20111026

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©Newton Press

巨大氷惑星形成 ©Newton Press

V Eimp = - p dV V0d ~ Eimp [g/cm3] f ~ N 2.40 f 3 2dN Eroll Suyama et al. submitted to ApJ 10-4g

KOKUBO AND IDA20 KOKUBO AND IDA FIG. 4. Time evolution of the maximum mass (solid curve) and the mean mass (dashed curve) of the system. than this range are not statistically valid since each mass bin often 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 FIG. 4. Time evolution of the maximum mass (solid curve) and the mean mass (dashed curve) of the system. FIG. 3. Snapshots of a planetesimal system on the a–e plane. The circles than this range are not statistically valid since each mass bin oftenrepresent planetesimals and their radii are proportional to the radii of planetesi- has only a few bodies. First, the distribution tends to relax to a

FORMATION OF PROTOPLANETS FROM PLANETESIMALS 23 [kg] [yr] 1×1024 7×105 3×1025 4×107 8×1025 2×109FIG. 7. Snapshots of a planetesimal system on the a–e plane. The cir- FIG. 8. The number of bodies in linear mass bins is plotted for t = 100,000,

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1134 KOKUBO, KOMIN Fig. 2.—Snapshots of the system on the a-e (left) and a-i (right) planes at t ¼ 0, 1are proportional to the physical sizes of the planets.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 smallerplanet. 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 ofprotoplanets. In most runs, these planets are smaller scatteredplanets. Thus we obtain a high efﬁciency of h fa i ¼ 0:79 Æ 0:15.The accretion timescale is hTacc i ¼ ð1:05 Æ 0:58Þ ; 108 yr. Theseresults are consistent with Agnor et al. (1999), whose initial con-

1226 MACHIDA ET AL.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 ˜p and the central density c on the midplane are denoted above each of the t ˜ ls. The velocity scale in units of the sound speed is denoted below each panel.

20111026

by noinoi79528 on Oct 25, 2011

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