The Origin of the Moon

京大での大学院講義「惑星物理学」で用いたスライドです。

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1. 2017೥6݄15೔ɹ࿭੕෺ཧֶ 2017೥౓ߨٛ The Origin of the Moon େֶӃཧֶݚڀՊ Ӊ஦෺ཧֶڭࣨɹࠤʑ໦وڭ
2. ݄ͷىݯͷݚڀ࢙ • ᴈ໌ظʢلݩલʙ1960೥୅ʣ • ։Խظʢ1970೥୅ʙ1980೥୅ʣ • ԁख़ظʢ1990೥୅ʙ2000೥୅લظʣ • ࠞཚظʢ2000೥୅ޙظʣ • ֵ໋ظʢ2010೥୅ʣ • ࠞ໎ΛۃΊΔݱ୅
3. ᴈ໌ظ
4. • ݹࣄه
 ΠβφΪϊϛίτ͕ӈ໨Λચ͍݄ಡ໋͕஀ੜʢࠨ໨͕ఱরେਆʣ • چ໿੟ॻ
 ૑଄ओ͕4೔໨ʹఱͷଠཅͱ݄ͱ੕Λ஀ੜͤͨ͞ • Τδϓτ
 ૑଄ओϥʔͷࠨ໨͕݄ͱͳͬͨʢӈ໨͕ଠཅʣ • தࠃ
 ૑଄ਆ൫ݹͷӈ໨͕݄ͱͳͬͨʢࠨ໨͕ଠཅʣ ਆ࿩ʹ͓͚Δ݄ͷىݯ
5. XIII. On the Precession of a Viscous Spheroid, and on the remote History of the Earth. By G. H. Darwin, M.A., Fellow of Trinity College, Cambridge. Communicated by J. W. L. Glaisher, M.A., FM.S. Received July 22, —Read December 19, 1878, Plate 36. The following paper contains the investigation of the mass-motion of viscous and imperfectly elastic spheroids, as modified by a relative motion of their parts, produced in them by the attraction of external disturbing bodies ; it must be regarded as the continuation of my previous paper/" where the theory of the bodily tides of such spheroids was given. The problem is one of theoretical dynamics, but the subject is so large and complex, that I thought it best, in the first instance, to guide the direction of the speculation by considerations of applicability to the case of the earth, as disturbed by the sun and moon. In order to avoid an incessant use of the conditional mood, I speak simply of the earth, sun, and moon ; the first being taken as the type of the rotating body, and the two latter as types of the disturbing or tide-raising bodies. This course will be justi- “Fission Theory” ʹΑΔ݄ܗ੒γφϦΦ
6. ݄ͷىݯઆ ั֫આ ෼྾આ ૒ࢠઆ ݪ࢝஍ٿ͕ߴ଎ճసʹΑΓ;͘ΒΈ
   ͦͷҰ෦͕ͪ͗Ε݄͕ͯ஀ੜ ஍ٿيಓ෇ۙͰͷඍ࿭੕ͷूੵʹΑΓ
   ஍ٿͱ͸ಠཱʹ݄͕ܗ੒ ஍ٿͱ͸ผͷ৔ॴͰ࡞ΒΕ݄͕ͨ
   ஍ٿͷۙ͘Λ௨ͬͨͱ͖ʹัΒ͑ΒΕͨ
7. ։Խظ
8. Lunar Rock by Apollo 11
9. Constraints of Moon Formation (1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001] suming that similar proportions of material me from the silicate portions of the proto- rth and Theia. Only if the proto-Earth and eia ⌬17O values were identical to within 03‰ would it be possible that the average 7O value of the Moon plots within 0.005‰ the terrestrial fractionation line. Some computer models assume a larger e for the impactor, i.e., a mass ratio of 7:3 tween the proto-Earth and Theia (2, 13). l these models assume that the Earth had ly achieved about two-thirds of its final ass after the Giant Impact, because a larger oto-Earth would produce greater angular omentum for the Earth-Moon system than at observed. Models assuming that the oto-Earth had reached just 66% of its mass er the Giant Impact (2, 3) and identical 7O of the Moon and Earth require that late coming material came from the same res- voir as the material that made up Theia and system or that oxygen isotope alteration continued on icy planetesimals (18). How- ever, computer simulations of the colli- sional growth stage of the inner solar sys- tem (19) demonstrate that terrestrial planets were fed from a zone with a heliocentric distance of 0.5 to 2.5 astronomical units and beyond. Regardless of how heteroge- neous the early inner solar system was at the beginning, it developed toward a homo- geneous composition by collisional growth. This is endorsed by the small ⌬17O differ- ences of about 0.6‰ observed for the Earth-Moon system, Mars, and Vesta com- pared with more than 10‰ differences among chondrites. Collisional growth will smooth out pre-existing heterogeneities but is unlikely to result in identical oxygen isotopic compositions for all planets be- cause a correlation between final heliocen- tric distance and average provenance of a planet is predicted (19). The differences in ⌬17O among large planetary embryos and g. 1. Comparison between conventional and w laser 16O, 17O, and 18O measurements of nar samples. ⌬17O gives displacement from Fig. 3. The ⌬17O values for lunar samples plot within standard deviation (2␴ i ) error of Ϯ 0.016‰ (long-dashed lines) on the TFL. If the impactor had formed from the same raw ma- terial as Mars or the HED parent body, then all lunar samples must have obtained, within 2%, the same portion from the impactor and proto- Earth as obtained by Earth using the triple standard error of the mean (3␴ mean ) as signif- icant, shown by short-dashed lines. On average, the H-chondrites plot 0.7‰ above the TFL, allowing a maximum of 3% chondritic material mixed into any of the studied lunar samples, 2␴ confidence level. Other chondrite groups like L, LL, or carbonaceous chondrites show an even larger deviation from the TFL and, there- [Wiechert et al., Science, 2001]
10. ݄ͷىݯઆ ั֫આ ෼྾આ ૒ࢠઆ ݪ࢝஍ٿ͕ߴ଎ճసʹΑΓ;͘ΒΈ
    ͦͷҰ෦͕ͪ͗Ε݄͕ͯ஀ੜ ஍ٿيಓ෇ۙͰͷඍ࿭੕ͷूੵʹΑΓ
    ஍ٿͱ͸ಠཱʹ݄͕ܗ੒ ஍ٿͱ͸ผͷ৔ॴͰ࡞ΒΕ݄͕ͨ
    ஍ٿͷۙ͘Λ௨ͬͨͱ͖ʹัΒ͑ΒΕͨ ߴ଎ճస͕೉͍͠
    
    ֯ӡಈྔ͕େ͖͗͢Δ ݄ͷ಺෦ߏ଄͕આ໌Ͱ͖ͳ͍
    
    ݄Λ࢒ͤͳ͍ ั֫֬཰͕௿͍
    
    Խֶత੍໿Λຬͨͤͳ͍
11. [Schreiber & Anderson, Science, 1970] ݄͸νʔζͰͰ͖͍ͯΔʁ
12. δϟΠΞϯτΠϯύΫτઆ [Hartman & Davis, Icarus, 1975] [Cameron & Ward, LPI Conference, 1976]
13. 520 BENZ, SLATTERY, AND CAMERON T: 7.76217 [ -2.0. 2.0. -2.0. 2.01 T: 8.83375 ( -2.0. 2.0. -2,0. 2.0] ,,:iii:i~iiiiii!iii!i,li!~iliiiiiii~!!!iiii:~iii~:i ,: T: 9,q0986 ( -2.0. 2.0. 2.0, 2.01 T: 11.03161 I -~.0. ~,.0, -q,0. ~.0] /,,l--¢/ t~ FIG. 2. Snapshots of run 1. (u~ = 0 km/sec; rmi, = 0.77Rearth; Eint = 107 erg/g). Velocity vectors are plotted at particle locations. The velocity has been normalized to its maximum value in each frame. Time and coordinates of the four corners of the plotted field are given in the upper line (in units defined in Section 3). For particles in the vapor phase a "O" is plotted. before the time at which the particles spread out in space. Since this happens af- ter the time of closest approach, the trajec- and this completes the description of the equation of motion. 520 BENZ, SLATTERY, AND CAMERON T: 7.76217 [ -2.0. 2.0. -2.0. 2.01 T: 8.83375 ( -2.0. 2.0. -2,0. 2.0] ,,:iii:i~iiiiii!iii!i,li!~iliiiiiii~!!!iiii:~iii~:i ,: T: 9,q0986 ( -2.0. 2.0. 2.0, 2.01 T: 11.03161 I -~.0. ~,.0, -q,0. ~.0] /,,l--¢/ t~ FIG. 2. Snapshots of run 1. (u~ = 0 km/sec; rmi, = 0.77Rearth; Eint = 107 erg/g). Velocity vectors are plotted at particle locations. The velocity has been normalized to its maximum value in each frame. Time and coordinates of the four corners of the plotted field are given in the upper line (in units defined in Section 3). For particles in the vapor phase a "O" is plotted. before the time at which the particles spread out in space. Since this happens af- ter the time of closest approach, the trajec- and this completes the description of the equation of motion. T: 9,q0986 ( -2.0. 2.0. 2.0, 2.01 T: 11.03161 I -~.0 /,,l--¢/ t~ FIG. 2. Snapshots of run 1. (u~ = 0 km/sec; rmi, = 0.77Rearth; Eint = 107 erg/g plotted at particle locations. The velocity has been normalized to its maximum Time and coordinates of the four corners of the plotted field are given in the upp in Section 3). For particles in the vapor phase a "O" is plotted. before the time at which the particles spread out in space. Since this happens af- ter the time of closest approach, the trajec- tories of the various clumps forming after collision are calculated accurately. The total "viscous" force therefore be- comes F visc= F/bulk -I- F~ rag and this completes t equation of motion. 4.2. Energy Conserva The variation of t given by thermodynam du d--i = - P BENZ, SLATTERY, AND CAMERON 2.0. -2.0. 2.01 T: 8.83375 ( -2.0. 2.0. -2,0. 2.0] i~!!!iiii:~iii~:i ,: 2.0. 2.0, 2.01 T: 11.03161 I -~.0. ~,.0, -q,0. ~.0] /,,l--¢/ t~ f run 1. (u~ = 0 km/sec; rmi, = 0.77Rearth; Eint = 107 erg/g). Velocity vectors are ations. The velocity has been normalized to its maximum value in each frame. of the four corners of the plotted field are given in the upper line (in units defined ticles in the vapor phase a "O" is plotted. T: 1%68976 COLLISIONAL ORIGIN OF THE MOON -6.0. 6.0. -6.0. 6.0} T: 22.19287 -6.0, 6.0, -6.0. 6.01 521 ", S s 3. " j'q~k','" '. 0 ~,'e~4 " FIG. 2--Continued. i % where dQ is the amount of energy absorbed its first derivative, to assure the continuity T: 1%68976 COLLISIONAL ORIGIN OF THE MOON -6.0. 6.0. -6.0. 6.0} T: 22.19287 -6.0, 6.0, -6.0. 6.01 521 ", S s 3. " j'q~k','" '. 0 ~,'e~4 " FIG. 2--Continued. i % where dQ is the amount of energy absorbed its first derivative, to assure the continuity Giant Impact by SPHʢॳʣ [Benz et al., Icarus, 1986]
14. Constraints of Moon Formation (1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001] Giant Impact ʹΑͬͯܗ੒͞ΕΔप࿭੕ԁ൫ͷ ~80% ͕ Impactor ىݯͷϚϯτϧ෺࣭Ͱ͋Δ
15. ԁख़ظ
16. ଠཅܥܗ੒ඪ४ཧ࿦ʢྛϞσϧʣ  
    
    
    
     
     
    ©Newton Press [Hayashi et al., 1985]
17. KOKUBO AND IDA system on the (a) a–e and (b) a–i planes. The circles represent planetesimals and their radii are system initially consists of 3000 equal-mass (1023 g) bodies. We used the radii of planetesimals five umbers of planetesimals are 1533 (t 5 5000 years), 1294 (t 5 10,000 years), and 1059 (t 5 20,000 years). [Kokubo & Ida, Icarus, 1996] OLIGARCHIC GROWTH OF PROTOPLAN runaway stage, typical orbital s ing is about 10r mass of protopl rial, and the sem is a general pr in a disk when g are effective. If we assume the final stage planets is estim model that is 5 model, the sur given by S 5 510 4 Adopting this S b Q 0.07 AU a b Q 2 AU at 7 b Q 8 AU at 2 Earth mass. In mass and the o smaller than th oligarchic grow planetary accre FIG. 4. The same as Fig. 1 but for the system initially consists of 4000 equal-mass planetesimals (m 5 3 3 1023 g). The radius increase orbital separati factor is 6. In the final frame, the filled circles represent protoplanets region, if the ra [Kokubo & Ida, Icarus, 1998] ๫૸੒௕ˍՉ઎੒௕
18. ORIGIN OF MOON AND SINGLE IMPACT HYPOTHESIS 129 [Cameron, Icarus, 1997] Giant Impact by SPH
19. Roche radius, whereas Fig. 3 is a rather extended disk case (run 9). The extension of a disk is indicated by J disk /M disk , where J disk is the total angular momentum of the starting disk. For the disks in Figs 2 and 3, J disk /M disk are0:692 GM ! a R and 0:813 GM ! a R , respectively. e Figure 3 The same snapshots as in Fig. 2 but for run 9 of a more extended disk (Jdisk =Mdisk ¼ 0:813 GM ! aR ). At t ¼ 1,000 the largest moon mass is 0.71ML . [Ida et al., Nature, 1997] FIG. 2. Snapshots of the circumterrestrial disk projected on the R–z plane at t = 0, 10, 30, 100, 1000TK for runs (a) 29a, (b) centered at the coordinate origin stands for Earth. Circles represent disk particles and their size is proportional to the physical siz [Kokubo et al., Icarus, 2000] Moon Formation by N-body
20. Moon Formation Simulations ਺ϲ݄ʙ਺೥Ͱɺͻͱͭͷ݄͕Ͱ͖Δ
21. ............ mical adio- 82Hf- n in mpo- ation Solar The accu- Solar rites. drite ation 5,11,12. apid ation that of the rs of rep- . The es is, ases), bon- , but in all same ore a ratio p to ble at he W gueil okke- ollec- MS), for Ste Marguerite is our preferred approximation for the initial 182Hf/180Hf ratio of the Solar System. This precisely defined value is in agreement with previous estimates obtained from internal chondrite isochrons16, the comparison of W isotopes in iron meteorites and chondrites16,30, and the W isotope compositions of Figure 1 1w values of carbonaceous chondrites compared with those of the Toluca iron meteorite and terrestrial samples analysed in this study. The values for Toluca, Allende, G1-RF and IGDL-GD are the weighted averages of four or more independent analyses. Also included are data from ref. 16 (indicated by a), ref. 30 (b), and ref. 2 (c). For the definition of 1w see Table 1. The vertical shaded bar refers to the uncertainty in the W isotope composition of chondrites. Terrestrial samples include IGDL-GD (greywacke), G1- RF (granite) and BB and BE-N (basalts). [Kleine et al., Nature, 2002] with the f Hf/W of ,12 for the BSE15 provide the basis for such a calculation. The D1w value of the BSE is þ2, and a plot of D1w versus the mean time of core formation is shown in Fig. 2. A two- stage model age for the BSE of 29 Myr since the formation of the Figure 1 Hf–W systematics for the early Solar System. Shown is a plot of 1w versus 180Hf/183W represented as f Hf/W (see Table 1 for definitions of 1w and f Hf/W). a, Data for metal and silicate fractions from ordinary chondrites Dalgety Downs (L4) and Dhurmsala (LL6), and from carbonaceous chondrites Allende and Murchison, define a good fossil isochron, identical within error of the individual isochrons for the two ordinary chondrites. Least-squares fitting of the data include the Allende and Murchison whole-rock data, but exclude the Allende CAI. Including or excluding the Murchison and Allende whole-rock data or the CAI data does not significantly change the slope or the intercept. Our Juvinas eucrite datum plots on the eucrite isochron6. The Moon, with a residual 1w ¼ 1.3 ^ 0.4 from 182Hf decay27 and f Hf/W ¼ 18 defined by the lunar La/W ratio28, falls within error on the extension of the tie-line between the bulk chondrite (CHUR) and bulk silicate Earth (BSE) points. b, Magnified area for bulk chondrite data. Dotted curves show the 2j error band. Our results are consistent with E-chondrite data19, the zircon data for the Simmern Figure 2 Models for timing of core formation in the Earth. Shown is the expected radiogenic 182W/183W value in the Earth relative to chondrites ðD1w ¼ ½1w ðBSEÞ 2 1w ðCHURފ for a range of mean times of core formation (given by T 0 2 kTl cf ; where T 0 is the age of the Solar System and kTl cf is the mean age of core formation; see ref. 14) in the Earth for two different models of core segregation: a two-stage model, and a magma ocean model. For the D1 w value of þ1.9 ^ 0.20 reported in this work, we obtain as shown a two-stage model age of 29.5 ^ 1.5 Myr and a mean time of core formation of [Yin et al., Nature, 2002] Age of the Moon Formation CAI ܗ੒͔Β໿3,000ສ೥ޙʹ last giant impact = ݄ܗ੒
22. “CAI ܗ੒͔Β໿3,000ສ೥ޙ ݪ࢝஍ٿʹՐ੕αΠζͷݪ࢝࿭੕͕ࣼΊিಥ͠ ඈͼࢄͬͨϚϯτϧ෺࣭͕प࿭੕ԁ൫Λܗ੒͠ ͦΕΒ͕໿਺೥͔͚ͯूੵ͠ ݄͕஀ੜͨ͠”
23. ಓ͸ԕ͍͚Ͳɼ ·ͩͩΕ΋஌Βͳ͍͜ ͱΛࣗ෼͕࠷ॳʹ஌Δ͜ ͱͷتͼ΍Θ͘Θ͘ ͦΕ͕޷͖͔ͩΒɼ ݚڀΛଓ͚͍ͯΔͷͩͱࢥ͍·͢ɻ “ࠃޠ” ͷڭՊॻʹࡌΔ
24. ࠞཚظ
25. Constraints of Moon Formation (1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001] Giant Impact ʹΑͬͯܗ੒͞ΕΔप࿭੕ԁ൫ͷ ~80% ͕ Impactor ىݯͷϚϯτϧ෺࣭Ͱ͋Δ
26. ty of Earth gsten9 and have a fully sfactory as particularly on process rgy release, substantial the imme- part of the antle of the thought to mperatures, material is re there are icate) then ate at high he core and hese equili- mantle may ron at high significant: nd the fate nventory of ever, much own to the hours after thermally re-forming ed earlier). not expect onship that mperature, mic condi- imes2,11. have been ere impor- sphere was is, however, tmosphere gma ocean pour is that describes the melting responsible for the generation of basaltic magma, the dominant volcanism on Earth and most voluminously expressed at the low mantle pressures immediately beneath mid-ocean ridges. Recent work13,14 suggests that this picture may not apply for the deeper part of Earth’s mantle, so that freezing may begin at mid-depths. Even so, there will eventually come a point (perhaps as soon as a few thousand years) after a giant impact when the bottom part of the mantle a b c Lunar-forming giant impact Core Core Magma disk Silicate vapour atmosphere Radiative cooling Blobs of iron settling to core Partly solidified mantle Rest of disk falls back on Earth Newly formed Moon, mostly or partly molten Figure 2 | The effect on Earth of the giant impact that formed the Moon. a, A giant planetary embryo collides with the nearly complete Earth. b, A magma disk is in orbit about Earth, while blobs of iron from the planetary Mixing in the Magma Disk [Stevenson, Nature, 2008] [Pahlevan & Stevenson, EPSL, 2007] ݪ࢝஍ٿͱݪ݄࢝ԁ൫ͷؒͰ ਺100೥ؒ mixing ͢Ε͹Α͍
27. e Astrophysical Journal, 760:83 (18pp), 2012 November 20 Salmon & Canup Table 3 Hybrid Simulation Parameters Ld /Md Ld Md Min Mout q amax ( √ GM⊕aR ) (LEM) (M ) (M ) (M ) (R⊕ ) 0.843 0.304 2.00 2.00 0.00 N/A 2.9 0.843 0.365 2.50 2.50 0.00 N/A 2.9 0.955 0.345 2.00 1.00 1.00 5 4 0.960 0.347 2.00 1.00 1.00 3 4 0.965 0.348 2.00 1.00 1.00 1 4 0.955 0.414 2.40 1.20 1.20 5 4 0.960 0.416 2.40 1.20 1.20 3 4 0.965 0.418 2.40 1.20 1.20 1 4 0.899 0.325 2.00 1.50 0.50 5 4 0.901 0.326 2.00 1.50 0.50 3 4 0.904 0.326 2.00 1.50 0.50 1 4 0.899 0.390 2.40 1.80 0.60 5 4 0.901 0.391 2.40 1.80 0.60 3 4 0.904 0.392 2.40 1.80 0.60 1 4 0.888 0.401 2.50 2.00 0.50 5 4 0.890 0.402 2.50 2.00 0.50 3 4 0.892 0.403 2.50 2.00 0.50 1 4 0.880 0.477 3.00 2.50 0.50 5 4 0.882 0.478 3.00 2.50 0.50 3 4 0.884 0.479 3.00 2.50 0.50 1 4 0.986 0.356 2.00 1.00 1.00 5 6 1.009 0.365 2.00 1.00 1.00 3 6 1.036 0.374 2.00 1.00 1.00 1 6 0.986 0.427 2.40 1.20 1.20 5 6 1.009 0.437 2.40 1.20 1.20 3 6 1.036 0.449 2.40 1.20 1.20 1 6 0.914 0.330 2.00 1.50 0.50 5 6 0.926 0.335 2.00 1.50 0.50 3 6 0.940 0.339 2.00 1.50 0.50 1 6 0.914 0.396 2.40 1.80 0.60 5 6 0.926 0.401 2.40 1.80 0.60 3 6 0.940 0.407 2.40 1.80 0.60 1 6 0.900 0.406 2.50 2.00 0.50 5 6 0.909 0.411 2.50 2.00 0.50 3 6 0.920 0.416 2.50 2.00 0.50 1 6 0.890 0.482 3.00 2.50 0.50 5 6 0.898 0.487 3.00 2.50 0.50 3 6 0.907 0.492 3.00 2.50 0.50 1 6 1.068 0.386 2.00 1.00 1.00 1 7 1.068 0.463 2.00 1.20 1.20 1 7 0.998 0.361 2.00 1.00 1.00 5 8 1.043 0.377 2.00 1.00 1.00 3 8 1.099 0.397 2.00 1.00 1.00 1 8 0.998 0.433 2.40 1.20 1.20 5 8 1.043 0.452 2.40 1.20 1.20 3 8 1.098 0.476 2.40 1.20 1.20 1 8 Figure 2. Snapshots of the protolunar disk, projected on the R − z plane, at t = 0, 0.03, 1, 30, 200, and 1000 years, for Run 34 using the hybrid model with a fluid inner disk. The size of circles is proportional to the physical size of the corresponding particle. The horizontal thick line is the Roche-interior disk. The [Salmon & Canup, ApJ, 2012] ೪ੑϞσϧ Roche ൒ܘҎ಺͸ ྲྀମతʹৼΔ෣͏ ɾݻମ΁ͷڽॖ ɾ෺࣭ͷ༌ૹ N ମܭࢉ Roche ൒ܘҎԕ͸ ݻମతʹৼΔ෣͏ ɾিಥ߹ମ੒௕ ݄ͷܗ੒࣌ؒ ~1,000೥
28. Constraints of Moon Formation (1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001]
29. lunar material Junjun Zhang1*, Nicolas Dauphas1, Andrew M. Davis1, Ingo Leya2 and Alexei Fedkin1 A giant impact between the proto-Earth and a Mars-sized impactor named Theia is the favoured scenario for the formation of the Moon1–3. Oxygen isotopic compositions have been found to be identical between terrestrial and lunar samples4, which is inconsistent with numerical models estimating that more than 40% of the Moon-forming disk material was derived from Theia2,3. However, it remains uncertain whether more refractory elements, such as titanium, show the same degree of isotope homogeneity as oxygen in the Earth–Moon system. Here we present 50Ti/47Ti ratios in lunar samples measured by mass spectrometry. After correcting for secondary effects associated with cosmic-ray exposure at the lunar surface using samarium and gadolinium isotope systematics, we find that the 50Ti/47Ti ratio of the Moon is identical to that of the Earth within about four parts per million, which is only 1/150 of the isotopic range documented in meteorites. The isotopic homogeneity of this highly refractory element suggests that lunar material was derived from the proto-Earth mantle, an origin that could be explained by efficient impact ejection, by an exchange of material between the Earth’s magma ocean and the protolunar disk, or by fission from a rapidly rotating post-impact Earth. Apart from the effects of radioactive decay, the isotopic compositions of most terrestrial rocks are related by the laws of mass-dependent fractionation. Meteorites show departures from this rule that can be ascribed to unusual chemical processes, inheritance of nucleosynthetic anomalies, or nuclear transmu- tations (cosmogenic effects and radioactive decay). In the zoo of elements that show well-documented isotopic anomalies at a bulk planetary scale5–8, highly refractory titanium, with large nucleosynthetic anomalies on 50Ti, is the most promising to assess the degree of homogeneity in the Earth–Moon system9. Taking advantage of our new chemical procedure for titanium separation and developments in multicollector inductively cou- pled plasma mass spectrometry (MC-ICPMS; see Methods and ¬2 ¬1 0 1 2 3 4 5 6 50Ti Pre-exposure lunar value ( 50Ti = ¬0.03±0.04) ε ε Ordinary chondrites Enstatite chondrites Moon Earth Carbonaceous chondrites Achondrites CI CM CR CO CV CK EH EL H L LL HEDs Angrites Aubrites Ungrouped Acapulcoite Figure 1 | Titanium nucleosynthetic heterogeneity, "50Ti = [(50Ti/47Ti)sample/(50Ti/47Ti)rutile 1]⇥104, for carbonaceous, [Zhang et al., Nature Geo., 2012] m a magma tion of the 6Sm–142Nd ntradicting rocks were d were used illion years component mainly by of the lunar n terms of sotope data Ta-derived icating that st ,60 Myr ith Sm–Nd d terrestrial ction with strains the rmation of f the lunar is derived opes in the of the giant oxygen iso- wo KREEP- m (K), rare Ti and five fourfold to nitored the Hf/W ratios. ossible con- ble effect on atively short (e 5 0.01%) 15556 and tions larger s are given here have d agree with h samples3. cates that this anomaly might be due entirely to cosmogenic 182W. Kleine et al.3 reported elevated e182W < 2 for a magnetic separate from high-Ti mare basalt 79155 but we determined Hf/W 5 7.5 for an aliquot from the same magnetic separate, most probably indi- cating the presence of some ilmenite and hence cosmogenic 182W in this separate. The calculated cosmogenic 182W component is ,1.7 –2 –1 0 1 2 3 4 5 –2 –1 0 1 2 3 4 5 e182W Ref. 3 This study Ref. 5 Corrected in this study KREEP-rich samples Low-Ti mare basalts High-Ti mare basalts 14310 15445 62235 65015 68115 68815 72155 79155 75075 77516 70035 70017 70035 15475 15555 (WR) 15499 15556 15058 15555 75035 74255 74275 12004 Figure 1 | e182W of lunar metals analysed in this study compared with data from refs 3 and 5. Some of the previous data (shown with black dots inside the symbols) were corrected for cosmogenic 182W (see the text for details). [Touboul et al., Nature, 2007] ೉شൃੑݩૉͷಉҐମ΋Ұக
30. Constraints of Moon Formation (1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001] (6) ೉شൃੑݩૉͷಉҐମൺ͕஍ٿͱ΄΅Ұக [Touboul et al., 2007] ͙͢ʹڽ݁ͯ͠͠·͏ݩૉ͸े෼ʹ mixing Ͱ͖ͳ͍
31. and vapor, which requires a solution model th coefficients for trace elements at the tem (T=2500 K–3500 K). At present, no such Fig. 1. Chemical fractionation on an unstratified Earth. A single convective column characterizes the Earth from the deep magma ocean, where only one phase is present, through the top of the two-phase atmosphere. Rainout of Mg-rich droplets in ascending parcels shifts the composition of the upper atmosphere towards an Fe-rich vapor -2 -1 0 0 0.2 0. log P (bars) Fe/Fe+Mg liqu parc vap Fig. 2. Chemical structure of the silicate vapor atmosp rainout. The parcel represents the composition of the at suspended in a fayalitic vapor) and shifts with altitude t as the droplets separate via rainout. The lower atmo convection from the underlying magma ocean an composition. This calculation assumes that 40% of the every three-fold decrease in pressure (fL =0.4). This par the top of the atmosphere – a two-fold enhancement in t enhancement is comparable to a widely postulated silica has observable consequences (see text). 438 K. Pahlevan et al. / Earth and Planetary Science Letters 301 (2011) 433–443 [Pahlevan et al., EPSL, 2011] “Unstratified” Magma Disk ೉شൃੑݩૉʹ͍ͭͯ΋ mixing ͷՄೳੑΛఏҊ
32. Constraints of Moon Formation (1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001] (6) ೉شൃੑݩૉͷಉҐମൺ͕஍ٿͱ΄΅Ұக [Touboul et al., 2007]
33. lunar glasses are given in Table of all the bulk lunar sample (±2rSD ) which is identical to t et al. (2010) for bulk sil À0.29 ± 0.08 (±2rSD ). The ave alts (d30Si = À0.31 ± 0.07, 2r (2007) and Fitoussi et al.’s (201 of d30Si = À0.30 ± 0.05& (2rS narrow observed range of Si is the variety of samples observed lunar lithologies analysed in within error (2rSD ): d30SiLo d30SiHigh-Ti basalt = À0.32 ± 0.09 0.05; d30SiHighland rocks = À0.27 Fig. 2. d29Si versus d30Si plot. The error bars represent ±2rSEM for the samples. The calculated slopes for mass dependent equilibrium fractionation (0.5178) and mass dependent kinetic fractionation (0.5092) are also plotted. 30 Fig. 4. Histograms of d30Si values and bulk silicate Earth samples (BS The lunar breccia from Chakrabart [Armytage et al., GCA, 2012] Si ಉҐମൺ΋Ұக
34. Constraints of Moon Formation (1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001] (6) ೉شൃੑݩૉͷಉҐମൺ͕஍ٿͱ΄΅Ұக [Touboul et al., 2007] Si ಉҐମ෼഑ʹ͸ѹྗʢʹαΠζʣґଘੑ͕͋Δ (7) Si ಉҐମൺ͕஍ٿͱ΄΅Ұக [Armytage et al., 2012]
35. Hf-W Chronometry ͷऑ఺ [Sasaki & Abe, PPV, 2005] Ͳ͏ߟ͑ͯ΋ Hf-W ܥͷ׬શฏߧԽ͸࣮ݱͰ͖ͳ͍
36. T. SASAKI AND Y. ABE: IMPERFECT EQUILIBRATION OF HF-W SYSTEM 1041 The age of the last giant impact as a function of the resetting ratio h giant impact, fitting to the observational data (ϵ = 2) from Earth es. The number of giant impacts is assumed to be five. The initial s ϵ = 10 at t = 10. The formation age of the Earth for perfect ng (resetting ratio = 1) is about 30 Myr, in agreement with a us study (Yin et al., 2002). ilicate equilibration. This would not be a realistic Fig. 7. The age of the last giant impact as a function of the resetting ratio of each giant impact, fitting to the observational data (ϵ = 2) from Earth samples. The number of giant impacts is 2 to 10 from left to right. The initial state is ϵ = 10 at t = 10. [Sasaki & Abe, EPS, 2007] [Wood & Halliday, Nature, 2005] Age of the Moon Formation? Hf-W chronometry Ͱ͸ ݄ܗ੒ͷ೥୅͸ܾ·Βͳ͍
37. 2.3. Initial Conditions We follow Canup & Asphaug (2001) and Canup (2004) for the orbital parameters of the impactor for which the most massive satellite is expected. The masses of the proto-Earth and the im- pactor are assumed to be 1.0 and 0:2 MÈ, where MÈ is the Earth mass. The radii of the proto-Earth and protoplanet are rE ¼ 1:0 and 0:64r , respectively. Note that no significant differences in Fig. 1.—Giant impact simulation with EOS-1, which represents a state in which most of the impactor mass is vaporized. Left, face-on views of the system; right, edge- on views. The numbers in the upper right corners of the panels show the time in units of hours. The color represents log-scaled density (the units are 0 ¼ 12:6 g cmÀ3). WADA, KOKUBO, & MAKINO 1182 Vol. 638 [Wada et al., ApJ, 2005] ߴղ૾౓֨ࢠ๏ʹΑΔ G.I. ܭࢉ ৠൃͨ͠ݪ݄࢝ԁ൫಺ʹিܸ೾ཱ͕ͪ·ͬͯ͘ ԁ൫͕֯ӡಈྔΛࣦ͍਺೔Ͱશͯ஍ٿʹམԼʂʁ
38. ֵ໋ظ
39. Ćuk & Stewart, Science (2012) -200 -150 -100 -50 0 50 100 150 200 0 20 40 60 80 100 Resonant angle (°) Time (kyr) D 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Earthís spin period (hr) C 0 0.1 0.2 0.3 0.4 0.5 0.6 Eccentricity B 4 5 6 7 8 9 10 Semi-major axis (RE ) A Synchronous at perigee Fig. 3. Tidal evolution of the Moon through the evection resonance, starting with an Earth spin 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0 20 40 60 80 100 120 Earth+Moon angular momentum Time (kyr) P=2.25 hr QE=48 QM=48 P=2.25 hr QE=96 QM=97 P=2.5 hr P=2 hr P=3 hr 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0 20 40 60 80 100 Earth+Moon angular momentum Time (kyr) QE=48 QM=48 QE=96 QM=97 QM=117 QM=73 QM=57 A B Fig. 4. Change in total angular momentum of the Earth-Moon system during tidal evolution of the Moon for different simulation parameters. (A) Simulations starting with Earth’s spin period of 2.5 hour with different tidal quality factors for Earth (QE = 96, where not noted otherwise) and the Moon (QM ) (B) Simulations starting with 2-, 2.25-, 2.5-, and 3-hour spin periods for Earth (QE = 96 and QM = 97 RESEARCH ARTI ஍ٿ-݄-ଠཅͷؒͷӬ೥ڞ໐Ͱܥͷ֯ӡಈྔ͕ݮগ
40. Constraints of Moon Formation (1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001] (6) ೉شൃੑݩૉͷಉҐମൺ͕஍ٿͱ΄΅Ұக [Touboul et al., 2007] (7) Si ಉҐମൺ͕஍ٿͱ΄΅Ұக [Armytage et al., 2012]
41. Collision Scenarios w/o angular momentum constraints formed from a magma ocean ( 5), implying an intensely energetic fi ery start at a time when heat-producing short-lived nuclides (26Al and 60Fe) were extinct. Third, the oxygen isoto- silicon isotopic composition of Earth and the Moon ( 13) is not readily explained; the rain- out process is expected to generate a silicon isotopic difference, so the problem persists. ene Th ma los ure mo der els deb pro equ the cat wit fere Ear A Standard impactor Small impactor Large impactor B C Collision scenarios . Examples of the three new models of the Moon-forming Giant Impact, each of which allows more angular momentum to be lost and thereby achieves oxygen isotopic compositions that cannot be resolved between Earth and the Moon. ( A ) “Standard” impactor, 10% of Earth’s fi nal mass, works with “hit and run” collision ( 14 ). ( B ) “Small” impactor, 2.5% of Earth’s fi nal mass ( 1 ). ( C ) “Large” impactor, 45% of Earth’s fi nal mass ( 2 ). (A) ࣭ྔൺ 10:1 Ͱ “Hit-and-Run” collision [Reufer et al., 2012] (B) ࣭ྔൺ 40:1 Ͱ “Fission-like” collision [Ćuk & Stewart, 2012] (C) ࣭ྔൺ 1:1 Ͱ “Twins” collision [Canup, 2012] [Halliday, 2012]
42. Fig. 1a. Five snapshots from the 30° impact angle and 1.30 vesc impact velocity case (cC06) showing cuts through the impact plane. Color coded is the type and origin of s 221 (2012) 296–299 297 “Hit-and-Run” Collision [Reufer et al., Icarus, 2012]
43. otential Moon-formation events for arios with less angular momentum. he total angular momentum by add- the impactors generated successful he slower-spinning planets. Because mentum is carried away with debris rosive giant impacts, the spin period t decreases. Thus, the spin state of required to be near fission before or oon-forming impact in our scenario e, last entry in Table 1). However, the spin of each body and the impact geometry) is near the stability limit. Our candidate Moon-forming events have more than double the kinetic energy of previous scenarios, and the impact velocities were suf- ficient to substantially vaporize silicates (33). As a result, the silicate atmosphere and vapor-rich disk are more massive and hotter than found in previous work (34). At the resolution of the simulations, the projectile-to-target mass ratio is uniform from the atmosphere to the Roche radius. mation of the rom Earth’s mple impact impactor at nd b = −0.3 E Earth spin- period of 2.3 able 1). Gray e the Roche F) View of in the lower ooking down ockwise spin olors denote mantles and f the Earth ctor. The disk by material rom Earth’s the impact nd movie S1). misphere view colors de- lanet (blue), yellow), and (H) Density rial plane of planet, which fied. VOL 338 SCIENCE www.sciencemag.org on November 25, 2012 www.sciencemag.org Downloaded from “Fission-like” Collision shifted inward. Eventually, the lunar semimajor axis evolved within 5RE , whereas the Moon main- Earth-Moon system with its current momentum and found that capture in the evection resonance and the Moon is within ~50% of the value op- timal for their balance (26). This balance of tides Fig. 2. Summary of the range of outcomes for expected terminal giant impacts onto the proto-Earth: Mproj ≤ 0.1ME and 1 to 3Vesc (Vesc ~ 10 km s−1). The target was a 0.99ME body with a 2.3-hour spin. Projectiles had no spin and masses of 0.026, 0.05, or 0.10ME . The radius of each filled colored circle is proportional to the satellite mass; the black circle indicates MS = 1.0MM . Color indicates the difference in projectile composition between the silicate disk and silicate Earth. Within a colored circle, a gray dot denotes too much iron core mass fraction in the disk. The number above each symbol gives the final mass of the planet; bold numbers indicate cases that satisfy the relaxed Moon-formation criteria in Table 1. Collisions in the middle region of the figure, head-on and slightly retrograde impacts from 10 to 30 km s−1, are the best fit to the observational constraints for Moon-forming impacts. RESEARCH ARTICLE [Ćuk & Stewart, Science, 2012]
44. into a single moon at an orbital distance of about 3.8R⊕ , where R⊕ is Earth’s radius (19, 20), MM MD ≈ 1:9 LD MD ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2:9GM⊕R⊕ p   − 1:1 − 1:9 Mesc MD   ð1Þ where Mesc is the mass that escapes from the disk as the Moon accretes. To estimate MM , we used Eq. 1 and made the favorable assumption that Mesc = 0. We tracked the origin (impactor versus tar- get) of the particles in the final planet and the disk. To quantify the compositional difference be- tween the silicate portions of the disk and planet, we define a deviation percentage dfT ≡ [FD,tar /FP,tar − 1] × 100 (2) where FD,tar and FP,tar are the mass fractions of the silicate portions of the disk and of the planet derived from the target’s mantle, respectively (21). Identical disk-planet compositions have dfT = 0, whereas a disk that contains fractionally more impactor-derived silicate than the final planet has dfT < 0, and a disk that contains fractionally less impactor-derived silicate than the final planet has dfT > 0. Prior impact simulations (1–3, 14, 15) that consider g ≡ Mimp /MT ≈ 0.1 to 0.2 produce disks with −90% ≤ dfT ≤ −35% for cases with MM > ML , where ML is the Moon’s mass. Results with larger impactors having g = 0.3, 0.4, and 0.45 are shown in Figs. 1 and 2 and Table 1. As the relative size of the impactor (g) is increased, there is generally a closer compositional match be- tween the final disk and the planet. For g ≥ 0.4, some disks have both sufficient mass and an- gular momentum to yield the Moon and nearly identical silicate compositions to that of the final Fig. 1. An SPH simulation of a moderately oblique, low-velocity (v∞ = 4 km s–1) collision between an impactor and target with similar masses (Table 1, run 31). Color scales with particle temperature in kelvin, per color bar, with red indicating tempera- tures >6440 K. All particles in the three-dimensional simulation are overplotted. Time is shown in hours, and distances are shown in units of 103 km. After the initial impact, the plan- ets recollided, merged, and spun rapidly. Their iron cores migrated to the center, while the merged structure developed a bar- type mode and spiral arms (24). The arms wrapped up and finally dispersed to form a disk containing ~3 lunar masses, whose silicate composition dif- fered from that of the final planet by less than 1%. Because of the near symmetry of the colli- sion, impactor and target material are distributed approximately proportion- ately throughout the final disk, so that the disk’s dfT value does not vary ap- preciably with distance from the planet. REPORTS on November 25, 2012 www.sciencemag.org ownloaded from “Twins” Collision larger impactors having are shown in Figs. 1 and relative size of the impac is generally a closer co tween the final disk and some disks have both s gular momentum to yiel identical silicate compos material are distributed approximately proportion- ately throughout the final disk, so that the disk’s dfT value does not vary ap- preciably with distance from the planet. Fig. 2. Compositional differ- ence between the disk and final planet (dfT ) (Eq. 2) produced by simulations with (A) g = 0.3 and (B) g = 0.4 (triangles) and 0.45 (squares) versus the pre- dicted mass of the moon that would accrete from each disk (MM ) (Eq. 1) scaled to the final planet’s mass (MP ). There is a change in y axis scales between the two plots. Gray, purple, dark blue, light blue, green, yellow, orange, and red points corre- spond to vimp /vesc = 1.0, 1.1, 1.2, 1.3, 1.4, 1.6, 1.8, and 2.0, respectively. The open square is run 60* from Table 1, which includes pre-impact rotation. Forming an appropriate-mass Moon mass requires MM /MP > 0.012, the region to the right of the vertical solid line. Constraints on dfT needed to satisfy Earth-Moon are shown by horizontal lines for oxygen (solid), titanium (dotted), and chromium (dot-dashed), assuming a Mars-composition impactor. www.sciencemag.org SCIENCE VOL 338 23 NOVEMBER 2012 get) of the particles in the final planet and the disk. To quantify the compositional difference be- tween the silicate portions of the disk and planet, we define a deviation percentage dfT ≡ [FD,tar /FP,tar − 1] × 100 (2) where FD,tar and FP,tar are the mass fractions of the silicate portions of the disk and of the planet derived from the target’s mantle, respectively (21). Identical disk-planet compositions have dfT = 0, whereas a disk that contains fractionally more impactor-derived silicate than the final planet has dfT < 0, and a disk that contains fractionally less impactor-derived silicate than the final planet has dfT > 0. Prior impact simulations (1–3, 14, 15) that consider g ≡ Mimp /MT ≈ 0.1 to 0.2 produce disks with −90% ≤ dfT ≤ −35% for cases with MM > ML , where ML is the Moon’s mass. Results with larger impactors having g = 0.3, 0.4, and 0.45 are shown in Figs. 1 and 2 and Table 1. As the relative size of the impactor (g) is increased, there is generally a closer compositional match be- tween the final disk and the planet. For g ≥ 0.4, some disks have both sufficient mass and an- gular momentum to yield the Moon and nearly identical silicate compositions to that of the final simulation are overplotted. Time is shown in hours, and distances are shown in units of 103 km. After the initial impact, the plan- ets recollided, merged, and spun rapidly. Their iron cores migrated to the center, while the merged structure developed a bar- type mode and spiral arms (24). The arms wrapped up and finally dispersed to form a disk containing ~3 lunar masses, whose silicate composition dif- fered from that of the final planet by less than 1%. Because of the near symmetry of the colli- sion, impactor and target material are distributed approximately proportion- ately throughout the final disk, so that the disk’s dfT value does not vary ap- preciably with distance from the planet. Fig. 2. Compositional differ- ence between the disk and final planet (dfT ) (Eq. 2) produced by simulations with (A) g = 0.3 and (B) g = 0.4 (triangles) and 0.45 (squares) versus the pre- dicted mass of the moon that would accrete from each disk (MM ) (Eq. 1) scaled to the final planet’s mass (MP ). There is a change in y axis scales between the two plots. Gray, purple, dark blue, light blue, green, yellow, orange, and red points corre- spond to vimp /vesc = 1.0, 1.1, 1.2, 1.3, 1.4, 1.6, 1.8, and 2.0, respectively. The open square is run 60* from Table 1, which includes pre-impact rotation. Forming an appropriate-mass Moon mass requires MM /MP > 0.012, the region to the right of the vertical solid line. Constraints on dfT needed to satisfy Earth-Moon compositional similarities are shown by horizontal lines for oxygen (solid), titanium (dotted), and chromium (dot-dashed), assuming a Mars-composition impactor. on November 25, 2012 www.sciencemag.org Downloaded from [Canup, Science, 2012]
45. standard “Fission-like” “Twins” [Simulations by Miki Nakajima]
46. ࠞ໎ΛۃΊΔݱ୅
47. he a ic sk of al ay n- th e- e- 1Þ m ed 2Þ he ng m- he ic o- a of sk et colors. In the canonical scenario, the impactor grazes around the target’s mantle and is deformed. Due to the low impact velocity, material supposed to end up in or- bit around the Earth must not be decelerated too strongly in order to retain enough velocity to stay in orbit. This is only achieved for the parts of the impactor mantle most distant to the point of impact, and some minor part of the target’s mantle. But if impact velocity is increased from 1.00 (cA08) to 1.30 vesc (cC01), parts from dee- per within the target mantle receive the right amount of energy for orbit insertion, Fig. 1a. Five snapshots from the 30° impact angle and 1.30 vesc impact velocity case (cC06) showing cuts through the impact plane. Color coded is the type and origin of the material. Dark and light blue indicate target and impactor iron; Red and orange show corresponding silicate material. The far right shows the situation at the time of impact. At 0.52 h, it can be seen how the impactor ploughs deep through the targets mantle and pushes considerable amount of target material into orbit. A spiral arm of material forms and gravitationally collapses into fragments. The outer portions of the arm mainly consist of impactor silicates and escapes due to having retained a velocity well above escape velocity. The silicate fragments further inward are stronger decelerated and enter eccentric orbits around the target. The impactor’s iron core also looses much of its angular momentum to the outer parts of the spiral arm and re-impacts the proto-Earth. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) carus 221 (2012) 296–299 297 “Hit-and-Run” Collision? [Reufer et al., Icarus, 2012] 2) suggests that this issue can be resolved if Theia arable to that of the proto-Earth. In this case, both on-forming disk are a roughly even mixture of the Theia. (This scenario relies on the angular momen- h–Moon system later decreasing via an evection he Sun (C ´ uk and Stewart, 2012).) e number of terrestrial planet formation simula- imate the statistical likelihood that Theia’s mass to the proto-Earth. To do this, we simply look at of mass ratios for Earth analogs struck by Theia mulations. This distribution is shown in Fig. 17, he parameter c, which is the ratio of Theia’s mass mass of Theia and the proto-Earth at the time of he Earth and Moon evenly enough, Canup (2012) must have had cJ 0:4. In Fig. 17, we see that such found in any of our simulations. Out of the 104 nerated in our collisions, the largest recorded c y 8.7% of our Earth analogs experienced impacts e impacts with cJ 0:4 must be exceedingly rare, omparably massed Theia and proto-Earth is a very This result agrees with Jacobson and Morbidelli found that major mergers between protoplanets ses are rare. mparable masses for Theia and the proto-Earth, l. (2012) and C ´ uk and Stewart (2012) invoke a if the proto-Earth was spinning very rapidly before impact. Because of this finding, we also look at our collision statistics for last major mergers on Earth analogs that involve impacting bodies with masses below 0:1 M È . These are also shown in Fig. 18. We see that smaller impactors do collide with the Earth at higher velocities, but Fig. 18. The cumulative distribution of impact velocities between Earth and Theia analogs in the ANN simulations. Theia analogs are split into three different mass bins: m = 0.025–0.05 M È (solid line), m = 0.05–0.1 M È (dashed line), and m > 0:1 M È (dotted line). Impact velocity is calculated in terms of the mutual escape velocity of the Earth and Theia analogs. N.A. Kaib, N.B. Cowan / Icarus 252 (2015) 161–174 171 [Kaib & Cowan, Icarus, 2012] N ମܭࢉͰ Giant Impacts ͷաఔΛ௥ͬͨͱ͜Ζ িಥ଎౓͕ඞཁͳେ͖͞ʹୡ͠ͳ͍͜ͱ͕൑໌
48. (Agnor et al. 1999) is necessary after the giant impact stage. 3.3. Statistics of Spin In 50 runs of the realistic and perfect accretion models, we have 128 and 124 planets that experience at least one accretionary collision, respectively. The average values of each an isotropic distr the obliquity rang distribution whic and Kokubo & I K–S probabilities accretion models, spin anisotropy p Figure 3. Left: average spin angular velocity of all planets formed in the 50 runs of the realistic (circle) and mass M with mass bin of 0.1 M⊕ . The error bars indicate 1σ and the dotted line shows ωcr. Right: normal curve) and perfect (dashed curve) accretion models with an isotropic distribution (dotted curve). (A color version of this figure is available in the online journal.) [Kokubo & Genda, ApJ, 2010] he es of ty a ct io a o- he uf- v- de is he nd of re, ng a net ial ite ile ile %. en ly he m- ur ng ial nd ial m is a he m- esc ng is- a- ts, in on n- n- he g. es of hat he ve nal e- sk disk (table S1). The results imply a more narrow range for potential Moon-formation events for impact scenarios with less angular momentum. Increasing the total angular momentum by add- ing spin to the impactors generated successful disks from the slower-spinning planets. Because angular momentum is carried away with debris from these erosive giant impacts, the spin period of the planet decreases. Thus, the spin state of Earth is not required to be near fission before or after the Moon-forming impact in our scenario (for example, last entry in Table 1). However, the total angular momentum of the event (from the spin of each body and the impact geometry) is near the stability limit. Our candidate Moon-forming events have more than double the kinetic energy of previous scenarios, and the impact velocities were suf- ficient to substantially vaporize silicates (33). As a result, the silicate atmosphere and vapor-rich disk are more massive and hotter than found in previous work (34). At the resolution of the simulations, the projectile-to-target mass ratio is uniform from the atmosphere to the Roche radius. Fig. 1. Formation of the lunar disk from Earth’s mantle. Example impact of a 0.05ME impactor at 20 km s−1 and b = −0.3 onto a 1.05ME Earth spin- ning with a period of 2.3 hours (‡ in Table 1). Gray circles denote the Roche radius. (A to F) View of SPH particles in the lower hemisphere looking down the counterclockwise spin axis, where colors denote the silicate mantles and iron cores of the Earth and the impactor. The disk is dominated by material originating from Earth’s mantle near the impact site (fig. S1 and movie S1). (G) Lower hemisphere view with particle colors de- noting the planet (blue), atmosphere (yellow), and disk (green). (H) Density in the equatorial plane of the disk and planet, which is stably stratified. EMBER 2012 VOL 338 SCIENCE www.sciencemag.org on November 25, 2012 www.sciencemag.org Downloaded from “Fission-like” Collision? িಥഁյͷޮՌ΋ߟྀ͢Δͱ ݪ࢝஍ٿΛߴ଎ճసͰ͖ͳ͍ [Ćuk & Stewart, Science, 2012]
49. into a single moon at an orbital distance of about 3.8R⊕ , where R⊕ is Earth’s radius (19, 20), MM MD ≈ 1:9 LD MD ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2:9GM⊕R⊕ p   − 1:1 − 1:9 Mesc MD   ð1Þ where Mesc is the mass that escapes from the disk as the Moon accretes. To estimate MM , we used Eq. 1 and made the favorable assumption that Mesc = 0. We tracked the origin (impactor versus tar- get) of the particles in the final planet and the disk. To quantify the compositional difference be- tween the silicate portions of the disk and planet, we define a deviation percentage dfT ≡ [FD,tar /FP,tar − 1] × 100 (2) where FD,tar and FP,tar are the mass fractions of the silicate portions of the disk and of the planet derived from the target’s mantle, respectively (21). Identical disk-planet compositions have dfT = 0, whereas a disk that contains fractionally more impactor-derived silicate than the final planet has dfT < 0, and a disk that contains fractionally less impactor-derived silicate than the final planet has dfT > 0. Prior impact simulations (1–3, 14, 15) that consider g ≡ Mimp /MT ≈ 0.1 to 0.2 produce disks with −90% ≤ dfT ≤ −35% for cases with MM > ML , where ML is the Moon’s mass. Results with larger impactors having g = 0.3, 0.4, and 0.45 are shown in Figs. 1 and 2 and Table 1. As the relative size of the impactor (g) is increased, there is generally a closer compositional match be- tween the final disk and the planet. For g ≥ 0.4, some disks have both sufficient mass and an- gular momentum to yield the Moon and nearly identical silicate compositions to that of the final SPH simulation ately oblique, y (v∞ = 4 km n between an nd target with sses (Table 1, lor scales with mperature in color bar, with ing tempera- K. All particles e-dimensional re overplotted. own in hours, ces are shown 103 km. After mpact, the plan- ded, merged, rapidly. Their migrated to the e the merged veloped a bar- and spiral arms rms wrapped ally dispersed disk containing masses, whose mposition dif- that of the t by less than se of the near of the colli- ctor and target e distributed ely proportion- ghout the final t the disk’s dfT not vary ap- with distance anet. mpositional differ- en the disk and final (Eq. 2) produced by with (A) g = 0.3 = 0.4 (triangles) and REPORTS on November 25, 2012 www.sciencemag.org Downloaded from “Twins” Collision? [Canup, Science, 2012] 20Ne/22Ne 10 11 12 13 40Ar/36Ar 2,000 4,000 6,000 8,000 10,000 21Ne/22Ne 0.07 20Ne/22Ne 10 11 12 13 a Iceland; this study MORB (2ΠD43) Iceland; ref. 18 Air Air Iceland mantle source Iceland mantle source Solar wind b 0.04 0.03 0.05 0.06 Figure 1 | Differences in neon and argon isotopic composition between MORB and the Iceland plume. a, Neon three-isotope plot showing the new analyses of the DICE 10 sample (filled circles) from Iceland in comparison to previously published data for this sample (open circles; ref. 18) and the gas-rich ‘popping rock’ (2PD43) from the north Mid-Atlantic Ridge (open triangles; ref. 17). Error bars are 1s, and forclarity, twoprevious analyses18 with largeerrorbars have not been shown. Step-crushing of a mantle-derived basalt produces a linear trend that reflects variable amounts ofpost-eruptive air contamination in vesicles containingmantleNe.Theslopeofthelineisafunctionoftheratioofnucleogenic 21Ne to primordial 22Ne, with steeper slopes indicating a higher proportion of primordial 22Ne and, thus, a less degassed mantle source. The slope of the Iceland line based on the new analyses is consistent with that obtained previously18. Importantly, 20Ne/22Ne ratios of 12.8860.06 are distinctly higher than the MORB source 20Ne/22Ne of #12.5 as constrained from continental well gases20. b, Ne–Ar compositions of individual step crushes of the DICE 10 sample. 40Ar is generated by radioactive decay of 40K, and low 40Ar/36Ar ratios are indicative of a less degassed mantle. The data reflect mixing between a mantle component and post-eruptive atmospheric contamination. A least-squares hyperbolic fit through the data yields a 40Ar/36Ar ratio of 10,74563,080, corresponding to a mantle solar 20Ne/22Ne ratio of 13.8. This Ar isotopic ratio is used as the mantle source value for Iceland in Figs 2 and 3. Symbols as in a; error bars are 1s. Kinetic fractionation 10 13 Iceland; this study MORB (2ΠD43) a Air 20Ne/22Ne 3He/22Ne 12 11 3He/36Ar 40Ar/36Ar 5,000 10,000 15,000 20,000 25,000 30,000 b Air Iceland mantle source MORB (2ΠD43) mantle source 0.0 0.2 0.4 0.6 0.8 22Ne/36Ar 40Ar/36Ar 5,000 10,000 15,000 20,000 25,000 30,000 Air Sea water c 0.0 0.1 0.2 0.3 0.4 Degassing 0 1 2 3 4 5 6 Figure 2 | Differences in elemental abundances and isotope ratios between MORB and the Iceland plume. Errorbarsare1s.a,3He/22Neversus20Ne/22Ne; b, 3He/36Ar versus 40Ar/36Ar; and c, 22Ne/36Ar versus 40Ar/36Ar. The mantle source composition for 2PD43 (filled grey square in all panels) is based on the 40Ar/36Ar and 20Ne/22Ne ratios as defined in ref. 30, and the mantle source composition for Iceland (filled black square in all panels) is based on Fig. 1. The grey and black arrows at the top ofthe figure indicate how elemental ratios evolve asaresultofkineticfractionationandsolubilitycontrolleddegassing,respectively. Good linear relationships are observed between isotope ratios and elemental ratios, which reflect mixing between mantle-derived noble gases and post- RESEARCH LETTER 20Ne/22Ne 10 11 12 13 40Ar/36Ar 2,000 4,000 6,000 8,000 10,000 21Ne/22Ne 0.07 20Ne/22Ne 10 11 12 13 a Iceland; this study MORB (2ΠD43) Iceland; ref. 18 Air Air Iceland mantle source Iceland mantle source Solar wind b 0.04 0.03 0.05 0.06 Figure 1 | Differences in neon and argon isotopic composition between MORB and the Iceland plume. a, Neon three-isotope plot showing the new analyses of the DICE 10 sample (filled circles) from Iceland in comparison to previously published data for this sample (open circles; ref. 18) and the gas-rich ‘popping rock’ (2PD43) from the north Mid-Atlantic Ridge (open triangles; ref. 17). Error bars are 1s, and forclarity, twoprevious analyses18 with largeerrorbars have not been shown. Step-crushing of a mantle-derived basalt produces a linear trend that reflects variable amounts ofpost-eruptive air contamination in vesicles containingmantleNe.Theslopeofthelineisafunctionoftheratioofnucleogenic 21Ne to primordial 22Ne, with steeper slopes indicating a higher proportion of primordial 22Ne and, thus, a less degassed mantle source. The slope of the Iceland line based on the new analyses is consistent with that obtained previously18. Importantly, 20Ne/22Ne ratios of 12.8860.06 are distinctly higher than the MORB source 20Ne/22Ne of #12.5 as constrained from continental well gases20. Kinetic fractionation 10 13 Iceland; this study MORB (2ΠD43) a Air 20Ne/22Ne 3He/22Ne 12 11 3He/36Ar 40Ar/36Ar 5,000 10,000 15,000 20,000 25,000 30,000 b Air Iceland mantle source MORB (2ΠD43) mantle source 0.0 0.2 0.4 0.6 0.8 22Ne/36Ar 40Ar/36Ar 5,000 10,000 15,000 20,000 25,000 30,000 Air Sea water c 0.0 0.1 0.2 0.3 0.4 Degassing 0 1 2 3 4 5 6 Figure 2 | Differences in elemental abundances and isotope ratios between MORB and the Iceland plume. Errorbarsare1s.a,3He/22Neversus20Ne/22Ne; RESEARCH LETTER contamination processes are ruled out as the reason for the lower 129Xe/130Xe ratios at Iceland. The data in Fig. 3a demonstrate that the Iceland and MORB source mantles evolved with different I/Xe ratios, requiring the two mantle sources to have separated by 4.45Gyr ago with limited subsequent mix- ing between the two. As atmosphere is located near the origin in this plot (Fig. 3a), and mixing in this space is linear, adding subducted atmo- spheric Xe to the MORB source clearly cannot produce the Iceland source, based on its higher proportion of Pu- to U-derived fission Xe, is a conclusion that is independent of the absolute concentrations of noble gases andtherelativepartitioncoefficientsofthenoblegases withrespect to their radiogenic parents. The combined I–Pu–Xe system has been used to constrain the closure time for volatile loss of a mantle reservoir through the 129*Xe/136*XePu ratio1,2,6,25, where 129*Xe is the decay product of 129I decay and 136*XePu is 136Xe produced from 244Pu fission. 129I has a shorter half-lifethan244Pu,andasa resulthigher129*Xe/136*Xe ratios 6.6 6.8 7.0 7.2 7.4 129Xe/130Xe 40Ar/36Ar 2,000 4,000 6,000 8,000 10,000 Iceland mantle 129Xe/130Xe Air b 3He/130Xe 0 200 400 600 800 1,000 Air 129Xe/130Xe 6.6 6.8 7.0 7.2 7.4 7.6 7.8 MORB (2ΠD43) source Iceland mantle source a Figure 3 | Differences in Xe isotopic composition between MORB and the Iceland plume. a, Correlation between 129Xe and 3He in the ‘popping rock’ MORB (2PD43)17 and Iceland (DICE 10). Error bars are 1s. Data points are individual step crushes that reflect different degrees of post-eruptive atmospheric contamination in the vesicles. Air lies near the origin and the mantle compositions at the other end of the linear arrays. The straight lines are robust regressions through the data. Because mixing in this space is linear, the lines also represent the trajectories along which the mantle sources will evolve when mixed with subducted air. The new observations from Iceland demonstrate that the Iceland plume 129Xe/130Xe ratio cannot be generated solely through adding recycled atmospheric Xe to the MORB source, and vice versa. Thus, two mantle reservoirs with distinct I/Xe ratios are required. The mantle 129Xe/130Xe ratio of 6.986 0.07 for Iceland was derived from a hyperbolic least-squares fit through the Ar-Xe data (b) corresponding to a mantle 40Ar/36Ar ratio of 10,745. Note that given the curvature in Ar–Xe space, the 129Xe/130Xe in the Iceland mantle source is not particularly sensitive to the exact choice of the mantle 40Ar/36Ar ratio. LETTER RESEARCH [Mukhopadhyay, Nature, 2012] ஍ٿਂ෦ͷرΨεಉҐମෆۉҰ ஍ٿਂ෦·Ͱ melting ͍ͯ͠ͳ͍
50. cases can be found in the Methods). We calculate the that the feeding zones of the impactor and the planet are he same distribution, using a two-group Kolmogorov– probabilities shown in the plots and in Table 1). In 3 out e feeding zones contributing to the Moon and those con- e planet are consistent with being drawn from the same of the proto-Earth was mixed into the Moon (as suggested by detailed collision simulations showing a 10%–40% contribution from the proto- Earth14). For the typical 20% mix of proto-Earth material with the impactor material forming the Moon (as found in simulations), 35% of cases are consistent with their feeding zones being drawn from the same parent distribution, and the success rate increases further for a 50 100 50 100 50 100 N 50 100 0.5 1 1.5 2 2.5 3 3.5 4 0 50 100 a (AU) a N P = 123, N I = 97 P = 0.0039 10%, P = 0.023 20%, P = 0.13 30%, P = 0.32 40%, P = 0.67 cjs15 number 1 0 20 40 60 0 20 40 0 20 40 N 0 20 40 1 2 3 4 0 20 40 a (AU) cjs1 number 4 10%, P = 6.7 × 10−27 N P = 128, N I = 78, P = 1.1 × 10−29 20%, P = 5.1 × 10−18 30%, P = 2.7 × 10−10 40%, P = 0.052 b distribution of planetesimals composing the planet and the case where the origins of the planetesimals composing the the impactor (blue) areconsistent with being sampled from the tribution for the expected typical 20% contribution of planetary on-forming impacts (Kolmogorov–Smirnov test probability se where the planet and impactor compositions are inconsistent (P , 0.05), but become consistent once a large (40%) contribution of material from the planet is considered. The lower plots in each panel show the results when different contributions from the planet are assumed (four cases are shown 10%; 20%; 30% and 40%). The cumulative distribution for these cases as well as all other planet–impactor pairs in Table 1 can be found in the Methods. 9 A P R I L 2 0 1 5 | V O L 5 2 0 | N A T U R E | 2 1 3 G2015 Macmillan Publishers Limited. All rights reserved ProtoEarth ≒ Theia? [Mastrobuono-Battisti et al., Nature, 2015] planetesimals rather than 1000. The final four cases (EEJS 9- 12) also had 2000 planetesimals but had eJ ¼ 0:07 and eS ¼ 0:08.  JSRES (‘‘Jupiter and Saturn in RESonance”). Jupiter and Saturn were placed in their mutual 3:2 mean motion resonance, follow- ing directly from simulations of their evolution in the gaseous Solar Nebula (Morbidelli et al., 2007): aJ ¼ 5:43 AU; aS ¼ 7:30 AU; eJ ¼ 0:005, and eS ¼ 0:01, with a mutual inclination of 0.2°.  JSRESECC (‘‘Jupiter and Saturn in RESonance on ECCentric orbits”). As for JSRES but with eJ ¼ eS ¼ 0:03. The EJS and EEJS simulations assume that Jupiter and Saturn did not undergo any migration. The EEJS simulations are more self-consistent than the EJS simulations, because scattering of remnant planetesimals and embryos tends to decrease the eccen- ricities and semimajor axes of Jupiter and Saturn (e.g., Chambers, 2001). Thus, to end up on their current orbits, Jupiter and Saturn would have had to form on more eccentric and slightly more dis- ant orbits. The CJS, JSRES and JSRESECC simulations all follow rom the Nice model and assume that Jupiter and Saturn’s orbits changed significantly after their formation, with Saturn migrating outward and Jupiter inward (Tsiganis et al., 2005). If migration of he giant planets is really associated with the late heavy bom- bardment (Gomes et al., 2005; Strom et al., 2005), then at least most of the migration of Jupiter and Saturn must have occurred ate, well after the completion of the terrestrial planet formation process. from Abe et al. (2000). The ‘‘water mass fraction”, WMF, i.e. the water content by mass, varies with radial distance r as WMF ¼ 10À5 ; r < 2AU 10À3 ; 2AU < r < 2:5AU 5%; r > 2:5AU 8 > < > : ð4Þ This water distribution is imprinted on planetesimals and em- bryos at the start of each simulation. During accretion the water Fig. 2. Sample initial conditions for a disk with R $ rÀ3=2 containing 97 planetary embryos and 1000 planetesimals. Embryos are shown in gray with their sizes proportional to their mass(1/3) (but not to scale on the x axis). [Raymond et al., Icarus, 2009] planets is hnM i ’ 2:0 Æ 0:6, which means that the typical result- ing system consists of two Earth-sized planets and a smaller planet. In this model, we obtain hna i ’ 1:8 Æ 0:7. In other words, one or two planets tend to form outside the initial distribution of protoplanets. In most runs, these planets are smaller scattered planets. Thus we obtain a high efficiency of h fa i ¼ 0:79 Æ 0:15. The accretion timescale is hTacc i ¼ 1:05 Æ 0:58 ð Þ ; 108 yr. These results are consistent with Agnor et al. (1999), whose initial con- ditions are the same as the standard model except for Æ1 ¼ 8. The left and right panels of Figure 3 show the final planets on the a-M and M–e, i planes for 20 runs. The largest planets tend to cluste same s ha1 i. M larges are ha 0:06 Æ hM2 i’ 0:05, a in som one, w find a Fig. 2.—Snapshots of the system on the a-e (left) and a-i (right) planes at t ¼ 0, 106, 107, 1 are proportional to the physical sizes of the planets. KOKUBO, KOMINAMI, 1134 [Kokubo et al., ApJ, 2006] ͦ΋ͦ΋ݪ࢝஍ٿͱিಥఱମ͸ಉ͡ࡐྉͰܗ੒ ॳظ৚͕݅ۃΊͯዞҙతʢඪ४γφϦΦͰ͸ͳ͍ʣ ݁Ռ͸ॳظ৚݅Λ൓өͨࣗ͠વͳؼ݁ʹ͗͢ͳ͍
51. 5 2330, pic com- ve to the he metal rocks, we erized by E, as well al within e incorp- into the pactor is bout the e grossly W present it is very s. This is ous lunar gimpac- µ182W –10 0 10 20 30 40 50 68815,396 68115,114 Average 68115,114 68815,394 Figure 1 | Values of m182W of lunar metals separated from KREEP-rich impact melts analysed by negative thermal ionization mass spectrometry in this study. The data for 68115,114, 68815,394, and 68815,396 are shown as circles, diamond, and square respectively; error bars for our analysis show internal precision of one single measurement, for which the 2 standard deviations (s.d.) external reproducibility is ,4.5 ppm, as demonstrated by replicated standard measurements over the two year period. The white-dotted circle corresponds to the average of the three replicated analyses of 68115,114 ndances m182W 5.3 6 4.6 1.5 6 2.6 3.0 6 1.7 3.3 6 3.8 8.1 6 2.5 0.4 6 2.9 0.6 6 5.1 LETTER RESEARCH [Touboul et al., Nature, 2015] of 10.27 6 0.04 is significantly higher than the previously obtained mean value of 0.09 6 0.10 for lunar metal samples (ref. 10), but for non-irradiated samples (68115, 68815) there is good agreement between our data and previous data (Fig. 2). For more strongly irra- diated samples, however, the e182W of the metals tends to be slightly lower10, resulting in an overall decrease of the mean e182W inferred from the lunar metals. Therefore, the higher pre-exposure e182W of 10.27 6 0.04 determined here reflects not only the better precision of our measurements, but also that the previous study10 did not fully quantify neutron capture effects in the metals. The well-resolved 182W excess of the Moon compared to the pre- sent-day BSE (Fig. 2) places important constraints on the occurrence, mass and timing of the late veneer as well as on the origin of the Moon. Below we first evaluate the magnitude of any e182W difference between the BSE and the Moon induced by the late veneer, and then we assess whether there is a resolvable 182W anomaly in the Moon resulting from the mixing of impactor and proto-Earth material during the giant impact. The mass and composition of the late veneer is constrained through absolute and relative HSE abundances and ratios of S, Se and Te in Earth’s primitive mantle2,19,20. On this basis, the late veneer probably had a carbonaceous-chondrite-like composition with a minor fraction of iron-meteorite-like material16, corresponding to ,0.35% of Earth’s mass. This composition can explain several geo- chemical signatures of the Earth’s mantle, including its chondritic Os/ Ir, Pt/Ir and Rh/Ir but suprachondritic Ru/Ir and Pd/Ir, as well as its 187Os/188Os value2 and Se–Te systematics19. Mass balance considera- –4 –3 –2 –1 0 0 1 2 ε180Hf ε182W 68115 12034 14310 14321 62235 14163 KREEP-rich samples ε182W pre-exposure 68815 Figure 1 | Plot of e182W versus e180Hf determined for KREEP-rich samples. e182W has been internally normalized to 186W/184W 5 0.92767: elsewhere this is referred to as e182W (6/4) (see Methods and Table 1). Solid line is a best-fit –0.2 0 0.2 0.4 0.6 14321, 1827 (n = 2) 14321, 1856 (n = 6) 68115, 295 (n = 4) 68115, 112 (n = 3) 68115, 112 (n = 4), ref. 10 BCR-2 (n = 22) AGV-2 (n = 12) BHVO-2 (n = 3) 68815, 400 (n = 2) 68815, 400 (n = 4), ref. 10 KREEP-rich samples Terrestrial rock standards ε182W Figure 2 | e182W data of KREEP-rich samplesandterrestrialrock standards. Top panel, data from this study (filled symbols) and for metal samples from ref. 10 (open symbols). Data points of 68115 and 68815 (this study) were corrected for a minor contribution from meteoritic contamination at the lunar surface (Table 1). Error bars indicate external uncertainties derived from the 2 s.d. obtained for terrestrial rock standards analysed in this study (if N , 4) or 95% confidence interval of multiple solution replicates of a sample (if N $ 4) (Extended Data Table 1). Bottom panel, data from terrestrial rock standards. Top panel, weighted mean (n 5 5) e182W 5 10.27 6 0.03 (95% confidence 182 [Kruijer et al., Nature, 2015] Θ͔ͣͳ W ಉҐମͷࠩ G.I. ௚ޙ͸׬શʹ identicalɾͦͷޙͷఱମিಥͰมԽ
52. m the deformed e to the Moon. a ocean can be (element parti- rinciples of the xperimental data ivine and ultra- of magma ocean red value of Mg# ained by a broad g (920–80%) or ree of chemical on the process pact and partial modify the composition (e.g., ref. 24). The present model could also explain the presence of a small Fe-rich core,25) if the influence of reduction at high proto-Earth proto-Earth impactor impactor magma ocean vapor jet (a) (b) Fig. 4. Schematic drawing of processes of ejection of materials upon a giant impact. (a) A case where the proto-Earth does not have a magma ocean. (b) A case where the proto-Earth has a magma ocean. fate of ejected materials depends on the ratio h/R and materials with only for modest value of h/R and velocity will become the source of the Moon. km/s) re. The temperature g the relation [1] in o temperature at the are summarized in : volume, q: a non- oÞq (q 9 1 for solids, [Karato, Proc. Jpn. Acad., 2014] Giant Impact on Magma Ocean Magma Ocean ঢ়ଶͷݪ࢝஍ٿ΁ͷ Giant Impact ࡉ໺ࣣ݄ˏੜଘֶ͕ؗ਺஋ܭࢉʹΑΓઈࢍݕূத
53. High-Energy Giant Impact ஍ٿͷϚϯτϧ͸ G.I. Ͱ͍ͬͨΜશͯৠൃͨ͠ʂʁ [Wang & Jacobson, Nature, 2016]
54. Multiple Impact Scenario NATURE GEOSCIENCE DOI: 10.1038/NGEO2866 ARTICLES a −60 −45 −30 −15 0 15 30 45 60 V imp /V esc V imp /V esc 1.0 1.4 2.0 3.0 4.0 1.0 1.4 2.0 3.0 4.0 M moon M moon 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 b 1.0 0.5 0.1 9 5 2.4 1 10 20 30 40 50 60 Impact angle, (°) β |δf T | (%) |δf T | (%) a L imp /L EM L final /L EM −4 −2 0 2 4 M sat /M moon 10−2 10−1 100 b 1.0 1.5 2.0 2.5 3.0 |δf T | < 10 Graze and merge Hit and run Partial accretion / max = 0.00 ω ω / max = 0.25 ω ω / max = 0.50 ω ω NATURE GEOSCIENCE DOI: 10.1038/NGEO2866 ARTICLES a −60 −45 −30 −15 0 15 30 45 60 V imp /V esc V imp /V esc 1.0 1.4 2.0 3.0 4.0 1.0 1.4 2.0 3.0 4.0 V imp /V esc 1.0 1.4 2.0 3.0 4.0 M moon M moon M moon 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 b 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 c 1.0 0.5 0.1 9 5 2.4 1 10 20 30 40 50 60 Impact angle, (°) β −60 −45 −30 −15 0 15 30 45 60 Impact angle, (°) β |δf T | (%) |δf T | (%) |δf T | (%) a L imp /L EM L final /L EM L imp /L EM −4 −2 0 2 4 M sat /M moon 10−2 10−1 100 b −6 −4 −2 0 2 4 6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 |δf T | < 10 Graze and merge Hit and run Partial accretion / max = 0.00 ω ω / max = 0.25 ω ω / max = 0.50 ω ω Figure 4 | Final satellite mass and system angular momentum. a, Mass of the formed satellite using equation (2) as a function of impact angular momentum for !=0.25!max rotation. The colours correspond to di￿erent collisional regimes (hit and run—impactor escapes partially intact; graze and merge—impactor impacts the target twice; partial accretion—addition of mass to the target). b, The final angular momentum of all the systems that created a satellite. The di￿erent styles of markers represent di￿erent initial rotations. The darker horizontal lines represent the initial planetary angular momentum value with colours corresponding to the colours of the markers. Disks containing <100NSPH were omitted. −60 −45 −30 −15 0 15 30 45 60 V i V imp /V esc 1.0 1.4 2.0 1.0 1.4 2.0 3.0 4.0 V imp /V esc 1.0 1.4 2.0 3.0 4.0 M moon M moon 0 10 20 b 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 c 1.0 0.5 0.1 9 5 2.4 1 0 10 20 30 40 50 60 Impact angle, (°) β −60 −45 −30 −15 0 15 30 45 60 Impact angle, (°) β −60 −45 −30 −15 0 15 30 45 60 Impact angle, (°) β %) |δf T | (%) |δf T | (%) Figure 3 | Disk properties in the angle–velocity phase space. a–c, Initial planetary rotation rate !=0.10!max (a), !=0.25!max (b) and !=0.50!max (c). The marker size corresponds to disk mass and the colour to the compositional di￿erence between the silicates in the final planet and disk. For comparison, the grey circles in the upper left corner represent a disk mass of 0.1, 0.5 and 1 MMoon. Markers are shifted horizontally according to the mass ratio, from left to right (9, 5, 2.4, 1%). The grey dots indicate disks that have an iron content larger than the estimated lunar core mass of 0.1Mmoon. Disks containing <100 smoothed particle hydrodynamics (SPH) particles were omitted. retrograde impactors often fail to form a disk with enough angular momentum to accrete a moonlet. L final /L EM M sat / 1 b Figure 4 the form moment collision and mer of mass that crea initial rot angular m markers. high-en Fig. 3). rotation good ag erosion due to t the Met For period Howeve planets, momen impacts momen retrogra angular [Rufu et al., Nature Geo., 2017] 20 ճఔ౓ͷিಥͰܗ੒͞Εͨ moonlets ͷूੵ িಥதͷ previous moonlets ͷ҆ఆੑʹ͍ͭͯ͸ෆ໌
55. acquire larger late-accreted masses than those in the Grand Tack simu- lations (see Fig. 1), because the planetesimal population is more dis- persed in the classical scenario and therefore decays more slowly. necessary,whereM› representsanEarthmass. Thismassdoe contributions from the era known as the Late Heavy Bomb Current mass estimates for this very late (approximately 500 condensation) accretion are21 1023M›, which we added to accretedmassesofoursynthetic Earth-like planets, butitonly for about 2% of the chondritic mass and therefore does no important part in our analysis of the correlation. The chondritic mass can only be identical to the late-accre or to the Late Veneer mass if the Moon-forming event strip the HSEs from Earth’s mantle or was the last episode of gr Earth’s core, respectively (as is traditionally assumed). Howe conditions are not necessarily true. Consider that some p colliding with Earth after the Moon-forming event might h differentiated, so that their HSEs were contained in their cor of these cores had merged with Earth’s core22, then the late mass would clearly be larger than the chondritic mass, beca would be no HSE record of this fraction of the projectile Earth’s mantle. Additionally, in this case, given thatiron (and HSEs) would have beensimultaneously added to Earth’s man core, the chondritic mass would be larger than the Late Ven which is geochemically defined as the mass accreted to Earth core has stopped growing. In fact, as explained in detail in the Methods and in Exten Figs3and4,itisunlikelythatmorethan50%ofaprojectile’sco reaches Earth’s core, otherwise geochemical models cannot r the tungsten isotope composition of Earth’s mantle23. Moreov late-accreted mass, delivered in only a few objects so as to ex relative HSE abundances of Earth and Moon12, would have lef able isotopic signature on Earth relative to the Moon24,25. T when considering these more complex possibilities, geochem ence constrains the late-accreted mass probably not to exceed (see Methods). For these reasons, we first make the usual assumption tha accreted mass and the HSE-derived chondritic mass are ide Running geometric mean of all Earth-like planets Running geometric mean of only Earth-like planets from Grand Tack simulations Earth-like planets from classical simulations Earth-like planets from Grand Tack simulations 10 100 50 20 30 15 150 70 10–4 0.001 0.01 0.1 1 Relative late accreted mass Time of last giant impact (Myr) Figure 1 | The late-accreted mass relative to each synthetic Earth-like planet’s final mass as a function of the time of the last giant impact. Triangles represent Earth-like planets from the first category: classical simulations with Jupiter and Saturn near their contemporary orbits7,8. Circles [Jacobson et al., Nature, 2014] Age of the Moon Formation? ஍ٿϚϯτϧͷ HSE ྔ Λઆ໌͢ΔͨΊʹ͸ɺ ࠷ޙͷ G.I. ͸ CAI ܗ੒ ޙ ~100My Ͱ͋Δ΂͖ ஍ٿϚϯτϧͷ HSE ա৒ ɹˠ ஍ٿܗ੒ޙͷ late veneer ※ Grand Tack Model ΛԾఆͨ͠৔߹ͷ೥୅Ͱ͋Δ
56. ~1% come back to strike the Moon within 400 million years (My) (Fig. 1) (8). Because the Moon only has ~25 ancient (Pre-Nectarian) lunar basins (16), probably made by the impact of diameter D > 20 km projectiles >4.1 Ga (13, 17), an impact probability of ~1% implies the GI ejecta popula- tion could—at best—only contain a few thou- sand D > 20 km bodies (the order of 25/0.01). Mass balance therefore requires the majority of GI ejecta to be in a steep size frequency distribu- tion dominated by D < 20 km bodies (8). This leads us to predict that ~1010-km-sized projec- tiles were thrown out of the Earth-Moon system (fig. S8) (8). Although GI simulations lack the resolution to confirm the nature of this steep size frequency distribution, insights gleaned from numerical impact experiments on D = 100 km bodies show that such steep slopes are common outcomes when the targets are largely left intact (6). An analog in nature for this may be the formation of the ~500-km Rheasilvia basin on the D = 530 km asteroid Vesta; the largest body in Vesta’s family of fragments is D ~ 8 km, a factor of 70 smaller than Vesta itself, whereas the exponents of its cumu- lative power law size distribution are extremely steep, with –3.7 and –8 observed for D > 3 km and > 5 km bodies, respectively (fig. S6) (7, 8, 18). The shape of this size distribution implies that much of the mass of GI ejecta was initially in the form of 0.1 < D < 20 km fragments rather than of dust and small debris (8). A consequence of a steep GI ejecta size fre- quency distribution is that the fragments should undergo vigorous collisional evolution with themselves. Tests using collision evolution codes (13, 19) indicate that D < 1 km bodies rapidly demolished themselves, enough so to reduce the population by several orders of magnitude in mass within 0.1 to 1 My of the GI (fig. S8) (8). This would lead to a huge dust spike, with small particles either thrown out of the solar system via radiation pressure or lost to the Sun via Poynting-Robertson drag (14, 20). The surviving Fig. 2. Compilations of impact ages found within chondritic meteorites. (A) A representation of 40Ar-39Ar shock degassing ages for 34 ordinary and enstatite chondrites whose mean ages are between ~4.32 billion and 4.567 billion years (9–11). All samples were heavily shocked, shock-melted, or otherwise had some evidence for having been part of a large collision. To create this age-probability distribution, we separated the sample ages by parent body (EL, EH, E-melt/Aubrites, L, LL, and H chondrites) and computed the sum probability of ages within each class by adding Gaussian profiles, with centers and widths corresponding to the most probable age and 1s errors of each dated sample (8). The profiles were then normalized before they were summed in order to prevent any single class from dominating the distribution (fig. S9A). We caution that systematic errors in measured Ar decay rates could make these ages slightly older (8). (B) The age-probability distribution of U-Pb ages for 24 L, LL, and H chondrites (table S1) created by using the same method (fig. S9B). U-Pb ages >60 My after CAIs are interpreted to be from impact heating alone, whereas those <60 My after CAIs are an unknown mixture of formation, metamorphic, and impact ages (26). Both distributions show a feature ~80 to 120 My after CAIs (~4.45 to 4.49 Ga). Fig. 3. A sample comparison between our model and ran- domly derived 40Ar-39Ar shock degassing ages for asteroidal meteorites. (A) The combined 40Ar-39Ar age distribution, in blue, was created by assuming that leftover planetesimals and giant RESEARCH | REPORTS [Bottke et al., Science, 2015] , PLANETARY SCIENCE INSTITUTE By Eric Hand It was the biggest cataclysm the solar system has ever seen. About 100 million years after the planets began to take shape, a Mars-sized body crashed into the proto-Earth, creating a halo of hot debris that coalesced into the moon. There was collateral damage, it turns out. Scientists now suspect that fragments of the giant impact were flung all the way to the fledgling asteroid belt. When this plan- way to probe that.” Scientists have long tried to pin down the age of the moon by analyzing lunar samples returned from the Apollo missions. But be- cause of disagreements about the isotope systems used for dating, the calculated ages vary from about 30 million years after the start of the solar system to 100 million or even 200 million years younger. A more precise age would help scientists work out that 10 billion kilometer-sized bodies would have been flung out into the solar system— where many of them could strike asteroids. Asteroids constantly collide with each other, but at relatively slow speeds. Some high-speed projectiles from the giant im- pact, in contrast, would have struck at speeds upward of 10 kilometers a second, melting and transforming asteroid miner- als into darker, glassy materials. The shock heating would also have altered a standard radio active “clock” used for dating, in which a radioactive isotope of potassium decays into argon that remains trapped in the crys- tal structure of the rock. “If you heat it up enough, argon moves through the crystal structures, and you can reset [the clock],” says study co-author Tim Swindle, director of the Lunar and Planetary Laboratory at the University of Arizona in Tucson. Searching through the literature for me- teorites that had already been dated, the team found 34 samples that fit their profile: those with shock-heating alteration and ancient argon ages. A significant fraction of these 34 samples have ages that cluster around 105 million years after the solar sys- tem began; that, the team believes, is the age of the moon-forming impact. Other scientists are excited about the method but worried about the small sam- ple size. The authors used their own judg- ment to identify meteorites with the right type of shock heating, and their 34 meteor- ite samples could hail from as few as five or six parent asteroid bodies. “Is that really representative of everything the asteroid belt saw?” asks Sarah Stewart, a planetary scientist at the University of California, Davis. “It’s not a robust conclusion, but it’s a robust method.” Swindle says the new moon age estimate—a Moon-forming impact left scars in distant asteroids Planetary collision dated through analysis of meteorites PLANETARY SCIENCE The giant impact that formed the moon may have flung copious debris into the solar system. on April 16, 2015 www.sciencemag.org Downloaded from (c) Science Age of the Moon Formation? Giant Impact Ejecta ͕ߴ଎Ͱখ࿭੕ʹিಥɾ೥୅Λ Ϧηοτͨ͠ূڌ͕ᯁੴʹࠁ·Ε͍ͯΔ͸ͣ ※ αϯϓϧ͕গͳ͗͢ΔˍϞσϧ͕γϯϓϧ͗͢Δ
57. ݁ہ Ͳ͏ͨ͠Β͍͍ͷʁ
58. • ֤ Giant Impact Ϟσϧͷଥ౰ੑ͕Θ͔Βͳ͍
 ˠ ଟ༷ͳ Giant Impact ͷΑΓৄࡉͳܭࢉΛߦ͏ • ஍ٿͱ݄ͷԽֶ૊੒͕Ұக͍͗ͯ͢͠Δʁ
 ˠ ৽ͨͳ݄ͷੴΛऔಘɾαϯϓϧόΠΞεΛআ͘ • શͯͷԽֶσʔλΛຬͨ͢ղ͕ଘࡏ͠ͳ͍
 ˠ ͍ͬͦ Giant Impact આ͔Β཭Εͯߟ͑ͯΈΔ • ݄ܗ੒೥୅ΛͲ͏΍ܾͬͯΊΔʁ
 ˠ ݄ͷࢎૉಉҐମൺΛ࣋ͭܽยˏᯁੴΛ୳͢