Water UV-shielding in the Terrestrial Planet-forming Zone: Implications for Oxygen-18 Isotope Anomalies in ${{\rm{H}}}_{2}^{18}{\rm{O}}$ Infrared Emission and Meteorites

Dust And LInes (DALI) is a physical–chemical code that accounts for radiation transfer and 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 self-shielding. For this project, H₂O UV-shielding has been additionally accounted for; see Bosman et al. (2022) for details. We utilize a model derived from the AS 209 and corresponding stellar spectrum from Zhang et al. (2021), and explore the effect of H₂O UV-shielding and Lyα radiation in a flat versus thick model and two levels of dust settling. We include the ¹⁸O 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 Lyα radiation using another code, detailed in the following section. The results from the separate Lyα 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 H₂O and ${{\rm{H}}}_{2}^{18}{\rm{O}}$.

Excitation data for both ortho- and para-${{\rm{H}}}_{2}^{18}{\rm{O}}$ were compiled into a file identical to the format from the Leiden LAMDA database (Schöier et al. 2005). ¹ Line excitation data were obtained via the HITRAN database (Gordon et al. 2022) ² and collisional data from the ${{\rm{H}}}_{2}^{16}{\rm{O}}$ 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.

The inclusion of the Lyα is derived from a radiation transfer code described by Bethell & Bergin (2011). Briefly, this code calculates the transport of both FUV-continuum and Lyα photons. FUV photons are solely affected by the dust distribution, while Lyα is additionally affected by resonance line scattering. An initial distribution of H and H₂ is derived using the thermochemical calculation from DALI, and Lyα 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 Lyα-affected radiation field is combined with the DALI radiation field. The effects of a separate stellar input spectrum are normalized out of the Lyα radiative transfer results, and a depletion or enhancement factor across wavelengths covered by the Lyα line and its line wings is calculated. The original DALI radiation field contains Lyα emission as it would exist if Lyα photons scattered normally off of small dust grains only, identically to continuum-UV photons.

We find an ${{\rm{H}}}_{2}^{18}{\rm{O}}$-rich environment high up in the molecular region of the disk. Enhanced ${{\rm{H}}}_{2}^{18}{\rm{O}}$ exists in models that range in flaring angle and dust settling parameters. Four models were explored with two different values for scale height and dust settling, and these individual models are detailed in the Appendix of Bosman et al. (2022). The following figures and discussion are based on the flattest and most highly settled model, which reproduce H₂O and CO₂ spectra simultaneously (see Bosman et al. 2022). In this model, a region where H₂O/${{\rm{H}}}_{2}^{18}{\rm{O}}$ dips to approximately 45% of the initial ISM ratio exists at a z/r of 0.16–0.2 at r = 0.1–1 au, as seen in Figure 1. The upper boundary of this layer corresponds to where CO becomes optically thick enough to self-shield, producing an environment were C¹⁸O continues to photodissociate while C¹⁶O does not, releasing free ¹⁸O. Much of the free ¹⁸O finds its way into water molecules, enhancing the ${{\rm{H}}}_{2}^{18}{\rm{O}}$ abundance, thus providing a lower ratio between H₂O and ${{\rm{H}}}_{2}^{18}{\rm{O}}$ (≈ 300). The most common ¹⁸O destruction mechanisms come in the form of interactions with H₂ to form ¹⁸OH and an extra H atom. ¹⁸OH can then interact with an H₂ atom to form ${{\rm{H}}}_{2}^{18}{\rm{O}}$. The main cycle of ¹⁸O once the chemistry has reached equilibrium is shown in Figure 2. The ratio returns to an ISM level at z/r ≈ 0.16 when C¹⁸O starts to be shielded, cutting of the supply of free ¹⁸O. Near the same z/r, within 1 au, H₂O UV-shielding aids in shielding C¹⁸O to a point where its photodissociation rate is extremely low, many orders of magnitude lower than an environment where H₂O UV-shielding would be ignored.

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Beyond ∼1 au, the water abundance drops, yet a non-ISM ratio still exists. CO self-shielding continues to dominate, continuing to produce a ¹⁸O-enhanced environment, thus a continued low ratio of H₂O to ${{\rm{H}}}_{2}^{18}{\rm{O}}$; however, there exists very little water vapor in the gas phase beyond r = 1 au. The ${{\rm{H}}}_{2}^{18}{\rm{O}}$-enhanced region exists between a top-down vertical CO column of 10¹⁷ and 10¹⁹ cm⁻², an H₂ column of 10¹⁹ and 10²² cm⁻², and below an H column of 10²¹ cm⁻². This ${{\rm{H}}}_{2}^{18}{\rm{O}}$-enhanced region coexists with large temperature gradients. Within 1 au, the thermal range from the bottom of this layer to the top is 500–2000 K. Beyond 1 au the gradient is larger, ranging from 100 to 4000 K.

We find that most Lyα photons do not reach the H₂-dominated zone of the disk, including where the ${{\rm{H}}}_{2}^{18}{\rm{O}}$-rich region exits. The Lyα emission feature is 25 times less bright in the radiation field of the disk at the location of the ${{\rm{H}}}_{2}^{18}{\rm{O}}$-rich region than it would be if the transfer of Lyα photons was disregarded. Despite the decrease in overall UV flux, the ${{\rm{H}}}_{2}^{18}{\rm{O}}$-rich region exits over the same spatial extent of the disk compared to a model that does not account for Lyα scattering off of hydrogen atoms. The limit at which scattered Lyα photons have a decreasing contribution to the radiation field corresponds to a z/r ≈ 0.25, or where the H-to-H₂ 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 thermochemical 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 H₂ and H. This results in a H-to-H₂ transition within the work that exists higher in the disk as compared to Bethell & Bergin (2011). Additionally, in Bethell & Bergin (2011) the H-fraction drops to near zero while H₂ is dominate, while in DALI there exists a population of free H atoms in the H₂-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 increase the chance for Lyα photons to be absorbed by dust.

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 (Bosman et al. 2017, Appendix B) that estimates the flux of water lines over the full extent of the MIRI wavelength range. We find that IR bright H₂O lines emit high up in the disk, proving to be optically thick across all IR wavelengths (see A. D. Bosman et al. 2022, in preparation for detail). Isolated and bright ${{\rm{H}}}_{2}^{18}{\rm{O}}$ emission lines are rare, but a handful of lines will be accessible and distinguishable from H₂O with the MIRI instrument. We find eight distinct lines listed in Table 1 and highlighted in Figure 3. These lines exist between 19 and 27 μm; notably a region in MIRI with a lower sensitivity compared to shorter wavelength ranges.

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Each ${{\rm{H}}}_{2}^{18}{\rm{O}}$ line emits from distinct heights within the disk, and may partially emit from the ${{\rm{H}}}_{2}^{18}{\rm{O}}$-enhanced region; thus, when converting from ${{\rm{H}}}_{2}^{18}{\rm{O}}$ emission to an H₂O abundance, a ratio below that of the ISM should be used. One of the brightest and most isolated lines is the ${{\rm{H}}}_{2}^{18}{\rm{O}}$ 8_(7,2) − 7_(6,1) (27 μm) transition. We find that this transition starts to become optically thick and emits primarily in the enriched ¹⁸O region. We find this to be true for seven out of the eight identified lines. The ${{\rm{H}}}_{2}^{18}{\rm{O}}$ 9_(7,2) − 9_(4,5) transition (22.77 μm) appears to primarily emit below the ${{\rm{H}}}_{2}^{18}{\rm{O}}$-enriched region; thus, if using this line to determine an H₂O abundance, the conversion factor will be closer to an ISM value of 550.

A weighted ratio between H₂O and ${{\rm{H}}}_{2}^{18}{\rm{O}}$ must be used in order to extrapolate to an H₂O abundance and distribution using ${{\rm{H}}}_{2}^{18}{\rm{O}}$ observations. We have identified eight transitions of ${{\rm{H}}}_{2}^{18}{\rm{O}}$ that are observable with JWST, and calculate the weighted ratio of H₂O to ${{\rm{H}}}_{2}^{18}{\rm{O}}$ that should be assumed based on our AS 209 model, and the vertical layers where we predict the emission arises. We compute weighted averages of H₂O/ ${{\rm{H}}}_{2}^{18}{\rm{O}}$ using the relative spatial contribution from where each line is emitting from, as calculated by DALI.

Our first example comes from the ${{\rm{H}}}_{2}^{18}{\rm{O}}$ 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 ${{\rm{H}}}_{2}^{18}{\rm{O}}$ enhanced region. We use the following equation to calculated a weighted H₂O/${{\rm{H}}}_{2}^{18}{\rm{O}}$ value:

$$\begin{eqnarray}&&W=\displaystyle \frac{{\sum }_{i=1}^{n}{w}_{i}{\chi }_{i}}{{\sum }_{i=1}^{n}{w}_{i}},\end{eqnarray} \tag{ 2 }$$

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 H₂O/${{\rm{H}}}_{2}^{18}{\rm{O}}$ value in a cell. Using this formalism, we find the average H₂O/${{\rm{H}}}_{2}^{18}{\rm{O}}$ coming from this transition is ∼400. The ${{\rm{H}}}_{2}^{18}{\rm{O}}$ at 22.77 μm appears to emit from a drastically different region in the disk; thus, its average H₂O/${{\rm{H}}}_{2}^{18}{\rm{O}}$ is 540, nearly identical within the margin of error to the typically used ISM estimate. We list the calculated weighted averaged determined for the eight identified bright and isolated ${{\rm{H}}}_{2}^{18}{\rm{O}}$ transitions in Table 1. There is a general trend that transitions from smaller wavelengths trend toward 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 ${{\rm{H}}}_{2}^{18}{\rm{O}}$-enhanced region. To reduce the uncertainty in the H₂O/${{\rm{H}}}_{2}^{18}{\rm{O}}$ ratio, transitions associated with low Einstein A-coefficients could be preferentially used. These differences are small and up to a factor of 2. 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.

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In the ${{\rm{H}}}_{2}^{18}{\rm{O}}$-enhanced region, C¹⁸O abundance drops and the ¹²CO-to-C¹⁸O ratio increases by upward of four orders of magnitude. Measuring the ¹²CO-to-C¹⁸O ratio using lines of CO that emit from this region could help confirm the presence of this ¹⁸O-rich region and even calibrate uncertainties in the true ratio between H₂O and ${{\rm{H}}}_{2}^{18}{\rm{O}}$. 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 NIRSPEC and the Very Large Telescope's CRIRES. The C¹⁸O column densities in the ${{\rm{H}}}_{2}^{18}{\rm{O}}$-rich region range from 10¹² to 10¹⁵ cm⁻¹² and are predicted to produce optically thin C¹⁸O 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 ${{\rm{H}}}_{2}^{18}{\rm{O}}$-enhanced region. In these studies only CO and ¹³CO observations were reported, making it currently impossible to use these observations to corroborate our predicted ¹⁸O-rich region within 1 au. The only work that set out to measure ¹²CO/C¹⁸O and ¹²CO/C¹⁷O is found in Smith et al. (2015). This study observed nine young stellar objects (YSOs), three of which were optically thick disks. These three disks show tentative increase in the ¹²CO/C¹⁸O well above the ISM-measured value; however, it was noted that significant systematic uncertainties were 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 ¹⁸O enhancement within the radial extent of planet formation.

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 ¹⁸O-rich (and ¹⁷O-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 C¹⁸O and C¹⁷O relative to CO producing gas enriched in ¹⁸O and ¹⁷O (Lyons & Young 2005; Miotello et al. 2014). In this work, we find that the addition of H₂O UV-shielding not only continues the ¹⁸O enrichment within the inner disk, but enhances it compared to results solely based on CO self-shielding. We find a depletion of C¹⁸O approaching a factor of 10³ high up in the disk between 0.1–30 au at a ∼z/r = 0.2-0.3. This is a reservoir rich with ¹⁸O, enhancing the ¹⁸O isotopologues for many different volatile species, including water vapor and ice.

Vertical mixing may act as a mechanism to deliver the ¹⁸O-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 submillimeter observations exhibit nondetections (Salyk et al. 2011; Du et al. 2015; Carr et al. 2018; Bosman & Bergin 2021; Bosman et al. 2022). Thus, while the ${{\rm{H}}}_{2}^{18}{\rm{O}}$-rich regions reside 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 astronomical units that suggested that meteoritic ¹⁸O 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 downward forming water ice via grain surface chemistry. These ices will need to be transported to the inner few astronomical units, 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 ¹⁸O is placed directly into water in surface layers above the inner disk spatially closer to the region where meteoritic progenitors originate.