The formation of stars and planets Day 4, Topic 3: Agglomeration of particles Lecture by: C.P. Dullemond.

The formation of stars and planets

Day 4, Topic 3:

Agglomeration of particles

Lecture by: C.P. Dullemond

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

Dust coagulation

From dust to planets

1m 1mm 1m 1km 1000km

Observablein visual, infrared

and (sub-)mm

Observablewith

DARWINTPF etc.?

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

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)

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


•Produced by particle-cluster aggregation

•Higher /m than compact ones, i.e. slightly slower settling

• /m ∝ m-1/3

Compact Porous


•Produced by cluster-cluster aggregation (hierarchical growth)

•Very high /m, i.e. very slow settling

• /m ∝ m with -1/3<<0

Compact Porous Fractal

Interplanetary dust particles (IDPs)

Modeling of grain-grain collision

Carsten Dominik

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benötigt.


Carsten Dominik


benötigt.



benötigt.

Carsten Dominik



benötigt.

Carsten Dominik



benötigt.

Carsten Dominik

Magnetic aggregation

Carsten Dominik, Hendrik Nübold


benötigt.

Coagulation equation

mass1 2 3 4 5 6 7 8 9 10 11 12

Hit and stick between aggregates:

Size distribution function (discrete version):

€

N i = Number/cm3 of aggregates with i monomers


The coagulation equation (discrete form) becomes:

€

dNkdt

= − σ i,kΔvi,kN iNki=1

n

∑ + σ i,k−iΔvi,k−iN iNk−ii=1

k−1

∑

€

i,k = Cross-section for collision between i and k

€

Δvi,k = Average relative velocity between i and k

€

n = Total number of size-bins modeled

Problem with this approach:Need 1030 bins... Impossible!!


Introduce continuous distribution function:

€

f (m)dm = Number of particles per cm3 with mass between m and dm

Now make discrete bins, with bin width Δm ~ m. This way each logarithmic mass interval is equally well spaced!

The coagulation equation becomes:

€

df (m)

dt= − σ (m,m') Δv(m,m') f (m') f (m) dm'

0

∞

∫

+ σ (m,m −m') Δv(m,m −m') f (m') f (m −m') dm'0

m / 2

∫

Brownian motion


benötigt.

Sedimentation-driven coagulation

Equator


Equator


Equator


Equator


Equator


Equator


Equator


Equator


One-particle model


One-particle model


One-particle model


One-particle model


One-particle model


One-particle model


One-particle model

Parallel with weather on Earth

Rain falling from a cumulus congestus cloud

Parallel with weather on Earth

Rain falling from a cumulus congestus cloud



benötigt.

Full model with turbulence


benötigt.

Parellel with weather on Earth

Cumulonimbus cloud, most probably with severe hail


Layered structure of giant hail stone


Hierarchical structure of giant hail stone

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

Effect of pure growth on SED of disk

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

Porous grains: one-particle model

Porosity does not prolong time scale!!

Porous grains: one-particle model

Porosity only makes end-products larger/heavier

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 (>1m/s) collision: desintegration

(Blum et al.; Dominik et al.)

• Extremely simple model treatment: if(v>1m/s) then destroy (put mass back into monomers)

Coagulation with fragmentation


benötigt.

Collisional cascade in debris disks

Thebault & Augereau (2003)

The formation of stars and planets Day 4, Topic 3: Agglomeration of particles Lecture by: C.P. Dullemond.

Documents

small grains big grains

planet dust coagulation

dullemond slide

fragmentation slide

aggregation of monomers

evolution of dust

different speeds slide

compact porous slide