008.13502v1 [astro-ph.GA] 31 Aug 2020

5Department of Astronomy, University of Massachusetts, Amherst, MA01003, USA
c ESO 2020
Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik,
Albert-Ueberle-Str. 2, 69120 Heidelberg,
September 1, 2020
Germany
7
Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, INF 205, 69120 Heidelberg, Germany
8
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
9Centre for Astrophysics and Planetary Science, University of Kent, Canterbury CT2 7NH, UK
10 Atomic and molecular gas properties during cloud formation
School of Physics and Astronomy, Cardi↵ University, Queen’s Buildings, The Parade, Cardi↵ CF24 3AA, UK
11
Schooland Astronomy,
The University
1 of Physics
11
1 E.C. Stoner
2 Building,32
4of Leeds,5 Leeds LS2 9JT, UK

2008.13502

6
Astronomy& Astrophysics manuscript no. main

J. Syed , Y. Wang , H. Beuther , J. D. Soler , M. R. Rugel , J. Ott , A. Brunthaler , J. Kerp , M. Heyer , R. S.
Klessen6, 7 , Th. Henning1 , S. C. O. Glover6 , P. F. Goldsmith8 , H. Linz1 , J. S. Urquhart9 , S. E. Ragan10 , K. G.
Received XX May XXXX; acceptedJohnston
12 August
11 , and2020
F. Bigiel4
1

Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
ABSTRACTe-mail: syed@mpia.de
2
Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany3
National Radio Astronomy Observatory, PO Box O, 1003 Lopezville Road, Socorro, NM 87801, USA
4
Context.
Molecular
Argelander-Institut
für clouds,
Astronomie,which
Auf dem harbor
Hügel 71, the53121birthplacesBonn, Germany of stars, form out of the atomic phase of the interstellar medium (ISM). To
5
Departmentof Astronomy,
Universityof Massachusetts,
Amherst,
USA the spatial and kinematic relationships between atomic and molecularunderstandthis
transition
process,
it is crucial
toMA01003,
investigate
6
Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg,gas. Germany
7
Universität
Interdisziplinäres
für Wissenschaftliches
Rechnen,
INF 205,
69120ISM
Heidelberg,
Aims.
We aimHeidelberg,
to characterize
theZentrum
atomicand molecularphasesof theand Germany
set their physical properties into the context of cloud8
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA9formation
processes.
Centre for
Astrophysics and Planetary Science, University of Kent, Canterbury CT2 7NH, UK
10SchoolofPhysics
and Astronomy,
Cardi↵
University,
Queen’s Buildings,
Theby
Parade,Cardi↵of
CF24
3AA,
UK
Methods.
We
studiedthecoldneutralmedium
(CNM)
means
H
i
self-absorption(HISA) toward the g(ard)-29(25)-.1419-lh1(T)11School of Physics and Astronomy, E.C. Stoner Building, The University of Leeds, Leeds LS2 9JT, UK
Received XX May XXXX; accepted 12 August 2020
ABSTRACT
Context. Molecular clouds, which harbor the birthplaces of stars, form out of the atomic phase of the interstellar medium (ISM). To

understand this transition process, it is crucial to investigate the spatial and kinematic relationships between atomic and moleculargas.
Aims. We aim to characterize the atomic and molecular phases of the ISM and set their physical properties into the context of cloudformation processes.
Methods. We studied the cold neutral medium (CNM) by means of H i self-absorption (HISA) toward the giant molecular filament
GMF20.0-17.9 (distance=3.5 kpc, length ⇠170 pc) and compared our results with molecular gas traced by 13 CO emission. We fitted
baselines of HISA features to H i emission spectra using first and second order polynomial functions.
Results. The CNM identified by this method spatially correlates with the morphology of the molecular gas toward the western region.
However, no spatial correlation between HISA and 13 CO is evident toward the eastern part of the filament. The distribution of HISA
peak velocities and line widths agrees well with 13 CO within the whole filament. The column densities of the CNM probed by HISA
are on the order of 1020 cm 2 while those of molecular hydrogen traced by 13 CO are an order of magnitude higher. The column density
probability density functions (N-PDFs) of HISA (CNM) and H i emission (tracing both the CNM and the warm neutral medium,
WNM) have a log-normal shape for all parts of the filament, indicative of turbulent motions as the main driver for these structures.
The H2 N-PDFs show a broad log-normal distribution with a power-law tail suggesting the onset of gravitational contraction. The
saturation of H i column density is observed at ⇠25 M pc 2 .
Conclusions. We conjecture that di↵erent evolutionary stages are evident within the filament. In the eastern region, we witness theonset of molecular cloud formation out of the atomic gas reservoir while the western part is more evolved, as it reveals pronounced
H2 column density peaks and signs of active star formation.
Key words. ISM: clouds – ISM: atoms – ISM: molecules – ISM: kinematics and dynamics – radio lines: ISM – stars: formation

feature. H i self-absorption features with line widths

120
HI
HISA
13
CO

100

10

60

50

agree with the momeasurements agatical depths in the
derlines the robus
the two subregion

0

3.2. Kinematics

100

40
20
0

We smoothed th
1.5 km s 1 and ap
consistent in our asity of > 1.25 K(⇠
100
20 km s 1 are consof HISA and 13 COof HISA in the ea
50⇠44 46 km s 1 .
velocities from ⇠40show a coherent2014).
150
Although ther
Spectrum 5
Spectrum 6
locity at some po
velocities reveal g
100sion in both the ea
velocities are a coare trustworthy, ev
50gree of line-of-sig
ment. The HISA sgion reveal large lFig. 3.0 Comparison of baseline fits toward continuum emission.
Thesouth ofof HISA
black curveof H i 60emission
20 shows
40 an example
60
80 spectrum
2040
80 centered
6 km s 1 .inPossibles 1 ]that is contaminatedvLSR [kmbys 1continuum]` = 18.95 , b v=
0.03
emission.
LSR [kmarediscussed in S
13
The dashed magenta and green curve show a second and firstTheorder
CO lin
Fig.
4.
H
i
(T
)
and
extracted
HISA
spectra(TT)
towardtherepolynomial onfit to the velocity channelso↵ of onthe H i spectrumandat show
33.5–line wid
gions markedbytheyellow
circlesinthebottom
panel
of
Fig.
1.
The
(Fig. 9). Assumin
43.0
km s 1 and 56.0–65.5 km s 1 , respectively. Due to the continuumcolors are the same as described in Fig. 2.
contamination, the second order polynomial yields a bad fit toexpected
the HISAthermalriump (LTE), the thbaseline.
8 ln2 kB T k /(µmH
stant, kinetic temp
3. Results
Figure 4 shows our baseline fitting procedure and extracted
and the CO molec

25

0

25

50

75

100

125

150

vLSR [km s 1]
Fig. 2. H i, HISA, and 13 CO spectra. The black curve shows an example spectrum of H i emission (T on ) from 80 km s 1 to 160 km s 1 averaged over an area of 18000 ⇥ 18000 centered in ` = 19.9 , b = 0.5 .
The dashed red curve is a second-order polynomial fit (T o↵ ) to theabsorption-free channels of the H i spectrum at 33.5–43.0 km s 1 and
56.0–65.5 km s 1 (see Sect. 2.2). We estimated the HISA spectrum bythen subtracting the H i spectra from the fitted background emission.
The GRS 13 CO spectrum (Jackson et al. 2006) covering velocities from
5 km s 1 to 135 km s 1 is shown in blue and has been multiplied by afactor of ten for better visibility.

To reliably identify HISA features, it is crucial to know the13COと⽐較,

emissionin the absence of a HISA cloud. Many methods have
⾃⼰吸収してないHIプロファイルを2次関数で再現
been tested to estimate T o↵ in Eq. (1) (e.g., Gibson et al. 2000;
Kavars et al. 2003; Li & Goldsmith 2003; Krčo et al. 2008;
Wang et al. 2020b). Wang et al. (2020b) tested estimating thebackground spectrum T o↵ by measuring several o↵ positions o↵set from apparent absorption features at slightly shifted lines ofsight. Their spectra partly show large variations depending on
the line of sight, so the assumption that the H i background emission stays spatially constant does not really hold. Therefore, we
refrain from selecting actual o↵ positions to estimate T o↵ . In-

TB [K]

50

TB [K]

150

75

spatial correlation

2008.13502

TB [K]

TB [K]

80

1 km ssecondorder
polynomialfrom
fits,emission
with a troughs.
> 0. Forthose
we theare difficult
to di↵erentiateThekine-spectra,
ing. However,matic first
information
emissionis thereforeacrucial
shows significant
usedorder offitsmolecular
instead.lineFigure
3 presents
comparison
be13
in our analysis.
CO emission at
tween
first and second order polynomial fits toward a position
ern side of the clthat is contaminated by di↵use continuum emission, whichcanenvelop the denser
150
Spectrum 1 of the absorption
Spectrum2
contribute to the broadening
profile.
dicate the presenc

Spectrum 3

Spectrum 4

we
ve
se
in
s-

2008.13502

Optical depthude-

H i emission
is mostattributed
to the background,which is not assostrong
emissionAs
strongcontinuum
Depending on the brightnessof thecontinuum
continuum
sourceandthe H i sources.
A&A proofs:
manuscriptno.
mainciated with GMF20.0-17.9. We derived the H i column
densitycorrection
opacity
optical depth, the absorption
spectrumcandiscrete
approach zero.
Due sources,
to map shown
are
point
thisinmethod
results
an in-into account! sources
the top panelof Fig. in
11 takingonly
density
by a factor
theTnoiseinthespectra,thespectracanexhibitbrightness
temT o↵onthe nearside gas at 3.5 kpc.
complete
censusof
opticaldepthmeasurements
(see
Wang
et
al.
⌧HISA
= ),lnwe1can then
(1) baselines of HISA spectra. For the baseline fitting, we further
peratures
smallerthe
thanHzero,
which is not
physically(=
T HISAcalculatei, column
densityof meaningful.
theThe derived co
T HISApT
To↵ report
cont2020a,
acompilationofall
opticaldepthmeasurementsin
We therefore
a lower
limit forfor
the opticaldepth where thecold H i gas using the generalform (Wilson et thanal. 2013)
more smoothed the H i emission maps spatiallyto an angulasion
stemmingfroabsorption T on becomes smaller
5
.
00
the
THOR
survey).
Consequently,
theintrinsic
structureofindiresolution
of
⇥
=
80
to
enhancethebrightness
sensitivity.
Besides strong continuum sources we observe weak conG19.075-0.287
13 (3.5 kpc) side of tvidualH i clouds
be determined.
Somecontinuum
emistinuumZemission throughout
the !Galactic
plane.cannot
This compo2
Irrespective of the actual presence of CO emission at indi
been obtained usin
⌧
N
T
dv
nent
has
brightness
temperatures
between
10
and
50
K.
For
the
bg
H
s
sourcesalso
show
extendedstructures.
Therefore,
finding18 parameter p ⌘ sion
(1)
with thedimensionless
T
e
/T
debg
o↵
vidualpositions,
every
pixel
spectrumissearched
for HISA and= 1.8224 ⇥ 10 derivation of⌧ (T, we employed(2)the comthes ,Hv)i column densitiesetal.
2018) and e
2
1
1
cm
km
sJ. Syedreliableo↵positions
could
pose
As
we
exploitedscribing the fraction binedofKbackgroundemission
theal.:
opticallyetAtomicandmoleculargasproperties33.5
duringcloud
formation
fittedat thedifficulties.
velocities
43.0
kms and 56.0 65.5 km s 1
THOR data as in
the
case
of in
HISA.
The
continuum
emiset al. (2019)
1the data
thin limit (Feldt 1993).
a HISA
spindatatemperatureT s omittingsionAssuming
has been subtracted
duringreduction
as describedin
THOR-only(VLA
C-configuration)
for thismeasurement,
velocity
range
associated withReid
GMF20.0-17.9.
In
Sect. 2.1. However,evenweweak
continuum
emissioncanstill in- H i emission. The THOR-only
the Galacticplane1filterout
mostlarge-scaledata(Twhere T s is thespin (Ttemperatureof
atomichydrogen
and
⌧
,
v)
the
first
cycle
of
the
fitting
procedure,all
spectraarefittedwithsclouds⇠ 100K),
weobserve
the
H
i
cloud
in
absorption.
The
43
and
56
km
s
,
which
gives
a
mean
opticaldepth
sfluence
the observed brightness
temperature.
If weneglect
weak
Articlenumber,
page
3
of
21
to
the
Galactic
ceno
2
describes theabsorption
optical depth.
HH ii emission
emission
of
less
than
30
K,(Fig.
often
justThis
within
the noise.
secondorder
polynomial
functions( f (x) =ax + bx + c).asSpec
featureemission,
is furthermore
dominated
by
CNM
since
12).
is
a
reasonableapproximation
thecontinuum
the reveal
measured
willthebe underes0that gives
theproduce
atomicgao
1 cantimatedasweakcontinuum
emissionsuppressasignificant
tra
that
are
contaminatedcontinuum
emission
bad
Therefore,
wecanneglect
theemission
ofderived
the H i cloudin Eq.
(8)(2020a)
the absorption is proportional to T s . By measuring on and o↵ map
bybyWang
et al.
a mean0
20
40
60 is similar
80
fraction of H i emission (e.g., Bihr et al. 2015). Consequently,
for a giv
secondorder
polynomial
fits,
with
a
>
0.
For
those
spectra,w
positions,thewederived
can directlycomputetheoptical
depth
of
H
i.
The
of
⇠1.0
when
averaged
over
the
whole
filament.
and
set
T
=
0.
We
can
then
calculatetheopticaldepth
withouto↵underestimated. We took1
H i column densities will be
v
[km
s
]
LSR
スピン温度は仮定
verticaldensity pro
usedfirst order However,fits instead.
presents
a comparison
optical depth
is givenby (seewhen
Bihret al. 2015;
etdensityal.
2020b)
this e↵ect
into accountcomputingthe o↵
H iWangcolumnmeasuringanpositionby
thisFigure
optical3 depth
measurement
is abe
lo
(see
Bihr
et
al.
2015,
Eq.
9).
estimatethegas
fr
tweenFig.firstsecondpolynomial
fits
towarda position
tauは推定12. and
Opticaldepth ordermeasurement
toward H
the
Hregionii regionlocatedG19.075-0.287
isaGalacticii
in
In contrast
a6! to Wang et al. (2020a), where they used
each
line
of sourc
sight(Wang etby
al. di↵use2018). The continuum
plot shows the opticaldepth
as whichthat isG19.075-0.287
contaminatedemission,can!
plane.
As
nostrongextragalactic
continuum
toselectcontinuum
sources,
wemeasuredtheoptiTthresholdTa function of LSR velocity and was computed using Eq. (9). For someono↵T oncontinuum
to profile.
the
Galactic
mio
contributetotifiedthebroadeningof
the absorption
towardthebrightest⌧ = ln cal depth of atomic, hydrogen(8)
towardthepositionof
GMF20.0-17.9,
thechannels,theabsorption
spectrumsaturatesandthemeasured
optical
⌧
=
ln
.
(9)
simplified T
T contwith brightness temperatures
sources
to not su↵er depth is a lower limit of ⌧ = 1.6, which is indicated by thecont > 200
horizontal
Therefore,
due toTKgas
contproperties during
measurementhas
drawbacks
inthecurrent
investiga
J.
Syed
et
al.:
Atomicandmolecular
cloud
formationfrom low saturation limits since we expect the optical depth to be dottedline. The gray shaded area indicates the velocity range between
H i accountemissionatt
we have
intoanisopachigh. Four sources have been identified with this threshold. The 43 and 56 emission
km s 1 , wheredata,
HISA features
have tobeentakeextracted.
Dependingonthebrightnessofthecontinuum
sourceandtheHi
T onmeasured
andthe Hoffilamenti thesebrightness
temperaturea tion from the far side H i beyondciatedo↵ isTable 1. where
Derived massesof theTgiant
molecular
GMF20.0-17.9.
opticaldepthssourcesvary
between 0.5 towardandwith GMF2
the locationof thestrong continuum
sourceand o↵setfromthe source,
opticalthesource
absorption
spectrumcanapproach
zero.
Due
to
2.5 (lower backgroundlimit). We selected
the depth,
continuum
G19.075map that
shown
the
To first approximation, we assumed
the inoptical(Wang
et al.
2018)asa representative
sourcefor M(HISA)
the opticalrespectively.
The
brightness
temperatureT
describes
theconRegion
M(H0.287)
M(Hi)
M(HISA)
f
f
f
the
noise
in
the
spectra,thespectracanexhibitbrightness
temcont
2
HISA
HISA
i
thethenearside gasforeathe backgroundis similarHto
that ofmeasureddepth as it is not in the 5 saturation at most velocities between 1 https://github.com/tvwenger/kd

tinuum level of the backgroundsourcea↵ectedH
peratures
than
which
not
(Tsmaller= 20isK)not(T= 40 K)by(T si =is20
K) physically(T s =
40 K) meaningful.
sthat
s zero,therefore
adopted2 ⇥Article⌧(vLSR
) for
the
whole
map annumber,
page
11
of
21
absorption.
Theadvantageof
thismethodisthedirectmeasureWe
therefore
report
a
lower
limit
for
the
optical
depth
where
the
[M ]
[M ]
[M ]
[M ]
the H i column density for the optical depth per ve
ment
of
the
However,theHICA
methodrequires5optical depth.
5
5
(a)
3
4
(a)
than
5 .Given4%
Total
3.5 ⇥ 10
2.6 ⇥ 10 (4.6 ⇥absorption
10 )4.6T⇥on10becomes
1.3 ⇥smaller
10
1%nel.
75% (130%)the correctedmean
optical depth of 2 ⇥strongcontinuum
emissionAs
moststrongcontinuum
55sources.
33Besides
continuum
sources
we correction
observeweak
conEast1.1 ⇥ 10
1.2 ⇥ 10
1.9 ⇥strong10
5.7 ⇥ 102%opacity
5%110%factor⌧/(1 e ⌧ ) increases the msourcesare discrete point
sources, this2.6method
results
in an in- 1%density plane.
ThisofcompoWest
2.3 ⇥ 105
1.5 ⇥ 105tinuum emission⇥ 103 throughout
7.5 ⇥ 103 the Galactic
65%
by3%
a factor⇠2.
complete census of optical depth
measurements
(see
Wang
et
al.
nent has brightness temperatures between
10derived
and 50column
K. For densities
theThe
13 acalculated
Notes.
The
masses
were
for
each
part
of
the
filament
as
well
as
the
whole
filament
markedbytheredpolygons
in
Fig.
11.
The
second are a result of th
2020a,
forcompilationofall
opticaldepthmeasurements
inFig. 2. H i, HISA, and CO spectra. The black
curve
shows
an
exam13derivationof the1 The
H ithird
columndensities
employed
thecomstemming
from
both
the
kinematicfar (12.0 kp
column gives
the molecularhydrogenmass as tracedbyCOintrinsic
emission.
columnshows
thesiontotalweatomichydrogenmass
inferred
from
the
1 the
the
THOR
survey).
Consequently,
structureofindiple spectrumofHiemission
(T
)
from
80
km
s
to
160
km
s
averonoptical depth and continuum
corrected
H i emission.
fourth andfifthascolumnpresent
theof
massof thekpc)
coldhydrogentracedby
HISAThe kinematic dis
binedTheTHOR
data
in thecase
HISA.
Theatomic
continuumemis(3.5
sideof
the Milky
Way.
00
00
vidualHicloudscannotbedetermined.
Somecontinuum
emisaged over
an
area
of
180
⇥
180
centered
in
`
=
19.9
,
b
=
0.5
.
with an assumed spin temperature of 20 and 40 K, respectively. The last three columns give the corresponding mass fractions with respect to thesion hasbeen
duringreduction
described
inobtainedasusing
the Kinematic
Distance Utiliti
The dashedred
is a also
second-orderpolynomialfit(T o↵subtracted) Therefore,
to theH2 mass.
sioncurve
sourcesshow extended
structures.
findingdatabeen(a)2.1.
However,even
weak
emissionstill
in- the Galactic rotation
al.and2018)
andemploying
This mass
was calculated
using
corrected
Hati emission
betweenand
56 kmexploiteds 1 , 20.6continuum> ` >et17.6
1.25 <
b <can+0.5.
absorption-freechannelstheH ithespectrum
33.5–43.0
km s431As
andreliableo↵ofpositions
could Sect.
pose
difficulties.
weReid et al.
(2019).
Since
the distribution of the atfluencethebrightness temperature.
If weneglect
weak
56.0–65.5 km THOR-onlys 1 (see Sect. (VLA
2.2). We
estimatedthe HISA
spectrumC-configuration)
dataobserved
for this bymeasurement,theGalacticplane
approximately axisymmetricthen subtractingtheH ioutspectratheal.fitted
emission.
continuum
emission,the2.measured
itoemission
beisunderesTable
Resultsdataof the H
fits
the
N-PDFs.will
wedatafiltermostfrom
large-scale
H ibackgroundemission.
The
THOR-only
ferometric(Ossenkopf-Okadaet2016).
We derived
each
仮定するスピン温度によって,質量は約3倍異なる.
13
The GRS
COreveal
spectrum(Jackson
et
al.
2006)
coveringfrom the noise.
the suppress
Galactic center(Kalberla & Dedes 2008), we
N-PDF
from
theHregions
markedbytheredpolygons
invelocities
Fig.
11, continuum
timatedasweakemissiontocana significant
iemission
of
less
than
30
K,
often
just
within1
1
2
5 km srespectively.
to 135 km
s is shownin blueand haslow
beenmultiplied
hNHthei [cmatomic] Width
PL index↵
However,
if we take
into accountcolumnden- by a Componentthatgas density
distribution
in the vertic

A&A proofs: manuscript no. main2008.13502
V
450

55

400

whole filament

350

50vHI [km s

1]

300
250

45

200
150

40

100
Fig. 15. H i-to-H2 transition. The plot shows the H i mass surface density
traced by H i emission as a function of the total hydrogen mass surface
density. The black solid line indicates a 1-to-1 relation. The dashed blueline shows a fit to the mean of the distribution.

50

35
35

40

45

50

55

55
eastern region

4.4. Spatial correlation between atomic and molecular gas

300
250

50
vHI [km s

1]

200
45

150
100

40

50
35
35

40

45

50

55

55
western region

0
300
250

50
200

1]

vHI [km s

The Histogram of Oriented Gradients2 (HOG) is a method basedon machine vision to study the spatial correlation in the emission
by two or more spectral line tracers across velocity channels in
an unbiased and systematic way. In Appendix B we briefly outline the basic principles involved in this method. A comprehensive description is given by Soler et al. (2019).
We applied the HOG on each part of the filament to investigate the spatial correlation between H i and 13 CO. The output of
the HOG analysis is a matrix where the rows and columns correspond to the di↵erent velocity channels in each tracer, as shownin Fig. 16. The number in each matrix position corresponds tothe projected Rayleigh statistic (V), which is an optimal estimator of the morphological correlation between the velocity channel maps as evaluated by the orientation of its intensity gradients.
High values of V correspond to high spatial correlation and values of V ⇡ 0 correspond to very low spatial correlation. The intensity gradients are calculated using a Gaussian derivative kernel whose width determines the spatial scales under consideration. To exploit the available spatial resolution, we selected aderivative kernel size that matches the synthesized beam size of
the GRS 13 CO data, that is, 4600 . The projected Rayleigh statisticp
is a measure of the significance of the spatial correlation, V ⇡ 2is roughly the equivalent of a 1 deviation from complete lack ofcorrelation, which corresponds to a flat distribution in the angles
between the intensity gradients. However, the significance of theresult also has to be evaluated with respect to the chance correlation that may be present between the velocity channel maps. We
use the standard deviation of V in the velocity range between 10
and 90 km s 1 as an estimate of the amplitude of the chance coragainst
which densities
we can evaluate
the significanceFig. 11. Top panel: H i column densities of the combined WNM and CNM seen in Hrelationi emission.
The column
were corrected
for optical of the Vvalues.
This
assumesthat there
are enoughindependent
depth, weak di↵use continuum emission, and the kinematic distance ambiguity. The
opticaldepth
is measured
towardthe continuum
source velocitymaps
in 3.3.3).
the selectedvelocityofrange.
G19.075-0.287 and is applied to correct the column densities throughout the wholechannel
cloud (seeSect.
The position
G19.075-0.287 isindicated by the green cross. Middle panel: The H i column densities of the CNM inferredfrom16
HISA
featuresa spindistribution
temperaturebetween
ofFigurepresents
theassuming
correlation
Hi
13
T HISA = 40 K and a background fraction of p = 0.9. Bottom panel: H2 column densities
inferred
fromall13 CO
asof
a tracer.
We assumedan H2 /13 CO
and
CO
for
parts
the
filamentasafunctionofvelocity.
ratio of 3.4⇥105 . The red dashed polygons in each panel indicate the eastern and westernof the filamentthat areanalyzed
separately.
Wepartobservea significant
spatialcorrelationin Thethe white
velocity chanand black contours indicate the column density thresholds that were used for the derivationof
thecolumndensityprobability
densityfunctions1nels around vHI ⇡ v13 CO ⇠ 43 km s and ⇠ 47 km
s 1 toward the(see Sect. 4.2).
west. However, the eastern part of the filament shows no signifi-

0

45

150
100

40

50
35
35

40
45
vCO [km s

50

55

0

1]

Fig. 16. HOG correlation plane of the filament as marked by the redpolygons in Fig. 11. This figure presents the computed correlation between H i and 13 CO across velocities defined by the projected Rayleighstatistic. The white line shows a 1-to-1 correlation across velocities. The
blue contours show the 5 level on V. Large values of V indicate a highspatial correlation. Values of V close to zero indicate a negligible spatial
correlation.

2008.13502
10

10

10

1020

1021

Probability density

101

10

10

1022

10

1020

1021

101

whole filament Ts = 40 K

10

10

1022

10

10 1

10 1

10 1

10 2

10 2

10 2

1021

101

1022

1023

101

102

1021

whole filament H2= 0.57= 2.99100

10 3 1
10

100

101

1022

1023

102

10 3 110

eastern H2

100= 0.54= 4.3410 2

10 2

NH / NH

10 3 1
10

100

101

NH / NH

102

1022

1023

102

100

10 2

102

101

= 0.58= 2.81

10 1

101

100

western H2

10 1

100

western HISA Ts = 40 K

101

10 1

10 3 1
10

1022

0

1021

101

10

= 0.28

10

100

1021

= 0.30
0

10

10

101

eastern HISA Ts = 40 K

= 0.29101020

0

10 3 1
10

Probability density

10

10 3 1
10

100

101

102

NH / N H

Fig. 13. Top panels: N-PDFs traced by H i emission. The distributions are derived from the H i column densities that have been corrected for opticaldepth and continuum emission (top panel of Fig. 11). Middle panels: The N-PDFs of the gas traced by HISA. Bottom panels: H2 N-PDFs traced
by 13 CO. The left panels show the derived N-PDF of the whole filament (east+west), respectively. The middle and right panel show the N-PDFs
of the eastern and western part of the filament, respectively. The blue curves indicate the log-normal fits to the distribution. The red vertical dashedand solid lines mark the column density threshold (last closed contour) and mean column density, respectively. The red solid lines in the lower
panels indicate the fit to the power-law tail.

A&A proofs: man

Fig. 15. H i-to-H2 transition. The plot shows the H i mass surface density
traced by H i emission as a function of the total hydrogen mass surface
density. The black solid line indicates a 1-to-1 relation. The dashed blueline shows a fit to the mean of the distribution.

Ian W. Stephens,1 Manuel Fernández-López,2 Zhi-Yun Li,3 Leslie W. Looney,4 and Richard Teague1

2008.04952

Draft version August 13, 2020
Center Typeset
for Astrophysics
Harvard &style
Smithsonian,
60 Garden Street, Cambridge, MA 02138, USA ian.stephens@cfa.harvard.ed
using LATEX| twocolumn
in AASTeX63

tuto Argentino de Radioastronomı́a (CCT-La Plata, CONICET; CICPBA), C.C. No. 5, 1894, Villa Elisa, Buenos Aires, Arge
3 Astronomy Department, University of Virginia, Charlottesville, VA 22904, USA
4 Department of Astronomy, University of Illinois, 1002 West Green Street, Urbana, IL 61801, USA

Low Level Carbon Monoxide Line Polarization in two Protoplanetary Disks: HD 142527 and IM Lup

to2 ApJon August11, W.
2020)
Ian W. Stephens,1 Manuel Fern(Acceptedández-López,
Zhi-YunLi,3 Leslie
Looney,4 and Richard Teague1
1 Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA ian.stephens@cfa.harvard.edu

ABSTRACT

2 Instituto Argentino de Radioastronomı́a (CCT-La Plata, CONICET; CICPBA), C.C. No. 5, 1894, Villa Elisa, Buenos Aires, Argentina
3 Astronomy Department, University of Virginia, Charlottesville, VA 22904, USA

Magnetic fields
are expected
to play an important role in accretion processes for circumstellar disks.
4 Departmentof Astronomy, University of Illinois, 1002 West Green Street, Urbana, IL 61801, USA
Measuring the magnetic field morphology is difficult, especially since polarimetric (sub)millimeter(Accepted
on August2020)
continuum observations may not trace
fieldstoinApJ
mostdisks. 11,
The
Goldreich-Kylafis (GK) e↵ect suggeststhat line polarization is perpendicular or parallel to the magnetic field direction. We attempt to
ABSTRACT
observe CO(2–1), 13 CO(2–1), and C18 O(2–1) line polarization toward HD 142527 and IM Lup, which
are expected to play an important role in accretion processes for circumstellar disks.
are large,Magnetic
bright fields
protoplanetarydisks. We use spatial averaging and spectral integration to search
Measuring the magnetic field morphology is difficult, especially since polarimetric (sub)millimeterfor signals
in both disks, and detect a potential CO(2–1) Stokes Q signal toward both disks. The
continuum observations may not trace fields in most disks. The Goldreich-Kylafis (GK) e↵ect suggests
total CO(2–1)
polarizationis fractions
are or
1.57± 0.18%and1.01 ± field
0.10%
for HD We
142527
andtoIM Lup,
that line polarization
perpendicularparallelto themagnetic
direction.
attempt13
respectively.
Our Monte
Carlo andsimulations
that thesesignals
are marginal.
also stackobserve CO(2–1),
CO(2–1),
C18 O(2–1)indicate
line polarization
towardHD 142527
and IM Lup,We
which
large, bright
protoplanetarydisks. Werotation,
use spatial
averaging
andwasspectral
integration
searchStokes areparameters
basedon the Keplerianbut
no signal
found.
Acrosstothe
disk traced
00
in both thedisks,
detecta potential
CO(2–1)signaltoward bothdisks. Theless thanby dustforofsignals
HD 142527,
3 and
upper
limitsfor Pfrac
at 0.5Stokes(⇠80Qau)resolution
are typicallyCO(2–1) polarization
fractions are 1.57 ± 18
and 1.01 ± 0.10% for HD 142527 and IM Lup,
3% fortotal
CO(2–1)
and 13 CO(2–1)
and 4% for C 0.18%
O(2–1).
For IM Lup the 3 upper limits for theserespectively. Our Monte Carlo simulations indicate that these signals are marginal. We also stack
three lines
typicallybased
less onthan
4%, and
12%,but
respectively.
ontraced
our stacking
Stokesareparameters
the3%,
Keplerianrotation,no signal wasUpper
found. limits
Acrossbased
the disktechniqueare ofupHD
to 142527,
a factortheof 3⇠10lower,
thoughstacking
areasau)canpotentiallyaveragelessoutthansmall-scaleby dustupper
limitsfor Pfrac
at 0.500 (⇠80
resolution
are typically
13 also compare our 18
polarization
1.3 mmto forobservations
at
3% for structure.
CO(2–1) andWeCO(2–1) and 4% for C continuumO(2–1). Forpolarization
IM Lup the 3at upper
limitsthese
lines
are typicallyless than
4%, and 12%,inrespectively.
Upperdust
limitsbased
our142527
stacking shows a
870 µmthree
fromprevious
studies.
The3%,polarization
the northern
trapof onHDtechniqueare upa factor of ⇠10
lower,
stacking
areas
potentiallytoaverageout small-scalesignificant
changein tomorphology
andan thoughincreasein Pfrac
ascan
compared
870 µm.
For IM Lup, thepolarization structure. We also compare our continuum polarization at 1.3 mm to observations at
1.3 mm polarization may be more azimuthal and has a higher Pfrac than at 870 µm.
870 µm from previous studies. The polarization in the northern dust trap of HD 142527 shows asignificant change in morphology and an increase in Pfrac as compared to 870 µm. For IM Lup, theIn the limit v3d/h^>C, A b, and 9Í, the magnetic
field direction is the natural choice for the quantization
axis. We denote by n±,
and nb the number densities
of molecules in the ma = ± 1, w0 = 0, and= 0 sublevels. In
the absence of circular polarization, n+ —ON MAPPING THE MAGNETIC FIELD DIRECTION IN MOLECULAR
CLOUDS= n±. The emissionBYandabsorption
coefficientsare
POLARIZATION MEASUREMENTS
completely determined
byGoldreich
the sublevel
numberdensiPeterand Nikolaos
D. Kylafis
California
Institute of element
Technology, Pasadena,
California
ties, the reduced dipole
matrixof thetransiReceived 1980 July 21; accepted 1980 October 6
tion d, and the angle y between the propagation
L76
GOLDREICH AN
ABSTRACT
directionnandmagnetic
field
directionb.
We predict that interstellar radio-frequency lines possess a few percent linear polarization, procoefficients are related to d bythat (1) the ofradiative
transition rate
is at least comparable
to the collision rate,The(2) Einstein
theThevidedequationradiative
transferin component
optical depth is moderate and anisotropic, and (3) the number of extrema of the velocity comform isponent along the line of sight through the source is small. If the Zeeman splitting exceeds both
_ 64ir4dV_ 327r4d2
p
198lApJ...243L..75G

at 15
The Astrophysical Journal, 243:L7S-L78, 1981 January© 1981. The American Astronomical Society. All rights reserved. Printed in U.S.A.

the collisional frequency and the radiative transition rate, then the polarization is aligned either
perpendicular to or parallel to the projection of the magnetic field on the plane of the sky.
Subject headings: interstellar: magnetic 3fields — polarization — radiative transfer^- S] ,

I. INTRODUCTION<? =±,11,

a,i

3hc3

(1)

’

'öa'i’ _ 3hH '(4)The rate equations which govern the sublevel populations
arewrittenasequilibrium. The radiative transfer issolved
with
the

where
I*, and I\\ are the specific intensities
radiation
aid of theof
Sobolev
approximation in § III. Asymptotic
It is not generally appreciated that many interstellar
solutionsforthemagnitude
the polarization in theradiofrequency lines
may possesspolarizedalong
ê± =measurable(b X amounts
ñ)/sin y limits
andof highe\\and=low(boptical— ofdepth
are given
com= and—Aa,bn±+ 9î±(^6 — n±) — C'(n± — no)of linear polarization. Our aim is to describe the circumparedwiththeresultsofnumerical
computations
inhstancescos 7)/sin
7, linears is polarization
the pathwilllength
along n, and </>„ isunder whicharise.
§ IV. Section V is devoted to a discussion of the+ mainC[nb exp ( — hvr/kT) — n+] ,Analysisof a simple modelprofile
problem suffices
to illustratethenormalized
function.
The
absorption
coeffiresults
and
their
potential
forapplication.
all of the important physics.
cientsanda hypotheticalsource functions
We consider
molecule whicharepossesses
II. BASIC EQUATIONS
two levels between which radiative and collisionaltransitions of frequency vr can occur. The upper and3 angular momenta Fa = 1 andlower levels have totalb line formation in
Fh = 0, respectively. We investigate
a medium in which the macroscopic velocity differences
are much greater than the thermal velocities of themolecules, a condition
met in molecularv
3 generally
2
clouds.
±We assume that the Zeeman splitting fjßß/h issmaller than the Doppler width Ay, so that circularpolarization does not arise. In this Letter we make theadditional assumption that the Zeeman splitting ismuch larger thanrate C and the spon=the collision2
taneous and stimulated radiativetransition ratesb
Aa,b and 9î. We reserve discussion of the more difficult
case, in which this condition is not satisfied,2to a laterand more detailed paper. The known densities andexpected magnetic
field 2strengths in interstellar clouds
11
2
are such that ijßß/h is much greater
than
C,
A
,b,
and
b
a
9Î for most centimeter and millimeter wavelengthlines.
Rotation endows molecules with minimum magnetic¿± = (27t)k\\ = (27t)C(n — n±) ,s}2= magnetic— Aa,bno + 3îo(% — no) — 2C'(n0 — n±)
In the limit v3d/h^>C, Aatb, and^9Í, thefield direction is the natural choice for the quantization
C[nh exp { — hvr/kT) — no] ,axis. We denote by n±,
and nb the number +densities
of molecules in the ma = ± 1, w0 = 0, and= 0 sublevels. In the absence of circular polarization, n2n+ — + nonb = n = constant .
(5)±= n±. The emission and absorption coefficients are
2completely determinedby the sublevel number densiHereof C
0ties, the reduced dipole matrix element
the andtransi-C' are collisional transition rates, and Ttion d, and the angle y betweenisthe
thepropagation
kinetic temperature. The net rates of stimulated
direction n and magnetic field directionb.
absorption and emission are
The equation of radiative transfer in component
form is{nb — n cos y — n sin 7) , (2)^ZL
c (n — n±) ’^- S3] ,

9Î+ = (1)<? =±,11,

S

^

2
_ hvf
(n± cos 7 + ^0 sin
v intensities of radiation
where 7)
I*, and I\\ are the ,specificpolarized2 along ê± = (b X ñ)/sin y and 5Ro
e\\ = (b Bg¿—s dv<t>v S ~I II sin2 77)/sin7)7, s’ is the path length along n, and </>„ is3
c (n — n± cos y — nh 0cossin
the normalized profile function. The absorption coefficients and source functions are

III. SOBOLEV APPROXIMATION

3

COs2

(6)

Í

(-W^bb)] j

198lApJ...243L..75G

v. DISCUSSION© 1981. The American Astronomical Society. All rights reserved. Printed in U.S.A.
To our knowledge, there are no reports of linearlypolarized radio-frequency lines other than those associated with maser emission from OH, H20, and SiO.
Goldreich, Keeley, and Kwan (1973a, b) attributed
fl , 10 (C + 3Cf) (nb - na)l
the linear polarization in the maser lines to the same
(17)
IN MOLECULAR
CLOUDS
L ON MAPPING
3
Aa,b THE MAGNETIC
nb
J , FIELD DIRECTION
basic mechanism
described
in this Letter. A special
L76
GOLDREICH AN
BY POLARIZATION MEASUREMENTS
feature of maser line formation is that, since the opticalfor TAU ^>> 1. There is an extra requirement for theis negative, the radiative
maycoefficientsbe aniso- are related to d byPeter
Nikolaosdepth
D. Kylafis
Thetransfer
Einsteinvalidity of equation (16), namely
31 Goldreich|/|andAi +tropic even for |r| »1. The 21 cm line presumably
A2 + A31 <<C 1 must be satisfied.California Institute of Technology, Pasadena, California
4
hasOctober
P<^\
which
Received 1980for
JulyP21;areaccepted 1980
6 because C/Aa,b^> 1 in all clouds_for64ir
dV_ 327r4d2
Several general features of the expressionsp
TAU = 0(1). It is not clear what a,imagnitude of3(4)worth noting. The maximum value of P occurs
at
ABSTRACT
3hc’'öa'i’ _ 3hH 'polarizationtoexpectforlines
formedinmolecular
7 = tt/2. Anisotropicr isinterstellara requirement
for P ÿ*lines
0; possess a few percent linear polarization, proWe predict thatradio-frequency
clouds. Certainly C/A < 1 in the source regions off(<X, ß) =vided
1 forthat
Ai =(1)Athe
A3. Collisional
excitationtransition
rate is atisleast comparable to the collisionaibrate, (2)Thethe rate equations which govern the sublevel popula2 = radiative
many ofmillimeterlines.
The major unisotropic, opticalso P isdepth
smalllarge andvaluesof (C +and
3C')/
is formoderateanisotropic,(3) the number
extrema ofwavelength
the velocity
comtionsarewritten as
certainty
is the splitting
scale ofexceeds
the spatial
Aafi. In ponent
addition,
P ocline
TAU
for through
TAU <3C
and is small.
along theof sight
the1,source
If the Zeemanboth variations of thethe radialisvelocity
is monotonie, or nearly
the1 collisional
the radiative
then the Ifpolarizationaligned either
P « TAU“for TAU frequency>>> 1. Theandlargestvalues oftransition
P are rate,velocity.
the plane
the sky.throughso, field
alongontheline ofof sightthe clouds,+then
attained perpendicular
for TAU ~ 1.to or parallel to the projection of the magnetic= —Aa,bn±9î±(^6 — n±) — C'(n± — no)
TheTAU
Astrophysicalfor« 1, andJournal, 243:L7S-L78, 1981 January 15

2008.04952

Subject headings: interstellar: magnetic fields — polarization — radiative transfer+ C[n exp ( — hv /kT) — n+] ,br
I. INTRODUCTION
equilibrium. The radiative transfer is solved with theaid of the Sobolev approximation in § III. Asymptotic
It is not generally appreciated that many interstellar
solutions for the magnitude of the polarization in theradiofrequency lines may possess measurable amounts= and— comAa,bno + 3îo(% — no) — 2C'(n0 — n±)limits of high and low optical depth are^given
of linear polarization. Our aim is to describe the circumpared with the results of numerical computations instances under which linear polarization will arise.
+main
C[nh exp { — hvr/kT) — no] ,§ IV. Section V is devoted to a discussion of theAnalysis of a simple model problem suffices to illustrate
results and their potential for application.
all of the important physics.
We consider a hypothetical molecule which possesses
2n± + nonb = n = constant .
(5)
II. BASIC EQUATIONS
two levels between which radiative and collisional
In the limit v3d/h^>C, Aatb, and 9Í, the magnetictransitions of frequency vr can occur. The upper and
C and C' are collisional transition rates, and T
field
direction is the natural choice forHere
the quantization
lower levels have total angular momenta Fa = 1 andaxis. We denote by n±,
and nb the isnumberdensities temperature. The net rates of stimulated
the kinetic
Fh = 0, respectively. We investigate line formation inofmolecules
in
the
m
=
±
1,
w
=
0,
and
=
0 suba0
a medium in which the macroscopic velocity differences
absorption
and emission arelevels. In the absence of circular polarization, n+ —are much greater than the thermal velocities of the= n±. The emission and absorption coefficients aremolecules, a condition generally met in molecular
COs2
completely determined by the sublevel number
densiclouds.
9Î+
=
S
^
ties, the reduced dipole matrix element of the transiWe assume that the Zeeman splitting fjßß/h istion d, and the angle y between the propagation
smaller than the Doppler width Ay, so that circular
direction n and magnetic field direction b.
polarization does not arise. In this Letter we make theBg¿
The equation of radiative transfer in component
2additional assumption that the Zeeman splitting is
5Ro
(6)
s
dv<t>
S
~I
II
sin
7
v
form
is
3
much larger than the collision rate C and the spontaneous and stimulated radiative transition rates^- S3] ,<? =±,11,(1)
Aa,b and 9î. We reserve discussion of the more difficult
III. SOBOLEV APPROXIMATION
case, in which this condition is not satisfied, to a later
where I*, and I\\ are the specific intensities
and more detailed paper. The known densities and
It ofis radiation
extremely difficult to solve the coupled equations
polarized
along
ê±
=
(b
X
ñ)/sinyande\\ = (b —expected magnetic field strengths in interstellar cloudsof radiativetransferand statistical equilibrium in a noncos line7)/sin7, ours isnumericalthe pathresults,
length while
alongn, dashedand </>„ one
is correspondsarethat ijßß/h isasmuch
greaterthan C,depth
Aa,b, TAU.
and The hsolid
Fig.such
1.—Polarizationa functionof optical
gives
the
theare:normalized
absorption
medium.
in the limit that themost centimeter
and Themillimeterto9Îthefor
asymptotic
expression (17).
values ofwavelength
the parameters used
Ai = A2 profile= 1 X function.
10-9 s-1, A3The= 0,stationary
Xr = c/vr coeffi= 0.3
cm, C/Aa,bFortunately,=2
cientsareimply 7thermal
0.212,
andand\ =sourcea = ßfunctions= 0, which= tt/2. P ocvelocities
sin 7 is an excellines.C/Aa,b = 0,T = 10K, 7bb = 2.7 K. The angles are: 0 = tt/2,
are much smaller than the macrolent Rotation
approximation
for
all
TÁU.
endows molecules with minimum magnetic3

scopic velocity differences, a simple approximateheir contributions to the polard the combined radiation willction of the polarization of the
POLARIZATION OF MOLECULAR LINES AT RADIO FREQUENCIES: THE CASE OF DR 21(OH)ularLINE
to themagnetic field.
P. C. Cortes, R. M. Crutcher, and W. D. Watson
mpact, external sourceofReceivv
raed 2005 February 23; accepted 2005 April 7
e optical depths as in the above
ABSTRACT
direction
perpendicular
to theWe present
polarization observations
in DR 21(OH ) from thermal dust emission at 3 mm and from CO J ¼ 1 ! 0line emission. Theassociatedobservations werewith
obtained using the Berkeley-Illinois-Maryland Association (BIMA) array.
ular distribution
Lai et al. observed this region at 1.3 mm for the polarized continuum emission and also measured the CO J ¼ 2 ! 1
Ourthecontinuumpolarization
results are consistent with those of Lai et al. However, the direction of therectionpolarization.
thanisangulardislinear polarization for the J ¼ 1 ! 0 is perpendicular to that of the CO J ¼ 2 ! 1 polarization. This unexpectede J ¼ 1;Mwas¼explored
0 substatebesolutions to the multilevel radiative transfer equations for a gas withresultby obtainingwill
numerical
optical depths. We find that in addition to the anisotropic optical depths, anisotropic excitation due totion ofanisotropic
thisradiationa source of radiation that isthan
externalwill
to the CO is needed to understand the orthogonality in the directions ofpolarization. The continuum emission by dust grains at the core of DR 21(OH ) is sufficient to provide this exters. Thenal radiation.
J ¼ 1;TheMCO¼polarization
0 substatemust arise in relatively low density (n " 100 cm#3 ) envelope gas. We infer
B " 10 !G in this gas,
whichtheimpliesthat the envelope is subcritical.
ed in comparison
with
other
Subject headinggs: ISM: magnetic fields — ISM: molecules — polarization — stars: formation
ation thatemerges from the gas
on of " radiation, parallel to the
1

1

2

H2

1. INTRODUCTION
The star formation process is one of the most complicatedorecomplicatedbecausethe includes
problems
in current astrophysicalresearch.of
Its study
several physical parameters, of which the magnetic field is thens,conclusions
apply
leastanalogous
observed. Magnetic
field observations are
divided into meaof the Zeeman
effect(inJorder
to2
obtainthemagnetic
nsurements
associated
with
the
¼
!
1
field strength in the line of sight) and linear polarization observations of star-forming regions. Dust polarization is believed to be permolecule.
pendicular to the magnetic field under most conditions (Lazarian
velocity
and2003);
hence, dustgradientspolarization has beenusedexteras a major probe formagnetic field geometry. In order to efficiently measure the dust
hthe
present,
theinformation
direction
thefield mor- Fig. 5.—Fractional polarization P calculated for the CO transitions J ¼
polarization and infer
about theof
magnetic
high-resolution
observations
are required.
The BIMA
atphology,
isemitted
by
the
gas
is
demillimeter interferometer has been used to obtain high-resolution 1 ! 0 and J ¼ 2 ! 1 as a function of the LVG optical depth for the CO J ¼
maps inof
severalstar-forming
cores(Rao etof
al. an1998; Girart & 1 ! 0 transition. Here T
ance
these
two
causesgas ¼ 28 K and Tsource ¼ 42 K. Each pair of curves
Crutcher 1999; Lai et al. 2001, 2002, 2003). These resuls.5are5(Qq1.421164001.421164-28.645.mBT-0.0001Tc9-23(r)0o)-3-23.1(e)0962676.7(h)26.-168epths4(-)0..1.1(r)13.5(e-236
represents calculations for a different density of molecular hydrogen: 25, 75,
nce is not, however, the same!3
. In the upper panel , the velocity gradient is characterized by # ¼
and
225
cm
¼ 1 ! 0 transition. The dust
0:1. In order to test the robustness of the calculation, we decreased the degree of(OH) is much higher at the CO
anisotropy by setting # ¼ 0:3. This is shown in the lower panel.
y than the CO J ¼ 1 ! 0 fre-Annu. Rev. Astron. Astrophys. 2012.50:29-63. Downloaded from www.annualreviews.org
Access provided by Tokushima University on 11/24/20. For personal use only.

Magnetic Fields
in Molecular Clouds
Richard M. Crutcher
Department of Astronomy, University of Illinois, Urbana, Illinois 61801;
email: crutcher@illinois.edu

Annu. Rev. Astron. Astrophys. 2012. 50:29–63

Keywords

First published online as a Review in Advance on
May 29, 2012

ambipolar diffusion, dust polarization, magnetohydrodynamic (MHD)
turbulence, spectral-line polarization, star formation, Zeeman effect

The Annual Review of Astronomy and Astrophysics isonline at astro.annualreviews.org
This article’s doi:
10.1146/annurev-astro-081811-125514
c 2012 by Annual Reviews.
Copyright !
All rights reserved
0066-4146/12/0922-0029$20.00

Abstract
This review examines observations of magnetic fields in molecular clouds
and what those observations tell us about the theory of molecular cloud
evolution and star formation. First, the review briefly summarizes classesof theoretical models of molecular clouds and specific predictions of themodels that can be tested by observation. Then, the review describes thetechniques for observing and mapping magnetic fields in molecular clouds,
followed by discussion of important examples of observational studies using each technique. A synthesis of results from all observational techniquessummarizes the current state, which is that though magnetic fields generally dominate turbulence, there is no definitive evidence for magnetic fields
dominating gravity in molecular clouds or for ambipolar-diffusion-driven
star formation. Finally, the review discusses prospects for advances in ourobservational capabilities with telescopes and instruments now beginning
operation or under construction.

29

center.
andthird self-calibrations were infinite, 25 s, and 10 s,
Delivered data
were manuallycalibrated
the Northrespectively.
Self-calibration
improved
thebycontinuum
AmericanARC sta↵ using
theHD
CommonAstronomy
StokesI signal-to-noise
ratio for142527 and
IM LupSoftwareApplications
packageet al.
bya factorof 6 and 3, (CASA)
respectively.
The(McMullin
self-calibration
2007). J1427–4206
was used Stokes
as theI flux
solutionsfrom the continuum
wereandthenbandappass tocalibrator,
J1610–3958
wasVthecalibrator,plied
the continuum
Stokes QU
andphase
the spectral
line
and J1517–2422
wasthespectral
polarization
ALMA
StokesIQU V . For
eachline, calibrator.
we subtractedtheBand 6 observations
havea typical
absolute flux
uncercontinuum
emission byfitting
the continuum
using
the
tainty of 10%,and thepolarization
uncertainties
as we
debaseband’sline-freechannels.
To cleanthe images,
terminedby theD-termslessthan weighting
a 5%.
use
the CASA
task
tcleanwere
using
Briggswith
We imaged
the continuum
lines
a robust
parameterof 0.5. The andfinal spectral
continuum
andusing
line
CASA v5.6.0.
construct
the arecontinuum
synthesized
beamsToandnoise levels
reported images,
in Table 1. All images in this paper have been corrected forthe primary beam. The pixel size for our maps is 0.00 11.
From the Stokes IQU images, we constructed polarized intensity (PI ), Pfrac , and position angle ( ) maps
where:Thus,
given
the thepolarization
P,
one
can
estimator
distribution
isobserved
peakedat 0behavior
and similar to
exponential.
understandnoise
ofanthese
StokesWhen transforming
to a Gaussianwith the SNR,it develops
an incalculate
truepolarization
Pc by¯ndingtheters. theWe thusanalyze
the CO(2–1)
StokesQU
termediate
minimumthatcomplicatesitsoverallshape.
In
contrast,
maximumthebefore
most probablevalue)of thePDF
the(i.e.
theprimary
correctiofor λonaround1,mapsthe distribution
transforms
from beama Rayleigh-likein
Eq. (18).
one to aFor
Gaussian
oneHD
without
introducing
extremum,both
142527anda secondary
IM Lup,the noisForvery thesigni¯cantpolarization
detections
which
is similar
Rice caseStokes
andwillQUbe further
discussedtheentireto CO(2–1)
V cubesare infit v(P& 5 3.1.
!P ),thethesimple
is valid(see
SectionGivenmarginalhigh-SNR
gain of using limit
λ = 2 andits induced
withaGaussian,withanaverage
value
of
0.0
complexity on the2006,
distribution,
we consider λ = 1 as our optimal ±Vaillancourt,
Eq. (12)):
We check for any
in each cube
solution.
qffiffispatial
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffivariation
ffiffiffiffiffiffiffiffiffiffiffiffi
Weatingthen propose
following(MAS)meanesti- sq
2 modified
a moment
6Q maps: rootð19Þ
Pthe#
þ U 2(i.e.,'asymptotic! 2Pthecmator:
the spectrum).2 2 The average value in these mi /σ− e−pand
21
3.3
±
0.2
mJy,
. the noise is once again Gaussi(20)p̂MAS = pi − σ
15500
2pi
noise characteristics do not change for emission
February 28
We Advance
showAccessinpublication
Fig. 2014
3 its
transformation curve, together witho↵ the disk, nor fordi↵erent velocity bins. As

2008.04952

MNRAS 439, 4048–4056 (2014)dsome other classical estimators, demonstrating how it extrapolates
A novel estimator of the polarization amplitude from normally
Stokes parameters
S. Plaszczynski,1‹ L. Montier,2,3 F. Levrier4 and M. Tristram1
1 Laboratoire de l’Accélérateur Linéaire, Université Paris-Sud 11, CNRS/IN2P3, Orsay, France
2 Université de Toulouse, UPS-OMP, IRAP, F-31028 Toulouse cedex 4, France

3 CNRS, IRAP, 9 Av. colonel Roche, BP 44346, F-31028 Toulouse cedex 4, France

4 LERMA/LRA, ENS Paris et Observatoire de Paris, UMR 8112 du CNRS, 24 rue Lhomond, F-75231 Paris cedex 05, France

Accepted 2014 February 7. Received 2014 February 6; in original form 2013 December 6

PI =

p

Q2 + U 2

Pfrac = PI /I✓ ◆1
U= arctan
.
2
Q

(1)
(2)
(3)

Since PI can only be positive, it has an inherit bias toward positive values. We de-bias the values following
Hull & Plambeck (2015). In our images, we show thepolarization as line segments. These segments are typically called “vectors.” While we adopt this custom, we

ABSTRACT

We propose a novel estimator of the polarization amplitude from a single
normally distributed (Q, U) Stokes components. Based on the properties ofand dubbed modified asymptotic, it meets several desirable criteria: (i)whole positive region; (ii) its distribution is continuous; (iii) it transformsignal-to-noise ratio (SNR) from a Rayleigh-like shape to a Gaussian on
and reaches its components’ variance as soon as the SNR exceeds 2; aand can therefore be used on large data sets. We also revisit the construcconfidence intervals and show how the Feldman–Cousins prescription e
issue of classical intervals lying entirely in the unphysical negative dom
can be used to identify statistically significant polarized regions and con
for polarization data. We then consider the case of a general [Q, U] co
perform a generalization of the estimator that preserves its asymptotic p
Figure 3. Transformation curveof the MAS estimator (in red). We alsothat its bias does not depend on the true polarization angle, and provide anshow some other classical estimatorin value,
lighttogether
blue,withtheits asymptotic
its variance.curves:
The estimator
variance, provide a pow
of
the
true
polarization
amplitudethat
follows
anunbiased
Gaussian(equation 15), in blue the most probable (Wardle & Kronberg 1974) andin distas low as 2. These results can be applied to the much more general caseblack the ML (Simmons & Stewart
discontinuous
normally 1985).
distributedThey
randomarevariablefrom Cartesian toandpolar thecoordinates

latter two non-analytic. Also Key
shown
inpolarization
green is– thecurve
the–posteriorwords:
methods:
data ofanalysis
methods: statistical.
mean Bayesian estimator (Quinn 2012) with a uniform prior on p0 /σ . The
Unlike in the angular case where the
I N T represents
RO D U C T I O Nthe naive estimator.
dashed1line
1arctan u is unbiased (Vinokur 1965), ge
The advent of high precision experiments dedicated to measuring
the radiation polarization on cosmological scale or exploring the2qestimate for the amplitude from a single! (q, u2

Figure 1. 1.3 mm continuum polarimetric map toward
HD 142527. Color-scale shows the polarized intensity PI .
Red and blue vectors show the direction of the polarization(i.e., vectors are not rotated). Red and blue vectors areshown for Pfrac smaller than and larger than 5%, respectively (i.e., all blue vectors have higher Pfrac than the red).
Vectors are shown for signal-to-noise ratio >3 for Stokes I
and PI and for Pfrac < 40%. Contours show the Stokes I
emission, with levels of [3, 10, 25, 50, 100, 200, 325, 500,
750, 1000] ⇥ I , where I = 37 µJy bm 1 .

Figure 3. Comparisons of the 1.3 mm and 870 µm dust continuum polarization for HD 142527. The first and second panels
show the 1.3 mm and 870 µm polarized intensities overlaid with Stokes I contours and polarization vectors (all vectors are
the same size for clarity). Observations at 1.3 mm have been regridded to the 870 µm pixel size and smoothed to the 1.3 mm
resolution (Table 1). 1.3 mm Stokes I contours are drawn for [4, 150, 500, 2000] ⇥ I,1.3 mm , where I,1.3 mm = 37 µJy bm 1 ,and 870 µm Stokes I contours are drawn for [3, 25, 60, 250] ⇥ I,870 µm , where I,870 µm = 80 µJy bm 1 . The third panel shows
the ratio between the polarization fractions at 1.3 mm and 870 µm. The fourth panel shows the di↵erence between the 1.3 mm
and 870 µm polarization angles. The latter two panels have a square root stretch for the color scale.

Figure 4. Same as Figure 3, but now for IM Lup. 1.3 mm Stokes I contours are drawn for [4, 150, 500, 2000] ⇥ I,1.3 mm ,where I,1.3 mm = 22 µJy bm 1 , and 870 µm Stokes I contours are drawn for [3, 100, 250, 900] ⇥ I,870 µm , where1.
I,870 µm = 100 µJy bm

Line Polarization toward HD 142527 and IM Lup

2008.04952
11

Figure 11. Stacking based on Keplerian rotation of selected quadrants (90 wedges in disk plane) via GoFish. The top row
shows selected quadrants overlaid on the moment 0 maps (integrated over same velocity interval as Figures 5 and 6). The left
two images show the quadrants for HD 142527, and the right two images show quadrants for IM Lup. The number range next
to each quadrant correspond to the quadrant’s angle range from the disk’s axis, starting from PAred . The middle row shows 8
panels where we stack for the quadrants shown in the top row for HD 142527. The top four of these panels correspond to thefirst HD 142527 image, while the bottom four correspond to the second image. The bottom left of each of the 8 panels shows
the minimum and maximum radii, rmin and rmax , used for the quadrant. The bottom right of each panel shows the angle rangeof the quadrants indicated in the top panels. The 8 panels on the bottom row are like the middle row, except for IM Lup.

hens et al.

re given as ranges in Tathe 3 upper limits vary
velocity interval and (foradrant analyzed. We reum 3 upper limit foundty interval and quadrant.
xel analysis, the stacking
ng lower 3 upper limits

e executed
one thousand
Figure 9. HD 142527 IQU V CO(2–1) spectra, stacking
on the Keplerian profile of the disk via GoFish acrossthebasedTable
2 upper limits
the entire disk out to a radius of 3 . The stacked Stokes I
signal has been divided by 170.
. In
these runs, we ranhe mass, inclination, andKeplerian profile strongly
For the mass, we assume
is 15% of the estimatedinclination and position
he Gaussian noise is 5 .
alue in Table 2 is typical,
ns of these values over thet identical to their values.
Figurestandard
10. IM Lup IQUdeviation
V CO(2–1) spectra, stacking based
ypicalon the Keplerian profile of the disk via GoFish across theentire disk out to a radius of 4 . The stacked Stokes I signal
ts value.
has been divided by 170.
d for stacking slightly af00

00

2008.04952

Ural Federal University, 51 Lenin Str., 620051 Ekaterinburg, Russia
Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, AS/NTU No.1, Sec. 4,Theeffectluminosity
on the protoplanetary disk
Roosevelt
Rd,ofTaipei
10617, Taiwan,outbursts
R.O.C.
4

2009.01888

dynamics
Preprint online version: September 7, 2020

Eduard I. Vorobyov1,2,3 , Vardan G. Elbakyan2 , Michihiro Takami4 , and Hauyu Baobab Liu4

ABSTRACT

1

University of Vienna, Department of Astrophysics, Vienna, 1180, Austria
e-mail: eduard.vorobiev@univie.ac.at
Aims.
Response of a protoplanetary disk to luminosity bursts of various duration is studied with the purpose to determine the e↵ect of2
Research Institute of Physics, Southern Federal University, Rostov-on-Don, 344090 Russia
3 the bursts on the strength and sustainability of gravitational instability in the disk. A special emphasis is paid to the spatial distribution
Ural Federal University, 51 Lenin Str., 620051 Ekaterinburg, Russia
4 of gas and grown dust (from 1 mm to a few cm) during and after the burst.
Institute of Astronomy and Astrophysics, Academia Sinica, 11F of Astronomy-Mathematics Building, AS/NTU No.1, Sec. 4,
Roosevelt Rd,NumericalTaipei 10617, hydrodynamics
Taiwan, R.O.C.
Methods.
simulations using the FEOSAD code were employed to study the dynamics of gas and dust in

the thin-disk
limit.
Dust-to-gas
Preprint
online version:
September
7, 2020 friction including back reaction and dust growth were also considered. Bursts of various duration (from100 to 500 yr) were initiated in accordance with a thermally ignited magnetorotational instability. Luminosity curves for constantABSTRACT
and declining-magnitude bursts were adopted
to represent two typical limiting cases for FU-Orionis-type eruptions.
Results.
The
the burst
isoftovarious
reducethe strengthof thegravitational
instability
byofheating and expanding the disk. The
Aims.
Responseof ashort-term
protoplanetarye↵ect
disk to ofluminosity
burstsdurationis studied withpurpose to determine
the e↵ectthebursts onbursts
the strength
andduration
sustainabilityof gravitationalin the disk.period
A specialof
emphasis
is paid canto thecompletely
spatial distribution
longestwithcomparable
toinstability
the revolution
the spiraldissolve the original two-armed spiralof gas and grown dust (from 1 mm to a few cm) during and after the burst.
patternNumericalin the gas
disk by theend ofusing
thetheburst,
while
weakentheandspiral
Methods.
hydrodynamics
simulations
FEOSAD
codethewereshortest
employed bursts
to study only
the dynamics
of gasdust inpattern. The reaction of grown dust
tothin-disk
the burst
somewhatdi↵erent.
Thereaction
spiral-like
distribution
withBursts
deepof cavities
in theinter-armed regions transforms into athelimit.isDust-to-gas
frictionincluding backand dustinitial
growth werealso considered.
various duration
(from
100
to
500
yr)
were
initiatedinaccordancewithathermally
ignitedmagnetorotational
instability.
Luminosity
curvesforconstantring-like distribution with deep gaps. This transformation is most expressed for the longest-duration bursts. The long-term e↵ect ofand declining-magnitude bursts were adopted to represent two typical limiting cases for FU-Orionis-type eruptions.
the burst
dependse↵ect
on ofthetheinitialdisk
conditions
the onset instabilityof the burst.
In andsome
cases,thevigorous
Results.
The short-term
burst is to
reducethe strength atof gravitationalby heating
expanding
disk. The disk fragmentation sets in several
longestbursts years
with duration
the revolution
period ofin
thethespiralcan completely
the original
two-armed
spiralwith masses in the giant-planet mass
thousandaftercomparable
the burst,towhich
was absent
model
withoutdissolve
the burst.
Severalclumpspatternin form
the gas indisktheby theend diskof the burst,
whileAfterthe shortest
burstsonly
weaken the spiralpattern.theThespatial
reaction distributionof grown dust of grown dust is characterized by
range
outer
regions.
thedisk
fragmentation
phase,
to the burst is somewhat di↵erent. The spiral-like initial distribution with deep cavities in the inter-armed regions transforms into a
multiple
sharp withrings
locatedfromtens to hundredsof astronomical
units. The
arrangement
and sharpnessof the rings depends on the
ring-like
distribution
deep
gaps. Thistransformation
is most expressed
for the longest-duration
bursts.
The long-term e↵ectoftheburst depends
on theinitial disk di↵usion.
conditions at The
the onsetof the burst.
In somevigorous
disk asfragmentation
severalstrengthof dustturbulent
wide-orbit
rings
arecases,
likelyformedthe resultsets
ofindust-richclump dispersal in the preceding
thousand years after the burst, which was absent in the model without the burst. Several clumps with masses in the giant-planet mass
gravitationally unstable phase.
range form in the outer disk regions. After the disk fragmentation phase, the spatial distribution of grown dust is characterized byConclusions.
Luminosity
similarin magnitude
FU-Orionis-type
eruptionshave
a profound e↵ect on the dynamics ofmultiple
sharp rings locatedfrom tensbursts
to hundredsof astronomical
units. Thetoarrangement
and sharpnessof the ringscan
depends
on thestrengthof dustturbulentdi↵usion. The wide-orbit
areburst
likely formed
as theisresultof dust-rich clump
the preceding
gas anddust
in protoplanetarydisks rings
if thedurationcomparable
to or dispersal
longerinthan
the dynamical timescales. In this context,
gravitationally unstable phase.
the spatial morphology of the gas-dust disk of V883 Ori, a FUor-like object that is thought to be in the outburst phase for more thanConclusions. Luminosity bursts similar in magnitude to FU-Orionis-type eruptions can have a profound e↵ect on the dynamics ofa century
the unknown
onset
date, may
be usedto or
aslongertest caseforthe burst
modelsconsideredhere. A potential relation of thegas
and dust inwith
protoplanetarydisks if the
burst durationis comparable
than thedynamical
timescales.
In thiscontext,
thespatial morphologyof the gas-dustof V883a FUor-likeobjectthat is thought
be in theoutburst
phase fortomore
obtainedring structures
to adiskvarietyofOri,
gaps
and rings
observed
in TtoTauri
disksremains
be thanestablished.
a century with the unknown onset date, may be used as test case for the burst models considered here. A potential relation of theobtainedring structures
to a variety of gaps
and –
rings
observed
in T Tauri–disks
remains to be established.
Key words.
Protoplanetarydisks
Stars:
protostars
instabilities
Key words. Protoplanetary disks – Stars: protostars – instabilities

ntroduction
ntroduction

ostellar accretion is a fundamental process in the theory ofpanying rise in the diskpanying
temperature
leads
sublimationof icyrise
intothedisk temperatureleads to sublimation of
mantles from dust grains,
this shifting
thedustice lines(Cieza thiset al. shifting the ice lines (Cieza etmantlesfromgrains,2016). Luminosity bursts can also trigger the chemical gas-phase