GAS-PHASE CONDENSATIONOF SUBMICRON-SIZED SILICATE CRYSTALSBEHIND PLANETESIMAL BOW SHOCKS
Hitoshi Miura1,2, Kyoko K. Tanaka3, Tetsuo Yamamoto3, Taishi Nakamoto4, Jun Nozawa1, Katsuo
Tsukamoto1, Junya Yamada1
1Tohoku Univ., Japan, 2E-mail: miurah@ganko.tohoku.ac.jp，3Hokkaido Univ., Japan, 4Tokyo Institute of Technology, Japan.

SUMMARY: We numerically simulated the dust heating and evaporation behind a planetesimal bow shock based on the one-dimensional planeparallel shock-wave heating model. The dust vapor rapidly cools due to the adiabatic expansion of the shocked gas. We obtained an analytic
formula of the cooling timescale of the vapor. The vapor becomes highly supersaturated and ﬁne silicate crystals with various morphologies
could condense. We estimated the typical size of condensates as 1 µm or less by using the classical nucleation theory. These estimated propertiesof condensates match well with ﬁne silicate crystals observed in matrix of primitive meteorites. This suggests that they have formed in therapidly cooling silicate vapor behind the planetesimal bow shock in early solar nebula.

1

Condensation in Highly Supersaturated Silicate Vapor

There are several lines of ev(b)(a)(c)
idences in interplanetary dust
particles (IDPs) and chondritic
meteorites that the dust condensed in the conditions far
from equilibrium in the earlysolar nebula (see Fig. 1). It
was suggested that these ﬁnesilicate crystals of various morFigure 1: (a) Enstatite whisker in IDPs [1]. (b)phologies form by a homogeUltra-ﬁne particles in matrix of Allende meteneous nucleation and successive
orite [2]. (c) Fine olivine crystals in matrix ofcrystal growth in a highly superAllende meteorite [3].
saturated silicate vapor [4, 5].
The morphologies depend on the condensation temperature Tc and supersaturation ratio σ. The numerical simulations of shock-wave heating showed that theplanetesimal bow shock could generated highly supersaturated silicate vapor [6].
In this study, we consider the typical size and morphologies of ﬁne silicate crystals
condensed behind the planetesimal bow shock. They can be estimated from thecooling timescale and vapor density based on the classical nucleation theory [7].

24

The typical size of condensates r∞ can be estimated from the cooling timescale and the vapor
density as [7] (see Fig. 4)
r∞ ∼ 1 (Λ/105) µm,dvr
1 ∂p=−,dtρ ∂rwhere l is the mean free path of the vapor
molecules. The calculated size of condensates foreach case is listed in a table below. It is found thatthe typical size of condensates is ∼ 1 µm or less.

case(spatial scale)

L2n14v10c1
L2n15v08c1
L2n15v08c1
L2n14v10c1
L3n14v10c1
L3n14v10c2
L3n14v10c1
L3n14v10c1
L3n14v10c2

expantion velocity:(1)planetesimal

radius:gas

We adopt the one-zone approximation (vr ∼ dR/dt, ∂p/∂r ∼ −p/R),
bow shockequationofstate(p = Kργ ),and mass conservation (σ = πR2ρ =const.).

before expansion
dust
evaporation

vapor
cools
pressure, density, temperature

Relaxation Zone (RZ)
(Miura et al., in prep.)↓(5)

where Λ ≡ τsat/τcoll and τcoll = (4πr02αn0vth)−1 isthe collision interval of vapor molecules. r0 is themolecule radius, α is the sticking probability, n0
is the number density of vapor molecules, and vth
is the thermal velocity. Substituting Eq. (4) into
τsat, we obtain()( )()−1R0αlr∞ ∼ 1µm,
(6)100 km0.1
1 cm

Cooling Timescale by Adiabatic Expansion

Equation of motion for expansion:

Typical Size of Condensates

Hydrodynamic Expansion (HE)(this study)

Figure 4: Typical size ofcondensate [7]．

dust radius evap. fraction vapor density mean free path size[µm]
[g cm−3]
[cm]
[nm]
0.1
101.0
1.00.10.11.010
1.00.15
3.1 × 10−2
0.93
1.1 × 10−4
0.27
0.56
0.19
2.8 × 10−4
3.8 × 10−3

6.1 × 10−11
9.5 × 10−11
1.7 × 10−9
9.0 × 10−14
7.1 × 10−11
1.3 × 10−11
1.5 × 10−10
2.5 × 10−13
3.2 × 10−13

37
23
1.3
2.5 × 10431170
15
8.9 × 103
6.9 × 103

2743
770
<1?
32
5.9
67
<1?
<1?

Normalized equation of motion:

5d2R̃−2γ+1,=R̃
dt̃2(2)RZ

where R̃ = R/R0 and t̃ = t/ts0 (R0is the initial radius and ts0 ≡ R0/cs0
with initial sound speed cs0). γ is theratio of speciﬁc heat.

HEFrom the solution of Eq. (2) (seeFig. 2), we obtain an analytic expression of cooling rate:( )dT= −aγ T0/ts0,
(3)
dt HE

Figure 2: Schematic of planetary bow
shock (top). Solution of Eq. (2) (bottom).

where aγ ∼ 0.3 − 0.4.
The timescale in which the supersaturation ratio changes:τsat,HE ∼ 10−2(R02ρ0/p0)1/2(4)

We consider the condensation of forsterite (Mg2SiO4) in H2 atmosphere.

Vapor Density3000temperature [K]Fig.
3 shows a result ofnumerical simulations for dust
evaporation behind the shockfront.
The solid dust particles with radius of 0.1 µm
are abruptly heated by the gas
frictional heating just behindthe shock front, then evaporate
completely (panel a). As a result, silicate vapor forms (panelb). In this case, the vapor density is 6 × 10−11 g cm−3.

Fig.
5 shows the supercooling ∆T = Te − Tc, where Te
is the equilibrium condensation
temperature and Tc is the actual condensation temperature[7]. The red, blue, and green
regions indicate the experimental conditions that bulky-,platy-, columnar-, and needletype crystals condensate, respectively [4]. It is found thatplaty, columnar-, and needletypes form in rapidly cooling silicate vapor (small Λ). Since ourmodel suggests that Λ < 105,the bulky- and platy-types will
be obtained in the case of typical silicate dusts (µ = 20 [7]).
The morphological property isvery similar to that observed inprimitive meteorites [3].

columner and needle
platybulky

Figure 5: Supercooling at condensation inrapidly cooling vapor [7] and experimental condition in which each type of crystal condenses[4].

References

(a)
2000

[1] Bradley, J.P. et al., (1983). Nature 301, 473-477.

radiation

1000
dust

gas

[2] Toriumi, M., (1989). Earth Planet. Sci. Lett. 92, 265-273.

evaporation

0density [g cm-3]3Morphologies of Condensates

10-9[3] Nozawa, J. et al., Icarus submitted.

(b)

dust

[4] Kobatake, H. et al., (2008). Icarus 198, 208-217.

10-10[5] Yamada et al., in prep.

silicate vapor
10-11-100-50

050
distance from shock front [km]100

[6] Miura, H. et al., (2008), Poster Presentation on Silicate Dust in Protostars: Astrophysical, Experimental, and Meteorite Links, University of Tokyo, Japan, July 25–26.
[7] Yamamoto, T. and Hasegawa, H., (1977). Prog. Theo. Phys. 58, 816-828.

Figure 3: Numerical result of dust evaporation
behind shock front (case L2n14v10c1).

The 1st International School of Planetary Sciences “Dust in Space”
P-19, January 5-9, Kobe, Japan