Astronomy
&
Astrophysics
A&A 664, A174 (2022)
https://doi.org/10.1051/0004-6361/202243319
© J. L. Vergely et al. 2022
Three-dimensional extinction maps: Inverting inter-calibrated
extinction catalogues?
J. L. Vergely1, R. Lallement2, and N. L. J. Cox3
1ACRI-ST, 260 route du Pin Montard, 06904, Sophia Antipolis, France
e-mail: jean-luc.vergely@acri-st.fr
2GEPI, Observatoire de Paris, PSL University, CNRS, 5 Place Jules Janssen, 92190 Meudon, France
e-mail: rosine.lallement@obspm.fr
3ACRI-ST, Centre d’Etudes et de Recherche de Grasse (CERGA), 10 Av. Nicolas Copernic, 06130 Grasse, France
Received 12 February 2022 / Accepted 11 May 2022
ABSTRACT
Context. Three-dimensional (3D) maps of the extinction density in the Milky Way can be built through the inversion of large cata-
logues of distance-extinction pairs for individual target stars. Considerable progress is currently achieved in this field through the Gaia
mission. Available catalogues are based on various types of photometric or spectrophotometric information and on different techniques
of extinction estimations.
Aims. The spatial resolution of the maps that can be achieved increases with the spatial density of the target stars, and, consequently,
with the combination of input catalogues containing different target lists. However, this requires careful inter-calibration of the cata-
logues. Our aim is to develop methods of inter-comparison and inter-calibration of two different extinction catalogues.
Methods. The catalogue we used as reference for inter-calibration is a spectrophotometric catalogue. It provides a more accurate
extinction than a purely photometric catalogue. In order to reduce the dimension of the problem, a principal component analysis was
performed in (G,GB,GR,J, H, K) multi-colour space. The subspace constituted by the two first components was split into cells in
which we estimated the deviations from the reference. The deviations were computed using all targets from the reference catalogue that
were located at a short spatial distance of each secondary target. Corrections and filtering were deduced for each cell in the multi-colour
space.
Results. We applied the inter-calibration to two very different extinction datasets: on the one hand, extinctions based on both spec-
troscopy and photometry, representing 6 million objects and serving as a reference, and, on the other hand, a catalogue of 35 million
extinctions based on photometry of Gaia eDR3 and 2MASS. After calibration, the dispersion of the extinction among neighbouring
points in the second catalogue is reduced, regardless of whether reference targets are present locally. Weak structures are then more
apparent. The extinction of high Galactic latitude targets is significantly more tightly correlated with the dust emission measured by
Planck, a property acquired from the first catalogue. A hierarchical inversion technique was applied to the two merged inter-calibrated
catalogues to produce 3D extinction density maps corresponding to different volumes and maximum spatial resolution. The maxi-
mum resolution is 10 pc for a 3000 pc ×3000 pc ×800 pc volume around the Sun, and the maximum size of the maps is 10 kpc ×
10 kpc ×800 pc for a resolution of 50 pc. The inclusion of the spectroscopic survey data increases the dynamic range of the extinction
density, improves the accuracy of the maps, and allows the mapping to be extended to greater distances to better constrain the remark-
able '2.5 kpc wide dust-free region in the second quadrant in particular, which now appears as a giant oval superbubble. Maps can be
downloaded or used by means of on-line tools.
Key words. ISM: clouds – dust, extinction – ISM: structure – local insterstellar matter
1. Introduction
As repeatedly noted for the past several years, Gaia data are
both massive and of unprecedented quality. They revolutionize
our knowledge of the Milky Way (Gaia Collaboration 2021). The
unique catalogue of parallaxes of Gaia adds the third dimension
of space, radial distance. The combination of information about
stellar positions, velocities, atmospheric parameters, and chem-
ical abundances adds the temporal dimension, that is, the age
of stars and the global history. In parallel, massive stellar sur-
veys from ground or space, either photometric or spectroscopic,
add a wealth of information. The surveys complement Gaia data
for faint objects in the visible and add further spectral bands,
especially in the infrared. Gaia and massive surveys provide all
?3D maps are only available at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.
u-strasbg.fr/viz- bin/cat/J/A+A/664/A174
ingredients entering the determination of individual extinctions
for a huge quantity of stars in the Galaxy. All extinctions, and
more specifically, all measured spatial gradients of extinction,
may feed tomographic inversion to obtain the 3D distribution of
the Galactic extinction density (Chen et al. 2019;Green et al.
2019;Lallement et al. 2019,2022;Leike et al. 2020;Rezaei
Kh. et al. 2020;Babusiaux et al. 2020;Hottier et al. 2020).
These 3D extinction density maps allow interpolating extinc-
tions everywhere from the 3D maps. This estimator can replace
photometric or spectro-photometric determinations if these are
too uncertain or not available. In this paper, we generate the
3D extinction density by applying tomography algorithms pre-
sented in Vergely et al. (2001,2010), which was extended to a
hierarchical approach in Lallement et al. (2019).
The distance to individual targets can be deduced from their
parallax, if available, or estimated from differences between
observed and modelled luminosity. The choice of the method
A174, page 1 of 16
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A&A 664, A174 (2022)
depends on the parallax uncertainty. In some cases, the paral-
lax distance may also enter a Bayesian determination along with
photometric data. Extinction is always deduced from the compar-
ison between data and models. By principle, the most accurate
determination of the extinction is based on the combination
of high- or medium-resolution spectroscopy and photometric
measurements (Sanders & Das 2018;Queiroz et al. 2020).
The set of observed spectral features allows constraining the
temperature, gravity, and metallicity, and these spectroscopic
atmospheric parameters then enter the photometric analysis.
Knowing them reduces the uncertainty on the extinction con-
siderably. Observational limitations unfortunately mean that the
catalogues of targets that are observed in spectroscopy are con-
siderably smaller than photometric catalogues, although huge
progress has been achieved due to multiplex instrumentation
(e.g., the Apache Point Observatory Galactic Evolution Exper-
iment (APOGEE), the Radial Velocity Experiment (RAVE),
the Large Sky Area Multi-Object Fiber Spectroscopic Tele-
scope (LAMOST), the GALactic Archaeology with HERMES
(GALAH), the Sloan Extension for Galactic Understanding and
Exploration (SEGUE). Conversely, purely photometric deter-
minations of the extinction are less precise, but the order of
magnitude of the number of available targets is far higher than
that for spectroscopy (see Anders et al. 2019). Additionally,
considerable improvement is brought by including infrared pho-
tometry in combination with blueward wavelength domains. All
3D maps quoted above make use of infrared 2MASS photometry
along with data in the visible. Finally, narrow-band photometry
allows more accurate extinctions (Sale et al. 2014).
Ideally, information would be maximised by using distinct
extinction catalogues simultaneously in a unique inversion. This
has already been attempted in the past in several ways: (i)
extinction catalogues from different ground-based photomet-
ric systems (Lallement et al. 2014), (ii) extinctions based on
photometry and using equivalent widths of diffuse interstellar
bands as proxies for the extinction (Capitanio et al. 2017), and
(iii) extinctions from both ground-based and Gaia photometry
(Lallement et al. 2018). However, merging catalogues may be
the source of artefacts during the inversion if some systematic
differences are present, as in the following simple example. We
assume that in one region of the sky, a first catalogue contains
nearby stars for which extinction is overestimated, while a sec-
ond catalogue contains more distant stars and their extinction is
correctly estimated or slightly underestimated. During the tomo-
graphic inversion, the erroneous underestimated radial gradient
found in the transition region between the two altitude ranges
will result in the formation of an artificial dust layer just below
this area. This shows that catalogues must be assembled very
carefully.
There are several types of sources for differences between the
catalogues. First, each type of photometric measurement has its
own calibration, which is often based on the use of non-reddened
standard stars. The choice of the calibration stars differs from
one technique to the next. Moreover, some standard objects may
be weakly extincted. This affects the inversion at a short dis-
tance. Second, the stellar models that are used as references vary,
and the techniques of data-model comparison vary as well. Neg-
ative extinctions are allowed or prohibited, depending on the
techniques. Third, the surveys may focus on specific types (e.g.
red giants). The distributions of estimated extinctions and their
errors, as well as the spatial distribution of the targets, reflect this
choice. Merging data for sources distributed in a specific way
requires an extremely precise determination of the extinctions
and their errors. Finally, errors on extinctions linked to different
stellar types and/or different regions may arise from various
types of errors on distances for these object types and/or these
regions. If systematic effects due to brightness and/or crowding
are not perfectly contained in the quoted errors, this may produce
artefacts for all catalogues that are used.
A simple way to inter-calibrate two sources is to use the
series of objects that are common to the two catalogues and com-
pute the relation between the extinctions from the two sources.
This approach was used in the studies quoted above. This way
may be appropriate if the discrepancies are related to a dominant
effect, such as the extinction level, and if they do not significantly
depend on stellar type. In the opposite case, using this method
may become the source of errors that make the merging counter-
productive. Moreover, this simple method requires the existence
of a large number of common targets. Our goal here is to develop
and test a more accurate method of inter-calibration that is appli-
cable to two fully disconnected datasets. The unique requirement
is that a significant fraction of the targets in each catalogue are
located in the same region in 3D space. Section 2describes the
two catalogues we used to illustrate the inter-calibration tech-
nique. Section 3describes the basic principles of the method,
along with the application to the two datasets. Section 4contains
validation tests on the individual extinctions in order to assess
the inter-calibration method. Section 5describes the results of
several inversions of the entire dataset made from the reference
and the corrected catalogues. Section 6contains a summary and
discusses further improvements.
2. Data
As already mentioned, we chose to inter-calibrate two very dif-
ferent types of catalogues that contain extinctions estimated from
both spectroscopy and photometry for the reference catalogue,
and extinctions estimated from photometry alone for the second
catalogue. In addition, the distances are estimated differently in
the two catalogues. In the reference catalogue, Gaia parallaxes
are used as prior values for the distances, and the final distance
is determined from the parallax, the set of photometric data, and
from the spectral type deduced from spectroscopy. As a result,
targets with very uncertain parallaxes enter the catalogue. In the
second catalogue, the accuracy of the Gaia parallax is required,
and, at variance with the reference catalogue, the distance is
entirely based on the parallax. Finally, extinctions are forced to
be positive in the first catalogue, which is not the case in the
second catalogue.
In contrast to the input data and techniques that are very dif-
ferent, the target distance ranges are similar in the two sources,
as shown in Fig. 1(top panel). This is a necessary condition
for the inter-calibration. Subsequently, extinctions are expected
to be distributed in similar intervals, as shown in Fig. 1(bot-
tom panel). The two extinction distributions peak at about the
same value, but their shapes are quite different. This is caused
by two facts. First, when photometry alone is used, the uncer-
tainties are often of the same order as the estimated extinction,
and the dispersion is large. Conversely, stellar spectra add strong
constraints, and the uncertainties on the extinction are strongly
reduced, which results in a much smaller dispersion. The sec-
ond cause is the imposed positive value for the extinction in the
spectroscopic catalogue, while negative values are permitted in
the second catalogue. The very small number of slightly nega-
tive values of the extinction from the spectroscopic catalogue in
Fig. 1is due to the empirical inter-calibration of the two sources
(see next section and the appendix).
A174, page 2 of 16
J. L. Vergely et al.:Three-dimensional extinction maps: Inverting inter-calibrated extinction catalogues
2.0 x106
1.5
1.0
0.5
0.0
Target number
500040003000200010000
DISTANCE (pc)
300
200
100
0
x103
PHOTO
SPECTRO
1.6 x106
1.2
0.8
0.4
0.0
Target number
2.01.51.00.50.0-0.5
Extinction (mag)
1.0
0.8
0.6
0.4
0.2
0.0
x106
Fig. 1. Characteristics of the two catalogues. Top: histograms of
target distances: Gaia-2MASS extinction catalogue (red), and spectro-
photometric catalogue (black). The left axis corresponds to the photo-
metric catalogue, and the right axis corresponds to the spectroscopic
catalogue. Bottom: same as in the top panel for extinction values.
2.1. Catalogue based on spectroscopic surveys
The reference catalogue is based on two analyses by Sanders
& Das (2018) and Queiroz et al. (2020) of ground-based
spectroscopic survey data and associated available photometric
and astrometric measurements of the survey targets. The authors
used the stellar parameters derived from the initial spectroscopic
analysis of the surveys as input as well as Gaia DR2 paral-
laxes, when available, and performed a Bayesian estimate of all
parameters, including extinctions, distances from astrometry and
photometry, and ages. The photometric data used in both works
are from the SDSS (u; g; r; i; z), Pan-STARRS (gP; rP; iP; zP),
2MASS (J; H; Ks), APASS (B;V), WISE (W1;W2), and Gaia
(G,GB,GR, GRVS). Our goal is to illustrate the inter-calibration
of two (not three) very different datasets and the subsequent
correction of one of them. We therefore preliminarily merged
the two spectroscopy-based catalogues. Before merging the two
sources, we performed various corrections that are described in
Appendix B.
The analysis by Sanders & Das (2018) included targets from
the APOGEE, LAMOST, RAVE, SEGUE, GES, and GALAH
surveys (Majewski et al. 2017;Deng et al. 2012;Steinmetz et al.
2006;De Silva et al. 2015;Gilmore et al. 2012;Yanny et al.
2009). The authors used the catalogues available in 2018. Their
study is based on PARSEC isochrone fitting (Bressan et al. 2012;
Chen et al. 2015;Tang et al. 2014) and makes use of several prior
relations and parameter estimates: mass estimates from spectro-
scopic parameters (Das & Sanders 2019); an elaborate Galactic
model for distances, ages, and metallicities (Binney et al. (2014);
Queiroz et al. (2018); Bovy (2017)); and, of importance here,
a Galactic extinction prior based primarily on the Green et al.
(2018) maps; the Marshall et al. (2006) maps at low latitudes in
regions not covered by the Green et al. (2018) study; and finally,
the Drimmel et al. (2003) model in regions not covered by any
of the two previous maps. We chose to use this extinction cata-
logue as the reference for the calibration because this extinction
prior was used. The prior enhances the quality of the extinction
determination. Another reason to choose this catalogue was our
particular interest in the very nearby InterStellar Medium (ISM),
that is, very weak extinctions, and our previous determination of
the zero point for the extinction AVfrom this catalogue based
on nearby white dwarf (WD) absorption measurements in the
UV (detailed in Appendix A). We selected all targets flagged
best from the published catalogue for a total number of 3 318 118
stars, and we removed our estimated bias of 0.01 mag in AVfrom
all extinctions. We did not add any other flag.
Queiroz et al. (2020) derived stellar parameters, includ-
ing extinctions, for the same spectroscopic surveys except for
SEGUE. Their catalogue was based on the StarHorse Bayesian
analysis tool (Queiroz et al. 2018;Anders et al. 2018). Impor-
tantly, Queiroz et al. (2020) used updated catalogues, in particu-
lar, APOGEE DR16, GALAH DR2, LAMOST DR5, GES DR3,
and RAVE DR6, which resulted in a significant increase in the
number of targets in comparison with Sanders & Das (2018). We
excluded objects that were already present in the first catalogue
from this catalogue. The authors fitted PARSEC stellar evolu-
tionary model tracks (Bressan et al. 2012;Marigo et al. 2017). As
priors, they used the initial mass function from Chabrier (2003)
for all Galactic components, exponential spatial density profiles
for thin and thick discs, a spherical halo, and a triaxial (ellip-
soid plus spherical) bulge-bar component, broad Gaussians for
the age, and mass distribution functions. They used the normal-
isation of each Galactic component, as well as the solar position
reported by Bland-Hawthorn & Gerhard (2016). No prior on 3D
extinction was introduced. In the case of APOGEE, they used
the 2D AVprior provided in the survey catalogue. After appli-
cation of filters based on several StarHorse and Gaia flags and
an empirical filtering or correction based on Gaia photometry
and Planck dust emission (described in Appendix B), the num-
ber of additional targets from this Queiroz et al. (2020) catalogue
is 2 375 074 targets.
2.2. Gaia-2MASS catalogue
Our second catalogue of data is the one described in Lallement
et al. (2022). It is a series of 35 463553 extinctions derived from
Gaia G, Bp, and RP and 2MASS J, H, and Kphotometric data on
the one hand, and Gaia eDR3 parallaxes on the other hand. The
targets were selected according to their accurate photometry and
relative uncertainties on parallaxes better than 20%. The extinc-
tion was estimated based on preliminary established empirical
colour-colour relations that were deduced from weakly reddened
stars (Ruiz-Dern et al. 2018) and the most recent extinction
laws1. The method is described in detail in this article, as is
the hierarchical inversion of this homogeneous dataset, following
the technique described in Capitanio et al. (2017) and Lallement
et al. (2019). The inverted 3D extinction density map has been
shown to have an increased dynamic range and reaches larger
distances than the earlier map derived from Gaia DR2. We have
kept the catalogue in its entirety.
3. Inter-calibration
3.1. Basic principle
The inter-calibration method is based on the fact that co-spatial
target stars experience the same extinction, that is, regardless
1https://www.cosmos.esa.int/web/gaia/edr3-extinction-
law
A174, page 3 of 16
A&A 664, A174 (2022)
of the position of these targets in the colour-colour or colour-
magnitude diagrams, extinction estimates from two catalogues
should produce equivalent results for stars that are neighbours
in space. We chose a reference catalogue and assumed that it
provided the most accurate results. We then considered all pho-
tometric bands used for the second catalogue. After correcting
the different fluxes in all bands for the effects of extinction
(using the extinctions given in the catalogue) and deriving the
de-reddened absolute magnitudes, a principal component analy-
sis (PCA) was implemented in (G,GB,GR,J, H, and K) space in
order to work in a low-dimensional subspace. This subspace was
then divided into cells. For each star belonging to a given cell,
we compared the estimated extinction with extinctions of neigh-
bor targets from the reference catalogue located in 3D space at
distances shorter than a chosen value D, and we estimated for
each cell the systematic differences in extinction between the
two catalogues. We additionally defined some criteria to exclude
peculiar data.
The technique is not based on comparisons between extinc-
tions of targets in common to the two catalogues, that is, it does
not require any overlap. It is more general and can be applied to
catalogues using very different types of targets, different types
of extinction estimate, photometric and/or spectroscopic sources
in different wavelength domains, or various types of absorption
data. Finally, we draw attention to the fact that this method can
be used for an internal calibration of a single catalogue, that is,
a search for biases associated with various stellar types. This is
beyond the scope of the present work. Instead, we aim at esti-
mating corrections or filtering data from the second catalogue to
ensure compatibility with the reference.
3.2. Choice of catalogues
As we stated above, our goal is to develop and test an inter-
calibration method on two very different types of extinction
estimates. For this reason, we selected a purely photomet-
ric determination and a hybrid determination based on spec-
troscopy and photometry. The photometric extinctions (Ephot)
were derived from the three Gaia photometric bands (G,GB, and
GR) and the three 2MASS photometric bands (J, H, and K). They
were obtained by comparing the observed magnitudes with refer-
ence magnitudes in this six-dimensional space (Babusiaux et al.
2020). The quality of the extinction estimator depends on the
stellar type of the star and therefore on its position in this multi-
dimensional space. For example, and in general, the extinction
estimates of hot main-sequence stars are much more accurate
than the extinction estimates of cold stars (Vergely et al. 1998).
In some places in the HR diagram, unresolved ambiguities can
be expected to lead to biases in the extinction estimate. Dur-
ing the process, the location of the object in multi-colour space
or colour-magnitude space is displaced, and along the displace-
ment, more than one position with a high probability of existence
and different values of the extinctions can be encountered. In this
case, it is difficult to solve for the ambiguity, although it helps to
know the distance.
The addition of spectroscopic data provides strong con-
straints on the stellar type. The results on the extinction are
therefore more accurate. For the same distance and luminosity,
the quoted uncertainties on the extinctions in spectroscopy-based
catalogues are smaller than the quoted errors in the purely photo-
metric determination. In order to carry out the inter-calibration,
the spectroscopic extinctions (Espec) should therefore be taken
as the reference, which means that by assumption, the spectro-
scopic extinctions are considered to be unbiased and affected
by negligible errors compared to the errors of the photometric
extinctions. We therefore attempted to correct the photometric
extinctions for possible biases that depend on the position in
multi-colour space, so that they agreed with the spectroscopic
extinction measurements. In other words, the goal of this inter-
calibration is above all to work with a homogeneous set of
objects and to avoid systematic shifts in extinction depending
on the origin of the latter. The photometric catalogue provides
monochromatic extinctions A0at 550 nm, while the spectro-
scopic catalogues estimate AV, the extinction in the Vband.
Both quantities are very similar. We expect only weak system-
atic differences, and these differences are taken into account in
the results of the inter-calibration.
3.3. Selecting a target sub-sample for the calibration
The inter-calibration was carried out using subsets of the pho-
tometric and spectroscopic extinction data. As the aim is to use
spatially co-located stars from the two catalogues and compare
their extinctions, we selected stars in a 3 kpc sphere. For the
spectroscopy, we restricted the selection to stars with distance
errors smaller than 25 pc and errors on the extinction estimate
smaller than 0.15 mag. For the photometry, we selected objects
with a parallax error smaller than 10%. This selection allowed
us to cover the entire colour space with a significant number
of objects, namely 1.2 million spectroscopic extinction values
(out of a total of 5.7 million) and 29 million photometric extinc-
tion values (out of a total of 35.5 million). The purpose of this
pre-selection was to calculate the inter-calibration corrections
as accurately as possible. After the corrections were calculated,
they were applied to the entire photometric catalogue.
3.4. De-reddening and choice of colour-colour space
The first step was the calculation of the absolute de-reddened
magnitudes of the stars from the photometric catalogue. The
determination of the band-by-band extinctions was obtained by
using the absorption in the visible provided by the catalogue,
which was transformed to the other magnitudes (G,GB,GR,J,
H, and K) using the extinction coefficients given by the appro-
priate Gaia link2. Both sets of coefficients were attempted for
main-sequence stars on the one hand, and for giants and for
the top of the main sequence on the other hand. These extinc-
tion coefficients account for the wide bandpasses (especially
the Gband) and the resulting influence of the star temperature
on the extinction, and their use reduces this well-known source
of uncertainties. It has a shortcoming, however. This operation
requires an iterative calculation due to the implicit form of the
equations. The iterative calculation may induce classification
errors if there are problems with the convergence or/and if there
are bi-modal solutions. This happened in very rare cases, and we
eliminated the corresponding targets. A small number of objects
was rejected at this stage (about 20 000). All other objects were
de-reddened in all bands. Uncertainties on the stellar type due
to the wide bandpasses are also reduced by the inter-calibration
technique itself, namely the fact that we compare the extinctions
of targets located in the same volume, in which all stellar types
co-exist in general.
The second step was to define the space in which the inter-
calibration was to be performed. In order to normalise the
magnitudes before the PCA, they were centred and reduced
2https://www.cosmos.esa.int/web/gaia/edr3-extinction-
law
A174, page 4 of 16
J. L. Vergely et al.:Three-dimensional extinction maps: Inverting inter-calibrated extinction catalogues
Fig. 2. Distribution of the stars of the second catalogue in C1-C2 space,
where C1 and C2 are the first two principal components in the de-
reddened centred reduced (Gcr, GBcr, GRcr, Jcr, Hcr, and Kcr) space
and carry 99.9% of the variance. The colour scale refers to the loga-
rithm of the target number. The red line shows the average displacement
of a star due to a 1 mag absorption in the visible. Top: before the
inter-calibration. Bottom: after the inter-calibration (see Sect. 3.6).
(Gbecomes Gcr, etc.): For each magnitude, the mean was
subtracted, and the whole was divided by the standard devia-
tion. We then performed a PCA, which showed that 99.9% of
the variance was carried by two components that we called C1
and C2 (see Fig. 2). Components 3, 4, 5, and 6 carry relatively
little information in terms of variance, as shown in Fig. 3. The
components C1 and C2 are linear combinations of the reduced,
centred, de-reddened magnitudes Gcr, GBcr, GRcr, Jcr, Hcr, and
Kcr:
C1 =0.409 Gcr +0.411 GBcr +0.404 GRcr +0.411 Jcr
+0.408 Hcr +0.407 Kcr
C2 =−0.364 Gcr −0.151 GBcr −0.613 GRcr +0.200 Jcr
+0.436 Hcr +0.489 Kcr.
Based on these equations, a 10% error in parallax amounts
to an error of the order of 0.3 mag for C1 (the centred reduced
normalisation is about 1.6 for all photometric bands) and close to
0 for C2 (due to sign compensations). The errors on the observed
magnitudes were used as a selection criterion: less than 0.05 mag
for 2MASS bands, GBand GRbands, and less than 0.02 mag
on G.
The previous equation shows that C1 is a weighted sum
of the absolute magnitudes, which can be seen as a kind of
absolute luminosity. C2 is roughly the difference between the
magnitudes (J, H, and K) and the magnitudes (G,GB, and GR),
which gives an idea of the slope of the spectrum between the
infrared and the visible. C2 therefore is a colour that is strongly
correlated with the effective temperature of the star. It is inter-
esting to note that what distinguishes one star from another in
magnitude space (Gcr, GBcr, GRcr, Jcr, Hcr, and Kcr) happens
mainly in 2D space. We work in this space for practical reasons,
namely the simplification of representations and reduction of the
computation times.
3.5. Extinction differences
For practical reasons, the inter-calibration was carried out in
this C1-C2 2D space, which was divided into cells of size
(0.25 mag ×0.25 mag). We considered that in a given cell, we
can define a category of homogeneous stars that can be cal-
ibrated with the spectroscopic data. We show below that this
assumption is not always verified and that it is possible to iden-
tify cells where it is not possible to inter-calibrate the data
correctly. Each cell contains a number of objects that are spa-
tially collocated with the objects in the spectroscopic catalogue.
The objects in the spectroscopic catalogue that are within 25 pc
of the stars in a given cell were selected, and we assumed that the
photometric and spectroscopic extinctions are similar within the
errors on average. The average difference between photometric
and spectroscopic extinction gives an estimator of the correc-
tion to be made to the photometry in this given cell. It is also
possible to calculate the standard deviation of the extinction dif-
ference. If this standard deviation is very large, it can give an
idea of the error on the photometric extinction, knowing that
the error on the spectrometric extinction is considered negligi-
ble. The standard deviation was calculated in two different ways:
according to the classical method, and according to a robust
method that allows decreasing the influence of extreme values
(stdrob(X)=median(abs(X−median(X)))/0.6745).
It may appear inappropriate to use reference stars located in
volumes around each target instead of using those at similar dis-
tance and at small angular separation because the extinction is
a line-of-sight phenomenon. However, there are complex com-
pensating effects. The more distant the cells, the smaller the
angular separations, but simultaneously, the higher the angu-
lar fluctuations of the foreground extinction. Conversely, the
angle subtended by a nearby cell is wide, but the fluctua-
tions due to the local clouds as a function of the direction are
small.
Figure 4shows the corrections in AVthat are to be applied to
the photometric extinctions in order to homogenise them with
the spectroscopic extinctions. The corrections that are to be
applied are smaller than 0.3 mag in most cells. However, in some
specific regions of the (C1,C2) plane, especially at low values of
C1, the corrections can reach 1 mag and more. As we will show
below in (G,GB–GR) space, the effects of the corrections are sig-
nificant for the branch of giants, the turn-off, and the bottom of
the main sequence. In general, the HR diagram is better resolved,
which suggests that the corrections are effective.
Figure 5shows the standard deviations std and stdrob of
the difference between photometric and spectroscopic extinc-
tions in the (C1, C2) cells. When we neglect the errors in
A174, page 5 of 16
A&A 664, A174 (2022)
Fig. 3. Same as Fig. 2for C3-C4 space (left) and C5-C6 space (bottom), which carry 0.01% and less than 0.005% of the variance, respectively. The
colour scale refers to the logarithm of the target number.
Fig. 4. Mean difference Ephot −Espec in each cell of the de-reddened
(C1,C2) plane.
the spectroscopic extinction, then this standard deviation is a
measure of the error in the photometric extinction. The represen-
tation of the differences in the form of histograms in certain areas
of the plane (C1, C2) shows a bi-modal behaviour of the distri-
butions. This means that the photometric extinction estimation
is ambiguous and that there are two distinct potential solutions
in this area of the colour space. When the histograms are very
broad, a continuum of solutions makes the extinction estimate
uncertain. Figure 6shows two examples of histograms obtained
in regions of the plane (C1, C2) with a weak (strong) standard
deviation of the extinction differences.
3.6. Application of the inter-calibration
The inter-calibration makes use of the mean value of the differ-
ence (Ephot −Espec) and of its standard deviation in each cell. Two
resulting actions were implemented. The first action is a star-by-
star correction according to the cell of the star. Figures 2and 7
show the effect of the correction in the (C1, C2) and (G,GB–GR)
planes. In both cases, the dispersion is reduced after correction.
In the (G,GB–GR) plane, the red giant branch is corrected in
the expected direction. The second action is a filtering. If the
classical standard deviation of the differences (Ephot −Espec) was
larger than 0.5 mag, then the cell is rejected, that is, the stars
with photometric extinctions belonging to the cell were not used
in the future tomography. We obtained a bi-modal distribution
in a C1-C2 cell when there are two solutions for the reference
targets that are distant in the colour-magnitude diagram because
they have different extinctions. We conservatively chose to reject
such cells to avoid largely erroneous estimates of the correction.
The price to pay is the simultaneous rejection of some correct
data points. The choice of a threshold of 0.5 mag resulted in a
loss of about 5% of photometric extinctions and enabled us to
reject bi-modal or overly spread Ephot-Espec distributions.
4. Inter-calibration validation tests
There are several ways to test the effect of the correction. Some
are internal, such as simple tests of changes in homogeneity and
consistency of the corrected dataset. Others may use independent
measurements: we performed tests of this type using the Planck
optical thickness at 353 GHz (Planck Collaboration XI 2014).
If the reference values are accurate and the inter-calibration
effectively corrects for small biases associated with the colours
and the extinction level, we expect a decrease in dispersion
of data points forming the line-of-sight extinction profile for
any direction. This must be true also in regions of space that
are devoid of targets of reference because the correction is
established from the whole series of deviations measured for
targets of a given type, regardless of their location. A line-of-
sight extinction profile built from initial (i.e. prior to correction)
distance-extinction pairs reveals a dispersion with two sources,
the actual angular variability of the extinction, and the combina-
tion of uncertainties and biases. Figure 8displays two examples
of tests illustrating the disappearance of a fraction of the dis-
persion. We selected from the photometric catalogue all targets
located within 0.5◦from two specific directions, here (l,b) =
(60.7◦, +0.2◦) and (l,b) = (76◦,−2◦). For each direction, we
A174, page 6 of 16
J. L. Vergely et al.:Three-dimensional extinction maps: Inverting inter-calibrated extinction catalogues
Fig. 5. Standard deviation of Ephot −Espec in each cell of the de-
reddened (C1,C2) plane. Top: Classical standard deviation. Bottom:
robust standard deviation.
separated the data into two groups according to the sign of the
computed inter-calibration correction to be applied. For each
group, we averaged the data into 200 pc distance bins. The figure
shows that for both directions, data moving down are all above
data moving up. This shows that the dispersion around the aver-
age profile, also shown in the figure, will decrease. The same
trend is obtained when tests were performed at different lati-
tudes and longitudes. The two figures also display the number
of distance-extinction pairs of stars from the catalogue of refer-
ence located in the same solid angle and the same distance bin as
the photometric targets. The decrease in dispersion is not limited
to regions with high densities of reference targets, but extends to
regions that are devoid of these targets. This demonstrates that
an effective correction is spread in space, and not only close to
reference targets.
Another test can be performed using 2D images. Figure 9
displays the pre- and post-correction extinctions for targets of
the second catalogue located in an area at low Galactic latitude
Fig. 6. Two illustrative examples of Ephot −Espec histograms. Top:
(C1,C2) plane cell with a weak standard deviation. Bottom: same as
in the top panel for a strong standard deviation.
below Perseus. There are subtle changes due to the correction
in this area. To highlight these very weak changes, an image
based on the same targets, this time colour-coded according to
the dust optical thickness deduced from Planck data (Planck
Collaboration XI 2014), is shown for comparison. The Planck
image shows that filamentary structures that are best seen with
Planck appear slightly more clearly after the correction.
Finally, a validation based on the comparison with the dust
emission can be performed, provided it is restricted to high
latitudes. Because the dust is located at a short distance from
the Plane (within '200 pc; see e.g. Lallement et al. 2022), the
absorbing dust for most high-latitude targets is the totality of
the dust seen in emission, and a tight correlation between the
extinction and the dust optical thickness is expected. We used the
Planck optical thickness because it provides the highest angular
resolution over the sky and does not enter any extinction prior
used in the inter-calibrated catalogues. Figure 10 displays all pre-
and post-correction extinctions for all targets of the second (pho-
tometric) catalogue located above b= +40◦as a function of the
A174, page 7 of 16
A&A 664, A174 (2022)
Fig. 7. Distribution of stars in the (G,GB,GR) plane before extinction
correction (top graph), after correction for initial extinction (middle),
and after correction for inter-calibrated correction (bottom).
3
2
1
0
Av (mag)
3000200010000
Distance bin (pc)
40
30
20
10
0
Number of targets of reference
3
2
1
0
Av (mag)
300025002000150010005000
Distance bin (pc)
4
3
2
1
0
Number of targets of reference
Fig. 8. Illustration of the correction. Left: initial extinction of all
targets from the photometric catalogue within 0.5◦of the direction
(l,b) = (60.7◦, +0.2◦). Data are averaged into 200 pc distance bins and
separated into two groups according to the sign of the computed cor-
rection to be applied. Red shows an upward correction (extinction
increase), and black shows a downward correction. The thin black line
indicates the average for all data. Black (red) points lie below (above)
the average value, showing that the corrections we applied reduce the
scatter. The histogram represents the number of spectroscopic extinc-
tions in the same region of the sky and their distribution in the same
distance bins. Right: same as left for the direction (l,b)= (76◦,−2◦).
Significant corrections are visible in regions that are devoid of reference
targets (below 600pc and between 1200 and 1800 pc.)
Planck 353 GHz optical thickness τ353. For all these targets, the
extinction is very weak, often of the order of the uncertainty. Lin-
ear fits to τ353 are shown, and the slope is slightly higher after
correction. More importantly, the dispersion around the linear fit
is significantly reduced (χ2decreases by 32%). This shows that
even for these very weak extinctions, the inter-calibration brings
some improvement, and that some reliability of the spectroscopic
data has been transmitted to the photometric extinctions. Part of
this reliability may be due to the extinction prior used by Sanders
& Das (2018) for all targets or by Queiroz et al. (2020) for the
subset of APOGEE targets, and may be transferred to the final
maps discussed in the next section. However, as already pointed
out, this transmission is not directional, but goes through the
location of the targets in multi-colour space C1-C2.
-39
-38
-37
-36
-39
-38
-37
-36
-39
-38
-37
-36
164 162 160 158 156
Fig. 9. Illustration of the correction. Top: Planck τ353 GHz dust optical
thickness in the direction of photometric targets in a region of the sky in
the low Galactic latitude part of the Taurus-Perseus area. The image is
used to show weak filamentary structures. Middle: corrected extinction
for the same targets. Bottom: initial extinction for the same targets. The
colour scale is identical to the one used in the middle image. The subtle
variations in the pattern in the middle image agree better with Planck
structures. Stars from the reference catalogue are not displayed in the
images.
Fig. 10. Illustration of the correction. Red dots show the initial extinc-
tion for all targets of the photometric catalogue above 40◦Galactic
latitude as a function of the optical thickness of the interstellar dust
at 353 GHz, as measured by Planck (Planck Collaboration XI 2014).
Black dots show the corrected extinction for the same targets. A linear
fit to Planck τ353 gives a significantly lower χ2value for the corrected
extinctions, showing that some biases have been corrected.
5. Inversion of merged catalogues
We have applied the hierarchical inversion technique presented
in (Vergely et al. 2010) and Lallement et al. (2019) to the merged
catalogue composed of the reference catalogue and the inter-
calibrated one. This technique uses spatial correlation lengths in
A174, page 8 of 16
J. L. Vergely et al.:Three-dimensional extinction maps: Inverting inter-calibrated extinction catalogues
order to allow estimating extinction density everywhere. Several
extinction density maps were computed for several maximum
spatial resolutions and extents. We recall that the best achievable
resolution (or minimum achievable spatial correlation length)
depends on the spatial density of the target star and on distance
uncertainties, that is, it decreases with the distance to the Sun and
the opacity encountered in the various regions. For these reasons
and to reduce the computational time, maps covering a large vol-
ume were computed with a larger correlation length. The series
of maps correspond to volumes ∆X×∆Y×∆Zof
– 10 000 pc ×10 000 pc ×800 pc for R=50 pc
– 6000 pc ×6000 pc ×800 pc for R=25 pc,
– 3000 pc ×3000 pc ×800 pc for R=10 pc,
where Ris the size of the minimum correlation length, corre-
sponding to the last iteration of the inversion. The extinction
density maps can be explored and exploited using a dedi-
cated application, called G-Tomo, deployed on the EXPLORE
website3. We illustrate the results by showing examples of
extinction density images in three selected planes for the first,
second, and third map. The fourth map will be studied in more
detail and compared with other tracers of the dense ISM in
a forthcoming dedicated article. Figure 11 displays the extinc-
tion density of the first map in the XY plane, parallel to the
Galactic Plane and containing the Sun. The minimum correla-
tion length of 50 pc allows showing only large structures. Several
iso-contours of the extinction density are drawn to delineate the
most opaque and most transparent areas. Because the number
of targets is very limited beyond 3 kpc and because the dis-
tribution of these distant targets is very inhomogeneous, this
map reveals structures only in several distant regions, while in
others, the solution is strongly influenced by the homogeneous
prior used in the first iteration of the hierarchical inversion.
We drew an isocontour that delimits regions possessing a target
density below one per 100 ×100 ×100 pc−3and where the inver-
sion cannot be performed, even at the lowest spatial resolution.
Figure 11 also shows the extinction density from the same 3D
map in vertical planes containing the Sun and oriented along the
axis Sun-Galactic centre (the meridian plane) and along the tan-
gential direction to the Sun circle (the rotation plane). We refer
to Lallement et al. (2019,2022) for an identification of the main
structures. In our former map based on Gaia e-DR3 and 2MASS
photometric data (Lallement et al. 2022), we emphasised the
wavy pattern of the dust distribution along the Z-axis. This pat-
tern is seen in many regions. We also pointed out the similarity
the mean vertical peak-to-peak amplitude (about 300 pc) and the
vertical period of the spectacular snail-shaped stellar kinemati-
cal pattern discovered in Gaia data by Antoja et al. (2018). The
more extended new map shows that the wavy pattern seems to
disappear at large distances along the X-, -X-, and -Y-axes, and
seems to persist along the +Y-axis (see Fig. 11 middle and bot-
tom). However, more data are needed to confirm the pattern at
these distances.
Figure 12 is identical to Fig. 11 for the second map, which
covers only 6 kpc by 6 kpc along the Plane. Here the maximum
resolution, corresponding to a correlation length of 25 pc, allows
showing many more details. As explained above, the maximum
resolution is not achieved everywhere. In the frame of the hier-
archical technique, the resolution is even limited by the target
density. For this reason, the highest resolution is achieved in
regions with high target density, and the map is more detailed
than the previous one. Conversely, in regions with very few
targets, the map is similar to the previous one.
3https://explore-platform.eu
In addition to structures discussed in previous works, the two
maps in Figs. 12 and 11 reveal a gigantic, oval cavity in the sec-
ond quadrant very clearly. This 2.5 kpc by 2.0 kpc region devoid
of dust has previously been overlooked because its far boundary
was not clearly delineated because the mapping extent was lim-
ited or the resolution was too poor. Here its entire contours are
drawn rather precisely. This remarkable, huge structure is ori-
ented very differently from other cavities and chains of clouds,
and it suggests a local phenomenon, at variance with structures
triggered by external perturbations (dwarf galaxy crossing, bar
and arm resonances; see Antoja et al. 2018;Khoperskov et al.
2020). The most likely origin for this huge cavity is a large series
of supernovae. Comparisons with O, B star associations will help
tracing the history of this region.
Figure 13 is similar to Figs. 11 and 12 for the third map. It
covers only 3 kpc by 3 kpc and shows the result of a hierarchical
inversion with a smaller final correlation length of 10 pc.
Isocontours of equal extinction densities are drawn on each
map for the same series of extinction density levels (see Fig. 11
for details). Contours delineating the densest regions appear
gradually from the lower to the higher resolution map. This is
a natural consequence of the decreasing correlation kernel, and
it arises because the integrated extinction can be distributed in
smaller volumes in the high-resolution maps.
6. Summary and discussion
We have devised a technique of inter-calibrating extinction cata-
logues that were based on different data and different techniques
of extinction estimates. Our goal was suppressing biases or arte-
facts in 3D maps of extinction density that are produced by the
inversion of merged catalogues. The inter-calibration was based
on extinction comparisons for targets from different catalogues
that are located in the same region of 3D space. It was based
on the principle that all estimated extinctions should be equal at
the same location, regardless of the method, input data type, and
stellar type. The comparison was conducted cell by cell in a sub-
space constituted by the two first components of a PCA initially
performed in the (G,GB,GR,J, H, and K) multi-colour space.
One main advantage of this technique is its potential applica-
tion to two catalogues for which the targets do not overlap.
This allows using catalogues based on photometry in different
wavelength ranges. The only requirement is that in at least one
region of space targets from the different sources co-exist and are
numerous enough to establish some statistical relations. Outside
this region, other targets may be distributed differently. This is
a second advantage because it allows the use of catalogues that
consist of targets that are mostly located in different regions of
space.
As an illustration, we used as the catalogue of reference for
the inter-calibration a spectrophotometric catalogue, and we per-
formed the inter-calibration on a purely photometric catalogue,
previously presented in Lallement et al. (2022). The combina-
tion of spectroscopy and photometry provides a more accurate
extinction, and the inter-calibration allows transferring part of
this accuracy to the other data. In order to reduce the dimen-
sion of the problem, a PCA was performed in the (G,GB,GR,
J, H, and K) space by associating colours used for the consti-
tution of the catalogue. The subspace constituted by the two
first components was split into cells, in which deviations from
the reference were estimated. These deviations were computed
using all targets from the reference catalogue located at a short
distance of each secondary target in 3D space. Corrections and
filtering were deduced in each cell in multi-colour space. The
A174, page 9 of 16
A&A 664, A174 (2022)
-4000
-2000
0
2000
4000
-4000 -2000 0 2000 4000
X axis
Y axis
5
4
3
2
1
x10-3 mag pc-1
giant
oval
cavity
-400
-200
0
200
400
-4000 -2000 0 2000 4000
Z axis
X axis
-400
-200
0
200
400
-4000 -2000 0 2000 4000
Y axis
Z axis
Fig. 11. Inverted 3D dust distribution. Top: extinction density in the XY plane containing the Sun. The orientation is parallel to the Galactic Plane.
The map is at the lowest resolution (correlation length of 50 pc). The Sun is at (0,0). Units are in parsecs. The colour scale is the same for all maps
and is shown in Fig. 12. The thick dashed-dot black line shows the distance beyond which cells may be devoid of targets (see text for caveats at large
distance). Iso-extinction density contours are drawn for 1×10−5(red), 5×10−5(dashed pink), 1×10−4(dashed light orange), 2×10−4(dashed
orange), 5×10−4(red), 1×10−3(orange), 2×10−3(brown), 5×10−3(dark green), 1×10−2(dashed light green), 2×10−2(blue) mag pc−1. A giant
cavity devoid of dust lies between longitudes l '85◦and l '145◦.Middle: extinction density in the XZ (meridian) plane. The Galactic centre is to
the right. Bottom: extinction density in the YZ (rotation) plane. The sense of rotation is to the top.
A174, page 10 of 16
J. L. Vergely et al.:Three-dimensional extinction maps: Inverting inter-calibrated extinction catalogues
-3000
-2000
-1000
0
1000
2000
3000
-3000 -2000 -1000 0 1000 2000 3000
X axis
Y axis
5
4
3
2
1
x10-3 mag. pc -1
-400
-200
0
200
400
-3000 -2000 -1000 0 1000 2000 3000
Z axis
X axis
-400
-200
0
200
400
-3000 -2000 -1000 0 1000 2000 3000
Y axis
Z axis
Fig. 12. Same as Fig. 11 for the less extended 6 kpc ×6 kpc ×0.8kpc map inverted with a correlation length of 25 pc. The colour scale is the same
for all images.
A174, page 11 of 16
A&A 664, A174 (2022)
-1500
-1000
-500
0
500
1000
1500
-1500 -1000 -500 0 500 1000 1500
X axis
Y axis
5
4
3
2
1
x10-3 mag pc-1
-400
-200
0
200
400
-1500 -1000 -500 0 500 1000 1500
X axis
Y axis
-400
-200
0
200
400
-1500 -1000 -500 0 500 1000 1500
Y axis
Z axis
Fig. 13. Same as Fig. 12 for the 3kpc ×3 kpc ×0.8 kpc map inverted with a correlation length of 10 pc.
A174, page 12 of 16
J. L. Vergely et al.:Three-dimensional extinction maps: Inverting inter-calibrated extinction catalogues
same technique can be applied to a different multi-colour space
or to any multi-dimensional space associating the different types
of measurements entering the determination of the extinction.
We have used several validation tests and showed that the
technique produces a merged catalogue that is significantly more
self-coherent by comparison with a simple concatenation of data,
including in regions of space that are devoid of reference targets.
We emphasise that the same method can be also successfully
applied to a single dataset to detect biases and increase the inter-
nal self-coherence. We also note that this work contains some
arbitrary choices of reference values. Further work is planned on
the various criteria and the search for the best references. Gaia
Data Release 3 will be used for this purpose.
We have inverted the merged catalogue to produce several 3D
distributions of extinction density in various volumes and for dif-
ferent resolutions comprised between 50 pc and 5 pc, following
the technique presented in Vergely et al. (2010) and Lallement
et al. (2019). The addition of spectroscopic data allows us to
reach larger distances from the Sun and to improve the quality of
the map. The wavy pattern around the Z-axis is confirmed and
better delimited. Based on our previous maps (Lallement et al.
2022), we suggested that it is connected with the spectacular
snail-shaped stellar kinematical pattern discovered in Gaia data
(Antoja et al. 2018), whose origin is currently debated. Future
Gaia data and further studies are expected to shed light on this
peculiar local pattern. Some cavities are more clearly revealed,
in particular, a 2.5 kpc ×2 kpc region that is fully devoid of dust
in the second quadrant. Further work is needed to understand its
oval shape, which is more suggestive of a superbubble than of
an inter-arm region. New Gaia data for the locations of massive
stars and 3D motions will help trace the formation of this huge
cavity.
Acknowledgements. We thank our referee for his very careful reading of the
manuscript and his many constructive remarks which helped to improve the
clarity of the text and the presentation of the figures. J.-L.V. and N.L.J.C.
acknowledge support from the EXPLORE project. EXPLORE has received
funding from the European Union’s Horizon 2020 research and innovation
programme under grant agreement no. 101004214. J.-L.V. acknowledges sup-
port from the THETA Observatoire des Sciences de l’Univers in Besançon.
This research or product makes use of public auxiliary data provided by
ESA/Gaia/DPAC/CU5 and prepared by Carine Babusiaux. This research has
made use of the SIMBAD database, operated at CDS, Strasbourg, France. This
work has made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Process-
ing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/
gaia/dpac/consortium). Funding for the DPAC has been provided by national
institutions, in particular the institutions participating in the Gaia Multilateral
Agreement. This work also makes use of data products from the 2MASS, which
is a joint project of the University of Massachusetts and the Infrared Processing
and Analysis Center/California Institute of Technology, funded by the National
Aeronautics and Space Administration and the National Science Foundation.
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40 x10-3
35
30
25
20
15
10
5
0
Integrated extinction AV (mag)
16 x10-3
12840
Av from PII absorption (mag)
40
35
30
25
20
15
10
5
0
x10-3
60 x10-3
50403020100
Av from UV-estimated N(H) (mag)
Fig. A.1. Comparison between extinctions estimated from UV absorp-
tion lines in the spectra of nearby white dwarfs and extinction values
integrated in a preliminary 3D map (see text). Left: Using P II ion
columns from Lehner et al. (2003) and phosphorus depletions from
Jenkins (2009). Black arrows correspond to estimated negative values
and show the corresponding upper limits. The dot-dashed black line is
a linear fit using only positive values. Right: Using N(H) columns esti-
mated by Jenkins (2009) from P, O, Si, and Fe ions. The dot-dashed
black line is reported from the left panel. Both estimates indicate a
positive bias on AVof about 0.01 mag.
Appendix A: Extinction bias estimate from
absorption lines in white dwarf UV spectra
Extinctions estimated by Sanders & Das (2018) are forced to
be positive, which may induce a small bias at very low extinc-
tions. Because this may introduce systematic effects during the
combination with the Queiroz et al. (2020) catalogue, in which
extinctions are allowed to be negative, we searched for a quan-
tification of a potential small bias. To do this, we performed a
preliminary inversion of the Sanders & Das (2018) catalogue
alone, using the 3D distribution from GAIA-2MASS photometry
(Lallement et al. 2019) as a prior. Because the error bars of the
Sanders & Das (2018) catalogue are very small, its content con-
strains the 3D distribution of extinction at very short distance,
where the prior has no effect. As a result, if a bias does exist, it
should be reflected in the opacity density at the short distances
found in this preliminary inversion.
In parallel, we searched for gaseous absorption lines in the
UV spectra of nearby WDs with the goal of estimating the
extinction at short distance in a different way, assuming a classi-
cal relation between dust and gas. An appropriate species is the
PII ion, which has a small depletion and has been shown to be
relatively well correlated with the gas column (see Jenkins 2009,
and references therein). We used the results from Lehner et al.
(2003), and in particular, measurements of P I I ion columns as
well as the phosphorus depletion estimates from Jenkins (2009)
to transform the P I I columns into N(H), then into extinction AV
using AV= 3.1* N(H) / 6×1021 for about 30 nearby WDs.
Fig. A.1 (left) shows the extinction integrated in the 3D map
described above between the Sun and each WD as a function of
the extinction estimated from P I I absorbing columns along the
path to the targets. Although the uncertainties on both quantities
are large, the extrapolation of the average relation between the
two quantities shows that for null columns of gas, the extinction
integrated in the map is positive and about 0.01 mag, suggesting
a bias on this order.
Later on, and for most of the Lehner et al. (2003) nearby
WDs, Jenkins (2009) estimated the gas column using all avail-
able absorption data for P, O, Si, and Fe in combination. Fig. A.1
(right) shows the extinction integrated towards the slightly differ-
ent set of WDs as a function of the extinction from N(H) using
the same AV/N(H) relation as above. The bias deduced in this
way is similar. As a result, we removed 0.01 mag from all
the extinction measurements from the Sanders & Das (2018)
catalogue.
Appendix B: Merging the two extinction catalogues
based on spectroscopy and photometry
As described in section 2.1, the methods used by Sanders & Das
(2018) and Queiroz et al. (2020) to estimate the stellar parame-
ters and extinctions differ in several aspects. Due to the use of a
prior on the 3D distribution of extinction in the former catalogue
and the existence of a global quality flag (best), we kept all good-
quality data (best = 1) and removed the small bias described in
the previous section. In the case of the latter catalogue, we per-
formed several selections and searches for biases, as described
below.
Appendix B.1: Data selection
In the case of the Queiroz et al. (2020) catalogue, we made use
of the various flags tabulated by the authors and additionally
excluded some targets based on the Gaia measurements. We list
below the criteria for target exclusion.
– For APOGEE data, the absence of the Avprior input.
– For all surveys, the presence of uncal, or TEFF-LOGG-m-h-
ALPHA-PARALLAX-Ggaia, in the input flags.
– For all surveys, the presence of bad,high, or warn in the
output flags.
– When Gaia parallaxes are used,
–ruwe ≥1.4, or ipd frac multi peak ≥2
– a high bp-rp flux excess factor, namely C ≥3σ(G)with C
and σ(G)computed following Table 2 and Equ. 18 from
Riello et al. (2021)
– The presence of bright, angularly close targets being a poten-
tial source of bias during the spectroscopic observation. We
used Gaia eDR3 astrometry and photometry to select stars
within 10 µarcsec from each catalogue target. We computed
aweight function Wof these secondary stars in the form of a
sum of their potential contaminating flux C f . We used for Cf
the G-band flux fG and the angle θwith the catalogue target,
W= Σ f G i/f G0/θi
where fG0is the G-band flux of the catalogue target. We
excluded targets with w≥0.7. This quantity was adjusted
after a search for visible effects of a high value of win the
form of outliers in line-of-sight extinction profiles. Based on
this criterion, we excluded about 7,500 targets.
Appendix B.2: Additional empirical corrections using the dust
emission
We used the dust optical depth at 353 GHz measured by Planck
(Planck Collaboration XI 2014) to select directions of very weak
extinction. The selection criterion was τ(353) ≤2.1 10−6, which
corresponds approximately to AV≤0.1 mag, according to the
average relation E(B-V) = 1.5·104τ(353) from Remy et al.
(2018) and assuming AV= 3.1 E(B-V). All the selected sight
lines correspond to high latitudes, and for this reason, the large
majority of the target stars are located beyond the dust layer.
For all these sightlines, we removed from the catalogue extinc-
tion AV(c) the weak amount of extinction corresponding to the
Planck optical depth AV(P), using the above relation. For each
A174, page 14 of 16
J. L. Vergely et al.:Three-dimensional extinction maps: Inverting inter-calibrated extinction catalogues
catalogue separately, we then computed the average difference
AV(c)-AV(P) for targets belonging to temperature-gravity log(g)-
Tefftwo-dimensional cells. The Teffgrid extends from 3500 to
9000 K in steps of 250 K, and the log(g) grid extends from 0 to
5 by steps of 0.25. The distribution of AV(c)-AV(P) in each cell
was fitted to a Gaussian distribution. The central value was con-
sidered as a bias for the corresponding cell in the corresponding
survey. The standard deviation was added quadratically to the
catalogue uncertainty for all stars in the Teff-log(g) cell (regard-
less of the Planck value). Fig. B.1 shows the values of the biases
determined using this empirical method. Some cells are empty
and correspond to numbers of targets that are too low to allow a
bias estimate.
A second filtering and correction was performed on the basis
of the Gaia photometric fluxes. To do so, we used the updated
Gaia eDR3 values. After the above correction we distributed all
targets in directions of low dust emission in GB-(GB-GR) two-
dimensional cells. Here again, one would expect a distribution
of AV(c)-AV(P) centred around zero. We fitted the distribution
to a Gaussian and estimated a bias and an additional uncertainty
in the same way than for the log(g)-Teffbins. Additionally, for
each interval for GB, we excluded targets in (GB-GR) cells with
very high bias or dispersion. This last step was performed by eye.
The intervals, biases, additional uncertainties, and exclusions are
listed in Table B.1.
Fig B.2 shows the histogram of all extinctions AV(c)-AV(P)
before and after application of the filtering and empirical cor-
rections for all stars with τ(353) ≤2.1 10−6. About 25 % of
the targets are excluded if all constraints are applied. The wings
of the distribution were largely reduced and the width of the
distribution has decreased.
5
4
3
2
1
0
8000 7000 6000 5000 4000
1.2
1.0
0.8
0.6
0.4
0.2
0.0
5
4
3
2
1
0
8000 7000 6000 5000 4000
-1.5
-1.0
-0.5
0.0
0.5
5
4
3
2
1
0
8000 7000 6000 5000 4000
1.0
0.5
0.0
-0.5
5
4
3
2
1
0
8000 7000 6000 5000 4000
1.5
1.0
0.5
0.0
5
4
3
2
1
0
8000 7000 6000 5000 4000
0.25
0.20
0.15
0.10
0.05
0.00
-0.05
Log(g)
Log(g)
Tef f
Log(g)
Log(g)
5
4
3
2
1
0
8000 7000 6000 5000 4000
0.30
0.25
0.20
0.15
0.10
0.05
Log(g)
5
4
3
2
1
0
8000 7000 6000 5000 4000
0.14
0.12
0.10
0.08
0.06
5
4
3
2
1
0
8000 7000 6000 5000 4000
0.35
0.30
0.25
0.20
0.15
0.10
0.05
5
4
3
2
1
0
8000 7000 6000 5000 4000
0.35
0.30
0.25
0.20
0.15
0.10
0.05
5
4
3
2
1
0
8000 7000 6000 5000 4000
0.7
0.6
0.5
0.4
0.3
0.2
Tef f
Fig. B.1. Empirical corrections of the extinction (in mag) and additional
uncertainties based on low dust emission regions (see text). Left: From
top to bottom: APOGEE, GALAH, GES, LAMOST, and RAVE empir-
ical corrections. Blank cells correspond to an absence of targets. No
correction was made for other targets with higher dust emission that lay
in the same cell. The colour scale varies from one survey to the other.
Right: Additional empirical uncertainties. Because it contains very few
targets, we arbitrarily added uncertainties similar to those of LAMOST
for the GES survey.
60 x103
50
40
30
20
10
0
target number
1.51.00.50.0
Extinction (mag)
NO correction, NO flag
After correction, filtering
Fig. B.2. Histogram of the extinctions for the set of stars with low dust
optical thickness before and after filtering and introduction of empirical
corrections.
A174, page 15 of 16
A&A 664, A174 (2022)
Table B.1. Second empirical correction based on low-extinction regions: For each GBmagnitude interval, we list the allowed interval for GB-GR,
the bias, and the standard deviation to be quadratically added to the other terms.
GBinterval 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20
GB-GR>0.58 0.5-1.5 >-0.09 0.02-1.63 0.02-1.63 0.03-1.54 0.03-1.45 0.0-1.5 0-1.55 0.6-1.5 <1.1
Corr-Av 0.0329 0.0324 0.0513 0.0547 0.0504 0.0418 0.0316 0.0273 0.0088 -0.0244 -0.1044
σ(c) 0.09 0.10 0.09 0.08 0.08 0.09 0.105 0.115 0.13 0.19 0.34
A174, page 16 of 16
