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 coagulation
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
1mm 1m
1km
1000km

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”
Compact
Porous
Fractal
Produced by cluster-cluster aggregation (hierarchical growth)
Very high  /m, i.e. very slow settling
 /m ∝ m with -1/3<<0

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:
= Cross-section for collision between i and k
= Average relative velocity between i and k
= Total number of size-bins modeled
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
The coagulation equation becomes:
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 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 (>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)

48. Coagulation with fragmentation

49. Collisional cascade in debris disks
Thebault & Augereau (2003)