The Astrophysical Journal, 645:757–765, 2006 July 1 Copyright is not claimed for this article. Printed in U.S.A.
TRACKING LARGE-SCALE PROPAGATING CORONAL WAVE FRONTS (EIT WAVES) USING AUTOMATED METHODS M. J. Wills-Davey Department of Space Studies, Southwest Research Institute, Boulder, CO 80302;
[email protected] Received 2003 October 9; accepted 2006 March 12
ABSTRACT Recently developed mapping algorithms allow automated tracking of a propagating coronal wave, enabling the finding of reproducible fronts and propagation trajectories. Coronal observations taken by the Transition Region and Coronal Explorer (TRACE ) on 1998 June 13 show a large-scale bright wave front, comparable to ‘‘EIT waves’’ seen with the Extreme Ultraviolet Imaging Telescope aboard the Solar and Heliospheric Observatory ( SOHO EIT ). Cross sections measuring density perturbations show roughly Gaussian wave structure, suggesting a single propagating compression front. The wave fronts are also found to propagate nonuniformly, unlike the circular fronts often seen with SOHO EIT. Any perceived dissimilarity between EIT waves and the bright propagating fronts seen by TRACE, however, can be explained by differences in the typical observing sequences of the two instruments. Subject headingg s: methods: data analysis — Sun: activity — Sun: corona — waves
1. INTRODUCTION
early theories. Observed primarily by the Extreme Ultraviolet Imaging Telescope aboard the Solar and Heliospheric Observatory (SOHO EIT ), ‘‘EIT waves’’ appear as large, diffuse, often circular propagating fronts traveling away from some flaring regions. They move at a fraction the speed of Moreton waves (300 km s1) and are seen much more frequently (by more than an order of magnitude). They are strongly associated with coronal mass ejections (Biesecker et al. 2002), and the flares that produce them often exhibit ‘‘coronal dimming’’ (Harra & Sterling 2001). Like Moreton waves, EIT waves seem to coincide with type II radio bursts (Klassen et al. 2000). In fact, the most recent studies citing Moreton waves have all found that an EIT wave is instigated by the same event ( Thompson et al. 2000; Eto et al. 2002; Warmuth et al. 2001; Vrsˇnak et al. 2002). New theories have been put forth trying to relate the two types of fronts. Warmuth et al. (2001) postulates that EIT waves are the remnants of Moreton waves, expanded and decelerated over time. Chen et al. (2002) sees any EIT wave as a slow compressive ‘‘wake’’ following a much faster, piston-shock-driven Moreton wave. Unfortunately, the average lifetime of a Moreton wave (8 minutes) is much less than the typical SOHO EIT observation cadence of 15 minutes, so validation of theories is difficult using EIT as the sole source of coronal data. Since EIT wave events are notoriously dim and diffuse—with front widths of many Mm typically distinguishable from the background by only a few percent—there is an additional difficulty with identifying their locations at all. Bright wave fronts can be tens of Mm wide, and their edges are often ill-defined by the second SOHO EIT observation. Because analysis of these phenomena requires some identification of position and trajectory, researchers often opt for the most useful visual definition; depictions can be arrows showing the front’s position, or a line drawn in along the leading edge of the ‘‘bright front’’ as seen in differenced data. Because the fronts are inherently diffuse, it is important to treat such labels as mere suggestions of position, and not representations of exact wave structure. Work presented by Wills-Davey & Thompson (1999) used such visual identification in following the EIT wave considered here, but—as our conclusions show—the use of observer tracking led to inherent bias in the final results. This research can be seen as a follow-on to Wills-Davey & Thompson (1999), but using more accurate,
Propagations across the solar disk were both observed and theorized long before the advent of dynamic coronal imaging. The earliest studies (Richarson 1951; Becker 1958) examined sympathetic flaring, postulating unseen waves as a trigger mechanism between events. Moreton & Ramsey (1960) were the first to present direct observations of any propagating fronts. These ‘‘Moreton waves’’ were sharp wave fronts, instigated by flaring regions, that appeared as propagating depressions in chromospheric data. They traveled substantially faster than the local sound speed (O 10 km s1), typically moving at 1000 km s1. To account for the high velocity, theorists looked to the solar corona. Meyer (1968) and Uchida (1968) offered complementary theories to explain how a coronal magnetoacoustic wave would lead to a Moreton wave effect. Meyer (1968) reasoned that a stratified corona would act as a wave guide, trapping the wave front low down and causing it to ‘‘dip’’ into the chromosphere. Uchida (1968) assumed the same initial conditions, but instead required the propagating waves to be shock fronts. This ‘‘hydromagnetic disturbance’’ would ‘‘plow’’ into the chromosphere and might extend up to the highest reaches of the corona. By invoking shocks, Uchida (1968) created a model that could account for velocity differences between events, a variation not considered in the Meyer (1968) model. Subsequent study only seemed to confirm the relation between coronal propagations and Moreton waves. Concentrated field structures were found to cause deflection ( Uchida 1970; Uchida et al. 1973). Such an effect could account for the high directionality of Moreton waves seen in the data (Smith & Harvey 1971). The extension of shock fronts into the upper corona even offered a single source for Moreton waves and type II radio bursts ( Uchida 1974). However, when dynamic coronal observations finally became available—with the launch of the Yohkoh satellite (Ogawara et al. 1992) and its Soft X-Ray Telescope (SXT )—there was little evidence of the predicted hydromagnetic disturbances, although the few that were observed (Khan & Aurass 2002; Hudson et al. 2003) seemed to confirm the Uchida (1968) theory. There are frequent observations of large-scale coronal pulse propagations, but they are not the fast, highly directed waves envisioned in the 757
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Fig. 1.—The 1998 June 13 wave event as observed by SOHO EIT. The TRACE field of view is shown in all three frames. (a) Original SOHO EIT Fe xii observation. Here the front is sufficiently dim that it is unobservable in a still image, although it is visible in movies. (b) Event data with a pre-event image subtracted from it as seen by SOHO EIT. While the wave only appears dimly, the related dimming region can be clearly seen. For the effects of the wave to become visible in multiple frames, these running difference data must also be watched dynamically. This differs from the TRACE base difference data shown in Fig. 2, where the front is clearly visible in stills. (c) Mapping reproduced from Thompson & Myers (2006). This mapping shows the shape and position of the leading edge of the front over time. Thompson & Myers (2006) classify events on a scale from Q0 to Q5; this event was considered a Q4. The gray region is the active region from which the wave originated, while the lines map the edge of the observed front. Solid lines refer to clearly apparent front locations; where dashed lines are shown, the front was less well defined.
reproducible methods. These new methods also tell us a great deal more about the underlying physical attributes of the wave front. This work presents automated techniques for recording dynamic wave position. For accurate wave mapping to be possible, the complete structure of the front must be taken into account. Position must be definable, but it should relate to a physical property of the wave, not a convenient visual cue in the data. The large cross section of EIT waves is actually an asset; twodimensional measurements normal to the front are critical. Variations in the size and shape of the cross section, especially when comparing multiple points along the front, offer information on the nature of the propagation. The internal intensity structure can reveal a great deal about the wave itself and will give details about its interaction with the surrounding medium. When the cross-sectional variations are coupled with the front’s spatiotemporal position, a different type of diagnostic may even be possible. Variations in the wave front can be used to determine the nature of the local plasma—a sort of ‘‘quiet Sun’’ coronal seismology. Since the wave’s speed depends uniquely on the local temperature, density, and magnetic field, the front’s trajectory and the variability therein can be tied to local variations of these properties. For such a technique to be useful, however, wave observations must have a much higher cadence than is generally available, and all aspects of the wave itself must be measured with much greater precision. Some properties of the plasma itself and of the nature of the wave itself ( particularly any nonlinearities) must also be taken into account. While this is perhaps a goal to strive for rather than an application of our current understanding, its promise certainly cannot be ignored. Any of these applications call for detailed and in-depth analysis, which requires that research moves beyond visual tracking and instead takes advantage of automated techniques and machine vision. In this study, I offer the first results of a wave mapped under such conditions. The precision available through automation makes it possible to glean new information from the subtleties in the data. Using data from the TRACE telescope (presented in x 2), x 3 describes the techniques of analysis. Section 4 then shows how the results of these methods differ from those presented in other wave mapping studies. These differences are expanded on in x 5 with a discussion of the SOHO
EIT observation campaigns and the current understanding of EIT waves. 2. DATA The wave event recorded by the TRACE telescope on 1998 June 13 was also observed as an EIT wave by SOHO. The front is sufficiently dim that it is not visible in any individual images of the original Fe xii SOHO EIT data; rather, it is picked out visually when the data are shown as a movie. However, when pre-event data are subtracted (‘‘difference imaging’’), the wave appears clearly in a single still frame. This front had a short lifetime (20 minutes) for an EIT-observed event but is recorded as a reasonably well seen EIT wave transient ( Thompson & Myers 2006). Figure 1 shows three aspects of the 1998 June 13 EIT observation: panel a is the original SOHO EIT Fe xii image, panel b shows the EIT event data with the previous pre-event observation subtracted from it, and panel c is a mapping of the event taken from Thompson & Myers 2006. (As the subtracted images in Fig. 1b are chronologically consecutive, this particular frame can be described as either a ‘‘base difference’’ or a ‘‘running difference’’ image; both terms are described in detail in x 3.) In each frame, the TRACE field of view has been superimposed over the EIT image. Figure 1c shows the position of the wave’s leading front as a function of time as observed by SOHO EIT; the solid line refers to a clearly defined front, while the dashed lines are a less confident mapping. The TRACE observation of the wave extends over 15:25– 15:45 UT. At the end of this period, the front has left the field of view, and there is a 10 minute data dropout, limiting the possibility of observing any additional effects due to the front. Over the 20 minute window, the front is seen in two EUV wavelengths for a total of 28 observations. The coincidence between the TRACE observation and the well-defined section of the SOHO EIT data allows for detailed analysis of a known EIT wave using highresolution, high-cadence data. 3. AUTOMATED TRACKING OF THE 1998 JUNE 13 EVENT The event from 1998 June 13 can be seen in both Fe ix/x (1 MK ) and Fe xii (1.5 MK ) data. To utilize both wavelengths in a single tracking of the front, a narrowband filter ratio method
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(available as trace_teem.pro in the IDL SolarSoft software library; Freeland & Handy 1998) is used to combine the data and produce local temperatures and emission measures. Assuming a collisionally excited, optically thin medium, the intensity at any pixel in an image can be described as Z ð1Þ Itel (x) ¼ ds n2e Rtel (T ) integrated over the column depth, where Itel is observed intensity flux in units of DN s1, ne is the electron density, and Rtel (T ) is the temperature response kernel of the particular narrowband filter. Each passband has a unique Rtel , derived from the atomic physics. In the EUV passbands, different Rtel are defined through an overlapping range of T. Within a limited temperature range (usually 0.9–1.5 MK ), the ratio of two response kernels creates a monotonically increasing function. If a structure observed in two passbands is considered isothermal, it follows from equation (1) that the ratio of the intensity fluxes will equal the value of the response function ratios at the structure’s temperature. The emission measure Z ð2Þ EM(x) ¼ ds n2e is then solved for by dividing equation (1) by Rtel (T0 ), where T0 is the temperature found using the ratios. The filter-ratio method relies on isothermality over the entire column depth of a pixel. There is some doubt as to whether such calculations are accurate. Schmelz (2002) and Martens et al. (2002) argue that this technique may incorrectly determine that structures with spatial temperature variation are isothermal. They show that different filter ratios calculated for the same region produce inconsistent results. Despite the controversy over the use of narrowband filter ratios, this appears at present to be the most reasonable way to combine the two data sets. The dynamic variation of the front in the Fe xii data is substantially different than that shown in the Fe ix/x data. It would appear that the two data sets show different aspects of a single event. To choose to study one data set as opposed to the other may misrepresent the event; it would certainly be an arbitrary elimination of likely valuable information. Therefore, regardless of the potential temperature inaccuracies, a combination of the two data sets should still give the most complete dynamic picture. While values for emission measure are presented, the bulk of the analysis relies on largescale coronal dynamics. Future studies may show that the values given here are problematic, but properties such as the wave front trajectory, or the rate of intensity change within the wave’s cross section, should be relatively unaffected. Independent of the calculation method, any integrated emission measure still suffers from the potential column depth or lineof-sight problems caused by observing through optically thin media, as well as a two-dimensional/ three-dimensional ambiguity. Some of these issues can be isolated by using only difference images in the tracking. By subtracting an image taken at an earlier time, one reduces the data to the changes between the two images. These observations are in a sufficiently quiet region that the only dynamic events are related to the wave front. This makes it likely that the major changes in the field of view (and therefore the most prominent features in the difference images) relate to the wave. By confining this study to the changes only, it should be possible to limit measurements to the effects of the wave front, removing any potential problems from line-of-sight or column depth issues.
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Three types of difference images can be created, depending on the desired results. The difference images most often used are often called ‘‘running difference’’ images. These subtract the frame immediately previous, showing the changes that take place from image to image. The resulting data are the discrete time derivative of the solar emission. Running difference images are often used for determining the velocities of dim, coherent structures, such as coronal loop oscillations, and can show extremely subtle dynamics. While this technique is ideal for deriving and tracking movement, it is important to realize that such piecewise subtraction makes global structural comparisons impractical: it is possible to find the motion of a loop, but not its cross section. ‘‘Base difference ’’ images are produced by subtracting a single pre-event image from all subsequent data. With this method, it is possible to study the total integrated change within a region as a function of time; these data are normalized relative to the initial pre-event image and are comparable to each other. Base differencing is useful for determining intensity changes, such as ‘‘coronal dimming’’ associated with coronal mass ejections, or for determining absolute morphology differences relative to initial conditions. Examples of the use of base difference images can be seen in Howard & Harrison (2004) and others. In cases of extremely complex dynamics, however, or where the background itself changes (as with solar rotation over long periods of time), base difference images are prone to inaccuracy.1 The most reliable results require that areas unaffected by the dynamic event in question remain largely unchanged over the length of the data set. A variation on base difference images, ‘‘percentage difference’’ images, can be seen in Wills-Davey & Thompson (1999) and Warmuth et al. (2004b). In the case of percentage difference images, each base difference frame is then divided by the initial pre-event image. This produces difference images in which all values show positive or negative changes scaled relative to the initial image as a percentage (i.e., values of a bright wave at 0.3 would indicate a 30% increase above the background.) Since the goal is to map an intensity propagation over a number of time steps, the analysis of the 1998 June 13 wave event requires base difference images. Figure 2 shows sample stills of the combined 1998 June 13 emission measure data and the corresponding base difference images. After subtracting out the initial conditions, the remaining intensity increase can be interpreted as wholly due to the propagating event. The morphology of this intensity perturbation contains a great deal of physics and will become one of the prime information sources when the data are scrutinized and interpreted. 3.1. Necessity for Automation When viewed as a movie, the original 1998 June 13 TRACE observations are quite dramatic, with the wave’s propagation easily observable by the unaided eye. However, when images from this same event are viewed individually (as in Fig. 2, top row), the wave is virtually unobservable in the TRACE emission measure data; the base difference images (Fig. 2, bottom row ) are required to properly follow the front. Even in the difference image stills, the bright front eventually becomes difficult to define as a coherent structure; only dynamic imaging allows the viewer to coherently follow the wave in its entirety. These observational difficulties not only make apparent the extreme dimness and diffuseness of such a wave event, but they 1 In some cases, solar rotation effects can be compensated for by using image distortion, allowing for the study of longer time intervals. Such image manipulation methods are discussed in DeForest (2004).
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Fig. 2.—Sample emission measure data derived from the Fe ix/x and Fe xii TRACE observations from 15:25–15:45 UT, 1998 June 13. The times given are the averages of the times of the two different passband observations used to create each image. The top row is in units of derived emission measure, related in the color bar at the left. The bottom row shows the base difference images corresponding to the frames in the top row. The color gradation in the difference images has been enhanced to show morphology.
also speak to the prowess of the human eye in the detection of motion. Human observers are extremely adept at filtering through noise and will interpret the structural relationships of even dim, diffuse movement. Because it is so easy for observers to visually identify motion, most previous research done on EIT waves has relied on visual inspection (Thompson et al. 1998; Biesecker et al. 2002; Eto et al. 2002). When SOHO EIT data are used, this technique is not unreasonable. Fronts observed in the SOHO EIT data appear to experience considerable diffusion, perhaps as a result of the long duration (12–18 minutes) between exposures. While the waves themselves may be visible in movies, when tracking and identifying them in stills, the observer may be forced to derive a coherent front from an ill-defined collection of positive points in noisy difference images, where edge detection is at best difficult. Work by Ballai & Erde´lyi (2003) demonstrates the difficulty of using automated techniques to find fronts in SOHO EIT data. In those studies, attempts were made to find and map the cross sections of some of the Thompson & Myers (2006) EIT wave transients. In each case, wave fronts that could be observed visually by the researchers in movies could not be isolated using an automated process; the spatial position of the wave front was indistinguishable from noise, even when difference images were examined. In cases with especially dim wave fronts, observers may discount still images entirely, relying solely on the eye’s ability to detect motion. Often, the location of a front is drawn based purely on movie observations, with the viewer extrapolating back to an often indeterminate difference image. If such measurements are then displayed as a series of stills, the results can appear confusing and even arbitrary. The problem with relying on visual inspection to find and measure wave fronts is one of reproducibility. Because the data are typically dim or diffuse, the location of the front can be difficult to isolate, and different observers may produce different results. Figure 3 shows a single EIT wave event (from 1997 September 24) as examined by both Biesecker et al. (2002) and DeForest (2004). (Each difference image has undergone sepa-
rate scaling and enhancement to bring out features, but both show the same EIT data.) While both studies identify the same region as the western edge of the front, in Figure 3a Biesecker et al. (2002) points out the eastern wave front edge as being near the equator and very close to the limb. DeForest (2004), in Figure 3b, has drawn a circle to show the front in its entirety. Here the location of the eastern edge appears to be farther south and west than that described by Biesecker et al. 2002. While the differences in front position seem entirely reasonable considering the size and noisiness of the event, the separation is 20 . Some studies involving EIT waves (e.g., Shibata et al. 2002) require an uncertainty much smaller than this to sustain their arguments. If research concerning coronal propagations is to demand a reasonable level of accuracy, the front-mapping techniques must become reproducible. Since the human eye cannot be calibrated, this requires automation. 3.2. Determining Wave Fronts When the 1998 June 13 event is observed in base difference images, it appears primarily as a wide bright front. Visual inspection studies of EIT waves have generally followed the leading bright edge when determining properties such as wave position or velocity. However, when intensity variation over a cross section of the front is examined, it reveals a roughly Gaussian shape, with the peak change in intensity near the midline of the front. The varying intensity changes are likely due to local compression caused by the propagating MHD wave (Wills-Davey 2003). If the wave is considered to be a compressive front, then the best definition of its ‘‘location’’ is probably the centroid of the front, along the line of maximum compression. While the bright leading edge stands out visually in a two-dimensional image, it is really just the transition of the Gaussian from positive to zero and is not a physically meaningful region within the front. For the automated tracking methods discussed in this paper, the ‘‘front’’ is defined as the point along the wave of greatest compression and intensity—the maximum of the Gaussian. Because such a front will manifest itself as a positive intensity change, the data can
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Fig. 3.—Examples from two different series of running difference images of a wave event observed by SOHO EIT on 1997 September 24. (a) Analysis as presented by Biesecker et al. 2002; panel (b) is from DeForest 2004. A comparison of the figures reveals that the two studies place the eastern edge of the front in different places, separated by 20 . This variation is quite large, considering that the results of some ‘‘EIT wave’’ studies rely on much higher accuracy.
be even further constrained by only considering points of positive change. When the front in the 1998 June 13 data was analyzed in each difference image, 10 of the 13 frames displayed measurable fronts. ( For the first and the last two frames, too little of the bright front is in the field of view to fit a Gaussian to the profile.) For a given image, the data are divided into pixel-wide vertical bins, and local maxima are found along these bins. Since the front is not generally observable over the width of the entire field of view, the position of the front will be apparent in only a fraction of the vertical bins. (The front progresses into the east side of the image gradually and never extends west out of the field of view.) The front is easily defined by the clustering of local maxima points along a reasonable line; local maxima in bins to the east and west tend to scatter randomly. This random scatter allows the east-west boundary of the front to be determined, and the vertical bins outside this boundary are eliminated from consideration for the purposes of this image. In addition, any sources of noise in the bins that contain the front (for instance, bright points or ejecta) are reduced. In some cases, this noise reduction can be used to better define the front. After filtering, the points on the wave front are fit with a smoothed spline to remove additional scatter from the derived shape of the front. The result is a one-dimensional front that shows variation, but where the scatter of the Gaussian maxima has been suppressed. Such one-dimensionality is essential if one is to ultimately determine propagation trajectories. The final fronts are shown as the thick black lines in Figure 4. With this particular front-finding technique, two regions of the data proved problematic. The northeast corner suffers from noise limitations. By the time the front reaches this region, the amplitude of the wave has decreased to the point at which a Gaussian fit is difficult and the point of maximum compression is hard to find. In addition, the measurement of the last two fronts occurs with a significant portion of the wave outside of the field of view. While it appears that TRACE is still observing the maximum intensity, this may account for the apparent slowing at the front in the final measurement. The inherent dimness of the northwest corner also makes the data too noisy to locate a bright front in base difference images. Therefore, no wave is recorded in this section of the image
when the mapping algorithms are used. This does not mean the front does not pass through this region. In fact, Wills-Davey (2003) shows evidence (primarily in loop motions observed visually) that the wave does affect the northwest corner of the field of view; it is simply not measurable using the current techniques. If this region is to be analyzed, methods must be developed that track the progress of feature motion, and not just intensity. 3.3. Determining Trajectories Knowing the position of the front over time, it is possible to determine trajectories traveled by the impulse. The front shows so much variation as it propagates that radial trajectories are unrealistic. Even straight lines from front to front would appear jerky, and would not smoothly reproduce the curving required to turn the wave to the northeast. More meaningful paths can be determined by subjecting the measured wave fronts to a time gradient. With each front displayed at its known position in the field of view and assigned a constant value in units of seconds, the data are convolved with a smoothing kernel over each pixel until there are well-defined time gradients between the fronts. The gradients are then broken down into 10 s contours, shown in Figure 4 as the thin black lines. Although the new contours are still piece-wise measurements of the wave’s motion, they have the advantage of being both closer spatially and inherently smoother. Several options exist for determining the appropriate path traversed by a point on the initial wave front. A simple method assumes conservation of all points along the front, with paths equally spaced at each interval. While such measurements are straightforward, they rely on inherent accuracy in the measurement of the fronts, and are based on the observer’s results, rather than any physical premise. Alternatively, the Huygens Principle—in which a front expands unchanged until it is deformed in some way—could be applied. Trajectories would propagate away locally normal to the front, changing to the new local normal when they encountered the next front. This study uses a variation on the Huygens Principle. Assuming smooth fronts with no cusps, the Huygens Principle can be time-reversed, so that a point on one front advancing to the closest position on the next front must intersect an area normal to its trajectory.
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Fig. 4.—Automated mapping of the propagation front from the 1998 June 13 TRACE data. The thick black lines identify the position of each front, determined by finding the line of maximum intensity within the wave cross section. The first, fifth, and tenth fronts have been labeled with their corresponding times from Fig. 5: the first and tenth shown in black, and the fifth in white, for clarity. The thin black lines are ‘‘minifronts,’’ interpolated smoothly between the measured fronts at 10 s intervals. Despite some high-frequency spatial noise and artifacts, the basic areas of speeding up, slowing down, and turning are apparent. The white lines are one possible calculation of natural trajectories between the fronts. From right to left, the three thick white lines correspond to tracks 1, 2, and 3 in Fig. 5, where the cross sections of these trajectories are mapped out.
To determine the most ‘‘natural’’ trajectories, 40 equidistant points were chosen along the earliest 10 s contour. The points did not extend to the ends of the contour, so that edge effects would be minimized. A calculation was made from each point to determine the closest point on the next 10 s contour. This point on the next contour became the new initial condition, and the calculation was repeated. In this way, trajectories were found for all 40 initial conditions. The white lines in Figure 4 show trajectories found using this method. Time-reverse Huygens plotting works best when applied to smooth fronts with no cusps, on images of extremely high resolution. Because these data are only 512 ; 512 pixels, the lack of resolution leads to artificial trajectory ‘‘clumping.’’ When the size of a pixel starts to become a significant percentage of the spacing between trajectories, two paths may converge to the same position (pixel) in the ‘‘closest-point’’ calculation. Unfortunately, the nature of the time-reverse Huygens plotting constrains overlapped trajectories to essentially merge. As a result, there are many
fewer points along the last front than the first, and the process is not reversible. These data are strongly affected by this problem, with the 40 initial trajectories in Figure 4 ultimately consolidating down to just nine. Because of the clumping,’’ it is unlikely that the trajectories mapped here accurately represent the path of the front. However, the resulting mappings do generally follow the wave’s path, and to first order they can describe its motion. Plans for future mapping techniques call for incorporating some synthesis of forward and time-reverse Huygens plotting and finding a way to compensate for the pixelization. 4. PROPERTIES OF THE 1998 JUNE 13 EVENT Having determined both the position of the wave front as a function of time and possible trajectories followed by a point on the front, it is possible to draw basic morphological conclusions from the TRACE data that may not be apparent in the SOHO EIT observations.
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Fig. 5.—Three graphs plot density enhancements along the trajectories denoted by the thick white lines in Fig. 4. As explained in x 4.1, density reductions in the dimming regions have been omitted for visual clarity. Each plot is labeled with its corresponding time; time increases with higher plots. All density enhancements are determined with respect to the emission measure data from 15:26:49 UT, before the wave entered the TRACE field of view.
4.1. Front Cross Section The fronts shown in Figure 4 were calculated based on the point of maximum intensity in a vertical cross section. Therefore, an intensity measurement in each base difference image along any one of the trajectories should show some variation that can be identified as the wave front. Three of the trajectories have been chosen (shown as thick white lines in Fig. 4) to examine the intensity dynamics of the wave in space and time. The starting points of these paths are roughly evenly spaced along the first measured wave front, and they each travel through distinct regions. Note that the tracks (and the fronts) are noticeably different from those produced by Wills-Davey & Thompson (1999). This is primarily a consequence of the automated measurement techniques. As the human eye cannot be calibrated, the fronts measured by Wills-Davey & Thompson (1999) are not reproducible and are prone to human error. The data presented here are both reproducible and quantifiable, making them much more applicable to scientific research. For a given observation, each path is divided into 100 equally spaced points. Since the data are inherently noisy, each path is treated as a band, and the value at any single point is determined
by averaging it with several pixels on either side. With an average calculated for each point, the result is a one-dimensional wave profile that is essentially a ‘‘slice’’ through the image. Equation (2) can be applied discretely to the TRACE emission measure data to determine local density enhancement, such that rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EM(x) ¼ ne ; h
ð3Þ
where EM are positive changes in the base difference images and h 100 Mm. ( The value we use for h corresponds roughly with the width of the wave observed here. It was also observed by Warmuth et al. [2004a] to correspond to the height of EIT waves observed on the limb.) Figure 5 shows density enhancement profiles along the three chosen trajectories over 12 time steps. For visual clarity, only regions of increased density (i.e., a compression wave) are shown. While Figure 2 does show evidence of considerable dimming behind the wave — dimming that in and of itself has been shown to have scientific significance (Howard & Harrison 2004; Harrison et al. 2003 and others) — the amount of dimming is so great that
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including it here would detract from the comparatively dim enhancements being tracked by the algorithm. In Figure 5, the wave front is clearly visible as a single pulse over a number of frames. All three trajectories show it moving at roughly constant speed. Along tracks 1 and 2, the wave appears to suddenly come into existence at 15:29:42 UT. This can be explained one of three ways: (1) the front started out traveling much faster and moved into the field of view after 15:28:19 UT, (2) it was originally a substantially different temperature and heated (or cooled ) into the observed TRACE filter passband, or (3) the front somehow consolidated in place in that same time interval. Interestingly, the first and second tracks also show that the height and width of the density enhancement actually increases for the first few frames. Track 3 shows this behavior later, in the 15:31:04–15:35:39 UT time interval. Since an unaffected wave would show a persistent drop-off in pulse amplitude, this suggests that there may be some extended external influence acting on the wave front. Eventually, the pulse either leaves the field of view or fades to serial brightenings of individual structures. Along track 1, for instance, there are coronal features at 140 and 200 Mm, and from 15:37:20 UT on, the density enhancement decays in the first structure and then reemerges in the second. Both the second and third tracks show nearly identical sets of four spikes just past their midpoints. While not visible as a coherent coronal structure in Figure 2, it may be the same set of loops lying perpendicular to both paths (which are traveling roughly parallel past their midpoints in Fig. 4). A strong, persistent enhancement spike appears at 15:31:04 UT about 100 Mm along the second trajectory. This spike corresponds to bright ejecta that occur contemporaneously with the wave. Harra & Sterling (2003) examined these ejecta using SOHO CDS data and showed that the ejecta behave independently of the front. The spike in track 2 persists through the entire wave observation, and convolves with the front from 15:31:04 through 15:34:19 UT, resulting in an overestimate of the effect of the wave. Figure 5 shows that, along a given trajectory, a wave front appears to maintain (or regain) coherence. This occurs even when the wave passes across multiple loop structures: several peaks will form, and often the wave will reemerge as a single front. The EIT wave would seem to be a single coherent structure; this contradicts some of the postulations put forth by Harra & Sterling (2003). In their examination of difference images from the 1998 June 13 event, they conclude that the leading edge of the bright front (called the ‘‘weak wave’’) and the trailing edge of the bright front (called the ‘‘bright wave’’)2 are in fact two different, dissociated wave fronts. The widening of the pulse in the first few time steps (actually associated with an increasing density enhancement) is then interpreted as the ‘‘weak wave’’ traveling at a faster velocity than the ‘‘bright wave.’’ Such an analysis in inconsistent with the data shown in Figure 5. While the mapped wave fronts presented in Figure 4 correlate with the local maxima of the pulses, the Harra & Sterling (2003) ‘‘waves’’ correspond to the zero crossings on either side of the intensity enhancement. The two-wave interpretation may be the artifact of a predominantly visual analysis; it is possible to 2
Based on their data, they may alternatively be arguing that the leading edge of the dimming region is a wave. Eventually, the edge of the dimming region (associated with the related coronal mass ejection) becomes static, while the trailing edge continues to propagate away with the pulse. Their data only show fronts through 15:36:01 UT, during which time the dimming region is still forming and before the two dissociate.
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distinguish two ‘‘waves’’ in base difference images because it is easier for the eye to identify a change between positive and negative than intensity enhancement gradations. 4.2. Propagation Dynamics To understand the way the front propagates in space, I examined trajectories determined using the time-reverse Huygens plotting. Automated results show that the front originates outside of the field of view on the southern edge (at the site of a flare observed by SOHO EIT ) and propagates north and northeast. However, after a few time steps, the motion is no longer radial. The eastern edge of front moves relatively uniformly toward the northeast, while the western edge starts by propagating northward and then turns toward the northeast. The mean propagation velocity is 300 km s1, although the velocities vary between 100 and 600 km s1 at different points in space and time. The velocity variations are due primarily to the turn. Looking at Figure 4, the region in which the front appears to turn (the center of the field of view) is noticeably dimmer than other areas through which the front passes. This dim area may correspond to a region of lower density, presenting two possible explanations for the observed turn. If the front is a magnetoacoustic wave, it could be a genuine refraction. Uchida et al. (1973) show that fast magnetoacoustic waves will refract away from regions of lower density. However, in a region that is so dim, it can be difficult to find and map a propagating intensity increase. It is possible that the front continues to move into the northwest region and is simply not observable. Regardless of the direction of the wave’s ultimate propagation, fronts in Figure 4 do indicate that it speeds up as it passes through the central, dimmer region. If the wave is Alfve´n-dominated, it will speed up in less dense areas. The variations in the speed and direction of this particular wave front make it reasonably definable as a fast hydromagnetic disturbance, as postulated by Uchida (1968, 1970) and Uchida et al. (1973). The wave is coherent, yet appears to be buffeted and change with respect to local density and magnetic field. While this event is not associated with a Moreton wave (Wills-Davey & Thompson 1999), it is consistent with the physics first put forth about coronal propagations. 5. CONSTRAINTS OF SOHO EIT OBSERVATIONS Other wave fronts so often seen by SOHO EIT are less easily identified as Uchida (1968) ‘‘hydromagnetic disturbances.’’ A typical EIT wave observation consists of a bright, simple wave front, propagating globally and largely uniformly through regions of low activity at velocities of 25–450 km s1. The TRACE observation discussed here does not fit the definition of a typical EIT wave. In studies to date, EIT waves show remarkable consistency in size, shape, and velocity. There are two possible reasons for this — either the physics of the corona constrains EIT wave events to be similar, or SOHO EIT preferentially observes events of a particular size and shape. While not discounting the first possibility, the second is worth examining. In order to meaningfully analyze a dynamic event, an instrument must acquire three images of the event in progress; to observe an event using difference images, four images are required. Most EIT wave data are obtained during the SOHO EIT CME Watch, a program that has the advantage of full-disk observations but uses a much slower cadence than typical TRACE observing runs. For something to be seen over four exposures during a CME Watch, it must have a lifetime of >45 minutes. This constrains SOHO EIT to preferentially observe long-duration wave events.
No. 1, 2006
TRACKING LARGE-SCALE PROPAGATING WAVE FRONTS
In addition, there is a maximum speed at which a front can travel and remain observable on the solar disk for 45 minutes. Assuming maximum possible travel distance, a wave front moving at constant velocity can travel no faster than 480 km s1. Events instigated closer to disk center are even more velocityconstrained. This may explain why no particularly fast waves have been observed by SOHO EIT, as well as why there has been so much difficulty correlating Moreton waves (which generally travel >600 km s1) and EIT wave observations. The observable velocity range for SOHO EIT is at the low end of possible coronal fast-mode speeds, and EIT waves are typically seen to propagate at 25–450 km s1. At such speeds, many events must travel a significant distance to achieve a lifetime observable by the SOHO EIT CME Watch. It also must remain sufficiently coherent to still be identifiable in the final frame. For a front to remain coherent over a great distance relative to its wavelength (or here, the width of the pulse), it must initiate as an uncomplicated structure (for instance, circular) and experience little interference. It would appear that the observational conditions constrain SOHO EIT to record a limited range of events: wave fronts with simple structures and long lifetimes, that ultimately extend over a large percentage of the solar disk. Even if myriad EIT wave shapes and lifetimes were possible, SOHO EIT would still only observe the large, simple wave fronts considered typical EIT waves.
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observations. Already, the subtle dynamics of some wave events (e.g., reflection off of an active region to produce a secondary front) have been revealed by TRACE’s high temporal resolution. Because of the variety of waves seen by TRACE, significantly more detailed measurement techniques are required. Most bright fronts are not as well-defined as that of 1998 June 13. Many events show no bright front at all, and are instead manifested as a propagating effect on surrounding loop structures. Such fronts are easily identified visually; the difficulty is in the automation. Comparison between the available TRACE and SOHO EIT data sets suggests that the large, global waves that constitute the bulk of the existing research may be a subset of a much larger category of coronal propagations. Current instruments are inadequate for general observation of such wave events—TRACE is limited spatially and SOHO EIT is limited temporally. Complete observation and understanding of coronal wave fronts requires a full-disk EUV imager with a continuous subminute cadence, and (ideally) high dynamic range, so that even the dimmest events can be studied. Until new instruments and data become available, wave studies with current instruments are vital, both to enhance our understanding of coronal dynamics and to develop useful automated observing methods for the immense amount of data that can be expected in the future, from programs such as Solar-B ( Davis 2000) and the Solar Dynamics Observatory (SDO; Schwer et al. 2002).
6. DISCUSSION At present, the 1998 June 13 event is the most promising observation provided by TRACE of a large-scale coronal propagation. While other wave fronts have also been studied (i.e., Wills-Davey 2003), these data benefit from long exposures, the lack of a direct flare observation, and the fact that the front passes across the entire field of view. Preliminary examination of the TRACE data shows a whole range of events, from subfields of larger, EIT-observed waves to small events with lifetimes
