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
around TMC-1A, as previously reported. In contrast, a more extended structure is detected in C18O, although it isstill elongated with a deconvolved size of 3 3 × 2 2, indicating that C18O traces mainly a ﬂattened envelope2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

4.3. Rotating Disk Models

Aso et al.

observations. The mean position is not measured at low
In the previous section, the detailed analysis velocitiesof the PV(∣ %V ∣  1.2 km s1), where the emission shows
diagram cutting along the disk major axis was presented
extended tostructures, which is unsuitable for this analysis. We
characterize the nature of rotation, which suggests theexistence
also
note that a similar analysis was performed by Yenof a Keplerian disk in the innermost part of the envelope.
this
et al. In(2013).
section, physical conditions of the Keplerian diskareFigure9 shows the mean positions of the PV diagram along
O channel
investigated based on model ﬁttings to the C18themajor axis on a log R  log V diagram. The abscissa
maps. To quantify physical parameters of the disk
aroundshows
the mean positions measured as offset positions from theJ = 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,
Dutrey et al. 1994). When a standard disk model isThecomparedordinate is the relative-projected velocity assuming that theto notewith these observed C18O channel maps, it is importantsystemic
velocity is 6.4 km s1. 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
law index close to the Keplerian law, suggesting that
the C18O
rotation).
Importantly, there seems to be a break point at R ∼
1thought
to where the power changes. We performed a χ2
emission in this range with ∣ %V ∣  2.4 km s is 70–80
AU,arise from the possible Keplerian disk. We intend, therefore,toﬁtting to Figure
9 with a double power model as follows:
ﬁt the channel maps within this velocity range, with rotating
pindisk models.
⎧⎪ Vb ( R Rb )Figure 7. 2D mean positions of the C18O (J = 2–1) emission in TMC-1A.
( R - Rb )
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 )

・

3

elescope Science Institute, Baltimore, MD 21218, USA•
August 2015

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

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. Proposed metallicity thresholds for planet formation do not significantly
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 pastestimates, formed after 80% of Earth-like planets. However, if existing gas within virialised
dark matter haloes continues to collapse and form stars and planets, the Universe will form
over 10 times more planets than currently exist. We show that this would imply at least a
92% chance that we are not the only civilisation the Universe will ever have, independent ofarguments involving the Drake Equation.
Key words: planets and satellites: terrestrial planets, planets and satellites: gaseous planets,
galaxies: formation

RODUCTION

imates of the planet formation history of the Universe
99; Lineweaver 2001) suggested that the Earth formed
80% of other similar planets, even when considering polactic habitable zones (Lineweaver et al. 2004). Since thatusands of exoplanets have been found, aided by the Kepler
Lissauer et al. 2014). Many advances have been made in
ecade, especially in our understanding of how planet forepends on the mass and metallicity of the host star (Fischer
2005; Buchhave et al. 2012; Wang & Fischer 2013; Lisal. 2014; Buchhave et al. 2014; Gonzalez 2014; Reffert

mass function (IMF) is assumed to follow Chabrier (2003) from 0.1
to 100 M .

2

METHODOLOGY

While planet formation can depend on host star mass, new stars’
masses are drawn from a nearly universal distribution (Chabrier2003). When averaged over an entire galaxy, the planet formation
rate (PFR) is then proportional to the galaxy’s star formation rate,
modified by the PFR’s metallicity dependence. Using a power-law
parametrisation for this metallicity dependence (see, e.g., Fischer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
interpret our observations, we develop a magneto-centrifugally driven disc-wind model.
Results. Our analysis of the UVES spectrum shows that HD 98922 is a young (∼5×105 yr) Herbig Be star (SpT=B9V), located at−7−1
a distance of 440±60
50 pc, with a mass accretion rate ( Ṁacc ) of ∼(9±3)×10 M⊙ yr . SINFONI K-band AO-assisted imaging shows aspatially resolved circumstellar disc-like region (∼140 AU in diameter) with asymmetric brightness distribution. Our AMBER/VLTI
UT observations indicate that the Brγ emitting region (ring-fit radius ∼0.31±0.04 AU) is smaller than the continuum emitting region(inner dust radius ∼0.7±0.2 AU), showing significant non-zero V-shaped diﬀerential phases (i.e. non S-shaped, as expected for arotating disc). The value of the continuum-corrected pure Brγ line visibility at the longest baseline (89 m) is ∼0.8±0.1, i.e. the Brγ
emitting region is partially resolved. Our modelling suggests that the observed Brγ line-emitting region mainly originates from a discwind with a half opening angle of 30◦ , and with a mass-loss rate ( Ṁw ) of ∼2×10−7 M⊙ yr−1 . The observed V-shaped diﬀerential phases
are reliably reproduced by combining a simple asymmetric continuum disc model with our Brγ disc-wind model.
HR observationsConclusions.
of the Brγ emitting
regionthe
inBrγ
HDemission
98922 of HD 98922 can be modelled with a disc wind that is able to approximately reproduce
In conclusion,
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)

Key words. stars: formation – stars:circumstellar matter – stars: pre-main sequence – stars: variables: Herbig Ae/Be: individual

objects: HD 98922 – techniques: interferometric – techniques: high angular resolution

・
1. Introduction

Send oﬀprint requests to: A. Caratti o Garatti, e-mail:alessio@cp.dias.ie⋆
Based on observations collected at the VLT (ESO Paranal, Chile)with programmes 075.C-0637(A), 083.C-0236(A-D), 090.C-0192(A),090.C-0378(A) and 090.C-0371(A)Herbig Ae/Be stars are intermediate-mass pre-main-sequencestars (2–10 M⊙ ; see e.g. Herbig 1960; Waters & Waelkens 1998).
Article number, page 1 of 16

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
velocity (LSR) [km/s]

5. Results from VLTI/AMBER interferometry andgeometric modelling

100 mas5.1. Interferometric observables: Visibilities, differential
phases, and closure phase

11.7

Dec. (J2000)

11.6 -53:22:11.5 11.4

11.3

Flux

limit constraint on the spectral
type and
SpT∼M0 and-400 -200
0 mass200 of400M∗ ∼0.5 1.4M⊙ .
To better display the observed brightness asymmetry in thedisc, the1.3
lower panel of Figure 3 shows an intensity ratio image
that is computedfrom two SINFONI K-band continuum images
1.2(between 2.15 and 2.16 µm) with PAs of 0◦ and 180◦ , respectively. The
1.1 central unresolved PSF disappears (ratio value ∼1),
whereas the bright NNE arc becomes clearly visible (ratio values
between1.0
1.5 and 5) in the image. Apart from the aforementioned
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.
It is worth mentioning that the PIONIER/VLTI reconstructed
images of the HD 98922 inner disc (see Figure 2 in Kluska et al.
2014), show a similar brightness disc asymmetry, namely thenorth-eastern side of the disc is brighter than the south-westernside. These interferometric data were acquired between 20 December 2012 and 20 February 2013 (Kluska priv. comm.), simultaneous with our AMBER and SINFONI observations. The
observed PIONIER disc has, however, a size of ∼3-4 mas (∼11.5 AU), which is well within the (spatially unresolved) PSF.
This suggests that the disc might have a similar morphology
from ∼1 to 60-70 AU from the source and that the origin of thisbrightness asymmetry might be the same.
The Brγ line is the only emission line detected over the Kband continuum of the analysed SINFONI spectral-images. Thisemission is not spatially resolved, being enclosed within 60 mas(or ∼26 AU) from the central source.

Image ratio PA 0/180 deg
31.7

11:22:31.6

R.A. (J2000)
0.29

0.87

1.5

2.1

2.6

3.2

3.8

4.4

5

5.6

6.2

Fig. 3. Upper Panel: SINFONI K-band continuum image (between 2.15
and 2.16 µm). Labelled fluxes are in W m−2 µm arcsec−2 . Contour levels
are 4, 5, 50, 150, 250, 400, 500, and 1000 σ. Lower Panel: Intensity
ratio image of two SINFONI K-band continuum images (between 2.15
and 2.16 µm) taken at PA of 0◦ and 180◦ , showing the asymmetric discemission. Contours show the K-band continuum of the PA=0◦ image(see upper panel), and give the position of both symmetric PSF in thecentre, and asymmetric disc emission. Contour levels are as in the continuum image.

−11

−1

−2

−1

density in our data is ∼5×10 erg s cm µm , which corresponds to K ∼ 9.8 mag or MK ∼ 1.6 mag at the estimateddistance of 440 pc. Adopting the Siess et al. (2000) evolutionary
tracks and assuming an age of ∼5×105 yr for any possible undetected companion, the MK estimate provides us with an upper

Our VLTI/AMBER observations provide us with four direct
observables, namely the Brγ line profile, visibilities, diﬀerential phases, and closure phases. These observables allow us
to retrieve information about the inner-disc emitting region of
HD 98922, in particular the size and kinematics of the Brγ emitting region, as well as its displacement with respect to the continuum emission.
First of all, we stress that observations in both VLTI runs
were taken with the same AMBER settings and UT configurations, which result in similar projected baselines and position
angles (see Cols. 10 and 11 of Table 1). The results from bothruns are identical inside the error bars. However, those from thesecond run (28 February 2013) are clearly much less noisy thanthose from the first run (26 December 2012) owing to the longer
total integration time. For this reason, in this section we only
present the results from the second run (Figure 4), whereas thosefrom the first run are shown in Appendix A (Figure A.1). The
diﬀerent panels in Figures 4 and A.1 show (from top to bottom)
the Brγ line profile (upper panels), visibilities (middle upper
panels), diﬀerential phases (middle lower panels), and closure
phases (lower panels).
The wavelength-dependent visibilities (middle upper panelsof Fig. 4 and A.1) clearly increase across the Brγ line-profile atall baselines. This indicates that the Brγ emitting region is morecompact than the continuum emitting region. Previous spectrointerferometric studies of HD 98922 at medium resolution (R =1500) have also detected an increase in the visibility within theBrγ line (Kraus et al. 2008) with baseline lengths up to 60 m.
Our HR mode AMBER observations allow us, for the first time,
to measure the visibilities and phases in ∼30 diﬀerent spectral

A&A proofs: manuscript no. astroph
Table 3. Disc-wind accretion model parameters: range of explored values and values for our best-fit model P5

Parametera
Half opening angle (θ1 )Inner radius - ω1 (R∗ )Outer radius - ωN (R∗ )Acceleration parameter (β)
Mass load parameter (γ)
Mass-loss rate - Ṁw (M⊙ yr−1 )Article number, page 6 of 16

Range of Values

Model P5◦30◦
3 (0.1 AU)
30 (1 AU)53
2×10−7◦

20 –60
2–3 (0.07–0.1 AU)
4–30 (0.13–1 AU)
3–7
2–5
10−8 –3×10−7

Notes. (a) See Weigelt et al. (2011) for definition and detailed description of the listed disc-wind model paramet

8

show a red-shifted peak in the diﬀerential phases. On the other
hand, it is worth noting that the HD 98922 NIR continuum emis-

servables are approximatively wthat V-shaped diﬀerential phases

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

log Mcore (M☉)

0.5

!2.2

!2

!1.8

!1.6

!1.4

M10

B5

k = 2.17

!2.5
!2.4

!2.2

!2

!1.8

!1.6

!1.4

B20

0
!0.5
!1
!1.5
!2

k = 2.40

!2.5
!2.4

0.5

!2.2

!2

!1.8

!1.6

k = 2.47

!1.4

M20

All

0
!0.5
!1
!1.5
!2

k = 2.58

!2.5
!2.4

!2.2

!2

!1.8

!1.6

!1.4

log Rcore (pc)11

k = 2.17