arXiv:1209.110

Key words: accretion, accretionent to a maximum gravitational stress that a disc can withstand without
0.02, which is much smaller than the values typically- gravitation - instabilities - hydr
it ⇡ 0.013
t is therefore easier for self-gravitating discs to fragment than has been
past studies.
SFN 速報 10月号の終わり9本+11月号1本
担当：片岡, accretion discs - protoplanetary discs - planets and satellites: formationties - hydrodynamics
1 INTRODUCTION

On the convergence of the critical cooling timescale for the fragmentation of self- gravitating discs

Historically,
Farzana Meru and Matthew
R. Bate there have been two key quantities that have been used
to determine whether a self-gravitating disc is likely to fragment.
Gammie (2001)
in addition
to the stability
crite-1964),
Theshowed
first is thatthe stability
parameter(Toomre

used
ment.

概要：重力不安定円盤のシミュレーション。空間分解能をあげていった時の収束性を調べた。
β = 10β = 12

rion above, the disc must cool at a fast enough rate. Using shearing
sheet simulations, he showed that if the cooling timescalecs epcan beQ=,parametrized as⇡⌃G※重力不安定による円盤分裂の判定条件1:Toomre’s Q(1)c freo thes thenitese less4

Q<1で円盤が分裂。

log column density [g/cm2]

http://arxiv.org/abs/1209.1107
6
Farzana Meru and Matthew R. Bate(1)where cs is the sound speed in the disc, ep is the epicyclic fre= tcool ⌦,(2)
discs is approximately equal to the※判定条件2 : Coolingquency,
timescale which for Keplerianβ<βcritで円盤は分裂。充分早く冷えないといけない。
angular frequency, ⌦, ⌃ is the surface mass density and G is thewhere
2gravitational constant. Toomre (1964) showed that for an infinites今回の話題：critical cooling timescale✓の 数値計算への依存性。
◆ 1
imally thin discto fragment,
the stability parameter must be lessducool
数値計算から、β=6-7(γ=5/3の時)と言われてきた。しかし、収束していなかった。
t
=
u
,
(3)
thancoola critical value,
dt Qcrit ⇡ 1.
使ったのはSPHコードとグリッドコード(FARGO)。

u is the specific internal energy and du/dt is the total spe0
cific cooling rate,? thenforfragmentation
werequire.
.
crit
farzana.meru@phys.ethz.ch-> これが、今までの計算でうまく行かなかった原因。
According to Gammie (2001), crit ⇡ 3 for a ratio of specificFigure 2. Surface
rendered
image of&two Armitage
identical simulations
carried outcarriedusing = 10
(leftthreepanel) and = 12 (right panel), using 16m SPH
heats,=mass
2.density
Rice,(2005)
out
βが終息するのは>20、もしかしたら、30。それまで考えられてきたものの3-5倍大きい。
c Lodato0000
particles. Fragmentation occurs for= 10 butRAS
not for = 12. These Convergence
simulations are performed
with
(↵
, SPH
) = (0.1, 0.2).
SPH
of fragmenting
self-gravitating
discs
7
cool
結果、critical cooling timescaleは数値粘性に強く寄ってしまうことがわかった。

左：SPH, 右：FARGO, □：分裂しない, ▲：分裂した
Simulation nameNo ofradial cells

No ofazimuthal cells

Fragmented?

55.1

RESULTSThe convergence rate ofcrit with SPH

197k cells-beta0.5
256
768
0.5
Yes
Table 1 summarises the results of the SPH simulations, using ↵SPH ,197k cells-beta1
256
768
1
Yes
SPH ) = (0.1, 0.2), carried out by Meru & Bate (2011a) and those
197k cells-beta2
256
768
2
No
performed for this paper. Meru & Bate (2011a) found borderline
197k cells-beta3
256
768
3
No
simulations which they defined to be discs which showed signs
197k cells-beta4
256
768
4
No
of fragmentation but the fragments sheared apart rapidly (within
786k cells-beta3
512
1536
3
Yes
786k cells-beta3.5
512
1536
3.5
Yes
1 ORP) and no further signs of fragmentation were seen. We find786k cells-beta4.5
512
1536
4.5
Yes
that borderline simulations can in fact range a span of values.
786k cells-beta5
512
1536
5
Yes
However, since ultimately they are discs that do not end up frag786k cells-beta5.5
512
1536
5.5
Yes
menting, we now simplify this terminology and refer to them as
786k cells-beta6
512
1536
6
No
non-fragmenting simulations. Figure 1 shows a summary of the
786k cells-beta10
512
1536
10
No
SPH results. This figure is the same as Figure 3 of Meru & Bate
3.1m cells-beta10
1024
3072
10
Yes
(2011a) but with the the addition of the new SPH results presented
3.1m cells-beta12
1024
3072
12
Yes
in this paper. Meru & Bate (2011a) found no evidence for con3.1m cells-beta13
1024
3072
13
No
vergence, but the addition of the new high resolution calculations
13m cells-beta11
2048
6144
11
Yes
now provides evidence for a very slow convergence of crit with
13m cells-beta14
2048
6144
14
Yes
13m cells-beta15
2048
6144
15
Yes
increasing resolution. Figure 2 shows two of the highest resolution
13m cells-beta16
2048
6144
16
Yes
SPH simulations (16 million particles) carried out using = 1013m cells-beta18
2048
6144
18
No
and = 12. It can clearly be seen that at this resolution, fragmen50m cells-beta18
4096
12288
18
Yes
tation occurs for = 10 but not for = 12. To estimate the rate
50m cells-beta20
4096
12288
20
Yes
Figure3. Graph of weagainst
resolutionof thenon-fragmenting (openof convergence
fit a formulaof theform
Figure1.
Graphofagainstresolutionofthenon-fragmenting
(open
50m
cells-beta22 column
4096 density12288
22
Yes(1,1) emission in star-forming regions
Estimatingfromammoniasquares) and fragmenting (solid triangles) FARGO simulations carried out
squares)andfragmenting(solidtriangles)
SPH
simulations.
This
figure50m cells-beta24
4096
12288
24
No
contains the results presented by Meru & Bate (2011a, their Figure 3) as using q = 1.41. The solid line, obtained by fitting equation 23, shows acrit
dividing line between the fragmenting= and non-fragmenting cases and the(23)well asthe new simulations
highlighted
in Table
1. The solid line,
obtained
L.K.
Morgan1,
T.J.T.
Moore1,
J. Allsopp1
and
D.J. Eden1
1
+
l
grey
regioniswherefragmentation
cantakeplace.
The graph shows clear
Table
Tableequation
showing23,
theshows
simulations
carriedusing theFARGO
and the andby2.fitting
a dividing
lineout
betweenfragmentingof convergence of results with increased resolution. The converkey fragmenting
results.
Theandsimulations
are performed
using the artificial
non-fragmenting
cases
the grey regionis where fragmentation
can take evidence
where l is the linear spatial resolution, is a constant and is the
http://arxiv.org/abs/1204.6041(which1
viscosity= 1.41.
place.parameter,
The graphq shows
clear evidence of convergence of results with in- gence rate is second order with spatial resolution. The dotted line
3
convergence rate. For SPH, we simply take l / Npart. We fit this21.
creased resolution. These simulations are carried out with (↵,) coincides well with the solid line) is obtained by fitting equation
SPH

SPH

= (0.1, 0.2). The convergence rate is first order with spatial resolution. The
derstanding
the(whichresultspresented
Section
5.3.3(whichonly havedotted line
coincides
wellinwith
the solidline)
is obtainedby fitting
dataequation
points at15.the lowest three resolutions) we fit equation 23 to thedata presented in Figure 1 but exclude the highest resolution simulations. We find crit = 17.4 and = 1.03, so excluding the lastpoint does not alter the fit significantly due to the slow convergence

formula to the values of in Figure 1 that lie half way between
the lowest non-fragmenting value1 of and the highest fragment2 resolution, i.e. the fragmentationvalue
of simply
for each, where Ncells is the number
For ing
FARGO, wetakenumericall / Ncells
boundary.
We finda goodresolution
fit is obtainedwith crit= 15.6±1.0
of grid
cells. Notethat thatthe linear
is inversely
proportional
andsquare= root1.08of± the
0.05.
The valueof becauseshows thethatcalculation
the rate ofisconto thenumberof cells
is first
spatial toresolution.
For the benefit
of untwo vergencedimensional.
Weorder
fit thisinformula
the fragmentation
boundary

etic temperature is less than typical observational errors over thege of temperatures found in star-forming regions.

ln−0.282ln
τm(1,1)(?), where T∗Am represents
概要：アンモニア23GHz線を使った新しい質量推定方法の提案。
perature of the main line o
METHOD
optical depth of the main li
普通(J,K)=(1,1)と(2,2)の組み合わせを使って面密度を求めるが、(1,1)のみを使って質量を推定可
It can be seen that thecalculate 能。この方法は(2,2)が短時間の探査では受からないような原始星エンベロープの外側の方で有the column density of ammonia molecules in the (1,1)
temperature depends upon
効。
nsition following
equation A4 of ?,sured at the peaks of (1,1)
hν0!
the optical depth of the (18πν20 1 + e− kB Tex
N(1, 1) = 2
τ(ν)dν,(1)
range of T k for which we mhνcA
− k T0 Mapping Ammonia in Star-Forming Regions
5
ex
B
1−e
forming regions, we have e
and W3 presented in ? in awhere ν0 , T ex and τ are the line rest frequency, measured

Why circumstellar disks are so faint in scattered light: The case of HD 100546
Gijs D. Mulders1,2, Michiel Min1, Carsten Dominik1,3, John H. Debes4 and Glenn Schneider5
http://arxiv.org/abs/1210.4132
目的：円盤の散乱光を利用してダストの性質(サイズ)を制限する。
従来観測されている円盤の特徴：
1. 観測されている円盤は、等方~ちょっと前方散乱くらいだと思われている。
2. ディスクの明るさ(中心星の光に対するalbedo)は数%くらい(Fukagawa+ 2010)だが、dust albedoは0.5くらいのはずである。
3. 円盤のカラーはgrey~赤。
結果：ミクロンサイズのダストによる前方散乱は実効的アルベドを下げる。
応用：HD100546→ ダストサイズは2.5μm以上。intermediate size : too bright, small dust : disk color isblue

of different sizes. The effective albedo (solid line) is defined as the fraction of lights the real albedo, see text (dotted line). The green area denotes the range of observed
ges. The small, medium and large panels correspond to a particle size of 0.08 µm,

ss sections comethe geometricaltion comes fromrticle and is also
t is than directly
particles is,

0.5.

Gijs D. Mulders et al.: Scattering paper(1)tered lightangle-integrated
ing becomes ineigh scattering –ved wavelengthose to isotropich the scatterings the forward di-ction by a partinto the disk, andsee Fig. 1, largethat scatter prescattering crosscattered into ourpected from theefore we define
nt the part of thetween angles θ1

θdθ

.

(2)

Fig. 1. Visualization of anisotropic scattering properties of different dust species. Displayed are: a small particle in the RayleighFig. 3. Phase function of a large dust grain (2.5 µm, red line),limitan(2πa < λ) in blue, an intermediate sized particle (2πa ∼ λ) in gray and a large particle (2πa > λ) in red. The angle between
disk surface and incident stellar light is 3 degrees, equal to the flaring angle minus aspect ratio of the surface at 200 AU. Theintermediate size dust grain (0.25 µm, grey line) and a small thedustphase functions at 0.6 µm are plotted in polar coordinates, and normalized such that surfaces are equal (square root of intensity).
grain (0.08 µm, blue line) at 0.6 µm. The green area marksThethearrows indicate the direction and magnitude of light scattered towards the observer.
range of observed angles for HD 100546, between 34◦ and 126◦ .
θ = 0o refers to forward scattering and θ = 180o to backward
rived from observations (Kalas et al. 2005; Krist et al. 2010; the forward scattering peak, the disk image does not appear to
Outflow
Source
ALMA
Imaginglogue
Maser
scattering. Structure and Velocity Field of Orion
haveSiOa strong Isotopobrightness asymmetry,
and caneven appear backGolimowski
et al. 2011), I:
while
an albedo of 0.5
is predicted ofand Thermal Emission

on basis of the grain radius of ∼1 µm derived from asymmetries in the disk images.

For large particles this effective albedo can be smaller than 3.0.5
Disk color, caused by the wavelength dependence of thealbedo. Dust grains in the interstellar medium have a grey
when the phase function is sufficiently peaked towards the forscattering
at optical to near-infrared
FlorianNiederhofer,
Elizabeth Humphreys
andcolor
CiriacoGoddi wavelengths (e.g.
ward scattering
direction.
Whitney 1995), whereas more evolved objects such as debris disks (e.g. Golimowski et al. 2006; Debes et al. 2008),
comets (Jewitt & Meech 1986) and Kuiper Belt objects(e.g.
3 Luu & Jewitt 1996) can have redder colors, indicating that larger than ISM grains are present (e.g. Wolf et al.
2012). Most protoplanetary disks have grey colors (e.g.
Fukagawa et al. 2010), though some disks exhibit redder colors: HD 141569 (Clampin et al. 2003), GG Tau (Krist et al.
2005) and HD 100546 (Ardila et al. 2007).

http://arxiv.org/abs/1210.2526

ward scattering (Min et al. 2010). We will describe this effect inmore detail in section 2.
We have applied this strong forward-scattering dust modelto the well-studied protoplanetary disk of HD 100546, forwhich scattered light images are available from 0.4 to 1.6 µm
Augereau et al. (2001); Ardila et al. (2007), and we present a
new image at 2.22 µm in section 3.1. After constructing a geometric model of the disk in section 3.3, we derived the grain
size from the observations in sections 3.4 and 3.5. We will also
discuss how the derived grain size compares to those of othersize indicators in the discussion.

概要：ALMA SVデータでOrion BN/KLでSiOを検出。outflowをトレース。

2. Scattering by protoplanetary dust

Orion BN/KN領域：d=418pc, 大質量星形成領域。
To extract the grain size from scattered light images, these In this section we will briefly discuss the basis of the scatterthree aspects (moderate brightness asymmetries, low albedos,

ing properties of protoplanetary dust (Mie 1908; Van der Hulst

To solve this problem, we have studied the effects of

The fraction of light that is scattered by a dust grain in all di-disk that is not observed edge-on (Fig. 1). The resulting few percent are scattered towards the observer, resulting in a low ’effective’ albedo (Dullemond & Natta 2003). Because the observer of
an inclined disk sees only a part of the phase function outside ofparticles much larger than the wavelength of incident radiation,
the total extinction cross section of the particle is comprised ofthree components: absorption (Cabs ), reflection/refraction (Cref ),and diffraction (Cdiff ).

1957; Bohren & Huffman1983) v=0,
and its influenceon the obfive rotational transitions (J=5-4 and J=6-5)
oftothethreemonoxideisotopologues
28SiO
1, 2 andneutralred colors)
havesilicon
to be modelledsimultaneously. Thisis challenging, because small dust grains have low albedos but served brightness and color of scattered light images.
29SiO v=0 and 28Si18O v=0 in the frequency
range
from
214
to
246
GHz
very blue colors. Large grains have neutral to red colors but alsohigh albedos. We call this “the color and brightness problem of 2.1. Single scattering albedo→これらのSiOはoutflowをトレースしていることを確認。(18km/s, 5000AU)
scattered light images”.
anisotropic scattering on the observed brightness and colors. rections is given by the single scattering albedo, ω. For particles
更に、100AU以内のoutflowの根本の観測をしていると思われる。
Particles that are large enough become extremely forward scat- much smaller than the wavelength the albedo is very low sincetering. The bulk etof thescatteredlight is concentrated
in the forlight is absorbedby the ofparticle.
When thesize of the parF. Niederhoferal.:Outflow
StructureandmostVelocity
Field
Orion
SourceI
ward peak - which is outside the range of observed angles for a ticle increases, the single scattering albedo also increases. For

2

Fig. 7. Fitted positions of the 28 SiO v=1 emission. The crosses
are color coded by velocity. We see that there is a clear velocity gradient along the northwest-southeast direction, with blueshifted emission in the eastern part and red-shifted emission in
the western part. This is in good agreement with the result obtained by Matthews et al. (2010) from VLBA data for the v=1
J=1-0 transition. The size of the image is about 160 AU x 160
AU.

Fig. 9. Intensity-weighted velocity (moment
J=5-4 28 SiO line emission with overlaid con
J=2-1 28 SiO total intensity (Plambeck et a
els with fluxes >1 Jy beam 1 or 4 times thchannel with the brightest emission, were u
lipses indicate the positions (Shuping et al.
mate sizes (estimated from Shuping et al. 2
sources IRc4, IRc7, IRc11 and IRc12. Sour

tflow Structure and Velocity Field of Orion Source I

The crosses
clear veloc- Theof thermodynamics
on gravitational
filament
Fig.impact
9. Intensity-weighted
velocity(moment 1) collapse:
map of thev=0 formation and magnetic fieldwith blue- amplification
28
J=5-4 SiO line emission with overlaid contours from the v=0
emission in J=2-1 28 SiO total intensity (Plambeck et al. 2009). Only pixPeters1, Dominik R. G.
Schleicher2, Ralf S. Klessen3, Robi Banerjee4, Christoph Federrath5,
e result ob- Thomas
els with
fluxes >1
beam 1 Sur7
or 4 times the rms noise of the
J. Smith6
andJySharanya
for the v=1 Rowan
channel with the brightest emission, were used. The white el0 AU x 160 lipses indicate the positions (Shuping et al. 2004) and approxiポリトロープ指数を変えてコアの重力収縮を計算。磁場が増幅されるか調べた。
mate sizes (estimated from Shuping et al. 2004) of the infrared
P sources= kρΓ, IRc4, IRc7, IRc11 and IRc12. Source I is marked with
Γ>1 → virialized core, turbulent, amplified magnetic fielda white cross. The newly discovered infrared source SOF1 (deΓ<1 → 早い降着、シートやフィラメントを作る。磁場はcoherentだがexp増幅。
Buizer et al. 2012) is indicated as a circle in the upper left corner. The two white crosses in the blue arc labeled ‘Goddi’ and‘Zapata’ are the points of interaction between Source I and BN
Aremolecular
high-mass
stars driven
by ionization
feedback?
as derived
by outflows
Goddi etaroundal. (2011a)
and Zapata
et al. (2009),
respectively.
Thomas Peters1, Pamela D. Klaassen2, Mordecai-Mark Mac Low3, Ralf S. Klessen4 and Robi
Banerjee5
northwest-southeast outflow that originated from a close enhttp://arxiv.org/abs/1209.5858
counter of Source I and the BN object approximately 500
years ago (Goddi et al. 2011a; Bally et al. 2011).
Episodic
radiative
their roleiii) The accretion,center of protostellar
the “blue arc”
to the feedback,north-westandof Source
I in low-mass star for- mation
falls in between two independent measurements of the cenDimitris
Stamatellos1,
Whitworth1
andIDavid
A. BN
Hubber2
ter ofdynamical AnthonyinteractionP. between
Sourceand theobject (Goddi et al. 2011a; Zapata et al. 2009; Figure 9).
http://adsabs.harvard.edu/abs/2012arXiv1209.0765S
We speculate that this blue-shifted emission, similarly to the
red-shifted emission from the “red arm”, could arise from
概要：episodic accretionによって円盤の分裂が決まる。
remnant material that was stripped away from the interact星のburstは数千年に一度数百年続くものと思われている。
ing objects with moderately velocity.

=5-4 28 SiO
iO total in- Episodic accretion -> episodic radiative heat up -> disk becomes stable
CARMA. (でも、バーストとバーストの間で十分冷えるから円盤は分裂する。)
4.1.2. The v=0 29 SiO Emission.6 and 3.7 計算：SPH, with radiation + episodic accretion
Figures 10 and 11 show the ALMA moment 0 and moment 1of Source I. 結果：円盤分裂条件
29
with the contours
white line. maps of the SiO J=5-4 transition, overlaid
28
of
the
total
intensity
of
the
CARMA
SiO
v=0
1. 数千年よりアウトバーストの間隔が長い。 J=2-1 emission(Plambeck et al. 2009). The structure of 29 SiO J=5-4 line fold arm” aris- lows the 28 SiO J=2-1 contours by Plambeck et al. (2009) quite
erlaps well well (Figure 10). The 29 SiO J=5-4 emission appears more comIRc11 and pact than the 28 SiO J=5-4 emission but has an overall similar
gh-velocity morphology, with the southern lobe of the outflow being morecannot ex- extended than the northern lobe (e.g. compare Figures 8 and 10).
The velocity field shows a much clearer blue-red asymfilamentary
reminiscent metry than the 28 SiO perpendicular to the outflow axis (along2. 静かなときに降着率が低い。
6 Stamatellos, Whitworth, & Hubber

Figure 1. Evolution of the accretion disc around the primary protostar forming in a collapsing turbulent molecular cloud core. The
colour encodes the logarithm of column density, in g cm−2 . The different rows present time sequences from 85 to 91 kyr for different
treatments of the protostellar radiative feedback. Top row (ea0), no radiative feedback: the disc around the primary protostar increases
in mass, becomes gravitationally unstable, and fragments to form 2 low-mass stars and 1 planetary-mass object. Middle row (ea1),
continuous accretion and continuous radiative feedback: the disc grows in mass, but radiative feedback keeps it sufficiently hot so thatit does not fragment. Bottom row (ea2), episodic accretion and episodic radiative feedback: the disc becomes gravitationally unstable(first column) but the growth of GIs is suppressed by heating due to an accretion burst (second column); however, after this burst thedisc cools again, GIs quickly develop, and eventually the disc fragments; one low-mass star forms in the disc.

Sputtering
inetobliqueC-type shocks
tion (Bateal. 2002; Goodwin
et al. 2004a; Attwood et al.

disc; this leads to more material driven inwards in the discand eventually onto the protostar, and therefore more enis released
that heats and stabilises the disc, dampening
S. Van Loo1, I. Ashmore2, P. Caselli2, S. A. E. G. Falle3ergy
and
T. W. Hartquist2
any spiral structure. The disc is therefore in a self-regulating
stable state (Lodato & Rice 2004, 2005).
4.2 Continuous radiative feedback
http://arxiv.org/abs/1209.4041
These results agree with the studies of Bate (2009b) &In this run (ea1; Fig. 1, middle panel) mass accretes conOffner et al. (2009), which show that when protostellar ratinuously onto the protostar, and gravitational energy is
C-shockモデルでsputteringでマントルとコアを壊すMHDシミュレーション。
diative feedback is included, disc fragmentation is generally
radiated away according to Eq. 3. Therefore the protostar
suppressed and fewer low-mass stars and brown dwarfs form.
初めてのobliqueC-typeshockでの計算。
continuously heats
its environment.
The luminosity of the
protostar varies from 10 − 200 L" (Fig. 2, middle panel). As
粒子として中性粒子、ion,
electron,in the previous case the disc aroundthe ２種類のダスト流体を考える。科学計算も同時に行う。
primary protostar
4.3 Episodic radiative feedback
grows in mass (up to ∼ 0.4 M" ; see Fig. 3, middle) and exmantle
sputteringはv>10km/s,
20-25km/s以上では完全に気化する。この時、コアのsputteringも始ま
tends in radius (out to ∼ 100 AU). The disc is continuously
In this run (ea2; αMRI = 0.1, ṀBRG = 10−7 M" yr−1 ; Fig. 1,
heated by the protostar and therefore it is stabilised against
bottom panel) mass accretes onto the protostar episodically
り、SiOも作られる。
fragmentation, despite its large mass. The temperature atusing the model described in detail in Section 3. The mass
100 AU remains relatively high at around 50 K at all times
flows into the inner disc region and then it accretes onto the(Fig. 4a, blue line), and the corresponding Toomre paramprotostar only when the conditions are right for the MRI toeter is always larger than 2 (Fig. 4b, blue line), indicating
operate. The accretion rate is low (10−7 M" yr−1 ) when the
Imprints
ofMolecular
Cloudsin
RadioContinuum
Imagesa stable disc. There are occasions when the disc becomes
MRI is inactive, and high (∼ 10−3 M" yr−1 ) when the MRI
marginally unstable and spiral arms start developing in theis active. Therefore, the release of energy from the protostar
2009; Bate 2009a; Offner et al. 2009).

F. Yusef-Zadeh

電波連続はでの暗黒星雲の発見報告。→radio dark cloud（濃い分子雲に対応）

電波で暗い理由：free-free absorption coefficient がν^-2.1 なので、低周波数側で吸収が強いから。

この手法の強み：磁場の強さ（周りの分子雲と比べて電子の経路が違うことによる比熱的放射の違いを利用）や分子雲の奥行き方向の厚さがわかる。
5例：Sgr A, Sgr B2, radio Arc, Snake filament, G359.75-0.13-> dark featureは分子輝線やダスト放射と反相関であることを照明。→将来の電波連続波観測で星形成領域での冷たい分子雲がみつかるのではないか？

Figure 1. (a) Top—the integrated gray-scale emission of the HCN (1–0) line from IRDC G359.75-0.13 over velocities between −22.9 and −8.5 km s−1 based on
MOPRA observations with a resolution of ∼39## . (b) Middle—similar to (a) except showing the distribution of radio continuum emission at 3.5 cm based on GBT
G359.75-0.23の例。赤：HCN(1-0)line, 緑：3.5cm 連続波。
observation with a spatial resolution of 88## . (c) Bottom—a color composite image showing (a) and (b) in red and green, respectively. (d) Right—a Cross cut, as drawnin (a), made at constant l = 16# 36## showing the intensity profiles of HCN line emission in red and of 3.5 cm continuum data in blue.
(A color version of this figure is available in the online journal.)

Figure 3(c). Given the mismatch between the 2# resolution ofcross cuts at b = −3# 45## across the 6 cm and molecular line

continuum data, the distribution of molecular gas is similarof molecular line emission coinciding with two dips in the 6 cm
image with deficient radio flux of roughly 400 and 300 mJy.
These dips correspond to RDC-1 and RDC-2, and imply thatthe diameters of RDC-1 and RDC-2 are roughly 4/5 and 3/5 ofthe depth of the ionized medium surrounding the cloud.

Phosphorous
chemistryin the shocked
region
L1157 B1
molecular line data
based on AST/RO
observations
and radio
images, as shown in Figure 3(d). The cross cuts show two peaks
to that of darkradioandclouds.
continuum image reveals
Takuhiro
Aota1
YuriThe
Aikawa1

detailed morphological structures of a giant molecular cloud
on arcsecond spatial resolution especially at the boundary of
http://arxiv.org/abs/1210.7900
the molecular cloud near the continuum source. We also madeL1157B1領域(shock region)でのリンの化学進化計算。C-shockmodel。
3
太陽組成に比べて宇宙空間のリン化物は少ない。
PNは見つかっているが(Ori(KL), W51M, and Sgr B2) POはnon-detection (Ori(KL), and Sgr B2)
L1157 : low mass, class 0
L1157 B1 : outflowと星間ガスのshock region。これをモデル計算する。
結論：観測を説明するためには、10^-9のPは固相から気相へPH3かPでsputteringで出る。Nの量は多く(10^-5以上)、ショックガスの温度は2000K以下だった。

10

Aota & Aikawa

O

Figure 3. Reaction network of P-bearing species in the shocked gas.

10 5order to reproduce the observed abundance of PN and the non
detection of PO. The result tells us how large of a fraction of P isin the relatively volatile component in the solids that is desorbed
to the gas phase via sputtering in the C-shock.

Initial N atom

odel B

3. RESULT

undance

3.1. Model A

0 × 10−5
5 × 10−7
6 × 10−8
4 × 10−8

Figure 2 shows the time evolution of P-bearing species inModel A. Abundances are relative to the number density ofhydrogen nuclei (nH ). Major chemical reactions of P-bearing
species are shown in Figure 3. At first, P is in PH3 , which reacts
with H atoms, converting them to P atoms:

with atoms
in molecubelow). Wer as the iniof the shock
ecular cloudH + PH3 → PH2 + H2

(1)

H + PH2 → PH + H2

(2)

H + PH → P + H2 .

(3)

HPO+ + H2 O → PO + H3 O+ .

(5)

PO + N → PN + O(6)

PH + N → PN + H.

(7)

These reactions have activation barriers of 735 K, 318 K, and
416 K, respectively, and thus become active only when the gas
temperature is higher than ∼100 K, i.e., from t = several 102 yr
to a few 103 yr in our model. P atoms react slowly with H3 O+
to form PO:
P + H3 O+ → HPO+ + H2
(4)

lative to hyr abundance
not detected
90). If all Pdels predict
ily detected
phorus thus
clouds (e.g.,solid is unH3 ice is as
hat only thisupon heatr (1994), we

PN is then formed by the following reactions:

For comparison with the observation, we refer to the abundances at the dynamical timescale of the outflow of L1157,∼104 yr (Umemoto et al. 1992). In Figure 2, PN abundanceis lower, and PO abundance is much higher than observed in
L1157 B1. Considering reactions (6) and (7), it is clear thatthe abundances of PN and PO depend on that of N atoms. In
the current model, the dominant form of nitrogen is N2 , and N
atoms are formed by the collisional dissociation of N2 ,solid phaseion of P isputtering in
A easy, the−8. We notetional to theinitially) inabundance
bundance inN2 + Fe+ → N + N + Fe+ ,3