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. Dust coagulation 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. Compact Porous Fractal 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

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. = Cross-section for collision between i and k = Average relative velocity between i and k = Total number of size-bins modeled Coagulation equation The coagulation equation (discrete form) becomes: Problem with this approach: Need 1030 bins... Impossible!!

18. The coagulation equation becomes: 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 (>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)