A&A proofs: manuscript no. 45143corr

Skaf et al.: The

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

expressed as:
r
GM?
,
⌦K =
3
a

ÚÛÙWı¿%¥%AL(6)

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

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

11. Evolution of the projected distance and relative intensity profile of C1 over the years, from di↵erent instruments (colour-coded inwithFig.
✓
the
angle
betweenthesetclump
the
direction
0 defining
Skaf
et al.:
Thedata hasPictoris
system:Setting
on the pllegend).
The intensity
forthe VISIR
and NEAR
been
to scalewithandthe T-ReCS
data
by Li etconstraintsal. (2012).
Fig. 11. Evolution of the projected distance and relative intensity profile of C1 over the years, from di↵erent instruments (colour-coded in theperpendicular
to the line of sight. Since the Keplerian speedislegend). The
intensity for the VISIR and NEAR data has been set to scale with the T-ReCS data by Li et al.DÀIJ{[Ã&(2012).
ô3üFEΩæøîB&¿h¡¬√;;ƒ¬≈g∆«3»:¬…8¬√3
Clumps
C1
C2
C3
C4
constant for a circularorbit (⌦K = ✓/t), theprojected
sepaClumps
C3 29.3±0.3
C4 -15.2±0.3
Projected separation (au)C1 56.1±0.3C2 -35.2±0.3
as a functionof time for a given orbital
radiusisFig. 1. Image of the disk at 12 µm, using a PCA reduction (bottom), and a ClasImg reduction performed with SpeCal. The disk has beenration,
rotated x[t, a],∏%ÕŒANO3œ¿h¡¬√;;ƒ¬≈œDÀdp&¡:–9¬:&–√…—¬K“&”–…ƒ–≈&Table 2. Projected separationsof the clumps
observedwith 56.1±0.3
NEAR. Negative
signs are29.3±0.3
for the NE sideof the disk.
Projected
separation(au)-35.2±0.3-15.2±0.3
by 30 degrees in those images with respect to due north. Labels indicate the dust clumps described in Sect. 4.
expressed
as:Table 2. Projected separations of the clumps observed with NEAR. Negative signs are for the NE side of the disk.
UV9dÚŒAÛÙôöA®©Y@{Ifwıˆ˜¯V3˘òabIJ3˙`&&≫to&˚ò¸˝˛ˇ&†°‘’÷î◊ÿŸdB⁄8»:8K¢£€
Fig. 7. Surface brightness profile of the PCA image (red), and ClasImg image (orange). The y-axes correspond
the ClasImg on the left andof thetheprojected 0
intensity profiles
for the NEAR2019 data, to- around 56 au. At face value, this would suggest that we are w
1r
PCA on the right. Labelsof the clumps have been Fig.
added10.
forPosition
convenience.
of C1 in the PCA image of the 2019 data. Two Gausgether
with the intensity
ALMA
data.
Forforconsistency,
weused
thetostar’saroundnessingdi↵erent
whose
projected
positionsofthe projected
profilesthe NEAR
2019
data,
56 au.two
At facevalue,clumps
this would
suggestthat weare wit- hap
BC!"\&¶´A3ÀÍ#î#""&”¬;p&$F%&ïE3'(÷î)#!*+∏∏\!•&√”p&&
GM
B
C
⇤ C
BBBpc✓ fordata.
distanceof the19.63
theseobservations,thus
to coincide.
Suchclumps
a conclusion
should, however,be taken w
with
ALMA
Forthreeconsistency,
we usedtheincluding
star’s nessing
two di↵erent
whose projected
positions happen
Csian curves have been added in dashed lines to show the substructures x[t, gether
a]
=
a
cos
t.
.
(8)
C
0 these three@di↵erences
potentiallyslightpc
withobservations,the3 twoAaforementioned
great caution.
PV diagrams
the CO belines
do withindeed a
distanceof 19.63
forthus including pa-to coincide.
Such aTheconclusion
should,ofhowever,
taken
−3
a
$GHïòH3•Ùö,îp&&5
×
10&
within the disk and the brown line corresponds to the final fit.
pers regarding
positionswithof theAlthough weclump shouldbe radiallyspannpotentiallyslightthedi↵erences
thestructures.
two aforementioned
pa- de-greatsuggest
caution.that
ThethePVgas
diagramsof the COlines doextended,
indeed also
Skaf et al.: The

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

expressed as:
r
GM?
,
⌦K =
a3

(6)

with a being the semi-major axis and G being the gravitational constant. The projected separation, x0 , at the first epoch is
tect with
VISIR
well-resolved(C2) inthe NE we
part
of
⇠100
authe
forgastheclump
orbitalradius.
If the dust
clumpspanning
was to hav
persregardingthea positionsof theclump
structures.
Althoughdesuggestthatshouldbe radiallyextended,
given
by: thetecta well-resolved
the NE partisofnot
thevery⇠100similar
au for radial
the orbital
radius.then
If thedust clump
to haveadisk,with
theVISIR
correspondencewith clump
the CO(C2)gasin
distribution
extension,
it could
appearwas
brighter(becaus¯VIJ)#"¶ß3™#W-®©& To
estimatethebestmodelsmatching
the
data
given
the
error
disk,
the correspondence
withthetheclump
CO gason
distribution
is notradialextension, then(becauseof lu
conclusive.
Not only does
the NE sidein very
ALMAsimilar
highertemperatures)at ititscould
innerappear
edge,brighter
while thepeak CONotatonly
does
clump
on
the2000
NE33sideintemperatures)at its inner
edge,
while
peak CO lumiimages
peak
about
25the
au,grid
as opposedtoau modelsin ALMA
the VISIRhigher
nositycould
be locatedfurtherout,
thustheexplaining
the appar
bars,conclusive.
wegenerated
a
of
of
two
parameters,a¯VIJ)∏%¶ß3™+W-®©&
5.3. Temporal evolution of C1’s
projected distanceimages
peak
at
about
25
au,
as
opposed
to
33
au
in
the
VISIR
nositycould
belocatedfurtherout,
thus
explaining
theapparent
image, but it is also related to a much broader projected struc- discrepancy. In addition, the di↵erent transitions of CO gas w
but it is also
relatedto (⇠70
a muchstrucIn
the di↵erentof CO gasand
willthe dwiththefollowingpriors:aube more(step
0.1excitedau)and transitions
and image,
x0 ,especially
ture,
in CO
J=3-2
au),broader
than atprojected
11.2555µm.
On60
thediscrepancy.
oraddition,
lessdependingon temperatureespeciallyincontrary,
CO J=3-2there(⇠70isau),
thanmatch
at 11.25µm. Onthe
thepro-be moreor less
excited partners
dependingonnon-LTEtemperature
denSW side,on thea goodbetweensity ofcollisional(in2
as isandthethecase
for P
Figure 11 presents the intensity profiles of the diskv3./î&for each 51.9ture,
53.9
au
(step
0.05
au),
respectively.
Asaresult
of
a
SW
side,
on
the
contrary,
there
is
a
good
match
betweentheprosityofcollisional
partners(innon-LTE
as
is
the
case
for
Pic,
jected location of C1 and that of the CO gas clump. A small o↵- Matrà et al. 2017) and they are not necessarily representative
jectedof C1 and that of the CO gasFig.
clump.
small o↵- of
Matrà
etpositional. 2017) ofandC1
are not
necessarily
representativeof Fig12.A Evolution
the
over
the
16gas
years
of observaepoch around the location
of
C1.
The
T-ReCS
measurements
ÓÔ0DÏ312p&®3p&◊4567&minimization,set (⇠6locationau) of C1
between
ALMAableand VISIR
observations
is vistheunderlying
COtheyordominant
speciesspatial distributi
we
were
to
constrainthesemi-majoraxisofset (⇠6 au) of C1 between ALMA and VISIRtions
observations
is vis- forthe VISIR
underlying
or dominantgas species
distributions(20(redclumpsquaresandCO
NEAR,
redThesecircles
for spatial
T-ReCS).
The
ible
in
Fig.
14,
but
this
cannotbeattributed
totheorbital(e.g.,
Kraletal.
2016).
questionsclearly
go beyond+0.4+0.5
from 2003 and 2010 were obtained from the plots in Telesco C1 toible in
Fig.
14,
but
this
cannotbeattributed
to
the
clump
orbital(e.g.,
Kraletal.
2016).
These
questionsclearlygobeyondthea according= 56.1 theau (andxbest
52.8implying
au).
More
detailsare
0 =motionanalysisSect.
5.4,
possibly
theinpresent
paper,
andwe thisleave
thistoopenbedisanissue
openbut
is
Keplerianmodel
isscopeoverlaid
blue
togetherwiththeto1-sigma
0.3
0.5 scopeÂPBI{38WÖÉÈùSTh[\motionaccording totothe
analysis
in in
Sect.
5.4,
possibly
implyingof theofpresent
paper,
and we
leave
be
an
0.4
et a
slightlydi↵erentdistribution
distribution
dust
andcomponents.
for investigationinstudies.
et al. (2005) and Li et al. (2012), after updating the star’s dis- given
persion(lightblue),forcorresponding
R future=studies.
56.1
inFigure12).
aa slightlydi↵erent
of ofthethedust
andgasgascomponents.
investigation
in to
future0.3 au. Also displayed:
However, wewenotenotethat
thatMatrà
Matràet etal.al.
(2017)
arguedwhilethe data for a 2:1 (orange) and 3:2 (green) resobest
modelsfitting
However,(2017)
arguedthatthatwhiletance to 19.63.
Telescoetal.ofof(2005)
measured
for C1 of 52 au
the projected
projectedlocation
location
CO
clump
is
around50a
au,
its dethe
thetheCOclump
is around
50 au,
its position
denances.
7. Originand andfate fateof C1of C1
projectedstellocentric
stellocentricdistancedistance(deducedfromposition-velocity7. Origin
projected(deducedfromposition-velocity
The apparent projected separation of the clump is clearly in- in Dec.
7.1
2003,
while
Li
et
al.
(2012)
obtained
54
au,
then
spec(PV)diagrams
diagramsofofCO
COintensity)
intensity)
peaks,
in reality,⇠ au.
85 Thisau. This As shown in Sect. 5.4, the location of C1 over the 2003-2(PV)
peaks,
in reality,at ⇠at85
As shown in Sect. 5.4, the location of C1 over the 2003-2019+0.6
Fig. 2. Contrast curve at 5 as measured along the creasing
disk spine acrossaseemsatotodisplacement
contradictthetheresults
results
orbitalanalysis(Sec.
over time,suggestive of a global outward motion of C1. ulated
seems
contradictof ofourourorbitalanalysis(Sec.
5.4),5.4),ofroughly2.0
au.
The
authors
periodislattercompatible
witha circular
Keplerianorbita wit
Sinperiodis compatible
witha circular
Keplerianorbit with
0.6
width
of
1",
as
measuredonthe
PCA
image.
The
contrast
of
Pic
b
which
the
semi-major
axis
of
the
dust
clump
is
constrained
to
lie
which
the
semi-major
axis
of
the
dust
clump
is
constrained
to
lie
+0.4
Fig. 8. Images of the centro-symmetrical subtractionof eventhe disk
at obvious when plotting its measured position concluded that the clump is moving at Keplerian
56.156.1au0.3semi-majoraxis. axis.
Duringthe review
processprocess
for the hav
auvelocity,semi-major
the review
for
This
is
more
cor-Duringwithrespect
to
the
star
and
its
distance
to
the
star
is
indicatedbythe
11.25 µm, obtained with VISIR in 2004 on VLT UT3 (top) and at+2.0
tro
Articlepage
1010oforbital
1515
Articlenumber,number,page
ofversustime
ona
16-yearbaseline,as
inFigure12(redcirclesau.
Whenconsidering
respondingtoanradiusof54.3
greylines.
1.2
3. Spectra of Pictoris b obtained by fitting forward BT-Settle
11.7 µm obtained in 2015 (bottom). In both images, the disk has rotated, Fig.
et‹&›ﬁóïGü3¢£®©3wxP!""+Õﬂ‡·W&
data,tored
for 2004,
2015, and(color-coded2019 a instellar
modelsdata squares
obtained withseveral instruments
the distance of 19.63 pc (Gaia Collaboration et al. 2021)
respectively, 33 and 34 with respect to the north.for 2003 and 2010(20
+2.0&&&&‚¨B„‰SwÂÊÁ3ËShÈÍÎÏAÌÍÎÂSwÓÔ3gÒÈdata). This outward
motiontheflux
projected
distance
is likely
to by insteadlegend).
The ofupper
limit of the
NEAR data
is marked
a green of 19.28 pc, the orbital radius changes to 54.7
sioau, accos(✓0 ) =

x0
,
a

(7)

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

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

5.3. Temporal evolution of C1’s projected distance

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

t.

r

1
GM⇤ CCCC
C.
a3 A

(8)

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

13

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

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

Lunar Impactors(d>20 km)

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

15

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

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

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

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

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

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

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

Accepted XXX. Received YYY; in original form ZZZABSTRACT

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

16

]#.Á"'Á÷ÿ."–<|}~RU^

Dec.J2000( 0 00 )arXiv:2303.162

2000
B)

streamer. The lack of a velocity gradien
Accepted XXX. Received YYY;
inoriginal
form
ZZZ⇤ occurs
may indicate
that
the
gas
motionSourceR.A.
Ellipse size
Position angle
Peak
I
M
J2000
1.3 mmdust
B)(⌘ <4 M(00 ⇥ 00 )( ) et al. 2020).
(mJy)(mJy/beam) (10)± 0.0013
7 ± 0.0013–24.24.30.934 ± 0.017
0.49 (±0.01) ⇥ 0.33 (±0.01)
74 ± 20158 ± 14A1+A2
71 ± 16:26:26.39074
1.6±0.8
N
X
ABSTRACT
3 ± 0.0001 W –24.24.30.787 ± 0.002
0.32 (±0.04)⇥ 0.16 (±0.03)
43 ± 5121 ± 2 B
80 ± 16:26:26.30631
1.2±0.6± 0.0001
1√YZ[Z2 ± 0.0002 –24:24:29.669 ± 0.005 0.71 (±0.01)⇥ 0.12 (±0.02)
0.8
59 ± 1 stars± 16:26:25.6312
0.3 in multiple
0.6±0.3
W 23.7± 0.0002
Morethan 50%10.0of± solar-mass
form
sys
4

S. Mercimek et al.

4 DISCUSSION: ON THE ORIGIN+
star and planet formation processes at the protostellar ss, ellipse size, position angle, integrated and peak intensity of the continuum emissionTheat 1.3FAUST
mm towards
sources
A1+A2,
B,
and
W.
Table
1.
Peak
coordinates,
ellipsesiz
ALMA
observationsofth1623-2417
protostellar
systemat50
auangularresolutios derived from the integrated intensity assuming a dust temperature of 20 50 K.
(⇤ ) The dust mass, Mdust , is derived fr
reveal
for
the
first
time
the
gas
kinemaprobes the disks of VLA 1623A, B, andXf?9ì4û%W, and the circu
component, VLA
1623W.
Specifically,
AL\B<>)*,(#")◊.oØ%
firstof VLA 1623W.
!L!L time, the gas in the disk-envelopeof the gas in the disk is contaminatedbythea contour indicates the 25f level of the CS(5–the following(i)streamers
the
molec
et emission
al. structures:2018).from
The magenta
contour
i
3
"
⇠
6
⇥
10
M
.
, andonthe
mass
disk
largerscalesof1623W
inits
Fig.disk,
2 withandpanels
a)
and
b)
of
Fig.
4.
n the velocity interval 3.4 – 4.2 km1√YZ[Zs 1 , which Mmapped
4)
emission
integrated
on
the
veloc
Keplerianmotionon
50!v
In the channel connecting
maps at high velocities,
instead,the outflow
peaks
of walls
the
ity walls associated with VLA 1623A (from kinematicallytheenvelope
andcavitiprobestheoutflow
cavityatheprotostellar
mass
(M
⇠
0.45
.45
45
M
3H=
18
18 O emi
blue- and red-shifted emission are locatedalong
the2022).
disk majoraxis,
C O emission probes the circumbinary disk
Ohashi
et
al.
The
C
of
the
streamers,
as
well
as
the
spatial(⇠1300
au)
and
ve
on
scales>auandconnectspatia1000
andtheemissionismorecompact
and
peaks
at
smallerdistancesd the A1+A2 binary
systemandtheoutflow
and the envelope around the A1+
X
sidesrespectof theedge-on
disk
of
VLA
162
formedin different
cores,
interacting
between
forA+B
increasing
velocities
with
to
V
fied through CS (5–4) emission (Ohashi et al. and(W)
asexpectedinasys
cavity 3walls first identified throug
Keplerianrotating
disk.
o traces a bright elongated structure south of system18"disk ⇠In
6⇥10
M
)
with
the
envelope
duringits
formation.
thelattercase,
thestreame2022).
C
O
(2–1)
also
tracesab
18Moreover, C O shows emission towards the
The previous molecularand
lineB.
study towards
VLA
1623W
(Murillothecircumbinary
disk.
Moreover,onto
VLA
1623W,
thus
concurring
to
set
its
final
mass
a
18
nuum, as well as an elongated structure to the
et al. 2013) showed only C O(2–1) VLA
blueshifted
emission
towards
1623W diskhave
continuum,
as w
Molecular
streamersbeenobs
1√YZ[Z!vthe
of W, roughly along
disk position angle.
the northern disk side, plausibly due to lower sensitivity. Indeed, weNorth
and tothecomponents
Southof W,molroug
Keywords:
ISM:
kinematics
anddynamics
–
ISM:
tems,
e.g.,
betweentheof
n cannot be due to a jet or an outflow as it isfind that the blue-shifted disk side is brighter than the red-shifted 17+

4

S. Mercimek et al.

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

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

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

A] 20 Apr 2023

2

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

The distance to the Serpens South cluster from H O masers

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

April 24, 2023
1

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

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

9&
:&
P&
;&
r&
{&
f&
T&
h&
[

motion is shown as a black arrow in Fig. C.3 and has values ofµ↵ cos = 0.83 and µ = 5.18 mas yr 1 .
To obtain proper motions of sources in the rest frame of
the molecular cloud complex, we had to remove the expected
proper motion from Galactic rotation. We used a rotation velocity for the LSR of ⇥0 = 239 km s 1 , a distance to the Galactic
center of R0 = 8.3 kpc (Brunthaler et al. 2011), and a Solar motion of U0 = 11.10 km s 1 , V0 = 12.24 km s 1 , and
W0 = 7.25 km s 1 (Schönrich2010).
Theinresulting
Fig. 2: Spatial distributionetof theal.
water maser
spots. The numbers
the corners indicate thestellar
velocity channel in km s . The symbols
are color-coded by epoch (see the figure legend). The spots used for the astrometric fits are filled with crosses (see Sect. 3.2).
motions from this subtraction are shown in Fig. 4. We note thatin this figure sources in the 1_Ù√ê<0∏b_4`-!T<f%west of Serpens South have propermotions mostly pointing
towardthewhereasin the velocity channel in km s . The symbols
Fig. 2: Spatial
distributionof the south,
water maser spots.
The numberssourcesin the corners indicate
MNOPabUcd%v\û%efC}Ucd%Í\RglH<4û%
color-coded by epoch (see the figure legend). The spots used for the astrometric fits are filled with crosses (see Sect. 3.2).
the east of W40 have areRAproper motions mostly pointing towardhi§7Hb_<°the west. This may result from an interaction
between W40 and
Serpens South. The proper motions of stars in W40 have mag1
nitudes ⇡ 2 mas yr , which correspond to tangential velocitiesj<ÔÂ8klçKKKKKKC!lH@7ì=%⇡ 4 km s 1 for a distanceof 440.7
pc.spots detected in the velocity range V = 9.76 to 10.81 km s . (a) Measured absolute spot]#)#Rm$<á<MNOPoØnoHp“@qrWNCst∏uZvZ01R%
Fig. 3: Astrometricfits to water maser
positions, shown as blue squares. The dashed black line is the fitted model. Expected positions from the best-fit model are shown as
noHp“CwxÜTä%y%!,$8%!ä<z{|8p“}Cn2lHä
black
dots.
(b)
Measured
positionsandbest-fit
model
after
propermotionsareremoved.
(c)
Residualsoftheastrometric
fit
in
RA
Shimoikura et al.(top panel)(2019)
suggest that an outer expanding
and Decl. (bottom panel).
shell created by the W40 HII region is interacting with the dense Fig. 4: Spatial distribution of Gaia sources (green star symbols)
et al. 2022) associated with CARMA–6. We note that the directhe Serpens
South and W40 regions. The arrows indicate theirtion of the maserandproper motion
is close to in
perpendicular
to thegas associated with Figure
theC.3Serpens
South
young
cluster,thatshows the proper motions of the maser source and large-scale molecular outflow, which is oriented in the southeastdirection (see Fig. 3 in Ortiz-Leónet al. 2021).
the Gaia sources.(a)The Gaia sources have a mean value of northwest
propermotions. The red star and red arrow mark the location of(b)(c) This
this interaction induced
star
formationinthecluster(seealso(µ cos , µ ) = (0.37, 6.06) mas yr , with a mean error suggests that the masers are most likely associated with a diskof 0.2 mas yr . We also show proper motions of five radio con- wind. We will investigate this in a forthcoming paper.
thekmwatermaser
associatedwith CARMA–6 and the proper moFig. 3:sources
Astrometricfits to by
water
maser
detected
range V=9.76 to 10.81
s . (a) Measured
absolute
spot
Nakamura et al. 2017).
Shimoikuraetal.
(2019)
estimateantinuumin W40 derived
Ortiz-León
etspotsal. (2018).
The in the velocity
positions,as bluesquares.
The
dashedblackofline isOn
thethefitted
model.
positionsfromarethelarger
best-fit model are shown asother hand,the Expectedmotions of mostGaia sourcesmasersource shown
has a propermotiondifferent
fromthe motion
1tion
the astrometricfits. The cyan arrows indicate propertheGaiasources
locatedin theofwestof⇠3
the Serpens
Southsregion.
inmagnitude
thantheexpected
proper motion
due tofrom
Galactic
black
dots.
(b)
Measured
positionsandbest-fit
model
after
properis
motions
are removed.
(c)Residualsof the astrometric
fit in RA.
Thissimilarexpansion velocity for
the
shell
km
This
expectedsince
the maser
emissionarises from gas that rotation (see, e.g., Dzib et al. 2017) for objects at the location(topispanel)
and
Decl.
(bottom
panel).
may be moving along a jet or along a disk wind (Moscadelli of the Serpens South and W40 regions. The
expected proper of stars in W40 that have VLBA astrometric solutions
to themagnitude
the velocityof the Gaia sources in W40 motions
raged VLBA
spectraof the ofwater
maser emis1(Ortiz-León
etthatal.
2015). We subtracted the expected proper moProper2022) associated with
CARMA–6. We notethe direcd toward CARMA–6.
were4.2. obtainedin- 4 that the Gaiaettional.sources(⇡ 4 km s They). However,wemotionssee byin Fig.
of the maser proper motion is close to perpendicular to thetionwhichof istheSerpens
South and W40 regions due to Galactic rotaoutflow,orientedin the southeastFigure
C.3Serpens
showsandthe propermotions ofbelong
the maser source
and large-scale molecularr the area thatcoversall detected
spots,
theirat thewesternmost
side
of
South
to
“filament
A”
the Gaia sources. The Gaia sources have a mean value of northwest direction (see Fig. 3 in Ortiz-León et al. 2021). This18
1, µ ) = (0.37,
tion
from
the propersuggeststhat the masers
are most
likely associatedwith a diskmotions shown here. The background shows
cosdashed
6.06)
mas Shimoikura
yr , with a mean error
ndicated in thelegends.
line
atof
tracedby C TheO atvertical
6 km(µ
s
(see
Fig.
12
et
al.
2019),
of 0.2 mas yr . We also show proper motions of five radio con- wind. We will investigate this in a forthcoming paper.
1
the H2 column density map obtained with Herschel (André et al.
sourcesinFig.
W40 derivedbyOrtiz-León et al.that(2018). thisThemarks thevelocity
oftinuum
thetheircloud.
andsystemic
the model
shown
in
18
suggests
filament
19
maser source has a proper motion different from the motion of
On the other hand, the motions of most Gaia sources are larger
1

1

(a)

(b)

(c)

1

LSR

4.2. Proper motions

1

↵

1

LSR

Article number, page 4 of 13

↵

1

1

1

short title: Protostellar Outflows

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

Abstract

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

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

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

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

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

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

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

Worcester State University
486 Chandler St.

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

20

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

the mass evolution of the protostar, the infalling envelope, and the outflow mass. Section 2.3
calculates :() by numerical solution of the equation of motion of an infalling shell. Section 2.4

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

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

特にコア散逸過程の物理が不明

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

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

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

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

2.1. Protostellar Mass Accretion Rate

which are negligibly small compared to the core scale.

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

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

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

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

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

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

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

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

⨀

⨀

8

8

K

K

なっているのか？

7

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

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

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

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

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

緩和時間を恣意的に与えて、モデル結果を

paraboloidal cavity.

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

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

2

1

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

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

stro-ph.GA] 24 Apr 2023

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

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

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