The Existing Frameworks of Delivery of Major Volatiles and the Feasibility of Mars-Mass Planetary Embryos as the Major Volatile Contributors to Bulk Silicate Earth

This model of addition of volatile elements to Earth via late accreting materials has been the most popular (Chou et al., 1983; Holzheid et al., 2000; Kimura et al., 1974; Walker, 2009). The hypothesis considers Earth to have accreted almost “dry” in the main accretion phase and remained volatile-free through the last Moon-forming giant impact (Fig. 1a). This is followed by adding volatile-rich material with a mass of 4.86 ± 1.63 × 10⁻³ M_E (M_E-Mass of Earth) (Walker, 2009; Morbidelli and Wood, 2015). The late veneer hypothesis is chiefly based on the observation that the HSE concentration in the BSE is significantly higher than what is expected after the equilibrium core–mantle differentiation. Low-pressure, high-temperature alloy melt–silicate melt partitioning experiments showed that HSEs are partitioned strongly to the alloy melt compared with the equilibrium silicate melt (Holzheid et al., 2000; O'Neill et al., 1995). This led to the suggestion that a small fraction of chondritic materials should be added to the BSE after core formation is complete.

The nature of this late-added material has been studied and debated. Most studies argued for a carbonaceous chondrite (CC) origin of the late veneer (Budde et al., 2019; Dauphas et al., 2002; Dauphas and Marty, 2002; Fischer-Gödde and Becker, 2012; Wang and Becker, 2013). For instance, Dauphas and Marty (2002) argued for an outer solar system CC origin of the late veneer based on noble metals such as osmium and noble gases such as krypton and xenon. Similar arguments have been made based on the elemental and isotopic signatures of siderophile elements (osmium isotopes and Ru/Ir, Pt/Ir, Pd/Ir—Fischer-Gödde and Becker, 2012; S-Se-Te estimates—Wang and Becker, 2013; Mo isotopes—Budde et al., 2019). In addition, the D/H signature of Earth’s ocean is very similar to the D/H signature of the CCs (Alexander, 2017, 2022; Drake and Righter, 2002). Alexander (2017) discussed the D/H ratio of bulk Earth as closest to the D/H signature of CI and CM chondrites. Piani et al. (2018) measured the D/H in six CM chondrites, which further confirmed that the CM chondrites hosted components that are considered to be the ubiquitous water reservoir in the inner protoplanetary disk. In contrast, an inner solar system origin of late veneer has also been proposed (Dauphas et al., 2004; Fischer-Gödde and Kleine, 2017; Hopp et al., 2020). Dauphas et al. (2004), based on the Mo-Ru isotopic systematics, argued that the late veneer constituted the same material as Earth. Dauphas et al. (2024) modeled Earth’s accretion using the isotopic signatures of various lithophile and siderophile elements and argued that the Earth was accreted primarily in the following two different stages: The first 60% of the Earth was dominated by inner solar system material, and the second stage was dominated by inner solar system material, with a minor contribution of outer solar system chondrites. Moreover, the inner solar system origin of late veneer was also later validated by new estimates of the Ru isotopes in CCs (Fischer-Gödde and Kleine, 2017), which showed distinct values compared with those of Earth and consequently pointed toward an inner solar system origin of late veneer. Another line of evidence for the inner solar system origin of the late veneer is the ²H/¹H signature of Earth. For instance, the H isotope value of enstatite chondrites (−100 to −150‰) falls within the range of Earth’s mantle (−220 to −20‰; Piani et al., 2020); this provides further geochemical evidence for inner solar system objects supplying volatiles to Earth.

However, Earth’s LEVE budget may not explicitly require contributions from the late veneer, and the structure and the compositional makeup of the late veneer may pose a challenge in explaining the BSE LEVE. For instance, it has been observed from recent high-pressure S partitioning between alloy melt and silicate melt (Suer et al., 2017) that S becomes less siderophile at high pressures (e.g., ∼55 GPa). This, in turn, lowers the estimated mass of the veneer required to be delivered to explain the BSE S content. More recently, molecular dynamics simulations have also shown that the isotopic signature of S, Se, and Te can be established by protoplanetary differentiation and would not require a significant contribution from the late veneer (Wang et al., 2023). Current estimates of high H content in the inner solar system enstatite chondrites (Piani et al., 2020) also argue that Earth might have received a substantial portion of at least one of the LEVEs very early on in its growth, which therefore makes the requirement for late veneer less compelling. Moreover, the retention of the late veneer material in Earth’s mantle could be challenging, especially if the required late veneer component was in the cores of differentiated bodies. For example, it remains uncertain how much core materials could be retained in the silicate MO or solid matrix. Strong density contrast should facilitate Fe-rich metallic core materials sinking to the base of the MO efficiently. Furthermore, short-lived mechanical instabilities (<1 day) could allow the metal droplets to percolate to the core through the solid silicate matrix of the unmolten mantle beneath the MO (Korenaga and Marchi, 2023). Finally, the relative abundance of the major volatiles in the BSE is not in chondritic ratios (Fig. 2; e.g., Bergin et al., 2015; Chi et al., 2014; Dasgupta and Grewal, 2019; Grewal et al., 2019; Hirschmann, 2016; Marty, 2012). Therefore, even if chondritic late veneer was responsible for delivering some or all of the terrestrial volatiles, such materials should have been processed for differential loss of LEVEs. Alternatively, other processes should have delivered LEVEs to prelate veneer proto-Earth in sufficient quantities such that the chondritic LEVE abundance pattern of the late veneer could not overprint the LEVE ratios established during prior episodes of growth of proto-Earth.

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FIG. 2.

The present-day bulk silicate Earth (BSE) estimates of C, N, H, and S normalized to their average CI-chondrite estimate. The BSE LEVE estimates are from different studies based on various approaches, as given in the legend. The BSE C budget remains the most debated. The C estimates are from Hirschmann (2018) (H18), Marty et al. (2020) (M20), and Sun and Dasgupta, 2023 (2022) (SD22). The N estimate is from M20 and H estimate is from Marty (2012) (M12). The S estimate is from Palme and O’Neill (2014) (PO14). The general trend is that the C abundance in BSE is higher than that of N and is almost similar to that of S.

The idea of cometary delivery of volatiles (Fig. 1b) has been a natural extension of the idea of late delivery of volatiles to a predominantly “dry” Earth (Fig. 1a). The advent of this idea dates back to 1960s–1970s, when it was thought that Earth’s oceans, atmosphere, and organics were delivered by volatile-rich bodies that originated at large heliocentric distances with a significant possibility of colliding with Earth (Anders and Owen, 1977; Chyba et al., 1990; Oró, 1961). In addition, dynamical studies have also looked at the cometary delivery to Earth (Joiret et al., 2024, 2023; Morbidelli et al., 2000; Raymond et al., 2004). The volatile delivery for comets has been mostly constrained based on the noble gas signature of Earth’s present-day atmosphere and mantle (Marty, 2012; Marty et al., 2016; Owen and Bar-Nun, 1995). For instance, Ar/Kr/Xe ratios of Earth’s atmosphere were thought to be established by the delivery of cometary ice (Owen and Bar-Nun, 1995). More recent estimates have accounted for a 20% contribution of cometary material to explain the noble gas (i.e., Kr and Xe) signature of Earth’s atmosphere (Bekaert et al., 2020; Marty et al., 2017). The estimates based on ¹³²Xe/C, ¹³²Xe/N, and ¹³²Xe/H₂O of the chondrites and the comets yield a variety of cometary contributions to Earth’s volatile budget that range from <0.07% to as high as 80% (Bekaert et al., 2020), whereas halogens in comets (Dhooghe et al., 2017) and chondrites (Clay et al., 2017) suggested an extremely minor contribution of cometary volatiles (<0.5%; Bekaert et al., 2020). However, the biggest challenge to the cometary delivery of LEVEs to Earth is the isotopic signature of N, H, and C in Earth’s mantle. The isotopic signature of Earth in terms of N and H points toward a chondritic nature of Earth’s N and H inventory (Marty et al., 2016; Alexander et al., 2012) and not that of comets (e.g., see reviews by Marty and Yokochi, 2006; Dasgupta and Grewal, 2019; Dasgupta et al., 2024). Moreover, the isotopic and elemental abundance of LEVEs in comets is not well constrained and is based only on a few measured comets (Bekaert et al., 2020; Marty et al., 2016). If we consider that the late veneer material (0.5% of present-day Earth mass) was wholly made up of comets, then the budget of volatiles supplied to a volatile-free proto-Earth would be significantly more than the present-day BSE estimates. For instance, atmospheric ³⁶Ar would be almost 2–3 orders of magnitude higher than the present-day budget. Similarly, a much higher budget of C and N would be delivered to Earth’s mantle. Therefore, cometary delivery is not thought to be the main mechanism that established the present-day budget of C, N, and S unless the comets were severely processed in terms of their volatile budget and compositions.

2.3. LEVE delivery by differentiated planetesimals

The traditional models are based on the premise that Earth received its LEVEs from volatile-rich late-impacting bodies that were undifferentiated (Fig. 1a, b; Supplementary Table S1; Albarède, 2009). However, the C, N, H, and S budgets in the BSE are differentially depleted relative to the chondrites, although the estimated extent of depletion varies from one study to another (Fig. 2; Supplementary Table S1; Halliday, 2013; Marty and Zimmermann, 1999; Marty et al., 2020; Hirschmann, 2018).

Hirschmann (2018), building on Bergin et al. (2015), estimated a C concentration of 110 ± 40 ppm using the CO₂/Ba ratio of the mantle-derived basalts. In contrast, Marty et al. (2020) estimated a C budget of 330–450 ppm for the BSE based on the C/³He analysis of CO₂-rich volcanic gases, corrected for degassing by using the noble gas ratio of ⁴He/⁴⁰Ar. Sun and Dasgupta (2023) also estimated an average C budget of 330–400 ppm for the Ocean Island Basalts (OIB) source regions, which may also be the less degassed mantle domains akin to the BSE. For N, the N₂/Ar ratio of the magmatic gases has been used to estimate 2.1–3.5 ppm of N in the BSE (Hirschmann, 2018; Marty et al., 2020). In the case of S, the chalcophile element and S geochemistry of basalts have been used to estimate a bulk budget of 200–225 ppm S in the BSE (Hirschmann, 2016). Finally, the H budget of the BSE has been calculated to be∼110 ppm based on the water content of oceanic basalts (Marty, 2012). Although the BSE S and H budgets have been debated less in current literature, even these estimates remain highly uncertain. Nevertheless, the current estimates reveal that the major volatiles in the BSE are variably depleted with respect to CC. This promoted the idea that perhaps the terrestrial volatile delivery was dominated by thermally processed objects rather than unmodified chondrites.

One mode of thermal processing of parent bodies is where the bodies undergo complete differentiation to produce a silicate mantle (MO), an alloy melt core, and an atmosphere (Fig. 1c; Li et al., 2016; Dasgupta and Grewal, 2019; Grewal et al., 2019, 2021a; Hirschmann et al., 2021; Lichtenberg et al., 2019; Rubie et al., 2015, 2011; Young et al., 2023). The depletion pattern of C, N, H, and S has been explained by various models that have attempted to incorporate a geochemical differentiation scheme coupled with various accretionary scenarios to establish the present-day BSE estimates of Earth (Chen and Jacobson, 2022; Dasgupta and Grewal, 2019; Grewal et al., 2019; Gu et al., 2024; Hirschmann, 2016; Sakuraba et al., 2021; Shi et al., 2022). Some of these models have used dynamically constrained N-body simulation outputs for their geochemical model, which in turn is controlled by the solubility of these volatiles in the silicate melt as well as the partitioning of these volatiles between alloy melt and silicate melt (Chen and Jacobson, 2022; Gu et al., 2024; Sakuraba et al., 2021; Shi et al., 2022). In addition, these models, in various degrees, have tried to incorporate different physical processes such as impact erosion (Gu et al., 2024), core formation (Gu et al., 2024; Sakuraba et al., 2021; Shi et al., 2022), and MO degassing (e.g., Li et al., 2023) to establish the present-day estimates of C, N, H, and S. These estimates rely heavily on the high pressure (P)–temperature (T) experimental studies, which are mostly restricted to modest P-T conditions. The P-T of these experiments were conducted for conditions of small protoplanets and terrestrial embryos (0.5 GPa ≤P≤20 GPa and temperatures up to 2500 K; Boujibar et al., 2014; Dasgupta et al., 2009; Grewal et al., 2019; Malavergne et al., 2019). Recently, experiments were conducted at pressures beyond 20 GPa, reaching up to 108 GPa, and temperatures up to 5500 K (Blanchard et al., 2022; Huang et al., 2024; Jackson et al., 2021; Roskosz et al., 2013; Suer et al., 2017; Tagawa et al., 2021). Even though these experiments covered a significant range of P-T, they did not reach conditions of planetary differentiation that could lead to complete vaporization, such as those that may be realized in the aftermath of giant impacts (Caracas and Stewart, 2023; Ćuk and Stewart, 2012), where pressures go significantly above 100 GPa (Lock and Stewart, 2019) and temperatures reach around 7000 K (Nakajima and Stevenson, 2014). Moreover, the chemical system in which these studies were performed also needs to be more realistic to mimic the chemical compositions of our early solar system MO, which are considered to be peridotitic. The main experimental challenge lies in retrieving such ultramafic glasses. More importantly, the accretionary pathways that result in widespread differentiation also cause a significant loss of the volatiles in the form of proto-atmosphere overlying the surficial MOs developed in these bodies (Hirschmann et al., 2021; Lammer et al., 2020; Pringle et al., 2014). Furthermore, studies of achondrite meteorites reveal that differentiation leads to significant volatile loss (Harries et al., 2023; Newcombe et al., 2023; Peterson et al., 2024, 2023a, 2023b; Sarafian et al., 2017; Stephant et al., 2021). For instance, based on SIMS measurement of H₂O in nominally anhydrous minerals, the H₂O estimates in the parent bodies of ungrouped achondrites, aubrites, partially differentiated acapulcoites–lodranites, ureilites, and eucrites yielded values of 3–13 ppm (Newcombe et al., 2023), <10 ppm (Peterson et al., 2023a), <38 ppm (Peterson et al., 2024), 2–20 ppm (Peterson et al., 2023b), and ∼12–23 ppm (Stephant et al., 2021), respectively. Therefore, it remains a challenge for the models where differentiated bodies alone are invoked to establish the absolute LEVE budget of Earth. In fact, given that the volatile budget was delivered throughout the entire phase of Earth’s accretion, it is likely that undifferentiated, primitive objects also contributed to the LEVE budget. For instance, Péron et al. (2021) argued, based on the Kr isotopic compositions of OIBs, that Earth accreted undifferentiated, CC-like bodies very early on during the main phase of Earth’s accretion.

2.4. LEVE delivery by the last giant impactor

N-body simulation studies of Earth’s accretion have argued that around 80% of Earth’s growth happened by accretion of large differentiated Moon-Mars mass embryos (Raymond and Morbidelli, 2022). These high-energy accretion events could have sterilized Earth of the budget of LEVEs that it acquired from the start of its accretion (Albarède, 2009; Chyba et al., 1990; Halliday, 2008; Schlichting and Mukhopadhyay, 2018). Therefore, the next logical question is whether the Moon-forming last giant impact could deliver the LEVEs, as there would be less probability of loss via any major impacts afterward. Various works have argued that the last giant impact could have been an essential event in determining the orbital (Ćuk and Stewart, 2012; Gabriel and Cambioni, 2023) and elemental characteristics of Earth (Fig. 1d; Grewal et al., 2019; Li et al., 2016; Mezger et al., 2021; Sleep, 2016). This last giant impact is thought to have involved the impact of a Mars-sized giant impactor to a Venus-sized proto-Earth (Fig. 1d; Halliday and Canup, 2022). More importantly, the last giant impact has been argued to have been capable of setting up the present-day BSE LEVE budget. For instance, Grewal et al. (2019) argued that a Mars-sized differentiated impactor would have been sufficient to deliver the present-day budget of C, N, and S. In another work, Mezger et al. (2021) argued that the Moon-forming giant impactor could have delivered the moderately volatile elements to the volatile-free proto-Earth. More interestingly, Sleep (2016) argued that the core of the final giant impactor, Theia, could have acted as the late veneer material and could have supplied the present-day HSE budget of Earth’s mantle. A major uncertainty with this mechanism of volatile delivery is the lack of knowledge on the chemical and physical properties of the last giant impactor. There is a dearth of estimates of Theia’s bulk LEVE budget, with the existing estimates being hugely model dependent (e.g., Grewal et al., 2019, 2024). Specifically, some models of LEVE delivery that involve Theia, which likely was a differentiated object, did not fully consider MO-atmosphere fractionation (e.g., Grewal et al., 2019) or did not consider the influence of possible growth scenarios for Theia (e.g., Grewal et al., 2024). Similarly, all of these models focused entirely on the silicate reservoir of the Mars-size planetary embryo to deliver the BSE volatiles; they ignored entirely the possible contributions from the embryo’s core. Finally, the giant impact hypothesis cannot alone explain the Moon’s volatile-depleted nature and establish Earth’s volatile distribution.

Motivated by the knowledge gap around the feasibility of Theia bringing LEVE to Earth, in the second part of the study, we present a geochemical model that combines different accretion scenarios to estimate the budget of C, N, H, and S in the silicate and metallic reservoir of a Mars-mass embryo. An approach such as this was adopted before (Chen and Jacobson, 2022; Gu et al., 2024), where N-body simulations were combined with geochemical and other physical models. In contrast, our model is more simplistic and aims to provide deeper insights into the evolution of the C, N, H, and S inventory of the main reservoirs of a planetary embryo. Although simple, the end-member accretion scenarios used here provide a framework of accretion and geochemical evolution going hand in hand. In the following sections, we describe the methodology followed by the results of our model and their implications.

3.1. General framework

Objects of different sizes and masses populated the early solar system. The objects ranged in size from smaller than Vesta to almost the size of Mars. The masses and sizes of the bodies are documented in the Supplementary Data (Supplementary Table S2). The embryos modeled here are all Mars-mass bodies, built by various accretion scenarios, which differ by the combination of body masses that come together to make the final embryo. The mass of the planetary embryo is fixed at Mars mass, as dynamical studies usually considered a large fraction of their planetary embryos to be Mars mass. Moreover, SPH studies also considered Theia to be Mars mass (discussed in Halliday and Canup, 2022). Grewal et al. (2021a) took an approach similar to this for tracking the N budget of the BSE from different accretional scenarios. We grew a Mars-mass body by the following scenarios—(1) Accreting only Vesta-mass bodies (Vesta); (2) accreting only intermediate mass (the mass of the body lying between that of Vesta and Moon [Supplementary Table S2]) bodies (Int); (3) accreting only Moon-mass bodies (Moon); (4) accreting Vesta-mass bodies to form intermediate mass bodies, which are then used to make a Mars-mass body (Vesta-intermediate-Mars); (5) accreting intermediate-mass bodies to form Moon-mass bodies, which are then used to grow a Mars-mass body (intermediate-Moon-Mars); (6) accreting only Vesta-mass bodies to form intermediate-mass bodies, which are used to form Moon-mass bodies, which in turn are used to construct a Mars-mass body (Vesta-intermediate-Moon-Mars).

We couple geochemical fractionation calculations involving three reservoirs, that is, alloy melt, silicate MO, and a gaseous atmosphere, with these accretion scenarios to determine the C, N, H, and S abundances in these protobodies. This follows an approach that has been adopted in some recent studies (Grewal et al., 2021a, 2024; Gu et al., 2024; Hirschmann, 2016; Pathak and Dasgupta, 2024; Shi et al., 2022) and reviewed by Dasgupta and Grewal (2019) and Dasgupta et al. (2024). The solubility of C, N, H, and S in the silicate melt or MO is dictated by the vapor pressure of the gaseous species of that element in the overlying atmosphere. This sets up the volatile budget in the silicate melt, which also undergoes simultaneous alloy melt–silicate melt partitioning between the MO and the metallic core. The mass balance can be represented by the following equations:

The concentration of the volatile in the silicate MO is represented by the following:

We couple the geochemical fractionation model with the accretion model in a self-consistent framework. The equilibration pressure after each impact is based on the prescription of Badro et al. (2015) and Tagawa et al. (2021) along with an associated temperature increase of the target body estimated from Rubie et al. (2011, 2015), and acceleration due to gravity of the growing body and density of the postimpact body are all calculated in a self-consistent manner with each impact. The equilibration pressure for the core of the impactor and the MO takes place at a fixed fraction of the core–mantle boundary pressure (Badro et al., 2015; Tagawa et al., 2021). The core–mantle boundary pressure of the embryo is fixed at 21 GPa (Rivoldini et al., 2011). At each iteration, the equilibrium pressure for the LEVE partitioning parameterizations is considered to be at the fixed fraction of this pressure.

The impactors first undergo the three-reservoir core–mantle (MO)–atmosphere fractionation, which sets up the volatile budget of the impactor’s core, its silicate MO, and its atmosphere. After the three-reservoir differentiation of these bodies, their atmospheres are lost to space. Following that, the impactors are added to the target body. After accretion of each impactor to the target body, the new LEVE budget that is available for further three-reservoir fractionation is that of the target’s MO volatile budget, the impactor’s MO volatile budget, and the impactor’s core volatile budget. Upon impact, the impactor’s MO adds to the target’s MO, with the impactor’s core completely involved in chemical equilibrium with the target’s MO. Following chemical equilibration, the impactor’s core merges with the target’s core. The atmosphere is lost after every iteration of the geochemical fractionation, which is a reasonable assumption for small bodies leading up to the size of Mars (Young et al., 2023). We varied parameters such as fO₂ prevailing during differentiation (from IW−2 to IW+2, where IW stands for fO₂ set by equilibrium coexistence of Fe-metal and FeO), the silicate-mass fraction (SMF), the depth of the MO, and the initial LEVE budget of the undifferentiated building blocks (initial LEVE concentration documented in Supplementary Table S1). We have discussed the choice of these parameters in the Supplementary Data in more detail.

5.1. Influence of accretional parameters on the Mars-like embryo LEVE budget

5.2. LEVE ratios of the silicate reservoir of the planetary embryo

One key goal of our new calculations was to test whether a main geochemical reservoir in a planetary embryo can achieve LEVE absolute and/or relative abundance similar to that of the BSE. In other words, whether a large impactor that likely contributed to the growth of Earth could bring in the geochemical characteristics of the LEVEs that are observed in present-day Earth. Furthermore, if such desired characteristics are indeed achieved in a Mars-mass embryo, the question is what accretional conditions allow such characteristics to be achieved.

5.3. The BSE LEVE budget and its relation to the LEVE budget of the embryo’s condensed reservoirs

The range of LEVE budgets estimated for the giant impactor or the planetary embryo in this study represents the volatile budgets of the Moon-forming giant impactor, Theia, or a similar type of giant impactor, which may not necessarily have been the final giant impactor. We observed that the MO of a Mars-mass embryo can achieve C, N, H, and S budgets relative to each other that resemble the present-day BSE ratios if the embryo accreted from bodies that underwent differentiation under relatively oxidizing conditions (fO₂ ≥ IW−1; Fig. 6). However, most of the MO LEVE estimates for the embryo obtained from our modeling are at least 1–2 orders of magnitude lower than the present-day BSE abundances. Therefore, none of the accretion scenarios that produce a Mars-mass giant impactor would deliver a sufficient LEVE budget to Earth’s mantle to account for the present-day LEVE abundances in the BSE if a perfect core merger occurred between the embryo and the volatile-free proto-Earth. A recent study also argued that a Mars-mass giant impactor would contribute only a minimal amount of LEVEs to the Earth (Grewal et al., 2024). However, that study did not consider the accretionary growth of the embryo, leading to a difference in the required C, N, H, and S budgets in the Moon-forming impactor compared with our results.

In the case of the core of our modeled embryo, although the most oxidizing conditions (IW+2) result in a superchondritic C/N and H/N ratios (Fig. 3b), these ratios are far more extreme than those estimated for the present-day BSE. In contrast, under reducing conditions (e.g., IW−2; Fig. 4b), the core LEVE pattern for C, N, and H is a much closer match to the BSE abundance pattern. The LEVE ratios in the core of the embryo depend on both the LEVE budgets in the silicate MO and the alloy melt–silicate melt partition coefficients of the LEVEs. For S and H, the fO₂ variations do not produce significant differences in their relative core abundances. However, the effects on C and N are more pronounced. Under the most oxidizing conditions (IW+2), a relatively larger budget of C dissolves into the MO; this results in a greater budget of partitioning of C into the impactor’s core. In contrast, the budget of N dissolved in the MO is lower under these oxidizing conditions, which leads to a lower sequestration of N in the core. This coupled effect generates an extreme superchondritic C/N ratio in the core (Fig. 3b). Conversely, under the most reducing conditions (IW−2), a lower C budget dissolves in the MO and results in reduced sequestration of C in the core. Simultaneously, a larger N budget dissolves in the MO, which leads to increased N sequestration in the core. This behavior arises because N is less siderophile under reducing conditions (e.g., IW−2) compared with oxidizing conditions (e.g., >IW−1) (Grewal et al., 2021a). Consequently, the C/N ratio in the core under the most reducing conditions is still superchondritic but is much closer to the BSE estimate (Fig. 4b).

Notably, in terms of the absolute budget, our estimated LEVE content in the core of the planetary embryo overlaps with and in some cases exceeds the present-day BSE budget (Figs. 3b and 4b). Therefore, if there was partial equilibration between the impactor’s core and proto-Earth’s silicate MO, significantly more C, N, H, and S would have been available for subsequent three-reservoir fractionation. This would ultimately result in an increased volatile budget in the MO of post-impact Earth. Similarly, if a fraction of the impactor’s core became entrained in the silicate matrix underlying the MO, the LEVE budget delivered to the silicate reservoir of the volatile-free proto-Earth could have been significantly higher. Stranded metal could subsequently mix into the silicate matrix beneath the MO through solid-state convection; this would further supplement the LEVE supply from the silicate portion of the embryo. The effectiveness of the impactor’s core in supplying LEVEs to the silicate Earth depends on the fraction of core material that becomes trapped in the silicate matrix. This, in turn, is controlled by the dynamics of metallic melt percolation and the extent of the impactor’s core breakup (Röhlen et al., 2025). However, such detailed considerations are beyond the scope of this study.

Our model in this study represents an end-member scenario in which accretion and merger involve fully differentiated bodies. While this is possible, smaller, undifferentiated bodies may also have contributed directly to the mantle of the growing Earth without experiencing core formation. Such contributions could significantly increase the volatile budget of the MO without sequestrating volatiles into a core. For example, recent work has highlighted the role of undifferentiated bodies in delivering water to the Earth (Newcombe et al., 2023). We suggest that the quantity of volatile-rich, undifferentiated bodies required to match the present-day BSE budget is influenced not only by the volatile contributions from the silicate portions of differentiated embryos but also by the fraction of each embryo’s core that became trapped at the base of Earth’s silicate MO.

5.4. Implications for solar system dynamics

We argue that the silicate MO of the modeled planetary embryos needs to evolve to oxidizing conditions (logf O₂ ≥ IW−1) to have some resemblance to the BSE abundance pattern of the LEVEs. However, the cores of planetary embryos achieve a chondrite-normalized LEVE (in particular C, N, and H) pattern, akin to the BSE pattern at reducing conditions. This implies that a range of differentiated planetary embryos could supply the BSE-like volatile patterns, depending on whether the silicate versus the metallic reservoir plays the most important role.

The evolution of planetary bodies in the inner solar system to highly oxidizing conditions can be evaluated in the context of the timing of giant planet instability. This instability refers to the time period of chaotic dynamical disruption caused by interplanetary gravitational interactions (Tsiganis et al., 2005). However, the timing of such instability varies significantly, ranging from less than 10 million years (Clement et al., 2018; Liu et al., 2022; Walsh et al., 2011) to 100 million years after the solar system’s formation (Nesvorný et al., 2018; Ribeiro R de et al., 2020), depending on the processes invoked to trigger it. For the Mars-mass embryos to evolve to high fO_2s, they probably accreted a substantial amount of oxidized material, potentially delivered from the outer solar system. Dynamical accretion models suggest that such implantation of oxidized materials (Raymond and Izidoro, 2017) into the terrestrial planet-forming region is feasible during the period of giant planet instability. Consequently, the timing of this instability serves as an earliest time line, beyond which embryos could achieve high fO₂s (logf O₂ ≥ IW−1). Reduced conditions in the metal-silicate systems could have been present in the terrestrial planet-forming regions from the very early part of the solar system, however. Hence, early planetary embryonic cores could have achieved a BSE-like LEVE budget and could have contributed to building proto-Earth’s LEVE budget through core breakup and mixing during planetary collisions at timescales as early as <10 million years of the solar system’s formation.

5.5. Assumptions and caveats

Although our models provide important insights into the possible modes of volatile delivery to the growing Earth, our study made important assumptions, as other studies have done. First, the redox evolution of the growing bodies was not considered in a self-consistent manner. The entire process of accretion and equilibration in our models took place at fO₂ between IW−2 (most reduced) and IW+2 (most oxidized), which is a reasonable assumption as all terrestrial bodies such as Earth, Mars, and iron meteorites record fO₂ around these values (discussed more in the Supplementary Data; Righter et al., 2016). However, it is possible that each growth scenario was coupled with changes in the fO₂ conditions of differentiation (e.g., Rubie et al., 2015). Moreover, the evolution of fO₂ conditions to higher values (more than IW) is quite possible through the auto-oxidation of MO by stabilization of Fe³⁺ in deep MO (Armstrong et al., 2019; Deng et al., 2020; Hirschmann, 2022) or by addition of more oxidizing materials during the late stages of accretion. Second, our model assumes the loss of atmosphere at all steps of the accretion. This is also not unreasonable, as the gravitational forces of these small bodies are not large enough to hold onto an atmosphere. However, for a better representation of the contribution of atmospheric retention in the volatile budget of these bodies, one could consider a fraction of the atmosphere being retained in the embryo. Another crucial assumption was that the target mantle is completely molten, irrespective of the energetics of the impact. This is reasonable for bodies during the early stages of growth but not for the late stages when a small impactor may not be able to melt a big target. For instance, a Vesta-mass impactor would not necessarily melt the entire Mars-mass target’s mantle. Therefore, the effective MO-core ratios for equilibration could be different than those conceived in our models. Similarly, before each impact event, the MO of the accreting bodies may undergo partial to complete solidification, especially with the atmospheric blanket effect removed (e.g., Korenaga, 2023; Miyazaki and Korenaga, 2019). Therefore, the MO LEVE budget that is estimated here is an upper bound as more LEVEs are expected to outgas from the MO, and subsequently get lost, through crystallization; and only a limited portion is expected to remain via incorporation in the solid matrix and via entrapment of interstitial melt (e.g., Dasgupta et al., 2024; Hier-Majumder and Hirschmann, 2017; Pal and Dasgupta, 2024). The pattern of LEVE is expected to be modified via MO crystallization, which is not considered in our study.