2016年2月21日　NHKカルチャー梅田教室

惑星科学最前線 　～太陽系誕生の謎～

京都大学 宇宙物理学教室　佐々木貴教

講座の内容

✤ 現在の太陽系の姿　8つの惑星とその衛星、そして無数の小天体たち

✤ 太陽系形成論のレビュー　標準理論（京都モデル）の概要とその拡張の歴史

✤ 系外惑星の発見、そして汎惑星形成理論へ 　多様な惑星系の作り方；第二の地球は存在するか？

太陽系形成論標準モデル 「京都モデル」

太陽系の構成メンバー

地球型惑星 　　水星 　　金星 　　地球 　　火星

巨大ガス惑星 　　　木星 　　　土星

巨大氷惑星 　　天王星 　　海王星

(c) ikachi.org

太陽系形成標準理論（京都モデル）

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巨大氷惑星形成

太陽系の起源モデル

天動説から地動説へ ・Newton (1687)：「プリンキピア」

20世紀以前 ・Kant (1755), Laplace (1796)：星雲説

20世紀以降 ・Safronov (1969)：コア集積モデル ・Cameron (1978)：重力不安定モデル ・Hayashi et al. (1985)：コア集積モデル

林忠四郎（1920-2010）

ὼ⥄ޔ߇ߥߪߢߩߟ┙ߦធᓎ⋤ߦᵴ↢ߩޘᚒߪቝቮ‛ℂޟᨋ)ޠࠆߡߞ┙ߦᓎߢὐߚߒߦ⏕ࠍሽߩ࿃ᨐ㑐ଥߩ 1988)

・恒星進化における 　　「林フェイズ」

・恒星の進化経路 　　「林トラック」

・恒星半径に対する 　　「林の境界線」

・原始太陽系円盤 　　「林モデル」

原始太陽系円盤の２つのモデル

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京都モデル（林モデル） キャメロンモデル

地球型惑星・巨大ガス惑星・巨大氷惑星の作り分け 　→ 太陽系形成に関しては、京都モデルの方に軍配

(c) Alan P. Boss

京都モデルの基本概念円盤仮説 ・惑星系は原始惑星系円盤から形成される ・円盤は最小質量のガスとダストから構成される

微惑星仮説 ・ダストの集積によって微惑星が形成される ・微惑星の集積によって固体惑星が形成される ・固体惑星にガスが降り積もることによって 　ガス惑星が形成される 　　　　　　　　　　　　 [林忠四郎 他, 1985]

分子雲から主系列星への進化

(c) Yusuke Tsukamoto

（１）星間分子雲の収縮とコアの形成 （２）原始星の形成と成長 （３）主系列星への進化

星形成の ３段階

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原始惑星系円盤分子雲コア

分子雲コアの収縮 　 重力と遠心力のつりあい 原始惑星系円盤が形成

(c) NASA

原始太陽系円盤の組成一般に円盤質量の99%はガス（水素・ヘリウム） 残りの1%がダスト（固体成分）

・現在の太陽系の惑星の固体成分（約10-4M太陽） 　　→ すりつぶして円盤状にならす ・固体成分の約100倍の質量のガス成分を加える

最小質量円盤モデル（林モデル）

原始太陽系円盤の初期質量は約10-2M太陽 重力と遠心力の釣り合いから半径は約100AU Snow line 以遠では水が凝結し固体面密度が上昇

原始惑星系円盤の観測

実際に様々な形の円盤が観測されている 　→ 原始惑星系円盤は確かに存在する！

Subaru

ALMA

微惑星形成シナリオと様々な困難

ダスト (≲µm) 惑星 (≳103km)

原始惑星系円盤

微惑星 (≳km)

惑星形成と微惑星形成

!5ice

+rock

ice+rock

rock

Itokawa (~0.5km)

rock

重力集積分子間力集積

+ ダスト層の自己重力不安定? スノーラ

イン

(~1-3AU?)

直接合体成長

ダストの自己重力不安定

ダスト 微惑星

μm mm m km

静電反発障壁跳ね返り障壁

中心星落下障壁衝突破壊障壁

乱流障壁

☓☓☓

☓☓

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���������� ダストの合体成長

ダストの合体成長 　→ 微惑星形成

微惑星の円盤が形成

(c) Toru Sayama

氷微惑星は形成可能

岩石微惑星は破壊が 卓越し形成不可能

微惑星の合体成長数kmサイズの 微惑星が形成

互いに衝突・合体 を繰り返し成長

↓

暴走的成長 　大きい粒子ほど成長が速い

秩序的成長 　全ての粒子が同じ速度で成長

(c) Kouji KANBA

多体問題専用計算機 GRAPE多体（微惑星）の重力計算 　→ 計算量が膨大になる

粒子間相互作用の部分だけを 専用計算機で計算したい 　→ GRAPE 誕生！

GRAPE-6 と 牧野淳一郎教授(c) Junichiro Makino

20 KOKUBO AND IDA

FIG. 3. Snapshots of a planetesimal system on the a–e plane. The circlesrepresent planetesimals and their radii are proportional to the radii of planetesi-mals. The system initially consists of 3000 equal-mass (1023 g) planetesimals.The numbers of planetesimals are 2215 (t = 50,000 years), 1787 (t = 100,000years), and 1322 (t = 200,000 years). In the t = 200,000 years panel, the filledcircle represents a protoplanet (runaway body) and lines from the center of theprotoplanet to both sides have the length of 5rH.

the mass ratio keeps increasing when α <−2. If α >−2, meanmass should be similar to themaximummass, so that the increasein the mass ratio would stall soon. Note that our definition ofrunaway growth does not necessarily mean that the growth timedecreases with the mass of a body, but that the mass ratio of anytwo bodies increases with time as shown below.The evolution of the distributions of the RMS eccentricity and

the RMS inclination is plotted in Fig. 6. Let us focus on the massrange 1023 ≤m≤ 1024 g. The values for the mass range larger

FIG. 4. Time evolution of the maximum mass (solid curve) and the meanmass (dashed curve) of the system.

than this range are not statistically valid since eachmass bin oftenhas only a few bodies. First, the distribution tends to relax to adecreasing function of mass through dynamical friction among(energy equipartition of) bodies (t = 50,000, 100,000 years).Second, the distributions tend to flatten (t = 200,000 years). Thisis because as a runaway body grows, the system ismainly heatedby the runaway body (Ida and Makino 1993). In this case, theeccentricity and inclination of planetesimals are scaled by the

FIG. 5. The cumulative number of bodies is plotted against mass att = 50,000 years (dotted curve), 100,000 years (dashed curve), and 200,000years (solid curve). A runaway body at t = 200,000 years is shown by a dot.

暴走的成長の様子

平均値

最大の天体

微惑星の暴走的成長 　→ 原始惑星が誕生する

20 KOKUBO AND IDA

FIG. 3. Snapshots of a planetesimal system on the a–e plane. The circlesrepresent planetesimals and their radii are proportional to the radii of planetesi-mals. The system initially consists of 3000 equal-mass (1023 g) planetesimals.The numbers of planetesimals are 2215 (t = 50,000 years), 1787 (t = 100,000years), and 1322 (t = 200,000 years). In the t = 200,000 years panel, the filledcircle represents a protoplanet (runaway body) and lines from the center of theprotoplanet to both sides have the length of 5rH.

the mass ratio keeps increasing when α <−2. If α >−2, meanmass should be similar to themaximummass, so that the increasein the mass ratio would stall soon. Note that our definition ofrunaway growth does not necessarily mean that the growth timedecreases with the mass of a body, but that the mass ratio of anytwo bodies increases with time as shown below.The evolution of the distributions of the RMS eccentricity and

the RMS inclination is plotted in Fig. 6. Let us focus on the massrange 1023 ≤m≤ 1024 g. The values for the mass range larger

FIG. 4. Time evolution of the maximum mass (solid curve) and the meanmass (dashed curve) of the system.

than this range are not statistically valid since eachmass bin oftenhas only a few bodies. First, the distribution tends to relax to adecreasing function of mass through dynamical friction among(energy equipartition of) bodies (t = 50,000, 100,000 years).Second, the distributions tend to flatten (t = 200,000 years). Thisis because as a runaway body grows, the system ismainly heatedby the runaway body (Ida and Makino 1993). In this case, theeccentricity and inclination of planetesimals are scaled by the

FIG. 5. The cumulative number of bodies is plotted against mass att = 50,000 years (dotted curve), 100,000 years (dashed curve), and 200,000years (solid curve). A runaway body at t = 200,000 years is shown by a dot.

軌道長半径 [AU]

軌道離心率

質量 [1023 g]

時間 [年][Kokubo & Ida, 2000]

寡占的成長の様子FORMATION OF PROTOPLANETS FROM PLANETESIMALS 23

FIG. 7. Snapshots of a planetesimal system on the a–e plane. The cir-cles represent planetesimals and their radii are proportional to the radii ofplanetesimals. The system initially consists of 4000 planetesimals whose to-tal mass is 1.3× 1027 g. The initial mass distribution is given by the power-law mass distribution with the power index α = −2.5 with the mass range2× 1023 ≤m≤ 4× 1024 g. The numbers of planetesimals are 2712 (t = 100,000years), 2200 (t = 200,000 years), 1784 (t = 300,000 years), 1488 (t = 400,000years), and 1257 (t = 500,000 years). The filled circles represent protoplanetswith mass larger than 2× 1025 g and lines from the center of the protoplanet toboth sides have the length of 5rH.

there is no supply of small bodies. Figure 9 shows the snapshotof another run at t = 500,000 years. Two large protoplanets withmass 1–3× 1026 g with an orbital separation of about 10rH areformed. The two protoplanets contain 38% of the system mass.

FIG. 8. The number of bodies in linear mass bins is plotted for t = 100,000,200,000, 300,000, 400,000, and 500,000 years.

In Fig. 10, we plot the maximum mass and the mean mass ofthe system against time. The time evolution of the RMS eccen-tricity and inclination of the system is plotted in Fig. 11. Thevalues are scaled by the reduced Hill radius of the maximumbody. The reduced Hill radius is given by h= rH/a. After about20,000 years, the scaled RMS eccentricity and inclination are al-most constant, ⟨e2⟩1/2 ≃ 6hmax and ⟨i2⟩1/2 ≃ 3.5hmax. This resultagrees with the estimation of Ida and Makino (1993). They esti-mated the equilibrium eccentricity and inclination of a planetes-imal system perturbed dominantly by a protoplanet under gasdrag. They found that when the mass of a protoplanet becomes

軌道離心率

各場所で微惑星が暴走的成長 　→ 等サイズの原始惑星が並ぶ

寡占的成長とよぶ

＝

各軌道での原始惑星質量 [kg] 形成時間 [yr]

地球軌道 1×1024 7×105

木星軌道 3×1025 4×107

天王星軌道 8×1025 2×109軌道長半径 [AU][Kokubo & Ida, 2000]

原始惑星から惑星へ������)-/

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軌道長半径 [AU]

地球型惑星 　原始惑星同士の合体

巨大ガス惑星 　原始惑星のガス捕獲

巨大氷惑星 　原始惑星そのまま

snow line

(c) Eiichiro Kokubo

ジャイアントインパクト

原始惑星同士の巨大天体衝突を繰り返し, 現在の惑星へ(c) NASA

ジャイアントインパクト

軌道長半径 [AU]

軌道離心率

planets is hnM i ’ 2:0 ! 0:6, which means that the typical result-ing system consists of two Earth-sized planets and a smallerplanet. In thismodel, we obtain hnai ’ 1:8 ! 0:7. In other words,one or two planets tend to form outside the initial distribution ofprotoplanets. In most runs, these planets are smaller scatteredplanets. Thus we obtain a high efficiency of h fai ¼ 0:79 ! 0:15.The accretion timescale is hTacci ¼ 1:05 ! 0:58ð Þ ; 108 yr. Theseresults are consistent with Agnor et al. (1999), whose initial con-ditions are the same as the standard model except for !1 ¼ 8.

The left and right panels of Figure 3 show the final planets onthe a-M andM–e, i planes for 20 runs. The largest planets tend to

cluster around a ¼ 0:8 AU, while the second-largest avoid thesame semimajor axis as the largest, shown as the gap around a ¼ha1i. Most of these are more massive thanM%/2. The mass of thelargest planet is hM1i ’ 1:27 ! 0:25M%, and its orbital elementsare ha1i ’ 0:75 ! 0:20 AU, he1i ’ 0:11 ! 0:07, and hi1i ’0:06 ! 0:04. On the other hand, the second-largest planet hashM2i’ 0:66 ! 0:23M%, ha2i ’ 1:12 ! 0:53AU, he2i ’ 0:12 !0:05, and hi2i ’ 0:10 ! 0:08. The dispersion of a2 is large, sincein some runs, the second-largest planet forms inside the largestone, while in others it forms outside the largest. In this model, wefind a1 > a2 in seven runs.

Fig. 2.—Snapshots of the system on the a-e (left) and a-i (right) planes at t ¼ 0, 106, 107, 108, and 2 ; 108 yr for the same run as in Fig. 1. The sizes of the circlesare proportional to the physical sizes of the planets.

Fig. 3.—All planets on the a-M (left) and M–e, i (right) planes formed in the 20 runs of the standard model (model 1). The symbols indicate the planets first(circles), second (hexagons), third (squares), and fourth (triangles) highest in mass. The filled symbols are the final planets, and the open circles are the initialprotoplanets in the left panel. The filled and open symbols mean e and i in the right panel, respectively. [See the electronic edition of the Journal for a color versionof this figure.]

KOKUBO, KOMINAMI, & IDA1134 Vol. 642

長い時間をかけて原始惑星同士の軌道が乱れる 　→ 互いに衝突・合体してより大きな天体に成長

[Kokubo & Ida, 2006](c) Hidenori Genda

Break：月の起源

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

ジャイアントインパクト説

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

(c) Wikipedia

巨大天体衝突による円盤形成

原始地球に火星サイズの原始惑星が衝突

飛び散った破片が地球の 周囲に円盤を形成

(c) Robin Canup

[Canap & Asphaug, 2001]

円盤中での月形成

[Ida et al., 1997]

周地球円盤内で月形成

現在の月の位置よりも かなり内側（約 1/20）

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

巨大ガス惑星の形成

原始惑星に円盤ガスが暴走的に流入 → ガス惑星へ

(c) NVIDIA

ガス捕獲による巨大ガス惑星形成原始惑星は重力により周囲の円盤ガスを捕獲 ・10地球質量以下 → 大気圧で支えられて安定に存在 ・10地球質量以上 → 大気が崩壊・暴走的にガス捕獲

軌道付近に残っているガスを全て加速度的に捕獲 　→ 急激に質量を増し木星・土星へと成長する

(c) Nagoya U

ガスの流れの数値シミュレーション

(c) Takayuki Tanigawa

巨大ガス惑星の形成の様子

and goes downward (upward) according to the Keplerian shearmotion. The shocks (crowded contours near the Hill radius) canbe seen in the upper right and lower left regions near the proto-planet. In this model, the shock front almost corresponds to theHill radius (Fig. 4, left). When the gas approaches the proto-planet, the streamlines are bent by the gravity of the protoplanet.According to Miyoshi et al. (1999), the gas flow is divided intothree regions: the pass-by region ( xj jk rH), the horseshoe region(xP rH and yj jk rH), and the atmospheric region (rP rH). Notethat although Miyoshi et al. (1999) classified the flow pattern intheir two-dimensional calculation, their classification is useful fora global flow pattern in three dimensions. In the pass-by region,the flow is first attracted toward the protoplanet and then causes ashock after passing by the protoplanet. At the shock front, thedensity reaches a local peak and the streamlines bend suddenly.On the other hand, the gas entering the horseshoe region turnsaround because of the Coriolis force and goes back. The outer-most streamlines in the horseshoe region (i.e., the streamlinespassing very close to the protoplanet) pass through the shockfront, whereas the gas on the streamlines far from the protoplanetdoes not experience the shock. In the atmospheric region, the gasis bound by the protoplanet and forms a circumplanetary diskthat revolves circularly around the protoplanet in the prograde(counterclockwise) direction.

Although the streamlines on the z ¼ 0 plane (Fig. 4, left) aresimilar to those in recent two-dimensional calculations (e.g., Lubowet al. 1999; Tanigawa & Watanabe 2002a), there are important

differences. In the two-dimensional calculations, a part of the gasnear the Hill sphere can accrete onto the protoplanet. Lubow et al.(1999) showed that only gas in a narrow band distributed from thelower left to the upper right region against the protoplanet fory < 0 spirals inward toward the protoplanet, passes through theshocked region, and finally accretes onto the protoplanet (for de-tails, see Figs. 4 and 8 of Lubow et al. 1999). On the other hand,in our three-dimensional calculation, gas only flows out from theHill sphere and thus does not accrete onto the protoplanet on themidplane. The left panel of Figure 4 shows that although gas flowsinto the Hill sphere, some of the gas flows out from the centralregion. The right panel of Figure 4 is a three-dimensional view atthe same epoch as the left panel. In this panel, only the stream-lines flowing into the high-density region of rTrH are drawnfor z " 0 and are inversely integrated from the high-density re-gion. This panel clearly shows gas flowing into the protoplanet inthe vertical direction.To investigate the gas flowing into the protoplanet system in

detail, in Figure 5 we plot the streamlines at the same epoch asFigure 4, but with different grid levels (l ¼ 3, 5, and 7). In thisfigure, each of the top panels shows a three-dimensional view,while each of the bottom panels shows the structure on the crosssection in the y ¼ 0 plane. Note that, in the bottom panels, thestreamlines are projected onto the y ¼ 0 plane. Figure 5a showsonly the streamlines in a narrow bundle flowing into the proto-planet system. This feature is similar to that shown in two-dimensional calculations (Lubowet al. 1999;Tanigawa&Watanabe

Fig. 4.—Structure around the Hill sphere for model M04 on the midplane (left) and in three dimensions, shown in bird’s-eye view (right). The gas streamlines (redlines), density structure (color), and velocity vectors (arrows) are plotted in both panels. The dashed circle in the left panel represents the Hill radius. The size of the domainis shown in each panel.

MACHIDA ET AL.1226 Vol. 685

Fig. 1.—Time sequence for model M04. The density (color scale) and velocity distributions (arrows) on the cross section in the z ¼ 0 plane are plotted. The bottompanels (l ¼ 3) are 4 times the spatial magnification of the top panels (l ¼ 1). Three levels of grids are shown in each top (l ¼ 1, 2, and 3) and bottom (l ¼ 3, 4, and 5) panel.The level of the outermost grid is denoted in the top left corner of each panel. The elapsed time tp and the central density !c on the midplane are denoted above each of thetop panels. The velocity scale in units of the sound speed is denoted below each panel.周囲の円盤ガスが原始惑星の重力圏内に捕獲される

(c) Takayuki Tanigawa

周惑星円盤内で衛星が形成

(c) Takayuki Tanigawa

イオ エウロパ ガニメデ カリスト

タイタン(c) Wikipedia

巨大氷惑星の形成

円盤散逸後に原始惑星が形成 → ガスを纏えず氷惑星へ

太陽系形成標準理論（京都モデル）

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巨大氷惑星形成

Advanced: 新しい太陽系形成シナリオ

太陽系形成論の様々なモデル

（円盤ガスの自己重力不安定による惑星形成モデル）

微惑星形成＋コア集積＋ガス集積によるその場形成モデル

ガス惑星の移動を考慮した “Nice Model”

ガス惑星の複雑な移動を考慮した “Grand Tack Model”

惑星形成領域を限定する “Local Planet Formation Model”[Sasaki et al., in prep.]

[Walsh et al., 2011]

[Gomes et al., 2005; Morbidelli et al., 2005; Tsiganis et al., 2005]

[Hayashi et al., 1985]

[Cameron, 1978]

各天体の軌道

(c) wakatsuki

“Nice Model”

・太陽系はもともと 水金地火木土海天 だった

・巨大惑星は現在よりもコンパクトな領域に固まっていた

・巨大惑星同士の重力散乱の結果、海が外に飛ばされた

・海によってエッジワースカイパーベルト天体が散乱された 　　→ 散乱された証拠が外縁天体の軌道に残されている

・散乱された天体の一部が地球や月にも落下してきた 　　→ 後期重爆撃期の証拠が月のクレーターに残されている

・太陽系は 水金地火木土天海 になった

[Gomes et al., 2005; Morbidelli et al., 2005; Tsiganis et al., 2005]

惑星落下問題

Type I migration（M < 10M+） 等温円盤での migration による落下が速すぎる 　→ 原始惑星が円盤内に生き残れない [Tanaka et al., 2002]

Type II migration（M > 50M+） 惑星重力により gap を形成し、円盤降着とともに落下 　→ a > 1AU にガス惑星を残せない [Hasegawa & Ida, 2013]

Type III migration（M ~ 30M+） Corotation torque の positive feedback 　→ 超高速移動＆向きが予測不可能 [Masset & Papaloizou, 2003]

“Grand Tack Model” [Walsh et al., 2011]

(c) http://www.exoclimes.com

Type I migration のカオス性

© F. Maseet

円盤との重力相互作用による惑星軌道移動 ー 混沌 新たな物理：惑星軌道移動

円盤温度勾配、流体素片熱輸送、 乱流拡散等を考慮する 　→ 移動方向が変わる（ただし高速） 　　　　　[Paardekooper et al., 2010, 2011]

乱流による密度ゆらぎからの重力摂動 　→ ランダム運動を引き起こす 　 [Ida et al, 2008, Okuzumi & Ormel, 2013a, b]

いずれにしても惑星は円盤ガスとの相互作用で動き回る

Migration TrapPossible%migra3on%trap:%type%I%%

! %adiaba3c%+%isothermal%disk%

,,,,,e.g.,,Paardekooper,&,Papalouzou,(2009),,Paardekooper,et,al.,(2010,,11),,,,,,,,,,,,,,,,,Kretke,&,Lin,(2012),

! %gas%density%jump%

adiabatic isothermal

“saturation” of corotation torque: delicate

0.1AU 1AU 10AU

dead zone (DZ)

inner disk edge or DZ inner edge Masset,et,al.,(2006),Ogihara,et,al.,(2010)

DZ outer edge Hasegawa,&,Pudritz,(2012),Regaly,et,al.,(2013)

ice line Kretke,&,Lin,(2007)

theory: not clear�

see Y. Hasegawa’s talk�

[Ida-san’s talk]

“Local” Planet Formation Model Solar%system:%“local”%forma3on??%

! %I1995,:,uniform,disk,w/o,orbital,migraDon,! ,1995I,:,uniform,disk,with,orbital,migraDon,! ,New,idea:,nonIuniform,disk,,,,,,,,,,,,,,,,,,,,,,,,start,from,2,narrow,disk,regions??,,,,,,,,,,,,,,,,,,,,,,,,,migraDon,trap?,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,‘Grand,Tack’,model?,(Walsh+,2011),

0.1AU 1AU 10AU

Me V E Ma J S U N

close%scaLering%&%giant%impacts%,,Morishima+,(2008),,,Hansen,(2009),,

induced%forma3on%of%Saturn%,,Kobayashi,,Ormel,,Ida,(2012)%diffusion%via%planetesimal%scaLering%,,Fernandez,&,Ip,(1994),secular%perturba3on%by%JS%in%2:1%,,Nice,model,,

~2M⊕� 50I100M⊕�

[Ida-san’s talk]“ちゃんとした論文は出ていないが多くの人が何となく思っている”

[Sasaki et al., in prep.]