FORMATION CONDITIONS OF ICY MATERIALS IN COMET C/2004 Q2 (MACHHOLZ). II. DIAGNOSTICS USING NUCLEAR SPIN TEMPERATURES AND DEUTERIUM-TO-HYDROGEN RATIOS IN COMETARY MOLECULES

High-S/N ratios of H₂O emission lines enabled us to determine the abundance ratio between ortho- and para-H₂O precisely. We adopted the fluorescence excitation model to the water hot-bands in the 2.9 μm region. The basic ideas were described in detail by Dello Russo et al. (2004, 2005). In the model, H₂O molecules are excited from the ground state to the upper vibrational states by the solar radiation field, and the population distribution of the vibrational ground state is assumed to follow a Boltzmann distribution at a given rotational temperature. The population distribution in the ground vibrational state is assumed to be maintained by frequent intermolecular collisions in the inner coma. Wavelengths and Einstein's A coefficients of the transitions related to the water hot-bands were taken from Barber et al. (2006). The high-dispersion solar spectrum in the near-infrared was calculated by Kurucz's spectrum synthetic code (Kurucz 1994; Fontenla et al. 1999).

There are two free parameters for the fluorescence excitation model, the rotational temperature of H₂O in the vibrational ground state (T_rot) and the abundance ratio between ortho- and para-H₂O (OPR). We have fitted the observed spectrum near 2.9 μm with the modeled spectrum by minimizing the reduced-χ² to determine the best T_rot and OPR. Errors in the measured line flux and in the telluric transmittance are considered in the model fitting.

Figure 3 shows the modeled spectrum of H₂O compared with the observed spectrum. There is not a perfect match between the observed and modeled spectrum of water for some lines. Uncertainties in Einstein's A coefficients for water hot-band transitions used in the model calculation may cause these errors (Dello Russo et al. 2004, 2005). Moreover, one of the emission lines labeled as "SH" in Barber et al. (2007) was also found in our spectrum. These "SH" lines are caused by the transitions from the "high-v but low-J" levels having energies in the range from ∼10,000 to ∼15,000 cm⁻¹ (Barber et al. 2007). Since the excitation mechanism for these SH lines is not well understood, we did not use "SH" lines for the model fitting. There were some unidentified lines in our spectrum and some of these may be "SH" lines.

Zoom In Zoom Out Reset image size

The best-fit values of T_rot and OPR are 85 ± 5 K and 3.13^+0.56_−0.42, respectively. Errors are 1σ error-levels (corresponding to the reduced-χ²⩽ reduced-χ²_min + 1). The obtained OPR is interpreted as the nuclear spin temperature (Mumma et al. 1987). The best OPR value could give a lower limit of the nuclear spin temperature, T_spin ⩾ 34 K. Note that the 95% confidence limit is 27 K, which is estimated based on the reduced-χ²⩽ reduced-χ²_min + 4.

The OPR of water in C/Machholz had been also reported based on the near-infrared water hot-band emission spectrum, which was also taken by Keck II/NIRSPEC by Bonev et al. (2007). They reported OPR = 2.86 ± 0.17 (T_spin ⩾ 34 K) and their OPR is consistent with our measurements.

In our spectra of C/Machholz, three emission lines of CH₄ were detected, i.e., R0, R1, and R2 of the ν₃ vibrational band. Methane has three nuclear spin modifications of A, E, and F. The emission of R0 belongs to A, and the emission of R1 belongs to F while the emission of R2 is a composite of E and F.

We reproduced the emission spectrum of CH₄ using the fluorescence excitation model by the solar radiation. The vibrational ground state of CH₄ was assumed to be thermalized (Gibb et al. 2003; Kawakita et al. 2005). In this case, the population distribution among the rotational levels in the vibrational ground state can be specified by both the rotational temperature (T_rot) and the nuclear spin temperature (T_spin). These two parameters could be determined from our observations. The best-fit values of T_rot and T_spin were determined based on the minimizing reduced-χ² method as done for H₂O. Errors in the measured line flux and in the telluric transmittance are considered in the model fitting. The best-fit rotational temperature is T_rot = 90⁺¹⁰₋₈ K (±1σ error-levels) and the lower limit of nuclear spin temperature is derived as T_spin ⩾ 40 K corresponding to the ±1σ error-levels (the 95% confidence limit is T_spin ⩾ 36 K). Figure 4 shows the observed spectrum compared with the modeled spectrum of CH₄ where T_rot = 90 K and A:E:F ratios are 5:2:9 (equilibrium ratios in high-temperature limit).

Zoom In Zoom Out Reset image size

The rotational temperature of CH₄ is consistent with T_rot of H₂O listed in the previous subsection. The consistency in T_rot between H₂O and CH₄ supports the validity of the assumption that molecules were thermalized well by intermolecular collisions in the inner coma. Regarding the nuclear spin temperature, the temperature range inferred from CH₄ (⩾ 36 K, 95% c.l.) is consistent with that of H₂O (⩾ 27 K, 95% c.l.). Consistency between the nuclear spin temperatures of H₂O and CH₄ was also found in comet C/2001 Q4 (NEAT) in which the nuclear spin temperatures of H₂O, NH₃ and CH₄ were consistent with one another (about 32 K; Kawakita et al. 2006).

The strongest vibrational emission band of CH₃D in comet is the ν₄ vibrational band around 3000 cm⁻¹, which is close to the ν₃ vibrational band of CH₄ (Kawakita & Watanabe 2003). Both CH₄ and CH₃D could be recorded simultaneously on the same echelle order by the NIRSPEC and it is easy to compare strengths of emission lines between CH₄ and CH₃D. We searched for emission lines of CH₃D ν₄ band in our spectrum of C/Machholz. Figure 5 shows a tentative detection of the ^RR(3, 3) emission line of CH₃D ν₄ band at 3053.84 cm⁻¹ (rest). Although we had searched for other emission lines of CH₃D in our spectra, we could not find any lines except the line shown in Figure 5. A modeled spectrum of CH₃D is also plotted in Figure 5. Here we employed the fluorescence excitation model of CH₃D (Kawakita & Watanabe 2003). The ground vibrational levels are assumed to be thermalized by intermolecular collisions in the inner coma. The rotational temperature of CH₃D is assumed to be 90 K that is the same as T_rot found in CH₄. The modeled spectrum of CH₃D (scaled to fit to the observation at 3053.84 cm⁻¹) demonstrates that the emission lines of CH₃D except ^RR(3, 3) were too weak to be detected, namely, the other emission lines are below 1σ error levels in Figure 5. If the emission line at 3053.84 cm⁻¹ is assumed to be from CH₃D, the D/H ratio in methane could be obtained. The measured line flux and the corresponding g-factor is listed in Table 3. We also assumed that the photodissociation lifetime of CH₃D is similar to that of CH₄ (this means that the lifetime of CH₃D is much longer than the traveling time along the slit from the nucleus as in the case of CH₄). Thus, the D/H ratio in methane was determined to be (3.8 ± 1.3) × 10⁻³ (±1σ error-levels).

Zoom In Zoom Out Reset image size

However, we note that the emission line at 3053.84 cm⁻¹ might be caused from other molecules, e.g., CH₃OH. Since there are many ro-vibrational transitions of CH₃OH around 3000 cm⁻¹, we must be careful to identify a very weak emission line around 3000 cm⁻¹. There is no detailed report about line assignments for CH₃OH near 3000 cm⁻¹ (the ro-vibrational spectrum of CH₃OH is very complicated). Multiple detections of CH₃D emission lines are necessary to confirm the existence of CH₃D in cometary coma. Therefore, we may have to consider our result as an upper limit. The upper limit of the D/H ratio in methane is estimated to be 6.4 × 10⁻³ (95% c.l.).¹

The D/H ratio of a molecular species is a powerful diagnostic tool to reveal molecular formation conditions. In the case of comet Hale-Bopp, Meier et al. (1998b) demonstrated that the D/H ratios of water and hydrogen cyanide were consistent with the deuterium fractionation in a dense molecular cloud at about 30 K. Although this temperature was based on the ion–molecule chemistry in the gas phase (Millar et al. 1989), the gas-grain chemistry trends to produce similar D/H ratios under higher temperature conditions. Thus, Meier et al. (1998b) concluded that the formation temperature of the cometary molecules was higher than 30 ± 10 K. Note that the observed D/H ratios in comet Hale-Bopp could not be explained even by the recent physicochemical model of the solar nebula considering gas-grain chemistry (Willacy 2007). The gas phase chemistry might play an important role in forming simple molecules such as H₂O and HCN, while more complex molecules such as CH₃OH could not be produced efficiently by the gas phase chemistry only.

In the case of C/Machholz, we could estimate the formation temperature of methane based on a similar discussion as described above (Meier & Owen 1999; Meier et al. 1998b). Based on the ion–molecule chemistry in a dense molecular cloud (Millar et al. 1989), the upper limit of the D/H ratio in methane in C/Machholz could be interpreted as the temperatures higher than about 25 K. Since the gas-grain chemistry tends to produce similar D/H ratios under higher temperature conditions than ion–molecule chemistry, the lower limit of the formation temperature is considered to be about 25 K.

Furthermore, the D/H ratio of H₂O in C/Machholz was also reported by Biver et al. (2005) based on their radio observations. They reported the upper limit for water: D/H <2.2 × 10⁻⁴. This upper limit is significantly lower than the typical D/H ratio in water (about 3 × 10⁻⁴) previously observed in the three Oort Cloud comets (1P/Halley, C/Hyakutake, and C/Hale-Bopp). As discussed above, temperatures determined based on the deuterium fractionation by ion–molecule chemistry in a dense molecular cloud (Millar et al. 1989) could be interpreted as the lower limit of the formation temperature of the molecules. Thus, the upper limit of the D/H ratio in water in C/Machholz corresponds to the lower limit of about 35 K for the temperature at molecular formation while the lower limit of about 25 K was inferred from our observations of methane in C/Machholz (Figure 6). The temperature ranges derived from the D/H ratios in both water and methane are consistent with each other.

Zoom In Zoom Out Reset image size

Thus, icy materials in C/Machholz were probably produced at higher temperatures than the three Oort Cloud comets having D/H ∼3 × 10⁻⁴ in water. The icy materials in C/Machholz might form or be processed in the inner (i.e., warmer) region of the solar nebula than the three Oort Cloud comets. An alternative explanation is that the cometary materials formed (or were processed) in the same region of the solar nebula but at different epochs (physical conditions in the solar nebula, such as temperature, ionization degree, UV and X-ray radiations, mass accretion rate, and so on. varied with time even at the same distance from the proto-Sun; Villanueva et al. 2006).

We also note that the radial mixing of cometary materials in the solar nebula might play an important role in modifying the D/H ratios in cometary molecules (materials with different D/H ratios might be mixed together; Horner et al. 2007; Willacy 2007). In such cases, the observed D/H ratio in a molecular species represented an averaged value for the mixtures of ices that have different D/H ratios. If the radial mixing of materials occurred in the solar nebula, more sophisticated interpretation is necessary for our observations and we conclude that the molecules processed in the warm region (such molecules had lower D/H ratios) contributed to the cometary ices in addition to the materials formed or processed at lower temperatures. The fraction of materials processed in the warm region might be larger than typical Oort Cloud comets for C/Machholz.

It is usually considered that the radial transportation of refractory grains occurred from the hot inner region (where CAI-type minerals found in the STARDUST sample (Brownlee et al. 2006) formed and where amorphous silicate grains were annealed and crystallized (Wooden 2008)) to the outer region (comet-forming region) in the solar nebula. However, it is unclear whether gases processed in the hot or warm region was transported to the outer solar nebula. Although both the X-wind model (Shu et al. 1996) and the turbulent mixing model (Bockelée-Morvan et al. 2002; Ciesla 2007) can mix dust grains radially, Huebner (2008) argued that turbulent mixing can be ruled out because there is no evidence that the frozen gases in the comet nucleus have ever been exposed to the high-temperature chemical reactions expected in the inner solar nebula. Turbulent mixing might not be significant and it was not responsible for the long-distance transportation from a very inner, hot region (∼0.1 AU from the proto-Sun) to the comet formation regions in the outer solar nebula.

Radial mixing of planetesimals caused by the dynamical perturbation of giant planets might form a comet as an aggregate of multiple planetesimals that have different chemistry (i.e., heterogeneous nucleus). Chemical heterogeneity in comets is not clear. Although some comets show heterogeneity in chemistry (DiSanti & Mumma 2008), it is unclear whether the heterogeneity is nature or nurture (composition of icy materials near the surface might have been affected by solar heating at multiple passages around the Sun). Since there is no evidence for the chemical heterogeneity in C/Machholz, we assumed that the nucleus of the comet is homogeneous. Namely, the D/H ratios and other properties of ices reflect the formation (and/or condensation) conditions of ices in the comet.

In the case of C/Machholz, the lower limits of nuclear spin temperatures were obtained for both H₂O and CH₄ and they are consistent with each other. The lower limit derived from H₂O is consistent with the nuclear spin temperatures found in the Oort Cloud comets (∼30 K). However, the lower limit derived from CH₄ seems to be higher than the typical nuclear spin temperature. In order to interpret our result, we should clarify what is indicated by nuclear spin temperature.

The real meaning of the nuclear spin temperature is still debated. Many authors (Mumma et al. 1993; Irvine et al. 2000; Kawakita et al. 2004; Dello Russo et al. 2005; Bockelée-Morvan et al. 2005; Crovisier 2007) discussed possible explanations for the abundance ratios of nuclear spin modifications such as OPR (or the nuclear spin temperature) in comets from various points of view:

• 1.  
  equilibration of nuclear spin modifications within the coma through chemical reactions,
• 2.  
  equilibration on (or near) the nucleus surface at sublimation,
• 3.  
  equilibration in the interior of cometary nucleus during 4.6 Gyr,
• 4.  
  equilibration before icy grains incorporated into cometary nucleus in the solar nebula.

The explanations of (1), (2), and (3) had been discussed and ruled out in previous studies (Irvine et al. 2000; Kawakita et al. 2004; Bonev et al. 2007; Crovisier 2007). However, readers may consider the explanation (3) to be valid. In previous studies, it is considered that the comet nucleus internal temperatures depend upon the comet orbital history and are expected to be different between short- and long-period comets, whereas the observed nuclear spin temperatures are almost the same (∼30 K) for both classes of comets. However, if the materials near the nucleus surface are porous and their thermal conductivity is extremely low, the temperature environment inside the nucleus since the comet formation may not have been so different for long- and short-period comets. Thus, the explanation of (3) may not be ruled out.

The most likely explanation is (4) and it means that the abundance ratios of nuclear spin modifications are cosmogonic indicators. If the abundance ratio of nuclear spin modifications of a molecular species last equilibrated in solid, the nuclear spin temperature analysis based on the rotational energy levels in the gas phase is meaningless because the rotational levels of the molecular species have different energies in the solid phase.

However, the nuclear spin temperatures of both H₂O and NH₃ were usually consistent with each other for a comet in the case that both nuclear spin temperatures were obtained. In particular, nuclear spin temperatures of H₂O, NH₃, and CH₄ were consistent in comet C/2001 Q4 (NEAT; Kawakita et al. 2006). It is not likely that we can find such consistency in each comet if nuclear spin temperatures derived based on rotational energy levels in the gas phase are meaningless. The abundance ratios of nuclear spin modifications might equilibrate in the gas phase or on the surface of cold grains but very weakly bounded to the surface (namely, under the condition where the rotational energy levels are not so different from the gas phase). The mechanism(s) to equilibrate the nuclear spins of molecular species must be investigated in future, especially in the laboratory.

If nuclear spin temperatures reflect the temperature conditions where the molecules formed or had been processed, comparison between nuclear spin temperatures and the temperature range inferred from D/H ratios in the same molecular species is interesting. In Figure 6, the ranges of nuclear spin temperatures of H₂O and CH₄ are shown. The nuclear spin temperatures are consistent with the temperature ranges indicated by the D/H ratios. This fact also supports the hypothesis that the nuclear spin temperature reflects the physical temperatures where the molecules formed or had been processed in the solar nebula.

On the other hand, the mixing ratio of methane to water in C/Machholz is similar to the typical Oort Cloud comets as reported in Kobayashi & Kawakita (2008). From the viewpoint of organic chemistry, C/Machholz is normal except for C₂H₂ (which is depleted). If the temperature where cometary molecules formed and the temperature where they last condensed were different from each other, both the normal mixing ratios in C/Machholz and the higher temperatures indicated from the D/H ratios and the nuclear spin temperatures in the comet could be explained simultaneously.

For example, the icy grains that formed in the presolar molecular cloud (at ∼25–30 K) and fell onto the outer solar nebula (> ∼ 30 AU from the proto-Sun) might not experience such high-temperature conditions that the ices evaporated (Lunine et al. 1991). They accreted inward in the solar nebula and then they were finally incorporated into comets in the comet-forming region (from 5 to 30 AU from the proto-Sun according to the "Nice" model; Morbidelli et al. 2008). In contrast, part of the interstellar ices experienced higher temperature conditions and they evaporated once at their infall onto the solar nebula surfaces by accretion shock heating if they fell onto the region within ∼30 AU from the proto-Sun (Lunine et al. 1991). After that they condensed again and were incorporated into comets in the solar nebula. Mixing ratios of cometary volatiles might reflect temperatures at the molecular condensation and might not reflect their formation conditions.

Thus, icy materials in C/Machholz might be processed in the warm region of the solar nebula (D/H ratios and OPRs were modified by chemical reactions) before they were incorporated into comets. Although turbulent mixing might be too weak to transport the dust grains from the very hot inner region (∼0.1 AU) to the comet forming regions, they might be able to transport the processed materials from the warm region (∼several AU) to the colder region (a few tens of AU) in the solar nebula. Temporal variation of temperature in the solar nebula may also be important.