Star	  Forma)on	
  Newsle0er	
  #262	
  53-­‐57本目	
麻生 有佑	

Angular	  Momentum	  Exchange	
  by	
  Gravita)onal	
  Torques	
  and	
  Indall	  in	
  the	  Circumbinary	  Disk	  of	
  the	
  Protostellar	
  System	  L1551	
  NE	
  Shigehisa	
  Takakuwa	
  et	
  al.	  (2014)	
  Ø Class	
  I	
  protobinary	  L1551	
  NE,	  C18O	
  3-­‐2,	
  13CO	
  3-­‐2,	
  0.9-­‐mm連続波,	
  ALMA	  Ø 過去のSMAより空間分解能が面積で1.6倍、感度が輝度温度で6倍良くなった。	
  Ø ALMAではじめて、	  -­‐	
  連続波ではcircumbinary	
  disk上で輝度の分布(粒々)	
  -­‐	
  C18Oではケプラー回転からずれた高速度成分	
  Ø 連続波ではbinaryの南北にprotostellar	
  diskとprotobinary	
  diskの隙間が見えるが、C18Oでは隙間はない。	
  Ø C18Oの速度構造は、高速成分やmom1のridgeが長軸からずれる。	
  Ø 短軸PV図で速度勾配あり。	
  Ø SMAで求めたケプラー回転成分を引くと、連続波circumbinary	
  disk上で高速成分が見える。	
  Ø 流体シミュレーションで再現(4x104	
  yrの準静的状態)。	
  Ø 連星系のRoche	
  poten)alでは重力によるトルクを受けて、角運動量を得たものが角運動量の小さい部分にぶつかり、ショックを作る。	
  Ø ラグランジュのL2とL3(連星を結んだ線上)にストリームができる。	

– 27 –

Angular	
  Momentum	  Exchange	
  by	
  Gravita)onal	
  Torques	
  and	
  Indall	  in	
  the	  Circumbinary	  Disk	  of	
  the	
  Protostellar	
  System	  L1551	
  NE	
  Shigehisa	
  Takakuwa	
  et	
  al.	  (2014) の続き	  – 26 –b) Robust = +0.5c) > 80 kλd) Circumstellar Disks Subtracted

140 AUa) C18O + Cont.

b) C18O (cont. subtracted)

Declination (J2000.0)

Declination (J2000.0)(K)a) Natural

Right ascension (J2000.0)

30 –Fig. 2.— a) ALMA image of the C18 O (J=3-2) plus–continuum
emission of L1551 NE
integrated over the velocity range from VLSR =2.67 km s 1 to 10.56 km s 1 , superposed on
the 0.9-mm dust-continuum image of L1551 NE (colors; same as in Figure 1). Contour levels
Fig. 1.— ALMA 0.9-mm dust-continuum images of L1551 NE with di↵erent imaging methb) Kepleriana) ALMA OBS
ods; a) Image with the Natural weighting, b) Image with the robust parameter of +0.5, c)
are 3 , 10 , 30 , and then in steps of 20 (1 = 14.8 mJy beam 1 km s 1 ). Crosses denote
Image using the visibility data at the uv distance higher than 80k with the Uniform weightthe positions of the protostellar binary, and a filled ellipse at the bottom-right corner theing, and d) same as that in panel c but after the subtraction of the central circumstellar-disk
components. Contour levels start from 0.107 K ⇥2 in steps of ⇥2 until ⇥18, and in steps
synthesized beam of the C18 O plus continuum image (0.00 82⇥0.00 49; P.A.=15.9 ). b) ALMA-1of ⇥6 until
andthen9.8-10.5
in stepskmof s⇥15.
levels of9.2-9.7
the images
in panelsc) a, b, 4.2-4.7; 8.5-9.1 km s-1a) ⇥30,b)1 noise 3.5-4.1;
2.7-3.4;
km s-118
image of the C18 O (J=3-2) emission of L1551 NE after the subtraction of the continuum
and c and dCareO
0.105 K, 0.090 K, and 0.107 K, respectively. Filled ellipses at the bottomENNright corners show the synthesized beams, and the beam sizes are 0.00 94⇥0.00 57 (P.A.=20.2 ),level (contours), superposed on the 0.9-mm dust-continuum image (colors). Contour levels
WN
0.00 85⇥0.00 50 (P.A.=15.2 ), and 0.00 72⇥0.00 36; P.A.=9.1 for panels a, b, and c and d, respectively.
and symbols are the same as those in panel a).
The lower-leftandupper-rightcrosses
indicatethecentroid
positionsofthe2-dimensionalE
Right ascension (J2000.0)– 29 –VLSR (km s-1)

VLSR (km s-1)

ES

140 AUd)c) OBS - KEP

e)

f)

13CO

Fig. 4.— Maps of high-velocity blueshifted (blue contours) and redshifted (red) C18 O (J=32) (upper panels) and 13 CO (J=3-2) emission (lower) in the velocity regions as labeled,d) Numerical Simulation

VLSR (km s-1)

Right ascension (J2000.0)

Declination (J2000.0)

S

WS

Voff (km s-1)

Declination (J2000.0)

Gaussian fittings to the dusty components associated with Sources A and B, which we regard
as the positions of Sources A and B.
W

Right ascension (J2000.0)

Fig. 5.— a) Intensity-weighted mean velocity (moment 1) map of the C18 O (J=3-2) emission

– 35 –

Angular	
  Momentum	  Exchange	
  by	
  Gravita)onal	
  Torques	
  and	
  Indall	  in	
  the	  Circumbinary	  Disk	  of	
  the	
  Protostellar	
  System	  L1551	
  NE	
  – (2014) の続き	  Shigehisa	
  Takakuwa	
  e–t	
  34al.	
  5 -1.0-0.5

0.0

vr [km s-1]

c
0.5

1.0

-1.0

-0.5

0.0

0.5

1.0

Arm A

Sh o ck400

st rota
Fa
e

4

w av

3

n
tio

2

vφ - vkep [km s-1]

b

log Σ
1

elope
Infalling env

aInfall– 32 –

L2

Source A
S h ockw

y [AU]

L3

ll
Infa

0

Source B– 38 –

200

[Fe
II] j
e

t

ave

ion

-200

Arm B

st rotat
Fa

-400
-400
-200
= 2.00 km s-1

0x [AU]

200

400 -400-200

0x [AU]

200

400 -400-200

0x [AU]

200

400

Declination (J2000.0)

Fig. 9.— Circumbinary disk reproduced by our AMR hydrodynamic simulation of gas accretion onto the protostellar binary at the stage of t = 4.13 ⇥ 104 yr (21.1 orbital periods ofthe binary). a) Color scale denotes the logarithmic surface density distribution. The surface-1
Jy pixis
Jy beam-1
densitynormalized so that the binary separation and the gas density at the outer boundary are unity. Arrows denote the gas velocity in the mid-plane of the protostellar binarya) Numerical
Simulationb) Numerical +Sim.
c) ALMA
Obs. the positions ofsystem.
The Roche
potential is overplayed
byALMA
contours.
Crosses
indicate
the protostellar
binary; the left and right crosses correspond to Source A (primary star) andArm A
Source B (secondary star), respectively. b) Color scale denotes a di↵erence betweenpthe rotation velocity and the Keplerian velocity in the mid-plane, v
vkep , where vkep = GM? /r,M? denotes the total massSourceof Sources
A and B, and r denotes a distance from the origin
Bwhich is defined by the center of the mass of the protostellar binary. The red regions ex140 AU
hibit faster rotation thanthat
SourceA expected from the Kepler’s law, and vice versa for the blue
regions. The logarithmic surface density is overplayed by contours, where the contour levels
Arm B
are log ⌃ =1, 0.5, 1.5, · · · 4. The spiral arms tend to exhibit faster rotation. c) Color scale
denotes the radial velocity vr in the mid-plane. The radial velocity is measured from theorigin. The logarithmic surface density
overplayed(J2000.0)
by contours. The spiral arms tend to
Right isascension
exhibit outflows (red), while the inter-arms tend to exhibit inflows (blue). Note that, inb) 0.9-mm
and c), extremely
high values
are obtained
near
the ALMA.
Roche robe
becauselevels
Fig.panels
7.— a)
dust-continuum
imageof L1551inside
NE andtaken
withContourthe Keplerian rotation around the origin is expected only outside the Roche lobe.

start from 2 in steps of 2 until 12 , and in steps of 6 until 30 , and then in stepsof 15 (1 = 2.6 mJy beam 1 ). The highest contour level is 90 . The lower-left andFig. Table
10.— Schematic
picture of thebinary system
L1551of
NEL1551
revealedNE
with the2. Parameters
forprotostellar
the TheoreticalModelpresent ALMA observation.
Parameter
Computer
Simulation Code
Execution Time
Simulation Box
Highest Resolution
Radius of Sink Particles
Boundary Radius
Image Pixel Size
Binary Separationa
Centrifugal Radius of Gasa
Disk Position Anglea
Disk Inclination Anglea
Total Binary Massa
Binary Mass Ratioa
Gas Number Density at the Boundary
Mean Molecular Weight
Temperature Profileb
Dust Opacityc
C18 O Abundanced

Value
ATERUI in NAOJ CfCA
3D AMR Code (SFUMARTO; Matsumoto 2007)
35 hours (512 Cores)(1740 AU)3
0.85 AU
3.4 AU
1740 AU
5 AU
145 AU
300 AU
167
-62
0.8 M
0.19
1.5 ⇥ 105 cm 3
2.3hrA
300 AU= 0.053 cm2 g 1

T (r) = max 23 K
0.9 mm
1.7 ⇥ 10 7

0.2

, 19 KrB
300 AU

0.2

ia Derived from the Keplerian-disk model fitting to the C18 O data taken with the SMA (Takakuwa

Surface	  Geometry	
  of	
  Protoplanetary	  Disks	
  Inferred	
  From	  Near-­‐Infrared	
  Imaging	
  Polarimetry	
  Michihiro	
  Takami	
  et	
  al.	  (2014)	
  Ø polarized	
  intensity	
  (PI)を使って、円盤のsurface	
  geometryを求める方法を開発。	
  Ø 以下の仮定のもと微分方程式を解く。	
  1. エッジオンに近くない。	
  2. NIRで光学的に厚い。	
  
3. 表面とは星からτ~1の場所。	
  4. 円盤は幾何的に薄い。	
  5. フレアは小さい（α–θ<<1）。	
  6. 中心星は点源。	
  7. 複数散乱は無視。	
  	
  Ø 散乱をmonochroma)cモンテカルロシミュレーションでモデル化し、今回の方法を検証。	
  (I) 密度分布を与え、τ=0.5,	
  1.0,	
  2.0の場所を計算する。	
  (II) PI分布をモンテカルロで計算する。	
  (III) (II)のPIを使って今回の方法で表面のgeometryを求め、(I)と比べる。	
  Surface	  Geometry	
  of	
  Protoplanetary	  Disks	
  Inferred	
  From	  Near-­‐Infrared	
  Imaging	
  Polarimetry	
  Michihiro	
  Takami	
  et	
  al.	  (2014)	
  の続き	
  Reproduced (i=18°)
Reproduced (i=49°)
τ = 0.5
τ=1
τ=2

P.A.=0°Model 1

τ=2

r (AU)r (AU)

P.A.=90°z (AU)x (AU)x (AU)x (AU)

P.A.=135°y (AU)(c)
PI / I0(10-6 pix-1)
i=49.5°

P.A.=45°r (AU)y (AU)(b)
PI / I0(10-6 pix-1)
i=18.2°Model 3
τ = 0.5
τ=1

z (AU)(a)log ρ(g cm-3)

Model 2x (AU)x (AU)x (AU)

Fig. 2.— (a) Density distributions assumed for the ID 300949 model (Model 1), the same model but =2,↵=3 (Model 2), and same as Model 2 but with a disk gap (Model 3, see text for details). White dashed,solid, and dotted curves show the positions for ⌧ =0.5, 1, and 2 from the star, respectively. (b)(c) Modeled
P I images using the Sprout code with a viewing angle of 18.2 and 49.5 , respectively. White lines show
the positions where we measured the P I fluxes to calculate the surface geometry of the disk (P.A.=0, 45,
90, 135, and 180 ).

P.A.=180°Ø 実際の観測Subaru-­‐HiCIAO	
  5天体に対して今回の方法を実行。	
  Ø 半径方向にPIの極大値があるが、zにはなく、sinθの傾きがその辺りで極大になる。	
  Ø 非軸対称性が見られるが、非軸対称な星の光度(hot	
  spotやinner	
  disk,	  companionの影響)を考えると表面の非軸対称性は小さくて良い。	
  Ø 残った非軸対称な表面geometryはスパイラルアームと重なる。	
  Ø ギャップはwallではなく、中心星からの光線が表面と平行な場所か、窪みかも。	
  r (AU)

Fig. 3.— The surface geometry of the disk derived using the measured P I flux in Figure 2 and Equation (10The parameters z and r are the height from the midplane and the distance from the star in the midplan
respectively. The red and blue curves show the geometry derived from the P I images with viewing angles
18 and 49 , respectively. Gray dashed, solid, and dotted curves show the positions for ⌧ =0.5, 1, and 2 fro
the star, respectively. The parameter S0 in each case is chosen for the best fit of the ⌧ =1 curve (see text22

23

Surface	  Geometry	
  of	
  Protoplanetary	  Disks	
  Inferred	
  From	  Near-­‐Infrared	
  Imaging	
  Polarimetry	
  Michihiro	
  Takami	
  et	
  al.	  (2014)	
  の続き	  nPI / n* (x10-7 pixel-1)

SAO
206462

Axisymmetric illumination,different S0 for different P.A.
(Case A)

Non-axisymmetric
illumination, S0=0
(Case B)
P.A.
60º
180º
220º
300º

z (AU)

Offset (AU)Axisymmetric illumination,
S0=0(same as Figures 2-6)

N

S0= 0
0.02
0.04

Offset (AU)z (AU)nPI / n*

MWC
758

S (=sin !)(10-7 pixel-1)

Angularresolutionr (AU)
P.A.= 300°
Angularresolution

PDS
70

z (AU)

P.A.
159º
339º

r (AU)r (AU)

P.A.
155º
335º

z (AU)MWC
480

z (AU)z (AU)

S (=sin !)(10-7 pixel-1)

Angularresolution

nPI / n*r (AU)
P.A.= 220°

P.A.
30º
90º
160º
250º

z (AU)z (AU)

2MASS
J1604

(10-7 pixel-1)

nPI / n*z (AU)

S (=sin !)(10-7 pixel-1)

Angularresolution

S (=sin !)nPI / n*

P.A.
60º
160º
265º
320º

P.A.= 180°

P.A.= 60°

Angularresolutionr (AU)r (AU)r (AU)

0.07,
0.09,
0.03 resolution is 0.00 06, corresponding to 8 AU in theFig. 4.— (top) P I image of SAO 206462 (Muto et al.0.06,
2012).
The
angularFig. 9.— Disk surfaces obtained for the following cases: (1) axisymmetric illumination, S0 =sin ✓0 =0, whereimage. The P I flux is scaled by the spatially integrated stellar I flux (see text for details). The region within 0.00 2 (28 AU)✓0 is the elevation angle of the position of a scattering event from the midplane at the innermost radius; (2)of the star is masked. The white dashed lines indicate the positions for which we derive the surface geometry. (bottom) The
results of the numerical integration for the individual P.A.s. For each P.A., the top figure shows the P I flux distribution; theaxisymmetric illumination, di↵erent S0 for di↵erent P.A.s to produce the axisymmetric structure at large
middle shows S=sin ✓, where ✓ is the elevation angle of the position of a scattering event from the midplane (see Figure 1);
radii (Case A); (3) S0 =0, non-axisymmetric illumination to produce the axisymmetric structure at large
the bottom shows the disk surface. The distance r is corrected for the disk inclination. The initial values of the numericalradii (Case B). See text for details. The P.A.s selected are the same as in Figures 4–8. As in Figures 4–8 theintegration S0 are set to be 0, 0.02, and 0.04 at 0.00 2 (corresponding to the projected radius of 28 AU) from the star, and thefainter curves show the results in the outer regions where the observed P I flux nP I /n⇤ ⇠ 0, and therefore
results are shown with solid, dashed, and dotted curves, respectively. Fainter curves at large radii show the results in the outerregions where nP I /n⇤ ⇠ 0, and the results are therefore not reliable (see text for details).
the results are not reliable.

SAO 206462

MWC 758

S1

SAO 206462

S1

S2

S2

S2

Offset (AU)Non-axisymmetric
illumination, S0=0
(Case B)

Offset (AU)Linear component
Offset (AU) subtracted

Non-axisymmetric
Angular illumination, S0=0
P.A.= 0º(Case
B)
resolution
Angularresolution

MWC 758

S1

Offset (AU)

Offset (AU)

S3

S2

S1

Offset (AU)

Offset (AU)

Surface	  Geometry	
  of	
  Protoplanetary	
  Disks	  Inferred	
  From	  Near-­‐Infrared	
  Imaging	
  Polarimetry	
  S3Michihiro	
  Takami	
  et	
  al.	  (2014)	
  の続き	  P.A.= 0ºP.A.

Linear component
subtracted

S3

Non-axisymmetric
illumination, S0=0
Offset (AU)
(Case B)

Linear component
subtracted

Non-axisymmetricLinear component
illumination,
Angular S0=0P.A.= 0º0ºsubtracted(CaseB)
resolution
P.A.
Angularresolution

0º

S3

S1
S1

90º
90º

90º

S2

180º

180º

z/z1

z/z1

0º
P.A.
0º

P.A.= 0º

90º

S2

P.A.

180º

180º

S1
S1
P.A.=P.A.=
360º360º(0º) (0º)

S2S2

270º270º

P.A.= 360º
P.A.= 360º
(0º)

(0º)

360º
(0º)360º

360º
(0º)

(0º)

r (AU)r (AU)r (AU)r (AU)r (AU)

270º

270º

360º
(0º)

r (AU)r (AU)r (AU)

Fig. 10.— (top) Spiral arms discussed for SAO 206462 and MWC 758. (bottom) Surface geometry for Case(B) at(top)di↵erent
P.A.s(left discussed
for each object)
and those
for whichwe subtracted
the linear component(right,Fig. 10.—
Spiralarms
for SAO
206462and MWC
758. (bottom)
Surface geometry
for Case
see the text for details). These are obtained at P.A.s with an interval of 30 , and each of them is shown with(B) at andi↵erent
P.A.s
(left
for
each
object)
and
those
for
which
we
subtracted
thelinearcomponent(right,arbitrary o↵set. The vertical arrows correspond to z/z1 = 1, where z1 is the disk height at the outermost
see theradius
text fordetails).
These
are obtained
P.A.s
with aninterval, 90
of ,30themis shown withr1 (seeTable 7).
The thickcurves showatthegeometries
for P.A.=0180, ,andand each
270 . ofBlue
curvesan arbitraryo↵set.
Theof verticalcorrespondto dashedz/z1 =curves
1, whereis thedisk The
heightthe outermost
show thepositionsthe spiralarrows
arms indicatedby blackin thez1upper
figures.
faintatblue
the ends
some thickof the blue
curvesare thethe positionsof arms
clearly ,seen
the topimage,
radius curves
r1 (seeatTable
7).of The
curvesshowgeometries
for not
P.A.=0
90 in
, 180
, and
270but. Blue curves
identified
as localat the disk
show thepositionsof concave-up
the spiralstructures
arms indicatedbysurface.
black dashed curves in the upper figures. The faint blue

curves at the ends of some of the blue curves are the positions of arms not clearly seen in the top image, but
identified as local concave-up structures at the disk surface.

Eﬀect	  of	  OH	
  deple)on	  on	
  measurements	
  of	
  the	
  mass-­‐to-­‐ﬂux	  ra)o	  in	
  molecular	
  cloud	
  cores	  Konstan)ons	
  Tassis	
  et	
  al.	  (2014)	
  Ø 分子雲中の磁場は、重力収縮を支えたり、cloud	
  fragmentaionを原始星が生まれるコ
アにしたりするが、その効果はM/ΦBに依存する。	
  Ø 分子雲がsubcri)calであれば、重力収縮が起きる前にambipolar	
  diﬀusionでsupercri)calなfragmentができる必要があるなどシナリオの違いを生む。	
  Ø ΦBはOHなどのZeeman効果で測るが、OHのabundanceが測定に与える影響を擬似観測で調べる。	
  Ø chemodynamical	  models	  -­‐-­‐-­‐	
  非平衡化学、nonideal	
  MHDで原始星コアの進化を追う。	
  パラメーターは、初期のM/ΦB、C/O,	
  イオン化率、温度。	
  Ø 擬似観測	
  -­‐-­‐-­‐	
  円盤状になるのでface-­‐onとする。nH2>104	
  cm–3を円盤、nH2>103	
  cm–3をコ
ア＋エンベロープとする。	
  Ø 高密度コアのM/Φ4とコア＋エンベロープのM/Φ3の比R’=(M/Φ4)/(M/Φ3)はモデルの違いや時間に対してほぼ一定。	
  Ø ΦBをOH-­‐mass-­‐weightedにしてZeeman擬似観測、MはOHの柱密度に比例。	
  Ø 高密度なほど磁場も強いが、OHはdepleteし、質量も減る。	
  à結果的にR’は真の値よりも小さく出て、モデル間の差も大きく、また初期にsubcri)calなほど小さく出て、高密度ほど小さく出た。	
  Ø MもΦBも過小評価するが、Mの方が影響が大きいàM/ΦBを過小評価。	
  à高密度(supercri)cal)で過小評価が酷いと、低密度(subcri)al)より小さくなる可能性も。	
  Figure 1. Actual value of R′ = (M/Φ4 )/M/Φ3 as a functionof central density of the core, for the various models used inthis work. Models correspond to symbols and line types as follows: Diamonds: magnetically subcritical; X: magnetcially critical; crosses: magnetically supercritical; solid lines: reference C/O,
depletionand dashedthe mass-to-flux
ratio high3T, OHζ; dotted
lines: C/O=1;
lines: low T; dot-dashed:
T; thick line: high ζ; thin line: low ζ.

Eﬀect	  of	  OH	
  deple)on	  on	
  measurements	
  of	
  the	
  mass-­‐to-­‐ﬂux	  ra)o	  in	
  molecular	
  cloud	
  cores	  Konstan)ons	
  Tassis	
  et	
  al.	  (2014) の続き	  Figure 1. Actual value of R′ = (M/Φ4 )/M/Φ3 as a functionof central density of the core, for the various models used inthis work. Models correspond to symbols and line types as follows: Diamonds: magnetically subcritical; X: magnetcially critical; crosses: magnetically supercritical; solid lines: reference C/O,
T, ζ; dotted lines: C/O=1; dashed lines: low T; dot-dashed: highT; thick line: high ζ; thin line: low ζ.

Figure 3. Scaling of the total (cumulative) mass (solid lines) andmagnetic flux (dotted lines) with radius, ′for a region of the cloud
Figure 2. Simulated observations of R = (M/Φ4 )/M/Φ3 as awith an outer boundary at 103 cm−3 . Each curve corresponds tofunction of central density of the core, for the various models useda diﬀerent evolutionary stage.
in this work. Symbols and lines as in Fig. 1.

the mass-to-flux
ratio of thecore isalsoZeeman
steady after
the
core”
and “core+envelope”
regionsusing
observaonsetandof dynamicalcollapse,
andlinebeforethe “resurrection”
tions
observationsof the OH
intenstity
respectively.
−3ofambipolar
diﬀusion,seen
atdensities
around1010 cmby
To do this, we assume that the magnetic field tracedThe	
  origin	
  of	
  complex	
  organic	
  molecules	
  in	
  prestellar	
  cores	  C.	
  Vastel	
  et	
  al.	  (2014)	
  Ø complex	
  organic	
  molecules	
  (COMs)とは6個以上の重元素を含む有機分子で、生命や惑星系形成の化学進化の理解にとって重要。	
  Ø hot	  cores,	
  low-­‐mass	
  hot	
  corinos,	
  Galac)c	
  Center	  cold	  clouds,	
  prestellar	
  coresで検出。	
  Ø モデルでは>30	
  Kの粒子表面で合成されるが、<20	
  Kの観測がある。	
  Ø Vasyunin	
  &	
  Herbst	
  (2013)でreac)ve	
  desorp)onというメカニズムを提唱。	
  Ø 表面化学反応の発熱によって、COMsが表面でできて離脱。	
  Ø CH3OCH3,	
  CH3CHO,	
  H2CCO,	
  CH3OHを再現、H2CO,	
  HCOOCH3,	
  CH3Oは再現せず。	
  Ø L1544	
  prototypical	
  starless	
  core、高密度2x106	
  cm–3,	
  低温度7	
  K,	
  deutera)on度が高い。	
  Ø Hershelでprestellar	
  coreとしては初めて水を検出abundanceは10–9àFUV光脱離(外側)	
  Ø 観測。IRAM	
  30	
  m,	
  周波数分解能50	
  kHz,	
  感度は4-­‐7	
  mK。	  
Ø E-­‐	  &	
  A-­‐	
  CH3OH,	
  13CH3OH,	
  CH3CHO,	
  t-­‐HCOOH,	
  H2CCO,	
  E-­‐CH3CCH,	
  C3Oを検出(1つ目以外初検出)	
  Ø 他のprestellar	
  coreで検出されているCH3OCH3,	
  HCOOCH3,	
  CH3Oは不検出。	
  Ø LTEモデル	
  -­‐-­‐-­‐	  パラメーターは線幅、VLSR,	
  Tex,	
  柱密度。	
  Ø CH3OHに対してはLVGモデル(柱密度、密度、温度)。	
  à低密度<105	
  cm–3を示唆、6800-­‐9600	
  AUに分布、水と同じく外側なので光脱離起因。	
  Ø 他の分子もTex>10	
  Kなので、同じ場所起因だろう。	
  Ø 化学モデルでgrain	
  mantleから気相への注入も調べた。	
  àC/O~0.5(Oが多い)、injec)on	
  rate~5x10–9	
  -­‐	
  10–8	  The	  origin	
  of	
  complex	
  organic	
  molecules	
  in	
  prestellar	
  cores	  C.	
  Vastel	
  et	
  al.	  (2014)	
  の続き	  – 15 –

Table 2. Column densities and abundances of COMs in L1544. Notes: a) LTE minimisation
procedure; b) assumed Tex =10 K; c) non-LTE LVG analysis (see text). The abundances x havebeen computed assuming N(H2 )=5 × 1021 cm−2 . The final error on the column densities andabundances is about a factor 2.
Fig. 3.— Results from the LVG analysis of the CH3 OH lines. The black lines show the χ2 =0.8
contour plot for N(CH3 OH)=3.8×1013 cm−2 ) and a size of 30” (dashed) and N(CH3 OH)=2.6×1013
cm−2 ) and size 100” (solid), the two extremes of the solutions with reduced χ2 ≤ 0.8. The greyline shows the densities and temperatures at diﬀerent distances from the center (diameter in arcsec
are marked along the curve) predicted for the structure of L1544 by CKB2012.

Species

Tex
(K)

C3 Ob
CH3 CHOat-HCOOHb
H2 CCOa
E-CH3 CCHa
CH3 OHc
CH3 OCH3 b
HCOOCH3 b
CH3 Ob10
17 ± 11027 ± 1
11 ± 2

Tk
(K)

10
10
10
10

n H2
(cm−3 )

3 × 104N(cm−2 )

x

2 × 1011
5 × 1011
5 × 1011
5 × 1012
2 × 1013
3 × 1013≤ 1 × 1012
≤ 6 × 1012
≤ 6 × 1011

5 × 10−11
1 × 10−10
1 × 10−10
1 × 10−9
5 × 10−9
6 × 10−9≤ 2 × 10−10≤ 1.5 × 10−9
≤ 1.5 × 10−10The	
  eﬀect	
  of	
  external	
  environment	
  on	
  the	
  evolu)on	
  of	
  protostellar	
  disks	  Eduard	  Vorobyov	
  et	
  al.	  (2014)	
  Ø コアの質量が円盤を介して中心星に落ちるモデルはisolatedなことが多いが、実際のコ
アはフィラメントの中にあるなど、外的環境の影響があるはず。	
  Ø >10	
  Myrで降着円盤があったり、観測(0.42	
  Myr)ではmain	  accre)on	
  phaseがisolatedシ
ミュレーション(0.12	
  Myr)より長く続いたりしている。àexternal	
  environmentの効果。	
  Ø R=10000	
  AUのコアの外に20000	
  AUまで一定密度の外成分を含んでシミュレーション。	
  Ø model	
  (1)	
  isolate、(2)内側と同じΩ、(3)Ωを0.1倍、(4)Ωを–0.1倍、(5)Ωを–1倍。	
  model	
  (1)	
  断続的にフラグメントができるが、)dally	
  dispersed。質量などはsteady	
  grow。	
  model	
  (2)	
  複数フラグメントができ、ミニ円盤もできる。	
  model	
  (3)	
  途中でフラグメントがなくなり、小さくなる(小さくなるのでフラグメントが起きにく	  い)。外の小さい角運動量がnega)ve	
  torqueを及ぼす。	
  model	
  (4)	
  急速に小さくなって見えなくなる。nega)ve	
  torqueが大きい。	
  model	
  (5)	
  小さくなった後に、逆回りのouter	
  diskとgapができる。outer	
  diskが内側に侵食。	
  Ø 星、円盤、エンベロープ(Σ=0.5	
  gcm–2で円盤と区別)の質量と円盤サイズ、sink	
  cellへのMdotと2000	
  AUでのMdot,infallの進化も調べた。	
  Ø 最終的なM*は外成分があるとisolatedの2倍以上。	
  Ø model	
  (2)と(5)で質量やサイズ、Mdotの進化がepisodic。	
  Model

Mcore
M⊙
0.63
0.63
0.63
0.63
0.63

βcore
%
0.53
0.65
0.48
0.36
0.36

Mext
M⊙
–
1.0
1.0
1.0
1.0

βext

Ωcore
km s−1 pc−1
0.56
0.56
0.56
0.56
0.56

C

r0
AU
1030
1030
1030
1030
1030

The	
  eﬀect	
  of	
  external	
  environment	
  on	
  the	
  evolu)on	
  of	
  protostellar	
  disks	  Eduard	  Vorobyov	
  Vorobyovet	
  al.	  et (al.:2014)の続き	  The eﬀect of external environment
1
2
3
4
5

Radial distance (AU)

10

100

1000

10000

10

100

1000

10000

0.4
0.05

0.2
0.0

0.02

-0.2
0.01

-0.4

0.005

-0.6

model 1

Gas surface density (g cm-2)

0.6

0.1

0.4
0.05

0.2
0.0

0.02

-0.2
0.01

-0.4

0.005

0.2

-0.6

model 2
10

100

1000

10000

10

100

1000

10000

-0.8
0.8
0.6

0.1

0.4
0.05

0.2
0.0

0.02

-0.2
0.01

model 3model 4model 5

0.005
10

100

1000

Radial distance (AU)

10000

10

100

-0.4
-0.6
1000

10000

Angular velocity (km s-1 pc-1)

-0.8
0.8

0.2

Gas surface density (g cm-2)

0.8
0.6

0.1

Angular velocity (km s-1 pc-1)

Gas surface density (g cm-2)

0.2

Angular velocity (km s-1 pc-1)

Radial distance (AU)

-0.8

Radial distance (AU)Fig. 1. Initial distribution of the gas surface density (leftand angularvelocity (right panels) in five considal.: The panels)
eﬀect of external
environment
ered models. The horizontal dotted line marks the zero angular velocity.

where γirr is the incidence angle of radiation arriving at thedisc surface (with respect to the normal) at radial distancer.
The stellar luminosity L∗ is the sum of the accretion
luminosity L∗,accr = GM∗ Ṁ /2R∗ arising from the gravitational energy of accreted gas and the photospheric luminosity L∗,ph due to gravitational compression and deuterium
burning in the stellar interior. The stellar mass M∗ andaccretion rate onto the star Ṁ are determined using theamount of gas passing through the sink cell. The propertiesof the forming protostar are calculated using a stellar evolution code described in Baraﬀe & Chabrier (2010). This
code is coupled with the main hydrodynamical code in realtime. However, due to heavy computational load the stellar
evolution code is invoked to update the properties of the
protostar only every 20 yr, while the hydrodynamical time
step may be as small as a few weeks and the entire duration of numerical simulations may exceed 1.0 Myr. The inn the inner Fig. 4. Similar to Figure 2 but for model 3.
put parameter for the stellar evolution code is the accretion
00 AU box
rate Ṁ , while the output are the radius and photosphericl evolution

–
2.5
0.033
0.019
1.2

(Dapp & Basu, 2009) The resulting initial distribution of
the gas surface density takes the following form!
√r02Σ0 2 for r ≤ Rcore ,
r +r0
Σ=
(8)
Σext
otherwise,
where√Σ0 is the gas surface density at the center of the core,r0 = Ac2s /πGΣ0 is the radius of the central plateau of thecore, Rcore is the radius of the core, cs is the initial soundspeed, and Σext is the density of the external environment,
the value of which is set equal to the gas surface
density"2
at the outer edge of the core (Σext = r0 Σ0 / Rcore+ r02 ).
In all models the value of A is set to 1.2 and the initial
temperature is set to 10 K.
To study the eﬀect of infall from the external environment characterized by varying angular momentum, we
adopt the following form for the initial radial profile of angular velocity Ω#Ωcore
for r ≪ Rcore ,Ω=(9)CΩcore for r ≫ Rcore ,

0
1.0
0.1
-0.1
-1.0

Σ0
g cm−2
9.2 × 10−2
9.2 × 10−2
9.2 × 10−2
9.2 × 10−2
9.2 × 10−2

Rcore
pc
0.05
0.05
0.05
0.05
0.05

Vorobyov et al.: The eﬀect of

calculate the masses of the fragments. The fragments wereidentified based on two conditions: 1) the fragment must bepressure-supported, with a negative pressure gradient withrespect to the center of the fragment and 2) the fragment
must be kept together by gravity, with the potential wellbeing deepest at the center of the fragment. The resulting
masses of the fragments lie in the 2.5–5.0 MJup range.
One can see in Figure 2 that the process of disk fragmentation in model 1 is not continuous but intermittent –time intervals showing fragments are alternatedby interVorobyov
et al.: The eﬀect ofvals showing no signs of disk fragmentation. The timescalewith which the disk fragments is determined by the ratio(Vorobyov et al., 2013a)
Tfr =

Md
,
Ṁinfall(10)

where Md is the disk mass and Ṁinfall is the rate of mass
infall from the parental core onto the disk. Taking 0.15 M⊙
and 10−6 M⊙ yr−1 for the typical values of Md and Ṁinfall(see Figs. 10 and 11), we obtain Tfr = 0.15 Myr, whichappears to agree (within a factor of unity) with a visuallyestimated value of Tfr ≈ 0.1 Myr (see Fig. 2). The lifetime
where Ωcore is the angular velocity of the core and C is aof fragments is usually shorter than 0.1 Myr, either due toFig.
Gas
surfacedensity ormaps
in modelvia2 tidal
in the inner
on3.thecentralprotostar
destruction
dimensionlessscaling
the angularFig.
2. Gas factor
surfacedefining
density maps
in modelvelocity
1 in the inner migration
1000
× 1000 AU
box2011;(top Vorobyovrow) and et
2000
×2013a),2000 AU box
torques(Stamatellos
et
al.,
al.,
in the external
environment.
The angularvelocity
profile1000 ×1000 AU box obtained
at several
evolution
times (as(middleand bottom
rows)
obtained
at several
evolutionin prolonged
periods
of diskevolution
without
in theeachexternal
panel) after
the formationof the central resultingtimes
between themarked
core andenvironmentis smoothly(as marked
in eachpanel)thatafter
thedisk
formationof the−2
fragments.
Finally,
it
is
worth
notingtheforms−2
protostar.
Theof
scale
is in log g cm .
joined at theouter edge
thebarcore.
centralprotostar.
The scaleis in log
g cm.
only onefragment
at a time,
whichbar
impliesthat
ejection
We have considered 5 models, the initial setup for which
Fig. 5.
Similarto Figure 2medium
but for due
model
of fragments
into
the intercluster
to 4.
gravitais shown in Figure 1. In particular, the left panels present
gravitationally unstable and prone to fragmentation in the tional many-body interaction in such a system is impossible
the radial distribution of Σ, while the right panels show
Vorobyov,panels 2012).
have a twice larger size. The early evolution inearly embedded stage of stellar evolution (Vorobyov, 2011). (Basu &otherΩ as a function
radial distance.
Model 1ofrepresents
a denAs many
fragment
can 1— themodel numerical
2 (t ≤ 0.12studiesMyr) isindicate,similar toa thatin modelFigureof
2 presents
the time evolution
the gas surface
Vorobyovet al.: The eﬀectbe
of external
environment
uniformly rotating
isolatedcore(noexternal
environment)
diskinto
is gravitationallyshowinga flocculent
driventhe disk innerunstableregions andprobably
onto spiralsity in model 1 in the inner 1000 × 1000 AU box. The
with mass 0.63
Mcomputationalrotational
and&noBasu,signs 2006,
of fragmentation.
Thisetisal.,
explained(Vorobyov
2010; Machida⊙ and ratio ofwholeregionextendstotogravitational
10000 AU. The time the starstructure& Nayakshin,2011),thisejectedthe intraclusby thefact that during
earlyinto
periodthe disk accretes
energy β = elapsed
0.51%. from
Modelsconsiderthecentral
same core
subthe 2–5
formationof thestar isindicated 2011a; Cha
the matterfromthe parental
rather by
than
from the(Basu &
Vorobyov,2012),coredispersed
tidal
merged intointhe
external
environment
angueachpanel. The
scale bar iswith
in logdiﬀerentg cm−2 andthe lower ter medium(Boley etenvironment.
al., 2010; Zhu et al., 2012) or even sursurface
density thresholdΣ = −1.5 gexcm−2 so torques external
lar velocities.
In particular,model is2 set
hastoalog
corotating
onto ofquasi-stable,
orbits evident
The eﬀect
the externalwide-separation
environment becomesthat the black
is notangularempty butfilled witha low den- vive and settle
ternal environment
with region
the samevelocityas that(Vorobyov,
model
1, thereare no starts
accretion
burststhe disk
at t 2013).
> 0.15InMyrwhen
its matterreaching
material
falling3onto
disk fromthe parentalof the core,sitywhile
in modelthe theangularvelocityof the core.
that could
be triggeredby fragments
the 2 besurface.
In this phase,the diskmigrating
evolution onto
in modelThe protostellar
disk inmodel 1than
becomes
external environmentis 10 times
smallerthatgravitationallyof thestar (seecomesFig. 11).
There diﬀerent
are also noejectionsstrikingly
fromthat in or
thesurvival
isolatedofmodel 1.
unstable
at
the
very
early
stage
of
evolution(asmanifested
core. Models 4 and 5 are characterized by a counterrotating
leaves usinstability
only with andone fragmentation
outcome – theleads toViolent Thisgravitational
by a spiral structure already present at t = 0.08 Myr) due to the fragments.
external environment.
In particular, in model 4 the exterin model
1 havebeen tidallyofdispersed.
almostcomplete
disintegration
the disk. The system now
a continuing mass loading from the infalling core. The first fragments
nal angular fragment
velocity forms
is tenintimes
smaller
absolute
valuethe disk
resembles a multi-component stellar system connected withthe disk
after t by
= 0.15Myr, whenthan that ofmass
the core,
while begin
in model5 the 0.1
external
angularfilaments, within which individual components tend
and radius
to exceedM⊙ and100 AU, re- 4.2. Thedense
eﬀect of external environment: corotating infall
velocity is equal
to thattheagreement
core by withabsolute
Innumerto form their own mini-disks. The masses of the fragments
spectively.
Thisofis in
manyvalue.
previousa rangefrom a few
Jupitersmodels 2-5 ical
the andradialdistributionof gassurfacethat
densityis needs In this spantheoreticalstudies,
indicating
the disk
sectionwe consider
models2 andto 3very-low-massin which a stars,
withtheismost
massive infragment
havingenvironmenta mass of 0.18 M⊙ .
to acquirea critical
0.1 M⊙) andgrow to ina critical prestellar
core
submerged
an external
identical. The
parametersof mass
every(>
areprovided∼modelthethenext
step,Figure
we consider
modelthe3 characterizedbysize (>
withcore.
3 presents
gas surTable 1.
∼ 50−100 AU) before gravitational fragmentation can corotating As
the externalrotating
at a ten times
ensue (Stamatellos & Whitworth, 2008; Rice et al., 2010; face density
maps in environment
model 2 at thesame evolution
times smaller
angularvelocitythan thatthe topcore.panels
Figurehave
4 presents
Vorobyov, 2011; Meru & Bate, 2012). We used the frag- as in Figure
2 for
the isolated
core.of The
gas×surface
densitymapsonin themodel
in thethesame spatracking
in Vorobyov(2013) to a size ofthe
1000
1000 AU
centeredstar,3 while
4. Results ment
Fig. 5.
Similaralgorithm
to Figure described
2 but for model
4.
tial box of 1000 × 1000 AU and at similar evolution times
In this section, we start with considering the properties ofas for the isolated model 1 (see Fig. 2). The early evo-

Fi

th
by
th
ep
an
an
rab
cen
som
F
ma
ye
ga
t=
T
wa
ev
len
tio
te
oro
co
tri
F
en
th
Th
20
ma
ev
sm
–
ma
sh

lie
4.3
ev
In
th
ex
du

Vorobyov et al.: The eﬀect of external environment

radius are calculated at each time step by disentangling t

disk andinfalling envelope on the computational mesh. WThe	
  eﬀect	
  of	
  external	
  environment	
  on	
  the	
  evolu)on	
  of	
  protostellar	
  disks	  do this in practice by adopting a surface density thres
old of Σ =0.5 g cm between the disk and envelope a
Eduard	  Vorobyov	
  et	
  al.	  (2014) の続き	  also using the radial gas velocity profile. This method is d
cr

The eﬀect of external environment

e inner
AU boxolutionn of theagmen-

up . The

Fig. 7. Development of a cavity in the disk. Shown withyellow arrows is the gas velocity field superimposed on thegas surface density in the inner 600×600 AU box in model 5.
The bar is in log g cm−2 .

Vorobyov et al.: The eﬀect of external environment

1000

10

100

1000 10100

1000 10100

1000 10

100

1e+4

1000

0.13 Myr
Myr
0.18 Myr
0.19 MyrAs the second
step, weconsider model
5 with 0.2external
environment counterrotating (with respect to the10core) with the same angular velocity at that of the core.
1
Figure 6 presents the gas surface density in model 5 in
0.1
the inner 1000 × 1000 AU box (top row) and in the inner
0.01
2000
× 2000 AU
box (middle
and bottom0.23rows).
The early
0.25 Myr
0.21 Myr
0.22 Myr
Myr
100
evolution(t ≤ 0.17 Myr) in models 4 and 5 is very similar
10 disk in both models is gravitationally unstable and
– the
1
shows
signs of fragmentation. The masses of the fragments
0.1 the 4.0–7.0 MJup range.
lie in0.01
Thesubsequentevolution of the disk in model 5 is how101001000 10100
1000 10
100
1000
100
1000 10ever quite diﬀerent from any
model
considered
so far. First,
Radialdistance(AU)the disk shrinks in size to just a few tens AU at t = 0.18 Myr
Fig.
Time seriesof azimuthally
averaged
gascounterotatsurface dendue
to8.
a strong
negative
torque exerted
by thesityinfalling
profiles material.
(Σ, solid Then,lines) showing
evolutioning
an outer thedisktime
forms
rotatingof
in model5. with respect to that of the inner,
inthe
thecavity
opposite
direction
heavily reduced disk. During this transformation, a notablecavity develops in the gas surface density at a radial discomeoffully
by ttens= 0.19Myr,withthe maximum
tance
the developedorder of a few
of AU.
This
process
is illusthe lowest
in thecavityandarthecontrastin Σ between
tratedin Figure7 showing
the gasvalue
velocity
field(yellow
maximum
values inon
thetheinnerouterdisks in
onthe
theinner
order
rows)
superimposed
gas andsurfacedensityof 900 andAs time600×600
AU40,
boxrespectively.
during a narrow
timeprogresses,
period of 8 thekyr.cavity
The
moves
to the central
star because
the diskmatterfrom theinfallofclosercounterrotatingenvelope
onto theis alreadyouter disk
throughcavitytoonto
the inner
disk, inexevident
at tflows= 0.175
Myr,theleadinga sharpreduction

Centrifugal radius, Rcf (AU)-2

Gas surface density (g cm )

100

1e+3
1e+2

outer edgeof the isolated coremodel 2model 3model 4model 5model 1

1e+1
1e+0
1e-1
1e-2
1e-3
100

1000

10000

Radial distance (AU)Fig. 9. Centrifugal radius Rcf as a function of radial distance in models 1–5.

Fig. 10. Left column: masses of the disk (solid lines), starlines),
and(dash-dotted
The(dashedradial profile
of R
model 2 (solid
red line) islines) as a funccf inenvelope
similartion
to thatmodel
1, exceptthat thethe matterof the ofex-the protostar in
of of
time
elapsedsinceformation
ternal environment is characterized by a gradually increas-−2

Vorobyov et al.: The eﬀect oscribed in detail by Vorobyov (2011, see fig. 1 and the pm
intaining text). The values of the disk radius and mass bocdepend somewhat on the adopted threshold. Neverthelesss
lower value of Σcr =0.1 g cm−2 results only in a few percecincrease in the net disk mass (see Fig. 2 in Dunham et ta
2014).
w
We found that our algorithm generally works well, abtmay somewhat overestimate the disk mass in the early Clae
0 stage (when the inner part of the infalling envelope m
frhave densities exceeding Σcr ) and somewhat underestima
the disk mass in the late Class I and Class II stages (whcthe disk spreads out and its density drops below Σcr in ict
outer parts). The envelope mass includes both the mattsin the core and external environment (when present). ino
The left column in Figure 10 presents the integrat
disk masses Md (solid lines), stellar masses M∗ (dashtlines) and envelope masses Menv (dash-dotted lines) astfunction of time passed since the formation of the cents
protostar, while the right column shows the correspondie
indisk radii Rd . Each row corresponds to a particular mod
as indicated in the figure. In model 1, the disk mass steada
grows and reaches a maximum value of Md ≈ 0.16 M⊙1et ≈ 0.2 Myr, gradually declining afterwards. The growK
rate of the protostar exceeds that of the disk and the fintmass of the star is expected to be about M∗ = 0.45 M
W
The envelope mass steadily decreases and the model ceters the class II stage, defined as the time when less thF
10% of the initial mass reservoir is left in the envelope,et ≈ 0.25 Myr. The disk grows in radius showing small radp
pulsations and reaches a maximum value of Rd ≈ 400 AUint ≈ 0.5 Myr. All in all, this model demonstrates a standambehaviour as has been found in previous numerical simuations of isolated collapsing cores (e.g. Vorobyov, 2011). in
The properties of the forming star plus disk systemfa
model 2 are strikingly diﬀerent from those of model 1. Firtnthe disk mass reaches a maximum value of 0.54 M⊙ , thrAtimes greater than that in model 1. Second, the disk mrdius exhibits large variations, which are indicative of asnificant radial motions within the disk caused by the graIn
iditational interaction between the fragments and elemenof spiral arms3 . Third, the central star experiences seve
episodes of sharp increase in mass caused by accretions
infalling fragments, the eﬀect discussed in more detailscaSection 6 below. The final stellar mass is expected tomaroundM⊙accretion. After t rates= 0.5throughMyr, there
is still
30%rFig. 11.0.8Mass
the sink
cell at
the
total
mass
available
for accretionr =5 AU(blacksolid lines)
and mass onto
infall theratesdisk+st
at gd