星形成ゼミ 2015/10/16 Newsletter #273 No.1‒5

担当；清兼和紘•

1. ALMA Observations of the Transition from Infall Motion to Keplerian Rotation aroundthe Late-phase Protostar TMC-1A
Yusuke Aso et al.
http://iopscience.iop.org/article/10.1088/0004-637X/812/1/27/
pdf;jsessionid=0B3863D44559BBF4AF43B7D21E1410E8.c1•

2. On The History and Future of Cosmic Planet Formation
Peter S. Behroozi, Molly Peeples
http://jp.arxiv.org/pdf/1508.01202v1•

3. A self-consistent, absolute isochronal age scale for young moving groups in the solar
neighbourhood
Cameron P. M. Bell, Eric E. Mamajek and Tim Naylor
http://mnras.oxfordjournals.org/content/454/1/593.full.pdf•

4. AMBER/VLTI high spectral resolution observations of the Brγ emitting region in HD
98922. A compact disc wind launched from the inner disc region
A. Caratti o Garatti et al.
http://jp.arxiv.org/pdf/1508.00798v1•

5. Anisotropic Formation of Magnetized Cores in Turbulent Clouds
Che-Yu Chen and Eve C. Ostriker et al.
http://jp.arxiv.org/pdf/1508.02710v1

1

Masahiro N. Machida7, Masao Saito8,9, Shigehisa Takakuwa3, Kengo Tomida10, Kohji Tomisaka 6, and Hsi-Wei Yen3
1

Department of Astronomy, Graduate School of Science, The University of Tokyo, 731 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
2
Subaru Telescope, National Astronomical Observatory of Japan, 650 North A’ohoku Place, Hilo, HI 96720, USA3• 1. ALMA Observationsof theSinica
Transition
from Infall
Motion P.O.
to Box
Keplerian
Rotationaround the Late-phase
Academia
Institute of Astronomy
and Astrophysics,
23-141, Taipei
10617, Taiwan
4
National Astronomical Obervatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan
Protostar TMC-1AChile Observatory,
5
Department of Earth and Planetary Sciences, Kobe University, Kobe 657-8501, Japan
6
National Astronomical Observatory of Japan, Osawa, 2-21-1, Mitaka, Tokyo 181-8588, Japan
Yusuke Aso et al. 7
Department of Earth and Planetary Sciences, Faculty of Sciences Kyushu University, Fukuoka 812-8581, Japan8
http://iopscience.iop.org/article/10.1088/0004-637X/812/1/27/
Nobeyama Radio Observatory, Nobeyama, Minamimaki, Minamisaku, Nagano 384-1305, Japan
9
SOKENDAI, Department of Astronomical Science, Graduate University for Advanced Studies, Japan
pdf;jsessionid=0B3863D44559BBF4AF43B7D21E1410E8.c1
10Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
Received 2015 January 12; accepted 2015 August 25; published 2015 October 6

ABSTRACT
We have observed the Class I protostar TMC-1A with the Atacama Millimeter/submillimeter Array (ALMA) inthe emissions of 12CO and C18O (J = 2–1)and 1.3mm dust continuum. Continuum emission with a deconvolved
size of 0 50 × 0 37, perpendicular to the 12CO outﬂow, is detected. It most likely traces a circumstellar disk
5 October 10
Aso et al. reported. In contrast, a more extended structure is detected in C18O, although it isaround TMC-1A, as previously
18
Table 13×2
2,
indicating
that
C
O traces mainly a ﬂattened envelope
stillelongatedwithadeconvolved
size
of
3
Summary of the Observational Parameters
18
surrounding the disk and the central protostar. C O shows a clear velocity gradient perpendicular to the outﬂow atContinuum
CO J = 2–1
C O J = 2–1
highervelocities,
indicativeof rotation, while an additional velocity gradient along the outﬂow is found at lower
ALMA (Extended), 2012 Nov. 6
L
TMC-1A
L
velocities. The radial proﬁleof the rotational velocity is analyzed in detail, ﬁnding that it is given as a powerlaw
L
R.A. (J2000) = 4 39
L
− 35
a 010
an index of L∼0.5 at higher velocities. This indicates that the rotation at higher velocities can be∝rdecl. (J2000) =25°41′45 with500
230.5380 GHz
219.5604 GHz
225.4336 GHz
explained as Keplerianrotationorbiting a protostar with a dynamical mass of 0.68 M: (inclination corrected). The
27 3
28 6
27 9
L
15.9–285.7
m
L
additional
velocity gradientof C18O along the outﬂow is considered to be mainly infall motions in the envelope.
2 × 0 90 (−178°)
1 06 × 0 90 (−176°)
1 01 × 0 87 (+0 . 87)
diagrams
0.16 km s
0.17 Position–velocity
km s
923 MHz made from models consisting of an infalling envelope and a Keplerian disk are
4.6 mJycomparedbeam
K
5.6 mJy beamwith the observations,revealing that the observed infall velocity is ∼0.3 times smaller than the free-fall
20 mJy beam
7.1 mJy beam
0.96 mJy beamL
J0522–364
L
velocity yielded by the dynamical
mass of the protostar. Magnetic ﬁelds could be responsible for the slow infall
L
CallistoLvelocity. A possible scenario
of Keplerian disk formation is discussed.
L
J0510+180
LThe Astrophysical Journal, 812:27 (20pp), 2015 October 10
Key words: circumstellar matter – stars: individual (TMC-1A) – stars: low-mass – stars: protostars
18

h

m

°

−1

−1

−1

−1

−1

−1

−1

Aso et al.

COinuum emission incontinuum emission
ted. Though the size
ilar to the beam size
be estimated from a
3 × 0 37 ± 0 05,
so measured from the20, δ(2000) = +25°
vious measurements
um peak position is
MC-1A in this paper.
ity of the continuum
g are 148.5 ± 2.2
ively. The dust mass
dust = (4.2 ± 0.9) ×
fﬁcient κ (1 THz) =an opacity index= 28 K (Chandler
ated from a ﬁtting to-1A at λ  20 μm.
e 4.2 × 10−2 M: if
100.
(moment 0) and the

1. INTRODUCTION

et al. 2013; Harsono et al. 2014)that are still deeply embedded
in protostellar envelopes.
Protoplanetary disks play key roles in the evolution of young
Despite the ubiquity of Keplerian disks in various protostellar objects (YSOs). In the early stages of star formation,
stellar stages, their formation process from protostellar
・ and angular momentum are transferred to the central stars
mass
envelopes is still controversial both theoretically and observathrough protoplanetary disks. In the later stages, these disks cantionally. Theoretical calculations of collapsing isothermal
become the sites of planet formation (e.g., Howard 2013).
spheres with ideal, nonmagnetized conditions, such as
Protoplanetary disks are ubiquitous around classical TTauri“inside-out collapse” models (Terebey et al. 1984; Shustars or Class II sources and have been observed in thermal dust
et al. 1987), provide a conventional picture of star and disk
continuumandmolecularlineemissionsatmillimeter
Figure 2. Moment and
0 (white contours) and 1 (color) maps of the CO (J = 2–1)
Figure 4.
Moment 0 (white
contours) andprotostar
1 (color) maps offorms
the C O (J = 2–1)
Figure 1. Continuum emission map of TMC-1A observed with ALMA.
Accordingmodels,a centralemission in TMC-1A. Contour levelsformation.
of the moment 0 map
are −3, 3, 6, 12,to theseemission in TMC-1A. Contour levels of the moment 0 map are −3, 3, 6, 12,Contour levels are −3, 3, 6, 12, 24, ... × σ, where 1σ corresponds to 0.96
submillimeter wavelengths since the 1990s. Keplerianrotation
24, ... × σ,
where 1σ corresponds to 0.034 Jy beam km s . A plus sign
mJy beam km
s . A plus sign
24, ...center× σ, whereof
1σ corresponds
to 8.1mJy beam . A plus sign shows the position of the continuum emission peak.
with a Keplerian disk at thea slowlyrotating
dense
shows the position of the central protostar (continuum emission peak). A ﬁlled
shows the position of the central protostar (continuum emission peak). A ﬁlled
A is
ﬁlledrevealed
ellipse at the bottom
leftcornerdenotesthe
ALMA
synthesized
beam;
for many of the disks (Guilloteau & ellipse
Dutreyat the 1998;
bottom left corner moleculardenotes the ALMA
synthesized
beam;as theellipsebottom left
corner denotes infall,
the ALMAwhich
synthesized beam;
cloud
core
gasat thebeginsdynamical
1 01 × 0 87, P.A. = +0 87. The deconvolved size of the continuum
1 02 × 0 90, P.A. = −178°. CO clearly traces the molecular outﬂow from1 06 × 0 90, P.A. = −176°. Blue and red arrows show the direction of the
03 ×al.
0 37 1999;± 0 05, P.A= +73° ± et
16°, al.
and the2000; Qi et al. 2004;
emission
is 0 50 ± 0 et
Guilloteau
Simon
TMC-1A, and the axis of the outﬂow(∼ −17°) is showna dashed line.
(Figure 2).
molecular outﬂow
from TMC-1A
observed momentum
in CO (J = 2–1) lineis
conservesitswithangularmomentum.
Largerangularelongation direction (73°) is shown with a white dashed line. Blue and red
arrowsshow
thedirectionofthemolecular
outﬂow
from
TMC-1Aobservedin
Hughes et al. 2009; Rodriguez et al. 2010). In the evolutionary 2 gradually transferred from the outer region of the dense corethe CO (J = 2–1) line (Figure 2).
18
stages earlier than TTauri stars, accreting protostars (Class I or
O ThereJ = 2–1 are some
3.2. Cand is redistributed in the disk as time goes
on.
12

1

1

18

1

1

12

12

12

1

Figure 8. PV diagrams of the C O (J = 2–1) emission in TMC-1A along (a) the major axis and (b) the minor axis (the ma
in Figure 1, PA = 73°). These PV diagrams have the same angular and velocity resolutions as those of the channel map
spacing from 3σ (1σ = 7.1 mJy beam1). Central vertical dashed lines show the systemic velocity (Vsys = 6.4 km s1), a
central position. Points with error bars in panel (a) are mean positions derived along the position (vertical) direction at eac
velocities along the outﬂow-axis direction for i = 70° and 40°.

The Astrophysical Journal, 812:27 (20pp), 2015 October 10

break radius can be estimate
break radius of 67 AU. Rb
and jp ∼ 1 × 10−3 km s1 p

Aso et al.

4.3. Rota

Figure 8. PV diagrams of the C18O (J = 2–1) emission in TMC-1A along (a) the major axis and (b) the minor axis (the major axis corresponds to the white dashed line
in Figure 1, PA = 73°). These PV diagrams have the same angular and velocity resolutions as those of the channel maps shown in Figure 5. Contour levels are 6σ
spacing from 3σ (1σ = 7.1 mJy beam1). Central vertical dashed lines show the systemic velocity (Vsys = 6.4 km s1), and central horizontal dashed lines show thecentral position. Points with error bars in panel (a) are mean positions derived along the position (vertical) direction at each velocity. Curves in panel (b) show escapevelocities along the outﬂow-axis direction for i = 70° and 40°.

break radius can be estimated to be ∼90 AU from the apparent
break radius of 67 AU. Rb ∼ 90 AU leads toM*p _ 0.6 M:
and jp ∼ 1 × 10−3 km s1 pc.
The Astrophysical Journal, 812:27 (20pp), 2015 October 10

Figure 9. Mean positions of the PV diagram along the major axis plotted on alog R−log V plane. The ordinate is not deprojected. Blue and red points show
blueshifted and redshifted components, respectively. Dashed lines show the
best-ﬁt lines with a double power law. In addition to the inner and outer power,
the “break” radius and velocity are included as free parameters. The best-ﬁt
parameters are Rb = 67 AU, Vb = 2.4 km s1, pin = 0.54 ± 0.14,
andpout = 0.85 ± 0.04. The error for (Rb, Vb) is ∼1%.

1
et al.
By using the break point (RAsob, Vb) = (67 AU, 2.4 km s ), thedynamical
mass
of
the
centralprotostarandthespeciﬁcangularobservations. The mean position is not measured at low
at Rb,thewhich
are notshows
inclination corrected, can be
In the previous section, the detailed analysis velocitiesof the PV(∣ %V ∣  1.2 momentum
km s1), whereemission
2 i  0.43 M and
M
M
sin

calculated
atjp  j sin i diagram cutting along the disk major axis was presented
topextended structures, which is unsuitable* for this* analysis. We :
4 km s1 pc,
characterize the nature of rotation, which suggests theexistence
7.7
q10
respectively.
Weshouldnote,
however,also note that a similar analysis was performed by Yenof a Keplerian disk in the innermost part of the envelope.
In
this
that
the
analysisusingcertain
representative
pointson a PVet al. (2013).
section, physical conditions of the Keplerian diskarediagrampresented
here
may
systematicallyunderestimate
Rb
Figure
9
shows
the
mean
positionsofthePV
diagramalong
O channel
investigated based on model ﬁttings to the C18thewhen
thelogspatialresolution
is nothigh enough, as discussed inR
V diagram.
The
abscissa
major axis on a log
maps. To quantify physical parameters of the disk
aroundAppendix
Takingpositions
this pointshows
the mean positions
measuredA.
as offset
frominto
the consideration, the realJ = protostar,
2–1
TMC-1A, we performed a χ2 ﬁtting to the C18Ocentral
which corresponds to the zero position on thechannel maps based on a standard rotating disk model(e.g., assuming that the distance of TMC-1A is 140 pc.
PV diagram,
8
Dutrey et al. 1994). When a standard disk model isThecomparedordinate is the relative-projected velocity assuming that the

1
to
note
with these observed C18O channel maps, it is importantsystemic velocity is 6.4 km s . Because there is no systematicfrom thebetween the blue- and redshifted components, wethat the observed C18O emission arises not onlyseparation
diskbut also from the envelope having rotation andconsider
additionalthat the central position and the systemic velocity are
motions as discussed in Section 4.1. Because ofplausible
this, it inis order to measure the relative position and velocity.
required that only the velocity channels where Figure
rotation9 showsisclear negative correlation between radius anddominant should be used for comparison with a diskvelocity,model. Asdemonstrating that the rotation velocity can beshown in Figure 9, there is a velocity range showingexpressed
the power-as a power-law function of the radius (spin-up
Figure 9. Mean positions of the PV diagram along the major axis plotted on alaw index close to the Keplerian law, suggesting that
the C18O
rotation).
Importantly, there seems to be a break point at R ∼
1
log R−log V plane. The ordinate is not deprojected. Blue and red points show
thought
to where the power changes. We performed a χ2
emission in this range with ∣ %V ∣  2.4 km s is 70–80
AU,
blueshifted and redshifted components, respectively. Dashed lines show thearise from the possible Keplerian disk. We intend, therefore,toﬁtting to Figure
9 with a double power model as follows:
best-ﬁt lines with a double power law. In addition to the inner and outer power,ﬁt the channel maps within this velocity range, with rotating
the “break” radius and velocity are included as free parameters. The best-ﬁtpin
disk models.
parameters are Rb = 67 AU, Vb = 2.4 km s1, pin = 0.54 ± 0.14,⎧⎪ Vb ( R Rb )Figure 7. 2D mean positions of the C18O (J = 2–1) emission in TMC-1A.
( R - Rb )andpout = 0.85 ± 0.04. The error for (Rb, Vb) is ∼1%.
We
use
a
disk
model
with
a
code
described
in
Ohashi
et
al.
⎨

V
(
R
)
(1 )
Gp
Each point indicates a 2D mean position at each channel weighted with the
pout
⎪
model
can
be describedwith 10 parameters( R  Rb ) .
⎩ Vb ( R Rb )O emission).
Error bars
intensity and 6σ cutoff(2014).
(σ is theTherms noiseleveldiskof C18are notbut aresummarized
smaller than theinpointsize. Dashedlines
show the
major
Table
2. Theradialdependenceof the disk
1plotted
By using the break point (Rb, Vb) = (67 AU, 2.4 km
the axis of the disk (73° and−17°, respectively), and theand sthe), minor
temperature T(R) and the disk surface densityTheΣ(R)are pin and pout, and the break point (Rb, Vb) are free
powers,dynamical mass of the central protostar and the speciﬁc
angularintersectionis the position of the central protostar (continuum emission peak).
described
asparameters. The best-ﬁt parameter set is (Rb , Vb, pin , pout ) 
The point
momentum at Rb, which are not inclination corrected,
can sizebe becomes smaller as the value of ∣V  Vsys ∣ becomes higher, and1points(67 AU, 2.4 km s1, 0.54 ± 0.14, 0.85 ± 0.04), where thecalculated at M*p  M* sin2 i  0.43 M: and jp green
 j sini correspond to a velocity range of ∣%V ∣  2.4⎛ km sR . ⎞q⎟
T (R)  T100 ⎜,(2)Rb and Vb are ∼1%, giving reduced χ2 = 1.6.
errors for
7.7 q 104 km s1 pc, respectively. We should note, however,⎝ 100 AU ⎠Because this reduced χ2 is close to the unity, we consider that
disk
that the analysis using certain representative points
on majora PV axis shown in Figure 8(a) is inspected here. Thisthe best ﬁt is reasonable. The error of each parameter is derived
ﬁgure shows
position getsdiagram presented here may systematically underestimate
Rb that the velocity gets higher(2  pas) Mthe200
4 (R ) R p R  R ,(3 )4.3. Rotating Disk Models

・3

In the previous section,
diagram cutting along thecharacterize the nature of roof a Keplerian disk in the insection, physical conditio
investigated based on momaps. To quantify physic
TMC-1A, we performed achannel maps based on a
Dutrey et al. 1994). Whenwith these observed C18O cthat the observed C18O e
diskbut also from the envemotions as discussed in S
required that only the ve
dominant should be used fo
shown in Figure 9, there is alaw index close to the Kepl
emission in this range witharise from the possible Kep
ﬁt the channel maps withindisk models.
We use a disk model wit(2014). The model disk casummarized in Table 2. T
temperature T(R) and thedescribed as

T (R)  T104 (R ) (2  p ) M(2p
2Q R outarger hostgalaxies
thanBaltimore,for Earth-likeplanets.
elescope
Science
Institute,
MD 21218,
USAThe Solar System

existing giant planets in the Milky Way, and consistent with pastof Earth-like• planets.
if existing gas
withinvirialised
2. OnHowever,
The History
andFutureof Cosmic Planet Formation
to collapse and form stars and planets, the Universe will form
thancurrently
WeS.
show
that this would
imply
at least aPeter
Behroozi,
Molly
Peeples
August2015 exist.
he only civilisation the Universe will ever have, independent ofke Equation. http://jp.arxiv.org/pdf/1508.01202v1

ABSTRACTellites: terrestrial planets, planetsand satellites: gaseous planets,

We combine constraints on galaxy formation histories with planet formation models, yielding
the Earth-like and giant planet formation histories of the Milky Way and the Universe asa whole. In the Hubble Volume (1013 Mpc3 ), we expect there to be ⇠ 1020 Earth-like and⇠ 1020 giant planets; our own galaxy is expected to host ⇠ 109 and ⇠ 1010 Earth-like and giant
planets,
respectively.
thresholds for planet formation do not significantly
mass function (IMF) is assumed
to follow
Chabrier Proposed(2003) frommetallicity
0.1
to 100 M .
affect these numbers. However, the metallicity dependence for giant planets results in later
typical formation times and larger host galaxies than for Earth-like planets. The Solar Systemformed at the median age for existing giant planets in the Milky Way, and consistent with past
2 METHODOLOGY estimates, formed after 80% of Earth-like planets. However, if existing gas within virialised
darkmattercollapse and form stars and planets, the Universe will form
While planet formation candependon haloes
host starcontinues
mass, new tostars’
10universal
times moreplanets
than currently exist. We show that this would imply at least a
masses are drawn from aovernearlydistribution(Chabrier92%
that weare not
the only civilisation the Universe will ever have, independent of2003). When averaged overan chance
entire galaxy,
the planet
formationarguments
involving
Drakerate,
Equation. 2 Behroozi & Peeples
rate (PFR) is then proportional
to the galaxy’s
startheformation
11

11

Galaxy Stellar Mass [Mo. ]

12

10

9

8

10

[Fe/

H] ≤

0.5

10

9

PFR

(1)

12

PFR

(Z(M⇤ ,t)/Z )aPFR(M⇤ ,t) = n
SFR(M⇤ ,t),hmi⇤
RODUCTION

Galaxy Stellar Mass [Mo. ]Redshift
Redshiftmodified by the PFR’s metallicity dependence. Using a power-law
8 4
0.5
0.2
0
8 4
0.5
0.2
0
2
1
2
1
Key
words:
planetsandsatellites:
terrestrial
andsatellites:
gaseousplanets,
10 planets, planets
10
Earth-like Planets Formed
Giant Planets Formed
parametrisation for this metallicity dependence (see, e.g., Fischer
Per Galaxy Per YearPer Galaxy Per Yeargalaxies:
formation
10
10& Valenti 2005; Gonzalez 2014), we model the planet formation
Milky Way Growth
Milky Way Growth
10
10rate of a galaxy as a function of its stellar mass (M⇤ (t)) and cosmic
time (t):
10
10
100
50
8

10

1
0.01

0.005

-1.5

mass function (IMF) is assumed to follow Chabrier (2003) from 0.1
to 100 M .
where n is the mean number of planets formed per star, a is theimatesoftheplanetformation
history
oftheUniverse
power-law dependence of planet incidence on metallicity, Z(M⇤ ,t)99; isLineweaver
suggestedmetallicity,that the Earthoothe galaxy’s2001)
mean gas-phasehm⇤ i =formed
0.67 M is the
80%meanof otherplanets, evenconsidering
masssimilarof a newly-formed
star when(Chabrier2003), andpoSFR(M⇤ ,t)
2 METHODOLOGY
1
lacticzones
that factors
is habitable
the galaxy’s
star (Lineweaver
formation rateetinal.M2004).
yr Since. Additional
usandsof exoplanets
been
found,andaided
by the Kepler(e.g.,
stellar initialhave
massfunctionsdensities)
influencing the
While planet formation can depend on host star mass, new stars’
PFR arediscussed
Appendix
A. have been made in
Lissauer
et al.
2014). inMany
advancesmasses are drawn from a nearly universal distribution (ChabrierFor giant inplanets(R > 6 R ; including,e.g.,forJupiter andecade, especially
our understandingof how planet2003). When averaged over an entire galaxy, the planet formation
Saturn),metallicity(specifically,
dependence
ependson thethemass
and metallicityof the[Fe/H])
host star(Fischer is longrate (PFR) is then proportional to the galaxy’s star formation rate,established(Fischer&
Valenti2005);
recentestimatessuggest2005; Buchhave et al. 2012; Wang & Fischer 2013; Lismodified by the PFR’s metallicity dependence. Using a power-law
al. 2014; Buchhave et al. 2014; Gonzalez 2014; Reffert
parametrisation for this metallicity dependence (see, e.g., Fischer
12

8

2

4

7

4
6
8
10
Time Since Big Bang [Gyr]2

1

Redshift

0.5

12

0

10

11

.

10

50%

9

10

90%

8

10

[Fe/

7

10

1

2

H] ≤

-1.5

4
6
8
10
Time Since Big Bang [Gyr]0.002

0.0002

Galaxy Stellar Mass [Mo. ]Earth-like Planet Formation
Volume Density

10

10

10

13.8

0.2

PFR·ND

Galaxy Stellar Mass [Mo. ]

10

1

12

1

8

2

4

4
6
8
10
Time Since Big Bang [Gyr]2

1

Redshift

0.5

12

13.8

0.2

0

Giant Planet Formation
Volume Density

11

10

10

.

50%

10

90%

9

10

PFR·ND

7

10

8

10

-5

2×10

0.007
0.0007
-5

7×10

7

12

13.8

10

1

2

4
6
8
10
Time Since Big Bang [Gyr]

12

13.8

Figure 1. Top-left panel: formation rate (in planets/yr) for Earth-like planets as a function of galaxy stellar mass and cosmic time. The dashed line indicatesthe median expected growth history of the Milky Way (Behroozi et al. 2013e). The dot-dashed line indicates [Fe/H]= 1.5, which has been suggested (Johnson& Li 2012) as the threshold metallicity for planet formation. Grey shaded areas indicate where galaxies are not expected to exist in the observable Universe.
Top-right panel: same, for giant planets. Bottom-left panel: Earth-like planet formation rate multiplied by galaxy number density as a function of stellar
mass and cosmic time, i.e., the volume density of planet formation (in planets/yr/comoving Mpc3 /dex). Contours indicate where 50% and 90% of all planet
formation has taken place. The symbol indicates the Milky Way’s stellar mass and age at the formation of the Solar System. Bottom-right panel: same, for
giant planets.

ameron P. M. Bell,1‹ Eric E. Mamajek1‹ and Tim Naylor2‹

partment of Physics & Astronomy, University of Rochester, Rochester, NY 14627, USA• 3. A self-consistent, absolute isochronal age scale for young moving groups inhool of Physics, Universityof Exeter, Exeter EX4 4QL, UK

ABSTRACT・

We present a self-consistent, absolute isochronal age scale for young (!200 Myr), nearby(!100 pc) moving groups in the solar neighbourhood based on homogeneous fitting of semiempirical pre-main-sequence model isochrones using the τ 2 maximum-likelihood fitting statistic of Naylor & Jeffries in the MV , V − J colour–magnitude diagram. The final adopted ages
for the groups are as follows: 149+51−19 Myr for the AB Dor moving group, 24 ± 3 Myr for the+6
β Pic moving group (BPMG), 45+11−7 Myr for the Carina association, 42−4 Myr for the Columba
association, 11 ± 3 Myr for the η Cha cluster, 45 ± 4 Myr for the Tucana–Horologium moving
group (Tuc–Hor), 10 ± 3 Myr for the TW Hya association and 22+4
−3 Myr for the 32 Ori group.
At this stage we are uncomfortable assigning a final, unambiguous age to the Argus associationas our membership list for the association appears to suffer from a high level of contamination,and therefore it remains unclear whether these stars represent a single population of coevalstars. Our isochronal ages for both the BPMG and Tuc–Hor are consistent with recent lithium
depletion boundary (LDB) ages, which unlike isochronal ages, are relatively insensitive tothe choice of low-mass evolutionary models. This consistency between the isochronal and
LDB ages instils confidence that our self-consistent, absolute age scale for young, nearby
moving groups is robust, and hence we suggest that these ages be adopted for future studiesof these groups. Software implementing the methods described in this study is available fromhttp://www.astro.ex.ac.uk/people/timn/tau-squared/.
Key words: techniques: photometric – stars: evolution – Hertzsprung–Russell and colour–
magnitude diagrams – stars: pre-main-sequence – open clusters and associations: general –solar neighbourhood.

I N T RO D U C T I O N

er the past couple of decades, hundreds of young low- andother measurements of dusty debris discs, substellar objects and, ofcourse, extrasolar planets (e.g. Janson et al. 2013; Chauvin et al.
5 et al. 2015).
2015; MacGregor

Downloaded from http://mnras.oxfordjournals.org/ at National Astronomical Observatory of Japan on October 13, 20

the solar neighbourhood
P.August
M. Bell,Ericform
E. 2015
Mamajekand Tim Naylor
epted 2015 AugustCameron
24. Received 2015
19; in original
June 24http://mnras.oxfordjournals.org/content/454/1/593.full.pdf

6arXiv:1508.00798v1 [astr•Laboratoire Lagrange, UMR 7293, Université de Nice Sophia-Antipolis, CNRS, Observatoire de la Côte D’Azur, BP 4229, 06304,
Nice Cedex 4, France
e-mail: Stephane.Lagarde@oca.eu; martin.vannier@unice.fr

4. AMBER/VLTI high spectral resolution observations of the Brγ emitting
8
UJF-Grenoble 1/CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble (IPAG) UMR 5274, 38041 Grenoble, France
regionin HD 98922. A compact disc wind launched from the inner disc region
e-mail: Fabien.Malbet@obs.ujf-grenoble.fr
A.
CarattiGaratti
Received
date; oAccepted
date et al.
http://jp.arxiv.org/pdf/1508.00798v1
ABSTRACT

Context. High angular and spectral resolution observations can provide us with fundamental clues to the complex circumstellar
structure of young stellar objects (YSOs) and to the physical processes taking place close to these sources.
Aims. We analyse the main physical parameters and the circumstellar environment of the young Herbig Be star HD 98922.
Methods. We present AMBER/VLTI high spectral resolution (R=12 000) interferometric observations across the Brγ line, accompanied by UVES high-resolution spectroscopy and SINFONI-AO assisted
near-infrared(NIR) integral field spectroscopic data. To
A&A proofs:
manuscript no. astrophinterpret our observations, we develop a Table
magneto-centrifugally
driven disc-wind model.
1. Log of the VLTI/AMBER/FINITO observations of HD 98922 and calibrators.
Results. Our analysis of the UVES spectrum shows that HD 98922 is a young (∼5×105 yr) Herbig Be star (SpT=B9V), located at
HD 98922
Unit Telescope −7
SpectralWavelength
DIT
N
SeeingBaselines
PAs−1( ṀaccStart)Timeof[UT]End∼(9±3)×10M⊙ yr
a distance of 440±60
Observation
array
mode
range. SINFONI K-band AO-assisted imaging shows a
50 pc, with a mass accretion rate
Date
(µm)
(s)
( )
(m)
( )
spatially resolved circumstellar disc-like region 2012
(∼140
AU
in
diameter)withasymmetricbrightness
distribution.
Our AMBER/VLTI
Dec 2609:02
09:20
UT2-UT3-UT4
HR-K-F2.147-2.194
1100
0.7-0.8
44.1/60.6/89.4
219.3/103/76.7
2013 Feb 28 (ring-fit
04:50
05:32radius
UT2-UT3-UT4
HR-K-F2.147-2.1941540
0.9-1.2
220.9/104.9/78.8 emitting region
UT observations indicate that the Brγ emitting region∼0.31±0.04AU) is1 smaller
than43.9/61/89.4
the continuum(inner dust radius ∼0.7±0.2 AU), showing significant
non-zeroV-shaped
diﬀerential
phases(i.e.
non
S-shaped,
as expected for a
Calibrator
DateTime [UT]UT arraySpectralWavelength
DIT
N
Seeing
Uniform-disc
Name
Start
End
rotating disc). The value of the continuum-corrected
pure Brγ line
visibility
at themodelongestrange
baseline(89 m)
is diameter∼0.8±0.1,
i.e. the Brγ
(µm)
(s)
( )
(mas)
emitting region is partially resolved. Our modellingHD suggests
the observed
Brγ HR-K-F
line-emitting
regionoriginates from a disc60276
2012 Decthat
26
07:50
08:03
UT2-UT3-UT4
2.147-2.194
1200 mainly
0.9-1.0
0.92±0.06
HD 103125
2013 Feb 28
04:08
04:42
UT2-UT3-UT4
1
70
0.9-1.5
0.88±0.06◦−7 HR-K-F −12.147-2.194
wind with a half opening angle of 30 , and with a mass-loss rate ( Ṁw ) of ∼2×10 M⊙ yr . The observed V-shaped diﬀerential phases
are reliably reproduced by combining a simple
asymmetric continuum disc model with our Brγ disc-wind model.
Notes. (a) Detector integration time per interferogram. (b) Number of interferograms. (c) High spectral resolution mode in the K-band using the(d)fringe tracker
UD diameterfrom JMMC Stellar
Diameters
Catalogue- JSDC(Lafrasse
et al. 2010).
HR observationsConclusions.
of the Brγ emitting
regionthe
inBrγ
HDemission
98922
In conclusion,ofFINITO.
HD 98922
cantaken
be modelledwitha discwind
thatis ableto approximately reproduce
all interferometric observations if we assume that the intensity distribution of the dust continuum disc is asymmetric.

theet al.
ectral. The
es per(tart-sky
, and
time
using
FoV)

a

b

c

′′

◦

a

b

c

d

′′

Table 2. HD 98922 stellar and disc parameterslibrary (Husser et al. 2013), which provides high-resolution
Key words. stars: formation – stars:circumstellar
matterstars:
pre-mainsequence – stars: variables: Herbig Ae/Be: individual(R=500 000) synthetic
spectra–basedon thestellar atmospherecode PHOENIX.
The spectral resolution
was then reduced
toobjects: HD 98922 – techniques: interferometric– techniques:
high angularresolution
Stellar Parameter

Value
Referencethat of the UVES observations by convolving the synthetic spec60
tra with a Gaussian profile (IRAF task gauss). We constructedDistance440±50 pc
1
a grid of spectra and varied diﬀerent stellar parameters, namely
T eﬀ
10 400±200 K
1,2
T e f f (from 9000 to 11 000 K, ∆T = 200 K), log g (from 3.0 to
S pT ype
B9V
1,2
4.5, ∆log g = 0.5), and [Fe/H] (from -1 to 1, ∆[Fe/H] = 0.5). Bothlog g
3.5±0.2
1
observed
andsynthetic
spectrawere
thennormalisedtothecon[Fe/H]-0.5±0.2
1
Send oﬀprint requests to: A. Carattitinuum.
o OurGaratti,
e-mail:own IDL programme was used to match the UVES
M∗
5.2±0.2 M⊙
1alessio@cp.dias.ie
spectrum with the best-fitting model in three steps. First, by comR∗
7.6±0.6
1
2 R⊙⋆
paring
the
wings
of
the
Balmerlines
thestellargravitywasinL∗
640±130
L
1⊙
Based on observations collected at the VLT(ESOParanal,Chile)
160
ferred. In this case, Balmer lines from H11 to Hγ were used (the ⊙ age
5×105 yr1with programmes 075.C-0637(A), 083.C-0236(A-D),
090.C-0192(A),Hβ line was excluded
because it is too aﬀected by circumstelMV-1.75±0.3 mag
1
lar emission). Second, the eﬀective temperature (T eﬀ ) of the star
m
6.77
mag
3 number, page 1 of 16
ArticleV
090.C-0378(A) and 090.C-0371(A)was obtained by comparing observed and theoretical equivalentAV
0.3
3widths (EWs) of lines sensitive to T eﬀ , namely the He i lines (at
mK
4.28
4
4026, 4120, 4145, 4470 Å), and the Ti ii line at 4176 Å. Finally,
Fobs (K)/F∗ (K)4.3
1
the metal abundance was inferred by comparing the iron abuni
20◦
5
dances for a well-defined set of Fe i and Fe ii lines. As a result,vrot sin i50±3 km s−1
6
we obtained the stellar eﬀective temperature, gravity, and metalṀacc(9±3)×10−7 M⊙ yr−1
4+1
licity, namely T eﬀ = 10 400±200 K (i.e. spectral type B9V), log g= 3.5±0.2, and [Fe/H] = -0.5±0.2. The best-fitting synthetic References. (1) This work; (2) Thé et al. (1994); (3) Manoj et al.
spectrum, normalised to the stellar continuum, is shown in Fig- (2006); (4) Garcia Lopez et al. (2006); (5) Hales et al. (2014);
ure 2 (red solid line) superimposed on the observed spectrum (6) Alecian et al. (2013);(in black). For comparison, Fig. 2 also shows a normalised syn-・

1. Introduction

Herbig Ae/Be stars are intermediate-mass pre-main-sequencestars (2–10 M ; see e.g. Herbig 1960; Waters & Waelkens 1998).

Fig. 1. UVES/VLT flux-calibrated spectrum of HD 98922.

7

A. Caratti o Garatti et al.: AMBER/VLTI HR observations of the Brγ emitting region in HD 98922

A&A proofs: manuscript no. astroph

Flux
Visibility

Differential Phase [°]Differential Phase [°]Closure Phase [°]Dec. (J2000)

Closure Phase [°]11.7

11.6 -53:22:11.5 11.4

11.3

Visibility

Flux

visibilities of the blue-shifted wings are systematically smaller discs produced by tidal interactions (see e.g. Tuthill et al. 2001;
Carattio Garatti
AMBER/VLTI HR observ
than those of the red-shifted wings. This might indicate that, at Demidova & GrininA.2014;
Marinoet etal.al.:
2015).
A&A proofs: manuscript no. astrophhigh velocities, the red-shifted Brγ emitting region is slighlty
To investigate the origin of the asymmetries in the HD 98922
velocity (LSR) [km/s](LSR) [km/s] one, or that there is a highly disc intensity distribution, we should analyse large- and smallmore compact thanvelocity
the blue-shifted
limit constraint on the spectral
type and
SpT∼M0 and-400 -200
0 mass200 of400-400 -2000
200 400
asymmetric continuum.
scale asymmetries.
M∗ ∼0.5 1.4
M⊙ .
Diﬀerential phases (Φ;lower middle panels of Fig. 4 andAsymmetries on small scales include i) asymmetric inner
To better display the observed brightness asymmetry in the
Observed Spectrum
1.3measure the displacement
Model ofSpectrumA.1)
the line-emitting region with brightness distribution, due to shadowing caused by the vertidisc, the1.3
lower panel of Figure 3 shows an intensity ratio image
that is computedfrom two SINFONI K-band continuum images
respect to the continuum-emitting region. For example, the ac- cally extended structure of the inner rims (which can appear un1.2
1.2(between 2.15 and 2.16 µm) with PAs of 0◦ and 180◦ , respeccuracy
reachable with a 90 m baseline and with Φ ∼10◦ is usually asymmetric if the disc geometry is not exactly face-on;
tively. The
1.1 central unresolved PSF disappears (ratio value ∼1),about
0.14 mas, or 0.06 AU at a distance of 440 pc. Therefore see e.g. Monnier et al. 2006), or ii) brightness peaks and gaps
1.1
whereas the bright NNE arc becomes clearly visible (ratio values
the observed displacements provide us with a very sensitive along the disc azimuthal angle.
between1.0
1.5 and 5) in the image. Apart from the aforementioned
measurementof the gas kinematics on scales of a few stellar
The large scale asymmetry is represented by the diﬀerent
1.0
elongated peak, there is a dip at PA∼0◦ and a second arc-shaped
0.9
peak towards the north-west that is less bright.
radii. For the first time in this object, we detect a clear pho- brightness distribution between the NNE and SSW side of the
It is worth mentioning that the PIONIER/VLTI
reconstructed
PBL 43.9m, PA 220.9°
tocentre shift of theModelBrγPBL
line43.9m,
withPArespect
220.9° to its continuum at disc (whose ratio is about 2.5). This feature is detected at both61.0m,
Model PBL 61.0m, PA 104.9°
images of the HD 98922 inner disc PBL(see
Figure PA
2 in104.9°
Kluska et al.
PBL 89.4m, PA 78.8°
the 61 m and 89 m baselines.
The line
is observed VLTI (AMBER and PIONIER) and SINFONI spatial scales.
Model PBL 89.4m,
PA displacement
78.8°2014), showasimilarbrightness
disc
asymmetry,
namely
the
0.8
0.8
in
diﬀerent
velocity
channels(bothblueandred-shifted).
NoThe diﬀerent emission between forward and backward scatnorth-eastern side of the disc is brighter than the south-western
tably, diﬀerential phases in both blue- and red-shifted channels tering could be the simplest explanation. The fact that the brightside. These interferometric data were acquired between 20 December 2012 and 20 February 2013 (Kluska priv. comm.), sihave the same sign, and therefore they do not exhibit the typ- ness asymmetry lies approximately in the direction of the system
0.6
0.6
multaneouswith our AMBER and SINFONI observations. The
ical “S” shape usually observed in rotating discs. Additionally, axis also supports this hypothesis. On the other hand, this asymobserved PIONIER disc has, however, a size of ∼3-4 mas (∼1the red-shifted channels in both baselines show larger diﬀeren- metry is observed both at large (SINFONI) and small (VLTI)
1.5 AU), which is well within the (spatially unresolved) PSF.
0.4
tial0.4
phases with respect to the blue-shifted ones. Because these scales, and the SINFONI data are likely dominated by scattered
This suggeststhat the disc might have a similar morphology
are line-to-continuum phases, the observed shifts in the diﬀer- light, whereas the VLTI data are possibly dominated by thermalfrom ∼1 to 60-70 AU from the source and that the origin of thisbrightness asymmetry might be the same.
ential phases could be caused by continuum shifts, line shifts, emission. These considerations are in favour of an intrinsic perThe 0.2
Brγ line is the only emission line detected over the Kor 0.2
both. The maximum value of the line/continuum displace- turbation of the disc.
band continuum of the analysed SINFONI spectral-images. Thisment
is 0.02±0.04 mas, 0.14±0.04 mas, and 0.16±0.03 mas for
In principle, disc warping is the most plausible explanation.
emission is not spatially resolved, being enclosed within 60 mas
the0.043.9 m, 61 m, and 89.4 m baselines, respectively.
Recently Demidova & Grinin (2014) modelled the disc asymme(or ∼26 0.0
AU) from the central source.
PBL 43.9m, PA 220.9°PBL
43.9m,that
PA 220.9°
Finally, it is alsoModelworth
notingthe closure phases do not try of LkHa 101 (a Herbig Ae star; see e.g. Tuthill et al. 2001),
60
60
PBL 61.0m, PA 104.9°
Model PBL 61.0m, PA 104.9°
PBL 89.4m, PA 78.8°
Model
PBL
89.4m,
PA
78.8°within the error bars which shows a warped disc. Such asymmetry is very similarshow
anysignificant
deviationfromzero
50 from VLTI/AMBER interferometry and50
5. Results
(see
lower
panels
of
Figs.
4
and
A.1);
we measure an average to that observed in HD98922 (see e.g. Figure 1 in Tuthill et al.
40geometricmodelling40
100 mas
◦
◦
value
of
-0.44
±2.55
.
2001). The warp is generated by the tidal eﬀects of a low-mass
30
30
5.1. Interferometricobservables: Visibilities, differential
companion (with mass ratio q ranging from 0.1 to 0.01) with
20
phases, and closure phase20
its 7.
orbit
slightlyphases
inclinedwiththe disc
TheFig.
Diﬀerential
for thethreerespectobservedtobaselines(as plane.
in Fig. 4),
10
5.2.10Geometric modelling: size of Brγ and continuum
Our VLTI/AMBER
observations provide us with four direct
warp heightvariesas the companion
extracts
matterdisc
outmodelof thecalculated
for
the
best
disc-wind
model
P5
plus:
symmetric
0 namely the Brγ line profile, visibilities, diﬀerenobservables,
0emitting region
mid-planeof thedisc. Thesean azimuthal(a,upper panel),
asymmetricdiscperturbations
model with a generate
counter clockwise(b,tial phases,-10 and closure phases. These observables allow us
panel),ofand(c, lower
disc-wind rotaasymmetry
theclockwise
extinction.
As a panel)
result,disctheandilluminationof theOur-10AMBER high spectral resolution data also provide us withmiddle
toretrieveinformation
about
the
inner-disc
emitting
regionof
Image ratio PA 0/180 deg-20-20
diﬀerential
phases of the first and last baselines are
discForby clarity,
the starthebecomesasymmetric.
HD 98922, in particular the size and kinematics of the Brγ emita measurementof the visibilities for the pure Brγ line-emittingtion.
◦◦+20
andof-20HD, respectively.
-30 as well as its displacement with respect to the con-30 in the diﬀerent spectral channels across the Brγ emissionshifted
ting region,
Inbythecase98922, the SINFONI data exclude theregion31.7
11:22:31.6
tinuum emission.
-40
line-40(see Figure 5). The continuum-corrected line visibilities are presence of a companion as close as ∼20 AU from the cenR.A. (J2000)
First 90of all, we stress that observations in both VLTI runs
tral source down to ∼0.5 M⊙ (see Sect. 4, i.e. q≥0.1). Morefundamental for measuring the size of the Brγ line-emitting re-On
were taken with the same AMBER settings and UT configurathethe
other
hand, it is morediﬃcult to image
estimate
theKluska
accuracy
over,
VLTI/PIONIER
reconstructed(see
et al.
2.1
4.4
0.29
0.87
1.5
2.6
3.2
3.8
5
5.6
6.2
gion.
tions, which result in similar projected baselines and position
135 Within the wavelength region of the Brγ line emission, theof the Ṁw value as inferred from our best-fit model, but it is2014) does not show any evidence of a close binary (up toangles (see Cols. 10 and 11 of Table 1). The results from bothmeasuredvisibility
has
two
components:thepureline-emitting
probably of the same order as the Ṁacc value, owing to the use
45
90
runs are identical inside the error bars. However, those from thea few AUs from the star), but for these data no sensitivity
part and the continuum-emitting part, which includes continuumof
our simplified model of the disc wind and to the uncertainties
second run (28 February 2013) are clearly much less noisy than45
is provided. Indeed, given the VLTI/PIONIER sensitiviemission from both the circumstellar environment and the un-inlimit
the fit of the Brγ line profile and intensity. As a result, their ra- F
those from the first run (26 December 2012) owing to the longer
ties
(see
e.g. Absil et al. 2011), the dynamical range of the re0
resolved
centralstar.
Therefore,
following
Weigeltetal.
(2007),
0
total integration time. For this reason, in this section we only
tio is well within the expected range of values. It should also be (Fig. 3. Upper Panel: SINFONI K-band continuum image (between 2.15
constructedimage
shouldbe loweror theequal
towind100 (Kluska
theemissionline
visibility
V
in
each
spectralchannelcanbepresent
theresultsfromthesecondrun(Figure4),
whereasthose
Brγ
noted that in ourbest-fit
modelof HDthan
98922
disc
starts b-45
and 2.16 µm). Labelled fluxes are in W m−2 µm arcsec−2 . Contour levels
priv.
comm).
This roughly
gives
a lower
limit thatof Hthe∼ wind10.2 magwritten as
are 4, 5, 50, 150, 250, 400, 500, and 1000 σ. Lower Panel: Intensity from the first run are shown in Appendix A (Figure A.1). The
in
the
close
vicinity
of
the
star.
This
can
mean
at v
-45
-90
or Mpartiallyat the as
adopteddistanceof 440ofpc.
Byadopting dratio image of two SINFONI K-band continuum images (between 2.15 diﬀerent panels in Figures 4 and A.1 show (from top to bottom)
H ∼ 2 mag!
least
originatesaresultofinteraction
theaccretionand 2.16 µm) taken at PA of 0◦ and 180◦ , showing the asymmetric disc the Brγ line profile (upper panels), visibilities (middle upper
the Siesset al.
(2000) evolutionary
tracks4), weFBrγ|Ftot Vtot |2 + |Fc Vc |2 − 2 Ftot Vtot Fc Vc · cosΦ, (2)disc-135VBrγ =with themagnetosphere.
In this casethe(seeṀw /Sect.
Ṁacc ratio
canob- remission. Contours show the K-band continuum of the PA=0◦ image panels), diﬀerential phases (middle lower panels), and closure
tain
an
upper
limit
for
the
mass
of
any
undetectedcompanionubehigher
than
that
used
in
the
theoryofthemagneto-centrifugal-90(see upper panel), and give the position of both symmetric PSF in the phases (lower
panels).
-180
proofs:manuscript
astrophwhere
FBrγ2.162
is the 2.164
wavelength-dependent
line2.172
flux, Vtot (Ftot ) isdisc
2.160 2.162 2.164visibilities
2.166 (middle
2.168 2.170
2.172
of ∼0.4–0.5
MA&A
. Our
reasoning
thatoftheof a a2.160
2.166 2.168 2.170
centre, and asymmetric disc emission. Contour levels are as in the con⊙for
The wavelength-dependent
upper panels
wind (0.1),
exampledue toimplies
theno.
eﬀect
the presence
mechanism
tinuum image.
[µm] the Brγ line-profile atthe measured total visibility
low-mass
object(M∗ ≤ (see0.5 M
or a massive
protoplanetcanλ [µm] (flux) in the Brγ line, Vc (F c ) isof
of Fig. 4 and A.1) clearly increaseλacross⊙ ) Illarionov
the magnetic
propellere.g.
& Sunyaev
1975).
Table 3. Disc-windmodel parameters:
range
exploredvalues and orvaluesforobservations.
our best-fit model
all baselines. This indicates that the Brγ emitting region is more
the visibility (flux) in the continuum,and Φ isaccretionthe measured
not be ruled
outofbyboth SINFONI
VLTI
As P5
a
compact
the continuum
emitting
Previous
spectro- resolution of wavelength-diﬀerential phase within the Brγ line.
consequence the hypothesis of a warped disc, originating from 2
Fig. 4.than
AMBER
observationof region.
HD 98922
at spectralFig.
9.
Comparisonofourinterferometricobservations
withtheinter−11−1−2−1
density in our data is ∼5×10 erg s cm µm , which cor- interferometric studies of HD 98922 at medium resolution (R =R=12 000 (28 Feb 2013). From top to bottom: wavelength dependence ferometric
In ouranalysis,derived
we alsothe intrinsic
Brγa verylow-masscompanion (i.e. with mass ratio in the range of H
observables
fromincluded
our best disc-windmodel
P5photoplus 7.
aDiscussion
responds to K ∼ 9.8 mag or MK ∼ 1.6 mag at the estimated 1500) have also detected an increase in the visibility within the
Parameter
Range of Values
Model P5of lineflux,(Kraus
visibilities,
wavelength-diﬀerential
anddisc model.feature
From topbottom,observed
line profile
spheric absorptionof toHD
98922,
using aBrγ
synthetic
spec- 0.1–0.01), still holds.
distance of 440 pc. Adopting the Siess et al. (2000) evolutionary Brγet al. 2008)
with baseline lengthsphases,
up to 60
m. closure phase asymmetrict5◦◦observedatthree
diﬀerent
projected
baselines(seelabelsinfigure).
For(grey)
and
model
line
profile(pink),
observed
visibilities
(grey
dots
with
trum with the spectral type and surface gravity values as in Ta-Half
7.1. opening
An asymmetrictracks and assuming an age of ∼5×10 yr for any possible un- Our HR mode AMBER observations allow us, for the first time,
angle (θ1disc) emission 20 –60
30◦
of thefirst diﬀerent
and last spectral
baselines are shifted error
bars)
and
model
visibilities(colouredlines),
observedandmodel
detected companion, the MK estimate provides us with an upper toclarity,
measurethe
thediﬀerential
visibilities phases
and phasesin ∼30ble 2.
Inner radius - ω1 (R∗ )
2–3 (0.07–0.1 AU) 3 (0.1 AU) o
7.2. Inner circumstellar
structure of
HD 98922
by +30◦ and -30◦ , respectively.
Asymmetries
in the disc brightness
distribution
are not uncom- M
wavelength-diﬀerential
phases,and observed
and model
closuredphase. Outer
The
size
of
the
continuumwasobtained
using
the
AMBER
radius - ωN (R∗ )4–30 (0.13–1 AU) 30 (1 AU)
Article number, page 6 of 16
mon as they havebeen observed at NIR wavelengths in several o
GTO archival data at low resolution. By fitting a circular sym-Acceleration
parameter(β)
3–7
5
Our interferometricobservations
that theBrγ Telescopeline visibilh
HerbigAe/Be stars and
CTTSs withshow
the Hubble
Space
metric Gaussian model, we derived a Gaussian half width at halfMass
loadparameter(γ)
2–5 indicating that
3 the
ities
are
higher
than
those
of
the
continuum,f(HST) or with ground-based
telescopes
through
AO assisted
−1
−8
−7
−7
channels across the Brγ line with baseline lengths up to 90 m, maximum (HWHM) radius of 1.8±0.3 mas (or ∼0.79±0.13 AUMass-loss
Brγ emitting(∼0.3
than K
rate-regionṀw (M⊙isyrlessimaging) extended10(see–3×10
imagingorinterferometrice.g. AU
Kristinetradius)
al.2×102005;
at thea distanceof (see
440 e.g.
pc). Marino
A similarof d)
1.6±0.3
masbe(or the continuum emitting region (∼0.7 AU in radius). The pureproviding a higher spatial and spectral resolution. Furthermore, andouter discet al.value2015);
arcs canDullemond & Monnier 2010). These images of spatially re- i(a)Notes.
See
Weigelt
et al.
(2011)
for Brγ
definition
anddetailedofdescriptionof thelistedmodel
paramet∼0.70±0.13
wasdensity
inferredby fitting
a ringmodel
witha ringour data indicate that the visibilities from the three baselines are also
produced AU)
by dustvariations
andstellocentricgrainline
visibility
HDrange98922
0.8
atdisc-windtheasymmetries,
longestbaselinesolveddiscs
display
a wideof isspectacular
in- c
width
of 20% ofring radius.
slightly asymmetric with respect to the Brγ peak, namely the size
segregation;e) thearcsinnerand rings
can also originate from warped cluding(89 m), arcs
indicating
that
the
Brγ
originatesfromaspatially(e.g. Fukagawa et al. 2006; Krist et al. 2012), gapsex- aand dips phases.
(e.g. Krist
al.other2005), servables
warps (e.g.areGolimowski
et al. wiapproximatively
show a red-shiftedpeakin theOnetthe
Article number,page
7 of diﬀerential
16
Article number, page 12 of 16
hand, it is worth noting that the HD 98922 NIR continuum emis- that V-shaped diﬀerential phases

8Anisotropic Formation of Magnetized Cores in Turbulent Clouds•

Che-YuFormation
Chen1 and Eve
Ostriker1,2
5. Anisotropic
ofC.MagnetizedCores in Turbulent Clouds
Che-Yu Chen and Eve C. Ostriker et al.
cychen@astro.umd.edu, eco@astro.princeton.edu
http://jp.arxiv.org/pdf/1508.02710v1
ABSTRACTIn giant molecular clouds (GMCs), shocks driven by converging turbulent flows
create high-density, strongly-magnetized regions that are locally sheetlike. In previous
work, we showed that within these layers, dense filaments and embedded self-gravitating
cores form by gathering material along the magnetic field lines. Here, we extend theparameter space of our three-dimensional, turbulent MHD core formation simulations.
We confirm the anisotropic core formation model we previously proposed, and quantify
the dependence of median core properties on the pre-shock inflow velocity and upstream
magnetic field strength. Our results suggest that bound core properties are set by the
total dynamic pressure (dominated by large-scale turbulence) and thermal sound speed
cs in GMCs, independent of magnetic field strength. For models with Mach number
between 5 and 20, the median core masses and radii are comparable to the critical
Bonnor-Ebert mass and radius defined using the dynamic pressure for Pext . Our resultscorrespond to Mcore = 1.2cs 4 (G3 ⇢0 v0 2 ) 1/2 and Rcore = 0.34cs 2 (G⇢0 v0 2 ) 1/2 for ⇢0 andv0 the large-scale mean density and velocity. For our parameter range, the median
Mcore ⇠ 0.1 1M , but a very high pressure cloud could have lower characteristic coremass. We find cores and filaments form simultaneously, and filament column densities
are a factor ⇠ 2 greater than the surrounding cloud when cores first collapse. We also
show that cores identified in our simulations have physical properties comparable tothose observed in the Perseus cloud. Superthermal cores in our models are generally
also magnetically supercritical, suggesting that the same may be true in observed clouds.
Subject headings: ISM: magnetic fields — MHD — turbulence — stars: formation

9
1.

Introduction

–4–

Bps

!ps
L
Bps

!ps

Bps

R

L’ = 2R

!fila
R

!’

~

!’

R

Fig. 1.— Schematic of the anisotropic condensation process. The blue region (top left) shows asection of the post-shock layer created by a converging flow. Contraction initially begins along thedirection of the post-shock magnetic field, which is nearly parallel to the post-shock layer. This
contraction is indicated for a cylinder of initial length L and radius R (top right). When the lengthof the cylinder has shrunk to satisfy L0 ⇠ 2R, it can be treated as an isotropic sphere with radiusR, which will collapse if the self-gravity overcomes thermal pressure. Contraction along the postshock magnetic field creates dense filaments, and the densest regions within the filament continue
contracting as quasi-spherical cores (bottom left).

Table 1: Summary of the post-shock properties measured and derived from simulations.
cloud conditions
v0
B0(km/s)(µG)

Model

simulated post-shock properties⇤
nps
B ps
vrms
ps
3
3
(10 cm ) (µG)
(km/s)

corresponding physical scales†
Rmag,sph Mth,sph Rth,sph Lmag,crit
(pc)
(pc)
(pc)
(pc)

Mmag,sph
(pc)

M5B10
M10B10
M20B10

1
2
4

10
10
10

12.1
18.7
32.6

43.0
66.8
121

0.25
0.16
0.09

0.44
0.57
0.79

7.64
12.0
23.5

0.14
0.14
0.14

1.26
1.02
0.77

0.07
0.06
0.05

0.19
0.18
0.19

M10B5
M10B10
M10B20

2
2
2

5
10
20

31.8
18.7
9.89

59.3
66.8
70.9

0.35
0.41
0.16
0.57
–
10
–
0.08
0.98

2.90
12.0
51.3

0.07
0.14
0.28

0.78
1.02
1.40

0.05
0.06
0.08

0.10
0.18
0.37

⇤

Post-shock properties are measured at t = 0.2 Myr in each model, averaged over the whole post-shock layer. The timescale
is chosen so the downstream properties are measured before the post-shock layer becomes strongly self-gravitating.
†See Equations (1) and (11)-(14) for definitions of physical scales.

Increasing Mach number
M5
M10

0.4

M20

0.4

0.3

0.3

0.2

4.

0.75 Myr 0.1

0
0

0
10

0.4

X [pc]

0.6

0.4

0.4

0.3

0.3

22

22

22
22

0.2
0.2
Post-shock
Environment and0.2
Structure
Formation

0.1
0.2

Y [pc]

Y [pc]

Y [pc]

Y [pc]

B10

which uses the largest closed gravitational potential contours around single local minimums as corelog (N/cm-2)
150 µG
boundaries.
We then select the gravitationally bound cores as thosewithnegativet =0.59
Myr,
B *=2000 total energy
1(sum of gravitational,
magnetic, and thermalenergy). It is then straightforward
to measure the 23
t =0.75 Myr, B *=2000
t =0.51 Myr, B *=2000
t =0.4 Myr, B *=2000
1mass and size for each identified
23
1 core.
1
23a core, we first find the plane 23
For the magnetic0.9flux within
0.9that includes the minimum of the
0.9 core’s gravitational potential 0.9
and is perpendicular to the average
0.8
0.8magnetic field direction within0.8the core. This plane separates 0.8
the core into an upper half and a
0.7
22.5
0.7lower half, and we can measure
0.7 the magnetic flux
0.7
core by summing up B · n̂ in 22.5
B through the22.5
22.5
0.6
0.6either the upper or lower half 0.6
of the core surface (see CO14). 0.6The normalized mass-to-magneticp
0.5flux ratio of the core is therefore
0.5
0.5⌘ M/ B · 2⇡ G. 0.5

0.8

0.51 Myr 0.1

4.1.
0.2

21.5

0.1
Post-shock
Layer
0
0.4
0.6
0.8
10
X [pc]

0
0

21.5

0.2

0.2

0.4

0.4

X [pc]

0.40 Myr
0.6

0.6

0.8

0.8

1

1

21.5

21.5

The post-shock results from our simulations are summarized in Table X1.[pc]Similar to CO14, welog (N/
150 µG the post-shock properties at t = 0.2 0Myr, a timescale that is short enough that no coresmeasuredcm-2)
t =0.59 Myr, B *=2000 2
have formed, yet long enough for the post-shock region to1 reach a steady-state solution as derived 23
t =0.6 Myr, B *=2000
t =0.51 Myr, B *=2000
t =0.59 Myr, B *=2000
1in Section 2.1 of CO14. In fact,
1 the23 timescale tsg necessary for
1 the
23 post-shock layer to become 23
0.9
0.9self-gravitating can be derived 0.9
0.9
by considering when the gravitational
weight,Increasing B
B10
0.7

0.6

0.6

Y [pc]

0.5
2

0.8

0.8

2
⇡G⌃ps 2
⇡G (2⇢0 v0.7
0 tsg )
=
, 0.7
22.5
2
2 0.6
0.6

0.5

0.5

Y [pc]

0.7

Y [pc]

0.8

M10

0.8

B20

Y [pc]

B5

(9)

22.5

22.5
22.5

0.5

Although the physical conditions0.4within the post-shock layer do not vary
0.4 much in time during the initial stages
0.4
22
of evolution, its thickness grows (approximately
linearly in time) because mass22is accumulated from the continual 22
0.3
0.3
0.3
22
inflow. The evolution of the layer’s thickness is consistent with the0.3expectation Hps = (2⇢0 v0 /⇢ps )t (see Figure 2).
0.4

0.2

0.2

0.1

0.60 Myr 0.1

0
0

0
10

0.2

0.4

X [pc]

0.6

0.8

0.2

0.2

0.51 Myr 0.1
21.5

0.2

0.4

X [pc]

0.6

0.1

0.8

0
10

0
0

0.2

0.59 Myr
21.5

0.2

0.4

0.4

X [pc]

X [pc]

0.6

10.6pc

0.8

0.8

1

1

Fig. 3.— An example from one of our simulation runs showing the structure formed in the postshock layer (in column density; color map) for models with di↵erent inflow Mach numbers andbackground magnetic fields. Magnetic field directions in the post-shock layer are also shown (pinksegments).

10

21.5

21.5

0.5

M5

0.5

0

0

!0.5

!0.5

!1

!1

!1.5

!1.5

!2

!2

k = 2.83

!2.5
!2.4

– 29 –

el to the magnetic field. This also gives the post-shock column density at/ M1/2 (Equation (25)).

median core mass and radius depend on inflow velocity as Mcore =1
The =mass-radiusrelationshipmeasured. fromour suggests
simulations that(diamonds)
compared with)) 1 Fig.
and13.—
Rcore
0.028 pc
(v0 / (km/s))
Thisthe coretheobservation
results
from
Perseus(asterisks),
using
the
medianvaluesofthebinnedcounts. Forll be, respectively, a factor 0.99 and 0.71 lower than the Bonnor-Ebert
both the simulations and observations, the vertical bars represent the ±25% values in each2 ) bin. The
dius computed
using
the
sound
speed
and
total
dynamical
pressure
(⇢
v
1.96
2.16
0
0
best-fit power laws (dotted lines) are M / R – forfor our simulations.
28 –Perseus, and M / R
ions (19) and (20)). This result is similar to the scaling for characteristic
Padoan et al. (1997), but our measured coefficient is higher by a factor

log Mcore (M☉)

0.5

!2

!1.8

!1.6

!2.4

0.5

0

0

!0.5

!0.5

!1

!1

!1.5

!1.5

!2

!2

k = 2.40
!2.4

0.5

!2.2

!2

!1.8

!1.6

0

0

!0.5

!0.5

!1

!1

!1.5

!1.5

!2

!2

k = 2.58
!2.4

!2.2

!2

!1.8

!1.6

!1.4

!2

!1.8

!1.6

!1.4

B20

k = 2.47
!2.4

0.5

!2.5

!2.2

!2.5

!1.4

M20

k = 2.17

!2.5

!1.4

M10

!2.5

implying that Ncore is not a constant over cores with di↵erent masses and sizes.5 This means that
Table 4: The fitted Mass-size relationship from
it is possible that there is no “universal” core column density, but simply
a weak dependence of
our simulations, Mcore /M = A(Rcore /pc)k .
Ncore on parameters, which is difficult to identify from the present models. For example, the postour simulations
have physical properties
to those observed3 ) very ksimilarA (⇥10R-squareshock column density at theModeltime of corecollapsevaries as Nps/ (n0 v0 )1/2 (see Equation (25)),y et andal. 2010a).
In addition,
we foundsimilardistributionsof density
M5appear±statistical
0.18
0.94
filament column
densities
to33.57
follow
a 2.83similartrend. Ifthemean core column
is alsomultiple of this, (Figure
then
it wouldvary
only
a factorforour models, which all haveM10
2.40 ±
0.23
0.82
ationsanda observations
11).10.28
Webysuggestthat twothe“super-Bonnor3
n0 = in1000
cm andethavevarying areby36.14aprobably
factor four.
We
do indeeda highermean Ncore for
0M20
2.58 ±
0.21
0.86 findby
dentified
Sadavoyal. v(2010b)
notsupportedmagnetic
22 cm 2 ). Further investigations,v0 = 4 km/s (4.8 ⇥ 1022 cm 2B5) compared4.31
to v0 = 12.17
km/s
(3.0
⇥
10
± 0.220.64
llapsegravitationally,
most coreswithtohigh
M/MBE in our simcore
bothobservational and sincecomputational,areneededreachaclearerB20
17.66
2.47 ± 0.12
0.88conclusion.

high

!2.2

B5

!2.2

!2

!1.8

!1.6

!1.4

All

k = 2.17

!2.5
!2.4

!2.2

!2

!1.8

!1.6

!1.4

log Rcore (pc)values, indicating that these cores are magnetically supercritical
All

5

4.45

2.17 ± 0.08

0.81

Composite distribution of cores from di↵erent models show a smaller value of k, and more dispersion, than
individual models.

a composite
mass-radius relation for our simulated prestellar cores comtimescale in our simulations.
n in observations, Mcore / Rcore k with k = 2 2.5 (e.g. Kirk et al. 2013).
2. Filamentary structures formed in the post-shock regions are similar to those found in observed relation
is sometimes interpreted as implying a “universal” core survations, with dense cores embedded within filaments (Figure 3). We measured the filamentsults suggestthat efficiency
there mighta weakofontheformation(FFE) beto bearound dependence
50% (dependent
thecorechoicesurfaceof column density
2
thresholdof filament;2), independent
the pre-shockconditions.
We alsoon coremassTableor radius(Figureof 14).
We alsofind thatthe found thatore / ⇡Rcore
the filament columnk density at the time when cores start to collapse is proportional to the
mass-size relation M / R is larger for individual models with consistentmean post-shock column density; Nfila (tcoll ) ⇡ 1.8N ps (Figure 6).
an the composite from heterogeneous environments (Figure 15).
3. Our velocity space-time diagrams (Figure 4) show clear evidence that the mass-gatheringflows that create cores and filaments are highly anisotropic. Until late times, flow along

Fig. 15.— Scatter plot of Mcore vs. Rcore in di↵erent models (each point represents one core formedin corresponding model), as well as the fitted power-law relationship M / Rk (dashed lines) withthe k values listed on the bottom right of each panel.

11