THE NEOWISE-DISCOVERED COMET POPULATION AND THE CO + CO₂ PRODUCTION RATES

During the cryogenic mission, NEOWISE was the most prolific discoverer of comets, other than the Sun-grazing comets observed by Solar and Heliospheric Observatory. NEOWISE discovered 18 comets during the prime mission and discovered activity on an additional three small bodies. Since the beginning of the reactivated mission, NEOWISE has discovered four additional comets.¹¹ For the prime mission discoveries, about half of the comets are designated long-period comets (LPCs; comets with orbital periods >200 years). For the reactivated mission half of the comets discovered are LPCs.

The new NEOWISE comets (see Figure 1) form an interesting population that has been discovered based on their thermal emission in the infrared, rather than reflected visible light. This is particularly important as the low albedos of the nuclei (Lamy et al. 2004) and potentially the darker refractory grains (Bauer et al. 2012a) make discovery in reflected light difficult until cometary activity increases the brightness dramatically upon approach to perihelion. The large-grain dust component may be comprised of dark, refractory grains that facilitate detection and study at IR wavelengths out to greater distances than can be reached by reflected light. Finally, strong gas emission lines of CO (4.67 μm) and CO₂ (4.23 μm) fall within the NEOWISE 4.6 μm channel (≥80% peak throughput from 4.13 to 5.14 μm; Wright et al. 2010), allowing abundance constraints to be set on these species. CO is otherwise only observable from the ground for bright comets, or if the comet's geocentric velocity is large enough that the comet lines are sufficiently Doppler shifted from their telluric counterparts (see Dello Russo et al. 2009). Emitted CO₂ is only detectable directly from space (Bockelée-Morvan et al. 2004). In this paper, we describe this NEOWISE-discovered population in detail, including analysis of the dust, constraints on the nucleus sizes, and gas production rates of various species. We provide a wider context for the CO + CO₂ analyses by exploring the CO + CO₂ production in the full comet sample from the 163 comets, roughly a quarter of which show 4.6 μm band excess attributable to CO or CO₂ gas emission. Because the NEOWISE W2 band encompasses both CO and CO₂ features, it is difficult to separate their relative contributions; however, CO is generally more than a factor of 11 times weaker than the CO₂ feature (see Section 4.6).

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Where H₂O-driven sublimation begins beyond 6 AU and can lift optically detectable sub-micron dust, comets are variable objects that become obviously active typically somewhere inside 4 AU when they cross the point at which water–ice sublimation becomes the dominant driver of activity (Meech & Svøren 2004). However, the exact details of when and how active they will become remains difficult to predict as these events are sensitive to variations in their compositions. In the outer solar system, water–ice is very common, yet other common ices exist as well that can sublimate rapidly at distances greater than 4 AU. For the last several decades, comets have been grouped into dust-rich and gas-rich categories that may not necessarily correlate with their dynamical age or origin (A'Hearn et al. 1995). In most circumstances, water–ice sublimation likely drives their activity near perihelion, but at larger distances other common volatile constituents like CO and CO₂ may be the primary driver. Recent studies have shown that the CO or CO₂ production rate relative to H₂O increases with heliocentric distance (A'Hearn et al. 2012), but these analyses are based on a limited sample. Some in-situ measurements, for example with comet 103P/Hartley 2 (see A'Hearn et al. 2011), suggest different source regions for CO₂ and H₂O on the surface. To date, only 40 comets have had their CO or CO₂ production rates constrained from space-based observations (see Bockelée-Morvan et al. 2004; Pittichova et al. 2008; Bauer et al. 2011, 2012a; Ootsubo et al. 2012; Reach et al. 2013). The NEOWISE sample represents a uniform survey of CO + CO₂ production collected with a single space-based instrument with consistent instrumental response. This sample nearly doubles the sample of measured CO + CO₂ production rates in comets reported in the literature. Moreover, the 12 and 22 μm channel observations set firmer constraints on the nucleus and dust contributions to the signal than do 2-band constraints such as those provided by Spitzer Space Telescope (SST; Reach et al. 2013), allowing the gas contribution to be separated.

During the fully cryogenic portion of the mission, simultaneous exposures in the four WISE wavelength bands were taken once every 11 s, with exposure durations of 8.8 s in W3 and W4, and 7.7 s in W1 and W2 (Wright et al. 2010). The number of exposures acquired for each moving object depends on its rate of motion across the sky, as well as the rate of survey progression. A total of 8 exposures were collected for areas on the sky on the ecliptic on average at each pass, rising to several hundreds of exposures near the ecliptic poles. For most moving objects, this cadence resulted in collecting ∼12 exposures uniformly spaced over ∼36 hr (Mainzer et al. 2011a; Cutri et al. 2012). Note that WISE may have observed a subset of its full sample of observations of any particular solar system object while it was in different parts of the sky, i.e., when several weeks or months had passed since the previous exposure (e.g., comet 67P; Bauer et al. 2012a), often providing data at different viewing geometries. Henceforth, we refer to the series of exposures containing the object in the same region of sky as a "visit," or "epoch." The spatial resolution in the WISE images varies with the wavelength of the band. The FWHM of the mean point-spread function (PSF), in units of arcseconds was 6.1, 6.4, 6.5, and 12.0 arcsec for W1, W2, W3, and W4, respectively (Wright et al. 2010; Cutri et al. 2012).

As with the comets we have previously studied (Bauer et al. 2011, 2012b), some analysis was improved by stacking at the objects' rates of motion to increase the signal-to-noise ratio (S/N). For each body, the images were identified using the WISE image server (http://irsa.ipac.caltech.edu/applications/wise), as described by Cutri et al. (2012). Images were stacked using the moving object routine, "A WISE Astronomical Image Co-adder" (AWAIC; Masci & Fowler 2009). Figure 1 shows the variation in morphology of the subset of cometary objects discovered by WISE/NEOWISE.

During the fully cryogenic prime mission, 163 comets were detected by WISE/NEOWISE with an S/N ≥ 5 in the stacked image from at least one band. Of these, 94 were detected with an S/N ≥ 5 in single-exposure images by the WISE moving-object pipeline sub-system (WMOPS). The additional 69 comets were found by co-adding the exposures at each visit. Of the comets detected, 57 were LPCs and 106 were short-period comets (SPCs; comets with orbital periods <200 years), according to present designations.¹²

We report here on the comets discovered by WISE/NEOWISE. We also discuss the total sample of comets that show 4.6 μm excess, likely attributable to CO + CO₂ emission. A summary of their WISE/NEOWISE observations are shown in Table 1. Note that LPCs are indicated by a "C/" prefix to their designations.

As of 2015 June, there were a total of 25 cometary body discoveries made by data from the WISE spacecraft. These include three distinct categories. Comets 237P, 233P, and P/2009 WX51 (Catalina) were known objects at the time of the discovery of their activity, but were not known to be previously active. NEOWISE reported coma and trails for these objects as they were imaged during the prime mission. Additionally, WISE discovered 18 new comets during the prime mission, which were named for the spacecraft discovery. These two groups represent a significantly different sample apart from other cometary discoveries, since each comet, or its active nature, was first discovered at thermal IR wavelengths, while comets discovered from ground-based telescopes are selected based on optical observations. Note that this sample could include a further member, 2010 KG43, a body on a centaur-like orbit that was reported to have activity when viewed by the Palomar Transient Survey (Wasczac et al. 2013). The WISE discovery observations of this object, taken at a significantly different epoch, showed no coma or extended emission.

In the first year, the reactivated NEOWISE mission has discovered three new active comets. These comets (each called NEOWISE) were discovered from their 4.6 μm signal, and so may have yet a different set of selection biases apart from those found in the prime mission or ground-based searches. A fourth comet, P/2015 J3 (NEOWISE) was discovered on 2015 May 15, after the first submission of this manuscript.

Throughout the fully cryogenic portion of the WISE/NEOWISE mission most comets exhibited their highest S/N in the 12 and 22 μm channels, as the dust, often dark and composed of refractory grains (see Bauer et al. 2011, 2012a), provided strong thermal signal relative to the background. However, a total of 56 comets showed some signal in the 4.6 μm channel, and often also at 3.4 μm. While dust thermal emission dominates the 12 and 22 μm bands, the 3.4 μm channel is dominated by the reflected light of the dust. Weak molecular emission lines, primarily from O–H and C–H related species, fall within this channel, but this signal typically is significantly less than that of the dust signal, i.e., ∼30% or less of the total signal (see Bockelée-Morvan et al. 1995; Reach et al. 2013). However, strong molecular emission lines of CO (4.67 μm) and CO₂ (4.23 μm) exist within the 4.6 μm bandpass (see Pittichova et al. 2008; Bauer et al. 2011, and Reach et al. 2013). The CO and CO₂ emission bands are strong enough to manifest excess flux within the 4.6 μm channel, apparent when the dust signal contribution is constrained by the 3.4 μm signal and the 12 and 22 μm thermal flux. Often, there are additional morphological differences between the 4.6 μm signal and the other bands. Moreover, the shape of the comets in the 3.4 μm channel often matches better the 12 and 22 μm signal, likely attributable to dust (Figure 2).

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A total of 39 comets observed during the prime mission exhibited 4.6 μm band flux excess, attributable to CO to CO₂ emission; two of the comets, C/2009 K5 and C/2010 FB87, exhibited 4.6 μm band excess in the post-cryo mission observations. A quarter of the comets observed during the prime mission, then, exhibited 4.6 μm excess. The rate of occurrence of W2 excess differed for the comets observed thus far during the NEOWISE-Reactivation mission, which are about 2/3rds of the total (Bauer et al. 2014). However, the match is nearly identical among the prime and reactivated mission comets observed with any significant W2 signal; both samples have ∼2/3 with 4.6 μm excess. We included in our sample of W2 excess the comets NEOWISE from the reactivated mission, three of which show 4.6 μm excess.

The counts were converted to fluxes using the band-appropriate magnitude zeropoints and 0th magnitude flux values provided in Wright et al. (2010). 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. The extracted magnitudes for the 11 arcsec aperture were then converted to fluxes (Wright et al. 2010; Mainzer et al. 2011b) and are listed in Table 2. Proper aperture corrections are required for accurate photometry (Cutri et al. 2012), in addition to the color corrections mentioned above. With these corrections, the derived magnitudes are equivalent to the profile-derived magnitudes providing there are no artifacts, saturation, or confusion with other sources in the apertures of the objects.

In order to extract the nucleus signal for the WISE/NEOWISE comet discoveries, we used routines developed by our team (Lisse et al. 1999 and Fernandez et al. 2000) to fit the coma as a function of angular distance from the central brightness peak along separate azimuths, as applied in Bauer et al. (2011, 2012a). 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 for the matching phase of the mission (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 fit 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. For most comets, the coma model fit residuals yielded uncertainty in the photometry of the extracted point-source ∼10% for the W3 and W4 images; these uncertainties were similar to the photometric uncertainties in the combined nucleus and coma signals. However, higher residuals ∼30% were seen for comets C/2010 L5 and C/2010 J4, and are therefore noted as possible upper limits to the nucleus sizes. We also note below that WISE imaged the predicted position of C/2010 L5 in January, before its discovery and did not detect the comet. The detection threshold is less than, but on the order of, the listed nucleus size in Table 3 (E. Kramer et al. 2015, in preparation).

The extracted nucleus signals in W3 and W4 were fit to a NEATM model (Harris 1998; Delbo & Harris 2002; and Mainzer et al. 2011b) with fixed beaming (η) parameters. The fits to only 2 extracted thermal flux points, with increased uncertainties from the raw extractions, were too poorly constrained to leave η as a free parameter to the fit such that it converged to physically realistic values between 0.5 and 3.0 For each comet, fits were used with beaming parameter values fixed to 0.8, 1.2 (Stansberry et al. 2008), and 1.0 (Fernandez et al. 2013). Note that each attempt of a fit 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. Table 3 presents the fit results and uncertainties, while it should be noted that, owing to the uncertainty inherent in the thermal models, there is an additional ∼10% uncertainty in the derived diameter values (Mainzer et al. 2011b, 2011c). The interpolated corrections for temperature are largest in W3. Note that for P/2015 J3 (NEOWISE), the size was based on the W2 signal assuming no coma contamination for an object with a beaming parameter of 1.

Unlike the asteroids, in most cases the visual band magnitudes of the nuclei were unmeasured. Nuclei were either obscured by activity at shorter wavelengths, or were not measured at distances where they were inactive. Since only the 12 and 22 μm channel images were used (except for P/2015 J3), the albedo was relatively unconstrained. For the thermal fits of the diameters, the geometric visible albedo (p_v) was free, but always converged near the initial condition of a few percent. We used the beaming parameter that provided the smallest fit residuals; those η values are listed in Table 3. An assumed 0.2 uncertainty in h is included in the listed diameter uncertainty. However, the uncertainty in p_v would have negligible effect, and so no uncertainty from that term is included with the diameter values listed in Table 3.

From the total NEOWISE/WISE observed sample of comets during the prime mission, 62 comets (or 38%) showed significant signal in W2, as shown in Tables 1 and 2. Not all comets that show significant signal in W2 have significant 4.6 μm flux excess. Some of the signal in W2 is due to the thermal and reflected light emission of the dust. In order to constrain the dust (and potentially nucleus) thermal and reflected light flux component, it is necessary to extrapolate from the thermal and shorter wavelengths. We fit a Planck function to the W3 and W4 flux, and a solar spectrum to the W1 flux for each comet. Using these two components, we determined the predicted flux at W2 (see Figure 3). We consider the flux in excess of the dust (and nucleus) signal when the flux is significantly (at the 3σ level) above the estimated dust and nucleus signal. We use this criterion to be certain of the excess. For those few cases (107P, 169P, and C/2009 F6) where there is weak or no significant W1 signal, we calculate the reflected light signal from the dust thermal signal and assume a corresponding emissivity of 0.9, and a surface reflectance of ∼0.1 to convert this to a reflected light component. For the objects lacking thermal flux measurements (C/2014 C3, P/2014 L2, C/2014 N3, and C/2009 K5), we make the reverse assumptions and extrapolate the thermal component (Stevenson et al. 2015). Using these methods, 42 comets show W2 excess. The excess flux is then converted into CO₂ production estimates using the method described in Bauer et al. (2011, 2012a, 2012b).

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We noted in Section 2.3 that the 3.4 μm coma signal is likely dominated by dust. However we note here that though that is probably true in most cases when the comet has a moderate to high dusttogas ratio, for rare gassy comets it may be that a small but significant component of the signal may be due to weak emission lines, leading to an overall significant contribution to the signal by emissions from organics and OH. Because this is the only reflected light baseline point, the 3.4 μm-based dust reflected light scaling could lead to uncertainties in the baseline fit in some cases. The result would be an underestimate of the CO + CO₂ production. We also note, however, the case of C/2006 W3 (Christiansen), which had a reportedly high gas content (see de Val-Borro et al. 2014), yet for which we had no significant W1 signal, and derived a high CO + CO₂ production.

The CO₂ production rates (${Q}_{{\mathrm{CO}}_{2}}$) are provided as a proxy for the combine CO + CO₂ production (see Section 4.6) , and as a convenience for analysis of the behavior of the comets, with noted limitations regarding the true fraction of the CO and CO₂ species present. The listed uncertainties in the derived CO₂ production rates are the combination of two components. The first component is the uncertainty in the calculated dust contribution as constrained by the W1, W3, and W4 photometry, a comparatively small component owing to the requirement that the flux is significantly (at the 3σ level) above the estimated dust and nucleus signal. The second component in the listed uncertainty is from the uncertainty in the W2 signal photometry, and is added in quadrature with the dust model uncertainty. Possible systematic sources of uncertainties, such as large variations in the fraction of CO relative to CO₂ or contributions to the W1 flux from non-dust signal, are not included in the tabulated uncertainty values.

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, 2012a, 2012b), 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 calculate the effective area for the dust using 9, 11, and 22 arcsec radius apertures. For the thermal bands, this derived area has a factor of the emissivity, , 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 (A'Hearn et al. 1984). We call this factor fρ, as introduced by Lisse et al. (2002) and used in Kelley et al. (2013), which is listed in Table 4. The value of fρ assumes that the observed flux is attributable primarily to the dust continuum emission and is the product of the emissivity, , 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 fρ values multiplying the observed surface brightness of the comet, I_λ, by ρ and dividing by the Planck function, Bλ (Tb), where Tb is the fitted blackbody temperature of the dust. The effective area is derived from this quantity by multiplying by πρ/ using an assumed value of ≈ 0.9. Our uncertainties come from the standard deviation between the derived values for 9, 11, and 22 arcsec apertures. Note that we do not correct fρ values for phase angle (the Sun–target–observer angle) effects, and where we are assuming an idealized 1/r behavior in our estimates of uncertainty, we do not find strong deviations in most cases.

Table 4.  Dust and W2 Excess Analysis Results

Visit	Rh	Delta	${Q}_{{\mathrm{CO}}_{2}}$ a	fρ	Afρ	Teff (K)
	(AU)	(AU)	(log10 molecules s−1)	(log10(cm))	(log10(cm))
P/2009 WX51	1.26	0.76	25.20 +/−0.12	0.72 +/−0.07	0.58 +/−0.08	241 +/−7
233P	1.80	1.43	25.04 +/−0.11	1.18 +/−0.10	0.58 +/−0.09	213 +/−1
P/2010 K2	1.29	0.73	25.74 +/−0.13	1.10 +/−0.08	0.68 +/−0.11	257 +/−2
P/2010 N1	1.55	1.08	25.49 +/−0.14	1.19 +/−0.10	0.67 +/−0.08	233 +/−1
C/2010 L5 Epoch1	1.21	0.65	26.43 +/−0.08	2.12 +/−0.08	1.63 +/−0.10	240 +/−1
C/2010 L5 Epoch2	1.60	1.15	25.08 +/−0.08	1.18 +/−0.08	0.04 +/−0.06	213 +/−3
C/2010 FB87 Epoch3	2.92	2.75	26.48 +/−0.11	3.4 +/−0.3	2.64 +/−0.14	257 +/−2
C/2014 C3	1.90	1.60	25.82 +/−0.08	2.2 +/−0.2	1.45 +/−0.05	207
P/2014 L2	2.26	1.98	27.38 +/−0.08	3.1 +/−0.3	2.35 +/−0.10	195
C/2014 N3 Epoch1	4.43	4.27	26.43 +/−0.10	3.2 +/−0.2	2.51 +/−0.11	136
C/2014 N3 Epoch2	3.96	3.79	26.51 +/−0.11	3.6 +/−0.2	2.78 +/−0.10	144
SPCs With 4.6 μm Excess
29P	6.21	6.04	27.84 +/−0.09	4.61 +/−0.25	3.79 +/−0.05	130 +/−13
30P	1.92	1.56	26.18 +/−0.17	2.64 +/−0.08	1.98 +/−0.05	225 +/−3
65P	2.46	2.25	27.28 +/−0.09	3.60 +/−0.08	2.70 +/−0.06	164 +/−1
67Pb	3.32	3.31	25.87 +/−0.14	2.16 +/−0.07	0.94 +/−0.26	183 +/−4
74P Epoch 1	3.61	3.44	25.88 +/−0.10	2.87 +/−0.09	2.23 +/−0.08	158 +/−1
74P Epoch 2	3.74	3.51	26.22 +/−0.15	3.04 +/−0.09	2.36 +/−0.11	153 +/−1
77P	2.99	2.80	25.45 +/−0.15	2.29+/0.08	1.68 +/−0.08	178 +/−2
81P	2.22	1.87	27.18 +/−0.14	3.59 +/−0.08	2.77 +/−0.05	178 +/−3
94P	2.27	1.94	25.91 +/−0.15	2.43 +/−0.08	1.51 +/−0.13	180 +/−1
100P	2.23	1.98	25.44 +/−0.12	1.49 +/−0.09	1.46 +/−0.05	217 +/−1
103P	2.29	2.04	25.72 +/−0.10	1.56 +/−0.09	1.17 +/−0.05	206 +/−1
116P	2.82	2.64	25.84 +/−0.12	2.88 +/−0.08	1.94 +/−0.06	157 +/−1
118P	2.09	1.75	26.71 +/−0.09	3.13 +/−0.07	2.30 +/−0.04	173 +/−3
143P	3.25	3.08	25.45 +/−0.32	2.19 +/−0.10	0.48 +/−0.05	173 +/−2
149P	2.80	2.52	25.52 +/−0.10	2.10 +/−0.09	1.34 +/−0.07	162 +/−2
169P	2.27	1.94	25.75 +/−0.15	1.69 +/−0.10	0.68 +/−0.07	203 +/−3
217P	2.46	2.15	26.02 +/−0.10	2.63 +/−0.07	1.86 +/−0.27	169 +/−1
P/2009 Q4	2.32	2.02	25.23 +/−0.17	1.53 +/−0.05	0.99 +/−0.08	182 +/−4
P/2010 A3	1.85	1.50	25.86 +/−0.11	2.15 +/−0.09	1.37 +/−0.07	191 +/−1
P/2010 H2	3.15	2.89	25.96 +/−0.10	3.06 +/−0.08	2.20 +/−0.06	143 +/−3
LPCs with 4.6 μm Excess
C/2005 L3	8.21	8.08	26.91 +/−0.10	3.92 +/−0.08	3.15 +/−0.09	102 +/−2
C/2006 S3	7.23	7.16	26.55 +/−0.14	3.93 +/−0.07	3.05 +/−0.05	104 +/−1
C/2006 W3	4.15	4.02	27.88 +/−0.09	4.76 +/−0.07	3.83 +/−0.01	133 +/−3
C/2007 Q3 Epoch 1	2.50	2.25	27.55 +/−0.10	4.18 +/−0.08	3.53 +/−0.05	192 +/−2
C/2007 Q3 Epoch 2	3.45	3.27	26.68 +/−0.10	3.85 +/−0.07	2.91 +/−0.04	144 +/−1
C/2008 FK75	4.77	4.66	25.97 +/−0.12	3.53 +/−0.09	2.65 +/−0.08	120 +/−1
C/2008 N1 Epoch 1	3.08	2.93	25.93 +/−0.10	2.96 +/−0.08	2.07 +/−0.08	150 +/−2
C/2008 N1 Epoch 2	3.76	3.53	25.99 +/−0.32	2.68 +/−0.09	2.01 +/−0.09	136 +/−2
C/2008 Q3	3.97	3.79	26.47 +/−0.10	2.95 +/−0.08	1.98 +/−0.06	139 +/−3
C/2009 K5	2.65	2.45	27.06 +/−0.10	3.35 +/−0.2	2.63 +/−0.09	176 +/−1
C/2009 P1	6.33	6.23	27.16 +/−0.10	4.03 +/−0.09	3.17 +/−0.10	111 +/−1
C/2009 U3	1.67	1.29	26.34 +/−0.10	2.15 +/−0.08	1.64 +/−0.05	201 +/−2
C/2010 J1 Epoch 1	1.84	1.56	25.94 +/−0.37	2.48 +/−0.08	2.07 +/−0.07	229 +/−5
C/2010 J1 Epoch 2	2.49	2.20	25.71 +/−0.16	1.88 +/−0.09	1.23 +/−0.08	222 +/−3

Notes.

^a ${Q}_{{\mathrm{CO}}_{2}}$ production rates are a proxy for the combined rates derived from CO + CO₂ emission (Section 3.3). ^bfrom Bauer et al. (2012a).

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The derived dust and production rates are listed in Table 4. It should be noted that for the comets without W3 or W4 signal, it is not possible to derive fρ values directly from measurements. Therefore, we estimated these values based on the means of the (fρ − Afρ ) values (denoted Δ_(fρ−Afρ)) from our comet sample that had W1 and W3 or W4 signal. We found a mean value of Δ_(fρ−Afρ) = +0.74 +/−0.29 from these comets; therefore, listed values for C/2009 K5, C/2010 FB87, C/2014 C3, P/2014 L2, and C/2014 N3 are simply the W1 derived Afρ values +0.74, with 0.29 added to the Afρ uncertainty in quadrature.

The values for Δ_(fρ−Afρ) were for active comets. The distributions of Δ_(fρ−Afρ) were similar for long and short period comets. The mean offset in the log values corresponds roughly to the a factor of 5.5 difference, which is less than, but within a factor if 1.6 of, what may be expected for a 3.4 μm albedo of ∼0.1 and emissivity of ∼0.9 for the same dust particles. The mean for Δ_(fρ−Afρ), however, is notably different when considering R_h (see Figure 4). The number of SPCs in this sample is too small at large R_h to be statistically significant. Yet, for the LPCs in our sample, for R_h < 3 AU, 〈Δ_(fρ−Afρ)〉 = +0.57 +/−0.14, and for R_h < 3 AU, 〈Δ_(fρ−Afρ)〉 = +0.86 +/− 0.10. This could be indicative of larger grains being lifted by activity at greater distances rather than shorter, or possibly, and perhaps more likely, the persistence of larger grains that remain in the dust coma after peak activity.

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A total of 21 comets were discovered by WISE/NEOWISE during the prime mission, and 4 additional comets have been discovered during the first year of the NEOWISE reactivated mission. Of these 25 objects, 12 are designated LPCs, and those 10 observed during the prime mission have yielded constraints on their nucleus size and dust, along with CO₂ production rates. This gives us a good statistical basis to search for differences between SPCs and LPCs that may be attributed to formation conditions. This small set, a subset of the larger set of 163 comets observed, allows for an unprecedented comparison of nucleus sizes between SPCs and LPCs, for example, using the same methods for each comet. The same methodology does not mean there is no variation on the efficacy of the methods, however, as each comet's behavior varies greatly. Constraints on dust and CO₂ production require the comet be active, or recently active in the case of the dust, where the presence of strong activity during the WISE observations obviously hampers the derivation of nucleus sizes. We provide a description for each comet's behavior below (see also Figure 1).

237P/LINEAR (2002 LN13): Activity was first seen in this JFC by WISE 190 days after its perihelion while at a distance of 2.70 AU from the Sun. No significant signal was observed in W1 or W2. A faint dust tail was apparent, as was a central condensation, easily separable from the dust, which yielded a nucleus size of ∼2 km.

233P/La Sagra (2009 WJ50): WISE viewed this Encke-type comet very close to its perihelion distance, at 1.81 AU from the Sun, just 34 days before perihelion. The comet's faint tail indicated activity, and significant W2 excess that yielded a CO₂ production rate of 1.1 × 10²⁵ molecules per second. A strong central peak in the stacked image yielded an extracted nucleus flux corresponding to a size ∼1 km.

P/2009 WX51 (Catalina): WISE viewed this NEC 61 days after its perihelion (q = 0.8 AU), when it was at a distance of 1.26 AU from the Sun. The comet displayed a tail, and significant W2 excess yielded a CO₂ production rate of 1.6 × 10²⁵ molecules per second. The W3 and W4 signals showed a strong central condensation, and the extracted nucleus flux yielded a size of <0.5 km.

P/2010 B2 (WISE): The first WISE-discovered comet, 2010 B2 (WISE), was detected on 2010 January 23, just 32 days after its perihelion, at 1.64 AU, and again on 2010 August 5, at an outbound heliocentric distance of 2.49 AU. With a Jupiter Tisserand invariant (T_J) of >3, and a semimajor axis less than Jupiter's, the comet was categorized as an Encke-type JFC. The first visit in January showed obvious activity, and detections in all four bands. The second visit showed significant signal only at 12 and 22 μm. The extracted flux from W3 and W4 in the first visit yielded nucleus size estimates, and showed W2 excess in the total signal. Our size estimate of 0.99 +/−0.15 km implies the nucleus comprises less than a quarter of the total signal in the bands. The strength of the thermal signal in the second visit suggests the comet was still active at a distance of 2.5 AU, or that the dust component was still significant (∼50% of the total signal), but did not have sufficient extended signal to remove the coma as was possible in the images from the first visit.

P/2010 D1 (WISE): This comet, the second discovered by WISE on 2010 February 17, was detected only at one visit by WISE, 237 days after its perihelion, at a heliocentric distance of 3.02 AU. A faint coma and tail was shown in the stacked W3 and W4 images, making it identifiably a comet. However, extracted W1 and W2 signals were very faint, near the level of the noise, at or below 3σ. The extracted nucleus signal yielded a diameter of 2.5 km.

P/2010 D2 (WISE): The third comet discovered by WISE was also a JFC, and it was detected only at one epoch by WISE curing the fully cryogenic mission, on 2010 February 26. The images were taken very near to its perihelion, within 8 days, at 3.66 AU. As with P/2010 D1, the coma was faint, but present, yet lacked a distinctly extended tail. Removal of the coma signal yielded a nucleus size estimate of 4.65 km. In addition to strong flux in W3 and W4, the signal in the stacked images showed faint (5σ) signal in W1, but no significant signal in W2 that may have indicated CO₂ or CO emission down to production limits (1σ) of 3 × 10²⁵ and 3 × 10²⁶ molecules s⁻¹, respectively.

C/2010 D3 (WISE): The first LPC discovered by WISE was detected at two separate epochs during the cryogenic survey. The first visit spanned 5 days centered around 2010 February 26 when the comet was 189 days prior to perihelion at a distance of 4.28 AU, and again outbound, 60 days after perihelion, when the comet was at a heliocentric distance of 4.52 AU. No significant W2 was detected in either visit, although weak W1 signal was seen during the first visit, allowing for CO₂ and CO production rate limits of 4 × 10²⁵ and 4 × 10²⁶ molecules s⁻¹, respectively. Faint coma is discernable in the stacked images of W3 and W4 during both visits, and the extracted nucleus signal yielded an estimated size of 4.3 km.

C/2010 D4 (WISE): This LPC was discovered on 2010 February 28, 335 days after it perihelion, at a rather distant 7.43 AU from the Sun. A second visit occurred over 2010 July 5, when the comet was at a larger heliocentric distance of 7.66 AU. The comet is not very active in the WISE images. No significant signal is present in W1 or W2, and the signal in W3 and W4 nearly match the WISE PSF, and are likely dominated by the nucleus. The 12 and 22 μm flux measurements from both visits yield a diameter of ∼25 km.

C/2010 DG56 (WISE): When this LPC was discovered, at a distance of 1.95 AU from the Sun, 3 months prior to it perihelion, no signs of significant activity were apparent. The stack of its PSF-like images for this first visit yielded a diameter of 1.5 km. When the comet was imaged again at a heliocentric distance of 1.87 AU on 2010 July 26, the comet was quite active, enough to sufficiently obscure the nucleus, so that its signal could not be extracted from this second visit. However, though a slight W2 excess was possibly present, it was not above a 3-σ uncertainty.

C/2010 E3 (WISE): Imaged when it was only marginally active, this LPC is on a parabolic orbit. The extracted nucleus signal yielded a size of 0.4 km, and no significant W2 or W1 signal was present. The comet was at a distance of 2.3 AU from the Sun at the time, very near its perihelion distance of 2.27 AU, which occurred one month after its discovery.

C/2010 FB87 (WISE-Garradd): First observed inbound, the comet's image nearly matched the WISE spacecraft's PSF in W3 and W4, and showed no significant signal in W1 or W2. These first observations were made when the comet was at a distance of 3.62 AU from the Sun, 224 days before perihelion. The comet was imaged a second time, still 108 days before its perihelion, while at a heliocentric distance of 3.04 AU. A faint coma and tail were apparent in the images. WISE detected W1 and W2 signal during its second visit, but no significant W2 excess. However, when the comet was imaged by WISE a third time, in the post-cryogenic portion of the prime mission, W2 excess was present. The comet was then outbound at a heliocentric distance of 2.92 AU, 66 days following its perihelion at 2.84 AU.

C/2010 G3 (WISE): This LPC was detected on two separate visits, both during the fully cryogenic phase of the WISE mission, and both while the comet was outbound. The first was within 4 days of perihelion, and the second 83 days after perihelion. With the furthest perihelion distance (4.9 AU) of the WISE/NEOWISE-discovered comets, one might expect CO or CO₂ to have driven the activity. Surprisingly, no significant W1 or W2 signal was seen at either visit, yet W3 and W4 images revealed both dust coma and tail. However, the dust modeling suggests that the activity occurred more than a year prior to the observations, and that potentially, the dust was composed of large-particles that lingered after the outburst. At such distances it was unlikely that CO₂, but rather that CO, was a possible driver. If so, the time of outburst, 726 days prior to perihelion, would have sufficiently preceded the WISE observations that the CO would have photo-dissociated. The predicted time scales for CO dissociation at 4.9 AU are ∼370 days or less (Huebner et al. 1992), and ∼90 days for CO₂.

C/2010 J4 (WISE): Comet C/2010 J4 was detected on two visits in 2010 May, the first two days before its 2010 May 3 perihelion and the second 9 days after. This parabolic comet had a perihelion distance of 1.09 AU, and came within 0.31 AU of the Earth's orbit. Both sets of observations showed significant coma and dust tails. W2 signal was significant in the stacked images of both visits; however, no significant excess above the dust thermal contribution was seen. The dust signal heavily dominated the total signal, and the extracted nucleus flux and derived diameter should therefore be taken as an upper limit.

P/2010 JC81 (WISE): This comet was detected twice during the WISE prime mission. The first visit was during the 4-band fully cryogenic period, when the comet was at a heliocentric distance of 3.9 AU, and the second was during the post-cryogenic period, when the comet was 2.65 AU from the Sun. The first and second visits were 350 and 180 days, respectively, before the comet reached its perihelion at 1.8 AU from the Sun, and before activity was noted by ground-based observations. The stacked images of both visits show a near-bare PSF-like surface brightness profile. The fitted temperature, about 40 K above the blackbody temperature, was consistent with a nucleus with a beaming parameter ∼0.8. No strong indication of W2 excess was present in the fully cryogenic mission data, and the W1 and W2 fluxes in the second visit were also consistent with a bare nucleus with a beaming parameter near 0.8, and a visual-wavelength albedo on the order of a few percent. We note that it is possible for comets to be very active even out to large heliocentric distances, though small comets have been observed without coma as well. P/2010 JC81 should be an interesting candidate for study upon its return in 2034 for signs of a large nucleus.

P/2010 K2 (WISE): This JFC was detected only once during the WISE fully cryogenic mission, and it exhibited a faint tail in W3 and W4. The images were taken when the comets was at a distance of 1.29 AU from the Sun, less than a tenth of an AU from its perihelion distance, and within 41 days of its perihelion passage. There was a clear W2 excess in the flux, which yielded a CO₂ production value of 1.3 × 10²⁵ molecules per second. The extracted nucleus flux was consistent with a sub-kilometer size diameter.

C/2010 KW7 (WISE): This LPC was imaged by WISE during the fully cryogenic mission 255 days prior to its perihelion and again 148 days before perihelion, at heliocentric distances of 3.7 and 3.0 AU, respectively. No significant W1 or W2 signal was seen in either data set. However, the W3 and W4 signals were strong, and the W3 and W4 brightness profiles matched WISE PSFs for the two band-passes. The data yielded a nucleus size for this body of ∼6 km. Activity was later identified by observations taken at Spacewatch (c.f. Scotti & Williams 2010) 17 days following is perihelion at 2.57 AU from the Sun.

245P/WISE (2010 L1): Activity was clearly shown in the first set of images WISE obtained of this JFC. The stacked images yielded no significant W1 or W2 flux values. The data were taken 120 days after the comet's perihelion, when it was at a distance of 2.6 AU from the Sun. The nucleus signal extracted from the stacked images yields a diameter of ∼1.5 km.

C/2010 L4 (WISE): A dust coma and tail were apparent in the individual images of this LPC, taken 112 days before its perihelion while the comet was at a distance of 3 AU. The stacked images showed no significant signal in the two shortest band passes. The extracted nucleus signal corresponded to a diameter of 3.4 km.

C/2010 L5 (WISE): The comet C/2010 L5 was the only WISE-discovered Halley type comet (HTC). It was strongly active when it was first detected 52 days after its perihelion, and again 85 days after. W2 excess was apparent in both of these visits, and yielded CO₂ production rates of 2.7 × 10²⁶ and 1.2 × 10²⁵ molecules per second, respectively. Because the comet was so active, the extracted nucleus signal, yielding a diameter of ∼2 km, should be regarded as an upper limit. This is further supported by a non-detection at the comet's predicted location in January (E. Kramer et al. 2015, in preparation). Large-grain dust modeling suggests that the comet's peak activity was near perihelion (Table 6). However, its worth noting that CO₂ dissociation lifetimes are ∼5 and 10 days for the comet's heliocentric distances of 1.2 and 1.6 AU, respectively, while CO₂ and CO lifetimes are ∼22 and 39 days at these distances. It is unlikely, then, that outgassing had completely ceased very soon after perihelion. This particular case is discussed in detail in E. Kramer et al. (2015, in preparation).

P/2010 N1 (WISE): This inbound JFC was discovered at a heliocentric distance of 1.55 AU, 41 days prior to its perihelion. The comet was moderately active, but showed a strong W2 excess and yielded CO₂ production rates of 3.1 × 10²⁵ molecules per second. The extracted nucleus flux was consistent with a solid surface diameter of 0.9 km.

P/2010 P4 (WISE): The final comet WISE discovered during the prime mission was a JFC, detected 31 days after its perihelion. The stacked image revealed a faint tail with a morphology consistent with dust particles emitted long before perihelion. No significant W1 or W2 signal was detected, and the extracted nucleus signal matched a body with a diameter of 1.2 km.

C/2014 C3 (NEOWISE): As with all three comets discovered during the first year of the NEOWISE reactivated mission, no nucleus sizes could be confidently derived from the W1 and W2 images, owing to the level of activity and dust signal observed at these bandpasses. However, all three comets discovered by the reactivated NEOWISE mission to date showed 4.6 μm channel excess. This LPC showed W2 excess that yielded CO₂ production rates of 6.6 × 10²⁵ molecules per second at a heliocentric distance of 1.9 AU, 29 days after its perihelion.

P/2014 L2 (NEOWISE): The second comet discovered during the reactivated NEOWISE mission was a JFC. NEOWISE imaged the comet 37 days before it reached perihelion, at a distance of 2.26 AU from the Sun. The stack images revealed a remarkably extended morphology in W2 relative to the more compact dust coma and tail in W1, and yielded a CO₂ production rate of 2.4 × 10²⁷ molecules per second.

C/2014 N3 (NEOWISE): This LFC was discovered by NEOWISE at a distance of 4.4 AU, 251 days prior to its perihelion, and it showed a faint tail and coma in the stacked images. The W2 excess yielded a corresponding CO₂ production rate of 2.7 × 10²⁶ molecules per second, although CO production at a rate of 2.9 × 10²⁷ molecules per second is the more likely driver at the distances the comet was observed. A second visit occurred 90 days before perihelion (R_h = 3.96 AU), and apparent W2 excess yielded CO production rates of 3.9 × 10²⁷ molecules per second.

P/2015 J3 (NEOWISE): The latest NEOWISE comet discovery was made on 2015 May 15 at a distance of 1.67 AU from the Sun. The JFC showed no indication of activity morphologically, but in ground-based follow-up images there was a faint tail. Size estimates for the nucleus are 2.3 +/−0.7 km, and reflectance 0.02 +/−0.02, based on JPL's Horizons rough estimate of the visual-band nuclear magnitude at 18.5.

2010 KG43: This body, on a centaur-like orbit, was found to be active by Waszczak et al. (2013), but has not been confirmed as a comet. Significant flux values were observed in W3 (3.3 +/−0.6 mJy) and W4 (9 +/−2 mJy) during the prime mission, yielding a preliminary diameter of 4 +/−1 km, and an albedo of 0.2 +/−0.02 for the object, assuming a beaming parameter near 1. This body is not included in the further analyses, since it's official cometary status remains undetermined.

The nucleus sizes of the discovery comets listed in Table 3 are shown as cumulative distribution plots in Figure 5. This sample is not large enough to make definitive conclusions as to the size frequency distribution power-law exponents for the total or sub-samples of LPCs and SPCs. Additionally, these samples are not de-biased in any way. However, because they were discovered by the WISE spacecraft, neither are they pre-selected by a strong visual reflectance bias. The data also includes two possible upper limits for the LPCs. However, these fall well below sizes that would influence the mean fractional sizes of the samples. An analysis using a minimum-variance unbiased estimator (MVUE) routine based on Feigelson & Babu (2012) was utilized to examine a power-law relation. The results were inconclusive, with the LPC sample yielding a size frequency distribution power-law exponent, α, of 1.4 +/−0.2, and the SPC sample yielding α = 1.6 +/−0.2.

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Figure 5 suggests that the LPC nuclei are, on average, larger than the SPC nuclei, by something like a factor of ∼2. This conclusion is consistent with a similarly sized sample of LPCs presented in Lamy et al. (2004) compiled from sizes in the literature. Statistically, however, the sample sizes are small; a Kolmogorov–Smirnov test of the NEOWISE discovered LPC and SPC size distributions yields a 94% confidence that the diameters come from different distributions. One of the sources in the Lamy et al. (2004) compilation of diameters was Meech et al. (2004), which concluded from visual-wavelength data that there was no average size difference between LPCs and SPCs while using an assumed geometric albedo. Note also that our sample contains SPCs with nuclei larger than 10 km in diameter. SPC nuclei on these scales were also measured in the SEPPCoN sample reported by Fernandez et al. (2013).

Of the 21 comets discovered by WISE during its prime mission, 9 (6 LPCs and 3 SPCs) were found to have extended emission due to dust tails. We employed the well-described Finson–Probstein (Finson & Probstein 1968) method to model these dust tails in order to constrain the size and age of the particles that comprised those tails. The Finson–Probstein method assumes that once a particle leaves the surface of a comet, its motion is only governed by solar radiation pressure and solar gravity, thereby allowing the particle motion to be parameterized using the ratio of these two forces, called β:

$$\begin{eqnarray*}&&\beta ={F}_{\mathrm{rad}}/{F}_{\mathrm{grav}}\end{eqnarray*}$$

where F_rad is the force due to solar radiation and F_grav is the force due to solar gravity. Putting in the appropriate values for F_rad and F_grav and collecting the constant terms yields the ratio

$$\begin{eqnarray*}&&\beta =\displaystyle \frac{{{CQ}}_{{pr}}}{{\rho }_{d}a}\end{eqnarray*}$$

where ρ_d is the particle density [g cm⁻³], a is the particle radius in cm, Q_pr is the scattering efficiency due to radiation pressure, and the factor C = 5.78 × 10⁻⁵ g cm⁻² comes from collecting all the constants into a single term. Thus, we can see that β is inversely proportional to the size of the particle: larger β values correspond to a smaller particle size, and vice versa.

The β parameter is incorporated into the equation of motion, which is then integrated for a range of β values using a numerical integrator (based on the work of Lisse et al. 1998, with the version used here described in further detail in Kramer 2014). For each comet, we ran the models for 5 years in 1-day increments, with β values ranging from 0.0001 (roughly cm-sized particles) to 3.0 (sub-micron sized particles). This allowed us to fully explore the reasonable parameter space for each comet tail. The software returns a matrix of points that can be plotted as curves of constant emission date (synchrones) or curves of constant β (syndynes). The models were over-plotted on each corresponding W4 image, allowing the best β and time since emission to be found for each comet.

In order to determine the heliocentric distance at which strong emission occurred, we find the synchrone that most closely matches the brightest part of the tail, giving the number of days since the emission occurred. We then step back in the comet's orbit using the online tool Horizons from JPL to find the heliocentric distance of the comet at that time. The β values listed in Table 6 do not mean that there were no small grains released, but more likely that either they have all been swept away already or that they are not optically active at W3 and W4 wavelengths. We further emphasize that this is not necessarily the only time that emission occurred for the comet; it is only where strong emission of particles which are still in the image frame occurred. Similarly for the interpretation of the syndynes, we note that the β values listed in Table 6 correspond to the brightest part of the tail, and there are likely particles both larger and smaller than suggested by the best β. The results of this method are shown in Table 6, as well as in Figure 6.

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Figure 7 shows the distribution of effective dust temperature based on the W3 and W4 band thermal fluxes. These may be effected by more than the dust temperature, namely variations in emissivity with silicate emission features (cf. Hanner & Bradley 2004). However, in a gross sense, these values are consistent with isothermal bodies with emissivity ∼0.9. The standard deviation of the points from the thermal curve is +/−17 K.

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The presence of CO or CO₂ manifests as a flux excess above the dust signal, as well as a difference in the morphology in W2 (Sections 2.3 and 3.3). WISE detected 163 comets during the prime WISE/NEOWISE mission. We found significant W2 flux excess in 40 comets, listed in Table 4. Assuming CO₂ was the dominant source of the W2 excess for all 40, we have converted the flux excess into CO₂ production rate values (molecules per second), or ${Q}_{{\mathrm{CO}}_{2}}$. Of course, this is not valid for all the 40 comets. We know significant CO was detected for 29P (Senay & Jewitt 1994) and for C/2009 P1 (Garradd; Feaga et al. 2014), observed at 6.2 and 6.3 AU, respectively, in the NEOWISE data. However, these values are readily convertible to approximate CO production rates (Q_CO) by multiplication of the ratio of CO₂ to CO fluorescence efficiencies (${g}_{{\mathrm{CO}}_{2}}/{\text{}}{g}_{\mathrm{CO}}$ = 11.6; see Crovisier & Encrenaz 1983). The conversion to hypothetical ${Q}_{{\mathrm{CO}}_{2}}$ production rates facilitates possible comparisons between CO₂ and CO dominant behavior, and how it may be related to the quantity of dust present. We note, as discussed in Section 3.3, the listed uncertainties in the derived CO₂ production rates are the combination of the uncertainty in the calculated dust contribution as constrained by the W1, W3, and W4 photometry, added to the uncertainty from the W2 signal. Possible systematic sources of uncertainties, such as large variations in the fraction of CO relative to CO₂ or contributions to the W1 flux from non-dust signal, are not included in the tabulated values.

The ${Q}_{{{CO}}_{2}}$ proxy and fρ values are plotted as a function of heliocentric distance in Figure 8. Except that the 15 LPCs may be more active than 24 SPCs at heliocentric distances greater than 4 AU, no differentiating trend is readily apparent for CO₂ production. To identify correlations, a Kendall-τ test was applied to the LPC and SPC distributions for comet heliocentric distance with CO₂ production and with fρ; high τ values near 1 indicate a correlation between the two parameters, and low values (∼ −1) indicate anti-correlations, where values near zero indicate no correlation. A second variable, the two-sided probability parameter, or p-value, is a test for a null hypothesis, such that a low p-value indicates a higher likelihood of the result indicated by the τ value. For example, a well-correlated pair of parameters, but poorly sampled, would have τ and p-value close to 1, and well-sampled correlated pair would have τ ∼ 1 and the p-value ∼0, but a well-sampled, but random, pair of parameters would have both values close to zero. Inside of 4 AU, the Kendall-τ test yielded τ values near 0 (0.18 and −0.10 for LPCs and SCPs, respectively), with low significance (p-values of 0.39 and 0.57 for LPCs and SPCs, respectively). Both SPCs and LPCs appear to have similar distributions given the limited sample. This find, in and of itself, is a significant constraint on current solar system formation theories. Dones et al. (2004), for example, place the source of Oort cloud comets and KBOs to be near Jupiter and near Neptune, respectively. However, A'Hearn et al. (2012) suggest that volatile abundances are similar for differing dynamical classes of comets, implying a comparable formation environment between the CO and CO₂ sublimation zones. This data set may affirm this notion, which places profound constraints on the various solar system scenarios, specifically regarding planetary migration. Such theories (see Morbidelli et al. 2008; Walsh & Morbidelli 2011) which have previously suggested different formation regions for cometary types, may have to account for the comparable compositional profiles between differing comet dynamical populations.

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Unsurprisingly, fρ values correlate well with SPCs (τ = 0.5, p-value = 0.02) and LPCs (τ = 0.4, p-value = 0.02) alike, as suggested previously (see Kelley et al. 2013). When the two values are ratio-ed (log₁₀ ${Q}_{{\mathrm{CO}}_{2}}$ − log₁₀ fρ), as in Figure 9, we find a relation of ${{R}_{{\rm{h}}}}^{-2}$. Inverse proportionality with R_h have been seen with OH and CN (A'Hearn et al. 1995), yet the relationship with CO₂ is particularly clear. Furthermore, where the A'Hearn et al. (1995) gas-to-dust ratio appears to go as ${{R}_{h}}^{-1/2}$, what we find with respect to CO₂ gas is considerably steeper. Such behavior, whereby an increase in CO₂ gas production lacks a corresponding increase in dust production, was noted in 103P (A'Hearn et al. 2011). This relation persists out to 4 AU, where the trend deviates. If CO₂ is expected to drive activity more within these ranges of R_h, this may indicate that the bulk of CO₂ may be endogenic with the dust. Alternatively, or possibly concurrently, it may be that CO reaches its maximum production before 4 AU if it resides at depth and its sublimation is not driven directly by surface insolation of, say, near-surface CO ice, while CO₂ is.

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We found limited overlap between the Akari (Ootsubo et al. 2012; hereafter O12) and SST (Reach et al. 2013; hereafter R13) observations. A total of 13 objects shared reported observations that allowed comparisons with the NEOWISE sample's somewhat larger time intervals. These results are summarized in Figure 10. The fidelity of the comparisons, however, are somewhat limited in several respects. Neither the R13 nor O12 observations provided fρ values, so that only gas production rates could be compared. Furthermore, O12 provided spectrally derived relative abundances, information we did not have, so that in order to make comparisons with our values, we converted the CO and CO₂ rates into proxy CO₂ production rates by dividing the O12 CO rate by 11.6, the scaling factor between the line strengths, and adding it to the reported CO₂ rate. Also, many of the comets that overlapped nonetheless were observed at similar times and heliocentric distances. Finally, we did not compare the limits of the non-detections in O12 and R13, but only detections. We found that, similar to the behavior for other species as analyzed in A'Hearn et al. (1995), variations in individual comet behavior did not clearly indicate trends with heliocentric distance for our proxy CO₂ values. What we found with the aggregate total sample shown in Figure 8, with dispersed behavior, seemed to match with the stochastic nature of cometary emission seen in Figure 10.

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