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星・惑星系の形成過程 入門

中本泰史

(東工大)

2012年9月10-13日 惑星科学フロンティアセミナー：北海道むかわ町

1. 形成過程の概観

2. 分子雲の重力収縮

3. 原始惑星系円盤

4. 固体微粒子の進化

5. 微惑星から惑星へ

6. 惑星系の形成

7. 特論：隕石の起源と惑星形成

1mm

隕石

鉄隕石

5%

石鉄隕石

1%

石質隕石

エイコンドライト

8%

コンドライト

86%

普通コンドライト

90%

炭素質コンドライト

4%

エンスタタイトコンドライト

2%

他

4%

H

L

LL

- T タウリ型星期

時期

~ 1 - 3 Myr after

CAI

期間

_{~ 2 Myr}

- 溶融 & 固化

前駆体

_{< 650 K}

温度上昇

_{> 10}

4

_K/hr

最高温度

_{~ 1600 -}

2000 K

液体状態

継続時間

~ 数分

冷却

_{~ 1 - 1000}

K/hr

- サイズ

0.1 – 1 mm

- 大量に存在 (up to 80%)

- 複数回加熱を受けている

1mm

“Flash Heating”による形成

コンドリュール

6

7

8

太陽系の形成に特化したモデル：

The Grand Tack Scenario (Morbidelli et al 2012)

LETTER

A low m ass for M ars from Jupiter’s early

gas-driven m igration

K evin J. W alsh1,2, Alessan dro M orbidelli1, Sean N. Raym on d3,4, David P. O’Brien5& Avi M . M an dell6

Jupiter and Saturn formed in a few million years (ref. 1) from a gas-dominated protoplanetary disk, and were susceptible to gas-driven migration of their orbits on timescales of only 100,000 years (ref. 2). H ydrodynamic simulations show that these giant planets can undergo a two-stage, inward-then-outward, migration3–5_{. The}

ter-restrial planets finished accreting much later6_{, and their}

character-istics, including M ars’small mass, are best reproduced by starting from a planetesimal disk with an outer edge at about one astronom-ical unit from the Sun7,8₍₁

AU is the Earth–Sun distance). H ere we

report simulations of the early Solar System that show how the inward migration of Jupiter to 1.5AU, and its subsequent outward

migration, lead to a planetesimal disk truncated at 1AU; the

terrest-rial planets then form from this disk over the next 30–50 million years, with an Earth/M ars mass ratio consistent with observations. Scattering by Jupiter initially emptiesbut then repopulatestheaster-oid belt, with inner-belt bodies originating between 1 and 3AU and

outer-belt bodies originating between and beyond the giant planets. This explains the significant compositional differences across the asteroid belt. The key aspect missing from previous models of ter-restrial planet formation is the substantial radial migration of the giant planets, which suggests that their behaviour is more similar to that inferred for extrasolar planets than previously thought.

H ydrodynamicsimulationsshow that isolated giant planetsembed-ded in gaseous protoplanetary disks carve annular gaps and migrate inward9_{. Saturn migrates faster than Jupiter; if Saturn is caught in the}

2:3 mean motion resonancewith Jupiter (conditionsfor thisto happen are given in Supplementary Information section 3), where their orbital period ratio is 3/2, generally the two planets start to migrate outward until the disappearance of the disk3–5,10_{. Jupiter could have migrated}

inward only before Saturn approached itsfinal mass and wascaptured in resonance. The extents of the inward and outward migrations are unknown a priori owing to uncertainties in disk properties and in relativetimescalesfor thegrowth of Jupiter and Saturn. Thuswesearch for constraints on where Jupiter’s migration may have reversed (or ‘tacked’, using a sailing analogy).

The terrestrial planets are best reproduced when the disk of plane-tesimals from which they form istruncated, with an outer edge at 1AU

(refs 7, 8). These conditions are created naturally if Jupiter tacked at , 1.5AU. H owever, before concluding that Jupiter tacked at this

dis-tance, a major question needs to be addressed: can the asteroid belt, between 2 and 3.2AU, survive the passage of Jupiter?

Volatile-poor asteroids(mostly Stypes) arepredominantin theinner asteroid belt, while volatile-rich asteroids(mostly C types) arepredom-inant in theouter belt. Thesetwo main classesof asteroidshavepartially overlapping semimajor axis distributions11,12_{, though C types}

outnum-ber Stypesbeyond , 2.8AU. W eran a suiteof dynamical simulationsto

investigate whether this giant planet migration scheme is consistent with the existence and structure of the asteroid belt. Because of the many unknownsin giant planet growth and early dynamical evolution,

we present a simple scenario that reflects one plausible history for the giant planets (Fig. 1). W e provide an exploration of parameter space (see Supplementary Information) that embraces a large range of pos-sibilities and demonstrates the robustness of the results. In all simula-tions, we maintain the fundamental assumption that Jupiter tacked at 1.5AU.

Figure 2 shows how the migration of the giant planets affects the small bodies. Thedisk interior to Jupiter hasa mass3.7 timesthat of the Earth (3:7M+ ), equally distributed between planetary embryos(large)

1_{Universite´deNice –Sophia Antipolis, CNRS, Observatoiredela Coˆted’Azur, BP4229, 06304 Nice Cedex4, France.}2_{Department of Space Studies, Southwest Research Institute, 1050 Walnut Street, Suite}

300, Boulder, Colorado 80302, USA.3_{Universite´de Bordeaux, Observatoire Aquitain des Sciences de l’Univers, 2 Rue de l’Observatoire, BP 89, F-33270 Floirac Cedex, France.}4_{CNRS, UMR 5804,}

Laboratoire d’Astrophysique de Bordeaux, 2 Rue de l’Observatoire, BP 89, F-33270 Floirac Cedex, France.5_{Planetary Science Institute, 1700 East Fort Lowell, Suite 106, Tucson, Arizona 85719, USA.} 6_{NASA Goddard Space Flight Center, Code 693, Greenbelt, Maryland 20771, USA.}

Jupiter Saturn Neptune Uranus Jupiter Saturn Uranus Neptune Tim e (kyr) S e m im a jo r a x is ( A U ) 100 10 10 5 0 0 200 400 600 M a s s ( M ) a b

Figure 1|The radial migration and mass growth imposed on the giant planets in the reference simulation. a, M ass growth; b, semimajor axis. A fully-formed Jupiter startsat 3.5AU, a location expected to be highly favourable

for giant planet formation owing to the presence of the so-called snow line21_.

Saturn’s 30 M+ core is initially at , 4.5AUand grows to 60 M+ as Jupiter

migrates inward, over 105years. Inward type-I migration of planetary cores is inhibited in disks with a realistic cooling timescale23–26_{; thus Saturn’s core}

remainsat 4.5AUduring thisphase. Similarly, thecoresof Uranusand Neptune

begin at , 6 and 8AUand grow from 5 M+ , without migrating. Once Saturn

reaches 60 M+ its inward migration begins25, and is much faster than that of

the fully grown Jupiter27_{. Thus, on catching Jupiter, Saturn is trapped in the 2:3}

resonance3_{. H ere this happens when Jupiter is at 1.5}

AU. The direction of

migration is then reversed, and the giant planets migrate outward together. In passing, they capture Uranus and Neptune in resonance and these planets are then pushed outwards as well. Saturn, Uranus and Neptune reach their full mass at the end of the migration when Jupiter reaches 5.4AU. The migration

rate decreases exponentially as the gas disk dissipates. The final orbital configuration of the giant planets is consistent with their current orbital configuration when their later dynamical evolution is considered28,29_(see

Supplementary Information section 3 for extended discussion).

2 0 6 | N A T U R E | V O L 4 7 5 | 1 4 J U L Y 2 0 1 1

Macmillan Publishers Limited. All rights reserved

©2011

Walsh et al. 2011

・ガス惑星/氷惑星

・地球型惑星

・小惑星

・...

Walsh et al. 2011

(Kerr 2011)

コンドリュール形成モデル

・

衝撃波加熱

・雷加熱

・

X-Windモデル

3. 衝撃波加熱仮説： コンドリュール形成

衝撃波加熱

1. 衝撃波の発生

2. 衝撃波内部での加熱機構

3. ダスト粒子内部の現象

1. 衝撃波発生

1. 衝撃波発生

m

_gr

C

_gr

dT

gr

dt

=

p

a

2

1

2

r

gas

V

3

-4

p

a

2

s

T

_gr

4

T

_max

₌

1

2

s

r

gas

V

3

é

ë

ê

ù

û

ú

1/ 4

簡単な見積もり

最高温度到達時：

dT

_gr

dt

=

0

=

1700

n

gas

10

15

cm

-

3

æ

è

ç

ö

ø

÷

1/ 4

V

10 km s

-

1

æ

è

ç

ö

ø

÷

3 / 4

K

radius

a

_gr

: 0.01

m

m – 1 cm

emissivity

: size dependent

evaporation rate : pure forsterite

r

_gr

da

gr

dt

æ

è

ç

ö

ø

÷

evap

= -

J

_evap

m

_gr

dv

gr

dt

= -

p

a

gr

2

C

D

2

r

v

rel

2

m

_gr

C

_gr

dT

gr

dt

= -L

rad

- L

evap

Basic Equations for Dust Particles:

+G

_rad,gas

+G

_rad,dust

+G

_drag

post-shock

pre-shock

Chemical Reactions：32 species, 167 reactions

¶

¶

x

( )

r

v

=

0

¶

¶

x

r

v

2

₊

_p

(

)

=

0

¶

¶

x

1

2

rv

2

₊

_E

₊

_P

æ

è

ç

ö

ø

÷

v

é

ë ê

ù

û ú

= G

_H

2

form

- L

Ly

a

- L

H

2

diss

- L

H

2

O(V)

- L

H

2

O(R)

- L

_CO(V)

- L

_CO(R)

- L

_OH(R)

- L

_grain

dy

_i

dt

=

n

H

_j

₌

1

32

å

k

_jk

y

_j

y

_k

k

=

1

32

å

+

n

_H

2

l

=

1

32

å

m

=

1

32

å

k

_lmn

y

_l

y

_m

y

_n

n

=

1

32

å

V

_s

= 10 km s

-1

_{, n}

pre

=10

14

cm

-3

, a

0

= 0.1 mm

Gas Temperature

Dust Temperature

Gas Number Density

衝撃波後面の構造

Iida, Nakamoto, Susa, & Nakagawa (2001) Icarus

Chondrule Forming Shock Waves: Peak Temperature

1. 衝撃波発生

複合コンドリュ−ル

▶二個以上のコンドリュールが付着

二つのコンドリュールが

溶融状態を経験中に

_衝突

▶コンドリュール全体の

_数%

_存在

原始太陽系星雲中のダストの直接衝突は低頻度

分裂ー衝突モデル

〜複合コンドリュール形成の1モデル〜

(Miura, Yasuda, and Nakamoto 2007)

衝突頻度

~0.36

存在割合

~0.05

コンドリュールの数

複合コンドリュールの数

>>

分裂片同士の衝突

衝突付着条件

25

50

75

100

0

0

0.25

0.50

0.75

1.00

We

X

合体

振動分離

伸張分離

分裂片同士は

ほとんど付着。

パラメータ

X

相対速度:

u

d

s

d

l

x

1

0.5

0

We

0

50

100

液滴の衝突実験 (水)

(Ashgriz and Poo 1990)

We =

r

v

2

g

/

R

=

動圧

表面張力

計算結果(ns1-nl1)

伸張分離

合体

破壊

We

x

1200

600

200

100

相対速度(cm/s)

1

0.8

0.6

0.2

0

0.4

1

₁₀

₁₀₀

₁₀₀₀

計算結果(ns1-nl1)

伸張分離

合体

破壊

We

x

1200

600

200

100

相対速度(cm/s)

1

0.8

0.6

0.2

0

0.4

1

₁₀

₁₀₀

₁₀₀₀

1. 衝撃波発生

衝撃波の起源は何か？

・

降着衝撃波

分子雲コアからの降着流による衝撃波

・

自己重力円盤内密度波

自己重力不安定なガス円盤内の密度波

・

微惑星前面のバウショック

木星により大きなランダム運動を獲得した

微惑星前面に発生するバウショック

・

星風による円盤上層衝撃波

X線フレアによる星風とそれによる衝撃波

重力不安定による衝撃波の生成

_{Boss & Durisen 2005, ApJ}

2AU

20AU

コンドリュール形成に

適当な衝撃波

ショック源は何か

– コンドリュール前駆体を融かせるほど強い

– 数百万年にわたって起こる

微惑星まわりの

バウショック

Hood (1998), Weidenschilling et al. (1998),

Ciesla et al. (2004)

木星による高速

微惑星形成と

微惑星前面の

バウショック形成

y = 110 km

直線上での

ガス密度分布

500

300

100

Planetesimal Bow Shocks

0.0

1.0

2.0

3.0

4.0

5.0

ρ

g

[10

-10

g cm

-3

]

y = 110 km

-200 0 200 400 600 800

x [km]

y

[k

m

]

【結果】

解離・再結合

なし

解離・再結合

あり

解離入り計算

ρ=10

_g/cm

_{, v=12km/s の場合}

微惑星

[K]

[K]

微惑星

温度

低下

密度

上昇

（解離）

温度

上昇

（再結合）

ρ=10

_g/cm

_{, v=12km/s の場}

合

[K]

微惑星

流線

0

50

10

₀

15

₀

20

₀

-2

00

-1

00

0

10

0

20

0

30

0

40

0

50

0

60

0

st

re

am

lin

e 1

st

re

am

lin

e 2

st

re

am

lin

e 3

st

re

am

lin

e 4

st

re

am

lin

e 5

st

re

am

lin

e 6

バウショックに突入した粒子の熱履歴

• パラメータ

– x

_imp

= 80 – 400 km

– a = 0.1, 1, 10 mm

• 粒子に働く力

– ガス摩擦

• 粒子の加熱と冷却

– ガス摩擦加熱、放射冷却

x

_imp

微惑星

ダスト

• 軌跡に沿った粒子の温度

【結果】

T

d

[K]

0

400

800

1200

1600

2000

2400

0

400

800

1200

1600

2000

2400

-200 0 200 400 600 800

x [km]

300

200

100

y

[k

m

]

ρ

₀

＝10

-8

_{g cm}

-3

V

₀

= 8 km s

-1

-11

-10

-9

-8

-7

-6

1

10

100

【結果】 コンドリュール形成可能領域

• V

_g

- ρ

_g

空間でのコンドリュール形成可能領域

V

_g

[km]

lo

g

10

(

ρ

g

[g cm

-3

])

融ける

融けない

r

t

0

1

3

10

30

CAI形成

分化天体形成

[AU]

[Myr]

1

3

10

原始惑星系円盤形成

微惑星形成

原始太陽

誕生

コンドリュール形成

彗星形成

0.05

円盤ガス散逸

木星形成

地球型惑星

形成

太陽系初期の進化

(中本 私見 2012)

課題

1. コンドリュール形成そのものを理解できるか

参考文献

•

Akaki, T., and T. Nakamura, 2004, The Formation Process of Adhering and Consorting

Compound Chondrules Inferred Their Petrology and Major-Element Composition,

Workshop on Chondrites and the Protoplanetary Disk, abstract no.9021

•

Ashgriz, N., and J. Poo, 1990, Coalescence and separation in binary collisions of liquid

drops, Journal of Fluid Mechanics, vol. 221, 183-204.

•

Boss, A., and R. Durisen, 2005, Chondrule-forming Shock Fronts in the Solar Nebula: A

Possible Unified Scenario for Planet and Chondrite Formation, The Astrophysical Journal,

Vol 621, L137-L140.

•

Ciesla, F., L. Hood, and S. Weidenschilling, 2004, Evaluating planetesimal bow shocks as

sites for chondrule formation,

Meteoritics & Planetary Science, Vol. 39, 1809-1821

•

Dauphas, N., and M. Chaussidon, 2011, A Perspective from Extinct Radionuclides on a

Young Stellar Object: The Sun and Its Accretion Disk, Annual Review of Earth and

Planetary Sciences, vol. 39, 351-386

•

Gooding, J., and K. Keil, 1981, Relative abundances of chondrule primary textural types in

ordinary chondrites and their bearing on conditions of chondrule formation, Meteoritics, vol.

16, 17-43.

•

Hood, L., 1998, Thermal processing of chondrule and CAI precursors in planetesimal bow

shocks, Meteoritics & Planetary Science, vol. 33, 97-107.

参考文献

•

Iida, A., et al, 2001, A Shock Heating Model for Chondrule Formation in a Protoplanetary

Disk, Icarus, Vol 153, 430-450

•

Kerr, R., 2011, Planetary Two-Step Reshaped Solar System, Saved Earth?, Science, Vol

332, 1255-

•

Miura, H., S. Yasuda, and T. Nakamoto, 2007, Fragment-Collision Model for Compound

Chondrule Formation: Estimation of Collision Frequency, Workshop on the Chronology of

Meteorites and the Early Solar System, No. 1374, 116-117

•

Miura, H., S. Yasuda, and T. Nakamoto, 2008, Fragment-Collision Model for Compound

Chondrule Formation: Size Ratio of Secondary to Primary, 39th Lunar and Planetary

Science Conference, LPI Contribution No. 1391., p.1215

•

Morbidelli, A., et al, 2012, Building Terrestrial Planets, Annual Review of Earth and

Planetary Sciences, vol. 40, 251-275

•

Sekiya, M., T. Nakamura, 1996, Condition for the formation of the compound chondrules

in the solar nebula, Twentieth Symposium on Antarctic Meteorites, No 9, 208

•

Walsh, K., et al, 2011, A low mass for Mars from Jupiter’s early gas-driven migration,

Nature, Vol 475, 206–209

•

Wasson, J., et al, 1995, Compound chondrules, Geochimica et Cosmochimica Acta, vol.

59, 1847-1869

•

Weidenschilling, S., F. Marzari, and L. Hood, 1998, The Origin of Chondrules at Jovian

Resonances, Science, Vol. 279, 681