How asteroids grow
Anders Johansen (Lund University)
“Star and Planet Formation For All”, Lund, February 2014
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Planets and exoplanets
I
First exoplanet was discovered in 1995
I
The Kepler satellite identified over 2300 exoplanet candidates
in the 16-months data (Batalha et al., 2013)
(Mayor & Queloz, 1995)
⇒ 50% of stars have planets within 0.4 AU
(Fressin et al., 2013)
⇒ Most exoplanets in close orbits are super-Earths or small
Neptunes
⇒ Nature is very efficient at turning dust and ice into planets
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Classical picture of planet formation
Planetesimal hypothesis of Viktor Safronov 1969:
Planets form in protoplanetary discs around young stars as planetesimals collide to form ever larger bodies
1. Dust to planetesimals
µm → km: contact forces
2. Planetesimals to protoplanets
km → 1,000 km: gravity (run-away accretion)
3. Protoplanets to planets
Terrestrial planets: protoplanets collide
(107 –108 years)
Gas and ice giants: 10 M⊕ core accretes gas (< 106...7 years)
Severe problems with classical model:
1 Growth of macroscopic particles is frustrated by erosion and bouncing
2 Planetesimals colliding at high speeds will shatter each other
3 Core formation takes much longer time than the life-time of the nebula
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Planet formation with pebbles
Pebble hypothesis:
Planetesimals form by gravitational collapse of dense clumps of pebbles and planets form mainly by pebble accretion onto planetesimals
1. Dust to pebbles
µm → cm: coagulation and condensation
2. Pebbles to planetesimals
km → 100–1,000 km: particle concentration and gravitational collapse
3. Planetesimals to planets
Terrestrial planets: pebble accretion, giant impacts (106 –108 years ?)
Gas and ice giants: pebble accretion to 10 M⊕
( 106 years)
See Protostars and Planets VI reviews by Johansen et al. (2014) and Chabrier, Johansen, et al. (2014)
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Dust to pebbles
(Zsom et al., 2010)
I Collisions between dust
aggregates can lead to sticking,
bouncing or fragmentation
(Güttler et al., 2010)
I Sticking for low collision speeds
and small aggregates
I Bouncing prevents growth beyond
mm sizes (bouncing barrier)
I Further growth may be possible
by mass transfer in high-speed
collisions (Windmark et al., 2012) or by
ice condensation (Ros & Johansen, 2012)
→ SPFFA talk by Katrin Ros
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Pebbles to planetesimals
t=80.0 Ω−1
+10.0
+0.0
+0.0
−10.0
−10.0
+0.0
x/(ηr)
+10.0
+20.0 −20.0
−10.0
t=120.0 Ω−1
FP
z/(ηr)
FG
−10.0
−20.0
−20.0
v Kep (1− η )
z/(ηr)
+20.0
+10.0
+0.0
x/(ηr)
−20.0
+20.0
+10.0
t=160.0 Ω−1
+20.0
+20.0
+10.0
+10.0
+0.0
+0.0
−10.0
z/(ηr)
z/(ηr)
t=40.0 Ω−1
+20.0
−10.0
−20.0
−20.0
−10.0
+0.0
x/(ηr)
+10.0
+20.0 −20.0
−10.0
+0.0
x/(ηr)
−20.0
+20.0
+10.0
unstable to streaming instability
y/H
(Youdin & Goodman, 2005; Youdin & Johansen, 2007)
I Particles pile up in dense filaments
0.10
0.10
0.05
0.05
0.00
0.00
−0.05
y/H
I The radial drift flow of particles is linearly
−0.05
(Johansen & Youdin, 2007; Bai & Stone, 2010a)
−0.10
−0.10
I Particle concentration triggered above a
0.00
x/H
0.05
0.10
−0.10
−0.05
0.00
x/H
0.05
10−6
0.10
t = 337.5 Ω−1
−0.10
0.10
269
Z = 0.020
0.05
threshold metallicity around Z ≈ 0.015
µ
0.00
R/km
162
z/H
(Johansen et al., 2009, 2012; Bai & Stone, 2010b,c)
−0.05
10−7
97
−0.05
I Possible to concentrate particles down to mm
sizes at 2.5 AU
−0.10
−0.10
10−8
−0.05
0.00
x/H
0.05
0.10
58
325
330
t/Ω−1
335
(Carrera, Johansen, & Davies, in prep)
→ SPFFA talk by Daniel Carrera
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Planetesimals to planets
0.10
z/H
Σp/<Σp>
5.0
0.05
y/H
t=120 Ω−1
0.10
0.05
0
−0.05
−0.10
0.0
0.10
−1
0.05 t=0.0 Ω
0.00
−0.05
−0.10
0.00
x/H
108
107
−0.10
0.10
t=131 Ω−1
∆t/yr
−0.05
t=134 Ω−1
y/H
0.05
−0.05
−0.10
−0.10
106
105
104
103
10−1
0.00
−0.05
0.00
x/H
0.05
0.10
−0.05
0.00
x/H
0.05
0.10
Core growth to 10 M⊕
Planetesimals
nts
gme
Fra
100
Pebbles
101
102
r/AU
⇒ Pebble accretion speeds up core formation by a factor 1,000 at 5
AU and a factor 10,000 at 50 AU
(Lambrechts & Johansen, 2012; also Ormel & Klahr, 2010; Morbidelli & Nesvorny, 2012)
⇒ Cores form well within the life-time of the protoplanetary gas disc,
even at large orbital distances
I
Requires large planetesimal seeds, consistent with turbulence-aided
planetesimal formation → SPFFA talk by Michiel Lambrechts
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Evidence for giant impact stage
(Wetherill, 1985)
I The Moon’s mean density is very low, with uncompressed density
ρ = 3.3 g cm−3 [Earth’s uncompressed density: ρ = 4.4 g cm−3 ]
I The Moon is highly differentiated – with a dense core, a mantle, and a
crust – but must be lacking iron and volatiles
⇒ Moon formed from the impact debris after Mars-sized protoplanet
impacted the young, differentiated Earth
⇒ Taken as evidence for giant impact stage of classical planet formation
? Any evidence for pebble accretion? YES – encoded in the asteroid sizes
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Asteroid birth sizes
Asteroid size distribution
103
dN/dR [km−1]
102
101
100
10−1
10−2
10−3
100
1000
D [km]
I Size distribution of asteroids shows distinct bumps at diameters D = 120
km and D = 350 km
I Forming asteroids from km-sized planetesimals does not reproduce the
first bump – bump is primordial
(Bottke et al., 2005)
I Asteroids must be born BIG (100 – 1000 km) in order to not overproduce
asteroids with diameters less than 100 km
(Morbidelli et al., 2010)
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Planetesimal formation
109
25
50
R [km]
100
200
400
qM = 1.31 +/− 0.07
8
10
dN/dM [M−1
22 ]
107
106
105
104
103
1283, 5.0×MMSN
2563, 5.0×MMSN
5123, 5.0×MMSN
2563, 2.5×MMSN
2563, 1.0×MMSN
102
1020
1021
1022
M [g]
1023
1024
I Streaming instability leads to concentration of pebbles and to
planetesimal formation
(Johansen et al., 2014, Protostars and Planets VI, arXiv:1402.1344 )
I Higher resolution gives smaller planetesimals
(PRACE grant “PLANETESIM”)
I Birth sizes of planetesimals show no sign of a bump – most of the
planetesimals are small but most mass is in the largest bodies
I Powerlaw in dN/dM ∝ M −q is approximately q = 1 . . . 1.5
I Gravitational collapse of clumps → SPFFA talk by Kalle Jansson
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Chondrules
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I
I
I
I
Meteorites recovered on Earth are fragments of asteroids
Oldest condensates in the Solar System are CAIs with a
narrow age range of 4567.30 ± 0.16 Myr (Connelly et al., 2012)
Primitive meteorites (chondrites) contain a large fraction of
0.1-1-mm-sized chondrules (formed over the first 3 Myr)
Chondrites contain up to 80% of their mass in chondrules
What role did chondrules play in asteroid formation?
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Chondrule accretion
∆v ≈ 50 m/s
Chondrule spirals towards
asteroid due to gas friction
Bondi radius:
GM
RB = (∆v
)2
Large chondrule is scattered
by protoplanet
Ṁ = πRB2 ρc ∆v ∝ R 6
(Lambrechts & Johansen, 2012)
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Planetesimal size distribution
1000 10
R [km]
100
1000
Lower pressure support
104
104
103
103
102
102
101
101
100
100
10−1
10−15
10
4
dN/dR [km−1]
105
10−2
105
Steeper chondrule size distribution
Larger chondrules
10
104
103
103
102
102
101
101
100
100
10−1
10−1
10−2
10
dN/dR [km−1]
dN/dR [km−1]
105
R [km]
100
Nominal model
dN/dR [km−1]
10
106
10−2
100
R [km]
1000 10
100
R [km]
1000
I The nominal model reproduces four features of the asteroid size
distribution: the bump at R = 60 km, the steep size distribution up to
R = 200 km, the bump at R = 200 km and the shallow size distribution
for the largest sizes (Johansen, Mac Low, Lacerda, & Bizzarro, in prep)
I Variation in the parameters gives different realisations of the asteroid belt
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Implications
(Elkins-Tanton et al., 2011)
I Asteroids grew primarily by chondrule accretion
I Size distribution of asteroids shows evidence of this chondrule accretion
I General validation that pebble accretion occurred in the Solar System
I Pebble accretion likely driven by icy pebbles beyond the ice line
I Planetesimals in the terrestrial planet formation region grew by accreting
chondrules – could this explain rapid formation of Mars?
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