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The Origin of the Moon
佐々木 貴教
月
・人類が降り立った唯一の地球外天体
・地球からの距離:38万4400km
・半径:1737km(地球の0.27倍)
・質量:7.3 1022kg(地球の0.012倍)
・地球に常に同じ面を向けている
・地球と比べてコア(Fe)が小さい
表 ...
月の起源の研究史
• 黎明期(紀元前∼1960年代)
• 開化期(1970年代∼1980年代)
• 円熟期(1990年代∼2000年代前期)
• 混乱期(2000年代後期)
• 革命期(2010年代)
• 混迷を極める現代
黎明期
• 古事記

イザナギノミコトが右目を洗い月読命が誕生(左目が天照大神)
• 旧約聖書

創造主が4日目に天の太陽と月と星を誕生させた
• エジプト

創造主ラーの左目が月となった(右目が太陽)
• 中国

創造神盤古の右目が月となった(左目が...
XIII. On the Precession of a Viscous Spheroid, and on the remote History of the Earth.
By G. H. Darwin, M.A., Fellow of Tr...
月の起源説
捕獲説
分裂説
双子説
原始地球が高速回転によりふくらみ,
その一部がちぎれて月が誕生
地球軌道付近での微惑星の集積により,
地球とは独立に月が形成
地球とは別の場所で作られた月が,
地球の近くを通ったときに捕らえられた
開化期
Lunar Rock by Apollo 11
Constraints of Moon Formation
(1) 地球ー月系の角運動量(Ltotal が保存)
(2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones & P...
月の起源説
捕獲説
分裂説
双子説
原始地球が高速回転によりふくらみ,
その一部がちぎれて月が誕生
地球軌道付近での微惑星の集積により,
地球とは独立に月が形成
地球とは別の場所で作られた月が,
地球の近くを通ったときに捕らえられた
高速回転が...
[Schreiber & Anderson, Science, 1970]
月はチーズでできている?
ジャイアントインパクト説
[Hartman & Davis, Icarus, 1975]
[Cameron & Ward, LPI Conference, 1976]
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!...
Constraints of Moon Formation
(1) 地球ー月系の角運動量(Ltotal が保存)
(2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones & P...
円熟期
太陽系形成標準理論(林モデル)
©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 co...
ORIGIN OF MOON AND SINGLE IMPACT HYPOTHESIS 129
[Cameron, Icarus, 1997]
Giant Impact by SPH
Roche radius, whereas Fig. 3 is a rather extended disk case (run 9).
The extension of a disk is indicated by Jdisk/Mdisk, ...
Moon Formation by N-body
N = 1,000
~3hours@MacPro
数ヶ月∼数年で、ひとつの月ができる
Giant Impact by SPH
[Canup & Asphaug, Nature, 2001]
1. Hf-W Chronometry
 Hf →  W(半減期 ∼ 9My)182 182
・Hf:親石性 W:親鉄性
・Hf, Wともに難揮発性元素
metal/silicate分離
年代を示す時計!
t =τでコア形成による平衡化
が起き...
Giant Impact による平衡化プロセス
3. Equilibration by G.I.
Giant Impact !
全球的なマグマオーシャン
(target + impactor)のマントル
と impactor のコアの mixt...
l
-
-
n
-
n
r
e
-
r
.
e
n
.
d
n
t
e
f
-
e
,
,
-
t
l
e
a
o
o
t
W
l
-
-
,
for Ste Marguerite is our preferred approximation ...
“CAI 形成から約3,000万年後
原始地球に火星サイズの原始惑星が斜め衝突し
飛び散ったマントル物質が周惑星円盤を形成し
それらが約数年かけて集積し
月が誕生した”
は遠いけど,まだだれも知らないことを自分が最初に知ることの喜びやわくわ
れが好きだから,研究を続けているのだと思います。“国語” の教科書に載る
混乱期
Constraints of Moon Formation
(1) 地球ー月系の角運動量(Ltotal が保存)
(2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones & P...
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
quil...
ophysical Journal, 760:83 (18pp), 2012 November 20 Salmon & Canup
Table 3
Hybrid Simulation Parameters
Ld /Md Ld Md Min Mo...
Constraints of Moon Formation
(1) 地球ー月系の角運動量(Ltotal が保存)
(2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones & P...
lunar material
Junjun Zhang1
*, Nicolas Dauphas1
, Andrew M. Davis1
, Ingo Leya2
and Alexei Fedkin1
A giant impact between...
Constraints of Moon Formation
(1) 地球ー月系の角運動量(Ltotal が保存)
(2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones & P...
and vapor, which requires a solution mod
coefficients for trace elements at the
(T=2500 K–3500 K). At present, no s
Fig. 1....
Constraints of Moon Formation
(1) 地球ー月系の角運動量(Ltotal が保存)
(2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones & P...
lunar glasses are given in Ta
of all the bulk lunar sam
(±2rSD) which is identical
et al. (2010) for bulk
À0.29 ± 0.08 (±2...
Constraints of Moon Formation
(1) 地球ー月系の角運動量(Ltotal が保存)
(2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones & P...
Hf-W Chronometry の弱点
[Sasaki & Abe, PPV, 2005]
どう考えても Hf-W 系の完全平衡化は実現できない
T. SASAKI AND Y. ABE: IMPERFECT EQUILIBRATION OF HF-W SYSTEM 1041
ge of the last giant impact as a function of the resetti...
2.3. Initial Conditions
We follow Canup & Asphaug (2001) and Canup (2004) for the
orbital parameters of the impactor for w...
革命期
Ćuk  Stewart, Science (2012)
-200
-150
-100
-50
0
50
100
150
200
0 20 40 60 80 100
Resonantangle(°)
Time (kyr)
D
2.5
3
3.5...
Constraints of Moon Formation
(1) 地球ー月系の角運動量(Ltotal が保存)
(2) 地球より低密度(コアが小さい)[Hood  Zuber, 2000]
(3) 揮発性元素が強く枯渇 [Jones  Pal...
Collision Scenarios
w/o angular momentum constraints
formed from a magma ocean (5), implying an
intensely energetic fiery s...
Fig. 1a. Five snapshots from the 30° impact angle and 1.30 vesc impact velocity case
(cC06) showing cuts through the impac...
Moon-formation events for
th less angular momentum.
angular momentum by add-
actors generated successful
er-spinning plane...
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
ffiffiffiffiffiffiffiffiffi...
standard
“Fission-like” “Twins”
[Simulations by Miki Nakajima]
混迷を極める現代
colors. In the canonical scenario, the impactor grazes around the target’s mantle
and is deformed. Due to the low impact v...
(Agnor et al. 1999) is necessary after the giant impact stage.
3.3. Statistics of Spin
In 50 runs of the realistic and per...
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
ffiffiffiffiffiffiffiffiffi...
s can be found in the Methods). We calculate the
the feeding zones of the impactor and the planet are
ame distribution, us...
330,
om-
the
metal
s, we
d by
well
thin
orp-
the
or is
the
ossly
sent
very
his is
unar
pac-
µ182W
–10 0 10 20 30 40 50
688...
the deformed
o the Moon.
ocean can be
element parti-
nciples of the
rimental data
ne and ultra-
magma ocean
value of Mg#
e...
acquire larger late-accreted masses than those in the Grand Tack simu-
lations (see Fig. 1), because the planetesimal popu...
~1% come back to strike the Moon within 400
million years (My) (Fig. 1) (8). Because the Moon
only has ~25 ancient (Pre-Ne...
結局
どうしたらいいの?
• 各 Giant Impact モデルの妥当性がわからない

→ 多様な Giant Impact のより詳細な計算を行う
• 地球と月の化学組成が一致しすぎている?

→ 新たな月の石を取得・サンプルバイアスを除く
• 全ての化学データを満...
h the disk in so short a time
e have no evidence yet that
erior is substantially differ-
th’s near surface in oxygen
on di...
o
i T
k ab
W WPH
i!!
(c) Tetsuya Kawase
New Perspectives by WPH
• 各 Giant Impact モデルの妥当性がわからない

→ 多様な Giant Impact のより詳細な計算を行う
• 地球と月の化学組成が一致しすぎている?

→ 新たな月の石を取得・サンプルバイアスを除く
• 全ての化学データを満...
Moon formation sasaki
Moon formation sasaki
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The Origin of the Moon

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Moon formation sasaki

  1. 1. The Origin of the Moon 佐々木 貴教
  2. 2. 月 ・人類が降り立った唯一の地球外天体 ・地球からの距離:38万4400km ・半径:1737km(地球の0.27倍) ・質量:7.3 1022kg(地球の0.012倍) ・地球に常に同じ面を向けている ・地球と比べてコア(Fe)が小さい 表 裏 •  ik d T   T (Fe) hT 0
  3. 3. 月の起源の研究史 • 黎明期(紀元前∼1960年代) • 開化期(1970年代∼1980年代) • 円熟期(1990年代∼2000年代前期) • 混乱期(2000年代後期) • 革命期(2010年代) • 混迷を極める現代
  4. 4. 黎明期
  5. 5. • 古事記
 イザナギノミコトが右目を洗い月読命が誕生(左目が天照大神) • 旧約聖書
 創造主が4日目に天の太陽と月と星を誕生させた • エジプト
 創造主ラーの左目が月となった(右目が太陽) • 中国
 創造神盤古の右目が月となった(左目が太陽) 神話における月の起源
  6. 6. 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” による月形成シナリオ
  7. 7. 月の起源説 捕獲説 分裂説 双子説 原始地球が高速回転によりふくらみ, その一部がちぎれて月が誕生 地球軌道付近での微惑星の集積により, 地球とは独立に月が形成 地球とは別の場所で作られた月が, 地球の近くを通ったときに捕らえられた
  8. 8. 開化期
  9. 9. Lunar Rock by Apollo 11
  10. 10. Constraints of Moon Formation (1) 地球ー月系の角運動量(Ltotal が保存) (2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000] (3) 揮発性元素が強く枯渇 [Jones & Palme, 2000] (4) 表面が大規模溶融を経験 [Warren, 1985] (5) 酸素同位体比が地球とほぼ一致 [Wiechert et al., 2001] ng that similar proportions of material rom the silicate portions of the proto- and Theia. Only if the proto-Earth and ⌬17 O values were identical to within would it be possible that the average value of the Moon plots within 0.005‰ terrestrial fractionation line. me computer models assume a larger r the impactor, i.e., a mass ratio of 7:3 n the proto-Earth and Theia (2, 13). ese models assume that the Earth had chieved about two-thirds of its final fter the Giant Impact, because a larger Earth would produce greater angular ntum for the Earth-Moon system than bserved. Models assuming that the Earth had reached just 66% of its mass he Giant Impact (2, 3) and identical of the Moon and Earth require that late ng material came from the same res- 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 ⌬17 O 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 ⌬17 O among large planetary embryos and Comparison between conventional and ser 16 O, 17 O, and 18 O measurements of amples. ⌬17 O gives displacement from Fig. 3. The ⌬17 O 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]
  11. 11. 月の起源説 捕獲説 分裂説 双子説 原始地球が高速回転によりふくらみ, その一部がちぎれて月が誕生 地球軌道付近での微惑星の集積により, 地球とは独立に月が形成 地球とは別の場所で作られた月が, 地球の近くを通ったときに捕らえられた 高速回転が難しい & 角運動量が大きすぎる 月の内部構造が説明できない & 月を残せない 捕獲確率が低い & 化学的制約を満たせない
  12. 12. [Schreiber & Anderson, Science, 1970] 月はチーズでできている?
  13. 13. ジャイアントインパクト説 [Hartman & Davis, Icarus, 1975] [Cameron & Ward, LPI Conference, 1976]
  14. 14. 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 = 107erg/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 = 107erg/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. ,,:iii:i~iiiiii!iii!i,li!~iliiiiiii~!!!iiii:~iii~:i,: T: 9,q0986 ( -2.0. 2.0. 2.0, 2.01 T: 11.03161 /,,l--¢/ t~ FIG. 2. Snapshots of run 1. (u~ = 0 km/sec; rmi,= 0.77Rearth; Eint = 1 plotted at particle locations. The velocity has been normalized to its m Time and coordinates of the four corners of the plotted field are given in 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 comple equation of mot 4.2. Energy Con The variation given by thermo du d--i = ENZ, SLATTERY, AND CAMERON 2.0. 2.01 T: 8.83375 ( -2.0. 2.0. -2,0. 2.0] .0, 2.01 T: 11.03161 I -~.0. ~,.0, -q,0. ~.0] /,,l--¢/ t~ (u~ = 0 km/sec; rmi,= 0.77Rearth; Eint = 107erg/g). Velocity vectors are The velocity has been normalized to its maximum value in each frame. our corners of the plotted field are given in the upper line (in units defined n 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 SPH(初) [Benz et al., Icarus, 1986]
  15. 15. Constraints of Moon Formation (1) 地球ー月系の角運動量(Ltotal が保存) (2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000] (3) 揮発性元素が強く枯渇 [Jones & Palme, 2000] (4) 表面が大規模溶融を経験 [Warren, 1985] (5) 酸素同位体比が地球とほぼ一致 [Wiechert et al., 2001] Giant Impact によって形成される周惑星円盤の ~80% が Impactor 起源のマントル物質である
  16. 16. 円熟期
  17. 17. 太陽系形成標準理論(林モデル) ©Newton Press[Hayashi et al., 1985]
  18. 18. 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 ass 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 aFIG. 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 sepa factor is 6. In the final frame, the filled circles represent protoplanets region, if t [Kokubo & Ida, Icarus, 1998] 暴走成長&寡占成長
  19. 19. ORIGIN OF MOON AND SINGLE IMPACT HYPOTHESIS 129 [Cameron, Icarus, 1997] Giant Impact by SPH
  20. 20. 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 (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 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] Moon Formation by N-body
  21. 21. Moon Formation by N-body N = 1,000 ~3hours@MacPro 数ヶ月∼数年で、ひとつの月ができる
  22. 22. Giant Impact by SPH [Canup & Asphaug, Nature, 2001]
  23. 23. 1. Hf-W Chronometry  Hf →  W(半減期 ∼ 9My)182 182 ・Hf:親石性 W:親鉄性 ・Hf, Wともに難揮発性元素 metal/silicate分離 年代を示す時計! t =τでコア形成による平衡化 が起きたとすると ε(t) = f (τ) ※初期比は始源的なコンドライトから決定 ε(t) = 182 W /184 W( ) 182 W /184 W( )CHUR −1         ×104 ε(t) が観測可能量なのでコア 形成年代τが求まる
  24. 24. Giant Impact による平衡化プロセス 3. Equilibration by G.I. Giant Impact ! 全球的なマグマオーシャン (target + impactor)のマントル と impactor のコアの mixture 現在の地球 マントルと impactor のメタルとの間で平衡化が起こり、 コア形成の際に過剰  Wがコアに持ち去られる182 impactorのメタル粒 によってマントルが平衡化
  25. 25. l - - n - n r e - r . e n . d n t e f - e , , - t l e a o o t W l - - , for Ste Marguerite is our preferred approximation for the initial 182 Hf/180 Hf 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 180 Hf/183 W 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 182 Hf 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 182 W/183 W value in the Earth relative to chondrites ðD1w ¼ ½1wðBSEÞ 2 1wðCHURފ for a range of mean times of core formation (given by T 0 2 kTlcf; where T 0 is the age of the Solar System and kTlcf 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 形成から約3,000万年後に last giant impact = 月形成
  26. 26. “CAI 形成から約3,000万年後 原始地球に火星サイズの原始惑星が斜め衝突し 飛び散ったマントル物質が周惑星円盤を形成し それらが約数年かけて集積し 月が誕生した”
  27. 27. は遠いけど,まだだれも知らないことを自分が最初に知ることの喜びやわくわ れが好きだから,研究を続けているのだと思います。“国語” の教科書に載る
  28. 28. 混乱期
  29. 29. Constraints of Moon Formation (1) 地球ー月系の角運動量(Ltotal が保存) (2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000] (3) 揮発性元素が強く枯渇 [Jones & Palme, 2000] (4) 表面が大規模溶融を経験 [Warren, 1985] (5) 酸素同位体比が地球とほぼ一致 [Wiechert et al., 2001] Giant Impact によって形成される周惑星円盤の ~80% が Impactor 起源のマントル物質である
  30. 30. 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 high icant: e fate ory of much o the after mally ming rlier). xpect p that ature, ondi- 11 . been mpor- ewas 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 Mixing in the Magma Disk [Stevenson, Nature, 2008] [Pahlevan & Stevenson, EPSL, 2007] 原始地球と原始月円盤の間で 数100年間 mixing すればよい
  31. 31. ophysical 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 mulation parameters with a Roche-interior fluid disk and Roche- 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] 粘性モデル Roche 半径以内は 流体的に振る舞う ・固体への凝縮 ・物質の輸送 N 体計算 Roche 半径以遠は 固体的に振る舞う ・衝突合体成長 月の形成時間 ~1,000年
  32. 32. Constraints of Moon Formation (1) 地球ー月系の角運動量(Ltotal が保存) (2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000] (3) 揮発性元素が強く枯渇 [Jones & Palme, 2000] (4) 表面が大規模溶融を経験 [Warren, 1985] (5) 酸素同位体比が地球とほぼ一致 [Wiechert et al., 2001]
  33. 33. 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 50 Ti/47 Ti 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 50 Ti/47 Ti 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 50 Ti, 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] magma of the –142 Nd dicting s were e used n years ponent nly by lunar ms of e data erived g that 60 Myr m–Nd estrial n with ns the ion of lunar erived in the e giant en iso- REEP- ), rare nd five fold to ed the ratios. e con- fect on y short 0.01%) 56 and larger given e have ee with mples3 . cates that this anomaly might be due entirely to cosmogenic 182 W. Kleine et al.3 reported elevated e182 W < 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 182 W in this separate. The calculated cosmogenic 182 W 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 | e182 W 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 182 W (see the text for details). [Touboul et al., Nature, 2007] 難揮発性元素の同位体も一致
  34. 34. Constraints of Moon Formation (1) 地球ー月系の角運動量(Ltotal が保存) (2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000] (3) 揮発性元素が強く枯渇 [Jones & Palme, 2000] (4) 表面が大規模溶融を経験 [Warren, 1985] (5) 酸素同位体比が地球とほぼ一致 [Wiechert et al., 2001] (6) 難揮発性元素の同位体比が地球とほぼ一致 [Touboul et al., 2007] すぐに凝結してしまう元素は十分に mixing できない
  35. 35. and vapor, which requires a solution mod coefficients for trace elements at the (T=2500 K–3500 K). At present, no s 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 logP(bars) Fe/Fe+Mg Fig. 2. Chemical structure of the silicate vapor at rainout. The parcel represents the composition of t suspended in a fayalitic vapor) and shifts with altitu as the droplets separate via rainout. The lower convection from the underlying magma ocean composition. This calculation assumes that 40% o every three-fold decrease in pressure (fL =0.4). Thi the top of the atmosphere – a two-fold enhancemen enhancement is comparable to a widely postulated 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 難揮発性元素についても mixing の可能性を提案
  36. 36. Constraints of Moon Formation (1) 地球ー月系の角運動量(Ltotal が保存) (2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000] (3) 揮発性元素が強く枯渇 [Jones & Palme, 2000] (4) 表面が大規模溶融を経験 [Warren, 1985] (5) 酸素同位体比が地球とほぼ一致 [Wiechert et al., 2001] (6) 難揮発性元素の同位体比が地球とほぼ一致 [Touboul et al., 2007]
  37. 37. lunar glasses are given in Ta of all the bulk lunar sam (±2rSD) which is identical et al. (2010) for bulk À0.29 ± 0.08 (±2rSD). The alts (d30 Si = À0.31 ± 0.07, (2007) and Fitoussi et al.’s ( of d30 Si = À0.30 ± 0.05& ( narrow observed range of S the variety of samples obser lunar lithologies analysed within error (2rSD): d30 d30 SiHigh-Ti basalt = À0.32 ± 0.05; d30 SiHighland rocks = À Fig. 2. d29 Si versus d30 Si 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 d30 Si val and bulk silicate Earth samples The lunar breccia from Chakra[Armytage et al., GCA, 2012] Si 同位体比も一致
  38. 38. Constraints of Moon Formation (1) 地球ー月系の角運動量(Ltotal が保存) (2) 地球より低密度(コアが小さい)[Hood & Zuber, 2000] (3) 揮発性元素が強く枯渇 [Jones & Palme, 2000] (4) 表面が大規模溶融を経験 [Warren, 1985] (5) 酸素同位体比が地球とほぼ一致 [Wiechert et al., 2001] (6) 難揮発性元素の同位体比が地球とほぼ一致 [Touboul et al., 2007] Si 同位体分配には圧力(=サイズ)依存性がある (7) Si 同位体比が地球とほぼ一致 [Armytage et al., 2012]
  39. 39. Hf-W Chronometry の弱点 [Sasaki & Abe, PPV, 2005] どう考えても Hf-W 系の完全平衡化は実現できない
  40. 40. T. SASAKI AND Y. ABE: IMPERFECT EQUILIBRATION OF HF-W SYSTEM 1041 ge of the last giant impact as a function of the resetting ratio nt impact, fitting to the observational data (ϵ = 2) from Earth he number of giant impacts is assumed to be five. The initial = 10 at t = 10. The formation age of the Earth for perfect resetting ratio = 1) is about 30 Myr, in agreement with a udy (Yin et al., 2002). ate 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 では 月形成の年代は決まらない
  41. 41. 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, MAKINO1182 Vol. 638 [Wada et al., ApJ, 2005] 高解像度格子法による G.I. 計算 蒸発した原始月円盤内に衝撃波が立ちまくって 円盤が角運動量を失い数日で全て地球に落下!?
  42. 42. 革命期
  43. 43. Ćuk Stewart, Science (2012) -200 -150 -100 -50 0 50 100 150 200 0 20 40 60 80 100 Resonantangle(°) Time (kyr) D 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Earthísspinperiod(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-majoraxis(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+Moonangularmomentum 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+Moonangularmomentum 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 地球-月-太陽の間の永年共鳴で系の角運動量が減少
  44. 44. Constraints of Moon Formation (1) 地球ー月系の角運動量(Ltotal が保存) (2) 地球より低密度(コアが小さい)[Hood Zuber, 2000] (3) 揮発性元素が強く枯渇 [Jones Palme, 2000] (4) 表面が大規模溶融を経験 [Warren, 1985] (5) 酸素同位体比が地球とほぼ一致 [Wiechert et al., 2001] (6) 難揮発性元素の同位体比が地球とほぼ一致 [Touboul et al., 2007] (7) Si 同位体比が地球とほぼ一致 [Armytage et al., 2012]
  45. 45. Collision Scenarios w/o angular momentum constraints formed from a magma ocean (5), implying an intensely energetic fiery start at a time when heat-producing short-lived nuclides (26 Al and 60 Fe) 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 final mass, works with “hit and run” collision (14). (B) “Small” impactor, 2.5% of Earth’s final mass (1). (C) “Large” impactor, 45% of Earth’s final mass (2). (A) 質量比 10:1 で “Hit-and-Run” collision [Reufer et al., 2012] (B) 質量比 40:1 で “Fission-like” collision [Ćuk Stewart, 2012] (C) 質量比 1:1 で “Twins” collision [Canup, 2012] [Halliday, 2012]
  46. 46. 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” Collision [Reufer et al., Icarus, 2012]
  47. 47. 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 ower own spin note and arth disk erial th’s pact S1). view de- ue), and nsity e of hich 38 SCIENCE www.sciencemag.org onNovember25,2012www.sciencemag.orgDownloadedfrom “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]
  48. 48. 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 onNovember25,2012www.sciencemag.orgownloadedfrom “Twins” Collision larger impactors h are shown in Figs relative size of the is generally a clo tween the final dis some disks have gular momentum identical silicate co 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 are shown by horizontal lines for oxygen (solid), titanium (dotted), and chromium (dot-dashed), assuming a Mars-composition im 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. onNovember25,2012www.sciencemag.orgDownloadedfrom [Canup, Science, 2012]
  49. 49. standard “Fission-like” “Twins” [Simulations by Miki Nakajima]
  50. 50. 混迷を極める現代
  51. 51. 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” Collision? [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- te 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. rable 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 MÈ. 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 MÈ (solid line), m = 0.05–0.1 MÈ (dashed line), and m 0:1 MÈ (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 体計算で Giant Impacts の過程を追ったところ 衝突速度が必要な大きさに達しないことが判明
  52. 52. (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 d the obliquity distribution w and Kokubo K–S probabil accretion mod spin anisotrop Figure 3. Left: average spin angular velocity of all planets formed in the 50 runs of the realistic (circle) mass M with mass bin of 0.1 M⊕. The error bars indicate 1σ and the dotted line shows ωcr. Right: no 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 ntle. Example impact a 0.05ME impactor at km s−1 and b = −0.3 to a 1.05ME Earth spin- g 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 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 ntle near the impact (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 onNovember25,2012www.sciencemag.orgDownloadedfrom “Fission-like” Collision? 衝突破壊の効果も考慮すると 原始地球を高速回転できない[Ćuk Stewart, Science, 2012]
  53. 53. 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 aining whose n dif- of the s than e near colli- target ibuted ortion- e final k’s dfT ry ap- stance onal differ- isk and final produced by A) g = 0.3 iangles) and REPORTS onNovember25,2012www.sciencemag.orgDownloadedfrom “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 0.040.03 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 21 Ne to primordial 22 Ne, with steeper slopes indicating a higher proportion of primordial 22 Ne 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, 20 Ne/22 Ne ratios of 12.8860.06 are distinctly higher than the MORB source 20 Ne/22 Ne of #12.5 as constrained from continental well gases20 . b, Ne–Ar compositions of individual step crushes of the DICE 10 sample. 40 Ar is generated by radioactive decay of 40 K, and low 40 Ar/36 Ar 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 40 Ar/36 Ar ratio of 10,74563,080, corresponding to a mantle solar 20 Ne/22 Ne 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 30,000b 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,3 He/22 Neversus20 Ne/22 Ne; b, 3 He/36 Ar versus 40 Ar/36 Ar; and c, 22 Ne/36 Ar versus 40 Ar/36 Ar. The mantle source composition for 2PD43 (filled grey square in all panels) is based on the 40 Ar/36 Ar and 20 Ne/22 Ne 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 0.0720Ne/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 0.040.03 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 21 Ne to primordial 22 Ne, with steeper slopes indicating a higher proportion of primordial 22 Ne 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, 20 Ne/22 Ne ratios of 12.8860.06 are distinctly higher than the MORB source 20 Ne/22 Ne 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 30,000b 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,3 He/22 Neversus20 Ne/22 Ne RESEARCH LETTER contamination processes are ruled out as the reason for the lower 129 Xe/130 Xe 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 gasesandtherelativepartitioncoefficientsofthenoblegaseswithrespect 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 129 I decay and 136 *XePu is 136 Xe produced from 244 Pu fission. 129 I 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 129 Xe and 3 He 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 129 Xe/130 Xe 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 129 Xe/130 Xe 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 40 Ar/36 Ar ratio of 10,745. Note that given the curvature in Ar–Xe space, the 129 Xe/130 Xe in the Iceland mantle source is not particularly sensitive to the exact choice of the mantle 40 Ar/36 Ar ratio. LETTER RESEARCH [Mukhopadhyay, Nature, 2012] 地球深部の希ガス同位体不均一 地球深部まで melting していない
  54. 54. 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 NP = 123, NI = 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 NP = 128, NI = 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 here 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] 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 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 rd 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 hnai ’ 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 fai ¼ 0:79 Æ 0:15. The accretion timescale is hTacci ¼ 1:05 Æ 0:58ð 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, KOMI1134 [Kokubo et al., ApJ, 2006] そもそも原始地球と衝突天体は同じ材料で形成 初期条件が極めて恣意的(標準シナリオではない) 結果は初期条件を反映した自然な帰結にすぎない
  55. 55. 330, om- the metal s, we d by well thin orp- the or is the ossly sent very his is unar pac- µ182W –10 0 10 20 30 40 50 68815,396 68115,114 Average 68115,114 68815,394 Figure 1 | Values of m182 W 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 nces W 6 4.6 6 2.6 6 1.7 6 3.8 6 2.5 6 2.9 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 e182 W of the metals tends to be slightly lower10 , resulting in an overall decrease of the mean e182 W inferred from the lunar metals. Therefore, the higher pre-exposure e182 W 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 182 W 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 e182 W difference between the BSE and the Moon induced by the late veneer, and then we assess whether there is a resolvable 182 W 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 187 Os/188 Os value2 and Se–Te systematics19 . Mass balance considera- –4–3–2–10 0 1 2 ε180Hf ε182W 68115 12034 14310 14321 62235 14163 KREEP-rich samples ε182Wpre-exposure 68815 Figure 1 | Plot of e182 W versus e180 Hf determined for KREEP-rich samples. e182 W has been internally normalized to 186 W/184 W 5 0.92767: elsewhere this is referred to as e182 W (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 | e182 W 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) e182 W 5 10.27 6 0.03 (95% confidence 182 [Kruijer et al., Nature, 2015] わずかな W 同位体の差 G.I. 直後は完全に identical・その後の天体衝突で変化
  56. 56. the deformed o the Moon. ocean can be element parti- nciples of the rimental data ne and ultra- magma ocean value of Mg# ed by a broad 920–80%) or e of chemical n the process ct 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. m/s) The temperature he relation [1] in mperature at the e summarized in olume, q: a non- (q 9 1 for solids, [Karato, Proc. Jpn.Acad., 2014] Giant Impact on Magma Ocean Magma Ocean 状態の原始地球への Giant Impact アイデアの提案だけで数値計算等は行われていない
  57. 57. 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. Thismas contributions from the era known as the Late Heavy Bo Current mass estimates for this very late (approximately condensation) accretion are21 1023 M›, which we adde accretedmassesofoursynthetic Earth-like planets, butit for about 2% of the chondritic mass and therefore doe important part in our analysis of the correlation. The chondritic mass can only be identical to the late-a or to the Late Veneer mass if the Moon-forming event s the HSEs from Earth’s mantle or was the last episode o Earth’s core, respectively (as is traditionally assumed). H conditions are not necessarily true. Consider that som colliding with Earth after the Moon-forming event mig differentiated, so that their HSEs were contained in their of these cores had merged with Earth’s core22 , then the mass would clearly be larger than the chondritic mass, would be no HSE record of this fraction of the proje Earth’s mantle. Additionally, in this case, given thatiron ( HSEs) would have beensimultaneously added to Earth’s m core, the chondritic mass would be larger than the Late which is geochemically defined as the mass accreted to E core has stopped growing. In fact, as explained in detail in the Methods and in E Figs3and4,itisunlikelythatmorethan50%ofaprojectile reaches Earth’s core, otherwise geochemical models cann the tungsten isotope composition of Earth’s mantle23 . Mor late-accreted mass, delivered in only a few objects so as relative HSE abundances of Earth and Moon12 , would hav able isotopic signature on Earth relative to the Moon24,2 when considering these more complex possibilities, geoc ence constrains the late-accreted mass probably not to ex (see Methods). For these reasons, we first make the usual assumption accreted mass and the HSE-derived chondritic mass are 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 1005020 3015 15070 10–4 0.001 0.01 0.1 1 Relativelateaccretedmass 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? 地球マントルの HSE 量 を説明するためには、 最後の G.I. は CAI 形成 後 ~100My であるべき 地球マントルの HSE 過剰  → 地球形成後の late veneer ※ Grand Tack Model を仮定した場合の年代である
  58. 58. ~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 40 Ar-39 Ar 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 40 Ar-39 Ar shock degassing ages for asteroidal meteorites. (A) The combined 40 Ar-39 Ar age distribution, in blue, was created by assuming that leftover planetesimals and giant RESEARCH | REPORTS [Bottke et al., Science, 2015] ,PLANETARYSCIENCEINSTITUTE By Eric Hand I t 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 radioactive “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. onApril16,2015www.sciencemag.orgDownloadedfrom (c) Science Age of the Moon Formation? Giant Impact Ejecta が高速で小惑星に衝突・年代を リセットした証拠が隕石に刻まれているはず ※ サンプルが少なすぎる&モデルがシンプルすぎる
  59. 59. 結局 どうしたらいいの?
  60. 60. • 各 Giant Impact モデルの妥当性がわからない
 → 多様な Giant Impact のより詳細な計算を行う • 地球と月の化学組成が一致しすぎている?
 → 新たな月の石を取得・サンプルバイアスを除く • 全ての化学データを満たす解が存在しない
 → いっそ Giant Impact 説から離れて考えてみる • 月形成年代をどうやって決める?
 → 月の酸素同位体比を持つ欠片@隕石を探す
  61. 61. h the disk in so short a time e have no evidence yet that erior is substantially differ- th’s near surface in oxygen on directly from Earth. mplanetary disk that is de- from Earth, it seems nec- ve an impact that violates r-momentum constraint. cientists have suggested ities. One is to hit an Earth dy close to fission with a projectile. That could be s impact-triggered fission. sibility is for the collision etween two ”sub-Earths,” each about half an Earth 2 presents hydrodynamic f three kinds of giant im- the first—the standard t of a smaller body collid- rth—satisfies the angular- constraint.9 But the other arios show how the mate- make the Moon can come Earth; for them to be can- must find a way of getting angular momentum. One doing so, proposed by and Sarah Stewart two is an evection resonance, he precession rate of the it matches Earth’s mean ut the Sun (see box 3). Al- resonance is well known, on to account for a loss of a b c Standard Fast-spinning Earth Sub-Earth TIME Figure 2. Hydrodynamic snapshots of giant impacts that might have been. In each of three cases, a projectile, whose mantle and core are shown in orange and white, respectively, obliquely hits Earth, whose mantle and core are shown in green and gray. Earth’s North Pole points out of the page. The aftermath of each collision, projected onto the equatorial plane, is pictured from left to right, with several hours elapsing between each snapshot. (a) In the standard scenario,9 the angular momentum of the impact equals that of the current Earth–Moon system, but the material that ends up in orbit is mainly projectile orange, a result at odds with the nearly identical isotopic ratios of oxygen, silicon, tungsten, and titanium observed in the real Earth and Moon. In the two other cases, (b) a small projectile smashes into a rapidly rotating planet,10 and (c) two bodies collide, each with half of Earth’s mass.13 In all three cases, very little metallic iron ends up in orbit, a result borne out by observation. But only in [Nakajima Stevenson, 2014] d e i- e a a- proto-Earth proto-Earth impactor impactor magma ocean vapor jet (a) (b) Fig. 4. Schematic drawing of processes of ejection of materials 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 re n he n n- s, terrestrial magma ocean origin of the Moon 101 [Karato, 2014] 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 0:64rE, respectively. Note that no significant differences in the results for smaller impactors (e.g., 0:1 MÈ) were found in our simulations. The initial orbits of the impactor are assumed to be parabolic, and the angular momentum is 0.86Lgraz, where Lgraz is the angular momentum for a grazing collision (Canup Asphaug 2001). Initially, the impactor is located at 4:0rE from the proto-Earth. 3. RESULTS 3.1. Disk Evolution and the Predicted Lunar Mass Figure 1 shows a typical time evolution of the giant impact with EOS-1 (model A). This model corresponds to the ‘‘late’’ impact model in Canup Asphaug (2001). After the first impact (t ’ 1 hr), the disrupted impactor is reaccumulated to form a clump at t ’ 3 hr, which finally collides with the proto-Earth at t ’ 6 hr. During the second impact, the impactor is destroyed, and a dense part of the remnant spirals onto the proto-Earth (t ’ 10 hr), and a circumterrestrial debris disk is formed around t ’ 18 hr. Note that many strong spiral shocks are generated in this process as seen in the density map (Fig. 2) and azimuthal density profile (Fig. 3). 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 ). Fig. 2.—Snapshot of the density field of model A at t ¼ 12:3 hr. Strong spiral shocks in the debris are resolved. WADA, KOKUBO, MAKINO1182 Vol. 638 [Wada et al., 2005] [Pahlevan Stevenson, 2007] ratio of 9:1 and a total mass of 1.05 ME (Canup, 2004). Both the impactor and the target are assumed to be differentiated bodies with a 30 wt% iron core and a 70 wt% silicate mantle. In these low-velocity collisions, the impactor loses kinetic energy during its grazing collision with the target, before it is dispersed into a disk around the target. The resulting proto-lunar disk is therefore mainly composed of impactor material. We will call this the ‘‘canonical scenario’’. When the assumption that no mass is lost is dropped however, the collisional angular momentum is no longer tightly constrained, as lost mass also carries away angular momentum. The total collisional angular momentum can therefore be con- siderably higher than the final angular momentum in the Earth–Moon system. With this additional degree of freedom, new regions in the collision parameter space be- come feasible. Apart from the disk mass, another interesting quantity is the origin of the mate- rial which ends up in the proto-lunar disk, especially for the silicate part. We call the fraction of target silicate to total silicate material in the disk fT ¼ ðMsilc targ=Msilc tot Þdisk ð1Þ where Msilc targ and Msilc tot denote the mass of the silicate fraction of the disk derived from the target, and the total disk mass, respectively. If we define a similar target-derived silicate fraction for the post-impact Earth, we can deduce a deviation factor dfT ¼ Msilc targ . Msilc tot disk . Msilc targ . Msilc tot post-impact Earth À 1 ð2Þ which directly reflects the compositional similarity between the silicate part of the proto-lunar disk and the silicate part of the post-impact Earth. Isotopic measurements show (Wiechert et al., 2001; Zhang et al., 2012) a strong isotopic similarity between the silicate fractions of today’s Moon and Earth. Assum- ing isotopic heterogeneity of the pre-impact bodies, this suggests that either the material of the bodies mixed during the collision or re-equilibrated their isotopic signatures after the collision. Either scenario is represented by a dfT $ 0 between to- day’s Earth and the Moon. The value of dfT right after the impact thus serves as a starting point, from which a re-equilibration mechanism leads to todays value of dfT $ 0. In a typical simulation of the canonical scenario, only about 30% of the disk material and 90% of the material of the post-impact Earth is derived from the target (the proto-Earth) respectively (Canup, 2004), yielding a dfT of À67%. 4. Results The new class of collisions presented here falls into the broad regime of slow hit-and-run collisions (Asphaug et al., 2006) with impact velocities between 1.20 and 1.40 vesc. Hit-and-run occurs up to half the time for collisions with impact velocities in this range. Because of the higher impact velocities in this type of col- lisions, substantial mass and angular momentum can be lost in the process. There- fore, the initial angular momentum is less constrained and can be considerably higher than the post-impact 1.0–1.1 LE–M angular momentum of the Earth–Moon- system. The higher impact velocities used in these simulations are also encouraged by more recent models of terrestrial planet formation (O’Brien et al., 2006). In hit- and-run collisions, a significant part of the impactor escapes, so that the disk frac- tion is enriched in target-derived materials compared to the canonical case. Fig. 1a shows four consecutive snapshots of such a hit-and-run collision. While the overall characteristics of the collision resemble the canonical scenario, here a considerable part of the impactor is ejected. 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, while the outer regions of the target mantle, retain too much velocity and leave the system, thereby removing mass and angular momentum. Both processes work to- wards increasing the target material fraction in the proto-lunar disk. While in run cB04 only $10% of the initial angular momentum is removed, $45% are removed in run cC06. We have found that collisions with an impact angle of 30–40° and impact veloc- ities of 1.2–1.3 vesc are successful in putting significant amounts of target-derived material into orbit, when using differentiated impactors with a chondritic iron/sil- icates ratio (30 wt% Fe, 70 wt% silicates) and masses between 0.15 and 0.20 ME. Some runs in this regime show an iron excess of 5 wt% in the proto-lunar disk and are rejected, as in previous work (Canup, 2004). While none of the runs done so far provide a ‘‘perfect match’’ in terms of the constraints from the actual Earth–Moon-system, several simulations come close to that. The best runs coming 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.) [Reufer et al., 2012] T. SASAKI AND Y. ABE: IMPERFECT EQUILIBRATION OF HF-W SYSTEM 10 [Sasaki Abe, 2007]
  62. 62. o i T k ab W WPH i!! (c) Tetsuya Kawase New Perspectives by WPH
  63. 63. • 各 Giant Impact モデルの妥当性がわからない
 → 多様な Giant Impact のより詳細な計算を行う • 地球と月の化学組成が一致しすぎている?
 → 新たな月の石を取得・サンプルバイアスを除く • 全ての化学データを満たす解が存在しない
 → いっそ Giant Impact 説から離れて考えてみる • 月形成年代をどうやって決める?
 → 月の酸素同位体比を持つ欠片@隕石を探す

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