A	  Keplerian	  disk	  around	  a	  Class	  0	  source:	  ALMA	  observa8ons	  of	  VLA	  1623A	
Murillo et al. 2013	

麻生有佑	  11月8日 星形成ゼミ	

1.	  Introduc8on	
Ø 星形成において円盤は鍵となる。	  
質量降着、角運動量分布・輸送、惑星形成・・・	  Class	  IIで回転に支えられた円盤、Class	  0で疑似円盤	  Ø 磁場	  磁場なしではClass	  0ではRout<100	  AU,	  R∝t3	  (Terebey	  et	  al.	  1984)	  ideal	  MHDでは円盤形成が抑制される	  (Mellon	  &	  Li	  2008)	  磁場と回転軸が平行でないと形成する	  (Hennebelle	  &	  Ciardi	  2009)	  Ø Class	  0の回転に支えられた円盤	  
HGC1333	  IRAS4A,	  L1527,	  VLA1623	  2つとも磁場が砂時計型、VLA1623はmisaligned	  HGC1333	  IRAS4AとVLA1623はmul8ple	  ーーーー＞進化段階と環境のどっちが円盤形成に効く？	  A&A proofs: manuscript no. nmurillo

2.	  Observa8ons	

1.3 mm continuum fluxes measured with ALMA

SourceVLA1623A
VLA1623B
VLA1623W

R.A.
16:26:26.390
16:26:26.309
16:26:25.636

Decl.
-24:24:30.688-24:24:30.588-24:24:29.488

Peak (mJy beam−1 )
93.1
93.5
21.6

Integrated (mJy)
201.3±1.2
96.3±0.737.3±0.9

VLA1623・・・	  3重原始連星、non-­‐coeval、ρ	  Oph	  (d~120pc)	  nd ifVLA1623A・・・Class	  the combination of thesefactors is more and our recalibrated data shows consistency
0、24µmより短い放射なし、Bから1.1”、Wから10”	  volutionary stage of a protostar when it comes levels. The synthesized beam size is 0.79## ×	  uum and 0.79## × 0.61## for C18 O, providing
a disk.
–1–0.5
回転則がR(Murillo	  &	  Lai	  and2013,	  MA)	   frthe continuum
line Semissiona Ø
triplenon-coeval なのかR
protostellar なのかは不明	  system to resolve

13; Chen et al. 2013) with a prominent outWe compare the ALMA 1.3 mm con1990) located in ρ Ophiuchus (d ∼ 120pc, that obtained with SMA for the same waveØ ALMA	  Cycle	  0,	  2012年4月8日,	  アンテナ16台,	  最長400	  m	  8). VLA1623 is composed of three contin- Murillo & Lai (2013). To compare, VLA1623+	  (3-­‐2),	  C18O	  (2-­‐1),	  12CO	  (2-­‐1)を検出	  Ø DCO
A1623A,a deeplyembedded Class 0 source is used since it was the most sensitive to the flu
18Oで0.0833	  shortwardof 24 µm;CVLA1623B,
a veryuse the same region and task (CASA’s imstat tØ 速度分解能	  km/s	  source separated 1.1## fromVLA1623A; and integrated flux for both datasets. For the SMA
18Oで0.79”×0.61”	  Ø空間分解能	  Css I source at a projected distance of 10" from has an integrated flux of 96.8±0.7 mJy, wh(チャネルマップは4チャネルをバインドしてる？)	  observationsof VLA1623 revealed that the data, VLA1623B has an integrated flux of 9onent, VLA1623A, has a disk-like structure shows that both observations are consistent.
which was mimicked in continuum. FurtherJCMT observations towards VLA1623 bs disk shows a velocity gradient characteristic (2002) detected C18 O (2-1) with a flux of 12.1

3.	  Results	  –	  1.3	  mm	  Con8nuum	

N. M. Murillo et al.: A Keplerian disk around a Class 0 source: ALMA observations of VLA1623A

Ø 分子流に直交した伸び。	  
Ø Bは24	  µmでも暗い。	  
Ø 赤外はSpitzer	  24,	  8	  µm	  Ø 左下は分子流の方向	183.	  Results	  –	  C O	  (2-­‐1)	
A&A proofs: manuscript no. nmurillo

Fig. 2. Observed C18 O (2-1): Left: Pure Keplerian rotation curves (v ∝ R−0.5 , red and blue) and infall (v ∝ R−1 , green) are overlaid on the PV
diagram. This suggests that the emission may be rotationally supported with M∗ ∼ 0.1-0.2 M% . Center: C18 O velocity map (Moment 1, halftone)
and intensity integrated (Moment 0, contours) maps. Contours are in steps of 3σ, 5σ, 10σ, 15σ, 20σ and 25σ with σ = 13 mJy beam−1 . VLA1623A
and B’s positions are marked with a square and triangle, respectively. Orange and blue lines indicate the image-space PV diagram cuts at PA =35◦ (left) and 125◦ (right), respectively. Right: Lack of velocity gradient suggests no outflow contamination on the C18 O emission. In both PV
diagrams contours are in steps of 3σ, 5σ, 10σ and 15σ where σ = 19 mJy beam−1 and the black lines indicate the systemic velocity and positionof VLA1623A.

Ø SMAより感度が上がったので南北にフィラメントを(初)検出。	  
Ø 短軸方向に速度勾配がないので分子流ではない(左図)。	  
Ø 長軸35°、短軸125°	  ∝R
Ø R–1は後のベストフィットモデルでjを決めている(Rcent=20	  AU)。	  
480

Original
Mirrored−1.0±0.214020

3locity - vlsr (km/s)

ted Flux (mJy)

602

∝R

−0.5±0.08VLA1623A: C18O (2-1)

18
3.	  Results	  –	  C O	  (2-­‐1)	

Fig. 2. Observed C18 O (2-1): Left: Pure Keplerian rotation curves (v ∝ R−0.5 , red and blue) and infall (v ∝ R−1 , green) are overlaid on the PV
diagram. This suggests that the emission may be rotationally supported with M∗ ∼ 0.1-0.2 M% . Center: C18 O velocity map (Moment 1, halftone)
and intensity integrated (Moment 0, contours) maps. Contours are in steps of 3σ, 5σ, 10σ, 15σ, 20σ and 25σ with σ = 13 mJy beam−1 . VLA1623Aand B’s positions are marked with a square and triangle, respectively. Orange and blue lines indicate the image-space PV diagram cuts at PA =35◦ (left) and 125◦ (right), respectively. Right: Lack of velocity gradient suggests no outflow contamination on the C18 O emission. In both PV
diagrams contours are in steps of 3σ, 5σ, 10σ and 15σ where σ = 19 mJy beam−1 and the black lines indicate the systemic velocity and positionof VLA1623A.
480

Original
Mirrored60−1.0±0.21

183

Radial Velocity - vlsr (km/s)

Integrated Flux (mJy)Ø ρ	  Ophでは前方の分子雲が吸収を起こす。	  
∝RVLA1623A: C O (2-1)Ø ∝ラインプロファイル(黒)を4	  Rkm/s付近で反転(橙)させたものと比べることで、システ
ム速度以外に2か所で吸収を確認した(青領域)。	  

40

20−0.5±0.08

20vlsr = 3.7km s−1−20Ø システム速度は3.4,	  3.8	  km/s
P.A. = 35とも言われている。	
◦1012

345

67Velocity (km s−1 )Fig. 3. C18 O (2-1) line profile. The unaltered spectral profile (black) isoverlaid with a portion of the spectral profile mirrored about 4.0 km s−1(orange). Light blue rectangles mark the widths obtained from the best
fit thin disk model (Table 3) of the foreground material (1.6 and 3 kms−1 ) and the envelope (4.0 km s−1 ). The horizontal line between 5 and6.5 km s−1 shows the velocity range used for the UV-space PV diagram.

3040506070

Radius (AU)Fig. 4. UV-space PV diagram of C18 O. vlsr = 3.7 km s−1 was used. The
red points indicate the red-shifted (v > 5.0 km s−1 ) emission. The velocity range covered in this diagram is indicated in Figure 3. Blue-shiftedemission (v < 2.8 km s−1 ) is not included in the diagram since it isgreatly affected by foreground emission (see Figure 3 and Section 3.2).
The points are fit with a power law of the form v = aRn . The solidline shows the fit to the high velocity points (v > 5.7 km s−1 ) while thedashed line shows the fit to the low velocity points (v < 5.7 km s−1 ).

※右下の線(5.0-­‐6.5	  km/s)はPVフィットに使った範囲。	

∝ R−0.5 , red and blue) and infall (v ∝ R−1 , green) are overlaid on the PVd with M∗ ∼ 0.1-0.2 M% . Center: C18 O velocity map (Moment 1, halftone)
ps of 3σ, 5σ, 10σ, 15σ, 20σ and 25σ with σ = 13 mJy beam−1 . VLA1623A
Orange and blue lines indicate the image-space PV diagram cuts at PA =ent suggests no outflow contamination on the C18 O emission. In both PV
mJy beam−1 and the black lines indicate the systemic velocity and position

e4.	  Analysis	  –	  P-­‐V	  diagrams	

4∝ R−1.0±0.21

Radial Velocity - vlsr (km/s)

3∝RØ UV上のPVフィット 	  （Lommen	  et	  al.	  2008）	  Ø blue側は含めず、>5	  km/s、
vsys=3.7	  km/s	  VLA1623A: C18O (2-1)−0.5±0.08

2Ø deconvolu8onの効果を防ぐため、マップ上での2次元ガP.A. = 35
ウシアンフィットに相当する作業をuv上でやった。	  
Fig. 4. UV-space PV diagram of C O. v = 3.7 km s was used. The
red points indicate the red-shifted (v > 5.0 km s ) emission. The velocity range
covered in this diagram is indicated in Figure 3. Blue-shifted Ø M*=0.22	  Mo,	  Rbreak~50	  AU	  (エラーバーに比べて冪のemission (v < 2.8 km s ) is not included in the diagram since it isgreatlyエラーが小さ過ぎ・・・)	
affected by foreground emission (see Figure 3 and Section 3.2). Ø 低速側はτや吸収の影響がThe points are fit with a power law of the form v = aR . The solidline shows the fit to the high velocity points (v > 5.7 km s ) while the
あるのでRbreakは広がり得る。	  
dashed line shows the fit to the low velocity points (v < 5.7 km s ).
vlsr = 3.7km s−1
◦1

30

40

50

60

70

Radius (AU)18lsr

−1−1−1n−1−1This suggests that the pure Keplerian disk extends to a radius of 50 AU.

4.	  Analysis	  –	  Modelling	  of	  C18O	  (2-­‐1)	
Ø モデルは輻射輸送を解かない。	  
Ø M*=0.2	  Mo,	  vsys=4.0	  km/sは固定、一様密度、温度はラインプロファイルに合うように決めた。	  
Ø フリーパラメーター	  line	  width	  vwidth	  (0.1-­‐1.0	  km/s),	  i	  (0-­‐90°),	  Rout	  (100-­‐200	  AU)	  吸収はラインプロファイルを再現するように速度上3か所にガウシアンのτを入れた。	  
Ø 見た目及び残差を比較してベストフィットを決めた。	  
(χ2フィットはしていないと思われる)	

does not correctly reproduce the blue-shifted peak. Chan
the C parameter does not resolve this issue, and changing
line width additionally broadens the wings. Furthermore, e18though fromtheintensity
integrated
map the spatial distribu
A&A proofs: manuscript no. nmurillo
appears to fit the observations, inspection of the channel
residuals show that the model does not quite agree with theservations (Figure B.3). Thus we determine that this scen
does not match the observations.
Infall plus Keplerian rotation: similar to the free fall
Keplerian case, but with the outer part of the envelope infal
Fig. 5. Cartoon illustrating the velocity structure distribution in the disk, shown here face on, for each model examined.
onto the rotationally supported disk (Figure 5). We consider
Table 2. Best Fit Thin Disk Model Results(1) 円盤上の自由落下	  a possibilityfrom AM
the Infallresultsof theUV-space PV diagParameter modelFree Fall Free
Fall + Keplerian Conserved+ Keplerian
Kepleriani (degrees)
55
55
55
55
55
(2) ケプラー円盤の外が自由落下	  (Figure4) whichshows
an inner180
region under
Keplerian rota
R (AU)
130
180
180
180
R (AU)
...
150
150
...
and
an outerregionof20 infall, witha criticalradius of ∼50(3) ケプラー円盤の外がj=C√(GM*Rcrit)を保存	  Table 3. Absorbing material for best
fit thin disk
modelthe inner rotating region (i.e. R < RThus,forcrit ) the velo(4) ケプラー円盤の外がインフォール	  Free Fall Free
+ Keplerian Conserved
AM Infall + Keplerianstructure
isfalldescribedby Equation
3, andKeplerian
for the outer infal
Envelope(5) ケプラー円盤のみ	
velocity (km s region)
4.0 (R ≥ R
4.0crit ) it is given
4.0
4.0
4.0
by: 7.5
opacity
7.0
7.0
7.0
7.0
width (km s )
0.9
0.99
0.99
0.99
! 0.99Foreground 1
velocity (km s )1.6 ∗ Rcrit1.6
1.6
1.6
GMr 1.6
opacity
5.0
5.0
5.0
5.0
5.0(4)について・・・	
v 0.89=width (km s ) infall
0.64
0.62 Vφ=Vrということ？	
0.64
0.64
RR
crit
Foreground 24.	  Analysis	  –	  Modelling	  of	  C O	  (2-­‐1)	

out

crit

−1

−1

−1

−1

velocity (km s−1 )opacitywidth (km s−1 )

3.0
0.39
0.39

3.0
0.29
0.34

3.1
0.29
0.34

3.05
0.29
0.34

3.0
0.29
0.34

As in the free fall plus Keplerian case, we run the model
different critical radii Rcrit to determine how far does each of4.	  Analysis	  –	  Model	  Results	

rtoon illustrating the velocity structure distribution in the disk, shown here face on, for each model examined.

est Fit Thin Disk Model Results

Parameteri (degrees)
Rout (AU)Rcrit (AU)Free Fall
55
130...

Free Fall + Keplerian55
180150Conserved AM
55
180
20

Infall + Keplerian55
180150Keplerian55
180...

Absorbing material for best fit thin disk model

Envelope
velocity (km s−1 )opacitywidth (km s−1 )Foreground 1
velocity (km s−1 )opacitywidth (km s−1 )Foreground 2velocity (km s−1 )opacitywidth (km s−1 )Free Fall

Free fall + Keplerian

Conserved AM

Infall + Keplerian

Keplerian

4.0
7.0
0.9

4.0
7.0
0.99

4.0
7.0
0.99

4.0
7.5
0.99

4.0
7.0
0.99

1.6
5.0
0.89

1.6
5.0
0.64

1.6
5.0
0.62

1.6
5.0
0.64

1.6
5.0
0.64

3.0
0.39
0.39

3.0
0.29
0.34

3.1
0.29
0.34

3.05
0.29
0.34

3.0
0.29
0.34

ベストフィット (円盤よりも吸収の数字が細かい・・・)	

esidual the best fit (discarding the filaments to the northscribe the velocity structure transition, we use the pØ それぞれのモデ
ルのベストフィットと観測の比較。	  
Ø 自由落下を含む
ものは短軸方向の勾配があるので却下。	  
Ø R–1回転(Rcrit=20	  AU,	  C=2)はblueの低速(R大)のずれとredの高速のずれから却下。	  4.	  Analysis	  –	  Model	  Results	
A&A proofs: manuscript no. nmurillo

Fig. 7. Free fall plus Keplerian case for three different Rcrit . The best
fit model (color) to the data (black) is obtained as Rcrit approaches Rout .
Right panels show PV diagram along outflow direction (P.A. = 125◦ ).
All contours and the model at Rcrit = 150 AU are the same as in Figure 6.

Fig. 8. Infall plus Keplerian case for three different Rcrit . The best fit
model (color) to the data (black) is obtained as Rcrit approaches Rout .
Right panels show PV diagrams along the disk’s major axis (P.A. =35◦ ). All contours and the model at Rcrit = 150 AU are the same as inFigure 6.

Rcrit~Routで合うのでのでケプラーの外にインフォールがあるかは不明。	  
cases examined, this model produces broader wings and higher
velocities at smaller radii, effects visible in the spectral profileand the PV diagram, respectively (Figure 6). Additionally, from
Keplerian case, we find that the best fit occurs as Rapproaches

of VLA1623. Holland et al
these conditions the disk’s centrifugal radius Rc is expected to ! tion with the JCMT, "findin
2#Ω3
grow proportional to t , where t denotes the time Rsincecollapse.
to the oc (AU) = 39 field perpendicular−14−1
To calculate the time since collapse for Rc = 150 AU, we use the also
4 × observed
10 rad0.
thesfield to beequation from Belloche (2013)
2" resolution with CARMA!

5.	  " D# iscussion	initialoutcloudcore rot" Ω is thecarried
polarization
ob$ ! where2Rout (AU)M∗ (M# )Menv b (M# )M∗ /MenvT bol (K)Lbol (L# )Lsubmm /Lbol c (%)

a0.2 km s−13m∗+da3 resolution ∼configuration,Rc (AU) = 39(6)
speed
andm
=0.975t. Assumin
∗+dG
1 M#
4 × 10−14 rad s−1tion.
−14From these−1 results werate Ω = 4 × 10
radsthewis
VLA1623 is not andaligned−1
where Ω is the initial cloud core rotation rate, ofa isathe
sound5disk,
field strength=0.2
kms,andwetheobtaint = 8.
Ø 上の式から年齢を導くとt=8.5×10	  yr	  a3speed and m∗+d = 0.975 G t. 5Assuming VLA1623gal
has radiusa rotation
find4 AU.
that rotationally
suppoof150
However,theØTからは10	  yr,	  分子流からはt=2.5×10	  yr	  −14−1bol10rate Ω = 4 ×
rad s and the sound speed in thedyncore is the Class 0 stages with siz
thismethod
is inconsistent with the−15of a =→回転が発達し過ぎなので他の要因があるはず。	  
0.2 km s , we obtain t = 8.5 × 10 yr for a centrifu- magnetic field direction and(Laddthroughet al. 1998)
andandthetheestimated
are large
magnetic
gal radius of 150 AU. However, the old age obtained
fragmenta8on,	  乱流、磁場と回転軸のずれ(84°)	  (2009),
is of tha fairly whichlarge rotationally
this method is inconsistent with the expected byageEvansfrom Tetbolal.ofconsistentwith Krumho(Ladd et al. 1998) and the estimated Class 0 lifetime
obtained istheyconceded
thatfor ρ Ophiuchus
th5
VLA1623A’s
misalignment
by Evans et al. (2009), which is of the order of 10yr,
althoughanorderofmagnitude
lower
than theØinclina8onの影響もあるが、他2天体に比べTbol,	  4
N. M. Murillo
et al.:
disk arounda Class 0 source:of VLA1623A
and rotational axis
they conceded
thatforAρKeplerian
Ophiuchus
the lifetime
is of 4ALMA
× 10observations
yr, rection
thermore,basedoutflow
observatdiskonsize
is sensitiveto th
an order ofLbolが小さいVLA1623は一番若いだろう。	  
magnitude lower than the above calculated
age. Furle 4. Class 0 sources with disk
cal timescale
between
0.2 and 2.5
×concentrated
profithermore, based on outflow observations, VLA1623’s
dynami- iscentrally	
discrepancy
mcal timescale Parameteris between 0.2NGC1333
and 2.5 IRAS4A2
× 104 yra (Andréet al. 1990;
Nakamura
et al.the2011).
indicates
L1527
VLA1623A
Ref. This between(degrees)
10.7 that there are∼85
55 and 1,2,3
VLA1623A’s disk may
Nakamura et ial.
2011). This indicatesother factorsΩ

310
0.08±0.02
5.6
0.01
51
1.9±0.93.6900.19±0.04
0.9
0.2
44
1.970.81800.22±0.02
0.8
0.28
10
1.1±0.21.21,2,3
1,2,34,5...
1,5,31,2,6...

6.	  Conclusions	Ø ALMA,	  Cycle	  0,	  Band	  6,	  extended,	  C18O	  (2-­‐1),	  con8nuum,	  VLA1623	  Ø PV図の解析とモデルフィットから150	  AU,	  0.2	  Moのケプラー円盤を同定。	  
Ø 磁場と回転軸のずれが効いているかもしれない。	  
Ø ケプラー円盤が見つかっているClass	  0の中で最も若い。	  
Ø Class	  0でも100	  AUサイズのケプラー円盤ができる。	  
Ø 進化段階よりも環境の影響が円盤形成に効くかもしれない。