Water UV-Shielding in the Terrestrial Planet-Forming Zone: Implications for Oxygen-18 Isotope Anomalies in H2-18O Infrared Emission and Meteorites

An understanding of the abundance and distribution of water vapor in the innermost region of protoplanetary disks is key to understanding the origin of habitable worlds and planetary systems. Past observations have shown H2O to be abundant and a major carrier of elemental oxygen in disk surface layers that lie within the inner few au of the disk. The combination of high abundance and strong radiative transitions leads to emission lines that are optically thick across the infrared spectral range. Its rarer isotopologue H2-18O traces deeper into this layer and will trace the full content of the planet forming zone. In this work, we explore the relative distribution of H2-16O and H2-18O within a model that includes water self-shielding from the destructive effects of ultraviolet radiation. In this Letter we show that there is an enhancement in the relative H2-18O abundance high up in the warm molecular layer within 0.1-10 au due to self-shielding of CO, C18O, and H2O. Most transitions of H2-18O that can be observed with JWST will partially emit from this layer, making it essential to take into account how H2O self-shielding may effect the H2O to H2-18O ratio. Additionally, this reservoir of H2-18O-enriched gas in combination with the vertical"cold finger"effect might provide a natural mechanism to account for oxygen isotopic anomalies found in meteoritic material in the solar system


INTRODUCTION
It is expected that the vast majority of solar-type stars host an exoplanet within 1 au (Johnson et al. 2010;Mulders et al. 2018). As a result, it can be assumed that the inner gaseous region of protoplanetary disks must be a hospitable environment for active planet formation. Typical temperatures place nearly all primary volatile carriers of carbon, nitrogen, and oxygen into the gas within surface layers providing a rich environment for astronomical observations and constraint (Pontoppidan et al. 2014). Volatiles (i.e. CO, H 2 O, CO 2 ) are potential starting points for the creation of complex molecules and the ice-coatings of pre-planetary pebbles (Wang et al. 2005;Gundlach & Blum 2015). These simple pre-cursors have been widely observed towards gas-rich disks within the 0.1-10 au region around young stars using the Spitzer space telescope (i.e. Carr & Najita 2008;Pontoppidan et al. 2010;Salyk et al. 2011a). Mapping the spatial extent and abundance of volatile molecules within the inner disk is essential knowledge used to piece together the connection between the chemical reservoir of a gasrich disk and the resulting planets.
The JWST mission will provide improved spectral resolution access to the inner disk region (JWST-MIRI: λ/∆λ = 2000 − 3000; Rieke et al. 2015), as compared to Spitzer 's InfraRed Spectrograph (λ/∆λ = 600; Houck et al. 2004). Nearly fifty disks will be targeted in the first set of JWST observations and will be used to enhance the study of emissions from volatiles in the terrestrial planet-forming zone. One molecule of high scientific impact is H 2 O. Based on previous observations and theoretical work, it is expected that H 2 O will be in high enough abundance such that its emission is optically thick (Carr & Najita 2008). The lesser abundant isotopologue H 18 2 O is also observable with JWST instruments, and, with reduced optical depth for its emission lines, will be used to infer the abundance and distribution of H 2 O using the ratio between 16 O and 18 O.
The most frequently used value for 16 O/ 18 O is 550. This value comes from Wilson (1999), and is the average observed ratio for five local ISM sources. This ratio has been seen to vary across the Galaxy following ( 16 O/ 18 O) = (58.8 ± 11.8)D GC + (37.1 ± 82.6) (1) where D GC is the distance of a source from the Galactic center (Wilson & Rood 1994). Within the environment of a protoplanetary disk, however, there are chemical processes that can alter this ratio. One such process is molecular self-shielding. Selfshielding is a process via which molecules, such as CO, N 2 , and H 2 , can protect themselves further from the source of radiation from the destructive effects of photodissociation from ultraviolet photons (van Dishoeck & Black 1988). These molecules are dissociated via a line process, as opposed to molecules with photodissociation cross-sections that are continuous at UV wavelengths (Heays et al. 2017). Thus, molecules closer to the radiation source can absorb UV photons allowing for the lines to become optically thick and, hence, self-shield molecules downstream from the source of UV photons. CO self-shielding can occur in gas-rich disks leading to a relative overabundance of 12 C 16 O compared to 12 C 18 O and 12 C 17 O in the warm disk region (Miotello et al. 2014) because the absorbing lines of the lesser abundant isotopologues have reduced opacity. This process can help explain relatively high C 16 O/C 18 O ratios that have been observed in a handful of protoplanetary disks (i.e. Brittain et al. 2005;Smith et al. 2009) and potentially might contribute to isotopic anomalies detected in asteroids and comets as compared to our Sun (Lyons & Young 2005;Nittler & Gaidos 2012;Altwegg et al. 2020). Bethell & Bergin (2009) demonstrated that, because of fast formation rates in hot (>400 K) gas, water can also self-shield. Further, this shielding is unique in that it not only shields itself, but shields over a wide range of wavelength space, similar to ozone in the Earth's atmosphere. Thus, water might also operate as a shield for other molecules, a process we call water UV-shielding.  (Ciesla & Cuzzi 2006;Banzatti et al. 2020).
One final consideration to the chemical make-up of the inner disk is Lyman-α (Ly-α) radiation. The Ly-α transition often contains the vast majority of the energy within the FUV range if present in a stellar spectrum of T Tauri stars (Herczeg et al. 2002;Schindhelm et al. 2012). It is readily observed towards young stars that are actively accreting and posses a gas-rich disk. The Ly-α transition occurs at 1216 Å and can photodissociate water (van Dishoeck et al. 2006). Ly-α is not often taken into account in radiation transfer codes, due to its added complexity of not only scattering off of dust but also atomic Hydrogen, causing the Ly-α photons to scatter isotropically below the hot atomic layer of the disk (Bethell & Bergin 2011). To explore the strength that both water and CO self-shielding will have on the oxygen isotopic ratio, Ly-α needs to be accounted for.
This paper is a companion to Bosman et al. (2022a), Bosman et al. (2022b), andDuval et al. (2022, in prep.) Bosman et al. (2022a) sets up protoplanetary disk models focused on the innermost region which take into account water UV-shielding and efficient chemical heating processes. These two processes are required in order for a thermo-chemical calculation to reproduce water line emission and observed excitation temperatures from Spitzer. Using the same modeling setup, Bosman et al. (2022b) shows that CO 2 -to-H 2 O ratios can also be achieved, strengthened by additional depletion of excess oxygen beyond the water snowline. Duval et al. (in prep) will focus on the impact of water UV-shielding on the chemical composition of the terrestrial planet forming region.
In this paper we will explore the abundances of both H 2 O and H 18 2 O in the inner most few au of protoplanetary disks where the excitation conditions are favorable for detection of rotational and vibrational emissions at mid-infrared wavelengths. This exploration will use the Spitzer observational legacy as a constraint (Pontoppidan et al. 2010;Salyk et al. 2011a), but look forward to JWST observations which will be observing systems where both Ly-α radiation and water UV-shielding will be present.
2. METHODS 2.1. Thermo-chemcial modeling: DALI DALI (Dust And LInes) is a physical-chemical code that accounts for radiation transfer, thermal and chemical calculations throughout a disk (Bruderer et al. 2012;Bruderer 2013). It contains an isotope chemical network (Miotello et al. 2014) and accounts for molecular selfshielding. For this project, H 2 O UV-shielding has been additionally accounted for, see Bosman et al. (2022a) for detail. We utilize a model derived from the AS 209 and corresponding stellar spectrum from Zhang et al. (2021), and explore the effect of H 2 O UV-shielding and Ly-α radiation in flat vs. thick model and two levels of dust settling. We include the 18 O isotopologue of every oxygen carrying species in our chemical network.
After an initial radiative transfer calculation, thermal balance, and chemical abundance distribution determination, we account for Ly-α radiation using another code, detailed in the following section. The results from the separate Ly-α radiative transfer calculation are combined with the initial disk radiation field as calculated by DALI. We then calculate a new thermal balance and chemical environment, containing the final distribution of H 2 O and H 18 2 O. Excitation data for both ortho-and para-H 18 2 O was compiled into a file identical to the format from the Leiden LAMDA database (Schöier et al. 2005). 1 Line excitation data was obtained via the HITRAN database (Gordon et al. 2022) 2 and collisional data from the H 16 2 O LAMDA file (Faure & Josselin 2008). This was used for ray-tracing calculations with DALI to determine which lines may be observable and from where in the disk they emit.

Inclusion of Lyman Alpha
The inclusion of the Ly-α is derived from a radiation transfer code described by Bethell & Bergin (2011). Briefly, this code calculates the transport of both FUVcontinuum and Ly-α photons. FUV photons are solely affected by the dust distribution, while Ly-α is additionally affected by resonance line scattering. An initial distribution of H and H 2 is derived using the thermochemical calculation from DALI, and Ly-α propagates throughout the distribution of gas and dust, scattered by atomic H in the H-rich layer, and eventually scattered and absorbed by dust.
After this calculation, the Ly-α-affected radiation field is combined with the DALI radiation field. The effects of a separate stellar input spectrum are normalized out of the Ly-α radiative transfer results, and a depletion or enhancement factor across wavelengths covered by the Ly-α line and its line wings is calculated. The original DALI radiation field contains Ly-α emission as it would exist if Ly-α-photons scattered normally off of small dust grains only, identically to continuum-UV photons.  Figure 2. The ratio returns to an ISM level at z/r≈0.16 when C 18 O starts to be shielded, cutting of the supply of free 18 O. Near the same z/r, within 1 au, H 2 O UV-shielding aids in shielding C 18 O to a point where its photodissociation rate is extremely low, many orders of magnitude lower than an environment where H 2 O UV-shielding would be ignored.
Beyond ∼1 AU, the water abundance drops, yet a non-ISM ratio still exists. CO self-shielding continues to dominate, continuing to produce a 18 O enhanced environment, thus a continued low ratio of H 2 O to H 18 2 O, however there exists very little water vapor in the gas phase beyond r=1 au. The H 18 2 O-enhanced region exists between a top-down vertical CO column of 10 17 and 10 19 cm −2 , an H 2 column of 10 19 and 10 22 cm −2 , and below an H column of 10 21 cm −2 . This H 18 2 O-enhanced region co-exists with large temperature gradients. Within 1 au, the thermal range from the bottom of this layer to the top is 500-2,000 K. Beyond 1 au the gradient is larger, ranging from 100-4,000 K.  We find that most Ly-α photons do not reach the H 2dominated zone of the disk, including where the H 18 2 Orich region exits. The Ly-α emission feature is 25 times less bright in the radiation field of the disk at the location of the H 18 2 O-rich region than it would be if the transfer of Ly-α photons was disregarded. Despite the decrease in overall UV flux, the H 18 2 O-rich region exits over the same spatial extent of the disk compared to a model that does not account for Ly-α scattering off of hydrogen atoms. The limit at which scattered Ly-α photons have a decreasing contribution to the radiation field corresponds to a z/r≈0.25, or where the H-to-H 2 ratio is ≈ 10 −5 . While in this disk model Ly-α did not reach into the molecular disk, Bethell & Bergin (2011) found that the molecular disk can be enhanced with Ly-α relative to FUV photons using the detailed disk physical models by D' Alessio et al. (2006). In this study, we use the thermo-chemical calculation within DALI and a chemical network to determine the H-fraction throughout the disk, while Bethell & Bergin (2011) used an analytical expression taking into account photodissociation and self-shielding processes while leaving out chemical destruction or creation pathways for H 2 and H. This results in a H-to-H 2 transition within the work that exists higher in the disk as compared to Bethell & Bergin (2011). Additionally, in Bethell & Bergin (2011) the Hfraction drops to near zero while H 2 is dominate while in DALI there exists a population of free H atoms in the H 2 -dominated region of the disk due to destructive chemical reactions. Thus, in the DALI disk, there are scattering events deep in the disk where in Bethell & Bergin (2011) there were none. The additional scattering events greatly increases the chance for Ly-α photons to be absorbed by dust.  (4,9) 19.78 3772.5 8.9 500 10 (4,7) -9 (1,8) 20.01 2265.3 1.9 510 11 (4,7) -10 (3,8) 22.03 2725.3 4.4 490 9 (7,2) -9 (4,5) 22.77 2581.7 0.031 540 9 (9,0) -8 (8,1) 23.17 3165.9 41. 420 9 (6,3) -8 (5,4) 26.83 2329.5 15. 410 8 (7,2) -7 (6,1) 26.99 2265.6 21. 400 Note-We quote each weighted average of the 16 O-to-18 O ratio with two significant figures following the level of certainty around the ISM value (assumed to be 550).

H 18 2 O Emission Spectrum
The bulk of the water content exists within a radius of 1 au. We use DALI to calculate the flux contribution per cell for each emitted line. In order to determine which water lines will be of high interest, we run a quick non-LTE ray tracing program , Append. B) that estimates the flux of water lines over the full extent of the MIRI wavelength range. We find that IR bright H 2 O lines emit high up in the disk, proving to be optically thick across all IR wavelengths (see Bosman et al. 2022 in prep for detail). Isolated and bright H 18 2 O emission lines are rare, but a handful of lines will be accessible and distinguishable from H 2 O with the MIRI instrument. We find eight distinct lines listed in Table  1 and highlighted in Figure 3. These lines exist between 19-27 µm; notably a region in MIRI with a lower sensitivity compared to shorter wavelength ranges. Our first example comes from the H 18 2 O 8 (7,2) − 7 (6,1) transition at 27 µm. As seen in Figure 4, much of the emission from this line originates from the H 18 2 O enhanced region. We use the following equation to calculated a weighted H 2 O/H 18 2 O value: where n is the number of cells in our model, w i is the relative emission contribution in a cell, and χ i is the  Table  1. There is a general trend that transitions from smaller wavelengths trend towards a weighted average of 550. This trend arises from the Einstein A-coefficient associated with each transition. Transitions with lower A values are more likely to emit from deeper within the disk at higher gas densities, thus farther away from the H 18 2 O-enhanced region. To reduce the uncertainty in the H 2 O/H 18 2 O ratio, transitions associated with low Einstein A-coefficients could be preferentially used. These differences are small and up to a factor of two. However, chemical studies will be looking for enhanced abundances of water vapor in this region, perhaps supplied by pebble drift (Banzatti et al. 2020). To isolate these chemical changes we need to correct for effects that can be understood; water UV-shielding is one of these effects.

Corresponding CO Infrared Observations
In    orders of magnitude. Measuring the 12 CO-to-C 18 O ratio using lines of CO that emit from this region could help confirm the presence of this 18 O-rich region and even calibrate uncertainties in the true ratio between H 2 O-to-H 18 2 O. The R and P branches for multiple vibrational transitions of CO and its isotopologues peak at ∼5 µm and are observable from the ground using high spectral resolution instruments such as Keck NIR-SPEC and VLT 's CRIRES. The C 18 O column densities in the H 18 2 O-rich region range from 10 12 -10 15 cm −12 and are predicted to produce optically thin C 18 O emission in the infrared. As summarized and expanded upon in Banzatti et al. (2022), over 100 T Tauri and Herbig disks have been observed with high-spectral resolution in the wavelength range of CO's vibrational lines which emit from ∼1000 K, corresponding to the temperature of the H 18 2 O-enhanced region. In these studies only CO and 13 CO observations were reported, making it currently impossible to use these observations to corroborate our predicted 18 O-rich region within 1 au. The only work that set out to measure 12 CO/C 18 O and 12 CO/C 17 O is found in Smith et al. (2015). This study observed nine YSO systems, three of which were optically thick disks. These three disks show tentative increase in the 12 CO/C 18 O well above the ISM-measured value, however it was noted at significant systematic uncertainties are associated with these measurements. A future study dedicated to deep observations of multiple disk systems could aid in upcoming MIRI observations of these regions, and put constraints on the 18 O-enhancement within the radial extent of planet-formation.

Impact of a different 16 O/ 18 O Ratio
Mass-independent fractionation of oxygen isotopes, with enrichment of the heavy isotopes, has been isolated within meteoritic material (Clayton et al. 1973;Thiemens & Heidenreich 1983). The origin of these isotopic anomalies requires a specific mechanism that creates an 18 O (and 17 O)-rich environment as compared to the natal stellar nebula and envelope (Clayton 1993). This fractionation must originate in the solar nebular disk or within the natal molecular cloud (Yurimoto & Kuramoto 2004;Lyons & Young 2005;Lee et al. 2008). CO self-shielding presents a mechanism to enrich gas in heavy isotopes, particularly on surfaces exposed to ultraviolet, as it selectively photodissociates C 18 O and C 17 O relative to CO producing gas enriched in 18 O and 17 O (Lyons & Young 2005;Miotello et al. 2014). In this work, we find that the addition of H 2 O UV-shielding not only continues the 18 O enrichment within the inner disk, but enhances it compared to results solely based on CO self-shielding. We find a depletion of C 18 O approaching a factor of 10 3 high up in the disk between 0.1-30 au at a ∼z/r=0.2-0.3. This is a reservoir rich with 18 O, enhancing the 18 O isotopologues for many different volatile species, including water vapor and ice.
Vertical mixing may act as a mechanism to deliver the 18 O-enhanced molecules to the planet-forming midplane. The "cold finger" effect (Stevenson & Lunine 1988;Meijerink et al. 2009) has been proposed a mechanism that will transport water and other organics efficiently from the atmosphere of the disk to the midplane. Due to vertical mixing, water from the gaseous atmosphere can transport down to the midplane where it locked onto grains as ice. The cold finger effect has been used to reconcile models in which high water abundances are predicted, yet corresponding sub-mm observations exhibit non-detections (Du et al. 2015;Salyk et al. 2011b;Carr et al. 2018;Bosman & Bergin 2021;Bosman et al. 2022b). Thus, while the H 18 2 O-rich regions resides high up in the disk atmosphere, vertical mixing can bring a portion of this reservoir down to the midplane and enrich meteoritic precursors. Lyons & Young (2005) explored a solution in the outer tens of au that suggested that meteoritic 18 O enrichment could be the result of CO self-shielding. In this model, oxygen atoms (enriched with heavy isotopes) produced via isotopic-selective CO self-shielding, are mixed downwards forming water ice via grain surface chemistry. These ices will need to be transported to the inner few au, perhaps by drift (Ciesla & Cuzzi 2006). However, current meteoritic evidence suggests the inner solar system is chemically separated from the outer ( 5 au) parts of the disk between 1 Myr and 3-4 Myr, potentially due to early formation of Jupiter's core (Kruijer et al. 2017). Our model shows that this vertical layer of enhanced 18 O is placed directly into water in surface layers above the inner disk spatially closer to the region where meteoritic progenitors originate.

CONCLUSION
In this Letter, we implement H 2 O UV-shielding and chemical heating in addition to CO self-shielding within a gas-rich disk environment. Focusing on the innermost region of the disk, a water vapor-rich reservoir exits within 1 au, and a H 18 2 O enhanced region exists where many water IR lines approach a τ = 1. In this region, the H 2 O-to-H 18 2 O ratio approaches 300, a significantly lower value than the assume ISM ratio of 550. We then seek use this context to provide insight into future JWST observations of H 18 2 O as it will act as a tracer for the abundance and distribution of gaseous H 2 O in the main planet formation zone.
1. In our disk model, the H 2 O-to-H 18 2 O ratio approaches 300 between a z/r≈0.16-0.2 and inside 1 au due to CO self-shielding. 3. In this model Ly-α radiation does not penetrate down to the molecular-rich region of the disk in the case of our relatively thin and 0.0045 M disk.
4. Vertical diffusive mixing, or the "cold finger" effect, could transport a significant amount of 18 Orich molecules to the planet-forming midplane to be incorporated into pre-planetary materials that reside in the terrestrial planet-forming zone.