Brownian motion growth: self-similar

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22 Φεβ 2014 (πριν από 3 χρόνια και 10 μήνες)

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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“)

d
z
(
t
)
d
t

v
s
e
t
t
(
z
(
t
)
,
a
(
t
)
)


s
a
(
t
)

g
a
s
(
z
(
t
)
)
v
t
h

K
2
z
(
t
)
d
m
(
t
)
d
t


a
2
(
t
)

t
i
n
y
d
u
s
t
(
z
(
t
)
)
v
s
e
t
t
(
t
)
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):

m
(
t
)

4

3

s
o
l
i
d
a
3
(
t
)
Distribution of the small dust:


t
i
n
y
d
u
s
t
(
z
)

0
.
0
1

g
a
s
(
z
)

0
.
0
1

g
a
s
2

H
p
e
x
p

z
2
2
H
p
2








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

10
0

10
-
8

10
-
6

10
-
4

10
-
2

Σ
dust

[g/cm
2
]

Dust coagulation+fragmentation model

10
-
8

10
-
6

10
-
4

10
-
2

Σ
dust

[g/cm
2
]

Grain size [cm]

10
-
4

10
-
2

10
0

Birnstiel
,
Dullemond

&
Ormel

2010

Meter
-
size barrier

1

m

1m
m

1
m

1k
m

Growth from

dust


to planetary building blocks

Brownian

motion

Differential

settling

Turbulence

Aggregation

Meter
-
size barrier

Sweep
-
up growth

Fragmentation

Rapid radial drift

More barriers...

1

m

1m
m

1
m

1k
m

Growth from

dust


to planetary building blocks

Brownian

motion

Differential

settling

Turbulence


Meter
-
size barrier

Sweep
-
up growth

Fragmentation

Rapid radial drift

Aggregation

Bouncing barrier

Zsom

et al. 2010,
Güttler

et al. 2010

Charge barrier

Okuzumi

2009

The “Lucky One” idea

1

m

1m
m

1
m

1k
m

Growth from

dust


to planetary building blocks

Brownian

motion

Differential

settling

Turbulence


Meter
-
size barrier

Sweep
-
up growth

Fragmentation

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

Particle abundance

The “Lucky One” idea

All the different collision outcomes...

Güttler et al. 2010

Fluffy grains, compaction, bouncing...

Zsom et al. 2010