The Kinematics and Excitation of Infrared Water Vapor Emission from Planet-forming Disks: Results from Spectrally Resolved Surveys and Guidelines for JWST Spectra

Water spectra in protoplanetary disks have so far been observed with instruments that fall under two main categories: space-based low-resolution spectrographs (e.g., IRS on Spitzer with maximum resolving power R ≈ 700), and ground-based high-resolution echelle spectrographs (e.g., Cryogenic Infrared Echelle Spectrometer (CRIRES) on the Very Large Telescope (VLT) with R ≈ 95,000). Each type of instrument presents specific advantages and disadvantages, which we illustrate in Figure 1. Space-based spectrographs provide wide spectral coverage (e.g., 10–37 μm with Spitzer-IRS, and now 4.9–28 μm with JWST-MIRI) but lose kinematic information on the observed emission, and blend together lines from multiple emission/absorption components and different chemical species. Conversely, ground-based spectrographs provide high resolving power that separates the emission from different lines and molecules and reveals the gas kinematics in high detail, but they can only observe in limited spectral windows of higher telluric transmission within the L, M, and N bands (Figure 1 and Table 1).

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In Figure 1 we report a water emission model for quick guidance on the structure of the spectrum across wavelengths. The model is described below in Section 4.3, and in this figure we use a temperature of 700 K, column density of 10¹⁸ cm⁻², and line FWHM of 15 km s⁻¹. We visually scale the model to approximately match the observed emission in DR Tau just for line identification (in Section 4.4 we will present actual model fits to the data). Purely rotational lines populate a large part of the spectrum at wavelengths longer than 10 μm, while rovibrational transitions in the bending and stretching modes present more compact bands at 4–9 μm and 2.5–3.5 μm, respectively. We include in the figure a sky transmission spectrum as obtained from the ESO SkyCalc application, set up for the Paranal site (altitude of 2640 m) and using airmass = 1 and precipitable water vapor (PWV) = 2.5 mm. Comparison of Earth's transmission to the water emission spectrum in the top two panels in Figure 1 demonstrates that ground-based instruments enable observations of the water spectrum only where it is relatively weak (the tails of rovibrational bands and a few rotational lines near 12.4 μm).

Using observations from space or from the ground, previous work has therefore focused on data sets or samples that were limited one way or the other, resulting in an incomplete view of the distribution and excitation of water in inner disks. Some studies analyzed large samples (up to ≈100 objects) of spectrally unresolved rotational water emission observed with Spitzer-IRS at 10–37 μm or Herschel-PACS/HIFI at 50–540 μm; due to the low resolving power and blending of emission lines, Spitzer spectra only provided degenerate model solutions for the properties (temperature and column density) of multiple molecules and no direct kinematic information on the radial location of emitting regions (Carr & Najita 2011; Salyk et al. 2011b; Pascucci et al. 2013), while Herschel observations provided very low detection rates of a few lines only (e.g., Riviere-Marichalar et al. 2012; Du et al. 2017).

Other studies analyzed small samples of high-resolution spectra from the ground, mostly biased toward highly accreting disks that had been observed with Spitzer to have strong water emission; these spectra provided first kinematic information on the water emission but were very limited in sensitivity and by strong telluric absorption (Pontoppidan et al. 2010b; Salyk et al. 2019) and, in the case of the 2.9 μm water band, by absorption in stellar photospheres (Banzatti et al. 2017). The properties of water emission as observed in different samples and different wavelengths have ranged from high temperatures in very optically thick regions in the L band (T ≈ 1500 K and N ≈ 10²⁰ cm⁻², found in only three disks so far; Carr et al. 2004; Doppmann et al. 2011; Salyk et al. 2022), to moderate temperatures and opacity in a narrow window in the N band (T ≈ 500–700 K and N ≈ 10¹⁸ cm⁻²; Najita et al. 2018; Salyk et al. 2019), down to cooler temperatures at mid- and far-infrared wavelengths (300–600 K; Carr & Najita 2011; Salyk et al. 2011b; Riviere-Marichalar et al. 2012; Liu et al. 2019). Apart from those analyzing Spitzer spectra, previous results were always based on small samples of 1–10 bright sources.

Supporting the scenario of water emitting from a radial range of disk regions, the combined analysis of spectrally unresolved mid- and far-infrared water spectra has suggested that water emission should come from disk surfaces from the dust sublimation radius out to 10 au or even larger radii (e.g., Antonellini et al. 2015; Blevins et al. 2016; Notsu et al. 2016; Woitke et al. 2018), where different emission lines probe a range of disk regions and layers depending on their upper-level energy and Einstein-A coefficient. However, a unified picture of water in inner disks across different emission bands, including the rovibrational lines in the near-infrared and calibrated on spectrally resolved water line kinematics, is still lacking. JWST now covers both the rotational lines at >10 μm (E_u ≈ 1000–6000 K) and the rovibrational lines from the bending mode (E_u ≈ 4000–10,000 K) simultaneously and at similar resolving power (R = 1500–3700 across Mid-Infrared Instrument, MIRI, wavelengths), providing unprecedented leverage on the excitation of water across inner disk radii. One goal of this paper is to support the analysis of JWST spectra by providing spectrally resolved line kinematics at multiple wavelengths from a suite of high-resolution ground-based spectrographs (Table 1). A comprehensive view of water in disks will require the combination of multiple instruments from the ground and space at least until a space-based infrared telescope with high resolving power (R >30,000) is possibly built (e.g., Pontoppidan et al. 2018; Kamp et al. 2021).

Water rovibrational emission spectra at 2.9–2.98 μm are included as observed with CRIRES (Kaeufl et al. 2004) on VLT as part of a survey from 2007–2008 (European Southern Observatory, ESO, Large Program 179.C-0151; Pontoppidan et al. 2011; Brown et al. 2013). The water spectra were obtained for ≈50% of the sample in that survey (35 out of 69 disks, mostly T Tauri stars) and were presented and analyzed in Banzatti et al. (2017), except for the very different spectrum with a much larger number of high-excitation lines observed in VV CrA S, which is published in Salyk et al. (2022). Additional spectra for 11 Herbig Ae/Be stars were presented in Fedele et al. (2011).

The T Tauri spectra included in this work were taken with a resolving power of ≈95,000 or ≈3 km s⁻¹, and most of them required correction for stellar photospheric absorption on top of telluric correction. The observed water emission lines were found to be generally as broad as the broad component of CO M-band emission (FWHM up to ≈100 km s⁻¹ in some disks), and in a few cases to include also weak narrower central emission similar to the kinematic structure of CO (for details, see Banzatti et al. 2017). An example L-band spectrum from CRIRES is shown in Figure 2, showing ≈15–20 prominent water lines that in some cases are blends of two nearby transitions (the blending of lines increases with line broadening, and is generally more severe than in the example shown here; see Figure 14 in Banzatti et al. 2017).

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Water rovibrational emission spectra at 5 μm are included as observed with iSHELL (Rayner et al. 2016, 2022) at the NASA Infrared Telescope Facility (IRTF), as part of an ongoing M-band survey of protoplanetary disks (Banzatti et al. 2022). iSHELL covers a wide portion of the observable M band at 4.5–5.25 μm in one shot, with only narrow gaps between the echelle orders at longer wavelengths, providing simultaneous observations of CO, H₂O, and H i (Banzatti et al. 2022). Most spectra were taken with the 075 slit and a resolving power of ≈60,000 or ≈5 km s⁻¹, while the narrower slit with ≈92,000 or ≈3.3 km s⁻¹ was used only for the brightest disks (mostly around Herbig Ae/Be stars, where water is not detected). The iSHELL spectra included here were reduced with Spextool v5.0.3 (Cushing et al. 2004) and have been presented in Banzatti et al. (2022) or obtained in 2022 January–July, for a total current sample of 60 disks. Multiepoch observations have been obtained for some disks and show variability (e.g., Figure 8 in Banzatti et al. 2022); in this work, we only include one epoch, and we will study the variability in a future publication.

The M-band water lines have been discovered in the disk of AS 205 N and reported for the first time in Banzatti et al. (2022), and in this new work we include all of the current detections from the rest of the survey. An example is presented in Figure 3. In the currently available M-band spectra, a total of ≈40 rovibrational water lines are observed (mostly from v = 1 and some from v = 2, see Table 2), some of which are blended with CO or H i emission. In this work, we make a weighted average of eight water lines that are not blended with CO to produce a stacked velocity profile with higher signal-to-noise ratio (S/N); these lines are marked in Table 2. At the S/N obtained in these spectra, the M-band water lines are consistent with having the same velocity profile; future higher-sensitivity spectra could be used to test for any change in rovibrational line profiles as a function of E_u .

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Water rotational emission spectra at 12.2–12.9 μm were obtained within a Large Program with VISIR (Lagage et al. 2004), and are presented and analyzed in this work for the first time. This survey used VISIR at the VLT right after its upgrade (Käufl et al. 2015) and over semesters between 2016 August and 2018 August (program IDs 095.C-0203 and 198.C-0104, PI: K. Pontoppidan). A spectrum is shown in Figure 4 as an example.

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The survey included three settings: two echelle settings centered at 12.27 and 12.41 μm to cover emission from H₂O lines and the 0-0 S(2) H₂ line at 12.2786 μm (and possibly OH), and one long-slit setting centered at 12.84 μm to include the [Ne ii] line at 12.8136 μm and two water lines with upper-level energy 3200 K. The central wavelengths of all settings were set to maximize the number of H₂O emission lines to be observed, a total of 11 (Table 2). We used the 075 slit providing a resolving power R ≈ 30,000 (or 10 km s⁻¹). The data reduction is based on a custom pipeline initially made for VISIR 1 data (Banzatti et al. 2014) and adapted to the upgraded VISIR. Appendix B reports more details on the observations and reduction.

The total numbers of spectra obtained in each setting, including multiple epochs and/or slit orientations for a given target, are: 60 spectra in the H₂O setting, 16 spectra in the H₂ setting, and 45 spectra in the [Ne ii] setting. Out of 64 targets, 22 were observed in at least two settings, and four targets were observed in all three settings (CrA-IRS2, SCrA, TCrA, and VVCrA; see Appendix B). To increase S/N, we have combined by weighted average spectra from multiple epochs and/or slit orientations obtaining one spectrum per object per setting. In the case of DR Tau, we averaged three epochs of data obtained earlier in program 088.C-0666 at higher S/N (Banzatti et al. 2014). The [Ne ii] detections obtained in this survey have been presented and analyzed in Pascucci et al. (2020); H₂O and [Ne ii] detections overlap in two disks only, RU Lup and VW Cha, but the lines have very different kinematic structure where [Ne ii] only traces gas at high blueshifted velocities of −50 to −200 km s⁻¹ in these two systems. No H₂ detections are reported from this survey, consistent with previous low detection rates (Bitner et al. 2008; Carmona et al. 2008).

Additional water rotational emission spectra at 12.2–12.4 μm are included as obtained with TEXES on Gemini (Lacy et al. 2002) with a resolving power of 100,000 or 3 km s⁻¹ and previously presented in Najita et al. (2018) and Salyk et al. (2019). In this work we consider only the highest S/N among these spectra, obtained in four disks (see Section 4.1).

There are some wide multiple systems in the sample (e.g., Prato et al. 2003; Manara et al. 2019; Panić et al. 2021): AS 205 (separation 13), DoAr 24E (GSS 31, 22), S CrA (13), VV CrA (19), DK Tau (24), UY Aur (09), T Tau (07), and KK Oph (16). In good seeing conditions, we aligned the slit along the system axes so that the main binary components could be extracted. AS 205 A is the brighter component in the north, AS 205 B the fainter component in the south. DoAr 24E A is the brighter component in the north, but it becomes fainter than the B component in the south in the L band and at longer wavelengths (Prato et al. 2003; Brown et al. 2013). Therefore, in our data, DoAr 24E B (S) is the brighter component. SCrA A is the brighter component in the northwest, SCrA B is the fainter component in the southeast; VVCrA A is the brighter component in the south, VVCrA B is the fainter component in the north (Sullivan et al. 2019a). DK Tau A, UY Aur A, T Tau A, and KK Oph A are the brighter components in the north in each system (e.g., Manara et al. 2019; Panić et al. 2021).

The first point we address in this work is about the line kinematics and emitting regions of water as spectrally resolved at multiple wavelengths, addressing questions (1) and (4) listed in Section 1. Previous work found that 2.9 μm lines are dominated by a broad emission component that matches the width of the broad component in CO emission lines in the same systems (Banzatti et al. 2017). At 12.4 μm, instead, line velocities were found to be narrower and match the narrow component in CO emission in a few disks where data was available (Banzatti et al. 2017; Salyk et al. 2019). With the new surveys and larger sample included in this work, it is now possible to expand the comparison between CO emission components and water emission lines on a larger number of detections and, for the first time, including water emission in the M band around 5 μm.

Figures 5 and 6 show a comparison of the H₂O line profiles using the CO line profiles observed in each object as reference. Line profiles from the fundamental v = 1 − 0 lines have been observed with VLT-CRIRES and IRTF-iSHELL (Pontoppidan et al. 2011; Brown et al. 2013; Banzatti et al. 2022), and have been decomposed into broad BC and narrow NC velocity components as described in Banzatti & Pontoppidan (2015) and Banzatti et al. (2022). Gaussian fits to these two components are then scaled to match the relative strength of water lines to visualize the broadening of water relative to each CO component. The 10 iSHELL spectra where H₂O is detected show that the kinematic profile of H₂O emission at 5 μm is broader than the NC but narrower than the BC in at least six out of 10 cases. In the other four cases (DO Tau, DF Tau, RNO 90, and V1331 Cyg), water lines are as broad as the BC. In DF Tau, and tentatively in RNO 90 too, water shows a double-peaked shape that matches the width of the BC. In V1331 Cyg, water is as broad as the BC and possibly has a narrower blueshifted absorption (see also Section 4.1.1); its near-infrared spectrum is overall more complex due to an uncommonly high excitation of both CO and water (see the L-band water spectrum in Doppmann et al. 2011), and will be analyzed in detail in a future work. Additional tentative detections are found in three more disks (UY Aur A, Elias 24, and HD 35929), which are all included in the plots in Appendix A.

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The 10 H₂O lines detected in the VISIR spectra show that the kinematic profile of H₂O emission at 12.4 μm is rather well matched by the narrow CO component in six out of 10 cases, within the uncertainty of the much lower pixel sampling and resolution of the VISIR spectra. The comparison between CO and H₂O lines is ambiguous in two cases (RU Lup and Elias 20), due to the low S/N of the water spectra. The case of VW Cha shows a broader water line with potentially a blueshifted absorption, which will be discussed in Section 4.1.1. The case of IRAS 04303 shows a very broad water line, similarly broad as the CO line; in this case, Figure 6 shows the complete CO line profile as observed, rather than decomposed into BC and NC as in the other objects, to illustrate the presence of a broad, deep, and blueshifted absorption component in the CO line (which is detected up to P38; i.e., this is another one of the highly excited blueshifted absorption spectra reported in Banzatti et al. 2022).

In Figure 7 we show fits to the 12.396 μm water emission line observed in the four highest-quality TEXES spectra from Najita et al. (2018) and Salyk et al. (2019). Water was detected in three more disks in Salyk et al. (2019), DoAr 44, HL Tau, and RW Aur, but with too low of S/Ns to apply this analysis. Given the higher resolution and S/Ns of these spectra, instead of using BC and NC individually as in Figures 5 and 6, we fit the full line shape with a two-Gaussian model based on the measured FWHM of BC and NC as was done for the 2.9 μm lines in Banzatti et al. (2017), to test whether there is evidence for both components contributing to the observed water line profile. The analysis of this small sample confirms that water rotational lines at 12.4 μm overall well match the shape of the NC, but it also shows that water lines include weak broad wings from a broader velocity component similar to the BC.

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All together, the picture emerging from the kinematics of spectrally resolved water emission observed between 2.9 and 12.4 μm is that water lines are broader at shorter wavelengths in the rovibrational bands and narrower at longer wavelengths in the purely rotational transitions. This suggests that rovibrational lines are excited predominantly (or exclusively) in an inner, hotter region as compared to the rotational lines, a region that may match that of the BC in CO. The rotational lines, instead, are dominated by an emission component that matches the NC in CO, at least down to upper-level energies of ∼4000 K as covered in the VISIR and TEXES spectra; lower-energy levels at longer wavelengths covered by JWST-MIRI remain to be spectrally resolved, and might be even narrower by being excited in outer disk regions (see Section 5). The fact that water lines at different wavelengths should have different FWHMs reflecting excitation from a wide range of emitting regions (broader to narrower from higher- to lower-level energies) has been the fundamental expectation of model predictions for some time (e.g., Blevins et al. 2016; Woitke et al. 2016), and this multiwavelength high-resolution data set directly confirms it for the first time. We will combine the picture emerging from line kinematics to that emerging from line excitation in Section 4.4.

4.1.1. Blueshifted Absorption in H₂O Spectra

Two peculiar cases to note in the context of water line profiles and their kinematic structure are those of VW Cha and V1331 Cyg (Figures 5 and 6). The water spectrum observed with VISIR in VW Cha shows a potential narrow absorption line blueshifted from the peak of the emission line (Figure 8). This emission+absorption structure is observed similarly in both water lines that are covered and detected in this object, and the absorption line is much narrower than the telluric lines (Appendix B); we cannot attribute this feature to any artifact possibly present in the VISIR spectra at the time of observation, and we present it here as a potential first detection of a blueshifted absorption feature in mid-infrared water spectra from disks. It should be noted that highly blueshifted [Ne ii] emission at −150 and −40 km s⁻¹ has been observed in VW Cha in this same VISIR survey (Pascucci et al. 2020), demonstrating the presence of an outflow that could also be linked to the absorption feature in the water lines (although if that is the case, [Ne ii] would trace an atomic part of the outflow at higher velocities).

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A unified scenario for emission and absorption in the context of an inner disk wind has been proposed to explain blueshifted narrow absorption lines that are observed on top of CO emission lines in other disks (Pontoppidan et al. 2011; Banzatti et al. 2022), conditions that have been found since earlier stages of disk evolution with additional complexity due to envelopes and multiple absorption components (Herczeg et al. 2011). A similar blueshifted absorption is possibly detected in the M-band water spectrum of V1331 Cyg (Figure 5), a known source of a large-scale jet and molecular outflow (Mundt & Eislöffel 1998; Wu et al. 2004). In this case, the blueshifted water absorption is very similar to the blueshifted CO NC in its centroid and FWHM. Additional epochs of high-resolution and high-sensitivity observations are required to further investigate these potential absorption components in infrared water spectra.

A second point that we investigate in this work is the excitation of water transitions from different energy levels as a function of stellar and disk properties, addressing questions (1) and (3) from Section 1. Previous work identified the following trends from spectrally unresolved water emission observed at 12–17 μm: (1) water detections are much higher in K and M stars as compared to earlier types (Pontoppidan et al. 2010a) and lower in M-dwarf disks (Pascucci et al. 2013), (2) water detections are lower in disks with inner dust cavities (Salyk et al. 2011b; Banzatti et al. 2017), (3) water line fluxes correlate with stellar luminosity in T Tauri stars (Salyk et al. 2011b) and, more strongly, with their accretion luminosity (Banzatti et al. 2020), (4) water line fluxes anticorrelate with the disk dust radius as spatially resolved with millimeter interferometry (Banzatti et al. 2020). As noted before, the analysis of water spectra is intrinsically a multidimensional problem where multiple star/disk properties affect the observed emission (see, e.g., discussion in Banzatti et al. 2020).

We provide in Figure 9 an overview of these and other trends by considering spectrally resolved water lines at 2.9, 5, and 12.4 μm, and spectrally unresolved water lines at 17 and 30 μm (from Spitzer-IRS), including the M-band spectrally resolved CO lines for reference. All of the line flux measurements included in this figure are reported in Appendix C. The line luminosity for each row of plots in the figure is, respectively, as measured in: the low-J v = 1 − 0 CO lines (Banzatti et al. 2022), the three water lines around 2.9285 μm (Banzatti et al. 2017), the 5 μm stacked line (Figure 5), the 12.396 μm line (Figure 6), and the few prominent water features around 17.25 and 30.7 μm included in the plots in Appendix A. In this work we do not reanalyze correlations that have already been presented and discussed in previous work, but we find it useful to include the full grid of plots in Figure 9 to combine in one place tracers, samples, and trends that have been previously considered only separately, for future reference. In this section, we briefly describe the general trends and any notable differences between different tracers, and remark that a comprehensive view of this kind will be increasingly valuable in future work to correctly interpret individual spectra and samples from JWST observations within the broader context of the global structure and evolution of molecular gas in inner disks (see guidelines in Section 5.2).

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Since CO lines provide the highest detection rates in molecular lines tracing inner disks (e.g., Salyk et al. 2011a; Brown et al. 2013; van der Plas et al. 2015) and a fundamental reference to interpret other molecular tracers, each data point in Figure 9 is classified according to the kinematic shape of its CO line using a line shape parameter S = FW10%/FW75% (the ratio of the line width at 10% and 75% of the peak flux). Lines identified as "triangular" have S > 2.5 (with broad wings and a much narrower line center, associated to disk+wind emission) and double-peaked lines have S < 2.5 (with typical line profiles associated to purely Keplerian, symmetric disk emission; see more on the definition and discussion of the line shape parameter in Banzatti et al. 2022).

Trends in CO luminosity—For reference to trends observed in water emission, we first describe trends in the CO line luminosity L_CO. L_CO as measured in this sample shows trends that are sometimes different or even opposite in the two types of lines (top of Figure 9): in particular, in triangular lines, L_CO presents a large scatter without an obvious trend as a function of M_⋆, while in double-peaked lines there is a strong positive correlation above 1 M_⊙ (and similarly is observed in L_acc). Other notable trends in L_CO are with disk inclination, infrared index n₁₃₋₃₀, and millimeter dust disk radius R_disk; the latter, excluding the weakest objects that are disks with inner cavities, presents an interesting anticorrelation similar to that found in water in Banzatti et al. (2020). The trends observed in L_CO are analyzed and discussed in J. Perez Chavez et al. (2023, in preparation).

Trends in 2.9 μm water luminosity—The 2.9 μm water sample was biased toward disks around T Tauri stars with moderate to high accretion rates (Banzatti et al. 2017), resulting in perceived high detection rates (∼45%; Table 1). The relatively small sample in this case does not allow to report strong trends, apart from a general agreement with those observed in CO.

Trends in 5 μm and 12.4 μm water luminosity—The samples at 5 μm and 12.4 μm are larger but provided detection rates of only ∼20%; despite that, some differences from the trends observed in CO emerge clearly. Water detections are exclusively found in objects that have a triangular CO line shape. These objects have in common a moderate accretion luminosity (0.1–1 L_⊙), T_eff < 6000 K, detection of jets and disk winds, and CO emitting from within the dust sublimation radius (see more discussion of triangular lines in Banzatti et al. 2022). The upper limits measured in the 5 μm water lines in some disks around intermediate-mass stars appear in stark contrast with their high CO luminosity, suggesting a different C/O ratio in these disks.

Trends in 17 and 30 μm water luminosity—Water line detections and luminosity at 17 μm and 30 μm, tracing lower-excitation transitions at 2400–3300 K and 1800 K, respectively, are still predominantly detected in disks with a triangular line shape. An important difference with the higher-excitation water lines at shorter wavelengths is the detection in a Herbig Ae disk (HD 163296, one of the few intermediate-mass stars that has a triangular line shape in CO, which has been associated with an inner disk wind; see Hein Bertelsen et al. 2016b; Banzatti et al. 2022) and in a few disks that have an inner dust cavity (DoAr 44, TW Hya, SR 9, and SU Aur). Detection of water in Spitzer-IRS spectra of these disks was previously reported in Fedele et al. (2012), Salyk et al. (2011b), and Banzatti et al. (2017). These cases demonstrate that rotationally cold water emission can still be observed in some disks with dust cavities and disks around Herbig Ae stars (plots of multiwavelength water spectra are included for reference in Appendix A).

General trends in water luminosity—Across different energy levels (and wavelengths), the water luminosity is in general higher in T Tauri disks than in Herbig disks. The nondetection of water in Herbig disks reflects a true decrease in luminosity and is not simply an S/N issue. In T Tauri disks, the water luminosity increases with accretion luminosity and with line shape parameter S, and decreases with disk inclination, infrared index n₁₃₋₃₀, millimeter disk radius R_disk, and radius of CO emission R_CO (estimated from the line width at 10%, as a tracer of the inner emitting radius for warm molecular gas; see Banzatti et al. 2022, for details). The higher detection rates of water in spectral lines with larger S values (e.g., AS 205 N and DR Tau) as observed at high resolution, therefore, are not simply due to the higher line-to-continuum contrast. Broader lines with lower S (e.g., in RNO 90) are more blended with nearby lines (e.g., CO, in M-band spectra) and do require a higher S/N per pixel to be detected, implying that their detection rate will be lower. However, two trends suggest an intrinsically decreasing water (and CO) luminosity due to (1) the S parameter itself, where triangular lines with S > 5 have a median luminosity that is ≈5 times higher than triangular lines with S < 5, and (2) the viewing angle, where disks with incl < 25° have a median luminosity a few times higher than triangular lines with incl ≈ 30°–50°. Both trends suggest that the geometry of emitting regions as viewed under different inclinations determines the observed properties of molecular spectra (see also Figure 6 in Banzatti et al. 2022).

The third point we address in this work is the relative excitation of water spectra across different bands and transitions, addressing questions (1) and (3) from Section 1. To do so, we describe the use of rotation diagrams of infrared water emission, which, for the first time, can be analyzed from spectrally resolved emission covering upper-level energies between 4000 and 9500 K. The rotation diagram technique has been thoroughly described for space applications in Goldsmith & Langer (1999), but has never been systematically applied to water emission from protoplanetary disks due to the lack of spectrally resolved line fluxes over a broad range in Einstein-A coefficients A_ul and in upper-level energies E_u . While this is not necessary with linear molecules in the simplest excitation conditions, covering a large range in E_u and A_ul is essential in the case of an asymmetric top polyatomic molecule like water, especially in circumstellar disks where the emission is not optically thin and non-LTE conditions may subthermally excite lines with high A_ul (Meijerink et al. 2009; Herczeg et al. 2012; Kamp et al. 2013). Below, we summarize previous explorations by Banzatti (2013) to describe how different conditions (line opacity, LTE/non-LTE excitation) produce distinct features in water rotation diagrams.

4.3.1. LTE Case

Rotation diagrams are defined such that, in conditions of optically thin emission at a single excitation temperature and in LTE, the fluxes from lines at frequency ν observed from an unresolved point source form a straight line as (see Larsson et al. 2002):

where F is the integrated line flux, Ω is the solid angle A/d² (A is the emitting area of the source, and d is the distance to the source), g_u is the statistical weight of the upper level, Q(T) is the partition function. Throughout this paper, we use E_u in units of kelvin and cgs units for the rotation diagram. The excitation temperature T and the column density N can be easily derived from the slope and intercept of a linear fit using Equation (1). This technique is useful, however, even when the emission becomes optically thick and/or the excitation deviates from LTE. In fact, in these cases the observed molecular line fluxes would produce specific curvatures and/or a large vertical spread in line fluxes in the diagram departing from the linear behavior given by the LTE optically thin case, as described in the following.

The basic properties of rotation diagrams of infrared water emission are displayed in Figure 10 using a single-slab model in LTE (described in Banzatti et al. 2012), with the temperature T and the column density N as free parameters. For this demonstration, we adopt a reference distance of 140 pc and a thermal line broadening of 1 km s⁻¹, and we fix the slab surface area A to a disk with radius 1 au. In the optically thin case (N = 10¹⁵ cm⁻², top left in the figure), water lines form a straight line in the diagram, with slope set by the temperature. It is worth noting that higher T increasingly populate transitions from higher energy levels, as indicated by the larger symbols in the figure. When the column density is increased, instead, line opacities increase and lines spread over the diagram following a specific pattern. When a line gets optically thick (τ ≫ 1) it "freezes" on the diagram, i.e., its intensity is only weakly dependent on the column density. This happens first to those lines with large A_ul (the low-energy, bottom-left corner of the diagram; see also Figure 11), as the line opacity is proportional to A_ul . The optically thin lines, instead, still follow Equation (1) and can rise in the diagram together with N.

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Therefore, unlike the case of a linear molecule like CO where a curve is produced, an increase in optical depth for the nonlinear water molecule spreads lines vertically in the diagram. The most optically thin lines (those with the lowest A_ul at any given bin in E_u ) define the upper edge of the spread, while the most optically thick ones progressively set the middle and lower edge (Figure 11). In these conditions, the vertical spread in the diagram is primarily sensitive to the column density. However, as Figure 11 shows, line intensities are larger at the center of the diagram, indicating that low-sensitivity spectra may only detect part of the full rotation diagram (as it typically happens with ground-based instruments; see Section 4.4).

4.3.2. Non-LTE Case

4.3.3. Disk Structure in LTE

After briefly describing general properties of the technique in the previous section, we now illustrate in Figure 12 for the first time rotation diagrams of spectrally resolved infrared water emission at energies of 4000–9500 K, for the small sample of disks where the emission is detected in this energy range (see Section 4.1). Previous attempts to retrieve line fluxes over a similarly large range were done by de-blending Spitzer-IRS spectra in Banzatti (2013), but were strongly limited by the low resolution of the data and blending between lines from different levels and molecules. Here, we simply measure and include in Figure 12 the total flux from ∼20 lines as observed in Spitzer-IRS spectra to extend the observed rotation diagram down to 1000 K, but we warn the reader that this is done for illustration only and that all of the measured fluxes are blends of multiple transitions. This problem will be solved with JWST-MIRI spectra, as discussed below (Section 5.2).

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The largest portion of the observed rotation diagrams is provided by M-band spectra, which cover the largest number of water lines from a single high-resolution spectrum (Section 2) and energies between 4000 and 9500 K. In this work, these lines are observed in the iSHELL spectra, which are flux calibrated using Wide-field Infrared Explorer (WISE) W2 photometry at 4.6 μm (Cutri et al. 2021). The high-energy end of these lines overlaps with lines extracted from L-band spectra previously observed with CRIRES (flux calibrated using WISE W1 photometry at 3.4 μm), while the lower-energy end overlaps with the rotational lines observed with VISIR and TEXES (flux calibrated using Spitzer-IRS, where available, or WISE W3 photometry at 12 μm). Overall, spectral lines from different instruments overlap well in the rotation diagram of each object apart from the L-band lines, which look under-excited as compared to the M-band lines in all disks. While real variability and the nonsimultaneous flux calibration may offset the emission as observed with different instruments at different times, the apparent systematic offset between rovibrational bands suggests a difference in their excitation (see Section 5).

Considering line fluxes from different instruments, the observed rotation diagrams show an overall curvature that is reminiscent of what is found from the 2D disk model in Figure 10 as due to emission from a range of temperatures at different disk radii. These curvatures could not be seen before in previous work that only covered <10 lines in a narrow portion of the diagram at 4000–6000 K (Pontoppidan et al. 2010b; Salyk et al. 2019), and are now most evident in the M-band spectra alone, as well as in combination with the Spitzer-IRS spectra. In addition to a curvature, lines from the Spitzer-IRS spectra spread vertically as expected in the case of large water column densities (Figure 10). The vertical spread is more visible than in the case of spectra from ground-based instruments, because these have more stringent sensitivity limits and only detect stronger lines close to the upper edge of the rotational spread (Figure 11). By better de-blending line fluxes at mid-infrared wavelengths and detecting weaker lines with lower A_ul , the analysis of JWST spectra will reveal the shape and spread in rotation diagrams in higher detail (see Section 5).

4.4.1. LTE Slab Fits

The overall picture emerging from this analysis is summarized in Figure 13, by combining results from Section 4 in terms of line excitation and kinematics as spectrally resolved at multiple wavelengths. LTE slab model fits show that the infrared water spectrum may probe moderately optically thick emission from hotter inner regions exciting the higher energy levels, to colder outer regions populating the lower-energy levels, qualitatively supporting general expectations from previous models (Section 1). The wide range of observable/observed inner disk water column densities (10¹⁷–10²⁰ cm⁻²) produced by previous works modeling water spectra from inner disks (Najita et al. 2011; Du & Bergin 2014; Walsh et al. 2015; Agúndez et al. 2018; Woitke et al. 2018) or estimated from spectrally unresolved disk observations (Carr & Najita 2011; Salyk et al. 2011b; Liu et al. 2019) demonstrates that this parameter, and more fundamentally the water vapor abundance as a function of disk radius and disk height (down to the disk midplane), are still, to date, critical unknowns (see discussion in Bosman et al. 2022).

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The similar column density found in slab fits to the spectra at different wavelengths (a few times 10¹⁸ cm⁻²) across the sample in Table 3 is therefore particularly interesting: recent models that include chemical heating and UV-shielding propose that this is the column density that ends up being probed in the disk surface due to the combination of the most prominent lines becoming optically thick, and the gas temperature steeply falling off at higher densities (Bosman et al. 2022). The results presented above suggest that water spectra across infrared wavelengths may trace gas where the right density for excitation is met at any given disk radius, resulting in a similar column density across radii but different excitation temperatures.

5.1.1. A Gradient in Excitation Temperature

5.1.2. Non-LTE Vibrational Excitation

5.1.3. A Gradient in FWHM and Emitting Regions

A total of ∼70 Class II protoplanetary disks are going to be observed with JWST spectrographs in Cycle 1, most of them with MIRI (Rieke et al. 2015) providing R ≈1500–3700 (80–200 km s⁻¹) between 4.9 and 28 μm (Labiano et al. 2021). The wide spectral coverage of MIRI includes the rovibrational bending mode and rotational lines of water vapor emission in disks for the first time at a similar resolution in the two bands (Spitzer-IRS did cover the water bending mode but only with the low-resolution module with R ≈60–120; Sargent et al. 2014). The higher resolving power of MIRI will de-blend many of the emission features previously observed with Spitzer (see example in Figure 14). Fundamental expectations from MIRI spectra are therefore a much improved characterization of the water (and OH) spectrum and its excitation across near- and mid-infrared wavelengths (James et al. 2022), a better characterization of the emission from some organic molecules (although their rovibrational bands near 14 μm will still be severely unresolved; see Figure 14), and the discovery of features from additional molecules previously unidentified in Spitzer spectra.

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MIRI will not provide, instead, measurements of the gas kinematics and the distinction between double-peaked (Keplerian) and triangular line shapes, between BC and NC (where present), and between emission and absorption components observed in inner disks (Figure 15). At most, MIRI is expected to partially resolve the wings of emission lines that are broader than ≈100 km s⁻¹ (Figure 15). By combining advantages and disadvantages, we describe in the following a number of guidelines for future work to support the analysis of space data and propose how the combination with ground data may be used to obtain a comprehensive understanding of molecular spectra from inner disks.

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5.2.1. The Emitting Regions and Excitation of H₂O

5.2.2. CO- and Water-rich Inner Disk Winds?

5.2.3. Measuring H₂O/CO Ratios in Inner Disks

With VISIR in echelle mode, the telescope chops off the slit due to the short slit of 41; the nod B positions are therefore used only for background subtraction. Mechanical oscillations of the grating between sequential chops and nods, and sometimes a difficult guiding on weak sources, introduce small shifts (between fractions of a pixel to a few pixels) in both the spatial and spectral directions on the detector. These are corrected by cross-correlation of the position of one echelle order (for the spatial direction) and telluric lines (for the spectral direction), during combination of individual chops and nods. This procedure ensures the correct combination of the point-spread function (PSF) as observed in different nods, and avoids producing an artificial PSF broadening and residuals from the shift of telluric lines. A similar procedure for the spectral direction was previously implemented for VISIR 1 data (Carmona et al. 2008; Banzatti et al. 2014).

Observing N-band water spectra from the ground is very challenging due the variability of Earth's atmospheric conditions, especially in the precipitable water vapor (PWV). Apart from exceptional conditions, the sky typically changes significantly between sequential nods and causes residuals from variable telluric lines in the spectra. In this VISIR survey, we carefully monitored the observing conditions nod by nod, and reject individual nods where the sky varied by more than 5σ from the mean sky variation in each observing block. Any remaining sky residuals were removed by averaging the signal over 10–15 pixels at the two sides of the PSF pixel by pixel in the spectral direction, fitting this average with a Savitzky-Golay polynomial smoothing filter, and then subtracting the fit from the PSF before extracting the 1D spectrum. We extensively tested this correction, which in previous work was performed using a simple median subtraction (Pontoppidan et al. 2010b; Banzatti et al. 2014), and found that it gives the best results in removing telluric residuals while minimizing noise addition to the spectral PSF. The 1D spectrum is then extracted using optimal extraction.

After the detector upgrade in 2016, strong high-frequency fringing was found to affect VISIR high-resolution spectra. In connection to that, the sensitivity was also found to be a factor ≈10 lower (Figure 21). In 2017 April, the entrance window of VISIR was replaced to solve this issue. This replacement removed completely the high-frequency fringing in the echelle mode, and suppressed it in the long-slit mode; however, the low-frequency fringing that was affecting VISIR 1 was still present in all modes (see, e.g., Figure 22). Since VISIR observations do not include flats, but fringing was found to not be stable enough to be removed simply by division with the standard, we fitted and removed fringes in each spectrum after extraction of the 1D spectrum and prior to telluric correction. Some fringe residuals remained when fringes varied between a science target spectrum and its telluric standard spectrum and in the spectra of binary systems, where the two components were observed in a different position on the detector as compared to the telluric standard.

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Telluric correction of the extracted 1D spectra was performed using observations of several bright asteroids and a few bright stars (Alpha Cen, Alpha Car, Alpha CMa = Sirius, Theta Sco = HR6553). Telluric observations were interspersed during science observations in order to ensure a good match (difference <0.1) in airmass and PWV with the science targets. This was achieved in most but not all cases. Differences in both airmass and PWV between science targets and telluric standards are compensated during reduction using telluric water and CO₂ lines. We have tested using the airmass and PWV values recorded in fits headers, but these average values do not fully capture real differences and variability happening during observations. We therefore scaled telluric water lines until they matched those observed in the science targets to find the best PWV correction, and do the same with a CO₂ line to find the best airmass correction. These correction factors were applied to the telluric spectra as an exponential correction of the form as in previous work (Pontoppidan et al. 2010b; Banzatti et al. 2014). The science and telluric spectra were then normalized to their continua, aligned by cross-correlation of telluric lines, and then divided after applying the airmass and PWV correction to the telluric spectrum.

Wavelength calibration of individual spectra was done by cross-correlation in each setting with an atmospheric model set on Paranal conditions (same model as above in Section 1.1). We fine-tuned the wavelength solution on low-PWV spectra that allowed us to use all of the observed telluric lines out to the detector edges (Figure 22), and then we applied that solution to all other spectra after shifting it by cross-correlation of sky lines in each spectrum.

We measured the spectral resolution of VISIR from unresolved O₃ lines detected in telluric absorption spectra. We used several asteroid observations obtained during the survey and consistently measure an FWHM of 10 km s⁻¹ (corresponding to R ∼ 30,000) in four O₃ lines detected in the 12.84 μm setting. In the other two settings, O₃ lines are much weaker and possibly detected only in a few spectra; these measurements are less consistent and provide FWHMs in the range 5–13.6 km s⁻¹, suggesting a similar resolution of R ≈30,000 also in echelle mode at 12.2–12.5 μm.

In terms of sensitivity, we find that VISIR 2 observations in the echelle and long-slit settings utilized here delivered a similar S/N per pixel (Figure 21). Using as reference spectra of DR Tau, T Cha, and Sz 73 taken in 2008–2012 (Pascucci & Sterzik 2009; Banzatti et al. 2014), the new sensitivity is ≈60% higher than VISIR 1 observations, after the different pixel sampling has been accounted for (VISIR 2 has a pixel/wavelength ratio larger by 60% than VISIR 1).