A NEW VIEW OF CORONAL WAVES FROM STEREO

The first observations of large-scale transient coronal waves, also known as EUV Imaging Telescope (EIT) waves, were made by the EIT (Delaboudinière et al. 1995) on board the Solar and Heliospheric Observatory (SOHO; Domingo et al. 1995). In many events, the EIT wave appears as a roughly circular diffuse emission enhancement propagating globally across the solar disk. This is particularly true when the magnetic structure on the Sun is simple (e.g., Thompson et al. 1998). When the global magnetic structure is more complicated, EIT waves can propagate inhomogeneously, avoiding strong magnetic features and neutral lines (e.g., Thompson et al. 1999), and generally stop near coronal holes (e.g., Thompson et al. 1999). Although EIT waves are found to be a quite frequent phenomenon, there are still some open questions. There is a debate as to whether EIT waves are "flare-driven" or "coronal mass ejection (CME)-driven" (e.g., Uchida 1968; Warmuth et al. 2001, 2004; Biesecker et al. 2002; Hudson et al. 2003; Zhukov & Auchère 2004; Cliver et al. 2005; Vršnak et al. 2006). Similarly, the physical nature of diffuse EIT waves (Vršnak 2005) is an active research topic, with different possible explanations, such as fast-mode MHD waves (e.g., Thompson et al. 1999; Wills-Davey & Thompson 1999; Wang 2000; Wu et al. 2001; Ofman & Thompson 2002; Warmuth et al. 2004; Ballai et al. 2005), slow-mode MHD waves (Krasnoselskikh & Podladchikova 2007; Wills-Davey et al. 2007; Wang et al. 2009), non-wave propagating disturbances related to magnetic field lines opening (e.g., Delannée 2000; Chen et al. 2002, 2005), restructuring associated with CME expansion in the low corona (Attrill et al. 2007a, 2007b), or a current shell around the expanding flux rope (Delannée et al. 2008).

The Solar Terrestrial Relations Observatory (STEREO; Kaiser et al. 2008) is the first mission dedicated to studying the three-dimensional evolution of solar eruptions, providing us with the opportunity to observe from two different directions simultaneously. STEREO consists of two identical spacecrafts orbiting the Sun at nearly 1 AU, with one ahead (STEREO A) and one behind (STEREO B) the Earth near the ecliptic plane. With observations from different angles, it becomes possible to constrain some of the debate about EIT waves. We briefly introduce our data in the next section, our observations and results are discussed in Section 3, and we present our conclusions in Section 4.

To study EIT wave morphology and propagation in the EUV, we take advantage of the two perspectives afforded by both STEREO–EUVI imagers (Wuelser et al. 2004; Howard et al. 2008). The EUVI instruments image the solar chromosphere and low corona in four emission lines: 171 Å (∼1 MK), 195 Å (∼1.5 MK), 284 Å (∼2 MK), and 304 Å (∼80,000 K) from the solar surface out to 1.7 R_☉. The pixel-limited spatial resolution of EUVI images is 16. In this study, we focus on EUVI observations in the 171 Å and in 195 Å passbands, with time cadences of 2.5 and 10 minutes, respectively. For comparison, we also use EUV data from SOHO–EIT.

To study the origin of the EIT wave, we augment our EUV observations with Hα, X-ray, and magnetogram data. Since such data are not available from the STEREO suite of instruments, we turn to other sources. Our Hα observations are derived from the Yunnan Astronomical Observatory (YNAO); we use soft X-ray data from Hinode–X-ray Telescope (XRT; Golub et al. 2007; Kosugi et al. 2007); and we obtain contemporaneous 1-minute cadence magnetograms from SOHO–Michelson Doppler Imager (MDI; Scherrer et al. 1995). Our XRT images were taken using the C-poly filter with a spatial resolution of 1028 and a cadence of 60 s or less.

On 2007 December 7, a diffuse EIT wave was observed at 04:25 UT, originating from AR 10977. This event occurred along with the eruption of a filament and the disappearance of the X-ray sigmoid. The Hα filament, which erupted at 04:33 UT, was associated with a B1.4 flare beginning at 04:35 UT. An associated CME was later observed by both STEREO–COR B and SOHO–LASCO.

3.1. Origin

Changes resulting from this eruption were observed in the photosphere, chromosphere, and corona. Figure 1(a) shows the corresponding Hα observations. The upper panel shows evidence of a small filament along the neutral line of AR 10977. After the eruption at ∼04:30 UT, a two-ribbon flare appears (lower panel). Similarly, the X-ray sigmoid shows evidence of an eruption (Figure 2(b)) by the sigmoid-to-arcade evolution (Hudson et al. 1998; Glover et al. 2002). At 04:20 UT, XRT observations show the sigmoid cospatial with the filament (upper panel). After the eruption, a series of flare loops appears, with their footpoints anchored to the two Hα flare ribbons. Close examination of the XRT data reveals that the sigmoid eruption was initiated near the center of the structure, close to the location of the filament.

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To better understand the effect of the eruption on the surrounding magnetic field, we examine MDI magnetograph data close to the eruption origin. Figure 1(c) shows the local magnetic field before and after the eruption; magnetic flux measurements are obtained from the area in the white box, which corresponds to the photosphere below the sigmoid eruption location. Figure 1(d) demonstrates that both the positive and negative magnetic flux decreased during the eruption. This result suggests that the magnetic cancellation occurred as part of the event.

3.2. Morphology

The related EIT wave was well observed by both EUVI A and B. Figure 2 shows the propagation of the EIT wave as observed by the two STEREO spacecrafts. At the time, their separation angle was 424. We examine the structure and dynamics of the EIT wave using running difference images of 171 Å and 195 Å data (see also the accompanying movie). The location of an equatorial coronal hole is identified by green contours.

The morphology of the EIT wave differs between the two EUV passbands. A weaker front is observed in the 171 Å data, while a brighter front appears in 195 Å. These results are consistent with those of Wills-Davey & Thompson (1999), who found marked differences between 171 Å and 195 Å observations of the same EIT wave event. Wills-Davey & Thompson (1999) suggested that such differences may relate to the relatively broad, overlapping nature of the EUV passbands themselves. In the case of thermal compression, the increased temperature of the compressed material causes changes in the emission at a given passband. Material in the lower corona, while normally bright at 171 Å, may appear to dim as it is heated; conversely, as cooler coronal plasma is heated into the adjacent 195 Å passband, an "overbrightening" is expected. We suggest that the observed differences between the 171 Å and 195 Å data in this instance may be due to the same effect.

Comparison of the EUV observations made by the two STEREO spacecrafts shows substantial differences in morphology early in the EIT wave's development. The images in Figure 2 are arranged so that EUVI A data are located above the corresponding EUVI B data. This allows us to easily see how the two perspectives differ, especially before 04:40 UT. Early on, the wave appears to propagate primarily eastward in EUVI A and primarily westward in EUVI B. These differences are particularly apparent in Figure 3, which shows contours of the relative positions of the projected EIT wave fronts. Interestingly, as the wave expands farther, it becomes more circular, and the observations of the two STEREO instruments become more similar. We note that Patsourakos et al. (2009) also noticed such a feature of the EIT wave independently.

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3.3. Wave Propagation

To study the dynamics of the EIT wave, we focus on 171 Å and 195 Å data. The data in 171 Å show a weaker EIT wave front, but have higher time cadence. The data in 195 Å have a more distinct wave front but suffer from a lower time cadence. In order to obtain the best information, we use both of them in this study. We consider wave motion along four different trajectories, represented by colored arcs in the top row of Figure 4. Each arc is a great circle projected on the photosphere which passes through the flare kernel. With the flare kernel as the origin, the wave position along each trajectory was determined in each frame using visual inspection. To account for observer error, each wave position was measured five times, and the mean distance values were used in the analysis.

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The lower three rows of Figure 4 show the positions of the wave front along each trajectory as a function of time. The left column corresponds to EUVI A and the right one to EUVI B. For each column, the top panels show EUVI images in 171 Å overlaid with the colored arcs. The second row are time–distance profiles giving the mean positions of the EIT wave fronts derived directly from observer measurements in 171 Å data. Error bars indicate the standard deviation of the measurements, "t2" and "t3" mark the EIT wave initiation time interval according to 171 Å data, which is 2.5 minutes. The third row are time–distance profiles of the EIT wave front in 195 Å, "t1" and "t4" mark the initiation time interval, 10 minutes according to the available 195 Å data. The bottom row displays a composite of time–distance profiles in 195 Å and 171 Å. The blue plus symbols mark the EIT wave front positions along the blue lines in the 171 Å images, which show that the EIT wave front propagating along the blue lines stopped at ∼04:40 UT, about 7 minutes ahead of the stop time determined from the data in 195 Å.

Table 1 show the linear fit velocities derived from the time–distance data in the given time intervals. The data show that the velocities derived from 171 Å data are larger than the corresponding velocities derived from 195 Å along the same path. This is consistent with the analysis of Long et al. (2008), who suggest that EIT wave velocities may have been underestimated due to the low (∼12 minutes) cadence of EIT data. Moreover, the velocities along the different paths are different from each other, especially the velocities along the blue lines, which are distinctly smaller than those along the other paths. Additionally, the values along the same path but from the different instruments are also different.

Table 1. Linear-fit Velocities (km s⁻¹) for EIT Wave

Direction	171A	171B	171 Time Interval (UT)	195A	195B	195 Time Interval (UT)
Red	260	228	04:30-04:50	194	215	04:35-05:15
Yellow	213	281	04:30-04:50	195	213	04:35-05:15
Green	262	228	04:30-04:50	194	215	04:35-05:15
Blue	198	149	04:30-04:40	78	80	04:25-04:45

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We note that the data in 171 Å shown in the second row of plots in Figure 4 have been divided into two groups, as indicated by the vertical dot–dashed lines marked by "t2," the data obtained before 04:30 UT, and "t3" those obtained after 04:30 UT. This classification is appropriate because the wave dynamics change markedly at this point in time. Before 04:30 UT, we believe that any observed motion is due, not to the EIT wave front, but rather to the expansion of the sigmoid. The EIT wave itself cannot be convincingly distinguished from the eruption as a whole until ∼04:30 UT, after which it is observed to propagate rapidly and ubiquitously. After 04:50 UT, the wave front becomes too faint to track reliably. From 04:30 UT to 04:50 UT, motions in different directions show similar trends, but some differences are visible. We calculate the linear-fit velocities along red, green, and orange lines in this period. For the linear-fit velocities along the blue lines, we calculated only from 04:30 UT to 04:40 UT because we find that the EIT wave front stopped propagating at ∼04:40 UT. The results are placed in the second and third columns and the time intervals are listed in the fourth column in Table 1.

However, the data at 195 Å shown in the third row in Figure 4 have even been divided into three groups by the dashed lines marked as "t1" (04:25 UT) and "t4" (04:35 UT). The first group obtained before 04:25 UT, the second group obtained between 04:25 UT and 04:35 UT and the last group obtained after 04:35 UT. Like the first group in 171 Å, the data of the first group in 195 Å do not appear to show distinct changes. During the period from "t1" to "t4," the locations of the EIT wave front began to change clearly. After "t4," the locations of the front changed rapidly. The data appear to show that the EIT wave undergoes a period of acceleration. However, we think that this is an illusion. Comparing the initiation time estimated from 195 Å with that estimated from 171 Å, we find that the time estimated from 195 Å is at least 5 minutes ahead of that in 171 Å. When we consider the initiation time to be "t2," we found that all except for the blue time–distance profiles showed a linear increase (see the bottom panels in Figure 4). We calculate the linear-fit velocities from 04:25 UT to 04:45 UT along the blue lines and from 04:35 UT to 05:15 UT along the other colored lines. The results are shown in the fifth and sixth columns of Table 1. The time intervals are listed in the right column.

Although the EIT wave showed a similar propagation along different directions, its velocity displayed variations with direction as well, implying that the propagation is not symmetric. In particular, the blue trajectory in Figure 4 shows little or no motion after 04:40 UT, which suggests that the southeastern front of the EIT wave suddenly "stopped." An examination of the nearby magnetic structures reveals the presence of an equatorial coronal hole (outlined by the green contours in Figures 2 and 4). Its position coincides with the EIT wave front at ∼04:40 UT, suggesting that it is the coronal hole that prevents the EIT wave from moving farther southeast. This result is consistent with other studies (e.g., Thompson et al. 1998; Veronig et al. 2006; Attrill et al. 2007b). Another issue that draws our attention is the velocity differences observed by EUVI A and B. As previously stated, efforts were made to correct for projection effects along the great circle arcs measured in Figure 4. However, we still find velocity differences (see Table 1), in spite of the correction. This suggests that a simple spherical correction using the photosphere as a reference is insufficient for adequately mapping EIT wave dynamics; the three dimensionality of these events must be taken into account.

Comparing differences between the EUVI A and EUVI B observations, several aspects deserve additional attention. Early in its lifetime, the EIT wave morphology (Figures 2 and 3) appears quite different depending on the perspective. However, as time goes on, the two views of the EIT wave start to look more alike.

Such a discrepancy can be easily accounted for if the CME eruption itself is taken into account. Early in its initiation, the CME expands upward through the lower corona. The presence of this early-stage CME, combined with projection effects, produces observations similar to those seen by EUVI A and B. Figure 5 shows how these aspects can influence the observational results. The upper two cartoons demonstrate the early and late stages of a CME eruption, respectively. The green semicircle in the left cartoon represents the CME and its associated coronal disturbance early in the eruption. At this point, the entire CME is still in the atmosphere layer observable in the 171 Å passband. The lines of sight (LOS) of EUVI A and B are represented by two sets of parallel arrows, with the orange lines indicating regions of the greater column depth. The middle row shows the likely EUVI B, EIT, and EUVI A observations resulting from such an eruptive process. Here, the orange areas mark the regions that appear brighter due to increased optical depth.

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When compared to actual observations (displayed in the bottom row), the similarities are striking. The leading EIT wave edge seen by EUVI A appears to be moving in the opposite direction to that seen by EUVI B; this comparison is shown even more clearly by the red and green contours in Figure 3, which morphology can be explained by projection effects alone if the CME itself is coupled to the EIT wave early in the eruption. Under such circumstances, part of the emission detected by EUVI comes from the "dome-like" structure of the CME before it leaves the lower corona.

As the eruption progresses, the top of the CME eventually leaves the layer where the emission is visible to EUVI (Figure 5, upper right). The result is an increasingly circular wave. As for the dynamics of the wave itself, our results for this event show similar velocity trends observed by each spacecraft, regardless of direction. However, there are still notable discrepancies between the corrected EUVI A and B measurements. These issues could come from a number of sources.

• 1.  
  It could be due to observer bias. Visual inspection is, by nature, observer-dependent, and diffuse wave fronts are notoriously difficult to measure, particularly near the limb or later in the life of the event.
• 2.  
  Different local MHD conditions could affect propagation. This is likely the case along the blue arc, which is apparently affected by the nearby coronal hole.
• 3.  
  The projection effect corrections might not be accurate. Such corrections assume that the wave exists as an infinitesimally thin layer at the photosphere, which is a poor approximation at best.

Considering the initiation time of the EIT wave, both the data in 171 Å and in 195 Å seem to support a time–distance fit of a linear increase, indicating constant velocity. According to this study, the low time cadence of 195 Å may mislead to a cursory examination to the conclusion that the EIT wave experiences an acceleration period at the beginning of the EIT wave propagation. Due to the low time cadence, the initiation time of the EIT wave is inaccurate. Therefore, the 195 Å with 10 minute cadence is not sufficient to prove EIT wave experienced an acceleration period.

Our measurement fits suggesting constant velocity are consistent with the new results of Kienreich et al. (2009), but differ from other previous findings. Warmuth et al. (2004) and Veronig et al. (2008) find that some EIT waves decelerate as they propagate, and Long et al. (2008) observe an increase and then decrease in EIT wave velocity. It is possible that the different results come from the different definition of the EIT wave initiation time. Rather than marking it as coincident with the first observed motion (which could well be related to the expansion of the sigmoid), we relate the onset to the first appearance of the well-defined bright front. Interestingly enough, if a similar assumption of the initiation time, 12:50 UT, of EIT wave is made for the work of Long et al. (2008), the time–distance profiles in 171 Å at the top panels in Figure 3 in that paper then also show a constant velocity, which is consistent with our results. Higher time cadence at 195 Å is required for future studies to reliably reconcile such results.

By taking advantage of STEREO's dual perspective, this study offers compelling evidence of the ways that observations are affected by the inherent three dimensionality of EIT waves. There is much evidence to suggest that EIT waves are confined to a layer within the lower corona (Thompson et al. 1999; Warmuth et al. 2004, 2005; Vršnak 2005), which recently this has been determined from STEREO observations as being ∼90 Mm (Patsourakos et al. 2009; Kienreich et al. 2009). However, we find that, in the early stages, the EUV intensity enhancement observed as an "EIT wave" is due, not only to density changes close to the surface, but also to the added column depth of the CME itself. When considered in the context of velocity incongruities between EUVI A and B, these results lend credence to the idea that EIT waves exist over some non-negligible height in the corona. It is apparent that such morphology, neglected for so long, can materially influence results if not taken into account, and must be considered in future analyses and modeling efforts.

We sincerely thank the anonymous referee for very helpful and constructive comments that improved this paper. The STEREO/SECCHI data are produced by an international consortium: NRL, LMSAL, NASA, GSFC (USA); RAL (UK); MPS (Germany); CSL (Belgium); and IOTA, IAS (France). Hinode is a Japanese mission developed and launched by ISAS/JAXA, collaborating with NAOJ as a domestic partner, NASA and STFC (UK) as international partners. Scientific operation of the Hinode mission is conducted by the Hinode science team organized at ISAS/JAXA. This team mainly consists of scientists from institutes in the partner countries. Support for the post-launch operation is provided by JAXA and NAOJ (Japan), STFC (UK), NASA, ESA, and NSC (Norway). SOHO is a project of international cooperation between ESA and NASA. YNAO/Hα telescope is run by the Yunnan Astronomical Observatory, Chinese Academy of Science. This work was supported by Program 973 grant 2006CB806303, by NSFC grants 10873030 and 40636031, and by CAS grant KJCX2-YW-T04 to YNAO. S.M. was also supported by NASA grant SP02H1701R and NNM07AB07C. M.J.W.D. and G.D.R.A. gratefully acknowledge NASA grant NNX09AB11G. J.L. was supported by NASA grant NNX07AL72G when visiting CfA.