Origin-of-life Molecules in the Atmosphere after Big Impacts on the Early Earth

Within days, a massive asteroid impact would leave the Hadean Earth with a global ∼2000 K rock and iron vapor atmosphere, the iron derived from the impactor’s core (Itcovitz et al. 2022). In the following months to years, energy radiated downward from the silicates would vaporize a large fraction of the ocean, adding steam to the atmosphere (Sleep et al. 1989). At this point, the steam should rapidly react with iron to generate H₂. Eventually, the iron vapor and then rock would rain out, leaving behind a steam-dominated atmosphere containing H₂, as well as CO₂ and N₂ from the preimpact atmosphere. The sequence of metal followed by silicate condensation with falling temperature is loosely analogous to the well-known condensation sequence of the solar nebula.

Furthermore, the massive impact would generate a melt pool on Earth’s surface inside the impact crater, which may contain reducing impact-derived iron. The atmosphere and melt pool could react to a redox-equilibrium state. This could add or sequester H₂ from the atmosphere, depending on whether the melt was more or less reducing than the atmosphere (Itcovitz et al. 2022).

Recently, Itcovitz et al. (2022) used a smoothed particle hydrodynamics (SPH) code with 0.5 × 10⁶–3 × 10⁶ particles of 150–250 km diameter to estimate the amount of H₂ generated as these processes unfold under several different impact scenarios on the Hadean Earth. In their fiducial case (i.e., their model 1A), they assumed that 100% of the iron delivered by an impactor is available to react and reduce a postimpact steam atmosphere. In another scenario, they assumed that only ∼15%–30% of the impactor iron reacts with the steam atmosphere based on their SPH simulations (their model 1B; Citron & Stewart 2022). For both cases, they also considered equilibration between the atmosphere and a melt pool (their models 2, 3A, and 3B). In their simulations, the melt pool is extremely reducing or more oxidizing, depending on whether they assumed that it contains a fraction of the impactor’s iron, and they used SPH models to predict the amount of iron accreted to the melt pool (Citron & Stewart 2022). Overall, they concluded that melt–atmosphere equilibration generates about as much H₂ as their fiducial case as long as the iron delivered to the melt–atmosphere system can equilibrate. However, if iron delivered to the melt pool sinks into Earth and cannot react with the atmosphere, then approximately 2–10 times less H₂ is produced compared to their fiducial scenario (see the erratum in Itcovitz et al. 2022).

Itcovitz et al. (2022) considered impactors between 2 × 10²¹ and 2 × 10²² kg and assumed that the preimpact Earth has 1.85 oceans of water, 100 bars of CO₂, and 2 bars of N₂. However, we investigate impacts as small as 10²⁰ kg, and our nominal model (Table 2) assumes only 0.5 bar of preimpact CO₂ motivated by models of the Hadean carbonate-silicate cycle (Kadoya et al. 2020) and assuming that little mantle-hosted carbonate is vaporized. Therefore, we use a similar model (Appendix A) to the one described in Itcovitz et al. (2022) to predict the postimpact H₂ for our alternative model assumptions (Table 2) and impactor sizes. Figure 2 shows the results.

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Table 2. Nominal Model Assumptions

Parameter	Symbol	Value
Preimpact ocean inventory	${N}_{{{\rm{H}}}_{2}{\rm{O}}}$	1.5 × 104 mol cm−2 (i.e., 1 ocean) a
Preimpact CO2 inventory	${N}_{{\mathrm{CO}}_{2}}$	12.5 mol cm−2 (i.e., 0.5 bar) b
Preimpact N2 inventory	${N}_{{{\rm{N}}}_{2}}$	36 mol cm−2 (i.e., 1 bar) c
Impactor mass	Mimp	1020–1022 kg
Iron mass fraction of the impactor	mFe,imp	0.33
Fraction of iron that reacts with atmosphere	XFe,atmos	1.0 d
Impact angle	⋯	45°
Impact velocity relative to Earth	⋯	20.7 km s−1
Eddy diffusion coefficient e	Kzz	106 cm2 s−1
Aerosol particle radius e	⋯	0.1 μm
Troposphere relative humidity	ϕ	1
Surface albedo	As	0.2
Temperature of the stratosphere	Tstrat	200 K
Rainfall rate	Rrain	1.1 × 1017 molecules cm−2 s−1 (modern Earth’s value)
HCN deposition velocity f	${v}_{\mathrm{dep},\mathrm{HCN}}$	7 × 10−3 cm s−1
HCCCN deposition velocity g	${v}_{\mathrm{dep},\mathrm{HCCCN}}$	7 × 10−3 cm s−1

Notes.

^a The source and inventory of surface H₂O throughout the Hadean is debated (Johnson & Wing 2020; Korenaga 2021; Miyazaki & Korenaga 2022), as is how much water is present on the modern Earth (e.g., Lécuyer et al. 1998 estimated 0.3–3 oceans in Earth’s mantle). Our nominal case of one modern ocean is one possibility among several. ^b Based on Hadean carbon cycle modeling in Kadoya et al. (2020). ^c Based on Figure 5 in Catling & Zahnle (2020). ^d This is the model 1A scenario for H₂ production described near the end of Section 3.1 and in Figure 2. ^e Assumed to be constant as a function of altitude. ^f Estimated based on the HCN hydrolysis rate in the ocean (Appendix C.4). ^g Assumed to be the same as HCN.

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Our calculations give two end-member scenarios for impact H₂ production, which we consider for subsequent calculations in this paper. The more optimistic case assumes that 100% of the impactor’s iron reacts with an atmosphere that is chemically isolated from a melt pool (model 1A in Figure 2). Following Zahnle et al. (2020), we adopt this scenario as our nominal model throughout the main text. This assumption produces a similar amount of H₂ as an atmosphere–melt system that retains most of the impactor’s iron (e.g., model 2 in Figure 2), which is consistent with Itcovitz et al. (2022). The model 2 calculation assumes that the melt pool has an initial oxygen fugacity of ΔFMQ-2.3, which is appropriate for a peridotite melt (Itcovitz et al. 2022). ⁵ However, our results are not sensitive to this assumption because, for model 2, initial melt oxygen fugacities between ΔFMQ and ΔFMQ-4 change the generated H₂ by a factor of at most ∼1.3.

The less optimistic case for H₂ production is model 1B in Figure 2, which assumes that only a fraction of the impactor iron reacts with an atmosphere (∼15%–30%) and that the latter does not react with a melt pool. We compute the fraction of available iron by extrapolating SPH simulations of impacts traveling at twice Earth’s escape velocity and colliding with Earth at a 45° angle (Appendix Figure A1), which is the most probable angle (Citron & Stewart 2022). Most simulations shown in the main text have a complementary figure in the Appendix that makes this alternative pessimistic assumption regarding postimpact H₂ generation.

After reactions between impact-derived iron and steam produce H₂, the atmosphere would radiate at a rate determined by the optical properties of water vapor (Zahnle et al. 2020). Chemical reactions would initially be rapid, forcing the whole atmosphere to chemical equilibrium. Methane is thermodynamically preferred at lower temperatures (e.g., more methane is preferred in a gas at 1000 K than a gas at 1500 K), so it should become more abundant as the atmosphere cools. Eventually, the atmosphere would reach a temperature where the reactions producing methane would be extremely sluggish compared to the rate of atmospheric cooling. At this point, the methane abundance would freeze, or quench. Ammonia would exhibit the same behavior as methane by initially rising in abundance and then quenching when the kinetics become slow. After several thousand years, water vapor condenses and rains out of the atmosphere to form an ocean.

We use the 0D kinetics-climate box model described in Appendix B to simulate these events. By simulating each elementary chemical reaction, the model automatically computes methane and ammonia quenching as the atmosphere cools and temperature-dependent reactions slow. We first consider gas-phase kinetics; later, we will also consider nickel-surface kinetics.

Figure 3 shows our model applied to a 1.58 × 10²¹ kg (∼900 km diameter) impactor. As the steam cools, ammonia quenches when the atmosphere is ∼1200 K, followed by CH₄ quenching at ∼950 K. After quenching, nearly half of the total carbon in the atmosphere exists as CH₄. After 4200 yr, the steam has largely rained out to form an ocean, leaving behind a H₂-dominated atmosphere containing CH₄ and NH₃. The NH₃ is soluble in water, so a fraction should be removed from the atmosphere by dissolution in the newly formed ocean; however, our simulations (e.g., Figure 3) do not account for this effect.

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Figure 4 shows the predicted atmospheric composition at the end of the steam atmosphere (e.g., at 4200 yr in Figure 3) as a function of impactor mass. The calculations use gas-phase reactions and our nominal model parameters (Table 2), including the assumption that 100% of the iron delivered by the impactor reacts with the steam atmosphere to make H₂. For example, a 10²⁰ kg impactor generates 1.2 × 10² H₂ moles cm⁻², which would have a partial pressure of 1.2 bars if the atmosphere did not contain water vapor. A 10²² kg impactor generates 1.1 × 10⁴ H₂ moles cm⁻², which would have a “dry” partial pressure of 23.8 bars. ⁶ We find that most of the CO₂ in the atmosphere is converted to CH₄ for impactors larger than 1.6 × 10²¹ kg (∼900 km diameter), and that bigger impacts generate more NH₃; e.g., a 10²² kg impactor makes 0.013 “dry” bars of NH₃. Reduced species like CH₄ and NH₃ are thermodynamically preferred in the thick H₂ atmospheres generated by bigger impacts. Large impacts generate large amounts of hydrogen because they deliver more iron, which more thoroughly reduces the atmosphere.

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The Figure 4 calculations might underestimate the CH₄ produced in the postimpact atmosphere because they ignore reactions occurring on nickel surfaces that can catalyze CH₄ generation. If the impactors that struck the Earth during the Hadean resembled enstatite chondrite or carbonaceous chondrite composition, they would have contained 1%–2% nickel (Lewis 1992, Table 15). This nickel would have coexisted with the rock and iron vapor atmosphere that lasted months to years following a massive impact (phase 1 in Figure 1). Metals, along with silicates, would have rained out as spherules covering the entire planet (Genda et al. 2017). As the impact-generated steam cooled, chemical reactions catalyzing CH₄ production could have occurred on nickel surfaces in the bed of spherules (Schmider et al. 2021). These surface reactions could lower the quench temperature of CH₄, causing more of the gas to be produced.

To estimate the effect of nickel catalysis on CH₄ production, we use our kinetics-climate box model (Appendix B) with the nickel-surface reaction network developed by Schmider et al. (2021). The network is based on quantum chemistry calculations and about a dozen experiments from the literature. Our microkinetics approach is distinct from the empirical one taken by, e.g., Kress & McKay (2004) because our model tries to capture each elementary step of catalysis, rather than use a parameterization that is specific to certain experimental conditions.

Figure 5 shows the quenched methane abundance as a function of impactor mass predicted by our model that includes nickel catalysts. The amount of CH₄ generated depends strongly on the amount of available nickel surface area. Nickel areas bigger than 0.1 cm² nickel cm⁻² Earth permit more CH₄ production compared to our gas phase–only model. Assuming a nickel area of 1000 cm² nickel cm⁻² Earth, a Vesta-sized impactor (2.6 × 10²⁰ kg, 500 km diameter) could convert most CO₂ in the preimpact atmosphere to CH₄.

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Unfortunately, a precise nickel surface area is hard to estimate. The correct value depends on how the rock, iron, and nickel spherules mix and precipitate to the surface and, furthermore, how effectively the atmosphere can diffuse through and react on exposed nickel. We do not attempt to compute these effects here and instead estimate possible upper bounds. Consider a 2.6 × 10²⁰ kg impactor (Vesta-sized) of enstatite chondrite composition containing 2% by mass Ni (Lewis 1992). If all of this nickel is gathered into 1 mm spheres, a plausible droplet size according to Genda et al. (2017), then the total nickel surface area is 3.4 × 10³ cm² nickel cm⁻² Earth. An impactor 10 times more massive would deliver 10 times more nickel, resulting in an upper bound Ni area that is 1 order of magnitude larger. Significantly smaller nickel particles are conceivable. There is experimental support for the formation of ultrafine <300 nm particles in the wake of impacts colliding with an ocean (Furukawa et al. 2007). For a Vesta-sized impactor, collecting all nickel into 100 nm particles has a nickel area 6 orders of magnitude larger than the 1 mm case: 3.4 × 10⁹ cm² nickel cm⁻² Earth. Overall, the larger nickel areas shown in Figure 5 may be within the realm of possibility. Alternatively, nickel might be buried by rock and iron when these materials condense out of the postimpact atmosphere, and the <0.1 cm² nickel cm⁻² Earth is available for catalysis. In this case, gas-phase kinetics would determine the conversion of CO₂ to CH₄.

Figures 4 and 5 optimistically assume that all iron delivered by the impactor reacts with steam to make H₂; however, this may not be the case (see Section 3.1). Therefore, in Appendix Figures A2 and A3, we recalculate Figures 4 and 5 but assume that only a fraction of the impactor’s iron reduces the steam atmosphere by extrapolating SPH simulations of impacts (model 1B in Figure 2). The resulting H₂, CH₄, and NH₃ production appears similar but shifted by a factor of ∼5 to larger impactors. The results are shifted by this amount because SPH simulations suggest that approximately one-fifth of the impactor iron is delivered to the atmosphere, while the rest is either embedded in Earth or ejected to space. We consider these supplementary calculations lower bounds for impactor-generated CH₄ and NH₃.

Several thousand years after a massive impact, the steam-dominated atmosphere would condense to an ocean, leaving behind a H₂-dominated atmosphere containing CH₄ and NH₃ (e.g., at 4200 yr in Figure 3). The reducing atmospheric state should persist for millions of years until the hydrogen escapes (Zahnle et al. 2020).

We simulate the long-term evolution of this hydrogen-rich atmosphere using a coupled 1D photochemical-climate model (Appendix C). Figure 6 shows our model applied to the atmosphere following a 1.58 × 10²¹ kg (∼900 km diameter) impactor. We assume a preimpact atmosphere with 1 bar of N₂ and 0.5 bar of CO₂ and simulate the cooling steam atmosphere with our kinetics-climate model (Section 3.2). Next, we use the end of the steam atmosphere simulation as initial conditions for our 1D photochemical-climate model.

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We find that N₂ and CH₄ photochemistry generates HCN in a hazy Titan-like atmosphere for about 1 million yr until it is halted by hydrogen escape to space. In this model, the dominant channel producing HCN is N + ³CH₂ $\to$ HCN + H, where ³CH₂ is the ground (triplet) state of the methylene radical derived from methane photolysis. There are two other important paths. The first is ${\rm{N}}+\mathrm{CH}\to \mathrm{CN}+{\rm{H}}$ followed by ${{\rm{H}}}_{2}+\mathrm{CN}\to \mathrm{HCN}+{\rm{H}}$, and the second is ${\rm{N}}+{\mathrm{CH}}_{3}\to {\rm{H}}+{{\rm{H}}}_{2}\mathrm{CN}$ and ${{\rm{H}}}_{2}\mathrm{CN}+{\rm{H}}\to \mathrm{HCN}+{{\rm{H}}}_{2}$. In all pathways, hydrocarbon radicals (e.g., ³CH₂ and CH₃) are sourced from photolyzed CH₄, and atomic N is derived from photolyzed N₂, which both occur at high altitudes (p < 10⁻⁵ bars; Appendix Figure A5). The largest chemical loss of HCN is photolysis followed by ${\rm{N}}+\mathrm{CN}\to {{\rm{N}}}_{2}+{\rm{C}}$. Other significant losses are paths that form HCCCN haze aerosols. The HCN production and loss in our model is comparable to pathways discussed in similar studies (Zahnle 1986; Tian et al. 2011; Rimmer & Rugheimer 2019). We determined the chemical paths most important for producing and destroying HCN by studying column-integrated reaction rates at 14,200 yr in Figure 6.

In Figure 6, HCN mixes to the surface and rains out in droplets of water at a rate of ∼10⁷ molecules cm⁻² s⁻¹. It also dissolves into the ocean at a similar rate, where we assume it is eventually destroyed by hydrolysis (not shown in Figure 6). To emulate HCN dissolution and destruction in the ocean, we assume a 7 × 10⁻³ cm s⁻¹ deposition velocity justified in Appendix C.4. Additionally, a relatively small amount of HCN polymerizes to haze particles in our model via ${{\rm{H}}}_{2}\mathrm{CN}+\mathrm{HCN}\to \mathrm{polymer}$ following Lavvas et al. (2008a), which falls and rains out in water droplets to the surface.

Our results differ from the simulations of Zahnle et al. (2020), which suggested that the duration of HCN production after an impact was limited by the rapid photolysis of methane. The Figure 6 simulation finds that the CH₄ lifetime is 4.8 million yr because, following photolysis, CH₄ efficiently recombines in a hydrogen-rich atmosphere from the following reaction, which is well known in the atmospheres of the giant planets in our solar system (Appendix Figure A4):

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

Zahnle et al. (2020) did not account for Reaction (3). The lifetime of cyanide production is therefore instead determined by the timescale of hydrogen escape to space. Significant hydrogen escape permits the destruction of most atmospheric CH₄ because Reaction (3) becomes inefficient, which in turn ceases CH₄-driven HCN production.

In Figure 6, HCCCN is primarily destroyed by photolysis and produced by the following reaction from acetylene and the cyanide radical:

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

A fraction of the produced HCCCN reacts to form aerosols via ${{\rm{C}}}_{4}{\rm{H}}+\mathrm{HCCCN}\to \mathrm{polymer}$ following Lavvas et al. (2008a). These polymers fall and mix toward the surface, where they rain out in droplets of water at a rate of ∼10⁸ molecules cm⁻² s⁻¹. Most gas-phase HCCCN is either destroyed by photolysis or incorporated into aerosols, causing vanishingly small surface HCCCN gas pressures (<10⁻¹⁶ bars).

Our model approximates haze formation with the following three reactions: C₂H + C₄H₂ → polymer + H, ${{\rm{H}}}_{2}\mathrm{CN}+\mathrm{HCN}\to \mathrm{polymer}$, and ${{\rm{C}}}_{4}{\rm{H}}+\mathrm{HCCCN}\to \mathrm{polymer}$. At 14,200 yr in Figure 6, the first pathway dominates, forming ∼1.8 × 10¹³ g haze yr⁻¹. At this same point in time, the second and third pathways produce 9 × 10⁷ and 2.8 × 10¹² g yr⁻¹, respectively. The total haze production rate (2.1 × 10¹³ g yr⁻¹) is comparable to the values estimated by Trainer et al. (2006) for the early Earth based on laboratory experiments. Haze particles fall and rain out to the surface, where they can hydrolyze and participate in prebiotic chemistry (Neish et al. 2010; Poch et al. 2012).

In Figure 6, impact-generated ammonia persists for nearly 10⁵ yr. The NH₃ is primarily destroyed by photolysis but then recombines from reactions with hydrogen:

$$\begin{eqnarray}&&\mathrm{NH}+{{\rm{H}}}_{2}+{\rm{M}}\to {\mathrm{NH}}_{3}+{\rm{M}},\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{\mathrm{NH}}_{2}+{\rm{H}}+{\rm{M}}\to {\mathrm{NH}}_{3}+{\rm{M}}.\end{eqnarray} \tag{ 6 }$$

Reactions (5) and (6) are relatively efficient in a hydrogen-rich atmosphere. Ammonia photolysis primarily occurs at the 10⁻³ bar altitude, while haze is largely produced above the 10⁻⁵ bar altitude. Therefore, haze particles partially shield ammonia from photolysis, extending the NH₃ lifetime (Sagan & Chyba 1997). Our model assumes that the haze particles are perfect spheres with optical properties governed by Mie theory. Observations of Titan’s haze have revealed that hydrocarbon haze particles have a fractal structure that absorbs and scatters UV more effectively than Mie spheres (Wolf & Toon 2010). Therefore, our model likely overestimates NH₃ photolysis in postimpact atmospheres.

Figure 6 assumes that all NH₃ is in the atmosphere and that it does not rain out, but the gas is highly soluble in water and should dissolve in the ocean, where it hydrolyzes to ammonium, ${\mathrm{NH}}_{4}^{+}$. In Section 4.4.2, we show that for an atmosphere with 0.3 mol cm⁻² NH₃ and a 371 K ocean at pH = 7, 4% of the NH₃ would persist in the atmosphere, while the rest would be dissolved in the ocean. For a hotter 505 K atmosphere with 6.8 mol cm⁻² NH₃, only 20% of the ammonia dissolves in the ocean because solubility decreases with increasing temperature (Section 4.4.2). Ammonia dissolution in the ocean would protect it from photolysis, perhaps lengthening the lifetime of ammonia in the atmosphere–ocean system. Overall, since our photochemical-climate model neglects NH₃ ocean dissolution and likely overestimates NH₃ photolysis, we probably underestimate the lifetime of NH₃ in Figure 6.

While HCN and HCCCN are produced in Figure 6, the surface temperature would be ∼390 K, primarily caused by H₂–H₂ collision-induced absorption (CIA), which has a significant greenhouse effect in thick H₂ atmospheres like this one of 8.5 bars total pressure. The atmosphere cools to ∼300 K after the H₂ escapes to space.

Figure 7 applies our model to various impactor masses. The results show the Hadean atmosphere 10,000 yr after the postimpact-generated steam atmosphere has condensed to an ocean. We choose 10,000 yr after ocean condensation because this is adequate time for the atmosphere to reach a quasi-photochemical steady state that does not change significantly until the hydrogen escapes (e.g., Figure 6). Figures 7(d) and (e) show a sharp increase in the HCN and HCCCN production for impactors larger than 10²¹ kg (∼780 km). Such large impacts generate CH₄/CO₂ > 0.1 (Figure 4), which makes a thick Titan-like haze (Trainer et al. 2006). Haze shielding causes CH₄ photolysis to be higher in the atmosphere and closer to N₂ photolysis; therefore, the photolysis products of both species can more efficiently combine to make cyanides (Appendix Figure A5). Additionally, HCCCN production requires acetylene (Reaction (4)), which is a haze precursor that accumulates when CH₄/CO₂ > 0.1. These Titan-like atmospheres have ∼10⁻⁹ bar surface HCN and HCN ocean deposition and rainout rates between 10⁷ and 10⁹ HCN molecules cm⁻² s⁻¹ persisting on hydrogen escape timescales (>1 million yr). The HCCCN is incorporated into aerosols before raining out to the surface at a rate of up to 10⁹ HCCCN molecules cm⁻² s⁻¹.

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In addition to photochemistry, lightning should also generate HCN (Chameides & Walker 1981; Stribling & Miller 1987). Appendix Figure A8 shows HCN production from lightning for the same time period as the Figure 7 simulation using the methods described in Chameides & Walker (1981). Assuming the same lightning dissipation rate as modern Earth’s, we find that lightning produces up to ∼10⁴ HCN molecules cm⁻² s⁻¹. This value is small compared to the 10⁷–10⁹ HCN molecules cm⁻² s⁻¹ produced from photochemistry after >10²¹ kg impacts.

Larger impacts generate a thicker H₂ atmosphere, which makes the atmosphere warmer (Figure 7(c)). For impactors of >10²¹ kg, which generate substantial HCN and HCCCN, the surface temperature is >380 K. Figure 7(f) shows that impactors that produce substantial haze shield the surface from <250 nm photons, which means that prebiotic schemes that require high-energy UV light (e.g., Patel et al. 2015) would need to rely on stockpiling of the nitriles for later use.

The Hadean Earth CO₂ concentration is uncertain. Models of the Hadean geologic carbon cycle argue for CO₂ levels between ∼10⁻⁵ and 1 bar at 4 Ga with a median value of ∼0.5 bar and a 95% uncertainty spanning 10⁻⁵ to 1 bar (Kadoya et al. 2020). However, these values might be unrealistically small because a large impact would warm surface rocks, possibly causing carbonates to degas, thereby increasing the atmospheric CO₂ reservoir. Up to ∼80 bars of CO₂ may potentially be liberated from surface carbonates (Krissansen-Totton et al. 2021).

Figure 8 explores the effect of different preimpact CO₂ abundances on HCN and HCCCN production in postimpact atmospheres. The simulations are snapshots of the atmosphere 10,000 yr after the impact-vaporized steam has condensed to an ocean. Larger preimpact CO₂ causes larger HCN and HCCCN production because it allows more CH₄ to form in the cooling steam atmosphere. As discussed previously, CH₄ is closely tied to photochemical cyanide generation. Regardless of the preimpact CO₂ concentrations, HCN and HCCCN production sharply increases for impactors larger than ∼10²¹ kg due to more efficient haze production (Figure 7, and corresponding text).

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Figure 9 shows the state of the atmosphere after impacts of various size assuming that 10 cm² nickel cm⁻² Earth is present in the steam atmosphere to catalyze methane production. The nickel causes more efficient conversion of CO₂ to CH₄ compared to the gas phase–only scenario (Figure 7), permitting greater production of HCN and HCCCN for smaller impactors. For example, a 5 × 10²⁰ kg (∼610 km) impactor that accounts for nickel catalysts (Figure 9) has comparable HCN and HCCCN production to a 1.6 × 10²¹ kg (∼900 km diameter) impactor if no nickel catalysts are assumed in the cooling steam atmosphere (Figure 7).

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A critical assumption in this section is that 100% of the iron delivered by impactors reacts with steam to generate H₂. As discussed in Section 3.1, it is possible that the postimpact atmosphere is less thoroughly reduced by impactor iron. Appendix Figures A6 and A7 recalculate main text Figures 7 and 9, assuming that a fraction (approximately 15%–30%) of the impactor iron reduces the steam atmosphere based on SPH simulations (model 1B in Figure 2). This alternative assumption requires that impactors ∼five times more massive are required to generate a haze-rich postimpact atmosphere with copious HCN and HCCCN production. For example, in Figure 7, recall that there is a sharp increase in cyanide production for impactors larger than 10²¹ kg (∼780 km). Appendix Figure A6, which instead assumes that a fraction of iron reduces the steam atmosphere, finds that the sharp increase in cyanide production occurs for impacts larger than 5 × 10²¹ kg (∼1330 km). However, the presence of nickel catalysts may permit large prebiotic nitrile production for smaller impactors, even under pessimistic postimpact H₂ generation (Appendix Figure A7).

Recently, Zahnle et al. (2020) performed calculations of postimpact atmospheres using simpler models than the ones used in this paper. Our results differ in several important ways. First, we find that our purely gas-phase model of the postimpact steam atmosphere (Section 3.2) predicts less CH₄ generation than the model used in Zahnle et al. (2020). For example, Figure 4 predicts that most CO₂ is converted to CH₄ for impactors larger than 1.6 × 10²¹ kg. Figure 2 (top panel) in Zahnle et al. (2020), which is a comparable scenario, suggests that a 5 × 10²⁰ kg impactor is required to convert most of the atmospheric CO₂ to CH₄. The difference is likely caused by different approaches to computing CH₄ quenching, or freeze-out, as the atmosphere cools. Our kinetics-climate model automatically computes CH₄ quenching by tracking the elementary reactions producing and destroying CH₄ along with many other atmospheric species. In most of our simulations of cooling postimpact atmospheres, CH₄ quenches when the temperature is between 900 and 1000 K. Zahnle et al. (2020) instead used equilibrium chemistry modeling with a parameterization for CH₄ quenching derived from kinetics calculations of H₂-dominated brown dwarf atmospheres (Zahnle & Marley 2014). This parameterization predicts ∼800 K CH₄ quenching temperatures. The different quenching temperatures between our model and the Zahnle et al. (2020) model suggest that the Zahnle et al. (2020) kinetics parameterization is likely not suitable for a cooling steam-rich atmosphere.

The new photochemical model predicts longer postimpact CH₄ lifetimes than the Zahnle et al. (2020) model. As mentioned previously, Zahnle et al. (2020) included CH₄ photolysis but neglected Reaction (3), which efficiently recombines photolysis products in hydrogen-rich atmospheres. In our model, these recombination reactions allow CH₄ to persist in most postimpact atmospheres until hydrogen escapes to space (∼millions of years). Zahnle et al. (2020) instead found that CH₄ is eradicated from the atmosphere before hydrogen escape.

Finally, nitrile production and rainout in our new model depend strongly on the presence of haze and the CH₄/CO₂ ratio, which was not the case in Zahnle et al. (2020). Our model finds that up to ∼10⁹ molecules cm⁻² s⁻¹ of HCN and HCCCN is rained out in hazy postimpact atmospheres with CH₄/CO₂ > 0.1 (Figure 7). When CH₄/CO₂ < 0.1, there is little haze, and HCN production is ∼<10⁵ molecules cm⁻² s⁻¹, and HCCCN production is negligible. Haze causes CH₄ and N₂ photolysis products to be close in altitude so that they efficiently react to make cyanides (Appendix Figure A5). Additionally, HCCCN generation requires C₂H₂ in our model (Reaction (4)), which is only abundant in hazy atmospheres. In contrast, Zahnle et al. (2020) found that the cyanide production rate in postimpact atmospheres is 10⁸–10¹⁰ molecules cm⁻² s⁻¹ regardless of the presence of haze and the CH₄/CO₂ ratio. Our results differ largely because our model is 1D (has vertical transport), while the Zahnle et al. (2020) model is a 0D box model. The HCN production depends on the proximity of CH₄ and N₂ photolysis, but a box model cannot account for this 1D effect. Furthermore, Zahnle et al. (2020) did not distinguish between different prebiotic nitriles (e.g., HCN and HCCCN) or determine their surface concentrations and rainout rates. Also, Zahnle et al. (2020) did not have a coupled climate model.

Cometary and lightning sources of HCN are relatively small compared to our estimated photochemical production rates in haze-rich postimpact atmospheres. Todd & Öberg (2020) calculated that comets could deliver ∼1.8 × 10⁵ HCN molecules cm⁻² s⁻¹ to the Hadean Earth, a value ∼4 orders of magnitude smaller than HCN from photochemistry in our most optimistic models. As discussed in Section 3.3, we find the HCN production from lightning in postimpact atmospheres to be at most ∼10⁴ HCN molecules cm⁻² s⁻¹, which is also small compared to UV photochemistry in a CH₄-rich atmosphere. This result agrees with Pearce et al. (2022), who also found that lightning-produced HCN is relatively insignificant.

Rimmer & Shorttle (2019) suggested that localized ultrareducing magma rich in carbon and nitrogen might outgas HCN and HCCCN. They imagined this gas interacting with subsurface water, causing high concentrations of dissolved prebiotic molecules and therefore a setting for origin-of-life chemistry. While this idea may have merit, their calculations do not account for graphite saturation in magma, which may inhibit outgassing of reduced carbon-bearing species like HCN (Hirschmann & Withers 2008; Wogan et al. 2020; Thompson et al. 2022). Additionally, Rimmer & Shorttle (2019) did not self-consistently account for the solubility of gases in magma, which has been been hypothesized to prevent the outgassing of H-bearing gases like CH₄ or HCN (Wogan et al. 2020). Therefore, we argue that a hypothesized volcanic source of HCN and HCCCN requires further modeling and experiments before it can be compared to a photochemical source but, in general, seems challenging.

Cerrillo (2022) recently used a climate model to predict the surface temperature of postimpact atmospheres with compositions predicted by Zahnle et al. (2020). They found surface temperatures of >600 K in some cases. However, the Cerrillo (2022) calculations do not include the effects of water vapor on the lapse rate in the troposphere. Latent heat from water condensation alters convection in the troposphere, greatly reducing the lapse rate when compared to a dry lapse rate. The result is a much cooler surface. Our climate calculations include the effects of water vapor on the lapse rate, which is why we predict surface temperatures of ≲500 K, even in the wake of a 7.9 × 10²¹ kg impact in Figure 7. All of our climate simulations of postimpact atmospheres allow surface liquid water.

If a postimpact atmosphere of 2000 mol cm⁻² H₂ is all lost to space (∼4 bars pure H₂ atmosphere, or ∼13% of the H₂ in an ocean), it would make the D/H of the ocean heavier by 1.4% by hydrodynamic escape and Rayleigh fractionation (following Equation (16) in Zahnle et al. 2019 using an escape fractionation factor of ∼0.9 appropriate for an atmosphere where H₂ dominates over CO₂). This may be an underestimate of the D/H shift because the immediate postimpact oxidation of iron by steam probably produces H₂ with a lower concentration of D than the steam that condenses into an ocean. Experiments show isotopic fractionation in the reaction of iron powder with steam at low temperatures (Smith & Posey 1957), but we are unaware of high-temperature experiments corresponding to postimpact conditions. In any case, cumulative big impacts during the Hadean that created highly reducing atmospheres would be expected to increase oceanic D/H additively, raising the ocean D/H from starting values that were 10% (Piani et al. 2020) to tens of percent (Alexander et al. 2012) lighter than the modern ocean. Such an evolution with intermittent hydrogen escape in the Hadean is consistent both with D/H constraints and with the xenon isotope record (Avice et al. 2018), in which ionic xenon is dragged out to space by early hydrogen escape, and the distribution of xenon isotopes becomes heavier (Zahnle et al. 2019).

The Hadean Earth may have had less land but was likely speckled with hot-spot volcanic islands similar to modern-day Hawaii (Bada & Korenaga 2018) and possibly had continental land (Korenaga 2021) where nitriles could accumulate. The majority of HCCCN and HCN produced in postimpact atmospheres would dissolve or rain out into the ocean, where it would be diluted and gradually removed by hydrolysis reactions (Miyakawa et al. 2002) or complexation with dissolved ferrous iron (Keefe & Miller 1996). However, some of the nitriles would be deposited in lakes or ponds on land. We consider, first, equilibrium with atmospheric p_HCN and, second, time-integrated deposition.

Nitrile concentrations in water bodies on land in equilibrium with the atmosphere according to Henry’s law would be too small to participate in prebiotic schemes that form ribonucleotides. Our models predict HCN surface pressures up to 10⁻⁹ bars (Figure 7). For a warm 373 K pond, Henry’s law predicts that the dissolved HCN concentration is 4 × 10⁻¹¹ mol L⁻¹. Yet ∼0.01 mol L⁻¹ HCN is required for polymerization (Sanchez et al. 1967), and published prebiotic schemes can use 1 mol L⁻¹ HCN (Patel et al. 2015).

Additionally, while nitriles are produced in postimpact atmospheres, water bodies on land would likely be too warm for prebiotic chemistry. In the Figure 6 simulation, substantial HCN and HCCCN production occurs in the aftermath of big impacts when the surface temperature is ∼390 K caused by a H₂–H₂ CIA greenhouse. Nickel catalysts permit big HCN and HCCCN production for surface temperatures as small as ∼360 K (Figure 9). Nucleotide building blocks are fragile at such hot temperatures, and conditions may not be conducive to an RNA world (Bada & Lazcano 2002).

We propose that cyanides produced in hot postimpact atmospheres may instead be preserved, stockpiled, and concentrated and used in prebiotic schemes at a later time, when the climate is colder. Cyanide rainout and stockpiling could occur for millions of years until HCN production is halted by H₂ escape to space (Figure 6). For example, if HCN rains out at 10⁹ molecules cm⁻² s⁻¹ over 1 million yr (Figure 7), then ∼1.4 g cm⁻² HCN could be stockpiled, assuming that all molecules are preserved. Once the H₂ escapes, the surface temperature would drop to ∼300 K (Figure 6), and over longer timescales, the carbonate-silicate cycle might settle on even colder climates because impact ejecta promotes CO₂ sequestration (Kadoya et al. 2020). In this cold climate, cyanide stockpiled into salts could be released as HCN or CN⁻ into water bodies on land because of rehydration, volcanic or impact heating (Patel et al. 2015; Sasselov et al. 2020), or UV exposure (Todd et al. 2022). Liberation of cyanide could enable the prebiotic schemes that make RNA.

Toner & Catling (2019) investigated a mechanism for stockpiling cyanides. Their thermodynamic calculations show that HCN can be preserved as ferrocyanide salts in evaporating carbonate-rich lakes. However, the Toner & Catling (2019) numerical experiments were at 273 and 298 K, which are far colder environments than the >360 K surface temperatures that coincide with large HCN production in postimpact atmospheres (Figure 9). Although Toner & Catling (2019) did not address stockpiling of HCCCN, cyanoacetylene can be captured by 4,5-dicyanoimidazole (DCI), a byproduct of adenine synthesis, to make crystals of 4,5-dicyanoimidazole (CV-DCI; Ritson et al. 2022), and it is possible that other capture mechanisms are yet to be discovered. Overall, the feasibility of stockpiling prebiotic nitriles in postimpact conditions requires further geochemical modeling and experiments.

We hypothesize that CH₄/CO₂ > 0.1 might be an important threshold required for a postimpact atmosphere to produce useful concentrations of nitriles for origin-of-life chemistry. Figure 10 shows HCN and HCCCN haze rainout as a function of the atmospheric CH₄/CO₂ mole ratio for every postimpact simulation in this paper. When CH₄/CO₂ > 0.1, the atmosphere is hazy, and HCN and HCCCN are delivered to the surface at a rate of up to ∼10⁹ molecules cm⁻² s⁻¹. In contrast, atmospheres with CH₄/CO₂ < 0.1 rain out less than 10⁵ HCN molecules cm⁻² s⁻¹ and have surface HCN concentrations of less than 10⁻¹³ bars (Figure 7). Such small HCN concentrations may be challenging to stockpile as ferrocyanides (Toner & Catling 2019). Additionally, modeled atmospheres with CH₄/CO₂ < 0.1 produce negligible HCCCN, yet the molecule is required in prebiotic schemes to synthesize pyrimidine (cytosine and uracil) nucleobase precursors to RNA (Powner et al. 2009; Becker et al. 2019; Okamura et al. 2019).

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The impactor mass required to generate an atmosphere with CH₄/CO₂ > 0.1 is uncertain. Our optimistic model, which considers the effect of nickel-catalyzed methane production, requires a >4 × 10²⁰ kg (>570 km) impactor (Figure 9). The lunar cratering record and abundance of highly siderophile elements in Earth’s mantle imply that between four and seven such impacts occurred during the Hadean (Marchi et al. 2014; Zahnle et al. 2020). Our least optimistic model needs a >5 × 10²¹ kg (>1330 km) impact to create a postimpact atmosphere with CH₄/CO₂ > 0.1 because it assumes that only a fraction of the iron delivered to Earth reacts with the ocean to create atmospheric H₂ (Appendix Figure A6). The Hadean only experienced zero to two collisions this large (Zahnle et al. 2020). The precise minimum impactor mass to make an atmosphere with CH₄/CO₂ > 0.1 depends on the importance of atmospheric equilibration with a melt pond (Section 3.1; Itcovitz et al. 2022), the fraction of impactor iron that reduces the atmosphere, and the effect of nickel and other surface catalysts on CH₄ kinetics.

An additional consideration is that any progress toward the origin of life caused by an impact could be erased by a subsequent impact that sterilizes the planet. For example, suppose a >500 km impact that vaporizes the ocean sterilizes the globe (Citron & Stewart 2022). With our most pessimistic calculations for postimpact CH₄ generation, a >1330 km (>5 × 10²¹ kg) impact is required to create an atmosphere that generates significant HCN and HCCCN. In this scenario, the last >1330 km impact favorable for prebiotic chemistry would likely be followed by a 500–1330 km impact that would destroy any primitive life without rekindling it. Alternatively, our optimistic model for postimpact CH₄ generation only requires a >4 × 10²⁰ kg (>570 km) impact to create an atmosphere with CH₄/CO₂ > 0.1. In this case, the final >570 km impact that might kick-start the origin of life is unlikely to be followed by a slightly smaller 500–570 km sterilizing impact.

A caveat to the reasoning in the previous paragraph is that ocean vaporization may not have sterilized the planet because microbes could have possibly survived in the deep subsurface (Sleep et al. 1989; Grimm & Marchi 2018).

In summary, we suggest that CH₄/CO₂ > 0.1 may be an important threshold for postimpact atmospheres to be conducive to the origin of life because they generate >4 orders of magnitude larger surface HCN concentrations and are the only modeled atmospheres capable of generating HCCCN. We find that the minimum impactor mass required to create a postimpact atmosphere with CH₄/CO₂ > 0.1 is between 4 × 10²⁰ and 5 × 10²¹ kg (570–1330 km). The value is uncertain for three reasons: (1) we do not know how effectively iron delivered by an impact chemically reduces the atmosphere (Section 3.1); (2) we do not know the importance of atmospheric equilibration with a melt pond (Section 3.1); and (3) it is hard to estimate a realistic surface area of nickel catalysts available during the cooling steam atmosphere (Section 3.2).

4.4.1. Hydrogen from Crust–Atmosphere Reactions

Perhaps the most significant caveat to the modeling effort described above is that we did not consider H₂ production from reactions between a hot postimpact atmosphere and solid, nonmelted crust. Section 3.1 explores the impact the H₂ made by two mechanisms: (1) reduction of the atmosphere by impact-derived iron and (2) atmospheric equilibration with a melt pond made by the impact. However, it is also conceivable that, while the atmosphere is hot and steam-rich in the ∼10³ yr following an impact (i.e., phase 2), water vapor could permeate through and react with the solid crust to produce H₂ by a process like serpentinization. Specifically, H₂O reduction by FeO in the solid crust could make H₂:

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

In our nominal model (Figures 4 and 7), we require a postimpact atmosphere to have >2 × 10³ H₂ mol cm⁻² (i.e., the equivalent of converting 13% of Earth’s ocean to H₂) in order to reach CH₄/CO₂ > 0.1 and big nitrile production rates. Assuming a crustal FeO content of 8 wt% (Takahashi 1986), 2 × 10³ H₂ mol cm⁻² could be produced by reacting water with FeO in the top ∼16 km of Earth’s lithosphere. The feasibility of extensive water–rock H₂ generation depends on the permeability of the crust and the pressure gradients driving subsurface fluid circulation. For example, low-permeability rocks with slow water circulation may not permit serpentinization of the upper crust within ∼10³ yr while the atmosphere is hot and steam-rich. A comprehensive model is outside the scope of this paper, but if attainable, significant water–rock reactions might produce a thick H₂ atmosphere after relatively small impacts (e.g., 10²⁰ kg), which favors CH₄/CO₂ > 0.1 and significant nitrile generation.

Another possibility, which we do not investigate in detail, is that atmosphere–crust reactions occur in the immediate aftermath of a giant impact (i.e., phase 1), rather than over ∼10³ as previously discussed. A large impact could produce a global ejecta blanket of mixed hot water and rock several kilometers thick. As water was vaporized to form a steam atmosphere, the water and rock slurry could chemically equilibrate, producing H₂.

Zahnle et al. (2020) attempted to account for atmosphere–crust interaction by equilibrating the postimpact steam atmosphere (phase 2) to a mineral redox buffer. For example, their Figure 5 assumes that the atmosphere has a fixed oxygen fugacity set by the FMQ buffer at an assumed 650 K methane quench temperature. The calculation predicts that most CO₂ is converted to CH₄ for impacts as small as ∼5 × 10¹⁹ kg, but Zahnle et al. (2020) did not determine whether such significant atmosphere–crust interaction is physically plausible.

4.4.2. Climate

A shortcoming of this work is that our climate model is relatively simple. Throughout Section 3, our climate code assumes an isothermal 200 K stratosphere and saturated adiabatic troposphere (i.e., relative humidity, ϕ = 1.0) and ignores clouds. However, many of our simulated postimpact atmospheres contain a hydrocarbon haze that should absorb sunlight and warm the stratosphere (Arney et al. 2016). Also, in a hydrogen-dominated atmosphere, water vapor has a larger molecular weight compared to the background gas, which could inhibit convection (Leconte et al. 2017) and perhaps cause low relative humidities. Furthermore, low-altitude clouds reflect sunlight and should cool a planet, while high clouds have a greenhouse warming effect (Goldblatt & Zahnle 2011).

Figure 11 attempts to show the uncertainty in our climate calculations as a function of three free parameters: stratosphere temperature, relative humidity, and low-altitude clouds, which we crudely approximate by varying the surface albedo. The calculation uses the composition of the atmosphere after a 5 × 10²⁰ kg impact in Figure 9 immediately after the steam atmosphere has condensed to an ocean. Our nominal climate parameters (T_strat = 200 K, ϕ = 1, A_s = 0.2) predict a 361 K surface temperature. A warm stratosphere caused by hydrocarbon UV absorption and high-albedo, low-altitude clouds might cause the surface to be ∼30 K colder than our nominal model, assuming water vapor is saturated. On the other hand, low relative humidities, which might be favored in convection-inhibited H₂-dominated atmospheres, increase the troposphere lapse rate, which warms the surface (Leconte et al. 2017). While Figure 11 gives a sense of the possible uncertainty in our climate calculations, it does not self-consistently simulate haze, relative humidity, and cloud feedback. A more comprehensive model is required to resolve these nuances.

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A further caveat is that our climate calculations ignore greenhouse warming from NH₃ (Table 1). We choose to disregard the influence of NH₃ because a substantial fraction of the gas should dissolve in the ocean (Zahnle et al. 2020), a process that our coupled photochemical-climate model cannot self-consistently account for. However, our climate model (Appendix D), when uncoupled to photochemistry, can partition gases between the atmosphere and ocean according to gas solubility and ocean chemistry. Below, we use this stand-alone climate model to determine the climate effects of NH₃ in a postimpact atmosphere. The NH₃ should dissolve into an ocean by Henry’s law, then hydrolyze to ${\mathrm{NH}}_{4}^{+}$:

$$\begin{eqnarray}&&{\mathrm{NH}}_{3}({\rm{g}})\leftrightarrow {\mathrm{NH}}_{3}(\mathrm{aq}),\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&{\mathrm{NH}}_{3}(\mathrm{aq})+{{\rm{H}}}_{2}{\rm{O}}\leftrightarrow {\mathrm{NH}}_{4}^{+}+{\mathrm{OH}}^{-},\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{{\rm{H}}}_{2}{\rm{O}}\leftrightarrow {\mathrm{OH}}^{-}+{{\rm{H}}}^{+}.\end{eqnarray} \tag{ 10 }$$

Therefore, the concentration of aqueous NH₃ (in mol kg⁻¹) is given by ${m}_{{\mathrm{NH}}_{3}}={p}_{{\mathrm{NH}}_{3}}{\alpha }_{{\mathrm{NH}}_{3}}$, where ${p}_{{\mathrm{NH}}_{3}}$ is the surface partial pressure of NH₃ in bars, and ${\alpha }_{{\mathrm{NH}}_{3}}$ is the Henry’s law constant (mol kg⁻¹ bar⁻¹). Reactions (9) and (10) give the ammonium concentration as ${m}_{{\mathrm{NH}}_{4}^{+}}=({K}_{9}/{K}_{10}){m}_{{\mathrm{NH}}_{3}}{m}_{{{\rm{H}}}^{+}}$, where K₉ and K₁₀ are equilibrium constants for each reaction. The Henry’s law constant for NH₃ (in mol kg⁻¹ bar⁻¹) is ${\alpha }_{{\mathrm{NH}}_{3}}\,=61\exp \left(4200\left(\tfrac{1}{T}-\tfrac{1}{298.15}\right)\right)$ (Linstrom & Mallard 1998). The equilibrium constants for Reactions (9) and (10) are approximately ${\mathrm{log}}_{10}({K}_{9})=-84.63\exp (-0.016\,1T)-4.05$ and ${\mathrm{log}}_{10}({K}_{10})=-39.96\exp (-0.006\,39T)-8.06$. We derived both of these parameterizations using the SUPCRT thermodynamic database (Johnson et al. 1992).

We implement this ocean chemistry into our stand-alone climate model (Appendix D) and compute the surface temperature after the 5 × 10²⁰ kg impact in Figure 9 once the steam atmosphere has condensed to an ocean. The mol cm⁻² of each gas are given in the Figure 11 caption. We use our nominal climate parameters (T_strat = 200 K, ϕ = 1, A_s = 0.2), assume that the total H₂O reservoir is 1 modern ocean (15,000 mol cm⁻²) with pH = 7, and account for the radiative effects of NH₃ in addition to the Table 1 opacities. The model predicts a 371 K surface temperature, which is 10 K warmer than calculations that do not include NH₃ opacities or ocean dissolution, and 96% of the ammonia reservoir is dissolved in the ocean.

Ammonia has a more substantial effect on climate after larger impactors. Consider the atmosphere after a 7.9 × 10²¹ kg impact in Figure 5 once steam has condensed to an ocean (0.008 mol cm⁻² CO₂, 11.5 mol cm⁻² CH₄, 32.6 mol cm⁻² N₂, 9122 mol cm⁻² H₂, 0.002 mol cm⁻² CO, and 6.8 mol cm⁻² NH₃). Our climate model, which includes NH₃ opacities and ocean dissolution, predicts a 505 K surface temperature with only 20% of the NH₃ dissolved in the ocean because solubility decreases with increased temperature. This is 42 K hotter than our model that ignores NH₃ greenhouse contributions (Figure 7). Overall, our climate calculations throughout most of this paper perhaps underestimate the greenhouse warming by 10 to ∼40 K by ignoring NH₃ opacities but instead may overestimate surface temperature because they do not account for the cooling effects of haze and low-altitude clouds (Figure 11). Additional warming from NH₃ would only be relevant for a fraction of the postimpact atmosphere, before ammonia is destroyed by photolysis (Figure 6).

4.4.3. Unknown Chemical Reactions and the Effect of Ions

We begin our derivation of the equations governing Photochem with modified versions of Equations (B.1), (B.2), and (B.29) in Catling & Kasting (2017):

$$\begin{eqnarray}&&\displaystyle \frac{\partial {n}_{i}}{\partial t}=-\displaystyle \frac{\partial }{\partial z}{{\rm{\Phi }}}_{i}+{P}_{i}-{L}_{i}-{R}_{i,\mathrm{rainout}}+{Q}_{i,\mathrm{cond}},\end{eqnarray} \tag{ C1 }$$

$$\begin{eqnarray}&&\begin{array}{l}{{\rm{\Phi }}}_{i,\mathrm{gas}}=-{K}_{\mathrm{zz}}n\displaystyle \frac{\partial }{\partial z}\left(\displaystyle \frac{{n}_{i}}{n}\right)\\ -{n}_{i}{D}_{i}\left(\displaystyle \frac{1}{{n}_{i}}\displaystyle \frac{\partial {n}_{i}}{\partial z}+\displaystyle \frac{1}{{H}_{i}}+\displaystyle \frac{1}{T}\displaystyle \frac{\partial T}{\partial z}+\displaystyle \frac{{\alpha }_{{Ti}}}{T}\displaystyle \frac{\partial T}{\partial z}\right),\end{array}\end{eqnarray} \tag{ C2 }$$

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{i,\mathrm{particle}}=-{K}_{\mathrm{zz}}n\displaystyle \frac{\partial }{\partial z}\left(\displaystyle \frac{{n}_{i}}{n}\right)-{w}_{i}{n}_{i}.\end{eqnarray} \tag{ C3 }$$

Table B1 explains the variables and their units. Equation (C1) states that molecule concentration (n_i in molecules cm⁻³) changes over time at a point in space because of vertical movement of particles $\left(\tfrac{\partial }{\partial z}{{\rm{\Phi }}}_{i}\right)$ and chemical reactions, rainout, or condensation/evaporation (P_i , L_i , R_i,rainout, and C_i,cond). The equation is 1D because it only considers vertical gas transport and differs from Equation (B.1) in Catling & Kasting (2017) because we explicitly include rainout and condensation. Equation (C2) states that the flux of gases (Φ_i,gas) is determined by eddy and molecular diffusion, and Equation (C3) assumes that the flux of particles (Φ_i,particle) is given by eddy diffusion and the rate at which particles fall through the atmosphere.

Many 1D photochemical models further simplify Equation (C1) by assuming that the total number density does not change over time (∂n/∂t ≈ 0). Using this assumption, Equation (C1) is recast in terms of evolving mixing ratios (f_i ) rather than number densities (see Appendix B.1 in Catling & Kasting 2017 for a derivation). Such models assume a time-constant temperature profile. The surface pressure is also prescribed, and pressures above the surface are computed with the hydrostatic equation. In order to guarantee that all mixing ratios in the atmosphere sum to 1, the models assume a background filler gas with a mixing ratio f_background = 1 − ∑_i f_i . Common choices for the background gas are N₂, CO₂, or H₂, depending on the atmosphere under investigation. By definition, the background gas is not conserved. This approach is valid for steady-state photochemical calculations and also reasonable for atmospheric transitions, which maintain an approximately constant surface pressure and atmospheric temperature. The Photochem code contains an implementation of this traditional approach to photochemical modeling.

Unfortunately, solving a simplified version of Equation (C1) in terms of mixing ratios does not work well for postimpact atmospheric modeling. For example, a postimpact atmosphere can contain 10 bars of H₂ that escapes to space over millions of years, lowering the surface pressure to a 1 bar N₂-dominated atmosphere (e.g., Figure 6). Traditional photochemical models fail to simulate this scenario because it is not reasonable to assume a single background gas and time-constant surface pressure. Additionally, most models fix the atmospheric temperature during any single model integration, but surface temperature should change significantly as impact-generated H₂ escapes to space.

Therefore, Photochem implements a code that solves Equation (C1) in terms of number densities (n_i ) without the assumption of fixed surface pressure or a background gas. This approach requires slight modifications to Equations (C2) and (C3), which we describe below. Consider the hydrostatic equation and ideal gas law,

$$\begin{eqnarray}&&\displaystyle \frac{\partial p}{\partial z}=\displaystyle \frac{-{gp}\bar{\mu }}{{N}_{a}{kT}},\end{eqnarray} \tag{ C4 }$$

$$\begin{eqnarray}&&p\,=\,{nkT}.\end{eqnarray} \tag{ C5 }$$

Substituting the ideal gas law into the hydrostatic equation yields

$$\begin{eqnarray}&&\displaystyle \frac{\partial }{\partial z}({nT})=\displaystyle \frac{-{gn}\bar{\mu }}{{N}_{a}k},\end{eqnarray} \tag{ C6 }$$

$$\begin{eqnarray}&&n\displaystyle \frac{\partial T}{\partial z}+T\displaystyle \frac{\partial n}{\partial z}=\displaystyle \frac{-{gn}\bar{\mu }}{{N}_{a}k}.\end{eqnarray} \tag{ C7 }$$

After rearrangement and substituting the definition of scale height,

$$\begin{eqnarray}&&\displaystyle \frac{1}{n}\displaystyle \frac{\partial n}{\partial z}=-\displaystyle \frac{1}{{H}_{a}}-\displaystyle \frac{1}{T}\displaystyle \frac{\partial T}{\partial z}.\end{eqnarray} \tag{ C8 }$$

Now consider the following expansion using the quotient rule:

$$\begin{eqnarray}&&\displaystyle \frac{\partial }{\partial z}\left(\displaystyle \frac{{n}_{i}}{n}\right)=\displaystyle \frac{1}{n}\displaystyle \frac{\partial {n}_{i}}{\partial z}-\displaystyle \frac{{n}_{i}}{{n}^{2}}\displaystyle \frac{\partial n}{\partial z}.\end{eqnarray} \tag{ C9 }$$

Substituting Equation (C8) into Equation (C9) and rearrangement gives

$$\begin{eqnarray}&&n\displaystyle \frac{\partial }{\partial z}\left(\displaystyle \frac{{n}_{i}}{n}\right)=\displaystyle \frac{\partial {n}_{i}}{\partial z}+\displaystyle \frac{{n}_{i}}{{H}_{a}}+\displaystyle \frac{{n}_{i}}{T}\displaystyle \frac{\partial T}{\partial z}.\end{eqnarray} \tag{ C10 }$$

Finally, we can substitute Equation (C10) into Equations (C2) and (C3) to derive new equations for the flux of gases and particles:

$$\begin{eqnarray}\begin{array}{rcl}{{\rm{\Phi }}}_{i,\mathrm{gas}} & = & -{K}_{\mathrm{zz}}{n}_{i}\left(\displaystyle \frac{1}{{n}_{i}}\displaystyle \frac{\partial {n}_{i}}{\partial z}+\displaystyle \frac{1}{{H}_{a}}+\displaystyle \frac{1}{T}\displaystyle \frac{\partial T}{\partial z}\right)\\ & & -{n}_{i}{D}_{i}\left(\displaystyle \frac{1}{{n}_{i}}\displaystyle \frac{\partial {n}_{i}}{\partial z}+\displaystyle \frac{1}{{H}_{i}}+\displaystyle \frac{1}{T}\displaystyle \frac{\partial T}{\partial z}+\displaystyle \frac{{\alpha }_{{Ti}}}{T}\displaystyle \frac{\partial T}{\partial z}\right),\end{array}\end{eqnarray} \tag{ C11 }$$

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{i,\mathrm{particle}}=-{K}_{\mathrm{zz}}{n}_{i}\left(\displaystyle \frac{1}{{n}_{i}}\displaystyle \frac{\partial {n}_{i}}{\partial z}+\displaystyle \frac{1}{{H}_{a}}+\displaystyle \frac{1}{T}\displaystyle \frac{\partial T}{\partial z}\right)-{w}_{i}{n}_{i}.\end{eqnarray} \tag{ C12 }$$

We then apply a finite-volume approximation to the Equation (C1) system of particle differential equations using the fluxes for gases and particles given by Equations (C11) and (C12), which results in a system of ordinary differential equations. We use a second-order centered scheme for all spatial derivatives except falling particles, which use a first-order upwind scheme for stability. Photochem evolves the finite volume approximately forward in time using the CVODE BDF method developed by Sundials Computing (Hindmarsh et al. 2005). The model assumes no background gas, and the surface pressure can evolve over time as, for example, gases escape to space. Additionally, our model computes a self-consistent temperature structure within each time step using the Clima radiative transfer code (Appendix D) assuming a pseudomoist adiabatic troposphere connected to an isothermal upper atmosphere.

An additional challenge of postimpact atmospheres is that the scale height changes by a factor of ∼10 or more when H₂ escapes, leaving behind a N₂- or CO₂-dominated atmosphere (Figure 6). Most relevant photochemistry occurs at pressures >10⁻⁷ bar, so we choose a model domain that starts at the surface and extends to an altitude that is approximately this pressure. However, suppose we choose a model domain extending to ∼1000 km (i.e., the 10⁻⁷ bar level), appropriate for a H₂-dominated atmosphere. After H₂ escapes to space, all relevant photochemistry would occur below 100 km, in the bottom several grid cells of the model. Therefore, the important photochemistry would be poorly resolved and inaccurate, and the extremely small pressures at the top of the model domain would likely cause numerical instability. Our solution is to adaptively adjust the model domain so it is always appropriate for atmosphere scale height. We use the rootfinding functionally in CVODE to halt integration whenever the pressure at the top of the atmosphere falls below 10⁻⁷ bars and lower the top of the model domain before continuing integration. This procedure is automatically done tens to hundreds of times during each postimpact integration.

Our chemical reactions, photolysis cross sections, and thermodynamic data used for all gas-phase kinetics are archived in a Zenodo repository at doi:10.5281/zenodo.7802962. Chemical reactions and thermodynamic data are in the file “reaction_mechanisms/zahnle_earth.yaml,” and photolysis cross sections are in the folder “xsections/.” All thermodynamic data are from the NIST Chemistry WebBook (Linstrom & Mallard 1998). The chemical and photolysis reactions are an updated version of rates presented in Zahnle et al. (2016).

In this paper, our model simulates rainout in droplets of water for the following species: particles, OH, CN, HCN, C₂H₄, NO, HO₂, N₂O, H₂O₂, O₃, NO₂, NO₃, HNO₂, HNO₃, C₂H₆, CH₃OH, CH₃CHO, C₃H₆, and CH₃CN.

Figure C1 shows Photochem applied to Earth and Titan compared to observations gathered from the literature. All boundary conditions and settings for each model are archived in the “ModernEarth” and “Titan” templates in Zenodo at doi:10.5281/zenodo.7802921. Our model of Titan fixes the surface CH₄ mixing ratio to a 0.015 volume mixing ratio, permits H₂ escape at the diffusion-limited rate, and allows aerosols to fall to Titan’s surface but otherwise has zero-flux boundary conditions. We ignore the effects of galactic cosmic rays, which causes our model to underpredict the nitrile haze production in the lower atmosphere (Lavvas et al. 2008b). Additionally, we neglect ion chemistry, which is argued to be important for the formation of large hydrocarbons (e.g., C₆H₆) but inconsequential for smaller molecular weight species. Despite these omissions, Photochem broadly reproduces the main cyanide chemistry on Titan.

Our photochemical-climate simulations of a postimpact atmosphere assume a HCN surface deposition velocity of 7 × 10⁻³ cm s⁻¹. Here we describe a simple model of HCN hydrolysis in the ocean that justifies this value.

Motivated by Appendix 3 in Kharecha et al. (2005), we imagine a two-box ocean model with a surface ocean of depth ∼100 m and a deep ocean (∼4 km). We assume that HCN transport into the ocean is governed by a stagnant boundary layer model (see Figure 3 in Kharecha et al. 2005), where it is destroyed by hydrolysis reactions. The HCN is mixed between the surface and deep ocean reservoirs by a turnover velocity, v_over, which we nominally take to be 1.2 × 10⁻⁵ cm s⁻¹, which is appropriate for modern Earth. Under these circumstances, the following system of ordinary differential equations governs the concentration of HCN in the surface and deep ocean:

$$\begin{eqnarray}&&\begin{array}{c}\displaystyle \frac{{{dm}}_{{\rm{HCN}},{\rm{s}}}}{{dt}}=\displaystyle \frac{{{\rm{\Phi }}}_{{\rm{HCN}}}}{{{Cz}}_{s}}-{k}_{{\rm{tot}}}{m}_{{\rm{HCN}},{\rm{s}}}\\ \,\,\,-\left(\displaystyle \frac{{v}_{{\rm{over}}}}{{z}_{{\rm{s}}}}\right)({m}_{{\rm{HCN}},{\rm{s}}}-{m}_{{\rm{HCN}},{\rm{d}}}),\end{array}\end{eqnarray} \tag{ C13 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{{dm}}_{\mathrm{HCN},{\rm{d}}}}{{dt}}=-{k}_{\mathrm{tot}}{m}_{\mathrm{HCN},{\rm{s}}}+\left(\displaystyle \frac{{v}_{\mathrm{over}}}{{z}_{{\rm{d}}}}\right)({m}_{\mathrm{HCN},{\rm{s}}}-{m}_{\mathrm{HCN},{\rm{d}}}).\end{eqnarray} \tag{ C14 }$$

Here ${m}_{\mathrm{HCN},{\rm{s}}}$ and ${m}_{\mathrm{HCN},{\rm{d}}}$ are the concentration of HCN in the surface and deep ocean, respectively, in mol L⁻¹; C is a constant equal to 6.022 × 10²⁰ molecules mol⁻¹ L cm⁻³; z_s is the depth of the surface ocean; and z_d is the depth of the deep ocean. We compute the temperature and pH-dependent hydrolysis rate coefficient, k_tot, following Miyakawa et al. (2002). Here ${{\rm{\Phi }}}_{\mathrm{HCN}}$ is the HCN flux into the ocean in molecules cm⁻² s⁻¹, which is determined by a stagnant boundary layer model:

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{HCN}}={v}_{{\rm{p}},\mathrm{HCN}}({\alpha }_{\mathrm{HCN}}{10}^{-6}{p}_{\mathrm{HCN}}-{m}_{\mathrm{HCN},{\rm{s}}})C.\end{eqnarray} \tag{ C15 }$$

We assume that the piston velocity of HCN is 5 × 10⁻³ cm s⁻¹, which is the same as the piston velocity of CO (Kharecha et al. 2005, Table 1). Also, ${\alpha }_{\mathrm{HCN}}$ is the Henry’s law coefficient for HCN. The flux of a gas can also be parameterized with a deposition velocity (${v}_{{\rm{d}},\mathrm{HCN}}$):

$$\begin{eqnarray}\begin{array}{rcl}{{\rm{\Phi }}}_{\mathrm{HCN}} & = & {n}_{\mathrm{HCN}}{v}_{{\rm{d}},\mathrm{HCN}}\\ & = & \displaystyle \frac{{p}_{\mathrm{HCN}}}{{kT}}{v}_{{\rm{d}},\mathrm{HCN}}.\end{array}\end{eqnarray} \tag{ C16 }$$

Assuming a steady state (${{dm}}_{\mathrm{HCN},{\rm{s}}}/{dt}={{dm}}_{\mathrm{HCN},{\rm{d}}}/{dt}=0$) and solving for ${v}_{{\rm{d}},\mathrm{HCN}}$ in Equations (C13)–(C16) yields

$$\begin{eqnarray}&&\begin{array}{c}{v}_{{\rm{d}},{\rm{HCN}}}={10}^{-6}{kT}{\alpha }_{{\rm{HCN}}}{{Ck}}_{{\rm{tot}}}{v}_{{\rm{p}},{\rm{HCN}}}\\ \times \,\displaystyle \frac{\left.{k}_{{\rm{tot}}}{z}_{{\rm{d}}}{z}_{{\rm{s}}}+{v}_{{\rm{over}}}({z}_{{\rm{d}}}+{z}_{{\rm{s}}}\right)}{{k}_{{\rm{tot}}}{z}_{{\rm{d}}}({v}_{{\rm{p}},{\rm{HCN}}}+{k}_{{\rm{tot}}}{z}_{{\rm{s}}})+{v}_{{\rm{over}}}\left({v}_{{\rm{p}},{\rm{HCN}}}+{k}_{{\rm{tot}}}\left({z}_{{\rm{d}}}+{z}_{{\rm{s}}}\right)\right)}.\end{array}\end{eqnarray} \tag{ C17 }$$

Here we assume that the temperature and pH of the ocean are uniform and that the temperature of the surface air is the same as the temperature of the ocean.

Figure C2 computes the deposition velocity of HCN using Equation (C17) over a wide range of ocean temperatures and pH. Kadoya et al. (2020) used a model of the geologic carbon cycle to argue that the Hadean ocean was moderately alkaline (pH ≈ 8). Therefore, we choose a HCN deposition velocity of 7 × 10⁻³ cm s⁻¹ for our nominal model because it is a reasonable approximation of the pH = 8 case over a wide range of temperatures. Additionally, we assume that HCCCN has the same deposition velocity as HCN, also caused by hydrolysis reactions in the ocean.

We have rerun our photochemical-climate simulations of postimpact atmospheres with order-of-magnitude larger and smaller HCN deposition velocities. The results are qualitatively unchanged. For example, assuming ${v}_{{\rm{d}},\mathrm{HCN}}=7\,\times \,{10}^{-4}$ cm s⁻¹ for a 2 × 10²¹ kg impactor in Figure 7 causes 1 order of magnitude smaller HCN ocean deposition. However, the HCN rainout and surface pressure are unchanged because HCN rainout dominates over the HCN ocean deposition.