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
corotation torque: delicate 0.1AU 1AU 10AU dead zone (DZ) inner disk edge or DZ inner edge Masset,et,al.,(2006), Ogihara,et,al.,(2010) DZ outer edge Hasegawa,&,Pudritz,(2012), Regaly,et,al.,(2013) ice line Kretke,&,Lin,(2007) theory: not clear <*EBTBO`TUBML>
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