imp 2 3 ~ 40 . 2 ~ E E N dN d f f E imp = - p dV V 0 V Suyama et al. submitted to ApJ μετͷ߹ମ μετͷ߹ମ ɹˠඍܗ ඍͷԁ൫͕ܗ (c) Toru Sayama ණඍܗՄೳ ؠੴඍഁյ͕ ӽ͠ܗෆՄೳ
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- Fig. 2.—Snapshots of the system on the a-e (left) and a-i (right) planes at t ¼ 0, 1 are proportional to the physical sizes of the planets. KOKUBO, KOMIN 1134 ͍࣌ؒΛ͔͚ͯݪ࢝ಉ࢜ͷيಓ͕ཚΕΔ ɹˠޓ͍ʹিಥɾ߹ମͯ͠ΑΓେ͖ͳఱମʹ <,PLVCP*EB > (c) Hidenori Genda
on the midplane (left) and in three dimensions, shown in bird’s-eye view (right). The gas stream MACHIDA ET AL. 1226 V 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 bottom 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. l 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 the ls. The velocity scale in units of the sound speed is denoted below each panel. पғͷԁ൫Ψε͕ݪ࢝ͷॏྗݍʹั֫͞ΕΔ (c) Takayuki Tanigawa
veloc- ity makes the accretion process slow and inefficient and thus Tgrow longer. This accretion inefficiency is a severe problem On the ot in circular o HD 192263 with Æ1e 1 for in situ f case. It is d slingshot m circular orb the magnet may be wea disks may b Terrestria Jovian plan planetary a key process systems. We confir holds in Æsolid ¼ Æ1 ð ¼ 1=2; 3= tions. We d systems dep disk profile growth tim and (17), re 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 the collection of planetesimals at 0.06 AU, a M] planet at 0.12 AU, the hot Jupiter at 0.21 U, and a 3 M] planet at 0.91 AU. Previous sults have shown that these planets are likely 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 g. 1. Snapshots in time of the evolution of one simulation. Each panel ots the orbital eccentricity versus semimajor axis for each surviving body. he size of each body is proportional to its physical size (except for the ant 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). ଟ༷ͳܥܗ <3BZNPOEFUBM >
noinoi79528
codeforeveryone
signer
mineo_matsuya
irocho
matleenalaakso
shiba_8ro
abap34
wagnerbeethoven
danielanewman
garrettdimon
mclloyd
panda_program
soudai
addyosmani
lauravandoore
denniskardys
paulrobertlloyd
pauljervisheath
eitanlees
sonatard
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