formation of anorthosite on the moon through magma ocean fractional crystallization

Accepted Manuscript Formation of anorthosite on the Moon through magma ocean fractional crystallization Tatsuyuki Arai, Shigenori Maruyama PII: S1674-9871(16)30204-3 DOI: 10.1016/j.gsf.2016.11.007 Reference: GSF 512 To appear in: Geoscience Frontiers Received Date: April 2016 Revised Date: 20 November 2016 Accepted Date: 25 November 2016 Please cite this article as: Arai, T., Maruyama, S., Formation of anorthosite on the Moon through magma ocean fractional crystallization, Geoscience Frontiers (2017), doi: 10.1016/j.gsf.2016.11.007 This is a PDF file of an unedited manuscript that has been accepted for publication As a service to our customers we are providing this early version of the manuscript The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain ACCEPTED MANUSCRIPT Pl starts to crystallize Calculation limit RI PT melt Mg# = 0.46, 1218oC TE D 30 EP 20 10 0 20 40 60 Solidification of LMO (%) 80 100 SC SiO2 Al2O3 FeO MgO CaO Na2O M AN U 40 Critical diameter of plagioclase, dpl (cm) 50 AC C Composition of melt (wt%) 60 Crystal fraction, φ 0.01 0.05 0.1 Typical size of plagioclase in the lunar anorthosite 0.2 0.3 0.4 0.5 0.59 Pressure (kbar) 4.6 ACCEPTED MANUSCRIPT Tatsuyuki Araia, Shigenori Maruyama b,* a Ookayama, Meguro-ku, Tokyo 152-8551, Japan Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 b Meguro-ku, Tokyo 152-8551, Japan RI PT Formation of anorthosite on the Moon through magma ocean fractional crystallization Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1 Ookayama, 10 SC 11 * 12 Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1 Ookayama, 13 Meguro-ku, Tokyo 152-8551, Japan 14 E-mail: smaruyam@geo.titech.ac.jp 15 16 EP TE D Keywords: Moon; anorthosite; magma ocean; MELTS; fractional crystallization AC C 17 M AN U Corresponding author Shigenori Maruyama ACCEPTED MANUSCRIPT 18 19 Abstract Lunar anorthosite is a major rock of the lunar highlands, which formed as a result of 21 plagioclase-floatation in the lunar magma ocean (LMO) Constraints on the sufficient 22 conditions that resulted in the formation of a thick pure anorthosite (Pl >95 vol.%) is a 23 key to reveal the early magmatic evolution of the terrestrial planets To form the pure 24 lunar anorthosite, plagioclase should have separated from the magma ocean with low 25 crystal fraction Crystal networks of plagioclase and mafic minerals develop when the 26 crystal fraction in the magma (φ) is higher than ca 40–60 vol.%, which inhibit the 27 formation of pure anorthosite In contrast, when φ is small, the magma ocean is highly 28 turbulent, and plagioclase is likely to become entrained in the turbulent magma rather 29 than separated from the melt To determine the necessary conditions in which 30 anorthosite forms from the LMO, this study adopted the energy criterion formulated by 31 Solomatov (2015) The composition of melt, temperature, and pressure when 32 plagioclase crystallizes are constrained by using MELTS/pMELTS to calculate the 33 density and viscosity of the melt When plagioclase starts to crystallize, the Mg# of melt 34 becomes 0.59 at 1291oC The density of the melt is smaller than that of plagioclase for P 35 >2.1 kbar (ca 50 km deep), and the critical diameter of plagioclase to separate from the 36 melt becomes larger than the typical crystal diameter of plagioclase (1.8–3 cm) This 37 suggests that plagioclase is likely entrained in the LMO just after the plagioclase starts 38 to crystallize When the Mg# of melt becomes 0.54 at 1263oC, the density of melt 39 becomes larger than that of plagioclase even for kbar When the Mg# of melt decreases 40 down to 0.46 at 1218 oC, the critical diameter of plagioclase to separate from the melt 41 becomes 1.5–2.5 cm, which is nearly equal to the typical plagioclase of the lunar 42 anorthosite This suggests that plagioclase could separate from the melt One of the 43 differences between the Earth and the Moon is the presence of water If the terrestrial 44 magma ocean was saturated with H2O, plagioclase could not crystallize, and anorthosite 45 could not form AC C EP TE D M AN U SC RI PT 20 ACCEPTED MANUSCRIPT 46 47 Introduction In contrast to the Earth where most of the Hadean geological record has been 49 eliminated by tectonics, the lunar surface preserves rocks formed during the early 50 magmatic evolution of the Moon Understanding how the lunar rocks formed is a key to 51 reveal the early evolution of the terrestrial planets RI PT 48 The lunar highland crust is mainly composed of anorthosite or anorthositic rocks 53 formed by the floatation of plagioclase in the lunar magma ocean (LMO) (e.g., Wood et 54 al., 1970; Warren, 1990; Ohtake et al., 2009) It has long been debated whether 55 anorthosite is a major rock of the lunar crust Lunar anorthosite was first discovered 56 from rock fragments in surface regolith sampled during the Apollo 11 mission (Wood et 57 al., 1970), and anorthosite rocks were first found during the Apollo 15 mission (James, 58 1972) These and other findings suggest that anorthosite is a primary component of the 59 crustal materials of the lunar highlands The Multiband Imager on the Selenological and 60 Engineering Explorer (SELENE) has enabled investigation of the composition of the 61 lunar crust at global scale (Kato et al., 2008) Ohtake et al (2009) reported extensive 62 pure anorthosite rock with over 95 vol.% of plagioclase exposed by large impact events; 63 the crustal thickness of anorthosite on the Moon has been estimated to be 50 km based 64 on the calculation of the excavation depth of the anorthosite (Yamamoto et al., 2012) 65 Pure anorthosite has also been reported from lunar rock samples (Warren and Wasson, 66 1979a) The findings by SELENE suggest that the pure anorthosite is a primary 67 component of the lunar highlands EP TE D M AN U SC 52 Anorthosite can form by floatation of low-density plagioclase in the magma due to the 69 density difference between plagioclase and melt (Wood et al., 1970) The extensive 70 occurrence of anorthosite on the Moon requires a global magma body, referred to as the 71 lunar magma ocean (LMO) (Yamamoto et al., 2012) The “giant impact” scenario has 72 sufficient energy to produce Moon-forming melt (Hartmann and Davis, 1975; Ida et al., 73 1997; Pritchard and Stevenson, 2000) AC C 68 74 However, the actual mechanism that resulted in the formation of the lunar anorthosite 75 is still controversial To form the pure anorthosite, plagioclase should separate from the 76 LMO with low crystal fraction If the crystal fraction in magma becomes higher than 77 40–60 vol.%, crystal networks of plagioclase and mafic minerals develop, making it 78 difficult to separate only plagioclase from the crystal networks (Philpotts et al., 1998; ACCEPTED MANUSCRIPT 79 Philpotts et al., 1999) On the other hand, if the magma ocean was highly turbulent with 80 low crystal fraction, the plagioclase would have likely become entrained in the magma 81 rather than being separated from the melt (Martin and Nokes, 1989; Abe, 1993; Tonks 82 and Melosh, 1993) In order to constrain the necessary conditions that allow the plagioclase to be separated 84 from the LMO, we have adopted the energy criterion for the onset of fractional 85 crystallization formulated by Solomatov (2015) Sakai et al (2014) used the same 86 formula to constrain the composition of the initial LMO, with their results indicating 87 that the lunar bulk composition is enriched in FeO compared with the bulk silicate Earth 88 (BSE), which makes a large density difference between plagioclase and melt enough to 89 separate plagioclase from the turbulent LMO However, Sakai et al (2014) only 90 discussed the conditions when plagioclase first starts to crystallize As the LMO 91 solidifies, the melt becomes enriched in FeO, and the density of the melt possibly 92 increases enough to allow plagioclase to float at the upper part of the LMO In this study, 93 we evaluated the necessary conditions that allow the plagioclase to separate from the 94 melt by taking into account changes in the composition, the density, and the viscosity of 95 melt SC M AN U TE D 96 RI PT 83 97 Calculation Method 98 2.1 Energy criterion for the onset of fractional crystallization by Solomatov (2015) In order to constrain the necessary conditions that result in the formation of lunar 100 anorthosite, a theoretical criterion is required, addressing the critical condition when 101 minerals start to separate from the magma EP 99 Several previous studies focused on the comparison between the downward flux of 103 settling velocity of minerals with the upward flux of convective velocity of magma 104 convection (Huppert and Sparks, 1981; Abe, 1993) However, the laboratory 105 experiments on convective suspensions showed that the particles eventually settle down 106 even when the settling velocity is much smaller than the convective velocity (Martin 107 and Nokes, 1988, 1989) This is because the convective velocity vanishes at the 108 boundary layer, and the particles cannot be re-entrained This experimental observation 109 suggests that the convective speed in the magma ocean is not the parameter scaling the 110 efficiency of the crystal settling 111 AC C 102 This study alternatively uses the energy criterion for the onset of fractional ACCEPTED MANUSCRIPT crystallization formulated by Solomatov (2015) A condition when fractional 113 crystallization starts was addressed based on the balance between the total amount of 114 energy released per unit time due to crystal settling and the mechanical work most of 115 which is spent to overcome viscous friction associated with convection (Solomatov and 116 Stevenson, 1993; Solomatov, 2015) The critical crystal size above which fractional 117 crystallization starts is shown as: 118 , 119 where fφ is a hindered settling function, g is the gravity, cp is the isobaric specific heat, 120 ∆ρ is the difference of density between crystal and melt, φ is the volume fraction of 121 crystals in the magma, α is the coefficient of thermal expansion of melt, ηl is the 122 viscosity of melt, and F is the surface heat flux The calculation results of Solomatov 123 and Stevenson (1993) are consistent with the experimental results of Martin and Nokes 124 (1989), though the crystal radius and the density difference between the particles and 125 the fluid were not fully constrained in their experiment 2.2 Hindered settling function M AN U SC (1) 126 127 RI PT 112 The hindered settling function represents the phenomenon that settling is hindered by 129 the presence of solid particles and the return flow of the interstitial fluid (Davis and 130 Acrivos, 1985; Huppert et al., 1991) For our calculations, we adopted the most 131 commonly used formula by Garside and Al-Dibouni (1977) and Richardson and Zaki 132 (1954): 133 f(φ) = (1 – φ)5.1 EP TE D 128 (2) It should be noted that it is difficult to simply apply the formula to the magma because 135 the correction also depends on the nature of interparticle forces (Davis and Acrivos, 136 1985) 137 138 AC C 134 2.3 Viscosity and density calculation 139 In order to constrain the viscosity and the density of the melt while the plagioclase 140 crystallizes from the LMO, its melt composition, temperature, and pressure must be 141 known This study used thermodynamic equilibrium software, pMELTS for P > 1GPa 142 (Ghiorso et al., 2002) and rhyolite-MELTS for P < GPa (Gualda et al., 2012) To 143 calculate compositional change of the melt through the solidification of the magma 144 ocean by using MELTS program, the crystallization model needs to be assumed ACCEPTED MANUSCRIPT 145 146 2.3.1 Solidification model of the LMO for MELTS/pMELTS 147 2.3.1.1 Bulk composition of the initial LMO 149 To calculate the compositional change of the melt, we assumed a bulk composition of the initial LMO to be the bulk silicate Earth (BSE; McDonough and Sun, 1995) RI PT 148 There has been no agreement about the lunar bulk composition (Taylor, 1982; Jones 151 and Delano, 1989; O'Neill, 1991; Snyder et al., 1992; Lognonné et al., 2003; Warren, 152 2005; Longhi, 2006 ) In order to constrain the necessary conditions that result in the 153 separation of the plagioclase from the LMO, the initial bulk composition must be the 154 one with the lowest estimated density Although most previous works concluded that the 155 composition of the initial LMO is enriched in FeO rather than BSE (Taylor, 1982; Jones 156 and Delano, 1989; O'Neill, 1991; Snyder et al., 1992; Lognonné et al., 2003), Mg# 157 =0.93 of olivine in the Mg-suite requires Mg#=0.89 for the lunar bulk composition to 158 generate such a high Mg# of olivine (Warren, 2005; Longhi, 2006) This suggests that 159 BSE (Mg#=0.89) can be considered as one of the possible lowest-density compositions 160 of the initial LMO This is also supported by recent giant-impact modeling on the 161 terrestrial magma ocean, indicating that more materials from the terrestrial magma 162 ocean with high Mg# contribute to the Moon compared to the impactor (Karato, 2014) 164 M AN U TE D 163 SC 150 2.3.1.2 Depth of the LMO In our calculations, we assumed that the initial depth of the LMO is 1000 km The 166 initial depth of the LMO is likely dependent on the available heat source The heat 167 sources of the LMO are the kinetic energy of the giant impact, gravitational settling 168 energy, and the distribution of radiogenic heating Another important and yet poorly 169 quantified energy source is tidal heating The proximity of the Moon to Earth was much 170 closer during its formation Harada et al (2014) suggested that strong tidal heating 171 caused an ultralow-viscosity zone 200–400 km from the center of the Moon, which 172 might be evidence that the Moon was probably molten at depths reaching 1000 km 173 when tidal heating was greatest The depth range of the deep moonquakes, estimated to 174 be 750–1400 km (Zhao et al., 2012), is generally thought to correspond to the boundary 175 between the base of the initial LMO and the primitive lower mantle The average depth 176 where deep moonquakes occur thus suggests that the LMO would also be molten at 177 depths reaching 1000 km AC C EP 165 ACCEPTED MANUSCRIPT As discussed in Sakai et al (2014), the depth range from 800 to 1738 km has 179 negligible effect on the compositional evolution of the LMO because the liquidus phase 180 at the pressure range is always olivine, and the volume of LMO at depths greater than 181 1000 km corresponds to only vol.% of the total volume of the Moon 182 RI PT 178 2.3.1.3 Oxygen fugacity of the LMO 184 The oxygen fugacity was fixed at the iron-wustite buffer In the case of mare basalt, fO2 185 is estimated to range from 10–13 to 10–16 based on intrinsic measurements and 186 thermodynamic gas equilibria calculations (Shearer and Papike, 2004; Wadhwa, 2008) 187 188 2.3.1.4 Calculation methods of MELTS/pMELTS SC 183 Using MELTS/pMELTS, the magma ocean fractionally crystallizes in steps with each 190 representing 1/10th of the total magma ocean volume Mafic minerals such as olivine 191 and pyroxene crystallized from ultramafic melt are assumed to separate from the melt M AN U 189 For every step, input pressure of the equilibrium calculation is set to be the middle 193 depth of the LMO (Fig 1a) Crystallization likely takes place at all depths of the LMO 194 because its adiabat lies between the solidus and the liquidus (Tonks and Melosh, 1990) 195 Because of the relatively small size of the Moon, the highest pressure at the core of the 196 Moon is only GPa However, the pressure condition where crystallization takes place 197 does not have large effects on the composition of the residual melt First, the liquidus 198 phase is always olivine though the stability field of pyroxene increases with pressure 199 Second the Mg–Fe partition coefficient between mafic minerals (olivine and pyroxene) 200 and melt not change for the pressure range of 0–5 GPa (Herzberg and Zhang, 1996) 202 203 204 EP The calculations can track SiO2, Al2O3, FeO, MgO, and CaO in the evolved melt, as AC C 201 TE D 192 well as temperature and pressure changing through the solidification of the LMO 2.3.2 Viscosity and density 205 Viscosity and density of the magma ocean can be constrained as long as melt 206 composition, temperature, and pressure are known Viscosity dependence on 207 composition and temperature of melt was modeled by Bottinga and Weill (1972), while 208 the viscosity dependence on composition, temperature, and pressure modeled by Lange 209 and Carmichael (1987) Sakamaki et al (2013) were the first to constrain the viscosity 210 of basaltic melt under room pressure and extrapolate it to high pressure conditions ACCEPTED MANUSCRIPT 211 212 2.4 Heat flux Convective heat flux of the magma ocean is an important factor for determining the 214 critical crystal size, df For a magma ocean in which case the Rayleigh number is 215 extremely high, convection is likely to be in a high-turbulence regime, rather than a 216 low-turbulence regime where the heat flux is proportional to Ra2/7 (Solomatov, 2015) 217 Based on Eq (2) from Solomatov (2015) and the Eqs (2.17a) from Siggia (1994), the 218 heat flux of the magma ocean is shown as: SC M AN U 219 220 RI PT 213 where 221 , (3) (4) is the Rayleigh number, Tm is the potential temperature, Ts is the surface temperature, L 223 is the depth of magma ocean, k is the coefficient of thermal conductivity, ߢ = k/ρcp is the 224 coefficient of thermal diffusivity, ߥ = η/ρ is the kinematic viscosity, η is the viscosity of 225 magma (Kraichnan, 1962; Siggia, 1994), and ρ is the density of magma Pr = ߥ/ߢ is the 226 Prandtl number, and λ is the aspect ratio for the mean flow We consider this to be a 227 rough estimate, and a more realistic scaling law for the heat flux of the magma ocean 228 should be established AC C EP TE D 222 229 230 2.4.1 Viscosity of magma 231 Viscosity of magma is one of the critical parameters determining the dynamics of the 232 magma ocean The important factor controlling the viscosity of magma is the volume 233 fraction of crystals in the magma, φ Magma becomes a Newtonian flow at a relatively 234 low crystal fraction, and one of the most popular equations of the viscosity of magma is 235 the Einstein-Roscoe relationship (Roscoe, 1952): 236 237 , (5) where φm is the maximum packing fraction of crystals When crystals are ideal spheres, ACCEPTED MANUSCRIPT 403 plagioclase in the magma will become ca 35–40 vol.% While plagioclase floats to the 404 surface of the LMO, the interstitial melt migrates downward due to the compaction, 405 resulting in the formation of pure anorthosite (Piskorz and Stevenson, 2014) Sakai et al (2014) suggested that dpl becomes ca cm when the initial composition of 407 the LMO is assumed to be BSE composition They also concluded that the initial 408 composition of the LMO is required to be enriched in FeO to produce a density 409 difference between plagioclase and melt large enough to make dpl small The results of 410 Sakai et al (2014) ultimately show that plagioclase could separate from the melt even 411 when the initial composition of the LMO is BSE composition SC RI PT 406 If the lunar bulk composition is more enriched in FeO or the basaltic melt actually 413 becomes enriched in FeO through the complex solidification of the LMO, plagioclase 414 could probably separate from the melt even when it starts to crystallize M AN U 412 415 416 4.2 Implications for the formation of the anorthosite on the Hadean Earth Understanding the surface environment of the Hadean Earth is important to reveal the 418 possible site for the emergence of life For efficient biogenic synthesis, land above the 419 sea level and nutrient-rich rocks might have been required to condense nutrients 420 (Maruyama et al., 2013) It is difficult, however, to generate granites in the Hadean, 421 because its formation requires plate tectonics supplying the water to the mantle through 422 subduction of hydrated oceanic crust Possible candidates for the land and nutrient-rich 423 rocks are the lunar highland crust of anorthosite and KREEP formed as a result of the 424 differentiation of the LMO EP TE D 417 Previous work suggests that the primitive Earth also might have melted wholly or 426 partially caused by kinetic energy of a giant impact, gravitational settling energy, and 427 radio-decay heating (Wood et al., 1970) At the late stages of terrestrial planetary 428 accretion, Mars-size impactors would have accreted to the growing Earth, which have 429 sufficient energy to substantially melt the Earth (Melosh, 1990) AC C 425 430 Although the discussion of the LMO cannot simply be applied to that of the terrestrial 431 magma ocean because minerals crystallizing from the magma and composition of melt 432 are different due to the different size between the Earth and the Moon, this study 433 assumes that the melt composition is generally the same with that calculated for the 434 Moon with BSE composition Previous works suggested that majorite crystallizes in the 435 cooling terrestrial magma ocean, which depletes Al of the residual magma ocean and ACCEPTED MANUSCRIPT hinders crystallization of plagioclase at a shallow depth of the ocean (Warren and 437 Wasson, 1979b; Anderson, 1981; Taylor, 1982) The residual melt would actually be 438 depleted in Al2O3 by crystallization of majorite, but only as much as about wt.% The 439 composition of melt generally follows the eutectic point by crystallizing olivine, 440 clinopyroxene, or garnet, and finally becomes basaltic in composition RI PT 436 When the melt composition is assumed to be the same as that calculated for the Moon 442 with BSE composition, dpl for the terrestrial magma ocean is calculated to be ca 1.1 cm 443 where g =9.8 kg/s2 and L =160 km (640 km×(1–0.75)) The results show that dpl for the 444 terrestrial magma ocean becomes about half of that for the LMO, because the large 445 gravity for the terrestrial magma ocean makes dpl small Plagioclase could separate from 446 the terrestrial magma ocean SC 441 Plagioclase crystallizes at relatively low pressures less than about GPa While GPa 448 corresponds to a depth of 200 km for the Moon due to its relatively small size, it 449 corresponds to a depth only reaching 30 km on the larger-gravity Earth Warren (1985), 450 therefore, suggested that thick anorthosite is unlikely to have formed in the terrestrial 451 magma ocean for this reason However, it is still premature to conclude that the 452 formation of anorthosite was hindered For Mars, iron-bearing, plagioclase-rich rocks 453 were detected at eight sites in the southern highlands based on near-infrared spectral 454 data of the Mars Reconnaissance Orbiter (Carter and Poulet, 2013) In spite of the 455 paucity of detections, the findings suggest that anorthosite formed globally from the 456 highly evolved magma produced by differentiation of the Martian magma ocean GPa 457 corresponds to a depth of only 80 km in Mars, which supports that anorthosite could 458 have formed during the early Earth EP TE D M AN U 447 The major difference between the Earth and Moon and their influence on the formation 460 of anorthosite is the presence water If the basaltic magma is saturated with water, 461 enstatite and amphibolite rather than quartz and plagioclase crystallize at the eutectic 462 point (Kushiro, 1990) This suggests that anorthosite could not form on the Earth if the 463 terrestrial magma ocean was saturated with the water AC C 459 464 Although the origin of the water on the Earth is still debated, one of the scenarios is 465 the “late-veneer” hypothesis in which the Earth and the Moon were dry just after the 466 formation of the Moon, and late-accretion of volatile-rich carbonaceous chondrites 467 beyond the asteroid belt supplied water to the “dry” Earth (Albarede, 2009) In this case, 468 it is possible that plagioclase crystallized from the “dry” terrestrial magma ocean and ACCEPTED MANUSCRIPT 469 anorthosite formed on the Hadean Earth Geological records of anorthosite crusts of the Hadean have been erased by tectonic 471 erosion on the Earth (Kawai et al., 2009; Yamamoto et al., 2009), or reprocessed by 472 impacts (Marchi et al., 2014) Once the anorthosite is subducted to a depth of 30 km, the 473 plagioclase changes to garnet due to the phase transition, and the density of the 474 garnet-composing “meta-anorthosite” becomes higher than the pyrolite (Kawai et al., 475 2009) The result suggests that the meta-anorthosite could easily be transported into the 476 mantle due to the density difference Future works should be focusing on the detection 477 of the geophysical evidences of meta-anorthosite buried in the deep interior of the 478 Earth SC RI PT 470 480 Acknowledgement M AN U 479 We appreciate the discussions and comments from Y Ueno, I Kushiro, which helped 482 improve our paper, and Dr James M Dohm for the improvement of the English This 483 work was partly supported by a grant from the Ministry of Education, Culture, Sports, 484 Science and Technology of Japan, Grant-in-Aid for Scientific Research on Innovative 485 Areas Grant Number 26106002 486 487 Figure Captions 488 Figure TE D 481 Summary of the results calculated by the MELTS/pMELTS (a) Inputted value of 490 pressure for the calculation (b) Modal abundance of minerals crystallizing from the 491 LMO (c) Compositional change of melt through the solidification of the LMO (d) Mg# 492 of melt, olivine and orthopyroxene AC C 493 EP 489 494 Figure 495 (a) Density of melt calculated for Mg#=0.59, 1291oC when plagioclase starts to 496 crystallize and Mg#=0.46, 1218oC when calculation ends Also shown is density of 497 anorthite The solid line denotes the density for the pressure-pressure of the LMO (b) 498 Viscosity of melt 499 500 Figure 501 Magma viscosity (a), surface temperature (b), Rayleigh number (c), and surface heat ACCEPTED MANUSCRIPT flux (d) on crystal fraction of the magma This study calculates Ts, Ra, and F by 503 substituting the physical parameters as constant value at a certain pressure (a) magma 504 viscosity, η, can be deduced from the equation (5) and the viscosity of melt in Fig 2b 505 Since φm is set to be 0.6, viscosity of magma becomes infinite at φ =0.6 (b) The surface 506 temperature of the LMO, Ts, could be calculated from the equation (3) and (6) (c) 507 Rayleigh number, Ra, was deduced from the equation (4) (d) Heat flux, F, was deduced 508 from the equation (3) RI PT 502 509 Figure 511 (a) Critical crystal size of plagioclase, dpl, on the pressure for φ =0.01–0.59 when 512 plagioclase starts to crystallize, melt Mg#=0.59, 1291oC The dpl becomes infinite at 2.1 513 kbar because of the density inversion between the melt and plagioclase (Fig 2a) Also 514 shown is the typical size range of plagioclase in the lunar anorthosite, 1.8–3 cm (James, 515 1972; Wilshire et al., 1972) (b) dpl when calculation ends, melt Mg#=0.46, 1218 oC M AN U SC 510 516 Figure 518 (a) Critical crystal size of olivine, dol, on the pressure for φ =0.01–0.59 when 519 plagioclase starts to crystallize, melt Mg#=0.59, 1291oC Also shown is the typical size 520 rage of olivine in the lunar dinite, 1–3 mm (Dymek et al., 1975) (b) dol, when 521 calculation ends, melt Mg#=0.46, 1218oC TE D 517 EP 522 523 References 524 Abe, Y., 1993 Thermal Evolution and Chemical Differentiation of the Terrestrial 526 527 528 529 530 531 532 533 534 Magma Ocean, Evolution of the Earth and Planets American Geophysical Union, AC C 525 pp 41-54 Albarede, F., 2009 Volatile accretion history of the terrestrial planets and dynamic implications Nature 461, 1227-1233 Anderson, D., L., 1981 Hotspots, Basalts, and the Evolution of the Mantle Science 213 Bottinga, Y., Weill, D.F., 1972 The viscosity of magmatic silicate liquids; a model calculation American Journal of Science 272, 438-475 Carter, J., Poulet, F., 2013 Ancient plutonic processes on Mars inferred from the detection of possible anorthositic terrains Nature Geoscience 6, 1008-1012 ACCEPTED MANUSCRIPT 535 536 537 Davis, R.H., Acrivos, A., 1985 Sedimentation of noncolloidal particles at low Reynolds numbers Annual Review of Fluid Mechanics 17, 91-118 Dymek, R., Albee, A., Chodos, A., 1975 Comparative petrology of lunar cumulate rocks of possible primary origin-Dunite 72415, troctolite 76535, norite 78235, and 539 anorthosite 62237, Lunar and Planetary Science Conference Proceedings, pp 540 301-341 RI PT 538 Garside, J., Al-Dibouni, M.R., 1977 Velocity-voidage relationships for fluidization and 542 sedimentation in solid-liquid systems Industrial & engineering chemistry process 543 design and development 16, 206-214 544 SC 541 Ghiorso, M.S., Hirschmann, M.M., Reiners, P.W., Kress, V.C., 2002 The pMELTS: A revision of MELTS for improved calculation of phase relations and major element 546 partitioning related to partial melting of the mantle to GPa Geochemistry, 547 Geophysics, Geosystems 3, 1-35 M AN U 545 548 Gualda, G.A.R., Ghiorso, M.S., Lemons, R.V., Carley, T.L., 2012 Rhyolite-MELTS: a 549 Modified Calibration of MELTS Optimized for Silica-rich, Fluid-bearing 550 Magmatic Systems Journal of Petrology 53, 875-890 551 Harada, Y., Goossens, S., Matsumoto, K., Yan, J., Ping, J., Noda, H., Haruyama, J., 2014 Strong tidal heating in an ultralow-viscosity zone at the core-mantle 553 boundary of the Moon Nature Geoscience 7, 569-572 555 556 Hartmann, W.K., Davis, D.R., 1975 Satellite-sized planetesimals and lunar origin Icarus 24, 504-515 EP 554 TE D 552 Herzberg, C., Zhang, J., 1996 Melting experiments on anhydrous peridotite KLB-1: Compositions of magmas in the upper mantle and transition zone Journal of 558 Geophysical Research: Solid Earth 101, 8271-8295 AC C 557 559 Huppert, H., Sparks, R.S., 1981 The fluid dynamics of a basaltic magma chamber 560 replenished by influx of hot, dense ultrabasic magma Contributions to 561 562 Mineralogy and Petrology 75, 279-289 Huppert, H.E., Kerr, R.C., Lister, J.R., Turner, J.S., 1991 Convection and particle 563 entrainment driven by differential sedimentation Journal of Fluid Mechanics 226, 564 349-369 565 566 Ida, S., Canup, R.M., Stewart, G.R., 1997 Lunar accretion from an impact-generated disk Nature 389, 353-357 ACCEPTED MANUSCRIPT 567 Ishibashi, H., Sato, H., 2007 Viscosity measurements of subliquidus magmas: Alkali 568 olivine basalt from the Higashi-Matsuura district, Southwest Japan Journal of 569 Volcanology and Geothermal Research 160, 223-238 572 573 574 575 576 History Science 175, 432-436 RI PT 571 James, O.B., 1972 Lunar Anorthosite 15415: Texture, Mineralogy, and Metamorphic Jones, J.H., Delano, J.W., 1989 A three-component model for the bulk composition of the Moon Geochimica et Cosmochimica Acta 53, 513-527 Karato, S.-i., 2014 Asymmetric shock heating and the terrestrial magma ocean origin of the Moon Proceedings of the Japan Academy, Series B 90, 97-103 SC 570 Kato, M., Sasaki, S., Tanaka, K., Iijima, Y., Takizawa, Y., 2008 The Japanese lunar mission SELENE: Science goals and present status Advances in Space Research 578 42, 294-300 580 581 582 583 584 585 Kawai, K., Tsuchiya, T., Tsuchiya, J., Maruyama, S., 2009 Lost primordial continents Gondwana Research 16, 581-586 Kraichnan, R.H., 1962 Turbulent Thermal Convection at Arbitrary Prandtl Number Physics of Fluids (1958-1988) 5, 1374-1389 Kushiro, I., 1990 Partial melting of mantle wedge and evolution of island arc crust Journal of Geophysical Research 95, 15929 TE D 579 M AN U 577 Lange, R.A., Carmichael, I.S.E., 1987 Densities of Na2O-K2O-MgO-MgO-FeO-Fe2O3-Al3O3-TiO2-SiO2 liquids: New 587 measurements and derived partial molar properties Geochimica et Cosmochimica 588 Acta 51, 2931-2946 590 591 592 593 594 Lejeune, A.-M., Richet, P., 1995 Rheology of crystal-bearing silicate melts: An experimental study at high viscosities Journal of Geophysical Research: Solid AC C 589 EP 586 Earth 100, 4215-4229 Lognonné, P., Gagnepain-Beyneix, J., Chenet, H., 2003 A new seismic model of the Moon: implications for structure, thermal evolution and formation of the Moon Earth and Planetary Science Letters 211, 27-44 595 Longhi, J., 2006 Petrogenesis of picritic mare magmas: Constraints on the extent of 596 early lunar differentiation Geochimica et Cosmochimica Acta 70, 5919-5934 597 Marchi, S., Bottke, W.F., Elkins-Tanton, L.T., Bierhaus, M., Wuennemann, K., 598 Morbidelli, A., Kring, D.A., 2014 Widespread mixing and burial of Earth's 599 Hadean crust by asteroid impacts Nature 511, 578-582 ACCEPTED MANUSCRIPT 601 602 603 604 Martin, D., Nokes, R., 1988 Crystal settling in a vigorously converting magma chamber Nature 332, 534-536 Martin, D., Nokes, R., 1989 A Fluid-Dynamical Study of Crystal Settling in Convecting Magmas Journal of Petrology 30, 1471-1500 Maruyama, S., Ikoma, M., Genda, H., Hirose, K., Yokoyama, T., Santosh, M., 2013 RI PT 600 605 The naked planet Earth: Most essential pre-requisite for the origin and evolution 606 of life Geoscience Frontiers 4, 141-165 609 610 611 612 613 614 615 complex: Part I Stratigraphy and structure of the banded zone SC 608 Mccallum, I.S., Raedeke, L.D., Mathez, E.A., 1980 Investigations of the stillwater McDonough, W.F., Sun, S.S., 1995 The composition of the Earth Chemical Geology 120, 223-253 Melosh, H.J., 1990 Giant impacts and the thermal state of the early Earth Origin of the M AN U 607 Earth and Moon Myers, J.S., Platt, R.G., 1977 Mineral chemistry of layered Archaean anorthosite at Majorqap qâva, near Fiskenæsset, southwest Greenland Lithos 10, 59-72 O'Neill, H.S.C., 1991 The origin of the Moon and the early history of the Earth—A chemical model Part 2: The Earth Geochimica et Cosmochimica Acta 55, 617 1159-1172 TE D 616 Ohtake, M., Matsunaga, T., Haruyama, J., Yokota, Y., Morota, T., Honda, C., Ogawa, Y., 619 Torii, M., Miyamoto, H., Arai, T., Hirata, N., Iwasaki, A., Nakamura, R., Hiroi, T., 620 Sugihara, T., Takeda, H., Otake, H., Pieters, C.M., Saiki, K., Kitazato, K., Abe, M., 621 Asada, N., Demura, H., Yamaguchi, Y., Sasaki, S., Kodama, S., Terazono, J., 622 Shirao, M., Yamaji, A., Minami, S., Akiyama, H., Josset, J.L., 2009 The global 623 distribution of pure anorthosite on the Moon Nature 461, 236-240 625 626 627 628 629 630 631 632 AC C 624 EP 618 Philpotts, A.R., Brustman, C.M., Shi, J., Carlson, W.D., Denison, C., 1999 Plagioclase-chain networks in slowly cooled basaltic magma American Mineralogist 84, 1819-1829 Philpotts, A.R., Shi, J., Brustman, C., 1998 Role of plagioclase crystal chains in the differentiation of partly crystallized basaltic magma Nature 395, 343-346 Piskorz, D., Stevenson, D.J., 2014 The formation of pure anorthosite on the Moon Icarus 239, 238-243 Pritchard, M.E., Stevenson, D.J., 2000 Thermal Aspects of a Lunar Origin by Giant Impact Origin of the Earth and Moon ACCEPTED MANUSCRIPT 634 635 636 637 Richardson, J.F., Zaki, W.N., 1954 The sedimentation of a suspension of uniform spheres under conditions of viscous flow Chemical Engineering Science 3, 65-73 Roscoe, R., 1952 The viscosity of suspensions of rigid spheres British Journal of Applied Physics 3, 267 Sakai, R., Nagahara, H., Ozawa, K., Tachibana, S., 2014 Composition of the lunar RI PT 633 638 magma ocean constrained by the conditions for the crust formation Icarus 229, 639 45-56 640 Sakamaki, T., Suzuki, A., Ohtani, E., Terasaki, H., Urakawa, S., Katayama, Y., Funakoshi, K.-i., Wang, Y., Hernlund, J.W., Ballmer, M.D., 2013 Ponded melt at 642 the boundary between the lithosphere and asthenosphere Nature Geoscience 6, 643 1041-1044 Sato, H., 2005 Viscosity measurement of subliquidus magmas:1707 basalt of Fuji M AN U 644 SC 641 645 volcano Journal of Mineralogical and Petrological Sciences 100, 133-142 646 Shearer, C.K., Papike, J.J., 2004 Oxygen fugacity of lunar basalts and the lunar mantle 647 Range of fO2 and the effectiveness of oxybarometers Oxygen in the Terrestrial 648 Planets 650 651 Siggia, E.D., 1994 High Rayleigh Number Convection Annual Review of Fluid Mechanics 26, 137-168 TE D 649 Snyder, G.A., Taylor, L.A., Neal, C.R., 1992 A chemical model for generating the sources of mare basalts: Combined equilibrium and fractional crystallization of 653 the lunar magmasphere Geochimica et Cosmochimica Acta 56, 3809-3823 EP 652 Solomatov, V.S., 2015 The terrestrial magma ocean hypothesis Gondwana Research 655 Solomatov, V.S., Stevenson, D.J., 1993 Suspension in convective layers and style of 656 differentiation of a terrestrial magma ocean Journal of Geophysical Research: 657 658 659 660 661 662 663 664 665 AC C 654 Planets 98, 5375-5390 Taylor, S.R., 1982 Lunar and terrestrial crusts: a constrast in origin and evolution Physics of the Earth and Planetary Interiors 29, 233-241 Tonks, W., Melosh, H., 1990 The physics of crystal settling and suspension in a turbulent magma ocean Origin of the Earth 1, 151-174 Tonks, W.B., Melosh, H.J., 1993 Magma ocean formation due to giant impacts Journal of Geophysical Research: Planets 98, 5319-5333 Wadhwa, M., 2008 Redox Conditions on Small Bodies, the Moon and Mars Reviews in Mineralogy and Geochemistry 68, 493-510 ACCEPTED MANUSCRIPT 666 667 668 Warren, P.H., 1985 The Magma Ocean Concept and Lunar Evolution Reviews in Mineralogy and Geochemistry 13 Warren, P.H., 1990 Lunar anorthosites and magma-ocean plagioclase-flotation hypothesis: Importance of FeO enrichment in the parent magma American 670 Mineralogist 75, 46 671 RI PT 669 Warren, P.H., 2005 “New” lunar meteorites: Implications for composition of the global 672 lunar surface, lunar crust, and the bulk Moon Meteoritics & Planetary Science 40, 673 477-506 675 676 Warren, P.H., Wasson, J.T., 1979a The compositional-petrographic search for pristine SC 674 nonmare rocks: Third foray Warren, P.H., Wasson, J.T., 1979b Effects of pressure on the crystallization of a "chondritic" magma ocean and implications for the bulk composition of the 678 Moon 679 M AN U 677 Wilshire, H.G., Schaber, G.G., Silver, L.T., Phinney, W.C., Jackson, E.D., 1972 680 Geologic Setting and Petrology of Apollo 15 Anorthosite (15415) Geological 681 Society of America Bulletin 83, 1083-1092 683 684 Wood, J.A., Dickey, J.S., Marvin, U.B., Powell, B.N., 1970 Lunar Anorthosites Science 167, 602-604 TE D 682 Yamamoto, S., Nakamura, R., Matsunaga, T., Ogawa, Y., Ishihara, Y., Morota, T., Hirata, N., Ohtake, M., Hiroi, T., Yokota, Y., Haruyama, J., 2012 Massive layer of pure 686 anorthosite on the Moon Geophysical Research Letters 39, n/a-n/a 687 EP 685 Yamamoto, S., Senshu, H., Rino, S., Omori, S., Maruyama, S., 2009 Granite subduction: Arc subduction, tectonic erosion and sediment subduction Gondwana 689 Research 15, 443-453 690 691 692 AC C 688 Zhao, D., Arai, T., Liu, L., Ohtani, E., 2012 Seismic tomography and geochemical evidence for lunar mantle heterogeneity: Comparing with Earth Global and Planetary Change 90-91, 29-36 AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT AC C EP TE D M AN U SC RI PT ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT Research Highlights The lunar anorthosite formed as a result of plagioclase-floatation of the magma ocean A sufficient condition that formed the thick anorthosite was constrained RI PT Plagioclase will be entrained just after plagioclase starts to crystallize Plaigoclase will separate from the magma when the melt becomes enriched in FeO If the terrestrial magma ocean was saturated with H2O, anorthosite could not AC C EP TE D M AN U SC form ... Viscosity of magma is one of the critical parameters determining the dynamics of the 232 magma ocean The important factor controlling the viscosity of magma is the volume 233 fraction of crystals in the. .. nonmare rocks: Third foray Warren, P.H., Wasson, J.T., 1979b Effects of pressure on the crystallization of a "chondritic" magma ocean and implications for the bulk composition of the 678 Moon. .. between the solidus and the liquidus (Tonks and Melosh, 1990) 195 Because of the relatively small size of the Moon, the highest pressure at the core of the 196 Moon is only GPa However, the pressure