12. 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]
13. 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]
15. 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]
18. 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
27. 多様な円盤から生まれる多様な惑星
円盤の質量の違い → ガス惑星の数と位置の違い
the escape velocity of protoplanets. This high random 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 Æ1e1
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 Æ1ð
¼ 1=2; 3=
tions. We d
systems dep
disk profile
growth tim
and (17), re
a
Mdisk T Tgrow diskT Tcont 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.]
原始惑星系円盤の質量
軌道長半径 (中心星からの距離)
[Kokubo Ida, 2002]
28. 惑星の移動に伴う惑星系の変化
earing continues through scattering. After
00 million years the 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).
タイプ I, II 惑星落下に
より惑星系の軌道が大き
くかき乱される
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).
多様な惑星系形成
[Raymond et al., 2006]
