Numerous chondritic impactors and oxidized magma ocean set Earth’s volatile depletion

Earth’s surface environment is largely influenced by its budget of major volatile elements: carbon (C), nitrogen (N), and hydrogen (H). Although the volatiles on Earth are thought to have been delivered by chondritic materials, the elemental composition of the bulk silicate Earth (BSE) shows depletion in the order of N, C, and H. Previous studies have concluded that non-chondritic materials are needed for this depletion pattern. Here, we model the evolution of the volatile abundances in the atmosphere, oceans, crust, mantle, and core through the accretion history by considering elemental partitioning and impact erosion. We show that the BSE depletion pattern can be reproduced from continuous accretion of chondritic bodies by the partitioning of C into the core and H storage in the magma ocean in the main accretion stage and atmospheric erosion of N in the late accretion stage. This scenario requires a relatively oxidized magma ocean (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} f_{{\mathrm{O}}_2}$$\end{document}log10fO2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gtrsim$$\end{document}≳ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{IW}}$$\end{document}IW\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-2$$\end{document}-2, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{{\mathrm{O}}_2}$$\end{document}fO2 is the oxygen fugacity, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{IW}$$\end{document}IW is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\log _{10} f_{{\mathrm{O}}_2}^{\mathrm{IW}}$$\end{document}log10fO2IW, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{{\mathrm{O}}_2}^{\mathrm{IW}}$$\end{document}fO2IW is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{{\mathrm{O}}_2}$$\end{document}fO2 at the iron-wüstite buffer), the dominance of small impactors in the late accretion, and the storage of H and C in oceanic water and carbonate rocks in the late accretion stage, all of which are naturally expected from the formation of an Earth-sized planet in the habitable zone.

consistent with classical models such as the Ringwood model 4 , which contains 10 wt.% CI chondrites in the building blocks as well as Wänke 5 who argued 20 wt.%. Recent works also suggest a similar range of 8 wt.%-20 wt.% 6,7 . As the most important point of this study was reproducing the V-shaped relative depletion pattern by considering realistic processes to the extent of today's observational uncertainties, adopting higher BSE abundances by a factor of a few does not change our conclusions.
Enstatite chondrites are also candidates for Earth's building blocks and might have supplied Earth's major volatile elements 8 . 25 We performed our model calculation for Enstatite chondrite-like impactors (see Supplementary Fig. S3 and S4) whose volatile abundances are listed in Table 1 (EC model) in the main manuscript. We set the same scenario as Fig. 2 and Fig. 3. Furthermore, we changed the redox state setting of the magma ocean since the relationship between them is still not comprehensively understood (Fig. S5). The current V-shaped C-N-H depletion pattern of BSE was successfully reproduced even with Enstatites chondritic building blocks when metal-silicate fractionation occurred under the oxidized condition(log 10 f O 2 ∼ log 10 f IW O 2 + 1), 30 but the requirement for the oxidization state was stricter than the nominal CI model (Fig. 4d). The final H abundance in the case where impactors of the EC model and intermediate oxidization state (log 10 f O 2 ∼ log 10 f IW O 2 − 2) was slightly smaller than the minimum estimate for BSE owing to the low content of H in the EC model. These results suggest that either accretion of H-rich materials (such as the CI model) or metal-silicate partitioning under oxidized conditions in the magma ocean (such as the EC model with the oxidized magma ocean) are required for reproducing the Earth's volatile composition.

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As Enstatite chondrites' chemical composition is reduced and has a large fraction of iron relative to other chondrites, 100% Enstatite chondrite accretion may not allow for this oxidized condition. However, core formation is a self-oxidizing process 9, 10 , and the actual redox state of the magma ocean as a function of that of accreting bodies is not fully understood. Thus, given the limitations of our understanding, our treatment to assume the building blocks and the magma ocean redox state as independent parameters should be justified. These results suggest that core segregation and atmospheric erosion by impacts solve the 40 discrepancy between BSE and chondrites to the extent of today's observational uncertainties.

Solubilities and partitioning coefficients
The element behaviour and the flux balance between the atmospheric erosion and the core segregation depend on the solubilities and partitioning coefficients that depend on P-Tf O 2 conditions. However, the exact conditions of the magma ocean have not been fully elucidated and the oxygen fugacity f O 2 in the magma ocean would have evolved over time 9 . Furthermore, each 45 partitioning coefficient as a function of P-Tf O 2 has not been well-established yet. In the current understanding, C and H have been found to be strongly siderophile 11,12 , while N acts as a mildly lithophile to mildly siderophile 13 , but these properties have not been fully achieved consensus. Given these limitations, in order to understand the physical behaviour of volatile element partitioning, we test cases where we varied each parameter separately, which help us to understand the element partitioning once these parameters are better constrained in the future. Supplementary Fig. S6 shows the dependence of the BSE volatile composition on the solubilities and partitioning coefficients.
C is generally thought to be a highly siderophile element [13][14][15] . C partition coefficient D C increases linearly with decreasing f O 2 under relatively oxidized conditions (log 10 f O 2 log 10 f IW O 2 − 3 to −1.5) but starts to decreases with decreasing f O 2 under more reduced conditions. As shown in Case (a), a higher D C leads to a smaller amount of C in BSE because C transportation to the core is enhanced. C would be significantly depleted compared with the current BSE when a high D C (D C = 5670 in 55 Case a) is assumed throughout the core formation. It has been proposed that C can be much less siderophile under high P-T conditions 16 , but adopting an extremely low value D C = 0.5 (Case b) still reproduce the current BSE's abundance. This is because the low solubility of C enables atmospheric erosion to buffer the effect to reduce partitioning into the core. C becomes less (more) soluble in silicate melt under more reduced (oxidized) conditions 17 . A lower S C leads to less C partitioned into the core, but its influence is smaller compared with that of D C in the range we investigated (Cases c and d).

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N partitioning depends chiefly on f O 2 rather than P and T 13 -N becomes more soluble and D N decreases with decreasing f O 2 [18][19][20] . However, with any values of D N considered, the current N content in BSE was finally reproduced (Cases e and f), which is the same for the solubility as well (Cases g and h). The final N content in BSE was determined by the balance of the supply and loss during late accretion owing to the low D N and S N as discussed in the main text, and thus the results are insensitive to D N and S N .
H is weakly siderophile at low pressure (∼20 GPa) and becomes much more strongly siderophile with increasing pressure 21 , and D H decreases with increasing f O 2 22 . Under relatively oxidized conditions (log 10 f O 2 log 10 f IW O 2 − 2), H is highly soluble in silicate melt 2 , while H becomes less soluble under more reduced conditions. We note that varying H solubility by a factor of 2 does not change the results significantly (Cases k and l). The core formation under highly siderophile condition (log 10 f O 2 ∼ log 10 f IW O 2 − 3.5) would result in a deficit of water in BSE owing to both enhanced partitioning into the core with 70 high D H (Case i) and a small H storage in the magma ocean as discussed in the main text. In contrast to previous findings, some recent experiments reported a much less siderophile property at high P-T for H 23,24 . Adopting a lower partitioning coefficient leads to a higher abundance in BSE, but the results are within the estimate of H content in the current BSE (Case j). Table S1. Parameter set of partitioning coefficients and solubilities for the parameter survey in Fig. S6.    Figure S1. Dependence of final volatile composition of BSE on the parameters which have minor influences. In all cases, the other parameters are the same with the nominal model. a. Influence of the surface temperature on the impact-induced atmospheric erosion in our model in the main accretion. We set 1,500 K in the nominal model and varied it from 1,000 K to 3,000 K. All plots are almost overlapped. b. Effects of the atmospheric erosion by giant impacts. We calculated for the cases where the erosion efficiency of giant impact is three times higher and lower than Schlichting model which we used for our nominal model. c. Dependence on the magma ocean depth. We varied the silicate melt mass fraction on accreting Earth to 20 wt.% (orange), 30 wt.% (red), and 60 wt.% (brown). We also tested the case where a shallow magma ocean is formed after the moon-forming giant impact (pink). d. Dependence on the suspended metal fraction in the magma ocean. The results for different metal fractions from 10 −6 to 10 −2 are plotted, but all lines are overlapped.   Supplementary Table S1. The cases R and m show dependence on D H in the reduced magma ocean case.