MFR). Long, sheared and twisted magnetic field lines along the SW-PIL were found in our extrapolation results. Therefore, we believe that an MFR was formed and existed before each eruption. Chatterjee & Fan 2013 studied the emergence of twisted flux rope in magnetohydrodynamic simulation. They suggest that the partial eruption and reformation of MFR can produce homologous eruptions. In their simulation, reformed MFR was appeared as X-ray sigmoid. In the present case, flux emergence was going on before the first eruption. It is possible that the erupting MFR, before the first eruption, could have emerged from the sub-photosphere. However, since there were continuous shearing motion and flux cancellation in the SW sub-region, spanning the three eruptions. Also, after partial eruption an erupting magnetic structure of similar morphology was reformed. Therefore we believe that, most probably the shearing motion and flux cancellation were the primary mechanisms that formed the erupting MFR along the SW-PIL.

At last, we want to discuss about the identical precursor phase (PP) activity in the AR. It was identified as a confined flare surrounding an island of positive flux at the left side of the SW sub-region. A complex magnetic configuration, semicircular quasi-separatrix layers (QSLs), was inferred to exist in the region. The magnetic configuration was almost the same before each eruption, we believe this was due to the reformation of identical magnetic structures in the region. It is arguable that the identical PP was due to reconnection at identically shaped QSLs, either due to flux emergence or shifting of the island itself. As a strong overlying magnetic strapping force, due to overlying magnetic field, was inferred above the MFR lying along the SW-PIL. Our study suggests that the PP flare facilitated the eruption by removing the overlying magnetic strapping force above the MFR.