Detectable Abundance of Cyanoacetylene (HC$_3$N) Predicted on Reduced Nitrogen-Rich Super-Earth Atmospheres

We predict that cyanoacetylene (HC$_3$N) is produced photochemically in the atmosphere of GJ 1132 b in abundances detectable by the James Webb Space Telescope (JWST), assuming that the atmosphere is hydrogen dominated and rich in molecular nitrogen (N$_2$), methane (CH$_4$) and hydrogen cyanide (HCN), as described by Swain et al. (2021). First, we construct line list and cross-sections for HC$_3$N. Then we apply these cross-sections and the model atmosphere of Swain et al. (2021) to a radiative transfer model in order to simulate the transmission spectrum of GJ 1132 b as it would be seen by JWST, accounting for the uncertainty in the retrieved abundances. We predict that cyanoacetylene features at various wavelengths, with a clear lone feature at 4.5 $\mu$m, observable by JWST after one transit. This feature persists within the $1-\sigma$ uncertainty of the retrieved abundances of HCN and CH$_4$. The signal is detectable for stratospheric temperatures $\lesssim 600$ K and moderate stratospheric mixing ($10^6 \, {\rm cm^2 \, s^{-1}} \lesssim K_{zz} \lesssim 10^8 \, {\rm cm^2 \, s^{-1}}$). Our results also indicate that HC$_3$N is an important source of opacity that future retrieval models should consider.

Cyanoacetylene (HC 3 N) is a linear molecule composed of two triple-bonded carbons bound at one end with a hydrogen atom and at the other with a nitrile group: carbon and nitrogen joined by a triple-bond. H−C ≡ C−C ≡ N. Because of its two energetic bonds, it is both physically stable and highly reactive in aqueous media (Ferris et al. 1968). It acts as both a molecular backbone and a source of chemical energy for prebiotic chemical synthesis (Powner et al. 2009;Becker et al. 2019). It can be produced from radical reactions between the cyano radical and acetylene and is a major product of the Miller-Urey synthesis (Miller 1953;Sanchez et al. 1966). There is extensive discussion among prebiotic chemists about whether HC 3 N is prebiotically plausible (Orgel 2002).
HC 3 N has been observed in the atmosphere of Titan from the ground, both in the gas phase (Bézard et al. 1992), and condensed into crystalline aerosol (Khanna 2005). According to retrieval from ALMA observations, the abundance of HC 3 N in the atmosphere of Titan is at about 100 ppb at 0.1 to 1 mbar, and drops by orders of magnitude with increasing pressure (Thelen et al. 2019).
Experimentally, the IR intensities of HC 3 N was studied in Bénilan et al. (2006); Douin et al. (2015). High-resolution spectroscopic analyses were reported by Bizzocchi et al. (2017); Jiang et al. (2021). Swain et al. (2021) analyzed of Hubble data of GJ 1132 b transmission spectra and find 0.5% concentrations of both HCN and CH 4 in an atmosphere with low mean molecular mass, implying the atmosphere is hydrogen-dominated. Swain et al. (2021) report that the atmosphere may be volcanic, and their photochemical models predict significant amounts of HC 3 N in the upper atmosphere. The analysis of Swain et al. (2021) has been challenged by Mugnai et al. (2021) and Libby-Roberts et al. (2021), who find no evidence of molecular features in the Hubble data. The analysis of Swain et al. (2021) and response by Mugnai et al. (2021) and Libby-Roberts et al. (2021) are the latest in an elaborate and conflicting literature attempting to determine the presence and nature of an atmosphere of GJ 1132 b (e.g. Schaefer et al. 2016;Southworth et al. 2017;Diamond-Lowe et al. 2018).
Regardless of whether GJ 1132 b has a reduced atmosphere, there is theoretical support for the persistence of volcanically derived highly reduced atmospheres on rocky exoplanets, owing to the persistence of elemental iron in the mantle (Lichtenberg 2021). It is possible that many Super Earth atmospheres resemble a warm Titan composition.
For this paper, we assume that the atmosphere reported by Swain et al. (2021) is the atmosphere of GJ 1132 b. Based on this assumption, we predict that HC 3 N is present in the upper atmosphere of GJ 1132 b in abundances detectable by the James Webb Space Telescope (JWST), and is an indication of a reduced atmosphere with a significant fraction of chemically active nitrogen and carbon species. In Section 2, we describe the method for constructing a line list of HC 3 N and the radiative transfer model and synthetic JWST pipeline used to calculate the transmission spectra. We present our results in Section 3, and discuss the promise and challenges for observing HC 3 N on GJ 1132 b, and the application of this work beyond GJ 1132 b, in Section 4.

METHODS
In order to make predictions about HC 3 N in the atmosphere of GJ 1132 b, we first predict the atmospheric composition as a function of atmospheric height (Section 2.1) and then develop a line list and cross-sections for HC 3 N (Section 2.2), to model the transmission spectrum of GJ 1132 b (Section 2.3). Finally, we simulate how that spectrum will look if observed by JWST (also Section 2.3). Swain et al. (2021) use the Argo model (Rimmer & Helling 2016) with the Stand2020 chemical network (Rimmer & Rugheimer 2019;Rimmer et al. 2021) and fixed surface conditions to predict atmospheric chemical profiles. Argo is a Lagrangian code that solves the photochemistry-transport equation:

Atmospheric Model
where n X (cm −3 ) is the number density of species X, t (s) is time, P X (cm −3 s −1 ) is the production rate of X, L X (s −1 ) is the destruction rate of X, and ∂Φ X /∂z (cm −3 s −1 ) accounts for the vertical transport.
We take the chemical profiles of Swain et al. (2021) as given. This is a self-consistent photochemical model atmosphere, and so the predictions of each of the species are interconnected. Such an atmosphere cannot be rich in carbon dioxide, for example, because carbon dioxide is not a predicted thermochemical or photochemical product in such a reduced atmosphere. We also explore the sensitivity of HC 3 N to the concentrations of HCN and CH 4 . To do this, we take the ±1 − σ errors for the retrieved abundances of HCN and CH 4 , from Swain et al. (2021), and apply or model to predict the effect on HC 3 N.
A set of temperature dependent cross sections and k tables were generated using a combination of the program ExoCross (Yurchenko et al. 2018) and the Python library Exo_k (Leconte 2020) on the corresponding grids used in PetitRADTRANS (Mollière et al. 2019). Figure 1 illustrates the vibrational bands used to generate the line list for HC 3 N.

Predicted Transmission Spectra
From the atmospheric model, planetary physical parameters, and line-opacities of different molecules; synthetic transmission spectrum was modelled using 'PetitRADTRANS' 1 (Mollière et al. 2019) both for a clear and cloudy atmosphere. The atmosphere was considered to be a composition of HC 3 N, HCN, CH 4 , C 2 H 2 , CO, CO 2 , H 2 O, N 2 O, and NH 3 . Rayleigh scattering from H 2 , He, and N 2 was considered, while Collision-induced absorption (CIA) opacities for H 2 -H 2 , and H 2 -He were included. A correlated-k approximation mode was used, which resulted in a spectrum of Spectral Resolution λ/∆λ = 1000. To model a cloudy atmosphere, a gray cloud deck was considered at 0.01 bar, which added an opaque cloud deck to the absorption opacity at the given pressure.
To study and analyse the detectability of molecular absorption features in the spectrum from JWST both for a clear and cloudy atmosphere, a noise simulator PandExo (Batalha et al. 2017) package was used. Following the details of modelling as mentioned in Zilinskas et al. (2020), NIRCam grisms in F322W2 (2.4-4 µm) and F444W (4-5 µm) mode, and the MIRI LRS instrument in Slitless mode (5-12 µm) were used to imitate the spectrum. Constant noise levels of 30 ppm for NIRCam and 50 ppm for MIRI LRS were taken with a saturation limit of 80% of full well capacity.

RESULTS
Here we present our results for the HC 3 N chemistry in the atmosphere of GJ 1132 b, the model transmission spectrum for GJ 1132 b, and the synthetic JWST spectra.
The model atmosphere of GJ 1132 b sufficient to explain the observations from Swain et al. (2021) which involves a surface chemistry set by degassing primarily of H 2 , He, N 2 , HCN, CH 4 and CO. Chemical profiles are shown in Figure 2.
A major photochemical product of CH 4 is ethane (C 2 H 6 ), which is then dehydrogenated to acetylene (C 2 H 2 ), which at the high temperatures of the atmosphere of GJ 1132 b can react directly with the photodissociation product of HCN to form HC 3 N. The total reaction proceeds as follows: Cyanoacetylene is destroyed by reaction with H (R2386 the reverse of R1686), and this simply restores the cyano radical (CN) and acetylene. This reaction has a barrier of ≈ 9500 K, and this will be important for the steep temperature sensitivity of upper atmospheric cyanoacetylene, discussed below. The dominant reaction destroying CN is R1483: which has a barrier of 2370 K. The acetylene undergoes hydrogenation back to C 2 H 5 , which then reacts with a hydrogen atom and breaks apart into two CH 3 radicals. At low temperatures, these would recombine to form ethane, but at high temperatures, the CH 3 will react with H 2 to reform CH 4 . The significant reactions are shown as functions of atmospheric pressure in Figure 2. We explore how HC 3 N varies as HCN and CH 4 are varied. We vary both HCN and CH 4 over the 1 − σ retrieved abundances of Swain et al. (2021) and plot the predicted HC 3 N profiles in Figure 3. HCN abundance determines the peak of the HC 3 N profile, with some influence from CH 4 . CH 4 also influences the overall shape of the HC 3 N profile.
We also explore how HC 3 N varies with temperature and chemical mixing, expressed by varying the eddy diffusion coefficient (K zz , cm 2 s −1 ). We performed a sensitivity analysis with fixed HCN and CH 4 at 0.5%, varying stratospheric temperature from 300 -1000 K (with fixed K zz = 10 7 cm 2 s −1 ), and eddy diffusion coefficient from 10 5 − 10 10 cm 2 s −1 (with fixed stratospheric temperature of 480 K).
The absorption lines corresponding to HC 3 N are very narrow, and a reason for that could be its abundance only in the upper atmosphere, i.e., at low pressure, where pressure broadening is minimal. To resolve these narrow absorption lines, we'd need high spectral resolution. At a Spectral Resolution of 100 and 1 transit, the peaks of HC 3 N at around 4.5 µm and 9 µm nevertheless seem distinguishable. If we increase the number of transits to 4, we see only a slight change in the values of error bars at higher wavelength regions, but it does not noticeably affect the error bars near HC 3 N features. Even after considering cloudy atmosphere, an HC 3 N feature is fairly detectable at around 9 µm when we have high HCN and CH 4 . In all cases except when HCN and CH 4 both are low, the 4.5 µm HC 3 N line is readily detectable. The absorption features of other major molecules viz. CH 4 and HCN are very prominent and have broad absorption lines in the generated spectrum, which aligns very well with their high abundance of those molecules, specifically in the higher pressure region as shown in the plot of pressure vs. mixing ratio of species. At least one of the HC 3 N features is detectable for stratospheric temperature 600 K, as shown in Figure 3, and eddy diffusion coefficient between 10 6 cm 2 s −1 K zz 10 9 cm 2 s −1 . If we decrease the spectral resolution to 50, we can still distinguish the HC 3 N feature at 4.5 µm for most of the models (except the model with 0.1% HCN and 0.1% CH 4 ), whereas HC 3 N feature at 9 µm remains undetectable for most of the models (except the model with 1.2% HCN and 1.6% CH 4 ). Thus, the spectral resolution of 100 is required to detect both the HC 3 N features simultaneously.
We see in Figure 3 that the mixing ratio of HC 3 N is strongly dependent on stratospheric temperature, and drops below 1 ppm in the upper atmosphere when T 700 K. The relative strength of these lines and others in the upper atmosphere is also affected by the temperature, and at high temperatures, 600 K, HC 3 N will be very difficult to detect. Above ∼ 700 K, no observable features remain.
This temperature sensitivity can be explained by R2386 (discussed above): The rate constant for this reaction between 450 − 800 K is effectively 2.5 × 10 −10 cm 3 s −1 exp(−9500 K/T ), and production does not change by more than a factor of a few over this range, and so balancing production and destruction at ∼ 10 −5 bar, one finds an analytic estimate of the peak mixing ratio of cyanoacetylene (x (HC 3 N)): x(HC 3 N) ≈ 4 × 10 −12 e 9500/T , 450 K ≤ T ≤ 800 K.
This explains the chemical mechanism for the loss of cyanoacetylene at higher stratospheric temperatures.   In this letter, we show that, if GJ 1132 b has observable amounts of CH 4 and HCN in its atmosphere, as reported by Swain et al. (2021), we predict it will have up to 0.5% of HC 3 N in its upper atmosphere due to photochemistry. Applying radiative transfer and accounting for the properties of JWST, we predict that cyanoacetylene (HC 3 N) will be observable by JWST, given what we presently know about the molecule.
There is some uncertainty about the HC 3 N line list (limited coverage of vibrational bands), but these uncertainties are small compared to the uncertain composition of the atmosphere, with retrieved HCN and CH 4 abundances spanning more than an order of magnitude and the predicted HC 3 N abundances spanning a factor of 30. These uncertainties were incorporated into the spectra and we found that spectral features of the molecules remain detectable at 0.1% mixing ratios of HCN and CH 4 , the low end of the 1 − σ error bars for these species retrieved abundances. More work will be needed, both experimental and theoretical, in order to make any strong claim about the shape and strength of HC 3 N features for temperatures 500 K, where otherwise energetically prohibitive and therefore yet unknown bands will be accessed, and the spectrum of HC 3 N could be significantly different. As we have found, however, HC 3 N abundance decreases to below detectable levels (concentrations of 10-100 ppm) at temperatures 600 K, at least in the reducing rocky planet atmosphere we explore. For our bulk atmospheric composition, HC 3 N may not be detectable at such high stratospheric temperatures because it will not survive in those temperatures, see Eq. (5). We found that HC 3 N concentrations were far less sensitive to the eddy diffusion coefficient, remaining detectable between values of 10 6 cm 2 s −1 and 10 10 cm 2 s −1 .
Even if GJ 1132 b does not have HCN, there are many planets, including, plausibly, many rocky planets that may host hydrogen-rich atmospheres rich in HCN (Tsiaras et al. 2016). Super Earths also may host reduced atmospheres because of quenched mantle differentiation (Lichtenberg 2021). For reduced atmospheres of rocky planets, HC 3 N is an important opacity source that retrieval models should take into account. . Simulated transmission spectrum of GJ1132b using Argo photochemistry model and Peti-tRADTRANS radiative transfer package for different HCN and CH 4 compositions. The cloud was modelled according to the power law function, considering a Gray cloud at P=0.01 bar. The spectrum is shown at a resolution of 100, which was generated by convolving the high resolution data (R=1000) with a Gaussian kernel of standard deviation=8.4506.
By itself, HC 3 N cannot be uniquely identified by observing one or two spectral features. Rather, it will be presence in the context of a hydrogen-rich exoplanet atmosphere. The probability that HC 3 N is an explanation for a given spectral feature must be assessed in the context of other molecular constituents as indicated by the full transmission spectra, such as H 2 (inferred from the scale height), CH 4 , and HCN. In this context, HC 3 N would be a further indicator of the presence of HCN, and a probe into prebiotically relevant mechanisms taking place on uninhabitable planets. This may give a window into the time when our planet was hot and hydrogen-rich (Genda et al. 2017), forming molecules that later may have been essential to the origins of life.  (Yurchenko et al. 2018)