2020೥7݄11೔ɹΦϯϥΠϯࢢຽߨ࠲ʮ෺ཧͱӉ஦ʯୈ̏ճ ݄ͷىݯΛղ͖໌͔͢ ژ౎େֶ Ӊ஦෺ཧֶڭࣨɹࠤʑ໦وڭ

http://sasakitakanori.com

✤ ᴈ໌ظʢلݩલʙ1960೥୅ʣ ✤ ։Խظʢ1970೥୅ʙ1980೥୅ʣ ✤ ԁख़ظʢ1990೥୅ʙ2000೥୅લظʣ ✤ ࠞཚظʢ2000೥୅ޙظʣ ✤ ֵ໋ظʢ2010೥୅ʣ ✤ ࠞ໎ΛۃΊΔݱ୅ ݄ͷىݯͷݚڀ࢙

✤ ᴈ໌ظʢلݩલʙ1960೥୅ʣ ✤ ։Խظʢ1970೥୅ʙ1980೥୅ʣ ✤ ԁख़ظʢ1990೥୅ʙ2000೥୅લظʣ ✤ ࠞཚظʢ2000೥୅ޙظʣ ✤ ֵ໋ظʢ2010೥୅ʣ ✤ ࠞ໎ΛۃΊΔݱ୅ ݄ͷىݯͷݚڀ࢙

• ݹࣄه ΠβφΪϊϛίτ͕ӈ໨Λચ͍݄ಡ໋͕஀ੜʢࠨ໨͕ఱরେਆʣ • چ໿੟ॻ ૑଄ओ͕4೔໨ʹఱͷଠཅͱ݄ͱ੕Λ஀ੜͤͨ͞ • Τδϓτ ૑଄ओϥʔͷࠨ໨͕݄ͱͳͬͨʢӈ໨͕ଠཅʣ • தࠃ ૑଄ਆ൫ݹͷӈ໨͕݄ͱͳͬͨʢࠨ໨͕ଠཅʣ ਆ࿩ʹ͓͚Δ݄ͷىݯ

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

݄ͷىݯઆ ั֫આ ෼྾આ ૒ࢠઆ ݪ࢝஍ٿ͕ߴ଎ճసʹΑΓ;͘ΒΈ ͦͷҰ෦͕ͪ͗Ε݄͕ͯ஀ੜ ஍ٿيಓ෇ۙͰͷඍ࿭੕ͷूੵʹΑΓ ஍ٿͱ͸ಠཱʹ݄͕ܗ੒ ஍ٿͱ͸ผͷ৔ॴͰ࡞ΒΕ݄͕ͨ ஍ٿͷۙ͘Λ௨ͬͨͱ͖ʹัΒ͑ΒΕͨ

✤ ᴈ໌ظʢلݩલʙ1960೥୅ʣ ✤ ։Խظʢ1970೥୅ʙ1980೥୅ʣ ✤ ԁख़ظʢ1990೥୅ʙ2000೥୅લظʣ ✤ ࠞཚظʢ2000೥୅ޙظʣ ✤ ֵ໋ظʢ2010೥୅ʣ ✤ ࠞ໎ΛۃΊΔݱ୅ ݄ͷىݯͷݚڀ࢙

Ξϙϩ11߸ɿ݄ͷੴͷ࠾औ

(1) ஍ٿʔ݄ܥͷ֯ӡಈྔʢLtotal ͕อଘʣ ݄ܗ੒Ͱຬͨ͢΂͖৚݅ ɹˠ ݄͸ߴԹͷঢ়ଶ͔Βελʔτ͍ͯ͠Δ ɹˠ ஍ٿ͸Ҏલʹߴ଎ճస͍ͯͯ͠͸͍͚ͳ͍ (2) ஍ٿΑΓ௿ີ౓ʢίΞ͕খ͍͞ʣ[Hood & Zuber, 2000] ɹˠ ݄͸΄΅ؠੴ͚ͩͰͰ͖͍ͯΔ (3) شൃੑݩૉ͕ڧ͘ރׇ [Jones & Palme, 2000] (4) ද໘͕େن໛༹༥Λܦݧ [Warren, 1985] (5) ࢎૉಉҐମൺ͕஍ٿͱ΄΅Ұக [Wiechert et al., 2001] ɹˠ ݄ͱ஍ٿͷؠੴ͸ಉ͡΋ͷ͔ΒͰ͖͍ͯΔ

݄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଄͕આ໌Ͱ͖ͳ͍݄Λ࢒ͤͳ͍ ั֫֬཰͕௿͍Խֶత੍໿Λຬͨͤͳ͍

δϟΠΞϯτΠϯύΫτઆ [Hartman & Davis, Icarus, 1975] [Cameron & Ward, LPI Conference, 1976]

✤ ᴈ໌ظʢلݩલʙ1960೥୅ʣ ✤ ։Խظʢ1970೥୅ʙ1980೥୅ʣ ✤ ԁख़ظʢ1990೥୅ʙ2000೥୅લظʣ ✤ ࠞཚظʢ2000೥୅ޙظʣ ✤ ֵ໋ظʢ2010೥୅ʣ ✤ ࠞ໎ΛۃΊΔݱ୅ ݄ͷىݯͷݚڀ࢙

ଠཅܥܗ੒ඪ४ཧ࿦ʢྛϞσϧʣ ©Newton Press [Hayashi et al., 1985]

KOKUBO AND IDA m on the (a) a–e and (b) a–i planes. The circles represent planetesimals and their radii are m initially consists of 3000 equal-mass (1023 g) bodies. We used the radii of planetesimals five s 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 PROTO runaway sta typical orbi ing is abou mass of pro rial, and th is a genera in a disk wh are effectiv If we as the final st planets is e model that model, the given by S 5 Adopting t b Q 0.07 A b Q 2 AU b Q 8 AU Earth mass mass and t smaller tha oligarchic g planetary a 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 sep factor is 6. In the final frame, the filled circles represent protoplanets region, if t [Kokubo & Ida, Icarus, 1998] ๫૸੒௕ˍՉ઎੒௕

ڊେఱମিಥʹΑΔԁ൫ܗ੒ [Canup & Asphaug, Nature, 2001] © Natsuki Hosono ݪ࢝஍ٿʹՐ੕αΠζͷ ݪ࢝࿭੕͕িಥ ඈͼࢄͬͨഁย͕஍ٿͷ पғʹԁ൫Λܗ੒ ͜ͷഁยΛࡐྉʹͯ͠ ݄͕ܗ੒͞ΕͨͷͰ͸ʁ

Roche radius, whereas Fig. 3 is a rather extended disk case (run 9). The extension of a disk is indicated by Jdisk /Mdisk , where Jdisk is the total angular momentum of the starting disk. For the disks in Figs 2 and 3, Jdisk /Mdisk are0:692 GM!aR and 0:813 GM!aR , respectively. Figure 3 The same snapshots as in Fig. 2 but for run 9 of a more extended disk (J disk =M disk ¼ 0:813 GM ! a R ). At t ¼ 1,000 the largest moon mass is 0.71M L. [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 centered at the coordinate origin stands for Earth. Circles represent disk particles and their size is proportional to the physic [Kokubo et al., Icarus, 2000] িಥഁยԁ൫͔Βͷ݄ܗ੒

݄ܗ੒γϛϡϨʔγϣϯ ਺ϲ݄ʙ਺೥Ͱɺͻͱͭͷ݄͕Ͱ͖Δ [Sasaki & Hosono, ApJ, 2018] [Simulation by Natsuki Hosono]

“ଠཅܥ࠷ݹͷ෺࣭͕ܗ੒͞Ε͔ͯΒ໿3,000ສ೥ޙ ݪ࢝஍ٿʹՐ੕αΠζͷݪ࢝࿭੕͕ࣼΊিಥ͠ ඈͼࢄͬͨϚϯτϧ෺࣭͕प࿭੕ԁ൫Λܗ੒͠ ͦΕΒ͕໿਺೥͔͚ͯूੵ͠ɺ݄͕஀ੜͨ͠”

✤ ᴈ໌ظʢلݩલʙ1960೥୅ʣ ✤ ։Խظʢ1970೥୅ʙ1980೥୅ʣ ✤ ԁख़ظʢ1990೥୅ʙ2000೥୅લظʣ ✤ ࠞཚظʢ2000೥୅ޙظʣ ✤ ֵ໋ظʢ2010೥୅ʣ ✤ ࠞ໎ΛۃΊΔݱ୅ ݄ͷىݯͷݚڀ࢙

(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 ىݯͰ͋Δ ݄ܗ੒Ͱຬͨ͢΂͖৚݅ [Simulations by Miki Nakajima]

(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] ݄ܗ੒Ͱຬͨ͢΂͖৚݅ (8) W ಉҐମൺ͕͔ͭͯ஍ٿͱҰக [Touboul et al., 2015]

✤ ᴈ໌ظʢلݩલʙ1960೥୅ʣ ✤ ։Խظʢ1970೥୅ʙ1980೥୅ʣ ✤ ԁख़ظʢ1990೥୅ʙ2000೥୅લظʣ ✤ ࠞཚظʢ2000೥୅ޙظʣ ✤ ֵ໋ظʢ2010೥୅ʣ ✤ ࠞ໎ΛۃΊΔݱ୅ ݄ͷىݯͷݚڀ࢙

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 Moon for different simulation parameters. (A) Simulations starting with Earth’s spin period of 2.5 with different tidal quality factors for Earth (QE = 96, where not noted otherwise) and the Moon (B) Simulations starting with 2-, 2.25-, 2.5-, and 3-hour spin periods for Earth (QE = 96 and QM RESEARCH A ஍ٿ-݄-ଠཅͷؒͷӬ೥ڞ໐Ͱܥͷ֯ӡಈྔ͕ݮগ

(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] ݄ܗ੒Ͱຬͨ͢΂͖৚݅ (8) W ಉҐମൺ͕͔ͭͯ஍ٿͱҰக [Touboul et al., 2015]

৽͍͠িಥγφϦΦͷఏҊ 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. 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” িಥ [Reufer et al., 2012] (B) ࣭ྔൺ 40:1 Ͱ “Fission-like” িಥ [Ćuk & Stewart, 2012] (C) ࣭ྔൺ 1:1 Ͱ “Twins” িಥ [Canup, 2012] [Halliday, 2012]

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 21 (2012) 296–299 297 “Hit-and-Run” িಥ [Reufer et al., Icarus, 2012]

Moon-formation events for th less angular momentum. angular momentum by add- actors generated successful er-spinning planets. Because is carried away with debris iant impacts, the spin period ses. Thus, the spin state of to be near fission before or ming impact in our scenario ntry 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. the th’s pact r at −0.3 pin- 2.3 Gray oche w of wer own spin note and arth disk erial th’s pact S1). view de- ue), and nsity e of hich 38 SCIENCE www.sciencemag.org on November 25, 2012 www.sciencemag.org Downloaded from “Fission-like” িಥ 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]

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” িಥ 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 fer- inal by 0.3 and pre- hat disk nal s a een dark ow, rre- 1.1, 2.0, are hich on. ass P > 0.012, the region to the right of the vertical solid line. Constraints on dfT needed to satisfy Earth-Moon compositional similarities es for oxygen (solid), titanium (dotted), and chromium (dot-dashed), assuming a Mars-composition impactor. [Canup, Science, 2012]

✤ ᴈ໌ظʢلݩલʙ1960೥୅ʣ ✤ ։Խظʢ1970೥୅ʙ1980೥୅ʣ ✤ ԁख़ظʢ1990೥୅ʙ2000೥୅લظʣ ✤ ࠞཚظʢ2000೥୅ޙظʣ ✤ ֵ໋ظʢ2010೥୅ʣ ✤ ࠞ໎ΛۃΊΔݱ୅ ݄ͷىݯͷݚڀ࢙

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.) 221 (2012) 296–299 297 “Hit-and-Run” িಥʁ [Reufer et al., Icarus, 2012] uggests that this issue can be resolved if Theia ble to that of the proto-Earth. In this case, both forming disk are a roughly even mixture of the a. (This scenario relies on the angular momen- oon system later decreasing via an evection Sun (C ´ uk and Stewart, 2012).) umber of terrestrial planet formation simula- ate the statistical likelihood that Theia’s mass he proto-Earth. To do this, we simply look at mass ratios for Earth analogs struck by Theia lations. This distribution is shown in Fig. 17, arameter c, which is the ratio of Theia’s mass ss of Theia and the proto-Earth at the time of Earth and Moon evenly enough, Canup (2012) t have had cJ 0:4. In Fig. 17, we see that such und in any of our simulations. Out of the 104 ated in our collisions, the largest recorded c 7% of our Earth analogs experienced impacts mpacts with cJ 0:4 must be exceedingly rare, parably massed Theia and proto-Earth is a very result agrees with Jacobson and Morbidelli nd that major mergers between protoplanets are rare. arable masses for Theia and the proto-Earth, 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൑໌ ඞཁͳ଎౓

(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 distrib the obliquity range distribution which and Kokubo & Id K–S probabilities o accretion models, r spin anisotropy par Figure 3. Left: average spin angular velocity of all planets formed in the 50 runs of the realistic (circle) and pe mass M with mass bin of 0.1 M⊕ . The error bars indicate 1σ and the dotted line shows ωcr. Right: normaliz 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] k (table S1). The results imply a more narrow nge for potential Moon-formation events for pact scenarios with less angular momentum. creasing the total angular momentum by add- g spin to the impactors generated successful ks from the slower-spinning planets. Because gular momentum is carried away with debris m these erosive giant impacts, the spin period the planet decreases. Thus, the spin state of rth is not required to be near fission before or er the Moon-forming impact in our scenario r 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. g. 1. Formation of the nar disk from Earth’s antle. Example impact a 0.05ME impactor at km s−1 and b = −0.3 to a 1.05ME Earth spin- ng with a period of 2.3 urs (‡ in Table 1). Gray cles denote the Roche dius. (A to F) View of H particles in the lower misphere looking down e counterclockwise spin s, where colors denote e silicate mantles and n cores of the Earth d the impactor. The disk dominated by material ginating from Earth’s antle near the impact e (fig. S1 and movie S1). Lower hemisphere view h particle colors de- ting the planet (blue), mosphere (yellow), and k (green). (H) Density the equatorial plane of disk and planet, which stably stratified. 2012 VOL 338 SCIENCE www.sciencemag.org on November 25, 2012 www.sciencemag.org Downloaded from “Fission-like” িಥʁ িಥഁյͷޮՌ΋ߟྀ͢Δͱ ݪ࢝஍ٿΛߴ଎ճసͰ͖ͳ͍ [Ćuk & Stewart, Science, 2012] ඞཁͳ ճస଎౓ ׬શ߹ମ ݱ࣮త߹ମ

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 ulation blique, 4 km een an et with ble 1, es with ure in r, with mpera- articles sional plotted. hours, shown . After e plan- erged, Their to the merged a bar- al arms apped persed taining whose n dif- of the s than e near colli- target ibuted ortion- e final sk’s dfT ry ap- stance onal differ- isk and final produced by A) g = 0.3 iangles) and REPORTS on November 25, 2012 www.sciencemag.org Downloaded from “Twins” িಥʁ [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 244 129 136 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

(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] ݄ܗ੒Ͱຬͨ͢΂͖৚݅ (8) W ಉҐମൺ͕͔ͭͯ஍ٿͱҰக [Touboul et al., 2015]

s can be found in the Methods). We calculate the the feeding zones of the impactor and the planet are ame distribution, using a two-group Kolmogorov– babilities shown in the plots and in Table 1). In 3 out ding zones contributing to the Moon and those con- anet 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 ibution of planetesimals composing the planet and the where the origins of the planetesimals composing the mpactor (blue) areconsistent with being sampled from the tion for the expected typical 20% contribution of planetary rming impacts (Kolmogorov–Smirnov test probability ere 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 ݪ࢝஍ٿ ≒ িಥఱମʁ [Mastrobuono-Battisti et al., Nature, 2015] netesimals rather than 1000. The final four cases (EEJS 9- also had 2000 planetesimals but had eJ ¼ 0:07 and eS ¼ 0:08. ES (‘‘Jupiter and Saturn in RESonance”). Jupiter and Saturn re placed in their mutual 3:2 mean motion resonance, follow- directly from simulations of their evolution in the gaseous ar Nebula (Morbidelli et al., 2007): aJ ¼ 5:43 AU; aS ¼ 0 AU; eJ ¼ 0:005, and eS ¼ 0:01, with a mutual inclination 0.2°. ESECC (‘‘Jupiter and Saturn in RESonance on ECCentric its”). As for JSRES but with eJ ¼ eS ¼ 0:03. e EJS and EEJS simulations assume that Jupiter and Saturn ot undergo any migration. The EEJS simulations are more onsistent than the EJS simulations, because scattering of ant planetesimals and embryos tends to decrease the eccen- es and semimajor axes of Jupiter and Saturn (e.g., Chambers, . Thus, to end up on their current orbits, Jupiter and Saturn d have had to form on more eccentric and slightly more dis- orbits. The CJS, JSRES and JSRESECC simulations all follow the Nice model and assume that Jupiter and Saturn’s orbits ed significantly after their formation, with Saturn migrating ard and Jupiter inward (Tsiganis et al., 2005). If migration of ant planets is really associated with the late heavy bom- ment (Gomes et al., 2005; Strom et al., 2005), then at least of the migration of Jupiter and Saturn must have occurred well after the completion of the terrestrial planet formation ss. Raymond et al. (2004, 2006), using data for primitive meteorites 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 Fig. 2.—Snapshots of the system on the a-e (left) and a-i (right) planes at t ¼ 0, 1 are proportional to the physical sizes of the planets. KOKUBO, KOMI 1134 [Kokubo et al., ApJ, 2006] ͦ΋ͦ΋ݪ࢝஍ٿͱিಥఱମ͸ಉ͡ࡐྉͰܗ੒ ॳظ৚͕݅ۃΊͯዞҙతʢඪ४γφϦΦͰ͸ͳ͍ʣ ݁Ռ͸ॳظ৚݅Λ൓өͨࣗ͠વͳؼ݁ʹ͗͢ͳ͍

௒ߴΤωϧΪʔিಥγφϦΦ ஍ٿͷϚϯτϧ͸ G.I. Ͱ͍ͬͨΜશͯৠൃͨ͠ʂʁ [Wang & Jacobson, Nature, 2016]

ෳ਺ճিಥγφϦΦ 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 dieren 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 dierent styles of markers represent dierent 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 im 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 dierence 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. Fi th m co an o th in an m h F ro g er d th p H p m im m re a [Rufu et al., Nature Geo., 2017] 20 ճఔ౓ͷিಥͰܗ੒͞Εͨ moonlets ͷूੵ িಥதͷ previous moonlets ͷ҆ఆੑʹ͍ͭͯ͸ෆ໌

࠷৽ͷݚڀ݁Ռ

d e - e a - n # d 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. R h A B C Fig. 3. A schematic diagram showing possible paths of materials ejected at a certain height. Only a fraction of materials goes to the orbit (shaded region) from which the Moon was formed. The 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. 2 e n e n n- s, ϚάϚΦʔγϟϯ஍ٿ΁ͷ G.I. ஍ٿͷϚάϚΦʔγϟϯ͕બ୒తʹ݄ԁ൫ʹ෼഑ʂ [Hosono et al., Nature Geo., 2019]

Earth 9 and a fully ory as ularly ocess lease, antial mme- of the of the ght to tures, rial is re are ) then high e and quili- e may t high icant: e fate ory of much o the after mally ming rlier). xpect p that ature, ondi- 11. been mpor- e was wever, phere ocean 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 ஍ٿͱ݄ԁ൫ͷؒͷ෺࣭ࠞ߹ [Stevenson, Nature, 2008] [Pahlevan & Stevenson, EPSL, 2007] ݪ࢝஍ٿͱݪ݄࢝ԁ൫ͷؒͰ ௕࣌ؒ෺࣭Λࠞ߹͢Ε͹Α͍

Canup (2004) Kokubo et al. (2000) Giant Impactʢ໿1೔ʣ ݄ͷܗ੒ʢ໿1݄ʣ ʁ Pahlevan & Stevenson (2007) ݄ԁ൫ͷྫྷ٫ਐԽ ʢ50೥ʙ100೥ʣ ຊདྷ͸݄ԁ൫ͷਐԽաఔΛ௥͏ඞཁ͕͋Δ͕ ௕࣌ؒͷܭࢉΛߦ͏͜ͱ͕Ͱ͖ͣෆՄೳͩͬͨ ݄ԁ൫ͷਐԽաఔΛܭࢉ [Sasaki & Hosono, 2018, 2020 submitted]

✤ ᴈ໌ظʢلݩલʙ1960೥୅ʣ ✤ ։Խظʢ1970೥୅ʙ1980೥୅ʣ ✤ ԁख़ظʢ1990೥୅ʙ2000೥୅લظʣ ✤ ࠞཚظʢ2000೥୅ޙظʣ ✤ ֵ໋ظʢ2010೥୅ʣ ✤ ࠞ໎ΛۃΊΔݱ୅ ݄ͷىݯͷݚڀ࢙ → ޫ͕ݟ͖͑ͯͨ…͔΋ʁ