# Dry late accretion inferred from Venus's coupled atmosphere and internal evolution

C. Gillmann, G. Golabek, S. Raymond, M. Schönbächler, P. Tackley, V.

Dehant, V. Debaille

► To cite this version:

C. Gillmann, G. Golabek, S. Raymond, M. Schönbächler, P. Tackley, et al. Dry late accretion inferred from Venus's coupled atmosphere and internal evolution. Nature Geoscience, 2020, 13 (4), pp.265-269.
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# Dry late accretion inferred from Venus's coupled atmosphere and internal evolution

C. Gillmann<fnref n="1" />, G. J. Golabek², S. N. Raymond³, M. Schönbächler⁴, P. J. Tackley⁴, V. Dehant<fnref n="5" />,⁶ and V. Debaille<fnref n="1" />

It remains contentious whether the meteoritic material delivered to the terrestrial planets after the end of core formation was rich or poor in water and other volatiles. As Venus's atmosphere has probably experienced less volatile recycling over its history than Earth's, it may be possible to constrain the volatile delivery to the primitive Venusian atmosphere from the planet's present-day atmospheric composition. Here we investigate the long-term evolution of Venus using self-consistent numerical simulations of global thermochemical mantle convection coupled with both an atmospheric evolution model and a late accretion N-body delivery model. We found that atmospheric escape is only able to remove a limited amount of water over the history of the planet, and that the late accretion of wet material exceeds this sink and would result in a present-day atmosphere that is too rich in volatiles. A preferentially dry composition of the late accretion impactors is most consistent with measurements of atmospheric H₂O, CO₂ and N₂. Hence, we suggest that the late accreted material delivered to Venus was mostly dry enstatite chondrite, consistent with isotopic data for Earth, with less than 2.5% (by mass) wet carbonaceous chondrites. In this scenario, the majority of Venus's and Earth's water would have been delivered during the main accretion phase.

The volatile inventory of terrestrial planets is of prime importance because it not only affects the atmosphere, surface conditions and potential habitability, but also influences mantle dynamics, the tectonic regime and volcanic outgassing<fnref n="1" />,². Uncertainties remain mostly due to the limited data on the early volatile reservoirs³ and to uncertain delivery scenarios³⁻<fnref n="5" />.

After core formation ceased, late meteoritic material delivery occurred on Earth, which contributed as a late accretion (LA) an additional ≈0.5–1.5% of Earth's mass<fnref n="5" />⁻⁷. Although advances have been made to constrain Earth's LA, the exact nature of that late material remains debated when it comes to other bodies. It must account for the abundances of highly siderophile elements in the Earth's mantle, but might also have contributed to water delivery to the Earth⁸. Although volatile-rich bodies, such as carbonaceous chondrites (CCs), have been considered as ideal candidates, especially if the Earth's mantle was left dry after the Moon-forming giant impact⁹, recent geochemical results argue for a LA on Earth that was mainly composed of dry material<fnref n="1" />, such as enstatite chondrites (EC)¹⁰.

Numerical results show that LA also occurred on Venus¹¹, but in the absence of samples from Venus, isotopic studies are limited to the planet's atmosphere<fnref n="1" />,²,¹². Venus's past is poorly constrained; however, it was suggested that Venus experienced a more straightforward evolution of its volatile inventory<fnref n="1" />,¹³. Such an evolution would involve less volatile recycling, as Venus shows no sign of a biosphere, standing water or global plate tectonics.

Although it has been suggested that, under specific conditions, liquid water was stable on Venus for long periods of time¹⁴, without a magma ocean there is no sufficiently strong oxygen sink to remove the oxygen that results from the eventual evaporation of a large water ocean caused by a runaway greenhouse effect<fnref n="1" />,¹⁵,¹⁶. Conversely, conditions during the global magma ocean phase are not compatible with the condensation of large bodies of water at the surface<fnref n="1" />,¹⁷; the condensation of water means the loss of the magma ocean and so the

loss of the strongest oxygen sink. Thus, large bodies of liquid water are difficult to accommodate on Venus both early and late during its evolution. It is therefore likely that Venus has been desiccated since its early evolution¹⁸, the extent and timing of which are still poorly constrained, and the recent surface conditions do not allow for water condensation and associated enhanced weathering<fnref n="1" />,¹⁷.

Venus's massive CO₂ atmosphere also contains about as much CO₂ as all the atmospheric, crustal and mantle reservoirs on Earth. Thus, the present-day atmosphere of Venus is closer to its primitive inventory of CO₂, whereas on Earth, a comparable amount has been incorporated into carbonates and the mantle<fnref n="1" />. Without volatile recycling, Venus is also less likely to develop Earth-like plate tectonics¹⁹, which explains the lack of a magnetic dynamo²⁰.

We propose a quantitative self-consistent model of Venus, focussing on the evolution of its volatile inventory since the LA. We combined N-body LA calculations¹¹ with a state-of-the-art coupled planet interior and atmospheric evolution model²¹. We modelled the consequences of LA on Venus's volatile history and the exchanges of three species (H₂O, CO₂ and N₂) between the planetary interior and atmosphere.

## The early evolution of Venus

The evolution of Venus starts with its accretion, when the bulk of the mass of the planet is delivered<fnref n="1" />. Both accretionary impacts and the atmosphere result in temperatures high enough to create a magma ocean²². Owing to hydrodynamic escape, the primordial atmosphere thins over a timescale of a few tens of million years¹²,¹⁵. For a slow-to-moderate solar rotation period, modelling work on the isotopic fractionation of noble gases indicates the loss of a terrestrial water ocean every 10⁵–10⁷ years. Models also suggest that the magma ocean solidifies rapidly over a period of ≈1 Myr¹⁷, when the atmospheric water content becomes small¹⁷,¹⁸ due to hydrodynamic escape. The mantle enters the phase of solid-state convection

<footnote n="1">¹Laboratoire G-Time, Université Libre de Bruxelles, Brussels, Belgium. ²Bayerisches Geoinstitut, University of Bayreuth, Bayreuth, Germany. ³Laboratoire d'Astrophysique de Bordeaux, CNRS and Université de Bordeaux, Pessac, France. ⁴Department of Earth Sciences, ETH Zurich, Zurich, Switzerland.</footnote>

<footnote n="5">⁵Université catholique de Louvain, Louvain-la-Neuve, Belgium. ⁶Royal Observatory of Belgium, Brussels, Belgium. ⁷e-mail: cgillman@ulb.ac.be</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1 | Volatile exchanges on Venus.** Mechanisms that affect the water content of Venus's atmosphere during the long-term evolution of the planet.</figcaption></figure>

(Fig. 1), which we model here. Afterwards, LA delivers the final part of the planetary mass via impacts⁵,⁶.

LA impacts have three main effects (all considered here): delivery of volatiles to the planet⁸, impact heating²³ and erosion of the atmosphere²⁻⁴. We use N-body simulations to study LA, with various simulated growth histories that are consistent with the masses of present-day terrestrial planets. As it is possible that the size and number of impactors have consequences for the evolution, we tested four distinct LA impact scenarios (Fig. 2). These represent median cases based on several hundred N-body simulations³¹: a single very large impact (Scenario A, R=1,819 km) (ref. ²⁵), 9 large impacts (Scenario B, R>500 km), 82 medium-sized collisions (Scenario C, R>125 km) and, finally, 244 small impactors (Scenario D, R>50 km). However, we note that, given the top-heavy nature of the impacting size distributions, the mass tends to be dominated by the few largest bodies. The timing of LA on Venus is still debated, and thus onset times that range from 50 to 150 Myr (ref. ²⁶) after the formation of Ca–Al-rich inclusions (CAIs) are used, marking the start of the evolution models. Impactors have either an EC-like composition²⁷,²⁸ (0.1% H₂O, 0.4% CO₂ and 0.02% N₂) or a CC composition²⁹,³⁰ (8% H₂O, 4% CO₂ and 0.2% N₂), which thus determines the amount of volatiles delivered by LA to the atmosphere of Venus³¹. Intermediate ordinary chondrite (OC) compositions are also considered (Supplementary Information).

## The consequences of volatile delivery

During the LA volatile delivery, strong escape mechanisms limit the accumulation of volatiles in the atmosphere. Thermal (hydrodynamic) escape dominates¹² the early evolution. As atmospheric water is photodissociated, the early hydrodynamic escape removes H₂ efficiently during the first few 100 Myr. As the removal of oxygen¹,¹²,³²,³³ by hydrodynamic escape is inefficient, it accumulates in the early atmosphere. However, the present-day atmosphere of Venus displays very little water or oxygen. Therefore, it must have been lost during the planetary evolution¹. During the main accretion stage, oxidation of the molten magma ocean can trap oxygen efficiently¹,¹⁵,³⁴, but from the LA stage onwards this sink only exists

<figure><img src="image_4.png" /><figcaption>**Fig. 2 | LA scenarios.** Four distinct LA impact scenarios were used in the coupled interior-atmosphere models assuming a LA that began at 100 Myr after the formation of the CAIs. The considered variation in the LA onset time is shown by the dashed line box. The total mass of Venus LA was found to be larger than Earth's by a factor of 2–3. *M*<sub>Venus</sub>, mass of Venus.</figcaption></figure>

in the form of oxidation of the newly emplaced lava flows³⁵ and thus its consequences on oxygen removal are limited (Supplementary Information).

Non-thermal escape removes less mass than hydrodynamic escape does. However, it removes oxygen and affects the long-term evolution of the atmosphere. The balance between oxygen left in the atmosphere by LA, hydrodynamic escape and the long-term sink of non-thermal escape (plus putative oxidation mechanisms³⁴), defines the upper limit of the LA volatile delivery and its composition.

As the removal of oxygen occurs on the timescale of billions of years, the entire evolution of Venus starting with LA needs consideration. To this end, the LA impact scenarios are incorporated into coupled atmosphere–interior evolution models that follow the model layout of Gillmann et al.²¹ with volcanic outgassing considered as an additional volatile source (Methods). We modelled the evolution of the atmospheric volatile inventory starting after the end of the magma ocean stage until present-day. Comparison between the final state of the simulated atmosphere and the present-day atmosphere composition enabled us to constrain the volatile content of the LA material.

Our main constraint is the bulk composition of the present-day atmosphere of Venus, which is well-established¹, with $11 \times 10^{18}$ kg of N₂ ($2 \times 10^{26}$), $10^{16}$ kg of H₂O ($2 \times 10^{-3}$ bar³⁴,³⁷) and $4.69 \times 10^{20}$ kg of CO₂ ($90.6$ bar³⁸) (Methods). Other major constraints available to narrow down Venus evolution scenarios are the noble gas isotopic ratios and the D/H ratio. Noble gas isotopic ratios ($^{36}$Ar/$^{38}$Ar and $^{20}$Ne/$^{22}$Ne) are thought to indicate that an early thermal escape fractionated these species¹,¹². However, this constraint on escape is weak, because it has been shown that no single solution meets the $^{36}$Ar/$^{38}$Ar and $^{20}$Ne/$^{22}$Ne fractionation¹². We still used this constraint to assess the hydrodynamic escape fluxes. The upcoming Venera D mission may improve the noble gas isotopic measurements and provide tighter constraints on Venus's evolution. The D/H atmospheric ratio shows an enrichment of deuterium relative to that of Earth by a factor 100, which indicates water loss from the Venus atmosphere³⁹. It is governed by a long-term non-thermal escape and its interaction with volcanic degassing sources of unknown composition⁴⁰, with additional effects from hydrodynamic escape⁴¹ and impacts⁴². Moreover, measurements show that the D/H ratio in the atmosphere of Venus changes with altitude³⁹, which limits its value as a constraint. Thus, modelling of the D/H ratio evolution is not feasible here.
<figure><img src="image_5.png" /><figcaption>**Fig. 3** | Evolution of water in the atmosphere of Venus. Time evolution of H₂O in the Venus atmosphere for MAX conditions assuming different LA compositions, labelled as CC material percentage of the total LA mass delivery. The LA scenario D that starts at 100 Myr after CAI formation is used.</figcaption></figure>

Estimating the maximum LA delivery

At the start of the evolution model, after the magma ocean has solidified, the initial water content of Venus's atmosphere is assumed to have been completely removed during earlier evolution¹. As our aim is to estimate the maximum volatile content of the LA, we chose the ideal initial conditions with no pre-existing water. Any oxygen that remained at the onset of the simulation also needs to be extracted from the atmosphere by the limited existing volatile sinks. This implies a reduced LA volatile delivery and reinforces our results. An early CO₂ atmosphere exists due to the magma-ocean outgassing, whereas N₂ is mostly trapped at the hot surface⁴³. The initial volatile pressures at the start of the LA were chosen to be 0 bar N₂⁴³ and H₂O, and 65 bar CO₂¹⁵. CO₂ degassing of the magma ocean is considered to be efficient due to its low solubility in magma, and a thick CO₂ atmosphere forms early on¹,¹⁷. The LA stage is characterized by volatile delivery due to impacts and subsequent volatile loss. Water delivery is dominated by impactors with a CC composition (if present) because of their high water content, whereas N₂ and CO₂ are deposited in large amounts by both CC and EC. Impact erosion effects⁴⁴ are noticeable but insufficient to prevent volatile build-up. Volcanic outgassing, which includes that caused by impact melting, also remains a second-order effect. The late evolution of atmospheric water content (from the end of the LA to present-day) is dominated by atmospheric escape and volcanic degassing, which also causes the slow accumulation of N₂ and CO₂ in Venus's atmosphere.

The major factor that limits H₂O evolution models is the 'escape envelope', which corresponds to the maximum amount of oxygen that can be removed by atmospheric escape between a given time and present-day⁴⁵ (Fig. 3a). It is obtained by cumulating losses based only on non-thermal escape processes from present-day, back to any given time in the past⁴⁶. Thus, models in which the delivered water and consequent H₂O equivalent pressures exceed the escape envelope are not able to lose sufficient amounts of volatiles to meet present-day observations and are rejected. All the models are evaluated against the present-day volatile content of the atmosphere. As an additional constraint, Venus must lose all molecular oxygen that it accumulated during its early evolution due to hydrodynamic escape¹,⁴⁶,⁴⁷.

The evolution of water abundances shown in Fig. 3 represents an equivalent water concentration based on the fluxes of O atoms from both water delivery and losses. For H₂O, two distinct cases arise: either (1) H₂O is removed, the atmosphere desiccates and only limited volcanic degassing during late evolution replenishes it

or (2) it remains in the atmosphere, which results in higher equivalent water pressures (>1 bar) for the rest of the evolution, which does not fit present-day observations of Venus. For CO₂ and N₂ the progression from one scenario to the other is much smoother (Extended Data Fig. 1).

The choice of non-thermal escape parameters is therefore crucial. Three main sets, which controlled the magnitude of volatile loss, were tested. The parameter set that allows the largest potential volatile deposition from the LA (that is, the most favourable to wet LA) was therefore considered as the upper limit for LA volatile content, and is denoted MAX. This end member is characterized by the maximum atmospheric escape⁴⁶, minimal outgassing²¹ and the use of the tangent plane model for the impact-induced atmospheric erosion⁴⁴. The parameter set called MIN causes the smallest loss and therefore the driest LA and is considered to be the most realistic¹. A third scenario with intermediate volatile loss is called MED. Extended Data Figs. 2 and Fig. 3 show the evolution with the MED and MIN parameters.

Figure 4a,b shows the relative agreement between the model results and observations using the relative accuracy of simulations ($α=1 - |M_{s,i} - M_{\text{obs}}|/M_{\text{obs},i}$, where *i* denotes the volatile species considered, and $M_s$ and $M_{\text{obs}}$ are the simulated and observed masses, respectively). Figure 4 summarizes the model results based on different LA onset times (Fig. 4a) and the four LA impact scenarios (Fig. 4b) for the cases that allow for a maximum volatile concentration in LA bodies. For comparison, Fig. 4c shows results for selected models using more realistic water losses. Based on H₂O only, the calculations show that a maximum of 2.5% of wet LA material consistently satisfies present-day conditions for a LA that began around 60–120 Myr after CAI formation (Fig. 4a). This is the equivalent of a single CC impactor ≈500 km in radius. The onset time of LA greatly affects the results in MAX cases, due to the additional losses it allows for. Late LA onsets (>150 Myr after CAI formation) are unlikely to fit the atmosphere composition data. Assuming an earlier LA onset (while keeping the same LA mass), the results for water imply a viable amount of up to 10–15% of wet LA material. However, N₂ and CO₂ evolution provide additional constraints, as their loss rates are lower than those of water¹,⁴⁶. Correspondingly, early volatile-rich LA models that satisfy the H₂O content are unable to simultaneously meet present-day N₂ and CO₂ measurements. In the case of LA that contains 10% CC material, the present-day amount of CO₂ is 22% off (≈20 bars), whereas N₂ is 40% off (≈0.7 bar). These discrepancies are larger than the total contribution of volcanic outgassing for CO₂ and N₂, respectively (Extended Data Fig. 4). Therefore, such a LA composition is in disagreement with the measured atmospheric composition data, and the excess of volatiles cannot be attributed to excessive outgassing. Therefore, the maximum contribution of CC in LA is <2.5% for LA onset times >100 Myr after CAI formation and <10% for earlier LA onsets. Thus, our results do not allow us to constrain the LA onset time on Venus, but rather, indirectly, the impact time of the last major wet impactor⁴⁵.

Figure 4b illustrates the interplay of total LA mass and the number of impactors. Larger masses result in more volatile delivery. However, for a given mass, many small impacts cause more atmospheric erosion than a smaller number of larger impactors. Thus, Fig. 4b implies that the size-frequency distribution of LA impactors has only minor effects on our conclusions, especially for water. In particular, we do not expect our results to change if the LA impactors had a size distribution that was less top-heavy and closer to the present-day asteroid size distribution. Figure 4c shows water-loss estimates based on the MIN parameter, which represent more accurately our current understanding of solar extreme ultraviolet (EUV) and water-loss evolution¹. MIN models are extremely restrictive and have a tighter limit on water delivery. The escape envelope shows a small slope, and thus is not able to constrain the LA onset time very well. This parameter set requires a dry LA scenario, with less than
<figure><img src="image_6.png" /></figure>

**Fig. 4** | Consequences of LA volatile content on present-day Venus atmosphere. **a–c.** Agreement (relative accuracy) between the model results and the present-day volatile content of Venus's atmosphere assuming a strong atmospheric escape (MAX parameter set) (**a,b**) and using a weak atmospheric escape (MIN parameter set) (**c**). **a,** Scenario D starting at 60–120 Myr after CAI and different LA compositions that range from an EC end member to 15% of the CC material. **b,** LA scenarios A–D with LA onset at 100 Myr after CAI and assuming the same variation of LA compositions as in **a. c.** Selection of simulations that employ scenarios C and D with different LA onset times. EC composition simulations display a deficit in $N_2$ relative to present-day atmospheric content. Red numbers indicate the post-magma ocean $CO_2$ pressure (bar) required as the initial condition to increase the $CO_2$ agreement at present-day to 100%. The perceptually uniform colour map is reproduced from ref. [5], EGU, StagLab 3.0, under a CC BY 4.0 licence.

2.5% CC (and >97.5% EC material), regardless of the LA onset time and implies that impactors may have been substantially desiccated[48].

In conclusion, the best fit between models and present-day Venus atmosphere shows that the LA on Venus was primarily composed of EC-like (dry) meteorites with at most 2.5% of the total mass exhibiting a CC (wet) composition. Venus and its atmosphere have therefore not received any major volatile deliveries after the end of the magma ocean. Numerical models suggest that the LA could have been homogeneous in the early solar system with comparable compositions, which include that for water[11,13,49]. In this case, our conclusions agree with previous suggestions based on isotopic studies for both Earth and Mars material[9,10,50] and indicate that the majority of volatiles was delivered to the terrestrial planets during planet formation, and thus, in the case of Earth, before the Moon-forming giant impact.

## Online content

Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41561-020-0561-x.

Received: 21 March 2019; Accepted: 26 February 2020;
Published online: 7 April 2020

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**Methods**

The coupled atmosphere-interior model considers four main aspects that define the long-term evolution of Venus: (1) volcanic degassing of volatiles, (2) atmosphere escape sinks, (3) surface condition evolution and (4) LA impacts. We tested three distinct parameter sets: MAX parameters (which allow for a maximum LA volatile contribution; see main text), MED parameters (average parameter; Supplementary Information) and MIN parameters (which allow for a minimum LA volatile contribution; see main text). Extended Data Figs. 5 and 6 give more details and the list of models is given in Supplemental Table 1. Based on present-day knowledge, the MIN parameter set is considered to be the most realistic¹. The MAX parameter set leads to extreme escape cases; it is used for the numerical models discussed in the main text because the extreme nature of this parameter set also ensures that results are robust to parameter variations. All the atmospheric volatile pressures are expressed assuming that this specific gas is the only one in the atmosphere, and are therefore a proxy of mass. As a reference, one terrestrial ocean corresponds to 265 bar, 1.39 × 10²¹ kg and a global equivalent layer of 2,900 m depth.

**Numerical modelling of thermochemical convection.** We modelled the mantle dynamics for a 4.5 Gyr period, from the end of the magma ocean stage until the present-day. We used the version of the code StagYY⁵² described in Armann and Tackley⁵³, Gillmann and Tackley⁵⁴ and Gillmann et al.²¹. The tectonic regime of the planet is not prescribed, but it is calculated self-consistently. In the present simulations Venus does not exhibit Earth-like plate tectonics. Supplementary Annex 1 contains a full description.

**Melt eruption and volatile outgassing.** Melt generated during the mantle convection and reaching the surface of Venus contributes to volatile outgassing of N₂, CO₂ and H₂O. The full description of the outgassing process and parameters can be found in Supplementary Annex 1. Extended Data Fig. 4 shows the impact and volcanic contributions.

**Solar evolution.** The long-term evolution of EUV flux from the Sun and solar wind affect atmospheric escape¹⁵,⁴⁶,⁵⁵. EUV flux decreases with time according to a power law⁵⁶, which assumes that the early Sun was a slow-to-moderate rotator, as suggested by recent studies¹⁵,⁷⁷. Luminosity increases with time, according to the faint young Sun hypothesis⁵⁸,⁵⁹ from 70% of present-day luminosity to the present-day value.

**Hydrodynamic and thermal escape.** Hydrodynamic and thermal escape describes the response of a primitive, hydrogen-rich atmosphere subjected to high-intensity EUV radiation. The atmosphere expands, hydrogen escapes and heavier species can be dragged along only for as long as the driving H flux persists. We used the energy-limited model of hydrogen escape described in Gillmann et al.⁴⁷ and based on previous work³³,³⁴,⁶⁰⁻⁶³. Maximum escape fluxes calculated for hydrogen are ≈3 × 10¹⁴ s⁻¹, consistent with estimates from recent work¹⁵,⁴⁶. Photodissociation splits water molecules into H and O atoms. As H escape is much more efficient than O escape, hydrodynamic escape generates an accumulation of O (possibly as much as 85 bars O²⁵,⁶³) that needs to be removed from the atmosphere: only early on can it be stored in the magma ocean. At the onset of the model, all the primordial water is thus assumed to have been removed from the atmosphere¹. Any oxygen remaining in the atmosphere reduces potential water delivery during the LA. Additionally, this means that most of the thermal escapes of oxygen and CO₂ occur during the magma ocean phase, before the onset of our model, and therefore controls the initial volatile inventory. CO₂ losses have been suggested to be low (<10 bar¹⁵,⁴⁶,⁶⁴,⁶⁵). N₂ was protected due to the cooling effect of CO₂ in the upper atmosphere¹. Later on, during and after the LA, oxygen and CO₂ are lost primarily by non-thermal escape mechanisms¹,⁴⁶,⁴⁷, due to the lack of a late long-lived hydrogen-rich atmosphere¹. Therefore, owing to its very limited losses during and after the LA, CO₂ thermal escape rates are not considered in the model. The error between modelled and observed present-day CO₂ pressures was determined and a corrected initial pressure necessary to reduce the error to zero was calculated (Fig. 4).

**Non-thermal escape.** Non-thermal escape covers the interaction of upper atmosphere particles with the high-energy radiation from the Sun, such as, for example, the EUV flux. The mechanisms involved are photochemical reactions⁶⁶, sputtering⁶⁷, ion pick-up⁶⁸ and plasma instabilities⁵⁵. Non-thermal escape dominates late evolution (3.5 billion years ago (Ga) to present), but also plays a role earlier on. We reconstructed past non-thermal escape fluxes in two stages: before and after 3 Ga, as detailed in the next two paragraphs. The cumulated effect of oxygen loss over time is shown as the escape envelope in Fig. 3. Non-thermal CO₂ losses are very small over the history of Venus²¹,⁴⁶.

**Recent water loss.** Recent water loss is calculated from O escape rates. Late evolution rates for the past 3 Gyr are calculated as in Gillmann et al.²¹,⁵⁴, based on simulations and present-day measurements⁶⁰ of atmospheric escape rates at solar minimum and solar maximum EUV conditions. An interpolation between those two values indicates how escape varies over a solar cycle, depending on the EUV flux. Solar maximum conditions of a present-day solar cycle correspond to the

solar minimum EUV conditions 2.5–2.8 Ga⁵⁶. Thus, we have access to the variation of escape rates for minimum solar conditions over the past 2.8 Gyr, which we extrapolate to mean escape rates used for the time period 0–3 Gyr before present-day. We used a cumulated present-day escape rate of 6 × 20²⁵ s⁻¹ (combining all O loss mechanisms), close to the maximum limit derived for present-day conditions¹. The reconstruction is consistent with simulations from Kulikov et al.⁴⁶.

**LA-era O excess removal.** The early non-thermal escape was calculated using numerical simulations⁶⁶ of the ion-pick-up loss flux based on a particle model⁶⁹ and taking into account the stronger early solar activity (EUV about 100 times the present-day value 4.5 Ga⁵⁹). Specifically, we used case 2b in Kulikov et al.⁴⁶ (moderate solar wind activity). This estimate corresponds to the effect of ion-pick-up only. The total escape, which accounts for all the mechanisms, is several times higher⁴⁴. MAX (main text and figures) and MED (extended data) parameter cases use a multiplication factor of 5 and 2.5, respectively (case 2b in Kulikov et al.⁴⁶), to account for higher and lower escape ranges. A low escape (case 4 in Kulikov et al.⁴⁶), which represents recent advances in the characterization of solar evolution¹,⁷⁰,⁷¹, is used in the MIN parameter cases. Further models use the lowest possible multiplicative factor (6) able to accommodate LA scenario D with the EC composition. Extended Data Fig. 6 compares parameters for these three cases. Although thermal escape remains unaffected by the presence of a magnetic field, non-thermal escape is affected. It is currently uncertain whether Venus had a magnetosphere in the past⁷², and there is currently no sign of a present-day magnetosphere. It has been suggested that, if Venus exhibited Earth-like conditions, it would probably still maintain a magnetic field at the present-day⁷². However, if Venus had a stratified core, it would not have generated a magnetic field⁷³. Given our present knowledge of the effects of magnetic fields, it is unknown whether the presence of a magnetosphere would result in decreased or increased atmospheric losses⁷⁴. In case the atmosphere is shielded, our conclusions are reinforced. Assuming an end-member scenario in which Venus had a magnetosphere during its entire evolution, which results in the maximum additional H₂O losses⁷⁴, leads to an increased maximum contribution of CC material in our models of up to 15%, 10% and 3% assuming MAX, MED and MIN parameter sets, respectively. However, the N₂ and CO₂ limits remain unchanged (Fig. 4).

**Surface oxidation sink.** Oxidation of the surface of Venus has been proposed as a possible oxygen sink³⁴,⁴¹ and would be consistent with the suggestion⁷⁵ of an oxidized basaltic surface. We performed additional numerical calculations that include surface oxidation to assess its consequences on the results of the model. We considered the following chemical reaction¹⁷: 2FeSiO₃ + ½O₂ → Fe₂O₃ + 2SiO₂.

Freshly erupted lava is able to react with oxygen while it is still hot. However, as the diffusion of oxygen in hot lava is slow, the process is inefficient. Results of the simulations and a full description of the calculations are available in Supplementary Annex 1. The effect of oxidation is noticeable, but only a small amount of up to a few bars of oxygen at most is removed from the atmosphere in this way.

**Surface conditions.** Surface temperature is calculated using a one-dimensional (1D), vertical, radiative-convective grey atmosphere model, as described in Gillmann et al.⁵⁴. The atmosphere is considered to be in hydrostatic equilibrium and in a regime similar to that of present-day. The equilibrium temperature of the planet evolves with solar luminosity. CO₂ and H₂O are the only greenhouse gases considered here. Over time, the CO₂ content of the atmosphere only varies moderately compared with those of present-day conditions. Water atmospheric concentration is more variable, but within the bounds of previously tested models²¹,⁵⁴. The surface temperatures calculated were found to be consistent with canonical values¹. Changes in surface temperature affect convection⁵⁴, but the consequences on the volatile repartition are marginal, due to the low outgassing efficiency. Simulations with a constant surface temperature show a 3% change in the atmospheric volatile inventory.

**LA scenarios.** We used a series of N-body simulations from Raymond et al.¹¹ to generate a population of impacting bodies for Venus's LA. These simulations provide plausible evolutionary histories that match our current interpretation of the constraints. In our simulations, Jupiter and Saturn were included on orbits consistent with their gas-driven orbital migration⁷⁶⁻⁷⁸. The terrestrial 'leftovers' were included on orbits consistent with simulations of terrestrial planet formation⁷⁹,⁸⁰: the orbital semi-major axis was randomly chosen between 0.5 and 1.7 au, the eccentricity between 0.1 and 0.6, and the inclination between 0 and 20°. The mass of the leftovers was drawn from a size distribution consistent with Bottke et al.⁸¹ and parameterized as dN/dD ~ D⁻q, where N is the number of objects of a given diameter *D* and *q* was chosen to be 1, 1.5 or 2. For the main set of simulations¹¹, terrestrial leftovers (minimum diameter of 1,000 km) represent a population totalling 5% of Earth's mass, which was found to deliver the correct amount of LA mass to Earth¹¹. Scenarios A and B adopted the stochastic LA framework of Bottke et al.⁸¹, who suggested that a top-heavy mass distribution could explain why Earth experienced a more substantial LA than that inferred for the Moon or Mars⁷,⁸². Owing to the limited number of impactors in scenarios
A and B, small number statistics has to be considered. For this purpose, these two scenarios employed median cases based on hundreds of N-body simulations from Raymond et al.¹¹. We also considered LA scenarios that involved smaller impactors³³. These higher-resolution simulations (scenarios C and D) use minimum diameters of 100 and 250 km. All the scenarios used here were found to deliver the correct amount of LA material to the Earth (0.25–0.75% of Earth's mass)⁵⁻⁷, which satisfies the highly siderophile element constraints. As a rule, they deliver a slightly larger mass as for the LA to Venus. This is consistent with the findings of Jacobson et al.²⁶. Our simulations start with fully formed terrestrial planets and a population of leftovers, which implies that 'time zero' for these simulations was the last giant impact on any of the terrestrial planets, (the Moon-forming impact, roughly 50–150 Myr after the CAI formation for Earth⁴⁴,⁸⁵). It has been shown that an early last giant impact on Venus implies a larger total LA mass of up to ≈20% of the planet's mass²⁶,⁷⁰. Such LA scenarios result in additional volatile delivery and are unlikely to accommodate CC material. We performed numerical calculations using a modified scenario D in which the LA onset is at 20 Myr after CAI formation and all impactor masses are scaled up, so the total LA mass is 10% of the Venus mass (Supplementary Table 1). The results indicate no more than 10% CC material is permitted to match the present-day H₂O atmospheric content, whereas N₂ and CO₂ deliveries do not match with present-day observations. We found the differences between models A to D to be small (Fig. 4), and mainly due to differences in total mass. This leads us to expect that the size distribution of the LA impactors is not a critical factor for atmospheric volatile content and that our model would still match the constraints for a different distribution more characteristic of those of the present-day asteroid belt.

**LA composition.** Two compositional end members were chosen: ECs²⁷,²⁸ or CCs²⁹,³⁰,³⁶. Reducing the water content of the EC end member does not affect the maximum mass of CC compatible with atmospheric constraints by more than 1%, because water delivery is dominated by the CC bodies. An EC H₂O concentration reduced by a factor ten has been tested without a notable change to the results (Supplementary Table 1). The effects of variations in CC water content are shown in Supplementary Information Table 1; our conclusions remain unaffected.

We performed several calculations with an OC end member instead of a CC composition⁸⁷,⁸⁸, using 1% H₂O, 1% CO₂ and 0.01% N₂. Lower water concentrations make this reservoir very similar to the EC end member and the resulting evolutions are close to those of the OC-only cases featured in Supplementary Table 1. The results for the OC LA scenarios indicate a correspondingly higher fraction of the wet end member with less than 45% OC with the MAX, 30% with the MED and 10% with the MIN parameter sets. This is (especially for MED) in line with the results obtained by Brasser et al.⁸⁹.

In scenarios B–D, the compositional variation is handled by assigning part of the LA impactors up to the desired mass fraction CC composition, whereas the bulk of the impactors have an EC composition. Those impactors with a CC composition are always assumed to collide with Venus during the first 20 Myr of the specific LA scenario to maximize volatile loss. For control models and scenario A, all the impactors have a uniform intermediate composition. Control models (Supplementary Table 1) exhibit marginal changes, which indicates they can accommodate 1–3% (weight) more CC material.

**Impact-induced atmosphere erosion.** Impacts can cause atmospheric loss due to atmospheric entry, ejecta material and vapour plume generation. Here, we used two approaches to model impact erosion²¹: (1) the tangent plane model¹⁴,⁹⁰ and (2) results from SOVA hydrocode simulations²⁴,⁹¹,⁹². The tangent plane model predicts the removal of all the atmospheric content above a plane tangent to the surface of the planet at the impact location, and thus each collision removes ≈10⁻³ times the mass of the atmosphere of Venus. We considered for the MAX and MED parameter models that all the LA impactors are large enough to cause atmospheric escape as described by the tangent plane model. The SOVA hydrocode results imply lower erosion rates and are used for MIN parameter models. For large bodies (R > 100 km), SOVA-derived erosion efficiencies are reduced by a factor of ≈4 compared to the tangent plane model. Here, the total amount of atmospheric erosion by a certain LA scenario is primarily dictated by the number of impacts. We neglected ground-motion atmospheric erosion⁹³, which may be important for large impacts (scenario A) but negligible for smaller ones (scenarios B–D). This mechanism would increase the impact erosion in scenario A and make it comparable to those of scenarios C and D, and thus lead to more uniform results across all mass-size distributions.

**Impact delivery of volatiles.** Volatile delivery depends on the impactor composition (see above) and the fraction of the volatiles released during the collision that remain in the atmosphere afterwards. This deposition efficiency must take into account the portion of impactor material retained and the outgassing of volatiles from the impactor material. Numerical simulations²⁴,⁹¹,⁹⁴ suggest that a minor fraction (10%) of the projectile can be lost back to space as ejecta material. We considered that only vaporized impactor material contributed to the outgassing of volatiles. We used a conservative value for the vaporized fraction of 40%⁹⁴⁻⁹⁶, which led to a deposition efficiency of 36%. In the case that a larger part of the projectile is vaporized, the conclusions presented in the main text are reinforced.

We tested low-end deposition efficiency factors (12%; Supplementary Table 1) with similar conclusions that led to a maximum EC fraction of ≈10% for the MAX parameters (less than 5% for MED and 2.5% for MIN).

**Impact heating.** Shock heating generates a high-temperature region in the planetary interior. Mantle volume and temperature increase in this thermal anomaly were treated here as in Gillmann et al.²¹,²³, taking into account impact velocities higher than the escape velocity¹¹,⁹⁷. Only impactors large enough (R > 150 km) to penetrate the lithosphere²¹,²³ were considered to have an important effect on the temperature structure of the planet's convecting interior. Smaller impactors only contributed to the atmosphere's evolution. Crustal vaporization was neglected. Compared to 3D geometry, the 2D geometry introduces an overestimation of the relative mantle volume affected by thermal anomalies²¹. In 2D and 3D, the ratio of affected volume to mantle volume varies with $R_{\text{anomaly}}^2/(R_{\text{Venus}}^2 - R_{\text{core}}^2)$ and $R_{\text{anomaly}}^3/(R_{\text{Venus}}^3 - R_{\text{core}}^3)$, where $R_{\text{Venus}}$, $R_{\text{core}}$ and $R_{\text{anomaly}}$ are the radii of the planet, its core and the isobaric core of the thermal anomaly, respectively⁹⁸. The ratio between these two values approximates the overestimation caused by geometry. For large impacts (R > 500 km), it is ≈3, whereas for medium-sized collisions (150 ≤ R ≤ 500 km) the factor is ≈7. Therefore, only one in three large impactors and one in seven medium-sized ones are considered to create a thermal anomaly.

## Data availability

The data that support the findings reported in this article are available as follows: code outputs of N-body simulations (impactors and collisions parameters) are available from figshare, with the identifier https://doi.org/10.6084/m9.fishshare.11829621. Data generated for the models displayed in the figures (equivalent pressure evolutions) are available from figshare, with the identifier https://doi.org/10.6084/m9.fishshare.11829621. Datasets generated during the current study as the present-day Venus atmosphere composition for the full complement of models are available in Supplementary Information.

## Code availability

The convection code StagYY is the property of P.J.T. and Eidgenössische Technische Hochschule (ETH) Zürich. It is available on request from P.J.T. (paul.tackley@erdw.ethz.ch). The N-body model MERCURY, used for the LA scenarios, is available at https://github.com/4xxi/mercury.

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## Acknowledgements

We thank F. Crameri for providing the perceptually uniform colour map used in Fig. 4a. We thank D. Rubie for his comments. We also thank R. Brasser and K. Zahnle, C.G., V. Dehant and V. Debaille were supported by BELSPO PlanetTOPERS IUAP programme and ET-HoME Excellence of Science programme. V. Debaille thanks the FRS-FNRS and ERC StG IsoSyC FP7/336718. M.S. acknowledges the National Center for Competence in Research 'PlanetS' supported by the Swiss National Science Foundation (SNSF). V. Dehant was financially supported by the Belgian PRODEX program managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office.

## Author contributions

C.G. wrote the atmosphere, outgassing and escape codes, and designed the coupling between models. C.G. and G.J.G. wrote the impact code. P.J.T. wrote the StagYY code. S.N.R. designed the N-body models and designed related simulations. C.G. and G.J.G. designed the set of StagYY simulations. C.G. ran all the simulations. All the authors discussed the results and contributed to the manuscript.

## Competing interests

The authors declare no competing interests.

## Additional information

Extended data is available for this paper at https://doi.org/10.1038/s41561-020-0561-x.

Supplementary information is available for this paper at https://doi.org/10.1038/s41561-020-0561-x.

Correspondence and requests for materials should be addressed to C.G.

Peer review information Primary Handling Editor: Stefan Lachowycz.

Reprints and permissions information is available at www.nature.com/reprints.
<figure><img src="image_7.png" /></figure>

**Extended Data Fig. 1 | Evolution of CO₂ and N₂ pressure.** Time evolution of a, CO₂ and b, N₂ abundances in the Venus atmosphere for three different LA compositions, labelled as CC material percentage of the total LA mass delivery. MAX parameters and LA scenario D starting at 100 Myr after CAI formation are used.
<figure><img src="image_8.png" /></figure>

**Extended Data Fig. 2** | Evolution of water in the atmosphere of Venus. Time evolution of H₂O in the Venus atmosphere for MED conditions assuming different LA compositions, labelled as CC material percentage of the total LA mass delivery. LA scenario D starting at 100 Myr after CAI formation is used.
<figure><img src="image_9.png" /></figure>

**Extended Data Fig. 3** | Evolution of water in the atmosphere of Venus. Time evolution of H₂O in the Venus atmosphere for MIN conditions assuming different LA compositions, labelled as CC material percentage of the total LA mass delivery. LA scenario D starting at 100 Myr after CAI formation is used.
<figure><img src="image_10.png" /><figcaption>**Extended Data Fig. 4** | Comparison of delivery mechanisms. Volcanic and impact sources for **a**, H₂O and **b**, CO₂. All shown cases employ MAX parameters and LA scenario D starting at 100 Myr after CAIs.</figcaption></figure>
<table><thead><tr><th>Parameter name</th><th>Parameter value</th></tr></thead><tbody><tr><td colspan="2"><strong>Mantle convection modeling</strong></td></tr><tr><td>Planetary radius</td><td>6052 km</td></tr><tr><td>Planetary mass</td><td>4.8673 x 10<sup>24</sup> kg</td></tr><tr><td>CMB radius</td><td>3110 km</td></tr><tr><td>Mantle depth</td><td>2942 km</td></tr><tr><td>Surface gravity</td><td>8.87 m/s<sup>2</sup></td></tr><tr><td>Surface temperature (for uncoupled cases)</td><td>740 K</td></tr><tr><td>Initial CMB temperature</td><td>4025 K</td></tr><tr><td>Specific heat capacity</td><td>1200 J/kg/K</td></tr><tr><td>Latent heat of silicate melting</td><td>600 kJ/kg</td></tr><tr><td>Reference viscosity</td><td>10<sup>20</sup> Pa s</td></tr><tr><td>Friction coefficient</td><td>0.5</td></tr><tr><td>Surface yield stress</td><td>100 MPa</td></tr><tr><td>Internal heating at present-day</td><td>5.2 x 10<sup>-12</sup> W/kg</td></tr><tr><td>Internal heating rate at model start</td><td>18.77 x 10<sup>-12</sup> W/kg</td></tr><tr><td>Half-life time of radiogenic heating</td><td>2.43 Gyr</td></tr><tr><td colspan="2"><strong>Volcanic outgassing modeling</strong></td></tr><tr><td>Volatiles eruption coefficient</td><td>10%</td></tr><tr><td>H<sub>2</sub>O concentration (initial; present-day)</td><td>80 ppm; 20 ppm</td></tr><tr><td>CO<sub>2</sub> concentration (initial; present-day)</td><td>400 ppm; 100 ppm</td></tr><tr><td>N<sub>2</sub> concentration (initial; present-day)</td><td>20 ppm; 5 ppm</td></tr><tr><td>Maximum eruption depth</td><td>300 km</td></tr><tr><td colspan="2"><strong>Atmosphere and escape modeling</strong></td></tr><tr><td>Solar irradiance (present-day)</td><td>2613.9 W/m<sup>2</sup></td></tr><tr><td>Initial CO<sub>2</sub> pressure (post magma ocean)</td><td>65 bar</td></tr><tr><td>Initial H<sub>2</sub>O pressure (post magma ocean)</td><td>0 bar</td></tr><tr><td>Initial N<sub>2</sub> pressure (post magma ocean)</td><td>0 bar</td></tr><tr><td>Equilibrium temperature (present-day)</td><td>232 K</td></tr><tr><td>Reference oxygen escape rate (non-thermal; present-day)</td><td>6.0 x 10<sup>25</sup> s<sup>-1</sup></td></tr><tr><td>Base of the exosphere</td><td>200 km</td></tr><tr><td>Radius of the extended atmosphere (in planetary radii)</td><td>8</td></tr><tr><td>Energy deposition efficiency (hydrodynamic escape)</td><td>15%</td></tr><tr><td>Exospheric temperature (hydrodynamic escape)</td><td>2000 K</td></tr><tr><td colspan="2"><strong>Impact modeling</strong></td></tr><tr><td>Efficiency of impact energy transfer into mantle</td><td>0.3</td></tr><tr><td>Impactor density</td><td>2700 kg/m<sup>3</sup></td></tr><tr><td>EC H<sub>2</sub>O content</td><td>0.1%</td></tr><tr><td>EC CO<sub>2</sub> content</td><td>0.4%</td></tr><tr><td>EC N<sub>2</sub> content</td><td>0.02%</td></tr><tr><td>CC H<sub>2</sub>O content</td><td>8%</td></tr><tr><td>CC CO<sub>2</sub> content</td><td>4%</td></tr><tr><td>CC N<sub>2</sub> content</td><td>0.2%</td></tr></tbody></table>

Extended Data Fig. 5 | List of parameters and values.
<table><thead><tr><th>Parameter</th><th>MAX</th><th>MED</th><th>MIN</th></tr></thead><tbody><tr><td>Oxygen escape scheme (from Kulikov et al., 2006)</td><td>Case 2b</td><td>Case 2b</td><td>Case 4</td></tr><tr><td>Multiplication factor for all mechanisms</td><td>5</td><td>2.5</td><td>6</td></tr><tr><td>Impact erosion scheme</td><td>Tangent plane</td><td>Tangent plane</td><td>SOVA models</td></tr></tbody></table>

Extended Data Fig. 6 | MAX, MED and MIN specific parameter sets.