WISE/NEOWISE PRELIMINARY ANALYSIS AND HIGHLIGHTS OF THE 67P/CHURYUMOV-GERASIMENKO NEAR NUCLEUS ENVIRONS

In order to extract the nucleus signal, we adapted routines developed by our team (Lisse et al. 1999, 2009, Fernández 1999, and Fernández et al. 2000, 2012) to fit the coma as a function of angular distance from the central brightness peak along separate azimuths, as done in Bauer et al. 2011. As per the description in Lisse et al. (1999), the model dust coma was created using the functional form f(Θ) × ρ⁻ⁿ, where ρ is the projected distance on the sky from the nucleus and Θ is the azimuthal angle. In order to compensate for the WISE instrumental effects, the model coma was then convolved with the instrumental PSF appropriate for AWAIC co-added images (see Cutri et al. 2012). Radial cuts through an image of the comet were made every 3° in azimuth, and the best-fit radial index, n, and scale, f, at each specific azimuth were found by a least-squares minimization of the model to the data along that azimuth. The pixels between 5 and 20 arcsec of the brightness peak were used to fit the model coma. The coma model fit residuals were ∼10% for the W3 and W4 images, similar to the photometric uncertainties in the nucleus and coma signals. We use the nucleus mean values of absolute magnitudes from Hubble Space Telescope observations reported in Lamy et al. (2006), i.e., H_V = 16.3, for our nucleus albedo calculations, as these constitute the highest spatial resolution nucleus measurements in the literature. Note that Tubiana et al. (2008) report H_V = 15.9, which would raise our derived albedos from VA and VB by factors of ∼1.4. We performed the extractions independently for the two visits, using the stacked images (Figure 1) to both average over the rotational variations and boost the signal-to-noise ratio (S/N). The higher S/N visit (see Figure 2), VA, had extracted nucleus signals 1.9 ± 0.17 mJy and 5.9 ± 0.9 mJy in W3 and W4, respectively, and were fit to an NEATM model (Harris 1998, Delbo et al. 2002, Müller et al. 2009, and Mainzer et al. 2011b) with a free beaming (η) parameter, yielding a diameter of 3.64 ± 0.39 km, an albedo (herafter p_v) of 0.04 ± 0.01, and an η value of 1.02 ± 0.17. The η value obtained in the free fit is similar to the mean value of η = 1.03 ± 0.11 found for 55 comets out of the sample obtained by Fernández et al. (2012) from a Spitzer survey of 100 Jupiter family comets. We obtained lower signal-to-noise extractions for VB (the comet was at a larger heliocentric distance during that visit), with W3 and W4 flux values of 0.28 ± 0.04 and 3.6 ± 0.8 mJy, respectively, yielding a diameter of 3.0 ± 1.4 km and p_v = 0.06 ± 0.03 for a fixed η value of 1.0. We held η fixed for the VB thermal fit since the free-fit solution converged to non-physical values of > π (Harris 1998). The diameter values are consistent with the average spherical radius value obtained by Kelley et al. (2008; 1.87 ± 0.08 km) and Lamy et al. (2008; 1.98 ± 0.05 km). A nucleus of this size will produce combined reflectance and thermal flux contributions of 3 μJy and 6 μJy in W1 and W2, respectively, well below the uncertainty of any flux or flux upper limits in those bands. Still, the flux contributions from the nucleus were subtracted from the flux values of the coma reported in Table 2.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Table 2. Coma Photometry Results

Visit	Coma Fluxa				Tdusta	W1 Afρa	W3 εfρa	W4 εfρa	$Q_{_{{\rm CO}_2 } } /Q_{_{{\rm CO}} }$a
	W1 (μJy)	W2 (μJy)	W3 (mJy)	W4 (mJy)	(K)	(cm)	(cm)	(cm)	(s−1)
VA	10 ± 7	180 ± 50	10.2 ± 0.4	50 ± 4	183 ± 4	8.7 ± 4	146 ± 24	147 ± 24	7.7(±2) × 1025 8.2(±2) × 1026
VB	···	···	2.8 ± 0.2	19 ± 2	169 ± 3	···	82 ± 10	90 ± 21	<1026,<1027

Notes. ^aEach co-added photometry point is listed for each visit (see the text). The fluxes here, in units of milli-Janskys for W3 and W4, and micro-Janskys for W1 and W2, and are reported for 11 arcsec aperture radius values, with the nucleus contribution to the signal removed. T_dust is derived from the blackbody fits to the coma flux values, where the expected blackbody temperatures are 157 and 140 K for VA and VB, respectively. Afρ is calculated from the 1.5 S/N signal in W1, and εfρ from the W3 and W4 coma fluxes, and are expressed in (cm) units along with the uncertainties. $Q_{{\rm CO}_2 }$ and Q_CO are derived from the W2 excess, assuming only a single species, either CO₂ or CO, is accountable for the entire excess signal.

Download table as:  ASCIITypeset image

Lisse et al. 1998 demonstrated how broadband photometry can be applied to determine the quantity and temperature of the coma dust. As in Bauer et al. (2011, 2012), we performed blackbody temperature fits to the dust coma region surrounding the nucleus, extracting the W3 and W4 measured nucleus flux contribution from the thermal signal. We also estimated the W1 and W2 nucleus contribution, based on the thermal fit results for the size and albedo computed using W3 and W4 and scaling the reflected light contribution to the appropriate phase angle, assuming an IR albedo twice that of the visual-wavelength albedo (Grav et al. 2011). W3 and W4 fluxes from the nucleus represent less than 11% of the total signal in the 11-arcsec aperture photometry for VA. The thermal fit was dominated by the dust coma to within the photometric uncertainty, and the uncertainty in the removed nucleus contribution was much less than the photometric uncertainty in the coma signal. For VB, the extracted nucleus fluxes comprise between 10% (W3) and 20% (W4) of the thermal flux in the 11 arcsec aperture. The associated uncertainties were still less than the aperture flux uncertainties, but are still included in the flux uncertainties listed in Table 2. The results of the dust thermal fits are listed in Table 2, and the dust fits for each visit are shown in Figures 2(A) and (B). The signal contribution from the nucleus, as estimated from the thermal fit results, was removed from the total flux in the derivation of the coma flux.

We calculate the effective area for the dust using 9 and 11 arcsec radius apertures, and find that the effective area matches across both thermal bands, W3 and W4. In fact, for the thermal bands, this derived area has a factor of the emissivity, ε, incorporated into the result. Division by the projected length scale of the apertures, i.e., the ρ value, and by the constant π, provides an aperture-independent means of comparison to the quantity of dust visible at particular wavelengths analogous to Afρ (Ahearn et al. 1984). We call this factor εfρ, as introduced by Lisse et al. (2002) and used in Kelley et al. (2012), which is listed in Table 2. The value of εfρ assumes that the observed flux is attributable primarily to the dust continuum emission and is the product of the emissivity, ε, the fractional area within an aperture filled by the dust, f, and the projected length scale of the aperture radius on the sky at the distance of the comet, ρ, expressed in centimeters. We compute our εfρ values multiplying the observed surface brightness of the comet, I_λ, by ρ and dividing by the Planck function, B_λ (T_b), where T_b is the fitted blackbody temperature of the dust, here 183K for VA and 169K at VB. The effective area is derived from this quantity by multiplying by πρ/ε using an assumed value of ε ≈ 0.9. Derived values for dust temperature, Afρ, εfρ, $Q_{{\rm CO}_2 }$ and Q_CO, from the 9 and 11 arcsec apertures match within the photometric uncertainty of the 11 arcsec coma flux signal (listed in Table 2).

Thermal fits of the dust to a blackbody were made using the W3 and W4 fluxes for VA and VB, and were found to exceed the expected blackbody temperature by ∼20%. This is not uncommon (cf. Lisse et al. 1998), but is usually seen for dust size distributions with a presence of small grains. Note that at the infrared wavelengths used by WISE, the observations are not sensitive to fine cometary dust on the order of 1 μm, which typically dominates the visible signal for coma photometry.

For VA, we find a W2 excess signal from the dust at the 2σ level. Scaling the dust blackbody curve and expected reflectance given a standard α = −3 power law for the particle size distribution (PSD; cf. Fulle 2004), with a neutral reflectance and a reflectance reddening law based on Jewitt & Meech (1986) averaged out to 3.5 μm, we employ the method from Bauer et al. (2011) to determine the excess flux. This is somewhat conservative in its approach for this particular comet, as the PSD is quite flattened relative to the standard PSD for 67P at these distances (see below). We emphasize that the detection is only 2σ above the dust flux estimates for W2. Using the methods outlined by Pittichová et al. (2008) and applied in the case of the WISE filter bands in Bauer et al. (2011, 2012), we find the production rate estimates listed in Table 2. We find no excess in the VB signal, and indeed no significant W2 signal at that time. The 1σ upper limits listed in Table 2 provide a relatively loose constraint on production during VB owing to the comet's heliocentric distance of 4.18 AU. The W1 signal listed in Table 2 is of an even lower S/N of 1.4. Still, we have calculated a corresponding Afρ value, and we use it later to constrain the dust properties, assuming any signal is primarily from the dust's reflected light.

Figures 1(C) and (D) show the dust morphology in the highest resolution thermal band, W3. Compared to the color Figures 1(A) and (B), the morphology is similar in both thermal bands. Finson–Probstein dust models (Finson & Probstein 1968) for various β parameters were performed using the comet viewing geometries at the time of VA and VB. The β parameter describes the ratio of the force on dust grains attributed to solar radiation pressure relative to solar gravity. In physical units, this gives the ratio (Burns et al. 1979; Finson & Probstein 1968)

$$\begin{equation} \beta = 1.19 \times 10^{ - 4} \frac{{Q_{{\rm pr}} }}{{\rho _d d}}, \end{equation} \tag{ 1a }$$

where ρ_d is the dust grain density in g cm⁻³, d is the grain diameter in cm, and Q_pr is the scattering efficiency for radiation pressure, with Q_pr ∼ 1 for grain sizes of d > λ (Burns et al. 1979), where λ is the wavelength of the observation. As the WISE bands are relatively insensitive to grains with d ⩽ λ, particularly with respect to the peak wavelength of scattered light from the Sun, this relationship applies. Larger β (⩾0.1) implies a stronger coupling to solar radiation pressure. Assuming a grain density ∼1 g cm⁻³, β values ∼0.01 correspond to grain sizes of ∼100 μm.

The value of β is incorporated into the equation of motion in the following way:

$$\begin{equation} \ddot{\bf x} +(1-\beta)\frac{{\it GM}_s}{{\bf |x|}^3}{\bf x}=0 \end{equation} \tag{ 1b }$$

where G is the universal gravitational constant, M_s is the mass of the Sun, and x is the vector position of the object. This is a simple equation of motion that can then be integrated for different values of β to track the motion of particles with a particular β value.

The computations used a numerical integrator written in Python (based on the work of Lisse et al., 1998), which took a set of β values, integrated the motion of the dust particles over the designated time interval, and returned the syndyne for each β input. A syndyne is the path of dust grains released from the nucleus of a comet continuously with a particular value of β. This created a set of curves (syndynes) that show the theoretical positions of dust with a particular β-value that was released starting at some initial time up to the time the image data were observed. Since the forces on particles of different β are relatively different, the syndynes will tend to fan out in the comet's orbital plane. If the data are truly represented by the syndynes, the curves will span the width of the dust tail when overplotted on the comet image. In the general case, the relative velocity of the grains from the comet's surface can be included into the integration, giving the curves a spread of some finite width. In this case, we are interested in matching the large-scale morphology, so the particles were given no initial velocity. The syndynes that best matched the data, for both visits, were two years old, 8–13 months before its 2009 February 28 perihelion, and for β ∼ 0.001, corresponding to dust grain diameters ∼1 mm.

We extracted thermal signal in the highest-resolution thermal band, W3, using a 9 arcsec aperture radius surrounding the central condensation of the comet (see Figure 2(C)). This aperture size corresponded to three times the W3 PSF FWHM (Cutri et al. 2012). After correcting for flux offsets between visits, the data were phased to a period of 12.65 hr (Lamy et al. 2008). The data were too sparsely sampled to confirm or refute the period. However, the data are consistent with the low amplitude (Δm = 0.4 ± 0.1) of brightness variation reported previously (Kelley et al. 2008) and implying a minimum a/b principal axis ratio of 1.45 ± 0.15 (cf. Meech et al. 1997).

We calculated the εfρ for the dust and found that the values matched across both thermal bands and apertures within the uncertainties. Converting these values into effective particle column densities leaves no significant increase in the number of grains as a function of decreasing wavelength, implying a discrete PSD slope much less than α = −3 (cf. Fulle et al. 2004). In fact, we find that between sizes of 11 μm and 22 μm, there is no excess area, implying that most of the dust in the aperture is of size 22 μm or larger, i.e., that the cumulative dust PSD is flat below 22 μm. This is likely caused by solar radiation pressure removing smaller grains from an old dust population, as significant dust emission has ceased some months before.

The dust trail analysis (Figure 1) in combination with the dust coma photometry places additional constraints on dust production. Dust production is better constrained using IR observations as compared to optical alone, since most of the mass resides in larger grains, while the optical signal is dominated by smaller grains (cf. Bauer et al. 2008). Assuming dust densities ∼1 g cm⁻³, we derive dust sizes ∼1 mm for the β ∼ 0.001 syndyne (see Equation (1a) and Figures 1(C) and (D)), the larger of the β values with orbits that possibly match the morphology. This implies an individual grain mass of 5 × 10⁻⁴ g. By multiplying our value of εfρ by πρ and dividing by an assumed emissivity value ε ∼ 0.9, we can derive an effective area. Our εfρ value derived from the 22 μm flux yields an effective total area of 1.4 × 10¹² cm², and with a mean individual grain area of 7.85 × 10⁻³ cm², yields a grain count of N_dust ∼ 1.8 × 10¹⁴ grains for the 11 arcsec aperture. This yields an average dust grain column density of 6 × 10⁻⁶ grains cm⁻² within ∼32,000 km of the nucleus, or an average density of ∼2 × 10⁻⁹ grains m⁻³. If we use the maximum grain size from Ishiguro (2008), we still derive 6 × 10¹² grains within the 11 arcsec aperture and a corresponding 8 × 10⁻¹¹ grains m⁻³, though the morphology suggests these will be concentrated in the dust tail. With a grain density of 1 g cm⁻³, we find a total mass of 9 × 10¹⁰ g within the 11 arcsec aperture for VA, similar to other JFC coma dust mass estimates (cf. Lisse et al. 2002). Scaling the length of the β ∼ 0.001 syndyne, a mean crossing time for the 11 arcsec aperture is ∼12 ± 3 days, yielding a mass-loss rate of ∼7 (±2) × 10⁴ g s⁻¹. Similar analysis of the VB data yields a comparable mass-loss rate of ∼4(±1) × 10⁴ g s⁻¹, i.e., in agreement with VA within the uncertainties of crossing time and measured flux. At the calculated mass loss for VA, the orbital mass loss is 1–1.5 × 10¹³ g orbit⁻¹, or on the order of other JFCs of similar size (cf. Reach et al. 2000; Lisse et al. 2002) which range between ∼10¹² and 10¹⁵ g orbit⁻¹. Note, however, that this is a lower limit, as the mean particle size may be larger than the 1 mm assumed from the morphological analysis of the dust. Also, these are based on only two spans of observations while the comet is outbound and at heliocentric distances where the water sublimation rate is low.

Reflected light signal is detected in W1 for only VA, and the detection is at the ∼1.4σ detection strength (9.0 ± 6.3 μJy for the coma flux, i.e., with the estimated nucleus signal removed). The W1 single VA S/N ∼ 1 detection presents an opportunity to constrain dust production and PSD, but it also provides a further constraint on the dust grain albedo at 3.4 μm (hereafter p_W1). Since a higher reflectivity will result in a brighter signal at shorter, i.e., reflected-light, wavelengths from the quantity of dust observed at thermal wavelengths, we can actually constrain the albedo. Smaller dust grains scatter light more efficiently per unit mass. A quantity of dust with the same effective area in all bands implies a PSD α ≪ 3, where the number of dust grains of a size d, N_dust(d), is proportional to d to the power −α. Fulle et al. (2004) found values of α between 3 and 3.5 for 67P at smaller heliocentric distances out to 2.7AU. The effective area of emitted light from the larger-grains must not exceed the effective area derived for the reflected light of the same dust observed at shorter wavelengths. For grain reflectivity ∼0.03, the effective areas match, leaving, as we saw, considerably fewer small grains to account for the fraction of an effective area left when subtracting out the contribution from grains with sizes at or in excess of ∼22 μm. In other words, the W1 signal is consistent with the quantity of dust seen in W3 and W4 if only 3% of the light is reflected. A more direct comparison is made by comparing the thermal band εfρ and W1 reflected light Afρ values. Both should describe the same quantity of dust. Within the uncertainties, assuming an emissivity near 0.9,

$$\begin{equation} p_{{\rm W}1} \approx 0.9\frac{{Af\rho }}{{\varepsilon f\rho }},\end{equation} \tag{ 2 }$$

which yields a value of p_W1 ≈ 0.053 ± 0.04. However, with such a low S/N detection, it is not unambiguously caused by noise. In such a case, the 3σ detection limit would still place the p_W1 ⩽ 0.12. To summarize, assuming the large-grain dust dominates both the reflected light at 3.4 μm (W1) and emitted light (W3 and W4), we find a mean grain p_W1 of 0.05 ± 0.04, or alternatively place a 3σ constraint on the large-grain p_W1 value of ⩽0.12; in any case, the large-grain reflectance is not consistent with bright ice-dominated grains.

If we assume a significant small-grained (a few microns or less in size) contribution to the coma brightness, such that the contribution of the small grains to the W3 and W4 signal was not significant, while the contribution to the W1 signal was significant, the resultant mean albedo would be less than 0.05, assuming small grains and large grains shared the same reflectance. If the grains were very dark at 3.4 μm, i.e., if pp_W1 ∼ 0.02, the small grains would account for 1.6 times the effective area accounting for the signal at W3 and W4. Assuming further that the majority of these small grains had diameters ∼3.4 μm, the derived value for the discrete size distribution α would be ∼2 to 2.3, considerably lower than the α = 3–3.5 reported by Fulle et al. (2004). Finally, though it may very well be the case that α ∼ 3–3.5 while 67P is more active, given the nearly equal εfρ values for W3 and W4, it is not likely that a power law adequately describes the size distribution of dust if small-grain particles are present at these distances while the comet is outbound. Such a bi-modal dust PSD may be possible if the large-grain dust, relatively unaffected by solar radiation pressure, is from a remnant trail, lingering from earlier activity, while more recent activity is weak, ejecting relatively few small dust grains from the surface.

Constraining the optical brightness without simultaneous optical imaging is complicated by the possibility of outburst during independent wavelength observations. Using the Minor Planet Center (MPC) database (http://www.minorplanetcenter.net) we find reported brightness values (of unspecified band-passes) between 18.4 and 20.4 (MPC 69186) spanning the time from 2009 November 22 through 2010 March 10. Similarly, reported brightness values range from 19.5 to 20.5 (MPC 71054) at the time of the June observations. Because the aperture size and accuracy of the reported photometry are unknown, one cannot use these as constraints to our PSD, as applied in Bauer et al. (2008), with the reported optical observations constraining particle sizes on the order of 0.5–1 μm. However, assuming an R-band brightness of ∼19 (±1) mag (i.e., near the 18.4 mag measurement corrected for phase and distance for VA) corresponds to the same aperture value as in VA, we derive an Afρ value of 14.2 (+21/−8) (in cm units), and find a p_vis ∼ 0.09 (+0.10/−0.06) for the quantity of dust detected in the thermal bands, roughly consistent with our value for p_W1. Similarly, for VB, assuming an R-band magnitude of ∼20, p_vis ∼ 0.06. As the presence of some small-grained dust cannot be completely ruled out, owing to the temperature excess (Section 2.2), these reflectances based on the reported visual band magnitudes should be considered as crude upper limits to the large-grain dust albedo.

It is important to note the similarities and differences between the observed behavior of 103P/Hartley 2 and 67P. We find in both comets evidence for a persistent trail, and clear evidence of large-grained particles at heliocentric distances far from each comet's perihelion (cf. Bauer et al. 2011). The CO₂ detection in 103P was clearly more pronounced, though it was observed at a considerably closer heliocentric distance, and evidence reported here exists for some CO₂ activity in 67P. Other comets show activity at large distances beyond 3 AU (cf. Stansberry et al. 2004; Lisse et al. 2004; Meech et al. 2009). Thus such behavior is not unprecedented. However, we might expect to find more evidence of the existence of small-grained dust than we do here, resulting in a more significant W1 flux. It must be emphasized that the W2 excess signal is only at the ∼2σ–3σ level relative to the expected dust contribution to the signal, and that the W2 signal in total is only a ∼4σ detection. With this in mind, a calculation can be made regarding the active area for the CO₂. Using the values for Z, shown in log units of mol s⁻¹ m⁻² in Meech & Svoren (2004), we compare our derived $Q_{{\rm CO}_2 }$ and Q_CO listed in Table 2 with the $Z_{{\rm CO}_2 } \sim 8 \times 10^{20}$ and Z_CO ∼ 1 × 10²² mol s⁻¹ m⁻², which yields an active area of ∼10⁵ m² and 4 × 10⁴ m², or 0.3% to 0.1% of the nucleus surface area, for CO₂ and CO, respectively, at a distance of 3.32 AU. Using Meech & Svoren (2004) to scale the reported water production rates from Combi et al. (2010), and assuming constant active area, we find a CO₂/H₂O production ratio ∼30% at 3.32 AU, provided the W2 signal excess is from CO₂ emission.