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

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

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

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” Compact Porous Produced by particle-cluster aggregation Higher  /m than compact ones, i.e. slightly slower settling  /m ∝ m-1/3

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

Interplanetary dust particles (IDPs)

Modeling of grain-grain collision Carsten Dominik

Modeling of grain-grain collision Carsten Dominik

Modeling of grain-grain collision Carsten Dominik

Modeling of grain-grain collision Carsten Dominik

Modeling of grain-grain collision Carsten Dominik

Magnetic aggregation Carsten Dominik, Hendrik Nübold

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

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!!

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!

Brownian motion

Sedimentation-driven coagulation Equator

Sedimentation-driven coagulation Equator

Sedimentation-driven coagulation Equator

Sedimentation-driven coagulation Equator

Sedimentation-driven coagulation Equator

Sedimentation-driven coagulation Equator

Sedimentation-driven coagulation Equator

Sedimentation-driven coagulation Equator

Sedimentation-driven coagulation One-particle model

Sedimentation-driven coagulation One-particle model

Sedimentation-driven coagulation One-particle model

Sedimentation-driven coagulation One-particle model

Sedimentation-driven coagulation One-particle model

Sedimentation-driven coagulation One-particle model

Sedimentation-driven coagulation 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

Sedimentation-driven coagulation

Full model with turbulence

Parellel with weather on Earth Cumulonimbus cloud, most probably with severe hail

Parellel with weather on Earth Layered structure of giant hail stone

Parellel with weather on Earth 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

Collisional cascade in debris disks Thebault & Augereau (2003)