brownian motion growth: self-similar

Dullemond & Dominik 2005

Brownian motion growth: self-similar

One-particle model

Equator

Sedimentation-driven growth („rainshower“)

One-particle model

Equator

Sedimentation-driven growth („rainshower“)

One-particle model

Equator

Sedimentation-driven growth („rainshower“)

One-particle model

Equator

Sedimentation-driven growth („rainshower“)

Warning: Not to scale! ;-)

Sedimentation-driven growth („rainshower“)Equation of settling of the big dust grain:

Equation of growth by sweep-up as the big grain falls:

Relation between m(t) and a(t):

Distribution of the small dust:

Sedimentation-driven growth („rainshower“)

Dullemond & Dominik (2005)

“Rainshower” in a disk

Dullemond & Dominik (2005)

Rain falling from a cumulus congestus cloud

Parallel with meteorology

Now with convection

Dullemond & Dominik (2005)

Cumulonimbus cloud, most probably with severe hail

Parallel with meteorology

Layered structure of giant hail stone

Parallel with meteorology

Main problem: high velocities

Particle size [meter]

30 m/s =100 km/h !!

Dust coagulation+fragmentation model

Birnstiel, Dullemond & Ormel 2010

Grain size [cm]10-4 10-2 100

10-8

10-6

10-4

10-2Σ d

ust [

g/cm

2 ]

Dust coagulation+fragmentation model

10-8

10-6

10-4

10-2Σ d

ust [

g/cm

2 ]

Grain size [cm]10-4 10-2 100

Birnstiel, Dullemond & Ormel 2010

Meter-size barrier

1m 1mm 1m 1km

Growth from ‘dust’ to planetary building blocks

Brownianmotion

Differentialsettling Turbulence

Aggregation

Meter-size barrier

Sweep-up growthFragmentation

Rapid radial drift

More barriers...

1m 1mm 1m 1km

Growth from ‘dust’ to planetary building blocks

Brownianmotion

Differentialsettling Turbulence

Meter-size barrier

Sweep-up growthFragmentation

Rapid radial drift

Aggregation

Bouncing barrier

Zsom et al. 2010, Güttler et al. 2010

Charge barrier

Okuzumi 2009

The “Lucky One” idea

1m 1mm 1m 1km

Growth from ‘dust’ to planetary building blocks

Brownianmotion

Differentialsettling Turbulence

Meter-size barrier

Sweep-up growthFragmentation

Rapid radial drift

Aggregation

Let’s focus on the fragmentation barrier

Windmark et al. 2012

How to create these seeds? Perhaps velocity distributions:Garaud et al. 2013; Windmark et al. 2012

Low sticking efficiency

Par

ticle

abu

ndan

ceThe “Lucky One” idea

All the different collision outcomes...

Güttler et al. 2010

Fluffy grains, compaction, bouncing...

Zsom et al. 2010