The Lunar Magma Ocean: Reconciling the Solidiﬁcation Process with Lunar Petrology and Geochronology

Earth and Planetary Science Letters 304 (2011) 326–336

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Earth and Planetary Science Letters

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The lunar magma ocean: Reconciling the solidiﬁcation process with lunar petrology and geochronology

Linda T. Elkins-Tanton a,⁎, Seth Burgess a, Qing-Zhu Yin b a Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences, USA b University of California at Davis, Department of Geology, USA article info abstract

Article history: The Moon is thought to have originated with a magma ocean that produced a plagioclase flotation crust as Received 3 November 2010 solidification proceeded. Ages of anorthositic crust range over at least 200 million years. The model for Received in revised form 31 January 2011 solidification presented here integrates chemical and physical constraints of lunar magma ocean solidification Accepted 4 February 2011 to determine (1) the final thickness of flotation crust generated by a fractionally solidifying magma ocean, Editor: T. Spohn (2) the timescale of crystallization before plagioclase is a stable phase, (3) the timescale of solidification after the formation of the plagioclase flotation crust, and (4) the post-overturn lunar mantle composition and Keywords: structure. We find that magma oceans of as much as 1000 km depth are consistent with creating an Moon anorthositic crust 40 to 50 km in thickness. Solidification of the magma ocean prior to formation of the magma ocean flotation crust may occur on the order of 1000 years, and complete solidification would require additional ten geochronology to tens of millions of years. Reconciling these short model timescales with radiometric dates of crustal samples anorthosite requires either a very late-forming Moon combined with finding older crustal ages to be incorrect, or calling on tidal heating of the crust by the early Earth to prolong solidification. Gravitationally driven overturn of cumulates during tidal heating provides a mechanism for creating the compositions and ages of the lunar Mg suite of crustal rocks. Further, we find that upon crystallization, the Moon likely began with an azimuthally heterogeneous, gravitationally stable mantle, after magma ocean cumulate overturn. This result may help explain the experimentally determined origin of picritic glasses at similar depths but from different source materials. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The lunar anorthosites span a large range of ages (e.g., Borg et al., 1999, 2002; Boyet and Carlson, 2007; Carlson and Lugmair, 1988; Samples from the lunar highlands first led to the hypothesis that Nyquist et al., 1995, 2010), and references used in Fig. 1), potentially the primordial Moon was at least partially molten and that from longer than it took the last silicate magma source regions in the this melt, anorthite plagioclase was buoyantly segregated, forming Martian mantle to differentiate as evidenced by isotopic measure- an anorthositic crust (Kaula, 1979; Smith et al., 1970; Solomon and ments (Nyquist et al., 1995). This age span has been proposed to Toksoz, 1973; Taylor and Jakes, 1974; Walker and Hays, 1977; Warren, represent the time required for the lunar magma ocean to solidify, 1985; Wood et al., 1970). The age of the anorthositic highlands though the ages can only be said with confidence to represent the (Nyquist and Shih, 1992; Nyquist et al., 1977) and references used in times that the minerals cooled sufficiently to retain all the radiogenic Fig. 1), their positive Europium anomalies and the corresponding daughter product of the applied geochronometer, and therefore negative anomalies in the mare basalts (e.g., Haskin et al., 1981; cooling can be decoupled from solidification. Morse, 1982; Ryder, 1982), and experimental evidence that plagio- Solidification of the Moon is directly dependent upon heat transfer clase is not present on the liquidus of mare basalts (Green et al., from the interior to space. Upon formation of a conductive plagioclase 1971a, 1971b) are all strong supporting evidence for an early, major lid, the heat loss regime changes from black-body radiation to differentiation event. conduction. The conductive lid is therefore the rate-limiting step in heat loss from the Moon, resulting paradoxically in far longer solidification times than those for larger planets without conductive lids (Elkins-Tanton, 2008). ⁎ Corresponding author at: Department of Earth, Atmospheric, and Planetary On the Moon plagioclase flotation is probably the only viable way Sciences, Massachusetts Institute of Technology, 77 Massachusetts Ave., 54-832, to form a conductive lid (Elkins-Tanton, 2008; Herbert et al., 1977). Cambridge, MA 02139, USA. Tel.: +1 617 253 1902. fi fi E-mail addresses: [email protected] (L.T. Elkins-Tanton), [email protected] No early ma c stagnant lid is likely to form before a signi cant crystal (S. Burgess), [email protected] (Q.-Z. Yin). fraction reaches the surface of the planet because the mafic magma

LUNAR FORMATION AND DIFFERENTIATION

a bcd e Solidification to the point of anorthosite ~10 Ma: Time to MO solidification MODELS FOR lid formation through growing lid in this study NOTE: Start time of SOLIDIFICATION models is arbitrary, constrained only by the ~220 Ma: Time to MO solidification range of (a) through (e) with tidal heating in lid (Meyer et al., (2010) and age (f) f g l o AGES FROM h n LUNAR i j m p CRUST k 4.57 4.56 4.55 4.54 4.53 4.52 4.51 4.5 4.49 4.48 4.47 4.46 4.45 4.44 4.43 4.42 4.41 4.4 4.39 4.38 4.37 4.36 4.35 4.34 4.33 4.32 4.31 4.3 4.29 Ga before present

Fig. 1. Lunar timeline. Ages pertaining to the formation of the Moon, magma ocean solidification, and anorthositic crust formation. The modeled age of giant impact and lunar magma ocean solidification, 4.51 Ga, could be moved to any age between 4.54 and 4.48 without being inconsistent with crustal age data, as discussed in the text. In black at left: The oldest calcium–aluminum inclusions in the meteorite Allende (Connelly et al., 2008). In red at top: (a) Moon formation (Yin et al., 2002), (b) Moon formation and differentiation (Kleine et al., 2005), (c) Moon formation and differentiation (Lee et al., 1997), (d) Moon formation and differentiation (Lee et al., 2002); (e) Lunar magma ocean N60% solid (Touboul et al., 2007). In yellow, at bottom, lunar crustal ages: (f) FAN 67075 by Sm–Nd (Nyquist et al., 2010); (g) Mafic fractions from anorthositic samples by Sm–Nd (Norman et al., 2003); (h) Pristine anorthosite 60025 by Sm–Nd (Carlson and Lugmair, 1988); (i) Yamato 86032 lunar highlands meteorite by Sm–Nd (Nyquist et al., 2006); (j) Zircon from lunar breccia 72215 by U–Pb (Nemchin et al., 2009); (k) Zircon from breccia 14321 by U–Pb (Nemchin et al., 2006); (l) Zircon from anorthosite breccia meteorite Dhofar 025 by U–Pb (Leont'eva et al., 2005); (m) FAN 60025 by both Pb–Pb and Sm–Nd (Borg et al., 2011); (n) Mg suite norite 78236 by Sm–Nd (Boyet and Carlson, 2007); (o) Zircon in granophyre 73235,673 by U–Pb (Meyer et al., 1996); (p) Ferroan anorthosite 62236 (Borg et al., 1999). For ages (f) through (p), the label rests on the error bar. Anorthosite ages are darker than ages for Mg suite or KREEP enriched rocks. Ages (h) and (m) are circled because they derive from the same rock, 60025.

ocean quench material is denser than its underlying silicate magma. 2. Geochronologic constraints If the lid is not compositionally buoyant, it will founder into the underlying liquid (Elkins-Tanton et al., 2005; Walker and Kiefer, 2.1. 182Hf–182W constraint and the interpretation of the lunar W isotope 1985; Walker et al., 1980). Planets with magmas at the surface cool data extremely quickly, even in the presence of an atmosphere (Abe, 1993, 1997; Abe and Matsui, 1985, 1986; Elkins-Tanton, 2008; Kasting, Because Hf is a lithophile element, W is moderately siderophile 1988). In contrast, a plagioclase flotation crust will slow the cooling of element, and 182Hf has a suitable half-life (9 Ma) over which it decays the planet significantly. to 182W, the 182Hf–182W system is ideally suited to constrain the An anorthositic flotation crust on the Moon, therefore, would have timescale of metal–silicate (core–mantle) differentiation of planetary its oldest portions closest to the surface, and would have been objects. After decaying for ~7 half-lives, the radiogenic parent (182Hf) underplated by subsequent flotation. In general, the age of the crust has almost completely converted to the daughter nuclide, rendering would diminish with depth, with two important caveats: The it an extinct chronometer. As a result, the 182Hf–182W chronometer structure of the crust may have been significantly disturbed by only yields information from the first ~60 Myr of our solar system. subsequent giant impacts (Wieczorek and Phillips, 1999), and early No discernable radiogenic in-growth of 182W should occur in rocks tidal heating from the Earth may have melted the interior of the crust formed ~60 Myr after solar system formation or later. and reerupted anorthosite onto the surface (Meyer et al., 2010). In the highly energetic Moon-forming giant impact of a Mars-sized The first goal of this study is to construct a self-consistent model body onto the proto-Earth, the system's temperature is thought to for fractional solidification of a lunar magma ocean, with predictions have reached 5000–10,000 K (Canup, 2004, 2008); thus any previous for the composition and structure of the resulting lunar mantle after memory of the isotopic clock must have been reset. The 182Hf–182W cumulate overturn to gravitational stability. We will build on the work clock would have been restarted from the formation of the magma by Meyer et al. (2010), Snyder et al. (1992), and Solomon and Longhi ocean of the post-giant impact Earth–Moon system. This system is (1977). The advances of this study include tracked liquid and solid thus used to date the Moon-forming impact and therefore the oxide components during fractionation, calculation of assemblage initiation of the final large magma oceans on Earth and Moon. densities using experimental data for each mineral phase, and The measured W isotopic composition of the Moon has evolved complete composition and temperature tracking during solid-state through four iterations in the last decade (Kleine et al., 2005; Lee cumulate overturn. From this we conclude that the lunar mantle is et al., 1997, 2002; Touboul et al., 2007). The initial results showing likely to be azimuthally heterogeneous over a wide radius range, large 182W excess (Lee et al., 2002; Kleine et al., 2005; see ages b, c, which with interstitial melt retention may explain the compositions and d in Fig. 1) are now all shown to be compromised by cosmogenic of mare basalts and picritic glasses. Adiabatic melting during cumulate 182W production via neutron capture of 181Ta at the lunar surface, overturn may further explain the origin of the Mg suite rocks. instead of indigenous radiogenic in-growth from 182Hf decay. The The second goal is to compare the timelines from this and other latest results of Touboul et al. (2007) do not contain any significant magma ocean solidification models to ages from returned lunar Ta-derived 182W, as a result of using larger amounts of Apollo samples samples and lunar meteorites, and discuss processes that might with cleaner separation of metallic grains free from Ta-rich silicate. reconcile the significant timeline disagreements. Here we propose a The results show that the lunar W isotopic composition is the same as structure to begin to clarify the ages obtained through geochronology, the Earth. W is now added to the group of elements (together with O and the results from geophysical modeling (Fig. 1). In these models and Cr) that show a remarkable similarity in their isotopic the Moon would cool too quickly to fit the wide range of anorthositic composition between the Earth and Moon (Touboul et al., 2007 and crustal ages, requiring either tidal heating or another explanation for references therein). Importantly, however, both the Moon and the the range in anorthosite ages. Earth are still radiogenic compared to chondritic uniform reservoir, 328 L.T. Elkins-Tanton et al. / Earth and Planetary Science Letters 304 (2011) 326–336 reflecting in-growth of 182W from a high Hf/W reservoir when 182Hf a period of time (e.g. Borg et al., 1999; Edmunson et al., 2009; Nyquist was still extant. et al., 1995). Similarity in W isotopic composition between the Earth and the In this figure the model results presented below are placed such Moon (Touboul et al., 2007) does not necessarily imply that the Earth– that magma ocean solidification begins at ~4.51; this start time is Moon system was formed after 182Hf had decayed (N60 Myr). The suggested only by the range of Hf–W ages and the age of the oldest calculated similarity in ε182W for samples of high-Ti, low-Ti and crustal material presented. The youngest age of the first anorthosite KREEP basalts (Fig. 2 of Touboul et al., 2007) does not necessarily flotation crust allowed by the collective data shown here is ~4.42 Ga, mean the Moon itself formed N60 Myr after the CAI formation. These constrained by the error bar on sample h. This age for initiation of data only reflect the prolonged internal silicate differentiation and formation of the anorthosite crust is also consistent with the extreme solidification of these chemical reservoirs within the Moon, which we error bar on Hf–W age e. Thus any model time for the giant impact will argue in this paper as due to the tidal heating of lunar crust by and initiation of the lunar magma ocean between 4.54 and 4.42 is early Earth. consistent with the ages now available. For isochron dating of any event, one needs both the radiogenic isotopic composition (y-axis), as well as parent/daughter elemental 3. Model parameters ratios (x-axis). The Touboul et al. (2007) results establish that the 182 184 W/ W ratios of both silicate Earth and the Moon are identical The heat generated upon accreting the Moon from post giant- within analytical uncertainty (y-axis). The question remains whether impact terrestrial disk material is sufficient to bring a significant 180 184 Hf/W ratios ( Hf/ W) for the bulk silicate Earth and Moon are portion of proto-lunar material above solidus temperatures (e.g., distinguishable. Canup, 2008; Solomon and Longhi, 1977; Wetherill, 1990; Wood et al., Because of strong partitioning of W into metallic core, the bulk 1970), making a whole-mantle magma ocean possible. silicate Earth and Moon's Hf/W ratio are estimated indirectly by using the chondritic Hf/U ratio to represent bulk silicate Earth (unaffected by core formation) multiplied by the U/W ratios of the terrestrial or 3.1. Depth of the magma ocean lunar mantle. U and W are so highly incompatible that the U/W ratio of the differentiated rocks of planetary surface reflects faithfully the This model considers the evolution of a convecting magma ocean deep mantle source regions' U/W ratio. Arevalo and McDonough with a depth of 1000 km. Lunar seismic data are ambiguous as to (2008) estimate the U/W ratio for the bulk silicate Earth to be 1.54±1 whether or not there are global seismic discontinuities (e.g., Khan at best. et al., 2000; Lognonne, 2005). Deep moonquakes occur between ~700 Given the substantial scatter in the U/W ratio measured in lunar and 1000 km depth (e.g., Nakamura et al., 1973). This depth may rocks, the lunar mantle's U/W ratio is unlikely known with only 4% contain a preferential zone of weakness, prone to fracture under tidal uncertainty (1.93±0.08), as claimed by Touboul et al. (2007). If there forces exerted on the Moon by the Earth, may in fact be the original is a small lunar core (Wieczorek, 2009), the estimated U/W ratio for depth of the magma ocean. the bulk Moon should be even smaller than 1.93. Thus, the bulk With a lunar radius of 1738 km, this model assumes some silicate Earth and Moon's U/W ratio, and Hf/W ratios by inference, are underlying lower mantle or mantle and core material. This magma not distinguished beyond 20% uncertainty. With these uncertainties, ocean is deeper than some other models (Hess and Parmentier, 1995; the age of the Moon-forming giant impact and the age of the Earth at Kirk and Stevenson, 1989; Warren, 1985). Previous estimates of +90 magma ocean thicknesses are based on Al2O3 contents of ~4 wt.% and 62 /− 10 Ma after CAI formation as argued by Touboul et al. (2007) is similarly uncertain. the assumption that all Al2O3 is in the plagioclase crust. With these assumptions, a magma ocean thinner than ~400 km cannot provide

sufficient Al2O3 to form the observed thickness of crust while a 2.2. Lunar crustal ages magma ocean greater than ~800 km thick would generate far too much crust. Our model crystallizes the aluminum-bearing Mg–Fe The antiquity of lunar highland anorthosites has been reported in spinel pleonaste in addition to plagioclase, and in addition alumina is the literature since the early 1970s, and has been a key point in the retained in the lunar interior in interstitial melts, and so our magma evolution of the magma ocean hypothesis (Alibert et al., 1994; Carlson ocean can be deeper, begin with a similar initial Al2O3 content, and and Lugmair, 1988). Subsequent re-analysis of much of this data still create an anorthositic crust in agreement with geophysical indicates that both the Rb–Sr and K–Ar systems are susceptible to measurements. open system behavior during impact events and thus may not yield a date representing the time of initial crystallization. Sm–Nd is far less 3.2. Lunar cumulate mineral assemblages mobile and therefore less likely to be reset during impact events and is therefore often preferred for lunar samples. U–Pb is a second highly We begin with the lunar bulk silicate composition of Buck and robust system, though particularly difficult to apply to the ferroan Toksöz (1980) (Table 1). The model fractionally crystallizes the anorthosites. Those highlands rocks that have been dated using U–Pb magma ocean in steps that each represent 1/1000th of the total ocean must contain an element of KREEP and therefore be a secondary melt volume and individually tracks SiO2, TiO2,Al2O3, FeO, MgO, CaO, of the lunar interior and often members of the Mg-suite of lunar Cr2O3, Sm, Nd, Lu, Hf, C, and OH (though all models run here are crustal rocks. Though interstitial melts are certainly present in the devoid of water and carbon, results of models including water will be anorthosite flotation crust, they are less likely to fractionate to the discussed in a separate paper). point that zircon could be stable. At the beginning of magma ocean solidification the dense iron- and In Fig. 1 we show a range of crustal rocks ages. This is not meant to magnesium-rich olivine and pyroxene crystallizing from the cooling be an exhaustive collection of all the ages available, and we have not magma are believed to have sunk to the bottom of the magma ocean. included model ages for other suites, such as the KREEP or high-Ti When approximately 80% of the lunar magma ocean solidified, basalts, which represent later still lunar interior processes. Fig. 1 anorthite began to crystallize and float upward through the more includes a range of ages that represent ferroan anorthosites and Mg dense magma ocean liquid; anorthite will continue to be added to this suite rocks. Two broad conclusions can be made that require flotation crust until the last dregs of the magma ocean solidify (Smith explanation: anorthosite flotation crust ages span 150 to 200 Myr; et al., 1970; Snyder et al., 1992; Wood et al., 1970). Once isolated by the Mg suite and KREEP-contaminated intrusives span nearly as broad the subsequent fractionating material, the composition of the solid is L.T. Elkins-Tanton et al. / Earth and Planetary Science Letters 304 (2011) 326–336 329

Table 1 Lunar magma ocean bulk compositions, renormalized.

This Ringwood and Morgan, Hertogen Buck and Toksöz Taylor Wänke and Warren Ringwood Ringwood O'Neill Snyder et al. study Kesson (1976) and Anders (1978) (1980) (1982) Dreibus (1984) (1986) et al. (1987) et al. (1987) (1991) (1992)

SiO2 47.1 44.7 43.4 48.5 43.8 44.3 46.3 43.4 44.3 44.6 48.5

TiO2 0.40 0.30 0.39 0.40 0.30 0.00 0.30 0.30 0.42 0.17 0.40

Al2O3 4.0 3.7 7.6 5.0 6.0 3.8 7.0 3.7 5.2 3.9 5.0 FeO 12.0 13.9 13.0 12.9 13.1 12.7 12.5 12.2 13.5 12.4 12.0 MgO 33.1 33.5 29.2 29.0 32.2 35.6 27.8 37.0 32.0 35.1 30.0 CaO 3.0 3.4 6.1 3.8 4.5 3.2 5.5 3.0 4.2 3.3 3.8

Cr2O3 0.30 0.40 0.30 0.30 0.00 0.37 0.50 0.32 0.36 0.47 0.30 Mg# 83.1 81.1 80.0 80.0 81.4 83.3 79.9 84.4 80.8 83.5 81.6

assumed to remain constant and is subtracted from the remaining clinopyroxene, 30% orthopyroxene, 40% plagioclase, and 10% oxides liquid, which evolves as crystallization proceeds. (consisting of 20 wt.% pleonaste (Mg,Fe)Al2O4, 30 wt.% chromite The small pressure range of the Moon means that an adiabat in its FeCr2O4, 20 wt.% ulvöspinel Fe2TiO4, and 30 wt.% ilmenite FeTiO3). well-mixed magma ocean will lie between its solidus and liquidus Oxide stability at 87 vol.% solidification is earlier than estimated by during much of solidification (Solomatov, 2000; Tonks and Melosh, lunar petrologists (90–95 vol.%, P. Hess and J. Longhi, pers. comm.). 1990), suggesting high crystal fraction and possible crystal networks. Otherwise, these mineral assemblages are a reasonable match to the Fluid theory indicates that at a degree of solidification between 10 and estimates of Hess and Parmentier (1995) and Van Orman and Grove 60% the solids form a stress-supporting network (Campbell and (2000), who state that ilmenite crystallization should begin 150 and Forgacs, 1990; Saar et al., 2001). This likely scenario led to the 100 km at a temperature between 1180 and 1125 °C. hypothesis of a significant viscosity jump in the solidifying magma At writing there are no complete experimental fractional crystal- ocean (Solomatov and Stevenson, 1993). lization studies of relevant lunar compositions on which to base these Lunar sample suites, however, indicate fractional crystallization of mineral assemblages. All previous studies including those we base our a lunar magma ocean including efficient flotation of anorthosite to its work upon used theoretical calculations of phase stability. These are surface, unimpeded by high crystal fractions or crystal networks (Smith et al., 1970; Wood et al., 1970). In this work we assume all This study Snyder et al. (1992) minerals sink or float according to their relative density with the 100 fi fl Cpx Pig An Ox coexisting liquid, ef ciently if not rapidly segregating from the uid. Opx Cpx An Ox Solomatov et al. (1993) demonstrated that particles smaller than diameter D with density difference Δρ between themselves and the Cpx Pig An magma ocean liquids would remain entrained in a magma ocean with Cpx An viscosity η and surface heat flux F, as given by Opx Ol Pig An

!1 ηα 2 ≈ 10 gF ð Þ D Δρ 1 g Cp

α scaled by thermal expansivity , gravity g, and heat capacity Cp (see Opx also Martin and Nokes, 1989; Tonks and Melosh, 1990). For plagioclase in the lunar magma ocean D is between a fraction of a millimeter and a few millimeters. For this simplified model we assume all plagioclase floats. 50 Opx While Spera (1992) suggests that mineral segregation from convective flow occurs only in boundary layers, persistent sinking or floating will result in minerals arriving at these boundary layers. Further, magmas that are saturated with plagioclase and a mafic phase at depth will be saturated with only plagioclase when advected near the surface (J. Longhi, pers. comm.). Thus focused downwellings from the upper boundary layer may deposit pyroxenes in the lower boundary layer, and return flow deposit plagioclase grains in the Olivine upper boundary layer. Anorthite lid growth may thus occur on the timescale of convection. Our models include fractionation of magma ocean cumulates in assemblages determined aprioriand shown in Fig. 2. The model Olivine crystallizes solely olivine from a starting pressure of 3.86 GPa, which corresponds to a depth of 1000 km on the Moon, until solids have filled the lunar interior to a pressure of 3.0 GPa. At this point the crystallizing Percent solid by volume 0 assemblage becomes 90% orthopyroxene (with ~2 wt.% Al2O3)and10% Fig. 2. Cumulate stratigraphy. Solidifying mantle mineral assemblages used in this olivine. This mineralogy is crystallized until ~80 vol.% solidification is paper (left) and by (Snyder et al., 1992) (right). Opx = orthopyroxene; Cpx = reached, at 0.6 GPa, when plagioclase and clinopyroxene also begin clinopyroxene; Pig = pigeonite; Ox = oxides, including ilmentite, as described in the crystallizing. The crystallizing assemblage from 0.6 GPa to 0.5 GPa is 20% text; An = anorthite feldspar (plagioclase). Width of mineral boxes indicates fraction in well-mixed phase assemblage. Note that when anorthite crystallizes it is assumed to olivine, 20% low-calcium clinopyroxene (with ~4 wt.% Al O ), 50% 2 3 float while other phases sink. This figure does not, therefore, represent the depth at fi plagioclase, and 10% orthopyroxene. From 0.5 GPa (~87 vol.% solidi ed) which the minerals reside after solidification, just the ranges in solidification over to the end of solidification the crystallizing assemblage contains 20% which they are assumed to form. Models assumed different initial depths. 330 L.T. Elkins-Tanton et al. / Earth and Planetary Science Letters 304 (2011) 326–336 based on empirical measurements and result a fractional solidification The solidus of the fractionally solidifying mantle is fit to the lunar sequence certainly accurate enough for this study. Both the bulk mantle solidus of Longhi (2003). Temperature is a contributing factor composition and the mineral assemblages were adjusted slightly from in density, which is important in these models; any similar smoothly Buck and Toksöz (1980) and Snyder et al. (1992), respectively, to allow decreasing solidus would give similar results. As crystallization solidification to proceed to 90% without running out of any of the proceeds, the solidus for the evolving liquid decreases to match major oxides (see Table 1 for bulk composition and Fig. 2 for mineral temperatures calculated from the MELTS program (Ghiorso and Sack, assemblages). Specifically, magnesium needed to be slightly enriched in 1995) using the evolving compositions from fractional crystallization the initial bulk composition to enable fractional solidification of the calculations in these models: entire magma ocean without running out of magnesia. The final 10% − − is assumed to solidify in bulk, and at some point during this solidification TrðÞ= −1:3714 × 10 4 r2−0:1724r + 1861−4:40ðÞ:2L +0:01 1; ð3Þ to be roughly analogous to KREEP. Along with, or perhaps instead of, adjusting the bulk composition where L is the remaining liquid fraction. and mineral assemblages, we could have used other of the many estimates for the bulk silicate Moon (Jones and Delano, 1989; Morgan 3.3. Heat flux and solidification timescales et al., 1978; O'Neill, 1991; Ringwood and Kesson, 1976; Ringwood et al., 1987; Taylor, 1982; Wänke and Dreibus, 1984; Warren, 1985, The cooling of the magma ocean can be modeled as a two-stage 1986). Most importantly, however, the specific results and conclu- process. First, heat is advected in a vigorously convecting body to a sions presented here do not vary greatly with the possible differences free liquid surface. Unlike Solomon and Longhi (1977) we propose in compositions or assemblages; as in all modeling efforts we must that the Moon will not have a solid conductive lid until plagioclase differentiate between first-order conclusions and more fragile results flotation creates the anorthositic crust. Modeling efforts concerning that are model dependent. the Moon-forming giant impact indicate high surface temperatures Compositions of mineral phases are calculated in equilibrium with (Canup, 2008), and any quenched mafic magma ocean liquids will the magma ocean liquid composition at that stage of solidification, have densities greater than their liquid counterparts and will sink using experimentally determined KDsformajorelementsand (Walker and Kiefer, 1985). We therefore model the lunar magma partition coefficients for trace elements; see Elkins-Tanton (2008). ocean as having a free surface until plagioclase flotation. The percentage of interstitial liquids retained during solidification A solidification time scale for this early stage can be calculated can also be varied in these models, and results are shown with 1 to using heat flux F from the planet expressed as the following balance 10 vol.% interstitial liquids. The density of each mineral phase at each between total planetary heat flux on the left and the sum of latent step is calculated as a function of composition, pressure, and tem- heat of crystallization of an increment of the magma ocean and perature (Fig. 3). secular cooling of the planet: Material is assumed to retain its solidus temperature as crystal- hi lization proceeds (Elkins-Tanton et al., 2003). The mineral densities dr 4 d 4πR2F = ρH4πr2 + πρC TR3−r3 ð4Þ are calculated using a Birch–Murnaghan equation of state that dt 3 p dt includes the effects of composition, temperature, and pressure. The ρ pressure profile of the lunar interior in GPa is calculated as: expressed in terms of planetary radius R, solid density , heat of fusion H, radius of solidification r, heat capacity C , and change in solid p − − temperature dT (dependent upon solidus slope). Total heat flux F can PrðÞ= −1:522 × 10 6 r2 + −8:963 × 10 5 r +4:76; ð2Þ be calculated as Stefan–Boltzmann radiation from the atmosphere where r is radius in km. 4 4 F = εσ T −T∞ ; ð5Þ

1700 where T is the surface temperature [K], T∞ is the blackbody equi- clinopyroxene oxides plagioclase librium temperature of the planet heated only by the Sun, σ is the 1600 Stephan–Boltzmann constant, and emissivity ε is a function of optical depth, here assumed to be unity. 1500 Plagioclase is always buoyant with respect to its coexisting liquid, 1400 resulting in density-driven rise to the top of the magma ocean (Fig. 3) (e.g., Smith et al., 1970; Warren, 1990; Wood et al., 1970). The 1300 growing conductive plagioclase lid becomes the rate-limiting step in heat loss from the Moon. At the point plagioclase solidification begins 1200 orthopyroxene in these models the remaining magma ocean is ~100 km deep. Radius [km] 1100 Heat flux is assumed to continue as convective and radiative until a olivine conductive lid 5 km thick is reached through solidification and flotation. 1000 interstitial Once a 5 km-thick lid is attained, when the magma ocean is about liquid 900 100 km deep, cooling through the lid is calculated solving the transient heat conduction equation in a spherical geometry for the solid lid. 800 During each step the requisite temperature loss to allow 1/1000 of the

2600 2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800 initial magma ocean volume to solidify is calculated including latent fi Density [kg m-3] heat of solidi cation and secular cooling of the body, as in Eq. (3).Heatis then conducted through the lid for the time required to match this new Fig. 3. Mineral densities. Cumulate phase densities as calculated in the model, as a temperature at the lid's bottom boundary, assuming the top boundary function of depth of initial crystallization from the magma ocean (note these depths is held at 25 K. The lid thickness is increased during each step by the will not perfectly match final pre-overturn cumulate depths, because plagioclase volume of plagioclase solidified during that step, assuming only flotation is not accounted for here). Only plagioclase feldspar is buoyant with respect to plagioclase floats (though the highest measured plagioclase content coexisting evolving magma ocean liquids (though note that late in solidification liquid fl densities rise in response to increased metal oxide content, and at the final stages of the anorthosite otation crust on the Moon is about 96%; (Shearer pyroxenes may be buoyant). et al., 2006), thus progressively slowing the process of cooling. L.T. Elkins-Tanton et al. / Earth and Planetary Science Letters 304 (2011) 326–336 331

4. Results and discussion Solidification of cumulate mantle pre-overturn (anorthite from solidifying layers 3 and 4) 1700 LAYER 4 opx + cpx + an + oxides 4.1. Fate of alumina: anorthositic crust, interstitial liquids, and pyroxenes LAYER 3 opx + cpx + an 1600 1% 10% interstitial With 1 vol.% of interstitial melt through the cumulate pile, this 1500 liquid model creates 45 km of anorthositic crust. The model of Snyder et al. LAYER 2 olivine + orthopyroxene (1992), in comparison, created ~28 km. Recent re-interpretation of 1400 the data collected from the Apollo seismic array suggests the global 1300 average crustal thickness varies between 40 and 45 km (Chenet et al., 2006; Hikida and Wieczorek, 2007; Wieczorek, 2009). In models 1200

with more retained interstitial liquid in the cumulate pile, a thinner Radius [km] anorthosite lid is built. With 10 vol.% of interstitial melt the resulting 1100 lid is only ~40 km thick. 1000 Interstitial melt is therefore an important consideration in magma LAYER 1 olivine ocean solidiﬁcation. These small melt fractions retain incompatible 900 elements in the deeper mantle, where otherwise the composition 800 would be a sterile pure olivine or olivine plus pyroxene composition. Interstitial melt also, therefore, sequesters alumina in the mantle and prevents its incorporation into the anorthositic lid. The alumina in Cumulate mantle after gravitationally-driven overturn interstitial melt and the alumina content of pyroxenes produces a non- 1700 anorthite from layers 3 and 4 zero alumina content of the lunar cumulate mantle, despite anorthite olivine + opx from lowest layer 2 ﬂotation, as shown in Fig. 4. 1600

Thus even with this simple model alumina is dispersed through 1500 olivine + opx from mid-layer 2 the lunar interior. Though the ﬂotation lid is here treated as pure anorthite feldspar, the lunar anorthositic crust is not pure anorthite, 1400 ol + opx from olivine upper but contains maﬁc minerals (e.g. Shearer et al., 2006 and references from layer 2 layer 1 therein) as well as Mg suite igneous rocks. 1300

In these models anorthite is forming and rising during the time of 1200 greatest evolution in the remaining magma ocean liquids (Fig. 4). The ol + opx from top of layer 2 Radius [km] first anorthite grains to solidify may coexist with pyroxenes with 1100 opx + cpx from layer 3 Mg#s (where Mg# is molar Mg/(Mg+Fe)) as high as 80, while the 1000 last anorthite to solidify may co-crystallize with pyroxenes with Mg# 50 or less (Fig. 5). This model therefore predicts a wide range of 900 opx + cpx + ox from layer 4 coexisting Mg#s, and also that the Mg#s should be correlated to degree of fractionation of the evolving magma ocean, and therefore to 800 depth in the anorthositic lid. Indeed the Mg#s of orthopyroxenes in 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ferroan anorthosites ranges from ~40 to 75 (Lucey et al., 2006), Mg# (molar Mg/(Mg+Fe)) of bulk cumulate mantle indicating a degree of fractionation equivalent to what is predicted in these models. Fig. 5. Cumulate Mg#s and oxides. Cumulate mantle compositional evolution with solidification from the bottom, shown with Mg# (molar Mg/(Mg+Fe)), for pre- and post-overturned lunar mantles. The model holds the extremely evolved liquid compositional constant during final ~30 km in radius to avoid computational errors; this is shown with a vertical line in Mg# in the pre-overturn figure. Cumulate Mg# profiles are given for 1, 5, and 10 vol.% retained interstitial liquid pre-overturn, and for Anorthositic crust at 37 wt% 1 vol.% post-overturn. Abbreviations as in Fig. 2. 1700 1%

1600 10% interstitial 4.2. Composition of the lunar cumulate mantle and overturn to gravitational 1500 liquid stability 1400 Once solidiﬁcation is complete, the modeled lunar interior in- 1300 variably has an unstable density gradient (denser near the surface than at depth) under its buoyant anorthosite lid (Hess and Parmentier, 1200 1995; Ringwood and Kesson, 1976; Spera, 1992). This unstable density Radius [km] 1100 gradient is created in three ways: by temperature, fractionation of magnesium and iron, and late solidiﬁcation of dense iron, chromium, 1000 and titanium-bearing oxides (Hess and Parmentier, 1995; Solomatov, 900 2000 and references therein). Temperature in the cumulate mantle is likely to lie along its 800 solidus, which is less steep than an adiabatic gradient. Shallow 0 5 10 15 cumulates, therefore, are cooler, hence denser than they would be in a

Al2O3 in bulk cumultes [wt%] stable adiabat, and deep cumulates are hotter and accordingly more buoyant (Solomatov, 2000). Second, fractional solidification of a Fig. 4. Alumina content of cumulate. Alumina content of bulk cumulate mantle magma ocean produces a relatively smooth decline in Mg# in following flotation of anorthositic crust and full solidification but before gravitationally cumulates, as all mafic phases incorporate magnesium in preference driven overturn. The alumina content of pyroxenes and interstitial melt combine to leave alumina in the mantle, available for inclusion in magma during melting events. to iron, progressively enriching iron in the evolving liquids, as Profiles are given for 1, 5, and 10 vol.% retained interstitial liquid. controlled by the minerals' Fe–Mg KD (Fig. 5, top; for KDs see Elkins- 332 L.T. Elkins-Tanton et al. / Earth and Planetary Science Letters 304 (2011) 326–336

Tanton, 2008). Fractionation of mafic phases therefore gradually The volume of each layer is preserved during the overturn and enriches the magma ocean liquids with iron and drives later, temperatures are adjusted for adiabatic rise and fall (Fig. 5, bottom; shallower cumulates to higher iron contents. Finally, titanium and Fig. 6). Because the model stops the evolution of the magma ocean chromium are relatively incompatible in cumulate minerals and are liquids in their last fractions, the Mg# of cumulates become constant progressively enriched in magma ocean liquids until dense, late-stage near the top of the cumulate mantle in Fig. 5, top. Preservation of oxides are stabilized and added to the cumulate assemblage near volume means these constant-Mg# cumulates fill the lowest mantle the lunar surface. The models with 1, 5, and 10 vol.% interstitial melt after overturn to a depth of almost 200 km (Fig. 5, bottom). This produce the unstable pre-overturn density gradients shown in Fig. 6, constant composition in the lowest mantle is an artifact of calculation. left. If the lunar magma ocean crystallized fractionally, the Mg# of cumu- A gravitationally unstable stratigraphy will overturn via Rayleigh– lates would continue to decrease rapidly rather than become constant. Taylor instabilities to a stable profile with intrinsically densest Each solidifying increment is assumed to maintain its solidus materials at the bottom, on timescales that depend on the rate of temperature (Fig. 6, right). Some of the rising materials may, upon thermally activated creep (Elkins-Tanton et al., 2005; Solomatov, decompression, reach super-solidus temperatures and re-melt. In 2000). The time of overturn depends upon a competition between the Fig. 6 the pre-overturn temperature profile is not the correct solidus rate of solidification and the time of onset of gravitational overturn. for each differentiated packet of cumulate mantle and so can only Overturn time is dependent upon the reciprocal of layer thickness be used as a rough guide to decompression melting. In this case the squared (Elkins-Tanton et al., 2003; Hess and Parmentier, 1995). hottest cumulates are high-Mg# olivine and will not melt during On the low-gravity Moon during the first 80% or so of solidification rise. Some of the pyroxene-bearing mid-mantle cumulate may overturn times range from the hundreds of thousands to millions of partially melt, however, on their ascent to the region just under the years, first because the layer thickness is small and second because anorthositic crust (lower panel of Fig. 5). We hypothesize that this the density gradient is shallow (Fig. 6). Overturn therefore will not overturn melting may be a source for lunar Mg suite rocks and other begin during the rapid-solidification stage. When solidification is igneous intrusives in the anorthosite flotation crust. nearly finished however, overturn times shrink to thousands of years The model predicts that melt during overturn would have a high because of the layer of high-density oxide-bearing cumulates at the Mg#, originating from material with Mg#s of ~80 to 90. Indeed, top. Here the time to initiate solid-state overturn is less than the time anorthite (calcium) content of plagioclases from the magnesian suite of required to complete solidification of the magma ocean (see below), lunar crustal rocks is positively correlated with the Mg# of coexisting and so overturn is likely to initiate before solidification is complete. orthopyroxenes, possibly indicating co-fractional crystallization from a The high-titanium late cumulates are thus likely to sink partly in the magma. Mg#s of pyroxenes range from about 30 to 90, while calcium liquid state, and leave traces of their composition in solid cumulates content of plagioclases ranges from 78 to 96 (Lucey et al., 2006). These during their fall, increasing the titanium heterogeneity of the lunar magnesian suite rocks intruded existing anorthositic crust and thus upper mantle. These models, however, assume for simplicity in these are both petrologically and chronologically consistent with production calculations and figures that the Moon is fully solid before overturn through melting during cumulate overturn. The likelihood that overturn begins. began before solidification was complete adds complexity to these The first prediction for internal structure after overturn is that calculations, though fractionation to first order would not be disturbed much of the iron- and titanium-bearing material will be at depth, with by overturn of existing sequestered solids. A further discussion of timing the possible exception of some cold, shallow titanium-bearing and ages is included in the next section. materials that did not participate in overturn and remain just under Both phase assemblage and composition affect density. These the lunar lid (Elkins-Tanton et al., 2002) and traces that are left behind create an initial density profile (Fig. 6, left) in which some mid-level as the sinking diapirs pass through shallower material. The second cumulates have the same density as lower-mantle cumulates, though prediction is that the lunar mantle will remain azimuthally hetero- their compositions differ. As they sink or rise under the influence of geneous in composition to the present day. gravity, they will reach a unique depth of mutual neutral buoyancy

1700

Luna 24 15065 1600 Pre-overturn 70215 12009 Mare 70017 15555 basalts 14072 15016 1500 15C 74275 12002 12022 Radius range of 14 Black 1400 azimuthally 17 VLT 14 VLT heterogeneous 74220 orange 15A 1300 cumulate mantle Picritic 14B for interstitial melt glasses 15 Red 1200 from 1 to 10% Post-overturn Radius [km] 1100 1% interstitial 1000 liquid 5% 900 10% Post-overturn Pre-overturn

800

2600 2800 3000 3200 3400 3600 800 1000 1200 1400 1600 Density [kg m-3] Cumulate mantle temperature [C]

Fig. 6. Cumulate density and temperature profiles. Cumulate mantle density and temperature profiles before and after solid-state overturn to gravitational stability. Left: Density of mantle mineral assemblages at reference pressure and solidus temperature; assumes mantle retains solidus temperature over period of solidification and carries temperature during overturn with only adiabatic adjustment and no conductive loss. Right: The pre-overturn temperature profile is the solidus adjusted for evolving bulk composition. After overturn the mantle is monotonic in density (left) but laterally heterogeneous in temperature and composition between ~1250 and 1450 km radius with 1 vol.% interstitial melt. Horizontal guidelines indicate radius ranges of compositional heterogeneity. The pressures and temperatures of origin of the mare basalts (rectangles) and picritic glasses (circles) are also given (for references see (Elkins-Tanton et al., 2004). Black symbols indicate high titanium content, while white symbols indicate low titanium. L.T. Elkins-Tanton et al. / Earth and Planetary Science Letters 304 (2011) 326–336 333 and the rising and sinking diapirs will stall adjacent to each other in 6 1 the lunar mantle. This phenomenon serves to juxtapose magma ocean Fraction solidified 5 0.9 materials with different temperatures at the same depth and appears as a zone of different temperatures at the same depth. 0.8

4 Fraction solidified by volume ]

These models indicate that, if it underwent compositionally driven -1 0.7 3 cumulate overturn, the Moon was unavoidably left with radius ranges in sec -2 its mantle containing laterally heterogeneous cumulates (Figs. 5 and 6). 0.6 All models run for the Moon result in a heterogeneous mantle, though 2 the radius range and exact compositions depend upon starting bulk 0.5 composition, mineral assemblage, and percent of retained interstitial 1 0.4

liquid. [Heat flux] [Jm 0 Fig. 6 (right) shows the depths and temperatures of origin of 10 0.3

Log Heat flux a wide variety of lunar volcanic compositions. An enduring problem -1 in understanding their provenance has been that magmas with 0.2 compositions that require different melting source regions appear to -2 0.1 have originated at similar depths in the lunar mantle. High-titanium -3 0 compositions are shown in black or gray, for intermediate titanium 0 1 2 3 4 5 6 7 content picritic glasses. In our reference model, with 1 vol.% inter- Time [Ma] stitial melt, the radius range of heterogeneous mantle closely matches the radius range of origin of the picritic glasses, while residues from Fig. 7. Heat flux and timeline to solidification. Surface heat flux from the solidifying Moon, and fraction of the initial magma ocean solidified, vs. time. In this model with overturn are predicted to create a heterogenous upper mantle for the 5 vol.% retained interstitial melt the 1000 km-deep magma ocean requires about mare basalts; an azimuthally heterogeneous lunar cumulate mantle 7 million years to fully solidify. The first 80%, however, with a free surface before may help explain the origin of such compositionally diverse magmas plagioclase flotation begins, solidifies on the order of 1000 years. from the same range of lunar depths. Isotopic and trace element data from lunar basalts analyzed by When plagioclase crystallization begins, the depth from the free Nyquist et al. (1977) similarly motivated them to suggest that the surface to the cumulate pile is only about 100 km. Thus, during the basalt source region was heterogeneous on a small scale, partly as a greatest majority of cooling, the Moon consists of a largely solid result of gravitational settling, and partly as a result of other fluid sphere with a solid conductive lid, and only a thin shell of liquid and dynamic processes. Here we provide a robust physical model for crystals between. The results of models in Herbert et al. (1977) largely producing the required heterogeneity. agree with results in this paper, while Solomon and Longhi (1977) The close coincidence between origin of the lunar magmas and predict 200 Myr to solidify the Moon. Their longer period relies not on model prediction of azimuthally heterogeneous mantle in Fig. 6 is tidal heating but on the existence of a conductive lid throughout the partly a product of assumptions about solidification mineralogy and process, a hypothesis we find unlikely. interstitial melt fraction, but all models for fractionally solidifying Despite the drastic decline in heat flux and lengthening of the magma oceans we have considered for any planet have produced cooling time of the final 20% of the lunar magma ocean by many heterogeneous regions in the planetary mantles. Fig. 6 also shows the orders of magnitude, the modeled range in time of anorthosite crust radius range over which the lunar mantle is predicted to be hetero- formation still cannot be reconciled with the geochronologic data geneous for a range of retained interstitial melt fractions. shown in Fig. 1. An additional ~200 million years of delayed solid- The temperature profile shown in Fig. 6 pertains only to the first ification and anorthosite formation is required beyond the point of few million years after overturn. The mare basalts and picritic glasses complete solidification modeled here. did not melt and erupt until ~500 million to ~1.5 billion years later The parameters that have the greatest influence on solidification (Shearer et al., 2006). The mantle may be mixed by convection and time in the model presented here are time of formation of a conductive will certainly relax through conductive heat exchange over that time lid; thermal conductivity through the lid; depth of the magma ocean at period. The temperature profile would certainly be different when the the time of formation of the lid; and additional cooling required by picritic glasses and mare basalts erupted. The compositions, though, melting during cumulate overturn. The first two do not appear to be are not likely to have been thoroughly mixed even by possible thermal viable processes to significantly change the timeline of solidification. convection. As described above, we do not believe that a conductive lid can be Experiments on the picritic glasses show their source mineralogy initiated before plagioclase flotation. Thermal diffusivity through the to be olivine plus pyroxene, in agreement with magma ocean lid may be faster than that used here (10− 6 m2 s− 1) if melt channels solidification models, but their compositions also include alumina, still exist, but this would only serve to speed cooling. titanium, and trace elements not likely to have been contained in the The depth of the magma ocean at initiation of the anorthosite lid may simple olivine plus pyroxene cumulates. Rather than calling on a be an important factor (Fig. 8). With a fixed-thickness conductive lid of primary melt from a deeper, undefined region of the Moon, melting 40 km, a magma ocean 200 km thick requires twice the time to cool of a and incorporation of interstitial melts and stringers of previously magma ocean 100 km thick; this is a simple scaling relationship of descended high-titanium late-stage cumulates may provide all the volume to surface area. Note, however, that an incrementally growing compositional range needed. lid (as shown in Fig. 8 as the reference model) cools about twice as fast as its constant-lid equivalent. In any case, however, no lunar magma ocean 4.3. Time to solidification and geochronologic constraints can be sufficiently deep to prolong solidification by 200 Myr. Lastly, cumulate overturn offers the possibility of additional melting through Heat loss from the Moon prior to formation of the conductive adiabatic decompression, as discussed above in connection to the Mg flotation lid is extremely rapid. Solidification of the first 80 vol.% of suite rocks. Overturn is likely to occur before the end of solidification the magma ocean, to the point that plagioclase begins to float, and thus deepen the existing magma ocean, but only fractionally requires only on the order of 1000 years. As soon as a conductive lid because of the high melting temperatures of these deep magnesian is established on the body solidification slows greatly, and the re- cumulates. maining 20 vol.% of the magma ocean requires about 10 million years The likeliest process to account for the difference in time to solidify in this reference model (Figs. 1 and 7). between modeled solidification and geochronology is tidal heating, 334 L.T. Elkins-Tanton et al. / Earth and Planetary Science Letters 304 (2011) 326–336

1100 et al., 1995). Throughout overturn and remelting and production of the Mg-suite rocks, the crust may have been remelting, and therefore 1050 resetting its geochronometers.

1000 5. Conclusions

950 The comparison of a linked physical and chemical model for solidification of an initially partially molten Moon with ages obtained 900 through geochronology of lunar samples leads to the following conclusions: 850 120 km fiducial model • Magma oceans of as much as 1000 km depth can create anorthosite 800 Magma ocean temperature [C] flotation crusts of as little as 40 to 50 km, because some alumina is 250 200 sequestered in pyroxenes and interstitial liquids at depth, and thus 750 50 km 100 150 plagioclase formation is reduced. • Solidification of ~80 vol.% of the magma ocean occurs on the order of 700 0 5 10 15 20 25 30 35 1000 years. Time [Myr] • The remainder of solidification, under the conductive anorthosite lid, requires on the order of 10 Myr in the absence of tidal heating. Fig. 8. Time for magma ocean solidification from the point of plagioclase flotation. • Reconciling this solidification time with the wide range of anortho- Dashed lines: A simplified model for magma oceans with depths of 50, 100, 150, 200, and 250 km below a lid with constant thickness 40 km. Solid line: Curve for the sitic crustal ages likely requires tidal heating from the Earth, which reference model presented here, under a growing lid; plagioclase begins to float when will melt and recycle the lunar crust (Meyer et al., 2010). the magma ocean is 130 km deep, but conductive calculations begin when the lid has • Solid-state cumulate overturn creates a lunar mantle azimuthally reached 5 km thickness, and the magma ocean is then ~120 km deep. Note that an heterogeneous in composition, consistent with the source regions incrementally growing lid roughly halves the time for solidification compared to a constant-thickness lid. of picritic glasses and mare basalts. • Solid-state cumulate overturn also produces adiabatic melting and likely injection of magmas into the anorthositic crust, consistent with creation, composition, and ages of the Mg suite lunar crustal as described in Meyer et al. (2010). Tidal heating of the Moon by the rocks. Earth is sufficient not only to slow solidification of the remnant interior lunar magma ocean, but also to hold portions of the crust above its closure temperatures, and in some cases to melt and re- Acknowledgments erupt portions of the crust (Meyer et al., 2010). Cooling of crustal minerals beneath their closure temperatures may therefore have The authors thank Rick Carlson, Larry Nyquist, and John Longhi occurred at any point along this timeline and is largely decoupled for their thoughtful and expert reviews that greatly improved this from magma ocean solidification. The collective age range, from all paper. This work is funded through an NSF Astronomy CAREER isotope systems used, thus represents the time over which the crust grant to Elkins-Tanton, and NASA LASER and Lunar Institute funding. was either solidifying or resetting through tidal heat. Q.-Z. Y. acknowledges the support by NASA Cosmochemistry grant These processes continue for ~200 Ma according to the dynamical (NNX08AG57G). simulations, adequate to explain the range of ages measured in lunar crustal rocks. The resulting crust will be heterogeneous and non- References monotonic in age and composition as a function of depth, and it would Abe, Y., 1993. Physical state of the very early Earth. Lithos 30, 223–235. be expected to contain rocks with ages ranging over ~200 Ma. Abe, Y., 1997. Thermal and chemical evolution of the terrestrial magma ocean. Phys. Melting and eruption produces a structure in which the youngest Earth Planet. Inter. 100, 27–39. Abe, Y., Matsui, T., 1985. The formation of an impact-generated H2O atmosphere and its rocks are at the surface, and age increases with depth, to the depth – fi implications for the thermal history of the Earth. J. Geophys. Res. 90, 545 559. where melting did not occur and magma ocean solidi cation processes Abe, Y., Matsui, T., 1986. Early evolution of the Earth: accretion, atmosphere formation, again prevail, and crustal age decreases with depth. This approxi- and thermal history. J. Geophys. Res. 91, E291–E302. mately reverses the age structure of the crust created by initial magma Alibert, C., Norman, M.D., McCulloch, M.T., 1994. An ancient Sm–Nd age for a ferroan fi noritic anorthosite clast from lunar breccia 67016. Geochem. Cosmochim. Acta 58, ocean solidi cation. The resulting crust will be heterogeneous and 2921–2926. nonmonotonic in age and composition as a function of depth, and it Arevalo, R.J., McDonough, W.F., 2008. Tungsten geochemistry and implications for would be expected to contain rocks with ages ranging over ~200 Ma. understanding the Earth's interior. Earth Planet. Sci. Lett. 272, 656–665. – Borg, L.E., Norman, M., Nyquist, L.E., Bogard, D., Snyder, G.A., Taylor, L., Lindstrom, M., This lengthy reheating event may also help explain the Hf W results 1999. Isotopic studies of ferroan anorthosite 62236: a young lunar crustal rock of Touboul et al. (2009), and is in agreement with their suggestion from a light rare-earth-element-depleted source. Geochem. Cosmochim. Acta 63, of a protracted solidification. 2679–2691. Further, and similar to the anorthosite crust, the Mg suite rocks are Borg, L.E., Shearer, C.K., Nyquist, L.E., Norman, M., 2002. Isotopic constraints on the origin of lunar ferroan anorthosites. Proc. Lunar Planet. Sci. Conf. 33, 1396. not all the same age. Overturn of gravitationally unstable cumulates is Borg, L.E., Connelly, J., Boyet, M., Carlson, R., 2011. The age of lunar ferroan anorthosite likely to occur on a timescale shorter than the tidal heating period of 60025 with implications for the interpretation of lunar chronology and the magma 200 Myr. Therefore if the source region of the Mg Suite is high-Mg ocean model. Proceedings of the Lunar and Planetary Science Conference, 42. Lunar and Planetary Institute, Houston TX. p. (abstract). cumulates rising during overturn, as suggested in the section above, Boyet, M., Carlson, R., 2007. A highly depleted moon or a non-magma ocean origin for then this source region would participate in the lengthy heating the lunar crust? Earth Planet. Sci. Lett. 262, 505–516. Buck, W.R., Toksöz, M.N., 1980. The bulk composition of the moon based on geophysical process created by tidal friction. The source region remains under the – fl fi constraints. Proc. Lunar Planet. Sci. Conf. 11, 2043 2058. otation lid, interacting with the nal dregs of the magma ocean, Campbell, G.A., Forgacs, G., 1990. Viscosity of concentrated suspections: an approach melting, and intruding the crust over a lengthy period of time. The based on percolation theory. Phys. Rev. 41A, 4570–4573. mechanism of extended tidal heating and partial remelting also offers Canup, R.M., 2004. Dynamics of lunar formation. Annu. Rev. Astron. Astrophys. 42, 441–475. an explanation for the overlapping ages of ferroan anorthosites and Canup, R.M., 2008. Accretion of the Earth. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. Mg-suite rocks (e.g. Borg et al., 1999; Edmunson et al., 2009; Nyquist 3366, 4061–4075. L.T. Elkins-Tanton et al. / Earth and Planetary Science Letters 304 (2011) 326–336 335

Carlson, R., Lugmair, G.W., 1988. The age of ferroan anorthosite 60025: oldest crust on a Nemchin, A., Timms, N., Pidgeon, R., Geisler, T., Reddy, S., Meyer, C., 2009. Timing and young Moon? Earth Planet. Sci. Lett. 90, 119–130. crystallization of the lunar magma ocean constrained by the oldest zircon. Nat. Chenet, H., Lognonne, P., Wieczorek, M.A., Mizutani, H., 2006. Lateral variations of Geosci. 2, 133–136. lunr crustal thickness from the Apollo seismic data set. Earth Planet. Sci. Lett. 243, Norman, M., Borg, L.E., Nyquist, L.E., Bogard, D.D., 2003. Chronology, geochemistry, and 261–275. petrology of a ferroan noritic anorthosite clast from Descartes breccia 67215: clues Connelly, J., Amelin, Y., Krot, A., Bizzarro, M., 2008. Chronology of the Solar System's to the age, origin, structure, and impact history of the lunar crust. Meteorit. Planet. oldest solids. Astrophys. J. Lett. 675, 121–124. Sci. 38, 645–661. Edmunson, J., Borg, L.E., Nyquist, L.E., Asmerom, Y., 2009. A combined Sm–Nd, Rb–Sr, Nyquist, L.E., Shih, C.-Y., 1992. The isotopic record of lunar volcanism. Geochem. and U–Pb isotopic study of Mg-suite norite 78238: further evidence for early Cosmochim. Acta 56, 2213–2234. differentiation of the Moon. Geochem. Cosmochim. Acta 73, 514–527. Nyquist, L.E., Bansal, B.M., Wooden, J.L., Wiesmann, H., 1977. Sr-isotopic constraints on Elkins-Tanton, L.T., 2008. Linked magma ocean solidification and atmospheric growth the petrogenesis of Apollo 12 mare basalts. Proc. Lunar Sci. Conf. 8, 1383–1415. for Earth and Mars. Earth Planet. Sci. Lett. 271, 181–191. Nyquist, L.E., Wiesman, H., Bansal, B.M., Shih, C.-Y., Keith, J.E., HArper, C.L., 1995. 146Sm– Elkins-Tanton, L.T., Van Orman, J., Hager, B.H., Grove, T.L., 2002. Reexamination of the 142Nd formation interval for the lunar mantle material. Geochem. Cosmochim. Acta lunar magma ocean cumulate overturn hypothesis: melting or mixing is required. 59, 2817–2837. Earth Planet. Sci. Lett. 196, 249–259. Nyquist, L.E., Bogard, D., Yamaguchi, A., Shih, C.-Y., Karouji, Y., Ebihara, M., Reese, Y., Elkins-Tanton, L.T., Parmentier, E.M., Hess, P.C., 2003. Magma ocean fractional crystal- Garrison, D., McKay, G., Takeda, H., 2006. Feldspathic clasts in Yamato-86032: lization and cumulate overturn in terrestrial planets: implications for Mars. Meteorit. remnants of the lunar crust with implications for its formation and impact history. Planet. Sci. 38, 1753–1771. Geochem. Cosmochim. Acta 70, 5990–6015. Elkins-Tanton, L.T., Hager, B.H., Grove, T.L., 2004. Magmatic effects of the lunar late Nyquist, L.E., Shih, C.-Y., Reese, Y.D., Park, J., Bogard, D., Garrison, D., Yamaguchi, A., heavy bombardment. Earth Planet. Sci. Lett. 222, 17–27. 2010. Lunar crustal history recorded in lunar anorthosites. Lunar and Planetary Elkins-Tanton, L.T., Hess, P.C., Parmentier, E.M., 2005. Possible formation of ancient Science Conference, 41. Lunar and Planetary Institute, Houston, TX, p. 1383. crust on Mars through magma ocean processes. J. Geophys. Res. Planets 110. O'Neill, H.S.C., 1991. The origin of the Moon and the early history of the Earth — a Ghiorso, M.S., Sack, R.O., 1995. Chemical mass transfer in magmatic processes IV. A chemical model. Part 1. The Moon. Geochem. Cosmochim. Acta 55, 1135–1157. revised and internally consistant thermodynamic model for the interpolation and Ringwood, A.E., Kesson, S.E., 1976. A dynamic model for mare basalt petrogenesis. Proc. extrapolation of liquid–solid equilibria in magmatic systems at elevated tempera- Lunar Sci. Conf. 7, 1697–1722. tures and pressures. Contrib. Mineral. Petrol. 119, 197–212. Ringwood, A.E., Seifert, S., Wänke, H., 1987. A komatiite component in Apollo 16 Green, D.H., Ringwood, A.E., Ware, N.G., Hibberson, A., Kiss, E., 1971a. Experimental highland breccias: implications for the nickel–cobalt systematics and bulk petrology and petrogenesis of Apollo 12 basalts. Proc. Lunar Sci. Conf. 2, 601–615. composition of the Moon. Earth Planet. Sci. Lett. 81, 105–117. Green, D.H., Ware, N.G., Hibberson, A., Major, A., 1971b. Experimental petrology of Ryder, G., 1982. Lunar anorthosite 60025, the pertrogenesis of lunar anorthosites, and Apollo 12 mare basalts, Part 1, sample 12009. Earth Planet. Sci. Lett. 13, 85–96. the bulk composition of the Moon. Geochem. Cosmochim. Acta 46, 1591–1601. Haskin, L.A., Lindstrom, M.M., Salpas, P.A., Lindstrom, D., 1981. On compositional vari- Saar, M.O., Manga, M., Cashman, K.V., Fremouw, S., 2001. Numerical models of the onset ations among lunar anorthosites. Proc. Lunar Planet. Sci. Conf. 12, 41–66. of yield strngth in crystal–melt suspensions. Earth Planet. Sci. Lett. 187, 367–379. Herbert, F., Drake, M.J., Sonett, C.P., Wiskerchen, M.J., 1977. Some constraints on the Shearer, C.K., Hess, P.C., Wieczorek, M.A., Pritchard, M.E., Parmentier, E.M., Borg, L.E., thermal history of the lunar magma ocean. Proc. Lunar Sci. Conf. 8, 573–582. Longhi, J., Elkins-Tanton, L.T., Neal, C.R., Antonenko, I., Canup, R.M., Halliday, A.N., Hess, P.C., Parmentier, E.M., 1995. A model for the thermal and chemical evolution of Grove, T.L., Hager, B.H., Lee, D.C., Wiechert, U., 2006. Thermal and magmatic the Moon's interior: implications for the onset of mare volcanism. Earth Planet. Sci. evolution of the moon. New Views Moon Rev. Mineral. Geochem. 60, 365–518. Lett. 134, 501–514. Smith, J.V., Anderson, A.T., Newton, R.C., Olsen, E.J., Wyllie, P.J., Crewe, A.V., Isaacson, M.S., Hikida, H., Wieczorek, M.A., 2007. Crustal thickness of the Moon: new constraints from Johnson, D., 1970. Petrologic history of the moon inferred frompetrography, gravity inversions using polyhedral shape models. Icarus 192, 150–166. mineralogy and petrogenesis of Apollo 11 rocks. Proc. Apollo 11 Lunar Sci. Conf. 1, Jones, J.H., Delano, J.W., 1989. A three-component model for the bulk composition of the 897–925. moon. Geochem. Cosmochim. Acta 53, 513–527. Snyder, G.A., Taylor, L.A., Neal, C.R., 1992. A chemical model for generating the sources Kasting, J.F., 1988. Runaway and moist greenhouse atmospheres and the evolution of of mare basalts: combined equilibrium and fractional crystallization of the lunar Earth and Venus. Icarus 74, 472–494. magmasphere. Geochem. Cosmochim. Acta 56, 3809–3823. Kaula, W., 1979. Thermal evolution of Earth and Moon growing by planetesimal Solomatov, V.S., 2000. Fluid dynamics of a terrestrial magma ocean. In: Canup, R.M., impacts. J. Geophys. Res. 84, 999–1008. Righter, K. (Eds.), Origin of the Earth and Moon. University of Arizona Press, Khan, A., Mosegaard, K., Rasmussen, K.L., 2000. A new seismic velocity model for the Phoenix, p. 555. Moon from a Monte Carlo inversion of the Apollo lunar seismic data. Geophys. Res. Solomatov, V.S., Stevenson, D.J., 1993. Nonfractional crystallization of a terestrial Lett. 27, 1591–1594. magma ocean. J. Geophys. Res. 98, 5391–5406. Kirk, R.L., Stevenson, D.J., 1989. The competition between thermal contraction and Solomatov, V., Olson, P., Stevenson, D.J., 1993. Entrainment from a bed of particles by differentiation in the stress history of the Moon. J. Geophys. Res. 94, 133–144. thermal convection. Earth Planet. Sci. Lett. 120, 387–393. Kleine, T., Mezger, K., Palme, H., Scherer, E., Münker, C., 2005. Early core formation in Solomon, S.C., Longhi, J., 1977. Magma oceanography 1: thermal evolution. Proc. Lunar asteroids and late accretion of chondrite parent bodies: evidence from 182Hf–182W Sci. Conf. 8, 583–599. in CAIs, metal-rich chondrites, and iron meteorites. Geochim. Cosmochim. Acta 69, Solomon, S.C., Toksoz, M.N., 1973. Internal constitution and evolution of the Moon. 5805–5818. Phys. Earth Planet. Inter. 7, 15–38. Lee, D.C., Halliday, A.N., Snyder, G.A., Taylor, L.A., 1997. Age and origin of the moon. Spera, F.J., 1992. Lunar magma transport phenomena. Geochem. Cosmochim. Acta 56, Science 278, 1098–1103. 2253–2265. Lee, D.C., Halliday, A.N., Leya, I., Wieler, R., Wiechert, U., 2002. Cosmogenic tungsten and Taylor, S.R., 1982. Planetary Science: A Lunar Perspective. Lunar and Planetary Institute, the origin and earliest differentiation of the Moon. Earth Planet. Sci. Lett. 198, 267–274. Houston, Texas. Leont'eva, E.M., Matukov, D.I., Nazarov, M.A., Sergeev, S.A., Shukolyukov, Y.A., Taylor, S.R., Jakes, P., 1974. The geochemical evolution of the Moon. Proc. Lunar Sci. Brandstaetter, F., 2005. First determination of the isotopic age of a lunar meteorite Conf. 5, 1287–1305. by the uranium–lead zircon method. Petrology 13, 193–196. Tonks, W.B., Melosh, H.J., 1990. The physics of crystal settling and suspension in a Lognonne, P., 2005. Planetary seismology. Annu. Rev. Earth Planet. Sci. 33, 571–604. turbulent magma ocean. In: Newsom, N.E., Jones, J.H. (Eds.), Origin of the Earth. Longhi, J., 2003. A new view of lunar farroan anorthosites: postmagma ocean Oxford University Press, New York, pp. 151–174. petrogenesis. J. Geophys. Res. 108, 2-1–2-15. Touboul, M., Kleine, T., Bourdon, B., Palme, H., Wieler, R., 2007. Late formation and Lucey, P., Korotev, R.L., Gillis, J.J., Taylor, L.A., Lawrence, D., Campbell, B.A., Elphic, R., prolonged differentiation of the Moon inferred from W isotopes in lunar metals. Feldman, B., Hood, L.H., Hunten, D., Mendillo, M., Noble, S., Papike, J.J., Reedy, R.C., Nature 450, 1206–1209. Lawson, S., Prettyman, T., Gasnault, O., Maurice, S., 2006. Understanding the lunar Touboul, M., Kleine, T., Bourdon, B., Palme, H., Wieler, R., 2009. Tungsten isotopes in surface and space–Moon interactions. In: Jolliff, B.L., Wieczorek, M.A., Shearer, C.K., ferroan anorthosites: implications for the age of the Moon and lifetime of its Neal, C.R. (Eds.), New Views of the Moon, 60. The Mineralogical Society of America, magma ocean. Icarus 199, 245–249. Chantilly, Virginia, pp. 83–202. Van Orman, J., Grove, T.L., 2000. Origin of lunar high-titanium ultramafic glasses: Martin, D., Nokes, R., 1989. A fluid-dynamic studyof crystal settling in convecting constraints from phase relations and dissolution kinetics of clinopyroxene-ilmenite magmas. J. Petrol. 30, 1471–1500. cumulates. Meteoritics 35, 783–794. Meyer, C., Williams, I.S., Compston, W., 1996. Uranium–lead ages for lunar zircons: Walker, D., Hays, J.F., 1977. Plagioclase floatation an lunar crust formation. Geology 5, evidence for a prolonged period of granophyre formation from 4.32 to 3.88 Ga. 425–428. Meteorit. Planet. Sci. 31, 370–387. Walker, D., Kiefer, W.S., 1985. Xenolith digestion in large magma bodies. J. Geophys. Meyer, J., Elkins Tanton, L.T., Wisdom, J., 2010. Coupled thermal-orbital evolution of the Res. 90, C585–C590. early Moon. Icarus 208, 1–10. Walker, D., Hager, B.H., Hays, J.F., 1980. Mass and heat transport in a lunar magma ocean Morgan, J.W., Hertogen, J., Anders, E., 1978. The Moon: composition determined by by sinking blobs. Proc. Lunar Planet. Sci. Conf. 11, 1196–1198. nebular processes. Moon Planets 18, 465–478. Wänke, H., Dreibus, G., 1984. Geochemical evidence for the formation of the Moon by Morse, S.A., 1982. Adcumulus growth of anorthosite at the base of the lunar crust. Proc. impact-induced fission of the proto-Earth. In: Hartman, W.K., Phillips, R.J., Taylor, G.J. Lunar Planet. Sci. Conf. 13, A10–A18. (Eds.), Conference on the Origin of the Moon, Kona HI, pp. 649–672. Nakamura, Y., Lammlein, D., Latham, G., Ewing, M., Dorman, J., Press, F., Toksöz, N., Warren, P.H., 1985. The magma ocean concept and lunar evolution. Annu. Rev. Earth 1973. New seismic data on state of deep lunar interior. Science 181, 49–51. Planet. Sci. 13, 201–240. Nemchin, A., Whitehouse, M.J., Pidgeon, R., Meyer, C., 2006. Oxygen isotopic signature Warren, P.H., 1986. Anorthosite assimilation and the origin of the Mg/Fe-related of 4.4–3.9 Ga zircons as a monitor of differentiation processes on the Moon. bimodality of pristine moon rocks: support for the magmasphere hypothesis. Proc. Geochem. Cosmochim. Acta 70, 1864–1872. Lunar Planet. Sci. Conf. 16, D331–D343. 336 L.T. Elkins-Tanton et al. / Earth and Planetary Science Letters 304 (2011) 326–336

Warren, P.H., 1990. Lunar anorthosites and the magma–ocean plagioclase-ﬂotation Wood, J.A., Dickey, J.S.J., Marvin, U.B., Powell, B.N., 1970. Lunar anorthosites and a hypothesis: importance of FeO enrichment in the parent magma. Am. Mineral. 75, 46–58. geophysical model of the moon. Proc. Apollo 11 Lunar Sci. Conf. 965–988. Wetherill, G.W., 1990. Formation of the Earth. Annu. Rev. Earth Planet. Sci. 18, 205–256. Yin, Q., Jacobsen, B., Yamashita, K., Blichert-Toft, J., Telouk, P., Albarede, F., 2002. A short Wieczorek, M.A., 2009. The interior structure of the Moon: what does geophysics have timescale for terrestrial planet formation from Hf–W chronometry of meteorites. to say? Elements 5, 35–40. Nature 418, 949–952. Wieczorek, M.A., Phillips, R.J., 1999. Lunar multiring basins and the cratering process. Icarus 139, 246–259.