Water in Protoplanetary Disks with JWST-MIRI: Spectral Excitation Atlas and Radial Distribution from Temperature Diagnostic Diagrams and Doppler Mapping

The infrared spectrum of water vapor has attracted increasing interest in the community since the discovery of its forest of lines in protoplanetary disks with the Spitzer-InfraRed Spectrograph (IRS;J. R. Houck et al. 2004) and ground-based spectrographs almost two decades ago (J. S. Carr & J. R. Najita 2008; C. Salyk et al. 2008). With >1000 transitions significantly contributing to spectra at 10–37 μm, but only ≈150 blended features of multiple transitions that could be distinctly observed with IRS (e.g., K. M. Pontoppidan et al. 2010b), water spectra are at the same time fascinating and challenging. Most of the attraction comes from the fact that they trace inner disks at radii where rocky and super-Earth planet formation is expected to happen (e.g., B. Bitsch et al. 2019; M. Lambrechts et al. 2019; A. Izidoro et al. 2021), as shown by water line profiles when observed at high resolving power from the ground (K. M. Pontoppidan et al. 2010a; J. R. Najita et al. 2018; C. Salyk et al. 2019; A. Banzatti et al. 2023b). Water is expected to trace and significantly contribute to a number of processes that are fundamental in star formation all the way to late phases of disk evolution and planet formation (e.g., E. F. van Dishoeck et al. 2014), from the dynamics and accretion of solids (e.g., F. J. Ciesla & J. N. Cuzzi 2006; K. Ros & A. Johansen 2013) to the development of habitable conditions (e.g., S. Krijt et al. 2023). Determining the water abundance in disks as a function of orbital distance and time remains one of the major goals for understanding these fundamental processes (e.g., R. Meijerink et al. 2009; K. M. Pontoppidan et al. 2014).

On the other hand, challenges come from the wide range of excitation conditions that water spectra trace in inner disks, including radial and vertical temperature and density gradients and nonlocal thermodynamic equilibrium (non-LTE) excitation (e.g., A. E. Glassgold et al. 2009; R. Meijerink et al. 2009; J. R. Najita et al. 2011; A. D. Bosman et al. 2022; A. Banzatti et al. 2023b). The key to distinguishing different processes and correctly interpreting the observed spectra to obtain a global view of water properties as a function of disk radius lies largely in the possibility of measuring the flux and kinematics of transitions from a wide range of Einstein-A coefficients (A_ul) and a large range in upper-level energy (E_u). With Spitzer-IRS spectra, the most critical limitation to the analysis of water emission properties has come from the low resolving power (R ∼ 600–700, or 450 km s⁻¹), blending multiple transitions and leaving fundamental degeneracies between temperature and column density in slab model fits (R. Meijerink et al. 2009; J. S. Carr & J. R. Najita 2011; C. Salyk et al. 2011). Despite the identification of some important trends with stellar temperature (K. M. Pontoppidan et al. 2010b; I. Pascucci et al. 2013), with stellar and accretion luminosity (C. Salyk et al. 2011; A. Banzatti et al. 2017, 2020), with the formation of an inner disk dust cavity (C. Salyk et al. 2011; A. Banzatti et al. 2017, 2020), and with the dust disk mass or radius as observed at millimeter wavelengths (J. R. Najita et al. 2013; A. Banzatti et al. 2020), the need for higher-resolution spectroscopy has clearly emerged as a priority for making progress in the field after Spitzer.

In spite of the paucity of high-resolution spectra due to the difficulty of observations through the Earth’s atmosphere, recent work using spectrally resolved data from ground-based spectrographs has made some progress after the Spitzer surveys. Infrared water spectra have been found to trace a temperature gradient in the inner regions of protoplanetary disks, when velocity-resolved line widths from a large range in energy levels have been obtained by combining data from different instruments (A. Banzatti et al. 2023b). A gradient is naturally expected by disk models (e.g., A. E. Glassgold et al. 2009; R. Meijerink et al. 2009) but evidence from the data has been slow to emerge. Early fits to Spitzer-IRS spectra initially assumed a single temperature that could well reproduce at least part of the data (J. S. Carr & J. R. Najita 2011; C. Salyk et al. 2011), while pointing out that spectral lines at longer wavelengths seemed to come from colder temperatures (C. Salyk et al. 2011; A. Banzatti et al. 2012). Later, some works explored using temperature gradients that could better reproduce a broader spectral range, in some cases including also far-infrared spectra (K. Zhang et al. 2013; S. M. Blevins et al. 2016; Y. Liu et al. 2019). This is an aspect in which the sharper spectral view provided by the James Webb Space Telescope Mid-Infrared Instrument (JWST-MIRI) can now advance the community understanding of water in inner disks (I. Kamp et al. 2023; E. F. van Dishoeck et al. 2023; T. Henning et al. 2024). Since the first MIRI observations, water emission from multiple temperatures has been confirmed by single-temperature fits to different parts of the emission (A. Banzatti et al. 2023a; D. Gasman et al. 2023; K. R. Schwarz et al. 2024) as well as two- or three-temperature simultaneous fits (K. M. Pontoppidan et al. 2024; M. Temmink et al. 2024) and radial gradient fits to parts of the rotational spectrum at MIRI wavelengths (T. Kaeufer et al. 2024; C. E. Romero-Mirza et al. 2024a).

The identification of multiple temperature regions and characterization of their properties is a significant step toward the goal of determining the water abundance as a function of orbital distance and disk age/evolution. However, the detailed analysis and interpretation of water spectra remains a challenge after two years of JWST observations. Slab model fits to the observed spectra across MIRI wavelengths give different temperature and column density estimates even when similarly simple slab model tools are used (e.g., A. Banzatti et al. 2023a; D. Gasman et al. 2023; K. M. Pontoppidan et al. 2024; K. R. Schwarz et al. 2024; M. Temmink et al. 2024; C. Salyk et al. 2025), and it is currently unclear how much of that depends on the spectral ranges and specific lines being included (or excluded) from the fits rather than from species contamination, spectra quality (including residual fringes), and non-LTE excitation effects that have long been known (R. Meijerink et al. 2009) but have not yet been accounted for in fitting MIRI water spectra.

At the increased resolving power of MIRI, line blending is still an issue for carefully measuring the emission from different energy levels, due to the overlap of multiple water transitions as well as the contamination from a number of atomic and molecular species. A common approach to correctly analyze water spectra and compare results from different studies has not yet emerged, and the identification of reliable lines for breaking degeneracies and isolating or controlling different effects (temperature from opacity gradients, LTE from non-LTE excitation) is still a priority.

It is desirable as a community to agree on a reliable line list and some simple diagnostics that will provide comparisons across samples without biases from different implementations of slab modeling tools and their (often untested) dependence on fitting different line ranges that do not properly account for contamination or non-LTE effects. As a contribution toward defining a common ground for community comparisons, in this work we provide a curated list of reliable single (unblended) lines and demonstrate their use to describe the excitation and kinematic properties of water spectra as observed with MIRI, to provide the community with useful tools for their analysis and interpretation in the growing number of disks being collected in current and future observing cycles. In particular, we develop a general definition of water temperature and column density diagnostic diagrams that will enable empirical, line-flux-ratio comparisons across samples and data sets, to support a broad understanding of water in different conditions and its study across multiple processes that shape inner disk evolution and planet formation.

This paper is organized as follows. In Section 3 we present a spectral atlas of water emission as a general reference to support line identification and analysis, with specific focus on aspects of line blending, contamination, opacity overlap, and non-LTE excitation that are important for a correct analysis of observed spectra. With the atlas, we demonstrate a curated list of single, unblended lines that provides the most reliable flux and broadening measurements to support global analyses of water in inner disks. Using this line list, in Section 4 we define four line ratios that provide a simple general definition of diagnostic diagrams for the temperatures and column density of water emission in individual sources as well as large samples. In Section 5 we present, for the first time, evidence for Doppler broadening of water lines in MIRI–Medium Resolution Spectrometer (MRS) spectra, as well as the detection of unresolved wind blueshifted absorption on top of disk-rotation broadened emission in a disk observed at high inclination. In Section 5.3 we will use this information to perform a simple Doppler mapping of water lines, which can provide an independent estimate of the emitting radii of lines from different upper-level energies. In Section 6 we will combine all of these findings into the discussion of the radial distribution of water in inner disks in terms of radial gradients and of the processes that regulate them, and we summarize the tools into a general recipe to support the analysis of water MIRI-MRS spectra in future samples.

The data analyzed in this work were taken with JWST (J. P. Gardner et al. 2023) between 2023 February and 2024 March. The disks were observed with the MRS (M. Wells et al. 2015; I. Argyriou et al. 2023) mode on MIRI (G. H. Rieke et al. 2015; G. S. Wright et al. 2023). MIRI covers the full wavelength range of 4.9–28 μm with resolving power of 1800–4000 (I. Argyriou et al. 2023; K. M. Pontoppidan et al. 2024; see also Section 5.1.1 in this work) with spatial resolution down to 02 at the shortest wavelengths. The sample included in this work comes from three GO programs in Cycle 1 that defined the JWST Disk Infrared Spectral Chemistry Survey (JDISCS; K. M. Pontoppidan et al. 2024; N. Arulanantham et al. 2025, in preparation): 14 disks from GO-1584 (PI: C. Salyk; co-PI: K. Pontoppidan), eight disks from GO-1640 (PI: A. Banzatti), and three disks from GO-1549 (PI: K. Pontoppidan) for a total of 25 disks. Sample properties are reported in Appendix A. The full sample is described in the overview paper by N. Arulanantham et al. (2025, in preparation). Here we focus on disk spectra of T Tauri stars; i.e., we exclude three disks around intermediate-mass stars (HD 163296, HD 142666, and HD 143006), and we also exclude one disk in a binary system (AS 205 S) that has strong fringe residuals and binary contamination at >18 μm in MIRI. Some spectra have been analyzed and presented before in papers from the JDISCS collaboration: CI Tau, GK Tau, IQ Tau, and HP Tau in A. Banzatti et al. (2023a), Sz 114 in C. Xie et al. (2023), FZ Tau in K. M. Pontoppidan et al. (2024), AS 209 and GQ Lup in C. E. Romero-Mirza et al. (2024a, 2024b), and DoAr33 in M. J. Colmenares et al. (2024).

All spectra were extracted with a wavelength-dependent aperture radius of 1.4 × 1.22λ/D and wavelength-calibrated with the JDISCS pipeline as described in K. M. Pontoppidan et al. (2024), which adopts the standard MRS pipeline (H. Bushouse et al. 2024) up to stage 2b and then uses asteroid spectra observed as calibrators to provide high-quality fringe removal and characterization of the spectral response function to maximize the signal-to-noise ratio (S/N) in channels 2–4 (while a standard star is used in channel 1). Target acquisition with the MIRI imager was adopted to place all targets and asteroids on exactly the same spot on the detector with subspaxel precision, to ensure similar fringes and maximize the quality of their removal. For the data included in this work, we used the latest available JDISCS reduction (version 8.2) that uses the MRS pipeline version 11.17.19 and Calibration Reference Data System context jwst_1253.pmap. Before the gas emission-line analysis presented in this work, all spectra were continuum-subtracted using a median smoothing and a second-order Savitzky–Golay filter with the procedure presented in K. M. Pontoppidan et al. (2024) updated to apply a final offset based on line-free regions as demonstrated in Appendix B. The continuum-subtracted spectra are included in Appendix H.

Figures 1–4 present an atlas of water emission as observed across MIRI spectra, using as an example the spectrum of CI Tau from A. Banzatti et al. (2023a). This spectrum is chosen for multiple reasons: its high S/N (≈450 around 17 μm), the detection of all molecules commonly found in disks (CO, H₂O, OH, HCN, C₂H₂, CO₂, and H₂), and the detection of a large number of atomic lines (dominated by H i with  ∼30 lines), which provide a useful template to illustrate contamination to water lines from other species. Moreover, CI Tau has been used in previous work as a base reference to identify the presence of cooler water at larger disk radii from excess emission in low-energy lines, for being a spectrum that can be described almost entirely by a single hot component (A. Banzatti et al. 2023a; C. E. Romero-Mirza et al. 2024a). This property also makes it a good example to isolate other excitation effects related to line opacity and non-LTE excitation, which will be demonstrated below in this section.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

The atlas is made using the functionalities of iSLAT (E. Jellison et al. 2024; M. Johnson et al. 2024) to compile and export simulated spectra for single-temperature slabs of gas in LTE (defined by an excitation temperature T in kelvin, column density N in cm⁻² and a slab emitting area in au²; e.g., J. S. Carr & J. R. Najita 2011; C. Salyk et al. 2011; A. Banzatti et al. 2012) for multiple molecules and visualize the individual transitions blended at the resolving power of MIRI, using line properties from HITRAN and HITEMP (see Appendix D; I. E. Gordon et al. 2022). Figures 1–4 show model spectra for emission at different temperatures: a “hot” water component (850 K) and a “warm” water component (400 K) as representative of typical temperatures found from slab fits to ground-based or MIRI spectra for a total sample of 10 disks in previous work (A. Banzatti et al. 2023b, 2023a; C. E. Romero-Mirza et al. 2024a; M. Temmink et al. 2024). While these temperature components have been found to describe well the rotational water emission across MIRI wavelengths (12–27 μm), with hotter emission generally dominating shorter wavelengths, an additional “cold” ∼ 170–200 K component, where detected, becomes prominent at longer MIRI wavelengths, in particular in two lines near 23.85 μm with upper-level energies of ≈1500 K (K. Zhang et al. 2013; A. Banzatti et al. 2023a; C. E. Romero-Mirza et al. 2024a; M. Temmink et al. 2024). This component is of particular interest because it traces a temperature consistent with the ice sublimation/condensation front (the “snowline”) in inner disks (120–180 K; e.g., J. B. Pollack et al. 1994; D. D. Sasselov & M. Lecar 2000; K. Lodders 2003). The different spectral line flux distribution of these three components across infrared wavelengths provides a useful general tool for their identification in MIRI spectra, as will be demonstrated in Section 4.

Other molecules are plotted in different colors to illustrate where water emission is contaminated by other species (and vice versa), including atomic lines (which are marked with dotted lines and labeled for identification). The adopted slab model parameters for each molecular model are reported in Appendix D; these are just representative models, not fits to the data, and include different rovibrational components for CO (A. Banzatti et al. 2022) and two components of OH to approximately reproduce their non-LTE excitation, but not the OH asymmetry from prompt emission, though very visible in the data (for detailed analyses on OH excitation in disks, see, e.g., J. S. Carr & J. R. Najita 2014; B. Tabone et al. 2021, 2024; M. Zannese et al. 2024). In the case of CO, the highest J level detected in the first vibrational level in CI Tau is P 69 with E_u ∼ 16,000 K, at 5.544 μm.

3.1. Using the Atlas

Figures 1–4 provide a general reference for several aspects that are helpful for the analysis of water spectra as observed with MIRI-MRS, which are elaborated on below:

1. 1.  
   The level of blending and confusion between different energy levels in each observed water line;
2. 2.  
   water lines that are single, i.e., not blended (at the MRS resolution) with other water transitions from different levels at typical disk temperatures;
3. 3.  
   the relative emission in higher- versus lower-E_u across MIRI wavelengths, which is connected to the emission from different temperatures;
4. 4.  
   contamination of water emission from other molecules and atoms;
5. 5.  
   saturation from line opacity overlap and non-LTE excitation of higher vibrational levels (v > 0).

3.1.1. Water Transitions from Different E_u

The first three points in the list can be visualized as follows. Under the water models in Figures 1–4, the individual transitions that make the observed blended emission are plotted with vertical dashed lines, color coded with a gradient from magenta (higher-E_u) to cyan (lower-E_u) to reflect the upper-level energy. As in iSLAT, the height of these lines in the plot is proportional to their intensity, to visualize their relative contribution in each blend. To provide a maximum case of line blending, we visualize lines from the 850 K model; at lower temperatures, the higher-energy transitions are less excited, and therefore more lines may be dominated by a single, lower-energy transition. However, in this sample, we find that disk spectra generally have the high-energy lines significantly excited and detected aside from a few exceptions (see Appendix H and C. Salyk et al. 2025). Therefore, the spectral atlas Figures presented here should provide a useful general guidance.

From these Figures, it is possible to obtain a quick idea of how many transitions contribute significantly to each observed line/blend, and whether higher- rather than lower-energy transitions are blended in a given observed line. In cases where line clustering is too dense and/or the coloring system is not sufficient to identify individual lines in Figures 1–4, we recommend using iSLAT¹⁷ to inspect interactively any line blends of choice for different temperature and column density values. With this procedure, we have identified a list of single (unblended) water lines whose properties reflect the emission from individual upper levels (Section 3.2); this list provides reliable measurements for a number of analysis goals, which will be demonstrated below.

3.1.2. Contamination from Different Species

For the fourth point, the atlas provides quick identification of contamination from other molecules and atoms. For lines with lower contrast in the Figure, we suggest the use of iSLAT for interactive visualization and inspection. Depending on their relative strength, most water lines between 12 and 16 μm are typically contaminated by lines from OH, HCN, C₂H₂, and CO₂. For this reason, in this work we only use a few lines in this region, lines that, in conditions found to be typical in this sample, are dominated by water emission (Figures 2 and 3). Atomic lines, in particular from H i, are scattered across MIRI wavelengths and also need to be carefully checked to avoid contamination.

Vice versa, the atlas can be used to identify atomic emission lines that are the least contaminated by water or other molecules. In the case of H i, the cleanest, strongest lines are (upper–lower levels): 9–6 (5.91 μm), 14–8 (8.66 μm), 10–7 (8.76 μm), 12–8 (10.50 μm), 10–8 (16.21 μm), and 8–7 (19.06 μm). These lines, when detected, can generally be measured from MIRI spectra even when water emission is present; measuring other H i lines requires subtracting a model for the contaminants first, usually water but sometimes OH or the organics. Other atomic species of common interest, including [Ne ii] and [Ne iii], are all contaminated by water or other molecules and should generally be measured in water-subtracted spectra, unless water emission is absent or very weak. Examples of the water-subtraction process using Spitzer spectra can be found in C. Salyk et al. (2011), E. Rigliaco et al. (2015), and with MIRI spectra in S. L. Grant et al. (2023).

3.1.3. Mutual Line Opacity Saturation

For the fifth point in the list above, the atlas identifies transitions that are of special interest for understanding the excitation and observed flux of specific water lines. Previous work showed that parts of the infrared organic emission features at 13–14 μm may become highly optically thick and saturate due to the dense line clustering. This was observed in extreme high-column density conditions by B. Tabone et al. (2023) in the emission feature of C₂H₂ as observed with MIRI in the protoplanetary disk of a low-mass star. It has not been demonstrated yet where this effect may matter for infrared water spectra, instead, in spite of the fact that line opacity overlap has previously been included in modeling Spitzer spectra (J. S. Carr & J. R. Najita 2011; C. Salyk et al. 2011). With the increased resolving power of MIRI-MRS, we can now better observe where line opacity overlap matters the most. In the case of water, the mutual opacity saturation becomes relevant in several ortho-para (O-P) line pairs that share the same E_u but have different statistical weight and overlap exactly or very closely in wavelength; in these cases, each line contributes to the opacity of the other line, and the observed blended line saturates at lower values of the column density. This effect can be easily identified with iSLAT, which overpredicts the flux of all of these line pairs by ignoring this mutual saturation effect.

To demonstrate the opacity saturation effect in the case of water lines, we add in Figure 5 a new model that uses the same parameters as the iSLAT hot water model, but made with a code that includes mutual line opacity saturation (spectools-ir; C. Salyk 2022). The simulated spectra from the two codes perfectly match, as they should (since they are equivalent, otherwise) except for the orto-para line pairs, where spectools-ir provides a very good match to the data in contrast to the iSLAT model. Therefore, line overlap should be accounted for when fitting water spectra, because many O-P lines pairs are close or coincident in wavelength, such that their fluxes do not simply add when the line's optical depth increases toward thick conditions. For details on existing code that implements this effect for water emission, see spectools-ir¹⁸ (C. Salyk 2022) and iris¹⁹ (C. E. Munoz-Romero et al. 2023).

Zoom In Zoom Out Reset image size

3.1.4. Non-LTE Excitation of Lines in v = 1 and v = 2

Another important effect included in the fifth point in the list above is related to non-LTE excitation. Non-LTE excitation of infrared water emission has been discussed in detail in previous work (R. Meijerink et al. 2009), and recently proposed to explain the observed suppression of the rovibrational bands in comparison to the excitation of pure rotational lines (see A. D. Bosman et al. 2022; A. Banzatti et al. 2023b). The origin of this effect comes from the very different critical densities of water lines from different bands, of the order of 10¹³ cm⁻³ for the rovibrational lines in comparison to 10⁸–10¹¹ cm⁻³ for the v = 0–0 rotational lines (see summary in Table 1 and Figure 13 of A. Banzatti et al. 2023b). This difference implies that rotational lines thermalize at lower gas densities, while rovibrational lines may be subthermally excited if the gas density of the emitting layers in inner disk does not reach ∼10¹³ cm⁻³.

To simulate the subthermal excitation of rovibrational lines, in Figure 1 we used a factor of 4 decrease in emission in comparison to the model of the rotational lines at longer wavelengths (see model parameters in Appendix D), which is enough to approximately reproduce the rovibrational band in CI Tau. A similar factor was found to approximately reproduce the rovibrational band also in the case of FZ Tau in K. M. Pontoppidan et al. (2024). Even with this global reduction factor, v = 2–1 lines are generally overpredicted in comparison to the v = 1–0 lines (Figure 1), pointing again to non-LTE excitation (for this effect in the case of CO lines, see, e.g., A. Banzatti et al. 2022; M. C. Ramìrez-Tannus et al. 2023). We remark that fits to higher-resolution (but much smaller spectral range) spectra from the ground suggested slightly higher temperatures of  ≈1000 K for the rovibrational water band near 5 μm (A. Banzatti et al. 2023b), which is dominated by higher energy levels (4500–9500 K), and therefore, it is more sensitive to gas at higher temperature. However, these higher-energy lines are much weaker and generally blended at the resolution of MIRI, where strong unblended lines are dominated by lower energy levels (Figure 1). We also remark that the suppression factor needed by the v = 1–0 lines in comparison to the rotational lines cannot be explained simply by a smaller emitting area (C. E. Romero-Mirza et al. 2024a), which is nonetheless demonstrated by velocity-resolved line widths from ground-based surveys (A. Banzatti et al. 2023b) and now also from MIRI spectra (Section 5.1).

The excitation mismatch between different vibrational levels is also very visible in the v = 1–1 lines, as resolved by MIRI-MRS and shown in this work for the first time. There is a large number of strong v = 1–1 lines intermixed to the v = 0–0 lines in the main rotational emission region at longer wavelengths (>10 μm; Figures 3 and 4), and these are overpredicted by fits to the v = 0–0 lines as expected in case of subthermal excitation of higher vibrational bands (R. Meijerink et al. 2009). It should be noted that the v = 1–1 lines are still overpredicted by the spectools-ir model in Figure 5, since it still assumes LTE. This is not an issue of the single-temperature approximation: the overprediction of v = 1–1 lines still happens even when modeling the water spectrum, as the sum of two temperatures or as a temperature gradient (by inspecting Figures reporting the best-fit models, the overprediction of some of these lines can in fact be recognized in K. M. Pontoppidan et al. 2024; C. E. Romero-Mirza et al. 2024a; M. Temmink et al. 2024).

As a simple test, we show in Figure 6 that these lines, similarly to the v = 1–0 band at shorter wavelengths, match the observed data reasonably well with the simple suppression of their flux by a single factor common to all lines. In the case of CI Tau, for the v = 1–1 lines, this factor is ∼2. For reference, Figure 7 shows the measured flux ratios in a v = 1–0 line (8.0696 μm) and a v = 1 − 1 line (24.91403 μm) with a v = 0–0 line (16.27136 μm), all with similar upper-level energy of  ≈​​​​​​4800 K and A_ul ≈ 10 s⁻¹. In comparison to LTE models used in this work (Section 4), the measured line fluxes cluster around a suppression of  ∼ 1/6 for the v = 1–0 lines and ∼1/3 for the v = 1–1 lines. The greater suppression in v = 1–0 lines is consistent with them being farther away from LTE due to their higher critical densities (≈10¹³ cm⁻³), requiring denser gas for thermalization. Based on this argument, and if the v = 0–0 lines at 12–28 μm with lower critical density (≈10⁸–10¹⁰ cm⁻³) are instead in LTE, the density of the water-emitting region should be >10¹⁰ cm⁻³ and ≪10¹³ cm⁻³ but probably different across the different disk radii that emit the different water lines (see Sections 4 and 5). A detailed analysis of the relative excitation of v = 1–0 and v = 1–1 lines to derive more specific gas density estimates is deferred to future work.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

3.2. List of Single Unblended Lines Used in This Work

With the list of single lines selected in Section 3, we can now proceed to an update and generalization of the distribution of water emission from different temperatures introduced in previous work. This Section demonstrates that by using a few, carefully selected line ratios it is possible to obtain a simple, model-independent view of the relative emission from water at different temperatures in inner disks before performing time-consuming fits with sophisticated models. For measuring emission-line properties from the spectra, we use iSLAT, which implements the least-squares minimization code lmfit (M. Newville et al. 2014) to perform single-Gaussian fits and measure the line centroid, FWHM, flux, and their uncertainties.

When fitting for two temperatures as well as a temperature gradient, previous work found CI Tau to be the disk most dominated by a hot water component, while GQ Lup to be one with strong emission from additional cooler water at larger radii (C. E. Romero-Mirza et al. 2024a). We show these two extreme cases in Figure 8 to illustrate how the temperature distribution in a MIRI spectrum can be visible by eye from the spectral line flux distribution, i.e., the distribution of line flux as a function of wavelength. This distribution is rather flat with wavelength (i.e., the strongest lines have similar flux across MIRI wavelengths) in the case of a hot-dominated spectrum (CI Tau), while it shows increasingly stronger lines at longer wavelengths when emission from cooler water is present (GQ Lup). This different spectral line flux distribution is exemplified at the bottom of the Figure using slab models at three temperatures representing properties found in previous work, as explained in Section 3 (assuming a cold component at 190 K, to represent results from fits to MIRI spectra; A. Banzatti et al. 2023a; C. E. Romero-Mirza et al. 2024a; M. Temmink et al. 2024), for reference.

Zoom In Zoom Out Reset image size

Leveraging the different spectral line flux distribution of different temperature components, previous work defined an empirical “cool water excess” by using the hot-dominated CI Tau spectrum as a comparative template for other disks, and by measuring excess emission in the lower-energy transitions from a large number of single lines measured across MIRI wavelengths (A. Banzatti et al. 2023a). In this work, we develop a simpler diagnostic that can be applied broadly to future analyses of disk samples observed with MIRI. We use: (i) a hot water model as the base to define the minimum flux in low-energy lines in the absence of emission from cooler water, and (ii) a curated, short list of emission lines from single transitions spanning E_u between 1400 and 6000 K that maximize data quality in terms of S/N and resolving power, absent of residual fringes, and absent of contamination from other species in typical emission conditions as observed in this work’s sample.

4.1. Diagnostic Lines for Temperature and Density

In Figures 9 and 10, we present the selected lines and demonstrate their use as proxies for temperature distribution and column density of the water spectra. These lines are reported in Table 1. From the main list of single lines defined above in Section 3, three are selected to span the entire range of E_u covered by MIRI at the two extremes (near 1500 and 6000 K, avoiding lines at higher E_u that are typically weaker and more likely to be affected by non-LTE excitation), and at intermediate E_u (near 3600 K). These transitions provide three flux ratios that capture the relative emission from different temperature components: the line flux ratio between transitions from 3600 and 6000 K (capturing the relative strength of a “warm” water component, here taken at ≈400 K), and the line flux ratio between transitions from 1500 and 3600 K or 6000 K (for the relative strength of a “cold” water component, here taken at ≈190 K).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Table 1. List of H₂O Transitions Used as Diagnostics

Wavelength	Transitions (Upper–Lower)	Aul	Eu
(μm)	(Format: )	(s−1)	(K)
Label: 1500 K (Temper. Diagnostic—Figures 10 and 11)
23.81676	000-000 8 3 6–7 0 7	0.61	1448
23.89518	000-000 8 4 5–7 1 6	1.04	1615
Label: 3600 K (Temperature Diagnostic—Figure 10)
17.50436	000-000 13 4 9–12 3 10	4.94	3646
Label: 6000 K (Temperature Diagnostic—Figure 10)
17.32395	000-000 16 8 9–15 7 8	41.5	6052
Label: 3340 K (Density Diagnostic—Figure 10)
13.50312 (a)	000-000 11 7 4–10 4 7	0.49	3341
22.37473 (b)	000-000 11 7 4–10 6 5	25.3	3341
Non-LTE Diagnostics—Figure 7
8.0696	010-000 10 5 6–11 6 5	5.95	4868
16.27136	000-000 15 5 10–14 4 11	9.23	4835
24.91403	010-010 9 6 3–8 5 4	18.6	4778

Note. For the 1500 K lines, in Figure 10 we take the combined flux of the two lines listed in this Table, as explained in Section 4. Lines are identified and inspected using iSLAT (E. Jellison et al. 2024; M. Johnson et al. 2024). Line properties are from HITRAN (I. E. Gordon et al. 2022). The full line list used for other parts of the analysis in this work is reported in Appendix C.

Download table as:  ASCIITypeset image

While the low-energy lines near 23.85 μm were already identified as good tracers of sublimation temperatures (∼150–180 K) of water in previous work (K. Zhang et al. 2013; A. Banzatti et al. 2023a), the two lines we use here to trace water at higher temperatures are selected from the 17–17.6 μm range, which achieves the highest S/N and a high resolving power at MIRI wavelengths (Section 5.1). The line selection from different options with similar E_u was made such that the 850 K reference model adopted in this work, labeled with “H” in Figure 10, has all line ratios with a value of ∼1, making it a convenient, easy reference. For this reason, the 1500 K line flux used in the diagnostic diagrams in this work is taken as the sum of the two transitions in Table 1.

Additionally, we identify two lines from the same upper level with E_u = 3341 K and statistical weight of 69 that have very different Einstein-A coefficients (A_ul): 0.49 and 25.3 s⁻¹. This line pair traces the spectral line flux distribution in MIRI spectra near the peak of maximum spread in the rotation diagram (Figure 9), and it is one of the few transitions with largely different A_ul from the same upper level we could find among single unblended lines that are strong enough to be typically detected in disks. The same line pair has been identified independently in D. Gasman et al. (2025). Such transitions can in principle provide useful measurements to help estimate the column density, as recently discussed in D. Gasman et al. (2023) where a selection of blended lines was used as an approximation. In fact, in optically thin conditions, the lower-A_ul transition from the same level will be weaker, while in optically thick conditions, the two transitions will have similar flux, and their flux ratio (defined in this work as the higher-A_ul line, labeled “b,” divided by the lower-A_ul line, labeled “a”) will reflect these two regimes. The hot model in Figure 10 is optically thick, and this line ratio is in fact close to unity. As described in detail in A. Banzatti et al. (2023b), a lower column density in the rotation diagram will be observed as a lower spread in the data, while the opposite will be seen with a larger column density. These different regimes are well illustrated by the two examples included in Figure 9. A caveat to keep in mind for the more optically thin of these lines, that at 13.50 μm, is that it is contaminated in case of strong organic emission relative to water, as note above for DoAr 25, GO Tau, and MY Lup.

4.2. Definition of General Water Diagnostic Diagrams

The diagnostic line flux ratios are shown in Figure 10 as measured across the entire disk sample included in this work. The spectra of CI Tau and SR 4 lie closest to the hot model (specifically with a slab radius of ∼0.5 au; left panel in Figure 10) as expected from visually inspecting their spectra, since both have a flat spectral line flux distribution (Figure 8 and Appendix H). The rest of the sample shows a wide range of diagnostic line luminosities (a factor of ​​​​​​≈100) and ratios (factors of ≈1–10) that can be interpreted in the framework of sequential combinations of discrete LTE components (the model series are fully explained and reported in Appendix D and Figure 25) as an approximation of radial gradients (Section 6.1). Each model track in Figure 10 corresponds to the 850 K model (H) plus a sequentially increasing emitting area of the 400 K component (H+W model series) and of a 190 K component (H+W+C model series). All disks in this sample require some emission from the warm component as indicated by the 3600/6000 K line ratio (middle and right panels), from about 2× the slab radius of the hot component (e.g., CI Tau) to about 6× that radius (the end of the model track in the Figure).

The 3340 K line ratio, sensitive to the column density of the 400 K component, indicates that water emission in this sample is moderately to highly optically thick (the data points cover the region between the dashed and solid lines in the middle panel, showing column densities from 5 × 10¹⁷ cm⁻² to 5 × 10¹⁸ cm⁻²). As noted above, in disks with strong organic emission relative to water, this line ratio is contaminated and shows values as low as ∼0.5, as measured in DoAr 25 and MY Lup.

Emission at colder temperatures becomes prominent in the 1500 K lines, and their ratio with the 3600 K and 6000 K lines. The 1500/3600 K line ratio in the right panel in Figure 10 shows that while about 50% of the sample lies between the H+W model tracks, consistent with a hot component plus a warm-water component, the other 50% requires additional emission from colder water. The H+W+C model track shown in the Figure to approximately align with the data points with the highest measured 1500/3600 K ratios shows areas of the cold component between 2× the slab radius of the warm component to about 6× that radius (the end of the model track in the Figure), as with the H+W model series above.

The position of a given disk in the diagnostic diagrams can therefore be used to obtain an estimate of the slab radii, column density, and relative emitting areas of different temperature components that are found from slab fits to their spectra, as well as for comparative analyses of different disks. For instance, both CI Tau and FZ Tau are dominated by a hot component with some contribution from warm water, as found in previous fits (K. M. Pontoppidan et al. 2024; C. E. Romero-Mirza et al. 2024a). Relative to CI Tau, the position of FZ Tau in Figure 10 indicates a more extended and more optically thick warm component, consistent with the results from radial gradient fits to the line fluxes (C. E. Romero-Mirza et al. 2024a). As for disks requiring emission from colder water, three disks that align with the H+W+C track in the diagram (GK Tau, GQ Lup, and IQ Tau) have indeed been found to have water emission down to sublimation temperatures near the snowline (∼170–200 K; A. Banzatti et al. 2023a; C. E. Romero-Mirza et al. 2024a). The line ratios in GQ Lup show more extended 400 and 190 K components in comparison to GK Tau, consistent with the more extended cold water area found by fits (C. E. Romero-Mirza et al. 2024a). In the larger sample included in this work, we now find a disk with an even stronger cold water component: IRAS 04385+2550, a more embedded disk in Taurus associated with the Herbig-Haro object HH 408 (K. Stapelfeldt et al. 1999; G. H. Schaefer et al. 2009; J. Bally et al. 2012) that might be in an earlier phase of strong pebble drift. Cases where the hot water emission is strongly reduced or absent and the observed spectrum can be reproduced mostly by a warm and/or cold water component may provide only lower limits in some line flux ratios, such as is found in MY Lup that is well reproduced by a single ∼300–400 K component (C. Salyk et al. 2025).

The coldest emission observed with MIRI has been modeled in a few disks in previous work, finding temperatures of 170–200 K (A. Banzatti et al. 2023a; C. E. Romero-Mirza et al. 2024a; M. Temmink et al. 2024). Here, we introduce a simpler diagnostic for the coldest temperature that is detected with MIRI: the flux asymmetry between the two 1500 K transitions, where cooler temperatures produce stronger emission in the 1448 K line at 23.867μm. In Figure 11, we demonstrate this new diagnostic by taking a grid of slab models between a temperature of 150 and 850 K and a column density between 10¹⁶ cm⁻² (giving optically thin emission) and 10¹⁹ cm⁻² (giving optically thick emission), spanning the entire range of conditions adopted above in this work. We simulate their spectra as for the models shown in Figure 4 and measure the line flux of these two transitions over the same range as done for the data. We then plot the model line ratio as a function of the slab temperature for the different column density curves in Figure 11. This model grid illustrates that temperatures above 320 K produce a stronger 1615 K line, or an equal flux in the two lines (a ratio of ∼1) in case of optically thick emission. At temperatures <320 K, the 1448 K line becomes increasingly stronger, especially for lower values of column density (optically thin emission).

Zoom In Zoom Out Reset image size

We distribute the line flux ratios measured in the sample along the 10¹⁷ cm⁻² model, assuming it represents an average column density for this component (as found for the coldest water detected in radial temperature profiles in C. E. Romero-Mirza et al. 2024a). With this column density, the line asymmetry gives evidence for a temperature of 170–200 K in five disks (IRAS-04385, GK Tau, IQ Tau, Sz 114, Sz 129),²⁰ five more for a temperature up to 220 K (HP Tau, GQ Lup, TW Cha, RY Lup, AS 205 N) and five more for a temperature of 220–250 K (VZ Cha, Elias 24, Elias 20, WSB 52, Elias 27). In general, these models show that a line ratio >1 requires temperatures <​​​​​​350 K and a ratio of >1.2 needs temperatures <220 K for any column density explored here. In total, therefore, more than 50% of this sample has evidence for water emission at temperatures 170–250 K, close to and consistent with that expected for the snowline region (K. Lodders 2003). These disks also have larger 1500/3600 K and 1500/6000 K ratios (the latter one shown in the right panel in Figure 11) indicative of having a greater reservoir of cold water, as demonstrated in Figure 10. To confirm the exact temperature and determine the column density of water near and across the snowline, lower-energy lines at longer wavelengths need to be included as previously provided from Spitzer or Herschel (K. Zhang et al. 2013; A. Banzatti et al. 2023a) or from a future far-infrared observatory (K. M. Pontoppidan et al. 2018; K. Pontoppidan et al. 2023; I. Kamp et al. 2021).

4.3. Trends with Accretion, Inclination, and Disk Size

In reference to previous work that found correlations in water emission as observed with Spitzer or ground-based instruments (C. Salyk et al. 2011; A. Banzatti et al. 2020, 2023b), it is important to test for correlations between the line fluxes and ratios used in Figure 10 and the accretion luminosity, one of the strongest correlations found before, and the disk inclination, for comparison to the inclination effects that will be shown later in Section 5. In Figure 12, we confirm with the new MIRI spectra that rotational water emission correlates with accretion and anticorrelates with disk inclination. The slope steepens with E_u in both cases, as found in A. Banzatti et al. (2023a) in the case of the correlation with accretion (linear correlation parameters are reported in Appendix E). These correlations support the idea that inner disk irradiation and heating determine the size of the emitting areas for water at different temperatures, as suggested in previous work (C. Salyk et al. 2011; A. Banzatti et al. 2023b, 2023a). The anticorrelations with disk viewing angle are less trivial to interpret, as they could depend on the geometry and obscuration of different regions between a vertical inner dust rim and the disk surface at larger radii; these trends will be further analyzed in future work. The water line ratios, instead, do not correlate with these properties, suggesting that the relative areas of emitting regions for water reservoirs at different temperatures are not set primarily by accretion and are independent of the viewing angle.

Zoom In Zoom Out Reset image size

Another known correlation to test in the context of water emission from inner disks is with disk sizes as measured at high angular resolution with the Atacama Large Millimeter/submillimeter Array (ALMA). In Figure 13, we show the trends between the three line ratios and the millimeter dust disk size following previous work (A. Banzatti et al. 2020, 2023a; see Appendix A for the millimeter data references). In this Figure, we include in the linear regression only the subsample of full disks around single stars and without millimeter inner dust cavities or signs of being in younger embedded phases (cloud/envelope contamination, including the case of IRAS-04385 associated with an Herbig-Haro outflow). The reason for this selection is to isolate the effects of gas and dust transport through the disk from other effects that may regulate the observed inner water vapor due to age and environment, inner disk depletion, and binary interactions (e.g., M. C. Ramìrez-Tannus et al. 2023; G. Perotti et al. 2023; S. L. Grant et al. 2024; C. Salyk et al. 2024; K. R. Schwarz et al. 2024). The measured line diagnostics in the context of these effects will be analyzed in upcoming papers.

Zoom In Zoom Out Reset image size

The anticorrelations detected in line ratios in the subsample of eight disks in Figure 13 (with regression parameters reported in Table 10 in Appendix E) correspond to what was previously found in four disks in A. Banzatti et al. (2023a), which used a larger line list but similar energy levels. The correlation is detected only in the 1500/6000 K and 3600/6000 K line ratios, suggesting that the underlying physical process regulates the flux (here interpreted as emitting area) observed in the 170–200 K and 400 K water components relative to the hot inner water reservoir, which is instead mostly regulated by accretion (A. Banzatti et al. 2023a). The 3340 K line ratio, instead, does not correlate with disk size, suggesting that the column density of the 400 K component is independent from the underlying process driving this correlation. The discussion of these correlations in the context of pebble drift delivering water ice to the snowline, following previous work, is provided in Section 6.

The figures in this Section are provided as future reference for fundamental dependencies of the observed line luminosities to system parameters, which will help interpreting water spectra of specific disks. Multiple factors play a role in driving the physical or chemical properties of the water-emitting regions in inner disks, and distinguishing their relative role in specific cases will not be trivial. However, based on previous work and Figure 12, we can expect that the water luminosity generally correlates with accretion, and with stronger correlation for higher energy levels. We can also generally expect that the viewing angle plays a role in how we observe water spectra, with a luminosity that decreases at higher inclinations.

Building upon previous work, the diagnostic diagrams defined above in Section 4 and Figure 10 demonstrate that different disks have different fractions of temperature components in their inner disk, showing up as a different spectral line flux distribution where hotter emission populates higher-E_u, and colder emission emerges at lower-E_u to the extent to which it is present in a given disk. This is consistent with results from ground-based higher-resolving-power spectra, which additionally measured a gradient in line widths with broader higher-energy lines and narrower lower-energy lines directly demonstrating a temperature gradient across disk radii (see Figure 13 in A. Banzatti et al. 2023b). The recent characterizations of the resolving power of MIRI (I. Argyriou et al. 2023; K. M. Pontoppidan et al. 2024) now open the way to test whether some water lines may be partially spectrally resolved. If this is true, we could determine their orbital region (not just the equivalent emitting area provided by the slab models used so far to fit MIRI spectra) from the observed kinematics and improve estimates of the radial distribution of water indicated by the line flux ratios in Figure 10.

In this Section, we present the detection and a first general analysis of disk-rotation Doppler line broadening measured in MIRI spectra. Even in this case, the list of single unblended lines presented in Section 3 turns out to be very important to provide the most reliable measurements of line widths across MIRI wavelengths.

5.1. Doppler Broadening of Emission Lines

Potential inclination effects on the observed MIRI spectra were pointed out in A. Banzatti et al. (2023a) in the case of the high-inclination (62 deg) disk of IQ Tau, which showed broader lines than the nominal resolving power and a more compact slab emitting area than in three other disks. In reference to this finding, Figure 14 shows the single water line at 17.35766 μm (E_u ∼ 2400 K) for selected targets where high-quality rovibrational CO lines are available at high resolving power from ground-based spectrographs. Figure 14 demonstrates that, just like the high-resolution CO lines, the MIRI water lines also become broader at higher disk inclinations, suggesting a similar effect of rotational Doppler broadening from gas in the disk. By extending the sample and systematically measuring the line widths in all disks, we can now conclusively test Doppler broadening as a general effect in MIRI spectra.

Zoom In Zoom Out Reset image size

Figure 15 presents clear evidence for disk-rotation Doppler broadening of line widths measured with MIRI. For water, we split the measured line widths (using the same line list presented above and reported in Appendix C) into three panels: one for rovibrational lines at <9 μm, one for rotational lines at <18 μm, and one for rotational lines at >18 μm. In each case, we show the median FWHM value as measured in single lines from the main line list (Section 3.2) in each disk to capture a representative line broadening in each wavelength range. The measured FWHM will be deconvolved to estimate physical emitting radii in Section 5.3. The top panel shows the line FWHM against disk inclination, which should show a positive trend when lines are broadened by Keplerian rotation in a similar inner disk region as observed from a range of viewing angles. The bottom panel shows the FWHM of MIRI lines against the FWHM of v = 1–0 CO lines measured at much higher resolving power (R > 50,000) with ground-based spectrographs in previous surveys (RU Lup, FZ Tau, GK Tau, and CI Tau with iSHELL from A. Banzatti et al. (2022), IQ Tau with CRIRES from J. M. Brown et al. (2013) as available on SpExoDisks²¹ (C. I. Wheeler et al. 2024), which should correlate if they are both broadened by Keplerian rotation in the inner disk. High-resolution spectra from the ground have already shown that CO and H₂O lines share a similar shape and broadening at 4.6–12.4 μm (for an overview, see A. Banzatti et al. 2023b), and the correlations now found with line widths from MIRI spectra extend this finding to wavelengths of >13 μm for the first time. At the lowest disk inclinations, the narrowest lines are consistent with the nominal MIRI resolving power (except for the rovibrational lines) as measured in previous work (I. Argyriou et al. 2023; K. M. Pontoppidan et al. 2024), which is reported in each panel of the Figure for comparison. In the case of the three water emission ranges illustrated in Figure 15, we show median values of the nominal resolving power of MIRI over the relevant wavelength ranges.

Zoom In Zoom Out Reset image size

For comparison to the H₂O lines, Figure 15 reports the trends observed in lines from other species (measured with average significance of 12σ–17σ in this sample): a single hot OH line at 14.62 μm (E_u = 10,754 K, the only single OH line we can find at MIRI wavelengths, which may include some contamination from organics depending on the relative strength; see Figure 3), a lower-energy OH line pair that overlaps in wavelength at 23.07 μm (with E_u ∼ 4100 K), the P26 line of v = 1–0 CO emission (one of the only three unblended CO lines in MIRI spectra with minimal contamination from water and other higher-energy CO vibrational lines, together with P25 and P27), and the H₂ 0–0 S(1) line near 17 μm, which is well separated from emission from other molecules (all other H₂ lines except for S(3) are too weak or significantly blended; see Figures 1–3). While water, CO, and partly OH show similar evidence for Doppler broadening, supporting their disk origin, the H₂ line width does not increase with inclination, suggesting that the line is typically unresolved. Another H₂ line that can be measured is the S(3) line at 9.665 μm (Figure 2). This line also provides evidence for being unresolved in MRS spectra (Figure 16), but it is blended in its wings with H₂O and OH lines, which can contaminate its measured FWHM in case of relative weak emission (e.g., FZ Tau). The other H₂ lines covered by MRS are all blended with H₂O but are still consistent with the local resolving power at each wavelength. That H₂ is unresolved in MRS spectra is consistent with a non-disk origin for H₂ emission, which is indeed observed to trace outflows and winds in young disks (e.g., Y.-L. Yang et al. 2022; N. Arulanantham et al. 2024; V. Delabrosse et al. 2024). Another option could be extended emission from larger disk radii (therefore narrower lines) than the emission from other molecules detected in MIRI spectra.

Zoom In Zoom Out Reset image size

5.1.1. Updates on the MIRI Resolving Power

The data in Figure 15 show that the narrowest lines are found at low inclinations, as expected from Keplerian broadening. We can therefore use MIRI spectra of low-inclination disks to measure the MIRI resolving power, as was done recently in K. M. Pontoppidan et al. (2024). This is done in Figure 16, where three targets are selected for their low inclination (FZ Tau, 22 deg, and RU Lup, 19 deg) and low stellar mass (Sz 114, 21 deg, 0.2 M_⊙), which provide the best conditions to have unresolved lines across the MIRI spectrum. Their line measurements are shown in reference to the MIRI resolving power from I. Argyriou et al. (2023), which used H i and forbidden lines from a planetary nebula, and K. M. Pontoppidan et al. (2024), which used water and CO lines from the protoplanetary disk of FZ Tau.

The characterization from K. M. Pontoppidan et al. (2024) is confirmed overall, including the much higher resolving power in channel 4 in comparison to that estimated in I. Argyriou et al. (2023). In this updated analysis, we identify a few sub-bands where the resolving power is slightly better than what was previously found in K. M. Pontoppidan et al. (2024), and we provide the updated profile in Figure 16 (the red dashed line) and tabulated in Table 11 of Appendix F. In particular, we identify the H₂ line at 17.035 μm as providing a useful anchor point showing a higher resolving power than what the nearby water lines show, suggesting that these might be partially resolved in disks. By taking the median value of measurements for this H₂ line in this sample, we estimate FWHM_MRS  ∼ 93 km s⁻¹, i.e., about ∼10 km s⁻¹ better than what was estimated in K. M. Pontoppidan et al. (2024) at this wavelength.

5.1.2. Doppler Broadening as a Function of E_u

Another very interesting trend emerges from considering line broadening as a function of upper-level energy E_u. This can be easily analyzed over small spectral ranges where the resolving power is approximately constant, to avoid confusing the signal with a changing resolving power with wavelength. This was one of the reasons why we selected lines between 14.4 and 17.6 μm in Section 3.2: the resolving power is approximately the same (see Figure 16), and there is a good number of single (unblended) lines that can be used for FWHM measurements. If water emission comes from a radially narrow region that can be well approximated with a single-temperature component, we should not expect an observable trend between the measured line FWHM and E_u. Instead, if water emission comes from a more extended disk region that has a larger temperature gradient as suggested by ground-based work (A. Banzatti et al. 2023b), we may be able to measure a trend between FWHM and E_u, where the lower-E_u lines should become increasingly narrower.

This is exactly what is observed in the data when comparing two disks that have previously been proposed to be in these two different situations. Figure 17 shows that the spectrum of GQ Lup, with one of the strongest and most extended cool water components found so far, has a clear trend between FWHM and E_u, while the same lines in CI Tau are flat with E_u. The rest of the sample is shown in Figure 26 in Appendix G. This finding provides new, independent confirmation of previous work that proposed water to trace an extended disk region in disks with increased emission from low-energy lines (A. Banzatti et al. 2023a; C. E. Romero-Mirza et al. 2024a). Line broadening will be applied in Section 5.3 to extract radial profiles from the observed water emission.

Zoom In Zoom Out Reset image size

5.2. Water and CO Absorption at High Inclinations

If lines observed with MIRI-MRS are rotationally broadened at high inclinations, as demonstrated in the previous Section, we could also expect to observe absorption on top of emission lines with different Doppler broadening, since this is observed at high resolution from the ground (e.g., K. M. Pontoppidan et al. 2011; J. M. Brown et al. 2013; A. Banzatti et al. 2022, 2023b). The best test case should be a high-inclination disk with deep blueshifted absorption observed in rovibrational CO emission from the ground, since absorption is observed to deepen at higher disk inclinations possibly due to a larger portion of an inner disk wind intercepted along the line of sight (K. M. Pontoppidan et al. 2011; A. Banzatti et al. 2022). In our sample, this is the case of IQ Tau, whose CO rovibrational line shape shows broad double-peaked emission (due to its high inclination of 62 deg) with at least one blueshifted absorption component (Figure 14, previously shown in J. M. Brown et al. 2013).

Figure 18 shows portions of the rovibrational CO and H₂O spectra from the MIRI spectrum of IQ Tau, confirming the scenario proposed above. The spectral lines of both molecules show a broader and more complex shape than in other disks in this work, a shape that can be excellently matched with the simple difference of two spectra (red total model in Figure 18): a hotter spectrum in emission at the radial velocity (RV) of the star (with FWHM = 150 km s⁻¹, much larger than the nominal resolving power at these wavelengths, as already shown in Figure 15), and a colder spectrum blueshifted by −7 km s⁻¹ (with FWHM = 80–90 km s⁻¹). The models used for absorption adopt a similar column density of 1–5 × 10¹⁷ cm⁻². While the models in this Figure are just for quick demonstration, we remark that the data seem to clearly show two aspects: that the absorption spectrum is blueshifted, and that it is cooler than the emission spectrum. The different temperature is most evident from the v = 2–1 CO lines, which are less absorbed than the v = 1–0, and in the water lines, where it is the low-energy lines that have the most significant absorption (see color coded transitions in Figure 18).

Zoom In Zoom Out Reset image size

This finding opens up the possibility to distinguish and study blueshifted absorption from inner disk winds in molecular disk spectra observed with MIRI. At the same time, it highlights the importance of having high-resolution molecular spectra from ground-based instruments, that easily distinguish absorption and blueshifted winds in the velocity-resolved line profiles (for a recent overview, see A. Banzatti et al. 2022), to support the analysis of MIRI spectra. Detailed analysis of the molecular wind absorption spectrum in IQ Tau and other disks is left for future work. For a detailed discussion of the analysis of water absorption spectra as observed with MIRI-MRS, see J. Li et al. (2024).

One immediate practical application in this work is that we can use measurements of absorption lines in IQ Tau, which have an FWHM of ≈7 km s⁻¹ (A. Banzatti et al. 2022) and are therefore surely unresolved with MRS, to improve the characterization of the MIRI resolving power at the shortest wavelengths. This is shown in Figure 16, where we add with empty red data points the measured FWHM of absorption lines from IQ Tau. These confirm that the resolving power is close to that estimated in I. Argyriou et al. (2023), and demonstrate that rovibrational CO and H₂O emission lines are generally partially resolved by the MRS in protoplanetary disks, consistent with their small emitting radius obtained from the large line broadening observed at high resolution from the ground (A. Banzatti et al. 2023b).

A decrease in rovibrational line broadening was in fact visible even in Figure 15 in disks at inclinations >50 deg (region marked with a red arrow), with IQ Tau providing the most extreme case where CO and H₂O lines decrease down to the MIRI resolving power. This suggests that rovibrational CO and H₂O absorption may be present and observable in MIRI spectra in disks at inclinations >50 deg, which should be checked when the rovibrational lines are to be analyzed. In the sample analyzed here, in addition to IQ Tau, absorption seems to be visible in GQ Lup and possibly Elias 20 and GO Tau. In the case that high-resolution spectra from the ground are available, they can provide useful guidance on whether to expect absorption to be present in a specific disk; however, ground-based observations are not always available nor possible for MIRI targets. Cases where absorption is not as significantly blueshifted as in IQ Tau (Figure 14), e.g., CI Tau, may only result in weaker lines and not be easily detected from the MIRI spectra alone (see previous discussion in A. Banzatti et al. 2023b).

5.3. Doppler Mapping of MIRI Water Lines

The data shown in Section 5 and Figures 14, 15, and 17 demonstrated that individual molecular lines in MIRI-MRS spectra may be rotationally broadened beyond the MIRI resolving power (except for H₂), depending on the disk inclination and the upper-level energy of the emitting lines. This finding, in addition to the strong correlations with the FWHM of rovibrational CO lines as observed from the ground at high resolving power, supports the idea that MIRI lines are rotationally broadened by the Doppler effect in an inner disk with an inside-out temperature gradient. In this Section, for simplicity we assume that the Doppler broadening can be simply described by Keplerian rotation in the disk; for an overview and discussion of the possible contamination by a slow disk wind to the narrow CO components, see K. M. Pontoppidan et al. (2011) and A. Banzatti et al. (2022).

In Figure 19, we illustrate one example of how Keplerian rotation in the disk broadens MIRI lines beyond the resolving power. With solid lines, we show the FWHM produced by gas in Keplerian rotation at 0.2 au (which should be appropriate for high-energy lines; see overview in A. Banzatti et al. 2023b) for a range of stellar masses between 0.25 and 1 M_⊙. With dashed lines, we show how the Keplerian models would be observed after convolution with the MIRI-MRS resolving power, by assuming . We do not include any thermal broadening component, as it is negligible (<5 km s⁻¹) at the temperatures relevant for this work (<1000 K; see, e.g., R. Meijerink et al. 2009; C. E. Romero-Mirza et al. 2024a; K. M. Pontoppidan et al. 2024). As can be seen from the models, Doppler broadening should become detectable in high-S/N spectral lines starting at inclinations as low as ∼​​​​​​20 deg, especially in disks around stars with larger mass.

Zoom In Zoom Out Reset image size

For comparison to the models, we include the 17.32 μm (E_u ∼ 6000 K) line from Table 1 tracing hot water emission for a representative sample of targets that spans the entire range in disk inclinations included in this work, with masses between 0.2 and 1 M_⊙ (color coded in the same way as the models, for comparison). This line is confirmed to be consistent with tracing disk radii at ∼0.2 au in a few disks that overlap with their stellar-mass model curve (e.g., CI Tau). Instead, disks falling above their stellar-mass curve indicate emission from smaller radii (IQ Tau), and those falling below indicate emission at larger radii (GQ Lup). For reference, we also show the H₂ line that reflects the MIRI resolving power near 17 μm (Section 5.1.1).

The simple Doppler mapping technique illustrated in Figure 19 is generally applied to multiple MIRI lines in Figure 20, providing a radial excitation profile with line upper-level energies as a function of their Keplerian emitting radius from the line broadening. In Figure 20, as examples, we include two disks that were previously identified to have a hotter and supposedly more compact versus a colder and supposedly more extended emission, the same disks shown in Figure 17. Here we use the line FWHM/2 = HWHM (for the Keplerian velocity V_Kepl from one side of the disk) as deconvolved with the local MIRI resolving power (Section 5.1.1), for the same sample of lines used for Figure 17. The radial excitation profiles in Figure 20 provide a new demonstration, completely independent from the temperature fits made in previous work, for the different distribution of water in these disks (A. Banzatti et al. 2023a; C. E. Romero-Mirza et al. 2024a): in CI Tau (large, multi-gapped disk dominated by a single hot water component, proposed to have a reduced icy pebble drift) confined within ≲0.35 au, and in GQ Lup (compact disk with strong warm and cold water components, proposed to have a stronger water enrichment from pebble drift) extending out to >​​​​​​1.5 au. A fit to the radial profiles in Figure 20 confirms the relative difference and slopes in radial gradients estimated from power-law fits to the line fluxes in C. E. Romero-Mirza et al. (2024a), highlighting the potential in future work to improve model fits to MIRI spectra by including both line excitation and line broadening.

Zoom In Zoom Out Reset image size

An important caveat to consider is that these regions are derived from the line broadening (which can be resolved in MIRI spectra) and only provide a characteristic emitting radius that does not reflect the full radial extent of the emission, which would be shown from the velocity of the typical double peaks from Keplerian rotation (which instead cannot be resolved in MIRI spectra). However, the Keplerian radii estimated from MIRI spectra can be used for relative comparisons between different disks and for comparing the relative emitting region of different lines in a given disk. For instance, CI Tau shows that rovibrational lines are emitted from smaller disk radii than the rotational lines, as found before in higher-resolution spectra from the ground (A. Banzatti et al. 2023b). The rovibrational lines in GQ Lup (incl = 60 deg) are instead very weak and possibly include absorption (see discussion in Section 5.2), providing only a few uncertain estimates in Figure 20.

For comparison to the water radial profiles, we include in Figure 20 the Keplerian radii estimated in the same way for the CO and OH lines that have been measured in this work (Figure 16 and Appendix C). The radial gradient in CO lines shows a very similar slope to the water gradient in both disks. The comparison to water profiles can be useful, but it should be kept in mind that these are only simple approximations of the CO distribution in the inner disk, because MIRI-MRS spectra cannot resolve the multiple CO components shown by ground-based spectra that fully resolve the line profiles (see, e.g., discussions in A. Banzatti et al. 2022; A. Banzatti et al. 2023b).

In this Section, we discuss some important applications of the tools and findings presented above to study MIRI water spectra in protoplanetary disks, with the intent to provide a helpful framework for community efforts and a common ground for comparisons across different samples.

6.1. The Radial Distribution of Water in Inner Disks

The diagrams in Figure 10 have been introduced for providing a simple, general view of the relative emission from water at different temperatures. These simple diagnostics can provide a helpful starting point before performing detailed fits with slab or more sophisticated models, and provide an empirical framework for comparisons across data sets and samples independently from different modeling tools. As described in Section 4, the position of a given disk in the diagnostic diagrams informs on whether a warm ∼400 K and a cold ∼170–200 K component significantly contribute to its water spectrum in addition to a hot ∼850 K component that is commonly (but not always) present, and on the column density of a ∼400 K component. These discrete components are only a convenient approximation of the radial gradient previously found in inner disks (A. Banzatti et al. 2023b), as shown in recent work from fits to the MIRI line fluxes (S. L. Grant et al. 2024; C. E. Romero-Mirza et al. 2024a; M. Temmink et al. 2024) and demonstrated for the first time from their Doppler broadening in this work (Figure 20).

6.1.1. Combining Line Flux and Broadening Information

The detection of Doppler broadening in MIRI lines provides additional physical information to improve the interpretation of the position of a given disk in Figure 10 in terms of the radial distribution of water. The line broadening in Figure 20 shows that a disk like CI Tau that sits close to the 1,1 point in the diagnostic diagram has lines from all E_u emitting from a compact inner disk annulus at ∼0.1–0.3 au, with only a slightly larger emitting radius for the lower E_u ∼ 1500 K. This explains why it has been found in previous work to be well reproduced by a single high-temperature component (A. Banzatti et al. 2023a; C. E. Romero-Mirza et al. 2024a). Instead, a disk like GQ Lup that sits along the W+H+C model track in Figure 10 shows a line broadening gradient in Figure 20 that corresponds to a much larger span of disk radii, with lower-E_u lines emitted from up to 10× larger radii than the higher-E_u lines. This explains why this disk has such strong 1500 K lines indicating a strong cold component, as shown above in this work and in C. E. Romero-Mirza et al. (2024a). An extended radial emitting region for water was generally expected from disk models and velocity-resolved surveys (Figure 13 in A. Banzatti et al. 2023b), but has never been directly observed from the broadening of water lines at >13 μm before this work.

We now compare the flux and broadening measurements from MIRI spectra in Figure 21, using the subsample of disks in this work where Doppler broadening is detected across all energy levels (Appendix A). Figure 21 shows the ratio of Keplerian radii (each radius obtained from the deconvolved half-width at half-maximum, HWHM, as in Figure 20) as a function of the diagnostic line flux ratios used above in this work. To use a representative Keplerian radius for each bin in E_u, we take the median radius of lines included in Figure 20 for each of these ranges: 1400–1700 K, 3000–4000 K, and 6000–6500 K. Figure 21 shows the example of the 1500/6000 K line ratios (their flux ratio and Keplerian radius ratio), which maximizes the range of values measured in the spectra (as the cold component should be generally the most radially extended). With the exception of IQ Tau (the same high-inclination disk where wind absorption is detected; see Section 5.2), the general trend in this Figure shows that a higher line flux ratio corresponds to emission in the cold component from larger disk radii. Therefore, the line broadening measurements independently support the interpretation of Figure 10 as providing a quick reference for the radial distribution of water in the inner disk, which we approximated above with three temperature regions, as illustrated in the right panel of Figure 21, adapted from A. Banzatti et al. (2023a).

Zoom In Zoom Out Reset image size

6.1.2. Radial Gradients in the Main Diagnostic Diagram

After demonstrating that both the line flux ratios and the line broadening show the radial distribution of water emission in inner disks, we illustrate in Figure 22 the interpretation of the main diagnostic diagram introduced in this work in the context of radial gradients. We adopt the parameterization in temperature and column density recently applied to fit water spectra for part of this sample in C. E. Romero-Mirza et al. (2024a). For a general demonstration, we adopt the power-law profiles adopted in that work as T = T₀(r/0.5 au)^−α and N = N₀(r/0.5 au)^−β with representative values from their best-fit results: T₀ = 450 K, N₀ = 1 × 10¹⁸ cm⁻², β = 1, and α between 0.4 and 0.7 (Figure 22). We also consider a cutoff radius for the radial profiles between 0.75 au and 10 au, beyond which the water column density drops to zero (as an approximation for the tapered profiles in C. E. Romero-Mirza et al. 2024a). In the diagnostic diagram, the line ratios provided by this grid of models reproduce the entire range of those measured in this sample (right panel in Figure 22) similarly to the discrete temperature components described in Section 4, again supporting that they can be used to approximate a power-law radial gradient (C. E. Romero-Mirza et al. 2024a; M. Temmink et al. 2024).

Zoom In Zoom Out Reset image size

Similarly to the discrete temperature components used in Figure 10, the power-law models in Figure 22 show that a larger 3600/6000 K line ratio indicates a less steep temperature gradient, where the inner disk has more emission from warm water at intermediate radii. A larger 1500/3600 K line ratio, instead, is indicative of colder water at larger distances out to the cutoff radius. Most of the sample included in this work can be well reproduced by gradients with temperature slopes between 0.7 (for the disks dominated by hotter emission, e.g., CI Tau) and 0.5 (for the disks with significant emission from colder water, e.g., GK Tau and GQ Lup), and cutoff radii between <1 au and 4 au, matching well the fit results found in part of the sample in C. E. Romero-Mirza et al. (2024a). This demonstrates that the main water diagnostic diagram introduced in this work (with the 1500/3600 K and 3600/6000 K line flux ratios) can be used as a simple proxy for temperature gradients too, and to provide input to more detailed fits. We note instead that the 3340 K line flux ratio introduced above as a diagnostic for the column density at ∼400 K shows a more complex dependence in the grid of power-law radial profiles, suggesting that it may be more degenerate than what the discrete components show in Figure 10. A more complete and detailed analysis of the diagnostic line ratios in terms of radial gradients is left to future work.

6.1.3. What Regulates the Water Abundance in Inner Disks?

The correlations reported in Section 4.3 are indicative of some of the major processes that determine the water distribution in inner disks. The emitting area of the hotter, optically thick inner water reservoir can be considered to be set by the disk irradiation and heating, based on the strong trend with accretion luminosity (Figure 12). Water lines at lower energy levels also correlate with accretion, but with a larger scatter that can be interpreted as due to other processes that become increasingly important for the colder water reservoir. Of these processes, radial transport of water ice toward the snowline especially through pebble drift, followed by ice sublimation that enriches the observed water vapor at low temperatures, continues to be supported by the correlations between the diagnostic line ratios and the pebble disk size (Figure 13). This builds evidence on modeling predictions and observational correlations that have emerged in previous work (F. J. Ciesla & J. N. Cuzzi 2006; J. R. Najita et al. 2013; A. Banzatti et al. 2020, 2023a; A. D. Schneider & B. Bitsch 2021; A. Kalyaan et al. 2021, 2023; J. Mah et al. 2024; A. Houge et al. 2025). By combining these correlations to the new analysis of radial gradients and Doppler broadening (Figures 20 and 22; see also C. E. Romero-Mirza et al. 2024a), this work now suggests that drift-dominated disks have shallower temperature gradients with an extended cold disk surface enriched by ice sublimation, while disks with strong pebble traps that reduce the influx of pebbles from the outer disk have steeper temperature profiles with much reduced emission from temperatures <300 K, as summarized in Figure 21.

The scatter in the larger sample in Figure 13 indicates that the outer millimeter disk radius may not be the best tracer of pebble drift through the snowline, as suggested in previous work. If multiple gaps are present in a disk, as commonly observed in ALMA images (S. M. Andrews 2020; J. Bae et al. 2023), the outer radius is set by the outer gap, while ice delivery through the snowline is regulated by the innermost gap (as long as it provides an effective trap to pebbles; A. Kalyaan et al. 2021, 2023; W. Easterwood et al. 2024). This highlights the importance for future work to investigate the dependence of the measured water line diagnostics on the observed inner gap properties from high-resolution ALMA images. As the sample of disks observed with MIRI grows, other system parameters that are emerging as important for pebble drift efficiency, including stellar mass, age, and multiplicity (e.g., C. Xie et al. 2023; S. L. Grant et al. 2024; F. Long et al. 2025) should become clearer.

One important caveat of the main diagnostic diagram based on water lines at MIRI wavelengths is that it is only partly sensitive to the snowline region expected at temperatures of 120–180 K (K. Lodders 2003). In fact, the power-law models in Figure 22 are sensitive to the colder region at <200 K only in the case of shallow temperature slopes. We suggest, however, that a simple power law (even with a tapered profile in column density) may not be the best approximation to the observed water spectra. In fact, the best-fit models in C. E. Romero-Mirza et al. (2024a) still underpredict the flux of the 1500 K lines, and the maximum asymmetry in the 1448/1615 K line ratio from the model grid in Figure 22 is only 1.1 (for cutoff radii at 10 au), lower than what measured in half of the sample included in this work (up to 1.3; Figure 11). A more complex radial profile that accounts for a surface layer beyond the midplane snowline may be necessary (Figure 21). To analyze in detail the water abundance near and across the snowline from midplane to surface, access to lower energy levels at >30 μm will be needed (e.g., K. Zhang et al. 2013; S. M. Blevins et al. 2016; A. Banzatti et al. 2023a), which would be provided by a future far-infrared observatory (K. M. Pontoppidan et al. 2018; I. Kamp et al. 2021; K. Pontoppidan et al. 2023).

Dynamic disk models including dust evolution and water processing are beginning to unfold how the observable water columns can evolve with time under the effect of pebble drift (A. D. Sellek et al. 2025; A. Houge et al. 2025). It would be very interesting in future work to generate evolutionary tracks of such models in the context of the diagnostic diagrams presented in this work, to add the time dimension to the interpretation of the diagnostic line ratios measured in this and future samples. Here we note that by integrating the water mass at temperatures of <300 K from the radial gradients in Figure 22 and converting those into a pebble mass delivered to the snowline using Equation (11) from C. E. Romero-Mirza et al. (2024a) gives pebble mass fluxes between a few 10⁻⁵ M_⊕ yr⁻¹ (in the case of steep temperature profiles with a small cutoff radius, representative of disks with pebble traps) and a few 10⁻⁴ up to 10⁻³ M_⊕ yr⁻¹ (in the case of shallow temperature profiles with a larger cutoff radius, representative of drift-dominated disks), see Appendix D. This range is consistent with typical predictions from dust evolution models (e.g., T. Birnstiel et al. 2012; J. Drazkowska et al. 2021; G. D. Mulders et al. 2021).

6.2. A Procedure for the Analysis of Water Spectra

We propose now in Figure 23 a simple general procedure for the analysis of water spectra, by combining the findings and tools presented above to the list of guidelines provided recently in A. Banzatti et al. (2023b), which was based on lessons learned from ground-based surveys of water emission from protoplanetary disks.

Zoom In Zoom Out Reset image size

6.2.1. Step 1—Spectral Line Inspection

The first step after reducing the spectra and subtracting the continuum (see Appendix B for guidelines on that step) is to inspect them carefully across MIRI wavelengths for the general identification of a series of properties. These properties, related to line blending and excitation, will be useful and in some cases fundamental for a correct analysis of water emission to study physical and chemical processes in inner disks.

Relative Emission in High- versus Low-energy Lines. With guidance from the atlas presented in this work, the identification of the general distribution of water temperature components can be visualized from the relative ratio of lines dominated by higher-E_u versus lower-E_u. The 16–18 μm range is well suited for the hot and warm components, by including lines with E_u from above 6000 K down to 2000 K (see Figure 4 in A. Banzatti et al. 2023a and Figure 17 in this work). The best lines at MIRI wavelengths where colder emission consistent with the snowline region emerges are two transitions around 23.85 μm (K. Zhang et al. 2013; A. Banzatti et al. 2023a; C. E. Romero-Mirza et al. 2024a; M. Temmink et al. 2024), including their relative asymmetry, which, at lower temperatures, is prominent in a stronger 1448 K line at 23.82 μm (Figure 9). This will give a first general impression of the global water distribution in the inner disk of a given target or sample; see, e.g., Appendix H for the sample in this work.

Contamination from other species. Next, before water emission lines shall be extracted and used for analysis, the atlas can be used for general reference of contamination from other species. To evaluate that carefully on individual targets, models that at least approximately reproduce the observed emission from other molecules should be used, as done in the example of CI Tau in Figures 1–4. With this process, it is possible to identify which water lines can be extracted and used for analysis without having to subtract other emission models. In this work, we provide a curated list of single unblended lines that should provide the most reliable measurements in most situations (Section 3); in the case of weak water relative to organic emission, lines at 12–16 μm should be checked for contamination and possibly removed from the list.

Absorption. If high-resolving-power infrared spectra are available from ground-based instruments, those can be used to check for the presence of absorption in the rovibrational lines. If not, the MIRI spectra at <9 μm should be inspected to identify potential blueshifted absorption (e.g., Figure 18), especially disks observed at inclinations >50 deg (Figure 15) that may generally have blueshifted absorption by intercepting an inner disk wind (K. M. Pontoppidan et al. 2011; A. Banzatti et al. 2022). Identifying absorption solely from MIRI data needs a strong absorption blueshift and a broad emission component and will likely be possible only in a limited number of cases. Ground-based observations demonstrate that absorption is rather common in rovibrational CO spectra and may be blended into emission producing weaker line fluxes in MIRI spectra (Figure 15 in A. Banzatti et al. 2023b), making their interpretation more challenging. In those cases where the absorption blueshift is large enough to enable detection in MIRI spectra, the rovibrational lines will provide a useful new probe of the molecular content of inner disk winds. To date, there is no evidence for absorption in the rotational lines (except for tentative evidence in VW Cha; see Figure 8 in A. Banzatti et al. 2023b), which could therefore be unaffected.

Opacity and non-LTE effects. There are specific lines that should be handled carefully depending on the analysis and modeling tools that are going to be used. As shown above in Section 3.1.3, there is a large number of ortho-para pairs of lines that overlap in wavelength, and where line opacity overlap is necessary to correctly model their combined flux. Not all modeling tools include line opacity overlap, including some of the thermo-chemical codes that are being used for the analysis of infrared spectra from disks, so these lines should, in that case, be excluded from the modeling.

Another important case that we have illustrated in this work is the presence of several v = 1–1 lines intermixed with v = 0–0 lines (Section 3.1.4). These should generally be populated in non-LTE conditions and will bias the results from model fits that assume LTE, either from simple slab models or more sophisticated disk models. These lines should either be ignored when fitting spectra with LTE models, or accounted for by implementing non-LTE excitation. The measured flux in these lines could be used to characterize the density of the emitting gas in the inner hot region where they are excited (R. Meijerink et al. 2009), expanding what ground-based spectra have initially provided (A. Banzatti et al. 2023b).

6.2.2. Step 2—Water Diagnostic Diagrams

After the water spectrum has been inspected and any contaminated lines removed, the line list provided with this work can be used to measure line properties for a series of general analysis steps. The fundamental lines listed in Table 1 can be directly used to obtain the line flux ratios and place any target on Figure 10 for a general identification of its radial water distribution in the inner disk, whether approximated with discrete components or as a temperature gradient, and in Figure 11 for the coldest water detected at MIRI wavelengths. Figure 23 visualizes the principal directions to interpret an object's position on the diagram in terms of a decreasing temperature slope, which increases the emitting area of an intermediate 400 K component, and an increasing reservoir at lower temperatures down to ice sublimation at the snowline. Objects that exceed the model series to the right of the diagram are increasingly dominated by a pure ≈400 K component, those that exceed the diagram at the top are increasingly dominated by a colder component down to ≈150 K. A comprehensive characterization of the region around the snowline will need the availability of high-resolution far-infrared spectra.

6.2.3. Step 3—Use Doppler Line Broadening, If Detected

While the water line-flux-ratio diagnostic diagrams have broad applicability to any observed MIRI spectrum, in the limited cases where Keplerian broadening by disk rotation is detected, the measured line widths can be used to better characterize the radial distribution of water across the different temperatures (Figures 20 and 21). Beyond the very simple Doppler mapping procedure presented above, which can be used for quick reference and comparison across objects, the advantage of using Doppler-broadened line widths will be in the simultaneous modeling of line excitation and broadening that can be done for specific cases in the future. These limited cases will also provide an important reference for comparison to the larger number of cases where lines are unresolved (or where stellar mass or disk inclination may be unknown) and only the line fluxes can be used in modeling the spectra (e.g., Figure 21).

From what we observed in this sample, the rovibrational lines at <9 μm are commonly Doppler-broadened due to their excitation in an innermost region within ≈0.1–0.2 au, as shown by fully spectrally resolved data from the ground (A. Banzatti et al. 2023b). In this case, future work should be able to use the observed flux and line broadening to study the density of a region near the inner disk wall, provided that non-LTE excitation is accounted for in the modeling.

The study of water emission in protoplanetary disks is now reaching the end of its second decade, with a plethora of spectra obtained from ground- and space-based observatories with a wide range of resolving powers (from 700 of Spitzer-IRS up to 90,000 of VLT-CRIRES and IRTF-iSHELL). By combining water spectra from multiple surveys, A. Banzatti et al. (2023b) recently summarized a series of fundamental questions, as follows:

1. 1.  
   Which inner disk region(s) do the infrared water lines trace, and are there multiple water reservoirs (with different temperature and density)?;
2. 2.  
   what is the water abundance in inner disks, and what regulates it (chemistry versus dynamics)?;
3. 3.  
   what is the relative role of different excitation processes, and is water emission excited in LTE?;
4. 4.  
   is water present in a molecular inner disk wind?; and
5. 5.  
   how can we correctly interpret the complex water spectra observed across infrared wavelengths within a unified picture of inner disks?

After two years of JWST observations, steps forward have been made in most of these topics, especially the detection of multiple temperature components or a temperature gradient in water emission from inner disks (see Section 1). In this work, by analyzing MIRI-MRS high-quality spectra observed in 25 disks as part of the JDISC Survey, we have learned and demonstrated some general properties of water in inner disks, as summarized below (following the numbered questions above).

1. 1.a  
   The line flux diagnostics introduced in this work demonstrate that water in inner disks is generally distributed with a radial temperature gradient that can be approximated with three discrete components in LTE (∼850 K, ∼400 K, and ∼170–200 K) or a power-law profile with negative index of ∼0.4–0.7 and cutoff radii of ∼1–10 au. The diagnostic line ratios measured in this sample are consistent with a continuum of radial profiles, from disks with a steeper gradient dominated by a compact hot region (e.g., CI Tau) to disks with a shallower gradient and a 2–10 times more extended region reaching ice sublimation temperatures (e.g., GK Tau, GQ Lup). The observed emission is typically optically thick at ≳400 K.
2. 1.b  
   The detection of Doppler line broadening from disk rotation demonstrates, for the first time at wavelengths >13μm directly from the line widths, that the observed water spectra emit from disk radii between the inner disk rim (≲0.1 au) and the water snowline (a few astronomical unit). This discovery opens up the possibility to combine line flux and broadening measurements across MIRI-MRS spectra, from the rovibrational band at <9 μm to the rotational lines at 10–28 μm, to estimate the water abundance and its evolution across the inner planet-forming region.
3. 2.  
   The line flux ratios of low (1500 K) and intermediate (3600 K) energy levels in comparison to the high levels (6000 K) anticorrelate with the ALMA dust disk radius in a selected sample of disks, supporting the role of icy pebble drift in regulating the water abundance within the snowline as proposed before (F. J. Ciesla & J. N. Cuzzi 2006; A. Banzatti et al. 2020, 2023a). The broader sample in this work, which includes a range of dust structures (including multiple gaps and inner dust cavities) in disks of single and multiple-star systems, and slightly younger embedded objects, shows a larger spread likely due to multiple effects related to age, dust depletion, stellar multiplicity, and the depth of dust gaps that should be investigated in future work.
4. 3.  
   Expanding on what was found in ground-based surveys (A. Banzatti et al. 2023b), MIRI spectra show that the excitation of the entire rovibrational band at 5–8 μm is not in LTE, and the broader line widths in this band demonstrate a smaller emitting radius than the v = 0–0 rotational band. Evidence for non-LTE excitation is demonstrated for the first time also in rotational lines in the first vibrational level (v = 1–1). The relative excitation of these different bands should enable obtaining estimates of the molecular gas density across inner disk radii.
5. 4.  
   Water is indeed present in a dense molecular region of inner disk winds at ≈1 Myr, as shown for the first time by detecting blueshifted absorption in rovibrational lines observed from the high-inclination disk of IQ Tau. Going forward, under specific geometric conditions, MIRI spectra may provide a new probe of the physical and chemical composition of inner disk winds close to their launching radii at the disk surface.
6. 5.  
   In this work, we have presented a number of guidelines and tools to identify, analyze, and interpret different excitation and broadening effects in water spectra as observed with MIRI-MRS, which should be beneficial to the community for producing reliable analyses and homogeneous comparisons across large data sets in the future. In particular, the diagnostic diagrams introduced in this work (Figures 10, 11, and 22) will make comparative analyses across >100 disks (the total sample obtained by the end of Cycle 2) sustainable without extensive computing time and without depending on the different assumptions and limitations of different modeling tools.

This work demonstrates that protoplanetary disk spectra observed with MIRI-MRS provide a large repository of information (the spectral line flux distribution and line broadening as a function of upper-level energy) about the distribution in temperature and density of water in planet-forming regions from the inner disk rim out to the snowline. This highlights the role of JWST as a leading observatory that will continue to deliver new discoveries on the origins of planetary chemistry (including water) for many years. While water emission from temperatures down to ice sublimation is detected in some disks (Figure 11; see also C. E. Romero-Mirza et al. 2024a), with only a handful of water lines with E_u ∼ 1000–1500 K observed with MIRI, a detailed characterization of the water abundance across the snowline will necessitate a high-resolution far-infrared observatory.

We thank the referee for providing multiple suggestions that improved the clarity and usefulness of this work. This work includes observations made with the NASA/ESA/CSA James Webb Space Telescope. The JWST data used in this paper can be found in MAST: 10.17909/7w5s-f430. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127 for JWST. The observations are associated with JWST GO Cycle 1 programs 1549, 1584, and 1640. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). The authors acknowledge support from NASA/Space Telescope Science Institute grants: JWST-GO-01640, JWST-GO-01584, and JWST-GO-01549. G.A.B. gratefully acknowledges support from NASA grant 80NSSC24K0149.

Facility: JWST - James Webb Space Telescope.

Software: Matplotlib (J. D. Hunter 2007), NumPy (S. van der Walt et al. 2011), SciPy (P. Virtanen et al. 2020), Seaborn (M. Waskom 2021), Astropy (Astropy Collaboration et al. 2013, 2018, 2022), LMFIT (M. Newville et al. 2014), iSLAT (M. Johnson et al. 2024), spectools_ir (C. Salyk 2022).

Tables 2, 3, and 4 report the sample properties and some fundamental measurements extracted in this work. All line measurements in this work are extracted using the “fit saved lines” function in iSLAT, which implements the least-squares minimization code lmfit (M. Newville et al. 2014) to perform single-Gaussian fits and measure the line centroid, FWHM, and flux and their uncertainties. The pixel flux errors are adopted as estimated from the JDISCS pipeline (K. M. Pontoppidan et al. 2024). When a line is not detected, the integrated line flux is just the integral of the pixels in the line range (which could be negative, if there are more negative pixels), and its error is from the propagation of pixel flux errors. Upper limits reported in the Figures in this work use the 2σ flux error.

The continuum-subtraction algorithm presented in K. M. Pontoppidan et al. (2024)²² is a very effective empirical procedure designed to remove broad dust features under narrow gas line emission. As noted in the original paper, the procedure may subtract a small fraction of the gas emission in some regions of dense clustering of lines. For this reason, in applying the method to this sample, we excluded the following regions: 6.4–6.91 μm for the most densely clustered part of the rovibrational water bands, 7.45–7.515 μm in case of strong H i emission (which sits on a cluster of water lines; see Figure 1), 13.4–14.1 μm for the broad Q-branches of HCN and C₂H₂, and 14.9–15 μm for the Q-branch of CO₂ when stronger than the nearby water emission. We also exclude the region at >28 μm where the MRS sensitivity drops (K. M. Pontoppidan et al. 2024). A modification we make to the algorithm is to apply two different smoothing windows and a number of iterations at short versus long wavelengths, with a separation at 8–10 μm; this is found necessary in most spectra in this sample to account for the different clustering of lines, the different spectral resolution, and the different dust features in the two wavelength ranges, with the long wavelengths often including more dust features (see, e.g., the case of GK Tau shown in A. Banzatti et al. 2023a).

Additionally, we use 200 line-free regions identified from the slab models in Figures 1–4 to apply a final small wavelength-dependent offset informed on where the flux is expected to be dominated by dust continuum. The list of continuum pixels is now included in the iSLAT release on GitHub.²³ We find that this final step helps in getting closer to the underlying continuum especially at <8 μm, where the clustered rovibrational bands of CO and water produce a pseudo-continuum, and at >​​​​​​20 μm, where fringe residuals would otherwise be interpreted as emission lines in the original code, pushing the continuum too low. This final offset turns out to also be important when molecular absorption is present, since the procedure from K. M. Pontoppidan et al. (2024) is built on the assumption that any gas feature in the spectrum is in emission (i.e., the algorithm assumes the continuum to be at the bottom of the spectrum, not at the top). Absorption spectra from a molecular inner disk wind (like the one identified in IQ Tau in Figure 18) or a stellar photosphere (e.g., in MY Lup as identified in C. Salyk et al. 2025, and included in Figure 36) would instead have the continuum in between or at the top of any gas features, and the line-free regions are fundamental in identifying the level of the actual continuum, especially in these cases (see the application of this procedure in F. Long et al. 2025). An example of this procedure as applied to CI Tau is shown in Figure 24.

Zoom In Zoom Out Reset image size

Tables 5 and 6 report the list of single unblended water transitions defined in Section 3 and used for the analysis in this work. The entire line list has been added to the GitHub repository of iSLAT and named “MIRI_general.” In addition to the water lines, we have included the unblended CO transitions (v = 1–0 P26 and P27, v = 2–1 P23 and P27) and some coincident pairs of OH transitions that are used for reference to water in this work, in addition to the single transition at 14.62 μm (Figures 16 and 20).

Table 5. List of Single Unblended Water Transitions Defined in Section 3 and Used for the Analysis in This Work

Wavelength	Transitions (Upper–Lower)	Aul	Eu
(μm)	(Level Format: )	(s−1)	(K)
5.34529	010-000 10 3 8–9 2 7	5.81	4420
5.63179	010-000 7 2 6–6 1 5	6.87	3335
5.64107	010-000 3 3 0–2 2 1	5.82	2744
6.07545	010-000 3 2 1–3 1 2	6.86	2617
6.14316	010-000 2 0 2–1 1 1	3.78	2395
6.1854	010-000 1 1 0–1 0 1	10.94	2360
6.34443	010-000 1 0 1–1 1 0	12.63	2328
6.43355	010-000 5 1 4–5 2 3	11.52	2878
6.49224	010-000 2 1 2–3 0 3	7.21	2412
6.52896	010-000 7 3 4–7 4 3	9.45	3543
6.97738	010-000 9 0 9–9 1 8	4.24	3614
6.99328	010-000 3 2 2–4 3 1	8.57	2609
7.14692	010-000 4 2 3–5 3 2	5.63	2745
7.21253	010-000 7 2 5–8 3 6	4.48	3442
7.27924	010-000 5 3 2–6 4 3	8.01	3065
7.30659	010-000 5 3 3–6 4 2	7.83	3059
8.0696	010-000 10 5 6–11 6 5	5.95	4867
9.90602	000-000 21 4 17–20 3 18	10.81	8270
10.1132	000-000 17 7 10–16 4 13	1.56	6371
10.76435	000-000 14 9 6–13 6 7	0.76	5302
10.85307	000-000 15 6 9–14 3 12	0.66	4996
11.00168	000-000 12 6 7–11 1 10	0.07	3501
11.17771	000-000 20 8 13–19 5 14	14.51	8556
11.26877	000-000 20 7 14–19 4 15	16.82	8257
11.64764	000-000 17 3 14–16 2 15	4.61	5483
11.70161	000-000 13 5 8–12 2 11	0.20	3783
11.96812	000-000 14 8 7–13 5 8	1.27	4985
12.26544	000-000 18 7 12–17 4 13	12.28	6953
12.5645	000-000 10 6 5–9 1 8	0.04	2697
12.89409	000-000 12 5 7–11 2 10	0.26	3310
12.98575	000-000 12 7 5–11 4 8	0.74	3759
13.13243	000-000 16 7 10–15 4 11	7.03	5763
13.29319	000-000 15 3 12–14 2 13	3.78	4431
13.31231	000-000 16 4 12–15 3 13	6.83	5213
13.50312	000-000 11 7 4–10 4 7	0.49	3340
14.34608	000-000 14 3 11–13 2 12	3.38	3941
14.42757	000-000 15 4 11–14 3 12	6.09	4668
14.51301	000-000 13 2 11–12 1 12	1.23	3232
14.89513	000-000 14 5 10–13 2 11	5.49	4198
15.62568	000-000 13 3 10–12 2 11	2.99	3474

Note. Line properties are from HITRAN (I. E. Gordon et al. 2022). The full line list is included in iSLAT at https://github.com/spexod/iSLAT.

Download table as:  ASCIITypeset image

Table 6. List of Single Unblended Water Transitions Defined in Section 3 and Used for the Analysis in This Work (Continued)

Wavelength	Transitions (Upper–Lower)	Aul	Eu
(μm)	(Level Format: )	(s−1)	(K)
15.83495	000-000 18 8 10–17 7 11	43.99	7252
15.96622	000-000 13 5 9–12 2 10	4.68	3721
16.27136	000-000 15 5 10–14 4 11	9.23	4835
16.50525	000-000 17 7 10–16 6 11	28.79	6371
16.54402	000-000 11 6 6–10 3 7	1.37	3082
16.59123	000-000 16 9 7–15 8 8	56.44	6369
17.10254	000-000 12 5 8–11 2 9	3.78	3273
17.14148	000-000 16 8 8–15 7 9	42.49	6053
17.19352	010-010 13 4 9–12 3 10	6.27	6005
17.32395	000-000 16 8 9–15 7 8	41.53	6051
17.35766	000-000 11 2 9–10 1 10	0.96	2432
17.50436	000-000 13 4 9–12 3 10	4.94	3645
17.56683	000-000 8 6 3–7 3 4	0.15	2030
17.59626	010-010 15 7 8–14 6 9	35.12	7686
18.25429	000-000 11 5 7–10 2 8	2.81	2857
19.12996	000-000 15 7 9–14 6 8	27.00	5214
19.24597	000-000 11 3 8–10 2 9	2.27	2608
19.34995	000-000 10 5 6–9 2 7	1.83	2472
19.68805	000-000 14 7 8–13 6 7	27.30	4696
20.42595	000-000 13 7 7–12 6 6	27.03	4211
20.66181	000-000 7 4 3–6 1 6	0.07	1339
21.33317	000-000 12 7 6–11 6 5	26.27	3759
21.61495	000-000 17 6 12–16 5 11	16.87	6073
21.7488	000-000 15 6 10–14 5 9	15.59	4953
22.08091	000-000 11 4 7–10 3 8	4.58	2732
22.13775	000-000 12 6 6–11 5 7	17.69	3507
22.37473	000-000 11 7 4–10 6 5	25.29	3340
22.99881	000-000 12 6 7–11 5 6	16.51	3501
23.31846	000-000 10 6 5–10 3 8	0.09	2697
23.81676	000-000 8 3 6–7 0 7	0.61	1447
23.89518	000-000 8 4 5–7 1 6	1.04	1615
24.05845	010-010 16 5 12–15 4 11	13.76	7640
24.41975	010-010 9 3 6–8 2 7	2.42	4179
24.91403	010-010 9 6 3–8 5 4	18.64	4778
25.14613	000-000 10 6 5–9 5 4	16.05	2697
26.05384	000-000 10 5 5–9 4 6	9.89	2481
26.25519	000-000 13 5 9–12 4 8	9.33	3721
26.64294	000-000 9 6 4–8 5 3	15.33	2346
26.72651	000-000 11 4 7–11 1 10	0.12	2732
26.90847	000-000 17 3 14–16 4 13	15.93	5483
27.0272	000-000 7 3 5–6 0 6	0.48	1175

Note. Line properties are from HITRAN (I. E. Gordon et al. 2022).

Download table as:  ASCIITypeset image

Table 7 reports the reference models used for the general water atlas in Figures 1 to 4. In the case of CO and H₂O, we use HITEMP data as currently available from HITRAN.org (L. S. Rothman et al. 2010; G. Li et al. 2015), which enables the identification of several higher-energy lines for the first time in disk spectra. HITEMP includes CO lines from E_u > 12, 000 K detected at 5.25–5.55 μm (Figure 1), as well as H₂O lines from E_u > 10, 000 K at 9–15 μm (which may require higher temperatures than the T = 850 K model in Figures 2 and 3). In the case of H₂O, HITEMP also includes a few, strong v = 0 − 0 lines with E_u =  7000–8000 K that are missing from HITRAN and are clearly detected at (with quantum numbers as in Table 5): 24.525 μm (22₁₂₂ − 21₀₂₁ and 22₀₂₂ − 21₁₂₁) and 23.536 μm (23₀₂₃ − 22₁₂₂). For CO, we de-couple the excitation of different vibrational bands to approximately reproduce their excitation, which is known to not be in LTE (e.g. Figure 11 in A. Banzatti et al. 2022).

Figure 25 and Table 8 illustrate the reference models used in Figure 10 for the water line-ratio diagnostic diagrams. The discrete temperature component models described in the main text above are summed up into an “H+W” and “H+W+C” series producing the model tracks shown in Figure 25 as follows. The H+W series takes the base hot model (850 K) and adds emission from a warm-water component (400 K) by progressively increasing its emitting area to mimic a larger warm-water-rich disk region. The specific models are labeled by the size of the emitting area of the warm model in reference to the hot model, e.g., the W2 model has twice the emitting radius as the hot model, W3 three times the radius, and so on. We explore models up to six times the hot model radius, as they are sufficient to cover the range of line ratios observed in this sample. To illustrate the effects of having a more optically thick (“TK”) or thin (“TH”) emission, we reproduce the W models with a 10 times larger and 2.5 times lower column density, which produce the H+W(TK) and H+W(TH) model series. The 3340 K line ratio is most sensitive to the column density of the 400 K component, producing the spread of models in the middle panel.

Zoom In Zoom Out Reset image size

Table 8. Series of Slab Models Used in Figure 10

Model	T	N	Rslab	Mgas	Combined	1500/3600 K	3600/6000 K	1500/6000 K	3400 K
	(K)	(cm−2)	(au)	(μM⊕)	models				b/a
H	850	1 × 1018	RH		H	0.97	1.01	0.97	0.79
W2	400	5 × 1017	RW = 2RH		H+W2	1.54	1.34	2.07	1.28
W2(TK)	400	5 × 1018	RW = 2RH		H+W2(TK)	1.30	1.69	2.18	0.93
W2(TH)	400	2 × 1017	RW = 2RH		H+W2(TH)	1.66	1.17	1.95	1.25
W3	400	5 × 1017	RW = 3RH		H+W3	1.94	1.75	3.39	1.76
W3(TK)	400	5 × 1018	RW = 3RH		H+W3(TK)	1.44	2.37	3.40	0.99
W3(TH)	400	2 × 1017	RW = 3RH		⋯	⋯	⋯	⋯	⋯
W4	400	5 × 1017	RW = 4RH		H+W4	2.26	2.30	5.20	2.26
W4(TK)	400	5 × 1018	RW = 4RH		H+W4(TK)	1.52	3.08	4.68	1.03
W4(TH)	400	2 × 1017	RW = 4RH		H+W4(TH)	2.92	1.66	4.86	2.39
W5	400	5 × 1017	RW = 5RH		H+W5	2.49	2.97	7.39	2.73
W6	400	5 × 1017	RW = 6RH		H+W6	2.65	3.74	9.91	3.15
C2	190	1 × 1017	RC = 2RW		H+W2+C2	1.77	1.34	2.37	1.27
C3	190	1 × 1017	RC = 3RW		H+W3+C3	2.82	1.75	4.92	1.77
C4	190	1 × 1017	RC = 4RW		H+W4+C4	4.33	2.29	9.91	2.28
C5	190	1 × 1017	RC = 5RW		H+W5+C5	6.30	2.96	18.64	2.76
C6	190	1 × 1017	RC = 6RW		H+W6+C6	8.72	3.76	32.78	3.18

Note. Other parameters that are assumed in the models: a thermal line broadening of 1 km s⁻¹ (FWHM), an instrumental+Doppler line broadening of 130 km s⁻¹. M_gas is the observable gas mass (the product of area, column density, and molecular weight) in units of micro-Earth masses.

Download table as:  ASCIITypeset image

For the H+W+C series, we take each model in the H+W series and add a water emission component close to the snowline region (here assuming 190 K to represent the range estimated in Figure 11) by progressively increasing its emitting area to mimic a larger cold-water-rich disk region. Similarly to how the H+W series is built, the specific models are labeled by the size of the emitting area of the cold model in reference now to the warm model, e.g., the C2 model has twice the emitting radius as the warm model, C3 three times the radius, and so on. Also in this case, exploring models up to six times the radius of the warm region is enough to cover the observed line ratios. The 190 K component does not contribute to the flux of the 3340 K lines because it is too cold; therefore, the “H+W” and “H+W+C” model series overlap perfectly in the middle panel of the Figure.

In Figure 25, we only label some models to avoid overcrowding the plot. The arrows show the directions defined by changes in column density (red arrows in the middle and right panels) and by adding a cold component (green arrows in the right panel). The three shaded areas in the right panel identify the regions covered between a pure H+W and an H+W+C model in the three opacity regimes explored for the warm component. The overall information provided by this grid of models is summarized in Figure 10: an increasing 3600/6000 K line ratio indicates a larger emitting area for the warm region, while an increasing 1500/3600 K ratio indicates increasing emitting area for the cold reservoir near the snowline. These effects are also consistent with what is found by considering a continuous radial gradient rather than discrete temperature components, as shown and discussed in Section 6.1.

Since line ratios are insensitive to specific value of the slab radius, the left panel in Figure 25 is provided to anchor the general models described here to the specific case of individual disks. The measured 6000 K line luminosity, as this line is optically thick, mostly reflects the size of the emitting area once the temperature is assumed to be represented well by a 850 K component. Placing an object on the grid of models in the left panel will inform on the approximate emitting area of the hot model, which then can be used to estimate the specific areas for the warm and cold models as described above. Placing an object in the middle panel, instead, will help break degeneracies between different possible solutions in the plot to the right, where W models with different column density and the addition or not of a cold component may lie very close in the diagnostic diagram (e.g., the H+W5 and the H+W4(TK)+C models).

The radial gradient models shown in Figure 22 are reported in Table 9. The models use power-law profiles following work by C. E. Romero-Mirza et al. (2024a) as T = T₀(r/0.5 au)^−α and N = N₀(r/0.5 au)^−β with these fixed values: T₀ = 450 K, N₀ = 1 × 10¹⁸ cm⁻², and β = 1, while α is varied between 0.4 and 0.7 and a cutoff radius R_cut between 0.75 and 10 au, beyond which the water column density drops to zero. The cold water vapor mass integrated over the temperature range >120 K (taken as the minimum sublimation temperature, from K. Lodders 2003) and <300 K (above which gas-phase formation becomes efficient; e.g., A. E. Glassgold et al. 2009), taken as having an origin from ice sublimation at the snowline, is used to estimate an icy pebble mass flux through the snowline using Equation (11) and the same parameter values in C. E. Romero-Mirza et al. (2024a), with a water molecule mass of 3 × 10⁻²³ g. This cold mass flux, called , is reported for each model in Table 9.

Table 9. Series of Slab Models Used in Figure 22

α	Rcut		1500/3600 K	3600/6000 K	1500/6000 K
	(au)	(M⊕ Myr−1)
0.4	0.75	0	1.57	2.40	3.76
0.4	1	0	1.96	2.73	5.36
0.4	2	133	3.86	3.02	11.7
0.4	5	788	7.76	3.04	23.6
0.4	10	1917	9.43	3.04	28.7
0.5	0.75	0	1.51	1.96	2.95
0.5	1	0	1.91	2.13	4.06
0.5	2	199	3.46	2.22	7.66
0.5	5	854	5.22	2.22	11.6
0.5	10	1285	5.40	2.22	12.0
0.7	0.75	0	1.36	1.37	1.88
0.7	1	19	1.67	1.43	2.39
0.7	2	239	2.42	1.43	3.47
0.7	5	550	2.62	1.43	3.75
0.7	10	550	2.62	1.43	3.75

Note. See the text in Appendix D for details on model parameters. Other parameters that are assumed in the models: a thermal line broadening of 1 km s⁻¹ (FWHM), an instrumental+Doppler line broadening of 130 km s⁻¹.

Download table as:  ASCIITypeset image

Table 10 reports linear regression parameters for significant correlations detected in this work. The data to reproduce these correlations are provided in Appendix A.

Table 11 reports updated fits to measured line FWHM to characterize the MIRI resolving power as presented in Section 5.1 and Figure 16. We only update the intercept in sub-bands at >10 μm, since the slope was already well characterized in K. M. Pontoppidan et al. (2024); the parameters for sub-bands not included in this Table are unchanged and can be found in Table 3 in K. M. Pontoppidan et al. (2024).

Figures 26 and 27 report additional plots to complement those shown in the main text above.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Figures 28–36 show a compact version of a water spectral atlas for all disks included in this work in reference to the three temperature components, as in Figure 8. The spectra are split into three regions that are most important for the analysis presented in this work: the rotational lines at ≈15–18 μm (typically dominated by water emission at higher temperatures), the rotational lines at ≈21–27 μm (in which cooler water emission, where present, becomes prominent), and, lastly, the rovibrational band from the bending mode at 5–8 μm. The region of organic emission at 12–15.5 μm is included in the JDISCS overview paper (N. Arulanantham et al. 2025, in preparation). The line list presented in Appendix C is identified with stars, color coded as in Figure 1. Targets in Figure 30 have some peculiarities: Sz 114 has the lowest stellar mass in this sample, IRAS 04385+2550 (labeled IRAS-04385 in the plots) is a younger more embedded disk (G. H. Schaefer et al. 2009), MY Lup has an inclination >70 deg and a cold water spectrum analyzed in C. Salyk et al. (2025), HT Lup is the spectrum of both A and B components of the triple system, and AS 209 and RY Lup have weaker molecular emission and larger fringe residuals than the rest of the sample.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size