Rehomogenizing the Earth-Moon system A giant impact formed the Moon, and lunar rocks provide insight into that process. Young et al. found that rocks on Earth and the Moon have identical oxygen isotopes. This suggests that well-mixed material from the giant impact must have formed both the Moon and Earth's mantle. The finding also constrains the composition of the “late veneer”: material sprinkled onto Earth after the Moon-forming impact. Science, this issue p. 493

Abstract Earth and the Moon are shown here to have indistinguishable oxygen isotope ratios, with a difference in Δ′17O of −1 ± 5 parts per million (2 standard error). On the basis of these data and our new planet formation simulations that include a realistic model for primordial oxygen isotopic reservoirs, our results favor vigorous mixing during the giant impact and therefore a high-energy, high-angular-momentum impact. The results indicate that the late veneer impactors had an average Δ′17O within approximately 1 per mil of the terrestrial value, limiting possible sources for this late addition of mass to the Earth-Moon system.

The Moon is thought to be the consequence of a giant collision between the proto-Earth and a planetary embryo (named Theia, “mother of the Moon”) ~108 years after the birth of the solar system (1, 2). However, the distinct oxygen isotopic signatures of solar system bodies (3, 4) has presented a problem for the impact hypothesis for the formation of the Moon (5, 6). In order to create an iron-poor Moon and simultaneously reproduce the angular momentum of the Earth-Moon system, early models required a glancing blow by a Mars-sized impactor that resulted in the Moon being composed mainly of impactor material (7). Therefore, in the general case the Moon and Earth should not be identical in their oxygen isotopic compositions. Nonetheless, until recently the Moon and Earth have been found to be indistinguishable in their oxygen isotope ratios (8–10). Proposed higher-energy giant impacts offer potential solutions to this conundrum (11), although at the expense of the need to shed substantial angular momentum from the system via orbital resonances (12).

Oxygen reservoirs comprising rocky bodies of the solar system are characterized by distinct relative concentrations of oxygen isotopes. These relative concentrations are customarily represented by Δ17O, the departure in 17O/16O relative to a given 18O/16O under the assumption that these two isotope ratios covary as a consequence of mass-dependent isotope fractionation. The small fractional differences in isotope ratios can be replaced with δ′17O = 103ln(17R/17R o ) and δ′18O = 103ln(18R/18R o ) (13) values, where 17R is 17O/16O, 18R is 18O/16O, and 17R o and 18R o refer to the initial isotope ratios (such as those characterizing bulk Earth) (14). These δ′ values are nearly equivalent to the fractional differences in per mil (‰) but are linearly related by the mass fractionation exponent β. The exact values for β depend on the processes involved in fractionation but are always near ½, as prescribed by oxygen isotope masses (13). With these definitions, Δ17O is written as Δ′17O = δ′17O – βδ′18O (1)A positive Δ′17O signifies that a reservoir is enriched in 17O relative to Earth, whereas a negative value signifies that a reservoir is relatively depleted in 17O compared with expectations from mass fractionation. At the scale of individual mineral grains, solar system materials exhibit variations in Δ′17O spanning ~200‰ (15). The dispersion in Δ′17O decreases drastically with mass. Differences in Δ′17O among meteorite whole-rock samples are ~5 to 8‰ (4, 16), representing parent asteroids with masses of ~1015 to 1017 kg. Differences between differentiated bodies with metal cores and silicate mantles are smaller still: Mars (6.4 × 1023 kg) has a Δ′17O value of about +0.3‰, whereas Vesta (2.6 × 1020 kg) has a value of −0.25‰ (17, 18). The reduced dispersion in Δ′17O with mass evidently reflects averaging as smaller rocky bodies coalesced to form larger bodies in the solar system (19, 20). Historically, the identical Δ′17O values for Earth and the Moon have stood out against this backdrop of variability in the solar system.

However, some high-precision measurements on lunar samples indicated that the Moon has a greater Δ′17O than that of Earth by 12 ± 3 parts per million (ppm) (21). The importance of this finding can be gauged by considering contours for Δ′17O Moon − Δ′17O Earth plotted as functions of the difference in Δ′17O between Theia and the proto-Earth and the difference in the fractions of the Moon and Earth inherited from Theia (Fig. 1A). The mass-balance equation plotted is (2)where x Theia, i refers to the oxygen fraction of body i derived from Theia (essentially, mass fractions of the bulk silicate portions of the bodies). For convenience, we also use the fractional difference δ Theia rather than the absolute difference in Eq. 2: (3)The implications of a difference in oxygen isotopic composition between the Moon and Earth depend on the fraction of Theia contained within Earth (Eqs. 2 and 3). Four recent proposed giant impact scenarios (5, 11, 12, 22) predict disparate differences in the Theia fractions in the Moon and Earth (Fig. 1A). If the difference in Δ′17O between Theia and the proto-Earth was zero, there is no oxygen isotope constraint on δ Theia (Fig. 1A). Similarly, if Earth and the Moon are composed of precisely the same concentrations of Theia, there is no constraint on differences in Δ′17O between Theia and the proto-Earth.

Fig. 1 Oxygen isotope mass balance diagram. (A) Contours of Δ′17O Moon − Δ′17O Earth in parts per milliion versus fractional differences in Theia content of the bulk silicate Moon and Earth and Δ′17O Theia − Δ′17O proto-Earth . The contour interval is 2 ppm. The pink region indicates that the contour intervals are consistent with the Δ′17O Moon − Δ′17O Earth reported by Herwartz et al. (21). The yellow region encompasses the contours consistent with our data ±2 SE. Corresponding values for δ Theia are shown at right. One set of δ Theia values applies if the fraction of the present-day bulk silicate Earth composed of Theia is 0.1, whereas the values in parentheses apply where the fraction of Theia in present-day Earth is 0.5. For comparison, the ranges in Theia contents of the Moon and Earth for four simulated Moon-forming impact scenarios are shown as dashed horizontal lines. The models include the “canonical” model requiring no subsequent angular momentum loss by Canup (2008; Canup08), the hit-and-run model of Reufer et al. (2012; RMBW012), and the high angular momentum scenarios, including Cuk & Stewart (2012; C&S012) and Canup (2012; Canup012). (B) The cumulative probability for Δ′17OTheia – Δ′17Oproto-Earth in per mil based on simulations in this study. Three cases are shown: those with late accreted mass to Earth <5%, those with late accreted mass <1%, and all simulations.

A positive Δ′17O of 12 ± 3 ppm for the Moon (21) requires a difference in the proportions of Moon and Earth composed of remnants of Theia because the contours representing this range of values (Fig. 1A, pink regions) do not include the center of the diagram (Fig. 1A). For a Mars-sized differentiated body with Δ′17O ~ ± 0.3‰ (such as Mars or Vesta), the difference in Theia contents between the Moon and Earth is ± 50% or more (Fig. 1A). For the case of a proto-Earth–sized Theia, the result is a difference of ± 8% or more (Fig. 1A). Alternatively, assuming enstatite-chondrite–like material better represents the terrestrial planet-forming region (23, 24), differences in oxygen isotope ratios between Theia and proto-Earth would have been smaller (~0.1‰) (21, 25), and the lunar Δ′17O of 12 ± 3 ppm (21) requires δ Theia values of 150 and 30% for the Mars and proto-Earthȓsized impactors, respectively (Fig. 1A). Such large δ Theia values would effectively remove the constraint imposed by oxygen isotopes that the Earth-Moon system was well mixed.

We analyzed seven Apollo 12, 15, and 17 lunar samples and one lunar meteorite and compared their 17O/16O and 18O/16O isotope ratios with those for a suite of terrestrial igneous samples. The 1- to 4-mg lunar samples include high-Ti mare basalts, low-Ti Mg-rich olivine cumulate basalts, a quartz normative basalt, and a highland anorthositic troctolite (table S1). The terrestrial samples include San Carlos mantle xenolith olivines, San Carlos mantle xenolith spinels, Mauna Loa basalt samples, Mauna Loa olivine separates, an anorthosite from the Bushveld complex, and a sample of Gore Mountain metamorphic garnet. We obtained our analyses (Table 1) using infrared laser heating (26) modified to include F 2 as the fluorinating agent and purification of the analyte O 2 gas for analysis of both 17O/16O and 18O/16O (27). We have improved our precision compared with many previous efforts by more thoroughly desiccating samples before analysis and by regular rebalancing of standard and sample ion beam intensities throughout the mass spectrometer analyses (28). We analyzed a range of lunar and terrestrial sample lithologies to account for the fact that β values vary with process (13, 29, 30). We use the traditional standard mean ocean water (SMOW) as the reference for δ′18O, but we use San Carlos (SC) olivine as the reference for Δ′17O when characterizing oxygen isotope reservoirs of rocks (28). We adopt a typical igneous β of 0.528 passing through the mean value for San Carlos olivine as our reference fractionation line for calculating Δ′17O (28).

Table 1 Summary of oxygen isotope data for lunar and terrestrial samples. Delta values are in logarithmic form as defined in the text. View this table:

Lunar basalts are relatively high in δ′18O as compared with SC olivine and terrestrial basalts (Fig. 2). Nonetheless, the basalts show no clear deviation from the reference β of 0.528, allowing direct comparison of Δ′17O values for these materials. No discernible difference exists in Δ′17O between SC olivine and lunar basalts powders (−0.001 ± 0.002, 1 SE) or fused beads (0.000 ± 0.003, 1 SE). The mean for all mafic terrestrial samples, representing terrestrial mantle and its melt products, is 0.000 ± 0.001‰ (1 SE). Adding in quadrature, the analytical uncertainty in the SC olivine and the standard error for the lunar samples yields a difference between lunar basalt and SC olivine of −0.001 ± 0.0048‰ (−1 ± 4.8 ppm, 2 SE), which is indistinguishable from zero. Other mafic terrestrial whole rocks and olivines are within this uncertainty range (Table 1). We found no resolvable difference in Δ′17O between lunar mantle melts represented by these basalts and terrestrial mantle and melts.

Fig. 2 Plot of Δ′17O versus δ′18O for lunar and terrestrial samples by using a fractionation line with β = 0.528 passing through San Carlos olivine as the reference. Only the powders of lunar samples are plotted. The gray region indicates the regions accessible through mass fractionation starting from SC olivine. Different fractionation laws are labeled with their defining β values. Error bars depict 2 SE for each measurement. Points lying inside of the gray region are consistent with simple one-stage, mass-dependent isotope fractionation relative to SC olivine, implying that they represent a single oxygen reservoir.

Our result does not agree with the conclusions of Herwartz et al. (21). Measurements on the one sample common to both studies (12018) agree within uncertainties when compared in the same reference frame (fig. S2) (28). It is therefore conceivable that an unfortunate difference in sample selection could be a plausible explanation for the difference between the studies.

The lunar highland sample has a significantly lower Δ′17O value of −0.016 ± 0.003‰ (1 SE) (or −16 ± 3 ppm), which is similar to a previous study (8). However, the terrestrial anorthosite sample has a similarly low value (Table 1). The low Δ′17O values for both the terrestrial and lunar highland anorthosites (anorthostic troctolite) imply a mass fractionation process related to formation of this rock type that results in low Δ′17O values (Fig. 2). The low Δ′17O value for the lunar highland rocks is not evidence for a distinction between the oxygen pools for the Moon and Earth because these samples are in the mass-fractionation envelope for Earth (Fig. 2), and low Δ′17O values are found in both terrestrial and lunar anorthosite-like rocks. One terrestrial mantle spinel sample also shows a measurable deviation from the β = 0.528 reference, implying a relatively low β value (Fig. 2).

Of course, in all cases invoking no difference in oxygen isotope ratios between Theia and proto-Earth results in no constraints on the relative Theia concentrations in the Moon and Earth. We can assess the purely statistical feasibility of two proto-planetary bodies having identical oxygen isotope ratios using the central limit theorem (19). Results suggest that a purely random sampling of asteroid-like materials would lead to variations in Δ′17O among planetary embryos of ~3 ppm (28). However, the larger difference between Earth and Mars testifies to the fact that Δ′17O was not distributed randomly in small bodies across the inner solar system.

Differences in Δ′17O between Theia and the proto-Earth have expected values of 0.15‰ (31) or 0.05 ‰ (32) on the basis of two recent N-body simulations of standard terrestrial planet-formation scenarios with hypothesized gradients in Δ′17O across the inner solar system. We used a planetary accretion model (33) that uses N-body accretion simulations based on the Grand Tack scenario (34). Our model differs from previous efforts in that we strictly limit our analysis to simulations that closely reproduce the current masses and locations of Earth and Mars and the oxidation state of Earth’s mantle, we use a multi-reservoir model (composed of silicate, oxidized iron, and water) to describe the initial heliocentric distribution of oxygen isotopes, and we include the effects of mass accretion subsequent to the Moon-forming impact (28). An example simulation (Fig. 3) and others like it show that the Δ′17O values of the colliding bodies rise together as the average Δ′17O values increase during accretion. Incorporation of more material from greater distances from the Sun as accretion proceeds accounts for the rise. Large planets such as Earth and Venus reflect an average of many embryos and planetesimals and so exhibit similar Δ′17O values with time, whereas stranded embryos averaging fewer components, such as Mars, show greater variation.

Fig. 3 A simulation of the oxygen isotopic evolution of the terrestrial planets and last giant (Moon-forming) impactor, Theia. The Δ′17O values of the growing Venus-like (green), Earth-like (blue), and Mars-like (red) planets are shown as a function of time as well as the value for the Theia-like impactor (black). (A) The case in which the water oxygen reservoir has Δ′17O = 3‰. (B) The case in which water Δ′17O = 100‰.

The cumulative distribution of Δ′17O differences between Theia and proto-Earth is shown for 236 simulations of planet growth (35) (Fig. 1B). The median Δ′17O Theia − Δ′17O proto-Earth is nearly 0 in these calculations for all simulations (Fig. 1B). However, our median predicted Δ′17O Theia − Δ′17O proto-Earth is +0.1‰ if we restrict our analysis to those simulations consistent with adding ≤1% by mass of a “late veneer” (LV) of primitive material post Moon-forming giant impact, as required by geochemical constraints (36). This median value combined with our measurement of Δ′17O Moon − Δ′17O Earth corresponds to δ Theia of +20 to –60% for the Mars-sized impactor scenario and +8 to −12% in the proto-Earth–sized impactor scenarios. The corresponding values for δ Theia using the previous 12 ± 3 ppm difference between Moon and Earth Δ′17O values (21) are +80 to +180% and +16 to +36%, respectively (Fig. 1A). The new measurements presented here are consistent with Earth and the Moon having near-identical Theia contents. Indistinguishable Δ′17O values of the Moon and Earth to the 5 ppm level of uncertainty suggests that the Moon-forming impact thoroughly mixed and homogenized the oxygen isotopes of Theia and proto-Earth.

Our interpretation has implications for the composition of the LV of primitive bodies that impacted the silicate Earth. A disproportionately larger flux of LV planetesimals is implied by a higher average 182W/184W for the Moon than for Earth and by previous estimates for the apparent differences in highly siderophile element (HSE) concentrations between the terrestrial and lunar mantles (37). The interpretation of these data is that the Moon and Earth began with the same W isotopic ratios, but that Earth inherited a greater fraction of low 182W/184W material in the form of chondritic planetesimals after the Moon-forming giant impact (38, 39). If we adopt the conclusion from the W isotopes that the Earth-Moon system was well mixed as a result of the Moon-forming impact, then the nearly identical Δ′17O values of Moon and Earth constrain the identity of the LV impactors by their oxygen isotope ratios. Estimates for the Earth/Moon ratio of the LV mass fluxes range from ~200 to 1200 (37, 40, 41). Using a late-veneer flux to Earth of 2 × 1022 kg (37) and a conservative maximum Earth/Moon flux ratio of 1200 (41), the difference in LV fractions comprising the silicate Earth and Moon is 0.00447. Combining this value with our measured value for Δ′17O Moon − Δ′17O Earth of zero (28) requires that the LV impactors had average Δ′17O values within ~0.2‰ or less of Earth, similar to enstatite chondrites (25). Alternatively, with our maximum permitted Δ′17O Moon − Δ′17O Earth of ± ~5 ppm, the calculated Δ′17O value for the LV is ±1.1‰. This value encompasses aqueously altered carbonaceous chondrites and some ordinary chondrites. For comparison, the same calculation using the 12 ppm difference between the Moon and Earth yields an LV Δ′17O of −2.7‰, suggesting that the impactors were composed mainly of relatively unaltered and dry carbonaceous chondrites (4). Our result suggests that if the LV was composed mainly of carbonaceous chondrites, the parent bodies must have included substantial fractions of high-Δ′17O water either in the form of aqueous alteration minerals or as water ice.

Supplementary Materials www.sciencemag.org/content/351/6272/493/suppl/DC1 Materials and Methods SupplementaryText Figs. S1 to S7 Tables S1 to S4 References (42–67)

Acknowledgments: We are grateful to NASA Johnson Space Center for approving use of the Apollo samples for this study. E.D.Y. acknowledges support from a grant from the NASA Emerging Worlds program (NNX15AH43G). D.C.R., S.A.J., and A.M. acknowledge support from the European Research Council Advanced Grant “ACCRETE” (contract 290568). Development of the Panorama instrument was supported by the Deep Carbon Observatory (Sloan Foundation), NSF, U.S. Department of Energy, Shell, the Carnegie Institution of Washington, and the University of California, Los Angeles. The complete data table for this study can be found in the supplementary materials.