星形成ゼミ 2022.10.7 SFN #354 29-35
片岡章雅

• 29. Star Formation Activity Beyond the Outer Arm II: Distribution and Properties of Star
Formation
Natsuko Izumi, et al.

• 30. Statistical properties and correlation length in star-forming molecular clouds: I. For- malism andapplication to observations
Jaupart and Chabrier• 31. Statistical properties and correlation length in star-forming molecular clouds: II. Grav- itational
potential and virial parameter
Jaupart and Chabrier• 32. Super-resolution trends in the ALMA Taurus survey: Structured inner discs and compact discs
Jennings et al.

• 33. A multiwavelength study of the W33 Main ultracompact HII region
Khan et al.

• 34. The morphology of CSCha circumbinary disk suggesting the existence of a Saturn-mass planet
N. T. Kurtovic et al.

• 35.Dynamical star forming history of Per OB2
Kounkel et al.

Super-resolution trends in the ALMA Taurus survey: Structured
inner discs and com- pact discs
Jeff Jennings, Marco Tazzari, Cathie J. Clarke, Richard A. Booth, Giovanni P. Rosotti

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⋆ The 1.33 mm survey of protoplanetary discs in the Taurus
molecular cloud found annular gaps and rings to be common inextended sources (> 55 au), when their 1D visibility distributions
were t parametrically. We rst demonstrate the advantages andlimitations of nonparametric visibility ts for data at the survey’s
0.12" resolution. Then we use the nonparametric model inFrankenstein (’frank’) to identify new substructure in three compact
and seven extended sources. Among the new features we identify
three trends: a higher occurrence rate of substructure in the survey’s
compact discs than previously seen, underresolved (potentiallyazimuthally asymmetric) substructure in the innermost disc ofextended sources, and a ’shoulder’ on the trailing edge of a ring indiscs with strong depletion at small radii. Noting the shoulder
morphology is present in multiple discs observed at higher resolution,
we postulate it is tracing a common physical mechanism. We further
demonstrate how a super-resolution frank brightness pro le is useful
in motivating an accurate parametric model, using the highly
structured source DL Tau in which frank nds two new rings. Finally
we show that sparse (u, v) plane sampling may be masking thepresence of substructure in several additional compact survey
sources.

・原始惑星系円盤のALMA連続波観測のモデリングの話。
・0.12秒角のTaurusサーベイデータを使う。
・ ttingはʼfrankʼというパッケージを使う。
・結果、3つのコンパクト天体と７つのextended天体で新たなsubstructureを発見した。
・見つけたトレンドは3つ
・以前よりコンパクト天体にsubstructureがある確率が高い
・extended天体の分解できてないsubstructureがある・ʼshoulderʼとよぶ構造がある
・特に、DL Tauは2つの新しいリングがあった。

干渉計の画像化• 電波干渉計のデータは、2次元空間情報(x,y)をフーリエ変換した2次元空間(u,v)の中で、離散的なデー
タとして手に入る。

• 離散的な(u,v)から元の画像を再現したいが、解は一意に決まらないので、色々なやり方が提案されている。

• 古典的にはCLEANという手法が提案されている。(x,y)空間でまあまあ明るい点源を有限個組み合わせて(u,v)空間を再現した上で、点源を適当なガウシアンでなましたもの。このガウシアン（ビーム）くらいの画像の粗さがある。

• 日本ではスパースモデリングを使って2次元画像を描くグループも。
• それとは別に、(u,v)空間を直接 ttingすることも可能。frank (Jennings et al. 2020)はこの種類。

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Galario (Tazzari et al. 2017)もこっち。そもそもALMA前の時代はこっちが多い。Andrews et alなど。

frank (Jennings et al. 2020)

Frankenstein, the flux reconstructor13• 1次元軸対称の天体を仮定して、(u,v)空間上でガウス過程を用いて1次元radial pro leを持ってくる手法• face-on円盤が得意=あまり傾いていると使えない• 非軸対称構造があると変な結果がでる• Galario(Tazzari et al. 2017)との違い：円盤のpro leを予め決めて、MCMCパラメー
タフィットをする。予め指定されたパラメー
タと違う構造が不得意（ガウシアンっぽいけ
どちょっとずれたリングの広がりとか）
Jennings et al. 2020

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Figure 7. Performance on di↵erent disc morphologies using mock observationsa) Input and reconstructed brightness profiles for a mock Gaussian disc with FWHM 0.200 , observed separately with the ALMA C43-3(synthesized beam FWHM 0.59 ⇥ 0.7000 , Briggs=0.5) and C43-6 (beam FWHM 0.13 ⇥ 0.1700 , Briggs=0.5, factor of 5 longer integration timethan C43-3; see Table 2) configurations. The beams’ minor axes are shown for reference. The frank fit to each of the 2 mock observations

• データはLong et al. (2018) and Long et al. (2019) で用いられた
Taurusのサーベイデータを用いる。彼女らはGalario codeを使って
parametric 4 tをした。
Jennings, Tazzari, Clarke, Booth, Rosotti
2 D( 1 L DJ( 1 R OJDODULR
IUD N( 1 L DJ( 1

R O

JDODULR

VU
D
,

5 9

IUD N

5 VL

E

DV OL

U

0

8

Tauの場合。カイ二乗値が向上している(42->23)• 例： ttingの比較。DO
Figure 1. Improved visibility fit accuracy better resolves disc structurea) A zoom on the Taurus survey visibilities for DO Tau (20 and 100 k_ bins, with 1f uncertainties shown for the 100 k_ points); the parametric fit from Longet al. (2019); the nonparametric frank fit; and the Fourier transform of brightness profiles extracted from the CLEAN image and CLEAN model.
b) Residuals of the parametric and frank visibility fits and the CLEAN model transform (20 k_ bins).
c) Brightness profiles for DO Tau corresponding to the visibility fits in (a).

• Long et al. (galario)は低基線、中基線であっているが、長基線でずれている。

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fi• 対してfrankは長基線もよく再現している。
the visibilities in (b) with frank gives an accurate recovery of thethe baselines at which the current data become noise-dominated.

frankの結果は信じられるかのデモ
リング幅が80masのとき• 実験：シンプルなモデルを

DV
(
RS
5 J
6
R R
D N

E

(
RS
5 J

V

D

J

DV

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6

5

幅に間違えているが、これは長基線の方がゼロになるまでデー
タが揃っていないことが問題。
実際のデータについてはここをよくチェックすれば良い。

frank:結構ずれる。
frank:ちょっとずれる
Super-resolution trends in the ALMA Taurus survey 5
中心も合わない

JVV• 特に40masリングの場合は大DV

リング幅が40mas

J

120masの分解能で擬似観測し、その結果をfrankで tして再現できているかを見る。

frank:よく再現

リング幅が60mas

D N• DO Tauではうまく見えてい

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DV
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0
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DV
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D N

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R

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R R

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るが、他のデータではそうでもないfrankの結果は信じられるかのデモ2• 実験2：非軸対称な成Jennings, Tazzari, Clarke, Booth, Rosotti
R
R

R
[ R
[ R

[ ,D

[
[

[ ,D

R

R

R
R

D

J

分が乗っていたら
frankはどう応答する
か。

6

E

• 基本的には非軸対称成
R
RI[ ,DUFR[ ,DUFR

R

R
D R[ ,DUF
R

RII

分は区別できないので、CLEAN imageを確認したり、
imaginary part をみたり、residualをみたりして努力する

R

D
5 RII
1R

D ]

E J

1R

D ]

D

Figure 3. Low contrast, asymmetric substructure emulates an underresolved annular ring in a brightness profilea) The brightness profile of a Gaussian envelope, as well as the azimuthally averaged profile of the envelope summed with a 40 mas arc that spans 180o in
101

メインの結果
Super-resolution trends in the ALMA Taurus survey
DLF

5 VL D
P

DV L
)

0

D

5 9 P

( 1 LPDJ( 1 PR

D DP
ID N

LF

P9
P

5 VL
P

D

• 載せていないが T Tau Nは
Yamaguchi et al. 2021の
PRIISMの結果と同様に
gap/ringが見えていた。

D DP
ID N

P9
P

ち、24天体にfrankを適応。その中でsubstructureがあった10天体の結果を見せる。

( 1 LPDJ( 1 PR

5 9 P• Taurus 32天体データのう

5 D

7

D
DV L

)

D

5 D

0

Figure 4. Improved visibility model accuracy in frank fits to compact discs
For the compact discs in Sec. 4.1, a zoom on the visibilities (> 0.30 M_; 20 and 100 k_ bins, with 1f uncertainties shown for the 100 k_ points). The

顕著な例

Super-resolution trends in the ALMA Taurus survey
5 D

5 9 P

D

P9
P

parametric modelingでは、1.25Mλのfeatureを捉えられていなかった。

DV L

0

D

P9
P

5 9 P

)

5 VL DP

5 VL DP

5 9 P

D• 以前のLong et alの

VL DP( 1 LPDJ( 1 PR( 1 LPDJ( 1 PR

)

D DP
ID N

D

LF

7

Super

D DP
ID N

LF

DV

DV

2 7D

S DN

DU V

DU V

S DN

S DN

DU V

VU

D

D

• 97auと116auのリングは、( 1 L DJ( 1 RG OED JLong et al.では一つのbroad ringとして解釈されていた
0

DV

S DN

DU V

DU V

S DN

SDUD WUL
IUD N

DV

S DN

DU V

VU

• residualから考えられる非対称構
E
造はおもにgapのなかにある
D J

DV

8

D (

DV

0

7D

S DN

DU V

S DN

DU V

S DN

DU V

RIIV W

VU

5 9

5 9

Jennings, Tazzari, Clarke, Booth, Rosotti

ED J

DV

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8

DV

5 RIIV W

Star Formation Activity Beyond the Outer Arm II: Distribution and Properties of Star Formation
Natsuko Izumi

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The outer Galaxy beyond the Outer Arm represents a promising
opportunity to study star formation in an environment vastly different
from the solar neighborhood. In our previous study, we identi ed 788
candidate star-forming regions in the outer Galaxy (at galactocentricradii RG ≥ 13.5 kpc) based on Wide- eld Infrared Survey Explorer(WISE) mid-infrared (MIR) all-sky survey. In this paper, we investigate
the statistical properties of the candidates and their parental molecular
clouds derived from the Five College Radio Astronomy Observatory(FCRAO) CO survey. We show that the molecular clouds withcandidates have a shallower slope of cloud mass function, a larger
fraction of clouds bound by self-gravity, and a larger density than themolecular clouds without candidates. To investigate the star formation
ef ciency (SFE) at different RG, we used two parameters: 1) the
fraction of molecular clouds with candidates and 2) the monochromatic
MIR luminosities of candidates per parental molecular cloud mass. We
did not nd any clear correlation between SFE parameters and RG at
RG of 13.5 kpc to 20.0 kpc, suggesting that the SFE is independent ofenvironmental parameters such as metallicity and gas surface density,
which vary considerably with RG. Previous studies reported that theSFE per year (SFE/yr) derived from the star-formation rate surface
density per total gas surface density, HI plus H2, decreases withincreased RG. Our results might suggest that the decreasing trend is due
to a decrease in HI gas conversion to H2 gas.

・銀河系外縁部における星形成領域の統計的性
質の話
・>13.5kpcの領域でWISE MIR surveyで788の星形成領域をリストアップ済み
・FCRAO CO surveyをもちいて、分子雲の性質を調査
・core mass function CMFは、星形成領域候補を持っているとshallowになった・star formation e ciency SFEの銀河中心からの距離依存性を調べたが、明確な相関は得られなかった。

52

Kennicutt and Evans• 銀河系外縁部は金属量が低く、HIが支配的（H2分子は少ない）と言われている。13.5kpc以遠はガス面密度は下がる。->低金属
量、低ガス面密度環境• Kennicutt-Schmidt law で知られているように面密度に星形成率と相関すると考えられている。特に高面密度ではΣsfr
Σgas、低面密度ではΣsfr

Σgas^2と言われている。ここで、Σsfrは単位面積あたりの星形成率。

• 銀河系では、Σsfr /Σgasは15kpcまで測られている(Kennicutt and Evans 2012, review)が、13.5kpcまではコンスタントで、それ以降は下がっている

FCRAO CO data
• BKP catalog (Brunt et al.
2003)• 星形成領域が付随してい
る・していないでベキが違う• 重いクラウドのほうが星形
成が活発• 星形成領域候補がある分子雲・ない分
子雲のビリアル質量の違い• Mvir = 210

r dv^2とした。189/466でデータを出した COからH2を見積もる比は近傍のものを仮定。

• 星形成領域候補がある方は、主に思い側にあって、Mvir=MCOに乗っており、重力的に束縛されている。

• 星形成領域がない方は、質量軽い側で、関係から外れていて、重力的に束縛されていなさそう。

• 金属量は1/3以下なのに、COから質量求めるファクターは近傍と一緒。

Figure 6. Top: Relation between virial mass (Mvir ) and mass derived from CO intensity (MCO ). Red circles and yellow
squares show clouds with associated candidate star-forming regions with a contamination rate of their parental clouds of < 30
% (reliable) and
30 % (less reliable), respectively. Black open circles show clouds without associated star-forming regions.
The gray-dotted line shows the Mvir = MCO relation. The vertical gray-dotdashed line indicates the mass threshold (183.6
M ). The arrows indicate the upper limit (using dv = 0.98 km s 1 ) for 277 clouds for which the linewidths are not derived in
BKP catalog. Bottom: Relation between completeness of Mvir (number of clouds whose linewidth is derived / total number ofclouds) and MCO . The error bars represent Poisson errors (1 ).

hemisphere (Kerr et al. 1986) data. They provide plots ofthe H i surface density, !H i ðRÞ, from the second and third
Galactic quadrants (northern and southern data) as well as
the average surface density and find that the average radial
distribution at R > 13 kpc is well fitted by an exponential,!H i ðRÞ / expð#R=HRH i Þ, with HRH i ¼ 4 kpc. A relatively
flat rotation curve was used, similar to that derived by
Brand & Blitz (1993).
Dame (1993) and Lockman (1988) showed that minor(%2%) differences in the rotation curve can greatly affect thesurface density derived from the data with differences in thesurface density amounting to %50%. Based on the northernhemisphere data, Dame (1993) found a peak in surface
density near 12 kpc for a flat rotation curve but a nearly constant surface density out to 17 kpc when using the slightly
rising rotation curve of Kulkarni, Blitz, & Heiles (1982).
Wouterloot et al. (1990) attributed the peak in the H isurface density to gas associated with the Perseus arm andshow that the average of the northern and southern data
partially smooths the 12 kpc peak.
In addition to the surface density enhancement at 12 kpc,
the Wouterloot et al. (1990) plots of the outer Galaxy show

1:7 * 10

M&, while our distribution gives a mass

Fig. 1.—Azimuthally averaged H i surface density !H i (dashed curve)and H2 surface density !H2 (dotted curve) in the Galactic disk vs. Galactocentric radius R. Total H i plus H2 is shown as a solid curve. Mass does notinclude He.

e 14. Top: Galactocentric radius variation of fraction of molecular clouds with candidate star-forming regions (NSF /Nall )uds with MCO
183.6 M . The magenta squares and red circles show all the clouds with candidates and only clouds
eliable candidates, respectively. The error bars represent Poisson errors (1 ). The magenta and red dotted lines show
ult of least-squares fittings: NSF /Nall = 5.8(±2.5)RG - 52.3(±36.5) (magenta: all clouds with candidates) and NSF /Nall±2.1)RG - 64.0(±31.0) (red: only clouds with reliable candidates), respectively. Bottom: Galactocentric radius variation
number clouds with and without candidates. The red and orange bars show the number of clouds with candidates withmination rate of < 30 % (reliable) and
30 % (less reliable), respectively. The white bars show the number of clouds
t candidates. Only clouds with MCO 183.6 M are plotted. The gray areas indicate the concentrated areas consideredpiral arms.

Wol re 2003

• N̲SF/N̲allを見ると、銀河中心からの距離と若干性の相関。CO dark cloudの影響か？spiral arm がグレーのところにあるのに注意。

fi• H2ベースでみたらN̲SF/N̲allは定数か減ってるかも？

• LMIR/MCOはだいたいSFEを表しているとされている。

• MIRの輝度の距離相関はあんまなさそう。

Figure 16.
Left: Galactocentric radius variation of the integrated (total) monochromatic MIR luminosities of candidatestar-forming regions per parental cloud mass (LMIR /MCO ). Red circles and yellow squares show clouds with candidates with acontamination rate of their parental clouds of < 30 % (reliable) and 30 % (less reliable), respectively. The size of these markers
indicates the mass of their parental molecular clouds (small: MCO < 103 M , middle: 103 M  MCO < 104 M , large: 104 M
 MCO ). Magenta solid and dotted lines indicate median and mean values of only candidates with a contamination rate of lessthan 30 % (reliable), respectively. Cyan solid and dotted lines indicate median and mean values of all candidates. These values
are calculated in a 0.5 kpc binning from RG of 13.5 to 20.0 kpc. The gray areas indicate the concentrated areas considered to be
spiral arms. Correlation coefficients (CC) are noted in the bottom right corners. Right: Galactocentric radius variation of theindividual monochromatic MIR luminosities of candidate star-forming regions per parental cloud mass (LMIR /MCO ). Notations
are the same as in the left panels.

• 論文としての結論：N̲SF/N̲allもL̲MIR/M̲COも13.5-20.0kpc領域において際立って下がっているわけではない。→SFEは環境によらないのでは

Statistical properties and correlation length in star-forming molecular clouds: I. For- malism and application to observations
Etienne Jaupart, Gilles Chabrier ⋆ The proper characterization of the general statistical behavior of these uctuations, from a limited sample of observations or
simulations, is of prime importance to understand the process of star formation. In this article, we use the ergodic theory for any random eld of uctuations, ascommonly used in statistical physics, to derive rigorous statistical results. We outline how to evaluate the autocovariance function (ACF) and the characteristic
correlation length of these uctuations. We then apply this statistical approach to astrophysical systems characterized by a eld of density uctuations, notably starforming clouds. When it is dif cult to determine the correlation length from the empirical ACF, we show alternative ways to estimate the correlation length. We showthat the statistics of the column-density eld is hampered by biases introduced by integration effects along the line of sight and we explain how to reduce these biases.
The statistics of the probability density function (PDF) ergodic estimator also yields the derivation of the proper statistical error bars. We provide a method that can beused by observers and numerical simulation specialists to determine the latter. We show that they (i) cannot be derived from simple Poisson statistics and (ii) become
increasingly large for increasing density contrasts, severely hampering the accuracy of the low and high end part of the PDF because of a sample size that is too small.
As templates of various stages of star formation in MCs, we then examine the case of the Polaris and Orion B clouds in detail. We calculate, from the observations, theACF and the correlation length in these clouds and show that the latter is on the order of ∼1% of the size of the cloud.
Statistical properties and correlation length in star-forming molecular clouds: II. Grav- itational potential and virial parameter
Etienne Jaupart, Gilles Chabrier ⋆ In the rst article of this series, we have used the ergodic theory to assess the validity of a statistical approach to characterize various
properties of star-forming molecular clouds (MCs) from a limited number of observations or simulations. This allows the proper determination of con dence intervals
for various volumetric averages of statistical quantities obtained form observations or numerical simulations. In this joint paper, we apply the same formalism to adifferent kind of (observational or numerical) study of MCs. Indeed, as observations cannot fully unravel the complexity of the inner density structure of star forming
clouds, it is important to know whether global observable estimates, such as the total mass and size of the cloud, can give an accurate estimation of various key
physical quantities that characterize the dynamics of the cloud. Of prime importance is the correct determination of the total gravitational (binding) energy and virial
parameter of a cloud. We show that, whereas for clouds that are not in a too advanced stage of star formation, such as Polaris or Orion B, the knowledge of only theirmass and size is suf cient to yield an accurate determination of the aforementioned quantities from observations (i.e. in real space). In contrast, we show that this is nolonger true for numerical simulations in a periodic box. We derive a relationship for the ratio of the virial parameter in these two respective cases.

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エルゴード理論を用い、統計的性質を導く、という手法の開発と、その星形成領域への適用
分子雲の質量とサイズというりょうが最も重要である

A multiwavelength study of the W33 Main ultracompact HII region
Sarwar Khan, Jagadheep D. Pandian, Dharam V. Lal, Michael R. Rugel, Andreas Brunthaler, Karl M. Menten, F. Wyrowski, S-N. X.
Medina, S. A. Dzib, H. Nguyen ⋆ The dynamics of ionized gas around the W33 Main ultracompact HII region is studied using
observations of hydrogen radio recombination lines and a detailed multiwavelength characterization of the massive star-forming region
W33 Main is performed. We used the Giant Meterwave Radio Telescope (GMRT) to observe the H167α recombination line at 1.4 GHz
at an angular resolution of 10 arcsec, and Karl. G. Jansky Very Large Array (VLA) data acquired in the GLOSTAR survey to study the
dynamics of ionized gas. We also observed the radio continuum at 1.4 GHz and 610 MHz with the GMRT and used GLOSTAR 4−8
GHz continuum data to characterize the nature of the radio emission. In addition, archival data from submillimeter to near-infrared
wavelengths were used to study the dust emission and identify YSOs in the W33 Main star-forming region. The radio recombinationlines were detected at good signal to noise in the GLOSTAR data, while the H167α radio recombination line was marginally detectedwith the GMRT. The spectral index of radio emission in the region determined from GMRT and GLOSTAR shows the emission to be
thermal in the entire region. Along with W33 Main, an arc-shaped diffuse continuum source, G12.81−0.22, was detected with the GMRT
data. The GLOSTAR recombination line data reveal a velocity gradient across W33 Main and G12.81−0.22. The electron temperature isfound to be 6343 K and 4843 K in W33 Main and G12.81−0.22, respectively. The physical properties of the W33 Main molecular clump
were derived by modeling the dust emission using data from the ATLASGAL and Hi-GAL surveys and they are consistent with theregion being a relatively evolved site of massive star formation. The gas dynamics and physical properties of G12.81−0.22 are consistent
with the HII region being in an evolved phase and its expansion on account of the pressure difference is slowing down.

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The morphology of CSCha circumbinary disk suggesting the existence of a Saturn-mass planet
N. T. Kurtovic, P. Pinilla, Anna B. T. Penzlin, M. Benisty, L. Pérez, C. Ginski, A. Isella, W. Kley, F. Menard, S. Pérez, A. Bayo ⋆ Planets
have been detected in circumbinary orbits in several different systems, despite the additional challenges faced during their formation insuch an environment. We investigate the possibility of planetary formation in the spectroscopic binary CS Cha by analyzing its
circumbinary disk. The system was studied with high angular resolution ALMA observations at 0.87mm. Visibilities modeling and
Keplerian tting are used to constrain the physical properties of CS Cha, and the observations were compared to hydrodynamic
simulations. Our observations are able to resolve the disk cavity in the dust continuum emission and the 12CO J:3-2 transition. We nd
the dust continuum disk to be azimuthally axisymmetric (less than 9% of intensity variation along the ring) and of low eccentricity (of0.039 at the peak brightness of the ring). Under certain conditions, low eccentricities can be achieved in simulated disks without theneed of a planet, however, the combination of low eccentricity and axisymmetry is consistent with the presence of a Saturn-like planet
orbiting near the edge of the cavity.

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Dynamical star forming history of Per OB2
Marina Kounkel, TingYan Deng, Keivan G. Stassun ⋆ We analyze the internal dynamics of young stars towards Perseus using Gaia
EDR3 data, including Per OB2 and California Cloud. Interpreting the current dynamics, we speculate that Per OB2 may have formed
from two separate clouds that have begun forming stars in a close proximity of each other. IC 348 is caught in the middle between thetwo of them, inheriting kinematics of both, and it stands out as a possible site of cloud cloud interaction. We also consider a possibilityof a past supernova in Per OB2 - while one had likely occurred, it did not appear to have caused any obvious triggered star formation,
but it has created a shock which has swept away the molecular gas away from IC 348. Finally, we examine a recently proposed shell
between Taurus and Perseus. While its origin is unknown, we nd no support for an expanding bubble in stellar kinematics, nor can we
identify a likely progenitor for a supernova that may have caused it, disfavoring this scenario in the formation of this apparent shell.

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