The ¹²CO₂ and ¹³CO₂ Absorption Bands as Tracers of the Thermal History of Interstellar Icy Grain Mantles

In this set of experiments, 50 ML of water and various amount of CO₂ were co-deposited on the sample at 10 K, to make the following CO₂:H₂O mixtures: 5:100, 10:100, 15:100, 20:100, 25:100, 30:100, 40:100, and 50:100. After deposition, the ice mixtures were heated linearly from 10 to 200 K at 0.1 K s⁻¹. Figures 1–3 show the absorption bands ν₃, ¹³CO₂ ν₃, and the combination modes of a 50:100 CO₂:H₂O mixture at selected temperatures during heating. Figure 4 shows the integrated band area of the ν₃ peak at around 2350 cm⁻¹ for CO₂:H₂O mixtures of different mixing ratios during the heating up.

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The CO₂ ν₃ mode shows an asymmetric peak centered at about 2365 cm⁻¹ at low temperatures. He & Vidali (2018) has shown that the ν₃ peak of CO₂ on water ice surface is dependent on the CO₂ coverage. As the coverage increases from zero to more than two layers (L), the peak shifts from ∼2347 to ∼2376 cm⁻¹. The shape and position of the spectra in Figure 1 at low temperatures are qualitatively similar to the submonolayer spectra shown in Figure 1 of He et al. (2017). As the ice is heated to the 70–80 K range, a peak at ∼2378 cm⁻¹ emerges, which is a signature of "pure" crystalline form of CO₂ after segregation has taken place. Between 80 and 100 K, the ν₃ band area of CO₂ decreases. This is due to the desorption of weakly bound CO₂ on the surface of water ice (including the surface of pores). The remaining CO₂ molecules that are trapped inside the water ice matrix have an absorption peak at around 2345 cm⁻¹ that redshifts with temperature. Between 100 and 150 K, the CO₂ amount decreases linearly with temperature. This slow desorption is induced by the compaction of ASW, and CO₂ molecules are pushed out of the water matrix during the pore collapse of ASW. Between 150 and 155 K, water crystallizes and all of the remaining CO₂ desorbs from the ice. This is referred to as the "molecular volcano desorption" (Smith et al. 1997).

A similar trend is also seen in the ν₃ ¹³CO₂ band. When CO₂ segregates, a peak at 2282 cm⁻¹ emerges. This peak is characteristic of ¹³CO₂ with natural isotopic abundance (He et al. 2017) and is more sensitive to segregation than the ν₃ peak of CO₂ at around 2376 cm⁻¹. During the heating from 10 to 140 K, the peak redshifts from about 2280 cm⁻¹ to about 2276 cm⁻¹, and the width becomes narrower with temperature. To see more clearly how the peak position and width change with temperature, we used one broad Gaussian lineshape and one narrow Lorentzian lineshape to fit ¹³CO₂ in disordered and ordered (crystalline) CO₂, respectively. Although the disordered component has an asymmetric shape, for simplicity we still use a Gaussian function. This fitting scheme is sufficient to reliably obtain the peak position and the width. Figures 5 and 6 show the center position (μ) and the full width at half maximum (FWHM) of the Gaussian fit, respectively. Both the center position μ and FWHM decrease with temperature roughly linearly. The best-fitting parameters with a 95% confidence interval are

$$\begin{eqnarray}&&\mu =(2280.16\pm 0.06)-(0.030\pm 0.0006)T,\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\mathrm{FWHM}=(8.6\pm 0.7)-(0.022\pm 0.001)T,\end{eqnarray} \tag{ 2 }$$

where the unit is cm⁻¹ for μ and FWHM, and Kelvin for T. These simple functions will be useful for the analysis of the observed ¹³CO₂ profile, to be discussed below.

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Figure 3 shows the region of the ν₁ + ν₃ ¹²CO₂ mode at around 3700 cm⁻¹, ν₁ + 2ν₂ ¹²CO₂ mode at 3600 cm⁻¹, as well as a peak at ∼3650 cm⁻¹. The 3650 cm⁻¹ peak can be attributed to ¹²CO₂ on the surface of water. This feature is common in CO₂:H₂O mixtures or CO₂ on the surface of water at low temperatures. The ν₁ + ν₃ and ν₁ + 2ν₂ combination modes are broad at low temperatures. As the CO₂ segregates, a sharp feature emerges for both combination modes. After weakly bound CO₂ has desorbed from the surface, the 3600 cm⁻¹ peak is barely seen, but the peak at 3700 cm⁻¹ is still clearly visible. Its position and width are no different from the 3-coordinated dangling bond of amorphous water annealed at similar temperatures. We attribute this peak to the dangling bond of ASW, although we do not exclude the possibility that the ν₁ + ν₃ mode of CO₂ may also have a small contribution to this peak.

Prior laboratory measurements (Hodyss et al. 2008; He & Vidali 2018) have shown that the segregation and crystallization of CO₂ is accompanied by changes in the bending, asymmetric stretching (for both ¹²CO₂ and ¹³CO₂), and combination modes. The bending mode absorption at ∼650 cm⁻¹ is an important feature that is used to characterize CO₂ ice (Pontoppidan et al. 2008). Toward heavily embedded YSOs, the bending mode is easier to observe than the combination modes or the ν₃ of ¹³CO₂ because of the brighter continuum emission at 15 μm. However, the bending mode band is close to the lower limit of our infrared detector, and the signal is weak. Following our previous work on CO₂ ice (He & Vidali 2018), we use the ν₁ + ν₃ combination mode at around 3700 cm⁻¹ to quantify the segregation. The analysis of segregation based on the combination mode at 3700 cm⁻¹ should not differ from that using the bending mode at ∼650 cm⁻¹.

We decompose the profile of the combination mode at ∼3700 cm⁻¹ into two components, one broad Gaussian component centered at ∼3703 cm⁻¹ attributed to disordered CO₂, and one sharp Lorentzian component centered at 3708 cm⁻¹ attributed to (poly)crystalline CO₂. An example of the fitting is shown in Figure 7. We defined the "degree of crystallinity" (DOC) as the fraction of CO₂ in the (poly)crystalline form (the Lorentzian component),

$$\begin{eqnarray}&&\mathrm{DOC}=\displaystyle \frac{{A}_{\mathrm{crystalline}}}{{A}_{\mathrm{crystalline}}+{A}_{\mathrm{amorphous}}}\,,\end{eqnarray} \tag{ 3 }$$

where A_crystalline and A_amorphous are the band area of the Lorentzian component and Gaussian component, respectively. We calculate DOC of the experiments presented in Section 3.1. The results are shown in Figure 8.

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From Figure 8, it can be seen that the segregation strongly depends on both concentration and temperature. Here we performed the experiments at a fixed heating ramp rate. It is possible that different ramp rates would also yield different segregation ratios. To use CO₂ segregation to trace the temperature history of the ice mantle would require a systematic study of the segregation over the entire parameter space of time, temperature, and concentration, which is a very time consuming set of measurements. Here we take a simpler approach and focus on one parameter at a time. A set of isothermal experiments were devoted to determine the temperature that maximizes the segregation. We deposited 50 ML of water and 30 ML of CO₂ simultaneously onto the sample at 10 K, then flash-heated the sample at a rate of 0.5 K s⁻¹ to a target temperature and kept it at that temperature for 2 hr while monitoring the ν₁ + ν₃ mode. The band area of the Lorentzian component at different target temperatures as a function of time is shown in Figure 9. It can be seen that 72 K is the most favorable temperature to form crystalline CO₂ in CO₂:H₂O mixtures. Below 72 K the mobility of CO₂ is not enough for segregation of CO₂ to occur to the fullest extent, while above 72 K the desorption of CO₂ starts to play a significant role. At 70 and 68 K, the segregated CO₂ does not reach maximum after 2 hr. To verify that the highest degree of segregation is indeed achieved at 72 K instead of 68 K or 70 K, we use a function to fit the curves and try to find the saturation level. Öberg et al. (2009) found that the segregation during isothermal experiments cannot be fit by a single exponential function. Two exponential functions are required to fit it. They attributed the two parts of the segregation to two distinct mechanisms of segregation—surface processes and bulk processes. Here we focus on the second part of the segregation only and use the function $a(1-\exp (-{bt}))+c$ to fit the 68–72 K curves after the first 10 minutes. The fittings are extrapolated to 4 hr to show the saturation level, from which it is clear that 72 K is the favorable temperature that maximizes the segregation. Based on Figure 8, the temperature at which the DOC maximizes is similar for all concentrations. Therefore, it is fair to assume that this favorable temperature, 72 K, works for all concentrations.

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After finding this most favorable isothermal experimental temperature, we fix the temperature and try different concentrations to obtain the lowest concentration required for the formation of "pure" crystalline CO₂. We fixed the amount of water deposited at 50 ML and selected the CO₂ dose to be: 2.5, 5.0, 7.5, 10, 11.5, 12.5, 15, 20, and 25 ML. After the co-deposition at 10 K, the ice mixtures were heated to 72 K at a ramp rate of 0.5 K s⁻¹ and then kept at 72 K for 2 hr. Figure 10 shows the DOC as a function of isothermal experimental time at different target temperatures. It can be seen that below the CO₂:H₂O = 23:100 concentration, the DOC is almost zero. We thus conclude that 23% is the threshold concentration to obtain "pure" crystalline CO₂ in CO₂:H₂O mixtures.

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CO₂ is one of the main components of ISM ice mantles. In some of the observed sightlines, CO₂ is in the "pure" crystalline form, as seen from the double splitting of the bending absorption profile. This splitting feature has been proposed to be a candidate tracer of the thermal history of the ice mantle. Prior laboratory studies (Ehrenfreund et al. 1999; Hodyss et al. 2008; Öberg et al. 2009) have found that the segregation of CO₂ from ice mixtures is a function of temperature, and the segregation is irreversible with temperature. Experiments in this work show that the segregation of CO₂ from a CO₂:H₂O mixture is not only temperature dependent but also strongly affected by the concentration of CO₂. In fact, if the concentration of CO₂ is too low, pure crystalline CO₂ never forms, regardless of the thermal history. According to our measurements, the concentration threshold for CO₂ segregation is 23:100. This is larger than the average CO₂/H₂O column density ratio observed toward massive YSOs (17 ± 3%; Gerakines et al. 1999) and comparable to the ∼25% ratio of the low-mass YSOs (Pontoppidan et al. 2008). The segregated CO₂ detected in these sightlines (e.g., S140 IRS1) might thus probe CO₂/H₂O concentrations that are enhanced at certain locations along the sightline or in certain ice layers.

Our experiments show that the ¹³CO₂ absorption profile at around 2280 cm⁻¹ is a good tracer of the thermal history of the ice mantle, even if there is no sign of the very narrow feature of segregated crystalline CO₂. Figures 5 and 6 show that both the peak position (in cm⁻¹) and width decrease with increasing temperature, but they are not sensitive to CO₂ concentration. This isolates the effect of temperature from the effect of concentration, and thus provides an easy tool for the determination of the thermal history. Next we try to fit the ¹³CO₂ spectra in Boogert et al. (2000) based on our laboratory measurements. We visually examine the observed spectra and separate them into two groups: group 1 without a significant narrow blue peak at 2283 cm⁻¹, and group 2 with it. Spectra in group 1 are fit with a single Gaussian function, while spectra in group 2 are fit with one Gaussian function for disordered CO₂ and one Lorentzian function for crystalline CO₂, as shown in Figures 11 and 12. The best-fit peak position, FWHM as well as the calculated temperature based on the Gaussian component using Equation (2) are also shown for each spectrum. For group 2, the magnitude of both components are also shown.

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The temperatures quoted in Figures 11 and 12 are based on the laboratory timescale. In a typical astrophysically relevant timescale, the warming up of the ice is over a much longer time, and a lower temperature is expected to yield the same structural changes in the ice mixture. To translate the ice's temperature in the laboratory timescale T_lab to the temperature in astronomical conditions T_ast, an Arrhenius-type expression can be used to describe the rate of segregation:

$$\begin{eqnarray}&&k=\nu \exp (-{E}_{\mathrm{seg}}/T),\end{eqnarray} \tag{ 4 }$$

where ν and E_seg are the prefactor and the energy barrier (in unit of degree Kelvin) for CO₂ segregation, respectively. The timescale for segregation to happen can be approximated by t ∼ k⁻¹. The temperature at which segregation happens most efficiently is

$$\begin{eqnarray}&&T=\displaystyle \frac{{E}_{\mathrm{seg}}}{\mathrm{ln}(\nu t)}.\end{eqnarray} \tag{ 5 }$$

In laboratory experiments, the timescale t_lab is on the order of seconds. Under astronomical conditions, the freefall time between distances that have temperatures of 70–90 K for a low-mass star is 75 yr (Pontoppidan et al. 2008). Rotation will slow down this process, but 10²–10³ yr for the temperature range where segregation takes place is a reasonable estimate. The lifetime of hot cores around massive YSOs is 30,000 yr (Charnley et al. 1992). These hot cores have temperatures exceeding 100 K, but there is a gradient outside of that where ices have not yet evaporated and are heated during that time. We adopt the range of 10²–10⁵ yr for the segregation timescale under astronomical conditions. The conversion factor from the laboratory timescale to an astronomical timescale is

$$\begin{eqnarray}&&\displaystyle \frac{{T}_{\mathrm{ast}}}{{T}_{\mathrm{lab}}}=\displaystyle \frac{{ln}(\nu {t}_{\mathrm{lab}})}{{ln}(\nu {t}_{\mathrm{ast}})}.\end{eqnarray} \tag{ 6 }$$

The prefactor ν is not well characterized. Öberg et al. (2009) performed isothermal experiments of 1:2 CO₂:H₂O mixtures and reported a prefactor of $2\times {10}^{5\pm 1}$ s⁻¹ for segregation. This prefactor likely reflects a combined effects of CO₂ diffusion on ASW and the collapse of pores in ASW. Using this prefactor, the conversion factor can be calculated to be in the 0.3–0.4 range. If we assume that the segregation is dominated by the diffusion of CO₂ on the pore surface of ASW and take the laboratory determined prefactors for volatile molecules such as CO, N₂, CH₄, which are mostly in the 10^8 ± 1 range (He et al. 2018), then the conversion factor is in the 0.4–0.5 range. In summary, to convert the temperature in the laboratory timescale to that of the warming up of a interstellar cloud, a factor 0.4 ± 0.1 should be considered. With a correction for timescale taken into account, the dependence of segregation on both concentration and temperature shown in Figure 8 should be useful in models of YSO envelopes.

In the sightline of W33A, the ¹³CO₂ absorption peak is centered at 2277 cm⁻¹, which corresponds to a temperature of 105 K in the laboratory timescale. But if we plug T = 105 K into Equation (2), the calculated FWHM = 6.3 cm⁻¹ is much smaller than that for the observed one, 9.0 cm⁻¹. Note that this is likely not due to contamination by CO mixed in the ices, because W33A has a smaller contribution from CO (10%) compared to other YSOs, e.g., NGC 7538 IRS9 (20%; Pontoppidan et al. 2008). This inconsistency is likely due to the nonuniform temperature along the sightline. For this reason, we use the peak position in Equation (1) instead of the FWHM in Equation (2) to determine the temperature. In general, the best-fit temperature in Figure 11 should be understood as the average temperature along the sightline.

So far, we used CO₂ in water ice to obtain the temperature of the ice. Now we put the temperature traced by ¹³CO₂ in the context of the observed sightlines. Of the targets with a single "disordered" ¹³CO₂ component (Figure 11), the peak of R CrA IRS2 (TS13) has the largest wavenumber, and thus the lowest temperature. The space temperature of (0.4 ± 0.1) ×(23 ± 12) K is well below that for CO sublimation, and indeed this sightline harbors an exceptionally large apolar CO component (Vandenbussche et al. 1999). The two other high-quality spectra of the low-mass YSO HH 100 IR and the massive YSO W33A show ¹³CO₂ bands peaking at smaller wavenumbers, corresponding to space temperatures of (0.4 ± 0.1) × (55 ± 9) K and (0.4 ± 0.1) × (105 ± 7) K, respectively. Indeed, the CO profile of W33A is dominated by polar CO ices (Pontoppidan et al. 2003), indicating that the volatile apolar CO ices have sublimated, and a significant abundance of warm CO gas is detected in this sightline (Mitchell et al. 1990). The relatively high ¹³CO₂ temperature for HH 100 seems puzzling considering the large abundance of apolar CO (Pontoppidan et al. 2003). This likely reflects a large temperature gradient in the HH 100 YSO envelope, with colder apolar CO dominating the ices at larger radii. One should also consider the possibility that the CO₂:H₂O ices are formed earlier in the cloud history in less shielded conditions on warmer grains than the volatile CO. Then, the ¹³CO₂ profile reflects the formation temperature. This can be tested by observations toward background stars tracing quiescent clouds. Unfortunately, the ISO/SWS spectrum of Elias 16, a background star of the Taurus Molecular Cloud, is of low quality, but will be vastly improved when observed with JWST in the near future. For a discussion regarding the targets with segregated crystalline ¹³CO₂ (Figure 12), we refer the reader to Boogert et al. (2000) and van der Tak et al. (2000), who show that the degree of segregation correlates with the dust temperature as the YSO envelope becomes less massive and hotter over timescales of a few times 10000 yr.

In the second group (Figure 12), we used one broad Gaussian and one narrow Lorentzian to fit the spectra. The temperatures are derived from the broad component using Equation (1). Boogert et al. (2000) used a narrow Gaussian instead of a Lorentzian to fit the 2283 cm⁻¹ feature. They found that the narrow feature is present only toward high-mass protostars, even though not all high-mass protostars have the narrow feature (see Boogert et al. 2000 for a detailed discussion). In these four sightlines, the temperatures are all relatively high, in agreement with the previous proposition that segregation indicates thermal processing. Because of more free parameters being used in the fitting, the uncertainty in temperature is much larger than in group 1. Furthermore, the signal-to-noise ratios of the spectra from S140:IRS1 and W3:IRS5 are not good enough for an accurate determination of the peak position of the disordered component. To better constrain the temperature would require a better signal-to-noise ratio of the spectra. The JWST is expected to cover these regions at orders of magnitude better sensitivity and somewhat larger spectral resolution (R = 3000 versus 2000), and more accurate temperature determination and sorting of features between different classes of objects will be possible. The bending mode profile at 15 μm can also be used as a supplementary tool to further constrain the temperature.

Previously, Boogert et al. (2000) compared the observed spectra with the laboratory measurement of Ehrenfreund et al. (1999). They found a similar redshift and a narrowing of the ¹³CO₂ peak as the temperature of the CO₂:H₂O mixture was increased. They also found that during heating a 1:0.92:1 H₂O:CH₃OH:CO₂ mixture, the peak position and width changed, but with a different temperature dependence than that of a CO₂:H₂O mixture. Therefore, Boogert et al. (2000) concluded that while ¹³CO₂ traces segregation, it is not suitable for temperature determinations, because the temperature effect could not be separated from composition effects. In their experiment, the concentration of CH₃OH is much higher than what is typically observed. CH₃OH is formed mostly on dust grains by the consecutive hydrogenation of CO after the heavy CO freeze-out. This formation mechanism is corroborated by both laboratory measurements (Hama & Watanabe 2013) and observations (Boogert et al. 2011), which show that CH₃OH is mostly found in high-extinction regions. Conversely, CO₂ is mostly found in a water-rich environment, consistent with the scenario that CO₂ is formed together with water. Although most recent laboratory experiments found that CH₃OH can also be formed before the heavy freeze-out of CO by the reaction between CH₃ and OH (Qasim et al. 2018), the question still remains of how much CH₃OH can be formed this way. Based on the current state of knowledge, it is safe to assume that CO₂ primarily interacts with water instead of with CH₃OH in the ice, and therefore it is justifiable to ignore the effect of CH₃OH on the ¹³CO₂ absorption profile. This assumption seems less applicable to CO mixed in the ices, as discussed below.

Previous analysis of the CO₂ bending mode absorption profile at 15 μm and the blue component of CO absorption profile at 4.7 μm reveals that 10–30% of the CO₂ molecules are mixed with CO (Pontoppidan et al. 2003, 2008). This group proposed that "pure" crystalline CO₂ can be formed either by thermally induced CO₂ segregation from a CO₂:H₂O mixture, or by CO desorption from a CO:CO₂ mixture. The mechanism of segregation is closely related to the mechanism of CO₂ formation. So far there are mainly two categories of mechanisms proposed to explain the formation of CO₂ molecules on grains. The first category involves pure thermal reactions among CO, O, H, and OH. Although several questions still remains, such as the relative contribution of CO+O (Roser et al. 2001) and CO+OH (Zins et al. 2011), and whether the reaction involves HOCO (Ioppolo et al. 2011), it is clear that water is formed on grains at the same time as CO₂ via reactions with hydrogen: O + H→OH, OH+H→H₂O. The experimental results and the temperature tracing method proposed in this study mostly apply to the CO₂ that is formed together with water by thermal processes. The second category of CO₂ formation mechanism involves energetic processing of the pure CO in the top layers of the ice mantle. Laboratory experiments have shown that CO₂ can be formed by the bombardment of analogs of cosmic rays with CO ice (Gerakines & Moore 2001; Loeffler et al. 2005; Jamieson et al. 2006). However, other molecules that should have also been produced in the energetic processing of CO, such as C₃O₂ (Jamieson et al. 2006), were not observed in the same sightline as CO₂ (Pontoppidan et al. 2008). The reason why a fraction of CO₂ is in a CO-rich environment is still puzzling. If cosmic ray bombardment is important for CO₂ formation, the compaction of the ASW and the segregation of CO₂ from CO₂:H₂O mixtures may also be affected by cosmic rays. It would be less relevant to characterize the ice mantle by temperature than to use the fluence of cosmic rays. In any case, the use of CO₂ segregation or ¹³CO₂ to trace the temperature history of the ice mantle is only valid under the assumption that cosmic ray irradiation is not the dominant mechanism for CO₂formation.