The Causes of Quasi-homologous CMEs

The event sample of Wang et al. (2013) consists of 281 QH CMEs that originated from 28 super ARs in SC 23. The CMEs are all listed in the SOHO/LASCO CME catalog⁷ (Yashiro 2004), and their source ARs have been determined,⁸ following the process described in Wang et al. (2011). It is based on a combination of flares and EUV dimmings or waves, as they are strong evidence for the presence of CMEs. In particular, in the present work, we use localized flare-associated features, such as flare kernels, flare ribbons, and post-flare loops in order to determine the (portions of the) PIL relevant to the individual CME.

Another two well-studied CME-rich ARs, NOAA AR 11158 and 11429, are added into the sample for detailed case study, as they were observed during the SDO (Pesnell et al. 2012) era, allowing an in-depth study of the associated flare emission using coronal imagery from AIA (Lemen et al. 2012) and the involved coronal magnetic field structure and evolution based on vector magnetic field measurements from HMI (Schou et al. 2012; Hoeksema et al. 2014). Out of all of the events, 188 QH CMEs exhibit a waiting time of less than 18 hr; thus, we assume them to be physically connected.

Due to limitations in the observational data, not all of the 188 QH CME events could be successfully assigned to one of the three categories introduced above, i.e., whether to originate, from the exactly same portion of a PIL, from different portions of the same PIL or from a different PIL within the same AR as their predecessor. The CMEs assigned to the first category (the latter two categories) are defined as S-type (D-type) QH CMEs. Note that QH CMEs were assigned to the second category only when they originated from totally different portions of a long PIL (with non-overlapped post-flare loops, ribbons, etc.). In total, we were able to clearly identify the magnetic sources of 142 QH CMEs. Among them, 90 are classified as S-type, accounting for 63%; 52 are classified as D-type, accounting for 37%. Selected QH CMEs are discussed in detail in the following two subsections, in order to demonstrate the identification process. The preceding CME is referred to as CME1, and the following CME is referred to as CME2. The associated flares are accordingly referred to as flare1 and flare2.

S-type QH CME from NOAA AR 9026. NOAA AR 9026, observed in the form of a large bipolar sunspot region with a δ-spot (Figure 1(a)), was a highly CME-productive AR that launched at least 12 CMEs during its disk passage. Note that the strong positive polarity at $[-300^{\prime\prime} ,320^{\prime\prime} ]$ in Figure 1(a) belongs to AR 9030. Figure 1 shows the magnetic source location, morphology, and time evolution of an S-type CME and its predecessor that both originated from the main PIL, located within the yellow box L1 in Figure 1(a). Figures 1(b)–(d) show the evolution of the CME1-associated M7.1 flare1, as observed by TRACE (Handy et al. 1999) at 1600 Å, while the white-light appearance of CME1 in LASCO/C2 (Brueckner et al. 1995) is shown in Figure 1(e). Figures 1(f)–(i) show the corresponding features of CME2 and its associated X2.3 flare2. From Figure 1 it is evident that the chromospheric ribbons of both flare1 and flare2 appear and evolve along the same part of the main PIL of the AR. Thus, CME2, with a waiting time of 1 hr, is classified as an S-type CME.

S-type QH CME from NOAA AR 9236. NOAA AR 9236 produced more than 15 CMEs during its disk passage. The AR hosted a δ-spot of positive polarity surrounded by scattered elements of negative polarity (see Figure 2(a)). The PIL of interest is located within the yellow box L1. The two CMEs (see Figures 2(e) and (i)) were associated with an X2.3 and an X1.8 flare, respectively. The corresponding TRACE 1600 Å observations (Figures 2(b)–(d) and (f)–(h), respectively) reveal that the ribbons of the two flares appeared at the same location. CME2 had a waiting time of 7 hr and is thus classified as an S-type event. Note that these two CMEs were also classified as homologous events in Zhang & Wang (2002) and Chertok et al. (2004).

S-type QH CME from NOAA AR 11158. NOAA AR 11158 was the first super AR in SC 24 and produced more than 10 CMEs during disk passage. A pair of opposite polarities in the quadrupolar AR (outlined by the yellow box L1 in Figure 3(a)) produced a number of CMEs within 2 days. Most of the CMEs were front-side, narrow events and missed by LASCO. However, they were all well captured by STEREO/COR1 (Kaiser et al. 2008). The CMEs shown in Figures 3(e) and (i) were associated with an M2.2 and a C6.6 flare, respectively (see Figures 3(b)–(d) and (f)–(h)). The mass ejections (marked by the white arrows in Figures 3(d) and (h)) shared the same source location. CME2, with a waiting time of 2.2 hr, is thus classified as an S-type QH CME. The cyan curve A1 in Figure 3(a) indicates the projection of the flux rope axis along the related PIL at Time1, i.e., before the occurrence of CME1. The pink curve A2 indicates the flux rope axis position at Time2, i.e., at a time instance after CME1 happened but before CME2 was launched. The lines C1 and C2 mark the position of two vertical cuts that will be used to derive some flux rope parameters at the two time instances. For details see Section 3.2.

D-type QH CME from NOAA AR 10030. NOAA AR 10030 adhered to a quadrupolar configuration (see Figure 4(a)) and produced at least eight CMEs during disk passage. A CME and its QH predecessor are shown in Figures 4(i) and (e). The yellow boxes L1 and L2 in Figure 4(a) enclose the pairs of opposite polarities, relevant to the respective CMEs, CME1 and CME2, and defining the accordingly relevant PILs (PIL1 and PIL2, respectively). CME1 was accompanied by an X3.0 flare (see Figures 4(b)–(d)). Though an extra ribbon appeared in the positive polarity in L2 in Figure 4(b), the helical structure marked by the white arrow in Figure 4(b) and the observed chromospheric ribbons support that CME1 originated from L1. Figures 4(f)–(h) show the time evolution of the chromospheric ribbons of the CME2-associated M1.8 flare2, clearly aligned with PIL2. CME2, with a waiting time of 1 hr, thus is classified as a D-type CME. Already Gary & Moore (2004) demonstrated that the two CMEs should have originated from two different magnetic flux tube systems, and further argued that the observational signatures matched a breakout scenario.

D-type QH CME from NOAA AR 10696. NOAA AR 10696, similar to NOAA 9236, consisted of a concentrated negative-polarity region surrounded by scattered small positive-polarity patches (see Figure 5(a)). It produced more than 12 CMEs. The yellow boxes L1 and L2 in Figure 5(a) mark the source locations of CME1 and CME2, respectively. Figures 5(b)–(d) and (f)–(h) show the evolution of the associated M5.0 and M1.0 flare, respectively. Figures 5(e) and (i) show the appearance of the CMEs in LASCO/C2. The white arrows in Figures 5(d) and (h) mark the post-flare loops associated with the two CMEs, further supporting that they originated from different flux tube systems. CME2 had a waiting time of 2.8 hr and is therefore classified as a D-type QH CME.

D-type QH CME from NOAA AR 11429. NOAA AR 11429, a super AR in SC 24, produced more than 12 CMEs during disk passage. The AR exhibited a complicated topology with a δ-spot. The two yellow boxes L2 and L1 in Figure 6(a) mark the magnetic source locations of a CME and its QH predecessor. The cyan curve A1 indicates the projection of the flux rope axis along PIL2 at Time1, i.e., before the occurrence of CME1. The cyan line C1 marks the position of a vertical plane that is perpendicular to A1 at Time1. The pink curves A2 and C2 are the corresponding axis and plane for PIL2 at Time2, i.e., a time instance after CME1 happened but before CME2 was launched. See more details in Section 3.3. The time evolution of the flares that accompanied the two CMEs, an X5.4 and an X1.3 flare, is shown in Figures 6(b)–(d) and (f)–(h), respectively. The white arrow in Figure 6(h) marks the post-flare loops of CME2, while the black arrows in Figures 6(f)–(h) mark the post-flare loops of CME1. CME2, with a waiting time of 1 hr, is classified as a D-type CME, in agreement with its classification by Chintzoglou et al. (2015).

The waiting time distribution of the 188 CMEs (with waiting times <18 hr) is shown as a black curve in Figure 7, exhibiting a Gaussian-like distribution with a peak at about 7.5 hr, suggesting that they are physically related. The distributions of precisely located S- and D-type QH CMEs are shown as a blue curve and a red curve in Figure 7, respectively. The two are distinctly different from each other: the former peaks at 7.5 hr, while the latter peaks at 1.5 hr, strongly supporting that these two types of QH CMEs may be involved in different physical mechanisms. Another slightly lower peak appears around 9.5 hr in the waiting time distribution of D-type QH CMEs. One possible reason is that in some cases, a CME triggers a D-type QH CME in a short interval of around 1.5 hr, after which the first CME's source region undergoes an energy replenishment and produces another QH CME with an interval around 7.5 hr. However, the third CME would be classified as a D type, as it originates from a different source location from its predecessor, with a waiting time of around 6 hr. Considering the 3 hr bin size of the distribution, a peak around 9 hr may be reasonable. Another possible reason is that those D-type QH CMEs with waiting times around 9.5 hr may follow a different mechanism from the ones with short waiting times (around 1.5 hr). This work aims to find the most possible (but not only) scenario for the two types of QH CMEs.

Zoom In Zoom Out Reset image size

In order to explore the different underlying mechanisms, the aforementioned S-type CME in AR 11158 and D-type CME in AR 11429 are analyzed in detail in the next section. These two cases were observed during the SDO era, allowing for sophisticated modeling of the 3D coronal magnetic field, based on the measurements of the photospheric magnetic field vector at a high spatial resolution from SDO/HMI.

It is widely accepted that the expulsion of a CME is determined by the inner driving force (associated with, e.g., an erupting flux rope) and the external confining force (exerted by the large-scale, surrounding coronal magnetic field; e.g., Wang & Zhang 2007; Liu 2008; Schrijver 2009). In order to investigate the involved mechanisms, the knowledge of the 3D coronal magnetic field is necessary. A method developed by Wiegelmann (Wiegelmann 2004; Wiegelmann et al. 2012) is employed for the two selected cases, to reconstruct the 3D potential (current-free) and nonlinear force-free (NLFF) fields in the corona, based on the surface magnetic vector field measurements from HMI.

A magnetic flux rope, characterized by magnetic fields twisted about a common axis, may become unstable and act as a driver for an eruption (e.g., Amari et al. 1999; Török & Kliem 2005). A flux rope can be identified using a combination of topological measures deduced from the employed NLFF models, e.g., in the form of the twist number T_w and the squashing factor Q (Liu et al. 2016b). T_w gives the number of turns by which two infinitely approaching field lines, i.e., two neighboring field lines whose separation could be arbitrarily small, wind around each other, and it is computed by

$$\begin{eqnarray}&&{T}_{w}=\displaystyle \frac{1}{4\pi }{\int }_{L}\alpha {dl},\end{eqnarray} \tag{ 1 }$$

where α is the force-free parameter, dl is the length increment along a magnetic field line, and L is the length of the field line (Berger & Prior 2006; Liu et al. 2016b). Q is a measure of the local gradients in magnetic connectivity; regions with high values of Q are referred to as quasi-separatrix layers (QSLs; Titov et al. 2002; Titov 2007).

The cross section of a flux rope with twisted field lines treading the plane would be visible as a region of strong T_w enclosed by a surface of high Q values separating the magnetic fields of the flux rope from its magnetic environment. The location of the local extremum T_w in the cross section of a coherent flux rope is a reliable proxy of the location of its central axis. Additionally, a cross section perpendicular to the axis of the flux rope (e.g., the section at the apex point of the flux rope axis) would allow the axis to run through the plane horizontally, so that the in-plane vector field will show a clear rotational pattern around the axis, which is represented by the point where T_w is maximal.

The external confining force can be measured by the decay index

$$\begin{eqnarray}&&n=-\displaystyle \frac{d\mathrm{ln}\ {B}_{\mathrm{ex}}(h)}{d\mathrm{ln}\ h},\end{eqnarray} \tag{ 2 }$$

where h is the radial height from the solar surface and B_ex is the horizontal component of the strapping potential field above the AR. Basically, n measures the run of the strapping field's confinement with height. Theoretical works predict the onset of torus instability when n is in the range of $[1.5,2.0]$ (Kliem & Török 2006), while observations of eruptive prominences suggest a critical value $n\sim 1$ (Filippov 2013; Su et al. 2015). It is suggested that the former value is representative for the top of the flux rope axis, while the latter value is typical for the location of magnetic dips that hold the prominence material (Zuccarello et al. 2016). Therefore, $n=[1,1.5]$ are used as critical decay index values for our analysis. Torus instability sets in once the axis of the flux rope reaches a height in the corona at which the strapping potential fields decrease fast enough (Török & Kliem 2005); thus, the vertical distribution of n, along the axis of the flux rope, will hint at its instability.

Since a physical relation is assumed to exist between the QH CMEs (CME2 and its predecessor, CME1), we may expect a change in the magnetic field configuration of the CME2's source location after CME1, detectable in the form of a change of the related parameters defined above (T_w, Q, and n). Therefore, we deduce these parameters from the NLFF models (for T_w and Q) and potential models (for n) of the pre-CME1 and post-CME1 (i.e., pre-CME2) corona as follows:

• 1.  
  Locate the axis of the flux rope using the method of Liu et al. (2016b), which calculates the twist maps in many vertical planes and traces the field line running through the peak T_w point at each map. All traced field lines should be coinciding with each other if a coherent flux rope is present. The line is then considered to represent the flux rope axis.
• 2.  
  Calculate T_w and Q in a vertical plane perpendicular to the flux rope axis. The in-plane vector field, ${{\boldsymbol{B}}}_{\parallel }$, can provide additional evidence of the presence of a flux rope in the form of a clear rotational pattern, centered on the flux rope axis position.
• 3.  
  Calculate the decay index n in a vertical plane, aligned with the flux rope axis and extending from the flux rope axis upward, as a function of height in the corona.

Using the above-introduced models and concepts, we investigate the pre-CME1 and post-CME1 (pre-CME2) coronal magnetic field configuration of the two mentioned cases in NOAA AR 11158 (Section 3.2) and 11429 (Section 3.3) in great detail. The quality of the NLFF extrapolation in this paper is shown in Appendix A.

As demonstrated in Section 2.2, the S-type CME and its predecessor originated from the same PIL within NOAA 11158. We study the magnetic parameters at the CMEs' source location (L1) at two time instances: once before CME1, at 2011-02-14T17:10:12 UT (Time1), and once after CME1 but before CME2, at 2011-02-14T18:10:12 UT (Time2).

At both times, we find a flux rope structure from the constructed corona field (see Figures 8(g) and (h)). The magnetic properties of the pre- and post-CME1 flux rope in a vertical plane perpendicular to its axis are shown in Figures 8(a)–(c) and (d)–(f) (from left to right: Q, T_w, and ${{\boldsymbol{B}}}_{\parallel }$), respectively. The footprints of the vertical planes at the two times are marked as C1 and C2 in Figure 3(a). Their vertical extensions are indicated by the yellow lines in Figures 8(g) and (h). At Time1 (pre-CME1), a region of strong twist (Figure 8(b)) is surrounded by a pronounced Q-surface (Figure 8(a)). The diamonds in Figures 8(a)–(c) mark the location where T_w is strongest, at $T=-1.94$, and are assumed to represent the 3D location of the flux rope axis, at a coronal height of $h\gtrsim 2$ Mm. The in-plane vector magnetic fields, ${{\boldsymbol{B}}}_{\parallel }$ (Figure 8(c)), show a clear rotational pattern, centered around the flux rope axis, suggesting a left-handedness of the flux rope, since the blue arrows indicate the vector fields with the normal components going into the plane. The field lines passing through the strong twisted region are shown in Figure 8(g) in cyan, even adhering to a Bald Patch (BP), a set of field lines that graze the photosphere at the PIL (see, e.g., Titov et al. 1993). A representative field line in the BP is plotted as a white line, which is determined by the criteria introduced in Titov & Démoulin (1999, Equation (32)).

Zoom In Zoom Out Reset image size

At Time2 (post-CME1), the highest value of twist in the vertical plane perpendicular to the flux rope axis is found as ${T}_{w}=-2.11$, marked by the diamonds in Figures 8(d)–(f). Again, a region of strong twist (Figure 8(e)) is surrounded by a pronounced Q-surface (Figure 8(d)), but located lower in the model corona (height of the flux rope axis $h\lesssim 2$ Mm). The fields traced from the high-T_w region are shown in Figure 8(h) as pink curves. For comparison, the outline of the flux rope at Time1 is shown again as cyan curves. The more potential arcade fields (white lines) are traced at Time2 but from the coordinates of the top of the flux rope at Time1.

The direct comparison between the pre- and post-CME1 model magnetic field configuration suggests that the upper part of the flux rope might erupt during CME1, while the lower-lying part of the flux rope seems to remain. In order to check the conjecture, we further trace the field lines within the pre-CME1 corona from exactly the same starting locations used for tracing the post-CME1 flux rope (i.e., the high-T_w region enclosed by the high-Q boundary at Time2; see Figures 8(d) and (e)). The traced pre-CME1 field configuration (red lines in Figure 8(h)) clearly differs from the post-CME1 field structure (pink lines in Figure 8(h)), which may suggest two possibilities: (i) the flux rope totally erupted during CME1, after which a new one emerged, or reformed; and (ii) the flux rope underwent a topology change in which part (not simply the upper part) of it was expelled during CME1, while the other part was left, being responsible for CME2. See Appendix B for some details on CME2.

We also calculated the unsigned vertical magnetic flux from the strong T_w region in the aforementioned planes. No strong twist region exists outside of the flux rope; thus, instead of doing an image-based flux rope recognition, we directly select the regions with $| {T}_{w}| \gtrsim 1.25$. $| {T}_{w}| =1.25$ is a threshold value for kink instability (Hood & Priest 1981; Török & Kliem 2003). The flux is calculated by

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{1.25}={\int }_{{A}_{1.25}}| {{\boldsymbol{B}}}_{\perp }| {dA},\end{eqnarray} \tag{ 3 }$$

in which ${{\boldsymbol{B}}}_{\perp }$ is the magnetic field perpendicular to the vertical plane and dA is the element area. The planes are perpendicular to the axes of the pre- and post-CME1 flux ropes; thus, the vertical magnetic flux can represent the axial flux of the flux rope. The unsigned vertical magnetic flux (given at the the header of Figures 8(a) and (d)) decreased from $4.52\times {10}^{19}$ Mx at Time1 to $3.10\times {10}^{19}$ Mx at Time2, which can be due to either ejection or simple redistribution of twisted field lines, since twist is not supposed to be conserved during the flux rope evolution. However, CME1 has been confirmed to be related to source location L1 based on observation; as discussed in Section 2.2, the decrease here is more likely to support a twist release through eruption rather than redistribution.

We cannot make a definite conclusion on whether the flux rope at Time2 is a partial eruption remnant or is a newly emerged/reformed one. However, the pre-CME1 flux rope has a BP, and the post-CME1 rope has some nearly potential loops right above it. Thus, we prefer a partial expulsion model (Gibson & Fan 2006), consisting of a coherent flux rope with a BP, to explain the eruption process: the field lines in the BP are not free to escape, so that during the writhing and upward expansion of the ends of the field lines, a vertical current sheet may form, along which internal reconnection may occur and finally split the flux rope into two parts. The white arcades in Figure 8(h) could be the post-eruption loops, which may also support that part of the flux rope erupted with CME1.

Figures 9(a) and (b) show the distribution of the decay index n as a function of height above the flux rope axis, for Time1 and Time2, respectively. The projections of the flux rope axis at the two times are indicated by the curves A1 (for Time1) and A2 (for Time2) in Figure 3(a). The solid black lines in Figure 9 indicate the height where n = 1 and n = 1.5. It is evident that, for both time instances, the vertical run of n varies strongly along the flux rope, with the n = 1.5 level being located at a height above 48 Mm at one end and around 16 Mm at the other end of the flux rope. The height where n = 1 varies less dramatically along the flux rope and is located at the height around 10 Mm. Comparison of the n = 1.5 level at Time1 and Time2 (represented by the dotted and solid black curves in Figure 9(b), respectively) suggests that the critical height at the southeastern end (x = 0 Mm in Figure 9) is lowered by about 8 Mm. In the remaining part of the flux rope, no significant change was detected, which indicates that the external confining force was not lowered significantly by the first eruption. The critical height, both before and after CME1, was located relatively low in the solar atmosphere (e.g., n = 1 at $h\approx 10$ Mm), but still far above the height of the flux rope axis (red lines in Figures 9(a) and (b)), located below 3 Mm at both times. The maximal n at the flux rope axis reaches 0.80 at Time1 and 0.44 at Time2, which are both lower than the critical n = 1.5 for torus instability. The results argue against torus instability in triggering the two QH CMEs.

Zoom In Zoom Out Reset image size

Sun et al. (2012) studied the long-term evolution of NOAA AR 11158 and showed that the fast emergence and continuous shear of a bipolar photospheric magnetic field (L1 in Figure 8) accumulated a large amount of magnetic free energy before the onset of a series of QH CMEs. They showed that the emerging fields reconnected with preexisting fields, which finally led to the eruptions. Together with our analysis, their results hint at a multistage energy release process during which the magnetic free energy is released owing to the successive eruptions from the same bipolar region (L1 in Figure 8). Meanwhile, the energy was replenished through the shearing motion and ongoing flux emergence. We also calculate the magnetic free energy in the entire extrapolation volume at the two time instances (shown as E_F in Figures 8(b) and (e)) by

$$\begin{eqnarray}&&{E}_{F}={\int }_{V}\displaystyle \frac{{B}_{N}^{2}}{8\pi }{dV}-{\int }_{V}\displaystyle \frac{{B}_{P}^{2}}{8\pi }{dV},\end{eqnarray} \tag{ 4 }$$

where B_N is the NLFF field, B_P is the potential field, and dV is the element volume. E_F shows a slight increase by 5% from Time1 ($2.06\times {10}^{32}$ erg) to Time2 ($2.17\times {10}^{32}$ erg), which is against the expectation that the magnetic free energy would decrease after CME1, since CME1 should have taken part of the free energy during the multistage energy release process. The slight increase could be due to the small fraction of the big, fast-evolving AR that the erupting bipolar system accounts for, and/or the fast accumulation of the magnetic free energy by flux emergence and shear motions. Besides, the free energy calculated from the model coronal field has an uncertainty of around 10% (Thalmann et al. 2008), so that no definite conclusion on the loss of free energy during CME1 could be made here.

As discussed in Section 2.3, a D-type CME and its predecessor originated from two different locations within NOAA 11429, separated by a waiting time of just 1 hr. A physical relation is assumed to exist between the two QH CMEs; thus, a change at the source location of CME2 after CME1 is expected (see Section 3.1). Therefore, we study the magnetic parameters at the source location (L2) of CME2 at two time instances in the following, once before CME1, at 2012-03-06 23:46:14 UT (Time1), and once after CME1 but before CME2, at 2012-03-07 00:58:14 UT (Time2).

Figure 10 shows the T_w, Q, in-plane vector field (${{\boldsymbol{B}}}_{\parallel }$) maps and the traced flux ropes for AR 11429. Through checking the T_w and Q maps in many vertical cuts across PIL2, we found three possible flux ropes at Time1. The peak T_w point resides in the middle structure; thus, we again identified the axis of the middle rope with the peak T_w point and then placed a plane perpendicular to the flux rope axis. The plane's footprint is marked as C1 in Figure 6(a), and its vertical extent is marked by the yellow vertical line in Figure 10(g). Figures 10(a)–(c) show the distribution of Q, T_w, and ${{\boldsymbol{B}}}_{\parallel }$, respectively, calculated in the plane. The axis of the middle flux rope, with a peak value T_w = 1.86, is indicated by diamonds. The in-plane vector field, ${{\boldsymbol{B}}}_{\parallel }$, displays three clearly rotational patterns with opposite handedness, alternately. This supports that there were three flux ropes present along PIL2 at Time1. A configuration with two vertically arranged flux ropes, i.e., a so-called double-decker flux rope, has been studied (Liu et al. 2012; Kliem et al. 2014). However, a similar configuration, with three flux ropes presented here, is barely reported to our knowledge; we name it a triple-decker flux rope, analogically. The blue arrows indicate the vector magnetic fields, with the vertical component going into the plane; thus, the upper one and the lower one (FR³₂ and FR¹₂ in Figure 10) are left-handed (i.e., the in-plane vector field exhibits a counterclockwise sense of rotation), while the middle one (FR²₂) is right-handed. The squares and triangles in Figures 10(a) and (b) mark the position of the axes of FR³₂ and FR¹₂, with local peak values ${T}_{w}=-1.82$ and ${T}_{w}=-1.49$, respectively. The plane is not perpendicular to the axes of FR³₂ and FR¹₂, positions of which do not correspond well with the rotational centers of the ropes' in-plane fields; thus, the symbols are not marked in Figure 10(c). Figure 10(g) depicts the structure of the flux ropes, FR³₂ in blue, FR²₂ in orange, and FR¹₂ in cyan. A longer, strongly twisted rope (marked as FR₁ in Figures 10(g)–(h)) is aligned with PIL1 and results in CME1. The white lines in Figure 10(g) represent some nearly potential arcades above the flux ropes. Note that the southwestern end of FR₁ was located close to the triple-decker flux rope along PIL2, and part of the arcade field was overlying both the southwest end of the CME1-associated flux rope and the eastern part of the tripple-decker flux rope. Therefore, we may assume that the eruption of FR₁ easily affected the triple-decker flux rope in various ways, e.g., by removing the common overlying arcades, disturbance, compressing the neighboring fields through expansion of the post-eruption loop system below the erupted flux rope, and even reconnecting with the neighbor fields during expansion.

Zoom In Zoom Out Reset image size

At Time2 (see Figures 10(d)–(f)), the upper two flux ropes along PIL2 evidently disappeared from the extrapolated domain, while the lower one was then located higher, with a peak value ${T}_{w}=-1.81$ (indicated by triangles) located at $h\sim 6$ Mm. The whole structure also appears expanded compared to that at Time1. The in-plane vector field, ${{\boldsymbol{B}}}_{\parallel }$, exhibits a rotational pattern around the maximum value of T_w, which is evidence for the presence of a flux rope (Figure 10(f)). The footprint of the vertical plane is marked as C2 in Figure 6(a), and its vertical extent is marked as a yellow line in Figure 10(h). Field lines traced from the strong T_w region at Time2 are shown in pink in Figure 10(h). For comparison, the flux rope that was present at Time1 is shown as cyan lines. Comparison of FR₂¹ at Time1 and Time2 reveals that it elevated and expanded, as well as gained internal twist. The vertical magnetic fluxes calculated by Equation (3) from the strong T_w region ($| {T}_{w}| \gtrsim 1.25$) of the lowermost structure of the triple-decker flux rope ($h\lesssim 5$ Mm at Time1 and $h\lesssim 8$ Mm at Time2), i.e., the representation of the axial magnetic flux of the lower flux rope (shown at the headers of Figures 10(a) and (d)), indicate an increase by 2.48 times (from $2.28\times {10}^{19}$ Mx at Time1 to $5.66\times {10}^{19}$ Mx at Time2), supporting the enhancement of the twist. The upper two flux ropes, with opposite handedness, clearly disappeared from the system with almost no remnant left behind. A QSL exists between the two ropes (strong Q line at around 8.5 Mm in Figure 10(a)). Thus, we prefer annihilation due to local reconnection that started from the QSL, rather than expulsion, to account for the absence of them at Time2. Annihilation of the ropes would cause a decrease of the local magnetic pressure, which is likely to allow FR¹₂ to rise, expand, and finally erupt, giving rise to the faint CME2.

Further support for this scenario is given by the evolution of the observed chromospheric ribbons as shown in Figure 11. At the beginning of flare1, two ribbons, labeled ${{\rm{R}}}_{1}^{1}$ and ${{\rm{R}}}_{1}^{2}$ in Figure 11(a), expand on both sides of PIL1. While ${{\rm{R}}}_{1}^{2}$ grew southward in time (Figure 11(b)), two more faint and small ribbons, ${{\rm{R}}}_{1}^{3}$ and ${{\rm{R}}}_{1}^{4}$, became visible along PIL2 (Figure 11(c)). In comparison to the flux ropes shown in Figures 10(g) and (h), this pair of ribbons indicates the involvement of FR₂² and FR₂³ in the magnetic process. The two ribbons showed no clear sign of development that departed from or along the PIL, which may be evidence for a local, small-scale reconnection process. FR₂² and FR₂³ should have reconnected and annihilated during the first eruption. After flare1/CME1, the lower flux rope became unstable as well and erupted, giving rise to a further pair of flare ribbons, ${{\rm{R}}}_{2}^{1}$ and ${{\rm{R}}}_{2}^{2}$, at the beginning of flare2.

Zoom In Zoom Out Reset image size

Note that there still existed a flux rope at PIL1 after CME1, though we cannot determine whether it is a remnant or a newly emerged/reformed one. A similar analysis is performed across PIL1. See Appendix C for details. The magnetic free energy in the extrapolated pre- and post-CME1 corona volume (shown as E_F in Figures 10(g) and (h)) shows a decrease of 25% (from $10.61\times {10}^{32}$ erg at Time1 to $8.01\times {10}^{32}$ erg at Time2), which is beyond the uncertainty (10%), implying a clear energy release with CME1.

Figures 12(a) and (b) show the distribution of the decay index n as a function of height above the axis of the lower flux rope at PIL2, for Time1 and Time2, respectively. The projection of the flux rope axis at the two times is indicated by the curves A1 and A2 in Figure 6(a). The solid black curves mark the height where n = 1 and n = 1.5. The height at which n = 1.5 varies between h = 30 Mm and 50 Mm along the flux rope axis, while the height at which n = 1 shows a similar trend but at lower heights (about 15 Mm lower). The dotted lines in Figure 12(b) are critical heights at Time1 for comparison. The red lines indicate the height of the flux rope axis, which both are lower than 6 Mm at the two time instances. No significant change is found, suggesting that CME1 may not significantly lower the constraining force of the overlying field. At both times, the predicted critical height for the onset of torus instability (n = 1.5) is located much higher in the corona than the axis of the flux rope. In addition, the observation-based critical height (where n = 1) is located clearly above the flux rope. The maximal n at the flux rope axis is 0.59 at Time1 and 0.53 at Time2, both lower than the critical value n = 1.5, also suggesting that torus instability may not have been the direct trigger for the two CMEs.

Zoom In Zoom Out Reset image size

We conclude for the D-type CME and its predecessor from NOAA AR 11429 that their magnetic source regions were located very close to each other and bridged by the same large-scale potential field arcade. The first occurring CME1 (associated with the flux rope along PIL1) destabilized the magnetic environment of the nearby flux tube system (above PIL2), leading to the reconnecting annihilation of the upper two flux ropes along PIL2, which decreased the local magnetic pressure and led the lower flux rope along PIL2 to rise, expand, and finally erupt as well (during flare2, and causing the associated CME2). See Appendix D for some details of CME2.