hypothesis protoplanet

A Standard Scenario for
Formation of Planetary Systems
Eiichiro Kokubo (NAOJ)
Outline
Introduction
•
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
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 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
protosun
gas
protoplanetary disk
dust
planetesimals
protoplanets
terrestrial planets gas giants
ice giants
From Dust to Planetesimals
Gravitational Instability of a Dust Layer
1.
2.
3.
4.
Formation of a dust layer
Increase of the dust layer density
Gravitational instability and fragmentation
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
r −α
gcm−2
planetesimal: Σd = 10ǫice fd
1rAU−α
gcm−2
gas: Σg = 2400fg
1 AU
ǫice = 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⊙
1/2
Assumptions
• in situ formation, perfect accretion
AU
From Planetesimals to Protoplanets
Terminology
Random Velocity
•
deviation velocity from a non-inclined circular orbit
2
2 1/2
vK
vran ≃ e + i
e : eccentricity, i : incination, vK : Kepler circular velocity
Hill (Roche/Tidal) Radius
•
radius of the potential well of an orbiting body
1/3
m
rH =
a
3M∗
M∗ : central body mass, m : orbiting body mass, a : semimajor axis
Growth Mode
d
dt
M1
M2
M1
=
M2
1 dM2
1 dM1
−
M1 dt
M2 dt
1 dM
∝ Mp
relative growth rate:
M dt
orderly growth
p<0
runaway growth
p>0
Growth Rate
R
M
m
dM
≃ nπR2 1 +
dt
vrel ≃ vran , n ∝
Test body:
M, R, vesc
Field bodies:
n (number density), m
2
vesc
2
vrel
−1
,
vran
Random velocity controls
•
•
the growth mode
the growth timescale
1 dM
−2
vrel m ⇒
∝ M 1/3 vran
M dt
vesc ∝ M
1/3
, R∝M
1/3
, vrel < vesc
Runaway Growth of Planetesimals
yr
self-gravity of planetesimals
dominant for random velocity
vran 6= f (M )
yr
e
⇓
1 dM
−2
∝ M 1/3
∝ M 1/3 vran
M dt
runaway growth!
yr
a (AU)
(EK & Ida 2000)
Runaway Growth of Planetesimals
nc
11
d log nc
≃−
d log m
8
23
m (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 a
protoplanet with M >
∼ 100m
0.15
vran ∝ rH ∝ M 1/3
⇓
0.1
1 dM
−2
∝ M 1/3 vran
∝ M −1/3
M dt
orderly growth!
0.05
(Ida & Makino 1993)
Orbital repulsion
0
0.4
orbital separation: b ≃ 10rH
0.6
0.8
1
1.2
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 time
tgrow
≃
3/2 a (3/2)(2−α)
1 AU
1/3 M∗
M⊙
3/5 −1/2
ρp
b
M
1.3 ×
M⊕
2 gcm−3
10rH
a (7/5)α+3/5 m 2/15 M −1/6
∗
years
1 AU
1018 g
M⊙
105 fd−1 fg−2/5 ǫ−1
ice
M⊕
−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
0
0.5
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 Formation
Critical Core Mass for Gas Accretion
Mc,cr ≃ 10M⊕
(e.g., Ikoma+ 2000)
Lifetime of Disk Gas
tdep ∼ 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⊕ =⇒

−2
fd



2.5
AU


10

a > ain ≃
aice = 2.7 AU

−2



fd

 3.5
AU
2
fd >
∼ 10
2<
∼ fd <
∼ 10
fd <
∼2
Outer Boundary: tgrow (10M⊕ ) < tdep =⇒
14/27
a < aout ≃ 6.4fd
ǫ
ice
4.2
10/27 tdep
107 years
−10/27
(α = 3/2, M∗ = M⊙ , fd = fg )
Habitat Segregation
gas giant range
ain <
∼a<
∼ aout ∩ a <
∼ aice
ain <
∼a<
∼ aout
ice giant range
ain <
∼a<
∼ aout ∩ a >
∼ aice
terrestrial range
AU
Diversity of Planetary Systems
fd
t grow (10 M ) < t dep
M iso >10 M
ain
terrestrial planets
gas giants
aout
ice giants
a ice
a
massive 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 of
Jupiter (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