# Water UV-shielding in the terrestrial planet-forming zone: Implications for
carbon dioxide emission

Arthur D. Bosman University of Michigan, LSA astronomy
1085 S University
Ann Arbor, MI 48109, USA  Edwin A. Bergin University of Michigan, LSA
astronomy
1085 S University
Ann Arbor, MI 48109, USA  Jenny K. Calahan University of Michigan, LSA
astronomy
1085 S University
Ann Arbor, MI 48109, USA  Sara E. Duval  University of Michigan, LSA astronomy
1085 S University
Ann Arbor, MI 48109, USA

###### Abstract

Carbon Dioxide is an important tracer of the chemistry and physics in the
terrestrial planet forming zone. Using a thermo-chemical model that has been
tested against the mid-infrared water emission we re-interpret the CO2
emission as observed with Spitzer. We find that both water UV-shielding and
extra chemical heating significantly reduce the total CO2 column in the
emitting layer. Water UV-shielding is the more efficient effect, reducing the
CO2 column by $\sim$ 2 orders of magnitude. These lower CO2 abundances lead to
CO2-to-H2O flux ratios that are closer to the observed values, but CO2
emission is still too bright, especially in relative terms. Invoking the
depletion of elemental oxygen outside of the water mid-plane iceline more
strongly impacts the CO2 emission than it does the H2O emission, bringing the
CO2-to-H2O emission in line with the observed values. We conclude that the CO2
emission observed with Spitzer-IRS is coming from a thin layer in the photo-
sphere of the disk, similar to the strong water lines. Below this layer, we
expect CO2 not to be present except when replenished by a physical process.
This would be visible in the ^13CO2 spectrum as well as certain ^12CO2
features that can be observed by JWST-MIRI.

proto-planetary disks – astrochemistry – line formation

††journal: ApJ††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)

##  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 the 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.

Towards proto-planetary 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 au (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), as well as the elemental
abundance of C (See Fig. 1 in Bosman et al., 2018a).

The interplay between dust growth, dynamics, and chemistry in the outer (tens
of au) disk might also significantly impact the abundance of CO2 in the inner
few au 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 au 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 iceline. Furthermore between the H2O and CO2
icelines, 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 mid-plane.

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 it requires the emission 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 thermo-
chemical 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

Table 1: Elemental abundances w.r.t H Element | Abundance w.r.t. H
---|---
H | 1.0
He | $7.59\times 10^{-2}$
C | $1.35\times 10^{-4}$
N | $2.14\times 10^{-5}$
O | $2.88\times 10^{-4}$
Mg | $4.17\times 10^{-9}$
Si | $7.94\times 10^{-8}$
S | $1.91\times 10^{-8}$
Fe | $4.27\times 10^{-9}$

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 photo-
dissocation (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 Lyman-$\alpha$
(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 time-scale in the region of interest are short, we solve for
statistical equilibrium (Anderson et al., 2021).

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$\mu$m we denote this as the $01^{1}0-00^{0}0$
$Q$-branch, but it is implied that this includes a smaller contribution of the
more highly excited $02^{2}0$–$01^{1}0$, $03^{3}0$–$02^{2}0$ , 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 $3\times 10^{18}$ cm-2 and a excitation
temperature of 500 K, as done in (Bosman et al., 2022), while for CO2 we use a
column of $3\times 10^{15}$ 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

Figure 1: CO2 abundance for the thin model with a large grain fraction of
99.9% for variation in the thermo-chemical model. Red contour shows the region
from which 90% of the CO2 $01^{1}0$–$00^{0}0$ $R(20)$ emission line
originates, the yellow contour shows the region from which 90% of the H2O
$11_{3,9}$–$10_{0,10}$ line flux at $17.2\mu$m originates, the orange line
shows the continuum $\tau_{\mathrm{15}\mu\mathrm{m}}=1$ surface and vertical
yellow and red bands show the locations of the H2O (0.4 au ) and CO2 (1.2 au)
mid-plane icelines, respectively.  Figure 2: Gas temperature as function of
the cumulative vertical CO2 column at the location of the mid-plane H2O
iceline (0.4 au). The CO2 column is a proxy for the location in the disk,
higher column being deeper into the disk. In the base DALI model, CO2 is
present at a significant abundance over most of the vertical extent of the
molecular layer and so the CO2 temperature changes continuously with
increasing CO2 column or increasing depth. In the heating and shielding model,
after reaching a column of about $10^{16}$ cm-2 at a temperature of 600 K, the
CO2 abundance drops significantly. Only very deep into the disk when the
temperature has dropped down to 200 K, does the CO2 abundance reach
appreciable levels and does the vertical CO2 column increase again with depth.
This causes the strong jump in the temperature profile.  Figure 3: H2O and CO2
spectra convolved to a R of 3000 around the CO2 $01^{1}0$–$00^{0}0$
transition. Top panels shows slab model spectra using parameters that
reproduce the observational data (Salyk et al., 2011). The four panels below
show the DALI output spectra for the thin disk structure with 99.9% large,
settled grains. The second panel shows the base DALI model, the third base
DALI with water UV-shielding, the fourth base DALI with water UV-shielding and
extra chemical heating and the fifth panel shows the same model as the fourth
panel, with now assuming emission can only originate from the region within
the water mid-plane iceline. The slab models clearly predict a CO2 feature at
15 micron that is weaker than the surrounding waterlines, while most DALI
models show a brighter CO2 feature compared to the water lines. Only when
combining water UV-shielding, extra chemical heating and a restricted radial
emitting region does the thermo-chemical flux ratio come close to the observed
flux ratio as exemplified by the slab models.

###  3.1 CO2 abundance

Figure 1 shows the CO2 abundance structure for the flat model with a large
grain fraction 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 mid-plane, and out to the CO2 iceline. There is some additional
structure as CO2 vapor is absent in the inner $\sim$ 0.2 au and in a region
around 0.7 au near the disk mid-plane, 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 photo-sphere (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 second panel of Fig. 1). The warm surface layer becomes thinner and the
region of high CO2 abundance ($\sim$10-6) is restricted to below z/r $\leq$
0.1. In this model, CO2 vapor returns to the high abundance value around the
$\tau_{\mathrm{15}\mu\mathrm{m}}=1$ layer. The decrease of the CO2 abundance
is driven by the slower photo-dissociation 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 that H2O can start to block the UV radiation, as such
OH cannot be used as tracer of H2O UV-shielding (see Appendix A).

Increasing the chemical heating after photo-dissociation 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., Fig. 1 of
Bosman et al., 2018a).

Figure 1 also shows the emitting area of the $01^{1}0$–$00^{0}0$ $R(20)$ line
as an irregular red box. This line has an upper level energy of $\sim$1250 K
of which $\sim$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 few $\times 10^{-7}$. Lines with lower
rotational excitation will emit from a slightly larger radial region. As can
be seen in Fig 1 the CO2 emitting area extends to layers exterior to the water
mid-plane iceline 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 function of the vertical, top-down CO2
column at the radius of the water iceline. 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 structure. In the non-
shielding 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 $10^{16}$ 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, that have very high density the
statistical-equilibrium that is calculated tends towards 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
$\sim 10^{16}$ 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
$\tau_{\mathrm{15}\mu\mathrm{m}}=1$ surface ($\sim$200 K). Contribution for
columns $>10^{16}$ cm-2 should thus be negligible. Contrast this with the
models without shielding, where the temperature is $\sim$ 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 $\mu$m CO2 vibrational
band. The baseline DALI models predicts relatively stronger CO2 emission when
compared to the surrounding H2O line forest. The CO2 $01^{1}0$–$00^{0}0$
Q-branch is a factor few brighter than the surrounding water lines and the
individual CO2 $01^{1}0$–$00^{0}0$ $P$ 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 with the slab
models in Fig. 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. CO2 in this model remains too bright when compared to the surrounding
water emission. However, as noted earlier, the CO2 emitting region extends
further than the H2O emitting region. Additional spectra from different
physical structures find similar results (See App. B).

Figure 3 also shows the H2O and CO2 spectra in the case where we assume that
the emission of both is contained radially to within the water mid-plane
iceline (see fig. 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 for the Spitzer-IRS observations.

##  4 Discussion

###  4.1 CO2 column

The thermo-chemical model with water UV-shielding and chemical heating
consistently predict a CO2 column in the surface layers that is around
$10^{16}$ cm-2. This is orders of magnitude lower than the $10^{18}$ 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
$3\times 10^{14}$–$3\times 10^{16}$ cm-2, with additional non-detection
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 is
colder ($<$500 K) than the inferred temperatures from the CO2 Spitzer-IRS
observations ($\sim$700 K; Salyk et al., 2011). This could imply that the
radial temperature profile in the disk is impacting the shape of the
$01^{1}0$–$00^{0}0$ $Q$-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
Ly-$\alpha$. The photodissociation cross-section of CO2 is modest near
Ly-$\alpha$ 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 Ly-$\alpha$ 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, and derive the elemental
composition of the gas and explore disk physical processes, it is important to
understand 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 as water vapor. However, our models predict that
water UV-shielding has a strong influence on the CO2 vertical abundance
distribution (Fig. 1) which has significant impact on the column distribution
within different thermal layers (Fig. 2).

With higher spectral resolution when compared to Spitzer/IRS, JWST (NIRSPEC
and MIRI) offer an opportunity to observe CO2 vapor with MIRI being able to
isolate individual P and R branch lines around 15 $\mu$m and potentially
detect ^13CO2 (Bosman et al., 2017). In Fig. 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,
Fig. 1). In this case, the relative strength of the two $10^{0}0-01^{1}0$
Q-branch features at 13.90 and 16.20 $\mu$m is high, 20% of the main
$Q$-branch, while in the model without water UV-shielding, these features are
about a factor 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
$01^{1}0$–$00^{0}0$ $P(19)$–$P(27)$ and $R(19$)–$R(27)$ lines, around 10%
w.r.t. the main CO2 $Q-$branch. These lines can thus be used as a yard stick.
If the peak of $Q-$branch features at 13.90 and 16.20 $\mu$m is higher than
the than the $01^{1}0$–$00^{0}0$ rotational lines, this indicates deep, warm
CO2. It should be noted that many of the CO2 emission features have nearby H2O
lines, that will be blended in observations. Simultaneous fitting of the water
spectrum is thus required.

Figure 4: Normalized spectra convolved to a 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 $10^{5}$. CO2 is assumed
to only be present within the water mid-plane 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 normalize to the ^12CO2
$01^{1}0$–$00^{0}0$ $Q$-branch peak and are zoomed in on three regions with
$Q$-branches of interest. While the individual $01^{1}0$–$00^{0}0$ $P$ 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 derived the deeper abundance structure.

###  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. Formation of OH is only efficient at high
enough temperatures that the reaction barrier of the O + H2 reaction can be
over come. 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 $\mu$m, emits more strongly from colder gas a 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 Fig. 3. As the radially restricted emission reproduces the
CO2-to-H2O flux ratios from the observations. This implies that a 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 mid-plane icelines will constantly be reprocessed
into H2O which can then be trapped in the mid-plane ice. We note that trapping
CO2 in the H2O ice would still create a CO2 rich atmosphere outside of the H2O
iceline due to 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 no planned space mission that will cover
this wavelength range with a medium or high spectral resolving power
($\lambda/\Delta\lambda>10000$). As such, the emitting area from CO2 will have
to be extracted from analysis of the velocity unresolved spectra. Comparison
with the 4.3 $\mu$m 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
iceline (see Appendix C). The feature strength ratio between the 4.3 $\mu$m
band and the 15$\mu$m band could thus be a measure for 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 $\mu$m using the thermo-chemical 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 $10^{16}$ cm-2, two orders less than the CO2 column prediction without
water UV-shielding, $\sim$$10^{18}$ 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
$01^{1}0$–$00^{0}0$ $Q$-branch on the one hand and the two $10^{0}0-01^{1}0$
Q-branch features at 13.90 and 16.20 $\mu$m or the main ^13CO2 $Q$-branch on
the other hand.

We find the best agreement between thermo-chemical 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”, that is the
sequestration of oxygen in the form of water on the mid-plane ice outside of
the mid-plane water iceline. 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 mid-plane iceline, even in the disk atmosphere.

The authors thank the referees for their constructive reports that improved
the quality of the paper. ADB and EAB acknowledge support from NSF
Grant#1907653 and NASA grant XRP 80NSSC20K0259.

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##  Appendix A OH spectra

The Hydroxide radical, OH, is a critical intermediate in the 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 photo-dissociation
(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 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 mid-plane iceline and do an
inter-model comparison only.

The OH LTE spectra are show in Fig. 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 the 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.

Figure 5: Spectra of OH, CO2 and H2O for the base and H2O UV-shielding and
chemical heating models. The emitting region has been constrained to the
radial region within the water mid-plane iceline and the spectra have been
convolved to R=3000. LTE excitation is assumed for OH.

##  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 Fig. 3. The variations show, however that both more
dust, as well as 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 the CO2 production.

Figure 6: As Fig. 3 but from the thin model with a surface layer gas-to-dust
ratio of $10^{4}$.  Figure 7: As Fig. 3 but from the thick model with a
surface layer gas-to-dust ratio of $10^{4}$.  Figure 8: As Fig. 3 but from the
thick model with surface layer gas-to-dust ratio of $10^{5}$.

##  Appendix C Predictions for CO2 at 4.3 $\mu\mathrm{m}$

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

As with the 15$\mu$m 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$\mu$m feature than it has on the 15$\mu$m 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 $\mu$m flux from the thermo-chemical models is below that of the slab
model that fits the 15 $\mu$m flux. As with the water 6.5 $\mu$m emission,
this is due a sub-thermal 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$\mu$m feature is $\sim 10^{15}$ cm-3 (Bosman et al.,
2017). As the predicted continuum around 4.3 $\mu$m for this model is 0.45 Jy,
a high continuum S/N, $>$150, is required to detect the full, truncated model.

Figure 9: CO2 spectra around 4.3$\mu$m 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 mid-plane
iceline. The light grey spectra show the slab model that fits to the
observations, using a $N_{\mathrm{CO}_{2}}=3\times 10^{15}$ cm-2 and T = 700K.
In contrary to the 15 $\mu$m feature, the thermo-chemical models, are all
significantly weaker than the slab model.