星形成ゼミ
2020/09/04
SFN 334 #8-#14

長谷川哲夫（国立天文台）

1

Institute of Observational Sciences (ARIES), Manora Peak, Nainital, 263002, India.; Instituto Argentino de Radioas5
tronomíaNew(CCT
La Plata,
CONICET;CICPBA;
UNLP), C.C.5,(1894) Villasystem
Elisa, Buenos
Aires, Argentina.;
Indianinsights
intheHII
regionG18.88−0.49:
hub-filamentandaccretingfilaments
334
6
Institute of Technology Gandhinagar Palaj, Gandhinagar, 382355, India.; University of Hyderabad, Hyderabad K. Dewangan1, D. K. Ojha2, Saurabh Sharma3, S. del Palacio4, N. K. Bhadari1,5 and A. Das6
#8 L.
500046,
India.
2020 ApJ 903, 13D
E-mail contact:
lokeshd at prl.res.in

We present an analysis of multi-wavelength observations of an area of 0.27 deg × 0.27 deg around the Galactic H ii
region G18.88−0.49, which is powered by an O-type star (age ∼105 years). The Herschel column density map reveals
a shell-like feature of extension ∼12 pc × 7 pc and mass ∼2.9 ×104 M⊙ around the H ii region; its existence is further
confirmed by the distribution of molecular (12 CO, 13 CO, C18 O, and NH3 ) gas at [60, 70] km s−1 . Four subregions
are studied toward this shell-like feature, and show a mass range of ∼0.8–10.5 ×103 M⊙ . These subregions associatedwith dense gas are dominated by non-thermal pressure and supersonic non-thermal motions. The shell-like feature
is associated with the H ii region, Class I protostars, and a massive protostar candidate, illustrating the ongoingearly phases of star formation (including massive stars). The massive protostar is found toward the position of the
6.7 GHz methanol maser, and is associated with outflow activity. Five parsec-scale filaments are identified in thecolumn density and molecular maps, and appear to be radially directed to the dense parts of the shell-like feature.
This configuration is referred to as a “hub-filament" system. Significant velocity gradients (0.8–1.8 km s−1 pc−1 ) are
observed along each filament, suggesting that the molecular gas flows towards the central hub along the filaments.
Overall, our observational findings favor a global non-isotropic collapse scenario as discussed in Motte et al. (2018),
which can explain the observed morphology and star formation in and around G18.88−0.49.
4
L. K. Dewangan et al.
Acceptedby The Astrophysical Journal
https://arxiv.org/pdf/2009.05249.pdf

Table 1
List of di↵erent surveys utilized in this paper.

The
cloudsSurvey structure and characteristic scales of molecular
Wavelength/Frequency/line(s)Resolution (00 )Reference

Multi-Array Galactic
Plane Imaging Survey 1
203cm⇠6
Helfand
2 et al. (2006)
Sami
Dib1 , Sylvain
Bontemps(MAGPIS), Nicola Schneider2 , Davide Elia
, Volker Ossenkopf-Okada, Mohsen
The HI/OH/Recombinationline
survey
of
the
inner
Milky
Way
(THOR)
1–2
GHz⇠25
Beuther
et al. (2016) 9
4
5
6
7
8
Shadmehri
Doris
Arzoumanian , Frédérique Motte , Mark Heyer
NRAO VLA Sky ,Survey(NVSS)
21 cm, Åke Nordlund⇠45 and Bilal
CondonLadjelate
et al. (1998)
12
CO, 13 CO, C18 O (J = 1–0)
⇠20
Umemoto et al. (2017)
1FUGIN survey
Laboratoired’AstrophysiquedeBordeaux,
UniversitédeBordeaux,
CNRS, B18N, alléeGeoﬀroySaint-Hilaire,
APEX Telescope Large Area Survey of the Galaxy (ATLASGAL)
870 µm⇠19.2
Schuller et al. (2009)2
333615,
France;PlaneI. Survey
Physikalisches
Zülpicher
Straße 77,50937 Köln,
Herschel Pessac,
Infrared Galactic(Hi-GAL) Institut, Universität zu Köln,70–500µm⇠5.8–37
MolinariGermany;et al. (2010a)
4 et al. (2005)
Spitzer MIPS
Inner GalacticePlane
Survey (MIPSGAL)
24 µm 100, Roma, 00133,⇠6
Carey
Istitutodi Astrofisica
Planetologia
Spazialli, INAF, via Fosso del Cavaliere
Italy;
Department
Spitzer Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE)
3.6–8.0 µm⇠2Benjaminet al. (2003)
5of Physics, Faculty of Sciences, Golestan University, Gorgan 49138-15739, Iran; nstituto de Astrofísica e Ciências
theH ii regions
are uniform
sphericallyFigure 3a shows
the Portugal;
Herschel 6temperature
do Espaço,
Universidade
doand
Porto,
CAUP, symmetric.
Rua das Estrelas, PT4150-762,
Porto,
Institut de (TPlanétologied ) map
2
7
THOR surveyde
providessix radio
continuum
mapsAlpes,of CNRS,our selected
targetarea aroundG18.88 of0.49.
We
etThed’Astrophysique
Grenoble,
Université
Grenoble
Grenoble,
France;Department
Astronomy,
8find the presence of warm dust emission (T = 23.5–
at 1–2 GHz (beam size ⇠2500 ; noise level ⇠0.3–1 mJy

Hub-filament system in the HII region G18.88-0.49

11

距離 ~5.0 kpc
W39 HII region complex の一部

IRDC
G18.937−0.434

MIR bubbles

G18.88−0.49
SDC18.888−0.476

Figure 1. a) The panel shows a large-scale view of the complex W39 (selected area ⇠ 1 .2 ⇥ 1 .2 centered at l = 19 .176; b = 0 .333)
using the Herschel 70 µm continuum image. The MAGPIS 20 cm continuum contour (in cyan) is also overplotted with a level of 3.0 mJy
beam 1 . The ATLASGAL dust continuum clumps at 870 µm (from Urquhart et al. 2018) are also overlaid on the Herschel image (seehexagon symbols). An asterisk refers to the position of the exciting star(s) (l = 19 .025; b = 0 .38), which was previously reported by
Kerton et al. (2013) (see also Li et al. 2019). The dotted-dashed box (in yellow) encompasses the area shown in Figure 1b, which is thetarget area of this paper. The scale bar referring to 15 pc (at a distance of 5.0 kpc) is shown. b) Three color-composite map (Spitzer 24 µm(red), 8.0 µm (green), and 3.6 µm (blue) images in log scale) of an area (⇠0 .27 ⇥ 0 .27 centered at l = 18 .857; b = 0 .469) containing
the H ii regions G18.88 0.49 and G18.937 0.434. The position of the H ii region G18.937 0.434 is obtained from Anderson et al. (2011),
while the position of the H ii region G18.88 0.49 is taken from Lockman (1989) (see blue crosses). The scale bar referring to 5 pc (at adistance of 5.0 kpc) is shown. Dashed arrows show the locations of the IRDCs, while solid arrows and dashed circles highlight two MIR
bubbles. The positions of a water maser and a 6.7 GHz methanol maser are marked by an upside down triangle and a star, respectively.

Hub-filament system in the HII region G18.88-0.49

13

Herschel

16

L. K. Dewangan et al.

“Edge-DoG”処理

FUGIN

hub−filament system
fo

o1
i2
n2

j1

k1

o2

k2
l2 m2

l1

fk

j2
n1

fn

fl

i1

m1
Hub-filament system in the HII region G18.88-0.49
0

2

4

6

8

10

2

4

6

8

10

0

fo

fk
A

t3

B

t9

t7

fl

D

t5

t4

3

5

7

9

Hub-filament system in the HII region G18.88-0.49

00a) 1 k

2

4

7

9

11

14

K

1

3

k2

c8
11 c9

c10 c6
c13 j2
c7

2

4

6

8

10

7

9

j1

j2

c2
c4
c5

c1
c3

0

K

d)

1

3

5

7

9

11

fn

fm

11

k2

l1

l2

l2

12

0

f)

2

5

7

10

12

15

K

f)

m2

m1

j2

5

e)

e)

j1

c12
9

7

l1

m2

m1

0

i2

5

k1

K

b)

i1

14

d)

19

13

11

Figure 6. a) FUGIN integrated intensity (or moment-0) map of 13 CO (see also Figure 5b). Seven solid lines represent the axes (i.e.,“i1–i2”, “j1–j2”, “k1–k2”, “l1–l2”, “m1–m2”, “n1–n2”, and “o1–o2”), where position-velocity diagrams are extracted in Figures 9a– 9g.
The dotted box (in white) encompasses the area shown in Figure 6b. b) Overlay of the positions of NH3 emission (see plus symbols;from Li et al. 2019) on a two color-composite map (moment-0 map of 13 CO (red) and 1950 MHz (green) images). The moment-0 map of
13 CO is processed through an “Edge-DoG” algorithm. c) The panel shows a hub-filament system around the H ii region G18.88 0.49 aspresented in Figure 3d. The panel also displays the positions of Class I YSOs (filled circles), flat-spectrum sources (filled diamonds), and0
2 We 4
6 Class
8 I YSOs
10 and1202using the
5 Spitzer
7 photometric
10
12 data15(seethe ATLASGAL clumps (empty hexagons).
identified
flat-spectrum sources
K details). A shell-like feature is shown by a filled tomato
Figure 10 and also text for more
K contour at N (H2 ) = 21 ⇥ 1021 cm 2 , and a filledcyan contour at N (H2 ) = 26.4 ⇥ 1021 cm 2 highlights four subregions. In each panel, the scale bar is the same as in Figure 1b. In panels“a” and “b”, the position of a 6.7 GHz methanol maser is marked by a star.

k1

pc
m/s/

3

fl

0

11

9

K

c)

K

1

fo
i2

fm

Figure 3. a) Herschel temperature map. A solid contour (in black) is shown at Td = 23.7 K in the figure. b) Herschel column density(N (H2 )) map. Filamentary structures are traced in the column density map at a contour level of 14.1 ⇥ 1021 cm 2 (white contour). A
solid contour (in black), at N (H2 ) = 21 ⇥ 1021 cm 2 , traces a shell-like feature in the figure. c) Overlay of the N (H2 ) contours on a
two color-composite map (8.0 µm (red) and 1950 MHz (green) images). A dotted-dashed contour (in yellow) is drawn at N (H2 ) = 14.1 ⇥1021 cm 2 . A solid white contour at N (H2 ) = 26.4 ⇥ 1021 cm 2 highlights the four subregions, A, B, C, and D. d) The panel shows ahub-filament system around the H ii region G18.88 0.49. A filled contour displays the shell-like feature at N (H2 ) = 21 ⇥ 1021 cm 2 . A
solid contour (in spring green) at N (H2 ) = 26.4 ⇥ 1021 cm 2 shows the four subregions as labeled in Figure 3c. Five filaments seen in the
Herschel column density map are highlighted by solid lines (fk, fl, fm, fn, and fo), and are also labeled in the figure. Nine small regions (t1to t9) are also indicated by boxes in the figure, where molecular spectra are extracted (see Figure 4). In each panel, the scale bar, star,and crosses are the same as in Figure 1b.

10

c11

c)

1

7

c16

14

c17

Kj1

i2

i1
t6 fn
0

8

11

fk

t1

K

6

9

c15

t2

4

7

b) i1

0

C

2

4

4

c14

G18.88−0.49

0

2

K

a) 1 km/s/pc

2

b)

13

K

t8
G18.937−0.434

0K
hub−filament system
19a) 1 km/s/pc
Hub-filament system in the HII region G18.88-0.49

0

19

13

K

hub−filament system

fm

2

5

7

10

12

n1

n2

15

K

n2

n1
g)

0

1

3

5

7

9

0

11

1

3

5

7

9

11

d)

c)

k2

k1

0

2

4

6

8

10

2

5

7

10

12

15

0

FUGINo113CO

g)

l2

l1

12

0

K

K

K

2

5

7

o1

o2

o2

Figure 9. Position-velocity diagrams along the axes a) “i1–i2”, b) “j1–j2”, c) “k1–k2”, d) “l1–l2”, e) “m1–m2”, f) “n1–n2”, and g)“o1–o2” as marked in Figure 6a. In each panel, a horizontal dotted-dashed line is shown at Vlsr = 65 km s 1 , and a reference bar at 1 kms 1 pc 1 is also drawn to facilitate the tracing of velocity gradients.

10 Figure
12 9. 15Position-velocity diagrams along the axes a) “i1–i2”, b) “j1–j2”, c) “k1–k2”, d) “l1–l2”, e) “m1–m2”, f) “n1–n2”, and g)ARI

24 August 2018

12:52

Protostar
growing instellar mass

5

Time

6
HII region

ProtostellarProtaccretion
accr

Inflows

IR-quiet high-mass protostar

Protostellar
tostellar
core

Outflow

UV

Low-massstellar embryo

UV

HII region

Ionization,
expansion

HII REGION PHASE (~105–106 years)

HIGH-MASS PROTOSTELLAR PHASE (~3 × 105 years)

ProtostellarProtaccretion
accr

Inflows

IR-bright high-mass protostar

Starless MDC phase (~10 years)
Intermittent
gas inflows

High-massstellar embryo

HII REGION PHASE (~105–106 years)

Ionization,
expansion
64

Motte

Bontemps

LouvetSchematic evolutionary diagram proposed for the formation of high-mass stars. ! Massive filaments and spherical clumps, calledridges and hubs, host MDCs (0.1 pc) forming high-mass stars. " During their starless phase, MDCs only harbor low-mass prestellar
cores. # IR-quiet MDCs become protostellar when hosting a stellar embryo of low mass. The local, 0.02 pc, protostellar collapse isaccompanied by the global, 0.1–1 pc, collapse of MDCs and ridges/hubs. $ Protostellar envelopes feed from these gravitationallydriven inflows, leading to the formation of high-mass protostars. The latter are IR-quiet as long as their stellar embryos remain low inmass. % High-mass protostars become IR-bright for stellar embryos with mass larger than 8 M⊙ . & The main accretion phaseterminates when the stellar UV field ionizes the protostellar envelope and an HII region develops. Adapted from Tigé et al. (2017) withpermission. Abbreviation: MDC, massive dense core.

Protostar
growing instellar mass

6

High-massstellar embryo

OB starcluster

MDC

0.02 pc

MASSIVE DENSE CORE PHASES

IR-bright high-mass protostarRidgeor hubProtostellar MDC phase

0.01–10 pc

Low-mass
prestellar core

Intermittent
gas inflows

5

Low-massstellar embryo

Outflow

Protostellar
tostellar
coreIR-quiet high-mass protostar

4

Figure 8

MDC

Massive dense
core (MDC)

Low-mass
prestellar core3

Protostellar MDC phase

Starless MDC phase (~10 years)

Massive dense
core (MDC)

4

OB starcluster

4

2

Ridge
or hub0.1 pc4

1–10 pc

MASSIVE DENSE CORE PHASES

1–10 pc

MDC

Molecular cloud complex

MDC

0.02 pc

Figure 8
3

Molecular cloud complex

Time

1

HIGH-MASS PROTOSTELLAR PHASE (~3 × 105 years)

Annu. Rev. Astron. Astrophys. 2018.56:41-82. Downloaded from www.annualreviews.org
Access provided by Kokuritsu-Tenmondai Libr. - National Observatory of Japan on 03/24/20. For personal use only.

AA56CH02_Motte

2

Time

0.01–10 pc

1Annu. Rev. Astron. Astrophys. 2018.56:41-82. Downloaded from www.annualreviews.org
Access provided by Kokuritsu-Tenmondai Libr. - National Observatory of Japan on 03/24/20. For personal use only.

Motte+2018

Time

0.1 pc参考et d’Astrophysique de Grenoble, Université Grenoble Alpes, CNRS, Grenoble, France; 7 Department of Astronomy,
8
University
Massachusetts,
Amherst, MA 01003,
Centre clouds
for Star and Planet Formation, the Niels Bohr
Theofstructure
and characteristic
scales USA;of molecular
335
Institute and the1 Natural History 1Museum of Denmark,
University
2
3 of Copenhagen, Øster2 Voldgade 5-7, DK-1350,
4Sami
9 Dib , Sylvain Bontemps , Nicola Schneider , Davide Elia , Volker Ossenkopf-Okada , Mohsen Shadmehri ,#9Denmark; Instituto de Radioastronomía Milimétrica, IRAM Avenida Divina Pastora 7, Local 20, 18012, Granada,
5
6
7
8
9
Spain Doris Arzoumanian , Frédérique Motte , Mark Heyer , Åke Nordlund and Bilal Ladjelate
2020 A&A 642, A177

E-mail contact: sami.dib at gmail.com
The structure of molecular clouds holds important clues on the physical processes that lead to their formation andsubsequent dynamical evolution. While it is well established that turbulence imprints a self-similar structure to theclouds, other processes, such as gravity and stellar feedback, can break their scale-free nature. The break of selfsimilarity can manifest itself in the existence of characteristic scales that stand out from the underlying structure
generated by turbulent motions. In this work, we investigate the structure of the Cygnus-X North and the Polaris
Flare molecular clouds which represent two extremes in termsof their star formation activity. We characterize the11
structure of the clouds using the delta-variance (∆-variance) spectrum. In the Polaris Flare, the structure of the cloudis self-similar over more than one order of magnitude in spatial scales. In contrast, the ∆-variance spectrum of CygnusX North exhibits an excess and a plateau on physical scales of ≈ 0.5 − 1.2 pc. In order to explain the observations
for Cygnus-X North, we use synthetic maps in which we overlay populations of discrete structures on top of a fractal
Brownian motion (fBm) image. The properties of these structures such as their major axis sizes, aspect ratios, andcolumn density contrasts with the fBm image are randomly drawn from parameterized distribution functions. We areable to show that under plausible assumptions, it is possible to reproduce a ∆-variance spectrum that resembles theone of the Cygnus-X North region. We also use a "reverse engineering" approach in which we extract the compact
structures in the Cygnus-X North cloud and re-inject them on an fBm map. The calculated ∆-variance spectrum using
this approach deviates from the observations and is an indication that the range of characteristic scales (≈ 0.5 − 1.2pc) observed in Cygnus-X North is not only due to the existence of compact sources, but is a signature of the whole
population of structures that exist in the cloud, including more extended and elongated structures
Accepted by Astronomy & Astrophysics
https://ui.adsabs.harvard.edu/pdf/2020arXiv200708533D/abstract

The First Extensive Spectroscopic Study of Young Stars in the North America andPelican Nebulae Region
Min Fang1 , Lynne A. Hillenbrand1 , Jinyoung Serena Kim2 , Krzysztof Findeisen3, Gregory J. Herczeg4 ,6John M. Carpenter5 , Luisa M. Rebull6 and Hongchi Wang7

S. Dib et al.: Characteristic scales in molecular clouds

Fig. 1. Column density maps of the Cygnus-X North cloud (left) and the Polaris Flare cloud (right). Column densities are displayed in units of thevisual extinction using the conversion NH2 /AV = 0.94 ⇥ 1021 cm 2 .

Fig. 2. Column density distribution function in the Cygnus-X North cloud (left panel) and the Polaris Flare cloud (right panel). The full red lines
in both panels show a fit by a lognormal function in the low column density regime (.5 ⇥ 1021 cm 2 in Cygnus-X North and .1 ⇥ 1021 cm2 in
Polaris). The dashed line is a fit to the power-law regime that is observed in both regions in the intermediate column density regime, while thetriple-dot dashed red line in the case of the Cygnus-X North region is a fit to the shallower power law in the high column density regime.

ments or clumps) and the second, shallower PLT to the collapseof dense cores.

4. Analysis: the -variance method
We quantified the structure of molecular clouds using the variance method. The method was originally introduced in
Stutzki et al. (1998) and Zielinsky & Stützki (1999) and is a generalization of the Allan variance (Allan 1966). In this work, weused an improved version of the method presented in Ossenkopf
et al. (2008a)2 .
Here, we briefly present a summary of the main steps andcharacteristics of the method. For a 2D field A(x, y), the variance on a scale L is defined as being the variance of the
convolution of A with a filter function L such that
2

(L) =

1
h(A ⇤
2⇡

2
L ) i x,y .

(1)

For the filter function, Ossenkopf et al. (2008a) recommend
the use of a “Mexican hat” that is defined as
" 2
#
r2
r
r2
4 (L/2)4222ee (vL/2)e (L/2) ,(2)
L (r) =⇡L2
⇡L2 (v2 1)
where the two terms on the right side of Eq. (2) represent the core
and the annulus of the Mexican hat function, respectively, and v
is the ratio of their diameters (we used v = 1.5). For a faster andmore efficient computation of Eq. (1), Ossenkopf et al. (2008a)
performed the calculation as a multiplication in Fourier space,
and thus, the -variance is given by
Z Z
1
2
(L) =
P | ¯ L |2 dk x dky ,(3)2⇡
where P is the power spectrum of A and ¯ L is the Fourier transform of the filter function. If P can be described by a power law,and if is the exponent of the power spectrum, then a relation
exists between the exponent of the power law that describes the-variance (↵) and (Stutzki et al. 1998), and this is given by
2(L) / L↵ / L

2

.

(4)

& Mac
2009;
andLow
thus,2002;
the Federrath-varianceetisal.
given
byBertram et al. 2015).
In most cases, theZ -variancehas
beenused to investigate theZself-similar
natureofthecloudsandexaminewhether the slope
1
2=
Pself-similar(3)| ¯ L |2 dk x dkregimey,of the (L)-varianceinthevariesfrom cloud2⇡
to cloud and, in the case of simulations, whether it depends
on theproperties
the turbulent
motions
that¯ Laregenerated
where
P is theofpower
spectrumof A andis theFourier transin theformclouds.
However,ithasalready
been
demonstratedof the filter function. If P can be described by athat
power law,
the methodof detecting
breakpoints.
Ossenkopf
and if is iscapable
the exponentof thepower
spectrum,then &a relation
Mac Low 2002 found, when applying the method to numeriexists between the exponent of the power law that describes thecal models of molecular clouds where turbulence is driven on-variance (↵) and (Stutzki et al. 1998), and this is given byvarious physical scales, that the -variance departs from the selfsimilar2 regime on
physicalscales where turbulence is injected
2/ L↵Using/ L extinction.
(4)
into the (L)clouds.
maps, Schneider et al. (2011)
found that low-mass star-forming clouds have a double-peakof ↵ caninferred fromthe rangeof spatial
structure The
in thevalue-variancewith becharacteristic
size scales
aroundscalesover
which
the that-variance
displays
a self-similar⇡1 and⇡4 pc.
They
proposethe physicalprocess
governing behavior
and
can
be
tied
to
the
value
of
.
The
bars of thestructure formation could be the scale at which eithererror
a large-variance shockon a given
are computed
the counting
scale supernova
or an scale
expanding
H II regionfrom
sweeping
error
determinedbythefinitenumberofstatisticallyindependent
through the diffuse medium are broken at dense clouds, which
the filtered
map and the variance of the variturnsmeasurements
the well-orderedinvelocity
into turbulence.

ances (i.e., the fourth moment of the filtered map). Characteristic
scales are
scales atofwhich
there isNortha breakof Polaris
the self-similarity
5. Spatial
structure
Cygnus-X
andand which show up in the -variance spectra as break points,
We applied-variancepoints.
methodAnyto theunderlying
column density
maps ofbehavior
peaks,theor inflection
self-similar
Cygnus-X
North
andPolaris.
As
statedabove,
thesetwoof the cloud can be entirely perturbed on many regions
or all physicalwere scales
selected
becauseare ofsignificantly
both
if thereis atheyvariety
structures different,
that coexist
in in
the cloud.
termsTheof theircolumndensity
distribution(i.e.,
Fig.
2)
and
their
-variance has been employed to analyze the structure ofstar formation
activity. While
Polarisofobserved molecular
clouds(e.g., harbors
Bensch aetpopulation
al. 2001; Campeggio
starless cores, it is still a region with no ongoing star formation
et al. 2004; Sun et al. 2006; Ossenkopf et al. 2008b; Rowles
and a modest contrast in column density. On the other hand, the& Froebrich 2011; Schneider et al. 2011; Russeil et al. 2013;
Cygnus-X North cloud is a region with a much higher star forElia
al. a2014)
wellcontrast
as simulated
molecularmationrateetandmuch aslargerin column
densities clouds(see (e.g.,
Fig. 2,et al. for2012;calculating
Schneider ettheal. 2016b).
The can be
2 alsoThe Hennemann
IDL package-variance-variance
spectraforbothcloudsaredisplayed
in
Fig.
3.
The
found at https://hera.ph1.uni-koeln.de/~ossk/Myself/-variance
spectrumof
Polarisdisplaysaself-similar
behavdeltavariance.html
ior above the resolution limit, and this self-similarity extends
for more
A177,than
pageone4 of order
18 of magnitude in spatial scales (from⇡0.03 to ⇡0.6 pc). A power-law fit to the -variance of Polaris in
the range [0.035–0.6] pc yields a value of the power-law exponent of ↵ = 0.4 ± 0.003, and this implies a value of = 2.4.
On scales larger than 0.6 pc, the self-similarity is perturbed,
possibly due to the existence of a large filamentary structure

Cyg
mat
Fig
-v
-v
ior
for
⇡0.
the
nen
On
pos
(i.e
the
Pol
tech
Oka
larg
line
whe
rou
tion
and
in t
low
spe
den
reso
incr
dep
spe

play

star formation activity. While Polaris harbors a population ofstarless cores, it is still a region with no ongoing star formation
and a modest contrast in column density. On the other hand, theCygnus-X North cloud is a region with a much higher star formation rate and a muchlarger contrast in column densities (seec etpFig. 2, also Hennemannal. 2012; Schneider et al. 2016b). The
0.6for both clouds are displayed in Fig. 3. The-variance spectra
3-variance
0.0spectrum of Polaris displays a self-similar behavr
where P is the power spectrum of A and ¯ L is the Fourier trans- ior abovela the resolution limit, and this self-similarity extends
mi thanform of the filter function. If P can be described by a power law, for-simore
one order of magnitude in spatial scales (fromlf
and if is the exponent of the power spectrum, then a relation Se⇡0.03
to ⇡0.6 pc). A power-law fit to the -variance of Polaris inexists between the exponent of the power law that describes the the range [0.035–0.6] pc yields a value of the power-law expo-variance (↵) and (Stutzki et al. 1998), and this is given bynent of ↵ = 0.4 ± 0.003, and this implies a value of = 2.4.
On scales larger than 0.6 pc, the self-similarity is perturbed,
2 peak↵0.5 - 1.2
Broad(L) / L / L 2 . pc
(4) possibly due to the existence of a large filamentary structure
以前の12CO J=2-1, 13CO J=1-0輝線による研究では(i.e., the MCLD 123.5+24.9 structure), though substructured, in
The value of ↵ can be inferred from the range of spatial
the region.
scale-freenature of the -variance spectrum of
β = The3 - 3.2
だった←空間分解能が不十分であった？
scales over which the -variance displays a self-similar behavPolaris is consistent with earlier findings using the -variance
ior and can be tied to the value of . The error bars of thetechnique for the same cloud (Bensch et al. 2001; Ossenkopf-variance on a given scale are computed from the counting
Okada & Stepanov 2019). However, Bensch et al. (2001) founderror determined by the finite number of statistically independent
larger values of (⇡3 from observations in the 12 CO (J = 2 1)
measurements in the filtered map and the variance of the variline and ⇡ 3.2 from observations in the 13 CO (J = 1 0) line)
ances (i.e., the fourth moment of the filtered map). Characteristic
when the -variance spectrum is fitted over a spatial range that isscales are scales at which there is a break of the self-similarity
roughly
to thedashedone used
this study. The spatial resoluFig. 3. Delta-variance functions
calculatedforthe
Cygnus-X
North
cloud
(left)
andthe
PolarisFlare
cloud(right).similar
The vertical
blackinlines
and which show up in the -variance spectra as break points,tion
the inobservations
they usedin both panels mark the position of the spatial resolution for each of these two regions. The vertical dashedredoflines
the case of Polaris
markarethe2.20 and 0.780 , respectively,
peaks,
orinflection
points.
Anyunderlying
self-similar
behavior
spatial range over which the power-law fit is performed. We do not attempt any fit in Cygnus-X North because
the underlying
regimeofisthe observations presented
and arelower thanself-similar
the resolutionof thecloud can(seebe Sect.
entirelyheavily perturbed by the presenceof structures
6.3). perturbed on many or all physical in this work (⇡0.30 ). Ossenkopf 2002 showed that the use ofscales if there is a variety of structures that coexist in the cloud.
low-J CO isotopologues leads to somewhat steeper -variance
Fig. 14. Examples of synthetic
maps generated
by overlaying
structures(2DofGaussians,
N = 300)
on top of antofBm
image with = 2.4. The
The -variancehas been employed
to analyze
the structure
spectrathans thethe underlying column
resolutionof
limit
black
lines
inmolecularFig. 3) anda broadpeak
atdistribution
ofthe2001;
basicfunctions
propertiesofofthe
fBmaspect
imagesthatoneare correspondingknown
toposobserved
clouds(e.g.,
Benschet al.
Campeggio
properties
the(dashedstructures
are randomly
sampled
from
ratio
(Eq.
(9)),
size
of
the
major
axis (Eq.
density
structure.
Theinclude
exact relative
effect of the lower
spatial(10)), andarounddensity⇡0.5 0.12
pc. A reasonableassumption
make Ossenkopf
isherethat sharesessstructure.
In=a 2.5,
secondstep, wediscrete
et al.(11)).
2004;
Sun
et al.to2006;
et atheal.self-similar
2008b;
Rowlescolumncontrast(Eq.
All
modelsshown
same valuesof resolution,
(L
=
0.025
pc,
L
=
5
pc),
(
f
=
3, fmax = 12),whichc1,min effectively smoothes
1,max the map andmin possibly
the existence of many small-scaledense2011;
structures(e.g., etcores,
structures
specific
an existing fBm& Froebrich
Schneideral. 2011;
Russeilwith
et al.
2013; characteristics on top
00 of ofincreases
thevalues,compared
to
the
role
of
the
opticaland( c,minand= 1,filaments)
3).
Alletsyntheticmaps
areconvolved
witha beamwhose
FWHMof=these
18.2structures.
c,max = inclumps,Cygnus-X
North asaltersandinvestigate
how
the inclusion
impacts theElia
al. 2014)
welltheas underlysimulated molecular
clouds(e.g.,
depths of Lastly,
these molecular
tracershow
in steepening the -varianceing (i.e., primordial) self-similar structure of the gas that had shape of the -variance spectrum.
we investigate
2 The IDL package for calculating thespectrum,
is
not
yet
entirelyclear.
-variance
canbeexisted before these structures formed. However, it remains an the shape of the -variance is modified in the presence of an
Inthatcontrast
to Polaris, theby -varianceof Cygnus-X North disfoundthe atstar-forming
https://hera.ph1.uni-koeln.de/~ossk/Myself/
open question
massiveregionsuchroundish
as entire strucpopulation of structures
are wecharacterizedbottompanel)whether
show athat
existenceof moreIn summary,are shapeable withtodistrishow
that
it is possible to reprodeltavariance.html
plays
a
more
complexasteepslope above the spatial
Cygnus-X North had, at an earlier stage, a spatial distribution bution functions of their sizes, elongations, and column density

Spatial resolution

Spatial resolution

more efficient computation of Eq. (1), Ossenkopf et al. (2008a)
performed the calculation as a multiplication in Fourier space,
and thus, the -variance is given by
Z Z
1
2
(L) =
P | ¯ L |2 dk x dky ,(3)
2⇡

Cygnus Northのスペクトルは、Polaris的な self-similar structure (β = 2.4) の上にsmall-scale dense
structures (e.g., cores, clumps, and filaments) を乗せることで再現できるか？

→ Yes

1. Start from the fractal Brownian motion (fBm)tures image(i.e., larger structures for the same major axis size) results duce -variance spectra that resemble that of the Cygnus-Xof (column) density similarA177,
to thatof 4Polaris.
is a plausible contrasts.
pageof higher
18 Thisspatial
in2.
-variance
spectra
that
peak
at
scales,andassumption
given
that,
prior
to
the
formationofmassivestars
Include discrete structures to investigate
itsthose North region under reasonable assumptions of the size districasesa poor fitintothethe
observationsof Cygnus-X
butions
structures, their aspect ratios, and column density
in thepresent
region, turbulence
Cygnus-X
North cloud,
like in 6.1.North.
Fractal Brownian
motionof
maps
impacts
to intheΔ-variancespectrumPolarisand elsewhere
the ISM,
mustofhave
been
dominatedbyWe
now
exploretheeffectvarying
the distribution
funccontrasts.
Broadly
speaking, reproducing the -variance specshearing motions. Large-scale converging flows may be respon- Fractal Brownian motion images (Peitgen & Saupe 1988) aretion
ofcolumngas
densitycontrast.
Inpresence
addition
to ofthefiducial
trum ofofthe
3.
Δ-variancespectrumin theoften
used as a surrogate
ISMCygnus-X
maps thanksNorthto theirregion
visual requires a size distribution
sible
fortheaggregatingin specificregions
thatwould be the
case
with
=
2.5,
we
constructedsynthetic
maps
with
=
2
that
is
steeper
than
the
size
distributionof structures detected inparental
structuresof ridges and hubs.
Compressive motions
due similarity with cloud features (e.g., Stutzki et al. 1998; Bensch
entirepopulationofstructurescharacterized
et
al.
2001;
Miville-Deschênes
et
al.
2003;
Elia
et
al.
2014,
2018).
to feedback
stars in specificregions of Cygnus-Xand= 3.from
Wemassive
also generated
additional
maps in which the CO surveys, such as the HCS survey, and shallower than the one
full description of their analytic properties is presented inNorthcandistribution
also modify the spatial
distribution
oftheirthe (column)
byfunctionsofvalueof is fixed to 2.5 and varied the valuessizes,of the Alower
and inferred from the Hi-GAL submm survey. We also show that thedensity field. However, massive star formation is localized in Stutzki et al. (1998). Here, we simply review their basic propupper
limitsonthecolumndensitycontrast,.
We
consideredobservations
arepower
bestspectrum
fitted when
are allowed to haveelongations,andcolumndensitycontrasts
Cygnus-X North and not distributed across the entire ccloud erties. Firstly, theirradially averaged
exhibitsstructuresa(Beerer
et al.
We1,speculate
here
the underlying,“pri- earlier)power-law
behavior
with anratios
exponent
E +predominantly
2H, where E is the &3.
cases
with
( 2010).
3;thatfiducial
case shown
andaspectthat=arec,min =
c,max =
mordial,”North
cloud(resembled
that
Euclidiandimension (E = 2 for 2D images) and H is the Hurst
cases
withstructure( c,minin=the1,Cygnus-X
=
5)
and
=
1,
=
10).
c,max
c,min
c,max

where NG is the added column density of the 2D Gaussian structure, Npeak is its peak value, x0 and y0 are the coordinates of thepeak, and the terms a, b, and c are given by:cos2 (✓) sin2 (✓)
+
2 21
2 22
sin(2✓) sin(2✓)
b=
4 21
4 22

S. Dib et al.: Characteristic scales in molecular cloudsa=c=

sin2 (✓) cos2 (✓)
+
.
2 21
2 22

(8)

In Eq. (8), 1 and 2 are the standard deviations of the 2D
Gaussian along the major and minor axes, respectively, and ✓is the angle between the Gaussian function major axis and thex-axis, defined in the counterclockwise direction. We generated
a very large number of synthetic maps on which we superimposed one or several 2D Gaussian structures over fBm images ina controlled manner. All fBm images have a value of = 2.4,
similar to the value found in the Polaris cloud, and a resolutionof 1000 ⇥ 1000 pixels. For individual structures, we varied the
aspect ratio of the 2D Gaussian, f = ( 1 / 2 ), over a range of 1
to 10. The peak value of the 2D Gaussians is expressed in termsof the mean value of the fBm image, Npeak = c hNfBm i, and theFig.column
4. fBm images= 2.5between
and withthe
resolutions
2502D
⇥ 250
pixdensitywith
contrast
peak ofofthe
Gaussianels and(top theleft),mean
500 ⇥value
500 pixels
right),
andvaried
1000 ⇥between
1000 pixelsof the(top
fBm,
1 and
c , is(bottomleft).
Theexplored-variance
three cases
are compared
10. Wealso
thespectra
effectforof allvarying
the absolute
size ofin thebottom-rightsubpanel.
All
displayaself-similar
regimewith
an as
the Gaussian function with respect to the image size, as well
exponentof thelaw of↵=2 (i.e., Eq.functions(4)). All inmaps
the effectof power
includingmultiple
Gaussian
thearefBm
normalized by their own mean value, and the vertical offset between
images.
the three -variance functions simply reflects the effect of this different
Figure 6 displays five realizations of an fBm with superimnormalization.
posed Gaussian structures. The 2D Gaussians all have c = 5,
1 = 50 pixels, and an aspect ratio f = ( 1 / 2 ) that is varied Fig. 5. fBm images with values of ranging from 2 to 4 in steps of 0.5.
andbetween
3D (E =1 3)
fractaldimensions.
Thiswill be given
by:maps are All maps have a resolution of 1000 ⇥ 1000 pixels. The -variance figand
10. The-variance
functionsof these
displayed in the bottom-right panel of Fig. 6 and are compared ures for all cases are compared in the bottom-right subpanel. All display
3
a self-similar regime with an exponent of the power law of ↵ =2
tothe-variance
function
of
a
pure
fBm
image
with
= 2.4.
D2 = D3.
(6)TheEq.6.(4)).
All mapsstructures
are normalizedownmeanimagevalue.with
The =inclusion2of an additional structure in the fBm image increases (i.e.,Fig.
2D Gaussian
injectedbyontheir
top ofan fBmrandomnumberseriesgeneratingthephases
has
been
kept
the
same
in
2
the value ofon all spatial scales. The increment of the 2.4. The 2D Gaussian functions have an aspect ratio ( f = 1 / 2 ) that
all maps.
In
this paper,
we usedimagesas a -variancereference offortheself-variancefunction
withfBm
respect
to thepure is varied in the range [1–10], and all have a value of c = 5 and a fixedsimilarthey canobtained
fBm structures
reaches a sincemaximumon bea scalethatwith
is onpreconditioned
the order of the size of 1 = 50 pixels. All maps are normalized to their mean value.
statisticalproperties(e.g.,
Stutzki
et
al.
1998;
Shadmehri&
Bottom-rightcorrespondingratio-variance
functionscalculated
to thefigure:area-to-boundaryof mapsof different
sizes forequivalent diameter of the injected structure. Figure 6 shows that according
case,absoluteand theseare comparedto the -variancefunction of the
Elmegreen
2011;ratio
Eliaisetreduced,
al. 2018).
4 ofdisplaysthree
fBmthe so eachthat thescaleof the -varianceis only comparable
as the aspect
theFigurepositionthe pointwhere
underlying
fBm
image.
imagesgenerated
a valueof = 2.5 inandthefor -variancethree resoludeviationfrom withthe fBmis maximized
func- in the limit of very large maps. Figure 5 displays the same typetions:⇥ 250
pixelsspatial(top left),500
pixels (toptheright),
tion250moves
to larger
scales.
If ⇥we500
approximate
surface of fBm images, but in this case all images have a fixed resolu3
andof1000⇥
1000
pixels(bottom
left).
The
bottom-rightpanel
and thebetweenthe 2D Gaussian by the area that lies within [2 1 , 2 2 ] in(i.e., tion ofIn1000
Fig.⇥8,1000
we pixels
investigate
thevalueeffectofof isthevaried
surfacearea byFig.where
4 displays-variance
functionscalculated forthese three
A&A
A177(2020)
4 (in stepsof0.5).642,
Whilein Fig.
4 thedistribution
most theof thethe equivalentdiameteris then 2 andincreasing
the numberof structures
thatarephasesuperimposed
onto
psignal lies),
fBm
images.
The
self-similar
regimeisobserved
in
all
cases
and
variesfrom imagefBm
to image,the sameofgiven by Deq ⇡ 4
the underlying
image.inInFig
this5 figure,onedistribution
or several simi1 2 . The measured positions of the points
extends
tolargerspatialscales
for
cases
with
a
higherspatialphases
is
kept,
so
that
the
basic
“shape”
of
the
image
remainsof maximum deviation in the -variance functions in Fig. 6 do lar structures (all with c = 3, f = 5, and 1 = 50 pixels) areresolution.
The fBm
imagesare periodic,
and, if wedeviation
were using
a thesuperimposed
same. Increasingof produces
a gradualsmoothindeed confirm
thatthe positionof maximum
is well
ontothethevaluefBm images(all with
1000 ⇥ 1000
pixelsperiodic
analysis, bytheD -variancespectra would be perfect powerof the image
the Thetransferof powerfrominhighapproximatedand due= to
2.4).
lower-rightpanel
Fig.to8 lowshows
eq . A deviation from this value (by up to ingresolution
laws.
However,
in
order
to
comparethem
totheobservationalfrequencies.
bottom-rightpanel
in Fig.
5 displays⇡30%) can be observed for smaller structures (i.e., in this case, spatialthat increasing
theThesurfacearea of theinjected
structures
has a
data,
performed
theascalculationsof wellthe resolved-varianceonwith
cut thesignificant
corresponding
functionseach ofon
these
thewe
most
elongated)
they are lessthe agrid.
impact-variance(i.e., linearwith thefornumber)the cases.
increaseat the mapboundaries.
two effects.
First, between
there is athe Asofexpected,
thespatial-variance
power-law
We explored
the This
effectcut
ofhasvarying
the contrast
the 2 onscales functions
that are onare
thescale-freeorder of thesize of thenaturallimit2Dto Gaussian
the size ofany structurethat the -variance
whose
given
by ↵ =
injected
structureand thesounderlying
fBm image. functions
structures.
Weexponent
also noteisan
increasein the 2.
width of the excess
spectrumat thescales.where
Second,statisticalFigure flattens
7 displays
fivelargest
realizations
thethevalueof c = of the -variance spectrum up to scales of 250 pixels (i.e., larger
significanceof i thestructures
close
to themapallboundaries
isNpeak / hNfBm
is varied
between
1 and
5. Forcases, the other
than
the
sizes
of
the
individual
structures
themselves)
when there
Fractal Brownian motion maps with additional structure
reduced.
This arechangesof 6.2.
parameters
fixedtheto denominatorf = 5 and 1in=the
50normalization
pixels. All images
are several structures. This is the direct signature of the 250 pixel
thehave-variance
when
computingmean
properties
of
the
map
now explore
the theeffectof discrete
structuresa resolution of 1000 ⇥ 1000 pixels, and the underlying fBm Weseparation
betweenstructures.
We also
explore on
the theeffectspectrum.
structures
superimpose
on image
top
hasconstruction,
an exponentthe
ofmean= 2.4.
The lower-right panel in Fig. 7 dis- -varianceof changing
the sizeTheof thestructurewe
withrespect to the
3 Byvalue of the fBm is zero. We applied anoffBm
imagesaregeneralized
2D
Gaussianfunctions
that
are
plays
the
corresponding-variance
functions,which,
here
once
size
while
fixingtheaspectratio
andcolumndensitycontrast.
arbitrary offset to the maps in order to insure that all values were posiby: 9 displays five realizations with f = 5, c = 3 but whereagain,are compared
the -variancethe fBm
Figure 7 given
Figuretive.
The maps
were then to
normalized
by theirof
meanvalue.image.
The addition
thatoffset
higherthe self-similar
16.67 pixels. The -variance 2funcc ) between
1 is varied between 150 andof ashowsconstant
for contrasts
the whole (mapdoes not alter
the shape of fBm
the and2(x, y)for= Nthesea(x x0are)2 +displayed2b(x x0 )(yy0lower-right) + c(y y0 ) panel)],
peak exp[
the injectedstructure
to higher
valuesof thepixels
onspatial NGtions
realizationsin thevariance
spectrum
since thelead
relativedifferences
betweenremainthescalessame. equal to Deq .
(7)theof Fig. 9. Here as well, the increment in 2 with respect toFig. 10. Maximum deviation of the -variance function in the presenceof structures from that of a pure fBm as a function of the quantity A 2c ,where A is the area covered by the discrete structure(s) and c is thecolumn density contrast between the peak of the structure and the meanvalue of the underlying fBm. The dashed line has a slope of one.

Fig. 10. Maximum deviation of the -variance function in the presence 4
roundish than the ones detected in molecular line observations .
of structures from that of a pure fBm as a function of the quantity A 2c ,The distribution functions in Fig. 11 are normalized and are thus
where A is the area covered by the discrete structure(s) and c is thetransformed
into probability
distribution
columndensity contrast
between thepeak of the functions.
structure and the mean
aspect ratioof hasthe aHi-GAL
value ofFor
thetheunderlying
fBm.distributions
The dashed line
slope of andone. FCRAOHCS clouds and clumps, (dN/d f )norm (Fig. 11, middle panel),
we find that these distributions are best approximated by thefollowing
thanfunction:
the ones detected in molecular line observations4 .
Fig. 9. 2D Gaussian structures injected on top of an fBm image with roundish= 2.4. The Gaussian functions all have an aspect ratio f = 0.2, a col- The distributionfunctions in Fig. 11 are normalized and are thus!
umn density contrast between the peak of the 2D Gaussian and the mean transformed
dN into probability distribution functions.
= ratio⌘ f +distributions
Af .
value of the fBm, c = 3, and a value of 1 that is varied between 150 log
For theaspectof the Hi-GAL and FCRAO(9)df
and 16.67 pixels. Bottom-right figure: corresponding -variance func- HCS cloudsnorm
Dib11,
et al.:
Characteristicscal
and clumps, (dN/d f )normS.(Fig.
middlepanel),
tions calculated for each case, and these are compared to the -variance we find that these distributions are best approximated by the
Fitting the distributions of aspect ratios for the Hi-GAL (forfunction calculated for the underlying fBm image.
Fig. 9. 2D Gaussian structures injected on top of an fBm image with followingf > 1) function:and HCS (for f > 2.5) clouds yields [⌘ = 1.15 ±by= 2.4. The Gaussian functions all have an aspect ratio f = 0.2, a col0.04, A! f = 0.75 ± 0.13] and [⌘ = 0.37 ± 0.01, Af = 0.41 ± 0.10],
maumnanddensitycontrastsuch
betweenthe peakof thein2DtheGaussianthe meandN
filaments
as thosefoundcolumnanddensity
map respectively.
The results of the corresponding fits are shown inlog= ⌘ f + Af .
(9)
value
the fBm, North
is varied internal
between 150
c = 3, and1 thatcomplex
of ofCygnus-X
maya value
have ofa morestruc- Fig.
et(dashed red lines,
middle panel). For any other chosend f11norm
andture16.67thanpixels.
figure: corresponding-variance func2D Bottom-right
Gaussian functions,
we aim to understandwhich value of ⌘, the corresponding value of A f can be calculated bydy
tions
calculated forofeach
and theseare comparedto thefunctions-variancethat
R fmaxcombination
the case,parameters
leads
to -variance
Fitting the
distributions
aspectforwherethe Hi-GAL(dN/dofrequiringthatf )normd f ratios= 1, andfmin and(forfmax
function calculated for the underlying fBm image.
tio
are similar to that of the Cygnus-X North region. More broadly, f > 1) and HCSfmin(for f > 2.5)
cloudsyields [⌘ =In the
1.15same±are the lower and upper limits on
f , respectively.
toour aim is also to understand the sensitivity of the -variance 0.04,
A
=
0.75
±
0.13]
and
[⌘
=
0.37
±
0.01,
A
=
0.41
±
0.10],fvain,f we fitted the normalized distribution functionof the size ofthe choiceof thedistributionfunctionsthat characterizethandtofilaments
suchas thosefound inthe column
density mapthe respectively. The results of the corresponding fits are shown instatistical propertiesof havethe structures.
of Cygnus-X
North maya more complex internal struc- Fig.4 11
lines,weremiddlepanel).
ForCuTEx
any otherchosenthThe(dashed
Hi-GALredsources
extracted
with(Molinari
et al.
The
distribution
of
sizes
and
aspectratiosofcores
andture than 2D Gaussian functions, we aim to understand which value2016),
designed to identify
relatively
roundishsources. In byprinof which⌘, theiscorresponding
valueof A f canbe calculatedisR
clumpsinmolecular
cloudsislikelytodependonthedensityf
max
ciple,
duringthedetection
step,
it
keeps
only
structures
with
both
minor
combination of the parameters leads to -variance functions that requiring that(dN/d f )d f = 1, and where fmin andfmax
Xclump identification
algorithm.
To illus- and major axesfmin
ranging fromnorm
1 to 3 instrumental point spreadfunctions.
are tracer
similarastowell
thatasofonthetheCygnus-X
North region.
More broadly,
the lower andupper
limitson f ,guess,respectively.
In the fit
same
in to
Fig.understand11 we compare
the size (i.e.,
axis; L1 , areSubsequently,
startingfrom
this initial
the 2D Gaussianthat isisourtrate
aim this,is alsothe sensitivityof themajor-variance
vain,
wefittedthenormalized
distributionfunction
of
the
size
of
used
to
determine
the
flux
as
well
as
the
final
estimate
of
the
two
axes
left choicepanel) of
andratio ( functions
f , middle thatpanel)
distributions
to thetheaspect
distribution
characterize
the ofof
has an additional tolerance to adjust itself on the source profile, so thatstructures
found
in
the
Herschel
infrared
GalacticPlane
surveystatistical properties of the structures.
4 The Hi-GAL sources were extracted with CuTEx (Molinari et al.
slo
one can find one (or both) of the two axes shorter than 1 RMS or longer(Hi-GAL;
Molinari
et
al.
2016;
Elia
et
al.
2017)
and
in
the
Five
The distribution of sizes and aspect ratios of cores and 2016),
is designed
relatively roundish
sources.
In theprin-two
thanwhich
3 RMS.
Usually,tonoidentify
large differences
are foundbetweenrelCollege
Radio Astronomy(FCRAO)
COdensity
survey of ciple,
clumpsin molecular
clouds isObservatory
likely to dependon theduringthe thedetection
it keeps
withcontrary,both minor
so thatratio isstep,neverlargeronlythanstructures⇡4. On thealgothe as
outer
(HCS;
Heyer
et al. 1998; Dib
et al. 2009).
Struc- andaxes,
Cy
tracerwellGalaxy
as on theclump
identification
algorithm.
To illusmajor usedaxes ranging
from1 to 3from
instrumental
pointsuchspreadfunctions.
rithmsto extractsources
CO surveys,
as theone used
Hi-GALare theextracted
frommajor
250 µmemissionastratetures
this,inintheFig.
11 wesurvey
comparesize (i.e.,axis;
L1 , Subsequently,
fromthisisinitial
the 2D Gaussianapproach
fit that is in
in Heyer etstartingal. (2001)
thatbasedguess,on a friend-of-friend
maps
(78
952
objects
intotal),
whereastheHCS
surveyisbased
to determine the flux as space,well asdothenotfinal
estimateof the two
position-position-velocity
have
any constraint
on axessourceleft panel) and aspect ratio ( f 12
, middle panel) distributions of usedthA177, page 6 of 18
page 7 ofratio
18 of clouds
Fig. 11. Fractional probability distribution functions of the size of the major axis (left) A177,
and aspect(middle)
found
in
the
250
µm
on
the
(1–0)
transitionCOmolecularline
observations,has
anadditional
tolerancetoadjustitselfonthesourceprofile,sothatsize. If the CO emission is kinematically connected over an elongatedstructures found in the Herschel infrared Galactic Plane survey
sp
in
which
10
156
discrete
structures
wereidentified.
The
clouds
one
can
find
one
(or
both)
of
the
two
axes
shorter
than
1
RMS
or
longermaps of the Hi-GAL survey (Molinari et al. 2016; Elia et al. 2017; full line) and in the 12 CO FCRAO HCS survey(Heyer
et
al.
2001;
Dib
et
al.
2009;
area,
such
a
structuremight
beidentified
asasinglesourcewithalarge(Hi-GAL; Molinari et al. 2016; Elia et al. 2017) and in the Five
3 RMS.
clumpsreportedin Observatory
the
Hi-GAL survey
are COostensibly
ratio.Usually, no large differences are found between the twothdashed line). The distribution of column density contrast is assumed to be a power law. The distributions ofLand
f areAstronomy
fitted withparameterized
1 andCollegeRadio(FCRAO)survey moreof thanaspect
axes,
so
that
the
ratio
is
never
larger
than
⇡4.
On
the
contrary,
algofunctions. The values of the parameters of the fit are reported in the main text.
tip
the outer Galaxy (HCS; Heyer et al. 1998; Dib et al. 2009). Strucrithms used to extract sources from CO surveys, such A177,
as the page
one used
9 of 18
tures in the Hi-GAL survey are extracted from 250 µm emission in Heyer et al. (2001) that is based on a friend-of-friend approach inthmaps (78 952 objects in total), whereas the HCS survey is based position-position-velocity space, do not have any constraint on sourcesp
12
on the(1–0)
transition in
CO column
molecular line observations, size. If the CO emission is kinematically connected over an elongatedhave,
statistically,
higherthe major axis, (dN/dL1 )norm . Here again, we find that the data is self-gravitating structures willCy
in by).
which 10 156 discrete structures were identified. The
area,assuch
a structuresource witha largedensity contrasts at time goes
best fitted with a function that is given by:
Fig.clouds
16. Samethefigure mightwith be⇠ identified= 0.4, as⌘ a=single
0.35,= 2.5,
andres
and likeclumpsin thethe
Hi-GALsurvey are ostensibly more aspect ratio.
As stated above, we would
to reported
understandsensitivity

log

!
dN
= ⇠ L1 + AL1 .
dL1 norm(10)of the -variance spectrum in relation to the underlying distribution functions of the different parameters, and, as a by-product,

Ns = 300 displayed in Fig. 15 but additionally showing the -variancespectra of individual realizations with this set of parameters.
A177, page 9 of 18

va
co
to

doi:10.1088/2041-8205/759/1/L26⃝
C 2012. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

STRUCTURED MOLECULAR GAS REVEALS GALACTIC SPIRAL ARMS
Tsuyoshi Sawada1,2 , Tetsuo Hasegawa2 , and Jin Koda3

1 Joint ALMA Office, Alonso de Córdova 3107, Vitacura, Santiago 763-0355, Chile; sawada.tsuyoshi@nao.ac.jp
2 NAOJ Chile Observatory, Joaquı́n Montero 3000 Oficina 702, Vitacura, Santiago 763-0409, Chile
The Astrophysical Journal Letters,
759:L26 (6pp), 2012 November 1
Sawada, Hasegawa, & Koda
3 Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA

Received 2012 August 8; accepted 2012 October 4; published2012 October 17130+1° (a) H-1

TMB( CO J=1–0) [K]2

ABSTRACT

4

6

We explore the development of structures +1°
in molecular gas in the Milky Way by applying the analysis of the(b)distribution
L-1
brightness distribution function and the brightness
index (BDI) in the archival data from the Boston
University–Five College Radio Astronomy Observatory 13 CO J = 1–0 Galactic Ring Survey. The BDI measures
the fractional contribution of spatially confined bright molecular emission over faint emission extended over large
0° This relative quantity is largely independent of the amount of molecular gas and of any conventional, preareas.
conceived structures, such as cores, clumps,0°or giant molecular clouds. The structured molecular gas traced byhigher BDI is located continuously along the spiral arms in the Milky Way in the longitude–velocity diagram. This
clearly indicates that molecular gas changes its structure as it flows through the spiral arms. Although the high-BDI
50 pcof ongoing stargas generally coincides with H ii regions, there is also some high-BDI gas with no/little signatureformation. These results support a possible–1°
evolutionary sequence in which unstructured, diffuse gas transforms–1°
43°spiral arms,
42° followed41°
40°
itself into a structured state on encountering theby star formationand 39°an eventual38°
return to
Galactic
Longitude[degrees]
36°
35°
34°
the unstructured state after the spiral arm passage.
Key words: Galaxy: disk – ISM: molecules– radio lines: ISM
0log10(Fraction of Pixels)

Sawada+2012a
Sawada+2012b

The Astrophysical Journal Letters, 759:L26 (6pp), 2012 November 1

Galactic Latitude [degrees]

参考

–1
–2

(c)

H-1
L-1

Paper I quantified this structural evolution, by introducing
1. INTRODUCTION –3
the brightness distribution function (BDF) and brightness disA stellar spiral potential causes a large –4
amount of gas totribution index (BDI). In particular, the BDI is a measure ofaccumulate along the spiral arms (e.g., Wada & Koda 2004;
the fractional contribution of spatially confined bright molecu–5
Dobbs et al. 2006; Shetty & Ostriker 2006; Wada 2008). The
lar emission over faint emission extended over large areas and–6concentration and compression of the molecular
gas in spiralcan be derived directly from velocity channel maps without preshocks leads to active star formation (e.g., Roberts
1969; Rand
assumption of structures. Their analysis, however, is limited to–7
2 4 are6 8 1014 16 small region, and it is important to determine the1993; Knapen et al. 1996), and indeed, most –2
H ii0regions
this12
relatively
found along the narrow dust lanes and molecular spiralarms
in J=1–0)
BDF
TMB
(13CO
[K]and BDI over the Milky Way disk to reveal whether thisexternal spiral galaxies (Rand et al. 1999; Scoville et al. 2001;
important structural evolution is a general, fundamental process
Figure1. Velocity
regions (a)H-1 and (b)of
L-1.
averaged TMB in athat
5 kmleads
s−1 channel
and 30–35
km s−1, respectively)
Egusa
et al.channel2011).maps
Theof thephysicalconditions
theThemolecular
to star(50–55
formationacrossspiralarms. is shown in thesamegaslinearscale.
(c)
The
BDFs
in
these
regions.
also appear to change upon the entry into a spiral arm.
In this Letter, we apply the analysis developed in Paper I to
Analyses of the CO line ratios suggest that the molecular gas
archival 13 CO J = 1–0 line emission data covering the majority
becomesdenserand/orwarmerinspiralarms(Sakamotoetal.
of the Galactic
first
the maps of the two characteristic regions, H-1 and L-1 (their
T1 , T
1.5, 4, ∞) (K). A
thresholds
as Paperplane
I, (Tin
0 , the2 , TGalactic3 ) = (1,quadrant.
1997; Sempere& Garcı́a-Burillo
Tosakiet In
al.H-1,
2002). high BDI denotes dominance of compact, bright structures.
selections
and propertiesare discussed1997;
in Section
3.2).
remarkable
contrastof the in
COthe
J spatial= 2–1/J= 1–0
the A
emissionshowshigh contrast
structure,i.e.,ratio The BDIs in the regions
H-1 AND
and L-1are −0.63 and −2.15,
2. DATAANALYSISUniversity of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA; 3 University of Washington, Department of
Astronomy,WA, 98195,Spectroscopic
U.S.A; 4 Kavli InstituteforYoung
Astronomy
Peking University,
YiheyuanFirst Extensive
Study ofStarsandin Astrophysics,
the North America
and Pelican
335 TheSeattle,
55, HaidianQu, 100871
Beijing, China; Joint ALMA Observatory, Alonso de Cordova 3107 Vitacura, Santiago, Chile;
Nebulae
Region6#10
Infrared Science Archive (IRSA), IPAC, 1200 E. California Blvd., California Institute of Technology, Pasadena, CA
1
1
3
4
7
Min Fang, LynneA. Hillenbrand, Jinyoung
Kim2, Krzysztof
Findeisen, GregoryJ. Herczeg, John of
M.Sciences,
91125, USA;
PurpleMountainObservatory
andSerena
Key Laboratoryof Radio
Astronomy,
ChineseAcademy5
6
7
Carpenter, Luisa
M. Rebulland Hongchi
2 West Beijing
Road,
210008
Nanjing,
China Wang2020 ApJ 904, 146F

E-mail contact: mfang.cn at gmail.com
We present a spectroscopic survey of over 3400 potential members in the North America and Pelican nebulae (NAP)
using several low-resolution (R≈1300-2000) spectrographs: Palomar/Norris, WIYN/HYDRA, Keck/DEIMOS, and
MMT/Hectospec. We identify 580 young stars as likely members of the NAP region based on criteria involving
infrared excess, Li I 6708 absorption, X-ray emission, parallax, and proper motions. The spectral types of individual
spectra are derived by fitting them with templates that are either empirical spectra of pre-main sequence stars, ormodel atmospheres. The templates are artificially veiled, and a best-fit combination of spectral type and veilingparameter is derived for each star. We use the spectral types with archival photometry to derive V-band extinction
and stellar luminosity. From the H-R diagram, the median age of the young stars is about 1 Myr, with a luminosity
dispersion of ∼0.3–0.4 dex. We investigate the photometric variability of the spectroscopic member sample using ZTF
data, and conclude that photometric variability, while present, does not significantly contribute to the luminosity
dispersion. While larger than the formal errors, the luminosity dispersion is smaller than if veiling were not taken
into account in our spectral typing process. The measured ages of stellar kinematic groups, combined with inferredages for embedded stellar populations revealed by Spitzer, suggests a sequential history of star formation in the NAP
region.
Accepted by ApJ
https://arxiv.org/pdf/2009.11995

The chemical structure of young high-mass star-forming clumps: (II) parsec-scale COdepletion and deuterium fraction of HCO+
S. Feng1,2,3 , D. Li1,4 , P. Caselli5 , F. Du6,7 , Y. Lin8 , O. Sipilä5 , H. Beuther9 , Patricio Sanhueza3 , K.

1212

MA 02138, USA; 14 Institute for Astrophysical Research, Boston University, Boston, MA 02215, USA; 15 Centro
deAstrobiología(CSIC,structure
INTA), Ctra.
de Torrejóna Ajalvir
km. 4, Torrejón
Ardoz,
E-28850 Madrid,
The chemicalof young
high-mass
star-forming
clumps:de(II)parsec-scale
CO Spain;
335
16
Shanghai
Astronomical
Observatory,
Chinesedepletionanddeuterium
fractionof Academy
HCO+ of Sciences, 80 Nandan Road, Shanghai 200030, People’s
17#11
Republic of China;
Kavli
Institutefor Astronomy
and Astrophysics,
PekingUniversity, 53 Yiheyuan Road,
Haidian
1,2,3
1,4
5
6,7
8
5
9
10,11
18 Sipilä , H. Beuther , Patricio Sanhueza , K. Tatematsu
S.
Feng
,
D.
Li
,
P.
Caselli
,
F.
Du
,
Y.
Lin
,
O.
,
S.
Y.
District, Beijing 100871, People’s Republic of China;
School of Astronomy and Space Science, Nanjing University,
2
12
9
13
14
3
15
16
17
19 , T. Liu , K. Wang , Z. Y. Zhang , S. Zahorecz3,18,
Liu ,Avenue,
Q. ZhangNanjing, Y. Wang, T. Hogge, I.Republic
Jimenez-Serra, X. Lu163 Xianlin
210023,People’sof China;
Department of Physical Science, Graduate School
19
2
1
G. Li
, H. Prefecture
B. Liu and J.
Yuan
of Science,
Osaka
University,
1-1 Gakuen-cho,Naka-ku, Sakai, Osaka 599-8531, Japan
2020 ApJ 901, 145F

E-mail contact: siyi.s.feng at gmail.com
The physical and chemical properties of cold and dense molecular clouds are key to understanding how stars form.
Using the IRAM 30 m and NRO 45 m telescopes, we carried out a Multiwavelength line-Imaging survey of the 70 µm
dark and bright clOuds (MIAO). At a linear resolution of 0.1–0.5 pc, this work presents a detailed study of parsec-scale
CO depletion and HCO+ deuterium (D-) fractionation toward four sources (G 11.38+0.81, G 15.22-0.43, G 14.49-0.13,
and G 34.74-0.12) included in our full sample. In each source with T < 20 K and nH ∼ 104 –105 cm−3 , we comparedpairs of neighboring 70 µm bright and dark clumps and found that (1) the H2 column density and dust temperatureof each source show strong spatial anticorrelation; (2) the spatial distribution of CO isotopologue lines and dense
gas tracers, such as 1–0 lines of H13 CO+ and DCO+ , are anticorrelated; (3) the abundance ratio between C18 O and
DCO+ shows a strong correlation with the source temperature; (4) both the C18 O depletion factor and D-fractionof HCO+ show a robust decrease from younger clumps to more evolved clumps by a factor of more than 3; and (5)preliminary chemical modeling indicates chemical ages of our sources are ∼8 × 104 yr, which is comparable to theirfree-fall timescales and smaller than their contraction timescales, indicating that our sources are likely dynamicallyand chemically young.
Accepted by ApJ
https://doi.org/10.3847/1538-4357/abada3

Hydrodynamical simulations of protoplanetary disks including irradiation of stellar photons. I. Resolution study for Vertical Shear Instability (VSI)
Lizxandra Flores-Rivera1 , Mario Flock1 and Ryohei Nakatani2
1

Max Planck Institute for Astronomy, Germany; 2 RIKEN, Japan

E-mail contact: flores at mpia.de

13

In recent years hydrodynamical (HD) models have become important to describe the gas kinematics in protoplanetaryHydrodynamical simulations of protoplanetary disks including irradiation of stellar photons.
Resolution study
for Vertical
Shear Instability(VSI)irradiation of stellar pho- tons.
Hydrodynamical
simulationsof protoplanetarydisks including
335 I.
1 for Vertical Shear
study
Instability(VSI)2
Lizxandra
Flores-Rivera, Mario Flock1 and Ryohei
Nakatani#12 I. Resolution
1

1
1
2
2
Lizxandra
Flores-Rivera, Mario Flockand Ryohei
Nakatani
Max Planck
Institutefor Astronomy,
Germany;
RIKEN,
Japan

2020 A&Aflores
644A, 50F
E-mail contact:
at mpia.de

In recent years hydrodynamical (HD) models have become important to describe the gas kinematics in protoplanetarydisks, especially in combination with models of photoevaporation and/or magnetic-driven winds. Our aim is toinvestigate how the Vertical Shear Instability (VSI) could influence the thermally-driven winds on the surface of
protoplanetary disks. In this first part of the project, we focus on diagnosing the conditions of the VSI at the highest
numerical resolution ever recorded and allude at what resolution per scale height we obtain convergence. At the sametime, we want to investigate the vertical extent of VSI activity. Finally, we determine the regions where EUV, FUV
and X-Rays are dominant in the disk. We perform global HD simulations using the PLUTO code. We adopt a global
isothermal accretion disk setup, 2.5D (2 dimensions, 3 components) which covers a radial domain from 0.5 to 5.0 and an
approximately full meridional extension. Our simulation runs
13 cover a resolution from 12 to 203 cells per scale height.
We determine the 50 cells per scale height to be the lower limit to resolve the VSI. For higher resolutions, greaterthan 50 cells per scale height, we observe the convergence for the saturation level of the kinetic energy. We are alsoable to identify the growth of the ‘body’ modes, with higher growth rate for higher resolution. Full energy saturation
and a turbulent steady state is reached after 70 local orbits. We determine the location of the EUV-heated region
defined by the radial column density to be 1019 cm−2 located at HR ∼9.7 and the FUV/X-Rays-heated boundary
layer defined to be 1022 cm−2 located at HR ∼6.2, making it necessary to introduce the need of a hot atmosphere.
For the first time, we report the presence of small scale vortices in the r-Z plane, between the characteristic layers oflarge scale vertical velocity motions. Such vortices could lead to dust concentration, promoting grain growth. Our
results highlight the importance to combine photoevaporation processes in the future high-resolution studies of the
turbulence and accretion processes in disks.
Accepted by Astronomy & Astrophysics
http://arxiv.org/pdf/2010.06711

Lupus DANCe. Census of stars and 6D structure with Gaia-DR2 data
P.A.B. Galli1 , H. Bouy1 , J. Olivares1 , N. Miret-Roig1, R.G. Vieira2 , L.M. Sarro3 , D. Barrado4 , A.
14
Berihuete5 , C. Bertout6 , E. Bertin6 and J.C. Cuillandre7

Astrofísica, INTA-CSIC, ESAC Campus, Camino Bajo del Castillo s/n, 28692 Villanueva de la Cañada, Madrid,
Spain; 5 Dept. Statistics and Operations Research, University of Cádiz, Campus Universitario Río San Pedro s/n,
Lupus DANCe. Census6 of stars and 6D structure with Gaia-DR2 data
335 Puerto
11510
Real, Cádiz, Spain; Institut d’Astrophysique de Paris, CNRS UMR 7095 and UPMC, 98bis bd Arago,
7 Bouy1, J. Olivares1, N. Miret-Roig1, R.G. Vieira2, L.M. Sarro3, D. Barrado4, A. Berihuete5, C. Bertout6,
P.A.B.France;
Galli1, H.
#13 Paris,
75014
AIM Paris Saclay, CNRS/INSU, CEA/Irfu, Université Paris Diderot, Orme des Merisiers,
6
7
France E. Bertin and J.C. Cuillandre
2020 A&A 643A, 148G
E-mail contact:phillip.galli at u-bordeaux.fr

Context: Lupus is recognised as one of the closest star-forming regions, but the lack of trigonometric parallaxes in the
pre-Gaia era hampered many studies on the kinematic properties of this region and led to incomplete censuses of its
stellar population.
Aims: We use the second data release of the Gaia space mission combined with published ancillary radial velocity
data to revise the census of stars and investigate the 6D structure of the Lupus complex.
Methods: We performed a new membership analysis of the Lupus association based on astrometric and photometricdata over a field of 160 deg2 around the main molecular clouds of the complex and compared the properties of thevarious subgroups in this region.
Results: We identified 137 high-probability members of the Lupus association of young stars, including 47 stars
that had never been reported as members before. Many of the historically known stars associated with the Lupus
region identified in previous studies are more likely to be field stars or members of the adjacent Scorpius-Centaurus
association. Our new sample of members covers the magnitude and mass range from G ≃ 8 to G ≃ 18 mag and from0.03 to 2.4 M⊙ , respectively. We compared the kinematic properties of the stars projected towards the molecular
clouds Lupus 1 to 6 and showed that these subgroups are located at roughly the same distance (about 160 pc) andmove with the same spatial velocity. Our age estimates inferred from stellar models show that the Lupus subgroups
are coeval (with median ages ranging from about 1 to 3 Myr). The Lupus association appears to be younger thanthe population of young stars in the Corona-Australis star-forming region recently investigated by our team using
a similar methodology. The initial mass function of the Lupus association inferred from the distribution of spectral
types shows little variation compared to other star-forming regions.
Conclusions: In this paper, we provide an updated sample of cluster members based on Gaia data and construct themost complete picture of the 3D structure and 3D space motion of the Lupus complex.
Accepted by A&A
http://arxiv.org/pdf/2010.00233
14

15

181-8588, Japan; Department of Astronomical Sciences, SOKENDAI (The Graduate University for Advanced Stud3ies), 2-21-1
Osawa, Mitaka, accretion
Tokyo 181-8588,
Japan;
Instituto
RadioastronomíaA
photoionizeddiskarounda youngdehigh-massstar y Astrofísica, Universidad Nacional
335
4
Autónoma de México, P.O. Box 3-72, 58090, Morelia, Michoacán, México; Departamento de Astronomía, Universidad
1
1,2
3
E. el
Guzman, Paricio1515,
Sanhueza, Luis Zapata, GuidoGaray4 and Luis Felipe Rodriguez3#14deChile,Andres
CaminoObservatorio
Las Condes,
Santiago,
Chile2020 ApJ 904, 77G

E-mail contact: andres.guzman at nao.ac.jp
We present high spatial resolution (52 au) observations of the high-mass young stellar object (HMYSO) G345.4938+01.4677
made using the Atacama Large Millimeter/sub-millimeter Array (ALMA). This O-type HMYSO is located at 2.38
kpc and it is associated with a luminosity of 1.5 × 105 L⊙ . We detect circumstellar emission from the H38β hydrogen
recombination line showing a compact structure rotating perpendicularly to the previously detected radio jet. We
interpret this emission as tracing a photo-ionized accretion disk around the HMYSO. While this disk-like structure
seems currently too small to sustain continued accretion, the data present direct observational evidence of how disks
can eﬀectively survive the photo-ionization feedback from young high-mass stars. We also report the detection of alow-mass young stellar object in the vicinity of the HMYSO and suggest that it forms a high-mass and low-mass starbinary system.
Accepted by The Astrophysical Journal
https://arxiv.org/pdf/2010.00244

APEX-SEPIA660 Early Science: Gas at densities above 107 cm−3 towards OMC-1
A. Hacar1,2 , M. R. Hogerheijde1,3, D. Harsono4 , S. Portegies Zwart1 , C. De Breuck5 , K. Torstensson5 ,W. Boland6 , A. M. Baryshev6 , R. Hesper6 , J. Barkhof6 , J. Adema6 , M. E. Bekema6 , A. Koops6 , A.
Khudchenko6 and R. Stark7
Leiden Observatory, Leiden University, P.O. Box 9513, 2300-RA Leiden, The Netherlands; 2 University of Vienna,
Department of Astrophysics, Türkenschanzstrasse 17, 1180 Vienna, Austria; 3 Anton Pannekoek Institute for Astonomy, University of Amsterdam, the Netherlands; 4 Institute of Astronomy and Astrophysics, Academia Sinica, No.1,
Sec. 4, Roosevelt Rd, Taipei 10617, Taiwan, R.O.C.; 5 European Southern Observatory, Karl Schwarzschild Strasse 2,85748 Garching, Germany; 6 Netherlands Research School for Astronomy (NOVA), Kapteyn Astronomical Institute,
Landleven 12, 9747 AD Groningen, The Netherlands; 7 Netherlands Research School for Astronomy (NOVA), Leiden
Observatory, Leiden University, P.O. Box 9513, 2300-RA Leiden, The Netherlands
1E-mail contact: alvaro.hacar at univie.ac.at
16
Context: The star formation rates and stellar densities found in young massive clusters suggest that these stellar
7−3systems originate from gas at densities n(H2 )=10 cm . Until today, however, the physical characterization of this