Detection of Cyclopropenylidene on Titan with ALMA

First, the spectral lines of CO (Spw 4 and 5) were fitted using a model that allowed continuous variation of the temperature profile between 100 and 500 km, while CO was fixed at a constant mixing fraction of 49.6 ppm as determined by Serigano et al. (2016). The a priori temperature profile was constructed by interpolating measurements from the Huygens Atmospheric Structure Instrument and Cassini radio science observations to Titan's subobserver latitude (∼26°) below 100 km (Fulchignoni et al. 2005; Schinder et al. 2012), and disk-averaged retrieval results from 2015 ALMA observations of Titan (Thelen et al. 2018) were used at altitudes >100 km. Temperature a priori errors were set to 5 K in all atmospheric layers (0–1200 km), which allowed NEMESIS to obtain a fit to the data while limiting artificial vertical structure (ill-conditioning) in the retrieved temperature profile. Different frequency offsets from the line center sounded to different atmospheric depths (altitudes, or pressure levels), as shown by the contribution functions in Figure 1. The a priori and final retrieved temperature profiles are also indicated.

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Next Spw 1¹² was modeled to fit visible lines of known molecules: C₂H₅CN and C₂H₃CN. The temperature profile was fixed at the earlier retrieved profile from Spw 4 for 2016. Various gas profile types were investigated for the nitriles, adjusting the profiles to achieve the best fits.

We first tried using minimalist step functions (uniform volume mixing ratio above a fixed pressure level, and zero below) for the vertical distribution of each gas. From previous experience (e.g., Cordiner et al. 2015; Lai et al. 2017) we found that these worked well for trace (low abundance) nitriles in the ALMA spectrum where there is little information that can be obtained about the vertical profile. For C₂H₃CN we adopted a step altitude at 300 km. For C₂H₅CN, there was sufficient sensitivity to the altitude of the step to affect the quality of the fit, which was determined from Spw 1 and thereafter fixed at 250 km (see the Appendix). Initial fitting is shown in Figure 2.

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Having fitted the features of the known nitrile gases as well as possible, we proceeded to try adding additional gases to the model in an attempt to detect any weak lines due to a new species, including i-butanenitrile and n-butanenitrile (C₃H₇CN), propynenitrile (cyanodiacetylene, HC₅N), and others, using lines from the JPL catalog (Pickett et al. 1998; https://spec.jpl.nasa.gov). In both Spw 1 and 6, we found a significant improvement to the model fit after introducing the gas c-C₃H₂ (cyclopropenylidene) using spectroscopic lines from CDMS originally determined by Bogey et al. (1986) and Vrtilek et al. (1987) with a trial step function model with a step at 300 km or higher.

In Spw 1 two significant lines were detected at 251314.3 MHz (blend of ${7}_{\mathrm{0,7}}\to {6}_{\mathrm{1,6}}$ and ${7}_{\mathrm{1,7}}\to {6}_{\mathrm{0,6}}$ transitions) and 251527.3 MHz (${6}_{\mathrm{2,5}}\to {5}_{\mathrm{1,4}}$), as shown in Figure 3. We note that these two emissions are the strongest expected spectral features of c-C₃H₂ in Spw 1, and show close to the expected proportions of relative intensities.

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Similarly, in Spw 6, despite the noise level being higher in ALMA Band 7 than in Band 6 (Spw 1), we made two further detections of lines of c-C₃H₂: 351781.6 MHz (blend of the ${10}_{\mathrm{1,10}}\to {9}_{\mathrm{0,9}}$ and ${10}_{\mathrm{0,10}}\to {9}_{\mathrm{1,9}}$ doublet) and 351965.9 MHz (blend of the ${9}_{\mathrm{1,8}}\to {8}_{\mathrm{2,7}}$ and ${9}_{\mathrm{2,8}}\to {8}_{\mathrm{1,7}}$ doublet), see Figure 4.

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To further test the detection of c-C₃H₂, we calculated a Δχ² curve for different amounts of the gas in a forward model, using a step function at 350 km. In this case, χ² = Σ_ν [(S_ν − I_ν)/σ_ν]² is a metric of the spectral goodness of fit, where S_ν is the data spectrum, I_ν is the model spectrum, and σ_ν is the spectral noise estimate. However, note that this is not the same definition as the more commonly used reduced chi-square metric: χ²/n, where n is the number of spectral points minus the number of degrees of freedom (model parameters). In this case therefore a good fit occurs when χ² ≃ n (rather than χ²/n ≃ 1). We then define Δχ² as the improvement to χ² for various model trial abundances: ${\rm{\Delta }}{\chi }^{2}={\chi }_{q}^{2}-{\chi }_{0}^{2}$, where ${\chi }_{0}^{2}$ denotes the best-fit model in absence of the trial gas, and ${\chi }_{q}^{2}$ is the same metric when an amount q of the trial gas is present in the model (Teanby et al. 2009, 2018; Nixon et al. 2010, 2013b). An improved fit results in a Δχ² that decreases below zero, and worsening the fit results in Δχ² that increases above zero.

Results are shown in Figure 5. A strong minimum is seen for a volume mixing ratio of q = 0.5 ppb in Band 6, with Δχ² reaching −21.24, indicating a $\sqrt{21.24}$ = 4.6σ significance to the result. For Band 7, a minimum is reached at mole fraction q = 0.25 ppb with Δχ² = −18.69 (4.3σ). Both results are significant, although the mixing ratio determined in each case is somewhat different (but consistent within error bars, as shown later in Section 4). The combined significance of the detection is 6.3σ.

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Retrieved abundances for c-C₃H₂ with various profiles are described in Section 4.

Fitting for Spw 2 and 3 was accomplished by initially using the retrieved temperature profile from Spw 4, and also scaling a 250 km step model for C₂H₅CN and 300 = km step model for C₂H₃CN. In addition, we included HCN which contributed a continuum slope in these windows due to the wings of the strong $3\to 2$ line at 265886 MHz whose line center lies outside the bandpass. Then, 300 km step model profiles models for c-C₅H₅N (Spw 2) and c-C₄H₄N₂ (Spw 3) were introduced, but resulted in no significant improvement to the fit as measured by a reduced χ² test. Instead, upper limits for c-C₅H₅N and c-C₄H₄N₂ were determined (see Section 4.) The final fit for these spectral windows is shown in Figure 6.

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The propagation of errors in the retrieval process follows the formalism described in Irwin et al. (2008), and further elaborated in Section 3.5 of Nixon et al. (2008, hereafter N08). This includes a combination of a priori and measurement error (Equation (1) of N08), with the error from the earlier temperature propagated as additional measurement error (Equation (2) of N08). In addition, we needed to make a further error allowance for apodization, which reduces independent information in the spectrum. Due to the Hanning apodization applied during the Fourier transform, neighboring spectral channels become correlated, and the S/N in our retrieval will be overestimated by a factor equal to the square root of the number of channels per resolution element—two channels per resolution element for Hanning apodization. At the same time, there is a small gain of 1.095 from averaging information across two successive correlated channels,¹³ so the final error bars are increased by a factor $\sqrt{2}/1.095=1.291$. This factor has also been applied to correspondingly reduce the detection significances (σ levels) throughout the paper.

We initially fitted the c-C₃H₂ emissions with a step function model, where the gas abundance was zero below a step altitude and a uniform value above. The overall profile was then scaled to achieve a best fit. The effect of changing the altitude of the step was also explored, since lower steps increased the pressure broadening of the lines that became greater than the observed line widths.

We also investigated a more realistic gas profile, with an abundance decreasing downwards to a condensation altitude, using a four-parameter gradient model. This model was defined by two (p, q; pressure, mixing ratio) coordinates defining a straight-line, logarithmically decreasing VMR between (p_u, q_u) (upper point) and (p_l, q_l) (lower point). Above p_u the VMR was assumed constant at q_u and below p_l the VMR dropped to zero. The upper pressure level was set to be p_u = (5.0 ± 2.0) × 10⁻¹¹ bar, or approximately 1100 km, the altitude of the Ion and Neutral Mass Spectrometer (INMS) measurements of the C₃H₂H⁺ (protonated) ion. The initial value for the abundance at this altitude was set to be q_u = (3.4 ± 1.0) × 10⁻⁶ in line with the INMS ion measurements (Vuitton et al. 2007). The initial value for the lower point was set to be: p_l = (1.0 ± 0.5) × 10⁻⁴ bar, q_l = (2.0 ± 1.9) × 10⁻⁹ , a pressure level corresponding to approximately 300 km, and allowing a lenient variation of abundance.

Scaled step function solutions for c-C₃H₂ from Window 1 (Band 6) and Window 6 (Band 7) are shown in Figure 7, along with best-fit gradient model profiles. Numerical results are given in Table 3. Retrievals for cyclopropenylidene showed low sensitivity to the altitude of the step, with a weak minimum at 300–400 km. The resulting abundances and columns were slightly different in 2016 and 2017. For a step function of 350 km we obtained a VMR of 0.50 ± 0.14 ppb and column abundance of 3.5 × 10¹² cm⁻² in 2016, but somewhat lower VMR (0.28 ± 0.08) and column abundance (1.5 × 10¹²) in 2017. This implies either (a) that the global abundance had decreased from 2016 to 2017, or, (b) if the real abundance was constant, then a mean value of 0.33 ± 0.07 ppb for the 350 km step profile.

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Retrieved parameters for the gradient model retrievals in 2016 and 2017 are shown in Table 4, along with parameters for a weighted mean profile of both years.

Upper limits for c-C₅H₅N and c-C₄H₄N₂ were determined using the Δχ² method outlined for c-C₃H₂ in Section 3.2. In this case, the 1, 2, and 3σ upper limits are indicated at the trial abundances where the Δχ² reaches +1, +4, and +9, respectively (Nixon et al. 2012). Results are shown in Figure 8 and Table 5. A shallow minimum was detected for c-C₅H₅N, however the spectrum does not show obvious emissions consistent with expected spectral lines, therefore we believe this to be likely due to random spectral noise (although worthy of a more sensitive follow-up observation to be sure).

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The molecule cyclopropenylidene (c-C₃H₂) was discovered in the interstellar medium (ISM) by Thaddeus et al. (1985) through extensive laboratory and theoretical analysis to unearth the origin of several prominent, but previously unidentified, lines seen on radio astronomical spectra. Following this discovery, the molecule has been found to be ubiquitous in the galaxy (Fosse et al. 2001) and easily detectable due to the relatively large dipole of 3.43(2) D (Kanata et al. 1987) caused by the unpaired electrons on the bivalent carbon atom. In addition, c-C₃H₂ is a light molecule with a small partition function, which also works in favor of detection. One of its linear isomers, propadienylidene (H₂CCC; see Figure 9), has since been detected in the ISM (Cernicharo et al. 1991) while propynylidene (HCCCH) has not been observed. Note that propadienylidene is higher in energy than cyclopropenylidene, and therefore metastable, so that the observed ratio of 10 or more for c-C₃H₂/H₂CCC is expected.

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The Cassini INMS instrument measured peaks at m/z 38 and 39 in samples of Titan's upper atmosphere that were attributed to the presence of C₃H${}_{2}^{+}$ and various isomers of C₃H${}_{3}^{+}$ (Vuitton et al. 2006, 2007). Although the molecular structure was not directly measurable, modeling of the mass spectrum implied ion number densities of 0.0016 cm⁻³ (C₃H${}_{2}^{+}$), 34 cm⁻³ (c-C₃H${}_{3}^{+}$), and 1.6 cm⁻³ (l-C₃H${}_{3}^{+}$) respectively. Determining the ratio of l-C₃H${}_{3}^{+}$/c-C₃H${}_{3}^{+}$ was deemed to be of major importance by Vuitton et al. (2007; and the subject of laboratory investigation), since the linear propargyl ion is able to react to form heavier species, including possibly benzene (Wilson & Atreya 2004), while the cyclopropenylidene ion is essentially a terminal species, leading to c-C₃H₂.

Various mechanisms have been proposed for the formation of c-C₃H₂ and it is not clear at the present which mechanisms are the most important. In the original work of Thaddeus et al. (1985) on the ISM detection, cyclopropenylidene was produced by dissociative electron recombination of the cyclopropenylium cation, c-C₃H${}_{3}^{+}$:

$$\begin{eqnarray}&&{\rm{c}} \mbox{-} {{\rm{C}}}_{3}{{\rm{H}}}_{3}^{+}+{{\rm{e}}}^{-}\to {\rm{c}} \mbox{-} {{\rm{C}}}_{3}{{\rm{H}}}_{2}+{\rm{H}}\end{eqnarray} \tag{ 1 }$$

while c-C₃H${}_{3}^{+}$ is produced from C₂H₂ in two steps. First the fast ion–molecule reaction:

$$\begin{eqnarray}&&{{\rm{C}}}^{+}+{{\rm{C}}}_{2}{{\rm{H}}}_{2}\to {\rm{c}} \mbox{-} {{\rm{C}}}_{3}{{\rm{H}}}^{+}+{\rm{H}}\end{eqnarray} \tag{ 2 }$$

followed by the slower radiative association (hydrogenation):

$$\begin{eqnarray}&&{\rm{c}} \mbox{-} {{\rm{C}}}_{3}{{\rm{H}}}^{+}+{{\rm{H}}}_{2}\to {\rm{c}} \mbox{-} {{\rm{C}}}_{3}{{\rm{H}}}_{3}^{+}.\end{eqnarray} \tag{ 3 }$$

Alternatively the C₃H${}_{3}^{+}$ ion has been proposed to be produced from acetylene via many other possible ion–molecule reactions by Vuitton et al. (2019), for example

$$\begin{eqnarray}&&{\mathrm{CH}}_{3}^{+}+{{\rm{C}}}_{2}{{\rm{H}}}_{2}\to {{\rm{C}}}_{3}{{\rm{H}}}_{3}^{+}+{{\rm{H}}}_{2}\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&{{\rm{C}}}_{2}{{\rm{H}}}_{5}^{+}+{{\rm{C}}}_{2}{{\rm{H}}}_{2}\to {{\rm{C}}}_{3}{{\rm{H}}}_{3}^{+}+{\mathrm{CH}}_{4}.\end{eqnarray} \tag{ 5 }$$

Walch (1995) and Guadagnini et al. (1998) investigated the reactions of CH(X²Π) (methylidyne) with C₂H₂, predicting that various isomers of both C₃H₃ and C₃H₂ can result. From this point, several outcomes are possible: the products can stabilize into a less-reactive species, such as c-C₃H₂, or else can undergo further reactions to form heavier hydrocarbons. In particular, it was noted that both C₃H₃ and C₃H₂ can dimerize, forming benzene (C₆H₆) and para-benzene (C₆H₄) respectively, and therefore C₃H₃ and C₃H₂ are important stepping stones to polycyclic aromatic hydrocarbons (PAHs).

The work of Canosa et al. (1997) further clarified pathways to the formation of C₃H₂ from reactions of the methylidine radical (CH) with unsaturated C₂H_x hydrocarbons, such as

$$\begin{eqnarray}&&\mathrm{CH}+{{\rm{C}}}_{2}{{\rm{H}}}_{2}\to {{\rm{C}}}_{3}{{\rm{H}}}_{2}+{\rm{H}},\mathrm{or}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&\mathrm{CH}+{{\rm{C}}}_{2}{{\rm{H}}}_{4}\to {{\rm{C}}}_{3}{{\rm{H}}}_{3}+{{\rm{H}}}_{2}.\end{eqnarray} \tag{ 7 }$$

In the above reactions, CH is envisaged to add to the carbon–carbon double or triple bond. C₃H₃ can be converted to C₃H₂ by hydrogen loss through photodissociation (e.g., Hébrard et al. 2013):

$$\begin{eqnarray}&&{{\rm{C}}}_{3}{{\rm{H}}}_{3}+{\rm{h}}\nu \to {{\rm{C}}}_{3}{{\rm{H}}}_{2}+{\rm{H}}.\end{eqnarray} \tag{ 8 }$$

The C₃H radical may also result from the methylidine insertion reactions, which can lead to C₃H₂ via several steps, first charge transfer:

$$\begin{eqnarray}&&{{\rm{H}}}^{+}+{{\rm{C}}}_{3}{\rm{H}}\to {{\rm{C}}}_{3}{{\rm{H}}}^{+}+{\rm{H}}\end{eqnarray} \tag{ 9 }$$

followed by hydrogenation (Equation (3)) and then dissociative recombination (Equation (1)) as before. Subsequently, Canosa et al. (2007) showed that C₂ reactions may also be important, e.g.,

$$\begin{eqnarray}&&{{\rm{C}}}_{2}+{{\rm{C}}}_{3}{{\rm{H}}}_{8}\to {{\rm{C}}}_{3}{{\rm{H}}}_{2}+{{\rm{C}}}_{2}{{\rm{H}}}_{6}\end{eqnarray} \tag{ 10 }$$

as used in the photochemical model of Krasnopolsky (2009). The branching ratios between aliphatic and aromatic pathways in many of these reactions, especially at low temperatures, are important and often poorly known.

In Figure 10 we compare our retrieved gradient models to photochemical model predictions of Hébrard et al. (2013) and Vuitton et al. (2019). In fact, the models arrive at a column abundance rather similar to our retrieved amount of ∼10¹² cm⁻². It is difficult to pronounce whether the differences in the vertical profile shape are significant or not, since we have very little constraint on this at the present.

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The astrobiologically important species pyridine (c-C₅H₅N) and pyrimidine (c-C₄H₄N₂) are nitrogen-containing heterocyclic ring molecules resembling a benzene ring with either one or two of the C–H members replaced by a nitrogen atom. Pyrimidine in particular is of significant biological importance since it forms the backbone ring structure of several key biological molecules—specifically the nucleobases uracil (in RNA), cytosine (in RNA and DNA), and thymine (in DNA). These molecules can potentially be formed from pyrimidine after the chemical substitution of functional groups (-NH₂, -CH₃ and =O) in place of hydrogen, as indicated in Figure 11. Indeed, laboratory experiments (Nuevo et al. 2014) have shown that UV irradiation of pyrimidine in the presence of H₂O, CH₄, CH₃OH, and NH₃ can form uracil and cytosine—but not the more complex thymine—a possible clue as to why thymine appears only in DNA but not RNA, and further evidence that RNA may have preceded DNA. Similar processes may be taking place in space, including the atmosphere of Titan. Indeed, laboratory simulations of Titan's atmosphere, using multiple experimental techniques such as gas chromatograph mass spectroscopy (GC-MS), pyrolysis mass spectroscopy, Raman and reflectance spectroscopy, etc. have been successful in positively identifying the nitrogen heterocycles (Khare et al. 1984; Ehrenfreund et al. 1995).

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To date, neither pyridine nor pyrimidine have been detected in astrophysical sources, despite searches in molecular clouds (Simon & Simon 1973; Kuan et al. 2003, 2004; Cordiner et al. 2017; McGuire et al. 2018) and in the envelopes of evolved stars (Charnley et al. 2005), although pyridine and quinoline (two-membered N-heterocycle rings) derivatives have been found in meteorite samples (e.g., Stoks & Schwartz 1982; Martins 2018). Peeters et al. (2005) have shown that these molecules are relatively unstable against UV irradiation compared to benzene, but could survive for 10–100s of years in dense clouds where UV flux is attenuated, and therefore potentially in Titan's thick atmosphere.

The potential presence of the nitrogen heterocyclic molecules pyridine and pyrimidine in Titan's atmosphere may be inferred from the detection of C₅H₅N H⁺ and C₄H₄N₂ H⁺ ions in Cassini mass spectra (Vuitton et al. 2007) at m/z 80 and 81 (seen in their Figure 2). As with the hydrocarbons, the elucidation of structure from the mass spectra alone is not possible, therefore for example protonated forms of branched acyclic molecules such as penta-2,4-dienenitrile or 2-methylene-3-butenenitrile could be responsible for the mass 80 peak instead.

Formation pathways for the N-heterocycles are currently quite uncertain. For example, Fondren et al. (2007) suggest that efficient ion–molecule association reactions with HCN could form pyridine and pyrimidine from smaller ions:

$$\begin{eqnarray}&&{{\rm{C}}}_{4}{{\rm{H}}}_{4}^{+}+\mathrm{HCN}\to {{\rm{C}}}_{5}{{\rm{H}}}_{5}{{\rm{N}}}^{+}+{\rm{h}}\nu \end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{{\rm{C}}}_{3}{{\rm{H}}}_{3}{{\rm{N}}}^{+}+\mathrm{HCN}\to {{\rm{C}}}_{4}{{\rm{H}}}_{4}{{\rm{N}}}_{2}^{+}+{\rm{h}}\nu .\end{eqnarray} \tag{ 12 }$$

A more exotic mechanism for the formation of pyridine through ring expansion of pyrrole by methylidyne has been observed in the gas phase by Soorkia et al. (2010):

$$\begin{eqnarray}&&\mathrm{CH}+{{\rm{C}}}_{4}{{\rm{H}}}_{5}{\rm{N}}\to {{\rm{C}}}_{5}{{\rm{H}}}_{5}{\rm{N}}+{\rm{H}}.\end{eqnarray} \tag{ 13 }$$

More recently, Balucani et al. (2019) have investigated a pathway to pyridine that begins with an attack on C₆H₆ by N(²D), leading to a chain of unstable intermediate products that may decay to c-C₅H₅N.

The relative importance of these various channels is highly uncertain at the present time, leading to difficulties in incorporating these molecules into photochemical models. For example Krasnopolsky (2009) included just one hypothetical formation pathway for pyridine by the radical-molecule reaction

$$\begin{eqnarray}&&{{\rm{C}}}_{3}{\rm{N}}+{{\rm{C}}}_{2}{{\rm{H}}}_{6}\to {{\rm{C}}}_{5}{{\rm{H}}}_{5}{\rm{N}}+{\rm{H}}\end{eqnarray} \tag{ 14 }$$

while in Loison et al. (2015) only the aliphatic isomer C₂H₅C₃N is discussed.

Our analysis indicates 2σ upper limits of ∼1.15 ppb and ∼0.85 ppb for c-C₅H₅N and c-C₄H₄N₂, respectively (constant profile above 300 km), which may in the future be used to place some constraints on photochemical models as these become more sophisticated and add more detailed treatment of cyclic molecule formation.

In Spw 1, sufficiently strong lines of C₂H₅CN were seen that there was noticeable pressure-induced line broadening, allowing an optimum altitude for a step function model to be determined. Figure 12 shows the effect of changing the step function altitude for C₂H₅CN.

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The goodness of fit for all models is compared in Table 6. The best-fit solution for C₂H₅CN is a step function at 250 km with a uniform VMR of 5.0 ± 0.07 ppb and column abundance 2.2 × 10¹⁴ cm⁻². A comparison of retrieved profiles can be seen in Figure 13(a).

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A gradient model was also tested, using similar initial conditions to those used for c-C₃H₂, as described in Section 3.2, except that the initial abundance at the 1100 km altitude was set to q_u = (5.0 ± 1.0) × 10⁻⁷ in line with the INMS measurement of C₂H₅CN H⁺. Initial and retrieved parameters for the C₂H₅CN gradient model are given in Table 7.

A list of the ground-state and vibrationally excited lines detected in Spw 1 is given in Table 8.

In the next section the implications of the results for C₂H₅CN are discussed.

The ion C₂H₅CN H⁺ was inferred from early Cassini INMS mass spectra of Titan's upper atmosphere (e.g., Vuitton et al. 2007), and the first identification of ethyl cyanide (propionitrile) in the neutral atmosphere was achieved using ALMA by Cordiner et al. (2015). Nitrile molecules have a large molecular dipole (∼4.0 D for small nitriles, equivalent to 70% of an equivalent ionic bond), causing them to have strong rotational spectra. This was undoubtedly a reason why methyl cyanide (acetonitrile, CH₃CN) was first detected at submillimeter wavelengths (Bezard et al. 1992), and despite intensive searching has yet to be detected in the infrared (Nixon et al. 2010).

The detection of C₂H₅CN by Cordiner et al. (2015) in ALMA Band 6 data at ∼220–240 GHz was close to the region observed in this work, with an abundance of ∼9 ppb (300 km step model) derived from disk-averaged observations in July 2012. Several years later, follow-up work by Palmer et al. (2017) also in Band 6 near 230 GHz determined a disk-average abundance of 7.2 ± 0.29 ppb for early 2014, while Lai et al. (2017) measured 7.37 ± 0.32 ppb from 2015 April data in Band 7 near 348 GHz. Our measurement of 8.5 ± 0.2 ppb (using a directly comparable 300 km step model) based on 2016 data falls in the mid-range of the previous measurements, and indicates that the global abundance was not changing substantially in this period.

The vertical profile of propionitrile (as a global average) remains problematic. As pointed out by Cordiner et al. (2015) and also by Lai et al. (2017), photochemical models typically overestimate the abundance of this gas compared to retrieved abundances (see Figure 13(b)), especially in the lower stratosphere, indicating a possible missing loss mechanism. The model which best replicates the data is that of Willacy et al. (2016; Model C), which includes loss by condensation, sedimentation, and haze formation. Despite the abundance at 100–300 km appearing significantly too high, the column abundance of ∼10¹⁴ cm⁻² is of the same order of magnitude as our results. Other models (Loison et al. 2015; Vuitton et al. 2019) substantially overestimate the column by a factor of ∼100, by continuing significant gas mixing fractions down to the tropopause.