Electric charging of dust aggregatesand its effect on dust coagulationin protoplanetary disks
Ref. : S. Okuzumi, arXiv:0901.2886

Satoshi Okuzumi(GSHES, Kyoto Univ.)1

Mutual sticking of dust aggregates:
the first step toward planetesimal formation
Growth of small (<<km) dust aggregates
Gravitational accretion (too weak) Sticking by van der Waals force

Experiment (e.g. Wurm & Blum 1998) ：An ensemble of dust monomers
undergoes ballistic cluster-cluster
aggregation (BCCA)’.

StickingBCCA(Ballistic Cluster-ClusterAggregation)

Fractal dim.:Internal Density:（N: # of constituent monomers）
2

Disk IonizationDust ChargingCan Dust Grow?
cosmic raysGas disks should be weakly ionized by
Galactic cosmic rays or stellar X-rays.
Dust charges up negatively by absorbing
free electrons.

 Long-range repulsion force
emerges between aggregates―

Sticking―?

Question:
Can dust aggregates inprotoplanetary disks overcome
this electrostatic repulsion barrier?
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Aim of this study
We investigate how the electric charging of dust aggregates
can affect their collisional growth in protoplanetary disks.

Step 1: Formulating how to solve the dust charge state ofdust aggregates in protoplanetary disks.
Step 2: Examining whether BCCA growth is inhibited by theelectrostatic repulsion or not.

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Equilibrium charge state of dust in weakly ionized gas
gas

We need to solve dust charge stateand gas ionization state self-consistently.

ionization

Previous studies (e.g. Sano+ 2000; Ilgner & Nelson 2006)- Numerically solve using complicated reaction schemes- Very inefficient if we consider dust growing into large aggregatesion(i)

ionization
gas-phaserecombination(not important)absorption

absorption

This study: solves as analytically as possible

electron(e)dust (d)ion：ionizationelectron：absorption by dust

recombination ion-neutral reaction: rate coefficients

dust：

neutrality：： ionization rate
～10-17 - 10-22 [/s]5

Semianalytical solution of dust charge state
We have found a single equation determining the self-consistent solution.
(Okuzumi, arXiv:0901.2886)
Comparison with full-numerical solutions

The aggrement between the semialalytic and full-numerical calculations is very good!!
6Can dust aggregates overcome electrostatic barrier?
dust-dust collision cross section

Two aggregates can collide
only if

We examine whether dust aggregates can satisfy this criterion in protoplanetary disks.
Disk model: Minimum mass solar nebula
Ionization source: Galactic cosmic rays?

Dust monomer size: 0.1mGrowth mode: Cluster-cluster aggregation (D=2)
Source of relative motion:- Brownian motion- Sedimentation toward midplane- Turbulence
7Kinetic energy vs electric repulsion energy
Example: r = 5 AU; z = H; no turbulence(monomer size)

N: number of monomers in an aggregate
a: size(radius) of the aggregate

Ekin(thick solid curve):
kinetic energy of colliding aggregates
Eel(thin solid curve):
electric energy between the aggregatesjust before collision

At size a » 10m, the electric repulsion energy exceeds the kineticenergy  BCCA growth freezes out at this stage!!
8Ekin vs Eel at different disk positions (no turbulence)
Different altitudes (distances from the midplane)snow line

Different distances from the central star

■ For z. H(scale height), the growth``barrier’’ appears at r = 1AU – 100AU !!
■ The barrier is stronger inside the snow line
(less solid material  more free electrons
 more charging-up of an aggregate).

■ The growth barrier disappears
only at high ( z>2H ) altitudes
because of fast sedimentation
velocity.
9Effect of turbulenceGas turbulence induces relative motion between aggregates.
 Does turbulence help the aggregates to overcome the electric barrier?

The left figure shows that the electricbarrier disappears if the turbulence is
as strong as  > 10-2
MRI-driven turbulence:  » 10-2
(e.g. Sano+97)

Dust aggregates canovercome the electric barrier
in MRI-active regions.
10Strong turbulence seems to be preferable to dust growth,
but…

This causes another growth barrier--- collisional fragmentation of aggregates!
If  » 10-2 , maximum collisional velocity is » 100m/s .
On the other hand, the collisional fragmentation is catastrophic
for v > 30m/s (Wada+08).
 It is very unlikely that aggregates in such strong turbulence
can avoid collisional destruction!
Growth in weakly turbulent regions  electrostatic repulsion barrier
Growth in strongly turbulent regions  fragmentation barrier
The electric charging of aggregates, together with collisional fragmentation, may
impose a very strict limitation on dust growth in protoplanetary disks.
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Bimodal growth hypothesis
We have seen that it is likely that BCCA growth should freeze out
in its very early stage.
 What happens after the freeze-out ?
A simple estimation suggests that an irregularlycompact (i.e. more compact than standard BCCAclusters) aggregate can collide with frozen-out
aggregates.
We expect that the freeze-out of BCCA isfollowed by a bimodal growth in which only asmall population of irregularly compact
agrgegates continue to grow by sweeing up thelarge population of frozen-out BCCA clusters(see the right figure).
disk midplanefrozen-out BCCA clusters
oligarchic boulder

12Summary
We have investigated the electric charge state of dust aggregates andexamined the effect of the charging on dust coagulation in
protoplanetary disks.
* We have discovered a semianalytic formula for dust charge state in weakly
ionized gas (e.g. protoplanetary disks). This formula can be used for an arbitrary
ensemble of dust aggregates, and will be easily implemented in coagulation
equation solvers.
* Using the formula, we examined whether dust aggregates in protoplanetarydisks can overcome the electrostatic barrier. We have found that BCCA growth isstrongly inhibited by the electric repulsion and eventually freezes out.
•The combination of electric charging and collisional fragmentation may strictly
limit dust coagulation in protoplanetary disks.
* The freeze-out of BCCA growth may be followed by an bimodal growth in which
only a small fraction of aggregates can continue to grow.
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