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From pebbles to planets
Anders Johansen (Lund University)
with Michiel Lambrechts, Katrin Ros, Andrew Youdin, Yoram Lithwick
From Atoms to Pebbles – Herschel’s View of Star and Planet Formation
Grenoble, March 2012
1 / 11
Anders Johansen
From pebbles to planets
Overview of topics
Size and time
Dust
µm
Pebbles
cm
Planetesimals
10−1,000 km
Planets
10,000 km
1
From dust to pebbles by ice condensation
Ros & Johansen (in preparation); poster by Katrin Ros
2
From pebbles to planetesimals by streaming instabilities
Johansen, Youdin, & Lithwick (2012)
3
From planetesimals to gas-giant cores by pebble accretion
Lambrechts & Johansen (submitted); poster by Michiel Lambrechts
2 / 11
Anders Johansen
From pebbles to planets
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
3 / 11
Anders Johansen
From pebbles to planets
Planetesimal accretion
Planetesimals passing within the
Hill sphere get significantly
scattered by the protoplanet
The size of the protoplanet
relative to the Hill sphere is
r −1
Rp
α≡
≈ 0.001
RH
5 AU
Rate of planetesimal accretion
Ṁ = πRp2 FH
Without gravitational focusing
2
Ṁ = α2 RH
FH
Planet
With gravitational focusing
Gravitational cross section
Hill sphere
2
Ṁ = αRH
FH
4 / 11
Anders Johansen
From pebbles to planets
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
2
Ṁ = αRH
FH
⇒ Only 0.1% (0.01%) of planetesimals entering the Hill sphere
are accreted at 5 AU (50 AU)
⇒ Time to grow to 10 M⊕ is
∼10
Myr at 5 AU
∼50
Myr at 10 AU
∼5,000 Myr at 50 AU
5 / 11
Anders Johansen
From pebbles to planets
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 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
6 / 11
Anders Johansen
From pebbles to planets
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
7 / 11
Anders Johansen
From pebbles to planets
Time-scale of pebble accretion
x/H
t=131 Ω−1
Mc/M⊕
−0.05
−0.10
0.10
t=134 Ω−1
10−2
10−3
U
10−1
50A
100
Hill
Drift
PA
U
y/H
0.00
∆=0.05, Z=0.01
101
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
5.0A
U
z/H
0.05
Σp/<Σp>
5.0
0.5A
0.10
U
50A
U
5.0A
U
50A
U
5.0A
Pluto
y/H
0.05
10−4
0.00
10−5
−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
Ceres
0.5AU
5.0AU
100 101 102 103 104 105 106 107 108
t/yr
⇒ Pebble accretion speeds up core formation by a factor 1,000 at 5
AU and a factor 10,000 at 50 AU
(Lambrechts & Johansen, submitted to A&A; see also Ormel & Klahr 2010)
⇒ Cores form well within the life-time of the protoplanetary gas disc,
even at large orbital distances
But requires large planetesimals to begin with. . .
Anders Johansen
From pebbles to planets
8 / 11
Formation of large planetesimals
t=120.4
0.05
y/H
(Johansen & Youdin 2007; Bai & Stone 2010)
0.10
0.00
−0.05
Planetesimals with d ∼ 1000 km
form by gravitational collapse
t=140.4
20.0
Σp/<Σp>
0.0
N=13
Mbound= 1.34
M1= 0.44
M2= 0.19
M13= 0.0061
N=7
Mbound= 1.35
M1= 0.95
M2= 0.16
M7= 0.029
N=7
Mbound= 1.35
M1= 0.59
M2= 0.49
M7= 0.020
N=3
Mbound= 1.47
M1= 0.75
M2= 0.70
M3= 0.014
N=9
Mbound= 1.42
M1= 0.45
M2= 0.33
M9= 0.012
N=6
Mbound= 1.46
M1= 0.63
M2= 0.59
M6= 0.021
N=7
Mbound= 1.37
M1= 0.54
M2= 0.31
M7= 0.0052
N=3
Mbound= 1.44
M1= 0.63
M2= 0.59
M3= 0.22
−0.10
0.10
Collisions with shear
ε=0.3
0.05
y/H
⇒ Asteroids born big?
t=130.4
1283
No collisions
Streaming instabilities lead to
concentration of cm-sized pebbles
0.00
−0.05
(Morbidelli et al. 2009)
−0.10
0.10
Collisions without shear
ε=0.3
0.05
y/H
Scaling to Kuiper belt gives twice
as large planetesimals
(Johansen, Youdin, & Lithwick 2012)
0.00
−0.05
−0.10
0.10
Collisions with shear
ε=1.0
0.05
y/H
⇒ Explains why Kuiper belt objects
are larger than asteroids
0.00
−0.05
⇒ Largest planetesimals can grow to
cores by pebble accretion
−0.10
−0.10 −0.05
0.00
x/H
0.05
−0.10 −0.05
0.00
x/H
0.05
−0.10 −0.05
0.00
x/H
0.05
0.10
9 / 11
Anders Johansen
From pebbles to planets
Formation of icy pebbles
Pebbles are observed in abundance in nearby
protoplanetary discs
(e.g. Testi et al. 2003; Wilner et al. 2005)
How do pebbles form so efficiently?
Near ice lines pebbles can form like hail stones
⇒ Efficient formation of cm-dm sized icy pebbles
near ice lines
(Ros & Johansen, in preparation; poster by Katrin Ros)
10 / 11
Anders Johansen
From pebbles to planets
Summary of talk
Dust
Pebbles
Ice condensation
1
Planetesimals
Gravitational instability
Cores
Pebble accretion
Ice condensation leads to efficient formation of pebbles near ice lines
(Ros & Johansen, in preparation; poster by Katrin Ros)
2
Streaming instabilities form large planetesimals (∼Ceres or ∼Pluto)
(Johansen, Youdin, & Lithwick 2012)
3
Large planetesimals grow rapidly by pebble accretion, explaining the
giants of the solar system as well as gas giants in wide orbits
(Lambrechts & Johansen, submitted; poster by Michiel Lambrechts)
⇒ Icy pebbles may play important role in planet formation
⇒ Planet formation can be probed and constrained through
observations of water vapour and pebbles
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Anders Johansen
From pebbles to planets