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※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 less⇡⌃G

4

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

197k cells-beta0.5
197k cells-beta1
197k cells-beta2
197k cells-beta3
197k cells-beta4786k cells-beta3786k cells-beta3.5786k cells-beta4.5786k cells-beta5786k cells-beta5.5786k cells-beta6786k cells-beta10
3.1m cells-beta10
3.1m cells-beta123.1m cells-beta1313m cells-beta1113m cells-beta14
13m cells-beta1513m cells-beta1613m cells-beta18
50m cells-beta18
50m cells-beta2050m cells-beta2250m cells-beta24

256
256
256
256
256
512
512
512
512
512
512
512
1024
1024
1024
2048
2048
2048
2048
2048
4096
4096
4096
4096

768
768
768
768
768
1536
1536
1536
1536
1536
1536
1536
3072
3072
3072
6144
6144
6144
6144
6144
12288
12288
12288
12288

Fragmented?
0.5
1
2
3
4
3
3.5
4.5
5
5.5
6
10
10
12
13
11
14
15
16
18
18
20
22
24

Yes
Yes
No
No
No
Yes
Yes
Yes
Yes
Yes
No
No
Yes
Yes
No
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
No

Table 2. Table showing the simulations carried out using FARGO and the
key fragmenting results. The simulations are performed using the artificial
viscosity parameter, q = 1.41.

derstanding the results presented in Section 5.3.3 (which only havedata points at 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

Figure 3. Graph ofagainst resolution of the non-fragmenting (opensquares) and fragmenting (solid triangles) FARGO simulations carried out
using q = 1.41. The solid line, obtained by fitting equation 23, shows adividing line between the fragmenting and non-fragmenting cases and thegrey region is where fragmentation can take place. The graph shows clear
evidence of convergence of results with increased resolution. The convergence rate is second order with spatial resolution. The dotted line (whichcoincides well with the solid line) is obtained by fitting equation 21.
12, where Ncells is the number
For FARGO, we simply take l / Ncellsof grid cells. Note that the linear resolution is inversely proportional
to the square root of the number of cells because the calculation is
two dimensional. We fit this formula to the fragmentation boundary

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

METHOD

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

calculate 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)
効。
nsition following
equation A4 of ?,hν0!
8πν20 1 + e− kB Tex
N(1, 1) = 2
τ(ν)dν,(1)hνcA− k T01 − e B ex
where ν0 , T ex and τ are the line rest frequency, measured

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. For2

tflow Structure and Velocity Field of Orion Source I

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