The formation of stars and planets

1
The formation of stars and planets

• Day 4, Topic 3
• Agglomeration of particles
• Lecture by C.P. Dullemond

2
Main planet formation scenario

• Dust particles in disk stick and form aggregates
• Aggregates continue to grow until gravity becomes
  important (planetesimals)
• Planetesimals agglomerate via gravitational
  interactions and form rocky planet
• Two ways from here
• Stays a rocky planet (like Earth)
• Accretes gas and becomes Jupiter-like planet

3
From dust to planets
Observable with DARWIN TPF etc.
Observable in visual, infrared and (sub-)mm
?
1?m
1km
1000km
1mm
1m
4
Grain coagulation

• What happens upon collision?
• They stick (creating a bigger aggregate)
• They stick and compactify
• They bounce
• They mutually destroy each other
• How many collisions? / What is evolution of dust?
• Brownian motion
• Turbulence
• Big grains settle to the midplane and sweep up
  small grains
• Big grains move on Kepler orbits, small grains
  are mixed with gas (slightly sub-Keplerian)
• Radial migration of grains at different speeds

5
Grain coagulation

• What happens upon collision?
• They stick (creating a bigger aggregate)
• They stick and compactify
• They bounce
• They mutually destroy each other
• How many collisions? / What is evolution of dust?
• Brownian motion
• Turbulence
• Big grains settle to the midplane and sweep up
  small grains
• Big grains move on Kepler orbits, small grains
  are mixed with gas (slightly sub-Keplerian)
• Radial migration of grains at different speeds

Microphysical (molecular dynamics) modeling
/ laboratory experiments
Dominik Tielens (1997), Dominik Nübold (2002)
/ Blum et al. (2000) Poppe, Blum Henning
(2000)
Global dust evolution modeling (with distribution
functions) based on a model of disk structure
Weidenschilling (1980, etc) Nakagawa Nakazawa
(1981) Schmitt, Henning Mucha (1997) Mizuno,
Markiewicz Völk (1988) Tanaka et al.
(2005) Dullemond Dominik (2005)
6
Growth is aggregation of monomers
Compact

• Produced by particle-cluster aggregation, if
  anything
• Lowest possible ?/m, i.e. fastest settling
  velocity
• ? /m ? m-1/3

7
Growth is aggregation of monomers
Compact
Porous

• Produced by particle-cluster aggregation
• Higher ? /m than compact ones, i.e. slightly
  slower settling
• ? /m ? m-1/3

8
Growth is aggregation of monomers

• Produced by cluster-cluster aggregation
  (hierarchical growth)
• Very high ? /m, i.e. very slow settling
• ? /m ? m? with -1/3lt?lt0

9
Interplanetary dust particles (IDPs)
10
Modeling of grain-grain collision
Carsten Dominik
11
Modeling of grain-grain collision
Carsten Dominik
12
Modeling of grain-grain collision
Carsten Dominik
13
Modeling of grain-grain collision
Carsten Dominik
14
Modeling of grain-grain collision
Carsten Dominik
15
Magnetic aggregation
Carsten Dominik, Hendrik Nübold
16
Coagulation equation
Size distribution function (discrete version)
Number/cm3 of aggregates with i monomers
Hit and stick between aggregates
1
2
3
4
5
6
7
8
9
10
11
12
mass
17
Coagulation equation
The coagulation equation (discrete form) becomes
Problem with this approach Need 1030 bins...
Impossible!!
18
Coagulation equation
Introduce continuous distribution function
Number of particles per cm3 with mass between m
and dm
Now make discrete bins, with bin width ?m m.
This way each logarithmic mass interval is
equally well spaced!
19
Brownian motion
20
Sedimentation-driven coagulation
Equator
21
Sedimentation-driven coagulation
Equator
22
Sedimentation-driven coagulation
Equator
23
Sedimentation-driven coagulation
Equator
24
Sedimentation-driven coagulation
Equator
25
Sedimentation-driven coagulation
Equator
26
Sedimentation-driven coagulation
Equator
27
Sedimentation-driven coagulation
Equator
28
Sedimentation-driven coagulation
One-particle model
29
Sedimentation-driven coagulation
One-particle model
30
Sedimentation-driven coagulation
One-particle model
31
Sedimentation-driven coagulation
One-particle model
32
Sedimentation-driven coagulation
One-particle model
33
Sedimentation-driven coagulation
One-particle model
34
Sedimentation-driven coagulation
One-particle model
35
Parallel with weather on Earth
Rain falling from a cumulus congestus cloud
36
Parallel with weather on Earth
Rain falling from a cumulus congestus cloud
37
Sedimentation-driven coagulation
38
Full model with turbulence
39
Parellel with weather on Earth
Cumulonimbus cloud, most probably with severe hail
40
Parellel with weather on Earth
Layered structure of giant hail stone
41
Parellel with weather on Earth
Hierarchical structure of giant hail stone
42
Time scale problem

• Growth at 1AU up to cm size or larger proceeds
  within 1000 years
• Virtually all the small grains get swept up
  before 10.000 years
• Seems to contradict observations of T Tauri and
  Herbig Ae/Be star disks

43
Effect of pure growth on SED of disk
44
What could save the small grains?

• Porous / fractal grains settle slower
• Grain charging reduces sticking probability
• Accretion replenishes small grains
• Highly reduced turbulence in dead zone

45
Porous grains one-particle model
Porosity does not prolong time scale!!
46
Porous grains one-particle model
Porosity only makes end-products larger/heavier
47
Fragmentation of grains

• Dust aggregates are loosely bound
  (van der Waals force between monomers)
• Collision speed decisive for fate of aggregate
• Slow velocity collision sticking
• Intermediate velocity collision
  compactification
• High velocity (gt1m/s) collision
  desintegration
• (Blum et al. Dominik et al.)
• Extremely simple model treatment if(vgt1m/s)
  then destroy (put mass back into monomers)

48
Coagulation with fragmentation
49
Collisional cascade in debris disks
Thebault Augereau (2003)