# The intrinsic reddening of the Magellanic Clouds as traced by background
galaxies – III. The Large Magellanic Cloud

Cameron P. M. Bell,1 Maria-Rosa L. Cioni,1 Angus H. Wright,2 David L.
Nidever,3,4 I-Da Chiang,5,6 Samyaday Choudhury,7,8 Martin A. T. Groenewegen,9
Clara M. Pennock,10 Yumi Choi,11 Richard de Grijs,7,8 Valentin D. Ivanov,12
Pol Massana,13 Ambra Nanni,14, Noelia E. D. Noël,13 Knut Olsen,4 Jacco Th. van
Loon,10 A. Katherina Vivas15 and Dennis Zaritsky16
1Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, D-14482
Potsdam, Germany
2Astronomisches Institut, Ruhr-Universität Bochum, Universitätsstr. 150,
D-44801 Bochum, Germany
3Department of Physics, Montana State University, P.O. Box 173840, Bozeman, MT
59717, USA
4National Optical–Infrared Astronomy Research Laboratory (NOIRLab), 950 North
Cherry Avenue, Tucson, AZ 85719, USA
5Institute of Astronomy and Astrophysics, Academia Sinica, No. 1, Section 4,
Roosevelt Road, Taipei 10617, Taiwan
6Center for Astrophysics and Space Sciences, Department of Physics, University
of California, San Diego 9500 Gilman Drive, La Jolla,
CA 92093, USA
7Department of Physics and Astronomy, Macquarie University, Balaclava Road,
Sydney NSW 2109, Australia
8Research Centre for Astronomy, Astrophysics and Astrophotonics, Macquarie
University, Balaclava Road, Sydney NSW 2109, Australia
9Koninklijke Sterrewacht van België, Ringlaan 3, 1180 Brussels, Belgium
10Lennard-Jones Laboratories, School of Chemical and Physical Sciences, Keele
University, Keele, ST5 5BG, UK
11Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218, USA
12European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748 Garching
bei München, Germany
13Department of Physics, University of Surrey, Guildford, GU2 7XH, UK
14National Centre for Nuclear Research, ul. Pasteura 7, 02-093 Warszawa,
Poland
15Cerro Tololo Inter-American Observatory, National Optical Astronomy
Observatory, Casilla 603, La Serena, Chile
16Steward Observatory and Department of Astronomy, The University of Arizona,
Tucson, AZ85721, USA
E-mail<EMAIL_ADDRESS>(CPMB)

(Accepted 2022 May 27. Received 2022 May 27; in original form 2022 January 10
)

###### Abstract

We present a map of the total intrinsic reddening across $\simeq$ 90 deg2 of
the Large Magellanic Cloud (LMC) derived using optical ($ugriz$) and near-
infrared (IR; $YJK_{\rm{s}}$) spectral energy distributions (SEDs) of
background galaxies. The reddening map is created from a sample of 222,752
early-type galaxies based on the lephare $\chi^{2}$ minimisation SED-fitting
routine. We find excellent agreement between the regions of enhanced intrinsic
reddening across the central ($4\times 4$ deg2) region of the LMC and the
morphology of the low-level pervasive dust emission as traced by far-IR
emission. In addition, we are able to distinguish smaller, isolated
enhancements that are coincident with known star-forming regions and the
clustering of young stars observed in morphology maps. The level of reddening
associated with the molecular ridge south of 30 Doradus is, however, smaller
than in the literature reddening maps. The reduced number of galaxies detected
in this region, due to high extinction and crowding, may bias our results
towards lower reddening values. Our map is consistent with maps derived from
red clump stars and from the analysis of the star formation history across the
LMC. This study represents one of the first large-scale categorisations of
extragalactic sources behind the LMC and as such we provide the lephare
outputs for our full sample of $\sim$ 2.5 million sources.

###### keywords:

Magellanic Clouds – galaxies: photometry – galaxies: ISM – surveys – dust,
extinction

††pagerange: The intrinsic reddening of the Magellanic Clouds as traced by
background galaxies – III. The Large Magellanic Cloud–References††pubyear:
2022

##  1 Introduction

The Magellanic Clouds contain stellar populations spanning all ages which
thanks to their proximity ($\sim 50-60$ kpc) have allowed a number of
investigations. The study of star formation at lower ($0.2-0.5$ Z⊙)
metallicities (e.g. Gouliermis, Hony & Klessen, 2014; Zivkov et al., 2018),
the extragalactic distance scale (and by extension the Hubble constant
$H_{0}$, e.g. de Grijs, Wicker & Bono, 2014; de Grijs & Bono, 2015; Riess et
al., 2019; Freedman et al., 2020), and the metallicity dependence of the
period–luminosity relation of variable stars (see e.g. Gieren et al., 2018;
Groenewegen, 2018; Muraveva et al., 2018; Ripepi et al., 2019) are examples of
investigations dependent upon an understanding of the amount and spatial
distribution of dust across the galaxies. These studies use stellar
populations of different ages to quantify the reddening in the Magellanic
Clouds which results in statistically significant differences (this is further
complicated by variations in metallicity, three-dimensional distributions of
the stars and dust, etc.). On average, reddening maps based on young stellar
populations such as Classical Cepheids or young open clusters produce maps
emphasising the high levels of reddening typical of those areas of ongoing or
recent star formation (Nayak et al., 2018; Joshi & Panchal, 2019); on the
contrary, maps based on older stellar populations such as red clump and RR
Lyrae stars systematically result in lower levels of reddening (see e.g.
Zaritsky et al., 2002; Muraveva et al., 2018; Górski et al., 2020; Cusano et
al., 2021).

The differences in colour excess, $\Delta E(B-V)$, can have a large influence
on the inferred value for the Hubble constant and on the three-dimensional
structure derived from stars (e.g. Ripepi et al., 2017; Choi et al., 2018).
For example, an $\Delta E(B-V)=0.06$ mag difference between Haschke, Grebel &
Duffau (2011) and Górski et al. (2020) studies, both using data from the third
phase of the Optical Gravitational Lensing Experiment (OGLE-III; Udalski,
2003), implies a difference in the value of the Hubble constant larger then 3
km s-1 Mpc-1 (see e.g. section 3.1 of Riess et al., 2009). The presence of
dust influences the location of stars in colour–magnitude diagram (CMD) which
is often used to select different stellar types to study their spatial
distribution (e.g. El Youssoufi et al., 2019) and kinematics (e.g. Niederhofer
et al., submitted). An independent map of the internal reddening of the
Magellanic Clouds would also reduce the residuals between data and models in
regions of the CMD which are used simultaneously to infer the reddening,
distance modulus and star formation history (SFH) of the galaxies (e.g. Rubele
et al., 2018; Mazzi et al., 2021). Small-scale reddening variations present in
maps obtained from individual stars (e.g. Tatton et al., 2021) and in specific
regions of the galaxies (e.g. De Marchi, Panagia & Milone, 2021) may not be
easy to reconcile with large-scale studies based on broadly distributed
tracers.

In Bell et al. (2019, hereafter Paper I) we piloted a method to map the
intrinsic reddening of a foreground extinguishing medium using the spectral
energy distributions (SEDs) of background galaxies. This approach takes away
the dependency on reddening values of stellar populations and allows us to
study the total reddening by sampling the full column depth of the
extinguishing medium. In Bell et al. (2020, hereafter Paper II) we applied
this method to a $\simeq$ 34 deg2 region of the Small Magellanic Cloud (SMC)
covered by both the Survey of the MAgellanic Stellar History (SMASH; Nidever
et al., 2017) and the Visible and Infrared Survey Telescope for Astronomy
(VISTA) survey of the Magellanic Clouds system (VMC; Cioni et al., 2011). In
Paper II, adopting galaxies with low intrinsic reddening, we found signs of
higher intrinsic reddening in the main body of the galaxy compared with its
outskirts. Our maps agree with those in the literature which were created
using young stars whereas there are some discrepancies with maps derived from
longer-wavelength far-IR emission and from old stars. These discrepancies may
be due to biases in the sample or uncertainties in the far-IR emissivity of
the optical properties of the dust grains. In this study, we map the total
intrinsic reddening across a $\simeq$ 90 deg2 region of the Large Magellanic
Cloud (LMC) combining observations from the SMASH and VMC surveys.

The structure of this paper is as follows. In Section 2 we describe the
processes involved in creating and fitting the SEDs of background galaxies as
well as provide a comparison of the results of the SED fitting with other
extragalactic studies. The details of how we create our intrinsic reddening
map of the LMC are presented in Section 3. We discuss our reddening map and
compare it with literature reddening maps of the LMC based on different
tracers in Section 4, and summarise our findings in Section 5.

##  2 Creating and fitting SEDs of galaxies

Figure 1: Stellar density distribution of the LMC from the VMC survey. The
colour bar refers to the number of stars per bin, where the bin size is of
$0.4\times 0.4$ arcmin2. The origin of the plot corresponds to the centre of
the LMC as given by the HYPERLEDA catalogue of Paturel et al. (2003). The
hexagons denote the positions of the SMASH fields that overlap with the VMC
coverage of the LMC. Black fields denote those for which $ugriz$ data are
available, whereas khaki fields represent those for which only $griz$ data are
available. The combined SMASH–VMC footprint is $\simeq$ 90 deg2. A gap at
$\Delta$RA $\simeq 0.7$ deg is currently being observed.

Our data set consists of optical $ugriz$ and near-IR $YJK_{\rm{s}}$ photometry
taken as part of the SMASH and VMC surveys, respectively, that cover the
wavelength range 0.3–2.5 $\mu$m. The combined SMASH–VMC footprint of the LMC
is shown in Fig. 1 and covers an area of $\simeq$ 90 deg2. We note two
significant differences regarding the SMASH data used in this study compared
to that used in Papers I and II. First, as shown by the different colour DECam
fields in Fig. 1, only the central regions of the LMC (black hexagons) are
fully covered by deep $ugriz$ data. The surrounding fields (khaki hexagons)
represent fields for which only $griz$ data are available. Second, whereas the
fields with full 5-band data consist of deep exposures (999 s in $uiz$ and 801
s in $gr$), in addition to three sets of short 60 s exposures in $ugriz$ with
large half-CCD offsets between each set (to cover the gaps between the CCDs),
fields with 4-band data consist only of two sets of short 60 s exposures in
$griz$ (again with half-CCD offsets to cover the gaps between CCDs; see
section 3 of Nidever et al., 2017 for details).

For the study of the LMC we have made three notable changes, relative to the
methodology applied to the SMC and laid out in Papers I and II; namely the
selection of background galaxies, the treatment of foreground Milky Way (MW)
reddening and the use of ancillary radio data to separate the Active Galactic
Nuclei (AGN) population prior to fitting the SEDs. We refer the reader to
Paper I of this series for a discussion of each step of the process, including
the choice of galaxy templates, redshift priors, extinction law, and
photometric uncertainties.

###  2.1 Selection of background galaxies

Figure 2: a: Near-IR $J-K_{\rm{s}},K_{\rm{s}}$ CMD of tile LMC 3_4. The blue
points denote objects selected as likely galaxies adopting the criteria of
Papers I and II (see text), whereas the orange points represent those that are
subsequently classified by lephare as ETGs. The error bars on the left denote
the median photometric errors as a function of $K_{\mathrm{s}}$-band magnitude
at 1 mag intervals b: As a, but the green points correspond to those for which
the $K_{\rm{s}}$-band sharpness index is greater than 0.5. c: Same as b,
however the pink points denote those of the green points lephare classifies as
galaxies and the brown points represent the subset of these classified as
ETGs. d: Histograms of the numbers of galaxies and ETGs as a function of
$J-K_{\rm{s}}$ colour. The dashed line at a colour of $J-K_{\rm{s}}=0.8$ mag
separates those that appear to be primarily blended stellar sources (at bluer
colours) and those that are predominantly non-blended, extended sources (at
redder colours).

The process of creating the galaxy SEDs has been extensively covered in Papers
I and II. However, in light of our SMC analysis we have made some minor
modifications that we describe below. In Paper II we noted that the number of
early-type galaxies (ETGs) in the central regions of the SMC was limited due
to incompleteness arising from the enhanced levels of crowding compared to the
less-dense outer regions. The central regions of the LMC are even more
affected by crowding and thus we have revised our selection in an effort to
increase the number of ETGs in our sample.

Before explaining our updated selection criteria, it should be noted that our
definition of an ETG is directly linked to the adopted templates in lephare.
The galaxy templates we adopt are the so-called AVEROI_NEW templates and we
classify an object as an ETG if lephare finds a lower minimum $\chi^{2}$
associated with the best-fitting galaxy template (compared to the best-fitting
stellar template) _and_ if the best-fitting galaxy template corresponds to a
spectral type of Ell or Sbc (see section 3.1 of Paper I for details regarding
the AVEROI_NEW templates).

Our selection of background galaxies is based on the VMC point-spread function
(PSF) photometric catalogues (see Mazzi et al., 2021 for details). Panel a of
Fig. 2 shows the CMD selection previously adopted in Papers I and II, namely
retaining those that satisfy the following: $J-K_{\rm{s}}>1$ mag,
$K_{\rm{s}}>15$ mag, an associated stellar probability of less than 0.33 and a
$K_{\rm{s}}$-band sharpness index greater than 0.5. To increase our sample of
ETGs we effectively need to include galaxies at bluer colours. If we simply
remove the colour cut, however, the use of the stellar probability still
severely limits the inclusion of bluer galaxies (see e.g. Fig. 2 of Paper I).

To assess how best to modify our galaxy selection, we first retain only those
objects with a $K_{\rm{s}}$-band sharpness index greater than 0.5 (Fig. 2b).
These objects are then processed through lambdar (see Section 2.2) and lephare
(see Section 2.4) to determine which ones are classified as galaxies and, more
specifically for our purposes, ETGs (the brown and purple points in Fig. 2c,
respectively). There is clearly a bimodality in the distribution of galaxies
and ETGs as a function of $J-K_{\rm{s}}$ colour. Dividing the ETG sample at a
colour of $J-K_{\rm{s}}=0.8$ mag and visually inspecting $K_{\rm{s}}$-band
image cut-outs we note that the vast majority of objects at bluer colours (of
which there are 369 in tile LMC 3_4, a tile in the outer disc of the LMC) are
stellar blends, whereas those at redder colours (of which there are 4430)
appear to be predominantly non-blended extended sources. Retaining such a
large number of stellar blends in our ETG sample would have a non-negligible
effect when creating the reddening maps. Furthermore, it is not feasible to
visually inspect all ($\sim$300,000) candidate ETGs across the combined
SMASH–VMC coverage of the LMC. The $J-K_{\rm{s}}$ colour distribution of known
QSOs, which is similar to that of galaxies, shows a clear edge at $0.8$ mag
which is also away from stellar sources (Cioni et al., 2013). The final number
of objects classified as ETGs in tile LMC 3_4 based on a revised colour
selection criteria ($J-K_{\rm{s}}>0.8$ mag) is 4430, which when compared to
the 3361 one would find using our previous selection criteria represents an
increase in sample size of almost a third.

###  2.2 lambdar photometry

Fluxes for each of our targets are measured using the Lambda Adaptive Multi-
Band Deblending Algorithm in R
(lambdar111https://github.com/AngusWright/LAMBDAR, v0.20.7; Wright et al.,
2016). This version has minor developments (with respect to v0.20.5 that was
used in Paper II), that improve the stability and fidelity of the PSF
estimation procedure. We use these new developments (and our knowledge that
our fields are crowded with point sources) to specify conservative
requirements on which sources are selected for use in the PSF estimation.
Specifically, we opt for a maximum number of point sources to be used in the
PSF estimation of 500 per-chip (a chip corresponds to a detector or a charge
coupled device in the VISTA and SMASH images, respectively), with a minimal
radial separation (from possible contaminating sources) of 10 pixels (or
$\sim$ $3.4$ arcsec). The latter condition often produces many more than 500
sources per-chip (especially in very crowded regions), and in these cases the
code iteratively increases the minimum radial separation until 500 sources are
selected; that is, the code selects the 500 most isolated point sources for
use in the PSF estimation.

Paper I provides a comprehensive discussion regarding the measurement of
fluxes in addition to the calibration of both the optical and near-IR data
sets onto an AB magnitude system. We adopt the fluxes measured using a default
circular aperture of diameter 3 arcsec. The $Y$-, $J$\- and $K_{\rm{s}}$-band
deep stacks from which lambdar measures the fluxes were downloaded from the
VISTA Science Archive (VSA; Cross et al., 2012) and have been processed by the
Cambridge Astronomy Survey Unit (CASU). Unlike the deep stacks used in Papers
I and II that were created using the VISTA Data Flow System (VDFS; Irwin et
al., 2004) v1.3, the deep stacks used in this study have been processed using
v1.5 (González-Fernández et al., 2018; see also the CASU
webpage222http://casu.ast.cam.ac.uk/surveys-projects/vista/data-
processing/version-log). The main difference between the two versions is in
the determination of the zero-points and as such we apply the offsets listed
in eqs. C7–C11 of González-Fernández et al. (2018) in addition to those noted
in section 2.4 of Paper I. The zero-point differences between the two versions
amount to $0.01-0.02$ mag which will have a minimal influence on our study
(cf. Fig. 2). Other differences refer to tiles, the combined product of deep
stacks, which we do not use. The $u$-, $g$-, $r$-, $i$\- and $z$-band data
were treated in exactly the same way as described in Paper I.

###  2.3 Accounting for foreground Milky Way reddening

Figure 3: _Top panel_ : Schlegel et al. (1998) foreground MW and residual
intrinsic LMC reddening map. The black polygons represent the positions of the
VMC tiles covering the LMC. The dashed white lines separate the LMC into
different quadrants. The white circle (centred at $\Delta\mathrm{RA}=0.5$,
$\Delta\mathrm{Dec}=1.0$ deg and with a radius of 3.8 deg) marks the region
within which the SFD98 $E(B-V)$ values are unreliable. _Bottom panel_ : SFD98
$E(B-V)$ values in each quadrant as a function of angular distance. The solid
points denote the median $E(B-V)$ value calculated from the SFD98 reddening
map between distances of 3.8 and 6 deg in steps of 0.1 deg and the associated
error bars represent the standard deviation in that annulus. The linear best
fit to the solid points in each quadrant is also shown as the straight black
line. The open points are the same in each panel and denote the median of the
four fits in steps of 0.1 deg covering the region within which the SFD98
$E(B-V)$ values are unreliable. The error bars signify the standard deviation
between the four fits.

To produce a dust map of the LMC we need to take into account the reddening
along the line-of sight. In Papers I and II we adopted a rather rudimentary
method to account for the foreground MW reddening towards the SMC by adopting
a mean $E(B-V)$ value for all objects based on the Schlegel, Finkbeiner &
Davis (1998, hereafter referred to as SFD98) reddening map purposefully
neglecting the main body and Wing of the SMC (see fig. 4 of Paper I). Whilst
such a treatment, to zeroth order, should adequately reflect the “average”
foreground MW reddening, it is likely to hide fluctuations or trends in
$E(B-V)$ across the SMC. In light of this, we hereby adopt a revised method
that we describe below.

The top panel of Fig. 3 shows the SFD98 foreground MW and residual intrinsic
LMC reddening map with the positions of the VMC tiles covering the LMC
overlaid333We use the Python module sfdmap
(https://github.com/kbarbary/sfdmap) to determine the SFD98 $E(B-V)$ value at
a given position.. The inner circle (centred at $\Delta\mathrm{RA}=0.5$,
$\Delta\mathrm{Dec}=1.0$ deg and with a radius of 3.8 deg) marks the region
within which the SFD98 $E(B-V)$ values are unreliable due to insufficiently
resolved temperature structures. Outside of this inner circle the SFD98
$E(B-V)$ values are believed to be reliable (see e.g. Schlegel et al., 1998;
Skowron et al., 2021) and clearly show a significant amount of substructure in
the high-latitude MW cirrus (this difference is especially noticeable in
regions to the south and to the north of the LMC). For objects farther than
3.8 deg from the centre of the inner circle we simply de-redden the fluxes
provided by lambdar using sfdmap. For objects within the inner circle,
however, we construct a radial $E(B-V)$ profile from linear extrapolations of
fits to regions outside of the inner circle.

The bottom panel of Fig. 3 shows the SFD98 $E(B-V)$ values as a function of
angular distance from $\Delta\mathrm{RA}=0.5$, $\Delta\mathrm{Dec}=1.0$ deg.
The solid points denote the median $E(B-V)$ value calculated in each quadrant
between the two white circles in steps of 0.1 deg using sfdmap and the
associated error bars represent the standard deviation in that annulus. The
best-fitting linear curve to the solid points in each quadrant is also shown
as the straight black line. The open points are the same in each panel and
denote the median of the four fits in steps of 0.1 deg covering the region
within which the SFD98 $E(B-V)$ values are unreliable. The error bars signify
the standard deviation among the four fits. These open points represent the
radial $E(B-V)$ profile that we adopt to de-redden the fluxes for objects that
lie within the inner circle i.e. objects within this region are de-reddened
according to their angular distance from $\Delta\mathrm{RA}=0.5$,
$\Delta\mathrm{Dec}=1.0$ deg. From Fig. 3 it is clear that there are enhanced
levels of reddening in the south-west quadrant with respect to the other three
quadrants, and this likely accounts for the observed offset between the
extrapolated line and the calculated radial profile within 3.8 deg in this
quadrant which is not observed in the other quadrants. At the time of
submission of our work to the journal, Chen et al. (2022) presented a dust map
of the MW derived from the SED of stellar sources within 5 kpc. They combined
astrometry from Gaia with optical and near-IR photometry from various large-
scale surveys towards the Magellanic Clouds. Their MW reddening map towards
the LMC shows an average $E(B-V)$ of 0.06 mag with values as high as 0.15 in
the south of the disc (an area outside our inner circle). The small
inhomogeneities and clumps in the inner regions do not appear to exceed this
value (their Fig. 10). Our extrapolation corresponds to an average $E(B-V)$ of
about 0.1 mag (Fig. 3) which is in line with the maximum values derived by
Chen et al. (2022), but may overestimates by a few percent the extinction
towards some specific lines of sights.

The extinction coefficients adopted to convert a given $E(B-V)$ value into an
extinction in a specific bandpass are those listed in eq. 1 of Paper I and
should be used in conjunction with the unscaled SFD98 $E(B-V)$ values as they
already take into account the Schlafly & Finkbeiner (2011) recalibration.
After de-reddening the fluxes and retaining only objects for which lambdar
measures positive fluxes in at least four out of the eight available
bandpasses, our full LMC sample contains 2,474,235 objects.

###  2.4 Fitting the SEDs with lephare

Papers I and II provide a comprehensive overview of fitting SEDs using
lephare444http://cesam.lam.fr/lephare/lephare. However, we briefly discuss the
notable difference in this work with respect to the earlier works in this
series. In Papers I and II we primarily included quasi-stellar object
(QSO)/AGN templates (hereafter collectively referred to as AGN) as the level
of AGN contamination in our sample was unclear. With no comprehensive
catalogue of AGN behind the SMC [except for the areas covered by, e.g, the
XMM– _Newton_ survey (Haberl et al., 2012) as well as incomplete spectroscopic
samples (e.g. Kozłowski, Kochanek & Udalski, 2011; Kozłowski et al., 2013)] we
included such templates to not only account for the presence of AGN, but also
to provide more flexibility with regards to fitting the SEDs. The inclusion of
the AGN templates in lephare likely resulted in degeneracies in the best-
fitting templates as the number of objects classified as AGN in the full SMC
sample was markedly higher than those lephare classified as galaxies (see
table 2 of Paper II). This, in addition to the previously adopted criteria for
selecting background galaxies from the deep VMC PSF photometric catalogues
(see Section 2.1), likely contributed to the low number of ETGs in the central
regions of the SMC.

Figure 4: Positions of the 54,612 radio sources detected in the 888 MHz ASKAP
EMU data towards the LMC (red points; Pennock et al., 2021) overlaid on the
full SMASH-VMC sample (black points).

In this study we make use of the recently published catalogue of radio-
detected sources in the direction of the LMC by Pennock et al. (2021) based on
888 MHz Australian Square Kilometre Array Pathfinder (ASKAP) Evolutionary Map
of the Universe (EMU) radio continuum survey data. These data cover $\simeq$
120 deg2 and the catalogue contains 54,612 sources separated into Gold, Silver
and Bronze categories (see section 3.2 of Pennock et al., 2021 for details).
Although the catalogue also contains both MW sources in the foreground of the
LMC as well as sources in the LMC itself, the vast majority of the radio
sources are background objects, and in particular, AGN. Fig. 4 shows that the
radio sources almost completely cover the full LMC sample, except for a
significant fraction of the lowest row of VMC tiles (LMC 2_3–LMC 2_7). We can
therefore use this catalogue to systematically and effectively remove AGN
contaminants – as well as foreground interlopers – from our sample and ensure
that we are not reliant upon lephare for such discrimination.

There are two primary reasons for separating the AGN from the full LMC sample.
First, as demonstrated in Paper I, it is difficult to use AGN to create a
reddening map due to the varying levels of intrinsic reddening. By removing
AGN from the full LMC sample, they are unable to be misclassified by lephare
and incorrectly incorporated into the creation of the reddening map. Second,
the vast majority of spectroscopic redshifts for objects behind the LMC are
associated with AGN. To test the validity of the lephare photometric redshifts
it is therefore best to fit such objects with more representative AGN
templates so as to minimise any potential biases introduced by using less
well-suited galaxy templates. Following Pennock et al. (2021), we adopt a
cross-match radius of 5 arcsec and find a total of 21,706 radio sources in the
full LMC sample. Whilst the Pennock et al. (2021) catalogue is complete down
to 0.5 mJy across the field and contains the majority of the spectroscopically
confirmed AGN in the combined SMASH–VMC footprint of the LMC, we still
identified an additional 122 AGN with spectroscopic redshift determinations
from v7.2 of the Milliquas (Million Quasars)
catalogue555http://quasars.org/milliquas.htm (Flesch, 2021) that were not
present and include these to create our final AGN sample comprising 21,828
sources. These sources are subsequently removed from the full LMC sample,
reducing its number to 2,474,235. Note that although the radio catalogue of
sources in the direction of the LMC provided by Pennock et al. (2021) is the
most sensitive to date, only $\sim$ 10–20 per cent of all AGN are radio-loud
(see e.g. Ivezić et al., 2002; Jiang et al., 2007). We are therefore no doubt
significantly underestimating the level of AGN contamination in our sample of
extragalactic objects behind the LMC, although the EMU end-of-survey
sensitivity should detect radio-quiet AGN out to $z\simeq 2$ (Norris et al.,
2011).

We run lephare as described in Paper II on both the full LMC and AGN samples.
We only use the empirical AVEROI_NEW galaxy templates for the LMC sample in
addition to the stellar templates, whereas for the AGN sample we replace the
galaxy templates with the 10 AGN templates described in Polletta et al. (2007,
see section 3.1 of Paper I for details regarding these template libraries). As
in Paper II, we allow additional intrinsic reddening [in terms of $E(B-V)$] to
vary and allow this additional reddening for all galaxy/AGN types. Typically,
additional reddening is only used for later-type galaxies (Sc and bluer/later;
see e.g. Arnouts et al., 2007) and AGN (see e.g. Salvato et al., 2009) on the
basis that the adopted templates may not fully account for the widely varying
levels of dust observed in such galaxies/AGN. For ETGs, and particularly in
the optical/near-IR regime we are interested in here, the range in dust is not
as extreme and so the assumption is that the adopted templates fully account
for their dust contents and thus additional reddening is not required. Our
method of using ETGs as reddening probes essentially builds upon this
assumption by suggesting that any additional reddening required by ETGs is due
to a foreground extinguishing medium, in our case the LMC. Tables 1 and 2
provide the lephare outputs for the 2,474,235 and 21,828 sources in the full
LMC and AGN samples, respectively. The associated $\chi^{2}$ values for the
best-fitting templates imply that 61 per cent of the full LMC sample are
galaxies (39 per cent stars) and 87 per cent of the AGN sample are AGN (13 per
cent stars). Of the 61 per cent of objects classified as galaxies in the full
LMC sample, 15 per cent (222,752) are classified as ETGs.

Table 1: A sample of the lephare output for the 2,474,235 sources in the full
LMC sample. We only show the ID, RA and Dec. (J2000.0), the best-fitting
photometric redshift with associated $1\sigma$ limits, the maximum likelihood
photometric redshift with associated $1\sigma$ limits, the best-fitting galaxy
template, the associated $\chi^{2}$ value for the best-fitting galaxy template
and the best-fitting $E(B-V)$ value. The full table available as Supporting
Information contains other parameters.

ID | RA (J2000.0) | Dec. (J2000.0) | $z_{\rm{BEST}}$ | $z_{\rm{BEST}}^{-1\sigma}$ | $z_{\rm{BEST}}^{+1\sigma}$ | $z_{\rm{ML}}$ | $z_{\rm{ML}}^{-1\sigma}$ | $z_{\rm{ML}}^{+1\sigma}$ | Template${}_{\rm{G}}^{a}$ | $\chi^{2}_{\rm{G}}$ | $E(B-V)$
---|---|---|---|---|---|---|---|---|---|---|---
| deg | deg |  |  |  |  |  |  |  |  | mag
1 | 73.77041 | $-75.72749$ | 0.4906 | 0.4645 | 0.5143 | 0.4694 | 0.3974 | 0.5147 | 54 | 2.1045 | 0.05
2 | 73.82095 | $-75.72746$ | 0.3292 | 0.3059 | 1.3738 | 1.1080 | 0.3329 | 1.5322 | 59 | 8.6474 | 0.00
3 | 73.78706 | $-75.72451$ | 0.0200 | 0.0200 | 0.0277 | 0.0128 | 0.0041 | 0.0310 | 49 | 71.1816 | 0.15
4 | 73.74649 | $-75.71641$ | 1.0280 | 0.7738 | 1.2179 | 0.9209 | 0.5290 | 1.1316 | 50 | 2.6083 | 0.15
5 | 73.50257 | $-75.71626$ | 0.5961 | 0.5347 | 1.1331 | 0.9244 | 0.5870 | 1.2578 | 57 | 3.1876 | 0.50
6 | 73.83151 | $-75.71592$ | 0.4862 | 0.4433 | 0.5389 | 0.4802 | 0.3976 | 0.5374 | 38 | 5.5756 | 0.00
7 | 73.48358 | $-75.71535$ | 1.3214 | 1.3109 | 1.3322 | 1.3297 | 1.3041 | 1.3635 | 62 | 15.4637 | 0.40
8 | 73.77131 | $-75.71414$ | 0.0555 | 0.0423 | 0.0667 | 0.0726 | 0.0423 | 2.8935 | 62 | 15.1095 | 0.05
9 | 73.76825 | $-75.71168$ | 0.9478 | 0.7439 | 1.2849 | 0.9306 | 0.5771 | 1.1749 | 62 | 4.7682 | 0.30
10 | 73.82471 | $-75.71136$ | 0.5050 | 0.4176 | 0.8201 | 0.5114 | 0.3058 | 0.7615 | 62 | 2.0733 | 0.10

a Best-fitting galaxy templates are as follows: (1–21) E, (22–37) Sbc, (38–48)
Scd, (49–58) Irr, (59–62) Starburst.

b Context is a numerical representation in lephare specifying the combination
of bands present in the input catalogue and is defined as
$\sum_{i=1}^{i=N}2^{i-1}$, where $i$ is the band number (in our case $u=1$,
$g=2$, …, $J=7$, and $K_{\rm{s}}=8$), and $N$ is the total number of bands.

Table 2: Same as Table 1, but for the 21,828 sources in the AGN sample.

ID | RA (J2000.0) | Dec. (J2000.0) | $z_{\rm{BEST}}$ | $z_{\rm{BEST}}^{-1\sigma}$ | $z_{\rm{BEST}}^{+1\sigma}$ | $z_{\rm{ML}}$ | $z_{\rm{ML}}^{-1\sigma}$ | $z_{\rm{ML}}^{+1\sigma}$ | Template${}_{\rm{Q}}^{a}$ | $\chi^{2}_{\rm{Q}}$ | $E(B-V)$
---|---|---|---|---|---|---|---|---|---|---|---
| deg | deg |  |  |  |  |  |  |  |  | mag
1 | 74.13216 | $-74.39312$ | 1.1025 | 1.0778 | 1.1794 | 1.1353 | 1.0840 | 1.1957 | 6 | 10.2503 | 0.45
2 | 73.66724 | $-74.35413$ | 0.7129 | 0.5553 | 0.9163 | 0.8019 | 0.6263 | 1.0059 | 4 | 3.3765 | 0.00
3 | 74.62965 | $-74.33360$ | 1.0313 | 0.7321 | 1.4235 | 1.0588 | 0.6518 | 1.5054 | 5 | 7.6673 | 0.15
4 | 73.07838 | $-74.29228$ | 0.3555 | 0.3540 | 0.3623 | 0.3559 | 0.3414 | 0.3722 | 10 | 121.5800 | 0.15
5 | 70.73015 | $-74.10165$ | 1.0855 | 1.0737 | 1.2082 | 1.1423 | 1.0872 | 1.2030 | 6 | 10.8134 | 0.10
6 | 70.58080 | $-74.08259$ | 1.0907 | 1.0138 | 1.1312 | 0.8248 | 0.6040 | 1.0886 | 3 | 8.9963 | 0.00
7 | 76.32935 | $-74.59744$ | 1.0284 | 1.0141 | 1.0474 | 1.0428 | 1.0138 | 1.1032 | 3 | 33.3055 | 0.35
8 | 76.59007 | $-74.57986$ | 1.2702 | 1.0548 | 1.2807 | 1.2378 | 1.0576 | 1.2750 | 10 | 9.9513 | 0.00
9 | 75.99906 | $-74.47083$ | 1.0737 | 1.0768 | 1.0807 | 1.0792 | 1.0655 | 1.0933 | 6 | 15.1357 | 0.40
10 | 77.26805 | $-74.42954$ | 0.3326 | 0.3187 | 0.3475 | 0.3332 | 0.3125 | 0.3541 | 1 | 52.6541 | 0.05

a Best-fitting AGN templates are as follows: (1) Seyfert 1.8, (2) Seyfert 2,
(3–5) type-1 QSO, (6–7) type-2 QSO, (8–9) Starburst/ULIRG, (10)
Starburst/Seyfert 2.

b Context is a numerical representation in lephare specifying the combination
of bands present in the input catalogue and is defined as
$\sum_{i=1}^{i=N}2^{i-1}$, where $i$ is the band number (in our case $u=1$,
$g=2$, …, $J=7$, and $K_{\rm{s}}=8$), and $N$ is the total number of bands.

Figure 5: Distribution of redshifts for galaxies (blue) and AGN (orange)
classified by lephare.

Fig. 5 shows the photometric redshift distributions for the 1,504,987 objects
classified as galaxies and the 19,017 objects classified as AGN in the full
LMC and AGN samples, respectively. As discussed in section 2.3 of Paper II, we
choose the photometric redshift from the median of the maximum likelihood
distribution ($z_{\rm{ML}}$) or if this is not available666$z_{\rm{ML}}$ is
only unavailable in cases of extremely poor fits ($\chi^{2}\gtrsim 1500$) and
this occurs in about 1 per cent of the galaxies. the one with the minimum
$\chi^{2}$ value ($z_{\rm{BEST}}$). The median redshift of both samples is
very similar ($z_{\rm{med}}=0.56$ and 0.57 for the galaxy and AGN samples,
respectively). Although this median redshift is almost identical to that of
the objects classified as galaxies behind the SMC in Paper II, we refrain from
making a direct comparison between the two galaxy populations due to the
combined effects of the different methods of selecting background galaxies as
well as the use of different template sets between the two studies. Any
conclusions drawn from such a comparison (e.g. the different distribution of
spectral types) should be treated with caution and not used to argue for
systematic differences between the two galaxy populations. Although such a
comparison would be worthwhile, this would necessitate a complete
redetermination and analysis of the SMC sample that is beyond the scope of
this study.

####  2.4.1 Effects of missing $u$-band data

Figure 6: Distributions of galaxies redshifts in the full LMC sample. The blue
line denotes galaxies for which the SED comprises all eight available bands
(from $u$ to $K_{\rm{s}}$). The orange line represents the same sample of
galaxies as shown by the blue line, however we have removed the measured
$u$-band fluxes and re-run through lephare. The green line illustrates
galaxies for which there are no $u$-band data available but have measured
fluxes in the seven remaining bands (from $g$ to $K_{\rm{s}}$).

It is worth noting that we have not yet discussed the effects of non-complete
$u$-band coverage across the combined SMASH–VMC footprint of the LMC. From
Fig. 1 it is evident that only the central regions of the LMC have $u$-band
data from SMASH, as well as a few isolated regions in the outskirts. In Fig. 6
we show the photometric redshift distributions for objects classified as
galaxies in the full LMC sample. There are three samples of galaxies shown in
Fig. 6: i) objects that have measured fluxes in all eight available bands
(from $u$ to $K_{\rm{s}}$), ii) as i) but with the $u$-band fluxes removed and
re-run through lephare and iii) objects for which no $u$-band data are
available, but which have measured fluxes in the remaining seven bands (from
$g$ to $K_{\rm{s}}$). The number of galaxies in each sample is limited to
350,000 to better illustrate systematic differences between the samples. The
effect of simply removing the $u$-band data (where available) is small but
noticeable, in the sense that there are some variations in the redshift
distributions across the whole redshift range, but overall the distributions
resulting from samples (i) and (ii) are broadly similar in terms of median
redshift and shape (cf. $z_{\rm{med}}=0.36$ for the 8-band SED sample and
$z_{\rm{med}}=0.44$ for the reprocessed sample after removing the $u$-band
data). The resulting samples of ETGs are also similar. In contrast, the
redshift distribution for objects for which no $u$-band data are available is
markedly different, both in terms of median redshift ($z_{\rm{med}}=0.59$) and
as regards the apparent dearth of galaxies at higher redshifts. These
differences likely stem from the SMASH observing strategy for which only
regions with full $ugriz$ coverage have deep exposures, whereas the regions
with only $griz$ coverage are covered by short exposures (see Section 2 for
details). The latter sample of ETGs will be similar to that of ETGs within the
same magnitude ranges resulting from deeper observations. This further
reinforces the importance of the $u$ band as a powerful diagnostic to
discriminate between low ($z\lesssim 0.5$) and higher redshift galaxies (see
e.g. Bellagamba et al., 2012; Bisigello et al., 2016) as well as the need for
homogeneous coverage (in terms of photometric bandpasses and exposure time)
across the survey area.

####  2.4.2 Comparison of spectroscopic and photometric redshifts for AGN
behind the LMC

Figure 7: Histogram showing the differences between the spectroscopically
determined redshifts of AGN behind the LMC and the corresponding photometric
redshifts calculated by lephare. The various statistics regarding the
comparison of the two redshift determinations are discussed in the text. Table
3: Spectroscopically determined and photometric redshifts for AGN behind the
LMC. The full table is available as Supporting Information.

Name | $z_{\mathrm{spec}}$ | $z_{\mathrm{phot}}$ | Ref.
---|---|---|---
PMN J0601–7238 | 0.001 | $0.014^{+0.031}_{-0.009}$ | 1
6dF J050434.2–734927 | 0.045 | $0.186^{+0.120}_{-0.121}$ | 2
MQS J053242.46–692612.2 | 0.059 | $0.058^{+0.041}_{-0.050}$ | 3
MQS J043522.69–690352.9a | 0.061 | $0.096^{+0.004}_{+0.004}$ | 3
PGC 3095709 | 0.064 | $0.158^{+0.068}_{-0.092}$ | 4
J050550.3–675017 | 0.070 | $0.155^{+0.071}_{-0.052}$ | 5
1E 0534–6740a | 0.072 | $0.234^{+0.006}_{+0.006}$ | 6
PGC 88452 | 0.075 | $0.086^{+0.024}_{-0.037}$ | 7
MQS J045554.57–691725.6 | 0.084 | $0.005\pm 0.003$ | 3
MQS J043632.30–704238.1 | 0.142 | $0.182^{+0.207}_{-0.116}$ | 3

Notes: aAssociated 1$\sigma$ limits on $z_{\mathrm{BEST}}$ are unphysical (see
section 2.3 and footnote 4 of Paper II for details).

bAssociated $\chi^{2}$ value for best-fitting stellar template is lower than
$\chi^{2}$ value for best-fitting AGN template.

References: (1) Ajello et al. (2020), (2) Jones et al. (2009), (3) Kozłowski
et al. (2013), (4) Cowley et al. (1984), (5) Dobrzycki et al. (2005), (6)
Crampton et al. (1997), (7) Cristiani & Tarenghi (1984), (8) Kozłowski et al.
(2012), (9) Wang et al. (1991), (10) Dobrzycki et al. (2002), (11) Tinney
(1999), (12) Geha et al. (2003), (13) Ivanov et al. (2016), (14) Kostrzewa-
Rutkowska et al. (2018).

As an additional test we compare the derived photometric redshifts to
spectroscopic redshifts of 189 AGN. Table 3 lists the comparison between the
values and Fig. 7 highlights a median difference of $\Delta
z_{\rm{med}}=-0.009$, where $\Delta z_{\rm{med}}=z_{\rm{spec}}-z_{\rm{phot}}$,
and median absolute deviation of $\Delta z_{\rm{MAD}}=0.191$. Note that of the
189 AGN in our sample, five (MQS J050010.83–700028.5, 1E 0547–6745, MQS
J054400.43–705846.2, MQS J043200.60–693846.5 and MQS J052528.91–700448.6) are
classified as stars by lephare. The statistics reported here, with the
exception of the bias, outlier fraction (OLF), are very similar to those
reported in Paper II for the sample of 46 AGN behind the SMC. From Fig. 7 it
is clear that there is an extended tail towards higher values i.e. the
spectroscopic redshift is larger than the photometric redshift and that this
is more prevalent at higher redshifts (see the full version of Table 3). To
test whether this tail is a consequence of our choice of AGN templates, we re-
fitted the SEDs using the AGN templates of Salvato et al. (2009). The tail
persists even though these templates also include AGN-host galaxy type hybrids
(Salvato et al., 2009). Note that studies have found that template-based
redshift estimates for AGN can be underestimated and that Gaussian and/or
hierarchical Bayesian process photometric redshift estimates perform
significantly better at $z>1$ (see e.g. Duncan et al., 2018a, b). Another
potential cause for the underestimated redshifts could be contamination from
neighbouring objects. Of the 28 AGN for which
$|z_{\rm{spec}}-z_{\rm{phot}}|>0.5$, 21 (75 per cent) have neighbouring
objects within 2 arcsec that likely affect the deblended SED of the AGN.

##  3 Internal reddening of the LMC

Figure 8: _Top panel_ : Reddening map covering the combined SMASH–VMC
footprint created using all objects classified as galaxies by lephare. _Bottom
panel_ : As the top panel, but using only objects classified as ETGs.

Fig. 8 shows the reddening map covering $\simeq$ 90 deg2 of the LMC based on
the 1,504,987 objects classified as galaxies by lephare in the full LMC sample
(top panel) in addition to the map created using only the subsample of 222,752
objects classified as ETGs (bottom panel). From Fig. 8 there are two striking
observations. First, it is clear that the use of all galaxies (as discussed in
Papers I and II) effectively masks the regions where significant amounts of
dust intrinsic to the LMC are expected (e.g. along the bar region). This is
primarily due to the inclusion of late-type galaxies which are much more
numerous than the ETGs and for which the best-fitting template requires
additional reddening (including lines of sight through the LMC that do not
exhibit significant amounts of reddening), resulting in the systematically
higher reddening values across the LMC in the top panel of Fig. 8 compared to
the bottom panel. It is only by creating the reddening map using ETGs (with
low levels of intrinsic dust themselves) that regions of high internal
reddening in the LMC become apparent. Second, there is an obvious difference
between the regions that include $u$-band data and those that do not (see also
Section 2.4.1). Comparing Figs. 1 and 8 it is evident that the regions for
which $u$-band data are available tend to exhibit lower levels of reddening
(except for the central regions) than regions for which these data are not
available. The enhanced reddening surrounding the galaxy beyond $3-4$ deg from
the centre might therefore not be real. The MW correction is applied directly
to the LAMBDAR fluxes prior to the SED-fitting (see Sec. 2.3). As we only
allow the additional reddening to vary from $0.0-0.5$ in $E(B-V)$, there are
no ETG galaxies for which the intrinsic reddening is negative.

Figure 9: _Left panel_ : $10\times 10$ arcmin2 resolution reddening LMC map
using objects classified as ETGs. _Middle panel_ : As the left panel, but with
the IRAS 100 $\mu$m dust emission contours overlaid to aid the reader in terms
of where enhanced levels of reddening (due to the presence of dust) are
expected across the LMC. _Right panel_ : Number density of ETGs.

Fig. 9 shows a $10\times 10$ arcmin2 resolution reddening map using the same
objects as shown in the bottom panel of Fig. 8 to better illustrate large-
scale patterns/features across the LMC. Each bin corresponds to the median of
the best-fitting $E(B-V)$ values and the median number of ETGs per bin is 63.
Of 3348 bins covering the combined SMASH–VMC footprint of the LMC, only 52 (2
per cent) have fewer than 10 ETGs per bin and these are distributed around the
outskirts, although there is an obvious dearth of ETGs also associated with
the vertical stripe shown in Fig. 8 resulting from missing VMC data (see the
right-hand panel of Fig. 9). It is also clear from Fig. 9 that there are fewer
ETGs in the central regions of the LMC, which are more heavily affected by
crowding. Across the central regions of the LMC we find that the minimum
number of ETGs in any given bin is 18, which although significantly lower than
the median of 63 across all bins, does not appear to be systematically
affected [in terms of the $E(B-V)$ value] with respect to the median $E(B-V)$
values in the neighbouring bins (for which the number of ETGs ranges from 20
to 82). However, there might be ETGs missing due to high extinction regions,
which will introduce a bias towards lower extinctions, since both crowding and
extinction increase inwards.

Also apparent from Fig. 9 is the excellent agreement between the regions of
enhanced reddening across the central regions of the LMC and the regions that
exhibit emission at longer wavelengths due to the presence of dust (as traced
by the IRAS 100 $\mu$m emission contours). The regions of the LMC for which
SMASH $u$-band data are available completely cover these regions and so the
transition from regions where we expect dust to be present to regions where
little/no dust is present is reflected in the reddening values determined from
the ETGs. Farther from the LMC centre, where no $u$-band data are available
(except for some small isolated regions; see Fig. 1) enhanced levels of
reddening again become noticeable. Given the lack of $u$-band data in these
regions, and the aforementioned agreement between the ETG-determined regions
of enhanced reddening and far-IR emission, one should treat the absolute
reddening values in these outer regions of the LMC with caution [although they
are, to within the uncertainties on the median $E(B-V)$, also consistent with
zero intrinsic reddening].

The use of ETGs to trace the intrinsic reddening of the LMC has been shown to
reproduce the pervasive enhanced levels of reddening across the LMC bar region
that we know are present from existing far-IR observations (see e.g. Chastenet
et al., 2017 and references therein). In addition, there are several isolated
regions for which the median reddening is further enhanced, with respect to
this low-level pervasive enhancement. These enhancements coincide with well-
known star-forming regions throughout the bar (e.g. N44, N105, N113, N120,
N144, and N206, as well as the Tarantula Nebula and the molecular ridge south
of 30 Doradus) as well as overdensities observed in morphology maps based on
young stars. Interestingly, highest median reddening [$E(B-V)=0.35$ mag;
$\Delta$RA $\simeq$ –4.2, $\Delta$Dec $\simeq$ 0.7 deg] lies far from the LMC
bar in a region that is not actively forming stars and for which there are no
hints of enhanced far-IR emissions in the IRAS 100 $\mu$m data (see Fig. 9).

Figure 10: Comparison of median SEDs for all ETGs in the bin with the highest
intrinsic reddening (see text) as well as neighbouring bins to the north,
south, east and west.

It should be noted, that this region of the combined SMASH–VMC footprint lacks
$u$-band data and so that could partly be responsible for the anomalous
reddening value. However, the lack of other such enhancements in regions that
lack $u$-band data suggests this is not the sole reason. Furthermore, the
number of ETGs used to compute the median reddening is almost identical to the
median across the whole LMC (cf. 61 and 63) and there is a clear overdensity
of ETGs with higher than average reddening values (see Fig. 8). Fig. 10 shows
a comparison’s between the median SED for all ETGs in the bin with the highest
intrinsic reddening and the ETGs in the neighbouring bins to the north, south,
east and west. Note that for comparison sake we have normalised all SEDs to a
$z$-band magnitude of 19.0 mag. Although there is very good agreement between
the SEDs across most of the optical/near-IR regime, there is a clear
difference in the $J$-band regime, such that the median SED of the ETGs in the
high reddening bin is $\simeq$ 0.5 mag brighter than those in the neighbouring
bins. This difference is likely the reason behind the anomalously high
intrinsic reddening in this particular bin and may be related to a higher
level of background substructure observed in the VISTA $J$-band deep stack
images covering this region of the sky.

The majority of the bins covering the combined SMASH–VMC footprint have
$E(B-V)=0.0$ mag [$E(B-V)_{\rm{mean}}=0.06$ mag] and a median uncertainty of
$\sigma_{E(B-V)_{\rm{med}}}=0.09$ mag. For bins with only a single ETG, or for
which all best-fitting reddening values are identical, we assume an
uncertainty of 0.05 mag corresponding to the spacing implemented in the SED
process. Table 4 lists the median reddening values, standard deviations and
the number of ETGs in each bin across the LMC footprint.

Table 4: Reddening values derived from ETGs within 3348 bins across the LMC. The full table is available as Supporting Information. $\Delta$RA (J2000.0) |  $\Delta$Dec. (J2000.0) | $E(B-V)_{\mathrm{med}}$ | $\sigma_{E(B-V)_{\rm{med}}}$ | No. ETGs
---|---|---|---|---
deg | deg | mag | mag |
$-2.54675$ | $-6.21777$ | 0.050 | 0.089 | 77
$-2.38055$ | $-6.21777$ | 0.050 | 0.074 | 58
$-2.21435$ | $-6.21777$ | 0.100 | 0.065 | 66
$-2.04816$ | $-6.21777$ | 0.050 | 0.059 | 47
$-1.88196$ | $-6.21777$ | 0.050 | 0.071 | 68
$-1.71576$ | $-6.21777$ | 0.000 | 0.105 | 52
$-1.54957$ | $-6.21777$ | 0.025 | 0.109 | 56
$-1.38337$ | $-6.21777$ | 0.000 | 0.083 | 58
$-1.21718$ | $-6.21777$ | 0.000 | 0.080 | 90
$-1.05098$ | $-6.21777$ | 0.000 | 0.089 | 63

##  4 Discussion

This study produced a map of the total intrinsic reddening of the LMC for a
$\simeq$ 90 deg2 region covered by both the SMASH and VMC surveys. Using ETGs
we have demonstrated the ability to identify regions with enhanced levels of
reddening that coincide with regions of enhanced far-IR emission. We proceed
to compare our reddening map with maps created from other tracers to determine
how well the various tracers agree in terms of both the line-of-sight
reddening values as well as dust distribution morphology. As with the
comparison in Paper II, in the figures presented below we do not make any
correction for the difference in the volume sampled between the reddening map
based on ETGs and those based on various LMC stellar components. If necessary,
we remove the foreground MW reddening from the literature maps following the
same prescription as described in Section 2.3. The SFD98 $E(B-V)$ values have
been demonstrated to be overall systematically overestimated (see e.g. Yuan et
al., 2013) and so whilst their use to de-redden the lambdar fluxes was
justified (as the extinction coefficients already accounted for this
overestimation), their use to de-redden the reddening values in the literature
maps would result in us effectively overestimating the foreground MW
reddening, and as such adopt a scaling of 0.86 to reflect the recalibration of
Schlafly & Finkbeiner (2011).

###  4.1 Literature LMC reddening maps

####  4.1.1 Inno et al. (2016)

As part of our comparison in Paper II we adopted the Cepheid sample of Joshi &
Panchal (2019), however here we instead adopt that of Inno et al. (2016).
Although the reddening values are in very good agreement, the latter covers a
larger area of the LMC disc and is thus preferable as a comparison data set.
Inno et al. (2016) studied the structure of the LMC disc using multi-
wavelength observations of Classical Cepheids (from the $V$-band in the
optical to the $W1$-band in the mid-IR). As part of this study, Inno et al.
(2016) used a multi-wavelength fitting of the reddening law to the apparent
distance moduli to determine the colour excess to individual Cepheids and thus
create a reddening map covering $\simeq$ 80 deg2 of the LMC disc. For more
details regarding the methodology, readers are referred to the works of
Freedman, Wilson & Madore (1991) and Gallart, Aparicio & Vilchez (1996) as
early examples. Inno et al. (2016) assumed a value of $R_{V}=3.23$, where
$R_{V}$ denotes the total to selective absorption, as part of their reddening
analysis and provide the individual reddening values in the form of $E(B-V)$.
The highest median reddening corresponds to $0.65$ mag whereas the mean
reddening corresponds to $0.02$ mag.

####  4.1.2 Choi et al. (2018)

Choi et al. (2018) used $g$\- and $i$-band data from SMASH to create a
$2.67\times 2.67$ arcmin2 resolution reddening map covering $\simeq$ 165 deg2
of the LMC from a sample of $\sim$ 2.2 million RC stars. As opposed to simply
adopting a given intrinsic RC $g-i$ colour, Choi et al. (2018) instead
measured the intrinsic colour radial profile using a “clean” RC sample based
on regions in the outskirts of the LMC that are essentially dust-free (see
their figs. 4 and 7). The stars in these regions were de-reddened using the
SFD98 dust map before constructing the intrinsic colour radial profile. The
reddening map was created by comparing the observed $g-i$ colour map and the
intrinsic $g-i$ colour map which is based on the intrinsic colour radial
profile. Note that the radial profile only covers an angular distance range of
2.7 to 8.5 deg (from the LMC centre) and thus Choi et al. (2018) adopted the
intrinsic RC colour at a distance of 2.7 deg for the innermost regions ($<2.7$
deg) and similarly the intrinsic RC colour at a distance of 8.5 deg for the
outermost regions ($8.5-10.5$ deg). To convert the $E(g-i)$ values presented
in the Choi et al. (2018) reddening map, we use the extinction coefficients
listed in eq. 1 of Paper I to yield $E(g-i)=1.617\times E(B-V)$. In the
resulting map the highest median reddening is of $0.35$ mag and the mean
reddening is of $0.02$ mag.

####  4.1.3 Skowron et al. (2021)

Skowron et al. (2021) used $V$\- and $I$-band data from OGLE-IV (Udalski,
Szymański & Szymański, 2015) to create a reddening map covering $\simeq$ 180
deg2 of the LMC using RC stars777http://ogle.astrouw.edu.pl/cgi-
ogle/get_ms_ext.py. The resolution of the reddening map varies from $1.7\times
1.7$ arcmin2 in the central regions to $\simeq$ $27\times 27$ arcmin2 in the
outer regions. Skowron et al. (2021) determined an intrinsic RC $V-I$ colour
radial profile by de-reddening the observed RC colours using the SFD98 dust
map. Note that the authors exclude the central 4.1 deg radius region around
the LMC centre due to the incorrect reddening values provided by the SFD98
dust maps as well as some outer regions due to spurious RC colour measurements
(see their section 4 for details). To estimate the intrinsic RC colour in the
inner and outer regions, Skowron et al. (2021) used spectroscopic information
from Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectra
of red giant stars taken from Nidever et al. (2020) to first calculate the LMC
metallicity gradient and then a sample of intermediate-aged (3–9.5 Gyr)
clusters to determine the variation of the intrinsic RC colour as a function
of metallicity. These two relations are then combined to provide an intrinsic
colour change as a function of distance from the LMC centre of –0.002 mag
deg-1 that is used to calculate the intrinsic RC colour in the aforementioned
excluded regions (see their fig. 13). $E(V-I)$ values are converted into
$E(B-V)$ using the relation from Cardelli, Clayton & Mathis (1989). We find a
highest median reddening of $0.28$ mag and a mean reddening to $0.01$ mag.

####  4.1.4 Cusano et al. (2021)

Cusano et al. (2021) used a combination of near-IR time-series photometry from
the VMC and optical light curves from OGLE-IV to study the structure of the
LMC as traced by $\simeq$ 29,000 RR Lyrae stars. As part of this analysis,
they also determined optical $E(V-I)$ reddening values by comparing the
observed colours of these stars to their intrinsic colour (based on an
empirical relation connecting the intrinsic colour of the star to its $V$-band
amplitude and period; see also Piersimoni, Bono & Ripepi, 2002). Although
Cusano et al. (2021) do not provide the individual $E(V-I)$ reddening values,
they do provide the individual $K_{\rm{s}}$-band extinction values (see their
table 3) and so we convert these to $E(B-V)$ values using the extinction
coefficient listed in eq. 1 of Paper I [$A_{K_{\rm{s}}}=0.308\times E(B-V)$].
The highest median reddening corresponds to $0.67$ mag and the mean reddenign
to $0.02$ mag.

####  4.1.5 Utomo et al. (2019)

Utomo et al. (2019) homogeneously reanalysed archival far-IR maps from
_Herschel_ in four Local Group galaxies (including the LMC at $\sim$ 1 arcmin
resolution) by fitting the SED of dust from 100 to 500 $\mu$m with a modified
blackbody emission model (see Chiang et al., 2018 for details regarding the
model fitting). For our purposes, we are interested in the dust mass surface
density, $\Sigma_{\rm{d}}$, returned by the best-fitting model, as this can
then be converted into $E(B-V)$ which can then be directly compared to the
values we derive using ETGs. IR emission across these wavelengths primarily
captures emission from relatively large dust grains that are in thermal
equilibrium with the local radiation field, and represent the bulk of the
total dust mass. The smaller grains however contribute to the reddening
because of their surface to volume ratio. We note that the dust map of the LMC
adopted in this work (Chiang et al. priv. comm.) differs slightly from that
calculated in Utomo et al. (2019) in two small ways. First, whereas Utomo et
al. (2019) adopt a simple power law (see their eq. 5), the dust map included
here instead uses a broken power law (see eqs. 2 and 3 of Chiang et al., 2021)
as this yields a better fit to the data (see Chiang et al., 2018). Second, as
a result of modifying the form of the fit, the emissivity at 160 $\mu$m (the
reference wavelength in Utomo et al., 2019 and which is determined by
calibrating the models to the Milky Way cirrus where the dust mass is known,
see e.g. Jenkins, 2009; Gordon et al., 2014) increases slightly to
$\kappa_{160\,\mu\rm{m}}=20.73\pm 0.97$ cm2 g-1 (cf. $18.7\pm 0.6$ cm2 g-1 in
Utomo et al., 2019).

In Paper II (see section 4.1.3) we demonstrated a method to convert
$\Sigma_{\rm{d}}$ to $E(B-V)$ following the formalism of Whittet (2003) and
for which it was necessary to make assumptions regarding the values of the
$V$-band extinction efficiency factor, $Q_{V}$, as well as the radius, $a$,
and density, $\rho_{\rm{d}}$, of the dust grains. Here we adopt a simpler,
albeit model-dependent, approach using the following conversion (see Draine et
al., 2014 and references therein):

$A_{V}=0.7394\left(\frac{\Sigma_{\rm{d}}}{10^{5}\,\mathrm{M_{\odot}/kpc^{2}}}\right)\,\mathrm{mag}$
(1)

and then convert $A_{V}$ into $E(B-V)$ as in (Cardelli et al., 1989). Despite
the different methods to convert $\Sigma_{\rm{d}}$ into $E(B-V)$, the median
difference in the resulting $E(B-V)$ values is only $\Delta
E(B-V)_{\rm{med}}=0.004$ mag. Furthermore, significant differences (greater
than the 0.05 mag level) affect only 1 per cent of the total number of pixels
covering the area of the LMC observed by _Herschel_ and coincide with the most
intense regions of star formation. As in Paper II, we do not need to subtract
the foreground MW contribution as this has already been accounted for as part
of the SED modelling.

####  4.1.6 Mazzi et al. (2021)

Mazzi et al. (2021) used near-IR VMC data to determine the SFH across $\simeq$
96 deg2 of the LMC with a spatial resolution of 0.125 deg2. The derivation of
the SFH consists of determining the linear combination of partial models that
best fit the observed $K_{\rm{s}},Y-K_{\rm{s}}$ and $K_{\rm{s}},J-K_{\rm{s}}$
colour–magnitude Hess diagrams. These models include the effects of
extinction, and so by finding the best-fitting combination of models, Mazzi et
al. (2021) determined a representative “mean” $V$-band extinction for each
subregion. We transform $A_{V}$ into $E(B-V)$ following Cardelli et al. (1989)
[$A_{V}=3.1\times E(B-V)$]. Note that we only adopt the $A_{V}$ values
resulting from the $K_{\rm{s}},J-K_{\rm{s}}$ fits due to possible issues with
the absolute $Y$-band calibration. Due to SFH analysis being performed on
discretised regions across the LMC, we are unable to compare this reddening
map to the map based on ETGs at a resolution of $10\times 10$ arcmin2. To
facilitate a comparison, we will degrade the resolution of the ETG reddening
map and discuss this map separately (see Section 4.2).

###  4.2 Comparing different reddening tracers

Figure 11: $10\times 10$ arcmin2 resolution reddening maps of the LMC. Each
panel refers to a different literature source/tracer. The contour in each
panel represents the low-level pervasive dust associated with the central
regions of the LMC as traced by the IRAS 100 $\mu$m emission. Note that the
colour bar range has been limited to $0\leq E(B-V)\leq 0.3$ mag to better
illustrate low-level features within the maps. Note also that the ETG
extinctions should be roughly twice that of the Cepheids, RR Lyrae and RC
values since the latter do not sample the full path through the LMC. Figure
12: As Fig. 11, but showing a $10\times 10$ arcmin2 resolution differential
reddening maps of the LMC, such that $\Delta
E(B-V)=E(B-V)_{\mathrm{ETG}}-E(B-V)_{\mathrm{tracer}}$. Note that the colour
bar range has been limited to $-0.3\leq E(B-V)\leq 0.3$ mag to better
illustrate low-level features within the maps.

Fig. 11 shows the comparison between the LMC reddening map based on ETGs and
the other maps resampled onto the same $10\times 10$ arcmin2 resolution. The
majority of the maps used in our comparison have higher spatial resolutions
than that shown in Fig. 11 and so some small-scale features (of the order of
tens of pc in size) will be masked. Despite this resampling, any large-scale
features present in the maps will be retained and evidenced in Fig. 11. In
addition, Fig. 12 shows the difference between the reddening map based on ETGs
and the literature maps such that $\Delta
E(B-V)=E(B-V)_{\mathrm{ETG}}-E(B-V)_{\mathrm{tracer}}$.

Whilst the various reddening tracers shown in Fig. 11 all exhibit enhanced
levels of intrinsic reddening in some areas across the central regions of the
LMC (in particular the Tarantula Nebula and the molecular ridge south of 30
Dor), not all are consistent with the morphology of the low-level pervasive
dust emission as traced by the IRAS 100 $\mu$m emission. In particular, we see
clear differences between the stellar tracers (Cepheids, RR Lyrae and RC) and
those that sample ETGs and far-IR emission. However, the dust emission or the
Cepheids maps are likely very highly biased (the former by heating sources,
the latter by being near regions of star formation) and therefore not
appropriate to compare to the values presented here. The older stars are more
likely to be representative of random lines of sight (modulo the factor of two
difference).

Reddening values derived from pulsating stars (Cepheids and RR Lyrae stars)
are lower in the central region of the galaxy (at the location of the bar)
compared to regions east, west and north of it. These tracers follow a spatial
distribution typical of young and old stars, respectively, with most of them
located within a structure of a few kpc along the line of sight (e.g. Inno et
al., 2016; Cusano et al., 2021). The lower level of reddening suggested by
pulsating stars in the bar region compared to ETGs could be explained by the
predominant location of these sources in front of the dust rather than behind
it. This is however unlikely because both types of variables occupy the entire
thickness of the galaxy. Whilst the sample of Cepheids and RR Lyrae stars are
highly complete they suffer from incompleteness/blending, due to crowding, in
the central regions (e.g. Holl et al., 2018). This effect reduces the
amplitude of variation with respect to that of isolated stars, and makes the
stars redder which corresponds to a lower reddening towards them (see eqn. 2
of Cusano et al., 2021). The western edge of bar is consistently reddened in
all maps, but the continuous extension towards the south is only prominent in
the maps derived from RR Lyrae and RC stars. The latter shows also reddening
in the central bar region, especially in the map from Choi et al. (2018). RC
stars sample the same range of distances as RR Lyrae stars, but are
significantly more numerous which may explain their capability to trace
reddening across a larger volume.

Similarly to our findings, the middle of the northern arm (a structure
parallel to the bar) shows the largest reddening values compared to the other
regions within it. Maps extending to the outer regions confirm enhanced
reddening values in the south. In our map, the region of 30 Dor and of the
molecular ridge south of it appear as reddened as the bar region. This may be
a selective effect due to a lack of ETGs in regions of high extinction and/or
crowding introducing a bias to lower reddening values (see also Sect. 3). Both
effects do influence the molecular ridge region whereas crowding is the
dominant effect in the bar region.

The differential reddening maps imply that, by sampling the full line of sight
of the LMC, the intrinsic reddening values inferred from the background
galaxies are on average higher than those inferred from stellar tracers. If we
allow for a factor of 2 difference to account for this depth effect and
consider that the median uncertainty on the reddening is of
$\sigma_{E(B-V)_{\mathrm{med}}}=0.09$ mag, we find that our map is consistent
with those from RC stars for which the highest median reddening differs by
$0.19$ mag (Skowron et al., 2021) and $0.26$ mag (Choi et al., 2018),
respectively. On the contrary, the highest median reddening for the dust
emission exceeds that of our map by $0.50$ mag, for the Cepheids by $0.60$ mag
and for the RR Lyrae stars by $0.62$ mag. Note that these values are not shown
in Fig. 12 because the reddening scale has been limited to $\pm 0.3$ mag to
better illustrate low-level features. The mean reddening differences are
however consistent with zero for all tracers.

Figure 13: Left panel: Reddening map of the LMC derived from the SFH study by
Mazzi et al. (2021). The spatial resolution corresponds to bins of $21.0\times
21.5$ arcmin2 whereas the area shown is the same as in Figs. 8, 9 and 11,
hence the white space in the south and not all bins shown in the north. The
contour represents the low-level pervasive dust associated with the central
regions of the LMC as traced by the IRAS 100 $\mu$m emission. Note that the
colour bar range has been limited to $0\leq E(B-V)\leq 0.3$ mag to better
illustrate low-level features within the maps. Middle panel: As the left
panel, but showing the ETG reddening map adopting the spatial resolution of
Mazzi et al.. Right panel: As the left panel, but showing the differential
reddening map, such that $\Delta
E(B-V)=E(B-V)_{\mathrm{ETG}}-E(B-V)_{\mathrm{SFH}}$. Note that the colour bar
range has been limited to $-0.3\leq E(B-V)\leq 0.3$ mag to better illustrate
low-level features within the map.

The comparison between our reddening map and the map derived from the SFH
analysis is shown instead in Fig. 13. In this case, the spatial resolution of
each map corresponds to bins of $21.0\times 21.5$ arcmin2. The SFH shows the
highest reddening values in star forming regions (30 Dor, Constellation III
and at the west end of the bar) which are not representative of the line-of-
sights we trace in our study. Apart from other localised overdensities
comparable to the size of a few bins the overall reddening is low. In
particular, the central bar region appears as extinct as the outer regions
whereas in our study the bar and the overall inner region of the galaxy appear
more extinct than its surroundings. By differentiating the SFH and ETG
reddening maps we obtain a rather smooth distribution which agrees within the
factor of 2 higher distance sampled by the ETGs. This suggests that a
significant fraction of the dust is located beyond the bar sampled by the SFH
analysis. The bar region is also affected by extreme crowding and in this
region the SFH analysis relies more heavily on RC and RGB stars than on main-
sequence turn-off and subgiant stars; these regions are associated to a low
likelihood (Mazzi et al., 2021).

To further inspect possible correlations between the ETGs reddening and the
reddening derived from the other tracers we plot in Fig. 14 the relation
between them. The best fit lines are clearly different from the one-to-one
relation, except for the reddening derived from the dust emission which
follows a similar trend, but is offset by about 0.5 mag. We already mentioned
earlier that despite the influence of heating sources there is a good
agreement with the distribution of the low-level pervasive dust emission
traced by the IRAS at 100 $\mu$m.

Figure 14: Comparison of the reddening values in the 10$\times$10 resolution
ETG reddening map and those of the other reddening tracers. Note that the
comparisons only include bins that cover the combined SMASH-VMC footprint of
the LMC. The solid line and shaded region in each panel represent the linear
best fit and corresponding 67 per cent confidence interval. The dashed line in
each panel denotes the one-to-one correspondence between the two reddening
tracers.

Figure 15 shows histograms of the distribution of reddening values for the
different samples. For all tracers, the peaks of the distributions correspond
to reddening values inferior to 0.1 mag. The slope of the distributions
towards higher reddening values is however different among the different
tracers. It is shallower for the dust emission based reddening than for the
stellar ones. The ETG reddening does not show a prominent tail, but rather a
wide peak where the distribution of values is confined within about 0.15 mag
for the majoirty of the sources.

Figure 15: Histograms showing the distribution of reddening values in the
10$\times$10 resolution reddening maps shown in Figs. 11 and 13. Note that the
histograms only include bins that cover the combined SMASH-VMC footprint of
the LMC.

Figure 16 shows the magnitude of ETGs after applying the reddenign correction.
This figure was created in the same way as that described for the reddening
map, but instead of taking the median value of all best-fit reddening values
in a given bin, we take the median of all extinction corrected J-band
magnitudes. Note that the J-band magnitudes are calculated from the LAMBDAR
fluxes and corrected for extinction using the relation shown in eqn. 1 of
Paper I. We use the J-band magnitude because it is available for almost all
ETGs (essentially 100%; 222736 out of 222752 ETGs), whereas for the optical
bands we notice a decrease in the number of ETGs with measured fluxes that
grows as one moves to bluer bandpasses, e.g. only 49% and 88% of ETGs have
measured u- and g-band fluxes, respectively. In the r-, i- and z-bands, we
have 97%, 98% and 99% completeness, respectively. The variation of the
magnitude of ETGs shows that they sample a different physical scale and
therefore a different amount of dust towards the inner and outer regions of
the LMC. This is due to the limitation by crowding in the centre and the
shallow exposures in the outermost area. More line of sights are needed to
describe the likely extinction in these areas compared to that in the
intermediate area where the magnitude of ETGs is fairly homogeneous at about
J=20.2 mag.

Figure 16: Map of the ETG extinction corrected J-band magnitude
($m_{J_{\mathrm{0}}}$) across the LMC at a resolution of 10$\times$10 arcmin2.

##  5 Summary

In this study, we have determined the total intrinsic reddening across
$\simeq$ 90 deg2 of the LMC based on the analysis of SEDs of background
galaxies. We followed a similar technique as developed in Paper I and extended
to the SMC in Paper II. The main steps involved in our procedure and the
conclusions are as follows.

  * (i)

We select $\sim$ 2.5 million background sources from the SMASH and VMC
catalogues of the LMC by combining colour-magnitude and morphological
criteria. We use lambdar to measure fluxes and construct SEDs from the optical
($ugriz$) to the near-IR ($YJK_{\rm{s}}$).

  * (ii)

We run the lephare $\chi^{2}$ code to fit the SEDs of the objects, which
include 21,828 spectroscopically confirmed AGN, and select 252,752 galaxies
with low levels of intrinsic reddening. The resulting reddening map reproduces
the pervasive enhanced levels of reddening across the LMC bar region with
enhancements associated with star forming regions and overdensities traced by
young stars.

  * (iii)

The calculated lephare photometric redshifts for 189 AGN are in very good
agreement with the spectroscopically determined redshifts ($\Delta
z=z_{\rm{spec}}-z_{\rm{phot}}=-0.009$).

  * (iv)

We compare our reddening map with publicly available maps of the LMC. For the
inner region, we find good agreement between our map and the distribution of
dust emission. The comparison with stellar tracers, however, is more
complicated owing to the variations amongst the reddening maps of the various
stellar populations. For those showing a significant level of reddening
associated with 30 Dor and molecular ridge we find discrepancies. Given the
reduced number of galaxies in highly extinguished and crowded regions, it is
possible our map is biased towards lower levels of reddening. In contrast, we
find agreement with those maps demonstrating reddening in the bar region and
in the outskirts of the galaxy. Given a factor of 2 difference, by sampling
the full line-of-sight, and the uncertainties in the reddening determinations
our map is consistent with maps derived from RC stars. Furthermore, the good
agreement with a SFH-based reddening map indicates that a significant fraction
of the dust is located beyond the bar.

  * (v)

We find that the regions lacking $u$-band data, mostly located in the
outskirts of the galaxy, sample ETGs similar to those within the same $griz$
magnitude ranges resulting from deep exposures.

In this study, we have extended and improved our technique to measure the
total intrinsic reddening of the LMC using background galaxies. The sample of
252,752 ETGs we used may seem small compared to the size of stellar samples
adopted for the same purpose, it is however extremely large if one considers
that the LMC lies in front of it. Future studies based on large spectroscopic
surveys (including surveys using the 4-metre multi-object spectroscopic
telescope (4MOST); e.g. Cioni et al., 2019) will provide spectra for hundreds
of thousands of background galaxies which will allow us to not only robustly
determine their redshifts but also to develop a complementary method to
quantify the total intrinsic reddening in the foreground Magellanic Clouds.

## Acknowledgements

This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme
(grant agreement no. 682115). This research was supported in part by the
Australian Research Council Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO3D), through project number CE170100013. Y.C. acknowledges
support from NSF grant AST 1655677. A.N. acknowledges support from the
Narodowe Centrum Nauki (UMO-2020/38/E/ST9/00077). The authors would like to
thank the Cambridge Astronomy Survey Unit (CASU) and the Wide Field Astronomy
Unit (WFAU) in Edinburgh for providing the necessary data products under the
support of the Science and Technology Facilities Council (STFC) in the U.K.
The authors would also like to thank S. Rubele for his work on creating the
deep, near-IR VMC PSF photometric catalogues. This study was based on
observations made with VISTA at the La Silla Paranal Observatory under
programme ID 179.B-2003. This project used data obtained with the Dark Energy
Camera (DECam), which was constructed by the Dark Energy Survey (DES)
collaboration. Funding for the DES Projects has been provided by the U.S.
Department of Energy, the U.S. National Science Foundation, the Ministry of
Science and Education of Spain, the STFC, the Higher Education Funding Council
for England, the National Center for Supercomputing Applications at the
University of Illinois at Urbana-Champaign, the Kavli Institute of
Cosmological Physics at the University of Chicago, the Center for Cosmology
and Astro-Particle Physics at the Ohio State University, the Mitchell
Institute for Fundamental Physics and Astronomy at Texas A&M University,
Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à
Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento
Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovacão,
the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the
Dark Energy Survey. The Collaborating Institutions are Argonne National
Laboratory, the University of California at Santa Cruz, the University of
Cambridge, Centro de Investigaciones Enérgeticas, Medioambientales y
Tecnológicas-Madrid, the University of Chicago, University College London, the
DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische
Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the
University of Illinois at Urbana-Champaign, the Institut de Ciències de
l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence
Berkeley National Laboratory, the Ludwig-Maximilians Universität München and
the associated Excellence Cluster Universe, the University of Michigan, the
National Optical Astronomy Observatory, the University of Nottingham, the Ohio
State University, the University of Pennsylvania, the University of
Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the
University of Sussex and Texas A&M University. Based on observations at Cerro
Tololo Inter-American Observatory, National Optical Astronomy Observatory
(NOAO Prop. ID: 2013A-0411 and 2013B-0440; PI: Nidever), which is operated by
the Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation. Finally, this
project has made extensive use of the Tool for OPerations on Catalogues And
Tables (TOPCAT) software package (Taylor, 2005) as well as the following open-
source Python packages: Astropy (The Astropy Collaboration et al., 2018),
matplotlib (Hunter, 2007), NumPy (Oliphant, 2015), pandas (McKinney, 2010),
and SciPy (Jones et al., 2001–).

## Data Availability

The data underlying this study are available in the study and in its online
supplementary material. The SMASH survey images used to create the galaxy SEDs
are publicly available at the NOIRLab Astro Data Lab
(https://datalab.noirlab.edu/). The deep stack VMC images of the LMC will be
released in 2022, whereas the individual observations are publicly available
at the ESO archive (http://archive.eso.org/cms.html). The galaxy SEDs will be
shared on reasonable request to the corresponding author.

## References

  * Ajello et al. (2020) Ajello M., et al., 2020, ApJ, 892, 105
  * Arnouts et al. (2007) Arnouts S., et al., 2007, A&A, 476, 137
  * Bell et al. (2019) Bell C. P. M., et al., 2019, MNRAS, 489, 3200 (Paper I)
  * Bell et al. (2020) Bell C. P. M., et al., 2020, MNRAS, 499, 993 (Paper II)
  * Bellagamba et al. (2012) Bellagamba F., Meneghetti M., Moscardini L., Bolzonella M., 2012, MNRAS, 422, 553
  * Bisigello et al. (2016) Bisigello L., et al., 2016, ApJS, 227, 19
  * Cardelli et al. (1989) Cardelli J. A., Clayton G. C., Mathis J. S., 1989, ApJ, 345, 245
  * Chastenet et al. (2017) Chastenet J., Bot C., Gordon K. D., Bocchio M., Roman-Duval J., Jones A. P., Ysard N., 2017, A&A, 601, A55
  * Chen et al. (2022) Chen B. Q., Guo H. L., Gao J., Yang M., Liu Y. L., Jiang B. W., 2022, MNRAS, 511, 1317
  * Chiang et al. (2021) Chiang I.-D., et al., 2021, ApJ, 907, 29
  * Chiang et al. (2018) Chiang I.-D., Sandstrom K. M., Chastenet J., Johnson L. C., Leroy A. K., Utomo D., 2018, ApJ, 865, 117
  * Choi et al. (2018) Choi Y., et al., 2018, ApJ, 866, 90
  * Cioni et al. (2019) Cioni M.-. R. L., et al., 2019, The Messenger, 175, 54
  * Cioni et al. (2011) Cioni M.-R. L., et al., 2011, A&A, 527, A116
  * Cioni et al. (2013) Cioni M.-R. L., et al., 2013, A&A, 549, A29
  * Cowley et al. (1984) Cowley A. P., Crampton D., Hutchings J. B., Helfand D. J., Hamilton T. T., Thorstensen J. R., Charles P. A., 1984, ApJ, 286, 196
  * Crampton et al. (1997) Crampton D., et al., 1997, AJ, 114, 2353
  * Cristiani & Tarenghi (1984) Cristiani S., Tarenghi M., 1984, A&A, 132, 351
  * Cross et al. (2012) Cross N. J. G., et al., 2012, A&A, 548, A119
  * Cusano et al. (2021) Cusano F., et al., 2021, MNRAS, 504, 1
  * de Grijs & Bono (2015) de Grijs R., Bono G., 2015, AJ, 149, 179
  * de Grijs et al. (2014) de Grijs R., Wicker J. E., Bono G., 2014, AJ, 147, 122
  * De Marchi et al. (2021) De Marchi G., Panagia N., Milone A. P., 2021, ApJ, 922, 135
  * Dobrzycki et al. (2005) Dobrzycki A., Eyer L., Stanek K. Z., Macri L. M., 2005, A&A, 442, 495
  * Dobrzycki et al. (2002) Dobrzycki A., Groot P. J., Macri L. M., Stanek K. Z., 2002, ApJ, 569, L15
  * Draine et al. (2014) Draine B. T., et al., 2014, ApJ, 780, 172
  * Duncan et al. (2018a) Duncan K. J., et al., 2018a, MNRAS, 473, 2655
  * Duncan et al. (2018b) Duncan K. J., Jarvis M. J., Brown M. J. I., Röttgering H. J. A., 2018b, MNRAS, 477, 5177
  * El Youssoufi et al. (2019) El Youssoufi D., et al., 2019, MNRAS, 490, 1076
  * Flesch (2021) Flesch E. W., 2021, MNRAS, 504, 621
  * Freedman et al. (2020) Freedman W. L., et al., 2020, ApJ, 891, 57
  * Freedman et al. (1991) Freedman W. L., Wilson C. D., Madore B. F., 1991, ApJ, 372, 455
  * Gallart et al. (1996) Gallart C., Aparicio A., Vilchez J. M., 1996, AJ, 112, 1928
  * Geha et al. (2003) Geha M., et al., 2003, AJ, 125, 1
  * Gieren et al. (2018) Gieren W., et al., 2018, A&A, 620, A99
  * González-Fernández et al. (2018) González-Fernández C., et al., 2018, MNRAS, 474, 5459
  * Gordon et al. (2014) Gordon K. D., et al., 2014, ApJ, 797, 85
  * Górski et al. (2020) Górski M., et al., 2020, ApJ, 889, 179
  * Gouliermis et al. (2014) Gouliermis D. A., Hony S., Klessen R. S., 2014, MNRAS, 439, 3775
  * Groenewegen (2018) Groenewegen M. A. T., 2018, A&A, 619, A8
  * Haberl et al. (2012) Haberl F., et al., 2012, A&A, 545, A128
  * Haschke et al. (2011) Haschke R., Grebel E. K., Duffau S., 2011, AJ, 141, 158
  * Holl et al. (2018) Holl B., et al.., 2018, A&A, 618, A30
  * Hunter (2007) Hunter J. D., 2007, Computing in Science & Engineering, 9, 90
  * Inno et al. (2016) Inno L., et al., 2016, ApJ, 832, 176
  * Irwin et al. (2004) Irwin M. J., et al.., 2004, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 5493, Optimizing Scientific Return for Astronomy through Information Technologies, Quinn P. J., Bridger A., eds., pp. 411–422
  * Ivanov et al. (2016) Ivanov V. D., et al., 2016, A&A, 588, A93
  * Ivezić et al. (2002) Ivezić Ž., et al., 2002, AJ, 124, 2364
  * Jenkins (2009) Jenkins E. B., 2009, ApJ, 700, 1299
  * Jiang et al. (2007) Jiang L., Fan X., Ivezić Ž., Richards G. T., Schneider D. P., Strauss M. A., Kelly B. C., 2007, ApJ, 656, 680
  * Jones et al. (2009) Jones D. H., et al., 2009, MNRAS, 399, 683
  * Jones et al. (2001–) Jones E., et al., 2001–, SciPy: Open source scientific tools for Python
  * Joshi & Panchal (2019) Joshi Y. C., Panchal A., 2019, A&A, 628, A51
  * Kostrzewa-Rutkowska et al. (2018) Kostrzewa-Rutkowska Z., et al., 2018, MNRAS, 476, 663
  * Kozłowski et al. (2012) Kozłowski S., et al.., 2012, ApJ, 746, 27
  * Kozłowski et al. (2011) Kozłowski S., Kochanek C. S., Udalski A., 2011, ApJS, 194, 22
  * Kozłowski et al. (2013) Kozłowski S., et al., 2013, ApJ, 775, 92
  * Mazzi et al. (2021) Mazzi A., et al., 2021, MNRAS, 508, 245
  * McKinney (2010) McKinney W., 2010, in Proceedings of the 9th Python in Science Conference, van der Walt S., Millman J., eds., p. 51
  * Muraveva et al. (2018) Muraveva T., et al., 2018, MNRAS, 473, 3131
  * Nayak et al. (2018) Nayak P. K., Subramaniam A., Choudhury S., Sagar R., 2018, A&A, 616, A187
  * Nidever et al. (2020) Nidever D. L., et al., 2020, ApJ, 895, 88
  * Nidever et al. (2017) Nidever D. L., et al., 2017, AJ, 154, 199
  * Norris et al. (2011) Norris R. P., et al., 2011, PASA, 28, 215
  * Oliphant (2015) Oliphant T. E., 2015, Guide to NumPy. CreateSpace Independent Publishing Platform, 2nd ed.
  * Paturel et al. (2003) Paturel G., Petit C., Prugniel P., Theureau G., Rousseau J., Brouty M., Dubois P., Cambrésy L., 2003, A&A, 412, 45
  * Pennock et al. (2021) Pennock C. M., et al., 2021, MNRAS, 506, 354
  * Piersimoni et al. (2002) Piersimoni A. M., Bono G., Ripepi V., 2002, AJ, 124, 1528
  * Polletta et al. (2007) Polletta M., et al., 2007, ApJ, 663, 81
  * Riess et al. (2019) Riess A. G., Casertano S., Yuan W., Macri L. M., Scolnic D., 2019, ApJ, 876, 85
  * Riess et al. (2009) Riess A. G., et al., 2009, ApJ, 699, 539
  * Ripepi et al. (2017) Ripepi V., et al., 2017, MNRAS, 472, 808
  * Ripepi et al. (2019) Ripepi V., Molinaro R., Musella I., Marconi M., Leccia S., Eyer L., 2019, A&A, 625, A14
  * Rubele et al. (2018) Rubele S., et al., 2018, MNRAS, 478, 5017
  * Salvato et al. (2009) Salvato M., et al., 2009, ApJ, 690, 1250
  * Schlafly & Finkbeiner (2011) Schlafly E. F., Finkbeiner D. P., 2011, ApJ, 737, 103
  * Schlegel et al. (1998) Schlegel D. J., Finkbeiner D. P., Davis M., 1998, ApJ, 500, 525
  * Skowron et al. (2021) Skowron D. M., et al., 2021, ApJS, 252, 23
  * Tatton et al. (2021) Tatton B. L., et al., 2021, MNRAS, 504, 2983
  * Taylor (2005) Taylor M. B., 2005, in Astronomical Society of the Pacific Conference Series, Vol. 347, Astronomical Data Analysis Software and Systems XIV, Shopbell P., Britton M., Ebert R., eds., p. 29
  * The Astropy Collaboration et al. (2018) The Astropy Collaboration, Price-Whelan A. M., Sipőcz B. M., Günther H. M., et al., 2018, AJ, 156, 123
  * Tinney (1999) Tinney C. G., 1999, MNRAS, 303, 565
  * Udalski (2003) Udalski A., 2003, Acta Astron., 53, 291
  * Udalski et al. (2015) Udalski A., Szymański M. K., Szymański G., 2015, Acta Astron., 65, 1
  * Utomo et al. (2019) Utomo D., Chiang I.-D., Leroy A. K., Sandstrom K. M., Chastenet J., 2019, ApJ, 874, 141
  * Wang et al. (1991) Wang Q., Hamilton T., Helfand D. J., Wu X., 1991, ApJ, 374, 475
  * Whittet (2003) Whittet D. C. B., 2003, Dust in the Galactic Environment. Bristol: Institute of Physics Publishing, 2nd ed.
  * Wright et al. (2016) Wright A. H., et al., 2016, MNRAS, 460, 765
  * Yuan et al. (2013) Yuan H. B., Liu X. W., Xiang M. S., 2013, MNRAS, 430, 2188
  * Zaritsky et al. (2002) Zaritsky D., Harris J., Thompson I. B., Grebel E. K., Massey P., 2002, AJ, 123, 855
  * Zivkov et al. (2018) Zivkov V., et al.., 2018, A&A, 620, A143