星形成ゼミ
2021/04/30
SFN 338 #34-#39

長谷川哲夫

1

to determine which is younger and which is older. 25/04/2017
Sz102 and Merin28
are the mostsourcesshow signs 27.82
of havingC40-3
40evolved15– 459 and1.00
Starformation
in‘the
Brick’:
ALMA
reveals
anactiveproto-cluster
inthe
Galactic
centrecloud
338
associated flows, not as well traced by CO as for the
younger sources.
19/07/2017
C40-6
40
18 – 3696
0.49
49.45

#34 G0.253+0.016

21/07/2017

C40-6

40

16 – 3696

0.81

46.42

Star formationin ‘the Brick’: ALMA reveals an active proto-cluster in the Galactic
2021 MNRAS.503…77W
centre cloud G0.253+0.016

Daniel L. Walker, Steven N. Longmore, John Bally, Adam Ginsburg, J. M. Diederik Kruijssen, Qizhou Zhang,
dust continuum
Jonathan D. Henshaw, Xing Lu, João Alves, Ashley T. Barnes, Cara Battersby, Henrik Beuther, Yanett A.
the ‘maser core
Contreras, Laura Gómez, Luis C. Ho, James M. Jackson, Jens Kauﬀmann, Elisabeth A. C. Mills, Thushara
230 GHz (Band
Pillai F G0.253+0.016, aka ’the Brick’, is one of the most massive (> 105 Msun) and dense (> 104 cm 3 ) molecular clouds
2016.1.00949.S (Pin the Milky Way’s Central Molecular Zone. Previous observations have detected tentative signs of active star formation, mostas a single point
notably a water maser that is associated with a dust continuum source. We present ALMA Band 6 observations with an
see Figure 1), usi
angular resolution of 0.13" (1000 AU) towards this ’maser
core’,
and report
evidence of active star formation
Star
formationin ‘the unambiguous
Brick’ 3
tor was configure
within G0.253+0.016. We detect a population of eighteen continuum sources (median mass 2 Msun), nine of which are driving
specific m
Table 1. Details of the three observed execution blocks. Listed are the observation dates, nominal array configurations, number of 12 m
bi-polarmolecular outflows as seen via SiO (5-4) emission. At the location of the water maser, we find evidence fortargeteda protostellar
antennas in the array, full range of antenna baseline lengths, atmospheric precipitable water vapour content (PWV), total time on source,with a spectral rebinary/multiple
withmulti-directional
and the bandpass, flux, andphasecalibrators used for each outflow
observation. emission. Despite the high density of G0.253+0.016, we find no evidence forspectral windows
high-mass protostars in our ALMA field. The observed sources are instead consistent with a cluster of low-to-intermediateDate
Array
Antennas
Baselines
PWVTime on source
Bandpass
Flux
Phase
detection in the umass protostars.
However, #the measured
outflow(minutes)
propertiescalibrator
are consistent
those expected for intermediate-to-high-mass(d/m/y)configuration(m)(mm)
calibrator withcalibratorof ⇠ 2.5 km
s 1.
star formation.
We conclude
are27.82
young and
rapidlyTitan
accreting,and may potentially form intermediateand
25/04/2017
C40-3
40 that
15 –the459 sources
1.00
J1924-2914
J1744-3116
5.6 GHz
19/07/2017
C40-6
40 The18 –masses
3696
0.49
49.45
J1924-2914
J1733-1304 of
J1744-3116
high-mass
stars inthe future.
and projected
spatialdistribution
the cores are generally consistentimately
with thermal
21/07/2017
C40-6
40
16 – 3696
0.81
46.42
J1924-2914
J1733-1304
J1744-3116
vidualfragmentation, suggesting that the large-scale turbulence and strong magnetic field in the cloud do not dominate ontheseexecution
scales,executionused 40and that star formation on the scale of individual protostars is similar to that in Galactic disc environments.
– 3696 m. Full dedust continuum and molecular line observations towards
the ‘maser core’ in G0.253+0.016 with ALMA at ⇠tral setup are giv
GHz (Band
6, 1.3 mm) as partwithof the Cycle
4 project
The Milky Way Project: Probing230
Star
Formation
First
Results on Yellowballs from2016.1.00949.S (PI: D. Walker). The observations were taken
DR2
as a single pointing centred on the source (G0.261+0.016,

see Figure1), using
only the main
12 m array.Johanna
The correla- Mori, Leonardo Trujillo,
Grace Wolf-Chase, C. R. Kerton, Kathryn
Devine,Anupa
Pouydal,
Aurora2.1 Imaging
tor was configured to target 7 spectral windows, 5 of which
Cossairt, Sarah Schoultz, Tharindu Jayasinghe,
Matthew Povich F Yellowballs (YBs) were first discovered during
targeted specific molecular transitions in the lower sideband
The ALMA
the Milky Way Project citizen-science initiative(MWP;
Simpsonal.
2012).
MWP
users
noticedcompact, yellow
regions pipel
in
with
a
spectralresolution ofet
⇠ 0.77
km
s 1of
. The
remaining
2
Figure 1. Three-colour
image
G0.253+0.016.
Red: ALMA
spectral windows were dedicated to broad-band continuum
block
were
comb
Spitzer Space Telescope mid-infrared (MIR) images
the Milky
Way plane
and asked
to explain these3 mm ofdust
continuum(Rathborne
et professionalal. 2014b), astronomers
Green:
detection in the upper sideband, with a spectral resolution
were then
image
1
8 µm
emission(Churchwell
et al.
2009), Blue:"yellow balls." Follow-up work by Kerton etSpitzer/GLIMPSE
al.
that bandwidth
YBs
likelytrace
compact
photo-dissociation
regionsof ⇠(2015)
2.5 km s determined. The total
aggregate
is approximately
GHz. Thedust
project
wasobserved
across(Battersby
3asindito offinal
Herschel/HiGAL
columndensity
et al. 2011;
associated with massive and intermediate-massstar 5.6
formation.
YBs
were
includedtarget objects
in a version
the imaging,Milkyvidual execution blocks between April and July 2017. Eachet whichal. 2016).
The whitecrosses
indicatethepositionswindow,and ran
Way Project launched in 2016 (Jayasinghe etMolinarial.
2016),
producedalisting
of
over
6000
YB
locations.
We
havemeasured
execution used 40 antennas, with baselines ranging from 15
of
known
water
masers(Luetal.
2019b).
The
white
circlecorre– 3696 m. Fulldetails
concerning
spec- a pilot region coveringCASA
distances, cross-match associations, physical properties,
andMIR
colorstheofobservations
500 YBsandwithin
the l= in
30 pipelin- 40tral setup
are
given
in Tablesbeam
1 & 2, field
respectively.
spondstotheprimary
of
view
of
the
ALMA
observachannels
in
each
degrees, b= +/- 1 degree region of the Galactic plane. We find 20-30high-mass star formation capable of becoming expandingtionreportedinthispaper.
2
tinuumwas then
H II regions that produce MIR bubbles. A majority of YBs represent intermediate-mass star-forming regions whoseplacement
2.1 Imaging
and spein evolutionary diagrams suggest they are still actively accreting, and may be precursors to optically-revealed windows
Herbig Ae/Befragmentation, suggesting that the large-scale turbulence and strong magnetic field in the cloud do not dominate on these scales,
and thatThestar Milkyformationon thescale ofindividual
protostars
is similar
thatResultsin Galactic
environments.
Way
Project:
ProbingStar
Formation
withtoFirston disc
Yellowballs
from DR2338#352021 ApJ…911…28W

The Milky Way Project: Probing Star Formation with First Results on Yellowballs from
DR2

Grace Wolf-Chase, C. R. Kerton, Kathryn Devine, Anupa Pouydal, Johanna Mori, Leonardo Trujillo, Aurora
Cossairt, Sarah Schoultz, Tharindu Jayasinghe, Matthew Povich F Yellowballs (YBs) were first discovered during
the Milky Way Project citizen-science initiative (MWP; Simpson et al. 2012). MWP users noticed compact, yellow regions inSpitzer Space Telescope mid-infrared (MIR) images of the Milky Way plane and asked professional astronomers to explain these"yellow balls." Follow-up work by Kerton et al. (2015) determined that YBs likely trace compact photo-dissociation regions
associated with massive and intermediate-mass star formation. YBs were included as target objects in a version of the Milky
Way Project launched in 2016 (Jayasinghe et al. 2016), which produced a listing of over 6000 YB locations. We have measured
distances, cross-match associations, physical properties, and MIR colors of 500 YBs within a pilot region covering the l= 30 - 40
degrees, b= +/- 1 degree region of the Galactic plane. We find 20-30high-mass star formation capable of becoming expanding
H II regions that produce MIR bubbles. A majority of YBs represent intermediate-mass star-forming regions whose placementin evolutionary diagrams suggest they are still actively accreting, and may be precursors to optically-revealed Herbig Ae/Be
nebulae. Many of these intermediate-mass YBs were missed by surveys of massive star-formation tracers and thus this catalog
provides information for many new sites of star formation. Future work will expand this pilot region analysis to the entire YB
catalog.

12

6

The Astrophysical Journal, 799:153 (9pp), 2015 February 1

Kerton et al.

Figure 4. MWP GLIMPSE/MIPSGAL images, 4.5 µm (blue), 8 µm (green), and 24 µm (red), showing yellowballs with (in white) and without (in yellow) RMS
counterparts. The top panel shows part of W 33, with a cluster of yellowballs located between two large bubbles. The lower panel shows two isolated yellowballs andtwo yellowballs associated with a larger H ii region (see the text for details). The Galactic coordinates of the image center and the angular size of the image are shownat the top of each frame.

8Figure 1. YB spatial distribution. Heliocentric distances and Galactic longitudes are plotted for all 493 YBs in the pilot region
with CO associations (diamonds). The average statistical uncertainty in the distance is ⇠ 0.5 kpc. Lines show the spiral arm
traces along this line of sight from Reid et al. (2016): Per = Perseus, SgN and SgF = Sagittarius near and far sections, ScN and
ScF = Scutum near and far sections, AqR = the local Aquila Rift feature, and AqS = the Aquila spur between SgN and ScN.
12

Wolf-Chase et al.

First Results on Yellowballs from DR2

13

The Hi-GAL compact-source catalog provided additional information about the near/far association for a subset of
our YB sample. The Hi-GAL distances were assigned by extracting 12 CO or 13 CO spectra along the line-of-sight toevery Hi-GAL source to determine the VLSR , and subsequently employing the Galactic rotation model of Brand &Blitz (1993). In the Hi-GAL catalog, three types of flags are used to indicate the quality of the solution to the near/far
distance ambiguity (EMS17). An entry of ‘G’ indicates the ambiguity was solved by matching the source position witha catalog of sources with known distances (e.g., H II regions, masers, etc.) or with features in extinction maps. If noneof these was available, the ambiguity was arbitrarily solved in favor of the far distance and a bad-quality (‘B’) flag was
assigned. If a distance estimate was unavailable, a null value (‘N’) was assigned. When a YB was associated with a
Hi-GAL source that had a ‘G’ designation, we assigned this Hi-GAL near/far association to the YB while using theBayesian distance calculator. For example, if a Hi-GAL source had near distance then we would set Pfar = 0. For twoof the sources (YB 1166 and 1204) the Bayesian distance calculator and the Hi-GAL near/far solution would not agree
due to details of the Galactic model, and we adopted the Pfar = 0.5 Bayesian distance. For sources that had a ‘B’ ornull flag we used the Pfar = 0.5 Bayesian distance. The distribution of our sources in the Galactic plane is shown in
Figure 1. As expected, there are noticeable source groupings along the spiral arm tracers (e.g., the SgN arm at ⇠2kpc), consistent with the weighting that the Reid et al. (2016) technique gives to the underlying spiral arm structure
model.
The assigned distances to YBs with Hi-GAL associations are provided in column 4 of Table 4; for comparison, thekinematic distances reported in the Hi-GAL compact-source catalog are also given in column 6. Variations between
our distances and those presented in EMS17 can be attributed to the fact that: 1) the Bayesian model used additional
information beyond a kinematic model to calculate distances, and 2) if EMS17 could not resolve the near/far ambiguity,
they assumed the far distance, whereas the Reid et al. (2016) distance calculator uses a Bayesian approach to resolve
the ambiguity.

Figure 3. As Figure 2. All quantities plotted are distance independent.
Figure 2. Physical properties of the YB–Hi-GAL matched sources. The lower-left and upper row histograms show physicalproperties from the EMS17 catalog rescaled using our newly calculated distances. For reference, main-sequence OB star lumiWe note that while the photometry was repeated six times per source, only one set of background-subtracted images
nosities (Crowther 2005) are indicated in the upper-right panel. The lower-right histogram displays the distance-independent
was used for the fitting. To see how well-fit the YB-only images were by a 2D Gaussian, we created a residual of
luminosity-mass ratio also from EMS17. See text for full discussion.

2D-Gaussian fit subtracted from the YB-only image, which we refer to as the “residual image” in the rest of thissection. We measured the magnitude of residuals, di↵erences in 8-µm and 24-µm peak locations, and di↵erences incorrections for extended sources. MIPS images were in units of MJy sr 1 so conversion to flux density involved only

9

16

Wolf-Chase et al.

First Results on Yellowballs from DR2

17

Figure 5. Radar-plot visualizations for five distance-independent quantities for di↵erent classes of objects. Values plotted are
medians, and the maxima are indicated for each radial line. Di↵erent classes are connected via di↵erent colored pentagons.
Left: Protostellar clumps and H II regions identified in the Hi-GAL survey (EMS17) are compared with YB–Hi-Gal matcheslacking counterparts in other surveys. Right: Four YB–Hi-GAL subsets are compared. The RMS and WISE-K subsets arealmost entirely high-mass star-forming regions, while the WISE-Q and YB–Hi-GAL only subsets are a mix of intermediate-mass
regions and young high-mass regions.

extend the KWA15 analysis to the larger DR2 sample and examine YB colors using additional IR wavelengths. The
histogram of the log(F12 /F8 ) results for DR2, similar to that shown in KWA15, is shown in Figure 6.
KWA15 found that the average value of their sample (-0.19) was more negative than the average color sample of
WISE H II regions (-0.09) (Anderson et al. 2012) and that the YBs in their sample without RMS counterparts had aneven more negative average of -0.23. The colors of our new YB sample yields an even more negative mean log(F12 /F8 )value of 0.43 ± 0.15. Size measurements (based on MWP user radii) confirm that our new YB sample indeed contains
a larger number of very compact sources. Whereas the mean (± standard deviation) diameter of the RMS-matched
YBs with distances from KWA15 is 0.94 pc ± 0.71 pc, the mean diameter of all YBs with good distance estimatesin our current sample is 0.75 pc ± 0.53 pc. The median diameters are smaller (0.77 pc and 0.63 pc, respectively),as relatively few YBs are significantly larger than 1 pc. The mean diameter of the subset of YBs with counterpartsin catalogs of H II regions and MYSOs (CORNISH, RMS, WISE-C,G,K) is 0.96 pc ± 0.62 pc and the mean (±standard deviation) log(F12/F8) color of these objects is -0.28 ± 0.31; however, the mean diameter of YBs lacking
such counterparts is 0.65 ± 0.45 pc and the mean log(F12/F8) color of this subset is -0.47 ± 0.24. Many compact YBs
were missed in the KWA15 sample, which was drawn from images at lower zoom levels, where citizen scientists would
have been more likely to notice large and bright YBs. Additionally, only YBs with RMS counterparts had associateddistances in the KWA15 sample; our current sample indicates that YBs with counterparts in catalogs of H II regions
and MYSOs are biased to physically larger objects.
In addition to measurements at 8 and 12 µm, we use longer MIR wavelengths at 24 and 70 µm to examine the
YB population in our DR2 sample. We show a MIR color-color plot in Figure 7 for the 219 YBs in our pilot region
with reliable 8-µm and 24-µm photometry as well as counterparts in the Hi-GAL survey (EMS17). The color-color
plot indicates sources with cross-matches in the RMS and WISE catalogs. The average H II region colors and H II
region - PNe cut-o↵ colors established by Anderson et al. (2012) are also indicated in Figure 7. WISE sources wereseparated into categories by Anderson et al. (2014): “K” for known, “G” for group, “C” for candidate, “Q” for radio
quiet. YBs with counterparts in the RMS catalog and/or WISE K, G, and C sources are, unsurprisingly, grouped
near the expected colors for H II regions. We find a significant number of sources with WISE Q (n = 44) or no

Figure 4. Bolometric Luminosity – Clump Mass plots for various subsets of the YB–Hi-Gal Sources. Red lines show Molinari
et al. (2008) clump evolutionary tracks. Small squares, along the vertical portion of each track, correspond to 5 ⇥ 104 year
intervals, and isochrones are the red short dashed lines. The blue upper diagonal line represents a 90th percentile lower limit for
Herschel -defined H II regions, and the blue lower diagonal line is a 90th percentile upper limit for the pre-stellar objects in the
EMS17 sample of Hi-GAL clumps(see text for details). For sources with good SED fits (black), mass and luminosity error bars
are shown (most are smaller than the symbol used). Sources with poor SED fits (grey) do not have error bars shown for mass.

10

338 Formation and evolution of protostellar accretion discs. I. Angular-momentum budget, gravitational#36 self-regulation, and numerical convergence2021 MNRAS.502.4911X
Formationand evolution of protostellar accretion discs. I. Angular-momentum budget,
gravitational self-regulation, and numerical convergence

Wenrui Xu, Matthew W. Kunz F We investigate the formation and early evolution of a protostellar disc from a magnetizedpre-stellar core using non-ideal magnetohydrodynamic (MHD) simulations including ambipolar diﬀusion and Ohmic dissipation.
The dynamical contraction of the pre-stellar core ultimately leads to the formation of a first hydrostatic core, after ambipolar
diﬀusion decouples the magnetic field from the predominantly neutral gas. The hydrostatic core accumulates angular momentum
from the infalling material, evolving into a rotationally supported torus; this ‘first hydrostatic torus’ then forms an accreting
protostar and a rotationally supported disc. The disc spreads out by gravitational instability, reaching ⇠30 au in diameter at⇠3 kyr after protostar formation. The total mass and angular momentum of the protostar-disc system are determined mainly
by accretion of gas from an infalling pseudo-disc, which has low specific angular momentum because of magnetic braking; theirremoval from the protostar-disc system by outflow and disc magnetic braking are negligible, in part because the magnetic field
is poorly coupled there. The redistribution of angular momentum within the protostar-disc system is facilitated mainly bygravitational instability; this allows formation of relatively large discs even when the specific angular momentum of infallingmaterial is low. We argue that such discs should remain marginally unstable as they grow (with Toomre Q ⇠ 1-2), an ideathat is broadly consistent with recent observational estimates for Class 0/I discs. We discuss the numerical convergence of ourresults, and show that properly treating the inner boundary condition is crucial for achieving convergence at an acceptablecomputational cost.

The
ALMA
Chemistry
Survey (PEACHES).
I. The Complex Organic Molecules
志：以下の３点に集中ClassPerseus
0/I phase— How
do protostellar
inPerseusdiscs
Embeddedaccretion
form andProtostars
grow?

Yao-Lun Yang, Nami Sakai, Yichen Zhang, Nadia M. Murillo, Ziwei E. Zhang, Aya E. Higuchi, Shaoshan
1. Simulationとして：prestellar
classCeccarelli,
0/I まで連 Tomoya
Zeng, Ana López-Sepulcre, Satoshi Yamamoto, Bertrand
Lefloch, Mathilde Bouvier,から
Cecilia• 重要なプロセスが全部入ったシミュレー
Hirota,Muneaki Imai, Yoko Oya, Takeshi Sakai, Yoshimasa
Watanabe F To date, about two dozen low-mass
続的に計算、広いパラメタ空間を探索
embedded
protostars
exhibitrich
spectrawithcomplexorganic
molecule(COM) lines. These protostars seem to possess
ションはまだない2.
Physicsとして：計算結果の解析から重要な物理
diﬀerent enrichment in COMs. However, the statistics of COM abundance in low-mass protostars are limited by the scarcity of• Diskの特徴を決定する主要なメカニズムがobservations.
This study introduces the Perseus ALMA Chemistry
Survey (PEACHES), which aims at unbiasedly characterizing
プロセス（含む相互作用）を突き止める
the chemistryofCOMs
towardtheembedded(Class0/I)
protostars
in the Perseus molecular cloud. Among the 50 embedded
何か、まだ完全には理解できていない
3.
Modelingとして：semi-analiticalあるいはsub-grid
protostars surveyed, 58protostars have CH3 OH, CH3 OCHO, and N-bearing COMs, respectively. The detectability of COMs
• Pre-stellar
coreの初期条件とprotostellar
depends
on neither
the averaged continuum brightness temperature,a proxy of the H2 column density, nor the bolometricmodel setを追求し、重くない計算からでも正し
luminosity
andthebolometrictemperature.
Fortheprotostars
withdetected COMs, CH3 OH has a tight correlation withaccretion diskとをつなげられない
11
CH3 CN, spanning more than two orders of magnitude in columnい結論を得られるようにする
densities normalized by the continuum brightness temperature,suggesting a chemical relation between CH3 OH and CH3 CN and large chemical diversity among the PEACHES samples at the6

W. Xu and M. W. Kunz
t=1024.46 kyr
M10 = 0.00001 M

z [au]

1000

t=1025.55 kyr
M10 = 0.0001 M

1000

t=1025.93 kyr
M10 = 0.001 M

1000

800

800

800

600

600

600

400

400

400

200

200

200

Pre-stellar flattening
and collapse
14

0
0

500

750

1000

t=1026.15 kyr
M10 = 0.01 M

20

z [au]

250

250

500

750

1000

t=1026.31 kyr
M10 = 0.02 M

20

0

15

15

10

10

10

250

500

750

1000

t=1026.64 kyr
M10 = 0.04 M

20

15

12

10

8
5

5

0

5

0
0

5

10

15

20

t=1027.00 kyr
M10 = 0.06 M

20

z [au]

0
0

5

10

15

20

t=1027.41 kyr
M10 = 0.08 M

20

0

15

15

10

10

10

5

5

5

0

0
0

5

10

x [au]

15

20

5

10

15

20

t=1027.84 kyr
M10 = 0.1 M

20

15

The first hydrostatic
core/torus

600log10 (nn [cm 3 ])0

4Gravitational instability
and disk spreading

0
0

5

10

x [au]

15

20

0

5

10

15

20

x [au]

Figure 1. Azimuthally averaged profiles at di↵erent epochs from our fiducial 3D simulation. The total mass enclosed within 10 au (including
the accretor mass), M10 , is provided for reference. Each panel displays the density (colour), magnetic-field lines (black streamlines), andvelocity (white quivers). Each row captures a di↵erent phase of evolution; from top to bottom: the flattening of the pre-stellar core
along magnetic-field lines and the advection-di↵usion of the magnetic field into an hourglass shape, the formation of the first hydrostatic
core/torus on ⇠au scales, and the spreading of the rotationally supported disc through gravitational instability.

⇡0.2 G, a value similar to that found in previous calculations

braking because of its high column density and weak coupling

12B [G]

midplane v [km s 1 ][g cm 2 ]midplane nn [cm 3 ]ore(Jijina
et al.in 1999).
backgroundlAppendix
centraldensityn0 = The
10 A.
cm
and dendetailed
Appendix
3 A.
orgravitational
potential
in
order
to
avoid
behavior
4 unphysical
500
cm,
attainedintheinitialstate
at10radiiWechooseaninitialcentraldensityn=
cm 3 andze r0 = 0.1 pc, representative of a0 typat
large
r
(see
AppendixA).
Adopting
a
mean
mass
us
c, provides
a numericalthatcharacteristic
coreThesize rfloor= 0.1
pc, physically
representativeof a typ- per neu0backgroundnaetal.Initial
1999).
den- rep2.1
conditions
tralofparticlemn =molecular
2.33m
for molecularhydroical
NH(Jijinaetal. 1999).
backgrounddenp (accountingcal
3 coredensitytheambient
gasThesurrounding
3
2.1
Initialconditions, attained
intheinitial
state
at
radii
3
Pre-stellar
flattening
The first hydrostatic Gravitational instability
conditions
sity
n
=
500
cm
,
attainedintheinitial
state
at
radii
1
gen
with
20%
He
by
number),the
total
self-gravitating
mass
is gasWeis excluded
fromthe calculation
ofinitial
the selferemploy
thesamephysicalconditions
for
all
simes
a
numerical
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that
physically
repr
0.436
pc,
providesanumerical
floor
that
physically
repicalinitialconditions
allsim- M behavior
enclosed
withinr0 avoid
isfor
then
'1.43
.initial
The andinitialtemperature
potential
inorder tounphysicalWethe
employthesamephysicalconditions
for all simn)thecollapsecore/torus
and diskandspreadingyalsamephysicalinitialconditions
forsurroundingall
simProtostellar disc formation
evolution 7
resents
densityoftheambient
moleculargasulations.
The
pre-stellar
core
isinitially
spherical,
with thefeetheambient
moleculargassurroundingore
isinitially
spherical,
with
the
of
the
gas
is
set
to
T
=
10
K,
givingan
initialisothermal
0a mean core
AppendixA).
Adopting
mass
perneuulations.
The
pre-stellar
isinitially
spherical,
with
the
in
the
core;
this
gas
is
excludedfromthecalculationoftheselfThepre-stellar
core
isinitially
spherical,withthenumberdensityneutrals
given
by
初期条件
xcluded
from
the
of
the
sound
speed
cs0calculation
⌘of
(kof
)1/2
'self0.188
s 1.
given
BT
0 /m
navoidebmngravitational
= by
2.33m
(accountingforhydrop potential
inorder
tomolecularunphysicalbehavior
numberdensityneutrals
given
by km
nsity
of
neutrals
given
by
1015
1015
1015
⇢
The
is threaded
by aninitially
vertical magal
inat
order
to
unphysicalbehavior
4
W.
Xu
M.
W.
large
r core(seeavoid
AppendixA).
Adopting
a Kunzmean uniform,
mass
per neu% He
bynumber),theandtotal
self-gravitatingmass⇢n1024.46kyr
1026.15kyr1027.00 kyr
0⇢ nnetic
nmass
13
13
13
particle
mwith
2.33m
(accounting
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ed density
ral
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=
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ical
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101
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103 dust
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ained
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104
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byaninitially
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0.436
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/r
'
1.22
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.
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thatphysically
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0.436
providesanumerical
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physicallyrep)(63G)(Mouschovias&
Spitzer1976).
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1/2
lapse,(Mouschovias& Spitzer1976).
3 The
3
3pc, providesanumerical
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that
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25the
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mbientmolecular
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e
ratio
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magof
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1010
m-1.27r
'
.the
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gas
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ed
from
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ofissupercriticaltheself- from the calculationsc
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We usea spherical-polar grid withan outer radial boundhis
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Goodman1998).
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the
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afor
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r
,
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, the
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10
10
101
0rder
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in order 14
to avoid1 unphysical behavior
togravitational
avoid unphysicalbehavior
18
/2
ary
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)
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10angularvelocity⌦0&= Spitzer
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/r
1.22
⇥ 10
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sa mean.domainThis massangularmomentum
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order
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0'
s0
0 '
ocity
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= large
0.2c
1.22
⇥
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s .of
This
(Mouschovias
1976).
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0mean
at
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AppendixA).
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per
r/r
(see
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a10
mass
perneuneu100
100). Adopting
arto
mean
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per
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betweenrotationalandthermalenergydial boundary
at rin2 = 1 3 au. The
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can
be
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seeA).atAdoptingmean
perneutomass-to-flux
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ratio
betweenrotationalandthermalenergy2.2ofstatel(accountingout
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101
102
103
100
101
10
10
100
101
10
10
n
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tral
particlem
2.33m(accountingformolecularhydron2 =forratio
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again
consistentwitha p
typicalNH3 corefor(Bar⌦(r)
=
⌦
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)
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,
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withafiducial
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per
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03 core (Baragain
consistentNHe mranco=
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gengen
with
20%
He
byTo
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with
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He
by
number),thetotal
totalself-gravitating
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101
101
er),
the
total
self-gravitatingmassFor
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simplicity
andcomputational
expediency,
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specific
angularmomentumalongradiallines.
(dr/r ⇡ 0.05). To reduce computational cost, we only simuoodman
1998).
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mass
vr
angularmomentum
in
the
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set
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is0totalthen'1.43
Mspecific.simulations
The
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. The
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'1.43
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.
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We
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passingthat
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recentofprotomodelthethermalevolutionofthesystemusing
thefollowing
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100 boundary condition at thevmentum
in
the
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part
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at
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the
angularvelocitytolate100✓ 2 [0, ⇡/2] with a reflecting
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ithin
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. 0Theinitialtemperature
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.
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the
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2 [0, ⇡]
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1/2
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10 1
10 1 we only simulate
set
to
T
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1/2
1 givingo(r/rbetweenrotationalandthermalenergy
a
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.
2sound
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specific
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m
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/m
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We
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strength
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998).
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netic
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This
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that
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102
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103 size,withstrength
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100
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5 of lapse,
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resultingin a midplane d✓ ⇡ 100.03
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1
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hasapproximately
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central
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for
colon
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10 1
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–10
)the
and
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mimickouschoviasmax |B|
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tion represents
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witha fiducial resolution of 16
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2)(63G)(Mouschovias&mass-to-flux
SpitzerThe
Non-ideal
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10 2
mentumalongradialcore
hashassupercriticalmass-to-flux
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to abreak-point
cylindricaling(athigher densities).
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outevolution
toRlines.
a hascylindrical
sc
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000,
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(2020)
cells
for
2
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⇡].
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3
3
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contrast,
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to
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10
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that
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of
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most
To
test
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4
4erdisc
For
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'
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10 4
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今回はOhmic
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on1initialdentninto
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Section6
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/r
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0
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14
1
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10
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10we vary
10 rin between
102
103
In particular,
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au
3
ar
a ratio
betweenrotationalenergyocity⌦)corresponds= 0.2c/rto
1.22⇥
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0 ands0to
cmprotostar
smallercharacteristic
size.
corresponds
a0 '
ratio
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byKunz
Mouschovias(2010,
see
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r
[au]
r
[au]
r
[au]
een
rotationalandthermalenergy
MNRAS
000,
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(2020)
and 2 au and increase the ✓ resolution by up to a factor of 4.
by
of'0.011,
again
consistentwith
typicalNH3 corecore(Bar13 (Bars to figuresa ratio
betweenrotationalandthermalenergyHall効果やdust
evolution
condition
is4a
meant
to
represent
awith
later
of
'0.011,
again
consistenta atypicaland4b),at leastup
todensities
nNH
cm 3 ,
n &3 10t witha typical
NH(Bar3 coreranco&Goodman1998).
To
avoid
excessively
highspecific
again
consistent
witha1998).
typical(Bar3 corecollapse.
By
ourinitialcondiranco& contrast,
GoodmanTo NH
avoid
excessively
highspecific
at
which
point
thehighcentraltemperature
becomes
K andaveraged quantities at di↵erent epochs from our fiducial 3D simulation. Each column plots three
Figure2.
Radialprofiles&100
of azimuthallyTo
excessively
specific
効果はfuture
workで
angularmomentumin the outerpartof our domain(wherent avoid
epochscorresponding
to a row in
Fig. 1. To facilitate comparison, earlier epochs are also plotted in later panels using thin lines. 13
oodman1998).
To
avoid
excessively
highspecific
rlier
phase
of
the
evolution,
where
most
angularmomentum
in
the
outer
part
of
our
domain(whereapproaches
7/5.
We
plan
to
refinethisEoS
forfuturework.
outer partof
ourdomain(where2.5 Boundary conditions
r/r
can
be
at
most
⇠10),
we
set
the
angularvelocity
toof0
omentumin thepartof ourdensity
domain (wherehas
uniform
canbeouter
at most0 approximately
2 ⇠10),
),Rsc
wer/r
set
the angularvelocity
towe set the angular velocity to

10

0

0
14.5

10

10
10

0

10

1027.41 kyr

10

0

0

10

10
10

10

0

10

1028.33 kyr

14.0
10

10

13.0
12.5
12.0
0

102

101

Keplerian out to 10au

11.5

10

100 0
10

101

102

r [au]
Figure 5. Rotation profile of the disc at the end of the fiducial 3D
simulation.

11.0

1028.76 kyr

10.5
0

0

10

10
10

0

10

1021

10

x [au]

010x [au]

Figure 3. Snapshots of midplane density in the fiducial 3D simulation. The first four panels correspond to the last four epochs
shown in Fig. 1. The initially axisymmetric first hydrostatic torus
develops spiral arms due to gravitational instability. These spirals
transport angular momentum outward, spreading the disc and aiding protostar accretion. The disc size oscillates as spirals emerge
and disperse.

16

protostar
disc
total

0.150
0.125

14

Rd [au]

0.100

12

1020
1019
1018

1016
1026

1028

1029

1039

pseudo-discenvelope
outflowmagnetic
gravitational
inwardoutward

1038
1037

8

1035
1026

0.025

6

質量と角運動量
1. どちらも pseudo-disk から
2. Outflow の寄与は小さい
2. はMachida&Hosokawa13や

1040

0.050

0.000

1027

1041

1036

半径 20au の球殻を通過するの inflow が支配的t [kyr]10

0.075

pseudo-discenvelope
outflow
inwardoutward1017

Lz flux [g cm2 s 2 ]“Protostar” = mass at r < 1au

M [M ]

r 3/2

13.5

1027.84 kyr

10
10

0

mass flux [g s 1 ]y [au]

10y [au]

103

1027.00 kyr[kyr 1 ]1026.64 kyrlog10 (nn [cm 3 ])y [au]

10

1027

1028

1029

Tomida+19の結論と異なる。
より現実的な磁場散逸を取り入れた結果 toroidal field が弱くなったためとしている。

t [kyr]

4
1027

1028

t [kyr]

1029

1027

1028

1029

t [kyr]Figure 4. Time evolution of protostar mass, disc mass and disc sizein the fiducial simulation.

Figure 6. Contribution to mass and angular-momentum flux
through a 20-au sphere from di↵erent mechanisms. Both mass flux
and angular-momentum flux are dominated by inflow (accretion)from the pseudo-disc.

14

protostar-disc system, which is shown in Fig. 8. We see a rel-

Toomre Q

Lz flux [g cm2 s 2 ]r [au]Lz [g cm2 s 1 ]radial force density [dyn cm 3 ]n at M10 = 0.01 M is close to the M –Lz relation of
Figure 9. Angular-momentum flux due to di↵erent mechanisms
protostar-disc system for M . 0.05 M , but the slope of
10 W. Xu and M. W. Kunz
through spherical shells
di↵erent radii,
averaged for t >andatevolution
9
protostar-disc
M –Lz relation becomes less steep at laterProtostellar disc formation
質量・角運動量はどこから来るか
角運動量の再分配
1028 kyr. The axisymmetric hydrodynamic flux (grey) corresponds, suggestingmagnetic
that magnetic
continues
to decrease
braking hasbraking
reduced angularmomentumby about1041
to advection
with the mass accretion and outflow and does not con1.5
an
order
of
magnitude.
14
lar momentum
after
protostarformation.
gravity (negative)
10
tributetotheradial transport of angularmomentum with respecthydro-axisymmetricmagnetic
We can also look at when and how
magneticbraking hapthermalpressure
1.0
is also worth
pointingout
whymagneticbrakingcanbehydro-nonaxisymmetricgravitational
to the gas. Inside the disc, the transport of angular momentum
pens. In Fig. 8 we also plot the Mmagnetic(< r)–Lz (< r) relationpressure
10 16
ortant in theis always
unimportant
inthewith0.5respect to the gas is dominated by gravitational instability,
atpseudo-disc
M10 = 0.01 M but, whichis around
the
epoch
of
protostarmagnetic tension
Protostellar disc formation
formation.
This
curve
has
a
slope
of
⇡2,
consistent
with
that
18
which produces the non-axisymmetric hydrodynamic flux (blue)
ostellar disc.
Thisismainlybecausethedensityandcolcentrifugal
100.0
a flattened core with uniform column
density and rotaall support
and gravitational stress (green).
density in oftheprotostellar disc are muchhigherthan in
Vorobyov & Basu 2007; also seetion. This suggests that the bulk of the pre-stellar core has
10 20
0.5
1994; Tomida et al. 2017).
pseudo-discundergone(for example,
Figsof 1magnetic
and 2),
which
makes
a similarsee
amountbraking.
This
is reaWe also comment that, historica
sonableof magnetic
brakingtakes place atimthe
22
magnetic 10field
lesssince
wellmost
coupledand less
dynamically
1.0
ity is often considered to regulate
beginningof the collapse phase; once the collapse becomes
Basu97のsemiangular-momentum transport within the disc. ature
The bysumof radiative coolant. The distinction
between a dense, non-magnetizedbalancing
dynamical (with near free-fall velocity), braking is generally
1.5 0
10 24
10
101
102
these two terms first increases then decreases backzero,
spiral to
shocksand turbulence. Th
and a thin,slower
magnetizedpseudo-dischasandalso
beenobthan the modelと類似
timescaleof collapse
angularmomenanalyticr [au]
first
proposedby Paczynski (1978)
tumisapproximately
conserved.
The
M
(<
r)–L
(<
r)
re26
z
suggestingthat
gravitational
instability
takes
angularmoed, for instance,
in Masson
et al.2 (2016). 3
10
1
100
104
model due to the adoption of a b
lationat M1010 = 0.01 M 10is close to 10
the M –Lz relationofmentumfrom the inner
the disc
and deposits
it in theFigure9. Angular-momentum
flux partdue to ofdi↵erentmechanisms[au] M . 0.05 M , but the slope ofgravitational
instability controls dthe protostar-disc systemr forthroughspherical
shellsatdi↵erent
radii,
averagedfort>outer part of the disc. This transport of angularspreading
momentum(angular-momentum tra
the protostar-disc M –Lz relation becomes less steep at later
kyr. Theaxisymmetrichydrodynamic
flux (grey)
corresponds
Figure 7. Radial force density from gravity and various supporting
Figure 8.1028
Relation
betweenthe total mass
M and angularmomenthey should
equally important.
time,suggesting
thatfrommagneticbraking
continueswhen
to decrease
leads
to
disc
spreading,
and
is
the
main
thatbealto
advection
with
the
mass
accretionandoutflowanddoes
conforcesatthemidplane,taken
ourfiducial
simulation
tum
L
of
the
protostar-discsystem(blueline).
HereM
canbe not mechanismz
VOLUTIONangular
OF DISC
SIZE
AND
MASS
state,
therateof heating and ang
momentumafter
protostarformation.
tributetoprotostar
theforradialof angularwith and
respect
M10 = 0.01 M . Althoughsomesupporting
forcesare of the sameconsidered
as a proxytime.transport
Above
⇠0.1
M when, wemomentum
see aoutflow
power-lawlowsaccretion
magneticbrakingsince both are pr
arecomparable
It
is
also
worth
pointingout
whymagneticbraking
canbeto thegas.of Inside
the reference,
disc, the transportof theangularmomentumorder of magnitude as gravity, the sum of them (grey line) remains
scaling withslope
⇡1.5. For
we also plot
relation
he previous
sectiondiscussed
the
mass
and
angularthe
disc
are
weak.
which gravitational instability ext
importantinwe
the formation
pseudo-discbut
is always
to
gasat
istwo
dominated
gravitational
instability,
insufficient
to balance
gravityin the pseudo-disc,and unimportantthepseudobetween withMin(<respectr) andLzthe(<r)
di↵erentby
epochs:the initial
Protostellar
discand
evolution
9 in thetial rotationdisc(Gammie 2001).
producestheandnon-axisymmetrichydrodynamic
flux
disc.
This is mainly because
the density
and coldiscbudget
is inprotostellar
near free-fall.
conditionwhich(solidgrey importantline)
when MM , whichis (blue)mentumof theprotostar-discsystemas a whole.
10 = 0.01
One
consequenceof
thisgravitational
Figure 10. Toomre Q (computed using azimuthally averaged proandgravitational
stress(green).
aroundprotostarformation(dashedgreyline).
umn density in the protostellar disc are much higher than infiles)
in the fiducial
3D simulation.
Each
curve
corresponds
to a
we will focus
on the redistribution of angular momenspreadingis thatthe disccannowhave significantly
higher1052
the pseudo-disc (for example, see Figs 1 and 2), which makes
panel in Fig. 3. The gravitationally unstable disc generally has Q
5.3
Predicting
disc evolution
within the theprotostar-discsystem,which
determinesthespecific
angularmomentum than the pseudo-disc inflow thatmagnetic field less well coupled and less dynamically imbetween
1 and
4 2.
tension
(see
Fig.
7).
Althoughtheinitialmass-to-flux
ratio
Magnetic
breaking
重力不安定性によるself-regulation
angular-momentum
transport within
the disc.
sum of Fig.
The mass.
distinction
between disca dense,non-magnetizedUsing
the idea aof gravitational seution fieldof discsizeresolution)and(atportant.
35-au
in a protostellar
survey.
There
feeds the protostar-discsystem.
ForTheexample,5 showsof the pre-stellar
is justsupercriticaland Bz /⌃ to zero,these two coreterms
first slightly
increases
then decreases
backa thin, magnetizedalso been obtal mass M and angular momentu
are alsodisc
someanddi↵erencesin the initialpseudo-discconditions,has
includingsignificant
in ⌦ instability
betweenthe angulardisc
pseudo-disc;does notsuggesting
decreasesignificantly
duringmostof thetakes
infall,the andthat jump
gravitational
mo- the system,
served,instance,near-criticalin Masson etal. (2016).
one can obtain a robust es
our adoptionof fora stronger,
initialmagnetic field,
3.0
pressurementum
gradientandmagnetic
forcesremainatleastafactorsimilar
jumps
in
v
are
also
visibleinthemiddle
right
panel
from
the
inner
part
of
the
disc
and
deposits
it
in
the
sity
profile,mass, and size of thewhich could
leadto
substantiallyweakeroutflowassuggested
15of a few outersmallerthanthetransport
acceleration
is &50%momentumof1051
Angularmomentumtransport
by gravitational
partof2.gravity,
theThisdisc.andThisof angularof the possible
disc is known. Here we per
2.5
by resultsfrom Machida& Hosokawa(2013). Overall,instability
it is
of
Fig.
makes
havingrelatively
large
discs
free fall leadsin thetobulk
of spreading,pseudo-disc.
Still,
thismainis notmechanism
to say that that aldisc
andis theisothermal disc (with sound speed
importantto verify in futurestudiesour result is
5 EVOLUTIONOF DISC
SIZEwhether
AND
MASS
even
whenarethepseudo-disc
low thespecific
angularmomen10 forcesthese retarding
unimportant.
On thehas
contrary,
time evolution
afterapplicablethe formation
of
the
first
hydrostatic
core/torus,
lows
protostaraccretionwhen
outflowandmagneticbraking
Since we know most of the disc sh
2.0
over a broader range of initial parameters. Finally,
formationoftheself-similarcolumndensity
profilerequiresainitialcondition
thealthoughpreviousobservations
section we discussed
thehighmass
andandangulardue
magnetic braking.
intum
the disc
areto
weak.
we may assume that the whole discnote Inthat,of relatively
specific
densewetorus
becomesgravitationallyunstable,
reprotostarsystemformation
small but One
nontrivial
ratio between these forces and self gravmomentum
budgetof theprotostar-discasa whole.
disc
5 important consequence of this gravitational 1.5
simplicity, we also assume
angularmomentuminoutflows(e.g.,
Bjerkeli
et
al.
2016)
are
p that the(M10 = 0.01M ) Gravitans so for therest
offocus
our fiducial
simulation.
ity (similar
to theisrolepressure
in thecollapse higher
Nowusedwe as
will
the outflows
redistributionof angularmomenspreading
thatofthe
disc cannow sphericalhave significantly
M
GM/R3 . T
? ⇡ M and (R) ⇡sometimes
evidenceonthatcanremovea
sig1.5Lz M
model ofspecificLarsonangular1969), momentum
and this setsa characteristic
accre50
10tum
withintheprotostar-discsystem,which
determinestheal instability
plays
animportant
role
for
disc
growth,Spiralshockによるディ
thanthepseudo-disc
inflow
that
1.0
of
the
disc
is
then
nificant amount of angular momentum, this argument is nottion ratefeeds
thatthedepends
only 1027.5
on system.
the isothermal
sound
speed
1026.51027.01028.01028.51029.02revolutionof discsize
and mass.
10
10 1outflowand
protostar-disc
For example,
Fig.
5 shows a
5.2
Gravitational
self-regulation
groundedfirmlyunlessthe
mass-loss
rate
by
and thetransports
angularmomentumoutwardspreads
c
GM
t
[kyr]
cs and Gsignificant(for a given
mass-to-flux
ratio).
The
mass
accretions0 効果は、本
スク加熱の
M
[M
]
jump in ⌦ between the disc and the pseudo-disc;⌃(R) ⇡.
of thedisc arealso known.
disc. accretion
To seerate
this
e↵ect
clearly,
we plot the contriburate calculated
fromtheself-similar
model
of
Basu
(1997)
is⇡GQ
R30
similarjumps
in v 1are also
visible in oftheamiddle
right panel thin isothermalThe
gravitational
stability
geometrically
For the remainder of this section, we focus only on the
35
シミュレーションにはAngularmomentumtransport
by gravitational
instability
13cs /G of⇠ 2Fig.
⇥ 102. This
M makesyr , similartoour result.
ng
Figure8.5.1
Relation
betweenthemass M andangular momenfrompseudo-discdi↵erentstresses
to totalthehavingrelatively
largeevolution
discs possible
Figure 11.
Similarto Fig.
10 butshows timeof theinflow(accretion),
as itangular-momentum
largely determines the flux
Thisdefined⌃ / R 3/2
disc
can
be
described
bytheToomreQparameter,
asprofile is also obse
entum Lz of the protostar-disc system (blue line). Here M can be
even
when
the
pseudo-dischas
lowspecific
angularmomenToomre
Qprofile.
The
disc
size
is
also
plotted(whitecurve)
for
含まれていない。
Soon
after
the
formation
of
the
first
hydrostatic
core/torus,
mass
andangular-momentum
budgetoftheprotostar-disc
regulateddisc evolution of Voroby
ugh spheres
ata proxydi↵erent
duringdiscinmeconsidered as
for time.radii
Above ⇠0.1
M , wesee a expansion
power-lawtum
due to magnetic braking.
reference.
the
dense
becomes
unstable,re- Angularsystem.
Theslope
exclusion
thereference,othermechanisms,
which
are and 4.3
size Rd and disc inner boundary R
momentum budget: magnetic brakingnsscalingwithof torus⇡1.5.ofFor
also plot
9. Theangular-momentum
fluxgravitationally
iswethesumtheofrelationhydrodymains
forLzgreatly
therestof ourfiducial
simulation.
oftenhighlythe problem.
angular momentum of the disc are
Q
=
1
–
2
の領域は非軸対称
obetween
M (<variable,r)soand(< r)
atsimplifies
twodi↵erent
epochs:the initialGravitac
s
ic advection(Reynoldsv =),0.01
magneticbraking
For the angular-momentum
budget, we focus on the rela15
r10
Q⌘.
instability
plays
an⇢v
importantrole
discconditiontional(solidgrey line) stress
and
when
M
M ,forwhich
is growth,
Z Rd (3)Thethesteep
dependenceof the angular-momentum
trans⇡G⌃
4cs0 Mtion
between
total
mass
and
angularmomentumofthe5.2
Gravitational
self-regulation
重力不安定性が発現aroundprotostarformation(dashedgreyline).
asit
transports
angularmomentumoutwardandspreadsxwell stress Br B /4⇡), and gravitational torque (gravMd ⇡2⇡RdR ⌃(R) ⇡port rate on disc column density (through Q) implies a self1/
Gd pros to ahas Qof thee) forransa selfleadsng (astable
rease
o-discining
ll butld belies a
d 11,
tween
milar
(e.g.,

5.3 Predicting disc evolution
Using the idea of gravitational self-regulation, for given total mass M and angular momentum Lz of the protostar-discsystem, one can obtain a robust estimate for the surface density profile, mass, and size of the disc if the thermal profileof the disc is known. Here we perform this estimate for an
isothermal disc (with sound speed cs0 ) as an example.
Since we know most of the disc should be marginally stable,
we may assume that the whole disc has constant Q = Q0 . For
simplicity, we also assume
p that the disc is not very massive, so
M? ⇡ M and (R) ⇡ GM/R3 . The surface density profileof the disc is thenrcs0GM⌃(R) ⇡
.
(4)
⇡GQ0
R3
This ⌃ / R 3/2 profile is also observed in the gravitationallyregulated disc evolution of Vorobyov & Basu (2007). For discsize Rd and disc inner boundary Rd,in ⌧ Rd , the mass andangular momentum of the disc are then
Z Rd
1/2
4cs0 M 1/2 Rd
Md ⇡2⇡RdR ⌃(R) ⇡,(5)
G1/2 Q00
Z Rdp2cs0 M Rd
Ld ⇡2⇡RdR ⌃(R) GM R ⇡
.
(6)
Q0
0
Since most angular momentum of the protostar-disc system
is within the disc, we have Ld ⇡ Lz , which gives
Lz Q 0,2cs0 M✓◆1/2
8cs0 Lz
Md ⇡
.
GQ0
Rd ⇡

(7)
(8)

Using the M –Lz relation of our fiducial simulation (extrapolated assuming a power-law slope of 1.5), the above estimate
gives disc mass ⇡0.15 M and size ⇡80 au when the protostar
reaches ⇡1 M .
In reality, a marginally gravitationally unstable disc is of-16results, and show that properly treating the inner boundary condition is crucial for achieving convergence at an acceptable
The Perseus
computationalcost. ALMA Chemistry Survey (PEACHES). I. The Complex Organic Molecules in Perseus
338#37 Embedded Protostars

The Perseus
ALMA Chemistry Survey (PEACHES). I. The Complex Organic Molecules
2021 ApJ…910…20Y
in Perseus Embedded Protostars

Yao-Lun Yang, Nami Sakai, Yichen Zhang, Nadia M. Murillo, Ziwei E. Zhang, Aya E. Higuchi, Shaoshan
Zeng, Ana López-Sepulcre, Satoshi Yamamoto, Bertrand Lefloch, Mathilde Bouvier, Cecilia Ceccarelli, Tomoya
Hirota, Muneaki Imai, Yoko Oya, Takeshi Sakai, Yoshimasa Watanabe F To date, about two dozen low-massembedded protostars exhibit rich spectra with complex organic molecule (COM) lines. These protostars seem to possess
diﬀerent enrichment in COMs. However, the statistics of COM abundance in low-mass protostars are limited by the scarcity ofobservations. This study introduces the Perseus ALMA Chemistry Survey (PEACHES), which aims at unbiasedly characterizing
the chemistry of COMs toward the embedded (Class 0/I) protostars in the Perseus molecular cloud. Among the 50 embedded
protostars surveyed, 58protostars have CH3 OH, CH3 OCHO, and N-bearing COMs, respectively. The detectability of COMs
depends on neither the averaged continuum brightness temperature, a proxy of the H2 column density, nor the bolometricluminosity and the bolometric temperature. For the protostars with detected COMs, CH3 OH has a tight correlation with
CH3 CN, spanning more than two orders of magnitude in column densities normalized by the continuum brightness temperature,suggesting a chemical relation between CH3 OH and CH3 CN and large chemical diversity among the PEACHES samples at thesame time. A similar trend with more scatter is also found between all identified COMs, hinting at common chemistry forthe sources with COMs. The correlation between COMs is insensitive to the protostellar properties, such as the bolometricluminosity and the bolometric temperature. The abundance of larger COMs (CH3 OCHO and CH3 OCH3 ) relative to thatof smaller COMs (CH3 OH and CH3 CN) increases with the inferred gas column density, hinting at an eﬃcient production ofcomplex species in denser envelopes.

Low-metallicity Young Clusters in the Outer Galaxy. III. Sh 2-127

Chikako Yasui, Naoto Kobayashi, Masao Saito, Natsuko Izumi, Warren Skidmore F In deep near-infrared imaging of
the low-metallicity ([O/H] = 0.7 dex) H II region Sh 2-127 (S127) with Subaru/MOIRCS, we detected two young clusters with
413 members (S127A) in a slightly extended H II region and another with 338 members (S127B) in a compact H II region. The
limiting magnitude was K = 21.3 mag (10 ), corresponding to a mass detection limit of ⇠0.2 M . These clusters are an orderof magnitude larger than previously studied young low-metallicity clusters and larger than the majority of solar neighborhood
young clusters. Fits to the K-band luminosity functions indicate very young cluster ages of 0.5 Myr for S127A and 0.1-0.5 Myr
for S127B, consistent with the large extinction (up to AV ' 20 mag) from thick molecular clouds and the presence of a compact
H II region and class I source candidates, and suggest that the initial mass function (IMF) of the low-metallicity clusters is
indistinguishable from typical solar neighborhood IMFs. Disk fractions of 28% ± 3% for S127A and 40% ± 4% for S127B are
significantly lower than those of similarly aged solar neighborhood clusters (⇠50%-60%). The disk fraction for S127B is 17
higherthan those of previously studied low-metallicity clusters (<30 %), probably due to S127B’s age. This suggests that a large

The Astrophysical Journal, 910:20 (38pp), 2021 March 20

Yang etThe
al. Astrophysical Journal, 910:20 (38pp), 2021 March 20

Figure 5. The spectra of Per-emb 44 (SVS 13 A) along with the best-ﬁtting model assuming Tex = 150 K. The ﬁtted spectra for each species are illustrated by coloredlines (solid and dashed) with the legends shown at the top of the ﬁgure. The frequencies of identiﬁable simple organic species, carbon-chain molecules, and theblended COMs emission, such as 13CH3OH and CH18
3 OH, are shown as blue vertical bars with the species listed next to it.

Yang et al.

Figure 5. (Continued.)χ2 minimization. We allowed the column density to vary by a few
orders of magnitude to ensure that a global minimum was found.
where the better ﬁtting models are modiﬁed less over generations.
We set up the genetic algorithm to search for the top two best-From the ﬁve ﬁtted column densities assuming ﬁve different
Tex, if a molecule is detected according to the criteria listed inﬁtting models with 30 generations. Then, the Levenberg–
Section 3.3, we took the mean column densities as the bestMarquardt χ2 minimization was applied to the two best-ﬁtting
ﬁtting column density, while the range of the column densities
models for 20 iterations to determine the best-ﬁtting models. The
indicates the uncertainty. If a species is considered nondetected
genetic algorithm aims to ﬁnd global minima, and the Levenberg–
2
inMarquardt χ minimization further ﬁnds the best-ﬁtting models(Section3.3), we used the synthetic spectra to derive the upper
the global minimums. The two best-ﬁtting models found by limit
the of the column density corresponding to the noise of thegenetic algorithm are often very similar, suggesting that therespectra.
isThe ﬁtted column density assumes an FWHM of 0 5
only one minimum. In the rare cases of two distinct global(150 au). Figure 5 shows an example of the ﬁtted spectra fortheminima, we selected the model with the lower χ2 values from Per-emb
44 (SVS 13 A), assuming Tex = 150 K. The ﬁtted
two best-ﬁtting models constrained by the Levenberg–Marquardt

substantial. The synthetic spectra were calculated for the size ofcontinuum emission (Table 2) to include the effect of beam
dilution. We allowed the line width to vary between 1.2 and3.5 km s−1 for a better ﬁtting quality and chose a range of thecolumn density for each molecule according to the strength ofthe emission.
The ﬁtting function in XCLASS includes several optimization
algorithms that can be used in sequence to reduce biases. We
conﬁgured the algorithm chain that starts with the genetic
algorithm followed by the Levenberg–Marquardt χ2 minimization. The genetic algorithm iteratively searches for the best-ﬁtting
parameters with generations that evolve like a natural selection,
10

spectra may under- or overestimate the strengths of sometransitions because the assumed excitation temperature may not
be the true excitation temperature.
To benchmark this hybrid optimization process, we comparedthe ﬁtted column densities with the ﬁtting using the Monte Carlo
Markov chain (MCMC) algorithm on the most chemically richsource, Per-emb 44 (SVS 13 A). The MCMC algorithm uses the
afﬁne-invariant MCMC package EMCEE (Foreman-Mackey et al.
2013) to sample the parameter space. In this MCMC optimization,
we ﬁt both the excitation temperature and the column density. Fora single-species ﬁtting, we used 100 walkers with 100 iterations
after 30 burn-in iterations; for a combined ﬁtting of two species,

19

11

Figure 6. The column densities of Per-emb 44 (SVS 13 A) ﬁt using the hybrid algorithm, genetic and Levenberg–Marquardt χ2 minimization, and the MCMC
algorithm. The molecular species are annotated, and the gray line indicates the equality.

Figure 7. Summary of molecular detections. The sources are sorted by increasing R.A. from left to right. The detections are color-coded by the types of species:
S-bearing molecules in blue, carbon-chain molecules in pink, O-bearing COMs in green excluding N-bearing molecules, N-bearing COMs in brown, and other simple
organics in dark purple. The boxes with solid colors indicate emission and the empty boxes indicate absorption. The hatched boxes indicate both emission andabsorption are seen.

we used 500 walkers to better sample the parameter space. The
ﬁtting column densities from the hybrid (genetic and Levenberg–
Marquardt χ2 minimizations) method are consistent with that ﬁt

with the MCMC optimization (Figure 6). Moreover, our hybrid
method yields comparable uncertainties to those from the MCMC
method, validating our modeling approach.

20

The Astrophysical Journal, 910:20 (38pp), 2021 March 20
The Astrophysical Journal, 910:20 (38pp), 2021 March 20

Yang et al.

Yang et al.

discussed here are derived from the spectra taken from the areasurrounding the continuum peak, as explained in Section 3.1.
We focus on the chemistry of COMs toward the disk-forming
regions in this study. Therefore this study excludes any
molecules that are only detected outside the region ofcontinuum emission. A comparison of the chemical composition in protostellar envelopes (100–1000 au) requires observations with a larger maximum recoverable scale (θMRS).
The PEACHES sample shows a diverse chemistry of COMs,
from no molecule detected (e.g., B1-b N and L1455 IRS 2) torich spectra of COMs (e.g., Per-emb 13). Most protostars of the
PEACHES sample have simple molecules, such as SO, CS,
H13CN, and HDCO, and ∼60% of the sources have SO2 and34
SO. Emission of C2H can be easily identiﬁed from thespectra. However, C2H toward the continuum sources often
shows irregular line proﬁles together with velocity offsets andabsorption (Appendix E, Figure 21). Warm environments, suchas the outﬂow cavity wall, easily enhance the abundance ofC2H because of the elevated abundance of C+ (e.g., Zhang
et al. 2018; Imai et al. 2019). Thus, C2H emission tends toextend along with the outﬂow cavities, which means that 1D
spectra toward the continuum source are no longer representative of the abundance of C2H. Future studies will investigate
the comparison between unsaturated species and COMs using
follow-up observations with a higher dynamic range of thespatial distribution (from ∼100 au to several 1000 au scale).
Previous observations with single-dish telescopes have a beam
size of ∼3000 au (e.g., Higuchi et al. 2018). Thus, observations
that ﬁll in the spatial scale from several 100 au to 1000 au arenecessary.
Several sources have broad SiO emission, signiﬁcantly
contaminating the emission of CH3CH2CN and CH3CHO. In
comparison, the emission of COMs has relatively narrow line
width of a few km s−1. In the quantitative discussion below,
we exclude the spectral windows that are contaminated by the
SiO emission. For a few sources, such as Per-emb 26, we canstill distinguish the emission of CH3CH2CN and CH3CHO
from the broad SiO emission and include these identiﬁcation in
the detection statistics.
Figure 7 shows the number of COMs detected toward thePEACHES sample. Twenty-nine (58%) sources have detected
COMs. CH3OH is detected in 28 sources (56%), CH3OCHO is
detected in 14 sources (28%), and N-bearing COMs aredetected in 20 sources (40%). Compared to the COMs in the
CALYPSO survey (Belloche et al. 2020), the fraction ofsources that have methanol, ∼50%, is similar to that for the
PEACHES sample. Furthermore, 30% of the CALYPSO
sources have at least three species of COMs, while 28% of
the PEACHES sample have at least three species of COMs. In asmaller sample selected from several molecular clouds, vanGelder et al. (2020) found that 3 of 7 protostars show emissionof COMs.
To investigate the impact of protostellar properties on theappearance of COMs, we divided the PEACHES sample into
four groups according to the number of detected COMs from no
COM, at least 1, 5, and 10 species of COMs (Figure 8). The
compared protostellar properties include the bolometric luminosity (Lbol), the bolometric temperature (Tbol), and the meancontinuum brightness temperature (Tb,cont), where the Tbol and
Lbol are collected from Tobin et al. (2016) and Murillo et al.
(2016). Tbol traces the evolutionary stage of protostars withhigher Tbol for more evolved protostars (Myers & Ladd 1993;

Figure 8. The number of COMs detected toward the PEACHES sample
compared with the bolometric luminosity (Lbol), the bolometric temperature(Tbol), and the averaged continuum brightness temperature (Tb,cont) from top tobottom. The sample is divided into four groups with detected COM species of0, 1, 5, and 10, respectively. For each group, the circles show the meanvalues of the corresponding properties, while the error bars show the value
ranges. The number of sources in each group is labeled in parentheses. Lbol andTbol are taken from Tobin et al. (2016) and Murillo et al. (2016).

4. Results
4.1. Detection Statistics
We summarize the detection statistics in Figure 7, which
includes COMs, carbon-chain molecules, and simple molecules, such as CS, H13CN, SO, 34SO, and SO2. To derive thedetection fraction, we included the three sources that were
excluded from modeling because their source velocity was notreliable (Section 3.1), making a total of 50 sources. The COMs
13

Figure 12. Corner plot of the correlations of the column densities between CH3OH, CH3CN, CH3OCHO, and CH3OCH3. The color code follows that of Figure 11.
The annotated texts indicate the Pearson r (rd) and the logarithmic ratio of the two molecules (Ny/Nx) for the detection-only sample. The four most frequently detected
COMs are shown in this ﬁgure, while other COMs are shown in Figure 13.

the protostellar properties. After the normalization with Lbol
and Tbol (Figure 14, blue and black markers), the correlation
between CH3OH and CH3OCH3 weakens signiﬁcantly, whilerange from 0.76 to 0.93 (Figure 12). The Pearson r for the same
21
four species with all COM species has a median value of 0.86
with a range from 0.57 to 0.95 (Figure 13). The correlations

Figure 16. The column densities of CH3OH toward the PEACHES sample (excluding Per-emb 17) normalized by the averaged continuum brightness temperature as afunction of the minimum distance to the 10σ contour in the Planck 217 GHz observations. Due to the lower brightness at 217 GHz toward Per-emb 5 and Per-emb 25,
their minimum distances are calculated with 5σ and 3σ contours, respectively. The solid circles show the sources with detection of CH3OH, while the open circles
show the sources without detection of CH3OH.

Figure 17. The ratios of the COMs commonly found in the PEACHES and the CALYPSO survey (Belloche et al. 2020), as well as a few selected hot corinos. The
CALYPSO sources are categorized into three groups according to their COM abundance to CH3OH. Group 3 has no detection of CH2OHCHO. The column densities
of COMs toward IRAS 16293−2422 B are taken from Jørgensen et al. (2016) for CH3OH, Jørgensen et al. (2018) for C2H5OH, CH3OCH3, CH3OCHO, CH3CHO,
NH2CHO, and CH2OHCHO, and Calcutt et al. (2018) for CH3CN and CH3CH2CN. The column densities of COMs toward IRAS 16293−2422 A are taken from
Manigand et al. (2020) for CH3OH, C2H5OH, CH3OCH3, CH3OCHO, CH3CHO, NH2CHO, and CH2OHCHO, and Calcutt et al. (2018) for CH3CN and CH3CH2CN.
The column densities of COMs toward L483 are taken from Jacobsen et al. (2019). The column densities of COMs toward BHR 71 are taken from Yang et al. (2020),
assuming a Tex of 100 K for CH3OH. The purple hatched regions indicate the range of the peak abundance ratios to CH3OH from the warm-up models in Garrod(2013) that have three different speeds of the warm-up process.

abundance ratios in the warm-up models by Garrod (2013).
The models underestimate the abundance ratios for most of
the O-bearing COMs, while the ratios of CH2OHCHO andN-bearing COMs agree with the ratios derived from thePEACHES sample (Figure 17). Because we may underestimate
the column density of CH3OH due to the optical depth, theabundance ratio to CH3OH could be overestimated. If the ratios
derived from the PEACHES sample were lower by a factor offor the ﬁve COMs in the left, but the model would thenoverestimate the abundance ratios of CH2OHCHO, NH2CHO,
and CH3CH2CN. This disagreement may point to a dominant
gas-phase formation of (some) COMs other than CH3OH, assuggested by other studies (e.g., Balucani et al. 2015; Skouteris
et al. 2018; Vazart et al. 2020).
The well-correlated abundance of N-bearing COMs andO-bearing COMs (Figures 12 and 13) indicates no “N-/O-bearing
COMs differentiation,” which has long been discussed for23

luminosity and the bolometric temperature. The abundance of larger COMs (CH3 OCHO and CH3 OCH3 ) relative to thatof smaller COMs (CH3 OH and CH3 CN) increases with the inferred gas column density, hinting at an eﬃcient production of
Low-metallicity Young Clusters in the Outer Galaxy. III. Sh 2-127
338
complex species in denser envelopes.

#38

2021 AJ…161..139Y

Low-metallicity Young Clusters in the Outer Galaxy. III. Sh 2-127

Chikako Yasui, Naoto Kobayashi, Masao Saito, Natsuko Izumi, Warren Skidmore F In deep near-infrared imaging of
the low-metallicity ([O/H] = 0.7 dex) H II region Sh 2-127 (S127) with Subaru/MOIRCS, we detected two young clusters with
413 members (S127A) in a slightly extended H II region and another with 338 members (S127B) in a compact H II region. The
limiting magnitude was K = 21.3 mag (10 ), corresponding to a mass detection limit of ⇠0.2 M . These clusters are an orderof magnitude larger than previously studied young low-metallicity clusters and larger than the majority of solar neighborhood
young clusters. Fits to the K-band luminosity functions indicate very young cluster ages of 0.5 Myr for S127A and 0.1-0.5 Myr
for S127B, consistent with the large extinction (up to AV ' 20 mag) from thick molecular clouds and the presence of a compact
H II region and class I source candidates, and suggest that the initial mass function (IMF) of the low-metallicity clusters is
indistinguishable from typical solar neighborhood IMFs. Disk fractions of 28% ± 3% for S127A and 40% ± 4% for S127B are
significantly lower than those of similarly aged solar neighborhood clusters (⇠50%-60%). The disk fraction for S127B is higher
than those of previously studied low-metallicity clusters (<30 %), probably due to S127B’s age. This suggests that a large
fraction of very young stars in low-metallicity environments have disks, but the disks are lost on a very short timescale. These
results are consistent with our previous studies of low-metallicity star-forming regions, suggesting that a solar neighborhood
IMF and low disk fraction are typical characteristics for low-metallicity regions, regardless of cluster scales.

1324338 The Hawaii Infrared Parallax Program. V. New T-Dwarf Members and Candidate#39 Members of Nearby Young Moving Groups
The Hawaii
Infrared Parallax Program. V. New T-Dwarf Members and Candidate
2021 ApJ…911….7Z
Members of Nearby Young Moving Groups

Zhoujian Zhang, Michael C. Liu, William M. J. Best, Trent J. Dupuy, Robert J. Siverd F We present a search
for new planetary-mass members of nearby young moving groups (YMGs) using astrometry for 694 T and Y dwarfs, including
447 objects with parallaxes, mostly produced by recent large parallax programs from UKIRT and Spitzer. Using the BANYAN⌃ and LACEwING algorithms, we identify 30 new candidate YMG members, with spectral types of T0 T9 and distances of
10 43 pc. Some candidates have unusually red colors and/or faint absolute magnitudes compared to field dwarfs with similar
spectral types, providing supporting evidence for their youth, including 4 early-T dwarfs. We establish one of these, the variableT1.5 dwarf 2MASS J21392676+0220226, as a new planetary-mass member (14.6+3.2
1.6 MJup ) of the Carina-Near group (200 ± 50Myr) based on its full six-dimensional kinematics, including a new parallax measurement from CFHT. The high-amplitude
variability of this object is suggestive of a young age, given the coexistence of variability and youth seen in previously known
YMG T dwarfs. Our four latest-type (T8 T9) YMG candidates, WISE J031624.35+430709.1, ULAS J130217.21+130851.2,
WISEPC J225540.74 311841.8, and WISE J233226.49 432510.6, if confirmed, will be the first free-floating planets (⇡ 2 6
MJup ) whose ages and luminosities are compatible with both hot-start and cold-start evolutionary models, and thus overlap theproperties of the directly-imaged planet 51 Eri b. Several of our early/mid-T candidates have peculiar near-infrared spectra,
indicative of heterogenous photospheres or unresolved binarity. Radial velocity measurements needed for final membershipassessment for most of our candidates await upcoming 20 30 meter class telescopes. In addition, we compile all 15 known
T7 Y1 benchmarks and derive a homogeneous set of their eﬀective temperatures, surface gravities, radii, and masses.

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