Impacts of EUV Wavefronts on Coronal Structures in Homologous Coronal Mass Ejections

2.1.1. Eruption and Wave Initiation

2.1.2. Wave Propagation

Unlike the jet-associated wavefront, the primary wavefront propagated mainly in the northwest direction (Figure 3(b)). To study the wave propagation, we divided the solar disk into 24 sectors, each spanning 15° (Figure 3(a)) and centering on the midpoint of the conjugated HXR footpoints at 25–50 keV at 18:04:40 UT (Figure 2(g)). Each sector-shaped slice is converted to a one-dimensional slice by averaging over the azimuthal direction. Stacking up the slices chronologically yields the time–distance maps in Figure 4. One can see that the jet-associated wavefront is detected in Sectors 1–4 (labeled "JWF"), propagating at about 300 km s⁻¹, while the primary wavefront, which was initiated earlier, is detected mainly in Sectors 8–17, propagating at a speed exceeding 700 km s⁻¹ to as far as over 800 Mm away from the flaring site.

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The wave propagation seems to be modulated by the strength of the local field. Here we utilized a potential-field-source-surface (Schrijver & De Rosa 2003) model to shed light on this matter. In Figure 3(d), the starting points to trace field lines are randomly selected on the surface but weighted by magnetic flux so that there are fewer field lines in regions of weaker field. One can see that the magnetic field is generally weak to the north of AR 12371, through which the primary wavefront propagated. Another weak-field region is located to the immediate south of AR 12371, which may explain the propagation of the jet-associated wavefront in this direction.

Coronal structures that were impacted by the wave include an equatorial coronal hole (CH1), a north polar coronal hole (CH2; Figures 3(a) and (d)), and two quiescent filaments (F1 and F2; Figure 3(c)). Note the western end of F2 can be seen above the limb, embedded at the bottom of a coronal cavity (Figure 3(a)). Below we will investigate in detail the impact of the EUV wave on the aforementioned coronal structures.

2.1.3. Wave Impact on Coronal Structures

Wave & Coronal Holes—The wave impact on coronal holes can be seen through Sectors 4–8, which cover CH1, and Sectors 15–17, which cover CH2. In Figure 4, the wave transmission through CH1 is only detected in Sector 8, which covers the northern end of the crescent-shaped CH1, but not in Sectors 4–7. In contrast, the wave transmission through CH2 is detected in all sectors across it. Note that a stationary front was produced at the AR-facing boundary of CH1 (labeled "SF" in Figures 6(d)–(f); see also Figure 4, Sector 8). In addition, a wavefront moving away from CH2 toward the equator can be seen in the polar region above the limb in AIA 193 Å running difference images (see the animation accompanying Figure 3). It was also detected from the arc slits close to as well as above the limb up to 0.16 R_⊙ (∼110 Mm), starting at about 18:21 UT at PA ≈ 340° with an apparent speed of over 300 km s⁻¹ (labeled "RWF" in Figure 5). It soon became very diffuse at PA ≈ 330°, before being able to impact F2 at PA ≈ 310. The wavefront must be either reflected off or refracted out of CH2 because it propagated away from CH2 and appeared later than the arrival of the primary wavefront (labeled "PWF") at about 18:15 UT.

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Wave & Coronal Arcade—The wave transmission through an arcade of coronal loops was most clearly visible in 211 Å (see also the animation accompanying Figure 6), but also marginally visible in 193 Å (Sectors 21–23 in Figure 4). This arcade consists of coronal loops connecting positive flux in the eastern AR and negative flux to the east of AR (Figures 3(d) and 6(a)–(c)). The wavefront appears to propagate along these loops (indicated by red arrows in Figures 6(d)–(f)), initially at ∼600 km s⁻¹ (Figure 6(g)), but then significantly decelerated to ∼50 km s⁻¹ as it propagated toward the far (eastern) side of the arcade. The wavefront was enhanced in 211 Å (Figure 6(g)) but dimmed in 193 and 171 Å (Figures 6(h) and (i)), especially when it approached the eastern end of the arcade, where the propagation apparently stopped.

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Wave & Filaments—The wave transmission through the filaments F1 and F2 is detected in Sectors 10–12 (Figure 4). There is no discernible change of the primary wavefront as it traversed the filaments. In addition to the fast and sharp primary wavefront, one or two secondary wavefronts that are slow and diffuse are also visible in the corresponding time–distance maps. The secondary wavefronts are closely related with the filament disturbance in response to the impact of the primary wavefront, but this information is lost in the average over the azimuthal direction in each sector. We hence constructed time–distance maps (Figure 7) with linear slices across the two filaments (Figure 3(c)). We picked some reference points on the northern edge of the filaments along the slices (cyan crosses; Figure 3(c)), each corresponding to a horizontal reference line in the time–distance map (Figure 7). Note F1's eastern section bifurcated, labeled F1a and F1b. Under the impact of the primary wavefront, F1's displacement as large as 5–10 Mm can be seen in the time–distance maps southward of the reference line at around y = 110 Mm. F2's displacement is not quite visible, due to poorer contrast and more severe foreshortening nearer the limb. With the reference points we found that secondary wavefronts originated from the northern side of F1 and F2. These wavefronts initiated either from F1 soon after the impact of the primary wavefront at about 18:15 UT (Linear Slices 4 and 5; Figure 7), or when the displaced filament swung back, i.e., after the half period of the oscillation (Linear Slices 1–3). They are very diffuse and hence can be detected in various slits oriented in different directions, including the arc-shaped slices (Figures 5(a) and (b)). The speed was estimated to range from tens of kilometers per second to about 150 km s⁻¹.

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2.2.1. Eruption and Wave Initiation

2.2.2. Wave Propagation and Impact

To study the wave propagation, we again employed 24 sectors to cover the solar disk (Figure 9(a)), each spanning 15 deg and centering on the midpoint of the conjugated HXR footpoints at 25–50 keV at around 01:26:30 UT (not shown). Three representative sectors are shown in Figure 9(a). The primary wavefront propagated mainly southward and northward. The southward-propagating wavefront (marked by black arrows in Figures 9(b) and (c)) transmitted through CH1 along Sector A (Figure 9(d)), but not in other angular directions. The wavefront was weak inside CH1, and a stationary front formed at the AR-facing boundary of CH1, taking a similar crescent shape as CH1 (Figure 9(f)). The northward-propagating wavefront transmitted through CH2 along Sector B (Figure 9(e)). Unlike CH1, the transmission is seen in various angular directions covering the whole coronal hole, without a stationary front at the boundary. Along Sector C (Figure 9(f)), the transmission through the arcade to the east of AR 12371 is only marginally visible due to its proximity to the limb.

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Double or single secondary wavefronts can again be seen through virtual slices across the filament F1 (Figure 10). All the secondary wavefronts were associated with the filament disturbances between 20 and 40 Mm along the slices (marked by dotted lines in the top panel of Figure 10) at speeds of no more than 100 km s⁻¹. The filament disturbances are better discernible in time–distance maps constructed using original (middle panels) then running difference images (bottom panels); the reverse is true for the secondary wavefronts.

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At the onset of the M7.9 flare at about 08:10 UT on 2015 June 25, one can see two groups of sheared loops in 131 Å, apparently crossing each other (Figure 11(a)). These loops soon evolved into an eruptive RLS, reminiscent of tether-cutting reconnection (Liu et al. 2010). The RLS' southern leg was apparently kinked (Figures 11(b) and (c)). The primary wavefront emerged at about 08:15 UT, taking a loop shape (Figure 11(g)). From a virtual slit oriented along the expulsion direction, one can see that the wave initiation was again associated with the expansion and subsequent contraction of coronal loops overlying the RLS (Figures 11(i) and (j)). A representative 193 Å loop under contraction is marked by an arrow in Figure 11(h). The wave initiation time was around the HXR peak at 50–100 keV at 08:14:28 UT (Figure 1(d)).

In this event, the wave impact on coronal structures is best seen for CH2 and the arcade to the east of AR 12371 (Figure 12(a)). CH1 was located too close to the western limb, despite the fact that a stationary front again formed at its AR-facing boundary (Figure 12(b)). The primary wavefront also passed through filament F1 and produced a secondary wavefront propagating northward (Figure 12(b); see also the animation accompanying Figure 12). With sector-shaped slices centered on the flaring site, one can see through Sector A that the primary wavefront transmitted through CH2 (Figures 12(c), (d)–(f)). Though weaker inside CH2 than outside, generally the wavefront was slightly enhanced in 211 Å, significantly enhanced in 193 Å, but dimmed in 171 Å, suggesting that the plasma at the wavefront was warmed up to about 1.5 MK, an effect not clearly seen in the other two events. Sector B highlights the wavefront propagation along the arcade of coronal loops to the east of AR 12371, with an apparent deceleration (Figures 12(g)–(i)). The wavefront was initially shown as an enhanced feature in 211 and 193 Å, but not quite visible in 171 Å. However, when approaching the far side of the arcade, the wavefront was transformed into a dimmed feature in 171 and 193 Å, while remained enhanced in 211 Å, suggesting that the plasma at the wavefront was warmed up to about 2 MK, similar to the June 22 event (Figures 6(g)–(i)).

AR 12371 dominated the northern hemisphere during its disk transit. During the same period AR 12367 was the only major active region in the southern hemisphere; it was far away from AR 12371 and already close to the western limb on 2015 June 21 (see Figures 9(a) and (c)). Thus the EUV waves under investigation were propagating in similar coronal environments, interacting with similar coronal structures. This allows us to study these interactions from different viewing angles. On the other hand, the waves also derive their similarities from the homologousness of the eruptions, which are elaborated on below from three aspects.

First, the eruptions produced CMEs with similar morphology. All three CMEs exhibit a two-front morphology (Vourlidas et al. 2013): a halo outer front followed by an inner front with a more limited angular width (Figures 1(d)–(f)). The former is likely to be caused by the density compression at the primary wavefront, while the latter is identified with the RLS observed in the low corona, judging by its expulsion direction and spatial extent. Whether or not the wavefront is driven by the CME is debatable because of the asymmetry between the CME front with a limited angular width and the halo shocked front. Howard & Pizzo (2016) argued that the asymmetry could be explained by a blast wave and a flux rope erupting together. The contrast between a halo wavefront in the extended corona and a much narrower EUV wavefront on the surface suggests that the wave propagates in all directions in the relatively homogeneous high corona but is confined in the "valleys" of low Alfvén speed in the highly inhomogeneous low corona.

Second, the eruptions originated from the same segment of the AR's polarity inversion line, shared similar eruptive structure, and exhibited similar dynamics in the active region. The RLS in each event appeared to be kinked before erupting into higher corona (Figures 2, 8, and 11), hence we interpret it as a magnetic flux rope. The writhing motion indicates that the rope's magnetic twist has reached the threshold of the helical kink instability (Gilbert et al. 2007). The increase in twist can be accomplished by reconnections during the early phase of the flare (e.g., Wang et al. 2017b). Moreover, when the kinking RLS ascended, the overlying loops deflected, i.e., first expanded and then contracted (Figures 2, 8, and 11). A similar phenomenon was reported when a kinking filament "squeezed" through the overlying arcade (Liu & Wang 2009). Alternatively, the loop deflection is expected with the passage of a compressive wavefront followed by a rarefaction in pressure. This might be true in the June 22 and 25 events, in which the wavefront track in the time–distance map passes apparently through the "watershed" between loop expansion and contraction (Figures 2 and 11), but is not the case in the June 21 event (Figure 8). Hence we lean toward the former scenario.

Third, all three events show two major peaks in SXR or its time derivative, indicating two episodes of energy release (Figures 1(a)–(c)). In the June 21 and 22 events we did find two wavefronts: the primary wavefront was detected during the earlier episode of energy release; a narrower, jet-associated wavefront during the later episode (Figures 2 and 8, and accompanying animations). In the June 25 event, only the primary wavefront was detected; a second wavefront, even if it existed, could be easily missed because the second SXR peak is weaker compared with the other two flares, and the active region was close to the limb by that time.

The transmission of the primary wavefront through the bulk of the polar coronal hole CH2 was consistently observed on 2015 June 21 (Figure 9(e)), 22 (Figure 4 (Sectors 15–17)), and 25 (Figures 12(d)–(f)), with CH2 being imaged from quite different viewing angles, which minimizes the possibility of false detection. On the other hand, the transmission through the equatorial coronal hole CH1 was only seen at its southern end on June 21 (Figure 9(d)) and northern end on June 22 (Figure 4; Sector 8). We noticed that a bright stationary front formed at the AR-facing boundary of CH1 (Figures 6, 9 and 12), sustaining for an extended time period in each case. Hence we speculate that the primary wavefront only transmitted through the ends of CH1 because the bulk of wave energy was dissipated at the stationary front. Such stationary fronts also appear in numerical experiments when a fast-mode wave passes a coronal hole (e.g., Piantschitsch et al. 2017, 2018) or a quasi-separatrix layer (Chen et al. 2016). On 2015 June 22, a reflected/refracted front was seen to move away from the polar coronal hole at projected heights up to ∼110 Mm above the limb (Figure 5). We note that a similar height (∼80–100 Mm) was obtained for EUV waves using STEREO quadrature observations (Kienreich et al. 2009; Patsourakos et al. 2009).

The propagation of the primary wavefront along a coronal arcade consisting of east–west oriented loops was consistently observed in all three events (Figures 6, 9(f), and 12(g)–(i)). When we had a clear view of the whole arcade (June 22 and 25), we found the propagation speed was significantly decelerated as the wavefront propagated at the far side of the arcade (Figures 6(g)–(i) and 12(g)–(i)); but when the arcade was located close to the east limb (June 21), its far side was obscured by the perspective, and we found no clear deceleration (Figure 9(f)). Hence the deceleration was most likely a foreshortening effect involving the arched geometry and viewing angles. While the wavefront apparently slowed, it was enhanced in 211 Å and dimmed in 193 and 171 Å. We speculate that the arcade serves as a lens that "focuses" the waves toward the far end of the arcade, resulting in a local heating as evidenced by the different responses in 211 (Fe xiv), 193 (Fe xii), and 171 Å (Fe ix).

Under the impact of the primary wavefront from the south, the northward displacement of the filaments was negligible compared to the southward displacement (Figures 7 and 10). This can be understood by the Alfvén speed increasing with height in the low corona (below about 3 R_⊙) of the quiet Sun (Gopalswamy et al. 2001). As a result, the fast-magnetosonic wavefront tends to be refracted toward the surface, consequently inclining forward, which was indeed observed in some limb events (e.g., Hudson et al. 2003; Liu et al. 2012) and reproduced by numerical simulations (e.g., Wu et al. 2001; Grechnev et al. 2011). Upon arriving at a filament suspended in the corona, the compressive wavefront would push the filament forward due to the oblique front. The resultant displacement is expected to be small partly because of increasing magnetic field and plasma density toward the surface, and partly because of projection effects with the filament being located in the northern hemisphere. The filament then swings back and is expected to overshoot because of the rarefaction in the wake of the compressive wavefront, therefore, displaying a significant southward displacement. The second swing of the filament toward its original position would again exert pressure on the surface. Such impacts may produce the northward-propagating secondary wavefronts. These wavefronts are very diffuse probably because they originate at different times from different places along the filament. With speeds comparable to the sound speed, these secondary wavefronts are likely slow-mode waves.

The magnetic field in the polar coronal hole is open and hence predominantly vertical to the wave propagation, while in the coronal arcade the magnetic field is traced by coronal loops and hence parallel to the wave propagation. This reveals the nature of the primary wavefront, because only fast-magnetosonic waves can propagate in all directions with respect to the magnetic field. On the other hand, the stationary front at the boundary of the equatorial coronal hole makes it unlikely to interpret the primary wavefront as a slow-mode soliton (Wills-Davey et al. 2007; Long et al. 2017). Although compatible with the stationary front, both the current shell model (Delannée et al. 2007, 2008) and the continuous reconnection model (Attrill et al. 2007) cannot accommodate the transmission through, and the reflection/refraction from, the polar coronal hole (Long et al. 2017). The fast-mode shock wave in the field-line stretching model (Chen et al. 2002, 2005) is consistent with the primary wavefront in our observations, but it would be difficult for this model to explain why a slower front appeared only when the primary front impacted the filaments, had the slower front resulted from the stretching of field lines overlying the erupting flux rope.

The 2015 June 25 event is optimal for observing the transmission of the primary wavefront through the polar coronal hole and the coronal arcade (Figure 12(a)), as both structures were close to the disk center. Given that the wave propagates at the fast-magnetosonic speed, in the coronal hole the speed is

$$\begin{eqnarray}&&v=\sqrt{{v}_{{\rm{A}}}^{2}+{c}_{s}^{2}},\end{eqnarray} \tag{ 1 }$$

but in the coronal arcade

$$\begin{eqnarray}&&v={v}_{{\rm{A}}},\end{eqnarray} \tag{ 2 }$$

where ${v}_{{\rm{A}}}=B/\sqrt{4\pi {{nm}}_{p}}$ is the Alfvén speed, and ${c}_{s}\,=\sqrt{\gamma {k}_{B}T/{m}_{p}}$ is the sound speed. These speeds are insensitive to plasma temperature and density because of the square root. We made a rough estimate of the magnetic field strength by adopting typical values of plasma density number in the corona, i.e., n ∼ 10⁸ cm⁻³ for the coronal hole and 10⁹ cm⁻³ for the coronal arcade. We further assumed that the plasma temperature is in the range of 1–2 MK in the quiet Sun, and that the adiabatic index γ = 5/3. With the wave propagation speeds measured in the time–distance maps (Figures 12(d) and (g)), we found that B ∼ 2 G and plasma β ∼ 0.2–0.3 in the coronal hole, and that B ∼ 4 G and β ∼ 0.5–1 in the coronal arcade neighboring the active region. These numbers are comparable with previous results obtained by various methods (Liu & Ofman 2014, and references therein).

We have analyzed the coronal EUV waves associated with the three CMEs on 2015 June 21, 22, and 25, respectively. These homologous eruptions provide us a rare opportunity to investigate how the waves interact with coronal structures from three different viewing angles. Such observations help resolve the ambiguity and confusion due to projection and perspective effects, and yield new insight into the physics of EUV waves, as is highlighted below.

• 1.  
  The propagation both along the field in the coronal arcade and across the field in the coronal holes substantiates the primary wavefront as fast magnetoacoustic waves. The wave nature is further corroborated by the reflected/refracted wavefront bent away from the polar coronal hole.
• 2.  
  As the primary wavefront propagates along a coronal arcade toward its far end, a slow front is seen to "veer off" from the fast front in the time–distance maps (Figures 6 and 12). This is an effect of perspective and projection, which we suspect might be responsible for some of the slow fronts exhibiting similar features in time–distance maps (e.g., Chen & Wu 2011; Asai et al. 2012; Xue et al. 2013; Shen et al. 2014a). This offers an alternative scenario to those interpreting the slow front as a pseudo-wave produced by coronal restructuring associated with CMEs (e.g., Chen et al. 2005; Attrill et al. 2007; Delannée et al. 2008).
• 3.  
  Slow and diffuse wavefronts are produced by the primary wavefronts impacting on filaments, which may account for some extremely slow and diffuse "EIT" waves (e.g., Warmuth & Mann 2011).