Identifiable Acetylene Features Predicted for Young Earth-like Exoplanets with Reducing Atmospheres Undergoing Heavy Bombardment

The initial and boundary conditions discussed above are applied to calculate the temperature profile using the ATMOS 1D Global Climate model (Kasting et al. 1984; Pavlov et al. 2000; Haqq-Misra et al. 2008; Kopparapu et al. 2013; Ramirez et al. 2014).

The relevant greenhouse gases are ${{\rm{H}}}_{2}{\rm{O}}$ and ${\mathrm{CH}}_{4}$. ${\mathrm{CH}}_{4}$ is a very potent greenhouse gas, and at such high abundances, by itself, might not result in a temperate surface environment. At the same time, abundant ${\mathrm{CH}}_{4}$ is expected to produce a photochemical haze (Trainer et al. 2006), which will cool the planet's surface. This interplay, along with the surface heat flux due to impacts and latent heat from planet formation, make it very difficult to constrain the temperature. Because of this complex interplay, we treat ${\mathrm{CH}}_{4}$ as ${\mathrm{CO}}_{2}$ for the purposes of the climate model, to mitigate the greenhouse effect, and leave for the future a more accurate climate simulation that accounts for the many factors present on an Earth-like planet experiencing heavy bombardment. It is worth noting that the chemistry near the surface is not especially sensitive to the temperature profile in the sense that acetylene, hydrogen cyanide, and ammonia destruction, even at 100°C, is nevertheless dominated by photochemistry and diffusion. The temperature and eddy diffusion profiles are shown in Figure 2.

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The abundances of the shock chemical products correspond to exposure to a laser blast of a certain energy, and give us a number of molecules per joule of energy (S_i, for species i). We incorporate the experimental results in terms of surface fluxes, and preserve mass balance of the non-condensables by sequestering excess hydrogen and oxygen into water.

The surface flux can be expressed in terms of the average of this source function, the energy deposited via an impact, E_i, and the frequency of impacts ν_i: $\langle {E}_{i}{\nu }_{i}\rangle$. This product is considered to be evenly distributed over the surface of the planet, so the product is divided by the surface area of the planet to give the surface flux from the impact, Φ_{s, i} [cm⁻² s⁻¹]:

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{s,i}=\displaystyle \frac{{S}_{i}\langle {E}_{i}{\nu }_{i}\rangle }{4\pi {R}_{p}^{2}}.\end{eqnarray} \tag{ 1 }$$

The average of the energy deposition and frequency can be expressed as

$$\begin{eqnarray}&&\langle {E}_{i}{\nu }_{i}\rangle ={\int }_{{E}_{0}}^{\infty }\nu (E)\,{dE}.\end{eqnarray} \tag{ 2 }$$

The impact frequency is expressed in terms of crater diameter, D [m], as a power law (Wetherill 1975):

$$\begin{eqnarray}&&\nu ={\nu }_{0}{\left(\displaystyle \frac{D}{{D}_{0}}\right)}^{-\alpha },\end{eqnarray} \tag{ 3 }$$

where D₀ = 10⁴ m is a reference diameter, ν₀ = ν(D₀) and we take α = 1.3, which seems to agree with the lunar crater size distribution reasonably well. The diameter of the crater, in turn, can be related to the energy, also as a power law (Wetherill 1975), with constants taken from the literature (Hughes 2003):

$$\begin{eqnarray}&&D=4.8\times {10}^{-6}\,{\rm{m}}{\left(\displaystyle \frac{E}{1\mathrm{erg}}\right)}^{1/\beta },\end{eqnarray} \tag{ 4 }$$

where β can be between 3 (energy limited) or 4 (gravity limited) (Wetherill 1975). We choose β = 3. From the relationship between crater diameter and impactor mass from Wetherill (1975), we can parameterize the impactor frequency as a function of the mass deposition of impactors:

$$\begin{eqnarray}&&{\nu }_{0}=\displaystyle \frac{{\dot{M}}_{T}}{{M}_{0}},\end{eqnarray} \tag{ 5 }$$

where ${\dot{M}}_{T}$ [g s⁻¹] is the mass deposition rate and M₀ = 6.6 × 10¹⁷ g. Applying Equations (3)–(5) to Equation (2) and applying a high-energy cutoff for the impactor, E_max = 10³⁶ erg (assuming the maximum crater size of 1000 km and applying Equation (4)). We then integrate to find:

$$\begin{eqnarray}&&\langle {E}_{i}{\nu }_{i}\rangle =\displaystyle \frac{{\dot{M}}_{T}}{{M}_{0}}\displaystyle \frac{{E}_{0}}{1-\gamma }{\left(\displaystyle \frac{{E}_{\max }}{1\mathrm{erg}}\right)}^{1-\gamma },\end{eqnarray} \tag{ 6 }$$

where E₀ = 1.3 × 10¹² erg and γ = α/β = 0.43. We apply this result to Equation (1), along with S_i [molecules/J] from Table 1, taking our mass deposition rate during the heavy bombardment to be ${\dot{M}}_{T}=4.3\times {10}^{13}$ g yr⁻¹.

Table 1.  Experimental Yield of Species, Corresponding Surface Fluxes, and Atmospheric Lifetimes

Molecule	Si (mol J−1)	${{\rm{\Phi }}}_{i,s}$ (cm−2 s−1)	τ (yr)
$\mathrm{HCN}$	$5.4\times {10}^{-7}$	9.7 × 1012	30
${{\rm{C}}}_{2}{{\rm{H}}}_{2}$	8.6 × 10−7	1.6 × 1013	250
${\mathrm{NH}}_{3}$	1.1 × 10−7	1.9 × 1012	15

Note. Values for S_i are based on experimental results detailed here, values for Φ_i,s are from solving Equation (1) with Equation (6), and lifetimes are derived from our exoplanet model atmosphere using the STAND network and ARGO chemical model for photodestruction rates (see Section 6.1).

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The surface fluxes from Table 1 are incorporated into ARGO, a Lagrangian photochemistry and cosmic-ray atmospheric chemistry model (Rimmer & Helling 2016), that takes a prescribed temperature profile, which we determine using a climate model (discussed above), a high resolution (1 Å) UV field estimated for the 1 Gy Sun (Ribas et al. 2005, 2010), and a comprehensive chemical network, STAND (Rimmer & Rugheimer 2019), valid between 300 and 30,000 K incorporating H/C/N/O ions and neutral chemistry including complex hydrocarbons and amines, including the amino acid glycine (Rimmer & Helling 2016). The model solves the equation:

$$\begin{eqnarray}&&\displaystyle \frac{d[{\rm{X}}]}{{dt}}=P({\rm{X}})-L({\rm{X}})[{\rm{X}}]-\displaystyle \frac{\partial {\rm{\Phi }}({\rm{X}})}{\partial z},\end{eqnarray} \tag{ 7 }$$

where [X] (cm⁻³) is the concentration of chemical species X, itself a function of the atmospheric height, z. The production of X is denoted by $P({\rm{X}})$ [cm⁻³ s⁻¹] and loss by $L({\rm{X}})$ [s⁻¹], and the flux due to diffusion by ${\rm{\Phi }}({\rm{X}})$ [cm⁻² s⁻¹].

The model is Lagrangian, and keeps track of the timescales at which the parcel exists at a particular temperature and pressure, and then changes the temperature and pressure. Molecular diffusion is approximated using "banking" reactions. This model can be applied to planetary atmospheres from hot Jupiters and hot super-Earths, to Earth, and is even reasonably accurate for Jupiter (Rimmer & Helling 2016). We use the model with corrected downward diffusion (Rimmer & Helling 2019).

In order to account for gradual geological emissions of gases at the surface of the planet, a new outgassing process was added to the model. A new type of reaction was specified within the STAND network, which only takes place at the surface. This reaction converts a new "ground" species, GX, available at virtually infinite abundance, but not contributing to any other process, to the chemically active species. The rate of outgassing is controlled by the rate of this conversion as well as the time that the parcel spends at the surface. The rate is set to:

$$\begin{eqnarray}&&{R}_{\mathrm{out}}({\rm{X}})=\displaystyle \frac{{\rm{\Phi }}({\rm{X}})}{{\rm{\Delta }}z},\end{eqnarray} \tag{ 8 }$$

where ${\rm{\Phi }}({\rm{X}})$ [cm⁻² s⁻¹] is the surface emission flux, Δz [cm] is the height step of the atmospheric model, and ${R}_{\mathrm{out}}({\rm{X}})$ [cm⁻³ s⁻¹] is the effective rate at which species X is introduced into the atmosphere, and this last quantity is incorporated into the model.

For the network, we have updated the rate constants for some reactions, namely:

$$\begin{eqnarray}&&\begin{array}{l}{\rm{O}}+{\rm{O}}+{\rm{M}}\to {{\rm{O}}}_{2}+{\rm{M}},\\ {k}_{0}=1.67\times {10}^{-33}{\left(T/300{\rm{K}}\right)}^{-1},\end{array}\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&\begin{array}{l}{\rm{O}}+\mathrm{OH}\to {{\rm{O}}}_{2}+{\rm{H}},\\ k=3.28\times {10}^{-11}{\left(T/300{\rm{K}}\right)}^{-0.32},\end{array}\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&\begin{array}{l}{{\rm{C}}}_{2}{{\rm{H}}}_{2}+{\rm{H}}+{\rm{M}}\to {{\rm{C}}}_{2}{{\rm{H}}}_{3}+{\rm{M}},\\ {k}_{\infty }=3.01\times {10}^{-11}{\left(T/300{\rm{K}}\right)}^{1.09}\,{e}^{-1327/T},\end{array}\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&\begin{array}{l}{{\rm{C}}}_{2}{{\rm{H}}}_{2}+{\mathrm{CH}}_{3}+{\rm{M}}\to {{\rm{C}}}_{3}{{\rm{H}}}_{5}+{\rm{M}},\\ {k}_{\infty }=6.09\times {10}^{-9}{\left(T/300{\rm{K}}\right)}^{-5.98}\,{e}^{-6695/T},\end{array}\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{HCN}+{{\rm{C}}}_{2}{{\rm{H}}}_{3}\to {{\rm{C}}}_{3}{{\rm{H}}}_{3}{\rm{N}}+{\rm{H}},\\ {k}_{\infty }=1\times {10}^{-12}\,{e}^{-900/T},\end{array}\end{eqnarray} \tag{ 13 }$$

where Reaction (9) is from Javoy et al. (2003), Reaction (10) is from Robertson & Smith (2006), Reaction (11) is from Knyazev & Slagle (1996), Reaction (12) is from Diau et al. (1994), and Reaction (13) is from Monks et al. (1993). The value NIST provides for Reaction (13) is incorrect; they quote the 298 K value as though it is constant over all temperatures, whereas Monks et al. (1993) gives the rate constant as above. We have also removed the reaction

$$\begin{eqnarray}&&{{\rm{C}}}_{2}{{\rm{H}}}_{5}+\mathrm{HCO}+{\rm{M}}\to {{\rm{C}}}_{3}{{\rm{H}}}_{6}{\rm{O}}+{\rm{M}},\end{eqnarray} \tag{ 14 }$$

because the published rate constant was extracted indirectly from an experiment where atomic hydrogen was reacted with ${{\rm{C}}}_{2}{{\rm{H}}}_{4}$ and CO, and it is unclear whether the measured ${{\rm{C}}}_{3}{{\rm{H}}}_{6}{\rm{O}}$ resulted from the above reaction. In addition, we have updated the absorption cross sections for several photochemical reactions using the MPI-Mainz UV/VIS spectral atlas (Keller-Rudek et al. 2013).

Experimental results show that amounts of C₂H₂, HCN, and NH₃, significant for atmospheric chemistry, are generated in the impact simulation, transforming the atmosphere (see Table 2). Our spectroscopic analysis shows that the experimental atmosphere containing equimolar ratios of CO, CH₄, N₂, and H₂O is reprocessed, yielding several products, the dominant species among them being acetylene (C₂H₂) and hydrogen cyanide (HCN) in a mutual ratio of approximately 3:2, accompanied with less than a few percent of ammonia, ethylene, and carbon dioxide. Molecular hydrogen is generated mainly during the decomposition of methane and we estimate that each mole of methane ends up producing about 0.6 mol of H₂ (the remainder is retained in the products). Because the molecular hydrogen cannot be directly measured, and because it is expected to rapidly escape, we do not include it in the atmospheric model.

HCN in particular is well-connected to prebiotic chemistry, and is invoked in a host of different scenarios (Ferris et al. 1978; Ritson & Sutherland 2012; Xu et al. 2018). We apply the experimental chemical yields of C₂H₂, HCN, and NH₃ to a photochemistry/diffusion model in order to predict the atmospheric signatures of impacts. Specifically, we apply these results to a model atmosphere for an Earth-like exoplanet (Earth mass, Earth radius, 1 au away from a Sun-like star), with a bulk chemistry dominated by 80% N₂, 10% CO, and 10% CH₄ in the presence of surface liquid water and its saturated vapor. We include the impact-generated ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$, HCN, and ${\mathrm{NH}}_{3}$ as surface fluxes, as described in Section 3.2. The temperature profile and other details of this atmosphere are discussed in Section 3.1.

Here we discuss the chemistry of an Earth-like rocky exoplanet with a bulk atmosphere of 80% ${{\rm{N}}}_{2}$, 10% CO and 10% ${\mathrm{CH}}_{4}$, with water at vapor pressure. We assume this atmosphere is stable, and its stability is largely justified by indications from the geological record that Earth may have had this atmospheric composition during the Hadean (Yang et al. 2014). If the planet is lifeless, then high concentrations of CO can easily be maintained. High surface fluxes of ${\mathrm{CH}}_{4}$ could lead to it comprising 10% of the atmosphere, especially if the escape of ${{\rm{H}}}_{2}$ is slow. We first show the photochemistry without impacts.

The main consequence of the photochemistry before impacts is in the fixing of nitrogen high in the atmosphere, and the generation of large hydrocarbons that probably develop into an upper-atmospheric haze. This is consistent with experimental and other model results for gases with high concentrations of ${\mathrm{CH}}_{4}$ (Trainer et al. 2004, 2006; Arney et al. 2016), and that CO changes the character of the resulting haze (Hörst & Tolbert 2014). Significant amounts of hydrocarbons are also generated in the upper atmosphere, with ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ ranging from 1 ppm at 1 mbar, up to 1000 ppm at <10 μbar. For this atmosphere, ${{\rm{C}}}_{2}{{\rm{H}}}_{6}$ is over an order of magnitude more abundant throughout. This particular atmosphere has a large fraction of highly reduced carbon (−4, ${\mathrm{CH}}_{4}$), whereas the nitrogen is neutral (+0, ${{\rm{N}}}_{2}$), largely owing to the instability of ${\mathrm{NH}}_{3}$ in this environment. This combination leads to novel photochemistry for the fixed nitrogen, with the dominant species being diazomethane (${\mathrm{CH}}_{2}{{\rm{N}}}_{2}$), rather than hydrogen cyanide (HCN). The pathway for photochemical diazomethane formation is given in the Discussion (especially Section 6.1). It would be very difficult to observe any of these fixed nitrogen species in transmission on an exoplanet with present instruments, although this may be possible with future observational capabilities.

Following the calculations described above (Section 3.2), we incorporate the surface fluxes of C₂H₂, HCN, and NH₃. The dependence of the surface mixing ratios resulting from these fluxes, for different impact rates, is shown in Figure 3. The resulting atmosphere is shown in Figure 4. We also plot the atmosphere without the impact-generated species for comparison. It is clear that photochemistry alone cannot explain the high quantities of tropospheric ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$, HCN and ${\mathrm{NH}}_{3}$. The main effect of the photochemistry and diffusion is found in the upper atmosphere, where C₂H₂ is converted to C₂H₆ and HCN is converted to acrylonitrile. A trace amount of carbon dioxide is also produced at an atmospheric height of 30 mbar (an altitude of about 24 km). In addition, we predict that a high rate of impacts will generate a thick haze in the upper atmosphere. Kawashima & Ikoma (2018) have shown that this hydrocarbon haze may obscure some of the molecular features, and will affect the surface UV actinic flux, the effects of which can be predicted (Wolf & Toon 2010; Arney et al. 2016).

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The effect of impacts is determined not simply by the frequency of impacts, but also by the initial atmospheric composition. As a consequence of the C/O ratio (Rimmer & Rugheimer 2019), an atmosphere composed only of CO₂ and N₂ will have very different chemical tracers of impact history than a planet with a more reducing atmosphere, typically in the form of CO/CH₄. It is important to note that the more reducing atmospheres result in greater yields of life's building blocks due to impacts (Cleaves et al. 2008).

We find that, as a result of the impact, about 72% of the methane is decomposed, while more stable gases such as carbon monoxide and nitrogen experience losses of 28% and 13% respectively. The initial and resulting compositions are shown in Table 2. In previous studies referring to exploration of this system by selected ion flow mass spectrometry, we estimated that the laser spark plasma produces also ppm amounts of ethanol, propadiene, propane, methanol, butadiene, propene, acetone, and propanol (Civiš et al. 2004, 2016; Ferus et al. 2009, 2014, 2012).

We use the chemical profiles (Figure 4) in a TauREx radiative transfer model (see Methods), in order to predict transmission spectra for an Earth-sized planet around a Sun-like star (Figures 5 and 6). The first thing to note is that the large amounts of atmospheric methane obscure many of the other molecular features. Nevertheless, some of these features can be distinguished, even at a resolution of R = 300. The bulk composition of the atmosphere can be detected: in addition to ${\mathrm{CH}}_{4}$, a strong CO feature can be observed at 4.9 μm, ${{\rm{H}}}_{2}{\rm{O}}$ appears at 6.5 μm, and acetylene appears as a shoulder to the 3.3 μm ${\mathrm{CH}}_{4}$ feature, and as a lone feature at 10.5 μm. All the HCN features are masked by other features, and so we do not predict that HCN is a good tracer for impacts on a reducing atmosphere.

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Figure 6 emphasizes this acetylene shoulder, at roughly 3.05 μm, and this may be detectable using a combination of careful data reduction and atmospheric retrieval as with the nitrogen detection on HD 209458b (MacDonald & Madhusudhan 2017). Hazes may obscure some features on this exoplanet, and thick hazes may render the 3.05 μm acetylene shoulder difficult to detect, but should not obscure the 10.5 μm feature (Arney et al. 2016). We predict detectable amounts of acetylene (${{\rm{C}}}_{2}{{\rm{H}}}_{2}$) as a tracer of impact-induced chemistry on methane-rich rocky exoplanets.

Here we provide a description of the atmospheric processing of the impact-produced species, HCN, ${\mathrm{NH}}_{3}$, and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$. We also discuss the formation of ${\mathrm{CH}}_{2}{{\rm{N}}}_{2}$.

The lifetimes and profiles of all of these species are largely determined by atmospheric photochemistry, and the shape of their profiles is determined by how ultraviolet light at specific wavelengths penetrates the atmosphere. The depth at which photochemistry becomes important depends on the stellar spectrum, the bulk atmospheric composition, and the nature of the species in question. If there is an atmospheric window allowing near-ultraviolet light to penetrate deep into the atmosphere, at wavelengths where another species will absorb these wavelengths, then photochemistry will be active deep within the atmosphere. This can be visualized by a τ = 1 curve, showing where the optical depth, τ = 1 as a function of pressure. We show this curve in Figure 7.

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At the concentrations produced via impacts, hydrogen cyanide and acetylene are relatively stable (over > 1 yr timescales) within a ${{\rm{N}}}_{2}$, CO, and ${\mathrm{CH}}_{4}$ dominated atmosphere. They are primarily destroyed photochemically. The rates for the dominant destructive pathways for the three primary impact-generated chemical species, acetylene, hydrogen cyanide, and ammonia, are shown in Figure 8. The lifetimes of these species in the atmosphere are 250 yr for acetylene, 30 yr for hydrogen cyanide, and 15 yr for ammonia. The ammonia lifetime is in general agreement with Kasting (1982). We have included these lifetimes in Table 1.

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We now discuss the chemical pathways that lead to the destruction of HCN, ${\mathrm{NH}}_{3}$, and ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$. Much of the HCN is consumed by direct photodissociation or by reacting with products of acetylene, ${{\rm{C}}}_{2}{\rm{H}}$ and ${{\rm{C}}}_{2}{{\rm{H}}}_{3}$, leading to the production of acrylonitrile (${{\rm{C}}}_{3}{{\rm{H}}}_{3}{\rm{N}}$) and cyanoacetylene (${\mathrm{HC}}_{3}{\rm{N}}$), as shown in Figure 9.

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The lifetimes of ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ and HCN are largely regulated by ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ photodissociation:

$$\begin{eqnarray}&&{{\rm{C}}}_{2}{{\rm{H}}}_{2}+h\nu \to {{\rm{C}}}_{2}{\rm{H}}+{\rm{H}},\end{eqnarray} \tag{ 15 }$$

followed by production of diacetylene via

$$\begin{eqnarray}&&{{\rm{C}}}_{2}{\rm{H}}+{{\rm{C}}}_{2}{{\rm{H}}}_{2}\to {{\rm{C}}}_{4}{{\rm{H}}}_{2}+{\rm{H}}.\end{eqnarray} \tag{ 16 }$$

The diacetylene diffuses downward, and is photodissociated:

$$\begin{eqnarray}&&{{\rm{C}}}_{4}{{\rm{H}}}_{2}+h\nu \to {{\rm{C}}}_{2}+{{\rm{C}}}_{2}{{\rm{H}}}_{2},\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}&&\,\,\,\,\,\,{\to {\rm{C}}}_{2}{\rm{H}}+{{\rm{C}}}_{2}{\rm{H}}.\end{eqnarray} \tag{ 18 }$$

This destroys acetylene via Reaction (16), although much of the acetylene is restored from the photochemical destruction of diacetylene, but the excess atomic hydrogen rapidly destroys acetylene via the reaction:

$$\begin{eqnarray}&&{{\rm{C}}}_{2}{{\rm{H}}}_{2}+{\rm{H}}+{\rm{M}}\to {{\rm{C}}}_{2}{{\rm{H}}}_{3},\end{eqnarray} \tag{ 19 }$$

leading to ${{\rm{C}}}_{2}{{\rm{H}}}_{4}$ and ${{\rm{C}}}_{2}{{\rm{H}}}_{6}$. In addition, diacetylene photochemical products do not always return to acetylene, but will react with other hydrocarbon fragments to form photochemical haze particles.

Ammonia is far less stable, and its reaction pathway is relatively simple. Ammonia photochemistry leads predominantly to the formation of molecular nitrogen:

$$\begin{eqnarray*}\begin{array}{rcl}3({\mathrm{NH}}_{3}+h\nu & \to & {\mathrm{NH}}_{2}+{\rm{H}}),\\ {\mathrm{NH}}_{2}+{\mathrm{NH}}_{2} & \to & \mathrm{HNNH}+{{\rm{H}}}_{2},\\ \mathrm{HNNH}+{\mathrm{NH}}_{2} & \to & {\mathrm{NH}}_{3}+{{\rm{N}}}_{2}{\rm{H}},\\ {{\rm{N}}}_{2}{\rm{H}}+{\rm{M}} & \to & {{\rm{N}}}_{2}+{\rm{H}}+{\rm{M}},\\ 2({\rm{H}}+{\rm{H}}+{\rm{M}} & \to & {{\rm{H}}}_{2}+{\rm{M}}),\\ ----- & - & ----\\ 2{\mathrm{NH}}_{3}+3h\nu & \to & {{\rm{N}}}_{2}+3{{\rm{H}}}_{2}.\end{array}\end{eqnarray*}$$

Much of the atomic hydrogen goes on to form ${{\rm{H}}}_{2}$, as shown in the scheme above, but a significant fraction reacts with CO in a pathway to generate formaldehyde (see Figure 10) in addition to contributing to the hydrocarbon photochemistry.

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We do, however, observe the efficient formation of ethane, given the quantity of available free hydrogen. Ethane is generated from acetylene in the upper atmosphere by the reaction scheme:

$$\begin{eqnarray*}\begin{array}{r}\begin{array}{rcl}4({{\rm{C}}{\rm{H}}}_{4}+h\nu & \to & {{\rm{C}}{\rm{H}}}_{3}+{\rm{H}}),\\ 2({{\rm{C}}}_{2}{{\rm{H}}}_{2}+{\rm{H}}+{\rm{M}} & \to & {{\rm{C}}}_{2}{{\rm{H}}}_{3}+{\rm{M}}),\\ 2{{\rm{C}}}_{2}{{\rm{H}}}_{3} & \to & {{\rm{C}}}_{2}{{\rm{H}}}_{2}+{{\rm{C}}}_{2}{{\rm{H}}}_{4},\\ 2({{\rm{C}}}_{2}{{\rm{H}}}_{4}+{\rm{H}}+{\rm{M}} & \to & {{\rm{C}}}_{2}{{\rm{H}}}_{5}+{\rm{M}}),\\ 2{{\rm{C}}}_{2}{{\rm{H}}}_{5} & \to & {{\rm{C}}}_{2}{{\rm{H}}}_{4}+{{\rm{C}}}_{2}{{\rm{H}}}_{6},\\ 2(2{{\rm{C}}{\rm{H}}}_{3}+{\rm{M}} & \to & {{\rm{C}}}_{2}{{\rm{H}}}_{6}+{\rm{M}}),\\ ----- & - & ----\\ {{\rm{C}}}_{2}{{\rm{H}}}_{2}+4{{\rm{C}}{\rm{H}}}_{4}+4h\nu & \to & 3{{\rm{C}}}_{2}{{\rm{H}}}_{6}.\end{array}\end{array}\end{eqnarray*}$$

The ethane is also relatively stable, but is photodissociated, and the methyl radicals can either react to reform ethane, can react with hydrogen to reform methane, or can go on to participate in the haze chemistry.

Alternatively, acetylene can be stepwise hydrated (attacked by a hydroxyl radical and then hydrogenated) to form acetone. This latter series of reactions is not efficient enough to produce observable quantities of acetone. Both of these pathways are shown in Figure 11.

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The pathway for forming diazomethane is straightforward:

$$\begin{eqnarray}&&{\mathrm{CH}}_{4}+h\nu \to {}^{1}{\mathrm{CH}}_{2}+{{\rm{H}}}_{2},\end{eqnarray} \tag{ 20 }$$

$$\begin{eqnarray}&&{}^{1}{\mathrm{CH}}_{2}+{{\rm{N}}}_{2}+{\rm{M}}\to \,{\mathrm{CH}}_{2}{{\rm{N}}}_{2}+{\rm{M}},\end{eqnarray} \tag{ 21 }$$

$$\begin{eqnarray}&&{}^{1}{\mathrm{CH}}_{2}+{\rm{M}}\to {}^{3}{\mathrm{CH}}_{2}+{\rm{M}},\end{eqnarray} \tag{ 22 }$$

$$\begin{eqnarray}&&{}^{3}{\mathrm{CH}}_{2}+{{\rm{N}}}_{2}+{\rm{M}}\to {\mathrm{CH}}_{3}{{\rm{N}}}_{2}+{\rm{M}},\end{eqnarray} \tag{ 23 }$$

where M is any third body. The pathway for producing ${\mathrm{CH}}_{3}{{\rm{N}}}_{2}$ from triplet methylene is given by Xu & Lin (2010), and the pathway from singlet methylene by Braun et al. (1970). We use the rate constants given by these papers, replacing the reverse reactions in STAND2015 (Rimmer & Helling 2016).

Rocky exoplanets may have a wide range of bulk atmospheric compositions, and it is important to explore how our results are expected to change for a range of atmospheres. Here we use chemical equilibrium as our guide. Although impact-generated chemistry does not reproduce equilibrium at any temperature, the results presented here and in Ferus et al. (2017) indicate that trends in the experimental results follow trends in chemical equilibrium at temperatures ∼2000–5000 K. These trends allow us to explore predicted results over a range of compositions that are prohibitively broad in terms of experimental time and cost. This is also an important exercise for contextualizing our experimental results within a hypothetical exoplanet atmosphere, which is much more rich in ${{\rm{N}}}_{2}$.

We solve for chemical equilibrium at an atmospheric surface pressure of 1 bar at 300 K and equilibrium temperatures of 2000 K (6.67 bar) and 5000 K (16.7 bar), varying the amount of CO, ${\mathrm{CH}}_{4}$, ${{\rm{N}}}_{2}$, and ${\mathrm{CO}}_{2}$, and express our results in terms of three different ratios:

• 1.  
  ${{\rm{N}}}_{2}/(\mathrm{CO}+{\mathrm{CH}}_{4})$, where ${\mathrm{CO}}_{2}=0$, $\mathrm{CO}={\mathrm{CH}}_{4}$, and the ${{\rm{N}}}_{2}$ mixing ratio is varied from 0 to 0.95.
• 2.  
  $\mathrm{CO}/{\mathrm{CH}}_{4}$, where the ${{\rm{N}}}_{2}$ mixing ratio is fixed at 0.333, ${\mathrm{CO}}_{2}=0$, and CO and ${\mathrm{CH}}_{4}$ mixing ratios are varied between 0 and 0.667.
• 3.  
  ${\rm{C}}/{\rm{O}}$, where the ${{\rm{N}}}_{2}$ mixing ratio is fixed at 0.333, $\mathrm{CO}={\mathrm{CH}}_{4}$, and the ${\mathrm{CO}}_{2}$ mixing ratio is varied from 0 to 0.667.

The results of these calculations are plotted in Figure 12. The results are not predicted to be very sensitive to changes in ${{\rm{N}}}_{2}$/(CO + ${\mathrm{CH}}_{4}$) and CO/${\mathrm{CH}}_{4}$. The changes in abundance are within an order of magnitude for both species over a wide range of values, including the values selected for our hypothetical exoplanet. The C/O ratio, however, makes a big difference in the predicted results. We predict potentially observable quantities of acetylene (${{\rm{C}}}_{2}{{\rm{H}}}_{2}$) down to somewhere between ${\rm{C}}/{\rm{O}}\sim 1.1-1.5$. Below ${\rm{C}}/{\rm{O}}\sim 1.1$, ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ abundances drop off by several orders of magnitude.

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Hydrogen cyanide is a necessary feedstock molecule for photochemical reaction pathways leading to the selective high-yield synthesis of pyrimidine nucleosides, amino acids and lipid precursors (Ritson & Sutherland 2012; Patel et al. 2015). High rates of impacts provide a challenge for this synthetic pathway, due to the thick hazes that will result, which risk obscuring the 200–280 nm light needed for this chemistry. It has not been determined how effective these hazes will be in shielding the surface from UV light. Some prebiotic chemistry has been shown to occur within the haze particles themselves (Hörst et al. 2012). Additionally, HCN can be stored on the surface in the form of ferrous cyanide and other organometallic complexes, to be liberated by liquid water once the haze clears, after which the HCN photochemistry can proceed unimpeded (Ritson et al. 2018). Finally, the HCN produced, whether in its original form, as a salt, or as ferrous cyanide, can be subducted and would later be outgassed from vents again as HCN and other products, after the haze has cleared (Rimmer & Shorttle 2019).

The generation of ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$, HCN, and other products takes place in an extremely methane-rich atmosphere, and it is an open question about how this amount of methane could be sustained through an era of high impacts. Experiments suggest that the methane is destroyed by impacts, although not efficiently enough to significantly change its surface abundance. Coupled with UV light, energetic particles, and subsequent loss through formation of haze particles and escape of ${{\rm{H}}}_{2}$, it seems that a significant amount of methane must be outgassed at this time to restore that which was lost. Investigations into the redox state of the Hadean crust (Yang et al. 2014), and observations of Titan (see Table 2) and preliminary spectra from 55 Cnc e (Tsiaras et al. 2016), suggests this possibility can be realized both on the early Earth and now on other moons and planets.

Comparing spectra with and without impact shows that photochemistry alone is not sufficient to produce detectable quantities of ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$, as is apparent from Figure 6. This does not mean the presence of ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ is an unambiguous indicator of impacts. There are local scenarios where ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ could be outgassed in large quantities from extremely reducing volcanic plumes, similar to those of mud volcanoes on Earth (Rimmer & Shorttle 2019). If a planet's magmatic and crustal chemistry were very different from Earth's, it may be that these local volcanic plumes would be ubiquitous, in which case ${{\rm{C}}}_{2}{{\rm{H}}}_{2}$ could be one of the dominant atmospheric species. Acetylene, therefore, is a reliable impact signature only when the planet–star system is taken in context.