A Survey of CH₃CN and HC₃N in Protoplanetary Disks

During ALMA Cycle 2, the HC₃N 27–26 transition as well as the CH₃CN 14–13 K ladder were observed for the disks AS 209, HD 163296, IM Lup, LkCa 15, MWC 480, and V4046 Sgr (project code 2013.1.00226). Disk and stellar properties for each source are listed in Table 1. The MWC 480 data were previously presented in Öberg et al. (2015); these lines were reanalyzed in this work to ensure that all sources were treated consistently. During Cycles 3 and 4, as part of a line survey in disks (project code 2013.1.01070.S), the HC₃N 31–30 and 32–31 transitions and the CH₃CN 15–14 and 16–15 K-ladders were observed toward MWC 480 and LkCa 15.

Table 1.  Disk and Star Properties of Observed Sources

Source	Distance	Spectral	Age	M⋆	L⋆	${\dot{M}}_{\star }$	Disk Inc.	Disk PA	Mdisk	vLSR
	(pc)	Type	(Myr)	(M⊙)	(L⊙)	(10−9 M⊙ yr−1)	(deg)	(deg)	(M⊙)	(km s−1)
AS 209	143a	K5	1.6	0.9	1.5	51	38	86	0.015	4.6
IM Lup	161a	M0	1	1.0	0.93	0.01	50	144.5	0.17	4.4
LkCa 15	140	K3	3–5	0.97	0.74	1.3	52	60	0.05–0.1	6.3
V4046 Sgr	72	K5, K7	24	1.75	0.49, 0.33	0.5	33.5	76	0.028	2.9
MWC 480	142a	A4	7	1.65	11.5	126	37	148	0.11	5.1
HD 163296	122	A1	4	2.25	30	69	48.5	132	0.17	5.8

Note. Table adapted from Huang et al. (2017), where a full list of references can be found.

^aFrom Gaia Data Release 1 (Gaia Collaboration et al. 2016).

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A detailed description of the Cycle 2 observations can be found in Huang et al. (2017). Briefly, from 2014 to 2015 Band 6 observations were taken at two spectral settings, 1.1 mm and 1.4 mm, containing 14 and 13 narrow spectral windows, respectively. Baselines spanned 18–650 m, and the total on-source time was ∼20 minutes per source. Amplitude and phase calibration, as well as frequency bandpass calibration, were performed using observations of a quasar. Flux calibration was performed using observations of either Titan or a quasar. A portion of the CH₃CN 14–13 ladder (14₀–13₀, 14₁–13₁, and 14₂–13₂) is contained in a spectral window of 59 MHz with a channel width of 61 kHz (0.071 km s⁻¹) in the 1.1 mm spectral setting. The HC₃N 27–26 transition is contained in a spectral window of 117 MHz, also with a channel width of 61 kHz (0.075 km s⁻¹) in the 1.1 mm spectral setting.

The Cycle 3/4 observations are described in full in R. Loomis (2018, in preparation). This work made use of data taken in two Band 7 correlator setups at 0.9 and 1.1 mm, each containing four spectral windows of 1920 channels with channel widths of 975 kHz (∼0.99–1.06 km s⁻¹ for the lines of interest). Baselines spanned 15–650 m, and the total on-source integration time was ∼20 minutes per source. Phase calibration, bandpass calibration, and flux calibration were all performed using quasar observations.

Initial data calibration was performed by ALMA/NAASC staff. Two rounds of phase self-calibration were performed using the continuum emission from individual spectral windows, except for HD 163296, which was self-calibrated using averaged spectral windows due to weak continuum emission. Following continuum subtraction, the data cubes were imaged in CASA using the CLEAN task with a 3σ noise threshold. Briggs weighting was used with a robust parameter of 2.0 for all lines except those in the source V4046 Sgr; here, a value of 1.0 was adopted to improve the angular resolution, which was possible due to higher signal-to-noise ratios. To obtain channel maps, the data were regridded to 0.5 km s⁻¹ and 1.1 km s⁻¹ spectral resolution for the Cycle 2 and Cycle 3/4 observations, respectively. CLEAN masks were drawn by hand for lines with obvious emission (V4046 Sgr HC₃N 27–26 and CH₃CN 14₀–13₀ and 14₁–13₁). For all other lines, the 5σ continuum contour was used as the CLEAN mask.

A Keplerian mask was applied to the cleaned data cube to obtain moment zero maps, line spectra, and integrated flux densities for each transition. The use of Keplerian masks as CLEAN templates and for spectral extraction is well established (e.g., Rosenfeld et al. 2013a; Loomis et al. 2015; Öberg et al. 2015); details on the use of Keplerian masking for moment zero map generation will be presented in J. Pegues (2018, in preparation). Briefly, to construct appropriate masks, the Keplerian velocity of each image pixel was calculated based on its deprojected radius from the star, assuming disk and stellar parameters taken from the literature (Table 1). In each velocity channel, only pixels corresponding to the appropriate Keplerian velocity were included, and all other pixels were masked. The mask outer radii were chosen to encompass all HC₃N and CH₃CN emission. The masks were verified to fit the actual disk profile using H¹³CN emission (Guzmán et al. 2017), which has a more obvious Keplerian structure than HC₃N or CH₃CN. An example channel map with its Keplerian mask overlaid is shown in Figure 1 for the HC₃N 27–26 transition in V4046 Sgr; for all other lines and sources, similar figures can be found in the online Journal.

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View figure set (21 panels)

Tarball of figure set images

Since the moment zero maps are produced by summing only emission within the Keplerian mask, each moment zero pixel represents the sum of a different number of channels. The rms is therefore nonuniform across the moment zero map. We approximate the moment zero rms by bootstrapping: the same Keplerian mask used to obtain the moment zero map is applied to 1000 off-source positions. The rms per pixel is determined from the standard deviation of each mask pixel across all off-source moment zero maps. The median rms value is taken to be the representative moment zero rms, and is quoted in Table 2 and used to draw contours in Figures 2 and 4. The uncertainty in the integrated flux density was estimated from the standard deviation of the integrated fluxes within 1000 off-source Keplerian masks.

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In V4046 Sgr, the CH₃CN 14₀–13₀ line is blended with the 14₁–13₁ line (spectrum shown in Figure 2). Likewise, in MWC 480 the CH₃CN 15₀–14₀ and 15₁–14₁ lines are blended. To treat blended lines, two Keplerian masks (one centered on each line) were calculated and used to extract the emission from both lines, and the resulting moment zero map sums the total emission. To estimate the integrated flux density from each individual transition, we assume that emission is symmetric around the rest velocity of the source. The integrated flux for the lower-energy transition was therefore assumed to be twice the integrated flux of the lowest-velocity horn (i.e., velocities lower than the source velocity). The integrated flux of the higher-energy transition was taken to be the integrated flux of the total blended feature minus the integrated flux of the low-energy transition. To account for the added uncertainties in this procedure, an additional error of 30% the integrated flux was added in quadrature with the bootstrapped integrated flux uncertainty for blended lines.

A summary of the line observations is presented in Table 2. The CH₃CN 14₀–13₀ and HC₃N 27–26 transitions were targeted toward all six disks and, compared to the other observed CH₃CN and HC₃N transitions, are the brightest across the sample. We therefore use these lines to classify whether molecules are detected or not detected in a disk. A molecule is considered detected if emission >3 × rms is present within the Keplerian mask in at least three channels. We also tested a detection criterion of an SNR >3 for the integrated flux density and find the same status of detection versus nondetection for all transitions. Based on these criteria, HC₃N is detected toward all disks except IM Lup. CH₃CN is firmly detected toward three of six disks (HD 163296, MWC 480, and V4046 Sgr). In AS 209 and LkCa 15, CH₃CN is not seen at significant levels in individual channel maps but shows suggestive features at around a 3σ level in the moment zero maps, as well as positive integrated intensities in the radial profiles. Higher-sensitivity follow-up observations are required to confirm if these are indeed detections. For subsequent analysis, these lines are treated as nondetections (3σ upper limits).

Figure 2 shows the disk continuum maps as well as the CH₃CN 14₀–13₀ and HC₃N 27–26 line maps and spectra for each disk. In all cases, the molecular emission is more compact than the continuum emission. Comparing the nitrile emission across the sample, V4046 Sgr is by far the strongest emitter, with strong detections of both CH₃CN and HC₃N. Next strongest are HD 163296 and MWC 480, which both host strong HC₃N and moderate CH₃CN emission. AS 209 and LkCa 15 both exhibit moderate HC₃N and tentative CH₃CN emission, and neither molecule is detected in IM Lup.

Figure 3 shows the deprojected radial profiles for each transition. The uncertainties are estimated by dividing the median moment zero rms by the square root of the number of independent measurements (i.e., the number of pixels at each radius divided by the beam size in pixels, to account for beam convolution). For both CH₃CN and HC₃N, almost all detections exhibit centrally peaked emission. The exception is CH₃CN and HC₃N in AS 209, which peak at larger radii, indicative of a ringed structure; this can also be seen in the moment zero map (Figure 2). Although it does not have a large central dust cavity, AS 209 also exhibits a ring-like structure in the molecules H¹³CN, HC¹⁵N, DCN, H¹³CO⁺, and DCO⁺ (Guzmán et al. 2017; Huang et al. 2017), possibly due to dust opacity effects. Additionally, we note that when imaged with a smaller robust factor, HC₃N and possibly CH₃CN in V4046 Sgr show evidence of a central depression. Higher-resolution observations are required to confirm the morphology of these molecules at small scales.

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In V4046 Sgr, MWC 480, and LkCa 15, multiple transitions from the same molecule were observed. Figure 4 shows the moment zero maps for these additional transitions. The CH₃CN 14₁–13₁ and 14₂–13₂ lines were covered within the same spectral window as the 14₀–13₀ transition, and in V4046 Sgr these higher-K lines were strong enough to be detected. Additionally, for MWC 480 and LkCa 15 the CH₃CN 15₀–14₀ and 16₀–15₀ and HC₃N 31–30 and 32–31 lines were observed in a separate program (R. Loomis, 2018 in preparation). In MWC 480, CH₃CN 15₀–14₀, and HC₃N 31–30 and 32–31 were detected. These additional lines were not detected in LkCa 15.

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For molecules with multiple detections, rotational diagrams can be used to determine the disk-averaged column densities and rotational temperatures of emission (Figure 5). In most cases, only detected lines were used in fitting rotational diagrams; the exception is for HC₃N in LkCa 15, as only a single line is detected. In this case, the 3σ upper limits on the nondetected transitions were used to obtain an upper limit for the rotational temperature.

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Assuming LTE and optically thin emission, the disk-integrated flux density S_νΔV can be converted to an upper level population N_u (Goldsmith & Langer 1999):

$$\begin{eqnarray}&&{N}_{u}=\displaystyle \frac{4\pi {S}_{\nu }{\rm{\Delta }}V}{{A}_{\mathrm{ul}}{\rm{\Omega }}{hc}},\end{eqnarray} \tag{ 1 }$$

where S_ν is the flux density, ΔV is the line width, A_ul is the Einstein coefficient and Ω is the solid angle of the source. For a disk-averaged column density, Ω is the same for each transition of a molecule. To estimate Ω for each molecule, we use the deprojected radial profile of the brightest line (Figure 3) to identify the maximum angular extent of emission. Ω is taken to be the solid angle subtended by a circle with this radius. In turn, the total column density N_T and rotational temperature T_rot can be determined from the upper level populations given by the Boltzmann distribution:

$$\begin{eqnarray}&&\displaystyle \frac{{N}_{u}}{{g}_{u}}=\displaystyle \frac{{N}_{T}}{Q({T}_{\mathrm{rot}})}{e}^{-{E}_{u}/{T}_{\mathrm{rot}}}.\end{eqnarray} \tag{ 2 }$$

Here, g_u is the upper state degeneracy, Q is the molecular partition function, and E_u is the energy of the upper state (K). To calculate the partition functions for CH₃CN and HC₃N, we use the symmetric top and linear polyatomic approximations respectively (Gordy & Cook 1984; Mangum & Shirley 2015):

$$\begin{eqnarray}&&Q(T,{\mathrm{CH}}_{3}\mathrm{CN})=1.78\times {10}^{6}{\left(\displaystyle \frac{{T}^{3}}{{{AB}}^{2}}\right)}^{1/2},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&Q(T,{\mathrm{HC}}_{3}{\rm{N}})=\displaystyle \frac{{kT}}{{{hB}}_{0}}{e}^{{{hB}}_{0}/3{kT}},\end{eqnarray} \tag{ 4 }$$

where A, B, and B₀ are the rotational constants for CH₃CN and HC₃N.

The best-fit CH₃CN and HC₃N column densities and rotational temperatures are listed in Table 3. The rotational temperature of CH₃CN in V4046 Sgr is 29 ± 2 K and in MWC 480 is 73 ± 23 K. By comparison, the rotational temperature of CH₃CN was recently measured in the disk around the solar analog TW Hya to be 29 K; follow-up chemical modeling predicted abundant gas-phase CH₃CN between temperatures of ∼25–50 K, corresponding to the warm molecular layer of the disk (Loomis et al. 2018b). The measured rotational temperature in V4046 Sgr is consistent with these TW Hya results, while CH₃CN in MWC 480 is warmer. MWC 480 is a Herbig Ae star and hosts a stronger radiation field than the T Tauri stars TW Hya and V4046 Sgr, which may explain the warmer emission. However, we emphasize that given the line blending of CH₃CN (see Section 2.2) the rotational temperature is rather poorly constrained. Moreover, at densities below ∼10⁷ cm⁻³, the CH₃CN and HC₃N transitions targeted in this survey will be subthermally excited. Modeling in Loomis et al. (2018b) suggests that CH₃CN emission can arise from regions with densities down to 10⁶ cm⁻³; therefore, the rotational temperatures listed in Table 3 may underestimate the kinetic temperature of the emission region.

We note that in V4046 Sgr, the derived CH₃CN rotational temperature also corresponds to the kinetic gas temperature: for symmetric top molecules, the populations of different K levels with the same J value are a direct result of collisions (e.g., Loren & Mundy 1984). This is not the case for MWC 480 since the multiple lines detected consist of different J levels within the same K ladder.

HC₃N in MWC 480 has a measured rotational temperature of 49 ± 6 K, consistent within the uncertainties with the warm CH₃CN temperature found in the same source. Additional observations are needed to determine whether there is a real difference in the emission temperature (and therefore emission location) of CH₃CN and HC₃N within a disk. In LkCa 15, only one HC₃N line was firmly detected, resulting in a rotational temperature upper limit of 103 K.

Disk-averaged abundance ratios of HC₃N and CH₃CN with respect to HCN are calculated using the integrated fluxes listed in Table 2 and adopted rotational temperatures. H¹³CN integrated fluxes are taken from Guzmán et al. (2017); we assume a standard ¹²C/¹³C ratio of 70 (with an uncertainty of 15%) to convert to HCN column densities. HC₃N/HCN and CH₃CN/HCN abundance ratios are calculated for rotational temperatures of 30, 50, and 70 K corresponding to the range of observed rotational temperatures. In this treatment, we assume that HC₃N and CH₃CN are cospatial with HCN. If all molecules are emitting from the molecular layer between the midplane and the disk atmosphere, this is a reasonable approximation vertically; however, differences in the radial extent of emission for each molecule may introduce some error into the abundance ratios. IM Lup is excluded from this analysis since only upper limits are available for all species.

The derived abundance ratios are listed in Table 4. For all rotational temperatures, HC₃N is more abundant than CH₃CN. The CH₃CN abundance is on the order of a few percent with respect to HCN for all choices of rotational temperature. For a given rotational temperature, the CH₃CN/HCN ratios are consistent within the uncertainties with a single value across the entire disk sample. The derived HC₃N/HCN abundance ratios are a few percent for a 70 K rotational temperature but significantly higher (∼50% for AS 209, LkCa 15, and V4046 Sgr, and over 100% for MWC 480 and HD 163296) for a 30 K rotational temperature. In MWC 480, the only source with a well-constrained HC₃N rotational diagram, the derived temperature is close to 50 K; therefore, for at least the Herbig Ae stars, the 50 K abundances (∼20%) are likely the most reliable.

The physical model for V4046 Sgr is adapted from the parametric model of the V4046 Sgr disk described in Rosenfeld et al. (2013b) and is further developed in Guzmán et al. (2017). For fitting CH₃CN and HC₃N emission, we use the same physical disk model as that described in Guzmán et al. (2017).

Molecular abundance profiles are assumed to follow a power law, following, e.g., Qi et al. (2008, 2013):

$$\begin{eqnarray}&&X(r)={X}_{100}{\left(\displaystyle \frac{r}{{R}_{100}}\right)}^{\alpha },\end{eqnarray} \tag{ 5 }$$

where X is the abundance with respect to the total hydrogen density, X₁₀₀ is the abundance at the characteristic radius of R₁₀₀ = 100 au, and α is the power-law index. An outer radius cutoff R_out of 100 au was adopted based on the extent of emission in the deprojected radial profile (Figure 3). In the disk atmosphere, photodissociation is assumed to destroy most molecules, and the molecular abundances are attenuated by a factor of 10⁸ above z/r = 0.5. To account for depletion in the disk midplane, molecule abundances are attenuated by a factor of 10³ at temperatures below 25 K. This temperature does not correspond to a purely thermal freeze-out boundary for nitriles, but was chosen empirically based on the boundary where gas-phase CH₃CN disappears in the chemical model presented in Loomis et al. (2018b), and is also consistent with the ∼30 K rotational temperature found for CH₃CN in this disk. This depletion boundary is similar to the expected CO freeze-out temperature, and likely arises due to either a coincidence with the photodesorption boundary of the nitrile molecules, or an increase in gas-phase nitrile chemistry driven by CO sublimation.

CH₃CN and HC₃N were fit independently for the free parameters X₁₀₀ and α. While we use the same physical disk model as in Guzmán et al. (2017), the boundary conditions for the molecular abundance profiles are slightly different here; since we ultimately wish to normalize CH₃CN and HC₃N with respect to H¹³CN, we also refit the H¹³CN observations to ensure consistency.

The fitting was performed by generating synthetic observations of the brightest line emission, holding the gas density and temperature profiles constant and adopting the disk inclination, position angle, stellar mass, and systemic velocity listed in Table 1. The synthetic images had a spectral resolution of 0.5 km s⁻¹ and spanned −2.0 to 14.5 km s⁻¹ for CH₃CN (including both the 14₀–13₀ and 14₁–13₁ transitions) and -3.0 to 9.0 km s⁻¹ for HC₃N. The radiative transfer code RADMC-3D (Dullemond 2012) was used to calculate level populations for each synthetic image assuming LTE conditions. The vis sample Python package⁴ (Loomis et al. 2018a) was then used to sample the synthetic image at the u–v points of the observations. The likelihood function was calculated from the weighted difference between observations and the model in the u–v plane. The affine-invariant MCMC package emcee (Foreman-Mackey et al. 2013) was used to sample posterior distributions of both parameters X₁₀₀ and α. A flat prior was used for each parameter when generating new samples: 10⁻²⁰ < X₁₀₀ <  10⁻⁸ and −3 < α < 2. The resulting best-fit values are listed in Table 5. Figure 6 shows channel maps of the observations along with the best-fit model and residuals for CH₃CN and HC₃N (H¹³CN and CH₃CN 14₂–13₂ can be found in the Appendix); the observations are well reproduced by the model.

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Table 5.  Abundance Modeling Best-fit Parameters

	V4046 Sgr		MWC 480
	X100	α	X100	α
CH3CN	8.1 ± 0.4 × 10−12	0.6 ± 0.1	${7.9}_{-2.1}^{+2.7}\times {10}^{-13}$	−0.1 ± 0.3
HC3N	2.8 ± 0.2 × 10−11	1.3 ± 0.1	1.2 ± 0.1 × 10−11	0.8 ± 0.1
H13CN	1.2 ± 0.1 × 10−12	−0.5 ± 0.1	1.2 ± 0.2 × 10−13	−1.1 ± 0.1

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To ensure that the choice of depletion boundary does not significantly impact our results, the models were also run with an adopted depletion boundary of 19 and 30 K. For CH₃CN the best-fit X₁₀₀ at 19 and 30 K are within 25% of the 25 K value, and the best-fit α are within 15%. For HC₃N there was less than 3% change for both X₁₀₀ and α. The results are therefore not highly sensitive to the choice of depletion boundary. To further confirm the derived abundances, we use the best-fit X₁₀₀ and α values from the CH₃CN 14₀–13₀ line to create a synthetic image of the 14₂–13₂ transition. The higher-frequency transition is well reproduced by the lower-frequency best-fit values (shown in the Appendix), indicating that the adopted model is appropriate.

Since V4046 Sgr is a transition disk with a large inner gap, we also test whether a model with a large cavity produces a better fit to the observations. The fiducial model uses a cavity radius of 3 au based on the CO line emission and SED of V4046 Sgr (Rosenfeld et al. 2013b). An adopted 29 au radius, corresponding to the millimeter dust radius hole, produces a worse fit to the data for both molecules.

In Öberg et al. (2015), the CH₃CN 14₀–13₀ and HC₃N 27–26 profiles in MWC 480 were fit by obtaining the minimum χ² value from a grid of calculated abundance models. Here, we adopt the same parametric physical model for the disk density and temperature described in that paper but use the MCMC fitting procedure described in the previous section to constrain X₁₀₀ and α. This allows us to better explore the parameter space and therefore to obtain more robust constraints on the fit parameters and their uncertainties. Also in contrast to Öberg et al. (2015), we use RADMC-3D instead of the non-LTE LIME code for radiative transfer calculations to ensure consistency with the V4046 Sgr results.

To retrieve molecular abundances, we use the same power-law prescription (Equation (5)) as in Section 4.1. Again the abundances are attenuated above a z/r of 0.5 to account for photodestruction. We adopt a depletion boundary of z/r < 0.05, which roughly corresponds to the cutoff in the V4046 Sgr model. As in the V4046 Sgr model, this does not correspond to the nitrile freeze-out boundary but likely corresponds to where photodesorption of nitriles and/or CO-driven gas-phase chemistry become efficient. A higher cutoff of z/r < 0.2 was also tested, corresponding to the lower boundary of CH₃CN emission in the model of Loomis et al. (2018b). An outer radius R_out of 180 au was chosen, corresponding to the extent of emission in the MWC 480 radial profiles (Figure 3). The MCMC fitting procedure is otherwise the same as described above. CH₃CN, HC₃N, and H¹³CN were each fit with spectral resolutions of 0.5 km s⁻¹ and velocity ranges of 1–9.5 km s⁻¹, 0–14.5 km s⁻¹, and 0–14.5 km s⁻¹, respectively. The resulting model channel maps and residuals are shown in the Appendix. The best-fit values of X₁₀₀ and α are listed in Table 5. For both V4046 Sgr and MWC 480, CH₃CN and HC₃N appear to have increasing or flat abundance profiles, while H¹³CN shows a decreasing abundance profile.

Such as for V4046 Sgr, we can use the constraints from additional lines to confirm the validity of the best-fit model. For both depletion boundaries of z/r < 0.05 and z/r < 0.2, we created synthetic images of the upper-level CH₃CN and HC₃N lines based on the best-fit X₁₀₀ and α values from the lower-level lines. Rotational diagram calculations were performed for CH₃CN and HC₃N using the modeled fluxes. We obtain very similar rotational temperatures for z/r < 0.05 and z/r < 0.2 models: 20 and 23 K for CH₃CN, and 44 and 45 K for HC₃N, respectively. The HC₃N model temperatures are very close to the observed values, while the CH₃CN temperatures are low. Because the modeled CH₃CN rotational temperature is not substantially improved by increasing the z/r cutoff, a more complex parametric model is likely required to fully describe the disk physical and/or abundance structure. For instance, modeling of H₂CO emission in TW Hya required both a hot inner component and a cool extended component to match observations (Öberg et al. 2017); the possible presence of a warm inner component in MWC 480 would not be captured by the single power-law profile used in our models, resulting in a potential underprediction of the observed rotational temperature. We emphasize, however, that the observed rotational temperature of CH₃CN in MWC 480 is not well constrained due to a small lever arm in upper energy levels as well as line blending uncertainties, and may in reality be closer to the modeled rotational temperature. Of the two depletion boundaries, the z/r < 0.05 cutoff produced better fits to the higher-J lines as determined by the reduced χ², and therefore all future discussion pertains to the z/r < 0.05 model results. Channel maps for these models are shown in the Appendix.

The best-fit CH₃CN and HC₃N abundance profiles derived for V4046 Sgr and MWC 480 are shown in Figure 7, along with the derived radial column density profiles. For comparison, we also show the column densities of HC₃N and CH₃CN predicted by a disk chemistry model for a generic T Tauri star and disk (Walsh et al. 2014). CH₃CN column densities from the disk chemistry model are within an order of magnitude to those derived in this work for V4046 Sgr and MWC 480, while HC₃N column densities are underestimated by over an order of magnitude in the model. However, neither V4046 Sgr nor MWC 480 is well-described by the disk physical structure adopted by Walsh et al. (2014), and further tuning of models is required to make conclusive comparisons. Comparing the relative shapes of the radial column density profiles, the extremely centrally peaked profile in the model is not reproduced in the profiles derived in this work. However, we note that due to the high upper-state energies of the lines fitted (92 K for CH₃CN and 165 K for HC₃N), our observations are not sensitive to cool material and therefore may not reflect the true spatial distributions of the molecules.

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To illustrate this, we use the modeled best-fit abundance profiles to determine the fraction of emitting molecules (i.e., molecules in the upper energy state of the observed transition) in temperature bins from 10 to 200 K, following Bergin et al. (2013). The number density of a species in the upper energy state n_u is related to the total number density n_T by the Boltzmann distribution (Equation (2)). n_u is integrated over the disk to find the number of upper-state molecules in target temperature bins. The fraction of upper-state molecules in each temperature bin relative to the total number of upper-state molecules, f_u(T), is shown in Figure 8 as a cumulative distribution function.

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For both CH₃CN and HC₃N in V4046 Sgr and MWC 480, roughly half of the emitting molecules are in gas warmer than 50 K, with virtually no contribution from 30 K gas. This indicates that our observations are mostly probing warm emission. Since most gas in disks exists at <50 K temperatures, there may be a substantial amount of material that our observations are not sensitive to. As further discussed in Section 5, follow-up observations of lower-J transitions of HC₃N and CH₃CN will be helpful in addressing this issue.

Because the retrieved abundance profiles may depend on the physical disk structure assumed in the model, we also present the CH₃CN and HC₃N abundance profiles normalized with respect to HCN. This should be less sensitive to the details of the physical model structure assuming that all three molecules are emitting cospatially; this is already implicit in our model since we used the same freeze-out and photodissociation boundary conditions to retrieve molecular abundances within a given source. H¹³CN is converted to HCN using the standard isotopic ratio of 70 with an uncertainty of 15%.

The resulting CH₃CN and HC₃N abundance profiles with respect to HCN in V4046 Sgr and MWC 480 are shown in Figure 9. The derived gas-phase abundances with respect to HCN in the inner 100 au of the disks are on the order of a few percent for CH₃CN and a few tens of percent for HC₃N. These model-derived inner disk abundances are consistent with the range of disk-averaged abundances calculated assuming 30–70 K rotational temperatures (Table 4).

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5.1.1. Chemical Pathways

5.1.2. Nitrile Abundance Correlations

To explore the relationship among different nitrile-bearing species in our disk sample, Figure 10 shows the distance-normalized fluxes of the CH₃CN 14₀–13₀ and HC₃N 27–26 transitions each plotted against the H¹³CN 3–2 transition.

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The HC₃N emission strength has no clear relation to H¹³CN. However, interpreting this lack of correlation is complicated by the high upper energy of the HC₃N 27–26 line: with an excitation temperature of 165 K, this transition is not sensitive to cool HC₃N molecules, which may be abundant in some disks. Indeed, the enhanced HC₃N emission around the Herbig Ae stars compared with the T Tauri stars is consistent with a thermal effect (Figure 10), as there will be more hot molecular material around more luminous stars. Observations of lower-J HC₃N transitions are needed to determine whether the HC₃N chemistry is related to the other nitrile chemistry in disks.

From the available data, CH₃CN emission appears to correlate with H¹³CN, although more detections are required to establish if this relationship is real. We note that CH₃CN exhibits no such correlation with C¹⁸O emission strength; the tentative correlation with H¹³CN is therefore not simply a trend with the amount of gas in the disk. If additional data points confirm this correlation, it may be evidence for an active gas-phase contribution to CH₃CN formation, as this is currently the only chemical pathway with a direct link between HCN and CH₃CN. Other potential gas-phase and grain-surface channels to CH₃CN formation, which could explain a correlation with HCN but are not currently included in models, should also be explored.

5.1.3. Nitrile Spatial Correlations

The physical conditions of a protoplanetary disk set what chemistry can occur; while myriad properties have been proposed as chemical drivers in disks, we focus here on those that are, to some degree, testable based on the properties of our sample, namely the radiation field, disk structure, and evolutionary stage.

5.2.1. Radiation Field

The quiescent luminosity and accretion luminosity of a host star both contribute to the overall radiation environment in a disk. The FUV emission in T Tauri stars arises dominantly from accretion luminosity, while Herbig Ae stars should have significant FUV contributions from quiescent stellar photospheric emission in addition to accretion luminosity (e.g., Kurucz 1993; Matsuyama et al. 2003). Figures 11(a)–(b) shows the distance-normalized disk-integrated fluxes of CH₃CN 14₀–13₀ and HC₃N 27–26 plotted against the quiescent luminosity and the mass accretion rate of each star. For comparison, the CH₃CN 14₀–13₀ flux calculated for TW Hya based on the observations of Loomis et al. (2018b) is also included, with a bolometric luminosity and mass accretion rate taken from Van Boekel et al. (2017) and Herczeg & Hillenbrand (2008) respectively. For CH₃CN, we do not see any obvious trends with L_⋆ or ${\dot{M}}_{\star }$. This lack of correlation with the radiation field could indicate emission from the colder UV-shielded layers of the disk, but is also possibly due to the small number of CH₃CN detections. HC₃N appears to correlate with both the stellar luminosity and the mass accretion rate, suggesting that the UV field may play an important role in driving its chemistry. However, due to the high upper energy of the 27–26 transition, this could be due in part to the presence of hotter gas in high-UV environments rather than increased abundances of HC₃N; observations of lower-J HC₃N lines will be able to break this degeneracy.

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5.2.2. Disk Age

5.2.3. Inner Dust Cavity

We now compare the disk-averaged abundance ratios for our sample with the abundances measured in similar objects at different evolutionary stages. Low-mass protostars are the evolutionary precursors to the <2M_⊙ stars in this sample, while comets formed out of the midplane of the protosolar nebula and should preserve material from the time of planet formation. We note the environments in these different types of objects span a wide range of temperatures, densities, radiation fields, and other physical conditions.

As discussed in Section 4.3, for V4046 Sgr and MWC 480 the model-derived CH₃CN/HCN and HC₃N/HCN abundances in the inner 100 au are consistent with the range of disk-averaged abundances calculated for 30–70 K rotational temperatures. In this section, we use the range of disk-averaged abundances as a representaion of the inner 100 au of the disk in order to compare across the entire disk sample.

Figures 12(a)–(b) show the range of CH₃CN/HCN and HC₃N/HCN abundances measured in solar system comets (Mumma & Charnley 2011) compared to the gas-phase abundances measured in our disk sample. The disk abundances of CH₃CN are within a few percent of the values measured in solar system comets for sources with detections. The upper limits for AS 209 and LkCa 15 are somewhat lower but still possibly within a few percent of cometary.

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For HC₃N, the disk abundances are up to an order of magnitude higher than cometary for an adopted 30 K rotational temperature; however, given the warmer (50 K) HC₃N rotational temperature derived for MWC 480, we expect that the abundances calculated assuming a 30 K temperature overestimate the HC₃N/HCN ratio for the Herbig Ae disks at least. Restricting the comparison to the 50–70 K values, the HC₃N abundances are quite close to cometary.

Figure 12(c) shows the range of CH₃CN/HC₃N ratios measured in a sample of 16 low-mass protostellar envelopes (Bergner et al. 2017). HCN column densities toward these sources are not available; however, the CH₃CN/HC₃N ratio still provides a useful proxy for the relative efficiency of different complex nitrile chemistries. The ratios across the disk sample are mostly consistent with the values measured in protostellar envelopes, with the exception of V4046 Sgr, which is somewhat enhanced in CH₃CN/HC₃N compared to the other disks and protostars.

Based on this comparison, we see that the gas-phase nitrile abundances relative to other N-bearing molecules are consistent across various physical environments: disk molecular layers, protostellar envelopes, and the midplane of the solar nebula. We note that with these observations alone we cannot directly compare the comet- and planet-forming material in our sample with that of the protosolar nebula, as this would require extrapolations (i) from the molecular layer down to the midplane, and (ii) from gas-phase to ice abundances. Nonetheless, the consistency of nitrile abundances across a wide range of physical conditions demonstrates a robust nitrile chemistry with similar outcomes in different environments. CH₃CN abundance ratios (and upper limits) in particular appear to be especially regular both across the disk sample and in comparison with comets and protostars. Complex nitrile species should therefore be reliably produced in a variety of different star- and planet-forming environments.

While the abundances of N-bearing molecules appear internally consistent across a range of physical environments, there is evidence that the ratio of N- to O-bearing COMs in disks is distinct compared to other environments. In both comets and protostellar envelopes, the CH₃CN/CH₃OH ratio is typically on the order of a few percent (Mumma & Charnley 2011; Bergner et al. 2017). By contrast, in the one disk where CH₃OH has been detected (TW Hya), the column density ratio of CH₃CN/CH₃OH is about unity (Walsh et al. 2016; Loomis et al. 2018b), indicative of an oxygen-poor chemistry. Similarly, our observations covered a number of CH₃OH transitions in the 5–4 ladder, with no CH₃OH detections despite the strong nitrile emission. This suggests that the underabundance of gas-phase O- versus N-bearing COMs is systematic in disks. A nitrogen-rich, oxygen-poor chemistry is qualitatively consistent with an oxygen-starved environment due to, e.g., the depletion of H₂O and CO from the gas phase (Du et al. 2015). Such a scenario would indicate a predominantly gas-phase formation pathway for CH₃CN in disks. Another possible factor is if the photodesorption efficiency of intact CH₃CN is high compared to CH₃OH, which has been shown to photodesorb mainly as fragments (Bertin et al. 2016; Cruz-Diaz et al. 2016). Since photodesorption from grains is thought to be of primary importance in disks, compared to mainly thermal desorption in protostars and comets, this could also contribute to the observed discrepancy in CH₃CN/CH₃OH across circumstellar environments. Further exploration of the nitrile formation chemistry in disks using astrochemical models is needed to resolve the origin of this unique chemistry.