Beyond 3 au from the Sun: The Hypervolatiles CH₄, C₂H₆, and CO in the Distant Comet C/2006 W3 (Christensen)^∗

The spectra acquired at R_h = 3.25 au have the highest S/N. This permits examining how directly measured quantities (emission line intensity, Section 4.2) and retrieved quantities (column density, Section 4.3, and symmetric production rate, Section 4.4) vary with offset distance from the nucleus along the entrance slit. This ability to extract detailed spatial information was vital for identifying those lines of sight through the coma from which the emission is optically thick, and hence where the resulting production rates are most affected by uncertainties and parameters we cannot constrain from our observations. For our reported production rates we then use only the signal from those regions of the coma that were minimally affected by optical depth.

We measured the spatial intensity distribution of individual lines of CO and CH₄ at 3.25 au. The spatial profiles of the R1 and R0 lines of CH₄ are nearly identical, but CO exhibits a different spatial behavior, both to CH₄ and also among CO lines. Figure 2(A) compares profiles of the CO (R1) and CH₄ (R0) lines. While the CH₄ distribution is strongly peaked near the nucleus, the profile of CO is flatter in its central portion and decreases more slowly away from the nucleus than that of CH₄.

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Since the C₂H₆ lines were generally weaker, we combined spatial profiles for the three strongest emissions (${\nu }_{7}$ Q-branches), which we compare with that of CO (P1) in Figure 2(B). A similar spatial behavior is revealed: like methane, the more narrowly peaked ethane emission contrasts with the flatter distribution of CO. Finally, we compare the profiles of the CO R2 and R3 emissions in Figure 2(C).

What causes the different spatial behavior of CO emission when compared to methane and ethane? We consider two possibilities, and examine each in turn:

• 1.  
  CO was released (at least in part) from an extended source in the coma, while methane and ethane were released solely from the nucleus, and/or
• 2.  
  optical depth effects reduced the apparent flux near the nucleus, but more so for CO than for either hydrocarbon.⁷

The flattened appearance of CO profiles could be due to extended source production (e.g., Womack et al. 2017). Direct release of volatiles (CH₄, C₂H₆, CO₂, and CO itself) from the nucleus could also drag ice into the coma, similar to the release of ${\rm{H}}{}_{2}{\rm{O}}$ icy clumps (and grains) from 103P/Hartley 2 (A'Hearn et al. 2011; Mumma et al. 2011; Bonev et al. 2013; Fougere et al. 2013; Protopapa et al. 2014). In this scenario, a flattened spatial profile would be consistent with CO-rich clumps subliming slowly while transiting the region within the ∼1000 km from the nucleus that is covered by our CRIRES observations. However, the observed spatial profiles do not suggest extended release of methane and ethane. Of the three molecules we measured in C/2006 W3, CO has the lowest sublimation temperature. If CO-rich ice survived in the coma, we would expect CH₄ and C₂H₆ ices to also survive and thus their emissions to exhibit similarly broad spatial distributions. Although we cannot completely rule out production of CO from an extended source, the observed narrower profiles of methane and ethane argue against extended release of hypervolatiles.

As an alternative to a dominant release of CO from icy grains, the flattened appearance of the CO profiles is also consistent with optically thick conditions for lines of sight passing close to the nucleus (i.e., the central parts of the intensity distributions shown on Figures 2(A)–(C)). We quantitatively explore this possibility in the next section.

We retrieved the spatial profiles of column density (N ) by performing a Levenberg-Marquardt $\chi {}^{2}$ fit of modeled to measured spectra (e.g., Figure 1). This method is detailed in Villanueva et al. (2008) and Bonev et al. (2013). The quality of the fit depends on the mean rotational temperature (T_rot)⁸ for a given field of view (FoV). For a nucleus-centered aperture of 5 spectral × 5 spatial pixels (870 km × 935 km at the geocentric distance ${\rm{\Delta }}=3.00$ au, see Table 1), we found T_rot = ${20}_{-4}^{+6}$ K for C₂H₆ (Figure 1(A)), T_rot = 16 ± 3 K for CH₄, (Figure 1(B)), and T_rot = 14 ± 2 K for CO (Figure 1(C)). Our spectra did not allow for detecting any significant variation in T_rot along the slit. However, the retrieved column density (and production rate) is very insensitive to T_rot for the realistic range of ∼10–25 K. Therefore, for the simulations shown in this section, we fixed T_rot at 16 K. We verified that assuming another fixed value within 10–25 K or a gradient in T_rot along the slit did not alter the retrieved profile of N in any significant way. For example, when T_rot was varied (as a parameter) from 10 K to 20 K, the column density in the central FoV changed by less than 2σ uncertainty.

Figures 3(A) and (B) show the spatial distributions of the column density for CH₄ and CO, respectively. The column density is based on a ${\chi }^{2}$ fit to all emissions, which is significantly less sensitive to spatial fluctuations of individual line intensities. Because this fit encompasses multiple lines, our profiles of the column density are smoother in appearance than those in Figures 2 (A)–(C), which pertain to individual line fluxes.

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Each panel of Figure 3 shows two column density curves: green stars indicate retrievals using optically thin g-factors, while black squares show the results from a curve-of-growth analysis (Appendix), assuming that optical depth reduces the local pump intensity within the column and thus also the effective fluorescence efficiency. If optical depth is important, we expect the two column density curves (green stars and black squares) to diverge. This is not the case for Figure 3(A), suggesting that the CH₄ emission is nearly optically thin even in the center of the spatial profile. Conversely, Figure 3(B) suggests that optical depth significantly affects the CO emission in the central parts of the profile, consistent with the flatter appearance of the distributions of CO emission intensity, compared with those of CH₄ (and C₂H₆).

Figure 4(A) shows how the retrieved⁹ symmetric production rate (Q_sym, molecules ${\rm{s}}{}^{-1};$ Mumma et al. 2003) of CO varies with projected distance from the nucleus (ρ, km), assuming optically thin conditions. Conversely, Figure 4(B) shows how Q_sym varies with ρ when optical depth is included. The Q_sym (ρ) graphical relationship is commonly referred to as a "Q-curve" (Dello Russo et al. 1998; DiSanti et al. 2001; Bonev et al. 2006; Villanueva et al. 2011a; Paganini et al. 2013). Each value of Q_sym in Figures 4(A) and (B) was derived from measured column densities $\langle N\rangle$ according to the relationship:

$$\begin{eqnarray}&&{Q}_{\mathrm{sym}}=\ \displaystyle \frac{\langle N\rangle \ {A}_{\mathrm{FoV}}}{t({R}_{h})\ f(x)}.\end{eqnarray} \tag{ 1 }$$

In Equation (1), A_FoV (${{\rm{m}}}^{2}$) represents the "footprint" area corresponding to a rectangular aperture of 5 spectral pixels (the slit width) × 5 spatial pixels (870 × 935 km); t(R_h) (s) is the photodissociation lifetime of CO (t(R_h) = t(1 au) ${R}_{{\rm{h}}}^{2}$, where t(1 au) = 1.3 × $10{}^{6}$); and f(x) represents the fraction of all CO molecules that are sampled within the FoV. Spherically symmetric uniform outflow is assumed; see Yamamoto (1982) and the Appendix of Hoban et al. (1991). Since f(x) varies as approximately ${t}^{-1}$ for CO given our beam size, the product of t and f(x), and hence the extracted production rate is relatively insensitive to the adopted lifetime. However, f(x) depends directly on gas outflow velocity (v_exp, as discussed in Appendix). Importantly, for off-nucleus extracts, the column density $\langle N\rangle$ is the mean of two measurements obtained from FoVs equidistant from the peak intensity on opposite sides of the spatial profile. This approach minimizes the effects of possible asymmetries in the gas outflow (Xie & Mumma 1996); hence the term symmetric production rate.

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Figure 4 shows that the retrieved symmetric production rates initially increase with projected distance (ρ) from the nucleus until a "terminal" value is reached at ρ ∼ 1800 km. Each Q-curve is characterized by three quantities: the nucleus-centered production rate (Q_nc), the "terminal" value (Q_term), and the distance from the nucleus required to reach Q_term. The ratio Q_term/Q_nc is commonly referred to as the "growth factor" (GF). In comparing the Q-curves that result from our optically thin (Figure 4(A)) and optically thick (Figure 4(B)) treatments we point out the following features:

• 1.  
  The terminal production rates agree within the uncertainty.
• 2.  
  If optically thin g-factors are adopted (Figure 4(A)), the nucleus-centered production rate is much lower than the rate we obtain using an optical depth treatment (Figure 4(B)).

In both Q-curves the initial rise in retrieved production rate is related to net loss of flux from the nucleus-centered region, primarily because of atmospheric seeing and (possibly) small guiding inaccuracies. However, when optically thin g-factors are applied to an optically thick medium (Figure 4(A)), the nucleus-centered production rate is further underestimated (well beyond that caused by loss due to seeing) by (wrongly) assuming that the retrieved column density is directly proportional to the measured flux. Since optical depth effects are most significant at the peak intensity of the spatial distributions, the difference in the corresponding production rates is largest for the nucleus-centered extract.

The vast majority of molecular studies in comets have been restricted to heliocentric distances smaller than 2 au, where ${\rm{H}}{}_{2}{\rm{O}}$ has the highest production rate among volatiles (Mumma & Charnley 2011; Dello Russo et al. 2016). In contrast, C/2006 W3 (Christensen) remained outside R_h = 3.1 au throughout its apparition, but its exceptional brightness presented an extremely rare opportunity to sense a suite of primary volatiles. This comet was observed from several space- and ground-based facilities. As a part of its 18-comet survey (Ootsubo et al. 2012), Japan's infrared satellite AKARI observed C/2006 W3 pre-perihelion with low spectral resolution but wide spectral coverage (2.5–5 μm). These studies focused on CO₂, whose IR band at 4.3 μm was detected simultaneously with bands of ${\rm{H}}{}_{2}{\rm{O}}$ and CO. Observations of C/2006 W3 near 3.3 au were among the first science highlights of the Herschel Space Observatory, complemented by ground-based programs at Nanc̆ay and the IRAM radio telescopes (Bockelée-Morvan et al. 2010; de Val-Borro et al. 2014).

Figure 5 shows a compilation of CO production rates in C/2006 W3 measured by AKARI, IRAM, and ESO-VLT. The post-perihelion production rates measured near 4.0 and 4.7 au are consistent with insolation-limited outgassing ($Q\propto {R}_{{\rm{h}}}^{-2}$), while a steeper decrease is observed between 3.2 and 4.0 au (see also Table 2). For R_h < 3.35 au, the reported production rates span the range ∼2.0 to 5.5 (10${}^{28}$ molecules s⁻¹). Regardless of differences among individual measurements, these CO production rates are higher in C/2006 W3 than those measured in most previously studied comets, although these previous comets were observed significantly closer to the Sun.

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Our two measurements (R_h = 3.25 au; 2009 October 7 and 8) are in agreement, but are ∼1.4 times higher than Q(CO) from IRAM (R_h = 3.20 au; 2009 September 14) and ∼2.8 higher than Q(CO) from AKARI (R_h = 3.13 au; 2009 June 16). The presented measurements (which are weeks to months apart) are based on three very different techniques. Ootsubo et al. (2012) discuss that systematic uncertainties (e.g., due to different beam sizes) and modeling assumptions behind each technique can partly account for differences among the production rates (see also Dello Russo et al. 2009; Magee-Sauer et al. 1999). We note that differences in Q(CO) are not related to the assumed gas outflow velocity. Both infrared studies (ESO-VLT and AKARI) adopt similar values (∼440 m s⁻¹) of this parameter, in agreement with IRAM's measurements based on velocity-resolved rotational lines. Temporal variability in Q(CO) between the time of AKARI observations and those of ESO-VLT (∼4 months later) cannot be ruled out. AKARI's observations alone suggest a ∼30% decrease in Q(CO) from R_h = 3.66 to R_h = 3.13 au (pre-perihelion). In addition, AKARI observed the same infrared band as was targeted in our measurements, but at much lower spectral resolution. Q(CO) was then calculated assuming optically thin conditions and a band-integrated g-factor: g_band = 2.6 × 10⁻⁴ s⁻¹. For heliocentric radial velocity near zero (corresponding to AKARI's observation near perihelion), our optically thin model predicts $g{}_{\mathrm{band}}$ ≈ 1.2 to 1.5 × $10{}^{-4}$ s${}^{-1}$, depending on rotational temperature (Paganini et al. 2013; Villanueva et al. 2012; see also Goddard's Planetary Spectrum Generator; http://ssed.gsfc.nasa.gov/psg/). This difference in $g{}_{\mathrm{band}}$ accounts for most of the difference between CRIRES and ESO-VLT measurements. AKARI's lower value (3.13 au) is also consistent with optically thick CO, as suggested by our analysis at R_h = 3.25 au. Although we expect AKARI's very large FoV (∼43'') would diminish the influence of optical depth effects in their beam, their spatially integrated flux measurements might still include some contribution from the innermost (optically thick) regions of the coma, because CO column densities are highest near the nucleus.

A further and detailed comparison between the IRAM, AKARI, and ESO-VLT retrieval methods of Q(CO) is beyond the scope of this paper. Despite differences in productions rates (near perihelion) each of these studies brings unique and important insights: AKARI was essential as a window to CO₂ (not observable from the ground). AKARI results also helped in interpreting the imaging study by Spitzer (Reach et al. 2013) and the sources of forbidden OI emission detected from the Apache Point Observatory (McKay et al. 2012). Both investigations can be used to deduce the CO₂ production rate, but depend critically on knowledge of the CO/CO₂ ratio. Radio techniques were especially valuable for sensing a suite of volatiles (CO, CH₃OH, HCN, and ${\rm{H}}{}_{2}{\rm{S}}$, and CS) and of dust, for directly measuring gas outflow velocities, and for estimating the comet's comparatively large nucleus size (∼20 km). Importantly, the HIFI instrument (Herschel) detected rotational emission from ${\rm{H}}{}_{2}{\rm{O}}$ at 5 au from the Sun. ESO-VLT is essential for symmetric hydrocarbons (CH₄ and C₂H₆) and brings the best constraints on the post-perihelion decrease of the CO production rate with increasing R_h, since all other measurements of CO are clustered within R_h < 3.35 au. Synergistic interpretation of all these measurements provides the most in-depth view possible of the activity and composition of C/2006 W3.

Relative abundances (CH₄/CO, HCN/CO, etc.) often provide a better representation of coma composition than absolute production rates. Figure 6 shows the abundances of several molecules with respect to CO. This molecule is chosen as a baseline because, first, it is the species with the highest production rate, and second, CO was most frequently measured in C/2006 W3. For all species except ${\rm{H}}{}_{2}{\rm{O}}$ (R_h = 5 au) and NH₃, the abundance ratios X/CO are based on measurements with the same instrument and on the same date as for carbon monoxide; using contemporaneous measurements minimizes the effects of temporal variability. Using the same instrument-telescope combination also minimizes systematic uncertainties associated with and propagated from flux calibration and modeling parameters that are specific to the particular observing technique (Mumma et al. 2003; DiSanti & Mumma 2008; Ootsubo et al. 2012; Dello Russo et al. 2016).

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The AKARI relative abundances suggest that the coma of C/2006 W3 (Christensen) was rich in both CO and CO₂. The measured CO/CO₂ ratio (2.3 ± 0.3 and 3.5 ± 0.5 at R_h = 3.13 and 3.66 au, respectively) is the second highest (after 29P/SW 1) of all studied comets, including those observed beyond 2.5 au from the Sun. Regardless of R_h, only upper limits for CO production, and hence CO/CO₂, were achieved in most other comets in the AKARI survey, making C/2006 W3 a definitive outlier given its high CO coma abundance.

Post-perihelion abundances of ${\rm{H}}{}_{2}{\rm{O}}/\mathrm{CO}$ and NH₃/CO cannot be obtained from a single instrument-facility, but are included in Figure 6, given the lack of coverage in these species in distant comets. The upper limit ${\rm{H}}{}_{2}{\rm{O}}/\mathrm{CO}$ (green triangle in Figure 6) is estimated from near-contemporaneous measurements by Herschel (H₂O; R_h = 3.35 au) and IRAM (CO; R_h = 3.32 au). We extrapolated our production rate of CO from 4.73 to 5.0 au assuming an ${R}_{{\rm{h}}}^{-2}$ dependence (as we observed between R_h = 4.0–4.7 au; see above), and compared with Q(H₂O) and Q(NH₃) from Herschel (points marked with "x").

Overall, the revealed composition pertains to the coma at the time of observation, not necessarily to the bulk nucleus. The results summarized in Figure 6 provide a rare window to the coma abundances of primary volatiles in a distant comet. As such, they are especially valuable for constraining models for nucleus sublimation beyond R_h = 3 au, where differences in volatility are very important, as demonstrated for C/2006 W3 Christensen by the nucleus outgassing model of Kossacki & Szutowicz (2015), which roughly reproduces our observed post-perihelion decrease in CO production rate in this comet.

Like CO, the production rates of C₂H₆ and CH₄ in C/2006 W3 exceed their respective values as measured in a number of comets that were observed significantly closer to the Sun. In C/2006 W3 at R_h = 3.25 au, the three hypervolatiles scale approximately as CO/CH₄/C₂H₆ = 100/4.4/2.1. Table 3 compares these relative coma abundances to measurements in two other comets observed beyond 3 au from the Sun. The ratios CH₄/CO and C₂H₆/CO in C/2006 W3 at 3.25–3.26 au are consistent with the upper limits we report in C/2006 W3 at 4.73 au, and also with those reported for comet 29P/SW 1 at 6.26 au (Paganini et al. 2013).

Table 3.  Relative Abundances of the Hypervolatiles C₂H₆, CH₄, and CO in Comets Observed at R_h > 3 au

Comet	${R}_{{\rm{h}}}$[au]	Abundance			Technique	Reference
		C2H6	CH4	CO
	3.252	2.2 ± 0.3	4.8 ± 0.6	100	Remote sensing	This work
C/2006 W3	3.255	2.0 ± 0.3	4.0 ± 0.5	100
	4.73	<5.0	<9.9	100
67P/CG summer hem.a	3.15	11.9	4.8	100	in situ mass spectroscopy (∼10 km from the nucleus)	Le Roy et al. (2015)
67P/CG winter hem.a	3.15	16.5	2.8	100
29P/SW1	6.26	<2.2 (3σ)	<4.8 (3σ)	100	Remote sensing	Paganini et al. (2013)

Note.

^aLe Roy et al. measured the following relative abundances of hypervolatiles and water: C₂H₆/H₂O = 0.32 (SH) and 3.3 (WH); CH₄/H₂O = 0.13 (SH) and 0.56 (WH); CO/H₂O = 2.7 (SH) and 20 (WH); "SH" and "WH" designate summer and winter hemisphere, respectively.

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Le Roy et al. (2015) detected methane, ethane, and carbon monoxide in the coma of comet 67P/Churyumov-Gerasimenko (67P) using the ROSINA mass spectrometer on board the Rosetta space mission orbiter. The heliocentric distance of 67P (3.15 au) was very similar to that of our first observations of C/2006 W3 (3.25 au). However, the Rosetta in situ measurements reflect the local composition, approximately 10 km from the nucleus, rather than the line-of-sight-integrated composition afforded by remote-sensing measurements; this difference complicates a direct comparison with our results.

Emphasizing these caveats, Le Roy et al. nevertheless provided useful comparisons between the abundances of their detected species (relative to ${{\rm{H}}}_{2}{\rm{O}}$, which dominated 67P's outgassing) and those measured by ground-based telescopes in a number of comets within ∼2 au from the Sun. Here we extend this effort by comparing hypervolatiles in 67P and C/2006 W3, which are the only two comets for which measurements at R_h ≈ 3.2 au have been reported to date. In contrast to C/2006 W3 (which comes from the Oort cloud), 67P is an ecliptic (Jupiter-family) comet, most probably dynamically linked to the scattered Kuiper disk.

At the time of these Rosetta measurements, 67P was experiencing northern summer, with the northern pole in constant sunlight, while the southern pole was in permanent shadow. Le Roy et al. show that the abundances of each hypervolatile relative to ${\rm{H}}{}_{2}{\rm{O}}$ differed by factors of ∼4 (CH₄), ∼10 (C₂H₆), and ∼7 (CO) between the two hemispheres, with much lower X/H₂O ratios observed in the sunlit part of the coma (see Table 3, note a). Conversely, C₂H₆ /CO and CH₄/CO differed by less than a factor of 2 and followed the same trend, with ethane being more abundant than methane in both hemispheres. The in situ abundances of CH₄/CO in 67P are very similar to the column-integrated measurements in C/2006 W3, while C₂H₆/CO (and commensurately C₂H₆/CH₄) are distinctly higher.

Figure 7 includes 67P and C/2006 W3 in a diagram showing CO/CH₄ versus C₂H₆/CH₄ together with 17 comets observed between R_h of ∼2.0 and 0.35 au (after Mumma & Charnley 2011; Paganini et al. 2014, and DiSanti et al. 2014, 2016). For these comets, water production rates strongly dominated those of all other species, so that their CO/H₂O ratios are color-coded. Except for 67P (a space mission target), all other comets in the figure are from the Oort Cloud; CH₄ and CO measurements are significantly underrepresented in ecliptic comets because of geocentric Doppler shift limitations. Both species were recently detected (along with C₂H₆) in the ecliptic comet 45P/Honda-Mrkos-Pajusakova, with preliminary ratios CO/CH₄ ∼ 1.0 and C₂H₆/CH₄ ∼ 0.6 (DiSanti et al. 2017; CBET 4357).

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The scatter in the diagram showing CO/CH₄ versus C₂H₆/CH₄ is consistent with recent correlation analyses of infrared measurements by Dello Russo et al. (2016). These authors report correlation coefficients of 0.49, 0.71, and 0.18 between CO and CH₄, C₂H₆ and CH₄, and CO and C₂H₆, respectively. The larger spread of the CO/CH₄ measurements (y-axis in Figure 7) is consistent with the correlation found between these species, which is significantly weaker than the correlation between C₂H₆ and CH₄.

The underlying causes of the considerable scatter in Figure 7 might be a byproduct of differences in formative conditions and (possible) post-formative evolution. In particular, nebular models predict wide ranges in abundances of hypervolatile species within the large comet-forming region (Willacy et al. 2015; Drozdovskaya et al. 2016). At the same time, outgassing patterns that differ among species and with time were observed in 67P by Rosetta, with CH₄ showing a diurnal pattern that was distinctly different from the pattern of CO and C₂H₆ (Luspay-Kuti et al. 2015; Bockelée-Morvan et al. 2016; Fink et al. 2016). If similar effects are important among the larger population of comets, they might also contribute to the scatter in abundances derived by snapshot remote-sensing studies, such as those in Figure 7. Separating primordial from evolutionary effects in comets is an extraordinary difficult task, which will benefit from high-cadence campaign studies (see also Dello Russo et al. 2016; DiSanti et al. 2016).

The two in situ measurements of 67P are outliers in both CO/CH₄ and C₂H₆/CH₄. It will be interesting to compare these results from R_h = 3.15 au to their corresponding abundance ratios in 67P near perihelion, when the latter become available. Of the comets that were studied by remote sensing, C/2006 W3 (Christensen) has the highest abundance ratio of CO/CH₄. At R_h < 2 au, the most similar CO/CH₄ abundance ratios were measured in Hyakutake, C/2013 R1 (Lovejoy), C/2009 P1 (Garradd), Hale-Bopp, and C/1999 S4 (LINEAR), as indicated in Figure 7. This group also had CO/H₂O exceeding ∼10% (sometimes referred to as CO-rich comets), with the exception of C/1999 S4 LINEAR, which was depleted in all measured volatiles and has a large uncertainty in its CO/CH₄ ratio. Another notable comparator is C/2009 P1 (Garradd), in which the production rate of CO (but not ${\rm{H}}{}_{2}{\rm{O}}$) increased nearly monotonically from ∼2.5 au pre-perihelion to ∼2 au post-perihelion (McKay et al. 2015), with a value of ∼60% relative to water reported from observations at 2.0 au post-perihelion using the HRI-IR spectrometer on the Deep Impact flyby spacecraft (Feaga et al. 2014). A similar trend was not observed in C/2006 W3, at least post-perihelion, where Q(CO) decreased by a factor of ∼4 from 3.25 to 4.73 au (Figure 5).