An asteroidal origin for water in the Moon

The Apollo-derived tenet of an anhydrous Moon has been contested following measurement of water in several lunar samples that require water to be present in the lunar interior. However, significant uncertainties exist regarding the flux, sources and timing of water delivery to the Moon. Here we address those fundamental issues by constraining the mass of water accreted to the Moon and modelling the relative proportions of asteroidal and cometary sources for water that are consistent with measured isotopic compositions of lunar samples. We determine that a combination of carbonaceous chondrite-type materials were responsible for the majority of water (and nitrogen) delivered to the Earth–Moon system. Crucially, we conclude that comets containing water enriched in deuterium contributed significantly <20% of the water in the Moon. Therefore, our work places important constraints on the types of objects impacting the Moon ∼4.5–4.3 billion years ago and on the origin of water in the inner Solar System.

L unar sample studies have focused on the measurement of H (reported as equivalent amounts of OH or H 2 O) in lunar volcanic glass beads 1-3 , melt inclusions 1,2,4 and apatite in lunar basalts and highlands samples [5][6][7][8] . From this compilation of work the bulk silicate Moon (BSM) is estimated to contain between B10 and 300 p.p.m. H 2 O 4,9,10 . A few of these studies reported the identification of a primordial H-isotopic signature 2,7,8 , corresponding to Earth-like dD values between BÀ 200 and Bþ 180% (where dD ¼ [(D/H) sample /(D/H) SMOW -1] Â 1,000; SMOW: standard mean ocean water). Therefore, the similar nature of water (the term water is hereafter used to refer to H 2 O equivalent) in the Earth and Moon suggests that water locked up inside of the Moon was either inherited directly from the proto-Earth or delivered to the Earth-Moon system shortly after the formation of the Moon (Fig. 1) through impacting carbonaceous chondrite (CC)-type asteroids, since bulk D/H ratios for most CC-types 11 are consistent with those of terrestrial 12,13 and lunar water (Fig. 2).
Models for the differentiation of the Moon invoke the presence of a lunar magma ocean (LMO) and place the lifetime of this LMO to between B10 and 200 Ma after the Moon-forming event (as reviewed by Elkins-Tanton et al. 14 ), which necessitates that volatile accretion occurred relatively early in the Moon's geological history (Fig. 1). The final dregs of the LMO, enriched in incompatible elements such as potassium (K), rare-earthelements (REEs) and phosphorous (P)-collectively termed urKREEP-should have contained the vast majority of the lunar water, as OH would have been incompatible in the crystallizing mantle cumulates and the crust 10 . Lunar samples with a significant KREEP component, such as Mg-suite rocks and KREEP basalts 7,8 , are characterized by H-isotopic compositions that are similar to those estimated for the mantle source regions of picritic glasses and mare basalts 2,3,6 , suggesting that the crystallization of the LMO did not result in significant fractionation of the H isotopes of water. To retain volatiles in the LMO, a conductive lid is required, to have prevented significant loss of water via degassing of H-bearing species, and is consistent with the formation of an early anorthosite crust a few kilometres thick in the first few thousand years of the Moon's history 14 . It is likely that the lunar crust then grew by continuous underplating of more anorthositic materials over a period of between B10 and B200 million years until the LMO completely solidified, leading to the mantle cumulate overturn (see review by Elkins-Tanton et al. 14 ). This time period between lunar accretion and the overturn of mantle cumulates permits any water (and other volatiles) accreted to the LMO to be incorporated into the mantle source regions of mare basalts and picritic glasses (4B100 km deep 15 ), and the urKREEP liquid provided that impactors were able to breach the lunar crust. Crystallization of an insulating crust likely started only after B80% LMO crystallization 14 . During its initial growth the crust was likely hot and tenuous and perhaps even re-melted if tidal heating played an important role 14 , meaning not only that impactors could have reached the LMO melt pool but also that many early impact structures could have been erased during crustal underplating and modification. Therefore, volatile delivery through the earliest lunar crust into the LMO could have balanced out any potential loss of volatiles (accreted or indigenous) by degassing (before 80% solidification).
Studies that have modelled the flux of impactors to the Moon posit that it was likely that the time period between lunar accretion and differentiation received relatively fewer impact events than during the late heavy bombardment (LHB) (for example, Morbidelli et al. 16 ), but importantly this was not a quiescent time. Indeed, there are B12 preserved Pre-Nectarian lunar basins that have excavations depths around or greater than 34-45 km (ref. 17), which corresponds to the current estimates for lunar crustal thickness based on observations by the GRAIL spacecraft 18 . This demonstrates that large impacts occurred early in the Moon's history (albeit infrequently compared with the LHB epoch 19 ). In summary, the time interval for water delivery to the LMO, hereafter referred to as the late accretion window 'LAW', is conceptually restricted to between time zero (Moon formation) and up to B200 Ma thereafter. Importantly, the bulk of lunar water was delivered during LAW, which is distinct from a much younger basin-forming epoch on the Moon that is commonly referred to as the LHB, lunar cataclysm, or inner Solar System cataclysm 16,[20][21][22] .
It has been suggested that water could have been accreted together with the Moon-forming material in the so-called 'cold start' 9 . Whilst it is plausible that some water may have been retained since the Moon's formation 23 , it is highly unlikely that all of BSM water (up to 300 p.p.m. H 2 O) was accreted in this manner and survived LMO processing. Therefore, we envisage two scenarios that can account for the bulk water inventory of the Moon, the first that water was accreted solely during the LAW and no water was inherited from the Moon-forming material (scenario 1), and the second that a portion (we consider up to 25%) of the BSM water was accreted with Moon-forming materials and was then supplemented by water delivery during the LAW (scenario 2). In this study we utilize estimates of the water content of the BSM 4,9,10 and its H-isotopic composition 2,3,6-8 together with the current database for the bulk water contents of chondritic meteorites (Table 1, see Methods section), to determine the amount of water added to the early Moon by impacting objects. We consider a range of possible accretion scenarios during LAW to investigate the implications for the mass of water accreted and populations of accreting objects. This is constrained by the estimates for the proportion of lunar mass that was likely added post-lunar core-formation from studies of highly siderophile elements (HSEs) in lunar basalts (up to 0.02% lunar mass 24,25 ) and highly volatile elements in mare basalts and picritic glasses (up to 0.4% lunar mass 4,9 ). Our results indicate that carbonaceous chondrite types of impactors were the most important contributors of water to the lunar interior and that comets (with heavy water, Fig. 2) played a very small role.  (Table 2).

Mass
Importantly, because equilibrated ordinary (OC) and enstatite chondrites (EC) contain very little water ( Table 1) the mass of such types of chondritic material added to accrete even 10 p.p.m. H 2 O greatly exceeds the mass constraints imposed by HSE and highly volatile element abundances ( Table 2). As a consequence, although ECs are considered an ideal geochemical match for the BSM and the bulk silicate Earth, and Os isotope signatures may suggest a large contribution of OC-and EC-type objects in materials accreted to the Earth-Moon system during late accretion 28,29 , it is clear that these types of objects are unlikely to have contributed significant amounts of H 2 O to the lunar interior. The accretion during the LAW of CC material is consistent with the impact of CC-type asteroids during the LHB 20 . HSE data have been interpreted to mean that EC and OC impactors also played an important role during the LHB 30,31 , which may reflect a change in impactor populations over the first B500 million years of the Moon's evolution and, thus, dynamical mixing of material in the Solar System. The same data have also been interpreted, however, to represent a mixture of OC and CC impactors together with differentiated iron impactors [29][30][31][32] , in which case CC asteroids remained an important source of impactors.
Assessing the contribution of cometary water during LAW. The first scenario in this study assumes that the Moon accreted completely dry or that any primordial water was completely lost very early in the Moon's history, and that late-accretion delivered all of the water in the BSM. Considering a BSM of 100 p.p.m. H 2 O (the most recent BSM water estimates overlapping at this Where; D R is the resultant D/H ratio, H 2 O t refers to the total mass of water added (kg), fH 2 O is the proportion (fraction of total) of water accreted by a given type of impactor denoted with an A or B, characterized by D/H ratios D A or D B , respectively. The resultant isotopic ratios were subsequently converted into delta notation to ease comparisons. However, because cometary water, excluding comets 103P and 45P, has significantly elevated dD values compared with chondrites (see Methods section), the amount of cometary water that can be added to the lunar interior is far more restricted. In such cases, B2% H 2 O from Oort cloud comets can be mixed with 98% H 2 O derived from CI-chondrites, or B1% H 2 O is allowed from D-enriched Kuiper belt (DEK) comets ( Table 3). Mixing of cometary water with predominantly CV-, CM-or CO-type CCs, respectively, also result in minor cometary contributions of B6% for DEK comets and B15% from Oort cloud-like objects ( Fig. 4 and Table 3).
In scenario 2, we consider that the Moon accreted with between 1 and 25% of BSM H 2 O, with an initial dD value of À 200% (refs 2,3,6-8), and reached a final BSM water content of 100 p.p.m. H 2 O (in agreement with the constraints imposed by modelling of Elkins-Tanton and Grove 26 ) (equation (2)). Note that the lower the initial dD value is, the higher the maximum possible amount of H 2 O added from a cometary source.
Where; H 2 O i refers to the initial mass of water present in the LMO (kg), which varied between 1% and 25% of the total amount  of water (H 2 O t ), D i refers to the initial H-isotopic composition of the water in the LMO, H 2 O LA refers to the mass of water added during LAW (kg), fH 2 O is the proportion (fraction of amount added during LAW) of water accreted by a given type of impactor denoted with A or B, respectively, and all other parameters are the same as in equation (1). Mixing of water from CI-type CCs with water from CO, CM, CV-type CCs and DDK comets in different proportions can yield final dD values o þ 100% (Table 3), satisfying isotopic constraints 2,3,6-8 . If deuterium-enriched comets were involved in the addition of water during LAW then up to B14% H 2 O could have originated from Oort cloud-type comets and B5% H 2 O from DEK comets if the remaining water is assumed to come from CI-type chondrites (Fig. 5a), proportions that increase to B7 and B19% H 2 O originating from DEK and Oort cloud comets, respectively, if the remaining water came from CM-type chondrites ( Fig. 5b and Table 3). Significantly, in the case where CO-type CCs dominated the impactor population (Fig. 5c) Table 3). In addition, we considered that the LMO underwent some degassing 26,33 before prior to late addition (see Methods section) and found that the results limit the amount of initial water present before late addition (assuming degassed H-isotopic composition of B þ 800% (ref. 8)), which further restricts the amount of water contributed by D-rich comets (Table 4).

Discussion
To a first order, a dominantly asteroidal source of water accreted during the LAW is similar to the dominant source inferred for the subsequent basin-forming epoch of the Moon, based on geochemical 22,34 and mineralogical 20 markers, implying that asteroids and not comets dominated the impactor population hitting the Moon during its first 500 million years of geological history 35 . Although the source of objects delivered to the Earth-Moon system may have largely remained the same, the dynamical delivery could have been much different, as the basinforming epoch appears to have been characterized by asteroids with higher impact velocities compared with those during the early accretional epoch (LAW) (Bottke et al. 19 and references therein). We note that the accretion of CC-type material during      the LAW, that is required to account for the lunar H-isotope and water abundances in the lunar interior, is distinct from a late veneer dominated by EC-and OC-type objects that has been inferred from Os isotope studies of terrestrial rocks 28,29 . This dichotomy could imply that either the largest impactors that preferentially impacted the Earth due to stochastic accretion 19 were OC-and EC-type objects, while the population of smaller impactors included abundant CC objects that preferentially impacted the Moon, or that while the accreting objects had OC-and EC-type Os isotope signatures, they had CC-type water abundances and H-isotope signatures, consistent with other evidence that support the presence of planetesimal-types that are not represented in modern meteorite falls 36 .
On the basis of combined N isotopes and C/N ratios, the lunar interior seems to be best matched with CO-type CCs 37 38,39 , then the N-isotopic composition measured in mare basalts of between B À 2 and þ 27% (refs 37,38) should reflect the isotopic composition of the lunar mantle source regions from which the basalts were derived. If all of the N in the LMO was added during LAW (scenario 1) then mixing of CI-, CM-, COand CV-type CCs provide suitable matches for the origin of lunar N (Methods section and Table 1) and restrict cometary contribution of N to as much as B5% (Table 5). This is comparable to scenario 2, where considering the lowest mare basalt d 15 N value of À 2 % (ref. 37) to represent the N-isotopic signature of N accreted with Moon-forming materials before LAW, then up to B6% N could have been delivered by comets (Table 5). Still using scenario 2 but considering that the isotopic signature of N accreted when the Moon formed was consistent with that of the primordial Earth mantle, which is thought to be as low as B À 40 % (reviewed by Füri and Marty 40 ), increases the possible cometary contribution to a maximum of B8% of total lunar interior N.
Therefore, it appears that in order to add the appropriate amounts of H 2 O and N to the lunar interior during LAW, while keeping the H-and N-isotopic compositions in line with sample measurements, requires the contemporaneous accretion of the various types of CCs (mostly CO, CI, CM and CV), together with oB20% cometary input.
The very-low apparently indigenous lunar dD values of B À 600% reported by Robinson et al. 41 are quite anomalous. In fact, such low values have yet to be observed in terrestrial rocks, the lowest dD values being B À 220% for Earth's depleted upper mantle 13 . Therefore, such low values reported for an intrusive lunar rock 41 could potentially indicate the presence of a proto-solar component (dD value of B À 900% (ref. 42)) in the lunar mantle, in a similar way that has been used to explain Earth's noble gas record 43,44 and recent data from primitive terrestrial basalts 13 . If this source is indeed required to explain the extremely low H-isotopic compositions observed 41 , then this signature must have been added to the Moon from either material accreted from the proto-Earth or by the impactor involved in the formation of the Moon. Alternatively, such a low dD value could have arisen from contamination of a water-poor magma by solar wind-derived H present in the lunar regolith during magma ascent and emplacement.
The mantles of the early-Earth 13,45 the Moon 2,3,6-8 and Mars 46 all seem to be characterized by water with remarkably similar H-isotopic compositions, suggesting that the same types of accreting objects as those modelled here for the Moon delivered a vast majority of the water to the rocky planets in the inner Solar System. Likewise, isotopic analyses of differentiated meteorites 47 suggest that the interior of the eucrite parent body, probably the asteroid 4-Vesta, contained water characterized by H-isotopic signatures indistinguishable to that of the terrestrial planetary objects in the inner Solar System (Fig. 2).
Regarding the timing of volatile accretion to the Moon, major constraints are imposed by the time interval between lunar accretion and solidification of the LMO and overturn of mantle cumulates (B10-200 Myr after Moon formation 14 ) since there is water in the mantle source regions of the mare basalts 4,6 and picritic glasses [1][2][3]9 . It is possible that some water with Earth-like H-isotopic characteristics may have been accreted with the Moon-forming material, to explain the H-isotopic composition of water in the source regions for the picritic glasses (that were likely deep enough in the lunar mantle to have escaped processes such as degassing of H 2 (ref. 48)). To account for the H-isotopic composition of the primordial lunar mantle and the urKREEP reservoir together, it is necessary that any initial lunar water was complemented by the continuous accretion of water from CC-type objects to the LMO during LAW. Incidentally, late  accretion of material to the Earth-Moon system did not only affect their volatile inventories 49 but could also explain the recently identified difference between the bulk silicate Earth and BSM in terms of W isotopes 50,51 .
In summary, the lunar interior is characterized by an average bulk water content of the order of B100 p.p.m. based on samples studies 4,9,10 and we propose that the majority of this water was delivered during the ca. 10-200 million year-long LMO phase of lunar differentiation, with the possibility that some of this water was inherited proto-Earth-derived materials. This late accretion was dominated by water-rich carbonaceous chondrite asteroids, on the basis of H and N data, likely comprising a mixture of CO-, CI-, CM-and possibly CV-type CCs, with a minor contribution of water from deuterium-rich Oort cloud or Kuiper belt comets (much less than 20% of the total water in the BSM). Our work, therefore, confirms that the inner Solar System received a similar flux of asteroidal and cometary material for much of its early history from 4.5 billion years (this work and Dauphas et al. 52 ) to at least 3.9 Gyr (ref. 20) (LHB).

Methods
Mass balance calculations. For mass balance calculations, we considered a lunar radius of 1,737.4 km, a mantle density of 3,300 kg m À 3 , and varied the depth of the LMO from 400 to 1,000 km. We then calculated the mass of chondritic material added to the lunar interior that would result in BSM water contents of 10, 100 and 300 p.p.m. H 2 O, and considered both the addition of up to 0.02% lunar mass 24,25 and up to 0.4% lunar mass 4,9  Data for the average water contents of different carbonaceous, ordinary and enstatite chondrites that were used in these calculations are shown in Table 1. For carbonaceous chondrites, CI-, CM-, CV-, CO-and CR-refer to the different groups, named according to one prominent meteorite of the group, respectively Ivuna, Mighei, Vigorano, Ornans and Renazzo. OC stands for ordinary chondrites. The results of these calculations, presented in Table 2, allowed us to identify suitable impactors for the modelling presented below. For example, to add 10 p.p.m. H 2 O to the BSM through the accretion of enstatite chondrites alone implies the addition of 41% lunar mass for both 400-and 1,000-km-deep LMO, and, therefore, ECs were not deemed important carriers of water to the lunar interior. The same was also true for equilibrated ordinary chondrites (Table 2). Un-equilibrated ordinary chondrites were also not considered further on the basis of them having prohibitively high H-isotopic compositions (Table 1) for the mixing calculations. Note that all of the scenarios in this work consider that water was efficiently delivered to the Moon regardless of if it originated in asteroids or comets, that is, we have not attempted to calculate the proportions of volatiles lost during impact into the crystallizing LMO.
Mixing models. In the mixing models, literature data for the water abundances and D/H ratios of bulk carbonaceous chondrite meteorites were utilized. Carbonaceous, ordinary and enstatite chondrite meteorites are characterized by dD values mostly between B À 200 and þ 300% (refs 11,53-55). There is also a possibility that the asteroid parent bodies to the CCs may have once contained ice 11 . If the asteroids that delivered water to the Moon contained ice, in addition to their bulk water contents hosted in phyllosilicates and organic matter compounds, then less amounts of chondritic material than those given in Table 2 would have been accreted to the Moon to account for the bulk inventory of water in the lunar interior. Until ice on asteroids is identified and characterized, it remains difficult to quantify how much ice, if any, could have contributed to the mixing of different H-reservoirs within the Moon. Comets 103P/Hartley 2 (ref. 56) and 45P/Honda-Mrkos-Pajdusakova 57 contain water characterized by dD values between B þ 30 and þ 400%, whereas other comets studied (for example, 8P/Tuttle and 67P/Churyumov-Gerasimenko) contain water distinctly enriched in D, with dD values 4 þ 900% as reviewed by Hartogh et al. 56 In the modelling, the dD value for water in comet 67P/Churyumov-Gerasimenko ( þ 2,400% (ref. 58)) was used to represent DEK comets, the dD value for water in Oort-cloud comets was set to B þ 930% (see Hartogh et al. 56 for a review) , and the water dD for DDK belt comets was given the same isotopic composition as comet 103P ( þ 34% (ref. 56)).
The modelling for scenario 1 assumes no water in the lunar interior before lunar core-formation, and follows equation (1). We used the mid-range estimate for water content for the BSM of B100 p.p.m. H 2 O (refs 4,9,10) (equivalent to 3.94 Â 10 18 kg of H 2 O for a 400-km-deep LMO) and imposed an upper limit on the resultant dD values after mixing of o þ 100% to remain consistent with H-isotopic data obtained for lunar samples 2,3,6-8 . Only chondrites that were likely to have delivered significant amounts of water to the Moon without adding unrealistic amounts of chondritic material (Table 2) to the LMO were considered in the mixing calculations. Each chondrite-type (CI, CM, CO, CV) was considered in turn as being the most dominant chondrite in the impactor population (Table 3). CR-type CCs were not considered as being a significant part of the impactor population since the bulk dD value (Table 1) for such meteorites is significantly elevated with respect to the expected H-isotopic composition of the lunar mantle. In each case, the model extends from having 99% of the accreted water originating from CI-, CM-, CO-or CV-type CCs to having 99% of the water accreted from another type of chondrite or comet.
The two-component mixing models applicable to scenario 2 follow the same constraints as scenario 1 except that they assume that the Moon accreted with some water and late accretion added any remaining water needed to meet the BSM estimate of 100 p.p.m. H 2 O. These calculations follow equation (2) and consider an initial amount of water varying between 1% and 25% of the BSM estimate (that is, 1-25 p.p.m. for a bulk BSM water content of 100 p.p.m. H 2 O) characterized by a dD value of À 200% (refs 2,3,6-8). The model is also adapted to consider each type of CC (CI, CO, CM or CV) as being the dominant source (Table 3).
We also considered that water initially dissolved in the molten LMO might have experienced degassing through loss of H 2 , in a similar way as has been proposed to explain for example the elevated H-isotopic compositions of water (present as OH) measured in apatite in some lunar basalts 6 . Such degassing would have resulted in any remaining water in the LMO before late addition having an elevated dD signature of B þ 800% (following the work of Tartèse et al. 8 ). Therefore, we utilized equation (2) and allowed the model for scenario 2 to start with water having a dD signature of B þ 800% before the late addition of volatiles. All other parameters were kept the same (described above) and from this we were able to model the proportion of water that was initially in the LMO prior to late addition since the model is still constrained to a final H-isotopic composition of o þ 100% and to constrain the maximum contribution made by comets to the water inventory of the Moon assuming an initial H 2 O content of 1 p.p.m. prior to late addition (Table 4).
Bulk nitrogen content of the Moon and mixing calculations. Using the mass of each type of CC (CI, CO, CM and CV) accreted to an initially dry Moon during LAW (scenario 1) to end up with a BSM containing 100 p.p.m. H 2 O (Table 2), the average N contents for the various types of carbonaceous chondrites (Table 1, data sources 53,59 ), and assuming LMO depths of 400 or 1,000 km, we have estimated the amounts of N added to an initially N-free LMO, that is, the bulk N content of the BSM ( Table 5). Note that in some cases (e.g., CV CCs) the mass of chondritic material added, in order to accrete 100 p.p.m. H 2 O, exceeds the mass balance constraints imposed by HSEs. We then employed the mixing models described above for H 2 O to calculate the acceptable proportion of N contributed by comets (with d 15 N values B þ 700% as a lower limit, see Füri and Marty 40 and references therein) for scenario 1 (Table 5) and scenario 2 (Table 5), where it was assumed that the initial N-isotopic compositions of N were À 2% (ref. 37) and À 40% (Füri and Marty 40 and references therein) in the same way as was done for H 2 O ( Table 3). Notice that like for H 2 O, CR-type chondrites are unsuitable carriers of N due to their elevated d 15 N values (Table 1).
Data availability. All relevant data are available from the authors on request and/or are included with the manuscript (in the form of data tables or data within figures).