dedus,oninmhezed1).
red
ago
on
he
red
out
tong
ndroonbeng
afodherosly
eotetedherend

ebmaralandogy,G.
ode
09 –any mechanism for their formation and try
to reconcile these observations with theshock wave theory.

The Shock Wave Model
A shock wave is a sharp discontinuity between hot, compressed, high-speed gas(moving faster than the local speed ofsound) and cooler, less dense, slower moving gas. Gas overrun by a shock wave isabruptly heated, compressed, and accelerated. We envision the shock as a thin flatsurface (a plane) moving through an initially cool, quiet [turbulent velocities of !50 ms–1 (8)] nebula of gas and dust. For simplicity, we consider a normal shock traveling ina direction perpendicular to its front surface. We assume a cold background nebulatemperature T0 of 300 K. The ambient pressure of the nebula p0 is 1.00 " 10–5 bars. We
assume that the gas is ideal, diatomic mo-state, analytical relations (10) govern thepost-shock density, pressure, velocity, andtemperature (%1, p1, v1, and T1) in the gas(Fig. 2). Temperature and density increase
moderately behind the shock wave, whereaspressure increases significantly. For example, in an M 5 shock, pressure increases by
a factor of 29, density by a factor of 5, andtemperature by a factor of 5.8.
Solid particles are also affected by theshock wave. When a shock wave overruns
them, particles suddenly find themselves ina blast of wind moving at several kilometers
per second. Friction or drag from collisionsof gas molecules heats the particles, as does
中本(東京工業大学)，土居 政雄 (筑波大学)
thermal radiation
from泰史hot neighboring
particles. Particles lose heat by radiation
第19回理論懇シンポジウム@ 立教大，25-27 Dec. 2006
and evaporation(7, 11). In addition to gas
drag heating, particles can be heated radiatively and conductively by the hot postshock gas [at 1740 K in the M # 5 example]
until cooling begins (7) or a post-shock

原始太陽系星雲内部におけるmmサイズの流体力学的研究
三浦 均 (京都大学)

コンドリュール (始源的隕石の断面図)

Fig. 1. A transmitted
light image of a thinsection of Semarkona(LL3.0; USNM 1805 – 4),
an unequilibrated ordinary chondrite. This meteorite has experienced
virtually no thermal metamorphism and thus contains chondrules thatprobably preserve a
record of the preaccretional environment within
the protoplanetary nebula. Note the diversityof the chondrules (theround objects) and theirvarious sizes, shapes,
and textures. The arrowmarks a chondrule with
an igneous rim.

CIENCE

原始太陽系の珪酸塩ダスト融解現象

protoplanetary disk

proto-sun

H2 ガス + ダスト

Connolly & Love (1998), Science 280, 62! VOL. 280 ! 3 APRIL 1998 ! www.sciencemag.org

mmダストの加熱・融解→表面張力で球状に→急冷して再固化→ コンドリュール

どんなメカニズムがダストを融解し得たのか？
(Sorby 1877, Nature 15, 495)

that the chemical composition of the Earth and other terrestrial planets are not cosmic (compared to either the solar
photosphere or to CI chondrites, which are all matrix withno CAIs or chondrules), not only in the paucity of theirvolatiles (including hydrogen and noble gases) but in thedeÐciency of their moderate volatiles (Anders & Owen1977).
The model developed by Shu et al. (1996) in the context ofthe steady theory of magnetohydrodynamic X-winds (seeNajita & Shu 1994 ; Ostriker & Shu 1995) can provide aplausible thermal environment for the generation of CAIs
as well as a natural mechanism for the aerodynamic sizesorting and remnant magnetism of chondrules. Unfor-and major eruptions on timescales of thousands of years(e.g., Reipurth, Raga, & Heathcote 1993 ; Reipurth et al.
1997). The generation of protosolar Ñares in a Ñuctuating
X-wind model provides a natural timescale of tens ofminutes to a few hours for the multiple Ñash heating ofchondrules (Shu et al. 1997). By melting or softening therocky mantles of solids, the Ñares may also enhance thesticking probability and enable the collisional growth ofcompact rockballs of millimeter to centimeter size (seebelow). As a bonus, the accompanying irradiation by solar
cosmic-ray particles yields a possible mechanism for understanding the presence of several short-lived radioactivities
inferred to have been present in CAIs when they solidiÐed

コンドリュール形成モデル
X-wind modelLightning model

Electronic
Potential

radiation from star

Discharge(Lightning)
Charged Particle

in Gas DiskFIG. 1.ÈSchematic drawing of the X-wind model for the formation of CAIs and chondrules. On either side of a dead zone (the middle third of themagnetic Ñux trapped by the X-region) the Ðeld lines bend sufficiently inward or outward to force electrically conducting gas in the X-region to be funneledtoward the star or to be expelled in an X-wind. The case shown assumes that an outÑow of hot plasma in a coronal wind from the star and disk has helped
magnetocentrifugal e†ects to open the Ðeld lines in the dead zone, but the dead zone Ðeld lines could also be closed, as are those below the helmet dome,
without much a†ecting the discussion of our model. (After Shu et al. 1997).

e.g., Shu et al. (2001), ApJ 548, 1029

e.g., Pilipp et al. (1992), ApJ 387, 364

Shock-wave heating model
強いガス動圧shock front

nebula gas

unmelted dustgas flowgas drag heating

融解ダストの変形→変形コンドリュール？

Hood & Horanyi (1991, 1993), Ruzmaikina& Ip (1994), Iida et al. (2001), Desch &Connolly (2002), Ciesla & Hood (2002),
HM et al. (2002), HM & TN (2005, 2006a)

変形コンドリュール
コンドリュール3次元形状
3軸楕円体で近似
半径はそれぞれ A, B, C (ABC)

sphereprolate

プロレートコンドリュール

C / B/ 中軸)
C / B (短軸10.9Group-A : 多様な形状
真球に近いGroup-B : プロレート変形度は大きい(Group-B)
Group-B
Group-A

0.80.70.7

Porphyritic
Barred olivine
Crypto crystalline
0.80.9B / A (中軸B / A/ 長軸)

oblateTsuchiyama, priv. comm.

1

Tsuchiyama et al. (2003), LPSC, abst#1271

再固化したときの形状を反映？

本研究の目的

Deformed Chondrules
コンドリュール形状の多様性
3D shapes of chondrules

ガス流中における融解ダストの変形液滴の回転
gas flowsphereprolateC / B/ Middle)
C / B (Minor1droplet
仮定：回転軸ガス流の向き0.9Group-B
Group-A

0.80.70.7

Porphyritic
Barred olivine
Crypto crystalline
0.80.9B / A (MiddleB / A / Major)

oblate1

Tsuchiyama
et al.
(2003), LPSC,abst#1271
Tsuchiyama
et al.
(2003),LPSC,
abst#1271

衝撃波加熱でコンドリュール形状を説明できるか？

手法
CIP法 (Yabe et al. 2001, J.Comp.Phys. 169, 556) による3次元数値流体シミュレーション(HM & TN 2006b, Icarus, in press, astro-ph/0611289)

Eq. of cont.

∂ρ+ ∇ · (ρu) = 0∂t∂u−∇p + µ∇2 u + Fs + Fg+ (u · ∇)u =Eq. of motion∂tρ
1+g + ∇|Ω × r|2 + 2u × Ω∂p22=c
Eq. of states∂ρ

初期条件 : ガス流中に置かれた真球
ガス動圧
初期の液滴半径表面張力
粘性係数
角速度

：pfm = 104 dyne cm-2
：r0 = 1 mm：γs = 400 dyne cm-1：µ = 103 g cm-1 s-1：ω = parametergas flowdroplet

計算結果
ω = 100 s-1

z / r0y / r0

回転軸

ガス流x / r0x / r0

断面 ( 回転軸)

断面 (∥ 回転軸)

・回転軸に対して垂直方向に縮む・回転軸方向に伸びる(体積保存)→ プロレート形状になる！

なぜプロレートになるのか？
再固化直前は粘性が高い
変形が回転に比べて十分遅い→軸対称的なガス流 (ガス動圧)
プロレートに変形

さらに高速回転だとオブレート？

プロレート

オブレート

角速度ω
Rcr
軸対称ガス動圧を仮定し解析的に液滴形状を導出した(回転がない場合：Sekiya et al. 2003, PThPh. 109, 717)

液滴形状の解析的表式"!
rs = r0 1 + We /48(Rcr − R)P2 (cos θ)We pfm r0 / γs : Weber 数
R ρ r02 ω2 / <pfm> :無次元化された遠心力

z-axis (rotation axis)

ern
θeθez
rs

遠心力

R=tθ

平均化されたガス動圧

dropletgas flow

R < Rcr : プロレート
R > Rcr : オブレート

Figure 2: Settings for deriving the deformation of the droplet shape. The droplet
rotates around the z-axis and the gas flow is an axis-symmetry because of thedroplet rotation (see §1). The droplet radius rs is a function of the polar angle
θ. The unit normal of the surface is n and the unit tangential vector is tθ .

Rcr = 19/5

コンドリュール形状再現の条件
Rcr オブレート

50.6＝ 中軸 / 長軸100.8ギャップ？
1h2

O =

h1

O =

Weber number We

高速回転による
大変形オブレート形状は回転不安定により不可再固化時のガス動圧が→ 異なる2つの値を持つ？
0.9)

We ≡ pfm r0 /γs

4ガス動圧が強ければ0.7
大変形プロレート形状は
3
説明可group-B

65
ar 19
sekh
ndray
(Cha instabilit
shape otation)r(pure

ガス動圧が大きい (表面張力に対して)

プロレート

group-A√Oh ≡ µ/ ρr0 γs: Ohnesorge 数

00.0010.01

0.1

110squarednormalized
angular velocity
normalized
centrifugal
force RRR ≡ ρr02 ω 2 /"pfm #Figure 3: Axial ratio B/A of rotating high-viscous droplet exposed to highvelocity rarefied gas 遠心力が大きい
flow is plotted as (ガス動圧に対して)
a function of the squared normalized
angular velocity R ≡ ρr02 ω 2 /pfm and the Weber number We ≡ pfm r0 /γs . The

議論：異なる2つのガス動圧
less-dusty(a) low dust-to-gas mass ratio

dust-rich(b) high dust-to-gas mass ratio

周囲のダストの熱放射

ダスト温度

融点
再固化時に大きな相対速度
ダスト速度

再固化時には相対速度がほぼゼロ

ガス速度

大きなガス動圧

ガス動圧 ~ 0

コンドリュール形成領域の光学的厚さ τ<1 or >1→異なる2つのガス動圧が選択的に多くなる？
衝撃波面からの距離 [cm]Figure 12: H. Miura & T. Nakamoto

HM & TN (2006a), ApJ 651, 1272

まとめ(a) chondrule(b) simulation(c) reason for prolate

gas flow

time-averaged
gas flow
2: Three-dimensional external shapes of bodies: (a) prolate chondrule in
高速ガス流中で融解したmmサイズの珪酸塩ダストの変形• Figure
Allende Meteorite (CV3), (b) prolate droplet by our numerical simulation, (c)picture to explain the reason for prolate shape. (回転軸
適切な回転速度のもとプロレートになるガス流)• schematic• 衝撃波加熱モデルを強く示唆

mmサイズの流体力学的研究→原始太陽系星雲内部の物理的環境の推測