天文学概論（第７回）

系外惑星 2～「第２の地球」へ向けて～

東京工業大学　佐々木貴教

系外惑星 2～「第２の地球」へ向けて～

・系外惑星の統計データ・太陽系形成論から汎惑星形成論へ・生命を宿す惑星の発見へ向けて

系外惑星の統計データ

系外惑星の発見数の変化

発見されている系外惑星の特徴

手法ごとの発見されている惑星の特徴

視線速度法 トランジット法

重力レンズ法 直接撮像

AU

Mj

惑星が発見されている恒星の特徴

系外惑星のデータを調べる・The Extrasolar Planets Encyclopaedia

・Catalog of Exoplanets

・Exoplanet for iPhone/iPod touch/iPad

http://exoplanet.eu

http://www.planetary.org/exoplanets/

太陽系形成論から汎惑星形成論へ

太陽系形成標準理論（林モデル）

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巨大氷惑星形成

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

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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).

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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

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多様な惑星系形成

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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

宇宙は地球であふれてる！？

理論計算観測

地球型惑星が大量に存在していることを示唆恒星の 23% が 0.5～2.0 M地球 の惑星を持つ！？

ケプラー宇宙望遠鏡2009年3月に打ち上げトランジット観測により主に系外地球型惑星を探索

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

Habitable Zone 内の惑星たち

様々な Habitable Planet (Satellite)

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

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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

「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）・地球型惑星・Habitable Planet の発見（2010年）・系外惑星リング・衛星の発見・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

エンリコ・フェルミ（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

今後のスケジュール11/16　松井　銀河系・近傍銀河（１）11/30　石山　初期宇宙と構造形成（１）12/7　石山　初期宇宙と構造形成（２）12/14　松井　銀河系・近傍銀河（２） 12/21　高梨　超新星・宇宙論（１）1/11　高梨　超新星・宇宙論（２）1/18　佐々木　全体のまとめ

レポート❖ハビタブルプラネットについてまとめる

❖レポートボックスに提出〆切：11/24（木）17:00

❖A4用紙（枚数は問わない）

❖所属学科・学年・学籍番号・氏名を明記

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レポートでまとめてもらう内容

❖ハビタブルプラネットの定義（どんな種類の惑星が考えられるか？）

❖ハビタブルプラネットの形成過程（中心星形成から地球型惑星形成までを追う）

❖ハビタブルプラネットの観測手法（どの手法を用いて何を観測すればよいか？）

❖ハビタブルプラネットへの想い（自由に）