Water UV-shielding in the Terrestrial Planet-forming Zone: Implications for Carbon Dioxide Emission

Arthur D. Bosman; Edwin A. Bergin; Jenny K. Calahan; Sara E. Duval

doi:10.3847/2041-8213/ac7d9f

1. Introduction

Carbon dioxide, CO₂, is an important molecule in the interstellar inventory. CO₂ is a carrier of significant volatile carbon and oxygen in both interstellar (Boogert et al. 2015) and cometary (Mumma & Charnley 2011) ices. However, the lack of a permanent dipole and its abundance in Earth's atmosphere requires infrared space missions for astronomical observations. The chemistry of CO₂ is closely linked to CO, a common precursor to CO₂ and H₂O, with which CO₂ shares the OH radical as a precursor in both gas and grain-surface chemistry (e.g., Smith et al. 2004; Arasa et al. 2013). Such close chemical links to the main reservoirs of carbon and oxygen make CO₂ an important tracer of the carbon and oxygen elemental abundances, especially the overall C/O ratio. As the C/O ratio is proposed to link planet composition and formation history (Öberg et al. 2011), CO₂ likely has an important role to play in the unraveling of this complex problem.

Toward protoplanetary disks, CO₂ has most commonly been observed in emission using Spitzer-IRS (e.g., Carr & Najita 2008; Pontoppidan et al. 2010). CO₂ emission has been inferred to originate from the warm (>300 K) surface layers confined to within the inner few astronomical units (Salyk et al. 2011; Bosman et al. 2017). In these strongly irradiated disk surface layers, the abundance of CO₂ is sensitive to both the C/O ratio, through the abundance of its precursor OH (e.g., Woitke et al. 2018; Anderson et al. 2021), and the elemental abundance of C (See Figure 1 in Bosman et al. 2018a).

The interplay between dust growth, dynamics, and chemistry in the outer (tens of astronomical units) disk might also significantly impact the abundance of CO₂ in the inner few astronomical units where excitation conditions allow for detectable rovibrational emission. The low CO abundances in the outer disk are possibly pointing to a sequestration of carbon into CO₂ ices (Eistrup et al. 2016; Bosman et al. 2018b). This is seen in detailed models that link chemistry to dust evolution (Krijt et al. 2020). As these ices drift to inside the CO₂ sublimation front (or ice line), they could greatly impact the inner disk CO₂ abundance (e.g., Bosman et al. 2017; Booth et al. 2017). Thus, CO₂ might be a sensitive tracer of dust drift.

Gas dynamics in the inner few astronomical units could also impact the CO₂ abundance structure. Vertical mixing of water, followed by sequestration on large grains dubbed the "vertical cold finger effect," has been invoked to explain the limited extent of the water surface reservoir (Meijerink et al. 2009; Blevins et al. 2016; Bosman & Bergin 2021), and dynamical simulations have shown it to be effective (Krijt et al. 2016). Such sequestration would similarly affect CO₂ outside of the CO₂ ice line. Furthermore between the H₂O and CO₂ ice lines, the sequestration of water can impact the elemental abundances of carbon and oxygen, creating an environment in which CO₂ is inefficiently formed and the excess oxygen lost to water ice in the midplane.

The abundance of CO₂ is a crucial component in understanding the overall C/O ratio of gas and ices, but it also can be a probe of the overall disk chemical evolution, which is linked to the disk gas and dust physics. To fully understand these processes requires the emission to be analyzed in detail. Unfortunately, recent modeling efforts have difficulty in simultaneously predicting the H₂O and CO₂ fluxes in the mid-infrared (Woitke et al. 2018; Anderson et al. 2021). In this paper, we used an updated set of thermochemical models that has been tested against the infrared water observations (Bosman et al. 2022) to study the CO₂ abundance structure and emission from the inner disk regions. Crucially, our model includes the effects of water UV-shielding. This must be present given the large water columns (Bethell & Bergin 2009) leading to UV absorption at higher surface layers than would be set by the dust optical surface to UV photons; this can strongly alter the chemical structure of which CO₂ is a key component.

2. Methods

We use the DALI models from Bosman et al. (2022). These models include modification from standard DALI (Bruderer et al. 2012; Bruderer 2013) to better represent the inner disk regions. This includes more efficient H₂ formation at high temperature, more efficient heating following photodissociation (following Glassgold & Najita 2015), and water UV-shielding (Bethell & Bergin 2009). The models assume the AS 209 spectrum from Zhang et al. (2021) as input. Most of the UV in this spectrum is in Lyα (Herczeg et al. 2004). Four different physical structures are computed, two large grain fractions (99% and 99.9%) and two disk scale heights (h/R = 0.08 and 0.16 at R = 45 au). Model setup details are in Bosman et al. (2022). The elemental abundances used in the chemistry are given in Table 1. Abundances are based on Jonkheid et al. (2006), with reduced Mg, Si, S, and Fe. As the chemical timescale in the region of interest is short, we solve for statistical equilibrium (Anderson et al. 2021).

Table 1. Elemental Abundances w.r.t. H

Element	Abundance w.r.t. H
H	1.0
He	7.59 × 10⁻²
C	1.35 × 10⁻⁴
N	2.14 × 10⁻⁵
O	2.88 × 10⁻⁴
Mg	4.17 × 10⁻⁹
Si	7.94 × 10⁻⁸
S	1.91 × 10⁻⁸
Fe	4.27 × 10⁻⁹

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From the temperature and CO₂ abundance structure, we calculate the CO₂ emission spectrum using the molecular data as collected and computed in Bosman et al. (2017). The molecular excitation is calculated explicitly by balancing excitation and de-excitation from collisions and photon absorption and emission. Energy levels, line positions, and line strengths are from the HITRAN database (Rothman et al. 2013). Throughout this paper, we use the CO₂ level notation as used in Bosman et al. (2017). When talking about the main CO₂ feature around 15 μm, we denote this as the 01¹0 − 00⁰0 Q branch, but it is implied that this includes a smaller contribution of the more highly excited 02²0–01¹0, 03³0–02²0 , etc., Q branches.

For comparison with slab excitation models we use the model from Banzatti et al. (2012), using representative slab-model parameters from Salyk et al. (2011). For water, we use a column of 3 × 10¹⁸ cm⁻² and an excitation temperature of 500 K, as done in (Bosman et al. 2022), while for CO₂ we use a column of 3 × 10¹⁵ cm⁻² and a excitation temperature of 700 K. These effectively match the typical H₂O and CO₂ spectra and are excellent proxies for the observed emission spectrum.

3. Results

3.1. CO₂ Abundance

Figure 1 shows the CO₂ abundance structure for the flat model with a large grain fraction of 99.9%. In this baseline model, the CO₂ abundance is roughly distributed in two reservoirs. On the disk surface, there is the warm (>500 K), CO₂ layer with an abundance between 10⁻⁸–10⁻⁶ spanning the entire 0.1–1 au region, with a low-abundance tail to larger radii. Below this is a high-abundance, >10⁻⁶, cooler (100–500 K) CO₂ region that reaches all the way to the midplane and out to the CO₂ ice line. There is some additional structure as CO₂ vapor is absent in the inner ∼0.2 au and in a region around 0.7 au near the disk midplane, the former is caused by carbon sequestration in hydrocarbons, while the latter is caused by the efficient formation of water ice. The high-abundance, cool CO₂ reservoir extends to high in the disk photosphere (z/r > 0.1) and contributes to line formation. This CO₂ morphology is identical for the other physical structures.

When H₂O UV-shielding is included, both reservoirs are significantly impacted (see the second panel of Figure 1). The warm surface layer becomes thinner, and the region of high CO₂ abundance (∼10⁻⁶) is restricted to below z/r ≤ 0.1. In this model, CO₂ vapor returns to the high-abundance value around the τ_15μm = 1 layer. The decrease of the CO₂ abundance is driven by the slower photodissociation of H₂O, leading to lower OH production rates, which is critical for the production of CO₂. Furthermore, the CO₂ dissociation rate is not decreased by the same amounts as the H₂O dissociation rate. Unfortunately, the OH emission from disks is dominated by OH that is above the point where H₂O can start to block the UV radiation, as such OH cannot be used as a tracer of H₂O UV-shielding (see Appendix A).

Increasing the chemical heating after photodissociation only impacts the abundance in the warm surface layer. The increased temperatures increase the efficiency of the OH + H₂ → H₂O + H reaction, which has a high reaction barrier (1740 K; Baulch et al. 1992), leaving less OH for the OH + CO → CO₂ + H reaction, changing the H₂O to CO₂ abundance ratio (see, e.g., Figure 1 of Bosman et al. 2018a).

Figure 1 also shows the emitting area of the 01¹0–00⁰0 R(20) line as an irregular red box. This line has an upper-level energy of ∼1250 K, of which ∼250 K is in rotational energy. This is relatively low in comparison to the nearby water lines, many of which have upper-level energies of >2500 K. The emitting region of this line clearly traces the warm surface layer of the disk and extends over the full radial extent in gas where the CO₂ vapor abundance lies between 10⁻⁹ to a few ×10⁻⁷. Lines with lower rotational excitation will emit from a slightly larger radial region. As can be seen in Figure 1 the CO₂ emitting area extends to layers exterior to the water midplane ice line and, in almost all cases, the CO₂-emitting area is larger than that for the water vapor lines.

Figure 2 shows the gas temperature as a function of the vertical, top-down CO₂ column at the radius of the water ice line. Here, for ease in comparison, we show only two models, both with large grain fractions of 99.9%; one is the base DALI model and the other with extra chemical heating and water UV-shielding. These two models show sharply different structures. In the nonshielding model, CO₂ is abundant throughout the full vertical extent of the disk, so the temperature decreases relatively smoothly with increasing CO₂ column. In the water UV-shielding model, CO₂ is absent in the intermediate layers. As a result, the temperature drops sharply when the column reaches around 10¹⁶ cm⁻². The low CO₂ abundance in the intermediate layers is caused by the UV-shielding of water. The self-shielding of water stops the formation of OH, inhibiting the formation of CO₂. As CO₂ can dissociate at longer wavelengths compared to H₂O, dissociation of CO₂ is still possible; together, this strongly lowers the CO₂ abundance. In the deeper layers, all UV is blocked by the small dust. In these layers, which have very high density, the statistical equilibrium that is calculated tends toward the chemical equilibrium.

This abundance and temperature structure strongly constrains where the emission in the water UV-shielded model can originate from. Only a column of ∼10¹⁶ cm⁻² can contribute to the emission. CO₂ deeper into the disk exists at much lower temperatures, as well as at temperatures close to the τ_15μm = 1 surface (∼200 K). Contribution for columns >10¹⁶ cm⁻² should thus be negligible. Contrast this with the models without shielding, where the temperature is ∼300 K at a column of 10¹⁸, so two orders of magnitude higher columns can contribute to the emission in this model.

3.2. CO₂ Spectra

Figure 3 shows the H₂O and CO₂ spectra around the 15 μm CO₂ vibrational band. The baseline DALI models predict relatively stronger CO₂ emission when compared to the surrounding H₂O line forest. The CO₂ 01¹0–00⁰0 Q branch is a factor of few brighter than the surrounding water lines, and the individual CO₂ 01¹0–00⁰0 P and R branch lines are on par with the water lines. Both of these characteristics are inconsistent with Spitzer/IRS observations of typical disk systems as exemplified by the slab models in Figure 3.

Including water UV-shielding reduces the CO₂ flux. This is a direct consequence of the thinner upper atmosphere CO₂ layer. As the water emission is less strongly affected by the inclusion of water UV-shielding (Bosman et al. 2022), the ratio between water and CO₂ lines gets closer to the ratio in the slab models, but (in a relative sense) CO₂ emission is still too bright.

Including extra chemical heating, and thus increasing the gas temperature correspondingly leads to higher CO₂ infrared flux. However, as the increased temperature lowers the CO₂ abundance, the flux ratio between water lines and the main CO₂ feature decreases. As a result, the model with both water UV-shielding as well as chemical heating comes closest to the observed H₂O-to-CO₂ ratios. The CO₂ in this model remains too bright when compared to the surrounding water emission. However, as noted earlier, the CO₂-emitting region extends farther than the H₂O-emitting region. Additional spectra from different physical structures find similar results (See Appendix B).

Figure 3 also shows the H₂O and CO₂ spectra in the case where we assume that the emission of both is contained radially within the water midplane ice line (see Figure 1), perhaps due to the vertical cold finger effect (Meijerink et al. 2009). This cuts both the H₂O and CO₂ flux, but in general, the CO₂ lines are more strongly impacted than the H₂O lines. In the case of the model with shielding, extra chemical heating, and a truncated emitting region, the model H₂O and CO₂ spectra line up nicely with the slab-model spectra that are representative of the Spitzer-IRS observations.

4. Discussion

4.1. CO₂ Column

The thermochemical model with water UV-shielding and chemical heating consistently predicts a CO₂ column in the surface layers that is around 10¹⁶ cm⁻². This is orders of magnitude lower than the 10¹⁸ cm⁻² columns that follow from the models that do not include water UV-shielding. However, it is on the high end of the observed data where columns span the 3 × 10¹⁴–3 × 10¹⁶ cm⁻², with additional nondetection implying even lower CO₂ columns. As such, our models are not capturing the full variation in the observed population. They are, however, representative of a significant part of the full population.

The gas temperatures in our model at the outer edge of the CO₂ emission are colder (<500 K) than the inferred temperatures from the CO₂ Spitzer-IRS observations (∼700 K; Salyk et al. 2011). This could imply that the radial temperature profile in the disk is impacting the shape of the 01¹0–00⁰0 Q branch forcing the slab-model fit to a higher temperature, but lower column solution. This could also explain why the slab models consistently find a higher gas temperature for the CO₂ than for the H₂O (Salyk et al. 2011), whereas in the models they both emit from the same gas. With individual P- and R-branch lines of CO₂ and better-isolated lines of H₂O in the JWST-MIRI spectra, it should be possible to get a better handle on the gas temperature and column densities of both these species.

There are chemical pathways that could lead to lower CO₂ abundances. Increasing the gas temperature changes the balance between H₂O and CO₂ formation, which both rely on OH; as a result, a higher temperature lowers the CO₂ abundance. A temperature increase requires either a larger total UV flux or mechanical heating, as currently most of the energy in the UV photons is already converted into heat in the models (Bosman et al. 2022).

Another possible way to lower the CO₂ abundance (and decrease emission) is to increase its destruction rate. Two- and three-body gas-phase reactions that destroy CO₂ are few and inefficient (see Bosman et al. 2018a), whereas reactions due to an ionization source (cosmic rays and X-rays) are already included. This leaves the dissociation of CO₂ due to UV, which already is the main destruction pathway in the surface layers where CO₂ emission is being produced. The current stellar spectrum contains a significant amount of Lyα. The photodissociation cross section of CO₂ is modest near Lyα, and CO₂ is not efficiently dissociated in our model (Huestis & Berkowitz 2010; Archer et al. 2013; Heays et al. 2017). However, these cross sections are from measurements at room temperatures. At elevated temperatures, the UV cross section at Lyα increases by up to two orders of magnitude (Venot et al. 2018). Implementing these high-temperature cross sections, however, had little effect on the CO₂ distribution or spectra. In these models, the CO₂ abundance decreased by 10%–20% in the disk surface layers. As such, we deem that our chemical model is robust in its treatment of CO₂ destruction pathways.

4.2. Tracing the CO₂ Abundance Structure

To properly interpret the CO₂ mid-infrared flux, derive the elemental composition of the gas, and explore disk physical processes, it is important to understand the distribution of CO₂ throughout the disk. The models with water UV-shielding imply that CO₂ will only be present in a thin surface layer and will emit at a similar temperature to water vapor. However, our models predict that water UV-shielding has a strong influence on the CO₂ vertical abundance distribution (Figure 1), which has a significant impact on the column distribution within different thermal layers (Figure 2).

With a higher spectral resolution when compared to Spitzer/IRS, JWST (NIRSPEC and MIRI) offers an opportunity to observe CO₂ vapor with MIRI being able to isolate individual P- and R-branch lines around 15 μm and potentially detect ¹³CO₂ (Bosman et al. 2017). In Figure 4 we predict ¹²CO₂ and ¹³CO₂ features that can help elucidate the vertical abundance structure of CO₂. In the case without water UV-shielding, there is a significantly higher CO₂ abundance in the deeper layers below the nominal emitting surface region (see, Figure 1). In this case, the relative strength of the two 10⁰0 − 01¹0 Q-branch features at 13.90 and 16.20 μm is high, 20% of the main Q branch, while in the model without water UV-shielding, these features are about a factor of 2 weaker. ¹³CO₂ emission is also sensitive to these differences; this is in line with previous predictions (Bosman et al. 2017). Conversely, the models predict a nearly constant relative strength of the 01¹0–00⁰0 P(19)–P(27) and R(19)–R(27) lines, around 10% w.r.t. the main CO₂ Q branch. These lines can thus be used as a yardstick. If the peak of the Q-branch features at 13.90 and 16.20 μm is higher than the 01¹0–00⁰0 rotational lines, this indicates deep, warm CO₂. It should be noted that many of the CO₂ emission features have nearby H₂O lines, which will be blended in observations. Simultaneous fitting of the water spectrum is thus required.

**Figure 4.** Normalized spectra convolved to R = 3000 for the chemical heating model with (solid) and without (dashed) water UV-shielding assuming a thin structure with a surface layer gas-to-dust ratio of 10⁵. CO₂ is assumed to only be present within the water midplane radius for all these models. The top panel shows ¹²CO₂ and ¹3CO₂ in red and purple, respectively. The bottom panel shows the combined spectra. Spectra have been normalizing to the ¹²CO₂ 01¹0–00⁰0 Q-branch peak and are zoomed in on three regions with Q branches of interest. While the individual 01¹0–00⁰0 P- and R-branch lines show little differences in normalized flux, the various Q-branch features are impacted by the different abundance structures. Ratios between these can thus be used to derive the deeper abundance structure.
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4.3. Radial Extent of the Emitting Layer

In the chemical models, the radial extent of the emitting layer is naturally restricted by the presence of OH. The formation of OH is only efficient at high-enough temperatures that the reaction barrier of the O + H₂ reaction can be overcome. This effectively sets the maximal H₂O emitting area. As chemically CO₂ is linked to H₂O through the presence of OH, CO₂ is thus bound to a similar region from which emission can arise as the H₂O emitting region.

CO₂, however, due to the lower upper-level energies of the main transitions around 15 μm, emits more strongly from colder gas at large radii when compared to water transitions accessible to JWST. This is compounded by the higher CO₂ abundance in colder gas. Radially restricting the emission to warmer gas impacts the CO₂ emission more strongly than the H₂O emission. This can be seen in Figure 3. As the radially restricted emission reproduces the CO₂-to-H₂O flux ratios from the observations. This implies that the emitting areas are actually restricted more tightly than the chemistry implies and that a physical process like the "cold finger effect" is active (e.g., Meijerink et al. 2009; Bosman & Bergin 2021). This process impacts the H₂O directly by mixing it downward and locking up the water in the midplane ices (see, e.g., Krijt et al. 2016). This, in turn, impacts the chemical equilibrium of CO₂ due to the lower availability of oxygen, critical for the formation of CO₂. As CO₂ is constantly destroyed in the surface layers by UV, any available gaseous CO₂ between the H₂O and CO₂ midplane ice lines will constantly be reprocessed into H₂O, which can then be trapped in the midplane ice. We note that trapping CO₂ in the H₂O ice would still create a CO2-rich atmosphere outside of the H₂O ice line due to the back diffusion of the CO₂ gas (Bosman et al. 2018a).

This could be relatively easily tested by comparing velocity-resolved line profiles of CO₂ and H₂O; unfortunately, CO₂ is hard to do from the ground (e.g., Bosman et al. 2017) and currently there is no planned space mission that will cover this wavelength range with a medium or high spectral resolving power (λ/Δλ > 10000). As such, the emitting area from CO₂ will have to be extracted from the analysis of the velocity-unresolved spectra. Comparison with the 4.3 μm band, which can be observed with JWST-NIRSpec, could be helpful here as these lines originate from a radially more constrained region and are thus less affected by the abundance of CO₂ outside of the H₂O midplane ice line (see Appendix C). The feature strength ratio between the 4.3 μm band and the 15 μm band could thus be a measure of the radial extent of the total CO₂-emitting region.

5. Conclusions

We study the impact of water UV-shielding and chemical heating on the predicted CO₂ emission arising from within the terrestrial planet-forming zones of gas-rich disks around 15 μm using the thermochemical model DALI. Our base model finds a similar result as found in previously published models (Woitke et al. 2018; Anderson et al. 2021) in that the CO₂ is too bright relative to the H₂O emission.

We find that the water UV-shielding has a strong impact on the CO₂ abundance structure. With UV-shielding included, disk photospheric CO₂ is constrained to a thin layer close to the H/H₂ transition. This yields a CO₂ column of a few times 10¹⁶ cm⁻², two orders less than the CO₂ column prediction without water UV-shielding, ∼10¹⁸ cm⁻². The lower CO₂ column is in line with the observationally derived column. This suggests that water UV-shielding is present in disk systems, which is consistent with simple conclusions based on the inferred water vapor column (Bethell & Bergin 2009). This large change in column has a strong effect on the CO₂ emission, both in absolute terms, but particularly in the flux ratio between the main isotopologue 01¹0–00⁰0 Q branch on the one hand and the two 10⁰0 − 01¹0 Q-branch features at 13.90 and 16.20 μm or the main ¹³CO₂ Q branch on the other hand.

We find the best agreement between thermochemical model spectra prediction and observations if we invoke a radial restriction of the emitting area of both CO₂ and H₂O on top of the inclusion of water UV-shielding and extra chemical heating. The radial restriction increases the average temperature of the emitting gas, which appears to be required by observations. This has an impact on the chemistry, lowering the CO₂-to-H₂O abundance, as well as favoring the H₂O lines relative to the CO₂ lines as the H₂O lines have higher upper-level energies than the main CO₂ lines in the spectra.

We propose that this is evidence of the "cold finger effect", which is the sequestration of oxygen in the form of water in the midplane ice outside of the midplane water ice line. This process would lower the oxygen abundance until the C/O ratio reaches unity, locking all oxygen in CO and preventing the formation of both H₂O and CO₂, which rely on the presence of O or OH, outside of the water midplane ice line, even in the disk atmosphere.

The authors thank the referees for their constructive reports that improved the quality of the paper. A.D.B. and E.A.B. acknowledge support from NSF grant#1907653 and NASA grant XRP 80NSSC20K0259.

Software: Astropy (Astropy Collaboration et al. 2013, 2018), SciPy (Virtanen et al. 2020), NumPy (Van Der Walt et al. 2011), Matplotlib (Hunter 2007), DALI (Bruderer et al. 2012; Bruderer 2013).

Appendix A: OH Spectra

The hydroxide radical, OH, is a critical intermediate in CO, CO₂, and H₂O chemistry. As such, it is worth looking at the effects of H₂O UV-shielding and chemical heating on the OH emission. It should be noted that calculating OH emission is more complex than H₂O and CO₂ emission. H₂O and CO₂ emission are set by collision and radiation equilibrium. OH emission contains a contribution from highly excited OH that is produced in H₂O photodissociation (e.g., Carr & Najita 2014; Tabone et al. 2021). Furthermore OH collisional rate coefficients are not publicly available at present. Therefore, we calculate the OH excitation in LTE. This has an unfortunate side effect that OH emission arises predominantly from low-density gas at radii >10 au, yielding unrealistically high fluxes with line-to-continuum ratios >10 when convolved to an R of 3000. Fixing all of these issues would be possible with a non-LTE model, and possibly a density-dependent chemical heating rate in the gas, but that is beyond the scope of this paper. As such, we only consider a model with the OH abundance truncated to within the water midplane ice line and do an inter-model comparison only.

The OH LTE spectra are shown in Figure 5 in comparison to the H₂O and CO₂ spectra. Interestingly, the OH to H₂O line flux seems to be similar between the base and H₂O shielding and heating model. This is due to the OH column barely changing between the two models. The OH column is dominated by OH in the top layers of the atmosphere, when the density of H₂ gets high enough to efficiently form H₂O, the OH abundance drops significantly and the OH column barely increases with increasing depth from that point onward. As such, the only difference between the models is the temperature at which OH emits. The temperature change for the OH and H₂O emitting regions are similar, as such their line ratio does not change significantly. However, with the large number of non-LTE effects that can influence the OH emission, it definitely worth looking into OH emission in more detail in a further study.

Appendix B: Model Spectra for Different Physical Structures

Figures 6, 7, and 8 show the H₂O and CO₂ spectra for different variations of the physical structure. The same general trends hold as for the spectra for the reference structure in Figure 3. The variations show, however, that both more dust and a more puffed-up structure lead to a strong CO₂ Q branch relative to the surrounding water lines. More dust leads to lower gas temperatures in the surface layer, which promotes CO₂ production.

**Figure 6.** As Figure 3 but from the thin model with a surface layer gas-to-dust ratio of 10⁴.
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**Figure 7.** As Figure 3 but from the thick model with a surface layer gas-to-dust ratio of 10⁴.
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**Figure 8.** As Figure 3 but from the thick model with surface layer gas-to-dust ratio of 10⁵.
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Appendix C: Predictions for CO₂ at 4.3 μm

Aside from the strong feature at 15 μm, CO₂ has another strong vibrational band at 4.3 μm corresponding to the asymmetric stretch, the 00⁰1(1)–00⁰0(1) transition. This transition has an upper-level energy of 3350 K and a high Einstein A coefficient (>10 s⁻¹). JWSRT-NIRSpec is likely the first instrument that will be able to detect this band toward protoplanetary disks. At an R ≈ 3000, the lines in the bands will not be entirely separated, but the line peaks should be distinguishable (e.g., Bosman et al. 2017). Figure 9 shows the CO₂ model spectra at 4.3 μm.

**Figure 9.** CO₂ spectra around 4.3 μm convolved to R = 3000. Most flux is produced by the 00⁰1(1)–00⁰0(1) band, but there also is a contribution of the 01¹1(1)–01¹0(1) band. The top panel shows the spectra including the full extent of the CO₂ emission for base DALI (light blue) and our complete model with H₂O UV-shielding and extra chemical heating. The bottom panel shows the same models, but with the CO₂ emission constrained to within the H₂O midplane ice line. The light gray spectra show the slab model that fits to the observations, using an ${N}_{{\mathrm{CO}}_{2}}=3\times {10}^{15}$ cm⁻² and T = 700K. In contrast to the 15 μm feature, the thermochemical models, are all significantly weaker than the slab model.
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**Figure 9.** CO₂ spectra around 4.3 μm convolved to R = 3000. Most flux is produced by the 00⁰1(1)–00⁰0(1) band, but there also is a contribution of the 01¹1(1)–01¹0(1) band. The top panel shows the spectra including the full extent of the CO₂ emission for base DALI (light blue) and our complete model with H₂O UV-shielding and extra chemical heating. The bottom panel shows the same models, but with the CO₂ emission constrained to within the H₂O midplane ice line. The light gray spectra show the slab model that fits to the observations, using an ${N}_{{\mathrm{CO}}_{2}}=3\times {10}^{15}$ cm⁻² and T = 700K. In contrast to the 15 μm feature, the thermochemical models, are all significantly weaker than the slab model.
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As with the 15 μm feature, including water UV-shielding and chemical heating lowers the total flux in the CO₂ band, due to the lower CO₂ column in the disk model. Truncating the CO₂-emitting region has less of an effect on the 4.3 μm feature than it has on the 15 μm feature. This is due to the higher upper-level energy of the transition leading to a more centrally weighted emission profile. It is worth noting that in all cases, the predicted 4.3 μm flux from the thermochemical models is below that of the slab model that fits the 15 μm flux. As with the water 6.5 μm emission, this is due to a subthermal excitation of CO₂ in the surface layers of the disk (Bosman et al. 2022). This effect is especially notable as the critical density for the 4.3 μm feature is ∼10¹⁵ cm⁻³ (Bosman et al. 2017). As the predicted continuum around 4.3 μm for this model is 0.45 Jy, a high continuum signal-to-noise ratio, >150, is required to detect the full, truncated model.

Water UV-shielding in the Terrestrial Planet-forming Zone: Implications for Carbon Dioxide Emission

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Abstract

1. Introduction

2. Methods