Tempel 1

Icarus 191 (2007) 11–21 www.elsevier.com/locate/icarus

The nucleus of Deep Impact target Comet 9P/Tempel 1 ✩ Y.R. Fernández a,∗,1 , K.J. Meech a , C.M. Lisse b,1 , M.F. A’Hearn b,1 , J. Pittichová a , M.J.S. Belton c,1 a Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Drive, Honolulu, HI 96822, USA b Department of Astronomy, University of Maryland, College Park, MD 20742-2421, USA c Belton Space Exploration Initiatives, 430 S. Randolph Way, Tucson, AZ 85716, USA

Received 2 December 2002; revised 23 February 2003

Abstract On UT 2000 August 21 we obtained simultaneous visible and mid-infrared observations of Comet 9P/Tempel 1, the target of the upcoming NASA Discovery Program mission Deep Impact. The comet was still quite active while 2.55 AU from the Sun (post-perihelion). Two independent analyses of our data, one parameterizing the coma morphology and the other modeling infrared spectrophotometry, show that the nucleus’s cross section at the time the data were taken corresponds to an effective radius of 3.0 ± 0.2 km. Based on visible-wavelength photometry of the comet taken during this observing run and others in the summer of 2000, all of which show the rotational modulation of the nucleus’s brightness, we find that the infrared data were obtained near the maximum of the light curve. If we assume that the nucleus’s light curve had a peak-to-valley range of 0.6 ± 0.2 mag, then the mean effective radius is 2.6 ± 0.2 km. Visible-wavelength photometry of the nucleus, including data published by other groups, lets us constrain the nucleus’s R-band geometric albedo: 0.072 ± 0.016. The nucleus’s flux contributed about 85% of the light in the mid-infrared images. © 2003 Elsevier Inc. All rights reserved. Keywords: Comets, Tempel 1; Infrared observations

1. Introduction The Deep Impact spacecraft will be launched in late 2004 and fly by the Jupiter-family comet 9P/Tempel 1 on UT 2005 July 4 (Belton and A’Hearn, 1999). The centerpiece of the mission will be the release of a 370-kg projectile that will impact the nucleus and excavate a fresh crater, exposing (presumably pristine) subsurface material to space. The spacecraft will observe this collision (from 104 km away) and the resulting phenomena (until shortly before its 500-km closest approach). The properties of the crater will depend on the mostly unknown mechanical properties of the nucleus but the most likely model of ✩ This article originally appeared in Icarus Vol. 164/2, August 2003, pp. 481– 491. Those citing this article should use the original publication details. * Corresponding author. E-mail address: [email protected] (Y.R. Fernández). 1 Visiting Astronomer at W.M. Keck Observatory, which is jointly operated by the California Institute of Technology and the University of California.

0019-1035/$ – see front matter © 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2003.04.003

the event yields a crater that is roughly 100-m wide and 25-m deep. We are undertaking a vigorous campaign of ground-based observations prior to encounter in order to characterize the comet (Meech et al., 2000). For the design of the autonomous targeting software and mission instrumentation, it is crucial to know what the expected observational environment will be upon arrival. Our goal is to characterize fundamental properties such as: the nuclear size and reflectivity, the nuclear shape and spin state, and the near-nucleus, large-grain dust environment. All of these can affect the spacecraft’s ability to find and image a suitable impact location on the nucleus’s surface and successfully survive the passage through the inner coma. In this paper we report the first infrared study of the Tempel 1 nucleus and the determination of its size and albedo. Our analysis incorporates visible-wavelength data published by Lowry et al. (1999), Lowry and Fitzsimmons (2001), and Lamy et al. (2001), as well as some of our own ground-based data (Meech et al., 2003, in preparation). A companion paper by Lisse et

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al. (2003) discusses the Tempel 1 dust environment during the 1983 apparition. We will employ the results from that paper in the interpretation of the dust coma in our data. 2. Observations and data reduction 2.1. Conditions We observed Tempel 1 simultaneously using the Keck I 10-m and the University of Hawaii 2.2-m telescopes, both on Mauna Kea, over the three nights of UT 2000 August 20–22. We were awarded half-nights with the LWS instrument (Jones and Puetter, 1993) on the Keck telescope for mid-infrared (MIR) observations, but full nights with a Tektronix 20482 pixel (Tek2K) charge-coupled device (CCD) on the UH telescope for visible-wavelength observations. Clouds were evident on all nights; cirrus clouds were at times heavy on Night 1, mostly thin on Night 2 until the late morning, and very thick until just before dawn on Night 3. The geometry of the target and instrumentation of the observations are shown in Table 1. Among those nights, only the infrared data on August 21 and the visible data on August 21 and 22 were useful. Table 1 Target geometry and observing conditions UT date Heliocentric distance (AU) Geocentric distance (AU) Phase angle (◦ ) Sky conditions Visible seeing FWHM ( ) MIR seeing FWHM ( ) MIR wavelengths (µm)

August 20

August 21

August 22

2.540 1.668 14.30 Heavy cirrus 1.2–1.5 0.3 10.7

2.547 1.667 13.93 Cirrus 0.8–0.9 0.4–0.5a 8.9, 10.7, 11.7, 12.5, 17.9, 20.0

2.552 1.666 13.56 Thick cloud 0.5–0.8 0.5 8.9, 11.7

a Diffraction limit at 20 µm is 0. 5.

2.2. Visible observations The plate scale for the Tek2K at the f/10 Cassegrain focus was 0. 219 per pixel, yielding a 7. 5 × 7. 5 field of view (FOV). The gain was 1.74 e− ADU−1 , and the read-noise was 6 e− . Data were obtained through BVRI filters on the Kron-Cousins photometric system; we will concentrate on the R-band data here since they have the greatest signal-to-noise and are relatively untarnished by emission from the fluorescing gas coma. The central wavelength of that filter is 6460 Å and the full width at half maximum transmission is 1245 Å. Images were flattened using a median of dithered and tracked twilight sky images. The photometric calibration was obtained on UT 2000 September 29 by re-imaging (during photometric conditions) the star fields in which Tempel 1 had been on August 21 and 22. Experience has shown that this technique works extremely well to correct photometry suffering from  1 mag of extinction. The September data were calibrated using standard stars from the catalog of Landolt (1992). Observations of 225 standard stars from 5 fields at 6 different airmasses were used to determine the extinction coefficients, color terms, and zero points, which were stable during the night. None of the Landolt stars with poor sampling or known incorrect magnitudes was used. The error in the transformation from instrumental to final magnitudes was less than one percent. In order to correct for extinction in the August data, the magnitude offset, m, between the true magnitude and observed magnitude was computed for 12 field stars brighter than the comet in each frame. An average offset was computed for each frame, and applied to the comet photometry. On August 21, between 9:30 and 13:30 UT the extinction correction varied between 0.00  m  0.06 mag, so it was nearly photometric. However, between 13:36 and 15:00 UT the extinction correction rose to a maximum of 0.360 ± 0.003 mag. A registered and stacked image of the comet at this wavelength is shown in Fig. 1a. This is a ∼ 6000-s composite R-band image from nineteen images taken on UT 2000 August 21.

Fig. 1. Comet Tempel 1 on UT 2000 August 21. The greyscales are logarithmic. North, east, heliocentric velocity direction, and solar direction are marked. (a) Appearance in R-band. The comet’s coma is much stronger here than in mid-infrared wavelengths. This image is the composite of 19 separate images, hence the dotted nature of the background stars. (b) Appearance at a wavelength of 10.7 µm. The comet is only slightly wider than a point source. Striped wedges in the corners are artifacts of processing. Note the different spatial scales for the two images.

Nucleus of 9P/Tempel 1

The images were registered based on offsets measured from the centroids of about 19 field stars and the comet’s motion computed from its ephemeris. The tail is visible for several arcminutes (∼ 105 km in projection) away from the head. The integrated R-band magnitude within a 4-arcsec-radius circular aperture (centered on the comet’s photocenter) is 16.84 ± 0.01. If we account for the nucleus’s contribution to this number (magnitude about 18.6, Section 3.1), then we can calculate the dust production proxy Afρ (A’Hearn et al., 1984). We find Afρ = 71.0 ± 3.3 cm. 2.3. Infrared observations The plate scale was 0. 080 per pixel, yielding a 10. 24 FOV. Chopping and nodding were employed for these observations, with throws of 10 north and east. Flattening of the detector was done by first making two median images of the blank sky (one at high airmass and one at low airmass), and then subtracting the two. For absolute flux calibration we measured the brightness of the star Mirach (β Andromedae), whose fluxes are shown in Table 2. These are derived from the continuum function derived by Engelke (1992) and the effective temperature and stellar radius derived by Cohen et al. (1996), and are accurate to 5 percent at worst. Moreover we accounted for the star’s known, 9-micron, SiO-absorption band by convolving the 8.9-micron filter profile with the band profile published by Cohen et al. (1996); the correction factor to the star’s flux density from the Engelke function is 0.90. The LWS filters are about 10% wide, and given the relative slopes between the standard star’s and comet’s continua, the monochromatic color corrections were  0.01 mag. This is much smaller than the photometric uncertainty so the corrections were ignored. Primarily we used a filter centered at 10.7 µm and interleaved observations with filters at 8.9, 11.7, 12.5, 17.9, and 20.0 µm. To account for atmospheric extinction at 10.7 µm, about once per hour we measured an infrared-bright star, φ 1 Ceti, located about 3.2◦ to 3.6◦ from the comet in the sky. This star has visible-wavelength variations of only about 0.01 mag (Perryman, 1997), and a significant 12-µm flux of several janskys (Joint IRAS Science Working Group, 1988). With this time series of photometry we were able to account for hourscale variations in atmospheric extinction over the course of the night, since the intrinsic brightness of the star should stay constant. By interpolating a second-degree polynomial to the time series we thus could estimate the extinction at any time. The extinction was negligible at the beginning of the observations and about 0.5 mag by the end. Based on the scatter of the visibleTable 2 β And calibration λ (µm)

Flux (Jy)

8.9 10.7 11.7 12.5 17.9 20.0

302 236 198 174 85.9 68.9

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wavelength measurements of cloud extinction, we estimate that the error in this correction to the comet’s 10.7-µm photometry is at most 0.1 mag. For the other filters, where we only had measurements of the absolute flux calibrator Mirach and not a relative calibrator, we used an alternate method to account for extinction. First, by measuring the star’s photometry at the beginning and end of the shift we calculated the net extinction. We then assumed that the behavior of the atmosphere in these filters was similar to that at 10.7 µm. In other words, we assumed that the shape of the extinction-vs.-time plot was the same for all filters but the overall scale of that extinction was determined by our photometry. Since the extinction due to the cirrus was only a few hundredths of a mag up until about UT 13:30 (as indicated by the visible-wavelength observations), this correction introduces non-negligible error only for the 8.9 and 11.7 µm measurements, i.e., the two filters used after UT 13:30. For those filters, we estimate the error to this correction to be 0.1 mag. As a second-order correction, we compared the sky brightness in our comet images to that in our standard star images. At 10.7, 11.7, and 12.5 µm, the sky brightness is strongly correlated with the amount of cirrus in the field of view—since atmospheric water ice absorption bands are the main source of opacity at these wavelengths. (At 8.9 µm, ozone is the main culprit and cirrus clouds are too cold to influence the sky’s brightness. At 20.0 µm, the absorption bands are optically thick and thus opacity is fairly insensitive to the cirrus.) Using the sky’s brightness we can estimate the deviation from our assumed curve of the extinction-vs.-time. We estimate that the error here is about 0.05 mag. A list of the images and measured mid-infrared fluxes of the comet are presented in Table 3. The uncertainty estimates in the table derive from a combination of the statistical error in the photometry itself and the errors to the corrections described above. Infrared data from Night 1 and Night 3 are consistent with measurements from Night 2 but because of excessive clouds we were unable to measure enough standard stars to confidently account for extinction. Since these data from the other Table 3 Mid-IR Flux of 9P/Tempel 1a UT

λ (µm)

Flux (mJy)

11:39 11:41 11:56 12:10 12:42 12:58 13:17 13:42 13:58 14:15 14:43 14:59 15:16 15:23

10.7 10.7 12.5 10.7 10.7 20.0 10.7 10.7 8.9 10.7 10.7 11.7 17.9 10.7

46.7 ± 9.1 50.0 ± 3.6 79.4 ± 6.2 64.4 ± 4.7 46.9 ± 3.9 199.0 ± 42.3 65.7 ± 7.3 52.1 ± 5.9 27.0 ± 3.9 59.2 ± 6.9 53.8 ± 5.7 69.2 ± 8.2 < 196b 62.3 ± 7.4

a Data are for 2000 August 21. b 3-σ upper limit.

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nights are clearly inferior to the data from Night 2, they would be as likely to mislead us as help us and we have therefore omitted them from the table and from our analysis. The mid-IR appearance of the comet is shown in Fig. 1b. This composite, 1944-s image is a result of registering, reorienting (necessary for an altazimuth telescope), and stacking 6 images in the 10.7-µm filter. The signal-to-noise within a 0.8arcsec diameter aperture is about 50. The coma is much weaker in this image and that is partly due to the difficulty in detecting an extended, low-surface brightness feature with a groundbased MIR detector. The thermal background tends to swamp its signal.

3.1. Visible cross section and rotational context

Fig. 2. R-band photometry of the comet during the time of our observations. The aperture used was an 8-arcsec wide circle. The general trend is for a slight brightening over the course of August 21, and then a slight dimming over the course of August 22. To be consistent with an approximate 42-h period, we must have been observing near the light curve’s brightness maximum when we obtained our mid-IR data.

The analysis of the infrared data below requires an understanding of our visible-wavelength data. Unfortunately there is so much coma in the visible data that we were unable to confidently photometrically extract a signature of the nucleus. However the signature of the rotation of the nucleus is apparent in the photometry, and we can use this to find the rotational context. Figure 2 shows the R-band light curve obtained by us on UT August 21 and UT August 22. (The data themselves are listed in Table 4.) The aperture used was an 8-arcsec diameter circle. On the first night the comet was brightening while on the second night it was dimming, though the peak-to-valley range is only a few-hundredths of a magnitude. This is consistent with the expected value based on, e.g., 1997 observations reported by Lamy et al. (2001) when the comet had no coma, since the coma in our data would damp the nucleus’s photometric variation. Given that the period is approximately 42-h long (Meech et al., 2000), and assuming a reasonably symmetric, double-peaked light curve, the only way for the comet to have been dimming about 26 h after it was brightening is if the comet were near the midpoint or on the bright end of the light curve in the latter part

of UT August 21. The MIR data (Table 3) are consistent with this conclusion as well: a linear fit of the 10.7-µm photometry yields a slope of 1.8 ± 2.9 mJy per hour, which means that a, say, 30% increase in the nuclear brightness over the course of the observing period is feasible on the 1-σ level. Further evidence of this rotational context is shown in Fig. 3, which combines photometry from several datasets. In addition to the data in Table 4, we used data from our large Tempel 1 photometry database that will soon be published (Meech et al., 2003, in preparation); these data were obtained within a few months of our August observations, so the comet still showed a coma. The figure shows the data separated into three epochs (delineated by horizontal lines) and phased with a periodicity of 41 h. Since it is impossible to properly scale each epoch’s vertical axis with respect to the others (we do not know a priori the photometric behavior), the usual methods of searching for periodicities are unreliable. Instead we searched by eye for acceptable periods, where “acceptable” in this case means a period for which the trends in the data do not contradict each other and for which a two-peaked light curve is possible; an “acceptable” period is one where at no single rotational phase is there

3. Analysis and discussion

Table 4 R-band photometry of 9P/Tempel 1 Day

UT

R mag

Day

UT

R mag

Day

UT

R mag

August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21

09:32 09:59 10:06 10:12 10:20 10:26 10:33 10:40 10:47 10:54 11:00 11:07 11:14 11:21 11:29 11:37 11:44

16.862 ± 0.005 16.860 ± 0.005 16.865 ± 0.005 16.863 ± 0.008 16.869 ± 0.004 16.859 ± 0.010 16.869 ± 0.004 16.879 ± 0.006 16.865 ± 0.004 16.866 ± 0.008 16.867 ± 0.004 16.864 ± 0.010 16.871 ± 0.004 16.844 ± 0.004 16.842 ± 0.006 16.839 ± 0.004 16.833 ± 0.007

August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21 August 21

11:51 11:58 12:05 12:12 12:18 12:25 12:32 13:03 13:10 13:17 13:24 13:31 13:38 13:44 13:51 13:58 14:05

16.849 ± 0.004 16.843 ± 0.009 16.835 ± 0.004 16.840 ± 0.006 16.846 ± 0.004 16.841 ± 0.008 16.839 ± 0.004 16.836 ± 0.004 16.826 ± 0.004 16.837 ± 0.007 16.831 ± 0.004 16.834 ± 0.011 16.840 ± 0.005 16.839 ± 0.008 16.828 ± 0.005 16.849 ± 0.010 16.837 ± 0.006

August 21 August 21 August 21 August 21 August 21 August 21 August 22 August 22 August 22 August 22 August 22 August 22 August 22 August 22 August 22 August 22 August 22

14:12 14:19 14:26 14:33 14:40 14:46 11:09 11:23 11:31 11:40 12:17 13:24 13:32 14:20 14:29 14:37 14:44

16.835 ± 0.011 16.839 ± 0.006 16.834 ± 0.009 16.828 ± 0.006 16.842 ± 0.009 16.830 ± 0.006 16.841 ± 0.012 16.856 ± 0.011 16.847 ± 0.006 16.867 ± 0.011 16.849 ± 0.005 16.857 ± 0.009 16.851 ± 0.007 16.860 ± 0.005 16.856 ± 0.004 16.875 ± 0.004 16.865 ± 0.004

Nucleus of 9P/Tempel 1

Fig. 3. R-band photometry of the comet during three epochs in Summer 2000, phased by a 41-h periodicity. Note that the horizontal scale goes from −0.2 to 1.2 to facilitate seeing the wraparound. The horizontal lines separate the three epochs (E1, E2, E3) of observations; at top are 3 nights near UT August 21 (E1), including the data published in Table 4; at middle are 5 nights near UT September 7 (E2); and at bottom are 3 nights near UT September 29 (E3). These data will be published by us elsewhere (Meech et al., 2003, in preparation). Within each epoch the data have been scaled to a common geocentric and heliocentric distance, but among the epochs the vertical scale is arbitrary since that depends on the a priori unknown cometary activity and comatic brightness. The only two-peaked sinusoid that does not contradict the photometric trends on any day is one with a 41-h periodicity. August 21, the day from which we have MIR data, is marked in blue in the top panel, and appears to reside near a light curve maximum.

a brightening trend in one day’s data and a dimming trend in another day’s data. We found that a set of periods near 41 h were the only ones to meet the criterion, satisfyingly similar to the 42 h approximate period stated by Meech et al. (2000). The likelihood of this being a coincidence seems low. The data from August 21 and 22 are shown in blue and red, respectively, in the topmost third of the figure. One can visualize a two-peaked sinusoid through all of the data in Fig. 3 and this corroborates the notion that Tempel 1 was at or near the

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peak of its light curve when the MIR data were obtained on August 21. With the rotational context in hand, the next step is to estimate what the mean brightness of the nucleus should be. This requires understanding its phase behavior, i.e., the dependence of apparent brightness on phase angle. We used several published datasets to create Fig. 4, which plots the distanceindependent magnitude of the nucleus versus phase angle. Magnitudes without coma have been reported by Lowry et al. (1999), Lowry and Fitzsimmons (2001), and Lamy et al. (2001). We added a few other applicable data that are to be published by us (Meech et al., 2003, in preparation). Unlike the data from this set that were used in Fig. 3, these extra data for Fig. 4 show the comet as a bare nucleus. For the purposes of fitting a phase curve, we have collapsed the data into four representative points (lower right panel of Fig. 4). We have assigned the error bars based on our estimate of the true light curve midpoints, so the fit is only as good as these estimates. The formalism we use is to fit two parameters, absolute magnitude HR and slope parameter G (Bowell et al., 1989). Both are poorly constrained, with G about −0.17+0.45 −0.25 and HR about 14.5 ± 0.3. (Note that HR applies to R-band, not V-band, the absolute magnitude of which is usually expressed as H .) This is due to our being fairly uncertain about what exactly the amplitude of the light curve is. However this estimate of G is similar to what has been found for other nuclei (e.g., Fernández et al., 2000; Delahodde et al., 2001). Given the geometry in Table 1, the mean magnitude should therefore have been about 18.9 on UT August 21. To find the actual magnitude of the nucleus at the specific time we were observing, we need to know the light curve’s peak-to-valley range m. Based on previous observations of the bare nucleus

Fig. 4. Fits for the phase slope G and absolute magnitude HR of the nucleus of Tempel 1. Each of the first five panels represents one trial value of G, with various trial values of HR plotted. (From top to bottom the trial values are HR = 14.3, 14.4, 14.5, 14.6, and 14.7.) Diamonds indicate data published by Lamy et al. (2001); triangles, by Lowry et al. (1999) and Lowry and Fitzsimmons (2001). The squares and crosses represent unpublished data from 1998 and 2002, respectively, that are in our photometry database (Meech et al., 2003, in preparation). The sixth (lower right) panel displays the rigorous best fit to the plotted data.

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by Meech et al. (2000) and Lamy et al. (2001), we know that m  0.4. We can look for a statistically likely estimate of what the nucleus’s true range will be by using the current distribution of ranges of other comets. Jewitt et al. (2003) give a review of just such information and they find that nearly all comets have m  0.8 mag. Therefore, we adopt 0.6 ± 0.2 mag as a safe estimate for Tempel 1’s light curve range. Then the R-band magnitude of the nucleus at the time we obtained our infrared data was about 18.9 − 12 × m = 18.6. 3.2. IR data methodology The size and albedo of the nucleus can be determined through the measurements of both reflected sunlight and thermal emission. Ideally the nucleus would be seen untainted by emission from a coma but in our case Tempel 1 exhibited a significant visible-wavelength coma as well as a faint MIR coma, which we found by comparing the radial profile of the comet to that of a point source (i.e., a proxy, a standard star). Thus the comet’s spectrophotometry has contributions from both the dust and the nucleus. The two components of the flux must be separated before either component can be characterized. We used two methods to achieve this objective. One involves modeling the morphology of the dust coma, parameterizing the brightness as a function of cometocentric distance, ρ, and azimuth, Θ, and then interpolating to the central pixels and calculating the contribution of the coma to the central condensation. The second method involves modeling the shape of the broad-band spectrum built from our six (5 MIR and 1 visible) filter photometry, using separate models for the spectrum of the nucleus and the spectrum of the dust. Below we describe both methods and demonstrate that they give consistent results. 3.3. Dust morphology modeling The specific computer code to parameterize the coma’s surface brightness—a “coma-fitting technique”—has been developed independently by us (Lisse et al., 1999) and by others (e.g., Lamy et al., 1998). A thorough description of our method is given in the former reference and we only briefly outline it here. The morphology of the outer coma is parameterized azimuth-by-azimuth with a power law and scale factor and then interpolated into the inner coma and central condensation, letting us calculate the brightness of the coma in those central pixels coincident with the point-spread function (PSF) of the nucleus. The power law at a given azimuth is described by the slope, n, and scale, S, such that the surface brightness, F , is given by: F (ρ, Θ) = S(Θ)/ρ n(Θ) .

(1)

This model coma is convolved with the PSF—i.e., a sidereally tracked standard star observed near in time to the comet— before comparing with an image. The method assumes that along any given azimuth the coma brightness behaves as a single power law. This requirement is frequently violated for cometary gas comae so it is imperative to use images that are

sampling dust. The method also assumes that there are no short, curved jet features in the dust coma, and none is evident in Fig. 1. The high thermal background of the MIR images was very effective in making most of the coma invisible. This is good in the sense that it means that the nucleus’s signal is not swamped by the coma, but bad in the sense that it complicates our ability to find out just how much of the comet’s signal is due to that coma. (Conversely, a stronger coma would be easier to model using the aforementioned method, but then the nucleus would be harder to extract.) The clear difference in signal-to-noise ratio (S/N ) between the mid-IR coma and the visible coma suggested to us that one could try to analyze the morphology of the latter and apply that information to the morphology of the former. However this would require two assumptions of uncertain validity: (a) the slope of the coma’s brightness as a function of azimuth is the same across the two wavelength regimes; and (b) the grain dynamics of the inner coma are the same across the two wavelength regimes. The fundamental problem is that the two images span widely different spatial scales, and moreover the emission at the two wavelengths are due to predominant grain sizes that differ by a factor of roughly 5 to 10. A population of “fading” grains could significantly affect the coma’s radial profile as the dust travels out from the few 103 km seen in the mid-IR image to the few 104 km seen in the visible image. Indeed there is a strong indication that grains are fading from the fact that the radial profile of the visible image is steeper than 1/ρ at most of the azimuths. One may ask why one could not use this coma-fitting technique to at least photometrically extract the signature of the nucleus in the visible data, instead of using the indirect method of Section 3.1. The technique was indeed applied to the image in Fig. 1a, as well as to images created from stacking just a few images in a particular part of the night. We were able to find a residual point-like source in the photocenter of each image but we are not confident that these give reliable measurements of the nucleus: First, the residuals are much too faint to be nuclear. Second, we find no evidence of rotational modulation in the photometry of the residuals; the nucleus’s brightness should have changed by 20 or 30% over the course of the night. We surmise that the poor spatial resolution prevents us from obtaining a robust coma model and point-source residual. We conclude that the coma-fitting technique is inapplicable for the dataset both as a way to extract a nucleus and as an analog for the mid-IR coma. Thus, our safe choice for the mid-IR coma was to assume that it behaved like a steady-state, free-flow, canonical coma and showed a 1/ρ brightness profile along all azimuths. We created a model coma and convolved it with the MIR PSF to create a coma-only MIR image of the comet. The overall scale factor of this image is the parameter to be fit; the criterion for a “good” fit was whether the residual (image-minus-model) mimicked the shape of the PSF, since it should be just the emission from the point-source nucleus. We find that the profile of the residual image best matches the profile of the PSF when the residual’s (i.e., nucleus’s) contribution is 70 to 100% of the total flux. The close resemblance

Nucleus of 9P/Tempel 1

of the comet’s profile and the PSF is the reason for the ±15% uncertainty in the nucleus’s contribution. Figure 5 shows a profile comparison between the original comet, the model 1/ρ coma, and the residual. Also shown is the profile after a PSF has been subtracted from that residual—this profile straddles the zero counts line, indicating that we have accounted for all of the flux. Our confidence in the result is strengthened by the fact that if we do try to fit the MIR coma with other coma profiles (e.g., the visible-wavelength coma’s profiles) then we find about the same fraction of the flux is nuclear. Thus the nucleus’s contribution is fairly insensitive to the model coma behavior that is employed. From Table 3, the variance-weighted mean 10.7-µm flux is 54.1±3.5 mJy, so if 0.85±0.15 of the flux is nuclear, the nucleus’s brightness is 46.0 ± 8.6 mJy at that wavelength, including the modeling uncertainties. 3.4. Standard thermal model The last step for this analysis is to convert the radiometry into physical quantities. The basic radiometric method to obtain an effective radius, RN , and geometric albedo, p, is to solve two equations with these two unknowns, first done about 30 years ago (Allen, 1970; Matson, 1972; Morrison, 1973) and described in detail by Lebofsky and Spencer (1989): F (λvis ) Φvis 2 (2a) πRN p , 2 (r/1AU) π2    Fmir (λmir ) =  Bν T (pq, η, , θ, φ, r), λmir dφ d cos θ

Fvis (λvis ) =

Φmir , (2b) 4π2 where F is the measured flux density of the object at wavelength λ in the visible (“vis”) or mid-infrared (“mir”); F is the flux density of the Sun at Earth as a function of wavelength; r and  are the object’s heliocentric and geocentric distances, respectively; Φ is the phase function in each regime; Bν is the Planck function;  is the infrared emissivity; η is a factor to account for infrared beaming; and T is the temperature. The temperature itself is a function of , η, p, surface planetographic coordinates θ and φ, and the phase integral q, which 2 × RN

17

links the geometric and Bond albedos. The modeled body is assumed to be spherical, so RN is an “effective” radius. We employ the “standard thermal model” (STM) for slowrotators (Lebofsky et al., 1986) to derive the function T and evaluate Eqs. (2). In the STM, the rotation is assumed to be so slow and/or the thermal inertia so small that every point on the surface is in instantaneous equilibrium with the impinging solar radiation. This model has been used frequently to interpret radiometry of asteroids and its validity has been confirmed through occultation studies. The model is a valid one to use for a comet because (a) the comet’s rotation period is long (Meech et al., 2000), (b) the active fraction of the nucleus is small (A’Hearn et al., 1995) and thus does not dominate the thermal behavior, and (c) we have no reason to suspect that the thermal inertia of Tempel 1 or of active comets in general is pathologically high. However it should be noted that the STM is an extremum of thermal behavior, and while it is likely that cometary nuclei have low thermal inertia, there are only a few constraints on the matter (Julian et al., 2000; Groussin et al., 2000; Campins and Fernández, 2003). The other parameters to the models are , η, Φmir , Φvis , and q. Emissivity is close to unity and we assume  = 0.9. The beaming parameter is known for only a few asteroids but not for any comets and, among these parameters, is the largest contributor to the uncertainty. Among NEAs, which are of gross comparable size to Tempel 1, the known range covers about 0.7 to above 1 (Harris, 1998; Harris et al., 1998); we adopt 0.7  η  1.0 here. For Φmir we assume that the magnitude scales with the phase angle α: −2.5 log Φmir = βα, where, based on earlier work (Matson, 1972; Lebofsky et al., 1986), 0.005 mag/ deg  β  0.017 mag/deg. In the muchbetter studied visible regime, we use the H, G formalism to obtain Φvis . For G we use our constraint from Section 3.1, G ≈ −0.2. This determines q as 0.17; this parameter has only a minor influence on the final answer for RN . Now we solve Eqs. (2) with Fvis from Section 3.1 and Fmir from Section 3.3 (Note that since we have explicitly solved for the absolute magnitude HR in Section 3.1 and assumed a light curve amplitude, we actually do not need to bother with the true apparent brightness Fvis of the nucleus in Eq. (2a), but rather we already have Fvis /Φvis , saving the uncertainty in G from

Fig. 5. The breakdown of the MIR image of the comet into its contributions from the nucleus and coma. The subtraction has worked well, since the dot symbols straddle zero counts.

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the error budget.) We find that RN = 3.1 ± 0.3 km and p = 0.075 ± 0.020. We have no degrees of freedom, so a rigorous χ 2 fit is impossible. Instead we created a grid of trial values for RN and p to determine which models were plausible. For a model fit to be considered “good,” it had to pass within 1σ of each data point. The “best fit” and the “error estimates” we quote here are then merely the average and standard-deviation of the models from the grid that work. 3.5. Spectrophotometric modeling Our second method involves fitting the observed spectrophotometry to derived spectral shapes for the nucleus and dust. For this exercise we used the four measurements at singleobservation wavelengths in Table 3, the weighted average of the 10.7-µm measurements in Table 3, plus a derived R-band measurement that uses the same aperture size as the MIR data, for a total of six wavelengths. There is a subtlety here to this last point that should be explained. The required aperture for the R-band magnitude is a 0.8-arcsec diameter circle, since that is what was employed for the MIR data. However 0.8 arcsec is smaller than the R-band PSF. We solved this problem as follows. First for the nucleus, we created an artificial PSF (matching the seeing on UT August 21) to calculate what fraction of the light is contained within the necessary aperture. That value is about 75%. Second, we created an artificial coma with the same power-law profiles as seen in Fig. 1a. We then calculated the fraction of light within the necessary aperture both before and after convolving the coma with the PSF. The fraction is about 65%. These two fractions represent the amounts by which the naïve, 0.8-arcsec aperture photometry underestimates the true brightness of each component within such an aperture, and it is very convenient that both fractions are similar, since the actual relative contributions of the two components (nucleus plus coma) do not then significantly affect the answer. The final number we used for the comet’s brightness within the aperture is just the naïve aperture photometry divided by 70%, 17.62 ± 0.03 mag or 0.254 ± 0.008 mJy. For the thermal behavior of the nucleus, we employ the standard thermal model described above at all five MIR wavelengths, and a reflected solar continuum at the one visible wavelength. To make the problem tractable, we assume η = 0.9 and β = 0.01 mag/deg. For the dust, we use the results reported by Lisse et al. (2003) in their analysis of the IRAS measurements made during the comet’s 1983 apparition. They found that: (a) the mass distribution of the dust grains followed a m−0.7 power law, (b) there was no significant icy component to the grains, (c) the ratio of astronomical silicate to amorphous carbon was about 3 : 1, and (d) that the porosity index was such that the grain bulk density ρd followed a a −0.3 power law, where a is the grain radius. (Nonporous grains would have ρd independent of a.) Originally we had hoped to make an independent confirmation of both the dust and nuclear properties with our data, but we found that the data quality was not good enough to constrain them both—there are insufficient degrees of freedom. Using

the same model as outlined by Lisse et al. (1998) and Harker et al. (2002) (and was employed by Lisse et al. (2003) for the 1983 data), we were able to confirm the negligible ice component and the mass distribution power-law, but we were unable to constrain the fraction of astronomical silicate. Thus we made the assumption that the dust properties did not change significantly between 1983 and 2000 and just used the results from the IRAS analysis. Lisse et al. (2003) themselves note that the long-term trend in the post-perihelion infrared brightness (from IRAS) matched the long-term trend seen in the visible brightness from 1999 and 2000, which gives us further confidence that the properties of the comet’s dust production change little from orbit to orbit. The modeling is then straightforward χ 2 -fitting of a three parameter model: RN , p, and the overall scale of the dust’s ˙ contribution, which is represented by the total mass loss rate M. The results are shown in Fig. 6 as contour plots of various slices of the 3-dimensional χ 2 space. The radius was found to be 2.9 ± 0.5 km, but the albedo is constrained only as 0.05 ± 0.05. Both values are in agreement with our first analysis using coma morphology in Section 3.4. (If we were to use that section’s albedo as a further constraint on the spectrophotometric analysis, we would obtain RN = 3.1 ± 0.3 km.) The production rate M˙ can be constrained from the behavior of the 1-σ contour in Fig. 6; it is about 110 ± 70 kg/s. Gratifyingly, this is consistent with the approximately 102 kg/s that would be expected from the comet’s long-term photometric light curve, as analyzed by Lisse et al. (2003). 3.6. Removing light curve effects If p = 0.05 ± 0.05 from Section 3.5 and p = 0.075 ± 0.020 from Section 3.4, then the weighted average is p = 0.072 ± 0.016. If RN = 2.9 ± 0.5 km from Section 3.5 and RN = 3.1 ± 0.3 km from Section 3.4, then the weighted average is RN = 3.0 ± 0.2 km. This is the effective radius at the time we took our observations. To remove the effect of the light curve, recall that in Section 3.1 we demonstrated that we were likely near the maximum of the light curve, and we assumed that the peak-tovalley range is 0.6±0.2 mag. Thus a correction of δm = +0.3± 0.1 mag should be applied. √ This is equivalent to multiplying the radius by a factor f of 10−0.4δm = 0.88 ± 0.04, making the mean effective radius of the nucleus RN f = 2.6 ± 0.2 km. 4. Context A comparison of Tempel 1’s effective radius and albedo with those of other relevant objects is shown in Table 5. A more thorough sampling of nuclear radii is needed before the size distribution can be extracted, but the size of Tempel 1 is not atypical compared to its brethren. Tempel 1’s albedo is entirely consistent on the 1-σ level with many other nuclear albedos. The table does seem to show that the “normal” comets— i.e., those aside from Chiron—are straddling a consistently low range of albedos. Indeed the highest albedos belong to the Centaurs Chiron and (the currently inactive) Asbolus. Whether this is telling us something about the physical evolution of cometary

Nucleus of 9P/Tempel 1

19

Fig. 6. Results of fitting the spectrophotometry to a 3-parameter model of nucleus-plus-dust. Each panel represents a different trial value of the total dust mass loss rate, and shows the contour plot of χν2 (where ν is 3, the number of degrees of freedom) for that value. The largest contour is the 3-σ level, the next largest is 2σ , and the next is 1σ . The fourth contour shows the expected χν2 value for ν = 3 (i.e., where the probability is 50%). The grey rectangle shows the 1-σ range of radius and albedo derived from our morphological analysis of the coma’s contribution to the comet’s image (Section 3.4).

Table 5 Sample of well-constrained radii and albedos Object

Type

RN (km)

p (%)

Ref.

9P/Tempel 1 2P/Encke 10P/Tempel 2 19P/Borrelly 22P/Kopff 28P/Neujmin 1 49P/Arend–Rigaux 107P/Wilson–Harrington 1P/Halley 55P/Tempel–Tuttle C/1995 O1 Hale–Bopp 95P/Chiron (5145) Pholus (8205) Asbolus (10199) Chariklo

JFC JFC JFC JFC JFC JFC JFC JFC HFC HFC LPC ACe ICe ICe ICe

2.6 ± 0.2 2.4 ± 0.3 +0.2 5.3−0.7 2.4 ± 0.1 1.7 ± 0.2 10.6 ± 0.5 4.6 ± 0.2 2.0 ± 0.25 5.0 ± 0.1 1.8 ± 0.4 30 ± 10 80 ± 10 95 ± 13 33 ± 4 151 ± 15

7.2 ± 1.6 4.6 ± 2.3 3.0 ± 1.0 3.0 ± 0.5 4±1 6.0 ± 5.0 4.0 ± 1.0 5±1 4±1 6 ± 1.5 4.5 ± 3 15 ± 3 4.4 ± 1.3 13 ± 3 4.5 ± 1.0

1 2 3 4 5 6 7 8 9 10, 11 10, 11, 12 13, 14 15 14 16

Note. RN is effective radius. p is geometric albedo expressed as a percentage; the error is in percentage points, not a fractional error expressed as a percentage. Type indicates taxonomic group: “JFC” = Jupiter-Family Comet, “HFC” = Halley-Family Comet, “LPC” = Long-Period Comet, “ACe” = Active Centaur, “ICe” = Inactive Centaur. “Ref.” refers to the following: (1) this work; (2) Fernández et al. (2000); (3) A’Hearn et al. (1989), updated by Campins et al. (1995); (4) Soderblom et al. (2002) and Buratti et al. (2003); (5) Lamy et al. (2002); (6) Campins et al. (1987), updated by Campins et al. (1995); (7) Millis et al. (1988), updated by Campins et al. (1995); (8) Campins et al. (1995); (9) Keller et al. (1986); (10) Jorda et al. (2000); (11) Fernández (1999); (12) Fernández (2003); (13) Campins et al. (1994); (14) Fernández et al. (2002); (15) Davies et al. (1983); (16) Jewitt and Kalas (1998).

surfaces remains to be seen. For example, perhaps the specific mechanics driving cometary activity changes as an object evolves from the outer to the inner Solar System. A larger sam-

ple of cometary and outer Solar System albedos is needed, and SIRTF-era MIR observations will be useful for addressing this topic. 5. Conclusions We obtained simultaneous visible and mid-infrared (MIR) imaging observations of comet 9P/Tempel 1 on UT 2000 August 21 and were thus able to determine the effective radius RN and geometric albedo p of the nucleus, which will aid in the planning of the Deep Impact mission. We can make the following conclusions. 1. The comet is active at r = 2.55 AU from the Sun (postperihelion) and shows a significant coma at visible wavelengths but a much less extensive coma at mid-infrared wavelengths. The thermal background was too high to obtain good signal on the extended, low-surface brightness MIR coma. The nucleus shows up strongly in the thermal data but is impossible to reliably extract from the visible data. The comet’s R-band Afρ at the time of our observations was 71.0 ± 3.3 cm. This value pertains to an 8-arcsec wide circular aperture; the coma’s profile was steeper than canonical. 2. An analysis of R-band light curves obtained from many observers in summer 2000 let us derive the rotational context of our data. Our observations were apparently taken near a maximum in the light curve. Other published datasets that report magnitudes of the nucleus constrain the R-band absolute magnitude HR and phase darkening slope parameter G. Combining all of this allowed us to find that (a) HR = 14.5 ± 0.3, (b) G = −0.17+0.45 −0.25 , (c) a reasonable estimate for the peak-to-

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valley light curve range is 0.6 ± 0.2 mag, and (d) the R-band magnitude of the nucleus at the time of our observations was about 18.6. 3. By assuming that the MIR coma had a canonical 1/ρ structure, we were able to separate the comatic and nuclear contributions in the 10.7-µm data. The nucleus contributed a fraction 0.85± 0.15 of the total cometary signal. Using the standard thermal model for slow-rotators yields RN = 3.1 ± 0.2 km and p = 0.075 ± 0.020. 4. As a second tactic, we analyzed the six-filter broadband spectrophotometry (5 MIR filters between 8.9 to 20.0 microns, and 1 visible filter). The spectral shape of the dust is known from related work by Lisse et al. (2003), so we used this to constrain the nucleus’s contribution to the spectrophotometry and thus derive the radius and albedo independently of the previous, morphological method. We find that RN = 2.9 ± 0.5 km, but p is only constrained to 0.05 ± 0.05. 5. Our two analysis methods give consistent results, and combining them we have RN = 3.0 ± 0.2 km and p = 0.072 ± 0.016. The radius applies to the time of the observations, so knowing that we were near a maximum in the light curve and using the above light curve range gives a mean effective radius of 2.6 ± 0.2 km. The nucleus of Tempel 1 is not unusual in terms of either quantity compared to the known ensemble of comets. Acknowledgments The authors appreciate the work of Tom Morgan and the Keck TAC for allowing us to obtain these data; as well as the assistance of John Dvorak, Cynthia Wilburn, Joel Aycock, and Ron Quick in running their respective telescopes. We thank the JPL Solar System Dynamics group and the Centre de Données Astronomiques de Strasbourg for providing their online services, both of which we employed. We thank Tony Farnham, Gerbs Bauer, and Gian-Paolo Tozzi for contributing data to the Deep Impact project that was used in this analysis. Humberto Campins and another, anonymous referee provided helpful comments. Support for this work was provided by NASA Grant Nos. NAGW-4495, NAGW-5015, NAG-54080, and NAG-59006, and through University of Maryland and University of Hawaii subcontract Z667702, which was awarded under prime contract NASW-00004 from NASA. References A’Hearn, M.F., Campins, H., Schleicher, D.G., Millis, R.L., 1989. The nucleus of Comet P/Tempel 2. Astrophys. J. 347, 1155–1166. A’Hearn, M.F., Millis, R.L., Schleicher, D.G., Osip, D.J., Birch, P.V., 1995. The ensemble properties of comets: Results from narrowband photometry of 85 comets, 1976–1992. Icarus 118, 223–270. A’Hearn, M.F., Schleicher, D.G., Millis, R.L., Feldman, P.D., Thompson, D.T., 1984. Comet Bowell 1980b. Astron. J. 89, 579–591. Allen, D.A., 1970. Infrared diameter of Venus. Nature 227, 158–159. Belton, M.J.S., A’Hearn, M.F., 1999. Deep sub-surface exploration of cometary nuclei. Adv. Space Res. 24, 1175–1183. Bowell, E., Hapke, B., Domingue, D., Lumme, K., Peltoniemi, J., Harris, A.W., 1989. Application of photometric models to asteroids. In: Binzel, R., Gehrels, T., Matthews, M.S. (Eds.), Asteroids II. Univ. of Arizona Press, Tucson, pp. 524–556.

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