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