Star Formation
Newsletter
速報Seminar
2023/06/30
古屋 玲#364 29-42

まずは紹介しない論⽂の紹介

00Paris, France
5
Observatoire de Paris,
PSL University,
Sorbonne
Université,75014 Paris,
FranceModeling
the early
massejectionLERMA,in jet-driven
protostellar
Accepted January 12, 2022

outflows. Lessons from Cep E.
P. R. Rivera-Ortiz1, 2 , A. de A. Schutzer2 , B. Lefloch2, 3 , and A. Gusdorf4, 5

ABSTRACT
Instituto de Radioastronomı́a y Astrofı́sica, Universidad
Nacional Autónoma de México, P.O. Box 3-72, 58090, Morelia, Michoacán, Mexico
e-mail: p.rivera@irya.unam.mx
Context. Protostellar 2jets
outflows
areInstitut
an important
agentof starde formation
as38000
they
carry away a fraction ofUniv. and
Grenoble
Alpes, CNRS,de Planétologie etd’Astrophysique
Grenoble (IPAG),
Grenoble,
Francemomentum and energy,
whichisneededforgravitational
collapseandprotostellar
massaccretiontooccur.
3
Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geo↵roy Saint-Hilaire, 33615 Pessac,
Aims. Our goal is to provide
France constraints on the dynamics of the inner protostellar environment from the study of the
4
Laboratoire de Physique de l’ENS, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005
outflow-jet propagationParis,
away
from the launch region.
France5Observatoirede Paris, PSL University,
Sorbonne Université, LERMA,
75014
Paris, France
Methods. We have used
the axisymmetricchemo-hydrodynamicalcode
Walkimya-2D
to numerically model and repro-

1.06146v2 [astro-ph.SR] 4 Feb 2023

1

duce the physical and Accepted
CO emissionof the jet-driven outflow from the intermediate-mass protostar CepE-mm,
January 12,properties
2022
which was observed at ⇠ 800 au resolution in the CO J=2–1 line with the IRAM interferometer. Our simulations take
into account the observational constraints available on ABSTRACT
the physical structure of the protostellar envelope.
Context.
Protostellar jets
and outflows areimportantagent of star andformation
as they carry away
a fraction
Results. Walkimya-2D
successfully
reproduces
theanmain
qualitative
quantitative
featuresofofthe Cep E outflow andmomentum and energy, which is needed for gravitational collapse and protostellar mass accretion to occur.
the jet kinematics, naturally
accounting
for theirtime
variability.
Signaturesof internal
shocksAims. Our goal
is to provide constraints
on thedynamicsof the inner protostellar
environment
from the studyof the are detected as knots
outflow-jet
propagation
away
from the launch
region. the young emitted knots interact with the dense circumstellar
along the jet. In the early
times
of
the
ejectionprocess,
Methods. We have used the axisymmetric chemo-hydrodynamical code Walkimya-2D to numerically model and reproenvelope through high-velocity,
shocks,of whichstrongly
decrease
the COprotostar
gas abundancein the jet. As timeduce the physicaldissociativeand CO emission properties
the jet-driven
outflow fromthe intermediate-mass
CepE-mm,3
which was observed at ⇠ 800 au resolution in the CO J=2–1 line with the IRAM interferometer. Our simulations takeproceeds, the knots propagate
moresmoothly
throughtheenvelopeanddissociative
shocksdisappear
after
⇠
10
yr.
into account the observational constraints available on the physical structure of the protostellar envelope.
Results.
Walkimya-2D
successfully
the mainqualitativeand quantitativeof the Cepoutflowand dissociative phase in
The distribution of CO
abundance
along
thereproduces
jet showsthatthe latterbearsfeatures
memoryof Etheearly
the jet kinematics, naturally accounting for their time variability. Signatures of internal shocks are detected as knots
the course of its propagation.
of thefieldtheshows
thatknots
theinteract
jet material
mainlyconsists of gas entrained
along the jet.Analysis
In the early timesof thevelocity
ejection process,young emittedwith the dense
circumstellar
through andhigh-velocity,dissociative away
shocks, whichstrongly
the CO at
gas abundance
the jet. As
from the circumstellarenvelope
envelope
accelerated
fromthe decrease
protostar
700 au inscale.
Astimea result, the overall jet
3proceeds, the knots propagate more smoothly through the envelope and dissociative shocks disappear after ⇠ 10 yr.
mass-loss rate appearsThehigher
thantheactualmass-ejection
rateby
a memory
factorof⇠the3.early dissociative phase in
distributionof COabundance
along
the jet shows that thelatterbears
course of its propagation.
Analysisof the velocity fieldshows thatthe comparison
jet material mainlywith
consistsof gasentrained
Conclusions. Numericalthemodeling
of
the
Cep
E
jet-driven
outflowandtheCO
observations have allowedfrom the circumstellar envelope and accelerated away from the protostar at 700 au scale. As a result, the overall jet
us to peer into the outflow
mechanism
withunprecedented
and to retrieve the history of the mass-loss
mass-lossformation
rate appears higher
than the actual
mass-ejection
rate by a factordetail⇠ 3.
Conclusions. Numerical modeling of the Cep E jet-driven outflow and comparison with the CO observations have allowed
events that have shaped
outflow.
us to thepeer into
the outflow formation mechanism with unprecedented detail and to retrieve the history of the mass-loss
events that have shaped the outflow.

Key words. stars: formation— ISM: jets and outflows — astrochemistry
Key words. stars: formation — ISM: jets and outflows — astrochemistry01nctionbased
on COIt andH2 .noticing they outflows.
ts are easily
identified.
is worth
daptativeuses
seven alonglevelstheofjet,refinement,
pand radiallymesh
as they
propagate
wings
innercells,
bowshocks,
the slower mate096⇥of1024in a sincecomputational
domain (5 ⇥ts with the faster material ejected at later times. 4. Gas acceleration
au, allowing a resolution as high as 12.2 au pers appear to drive the formation of complex strucreflective
boundary
for theeWethe used
outflowacavity
as can beseen in thecondition
bottomandmovinga freeknots
outflowboundary
forg.axis
2. Fasttend toaccumulateconditionattheborders.
bow, increasing
at meshthe tip.is
After
her
The thesizedensityof thelarge enoughe knots located at distance > 15000 au display
uterboundaries do not a↵ect the simulation. Thea typical size of 1000 au.
cted
on gasthedensity
left sideof the assimulation
pects theto decreasea result of box withalconditions
injet
Table
1.
xpansionin the indicatedcourse of the
propagation.

分⼦流の成⻑が進むにつれ、先端でこわされる。
￼≃ 900yrs経った
後ろの領域ではCOが再⽣される(グラフのわずかな平坦部)

1500yrs￼
も経つとCOが再⽣された領域は
1e4 AU付近まで広がる(グラフの平坦部)

ooking in detail at the jet density field at e. g.
(second panel in Fig. 2), it appears that thedoes not decrease
along the narconditions:the monotonically
protostellar core
he density distribution of fast material along theanalyzedin Sectioncore,
5.2. we have adopted
on direction
describeis the
protostellar
500conditions
yr, a secondderived
outflow cavity
has now etformed.
alby Crimieral. (2010) from
utflow cavity has reached a size of ⇡ 15000 au andDtomodelingof the5000
dust
spectralenergy distribu00
up
a radius of aboutau (6at the distanceFig. 3. Cep E northern outflow lobe. Position-Velocity diagram
een
24µm
and
1300µm,using
theradiative
transmm), and the head of the outflow has reached a of the
CO J= 2–1 line emission along the jet main axis. Posi400
tions are in arcsec o↵set relative to the location of the driving⇥ 10 au (Ivezic(34 ). At&latertimes,1997).
the second
D2.8DUSTYElitzur
The temperaprotostar=Cep E-A. First contour and contour interval are 10%
ands
to reacha similar
radiusof ⇡ 5000
ed by
a brokenradialpower
law au.
T / r withion of Figure 2 reveals that a complex network of of the peak intensity. We have superimposed in yellow the beste range 50–300 K and = 0.4 in the range 7 K–
ense structures (n ⇠ 105 –106 cm 3 ) forms inside fitting solution (V Vlsr )/V0 = exp( 0 / ) where 0 = 690 au(Schutzertoet al. 2022).
Crimier’s
thecandensity
is ofassumed
w cavity verymodel,
early. One
note theprofile
presence
radius
70 first
au 1000
and yr.
toAsfollow
single radial
along
therjetin thecan beaseenin =eldistribution
at t= 1000 yr,n(r)=a filament
Cep E displays evidence of gas acceleration along the jetn0 ⇥has(r0formed/r)↵ . along
cated at R = 500 au, it is detected up to z = over a distance of 1000 au away from the protostar (Fig. 3).
er
to avoid density singularities in the limit r ! 0
nd appears as a thin, yellow, wiggling structure This e↵ect was reported and observationally characterizedmericalhave ofadopted
the byslightly
the jet. Wemodeling,also note thewepresencea ”shell”, or
Schutzer etal. 1.
(2022).
We showin the bottom
panel
Fig.
CO 2–1line emission
in theCep E-mm outflow as ob00
density
ch formedprofilein the dense protostellar envelope and of Fig. 4, theserved
synthetic
Position-Velocity
diagramof the (Lefloch et al. 2015).
with
the
PdBI
at
1
resolution
wly (⇠ 20 km s 1 ) as it propagates over 8000au CO gas along the main axis of the jet. Two kinematical
Four
main
velocity
components
are detected: a) the outflow
n0 the jet reached 40 ⇥ 103 au. This dense components arewhereasclearly
identified:i)alowvelocity
compo(1) cavity walls (black)↵ , the jet envelope of entrained gas to
at00 ) lowow)connects
8000 au (10from1velocities, in the range
nent,
between+0 and +10 km1s 1 up toemitting+ (r/r0 )[ 8; 3] km
and [ cavity
19; 14]kmii)
s a in the northern andwalls.
the source, associatedwiths the outflow
walls;
respectively;b) thejet, emitting at high veloci3 on the outflow morphology ap- high velocity southerncomponent,lobe,
that displaysa periodical
behavmericalresults=
109 cm, r0 = 100 au and ↵ = 1.9.
the mass
injectionand theod agreement with the NOEMA observations of ior, reflecting ties
in therange variability[ 135; 110]
kminternals 1 in the southern lobe (blue)
mulationtakes
thein rolein the fast material catches up with the slower
shocks, where
northernlobe(Fig. into
1). Asaccountcan be seen
Tableof2, gravity,and in the range [+40;+80] km s 1 in the northern lobe (red);withstratificationmaterial. Thec)jetthe
is detected
at terminala radial velocity
close tongth
andthethe source
radius of density
the outflow
cavity are cor- evidenced
southernbowshock
HH377, integrated in the1
Vj = 65 km s range
oduced;analysis.
this good Our
matchmodel
betweenincludes
observations
at z >[ 2000
frommier’sthe resulting
77, au64]kmthe
s 1source.
(green); d) the northern terminal bul-

まず、COが壊される

加速領域

nal
force as a source term, which reads:
ber, page 6 of 12

2 c20 r↵1 + (r/r0 ) )(2)

is the local sound speed. The inclusion of thisrm ensures hydrostatic equilibrium close to thelet NB integrated in the velocity range [+84,+97] km s 1 (magenta). First contour and contour interval are 20% and 10% of
the peak intensity in each component, respectively. The synthesized beam (100. 07 ⇥ 000. 87, HPBW) is shown in the bottom left
corner. The main axis of the northern and southern lobes of thejet are shown with black arrows. (Schutzer et al. 2022).

02

Mapping the distribution of OB stars and associations in Auriga
1¢11Alexis L. Quintana , Nicholas J. Wright and Robin D. Jeffries

1 Astrophysics Group, Keele University, Keele ST5 5BG, UK[astro-ph.SR] 17 Apr 2023

Accepted 2023 April 17. Received 2023 April 14; in original form 2023 February 15

ABSTRACTOB associations are important probes of recent star formation and Galactic structure. In this study, we focus on the Auriga
constellation, an important region of star formation due to its numerous young stars, star-forming regions and open clusters.
We show using Gaia data that its two previously documented OB associations, Aur OB1 and OB2, are too extended in propermotion and distance to be genuine associations, encouraging us to revisit the census of OB associations in Auriga with modern
techniques. We identify 5617 candidate OB stars across the region using photometry, astrometry and our SED fitting code,grouping these into 5 high-confidence OB associations using HDBSCAN. Three of these are replacements to the historical pairof associations - Aur OB2 is divided between a foreground and a background association - while the other two associations
are completely new. We connect these OB associations to the surrounding open clusters and star-forming regions, analyse themphysically and kinematically, constraining their ages through a combination of 3D kinematic traceback, the position of theirmembers in the HR diagram and their connection to clusters of known age. Four of these OB associations are expanding, withkinematic ages up to a few tens of Myr. Finally, we identify an age gradient in the region spanning several associations thatcoincides with the motion of the Perseus spiral arm over the last ⇠20 Myr across the field of view.
Key words: stars: kinematics and dynamics - stars: early-type - stars: massive - stars: distances - Galaxy: structure - open
clusters and associations: individual: Aur OB1, Aur OB2, Alicante 11, Alicante 12, COIN-Gaia_16, Gulliver 8, Kronberger 1,
NGC 1778, NGC 1893, NGC 1912, NGC 1960, Stock 8.

03

Table 5. RVs calculated for the new OB associations. #'+ is the numberof stars with a reliable measured RV. References are: (1): APOGEE, (2):Fehrenbach et al. (1992), (3): Grenier et al. (1999), (4): Gontcharov (2006),(5): Turner et al. (2011), (6): Chojnowski et al. (2017), (7): Gaia Collaboration
et al. (2018), (8): Zhong et al. (2020)

8

A. L. Quintana et al.

Assoc.

#'+RV (km s 1 )References

1

47

All but (6)252.13 ± 1.26

38(1), (6), (8)4314.64 ± 3.01

54

6.59 ± 4.31
4.12 ± 1.63

1.46 ± 7.45

(8)(1), (7), (8)(8)

4.4 Expansion and traceback age
Fig. 10 shows that many of the OB associations in Auriga haveages of several tens of Myr. Therefore, instead of using a linear
expansion model to determine their expansion age, we trace backthe associations using the epicycle approximation from Fuchs et al.
(2006), and correct for the local standard of rest (LSR) from thevalues of Schönrich et al. (2010). We gather RVs from the APOGEE
we have computed the intrinsic dispersion in distance and transverse
surveyandfrom
SIMBAD.
RVs
from
the
literaturearediscarded
velocities based on the method from Ivezi∆ et al. (2014) using the
if
they
lack
an
uncertainty
or
if
their
measurement
isconsideredobservational uncertainties. The distance dispersions typically range
unreliable. If some stars belong to both APOGEE and SIMBAD, weup to a few tens of pc, while the velocity dispersions range up to 3
taketheweighted
mean
of
the
two
values.
In
doing
so
we
obtaina1Figure7.
SpatialdistributioninGalactic
coordinates
of
the
5
new
OB
associations
in
Auriga.
The
backgroundextinction
map
and
the
featureshighlighted in
km s , consistent with that of other OB associations (Wright 2020).
04
this map are the same as in Fig. 1.
sample of 95 stars with RVs.
Figure 8. Transverse velocity distribution of the 5 new OB associations in
Auriga.

8

A. L. Quintana et al.

0. HR diagrams for the members of the new OB associations in Auriga. Isochrones have been shown from the rotating evolutionary models fromet al. (2012). Positions of some spectral types have been indicated on the top horizontal axis for clarity.

the best constraint on the age (e.g., for association 3) ore constraint was possible by any means (e.g., association 2).

USSIONection we discuss our findings and how the new Auriga OB
ons can help understand the star formation history of the
Our main results are outlined as follows:

have shown that both Aur OB1 and Aur OB2 are too exn PM and distance to be genuine OB associations, encour-aging us to revisit the census of OB stars and associations in theregion.
• We identified more than 5000 candidate OB stars across theregion using our SED fitter, with an estimated reliability of 90 %.
• We identified 5 new high-confidence OB associations in thearea that we analysed physically and kinematically, and estimatedtheir age through a combination of 3D kinematic traceback, theirlink to open clusters and star-forming regions with known ages,
and the distribution of members in the HR diagram. Only a small
fraction (⇠10 %) of the identified OB stars have been assigned to
Figure 7. Spatial distribution in Galactic coordinates of the 5 new OB associations in Auriga. The background extinction map and the features highlighted inthese associations.
this map are the same as in Fig. 1.

05

8

A. L. Quintana et al.

Figure 9. Galactic longitude as a function of SED-fitted distance for the 5 new OB associations in Auriga. The median error bars on distances are respectively⇠ 30 pc for associations 1 and 2, ⇠ 50 pc for association 3, ⇠ 70 pc for association 4 and ⇠ 160 pc for association 5.

Figure have
7. Spatial
distribution
Galactic
coordinates
the 5 new OB associations in Auriga. The background extinction map and the features highlighted in
Figure 10. HR diagrams for the members of the new OB associations in Auriga. Isochrones
been shown
from the inrotating
evolutionarymodelsof
from
Ekström et al. (2012). Positions of some spectral types have been indicated on the top horizontal
this mapaxis
are fortheclarity.
same as in Fig. 1.

06

星形成史研究として何がわかるかは, 記述なし.
(役に⽴つはずとの記述のみ)

12

このパネルに不定性の⼤きさを

A. L. Quintana et al.

描いていない理由の記述なし.

Figure 9. Galactic longitude as a function of SED-fitted distance for the 5 new OB associations in Auriga. The median error bars on distances are respectively⇠ 30 pc for associations 1 and 2, ⇠ 50 pc for association 3, ⇠ 70 pc for association 4 and ⇠ 160 pc for association 5.

現在(これを仮定としたとの記述もなし)

不定性の

不定性の

⼤きさ

⼤きさ

2 x 107 yrsまえ

不渦状腕と⼀致する星団は代わる
No.1&2.が渦状腕で誕⽣？

太陽系

太陽系

太陽系

Figure 12. Median positions of the OB associations across the X-Y plane from the present time to 20 Myr in the past, shown relative to the Local Standard of
Rest. Uncertainties on their position from the traceback have been shown as a blur. The Perseus spiral arm model, including its thickness, is from Reid et al.
Figure 10. HR diagrams for the members of the new OB associations in Auriga. Isochrones have been shown from the rotating evolutionary models from(2019).
The
symbolcorresponds
toclarity.
the position of the Sun.
Ekström et al. (2012). Positions of some spectral
types have
beenSunindicatedon the top
horizontal axis for07

Planet formation via pebble accretion in externally photoevaporating discs
1¢
1
1
Lin Qiao, Gavin A. L. Coleman, Thomas J. Haworth【前提知識のメモ】Pebbles : 固体の流れで、Pebble⽣成フ

1 Astronomy Unit, School of Physics and Astronomy, Queen Mary University of London, London E1 4NS,ロントからr⽅向内側に降着して惑星を成⻑させる.
UK
外部輻射

で円盤外縁部があっというまに光蒸発してしまう場合,
Pebbles⽣成フロントが円盤外縁部に速く到達する. このため

stro-ph.EP] 27 Mar 2023

Accepted XXX. Received YYY; in original form ZZZPeble降着に必要な固体供給が⽌まり惑星成⻑のための質量置き場としての役割も終わる. 逆に, 円盤が外部輻射から遮蔽さABSTRACT

れていれば, 質量置き場としての役割維持.

We demonstrate that planet formation via pebble accretion is sensitive to external photoevaporation of the outer disc. In pebble
accretion, planets grow by accreting from a flux of solids (pebbles) that radially drift inwards from the pebble production front.
If external photoevaporation truncates the outer disc fast enough, it can shorten the time before the pebble production front
reaches the disc outer edge, cutting off the supply of pebble flux for accretion, hence limiting the pebble mass reservoir for planet
growth. Conversely, cloud shielding can protect the disc from strong external photoevaporation and preserve the pebble reservoir.
Because grain growth and drift can occur quickly, shielding even on a short time-scale (< 1 Myr) can have a non-linear impact on
the properties of planets growing by pebble accretion. For example a 10 3 " planetary seed at 25 au stays at 25 au with a lunar
mass if the disc is immediately irradiated by a 103 G0 field, but grows and migrates to be approximately Earth-like in both massand orbital radius if the disc is shielded for just 1 Myr. In NGC 2024, external photoevaporation is thought to happen to discs
that are < 0.5 Myr old, which coupled with the results here suggests that the exact planetary parameters can be very sensitive tothe star forming environment. Universal shielding for time-scales of at least ⇠ 1.5 Myr would be required to completely nullify
the environmental impact on planetary architectures.
Key words: planets and satellites: formation – protoplanetary discs – (stars:) circumstellar matter – stars: formation

08

External photoevaporation and pebble accretion
出発位置 r = 25 AU

9

わずかに1x106 yrsだけ
外部輻射を遮蔽するだけで地球質量くらいまで成⻑できる

外部輻射場強度ごとに
横軸：出発位置
縦軸：最終質量のプロットが遮蔽時間を変えたパネルをセットにして掲載されている.

Figure 6. The final mass "final that the planetary embryos injected at 0init =25 AU reached as a function of shielding time Csh in discs evolved with FUV
tracks of different FUV, max values, indicated by different colors. There is anonlinear impact of shielding time on the planet’s final mass up to 1 Myr for
100 G0 .
FUV, max
Figure 4. Evolution of planetary embryo mass " ? against semi-major axis 0 in discs evolved with FUV tracks with FUV, max = 104 ⌧0 . In each subplot,
simulations with one specific shielding time Csh are included, and each colored curve represents the evolution trajectory of one planetary embryo in one discwith arrows indicating the direction of evolution. The initial planetary embryo core mass and semi-major axis (0init ) when injected is indicated by the circle.
Note that the plots only includes the simulations with 0init < 60 AU though the full 0init range simulated is 10 - 100 AU.

09

023

rXiv:2303.17784v1 [astro-ph.EP] 31 Mar 2023

gan Institute, Cornell University, Ithaca, NY 14853-6801
w Institute of Physics andEccentricity
Technology, Dolgoprudny,
Region,Planets
141700, Russia
Growth Moscow
of Massive
inside Cavities ofh Institute for Applied Mathematics,
Moscow, 125047,
Protoplanetary
Discs Russia
ment of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853-6801

M. M. Romanova1,2? , A. V. Koldoba3 , G. V. Ustyugova4 , D. Lai1,2 , R. V.
E. Lovelace1,2,5
1 Department of Astronomy, Cornell University, Ithaca, NY 14853-6801
2 Carl Sagan Institute, Cornell University, Ithaca, NY 14853-6801
3 Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141700, Russia
4 Keldysh Institute for Applied Mathematics, Moscow, 125047, Russia
5 Department of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853-6801

ABSTRACT
3 April 2023

We carry out hydrodynamical simulations to study the eccentricity growth of a 1ABSTRACT
30 Jupiter mass planet located inside the fixed cavity of a protoplanetary disc. The
carry outandhydrodynamical
simulations
to study thewith
eccentricity
growthofata 1-resonant locations,planet exchanges We
energyangularmomentumthedisc
30 Jupiter mass planet located inside the fixed cavity of a protoplanetary disc. The
planetgrows
exchangesdue
energyto
and Lindblad
angular momentum
with the disc at We
resonant
locations, several phases ofand its eccentricity
resonances.
observeand its eccentricity grows due to Lindblad resonances. We observe several phases of
eccentricity growthwheredi↵erent
eccentric
Lindbladeccentricity
growthwhere di↵erent
eccentric Lindblad
resonancesresonances
dominate from 1:3dominate from 1:3
up to 3:5. The maximum
valuesof eccentricity reachedin our simulations
are simulations
0.65upto
3:5.
The
maximum
valuesofeccentricity
reachedinourare
0.65過去の同様な計算に⽐べ、0.75. We calculate the eccentricity growth rate for di↵erent planet masses and discparametersand derive analyticalgrowthdependenciesrateon theseparameters.
We observethat masses and disc0.75.
We
calculatetheeccentricity
fordi↵erent
planetもっとも⼤きな離⼼率
the growth rate is proportional to both the planet’s mass and the characteristic discparameters
andderivedependencies
parameters.
mass for aanalyticalwide range of parameters.
In a separate on
set ofthesesimulations,
we derived the We observe thatになった(本⽂).
width of the 1:3 Lindblad resonance.
the growth rate is proportional to both the planet’s mass and the characteristic disc
Key words: accretion discs, hydrodynamics, planet-disc interactions, protoplanetary
mass for a wide rangeof parameters. In a separate set of simulations, we derived thediscs
width of the 1:3 Lindblad resonance.
Keywords: accretion discs, hydrodynamics,
planet-disc
protoplanetary
INTRODUCTION
A planet interacts
with the disc due tointeractions,the Lindblad andcorotation resonances (Goldreich & Tremaine 1979, 1980).
discs
Many massive exoplanets have high eccentricities. There
Lindblad resonances tend to increase the eccentricity of the1

is a wide distribution of eccentricities at di↵erent planet
masses and their distances from the star (see, e.g., Fig. 1
from Debras et al. 2021, which is based on the recent data

planet, while corotation resonances suppress the eccentricity growth (see also Goldreich & Sari 2003; Ogilvie & Lubow

10

Discussion
Sect. 6.1. キャビティのサイズ
Sect. 6.2. 先⾏研究との⽐較
Conclusions
1. ⻑時間にわたる離⼼率e成⻑は起こりうる.
2. 惑星のeは0.65-0.75と⼤きくなる傾向
3. 離⼼率成⻑は４段階を経る
4. 段階ごとの惑星質量の記述
5. 先⾏研究との⽐較
6. 粘性による成⻑時間を考えてもe成⻑は起こりうる7. 今後

Figure 3. Top 6 panels: waves forming in the inner disc in the Reference model at di↵erent times. Time is measured in periods ofrotation at r0 = 1. The color background shows the surface density. A small red dot shows the location of the planet, and small whitecircles show the locations of the spiral arms. The bottom panel shows the temporal evolution of the semi-major axis ap (red line) andeccentricity ep (blue line) of the planet’s orbit. The black vertical lines separate di↵erent phases of evolution, in which m = 1, 2, 3 or 4
spiral waves dominate.

11

Guyon55v1[astro-ph.EP]
27
Mar
2023
ph.EP] 27 Mar 2023

The

, Michael Bonnefoy , Faustine Cantalloube , H. Jens Hoeijmakers , Ulli Käufl , Markus Kasper ,Anne-Lise Maire6 , Mathilde Mâlin1 , Ralf Siebenmorgen19 , Ignas Snellen8 , and Gérard Zins19

Pictoris system: Setting constraints on the planet and the(Affiliations can be found after the references)?
disk structuresReceived
at mid-IR
wavelengths
with
NEAR
10/05/2022; accepted 08/03/2023

1,
2,
3
1
4
1
1
5
Nour Skaf, Anthony Boccaletti , Eric Pantin , Philippe Thebault , Quentin Kral , Camilla Danielski , Raphael

Galicher1 , Julien Milli6 , Anne-Marie Lagrange1 , ABSTRACT
Clément Baruteau7 , Matthew Kenworthy8 , Olivier Absil9 , Maud
18 +/- 2 Myrs 11
1012 , Nuria Huelamo13 , Philippe Delorme6 , Benjamin Charnay1 , Olivier
Langlois,
Johan
Olofsson,
Gael
ChauvinContext. Pictoris is a young nearby system hosting a well-resolved edge-on debris disk, along with at least two exoplanets. It o↵ers key
2,
14,
15,
16
6
17
18
19
19
opportunities
forcarrying
outdetailedstudiesoftheevolutionofyoungplanetarysystemsandtheirshaping
soon
after
the
end
of
the
planetary
Guyon, Michael Bonnefoy , Faustine Cantalloube , H. Jens Hoeijmakers , Ulli Käufl , Markus Kasper ,formation phase. Anne-Lise Maire6 , Mathilde Mâlin1 , Ralf Siebenmorgen19 , Ignas Snellen8 , and Gérard Zins19
Aims. We analyzed high-contrast coronagraphic images of this system, obtained in the mid-infrared, taking advantage of the NEAR experimentusing the VLT/VISIR instrument, which provides accessto adaptive
as wellasthe
phase
coronagraphy. The goal of our analysis is to investigate(Affiliations
canoptics,
be foundafter
references)both the detection of the planet Pictoris b and of the disk features at mid-IR wavelengths. In addition, by combining several epochs of observation,
Received
10/05/2022;
acceptedon
08/03/2023
we expect to constrain the position of the known clumps
and improve
our knowledge
the dynamics of the disk.
Methods. We observed the Pictoris system over two nights in December 2019 in the 10 12.5 µm coronagraphic filter. To evaluate the planet bflux contribution, we extracted the photometry at the expected position of the planet and compared it to the flux published in the literature as wellas the one we measured with SPHERE spectroscopy in the near-IR. ABSTRACT
In addition, we used previous data from T-ReCS and VISIR in the mid-IR,
updating the star’s distance, to study the evolution of the position of the southwest clump that was initially observed in the planetary disk back inContext. Pictoris is a young nearby system
hosting a well-resolved edge-on debris disk, along with at least two exoplanets. It o↵ers key
2003.
⼟星の環のような構造ではなく、フラックスの上限値から周惑星円盤のような構造が⽰唆される
opportunities
carryingout detailedof theable
evolutionof young onplanetarysystems
and their shaping
soon after
theoutend
the planetary
Results.
While for
we didnot detect
the planetstudiesb, we wereto put constraints
the presenceof circumplanetary
material,
rulingtheof
equivalentphase.
offormationa Saturn-likeplanetary ring around the planet. The disk presents several noticeable structures, including the known southwest clump. Using a
Aims. Weanalyzedhigh-contrast
coronagraphic
images weof thisin themid-infrared,
takingWe
advantageofthe
theclump
NEARorbits
experiment16-yearbaseline,sampledwith five epochsof observations,weresystem,
able to obtained
examine theevolutionof the clump.
found thatin
the VLT/VISIR
which
accesstoaddition
adaptive
optics,as wellas phasecoronagraphy.
The thegoalpresenceof our analysis
is toclump
investigate
a using
Keplerianmotion withinstrument,a semi-major
axis providesof 56.1+0.4
au.
In
to
the
known
clump,
theimagesclearly
showofasecond0.3
bothdetectionand of the
diskandfeaturesmid-IR wavelengths.
Inbe
addition,by combining
severalepochscorrelationsof observation,onthe thenortheastsideofofthe
theplanet
disk asPictoris
well as bpossibly
faintercloseratstructuresthat are yet toconfirmed.
Furthermore,
we foundwe expect
constrain
the position
the knownclumpsand improve
our knowledge
on thedynamics
the disk.
betweenthe toCOclumps detectedwithofALMA
and thenortheasternand southwesternclumpsin themid-IRof
images.
Methods. WeIf observed
the Pictoris
systemoverlocated
two nights
Decemberin the 10 amount12.5 µm
coronagraphic
thelimit
planet b
Conclusions.
the circumplanetary
material
wereat the inRocheradius,2019
the maximumof dustdeterminedfilter.
from Tothe evaluate
flux upper
flux contribution,
extracted
the photometry
positionthe planetand compared
it to theflux ofpublishedin the literaturearoundPictoris b we
wouldcorrespondto the massatofthe
anexpected
asteroid of
5 km inofdiameter.
Finally,
the Keplerianmotionthe southwesternclump asis wellas the one
we measured
with SPHERE
spectroscopy
in the presencenear-IR. of
In aaddition,from T-ReCS and VISIR in the mid-IR,
possibly
indicativeof a yet-to-bedetected planetor signals
vortex. we used previous dataクランプの軌道運動＠56AUを検出
updating the star’s distance, to study the evolution of the position of the southwest clump that was initially observed in the planetary disk back inKeywords. Exoplanets, Direct Imaging, High Angular Resolution
CO回転遷移輝線で観測されていたクランプとの対応も確認 12
2003.

A&A proofs: manuscript no. 45143corr

Skaf et al.: The

Pictoris system: Setting constraints on the planet and the disk structures at mid-IR wavelengths with NEAR

expressed as:
r
GM?
,
⌦K =
3
a

南⻄クランプ= C1(6)with a being the semi-major axis and G being the gravitational constant. The projected separation, x0 , at the first epoch is
given by:x0
cos(✓0 ) = ,a

Skaf et al.: The(7) constraints on the planet
Pictoris system: Setting

Fig. 11. Evolution of the projected distance and relative intensity profile of C1 over the years, from di↵erent instruments (colour-coded inwithlegend).
✓0 defining
the
angle
betweenthesetclump
the
direction
Skaf
et al.:
Thedata hasPictoris
system:Setting
on the pl
The intensity
forthe VISIR
and NEAR
been
to scalewithandthe T-ReCS
data
by Li etconstraintsal. (2012).
Fig. 11. Evolution of the projected distance and relative intensity profile of C1 over the years, from di↵erent instruments (colour-coded in theperpendicular
to the line of sight.
Since the Keplerian speed islegend). The
intensity for the VISIR and NEAR 狭いGaussianと幅広のplateauの２成分からなる。
data has been set to scale with the T-ReCS data by Li et al. (2012).
上のプロファイルは、Clumps
C1
C2
C3
C4
constant for a circularorbit (⌦K = ✓/t), theprojected
sepaClumps
C3 29.3±0.3
C4 -15.2±0.3
Projected separation (au)C1 56.1±0.3C2 -35.2±0.3
as a functionof time for a given Global
orbitalradiusisFig. 1. Image of the disk at 12 µm, using a PCA reduction (bottom), and a ClasImg reduction performed with SpeCal. The disk has beenration,
rotated x[t, a],16年間で内側の”狭いGaussian”成分が,outwardmotionTable 2. Projected separationsof the clumps
observedwith 56.1±0.3
NEAR. Negative
signs are29.3±0.3
for the NE sideof the disk.
Projected
separation(au)-35.2±0.3-15.2±0.3
by 30 degrees in those images with respect to due north. Labels indicate the dust clumps described in Sect. 4.
expressed
as:Table 2. Projected separations of the clumps observed with NEAR. Negative signs are for the NE side of the disk.
惑星bが中間で５σ上限で検出されなかった理由：主星のガス円盤からの放射￼≫toシステム雑⾳
軌道離⼼率は不明だが、Kepler運動的Fig. 7. Surface brightness profile of the PCA image (red), and ClasImg image (orange). The y-axes correspond
the ClasImg on the left andof thetheprojected 0
intensity profiles
for the NEAR2019 data, to- around 56 au. At face value, this would suggest that we are w
1r
PCA on the right. Labels
the clumps have been Fig.
added10.
forconvenience.
Positionof C1 in the PCA image of the 2019 data. Two Gausgether
with the intensity
ALMA
data.
Forforconsistency,
weused
thetostar’saroundnessingdi↵erent
whose
projected
positionsofthe projected
profilesthe NEAR
2019
data,
56 au.two
At facevalue,clumps
this would
suggestthat weare wit- hap
BC
cf.ofAOでの分解能は300mas,
コロナグラフの透過率は~32%@11.25
um,
GM
B
C
⇤ C
BBBpc✓ fordata.
distanceof the19.63
theseobservations,thus
to coincide.
Suchclumps
a conclusion
should, however,be taken w
with
ALMA
Forthreeconsistency,
we usedtheincluding
star’s nessing
two di↵erent
whose projected
positions happen
Csian curves have been added in dashed lines to show the substructures x[t, gether
a]
=
a
cos
t.
.
(8)
C
0 these three@di↵erences
potentiallyslightpc
withobservations,the3 twoAaforementioned
great caution.
PV diagrams
the CO belines
do withindeed a
distanceof 19.63
forthus including pa-to coincide.
Such aTheconclusion
should,ofhowever,
taken
−3
a
コントラストの5σ限界は,￼
5×10within the disk and the brown line corresponds to the final fit.
pers regarding
positionswithof theAlthough weclump shouldbe radiallyspannpotentiallyslightthedi↵erences
thestructures.
two aforementioned
pa- de-greatsuggest
caution.that
ThethePVgas
diagramsof the COlines doextended,
indeed also
Skaf et al.: The

Pictoris system: Setting constraints on the planet and the disk structures at mid-IR wavelengths with NEAR

expressed as:
r
GM?
,
⌦K =
a3

(6)

with a being the semi-major axis and G being the gravitational constant. The projected separation, x0 , at the first epoch is
tect with
VISIR
well-resolved(C2) inthe NE we
part
of
⇠100
authe
forgastheclump
orbitalradius.
If the dust
clumpspanning
was to hav
persregardingthea positionsof theclump
structures.
Althoughdesuggestthatshouldbe radiallyextended,
given
by: thetecta well-resolved
the NE partisofnot
thevery⇠100similar
au for radial
the orbital
radius.then
If thedust clump
to haveadisk,with
theVISIR
correspondencewith clump
the CO(C2)gasin
distribution
extension,
it could
appearwas
brighter(becaus
主星から~30AUのC3を初検出
To
estimatethebestmodelsmatching
the
data
given
the
error
disk,
the correspondence
withthetheclump
CO gason
distribution
is notradialextension, then(becauseof lu
conclusive.
Not only does
the NE sidein very
ALMAsimilar
highertemperatures)at ititscould
innerappear
edge,brighter
while thepeak CONotatonly
does
clump
on
the2000
NE33sideintemperatures)at its inner
edge,
while
peak CO lumiimages
peak
about
25the
au,grid
as opposedtoau modelsin ALMA
the VISIRhigher
nositycould
be locatedfurtherout,
thustheexplaining
the appar
bars,conclusive.
wegenerated
a
of
of
two
parameters,a
主星から~16AUのC4を初検出
5.3. Temporal evolution of C1’s
projected distanceimages
peak
at
about
25
au,
as
opposed
to
33
au
in
the
VISIR
nositycould
belocatedfurtherout,
thus
explaining
theapparent
image, but it is also related to a much broader projected struc- discrepancy. In addition, the di↵erent transitions of CO gas w
but it is also
relatedto (⇠70
a muchstrucIn
the di↵erentof CO gasand
willthe dwiththefollowingpriors:aube more(step
0.1excitedau)and transitions
and image,
x0 ,especially
ture,
in CO
J=3-2
au),broader
than atprojected
11.2555µm.
On60
thediscrepancy.
oraddition,
lessdependingon temperatureespeciallyincontrary,
CO J=3-2there(⇠70isau),
thanmatch
at 11.25µm. Onthe
thepro-be moreor less
excited partners
dependingonnon-LTEtemperature
denSW side,on thea goodbetweensity ofcollisional(in2
as isandthethecase
for P
Figure 11 presents the intensity profiles of the diskこの論⽂はfor each 51.9ture,
53.9
au
(step
0.05
au),
respectively.
Asaresult
of
a
SW
side,
on
the
contrary,
there
is
a
good
match
betweentheprosityofcollisional
partners(innon-LTE
as
is
the
case
for
Pic,
jected location of C1 and that of the CO gas clump. A small o↵- Matrà et al. 2017) and they are not necessarily representative
jectedof C1 and that of the CO gasFig.
clump.
small o↵- of
Matrà
etpositional. 2017) ofandC1
are not
necessarily
representativeof Fig12.A Evolution
the
over
the
16gas
years
of observaepoch around the location
of
C1.
The
T-ReCS
measurements
画像作成法の⽐較, 検証, 不定性評価 minimization,set (⇠6locationau) of C1
between
ALMAableand VISIR
observations
is vistheunderlying
COtheyordominant
speciesspatial distributi
we
were
to
constrainthesemi-majoraxisofset (⇠6 au) of C1 between ALMA and VISIRtions
observations
is vis- forthe VISIR
underlying
or dominantgas species
distributions(20(redclumpsquaresandCO
NEAR,
redThesecircles
for spatial
T-ReCS).
The
ible
in
Fig.
14,
but
this
cannotbeattributed
totheorbital(e.g.,
Kraletal.
2016).
questionsclearly
go beyond+0.4+0.5
from 2003 and 2010 were obtained from the plots in Telesco C1 toible in
Fig.
14,
but
this
cannotbeattributed
to
the
clump
orbital(e.g.,
Kraletal.
2016).
These
questionsclearlygobeyondthea according= 56.1 theau (andxbest
52.8implying
au).
More
detailsare
0 =motionanalysisSect.
5.4,
possibly
theinpresent
paper,
andwe thisleave
thistoopenbedisanissue
openbut
is
Keplerianmodel
isscopeoverlaid
blue
togetherwiththeto1-sigma
0.3
0.5 scope(に、かなりの稿を割き)⽰している.
motionaccording totothe
analysis
in in
Sect.
5.4,
possibly
implyingof theofpresent
paper,
and we
leave
be
an
0.4
et a
slightlydi↵erentdistribution
distribution
dust
andcomponents.
for investigationinstudies.
et al. (2005) and Li et al. (2012), after updating the star’s dis- given
persion(lightblue),forcorresponding
R future=studies.
56.1
inFigure12).
aa slightlydi↵erent
of ofthethedust
andgasgascomponents.
investigation
in to
future0.3 au. Also displayed:
However, wewenotenotethat
thatMatrà
Matràet etal.al.
(2017)
arguedwhilethe data for a 2:1 (orange) and 3:2 (green) resobest
modelsfitting
However,(2017)
arguedthatthatwhiletance to 19.63.
Telescoetal.ofof(2005)
measured
for C1 of 52 au
the projected
projectedlocation
location
CO
clump
is
around50a
au,
its dethe
thetheCOclump
is around
50 au,
its position
denances.
7. Originand andfate fateof C1of C1
projectedstellocentric
stellocentricdistancedistance(deducedfromposition-velocity7. Origin
projected(deducedfromposition-velocity
The apparent projected separation of the clump is clearly in- in Dec.
7.1
2003,
while
Li
et
al.
(2012)
obtained
54
au,
then
spec(PV)diagrams
diagramsofofCO
COintensity)
intensity)
peaks,
in reality,⇠ au.
85 Thisau. This As shown in Sect. 5.4, the location of C1 over the 2003-2(PV)
peaks,
in reality,at ⇠at85
As shown in Sect. 5.4, the location of C1 over the 2003-2019+0.6
Fig. 2. Contrast curve at 5 as measured along the creasing
disk spine acrossaseemsatotodisplacement
contradictthetheresults
results
orbitalanalysis(Sec.
over time,suggestive of a global outward motion of C1. ulated
seems
contradictof ofourourorbitalanalysis(Sec.
5.4),5.4),ofroughly2.0
au.
The
authors
periodislattercompatible
witha circular
Keplerianorbita wit
Sinperiodis compatible
witha circular
Keplerianorbit with
0.6
width
of
1",
as
measuredonthe
PCA
image.
The
contrast
of
Pic
b
which
the
semi-major
axis
of
the
dust
clump
is
constrained
to
lie
which
the
semi-major
axis
of
the
dust
clump
is
constrained
to
lie
+0.4
Fig. 8. Images of the centro-symmetrical subtractionof eventhe disk
at obvious when plotting its measured position concluded that the clump is moving at Keplerian
56.156.1au0.3semi-majoraxis. axis.
Duringthe review
processprocess
for the hav
auvelocity,semi-major
the review
for
This
is
more
cor-Duringwithrespect
to
the
star
and
its
distance
to
the
star
is
indicatedbythe
11.25 µm, obtained with VISIR in 2004 on VLT UT3 (top) and at+2.0
tro
Articlepage
1010oforbital
1515
Articlenumber,number,page
ofversustime
ona
16-yearbaseline,as
inFigure12(redcirclesau.
Whenconsidering
respondingtoanradiusof54.3
greylines.
1.2
3. Spectra of Pictoris b obtained by fitting forward BT-Settle
11.7 µm obtained in 2015 (bottom). In both images, the disk has rotated, Fig.
et⇦
南⻄クランプの運動検出のために2004年データをdata,tored
for 2004,
2015, and(color-coded2019 a instellar
modelsdata squares
obtained withseveral instruments
the distance of 19.63 pc (Gaia Collaboration et al. 2021)
respectively, 33 and 34 with respect to the north.for 2003 and 2010(20
+2.0
今回、使⽤した(複数の新しい)解析法で再解析(した画像のひとつ)
data). This outward
motiontheflux
projected
distance
is likely
to by insteadlegend).
The ofupper
limit of the
NEAR data
is marked
a green of 19.28 pc, the orbital radius changes to 54.7
sioau, accos(✓0 ) =

x0
,
a

(7)

with ✓0 defining the angle between the clump and the direction
perpendicular to the line of sight. Since the Keplerian speed isconstant for a circular orbit (⌦K = ✓/ t), the projected separation, x[t, a], as a function of time for a given orbital radius isexpressed as:

Fig. 10. Position of C1 in the PCA image of the 2019 data. Two Gaussian curves have been added in dashed lines to show the substructures
within the disk and the brown line corresponds to the final fit.

5.3. Temporal evolution of C1’s projected distance

Figure 11 presents the intensity profiles of the disk for eachepoch around the location of C1. The T-ReCS measurementsfrom 2003 and 2010 were obtained from the plots in Telesco
et al. (2005) and Li et al. (2012), after updating the star’s distance to 19.63.
The apparent projected separation of the clump is clearly increasing over time, suggestive of a global outward motion of C1.
This is even more obvious when plotting its measured position
versus time on a 16-year baseline, as in Figure 12 (red circles
for 2003 and 2010 data, red squares for 2004, 2015, and 2019data). This outward motion of the projected distance is likely tobe slowing down over time, indicating that the clump should becoming close to its maximum elongation.
We note that the overall profile of C1 has a two-mode shapewith a nearly Gaussian part inward and a plateau outward, indicative that the actual three-dimensional shape of the clump
is more complex. In particular, the clump can be azimuthally
and/or radially extended. In the latter, the di↵erential Keplerian0BBx[t, a] = a cos BBB@✓0

t.

r

1
GM⇤ CCCC
C.
a3 A

(8)

To estimate the best models matching the data given the error
bars, we generated a grid of 2000 models of two parameters, aand x0 , with the following priors: 55 60 au (step 0.1 au) and51.9 53.9 au (step 0.05 au), respectively. As a result of a 2
minimization, we were able to constrain the semi-major axis of+0.5
C1 to a = 56.1+0.4
0.3 au (and x0 = 52.8 0.5 au). More details are
given in Figure 12).
Telesco et al. (2005) measured a position for C1 of 52 auin Dec. 2003, while Li et al. (2012) obtained 54 au, then speculated a displacement of roughly 2.0+0.6
0.6 au. The latter authors
concluded that the clump is moving at Keplerian velocity, corresponding to an orbital radius of 54.3+2.0
1.2 au. When consideringa stellar distance of+0.4
19.63 pc (Gaia Collaboration et al. 2021)
0.3orbital radius changes to 54.7+2.0 au, acinstead of 19.28 pc, the
1.2
cording to Figure 8 in Li et al. (2012). This is a value that ought
to be compared to the obtained values described in the previous
section. Therefore, our measurement is in agreement, within theerror bars, with this revised value. We note that this value corresponds almost exactly to the projected separation of the clump in
the 2019 data, hence, the clump is supposed to be at its maximal
elongation.

13

(4)Early
Laboratoire
Lagrange, UMR7293,
UniversitéCôte d’Azur, the
CNRS,
Observatoire
Bombardmentof the Moon:
Connecting
Lunar
Craterde laCôte d’Azur,
Bouldervard
de l’Observatoire,
06304,
Nice Cedex 4, France
Recordto the Terrestrial
PlanetFormationDavid Nesvorný1 , Fernando V. Roig2 , David Vokrouhlický3 , William F. Bottke1 ,ABSTRACT
1
Simone Marchi , Alessandro Morbidelli4 , Rogerio Deienno1(1) Department of Space Studies, Southwest Research Institute, 1050 Walnut St., Suite
The lunar crater300,
recordfeatures⇠ 50 basins.
The radiometric dating of
Boulder,
CO 80302,
United States

Apollo samples indicates that the Imbrium basin formed relatively late – from
(2)
Nacional,
Rua Gal. –Jose
Cristinode weJaneiro,RJ a20921-400,
theObservatório
planet formation
perspectivesome' 3.9 77,
Ga.RioHeredevelopdynamical
Brazilmodel for impactors in the inner solar system to provide context for the interthe lunar crater
record.
The contributionof cometaryimpactors(3)pretation
Institute of Astronomy,Charles
University,
V Holešovičkách
2, CZ–18000
Prague 8,isCzechproduced
Republic most large impacts on the terresfound to be insignificant. Asteroids
彗星はほとんど効かない
trial worlds in the last ' 3 Gyr. The great majority of early impactors were rocky(4) Laboratoire Lagrange, UMR7293, Université Côte d’Azur, CNRS, Observatoire de la 初期の衝突体の⼤部分は、地球が形成されたあと、
planetesimals
leftBouldervard
behind at ⇠au after
the terrestrial
accretion.
Côte d’Azur,
de 0.5–1.5l’Observatoire,
06304,
Nice Cedex planet
4, France
約0.5-1.5AUの範囲に取り残された岩⽯質微惑星のThe population of terrestrial planetesimals was reduced by disruptive collisions
衝突によるin the first t ⇠ 20 Myr after the gas disk dispersal. We estimate that there were
ABSTRACT5⇠ 4 ⇥ 10 diameter d > 10 km bodies when the Moon formed (total planetesimal “地球型微惑星”数は，(上述の取り残された)ガス円盤がmass ⇠ 0.015 MEarth at t ⇠ 50 Myr). The early bombardment of the Moon 散逸した後，20Myrsでのdisruptive衝突にで激減.⽉形
成時に, d>10kmのbody(“地球型微惑星”?_)が4e5個
The lunarrecord features⇠ 50 basins.
radiometricof
was intense.
Tocrateraccommodate⇠ 50 known
basins, The
the lunarbasinsdatingthat formed
Apollo' samples
indicates
thathavethe Imbriumbasin formed
relatively
late of– frombefore4.35–4.41
Ga mustbeen erased.
The late
formation
Imbrium はあったと推定.
the planet formation perspective – some ' 3.9 Ga. Here we develop a dynamical
occurs with a ⇠ 15–35% probability in our model. About 20 d > 10-km bodies 今回のモデルで、Imbrium盆地が後期に形成される確率
model for impactors in the inner solar system to provide context for the interwere expected to hit the Earth between 2.5 and 3.5 Ga, which is comparable to は, 約15–35％.
pretation of the lunar crater record. The contribution of cometary impactors isthe number of known spherule beds in the late Archean. We discuss implications
found to be insignificant. Asteroids produced most large impacts on the terresof trial
our worlds
modelinfor
craterchronologies,
Late Veneer,thethelastlunar/Martian' 3 Gyr. The great
majorityof early impactors
were androckynoble
gases
in the Earthatmosphere.
planetesimals
left behindat ⇠ 0.5–1.5 au after the terrestrial planet accretion.
14

Lunar Impactors(d>20 km)

Lunar Impactors(d>20 km)Fig. 10.— Impacts of d > 20-km bodies on the Moon (log time scale in the left panel, linear
on the right). The plot shows the accumulated number of impacts since time t, where t = 0
is the birth of the solar system, and t ' 4.57 Gyr is the present time. The planetesimal,
asteroid and comet profiles are shows by red, green and blue lines, respectively; the blackline is the total impact flux. The vertical dash-dotted lines show the Moon formation in
our model (t = 42 Myr), estimated start of the known lunar basin record (t ' 190 or
T ' 4.38 Ga), Imbrium formation (t ' 650 Myr or T ' 3.92 Ga), and transition from theplanetesimal-dominated to asteroid-dominated impact stages (t ' 1.1 Gyr or T ' 3.5 Ga).
The numbers on the upper axis of the left panel indicate time T (in Gyr) measured looking
back from today.

15

21 Centro de Astrobiología (CSIC/INTA), Ctra.de Torrejón a Ajalvir km 4, 28806, Torrejón de Ardoz, Spain
22 Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

FAUST
VIII.
The
protostellar
disk
of
VLA
1623–2417
Wandits
streamers
23 Research Center for the Early Universe, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
imaged by ALMA
S. Mercimek,1,2¢ L. Podio,1 C. Codella,1,3 L. Chahine,4,5 A. López-Sepulcre,3,4 S. Ohashi,6 L. Loinard,7,8
D. Johnstone,9,10 F. Menard,3 N. Cuello,3 P. Caselli,11 J. Zamponi,11 Y. Aikawa,12 E. Bianchi,13,1
14,15,16 J. E. Pineda,11 , M. Bouvier,17 M. De Simone,18,1 Y. Zhang,6,19 N. Sakai,6 C. J. Chandler,20
G.
Busquet,XXX.
Accepted
Received YYY; in original form ZZZ
C. Ceccarelli,3 F. Alves,11 A. Durán,7 D. Fedele,1 N. Murillo,6 I. Jiménez-Serra,21 S. Yamamoto22,23
1 INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125, Firenze, Italy

2 Universià degli Studi di Firenze, Dipartimento di Fisica e Astronomia, via G. Sansone 1, 50019 Sesto Fiorentino, Italy

ABSTRACT
3 Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France

More
than
50%Université
of solar-mass
stars
form
in multiple
systems.
It is therefore crucial to investigate how multiplicity affects the
École doctoralede Physique,
Grenoble Alpes, 110
Rue de laChimie, 38400
Saint-Martin-d’Hères,FranceRIKEN Cluster for Pioneering Research, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan
18 O (2–1) observations of the VLA
star
andplanetformation
processes
attheprotostellar
stage.
We
reportcontinuumandC
Instituto de Radioastronomía y Astrofísica , Universidad Nacional Autónoma de México, A.P. 3-72 (Xangari), 8701, Morelia, Mexico
Instituto de Astronomía, Universidad Nacional Autónoma de México, Ciudad Universitaria, A.P. 70-264, Ciudad de México 04510, Mexico
1623-2417
protostellar system at 50 au angular resolution as part of the ALMA Large Program FAUST. The 1.3 mm continuum
NRC Herzberg Astronomy and Astrophysics, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada
18 O emission reveals, for the
Department of Physics and Astronomy, University of Victoria, Elliott Building, 3800 Finnerty Road, Victoria, BC V8P 5C2, Canada
probes
the
disks
of
VLA
1623A,
B,
and
W,
and
the
circumbinary
disk
of
the
A1+A2
binary.
The
C
Max-Planck-Institut für extraterrestrische Physik (MPE), Gießenbachstr. 1, D-85741 Garching, Germany
Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
first
time,
the
gas
in
the
disk-envelopeof
VLA
1623W.
We
estimatethedynamical
mass
of
VLA
1623W,
"
=
0.45
±
0.08
dyn
ORIGINS, Excellence Cluster Origins, Boltzmannstrasse 2, D-85748 Garching bei München, Germany
3
18
Departament de Física Quàntica i Astrofísica, Universitat de Barcelona (UB), c/ Martí i Franquès
1, 08028 Barcelona,
Spain
⇠
6
⇥
10
M
.
C
O
MInstitut, deand
the
mass
of
its
disk,
"
diskc. Martí i Franquès 1, 08028, Barcelona, Spain also reveals streamers that extend up to 1000 au, spatially andCiències del Cosmos (ICCUB), Universitat de Barcelona,
Institut d’Estudis Espacials
de Catalunya (IEEC),
c. GranCapità 2-4, 08034,
Barcelona,
Spain cavities of the A1+A2+B system with the disk of VLA 1623W. The presence
kinematicallyconnecting
theenvelopeandoutflow
Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
Southern Observatory,Karl-Schwarzschild-Strasse
2, 85748, Garching
bei München,
Germany
ofEuropean
thestreamers,
as
well
as
the
spatial(⇠1300au)
andvelocity
(⇠2.2
km/s)
offsetof
VLA
1623W
suggestthat
eithersourcesW
Department of Astronomy, University of Virginia, Charlottesville, VA 22904, USA
National
Radio Astronomy
Observatory,
PO Box O, Socorro,
NM 87801,
USA
and
A+B
formedindifferent
cores,
interacting
between
them,
or
that
sourceW
hasbeenejected
from
the
VLA
1623
multiple
Centro de Astrobiología (CSIC/INTA), Ctra.de Torrejón a Ajalvir km 4, 28806, Torrejón de Ardoz, Spain
Department duringof Astronomy,its
The Universityof Tokyo, 7-3-1
Hongo,
Bunkyo-ku,case,Tokyo 113-0033,
Japan
systemformation.
Inthelatterthestreamersmayfunnelmaterialfromtheenvelope
andcavitiesof
VLA
1623AB
Research Center for the Early Universe, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
onto VLA 1623W, thus concurring to set its final mass and chemical content.
4 Institut de Radioastronomie Millimétrique, 38406 Saint-Martin d’Hères, France
5
6
7
8
9

10
11
12
13
14
15
16
17
18
19
20
21
22
23

Key words: ISM: kinematics and dynamics – ISM: molecules – stars: formation – ISM: individual objects: VLA 1623–2417

Accepted XXX. Received YYY; in original form ZZZABSTRACT

測定の不定性を考えると, 固有運動測定と⽭盾せず,(Sect.4.3)
More than 50% of solar-mass stars form in multiple systems. It is therefore crucial to investigate how multiplicity affects ejection説は否定されない.
thestar and planet formation processes at the protostellar stage. We report continuum and C18 O (2–1) observations of the VLA

16

Gas-to-Dust⽐の不定性で説明

Dec.J2000( 0 00 )arXiv:2303.162

2000
B)

streamer. The lack of a velocity gradien
Accepted XXX. Received YYY;
inoriginal
form
ZZZ⇤ occurs
may indicate
that
the
gas
motionSourceR.A.
Ellipse size
Position angle
Peak
I
M
J2000
1.3 mmdust
B)(⌘ <4 M(00 ⇥ 00 )( ) et al. 2020).
(mJy)(mJy/beam) (10)± 0.0013
7 ± 0.0013–24.24.30.934 ± 0.017
0.49 (±0.01) ⇥ 0.33 (±0.01)
74 ± 20158 ± 14A1+A2
71 ± 16:26:26.39074
1.6±0.8
A
W
ABSTRACT
3 ± 0.0001 B –24.24.30.787 ± 0.002
0.32 (±0.04)⇥ 0.16 (±0.03)
43 ± 5121 ± 2 B
80 ± 16:26:26.30631
1.2±0.6± 0.0001
ストリーマー
2 ± 0.0002 –24:24:29.669 ± 0.005 0.71 (±0.01)⇥ 0.12 (±0.02)
0.8
59 ± 1 stars± 16:26:25.6312
0.3 in multiple
0.6±0.3
W 23.7± 0.0002
Morethan 50%10.0of± solar-mass
form
sys
4

S. Mercimek et al.

4 DISCUSSION: ON THE ORIGIN
N
star and planet formation processes at the protostellar ss, ellipse size, position angle, integrated and peak intensity of the continuum emissionTheat 1.3FAUST
mm towards
sources
A1+A2,
B,
and
W.
Table
1.
Peak
coordinates,
ellipsesiz
ALMA
observationsofth1623-2417
protostellar
systemat50
auangularresolutios derived from the integrated intensity assuming a dust temperature of 20 50 K.
(⇤ ) The dust mass, Mdust , is derived fr
reveal
for
the
first
time
the
gas
kinemaprobes the disks of VLA 1623A, B, andWについては,
W, and the circu
component, VLA
1623W.
Specifically,
C18Oのkinematicsから
firstof VLA 1623W.
S1
S1 time, the gas in the disk-envelopeof the gas in the disk is contaminatedbythea contour indicates the 25f level of the CS(5–the following(i)streamers
the
molec
et emission
al. structures:2018).from
The magenta
contour
i
3
⇠
6
⇥
10
M
.
, andonthe
mass
"
disk
largerscalesof1623W
inits
Fig.disk,
2 withandpanels
a)
and
b)
of
Fig.
4.
n the velocity interval 3.4 – 4.2 kmストリーマー
s 1 , which Mmapped
4)
emission
integrated
on
the
veloc
Keplerianmotionon
50
S2
In the channel connecting
maps at high velocities,
instead,the outflow
peaks
of walls
the
ity walls associated with VLA 1623A (from kinematicallytheenvelope
andcavitiprobestheoutflow
cavityatheprotostellar
mass
(M
⇠
0.45
M
3H=
18
18 O emi
blue- and red-shifted emission are locatedalong
the2022).
disk majoraxis,
C O emission probes the circumbinary disk
Ohashi
et
al.
The
C
of
the
streamers,
as
well
as
the
spatial(⇠1300
au)
and
ve
on
scales
>
1000
au
and
connectspatiaandtheemissionismorecompact
and
peaks
at
smallerdistancesd the A1+A2 binary
systemandtheoutflow
and the envelope around the A1+
Wsidesrespectof theedge-on
disk
of
VLA
162
formedin different
cores,
interacting
between
forA+B
increasing
velocities
with
to
V
fied through CS (5–4) emission (Ohashi et al. and(W)
asexpectedinasys
cavity 3walls first identified throug
Keplerianrotating
disk.
o traces a bright elongated structure south of system18"disk ⇠In
6⇥10
M
)
with
the
envelope
duringits
formation.
thelattercase,
thestreame2022).
C
O
(2–1)
also
tracesab
18Moreover, C O shows emission towards the
The previous molecularand
lineB.
study towards
VLA
1623W
(Murillothecircumbinary
disk.
Moreover,onto
VLA
1623W,
thus
concurring
to
set
its
final
mass
a
18
nuum, as well as an elongated structure to the
et al. 2013) showed only C O(2–1) VLA
blueshifted
emission
towards
1623W diskhave
continuum,
as w
Molecular
streamers
been
obs
ストリーマー
S2theof W, roughly along
disk position angle.
the northern disk side, plausibly due to lower sensitivity. Indeed, weNorth
and tothecomponents
Southof W,molroug
Keywords:
ISM:
kinematics
anddynamics
–
ISM:
tems,
e.g.,
betweentheof
n cannot be due to a jet or an outflow as it isfind that the blue-shifted disk side is brighter than the red-shifted 17

N

4

S. Mercimek et al.

Figure 2. Channel maps of the C18 O (2–1) emission on the low velocity range ([+0.2, +3.0] km s 1 ). The first contour is at 3f (4.2 mJy beam 1 ) and the ste
is 10f. The synthesized beam is shown by the black ellipse in the bottom-left corner of the first channel (beam: 0.00 53 ⇥ 0.00 44). The positions of VLA 1623A
B, and W are indicated by the white stars and are labelled in the first channel. The magenta contours in the channels from +1.0 km s 1 to +2.2 km s 1 indica
the outflow cavity walls probed by CS (5–4) emission (25f contour, from Ohashi et al. 2022).The northern, N, and southern, S1 and S2, streamers are labelle

Figure 3. Channel maps of the C18 O (2–1) compact emission around the VLA 1623W protostar (green star) at high red- and blue-shifted velocities, i.e. fro±2 km s 1 to ±4.2 km s 1 with respect to the VLA 1623W systemic velocity (+1.6 km s 1 ). First contours and steps are 3f (5.4 mJy beam 1 ). The veloci
offset with respect to +sys (W) is reported in the top right corner of each panel. The black contour is the 3f level of the 1.3 mm continuum emission, which
also shown by the gray scale background. The synthesized beam (0.00 48 ⇥ 0.00 40) is shown in the bottom left corner of the first channel.

Figure 2. Channel maps of the C18 O (2–1) emission on the low velocity range ([+0.2, +3.0] km s 1 ). The first contour is at 3f (4.2 mJy beam 1 ) and the stepis 10f. The synthesized beam is shown by the black ellipse in the bottom-left corner of the first channel (beam: 0.00 53 ⇥ 0.00 44). The positions of VLA 1623A,
B, and W are indicated by thewhite stars
labelled in the first channel. The magenta contours in the channels from +1.0 km s 1 to +2.2 km s 1 indicate
MNRAS
000, and
1–9 are(2022)
the outflow cavity walls probed by CS (5–4) emission (25f contour, from Ohashi et al. 2022).The northern, N, and southern, S1 and S2, streamers are labelled.

A] 20 Apr 2023

2

Max Planck Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany.
3
L la piscine, 38406E Saint Martin d’Hères, France.
Institut de radioastronomie millimétrique, 300 rue de4
Instituto de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México, Morelia, 58089, Mexico.
5
Instituto de Astronomía, Universidad Nacional Autónoma de México, Apdo Postal 70-264, Ciudad de México, Mexico.
6
MIT Haystack Observatory, 99 Millstone Road, Westford, MA 01886, USA
2
7
National Radio Astronomy Observatory (NRAO), 520 Edgemont Road, Charlottesville, VA 22903, USA

The distance to the Serpens South cluster from H O masers

1,
2
3,
2
4,
5
2
6
7
Gisela N. Ortiz-León , Sergio A. Dzib , Laurent Loinard , Yan Gong , Thushara Pillai , and Adele Plunkett

April 24, 2023
1

Instituto Nacional de Astrofísica, Óptica y Electrónica, Apartado Postal 51 y 216, 72000, Puebla, Mexico. e-mail:
ABSTRACT
gortiz@inaoep.mx
2
Max Planck Institut für Radioastronomie, Auf dem Hügel 69, D-53121 Bonn, Germany.
In this3 Letter we report Very Long Baseline Array observations of 22 GHz water masers toward the protostar CARMA–6, locatedInstitut de radioastronomie millimétrique, 300 rue de la piscine, 38406 Saint Martin d’Hères, France.
at the4 centeroftheSerpensSouth
youngcluster.
Fromtheastrometric
fits
to
maser
spots,
wederiveadistanceof
440.7±3.5pcforInstituto de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México, Morelia, 58089, Mexico.
5
the protostar(1%error).
This
represents
thebest
directdistance
determination
obtained
so
far
for
an
object
this
young
and
deeplyInstituto de Astronomía, Universidad Nacional Autónoma de México, Apdo Postal 70-264, Ciudad de México, Mexico.
6
embeddedthis highly
obscured 99
region.
Takingdepth
effects MA
into 01886,
account,
we obtain a distance to the cluster of 440.7 ± 4.6 pc. Stars
MITinHaystackObservatory,
Millstone
Road,
Westford,USA
7 in the optical that have astrometric solutions in the Gaia Data Release 3 are, on the other hand, all located at the periphery ofvisibleNational Radio Astronomy Observatory(NRAO),
520
Edgemont
Road,
Charlottesville,
VA
22903,
USA+51

the cluster. Their mean distance of 437 41 pc is consistent within 1 with the value derived from maser astrometry. As the maser
Aprilsourceis at24,
the2023
center of Serpens South, we finally solve the ambiguity of the distance to this region that has prevailed over the years.
Key words. astrometry – water masers – star forming regions – Serpens South – stars: low-mass – techniques: interferometric
ABSTRACTIn this Letter we report Very Long Baseline Array observations of 22 GHz water masers toward the protostar CARMA–6, locatedat the center of the Serpens South young cluster. From the astrometricfitsettoal.
maser
spots,
we derive
distance
440.7±3.5
pc forIntroduction
León
2017;
Herczeg
etaal.
2019;ofZucker
et al.
2019).
the protostar (1% error). This represents the best direct distance determination
obtainedetsoal.
far(2019)
for an object
this young
and deeply
instance, Herczeg
reported
distancesto subclus
embeddedinthishighlyobscuredregion.
Takingdepth
effects
intoaccount,
weobtainadistance
tothecluster
of
440.7
±
4.6
pc.
Stars
e Serpens South region hosts a rich protostellar cluster that and dark clouds in the Aquila Rift based on Gaia Data Rele
visible in the optical that have astrometric solutions in the Gaia Data Release 3 are, on the other hand, all located at the periphery ofs discoveredbyGutermuthetal.
(2008)
from
2
(DR2)
data
and
star
counts.
These
authors
found
distances+51 Spitzer imaging.
the cluster. Their mean distance of 437 41 pc is consistent within 1 with the value derived from maser astrometry. As the maser
18 S
e clustersourceis embedded
in a ofmassivefilament
438±11,478±6,to383±2,
and407±16
pc forover
Serpens
Main,
is at the center
SerpensmolecularSouth, we finallysolve(André
the ambiguityof the distancethis region
that
has prevailed
the years.

徐
々
に
暗
く
な
っ
て
い
る

motion is shown as a black arrow in Fig. C.3 and has values ofµ↵ cos = 0.83 and µ = 5.18 mas yr 1 .
To obtain proper motions of sources in the rest frame of
the molecular cloud complex, we had to remove the expected
proper motion from Galactic rotation. We used a rotation velocity for the LSR of ⇥0 = 239 km s 1 , a distance to the Galactic
center of R0 = 8.3 kpc (Brunthaler et al. 2011), and a Solar motion of U0 = 11.10 km s 1 , V0 = 12.24 km s 1 , and
W0 = 7.25 km s 1 (Schönrich2010).
Theinresulting
Fig. 2: Spatial distributionetof theal.
water maser
spots. The numbers
the corners indicate thestellar
velocity channel in km s . The symbols
are color-coded by epoch (see the figure legend). The spots used for the astrometric fits are filled with crosses (see Sect. 3.2).
motions from this subtraction are shown in Fig. 4. We note thatin this figure sources in the スペクトルの速度成分は複数あるのにwest of Serpens South have propermotions mostly pointing
towardthewhereasin the velocity channel in km s . The symbols
Fig. 2: Spatial
distributionof the south,
water 2),maser spots.
The numberssourcesin the corners indicate
固有運動解析(fig
視差推定(fig3)で使ったのは,color-coded by epoch (see the figure legend). The spots used for the astrometric fits are filled with crosses (see Sect. 3.2).
the east of W40 have areRAproper motions mostly pointing toward
網掛けした成分のみ
the west. This may result from an interaction
between W40 and
Serpens South. The proper motions of stars in W40 have mag1
nitudes ⇡ 2 mas yr , which correspond to tangential velocities
そのような弱点？
があったとしても⇡ 4 km s 1 for a distanceof 440.7
pc.spots detected in the velocity range V = 9.76 to 10.81 km s . (a) Measured absolute spotGaiaで周囲の星の固有運動から求めた距離とVLBAが⾼密度メーザーガスで
Fig. 3: Astrometricfits to water maser
positions, shown as blue squares. The dashed black line is the fitted model. Expected positions from the best-fit model are shown as
求めた距離が整合する. → Serp S.の「妥当な距離」が求まった.
black
dots.
(b)
Measured
positionsandbest-fit
model
after
propermotionsareremoved.
(c)
Residualsoftheastrometric
fit
in
RA
Shimoikura et al.(top panel)(2019)
suggest that an outer expanding
and Decl. (bottom panel).
shell created by the W40 HII region is interacting with the dense Fig. 4: Spatial distribution of Gaia sources (green star symbols)
et al. 2022) associated with CARMA–6. We note that the directhe Serpens
South and W40 regions. The arrows indicate theirtion of the maserandproper motion
is close to in
perpendicular
to thegas associated with Figure
theC.3Serpens
South
young
cluster,thatshows the proper motions of the maser source and large-scale molecular outflow, which is oriented in the southeastdirection (see Fig. 3 in Ortiz-Leónet al. 2021).
the Gaia sources.(a)The Gaia sources have a mean value of northwest
propermotions. The red star and red arrow mark the location of(b)(c) This
this interaction induced
star
formationinthecluster(seealso(µ cos , µ ) = (0.37, 6.06) mas yr , with a mean error suggests that the masers are most likely associated with a diskof 0.2 mas yr . We also show proper motions of five radio con- wind. We will investigate this in a forthcoming paper.
thekmwatermaser
associatedwith CARMA–6 and the proper moFig. 3:sources
Astrometricfits to by
water
maser
detected
range V=9.76 to 10.81
s . (a) Measured
absolute
spot
Nakamura et al. 2017).
Shimoikuraetal.
(2019)
estimateantinuumin W40 derived
Ortiz-León
etspotsal. (2018).
The in the velocity
positions,as bluesquares.
The
dashedblackofline isOn
thethefitted
model.
positionsfromarethelarger
best-fit model are shown asother hand,the Expectedmotions of mostGaia sourcesmasersource shown
has a propermotiondifferent
fromthe motion
1tion
the astrometricfits. The cyan arrows indicate propertheGaiasources
locatedin theofwestof⇠3
the Serpens
Southsregion.
inmagnitude
thantheexpected
proper motion
due tofrom
Galactic
black
dots.
(b)
Measured
positionsandbest-fit
model
after
properis
motions
are removed.
(c)Residualsof the astrometric
fit in RA.
Thissimilarexpansion velocity for
the
shell
km
This
expectedsince
the maser
emissionarises from gas that rotation (see, e.g., Dzib et al. 2017) for objects at the location(topispanel)
and
Decl.
(bottom
panel).
may be moving along a jet or along a disk wind (Moscadelli of the Serpens South and W40 regions. The
expected proper of stars in W40 that have VLBA astrometric solutions
to themagnitude
the velocityof the Gaia sources in W40 motions
raged VLBA
spectraof the ofwater
maser emis1(Ortiz-León
etthatal.
2015). We subtracted the expected proper moProper2022) associated with
CARMA–6. We notethe direcd toward CARMA–6.
were4.2. obtainedin- 4 that the Gaiaettional.sources(⇡ 4 km s They). However,wemotionssee byin Fig.
of the maser proper motion is close to perpendicular to thetionwhichof istheSerpens
South and W40 regions due to Galactic rotaoutflow,orientedin the southeastFigure
C.3Serpens
showsandthe propermotions ofbelong
the maser source
and large-scale molecularr the area thatcoversall detected
spots,
theirat thewesternmost
side
of
South
to
“filament
A”
the Gaia sources. The Gaia sources have a mean value of northwest direction (see Fig. 3 in Ortiz-León et al. 2021). This18
1, µ ) = (0.37,
tion
from
the propersuggeststhat the masers
are most
likely associatedwith a diskmotions shown here. The background shows
cosdashed
6.06)
mas Shimoikura
yr , with a mean error
ndicated in thelegends.
line
atof
tracedby C TheO atvertical
6 km(µ
s
(see
Fig.
12
et
al.
2019),
of 0.2 mas yr . We also show proper motions of five radio con- wind. We will investigate this in a forthcoming paper.
1
the H2 column density map obtained with Herschel (André et al.
sourcesinFig.
W40 derivedbyOrtiz-León et al.that(2018). thisThemarks thevelocity
oftinuum
thetheircloud.
andsystemic
the model
shown
in
18
suggests
filament
19
maser source has a proper motion different from the motion of
On the other hand, the motions of most Gaia sources are larger
1

1

(a)

(b)

(c)

1

LSR

4.2. Proper motions

1

↵

1

LSR

Article number, page 4 of 13

↵

1

1

1

short title: Protostellar Outflows

Can Protostellar Outflows Set Stellar Masses?
Philip C. Myers
Center for Astrophysics | Harvard and Smithsonian (CfA),
60 Garden Street
Cambridge, MA 02138, USA
pmyers@cfa.harvard.edu

Abstract

The opening angles of some protostellar outflows appear too narrow to match the expected

core-starmass
efficiency
!"#
=
0.3
−
0.5,
if
outflow
cavityvolumetracesoutflow
mass,
with
a
short title: Protostellar Outflows
conical shape and a maximum opening angle near 90 degrees. However, outflow cavities withMichael M. Dunham
Department of Physics, State University of New York at Fredonia paraboloidal shape and wider angles are more consistent with observed estimates of the SFE. This
280 Central Avenue
Fredonia, NY 14063, USA

paper presents a model of infall and outflow evolution based on these properties. The initial state

Philip C. Myersis a truncated singular isothermal sphere which has mass ≈ 1 -⨀ , free fall time ≈ 80 kyr, andCenter for Astrophysics | Harvard and Smithsonian (CfA),
small
fractions of magnetic, rotational, and turbulent energy. The core collapses pressure-free as
60 Garden
StreetCambridge, MAits02138,
protostarUSAand disk launch a paraboloidal wide-angle wind. The cavity walls expand radiallypmyers@cfa.harvard.edu
and entrain envelope gas into the outflow. The model matches SFE values when the outflow
SEF = 0.3-0.5という典型値に対し、
Ian W. Stephens
Department of Earth, Environment, and Physics
Worcester State University
486 Chandler St.
Worcester, MA 01602, USA

いくつかの分⼦流の開き⾓は狭すぎる。 mass increases faster than the protostar mass by a factor 1-2, yielding protostar masses typical of
MichaelM.
Dunham→ コアの破壊を開き⾓の⼤きい
the
IMF.
It
matches
observed
outflow
anglesiftheoutflow
mass
increases
atnearly
the
same
rate
DepartmentofPhysics,
State
University
of
New
York
at
Fredonia
分⼦流によると考えた場合、
asAvenue
the cavity volume. The predicted outflow angles are then typically ~50 deg as they increase
280
Central
SFEを説明できるか？ ̶> できる.
Fredonia, NY rapidly
14063,throughUSA the stage 0 duration of ~40 kyr. They increase more slowly up to ~110 deg during
その場合、放物線型の分⼦流

their stage I duration of ~70 kyr. With these outflow rates and shapes, model predictions appear

コア破壊機構として
Ian W. Stephensconsistent with observational estimates of typical stellar masses, SFEs, stage durations, and分⼦流だけ考えればよく、
Department of Earth, Environment, and Physics
外部機構(e.g., 輻射)など必要ない。
outflow angles, with no need for external mechanisms of core dispersal.

Worcester State University
486 Chandler St.

⇨ それは現実を無視しているでしょう。
⾔い⽅として、「コア破壊が分⼦流だけによる場合、本研究が⽰した条件であれば、それは機構としてありうる。」くらいが妥当か？

20

~ 1 km s . The parabolic shell lines indicate a bipolar outflow shell (Lee et al. 2000, Z19),

utward radial arrows indicating shell speed as given in Z19. For simplicity the central

maystructure
be consistentwithobservations(Z19),Rate
but radial motions are more compatible
and entrainment
flatteningofthedensityarenotshown. 2.1.
Protostellar
Mass Accretion
2. ofInfall-Outflow
Modeltrationmass accretion
rate CD*+ ⁄CE is derived from the rate at which a shell ofThis infall-outflow model (hereafter "IO model") isThean protostellar
idealized descriptionof a low-masswith the spherically symmetric initial model to be adopted here. Thus the assumed core geometrygas falls fromits andinitialradius6.5
to ×
accrete
10 K,
radius10% onto the protostar. The envelope consists of all
star-forming dense core, with typical initial mass 1envelope-⨀ , temperaturein Figure 1 is based on radial infall,
andonradialexpansion
outflow shells.
gas within
the initialcoreboundary
whichofis paraboloidal
not
au. Its mass components include the infalling envelope,
the protostellar
star-disk
system,andthein the outflow and not in the protostar.
The core estimates
free fall time is ofdenoted
as :$ fromangles
the initialandtruncation
fromIf outflow models match observed
opening
the radius
SFE,F, andit asis:$,-also
initial interior shells of radius F′, where 0 ≤ F′ < F.

The rate of envelope mass loss to the5important to determine whether
such ismodels
consistent
with observed protostar and coreoutflow
assumed toarebe CD.)/ ⁄CE = − D.)/ ⁄:# , for consistency with tapered mass accretion
ratesevolutionary
derived from outflow
observations
et al. evolution
1996, hereafterof
B96;
Curtisoutflow
et al. 2010),
masses, with the durations of theirstages,and(Bontemps
with thetheir
Figure 1. Sketch of IO model components in a plane containing the outflow axis and protostar at

protostar surveys (Fischer et al. 2017), and simulations (Schmeja & Klessen 2004, Vorobyov

angles. This paper addresses these points with a simple model of infall and outflow (hereafter IO

the center of a spherical initial core. For simplicity the central concentration of the core gas is notshown. The left panel shows the initial core. The right panel shows the core components after halfof a free-fall time, at the end of the Stage 0 phase. These components include the central protostar

このような観測事実を説明するために作るモデルにおいて、model) in a low-mass dense core.
さまざまな開き⾓の分⼦流をサンプルしたサーベイデータから導かれる

and disk, an infalling spherical shell at half the
6 initial radius (black), and paraboloidal outflow

shells (red and blue) due to wide-angle winds as in Lee et al. (2000), Z16 and Z19. Each outflow

shell spans the opening angle A&' evaluated at the core outer radius. Inward arrows show the7

経験的な関係をモデルに⼊れることは
The initial state of the IO model resembles
a singular isothermal sphere (SIS; Shu 1977)

radial inward motion of the infalling spherical shell. Outward arrows show the radial motion of
the paraboloidal outflow shells.

Low-mass single starsに限定した１次元の解析的モデル。
論理⽭盾では？
with relatively small fractions of magnetic, rotational, and turbulent energy. The core collapses
素過程の物理から組み⽴てるのではなく、 （このような扱いをしている項⽬が多数）
radially inward to form a disk and protostar, which launch episodic wide-angle wind shells. The
現象論的＆経験的関係を組み合わせているように⾒える。
The core evolution depends on the free fall time :$ within its initial truncation radius, on

the dispersal time scale :# for envelope mass loss to the outflow, and on the "infall time" :() for

the outermost shell to fall to the origin. Here :() > :$ due to dense gas dispersal by the outflow.
The "dispersal parameter" 8 ≡ :# ⁄:$ indicates the relative importance of infall and dispersal.

In the following, section 2.1 derives the protostar mass accretion rate. Section 2.2 derives

the mass evolution of the protostar, the infalling envelope, and the outflow mass. Section 2.3

calculates :() by numerical solution of the equation of motion of an infalling shell. Section 2.4

shells merge and push radially outward into the infalling envelope (Z16, Z19). In this model

quantifies the resulting relations between 8, :() , and 0. Section 2.5 uses these results to predict
final mass fractions of the protostar, envelope, and outflow as functions of 8. Section 2.6 describes

特にコア散逸過程の物理が不明

the relative rates of envelope mass flow to the outflow and to the protostar.

Figure 8. Evolution of core mass fractions U in the protostar (red), in the infalling envelope(green), and in the outflow (blue), for a protostellar system with representative dispersal parameter
81 = 2⁄M. The resulting U*+,$ = 0 = 0.44 lies within the usually estimated range 0 = 0.3-0.5. Asradial motions predominate except on the scales of the disk and the cavity-envelope interface,in Figures 6 and 7, Q = E⁄:$ is the ratio of accretion age E to core free fall time :$ . The accretion

The protostellar mass accretion rate CD*+ ⁄CE is derived from the rate at which a shell of

on initial core mass -(0) = 1.05 -⨀ . A vertical line indicates the adopted boundary between

2.1. Protostellar Mass Accretion Rate

which are negligibly small compared to the core scale.

envelope gas falls from its initial radius to accrete onto the protostar. The envelope consists of all
gas within the initial core boundary which is not in the outflow and not in the protostar.

The core free fall time is denoted as :$ from the initial truncation radius F, and as :$,- fromThe structure of this paper is as follows. Section 2 derives expressions for the mass

initial interior shells of radius F′, where 0 ≤ F′ < F.

The rate of envelope mass loss to theoutflow is assumed to be CD.)/ ⁄CE = − D.)/ ⁄:# , for consistency with tapered mass accretion
rates derived from outflow observations (Bontemps et al. 1996, hereafter B96; Curtis et al. 2010),
protostar surveys (Fischer et al. 2017), and simulations (Schmeja & Klessen 2004, Vorobyov

fractions of the protostar, envelope, and outflow, as functions of time and of the dispersal

age (top x-axis) is based on free-fall time :$ = 82 kyr, and the mass scale (right y-axis) is based20

evolutionary stages 0 and I, when the protostar and envelope masses are equal, and between stages
I and II, when the envelope mass is zero.

dxxの形で与えるから
mass at the 諸量を￼
end of stage 0 is 0.28=-−, the final
protostar mass is 0.46 - , and the final outflow
dtτ
dmass is 0.59 - . The evolutionary stage boundaries
are at E = 41 kyr and E = 103 kyr, and the−t/τanddのかたちの結果ばかりにstage durations
∆Edや￼
= 41
∆E = 62 kyr.
￼1 − eare−t/τekyr
In Figure 8, the SFE is 0 = 0.44, within the standard range of SFE values. The protostar
⨀

⨀

⨀

8

8

K

K

なっているのか？

7

parameter 8 ≡ :# ⁄:$ . Here 8 is the dispersal time scale :# normalized by the initial free-fall time

4. Outflow Opening Angles:$ . Section 3 presents the time history of these component masses depending on 8. Section 4

estimates of the SFE. It uses these results to predict the opening angle evolution for an expanding

describes observed outflow opening angles and presents cavity volume fractions for power-law

This section estimates final opening angles A of observed outflow cavities. It derives
さらに￼τ の与え⽅がよくわからないので、
the cavity volume dfraction for power-law cavity shapes, and relates the volume fraction to&'$

緩和時間を恣意的に与えて、モデル結果を

paraboloidal cavity.

サーベイ研究の結果にあわせているように⾒える。
4.1. Outflow Mass to Volume Ratio

As noted in Section 2.2, the SFE can be written in terms of the final outflow mass fraction21Line emission from filaments in molecular clouds
1?

2

1

F. D. Priestley , D. Arzoumanian & A. P. Whitworth

1 School of Physics and Astronomy, Cardi↵ University, Queen’s Buildings, The Parade, Cardi↵ CF24 3AA, UK

stro-ph.GA] 24 Apr 2023

2 Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

乱流convergによるフィラメント形成モデルが, 運動学的な特徴も再現できるかどうか？
Highly超⾳速のガス流⼊で形成されたフィラメントであっても, 13CO, HCN, N2H+輝線幅は、典型的には亜⾳速から遷⾳速.
Accepted XXX. Received YYY; in original form ZZZ
観測されたフィラメントが, このシミュレーションのように動的に形成されたものであれば,• 平衡解析は不可能であり,• フィラメントの存在を前提としたシミュレーションは, ⾮現実的な結果である可能性が⾼い.
ABSTRACT

Filamentary structures are often identified in column density maps of molecular clouds, and appear to be importantfor both low- and high-mass star formation. Theoretically, these structures are expected to form in regions where
the supersonic cloud-scale turbulent velocity field converges. While this model of filament formation successfully
reproduces several of their properties derived from column densities, it is unclear whether it can also reproduce theirkinematic features. We use a combination of hydrodynamical, chemical and radiative transfer modelling to predict theemission properties of these dynamically-forming filaments in the 13 CO, HCN and N2 H+ J = 1 0 rotational lines.
The results are largely in agreement with observations; in particular, line widths are typically subsonic to transonic,
even for filaments which have formed from highly supersonic inflows. If the observed filaments are formed dynamically,as our results suggest, no equilibrium analysis is possible, and simulations which presuppose the existence of a filament
are likely to produce unrealistic results.
Key words: astrochemistry – stars: formation – ISM: molecules – ISM: clouds – ISM: structure22

is observed (Palmeirim et al. 2013).
Figure 2 shows the 13 CO, HCN and N2 H+ line profiles2 at フィラメントが実際にHighly超⾳速の13
di↵erent evolutionary stages. The CO line is stronger and ガス流⼊で形成されたのであれば、初broader than the others, and is typically symmetric,
being althoughaccreted from a期に「フィラメント在りき」で、中⼼
sheet-like structure at an inclination
to the line of sight
et al. 2022), so that lines are
集中度の⾼い密度＆速度構造を仮定しin some cases ‘wings’ around the central line corresponding
to (Pineda
redshifted on one side たシミュレーションは、不適切。
of the filament and blueshifted on thethe inflowing material are visible. HCN profiles areasymmetother. The sheet itself is often suggested to have formed inric, showing the characteristic infall signature theof interface
redshifted
between two colliding molecular clouds (e.g. Bal最初期にはフィラメントが存在しない
four
et
al.
2015,
2017;
Inoue et al. 2018; Abe et al. 2021). As
self-absorption. However, this self-absorption is not due to という、現実的な計算（フィラメント
our models are cylindrically symmetric by construction, they
the inflowing material, which can also be seen are
asincapable
extendedof reproducing
these gradients, which would re形成を含めた計算？）が与える、密度
quire angular variationin the properties of the accreting gas.
wings in some cases. The velocity of the self-absorption
is ＆速度構造かそのような（中⼼集中度
However, synthetic line observations of turbulent molecularmuch lower than that of the inflow, and arises clouds
insteadfrom の⾼い密度＆速度）構造を与えるとの(Priestley & Whitworth2020) find that the resulting filamentary
do in fact tend to have velocity
the gravitational contraction of the dense central
filament.structures
保証はないから。
gradients perpendicular to their spines, even in the case ofN2 H+ profiles are symmetric, showing no self-absorption,andisolated clouds with no今後の計算研究は、対象天体の形成を
collision-induced layer. This suggests
have negligible emission from the inflowing material.
that supersonic turbulence by itself is capable of producing
含めて、self-consistentな設定で⾏う
thesheet-likestructuresinferred observationally, particularly
Figure 3 shows the evolution of line peak intensities andべき.
as some degree of compression
is necessary in order for the
full-widths at half maximum (FWHMs) with central
density.
accretingmaterial to be detectable in line emission.
6

4.6 Preexisting versus dynamical filaments

molecularlinesthat a7
It is common practice inFilament
theoretical studies
to assume
filament already exists at the outset of the model, in that theinitial radial density profile is quite centrally condensed (e.g.
Seifried & Walch 2015, 2016; Gutiérrez-Vera et al. 2023; Misugi et al. 2023). If filaments are actually structures formed via
turbulent accretion, this is inappropriate. Even if the initial
filament also has supersonic converging motions (e.g. Clarke
et al. 2016), there is no guarantee that the resulting densityand velocity profiles will resemble those in the more realistic
scenario where no filament exists at the outset, particularly
given that the definition of what counts as a filament seems
to be strongly related to the accretion shock (Priestley &Whitworth 2022). We suggest that future studies should focus on forming the objects of interest self-consistently (e.g.
Smith et al. 2012, 2013), in keeping with their presumed origins from cloud-scale turbulent motions (Mac Low & Klessen2004).

And
Arz

5 CONCLUSIONS

The filaments identified in molecular clouds are thought toform due to supersonic turbulent motions within these larger
objects. We investigate the observational consequences of this
scenario, specifically the predicted molecular line emission
properties of filaments formed via supersonic flows. These
are largely consistent with data; in particular, line widths
are trans- to subsonic, even for highly supersonic inflows. The
central filament dominates the line emission, making it difficult to identify signs of the accreting material. Signatures of
infall, such as redshifted self-absorption in the HCN J = 1 0line, are due to the contraction of the filament itself, rather
than the accretion flows it formed out of. Additional velocity
components would only be visible in the limit of almost total
shielding from the external UV field, and even then only foruum emission images produced with lime. These have identiCO isotopologues. Our results support the idea that filaments
cal spatial resolution
to the line PPV cubes, and should trace13+
in molecular clouds are dynamically-forming objects, which
ional transitions of CO (blue), HCN (orange)theandN
H(green),
for
M
=
1
(top
row)
and
2
column density almost exactly, as we assume a constantcannot be modelled as equilibrium structures, or considered
dust temperature of 10 K and the optical depth at this wavedensity from left to right.
in isolation from their environment.
4length is extremely low (⌧850 < 10 ). The filaments appear

I/K

Mach 3
4.5 Filament widths in di↵erent tracers
1 These profiles
0.99 Myrare averaged over the z axis between ±1 pc, but
It is expected theoretically (Priestley & Whitworth 2020) and4
di↵erences
between the average profiles and individual
cuts arefound observationally (Shimajiri et al. 2023) that the same
minor (Priestley & Whitworth 2022).
filament will appear to have di↵erent widths when observed
2 We average the line profiles within a radius of 0.05 pc of thein di↵erent tracers. This is due to the complex combinationof excitation,
abundance and optical depth e↵ects which re2 approximating the e↵ect of typical single-dishorigin,beam sizes
late the column density along the line of sight to the obfor nearby (⇠ 100 pc) filaments. As the line emissionserved
is dominatedline intensity. Figure 7 shows the spatial variation ofby the central filament, increasing the averaging radius
has a negthe integrated
line intensities perpendicular to the filament
the spatial resolution of our radiative transfer modligible0 e↵ect on the shape of the profiles, althoughspine.
the Asaveraged
1.0
0.5
0.0
0.5
1.0 els (0.01 pc) is much worse than that of the underlying SPH
intensities are lower.
v / km s 1
simulation, we compare the line data to 850 µm dust contin-23