17. 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
暴走的成長の様子
平均値
最大の天体
微惑星の暴走的成長
→ 原始惑星が誕生する
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
軌道長半径 [AU]
軌道離心率
質量[1023g]
時間
[Kokubo & Ida, 2000]
18. FORMATION OF PROTOPLANETS FROM PLANETESIMALS 23
FIG. 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,
寡占的成長の様子軌道離心率
各場所で微惑星が暴走的成長
→ 等サイズの原始惑星が並ぶ
寡占的成長とよぶ
=
各軌道での原始惑星
質量 [kg] 形成時間 [yr]
地球軌道 1×1024 7×105
木星軌道 3×1025 4×107
天王星軌道 8×1025 2×109
軌道長半径 [AU]
21. ジャイアントインパクト
軌道長半径 [AU]
軌道離心率
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 hnai ’ 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 fai ¼ 0:79 Æ 0:15.
The accretion timescale is hTacci ¼ 1:05 Æ 0:58ð 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, KOMIN1134
長い時間をかけて原始惑星同士の軌道が乱れる
→ 互いに衝突・合体してより大きな天体に成長
[Kokubo & Ida, 2006]
25. 巨大ガス惑星の形成の様子
MACHIDA ET AL.1226
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.周囲の円盤ガスが原始惑星の重力圏内に捕獲される