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Lecture 3:
Recent topics
0.10
z/H
Σp/<Σp>
5.0
0.05
y/H
0.10
−1
0.05 t=0.0 Ω
0.00
−0.05
−0.10
t=120 Ω−1
0.10
0.05
0
−0.05
−0.10
0.0
0.00
x/H
−0.05
−0.10
0.10
t=131 Ω−1
t=134 Ω−1
y/H
0.05
0.00
−0.05
−0.10
−0.10
−0.05
0.00
x/H
0.05
0.10
−0.05
0.00
x/H
0.05
0.10
“NBI summer School on Protoplanetary Disks
and Planet Formation”
August 2015
Anders Johansen (Lund University)
Copenhagen 2015 (Lecture 3)
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1 / 43
Topics
1
Wide-orbit exoplanets
2
Pebble accretion
3
Size distribution of asteroids
4
Nice model
5
Grand Tack model
6
Population synthesis with pebbles
7
Chondrule accretion
Copenhagen 2015 (Lecture 3)
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2 / 43
Classical core accretion scenario
1
Dust grains and ice particles collide to form km-scale planetesimals
2
Large protoplanet grows by run-away accretion of planetesimals
3
Protoplanet attracts hydrostatic gas envelope
4
Run-away gas accretion as Menv ≈ Mcore
5
Form gas giant with Mcore ≈ 10M⊕ and Matm ∼ MJup
(Safronov, 1969; Mizuno, 1980; Pollack et al., 1996)
All steps must happen within 1–3 Myr while there is gas orbiting the star
Copenhagen 2015 (Lecture 3)
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3 / 43
Life-times of protoplanetary discs
Stars in a star-forming region are pretty much the same age
Compare disc fraction between regions of different age
(Mamajek, 2009)
(Haisch et al., 2001)
⇒ Protoplanetary discs live for 1–3 Myr
Copenhagen 2015 (Lecture 3)
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4 / 43
Core formation time-scales
The size of the protoplanet relative to the Hill
sphere:
r −1
Rp
≡ α ≈ 0.001
RH
5 AU
Maximal growth rate by gravitational focussing
2
Ṁ = αRH
FH
⇒ Only 0.1% (0.01%) of planetesimals entering
the Hill sphere are accreted at 5 AU (50 AU)
Gravitational cross section
⇒ Time to grow to 10 M⊕ is
∼10
Myr at 5 AU
∼50
Myr at 10 AU
∼5,000 Myr at 50 AU
Copenhagen 2015 (Lecture 3)
Planet
Hill sphere
x=0
Other topics
x
5 / 43
Directly imaged exoplanets
(Kalas et al., 2008)
(Marois et al., 2008; 2010)
HR 8799 (4 planets at 14.5, 24, 38, 68 AU)
Fomalhaut (1 controversial planet at 113 AU)
⇒ No way to form the cores of these planets within the life-time of the
protoplanetary gas disc by standard core accretion
Copenhagen 2015 (Lecture 3)
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6 / 43
Pebble accretion
Most planetesimals are simply
scattered by the protoplanet
Planetesimal is scattered
by protoplanet
Pebbles spiral in towards the
protoplanet due to gas
friction
⇒ Pebbles are accreted from the
entire Hill sphere
Pebble spirals towards
protoplanet due to gas friction
Growth rate by planetesimal
accretion is
2
Ṁ = αRH
FH
Growth rate by pebble
accretion is
2
Ṁ = RH
FH
Copenhagen 2015 (Lecture 3)
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7 / 43
Relevant parameters for pebble accretion
Hill radius RH = [GM/(3Ω 2 )]1/3
Distance over which the gravity of the protoplanet dominates over the
the tidal force of the central star
Bondi radius RB = GM/(∆v )2
Distance over which a particle with approach speed ∆v is significantly
deflected by the protoplanet (in absence of drag)
Sub-Keplerian speed ∆v
Orbital speed of gas and pebbles relative to Keplerian speed
Hill speed vH = ΩRH
Approach speed of gas and pebbles at the edge of the Hill sphere
Copenhagen 2015 (Lecture 3)
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8 / 43
Pebble accretion regimes
2
100
Weak
Strong
τf=0.1
τf=0.01
τf=1
1
−1
10−3
10−3
y/rB
10−2
10−2
x/rB
−4 −2 0 2 4
−4
−2
0
2
4
10−1
100
101
y/rH
rd/rB
10
0
−1
102
−2
−2
tB/tf
Two main pebble accretion regimes:
−1
0
x/rH
1
2
(Lambrechts & Johansen, 2012)
1
Bondi regime (when ∆v vH )
Particles pass the core with speed ∆v , giving Ṁ ∝ RB2 ∝ M 2
2
Hill regime (when ∆v vH )
Particles enter Hill sphere with speed vH ≈ ΩRH , giving Ṁ ∝ M 2/3
Copenhagen 2015 (Lecture 3)
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9 / 43
Time-scale of pebble accretion
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
−0.05
0.00
x/H
0.05
0.10
−0.05
0.00
x/H
0.05
Planetesimals
106
105
104
103
10−1
0.00
Core growth to 10 M⊕
Fra
nts
gme
100
0.10
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
(Ormel & Klahr, 2010; Lambrechts & Johansen, 2012; Nesvorny & Morbidelli, 2012)
⇒ Cores form well within the life-time of the protoplanetary gas disc, even at
large orbital distances
Requires large planetesimal seeds to accrete in Hill regime, consistent with
planetesimal formation by gravitational collapse
Copenhagen 2015 (Lecture 3)
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10 / 43
The asteroid belt
1–2 million asteroids
larger than 1 km in main
belt between Mars and
Jupiter
Total mass is only
0.0005 ME
Interpolation between
terrestrial planets and
giant planets gives 2.5
ME in the primordial
asteroid belt between 2
and 3 AU
Asteroid belt depleted by
resonances with Jupiter
Copenhagen 2015 (Lecture 3)
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11 / 43
Growth of asteroids by pebble accretion
Put large (500 km) planetesimal in an ocean of pebbles:
0.02
2.0
t=2.0
ρp/ρg
t=0.0
0.01
y/H
0.0
0.00
−0.01
−0.02
0.02
t=6.0
log ρp:
t=12.0
y/H
0.01
0.00
−0.01
−0.02
−0.02
−0.01
0.00
x/H
0.01
0.02
−0.01
0.00
x/H
0.01
0.02
⇒ Prograde accretion disc forms around the protoplanet
(Johansen & Lacerda, 2010)
Copenhagen 2015 (Lecture 3)
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12 / 43
Asteroid rotation
Body
Ceres
2 Pallas
3 Juno
4 Vesta
5 Astraea
6 Hebe
The majority of large asteroids have axial tilt
α < 90◦
Called “direct” or “prograde” rotation
α
2o
60o
50o
29o
33o
42o
NP
α
n
Copenhagen 2015 (Lecture 3)
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13 / 43
Asteroid poles
Plot of asteroid pole axes
(from Johansen & Lacerda, 2010)
Largest asteroids have a tendency
to rotate prograde (1-2 σ)
... but there is a very large scatter
The two large retrograde asteroids,
2 Pallas and 10 Hygiea, are actually
spinning on the side
Planetesimal accretion yields slow,
retrograde rotation (Lissauer & Kary, 1991)
Prograde spin can also arise from
random effect of large impacts (Dones
& Tremaine, 1993) or due to collisions
between planetesimals within the
Hill sphere (Schlichting & Sari, 2007)
Copenhagen 2015 (Lecture 3)
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14 / 43
Primordial spin of planetesimals
B
A
2·10−5
−5
1·10
lz
0
ΩKτf=0.1
ε=10.0
Average
Cumulative
Keplerian
−1·10−5
ΩKτf=0.1
−2·10−5
ε=1.0
D
C
2·10−5
−5
1·10
lz
0
−1·10−5
ΩKτf=0.1
−2·10−5
ΩKτf=∞
ε=0.1
0
2
4
6
8
t/Ω−1
K
10
12
0
2
4
6
8
t/Ω−1
K
10
12
14
Prograde rotation with P ≈ (5 . . . 10) h induced for particles between centimeters
and a few meters
Spin can be randomised later in giant impacts
⇒ Predict that pristine Kuiper belt objects formed by gravitational collapse should
have prograde spin
Copenhagen 2015 (Lecture 3)
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15 / 43
Orbits of Kuiper belt objects
(Chiang et al., 2007; de Pater & Lissauer, 2010)
Kuiper belt objects reside beyond the orbit of Neptune
Pluto trapped in 3:2 resonance with Neptune – result of outwards migration of
Neptune
Scattered disc objects have high e and perihelion between 33 and 40 AU
Centaurs have perihelion within 30 AU – source of Jupiter family comets
Classical KBOs have low e and semimajor axes between 37 and 48 AU – future
target of New Horizons
Copenhagen 2015 (Lecture 3)
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16 / 43
Nice model
(Gomes et al., 2005)
Pluto’s resonant orbit with Neptune is explained by trapping during the migration
of Neptune through a primordial, massive Kuiper belt (Malhotra, 1993, 1995)
Planetesimals scattered inwards by N, U and S are ejected from the Solar System
by J, leading to a net outwards migration of the three outer giants
As Jupiter and Saturn cross their 2:1 mean motion resonance, the orbits of Uranus
and Neptune are excited and the primordial Kuiper belt is depleted (Tsiganis et al., 2005)
Explains modern architecture of the Kuiper belt and Late Heavy Bombardment of
the terrestrial planets and the Moon (Gomes et al., 2005)
Copenhagen 2015 (Lecture 3)
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17 / 43
Kuiper belt binaries
(Nesvorny et al., 2010)
At least 30% of 100-km classical KBOs are binaries
(Noll et al., 2008)
Nesvorny et al. (2010) modelled gravitational collapse of particle clumps to explain
why binary KBO can have similar colors
Found good statistical agreement in orbital parameters between simulations and
observed KBO binary systems
Almost no binaries in scattered disc – ionised by close encounters?
Copenhagen 2015 (Lecture 3)
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18 / 43
Cloud collapse to pebble piles
Simulate cloud collapse in 0-D collision code
(Wahlberg Jansson & Johansen, 2014)
High collision rates ⇒ Rapid energy dissipation ⇒
Contraction to solid density
(Wahlberg Jansson & Johansen, 2014)
⇒ High pebble fraction after collapse
⇒ Predict that comets like 67P/
Churyumov-Gerasimenko are pebble piles
Large Kuiper belt objects likely lost their porosity
by gravitational compression
(Brown, 2013)
Copenhagen 2015 (Lecture 3)
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19 / 43
Goosebumps on 67P
(Sierks et al., 2015)
(Mottola et al., 2015)
The Rosetta mission arrived at the comet 67P/Churyumov-Gerasimenko in 2014
Orbiter will follow 67P beyond perihelion
Structures in deep pits resemble goosebumps (Sierks et al., 2015)
Could be the primordial pebbles from the solar protoplanetary disc
But meter-sized pebbles hard to explain in light of radial drift
Philae’s first landing site shows characteristic particle scale of cm in smooth
terrains (Mottola et al., 2015)
Copenhagen 2015 (Lecture 3)
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20 / 43
Pebbles in the media!
Copenhagen 2015 (Lecture 3)
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21 / 43
Missing intermediate-size planetesimals
Sheppard & Trujillo (2010)
searched for Neptune
Trojans
Sensitive to planetesimals
larger than 16 km
Found no Trojans with
radius less than 45
kilometers
Dubbed them the missing
intermediate-size
planetesimals (MISPs)
Copenhagen 2015 (Lecture 3)
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22 / 43
Asteroid size distribution
Differential size distribution of
asteroids shows several bumps
Can be used to infer the degree of
depletion and collisional grinding
in the asteroid belt
Divide the history of the asteroid
belt into an early accretion phase
followed by an extended depletion
phase
Bottke et al. (2005a,b) evolved
the asteroid belt over billions of
years, starting from a size
distribution which matches the
current one for bodies larger than
120 km in diameter
Copenhagen 2015 (Lecture 3)
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23 / 43
Evolution of asteroid size distribution
Depletion factor of 100–200 gives good fit to
observed size distribution after 4600 Myr of
evolution
(Bottke et al., 2005)
Also satisfies the two constraints: (i) Vesta
only has a single large crater and (ii) there are
only 9 large asteroid familes
Observed size distribution of large asteroids is a
fossil of the size distribution at the end of the
accretion phase
Copenhagen 2015 (Lecture 3)
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24 / 43
Accretion phase of asteroids
Size distribution of asteroids shows distinct bumps at D = 120 km
and at D = 350 km
The first bump must be primordial
(Bottke et al., 2005)
Starting accretion phase with km-sized planetesimals produces way
too many asteroids with D < 100 km (Morbidelli et al., 2009)
Copenhagen 2015 (Lecture 3)
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25 / 43
Starting from planetesimals with D = 100 km
Starting with planetesimals with D = 100 km produces very few
fragments during the accretion stage
But the resulting size distribution is too steep for D > 100 km
(Morbidelli et al., 2009; Weidenschilling, 2011)
Copenhagen 2015 (Lecture 3)
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26 / 43
Asteroids are born big
The best results are obtained by setting the birth size distribution of
asteroids equal to the current observed size distribution of large
asteroids
Asteroids are born BIG
(Morbidelli et al., 2009)
Can we connect birth sizes to planetesimal formation models?
Copenhagen 2015 (Lecture 3)
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27 / 43
Birth sizes of planetesimals
109
25
50
R [km]
100
200
400
Asteroids (rescaled)
qM = 1.6
108
dN/dM [M−1
22 ]
107
106
105
104
3
10
102
1020
1283, Σp =
2563, Σp =
5123, Σp =
2563, Σp =
2563, Σp =
2563, Σp =
1021
23.9 g cm−2
23.9 g cm−2
23.9 g cm−2
12.0 g cm−2
6.0 g cm−2
2.4 g cm−2
1022
M [g]
Binary
1023
1024
Streaming instability leads to concentration of pebbles and to planetesimal
formation
Higher resolution yields smaller and smaller planetesimals
Powerlaw in dN/dM ∝ M −q with q ≈ 1.6 (Johansen et al., 2015)
Most of the planetesimals are small but most mass is in the largest bodies
Birth sizes of planetesimals show no sign of a bump at 50 km radii
Copenhagen 2015 (Lecture 3)
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28 / 43
Chondrules
Primitive meteorite parent bodies contain a large fraction of
0.1-1-mm-sized chondrules (formed over the first 3 million years)
Ordinary chondrites contain up to 80% of their mass in chondrules
What role did chondrules play in asteroid formation and growth?
Copenhagen 2015 (Lecture 3)
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29 / 43
104
Bondi accretion of chondrules
102
100
ng
oot
rsh
ove
Wea
tion
nta
k
e
m
i
Sed
ling
R/RB= 3.2×101
oup
c
2
ng
o
R/R
=
1.0×10
r
t
B
S
R/RB= 3.2×102
R/RB= 1.0×103
R/RB= 3.2×103
R/RB= 1.0×104
ic
etr
om
Ge
pli
10−2
R/RB= 1.0×10−1
R/RB= 3.2×10−1
R/RB= 1.0×100
R/RB= 3.2×100
R/RB= 1.0×101
cou
Racc/RB
∆v ≈ 50 m/s
R/RB= 1.0×10−4
R/RB= 3.2×10−4
R/RB= 1.0×10−3
R/RB= 3.2×10−3
R/RB= 1.0×10−2
R/RB= 3.2×10−2
Grav. focusing
Perfect sticking
10−4
10−3 10−2 10−1
100 101
tf/tB
102
103
104
Chondrule spirals towards
asteroid due to gas friction
Bondi radius:
GM
RB = (∆v
)2
Large chondrule is scattered
by asteroid
Ṁ = πfB2 RB2 ρc ∆v ∝ R 6
Copenhagen 2015 (Lecture 3)
(Ormel & Klahr, 2010; Lambrechts & Johansen, 2012)
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30 / 43
Asteroid sizes after chondrule accretion
106
1027
Nominal model (t=5.0 Myr)
Initial size distribution
Asteroid belt (× 540)
Embryos
No chondrule accretion
102
10−2
1024
1023
Smaller planetesimals
Larger chondrules
(t=2.0 Myr)
10
1025
Moon Mars
i
Ceres
1026
M [g]
dN/dR [km−1]
104
10−1
R5 Myr = 3119 km
R5 Myr = 498 km
R5 Myr = 199 km
Collisions
Smallest body i
Largest body i
10−3
0
1022
10−2
10
1021
100
10−4
0
1000
R [km]
1
2
3
t [Myr]
4
5
Chondrule accretion reproduces both the bump at R = 120 km and the steep size
distribution up to R = 200 km (Johansen et al., 2015)
Embryos with sizes between the Moon and Mars are also formed by rapid
chondrule accretion
Direct planetesimal accretion contributes only a minor amount of mass to the
embryos and the largest asteroids
Copenhagen 2015 (Lecture 3)
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31 / 43
Embryos in the asteroid belt
(Bottke et al., 2005)
Both planetesimal accretion and
chondrule accretion models produce
embryos in the asteroid belt
The embryos excite the
eccentricities and inclinations of
asteroids to their high values
(Wetherill, 1991; Petit et al., 2001)
Embryos also scattered asteroids to
Jupiter resonances
Embryos entirely removed from the
asteroid belt by perturbation from
Jupiter
Copenhagen 2015 (Lecture 3)
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32 / 43
The Grand Tack scenario
(Walsh et al., 2011)
The small mass of Mars (11% of Earth’s) is hard to explain in terrestrial planet
formation models
Jupiter could have migrated sufficiently far in to perturb the embryos in the
terrestrial planet formation region
As Jupiter and Saturn come to share a gap, they migrate outwards together (the
Grand Tack scenario of Walsh et al., 2011)
Best alternative to embedded embryos model for asteroid stirring, particularly if
one is concerned about Mars’ small size
Copenhagen 2015 (Lecture 3)
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33 / 43
Terrestrial planet formation with chondrules
10−1
10−2
10−2
Ceres
Moon Mars
10−3
10−4
10−4
Mmax
Chondrule contribution
Planetesimal contribution
No chondrules
Isolation mass
10−6
M [ME]
dN/dR [km−1]
100
t=0 Myr
t=1 Myr
t=3 Myr
t=5 Myr
100
10−5
10−6
100
1000
0
1
R [km]
4
5
100
t=0.0 Myr
t=0.5 Myr
t=1.0 Myr
t=2.0 Myr
100
dN/dR [km−1]
2
3
t [Myr]
10−1
10−2
10−2
Ceres
Moon Mars
10−3
10−4
M [ME]
10
10−4
Mmax
Chondrule contribution
Planetesimal contribution
10−6
10−5
10−6
10
100
1000
0.0
0.5
R [km]
1.0
t [Myr]
1.5
2.0
(Johansen et al., 2015)
Chondrule accretion leads to rapid formation of Mars-sized embryos in the
terrestrial planet formation region
Planetesimal accretion nevertheless more important than in the asteroid belt
Larger chondrules are accreted more efficiently
Copenhagen 2015 (Lecture 3)
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34 / 43
From planetesimals to planets
103
102
101
Mc/ME
Mc/ME
102
103
5AU
8AU
15AU
20AU
100
101
10−1
10−2
105
10−2
105
107
Z=0.02
100
10−1
106
t/yr
5AU
8AU
15AU
20AU
Z=0.005
106
107
t/yr(Lambrechts & Johansen, 2014)
The largest planetesimals accrete the remaining
pebbles and grow to planets in the next 1–5
Myr
Growth depends strongly on the amount of
heavy elements in the protoplanetary disc
(Z = 0.01 in the Sun’s photosphere)
(Lambrechts & Johansen, 2014)
Gas-giant planets like Jupiter form if Z is high,
in agreement with exoplanet surveys
Copenhagen 2015 (Lecture 3)
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(Buchhave, Latham, Johansen, et al., 2012)
35 / 43
The critical core mass
0%
20%
40%
60%
80%
10−2
⋅
M/(M
E/yr)
10−3
10−4
5AU
10−5
30A
⋅
M peb
5AU
U
10−6
⋅
M plan
10−7
τacc<τdisc
τacc>τdisc
10−8
10−9
10−1
(Ikoma et al., 2000)
U
30A
100
101
102
103
Mc/ME
(Lambrechts, Johansen, & Morbidelli, 2014)
The critical core mass for envelope collapse increases when the accretion rate
increases
Planetesimal accretion rates at 5–10 AU yield core masses of 10-20 Earth masses –
but the growth rate is too low to compete with gas dissipation
Pebble accretion rates yield very high critical core masses of 100–200 Earth masses
– in disagreement with measured core masses
Copenhagen 2015 (Lecture 3)
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36 / 43
Halting pebble accretion
Pebble accretion is stopped when the protoplanet grows massive enough to carve a
gap in the pebble distribution
Gap formation known for Jupiter-mass planets
(Paardekooper & Mellema, 2006)
Lambrechts et al. (2014) demonstrate that pebble accretion is stopped already at
20 M⊕ at 5 AU, with isolation mass scaling as
r 3/4
Miso = 20
M⊕
5AU
Copenhagen 2015 (Lecture 3)
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37 / 43
The critical core mass revisited
0%
20%
40%
60%
80%
10−2
⋅
M/(M
E/yr)
10−3
10−4
5AU
10−5
30A
⋅
M peb
5AU
U
10−6
τacc<τdisc
τacc>τdisc
10−8
10−9
10−1
U
30A
⋅
M plan
10−7
100
101
Mc/ME
102
103
(Lambrechts et al., 2014)
Protoplanets grow at the pebble accretion rate until pebble accretion is halted
abruptly
The envelope is then supercritical and collapses onto the core
Gives an excellent fit to Jupiter’s and Saturn’s heavy elements (Lambrechts et al., 2014)
Gas giants in wide orbits must have large cores masses (50-100 ME )
Explains dichotomy between ice giants and gas giants
Copenhagen 2015 (Lecture 3)
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38 / 43
Including planetary migration
6
1000
3.0x10
1000
100
10.0
6
2.5x10
20.0
10
100
1
t0=2 Myr
0.1
0.1
r0 = 5.0 AU
r0 = 10 AU
r0 = 15 AU
r0 = 25 AU
r0 = 40 AU
r0 = 50 AU
tD=3.0Myr
Σpeb at 2 Myr
0.01
0.001
0.1
Z=1.0%
t0 [yr]
M [ME]
2
Σpeb [g/cm ]
2.0x106
1
5.0
1.5x106
10
1.0x106
MP in ME
10
1.0
0.1 0.5
0.01
1
0.5x106
0.1
1
5
10
20
30 40 50
5
10
15
r [AU]
20
25
30
r0 [AU]
35
40
45
50
Pebble accretion combined with protoplanetary disc evolution and planetary
migration (Bitsch, Lambrechts, & Johansen, 2015)
Jupiter analogue forms late (after 2 Myr) and far out (beyond 15 AU)
Migrates into 3 AU orbit while growing to 300 ME
Growth tracks can be bundled into a growth map
Early formed planets migrate to become hot and warm Jupiters
Formation after 2 Myr yields a range of planetary classes
Copenhagen 2015 (Lecture 3)
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39 / 43
Growth map with planetesimal accretion
5.0x106
1.0x106
4.5x106
0.9x106
1000
4.0x106
0.7x106
10
2.0x106
t0 [yr]
2.5x106
MP in ME
100
3.0x106
100
6
0.6x10
6
10
0.5x10
MP in ME
3.5x106
t0 [yr]
1000
0.8x106
6
0.4x10
1.5x106
0.3x106
1
1.0x106
1
0.2x106
0.5x106
5.0
0.1
0.1
5
10
15
20
25
30
r0 [AU]
35
40
45
50
0.1x106
0.1
4
6
8
10
12
14
r0 [AU]
Accretion of planetesimals can not form cores within 5 Myr, even if
planetesimal surface density enhanced by factor 8 (Bitsch et al., 2015)
Hard to form Jupiter at 5 AU due to the slow accretion rate and the
high migration rate
Copenhagen 2015 (Lecture 3)
Other topics
40 / 43
Emergence regions of planetary classes
(Bitsch et al., 2015)
Copenhagen 2015 (Lecture 3)
Other topics
41 / 43
Reaching the initial conditions for the Nice model
1000
100
MP [ME]
10
1
0.1
0.01
0.001
Jupiter
Saturn
Uranus
Neptune
tD=3.0Myr
5
(Gomes et al., 2005)
10
15
r [AU]
20
25
(Bitsch et al., 2015)
In the Nice model the giant planets orbit initially in a compact configuration
Natural consequence of planetary migration combined with rapid pebble accretion
Orbital architecture of the Nice model can be explained if the planetary embryos
emerge after 1.5–2 Myr in initial orbits between 20 and 25 AU
What happened to the embryos that formed closer to the Sun?
Copenhagen 2015 (Lecture 3)
Other topics
42 / 43
Summary
Models and experiments of dust coagulation / fragmentation /
bouncing are very advanced now
Ice condensation may be another necessary ingredient for efficient
formation of pebbles
Particle clumping by streaming instabilities / pressure bumps /
vortices is by now a robust phenomenon studied by several groups
with independent codes
Pebble accretion is very efficient at growth from planetesimals to
planets – the full importance of this new growth mechanism is still
being explored
Asteroid belt and Kuiper belt may be sculpted by gravitational
collapse, pebble accretion and planetesimal collisions
Copenhagen 2015 (Lecture 3)
Other topics
43 / 43