Inner coma imaging of Comet Levy (1990c) with the Hubble space telescope

ICARUS97, 85-98 (1992)

Inner Coma Imaging of Comet Levy (1990c) with the Hubble Space Telescope 1 H. A. WEAVER Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, Maryland 21218 M. F. A'HEARN Astronomy Program, University of Maryland, College Park, Maryland 20742 P. D. FELDMAN Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218 C. ARPIGNY Institat d'Astrophysique, Universit~ de Liege, B-4000 Liege, Belgium W. A. BAUM Astronomy Department, University of Washington, Seattle, Washington 98195 J. C. BRANDT Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado 80309 R. M. LIGHT Lick Observatory, University of California, Santa Cruz, Santa Cruz, California 95064 AND J. A. WESTPHAL Division of Geologic and Planetary Science, California Institute of Technology, Pasadena, Califi~rnia 91125 Received September II, 1991; revised February 17, 1992

virtually the full spatial resolution capability of the HST. The images show a highly asymmetrical coma in which the sunwardfacing hemisphere is more than a factor of 2 brighter than the tailward hemisphere, consistent with volatile sublimation occurring primarily on the dayside of the nucleus. The azimuthal dependence of the spatial brightness distribution on the sunward side is roughly Gaussian with FWHM - 135° and an axis of symmetry that is nearly coincident with the projected Sun-comet line. While the azimuthal profile is clearly not consistent with isotropic emission of dust into the sunward hemisphere, the profile width is significantly larger than the widths of dust jets observed by the Halley Multicolor Camera on the Giotto spacecraft (H. J. Reitsema et al. 1989, Icarus 81, 31-40). Radial brightness profiles perpendicular to the Sun-comet line are very symmetric about the nucleus and follow approximately a p-1

Comet Levy (1990c) was observed with the Hubble Space Telescope (HST) on UT 27 September 1990 when both the heliocentric and geocentric distances were - 1 AU. Two sets of images of the comet were taken 6.5 hr apart with the WideField Camera (WFC) through a broadband red filter that was selected to isolate continuum emission peaking sharply at the nucleus. A single WFC pixel projected to a distance of - 7 8 km at the comet, and deconvolution techniques were used to recover

1 Based on observations with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universitiesfor Research in Astronomy, Inc., under NASA Contract NAS5-26555. 85

0019-1035/92$5.00 Copyright © 1992by AcademicPress, Inc. All rights of reproductionin any form reserved.

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law (where p is the projected distance to the nucleus). For the time-averaged radial brightness profile, the relative /-band luminosity increases linearly with aperture size over the entire range 0'.'1 -< p -< 10". However, the coma of Comet Levy is definitely not in steady state. Detailed analysis of the images appears to show a hemispherical arc of dust propagating through the coma with an average projected velocity of -0.16 km sec -~. Periodic occurrences of similar dust arcs could be responsible for the temporal variability in the continuum photometry observed from the International Ultraviolet Explorer (P. D. Feldman et al., Icarus 95, 65-72.) and from the ground (D. G. Schleicher et al. 1991, Icarus 94, 511-523). ~ 1992Academic Press, Inc.

I. INTRODUCTION Comet L e v y (1990c) was discovered in May 1990 and by midsummer it became clear that this comet would be an outstanding candidate for an extensive observational campaign. Monitoring of the comet's lightcurve in late August with the International Ultraviolet Explorer (IUE) (Feldman et al. 1992) and from ground-based telescopes (Schleicher et al. 1991) demonstrated that there was significant temporal variability with an apparent period o f - 1 8 hr. Immediately questions were raised concerning the possible sources of this temporal activity. Were there pockets of volatile material on the surface of Comet L e v y ' s nucleus that became active every time they rotated into sunlight? Such a scenario would imply that L e v y ' s nucleus was much like that of Comet Halley: primarily covered with a nonvolatile crust with the coma being produced by " j e t s " of dust and gas emanating from the volatile regions. H o w e v e r , Comet Levy is probably a dynamically " n e w " comet making its first passage through the inner Solar System (B. G. Marsden, private communication, 1991), so the surface of its nucleus may not yet have the insulating crust that is thought to evolve as comets make repeated passages close to the Sun (Houpis et al. 1985). Thus, an alternative picture is that the surface of Comet L e v y could be coated rather uniformly with volatile material, and the periodicity caused by very different cross sections of a highly elongated nucleus being rotated into sunlight. Then the production of gas and dust in the coma would presumably be much more isotropic. In either case, it seemed clear that high spatial resolution imaging of the inner coma would provide important insights into the nature of Comet L e v y ' s nucleus. Thus, we submitted a Target of Opportunity proposal for Director's Discretionary time on the Hubble Space Telescope (HST) to study the inner coma of Comet L e v y . The proposal was approved, and this paper describes the subsequent H S T observations and data analysis.

II. OBSERVATIONS A. General Considerations

Comet L e v y was observed with the H S T on UT 27 September 1990, which was approximately 5 months after H S T was launched. At that time the observatory was still in an immature stage with regard to performing scientific investigations. In particular, the H S T ' s ability to track Solar System targets, which have apparent motions relative to the stars used by the H S T f o r pointing control, was still under development. Thus, a rather modest imagingonly program was executed consisting of short-duration exposures that did not require the telescope to follow the motion of the comet ( " a m b u s h " observations). Since L e v y was a new comet with relatively uncertain orbital elements, there was some concern that ephemeris inaccuracies might preclude placing the comet within the H S T ' s field-of-view (FOV). Thus, all imaging was performed with the Wide-Field Camera (WFC), which has the largest FOV (-154") but the lowest spatial resolution (0"! pixel 1) of the H S T c a m e r a modes. At the time of the Comet Levy observations, both the heliocentric (R) and geocentric (A) distances were - 1 AU (R = 1.055 AU and = 1.069 AU), and one WFC pixel projected to 78 km at the comet. The program consisted of two separate visits to the comet, separated in time by - 6 . 5 hr in order to sample the comet at two different phases in its activity. The two visits could not be separated by exactly half the iightcurve period (as determined from 1UE and ground-based observations) because that would necessarily place one of the observation windows into a time when the H S T passed through the South Atlantic Anomaly, during which period observations are precluded due to the high particle background. The observing program was identical for both visits. In each case four images were obtained. Three were taken through the F785LP filter (with an effective wavelength of - 8 8 0 0 A, which is somewhat redder than the standard /-band) with integration times of I, 2, and 4 sec. One image was taken through the F439W filter (similar to standard B-band) with an integration time of 2 sec. E x p o s u r e times were restricted to less than 4 sec in order to keep the trail of the comet to less than the width of one pixel. Only the two 4-sec images through the F785LP filter are discussed in this paper. The shorter duration images through the F785LP filter provided no additional information on the spatial brightness distribution and had lower signal-to-noise ratios compared to the 4-sec images. The images through the F439W filter were severely underexposed and contain useful data only within - 1 " of the nucleus. For the initial pointings during both visits, the comet was found within a few arcseconds of its expected posi-

IMAGING OF COMET LEVY (1990c) WITH HST

tion, which is consistent with the uncertainties in the comet's ephemeris. However, in the 36 min needed to obtain the four images for each visit, the pointing drifted by - 15"-17". The magnitude of this drift is consistent with what is expected due to gyro drift error (the pointing was performed under gyro control), and the drift itself had no significant impact on the success of the scientific program. B. Data Reduction

All of the Comet Levy images were processed using the Routine Science Data Processing system (the "pipeline") at the Space Telescope Science Institute. This system implements the general procedure for reducing WFC images described in detail by Lauer (1989). Briefly, the data reduction steps consist of: (1) correction of a problem in the analog-to-digital conversion, (2) bias subtraction, (3) preflash subtraction (the CCDs were "preflashed" prior to taking the Comet Levy images in order to improve the ability to measure low-level signals), (4) dark current subtraction (unimportant for the Levy observations), and (5) fiat-field correction. The fiat-field image was generated on-orbit by observing the illuminated Earth and had no unusual features in the region of the CCD containing the comet. Cosmic ray events in the WFC are detected at the typical rate of - 2 . 2 sec -1 (Holtzman et al. 1991), but larger values are observed when the telescope passes near the South Atlantic Anomaly. Usually these events significantly affect the intensities in only a few pixels (often just one pixel). By comparing the Comet Levy images to a median-filtered image (using a filter window of 3 x 3 pixels), most single-pixel artifacts were easily removed using an automatic (i.e., computer) procedure. However, the procedure does not work well in regions where the intensities are comparable to the intensities induced by the cosmic ray events, such as near the nucleus. After running the cosmic ray rejection algorithm on the Levy images, a few features remain which appear to be singlepixel artifacts in the original images. Although the images could be improved cosmetically by removing these features by hand, this was not done on the principle that one should generally avoid making manual (subjective) corrections to data. While some of the data processing described in subsequent sections magnifies the effects of unremoved artifacts, it is usually possible to distinguish these image artifacts from real features. C. Image Deconoolution

The raw images of Comet Levy clearly show the effects of H S T 's spherical aberration (Burrows et al. 1991). The spatial brightness profile of the comet (discussed in the next section) is severely "flattened" near the nucleus due to the large extent of the H S T point spread function (PSF).

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In order to recover H S T ' s full spatial resolution capability, the Lucy-Richardson technique was used to deconvolve the images (Lucy 1974, Richardson 1972). The Lucy-Richardson deconvolution algorithm is an iterative method for extracting the " t r u e " intensity distgibution from images which have been blurred by the effects of the measurement process (e.g., blurring caused by the aberrated HSTprimary mirror for the problem considered here). The starting point in the iteration scheme is a uniform image in which each pixel intensity is set equal to the average pixel intensity in the observed image. Successive iterations then increase the likelihood (in a statistical sense) that the observed brightness distribution is the convolution of the estimated distribution (i.e., the deconvolved image) with the H S T PSF. Formally, the nth approximation of the deconvolved image is convolved with the PSF, divided by the observed image, the reciprocal taken, convolved again with the PSF, and multiplied by the nth approximation to form the (n + 1)st approximation of the deconvolved image. Further details can be found in the references given above. One shortcoming of the Lucy-Richardson technique is the inability to decide exactly where to stop the iteration process. A common method is to perform a X2 test comparing the observed image to the deconvolved image convolved with the PSF. However, as discussed by Lucy (1974), this procedure is not without pitfalls and still contains a subjective component. The procedure we followed is discussed later in this section. Deconvolutions were performed on a 211 × 211 pixel subregion centered on the nucleus of the original 1600 × 1600 pixel image. Near the periphery of this subregion the cometary signal was already becoming too weak to allow useful deconvolution. Accurate deconvolved images can be produced only if accurate PSFs are available. The PSF used to deconvolve both Comet Levy images was derived from the image of a star in the young cluster NGC 1850, which was imaged with the WFC through the F785LP filter on 20 September 1990. The stellar image was "cleaned" using DAOPHOT (Stetson 1987) to subtract other stars in the field. The center of the star used for the PSF was within 2 pixels of the location of the nucleus for one of the Comet Levy images and - 2 7 pixels from the location of the nucleus in the other Levy image. Simulations indicate that the same PSF can be used to deconvolve both Comet Levy images. The Comet Levy images were also deconvolved using other observed PSFs and theoretical PSFs. While small differences among the various deconvolved images can be discerned, the basic morphology of the coma is unaffected by the specific choice. The deconvolved images of Comet Levy presented here are mosaics created from a number of different images, each of which was produced using a different number of

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Lucy iterations. The inner l" of the coma was taken from a deconvolved image produced using 100 Lucy iterations. After 100 iterations the spatial brightness profile in the inner coma is "converging" in the sense that further iterations do not significantly change the pixel intensities. (For example, after 100 iterations the peak pixel intensity is - 7 times brighter than the value for the raw image and only - 4 % brighter than the value obtained after 90 iterations.) In moving from 1" to 5" from the nucleus, the mosaic uses fewer and fewer Lucy iterations (10 fewer Lucy iterations for every step of 0'.'5). At a distance of -5" from the nucleus, the mosaic uses a deconvolved image produced with only l0 Lucy iterations. In the outermost coma (more than 5'.'5 from the nucleus for one image and more than 7" from the nucleus for the other image), the mosaic simply uses the raw data (i.e., no deconvolution). Creating a mosaic deconvolved image in this way is justified (and preferred) for two reasons. First, the spatial scale over which the brightness distribution changes significantly becomes larger as one moves from the inner to the outer coma. Thus, the deconvolution algorithm should converge with fewer iterations in the outer coma and is not needed at all in those regions of the coma where the brightness distribution changes only on spatial scales larger than the extent of the PSF (-2-3"). Second, the deconvolution algorithm is ill-behaved when used with poor quality data. Since the signal-to-noise ratio of the cometary data falls rapidly with increasing distance from the nucleus, the use of the Lucy algorithm with many iterations produces numerous artifacts when applied to the outer coma. III. S P A T I A L M O R P H O L O G Y

A. Raw and Deconvolved Images The raw and deconvolved images of Comet Levy are shown in Fig. 1. All images are displayed using the same logarithmic intensity scale. Since the surface brightness distribution falls so rapidly with distance from the nucleus, displaying the images with a linear scale would show only the few brightest pixels. The most striking feature in all the images is the strong sunward-tailward brightness asymmetry, indicating that dust is emitted primarily from the sunlit side of the nucleus. The inner coma of the deconvolved images has a fan-like structure. As discussed in the previous section, the deconvolved images have a spatial brightness distribution which is much more sharply peaked toward the nucleus. (Note that there are no white pixels in the raw images.) B. Multiplication by p In a simplified model in which the coma is formed by the steady-state, isotropic ejection of material from an

unresolved (i.e., point) source, the surface brightness distribution of the coma will follow a p- ~law, where " p " is the projected distance to the nucleus. Although real comets display significant deviations from this simple picture, it is still true that spatial brightness profiles of comets observed in continuum light are often approximately p-1 in character. Thus, coma features are seen most readily after first multiplying images by the projected distance of each pixel from the nucleus. The latter (i.e., p) is calculated assuming that the nucleus is coincident with the center of the light distribution. The center of the light distribution can vary by a few tenths of a pixel depending on the algorithm employed and the size of the region used to determine the center. We used a 5 pixel region centered on the nucleus and took the average of the values determined from two different algorithms (the IMCNTR package in IRAF and a technique based on the DAOPHOT center-finding algorithm). Figure 2 shows the same four images displayed in Fig. 1 after multiplication by p. Besides the gross morphology seen in Fig. l, other aspects of the underlying structure in the coma become evident in Fig. 2. The severe flattening of the surface brightness distribution in the raw images and its removal by deconvolution is seen quite clearly. More importantly, the temporal changes in the Comet Levy images are now much more evident. The earlier image (on the left-hand side of the figure) shows a brightening near the nucleus on the sunward side, while the later image (on the right-hand side) shows a brightening farther out in the coma on the sunward side. As discussed in more detail later, this is evidence that the level of dust activity increased shortly before the time of the first exposure, producing an arc of dust which then propogated outward through the coma. There also appears to be a depression on the tailward side at - 2 " from the nucleus in both deconvolved images. Since the feature is located many pixels from the peak of the brightness distribution, it is unlikely to be an artifact of the deconvolution. Deconvolved images produced using different PSFs also show the feature. If the light observed on the tailward side of the nucleus is due primarily to scattered light from grains emitted on the sunward side, then the depression might represent a "dynamical shadowing" effect of the type described by Wallace and Miller (1958). We note that a similar feature may have been detected in Comet Halley (Hoban et al. 1989), although it was -15 times farther from the nucleus than the feature in Comet Levy. Quantitative information on the spatial morphology was obtained by extracting radial brightness profiles for four quadrants (i.e., 90° sectors) in each image. Figures 3 and 4 show these profiles for the raw and deconvolved images, respectively. Each displayed value represents the average intensity for all the pixels in the quadrant within a fixed

IMAGING OF COMET LEVY (1990c) WITH HST range of radii (typically 0" 1). Except in the case of the peak pixel, the error bars represent the standard deviations of the individual pixel intensities which were included in the average. For the peak pixel the error bar is the estimated noise in the intensity due to photon counting statistics and CCD readout noise; the peak signal-to-noise ratio is - 6 0 for both images. Also, a value of p = 0"029 is assigned to the peak pixel because we estimate (from numerical modeling) that a square pixel centered on a pure p - l surface brightness distribution would have the same intensity as the line of sight value along p = 0"029. The projected vector to the Sun bisects the quadrant shown at the upper left of each plot. Thus, the upper-lefthand plot is the sunward quadrant and the lower-righthand plot is the tailward quadrant. The solid line in each plot is the expected profile for isotropic, uniform outflow with constant velocity (i.e., a pure p - 1 surface brightness distribution). The intensities in the sunward quadrant are larger than the intensities in the tailward quadrant by more than a factor of 2. The intensities in the other two quadrants are nearly equal to each other and also are approximately equal to the mean of the intensities in the sunward and tailward quadrants. A single line-cut perpendicular to the Sun-comet vector (not plotted) fairly closely follows a p -1 variation right up to the brightest pixel. The sunward quadrant shows the largest deviations from uniform, isotropic outflow. One of the images shows a clear " h u m p " in the innermost coma while the other image has a hump farther out in the coma. This behavior is completely consistent with the description discussed above with regard to the images in Fig. 2. The depression in the tailward quadrant can only be seen in the plots for the deconvolved images. Except for this depression, the tailward brightness profile follows a O-1 law remarkably well. By examining the profiles in all four quadrants, there is some indication that the depression is more extended azimuthally for the earlier image (i.e., the one with the hump in the inner coma). Azimuthal spatial brightness profiles derived from the deconvolved images are shown in Fig. 5. The images of Comet Halley taken by the Giotto Halley Multicolor Camera (HMC) showed multiple narrow-angle dust structures, usually referred to as "jets" (Keller et al. 1987). Detailed analysis of these structures (Reitsema et al. 1989) revealed that most of the dust in the coma of Halley at the time of the observations was emitted in three jet-like structures. In the azimuthal direction, these structures were approximately Gaussian in shape with F W H M 50o-85 ° . While the azimuthal brightness profiles of Comet Levy are also rather Gaussian in appearance, the profile widths are much broader with F W H M - 135°. Nevertheless, the dust emission in Comet Levy is clearly not isotropic over the sunlit hemisphere.

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The spatial resolution of the Giotto HMC was several hundred times better than HST's resolution on Comet Levy, and this may partly explain why the H S T Levy images do not show narrower features. Poor spatial resolution smooths multiple narrow jets into a single broad feature. Examination of HMC images taken well before the time of closest approach demonstrates that one loses the ability to distinguish individual jets as the spatial resolution is degraded. Thus, the presence of a broad dust fan in the HST images of Comet Levy may not rule out the existence of Halley-like dust jets in Levy, although this seems unlikely since even ground-based images of Comet Halley showed jet-like structures (cf. Sekanina and Larson 1986). C. Subtraction o f a p-I Image

As mentioned previously, a comet having uniform, isotropic outflow of dust from a point source would have a pure p - i spatial brightness profile at small a. We have constructed an image of this "ideal" comet, convolved it with the H S T PSF, and then subtracted it from the observed Comet Levy images. The intensity of the model comet is normalized so that it asymptotically matches the intensity in the observed Comet Levy image along the perpendicular to the Sun-comet line. These difference images are shown in Figs. 6 and 7. Since the brightness profile varies so strongly with distance from the nucleus, there was some concern that the morphology produced in the difference image would depend on the relative alignment of the observed and model images. Thus, we constructed a matrix of difference images, each having a different relative alignment. In the central frames of Figs. 6 and 7, the photocenter of the observed and model images are exactly aligned. For all other frames, the model has been shifted by - 0 . 5 pixel relative to exact alignment in the direction indicated by the placement of the frame in the figure. As Figs. 6 and 7 demonstrate, the same basic coma morphology is evident in all images. Each image shows a sunward-facing fan whose axis is approximately aligned with the Sun-comet vector. As expected from the earlier discussion, the difference between the first Levy image and the model (Fig. 6) shows more of a brightening in the inner coma than the difference between the second Levy image and the model (Fig. 7). Also, the azimuthal dependence of the fan is consistent with the plots shown in Fig. 5. IV. TEMPORAL VARIABILITY A. Difference Image

Figure 8 shows an image obtained by subtracting the first Comet Levy image from the second one taken 6.5 hr

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later, multiplying each pixel's intensity by its distance from the optocenter, and then smoothing the result with a 3 x 3 pixel boxcar. The photocenters of the two images were aligned prior to subtraction. Two azimuthal profiles for this image are shown in Fig. 9, while the radial brightness profiles as a function of quadrant are shown in Fig. 10. (The deconvolved difference image shows the same general morphology as Fig. 8, but the deconvolved image is smaller since the deconvolution is not valid for P 5". Also, the radial brightness profiles derived from the deconvolved difference image are quite similar to those shown in Fig. 10.) In Fig. 8 there is a region of negative intensities in the inner coma on the sunward side and a region of positive intensities in the outer coma on the sunward side. The position angle of the positive region is not dependent on the exact alignment of the two input images prior to subtraction. The position angle of the negative region does change with the relative alignment, but by examining the spatial brightness profiles for the two individual images it is clear that the negative region should be located in the sunward quadrant. An independent analysis of the Comet Levy images was performed by fitting the isophotes in each 4-sec image with ellipses (Malumuth, Norman, and Brandt, private communication, 1991). A difference image was then constructed by subtracting one model ellipse image from the other, and the resulting coma morphology was completely consistent with that displayed in Fig. 8. The morphology observed in Fig. 8, and depicted graphically in the spatial brightness profiles, demonstrates that the coma of Comet Levy was not in steady state. At a distance of-1'.'5 on the sunward side of the nucleus, the first image is significantly brighter than the second. At a

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distance of - 6 " on the sunward side of the nucleus, the second image is significantly brighter than the first. We propose that the rate at which dust was emitted from Comet Levy's nucleus peaked shortly before the time of our first HST observation. Most of the dust associated with the increase in activity was ejected on the sunward side of the nucleus. Thus, we seem to be witnessing an arc of dust propagating through the sunward side of the coma. We note that similar arcs were detected at much larger distances from the nucleus in ground-based images obtained on 17 September 1990 (Larson and Levy 1990) and on 26-27 September 1990 (our own unpublished data taken contemporaneously with the HST data). B. Dust Velocity From the positions of the positive and negative arcs in Fig. 8, the average projected velocity of the dust between these two points can be derived. Our best estimate for the velocity is 0.16 km sec- 1based on a close examination of the radial spatial brightness profile for a small region of azimuthal angles centered on the Sun-comet line where the intensities are peaked. However, as is evident from Fig. 10, the minima and maxima in the spatial brightness profiles are rather broad and somewhat asymmetrical, so the choice for the positions of the minima and maxima has a subjective component. Roughly speaking, the minimum intensity in the difference image occurs at -I':5 from the nucleus, while the maximum intensity occurs at - 6 " from the nucleus. Thus, the separation is -4'.'5 which corresponds to a projected velocity of 0.15 km sec -~. In our view, it is difficult to justify a separation that differs by more than -0':5 from our " b e s t " estimate based on an

FIG. 1. A pair of raw and deconvolved 4-sec H S T WFC images of Comet Levy (1990c) taken through the F785LP filter (-/-band). Raw images are at the top and deconvolved images are at the bottom. The image on the left-hand side was taken 6.5 hr before the image on the right-hand side. The compass shows N(orth), E(ast), the direction to the S(un), and the velocity vector of the C(omet). Each pixel subtends 0':1 (78 km at the comet) and each of the four image frames subtends 21'.'1 x 21"1 (16,400 km x 16,400 km at the comet). All images show a highly asymmetrical coma with most of the emission being directed into the sunward-facing hemisphere. The deconvolved images show a fan-shaped coma whose axis of symmetry is nearly aligned with the Sun-comet line. Deconvolution increases the intensity of the peak pixel by a factor of - 7 . The PSF used to deconvolve the images is shown at the same spatial scale in the lower right-hand corner. FIG. 2. The same images shown in Fig. 1 have been multiplied by the distance of each pixel from the photocenter, enabling one to see coma features that would otherwise be diluted by the rapid decrease in brightness with increasing distance from the nucleus. The compass and image frame sizes are exactly as described in Fig. 1. The position of the nucleus is marked in each frame with " + ." The cometary image to the left is brighter in the inner coma (p -< 2"), while the image to the right is brighter in the outer coma (p - 6'3, consistent with the hypothesis that an increase in cometary activity occurred shortly before the time the first image was obtained producing a shell of dust on the sunward side which then propagated through the coma. Image deconvolution was performed only over the circular regions that are evident in the bottom half of the figure. FIG. 8. A difference image obtained by subtracting one raw HST image from another taken 6.5 hr later, multiplying each pixel's intensity by its distance from the optocenter, and then smoothing the result with a 3 x 3 pixel boxcar. Assuming that the negative feature in the inner coma is physically related to the positive feature farther out, we suggest that this difference image is showing an arc of dust moving sunward through the coma with an average projected velocity of -0.16 km sec -1. The position of the nucleus is marked with " + ." The compass in the lower righthand corner has the same meaning as that for Fig, 1. Each pixel subtends. 0':1 (78 km at the comet) and the full image frame subtends 18"6 × 20"8 (14,500 km x 16,100 km at the comet).

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FIG. 3. Radial spatial brightness profiles for the two images at the top of Fig. 2 (i.e., the raw data multiplied by p). The values plotted were obtained by taking, at s u c c e s s i v e radii, the average intensity over a particular quadrant (using our c o n v e n t i o n that angles are m e a s u r e d counterclockwise from the direction of increasing C C D columns, plots a, b, c, and d are averages over the following azimuthal angles, respectively: 90°-180 °. 0°-90 °, 180°-270 °, and 270°-360°). The S u n - c o m e t line bisects the q u a d r a n t s displayed in (a) and (d), with the vector pointing toward the sun lying in (a). Also plotted is the spatial profile for a steadystate, spherically s y m m e t r i c model comet, which m a t c h e s the observed distributions asymptotically in a direction perpendicular to the S u n c o m e t line. The data s h o w a large (factor of - 2 ) s u n w a r d - t a i l w a r d brightness a s y m m e t r y . In the s u n w a r d quadrant (a), one observed image s h o w s a peak at - 1':5 from the nucleus, while the other image has a peak at - 6 " from the nucleus. The plots showing data from the second image (upper right-hand side of Fig. 2) appear to have slightly thicker lines, since those data are plotted with error bars included.

indicates that muliplying by p can produce a shift in the positions of peaks in spatial brightness profiles by -1-2". Since this shift affects the peak positions in both images, the difference in the peak positions seems to be essentially unaffected, so we do not believe that our derived velocity is significantly changed by this effect. Second, in discussing the data from the difference image it should be noted that the velocity was derived by dividing the distance between the inner and outer arcs by 6.5 hr, since the second image was taken 6.5 hr after the first image. For a temporal variation that is purely sinusoidal, the velocity is obtained by dividing the distance between adjacent peaks and valleys by one-half of the lightcurve period (i.e., -8.5 hr according to Feldman et al. 1992). However, as discussed later, the temporal variation of the dust production rate in Comet Levy is clearly not purely sinusoidal. The true dust velocity might differ significantly from the projected value, if the dust emission is concentrated into narrow jets near the line of sight. Since the Comet Levy images show no strong evidence for narrow jets, we suspect that the projection effects are small. Even for the case of a narrow jet aligned along the Sun-comet line, the projection effect will only be -20% (i.e., since the Sun-comet vector lies - 3 4 ° out of the plane of the sky, a measured projected velocity o f - 0 . 1 6 km sec ' corresponds to a true velocity of -0.19 km sec-f). The dust velocity derived from the HST Levy images

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analysis of Figs. 8 and 10, which implies that the average projected velocity lies in the range 0.14-0.18 km sec I A projected dust velocity near 0.16 km sec i is also indicated by inspection of the individual images (as opposed to looking solely at the difference image). Examination of the data from the two deconvolved images (lower half of Fig. 2 and Fig. 4a) shows a peak in one image at - l " from the nucleus and a peak in the other image at -6". A similar morphology is suggested by the raw images (upper half of Fig. 2 and Fig. 3a), although the severe "flattening" of the spatial brightness profile due to the poor PSF makes drawing a conclusion about the dust velocity much more difficult in this case. However, we should point out that there are possible systematic errors associated with our analysis. First, we have derived a velocity by examining spatial brightness profiles for images in which the intensities have been multiplied by p. Our numerical modeling (described later)

x

0

I00

b

a

x

0

0 5 10 15 Arcsee from Center

5 10 15 Arcsec from Center

400

400

o 300

~ 300 X

X

2o0

100

~

20O

~

100

e

~

0

0 5 10 15 Aresee from Center

0

d 0 5 10 15 Aresee from Center

FIG. 4. Same as Fig. 3 except for the d e c o n v o l v e d images (i.e., the two images displayed in the lower half of Fig. 2). The plots showing data from the second image (lower right-hand side of Fig. 2) appear to have slightly thicker lines, since those data are plotted with error bars included.

IMAGING O F C O M E T LEVY (1990c) WITH HST ~'~ 4oo

"~ 400

,~. 3 0 0

~, aoo

200

200

"~ cL 100

i i • a. . . . . . . . . . . . . . . . . . . . .

o

o

N

'

i00

0

100 200 300 400 Angle (Deg)

100 200 300 400 Angle (Deg)

"~ 400

~" 400 0

Q.

'i

o

~ 300

300 200

~

tO0

"-" 100 i. . . . . . . . .

0

.........

100 200 300 400 Angle (Deg)

200 i I I

0

0

93

the gas; at the spatial resolution considered here this decoupling point can be considered coincident with the nucleus). After a time t the grain reaches the hump at a projected distance of -1'.'9 from the nucleus (the projection factor is 0.83). At t + 6.5 hr the grain reaches the hump at -6"6. (The positions of the humps are the values after removing the distortion caused by muliplying the image by p; the l-dim model described later was used to estimate the magnitude of this distortion.) Much later the grain reaches the " a p e x " point at which time its velocity becomes zero and it starts to turn tailward. For a given apex distance, one can then write down three independent equations of motion for the grain in the three unknowns, O0, a p t , and t. Although the exact apex distance is also unknown, we have obtained ground-based/-band images of Comet Levy on UT 26-27 September 1990 which indicate that the apex is more than 50" from the nucleus.

100 200 BOO 400

Angle (Deg)

FIG. 5. Azimuthal spatial brightness profiles: (a) and (b) are for an inner (1" -< p <- 1"5) and an outer (5" -< p ~ 5'.'5) annulus, respectively, for the image in the lower left-hand corner of Fig. 2. Angles are measured counterclockwise from the direction of increasing CCD columns. Celestial North is at an angle of 202 ° and East is at 292 °. Plots (c) and (d) show the same thing for the image in the lower right-hand corner of Fig. 2. All plots show that the emission is roughly Gaussian with F W H M = 135° and has an axis of symmetry approximately aligned with the S u n - c o m e t line (the dashed vertical line gives the position angle of the vector pointing toward the Sun). The spike in (c) is probably caused by an unremoved cosmic-ray event.

seems surprisingly low. The historical evidence on the speeds of expanding coma halos, as summarized by Bobrovnikoff (1951), indicates values o f - 0 . 5 - 1 km sec-~. Most of the early work on cometary dust tails estimated that the dust velocity at -50-100 km from the nucleus (where the dust and gas become decoupled) is -0.5 km sec -I (cf. Finson and Probstein 1968). More recent models give considerably lower dust velocities with values approaching the number observed for Comet Levy for grains having radii larger than - 2 k~m (cf. Gombosi et al. 1986). However, the velocities predicted from the hydrodynamic models depend on many factors, some of which are poorly known, so drawing a definite conclusion about the size of the dust from this consideration alone is difficult. Further information on the size and nature of the dust in Comet Levy can be obtained by examining the dynamics of a grain in the dust arc that is emitted along the Sun-comet direction. In the frame of the comet, the grain experiences a constant acceleration (apt) due to solar radiation pressure that is directed opposite to its initial motion. We assume that the true initial grain velocity is v0 (i.e., v0 is the velocity of the grain as it decouples from

I

-50

,

,

,

,

I

,

,

,

,

0

I

50 Intensity

I

100

(ADU)

FIG. 6. The difference between the first raw Comet Levy image and a model comet image having a pure p-~ surface brightness distribution. The model image was convolved with the H S T P S F prior to subtraction. In the central frame, the centroids of the observed and model images are exactly aligned. For all other frames, the model has been shifted by ~0.5 pixel (in the same direction the frame is displayed relative to the central frame) relative to the centroid of the observed image in order to show the sensitivity to small misalignments o f the images. Each of the nine frames subtends 21'.'1 x 21".1 (16,400 km x 16,400 km at the comet). In all cases, the images show the same basic morphology; a sunwardfacing fan whose axis is approximately aligned with the S u n - c o m e t vector.

94

W E A V E R ET AL.

t..,

6o 4o

20

~"

60

~

4o

~

20

b

N

0

~ 0 e~ < --20

~.~ - 2 0 Q.. - 4 0 x

-40

-60

x

-60

5 10 15 Arcsec from Center

60

0 5 10 15 Arcsec from Center

"~ e

40

60

d

40

20

'~

20

X

0

x

-20

-40

-40:

-601

-60

0 5 10 15 Arcsec from Center

i

L

L

.

.

.

.

50

•

,

L

L

0

L

50

1

~

,

J

1 O0

hH c~si[y (AI)i) FIG. 7. Same as Fig. 6 except for the second raw C o m e t L e v y image, which was taken 6.5 hr after the first image.

Assuming that the apex lies at projected distances between 50" and 100" from the nucleus (all of the quantities below, except a p d / Q p r, become essentially independent of the apex distance as long as the latter is larger than -50"), and allowing for the full range of " r e a s o n a b l e " values for the positions of the " h u m p s , " the equations of motion give the following limits:

S

0

-20

5 10 15 Arcsec from Center

FIG. 10. Radial spatial brightness profiles showing the temporal changes in the H S T C o m e t L e v y images. T h e radial brightness profile was extracted for four quadrants of the image s h o w n in Fig. 8. The sunward-facing quadrant (a) s h o w s a p r o n o u n c e d m i n i m u m and maxim u m that we propose represents the motion of a dust arc through the coma. If this interpretation is correct, then the projected dust velocity is --0.16 km sec i.

0.17-< o 0 - < 0 . 2 2 k m s e c 0.015 ~

1

Opt. --% 0 . 0 5 1 c m s e c

2

and 1.9 -< t --< 3.3 hr. Thus, the ratio of the solar radiation pressure force to the solar gravitational force (fi) falls in the range

0

........

' " 1 '

.........

'a .......

) L

"6"

-20

X

i

~ -4o

< x

40

e-~

20

The product of the grain radius (a) and density (Pd) is related to /3 and the radiation pressure efficiency factor (Qpr) by (Burns et al. 1979)

0

N ~

0.028 -
60

¢)

<

8O

--60

,.

0

L. . . . . . . . .

100 2 0 0 3 0 0 4 0 0 Angle (Deg)

apd = (0.57)Qpr//3.

-20 0

100 2 0 0 3 0 0 4 0 0 Angle (Deg)

FIG. 9. A z i m u t h a l spatial brightness profiles for the image s h o w n in Fig. 8: (a) is for an inner a n n u l u s (1" -< p ~ 1'.'5) and (b) is for an outer a n n u l u s (5" -< O -< 5'.'5). Angles are defined exactly as described for Fig. 5. The d a s h e d vertical line gives the position angle of the vector pointing toward the Sun. The spike in (a) is probably caused by an u n r e m o v e d cosmic-ray event in one of the c o m e t a r y images.

Thus we find 5.9 -< apa/Qp r <- 20/2m g cm 3. In the geometrical optics limit

(Qpr =

1)

5.9 -- apd <-- 20 /zg g cm -3 (geometrical optics).

IMAGING OF COMET LEVY (1990c) WITH HST

For a grain with the same optical properties as the grains in Comet Halley (1.6 -< Qpr ~ 2.2 for a -> 0.5 ~m; Hoban 1989) 9.4 - apd <-- 44 /xm g

cm -3

(Halley-like grains).

We emphasize that the above derived limits on/3 and apd are valid only if projection effects are insignificant. If

the latter is true, then the simplest interpretation for the observed dynamical behavior is that the dust arcs consist primarily of large grains (for Pd = 1 g cm-3, a - 5/~m). However, then one is faced with the problem of explaining how such large grains could dominate the light observed in the H S T images. Grains having radii in the range 0.5-2 ~m should be efficient scatterers in the/-band region, and they should be much more abundant than the larger grains if the Levy dust size distribution is similar to that of Halley (cf. Mazets et al. 1987). On the other hand, we note that Mie theory calculations at shorter wavelengths (specifically, at h = 4845 ,~ and ~ = 6840 ,~) indicate that, even for the Halley dust size distribution, approximately half of the radiation measured at wavelength h0 is scattered by grains having radii --4h 0 (Hoban et al. 1989). Thus, the dynamical constraint favoring large grains in the Levy dust arc may not be incompatible with the requirement that these grains also contribute the bulk of the scattered light at h - 0.9/xm. We also note that the values obtained here for the dust ejection velocity and for/~ are consistent with the v0, /3 relationships derived from the study of various dust features observed in the coma and tail of a number of comets (Sekanina 1988, Richter and Keller 1988). For example, the range of values 0.17-0.22 km sec-1 for v0 corresponds, according to these empirical laws, to values of 0.015-0.130 for/3, a range which encompasses the limits we derive for this parameter in Comet Levy. In an independent analysis of these H S T images, Fulle et al. (1991) reached somewhat different conclusions. They found that the dust velocity near the nucleus (the true velocity, not the projected value) was 0.35 km secand that/3 = 0.36 (no error estimates are reported). They contend that our conclusions are incorrect because we analyzed features located within - 2 " of the nucleus, which are not reliable. Fulle et al. ignored this inner coma and instead extracted radial brightness profiles out to p 40", revealing at least three more arcs ( " a r c " here means either a positive or a negative feature in the difference image). They used a model to fit the data in the outer coma, and then used that same model to infer the velocity in the near-nucleus region. As discussed earlier, we do not believe that our analysis of features within 2" of the nucleus are subject to any large systematic error. We concentrated on the innermost coma because that is where H S T can make

95

a u n i q u e contribution to the imaging of Comet Levy; the H S T data for p > 5" are of considerably poorer

quality than those obtained from large ground-based telescopes (including our own unpublished ground-based images). Nevertheless, it appears to us that the radial brightness profiles presented by Fulle et al. are consistent with a projected velocity of -0.16 km sec-I in the region 20-30" from the nucleus (i.e., divide the separation of adjacent peaks (or valleys) in the Fulle et al. profile by a period of 17 hr), and that these results are also consistent with our ground-based data in the same region of the coma. The principal point of contention concerns the velocity in the near-nucleus region. Fulle et al. claim that the dust leaves the nucleus at a fairly high velocity (0.35 km sec 1), while our value is considerably lower (-0.19 km sec -~ after taking into account radiation pressure). In the Fulle et al. model the dust is strongly decelerated while in our picture the deceleration is about 10 times weaker. Both analyses give a dust velocity of -0.16 km sec- 1 for 0 - 20". But in the Fulle et al. model the dust apex distance is -30" from the nucleus, which is inconsistent with the groundbased data. Finally, we note that Fulle et al. claim that the spatial morphology in the Levy images is caused by the uniform rotation of a nucleus having two active areas on opposite sides of the nucleus with a period of 12 hr. Such a scenario would require that the lightcurve have a 12-hr period, which is inconsistent with the I U E and ground-based data. C. R e l a t i v e P h o t o m e t r y

Figures 1la and 1lb show relative photometry extracted from the Comet Levy images. The percentage change in the comet's brightness depends strongly on the aperture size. For the smallest apertures, the temporal variation is -30%. For apertures which are -12"-14" across (total width), the total fluxes contained in the two H S T images are almost identical. D. M o d e l i n g

We have attempted to reproduce the general morphology observed in the H S T images of Comet Levy using a one-dimensional radial outflow model in which the production rate of dust varies with time (the model follows the method of Kaneda et al. 1986). Two production rate functions were investigated: a constant background source plus a sinusoidal temporal variation, and a constant background source plus a periodic step function (i.e., an outburst-type phenomenon). The model assumes that the dust travels with a single velocity, that there is no solar radiation pressure, and that the temporal variability is purely periodic (i.e., only a single frequency of variation, or harmonics of that value, is allowed).

96

W E A V E R ET AL. 5

5

-5 -15 -25

V. A B S O L U T E

_

f

a)

-5 -15

-25 a

b

~- - 3 5

a. - 3 5

0 2 4 Half-Aperture

0 2 4 6 8 Half-AperLure (aresec)

106

6 8 (arcsee)

14

105 104

' ~ 10

~

'~ 103 c

1o 2

0.1 1.0 Half-Aperture

a

I

10.0 (arcsec)

6 0.1 1.0 Half-Aperture

d 10.0 (arcsec)

FIG. 11. P h o t o m e t r y of C o m e t Levy: (a) and (b) show the temporal variation (in % difference) in the c o m e t ' s brightness as a function of aperture size for two images separated by 6.5 hr. In (a) we compare " b o x " (K]) p h o t o m e t r y to " c i r c l e " ( + ) photometry for the raw data. In (b) we c o m p a r e circle p h o t o m e t r y for the raw data ( + ) to circle photometry for the d e c o n v o l v e d data (5). Both (a) and (b) d e m o n s t r a t e that the o b s e r v e d temporal variation is a strong function of the aperture size. In (c) we s h o w the count rate (in A D U sec [) for the average of the two c o m e t images as a function of the aperture size. The raw data ( + ) show a severe " f l a t t e n i n g " effect in the inner coma, while the deconvolved data ( 5 ) d e m o n s t r a t e that the c o m e t a r y flux is a linear function of the aperture size over the entire range 0"1 <- p -< 10" (compare the data to the solid line). Plot (d) s h o w s the same data as (c) e x p r e s s e d in terms of /-magnitude.

Although we did not conduct an exhaustive search over the available phase space, it appears that no combination of different input parameters to the model can reproduce the observed spatial brightness profiles. While the gross morphology of the coma (e.g., separations and amplitudes of peaks and valleys in the brightness distribution) can be reasonably well matched with appropriate choices of model parameters, the fit of the model to the data is clearly unsatisfactory in detail, especially with regard to the shape of the brightness profile. There are many possible explanations for this discrepancy including: (1) the coma of Comet Levy is strongly anisotropic, which may imply that a onedimensional model is simply inappropriate, (2) the production rate function may be more complex than what we have assumed, and (3) there is a dispersion of velocities (e.g., velocity sorting according to grain size) instead of the monokinetic case we have considered. A more sophisticated model is being developed (Samarasinha, private communication, 1991) that could remedy most of the current deficiencies.

PHOTOMETRY

Figures 1 lc and I ld show absolute photometric information for the average of the two H S T Comet L e v y images. The flux in the coma as a function of aperture size is plotted for both the raw and the deconvolved data. The flux is expressed in two different units: ADU sec J, which is an instrumental unit, a n d / - b a n d magnitude, which is the usual astronomical unit. The formulas in H o l t z m a n et a/. (1991) and Harris et al. (1991) were used to convert from instrumental units into astronomical units. We conservatively estimate that the error in the absolute magnitude is - 0 . 4 mag. The precision in the relative fluxes plotted in Fig. 11 is considerably better ( - 1 0 % ) . As defined here, the " m a g n i t u d e " of the comet is to be interpreted in the following way: the c o m e t a r y flux within the specified aperture size is equal to the total flux for a star of that same magnitude, where " t o t a l " means that the stellar flux has been integrated o v e r the entire stellar image (i.e., integrate o v e r a radius of - 3 " for an H S T stellar image). For the time-averaged deconvolved data, the flux increases linearly with aperture size o v e r the entire range of radial distances considered in this paper (0'.'1 -< p -< 10"). The following formula represents the r e l a t i v e / - b a n d magnitude to within 10%, 1 = - 2 . 5 l o g p + 10.45, where p is the aperture radius in arcseconds. As mentioned earlier, the absolute error is - 0 . 4 mag. The raw data show a severe "flattening" in brightness within - 1 " of the nucleus, consistent with expectations from convolution of the comet's brightness distribution with the H S T ' s PSF. VI. C O N C L U S I O N S

Images of Comet L e v y were obtained with the H S T at a spatial resolution of - 7 8 km. These images show a highly asymmetrical coma in which the sunward-facing hemisphere is more than a factor of 2 brighter than the tailward hemisphere, consistent with volatile sublimation occurring primarily on the dayside of the nucleus. The azimuthal dependence of the spatial brightness distribution on the sunward side is roughly Gaussian in shape with F W H M - 135 ° and an axis of s y m m e t r y that is nearly coincident with the projected S u n - c o m e t line. Radial brightness profiles perpendicular to the S u n - c o m e t line are very symmetric about the nucleus and follow a p-J law rather closely to the limit o f l i S T ' s spatial resolution. For the time-averaged surface brightness distribution, the relative/-band magnitude increases linearly with aperture size over the entire range 0'.'1 -< p -< 10".

97

IMAGING OF COMET LEVY (1990c) WITH HST

Comet Levy was clearly not in steady state, and the high spatial resolution H S T images permitted a detailed examination of the inner coma where changes due to temporal variability are most pronounced. The temporal variability in Levy appears to be associated with the release of an arc of dust into the sunward hemisphere. The intensity in the arc is consistent with the amplitude of photometric variations observed from I U E and the ground. The average projected velocity of the dust in the arc in the near-nucleus region is 0.16 - 0.02 km sec-~, where the uncertainty represents our best estimate of the various possible sources of systematic error. The true dust velocity might differ significantly from the projected value, if the dust emission is concentrated into a narrow jet near the line of sight, but this does not appear to be the case for Comet Levy. The projected and true velocities probably differ by only - 2 0 % or less, which means that the true dust velocity is unlikely to be larger than -0.22 km sec - 1. Assuming that projection effects are insignificant, the ratio of the solar radiation pressure force to the solar gravitational force is very small (0.028 -
ACKNOWLEDGMENTS First and foremost we thank Riccardo Giacconi for granting us Director's Discretionary telescope time to perform this investigation. Timely ephemeris support from Don Yeomans was crucial in making this program feasible. The program's successful execution was due to the dedicated support from many people working in the H S T ground system, but we especially thank Glenn Schneider for his careful scrutiny of the entire observing plan, and the STScI's Moving Targets group (Marc Buie and Andy Lubenow) for general support. We thank Rick White for allowing us to use his deconvolution program and for numerous discussions on deconvolution issues. Ed Smith assisted with some of the data reduction and analysis. Hashima Hasan provided help in constructing theoretical PSFs. Dave Schleicher provided information on ground-based observations of Comet Levy prior to publication, as well as many insightful comments concerning the comet's temporal variability. We thank Nalin Samarasinha for discussions concerning his modeling of Levy's temporal variability and Michel Festou for discussions on dust velocities. The comments of two reviewers (Stephen Larson and an anonymous referee) helped to clarify some aspects of the paper. We thank Marco Fulle, Fabio Pasian, and Piero Benvenuti for several stimulating discussions concerning the analyses of the H S T images. Support for this work was provided by N A S A through Grant GO-3064.01-87A from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA Contract NAS5-26555.

REFERENCES BOBROVNIKOFF, N. T. 1951. Comets. In Astrophysics (J. A. Hynek, Ed.), pp. 302-356. McGraw-Hill Book Company, Inc., New York. BURNS, J. A., P. L. LAMY, AND S. SOTER. 1979. Radiation forces on small particles in the Solar System. Icarus 40, 1-48. BURROWS, C. J., et al. 1991. The imaging performance of the Hubble Space Telescope. Astrophys. J. 369, L21-L26. FELDMAN, P. D., S. A. BUDZIEN, M. C. FESTOU, M. F. A'HEARN, AND G. P. TOZZI 1992. Ultraviolet and visible variability of the coma of Comet Levy (1990c). Icarus 95, 65-72. FINSON, M. L., AND R. F. PROBSTEIN 1968. A theory of dust comets. I. Model and equations. Astrophys. J. 154, 327-352. FULLE, M., F. PASIAN, AND P. BENVENUTI 1991. HST observations of the inner coma of Comet Levy 1990c. Ann. Geophys., in press. GOMBOSI, T. I., A. F. NAGY, AND T. E. CRAVENS 1986. Dust and neutral gas modeling of the inner atmospheres of comets. Rev. Geophys. 24, 667-700. HARRIS, H. C., W. A. BAUM, D. A. HUNTER, AND T. J. KREIDL 1991. Photometric calibration of the HST wide-field/planetary camera. I. Ground-based observations of standard stars. Astron. J. 101, 677694. HOBAN, S. 1989. Comet Halley: An Optical Continuum Study. Ph.D. thesis, University of Maryland. HOBAN, S., M. F. A'HEARN, P. V. BIRCH, AND R. MARTIN 1989. Spatial structure in the color of the dust coma of Comet P/Halley. Icarus 79, 145-158. HOLTZMAN, J. A., et al. 1991. Stellar photometry with the Hubble Space Telescope wide-field/planetary camera: A progress report. Astrophys. J. 369, L35-L40. HooPIS, H. L., W.-H. IP, AND D. A. MENDIS 1985. The chemical differentiation of the cometary nucleus: The process and its consequences. Astrophys. J. 295, 654-667. KANEDA, E., O. ASHIHARA, M. SHIMIZU, M. TAKAGI, AND HIRAO, K.

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RICHARDSON, W. H. 1972. Bayesian-based iterative method of image restoration. J. Opt. Soc. Am. 62, 55-59.

KELLER, H. U., et al. 1987. Comet P/Halley's nucleus and its activity. Astron. Astrophys. 187, 807-823. LARSON, S., AND D. LEVY 1990. Comet Levy (1990c). IAUC 5098. LAtJER, T. R. 1989. The reduction of wide-field/planetary camera images. P A S P 101, 445-469. Lucy, L. 1974. An iterative technique for the rectification of observed distributions. Astron J. 79, 745-754. MAZETS, E. P., R. Z. SAGDEEV, R. L. APTEKAR, S. V. GOLENETSKll, YU A. GURYAN, A. V. DYACHKOV, V. N. ILYINSKII, V. N. PANOV, G. G. PETROV, A. V. SAVVlN, I. A. SOLOKOV, D. D. FREDRICKS, N. G. KHAVENSON, V. D. SHAPIRO, AND V. I. SHEVCI-IENCKO1987. Dust in Comet P/Halley from Vega observations. Astron. Astrophys. 187, 699-706. REITSEMA, H. J., W. A. DELAMERE, A. R. WILLIAMS, D. C. BOICE, W. F. HUEBNER, AND F. L. WHIPPLE 1989. Dust distribution in the inner coma of Comet Halley: Comparison with models. Icarus 81, 31-40.

RICHTER, K., AND H. V. KELLER 1988. The anomalous dust tail of Comet Kohovtek (1973 XII) near perihelion, Astron. Astrophys. 206, 136-142. SCHLEICHER, D. G., R. L. MILLIS, D. J. Os1P, AND P. V. BIRCH 1991. Comet Levy (1990c): Groundbased photometric results. Icarus 94, 511-523.

SEKANINA,Z. 1988. Outgassing asymmetry of periodic Comet Encke. Ii. Apparitions 1868-1918 and a study of the nucleus evolution. Astron. J.

96, 1455-1475, and reference therein. SEKANINA, Z.. AND S. M. LARSON 1986. Dust jets in Comet Halley observed by Giotto and from the ground. Nature 321, 357361. STETSON, P. B. 1987. DAOPHOT: A computer program for crowdedfield stellar photometry. PASP 99, 191-222. WALLACE, L. D., AND F. D. MILLER 1958. lsophote configurations for model comets. Astron. J. 63, 213-219.