Spectrally Resolved Mid-infrared Molecular Emission from Protoplanetary Disks and the Chemical Fingerprint of Planetesimal Formation

To determine the HCN and ${{\rm{H}}}_{2}{\rm{O}}$ emission line profiles, we first subtracted a local linear slope to the continuum, determined from neighboring wavelength regions located just beyond the line emission region. The profiles of the bright ${{\rm{H}}}_{2}{\rm{O}}$ lines in the 805 cm⁻¹ setting were used to set the velocity extent of the line emission region (±25 km s⁻¹).

The line profiles of the water and organic emission in both the AS 205 N and DR Tau spectra are consistent with each other within the noise. As shown in Figure 5, the HCN line profile in the AS 205 N spectrum is consistent with that of the ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ emission and with that of the weak ${{\rm{H}}}_{2}{\rm{O}}$ line at 779 cm⁻¹. Because the profiles of the HCN R22 and R23 lines for AS 205 N were similar, we averaged them together to obtain a higher signal-to-noise profile; the individual lines were scaled to a common line flux and the profiles averaged. The HCN emission has an FWHM of ∼20 km s⁻¹ and peaks at v_helio ∼−4 km s⁻¹. The top panel of Figure 5 compares the average line profile of the HCN lines (R22 and R23) with the profile of the ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ R21 line. The lower panel of Figure 5 compares the average of all three organic lines (HCN R22, HCN R23, and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ R21) with the 779 cm⁻¹ water line. The ${{\rm{H}}}_{2}{\rm{O}}$ 779 cm⁻¹ and HCN lines are similar in strength and detected at a similar signal-to-noise ratio.

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The bright water lines in the 805 cm⁻¹ setting on AS 205 N provide a better estimate of the water line profile. To define the water line profile, we examined the higher energy lines, which have good telluric correction (808, 807, and 806 cm⁻¹), and excluded the lower energy water lines (803, 804 cm⁻¹), which have stronger telluric absorption and less certain line profiles. Figure 6 compares the average HCN line profile with the profile of the 808 cm⁻¹ ${{\rm{H}}}_{2}{\rm{O}}$ line, which is closer in excitation to the HCN lines. The profiles of the two other water lines compare similarly. All three water lines are discussed in greater detail in J. S. Carr et al. (2018, in preparation).

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Given the wavelength calibration uncertainty and the limited signal-to-noise ratio of the HCN profile, the water and HCN profiles appear consistent with each other. Echoing the result found here, Mandell et al. (2012) found that the line profiles of the HCN and ${{\rm{H}}}_{2}{\rm{O}}$ emission lines observed in the L-band with CRIRES were consistent with each other, although at a much lower signal-to-noise ratio.

Similar results are found for the water and HCN emission from DR Tau. Figure 7 shows the average water line profile, obtained by scaling the three bright water lines in the 805 cm⁻¹ setting to the same equivalent width and averaging. The resulting profile is centrally peaked, with an FWHM of 13 km s⁻¹ and centered at v_helio of 25 km s⁻¹. The HCN line profile overlaps the ${{\rm{H}}}_{2}{\rm{O}}$ lines in velocity and appears consistent with the ${{\rm{H}}}_{2}{\rm{O}}$ profile given the limited signal-to-noise ratio of the detection.

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The water line emission properties we measure are in good agreement with earlier observations of water emission from DR Tau. Observations with VISIR found the same v_helio for the 806 and 805 cm⁻¹ water lines (Banzatti et al. 2014). Our measured FWHM of the MIR water emission (13 km s⁻¹) is consistent with that of the L-band water emission from DR Tau measured with Keck/NIRSPEC (18 km s⁻¹; Brown et al. 2013b) given the lower spectral resolution of the NIRSPEC spectrum (12 km s⁻¹). From the NIRSPEC spectrum, Brown et al. (2013b) inferred that the water emission extends outward in disk radius to at least 0.4 au, i.e., to a projected velocity of at least 7 km s⁻¹ for the stellar mass (0.4 M_⊙; Isella et al. 2009) and source inclination (i = 13°; see also Pontoppidan et al. 2011). At the higher resolution of the TEXES observations, we find that the MIR water emission extends to lower velocities and therefore larger disk radii (Section 4.1).

More generally, the line center velocities of the molecular emission from DR Tau and AS 205 N are consistent, within the TEXES wavelength calibration uncertainty, with that of other infrared and submillimeter molecular emission from the sources and with their stellar velocities. Further details are provided in Appendix A.

To characterize the detected emission, we compared the observed emission features with simple spectral synthesis models of LTE emission from gaseous slabs of a given temperature, column density, and emitting area (e.g., Carr & Najita 2008, 2011; Salyk et al. 2011b). Although protoplanetary disks are not isothermal (vertically or radially) and may not be in vibrational LTE, isothermal slab models can provide good fits to the data. They also provide estimates of the physical conditions in the line emitting regions.

For each of the two observed targets, we first calculated synthetic spectra to match the IRS SH spectra and then generated high-resolution spectra using the same model parameters for comparison with the TEXES data. The reduction of the IRS SH data for AS 205 N (2004 August 28, AOR 5646080) and DR Tau (2008 October 8, AOR 27067136) followed the methods given in Carr & Najita (2011). The procedure and molecular linelists used in the modeling are also described in Carr & Najita (2011). While the molecular emission lines are not resolved with IRS (R = 600), the IRS spectra have the advantage of including many lines with different A-values and energy levels, which constrains the temperature and column density (e.g., Carr & Najita 2008, 2011; Salyk et al. 2011b). Thus, the IRS spectra complement the TEXES data, which include only a few lines spanning a limited range of excitation.

In the slab models, the dust continuum is assumed to be negligible in the layer of the atmosphere that produces the molecular emission, consistent with our expectations for disk atmospheres. Recent disk atmosphere models by Najita & Ádámkovics (2017), which include irradiation by UV continuum and Lyα, find that warm HCN and water are abundant in the disk atmosphere over a vertical column density of N_H ∼ 10²² cm⁻² in hydrogen nuclei. If we assume that the dust in the atmosphere is reduced by a factor of ∼100 compared to ISM conditions, as is inferred for T Tauri disks and attributed to grain settling (Furlan et al. 2006), the vertical optical depth of the HCN-emitting region is A_V ∼ 0.05 and much lower at MIR wavelengths.

3.2.1. AS 205 N

We first fit the IRS water emission spectrum from AS 205 N using synthetic spectra generated with the LTE slab emission model. As described above, the IRS spectra have the advantage of including many water lines with different A-values and energy levels, which constrains the temperature and column density (e.g., Carr & Najita 2008, 2011). The temperature and column density were determined by χ² fits to water features between 12 and 16 μm. The best fit to the AS 205 N IRS water spectrum (Figure 18) gives a temperature of 680 ± 80 K, a column density of ${N}_{{{\rm{H}}}_{2}{\rm{O}}}$ = 1.3(+0.9/ −0.5) ×10¹⁸ cm⁻², and an emitting area of $\pi {R}_{e}^{2}$ where R_e = 1.90 ± 0.14 au, for a distance of 130 pc (Wilking et al. 2008; Loinard et al. 2008; Mamajek 2008). The parameters are given in Table 3. Note that in fitting the IRS spectra of water, temperature and column density are correlated (Salyk et al. 2011b) such that a higher bound on temperature corresponds to a lower bound on column density and a smaller emitting area.

Table 3.  Parameters for Slab Models

Source	Spectrum	T	R	N(${{\rm{H}}}_{2}{\rm{O}}$)	N(HCN)	N(${{\rm{C}}}_{2}{{\rm{H}}}_{2}$)	N(HCN)/N(${{\rm{H}}}_{2}{\rm{O}}$)
		(K)	(au)	(cm−2)	(cm−2)	(cm−2)
AS 205 N	IRS	680	1.90	1.3 (18)	4.2 (15)	1.5 (15)	0.0033
AS 205 N	TEXES	680	1.90	1.6 (18)	6.8 (15)	1.0 (15)	0.0043
DR Tau	IRS	690	1.33	9.3 (17)	5.7 (15)	6.8 (14)	0.0062
DR Tau	TEXES	690	1.33	4.6 (17)	4.4 (15)	⋯	0.0097

Note. The same temperature and emitting area are assumed for all species. For uncertainties, see text.

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To model the HCN and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ Q branch emission (at 14 μm and 13.7 μm respectively), we subtracted the synthetic water emission from the IRS spectrum. While LTE slab models provide a general match to the IRS water spectra, the fits are far from perfect (Carr & Najita 2011; Salyk et al. 2011b). Mismatches between the observed and model spectra are likely due to a range in temperature and column density in actual disk atmospheres, non-LTE level populations, and possibly missing transitions in the water line list or other unidentified features. Of relevance to the HCN and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ modeling, the water model appears to overcorrect for the few ${{\rm{H}}}_{2}{\rm{O}}$ features that fall within the Q branches. The location of these ${{\rm{H}}}_{2}{\rm{O}}$ features are marked in Figures 8 and 11. The pixels affected by these lines were ignored in the modeling.

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In modeling the HCN and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ emission, we assumed that they have the same emitting area and temperature as the ${{\rm{H}}}_{2}{\rm{O}}$ emission and adjusted the column density to match the flux in the Q branches. The assumption of similar emitting areas for ${{\rm{H}}}_{2}{\rm{O}}$, HCN, and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ is reasonable, given the similarity of their line profiles in the TEXES data. We find that the HCN and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ emission can be matched with column densities N_HCN = 4.2 (±0.2) × 10¹⁵ cm⁻² and ${N}_{{{\rm{C}}}_{2}{{\rm{H}}}_{2}}=1.5(\pm 0.2)\times {10}^{15}\,{\mathrm{cm}}^{-2}$. The shape of the Q branches is diagnostic of the rovibrational temperature of the gas. Comparison of the observed and model HCN spectra (Figure 8) shows that HCN is consistent with having the same ∼680 K temperature as ${{\rm{H}}}_{2}{\rm{O}}$. To explore the range of possible temperatures for the HCN emission, we held the emitting radius constant but allowed both temperature and column density to vary. This gave a best fit at T = 670 K with a range of 590–770 K, similar to the temperature range for ${{\rm{H}}}_{2}{\rm{O}}$. For ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$, the smaller width of the band and the water line at 13.69 μm prevented a definite determination of its temperature.

The parameters derived from the IRS spectra (Table 3) were then used to calculate LTE model spectra for comparison to the TEXES data. The IRS parameters work well for the TEXES ${{\rm{H}}}_{2}{\rm{O}}$ spectrum: the line ratios of the three best-measured water lines are reproduced, and the line fluxes are within 15% of the observed values. For the model plotted in Figure 9, the ${{\rm{H}}}_{2}{\rm{O}}$ column density was increased to ${N}_{{{\rm{H}}}_{2}{\rm{O}}}$ = 1.6(±0.1) × 10¹⁸ cm⁻² to match the line fluxes, although a small change in radius, temperature, or flux calibration would work equally well. The optical depths for the TEXES ${{\rm{H}}}_{2}{\rm{O}}$ lines are of order unity; therefore, the ratios of the three lines depend on both water temperature and column density. The match of the IRS-based model to the TEXES data (Figure 9) shows that the TEXES and IRS water emission are consistent with the same LTE temperature, column density, and emitting area.

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When the parameters used to fit the IRS spectra of HCN and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ are applied to the TEXES spectrum (Figure 10; dotted red line) we find that the HCN lines are underpredicted by 36% while the ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ line is overpredicted by 44%. A change in the joint emitting area of the molecules could not produce this effect. The line strengths in the TEXES spectrum can be fit (solid red line in Figure 10) by increasing the column density of HCN to 6.8(±0.5) × 10¹⁵ cm⁻² and decreasing the column density of ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ to 1.0(±0.1) × 10¹⁵ cm⁻².

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3.2.2. DR Tau

The same procedure was followed for DR Tau. The fit to the IRS water spectrum of DR Tau gave T = 690 ± 75 K, ${N}_{{{\rm{H}}}_{2}{\rm{O}}}$ = 9.3(+6.7/−3.4) × 10¹⁷ cm⁻², and R_e = 1.33 ± 0.07 au, assuming a distance of 140 pc (Figure 19 in Appendix B). After subtracting the model ${{\rm{H}}}_{2}{\rm{O}}$ spectrum, the HCN and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ Q branch fluxes were fit by adjusting the column densities, assuming the same emitting area and temperature as for the ${{\rm{H}}}_{2}{\rm{O}}$ emission. Figure 11 shows the resulting fit, with column densities of N_HCN = 5.7(±0.3) × 10¹⁵ cm⁻² and ${N}_{{{\rm{C}}}_{2}{{\rm{H}}}_{2}}$ = 6.8(±1.0) × 10¹⁴ cm⁻². While the ${{\rm{H}}}_{2}{\rm{O}}$ temperature of 690 K is consistent with the shape of the HCN Q branch, a higher temperature (∼800 K) improves the fit slightly, with an acceptable range of 700–1000 K. The ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ Q branch is relatively weak in DR Tau, and no conclusion about the ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ temperature is possible.

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When the water emission parameters derived from the IRS spectra are used to model the TEXES spectrum, the water line fluxes are overpredicted by nearly a factor of two (Figure 12). A reduction of the column density to ${N}_{{{\rm{H}}}_{2}{\rm{O}}}$ = 4.6(±0.2) ×10¹⁷ cm⁻² matches the line fluxes. The temperature could also be lowered to reduce the line fluxes, but then the observed line ratios would no longer match. The model ${{\rm{H}}}_{2}{\rm{O}}$ fluxes can also be reduced by decreasing the emitting area, or increasing the continuum flux (i.e., the flux calibration), but this would cause the HCN flux to be underpredicted. With the nominal IRS-derived model, the HCN line is overpredicted by ∼30%. To reproduce the observed HCN line strength (Figure 13) requires decreasing the HCN column density to 4.4(±0.8) × 10¹⁵ cm⁻². The prediction for the ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ R21 line (not shown) is consistent with the nondetecton of this line in the TEXES data.

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3.2.3. Variability

We find that the line profiles of the MIR HCN and ${{\rm{H}}}_{2}{\rm{O}}$ emission from DR Tau and AS 205 N are roughly symmetric and centered within a few km s⁻¹ of the stellar velocity (Appendix A). The emission also overlaps in velocity other known molecular emission diagnostics from the inner disk regions of these sources (rovibrational CO, ${{\rm{H}}}_{2}{\rm{O}}$, UV fluorescent ${{\rm{H}}}_{2}$; e.g., Salyk et al. 2008, 2011a; Schindhelm et al. 2012; Banzatti et al. 2014; Brown et al. 2013a, 2013b). These properties are consistent with emission from a rotating disk and not with high velocity outflows or inflows. Magnetocentrifugal winds and magnetospheric infall produce strongly blue- or redshifted emission and/or absorption features extending to ∼100 km s⁻¹ or more even at the relatively low inclination of our sources, e.g., forbidden optical line emission from winds (Hartigan et al. 1995; Simon et al. 2016) and magnetospheric infall emission/absorption profiles observed in H i (e.g., Edwards et al. 1994; Muzerolle et al. 1998a, 1998b; Folha & Emerson 2001).

Millimeter imaging and infrared spectroastrometric studies point to a low inclination for AS 205 N (i = 15° to include the units of degrees; as discussed in Salyk et al. 2014). Inclination estimates range from low to high for DR Tau, with spectroastrometric studies of the inner disk favoring a low inclination. The Pontoppidan et al. (2011) study of CO rovibrational emission found a good fit to their data assuming an inclination of 9°. Brown et al. (2013b) were able to fit their spectroastrometric L-band water observations with an inclination of i = 13°.

Photoevaporative disk winds are expected to produce observable blueshifts of 5–10 km s⁻¹ at these low inclinations (Font et al. 2004; Alexander 2008). In contrast, the water profiles of both sources studied here show, if anything, small redshifts rather than blueshifts. The water profile of DR Tau is +3 km s⁻¹ from the average of the reported stellar velocities (Petrov et al. 2011; Nguyen et al. 2012), and the AS 205 N profile is shifted by +4 km s⁻¹ (Melo 2003; Appendix A). The absence of a photoevaporative signature in the HCN and ${{\rm{H}}}_{2}{\rm{O}}$ profiles is not surprising. Driven from the disk surface by X-ray and UV irradiation, photoevaporative flows are likely to be atomic or ionized rather than molecular and unlikely to contribute to the molecular emission profile. Thus the line profiles of the HCN and ${{\rm{H}}}_{2}{\rm{O}}$ emission are best explained as arising in the inner disk.

The resolved line profiles also constrain the range of disk radii from which the emission arises. Au-sized projected emitting areas have been inferred for the MIR molecular emission from CTTS based on Spitzer spectra, which are spatially and spectrally unresolved (Carr & Najita 2008, 2011; Salyk et al. 2011b). From simple slab emission models, we infer water-emitting areas $\pi {R}_{e}^{2}$ with an R_e of 1.3 au for DR Tau and 1.9 au for AS 205 N (Section 3.2), similar to values previously reported in the literature. Salyk et al. (2011b) previously inferred water-emitting areas $\pi {R}_{e}^{2}$ with an R_e of 1.1 au for DR Tau and 2.1 au for AS 205 N using a similar approach.

Using the resolved line profiles, we can obtain an independent constraint on the range of disk radii responsible for the emission given the disk inclination and stellar mass for each source. For AS 205 N, with a stellar mass of M_* = 1.1 M_⊙ (Najita et al. 2015) and an inclination of i = 15, the observed ∼30 km s⁻¹ HWZI (half-width at zero intensity) of the ${{\rm{H}}}_{2}{\rm{O}}$ emission corresponds to an inner emission radius of 0.07 au. Emission from gas at 1.7 au would have a projected velocity of v sin i = 6.2 km s⁻¹, similar to the half-width of the flat-topped portion of the water line profile (Figure 6). Thus the line profile is consistent with ${{\rm{H}}}_{2}{\rm{O}}$ emission extending from 0.07 au to ∼2 au. The HCN profile of AS 205 N is similar to the ${{\rm{H}}}_{2}{\rm{O}}$ profile at low velocities, indicating that the HCN emission extends over a similar range of radii. Because of their lower signal-to-noise ratio, it is not possible to determine whether the wings of the HCN profile have the same velocity extent as the ${{\rm{H}}}_{2}{\rm{O}}$ profile. The HCN emission extends to at least ±15 km s⁻¹ from line center, i.e., inward in radius to at least 0.3 au.

For DR Tau, with a stellar mass of M_* = 1.2 M_⊙ (Andrews et al. 2013, using stellar evolutionary tracks from Siess et al. 2000) and i = 8°, the observed HWZI of at least 20 km s⁻¹ for the ${{\rm{H}}}_{2}{\rm{O}}$ lines corresponds to an inner emission radius of 0.05 au or smaller. Emission from gas at 1.4 au would have a projected velocity of v sin i = 4 km s⁻¹. We observe ${{\rm{H}}}_{2}{\rm{O}}$ emission throughout this range of velocities, and the strongly peaked profile suggests that the emission may extend beyond 1.4 au. Here we have adopted a lower inclination (i = 8°) than the values preferred by Pontoppidan et al. (2011; i = 9°, M_* = 1.0 M_⊙) and Brown et al. (2013; i = 13°; M_* = 0.4 M_⊙) to compensate for the larger stellar mass adopted here.

The similar line profiles and emission temperatures for HCN and water suggest that the two diagnostics probe the same volume of the disk atmosphere. First, the HCN and ${{\rm{H}}}_{2}{\rm{O}}$ profiles extend over approximately the same range of velocities in the case of both AS 205 N and DR Tau, consistent with the HCN and water emission arising from approximately the same range of disk radii in both systems. Second, the similar emission temperatures for HCN and water are consistent with the HCN and water emission arising from the same vertical height in the disk. Models of inner disk atmospheres irradiated by stellar UV and X-rays find that the gas temperature exceeds the dust temperature in the atmosphere and transitions from a hot (∼4000 K) atomic region at the top of the atmosphere to a warm molecular region (∼300–1000 K) at intermediate heights before reaching the dust temperature deeper in the atmosphere (Ádámkovics et al. 2014; Najita et al. 2011; Najita & Ádámkovics 2017). Both HCN and water are abundant in the intermediate layer—the warm molecular region—consistent with the similar line profiles and temperatures found here for the HCN and water emission.

The inferred temperatures and column densities of the HCN and water emission are also roughly consistent with thermal-chemical models of irradiated disk atmospheres. In comparison with the ∼700 K temperature and R_e ∼ 1.5 au emitting area found for the HCN and ${{\rm{H}}}_{2}{\rm{O}}$ emission, the reference model of Najita & Ádámkovics (2017) for a generic T Tauri disk atmosphere irradiated by stellar far-UV continuum, Lyα, and X-rays, is characterized at 1 au by vertically coincident warm (300–1000 K) HCN and water with vertical column densities (3 × 10¹⁵ cm⁻² and 2 × 10¹⁷ cm⁻², respectively) similar to the measured line of sight columns (∼5 × 10¹⁵ cm⁻² and ∼1 × 10¹⁸ cm⁻², respectively). Closer agreement may be possible with disk atmospheres more closely matched to the star+disk properties of the sources studied here.

Our results support the interpretation of the observed trend of increasing HCN/${{\rm{H}}}_{2}{\rm{O}}$ emission with disk mass as a possible chemical fingerprint of planetesimal formation and core accretion in action (Najita et al. 2013; Carr & Najita 2011). The core accretion model of planet formation is compelling in its ability to account for planet formation outcomes such as the existence of small rocky planets as well as ice and gas giants within the solar system and in the exoplanet population. But what does core accretion look like? Can any observations reveal whether known protoplanetary disks are actually engaged in core accretion? One approach is to look for observational evidence of the formation of planetesimals and protoplanets, which play no role in a competing theory of planet formation such as gravitational instability.

Observationally elusive, planetesimals are difficult to detect directly because of their small size, small mass, and intrinsic faintness. However, they may potentially reveal themselves through the chemical signature they induce in the gaseous disk within the snowline. When icy objects grow large enough (kilometer-sized or larger) to decouple from inward migration induced by gas drag, they are sequestered in the icy region of the disk beyond the snow line (beyond ∼1 au; Ciesla & Cuzzi 2006). The gas that accretes into the warm inner disk region within the snow line is thereby depleted of water (and oxygen), resulting in a higher C/O ratio than the disk overall. Thermal-chemical models of disk atmospheres predict that only a modest enhancement in the C/O ratio of the inner disk (factor of 2) is sufficient to induce a large, observable change in the HCN/${{\rm{H}}}_{2}{\rm{O}}$ ratio in the atmosphere (factor of 10), consistent with the range of observed molecular emission flux ratios (Najita et al. 2011).

As a result, molecular abundances in the inner disk (within the snow line) may encode evidence for icy planetesimal formation beyond the snowline. Because disks with higher masses are expected to grow planetesimals more rapidly, we expect to see the HCN/${{\rm{H}}}_{2}{\rm{O}}$ ratio in the inner disk increase with disk mass in systems undergoing planetesimal formation, a trend that is indeed observed (Najita et al. 2013; see also Figure 14). If this interpretation of the observed trend is correct, it implies that most T Tauri disks are in an advanced stage of planet formation, having built and sequestered large icy bodies beyond the snow line (Najita et al. 2013). This interpretation assumes that the HCN and ${{\rm{H}}}_{2}{\rm{O}}$ emission arise from the same volume of the disk atmosphere. In finding that MIR HCN and water emission probe the same volume of the disk atmosphere, our results support the hypothesis that the trend between the HCN/${{\rm{H}}}_{2}{\rm{O}}$ flux ratio and disk mass is evidence for planetesimal formation.

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The inference that planet formation is well advanced in most T Tauri disks is supported by a comparison of the mass of small solids present in T Tauri disks (the dust disk mass distribution) with the solids locked up in known exoplanet populations (Najita & Kenyon 2014). The comparison shows that there are fewer small solids in T Tauri disks than in the known exoplanets. If T Tauri disks are the birthplaces of planets, their low inventory of solids implies that they are by no means unevolved "primordial disks." More likely, most of the solids in most T Tauri disks have already grown into large sizes that are invisible to millimeter observations (beyond cm sizes) and/or they have been concentrated at small radii (within a few au) where they are optically thick at millimeter wavelengths. The trend of HCN/${{\rm{H}}}_{2}{\rm{O}}$ versus disk mass goes a step further and implies that the solids beyond the snow line have grown much beyond cm size and large enough to decouple from gas drag (i.e., kilometer-sized or larger).

This picture is consistent with the short timescale inferred for planetesimal formation in the solar system. Radiometric analyses of meteorites find that differentiated planetesimals accumulated soon after the formation of calcium aluminum inclusions (CAIs), i.e., that planetesimal formation was well underway at the onset of the T Tauri epoch of solar system history (Kleine et al. 2009; Dauphas & Chaussidon 2011).

Figure 14 plots as a function of disk mass the HCN/${{\rm{H}}}_{2}{\rm{O}}$ flux ratio measured from IRS spectra for the sources reported in Najita et al. (2013; red diamonds) and the sources studied here (blue diamonds). The HCN flux shown includes a correction for water emission blended with the HCN Q branch. The water flux shown is the sum of the water emission features at 17.12, 17.22, and 17.36 μm, and disk masses are derived from submillimeter continuum emission (Najita et al. 2013, 2015).

The trend of HCN/${{\rm{H}}}_{2}{\rm{O}}$ versus disk mass, while clearly apparent, has significant scatter. Multiple factors may be responsible for the scatter. The extent of planetesimal formation in the giant planet region may differ between sources of similar outer disk mass. Excitation effects may reduce HCN emission in inner disks with lower densities (Section 4.5). HCN and ${{\rm{H}}}_{2}{\rm{O}}$ may not always probe the same volume.

Any time variability in the HCN/${{\rm{H}}}_{2}{\rm{O}}$ emission ratio (Section 3.2.3) will also contribute to the observed scatter. Figure 14 shows the larger HCN/${{\rm{H}}}_{2}{\rm{O}}$ ratios we would infer from the TEXES data (blue circles) if the larger HCN/${{\rm{H}}}_{2}{\rm{O}}$ column density ratios found for the TEXES data (compared to the IRS data) reflect time variability (Section 3.2.3) and if the change in the inferred column density ratio (Table 3) translates into a change in the HCN/${{\rm{H}}}_{2}{\rm{O}}$ flux ratio. Accordingly, the flux ratios of AS 205 N and DR Tau in the TEXES data are shown enhanced by factors of 1.3 and 1.6, respectively, over their IRS flux values. The magnitude of the variability in the HCN/${{\rm{H}}}_{2}{\rm{O}}$ flux ratio found for AS 205 N and DR Tau is similar to the magnitude of the scatter observed in the relationship of HCN/${{\rm{H}}}_{2}{\rm{O}}$ versus disk mass. (The overall trend of HCN/${{\rm{H}}}_{2}{\rm{O}}$ flux ratio with disk mass extends, of course, over a much larger range of values.) Further study of variability in HCN/${{\rm{H}}}_{2}{\rm{O}}$ ratio is needed to understand whether this range of variability is typical of T Tauri disks.

Changes in molecular emission from the inner disk could arise from changes in the instantaneous UV field (driven by variations in stellar accretion), instantaneous local accretion heating (e.g., from time-varying energy dissipation due to the magnetorotational instability), grain settling or dust-lofting events in the disk atmosphere (e.g., due to disk turbulence), or other effects. These processes affect the photochemistry of the disk atmosphere, the depth of the warm disk atmosphere that can produce MIR molecular emission, and the depth to which we can see into the atmosphere. Because the HCN emission tends to be concentrated toward the top of the atmosphere, whereas water emission can extend deeper (e.g., Najita & Ádámkovics 2017), these processes can enhance or reduce the HCN/${{\rm{H}}}_{2}{\rm{O}}$ flux ratio.

A concrete illustration of the role of one process, accretion heating, in altering the molecular emission ratio comes from observations of the extreme outburst observed from EX Lupi (Banzatti et al. 2012). The Spitzer water emission increased dramatically in outburst, while emission from the organics completely disappeared. More modest accretion variability may produce more modest changes in the relative molecular fluxes.

Our constraints on the range of disk emission radii for HCN and water also bear on the abundance ratios inferred for inner disks. Molecular abundances can probe the extent to which inner disks are chemically active, i.e., whether inner disks actively synthesize molecules or primarily inherit their abundances from the interstellar medium or larger disk radii. As noted in Section 1, some earlier analyses of spectrally unresolved data inferred that inner disks have an HCN/water abundance that is significantly enhanced, by about an order of magnitude, relative to that of comets (Carr & Najita 2008, 2011). If comets are a surrogate probe of the chemical conditions in the giant planet region of the disk, where they are believed to have formed, the difference between the abundances of inner disks and comets can be interpreted as evidence for an active inner disk chemistry.

The low spectral resolution of Spitzer/IRS introduces potential uncertainty in the inferred column density ratios and abundances, because lines are blended and the spatial information from resolved line profiles is unavailable. In general, there can be signficant degeneracies between model parameters, even for LTE slab models (Carr & Najita 2011; Salyk et al. 2011b). Modeling assumptions may also differ.

In their modeling of Spitzer IRS spectra, Carr & Najita (2008, 2011) favored a fit with a smaller emitting area for HCN than water. In their minimum chi-square fits, in which the HCN emission is close to optically thick, the HCN emitting area is a factor of 3–12 smaller than the water emitting area, and the HCN/${{\rm{H}}}_{2}{\rm{O}}$ column density ratio is high (0.03–0.1; Figure 15, open red squares). In contrast, under the assumption of equal emitting areas for HCN and water, the HCN emission is optically thin, and the HCN/${{\rm{H}}}_{2}{\rm{O}}$ column density ratios are 4–30 times smaller than in the best fit but still fall within the confidence interval of fits to the HCN bandhead (see Carr & Najita 2011; Figure 15, solid red squares).

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Salyk et al. (2011b) also reported molecular column densities from simple slab fits to Spitzer IRS spectra under the assumption of equal emitting areas for all molecules. In contrast to the smaller wavelength region studied by Carr & Najita (2011; 12–16 μm), Salyk et al. (2011b) fit the strengths of water emission features from a much broader range of wavelengths (10–35 μm), among other differences in the modeling procedure. As shown in Figure 15, the molecular column density ratios reported by Salyk et al. (magenta squares) do not overlap those of Carr & Najita (2011; solid red squares), illustrating how different modeling choices (e.g., wavelength region studied, assumed line broadening, weight given to individual spectral features) can lead to different results, even in the context of simple slab models. In general, Salyk et al. found lower emission temperatures and higher column densities for water, a result that pulls the molecular column density ratios in Figure 15 toward the lower left of the plot.

Now with velocity-resolved spectra of water and HCN in hand—data that directly constrain molecular emitting radii and resolve line blends—we have, for the first time, an opportunity to directly assess some of the degeneracies in modeling Spitzer IRS spectra. For the two sources studied here, we find that the high-resolution water spectra are consistent with the high-temperature, low-column-density interpretation of the Spitzer water emission (see also J. S. Carr et al. 2018, in preparation). Similarly, we find that AS 205 N and DR Tau have approximately equal HCN and water emitting areas, which helps distinguish between high- and low-column-density solutions for the HCN emission as well. Assuming that the Spitzer HCN emission temperature applies to the TEXES HCN emission, the Spitzer and TEXES spectra can be fit with similar HCN/${{\rm{H}}}_{2}{\rm{O}}$ column density ratios.

The Spitzer HCN/${{\rm{H}}}_{2}{\rm{O}}$ column density ratios (Figure 15, red diamonds) are 0.0033 for AS 205 N and 0.0062 for DR Tau; the TEXES HCN/${{\rm{H}}}_{2}{\rm{O}}$ column density ratios (Figure 15, large red circles with black dots) are 0.0043 for AS 205 N and 0.0097 for DR Tau (3.2; Table 3). These values agree with the low end of the HCN/${{\rm{H}}}_{2}{\rm{O}}$ column density ratios reported by Carr & Najita (2011) and are closer to the average value of comets (blue symbols). For comparison, the range of molecular abundances measured for hot cores is also shown in Figure 15 (green cross).

These results endorse some aspects of earlier work and also suggest the need to extend our study to a wider variety of sources. We confirm for the two sources studied here that simple slab fits to their IRS spectra (following the methodology of Carr & Najita 2011) are consistent with the properties inferred from their TEXES spectra (Section 3.2). These results suggest a measure of confidence in our ability to infer abundances from lower resolution data. If the equal HCN and water emitting areas we find for the sources studied here also apply to the sources studied by Carr & Najita (2011), their HCN/${{\rm{H}}}_{2}{\rm{O}}$ column density ratios will be lower than the favored best-fit values and thereby alter our view of the level of chemical activity in inner disks. However, the results obtained here may not apply to other CTTS because AS 205 N and DR Tau are both very active sources with high accretion rates. High spectral resolution observations, similar to those presented here but of more typical T Tauri stars (like those studied in Carr & Najita 2011), are likely critical in order to measure with confidence molecular column density ratios that can be usefully compared to the abundances of comets and hot cores.

Finally, our results bear on models for the excitation of HCN. Bruderer et al. (2015) studied the possibility of non-LTE excitation of HCN, including excitation by collisions with ${{\rm{H}}}_{2}$ and radiative pumping by infrared photons. They concluded that infrared pumping is the major excitation mechanism for rovibrational HCN emission. This was particularly true for the 3 μm lines of the v₁ band, because the high critical densities of these transitions (${n}_{{{\rm{H}}}_{2}}\sim {10}^{13}\mbox{--}{10}^{14}\,{\mathrm{cm}}^{-3}$) are only present in their disk model well below the dust photosphere of the inner disk; the excitation of these transitions above the disk photosphere therefore relies on radiative pumping. In contrast, the critical density of the 14 μm lines of the v₂ band is lower (∼10¹¹ cm⁻³), and collisional excitation could affect the 14 μm emission from the inner 2 au of their disk model.

Using a disk model calculated specifically for the case of AS 205 N, Bruderer et al. predicted 3 and 14 μm line profiles and intensities for the HCN emission from the disk. They found that the 3 and 14 μm lines can have substantially different line profiles and that infrared pumping can excite the transitions in both bands out to large radii (∼10 au), producing very narrow line profiles.

To test these predictions, we compared the HCN line profiles of AS 205 N measured with TEXES in the MIR with the 3 μm line profiles from CRIRES (Mandell et al. 2012). We obtained an average profile for the 3 μm lines by averaging together the P5, P11, P12, and P13 lines, the cleanest HCN lines in the spectrum. The average 3 μm profile is compared to our average profile for the MIR lines in Figure 16. The MIR and 3 μm HCN profiles are remarkably similar.

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The velocity width for both line profiles (FWHM ∼ 20 km s⁻¹) is much larger than the ∼10 km s⁻¹ predicted by the Bruderer et al. models in which HCN is excited by infrared pumping out to ∼10 au. The discrepancy implies that either HCN is not abundant beyond a couple of au or that infrared pumping does not dominate at these radii. The Bruderer et al. model that best fits our observed width for the MIR lines is the "jump" model (see their Figure 10) in which the HCN abundance is assumed to be greatly reduced beyond ∼2 au. The radius of the abundance decrement is consistent with the emitting area derived from our modeling of the IRS spectra (Section 3.2). However, the same jump model also predicts a 3 μm line that is enhanced by radiative pumping and is much broader (∼45 km s⁻¹) than observed.

Collisional excitation is most likely the dominant excitation mechanism for the 14 μm HCN band. From fitting the Q branch at 14 μm (Section 3.2.1), we know that higher vibrational states, up to at least v₂ = 3, must be populated. Populating these vibrational states via infrared pumping would be difficult because of their weak radiative connection to the ground state. In the Bruderer et al. models, collisional excitation was found to be important for the 14 μm lines in the inner 2 au of the disk, consistent with our observed line profiles. The critical density of the HCN lines we observed with TEXES is ∼10¹¹ cm⁻³, not much higher than those of the observed rotational water lines $(3\times {10}^{10}\mbox{--}6\times {10}^{10}\,{\mathrm{cm}}^{-3}$) and similar to the density in disk atmosphere models where HCN is abundant (Ádámkovics et al. 2014; Najita & Ádámkovics 2017). All of this argues that the 14 μm transitions could be close to LTE.

The role of radiative pumping in exciting the 3 μm and MIR HCN lines is unclear, as the specific line profiles predicted by Bruderer et al. are not confirmed by the observations. The 3 μm profile is indistinguishable from the MIR profile, showing that they form over the same range of radii and suggesting that the two bands could share the same excitation mechanism. If radiative pumping does play a role, the details of how the radiative excitation occurs must differ from the description put forth in Bruderer et al. (2015).

In addition to comparing the line profiles, we can also compare the expected LTE emission line fluxes with the observed fluxes. Using the LTE slab model that we used to fit the Q branch of the 14 μm band in the IRS spectrum, we predicted the strength of the 3 μm HCN lines and compared it with the 3 μm line strength from Mandell et al. (2012; Figure 17). The simple LTE model produces a good match to the 3 μm HCN line flux in the CRIRES spectrum, better than the same model applied to the TEXES data (Figure 12). One should note that neither the CRIRES spectrum nor the TEXES spectrum were independently flux calibrated, and both these and the Spitzer IRS spectrum were observed years apart. Nevertheless, the intensity of the 3 μm and MIR lines, as studied here, are consistent with HCN being close to LTE.

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The similar 3 μm and MIR line profiles for AS 205 N, the warm vibrational temperature (≳700 K) implied by the fit to the 14 μm band in the IRS spectra, and the flux ratio of the 3 μm and MIR lines are all consistent with collisional exciation of the HCN within 1–2 au of the star. However, a significant uncertainty is whether the high densities required for collisional excitation of the 3 μm lines ($\sim {10}^{13}\mbox{--}{10}^{14}\,{\mathrm{cm}}^{-3};$ see Bruderer et al. 2015, Figure 4) are present in the region of the disk atmosphere where the HCN emission forms or whether a different excitation path is required to understand the observed 3 μm HCN transitions.

One possibility is that HCN is excited by collisions with atomic hydrogen rather than ${{\rm{H}}}_{2}$. In the disk atmosphere models of Najita & Ádámkovics (2017), atomic H and ${{\rm{H}}}_{2}$ are comparable in abundance in the region where warm HCN is abundant. For CO and SiO, the cross-sections for collisions with atomic H are considerably larger than for those with ${{\rm{H}}}_{2}$. If the same is true for HCN, it would help explain the apparent LTE excitation of HCN indicated by the results presented here.