WATER IN COMETS 71P/CLARK AND C/2004 B1 (LINEAR) WITH SPITZER

Comet 71P/Clark was observed once (r_h = 1.565 AU, a Spitzer-comet distance of 0.920 AU, and a phase angle of 378) in the second order of the short-wavelength, low-resolution module (SL2) on 2006 May 27.56 UT as part of a large Spitzer Cycle 2 comet survey, program identification (PID) 20021 (PI: C.E. Woodward), astronomical observation request (AOR) key 13818368, and processed with IRS reduction pipeline S15.3.0. The SL2 slit is 37 wide and provides 57'' of spatially resolved spectra (185 pixel⁻¹) with a spectral dispersion of 0.06 μm. Nine spectra (60 s × 5 cycles) at 5.2–7.6 μm were recorded in a 3 × 3 spectral map (executed with no peak-up), with 247 × 380 steps (perpendicular × parallel to the long-slit dimension). The comet was also observed with the long-wavelength, low-resolution (LL) module of IRS, which we used to verify the pointing of the spacecraft. Further analysis of the LL spectrum is beyond the scope of this paper.

Comet C/2004 B1 (LINEAR) was observed twice, both pre- and post-perihelion with the SL2 module as part of a multicycle Spitzer initiative to investigate the heliocentric evolution and activity of a given comet, PID 20104 (PI: D.H. Wooden). The SL2 spectra discussed here were derived from IRS spectral mapping observations obtained on 2005 October 15.22 UT (pre-perihelion, r_h = 2.210 AU) AOR key 15787008, and on 2006 May 16.24 UT (post-perihelion, r_h = 2.058 AU), AOR key 15791616. Pre-perihelion, three spectra (240 s × 5 cycles) were obtained from a 3 × 1 spectral map, while post-perihelion five spectra (60 s × 3 cycles) were generated from a 5 × 1 spectral map. Both AORs were executed using a mapping footprint of 250 steps (perpendicular to the long-slit dimension) with no peak-up on the comet nucleus, accompanied by appropriate shadow (background) observations. Spectral observations of comet C/2004 B1 (LINEAR) using the short-high (SH, 9.9–19.6 μm) module were also obtained, although detailed analysis of these spectra are beyond the scope of this manuscript.

A reconstruction of the pointing for the 71P/Clark SL2 spectral maps indicates that there is an 8'' perpendicular offset between the SL2 extraction position and the JPL Horizons⁵ ephemeris position of the comet nucleus at the epoch of our observations, Figure 1(c). This offset is confirmed by comparing the peak in the observed surface brightness distribution in the long-low (LL2, 14–20 μm) cube which is nearly coincident with the Horizons position, Figure 1(d). The spectral maps for both IRS pointings of C/2004 B1 (LINEAR) encompassed the peak in the surface brightness of the coma (Figure 1), hence SL2 extraction apertures centered on the nucleus are possible.

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The reduction of the spectra and wavelength calibration of the SL2 data follows the formalism discussed in detail by Kelley et al. (2006) and Woodward et al. (2007). "Hot-pixels" occasionally present in individual extractions derived from the spectral maps were removed and replaced by nearest neighbor interpolation, or ignored altogether. A summary of comet physical parameters, spectral extraction apertures, and derived water production rates (see Section 3) is given in Table 1.

As for C/2003 K4 (LINEAR), features observed between 5.8 and 7 μm above the continuum background in the 71P/Clark and C/2004 B1 (LINEAR) Spitzer spectra (Figure 2) coincide with the rovibrational structure of the ν₂ water band at the resolution of the short-low (SL2) spectrometer. In order to study whether water band emission fully accounts for the signal in excess of the continuum, these spectra were analyzed using a model of fluorescence water emission following the procedure described in Woodward et al. (2007). Details on the method, model and assumptions can be find in Woodward et al. (2007).

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In summary, we use the model of fluorescence water emission presented by Bockelée-Morvan & Crovisier (1989) which considers five excited vibrational states and their subsequent radiative cascades. Indeed, the ν₂ band, which dominates the water spectrum in the 5.8–7.1 μm spectral region, is significantly populated by radiative decay from higher excited vibrational states. The resulting emission rate of ν₂ is 2.41 × 10⁻⁴ s⁻¹ at r_h = 1 AU from the Sun. For computing the line-by-line fluorescence, 32 ortho and 32 para rotational levels are considered in each vibrational state. The rotational populations in the ground vibrational state is described by a Boltzmann distribution at a temperature T_rot. The gas expansion velocity, v_exp, was fixed to 0.8 km s⁻¹ and the water photodissociation rate was taken equal to 1.6 × 10⁻⁵ s⁻¹ (r_h = 1 AU). These parameters influence to a small extent the retrieved water production rates.

From the model output, synthetic Spitzer spectra are generated by convolving the intensity of the individual rovibrational lines with the instrumental spectral response of the spectrometer. The spectral resolution is determined to be 0.0614 ± 0.0027 μm from the pre-perihelion spectrum of C/2004 B1 (LINEAR), in good agreement with the SL2 spectral resolution (0.0605 μm) cited in the Spitzer IRS Data Hand Book v.3.2.⁶ Our derived value is used for the analysis of the comet spectra in this paper. A slightly higher value of the SL2 spectral resolution, 0.065 μm (determined from the wavelength calibration at the SL2 slit edge), was used in the analysis of the C/2003 K4 (LINEAR) spectra as spectral extractions of this comet were performed near the edge of the slit (see Sections 2.2 and 3.1 in Woodward et al. 2007).

The observed spectra are fitted with a composite curve consisting of the modeled water spectrum superimposed on a fifth-degree polynomial. This latter polynomial determines the underlying continuum due to dust emission. The best-fit modeled spectrum is searched for by applying a least-squares method that uses the gradient-search algorithm of Marquardt. The only free parameters of the model are the water production rate Q(H₂O) (or equivalently, the water column density), T_rot, the ortho-to-para ratio (OPR), and the polynomial for the continuum. However, the signal-to-noise ratio in the spectra of comets 71P/Clark and C/2004 B1 (LINEAR) post-perihelion is not high enough to constrain the OPR, so this parameter was fixed when analyzing these data.

Figure 2 shows the model fits superimposed on the observed spectra. In the right panels, B, D, and F, the continuum has been subtracted. The intensity of the water band in continuum-subtracted spectra and the retrieved T_rot, OPR and Q(H₂O) are given in Table 1.

As discussed in Woodward et al. (2007), the spectral resolution of Spitzer SL2 is too low to resolve the individual ortho and para water lines. Thus a fully independent estimate of the OPR and T_rot cannot be derived. However, a robust determination of these parameters is possible from model fitting and χ² minimization, because several para lines (near 6.12 and 6.4 μm) are well separated in wavelength from strong ortho lines, while several peaks, dominated by ortho lines, have their relative intensities essentially influenced by T_rot. Spectra obtained with high signal-to-noise ratios are of course requisite. Figure 3(a) shows iso-χ² contours in the (T_rot, OPR) region that provides the best fit to the C/2004 B1 (LINEAR) pre-perihelion spectrum. The coefficients of the polynomial describing the continuum background have been set to the values of the best fit. The reduced χ² obtained for the best fit is 0.97 in the 5.85–7 μm region. The weak inclination of the ellipses (i.e., their roundness at the scales of the plot) indicates that the two parameters are poorly correlated (Bevington & Robinson 1992). The linear correlation coefficient is equal to 0.034. In Figure 3(b), red iso-χ² contours are computed by fixing T_rot and OPR and then minimizing χ² with the coefficients of the polynomial and the water production rate left as free parameters. With respect to the iso-χ² contours computed with the previous method (superimposed in black), these χ² iso-contours extend a bit farther in T_rot, while they coincide along the OPR dimension. This demonstrates that T_rot is weakly correlated with the coefficients of the polynomial, whereas OPR is not correlated. Quoted uncertainties in Table 1 and throughout the paper are 1σ (68% confidence level) uncertainties computed from the diagonal elements of the covariance matrix. They correspond approximately to the Δχ² = 1 red contour in Figure 3(b). The joint confidence region for (T_rot, OPR), delimited by the Δχ² = 2.3 contour (Bevington & Robinson 1992), is not used here as these parameters are not physically linked.

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Model fits with residuals are shown in Figures 4 and 5, for 71P/Clark and C/2004 B1 (LINEAR), respectively.

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In the case of 71P/Clark, model fitting was performed for two different extraction apertures along the slit, 37 × 56 (top of Figure 4) and 37 × 179 (bottom of Figure 4). For the small-extraction aperture, there is significant disagreement at 6.35–6.40 μm (this region was masked during the fitting procedure to obtain successful results in the other domains). The intensity of the water band is less intense than expected from modeling, resulting in negative residuals. This low intensity is puzzling. At low temperatures, the 6.40 μm peak arises mainly from the 1₀₁–1₁₀ and 1₁₁–2₀₂ lines, whereas the 6.50 μm peak comes mainly from the 1₀₁–2₁₂ and 2₁₂–2₂₁ lines. The ratio of their intensities I(6.40 μm)/I(6.50 μm) decreases with decreasing T_rot (see Figure 5 of Woodward et al. 2007), but reaches a constant value of ∼ 0.4–0.5 at low T and fluorescence equilibrium. For the large-extraction aperture, the discrepancy is shifted towards the 6.45–6.50 μm domain (Figure 4). Therefore, it is likely that the misfit in the 6.35–6.50 μm range is related to incorrect background subtraction and/or instrumental artifacts. Outside this spectral domain, the agreement between our model of H₂O emission and the Spitzer spectra of 71P/Clark is good.

The best fits to the spectra of 71P/Clark correspond to rotational temperatures T_rot of 5 ± 13 K (large-extraction aperture) and 14 ± 4 K (small-extraction aperture), both consistent with T_rot< 18 K (similar values are found for OPR = 2.5 and 3.0). Indeed, the 6.50 μm peak is less intense than the 6.65 μm peak only for T_rot < 20 K (see Figure 5 of Woodward et al. 2007, where the emergent intensity of the H₂O ν₂ band is plotted as a function of rotational temperature). The reverse was observed in Spitzer spectra of C/2003 K4 (LINEAR) from which T_rot values ∼ 30 K were determined (Woodward et al. 2007).

The signal-to-noise ratio achieved in the C/2004 B1 (LINEAR) pre-perihelion water spectrum (∼50 in-band intensity on the 37 × 179 extraction aperture considered for model fitting) permits a determination of the water ortho-to-para ratio (OPR), as done from Spitzer spectra of C/2003 K4 (LINEAR; Woodward et al. 2007). The best fit, shown in Figure 5, corresponds to T_rot ≃14 ± 2 K and OPR =2.31 ± 0.18. Also shown in Figure 5 is the best fit obtained with the OPR fixed at a value of 3. The χ² is increased by Δχ² = 10 with respect to the best fit obtained with OPR =2.31.

The agreement between our model and the Spitzer spectrum is excellent, except for the structure at 6.85 μm where the predicted intensity is lower than observed with a 2σ discrepancy. Taking the 6.05 μm peak as a reference since its intensity is weakly dependent upon T_rot and OPR (cf., Figures 5 and 6 of Woodward et al. 2007), the intensity ratio I(6.85 μm)/I(6.05 μm) slowly increases with increasing T_rot (and decreasing OPR) (Figures 5 and 6 of Woodward et al. 2007). The observed ratio would be typical of T_rot∼ 50 K. However, the relative intensities of the other peaks (in particular, I(6.65 μm)/I(6.05 μm) and I(6.18 μm)/I(6.05 μm)) are indicative of a low T_rot. Model fitting to the 5.9–6.7 μm part of the spectrum yields the same results as those obtained from the whole spectrum. As discussed in Woodward et al. (2007), the band regions most sensitive to the OPR lie at 6.12 and 6.4 μm where the emission is dominated by para lines: model fitting with OPR = 3 results in excess emissions centered at 6.12 μm and 6.4 μm in the residuals. The discrepancy at 6.85 μm is likely related to instrumental effects or flaws in the background subtraction (the negative feature at 7 μm in the residuals is not explained either).

The best-fit modeled spectrum for C/2004 B1 (LINEAR) post-perihelion is shown in Figure 5. For this model fitting, we fixed the ortho-to-para ratio to the value OPR = 2.3 derived from the pre-perihelion data. The derived rotational temperature is T_rot = 23 ±  4 K. A similar value (T_rot = 20 K) is obtained with OPR = 3 (fit shown in Figure 2) and OPR = 2.5 (T_rot = 22 K). The agreement between our model and the Spitzer spectrum is rather good. The residuals with respect to the observed spectrum do not show any excess emission in the wavelength range 5.8–7.1 μm of water ν₂ band emission.

From the intensity of the ν₂ H₂O band measured on the spectra, we computed the water production rates of 71P/Clark and C/2004 B1 (LINEAR) using a Haser model for the water density (Table 1). Because the observations of comet 71P/Clark were affected by pointing offsets due to uncertainties in the ephemeris (Section 2), the production rates retrieved from the intensities measured in a small (37 × 56) and large (37 × 179) extraction aperture were used as a complementary check to the pointing offsets. Consistent values for Q(H₂O), equal to (1.08 ± 0.08)× 10²⁸ molecules s⁻¹ and (1.04 ± 0.08) ×10²⁸ molecules s⁻¹ for the small- and large-extraction apertures, respectively, are obtained applying offsets corresponding to the actual position of the nucleus with respect to the targeted position. This derived production rate for the 2006 perihelion is consistent with indirect estimations from the visual brightness at previous perihelia (Sekanina 1993).

The water production rate derived for C/2004 B1 (LINEAR) at r_h = 2.21 AU pre-perihelion is Q(H₂O) = (1.03 ± 0.02)× 10²⁸ molecules s⁻¹. At r_h = 2.06 AU post-perihelion, the measured Q(H₂O) is (4.74 ± 0.42) ×10²⁷ molecules s⁻¹, which suggests that the comet was more active pre-perihelion. This later conclusion is consistent with measurements of the total visual magnitude m_v of the comet. For 2005 October 21 and 2006 May 17, i.e., at dates close to the Spitzer observations, values m_v = 12.6 and 12.4 are reported, which correspond to heliocentric visual magnitudes of 11.1 and 11.8, respectively (Green 2005, 2006).

Water production rates were computed assuming a Haser parent-molecule distribution for the water density with the parameters given in Section 3.1. The signal-to-noise ratio achieved for C/2004 B1 (LINEAR) pre-perihelion permits the investigation of the radial distribution of water throughout the IRS SL2 spectral map (Figure1(a)). The intensity of the ν₂ band along nine extractions is plotted as a function of offset ρ in Figure 6(a). The ν₂ intensity varies as ρ^−0.54 north of the nucleus which suggests that the water distribution is extended in this direction. South of the nucleus, the intensity varies as ρ^−1.13, which is consistent with a Haser distribution. For comparison (Figure 6(a)), the surface brightness of the dust emission (derived from continuum measurements at 5.45 ± 0.08 μm in each of the nine apertures) decreases with increasing offset as ρ^−1.30 (southern and northern coma averaged).

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The extended water distribution is best evidenced in the "Q-curve" (see Mumma et al. 2003) shown in Figure 6(b) which plots the water production required to explain the H₂O band intensity at the different offsets, assuming a Haser distribution. The apparent Q(H₂O) increases by more than a factor of 2 from 1 × 10⁴ km to 4 × 10⁴ km. This extended distribution is suggestive of the presence of subliming icy grains in the coma of C/2004 B1 (LINEAR). At 2.1 AU from the Sun the lifetime of dirty ice grains ranges from 10⁴–10⁶ s for grains of radii 10⁻²–1 cm (Beer et al. 2006). This lifetime range corresponds to displacements within the coma of typically 10³–10⁴ km prior to complete grain sublimation. The lifetime of pure ice grains is considerably larger (Beer et al. 2006). Our measurements are most easily explained if pure icy grains or ices mixed with poorly absorbing materials are present in the coma of comet C/2004 B1 (LINEAR). However, modeling of such sublimation processes is beyond the scope of this paper.

The measured rotational temperatures (Table 1) may not correspond to physical gas temperatures. As the water molecules expand in the coma, the rotational populations within the ground vibrational state relax to a cold fluorescence equilibrium. Thermal equilibrium breaks down at distances which depend on the density of the collisional partners (mainly H₂O molecules and electrons), and which are directly related to the water production rate. Given the low water production rate of 71P/Clark and C/2004 B1 (LINEAR), and the observational circumstances (field of view, slit offset), we may expect molecules with non-LTE rotational populations within Spitzer IRS SL2 slit. Using a model of water rotational excitation and the methodology explained in Woodward et al. (2007), we have computed synthetic ν₂ band profiles for the observing conditions of 71P/Clark and C/2004 B1 (LINEAR) from Spitzer and the field-of-view corresponding to the extraction apertures. Effective T_rot were derived by fitting the synthetic spectra with the same procedure as used for the observed spectra.

For 71P/Clark, the predicted effective T_rot at 8''from the nucleus is 11–12 K for a kinetic temperature T_kin in the range 10–50 K and x_ne = 1, where x_ne is a multiplying factor to the electron density normalized to the Giotto 1P/Halley measurements. If our observations had been executed with the slit centered on the nucleus, we would have expected T_rot = 25 to 29 K with these model parameters. These results are for an aperture of 37 × 179, but similar numbers are obtained for a 37 × 56 aperture: 31–39 K on nucleus, 12–13 K for an offset of 8''. The size of the collisional region where water molecules are thermalized to the gas kinetic temperature is small with respect to the field of view, hence the predicted rotational temperature is weakly sensitive to the assumed T_kin. A relatively high T_rot is expected for a slit centered on the nucleus because molecules excited by collisions with hot electrons have a significant contribution to the signal. Rotational temperatures measured in 71P/Clark (14 ± 4 K and 5 ± 13 K for the small and large apertures, respectively) are consistent with modeling.

Model calculations pertaining to the observational circumstances of the C/2004 B1 (LINEAR) pre-perihelion data predict T_rot = 17–19 K for a 37 × 179 aperture and kinetic temperatures of 10–50 K. Note that low gas temperatures may be expected for this weakly active (Section 3.3) comet observed at 2.1–2.2 AU from the Sun. Overall, the agreement with the measured T_rot value (13.6 ± 2.1 K) is satisfactory.

In the case of C/2004 B1 (LINEAR) post-perihelion, the expected T_rot for a 37 × 179 extraction centered on the nucleus is T_rot = 17 K assuming T_kin = 30 K, with little dependency on the assumed T_kin since water molecules with non-LTE rotational populations are sampled. The measured T_rot of 23 ± 4 K is consistent with the model within 2σ. A better agreement could be obtained by increasing the electron density through the x_ne = 1 parameter.

The ortho-to-para ratio of 2.31 ± 0.18 measured in C/2004 B1 (LINEAR) corresponds to a spin temperature T_spin = 26⁺³₋₂ K. The ortho-to-para ratio in water has been measured in a dozen of comets (see Bonev et al. 2007, for a compilation of measurements before 2007), and ranges from ∼ 1.8 to the equilibrated value of 3 (T_spin from ∼ 23 to > 40 K). The OPR measured in C/2004 B1 (LINEAR) is in the low range of measured values in Oort cloud comets, yet comparable to OPR values reported by Mumma et al. (1988) and Dello Russo et al. (2005) for comets 1P/Halley and C/2001 A2 (LINEAR). Our new measurement for C/2004 B1 (LINEAR) suggests that OPR variation clearly exists among the population of Oort cloud comets.

The meaning of nuclear spin temperatures in cometary molecules is puzzling (Kawakita et al. 2004; Crovisier 2007). Nuclear spin temperatures may be related to the thermal conditions experienced by the molecules since their incorporation into cometary nuclei, or connected to their formation conditions and subsequent OPR re-equilibration in the solar nebula. Kawakita et al. (2004) have shown that there is no clear trend between the nuclear spin temperatures, production rate, heliocentric distance and orbital period of the comet, suggesting that the nuclear spin temperature is pristine (Kawakita et al. 2004). The measurement of the OPR (and corresponding nuclear spin temperature) in C/2004 B1 (LINEAR) is derived from observations conducted when the comet was at a heliocentric distance, r_h = 2.21 AU. This heliocentric distance is intermediate between the range r_h = 0.8–1.2 AU, where most OPR measurements were acquired, and the measurement in C/1995 O1 (Hale-Bopp) at 2.9 AU from the Sun. Our Spitzer measurement provides a new data point for future investigations of T_spin variations with heliocentric distance based on a statistically significant data set.

The modeled water spectrum wholly accounts for the emission in excess of the dust continuum background in the two comets (Figures 4 and 5). There is no emission excess at 6.2 μm that could be attributed to PAH emission. There is not significant evidence for moderately broad (Δλ ≃ 0.5 μm) emission peaking at 7.0 μm (arising from asymmetric stretching vibration of C–O) that could be due to carbonates minerals (Kemper et al. 2002; Crovisier & Bockelée-Morvan 2008). Such emission, if present, would have made the 6.85 μm peak of the H₂O band of less contrast than observed. In addition if carbonates where present, other narrow (Δλ ≲ 0.2 μm) emission features near 12.7 μm and 14.8 μm should be present (Kemper et al. 2002). The IRS spectra of comets C/2004 B1 (LINEAR) and 71P/Clark over this wavelength interval are featureless, Figure 7. Thus, carbonates are not present (or significantly abundant) in the comet comae created through quiescent sublimation processes or dermal jets from isolated active areas on the nucleus based on analysis of Spitzer spectra of three comets.

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Excess emission is present at 7.1–7.3 μm in the spectrum of 71P/Clark, and between 7.15 and 7.45 μm, peaking at 7.32 μm in the post-perihelion spectrum of C/2004 B1 (LINEAR) (Figures 4 and 5). Excess emission near 7.3 μm was also observed in the Spitzer spectrum of C/2003 K4 (LINEAR) (Woodward et al. 2007). The emission feature observed in C/2004 B1 (LINEAR) post-perihelion closely resembles that observed for C/2003 K4 (LINEAR), but is much more intense relative to the intensity of the water band than in C/2003 K4 (LINEAR): ∼ 10% the intensity of the water band in the post-perihelion spectrum of C/2004 B1 (LINEAR), ∼ 2% in C/2003 K4 (LINEAR; Woodward et al. 2007). Its contrast with respect to the continuum background is also more important in C/2004 B1 (LINEAR). The feature is not present in the pre-perihelion spectrum of C/2004 B1 (LINEAR). This suggests that the feature is not related to the absolute brightness of the comet. As discussed in Woodward et al. (2007), the origin of this feature is unclear. Based on examination of spectral extractions of standard stars used to calibrate the IRS campaign, this feature is not likely an instrumental artifact, although we cannot completely exclude this possibility.