Star Formation Newsletter#336 1-8
Yusuke Aso (KASI)

marksFigure
the positionon theofstar
onattheGaia
and withaccounting
benecessary
to detect any gas in this sy
1. ImageHDbased
38206
1.35
mmDR2
afterposition
processing
the CLEAN 3 Mwill
O
D
E
L
L
I
N
G
for propermotion.
algorithm.
The contours show the ±2, 4, 6, and 8σ levels. The white cross

Resolving the outer ring of HD 38206 using ALMA and constraining limits

marks the position on the star based on the Gaia DR2 position and accounting
on planets in the system
3.1 Disc
3 Mset-up
ODELLING
for proper motion.

15 and 365 m. The1‹received data 1were calibrated using
the standard
1
modellingprocedure used here follows tha
Mark Booth , Michael Schulz, Alexander V. Krivov,1 Sebastián Marino ,2,3 Tim D.The
Pearce3.1
Disc
set-upobservatory
calibration
2 in CASA version 4.7.74. The quasar J0609and Ralf Launhardt(2019). We model the dust radial and vertical dis
Astrophysikalisches
Institutund Universitätssternwarte,Friedrich-Schiller-Universität
Jena,
Schillergäßchen
2-3,standard
D-07745 Jena, Germany
1542 15
was
used
for
bandpassandphasecalibration
andtheactive
and
365
m.
The
receiveddata
werecalibrated
using
the
dricalThe
coordinates,φ, z), asuseda Gaussian.
Giv
Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany
modelling&(r,procedure
here follow
InstituteofAstronomy,
UniversityofCambridge,
MadingleyRoad,
Cambridge
CB3
0HA,
UK
Ø デブリ円盤から惑星の場所を制限できる。
galactic
nucleus
PKS
0521-36
asflux
calibrator.
The
correlator
wasobservatory calibration in CASA version 4.7.74. The quasar J0609- shows(2019).
some signsof asymmetry,
we defineraWe modelthe dust radial
and theverticset
toprovidefour
spectralwindows,
processingtwopolarizations
in
1542
was
used
for
bandpassandphasecalibration
andtheactiveØ HD38206: Herschel（θ~6"）からi=60°に近く、11 auと160 au（幅11aau）にベルト。Columba
Gaussianin terms of thea(r,drical coordinates,&(r,semimajorφ, z), as aaxis,
GaussianAccepted 2020 October 23. Received 2020 October 21; in original form 2020 September 1
eachofthese.
Whileone
spectralwindow
wascentred
at
the
CO
J
=
galactic
nucleus
PKS
0521-36
asflux
calibrator.
The
correlator
wasassociation (71 pc, 42 Myr、若い)。
radialshows
distribution,r, where
the semimajor
axis istsome signsof asymmetry,
we define
2–1
line
at
230.538
GHz,
with
3840
channels
of
width
0.5
MHz,
the
set
to
providefour
spectralwindows,
processingtwopolarizationsin
ALMA observations of HD 38206
1605
Ø ALMA Cy 1, 213, 215,
and2-1は検出無し。
a Gaussian
incos(φterms
ABSTR
A C T 228 GHz, 0.97"x0.75"。160 µmと合わせてダストβ=0.6。CO
1
−
e
− of
ω)the semimajor axis,
other eachthreecentralfrequencies
of
213,
215,
and
228
GHz
and
ofhad
these.
Whileone
spectralwindow
wascentred
at
the
CO
J
=
HD 38206
is an
A0V
starTablein theColumba
association,
hostingadebrisdisc
firstdiscovered
by
IRAS.
Furtherobservations
by, the semimajor axa(r, φ)= r distribution,2 r, where
1. Overview of the stellar parameters that haveradialSpitzerandHerschel
showed
that
the
disc
has
two
components,
likelyanalogoustotheasteroid
andKuiper
belts
of
the
Solar
1
−
e
been usedfortheanalysis.
128
channels
with
a
width
of
16
MHz
to
study
the
dust
continuum
2–1 line at 230.538 GHz, with 3840 channels of width 0.5 MHz, the⻄に⻑いsystem. The young age of this star makes it a prime target for direct imaging planet searches. Possible planets in the system
1 − e cos(φ−ωω)is the argumentØusingガウシアン3D離⼼リングモデル。
Parameter
Referenceemission.
where
e is
the=eccentricity
and
other
had
centralof the213,
215,observations
and 228of GHz
andKuiper
can bethreeconstrainedthedebrisfrequencies
disc. Here, Value
we present
first ALMA
the system’s
belta(r,
and
fitφ)
them
,
r
2
using a forward
MCMC
approach.
We
detectan extended
disc ofdust
peaking
at around180
au with a density
width of distribution
dis
(pc)
71.3
± 0.4
1 been1−eØdiscパラメーターはa0,
Δa,
M
,
i,
PA,
e,
ω。
The128imageof themodelling
shown
in
Fig.
1.
This
has
createdfromsurfaceisthengiven bychannels
with
a
width
of
16
MHz
to
study
the
dust
continuum
dust(J2000)05 43tentative
21.67 signs of 2an asymmetry best fit by an eccentricity of 0.25+0.10 . We use
140 au. The disc is close RA
to edgeon and shows−0.09"! eccentricity
Dec. (J2000)
33 26.91
2
the inversely
Fouriertotransformed
complexvisibilities
using
naturalemission.
the fitted parameters
determine
limits on−18
the massesof planets
interior
to thecold belt.
We determine that a minimumof four
2 and ω2 is the argu
wheree is the)z(a−aAge (Myr)4230, in order
toprocessing
clear the gap between
asteroid
and Kuiper
beltsplanets
are multifrequency
required, eachRwith
massof0.20.64(R )a minimum
1.7 ±
4 by
−is then
,
&(r,
φ, z)
∝ofdensity
exp −distribution
weightingandfollowed
withtheoffrom
The
image
of the discissynthesis,
shownin
Fig.MJ1.
This
has
been
createdsurface2
2 r 2given by
the system. If we make theassumption
thattheoutermostplanetis
responsibleforthestirring
the
disc,
the
location
of
its
9610
2
T (K)
2σ
2h
"
! r
the CLEAN
a synthesized(L )transformed
26 ±we7complex
4visibilities
L (Högbom
edgealgorithm
and theFourier
eccentricityof the disc, 1974).
then
canWe
more obtaintightly
predict
its eccentricity,
mass, and semimajor axis to betheinner
inversely
using natural
2
2
)
z
(a
−
a
+0.20al.
+0.5+12± 0.4
M
(M
)
2.4
4
0
)a
1606 beam
M. weighting
Boothet= 0.34−0.13 , mp = 0.7−0.3 M J , and ap = 76−13 au.
ofep size
0.97
beam
positionangle with σr = &(r,− 2 2 ,
log(g)× 0.75 arcsec
4.4 ± 0.3 and a4Øarcsec
Spwごとのビジビリティをスペクトル指数2.6としてフィット。
andmultifrequency
synthesis,
followedby processing√ φ, z) ∝, exp −
22σ
2h r◦words:
planet–discinteractions
circumstellar
matter– stars:
individual: theHD 38206– planetary
2 2 log 2
References.
(1)– Bailer-Joneset al.
(2018),(2) Gaiar2=2N
measuredfromnorth
to east.
We
measurerms
to systems – submillimetre:of −86.5
theKeyCLEAN
algorithm(Högbom1974).
We
obtainasynthesizedØ
nullmodelでχとなるように重みをスケール。RADMC3D,
EMCEE。
vis
Collaborationetal.
(2018),
(3)
Bell
et
al.
(2015),
andsystems.has seven free parameters – a0 , !a,Table 2. Parameters for the best-fitting
model. The uncertainties given for
To summarize, planetary
our model)amean−1(4)Stassunet al. (2018).
where
a
.
The
disc
is
seen
to
be
edge-on.
There
is
the
theposterior
Gaussian,)a is thebe σ beam= 23.5
µJy
beam
of
size
0.97
arcsec×0.75
arcsecandabeam
positionangle0√percentiles, ofof thedistribution.
Ø Herschelより幅広でエッジオン。
r =84th
ALMA observations of HD 38206 1607 the parameters are the 16thσandMdust , I, ", e, and ω.
◦ oftherefore,
consistent with thismodel anddeeperobservations
2north,2 log
2ofωtheare some
signs
asymmetryatomuchpeak
intheemission
Gaussian,and h is themeasuredfrom with
north
east.
We
measurethe ofrmsanticlockwise
to maximumof −86.5" is measuredfrom(FWHM)
whilstis measured
anticlockwise
will be necessary to detect any gas in this system.
Figure 1. Image of HD 38206 at 1.35 mm after processing with the CLEAN
bySpitzer/MIPS(Riekeetal. 2005), Spitzer/IRS(Moraleset al.
algorithm. The contours show the ±2, 4, 6, and8σ levels.
cross
0.18
±The
mJy
the isstar,whilst
the".
west
the
low
resolutionof these
we do)anoti
where
a is the. Theofdisc
seen
toGemini/T-ReCS
betofromedge-on.
Theremeanobservations,of the Gaussian,be
σIwhite23.5µJybeam−1east
1 0.02N T=
RO
D U C T I2.1
O N arcsec
2009),(Moerchen,
Telesco&Packham2010),
and0
marks the position on the star based on the Gaia DR2 position and accounting
モデル
3 M O D EofLaLplanetaryING
3.2 MCMCof thepeaks
keysigns
components
system,studying
debrisHerschel/PACS(Moraleset al. 2016). Byof
analysingboththetheresolved
for proper motion.
thefitemission
at of
2.9asymmetryarcsecfromthebutinwithaemission
lower
resolvedisc (FWHM)
and so havearbitrarily
set andh = h0.0
areAs onesome
withastar,
peakthemaximumof theGaussian,
is
◦)
◦)
◦)
discs enables us to understand the current make-up of a planetary
Herschel imagesaand(au)the full SED,
Morales
et al.
(2016)(M
demonstrate
!a
(au)
M
)
I
(
"
(
e
ω
(
0
dust the⊕ dust
3.1mJyDiscdensity
0.09±set-up
0.02arcsec
mJy.
We
do thenotexpectthistothegrains, wea differentialwe
size
0.18
±
0.02
2.1
east
of
star,
whilstwest
resolution
ofassumethese observations,dosystemparameters,
andof
its
formation
andevolution.
In
recentthe
Atacamathatthe system
is seento
close
tobe
edge
on and has For
two thebelts atlow
11 andTo find theflux
best-fitting
we
make
use
ofyears,the
EMCEE
module15 and 365 m. The received data were calibrated usingLargethe standard
Millimeter/submillimeter
Array(ALMA)used
has madeit possible
160
au. etThesystem+19
is thought to beamemberoftheColumbaThe
modellingprocedure
here
follows
thatofMarinoal.
+46 with the+0.016+0.10
power-law
α have=3.5, following
toaimagepointing
issue
thecentrelocationagreeswelltheemission
peaks
atPYTHON
2.9in phasearcsec
from
the
star,
but
a 143
lower
the+1.3
discindex
and+1.2soarbitrarily
set himplementation
ofin cylin-(Torres(Foreman-Mackeyal.
2013).
iswavelengths
aas
CASA version due
4.7.74. The
quasar
J0609observatory calibration in
184with
0.105
83.3
0.25−
49+22
toet
these
discs
at It
longWemuchthan
Myr (Bell,association
et−17
al. 2008),
givingit an ageof 42resolve(2019).
model the dust
radialfiner
anddetailvertical
distribution−36−1.3 84.3−1.2−0.09−0.015−251542 was used for bandpass and phase calibration andtheactive possible
waspreviously(forarecentreview,see
Hughes,Duchêne&
Mamajek&
Naylor2015).
The
young
age
of
this
systemmeans
thatdricalcoordinates,
&(r,
φ,the
z),
asmJy.
a Gaussian.
Given
the theimage
energydistribution
analysiwith flux
theexpectedofsystems
star
based
onnot
Gaia thisDR2to be Following
an Affine Invariant
Markov
chain
Monte
Carlo
(MCMC)
Ensembledensity
ofposition
0.09 ±
0.02
We
dothatexpectForthethespectral
dust grains,
we assumea differentia
galactic nucleus PKS 0521-36 as flux calibrator. The
correlator
Matthewswas2018). Ofshows
particularareasymmetry,whereboth debris
it is a prime as
candidate for direct imaging surveys, although no planets
someinterest
signs of
we definethe radial distribution
set to provide four spectral
windows, processingtwopolarizations
Sampler(Goodman&toWeare2010).
wefit
directly
tothebeen
discs
and
at
one
planethave
beenpaper,
observed.
Analysis
of
such
have
detected
far. Shannon well
et al. (2016)
developeda model(2016),
the minimum
to(Gaia
Collaboration
et In
al.
2018)
after
correcting
forso agrees
propera Gaussian
inthistermsofsemimajor
axis,a(r,centre
φ),ratherthanthewithwethesetpower-lawindex αgrain= −radius
3.5, follo
due
ain=least
pointing
issue
astheposition
the
phase
locationeach of these. While one spectral window was centred systems
at the COisJ ofprime
importancefor understanding
the interaction
for the minimum
mass of planets required to clear a gap in a two belt
radialdistribution,
r,
where
the
semimajor
axis
isdeterminedby∼6arcsec.
None
the
less,
our findingthat
theispeakin theis larg
data,
which
has
been
averagedto onechannelpergraintheradiussetenergy
toan emission
arbitrarily
motion.
2–1 line at 230.538 GHz,visibility
with 3840 channelsof width
0.5 MHz,thespectral
distribution
an
with
the
expected
positionofsystems
the include
starspectral
based
the
DR2
betweenplanets
and the disc. Examples
of suchdebris disconsystem.
TheyGaiause HD 38206
as anmaximum
exampleFollowingcase and show
1 − e cos(φ − ω)
+19
1
2
3

◦

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otherhadModelcentralfrequenciesof 213, parameters
215, and 228
andMiddle: Image residuals after subtracting the best-fitting model. The contours show
Figurethree
2. Left:image
for the best-fittingof theGHz
model.

+6−4

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represent
the minimum
numberand mass based on
the modelof Shannon"3 to determine that it must!
enoughbe muchwider thanpreviously
fromthe outermost
planet. The
timescaleplanetstill
stirring
y analogy with ourwouldleadistodefineda (marginally) sta
mass
mp thatfora1
Figure4. Constraints
on migration
the possibleofnumber
ofplanets
planets in theet gap
and theirsuchasdivergentplanetesimal-driven
pairs
of
al.
(2016)
and
using
K
=
16
and
K
=
20,
respectively(seeequations10
inassumed.
Forourpurposes,
weshallapproximate
the
edges
of
the
by
Mustill&Wyatt(2009)
asenario(12)in which
the
−
1
=
(3
−
e
)M
.
(14)
m
p
p
#
masses.2018)
grey
shaded region
thewithboundson 11).
the Themodel
horizontal dashed line represents the minimum number below(Morrison & 125
Kratteror sweeping
secularrepresents
resonances
one basedand
the planets themselves would already be close to b
aThe
Resolving
the
outer
ring
ofthe
HD
38206
using
ALMA
and constrainingp (1 + ep )#$limits
discwith
theetFWHM
theGaussian.
words,
ar, nearly-coplanar
in = are invalid (see equation 12).
3/2
which
equationsof Shannon
et al.a(2016)
Faberin&an
Quillen(2007)
equationsand of9).For
The fitted
crossandthedot In other‘lonely’ giantofplanet
eccentric
orbit(see(Zhengal.82017).
that planetesimals would already be co# argue
1 − ep2 theyplanetsin ±thesystem−spacing!a/2=three110
30theau.modelWhilstfollow-up, higher resolution
anumberive scenarios
exist,
cessary
to simplicity,
0onaout $9/2
Thus,we
wenow
have
equations,withunknowns.
represent
the minimum
and
mass
based
on
of Shannon
also
assumea twolog-uniform
and
equal
masses3
the planetary
ensuring andthe thegapargument
to be deo
≈ 1.53criterion
× 10 was Figure fromtpstability
planetin themodel, exceptthat the underlying
observations
may
the
real
distribution
is different
todistributionregion,
for the eccentricityofpairsweof planets(2016)
and usingK=and K
20, determine
respectively(seeequations10
whenfor all planets
inal.
the
gap.
Finally,
weis
assumethatthe=allegedplanets Ifthat
One etof
theunknowns
the16planet
eccentricity.
theplanetis
ep 3. Posterior
10 auの続き
only
by
Faber
& Quillen(2007)Marino
by numericalintegrations
material.
They thenalso isestimate
the minimum
1 established1still quite
1"
Whilst a non-zeroeccentricity
clearly preferred,a circular ringn
this,
the
uncertainties
onminimum
the
inner
edge
measuredareandstable
11). The
dashedline
represents
thenumberbelow
are onedynamicallyagainstmutualperturbation
overageof Schulz,
esonances"1/2!pericentre.
Mark
Booth
,1‹theMichaelAlexander
V.hereKrivov,
Sebastián,2,3!TimD.
Pearcees that forwith
−1 #
$the
eccentric,
thenthishorizontal
will
affectthedisceccentricity.
Therefore,
our range−3Mma
withinacertainofmassesandmayfailoutsidethat
range.
still
consistent
within3σuncertainties(definedbytheoutermostcontour2#
p To do this,ptheyplace them at separations
that awhich the equations of Shannon
et al.
(2016)(seetheequation
12). edge. In addition, wethe Forcentral star.
large
solikelyare
to2invalid
containreal innerg et
al. 2017).
and and
Ralf
Launhardt
×
yr,
(13)
ry
systemconstraints
on
the
disc
eccentricity
canprovideconstraints
ontheAnother
approach
is
to
put
the
suspected
planetsinaconfiguration
+6
1
M
M
1
au
Many studies derived stability criteria
forupdate
both lower
mass twoplanets$ Germany$ as those that correspond to a marginally stable sy
Astrophysikalisches
Institutund Universitätssternwarte,Friedrich-Schiller-Universität
Jena,
Schillergäßchen 2-3, D-07745 Jena,
(Bell
also
the otherparameters, now
using τ = 42−4 Myrand equaleg they
are. masses
thatisD-69117
spacedwidely Germany
enough of
to ensurestability,
place 1609
planetesimals
planeteccentricity.
The1996;
two2FabercanberelatedthroughtheequationMax
PlanckInstitutefor Astronomy,Königstuhl
17,
Heidelberg,
ALMA
observations
HD
38206
planetinthemodel,
exceptthat
theunderlying
stability
criterion
was(e.g.
Chambers,
Wetherill&
Boss&
Quillen2007;
Zhou,
au (Moraleset Road,al. 2016).
From
this,
we
et3 Instituteal. 2015)
and aw = 8.7of Cambridge,
the alleged planets
thetheexpectation
significant
of plan= a0 + !a, ep is
eccentricityisofthat
theaplanet,
and apfractionisaoutintegrationsof Astronomy, University
Madingley
Cambridge
CB3 0HA,
UKto invoke where
betweenthe planetary
orbits,andnumerical
ertainties(2018) show that
&SmithWyatt2009):
Lin 次がわかっている。惑星は必要か？
&(Mustill
Sun 2007;& Lissauer
2009,
among
others)and massive
only
established
by
Faber
&
Quillen(2007)
bynumerical
integrations
=
3.3
±
1.4
find
(assuming
Gaussian
uncertainty
propagation)N
on over the age of
semimajor
axis of the planet.
Therefore,
if of
weneighbouring
assume that thisbetweenthe orbits
planets
would
and analytic argumentsp to see whether, and theon whichtime-scales,with onesthat(Morrison
Kratter2016).
Onethanwayof applying
thesefailcriteria
! "!
"−1 #
!
"−3
hnets
to determine
it 4
must
wider
previously
fromthe outermost
planet.
The
timescaleforplanetstirring
is definedwithinamuch
certainrange
ofmassesand mayoutsidethat$
20 range.
and
N
=
4.8
±
2.0
and
m
=
and
m
a& be
(i)カスケードでダストができるほど微惑星が撹拌。
4p = 0.6 ± 0.3MJ for K = thesepptime-scaleisequivalent
to
the
age
of
the
systemandtheoutermost
1 It is ρonly the bodies
vfrag orbiting
Smaxexactly
planetesimals will be removed from the system. This idea
thesystem.
tothegapclearing
wasproposedby
Faber&
Quillen(2007).
First,
ld
satisfy=e.
(15)e
Accepted
2020
October
23.
Received
2020
October21;
inoriginal
form
2020
September
1
=
9.3
Myr
T
ed.
Formass
our planets
purposes,
we shallapproximate
ofsuspected
theJ for K by
MustillWyatt(2009)
as ShannonpAnother
approach theis toedges
putplanets
in a&configurations= 16(largefilledcircleandrespectively,
± the
0.14M
lower
planetin theresponsibleforstirring
the disc
was
employed
bycross,
et al. (2016) who
found
the system
clearingis solely
γ that1 gwould
cm−3 have30
mout
s−1to its
km The5 the
ap maximum number of0.28
relation to theirthey(ii)内側と外側のリングのギャップ。
estimateplanets
Nap in =theplanetsa chance
to 200survive.
#$hesystem
ith
the
FWHM
of
the
fittedGaussian.
In
otherwords,
thatisspacedwidelyenoughtoensurestability,
place
planetesimals
in other words, since our
3/2
!
"
!
"
!
"
in
Fig.
4).
In
data
allow
us
to
determinethatthetime-scaleofthechaoticzone
asafunctionoftheplanetmass
andQuillen 2007;mass
Zhou,
−1/2
−1
outer edge, we can find a familyof thensolutionsmass,
semi-major$7/2# afor its
2
mp that would still lead to a (marginally) stable system. Since
M
Mthe
%a/a
# a $9/2
wouldcertainlybestable,$00 whilst
disc gap woul
1
−
e
!a/2
=
110
±
30
au.
Whilstfollow-up,
higherresolutionIn
ourmodelling,
wehave
assumedasingleeccentricity
for
the
disc.
betweentheplanetary
orbits,andtoinvokenumerical
integrationsveclearedpaxiswithusing
simulations.
From
×
(6
out
(iii)⾮対称は動的相互作⽤。
that wassemimajor
not3 possible
theN-body
Herscheldataothers) and massive
Bis
S TwideRC–
T somethingaxis,theseand simulations,
eccentricity. Strictly
speaking, 100
theseare all lower
limitsthe planets
themselves would already discbeAclose
toAbecoming
unstable,
1.53
×a10
tp ≈
M
aucalculate
0.1
100 M⊕ Faber# In order todebris.
these
extremes,
ationsmay
determine
that
the
real
distributionisdifferent
toandanalyticargumentstoseewhether,
and
on
which
time-scales,
In
fact,
as
can
be
seen
from
this
equation,theinfluenceofplaneton,insidetheyderived
a
lower
limit
on
the
mass
of
each
planet,
m
nner
edge
p
HD
38206
is
an
A0V
star
in
the
Columba
association,
hostingadebrisdisc
firstdiscovered
by
IRAS.
Furtherobservations
by
–
we
find
that
the
gap
is
smaller
than
the
gap
assumedby
Shannone10
aulying these criteria
since a more massive, more distant, or more eccentric planet could
they argue that planetesimals would already be completely removedpe uncertainties
on
inner
edge
measured
are
still
quite
providethe following
formulae:theassuming
mass
planets
withtoathe
separationof K
mutualthese
planetesimals
willremovedfromthesystem.
This
idea
!the
"gap,
"−1equal
SpitzerandHerschel
showed
that
disc
has!
two
components,
likelyanalogous
andKuiperbelts
of theSolarathetheplanetesimal’s
eccentricity
isbe
strongertheclosertheplanetesimal
where
γshorterisa constantfactorbetween1system.
and 2, ρ is the density, v frag incertainty
etgap
al.
(2016)
andsothemassesrequired
to
clear
the
gap
are
lower
1/2
planetary
region,ensuringhere
the
to
be
devoidofanydebris$#uillen(2007).from
First,
stirasteroid
the discona time-scale
than
the
age
of the
−3
M
m
a
2
#
p
p
Ø
200
kmの微惑星がいくつかあったなら13
Myrで⼗分撹拌（Krivov&Booth18）。
Hill’sradii.
Modifying
theirequations
such
that
K
is
left
as
a
free
In
addition,weandso
likelytocontain
the
real
inner
edge.
system.
The
young
age
of
this
star
makes
it
a
prime
targetfor
directimagingplanetsearches.
Possibleplanetsinthesystemwas
employedby
Shannonetal.
(2016)
who
found
the
clearingthevelocityrequiredfor
destructive
collisions,max is the maximum
×
yr,
(13)
material.
They
then
also
estimatetheminimum
numberofplanets.
than
their
analysis.
is to the planet. Therefore, fora givenwide bydisc,
such
as that of HD 38206,
per
end of to theirin relation
In addition, following Section 4.2,log
we10can(ainconsider/aw ) the impactSthat+6 be constrained using the debris M
M
1
au
can
disc.
Here,
we
present
the
first
ALMA
observationsofthesystem’s
Kuiper
belt
and
fit
them
parameter,
we
find
that
$
$
Myr
(Bell
pdate
the
other
two
parameters,
now
using
τ
=
42
radiusofplanetesimals
inthecollisionalcascadeand Mdisc is the tota
time-scale
ofathechaoticzone
athesefunctionoftheplanetand= the inner edge of the disc. This is
Np on
do
this,
they
place
them
at
separations
thatasare
twice
asinnerlarge−4However,
results
shouldbemasstreatedwith caution. Shannon
the
disc
will
have
greater
eccentricity
atmodelling
its
edge
than
atWe
itsdetectsystem.ToSinceØ
⼩惑星帯とカイパーベルトのようにギャップは惑星を⽰唆。
the outermost
planetwill ahaveaisablesmallerusingaforward
MCMC
approach.
anextended
disc
of
dust
peakingataround
180
au
with
width
of
log
(1
+
gδ
)
#
$
min
mass
in the disc. For
we are using, ρ = 3.5 g cm−3
1/2
8.7 thatau (Morales
ettoaxisal.
2016).
From
this,
we
2015)
and unstable,awas=
10 the composition" !epa is "thethosecorresponda marginallystablesystem.
In thiscase,semimajor
using
simulations.
Fromsimulations,apoint!a,of the planet,andthatap iswhere
athese3/2 eccentricityout =0 +!good
etN-bodyal.
(2016)
showedthatatsomeequation(10)
breaks
down,
+0.10
M
κ
becoming
problemhas
beenstudiedbymultipleauthors
over
the
years
(see
in
#
outer
edge.
However,the resolutionofourobservationsisnot
We use 3.3,1/4
140 au. The disc is close to edge
on andshowsspacingのとき必要な個数。
tentative signs of an asymmetry
best fit by an eccentricity (10)of 0.25−0.09 .Section
Fromfind that a0 = 184 au and %a = 143 au. W=
m⊕if, wemp m
Ø uncertainty
同じ平⾯、同じ質量、円、log
uniform
the expectationis thata significant
fraction
of
3.3
±
1.4
ssuming Gaussian
propagation)
Nand
µ we
p =increasing, thisinsidetheyderiveda lower
limit
onplanetesimals
themassofresiding
eachplanet,thesemimajor
axis
of
the
planet.
Therefore,
assumethat this1980;pthe
theplanetmass
beyondpoint
nolongerreducesτ1
auM
ompletely
removede.g.
WisdomMustill
&four
Wyatt
2012;
Pearce &+Wyatt
2014;
the
fittedparameterstodetermine
limitsonmassesofplanets
interior
to
the
cold
belt.
We
determinethataminimumof"enoughtodetectsuch
avariationintheeccentricity
and
so
we
assumeobtained(logδ=
1 +mass,log(µ/10−7a)),byextrapolating
dust
singl
can
estimateM
min
disc
betweenorbitsofneighbouring
planetswouldremovedfrom10 (τ/yr)the
10assuming
K ⻄に⻑い=andNp = 4.8equal
±
2.0
and
mrequired,=p = 0.6 ± 0.3M
J forthepbe
the20gap,
assuming
mass
planets
witheacha separationofKmassmutualtime-scale
is andequivalent
to
the
age
of
the
systemandtheoutermost
1608
M.
Booth
et
al.
the
clearingtime(theirfigs
2
4).
Systemsareparticularly
,
in
order
to
clear
the
gap
betweentheasteroid
andKuiperbelts
ofplanetsarewithaminimumof
0.64
M
ギリギリ安定な最⼤個数。その2倍の間隔でもギリギリ掃ける（最⼩個数）。
3.7
evoid
of
any
debris&Kuchner2015).
Here,
we
use
the
formulasof
Pearce&J number of planets that Nesvold.
asingleeccentricity
throughout
and
set
a
=
a
and
also
the
minimum
areneededtoclear
thepower-law size distribution from dust grains up to Smax (although notlower0
the system. ItHill’s
isfilled
onlyradii.
thebodiesexactly
half-way
betweencircleand orbiting
cross,
respectively,
±ery
0.14M
J for K = 16 (large
planetthesystemsolelyresponsible
forouterstirring
disc
out
itsdisc,
Modifying
theirequations
such
that
K
is leftasaisfreethesystem.
If we
make
the
assumption
theoutermostplanetis responsible
forthethestirring
oftothethetakelocation
ofaccountitssusceptibletothiseffectifin
theyarethatyoung,
orage
have
a distantnumberofa planets.
Wyatt(2014),
which
into
thetheeccentricity
thegap
withintheofthesystem:that
estimating
total
disc
massedge
is ofhighlyuncertain
to a alac
whereathe isinnerof planet.
theouterduebelt,theplanets
that
would
have
a
chancetosurvive.
The
planetarysystemTherefore,
if
we
make
the
assumption
thattheoutermostplanetisundiscovered
planets.
It
would
be
interesting
to
put
some
constraints
ason
is
w
Ø
20
or
16ヒル半径離れた惑星が42Myr以内に間の微惑星を散らす。
4). In other words,
since
our
data
allow
us
to
determine
that
the
inner
edge
and
the
eccentricity
of
the
disc,
then
we
can
more
tightly
predictits
eccentricity,
mass,
and
semimajor
axis
to
be in
outer
edge,
we
can
find
a
familyofsolutions
for
its
mass,
semi-major
parameter,
we
find
that
belt.
Specifically,
thishappenswhen:!
"
are twice aswould
large
Combining
theirequations
(9)
and
(10),
we
find
on
the
number,masses,andlocationoftheallegedplanets
intheofknowledge
in
the
form
of
the
size
distributionandits
maximum+0.20+0.5of+12
thencertainlybestable,whilst
the
gap
would
be
nearly
free
the
inner
belt
(whichisassumedtobenarrow),
simultaneously
responsibleforthestirring
of
the
disc,
the
clearingal.
(2016).
, mp =
ap = 76−13 au.
ep = 0.34
in these are all lower limits
wide – something that was not possible with the#Herscheldata
J , andaxis,
andeccentricity.
Strictly
speaking,
−0.13
−0.3
$1/2
log10 would!0.7"M
cavity.
Such constraints
be tighter if the disc exhibited"3 Krivov &HD38206のg=1-2! strong extent; see"extremes,! κ " !these
Wyatt 2020, for further discussion on the totaystem. In thisdebris.
case,In order to calculateaw&
Quillen(2007)
aassumedM#Faberainthe3/2
inthat
equals1
for calculating the maximum numbe%&
ofsmaller
the inneredge
andeccentricity
of
the
disc,
then
we
can
solve
a
1
,
(11)
=
1
+
N
maximumfindthat the gap is
than
the
gap
by
Shannonasymmetries
(e.g.
Lee
&
Chiang2016;
Löhneetal.
2017),
or
if
an
"
!
"
!
p
in
since
a
more
massive,moredistant,ormoreeccentric
planet
could
1/3
−1/3
(10) matter
mp = formulae:
words:
planet–discinteractions– circumstellar– stars: mindividual:–=planetary systems –mass
submillimetre:
1 >mlog.
(12)NKey
of1 debris
discs)
p
M# HD 38206⊕ ,10
netesimals residing
p /2 −
provide the following
−
(3
−
e
)M
(14)
m
1+0.006Kpp#.
accurate
radialprofile
of
the
inner
edge
of
the
outer
disc
could
be
M
M
⊕
" of the system.
τ to clear
1 au
M"are
aw the2016)
and so theequations
masses requiredlower(13)–(15).
Duethe
togap
the
large
uncertainty
in discour onknowledge
forcalculatingtheminimum
numberof planets, µ
nd
7,
and
•:
20ヒル
stir
a
time-scale
shorter
than
125
a
(1
+
e
)
planetarysystems.
log! m "the! age"−1/3
p
p
1/3
10
d be removed from log (ain /aw )p
M# (e.g. Nesvold & Kuchner 2015;
inferred fromthe resolved
images4+α4+α1−0.006K
−
S
S
10
M
M
iven
by
their
analysis.
⊕ can consider"
max# , andmin τ is the age of the system. The relatio
discalso
parameters,
weFor
make
use
of allthatofInthesamplesfromaddition,
following
Section
4.2,
we
impactthat
mp /M
K half-way
between between(8)
Np =of the andthe minimum
numberofareneededtoclear
theplanets
Booth
et al. 2017).
Also,
for systems
observed
dust haveclose two
our parameters,
we
find
that
at
least
four
are
necessary
to with thethe=
Mdustx:.unknowns.
(7
Mdisc
Thus,
wehotnowequations,
three
16ヒル
observations
ofplanets
HD
38206
1609
4+α withlog(1 + begδALMA)
4+αmin
10
wever, these results
shouldtreatedwithcaution.
Shannon
S
−
S
toof
the
star, constraints
canbeedgederivedbyassuming
this
dust
to
stem
the
outermostplanet
will
have
on
the
inner
of
the
disc.
This
is
a
dust
min
our
MCMC
run,
solvingthesimultaneous
equations
for
each
set
where
κ
is
a
parameter
dependent
on
K.
They
first
assumed
a
wide
and
m
using
the
parameters
for
the
HD
38206
sy
gap
within
the
age
of
the
system:satisfy
thiscondition.
This
criterionis,therefore,satisfiedwhen
wep
he planetary system µ1/4
Oneof theunknowns is the planet
eccentricity. If the planet isfromcometsby
scattered
into
the
inner
systemby radiia chainbetweenof planetsthe
2016) showed
that
at
some
point
equation(10)
breaksdown,−7
problem
that
has
been
studiedmultipleauthors
over
the
years
(see
spacing,withseparation
of
K
=
20
mutualHill’s!
"外の惑星が永年摂動で円盤を直接撹拌。
discparameters.
Doing
wedetermine
that
would
Fig.
4al. withgrey region
representingby (e.g.
Spitzer/MIPS
et al.
2005),
Spitzer/IRS(Moraleset theassumeK= 16,
but
notsuchwhen
assumeKinterior= 20.toThis
impliesthatfor et(Rieke(logoutermost=+ logso(µ/10)),(9) awemin Ø
ldpreviously
be nearly δfreeof 3.7
eccentric,
thenaffectdisc theeccentricity.
Therefore,
our the allowe
10 (τ/yr) + 1
10
the outer
belt
Marinoal. 2018a).
However,
nonethisof willncreasingtheplanet.
The
isplanet
defined1timescale
I+0.5
N Treduces
U Cplanet
T I O N stirringaRO
in Dforthe planetfrom
massbeyond this
+0.20point no longer+12 neighbouring
planetorbits,
which
is
close
to
a
typicalseparation
in
log
e.g.
Wisdom1980;
Mustill
&
Wyatt
2012;
Pearce
&
Wyatt
2014;
2009),
Gemini/T-ReCS(Moerchen,
Telesco&Packham2010),
and10
wide
spacingof planets,
is notany
planetarysystem, mp =asa0.7
ap = 76it−13
au.possible
The
full
haveMustill
ep = 0.34
awMJ andthisforis thecasefor HD 38206,
so that we canonly use the gap
radiusBased canon theseresults,
we might
expect betwee
constraints
the disc
eccentricity
provideconstraints
on ther & Quillen(2007)−0.13(2009)
−0.3
edges
oftimethewhere
6onanalysing
質量感度10倍で⾒える。
one
key
components
system,studying
debrisHerschel/PACS(Moralesal.1)2016).
& ,ofofa planetary(11)=&1Wyatt+edge
N
earing(theirby
2 pand4).
Systems
areAsparticularly
afigs
inner
of %
the outerbelt,
islocation
yr.ThisThey both the resolved
Keplermultiplanet
systems.
In
this
case,
κ=
(4 et±
× system.
10By
"the
! the
"−1/3
! m ofa
in is thew
Nesvold&
Kuchner2015).
Here,
we
use
the
formulasof
Pearce&toconstrain
parametersofthepossibleplanetsin
this
1/3gap
to
clear
the
in
such
a
short
time,
no
matterhow
massive
they
are.
p
Mto
posterior
distribution
is $
shown
inMenables
Fig. g5.
planeteccentricity.
The demonstrate
two
canplanets.
be related
throughthe equation
mass
A largernumberof lower mass planusM
the current
make-upof aaplanetary
Herschel
imageswith
and
the
full
SED,
Moralesal.
(2016)=thewords,
1+0.006K
3/2be
inner
is #assumed
tonarrow),is"# aunderstandparameter
also
checkedslightly
tighterpacking,
Kof
= the
16,
and
found
the
makes
the problem
highlydegenerate,
since
the
same
gap
couldet betible toainthis
effectif beltthey(which
are young,or havea discs
distant⊕ outer
Wyatt(2014),
which
take
into
account
theeccentricity
planet.
2
log
!
"
!
"
None
the
less,
even
in
this
case,
there
are
reasonable
uncertainties
systemanditsformation
andevolution.
In
recentyears,
the
Atacamathatthesystem
is
seen
close
to
edge
on
and
has
two
belts
at
11
and
1/3
−1/3
$
#
(Mustill&
Wyatt2009):
6
10
1−An1attempt
to findinsystemhasandbeen
bythesimilar.
mthepNote that there is no stringent lower limit on theby manydifferent
planet9/2
M#planets
r resolution
pmaximumthat happens
equalsforcalculating
theeplanetsof
2 maderesultsequations
to clearedbeIn thiscase,=configurations.
(2± 0.2)× 10 yr.be a member of the Columba
anumberisc
being this
1−0.006K
pecifically,
when:
out
3
Combining
their(9)ofandand(10),
weκThefind
MMillimeter/submillimeterM"
Large
Array (ALMA)
has made
itviewpossible
160 au.
systemisnumberthoughtoftoassumptions.
⊕onseveralparametersinequations
(10)
and
(11),
planets
with
≈
1.53
×
10
t
In
this
degeneracy,
we
make
a
(8)
p
NaCo
Imaging
SurveyaroundYoungstars (ISPY),
using
et al. "(2016) applied
theirformulaeto4theHD
38206
for calculating
the minimum
numberoftoplanets,µ isdiscs
themass
a reality,
"
image
these
at
long ratio
wavelengths
inShannon
much
finer
than
association(Torres
et al. to2008),
it an
age of 42+6
bydifferent
planetsto!
ep for Planets
10
auat!uncertainty−4 Myr (Bell,All detailofinterval
themarbitraryand donot haveholdgiving
in e.
yet
3are would
masses
the
lower
end
of
the
satisfy
=
(15)
ep (τ
a/M
inthe
where
κ
is
a
parameter
dependent
on
K.
They
first
assumed
a
wide
a
1
,
and
τ
is
the
age
of
the
system.
The
relationshipbetweenNsystemusing
theparameters
known
at
the
time
=
30
Myr,
a
m
was
previously
possible(forarecentreview,see
Hughes,Duchêne&
Mamajek&
Naylor2015).
The
young
age
of
this=system means that
re
still
quite
in
p
#
p
w
Very
Large
Telescope(Launhardtetal.
2020).
No
planets
were!
"1/2 !
"−1 #
they
allow
us
to
make
specific
estimates.
Again
byanalogy
with
our
5
a
−urbations
1 > log10
.
(12)
$
p
−
1
=
(3
−
e
)M
.
(14)
m
−3
Figure4.
Constraintsonthepossiblenumberofplanets
inthegap and theirp interest#thatcandidate
equation
and
could
therefore
clear
the
gap
withinthesystemM# with separation
mpthe HDapK =(12)Matthews2018).
Of particular
are15
systems
bothdebrisit
isp aourselves
prime
for direct
imagingsurveys,noplanetsmthe parameters
for
38206
system
is
shown
in125
=pthe
au).
They
found
three
planets,each
a massau,awhereof
20themutualHill’sradii
between
MNRAS
500,
1604–1611(2021)
p using spacing,
in e
Solar
system,we confine
to a simple
scenario
inwithwhich
the althoughaddition, weandaw(9)alimits)180
detected,
find
that
most
stringentarep (1 +
masses.
The
greyshadedregionrepresents
theboundsbasedonthe model
× none the less they
yr,
(13)
discs
and
at least
oneifplanet
have been
observed.
of planets
such toto
have
been
detectedso far.
Shannonet al. (2016)a model a single eccentricity for the disc.
In ourmodelling,
wedeveloped
have
assumedage.
Inausummary,
multipleequal-massarecleared+6,presumedarerequiredclear
theFig. 4 with theneighbouring
grey
regionrepresenting
theallowedparameters.
of
1.4 MAnalysis
inhavethegap
are gap.
all in nearly-circular,
nearly-coplanar
J planets
planetorbits,
which
is
close
to
a
typicalseparation
inM
M
1of Faber & Quillen (2007) (see equations 8 and 9). The cross and the dot
$
$
Myr
(Bell
for
planets
atdistances
of
!70
au,
for
which
they
rule
out
planetsof−4
is of prime
importancefor understanding
the interaction
for theminimummass of planetsscenarios
required toclear a gap in a two beltr parameters, we
findonthatat least
four
planetsexpect
arenecessary
to
Thus,
we
now
have
two
equations,
with
three
unknowns.
orbits
(e.g.
&the
Rieke
2014),
althoughexist,
6 their
In fact,
as
canas
be
seen fromthisthe andinfluence
ofonatheplanetdeterminedsolelyalternative
from
a fit
to
the
SED
In
case,
ainSu
these
results,
we mightsystems.
between
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Dynamical stellar masses of pre-main sequence stars in Lupus and Taurus obtained with ALMA
surveys in comparison with stellar evolutionary models
Teresa A. M. Braun,1 Hsi-Wei Yen,1 Patrick M. Koch,1 Carlo F. Manara,2 Anna Miotello,2 andLeonardo Testi2, 3
1 Academia Sinica Institute of Astronomy and Astrophysics, 11F of Astro-Math Bldg, 1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan
2 European Southern Observatory (ESO), Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany

mixのjarXiv:2012.07441v1 [astro-ph.SR] 14 Dec 2020

11
INAF/Osservatorio Astrofisico di Arcetri, Largo Enrico
Fermi 5, I-50125 Florence, ItalyØ 正確なIMFのためにMspec（PMSでばらつく）をM
dynで校正。
Table 5. Measured parameters
face-on disks
in the Lupus region
Ø ALMA, 0.12"-0.25",
1-3forMyr,
Lupus& Taurus(~150 pc)。
ABSTRACT
Name
RA
Dec
A
dist line data of pre-main sequence (PMS) stars in the Lupus and Taurus
We
analysed iarchivalPmolecularØ ダスト円盤からi,PAを決められるもの30(Lupus) + 37 (Taurus)。
star-forming regions
obtainedwith ALMA surveys with an integration time of a few minutes per
[ ]
[ ]
[pc]
13stacked
We
the
data
CO and C3-2（あればCNも）をスタック。
O (J = 2–1 & 3–2) and CN (N = 3–2, J = 7/2–5/2)
Ø 輝線の感度が不⼗分でもCO, 120.0±15.0
C18
Oof160J=2-1,
Sz83
15:56:42.29 source.
-37:49:15.82
16.0
to enhance
ratios, and measured the stellar masses of 45 out of 67 PMS stars
Sz113 16:08:57.78 lines-39:02:23.21· · · the signal-to-noise···163Ø 薄いケプラー円盤を基準としたラインプロファイルをスタックして最⾼のS/NになるM
Sz114 16:09:01.83 from
-39:05:12.79
16.0
160.0
the Keplerianrotation
in162
their circumstellar disks. The measured dynamical stellar masses were*とvsys。
comparedtothestellarmassesestimatedfromthespectroscopic
measurements
with
seven
di↵erent
Note—We measured the inclination and position angles with theØ プロファイルをガウシアンフィットしてガウシアンの重みで±1σを積分して信号とする。
molecular-line data forface-onevolutionary
disks whose inclination
angleswerestellarmodels.
Wefound that the magnetic model of Feiden (2016) provides the best
measured to be  30 with the continuum data.
2で50%まで。
estimateof the stellar masses in the mass range of 0.6 M  M  1.3 M with a deviation of <0.7
Ø ピーク<4σや線幅<3chansは不採⽤。空間は95%フラックス半径。エラーバーはχfrom the dynamical masses, while all the other models underestimate the stellar masses in this mass
range by 20% to 40%. In the mass rangeof <0.6 M , the stellar masses estimated with the magnetic
Ø 3DモデルDALIでチェック。i>70°ではM*を30%過⼤評価。
3

13

+6.0
4.0
+6.0
4.0

18

+25.0
10.0

?

13

model of Feiden (2016) have a larger deviation (> 2 ) from the dynamical masses, and other, nonmagnetic stellar evolutionary models of Siess et al. (2000), Bara↵e et al. (2015) and Feiden (2016) show
better agreements with the dynamical masses with the deviations of 1.4 to 1.6 . Our results show
the mass dependence of the accuracy of these stellar evolutionary models.
Keywords: Pre-main sequence stars (1290), Circumstellar disks (235), Stellar masses (1614), Stellar
evolutionary models (2046)
1. INTRODUCTION

The mass is an important characteristic of a star. It
determines not only the luminosity and temperature of
the star, but also its evolution and feedback to the interstellar medium (Burkert 2004; Ceverino & Klypin 2009).
Furthermore, mass determination of a large sample ofyoung stars is essential to constrain the initial massfunction (IMF). The IMF is a key to understand thephysics of star formation and is also important to understand the evolution of stellar clusters and galaxies(Je↵ries 2012; Hopkins 2018).
One method widely adopted to determine stellar
masses uses the information of the luminosity and e↵ective temperature of a star. By incorporating the physical

Diagram) is compared to the theoretical evolutionary
tracks from the stellar evolutionary models to constrain
the mass and age of the star. The advantage of this approach is the large number of stars that it can be applied
to. With existing facilities it is possible to perform surveys on large samples of stars and provide data for the
spectroscopic method to determine stellar masses (e.g.,
Rigliaco et al. 2012; Herczeg & Hillenbrand 2014; Alcaláet al. 2017; Manara et al. 2017).
eff evolutionary models are in gooddyn
The di↵erent stellar
agreement for main sequence (MS) stars and have been
compared with various precise direct measurements ofstellar mass (e.g., from orbital motion of binaries).
Therefore, this method is considered reliable for MS

M*とi, R, Mgas, Σに相関はないのでバイアス無し。
全密度

分⼦密度

分⼦種による差も無し。

Ø ⾼感度観測とも合う（Dとiをスケール後）。
Ø T を５つに分けてM が中央値より3倍外れるものは連星候補。

Dynamical stellar masses of pre-main sequence stars in Lupus and Taurus obtained with ALMA
surveys in comparison with stellar evolutionary models
Teresa A. M. Braun,1 Hsi-Wei Yen,1 Patrick M. Koch,1 Carlo F. Manara,2 Anna Miotello,2 andLeonardo Testi2, 3の続き

1 Academia Sinica Institute of Astronomy and Astrophysics, 11F of Astro-Math Bldg, 1, Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan

mixのjarXiv:2012.07441v1 [astro-ph.SR] 14 Dec 2020

2 European Southern Observatory
17(ESO), Karl-Schwarzschild-Str. 2, D-85748 Garching, Germany
3 INAF/Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, I-50125 Florence, Italy

ABSTRACTØ M <0.6 M ではBHAC15, F16, SFD00が1.6σで合う。
Ø 0.6 ‒ 1.3 M はmagnetic F16のみ合う。他は2040%過⼩評価。
Ø magnetic F16が正しい場合、磁場でゆっくり収縮
するのでT Tauri期が⻑い可能性。
Ø しかし、magnetic F16は<0.6 Msunを説明できな
いので、星進化の物理がM に依ることを⽰唆。

We analysed archival molecular line data of pre-main sequence (PMS) stars in the Lupus and Taurus*
sunstar-forming regions obtained with ALMA surveys with an integration time of a few minutes per
source. We stacked the data of 13 CO and C18 O (J = 2–1 & 3–2) and CN (N = 3–2, J = 7/2–5/2)
lines to enhance the signal-to-noise ratios, and measured the stellar masses of 45 out of 67 PMS stars
sun dynamical stellar masses werefrom the Keplerian rotation in their circumstellar disks. The measured
compared to the stellar masses estimated from the spectroscopic measurements with seven di↵erent
stellar evolutionary models. We found that the magnetic model of Feiden (2016) provides the best
estimate of the stellar masses in the mass range of 0.6 M  M?  1.3 M with a deviation of <0.7
from the dynamical masses, while all the other models underestimate the stellar masses in this mass
range by 20% to 40%. In the mass range of <0.6 M , the stellar masses estimated with the magnetic
model of Feiden (2016) have a larger deviation (> 2 ) from the dynamical masses, and other, nonmagnetic stellar evolutionary models of Siess et al. (2000), Bara↵e et al. (2015) and Feiden (2016) show
better agreements with the dynamical masses with the deviations of 1.4 to 1.6 . Our results show*
the mass dependence of the accuracy of these stellar evolutionary models.
Keywords: Pre-main sequence stars (1290), Circumstellar disks (235), Stellar masses (1614), Stellar
evolutionary models (2046)

C14, BHAC15, F16: non-gray boundary、オパシ
ティが周波数で違う。
1. INTRODUCTION
Diagram) is compared to the theoretical evolutionary
tracks fromthe stellar
evolutionary models to constrain
The mass is an important characteristic of aPS99,
star. It Br12:
grayboundary。
the
mass
and
age
of
the
star. The advantage of this apdetermines not only the luminosity and temperature ofproachisthelarge
numberof stars that it can be applied
SFD00:
non-grayの解析的フィット。
the star, but also its evolution and feedback to the interto.
With
existing
facilities
it is possible to perform surstellar medium (Burkert 2004; Ceverino & Klypin 2009).
ü
対流のmixing
lengthもそれぞれ違う。
veys
on
large
samplesofstars
and provide data for the
Furthermore, mass determination of a large sample ofspectroscopic
methodtodeterminestellar masses (e.g.,young stars is essential to constrain the initialü massmagnetic
F16以外non-magnetic。
Rigliaco et al. 2012; Herczeg & Hillenbrand 2014; Alcaláfunction (IMF). The IMF is a key to understand thephysics of star formation and is also important to understand the evolution of stellar clusters and galaxies(Je↵ries 2012; Hopkins 2018).
One method widely adopted to determine stellar
Figure 6. Deviation between the spectroscopic and dynamical stellar
masses.uses
The namethe model is labelled
the upper
massestheofinformation
ofintheluminosity and e↵ecright corner of each diagram. Red crosses mark the mean deviations of the measurements in the respective mass ranges, andofinaTable
star.
incorporating
the physicaldashed vertical lines denote the three mass ranges. The calculatedtive
meantemperaturedeviations are shown
10. ByThe stars,
marked全密度

分⼦密度

et al. 2017; Manara et al. 2017).
The di↵erent stellar evolutionary models are in good
agreement for main sequence (MS) stars and have been
compared with various precise direct measurements ofstellar mass (e.g., from orbital motion of binaries).
Therefore, this method is considered reliable for MS

3. Numerical simulations
H2 mass–velocity relationship from 3D numerical simulations
3.1. Numerical setup
of jet-driven molecular outflows
A. H. Cerqueira1 , B. Lefloch2 , A. Esquivel3 , P. R. Rivera-Ortiz2 , C. Codella4,2 , C. Ceccarelli2 , The
and L.simulations
Podio4

presented here were performed usin
Yguazú-a code (Raga et al. 2000, 2002; Cerqueira et al.
1
LATO/DCET, Universidade Estadual de Santa Cruz, Rod. Jorge Amado, km 16, Ilhéus, BA, CEP 45662-900, Brazil
In its original version, the code was designed to solve
e-mail: hoth@uesc.br2
dynamic problems with a chemical network for the foll
CNRS, Univ. Grenoble Alpes, IPAG, BP 53, 38000 Grenoble, France‒γor exp(‒v/v )を説明できるか。
e-mail: bertrand.lefloch@obs.ujf-grenoble.frØ ジェット/ウインドが分⼦流を作るシナリオはm(v)∝v
atomic and ionic species: HI, HII, HeI, HeII, HeIII, CII
0
3
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 Ciudad de México,
A&A
645,
A135
(2021)
CIV, NI, NII, NIII, OI, OII, OIII, OIV, SII and SIII. F
MexicoØ collimated jetとambientの相互作⽤が有⼒。化学流体シミュレーションYguazu-aで混ざり具合も調べる。
4
INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
present work, we introduced the H2 molecule as a new s
Table 1.ØJet models.
2, 2, 8x104 au, 256x256x1024、5層、Δx=78.13au。半径5Δxのジェット。
and added three dissociation reactions for molecular hydroReceived 26 August 2020 / Accepted 1 December 2020
Model

vj,0
(km s 1 )A

H + H2 ! 3H ,
na
nj
⌘ Ta
Tj
⌧P
✓ ABSTRACT
Ntot
⌧e
3
3
(cm
) (cm
(K) shown
(yr)
)
(yr)
Context.
Previous) numerical(K)studies havethat in( protostellar
outflows, theoutflowing gas mass per unit velocity, or mass–

分⼦は原⼦の9倍
イオンは原⼦の1％

H of+a sample
H2 !of 2H + H2 ,velocity distribution m(v), can be well described by a broken power law / v . On the other hand, recent observations
DR_SS
212
0
100
100 stages
1 of 100– CO intensity–velocity––– closely related to m(v), follows 2an exponential
outflows at various
evolution1000
show that the
distribution,
law / exp( 100v/v0 ).
DR
212
0.15
100
1 100 1000––
4
5, 10, 20 and 50
e +outflows.
H2 !Wee + 2H .
Aims. In the present work, we revisit the physical origin of the mass–velocity relationship m(v) in jet-driven protostellar
DR_P
212
0.15
100
100
1 100 1000 200 6
45, 10, 20 and 50
A&A 645, A135 (2021)
investigate the respective contributions of the different regions of the outflow, from the swept-up ambient gas to the jet.
Methods. We performed 3D numerical simulations of a protostellar jet propagating into a molecular cloud using the hydrodynamical
used the collisional dissociation rates of mol
code Yguazú-a.
The code takes
intojetaccount
the most
atomicionic species
and wasto include the H2We
gas heating
Notes. vj,0 is the jet velocity in km s 1 ; A is the amplitude
of variationin thevelocity;na abundantand nj are
the andambient
mediumandmodified
jet (numericalandcooling.
particle) density; ⌘ = nj /na is the jet to ambient medium density ratio; T a and T j are the ambient medium and jet temperatures (in K); ⌧P is the hydrogen provided in Shapiro & Kang (1987) for these
Results. We find that by excluding the jet contribution, m(v) is satisfyingly fitted with a single exponential law, with v0 well in theprecession period, Ntot the number of different jet injection
period, andvalues.
⌧e is thevelocity variability
period. components in the mass–velocity relationship.
reactions.
We also calculated the cooling function consi
range of observational
The jetjet contribution
results in additional
This empiricalmass–velocity relationship is found to be valid locally in the outflow. The exponent v0 is almost constant in time and fora given
level
of
both
the
radiative
and the dissociative processes. For the
mixing between the ambient medium and the jet material. In general, v0 displays only a weak spatial dependence. A simple modeling ofcooling rate, we used the fit proposed by Lepp &L1157 outflow successfully reproduces the various components of the observed CO intensity–velocity
relationship.tive
Our simulations
5
With model DR_P, we aim to investigatethetheproperties of line
observations
yield
high gasvalues,cm 3along. Thisj & 10entrained
indicate that these components
trace
the outflow cavityof swept-up
and thenmaterial
the widejet, respectively.
(1983), which considers both the rotational and vibrationa
the L1157 outflow, kinematical studies
have revealed
Conclusions.
The CO intensity–velocity
is naturally explained
the jet-driven
outflowmodel. The entrained material
range of exponential
physical law
conditions
reflectsbythe
intrinsic
complexity
mix of which
ing from the two reactions, H-H2 and H2 -H2 , in bothplays
an importantthe jet,mass–velocity
profile.
convincing evidence of precession (Gueth et al. 1996;
Podio etroleal.in shapingof thewhich isoften associated with internal shocks thatand low-density regimes (n < ncr ⇡ 104 cm 3 ). The dis2016). In this simulation (and for model DR) we
that formation
the drive
Keyassume
words. stars:– ISM:thejetsformationand outflows of strong temperature and density gradients.

歳差や正弦パルス。

Ø 視線x⽅向からi傾ける。Δv=1 km/sでm(v)を計算。
Ø 初めにjetとambientをj=0, 1で区別して、混ざり具合を⾒る。 j<j を取り出せる。

mixのj
jet velocity varies
periodically with time, according to:

Adopting single initial values for temperature and density is most tive cooling function was taken from Shapiro & Kang (19likely an oversimplified description of the jet physical structure. Fig. 1 we show the different cooling functions: atomic (bluNtot
✓ 2⇡ ◆X
Nevertheless, the origin of the molecularassoci1. Introduction
molecular
dissociative (green line) and radiative coolin
We note however that the initial
jet temperature value adopted and outflows
ated with YSOs is still debated (see Lee 2020,v j = v j,0 · 1 + A
sin
·t ,
(5)
1 for a recent
line).
the simulations
are consistent
with
those
obtainedfrom⌧e,iOutflows from young stellar in
objects(YSOs) can exhibita review).
They
are believed
to be
the jetby-product of an interaci=1
observations
SiO, CO).
The
initial jet
den- wind,Together
great variety of morphologicalmolecularand physicalline
characteristics.
In (H
H2 , CO and H2 O have long been kno
tion
a morecollimatedjet and/or
produced inwithor
2 , between
4yr) and deeply
embeddedClass 0 protothe3star–diskand itssurrounding
medium(Ballysity inour simulations
is 100bycm(same interaction,
as in DC03),
which
where v j,0 is the jet velocity, A = v/v j,0 isthe
the youngest
adopted (10amplitude
play an important role in shocked gas cooling (Hollenb
stars ⌧(Andréet al. 2000), outflows
are easily
tracedusing determinedthe 2016). As
the wind and/or jetHowever,bow shock it
propagate into the ambiis lower
than thevaluesobservationally.
variation for the jet velocity variation, and
全密度& Neufeld
分⼦密度
e is the variabilMcKee
1979;andKaufman
1996; Flower & Pineau
walls advances
CO molecule and their presence is ubiquitous in star forming ent medium, the gas of the excavated cavity
isthejet-to-ambientdensityratio
whichcarriesthemostweightity period (t is the time). In our time-varying
models,N=1
tot they are a common manifestation of both
excites a profusion of molecular emissionDetailed
lines. For low
mass
regions, indicating thatobservational
studies have confirmed that line c
in modelingof the outflow.
or 4, and 5 . ⌧e,i . 50 yr (see Table 1). We
that although
YSOs in particular,
this canThis
take point
place via
one
of
three
main
low- noteand high-massstar formation
processes the(Wu dynamical
et al. 2004; evolution
from CO and H2 O can be as important as that from H2 i
was investigateddetailby Rosen& Smith(2004b).
Basedmechanisms(see Arceet al. 2007,
for ona comprehensive review):
Eq. (5) has been used here in an attempt toLeereproduce
model2020). On thethe otherhand, protostellar
jets werein
first
associFig. 3. Model DR at t = 400 yr. Distributions in the plane x = 0 of (a) j (tracer), (b) temperature, (c) v , (d) v , (e) total density n, and ( f )tostellar outflows (see e.g. Nisini et al. 2010a; Busquet
mix

z

y

H2 mass–velocity relationship from 3D numerical simulationsof jet-driven molecular outflows
A. H. Cerqueira1 , B. Lefloch2 , A. Esquivel3 , P. R. Rivera-Ortiz2 , C. Codella4,2 , C. Ceccarelli2 , and L. Podio4

ira et al.: Jet-cavity kinematical relationship1

LATO/DCET, Universidade Estadual de Santa Cruz, Rod. Jorge Amado, km 16, Ilhéus, BA, CEP 45662-900, Brazil
e-mail: hoth@uesc.br
2
CNRS, Univ. Grenoble Alpes, IPAG, BP 53, 38000 Grenoble, France
e-mail: bertrand.lefloch@obs.ujf-grenoble.fr
3
Fig. 8. ModelUniversidad
DR_SS at t = 400,
1200 andAutónoma
2000 yr (fromto bottom)Apartado
and for an inclination
angle i = 04510
30 . Left:
distribution
molecular
Instituto de Ciencias Nucleares,
Nacional
detopMéxico,
Postal 70-543,
Ciudadde of
México,mixdensity. Right: mass–velocity
gas column
relationship is depicted in black for each value of the jmix parameter, from jmix = 0.0 (first column) to
Mexicojmix = 1.0 (fourth column). The profiles were calculated considering the whole computational domain. The exponential best fit is drawn in red and
4
INAF, Osservatorio Astrofisico
Fermi 5, 50125 Firenze, Italy
the exponentdi
v0 Arcetri,is given forLargoeach jmixE.value.

Ø j が⼤きいと⾼速度成分増加àjet由来の分⼦ガスの寄与。
Ø 全質量と分⼦の差は先頭でのH2の乖離。

A. H. Cerqueira et al.: Jet-cavity kinemati

Received 26 August 2020 / Accepted 1 December 2020
ABSTRACT
Context. Previous numerical studies have shown that in protostellar outflows, the outflowing gas mass per unit velocity, or mass–

velocity distribution m(v), can be well described by a broken power law / v . On the other hand, recent observations of a sample ofoutflows at various stages of evolution show that the CO intensity–velocity distribution, closely related to m(v), follows an exponential
law / exp( v/v0 ).
Aims. In the present work, we revisit the physical origin of the mass–velocity relationship m(v) in jet-driven protostellar outflows. We
investigate the respective contributions of the different regions of the outflow, from the swept-up ambient gas to the jet.
Methods. We performed 3D numerical simulations of a protostellar jet propagating into a molecular cloud using the hydrodynamicalcode Yguazú-a. The code takes into account the most abundant atomic and ionic species and was modified to include the H2 gas heating
and cooling.
Results. We find that by excluding the jet contribution, m(v) is satisfyingly fitted with a single exponential law, with v0 well in therange of observational values. The jet contribution results in additional components in the mass–velocity relationship. This empiricalmass–velocity relationship is found to be valid locally in the outflow. The exponent v0 is almost constant in time and for a given level ofmixing between the ambient medium and the jet material. In general, v0 displays only a weak spatial dependence. A simple modeling ofFig. 9. Model
DR_P atthet = various
400, 1200,components
and 2000 yr andofforthe
an observed
inclination angle
i = 30 . The results arepresented for four
values of
the L1157 outflow successfully
reproduces
CO ofintensity–velocity
relationship.
Ourdifferent
simulations
the jet–ambient gas mixing degree jmix (from top to bottom): 0.0, 0.3, 0.6, 1.0. Left: maps of H2 column density obtained by integration over the
1 swept-up gas and the material entrained along the jet, respectively.
indicate that these components
trace
the
outflow
cavityofvelocity range between 1 and +150 km s . Right: mass–velocity relationship obtained for the molecular gas (black) and the fitted curve (red). The
0 The entrained material
exponent v0 is given foreach jmix value.
Conclusions. The CO intensity–velocity
exponential
law is naturally explained by the jet-driven outflow model.
plays an important role in shaping the mass–velocity profile.

Ø ⼤域的にも局所的にもexp(‒v/v )。
ß L1157のCO観測でも同じ傾向。
Close inspection of the mass–velocity relationships reveals profiles (case j = 0.0) and the presence of the jet as a bump
Key words. stars: formation–
ISM:
jets andoutflows
that the exponential
fitting(red curves) provides excellent solu- at v ' 40 km s for j= 1.0. Between these two extremes
mixのjØ
他の観測のv0(1.6-12.5)もage,
で説明
tions
over thewhole velocity range for jvaluesof 0.3. For we find great variability. Wei,
notejthatsomeresidual emission ismixhigher values of j , the high-velocity range of the distribution found in the low-velocity (1 < v < 20 km s ) range of the disv 10 km s is still accurately fitted, with a higher value of v , tribution, which can be fitted by two exponential functions. This
可能。
Nevertheless,the originof detailthe inmolecular
as can be seen in Fig. 9 (e.g., panels j = 0.6). This expresses
point is addressedin morethe followingoutflows
paragraph. associ1. Introduction
the fact that the jet contribution tends to make the mass–velocity
ated with YSOs is still debated (see Lee 2020, for a recent
distribution
shallower,
as discussed
above. On thetheØ
若いほど、説明に必要なj
Outflows from young stellar
objects(YSOs)
can exhibita otherthehand,mix（ジェットの寄
slopes in the intermediate velocity range depend onreview).
mixingThey are believed to be the by-product of an interacgreat
physicalcharacteristics.
In explain
Fig. 5. Model DR at t = 400 yr and an inclination
anglevariety
i = 30 . of
Themorphologicaltionthis:
betweenmorethatcollimatedjet and/or
wind,
level, andand weidentify two
mechanisms that may
the Thea results
we have discussed
so far referto theproduced
global mass–in or
400
yr,for fouri=30°与）が⼤きい。
results arepresented
different values of thethe jetand ambientof material
for v & 10Classkm s 0in thecase of swept-up
Hvelocity
relationship computed
over the whole computational
youngest(10 yr) and lackdeeplyembedded
protoby the star–diskinteraction,and its surrounding
medium (Ballygas mixing degree j (from top to bottom): 0.0,
0.3, (André
0.6, 1.0. Left:stars
et al. 2000), outflows are easily traced using the 2016). As the wind and/or jet bow shock propagate into the ambiH column density obtained by integration over the velocity
e of i = 60 . maps of全質量、分⼦COmolecule
and their presence is ubiquitous in star forming ent medium, the gas of the excavated cavity walls advances andrange,
between
+1
and
+150
km
s
.
Right:
mass–velocity
relationshiphe 0 km s <regions,
indicatingthat they are a common manifestation of both excites a profusion of molecular emission lines. For low mass
obtainedforthemoleculargas(black)
and
the
total
gas
(blue).
Bottom⽮印: パルスによるbump
g power law
分⼦密度
H swept-up
mass–
lowand high-massstar formation processes (Wu et al. 2004; YSOs in particular, this can take place via one of three mainn inside each panel: ( j = 1.0), the green dots correspond to the
mix
1

mix

mix

1

1

mix

0

mix

4.4. From large- to small-scale

4

1

mix

2

1

d 10 km s 1 <mix

A135, page 10 of 15

12

velocity relationship obtained by DC03 (see their Lee
Fig. 2).
We show2020).
On thethe other hand, protostellar jets were first associbest-fitting power laws m(v) / v to the velocity intervals v  10 km s 1

2

Fig. 10. Model DR_P at t = 1200 yr under an inclination of 30 . Top:map of H2 column density for jmix = 1.0. The location of the apertures
A1-A4 used to extract the mass–velocity relationships are drawn withblack circles. Bottom: mass–velocity relationship averaged over the circular apertures A1 to A4. The best exponential fits are drawn in dashedred. The value of v0 is given for each value of jet–ambient material
mixing ratio jmix = 0, 0.3, 0.6, 1.0.

縦が場所に対応。

mechanisms (see Arce et al. 2007, for a comprehensive review):
domain. However, the possibility of a local exponential fitting

positions.
bottom pa
We ve
consider athe mass–
the apertu
compariso
Our fivelocity di
fit m(v) /exponentia
flow is asomewhatrial ( jmix =between th
vides a ver
at all posi
for positio
These valmass–velo
A highposition A
appears th
velocity doutflow ca(intermitte
A clovelocity dtowards po
v = 25 km
tion is obs
In order t
the geommass–velo
times in th2000 yr, ato the plan
the mass–

5. Discu

5.1. Molec

Lefloch etH2 mass–velocity relationship from 3D numerical simulationsの続き
of jet-driven molecular outflows
A. H. Cerqueira1 , B. Lefloch2 , A. Esquivel3 , P. R. Rivera-Ortiz2 , C. Codella4,2 , C. Ceccarelli2 , and L. Podio4
A. H. Cerqueira et al.: Jet-cavity kinematical relationship1

LATO/DCET, Universidade Estadual de Santa Cruz, Rod. Jorge Amado, km 16, Ilhéus, BA, CEP 45662-900, Brazil
e-mail: hoth@uesc.br
2
CNRS, Univ. Grenoble Alpes, IPAG, BP 53, 38000 Grenoble, France
e-mail: bertrand.lefloch@obs.ujf-grenoble.fr
3
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510 Ciudad de México,
Mexico4
INAF, Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
Received 26 August 2020 / Accepted 1 December 2020

低速
ABSTRACT
⾼速
L1157の観測
Context. Previous numerical studies have shown that in protostellar outflows, the outflowing gas mass perunit velocity, or mass–
velocity distribution m(v), can be well described by a broken power law / v . On the other hand, recent observations of a sample ofIRAM
30 m, CO 2-1
outflows at various stages of evolution show that the CO intensity–velocity distribution, closely related to m(v),follows an exponential
law / exp( v/v0 ).
Aims. In the present work, we revisit the physical origin of the mass–velocity relationship m(v) in jet-driven protostellar outflows. We
investigate the respective contributions of the different regions of the outflow, from the swept-up ambient gas to the jet.
Methods. We performed 3D numerical simulations of a protostellar jet propagating into a molecular cloud using the hydrodynamicalcode Yguazú-a. The code takes into account the most abundant atomic and ionic species and was modified to include the H2 gas heating
and cooling.
Results. We find that by excluding the jet contribution, m(v) is satisfyingly fitted with a single exponential law, with v0 well in therange of observational values. The jet contribution results in additional components in the mass–velocity relationship. This empiricalmass–velocity relationship is found to be valid locally in the outflow. The exponent v0 is almost constant in time and for a given level ofmixing between the ambient
mixmedium and the jet material. In general, v0 displays only a weak spatial dependence. A simple modeling of
the L1157 outflow successfully reproduces the various components of the observed CO intensity–velocity relationship. Our simulations
indicate that these components trace the outflow cavity of swept-up gas and the material entrained along the jet, respectively.
Conclusions. The CO intensity–velocity exponential law is naturally explained by the jet-driven outflow model. The entrained material
plays an important role in shaping the mass–velocity profile.

合うモデル
i=10°, j =0.9

mixのj

Key words. stars: formation – ISM: jets and outflows

1. Introduction

Nevertheless, the origin of the molecular outflows associ-Fig. 11. Left: model DR_P at t = 1200 yr under an inclination of 10 (towards
the YSOs
observer).
Top: debatedmap of H(see= 0.9, inated withis still
Lee density
2020, forfor jmixa recent
2 column
the velocity
intervals
25 km
s 1 ] (top)and [30km s 1 ]a (bottom).
TheThey
5000 areau apertureused
the mass–velocity
distribution
Outflows
fromyoung [1stellarobjects(YSOs)
can 45
exhibitreview).
believed
to tobeextract
the by-productof an interacis drawn
by ofa circle.
Bottom: molecularmass–velocity
distribution
at position
A4. Wehave superposed
the best
exponential
greatvarietymorphologicaland physicalcharacteristics.
Inextractedtion between
a morecollimatedjet and/or
wind,
producedfitsinm(v)or /4components associated with velocity intervals [1 25 km s 1 ] (red) and [30 45 km s 1 ] (blue). The exponent value vi is given
exp(
v/v
)
to
the
i
the youngest (10 yr) and deeply embedded Class 0 proto- by the star–disk interaction, and its surrounding medium (Bally
for both velocity intervals. Right: ASAI observations of L1157-B1. Top : intensity–velocity distribution obtained in the CO J = 2–1 towards shockstars(André et al. 2000), outflows are easily traced using the 2016). As the wind and/or jet bow shock propagate into the ambiposition B1 in an aperture of about 4000 au (1100 at the distance to the source). The line profile is fitted by a linear combination of two exponential
COfunctions
molecule
theirpresence
in star forming ent medium, the gas of the excavated cavity walls advances andg1 and/ exp(
v/12.5)(blue),isgubiquitous
2 / exp( v/4.4) (red) (from Lefloch et al. 2012). Bottom: associated mass–velocity distribution, adopting a
excitesa profusionof molecularemissionlines.g1For
regions,
indicating
that
they
are
a
commonmanifestationof bothstandard CO-to-H2 abundance ratio and the excitation conditions
derivedby Leflochet al. (2012)
for the velocity
components
andlow
g2 . mass

Ø モデルの⾼速成分はjet shock impact region (Mach disk)だけではなく、フィラメント状。
Ø ⾼速分⼦流（L1157など）全体を⼲渉計で観測すればわかる。
全密度
分⼦密度
low- and high-mass star formation processes (Wu et al. 2004;
Lee 2020). On the other hand, protostellar jets were first associ-YSOs in particular, this can take place via one of three main
mechanisms (see Arce et al. 2007, for a comprehensive review):

Instituto Nacional de Astrofı́sica, Optica y Electrónica, Luis Enrique Erro 1, Sta. Ma. Tonantzintla, Puebla, CP 72840, Mexico

3 Instituto de Astrofı́sica de Canarias, Calle Vı́a Láctea S/N, E-38205 La Laguna, Tenerife, SpainMNRAS 500, 5552–5560 (2021)

doi:10.1093/mnras/staa3631

4 Byurakan Astrophysical Observatory,
Advance Accesspublication
2020Aragatzotn,
November 21 Armenia
Byurakan
0213,

Mark Booth ,1‹ Carlos del Burgo2,3 and Valeri V. Hambaryan

ABSTRACT

1,4

1 Astrophysikalisches Institut und Universitätssternwarte, Friedrich-Schiller-Universität Jena, Schillergäßchen 2–3, D-07745 Jena, Germany
2 Instituto Nacional de Astrofı́sica, Óptica y Electrónica, Luis Enrique Erro 1, Sta. Ma. Tonantzintla, Puebla, CP 72840, Mexico
3

Downloaded from https://academic.oup.com/mnras/article/500/4/5552/5998234 by KASI user on 12 Februde Astrofı́sica de Canarias, Calle Vı́a Láctea S/N, E-38205 La Laguna, Tenerife, Spain
Carina is a nearby young4 Instituto
stellarassociation.
far,0213,only
a small
Byurakan
AstrophysicalObservatory, So
Byurakan
Aragatzotn,
Armenianumber of stars have been clearly identified as members of
this association. In this paper, we reanalyse the membership of the association in light of Gaia DR2 data, in particular finding
Accepted
2020 November
13. Received 2020 November
form2020 July
17 is noteworthy as one of the few stars that hosts boththat HD 95086 is a potential
member(probabilityof 71 13;perin originalcent).
Thisstar
a detected debris disc and a directly imaged planet. It has previously only been considered as a potential member of the Lower
B S T RofA CtheT Scorpius–Centaurus association. We also reanalyse the age of the Carina association. Using
Centaurus Crux (LCC) –Apart
Carina is a nearby young stellar association. So far, only a small number of stars have been clearly identified as members ofa Bayesian inference codethisapplied
to infer a solution from stellar evolution models for the most probable (>99 per cent) members
association. In this paper, we reanalyse the membership of the association in light of Gaia DR2 data, in particular finding+1.1
that HDa potential member(probability
71 permuchcent). This
star is noteworthy
as one of the studies.
few stars thathosts bothwe have revised
Myr,youngerthan previous
Whilstof Carina, we infer an age
for95086
the isassociationof 13.3−0.6 ofa detected debris disc and a directly imaged planet. It has previously only been considered as a potential member of the Lower
HD 95086’s association membershipfrom LCC to Carina, the fact that we also find Carina to have a younger age, similar to that
Centaurus Crux (LCC) – part of the Scorpius–Centaurus association. We also reanalyse the age of the Carina association. Usingof LCC, means that the estimatesof HDcode
95086b’s
mass
remainHowever,
theprobableyoungerof Carina
a Bayesian inference
applied to infera solution
fromunchanged.
stellar evolution models
for the most(>99ageper cent)
members does mean that
+1.1
Myr, amuch
youngerpreviousclearlystudies. Whilst
we planet
have revised
Carina, wemember,infer an ageHDfor theassociationof 13.3−0.6hasthe companion to anotherof Carina
44627
(AB
Pic),
mass
thatthanis morein therather than brown
HD 95086’s association membership from LCC to Carina, the fact that we also find Carina to have a younger age, similar to thatdwarf range.
of LCC, means that the estimates of HD 95086b’s mass remain unchanged. However, the younger age of Carina does mean thatthe companion to another Carina member, HD 44627 (AB Pic), has a mass that is more clearly in the planet rather than brown
dwarf
range. – stars: evolution – stars: individual: HD 95086 – stars: kinematics and dynamics – planetarycircumstellar
matter

Key words:
Key associations:words: circumstellar
matter – stars: evolution – stars: individual: HD 95086 – stars: kinematics and dynamics – planetarysystems – open clusters andgeneral.

systems – open clusters and associations: general. DR2で再解析。デブリ円盤と惑星を持つ
Carinaの明らかなメンバーは少ない。Gaia
HD95086が71%でメンバー。確実なメンバーと星進化を使ってCarinaの年齢を13 Myrととて(2018a) compared to 20 and 45 bona fide members for Columba andも若く更新。HD44627の伴星が惑星質量ということになる。
1 I N T RO D U C T I O N(2018a)compared
Tuc-Hor,
respectively.to 20 and 45 bona fide members for Columba and1 I N T RO D U C T I O N There are a number of methods for determining the age of aIn thispaper, we reconsider the membership of the Carina
Tuc-Hor,
respectively.
star. These include using gyrochronology, X-ray emission, lithium
association in Section 2 based on the Gaia DR2 data. In doing so,
There are a number of methods
for determining
the ageofmodels.
a Not Inwethis
paper,
we isreconsider
themembermembershipof the Carina
depletion, chromosphericactivity, and stellar
evolution
proposethat HD 95086
a potential Carina
for the firstallmethods
workequally
well
for
all
spectraltypes
andevolution
time.
The
age
of
this
star
is
of
particularinterest
as
it
hosts
both
a
star. These include using gyrochronology, X-ray emission, lithium
association in Section 2 based on the Gaia DR2 data. In doing so,phases, and the accuracy for an individual star is usually not highdirectly imaged planet and a resolved debris disc. In Section 3, wedepletion, chromospheric activity,and 2012).
stellarevolutionmodels.
Not
thattheHD
95086
is a potential
Carinastellar
member for the first(see e.g. Vican
However,most stars
are thought
to form inwe propose
then reconsider
age ofthe association,
first by comparing
clustersfor
that allslowlydisperse into
associations(e.g. Ambartsumiantime.
evolutionmodelsthe Gaia
and then by interest
consideringas it hosts both a
all methods work equally wellspectraltypes
and evolution
The ageoftothis
starphotometry
is of particular
1947; Blaauw 1964) before dispersing completely into the Galactic

the kinematic evolution of the association. We conclude in Section 4

Downloaded from https://academic.oup.com/mnras/article/500/4/5552/5998234 by KASI user o

The age of the carina young association and potential membership
Accepted 2020 November 13. Received
November 13; in original form 2020 July 17
of HD 2020
95086

Institut d’Estudis Espacials de Catalunya, E-08030 Barcelona, Catalonia, Spain
Universidad de Chile, Camino el Observatorio 1515, Las Condes, Santiago de Chile, Chile
9
The Graduate
University
for Advanced Studies, SOKENDAI, Osawa 2-21-1, Mitaka, Tokyo 181-8588, JapanThe Explosion
10 in Orion-KL as Seen by Mosaicking the Magnetic Field with ALMANRAO Array Operations Center, P.O. Box O, Socorro, NM, USA
11Paulo C. Cortes1,2 , Valentin J. M. Le Gouellec3,4, Charles L. H. Hull2,5,12 , Josep M. Girart6,7 , Fabien Louvet4,8,
National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
Edward B. Fomalont1,2 , Seiji Kameno2,5,9 , George A. Moellenbrock10 , Hiroshi Nagai9,11 , Kouichiro Nakanishi9,11 , andReceived 2020 October 1; revised 2020 NovemberEric
3; Villard
accepted
2020 November 15; published 2021 February 2
2,3© 2021. The American Astronomical Society. All rights reserved.

8

1

National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA; paulo.cortes@alma.cl
2
Joint ALMA Observatory, Alonso de Córdova 3107, Vitacura, Santiago, Chile
3
European Southern Observatory, Alonso de Córdova 3107, Vitacura, Santiago, Chile
4
Université Paris-Saclay, CNRS, CEA, Astrophysique, Instrumentation et Modélisation de Paris-Saclay, F-91191, Gif-sur-Yvette, France
5
National Astronomical Observatory of Japan, NAOJ Chile, Alonso de Córdova 3788, Ofﬁce 61B, 7630422, Vitacura, Santiago, Chile
6
Institut de Ciències de l’Espai (ICE-CSIC), Campus UAB, Carrer de Can Magrans S/N, E-08193 Cerdanyola del Vallès, Catalonia, Spain
7
Institut d’Estudis Espacials de Catalunya, E-08030 Barcelona, Catalonia, Spain
8
Universidad de Chile, Camino el Observatorio 1515, Las Condes, Santiago de Chile, Chile
9
The Graduate University for Advanced Studies, SOKENDAI, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan
10
NRAO Array Operations Center, P.O. Box O, Socorro, NM, USA
11
National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
Received 2020 October 1; revised 2020 November 3; accepted 2020 November 15; published 2021 February 2

Abstract
We present the ﬁrst linear-polarization mosaicked observations performed by the Atacama Large Millimeter/
submillimeter Array (ALMA). We mapped the Orion-KLeinmann-Low (Orion-KL) nebula using super-sampled
mosaics at 3.1 and 1.3 mm as part of the ALMA Extension and Optimization of Capabilities program. We derive themagnetic ﬁeld morphology in the plane of the sky by assuming that dust grains are aligned with respect to the ambient
magnetic ﬁeld. At the center of the nebula, we ﬁnd a quasi-radial
Abstract magnetic ﬁeld pattern that is aligned with the explosive
We present
the ﬁrst linear-polarization
mosaicked au),observations
performedby thethe Atacama
Millimeter/transitions into a quasiCO outﬂow up to a radiusof approximately
12″ (∼5000
beyondwhichpatternLargesmoothlysubmillimeter Array (ALMA). We mapped the Orion-KLeinmann-Low (Orion-KL) nebula using super-sampled
hourglass shape resembling
morphology
in larger-scaleobservations
byprogram.
the James-Clerk-Maxwell
Telescopemosaics atthe
3.1 and
1.3 mm as part ofseen
the ALMA
Extension and Optimizationof Capabilities
We derive themagneticﬁeldmorphology
in
the
plane
of
the
sky
by
assumingthat
dust
grainsarealignedwithrespecttotheambient(JCMT). We estimate an average magnetic ﬁeld strength  B§  9.4 mG and a total magnetic energy of 2×1045 erg,
magnetic ﬁeld. At the center of the nebula, we ﬁnd a quasi-radial magnetic ﬁeld pattern that is aligned with the explosive
which is three orders oflessof approximately
than the 12″energythe explosiveCO
outﬂow.
that the ﬁeld has
CO magnitude
outﬂow up to a radius(∼5000 inau), beyond
which the patternsmoothlytransitionsWe
into aconclude
quasihourglass shape resembling the morphology seen in larger-scale observations by the James-Clerk-Maxwell Telescope
been overwhelmed by theoutﬂow and that a shock is propagating from the center of the nebula, where the shock front is(JCMT). We estimate an average magnetic ﬁeld strength  B§  9.4 mG and a total magnetic energy of 2×1045 erg,
which isthree orders
magnitude lessthe energy
the explosive
outﬂow. We center.
conclude that the ﬁeld has
seen in the magnetic ﬁeld
lines
at aofdistanceofthan∼5000
auin fromthe CO
explosion
been overwhelmed by the outﬂow and that a shock is propagating from the center of the nebula, where the shock front isseen in the magnetic ﬁeld lines at a distance of ∼5000 au from the explosion center.

Uniﬁed Astronomy Thesaurus concepts: Astrochemistry (75); Polarimetry (1278); Dust continuum emission (412);
Astronomy Thesaurus concepts: Astrochemistry (75); Polarimetry (1278); Dust continuum emission (412);
Star formation (1569);Uniﬁed(1302);(2086);
Interstellar
dust(836);
Youngstellar objects (1834);
StarProtostars
formation (1569);
ProtostarsShocks(1302); Shocks(2086); Interstellar
dust (836);Youngstellar objects(1834);
Interstellar(845)magnetic ﬁelds (845)
ALMA初の偏波モザイク。Orion-KL。磁場が中⼼の動径⽅向から外の砂時計へ。
Interstellar
magnetic ﬁelds

B=9.4 mG、CO分⼦流よりエネルギーが３桁⼩さい。
1. Introduction

The Orion nebula has been a subject of intense research since its
1.discovery
Introduction
by Fabri de Peiresc in 1610 (Miller 2016). Home to theTrapezium, a star cluster containing massive stars, the Orion

The Orion nebula has been
subject
intenseresearch
itsthenebulaaalso
hosts theof
closesthigh-mass
star-formingsinceregion to
Sun: the Orion integral-shaped ﬁlament (Johnstone & Bally 1999).
discovery by Fabri de Peiresc
in 1610 (Miller
to theﬁlament Homeis embeddedin theThis one-degree-long,
2200 Me2016).
Orion
A
cloud
(Ballyetal.
1987).
The∼100
M
50,000Mee OrionTrapezium, a star cluster containing
massive stars, the Orion
Molecular Core 1 (OMC1), located behind the Orion nebula
nebula also hosts the closest
high-mass
star-forming
regionto the(Genzel& Stutzki 1989)
at a distance of ∼414
pc (Menten
et al.
2007), is the densest and most molecule-rich part of the Orion A
Sun: the Orion integral-shapedﬁlament (Johnstone & Bally 1999).
cloud. OMC1 contains the Orion-KL nebula, which has beenmassive stars in the nebula, as suggested by the high-velocity
proper motions of BN, source I, and source x (Bally et al.
2017, 2020). This explosion affected the surrounding gas, as
shown by vibrationally excited H2 and [Fe II] emission thatreveals a spectacular network of collimated outﬂows known as the“Orion ﬁngers,” which extend for 0.1 pc in a wide-angle, conicalconﬁguration (Allen & Burton 1993; Colgan et al. 2007; Ballyet al. 2015). A plethora of observations of additional outﬂow
tracers conﬁrm this link between the outﬂow and the explosive
2
event. In the millimeter, the ﬁngers were detected in high-velocity
CO emission by the Submillimeter Array (SMA; Zapata et al.

massive stars in the nebula, as suggested by the high-velocity
proper motions of BN, source I, and source x (Bally et al.
2017, 2020). This explosion affected the surrounding gas, as
shown by vibrationally excited H and [Fe II] emission thatreveals a spectacular network of collimated outﬂows known as theAdvance Access publication 2020 September 11

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V. S. Veena,19 M. Wienen,2 F. Wyrowski,2 C. Agurto,20 F. Azagra,20 R. Cesaroni,9 R. Finger,12Affiliations are listed at the end of the paper
E. Gonzalez,20 T. Henning,10 A. K. Hernandez,21 J. Kainulainen,2,22 S. Leurini,2,23 S. Lopez,4F. Mac-Auliffe,20 P. Mazumdar,2 S. Molinari ,18 F. Motte,24 E. Muller,25 Q. Nguyen-Luong,15 R. Parra,20
Accepted 2020 May 22. Received 2020 MayJ.-P.
22; inPerez-Beaupuits
original form 2019 ,October
20
F. M.10Montenegro-Montes,20 T. J. T. Moore,14 S. E. Ragan ,1
A. Sánchez-Monge,19 A. Sanna,2 P. Schilke,19 E. Schisano ,18 N. Schneider ,19 S. Suri,19 L. Testi,19
K. Torstensson,20 P. Venegas,20 K. Wang26 and A. Zavagno5
ABSTRACT
Affiliations are listed at the end of the paper

Downloaded from https://academic.oup.com/mnras/article/500/3/3027/5904100 by KASI user on 12 February

V. S. Veena,19 M. Wienen,2 F. Wyrowski,2 C. Agurto,20 F. Azagra,20 R. Cesaroni,9 R. Finger,12
2,22
2,23
4
E. Gonzalez,20 T. Henning,10 A.
K.SEDIGISM
Hernandez,21survey:
J. Kainulainen,
S. Leurini,
S. Lopez,Themolecular
cloudsintheinner
GalaxyF. Mac-Auliffe,20 P. Mazumdar,2 S. Molinari ,18 F. Motte,24 E. Muller,25 Q. Nguyen-Luong,15 R. Parra,205
20 2‹ J. S. Urquhart 141
A. Duarte-Cabral,1‹ D. Colombo,
Ginsburg,
F. Schuller ,2J.-P. Perez-Beaupuits ,20 F. M.
Montenegro-Montes,
T. J. T. Moore, ,3‹S.A.E.
Ragan4 D.,Russeil,
9
11
12
L. D.
J. Barnes,7,8 M. T. Beltrán,
Beuther,10 S. Bontemps,
2 Anderson,6 P.19
19
A. Sánchez-Monge,19 A. Sanna,
P. Schilke,
E. Schisano,18 N. H.
Schneider,19 S. 15Suri,L.19Bronfman,
L. Testi,
11
13
14
2
2
T.
Csengeri,C.
L.
Dobbs,D.
Eden,
A.
Giannetti,
J.
Kauffmann,
M.
Mattern,
S.-N.
X. Medina,2
20
20
26
5
2,16
K. Torstensson, P. Venegas, K.K.
and Lee,A. Zavagno
M. Wang
Menten,2 M.-Y.
A. R. Pettitt ,17 M. Riener,10 A. J. Rigby ,1 A. Traficante ,18

We use the 13 CO (2–1) emission from the SEDIGISM (Structure, Excitation, and Dynamics of the Inner Galactic InterStellar
銀 河 系 内 側 の 10663 個
Accepted
2020 May
22. Received
May 22; inform the2019 October
10
Medium) high-resolution spectral-line
surveyof theinner2020
Galaxy,tooriginal
extract
molecular
cloud population with a large dynamicの分⼦雲。13CO 2-1。
range in spatial scales, using the Spectral Clustering for Interstellar Molecular Emission Segmentation (SCIMES) algorithm. This
work compiles a cloud catalogue with
aRtotalABST
A C T of 10 663 molecular clouds, 10 300 of which we were able to assign distances
⼤質量星形成と単独で
13
Westudyuse thesome
CO (2–1)
emission
fromthe SEDIGISM(Structure,
Excitation,
and Dynamics
of consisting
the Inner Galactic
InterStellar
and compute physical properties. Weof theglobalpropertiesof clouds
using
a science
sample,of 6664
Medium) high-resolution spectral-line survey of the inner Galaxy, to extract the molecular cloud population with a large dynamic 相関する分⼦雲の性質
well-resolved sources and for whichrange
the indistanceestimates
reliable.
In particular,
comparethe scaling
relations) algorithm. This
spatial scales,
using theare
Spectral
Clustering
for Interstellarwe
Molecular
Emission
Segmentation(SCIMESretrieved
work compiles
cloud
catalogue
a total of 10
molecular
300 of which
we werestar
able formation.
to assign distances はない。⼤きく、乱流
from SEDIGISM to those of other surveys,
and awe
explorethewithpropertiesof663
cloudswithclouds,
and 10without
high-massand computephysicalproperties.
study somethe global propertiesof clouds
using amassive
science sample,of 6664
Our results suggest that there is no single
globalpropertyof aWecloudthat ofdetermines
its ability
to formstars,consistingalthoughwell-resolved sources and for which the distance estimates are reliable. In particular, we compare the scaling relations retrieved が強く、⼤質量星を形
we find combined trends of increasing
mass, size,
surfacedensity,velocity
dispersion
thewithsub-sample
of clouds
from SEDIGISM
to thoseof othersurveys, andand weexplore theproperties offor
cloudsand without high-mass
starwith
formation. 成する分⼦雲は⼤局的
Our results
is noextreme
single global
propertya cloudthat determines
its ability
form massive
stars,
althoughongoing high-mass star formation. We
then suggest
isolatethat
thetheremostcloudsin oftheSEDIGISM
sample(i.e.toclouds
in the
tails
we
find
combined
trendsofincreasing
mass,
size,
surfacedensity,andvelocity
dispersion
forthesub-sample
ofcloudsof the distributions) to look at their overall Galactic distribution, in search for hints of environmental effects. We find that, for with な分布から外れている。
ongoing high-mass star formation. We then isolate the most extreme clouds in the SEDIGISM sample (i.e. clouds in the tails
most properties, the Galactic distributionof the mostextremecloudsis only
marginallydifferent
that of theeffects.
globalof the distributions)to lookat their overall
Galactic
distribution,
in search
for hints oftoenvironmental
We cloudfind that, fortheclouds,
Galactic distributionof theclouds
most extreme
cloudsis only marginallydifferent clouds
to that ofare
the global
population. The Galactic distributionmostof properties,
the largest
the turbulent
and thehigh-mass
star-forming
thosecloudGalactic
distribution ofWethe also
largestfind
clouds,thetheturbulent
and the high-masscloudslow
are thosethat deviate most significantly from population.
the globalThecloud
population.
that
leastclouds
dynamically
activestar-forming
clouds (withthat deviate most significantly from the global cloud population. We also find that the least dynamically active clouds (with low
velocity dispersion or low virial parameter)are situatedfurtherafield,aremostly
the afield,
leastmostly
populatedareas.
However,
we suspect
velocity dispersion
or low virial
parameter)
situated infurtherin the least
populatedareas. However,
we suspectthat partthese trends
may be affectedby someobservationalbiases (such ascompletenessand survey limitations),
and thusthat part of these trends may be affectedbyof someobservationalbiases(such
as completenessandsurvey limitations),
and thus
requirefurtherfollow
up
work
in
order
to
be
confirmed.
require further follow up work in order to be confirmed.
Key words: ISM: clouds – Galaxy: structure – stars: formation – galaxies: ISM, star formation.

Key words: ISM: clouds – Galaxy: structure – stars: formation – galaxies: ISM, star formation.

1

Yuji Ebisawa, Nami, KarlM.
The AstrophysicalJournal, Sakai
904:136 (13pp), 2020
December
1 Menten, Yoko Oya https://doi.org/10.3847/1538-4357/abc16f, and Satoshi Yamamoto© 2020. The American Astronomical Society. All rights reserved.
Department of Physics
and Research Center for the Early Universe, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
2
RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
3
Max-Planck-Institut
Auf
dem Hügel
69, Intensity
D-53121 Bonn,
Germany
Temperature Structurefürof Radioastronome,
the Pipe NebulaStudiedby theAnomalyof the OH
Received 2020 March 12; revised 2020 September
29;
accepted
2020
October
13;
published
2020
November 27
18 cm Transition1

Yuji Ebisawa1, Nami Sakai2, Karl M. Menten3

Abstract, Yoko Oya1

, and Satoshi Yamamoto1

Department of Physics and Research Center for the Early Universe, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
2
RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
3
Max-Planck-Institut für Radioastronome, Auf dem Hügel 69, D-53121 Bonn, Germany
Received 2020 March 12; revised 2020 September 29; accepted 2020 October 13; published 2020 November 27

We present observations of the four hyperﬁne structure components of the OH 18 cm transition (1612, 1665, 1667,
and 1720 MHz) toward a ﬁlamentary dark cloud, the Pipenebula, with the Green Bank Telescope. A statistical
Abstract
present observationsof the four hyperﬁne
structurecomponentsof the OH 18 cmoftransition(1612, 1665,
1667,
equilibrium analysis is We
appliedto the spectra,
and thekinetic
temperaturea diffusemolecular
gas surrounding
and 1720 MHz) toward a ﬁlamentary dark cloud, the Pipe nebula, with the Green Bank Telescope. A statisticaldense cores is determinedaccurately;
the derived
temperature
ranges offrom
40molecular
to 75 gas
K.surrounding
From this result, we assess
equilibrium
analysis is applied
to the spectra,
and the kinetic temperaturea diffuse
dense
cores
is
determinedaccurately;thederivedtemperature
ranges
from
40
to
75
K.
From
this
result,we assess from a nearby star
the heating effect on theﬁlamentary structure of the nebula’s “stem” region due to UV photons
the heating effect on the ﬁlamentary structure of the nebula’s “stem” region due to UV photons from a nearby starθ-Ophiuchi and a possible
ﬁlament–ﬁlamentcollisionin thetheand“stem”
and “bowl”
θ-Ophiuchi
and a possible ﬁlament–ﬁlamentcollisionin the interface
interface of theof“stem”“bowl” regions.
In the stem regions. In the stem
region, the gas kinetic temperature is found to be almost independent of the apparent distance from θ-Ophiuchi: theregion, the gas kinetic temperatureis thefound
to visible.
be almostindependentof theapparent
distance
UV-heating effect bystar is not
On the other
hand, the gas kinetic
temperatureis raised,as high asfrom θ-Ophiuchi: the∼75 K,
at theof the two ﬁlamentaryThis resultthe
provideswith additional
support for the is raised, as high as
UV-heating effect by thestarisinterface
not visible.
On the structures.
other hand,gasuskinetic
temperatureﬁlament–ﬁlament collision scenario in the Pipe nebula.
∼75 K, at the interfaceUniﬁedof thetwo ﬁlamentary structures. This result provides us with additional support for the
Astronomy Thesaurus concepts: Molecular clouds (1072); Interstellar molecules (849)
ﬁlament–ﬁlament collision scenario in the Pipe nebula.
the bowl region
exhibiting an extended
structure(849)
in the eastern
1. IntroductionMolecular clouds (1072);
Uniﬁed Astronomy Thesaurus concepts:
Interstellar
molecules
part. Since the Pipe nebula is a nearby (∼145 pc) object (Alves
The 18 cm transition of the hydroxyl radical (OH) has
extensively been observed toward molecular clouds, late-typestars and external galaxies (e.g., Harju et al. 2000; Darling &Giovanelli 2002; Caswell 2004; Hoffman et al. 2005; Wolak
al. 2012; Ebisawa et al. 2015, 2019; Xu et al. 2016; Li et al.
k etk2018). It is the Λ-type doubling transition in the groundrotational state, and consists of four hyperﬁne structure (hfs) lines
at 1612, 1665, 1667, and 1720 MHz. It is well known that theobserved intensity ratio of the four hfs lines is often different
from the ratio expected in the local thermodynamic equilibrium(LTE) condition; I1612: I1665: I1667: I1720  1: 5: 9: 1 (e.g., Harju
et al. 2000; Ebisawa et al. 2015). Such intensity anomalies can becaused by collisional and/or radiative processes among therotational states (Elitzur et al. 1976; van Langevelde et al. 1995;
Ebisawa et al. 2019). Ebisawa et al. (2015), on the basis of theirstatistical equilibrium calculations, reported that the intensity
ratio is sensitive to the gas kinetic temperature. They demonstrated that the gas kinetic temperature of warm (Tk  30 K)
molecular clouds can be determined accurately from theobserved intensities. Furthermore, the critical density of the& Franco 2007) with little star formation activity except for the
B59 region (Onishi et al. 1999), it has been a good target to
study molecular-cloud formation (Lada et al. 2008; RománZúñiga et al. 2010). Its magnetic-ﬁeld structure has been
investigated by polarimetry (Alves et al. 2008, 2014; Franco
et al. 2010). A bright B2 IV star, θ Ophiuchi (HD 157056), is
located about 3 pc away from the Pipe nebula (Figure 1), andfeedback with this star has been invoked for shaping thestructure and the formation process of the nebula (Onishi et al.
1999; Gritschneder & Lin 2012).
The velocity structure of the Pipe nebula was studied in the12
CO along with its isotopologue lines. Figure 2 shows theintegrated intensity maps of the 13CO (J  1–0) (cyan contours)
and 12CO (J  1–0 ) (red contours) lines by Onishi et al. (1999)
overlaid on the visual extinction (AK) map of Figure 1. The 12CO
map is prepared by integrating over the velocity range from 6 to
10 km s−1 (Onishi et al. 1999). As shown in Figure 2, the 13CO
line traces a ﬁlamentary structure elongated along the west toeast direction, which is seen in the visual extinction map. We
hereafter call this structure the W-E ﬁlament. On the other hand,

Green Bank Telescope, OH 18 cm, Pipe nebula。
the bowl region exhibiting an extended structure in the eastern
Introduction
正確なT1. =40-75
K。幹ではT がθ-Ophiuchiからの距離に依らないのでUV-heating無し。
part. Since the Pipe nebula is a nearby (∼145 pc) object (Alves
The 18 cm ⼆つのフィラメントの交差点に向かってT
transition of the hydroxyl radical (OH) has kが増加。フィラメント衝突。
& Franco 2007) with little star formation activity except for theextensively been observed toward molecular clouds, late-typestars and external galaxies (e.g., Harju et al. 2000; Darling &Giovanelli 2002; Caswell 2004; Hoffman et al. 2005; Wolak
et al. 2012; Ebisawa et al. 2015, 2019; Xu et al. 2016; Li et al.
2018). It is the Λ-type doubling transition in the groundrotational state, and consists of four hyperﬁne structure (hfs) lines
at 1612, 1665, 1667, and 1720 MHz. It is well known that theobserved intensity ratio of the four hfs lines is often
different
2−3

B59 region (Onishi et al. 1999), it has been a good target to
study molecular-cloud formation (Lada et al. 2008; RománZúñiga et al. 2010). Its magnetic-ﬁeld structure has been
investigated by polarimetry (Alves et al. 2008, 2014; Franco
et al. 2010). A bright B2 IV star, θ Ophiuchi (HD 157056), is
located about 3 pc away from the Pipe nebula (Figure 1), andfeedback with this star has been invoked for shaping thestructureand the formation process of the nebula (Onishi et al.
12

A. Eckart , F. Eisenhauer , M. Filho, F. Gao , E. Gendron , R. Genzel , S. Gillessen , R. Grellmann ,9119
M. Habibi , X. Haubois , F. Haussmann , T. Henning1 , S. Hippler1 , Z. Hubert16 , M. Horrobin6 , A. Jimenez Rosales9 ,The GRAVITY young stellar object survey
L. Jocou16 , P. Kervella10 , J. Kolb11 , S. Lacour10 , J.-B. Le Bouquin16 , P. Léna10 , H. Linz1 , T. Ott9 , T. Paumard10 ,1
IV. The1 ,CO
Oph at sub-au
G. Perrin10 , O. Pfuhl4 , M. C. Ramírez-Tannus
C. overtone
Rau9 , G. emission
Rousset10in, S.51Scheithauer, J.scales
Shangguan9 , J. Stadler9 ,9,15
10
9 2,3,59
O. Straub9 , C. Straubmeier6 , E.GRAVITY
Sturm9 ,Collaboration:
E. van Dishoeck, F. ?Vincent, S.1,2,3
von, F. Widmann,
M. Koutoulaki1,2,3,4,, R. Garcia Lopez, A.Fellenberg
Natta2 , R. Fedriani,
16
9 Garatti1,2,3 , T. P.6 Ray2 , D. Coffey2,1 , W.
9 Brandner1 , C. 9,6
11 7,8,11 , L. Klarmann1 ,A.
CarattioDougados,
P.
J.
V.
GarciaE. Wieprecht, M. Wiest , E. Wiezorrek , S. Yazici , and G. Zins
L. Labadie6 , K. Perraut16 , J. Sanchez-Bermudez1,18 , C.-C. Lin1,19 , A. Amorim8,17 , M. Bauböck9 , M. Benisty16,14 ,9J. P. Berger16 , A.(Affiliations
Buron9 , P. Caselli
Y. foundClénet10after, V. Coudé
du Foresto10 , P. T. de Zeeuw15,9 , G. Duvert16 , W. de Wit11 ,can ,bethereferences)
6,12
9
7,8,11
9
A. Eckart , F. Eisenhauer , M. Filho, F. Gao , E. Gendron10 , R. Genzel9,13 , S. Gillessen9 , R. Grellmann6 ,911
9
M. Habibi , X. Haubois , F. Haussmann , T. Henning1 , S. Hippler1 , Z. Hubert16 , M. Horrobin6 , A. Jimenez Rosales9 ,
16
10
11
10
L. JocouReceived, P. Kervella, J. Kolb2020, S. Lacour, J.-B.
LeOctober
Bouquin16, P. Léna10 , H. Linz1 , T. Ott9 , T. Paumard10 ,
22
March
/
Accepted
20
2020
G. Perrin10 , O. Pfuhl4 , M. C. Ramírez-Tannus1 , C. Rau9 , G. Rousset10 , S. Scheithauer1 , J. Shangguan9 , J. Stadler9 ,O. Straub9 , C. Straubmeier6 , E. Sturm9 , E. van Dishoeck9,15 , F. Vincent10 , S. von Fellenberg9 , F. Widmann9 ,9E. Wieprecht, M. Wiest6 , E. Wiezorrek9 , S. Yazici9,6 , and G. Zins11
ABSTRACT(Affiliations can be found after the references)

Context. 51 Oph is a Herbig Ae/Be star that exhibits strong near-infrared CO ro-vibrational emission at 2.3 µm, most likely originating

Received 22 March 2020 / Accepted 20 October 2020in the innermost regions of a circumstellar disc.
Aims. We aim to obtain the physical and geometrical properties of the system by spatially resolving the circumstellar environment of
ABSTRACTthe inner gaseous disc.
Context. 51 Oph
is aLarge
Herbig Ae/Be
star that exhibits
strong near-infrared
CO ro-vibrationalemission atto2.3spatiallyµm, most likely
originating
Methods. We used the second-generation
Very
TelescopeInterferometer
instrument
GRAVITY
resolvethe continin the innermost regions of a circumstellar disc.
uum and the CO overtone emission.
We
obtained
data
over
12
baselineswiththeauxiliary
telescopes
andderivevisibilities,
and theAims. We aim to obtain the physical and geometrical properties of the system by spatially resolving the circumstellar environment of
inner gaseous
differential and closure phases as athefunctionof disc.
wavelength. We used a simple local thermal equilibrium ring model of the CO emission
Methods. We used the second-generation Very Large Telescope Interferometer instrument GRAVITY to spatially resolve the continto reproduce the spectrum and COuum
lineanddisplacements.
the CO overtone emission. We obtained data over 12 baselines with the auxiliary telescopes and derive visibilities, and theResults. Our interferometric data differential
show thatstar
is marginallyresolvedWeat usedouraspatial
resolution,with ringa radius± 2.65 R .
and theclosurephasesas a function of wavelength.
simple local
thermal equilibrium
model ofof
the⇠10.58
CO emission
toreproducethespectrum
and
CO
line
displacements.
The K-band continuum emission fromthe disc is inclined by 63 ± 1 , with a position angle of 116 ± 1 , and 4 ± 0.8 mas (0.5 ± 0.1 au)
Results. Our interferometric data show that the star is marginally resolved at our spatial resolution, with a radius of ⇠10.58 ± 2.65 R .
across. The visibilities increase within
thecontinuum
CO lineemission,
indicatingthat
COa position
is emitted
The K-band
emissionfrom the discis inclined by
63 ±the1 , with
angle ofwithin
116 ± 1 , theand 4dust-sublimation± 0.8 mas (0.5 ± 0.1 au) radius.
across.
The
visibilities
increase
withintheCOlineemission,
indicating
that
the
CO
is
emittedwithinthedust-sublimation
radius. (NBy modelling the CO bandhead Byspectrum,
wederivethatthe weCOis thatemittedfroma fromhot a(Thot=(T1900–2800
K)andanddense
CO =modellingtheCObandhead
spectrum,
derivetheCOisemitted=
1900–2800
K)
dense
(N
CO =
21
2
21
2
(0.9–9) ⇥ 10 cm ) gas. The analysis
displacement
withrespectwith
to respect
the continuum
allowsustotoinfer
infer
that
(0.9–9) of⇥ 10thecm CO) gas.line
The analysisof the CO line
displacement
to the continuum
allows usthat theCOthe
is CO isemittedfrom awell
region within
0.10 ± 0.02theau across,well within the dust-sublimation
radius.
The inclination
andposition
position angleof theofCOtheline CO line
emitted from a region 0.10 ± 0.02 au
across,dust-sublimation
radius. The
inclination
and
angle
emitting region is consistent with that of the dusty disc.
emitting region is consistent with thatof theOur
dusty
disc.
Conclusions.
spatially
resolved interferometric observations confirm the CO ro-vibrational emission within the dust-free region
of
the
inner
disc.
Conventional
disc models exclude
the presenceof CO
in the dust-depleted
regions of Herbig
AeBe
Ad hoc region
Conclusions. Our spatially resolved interferometric observations
confirm
the COro-vibrationalemission
withinthestars.
dust-freemodels of the innermost disc regions, that can compute the properties of the dust-free inner disc, are therefore required.
of the inner disc. Conventional disc models exclude the presence of CO in the dust-depleted regions of Herbig AeBe stars. Ad hoc
Key words. accretion, accretion disks – stars: formation – techniques: interferometric – stars: pre-main sequence –models of the innermost disc regions,that can compute the properties of the dust-free inner disc, are therefore required.
stars: individual: 51 Oph

Key words. accretion, accretion disks – stars: formation – techniques: interferometric – stars: pre-main sequence –stars: individual: 51 Oph

1. Introduction

Circumstellar discs are crucial for understanding how stars andplanets form. In spite of the enormous wealth of data provided

regions, and this has only been possible for a few objects (Kraus
et al. 2008; Eisner et al. 2007; Lazareff et al. 2017; GRAVITY
Collaboration 2019). Still, this is a region of great importance,

VLTI, GRAVITY
CO ro-vibrational
2.3 µm
Herbig disk
連続波で10.6 Rsunの星と0.5 auの円盤。
COが0.1 au,
1900-2800 K, 0.99x1021 cm-2から。
dust-sublimationより内側。