11. random numbers that produce initial distribution of plane-
tesimals. Their results are qualitatively the same. We also
performed simulations of 2-D accretion where orbits of
暴走成長（寡占成長）の様子 planetesimals are confined to a plane and compared with
3-D a
OLIGARCHIC GROWTH OF PROTOPLANETS 177
is the
runaway stage, while most planetesimals remain small. The obtai
typical orbital separation of protoplanets kept while grow- more
ing is about 10rH. This value depends only weakly on the
mass of protoplanets, the surface density of the solid mate- 4.1. R
rial, and the semimajor axis. This self-organized structure
is a general property of self-gravitating accreting bodies Sna
質量 [1023g]
最大の天体
in a disk when gravitational focusing and dynamical friction t5
are effective. 1b. T
If we assume that the oligarchic growth continues till circle
the final stage of planetary accretion, the mass of proto- numb
軌道離心率
planets is estimated by M 2ab. In the solar nebula
model that is 50% more massive than the minimum mass 平均値 creas
model, the surface mass density of the solar nebula is tion,
given by locall
where
3/2
a the la
10 [g cm2] a 2.7 AU
1 AU larges
(12)
a 3/2 defini
4 [g cm2] a 2.7 AU. 1. It is
5 AU
mass,
時間 [年]
Adopting this and b 10rH, we have M 0.2M and mass
b 0.07 AU at 1 AU ( 10 g cm2), M 7M and away
bFIG. AU The maximum massgof the), and M 17M and
2 3. at 7 AU ( 2.4 cm2 planetesimals (solid curve) and away
their mean mass except the maximum (dashed curve) are plotted as a
b 8 AU at 25 AU ( 0.36 g cm2), where M is the
大きな天体がより大きくなる
function of time.
Earth mass. In the terrestrial planet region, the estimated
mass and the orbital separation of protoplanets are still
times
smaller than the present planets. This may suggest that
軌道長半径 [AU] 適当な間隔で原始惑星が並ぶ
oligarchic growth does not continue till the final stage of
FIG. 4. The same as Fig. 1 but for the system initially consists of planetary accretion in the terrestrial planet region. The
4000 equal-mass planetesimals (m 3 1023 g). The radius increase orbital separation may get larger in the terrestrial planet
13. ジャイアントインパクトの様子
1134 KOKUBO, KOMIN
軌道離心率
軌道長半径 [AU]
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.
長い時間をかけて原始惑星同士の軌道が乱れる
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 hna i ’ 1:8 Æ 0:7. In other words,
one or two planets tend to form outside the initial distribution of
→ 互いに衝突・合体してより大きな天体に成長
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 ð1:05 Æ 0:58Þ ; 108 yr. These
results are consistent with Agnor et al. (1999), whose initial con-
15. 1226 MACHIDA ET AL.
巨大ガス惑星の形成の様子
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.
周囲の円盤ガスが原始惑星の重力圏内に捕獲される
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
ls. The velocity scale in units of the sound speed is denoted below each panel.
t ˜
21. random velocity of planetesimals is pumped up as high as
the escape velocity of protoplanets. This high random veloc- On the ot
in circular o
多様な円盤から生まれる多様な惑星
ity makes the accretion process slow and inefficient and thus
Tgrow longer. This accretion inefficiency is a severe problem HD 192263
with Æ1 e1
for in situ f
Mdisk T cont Tdisk TgrowTdisk case. It is di
slingshot m
原始惑星系円盤の質量 circular orb
the magneti
may be wea
disks may b
Terrestria
Jovian plan
planetary a
key process
systems.
We confir
holds in
a Æsolid ¼ Æ1 ð
¼ 1=2; 3=
軌道長半径 (中心星からの距離) tions. We d
Fig. 13.—Schematic illustration of the diversity of planetary systems systems dep
against the initial disk mass for 2. The left large circles stand for central
disk profile
円盤の質量の違い → ガス惑星の数と位置の違い time
stars. The double circles (cores with envelopes) are Jovian planets, and the
others are terrestrial and Uranian planets. [See the electronic edition of the growth
25. earing continues through scattering. After orbital time scales and high inclinations. three categories: (i) hot Earth analogs interior to
00 million years the inner disk is composed Two of the four simulations from Fig. 2 the giant planet; (ii) Bnormal[ terrestrial planets
contain a 90.3 M] planet on a low-eccentricity
巨大惑星の移動に伴う惑星系の変化
the collection of planetesimals at 0.06 AU, a between the giant planet and 2.5 AU; and (iii)
M] planet at 0.12 AU, the hot Jupiter at 0.21 orbit in the habitable zone, where the temper- outer planets beyond 2.5 AU, whose accretion
U, and a 3 M] planet at 0.91 AU. Previous ature is adequate for water to exist as liquid on has not completed by the end of the simulation.
sults have shown that these planets are likely a planet_s surface (23). We adopt 0.3 M] as a Properties of simulated planets are segregated
be stable for billion-year time scales (15). lower limit for habitability, including long-term (Table 1): hot Earths have very low eccentric-
Many bodies remain in the outer disk, and ac- climate stabilization via plate tectonics (24). ities and inclinations and high masses because
巨大惑星が落下する際に
周囲の原始惑星の軌道を
大きくかき乱す
they accrete on the migration time scale (105
多様な惑星系形成
niscent of the recently discovered, close-in 7.5 M]
years), so there is a large amount of damping planet around GJ 876 (25), whose formation is
during their formation. These planets are remi- also attributed to migrating resonances (26).
g. 1. Snapshots in time of the evolution of one simulation. Each panel of each body’s inclination on the y-axis scale. The color of each dot
ots the orbital eccentricity versus semimajor axis for each surviving body. corresponds to its water content (as per the color bar), and the dark inner
he size of each body is proportional to its physical size (except for the dot represents the relative size of its iron core. For scale, the Earth’s water
ant planet, shown in black). The vertical ‘‘error bars’’ represent the sine content is roughly 10j3 (28).
