つぶらな衝突
ダストアグリゲイト衝突シミュレーション
和田 浩二
千葉工業大学惑星探査研究センター
田中秀和1，陶山徹2，木村宏3，山本哲生1
1北大低温研，2新潟科学館，3CPS

Background
Collisional growth of dust(< μm)?

Planetesimal formation(> km)

Structure evolution of dust aggregates in protoplanetary disks

When and how are aggregates compressed and/or disrupted ?
Numerical
simulation of dust aggregate collisions!
ダストアグリゲイト衝突の数値シミュレーション！

©NASAToday’s Topics:

ダストは大きくなれるのか？
z Collisional growth conditions for dust aggregates¾Can dust grow through high velocity collisions?
Wada et al. 2009, ApJ 702, 1490-1501

z Bouncing conditions for dust aggregates¾What causes aggregates to bounce?

Collisional Growth Conditions

Ballistic Cluster-Cluster Aggregation (BCCA)
9In the early growth stage, undeformed BCCAs are formed
because of their low collision velocity (< mm/s)
z A series of hit-and sticks ofcomparable aggregatesz Fluffy structure (fractal dimension df < ~ 2)

BCCA structures are compressed (df ~ 2.5) by collisions(Dominik & Tielens 1997; Wada et al. 2007, 2008; Suyama et al. 2008)

BackgroundCollision velocity of dust
in protoplanetary disks< several 10 m/se.g., ＜～50 m/s (Hayashi model, without turbulence)

Is it possible for dust to grow through collisions ?
Maybe possible in head-on collisions
Experimental: Blum & Wurm 2000, Wurm et al. 2005
Numerical: Dominik & Tielens 1997, Wada et al. 2008

What if in offset collisions ?

Ballistic Particle-Cluster Aggregation (BPCA)z Formed by one-by-one sticking of monomers

z Compact structure (fractal dimension ~ 3)Dust is expected to be compact
at high velocity collisions causing their disruption
Collisions of BPCA clustersimplication for growth and disruption of dust

Objective

Wada et al. 2008, ApJ 677, 1296-1308
Wada et al. 2009, ApJ 702, 1490-1501

Can dust aggregates grow ?
（even in offset collisions）
Numerical simulation ofHigh velocity collisions of BPCAs （& BCCAs ）9Degree of disruption (Growth efficiency)
Number of particles in the largest fragment

Grain interaction model
Johnson, Kendall and Roberts (1971); Johnson (1987); Chokshi et al. (1993)
Dominik and Tielens (1995,96); Wada et al. (2007)

Elastic spheres having surface energyNormalδ

SlidingrollingtwistingξsContact & Separations, ξ, ϕ > critical displacements

ϕEnergy dissipation

Ebreak: Energy to break a contact
Eroll : Energy to roll a pair of gains by 90˚A collision of BPCAs
8000+8000 ice particles (r=0.1μm, ξc = 8Å)Collision velocity = 57 m/s

CG by Dr. T. Takeda,
4D2Uproject, NAOJ

Growth efficiency averaged
vimp [m/s] (ice)f = Nlarge / Ntotal

110

Averaged for b2100f ≡ Nlarge / Ntotal: growth efficiency
f > 0.5 + growth~ 60 m/s

0.8f < 0.50.6- growth

0.49small dependence on N
0.200.1

110100Eimpact / (N Ebreak)1000

Amount of ejecta mass: Σ4 Nej , averaged
vimp [m/s] (ice)110

Averaged over b2

1009dependent on N
Σ4 Nej / Ntotal

0.8

The larger aggregates,
the smaller amount of ejecta.

0.6

0.40.2

00.1

1

10100

Eimpact / (N Ebreak)1000

Averaged growth efficiency : BCCA & BPCA
vimp [m/s] (ice)110

Averaged over b2

100

f = Nlarge / Ntotal

40 ~ 60 m/s
0.8Actual dust structure:
between BCCA and BPCA

0.6BCCA

BPCA

0.4

0.2

00.1

1

10100

Eimpact / (N Ebreak)1000Summary and Implications
zDust aggregates remain fluffly (fractal dimension ~ 2.5) .
Very fluffy planetesimals could be formed !?
Other processes to compress aggregates are necessary.

zIcy aggregates can grow at collision velocity < 60 m/s.
Planetesimals can be formed through collisions of dust.
Animation by Prof. H. Tanaka

Collisions of BPCA clusters ofdifferent sizes
N=32000+500, ice, ξc = 8Å, ucol = 70 m/s
b = 0.39

Bouncing Conditions

Bouncing Problem“Bouncing” prevents dust from growing
Dominik & Tielens 1997;
Previous numerical simulaitons: Wada et al. 2007, 2008, 2009;
Suyama et al. 2008, etc…

No bouncing

Collisional growth is feasible!

BPCA, N=8000+8000, ice, ξc = 8Å, ucol = 70 m/s ( Eimp = 42 NEbreak )Blum and Wurm 2008; Heißelmann et al. (in prep.)
SiO2 grain：~1.52 μm; porosity 85 %SiO2 grain (Aerosol 200)： ~12 nm; porosity 97%
Collision velocity: 0.15 – 4.5 m/sGüttler et al. 2009 (submitted to A&A)

ucol Stiking
Bouncing~ 1 m/s

Stiking
and/or fragmentation

Bouncing problem
z Why bouncing in experiments？
z What’s the condition for bouncing？

Hypothesis： Number of contacts controls？
Aggregates in numerical simulations：
Number of particles in contact with a particle（Coordination number, C.N.）＝ ２～４, on average
More C.N. in experiments？
→ Energy dissipation is difficult
due to immobility of particles？

ObjectivezTo reveal the dependence on coordination numberfor aggregate bouncing
Collision simulation of aggregate collisions
parameter : Coordination Number (C.N.)
Idea for making required C.N.：
Extracting particles randomly
from close-packed structure (C.N.=12)
aggregates with C.N. = ~12 to ~3

Initial conditions and settings
9 (hexagonal) close-packed aggregates：
mean C.N. ～ １１
• Number of particles：４１９７ （3 types randomly produced）

9 particle-extracted aggregates：
extraction rate f = 0.05 - 0.75
f = 0.2
mean C.N. = 8.8

f = 0.5
mean C.N. = 5.5

C.N.～12 (1 – f )f = 0.75
mean C.N. = 2.8

9Ice (E = 7.0 GPa, ν = 0.25, γ = 100 mJ/m , R = 0.1μm) , critical rolling displace. ξcrit = 8Å
9SiO2 (E = 54 GPa, ν = 0.17, γ = 25 mJ/m , R = 0.1μm) , critical rolling displace. ξcrit = 8Å
9 ucol = 0.1 - 22 m/s (Ice), 0.01 - 2.2 m/s (SiO2)
22

Examples of simulation (Ice)
C.N.= 11

C.N.= 8.8

ucol = 0.096 m/s ( Eimp = 0.66 Ebreak )ucol = 0.096 m/s ( Eimp = 0.53 Ebreak )C.N.= 5.5

C.N.= 2.8ucol = 0.38 m/s ( Eimp = 5.3 Ebreak )ucol = 0.38 m/s ( Eimp = 2.7 Ebreak )Examples of simulation (Ice)
C.N.= 11

C.N.= 8.8

ucol = 0.096 m/s ( Eimp = 0.66 Ebreak )ucol = 0.096 m/s ( Eimp = 0.53 Ebreak )C.N.= 5.5

C.N.= 2.8

ucol = 0.38 m/s ( Eimp = 5.3 Ebreak )ucol = 0.38 m/s ( Eimp = 2.7 Ebreak )Examples of simulation (Ice)
C.N.= 11

C.N.= 8.8

ucol = 1.5 m/s ( Eimp = 170 Ebreak )ucol = 1.5 m/s ( Eimp = 135 Ebreak )C.N.= 5.5

C.N.= 2.8

ucol = 1.5 m/s ( Eimp = 85 Ebreak )ucol = 1.5 m/s ( Eimp = 43 Ebreak )Examples of simulation (Ice)
C.N.= 11

C.N.= 8.8

ucol = 1.5 m/s ( Eimp = 170 Ebreak )ucol = 1.5 m/s ( Eimp = 135 Ebreak )C.N.= 5.5

C.N.= 2.8

ucol = 1.5 m/s ( Eimp = 85 Ebreak )ucol = 1.5 m/s ( Eimp = 43 Ebreak )Examples of simulation (Ice)
C.N.= 11

C.N.= 8.8

ucol = 22 m/s ( Eimp = 4.1 N Ebreak )ucol = 22 m/s ( Eimp = 4.1 N Ebreak )C.N.= 5.5

C.N.= 2.8

ucol = 22 m/s ( Eimp = 4.1 N Ebreak )ucol = 22 m/s ( Eimp = 4.1 N Ebreak )Examples of simulation (Ice)
C.N.= 11

C.N.= 8.8

ucol = 22 m/s ( Eimp = 4.1 N Ebreak )ucol = 22 m/s ( Eimp = 4.1 N Ebreak )C.N.= 5.5

C.N.= 2.8

ucol = 22 m/s ( Eimp = 4.1 N Ebreak )ucol = 22 m/s ( Eimp = 4.1 N Ebreak )Mean Coordination Number

Result：Bouncing Condition (Ice)
120.1

Collision velocity [m/s]
110Bouncing

1086

Mean C.N. < ~ 6

4Sticking

20
1e-5

1e-4

1e-3

0.01

0.1

Eimpact / (N Ebreak)110

Mean Coordination Number

Result: Bouncing Condition (SiO2)
120.01

Collision velocity [m/s]
0.1

1Bouncing

1086

Mean C.N. < ~ 64Sticking

201e-5

1e-4

1e-3

0.01

0.1

Eimpact / (N Ebreak)110

Result: Bouncing Condition
Mean Coordination Number(Ice, SiO2)
1210

No difference
between Ice and SiO2

86

Scaled wellby using Ebreak

4201e-5

1e-4

1e-3

0.01

0.1

Eimpact / (N Ebreak)110

Why C.N. = 6 ?
A particle is stable enough with C.N. = 6 in 3D:

Mean Coordination Number

C.N.@BPCA collisions
410ucol [m/s] 100 Ice, 8Å, 8000+8000

3.6

3.2

2.8

2.4

2
0.1

1

10

100

Eimpact / (N Ebreak)1000

Why C.N. = 4 ?
A particle is stable enough with C.N. = 6 in 3D:

Stable with at least C.N. = 4 in 3D:

1D2D

3D

aggregates produced by collisions
BPCA, N=8000+8000, ice, ξc = 8Å, ucol = 57 m/s ( Eimp = 27 NEbreak )Initial condition(C.N. = 3.8）
15288+15288

Collisions of collision-produced
aggregates（C.N.=3.8）

ucol = 0.38 m/s ( Eimp = 1.2×10-3 NEbreak )ucol = 0.77 m/s ( Eimp = 5.1×10-3 NEbreak )ucol = 1.54 m/s ( Eimp = 2.0×10-2 NEbreak )ucol = 17.4 m/s ( Eimp = 2.6 NEbreak )Structure is also important?
C.N. = 6

C.N. = 6C.N. = 2.35

C.N. = 4

Shen, Draine, and Johnson (2008)

New Calculations at Braunschweig
Structure is also important?
C.N. = 6

C.N. = 4

C.N. = 2.35

C.N. = 6

No!
Bouncing
only for C.N.=6

SummaryWe examine the bouncing condition, focusing on C.N. of aggregates.

zAlways sticking if C.N. < 6.
zCollision velocity for transition from bouncing tosticking is consistent with experimental results.
zcollision-produced aggregates have C.N. < 4

It is feasible to form planetesimals through direct collisions of dust aggregates.

Future work
¾dependence on size (and size ratio) of aggregates and offset collisionありがとうございました。