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ningfulconstraints
onand
the frequency
dust
properties
inThe
theofdisk
from(r) proﬁle is1
2
3
entativefrequency
coverageeach
ALMA(Tsukagoshi
et al.
2016).
Td,modelBands[3, k4, 5,is 6,the7, 8, 9, 10] as one
band set.
a givendeprojected
averaged
intensity
proﬁles
ofthe
dust
A
band
usedazimuthally
inbythesynthetic
multiband
analysis
inatGHz.
where
constantandThen,h is atthe
Planckobtainedﬁttingthetemperature
proﬁlediskAnalysis
midplane
Bthe DustBoltzmann
The
Synthetic
ALMA
MultibandofProperties
of
the
TW
Hya
,
which
corresponds
to
the
range
of
radius,
we
set
I
ν,syn
tinuumemission etobtainedby 2016),
the high-resolution
ALMA
constant.
We
note
that
we
simplyassumethatthesourceinAndrews
al.
(2012,
whichisderivedusing
radiative
Protoplanetary
Disk
February 20 However, since the uncertainty of dust size
Kim-etIOal.
(100%  x ) IO ,modelx ) IO ,model for ν=ν1,syn - (100%ervations.
function
is
S
=B
(T
)
and
the
dust
temperature
Td andtransfer calculations. Seongjoong
We noteKimthatthedistance
of
TW
Hya
is
ν accuracy
ν d 2,3,4
1
1
2
5
andTsukagoshi
ν2, where
theof amplitude
calibration
for ALMA,
HidekoNomura,Takashi,
RyoheiKawabe,and
Takayuki
Muto
ribution
opacity—as
well
as
the
structures
in
the
disk,
he Modeland
RadialIntensity
Proﬁles
at
Each
ALMA
Band
1
where
) Earthis thePlanckfunctionatdust
temperature
TBandsabsorption
is thedust
density)areconstant
assumed as d∼54pc
in Btheprevious
works,
but
weused
the coefﬁcientν(Tdofd andκMeguro-ku,
Department
and Planetary
Sciences,Tokyo
Instituteofx=10%
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data
for
3,
and
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he ofasEach
gaps
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National
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Osawa,
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181-8588,
Japan
Band
frequency
ν
and
τ
is
the
dust
optical
depth
for
which
we
adopt
3
the updated
ﬁrstALMA
part valueof thed∼59pc
synthetic
multiband
analysis,wealongthex=20%
lineOsawa,of sight
inTokyoEquation(1) (Warmels
for simplicity.
ν University for Advanced(Gaia
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et al. 2018,
The Graduate(SOKENDAI),
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alysis 20proﬁle (Jang-Condell & Turnerperature2012),
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ebruaryKim
etal.
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ate Usingtheradialatofβeach
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U

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Received
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and(r) andusing
Equations(1)–(3) and• calculation,
K674K24Kpoccl
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dustthe0,modelmodel
opticalτsolution
fromEquation(2).
whereBν(Tformal)ofisthethe
Planckfunction
atJanuary
dust
temperature
Td βandν,modelddepthproperties
withoutany
assumption
dust
temperature.
veEachtransfer
equation
dust
continuum
emission,
observed
intensity
Iobs(r),and spectral
index,
of
Band
by
that
the
dust
opacityobeys
law K.proﬁles,Tpower
IO3,syn using
Then, weestimate
temperature
385
602
787 for•ALMA
8Ky
K
massumingWld dustc opticala)surTd,syn(r),atthe radialThen,weobtainthemodelradialintensity
proﬁles,Iν,modelfrequencyνandτ
isproﬁlethedepth
for whichwe =5–60
adopt
ν
Abstract
rder
to
drop
the
assumeddust
temperature
and
then
β
ysis450
αobs, (r),togetherwith(1)the670
870 bandκν∝ν
UO1,syn,ofUO2190
βsyn, andEquationsandassumption(2). Finally, of
Tassumed. dustIn thiscase,thespectral
index
α at
the
dust
,syn ,GHz,
d,syn
each
ALMA
using
Equation(1) wewith
theAnalyzing
multiband
observationsof
dust
continuum
emission
is
one
of
the
usefultools
toconstrain
dust
ain 500
theimproved
radialproﬁlesofproperties,
needC0.4 . The observations were perIO (r9)720
 B10(Td (r ))[1continuum
exp ( that
UOemission(helpr ))]us, toUcanU0 (writtenO(1the)OphysicalTd,model(ofr )the
26setsK((2r) of
10disks.
au
O 950
τν,syna, syntheticβsyn] that satisfy
extract
the[T)d,synO  be0) asweproperties
understandproperties
protoplanetary
We ,perform
8
(r)
and
the
derivedτ(r).
Tν,modelitionald,modelobservations at a different
frequency.
high theresolutionmas×62.1
mas) by
ALMA multiband analysis to ﬁnd the best ALMAformed
band set forwith
constraining
dust properties(∼88.1
of the TW
Hya
h
O
k
T
(
r
)
by disk.
assuming
that
the
dust
opacity
obeys
the
power
law
n 385
this paper,
we perform
a synthetic
ALMA
multiband602
787
We ﬁnd that the Bandset amongUthe
combinations
ALMA Bands
4, 5, (r) proﬁle ishO [10, 6, e3] set isB the(rpossible)
O(Tsukagoshi
et al. of2016).
The [3,Td,model
2d best ALMA
β
B
(
r
)

3

C
,
(
3
)
450 to 670
870
6, 7, Sensitivity
8,.9, In10].setWe provides
also
ﬁnd twoconditions
thegood ALMA
setsdust
providing narrow constraint ranges on
Analysisysis
ﬁnd which
ALMA
band
us
good
κν2.2.
∝ν
this
case,
the
index
αUO (rofthehO spectral
k B Td (r )for
) bandobtainedbyﬁttingtemperature
proﬁlebetween
at the disk midplane
k
T
(
r
)
e

1
e

1
B
d
dust properties: (1) Band 9 or 10 is included in the band set, and (2) there arethe
enoughfrequency intervals
500
720
950 properties
es
in theondisk
fromstraints
the dust
in
the
TW
Hya
disk.
Then,
we
continuum
emissioncan bewrittenas that in
Andrews
et al. on(2012,
2016), whichisβ derived
thebands.
These arerelatedto theconditions
give
good constraints
dust properties:
the combinationof using radiative
Aftercalculating
the
model
radialintensity
proﬁlesand
ity this
proﬁlesof dust analysis
lymultibandtoALMAarchival
data
to
where
kthicktheconstanth..power-law
is the GPlanck) and low of TW Hya is
optically
thinBoltzmann
bands is required,and large
βand(β is theindex
dustnote
opacity,κν∝ν
B isand•M
m transfer
,( of
h,O d
kwe
calculations.
Wethatthe distance
B Td (r ) perform
frequency-independent
τ
and
β
a
h
O
e
U
(
r
)
0,modelmodel
O-resolution
ALMA
dust temperaturearepreferable.
To examinesynthetic thatanalysisthe multiband analysis tominewhetherthe results
derivedfromALMAarchival
data
constant.
note
that
we
simplyourassume
thesourceB (r ) archival
3We
C7, and,results,(K3we) 4]apply
assumedasd∼54pc
intheprevious
•
f
23I
1
c
y
B
=
B
=
ALMA
data
of
the
TW
Hya
disk
at
Bands
4,
6,
9.
The
Band
[9,
6,
set
providesthe dust works,
propertiesbut we used the
h
O
k
T
(
r
)
U
(
r
)
sensitivity
analysistoextract
theconstraintoftheB d ranges
O
ainty
of
dust
size
k
T
(
r
)
e

1
e

1
B d (T
heinTWdisk
are consistent
our
synthetic
functionSν=BandtemperatureTd∼59pc
the Hyadisk4xfromclose towith
theis
model
proﬁle,theBandthe[7, 6,dust
4] setgives
the dust
properties
deviating fromthe model
at all radii et al.Wz
ν whiled) analysis.
d andupdatedvalue(Gaia
Collaboration
2016).
B = temperature Td,syn, optical depth τν,syn, and opacity
synthetic
dust
uctures
in
the
disk,
(
100%

x
)
I
I
(
100%
x
)
I
.
Performwith
broad
a constraint
to specify
the accurateof
dust
temperature,
opticaldepth, and β. Since
Section2, we dust
describe how
thetoosynthetic
ALMA
multibandy proﬁlesabsorption
κrangedensity)areconstant(r)the and
Using
the
deriveding
thesethecalculations
for everyτradius,
we obtain
minimum βmodel(r), we calculate theνρd (ρ
d is the dust
kfeatures
iscoefﬁcienttheBoltzmann
constantandhvaluesisPlanck0,model• ofK βwhereGflam
Rl8KyK
c
B
these
are
expectedbythesynthetic
multiband
analysis,we
conﬁrmthat
thesynthetic
multiband
analysis isandmaximum
values
of
T
,
τ
,
and
β
,
which
correspondillaffectthedustpower-law
index
at
a
given
radius.
To
perform
thisanalysis,synysis derives
the dust properties.
Section3 describes
the (1) for
esolution
ALMA-I-optical(100% x ) I depth
to (100%  x ) I
at three
along
the
line
of
sight
in
Equation
simplicity.
frequency-dependentτν,model(r) from Equation (2).
consistentWe
with notethe results
derivedreal data.
constant.
that
we from
simplyassumethatthemlfrequencies,ν=[νsource, ν , ν ], as shown in Figure 2.
2012),
more
directweestablishtheparameter
spaceofsynthetic
intensityIatν,syn weradial
lts of synthetic
analysisand observationalthenty
dust size multiband
First,
wemethods:
derivethe) conditions
frequency-independent
proﬁlesThen,obtaintheradial intensity proﬁles, Iν,model(r), atKey
words:– theprotoplanetarydisks –Kstars:
individual(TW Hydrae)function
is
S
=B
(T
and
dust
temperature
Tcsurcandmodelννdd Synthetic•m,5(surmderstanding
of
the
3.
The
Resultsofthe
ALMA
Multiband
Analysisthreefrequencies,
which
are
pickedarbitrarily
among
ALMA
uired
band sets. We
will(r)explainthedust(r)properties
turesforin good
the disk,
τ
and
β
using
Equations(1)–(3)
and
the
each
ALMA
band
using
Equation(1) with the assumed
0,model
model
3.1.
The
Synthetic
Multiband
Analysis
Results
absorptionto
coefﬁcientκνρd, (ρthe dust
density)
are constantedusttemperature.
d is β
m
~
,
τ
and
.
Then,
we
Band
3–10,
correspondingTvedfromtheALMAdata throughmultibandd,synν,syn analysis
synIobs(r),affectdust archivalobserved
radialintensity
proﬁles,andThespectralindex,
We
performa synthetic
ALMA multiband
analysis (see
(r)
and
the
derivedτν,model(r).
Tsimplicity.
d,model1.
Introduction
originofgap
structures
the
TW Hya disk is also still
along
the
line
of
sight
in
Equation(1)
forSection2)
forallpossiblecombinationsof three in
bands
among
ure
proﬁle
and
then
•
G
0
(
(
B
1
)
*
,
.
constraint
rangesofdusttogether
properties
satisfying
the extract
consistency
between αthesynthetic
resultsandrealdata with
Bands 3–10. Among aof
total of 56 possible combina012),
more thedirectat synthetic
190
GHz,
the ALMA
assumption
obs(r),
undertions,
somedebate.
ALMA
band sets provide us narrow constraint
we deriveALMA
the frequency-independent
radialproﬁles
properties,
weneed
SinceFirst,
the high-resolution
observation
of
HL
Tau
0.4the, τ as, dustand β temperature, while therangeson the properties,
radialproﬁlesperof TsuchectionSectionwill
discuss
pointsimprovex ) Isomexobservations) IO ,modelothers
the4.rangeof (5100%, DustTd, dust opacity κν,T) etal.
26
KIO(,synrto10
au(100%)has
erstandingof the. The
wereO(r,model
2.2.ranges
Sensitivity
Analysisd,model(ALMA
Partnership2015),TWHya
been
one of thehave verybroad constraint
on the synthetic dust
τ
(r)
and
β
(r)
using
Equations(1)–(3)
and
the
ncy.
0,modelmodel
and dust
opacity
power-law
are the key parameters toproperties.
Since
the upper
limit of the index
synthetic β,
dusttibandanalysis.
Finally,
Section6withsummarizes
the concluformedhighresolution(∼88.1mas×62.1
mas)by
dustwhere
temperature.
Iν,modelis themodel
radialintensity
proﬁlederivedinrepresentative
protoplanetary
disks(PPDs)
thathave
axisym) is sensitive to the observational errors
temperature(Tobserved
radialintensity
proﬁles,I(r),
andspectralindex,
distinguishthe models
explaining
theoriginof those disk
multibandcalculatingtheintensity
proﬁles andin the synthetic
intensities between
20 andmodel
45 au, as shownradialin
metricringedstructure.
The central starHya isobs
awhichTThe
TauriTAfter
ALMA(Tsukagoshi
et ofal.TW
2016).
(r)
proﬁleis
esALMA
proﬁlethenofSection
our andmultiband
analysis.
d,model
2.1
and
x
are
the
observational
errors,vary
Figure2, we calculate
the average
normalized deviationofstructures.
Theyareexpectedtobehavedifferentlyindisk
αobsa(r),at ∼0.8
190
together
the assumptionofprovides us good star with(Andrews
et al. 2012).with
The gasmass of
MeGHz,
frequency-independentandβ, we perform afrom Tfor quantitativeτcomparison. Figure
1
T
The Astrophysical Journal, 872:179 (14pp), 2019 February 20

Kim et al.

Figure 1. Averaged values of (Td,syn,max−Td,model)/Td,model within 20 au<r<45 au. The bottom left triangle presents the values derived from the Band
[10, x1, y1] sets, and the top right triangle presents the values derived from theBand [x2, y2, 3] sets. The colors of the blocks indicate small errors as blue andlarge errors as red. The constrained Td,syn,max from the Band [10, 6, 3] set is∼21% larger than Td,model, on average, and this is the best band set.

O 3,model

O 3,synd,syn

O ,model1

2

O 3,model

ν,synO ,model3d,synd,syn,maxsynO ,synν,synsynFigure 2. Constraint range of radial proﬁles of synthetic dust temperature Td,syn(top), synthetic optical depth at ALMA Band 3 τB3,syn (middle), and synthetic
opacity power-law index βsyn (bottom) derived from ﬁve ALMA band
sets using the synthetic multiband analysis. The different colors represent

in the synthetic intensities between 20 and 45 au, as shown in
2, Analysis
we calculate
normalizedof
The Synthetic ALMA Figure
Multibandof the theDustaverage
Propertiesof the TW deviation
Hya
Protoplanetaryfrom Td,modelDisk
for quantitative comparison. Figure 1
Td,syn,max
B
2
2,3,4
examplesthe Kawabe
averaged
Seongjoong Kim1 , Hidekopresents
Nomura1 , Takashi
Tsukagoshiof, Ryohei, andnormalized
Takayuki Muto5 deviation
Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, JapanfromTd,modelwithin 20 au<r<45 au, thatof T Observatory of Japan,
National Astronomicald,syn,max
2-21-1 Osawa,
Mitaka, Tokyo 181-8588, Japan45
au
The Graduate University(SOKENDAI), 2-21-1(Osawa,
Mitaka, TokyoJapan (r )) / T/n 20ofStudies(r ) 181-0015,
 Td,modelis, for(1Advanced
r  20of Tokyo,
45 au )University
d,model (r ),Science,
au Td,syn,max
Department of Astronomy, School
Bunkyo, Tokyo 113-0033, Japan
Division of Liberal where
Arts, Kogakuin
1-24-2
Shinjuku-ku,
Tokyo
163-8677,
Japan
isNishi-Shinjuku,
the number
of:
grids
among
r=20–45 au.
nUniversity,
20–45 •au
Received 2018 September 10; revised 2019 January
27; accepted 2019 January 28; published2019 February 25
The bottom leftforBand [10, x1,• triangle )shows the
0 (results
6
% the
on:
Abstracty1] sets, and the
top right triangle shows•ad those% for the Band [x2,:Analyzing multiband observations of dust continuum emission is one of the useful tools to constrain dusty2, 3]thesets,
where
5,h
4],
y1=[8,7, 6, 5, 4, 3], :•propertiesc x1=[9,h 8, 7,
B6,disks.
i a synthetic
9
properties that help us to understandphysicalof the protoplanetary
We perform
ALMA multiband analysis tox2=[10,ﬁnd the best ALMA
set forthe dust properties
of 5,
the
TW Hya9, 8,
7,5],constraining
and y2=[9,8,According• bandc6,
B127, 6,
12
3 4].
:to
disk. We ﬁnd that the Band [10, 6, 3] set is the best set among the possible combinations of ALMA Bands [3, 4, 5,, whichtheconditions
calculation,theBand6, 3] set
us ranges
T
cALMA, givesJtR:d,syn,max
6, 7, 8, 9, 10]. We also ﬁnd two
for the•goodband[10,sets providing
narrow
constraint
on
dust properties: (1) Band 9 ordeviates
10 is included∼21%
in the bandfrom
set, and T(2) there are, enoughfrequency intervals betweend,model on average, within 20 au<r<
the bands. These are related to the conditions that give good constraints on dust properties: the combination ofβ
au. Itandislarge
theβ (βbest
setindex
among
all 56possible) and low band sets.
optically thick and thin bands45
is required,is the band
power-lawof dust opacity,κν∝ν
k analysisJ
dust temperature are preferable. BasedTo examineon
our synthetic
analysis results,
weapply the 1,
multiband
analysistheinFigureFigure2 toshows the
ALMA archival data of the TW Hya disk at Bands
4,
6,
7,
and
9.
The
Band
[9,
6,
4]
set
providesthe
dust
properties•~:
constraint
synthetic
dustof four goodclose to the model proﬁle, while
the Band [7, 6,ranges
4] set givesof
the thedust properties
deviating
fromproperties
the model at all radii•Th:with too broad a constraint range
to specify
the accurate
valuesof7,
dust3],
temperature,depth,
β. Since
ALMA
band
sets
([10,
[10,
6,optical3],multiband[9, 7,andanalysis
3],and[9, 6, 3])
these features are expected by the synthetic multiband
analysis,we
conﬁrmthat
thesyntheticis•r:and from
onerealbad
consistent with the results derived
data. ALMA band set ([7, 6, 3]) as examples selected

The Astrophysical Journal, 872:179 (14pp), 2019 February 20

Kim et al.

1
The Astrophysical Journal, 872:179 (14pp), 2019 February
20

Kim et al.

2

3

4

(top)
opac
sets
the d
[9, 6
show
the m

5

Figure 1. Averaged
values(14pp),
of (Td,syn,max
−Td,model)/Td,model within 20 au<
The AstrophysicalJournal, 872:179
2019 February
20

The Astrophysical Journal, 872:179 (14pp), 2019 February 20

Kim et al.

r<45 au. The bottom left triangle presents the values derived from the Band
Figure 6. 3D scatter plot of [Td,syn, τ190 GHz,syn, βsyn] derived from randomly generated intensities at the ALMA Band [10, 6, 3] set (bottom right) and their projected[10, x1, y1] sets, and the top right triangle2D
presents
valuesintensities
derivedhavefrom
thescatter plots. theThe generated
randomerrors of ±10% for Bands 6 and 3 and ±20% for Band 10 against the model intensities derived fromK, τ190 GHz,model
βmodelred points in the 2D scatter plots are the model values. The blue ellipses in the 2D scatter plots are the 1σ[Td,model=20
Band [x2, y2, 3] sets. The colors of the blocks
indicate
small=0.5,
errorsas=1.5].
blueTheandconﬁdence ellipse ﬁttings, which contain 68% of all points. The points show correlations between dust properties: τ190 GHz,syn and βsyn are getting smaller as Td,synfrom the Band [10, 6, 3] set islarge errors as red. The constrained Td,syn,max
becomes larger.
∼21% larger than Td,model, on average, and this is the best band set.
Equation (1), the derived constraints on the dust properties are
not able to reproduce the model values.

our synthetic multiband analysis results are consistent with thereal observational data.
Andrews et al. (2016) and Tsukagoshi et al. (2016) reported
the high spatial resolution dust continuum images of the TW
Hya disk at Bands 4, 6, and 7. We use the Band 4 and 6 data inTsukagoshi et al. (2016) and Band 7 ﬁts image at Sean
Andrews’s science home page.6 In the ALMA archive, we also
ﬁnd a Band 9 observation of the TW Hya disk (Schwarz
et al. 2016), which is low spatial resolution data. We retrieved

4. Applications of the Multiband Analysis to ALMA

(100%  x ) IO3,model - IO3,syn - (100% x ) IO3,model. DataPerformArchival
ing these calculations for every radius,
we3, obtain
minimum
In Section
we presentthe
the synthetic
multiband analysis
results and ﬁnd two conditions for the good ALMA band sets
and maximum values of Td,syn, τν,syn, andβsynconstraints, which oncorrespondderiving
accuratethe dust properties. In this
we apply x
theto ALMA archival(100%) Imultiband
to (100%  x ) IO ,model - IO ,syn -section,at threeO ,model analysis
dust continuum data of the TW Hya PPD at Bands 4, 6, 7, andfrequencies, ν=[ν1, ν2, ν3], as shown
9 in orderin
to Figurederive the 2.
dust properties and examine whether

6

Kim et al.

reported the variations of β on the frequencies by experimental
measurements for particles with different dust temperatures(Td=10–300 K) and chemical compositions (Mg- or Fe-rich
amorphous silicates). They suggested that β anticorrelates with
Td at a given frequency for Td>30 K due to the additional
absorption processes of the grains. They also found thecomplex β variations at λ 100 μm for the different Td andcompositions.
Despite those theoretical/experimental studies on β with thedust grain models, it is difﬁcult to fully understand thefrequency dependence of β of actual grains in PPDs. Therefore,
we simply assumed frequency-independent β in this work.
However, we need to be cautious that β can vary depending on
the frequency. In this case, we need additional observations at
different frequencies in order to constrain the dust properties.
5.3. Extension to ALMA Band 1

https://www.cfa.harvard.edu/~sandrews/data/twhya/7

3. The Results of the Synthetic ALMA Multiband Analysis

We ﬁnd that the frequency intervals between the bands
should be large enough for better constraints on the dust
properties through the multiband analysis. It infers that we canconstrain better dust properties if we add a lower-frequency
band instead of Band 3 (112 GHz) in the band sets. Since the
ALMA Band 1 receiver is developing now (Huang et al. 2016),
we perform the synthetic multiband analysis on the band sets
including Band 1 (40 GHz) in order to check the applicabilityof the multiband analysis.
Figure 10 presents the constraint ranges of the synthetic dust
properties, Td,syn(r), τB1,syn(r), and βsyn(r), derived from ﬁveband sets, including Band 1. The constraint ranges of the dust
properties derived from different band sets are represented
by different colors: yellow for the Band [9,7,1] set, purple for[9, 6, 1], blue for [10, 7, 1], red for [10,6,1], and green for[10, 5, 1]. The black solid lines are the model proﬁles of Td(r),τB1,model(r), and β(r) derived with the same method describedin Section 2.1.
The constraint ranges of Td,syn(r) are better than the ones
derived from the band sets including Band 3, such as the Band
[10, 6, 3] set. Similarly, the constraint ranges of τB1,syn(r) andβsyn(r) become much better than the ones in Figure 2 as well.
We calculate the same value as in Figure 1 for the band setswith ALMA Band 1 to estimate how Band 1 improves theconstraint range. Figure 11 presents the averaged normalized
deviation of Td,syn,max (left), τB1,syn,max (middle), and βsyn,max(right) from the model values for the Band [x2, y2, 1] sets (topright) compared to the Band [x1, y1, 3] sets (bottom left). The

Key words: methods: observational – protoplanetary disks – stars: individual (TW Hydrae)

3.1. The Synthetic Multiband Analysis Results••

We perform a synthetic ALMA multiband analysis (seeSection 2) for all possible combinations of three bands among
ALMA Bands 3–10. Among a total of 56 possible combinations, some ALMA band sets provide us narrow constraint
ranges on the radial proﬁles of Td,syn, τν,syn, and βsyn, while theothers have very broad constraint ranges on the synthetic dust
properties. Since the upper limit of the synthetic dust
temperature (Td,syn,max) is sensitive to the observational errors
Figure 2. Constraint range of radial proﬁles of synthetic dust temperature Td,syn(top), synthetic optical depth at ALMA Band 3 τB3,syn (middle), and synthetic
in the synthetic intensities between 20 and 45 au, as shown inopacity power-law index βsyn (bottom) derived from ﬁve ALMA band
Figure 2, we calculate the average normalized deviation ofsets using the synthetic multiband analysis. The different colors represent
Td,syn,max from Td,model for quantitative comparison. Figure 1
the different ALMA band sets: Band [7, 6, 3] set by yellow, [9, 7, 3] by purple,
presents
examplesthe andaveragednormalized
Figure 9.
Dotted lines show
Td (top), τB4of(middle),β (bottom) radial
proﬁles derived deviationfrom the Band [7, 6, 4][9,set 6,(left),
Band[9, 6,[10,4] setandandsmoothed
3] by
blue,
7,(middle),3] by red,
[10, 6, 3] by green. The black solid line
, andradial
βmodelproﬁleat ∼75 mas
andBand [7,of6, 4]Tset(right) withfrom
the ALMA
multibandwithin
analysis. The
solid lines are the
proﬁles of shows
Td,model, theTd,model20blackau<r<45
au,modelthat
modelof T(left)d,syn,maxd,model, τB3,model, and βmodel derived usinge τB4,model

1. Introduction

i

T

T:
%

0
0
The origin of gap structures in the TW Hya disk is also stillB :under debate.

Since the high-resolution ALMA observation of HL Tau(ALMA Partnership et al. 2015), TW Hya has been one of therepresentative protoplanetary disks (PPDs) that have axisymmetric ringed structure. The central star of TW Hya is a T Tauri
star with a mass of ∼0.8 M (Andrews et al. 2012). The gas-

Dust properties, such as dust temperature Td, dust opacity κν,and dust opacity power-law index β, are the key parameters to
distinguish the models explaining the origin of those disk
structures. They are expected to behave differently in disk

3

Figure 10. Constraint range of radial proﬁles of dust temperature Td,syn (top),
optical depth at ALMA Band 1 τB1,syn (middle), and opacity power-law index
βsyn (bottom) derived from ﬁve ALMA band sets using the synthetic multiband
analysis. The different colors represent the different ALMA band sets: the Band

from
tem
τB3,
βsyn
plot
Ban
set,
blac
proﬁ
τB3,

LETTER TO THE EDITOR

Resolving the MYSO binaries PDS 27 and PDS 37
with VLTI/PIONIER
E. Koumpia1 , K. M. Ababakr10 , W. J. de Wit2 , R. D. Oudmaijer1 , A. Caratti o Garatti3 , P. Boley4,5 , H. Linz6 ,S. Kraus7 , J. S. Vink8 , and J.-B. Le Bouquin9,?

•
•
•

1c
3 ,
9 7

d

R B
0
/
HKE
3 (,
7 ;74> 6 DC F

SP ue
~
ca
.( HKE ,8
9LM
OI (CM 9 c
R5 77 2C 77Se

School of Physics and Astronomy, E.C.LM
Stoner Building, University of Leeds, Leeds LS2 9JT, UKe-mail: ev.koumpia@gmail.com)
19001, Santiago de Chile, Chile
LM 23 ESO Vitacur, Alonso de Córdova 3107 Vitacura, CasillaLM
Dublin Institute for Advanced Studies, Astronomy & Astrophysics Section, 31 Fitzwilliam Place, Dublin 2, Ireland
4
Moscow Institute of Physics and Technology, 9 Institutski per., Dolgoprudny 141701, Russia
5A&A
623,Federal
L5 (2019)
Ural
University, 51 Lenin Ave., Ekaterinburg 620075, Russia
6
Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
1.0
7
Observations
University of Exeter, School of Physics, Astrophysics Group, Stocker Road, Exeter EX4 4QL, UK
Model (a)PDS 37
8
Armagh Observatory and Planetarium, College Hill, Armagh BT61 9DG, 0.8
Ireland
9
Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
0.6
10Erbil Polytechnic University, Kirkuk Road, Erbil, Iraq
1d0) CM
V

15
Observations
Model (a)

0.4

0.0
10
5
0
−5
−10

Residuals

Residuals

0.2

0Closure Phase (degrees)

PDS 37

V2

0.6
0.4

40

60

80

100

120

5

0

−10
10
5
0
−5
−10

140

60

80

0

−5

stars: pre-main sequence
−10
10
5
0
−5
−10
1. Introduction
100 120 140
60

Residuals

0.0
10
5
0
−5
−10
0

20

aN

−5

Flux w. disk 1 Flux w. 1
disk 2 Flux w. 2
Key words. stars: formation – binaries: close – techniques:Modelinterferometric– stars: individual: Flux
PDSw.27– stars: individual:Diameter
PDS 371 – Diameter 2

0.2

Residuals

20

PDS 37

100

120

140

Baseline(m)Baseline (m)stage during their lifetime. The origin of this high binarity and the binary parameters are poorly
understoodbecause observational
constraints are scarce, which is predominantly due to aFig.
dearth
of
known
young
massivebinarysystems.
1. Three di↵erent geometrical models compared with the observed visibilities (V 2 ) and closure phases of PDS 37. The black points with
Aims. We aim to identify and describe massive young
binaryerror
systemsin orderto fill indata,
the andgapstheof blue
our knowledgeof primordial
verticalbars arethe observed
triangles correspondto a representative best-fit model (a). The best-fit models correspond tobinarity of massive stars, which is crucial for our understanding
massivestara formation.
(panel a) aofbinary
withring surrounding the primary (Red. 2 ⇠10), (panel b) a binary with both companions resolved and some asymmetric
Methods. We observed the two massive young stellar objects(MYSOs)PDS 27and PDS
37 andat thehighestprovided2
flux toward
its primary
(Red.
⇠6),
(panelc) aspatial
binaryresolution
model withboth companions resolved (Red. 2 = 10).
by VLTI/PIONIER in the H-band (1.3 mas). We applied geometrical models to fit the observed squared visibilities and closure phases.
In addition, we performed a radial velocity analysis using published VLT/FORS2 spectropolarimetric and VLT/X-shooter spectroTable 1. Parameters of the models for PDS 37 and PDS 27.
scopic observations.
15 findings suggest binary companions for both objects at 12 mas (30 au) for PDS 27 and at 22–28 mas (42–54 au) for
Results.
Our
Observations
Observations
Model (a) PDS 37. This means
Model
(a)
PDS 37that they are among theclosestMYSOModel
binaries resolved
to date.
Flux weight
1 Flux w. 2
Flux w. ring
Inner diameter Width
PA (minor axis) Flatten ratio x2
y2
10mas(>8 M ) degreesmasmas
Conclusions. Our data spatially resolve PDS 27 and PDS 37ringfor the first time, revealing two of the closest andmas
most massive
YSO binary5 candidates to date. PDS 27 and PDS 37 are rare
but great laboratories 0.06
to quantitatively
inform 7.7
andtest the theorieson
PDS 37 (a) 0.5 ± 0.4± 0.05 0.44 ± 0.34
± 0.3
0.78 ± 0.25 14.0 ± 1.4
5±117.2 ± 0.3
24.3 ± 0.4
formation of such systems.
PDS 27 (a) 0.5 ± 0.4
0.5 ± 0.4
2.6 ± 0.4
4.7 ± 0.2
12.6 ± 1.2
8±5
0
0

1.0
0.8

Closure Phase (degrees)V2• n n mddb•
e T
- T db
Received 12 November 2018 / Accepted 20 February 2019
•
s
a 0
P c
ABSTRACTC
pkP D
PE
Context. Binarity and multiplicity appear to be a common outcome in star formation. In particular, the binary fraction of massive•
3 (,d) ) CMc
Y(OB-type) stars can be very high. In many cases, the further stellar evolution of these stars is a↵ected by binary interactions at some
10

40

60
80
Baseline (m)disk
PDS 37 (b)PDS 27 (b)PDS 37 (c)0.2 ± 0.1
0.33 ± 0.3
0.22 ± 0.18

0.001+0.054
0.001
0.49 ± 0.44
0.35 ± 0.28

0.28 ± 0.15
0.18 ± 0.16
0.11 ± 0.11

0.5 ± 0.3
00.32 ± 0.25mas
1.9 ± 0.2
5.4 ± 0.3
1.9 ± 0.2

mas
5 ± 0.3
3.0 ± 0.3
5 ± 0.3hydrodynamical 2 simulations establish that disks are viablex1
mas
25.8 ± 0.2
022.8 ± 0.1

y1
mas
y2 = 2.0 ± 0.3
03.4 ± 0.1x2
mas
22.7 ± 0.1
4.0 ± 0.2
22.8 ± 0.1

y2
mas
3.4 ± 0.1
11.5 ± 0.3
3.4 ± 0.1

[d.o.f.] (degrees of freedom) for the best-fit models a, b, and c are 10[11], 16[10], and 10[10], respectively, while
100
120
140Notes. For PDS 37 the reduced
agents for accretion (e.g., Rosen et al. 2016; Klassen et al. 2016;
Baseline (m)PDS27, the corresponing values for the best-fit models a and b are 10[12] and 12[11], respectively. Both visibilities and closure phases wereIn recent years, substantial progresshas been made inforthe
field
80

Kuiper & Hosokawa 2018). For a review on the topic, see
taken
into account.
of thehigh-mass
formation.
ThevarioustheoreticalscenarFig. 1. Three di↵erent geometrical models compared withobserved starvisibilities(V 2 ) andclosurephasesof PDS 37.
The blackpoints &with
Beltrán
de Wit (2016), Hartmann et al. (2016).
ios proposed
starbest-fit
formationsuggestthat mass
vertical error bars are the observed data, and the blue triangles
correspondfor
to ahigh-massrepresentativemodel (a).
The best-fit
models correspondto the formation of massive individual stars is becomAlthough2
actualseparationof the binary.
Based on the consistency of the high-contrast visibilities we observe. No such required degree
is accreted
a circumstellar
diskcompanions(Jijina & Adams
1996;(panel a) a binary with a ring surrounding the primary (Red.
⇠10),through(panel b)a binary with bothresolved
andsome asymmetricLETTER TO THE EDITOR

Resolving the MYSO binaries PDS 27 and PDS 37
with VLTI/PIONIER

dE. Koumpia1 , K. M. Ababakr10 , W. J. de Wit2 , R. D. Oudmaijer1 , A. Caratti o Garatti3 , P. Boley4,5 , H. Linz6 ,78, J. S. Vink , and J.-B. Le Bouquin
E. Koumpia et al.: Resolving the MYSO binaries PDS 27 and PDS 37 S.
withKraus
PIONIER

9,?

1

School of Physics and Astronomy, E.C. Stoner Building, University of Leeds, Leeds LS2 9JT, UKe-mail: ev.koumpia@gmail.com
2
ESO Vitacur, Alonso de Córdova 3107 Vitacura, Casilla 19001, Santiago de Chile, Chile
3
Dublin Institute for Advanced Studies, Astronomy & Astrophysics Section, 31 Fitzwilliam Place, Dublin 2, Ireland
4
Moscow Institute of Physics and Technology, 9 Institutski per., Dolgoprudny 141701, Russia )5
Ural Federal University, 51 Lenin Ave., Ekaterinburg 620075, Russia
6
Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
7
University of Exeter, School of Physics, Astrophysics Group, Stocker Road, Exeter EX4 4QL, UK
8
Armagh Observatory and Planetarium, College Hill, Armagh BT61 9DG, Ireland
9
Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
10Erbil Polytechnic University, Kirkuk Road, Erbil, Iraq

• 315 )-e s
woae
* 7
2
Fig. 2. Best-fit geometrical models (panel a) flattened ring (Red.
binary (R0() T ⇠r10) )and0( (panel
TmT b)cR
visibilities (V 2 ) and closure phases of PDS 27. The black •points
observ+ D with
9= verticalT
0 error0 bars are
% the
n~

a representative best-fit model. The two models show a similar fit, and therefore we show model b as•
, ,%()
%(, 7
•
e s
wob
p u
ABSTRACT•97et D 7 d. Binarity and multiplicity appear to be a common outcome in star formation. In particular, the binary fraction of massive
Assuming that theContext
extendedH-bandemission
is
due
to
hot
directly
test
the*theories o(OB-type) stars can be very high. In many cases, the further stellar evolution of these stars is))a↵ected aby binary interactions
at someRkghstage during their lifetime. The origin of this high binarity and the binary parameters are poorly understood because observational
constraints
are scarce,is predominantly due to a dearthTheof known young
massive binary systems. wavedust, the angular sizes
canbewhichestimated.
PIONIER7h R ( tion disk fragmentation
Aims. We aim to identify and describe massive young binary systems in order to fill in the gaps of our knowledge of primordial
binarity of massive stars, which is crucial for our understanding of massive star formation.
à37 at=the highest= spatial
7radid7 theoreticalTlength range (1.533 µm–1.772
is stellar
sensitive
thermalsupportthepr
Methods. We observed the µm)
two massive young
objects (MYSOs) PDSto
27 and PDS
resolution provided
Received 12 November 2018 / Accepted 20 February 2019

by VLTI/PIONIER in the H-band (1.3 mas). We applied geometrical models to fit the observed squared visibilities and closure phases.
In addition,
performed
radial (Red.
velocity2 analysis
using published
VLT/FORS2
2
Fig. 2. Best-fit geometrical models (panel a) flattened ring (Red.
⇠ 10)weand(panel b)abinary⇠ 12)) comparedwith theobserved spectropolarimetric and VLT/X-shooter spectroobservations.
visibilities (V 2 ) and closure phases of PDS 27. The black pointsscopic
with verticalerror bars are the observed data, and the blue triangles correspond to
Results. Our findings
suggestbinaryforfit.
both objects at 12 mas (30 au) for PDS 27 and at 22–28 mas (42–54 au) fora representative best-fit model. The two models show a similar fit,
and therefore
we showmodelb as acompanions
representative
PDS 37. This means that they are among the closest MYSO binaries resolved to date.
Conclusions. Our data spatially resolve PDS 27 and PDS 37 for the first time, revealing two of the closest and most massive (>8 M )binarydirectly
candidates
PDS of27youngand PDS
37 arerare but greatlaboratories
2
Assuming that the extended H-band emissionis dueYSO
to hottest tothedate.
theories
binaryformation
throughaccre- to quantitatively inform and test the theories onformationofsuchsystems.
dust, the angular sizes can be estimated. The PIONIER wave- tion disk fragmentation (Meyer et al. 2018). Our finding mightation of the dust in the temperature range 1500–2000 K. The nel as a possible mecha
angular distance of thefromstar canbinaries (<10 au), having• 4 dust
K()%(*4 the
0(-,
2 then0(, be2 estimated
8 7
R? T ?
• 0( - 7 * ) 7 315 *- ( , 7 * . 7 315 )- component. Such system
using
d
=
,
where
d
is
the
distance
of
the
dust
from
the
2
2 is sensitive
length range (1.533 µm–1.772 µm)
radisupportthetheoreticalpredictions
of
the
disk
fragmentation
chanT d to thermal• 315 )-drnkb 0( * 7 acRation of the dust in the temperature range 1500–2000 K. The nel as a possible mechanism for the formation of close MYSO
theTh
short-period (<10 d)angular distance of the dust from the star can then be•estimatedbinaries(<10au), having
a high-mass
and an accreting low-mass
315
*b
0*
.
7
Rutyi
8
d
star,
R?
and
T
?
are
the
radiusandtemperature
of
the
star,
and
T
d
using d =, where d is the distance of the dust from the component. Such systems are expected to be the progenitors of
Future interferometr
the short-period
massive spectroscopic
binaries.
Introductionhydrodynamical
simulations P
establish thatdisks are l
viableàe(<10 d)dn(e.g., VLTI)
b37
Sk
ac
star, R? and T ? are the radius and temperature of the1.star,and T disthedusttemperature.
The
stellar
PDS
and
PDS
27
Futureinterferometric radii
observations of
of
PDS
27
is the dust temperature. The stellar radii of PDS 37InandPDS years,
27 substantial progress has been made in the field agents for accretion (e.g., Rosen et al. 2016; Klassen et al. 2016;
recentand PDS 37 will provide a more complete uv-plane,
which
is
and
PDS 37 will provid
Kuiper& Hosokawa2018). For a review on the topic,see
are ⇠13 R and ⇠11.7 R , respectively (Vioque ofet al.
2018),
high-mass starformation.
Thebettervarioustheoretical scenarnecessaryforthecharacterizationofthesystems.
The
Beltrán
&deWitet(2016),
Hartmann
et al. (2016).
are
⇠13
R
R
,
respectively(Vioqueal.
2018),
while
their temperatureis ⇠17 500and
K (Ababakr⇠11.7
et al.
2015).
For
ios proposed forhigh-mass
mass
additional
datastar
willformation
make it suggest
possible thatto constrain
theAlthough
circum- the formation of massive individual stars is becoma dust temperature of 1500 K (graphite grains), an isangulardustthrough a circumstellar disk (Jijina & Adams 1996;
necessary for the betteaccretedstellar and circumbinary environment of the two components of
Key words. stars: formation – binaries: close – techniques: interferometric – stars: individual: PDS 27 – stars: individual: PDS 37 –stars: pre-main sequence

R? T ?2
2 T d2d

Gaia-2MASS 3D maps of Galactic interstellar dust within 3 kpc
R. Lallement1 , C. Babusiaux2, 1 , J.L. Vergely3 , D. Katz1 , F. Arenou1 , B. Valette4 , C. Hottier1 , and L. Capitanio1
1

l

•
A
• (71
•
•
• (,
T4
•
•
•
•
•

y

O

O

l2

i

g
S

rps o
O n
l
s ABSTRACTi S gfT4

O

gO
C % =sGaia stellar measurements are currently revolutionizing our knowledge of the evolutionary history of the Milky Way. 3D maps of theinterstellar dust provide complementary information and are a tool for a wide range of uses. We aimed at building 3D maps of thedust in the Local arm and surrounding regions. To do so, Gaia DR2 photometric data were combined with 2MASS measurements toderive extinction towards stars that possess accurate photometry and relative uncertainties on DR2 parallaxes smaller than 20%. We
applied to the individual extinctions a new hierarchical inversion algorithm adapted to large datasets and to a inhomogeneous target
distribution. Each step associates regularized Bayesian inversions along all radial directions and a subsequent inversion in 3D
of all their results. Each inverted distribution serves as a prior for the subsequent step and the spatial resolution is progressively
increased. We present the resulting 3D distribution of the dust in a 6 x 6 x 0.8 kpc3 volume around the Sun. Its main features are foundto be elongated along di↵erent directions that vary from below to above the mid-plane: the outer part of Carina-Sagittarius, mainly>??
located above the mid-plane, the Local arm/Cygnus Rift around and above the mid-plane and the fragmented Perseus arm are oriented
close to the direction of circular motion. The more than 2 kpc long spur (nicknamed the split) that extends between the Local Arm
and Carina-Sagittarius, the compact near side of Carina-Sagittarius and the Cygnus Rift below the Plane are oriented along l⇠40 to
55 . Dust density images in vertical planes reveal in some regions a wavy pattern and show that the solar neighborhood within ⇠500
pc remains atypical by its extent above and below the Plane. We show several comparisons with the locations of molecular clouds,
HII regions, O stars and masers. The link between the dust concentration and these tracers is markedly di↵erent from one region tothe other.

(

+C
am
n
54 BE
.M )
caO
P

s

iv:1902.04116v1 [astro-ph.GA] 11 Feb 2019

s

s
uP 3
s

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O
7 /+ OG AEDn()s ceu
1 8 55 gn
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u

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m

O

1 8 55•••

GEPI, Observatoire de Paris, PSL University, CNRS, 5 Place Jules Janssen, 92190 Meudon, France e-mail:rosine.lallement@obspm.fr
2
Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
3
ACRI-ST, Sophia-Antipolis, France
Fig. 3. Dereddened Hess diagram for a subset of stars with a paralla
4
ISTerre, Université Grenoble Alpes, France
relative uncertainty smaller than 10%. The grey scale corresponds to thsquare root of the stellar density. The Red Clump is the most promine
Received ; acceptedfeature which shape can be compared to Fig. 2 of Ruiz-Dern et a(2018).

OS

Key words. Dust: extinction;s‒g ISM: lines and bands; ISM: structure
O+ ; ISM: solar neighborhood) ; ISM:( Galaxy+ (+ =O
P f
Fig. 4. Comparison between the extinction A derived here and A d
1. Introduction
One form of 3D mapping of dust is the construction ofra- by Santiago et al. (2016) using APOGEE data.
terminedv sgag dial profiles of color excess
v or SOextinction, sightline by sightline. The first map produced in such a way was based on Hipmodels of the f
Milky Way require measurements+ parcoslPEvolutionaryg) ((Arenou
Oet al. 1992). Later on, maps of radial profiles
residuals) outliers, as illustrated in Fig. 1. The bright stars caof the spatial distribution of massive numbers of stars as well and their derivatives, i.e. reddening or extinction per unitibration
dis- is done using stars with G < 10.5 and is applied to a
dynamical, physical and chemical
properties, T4
all quan- tance, were built by GAEGO> A D AD astities>Gtheircurrently
AEDf‒stars with G < 11 mag. The colour range of our calibration
Marshall et al. (2006), Chen et al. (2013)provided by the ESA satellite Gaia (Gaia Col- and Schultheis et al. (2014) based on the Besançon model1.0of< (G K) < 5.6.
laboration P
et al. 2016, 2018b) and ground-basedt surveys. In this stellar tssynthesis (Robin et al. 2012)gand 2MASS,e The extinction coefficients
0SOare derived using the Fitzpatricpopulation
context, three-dimensional (3D) maps of the Galactic interstel0V0lar (IS) dust are an additional and mandatory tool since they allow de-reddening of stellar spectra and suppression of degeneracies between stellar temperature and dust reddening on the
one hand, and, on the other hand, since they may shed important
additional light on the star formation through the inter-play be-(2007) extinction law and the Kurucz Spectral En
GLIMPSE and VVV photometry, respectively. Majewski &et Massa
al.
ergy Distributions (Castelli & Kurucz 2003), as described(2011) derived individual stellar reddening and radial profiles
et al. (2018). The 2MASS transmissions are takeby combining SPITZER/GLIMPSE and 2MASS. Berry Danielski
et al.
(2012) used SDSS and 2MASS to constrain stellar SEDsfrom
andCohen et al. (2003) and the Gaia transmissions are thos
Weiler (2018). We are selecting here only the top of the HRD
reddening profiles using reddening-free empirical spectra.ofFolWe therefore adapted the surface gravity of the Kurucz spe
lowing a hierarchical Bayesian method devised by Sale (2012),

Gaia-2MASS 3D maps of Galactic interstellar dust within 3 kpc
R. Lallement1 , C. Babusiaux2, 1 , J.L. Vergely3 , D. Katz1 , F. Arenou1 , B. Valette4 , C. Hottier1 , and L. Capitanio1s

1

GEPI, Observatoire de Paris, PSL University, CNRS, 5 Place Jules Janssen, 92190 Meudon, France e-mail:rosine.lallement@obspm.fr
2
Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
3
ACRI-ST, Sophia-Antipolis, France
4
ISTerre, Université Grenoble Alpes, France

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iv:1902.04116v1 [astro-ph.GA] 11 Feb 2019

Received ; accepted

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ABSTRACT

Gaia stellar measurements are currently revolutionizing our knowledge of the evolutionary history of the Milky Way. 3D maps of theinterstellar dust provide complementary information and are a tool for a wide range of uses. We aimed at building 3D maps of thedust in the Local arm and surrounding regions. To do so, Gaia DR2 photometric data were combined with 2MASS measurements toderive extinction towards stars that possess accurate photometry and relative uncertainties on DR2 parallaxes smaller than 20%. We
applied to the individual extinctions a new hierarchical inversion algorithm adapted to large datasets and to a inhomogeneous target
distribution. Each step associates regularized Bayesian inversions along all radial directions and a subsequent inversion in 3D
of all their results. Each inverted distribution serves as a prior for the subsequent step and the spatial resolution is progressively
increased. We present the resulting 3D distribution of the dust in a 6 x 6 x 0.8 kpc3 volume around the Sun. Its main features are foundto be elongated along di↵erent directions that vary from below to above the mid-plane: the outer part of Carina-Sagittarius, mainly
located above the mid-plane, the Local arm/Cygnus Rift around and above the mid-plane and the fragmented Perseus arm are oriented
close to the direction of circular motion. The more than 2 kpc long spur (nicknamed the split) that extends between the Local Arm
and Carina-Sagittarius, the compact near side of Carina-Sagittarius and the Cygnus Rift below the Plane are oriented along l⇠40 to
55 . Dust density images in vertical planes reveal in some regions a wavy pattern and show that the solar neighborhood within ⇠500
pc remains atypical by its extent above and below the Plane. We show several comparisons with the locations of molecular clouds,
HII regions, O stars and masers. The link between the dust concentration and these tracers is markedly di↵erent from one region tothe other.

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Evolutionary models of the Milky Way require measurementsof the spatial distribution of massive numbers of stars as wellas their dynamical, physical and chemical properties, all quantities currently provided by the ESA satellite Gaia (Gaia Collaboration et al. 2016, 2018b) and ground-based surveys. In thiscontext, three-dimensional (3D) maps of the Galactic interstellar (IS) dust are an additional and mandatory tool since they allow de-reddening of stellar spectra and suppression of degeneracies between stellar temperature and dust reddening on the
one hand, and, on the other hand, since they may shed important
additional light on the star formation through the inter-play be-0i

Key words. Dust: extinction; ISM: lines and bands; ISM: structure ; ISM: solar neighborhood ; ISM: Galaxy

1. Introductionn

One form of 3D mapping of dust is the construction of radial profiles of color excess or extinction, sightline by sightline. The first map produced in such a way was based on Hipparcos (Arenou et al. 1992). Later on, maps of radial profiles
and their derivatives, i.e. reddening or extinction per unit distance, were built by Marshall et al. (2006), Chen et al. (2013)
and Schultheis et al. (2014) based on the Besançon model ofstellar population synthesis (Robin et al. 2012) and 2MASS,GLIMPSE and VVV photometry, respectively. Majewski et al.
(2011) derived individual stellar reddening and radial profiles
by combining SPITZER/GLIMPSE and 2MASS. Berry et al.
(2012) used SDSS and 2MASS to constrain stellar SEDs andreddening profiles using reddening-free empirical spectra. Following a hierarchical Bayesian method devised by Sale (2012),

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