A Standard Scenario for Formation of Planetary Systems Eiichiro Kokubo (NAOJ)
A Standard Scenario forFormation of Planetary Systems
Eiichiro Kokubo (NAOJ)
OutlineIntroduction
• Formation models
From Planetesimals to Protoplanets• Runaway growth of planetesimals• Oligarchic growth of protoplanets
From Protoplanets to Planets• Terrestrial planet formation• Gas giant formation• Diversity of planetary systems
Towards a More Realistic Scenario• Orbital Migration
(EK & Ida 2012; Raymond, EK+ 2014)
Introduction
Formation Modelsmodel disk mass (M⊙) building blocks alias
disk instability ≃ 1 protoplanets Cameron
core accretion ≃ 0.01 planetesimals Kyoto/Moscow
Disk Instability Model (Basu, Takahashi, Tsukamoto)• difficult to form solid bodies• origin of wide-orbit giant planets?• hybrid with core accretion possible (e.g., Inutsuka+ 2010)
Core Accretion Model• standard for solar system formation (Safronov 1969; Hayashi+
1985)• applicable to formation of exoplanets
Basic HypothesesDisk Hypothesis
• A planetary system forms from a light circumstellar disk(protoplanetary disk) that is a by-product of star formation.
• A protoplanetary disk consists of gas and dust.
Planetesimal Hypothesis• Planetesimals are formed from dust.• Solid planets are formed by accretion of planetesimals.• Gaseous planets are formed by gas accretion onto solid
planets (cores) (“core accretion” model).
(Safronov 1969; Hayashi+ 1985)
Standard Scenario
protoplanetary disk
planetesimals
protoplanets
terrestrial planets gas giants ice giants
gas
dust
protosun
From Dust to PlanetesimalsGravitational Instability of a Dust Layer1. Formation of a dust layer2. Increase of the dust layer density3. Gravitational instability and fragmentation4. Contraction of fragments into planetesimals
(e.g., Goldreich & Ward 1973)
gas
dust
Pairwise Coagulation of Dust Grains(e.g., Weidenschilling & Cuzzi 1993)
Disk Model
planetesimals
Surface Density Distribution
planetesimal: Σd = 10ǫicefd
( r
1AU
)−α
gcm−2
gas: Σg = 2400fg
( r
1AU
)−α
gcm−2
ǫice = 1 (r < aice) and 4.2 (r > aice): ice factor; fd, fg: scale factors
Ice Line (T ≃ 170K: H2O condensation temp.)
aice = 2.7
(
L∗
L⊙
)1/2
AU
Assumptions• in situ formation, perfect accretion
From Planetesimals to Protoplanets
TerminologyRandom Velocity
• deviation velocity from a non-inclined circular orbit
vran ≃(
e2 + i2)1/2
vKe : eccentricity, i : incination, vK : Kepler circular velocity
Hill (Roche/Tidal) Radius• radius of the potential well of an orbiting body
rH =
(
m
3M∗
)1/3
a
M∗ : central body mass, m : orbiting body mass, a : semimajor axis
Growth Mode
d
dt
(
M1
M2
)
=M1
M2
(
1
M1
dM1
dt−
1
M2
dM2
dt
)
relative growth rate:1
M
dM
dt∝ Mp
runaway growthp<0 p>0
orderly growth
Growth Rate
M m
RTest body: M, R, vesc
Field bodies: n (number density), m
dM
dt≃ nπR2
(
1 +v2escv2rel
)
vrelm ⇒1
M
dM
dt∝ M1/3v−2
ran
(
vrel ≃ vran, n ∝ v−1ran, vesc ∝ M1/3, R ∝ M1/3, vrel < vesc
)
Random velocity controls• the growth mode• the growth timescale
Runaway Growth of Planetesimals
(AU)
e
a
yr
yr
yr
(EK & Ida 2000)
self-gravity of planetesimalsdominant for random velocity
vran 6= f(M)
⇓
1
M
dM
dt∝ M1/3v−2
ran ∝ M1/3
runaway growth!
Runaway Growth of Planetesimals
(10 g)m 23
nc
dotted: 0 yr, dashed: 105 yr, solid: 2× 105 yr(EK & Ida 2000)
d log nc
d logm≃ −
11
8
Oligarchic Growth of ProtoplanetsΣ1 = 10, α = 3/2
0.4 0.6 0.8 1 1.2 1.4 1.6
0
0.05
0.1
0.15
(EK & Ida 2002)
Slowdown of runawayscattering of planetesimals by aprotoplanet with M >∼ 100m
vran ∝ rH ∝ M1/3
⇓
1
M
dM
dt∝ M1/3v−2
ran ∝ M−1/3
orderly growth!(Ida & Makino 1993)
Orbital repulsionorbital separation: b ≃ 10rH
(EK & Ida 1998)
Protoplanets
protoplanets
Isolation mass
Miso ≃ 2πabΣd = 0.16f3/2d ǫ
3/2ice
(
b
10rH
)3/2( a
1AU
)(3/2)(2−α)(
M∗
M⊙
)−1/2
M⊕
Growth timetgrow ≃ 1.3× 105f−1
d f−2/5g ǫ−1
ice
(
M
M⊕
)1/3 (ρp
2 gcm−3
)3/5 (b
10rH
)−2/5
( a
1AU
)(7/5)α+3/5(
m
1018 g
)2/15 (M∗
M⊙
)−1/6
years
(EK & Ida 2002, 2012)
Isolation Mass of ProtoplanetsStandard Protosolar Diskα = 3/2, M∗ = M⊙, fd = fg = 1
Terrestrial Zone• M ≃ 0.1M⊕
<∼ Mplanet
⇒ accretion of protoplanets
Jupiter-Saturn Zone• M ≃ 10M⊕ ≪ Mplanet
⇒ gas capture by protoplanets
Uranus-Neptune Zone• M ≃ 15M⊕ ≃ Mplanet
⇒ failed protoplanets (cores)?
From Protoplanets to Planets
Terrestrial Planet FormationGiant Impacts among Protoplanets
• Protoplanets gravitationally perturb each other to becomeorbitally unstable after gas dispersal (tdep ∼ 107 yr)
log tinst ≃ c1(b/rH) + c2
(e.g., Chambers+ 1996; Yoshinaga, EK & Makino 1999)
protoplanets
giant impacts
terrestrial planets
Giant Impacts of Protoplanets
0 0.5 1 1.5 2 2.5
0
0.2
0.4
two Earth-sized planets and one or two leftover protoplanets〈M1〉 ≃ 0.4Mtot, 〈M2〉 ≃ 0.3Mtot
e, i ≃ 0.1
(EK+ 2006, EK & Genda 2010, EK & Ida in prep.)
Conditions for Gas Giant FormationCritical Core Mass for Gas Accretion
Mc,cr ≃ 10M⊕
(e.g., Ikoma+ 2000)
Lifetime of Disk Gastdep ∼ 107 years
Conditions for Gas Giant Formation• Protoplanet mass: M > Mc,cr
• Protoplanet growth time: tgrow(Mc,cr) < tdep
=⇒ limited disk range
Formation Sites of Gas GiantsInner Boundary: M > 10M⊕ =⇒
a > ain ≃
2.5
(
fd10
)−2
AU(
fd >∼ 10)
aice = 2.7AU(
2 <∼ fd <∼ 10)
3.5
(
fd2
)−2
AU(
fd <∼ 2)
Outer Boundary: tgrow(10M⊕) < tdep =⇒
a < aout ≃ 6.4f14/27d
(ǫice4.2
)10/27(
tdep107 years
)−10/27
AU
(α = 3/2, M∗ = M⊙, fd = fg)
Habitat Segregation
terrestrial range ain <∼ a <∼ aout ∩ a <∼ aice
gas giant range ain <∼ a <∼ aout
ice giant range ain <∼ a <∼ aout ∩ a >∼ aice
Diversity of Planetary Systems
a
fd <M > Miso
gas giants
ice giants
10
a ice
terrestrial planets
ain aout
grow ( )M10t dept
massive disk → multiple giants → orbital evolution → close-in/eccentric planets
Toward a More Realistic Scenario
Unsolved ProblemsPlanetesimal Formation
• gravitational instability or coagulation?
Formation of Ice Giants• formed in the inner disk and migrated outward? (Fernandez
& Ip 1984)
Gas Disk Depletion• viscous accretion, photoevaporation or disk wind?
Origin of Small Bodies• how satellites, rings, asteroids, comets etc form?
And more ...
Extension of the Standard ScenarioAssumptions of the Standard Scenario
• Continuous power-law disk except the ice line• In situ formation (no radial migration)• Perfect accretion (no disruption)• Stable orbits
Key Processes (Origin of Diversity)• Discrete discontinuous disk (early disk evolution) (Inutsuka)
• Formation with migration• Collisional disruption (Kobayashi)
• Orbital instability/evolution (Chatterjee)
Orbital MigrationPlanet-Disk Interaction
• Type I migration– torque from planet-induced spiral arms– inward (also outward depending on disk property)
• Type II migration (Lyra, Dong, Kanagawa, Hasegawa)
– viscous evolution of the gas disk– inward– grand-tack model: mass depletion of the Mars-asteroid
belt region by the inward-then-outward migration ofJupiter (e.g., Walsh+ 2011)
• Planetesimal-driven migration (e.g., Ormel+ 2012) (Kominami)
– scattering of planetesimals– inward/outward
Orbital EvolutionPlanet-Planet Interaction
• Scattering ⇒ close-in planets, eccentric planets• Secular interaction ⇒ close-in planets, eccentric planets• Kozai mechanism ⇒ close-in planets• Orbital diffusion (expansion)
– Nice model: expansion of the compact giant planetsystem (e.g., Tsiganis+ 2005)
SummaryStandard Scenario: the Core Accretion Model
• Three stages:dust → planetesimals → protoplanets → planets
• Formation time ∼ 108–109 years
Habitat Segregation of Planets• Ice line ⇒ rock or ice• Mass and growth time of protoplanets and gas disk
lifetime ⇒ gas or not• Diversity of planetary systems with disk mass
Extension of the Standard Model• In situ formation → formation with migration• Perfect accretion → collisional disruption• Continuous power-law disk → discrete discontinuous disk