天文学概論（第７回）

系外惑星 2～汎惑星形成論～

東京工業大学　佐々木貴教

連絡先❖ Sasaki Takanori Online：http://sasakitakanori.com　“佐々木貴教”で検索してもすぐ見つかります　講義資料や参考図書の情報などを掲載します

❖ メール：takanori@geo.titech.ac.jp　本講義全体の代表メールアドレス

講義の感想, 質問, 要望, 相談惑星科学全般についての質問研究や研究者についての質問

系外惑星 2　～汎惑星形成論～

・太陽系形成論から汎惑星形成論へ　＊太陽系形成論のまとめ　＊汎惑星形成論へ・生命を宿す惑星の発見へ向けて

太陽系形成論から汎惑星形成論へ

太陽系形成論のまとめ

太陽系形成標準理論（林モデル）

原始惑星系円盤

微惑星の形成

微惑星の合体成長

地球型惑星形成

木星型惑星形成

©Newton Press

巨大氷惑星形成

原始惑星系円盤なぜ円盤状になるか？

! 分子雲が収縮すると、「角運動量保存の原理」に従い、収縮するほど回転が速くなる

! 回転の効果が効いて、平たい円盤状の構造になる

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子惑星系円盤が形成

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！

10-4g/cm3)

[g/cm3]

roll

imp23~40.2~

EE

NdNd

ff

Eimp = - p dVV0

V

Suyama et al. submitted to ApJ

微惑星の形成

ダストの合体成長　→ 微惑星形成

微惑星の円盤が形成

不明な点が多い重力不安定で形成？乱流が成長を妨害するダストの合体成長？中心星に落下する衝突で破壊される乱流渦中で形成？氷の昇華で密度上昇？

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

↓

暴走成長により少数の微惑星が急成長

火星サイズの原始惑星が形成

↓

暴走成長（寡占成長）の様子OLIGARCHIC GROWTH OF PROTOPLANETS 177

runaway stage, while most planetesimals remain small. Thetypical orbital separation of protoplanets kept while grow-ing is about 10rH. This value depends only weakly on themass of protoplanets, the surface density of the solid mate-rial, and the semimajor axis. This self-organized structureis a general property of self-gravitating accreting bodiesin a disk when gravitational focusing and dynamical frictionare effective.

If we assume that the oligarchic growth continues tillthe final stage of planetary accretion, the mass of proto-planets is estimated by M � 2�ab�. In the solar nebulamodel that is 50% more massive than the minimum massmodel, the surface mass density of the solar nebula isgiven by

� � �10 � a1 AU��3/2

[g cm�2] a � 2.7 AU

4 � a5 AU��3/2

[g cm�2] a � 2.7 AU.

(12)

Adopting this � and b � 10rH, we have M � 0.2M� andb � 0.07 AU at 1 AU (� � 10 g cm�2), M � 7M� andb � 2 AU at 7 AU (� � 2.4 g cm�2), and M � 17M� andb � 8 AU at 25 AU (� � 0.36 g cm�2), where M� is theEarth mass. In the terrestrial planet region, the estimatedmass and the orbital separation of protoplanets are stillsmaller than the present planets. This may suggest thatoligarchic growth does not continue till the final stage ofplanetary accretion in the terrestrial planet region. TheFIG. 4. The same as Fig. 1 but for the system initially consists of

4000 equal-mass planetesimals (m � 3 � 1023 g). The radius increase orbital separation may get larger in the terrestrial planetfactor is 6. In the final frame, the filled circles represent protoplanets region, if the radial excursion of planetesimals ea that isand lines from the center of the protoplanets to both sides have the proportional to the random velocity gets larger than 10rHlength of 5rH. The protoplanets are selected if their masses are larger than

due to, for example, the clearance of solar nebula gas in1/5 of the maximum mass of the system. The numbers of planetesimals arethe late stage of planetary accretion. The absence of gas1977 (t � 5000 years), 1514 (t � 10,000 years), and 1116

(t � 20,000 years). drag leads to the higher velocity dispersion and thus widerradial excursion.

In the jovian planet region, however, the oligarchicgrowth may be consistent with the formation of the presentare formed, while most planetesimals remain small. Theplanets. As for Jupiter and Saturn, which have massive gasfive protoplanets have the 34% of the total mass of theenvelopes, the estimated mass of protoplanets is as largesystem. The lines with the length of 5rH are drawn fromas the critical mass to onset the gas accretion onto thethe center of the protoplanets to both sides in the finalprotoplanets. As for Uranus and Neptune, which consistframe. This Hill radius is slightly modified to include onlymainly of solid material, the estimated mass of proto-the mass of a protoplanet. The separations are roughlyplanets and the orbital separation are consistent with theirconstant with the typical value of 5–10rH, which agreespresent values. These results suggest that jovian planetswell with the result of the two-protoplanet system and themay have been formed along the line of oligarchic growth.analytical estimation.However, we should be careful when we apply oligarchicgrowth to the jovian planet region. Oligarchic growth is4. CONCLUSION AND DISCUSSIONobtained from the local area simulation where the semima-jor axis is much larger than the width of the simulationWe have shown the oligarchic growth of protoplanets in

the post-runaway stage. Protoplanets with the same order region. It is uncertain that oligarchic growth takes placein the wide jovian planet region in the same way as the localmasses with the orbital separation larger than about 5rH

is the inevitable outcome of planetary accretion in the post- area simulation. Further work on this issue is required.

軌道長半径 [AU]

軌道離心率

ON RUNAWAY GROWTH OF PLANETESIMALS 185

FIG. 2. The number of bodies as a function of time.

f � 5. We study in detail how runaway growth starts and FIG. 4. The results of other two simulations at t � 20,000 years onthe a–e plane using different random numbers to produce the initialproceeds. We have done similar simulations with differentdistributions of planetesimals.random numbers that produce initial distribution of plane-

tesimals. Their results are qualitatively the same. We alsoperformed simulations of 2-D accretion where orbits ofplanetesimals are confined to a plane and compared with

3-D accretion. Note again that the time scale of the resultsis the value with f � 5 but not realistic one that should beobtained by adequate scaling. The accretion would proceedmore slowly in a real system.

4.1. Runaway Growth of Planetesimals

Snapshots of the system on the a–e and a–i planes att � 5000, 10,000, 20,000 years are shown in Figs. 1a and1b. The circles represent planetesimals and the radii of thecircles are proportional to the radii of planetesimals. Thenumber of bodies is plotted against time in Fig. 2. It de-creased from 3000 to 1059 in 20,000 years. In our calcula-tion, we consider runaway growth as that the largest bodylocally grows more rapidly than the second largest one,where ‘‘locally’’ means the range of the feeding zone ofthe largest body, and that the ratio of the mass of thelargest body and the mean mass grows with time. By thisdefinition, we see that two planetesimals run away in Fig.1. It is clearly shown in Fig. 3 that the ratio of the maximummass, the first runaway body (solid curve), to the meanmass (dashed curve) grows with time, in other words, run-away occurs. We have a similar figure for the second run-FIG. 3. The maximum mass of the planetesimals (solid curve) andaway body. The mass of the maximum body becomes 398their mean mass except the maximum (dashed curve) are plotted as a

function of time. times of its initial mass after 20,000 years, while the mean

時間 [年]質量 [1

023 g]

平均値

最大の天体

大きな天体がより大きくなる適当な間隔で原始惑星が並ぶ

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

ジャイアントインパクトの様子

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 " 0:79 ! 0:15.The accretion timescale is hTacci " 1:05 ! 0:58# $ ; 108 yr. Theseresults are consistent with Agnor et al. (1999), whose initial con-ditions are the same as the standard model except for !1 " 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 " 0:8 AU, while the second-largest avoid thesame semimajor axis as the largest, shown as the gap around a "ha1i. 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 " 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

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

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 ! 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 ! 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 ! 0 plane. Note that, in the bottom panels, thestreamlines are projected onto the y ! 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 ! 0 plane are plotted. The bottompanels (l ! 3) are 4 times the spatial magnification of the top panels (l ! 1). Three levels of grids are shown in each top (l ! 1, 2, and 3) and bottom (l ! 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

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

汎惑星形成論へ

バラエティに富む系外惑星系

標準的な惑星形成シナリオによって説明可能か？

惑星系の多様性を生み出す要素・原始惑星系円盤の質量の違い　 → ガス惑星の個数や位置の違いを生む？・形成中の惑星の中心星方向への落下（タイプ I 惑星落下 ＆ タイプ II 惑星落下）　 → 最終的な惑星の位置の違いを生む？・惑星の移動に伴う惑星系の変化　 → より多様な惑星系が形成される？・軌道不安定による惑星系の変化　 → 長い時間をかけて異なる惑星系へ移行？

多様な原始惑星系円盤

0

3

6

9

12

15

0.0001 0.001 0.01 0.1 1

牡牛座 へびつかい座

0.001 0.01 0.10.0001 1.0円盤の質量 [太陽質量]

発見数

太陽系復元円盤

宇宙には様々な質量を持つ原始惑星系円盤が存在　→ 円盤の質量の違いが多様な惑星系を生み出す！？

多様な円盤から生まれる多様な惑星

円盤の質量の違い → ガス惑星の数と位置の違い

protoplanets formmore massive planets thanMcr, they can-not become gas giants since giant impacts are possible onlyafter the depletion of most of the gas (Iwasaki et al. 2002;Kominami & Ida 2002). A planetary system formed fromthe light disk would consist of many relatively small solidplanets, terrestrial planets inside the snow border, andUranian planets outside the snow border.

6.4.2. Massive Disk (!1 ’ 100)

For the disk as massive as !1 ’ 100, Miso ’ 5 M! at 1AU, which is large enough for gas accretion within Tdisk.Gas giants can form in the inner disk (a " 1 AU). Further-more, in the massive disks, the growth timescale of proto-planets is so short that Tgrow < Tdisk even at large a.Therefore, several gas giants would form in relatively mas-sive disks with !1e30. Uranian planets would form outsidethe Jovian planets. We will discuss the massive disk case inrelation to the origin of observed extrasolar planets in moredetail below.

6.4.3. Medium (Standard)Disk (!1 ’ 10)

In the disk with!1 ’ 10, a planetary system similar to thesolar system is expected. In this disk, gas giants can formonly in the limited range beyond the snow border. Thisrange depends on Tdisk. For Tdisk " 108 yr, one or two gasgiants may form between the snow border and about 10AU. In this case, we have terrestrial planets, Jovian planets,andUranian planets from inner to outer system.

In Figure 13, we schematically summarize the predicteddiversity of planetary systems produced by the disk massvariation for disks with ! < 2.

It should be noted that in the oligarchic growth model weassumed the accretion in the gas disk. However, by defini-tion, Tgrow of Uranian planets beyond the Jovian planetzone exceeds Tdisk. After the dispersal of the gas disk, therandom velocity of planetesimals is pumped up as high asthe escape velocity of protoplanets. This high random veloc-ity makes the accretion process slow and ine!cient and thusTgrow longer. This accretion ine!ciency is a severe problem

for the formation of Uranian planets in the solar system(Levison & Stewart 2001). One possible solution to thisproblem is that Uranian planets form in the Jovianplanet region and are subsequently transported outward(Thommes, Duncan, & Levison 1999, 2002a).

6.5. Origin of Extrasolar Planets

The disk mass dependence of planetary systems suggeststhat the number of Jovian planets increases with the diskmass. However, initially formed Jovian planet systemswould not be the final configuration of planetary systemssince planetary systems with more than three giant planetsmay not be stable systems in the long term (e.g., Chambers,Wetherill, & Boss 1996;Marzari &Weidenschilling 2002). Aplanetary system of several gas giants may become orbitallyunstable against long-term mutual perturbations. After theejection of some planets or merging, orbitally stable planetsin eccentric orbits would remain, which may correspond toobserved extrasolar planets in eccentric orbits (Rasio &Ford 1996; Weidenschilling & Marzari 1996; Lin & Ida1997;Marzari &Weidenschilling 2002). In addition, interac-tions between gas giants and a residual relatively massivegas diskmay lead to significant orbital decay to a central star(e.g., Lin & Papaloizou 1993), which may correspond toextrasolar planets with short orbital periods (hot Jupiters)such as 51 Peg b (Lin, Bodenheimer, &Richardson 1996).

If an extremely massive disk with !1e200(Mdiske0:3 M# for ! $ 3=2) is considered, Figure 12 sug-gests that in situ formation of hot Jupiters at a " 0:05 AUsuch as 51 Peg b, " And b, etc., may be possible. However,dust particles may be evaporated at a " 0:05 AU in thedisk, which inhibits planetesimal formation, and/or ultra-violet and X-ray radiation from a T Tauri star may strip thegas envelope of a young gas giant (Lin et al. 1996). Hence,the migration model may be favored for hot Jupiterformation.

On the other hand, in situ formation of extrasolar planetsin circular orbits around a ’ 0:2 AU such as # CrB b andHD 192263 b is likely to occur in relatively massive diskswith !1e100 (Mdiske0:15 M#). The inhibition processesfor in situ formation for hot Jupiters do not apply to thiscase. It is di!cult for the migration (Lin et al. 1996) or theslingshot model (Rasio & Ford 1996) to explain planets incircular orbits at a ’ 0:2 AU because tidal interaction orthe magnetic field of a host star, which circularizes orbits,may be weak there. In situ formation in relatively massivedisks may be most promising.

7. SUMMARY AND DISCUSSION

Terrestrial and Uranian planets and solid cores ofJovian planets form through accretion of planetesimals. Inplanetary accretion, oligarchic growth of protoplanets is akey process that controls the basic structure of planetarysystems.

We confirmed that the oligarchic growth model generallyholds in the wide variety of planetesimal disks!solid $ !1%a=1 AU&'! g cm'2 with !1 $ 1, 10, 100 and! $ 1=2; 3=2; 5=2 by performing global N-body simula-tions. We derived how the characteristics of protoplanetsystems depend on the initial disk mass (!1) and the initialdisk profile (!). The oligarchic growth model gives thegrowth timescale and the isolation mass as equations (15)and (17), respectively, which are in good agreement with the

a

Mdisk T <Tgrow diskT <Tcont disk

Fig. 13.—Schematic illustration of the diversity of planetary systemsagainst the initial disk mass for ! < 2. The left large circles stand for centralstars. The double circles (cores with envelopes) are Jovian planets, and theothers are terrestrial and Uranian planets. [See the electronic edition of theJournal for a color version of this figure.]

678 KOKUBO & IDA Vol. 581

原始惑星系円盤の質量

軌道長半径 (中心星からの距離)

タイプ I 惑星落下月質量～10地球質量の天体に効くメカニズム天体が円盤に立てた密度波により角運動量を失う

タイプ II 惑星落下10地球質量以上の天体に効くメカニズム天体が円盤に溝を作り円盤とともに中心星に落下

理論的に予想される惑星の多様性

last section, the gas truncation by Mgas;vis seems to be incon-sistent with the observational data, but the migration conditionby Mgas;vis may be reasonable.)

In these calculations, !dep ! 106 107 yr. The time-dependentcalculation of disk evolution (Lynden-Bell & Pringle 1974)indicates that the disk mass declines on the viscous diffusiontimescale near Rm. If gas depletion in disks is due to theirviscous evolution, we would expect !dep to be comparable to!disk; acc (eq. [70]) near Rm " 10 AU. In order to match the ob-served properties of protostellar disks around classical T Tauristars, we adopt " ! 10#4, which corresponds to !dep=!disk; acc "1 at 10 AU.

The results of our simulations are shown in Figure 12 forthree series of models. In each case, the gas and core accretionare truncated by the conditions that correspond to those inFigure 9. The results show that the spatial distribution of the

gas-poor cores is not affected by the migration because it onlyaffects those planets that are able to accrete gas and to open upgaps. But for gas giant planets, equation (65) indicates that themigration timescale increases with their masses and semimajoraxes. The less massive gas giants are formed preferentiallywith relatively small semimajor axes, and they migrate to"0.04 AU in all the cases. This result is consistent with theobserved mass distribution of the short-period planets, whichappears to be smaller than that of planets with periods longerthan a few months (Udry et al. 2003).

Gas giant planets with !migP !disk migrate over extendedradial distance provided that the disk gas is preserved for asufficiently long time for them to form. For example, thecritical value of fdisk for the formation of gas giants is "3–8 ata " 1 AU where #ice ! 1 (see x 4.1). From equation (18), wefind that in disks with fdisk larger than the critical value, the

Fig. 12.—Similar plots as Fig. 9, but with the effect of type II migration included. The value of " -viscosity is taken as " ! 10#4 to be consistent with diskdepletion times "106–107 yr. (a) Gas accretion is truncated by Mg; iso and core accretion by Mc;iso; (b) Mg; iso and Mc;no iso; (c) Mg; th and Mc; iso. We adopt !ag ! 2rHin (a) and M$ ! 1 M% in (c).

DETERMINISTIC MODEL OF PLANETARY FORMATION. I. 409No. 1, 2004

軌道長半径 [AU]

惑星の質量 [M

E]

地球型惑星

巨大氷惑星

巨大ガス惑星

Hot Jupiter

巨大惑星の移動に伴う惑星系の変化stirred by interactions between bodies, andclearing continues through scattering. After200 million years the inner disk is composedof the collection of planetesimals at 0.06 AU, a4 M] planet at 0.12 AU, the hot Jupiter at 0.21AU, and a 3 M] planet at 0.91 AU. Previousresults have shown that these planets are likelyto be stable for billion-year time scales (15).Many bodies remain in the outer disk, and ac-

cretion and ejection are ongoing due to longorbital time scales and high inclinations.

Two of the four simulations from Fig. 2contain a 90.3 M] planet on a low-eccentricityorbit in the habitable zone, where the temper-ature is adequate for water to exist as liquid ona planet_s surface (23). We adopt 0.3 M] as alower limit for habitability, including long-termclimate stabilization via plate tectonics (24).

The surviving planets can be broken down intothree categories: (i) hot Earth analogs interior tothe giant planet; (ii) Bnormal[ terrestrial planetsbetween the giant planet and 2.5 AU; and (iii)outer planets beyond 2.5 AU, whose accretionhas not completed by the end of the simulation.Properties of simulated planets are segregated(Table 1): hot Earths have very low eccentric-ities and inclinations and high masses because

Fig. 1. Snapshots in time of the evolution of one simulation. Each panelplots the orbital eccentricity versus semimajor axis for each surviving body.The size of each body is proportional to its physical size (except for thegiant planet, shown in black). The vertical ‘‘error bars’’ represent the sine

of each body’s inclination on the y-axis scale. The color of each dotcorresponds to its water content (as per the color bar), and the dark innerdot represents the relative size of its iron core. For scale, the Earth’s watercontent is roughly 10j3 (28).

REPORTS

8 SEPTEMBER 2006 VOL 313 SCIENCE www.sciencemag.org1414

巨大惑星が落下する際に周囲の原始惑星の軌道を大きくかき乱す

they accrete on the migration time scale (105

years), so there is a large amount of dampingduring their formation. These planets are remi-

niscent of the recently discovered, close-in 7.5M]planet around GJ 876 (25), whose formation isalso attributed to migrating resonances (26).

Farther from the star, accretion time scales arelonger and the final phases take place after thedissipation of the gas disk (at 107 years), caus-ing the outer terrestrials to have large dynam-ical excitations and smaller masses, becauseaccretion has not completed by 200 million years;collisions of outer bodies such as these may beresponsible for dusty debris disks seen aroundintermediate-age stars (27). In the Bnormal[ ter-restrial zone, dynamical excitations and massesfall between the two extremes as planets formin a few times 107 years, similar to the Earth_sformation time scale (10). In addition, the averageplanet mass in the terrestrial zone is comparableto the Earth_s mass, and orbital eccentricitiesare moderate (Table 1).

Both the hot Earths and outer Earth-likeplanets have very high water contents Eup to9100 times that of Earth (28)^ and low iron con-tents compared with our own terrestrial planets(Table 1). There are two sources for these trendsin composition: (i) strong radial mixing inducedby the migrating giant planet, and (ii) an influxof icy planetesimals from beyond 5 AU fromgas drag-driven orbital decay that is unimpededby the scattering that Jupiter performs in ourown system. The outer terrestrial planets ac-quire water from both of these processes, butthe close-in giant planet prevents in-spiralingicy planetesimals from reaching the hot Earths.The accretion of outer, water-rich material di-lutes the high iron content of inner disk mate-rial, so water-rich bodies naturally tend to beiron-poor in terms of mass fraction. The highwater contents of planets that formed in thehabitable zone suggest that their surfaces wouldbe most likely covered by global oceans severalkilometers deep. Additionally, their low ironcontents may have consequences for the evolu-tion of atmospheric composition (29).

The spacing of planets (Fig. 2) is highlyvariable; in some cases planets form relativelyclose to the inner giant planet. The ratio of orbitalperiods of the innermost 90.3 M] terrestrialplanet to the close-in giant ranges from 3.3 to 43,with a mean (median) of 12 (9). We can there-fore define a rough limit on the orbital distanceof an inner giant planet that allows terrestrialplanets to form in the habitable zone. For a ter-restrial planet inside the outer edge of the hab-itable zone at 1.5 AU, the giant planet_s orbitmust be inside È0.5 AU (the most optimisticcase puts the giant planet at 0.68 AU). We applythis inner giant planet limit to the known sampleof extrasolar giant planets Eincluding planetsdiscovered by the radial velocity, transit, andmicrolensing techniques (1, 2)^ in combinationwith a previous study of outer giant planets(30). We find that 54 out of 158 (34%) giantplanetary systems in our sample permit anEarth-like planet of at least 0.3 M] to form inthe habitable zone (Fig. 3). The fraction ofknown systems that could be life-bearing maytherefore be considerably higher than previousestimates (30).

Fig. 3. Giant planetorbital parameter spacethat allows terrestrialplanets to form in thehabitable zone. The sol-id line indicates thelimit for outer giantplanets from (30). Thedashed line is an ap-proximate limit (0.5 AUwith eccentricity lessthan 0.1—the maximumeccentricity achieved inmost simulations—for asolar-mass star) insidewhich low-eccentricitygiant planets allow forthe formation of habit-able planets, derivedfrom our results and(15). We calculated the habitable zone (HZ, shaded area) by assuming the temperature to scale withthe stellar flux (i.e., the square root of the stellar luminosity), using a stellar mass-luminosity relationfit to data of (36). Open circles represent known giant planets that are unlikely to allow habitableterrestrial planets in the habitable zone. Filled circles represent known planets with low enoughorbital eccentricities to satisfy our criteria for habitable planet formation, deemed to be potentiallylife-bearing.

Fig. 2. Final configuration of our four simulations, with the solar system shown for scale. Eachsimulation is plotted on a horizontal line, and the size of each body represents its relative physical size(except for the giant planets, shown in black). The eccentricity of each body is shown beneath it,represented by its radial excursion over an orbit. As in Fig. 1, the color of each body corresponds to itswater content, and the inner dark region to the relative size of its iron core. The simulation from Fig. 1is JD-5. Orbital values are 1-million-year averages; solar system values are 3-million-year averages (35).See table S1 for details of simulation outcomes. Note that some giant planets underwent additionalinward migration after the end of the forced migration, caused by an articial drag force. This causedmany hot Earths to be numerically ejected, but had little effect outside the inner giant planet. Seesupporting online material for details.

REPORTS

www.sciencemag.org SCIENCE VOL 313 8 SEPTEMBER 2006 1415

多様な惑星系形成

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1軌道不安定による惑星系の変化惑星間の重力の影響が積み重なって最終的に互いの軌道が不安定化

異なる惑星系へ↓

Eccentric Planet の起源？

おまけ：重力不安定による惑星形成

原始惑星系円盤から直接ガス惑星が形成される可能性

生命を宿す惑星の発見へ向けて

生命存在条件生命の定義

(1) 自己と外界を区別する膜を持つこと(2) 代謝をすること(3) 自己複製をすること

惑星の表面に液体の水が存在すること

このような特徴を持った「生命」が生まれるための必要条件

これを便宜的に惑星科学における生命存在条件とする

Habitable Zone（生命居住可能領域）＊軌道半径＊液体の水が存在できる温度中心星の明るさによる＊ 惑星質量＊重力で大気が保持できるガス惑星にまで成長しない地球質量の1/3～3倍程度＊惑星大気＊温室効果が適度に効く水や二酸化炭素の量による

太陽型星の周りのHabitable Zone

様々な Habitable Planet (Satellite)

d

バイオマーカー（生物存在の証拠）生物活動によって作られたと考えられる物質（酸素、オゾン、植物の葉緑体、核爆発、、、）

大気にオゾンの吸収線を検出　　　　　　↓下層大気に大量の酸素が存在　　　　　　↓光合成を行う生命が存在！？

系外地球型惑星の超精密測光超精密分光観測が必要

地球型惑星発見へ向けての観測計画Kepler（2009年３月～）トランジット観測による系外地球型惑星の検出

Darwin（2015年以降）３機編隊の干渉計惑星の大気成分を検出

TPF（無期延期中）

「第二の地球」の発見へ向けて・巨大ガス惑星の発見（1995年）・惑星大気の観測（2002年）・惑星赤外線輻射（惑星の温度）の検出（2005年）・Super-Earth系の発見（2007年）・惑星の直接撮像（2008年）・系外惑星リング・衛星の発見・地球型惑星・Habitable Planet の発見・地球型惑星の直接検出（測光＆分光）・地球型惑星の大気成分・バイオマーカーの同定・地球外生命の発見！

フェルミのパラドックス

イタリアの物理学者（1901-1954）

Where are they?地球に似た惑星は恒星系の中で典型的に形成されうる ＝ 地球外文明はたくさんある？

これまで地球外文明との接触の証拠は皆無である = 地球外文明は存在しない？

天文学・生物学・数学・宇宙生物学等を巻き込む議論

参考図書

連絡先❖ Sasaki Takanori Online：http://sasakitakanori.com　トップページに講義資料へのリンクを載せておきます　参考図書の紹介とアマゾンへのリンクも載せておきます

❖ メール：takanori@geo.titech.ac.jp　本講義全体の代表メールアドレス

講義の感想, 質問, 要望, 相談惑星科学全般についての質問研究や研究者についての質問