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宇宙科学入門(2017年度後期)

 宇宙科学入門(2017年度後期)

学部生向け教養講義である宇宙科学入門で、惑星形成論+系外惑星に関する話をしてきました。そのときの講義資料です。

Takanori Sasaki

October 19, 2017
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  1. ݪ࢝࿭੕ܥԁ൫ '"('+, !  !+% ) ( !+*& '+ ! ) $

    #) ('+ ݪ࢝࿭੕ܥԁ൫ ෼ࢠӢίΞ ෼ࢠӢίΞͷऩॖ ɹॏྗͱԕ৺ྗͷͭΓ͍͋ ݪ࢝࿭੕ܥԁ൫͕ܗ੒ (c) NASA
  2. KOKUBO AND IDA FIG. 4. Time evolution of the maximum

    mass (solid curve) and the mean mass (dashed curve) of the system. thanthisrangearenotstatisticallyvalidsinceeachmassbinoften has only a few bodies. First, the distribution tends to relax to a ๫૸త੒௕ͷ༷ࢠ ฏۉ஋ ࠷େͷఱମ ඍ࿭੕ͷ๫૸త੒௕ ɹˠݪ࢝࿭੕͕஀ੜ͢Δ 20 KOKUBO AND IDA FIG. 3. Snapshots of a planetesimal system on the a–e plane. The circles represent planetesimals and their radii are proportional to the radii of planetesi- mals. The system initially consists of 3000 equal-mass (1023 g) planetesimals. FIG. 4. Time evolution of the maximum mass (solid curve) and the mean mass (dashed curve) of the system. thanthisrangearenotstatisticallyvalidsinceeachmassbinoften has only a few bodies. First, the distribution tends to relax to a decreasing 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). This is because as a runaway body grows, the system is mainly heated by the runaway body (Ida and Makino 1993). In this case, the eccentricity and inclination of planetesimals are scaled by the يಓ௕൒ܘ<"6> يಓ཭৺཰ ࣭ྔ<H> ࣌ؒ<೥> <,PLVCP*EB >
  3. Չ઎త੒௕ͷ༷ࢠ 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 of planetesimals. 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- 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 of يಓ཭৺཰ ֤৔ॴͰඍ࿭੕͕๫૸త੒௕ ɹˠ౳αΠζͷݪ࢝࿭੕͕ฒͿ Չ઎త੒௕ͱΑͿ ʹ ֤يಓͰͷݪ࢝࿭੕ ࣭ྔ [kg] ܗ੒࣌ؒ [yr] ஍ٿيಓ 1×1024 7×105 ໦੕يಓ 3×1025 4×107 ఱԦ੕يಓ 8×1025 2×109 يಓ௕൒ܘ<"6> <,PLVCP*EB >
  4. ݪ࢝࿭੕͔Β࿭੕΁ )-/ %  (  $  2 

    .3 ( ) -/(% -/ ) 0  #    " 4+ ݪ࢝࿭੕ͷ࣭ྔ<஍ٿ࣭ྔ> يಓ௕൒ܘ<"6> ஍ٿܕ࿭੕ ɹݪ࢝࿭੕ಉ࢜ͷ߹ମ ڊେΨε࿭੕ ɹݪ࢝࿭੕ͷΨεั֫ ڊେණ࿭੕ ɹݪ࢝࿭੕ͦͷ·· TOPXMJOF (c) Eiichiro Kokubo
  5. δϟΠΞϯτΠϯύΫτ يಓ௕൒ܘ<"6> يಓ཭৺཰ 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 hna i ’ 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 fa i ¼ 0:79 Æ 0:15. The accretion timescale is hTacc i ¼ 1:05 Æ 0:58 ð Þ ; 108 yr. These results are consistent with Agnor et al. (1999), whose initial con- clus sam ha1 i larg are 0:06 hM2 0:05 Fig. 2.—Snapshots of the system on the a-e (left) and a-i (right) planes at t ¼ 0, 106, 10 are proportional to the physical sizes of the planets. KOKUBO, KOMINAM 1134 ௕͍࣌ؒΛ͔͚ͯݪ࢝࿭੕ಉ࢜ͷيಓ͕ཚΕΔ ɹˠޓ͍ʹিಥɾ߹ମͯ͠ΑΓେ͖ͳఱମʹ੒௕ <,PLVCP*EB > (c) Hidenori Genda
  6. ଟ༷ͳݪ࢝࿭੕ܥԁ൫ Դڇ࠲ ΁ͼ͔͍ͭ࠲      ԁ൫ͷ࣭ྔ<ଠཅ࣭ྔ> ൃ

    ݟ ਺ ଠཅܥ෮ݩԁ൫ Ӊ஦ʹ͸༷ʑͳ࣭ྔΛ࣋ͭݪ࢝࿭੕ܥԁ൫͕ଘࡏ ɹˠԁ൫ͷ࣭ྔͷҧ͍͕ଟ༷ͳ࿭੕ܥΛੜΈग़͢ʂʁ
  7. ଟ༷ͳԁ൫͔Βੜ·ΕΔଟ༷ͳ࿭੕ ԁ൫ͷ࣭ྔͷҧ͍ˠΨε࿭੕ͷ਺ͱҐஔͷҧ͍ the escape velocity of protoplanets. This high random

    veloc- ity makes the accretion process slow and inefficient and thus Tgrow longer. This accretion inefficiency is a severe problem On the other in circular orb HD 192263 b with Æ1e 100 for in situ form case. It is diffic slingshot mod circular orbits the magnetic fi may be weak t disks may be m 7. Terrestrial Jovian planets planetary accr key process th systems. We confirme holds in th Æsolid ¼ Æ1 ða= ¼ 1=2; 3=2; tions. We der systems depen disk profile ( growth timesc and (17), respe a Mdisk T <T grow disk T <T cont disk Fig. 13.—Schematic illustration of the diversity of planetary systems against the initial disk mass for < 2. The left large circles stand for central stars. The double circles (cores with envelopes) are Jovian planets, and the others are terrestrial and Uranian planets. [See the electronic edition of the Journal for a color version of this figure.] ݪ࢝࿭੕ܥԁ൫ͷ࣭ྔ يಓ௕൒ܘ த৺੕͔Βͷڑ཭ <,PLVCP*EB >
  8. Weidenschilling &,Marzari (1996),,Lin,&,Id   a GM a GM a

    GM a GM a GM * * 3 * 2 * 1 *     $&,60 45 '"#, (t >~ 1My) /% , "# 2-+0'! 3. *) 1."#3. 00 a1 0  . 00 a1(. final e 0. 0. 0. 0. 0 1 يಓෆ҆ఆʹΑΔ࿭੕ܥͷมԽ ࿭੕ؒͷॏྗͷӨڹ͕ ੵΈॏͳͬͯ࠷ऴతʹ ޓ͍ͷيಓ͕ෆ҆ఆԽ ҟͳΔ࿭੕ܥ΁ ˣ </BHBTBXBFUBM > ᶃ ᶃ ᶄ ᶄ ᶅ ᶅ
  9. ࿭੕ͷҠಈʹ൐͏࿭੕ܥͷมԽ clearing continues through scattering. After 200 million years the

    inner disk is composed of the collection of planetesimals at 0.06 AU, a 4 M] planet at 0.12 AU, the hot Jupiter at 0.21 AU, and a 3 M] planet at 0.91 AU. Previous results have shown that these planets are likely to be stable for billion-year time scales (15). Many bodies remain in the outer disk, and ac- orbital time scales and high inclinations. Two of the four simulations from Fig. 2 contain a 90.3 M] planet on a low-eccentricity orbit in the habitable zone, where the temper- ature is adequate for water to exist as liquid on a planet_s surface (23). We adopt 0.3 M] as a lower limit for habitability, including long-term climate stabilization via plate tectonics (24). three categories: (i) hot Earth analogs interior to the giant planet; (ii) Bnormal[ terrestrial planets between the giant planet and 2.5 AU; and (iii) outer planets beyond 2.5 AU, whose accretion has 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 panel plots the orbital eccentricity versus semimajor axis for each surviving body. The size of each body is proportional to its physical size (except for the giant 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 dot corresponds to its water content (as per the color bar), and the dark inner dot represents the relative size of its iron core. For scale, the Earth’s water content is roughly 10j3 (28). λΠϓ* **࿭੕མԼʹ ΑΓ࿭੕ܥͷيಓ͕େ͖ ͔͖͘ཚ͞ΕΔ they accrete on the migration time scale (105 years), so there is a large amount of damping during their formation. These planets are remi- niscent of the recently discovered, close-in 7.5 M] planet around GJ 876 (25), whose formation is also attributed to migrating resonances (26). Far lon diss ing ical acc coll resp inte rest fall in a form pla to are plan 910 tent (Ta in c by ଟ༷ͳ࿭੕ܥܗ੒ <3BZNPOEFUBM >
  10. http://sasakitakanori.com ޻ֶࣾͷຊ ͷ෺ཧΛཧܥߴߍੜ΍ΤϯδχΞʹʮҰ໷௮͚ʯͰ఻तʂʂ ͷൿີʦ૿ิ൛ʧ ทɹ˙ຊମԁ ɹ4'өըΛ؍͍ͯΔͱɺ ʮ࣍ݩʯ ΍ ʮҟ࣍ݩʯ ͱ͍͏ݴ༿͕සൟʹग़

    ͖ͯ·͢ɻ ͔͠͠ɺ ͦͷ ʮ࣍ݩʯ ΍ ʮҟ࣍ݩʯ ͷҙຯΛയવͱ஌͍ͬͯ Δਓ͸ଟ͍ͱࢥ͍·͕͢ɺ ࣮ࡍͦ ΕΛཧղ͢ΔͱͳΔͱɺ ͔ͳΓ೉ ͍͠ͱࢥ͍·͢ɻ ɹͦ͜ͰຊॻͰ͸ɺ ͦͷ ʮ࣍ݩʯ ͱ ͸͍͍ͬͨԿͳͷ͔Λɺ ʮ૬ରੑཧ ࿦ʯ ʮࣗવ୯Ґܥʯ ͳͲͷجૅ͔Β ࠷ઌ୺ͷ ʮ%ϒϨʔϯʯ ·Ͱɺ ෼͔ Γ΍͘͢ղઆ͍ͯ͠·͢ɻ Ϋͳ෺ཧֶͷ਺ࣜΛಡΈղ͘ ΦͱΞΠϯγϡλΠϯํఔࣜ ทɹ˙ຊମԁ ɹ͜ͷӉ஦࿦ೖ໳Ͱ͸ɺ ֶज़ࢽʹܝ ࡌ͞Εͨ࢐৽͔ͭ෩มΘΓͳӉ஦ ࿦ͷԾઆΛωλʹɺ ͍ܰΤοηΠ෩ ͷϢʔϞΞΛ·͑͡ͳ͕Βཧ࿦ͷ ୉ޣຯΛ঺հ͠·͢ɻ ɹ·ͨɺ ඪ४తͳӉ஦࿦Λྫʹɺ ʮܭ ྔʯ ʮ઀ଓʯ ʮϦʔϚϯͷςϯιϧʯ ʮϦονͷεΧϥʔʯ ͱ͍ͬͨ΋ͷͷ ܭࢉ͔Βɺ ʮΞΠϯγϡλΠϯํఔ ࣜʯ ·Ͱɺ ߴ౓ͳ਺ֶΛߴߍੜ΍α ϥϦʔϚϯͰ΋ཧղͰ͖ΔΑ͏ʹॻ ͖Լ͍͖ͯ͠·͢ɻ ͷݯઘʹഭΔʂ ൃ໌త૝૾ྗͷಾ ทɹ˙ຊମԁ ɹੈل຤ʹ׆༂ͨ͠ൃ໌Ոɺ χί ϥɾςεϥɻ ൴͸ΤδιϯͷϥΠό ϧͰ͋Γɺ ࠷΋ڪΕΒΕͨஉͩͱݴ ΘΕ͍ͯ·͢ɻ ɹ஌໊౓ͷ఺ʹ͓͍ͯ͸Τδιϯʹ ᴴ͔ʹͻ͚Λͱ͍ͬͯ·͕͢ɺ ަྲྀ ిྗʹ͸͡·Γɺ ܞଳి࿩ͷݪܕͱ ΋ݴ͑Δಉௐճ࿏ͱߴप೾ൃిػɺ ిࢠϨϯδͷجૅͰ͋Δߴप೾೤ͷ ൃݟ΍ແઢૢॎٕज़ͳͲɺ ݱ୅ٕज़ ͷجૅΛ࡞ͬͨਓ෺ͷҰਓͰ͢ɻ ɹຊॻͰ͸ɺ ൴ͷࣗ༝ͳ૝૾ྗͷݯ ઘΛ୳Γɺ ൴ͷ૑Γग़ٕͨ͠ज़͕ݱ ୅ʹ͓͍ͯ΋຺ʑͱੜ͖ଓ͚͍ͯ Δ͜ͱΛࣔ͠·͢ɻ ˙ݱ ⾣ ⾣ ⾣ ⾣ ⾣ ˙ଠ ⾣ ⾣ ⾣ ⾣ ⾣ ⾣ ⾣ ˙ ʮ ⾣ ⾣ ⾣ ⾣ ˙ੜ ⾣ ⾣ ⾣ ⾣ *4#/ $ ɹˇ& ఆՁɿຊମ  ԁʴ੫ ʮଠཅܥ࿭੕ʯ ʮܥ֎࿭੕ʯ ͷ੒Γཱͪͱɺ ʮଠཅܥʯ ʮ࿭੕ʯ ͷܗ੒ཧ࿦ FS೥݄೔ޕޙ࣌෼@ଋNN ޻ֶࣾ ⼦࿭੕ ⽜ ͷ࿩ ủ ࿭ ੕ ܗ ੒ ࿦ Ứ ΁ ͷ ট ଴ ⽥ ࿭ ੕ ⽦ ͷ ࿩ ࠤ ʑ ໦ ɹ و ڭ ޻ֶࣾ ʮ࿭੕ܗ੒࿦ʯ ΁ͷট଴ ࠤʑ໦ɹوڭ Takanori Sasaki ⼦࿭੕ ⽜ ͷ࿩ ʮ࿭੕ܗ੒࿦ʯ ΁ͷট଴ ç ʦΧ ৽ץຊ͕ग़·ͨ͠ʂ