Creation and Evolution of Impact-generated Reduced Atmospheres of Early Earth

The origin of life on Earth seems to demand a highly reduced early atmosphere, rich in CH4, H2, and NH3, but geological evidence suggests that Earth's mantle has always been relatively oxidized and its emissions dominated by CO2, H2O, and N2. The paradox can be resolved by exploiting the reducing power inherent in the “late veneer,” i.e., material accreted by Earth after the Moon-forming impact. Isotopic evidence indicates that the late veneer consisted of extremely dry, highly reduced inner solar system materials, suggesting that Earth's oceans were already present when the late veneer came. The major primary product of reaction between the late veneer's iron and Earth's water was H2. Ocean-vaporizing impacts generate high pressures and long cooling times that favor CH4 and NH3. Impacts too small to vaporize the oceans are much less productive of CH4 and NH3, unless (i) catalysts were available to speed their formation, or (ii) additional reducing power was extracted from pre-existing crustal or mantle materials. The transient H2–CH4 atmospheres evolve photochemically to generate nitrogenated hydrocarbons at rates determined by solar radiation and hydrogen escape, on timescales ranging up to tens of millions of years and with cumulative organic production ranging up to half a kilometer. Roughly one ocean of hydrogen escapes. After the methane is gone, the atmosphere is typically H2- and CO-rich, with eventual oxidation to CO2 rate-limited by water photolysis and hydrogen escape.


Introduction
The modern science of the origin of life on Earth begins with Haldane (1929) and Oparin (1938). Both argued that a highly reduced early terrestrial environment-profoundly unlike the world of today, even with O 2 removed-was needed. Oparinʼs specific emphasis on methane, ammonia, formaldehyde, and hydrogen cyanide as primordial materials suitable for further development remains a recurring theme in origin-of-life studies (Urey 1952;Oró & Kamat 1961;Ferris et al. 1978;Stribling & Miller 1987;Oró et al. 1990;Ricardo et al. 2004;Powner et al. 2009;Sutherland 2016;Benner et al. 2019a). Although some of these materials-formaldehyde in particular-can be generated under weakly reducing conditions (Pinto et al. 1980;Benner et al. 2019b), others (such as cyanamide and cyanoacetylene) require strongly reducing conditions. The hypothesized reducing atmosphere inspired the famous and often-replicated Miller-Urey experiments, in which sparked or UV-irradiated gas mixtures spontaneously generate a wide range of organic molecules (Miller 1953(Miller , 1955Miller & Urey 1959;Cleaves et al. 2008;Johnson et al. 2008).
The geological argument against a reducing early atmosphere is nearly as old (e.g., Poole 1951), although often accompanied by the caveat that things could have been different before the rock record (e.g., Holland 1964Holland , 1984Abelson 1966;Walker 1977). The underlying presumption is that the atmosphere should have resembled volcanic gases. Modern volcanic gases are roughly consistent with the quartzfayalite-magnetite (QFM) mineral buffer, for which the redox state is determined by chemical reactions between ferrous (Fe +2 ) and ferric iron (Fe +3 ). At typical magma temperatures, QFM predicts that H 2 and CO would be present at percent levels compared to H 2 O and CO 2 , and that methane and ammonia would be negligible.
Some studies suggest that the Archean mantle had a similar redox state to today (Delano 2001;Canil 2002;Rollinson et al. 2017), while rare earth elements in zircons suggest a Hadean mantle consistent with QFM (Trail et al. 2012). Large uncertainties in observationally derived oxygen fugacities (±2 in ( ) f log 10 O 2 ) may obscure a secular trend, while some simplifying assumptions made in earlier f O 2 studies are open to question (Wang et al. 2019). (The redox state of rocks is usually described by oxygen fugacity f O 2 , which describes the formal abundance of O 2 gas in units of atmospheres.) Two recent studies that use filtered samples hint that ( ) f log 10 O 2 of the mantle increased by ∼1.3 from the early Archean to Proterozoic (Aulbach & Stagno 2016;Nicklas et al. 2019).
Concurrently, a body of experimental evidence has accumulated suggesting that ferrous silicates in Earthʼs mantle disproportionate under great pressure into ferric iron and metallic iron, with the latter expected to migrate to the core (Frost & McCammon 2008). This would leave the mantle, or at least part of the mantle, in a QFM-like state of oxidation from the time our planet first became big enough to be called Earth (Armstrong et al. 2019).
Given the incompatibility of a QFM mantle with a reduced atmosphere, workers have turned to impact degassing, in which gases are directly released into the atmosphere on impact (Matsui & Abe 1986;Tyburczy et al. 1986;Ahrens et al. 1989). Most impactors are much more reduced than the mantle and often better endowed (gram per gram) in atmophile elements (Urey 1952;Hashimoto et al. 2007;Schaefer & Fegley 2007;Sugita & Schultz 2009). Many meteorites, including ordinary chondrites and enstatite chondrites, contain substantial amounts of metallic iron and iron sulfides. Gases that equilibrate with these highly reduced meteoritic materials would be highly reduced themselves (Kasting 1990;Hashimoto et al. 2007;Schaefer & Fegley 2007, 2017Kuwahara & Sugita 2015), provided that there is enough iron to reduce all of the atmophiles in the impactor. But if there are more atmophiles to reduce than iron to reduce them, the gas composition can evolve to a much more oxidized state (Schaefer & Fegley 2017).
Several of the new impact-degassing studies (Hashimoto et al. 2007;Schaefer & Fegley 2007, 2017 calculate gas compositions in equilibrium with mineral assemblagesat fixed pressures, with temperature treated as an independent variable. These calculations often promise big yields of CH 4 and NH 3 at low temperatures. However, actual yields depend on the quench conditions in the gas as it cools after the impact. A cooling gas is said to have quenched when the chemical reactions maintaining equilibrium between species become so sluggish that the composition of the gas freezes (Zel'dovich & Raizer 1967). Quenching is mostly determined by temperature. Gas-phase reactions for making CH 4 from CO are strongly inhibited by low temperatures, and those for making NH 3 from N 2 are even more strongly inhibited. So unless an abundant catalyst were available to lower the effective quench temperature (Kress & McKay 2004), there is a tendency for the shockheated gas to quench to CO, N 2 , and H 2 . Of the new studies, only Kuwahara & Sugita (2015) have attempted to calculate quench conditions, but their results are problematic because they used the entropy of shocked silica to estimate the entropy of shocked carbonaceous chondrites, which results in artificially low temperatures and artificially large amounts of methane. Finally, in a full account, the quenched plume of impact gases would be mixed into, and diluted by, the preexisting atmosphere.
This study follows the lead of Genda et al. (2017aGenda et al. ( , 2017b and Benner et al. (2019a) in addressing how the largest cosmic impacts changed the ocean and atmosphere that were already present on Earth. We go beyond Genda et al. (2017aGenda et al. ( , 2017b and Benner et al. (2019a) in addressing not just the single largest impact but also a full range of sizes, extending to impacts 100 and even 1000 times smaller (Hadean Earth would have experienced scores of these). Our particular focus is on impacts that process the entire atmosphere and hydrosphere. This differs from previous studies of smaller impacts that find that the main product of impact is HCN, and this occurs only in atmospheres with C/O ratios greater than unity (Chyba & Sagan 1992). Section 2 provides a brief summary of impacts after the Moon formed as constrained by geochemistry and the craters of the Moon. Section 3 addresses impact-generation of methane-rich atmospheres on Earth. The emphasis is on impacts that are big enough to vaporize the oceans, as these produce long-lasting hot conditions at high pressures and, thus, can be highly favorable to methane and sometimes even to ammonia. Section 4 uses a simple model to address the subsequent photochemical evolution of these atmospheres. The emphasis here is on the fate of methane and the production of organic material and hazes on the photochemistry of nitrogen and the generation of HCN and other nitrogenated organics, and on hydrogen escape. Ammonia is (mostly) deferred to the Discussion.

The Late Veneer
The highly siderophile elements (HSEs) comprise seven heavy metals (Ru, Rh, Pd, Os, Ir, Pt, and Au) with very strong tendencies to partition into planetary cores. If Earthʼs mantle and core were fully equilibrated, almost all of its HSEs would be in the core, and the tiny remnant in the mantle would be highly chemically fractionated (Walker 2009;Rubie et al. 2015Rubie et al. , 2016Day et al. 2016). But this is not what is seen. Rather, the mantle contains a modest cohort of excess HSEs that, to first approximation, are present in roughly the same relative abundances that they have in chondritic meteorites (Day et al. 2016). One explanation is that the excess HSEs were dropped into the mantle and left stranded there some time after core formation was complete. If the mantleʼs HSEs were added with other elements in chondritic proportions, they correspond to about 0.5% of Earthʼs mass (Anders 1989). The late-added mass carrying the HSEs is usually called the "late veneer." The late veneer measured in this way is very big. Viewed literally, 0.5% of Earthʼs mass corresponds to a veneer 20km thick. Gathered into a sphere, it corresponds to a rocky world 2300km diameter-as big as Pluto, and more massive. We will call this the "maximum HSE" veneer. If the veneer were sourced from fragments of differentiated worlds, the veneer mass could be a little smaller or much bigger.
Historically, the late veneer was presumed volatile-rich, as would be expected if the last materials to fall to Earth fell from the cold distant outer solar system (Anders & Owen 1977;Wänke & Dreibus 1988;Dreibus et al. 1989;Marty 2012;Albarède et al. 2013;Halliday 2013). However, the late veneer now appears constrained by Ru isotopes to resemble either enstatite chondrites, enstatite achondrites (a.k.a., aubrites), or iron meteorites of type IAB and, thus, appears to come from the same deep inner solar system reservoir as Earth itself (Fischer-Gödde et al. 2015;Dauphas 2017;Fischer-Gödde & Kleine 2017;Bermingham et al. 2018;Carlson et al. 2018;Hopp & Kleine 2018). All of our samples of these materials are profoundly reduced and very dry. This apparently excludes the late veneer as the source of water on Earth (Fischer-Gödde & Kleine 2017; Carlson et al. 2018), and thus, the late veneer can be presumed to have impacted into an Earth already fully plenished with oceans, a view also consistent with oxygen isotopes (Greenwood et al. 2018). The late veneerʼs role changes from water bearer to water changer: it must now be viewed as a source of reducing power injected into Earthʼs near-surface environment (Pasek & Lauretta 2008;Genda et al. 2017aGenda et al. , 2017bBenner et al. 2019a).
The total reducing power delivered by the maximum late veneer can be illustrated by using all of its metallic iron to reduce water to hydrogen, in stoichiometry, Fe+H 2 O→ FeO+H 2 . The iron that accompanied the mantleʼs excess HSEs corresponded to 1×10 25 g of metal. Because the HSEs remained in the mantle, neither they nor the iron that came with them went to the core, and thus, we can be confident that the iron was oxidized at the surface, in the crust, or in the mantle. There is enough iron in the late veneer to reduce 1.8×10 23 moles of H 2 O to H 2 and FeO, which corresponds to reducing of 2.3 oceans of water to hydrogen.
If the late veneer were characterized by size-number statistics typical of stray solar system bodies, it is likely that most of the mantleʼs HSE excess was carried by a single Plutosized body (Sleep et al. 1989;Tremaine & Dones 1993;Bottke et al. 2010;Brasser et al. 2016;Genda et al. 2017a).
Comparison with the uncertain but apparently much smaller lunar HSE excess (Day et al. 2016) is consistent with the conjecture that the maximum HSE event was singular (Brasser et al. 2016;Morbidelli et al. 2018); although, this is not required, as there are other ways of explaining the scarcity of lunar HSEs that do not imply different accretion rates for Earth and Moon (see Kraus et al. 2015).
But even if the late veneer were delivered by one body, it does not follow that its mass was added to Earth in a moment. There is a considerable likelihood, estimated as 50% by Agnor & Asphaug (2004), that an impact results not in a merger but rather in the disintegration of the smaller body. The debris are distributed in a ring around the Sun coincident with Earthʼs orbit and swept up by Earth over tens or hundreds of thousands of years (Genda et al. 2017a(Genda et al. , 2017b. Few of the debris are swept up by the Moon, owing to the much greater gravitational cross section of Earth with respect to debris in quasi-circular orbits (Genda et al. 2017a). This kind of distributed event is likely to strand nearly all of its HSEs in the crust or at shallow depths in Earthʼs mantle, while the direct impact of a Plutosized body might be expected to drive much of the impactorʼs core directly into our own. Stranding all of the newly added HSEs in the mantle without fractionation fulfills a second independent requirement imposed by the mantleʼs Ru isotopes, which were not mass-fractionated by partitioning between the mantle and core (Fischer-Gödde & Kleine 2017; Hopp & Kleine 2018). Dividing the impactor into myriads of smaller particles would also be more effective at chemically reducing Earthʼs atmosphere and ocean. For example, Genda et al. (2017b) model a Moon-sized impactor and find that 60% of the iron would be divided into mm-size droplets. The overall picture resembles that suggested by Urey (1952), who wrote that "materials would have fallen through the atmosphere in the form of iron and silicate rains and would have reacted with the atmosphere (and hydrosphere) in the process." An important caveat is that a maximum HSE impact may not couple well to the oceans. A Pluto-sized impact would blanket Earth in tens of kilometers of impact ejecta, which is so much deeper than the oceans that much of the iron may have been buried before it could react with water. Under these conditions, the buried iron would have remained unoxidized in the upper mantle for a considerable period of time. We know from the presence of the HSEs and the unfractionated Ru isotopes that the iron was not removed to the core. The iron must therefore have strongly influenced the redox state of volcanic gases until its oxidation was complete. The effect of this is to prolong the influence of the maximum HSE event to geological timescales.
There is also a small chance that the late veneer is an illusion. It has been suggested that Earthʼs HSE excess may date to the Moon-forming impact itself (Newsom & Taylor 1989;Brasser et al. 2016;Sleep 2016). If so, the mantleʼs HSE excess overestimates the amount of reducing power delivered to Earth after the Moon-forming impact. A crude lower bound on the late veneer can be extrapolated from the lunar crater record (Sleep et al. 1989;Zahnle & Sleep 1997. This scaling suggests that the "minimum late veneer" delivered between 3% and 30% of the mass as the maximum HSE veneer. The large uncertainty, and large total mass striking Earth compared to the Moon, both arise from the high probability that all of the largest bodies in a given population hit the Earth (Sleep et al. 1989). Table 1 lists a representative sampling of maximum and minimum late veneer impacts. The number of bodies in any given size class is estimated from the cumulative relation N(>m)∝m − b , with 0.5<b<0.9, with the smaller number based on the number of lunar basins and with the larger number based on the total cumulative mass of the maximum late veneer using methods described by Zahnle & Sleep (1997). The number of oceans that can be vaporized assumes that 50% of the impact energy is available to evaporate an ocean (1.4×10 24 g) of water and heat the steam to 1500K. The number of oceans that can be reduced to H 2 assumes an EH enstatite chondritic composition with 33% Feby mass and that the reaction Fe+H 2 O→FeO+H 2 goes to completion. Other entries in Table 1 are discussed as they arise.
Evidence has recently emerged that Earthʼs molybdenumanother siderophile element but somewhat less so than the HSEs-has an isotopic composition distinct from Earthʼs HSEs (Budde et al. 2019). This has been interpreted by its discoverers to mean that Theia-the name widely given to the Moonforming impactor-was made of different stuff than the late veneer (Budde et al. 2019). Budde et al. (2019) even suggest that Theia was the source of Earthʼs water; although in our opinion, it seems equally plausible that Earthʼs distinctive Mo predates the Moon-forming impact. From our perspective here, it makes little difference whether Earthʼs water was delivered by Theia or predated Theia, because in either case, the water was present on Earth when the late veneer came.

Thermochemical Model
The redox state of gases in equilibrium with rocks is often described by mineral buffers that govern the capacity of the rock to consume or release oxygen. Three such buffers are described in Appendix A. Mineral buffering is most likely to matter when the rock-to-atmophile ratio is large, as it is in meteorites or for Earth-like planets considered as a whole. Mineral buffers are less obviously appropriate for describing the interaction of meteorites with oceans and atmospheres that are much bigger than the meteorite (Elkins-Tanton & Seager 2008). Only the very biggest post-Moon-forming impacts are big enough for a mineral buffer set by the impactor to apply on a global scale. For anything smaller, the oxygen in the atmosphere and ocean much exceeds the reducing power in the impactor, and hence, the reduced mineral buffers are exhausted before the atmosphere and ocean can fully equilibrate (Elkins-Tanton & Seager 2008;Schaefer & Fegley 2017). What this means is that, in most cases, a better approximation than hewing to a mineral buffer is to stoichiometrically remove the oxygen scavenged by metallic iron from the atmosphere and ocean and then compute the resulting equilibria among the gases.

Equilibrium Chemistry
We solve for five potentially major gases-H 2 , H 2 O, CO, CO 2 , and CH 4 -while presuming that other gases are minor. In particular, we treat nitrogen as a minor perturbation, and we ignore sulfur and chlorine. We treat the equilibrium chemistry of the atmosphere as a whole. We solve for the column number densities N j and for the partial pressures p j of the five species. The total pressure p is the weight of the atmosphere, where g is the gravity and m j is the mass of species j. Partial pressures p j are related to column densities and the total pressure by Note that, in general, ¹ p Nm g; j j j i.e., partial pressures are proportional to number fractions, not mass fractions.
In the five gas system, hydrogen and carbon are conserved: In the absence of a mineral buffer, oxygen is also conserved, The other two relations needed to close the system are chemical equilibria. We use the water gas shift reaction As is customary, partial pressures in Equations (6) and (7) are in atmospheres. Equilibrium constants given here are low-order curve fits (Zahnle & Marley 2014) generated using thermochemical data from Chase (1998). When oxygen is controlled by a mineral buffer, oxygen is not conserved, and a third chemical equilibrium reaction is needed to link the system to the mineral buffer. The mineral buffer supplies the oxygen fugacity f O 2 , which has units of pressure. We use We will suppose that the gas remains equilibrated with the mineral buffer until the metallic iron is either exhausted or physically removed from interaction with the gas. This fixes the total oxygen content of the atmosphere. Thereafter, the gasphase chemistry continues to evolve with oxygen conserved in response to further cooling until the gas-phase reactions themselves quench. It is convenient to treat nitrogen species as minor perturbations, solved separately for fixed amounts of the five important CHO species. Separating N also facilitates taking into account that nitrogen species quench at higher temperatures than H, C, and O. This simplification is accurate provided that NH 3 is not a major gas. Nitrogen is conserved, Two chemical equilibria are needed, one for ammonia Equations (10) and (11) reduce to a quadratic equation for NH 3 . In practice, HCN is never produced abundantly by shock heating in the large impacts and H 2 O-CO 2 atmospheres considered in this study. The chief source of HCN in this study is photochemical, discussed in Section 4 below.

Quenching
Chemical reactions are generally fast at high temperatures, and chemical equilibria are quickly established between major species. As the gas cools, chemical reactions between the more stable molecules slow down until, for all practical purposes, they stop, and the gas composition is said to have quenched or frozen (Zel'dovich & Raizer 1967). Here, we ignore possible catalysts and address only gas-phase chemistry, which is the most pessimistic case for methane and ammonia. We employ two quench points, one for the H 2 -H 2 O-CH 4 -CO-CO 2 system and a significantly hotter one for the H 2 -N 2 -NH 3 -HCN system.
We have characterized quench conditions for CO hydrogenation to CH 4 and for N 2 hydrogenation to NH 3 in browndwarf atmospheres Zahnle & Marley (2014). There, we devised curve fits to global quench temperatures for the key chemical systems using a time-stepping thermochemical kinetics code employing nearly 100 chemical species and more than 1000 chemical reactions. Our curve fits are degenerate between total pressure and the H 2 partial pressure, because these are the same in brown dwarfs. For making CH 4 , our model predicts that quenching is linear with p at low pressures but quadratic with p at high pressures. The low-pressure quench temperature is The timescale t c is in seconds. The high-pressure form is The quench temperature is the smaller of the two, Other published estimates of quench conditions in the CH 4 -CO-H 2 system (see Prinn & Barshay 1977;Line et al. 2011;Visscher & Moses 2011) are similar enough that they also predict CH 4 -dominated atmospheres for the cases where we predict them; the different chemical quenching times are explicitly compared in Zahnle & Marley (2014). Quenching in the NH 3 -N 2 system occurs at higher temperatures, There is considerable uncertainty regarding the mechanisms of N 2 hydrogenation, with resulting considerable uncertainty in quenching times. The older estimate by Prinn & Fegley (1981) predicts slower chemistry, while two more recent estimates (Line et al. 2011;Zahnle & Marley 2014) give similar results for conditions encountered here. In practice, the different kinetics predict similar chemical compositions (Zahnle & Marley 2014), because the NH 3 /N 2 ratio is not strongly sensitive to temperature. Figure 1 illustrates quenching after a Vesta-scale impact.

Cooling Times
Impacts that vaporize the oceans create globally hot, highpressure conditions that can last for thousands of years. The energy invested in evaporating water and heating the major atmospheric gases in an ocean-vaporizing impact is where the fiducial masses correspond to an ocean of water, a 100 bar CO 2 atmosphere, and a 1 bar N 2 atmosphere, respectively. Evaporating the oceans and heating the steam to the temperature of the condensing rock vapor are the big terms in the energy budget for impacts of this scale. This energy is compared to the impact energy If half of the impact energy is spent heating and vaporizing water (with the other half deeply buried and unavailable on timescales shorter than thousands of years, or promptly radiated to space at higher temperatures in the immediate aftermath of the event), a Vesta-size impact can evaporate and heat 2.3 oceans of water. The maximum HSE impact exceeds the Vestasize impact by a factor of 100. Put another way, an EH-like (high iron, enstatite chondritic) impact creates 100 times more steam than hydrogen. The characteristic cooling time t c is approximated by how long it takes for the steam atmosphere to cool to the quench point. Quench temperatures for methane and ammonia will be hotter than waterʼs critical point, so we ignore the latent heat released by condensation.
where A ⊕ is the area of the Earth, and F ir ≈1.5× 10 5 ergcm −2 s −1 is the radiative cooling rate of a terrestrial steam atmosphere with a 50% albedo after the Sun has reached the main sequence (ca. 50Myr). This cooling rate is valid provided that water clouds condense somewhere in the atmosphere (Abe & Matsui 1988;Nakajima et al. 1992). For methane, for which quench temperatures are of order 800K, the relevant cooling is from 1400 to 800K. Evaluated, which is of the order of 1000 yr for most cases we consider. For NH 3 , whose quench temperature is ∼300 K hotter than methaneʼs, the cooling time is about half as long.
If an impact is too small to fully vaporize the ocean, the ocean remains cool and acts as a heat sink that competes with thermal radiation to space. In the relevant case, the impact leaves the atmosphere much hotter than the ocean and mostly made of H 2 and water vapor. The lower atmosphere will therefore be stable against convection. Under these conditions, the flow of energy down to the ocean is limited by radiative transfer. To illustrate, compare the diffusive flux of downward radiation in the Eddington approximation (any astronomy textbook), to Earthʼs net cooling rate F ir . The gray approximation opacity of water vapor is κ≈0.1cm 2 g −1 (Nakajima et al. 1992). Assume 30 bar of 1100K steam as an example, for which the density at the surface is ρ=0.025gcm −3 and the surface temperature is 500K (both set by the boiling point). The temperature gradient appropriate to cooling the whole atmosphere is 600 (=1100-500)K over a 20km scale height. With dT/dz=3×10 −4 Kcm −1 , we estimate that » F 0.5 10 5 ergcm −2 s −1 , which is 30% of net cooling (F ir ) to space. The radiative flux  F is relatively small because ρκ is big. (In this example,  F would exceed F ir for impacts that generate less than 10 bar of steam.) We conclude that, in general, relatively little of the energy in a hot deep steam atmosphere will flow downward to the ocean. The chief exception would be if there is enough CO 2 that the much hotter atmosphere is nonetheless dense enough to sink in cooler steam. This might happen for smaller impacts in deep CO 2 atmospheres, and if it did, it would result in complications that we will not address here.

Results
We consider three classes of impact. (i) If the impact is big enough, it delivers enough iron to fully reduce all of the H 2 O and CO 2 at the surface. Under these conditions, the + « + Fe H O FeO H 2 2 equilibrium is likely to govern the oxidation state of the atmosphere throughout the cooling phase. Earthʼs maximum HSE impact was in this size range. The iron-wüstite (IW) buffer describes the simple reaction of iron and steam to make FeO (wüstite) and H 2 , and so it is likely to be kinetically favored in the short term. On longer timescales, the more reducing quartz-fayalite-iron buffer (QFI, effectively a buffer between iron and olivine) may dominate. Both mineral buffers favor CH 4 , but the QFI buffer would also consume most of the H 2 O in favor of H 2 . The latter outcome resembles the story proposed to explain the desiccation of Mars by Dreibus et al. (1989) and Kuramoto (1997).
A caveat is that, for impacts of this scale, the global ejecta blanket should have been tens of kilometers thick. Although the molten iron in the ejecta must have passed through the atmosphere and ocean to reach the surface- Genda et al. (2017b) estimate that more than half the iron is initially disseminated as mm-sized droplets-it is plausible that some of the iron was buried before it could react with H 2 O or CO 2 . If so, some of the reducing power of the impact would at first have been sequestered from the surface, only becoming Figure 1. Example of quenching after a Vesta-sized impact into an Earth with a pre-impact atmosphere containing 2bar CO 2 , 1bar of N 2 , and 1.85 oceans (500bar) of liquid water. Cooling (time) marches monotonically from left to right. Quench points for CH 4 and NH 3 H 2 -N 2 -NH 3 are indicated with stars. Solid lines show quenched compositions while dotted lines extend the equilibria to temperatures colder than the quench point for gas-phase reactions. Partial pressures are also affected by water condensation (T<650K).
available as reduced gases emitted to the atmosphere on a longer geologic timescale. Modeling the fate of iron in the postimpact mantle is beyond the scope of this study.
(ii) The oceans are fully vaporized but there is not enough metallic iron in the impact to reduce all of the H 2 O in the ocean to H 2 . Impacts on this scale leave much of the H 2 O and CO 2 unreacted. In such an impact, the ejecta blanket is not much thicker than the ocean is deep, and conditions at the surface are supercritical for water, promoting efficient chemical coupling of the water with the iron while the iron lasts (see Choudhry et al. 2014, and references therein). There are of the order of 10 such impacts in a representative maximum late veneer, and 1-3 in a minimum late veneer. We assume that in these events, the introduced Fe consumes oxygen from the water and CO 2 until all of the injected Fe is gone. Thereafter, the atmosphere evolves with its oxygen content (in H 2 O, CO, and CO 2 ) held constant. In these events, the steam atmosphere is deep, thick, and hot, and cooling is slow, conditions that strongly favor CH 4 and, to a lesser degree, NH 3 .
(iii) The impact is too small to fully vaporize the oceans. These events feature faster cooling times and lower atmospheric pressures, with the amount of steam generated proportional to the energy released by the impact. The lower pressures are generally much less favorable to CH 4 formation, but small impacts are interesting because there are more of them and they are likelier to be survived by life or its precursors. For small impacts, we will find that the QFM mineral buffer often generates a more reduced gas composition than predicted from scavenging by impact iron of the oxygen in the hydrosphere and atmosphere. For these events, we will presume that the ferrous iron already present in the crust is available as an additional sink of oxygen at the QFM buffer. These matters are discussed in more detail below.
We treat the volume of the ocean and the amount and state of carbon in the atmosphere before the impact as initial conditions. For water, we assume that 1.85 oceans of water (5km) were present at the surface. Bigger oceans allow for more extensive loss of hydrogen to space without desiccating the planet. We take the view, provisionally, that a much drier planet (=1 ocean) will not evolve to Earth as we know it.
Carbon reservoirs are not well constrained. Between surface, crust, and mantle, Earth may hold the equivalent of 200±100 bar of CO 2 (Sleep & Zahnle 2001;Dauphas & Morbidelli 2014). One end-member is hot and oxidized, with CO 2 being initially divided roughly equally between a melted QFM mantle and Henry Law partitioning of 100 bar of CO 2 in the atmosphere in the aftermath of the Moon-forming impact (Holland 1984;Abe 1997;Zahnle et al. 2007;Elkins-Tanton 2008). An oxidized mantle could have been consequent to a previous history of hydrogen escape or to iron-mineral disproportionation (Frost & McCammon 2008). CO 2 can also be generated from thermal decomposition of carbonate minerals if these were near the surface. Although we do not explicitly consider more reduced atmospheres (CO or CH 4 ) as initial conditions, we will find below that thick CO or CH 4 atmospheres can be long-lasting in the Hadean. The CO 2 atmosphere is the most oxidized and, hence, the most conservative case. We treat p CO 2 as a free parameter. Table 1 lists a sampling of possible Hadean impacts. Before impact, Earth is presumed to have had 1.85 oceans of water at the surface (500 bar, 28.3kmolscm −2 ) and one bar (36molescm −2 ) of N 2 in the atmosphere. The amount of CO 2 varies between examples. "100 bar" of CO 2 corresponds to 2300molescm −2 . Figures 2 and 3 show post-impact atmospheres for a wide range of impact sizes for 2 and 50 bar of CO 2 . Figure 2 shows column densities (molescm −2 ), which makes the chemical trends clear, while Figure 3 shows the same information as partial pressures. The reducing power of the impactors presumes high iron EH (enstatite) or H (ordinary) chondritic bodies (33% Fe by mass, which also approximates the bulk Earth). Impact energy assumes an impact velocity of 17kms −1 . Table 1 lists major product gases for each case. Many of the cases listed in the table are used as initial conditions for photochemical evolution in Section 3 below. If the Fe is incompletely used up, the corresponding impact mass can simply be scaled up; i.e., if half the Fe goes unreacted, the required impactor would have twice the mass.
The maximum HSE impact delivers marginally enough Fe to fully reduce the atmosphere and hydrosphere, which suggests that equilibration with a mineral buffer may be plausible. Table 1 lists several maximum HSE cases with 100 bar of CO 2 equilibrated to different buffers. The QFI buffer, which would also fully reduce the atmosphere and hydrosphere, seems likeliest if the reactions all go to completion. But if much of the iron is buried before it reacts, a more oxidized buffer might be more reasonable.
In the next category, the "Pretty Big" cases approximate the biggest impact in our lower bound late veneer, while "Ceres" and "Vesta" are impacts with the mass of the real Ceres and the real Vesta. These are all ocean-vaporizers, but none deliver nearly enough iron to fully reduce the ocean.  Quenched impact-induced transient atmospheres as a function of impactor mass (EH composition) for two pre-impact atmospheres, one with 50 bar of CO 2 and the other with 2 bar. Both have 1bar of N 2 and 1.85 oceans (500bar) of water on the surface. Inventories are shown in moles to highlight the chemical transformation. A Vesta-size impact is indicated by the shaded vertical bar. Potentially ocean-vaporizing impacts are indicated by lighter shading. A rough guide to the number of impacts of a given size is listed across the top. In these models, all reducing power is furnished by the quantitative reduction of the impactorʼs Fe to FeO; no mineral buffering is assumed. In the maximum late veneer impact (at right), nearly all CO and CO 2 are converted to CH 4 . compares outcomes as a function of pCO 2 for Ceres-sized impacts.
The third category is represented in Table 1 by two "sub-Vestas" and the lunar South Pole-Aitken impact that do not fully evaporate the oceans. These are small enough that life or its precursors might survive. These impacts are also too small to deliver enough metallic iron to reduce the ocean to the QFM composition. This means that the reducing power of Earthʼs mineral buffers-made active by the heat of the impact-needs to be taken into account. The South Pole-Aitken basin is an example of a relatively minor event. Table 1 lists two sub-Vestas. The first uses only the reducing power of the impact. This is the most pessimistic case. The other assumes equilibration with a crustal QFM mineral buffer, but at an arbitrary lower quench temperature of 650K. In effect, the second case asks what happens if supercritical water was in itself enough to ensure that the coupled H 2 -H 2 O-CO-CO 2 -CH 4 -N 2 -NH 3 system equilibrated on a 1000-yr timescale. This can be viewed as the optimistic limit on what sub-ocean-vaporizing impacts can do to generate species like CH 4 and NH 3 . Figure 5 illustrates the potential inherent in the more optimistic case. Here, we assume that the atmosphere and ocean remain chemically equilibrated with the crust or mantle at the QFM buffer while water remains supercritical; i.e., we set T q =650K. The QFM buffer is only weakly reducing because it has only Fe +2 to offer as a reductant. On the other hand, there is a great deal of Fe +2 available in impact-heated crust and mantle materials, although the crustal source is not inexhaustible.
To illustrate these considerations, in Figure 5, we estimate the depth in the crust (global average) to which FeO must be oxidized to Fe 3 O 4 (magnetite), assuming that the crust was 10% FeO by mass and that all of the FeO is oxidized to Fe 3 O 4 , and taking into account the reducing power delivered by the impact as metallic iron. Figure 5 presumes a pre-existing atmosphere with the equivalent of 2 bar of CO 2 and one bar of N 2 . The figure shows that, even in a Vesta-scale impact, the required reducing power can be extracted from FeO in the uppermost 3km of a QFM crust. Smaller impacts use less of Earthʼs FeO because they do not evaporate the entire ocean, while larger impacts (larger than 4×10 23 g in Figure 5) deliver more metallic iron than needed to maintain QFM.

Photochemical Evolution of Impact-generated Transient Atmospheres
Our goal in this section is to model the photochemical decay of the impact-generated transient reduced atmosphere. In particular, we are interested in what happens to methane. The key processes driving the atmosphereʼs evolution are ultraviolet photolysis and hydrogen escape. Thus, fundamentally, we are most concerned with counting the photons and apportioning their effects.

The Photochemical Model
In the photochemical model, we consider six major species: H 2 , CH 4 , H 2 O, CO 2 , CO, and N 2 . Minor species include HCN (nitriles), C 2 H n (a mix of C 2 H 2 , C 2 H 4 , C 2 H 6 ), and organic haze. Other molecules and free radicals that are considered include NO, NH, N( 4 S), N( 2 D), O( 3 P), O( 1 D), 3 CH 2 , 1 CH 2 , CH 3 , and OH. We refer to ground-state N( 4 S) as N, ground-state O( 3 P) as O, and ground-state 3 CH 2 as CH 2 . Key reactions are listed in Appendix B. Atomic H is implicit and lumped with H 2 for accounting purposes. Ions are not explicitly included, although the first-order effects of ion chemistry are taken into account as loss processes for CO 2 and CH 4 (Appendix C).
Our purpose is to construct the simplest model that captures the first-order consequences of photochemical evolution of unfamiliar atmospheres, while conserving elements and counting the photons. Anything more complicated (e.g., a 1D atmospheric photochemistry code) would necessarily introduce several poorly constrained free parameters. We therefore assume that the major atmospheric constituents are uniformly distributed vertically, affected only by the totality of chemical and physical sources and sinks. We treat each major species j as a column density N j (units of number per cm 2 ). Ultraviolet photons are sorted into several spectral windows, and the effects of photolysis are apportioned in accordance with the first-order consequences of photochemistry; these simplifications will be discussed in detail below. The columns are evolved through time by integrating dN j /dt. Hydrogen escape and the effectively irreversible photolysis of methane impose direction.
There are two first-order complications to the simplest model that demand attention. First, H 2 O-usually the most abundant gas after the impact-condenses to make oceans. Thereafter, its abundance at stratospheric altitudes where photolysis takes place is limited by the atmosphereʼs cold trap. Water vapor is key to these models because water vapor is often the major oxidant. The drier the stratosphere, the more slowly it evolves and the more likely it is to favor reduced products like hydrocarbons. A next-generation study might investigate the water vapor contents of self-consistent radiative-convective atmospheres, but this level of modeling goes beyond the scope of this study. Here, we treat stratospheric water vapor in the atmosphere as a free parameter.
The second complication is the shadow cast by organic hazes. Organic hazes are expected when methane is abundant and subject to UV photolysis (Trainer et al. 2006;Hörst et al. 2012Hörst et al. , 2018. The analogy is Titan. We expect Earthʼs hazes, when present, to be optically thick, much thicker than on Titan today, because UV irradiation of early Earth was at least 1000 times greater than of modern Titan. Here, we follow Wolf & Toon (2010) and parameterize haze optical depth as a function of haze production rate. Because water photolysis would be the major source of oxidants in a methane-rich atmosphere, the competition between hazes and water for UV photons creates a positive feedback in which one or the other dominates.

Irradiation
We divide the solar FUV and EUV spectrum into six windows that align with particular properties of the atmosphere ( Table 2). We neglect the Lyman continuum (80-91.2nm, current photon flux of 8×10 9 cm −2 s −1 ) as filtered out by atomic H. Absorption at wavelengths longer than the Lyman continuum usually leads to dissociation of molecules into two neutral species. Absorption at wavelengths shorter than the Lyman continuum usually ionizes the molecule, leaving the molecule provisionally intact as an ion.
The ancient Sun was a stronger source of EUV radiation than is the modern Sun. We scale the different channels according to the general rule that hotter source regions are relatively more enhanced by solar activity and were therefore relatively more enhanced when the Sun was young (Zahnle & Walker 1982;Claire et al. 2012). Enhancement factors for the different windows are listed in Table 2.
Total column photolysis rates Φ j (cm −2 s −1 ) for species j allow for competition for photons between species, where k is an index running over the species. This approach conserves photons, which is the principal requirement here. Photoionization is treated separately, Organic hazes, when present, may provide UV protection to the deeper atmosphere (Sagan & Chyba 1997;Pavlov et al. 2001;Wolf & Toon 2010). Wolf & Toon (2010) constructed a microphysical model of organic hazes of early Earth. They considered spherical haze particles and "fractal" haze particles, with the latter model much preferred by its authors. We fit power laws to the fractal haze optical depths listed in their Table S1 as a function of the haze production rate,  . Quenched impact-induced transient atmospheres as a function of how much CO 2 was in the atmosphere before the impact, for two sizes of impact, one ocean-vaporizing and one not. The pre-impact Earth has 1 bar of N 2 and 1.85 oceans (500bar) of water on the surface. The Ceres-sized (10 24 g) impact (EH) is big enough to convert thinner CO 2 atmospheres to CH 4 , but it does not have enough Fe to fully reduce the thicker CO 2 atmospheres. The smaller "sub-Vesta" impact is too small to fully vaporize 1.85 oceans; the chief effect is to make a lot of H 2 . Figure 5. The left-hand axis shows gas compositions as a function of impact mass when quenching is assumed to take place at 650K (waterʼs critical temperature). Solid lines for smaller impacts (M i <4×10 23 g) show gas compositions in equilibrium with the QFM mineral buffer. The right-hand axis shows the depth (shading) to which FeO in the crust must be oxidized to magnetite (Fe 3 O 4 ) to maintain equilibrium with the QFM buffer at 650K. Dashed lines for gas compositions generated by bigger impacts (M i >4×10 23 g) are determined by metallic iron delivered by the impact. These latter compositions are no more reduced than the otherwise comparable compositions seen for gas-phase quenching in Figure 2 above, but the assumed low 650K quench temperature favors CH 4 and NH 3 over H 2 .
The ultraviolet optical depth refers to 197 nm, and the visible optical depth refers to 564 nm. We have converted units from production in grams per year to the equivalent number of carbon atoms cm −2 s −1 , which are the units used in this paper. Haze production rates on early Earth can exceed 1×10 12 carbonatomscm −2 s −1 , which corresponds to UV and visible fractal haze optical depths of the order of 160 and 6, respectively.
Hazes can suppress H 2 O photolysis if the stratosphere is dry. This can lead to a positive feedback that encourages haze formation. As hazes thicken, there is less H 2 O photolysis and less oxidation, which favors more haze formation. The consequence of this positive feedback resembles a phase change, in which much of the carbon derived from methane photolysis polymerizes into a wide range of heavier, generally oxygen-deficient organics (which we loosely refer to as "haze") that precipitate to the troposphere and probably to the surface.
In wetter stratospheres, haze formation competes with oxidation consequent to H 2 O photolysis. The organics and hazes that form under these conditions will contain more oxygen, suggesting a relatively greater role for acids, aldehydes, carbonyls, and other more water-soluble molecules that are more likely to rain out when they reach the troposphere. These may be essential ingredients for genesis of ribose for the RNA world (see Benner et al. 2019b).

Photolysis
Methane photolysis is dominated by Lyα radiation. Methane photolysis at Lyα mostly yields an excited methylene radical 1 CH 2 plus hydrogen (Huebner et al. 1992). Singlet methylene can be collisionally de-excited to the less reactive triplet 3 CH 2 , or it can react with CH 4 or H 2 to make CH 3 radicals. We will refer to these small radicals generically as CH n . Both CH 2 and CH 3 react very quickly with atomic N from N 2 photolysis to make C-N bonds or with atomic O from CO 2 photolysis to make C-O bonds. The C-O bonds once formed are difficult to break photochemically. The N reactions are the primary sources of HCN in a CH 4 -N 2 irradiated atmosphere. We neglect the possible catalytic role of N 2 through the CH 2 N 2 (diazomethane) intermediary.
Competition for Lyα photons is limited. We do not expect scattering by atomic hydrogen to be significant, because the solar Lyα emission is much broader than the velocity dispersion in hydrogen atoms at atmospheric temperatures. CO 2 has a very small cross section to Lyα, only about 0.5% of methaneʼs. Both H 2 and CO have hot absorption lines that partially overlap with Lyα emission. Resulting fluorescence has been seen in planetary nebulae (Lupu et al. 2006) and cometary comae (Lupu et al. 2007), respectively. However, the effect requires ro-vibrationally excited H 2 and CO molecules and, hence, is unlikely to be important at relevant conditions. Waterʼs cross section at Lyα is about the same as methaneʼs, but we do not expect H 2 O to be abundant at the highest altitudes once the cold trap has been established in the lower atmosphere. What this all means is that, when methane is abundant, Lyα photochemistry takes place high in the atmosphere, aligning it with N 2 photolysis and generally favoring the production of organic hazes and nitriles. When methane is not abundant, Lyα photochemistry takes place deeper in the atmosphere, which better aligns methane photolysis with CO 2 photolysis and H 2 O photolysis, an alignment that favors methane oxidation and disfavors nitrile production.
Nitrogen (N 2 ) photolysis is dominated by several very strong narrow absorption bands that coincide with solar emission lines. Huebner et al. (1992) stress the importance of the overlap between a strong N 2 band and solar Ly γ (92.25nm). Comparison between the solar spectrum (Curdt et al. 2001) and the N 2 absorption spectrum predicted by Liang et al.
Notes. a Photoionizing EUV excluding the Lyman continuum. b EUV 2 excludes photoionizing radiation and radiation that photolyzes N 2 . c EUV-N 2 is the portion of non-photoionizing EUV that coincides with N 2 absorption. d Quiet Sun irradiance, photons cm −2 s −1 at 1 au. e Young Sun enhancement over modern quiet Sun.
from a suite of discordant experiments that the N 2 photolysis cross section at Ly γ is of the order of 2.5×10 −16 cm 2 . Nitrogenʼs chief competition for photons is with CO 2 , which has big cross sections of order 4×10 −17 cm 2 at wavelengths where N 2 absorbs. Molecular hydrogen also absorbs at some of these wavelengths, Ly γ in particular, but cross sections are generally smaller than 10 −18 cm 2 . For the quiet Sun at Earth, we estimate a total N 2 photolysis rate of 3.6×10 9 cm −2 s −1 , which agrees well with what Liang et al. (2007, their Figure2) compute for Titan when scaled to 1 au.
Photolysis between 91.2 and 100nm splits N 2 into a groundstate N atom and an electronically excited N( 2 D). The N( 2 D) can react with H 2 or CH 4 to make NH, react with CH 4 to make CH 2 NH, and react with CO 2 to make CO and NO (Herron 1999). Both NH and NO react rapidly with N to reconstitute N 2 . Otherwise, the most important N and NH reactions are with hydrocarbon radicals to make HCN and other nitriles, such as acetonitrile (CH 3 CN) and cyanoacetylene (HCCCN). Photolytic production of HCN has been predicted to work well in an N 2 -CO 2 atmosphere (Zahnle 1986;Tian et al. 2011). Photochemical organics have been hypothesized as a source of reduced nitrogen and reduced carbon that can be subducted by the mantle (Wordsworth 2016).
At the top of the atmosphere, CO 2 photolysis is dominated by EUV wavelengths between 91.2 (the Lyman limit) and 115nm. Weaker absorption at FUV wavelengths between 130 and 180nm can be as important if other absorbers are not abundant. At FUV wavelengths, CO 2 photolysis usually creates a ground-state CO molecule and a highly reactive O( 1 D) atom.
At the shorter wavelengths, photolysis can also yield electronically excited CO and a ground-state O atom (Huebner et al. 1992). We will assume that excited CO is de-excited by collisions.
The O( 1 D) atom is highly reactive, including reaction with CH 4 to liberate CH 3 . Key O( 1 D) reactions are listed in Appendix B. It can be de-excited to the less reactive O( 3 P) ground state by collisions with CO 2 , N 2 , and CO, but it reacts quickly with CH 4 and H 2 . By contrast, reactions of groundstate O with CH 4 and H 2 are negligibly slow at 300 K. We therefore take the initial reaction of O( 1 D) with CH 4 as the ratelimiting step for CH 4 loss from CO 2 photolysis. Subsequent reactions of O with free radicals like CH 3 are fast and result in CO bonds.
Carbon monoxide has a similar spectrum to N 2 , but unlike N 2 , few of its bands align with strong solar emission lines. CO dissociation into neutral atoms is dominated by the Lyman continuum (Huebner et al. 1992) and, hence, is relatively unimportant in hydrogen-rich atmospheres.
Water photolysis yields OH and H for FUV with λ<190 nm. If the stratosphere is very dry, organic hazes have potential to shield H 2 O from photolysis, especially at wavelengths λ>182 nm, where H 2 Oʼs cross section starts to fall off rapidly with increasing λ.
Because we do not distinguish between H and H 2 , hydrogen photolysis is important only as opacity.
Ammonia is swiftly photolyzed by UV radiation between 185<λ<215 nm at wavelengths where H 2 O and CO 2 absorptions are very weak. The products are highly reactive NH and NH 2 radicals (Huebner et al. 1992). These can lead to N 2 formation, but they can also react with hydrocarbons if the latter are plentiful.

The Methane Budget
Methane ends up either as organics or HCN, or is oxidized to CO or CO 2 . While CH 4 is preponderant, photochemistry following photolysis will tend to generate hydrocarbons (Lasaga et al. 1971;Yung & Pinto 1978;Zahnle 1986;Trainer et al. 2006;Hörst et al. 2018) and nitrogenous organics. When CO 2 is preponderant, methane is more often oxidized to formaldehyde (HCHO) or CO.
Methane can also be oxidatively attacked by products of H 2 O photolysis and CO 2 photolysis. The most important of these are O( 1 D) atoms from CO 2 photolysis (R32) and OH from H 2 O photolysis or reaction of O( 1 D) with H 2 . (Reactions of CH 4 with H and ground-state O atoms are slow unless the gas is much hotter than we have assumed, while reaction with N( 2 D) typically creates nitriles.) OH reacts fairly rapidly with CO to make CO 2 , and more slowly at room temperature with H 2 or CH 4 to yield H 2 O. The reactions of OH with H 2 and CH 4 are sensitive to temperature, while the reaction with CO is not. At 300K, OH+CO→CO 2 is about 20× faster than reaction with H 2 or CH 4 , and at 250K, it is about 100× faster.
Column oxidative loss of CH 4 is approximated by loss reactions with O( 1 D) from CO 2 photolysis and OH from H 2 O photolysis:

Hydrocarbons and Organic Hazes
Reactions between CH, CH 2 , and CH 3 lead to acetylene, ethylene, ethane, and eventually to more complicated hydrocarbons that can form a high-altitude haze. The chief competing reactions are those with O or OH radicals. We lump acetylene, ethylene, and ethane together as C 2 H n hydrocarbons. We equate the creation of CH n radicals to the appropriate destruction rate of CH 4 , Hazes are generally ineffective at shielding molecules from photolysis at wavelengths where an abundant gas absorbs strongly, because hazes make up a very small mass fraction of the atmosphere. Where hazes can matter is in shielding a gas of very low abundance at wavelengths that would otherwise be transparent. The cases of interest here are H 2 O, which can be cold-trapped, and NH 3 .

CO and CO 2 Budgets
The CO 2 budget is a balance between photolytic losses and CO oxidation, The latter reaction, although spin-forbidden, is important at high pressure in a dry CO-rich atmosphere in the absence of catalysts. The CO budget reverses the CO 2 budget and also includes the net oxidation of CH 4 as a source, while treating precipitation of organic hazes and nitriles as a carbon sink. This model of CO and CO 2 gives a better description of the sum of CO and CO 2 than it does of CO and CO 2 individually. Within the model, speciation between CO and CO 2 is sensitive to H 2 O (the only oxidant). We suspect that our model overpredicts CO at the expense of CO 2 .

Nitrogen and HCN Budgets
In the anoxic atmospheres relevant to this study, nitrogen chemistry leads either to nitriles (e.g., HCN)  The H 2 CN radical leads to HCN. Reaction paths through NO and HNO end in reactions with N that reconstitute N 2 . These are the most important paths when CO 2 is abundant. The NH radical can be important when H 2 is very abundant, but under these circumstances, NH is more likely to be recycled to N 2 than to react with CH n to form C-N bonds. Ground-state N reacts quickly with CH n to make HCN, or if CH n is not abundant, it can be recycled to N 2 through reactions with NH or NO, or following reaction with OH. For most cases of interest here, OH is strongly suppressed by reactions with abundant CO or H 2 . Ammonia can be abundant after some impacts. As a placeholder, we assume that it is photolyzed If methane is also abundant, ammonia photolysis probably leads to amines, but if H 2 is more abundant, ammonia photolysis will mostly end with reconstitution of N 2 . The fraction of NH 3 photolyses that lead to amines or nitriles is approximated by Reactions of NH n with H 2 will reconstitute NH 3 and can be ignored. Efficient formation of cyanamide (NH 2 CN) may require NH 3 . Net HCN, nitrile, and amine production is approximated by ⎛ where f 1x represents the fraction of excited N( 2 D) atoms produced that are available to make HCN, A convenient simplification is that these are reduced atmospheres with no net production of nitrogen oxides. The chief chemical sinks of HCN are addition reactions with OH and H. The direct reaction with OH has an exothermic branch with products CO and NH 2 , but the substantial rearrangements required to get these products require leaping over two energy barriers (Dean & Bozzelli 2000). The climb over the first barrier gives, as one possible set of products, atomic H and HNCO (isocyanic acid). Addition reactions with H or CH n can lead eventually to full hydrogenation through various intermediates including cyanamide and methlyamine. Like oxidation, these paths are expected to be kinetically inhibited.
The important physical sink is rainout. HCN is not very soluble in water (its Henry Law coefficient is not very high) but it is miscible. Total nitrile production is approximated by

Hydrogen and Hydrogen Escape
The most important loss process for hydrogen is escape and its most important sources are CH 4 photolysis and oxidation, and water photolysis. Zahnle et al. (2019) found that, for a wide range of solar EUV fluxes and hydrogen mixing ratios, hydrogen escape from a terrestrial CO 2 -H 2 atmosphere can be approximated by where A=2×10 12 cm −2 s −1 and B 2 =0.006. Here, we use S 1 from Table 2 to scale EUV radiation to the levels appropriate to the young Sun. Equation (47) blends the energy-limited escape (the limit where S 1 is small) with the diffusion-limited escape (the limit where S 1 is large). Photochemical destruction of H 2 is not a concern for the hydrogen budget because in the diffusion limit, H and H 2 escape almost equally easily. Equation (47) is readily generalized to other planets and other atmospheric compositions by recognizing that A is proportional to the density of the planet and¸= A B ( ) - where H H 2 and H a represent the unperturbed scale heights of H 2 and the background static atmosphere at the homopause, and b ia represents the binary diffusivity between H 2 and the background atmosphere. The latter is roughly the same for CO 2 , CO, N 2 , and CH 4 (Marrero & Mason 1972 Other things equal, the diffusion-limited hydrogen escape rate is about three times greater in CO 2 than in CH 4 . We take the variation of B as a function of m a into account in our models.
Sources of H 2 are photochemical or geological. The direct source is methane: each methane lost creates the equivalent of two H 2 molecules. Another source of H 2 is the water that oxidizes carbon from CH 4 to CO and CO 2 . In evaluating this source, we hold H 2 O constant. The presumption is that water is in equilibrium with an ocean and re-supplied to the stratosphere as needed. Some hydrogen is removed from the atmosphere when it is incorporated in precipitating organics and nitriles. For these, we assume an H/C ratio of unity. The total rate of change of hydrogen is then

Photochemical Results
Here, we present some illustrative examples of photochemical evolution for impacts of several scales.

Vestas
A Vesta-scale impact is at the upper limit of what life might survive or prebiotic biomolecules might survive. Vesta itself is 525 km diameter and has about 1% of the mass of the entire late veneer. There is energy enough to evaporate two oceans of water, which leaves few refugia unless the oceans were comparably enlarged. Figure 6 shows evolution after a Vesta-size impact into a hefty pre-impact atmosphere holding 5 bar of CO 2 and 1 bar of N 2 , and 1.85 oceans (500 bar) of H 2 O. If all of the Fe is used, the impact creates 3.9 bar of H 2 and converts about 9% of the 5 bar of CO 2 into CH 4 (see Table 1). Subsequent photochemical evolution assumes 1ppm H 2 O in the stratosphere, slightly drier than modern Earthʼs. Production rates of HCN, C 2 H n species, and haze are roughly 30× larger than those on modern Titan, or comparable to modern volcanic emissions of SO 2 or modern lightning production of NO. Cumulative precipitation of organics is about 5 cm. Hydrogen equivalent to 45 m of a global ocean escapes to space over the course of the event.
We estimate the surface temperature by assuming that the troposphere follows a moist adiabat, with the tropopause at the skin temperature, We put the tropopause at 0.1bar, as it is in most solar system planets with atmospheres (Robinson & Catling 2014). The solar constant F e =1.36×10 6 ergcm −2 s −1 and the Stefan- Earthʼs modern surface temperature is recovered with albedo A=0.3 and γ=1.15. For early Earth, the young Sun is 72% as bright as the modern Sun (S=0.72). If we take 0.3<A<0.5, the ∼6 bar atmosphere (1.6bar CO 2 , 0.55bar N 2 , 3.9 bar H 2 , 0.17bar CH 4 ) implies a surface temperature T surf ∼320K. A proper radiative-moist-convective model would be required to provide better estimates of surface temperature and tropopause conditions. Figure 7, a more productive scenario than Figure 6, is obtained if the reducing power of FeO in pre-existing mantle and crust is exploited by lowering the quench temperature to the critical point of water and imposing the QFM buffer, as discussed above in the context of Figure 5. For a Vesta-size impact striking 2bar of CO 2 , 1bar of N 2 , and 1.85 oceans (500bar) of H 2 O, the result is 1.8bar of H 2 and conversion of more than 90% of the CO 2 into CH 4 and more than 10% of the nitrogen into ammonia (see Table 1). The subsequent photochemical evolution in Figure 7 assumes a dry 0.1ppm H 2 O stratosphere. Such dryness might be expected in a deep greenhouse atmosphere illuminated by the faint young Sun. Predicted production rates of HCN, C 2 H n species, and haze are roughly 1000× larger than those on modern Titan for about 0.7Myr. Cumulative precipitation of organics is about 10m. Hydrogen equivalent to 60 m of a global ocean escapes to space over the course of the event.

A "Pretty Big" Impact
Figures 8 and 9 document the profound influence of stratospheric moisture on atmospheric evolution after a bigger impact, here a "pretty big" 2.5×10 24 g EH-type body striking a 5bar CO 2 , 1bar N 2 atmosphere over 1.85 oceans (500bar) of liquid H 2 O. This approximates the largest event in a minimum late veneer extrapolated from the lunar cratering record, as discussed in Section 2 above. The surface temperature before the impact may have been in the range 310<T<340K (estimated using Equation (50)). There is enough energy released by the impact to vaporize 20 oceans of water or melt the crust to a depth of tens of kilometers. It seems unlikely that life on Earth could survive the immediate effects of an impact of this scale, but surface conditions 10,000 years later are plausibly temperate enough. This is an interesting scale for setting the table for life of the future (Benner et al. 2019a).
If all of the new iron reacts with water and CO 2 , this impact generates 8.4 bar of H 2 and converts nearly all 5bar of CO 2 into 0.4bar of CH 4 . The mean molecular weight of the air is 3 and the scale height is 100 km. These are hydrogen atmospheres resembling Neptuneʼs more than modern Earthʼs. Viewed in transit, such an atmosphere would add about 10% to Earthʼs apparent diameter, or put another way, it would lead a distant observer to conclude that Earth had a density of just 4gcm −3 .
The photochemical evolution in Figure 8 assumes 1ppm H 2 O in the stratosphere. The outcome is somewhat similar to that following the Vesta impact, differing mostly in the lack of CO 2 . Most of the methane is eventually oxidized. A small fraction of the CH 4 is built up into organics, nitriles, and hazes. Production of HCN, hazes, and C 2 H n organics is roughly 10 times faster than on modern Titan. Cumulative precipitation of hazes and nitriles is of the order of half a meter, with perhaps another half-meter of partially oxidized organic matter (e.g., organic acids and aldehydes stemming from partial oxidation of hydrocarbons). Hydrogen from 50bar (0.2 oceans, 500m) of H 2 O escapes over 4Myr. Oxidation in the dry stratosphere is too slow to convert CO to CO 2 on the timescale of this event. Figure 9 is the same impact as Figure 8, but evolving with a stratosphere that is 10 times drier (0.1ppm H 2 O). The drier stratosphere might be appropriate given the strong greenhouse effect of the deep troposphere and the faint Sun. The outcomes are quite different. The low rates of stratospheric H 2 O photolysis frustrate oxidation of small organics and, thus, allow the buildup of thick photochemical hazes (τ vis ∼5 at 560 nm according to the fractal model). In this example, fully 60% of the Figure 6. Photochemical dissipation of an atmosphere after the impact of a Vesta-sized body. The pre-impact atmosphere contained 5bar of CO 2 and 1bar of N 2 over 1.85 oceans (500bar) of H 2 O. This example assumes a dry (1 ppm H 2 O) stratosphere. The optical depth of organic hazes at 564nm τ vis is shown against the left-hand axis. Production rates of HCN, C 2 H n species, and haze are plotted against the right-hand axis. The H 2 escape flux is also plotted against the right-hand axis. Note that in this case, nitrile production ("HCN") continues well after the other hydrocarbons have dissipated; the residual optical depth-of order unity at 250 nm-is from nitrogenous hazes. Figure 7. Photochemical evolution after a Vesta-size impact assuming that the atmosphere and ocean equilibrate with the QFM buffer at 650K (see Figure 5). The pre-impact atmosphere contained 2 bar of CO 2 ; otherwise, conditions are the same as for Figure 6. The case is listed in Table 1. Figure 8. Photochemical dissipation of an atmosphere perturbed by a pretty big 2.5×10 24 g impact. The pre-impact atmosphere contained 5bar of CO 2 and 1bar of N 2 over 1.85 oceans (500bar) of H 2 O. Partial pressures are shown against the left-hand axis. This example assumes 1ppm H 2 O in the stratosphere, like Earth today. Production rates of hazes, C 2 H n species, and HCN are indicated against the right-hand axis. The H 2 escape flux is also plotted against the right-hand axis. Hydrogen from 50bar (0.2 oceans, 500 m) of H 2 O escapes over the course of the event.
impact-generated CH 4 is converted into organic precipitates (hazes), which correspond in cumulate to a global blanket 10-20 m thick. On the other hand, production of organic nitrogen is no greater because in both cases, it is limited by the rate of N 2 photolysis. Conditions gradually grow less, reducing until the methane is fully titrated and an abrupt bleaching event clears the skies. In the end, about 40% of the CH 4 is oxidized to CO, and the hydrogen from 0.15 oceans of H 2 O escape to space.

The "Maximum HSE" Impact
Other things equal, there is a small but significant statistical chance, of the order of 10%, that the last of the world-sterilizing events was also the biggest of them. Surface environments will not be habitable until well after the impact, but much can be done to prepare the planet for a more hopeful future. This approximates the impact discussed by Benner et al. (2019a).
We document two versions of a maximum HSE event, one with a very dry stratosphere and one somewhat moister. The simulations presume the impact on Earth of a highly reduced Pluto-sized dwarf planet, at a time after the Moon-forming impact when there were still 100bar of CO 2 at the surface. Other initial conditions are 1bar of N 2 and 1.85 oceans of water (500bar). The biggest impact differs from smaller impacts in two key respects: there is more iron than CO 2 and H 2 O at the surface, and the ejecta blanket is much deeper than the oceans. The former means that the mineral buffer should be important, while the latter hints that much of the metallic iron might at first be buried.
For specificity, we presume that the atmosphere and ocean equilibrate with the IW mineral buffer and that the remaining metallic iron is oxidized later on geological timescales. With these particular assumptions, the impact converts all of the CO 2 and 15% of the water to CH 4 . About 60% of the water (one ocean) remains as H 2 O. Expressed in moles, the atmosphere after the impact contains 6000moles H 2 percm 2 (40% of the hydrogen in Earthʼs current oceans) and 2300moles CH 4 percm 2 . Expressed as pressure, after the impact, the dry atmosphere would at first hold 35 bar of H 2 and 14 bar of CH 4 , with a mean molecular weight of 6. Because the surface temperature would be high, a great deal of water would remain in the vapor phase, and the actual mean molecular weight and partial pressures of H 2 and CH 4 would be correspondingly higher.

Figure 10 documents photochemical evolution with an
Earth-like (1ppm H 2 O) stratosphere. As with the pretty big impacts, this stratosphere is moist enough that oxidation following water photolysis is more important than polymerization of CH 4 . The photochemical source of organic matter (C 2 H n , HCN, haze) is nonetheless large, of the order of 100× that of modern Titan. This case generates a cumulative global blanket of 25m of haze organics, plus another 5 m of partially oxidized organics and 5m of nitrogen-rich organics. Much of the nitrogenous material would be amines stemming from impact-generated NH 3 . The hydrogen from 2.3km of water escapes (leaving one ocean of water behind). Cases with still wetter stratospheres closely resemble this one. Figure 11 documents photochemical evolution with the drier (0.1ppm H 2 O) stratosphere. The dry stratosphere leads to highly reduced conditions and rapid photochemical organic haze production at 10 3 × the rate on modern Titan. Haze optical depths in the UV exceed 100; visible optical depths are in the range of 4-8. More than 70% of the methane is polymerized into organic matter equivalent to a cumulative deposit of the order of 300-500m deep. In addition, about 10 m of nitrogenous material reaches the surface, much of which stems from impact-generated NH 3 that is photolyzed in the presence of abundant hydrocarbons, rather than from photochemical HCN. The rest of the methane is oxidized to CO. The hydrogen from 1.7km of water escapes. Cases with even drier stratospheres closely resemble this one.
Despite the thick organic hazes, the climates of the postimpact atmospheres may have been dominated by the greenhouse effect from tens of bars of H 2 and CH 4 (Wordsworth & Pierrehumbert 2013), and the surface temperature may have been 350-450K, or higher.

Sub-Vestas
Finally, we consider two impacts that are small enough that life or its precursors ought to survive. These have the potential to build on what may already have been accomplished. We look at two cases, the first using the same approach as we used for ocean-vaporizing impacts, and, as this turns out to be rather Organic hazes form with optical depths of order 3-5 at 564nm (τ vis ). Haze optical depth is plotted against the left-hand axis. In this example, production rates of HCN and C 2 H n species, indicated against the right-hand axis, are very large, about 500× what they are on modern Titan, or 2% of modern biotic productivity. Cumulative organic precipitation is of the order of 100molescm −2 . Figure 10. Photochemical evolution of a maximum HSE impact-generated atmosphere assuming 1 ppm H 2 O in the stratosphere. Initial conditions (100 bar CO 2 , 1.85 oceans of water) may be appropriate to the largest of Earthʼs post-Moon impacts. Partial pressures are shown against the left-hand axis. Water vapor is mostly confined to the troposphere and presumes a surface temperature governed by total atmospheric pressure according to Equation (50). Organic C 2 H n , HCN, and haze production (dashed curves) are mapped to the right-hand axis. The rate of hydrogen escape is also mapped to the right-hand axis. Haze optical depth at 560 nm (τ vis ) is plotted against the left-hand axis.
disappointing, we consider a second case for which the assumptions are more liberal and the outcome more bountiful.
The first example, Figure 12, uses only the free Fe of the impact to reduce water and CO 2 . This case assumes 5 bar CO 2 and 1 bar of N 2 in the atmosphere and 1.85 oceans of water on the surface before the impact. The impact evaporates about half the ocean, leaving deep waters less disturbed and some subsurface environments continuously habitable.
The atmosphere immediately after the impact holds 6.2 bar, mostly of H 2 and CO 2 . This evolves after hydrogen escape into a 5.4bar CO 2 -N 2 -CO atmosphere, with about 1 bar of CO left at the end of the simulation. For a short time, the atmosphere provides a modest source of nitriles (comparable to modern Titan), but the cumulative production of organic material over the course of the event is equivalent to just 1mm of precipitate. Unlike many of the cases we consider, the results are independent of stratospheric H 2 O, because CO 2 is the oxidant. The H 2 from 15 m of water escapes.
The alternative sub-Vesta case ( Figure 13) begins with the scenario presented in Figure 5 above, in which the atmosphere and ocean equilibrate with the QFM buffer at the critical temperature of 650K. As in Figure 5, we assume that before the impact, the atmosphere held 2 bar of CO 2 and one of N 2 . The low equilibration temperature favors methane and ammonia, which are both rather abundant in a 2.3bar atmosphere volumetrically dominated by 1.5bar of H 2 (see Table 1); although, most of the mass is in CH 4 , CO 2 , and N 2 . For the photochemical evolution, we assume a dry stratosphere (0.1ppm H 2 O).
The story told in Figure 13 is eventful. At first, the atmosphere still holds enough CO 2 to be weakly oxidizing and organic production is modest, but after the CO 2 is gone, stratospheric conditions become much more reduced, and organic production becomes considerable and stays so for about 0.5Myr. This second phase ends abruptly when the methane disappears. Cumulative production of organics is in the range of 2.5-5 m of hydrocarbons and nitriles. The H 2 from 40 m of water escapes. The asymptotic state features about a bar of N 2 and CO each, the latter slowly oxidizing to CO 2 on geologic timescales. Benner et al. (2019a) have suggested that the greatest of the late veneer impacts (corresponding to those we simulate in Section 4.2.3) created a transiently reducing surface environment on Earth ca. 4.35 Ga and that this environment lasted for about 15 million years. They also suggest that the origin of the RNA world dates to this interval. They emphasized the difficulty in generating the simple N-rich organic molecules like cyanoacetylene and cyanamide needed to make purines and pyrimidines by paths other than highly reducing atmospheric chemistry. Although the dates and timing of events are less certain than Benner et al. (2019a) seem to suggest, in broad brush, we find ourselves in general agreement. The quantity of reducing power is determined from the excess HSEs in the mantle. The timescale is set by the EUV radiation emitted by the young Sun. With due allowance for the uncertainty in both, a timescale in the general range of 10-100Myr is obtained by simply dividing one quantity by the other, and it cannot be hugely wrong. As to when these events took place, opinions can differ, depending on how much weight one places on the ability of zircons to record the evolving conditions at the Earthʼs surface (Carlson et al. 2014).

Discussion
A possible problem posed by the biggest impact is that, although it brings the most reducing power, it is also the most likely to leave the surface too hot to promote prebiotic Figure 11. Same as Figure 10 but with a drier (0.1ppm H 2 O) stratosphere. Water vapor is mostly confined to the troposphere and presumes a surface temperature governed by total atmospheric pressure according to Equation (50). In this case, the evolution is characterized by a very reduced stratosphere and a great deal of Urey-Miller-like abiotic organic production that consumes most of the CH 4 . Organic (C 2 H n , HCN, and haze) production rates (dashed curves) are mapped to the right-hand axis. Haze optical depth at 560nm (τ vis ) is plotted against the left-hand axis. Figure 12. A non-ocean-vaporizing impact. This case assumes 5 bar CO 2 and 1 bar of N 2 before the impact. Quenching is determined by gas-phase reactions. Partial pressures (solid curves) are plotted against the left-hand axis, while fluxes (dashed curves) are plotted against the right-hand axis. Note the prolonged production of HCN in clear skies. Figure 13. A non-ocean-vaporizing impact that assumes that the atmosphere and ocean equilibrate with the relatively oxidizing QFM buffer at 650K (i.e., at waterʼs critical temperature). Quenching is not determined by gas-phase reactions. This case assumes 2 bar of CO 2 and 1 bar of N 2 before the impact. Partial pressures are shown. evolution, and for a long time. Even ignoring CO 2 and CH 4 , the greenhouse effect provided by tens of bars of H 2 could raise the surface temperature to 400K or more. Adding CO 2 or CH 4 or other greenhouse gases would make the surface still hotter. Impacts that are 10-to 100-fold smaller may therefore seem preferable, as these are more likely to leave the surface in a temperate state, albeit the reducing conditions do not last as long as for the bigger events. In a more recent study, Benner et al. (2019b) concede the potential advantages of less enormous impacts,while making a new point: the transience of highly reduced impact-generated atmospheres lets the prebiotic system exploit other chemical pathways pertinent to the RNA world that work better in weakly reduced (QFM mantle-derived) atmospheres. These make use of volcanic SO 2 (S in a deeply reduced atmosphere would be in H 2 S), borates, and even the highly oxidized Mo +6 .
An important opportunity that we have not quantitatively addressed is the delayed oxidation of impactor metallic iron that escaped immediate oxidation by the ocean or atmosphere. This iron would instead have been oxidized by recycled surface volatiles over the course of geologic time, which may have been millions or many tens of millions of years. If the chief oxidant were water, the chief volcanic gas would have been H 2 . But if the chief oxidant were CO 2 (probably in the form of subducted carbonate), volcanic gases could have included significant amounts of the much more useful CH 4 . Methane abundances are sensitive to pressure, but to give a specific example, CH 4 becomes the most abundant C-containing gas at the QFI buffer at 1400K under 300 bar pressure, and it is still 10% at 1600 K. In the latter regime-one in which CO 2 must have been abundant in the atmosphere (else no carbonate) and CH 4 was abundant in undersea volcanic gases-the chief photochemical products would have been HCN and small organic acids, aldehydes, and carbonyls. This regime could have lasted for a long time, possibly tens of millions years or more.

Ammonia
Large impacts can generate considerable amounts of ammonia from hot H 2 and N 2 . Ammoniaʼs fate involves many processes that are more complex than what we have been considering in this study. Nonetheless, the inherent interest of ammonia as a constituent of the prebiotic environment is great enough that we will risk some speculations.
Ammonia is highly susceptible to UV photolysis at 185<λ<215 nm, where its cross section is of the order of 3×10 −18 cm 2 , at wavelengths where the solar photon flux is much higher than at the shorter wavelengths where H 2 O and CO 2 absorb. The products are NH and NH 2 radicals (Huebner et al. 1992) that swiftly react with each other, with oxygen, or with hydrogen in a series of reactions that efficiently recombine N 2 (Kuhn & Atreya 1979). Without the protection of highaltitude UV absorbers, a bar of NH 3 would revert to N 2 in less than 10 4 yr on early Earth.
However, if the atmosphere were also CH 4 -dominated, as it likely would be were NH 3 abundant, the resulting hydrocarbon hazes might provide UV protection (Sagan & Chyba 1997). Perhaps more important is that a significant fraction of the NH and NH 2 radicals that photolysis creates will have good odds of reacting with hydrocarbons to make amines and nitriles. Under these conditions, the coupled hydrocarbon-ammonia photochemistry would lead to amines and nitriles (Miller 1953).
The other factor to consider with ammonia is that it is very soluble in cool water and, hence, likely to rain out and partition into the ocean. The Henryʼs Law coefficient for NH 3 in water is K H =4.6×10 −5 e −4200/ T moles l −1 atm −1 . Much of the dissolved NH 3 hydrolyzes to ammonium, NH 4 + . Ammonium abundance is related to NH 3 (aq) and pH by in which the base constant K b is a weak function of temperature (Read 1982), 4.75 2.5 10 298 . 52 b 5 Expressing [ ] -OH in terms of pH and the auto-ionization constant K w of water (which can be crudely approximated as a function of T by 14 0.03 298 7.5 10 298 w 5 2 ), the ammonium/ammonia ratio is If all of the nitrogen currently in Earthʼs atmosphere were converted to NH 3 , the equilibrium NH 3 gas pressure above an ocean with pH of 7.8 and temperature 298K would be just 100 mbar (yet enough to generate a considerable greenhouse effect). The other 1.56 bar of N would be dissolved in the oceans, 97% as + NH 4 . Hotter oceans are interesting. At 373K, other things equal, the + NH NH 4 3 ratio would drop to ∼2. The equilibrium NH 3 gas pressure over the ocean would be 0.02 bar. The other 1.54bar of NH 3 would be in the oceans, divided between + NH 4 and NH 3 . At 500 K, the pH would be another unit lower, and + NH 4 less abundant than NH 3 . The equilibrium NH 3 gas pressure in the atmosphere rises to 0.7-1.0 bar, with the rest of the N divided between NH 3 and + NH 4 dissolved in the ocean. In this case, the ammonia would probably be photochemically destroyed very quickly, although many of the products would be prebiotically interesting if CH 4 were also abundant.
This exercise suggests that NH 3 would last the longest as ammonium ions in cold seas under an organic haze, conditions rather similar to those sometimes imagined for early Titan. We speculate that ammoniaʼs powerful greenhouse effect can lead to a strong positive feedback between ocean temperature and exsolution that would in turn speed ammoniaʼs photochemical destruction. It is not obvious that keeping ammonia around for a long time is a better option for prebiotic purposes than a rapid dump of a wide variety of nitrogenous products into warm oceans. Here, we simply present these cases as end-members. Figure 14 presents a notional history of water, methane, and HSEs on early Earth in response to late great impacts. The last stage of this impact history is evident on the face of the Moon and is often called the "late heavy bombardment," often referred to as the "LHB." Water on Earth probably accreted before the Moon-forming impact, and the quantity of water on Earth was likely to have decreased during the late accretion of what the isotopic evidence shows were mostly water-poor bodies. Transient methane-rich atmospheres are generated by ocean-vaporizing impacts. Here, we presume that the mantleʼs excess HSEs were delivered mostly by a single impact, with light shading indicating an allowance for the HSEs dating to the Moon-forming impact itself. Major impacts are shown decreasing in magnitude as time passed, but the true order leaves much to chance; it is possible that the largest of the ocean-vaporizers was also the last. Each great impact left Earth in a state resembling somewhat the state of early Earth as sketched by Urey (1952) for periods that may have been less than a million years or as long as 100 million years, the duration depending on the size of the impact and on the flux of ultraviolet radiation from the young Sun.

Conclusions
Great impacts of Earthʼs late accretion-especially those that evaporated the oceans-differ from lesser impacts in several important ways. First, they delivered significant reducing power in the form of metallic iron to Earthʼs surface environments. We infer this because the characteristic isotopic fingerprints of the mantleʼs HSEs establishes the late veneer as kin to the enstatite chondrites, aubrites, and type IAB iron meteorites, all of which are profoundly reduced and bear ample metallic iron. The iron was oxidized in the crust or mantle, which we know because the HSEs are unfractionated, and hence, there was no significant loss of metal to the core. Water and CO 2 were the plausible oxidants; hence, hydrogen, carbon monoxide, and methane were the plausible products. Second, the high H 2 O and H 2 vapor pressures in a reduced steam atmosphere favor CH 4 and NH 3 over CO or N 2 , a preference that goes as the square of the pressure. Third, cooling after impact was slow because the thermal inertia of a hot steam atmosphere containing hundreds of bars of gas is large. It takes more than 1000 years to cool 270 bar (an ocean) of steam at the runaway greenhouse cooling rate. The result is that quench temperatures for gas-phase reactions in the CH 4 -CO-CO 2 -H 2 O-H 2 system drop to ∼800K or less, and quench temperatures for the NH 3 -N 2 -H 2 O-H 2 system drop to ∼1100K. Hence, both methane and ammonia form directly by gas-phase reactions.
How much methane actually forms depends on how much carbon was available to the atmosphere before the impact, on how much reducing power was delivered by the impact, how much of the delivered iron reacts with the atmosphere and ocean as opposed to being deeply buried under the ejecta, and on whether catalysts were active to reduce the quench temperature still further. In addition to atmospheric CO 2 and CO, available carbon inventories would include any CO 2 dissolved in the oceans, and any CO 2 in carbonate rocks that were not buried too deeply to be liberated by shock heating. Methane production could have been enormous. If, for example, we presume that a maximum-late-veneer scale impact took place on an Earth with a 100 bar of CO 2 atmosphere (perhaps left over from the Moonforming impact; Zahnle et al. 2007) and 5 km of water at the surface, there is enough time and reducing power to convert all of the carbon to methane, diluted in several tens of bars of H 2 . The resulting atmosphere is rather Neptune-like, with a scale height in the range of 50-100 km.
Another interesting aspect of the biggest impacts is that much of the delivered iron may have been too deeply buried in the ejecta blanket to be oxidized in the first few thousands of years after the impact. Under these circumstances, the iron must have been oxidized on a longer timescale set by broadly geological processes that govern the interchange of surface volatiles with crustal and mantle materials. Although we have not presented models of such a scenario here, we can expect that gases emitted from a mantle with extant metallic iron would be strongly reduced over an extended period of time. How important this impact coda might be to the origin of life depends on whether these gases included methane.
Earthʼs hydrogen-methane atmospheres would have been physically stable-they did not blow off-but they were subject to photochemical dissipation, as both hydrogen escape and methane photolysis are effectively irreversible. The rate the atmosphere evolves is set by the flux of solar far and extreme ultraviolet radiations. Here we use a zero-D photochemical model to simulate atmospheric evolution: we count the photons and apportion their effects. We find that the biggest late veneer impacts can generate (cumulatively) as much as 500 m of organic over tens of millions of years, while smaller impacts do commensurately less in commensurately less time.
The details of atmospheric evolution of the transient reduced atmosphere are mostly determined by quantities (i.e., bigger impacts have bigger impacts), but there is one ill-constrained modeling parameter-the stratospheric water vapor mixing ratio-to which the outcomes are sensitive. Moister stratospheres are relatively oxidizing, while drier stratospheres are profoundly reducing and resemble conditions on modern Titan but sped up by a factor of 1000. We see a sharp transition in photochemical products determined by the competition between oxidation and reduction. In our models, the transition appears to take place at stratosphere H 2 O mixing ratios in the range of 0.1-1 ppm, moisture levels that are not very different from Earth today. A more sophisticated model might predict a smoother transition, or a different critical water abundance for a sharp transition.
Lesser impacts are of course less impactful. Tens of smaller, non-ocean-vaporizing impacts will generate significant amounts of H 2 and CO but very little CH 4 or NH 3 unless catalysts were available to reduce the quench temperature. Hydrogen and CO are useful ingredients for a bootstrapping origin-of-life scenario in which the biochemical evolution began by catalyzing the kinds of chemical reactions that build hydrocarbons from CO and H 2 . But if the primary requirements for life are methane, ammonia, HCN, and their photochemical derivatives, only the biggest impacts or as of yet unknown chemistry will do.
From the points of view of the origin of life and biblical metaphors, the great impacts may be double-edged swords. In Figure 14. A schematic history of water, methane, and highly siderophile elements on Earth in response to late great impacts. "SPA" refers to an impact on the scale of the one that excavated the lunar S. Pole-Aitken basin-too small to evaporate the oceans-which is implied here by submerging SPAʼs pole under the waves. Major impacts are shown decreasing in magnitude as time passed, but the true order leaves much to chance; it is possible that the largest of the ocean-vaporizers was also the last. their aftermath, they leave Earth primed and ready to start life under a classic Urey-Miller H 2 -rich, CH 4 -rich, possibly even NH 3 -rich atmosphere that origin-of-life theorists have long favored. Unfortunately, at least with the biggest of them, the first act is an attempt to wipe out everything that had been accomplished before. What this suggests is that impactgenerated transient atmospheres may give a planet only one highly favorable roll of the dice. Smaller, less dangerous impacts can inject significant amounts of new H 2 or CO into the system that might be capable of building on previous progress, but these smaller impacts require unidentified catalysts or unidentified chemistry to generate large amounts of CH 4 or NH 3 . And even if all such conditions were met, there could not have many such impacts, probably no more than a dozen.
The two Fortran source codes and the BASH shells used to call the fortran codes are publicly available in a Zenodo repository at doi:10.5281/zenodo.3698264. These codes are built around planet characteristics specific to the early Earth. The FORTRAN codes have been compiled and tested using gfortran. Note added in proof. Two recent papers have undermined the Ru isotopic arguments against a carbonaceous chondrite-rich late veneer. Varas-Reus et al. (2019) show that mantle Se isotopes are carbonaceous chondritic and not enstatite chondritic; this is the first convincing evidence of a substantial outer solar system contribution to the late veneer. Fischer-Gödde et al. (2020) report that Earth's Ru isotopes are unique in the solar system, characterized by an even higher degree of s-process enrichment than the ECs or the type IAB irons. The new Ru isotopes no longer exclude a carbonaceous chondritic contribution to the late veneer. A heterogenous late veneer does not invalidate the arguments presented here, which focus on a small number of favorable events. Also, it should be understood that carbonaceous chondritic impacts are much less favorable to the in situ origin of life on Earth than more reducing impacts that interact with an ocean and generate organic matter here on Earth (Hashimoto et al. 2007).

Appendix A
We give three representative mineral buffers here. The QFI buffer is the most reduced buffer we consider, The oxygen fugacity of the QFI buffer is approximated by  The direct reaction of water with iron to make FeO and H 2 seems kinetically straightforward, and hence, the IW buffer seems appropriate for the interaction of hot iron and water. The fayalite-magnetite-quartz buffer (abbreviated FMQ or QFM) is representative of modern volcanic degassing and is regarded as typical of the modern Earthʼs mantle. It is the most oxidized mineral buffer that we consider. The generic QFM reaction is The oxygen fugacity of the QFM buffer can be approximated by Photoionizing photons (EUV 1 and S 1 in Table 2) are important for hydrogen escape but less important than photolysis for chemistry. To the first approximation, CO and N 2 usually survive photoionization intact by charge exchange. Photoionization of CO 2 usually creates + CO 2 ions, which can dissociate to CO after reaction with atomic H or O and can charge exchange with CH 4 to make + CH 4 , leaving CO 2 intact while ultimately disintegrating CH 4 . As we are not tracking H or O, we arbitrarily assume that 20% of CO 2 photoionizations generate CO CO ions CO 2 2 * Photoionization of water usually yields H 2 O + , which reacts with H 2 to make H 3 O + and H; with CH 4 to make H 3 O + and CH 3 ; and with CO to make HCO + and OH. Both H 3 O + and HCO + dissociatively recombine. The H 2 O + +CH 4 channel counts as a loss for CH 4 , while the HCO + channel counts as a source of OH. For cases of most interest to us here, H 2 O will be condensed at the surface and will not be a major constituent at the top of the atmosphere, the H 2 O photoionization terms will be small.
The chief chemical consequence of photoionization is that CH 4 is broken down into reactive CH n radicals. Direct photoionization mostly yields + CH 4 or + CH 3 , which, in subsequent reactions, are almost guaranteed to lead to the loss CH 4 . The other molecular ions also react with CH 4 , sparking chains of reactions that lead to CH n radicals. Exempli gratia., + N 2 can exchange with CO to make CO + , CO + can exchange with CO 2 to make + CO 2 , + CO 2 can react with CH 4 to free CH n radicals. The net where the X k factors crudely account for the branching patterns in the ion cascades: