THE DEPLETION OF WATER DURING DISPERSAL OF PLANET-FORMING DISK REGIONS

Water vapor emission has been observed in protoplanetary disks between 3 and 540 μm, with significant differences in detection rates, depending on the observed wavelength and on the mass of the central star. The most comprehensive survey of water emission in disks by a single instrument has been obtained by the IRS spectrograph on the Spitzer Space Telescope (Houck et al. 2004; Werner et al. 2004), which measured hundreds of water emission lines between 10 and 37 μm in over 60 disks. Spitzer observations showed that water emission is strongly dependent on the stellar spectral type and tentatively dependent on the evolutionary stage, with high detection rates in disks around solar-mass stars, low detection rates in disks around intermediate-mass stars, and similarly low rates in a small sample of "transitional" disks (1/6; see Table 1 and Pontoppidan et al. 2010a; Carr & Najita 2011; Salyk et al. 2015). Water emission at Spitzer wavelengths has been interpreted in most disks as coming from an optically thick surface layer within the snow line radius, at temperatures of 300–700 K (Carr & Najita 2011; Salyk et al. 2011a). Modeling of the velocity unresolved Spitzer spectra (Δv ∼ 400 km s⁻¹) provided estimates of the disk emitting region to the inner few au in disks (e.g., Najita et al. 2011; Antonellini et al. 2015; Walsh et al. 2015). At 12.4 μm, within the Spitzer-IRS range, a few water lines have been resolved in velocity in four disks with VLT-VISIR and Gemini-TEXES (Δv ∼ 15 and ∼ 3.5 km s⁻¹, respectively; Lagage et al. 2004; Lacy et al. 2002), providing support to the emitting regions estimated by models for the Spitzer spectra (Pontoppidan et al. 2010b; Banzatti et al. 2014; Salyk et al. 2015). At shorter wavelengths (∼2–3 μm), hotter water (T ≈ 900–1500 K) has been spectrally resolved and analyzed in only four disks so far, by Salyk et al. (2008) and Mandell et al. (2012) with Keck-NIRSPEC and VLT-CRIRES, and by Carr et al. (2004) with IRTF-CSHELL. At longer wavelengths (>55 μm), colder water has been surveyed in disks by Herschel-PACS, finding similarly low detection rates in disks around solar-mass as in disks around intermediate-mass stars (∼15% as based on the 63.3 μm line; see references in Table 1 and Rivière Marichalar et al. 2016).

Table 1.  Summary of Major Water Vapor Surveys in Protoplanetary Disks

λ	Instr.	Resol.	# Lines	Eu	T${}_{\mathrm{ex}}$	# Disks	${M}_{\star }\lt 0.2$	$0.2\lt {M}_{\star }\lt 1.5$	${M}_{\star }\gt 1.5$	Refs
(μm)				(K)	(K)		Detection Fractions (and sample sizes)
2.9–3	VLT-	100,000	$\approx 40$	8000–10,000	900	$\approx 40$	N/A	58% (24)	11% (18)	this work, (1)
	CRIRES				Sensitivity:		⋯	−15	−14.6
10–37	Spitzer-	700	$\approx 200$	700–6000	300–700	$\approx 100$	0% (5)	63%–85% (64)	0%–18% (27)	this work, (2)
	IRS				Sensitivity:		−15.7	−14.8	−13.7
55–200	Herschel-	1000–5000	$\approx 20$	100–1400	100–300	$\approx 120$	0% (10)	15% (80)	15% (27)	(3)
	PACS				Sensitivity:		−14.6	−14.5	−14

Note. Detection fractions are reported as percentages, individual sample sizes in brackets, and log sensitivities in erg cm⁻² s⁻¹ for the three stellar mass bins as indicated.

References. (1) Fedele et al. (2011), Mandell et al. (2012); (2) Pontoppidan et al. (2010a), Carr & Najita (2011), Salyk et al. (2011a), Pascucci et al. (2013); (3) Riviere-Marichalar et al. (2012, 2015), Meeus et al. (2012), Fedele et al. (2013), Blevins et al. (2016).

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Table 1 summarizes the properties, samples, and detection rates for all major surveys of water vapor in protoplanetary disks, including this work. The general trends identified to date are shown in Figure 1, and are compared to expectations produced by recent models of water in disks (Antonellini et al. 2015; Walsh et al. 2015).⁷ We investigate the measured line fluxes against the masses of the central stars, ${M}_{\star }$, as an alternative way to look at the spectral-type dependencies found by Pontoppidan et al. (2010a). Water line fluxes generally increase with stellar luminosity (Salyk et al. 2011a), and with stellar mass. Models explain this with the radial extent of the warm (>300 K) disk surface, where water vapor is abundant due to ice evaporation and efficient gas-phase formation, which increases to larger disk radii around more luminous stars. Model predictions agree well with the increase in Spitzer line fluxes measured in disks around stars of masses between 0.2 and $1.5\,{M}_{\odot }$, although 20%–40% of disks show significantly lower fluxes relative to what is expected from a pure luminosity effect. For ${M}_{\star }\gt 1.5\,{M}_{\odot }$, models produce water line fluxes $\gtrsim 10$ times stronger than observed for 80%–100% of the disk sample. The low water detection frequency at infrared wavelengths in disks around stars of ${M}_{\star }\gt 1.5\,{M}_{\odot }$ is still not understood (e.g., Walsh et al. 2015).

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In this work, we test the hypothesis that inside-out inner disk depletion may produce the progressive disappearance of water vapor emission at infrared wavelengths. If water vapor in inner disks is depleted from smaller to larger disk radii, an essential spectral region to include in the investigation of this process is where the hot water emits, in high-energy transitions at 2.9–3 μm (e.g., Mandell et al. 2012). In Sections 2 and 3 we describe the new survey of hot water emission as observed with CRIRES at 2.9 μm, and the comparative analysis with the CO data set at 4.7 μm. In Section 4 we report the discovery of a correlation between water line fluxes at 2.9–33 μm and the size of a gas-depleted region in the inner disk, as probed by rovibrational CO emission. We discuss the properties of these molecular gaps, and propose their potential for studies of the evolution of planet-forming disk regions, in Section 5.

The terms disk "gap" and "hole" have referred (sometimes interchangeably) to radial regions where the dust in the disk shows some degree of depletion, as compared to a continuous distribution adopted by models for disks considered "primordial" (e.g., Espaillat et al. 2012). In this work, we adopt these terms to identify inner disk regions of various sizes (namely ≈0.1–20 au), empirically defined to where molecular gas is depleted enough that its infrared emission (at wavelengths of 2.9–35 μm) is not detected. The term "gap" was utilized in Banzatti & Pontoppidan (2015) with this meaning, with the discovery of a strong correlation between velocity-resolved line widths and the $v2/v1$ vibrational ratios in rovibrational CO emission at 4.7 μm in a large survey of protoplanetary disks. By converting these measurements respectively into a characteristic CO emitting radius ${R}_{\mathrm{co}}$ and the vibrational excitation temperature, this correlation revealed cooler CO gas as larger gaps are formed in disks (i.e., as ${R}_{\mathrm{co}}$ increases). This observational finding suggests an inside-out depletion scenario, which is now being increasingly supported by independent modeling explorations (Hein Bertelsen et al. 2016; Woitke et al. 2016). To distinguish them from dust gaps or holes detected by other techniques, we call them "molecular gaps/holes," especially after the discovery in this work that they are shared by three of the most abundant molecules in disks: CO, H₂O, and OH (Sections 3 and 4). In the absence of constraints on the radial distribution of any undetected residual CO gas within the CO-depleted inner region, we use the terms "gap" and "hole" interchangeably. An upper limit to the CO column density of ≲10¹⁵ cm⁻² has been estimated by Carmona et al. (2016) in one of these gaps/holes, implying that very little residual CO gas is left (if any) in the inner CO-depleted region.

We take each 2.9 μm spectrum that has substantial stellar photospheric absorption and correct it by subtraction of the photospheric template that best matches its absorption spectrum. Given the limited grid of spectral-type templates obtained in this survey (Figure 2), the best matching template is usually easily identified for each science spectrum. We apply the following procedure to the spectral range between 2.925 and 2.935 μm, where the signal-to-noise ratio (S/N) is higher, the spectrum is less affected by detector or telluric gaps, and the H₂O and OH lines are more isolated and stronger (Figure 2). The template spectrum is first shifted to compensate for velocity differences with the science target by cross-correlating the H₂O and OH photospheric features in the science and template spectra. To match the science spectrum, the template is then artificially veiled to account for circumstellar disk emission and its absorption lines broadened. This is achieved by adding an excess flat continuum and by convolving the template spectrum with a Gaussian of variable width (for this technique, see also Hartigan et al. 1989, 1991; Basri & Batalha 1990). The best fit is found by minimizing the residuals after subtraction of the veiled and broadened template from the science spectrum, over a grid of veiling and broadening values. Residuals are measured as the standard deviation of pixel values from the median-smoothed de-veiled spectrum, in a spectral range free of disk molecular emission (2.930–2.934 μm). Figure 3 shows an example of the photospheric correction procedure as applied to the spectrum of VZ Cha; plots for all the other targets are reported in the Appendix. Table 4 lists, for each target, the best photospheric standard match and the estimated veiling at 2.9 μm. Veiling measurements may be refined in future work by using a denser sampling of template spectral types.

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The analysis of CO lines has been presented in Banzatti & Pontoppidan (2015), and here we provide a short summary. We built high S/N CO line profiles for each disk by stacking rovibrational transitions observed in the 4.7 μm spectra. The stacked line profiles preserve the line flux as well as the line shape, through a homogeneous analysis that we adopted for the entire disk sample. We stacked those lines that are most commonly available across the sample (due to the observing strategies and the detector characteristics), that have similar flux, and that are not blended with higher-level transitions. These requirements led us to typically use the v = 1 − 0 lines between P7 and P12, and the v = 2 − 1 lines between P3 and P6. Each line was normalized to its local continuum, re-sampled on a common velocity grid, and stacked by weighted average.

The v = 1 − 0 and v = 2 − 1 stacked line profiles were then used to identify and separate multiple emission components, where present. The v = 2 − 1 lines, with higher E_u (Table 3), are mostly excited in the hotter innermost disk region, while the v = 1 − 0 lines, with lower E_u, often show additional flux contributions from colder gas at larger disk radii. This has been empirically demonstrated through the systematic decomposition of CO lines, where a broad (inner) component "BC" is identified by the v = 2 − 1 lines that match the wings of v = 1 − 0 lines, and a narrow (outer) component "NC" is obtained from the residuals by subtraction of the v = 2 − 1 profile (which is dominated in flux by BC) from the v = 1 − 0 profile (which includes both BC and NC). An example of this procedure is included in Figure 4. In several disks, the two velocity components are clearly seen by visual inspection of the v = 1 − 0 lines, which show a narrower peak on top of broader wings (Bast et al. 2011; Herczeg et al. 2011; Banzatti & Pontoppidan 2015). Those disks that, following this analysis, have been found to have only one CO component (i.e., those where the v = 1 − 0 and v = 2 − 1 stacked line profiles match) have been identified as "single-component" disks ("SC"; e.g., SR21 in Figure 4).

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We use the stacked CO line profiles to reproduce the observed H₂O and OH emission features, to test if their shapes and width are equal to those of CO, implying that they emit from a similar disk region. We adopt the CO line profile at each rest wavelength of H₂O and OH transitions, combine them into a single feature if the lines are broad and overlap (which typically happens for the broad component), and then vary the peak flux of the combined line profile to fit the 2.9 μm spectrum (see Figure 4 and the Appendix).

H₂O and OH lines at 2.9 μm are typically detected in double-component disks only (i.e., when the BC is not detected in CO, H₂O and OH at 2.9 μm are typically not detected either). Where detected, H₂O and OH lines at 2.9 μm are dominated by a broad component that matches the CO BC profile (Figure 4 and Table 5); we therefore conclude that these lines are emitted at similar disk radii. This was first recognized in the 3–5 μm spectrum of EX Lupi by Banzatti et al. (2015), and applies to the majority of disks in the sample studied here (see Table 5). Disks that lack the CO broad component (the "single-component" disks) do not show H₂O emission at 2.9 μm either. This is the first hint that disks with evidence for an inner CO-depleted region are also depleted in water, which will be further detailed and discussed in the next sections. In these disks, OH is detected in a few cases. This finding agrees with previous work that detected OH but not H₂O in some disks around intermediate-mass stars (Mandell et al. 2008; Fedele et al. 2011); disks in this stellar mass bin are in fact found to typically have only a single, narrow CO component (Banzatti & Pontoppidan 2015).

Table 5.  Summary of 2.9–4.7 μm Emission Detections and Properties

Component	FWHM	R${}_{\mathrm{co}}$	CO	H2O	OH
	(km s−1)	(au)	(detection fractions)
Broad (BC)	50–200	0.04–0.3	25/25	15/20	17/20
Narrow (NC)	10–70	0.2–3	23/25	3/20	3/20
Single (SC)	6–70	0.3–20	28/28	1/10	4/10

Note. The definition of components in the first column is based on the analysis of 4.7 μm CO emission in Banzatti & Pontoppidan (2015), as summarized in Section 3.2. Details on individual sources are given in the Appendix.

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While H₂O and OH emission at 2.9 μm comes from similar disk radii as the CO broad component (∼0.04–0.3 au), a survey of velocity-resolved H₂O and OH emission at >2.9 μm is still missing, and is essential to determine which disk radii are probed at longer wavelengths. H₂O emission at 12.4 μm may come from a region at larger disk radii that matches the emitting region of the narrow CO component, as shown in Figure 5 for one disk. In fact, the 12.4 μm H₂O lines have lower energy than the 2.93 μm lines (Table 3), and may therefore match the colder/outer component of CO emission rather than the hotter/inner one.

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R${}_{\mathrm{co}}$ measures the location of CO emission in the disk by taking into account the stellar mass and disk inclination, which are both linked to the measured line FWHM through Kepler's law as

$$\begin{eqnarray}&&{R}_{\mathrm{co}}={(2\sin i/\mathrm{FWHM})}^{2}\,G\,{M}_{\star }\end{eqnarray} \tag{ 1 }$$

where ${M}_{\star }$ is the stellar mass, i is the the disk inclination, and G is the gravitational constant, and we take the line velocity at the half width at half maximum (FWHM/2), as in Banzatti & Pontoppidan (2015). As a reference comparison for ${R}_{\mathrm{co}}$, we take the midplane water snow line radius ${R}_{\mathrm{snow}}$, defined as

$$\begin{eqnarray}{R}_{\mathrm{snow}} & = & 2.1\,\mathrm{au}\,{({M}_{\star }/{M}_{\odot })}^{1/3}\,{({M}_{\mathrm{acc}}/{10}^{-8}{M}_{\odot }{\mathrm{yr}}^{-1})}^{4/9}\\ & & \times {({T}_{\mathrm{snow}}/160{\rm{K}})}^{-10/9}\end{eqnarray} \tag{ 2 }$$

where M_acc is the accretion rate and T_snow is the water freeze-out temperature. Equation (2) is the midplane snow line radius for a viscously heated disk as derived by Mulders et al. (2015)⁸ , who used ${T}_{\mathrm{snow}}=160$ K as in Min et al. (2011). This formula assumes that the disk midplane heating by stellar irradiation is negligible, and this has been shown to be valid for disks around stars younger than ∼3 Myr with mass up to $\sim 2\,{M}_{\odot }$ and accretion rates between 10⁻⁹ and 10⁻⁶ ${M}_{\odot }$ yr⁻¹ (Kennedy & Kenyon 2008; Min et al. 2011; Mulders et al. 2015). Some disks in our sample exceed these limits in stellar mass and age, while some have inner dust gaps that may change the disk temperature structure. For simplicity we adopt the same equation for the entire sample. By normalizing to ${R}_{\mathrm{snow}}$, we put ${R}_{\mathrm{co}}$ from individual disks in reference to a disk radius of equal temperature across the entire disk sample, as set by water ice evaporation in the disk midplane. ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}$ therefore enables a comparison of results from individual disks within a common reference framework.

Figure 8 shows that line fluxes of H₂O, OH, and CO decrease with increasing ${R}_{\mathrm{co}}/{R}_{\mathrm{snow}}$, i.e., as the inner gap radius increases and reaches the snow line radius.⁹ H₂O line fluxes at 2.9 μm show a decreasing linear correlation at radii −2 ≲ log R_co/R_snow ≲ −0.5, beyond which they fall under the detection limit ($\sim 2\times {10}^{-15}$ erg s⁻¹ cm⁻² distance/140 pc). A linear fit to the detected lines provides (using the Bayesian method by Kelly 2007):

$$\begin{eqnarray}&&{\mathrm{Flux}}_{140}{({{\rm{H}}}_{2}{\rm{O}})=-14.6\pm 0.2+({{\rm{R}}}_{\mathrm{co}}/{{\rm{R}}}_{\mathrm{snow}})}^{-0.8\pm 0.2}\end{eqnarray} \tag{ 3 }$$

where Flux₁₄₀ is the measured line flux normalized to a distance of 140 pc. At 12.5 and 33 μm, H₂O lines are detected out to log R${}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\sim -0.2$, and decrease only at log R${}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\gtrsim -1$. OH emission follows similar trends, but OH lines are tentatively detected up to larger disk radii (especially the cold lines at 30 μm). Variability in accretion luminosity may contribute to the order-of-magnitude scatter in line fluxes along these trends; however, a factor up to $\approx 10$ change in line fluxes has been observed so far only in the extreme accretion outburst of EX Lupi, and not during the typically lower variability of other young stars included in this sample (Banzatti et al. 2012, 2014, 2015). Similarly to H₂O and OH, the CO v = 1 − 0 line flux decreases with ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}$, but it is detected in disks well beyond the snow line radius. We interpret this as evidence that what regulates the observed H₂O and OH emission is the molecular gas left within the snow line radius, or in other words that H₂O and OH emission disappears as inner disks are depleted from the inside out to the snow line (i.e., as ${R}_{\mathrm{co}}$ grows larger and approaches ${R}_{\mathrm{snow}}$), beyond which the reservoir of water vapor is strongly limited due to freeze-out at low temperatures. CO gas is instead still detected beyond the snow line because it freezes out at lower temperatures (∼20 K), found at larger disk radii.

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As a basic test of this inside-out depletion scenario, we use a simple disk model composed of concentric rings of increasing radius, where each ring is a slab of gas described by one temperature and one column density as in Banzatti et al. (2012). We adopt power-law profiles to set how the temperature and column density of each ring decrease with increasing disk radius, as T(R) = T₀ (R/R₀)^−q and N(R) = N₀ (R/R₀)^−p. We calibrate the model using the observed CO line fluxes, by adopting model parameter values from the radial temperature profile measured by Banzatti & Pontoppidan (2015) in rovibrational CO emission, as ${T}_{0}=1300$ K, q = 0.3, ${N}_{0}={10}^{20}$ cm⁻², and p = 1. In Figure 8 (panel (g)) we show how the integrated CO line flux from the model decreases with increasing hole size, by removing one ring at a time from ${R}_{0}=0.03\,\mathrm{au}$ to ${R}_{\mathrm{out}}=100\,\mathrm{au}$ to mimic an inside-out removal of hotter to colder gas (the radial grid of disk rings is shown by the dots). A radially decreasing power-law temperature profile reproduces the decrease in the CO line fluxes as a curve, where as the hole radius increases, colder gas emission beyond the hole produces weaker CO lines at 4.7 μm. CO line fluxes that exceed the model at log R${}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\gtrsim -0.5$ come from disks where the emission is pumped by UV radiation (Brittain et al. 2003; Banzatti & Pontoppidan 2015).

The same ring slab model is then used for H₂O emission. Such a model produces line fluxes stronger than observed at 12.5 and 33 μm. We therefore include a step function for the column density, to simulate the presence of a radius in the surface of the disk beyond which water vapor is reduced by freeze-out or by chemistry in cold regions (e.g., van Dishoeck et al. 2013). We keep p = 1 as used for CO at disk radii smaller than $\approx 2.5\,\mathrm{au}$, and adopt p = 2.5 to produce a steeper decrease in water column density at larger disk radii (where the gas temperature decreases to ≲300 K). This model, shown in panels (a), (b), and (c) of Figure 8, approximately reproduces both the absolute fluxes and the wavelength-dependent radial decrease in water emission at 2.93–33 μm. A step function in the column density produces a decrease/cutoff in the 12.5 and 33 μm line fluxes at log R${}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\sim -0.5$, which is consistent with the observed water line fluxes in the Spitzer spectra.

The purpose of the ring slab model is to test in the simplest terms if an inside-out removal of disk gas can explain the observed line flux decrease within the snow line. Clearly, this simple model ignores several important factors that should be considered, such as a realistic physical disk structure, disk chemistry, and their adaptation to the formation and development of disk gaps. However, the model seems to have the key ingredients needed to qualitatively reproduce the observed data, by including a radially decreasing temperature and the inside-out removal of molecular gas. Detailed modeling of the water spectrum and of its dependence on disk regions of water vapor depletion at and beyond the snow line has been presented by Meijerink et al. (2009), Zhang et al. (2013), Blevins et al. (2016), Notsu et al. (2016). Recent explorations by Antonellini et al. (2016) for a disk around an intermediate-mass star found a wavelength-dependent decrease in the Spitzer water line fluxes for a grid of increasing inner disk hole sizes, in qualitative agreement with what we measure in the data out to the snow line radius (Figure 8, panels (b) and (c)). These models produce an excess flux when the gap reaches the snow line radius, contrarily to the observations (see Section 5.3).

The wavelength-dependent decrease in water vapor emission between 2.9 and 33 μm is summarized in Figure 9, where we show the temperature–radius (T–R) diagram originally defined for CO rovibrational emission by Banzatti & Pontoppidan (2015) and we color code the individual disks by their H₂O detections. For ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}$ between 0.1 and 1, all disks have lost their detectable H₂O emission at 2.9 μm (their line fluxes are $\lesssim {10}^{-15}$ erg s⁻¹ cm⁻² distance/140 pc), while some still retain detectable emission at 12 or 33 μm. Beyond the snow line (R${}_{\mathrm{co}}$/R${}_{\mathrm{snow}}=1$), H₂O emission between 2.9 and 35 μm is not detected in any disk. As a diagnostic of ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}$, we illustrate in Figure 9 the wavelength-dependent H₂O emission decrease shown earlier in Figure 6, here in reference to the increasing disk gap size.

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Figure 8 (panels (h) and (i)) shows molecular line flux ratios as measured in the CRIRES data set (2.9–4.7 μm). We find a constant OH/H₂O ratio of ∼0.4 in the range $-2\ \lesssim \mathrm{log}\,{{\rm{R}}}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\lesssim -0.5$. As for the CO/H₂O ratio, we find an increasing trend with increasing radius in the range $-2\lesssim \mathrm{log}\,{{\rm{R}}}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\lesssim -1$. This trend is due to a decreasing H₂O line flux, while the CO line flux is less steeply decreasing over these disk radii (Figure 8, panels (a) and (g)). By fitting the measured line ratios, we find the following linear relation (using Kelly 2007):

$$\begin{eqnarray}&&\mathrm{Flux}{(\mathrm{CO})/\mathrm{Flux}({{\rm{H}}}_{2}{\rm{O}})=1.0\pm 0.4+({{\rm{R}}}_{\mathrm{co}}/{{\rm{R}}}_{\mathrm{snow}})}^{0.4\pm 0.2}.\end{eqnarray} \tag{ 4 }$$

These trends are further analyzed and discussed in Section 5.3.

Water emission from protoplanetary disks has been detected by the Spitzer-IRS in more than 60 disks (see Section 1.1). This sample revealed two major trends: (1) water line fluxes increase with increasing stellar luminosity (and mass; see Figures 1 and 20, and Salyk et al. 2011a), and in contrast with the first trend, (2) the water vapor frequency is much higher in disks around stars of $0.2\,\lt$ ${M}_{\star }\lt 1.5$ ${M}_{\odot }$ (with a frequency of 60%–80%) than in disks around stars of ${M}_{\star }\gt 1.5$ ${M}_{\odot }$ (with a frequency of <20%; see Table 1, Figure 10, and Pontoppidan et al. 2010a). Recent chemical modeling of the molecular content of inner disks by Walsh et al. (2015), while able to reproduce the luminosity trend, was still unable to reproduce the absence of water emission in disks around intermediate-mass stars. We have demonstrated in Sections 3 and 4 that the strength of the infrared water spectrum is linked to an inside-out depletion scenario in disks by finding (1) a similar emitting region and detection frequency for the high-energy H₂O lines at 2.9 μm and the innermost CO gas (the broad component), (2) a wavelength-dependent decrease of water line fluxes, where hotter emission (as probed at 2.9 μm) decreases before colder emission (as probed at 33 μm), and (3) a correlation between the decrease of water line fluxes at 2.9–33 μm and the increase in size of an inner molecular hole measured from CO emission.

One major implication of this analysis is that the low frequency of water vapor detections in disks around ${M}_{\star }\gt 1.5$ ${M}_{\odot }$ is found to be linked to inner disk regions depleted in molecular gas out to or even beyond the water snow line, differently from most disks around solar-mass stars. Other independent techniques find signatures of inner holes in dust emission in a growing number of disks around intermediate-mass stars (e.g., Maaskant et al. 2013; Menu et al. 2015). With the analysis of disks that have CO emission observed at 4.7 μm and H₂O at 2.9 μm and/or 10–33 μm (Table 6), we also find that the depletion scenario is not limited to the known transitional disks or to disks around intermediate-mass stars. As shown in Figure 9, several disks around solar-mass stars show at least some degree of water depletion (those that we find to have $0.1\lesssim {R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\lesssim 1$). By interpreting results from Spitzer and VLT-CRIRES surveys in the context of this analysis (Figure 10), we could conclude that ≈20%–40% of disks around solar-mass stars may have molecular gaps in inner disks, while this fraction may be ≈80% for disks around intermediate-mass stars.

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The analysis of velocity-resolved molecular line spectra suggests a path of disk evolution where gas-phase CO and water are depleted from the planet-forming region in an inside-out fashion, a path that may be shared by disks around stellar masses of $0.3\lesssim {M}_{\star }$/${M}_{\odot }\lesssim 3.5$ (as probed in this sample). By detecting H₂O emission only at long wavelengths in SR 9, IM Lup, HD 35929, EC 82, TW Hya, DoAr 44, and HD 163296 (the last three of this list have been previously studied by Fedele et al. 2012; Zhang et al. 2013; Salyk et al. 2015), we propose that these disks may be in an intermediate phase of depletion ($0.1\lesssim {R}_{\mathrm{co}}$/${{\rm{R}}}_{\mathrm{snow}}\lesssim 1$) and still retain some water vapor in their planet-forming region. Disks that have 2.9–33 μm water line fluxes lower than $\approx 5\times {10}^{-15}$ erg s⁻¹ cm⁻² (distance/140 pc) have ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\gtrsim 0.5$ and have already depleted their molecular gas in the planet-forming region within the snow line. This line flux limit may be used to identify molecular holes/gaps in inner disks when only the line flux, and not the line profile or a direct image, can be obtained.

In Figure 9 we also include for comparison the case of disks around low-mass stars (M${}_{\star }\lt 0.2$ ${M}_{\odot }$), observed with Spitzer at 10–19 μm (Pascucci et al. 2013), divided by 10 to re-scale the strong emission observed from organic molecules (HCN and C₂H₂). Rovibrational CO emission at 4.7 μm has not been obtained for any of these disks so far, so we cannot include them in the T–R diagram. However, their spectra at Spitzer wavelengths could be distinguished from that of disks with large gaps by considering the emission from organics. Walsh et al. (2015) suggested that disks around low-mass stars may be too cold to produce strong water emissions. The luminosity dependence shown in Figure 1 may provide an explanation for the non-detection of water in these disks with Spitzer (only a tentative detection was reported by Pascucci et al. 2013): models produce fluxes at or below the measured sensitivity limits, due to a radial extent of the warm water-emitting layer that is ∼10 times smaller than in a disk around a solar-mass star (∼0.1 au; see Walsh et al. 2015). However, according to models, these disks would still show prominent organic emission lines from a disk atmosphere at 0.1–10 au, only mildly UV-irradiated as compared to higher-mass stars. Therefore, a continuous disk around low-mass stars would produce emission at least from organics at 13–15 μm, while no molecular emission at 10–19 μm may be the signature of inner disk depletion, with ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\gt 0.1$ also in disks around low-mass stars.

Previous studies proposed the idea that UV radiation may be responsible for the depletion of water vapor in inner disk surfaces, through an efficient photodissociation of H₂O into OH (Mandell et al. 2008; Pontoppidan et al. 2010a; Fedele et al. 2011; Brittain et al. 2016). Current thermochemical disk models, however, show that the balance at thermochemical equilibrium between the production and destruction of the water molecules produces large columns of water vapor, even in highly UV-irradiated disk surfaces (e.g., Woitke et al. 2009; Walsh et al. 2015). In fact, models produce more water emission than in less UV-luminous stars (or less massive stars; see Figure 1), because H₂O and OH are able to self-shield to UV radiation at the column densities typically measured in inner disks (≳10¹⁷ cm⁻²; Bethell & Bergin 2009). Therefore it is still unclear whether UV photodissociation alone may be responsible for a global depletion of water vapor in inner disks. Further, CO and H₂O emission at 2.9–4.7 μm recede at larger disk radii together (Section 3), and the CO molecule is able to self-shield to UV photodissociation at even lower columns (≈10¹⁵ cm⁻²; Bruderer 2013). As a consequence, a depletion of the molecular column densities to below the self-shielding limits may be required before UV photodissociation may deplete any residual CO and H₂O gas.

The destruction of H₂O by UV radiation has been observationally tested by measuring if OH emission is consistent with prompt emission from excited OH, produced by photodissociation of H₂O (Carr & Najita 2014). However, H₂O line fluxes increase (instead of decrease) with increasing UV radiation, by considering the accretion luminosity as a proxy (at least up to moderate accretion luminosities; see Banzatti et al. 2012, 2014, and Figure 21). The measured $v2/v1$ vibrational ratios of CO lines, which are sensitive to UV pumping and to the UV irradiation that reaches the disk (e.g., Thi et al. 2013), provide another way to test if and how H₂O line fluxes are linked to UV irradiation. The ratio $v2/v1$ decreases as water emission decreases from shorter to longer wavelengths, and $v2/v1$ is not anomalously high in several disks around intermediate-mass stars that show no water emission (Figure 9). However, the increase in $v2/v1$ with inner gap size for ${R}_{\mathrm{co}}\gtrsim 2\,\mathrm{au}$ demonstrates that enough UV radiation is present to pump the CO at large radial distances. In this regime of disk gaps around intermediate-mass stars, UV photodissociation of water could contribute more significantly to the depletion of residual water vapor. We find that this regime is activated after the inner disk region at $\lesssim 2\,\mathrm{au}$ has already been depleted from CO and water.

If not through UV photodissociation, the depletion of CO and H₂O may be initiated in inner disks by direct removal of disk gas. Disk photoevaporation by X-ray and UV photons potentially provides an inside-out dispersal mechanism, although this is proposed to be efficient only beyond the radius where the gas is gravitationally bound to the star (≳1–2 au in disks around solar-mass stars). Another removal mechanism could be through portions of MHD winds (e.g., Ferreira et al. 2006; Bai 2016) that may be probed at optical wavelengths through a low-velocity component in the forbidden oxygen lines (Simon et al. 2016). A slow disk wind has been proposed to contribute also to the CO narrow component in double-component disks (Bast et al. 2011; Pontoppidan et al. 2011a), and may play a role in the depletion of molecular gas in inner disks. A promising direction for future work is to test if wind models can reproduce the formation and development of the molecular holes revealed by the analysis of CO and H₂O velocity-resolved infrared spectroscopy.

In Figure 8, we showed linear trends in the CO/H₂O and OH/H₂O line flux ratios, as measured in the 2.9–4.7 μm lines observed with CRIRES. Both ratios were characterized only out to log ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\sim -1$, due to the absence of 2.93 μm H₂O detections at larger radii. To explore these trends over a larger disk region, we include in Figure 11 the line flux ratios as measured using H₂O line detections at longer wavelengths from the Spitzer data set, which is sensitive to emission at larger disk radii (Sections 3 and 4). We find that the CO/H₂O line flux ratio of all three water lines show similar radial trends. The increase in CO/H₂O is confirmed out to log ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\sim -0.7$ (Figure 11, left plot) by all three water lines. At larger radii, the Spitzer lines suggest a decreasing CO/H₂O out to the snow line radius. Beyond the snow line, lower limits show that the ratio may increase again.

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Following a similar procedure, we show the measured OH/H₂O line flux ratios in Figure 11, right plot. The constant ∼0.4 ratio with disk radius is also confirmed in this case by all three OH/H₂O ratios as measured at different wavelengths (2.93 μm using the CRIRES data, 12.5–12.6 μm and 30–33 μm using the Spitzer data). Some disks show a higher OH/H₂O ratio of ∼1.7 at 12.5–33 μm, perhaps linked to phases of stronger production of OH through increased UV irradiation (among these disks are, in fact, EX Lupi and DG Tau, where enhanced production of OH through UV photodissociation has been found by Banzatti et al. 2012 and Carr & Najita 2014). A decreasing trend of OH/H₂O may be present at log ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\gtrsim -0.7$. Beyond the snow line, lower limits suggest that the ratio may increase. Models propose that the OH/H₂O ratio in the observable column density of gas should increase significantly at the snow line, due to a drop in the column density of H₂O (e.g., Walsh et al. 2015). Future velocity-resolved observations must test if the 12.5–33 μm water lines have velocity profiles that match the 12.6–30 μm OH lines, indicating a similar emitting region (so far, no OH lines have been velocity-resolved at wavelengths $\gtrsim 10$ μm).

An open question is if these observed trends are due to the disk physical/chemical radial structure in a static "primordial" disk, rather than by the formation and evolution of disk gaps that may change it. The decrease of CO/H₂O and OH/H₂O at log ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\gtrsim -0.7$ out to the snow line radius may be due to changes in the disk chemistry as molecular holes expand out to the snow line radius. A promising direction for future modeling is to calibrate the disk chemistry with the measured molecular line flux ratios. The explorations suggested previously within the framework of models that include disk dispersal processes may provide important constraints on the evolution of planet-forming regions. Interesting in this context is, for instance, the notable discrepancy between the data and the model shown in Figure 8 (panel (b) and (c)), where Antonellini et al. (2016) predict an increase in water emission when disk gaps reach the snow line radius as due to a new reservoir of water emission released by photodesorption of icy grains (I. Kamp 2016, private communication). The fact that this is not observed in the data may suggest that the desorption efficiency is overestimated, either by the adopted desorption rates or because dust grains are larger (i.e., the total surface available for ice desorption is smaller) or are removed from disk surfaces. In the evolved disk of TW Hya, to reproduce weak water lines observed at $\gt 250$ μm with Herschel, Hogerheijde et al. (2011) proposed that icy dust grains may have been removed from the disk surface by settling toward the midplane, hiding a large reservoir of icy solids in a region shielded from UV irradiation and photodesorption.

JWST will provide R ∼ 3000 (or ∼100 km s⁻¹) spectroscopy of molecular spectra from the 2.9 μm lines included in this analysis (with JWST-NIRSpec) to the longer wavelengths covered by Spitzer (up to 28 μm, with JWST-MIRI). The observed molecular emission spectra will include CO, H₂O, OH, and CO₂. The broad spectral coverage will provide the data to study more molecular trends than those included in this work, and to better characterize the chemistry and its evolution when gaps form in disks. JWST also has the potential to study infrared molecular emission in disks around low-mass stars, and disk samples not limited to the closest star-forming regions at 120–180 pc. A JWST spectrum at 3–28 μm may distinguish the evolutionary phase of inner disks from the measured line fluxes and the molecular species detected (Figure 9), spanning a range of disk radii and gap sizes (∼ 0.05–20 au; Banzatti & Pontoppidan 2015) that is highly complementary to the larger scales probed by millimeter interferometry with the Atacama Large Millimeter Array ALMA ($\gtrsim 5\,\mathrm{au}$ at 140 pc; e.g., van der Marel et al. 2016) and by direct imaging techniques. The joint use of these observatories can transform our understanding of the development of disk gaps from the innermost disk regions to the larger-scale disk structures, and of the physical and chemical evolution of planet-forming environments.

We measure emission line fluxes by fitting a first-order polynomial continuum over neighboring pixels and by summing continuum-subtracted pixel flux values over the spectral range of each line. In the Spitzer-IRS spectra, to select pixels of continuum free from line emission, we use models of the strongest emitters at 10–35 μm, as identified in previous work (water, OH, HCN, C₂H₂, CO₂, HI; see, e.g., Carr & Najita 2011; Banzatti et al. 2012). The following are the ranges adopted: the 12.52 μm line is measured on 12.50–12.537 μm, and its continuum fitted on 12.48–12.5 μm and 12.7–12.72 μm (at the two sides of the line); the 33 μm line on 32.92–33.06 μm and its continuum on 32.53–32.63 μm and 33.4–33.47 μm; the 12.65 μm OH line on 12.64–12.68 μm and its continuum on 12.48–12.5 μm and 12.7–12.72 μm; the 30 μm OH lines on 30.245–30.385 μm and 30.62–30.73 μm, and their continua on 30.1–30.17 μm and 30.38–30.43 μm, and 30.57–30.62 μm and 30.73–30.83 μm (we sum the flux of these OH doublets to increase the S/N). OH detections at 30 μm are only tentative in some spectra of disks around intermediate-mass stars and will need to be confirmed by higher-spectral-resolution observations. Line flux errors are estimated as the standard deviation of the distribution of measured line fluxes after re-sampling the spectrum using the local noise, as in Banzatti et al. (2012). Following this procedure, we find values consistent within 1σ (or a few %) to those measured by Pontoppidan et al. (2010a), adopting as a test case the 17.22 μm water line. Line fluxes and errors are reported in Table 6; in all figures throughout this paper, line fluxes are normalized to a common distance of 140 pc for a homogeneous comparison, using distances from Table 2.

In the CRIRES spectra, line fluxes are measured in the continuum-normalized spectra and then flux calibrated using fluxes measured by the Wide-field Infrared Survey Explorer (WISE, Wright et al. 2010) at 3.35 and 4.6 μm, as released by Cutri et al. (2012, 2014). In some cases where the WISE 4.6 μm measurement disagrees with previous photometry, we adopt the Spitzer-IRAC measurement or an interpolated value between WISE measurements at 3.35 μm and 11.6 μm. The adopted continuum fluxes are reported in Table 2. Unlike in the Spitzer spectra, the lines observed with CRIRES are velocity-resolved and present a broad range of widths that makes it inappropriate to adopt fixed pixel ranges for their measurement. To adopt a homogeneous method, we therefore measure the line flux included within the full width at 10% of the line peak. Table 6 reports the fluxes and errors measured for the lines listed in Table 3. The four water lines at ∼2.93 μm are measured together into a single flux value, because in most spectra they are blended together due to their large line widths.

Figures 12 and 13 show the stellar photospheric correction of CRIRES 2.9 μm spectra as explained in Section 3.1. This procedure proves to be effective in correcting most science spectra—those that match well with a spectral template and where the disk gas emission lines are broader than the absorption lines from the same molecules in the stellar photosphere. In some cases, however, there is no unambiguous/acceptable spectral match with a template (in CW Tau, HT Lup, and IM Lup), or the disk emission lines are possibly as narrow as the photospheric lines (in FN Tau and TW Hya); in these cases, the residuals after photospheric correction leave larger uncertainties on potential detections of H₂O and OH and on their line profiles.

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Figures 14–19 show fits to CRIRES 2.9 μm spectra made by using the CO line profiles as models for H₂O and OH emission, as explained in Section 3.3. In addition to fitting the 2.9 μm data with the NC or BC separately (in those disks that have two CO components), we also combine NC and BC profiles in different fractions, a technique that we call Spectral Principal Component Analysis (SPCA), as being based on principal spectral components given by NC and BC (Figure 15). In the double-component disks, we can therefore test whether H₂O and OH are composed of one rather than two components, and which one dominates. To determine which model best represents the data among NC, BC, and their combination, we use the Akaike information criterion (Akaike 1974), defined as AIC = $2\times$ the number of free model parameters + the chi-square value. The criterion penalizes models with a larger number of free parameters, so that a simpler model is preferred unless the more complex model decreases the AIC number significantly (we adopt the criterion of a ΔAIC $\gt \,14$, corresponding to a 10⁴ higher probability of minimizing the information loss). In most cases, the chi-square value is enough to identify the best model between BC and NC.

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This procedure is generally robust against the photospheric correction performed on the 2.9 μm velocity-resolved spectra obtained by CRIRES (Section 3.1), because the disk emission lines are typically broader than photospheric lines from the same molecules (Figures 2, 4, 12, 13) and because the high resolving power of CRIRES allows the separation of emission components with different velocities. In two disks (FN Tau, TW Hya), however, photospheric lines have similar width as the possibly detected OH emission lines, while H₂O is undetected; their OH line fluxes and profiles are therefore highly uncertain (see Figure 18).

Overall, both non-detections and detections of weak emission advocate for the predominance of BC over NC in H₂O and OH emission at 2.9 μm. In a few cases, spectra are best fit with a combination of BC and NC: specifically AS 205, DR Tau, and SCrA N (and only OH in CW Tau). These three disks are also the only ones where NC was detected in the CO v = 2 − 1 lines, possibly due to the higher S/N and dust veiling in these spectra compared to other spectra in the survey (Banzatti & Pontoppidan 2015). Two other disks show tentative evidence for a weak NC, but its presence cannot be firmly established due to uncertainties from the photospheric correction: RU Lup and SCrA S. In all disks, the NC is about 2–10 times (or more) weaker in H₂O and OH than in CO, as compared to BC. In a few cases only, the OH profile is better matched by NC rather than by BC (DF Tau, RNO 90, VW Cha). In single-component disks, OH is detected only in EC 82 and TW Cha.

Figure 20 shows the measured H₂O and OH line fluxes plotted against the stellar + accretion luminosity, taken as a proxy for the irradiation and heating of inner disks. Only the OH line at 30 μm shows a steady flux increase with increasing luminosity, consistent with an increasing area of the warm disk emitting region. Hotter OH lines show rather a turning point at a luminosity of $\sim 3\,{\text{}}{L}_{\odot }$, beyond which line fluxes decrease (similar to that seen in the H₂O at 33 μm). Figure 21 shows the measured line fluxes plotted against the accretion luminosity alone, to highlight how line fluxes overall increase with accretion luminosity. The last two plots in the bottom right of the figure show the T-R diagram of CO emission, highlighting how there is no global trend between the sequence of CO gaps and the accretion luminosity and rate. OH emission is more frequently detected than water emission in disks, and is tentatively detected at 30 μm out to ${R}_{\mathrm{co}}$/R${}_{\mathrm{snow}}\sim 4$ (Figure 8) and up to larger luminosities (Figure 20), possibly supporting a still active photodissociation of trace amounts of H₂O gas. OH formation through water photodissociation populates higher energy levels first (e.g., the 12.6 μm line; see Carr & Najita 2014), though, which are less often detected in disks that have a large ${R}_{\mathrm{co}}$. It is therefore unclear whether a cold OH reservoir traced at 30 μm may be formed by photodissociation of H₂O or by gas-phase chemistry, known to be efficient at temperatures of 100–300 K (e.g., van Dishoeck et al. 2013). Future observations of velocity-resolved H₂O and OH lines at wavelengths longer then 2.9 μm will be able to test if two reservoirs of OH exist: one due to UV photodissociation of water (with similar line profiles for H₂O and OH, as found at 2.9 μm), which dominates the hotter OH lines, and one due to OH formation in cold environments where water formation and/or release to the gas phase is less efficient (by finding larger line profiles for H₂O and smaller line profiles for OH).

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