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 తͷ༷ࢠ ฏۉ ࠷େͷఱମ ඍͷత ɹˠݪ͕࢝ੜ͢Δ 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 يಓܘ<"6> يಓ৺ ࣭ྔ<H> ࣌ؒ<> <,PLVCP*EB >
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৺ ֤ॴͰඍ͕త ɹˠαΠζͷݪ͕࢝ฒͿ ՉతͱΑͿ ʹ ֤يಓͰͷݪ࢝ ࣭ྔ [kg] ܗ࣌ؒ [yr] ٿيಓ 1×1024 7×105 يಓ 3×1025 4×107 ఱԦيಓ 8×1025 2×109 يಓܘ<"6> <,PLVCP*EB >
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 ͍࣌ؒΛ͔͚ͯݪ࢝ಉ࢜ͷيಓ͕ཚΕΔ ɹˠޓ͍ʹিಥɾ߹ମͯ͠ΑΓେ͖ͳఱମʹ <,PLVCP*EB > (c) Hidenori Genda
veloc- ity makes the accretion process slow and inefficient and thus Tgrow longer. This accretion inefficiency is a severe problem On the othe 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 disks may be m 7. Terrestrial Jovian planets planetary accr key process th systems. We confirm 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.] ݪ࢝ܥԁ൫ͷ࣭ྔ يಓܘ த৺͔Βͷڑ <,PLVCP*EB >
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 ΑΓܥͷيಓ͕େ͖ ͔͖͘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 ଟ༷ͳܥܗ <3BZNPOEFUBM >
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