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 Models
model

disk mass (M⊙ )building blocks

alias

disk instability≃1

protoplanets

Cameroncore accretion≃ 0.01planetesimals

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 Hypotheses
Disk 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
protosungas

protoplanetary disk

dust

planetesimals

protoplanets

terrestrial planets gas giants

ice giants

From Dust to Planetesimals
Gravitational Instability of a Dust Layer
1. Formation of a dust layer
2. Increase of the dust layer density
3. Gravitational instability and fragmentation
4. Contraction of fragments into planetesimals(e.g., Goldreich & Ward 1973)
gas
dust

Pairwise Coagulation of Dust Grains(e.g., Weidenschilling & Cuzzi 1993)

Disk Modelplanetesimals

Surface Density Distribution
 r −αgcm−2planetesimal: Σd = 10ǫice fd
 1rAU−αgcm−2
gas: Σg = 2400fg
1 AUǫice = 1 (r < aice ) and 4.2 (r > aice ): ice factor; fd , fg : scale factors

Ice Line (T ≃ 170 K: H2 O condensation temp.)
aice = 2.7

L∗L⊙1/2Assumptions• in situ formation, perfect accretionAUFrom Planetesimals to ProtoplanetsTerminology
Random Velocity• deviation velocity from a non-inclined circular orbit
22 1/2vran ≃ e + ivKe : eccentricity, i : incination, vK : Kepler circular velocity

Hill (Roche/Tidal) Radius• radius of the potential well of an orbiting bodyrH =m3M∗

1/3aM∗ : central body mass, m : orbiting body mass, a : semimajor axis

Growth Modeddt



M1M2



M1=M2



1 dM2
1 dM1−M1 dt
M2 dt



1 dM
∝ Mprelative growth rate:
M dtorderly growth
p<0

runaway growthp>0Growth RateRMdM
≃ nπR2dt
m

Test body:

M, R, vesc

Field bodies:n (number density), m2
vesc
1+ 2vrel



1 dM
−2
vrel m ⇒∝ M 1/3 vran
M dt

−1, vesc ∝ M 1/3 , R ∝ M 1/3 , vrel < vesc
vrel ≃ vran , n ∝ vranRandom velocity controls• the growth mode
• the growth timescaleRunaway Growth of Planetesimals
yrself-gravity of planetesimals
dominant for random velocity
vran 6= f (M )yre⇓
1 dM−2∝ M 1/3∝ M 1/3 vran
M dt
runaway growth!

yra (AU)(EK & Ida 2000)

Runaway Growth of Planetesimals

nc

11d log nc≃−
d log m
823m (10 g)
dotted: 0 yr, dashed: 105 yr, solid: 2 × 105 yr(EK & Ida 2000)

Oligarchic Growth of Protoplanets
Σ1 = 10, α = 3/2

Slowdown of runaway
scattering of planetesimals by aprotoplanet with M >∼ 100m0.15vran ∝ rH ∝ M 1/3⇓0.1

1 dM−2∝ M 1/3 vran∝ M −1/3
M dtorderly growth!
0.05(Ida & Makino 1993)

Orbital repulsion
00.4

orbital separation: b ≃ 10rH
0.6

0.8

11.2

1.4

1.6

(EK & Ida 2002)(EK & Ida 1998)

Protoplanets

protoplanets

Isolation mass
3/2 3/2

Miso ≃ 2πabΣd = 0.16fd ǫice



b
10rH

Growth timetgrow≃

3/2 a (3/2)(2−α)
1 AU

1/3 



M∗M⊙

3/5 

−1/2

ρpbMM⊕
2 gcm−310rH a (7/5)α+3/5  m 2/15  M −1/6∗
years
1 AU1018 gM⊙
1.3 × 105 fd−1 fg−2/5 ǫ−1iceM⊕

−2/5(EK & Ida 2002, 2012)

Isolation Mass of Protoplanets
Standard Protosolar Disk
α = 3/2, M∗ = M⊙ , fd = fg = 1

Terrestrial Zone
• M ≃ 0.1 M⊕ < Mplanet∼⇒ accretion of protoplanets

Jupiter-Saturn Zone
• M ≃ 10 M⊕ ≪ Mplanet⇒ gas capture by protoplanets

Uranus-Neptune Zone
• M ≃ 15 M⊕ ≃ Mplanet⇒ failed protoplanets (cores)?

From Protoplanets to Planets

Terrestrial Planet Formation
Giant Impacts among Protoplanets• Protoplanets gravitationally perturb each other to become

orbitally 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
0.4

0.2

0
00.5

1

1.5

2

2.5

two Earth-sized planets and one or two leftover protoplanets
hM1 i ≃ 0.4Mtot , hM2 i ≃ 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 Giants
Inner Boundary: M > 10M⊕ =⇒ −2fd
2.5AU
10

a > ain ≃aice = 2.7 AU

 −2


fd

 3.5
AU2fd >∼ 10

2<∼ fd <∼ 10
fd <∼2Outer Boundary: tgrow (10M⊕ ) < tdep =⇒14/27

a < aout ≃ 6.4fd

ǫice4.2

10/27 tdep
107 years

−10/27(α = 3/2, M∗ = M⊙ , fd = fg )Habitat Segregationterrestrial range

ain <
∼a<
∼ aout ∩ a <∼ aicegas giant range

ain <
∼a<
∼ aoutice giant range

ain <
∼a<
∼ aout ∩ a >∼ aiceAU

Diversity of Planetary Systems
fdt grow (10 M ) < t dep

M iso >10 M

ainterrestrial planetsgas giants

aoutice giants

a iceamassive disk → multiple giants → orbital evolution → close-in/eccentric planetsToward a More Realistic Scenario

Unsolved Problems
Planetesimal 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 Scenario
Assumptions 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 Migration
Planet-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 Evolution
Planet-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 planet

system (e.g., Tsiganis+ 2005)

Summary
Standard 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