WISE/NEOWISE OBSERVATIONS OF COMET 103P/HARTLEY 2

For all but the night of 2010 April 17 and 2011 January 27 the Palomar, SOAR, Mauna Kea, and Steward observatory ground-based observing conditions for 103P were photometric, and provided magnitudes to within a few percent uncertainty. After acquisition, the ground-based images were bias-subtracted and flat-field corrected. The R-band photometry obtained from the ground-based observations is summarized in Table 2, including flux magnitudes and geometry corrected Afρ dust column values (A'Hearn et al. 1984) as well as magnitudes. The fixed 2.5 and 5 arcsec aperture radius values listed in Table 2 are chosen to highlight the activity near the comet's coma center. The values represent the average of the aperture signals in the individual images, but special analysis was performed for the 2010 April 18 and May 23 (Figure 2) observations. Larger aperture radius values of 11 and 22 arcsec were used to match the aperture sizes necessary to obtain the signal from the poorest resolution WISE bands. We stacked and median combined the May 23rd UH frames into a single image to reduce the contribution of background stars to the large aperture and background annulus signals. Photometric analysis yielded a reflected-light signal in these large aperture values for comparison to the WISE observations by adjusting the 2010 April 18 and May 23 aperture magnitudes to the May 10th WISE spacecraft-to-comet and comet heliocentric distance. Interpolation between the adjusted 2010 April 18 and May 23 magnitudes yielded 2010 May 10 magnitudes of 18.45 ± 0.02, and 18.11 ± 0.02, and Afρ values of 0.85 and 0.69, for the 11 and 22 arcsec aperture signal, respectively. Note that the interpolation correction was 0.04 mag, within the photometric uncertainty of the April 18 magnitudes and on the order of what might be expected for the change in viewing phase from 26.1 to 27.3 deg for a cometary body (with slope parameters between 0.02 and 0.035 mag deg⁻¹; Meech & Jewitt 1987). A single V-band 300 s exposure was taken the night of the 2010 May 23 observations, yielding V − R colors of 0.38 ± 0.03, or nearly solar.

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Table 2. R-band Optical Photometry

Date/Time	Airmass	mR, rap = 25	mR, rap = 5''	Afρ, 25	Afρ, 5''	Rhelio/Δ
(UT)				(log cm)	(log cm)
Apr 17, 12:02	1.70	19.90 ± 0.12	19.49 ± 0.19	1.08	0.94	2.49/2.52
Apr 18, 10:03	1.20	20.03 ± 0.04	19.62 ± 0.06	1.02	0.89	2.47/2.49
May 23, 13:52	1.12	19.46 ± 0.01	19.15 ± 0.01	1.00	0.82	2.19/1.81
Jul 13, 09:30	1.08	17.45 ± 0.02	16.87 ± 0.02	1.32	0.98	1.73/0.94
Aug 17, 03:56	2.46	15.99 ± 0.01	15.27 ± 0.01	1.49	1.05	1.43/0.52
Sep 3, 06:46	1.03	15.26 ± 0.02	14.54 ± 0.01	1.54	0.99	1.29/0.38
Nov 7, 09:35	1.44	13.60 ± 0.03	12.55 ± 0.01	1.70	1.02	1.07/0.17
Jan 27, 05:58	1.34	15.28 ± 0.20	14.63 ± 0.20	1.98	1.94	1.59/0.69

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The coma images were identified using the method described in the WISE archive explanatory supplement (http://wise2.ipac.caltech.edu/docs/release/prelim/expsup/), utilizing the WMOPS detections in combination with the single-frame (level 1b) archive source search. An additional frame with a near-edge detection (Modified Julian Date 55327.47018; see Table 1) was found from individually searching the archive scans spanning the dates of coverage (2010 May 10–11).

The WISE data were processed through the WISE Science Data System (WSDS) pipeline (Wright et al. 2010), to remove detector artifacts as well as bias and flat correct each image. The resultant images were stacked into the comet-centered images shown in Figure 1, using the WSDS co-adder routine specially adapted to stack according to the comet's rate of apparent sky motion. Aperture photometry was performed on the stacked images of each band for apertures using radii of 6, 9, 11, and 22 arcsec. Counts were converted to fluxes using the band-appropriate magnitude zero-points and zeroth-magnitude flux values provided in Wright et al. (2010), and an iterative fitting to a blackbody curve was conducted on the two long-wavelength bands to determine the appropriate color correction as listed in the same. Figure 3 shows the blackbody fit and the signal in W2, W3, and W4. The W1 image did not yield significant signal in any of the apertures. However, the reflected light signal was constrained by the visual wavelength data also shown on the graph. In Figure 3 fluxes, the flux contribution from the nucleus (see Figure 4) has been removed. Even so, note that the flux in W2 is significantly greater than the total dust reflected light and thermal contribution, suggesting another narrowband source of emission in the 4–5 μm range of the W2 passband.

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In order to extract the nucleus signal, we used routines developed by our team (Lisse et al. 1999 and Fernández et al. 2000) to fit the coma as a function of angular distance from the central brightness peak along separate azimuths. The extracted nucleus signals in W3 and W4, 0.7 ± 0.2 mJy and 2.6 ± 0.7 mJy, respectively, were fit to a NEATM model (Harris 1989, Delbo et al. 2003, and Mainzer et al. 2011b) with free and fixed beaming (η) parameters (Figure 4). Fits with η values fixed to 2.0, 1.2 (Stansberry et al. 2007), and 0.94 (Fernández et al. 2008) yielded diameters of 1.5, 1.1, and 0.9 (±0.2) km. The geometric mean radius, based on radar measurements (Harmon et al. 2010), is closer to 0.58 km, or a diameter of 1.16, more consistent with the η = 1.2 fixed value, and are closer to the 1.14 km diameter value derived from Spitzer measurements of the 2008 August 13, r_h = 5.4 AU, 22 μm flux obtained by Lisse et al. (2009). The η = 1.2 fixed fit yields an albedo of p_v = 0.038 ± 0.004, assuming an absolute magnitude of 18.8 consistent with a 0.6 km mean radius (Lisse et al. 2009). Note that each fit iteration requires an interpolation for surface temperature in the WISE bands (Wright et al. 2010), so that different flux values are derived for each final fit, as shown in Figure 4. The interpolated corrections for temperature are largest in W3. For decreasing η, the temperature increases. Note that the flux contribution from the nucleus in W2 was calculated to be less than 10⁻⁵ Jy, or significantly less than the uncertainty in the 4.6 μm flux. The W3 and W4 flux contributions from the nucleus were also subtracted from the total fluxes used to calculate the particle size distribution (PSD) shown in Figure 5.

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Observations of the 103P/Hartley 2 debris trail spanned the time period from May 4:13:35 to May 13:33:47, and a position on the sky of 13 leading to 4° trailing the comet, covering a range from −032 to +108 in delta Mean Anomaly (dMA). The debris trail of 103P is a low contrast feature with respect to the infrared background and requires co-addition to obtain reasonable signal-to-noise. The co-addition should be of the same trail features, for example, at the same dMA, to preserve any variations in the emission history.

W3 and W4 images were selected from the set of 113 WISE level 1b frames containing the trail, and the W3 images re-binned to the W4 pixel size. The background radiance of each image was fit with a two-dimensional low-order polynomial and subtracted from the image to reduce the effects of global radiance slopes. The resulting images were then shifted to bring the desired dMA to the center of a stacked (co-added) image of 508 columns × 200 rows, and rotated about that dMA to bring the projected orbit of 103P parallel to the stacked image rows. The co-added image thus contains the orbit along row 100 with the selected dMA at the center. The increment of dMA used was 004, and the number of images stacked at each dMA varied from 14 to 19. Figure 6(a) shows co-added images for a stack of W3 and W4 frames centered at dMA = 02.

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Radiance profiles normal to the trail were constructed from the mean and standard deviation of each row. Outlier rejection (of stars, instrumental artifacts, cosmic rays, etc.) was applied to each row using an iterative technique based on the theory of order statistics (Mandell 1964). The radiance profiles were fit to a Moffat (1969) function with an exponent of 0.5 to find the peak radiance, the position of the peak, and the FWHM. Radiance profiles derived from the two images shown in Figure 6(a) are plotted in Figure 6(b). The Moffat function, which is a modified Lorentz function, was chosen since it fits the peak, position, and shape of the radiance profile more accurately than the conventional Gaussian. The Lorentz form of the trail profile was originally suggested as a result of dynamical modeling of trail grains (D. Lien 1990, private communication). Data numbers (DNs) were converted to fluxes using the band-appropriate magnitude zero-points and zero-magnitude flux values provided in Wright et al. (2010). The peak profile in-band radiances are plotted as a function of dMA in Figure 7. In this and subsequent figures (Figures 8 and 9), vertical dotted lines delineate a region in which the trail radiances are influenced by the coma and tail radiances. This is due, in part, to the small angle between the sky-projected anti-solar vector and the projected anti-velocity vector (see Figure 1). However, it is mainly a result of the "boxcar-like" averaging effect of taking row means. It is also responsible for the peak radiance occurring at dMA = 0.16 rather than at the nucleus (dMA = 0) since the trail is brighter behind than in front of the comet. The mean radiance of the trail leading the comet is 0.05 MJy sr⁻¹ in W4 and 0.02 MJy sr⁻¹ in W3. Behind the comet, the trail peak radiance falls from 0.14 MJy sr⁻¹ at 02 dMA to 0.06 MJy sr⁻¹ at 104 dMA in W4 and 0.06 MJy sr⁻¹ to 0.04 MJy sr⁻¹ in W3.

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Comet 103P's signal at 4.6 μm is about 0.4 mJy for an 11 arcsec aperture. The contribution from the thermal and reflected light of the coma was calculated to be 0.03 mJy (see Figure 3). A large excess flux in the 4.6 μm band suggests other contributions, possibly from emission lines. Recent work with the Spitzer Space Telescope IRAC instrument's similar band-pass centered at 4.8 μm shows the most likely candidate emission lines to be from CO and CO₂ lines (Pittichova et al. 2008; Reach et al. 2009). With a band pass of ∼1 μm (Wright et al. 2010), the 4.6 μm band contains both the CO (4.26 μm) and CO₂ (4.67 μm) mid-IR emission bands. Water emission lines appropriate for the measured temperatures ∼200 K that reside in the mid-IR nearest the band pass cluster in the 2.7–33 and 5.5–6.3 μm range (Lisse et al. 2006; Woodward et al. 2007). The excess of the W2 flux is likely attributable to CO and CO₂ gas species, seen strongly in Hartley 2 by the EPOXI mission in 2010 (A'Hearn et al. 2011) and in previous apparitions (Weaver et al. 1994; Crovisier et al. 1997), while CO was found to be very underabundant in this comet and also in other comets as the dominant lines in the 4–5 μm spectral range by ISO (Crovisier et al. 1999; Woodward et al. 2008; Reach et al. 2009). Comet 103P's signal at 4.6 μm is about 0.4 mJy for an 11 arcsec aperture. The contribution from the thermal and reflected light of the coma was calculated to be 0.03 mJy (see Figure 3).

Using the analysis techniques as presented in Pittichova et al. (2008, see their Equations (4) and (5)) we convert our 4.6 μm band fluxes to the number densities and production rates shown in Table 4, assuming a gas ejection velocity of 0.62 km s⁻¹. We scale the contribution from the two species for relative CO₂:CO abundance of roughly 10:1, similar to previous oppositions (Weaver et al. 1994; Bhardwaj & Raghuram 2011) to arrive at our relative production values. These represent the unique constraints on these species abundances for 103P at these distances. We have no available measurement of H₂O production near the time of the WISE observations, so we are unable to provide reliable constraints on the CO₂/H₂O ratio. However, extrapolation to 2010 May 10 from the production models as shown in Meech et al. (2011) and from rates observed on 2010 July 26 by Mumma et al. (2011) yields H₂O values ∼3 × 10²⁶ mol s⁻¹, suggesting that a derived CO₂/H₂O ratio would be on the order of a few percent, i.e., a factor of a few lower than seen at perihelion during the EPOXI encounter (Weaver et al. 2011) and for previous orbits (Weaver et al. 1994). The CO₂/H₂O ratio may possibly decrease as a function of heliocentric distance.

The debris trail grain temperature (T_g) was calculated at each dMA from the ratio of the profile peak radiance in W3 to that in W4. The resulting temperatures were well represented over the range of trail distances (2.26 AU < r < 2.39 AU) by the relation T_g = 303/r^1/2_h ± 5 K, where r_h is given in AU and is in good agreement with the relation derived for IRAS trail comets with multiband detections (Sykes et al. 2005). As had been noted previously (Sykes et al. 1990), trail temperatures are significantly (∼10%) higher than the local equilibrium blackbody temperature. Possible explanations have been discussed extensively (Sykes et al. 1990, 2005; Sykes & Walker 1992); the least complex explanation assumes that randomly orientated trail grains maintain a latitudinal temperature gradient across their surfaces due to their very low thermal inertia. The optical depth, τ, of the trail at the profile peak radiance was derived using the above relation for T_g and assuming that the trail grains emit blackbody radiation, and is plotted in Figure 9 for each dMA observed. A solid line is drawn through the means of the W3 and W4 results and represents the values of τ used to integrate the trail mass. The peak optical depths for 103P lie within the range of values (0.3–16) × 10⁻⁹ found for the 34 comets surveyed by Spitzer (Reach et al. 2007) and (1.3–13.8) × 10⁻⁹ found for the eight IRAS trails (Sykes & Walker 1992).

The width of the trail, as derived from the FWHM of the radiance profile and the WISE centric distance to the trail, is shown in Figure 9. The trail reaches a minimum width of ∼65,000 km slightly behind the comet at dMA = 012, increases to a mean of ∼140,000 km ahead of the nucleus (−032 < dMA< −016), and increases to ∼170,000 km behind the nucleus at dMA = 104. Our value of 65,000 km near the nucleus is higher than the 40,000 km width found from 22 μm Spitzer photometric imaging (Lisse et al. 2009), however, this probably is due to the "contamination/averaging" previously discussed in the Analysis section. As such, it should be considered an upper limit to the trail width near the nucleus.

The velocity of trail grains can be deduced from measurements of the physical trail width (Sykes et al. 1986). Applying their Equations (1) and (2) to the above measurements of the width of the 103P trail and assuming isotropic perihelion emission, we derive a mean grain velocity relative to the nucleus of 3.6 ± 1.4 m s⁻¹. This is in good agreement with a radial velocity dispersion of the grains of 4 m s⁻¹ from preliminary radar observations (Harmon et al. 2010).

The grain size is the final element required to calculate the mass of the observed debris trail. Whereas we cannot measure the grain size directly, we can measure the ratio β = Force due to radiation/Force due to solar gravity = 1.14 × 10⁻⁴ Q_pr ρd⁻¹ (Burns et al. 1979) where Q_pr = efficiency for radiation pressure ≈1.0 for grains with d ≫ λ, ρ = grain density (g cm⁻³) and d = grain diameter (cm). Trail grains ejected from the nucleus experience a reduced force of gravity due to solar radiation pressure that changes the semimajor axis of their orbits from that of the parent comet (Sykes & Walker 1992). Figure 10 is a plot of the position of the peaks of the trail radiance profiles behind the nucleus versus dMA. The horizontal dashed line at pixel 100 is the position of the comet's orbit, that is, the zero velocity and zero β syndyne. Equation (2) from Sykes & Walker (1992) was used to calculate the positions of trail grains for a large set of β and find β_min giving a minimum χ² fit to the measured peak positions. The solid line is the zero velocity syndyne for β_min = 1.0 × 10⁻⁴. The dotted and dashed lines are for β_min ± 1σ. In the case where ρ = 1.0 g cm⁻³, β_min = 1.0 × 10⁻⁴ corresponds to a grain diameter = 1.1 cm, a diameter typical of dust trail particles (Sykes & Walker 1992; Reach et al. 2007), comet-associated meteoroids, and the icy grains imaged around the nucleus of 103P by the EPOXI spacecraft (A'Hearn et al. 2011). The ±1σ β_min values of 1.82 × 10⁻⁴ and 2.10 × 10⁻⁵ correspond to grain diameters of 0.63 and 5.4 cm, respectively. Note that the density for large particles may be ∼0.4 g cm⁻³ (Richardson et al. 2007) and thus the diameter of the particles may be 2–3 times larger. This result agrees with preliminary radar Doppler spectra that show a broadband echo from >1 cm diameter grains (Harmon et al. 2010).

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Our solution for β also gives an estimate of the age of the trail particles. Grains observed at dMA = 0.32 were emitted approximately 6.5 years (1 period) ago, while the grains observed most distant from the nucleus were emitted about 21 years (3.3 periods) ago.

103P is observed to have a significant trail of debris leading the comet. The minimum particle diameter ahead of the comet is that for which the effect of ejection velocity balances that of radiation pressure (Sykes et al. 1986; Lisse et al. 2004). Setting the above referenced Equation (2) (Sykes & Walker 1992) to zero and solving for β yields an estimate of the maximum value of β = 1.91 × 10⁻⁴ with corresponding minimum diameter of 0.59 cm in the leading portion of the trail (assuming ρ = 1).

The mass of the observed trail is estimated from the optical depth, peak normalized profile area, and β. If we assume that all the grains in a given field of view (FOV) are at the same temperature, then the optical depth, τ, is just the fraction of the FOV area at the trail that is filled by the projected areas of the grains, thus τ = πnR²/(αΔ)² where n is the number of grains of radius R within the FOV defined by the angular size of the pixel, α, and the WISE centric distance, Δ. The mass of the grains within the FOV is just the mass of a single spherical grain times the number of grains, that is, M_FOV = 4/3 πRρτ(αΔ)² where ρ is the grain density. In terms of β and the WISE W4 pixel size of 5.5 arcsec this reduces to M_FOV = 1.218 × 10¹³ τΔ²ρ/β (g pixel⁻²) where Δ is in AU. The total mass of the observed trail is then M_total = WLM_FOV, where the width of the trail, W, in pixels is the area under the peak-normalized radiance profile, and L is the length of the trail, in pixels, observed on the sky. In practice, since τ, Δ, and W vary with sky position, M_total was calculated as an integral along the trail length. Also, the portions of the trail ahead and behind the comet were treated separately, since each had a different value of β. This yields 3 × 10¹² g for the total mass of the trail leading the nucleus, and 4 × 10¹³ g for the longer trail section in the following portion, assuming ρ = 1 g cm⁻³. As previously noted (Reach et al. 2007), these values are lower limits to the trail mass because the full extent of the trail may not have been measured and larger grains may be present. The mass of the 103P trail is within the range of 3 × 10⁸ to 3 × 10¹¹ kg found for the eight trails observed by IRAS (Sykes & Walker 1992) and the range 4 × 10⁷ to 9 × 10¹⁰ kg found for six Spitzer comets "with reasonable total mass estimates" (Reach et al. 2007).

Given the age of the grains calculated above, we estimate the average mass loss rate of 103P meteoroids over 21 years is 62 kg s⁻¹ into the trail, which is greater by a factor of nine than the average orbital mass loss rate of ∼7 kg s⁻¹ into coma dust. This rate would amount to the loss per orbit of ∼1.5% of the mass of the comet's nucleus, assuming a density near 1 g cm⁻³. Our value falls within the range of 4–250 kg s⁻¹ found for the IRAS trails, but outside the range of 0.2–36 kg s⁻¹ for the Spitzer trails. If we exclude 2P/Encke and 29P/Schwassmann–Wachmann 1 from the IRAS list, then the IRAS range of mass loss rates for more typical JFC trails is 4–20 kg s⁻¹, totally within the range measured by Spitzer, and our value of 62 kg s⁻¹ for 103P is now well outside that range.