How can dust aggregates really grow bycollisions in protoplanetary disks?
Jürgen Blum
Institut für Geophysik und extraterrestrische Physik
Technische Universität zu Braunschweig
GermanyContents
1. An overview on planet formation
2. The minimum mass solar nebula model
3. Dust-particle condensation
4. What causes the dust grains to move (and to collide)?
5. What happens in a collision between two dust particles/aggregates?
6. How does dust agglomeration start?
7. Why do the dust aggregates not continue to grow the “fractal” way?
8. Collisions between high-porosity non-fractal dust aggregates
9. How large can dust aggregates really grow by direct sticking?
10. Is a dust-aggregate size of ~1 dm sufficient for the later formation ofplanets?
11. Can the dm-size barrier be shifted to larger sizes?
12. The next steps towards planetary-system formation
13. Conclusions

1.
An overview on planet
formation

A small chronology of the world

4,5 Gyr

Big bang; formation of the elements H and He
First stars and galaxies; first supernova explosions produce theheavy elements (C,N,O,Si,Fe,…)
Formation of the milky way
Formation of the solar system; at this point in time the interstellar
medium has been enriched with 1% heavy elements
Formation of the earth and the moon

4,45 Gyr
4,4 Gyr
4,2 Gyr
4 Gyr>3,5 Gyr>3,5 Gyr

Layer structure of the earth
Solid earth crust
Early ocean
Plate tectonics
Earth’s magnetic field
Origin of life

2,3 Gyr
1 Gyr
0 Gyr

Formation of oxygen-rich atmosphere; formation of ozone“Freeze-out” of inner earth coreToday

13,7 Gyr
13,4 Gyr
12 Gyr
4,567 Gyr

The five-stage process of planet formation
Protoplanetary dust

~1 µm

Planetesimals???

Agglomerationinteraction with gas importantno gravity~10 cminteraction with gas important
cumulative gravity potentially importantgas motion important~10 kmTerrestrial planets
Accretion ofplanetesimals~10,000 km
no interaction with gas
gravity dominates

Gas accretion
gravity dominates
escape velocity > thermal velocity(i.e. minimum mass ~10-15 Earth masses)
migration potentially important

Migration~100,000 km

Gas planets

The planets of the solar system

Terrestrial vs. gaseous planets

The planets of the solar system

Extrasolar planets
Z Planets around solar-type stars
Z Total of 333 extrasolar-planetcandidates (17 Dec 2008)
XSpectroscopically detected: 307
XTransits: 54
Z System with 2 or more planets: 31
Z Planetary systems in double stars: 30
Z Planetary systems in resonance: 5-7
Z Fraction of stars with planets: 0-25% (depending on
metallicity of the star)

Mass distribution of extrasolar planets
Udry et al. 2007

IcompletesamplePLANETSSTARS

Orbits of extrasolar planets

Wyatt 2008

About the metallicity of stars and theconnection to planets
13,7 GyrZ The search for planets around stars in globular Age of stars
in globularcluster has so far been unsuccessful; stars inclusters
globular clusters possess metallicities «1%.

Z The sun possesses a metallicity of ~1%.
Fischer & Valenti 2005

Z The mean metallicity ofstars with extrasolar
planets is >1%.

Age of thesun
Age of thestars withextrasolar
planets

0 Gyr

Star and planet formation belong together!
The sun and the planets of oursolar system formed at the sametime and from the same material
reservoir:
Z Elementary abundances
Z Age of the meteorites =age of the sun
Z Parallel angular momentum ofsun and planets

Cowley 1995

Star and planet formation belong together!
The sun and the planets of oursolar system formed at the sametime and from the same material
reservoir:
Z Elementary abundances
Z Age of the meteorites =age of the sun
Z Parallel angular momentum ofsun and planets

Radiometric dating:Material
Earth (Zircon, Australia)
Moon (highland rocks)
Meteorite (oldest from Mars)
Meteorite (chondrules)
Meteorite (CAI)

Age
4.40 Gyr
4.1-4.4 Gyr
4.5 Gyr
4.564 Gyr
4.567 GyrAge determination of the sun (evolutionarymodels and helioseismology data):
Authors
Age
Guenther & Demarque 1997
4.5±0.1 GyrBonnano, Schlattl & Paterno 2002
4.57±0.11 Gyr
Houdek & Gough 2007
4.68±0.02 Gyr

Molecular cloudStar formation –an overview© GEO, after Shu et al. 1987
Formation of gas-dust disk

“Clumping” of the dust

Formation of the sun by radialtransport of matter

Formation of isolated planetsMolecular clouds I

Molecular clouds II

Molecular clouds III

Molecular clouds IV:
dust and gas

Alves et al. 2001

Molecular clouds V: the interior

Bianchi et al. 2003

Alves et al. 2001

Molecular clouds VI: gravitational collapse

Bonnell et al. 2007

Stars form in clusters:
the open clusters h und χ Persei

HH 30Planet formation must be a (relatively) fast process!
Maximum lifetime of protoplanetary disks 107 years
Wyatt 2008

What have we learned so far?
Z The sun and our planets formed concurrently 4.567 billion years ago.
Z Extrasolar planetary systems can be similar to or different from thesolar system.
Z Dust plays a decisive role in the formation of the planets.
Z The lifetime of protoplanetary disks, the birthplaces of planets, is a few
million years.

2.
The minimum mass solar
nebula modelSolar-system data

Weidenschilling 1977

Inferred surface densities
Weidenschilling 1977

A power-law approximation:⎛ r ⎞Σ s ( r ) = 1700 g/cm 2 ⋅ ⎜⎟⎝ 1 AU ⎠−3 / 2

3.
Dust-particle condensation

The condensation sequence© NASA, after Shu et al. 1987

Z Formation of an accretion disk.
Z The disk is initially hotÆ few dust grains.
Z As the disk cools down, dust
particles condense.
Z Dust materials: oxides, silicates,organics, ices.
Z Particle sizes: sub-µm - µm.

Armitage 2007

4.
What causes the dust grains tomove (and to collide)?

The five-stage process of planet formation
Protoplanetary dust

~1 µm

Planetesimals???

Agglomerationinteraction with gas importantno gravity~10 cminteraction with gas important
cumulative gravity potentially importantgas motion important~10 kmTerrestrial planets
Accretion ofplanetesimals~10,000 km
no interaction with gas
gravity dominates

Gas accretion
gravity dominates
escape velocity > thermal velocity(i.e. minimum mass ~10-15 Earth masses)
migration potentially important

Migration~100,000 km

Gas planets

What causes the dust grains to move(and to collide)?
X Brownian motion (Weidenschilling 1984)
Z Vertical sedimentation, radial drift, azimuthal velocity
differences (Weidenschilling 1984)
Z Gas turbulence (magneto-rotational instability or selfinduced) (Balbus & Hawley 1991; Johansen et al. 2006;
Weidenschilling 1980; Sekiya 1998)

Blum et al.
2006Blum et al. 2006

What causes the dust grains to move(and to collide)?
Z Brownian motion (Weidenschilling 1984)
X Vertical sedimentation, radial drift, azimuthal velocity
differences (Weidenschilling 1984)
X Gas turbulence (magneto-rotational instability or selfinduced) (Balbus & Hawley 1991; Johansen et al. 2006;
Weidenschilling 1980; Sekiya 1998)

A MMSN model for the collision velocities
between protoplanetary dust grains
1 AU
Velocity contours
in cm/s
Critical velocity of
1 m/s
reachedfor 5-cm particles⎛ r ⎞Σ s ( r ) = 1700 g/cm 2 ⋅ ⎜
⎟
1
AU
⎝
⎠
Weidenschilling& Cuzzi 1993

−3 / 2

Alternative models
Desch 2007

Andrews & Williams 2007

Velocity contours in m/s

Velocity contours in m/s

1 AU

⎛ r ⎞
Σ s ( r ) = 20 g/cm 2 ⋅ ⎜⎟⎝ 1 AU ⎠Critical velocity of 1 m/sreached for 4-mm particles

−0.8

1 AU

⎛ r ⎞
Σ s ( r ) = 50500 g/cm 2 ⋅ ⎜⎟⎝ 1 AU ⎠Critical velocity of 1 m/sreached for >1-m particles

−2.17

5.
What happens in a collision
between two dust
particles/aggregates?

What happens in a collision between two dust
particles/aggregates?

Dominik & Tielens 1997

Adhesion force(van der Waals force)

Threshold velocity
for sticking

sticking

Heim et al. 1999

Restructuring

bouncing

Poppe et al. 2000

Heim et al. 2005

The importance of the threshold velocity for sticking
Z vSG ≈ vAG ≈ vFRvSG: threshold velocity for single-grain sticking
vAG: threshold velocity for fractal-dust-aggregate sticking
vFR: threshold velocity for dust-aggregate fragmentation.
Z The threshold velocity for dust-aggregate sticking is dependent on themonomer size.
Single-grain collisions
Poppe et al. 2000

sticking

bouncing

Dust-aggregate collisions
Blum & Wurm 2008

6.
How does dust agglomeration
start?

The initial growthStart with monomers at t0 = 0

P
R
I
N
C
I
P
L
E

Relative velocities due toBrownian motion, drift, gas
turbulenceObserve aggregate mass
(distribution) and structure at t > t0

Consider the simplest cases
BPCA

BCCA

Ballistic Particle-Cluster Ballistic Cluster-Cluster
Agglomeration
Agglomeration⇓⇓

ballistic hit-and-stick
impacts of single dust
particles into growing
dust agglomerateballistic hit-and-stick
collisions between
equal-mass dust
agglomerates

i = 1,024

i = 1,024

BPCA
N=2

BPCA
N=4

BPCA
N=8

BPCA
N=16

BPCA
N=32

BPCA
N=64

BPCA
N=128

BPCA
N=256

BPCA
N=512

BPCA
N=1024

BCCA
N=2

BCCA
N=4

BCCA
N=8

BCCA
N=16

BCCA
N=32

BCCA
N=64

BCCA
N=128

BCCA
N=256

BCCA
N=512

BCCA
N=1024

Consider the simplest cases
BPCA

BCCA

Ballistic Particle-Cluster Ballistic Cluster-Cluster
Agglomeration
Agglomeration⇓⇓

ballistic hit-and-stick
impacts of single dust
particles into growing
dust agglomerateballistic hit-and-stick
collisions between
equal-mass dust
agglomerates

i = 1,024

i = 1,024

The initial growth
Gas turbulence

E
X
P
E
R
I
M
E
N
T
S

Wurm &
Blum 1998

Differential sedimentation∅ 1.9 µm SiO2

∅ 1.9 µm SiO2

Blum et al. 1998
Brownian motion∅ 1.9 µm SiO2

Blum et al. 2000

The initial growth

M
O
D
E
L

monodispersity

hit-and-stick collisions

fractality

growthtimescale
determinedby collisiontimescale

The initial growth∅ 1.0 µm SiO2
Brownian motion

E
X
P
E
R
I
M
E
N
T
S

Z Hit-and-stick collisions
Z Mass-size relation m ∝ sD withD ≤ 2 (fractal aggregates)∅ 1.0 µm SiO2
Brownian motion∅ 1.0 µm SiO2
Brownian motion

Z Narrow (quasi-monodisperse)
mass spectra
Z Temporal mass growth follows apower law
Krause & Blum 2004

The initial growth
S
I
M
U
L
A
T
I
O
N

Z “Minimum Mass
Solar Nebula”
model
Z Hit-and-stick
collisions
Z Brownian motion+ turbulence
Z t = 0…30 yrs© Andras Zsom, MPIA Heidelberg

7.
Why do the dust aggregates notcontinue to grow the “fractal”
way?

The restructuring/compaction growth regime
Low impact energy: hit-and-stick collisions

Blum & Wurm 2000
Paszun & Dominik, pers.
comm.

Intermediate impact energy: compaction
Z Collisions result in sticking.
Z Impact energy exceeds energy to overcome rolling friction(Dominik and Tielens 1997; Wada et al. 2007).

Z Dust aggregates become non-fractal (?) but are still highly porous.

8.
Collisions between high-porosity
non-fractal dust aggregates

The experimental range

Blum & Wurm 2008
Background contours
by Weidenschilling &Cuzzi 1993

Z Sizes of protoplanetary dust aggregates:

1 µm

1 mm

Z Collision velocities of protoplanetary dust aggregates:
Z Protoplanetary dust materials:

oxidessilicates

10-4 m/s

organics

1m
10-2 m/s

1 km
1 m/s

10+2 m/s

icesno expt’s

expt’sExperimental outcomes in dust-aggregate collisions
STICKING+
NO COMPACTIONSTICKING+
COMPACTIONBOUNCING+
COMPACTIONBOUNCING+
FRAGMENTATIONBOUNCING +(PARTIAL) STICKING +FRAGMENTATION

Wurm & Blum 1998

Blum & Wurm 2000

Blum & Münch 1993

Blum & Münch 1993

Wurm et al. 2005b

Blum et al. 1998

Langowski et al. 2008

Heißelmann et al. (in prep.)

Schräpler & Blum (in prep.)

Paraskov et al. 2007

Blum & Wurm 2000

Teiser & Blum (in prep.)

Weidling et al. (subm.)

Wurm et al. 2005a

Teiser & Wurm 2008

Güttler & Blum (in prep.)

Paraskov et al. 2007

Güttler & Blum (in prep.)

Blum et al. 2000
Blum et al. 2002

Teiser & Wurm (in prep.)

Blum & Schräpler 2004

Lammel et al. (in prep.)

Krause & Blum 2004
Blum et al. 2006

Experimental outcomes in dust-aggregate collisions
STICKING+
NO COMPACTIONSTICKING+
COMPACTIONBOUNCING+
COMPACTIONBOUNCING+
FRAGMENTATIONBOUNCING +(PARTIAL) STICKING +FRAGMENTATION

An example of a fractal dust aggregate grown in a laboratory
experiment∅ 1.9 µm SiO2

Blum et al. 1998

Experimental outcomes in dust-aggregate collisions
STICKING+
NO COMPACTIONSTICKING+
COMPACTIONBOUNCING+
COMPACTIONBOUNCING+
FRAGMENTATION

Sticking due to deep penetration
PROJECTILES: v = 0.9 m/s; ∅ = 2-3 mm; ϕ = 0.07

TARGET:
dust particles: ∅ 0.1-10 µm SiO2 (irr.)
target ∅ = 25 mm; ϕ = 0.07

Langkowski
et al. 2008

BOUNCING +(PARTIAL) STICKING +FRAGMENTATION

Experimental outcomes in dust-aggregate collisions
STICKING+
NO COMPACTIONSTICKING+
COMPACTIONBOUNCING+
COMPACTIONBOUNCING+
FRAGMENTATIONBOUNCING +(PARTIAL) STICKING +FRAGMENTATION

Low coefficient of restitution as indication for compactionv = 0.4 m/s∅ = 3-5 mm
ϕ = 0.15
SiO2 (sph.)

Heißelmann et al. (in prep.)v = 0.2 m/s∅ = 2.5 mm
ϕ = 0.15
SiO2 (sph.)

Weidling et al. (subm.)

Experimental outcomes in dust-aggregate collisions
STICKING+
NO COMPACTIONSTICKING+
COMPACTIONBOUNCING+
COMPACTIONBOUNCING+
FRAGMENTATIONBOUNCING +(PARTIAL) STICKING +FRAGMENTATION

Breaking of inter-particle bonds

PROJECTILES:
dust particles: ∅ 1.5 µm SiO2 (sph.)∅ ~ 2 mm; ϕ = 0.15

Lammel et al.
(in prep.)

3D
Lammel et al. (in prep.)
SiO2, ϕ = 0.15; v = 5.1 m/s

2DExperimental outcomes in dust-aggregate collisions
STICKING+
NO COMPACTIONSTICKING+
COMPACTIONBOUNCING+
COMPACTIONBOUNCING+
FRAGMENTATIONBOUNCING +(PARTIAL) STICKING +FRAGMENTATION“High-velocity” impacts of dust aggregates∅ 0.6 mm SiO2 aggregate (ϕ = 0.35) projectile @ 8.4 m/s impact velocity onto solid SiO2 target

Teiser & Wurm 2009 in press

slope independentof velocity (~ MRN)

Güttler & Blum (in prep.)An attempt for categorization
Bouncing + compaction

Hit-and-stick

Mass transfer to projectile

Sticking + compaction

Fragmentation

Sticking by penetration

Fragmentation + erosion

Sticking + fragmentation

Fragmentation + mass transfer

9.
How large can dust aggregates
really grow by direct sticking?

The “facts”

Weidenschilling 1977

Z Collision velocity increases with increasing
aggregate size in all solar-nebula models.
Z Growth is limited by fragmentation.
Z Fragmentation threshold vth ≈ 1 m/s, but depends
on monomer size.
Andrews & Williams 2007

Blum & Wurm 2008

Desch 2007

Z Maximum aggregate sizeachievable bydirect collisional sticking:~ 1 dm for MMSN (Weidenschilling 1977)~ 1 mm for Andrews & Williams 2007 model~ 1 m for Desch 2007 model.

Weidling
et al.(subm.)

The growth range in the MMSN model

Blum &
Wurm 2008

How fast can we reach the decimeter size ?
Blum 2004~1dm

non-fractal growth~1
cm

restructuring
limit

~1
mm

1 AU
fractal growth
Minimum-masssolar nebula modeltaken from:
Hayashi et al. 1985

10
AU
100
AU
~1
µm

Growth timescale to dm size of ~103 years confirmed by more sophisticated model ofDullemond & Dominik 2005

10.
Is a dust-aggregate size of ~1 dm
sufficient for the later formationof planets?

At which size becomes gravity important ?
Z As long as the nebular gas is around(106 – 107 yrs), relative velocities
between (≤ km-sized) protoplanetary
bodies are ≤ 50 m/s.
Z Escape velocity vesc [m/s] ≈ d [km].
Z Typical rebound velocity of bouncing or
fragmenting projectile ~0.2 × vimp
(i.e. coefficient of restitution ~0.2).
Z Size above which impacting dust
aggregate must stick: dcrit ≈ 10 km.

Wyatt 2008

The growth range 1 dm … 1 km
Basically unsolved, due to the following problems:
Z Radial drift:radial velocity peaks at ~1 m bodies;drift timescale ~100 yr (“meter-size barrier“);smaller and larger bodies need longer
times (τ ∝ s -1 for s ≤ 1m; τ ∝ s for s ≥ 1m).

Z High collision velocities:

experiments suggest no direct sticking, butrather compaction and fragmentation.

The five-stage process of planet formation
Protoplanetary dust

~1 µm

Planetesimals???

Agglomerationinteraction with gas importantno gravity~10 cminteraction with gas important
cumulative gravity potentially importantgas motion important~10 kmTerrestrial planets
Accretion ofplanetesimals~10,000 km
no interaction with gas
gravity dominates

Gas accretion
gravity dominates
escape velocity > thermal velocity(i.e. minimum mass ~10-15 Earth masses)
migration potentially important

Migration~100,000 km

Gas planets

11.
Can the dm-size barrier beshifted to larger sizes?

Ways around the radial drift problem and/or the
fragmentation threshold
X Capture of m-sized bodies in turbulent eddies(Klahr & Bodenheimer 2006; Johansen et al. 2006a)

Z Suppressed radial drift in dust-dominated sub-disk
Z Fast growth of m-sized bodies in dust-dominated sub-disk due to highnumber densities, low relative velocities, and/or gravitational instability(Schräpler & Henning 2004; Johansen et al. 2006b; Johansen et al. 2007)

Z Fast growth of m-sized bodies by secondary accretion mechanisms(Wurm et al. 2001; Blum 2004)

Z Photophoresis at the inner edge of the (dust) disk
(Krauß & Wurm 2005)

Z …

Capture of macroscopic particles by long-living
gas vortices
Z Trapping of solid
objects in pressure
maxima and/or in
anticyclonic vortices.
Z Basically all solid
bodies with sizes
0.1-10 m are
efficiently captured.
Z No escape of dustwith sizes 0.1-1000 mfrom vortices.
Z Low relative velocities
within the vortices⇒ collisional growth ?
Z No shear inside
vortices.
Z Concentration of thedust particles in thecenters of the vortices ⇒ gravitational
instability ?
© H. Klahr (MPIA Heidelberg)

Δ: 1m dust particle

Ways around the radial drift problem and/or the
fragmentation threshold
Z Capture of m-sized bodies in turbulent eddies(Klahr & Bodenheimer 2006; Johansen et al. 2006a)

Z Suppressed radial drift in dust-dominated sub-disk
X Fast growth of m-sized bodies in dust-dominated sub-disk due to highnumber densities, low relative velocities, and/or gravitational instability(Schräpler & Henning 2004; Johansen et al. 2006b; Johansen et al. 2007)

Z Fast growth of m-sized bodies by secondary accretion mechanisms(Wurm et al. 2001; Blum 2004)

Z Photophoresis at the inner edge of the (dust) disk
(Krauß & Wurm 2005)

Z …

Gravitational instability (Johansen et al. 2007)© A. Johansen(Univ. Leiden)

http://www.strw.leidenuniv.nl/~ajohan/research.php#movies

Z In absence of turbulence, >cm-sized dust aggregates sediment towards the midplane of the
protoplanetary disk.
Z When the dust density exceeds the gas density, the gas in the midplane is forced to rotate at
Keplerian velocity. Due to the shearing between the midplane rotation and the layers
above/below the midplane, a Kelvin-Helmholtz instability forms.
Z Due to a local variation of the dust-to-gas ratio and, thus, the rotation speed, a “clumping
instability” occurs.
Z Gravitationally-bound dust ensembles are formed when the dust size exceeds ~0.1 m.
Z Direct formation of planetesimals with sizes up to 100-1 000 km, if fragmentation is negligible.
Z However, if collisions results in fragmentation, no net growth occurs (Johansen et al. 2008).

Ways around the radial drift problem and/or the
fragmentation threshold
Z Capture of m-sized bodies in turbulent eddies(Klahr & Bodenheimer 2006; Johansen et al. 2006a)

Z Suppressed radial drift in dust-dominated sub-disk
Z Fast growth of m-sized bodies in dust-dominated sub-disk due to highnumber densities, low relative velocities, and/or gravitational instability(Schräpler & Henning 2004; Johansen et al. 2006b; Johansen et al. 2007)

X Fast growth of m-sized bodies by secondary accretion mechanisms(Wurm et al. 2001; Blum 2004)

Z Photophoresis at the inner edge of the (dust) disk
(Krauß & Wurm 2005)

Z …

without gas flow
and charging

Fast growth of m-sized
bodies by secondary
accretion mechanisms(Wurm, Blum & Colwell 2001; Blum 2004)

dust
agglomeratewith gas flow or charging»1 - 100 m/s+

preplanetesimal

+

+

+
+

+

+

+

+

12.
The next steps towards
planetary-system formation

The five-stage process of planet formation
Protoplanetary dust

~1 µm

Planetesimals???

Agglomerationinteraction with gas importantno gravity~10 cminteraction with gas important
cumulative gravity potentially importantgas motion important~10 kmTerrestrial planets
Accretion ofplanetesimals~10,000 km
no interaction with gas
gravity dominates

Gas accretion
gravity dominates
escape velocity > thermal velocity(i.e. minimum mass ~10-15 Earth masses)
migration potentially important

Migration~100,000 km

Gas planetsAccretion of planetesimals
Z Gas friction is negligible
Z Typical collision velocity < escape velocity
X Gravitational sticking
X Collision probability increased due to gravitational focussing
Æ large bodies grow faster than small bodies

vr

Orbit without gravity
Orbit with graviy

Focussing factor

Escape velocity

2ve
Fg = 1+ 2
vr
Relative velocity at
infinity

Kokubo & Ida 2000

Formation timescales of terrestrial planets
Time$ (yr)Size

Process010-6 mCondensation of dust particles~ 103-104

0.1 m

Agglomeration with high sticking
probability

Stage 1? (< 107)§

10 km

Planetesimals with mass m0

Stage 2

Time# (yr)Mass

Process

~ 103

30 m0

~ 7×103105 m0~ 2×104

106 m0~ 6×104

107 m0~ 105

107,5 m0; 0,01-0,1 ME

Planetary embryos (isolated)~ 106-7

0.1-0.5 ME

Protoplanets (+ embryos; embryos are
slowly consumed)~ 107-8

1 ME

Planets on isolated orbits

Stage 3

$ Since the formation of the sun§ Dispersion of the nebula after ~107 years# Since the formation of planetesimals

Making terrestrial planets

Chambers 2001

Making terrestrial planets

Raymond et al. 2004

Overview of the formation of terrestrial planets
104 km

ACCRETION(Gravitation)

10 km
GRAVITATIONAL INSTABILITY(of an ensembles of dust aggregates) ?

10 cm
AGGLOMERATION(van der Waals force)

1 µm

The five-stage process of planet formation
Protoplanetary dust

~1 µm

Planetesimals???

Agglomerationinteraction with gas importantno gravity~10 cminteraction with gas important
cumulative gravity potentially importantgas motion important~10 kmTerrestrial planets
Accretion ofplanetesimals~10,000 km
no interaction with gas
gravity dominates

Gas accretion
gravity dominates
escape velocity > thermal velocity(i.e. minimum mass ~10-15 Earth masses)
migration potentially important

Migration~100,000 km

Gas planets

The formation of gas planets
Two hypotheses for the formation of the planets
Jupiter, Saturn, Uranus and Neptune:

Udry et al. 2007

1. Gravitational instability (Boss 2001; 2003; 2007)
Z Pro: fast process.
Z Con: unclear whether the process is feasible(problems with radiation transport);“Brown Dwarf Desert”.
2. Formation of a 10-15 ME solid core; gravitational accretion of gas(Pollack et al. 1996; Klahr & Bodenheimer 2006; Klahr & Kley 2006)

Z Pro: gas accretion on solid core well understood and fast(within ~300.000 yrs).
Z Con: formation of a 10-15 ME terrestrial planet within < 107 yrs
difficult; possible if (1) long-living eddies exist in the gas, which canefficiently trap m-sized bodies (in this case, no need for stages 2-3)or (2) if the mass density is sufficiently high.

Masses and sizes of extrasolar planets
Tests of the formation hypothesesof gas planets:
Æ Do extrasolar planets possessa core with more than ~1-2% of
the planetary mass?
Æ Simultaneous measurement ofmass and radius of extrasolar
planets.

Torres et al. 2008

Masses and sizes of extrasolar planets

SaturnJupiter

Torres et al. 2008

Core masses of extrasolar planets
Tests of the formation hypotheses of gas planets

Charbonneau et al. 2007

Prediction model 1: core mass / total mass ~0.01 – 0.02.
Prediction model 2: core mass ≥10-20 earth masses.

Core masses of extrasolar planets
Torres et al. 2008

Model 2Model 1

Santos et al. 2005

The formation of gas planets within 106-107 yrs (model 2)
Desch 2007:
modified model of solar nebula,
based on Nice model

Klahr & Bodenheimer 2006:
particle shearing within turbulence eddies

The formation of gas planets within 106-107 yrs (model 2)
Density

Klahr & Kley 2006

The formation of gas planets within 106-107 yrs (model 2)
Temperature

Klahr & Kley 2006

Has the formation of a gas planet been (indirectly)
observed in statu nascendi ?

http://hubblesite.org/newscenter/archive/releases/1999/03

http://hubblesite.org/newscenter/archive/releases/2003/02/image/b/

The five-stage process of planet formation
Protoplanetary dust

~1 µm

Planetesimals???

Agglomerationinteraction with gas importantno gravity~10 cminteraction with gas important
cumulative gravity potentially importantgas motion important~10 kmTerrestrial planets
Accretion ofplanetesimals~10,000 km
no interaction with gas
gravity dominates

Gas accretion
gravity dominates
escape velocity > thermal velocity(i.e. minimum mass ~10-15 Earth masses)
migration potentially important

Migration~100,000 km

Gas planets

Planet migration und reorganization
Excitation of spiral density waves in thegas by the planet; torque anisotropy
between inner and outer disk; in mostcases, the influence of the outer spiralwave dominates so that the planet loses
angular momentum and spirals radiallyinward. Stop of migration by (a) clearingof the nebula or (b) tidal friction with thecentral star.

http://www.maths.qmul.ac.uk/~masset/moviesmpegs.html

The Nice model for the dynamic evolution of the
giant planets of the solar system

Morbidelli et al. 2007
(Migration, resonances, clearing of nebula)

Desch 2007
(Prediction of the core masses of the giant
planets; modified solar-nebula model,
based upon Nice model)

13.
Conclusions

The five-stage process of planet formation
Protoplanetary dust

~1 µm

Planetesimals???

Agglomerationinteraction with gas importantno gravity~10 cminteraction with gas important
cumulative gravity potentially importantgas motion important~10 kmTerrestrial planets
Accretion ofplanetesimals~10,000 km
no interaction with gas
gravity dominates

Gas accretion
gravity dominates
escape velocity > thermal velocity(i.e. minimum mass ~10-15 Earth masses)
migration potentially important

Migration~100,000 km

Gas planets

CONCLUSION ON DUST AGGLOMERATIONZ The growth of protoplanetary dust from (sub-)micrometer to ~10 cm
in size (model dependent !) is caused by sticking collisions and israther well understood.
Z Initial growth timescales from µm to dm size are ~103 yrs (@1AU for
the MMSN model).
Z However, the further growth is still extremely speculative (andundoubtedly complex); direct collisional growth seems unlikely;
secondary growth mechanisms, high-number-density effects and/or
gravitational instabilities might be important.
→ work in progress … stay tuned!

REVIEW ARTICLESZ Blum, J. 2006. Dust Agglomeration. Adv. in Phys. 55 (7-8), 881-947.
Z Blum, J. & Wurm, G. 2008. The Growth Mechanism of Macroscopic
Bodies in Protoplanetary Disks. Ann. Rev. Astron. Astrophys. 46, 21-56.

THANK YOU FOR YOUR ATTENTION !
Acknowledgements
This work was supported by
DFG, DLR, ESA and TU Braunschweig
Many thanks to the
CODAG, ICAPS & IPE and the ICES teams
Many thanks to
Carsten Dominik, Carsten Güttler, Daniel Heißelmann, Anders Johansen,
Hubert Klahr, Willy Kley, Maya Krause, Christopher Lammel,
Doreen Langkowski, Dominik Paszun, Jens Teiser, René Weidling,
Gerhard Wurm, and Andras Zsom.

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