(1)A STUDY OF THE KINEMATIC EVOLUTION OF CORONAL MASS EJECTIONS J

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A STUDY OF THE KINEMATIC EVOLUTION OF CORONAL MASS EJECTIONS J. Zhang,¹K. P. Dere,²R. A. Howard,²and A. Vourlidas²

Received 2003 August 30; accepted 2003 December 1

ABSTRACT

We report the kinematic properties of a set of three coronal mass ejections (CMEs) observed with the LASCO (Large Angle and Spectrometric Coronagraph) on the Solar and Heliospheric Observatory (SOHO) spacecraft, which showed characteristics of impulsive, intermediate, and gradual acceleration, respectively. The first CME had a 30 minute long fast acceleration phase during which the average acceleration was about 308 m s²; this acceleration took place over a distance of about 3.3 R(from 1.3 to 4.6 R, height measured from disk center).

The CME characterized by intermediate acceleration had a long acceleration phase of about 160 minutes during which the average acceleration was about 131 m s²; the CME traveled a distance of at least 4.3 R, reaching a height of 7.0 Rat the end of the acceleration phase. The CME characterized by gradual acceleration had no fast acceleration phase. Instead, it displayed a persistent weak acceleration lasting more than 24 hr with an average acceleration of only 4.0 m s²throughout the LASCO field of view (from 1.1 to 30 R). This study demonstrates that the final velocity of a CME is determined by a combination of acceleration magnitude and acceleration duration, both of which can vary significantly from event to event. The first two CME events were associated with soft X-ray flares. We found that in the acceleration phase there was close temporal correlation both between the CME velocity and the soft X-ray flux of the flare and between the CME acceleration and derivative of the X-ray flux. These correlations indicate that the CME large-scale acceleration and the flare particle acceleration are strongly coupled physical phenomena occurring in the corona.

Subject headings: Sun: corona — Sun: coronal mass ejections (CMEs) — Sun: flares — Sun: X-rays, gamma rays

1. INTRODUCTION

In this paper, we investigate the kinematic evolution of coronal mass ejections (CMEs). CMEs are initiated and accelerated in the Sun’s corona and subsequently propagate into the heliosphere, causing interplanetary disturbances and geo- magnetic storms. CMEs are best observed by coronagraphs that use an occulter to block the solar disk’s dominant emission, thus allowing the detection of the faint light scattered by electrons in the corona. Most studies on CMEs are based on observations above a certain coronal height limited by the occulter used (e.g., >2.0 R). It has often been found that a CME has acquired its maximum speed and developed into a large-scale structure before it has emerged above the occulter.

In other words, the initiation and the early acceleration of CMEs are largely not observed, which sets a major limitation on the understanding of the origin of CMEs and also leads to confusion on the relationship between CMEs and surface phenomena such as flares and filament eruptions. In this paper, we present the detailed kinematics, including the height, velocity, and acceleration profiles, of a set of well-observed CME events from the Large Angle and Spectrometric Coro- nagraph (LASCO) instrument (ranging continuously from 1.1 to 30 R with three overlapping coronagraphs; Brueckner et al. 1995) on the Solar and Heliospheric Observatory (SOHO) spacecraft.

In the outer corona (e.g., >2.0 R), CMEs largely show constant speed or insignificant acceleration/deceleration.

Statistical studies on thousands of CMEs have found that the apparent speed (projected onto the plane of the sky, found by linear fitting to the height-time relation) ranges continuously from about 50 to 2500 km s¹with an average of 420–470 km s¹ based on several space-based coronagraphs including Solwind (Howard et al. 1985), the Solar Maximum Mission (SMM ) (Hundhausen, Burkepile, & St. Cyr 1994), and LASCO (St. Cyr et al. 2000; Moon et al. 2002;

Yashiro et al. 2003); the median speed in the distribution is about 50 km s¹ smaller than the average speed.

The measurement of CME acceleration is more difficult and highly depends on the effective field of view of observations, especially the availability of observations in the inner corona where major acceleration takes place. Based on a combination of ground-based Mauna Loa Solar Obser- vatory K-coronameter (1.2–2.4 R) and SMM (1.6–6.0 R) observations, St. Cyr et al. (1999) reported that the acceleration of 46 CME features (using a second-order polynomial fitting, or deriving a constant acceleration) ranged from218 to 3270 m s²with an average (median) value of 264 m s²(44 m s²).

Based on the velocity profiles of CMEs continuously tracked from the solar surface to 30 R, Zhang et al. (2001, hereafter Paper I) described the kinematic evolution of impulsive CMEs in a three-phase scenario: initiation, acceleration, and propagation. The initiation phase or slow-ascending phase can last tens of minutes before any significant acceleration takes place. The following acceleration phase lasts from a few minutes to an hour, with acceleration magnitude varying from 200 m s²to 7300 m s²for the four events they studied;

the distance CMEs travel in the acceleration phase also varies from less than one solar radius to several solar radii. This scenario of slow-ascending then fast-accelerating evolution

1Center for Earth Observing and Space Research, George Mason University, Fairfax, VA 22030.

2E. O. Hulburt Center for Space Research, Naval Research Laboratory, 4555 Overlook Drive SW, Washington, DC 20375.

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has also been found for other solar eruptive features, including EUV loop ejecta (Neupert et al. 2001), X-ray plasma ejection (Ohyama & Shibata 1997), and erupting filaments (Kahler et al.

1988; Plunkett et al. 2000; Wang et al. 2003). Following the acceleration phase, the propagation phase is simply a

‘‘developed’’ CME moving through the heliosphere with minor changes in speed and angular size.

The CME acceleration profile (derivative of the velocity profile), which is key to understanding CME kinematic processes, is not well known. Wood et al. (1999) showed acceleration profiles of two CMEs, but the limited cadence of coronagraph observations often does not allow one to derive the pattern of the acceleration. Nevertheless, high-cadence observations of solar eruptive features associated with CMEs indicate that acceleration in the early phase may be exponential, at least for certain fast events. By tracing a CME-associated erupting EUV feature observed by the Transition Region and Coronal Explorer (TRACE, 20 s cadence; Handy et al. 1999), Gallagher, Lawrence, & Dennis (2003) found that the acceleration can be best fit by an exponential rise followed by an exponential decay, with the peak acceleration at 1500 m s². Alexander, Metcalf, & Nitta (2002) also found an exponential form in the early acceleration of a CME-associated X-ray ejection observed by SXT (Soft X-Ray Telescope, 20 s cadence; Tsuneta et al. 1991) on the Yohkoh satellite, with the peak acceleration at 4800 m s². By studying a number of flare sprays and eruptive prominences, Vrsˇnak (2001) found that the majority of events showed a phase of exponential-like growth of the velocity. Similar results have been recently reported by Shanmugaraju et al. (2003).

It has been suggested that CMEs be simply grouped into two classes based on their kinematic behavior, namely, impulsive CMEs and gradual CMEs (Sheeley et al. 1999; see also Andrews & Howard 2000; Moon et al. 2002; Zhang et al.

2002). Gradual CMEs are found to have a very weak (<20 m s²) but persistent (lasting tens of hours) positive acceleration and low velocity (<400 km s¹) throughout the LASCO field of view (Sheeley 1999; Sheeley et al. 1999; Srivastava et al.

1999, 2000). On the other hand, impulsive CMEs are regarded as having short but strong acceleration in the low corona and constant speed above certain coronal heights. Nevertheless,

‘‘impulsiveness’’ is not well quantified with respect to key parameters such as acceleration duration or acceleration magnitude. The so-called impulsive CMEs in a simple two-class system may include CMEs with broad kinematic properties.

Some of these CMEs can be extremely impulsive, e.g., with acceleration at several thousand m s², as mentioned above.

Using the Mauna Loa K-coronameter only, MacQueen &

Fisher (1983) reported that a set of fast CMEs were accelerated within only 0.2 R above the limb, indicating that these fast CMEs were accelerated within a very short coronal distance.

Typical impulsive CMEs have been reported to have an acceleration of about a few hundred m s² (Wood et al. 1999;

Zhang et al. 2001). On the other hand, a fast CME can result from less impulsive acceleration (e.g., 100 m s²) but prolonged acceleration duration (a few hours) and prolonged acceleration distance (several solar radii) (Plunkett et al. 2000;

Vurchyshyn 2002).

In this paper, we present the full kinematic evolution of three CME events based on LASCO C1/C2/C3 observations. They were selected not only because they have well-observed velocity and acceleration profiles, but also to demonstrate the diversity of CME kinematic properties: one a typical impulsive CME, another a typical gradual CME, and another a CME with

intermediate properties. In complement to Paper I, in which CME velocity profiles are compared with flare soft X-ray flux profiles, in this paper we further compare the CMEs’ acceleration profiles with the derivative of the flares’ soft X-ray flux profiles. The correlation study between CMEs and flares may shed light on their physical relationship. We also measure the CMEs’ mass in order to calculate the mechanical forces needed for their acceleration. Many quantitative parameters of CME kinematics presented in this paper may provide constraints on theoretical models. Inx 2, we present the observations and data analysis. Inx 3, we present the results. Discussions are presented inx 4. Conclusions are given in x 5.

2. OBSERVATIONS AND DATA ANALYSIS The effectiveness of observing CME kinematics depends on the field of view and sensitivity of coronagraphs and the cadence of observations. The LASCO C1, C2, and C3 coronagraphs have a field of view of 1.1–3.0, 2.2–6.0, and 4.0–

30.0 R, respectively. The combined field of view of LASCO enables the investigation of the full kinematics of CMEs, including initiation, acceleration, and subsequent propagation processes. C2 and C3 are typical white-light coronagraphs that observe Thomson-scattered photospheric light from free electrons in the corona. C1, on the other hand, observes the emission of visible spectral forbidden lines from highly ionized elements in the corona. The main C1 lines are the green line of Fe xiv at 5302 A˚ (peak ionization temperature at 2.0 MK) and the red line of Fe x at 6376 A˚ (peak ionization temperature at 1.0 MK). The spectroscopic imaging capability of C1 is achieved by using a Fabry-Pe´rot interferometer. Before the SOHO interruption in 1998 June, the cadences of C2 and C3 were about 30 and 60 minutes (or 48 and 24 images per day), respectively; the cadences are about 20 and 30 minutes (or 72 and 48 images per day) since the interruption. For a CME of modest speed (e.g., 600 km s¹), C2/C3 (before 1998 June) were able to observe about 13 images of that CME. The slower the CME, the more CME images the observations can provide.

Therefore, the C2/C3 cadences are sufficient to study CME kinematics in their field of view.

The C1 observations usually took more images than C2 and C3; the average cadence combining all wavelengths was 10 minutes, or about 120 images per day. However, the detection of CMEs by C1 is more difficult than with C2 and C3.

The stray light level is very high in the C1 field of view because of its closeness to the bright disk. C1 was able to detect only large-density changes or changes in the temperature ranges to which C1 was sensitive in the inner corona. For the same reason, C1 was only sensitive to events originating very close to the limb; an event close to disk center would have already reached a high corona and become diluted when its flank reached the solar limb. C1 also had a highly irregular cadence because of its alternating observation modes in different spectral lines, with each spectral line taking alternate images in wavelengths at line center and off the line. The off- line images serve as background images to remove stray light from the on-line images in order to produce true coronal emission images. The effective cadence of C1 for a single spectral line was low, e.g., varying from 20 to 60 minutes, which is not sufficient to study the kinematics of CMEs, because CMEs have faster velocity changes in the inner corona than in the outer corona. We suggest that at least five CME images are needed in the C1 in order to make an effective study of CME kinematics in the low corona. This requirement

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does not appear to occur often, and, as a consequence, the C1 observations cannot routinely provide the same level of kinematic information of CMEs as the C2 and C3 do. Neverthe- less, because of the highly irregular cadence of C1, we are able to obtain good observations for a subset of CMEs which happen to occur both close to the limb and during the right C1 observation modes (e.g., events in Paper I and in this paper).

Note that C1 has not been functioning since the SOHO interruption in 1998 June. Therefore, any study using C1 observations must be before that date.

The knowledge of CME kinematics is based on the measurements of CME height versus time (H-T measurement), visually tracking certain CME features through a series of coronagraph images. When multiple coronagraphs are in- volved, it is important to make sure that the same CME feature is tracked. C1 images, which are emission-line images and sensitive to coronal temperature as well as density, are different from C2/C3 white-light images, which are sensitive to only density and not temperature. The internal structure of C1 CMEs does not seem to resemble that of the C2/C3 CMEs.

For instance, the helical structure of CMEs (Dere et al. 1999) often seen in C2/C3 images are generally not seen in C1 images. Nevertheless, it seems that the leading edge of CMEs is consistently seen in C1 and C2/C3 images. We believe that by tracking the leading edge only, we are measuring the same CME feature. As in many other studies, running difference images, which remove background and slowly evolving features and bring out transient changes such as expanding leading edges, are used in the measurement. Once a common feature is identified, the measurement itself is straightforward.

The uncertainty of height measurement is mainly attributed to selecting certain pixels along a radial path crossing the CME leading edge by visual inspection. It is subject to the sharpness of the CME leading edge. In our study, we put the uncertainty at 8 pixels in each image; this is about 0.05, 0.10, and 0.47 R

for C1, C2, and C3, respectively. We have asked several in- dividuals to make independent measurements and found the results to be consistent within the uncertainty we have stated.

Based on the H-T measurements, we use numerical derivative methods to derive CME velocity profiles as well as CME acceleration profiles. The numerical methods in this paper use Lagrangian interpolation of three neighboring points to obtain the derivative and the uncertainty at any given data point. Nu- merical derivative methods are not biased toward any form of kinematic evolution compared with prescribed-formula fitting methods. Simple-formula fitting methods are useful in obtain- ing basic CME parameters, e.g., average velocity and average acceleration. However, any simple formula may not be sufficient to describe the full kinematic evolution of CMEs because the functional form may change significantly with time and height (Zhang et al. 2001). The often-used first-order polynomial fitting method, which assumes constant CME speed (sufficient for CME propagation phase in the outer corona), is apparently not applicable in describing the CME’s early acceleration phase. The second-order polynomial fitting method, which assumes constant CME acceleration (applicable for a given period of the evolution), is not applicable for the entire range because the CME acceleration may change significantly from the inner corona to the outer corona. The exponential fitting method, which assumes an exponential increase with time of CME height, velocity, and acceleration, is apparently not applicable when the CME reaches certain coronal heights.

Therefore, numerical derivative methods are necessary for illustrating the complexity of CME kinematic evolution.

In this paper, we also measure CME masses in order to calculate the net mechanical force required for accelerating CMEs (this obvious task has not been done in Paper I). In the measurement, it is assumed that all scattered light comes from electrons in the plane of the sky. Since scattering efficiency monotonically decreases with increasing angle of the scattered electrons off the plane of the sky, the calculated mass tends to underestimate the actual mass. This underestimation effect should be minimal (less than a factor of 2) for the events studied in this paper, because they originate close to the limb.

For a detailed description of measuring CME masses using LASCO C2/C3 observations, refer to Vourlidas et al. (2000).

For each event, we obtain a single mass by averaging the masses measured in multiple C2/C3 images. We do not try to measure CME masses in C1 because of the difficulty in in- ferring column density from emission-line images without knowledge of the actual CME temperature.

Similar to Paper I, we use the GOES X-ray 1–8 A˚ full-disk flux as flare input to compare temporal relationships between CMEs and flares. Coronal disk observations, including EIT and SXT, are used for identifying source regions and coronal responses of CMEs; we do not present them in this paper because they are not essential for demonstrating CME kinematics.

3. RESULTS

3.1. CME 1: Impulsive Acceleration

We use a CME event that occurred on 1998 June 11 (Fig. 1) to illustrate the characteristics of CMEs that show impulsive acceleration. This event has been presented in Paper I. It is worth reexploring because the available observations of this event allow us to obtain a reasonably good acceleration profile in addition to the velocity profile presented in Paper I. This event has also been studied elsewhere for other purposes (Vourlidas et al. 2000; Raymond et al. 2000).

The observations of this CME are illustrated by nine selected EIT and LASCO C1, C2, and C3 images in Figures 1a–

1i. This CME can be clearly tracked from the solar surface to 20 Rduring the 4 hr it was in the LASCO field of view. Each image shown is a difference image in order to better show the CME leading edge; the times of the image and the subtraction image are given at the top of each panel. The bottom panel of the figure shows the GOES soft X-ray flux profile. The times of the nine CME images are indicated in this plot by arrows.

Apparently, the CME is closely associated with a GOES M1.4 class flare. We illustrate the detailed CME kinematics in Figure 2: the CME height-time (H-T ) plot, velocity-time (V-T ) plot, and acceleration-time (A-T ) plot are shown as discrete plus signs in Figures 2a, 2b, and 2c, respectively. The solid curves in Figures 2b and 2c are the GOES X-ray flux profile and derivative of the flux profile, respectively.

The H-T plot in Figure 2a shows that the slope of points does change with time as does the velocity. The H-T measurement is the base for all subsequent kinematic analysis.

Applying first-order polynomial fitting to the H-T points gives an average speed of 782 km s¹ for this CME; the second- order polynomial fitting gives an average acceleration of 21 m s². These numbers are indicated in the top left corner in the plot. These parameters are helpful in giving an overall quan- tification of the CME but are not useful in revealing the pattern of the CME’s kinematic evolution. The CME kinematics is better seen in its V-T plot (Fig. 2b). The velocity, which is derived by numerically differentiating the discrete height-time measurement, is also in the form of a discrete distribution. The

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uncertainty of the velocity (vertical error bar), which depends on the height uncertainty and the time interval between ad- jacent points, is apparently smaller than the characteristic scale of the velocity of this event. Note that the first velocity point at 09:01 UT is missing, because it has a negative value and thus is out of the plotting range due to incomplete interpolation in dealing with boundary points in numerical methods.

Based on the velocity profile (Fig. 2b), the kinematic evolution of this CME, as pointed out in Paper I, can be best described in a three-phase scenario: initiation phase, impulsive acceleration phase, and propagation phase. The initiation phase, characterized by a slow rise of some coronal structure,

lasted for about 1 hr (from 09:01 UT to 09:57 UT) with a speed less than 100 km s¹. The initiation structure seemed to be the coronal envelope of the associated active region, seen as a semicircular loop in Figures 1a and 1b. The existence of the initiation structure indicates changes of density and /or temperature surrounding the active region before the CME occurred. In this phase, the GOES soft X-ray also showed a slow and gradual increase, indicating that slow heating was occurring. However, this initiation phase occurred before the nomi- nal onset time of the associated flare (which was at 09:57 UT according to an NOAA report) and also before the onset of fast acceleration of the CME. The second phase, characterized

Fig.1.—CME/flare event on 1998 June 11. The difference images show the CME in time sequence for (a) EIT, (b–e) C1, ( f ) C2, and ( g–i) C3. The times of images and corresponding subtraction images are labeled at the top of each panel. The white circle indicates the solar limb. The GOES soft X-ray profile (solid line) is shown in the bottom panel. The times of CME images are indicated in the bottom panel by arrows along the profile.

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by a fast increase of velocity in the radial direction and a fast expansion of size in the lateral direction, lasted for about 30–50 minutes with a dramatic velocity increase of about 800 km s¹: from 304 km s¹at 09:56 UT to a peak velocity of 1104 km s¹ at 10:40 UT. The average acceleration in this phase was 308 m s², about 14 times higher than that averaged over the inner and outer corona. In the acceleration phase, the CME traveled a distance of about 3.3 R, from 1.3 to 4.6 R. Apparently, the soft X-ray flux increased rapidly along with the increase of the CME velocity (Fig. 2b). Following the fast acceleration, the third phase is simply a passive propagation phase without significant acceleration. For this event, it showed some deceleration. At 12:44 UT, when the CME front

reached a height of 13.5 R, the speed decreased to 767 km s¹ from its peak velocity of 1104 km s¹at 10:40 UT. The average deceleration in this period was about 45 m s².

We derived the acceleration profile of the CME (Fig. 2c) by numerically differentiating the calculated velocity, which was equivalent to second-order differentiation of the measured heights. Although the error bars in the acceleration are significantly larger than those in the velocity and height, the acceleration clearly showed a systematic change. Ignoring the first boundary point (at 09:01 UT), we found that the acceleration profile had a single peak at about 10:10 UT with a value of 402 m s². It had a fast rise phase (from about 09:40 UT to 10:10 UT) and then a fast decaying phase (from 10:10 UT to 10:40 UT). The cadence was not sufficient for us to determine the exact mathematical pattern of the profile. However, it is very interesting to note that there is a very good correlation between the CME acceleration profile and the soft X-ray derivative: they have a common rise phase, a common peak time, and a common decay phase. Combined with the fact that the CME velocity increase coincides with the soft X-ray flare’s flux rise (Paper I), the correlation shown here further strengthens the view that CMEs and flares are physically coupled phenomena.

It is also interesting to note that the CME was super- expanding along its lateral direction during the acceleration phase. It is well known that angular sizes of CMEs generally do not change with time in the outer corona; as the CME rises along the radial direction, it expands proportionally along the lateral direction. However, this kind of self-similar expansion pattern does not apply in the lower corona. At 09:41 UT (Fig. 1b), the CME-related structure had an initial lateral angular size of only 20, with the northern leg at position angle 66 and the southern leg at position angle 86. Note that the position angle is measured against the disk center and starts from the northern pole counterclockwise. At 10:07 UT and 10:11 UT (Figs. 1c and 1d ), the lateral angular size had increased to 50 and 70, respectively. We also found that the lateral expansion was not symmetric. By 10:11 UT, the southern leg expanded significantly by 40 farther south, while the northern leg expanded farther north by only 10. As a result, the CME appeared large and symmetric around the equator in the C2 and C3 fields of view although it was initiated in a relatively small coronal region in the middle latitude of the northern hemisphere.

3.2. CME 2: Intermediate Acceleration

The CME on 2000 October 25 is a good example of an intermediate CME, which are characterized by moderate and long acceleration. Events with similar kinematic characteristics have been reported elsewhere (Plunkett et al. 2000;

Vurchyshyn 2002). The morphological evolution of this CME is shown in Figures 3a–3i. The times of the images are indicated along with the X-ray profile in the bottom panel of Figure 3. Clearly, this CME is related to a C4.0 soft X-ray flare. Note that there is no C1 observation available for this event. A very faint brightness enhancement appeared above the C2 occulting disk at 08:50 UT (Fig. 3b); this time was close to that of the flare onset. The CME was clearly seen in the subsequent C2/C3 images. We cannot know whether there existed a distinct initiation phase before the onset of this flare because of a lack of C1 observations. As the flare flux rose, the CME rose and grew in angular size. Eventually, it became a halo CME with a visible brightening front surrounding the occulter. EIT observations showed a long-lasting large-scale

Fig.2.—Kinematic plots for 1998 June 11 CME: (a) height-time, (b) velocity-time, and (c) acceleration-time. The CME parameters are indicated by plus signs with error bars. The solid curves in (b) and (c) are the GOES X-ray profile and the derivative of the X-ray profile, respectively.

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loop arcade located at around N10 W66following the CME eruption. The soft X-ray images from SXT showed a similar loop arcade at the same location which appeared earlier than the EIT arcade. The surface region associated with the loop arcade seemed to be a decaying active region. There was no apparent filament or filament eruption associated with this event. The associated flare was an unusually long-rise, long-fall event; the flare started at 08:45 UT and peaked at 11:25 UT with a long rise phase of 160 minutes. It was this unusual aspect of this event that attracted our attention. We have wondered whether there existed a prolonged acceleration

phase for the associated CME. It can be seen that the CME- flare temporal correlation also holds for this long-duration event.

The kinematic plots of the CME H-T, V-T, and A-T are shown in Figures 4a, 4b, and 4c, respectively. The first- and second-order polynomial fitting to the H-T plot gives rise to the average velocity and average acceleration of this CME, which are 636 km s¹and 26 m s², respectively. Apparently, in general terms, this CME had a velocity and acceleration similar to those of the CME described in x 3.1 (CME 1).

However, detailed analysis revealed significant differences

Fig.3.—CME/flare event on 2000 October 25. The difference images show the CME in time sequence for (a–f ) C2 and ( g–i) C3. The times of images and corresponding subtraction images are labeled at the top of each panel. The white circle indicates the solar limb. The GOES X-ray profile (solid line) is shown in the bottom panel. The times of CME images are indicated in the bottom panel by arrows along the profile.

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between the two events. Based on the V-T profile (Fig. 4b), we found that the CME kept accelerating for a period of about 2 hr (from 08:50 UT to 10:42 UT), comparable to the flare rise time. The duration of its acceleration was about 2–3 times longer than that of CME 1. During the acceleration phase, the average acceleration was 131 m s², which was about 2.4 times smaller than that of CME 1. CME 2 had a peak speed of 954 km s¹, comparable to that of CME 1. The comparison here demonstrates that the velocity of a ‘‘developed’’ CME in the outer corona is determined by two factors: the magnitude and the duration of the acceleration.

Although the associated flare had a very long rise phase, the CME velocity evolution seemed to correlate with it (Fig. 4b).

The CME velocity monotonically increased along with the

rise of the flare flux. The acceleration ceased after the peak time of the flare. During the acceleration phase, the CME traveled a distance at least 4.3 R, from 2.7 to 7.0 R. The fact that the acceleration continued up to a height of 7 R seems inconsistent with the characteristics of a typical impulsive CME, which is commonly thought to have a constant speed at that height. The four events we studied in Paper I, which had a flare rise time ranging from a few minutes to 72 minutes and an acceleration distance ranging from a fraction of a solar radius to a few solar radii, had all shown good temporal correlation between the CME velocity and the flare flux. The event studied here, which had a much longer flare rise time and a much larger acceleration distance, also showed the same correlation. The CME acceleration–flare rise relation seems to be valid for all CME/flare events, no matter the magnitude and duration of the flare.

The acceleration profile for CME 2 (Fig. 4c) showed a single peak at about 10:26 UT; the peak acceleration was 192 m s². The acceleration profile was similar to the soft X-ray derivative profile; both had a common rise phase and a common decaying phase. Nevertheless, we noticed that the peak of the CME acceleration seemed to lag behind the peak of the soft X-ray derivative by about 30 minutes. This delay may not be significant since the cadence of CME observation was about 20 minutes. The delay may also be caused by the breakdown of the Neupert effect for long-duration events (Li, Emslie, &

Mariska 1993).

3.3. CME 3: Gradual Acceleration

In this section, we present an example of gradual CMEs, which are characterized by very weak but persistent acceleration and slow velocity throughout the LASCO field of view (Sheeley 1999; Sheeley et al. 1999; Srivastava et al. 1999, 2000). The event occurred on 1997 October 19; it has been studied before for other purposes (Dere et al. 1999; Srivastava et al. 1999). The morphological evolution of this CME is shown in Figures 5a–5i. There was no apparent GOES flare related with this CME (Fig. 5, bottom). The soft X-ray emission had been at a very low background level throughout the CME event; many small spikes superposed on the background may have been due to microflares randomly occurring across the disk. The CME was initiated above the east limb at latitude N14; there was no active region at this latitude and nearby longitudes. In the C1 field of view, the rising CME did not display a bright leading edge. Instead, the front appeared as a dark rim and the whole CME appeared as a dark bubble rising and expanding. The dark front of this CME in the inner corona was in contrast to the bright front often seen in impulsive and fast CMEs (Paper I). It seemed that the CME started from a small coronal feature best described as a cavity whose linear size was no larger than 0.2 R on the plane of sky (see Fig. 5a). The nonradial motion of the cavity was obvious. It started from the northern hemisphere at a latitude of 14 and tilted toward the equator as it rose. It appeared symmetric with respect to the equator when it moved into the C2/C3 field of view.

The detailed kinematic evolution of this CME is shown in Figure 6. Note that the time range for the plots is 32 hr, much longer than those of the previous two events. Also note that there is no GOES X-ray profile shown in the plots. The average velocity and average acceleration of the CME are 147 km s¹ and 4.3 m s², respectively. Apparently, there was no impulsive or fast acceleration phase during the evolution of this

Fig.4.—Kinematic plots for 2000 October 25 CME: (a) height-time, (b) velocity-time, and (c) acceleration-time. The CME parameters are indicated by plus signs with error bars. The solid curves in (b) and (c) are the GOES X-ray profile and the derivative of the X-ray profile, respectively.

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event. Based on the V-T plot (Fig. 6b), the CME reached a peak speed of 347 km s¹at 01:36 UT, 1997 October 20 when the CME was at a height of 19 R; this occurred after a 24 hr long gradual acceleration that started at 01:55 UT, 1997 October 19 from a height of 1.28 R. During this period, the average acceleration was only 4.0 m s², which was about 77 times smaller than that in the acceleration phase of CME 1 (308 m s²) and about 33 times smaller than that of CME 2 (131 m s²).

It is interesting to note that there existed a velocity plateau in the velocity profile (Fig. 6b). For a period of about 5 hr from 06 to 11 UT, which corresponded to the CME height

changing from about 2.0 to 3.4 R, the velocity of the CME did not seem to increase; instead, the velocity remained constant or decreased slightly. Note that there was a measurement gap between 05 and 08 UT during which the weak CME leading edge was hard to track, when it was close to both the outer edge of the C1 field of view and the inner edge of the C2 field of view. We put the plateau starting time at about 6 UT by simply extrapolating the velocity trend from before and after the gap. Before the plateau, the CME velocity continuously increased from about 10 to 80 km s¹for a period of about 4 hr; the respective height range was from 1.3 to 2.0 R. After the plateau, the CME velocity increased from 50 km s¹

Fig.5.—Gradual CME event on 1997 October 19. The difference images show the CME in time sequence for (a) EIT, (b–e) C1, ( f ) C2, and (g– i) C3. The times of images and corresponding subtraction images are labeled at the top of each panel. The white circle indicates the solar limb. The GOES X-ray profile (solid line) is shown in the bottom panel. The times of CME images are indicated in the bottom panel by arrows along the profile. Note that there is no flare associated with this CME.

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to about 350 km s¹over a period of 15 hr, corresponding to a height range from 3.4 to 19 R. The existence of a velocity plateau had been noticed before for this event (Dere et al.

1999; Srivastava et al. 1999). Dere et al. (1999) suggested that it might correspond to the period when the CME was opening the helmet streamer field lines.

The acceleration profile of this CME (Fig. 6c) showed an interesting quasi-sinusoidal variation with time. The acceleration decreased from an initial value of 7 to2 m s²from 2 UT (the earliest starting time of the CME) to 11UT, corresponding to a height range from 1.3 to 3.4 R. Later, the acceleration increased from2 to 12 m s²from 11 to 16 UT, corresponding to a height range from 3.4 to 5.5 R. Then the acceleration seemed to decrease again. It decreased from 12 to about5 m s²for a period of 11 hr from 16 to 03 UT (the next day),

corresponding to a height range of 5.5 to 22 R. During the whole process, the acceleration remained at a low level; the peak acceleration was only 12.1 m s², and the peak deceleration was about 5 m s². The velocity plateau mentioned above was found to occur during a CME evolution phase during which the acceleration decreased from positive to negative.

3.4. Summary of Results

To better illustrate the variation of CME kinematics for the three events presented above, we make composite kinematic plots in Figure 7 that show the CME height, velocity, and acceleration against time (left column), and the CME time, velocity, and acceleration against height (right column). In the time plots, the times of CMEs along the X-axis (in units of minutes) are relative to the flare onset time for the two CMEs associated with flares and are relative to the first CME measurement time for the gradual CME.

The kinematic differences between the three CMEs are obvious. In the H-T/T-H plots (Fig. 7, top panels), the different slopes of the curves indicate a high velocity for CME 1 and CME 2 but a very slow velocity for CME 3. Over the same period of 400 minutes, CME 1 and CME 2 have reached a height >20 R, while CME 3 only ascends to a height close to 3 R. The velocity plots (Fig. 7, middle panels), which show when and where CMEs gain their velocity, are more revealing than the height plots. While the height curves of CME 1 and CME 2 appear similar, their velocity curves show apparent differences. CME 1 gains its peak speed in a relatively short period (40 minutes) and short distance (3 R). On the other hand, CME 2 gains a similar peak speed over a longer period (2 hrs) and longer distance (6 R). CME 3, apparently a gradual CME, shows much slower speed gain over time and distance.

The acceleration plots (Fig. 7, bottom panels), reveal when and where the CMEs’ acceleration takes place. Clearly, there is a fast acceleration phase for CME 1 and CME 2. The CME 1 acceleration peaks at a low corona height (2 Rfrom disk center) and at a time less than 20 minutes after the flare onset.

The facts of the shortness (in both time and space) and high magnitude (400 m s² at the peak) of the acceleration qualify well CME 1 as an impulsive CME. CME 3 keeps a low acceleration (<12 m s²) from the surface to the outer corona and therefore is well qualified as a gradual event.

Compared with the impulsive event and the gradual event, CME 2 shows characteristics in between: its acceleration peaks in the high corona (5 R) after a long duration (more than 2 hr) of moderate acceleration.

We summarize a variety of measured parameters for the three CMEs in Table 1, including average velocity and average acceleration for the entire height range, acceleration duration in the acceleration phase, average acceleration within the acceleration phase, peak velocity, CME height at the peak velocity, CME traveling distance in the acceleration phase, peak acceleration in the acceleration phase, CME height at the peak acceleration, mass of the CMEs, net mechanical force required to accelerate the CMEs, and, finally, kinematic energy of the CMEs. The measured masses for CMEs 1, 2, and 3 are 5:0 10¹⁵, 1:7 10¹⁶, and 2:0 10¹⁵g, respectively. The net mechanical force is calculated simply by multiplying the average acceleration in the acceleration phase and the measured average mass; it is 1:5 10²⁰, 2:2 10²⁰, and 8:9 10¹⁷dyn, respectively. Apparently, the mechanical acceleration force required to accelerate the gradual CME is more than 2 orders of magnitude smaller than for the other two CMEs. The

Fig.6.—Kinematic plots for 1997 October 19 CME: (a) height-time, (b) velocity-time, and (c) acceleration-time. The CME parameters are indicated by plus signs with error bars. No X-ray profile is shown.

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Fig.7.—Composite kinematic plots for the three CMEs: impulsive (solid line), intermediate (dashed line), and gradual (dotted line). The left three panels show kinematic evolution versus time: height-time (top), velocity-time (middle), and acceleration-time (bottom). The right three panels show kinematic evolution versus height: time-height (top), velocity-height (middle), and acceleration-height (bottom).

TABLE 1

Properties of the Three CMEs

Parameter 1998 Jun 11 2000 Oct 25 1997 Oct 19

Characteristic... Impulsive Intermediate Gradual GOES flare ... M1.4 C4.0 No Average velocity (km s¹)... 782 636 147 Average acceleration (m s²) ... 21 26 4.3

Acceleration duration in acceleration phase (minutes) .... 30 160 1440

Average acceleration in acceleration phase (m s²) ... 308 131 4.0 Peak velocity (km s¹) ... 1104 954 347 Peak velocity height (R) ... 4.6 7.0 19 Acceleration distance in acceleration phase (R) ... 3.3 4.3 18 Peak acceleration in acceleration phase (m s²)... 402 192 12 Peak acceleration height (R)... 2.2 5.5 5.6 Mass (g) ... 5.0 10¹⁵ 1.7 10¹⁶ 2.0 10¹⁵ Net mechanical force (dyn) ... 1.5 10²⁰ 2.2 10²⁰ 8.0 10¹⁷ Kinematic energy (ergs s¹) ... 3.0 10³¹ 7.7 10³¹ 1.2 10³⁰

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kinematic energy, which is calculated based on measured CME mass and peak velocity, is 3:0 10³¹, 7:7 10³¹, and 1:2 10³⁰ergs for CMEs 1, 2 and 3, respectively.

4. DISCUSSIONS 4.1. CME Kinematics

For the three events studied in this paper, we have quanti- tatively obtained their acceleration properties, in addition to the commonly used velocity properties. There are three parameters used to characterize a CME’s acceleration: the duration of the acceleration, the magnitude of the acceleration, and the distance of the acceleration. The velocity of a CME, which is best measured in the outer corona, is simply the result of a combination of acceleration duration and acceleration magnitude, which have to be measured in the lower corona.

CME acceleration can vary significantly from event to event.

The acceleration of the three CMEs in this paper is 308, 131, and 4 m s² over periods of 30, 160, and 1440 minutes for CMEs 1, 2, and 3, respectively. Some CMEs can be extremely impulsive. In Paper I, Zhang et al. (2001) reported a CME event (1997 November 6) with an acceleration of 7300 m s²; the CME reached a speed of about 2100 km s¹in less than about 6 minutes. St. Cyr et al. (1999) reported the largest acceleration of 3270 m s²(CME on 1998 October 13) among 46 events with combined MK3 and SMM observations. Ex- tremely strong acceleration (e.g., >1000 m s²) of eruptive coronal features such as X-ray ejecta (Alexander et al. 2002) and EUV ejecta (Gallagher et al. 2003) have also been reported. These extremely impulsive eruptive events are associated with X-class flares. MacQueen & Fisher (1983) found that a class of events show fast but constant speed below a projected height of 0.2 Rabove the limb; these events must also be very impulsive because the acceleration takes place within a very short distance. On the other hand, there are CMEs characterized by very weak and long-duration acceleration, or so-called gradual CMEs (Sheeley 1999; Sheeley et al.

1999; Srivastava et al. 1999, 2000). Most CME events may reside in between the extremely impulsive ones and the gradual ones. The statistical study by St. Cyr et al. (1999) showed that CME acceleration was between218 and 3270 m s²with an average value of 264 m s² and a median value of 44 m s². The appearance of negative numbers is due to their use of second-order polynomial fitting to obtain the average acceleration over the entire measurable height range.

In other words, they did not distinguish the true acceleration phase from the following propagation phase. We summarize that true CME acceleration in the acceleration phase can vary by 3 orders of magnitude from several m s² to several thousand m s², while the acceleration duration can also vary by the same magnitude: from a few minutes to more than one thousand minutes.

It has been speculated that CMEs may have two distinct classes, impulsive CMEs and gradual CMEs, based on selected sets of events (Sheeley et al. 1999; Andrews & Howard 2000; Moon et al. 2002). However, we caution here that there is no compelling statistical evidence to support this classification. The statistical distribution of CME velocity always shows a continuous Gaussian distribution and shows no sign of a bimodal pattern (Howard et al. 1985; Hundhausen et al.

1994; St. Cyr et al. 2000; Moon et al. 2002; Yashiro et al.

2003). Statistics on the acceleration (including magnitude, duration, and distance) may set up a better observational test on this issue. The statistics on CME acceleration by St. Cyr

et al. (1999) did not show a bimodal distribution. Studies on thousands of LASCO C2/C3 CMEs showed that the average acceleration in the outer corona has Gaussian-like distribution for both fast and slow CMEs (Moon et al. 2002; Yashiro et al.

2003). A full assessment of true CME acceleration (during acceleration phase only, without contamination by averaging with the propagation phase) requires a large number of events of observation quality similar to or better than the events studied in this paper. Furthermore, the event on 2000 October 25 showed an intermediate acceleration with an acceleration duration of about 160 minutes and average magnitude of about 131 m s²; the acceleration continued until the CME reached a height of about 7.0 R. This event does not seem to fit well into either class, neither a commonly perceived impulsive one nor a gradual one. Events with similar kinematic characteristics have been reported (Plunkett et al. 2000; Vurchyshyn 2002). We argue that the two-class CME classification is oversimplified. We also do not intend to group CMEs into three classes. Whether the impulsiveness of a CME can decrease continuously, changing it to a gradual one, is still an open question.

4.2. Relationship between CMEs and Flares

We have suggested in Paper I that, for flare-associated CMEs, the two phenomena are strongly coupled, based on the correlation between CME velocity profiles and soft X-ray flare flux profiles. The observations presented in this paper further strengthen this view: in addition to the velocity coincidence, there is also a good correlation between CME acceleration profiles and soft X-ray derivative profiles. The peak of the CME acceleration matches the peak of the X-ray derivative very well for CME 1. For CME 2, although the acceleration peak was delayed by about 30 minutes with respect to the X-ray derivative peak, the delay was relatively small compared with the duration of the CME acceleration and the rise time of the flare (160 minutes). CME 3, which was not associated with any flare and displayed no fast acceleration, indicates that a CME can be initiated without a flare; on the other hand, it also indicates that the presence of a flare may be a signature of fast acceleration of a CME. Good correlation between CME kinematics and flare flux evolution has also been recently reported by Gallagher et al. (2003) and Wang et al. (2003).

There is also a possible good correlation between CME speed and X-ray flare peak flux (Moon et al. 2003). Therefore, we believe that CMEs and flares are physically integrated phenomena. There have been controversial arguments about the possible causal relationship between CMEs and flares and about which of these plays a dominant role in solar-terrestrial events (e.g., Kahler 1992, Gosling 1993, Dryer 1996). Our view regarding the relationship is that flares do not cause CMEs and vice versa; instead, they both are the results of more fundamental processes. This view is similar to what Harrison (1995) suggested: the flare and CME are signatures of the same magnetic ‘‘disease,’’ that is, they represent the responses in different parts of the magnetic structure to a particular activity; they do not drive one another but are closely related.

The suggested physical linkage between CMEs and flares is based on their temporal relationship. This linkage is not inconsistent with their spatial relationship. Some early inves- tigations noted the apparent spatial disparity between CMEs and flares: the flare regions are much smaller and commonly lie to one side of the CME span (Kahler et al. 1988; Harrison et al. 1990). We attribute the disparity in size to the

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superexpansion of CME structure in the lower corona during the acceleration phase. Our observations showed that CMEs were indeed initiated in the flare regions, and the initial CME sizes in both lateral and radial direction were much smaller than what was later observed in the outer corona (Fig. 1).

That the flare regions do not lie under the center of the CME span is attributed to the nonradial motion of CMEs in the lower corona. All three events in this paper showed that, whether the source regions were in the northern or southern hemisphere, the CMEs eventually appeared symmetric with respect to the equator.

To relate a CME with a flare is an issue relating particle acceleration on the small scale and bulk mass acceleration on the large scale. Flares are largely believed to be caused by nonthermal energetic particles produced in the corona. When these energetic particles precipitate from the corona into the chromosphere along magnetic field lines, they spontaneously produce hard X-ray emission through the Bremsstrahlung mechanism (Brown 1971). They also produce soft X-ray emission through evaporating chromospheric material into the corona (e.g., Li et al. 1993). There is a well-known Neupert effect, which states that the derivative of soft X-ray profiles resemble the corresponding hard X-ray profiles, especially during the soft X-ray flares’ rise phase (Neupert 1968; Dennis &

Zarro 1993). Therefore, the close temporal correlation between CME acceleration and the flare soft X-ray flux derivative indicates that the particle acceleration and large-scale CME acceleration are physically related. They are driven by the same physical process or by multiple processes that are physically coupled in the corona. Many workers studying flares have attributed the acceleration of energetic particles to the mechanism of magnetic reconnection. If this is true, magnetic reconnection may also play an important role in accelerating CMEs. We will discuss theoretical implications of this observation (including implications for several competing theoretical CME models) in a separate paper, in which a more robust study on CME kinematics and flare evolution will be carried out based on a larger set of well-observed CME/flare events (a survey of LASCO C1 CMEs).

5. CONCLUSIONS

In this paper, we have displayed the quantitative kinematic properties of three CMEs that showed characteristics of impulsive, intermediate, and gradual acceleration, respectively.

CME 1, which was associated with an M1.4 GOES soft X-ray flare, was found to have a distinct impulsive acceleration phase lasting about 30 minutes with an average acceleration of 308 m s². In the acceleration phase, it traveled a distance of about 3.3 R. CME 2 showed an intermediate acceleration

lasting about 160 minutes with an average acceleration of 131 m s²; it traveled a distance at least 4.3 R from about 2.7 to 7.0 R before reaching its peak velocity. This CME was associated with a C4.0 X-ray flare. For the two flare-associated CMEs, we have found that, in the CMEs’ acceleration phases, not only do their velocity profiles correlate with the flares’ flux profiles, but their acceleration profiles also correlate with the derivative of the flares’ flux profiles. CME 3, which had no fast acceleration phase and was not associated with any flare, had a persistent weak acceleration throughout the LASCO C1/C2/C3 field of view: it lasted about 24 hr with an average acceleration of only 4.0 m s², about 77 and 33 times smaller than those of CME 1 and CME 2, respectively.

Combined with other studies on well-observed solar eruptive events (St. Cyr et al. 1999; Sheeley 1999; Srivastava et al.

2000; Zhang et al. 2001; Alexander et al. 2002; Gallagher et al. 2003), we conclude that CME acceleration can vary by 3 orders of magnitude from several m s²to several thousand m s², while the acceleration duration can also vary by the same magnitude from a few minutes to more than one thousand minutes. The final CME velocity is a combined effect of the acceleration duration and the acceleration magnitude. A fast CME, which is often perceived to be accelerated impulsively, can however be accelerated over a significant duration and a significant coronal distance, e.g., CME 2. Whether there are two distinct classes of CMEs is still an open question. We do not intend to classify CMEs into three classes. It is worth investigating whether the impulsiveness of CMEs can decrease continuously and eventually lead to gradual CMEs.

In addition to the early findings about temporal correlation between CME velocity and flare soft X-ray flux (Zhang et al.

2001), we also find in this paper a good temporal correlation between CME acceleration and the derivative of flare soft X-ray flux. These correlations suggest that CME large-scale acceleration and flare particle acceleration are driven by the same physical process or by multiple processes that are physically coupled in the corona. It is possible that magnetic reconnection plays an important role in both CMEs and flares.

J. Zhang is supported by NASA grants NAG5-27027 and NSF SHINE grant ATM-0203226. J. Zhang thanks A.

Poland for proofreading. SOHO is a project of international cooperation between ESA and NASA. The LASCO instrument was constructed by a consortium of the Naval Research Laboratory, the University of Birmingham (England), the Max-Planck-Institut fu¨r Aeronomie (Germany), and the Laboratoire d’Astronomie Spatiale (France).

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