NUMERICAL SIMULATION OF AN EUV CORONAL WAVE BASED ON THE 2009 FEBRUARY 13 CME EVENT OBSERVED BY STEREO

The COR1 instruments are internally occulted coronagraphs and observe the inner solar corona in white light from 1.3–4 R_☉ (Thompson et al. 2003). Base difference images (where a pre-event image at 05:45 UT, is subtracted from all subsequent images) of COR1-A data are shown in the left panels of Figure 2. The COR1 images were taken with a temporal cadence of 10 minutes, and have a pixel size of 75. COR1-B also observed the CME as a halo event, first becoming apparent beyond the occulting disk at 06:55 UT. The non-differenced COR1-A data (not shown) show a helmet streamer located north of AR 1012, and open streamers to the south.

Zoom In Zoom Out Reset image size

The EUVI imagers observe the Sun out to 1.7 R_☉, and produce 2048 × 2048 images with a pixel size of 16 (Wuelser et al. 2004). We analyze the 195 Å EUVI images, which have a temporal cadence of 10 minutes. Base difference images from EUVI-B are shown in Figure 3. The base difference images are produced by first compensating for the solar rotation using SolarSoft's drot_map routine (http://www.lmsal.com/solarsoft), so that all images are de-rotated to the pre-event image time at 05:15 UT. Then, the pre-event image is subtracted from all subsequent images. Base difference images highlight real intensity changes, with bright areas showing an increase in emission with respect to the pre-event data.

Zoom In Zoom Out Reset image size

2.2.1. Coronal Dimmings

As well as showing the coronal wave bright front, base difference images also show depletions in intensity, known as "coronal dimmings." These are regions where the plasma density has dramatically decreased due to plasma evacuation along the "opened" magnetic field, usually occurring during an eruption (e.g., Hudson et al. 1996; Harra & Sterling 2001; Harra et al. 2007). Various works have shown that the core coronal dimming regions (i.e., black regions, bottom panels of Figure 1) located on either side of the bright post-eruptive arcade (PEA) mark the footpoints of the erupting flux rope (e.g., Webb et al. 2000; Mandrini et al. 2005; Crooker & Webb 2006; Attrill et al. 2006; McIntosh et al. 2007). The intensity drop in core coronal dimmings is substantial (typically ∼40%–60%; e.g., Chertok & Grechnev 2005).

We process the EUVI base difference data using the automatic dimmings detection algorithm described in Attrill & Wills-Davey (2009). Figure 4 shows the output from this algorithm. In addition to the core dimmings near to the PEA, secondary dimmings are also detected which develop remote from the active region and are spread across the solar disk. These secondary dimmings are more subtle than the deep, core dimmings and are not easy to identify by eye in the base difference data. We discuss the secondary dimmings further in Section 5.4.

Zoom In Zoom Out Reset image size

2.2.2. Persistent Brightenings

Prior to a detailed analysis of the magnetic field three-dimensional evolution, we validate the timing of the simulated CME by comparing its propagation with STEREO/COR1 observations. This validation is required for any further assumptions about the dynamic evolution and its relation to the observed coronal waves. Fortunately, the 2009 February 13 event was observed by both STEREO-A and STEREO-B simultaneously, in quadrature.

Figure 2 shows a side view of the CME propagation, comparing STEREO-A COR1 base difference white-light images with synthetic base difference white-light images generated from the simulation domain for 5:55, 6:15, and 6:35 UT. We would like to stress that both real and simulated data sets have been processed in the same manner, and the scale of the images has been chosen so that it provides the best display.

The comparison of the simulation (center column) with the base difference images (left column) is used to verify the structure of the CME. Comparison with the running difference images (right column) is used to verify the lateral extent. We emphasize that the outer shell of the CME is a very subtle feature, and is only really evident when successive frames are switched back and forth. Thus the reader is encouraged to examine the COR1 running difference movie available in the online journal (COR1_rdiff.mov), using the white arrows in the right column of Figure 2 as a reference. One can see that the simulated CME front and the global structure matches well to the observed CME.

Figure 3 compares the simulation results with STEREO-B EUVI data for the period 5:25–6:35 UT. The left panel of each pair shows an EUVI base difference image, while the right panel shows base difference images of the simulated mass density at a height of 1.1 R_☉ (about 70 Mm). We choose this height as it is consistent with calculations of the coronal wave bright front altitude from EUVI data (Patsourakos et al. 2009), as well as with previous height estimates from SOHO/EIT data (Section 1).

We mark the leading edge of the bright front in each base difference EUVI-B image with a dashed white circle. We emphasize that this circle has been drawn by eye, and simply indicates the maximum extent reached by the coronal wave in a given image. (The reader is encouraged to view the supplemental movies to Figure 3 available in the online journal: 195b_diff.mov, densityfrontdif.mov). Figure 3 shows that the expansion of the simulated wave front is in a good agreement with the observed one. Deviations are probably due to the fact that the actual EUVI emissions are not simply a representation of the mass density, but a rather complicated, integrated function of it.

The simulated bright front in Figure 3 becomes broader as it expands further from the active region. This is consistent with observed properties of coronal waves from SOHO/EIT data (Dere et al. 1997; Klassen et al. 2000; Podladchikova & Berghmans 2005). Areas of decreased mass density (corresponding to the core coronal dimming regions) can also be identified in the simulated data. We note that both the real and simulated bright fronts have an increasingly patchy, diffuse nature as the front expands away from the active region. We measured the expansion of the leading edge of the bright front in running difference data from 05:45–06:15 UT, which expands with an average velocity of ≈260 km s⁻¹. For comparison, the Alfvén velocity from the simulation (Figure 5) is ≈200 km s⁻¹.

4.2.1. Two-component Bright Front

Figure 6 compares snapshots at 06:05 UT from COR1-A, the simulated CME, and EUVI-A, all scaled to the same size. The COR1-A and EUVI images are running difference images, the simulation is a base difference image. Patsourakos & Vourlidas (2009) show a fit of the 3D CME model of Thernisien et al. (2006, 2009) to the COR1-A data for this event at 06:05 UT. This leads them to determine an extent for the CME in the low corona that is much too small to match the coronal wave in the corresponding EUVI data, since the 3D model is essentially made up of a spherical bubble attached to a conical leg. We note that a similar approach was also used in Patsourakos et al. (2009). In both papers, the authors interpret the apparent misfit between the CME model extension in the low corona and the EUVI coronal wave as evidence that the coronal wave and CME are different structures and conclude that the coronal wave is a fast-mode MHD wave.

Zoom In Zoom Out Reset image size

Our simulation results at 06:05 UT are shown in the middle panel of Figure 6. The simulation gives information about the low corona below 1.3 R_☉ (200 Mm), the region obscured by the occulting disk in the COR1 data. Comparison of the middle and right panels of Figure 6 show that the extension of the CME in the low corona maps very well to the coronal wave in the EUVI base difference data.

In particular, the simulation results show a secondary cavity located to the north of the main CME cavity (marked by the white arrow in the middle panel of Figure 6). Comparison with the corresponding EUVI base difference data shows secondary coronal dimmings developing at the same location (right panels, EUVI (A), Figure 4). Despite the lack of spectral diagnostics for secondary dimmings, this correlation between the secondary CME cavity and the secondary coronal dimmings is consistent with plasma evacuation.

A time-series movie of the simulated COR1-A white-light data (COR1joint1.mov) shows that the secondary cavity expands and merges with the main CME cavity, so that the low corona is really "opened" to a large lateral extent. This analysis demonstrates the important role of the simulation in developing an understanding of the true lateral extent of the CME in the low corona.

In Section 4.2.1 we noted that the higher intensity patches of the coronal wave front no longer expand as of ∼06:55 UT. Correspondingly, the simulation results show that the CME has stopped expanding significantly in a lateral direction by this time. (The reader is referred to movie COR1joint1.mov.)

Figures 7 and 8 show time-series plots of the simulation results matched to the STEREO-B (on-disk) and STEREO-A (limb) viewing angles, respectively. (The reader is encouraged to view the movies that correspond to these figures, SA.mov and SB.mov, available in the online journal.)

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The inner sphere shows the photosphere with the radial magnetic field strength from the magnetogram data. The outer sphere (light gray) is at a height of 1.1 R_☉ (70 Mm) and represents the altitude at which coronal waves are observed. The white contours represent the density-enhanced front (same as displayed in Figure 3). The green shade represents an iso-surface of mass density with a base ratio (ratio between the current image and pre-event image) of 1.1.

Selected core field lines of the magnetic flux rope are drawn in red and some surrounding field lines of a range of sizes are drawn in blue. Where the core flux rope field (red) reconnects with a surrounding field line (blue), the blue field line changes to red, indicating the new extended connectivity of the core flux rope field. Reconnections between surrounding magnetic field lines (i.e., blue and blue), are shown by the newly reconnected field line changing to yellow. The same magnetic field lines have been plotted in both Figures 7 and 8, so that we can study the same development from the two different perspectives.

Referring to Figure 7, we see that the green iso-surface of increased mass density approximately maps to the white contour at each time frame. Figure 9 shows a line profile of the density base and running differences, as well as the temperature along the path of the coronal wave at r = 1.1 R_☉ (shown by the black arrow in the top panel). It can be seen that the temperature jump (indicating the shock front) is ahead of the density increase associated with the coronal wave. This means that the green shade represents the CME front and not the shock. Indeed, comparison of the green iso-surface with the white-light simulation and observational data (Figure 6) further suggests that it represents the outer-most shell of the expanding CME. The existence of a major reconnection (discussed below) further suggests that the green iso-surface represents the actual CME rather than a shock, since there is a close matching between the reconnected magnetic field line (red) and the iso-surface.

Zoom In Zoom Out Reset image size

Reconnection of a given field line first occurs when the white contour reaches the vicinity of one of the reconnecting field lines. This applies both for reconnections between the flux rope and surrounding magnetic field (red), as well as for reconnections between surrounding fields (yellow). We therefore conclude that the reconnections are directly driven by the expanding CME.

Further, we observe a major reconnection between the core flux rope field (red) and the overlying field (blue) at 06:05–06:10 UT (marked by narrow white arrows in Figures 7 and 8). This reconnection transfers the connectivity of the core magnetic field from near the equator to a latitude of ∼60°. On comparison with Figure 6, this reconnection explains the development of the secondary cavity (Section 4.3), and dramatic lateral expansion of the CME in the low corona at this time.

These results show that where the core magnetic flux rope is able to reconnect with overlying or surrounding favorably orientated field, the CME "opens" up the low corona to a very large lateral extent. A clear example was reported in an observational study by Manoharan et al. (1996) concerning reconnection with a trans-equatorial loop and the subsequent formation of two dimmings in quiet-Sun regions. Figures 7 and 8 show that quiet-Sun loops across the whole range of sizes are deflected by the CME expansion. Where the orientation is favorable, reconnection occurs. Whether CMEs are large-scale by nature or become large-scale through nurture was considered by van Driel-Gesztelyi et al. (2008). From our results, we conclude that CMEs become large-scale by nurture, through stretching of the magnetic field and reconnection in the low corona with the surrounding magnetic environment (Pick et al. 1998).

It is difficult to separate temperature and density effects within single narrow bandpass observations (such as 195 Å used by EUVI) because line-of-sight effects make the optically thin EUV data complex to interpret, and because intensity changes can theoretically be caused by alterations in temperature and/or density. Indeed, observations have contributed evidence in favor of both temperature (e.g., Wills-Davey & Thompson 1999; Gopalswamy et al. 2000) and density (e.g., Warmuth et al. 2005; White & Thompson 2005; Wills-Davey 2006) enhancements.

Delannée et al. (2008) find that the plasma can be brightened from both a current shell around the expanding flux rope via Joule heating, as well as from an increase in density due to compression. They find that the emission from the current shell generates a more conspicuous brightening than that from the plasma compression; however, they note that "the dissipation of the current densities at low altitude would not be responsible for the observed structure." This work is consistent with our simulation results presented in Figure 3, which show that the coronal wave bright front is well described by the mass density enhancement at a height of 1.1 R_☉. We note that this does not exclude some additional contribution from temperature effects. Indeed, some heating component is expected as the plasma is compressed.

Delannée & Aulanier (1999) conjectured that fast expansion of the magnetic field should compress the plasma at the boundaries between expanding stable flux domains, naturally leading to the enhanced emission. Chen et al. (2002, 2005) showed that stretching of the overlying magnetic field leads to compression of plasma in the legs of the CME, producing an intensity enhancement. Attrill et al. (2007a) suggested that magnetic reconnections between the expanding CME and favorably oriented surrounding quiet-Sun magnetic field drive weak flare-like brightenings making up the bright front. The simulation demonstrates that the plasma is indeed compressed as a result of the expansion of the CME (Figure 3) and that stretching of the overlying magnetic field and magnetic reconnection with surrounding field do occur (see Figures 7 and 8). Although we only display selected field lines from the simulation (thus probably missing some stretching and magnetic reconnection events), these mechanisms are still constrained to the footpoints of overlying magnetic field lines (see Chen et al. 2002), and locations for favorable reconnection. They are not responsible for the emission of the entire bright front, only to the higher concentrations of intensity within it (Figure 3).

In order to directly drive compression between the expanding CME and surrounding magnetic field to the spatial extent covered by the coronal wave, it is necessary that the CME really expands to a massive, global extent low down (<200 Mm) in the corona. Our simulation results confirm (Figure 6 and Section 4.4) that this is indeed the case.

Stationary brightenings have previously been reported at coronal hole boundaries by, e.g., Thompson et al. (1998), Veronig et al. (2006), and Attrill et al. (2007b), and at separatrices formed in the large-scale magnetic topology (e.g., Delannée & Aulanier 1999; Delannée et al. 2007). Brightening "A" in Figure 1 is likely due to compression between the expanding CME and "open" magnetic field of the coronal hole to the East of AR 1012, since this brightening is also seen in the simulation results (Figure 3), which show enhanced mass density. Brightenings "B" and "C" in Figure 1 are located at the same place as ongoing magnetic reconnections seen in the simulation (Figures 7 and 10). Attrill et al. (2007a) reported persistent brightenings similar to these at the outer edge of deep, core dimming regions for two events during solar minimum of cycle 23. They suggested that these brightenings may be due to ongoing reconnection between the expanding flux rope and surrounding, favorably orientated magnetic field. Our results for this event are consistent with such an interpretation.

Zoom In Zoom Out Reset image size

Behind the expanding bright front, we detect localized regions of secondary dimming (Figure 4). Secondary dimmings were originally reported by Thompson et al. (2000). Such dimmings may be understood in a wave context (e.g., as in Wu et al. 2001), since a rarefaction shock develops trailing a large-amplitude perturbation (Landau & Lifshitz 1987). However, such dimmings would be short-lived, with a duration on Alfvén timescales (∼ few minutes) contrary to observations (Cliver et al. 2005; Delannée et al. 2007). Although secondary dimmings have a much lower average intensity level (e.g., ∼50 counts pixel⁻¹) before the event, compared to the core dimming (∼ 100 counts pixel⁻¹), the relative magnitudes of both the core and secondary dimmings are substantial (e.g., ∼50% and ∼20%, respectively). Further, like the core dimmings, the secondary dimmings remain at a reduced intensity level for an extended period (> 1 hr).

The locations of these secondary dimmings also appear to be closely associated with the magnetic fields reconnected through CME expansion. For example, Figure 6 shows a secondary dimming to the north of the source region that corresponds to the secondary cavity in the simulation seen at 06:05 UT. This dimming extends the CME cavity northward (see COR1join1.mov). Further evidence of this can be found in Figure 11 (also see Mandrini et al. 2007). These results show that overlying and neighboring magnetic field is "opened" through magnetic reconnection, extending the CME footprint in the low corona. Therefore, we also interpret the secondary dimmings in this event as being due to density depletion, although spectral diagnostics have yet to confirm or refute this interpretation.

Zoom In Zoom Out Reset image size

Our results show that the bright front observed in base difference EUV data and the CME are strongly coupled (e.g., Figure 6). These higher-intensity brightenings are due to the CME compressing the plasma (against both surrounding and overlying magnetic field). The brightest concentrations in the data and simulations in Figure 3 show correspondence with the regions of reconnection in Figure 7, both red and yellow field lines. Figure 10 shows a direct comparison.

When the CME has expanded to its maximum lateral extent, the brightest parts of the coronal wave either disappear or become stationary before fading (Section 4.2.1). This is the result of multiple factors: the CME is no longer directly compressing plasma, the overlying field has already stretched, and magnetic reconnections with surrounding favorably orientated field have had time to occur.

What remains is a weaker, more uniform component that is consistent with an MHD wave interpretation. The dynamic expansion of the CME is a highly energetic, impulsive event; therefore wave(s) are expected to be generated. The simulation results show that this weaker component exists throughout the expansion of the CME. The later frames of the simulation show that it continues to expand even after the considerable CME lateral expansion has finished. In this later stage, the coronal wave is freely propagating (e.g., Veronig et al. 2008). In the running difference EUVI-A data (195a_rdiff.mov), which highlights the leading edge of the disturbance, the Western expansion can be followed considerably later than in the base difference images, until at least 06:55 UT (cf. 06:25 UT, the reader is encouraged to compare the running and base difference movies for EUVI-A: 195a_rdiff.mov and 195a_diff.mov). It is more likely that the weaker component can be detected in running difference images, which better show subtle changes.

With this analysis, we believe we are able to reconcile the different (wave and non-wave) interpretations of coronal waves. When EIT waves were first discovered, they were studied using running difference data. This method highlights the (often faint) leading edge of the disturbance, making it useful for identifying waves; this technique was probably perpetuated because researchers (e.g., Thompson et al. 1999) originally identified their observations as a strong candidate for the predicted coronal counterpart to the chromospheric Moreton wave (Moreton 1960; Uchida 1968).

In the late 1990s, Delannée et al. (and later Chen et al. and Attrill et al.) preferentially used base difference images because they show real brightenings and dimmings (e.g., Chertok & Grechnev 2005). The motivation for using base difference images is due to the focus of these authors on coronal dimmings, which are strongly connected with coronal waves and CME events. It is not possible to study coronal dimmings with running difference images. However, base difference images do not show faint features so well. We have shown that the base difference brightenings are closely linked to the CME and magnetic field evolution; hence, the development of non-wave models.

For some time, both of these methods have been applied, with different studies producing disparate conclusions. In most cases, however, researchers have attempted to find a single solution—either wave or non-wave—applicable to all aspects of diffuse coronal wave events. Over time, this has led to seemingly contradictory evidence, selectively supporting wave or non-wave models, depending of the focus of the study. Zhukov & Auchère (2004) first introduced the concept of a coupled coronal wave, consisting of an eruptive mode and a wave mode, based on comparative analysis of EIT running and base difference data. Our results are consistent with such a picture. The combined observational and simulation results presented here allow us to firmly establish and understand the contribution from each of the various mechanisms. In retrospect, it is not surprising that wave and non-wave interpretations have failed to be reconciled when the different data sets highlight different things.

In interplanetary space, field lines following the Parker spiral connect the western longitudes of the Sun to spacecraft at 1 AU. When an impulsive electron event occurs in the corona, energetic particles travel along these field lines to 1 AU. However, sometimes impulsive electron events are clearly related to flares that occur on the eastern half of the solar disk, up to ∼1 R_☉ from the Parker spiral footpoint. Krucker et al. (1999) suggested that EIT waves might explain how the flare site and Sun-spacecraft magnetic field lines are connected. They concluded that at the time of electron release the EIT wave had not expanded far enough to reach the footpoints of the Parker spiral. However, by considering the EIT wave as a fast-mode MHD wave (which moves faster at higher altitudes due to decreasing density), they showed that the calculated wave front at higher altitude (∼1.5 R_☉) is fast enough to connect the flare site with the Sun-spacecraft field line.

We would like to suggest an alternative possibility. Our simulation results (Figures 7 and 8) show that reconnection between the core magnetic flux rope (intimately connected with the flare region) and the overlying or surrounding magnetic field occurs at a similar height range. The reconnection(s) subsequently displace the flux rope connectivity out of the flare region to a distance of ∼1 R_☉, consistent with observations.