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
Growth is aggregation of “monomers”
•Produced by particle-cluster aggregation
•Higher /m than compact ones, i.e. slightly slower settling
• /m ∝ m-1/3
Compact Porous
Growth is aggregation of “monomers”
•Produced by cluster-cluster aggregation (hierarchical growth)
•Very high /m, i.e. very slow settling
• /m ∝ m with -1/3<<0
Compact Porous Fractal
Modeling of grain-grain collision
Carsten Dominik
Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“
benötigt.
Modeling of grain-grain collision
Carsten Dominik
Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“
benötigt.
Modeling of grain-grain collision
Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“
benötigt.
Carsten Dominik
Modeling of grain-grain collision
Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“
benötigt.
Carsten Dominik
Modeling of grain-grain collision
Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“
benötigt.
Carsten Dominik
Magnetic aggregation
Carsten Dominik, Hendrik Nübold
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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
Coagulation equation
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!!
Coagulation equation
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
∫
Sedimentation-driven coagulation
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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
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
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
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