# Detectable Abundance of Cyanoacetylene (HC_3N) Predicted on Reduced
Nitrogen-Rich Super-Earth Atmospheres

Paul B. Rimmer Department of Earth Sciences, University of Cambridge, Downing
St, Cambridge CB2 3EQ, United Kingdom  Cavendish Laboratory, University of
Cambridge, JJ Thomson Ave, Cambridge CB3 0HE, United Kingdom  MRC Laboratory
of Molecular Biology, Francis Crick Ave, Cambridge CB2 0QH, United Kingdom
Liton Majumdar School of Earth and Planetary Sciences, National Institute of
Science Education and Research, HBNI, Jatni 752050, Odisha, India  Akshay
Priyadarshi School of Physical Sciences, National Institute of Science
Education and Research, HBNI, Jatni 752050, Odisha, India  Sam Wright
Department of Physics and Astronomy, University College London, Gower Street,
WC1E 6BT London, UK  S. N. Yurchenko  Department of Physics and Astronomy,
University College London, Gower Street, WC1E 6BT London, UK

(Revised NaN; Accepted NaN)

###### Abstract

We predict that cyanoacetylene (HC_3N) 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 as described by Swain et al.
(2021). First, we construct line list and cross-sections for HC_3N. 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
four transits. This feature persists within the $1-\sigma$ uncertainty of the
retrieved abundances of HCN and CH_4.

Extrasolar rocky planets, Exoplanet atmospheres, Exoplanets: individual GJ
1132 b

††journal: ApJL††software: Argo (Rimmer & Helling, 2016), petitRADTRANS
(Mollière et al., 2019), PandExo (Batalha et al., 2017)

##  1 Introduction

Cyanoacetylene (HC_3N) 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.
$\ce{H-C\\!\equiv\\!C-C\\!\equiv\\!N}$. 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_3N is prebiotically plausible (Orgel, 2002).

HC_3N 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_3N 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_3N 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_3N 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_3N 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_3N 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_3N on GJ 1132 b,
and the application of this work beyond GJ 1132 b, in Section 4.

##  2 Methods

In order to make predictions about HC_3N 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_3N
(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).

###  2.1 Atmospheric Model

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:

$\dfrac{dn_{\ce{X}}}{dt}=P_{X}-L_{X}n_{\ce{X}}-\dfrac{\partial\Phi_{X}}{\partial
z},$ (1)

where $n_{\ce{X}}$ (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 $\partial\Phi_{X}/\partial z$ (cm-3 s-1) accounts
for the vertical transport.

We take the chemical profiles of Swain et al. (2021) as given. We also explore
the sensitivity of HC_3N to the concentrations of HCN and CH_4. To do this, we
take the $\pm 1-\sigma$ 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_3N.

###  2.2 Line list and cross sections / k-tables for Cyanoacetylene

There existed no comprehensive IR line list for HC_3N applicable for a broad
range of temperatures. The experimental and theoretical information is rather
scarce for HC_3N, especially in IR, only for the room temperature (Bénilan et
al., 2006; Jolly et al., 2007; Douin et al., 2015; Bizzocchi et al., 2017;
Jiang et al., 2021). For this study, we have combined spectroscopic data
available for HC_3N in the literature to construct a line list as a best
estimate of the opacity of HC_3N in IR. Our synthetic HC_3N line list covers
the wavelength range from 2.5 to 10 $\mu$m and contains the fundamental
$\nu_{1},\nu_{2}$, $\nu_{3}$ and overtones $2\nu_{5}$, $2\nu_{6}$, $3\nu_{5}$,
$\nu_{1}+\nu_{7}$, $\nu_{2}+\nu_{4}$, $\nu_{2}+\nu_{6}$, $\nu_{2}+\nu_{7}$,
$\nu_{3}+\nu_{6}$, $\nu_{3}+\nu_{7}$, $\nu_{4}+\nu_{7}$, $\nu_{4}+\nu_{7}$,
$\nu_{5}+2\nu_{7}$, $\nu_{5}+\nu_{6}$ bands from this region. Only transitions
from the ground vibrational state are included.

We used the program PGOPHER (Western, 2017) to generate energies and Einstein
coefficients of HC_3N. Spectroscopic constants of $2\nu_{6}$,
$\nu_{5}+\nu_{7}$, $\nu_{6}+\nu_{7}$, $\nu_{6}+2\nu_{7}$, $\nu_{1}$,
$\nu_{2}$, $\nu_{3}$, $\nu_{1}+\nu_{7}$, $\nu_{2}+\nu_{7}$ and
$\nu_{3}+\nu_{7}$ were taken from the high-resolution IR studies by Bizzocchi
et al. (2017); Jiang et al. (2021). Other states of HC_3N from this IR region
have not been characterized experimentally. Their spectroscopic constants were
estimated using the constants of the same symmetry and were adjusted to
visually agree with the IR spectrum from Bénilan et al. (2006). The
corresponding transition-dipole moments were extracted from the ab initio work
by Dargelos & Pouchan (2020) computed at the high level of theory CCSD(T)-F12.

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 HC3N.

Figure 1: Absorption cross-sections of HC3N at $T=400$ K: vibrational bands
(fundamentals and overtones) used in the spectroscopic model are indicated in
the legend.

###  2.3 Predicted Transmission Spectra

From the atmospheric model, planetary physical parameters, and line-opacities
of different molecules; synthetic transmission spectrum was modelled using
‘PetitRADTRANS’ 111https://petitradtrans.readthedocs.io/en/latest/ (Mollière
et al., 2019) both for a clear and cloudy atmosphere. The atmosphere was
considered to be a composition of HC_3N, HCN, CH_4, CO, H_2O, C_2H_2, 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 $\lambda/\Delta\lambda=1000$. 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 $\mu m$) and F444W (4-5 $\mu m$) mode, and the MIRI LRS instrument in
Slitless mode (5-12 $\mu m$) 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.

##  3 Results

Here we present our results for the HC_3N 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_2H_6), which is then
dehydrogenated to acetylene (C_2H_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_3N. The total reaction proceeds as follows:

$\displaystyle\ce{HCN}+h\nu$ $\displaystyle\rightarrow\ce{CN}+\ce{H},$
$\displaystyle\mathrm{R5792};$ $\displaystyle 2\big{(}\ce{CH_{4}}+\ce{H}$
$\displaystyle\rightarrow\ce{CH_{3}}+\ce{H_{2}}\big{)},$
$\displaystyle\mathrm{R1520};$ $\displaystyle\ce{CH_{3}}+\ce{CH_{3}}+\ce{M}$
$\displaystyle\rightarrow\ce{C_{2}H_{6}}+\ce{M},$
$\displaystyle\mathrm{R143};$ $\displaystyle\ce{C_{2}H_{6}}+\ce{H}$
$\displaystyle\rightarrow\ce{C_{2}H_{5}}+\ce{H_{2}},$
$\displaystyle\mathrm{R1549};$ $\displaystyle\ce{C_{2}H_{5}}+\ce{H}$
$\displaystyle\rightarrow\ce{C_{2}H_{4}}+\ce{H_{2}},$
$\displaystyle\mathrm{R1538};$ $\displaystyle\ce{C_{2}H_{4}}+h\nu$
$\displaystyle\rightarrow\ce{C_{2}H_{2}}+\ce{H}+\ce{H},$
$\displaystyle\mathrm{R5841};$ $\displaystyle\ce{CN}+\ce{C_{2}H_{2}}$
$\displaystyle\rightarrow\ce{HC_{3}N}+\ce{H},$ $\displaystyle\mathrm{R1686};$
$\displaystyle----$ $\displaystyle------$ $\displaystyle\ce{HCN}+2\ce{CH4}$
$\displaystyle\rightarrow\ce{HC_{3}N}+4\ce{H2}.$ (2)

Cyanoacetylene is destroyed by reaction with H (R2386 the reverse of R1686),
but this simply restores the cyano radical (CN) and acetylene. The dominant
reaction destroying CN is R1483:

$\ce{CN}+\ce{H_{2}}\rightarrow\ce{HCN}+\ce{H},$ (3)

which has a barrier of $2370\,{\rm K}$. The acetylene undergoes hydrogenation
back to C_2H_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 CH4. The
significant reactions are shown as functions of atmospheric pressure in Figure
2.

We explore how HC_3N varies as HCN and CH_4 are varied. We vary both HCN and
CH_4 over the $1-\sigma$ retrieved abundances of Swain et al. (2021) and plot
the predicted HC_3N profiles in Figure 3. HCN abundance determines the peak of
the HC_3N profile, with some influence from CH_4. CH_4 also influences the
overall shape of the HC_3N profile.

The absorption lines corresponding to HC3N 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 4 transits, the peaks of HC3N at around 4.5 $\mu m$ and 9 $\mu m$
nevertheless seem distinguishable. Even after considering cloudy atmosphere,
an HC3N feature is fairly detectable at around 9 $\mu$m when we have high HCN
and CH4. In all cases except when HCN and CH4 both are low, the 4.5 $\mu$m
HC3N line is detectable. The absorption features of other major molecules viz.
CH4 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.

Figure 2: Left: Chemical profiles for GJ 1132 b, as mixing ratios as a
function of atmospheric pressure (bar), highlighting HC_3N. Taken from Swain
et al. (2021, their Fig. 11), with permission. Right: Rates, in units of cm-3
s-1, for critical reactions for the formation and destruction of HC_3N and its
precursors, as a function of atmospheric pressure (bar).  Figure 3:
Cyanoacetylene (HC_3N) mixing ratio as a function of atmospheric pressure
(bar), prediced for a 10% N_2, 90% H_2 atmosphere with the retrieved
abundances and errors of Swain et al. (2021): 0.5% + 0.7% - 0.4% HCN and 0.5%
+ 1.1% - 0.4% CH_4. C_2H_2 is set to 100 ppm.  Figure 4: Simulated
transmission spectrum of GJ1132b using Argo photochemistry model and
PetitRADTRANS radiative transfer package for different HCN and CH4
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. Figure 5: The range of
values in the JWST simulated observation using PandExo for different HCN and
CH4 compositions, after four transits and with a resolution of 100. The cloud
was modelled according to the power law function, considering a Gray cloud at
P=0.01 bar. The three colors denote the three JWST modes and instruments used,
which were NIRCam grism F322W2, NIRCam grism F444W, and MIRI LRS.

##  4 Discussion and Conclusion

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_3N in its upper atmosphere due to photochemistry.
Applying radiative transfer and accounting for the properties of JWST, we
predict that cyanoacetylene (HC_3N) will be observable by JWST, given what we
presently know about the molecule.

There is some uncertainty about the HC_3N 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_3N
abundances spanning a factor of 30. These uncertainties were incorporated into
the spectra and we found that spectral features of the molecule remain
detectable even at 0.1% mixing ratios of HCN and CH_4, the low end of the
$1-\sigma$ 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_3N features for temperatures $\gg
500$ K, where otherwise energetically prohibitive and therefore yet unknown
bands will be accessed, and the spectrum of HC_3N could be significantly
different.

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). HC_3N would be
an 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.

The authors thank Mark Swain for helpful comments on the paper. P. B. R.
thanks the Simons Foundation for funding (SCOL awards 599634). SY’s work was
supported by the STFC Project ST/R000476/1 and by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme through Advance Grant number 883830. S.W. was supported through the
STFC UCL CDT in Data Intensive Science (grant No. ST/P006736/1). , `Exo_k`
(Leconte, 2020), ExoCross (Yurchenko et al., 2018)

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