Halley

ICARUS 95, 73--85 (1992)

CN Jet Velocity in Comet P/Halley JAMES JAY KLAVETTER AND MICHAEL F . A ' H E A R N

Astronomy Department, University of Maryland, College Park, Maryland 20742 Received July 30, 1991; revised November 4, 1991

velocity. Section II describes the image processing techniques used to enhance jets. In addition to the methods in c o m m o n usage, shift differencing and renormalization, we demonstrate a technique of radial profile subtraction that has advantages o v e r the other methods. We also detail the method used to find the precise position of the jets. Section III details the p r o c e d u r e used to calculate the velocity, once the jets had been identified and measured. Section IV contains a discussion of the results and a comparison with other determinations o f the c o m a expansion velocity described in the literature. Unlike these earlier studies, the method described in this paper yields a direct determination of the projected velocity.

CN jet images provide a direct means of measuring the projected expansion velocity in the coma of Comet P/Halley. After processing of the CN images with a radial profile subtraction technique, we precisely determined the positions of the jets by Gaussian fitting in r- 0 space. All jets exhibited a linear portion in r - 0 space. By linear fitting to this portion, the distance from t h e n u c l e u s w a s m e a s u r e d for all jets that overlapped in azimuth in a time series, both within a night and from night to night. Since the time of the observation is known precisely, the projected velocity on the sky plane is simply v = A r / A t . Following specific features demonstrated the flow was approximately radial. We also found the velocity by measuring specific radial features in jets. The velocity found by both methods was consistent, although the latter had larger uncertainties and was used only as a confirmation of the validity of the former method. Due to projection effects, only a lower limit to the projected velocity could be found. From this large dataset (34 time s e r i e s of jets), we have measured a wide range of projected velocities, with the largest being v = 1.7 -+ 0.3 km sec -t at 50,000 km from the nucleus, the largest expansion velocity found for this region of the coma of Comet P/Halley. We find weak evidence of an acceleration in the region of the coma ranging from r = 20,000 to 80,000 km. Our findings are compared with other observations and theoretical m o d e l s . © 1992 AcademicPress, Inc.

II. IMAGE PROCESSING The basic dataset used in this investigation is the collection of images obtained at Perth Observatory with use of the standard International Halley Watch C N filter and described in A ' H e a r n e t al. (1986a) and H o b a n e t al. (1988). Details of the observing conditions can be found in H o b a n e t al. (1988) and its references. The images are at a scale of 1.8 arcsec per pixel. All images will be available on I H W CD-ROMs and through the Planetary Data System, Small Bodies N o d e (PDS-SBN). Table I lists the images used in this study; additional images were investigated but had to be rejected because of stellar contamination, poor seeing, or poor guiding. Images taken through the CN filter were chosen for this study because they have little contamination from the continuum ( A ' H e a r n e t al. 1986b) and because we have a high sampling rate for CN, both within a night (intranight) and on consecutive nights (internight). All images were first median filtered with a 3 x 3 pixel box to reduce spurious signals from cosmic rays and chip defects. These defects could otherwise affect the radial enhancement algorithms. As a check, the procedures described below were also applied to the original images. The same results were obtained, although occasionally with a larger uncertainty. Consequently, we are confident that median filtering in no way affects the results of the jet velocity.

I. INTRODUCTION The velocity of species in the cometary coma is a fundamental parameter used in many models of the coma and is essential for determination of molecular abundance. This paper will focus on measurements of the CN velocity in the coma o f Comet P/Halley as determined from the observed jets. Specifically, we have measured the velocity of the jets, not o f the ambient CN gas. CN data were used for convenience, but the velocity will be approximately the same for other molecules for at least most o f the coma investigated (see Combi 1989). The velocity of the jets on the sky plane was found by measuring the motion o f jets from images of Halley taken through the CN filter. The technique used is conceptually simple: identify a j e t ' s position, note how much it moves, and divide by the time interval to calculate the projected 73

0019-1035/92 $3.00 Copyright © 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.

74

KLAVETTER AND A'HEARN TABLE I Observations Date 1986

Start time (UT)

Exposure time (sec)

Heliocentric distance (AU)

Mar 11

20:20:32 20:13:27 17:59:13 21:01:46 16:55:17 19:08:09 18:23:38 19:03:28 21:20:01 15:18:17 20:04:15 19:56:04 17:29:44 18:32:38 19:33:50 21:02:17 14:05:46 16:01:04 18:29:20 12:39:05 17:16:39 13:23:51 14:53:00 18:27:24 11:20:50 I 1:36:32 15:08:45 12:15:19 15:25:37 17:46:04 10:04:54 13:45:19 11:42:12 17:36:11 11:28:47 14:38:39 11:38:21 14:46:12 16:03:18

300 300 300 600 300 600 600 300 300 300 600 600 600 600 600 600 600 900 900 900 900 900 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1800 1200 1800 1800 1800 1800 1800

0.87

Apr 04 Apr 06 Apr 07 Apr 09 Apr 14 Apr 15 Apt 16

Apt 17

Apr 23 Apr 24

Apr 25 Apr 26 Apt 27

Apr 28 May 01 May 02 May 09

1.24 1.27 1.28 1.3 I 1.39 1.41 1.42

1.43

1.52 1.54

1.56 1.57 1.58

1.60 1.64 1.65 1.76

Below, the image processing has been divided into three independent parts: (a) radial feature enhancement, (b) azimuthal jet fitting, and (c) radial cross correlation.

(a) Radial Feature Enhancement Although jets are not strictly radial features, processing in the radial direction affords the greatest enhancement of any simple technique. We discuss four methods of radial image enhancement. Rotational shift differencing has been described by Larson and Sekanina (1984). Azimuthal renormalization was used by Hoban et al. (1988) and Klinglesmith (1987). We emphasize the technique of profile subtraction, the method used for the figures in this

paper. Finally, we discuss some limited studies of model subtraction and future work that can be done with this method. Shift differencing. Shift differencing was the first published radial enhancement algorithm used to detect jets in Comet Halley unambiguously (Larson and Sekanina 1984). This method is based on a linear intensity derivative calculated by shifting the original image in the azimuthal direction, a rotation, and then subtracting. If this procedure is done with both positive and negative shifts and the results are then added, edges and other regions with a large second derivative are enhanced. (Klinglesmith (1981) described a simpler, single-shift algorithm in which the shift is not radial, but he still finds evidence for jet structure.) This algorithm has the advantage of enhancing weak and narrow radial features in the presence of a strong background. Although simple, both conceptually and computationally, shift differencing does have many disadvantages. First, it is inherently imprecise because the size of the shift must be adjusted according to the size of the feature being enhanced. Second, it necessarily introduces many artifacts into the processed images (see Larson and Sekanina 1984, for example). Even worse, shift differencing distorts the spatial information, partly due to the artifacts and partly due to the nature of the differencing. Finally, all photometric information is lost with this algorithm. Renormalization. The renormalization algorithm is a widely used technique of jet enhancement (see A'Hearn et al. 1986a, Klinglesmith 1987, Hoban et al. 1988, Cosmovici et al. 1988, Suzuki et al. 1990, Samarasinha and A'Hearn 1991). With this technique, the azimuthal values at each radius are renormalized to some fixed range, usually corresponding to the number of color levels in the individual's display device. Among the advantages of this technique are speed (since it is a simple mapping), high contrast of radial features, and magnification of low signalto-noise ( S / N ) j e t s (especially at large distances from the nucleus). In this regard, it is superior to the profile subtraction method described below. However, the renormalization algorithm has the disadvantage, shared with the shift differencing algorithm, that images processed by this method have lost all photometric information. This disadvantage is emphasized with images containing more than one jet, which is common with this dataset. Consequently, the renormalization technique is not as useful for measuring photometric properties as is the profile subtraction method described below. Profile subtraction. Subtraction of a radial intensity profile determined from the image itself has advantages over the shift-differencing and renormalization techniques. Profile subtraction, as well as renormalization, has the advantage of making the single assumption that there are discrete radial features to be enhanced with a

CN JET VELOCITYIN COMETP/HALLEY nearly uniform background. Profile subtraction also uses the data themselves to determine the background and jet components of the CN image. All photometric information is retained and the radial intensity profile of the isotropic component is computed. Most importantly for determining the projected velocity from the jets, spatial integrity in both the r and the 0 directions is maintained. The procedure we used to determine the radial profile is as follows. First, an accurate center of the original image was found. Although the presence of jets necessarily skews the results of any centering algorithm, especially if the jet or jets were on the same side of the nucleus, we found that the centroid of the marginal distributions near the nucleus was adequate as the " b e s t " center. " N e a r " was defined to be a box of at least 7-11" (4-6 pixels), but no more than 36-45" (20-25 pixels). Within this range, the center was relatively insensitive to the size of the marginal distribution sampled, such that centers were found to a precision of better than 0.18" (0.1 pixel). The next step was to convert the x - y image to an r-O image in order to simplify the processing in subsequent steps. This step was accomplished by computing the r-O pixel values using four-point interpolation of the x - y pixel values. Higher order interpolation did not change the resulting image appreciably. The range of radii was determined by the size of the chip and the position of the comet, but the number of 0 columns was arbitrary. We chose a minimum of twice the number of radii (rows) to ensure proper sampling. Typically a sampling interval of approximately 0.02 radians (1 °) was used in this study. Next, the radial intensity profile was found by a twostep process. First an average radial profile was derived by calculating the azimuthal median at each radius and subtracting the result from the original image. The median was used to lessen the effect of cosmic rays and field stars. The radial profile was then recomputed in a similar manner but used only the portion of the image least contaminated by jets. This profile, which represents the diffuse, presumably isotropic, component of the CN outgassing was then subtracted from the original image. Although we treated the CN as two components, discrete jets and an isotropic diffuse component, we did so as a convenience for enhancing the jets and do not imply anything about the source of the CN. At this point it was possible to reconvert back to an x - y plot, if desired. Figure 1 provides a comparison between the original image (Fig. la) and the image after subtraction of the radial intensity profile (Fig. lb). The jets are evident in Fig. lb, but look qualitatively different from those derived from the same original image by Hoban et al. (1988) (image at a phase of -0.75, cycle 3 in their Fig. 2) or Samarasinha and A'Hearn (1991) (image at a phase of -0.75, cycle 15 in their Fig. la), which used a renormalization algorithm. Figure lb gives a closer representation of

75

the appearance the jets would have without the isotropic CN background because it shows the gradual dissipation of the jets with distance from the nucleus. Unfortunately, the profile subtraction algorithm does not enhance any nonradial features (nor do the renormalization and rotational shift-differencing methods). Thus, the CN shells seen by Schulz and Schlosser (1989) are not evident in Fig. lb. Model subtraction. Another method of enhancing inhomogeneities in the surface brightness distribution of the coma would be to subtract a smooth distribution based on a model such as the Haser model. This method would have the advantage of enhancing all features, not just those explicitly modeled. Shells and jets, for example, could be enhanced with this method. However, choosing a model is arbitrary at some level because of the physical and chemical assumptions that are necessary. As an experiment, we subtracted a Haser model with arbitrary scaling from the CN images. The same basic features are seen as with the other algorithms. For velocity determination, however, this step is not necessary so we adopted the less model-dependent profile-subtraction method. In fact, as we show below, no image processing is absolutely necessary for velocity determination, but such measurements were more convenient and the process better visualized the processed images. (b) Azimuthal Jet Fitting

To find the projected velocity from jet motion, it is necessary to measure the position of each jet. We did this by simultaneously fitting a Gaussian to each jet in r-O space using the downhill simplex method (see Press et al. 1986). Thus, if inspection of the processed image showed N jets, N overlapping Gaussians were fitted to the image in the 0 direction at each pixel radius (1.8 arcsec). Although fitting of Gaussians may appear ad hoc, it will be shown that the jets are well fitted with this method. The Gaussian form fitted to each jet was

where z is the fitted pixel intensity, 0 is the pixel position, 00 is the position of the center of the jet, tr is the width of the jet, and B is a factor related to the brightness of the jet (height of the Gaussian). As will be detailed in the next section, only the position of the center of each jet is important to the determination of the projected velocity. The general suitability of the Gaussian fitting can be seen by inspection of Fig. 2. Figures 2a and 2b are examples of the fitting for two separate radial distances for the image shown in Fig. lb. Typical uncertainties in the position of the Gaussianjet are less than 0.01 rad. (-0.5°), except far

76

K L A V E T T E R AND A ' H E A R N

FIG. 1. An example of the radial profile subtraction method of jet enhancement. (a) Original image, (b) processed image for 27 April 1986 12:15 UT. Both are displayed with a logarithmic grayscale. While there is a definite asymmetry in (a), the jets are much more obvious in (b). In addition to the two obvious jets, there is a third, fainter jet to the northeast. Superposed over (b) are the fitted centers. The jet with lower signal-to-noise to the lower left (northeast) is plotted with smaller symbols and is barely discernible with this grayscale. Uncertainties in the position of the center are smaller than the symbol size for all jets. Note the close correspondence with the grayscale image, including the increased scatter of the fitted centers as the signal gets smaller with increasing distance from the nucleus.

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FIG. 2. Example of Gaussianjet fitting. (a and b) Plots from the r - 0 plot corresponding to the image of Fig. lb of the intensity versus azimuth at the specified nucleocentric distance, p = 22,013 km (a) or 39,440 km (b). The model, dashed line, is a sum of three Gaussians corresponding to the three jets and fits the data more precisely than choosing the local maximum pixel or some other simple scheme, especially at large distances from the nucleus where the data are noisier. The dotted line is a plot of the residuals (scale on right). Note added in proof. Fig. 2a has data as dashed line and model as solid line.

77

CN JET VELOCITY IN COMET P/HALLEY

above, which is equivalent to the radial profile subtracted. Indeed, this is another way to calculate the radial intensity profile of the diffuse CN component. The method of Gaussian fitting, however, is a great waste of computer time since the image processing step is approximately 1000 times faster. It is also unnecessary to use this method, because our results show that the radial intensity profiles obtained by the profile subtraction algorithm described above and this modified Gaussian fitting are approximately the same. (c) Radial Cross Correlation

FIG. 3. Results of Gaussian jet fitting. This logarithmic grayscale image, with the same scale as in Fig. l(b), is the Gaussian fit for the entire image, transformed to x - y space for comparison with Fig. l(b).

from the nucleus where the S / N ratio is low. The distance from the nucleus to which a given jet can be fitted precisely depends upon the strength of the jet but the limits become obvious from (1) inspection of the processed image, (2) the size of the formal uncertainty, and (3) the scatter in the nearby positions of the centers of the jet. Gaussian fitting is more precise than choosing the position of the maximum pixel or some other simple algorithm, as long as the profile is symmetric. However, the fitted Gaussian centers usually coincided (typically within 0.02 rad.) with the position of maximum pixel value for high S / N jets (within the uncertainty). Figure 3 also demonstrates the success of the Gaussian fitting algorithm. Figure 3 is a reconstructed image based on the Gaussian fits. Residuals in the intensity of this image compared with Fig. lb are typically no more than 1% of the local intensity and much smaller averaged over the entire image. Figure lb is also overlaid with a plot of the position of the centers of the jets; in this figure, formal uncertainties of the positions are smaller than the size of the symbols. Gaussian fitting is independent of the image processing discussed above. Although it is a help to know how many jets there are in the original image, this is not strictly necessary. The fitting can be performed N times assuming I jet, 2jets, up to N jets and inspection of the reduced X2 or inspection of the positions of the centers can be used to determine the number of jets. This fitting would have to have an extra parameter, a constant added to the equation

If the jets are moving strictly radially, it should have been possible to follow any radial structure from image to image, measuring the movement and then calculating the projected velocity. In the previous subsection, we described a method of fitting for the features in azimuth. Ideally, we should have been able to fit for those same features in the radial direction. Indeed, if the motion is radial, fitting in the radial direction might have been more natural. We attempted to cross correlate each time series of images by computing the FFT (fast-Fourier transform) of each column (which is the radial direction) in r-O space and then performing the standard cross-correlation techniques (see Press 1986). The distance determined by the cross correlation was then divided by the time interval between the images to obtain the projected velocity at each 0 (sampled every 0.02 rad (l°)). Our attempt to measure the jet velocity using crosscorrelation techniques was unsuccessful. The typical velocities obtained by this method were almost an order of magnitude smaller than any reasonable value because there was some feature near the nucleus which dominated the cross correlation. The distance from the nucleus of this feature is approximately the same as Eberhardt et al. (1987) found for the extended CO (less than 10,000 km), although any identification is uncertain. Consequently, we abandoned this approach for this study. Radial cross-correlation techniques will work only if the significant features of a time series have similar velocities. The jets must have a significant azimuthal component which can be correlated in the radial direction. This condition certainly does not exist for many of the jets (see Section IV). III. ANALYSIS Determination of the projected velocity was straightforward. Figure 4 shows the locations of the two bright jets (seen in Fig. lb) at three different times during the night as determined by the Gaussian fitting described in the last section. The projected velocity was computed by measuring the difference in radial distance along any azimuth and dividing by the time difference between the

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two observations. This a p p r o a c h a s s u m e s that the flow is radial. The overall a p p e a r a n c e of Fig. 4 is consistent with this assumption. Specific " f e a t u r e s , " such as those along the lines drawn in Figs. 4a and 4b, strengthen the assumption of radial outflow. Several other such features can be traced in the figure. C o m p a r a b l e behavior was seen for other jets on other nights. Figure 4b shows an almost periodic wavelike structure moving radially. Radial flow will be distorted by changing projection and real acceleration, but o v e r these timescales the expansion should be nearly radial. Projected velocities were determined by measuring the distance travelled by specific jet features in a given time interval. H o w e v e r , because the " c e n t e r s " of these features were difficult to determine, this method was less accurate than the method described below. Consequently, it was ultimately used only as a check on the better method. Since the flow was radial, it made more sense to plot the jet in an r - O representation, as in Fig. 5, which contains the same data as Fig. 4. A line was fitted to the obvious linear portion of each jet in the time series, as outlined by the b o x in Fig. 5. Higher order fits were generally not warranted, as determined by c o m p a r i s o n of the reduced X2 and visual inspection. We c o m p u t e d the radii f r o m these fits and divided by the time difference to get the projected velocity o v e r a range of 0. For those nights in which we had m o r e than two observations (images), we linearly fitted for the velocities at each nucleocentric distance. Uncertainties were p r o p a g a t e d throughout, with the largest uncertainties being in the linear fitting of the r - O plot. For a jet with quasicoherent structure, such as

seen in Figs. 4b and 5b, this method p r o b a b l y overestimated the uncertainty. This particular jet, h o w e v e r , was exceptional and consistency of m e t h o d o l o g y was judged to be more important than artificially reducing the formal uncertainty. For each night in which we had two or m o r e observations, we c o m p a r e d the velocity determined in this way with a simple pairing of features such that v = A r / A t and there was no indication of any systematic difference between the method of directly measuring features and the method of linear fitting. This procedure was applied to all jets for which there were two or more o b s e r v a t i o n s in one night. When the jets could be identified with some confidence f r o m night to night, the internight velocities were also measured. The results of the intranight and internight m e a s u r e m e n t s are listed in Tables II and III. Figure 6 is a plot of the intranight m e a s u r e m e n t s , scaled to heliocentric distance R = 1 AU by the relation vl AU = U ~ / R . Theoretical and observational evidence exists for this relation ( D e l s e m m e 1982), but the general conclusions presented in Section V will be the same for any reasonable scaling relation. In Fig. 6, the radial value along the abscissa is determined by computing the mean of the N radii for each azimuth, 0. In addition, the velocity range is listed in Table II or plotted in Fig. 6 only if there is overlap in 0 a m o n g the images used to calculate the projected velocity, so as not to extrapolate the linear fits discussed above. The area enclosed by the b o x e s in Figs. 5a and 5b shows the points actually used for the fits of those jets. Inspection of Fig. 6 reveals several interesting features. E v e n with a typical uncertainty of less than 0.1 km sec (see Table II), little overlap b e t w e e n the measured veloci-

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FIG. 5. The same plots as in Fig. 4 except in r-O space. The linear nature of a large fraction of the jet is obvious in this representation. Typical uncertainties are smaller than the size of the symbols. Lines were fitted to only the sections of the jets which overlapped in azimuth so as not to extrapolate the line, as shown by the box. In (a), for example, only the sections between approximately O = 1.6 and 2.1 were used to actually calculate the jet's projected velocity. Note the relative scale of the abscissa is the same for the two figures. Motion is not normalized to R = 1 AU.

ties is present. Both positive and negative gradients occur, although positive gradients are m o r e c o m m o n . Furthermore, an examination of Table II shows that about half the jets m e a s u r e d have velocities consistent with zero. Internight velocity determinations are generally smaller than intranight velocity values, as shown from a comparison o f Table II and Table III, but this is a selection effect as discussed below. IV. DISCUSSION C N jets provide a m e a n s of direct m e a s u r e m e n t of the projected C N velocity. The existence of radial features evident in Fig. 4 and other images d e m o n s t r a t e s that the expansion is a p p r o x i m a t e l y radial. Thus, the jets a p p e a r as nearly linear features in an r-O plot, as shown in Fig. 5. This can be shown mathematically for a simple rotator viewed pole-on with constant outflow velocity. U n d e r these conditions, r = vt and 0 = 00 + tot, where to is the angular velocity and 00 is an arbitrary constant (which will be set to zero). Eliminating the time variable, t, r = v/to 0, which is the formula for a spiral of A r c h i m e d e s - - a straight line on an r-O plot. E v i d e n c e indicates that C o m e t P / H a l l e y is not a simple rotator (see Belton and Julian 1990, S a m a r a s i n h a and A ' H e a r n 1991). H o w e v e r , nearly all of the jets are fit well by A r c h i m e d e a n spirals, which suggests that o v e r these small timescales, the projection of the rotation is simple and the local velocity is approximately constant for those jets m e a s u r e d for the projected velocity determination. In fact, the slopes m e a s u r e d for the time series on an r-O plot, such as Fig. 5, are slightly

different. This d e m o n s t r a t e s that while a jet is fit well by an A r c h i m e d e a n spiral, it is a slightly different A r c h i m e d e a n spiral at different times in the night. This difference is a major contribution to the calculated uncertainty in the final velocity for m a n y of the jets, even though it is a real effect due to projection or acceleration. An equivalent rotation period can be calculated from the a b o v e expression since the slope = v/to is m e a s u r e d from the r-O plot, and v is calculated as described in the last section. We stress that this is not necessarily a true rotation period. F o r the jet with the highest m e a s u r e d projected velocity, the calculated period is 6.3 - 0.9 days. We caution h o w e v e r , that this result must not be overinterpreted: the assumption o f P / H a l l e y as a simple rotator, even without any projection on the sky plane, is certainly false (Belton and Julian 1990, S a m a r a s i n h a and A ' H e a r n 1991). It is interesting, though, that this simple analysis is nearly consistent with the 7.4-day lightcurve rotation (Millis and Schleicher 1986) found for C o m e t P/Halley. Due to the complexities o f its rotation and the projection effects, it will be almost impossible to determine the rotation of P / H a l l e y f r o m c u r v a t u r e of its jets alone. Without a definitive rotation state of the nucleus of C o m e t P/Halley, it is impossible to model the effects of g e o m e t r y on our m e a s u r e m e n t s of the projected C N velocity. But geometric effects will be important, and will p r o b a b l y explain the gradients seen in Fig. 6. S a m a r a s i n h a and A ' H e a r n (1991) d e m o n s t r a t e d that simple jets can a p p e a r to h a v e very c o m p l e x m o r p h o l o g y due to the projection of the radially expanding jet f r o m the rotating and precessing nucleus. Theoretical justification (see C o m b i

80

KLAVETTER

able II Velocity Results of Intranight Measurements Normalized to R=IAU p range' (103 km) Date 1986

Jet" ID

N

Velocity range ~' (km sec-t)

Mar 11

1.6 4.8 3,0 t.8 6.1 5.9 0.9 3.5 1.8 3.5 5.9 1.4 3.7 5.9 2.1 4.7 6.1 0,0 1.2 3.7 1.2 3,5 0.0 2.1 5.5 0.0 2.1 4.4 0.8 3.2 1.1 4.2 0.8 3.2

2 2 2 2 2 2 2 2 3 4 4 3 3 3 2 2 2 2 2 3 2 2 3 3 3 2 2 2 2 2 2 2 3 3

Zero d Zero" Weak' 0.87 Zero" Weak" Zero a Zero" (I.93 1.54 0.95 Zero a 0.77 Weak' 1,71 1.11 0.59 Weak" Weak' 1.20 Weak" Weak" 1.89 1.64 Weak '~ Zero" Zero" 0.85 Weak' 0.95 1.13 1.42 Zero 'l 1,14

Apr 04 Apr 06 Apt 09 Apt 14 Apr 16

Apr 17

Apr 23

Apr 24

Apr 26 Apr 27

Apt 28

May 01 May 02 May 09

0.74

0.92 1.37 1.17 0.72 0.78 0.85 0.73

0.69

1.09 1.06

0,47 0.40 0.87 0.43 0.54

min

max

-+0.04

12

22

-+0.11 -+0.10 -+0.18

9 18 18 12

18 22 25 19

9 42 21 32

58 92 66 9(1

32

90

-+0.11 -+0.08

16 19

60 69

-+0.02

12 4

31

-+0.03 -+0.05 -+(I.01

59 26

85 40

-+0.06

13

32

-+0.18 ±0.02 -+0.04 -+0.05

-+0.49

43

" An identifier based on the approximate position of the jet 20,000-30,000 km from the nucleus measured (in radians) counterclockwise from the positive x axis (south/. t' Corresponding to 0 range. ' Distance from nucleus. " Measurement of moderate to high SIN data consistent with zero. " Too little signal for definitive measurement, but consistent with zero.

AND A'HEARN

than this value. Furthermore, Samarasinha and A'Hearn (1991) show that the lifetime of a single jet can be as little as 1 day, so large changes in geometry in a 24-hr period are not unusual. The internight velocity marked on Fig. 6 is a value almost exactly intermediate between the values corresponding to the two intranight velocities measured for that same jet, as is the case for all of the internight velocities listed in Table III. All the internight velocity values are weak lower limits to the instantaneous velocity. One half of the expansion velocities listed in Table II are zero, although a few are ambiguous due to low signal level. This result is expected since Samarasinha and A'Hearn (1991) have shown that the angular momentum vector of Comet P/Halley was almost perpendicular to the line of sight at the time of these observations. For a simple rotator, all jets on the equator would be moving nearly parallel to the line of sight and would show no curvature. Therefore, we would calculate nearly zero projected velocity, regardless of the true velocity. Since Halley is not a simple rotator and since jets probably originate from places other than the equator, it is not surprising that occasionally a jet with appreciable projected velocity is observed. With a much smaller dataset, it would be unlikely that a jet would be observed with a projected velocity near the true CN expansion velocity. Even with the large number of jets investigated in this work, we can only show that the calculated jet velocity is a lower limit. Table III Velocity Results of Internight Measurements Normalized to R = 1 AU p range' (10 ~ km) Date 1986 Apr 06-07 Apr 14-15 Apr 16-17 Apr 16-17

1989, Ip 1989) and some observational evidence (Lgmmerzahl et al. 1987) exist that the CN velocity increases in this part of the coma, from r ~ 10,000 to 80,000 km. Perhaps the larger number of positive slopes than negative ones in Fig. 6 provides weak evidence for this acceleration, but the geometry is unknown and the number of jets is too small to be certain. The internight results are somewhat less interesting because they represent an average of the apparent jet velocity over a time interval of approximately 24 hr. Our limited field of view precluded measurement of projected velocities greater than ~ 1 . 2 km sec -I, and all values of the internight projected velocity shown in Table III are less

Apr 16-17 Apr 23-24 Apr 24-25 Apr 26-27 May 01-02

Jet" ID

N

6.1 5.4 3.5 5.2 1.1 1,6 3.5 3.7 5.9 5.9 2.1 3.7 2.1 3.7 1,2 0.0 0.8 1. I

1 I 1 1 4 3 4 3 4 3 2 I 2 2 I 1 1 1

Velocity range ~ (km sec i)

min

max

(I.43

0.43

+0.01

22

36

(I.38

0.39

-+0.01

23

35

-+0.25

41

65

Zero J 0,77

0.00 Zero d

1.09

1. I 1

-+0.01

43

56

0.74

0.71

-+0.01

44

50

0.42

0.45

-+0.01

81

107

0.67

0.56

-+0.01

31

80

" An identifier based on the approximate position of the jet 20,000-30,000 km from the nucleus measured 1in radius) counterclockwise from the positive x axis (south). J' Corresponding to p range. ' Distance from nucleus. a Measurement of moderate to high S / N data consistent with zero.

CN JET VELOCITY IN COMET P/HALLEY

%"E x., v •~

2.0

'

'

'

I

'

'

'

I

'

1.8

'

'

/

' ' / I 27'Apt(0.0l) .~23Apt(2.09)

I

'

'

'

1.6 1.4

o >a~

1.2

16Apt ~ (5.93)/

c'-

1.0

6Ap

E

0.8

09

0.6

~

7

1 23-24Apt(2.0)9~3.67) /

J

24Apt(367)"~

.

S ~ 2 8A p t (4.36) ,

0.4 0

,

,

I

,

~ ,

,

I

,

,

,

I

23 A p t ( & l l ) ,

,

,

I

,

,

20 40 60 80 100 Distance from the Nucleus (103km)

FIG. 6. Results of projected CN velocity determination from jets measured during one night of observations (intranight). Jet 0.0 of 27 April has the greatest projected velocity, v = 1.7 _+ 0.1 km sec -I at 50,000 km. The positive and negative gradients are due to changing geometry conditions, although the larger number of positive slopes provides weak evidence for a true acceleration. For clarity, only April data are shown, although the four lines for March and May are similar (see Table II). Also shown is one of the night-to-night (internight) projected velocity determinations, in the middle of the graph. Unsurprisingly, it is in the middle of the values found for the corresponding intranight velocities. The typical uncertainty at each point is labeled in the upper left of the plot. Note that about half of the jets from Table II are not plotted since their projected jet velocity is consistent with zero. Data are normalized to R = 1 AU.

Independent support for the general methodology and velocity values listed in Table II comes from comparing the same physical jet on successive 7.4-day cycles. Samarasinha and A'Hearn (1991) identify the same jets which are seen on different cycles (see their Fig. lb and Table V). Using these identifications, we note that the projected velocities are approximately equal for the same physical jets, listed in Table IV (in a more compact form than Table II). It is unlikely that this would be true unless the jets were physically the same and the method of measuring the velocity was consistent. The small discrepancies in mean velocity listed in Table IV are most likely due to the incommensurability of our sampling with a 7.4 day period; our measurements are taken almost exactly 7 days apart. We attempted a statistical approach to the problem of finding the CN expansion velocity based on our measured projected velocities. For a random distribution of jets, the average of the projected velocity is known and we should be able to calculate the actual velocity under the assumption that the velocity is constant. The problem with this method was that the jets were not randomly oriented. One only need look at the distribution ofjets from Samarasinha and A'Hearn (1991) to see that we were measuring the same jets at similar phases, as discussed above (see Table

81

IV). That the jets are not randomly oriented was confirmed with our measurements: the weighted mean and unweighted mean velocity values were radically different. There have been almost as many values of coma velocity as there are measurements, although there is some clustering around the "canonical" value of 1 km sec-i. The velocity values for Comet P/Halley found by various observers using different techniques are summarized in Table V. Some of these determinations were based on assumptions that lead to erroneous conclusions. For example, A'Hearn et al. (1986b) assumed a 2.17-day period and calculated a preliminary value of 0.82 km sec -j, scaled to R = 1 AU, from the slope of jets in an r-O plot. Although they used some of the same data used in this work, their method was based on the assumption, now known to be incorrect, of a simple 2.17-day rotation period. Even the in situ measurement of gas velocity depends upon the unproven validity of some assumptions. In their original analysis, Krasnopolsky et al. (1986) also assumed simple rotation of 53 hr (2.2 days). At least two groups found the HCN velocity using radio line profiles (Schloerb et al. 1986 and Despois et al. 1986). Their line-

Table IV Similarities of the Same Physical Jet on Different 7.4-Day Cycles Normalized to R = 1 AU Physical a ID

Date 1986

Jet a ID

Mean velocity (km s e c - b

Gradient c

B

Apr 16 Apr 23

1.8 2. i

0.9 1.2

Positive Positive

A

Apr 16 Apr 23

3.5 4.7

1.5 1.0

Positive Positive

E

Apr 16 Apr 23

5.9 6.1

1.1 0.7

Negative Negative

B

Apr 17 Apr 24

1.4 1.2

Zero d Weak e

E

Apr 17 Apr 24 May 01 May 09

3.7 3.7 3.2 3.2

0.7 0.9 0.7 0.8

C

Apr 17 Apr 24 May 01 May 09

5.9 0.0 0.8 0.8

Weak e Weak e Weak e Zero d

Positive Positive Positive Positive

Using the notation of Samarasinha and A'Hearn (1991). See their Fig. I b and Table V. b An identifier based on the approximate position of the jet 20,000-30,000 km from the nucleus measured (in radians) counterclockwise from the positive x axis (south). c If the velocity increases with nucleocentric distance, the gradient is positive; otherwise it is negative. d Measurement of moderate to high S / N data consistent with zero. e Too little signal for definitive measurement, but consistent with zero.

82

KLAVETTER AND A'HEARN

TABLE V

Previous Coma Expansion Velocity Determinations For Comet P/Halley ~'

v (km sec i)/,

p range' (103 km)

Species

Note

Ref.

0.76 + 0.05 1.04 -+ 0.30 0.81 -+ 0.15 (0.87) -+ 0.12 J 0.9 +- 0.2 '~ 1.4 + 0.21 1.03 -+ ?? 0.82 -+ ?? (0.9) + 0.1 '/ (0.7-1.6) + ??a 1.87 _+ 0.14

1-4.0 0-6.3 0-10 0-20 0-11 0-11 -30 10-30 0-80 80-500 0-4.5

H20 HCN H20 HCN H,O H20 H20 CN OH CN CN

Giotto Radio Giotto Radio IR Spec. IR Spec. Giotto Jets Radio Shells G re e ns t e i n effect

L/ i mme rz a hl et al. 1987 Despois et al. 1986 K r a s n o p o l s k y et al. 1986 Schloerb et al. 1986 La rs on et al. 1987 Larson et al. 1987 L~immerzahl et al. 1987 A ' H e a r n et al. 1986 B o c k e l 6 e - M o r v a n et al. 1990 Schulz and S c h l o s s e r 1989 J a w o r s k i and Ta t um 1991

-50

CN

Jets

This w ork

1.7 -+ 0.3

~' See Celnik and S c h m i d t - K a l e r (1987) for a more complete list, including dust and ions. t, These values, except those noted, have been normalized to R = 1 AU for direct c o m p a r i s o n with Table II and Fig. 6. C o r r e c t i o n s are typically less than 10%. ' Distance from nucleus. ,1 A v e r a g e o v e r large range of R, not c orre c l e d to R = I AU. ~' Preperihelion m e a s u r e m e n t , not corrected to R = I AU. I Postperihelion m e a s u r e m e n t , not corrected Io R = 1 AU.

of-sight values o f v = 0.87 -+ 0.12 and 1.04 -+ 0.30 km s e c were an average of m a n y different geometries involving convolution of an a s s u m e d isotropic outgassing, which is k n o w n to be an oversimplification. There are similar a s s u m p t i o n s m a d e with the velocity determinations that use O H line radio data. Bockei6e-Morvan et al. (1990), for e x a m p l e , found v = 0.9 -+ 0.1 averaged o v e r all heliocentric distances observed. All of the results from radio line profiles are also highly model dependant. High-resolution infrared o b s e r v a t i o n s of H 2 0 line profiles allowed L a r s o n et al. (1987) to determine values of v = 0.9 -+ 0.2 km sec i (preperihelion) and 1.4 -+ 0.2 km s e c - l (postperihelion). T h e y also needed to m a k e a priori assumptions concerning the velocity distribution and ignored any variation in outflow velocity. Schulz and Schlosser (1989) calculated the CN velocity from CN shells ranging from 0.7 to 1.6 km sec I (with no uncertainty listed). The shell data will be discussed in a future work, but it is worth noting here that the distance from the nucleus of their m e a s u r e m e n t s ( - 4 × 105 km) is an order of magnitude greater than the distance appropriate to this work ( - 5 × 104 km). One recent m e a s u r e m e n t of the Greenstein effect for C N (Jaworski and T a t u m 1991) indicated a c o m a velocity as large as 1.86 -+ 0.14 (normalized to R = 1 AU), which is consistent with our m e a s u r e d value of the CN expansion velocity. Their velocity m e a s u r e m e n t s also show a large range, p e r h a p s due to similar geometrical effects as our m e a s u r e m e n t s . It is also possible that their p e a k velocities

correspond to the jet velocity and not the diffuse C N c o m p o n e n t of the coma. Their m e a s u r e m e n t s are m u c h closer to the nucleus (0-4500 km) than our m e a s u r e m e n t s (10,000-90,000 km), within the "collision z o n e " so it is possible that our m e a s u r e m e n t s m a y not be directly comparable. Theoretical studies of c o m e t a r y c o m a e have also found outflow velocities near the canonical 1 km sec-~ value (see Combi 1989, Ip 1989, Marconi and Mendis 1983). Theoretical studies, h o w e v e r , typically warn of the incompleteness of the physical and chemical a s s u m p t i o n s and are often fitted to the observational results listed above, which can lead to significant errors in the velocity. Theoretical studies have d e m o n s t r a t e d that the outflow velocity will have a positive gradient in the part of the c o m a studied in this work (Combi 1989, Ip 1989). Although impossible to say with certainty due to the geometrical considerations, our results are consistent with this acceleration. We have presented a method of directly determining the projected C N jet velocity, with a minimum set of assumptions. E v e n radial outflow is not a s s u m e d , but demonstrated. Three of the m e a s u r e m e n t s were v > 1.4 km s e c t at a distance of 50,000 kin, with uncertainties less than 0. I km s e c - J; all are lower limits. E v e n if there were some problem with specific data, these results indicate that the canonical value of 1 km s e c - 1for this portion of the c o m a is too small. Strictly speaking, if the motion observed is due to the motion of material and not a phase

CN JET VELOCITY IN COMET P/HALLEY

83

phenomenon, we measured the outflow velocity of the This investigation has not explicitly considered the jets. It is possible that this velocity is different from the source of the CN jets, since it is not relevant to the detervelocity of the diffuse CN, which could account for some mination of the expansion velocity. Yet, radiation presof the discrepancies seen in Table V between the various sure could possibly affect the results, if the jets originated velocity determinations of the coma of Comet P/Halley. from particles of a certain size. Samarasinha and A'Hearn Even with this direct determination of the projected (1991) have calculated the acceleration due to radiation CN velocity, uncertainties still exist in addition to the pressure for particles of a reasonable size and for gas. propagated formal error. The inescapable problem of the They found that radiation pressure effects are small for unknown geometry is the largest uncertainty. Without a r < 100,000 km, especially during April. These data were detailed model of the rotation state of Halley, it is impossi- near opposition, and any effect radiation pressure would ble to even attempt to model the changing geometry rigor- have on the displacement of the displacement of the CN ously. We chose a distance of 50,000 km from the nucleus jet would be mostly along the line of sight and would not as a reference to balance S / N considerations, centering effect the projection of the velocity vector on the sky errors, and comparison with most of the previously deter- plane. mined projected velocities. When the geometric effects One remaining uncertainty concerning this analysis is are at a minimum, motion in the sky plane of the jets will the functional form of the scaling to a common heliocenbe nearest the true expansion velocity. Thus, the jet with tric distance, 1 AU. Although the form we use, vl AU = the highest projected velocity (see Table II and Fig. 6) VX/-R has theoretical and observational justification may be most representative of the true velocity. (Delsemme 1982), it is impossible to determine this indeThe jets represented by Figs. 4a/5a and 4b/5b are exam- pendently due to the uncertain geometrical effects. Alples of nearly opposite extremes, with (a) being one of the though subsequent studies have indicated that this scaling best behaved jets and (b) one of the worst. Although the may be too simplistic (see Bockel6e-Morvan and CroviS / N is good for both jets out to -80,000 km from the sier 1987 or Huebner and Keady 1983), the general form nucleus, jet 2.1 (a) is much smoother. This is apparent in of the scaling is approximately correct. Furthermore, the both the x - y plot of Fig. 4 and the r-O plot of Fig. 5. Jet general results and conclusions of this study are not 0.0 (b), on the other hand, is almost wavelike in nature. strictly dependent on the details of the scaling relationship This is an illustration of the large differences found be- used. For example, with Delsemme's scaling, the correctween individual jets. Since following specific features is tion at the end of April, corresponding to the highest imprecise, time consuming, and somewhat subjective, we projected velocities measured, is only -1.25. The range chose a more uniform method of measuring the apparent of heliocentric distances during the latter part of April, jet movement. This method of linear fitting, detailed in corresponding to most of the plots in Fig. 6, is only the last section, provides a workable technique that is R = 1.4-1.6. Thus, only if the scaling law is significantly simple, yet accurate. For each time series of jets mea- different can these results be invalid. Some investigators sured, r-O plots similar to those in Fig. 5 were viewed to (Schloerb et al. 1986, for example) found no correlation determine the limits of the linear fitting. For the two jets of the expansion velocity with distance. Theoretically, it shown in Fig. 5, the box contains the data used in the is expected that there will be an increase of velocity as linear fits. We were conservative in our limits, preferring the heliocentric distance decreases since the energy input to work with the most linear portion at the expense of (heating) will be greater near the sun (see Combi 1989). using fewer data points. Certainly, there are variations Observational evidence for scaling with heliocentric disthat we have noticed in our analysis, but nothing was tance also exists (Delsemme 1982, Celnik and Schmidtlarge or consistent enough to detract from the overall Kaler 1987). Since the formal uncertainty due to any scalcorrectness of the method we chose to use. Although ing errors is impossible to calculate, we will use a 3ochoosing the limits of the linear portion is somewhat arbi- uncertainty to account for possible systematic errors. trary, we have found that this uncertainty is offset by the Thus, at 50,000 km from the nucleus, the maximum prolarge number of data points such that the cutoff point jected velocity is 1.7 - 0.3 km sec 1. Although the scaling chosen is relatively insensitive. For example, the differ- relationship we use is reasonable, it is still possible that it ence between the velocity measured for jet 0.0 when the is in error. If this were the case, the values listed in Tables fits are increased by as much as 5 points at the higher end II and III and shown in Fig. 6 would have to be divided (where the variation is the greatest) is less than 1 o-. Yet by -1.25 (the exact value being the square root of the jet 0.0 has some of the largest variations of any jet found, heliocentric distance tabulated in Table I) to renormalize another indication that the formal uncertainties listed in the values to their measured projected velocities. Table II are conservative. Thus, there is not enough eviThe CN projected velocity of the jets was measured, dence to justify any higher order method that would go but other species are thought to be coupled with the beyond this analysis. CN outflow and thus should have the same velocity, at

84

KLAVETTER AND A'HEARN

least in the inner part of the coma (-20,000 km, see Combi 1989). Preliminary reduction of C2 jets is consistent with the conclusions found from this work, but further analysis is necessary due to the contamination from the continuum. Eventually, this work will be extended to all the species observed, especially the dust, for comparison.

A'HEARN, M. A., S. HOBAN, P. V. BIRCH, C. BOWERS, R. MARTIN, AND D. A. KLINGLESMITH 1986a. Gaseous jets in Comet P/Halley. In Proceedings, 20th ESLAB Symposium, ESA SP-250, Vol. I, pp. 483-486.

V. CONCLUSIONS

BEETON, M. J. S., AND W. H. JULIAN 1990. A Model for the spin state of P/Halley. Bull. Amer. Astron. Soc. 22, 1089-1090.

The projected velocity for CNjets in the coma of Comet P/Halley is v = 1.7 -+ 0.3 km sec- ~, much higher than the canonical 1 km sec- 1. From these data, it is impossible to determine if this conclusion is also valid for the diffuse component of the CN gas. Even if only the jets are moving at 1.7 -+ 0.3 km sec-1 (while the isotropic component is at a lower velocity) this result will have important consequences for coma modeling since preliminary measurements show that the jets represent 10-50% of the observed CN flux. Furthermore, this result is secure: we have tested the general method by following specific features in the jets or by finding the maximum pixel value of the jet to determine the velocity. In all cases, the results are consistent with the values obtained using the method described in Section III. The specific conclusions are enumerated below. I. The maximum observed projected jet velocity is 1.7 _ 0.3 km sec ~ at a distance of 50,000 km from the nucleus, larger than any other observational or theoretical determination of the diffuse coma outflow speed for Comet P/Halley. This result is from a direct determination of the projected velocity, with no complicated models and few assumptions. 2. With these data, the most accurate determination of the projected CN velocity is from measurements of a time series taken during one night rather than from multiple nights, partly due to a selection effect and partly due to the larger change in geometry for internight velocity determinations. 3. The outflow is nearly radial, as demonstrated by following specific features in a jet's time series. 4. We have noticed weak evidence for an acceleration in the coma from about 20,000 to 80,000 km. However, it is impossible to uncouple this possible acceleration from the changing projection effects.

BOCKEL~E-MORVAN, D., J. CROVlSIER 1987. The role of water in the thermal balance of the coma. In Proceedings, Symposium on the Diversity and Similarity o f Comets. ESA SP-278, pp. 235-240.

VI. ACKNOWLEDGMENTS We thank Nalin Samarasinha and Susan Hobart for useful discussions. The observers who obtained many of these data deserve special recognition: Susan Hobart, Peter V. Birch, Craig Bowers, and Ralph Martin. In addition, J.J.K. thanks Athabasca and Reudi. Bob Millis and Mike Combi provided very useful reviews. We thank Vincent Patrick and the AVL for assistance with the grayscale figures. This work was supported by NASA Grant NAGW 1886 (formerly NSG 7322).

REFERENCES

A'HEARN, M. A.. S. HOBAN, P. V. BIRCH, C. BOWERS, R. MARTIN, AND D. A. KLINGLESMITH 1986b. Cyanogen jets in Comet Halley. Nature 324, 649-651.

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