星形成ゼミ #345 42-47
片岡章雅42. Protostellar Interferometric Line Survey of the Cygnus X region (PILS-Cygnus) -- First results: observations of
CygX-N30
S. J. van der Walt, L. E. Kristensen, J. K. Jørgensen, H. Calcutt, S. Manigand, M. el Akel, R. T. Garrod, K. Qiu
43. The impact of massive stars and black holes on the fate of open star clusters and their tidal streams
Long Wang (1 and 2), Tereza Jerabkova (3)44. In search of infall motion in molecular clumps III: HCO+ (1-0) and H13CO+ (1-0) mapping observations
toward the confirmed infall sources
Yang Yang, Zhibo Jiang, Zhiwei Chen, Yiping Ao, Shuling Yu
45. A Morphological Classification of 18190 Molecular Clouds Identified in 12CO Data from the MWISP Survey
Lixia Yuan, Ji Yang, Fujun Du, Xunchuan Liu, Shaobo Zhang, Zehao Lin, Jingfei Sun, Qing-Zeng Yan, Yuehui Ma, Yang
Su, Yan Sun, Xin Zhou
46. Global 3D Radiation Hydrodynamic Simulations of Proto-Jupiter's Convective Envelope
Zhaohuan Zhu, Yan-Fei Jiang, Hans Baehr, Andrew N. Youdin, Philip J. Armitage, Rebecca G. Martin
47. The HD 98800 quadruple pre-main sequence system. Towards full orbital characterisation using longbaseline infrared interferometry
S. Zúñiga-Fernández (1 and 2 and 3), J. Olofsson (3 and 1), A. Bayo (3 and 1), X. Haubois (2), J. M. Corral-Santana (2), A.
Lopera-Mejía (3), M. P. Ronco (1 and 4), A. Tokovinin (5), A. Gallenne (7 and 8 and 9), G. M. Kennedy (6), J.-P.
Berger (10)Astronomy & Astrophysics manuscript no. paper
September 13, 2021

©ESO 2021

The impact of massive stars and black holes on the fate of open
star clusters and their tidal streams
Long Wang1, 2 and Tereza Jerabkova3
1.04592v1 [astro-ph.SR] 9 Sep 2021

Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japane-mail: long.wang@astron.s.u-tokyo.ac.jp
2
RIKEN Center for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 648-0047, Japan3
European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk,
The Netherlands,e-mail: Tereza.Jerabkova@esa.int
Received June 15, 2021; accepted –, –ABSTRACT
Context. To investigate how the content of massive OB stars a↵ects the long-term evolution of young open clusters and their tidal

streams, and how such an e↵ect influences the constraint of initial conditions by looking at the present-day observations.
Aims. OB stars are typically in binaries, have a strong wind mass loss during the first few Myr, and many become black holes.
These a↵ect the dynamical evolution of an open star cluster and impact its dissolution in a given Galactic potential. We investigate
the correlation between the mass of OB stars and the observational properties of open clusters. Hyades-like star clusters are well
represented in the Solar neighborhood and thus allow comparisons with observational data.
Methods. We perform a large number of star-by-star numerical N-body simulations of Hyades-like star clusters by using the highperformance N-body code petar combined with galpy.
Results. We find that OB stars and black holes have a major e↵ect on star cluster evolution. Star clusters with the same initialconditions, but a di↵erent initial content of OB stars, follow very di↵erent evolutionary paths. Thus, the initial total mass and radiusof an observed star cluster cannot be unambiguously determined unless the initial content of OB stars is known. We show that thestellar counts in the corresponding tidal tails, that can be identified in the Gaia data, help to resolve this issues. We thus emphasise theimportance of exploring not only star-clusters, but also their corresponding tidal tails. These findings are relevant for studies of theformation of massive stars.

Young open star clusters are important stellar systems for understanding star formation and stellar evolution. Due to the stellar
and dynamical evolution, star clusters are evaporating their stars
and are in the process of becoming part of the Galactic field stel-• OB型星が星団に与える影響を考えた• OB型星はだいたいバイナリーで生まれる• OB型星は星風で質量を放出する• OB型星は最後はブラックホールになって
銀河ポテンシャルなどにも影響する• ヒアデス星団を念頭に、N体計算をやった• code: PETER + GALPY• 例えば、同じ星団の初期条件でも初期のOB星が違えば、結構違う進化パスをおう• 観測的にこれらを区別するには、Gaiaデータで見られたtidal tailを見るのが良いかもしれない。

Key words. star clusters – star formation – numerical methods

1. Introduction• アブストラクトの日本語まとめ

man 2019b; Fürnkranz et al. 2019; Meingast, Alves & Fürnkranz
2019; Tang et al. 2019; Zhang et al. 2020; Bhattacharya et al.
2021; Jerabkova et al. 2021). The kinematic properties of Galactic young star clusters (e.g. Kuhn et al. 2019; Monteiro & Dias
2019; Monteiro et al. 2020; Zhong et al. 2020; Angelo et al.
2021; Dias et al. 2021; Godoy-Rivera et al. 2021) and their extended structures (e.g. Pang et al. 2020, 2021; Meingast, Alves,• イントロのメモ• Gaiaのおかげではじめてopen cluster（散開星団）のtidal tail の星の分布がわかるようになってきた。
• もちろんkinematic structureやextended structureも• すると、星団の進化の議論もできるように。
• すべての星は初期には重力的に束縛されていた？
• 初期半径、質量、バイナリー率…
• OB星からの星風、輻射、超新星爆発によるフィードバックが聞く。これらは1Myrでガスを抜き去ってしまう。
すると、重力ポテンシャルも変わる。
• 上記のようなガスが抜け出すフェイズのあと、重力的に束縛されていれば、星団は再びビリアル化される。

• この研究では、OB星の影響はlong-termにも及ぶことを示す。
• OB星のwind mass lossは重力ポテンシャルをへらす。
• OB星のあとにはBHとかが残り、他の星と相互作用してlong-termにも影響する• 初期OB星はIMFによる。星形成がstochastic かどうかによってOB星の数は違うだろう• 特に、低質量散開星団では、IMFで決まるOB星の数の分散の影響は色濃く出るだろう。
• なるべく同じ初期条件で、どのくらい違いが出てくるのかを知りたい。

Fig. 2. Sketch of the formation and evolution of a star cluster (from left to right). The left: the gas embedded phase where star formation occurredalong the filaments in a few Myr, which were influenced by the gas flow in the large scale, the OB feedback and the stellar dynamics. The right:
after the gas expulsion, the bound star cluster re-virialised to a roughly spherical system, which is the initial condition in our models. With thethree black solid arrows we show that there are a number of evolutionary tracks a star cluster can take. In our case we focus on how the content
of massive stars can a↵ect the evolution of the cluster with otherwise identical initial conditions. We show that while this causes degeneracy
making it impossible to uniquely infer the initial conditions of an observed cluster, the properties of its tidal tails help to break the degeneracy andthus constrains the initial conditions, as marked by the gray solid arrow. The ultimate question (indicated by the gray dotted arrow) is then what
constraints can be placed on the gas-embedded phase of the star cluster.
Table 1. The initial and present-day coordinates of Hyades

Parameter

648 Myr ago

present-day

RA[deg]Dec[deg]
Distance[pc]pm(RA,cos(Dec))[mas yr 1 ]pm(Dec) [mas yr 1 ]radial velocity [km s 1 ]308.488
41.2174.575-0.904-0.740431.3167.98517.01247.501101.005-28.490
39.96

Notes. The evaluated coordinate of the Hyades 648 Myr ago by using
galpy and the observed present-day one in the ICRS frame (see Jerabkova et al. 2021; Gaia Collaboration et al. 2018, for more details)

formation and results in a largely gas-free star cluster. Phases(i)-(iii) are encompassed in the birth conditions as deduced byMarks & Kroupa (2012). All of these processes are contributing to the star cluster’s evolutionary path in a complex way as
depicted by the bottom solid arrow pointing to the gas-free starcluster. This point marks the start of our N-body simulations,where we assume the embedded pre-gas-expulsion cluster (grayshaded panel) has expanded and re-virialised after the residual
gas has been removed (Banerjee & Kroupa 2017). Thus, we do
not aim to simulate the formation of the cluster but the evolution
starts from the expanded gas-free state. The long-term evolutionof the star cluster and its tidal stream is controlled by the net effect from the stellar evolution, stellar dynamics and the Galactic
potential. In this work, we focus on how the content of massive
stars can a↵ect the evolution, which causes the degeneracy ofthe evolution track and brings the challenge to identify the initialcondition from the present-day observational property.
Observationally, gas-free star clusters are well resembled by
Plummer-like profiles (Plummer 1911; Röser et al. 2011; Röser

Table 2. The initial parameters of N-body models

M0 [M ]
Rh,0 [pc]800, 1000, 1200, 1400, 1600
0.5, 1, 2

Notes. The initial total masses M0 and the initial half-mass radii Rh,0of the star cluster model sets. The reference name of each set combines
the values of M0 and Rh,0 without the decimal point, such as M800R05,
M1000R1, M1600R2.

& Schilbach 2019a) and thus our initial set-up is empirically motivated. Using the initial coordinate described in Section 2.4.1 in
the Milky-way potential, we generate a grid of star-cluster models by varying the initial total masses M0 and the initial half-mass
radii Rh,0 (see Table 2). We combine each of M0 and Rh,0 , andthus, the total number of model sets is 15. The reference nameof each set is described in Table 2. To investigate the stochastice↵ect, it is necessary to carry out a large number of simulations
with di↵erent random seeds. Thus, for each set, we generate 300
models by randomly sampling the IMF from Kroupa (2001) withthe mass range of 0.08 150 M and the positions and velocities of stars from the Plummer density profile (Aarseth, Henon,& Wielen 1974). The stochastic eLong Wang and Tereza Jerabkova: The impact of massive stars on open star clusters
A&A proofs: manuscript no. paper

where ri is the position vector of each star or compact object in
the coordinate system used in the simulation. During the simulation, the origin point of the coordinate system follows the motion of the potential weighted center of the star cluster. Noticethat the definition of Rc from observation is di↵erent. Especially,
compact objects cannot be detected by observations. For massive
star clusters where many BHs exist, Rc in N-body models can bevery di↵erent from that of observations. In this study, only a few
BHs can form and their impact on the calculation of Rc is neglectable. We have confirmed this in our models.
In the Galactic potential, there is no precise definition of Rtid .
But we can obtain the rough estimation via
Rtid = Rgal
Fig. 3. The mass of the heaviest star (mmax ) and the total mass of OB
stars (MOB ) by randomly sampling the Kroupa (2001) IMF in each of
the 300 Hyades-like models. The initial total mass of each model is
1600 M .

M1600R2というセットの中の300初期条件にお•37.5
per cent of
the initial mass of the cluster. Thus, it is ex-pected that the dynamical impact from the OB stars can di↵er
ける、OB星の合計質量に対する、OB星の最大質
significant
model by model.

量の図（分散あるねえ）
varies from 150 M to 600M and m varies from 20 M to 140 M .
3.2.M The
stellar winds from OB stars
OB

⊙

⊙

max

⊙

⊙

•ToOB-minとOB-maxというモデルを選んだ。OB星
investigate how MOB a↵ects the present-day morphology, we
pickup the two models with the minimum and the maximumの総質量が一番大きいのと小さいの。
MOB in the M1600R2 set (hereafter named as “OB-min” and"OB-max" models, respectively). Fig. 4 compares the presentday positions and proper motions of stars in the ICRS frame

Mtid
3Mgal

! 13

(3)

(Binney & Tremaine 1987), where Rgal is the distance to the
Galactic center and Mgal is the e↵ective mass of the Galaxy (themass enclosed by Rgal ). In our analysis, we first calculate the(positive) Galactic potential at the cluster center (Pgal ) and thenapproximate Mgal via
Pgal rgal
Mgal =
G(4)

where G is gravitational constant. At the beginning, Mtid is unknown,
the total
mass
all map
objectsusedandasproper
themotions
starting
Fig. 4.thus
The comparisonof thenumberof
densityfor the ispositionsof stars at the age of 648 Myr in the two models with th
the maximum MOB from the M800R2 set (OB-min and OB-max models).
Mtidminimum. Then anda few
iterations are necessary to obtain the consistent
Rtid and Mtid . We stop the iteration when the di↵erence between
The reference data fromOB-min
Hyades are model;
shown as grey
horizon- where Nrh is the number of stars within Rh and the suffix “ref現在まで残る•the new
and
the
old
R
is
less
then
1
percent.
Whenrefers
the tocluster
tiduncertainties). Most of models havetal lines and regions (withthe parameters of the OB-max model. The values oreachesthelower
disruption
the iteration
not converge
to aare used for comparison. Rh and Mrh have largslightly
Rtid , Rh andphase,
Rc comparedto those ofmay
the obserMtid at 32 Myr
OB-maxmodel
200
Myr前に散逸した
vational
data. Thereis •a, degeneracy
between
MOBzero.
andMOnce
as shown in Fig. 5. Thus, their averaged values
0 thatpositive
value
of Rtid
i.e.,
Rtid becomes
Rfluctuations
tid is determany combinations of the two parameters can result in the simi-

24, 32 and 40 Myr are compared.

Long Wang and Tereza Jerabkova: The impact of massive stars on open star clusters

Long Wang and Tereza Jerabkova: The impact of massive stars on open star clusters• OB-minとOB-maxというモデルの統計量の比較• R_tid; 潮汐半径、M_tid, 潮汐半径ないの全質量, Rh;
half-mass半径、Rc; core radii• 最初の30Myrで、OB-maxモデルでは、Rtid Mtidが下がってるが、これはOB星の星風によるmass lossの影響。半分以上失う• 400Myrたつと、Rhがさがって、R_cが上がる→星団
がビリアル平衡から外れて散っていっている。

• OB-minモデルではなだらかな変化で、648Myr後も星団が生き残ってる。
Fig. 5. The comparison for the evolution of the global properties for
the OB-min and OB-max models shown in Fig. 4. From the top to thebottom: tidal radii (Rtid ), the total masses inside Rtid (Mtid ), the half-mass
radii (Rh ) and the core radii (Rc ). The vertical line refers to 30 Myr.

Fig. 5. The comparison for the evolution of the global properties for
the OB-min and OB-max models shown in Fig. 4. From the top to thebottom: tidal radii (Rtid ), the total masses inside Rtid (Mtid ), the half-mass
radii (Rh ) and the core radii (Rc ). The vertical line refers to 30 Myr.

have been disrupted. Such a trend depending on M0 suggests thatthe stellar wind mass loss at the beginning is not the only reason

have been disrupted. Such a trend depending on M0 suggests thatthe stellar wind mass loss at the beginning is not the only reason
for the divergent evolution like that of the OB-min and OB-max
models.
The values of T rh are shown in the second row of panels in
Fig. 7. Generally, the model with a short T rh loses mass faster,
but it is not the case for the two models in the M1600 set withT rh = 231.9 Myr and 255.4 Myr (hereafter named as R1 and R2
models, respectively). The R2 model has a large T rh but dissolute faster. In the meantime, some models in the M1600 set havelarger T rh than those of the M800 set, but the former has alreadybeen disrupted at the present day while the latter still survives.
Thus, the di↵erent evolution cannot be explained by T rh .
Instead, we find that the existence of BH binaries (BBHs)
play an important role. The total masses (MBH ), the number of
BHs at 32 Myr and the evolution of semi-major axies of BBHs

• もうちょい一般的傾向を見た• 60modelずつ5ビンに分けてR• larger M_OB -> RtidとMtidが小さい• 灰色がヒアデス星団。

Fig. 6. The comparison for the evolution of the global properties for allmodels with di↵erent M0 (represented by colors) and di↵erent Rh,0 (represented by markers and brightness of colors). From the top to the bottom are: Rtid , Mtid , Rh and Rc . The 300 models in each set are collected
into the bins of MOB . The error bars represent the standard deviation.
The observed values of Hyades are shown as horizontal lines or regions(with uncertainties).

A&A proofs: manuscript no. paper

has a di↵erent initial condition but shows similar properties (e.g.
mass, density and Rh ) at 32 Myr as those in the OB-max model,
they may have identical evolution after that. To investigate this,
we measure the di↵erence between models as
Mtid Mtid,ref=Mtid,ref

!2

+

Rh

Rh,refRh,ref!2

Nrh Nrh,ref+Nrh,ref!2(5)Article number, page 6 of 12• 似たような星団を適当に評価してピックアップ。

• 最初の32Myrは星風による質量損失とBBHの力学的加熱の2つが星団の質量をへらす• ブラックホールバイナリーの影響がつよい
ことがわかった• BBHの軌道長半径が下に書いてある• BBHの軌道長半径が下がっている→そのぶん星がkinetic energyをもらってふっとばされている
Fig. 7. The evolution of the global properties, from the top to the bottom: Rtid , Mtid , Rh , Rc and aBBH , for the models with a similar property at 32
Myr to those in the OB-max model. The columns separates the models with di↵erent M0 . For each M0 , a brighter color indicate a higher total massof BHs (MBH ). The half-mass relaxation time (T rh ) at 32 Myr are shown in the second row of panels. The values of MBH and the corresponding
numbers of BHs (in brackets) are shown in the last row of panels.

3.5. The structure of tidal streams

can be described as

Fi
mo
mo
els
mo
A

a small Mout and Nout . As the high-M0 model has a large MOB ,the dissolution of the star cluster is faster because of stronger
stellar wind mass loss and dynamical heating from BBHs. Thus,
the fraction of the number of stars inside Rtid ( ftid = Ntid /N where
N is the total number of stars) can help to estimate M0 and MOB
observed
star cluster.
Long Wang and Tereza Jerabkova: The impact of massive starsfor
onan
open
star clusters

Table 3. The parameters of the model set shown in Fig. 8Mode set
M800R2
M1000R1
M1200R05
M1400R05
M1600R05

MOB
27.0
207.2
165.5
348.8
456.9

Mtid
196.3
196.5
196.1
198.5
196.2

Mout
471.9
518.2
658.6
727.1
857.0

Ntid
186
184
173
202
180

Nout
735
761
958
973
1208

From the Gaia EDR3 catalogue, 862 objects with a similar magnitude cuto↵ were detected, 293 of which belong to theleading tail and 166 to the trailing tail. All Nout in Table 3 are Notes. The corresponding model set, the initial OB star mass (MOB ), thesignificantly higher than the observed counts. But it is difficult total mass inside Rtid (Mtid ) and outside Rtid (Mout ), the number counts
to make a solid conclusion based on the direct comparison of for stars with apparent G-band magnitude < 20 inside Rtid (Ntid ) andthe N-body model to the observation. For Gaia data, a strict se- outside Rtid (Nout ) for the five models shown in Fig. 8. Their Rtid ⇡ 6.5 pc
lection is needed to remove contamination and obtain signal in and Rh ⇡ 3.0 pc at 648 Myr. The mass unit is M .
the tails, which a↵ects completeness. With a looser constraint,
the contamination is higher. In addition, an unresolved binary is tidal streamは、これまでふっとばされThis result suggests one strategy to constrain the initial concounted as one object and large fraction of these are filtered out
dition of a star cluster. First, we find a group of models withby quality cuts applied to the Gaia data (Jerabkova et al. 2021). た星の履歴を持っている
Due to the overlap of objects along the line-of-sight and a higher di↵erent M0 and MOB that can result in the same Rtid , Mtid andRh . Then, we use ftid to determine which combination of M0 and
fraction of binaries inside the star cluster, the numbers of stars OB-minをreferenceとして、現在でな
might be underestimated. Meanwhile, the background contam- MOB best fits the observational data. Because of the high perforination is expected to be higher along the tails. A better solu- mance of petar, it is practically possible to generate a grid ofstar clusters models to achieve this goal.
tion is to use the N-body model as the reference to create mock るべく近いモデルを5個選んだ
observations considering the Gaia uncertainty and backgroundcontamination. Then compare the model with the observation to 4. Discussion and conclusion
obtain a better constraint. For such a purpose, the assumption 違いは、R_tidより内外にある星の数にof primordial binaries is also necessary. This will be our future In this work, we investigate how the content of OB stars a↵ects
e↵ort.
the long-term evolution of Hyades-like open star clusters and強く現れている(table3)•••

Article number, page 9 of 12• M0が大きいモデルはMOBも大きく、星風やBBHの影響で星がdissolutionされるのも早い• Gaia DR3では、862個が受かっていFig. 8. The comparison for the morphology, the density and the average mass of stars for the five models with di↵erent M0 and the minimum
referring to the OB-min model in the M800R2 set. For each model, the three sub-panels show the number density map of stars in the sphericalcoordinate system of the Galactocentric reference frame, the histogram of star counting (Ns ) and the average mass of stars (hms i) along thelongitude, respectively. The compacted objects (WDs, NSs and BHs) are excluded.

a small Mout and Nout . As the high-M0 model has a large MOB ,the dissolution of the star cluster is faster because of stronger

Table 3. The parameters of the model set shown in Fig. 8て、293/166個がleading/trailing tailに存在している。Noutの結果より小さい。

MNRAS 000, 1–24 (2021)

1?

Preprint 3 September 2021

2

Compiled using MNRAS L TEX style file v3.0

1

u (1g) , Yan-Fei Jiang (‹’ﬁ) , Hans Baehr , Andrew N.
2,41
p J. Armitage,
andRebeccaG.
MartinGlobal 3D Radiation Hydrodynamic Simulations ofs and Astronomy, University of Nevada, Las Vegas, 4505 S. Maryland Parkway, Las Vegas, NV 89154-4002, USA
onal Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA& Department of Astronomy, University of Arizona, 933 N Cherry Ave, Tucson, AZ 85721, USAs and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA1?
2
1

Proto-Jupiter’s Convective Envelope

Zhaohuan Zhu (1g) , Yan-Fei Jiang (‹’ﬁ) , Hans Baehr , Andrew N.
32,41
Youdin,PhilipJ.
Armitage,
andRebeccaG.
Martin1:2106.12003v2 [astro-ph.EP] 1 Sep 2021

Department of Physics and Astronomy, University of Nevada, Las Vegas, 4505 S. Maryland Parkway, Las Vegas, NV 89154-4002, USA
2 Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA
3 Steward Observatory & Department of Astronomy, University of Arizona, 933 N Cherry Ave, Tucson, AZ 85721, USAmber 2021
4 Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA

ABSTRACTThe core accretion model of giant planet formation has been challenged by the discovery of recycling flows between the planetary envelope and the disc that can slow
or stall envelope accretion. We carry out 3D radiation hydrodynamic simulations with
ABSTRACT
an updated opacity compilation
to modelproto-Jupiter’s
To isolate
thedisThe core accretion
model ofthe
giant
planet formation envelope.
has been challenged
by the3D e↵ects of convection
andrecycling,simulate
both isolated
spherical
coveryof recyclingflowswebetweenthe planetary
envelope andthe disc envelopesthat can slow
or stallinenvelope
We carry out
radiationwithand envelopes embedded
discs. accretion.
The envelopes
are3D
heatedathydrodynamic
given ratessimulations
to achieve
an updated opacity compilation to model the proto-Jupiter’s envelope. To isolate thesteady states, enablingcomparisons with 1D models. We vary envelope properties to
3D e↵ects of convection and recycling, we simulate both isolated spherical envelopes
obtain both radiativeandandconvective
solutions.
a passive
scalar,we observe
sigenvelopes
embeddedin discs. Using
The envelopes
are heatedat given
rates to achieve
steadyenabling comparisons
We vary
enveloperecycling
properties tonificant mass recycling
onstates,
the orbital
timescale. with
For1D
a models.
radiative
envelope,
obtainthe
bothdisc
radiative
and convective
solutions.
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observecan only penetrate fromsurfaceuntil ⇠0.1-0.2
planetary
Hill scalar,radii,wewhileforsignificant mass recycling on the orbital timescale. For a radiative envelope, recycling
a convective envelope,motion“dredgeup” thedeepertheforcantheonlyconvective
penetrate fromthe disccan
surfaceuntil ⇠0.1-0.2
planetary
Hillpart
radii,ofwhileenvelope so that the aentire
convective
envelope
is motion
recycledThis
recycling,
convective
envelope, theconvective
can efficiently.
“dredge up” thedeeperpart of theenvelopee↵ects
so that on
the theentireenvelopes’
convective envelope
is recycled
efficiently.
recycling,
however, has only limited
thermalstructure.
TheThisradiative
however, has only limited e↵ects on the envelopes’ thermal structure. The radiativeenvelope embedded in
the disc has identical structure as the isolated envelope. The
envelope embedded in the disc has identical structure as the isolated envelope. The
convective envelope hasa slightly
higherdensityhigher
when
it is whenembeddedin theindisc.
WeWe
convective
envelope
has a slightly
density
it is embedded
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a modified
1D approachwhich
can fully reproduce
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can fully
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withaa
10 M core, and the timescale to runaway accretion is shorter than the disc lifetime as
10 M core, and the timescale
to runaway
is shorterofthan
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in prior studies.
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discuss the implications
the efficient
recyclingon theasobin prior studies. Finally,
wechemical
discussabundances
the implicationsof theatmosphereefficient (especiallyrecyclingfor
onsuper-Earths
the observedof the planetaryand mini-Neptunes).
served chemical abundancesof the planetary atmosphere (especially for super-Earths
and mini-Neptunes). Key words: planets and satellites: formation - planets and satellites: gaseous planets

In original form 3 September 2021

- protoplanetary discs - radiation: dynamics - convection

Key words: planets and satellites: formation - planets and satellites: gaseous planets• 惑星コアにガスが降着する過程について、3次元輻射流体計算を使って調べた。
• 熱源を手で入れることで、輻射層と対流層それぞれ支配的な場合を作って、円盤ガスとどれくらい入れ替わるか見た。

• 輻射層が支配的な場合、0.1-0.2ヒルくらいしか入れない• 対流層の場合は、ガスが全部入れ替わる。
• （定性的な結果はあんまりこれまでの研究と変わらない？）• 1Dに使える式を作った。

The Astrophysical Journal, 747:47 (16pp), 2012 March 1

Tanigawa, Ohtsuki, & Machida• 1Dでは、Mizuno 1980で知られているように、10M地球くらいの固体コアがあれば、ガスが降着して暴走成長する• 3Dだと、そんなに単純じゃない• 例えばTanigawa et al. 2012
• 結果はEOSに依存する。
• isothermalだと周惑星円盤ができるし• 断熱だと圧力で支えられたガス球になる

Figure 17. Schematic picture of the flow structure of circumplanetary disks.
(A color version of this figure is available in the online journal.)•

is not easy to judge which factor causes the difference. Diskz-direction. In this region, radial velocity is very small andTanigawa
et al. would
2012
thicknessbe one of the reasons for that, even though
it is difficult for the gas to accrete inward throughthe disk
our disk thickness is not very different from theirs. Anothermidplane, as mentioned above. On the other hand, the gas at
possibility is gap formation. When a deep gap is formed, theR̃ ! 0.2 in the midplane shows significant outflow, which
contribution of the vertically accreting gas would become lesseventually escapes from the Hill sphere (see Figure 2). Thus

4

Z. Zhu et al.

Figure 2. The Rosseland mean opacities at di↵erent densities and temperatures from various databases. The colored region is where thedata are calculated and valid. The dashed curve labels the ⇢ T condition of a forming Jupiter’s envelope at the cross-over mass, ascalculated in Section 5.3.

the metal rich/poor environment, we vary the metal (beyond H and He) abundance accordingly. Both Planck mean
and Rosseland mean opacities have been generated using
the LANL opacity website. Since protoplanetary discs andplanet envelopes are cooler and less dense than stars, weonly calculate the opacity with temperatures from 0.5 eV to
1 keV (⇠5800 K to 107 K) and densities from 10 14 to 1 g
cm 3 . The density range where the LANL opacity is valid
depends on the temperature and element considered.
One advantage of the LANL opacity table over the
widely used opacities (mainly from Ferguson et al. 2005 andIglesias & Rogers 1996) in MESA (Paxton et al. 2011) is thatit includes opacities at high densities and low temperatures,the conditions found in the planet envelope/atmosphere. For
example, the MESA opacity table has a maximum opacity at⇢ ⇠ 0.01 g cm 3 and T ⇠ 3 ⇥ 104 K (Figure 3 in Paxton et al.
2011). This maximum opacity is artificial since the adopted
radiative opacity in MESA is only valid for ⇢ . 0.01 g cm 3
at T ⇠ 3⇥104 K, as shown in Figure 2. For ⇢ &0.01 g cm 3 , itis interpolated to connect to the electron conduction opacity (Cassisi et al. 2007) at much higher densities. Considering plasma screening and electron degeneracy e↵ects (e.g.
Pauli blocking, Armstrong et al. 2014), the LANL radiative
opacity is valid at much higher densities, covering the highpressure range that we are interested in (Figure 2). By comparison, we can see that, for a given temperature, the LANL

radiative opacity continues to rise with density even to ourupper density limit of ⇢ = 1g cm 3 , which is dramaticallydi↵erent from the MESA opacity.
2.4

Combining Opacities

Proto-Jupiter’s Envelope

Various opacities from di↵erent opacity databases, together
with their valid range, are shown in Figure 2. The top threepanels show the atomic, molecular, and dust opacities weadopt. The bottom two panels show the solar abundance
opacities used in MESA (Paxton et al. 2011) and ATLAS9(Castelli & Kurucz 2003). Since MESA and ATLAS9 arestellar structure codes, their adopted opacities miss the ⇢ T
condition of the planet interior.
Our combined opacities (LANL+Freedman+DSHARP)
are shown in Figure 3. At 100 K < T <1000 K, moleculesand dust coexist and they all contribute to the total opacity.
Since Freedman et al. (2008) didn’t provide the monochromatic opacity, we cannot derive the total monochromatic
opacity to calculate the mean opacities. Thus, we simply
pick the maximum between the molecular and dust mean
opacities as the total opacity. Considering that the molecularopacity is normally significantly smaller than the dust opacity, the derived opacity should approximate the real mean
opacity reasonably well. For the ⇢ T region that does nothave valid opacity data, we use the opacity at the smallest or

MNRAS 000, 1–24 (2021)

5

8
8

Z. Zhu et al.

Z. Zhu et al.

• 適当な円盤モデルを作り、その中に10地球質量のコアをおいた。r=5au• R=5 AU, the disc’s surface density is 488 g/cm2,

the midplane tempera- ture is 66 K, the midplanedensity is 7×10−11 g/cm3, and the disc’s aspectratio (H/R) is 0.037.
• 惑星の降着による明るさはL = GMpMp/rp, which is L
Figure 5. The density structure of the 3-D isolated sphere (the left panel) and 3-D envelope-in-disc (the right panel) simulations with
our fiducial setup. The green surface at the center is the iso-surface with a constant radial radiation flux. The iso-surface is not smooth
due to the convective motion within the envelope.

=5.92×1027 ergs/s• でも、実際には円盤が散逸していくともっと低くなるので、今回は手で1/10の明るさにしたものも• (Athena++
作った。
• FLDやM1とも違う輻射の解き方。
Figure 5. The density structure •of *片岡the 3-D (手で出てくるエネルギー量を適当にエンベ
isolated sphere (the left panel) and 3-D envelope-in-disc (the right panel) si
our fiducial setup. The green surface at the center is the iso-surface with a constant radial radiation flux. The iso-surfac• Jiang et al. (2014) のように輻射輸送を陽にとい
due to the convective motion withinロープに加熱機構として入れてるみたいです)the envelope.

Table 1. Di↵erent setups for isolated-sphere and disc models

L/(1.54 ⇥ 10 6 L )amax for dust
Tirr
tend /t p for 3-D spheretend /t p for 3-D disc

Fiducial

HighL

BigDustHotDisk

LowL

LowLBD

1
1 mm
66 K
7.68
7.20

10
1 mm
66 K
6.79
7.00

1
10 cm
66 K
7.10
7.01

1
1 mm
174 K
7.26
8.30

0.1
1 mm
66 K
6.94
7.18

0.1
10cm
66
5.47
8.00

た。+ reduced time approachdiative transfer methods, and compare them against the an-

2⇡ in the azimuthal direction. We have adopted a reflecting boundary condition in the ✓ direction and a periodic
boundary condition in the direction. The heat capacity
ratio is chosen as 1.4 and the mean molecular weight ischosen as 2.35, considering that the gas mainly consists ofmolecular hydrogen at our studied density and temperature
range. A global density floor of 10 10 -10 8 ⇢0 has normallybeen adopted. The smoothing parameter r s for the gravitational force is chosen as 0.1 rin .
For radiative transfer calculations, we have used the angular discretization with respect to the local coordinate (r, ✓,) in each cell. We have 8 longitudinal angles and 6 polar angles in the 3-D simulations (a total of 96 discrete directions
including both inward and outward directions) and 20 polar
angles in the 1-D simulations. At the outer radial boundary, we assume that there is incoming isotropic radiationfrom the background medium (e.g. stellar irradiation) witha temperature of 66 K. With such a boundary condition, our

alytical results.
Table 1. Di↵erent setups for isolated-sphere and disc models
When the envelope is radiative, we can calculate the envelope’s thermal structure analytically. For a steady state,
the second momentum equation of the radiative transfer
Fiducial HighL
equation becomes• 定常状態に移行した後に、陰解法でもう１回ときなおした(Jiang 2021).

r · Pr = T ⇢Fr ,• タイムステップは短くなっちゃうがいい感じに
とける

(11)

where Pr and Fr are the radiation pressure tensor and the radiation flux, and T is the total opacity. With the Eddington
approximation, we have
1 @Er
L= T ⇢.
3 @r
4⇡r2 c• 光速は、陽解法では1/2e5, 陰解法では1/10(12)where T is the total opacity (including the absorption andscattering opacity) and c is the speed of light. With irradiation from a blackbody having a temperature of T irr , we use
the two stream approximation to derive theat2⇡temperaturein the azimuthalL/(1.54 ⇥ 10 6 L )amax for dust
Tirr
tend /t p for 3-D spheretend /t p for 3-D disc

1
1 mm
66 K
7.68
7.20

10
1 mm
66 K
6.79
7.00

direction. We have adopted a reflect-

BigDustHotDisk

LowL

LowLBD

1
10 cm
66 K
7.10
7.01

1
1 mm
174 K
7.26
8.30

0.1
1 mm
66 K
6.94
7.18

0.1
10cm
66
5.47
8.00

diative transfer methods, and compare them aProto-Jupiter’s Envelope

1112

Z. Zhu et al.

Figure 8. The radial profiles of various quantities for 1-D (green curves), 3-D isolated sphere (blue curves), and 3-D disc (red curves)models with our fiducial setup. All quantities are spherically averaged over grids, except for the lower left panel which shows the sphericallyintegrated energy flux (solid curves: radiative fluxes, dotted curves: convective fluxes from Eg vr ). The energy fluxes have been averaged
over 20 snapshots over a time span of 0.2 planetary orbits. The energy fluxes, together with the pressure and temperature used in thelower right panel, have also been smoothed over 4 radial grids. The vertical dashed line in the temperature panel labels rH (which is also
very close to rB in our fiducial case). Clearly, convection is prohibited in the 1-D model so that r can be higher than rad .

• まず、3D isolated model
fiducial: 密度や温度には非対称構造はないが、亜音•
isymmetric and quiescent in the hotter disc or with the low
After understanding the results for our fiducial case, weFigure 7. The density (upper panels), temperature (middle panels), and vr (normalized to the local sound speed, lower panels) for four
3-D isolated sphere models at the ✓ = ⇡/2 plane at the end of each simulation. Convection in the HighL case is so strong that we adjust
the vr /c s colorbar for the HighL case to [-2, 2]. The left two models show convection while the right two models do not show convection.

速の対流が見えるcan study how di↵erent envelope parameters a↵ect the envelope structure. As shown in Figure 7, the higher luminosity
in “HighL” drives a much stronger convection. The colorbar
for vr /c s,0 is adjusted to [-2,2] accordingly, and we can clearly
see that the turbulence becomes transonic. Such transonicmotion does not provide enough time for the envelope to adjust itself from the turbulent motion. Thus, the density andtemperature structure is not axisymmetric. We can clearly
see turbulent features in the ⇢ and T panels. In the left panels of Figure 9, we see similar behavior as the fiducial case. In

opacity (from the bigger dust in the envelope). Most importantly, due to the spherical symmetry and the lack of motion,
the envelope structure is almost identical between 1-D and
3-D isolated sphere simulations. This is demonstrated in the
middle and right columns of Figure 9, where the green andblue curves perfectly overlap with each other in these radiative envelopes. The r is smaller than rad everywhere forboth the 1-D and 3-D models. The convective flux is also significantly smaller than the radiative flux, again confirmingthat the envelope is convectively stable. Due to the radiative• HighL: 対流 このパネルだけ速度[-2,2], 超音速乱流

in 1-D radiative simulations, r is smaller than rad in mostregions, except for a narrow r range in the LowL case wherer is barely higher than rad . Since the envelopes are radiative,
1-D and 3-D isolated sphere simulations are almost identical. On the other hand, the envelopes have not fully reachedsteady states with such a low luminosity (especially for the
LowLBD case). The envelopes are still contracting with significant vr so that the convective flux (Eg vr ) is still high. The
radiative flux in the LowLBD case is still higher than our input flux of 1.54⇥10 7 L . The radiative flux is actually close
to the convective flux suggesting that the energy increase
due to the contraction is mostly radiated away. Longer 1-D
radiative simulations suggest that steady states (when thecontraction stops) can be reached at t⇠20 planetary orbits(20 t p ).
4.2

3-D disc simulations

Due to the Keplerian shear, the 3-D disc simulations exhibit
spiral arms that extend from the planet. We can see density
concentration along the spirals in the upper panels of Figure

11. These spirals can also perturb the disc’s velocity structure (Rabago & Zhu 2021), as shown in the lower panelsof Figure 11 where the velocity perturbation ( vr ) suddenly
changes sign along the spirals at y/H=±1 when x/H=±2.
Goodman & Rafikov (2001) pointed out that the strength ofa spiral is mainly determined by the mass ratio between theplanet mass and the disc thermal mass (M p /Mth ). For the
Fiducial and the BigDust models, their disc temperatures
are the same and thus M p /Mth is also the same. Then, theiramplitudes of velocity perturbation at the spirals should also
be similar, as shown in Figure 11 (the leftmost and rightmost
bottom panels). For the HotDisk model, Mth , which is proportional to c3s , is a lot higher so that M p /Mth is a lot smaller
than our fiducial case. Thus, the excited spirals are much
weaker, demonstrated as the less apparent spirals in the ⇢panel and smaller vr /c s,0 in the velocity panel. Besides the
spirals, we can also see the planet-induced horseshoe orbit
at x/H⇠ ±0.5 when y/H=±2.
On the other hand, the envelope structure is very similar between the 3-D isolated sphere and the 3-D disc models.
For our fiducial case, the envelope is also convectively un-

12• 円盤の中においた場合• fiducial; 孤立のときとenvelope構造はあんまりか

Figure 11. Similar to Figure 7 but for 3-D disc simulations. vr is the velocity di↵erence between this snapshot and the initial condition(from the Keplerian shear). Again, convection in the HighL case is so strong that we adjust the vr /c s colorbar in the HighL case to [-2,2].

わらない。対流不安定っぽい。
no constant entropy region beyond 0.1-0.2 r . The density
and temperature profiles are almost identical to those in the
5.1 New procedures for 1-D
semi-analytical models• が、ちょっと温度低いくて密度高いがこれは円盤
isolated sphere calculations. Recycling does happen (as insection 4.3), but the timescale of recycling is longer than theBased on results from our direct 3-D simulations, we canthermal timescale of recycled material (Section 5.2). Thus,
improve previous 1-D modelsの幾何的な影響かも。それか、孤立モデルのほう
for calculating the envelope’s
the temperature structure is hardly a↵ected by the recycling
structure, mainly regarding the outer boundary condition
and is similar to that of an isolated sphere.
in the 1-D models. Previous が対流構造が外側まで続いているかも
approaches use the minimum
5

DISCUSSIONof the planet’s Hill radius and Bondi radius as the outer

B

Considering that the planet’s gravity does not abruptly

Z. Zhu et al.

• なぜ孤立モデルと円盤モデルで惑星エンベロープ構造

16

Z. Zhu et al.

にあんまりさがないのか？

• passive scalarをおいて、その動きを見た。
• *片岡 passive scalarなんだかわかんないんですが、テスト粒子的なふるまいと同じですかね。

• convective envelopeでは、物質が入れかわて散るが、radiative envelopeでは外側しかものが入れ替
わらない• 片岡メモ：big dust はopacity低いからあんま冷えない。hot diskは外側が熱いからあんま冷
えない→輻射層支配になりがち

Figure 12. The evolution of the passive scalar at the disc midplane for the fiducial model (upper panels), the big dust model (middle
panels), and the hot disc model (bottom panels) at di↵erent times (left to right panels) after the passive scalar is injected.

with f s = 1) to derive the envelope structure. Similar to the
traditional approach, r is calculated with the thermal di↵usion equation, and we switch to r = rad whenever r > rad .
Compared with our 3-D radiation hydrodynamical simula-simulations can only simulate very limited spatial and timescales. Thus, it is important to estimate the various timescales for the entire envelope. Particularly, we want to compare the recycled material’s cooling timescale with the re-Denmark
e-mail: sarel.vanderwalt@nbi.ku.dk
2
Department of Space, Earth and Environment, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
3
Institute of Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100
Torun, Poland
4
CY University, Observatoire de Paris, CNRS, LERMA, F-95000 Cergy, France
5
Departments of Astronomy and Chemistry, University of Virginia, Charlottesville, VA 22904 USA
6First
results:
observationsof Nanjing
CygX-N30
School of Astronomy and Space Science,
Nanjing
University,
163 Xianlin Avenue,
210023, People’s Republic of China
7
Key Laboratory of Modern
Astronomy and1Astrophysics (Nanjing
University),
Ministry of Education,
Nanjing
210023, People’s
1
1
2,3
1
4,
1
S. J. ofvander Walt , L. E. Kristensen , J. K. Jørgensen , H. Calcutt , S. Manigand , M. el Akel , R. T. Garrod5 , andRepublicChina

A&A proofs: manuscript no. main_arxiv

Protostellar Interferometric Line Survey of the Cygnus X region(PILS-Cygnus)

Received . . . ; accepted . . .

folded the dust-to-gas
rameter is not needed i
Furthermore, we correµmH instead of mH2 ,opacity of 0.43. We cmarginally optically th

K. Qiu6, 7

3.2. Molecular line em

1

rXiv:2109.03640v1 [astro-ph.SR] 8 Sep 2021

Niels Bohr Institute & Centre for Star and Planet Formation, University of Copenhagen, Øster Voldgade 5-7, 1350 Copenhagen K.,
Denmark
ABSTRACTe-mail: sarel.vanderwalt@nbi.ku.dk
2
Department of Space, Earth and Environment, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
Context. Complex
organic molecules (COMs) are commonly detected in and near star-forming regions. However, the dominant3
Institute of Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100
process in theTorun,
releaseof these COMs from the icy grains —where they predominately form— to the gas phase is still an open
Polandquestion. 4 CY University, Observatoire de Paris, CNRS, LERMA, F-95000 Cergy, France
5
Aims. We investigate
theoforigin
of COMemissionUniversity
in a high-mass
protostellar
source,CygX-N30
Departments
Astronomy
and Chemistry,of Virginia,
Charlottesville,
VA 22904
USA MM1, through high-angular6
School of Astronomy
and Space
Nanjingbroad
University,
163 Xianlin
resolution interferometricobservations
overScience,a continuous
frequency
range.Avenue, Nanjing 210023, People’s Republic of China
7
Key Laboratoryof Modern Astronomy
and Astrophysics(Nanjingof Education,
210023,
Methods. We used
32 GHz Submillimeter
Array (SMA)
observations
withUniversity),
continuousMinistry
frequency
coverage Nanjing
from 329
to 361People’s
GHz at an
Republic
angular resolutionof ⇠of100China
to do a line survey and obtain a chemical inventory of the source. The line emission in the frequency range

was used to Received
determineand excitation temperatures for the COMs. We also mapped out the intensity distribution of. . .column; accepteddensities...
the di↵erent species.
Results. We identified approximately 400 lines that can be attributed to 29 di↵erent molecular species and their isotopologues. We find
ABSTRACTthat the molecular peak emission is along a linear gradient, and coincides
with the axis of red- and blueshifted H2 CO and CS emission.
Chemical di↵erentiation
is detected
this gradient,
with
the O-bearing
speciespeaking
towards
one componentof theContext. Complex
organicalongmolecules(COMs) arecommonly
detectedmolecularin and nearstar-forming
regions.
However,the dominantsystem and process
the N- inandpeaking
the other.
Thetheychemical
gradientis o↵setfromparalleltheS-bearing
release of species
these COMs
from towards
the icy grains—wherepredominately
form—
to thegas but
phase
is still toan theopenaxis
through the question.
two continuum sources. The inferred column densities and excitation temperatures are compared to other sources where
Aims. We Only
investigate
the origin of
COM emission
in a HDO,
high-mass
protostellar
CygX-N30
MM1,
throughleading
high-angularCOMs are abundant.
one deuterated
molecule
is detected,
while
an uppersource,
limit forCH2 DOHis derived,
to a D/H
resolution interferometric observations over a continuous broad frequency range.
ratio of <0.1%.
Methods.
We usedthat
32 GHzSubmillimeter(SMA)COMobservations
withiscontinuous
coverageoffrom
to 361
GHz atanConclusions.
We conclude
theorigin of theArrayobserved
emissionprobablyfrequency
a combination
the 329
young
stellarsources00
angular resolutionof ⇠ 1material
to do a line
surveyand obtaina chemical
inventory ofathe
source.
The line andemissionin theclose
frequency
range
along with accretionof infallingonto
a disc-likestructuresurrounding
young
protostar
locatedto oneof thewas used to determine column densities and excitation temperatures for the COMs. We also mapped out the intensity distribution ofcontinuum sources.
Thisspecies.
disc and protostar are associated with the O-bearing molecular species, while the S- and N- bearing species
the di↵erent
on the otherResults.
hand arewith the othercore,which isto probably
protostarspecies
that isandslightly
more evolved
Weassociatedidentified approximately
400continuum
lines that canbe attributed
29 di↵erenta molecular
their isotopologues.
Wethanfind theother component
the system.
The lowisD/H
likelyreflects
pre-stellar
formedtheat warmthat theofmolecularpeak emission
alongratio
a linear
gradient,
and acoincides
withphasethe axiswhereof red-theandCOMs
blueshifted
H2 COonandCSicesemission.
temperaturesChemical(⇠ 30 K),
where theisdeuterium
fractionation
would
have
been inefficient.
The observations
andoneresultspresented
di↵erentiation
detected along
this gradient,with theO-bearingmolecular species
peaking towards
componentof thehere
and the N-ofandS-bearing
speciespeakingand
towardsother.resolution
The chemical
gradientis o↵set frombut parallelto theaxis
demonstratesystem
the importancegoodfrequency
coveragehigh theangularwhen
disentangling
the origin
of COMemission.

Fig. 1. Observed continuum
emissiona frequency of 345 GHz,
A&A proofs:
manuscript at
no. main_arxiv
showing the four continuum sources MM1a, MM1b, MM2, and MM3.
The beam is shown in the bottom-left corner, and has dimensions
000. 85 ⇥ 000. 66, with position angle 12.1 . The VLA radio sources VLA1,
VLA2, and VLA3 are labelled and marked with black crosses, with theemission peak positions of MM1a and MM1b shown by plus symbols,
and the dashed line representing the axis through these positions. Also
shown are the large-scale CO emission (red and blue arrows) and thedisc-like structure (dotted line) identified by Hutawarakorn et al. (2002).

Figure 2 shows a speof peak continuum em
ous frequency covera
approximately 400 m
the MM1 source, orLine identification wa
in Snyder et al. (200
SIS3 (Centre d’Analy
et Synthétiques; Vasteet al. 2001, 2005; En
1998) molecular spect
synthetic spectrum. Pr
to the synthetic spectr
observed spectrum inlines above 3 . From
ferent molecules and(CH3 OH, C2 H5 OH, C
The molecular tra
low, with the oxygen-b
species in Table 3, and4, together with SiO,
imately 40 lines thatlines (at frequencies n354.44896 GHz and2). A full list of detect
8.

mm and centimetre (cm) observations from the Very Large Array (VLA) telescope. VLA1 is located to the west and slightly
to the north of the MM1b submm peak, while VLA2 is to thenorth of the MM1a peak (southwest of MM1b). VLA3 is located very close to but slightly to the east of MM1a (see also
Rodríguez-Kamenetzky et al. 2020, for recent high-resolution
VLA observations of the region). The red and blue arrows reprethrough the two continuum sources. The inferred column densities and excitation temperatures are compared to other sources wheresent the large-scale CO emission (PA ⇠65 from north) centred
Key words.COMs
Astrochemistry;
formation;
Stars:
protostars;
ISM:
molecules;
Submillimeter:are abundant.Stars:
Only one
deuterated
molecule
is detected,
HDO,
while an ISM:
upper individual
limit for CHobjects:
derived, leading
to a D/H
2 DOH is W75N(B);at VLA2, with the dotted line representing the disc-like structure 3.3. Integrated molec
ratio of <0.1%.
ISM.
(PA ⇠155 ) traced by OH masers, as identified by Hutawarakorn
Conclusions. We conclude that the origin of the observed COM emission is probably a combination of the young stellar sources
et al. (2002).
The molecular peak p
along with accretion of infalling material onto a disc-like structure surrounding a young protostar and located close to one of the Fig. 19. Relative abundancesof each molecule relative to the column density of CH3 OH at each respective position. The white arrows represent
whetherthe dust
is opticallyintensity emission ma
continuum sources. This disc and protostar are associated with the O-bearing molecular species, while the S- and N- bearing species upper limits, whereas theToblackcheckbars represent
the uncertainties(see Tables
5, 6 and 7). thick or not, the first. Introduction
the ice a(Öberg
Nearmore
the evolved
forming
on the other hand are associated with the other continuum core,icals
whichinis probably
protostar 2016).
that is slightly
thanstars,
the where
step is to calculate the dust mass. Here, this is only done towards had more than one li
other component of the system. The low D/H ratio likely reflects
a pre-stellar
phase
the COMs
on theices at warm
T dust& 100 K,
thewherewater-rich
iceformed
mantels
sublimateo↵ the dust
the MM1a source, which is the brightest continuum source in weighting scheme —omplex organictemperatures
molecules(⇠(COMs;
molecules
with fractionation
at least sixwould
30 K), where
the deuterium
have beeninefficient.
The observations
resultswhere
presented
herecan be dithe field. The total mass (gas + dust) can be calculated using the emission-free region
grains,releasingCOMs
into the gasandphase,they
demonstratetheimportanceofgoodfrequency
coverageandhighangularresolution
whendisentangling
theoriginofCOMemission.
toms, of which at least one is carbon; Herbst & van Dishoeck rectly observed at submillimetre (submm) wavelengths (the sofollowing relation (e.g. Artur de la Villarmois et al. 2018):
crease the intensity an009) are foundKey
everywherein and nearstar-forming
regionswords. Astrochemistry;Stars:
formation; Stars:
protostars; ISM: molecules; ISM: individual objects: W75N(B); Submillimeter:
the molecule. Only un

In search of infall motion in molecular clumps III:
HCO+ (1-0) and H13 CO+ (1-0) mapping observations toward the confirmed infall sources
YANG YANG , 1, 2, 3 Z HIBO J IANG , 1, 2, 4 Z HIWEI C HEN , 1, 2 Y IPING AO , 1, 2, 3 AND S HULING Y U 1, 2, 3
1 Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China
2 Key Laboratory of Radio Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China
3 University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026, China
4 Center astronomy and Space Sciences, China Three Gorges University, Yichang 443002, China(Received April 26, 2021; Revised August 26, 2021; Accepted August 30, 2021)

Submitted to ApJ
ABSTRACTThe study of infall motion helps us to understand the initial stages of star formation. In this paper, we use
the IRAM 30-m telescope to make mapping observations of 24 infall sources confirmed in previous work.
The lines we use to track gas infall motions are HCO+ (1-0) and H13 CO+ (1-0). All 24 sources show HCO+
emissions, while 18 sources show H13 CO+ emissions. The HCO+ integrated intensity maps of 17 sources show
clear clumpy structures; for the H13 CO+ line, 15 sources show clumpy structures. We estimated the column
density of HCO+ and H13 CO+ using the RADEX radiation transfer code, and the obtained [HCO+ ]/[H2 ] and[H13 CO+ ]/[HCO+ ] of these sources are about 10 11 –10 7 and 10 3 –1, respectively. Based on the asymmetryof the line profile of the HCO+ , we distinguish these sources: 19 sources show blue asymmetric profiles, andthe other sources show red profiles or symmetric peak profiles. For eight sources that have double-peaked blueline profiles and signal-to-noise ratios greater than 10, the RATRAN model is used to fit their HCO+ (1-0) lines,
and to estimate their infall parameters. The mean Vin of these sources are 0.3 – 1.3 km s 1 , and the Ṁin areabout 10 3 – 10 4 M yr 1 , which are consistent with the results of intermediate or massive star formation inprevious studies. The Vin estimated from the Myers model are 0.1 – 1.6 km s 1 , and the Ṁin are within 10 3 –10 5 M yr 1 . In addition, some identified infall sources show other star-forming activities, such as outflows
and maser emissions. Especially for those sources with a double-peaked blue asymmetric profile, most of them
have both infall and outflow evidence.

Draft version September 3, 2021
Typeset using LATEX twocolumn style in AASTeX63

A Morphological Classification of 18190 Molecular Clouds Identified in 12 CO Data
from the MWISP Survey
Lixia Yuan,1 Ji Yang,1 Fujun Du,1 Xunchuan Liu,2 Shaobo Zhang,1 Zehao Lin,1 Jingfei Sun,1 Qing-Zeng Yan,1
Yuehui Ma,1 Yang Su,1 Yan Sun,1 and Xin Zhou1
1 Purple Mountain Observatory and Key Laboratory of Radio Astronomy, Chinese Academy of Sciences,September 9, 2021

A&A proofs: manuscript no. 41985corr

mation about their formation history. It is expected that di↵erent
formation processes, such as core fragmentation, disk instability,
dynamical interactions, or a combination of di↵erent formation
channels, leave imprints on the mass ratio, periods, eccentricities, and mutual orbit inclination of hierarchical systems (Kozai
1962; Lidov 1962; Whitworth 2001; Sterzik & Tokovinin 2002;
Lee et al. 2019; Tokovinin & Moe 2020). In the last decades,
observational and theoretical e↵orts have led to a better underTowards full orbital characterisation using long-baseline infrared
standing of the formation and dynamical stability of such mul?
interferometry
tiple systems (Kiselev & Kiyaeva 1980; Tokovinin et al. 2006;
Eggleton 2009; Tokovinin 2018a; Hamers et al. 2021).
S. Zúñiga-Fernández1, 2, 3 ?? , J. Olofsson3, 1 , A. Bayo3, 1 , X. Haubois2 , J. M. Corral-Santana2 , A. Lopera-Mejía3 , Wide binaries show a strong preference to be in hierarchicalsystems in low density young associations (Elliott et al. 2016a;
M. P. Ronco1, 4 , A. Tokovinin5 , A. Gallenne7, 8, 9 , G. M. Kennedy6 , and J.-P. Berger10
Elliott & Bayo 2016) and star-forming regions (Joncour et al.
2017). The fact that this relation is not seen in the same propor1
tion in denser environments or systems in the field suggests that
Núcleo Milenio de Formación Planetaria (NPF), Valparaíso, Chile
this could be the result of dynamical processing or the unfold2
European Southern Observatory, Alonso de Córdova 3107, Vitacura, Casilla 19001, Santiago de Chile, Chileing of hierarchical systems (Sterzik & Tokovinin 2002; Reipurth
3
Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña 1111, Valparaíso, Chile1, 2, 3 ??
3, 1
3, 1
2
2
3
4
Instituto de Astrofísica - Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul - Santiago, 8970117 , Chile& Mikkola 2012). In that regard, characterising young (1-100Myr), hierarchical systems helps to observe their early evolution.
5
Cerro Tololo Interamerican Observatory | NSF’s NOIRLab, La Serena, Casilla 603, Chile
The formation
channels of hierarchical systems
1, 4
5
7, 8, 96
10 cannot be easily
6
Department of Physics, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK
determined by only characterising field stars, where billions of7
Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland
years of dynamical evolution may have erased their formation
8
Universidad de Concepción, Departamento de Astronomía, Casilla 160-C, Concepción, Chile
history. Consequently, the study of young (1-100 Myr) hierar9
Unidad Mixta Internacional Franco-Chilena de Astronomía (CNRS UMI 3386), Departamento de Astronomía, Universidad dechical systems is an important step to better understand their
1
Fig. 1: Schematic view of HD 98800 orbital configuration. The
Chile, Camino
al Observatorio
1515, Las Condes,
Santiago, Chile
NúcleoMileniodeFormación
Planetaria(NPF),
Valparaíso,
Chile
formation pathway. Large-scale surveys provide crucial infor- BaBb subsystem hosts a circumbinary disk in polar configura2 10 Université Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France
mation that helps to discover such multiple systems, but they are tion and is orbiting around the AaAb binary in a highly inclined
European Southern Observatory, Alonso de Córdova 3107, Vitacura, Casilla 19001, Santiago
de Chile, Chile
not well suited to finely constrain their orbital architecture. We orbit with a semi-major axis of ⇡ 45 au.
3 Received; Accepted
high-precision
radial velocity (RV)
followInstituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av.need
Gran
Bretañaastrometry
1111,andValparaíso,
Chile
up observations of the identified hierarchical systems to accu4
Instituto de Astrofísica - Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna
4860,
Macul
- Santiago,
8970117
ratelyconstrain
parametersof their inner andouter orbits., Chile Recently, the orbital characterisation of hierarchical systems
ABSTRACT
5
Cerro Tololo Interamerican Observatory | NSF’s NOIRLab, La Serena, Casilla 603, ChileThe HD 98800 is a well-known hierarchical quadruple star hosting disks has provided new insights on the mechanism in6 Context. HD 98800 is a young (⇠ 10 Myr old) and nearby (⇠ 45 pc) quadruple system, composed of two spectroscopic binariessystem, and a member of the 10-Myr old TW Hydrae associa- volved in the formation of multiple systems and their interaction
Department of Physics, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL,tionUK(Torres et al. 2008). Located at 44.9 ± 4.6 pc from Earth ac- with the disk (Kraus et al. 2020; Czekala et al. 2021). To betorbiting
around each other (AaAb and BaBb), with a gas-rich disk in polar configuration around BaBb. While the orbital parameters
7
cording
to theWarszawa,latest reduction of
Hipparcos data1 (van Leeuwen ter understand the source of disk misalignment and the formaNicolaus
Copernicus
Astronomical
Centre,PolishAcademyof
Sciences,
Bartycka
18,00-716
Polandof BaBb and AB are relatively well constrained, this is not the case for AaAb. A full characterisation of this quadruple system can2007), corresponding to a parallax of 22.27 ± 2.32 mas, it contion process behind hierarchical systems, better information on
8 provide insights on the formation of such a complex system.
Universidad
deworkConcepción,
Departamentode Astronomía,
Casilla
160-C,
Concepción,
Chile
sists
of two pairs of spectroscopic binaries (hereafter, AaAb and well-characterised multiple systems’ architectures will be necAims.
The
goal
of
this
is
to
determine
the
orbit
of
the
AaAb
subsystem
andrefinetheorbitalsolution
of
BaBb
using
multi-epoch
BaBb, see Fig 1). Both binaries orbit each other with a semi- essary. In that regard, the full characterisation of the HD 98800
9Unidad Mixta
Internacional
Franco-Chilenade (VLTI)/PIONIER
Astronomía and(CNRS
UMI 3386), Departamentode Astronomía, Universidad deinterferometricobservations
with the Very Large
Telescope Interferometerradial velocities.
major axis of ⇡ 45 au (Tokovinin et al. 2014). The AaAb sys- quadruple system presents an opportunity to expand the sample
Methods.
The
PIONIERalobservations
provide relative
astrometricpositions Santiago,
and flux ratiosChilefor both AaAa and BaBb subsystems.tem is a single-lined spectroscopic binary (SB1) with a period of hierarchical systems hosting a protoplanetary disk.
Chile,
CaminoObservatorio
1515,
Las
Condes,of 262 days (Torres et al. 1995). The mass of the Aa was estiIn this work, we present new long-baseline infrared inter10 Combining the astrometric points with radial velocity measurements, we determine the orbital parameters of both subsystems.
Université
Grenoble
Alpes,CNRS,
IPAG,F-38000
Grenoble,
FranceResults. We refined the orbital solution of BaBb and derived, for the first time, the full orbital solution of AaAb. We confirmedmated from pre-main sequence evolutionary models as 1.1 ± 0.1 ferometric observations of both AaAb and BaBb subsystems, as
the polar configuration of the circumbinary disk around BaBb. From our solutions, we also inferred the dynamical masses of AaAbM (Prato et al. 2001). The BaBb subsystem is a double-lined well as new RV measurements from original observations and(MAa = 0.93 ± 0.09 and MAb = 0.29 ± 0.02 M ). We also revisited the parameters of the AB outer orbit.
spectroscopic binary (SB2) with a period of 315 days, the as- archival reduced spectra. The new interferometric observations
Received;
Acceptedpresented in resolve the relative position
Conclusions. The orbital parameters are relevant to test the long-term stability of the system and to evaluate possible formationtrometric orbital solution of this binary was firstof Ab with respect to Aa for the ⊙first
Aa
Ab
scenarios of HD 98800. Using the N-body simulation, we show that the system should be dynamically stable over thousands of orbitalBoden et al. (2005) using five Keck Interferometer (KI) epochs time, providing one of the missing keys for the full characterisaperiods and that it made preliminary predictions for the transit of the disk in front of AaAb which is estimated to start around 2026.combined with Hubble Space Telescope astrometry, and avail- tion of this quadruple system. Additionally, we also present two
We discuss the lack of a disk around AaAb, which can be explained by the larger X-ray luminosity of AaAb, promoting faster photo-able RV observations. From this orbital solution, Boden et al. new astrometric positions for BaBb, allowing us to refine the
ABSTRACTevaporation of the disk. High-resolution infrared spectroscopic observations would provide
radial velocities of Aa and Ab (blended(2005) estimated a parallax of 23.7 ± 2.6 mas, and dynamical orbital solution reported in Boden et al. (2005). With the newlines in contemporary observations), which would allow us to calculate the dynamical masses of Aa and Ab independently of themasses for Ba and Bb of 0.699 ± 0.064 and 0.582 ± 0.051 M , orbital solutions of AaAb and BaBb, we re-estimated the orbital
parallax of BaBb. Further monitoring of other hierarchical systems will improve our understanding of the formation and dynamicalrespectively. The BaBb pair also harbours a bright circumbinary parameters of the AB outer orbit, evaluate the dynamical stabilContext.
HD 98800 is a young (⇠ 10 Myr old) and nearby (⇠ 45 pc) quadruple system,composedof twoet al.spectroscopic
protoplanetary
disk (Skinner
1992; Zuckerman &binaries
Becklin ity of this system, and discuss possible formation scenarios forevolution of these kinds of systems.
1993), and BaBb.
ALMA observations
revealed
that theparameters
disk and the this 2+2 quadruple.
orbitingaround
each
other
(AaAb
and
BaBb),
withagas-rich
disk
in
polar
configuration
aroundWhiletheorbitalKey words. binaries (including multiple): close – stars: pre-main sequence – stars: individual: HD 98800 — techniques: high angularbinary orbital planes are perpendicular to each other (Kennedy
et al. 2019). Numericalof
simulations
suggest that thissystem’exotic’ (yetof resolution
BaBb andAB arerelatively well constrained, this is not the case for AaAb. A full characterisation
this quadruplecan— techniques:interferometricstable) configuration can be reached in some multiple systems, 2. Observations, astrometry, and RV
provide insights on the formation of such a complex system.
the so-called polar configuration (Verrier & Evans 2008; Farago 2.1. PIONIER observations and data reduction
Laskar 2010;
Aly et al.
Dynamical
studiesAims. The goal of this work is to determine the orbit of the AaAb subsystem and refine the &orbital
solutionof2018).
BaBb
usingevolution
multi-epoch

The HD 98800 quadruple pre-main sequence system

The HD 98800 quadruple pre-main sequence system

Towards full orbital characterisation using long-baseline infraredinterferometry?

rXiv:2109.02841v2 [astro-ph.SR] 8 Sep 2021

S. Zúñiga-Fernández
, J. Olofsson , A. Bayo , X. Haubois , J. M. Corral-Santana , A. Lopera-Mejía ,M. P. Ronco , A. Tokovinin , A. Gallenne, G. M. Kennedy , and J.-P. Berger• HD 98800 (10Myr, 45pc)• 4重星 AaAbとBaBb• AaAbのほうの軌道をよくきめた• VLTI/PIONEER• 質量も出た(M = 0.93 ± 0.09 and M = 0.29 ± 0.02 M ).
• 2026年にAaAbの前を円盤が通る• AaAbの周りに円盤がないのはX-線のせいか？