# The GLASS-JWST Early Release Science Program. III. Strong lensing model of
Abell 2744 and its infalling regions

Pietro Bergamini Dipartimento di Fisica, Università degli Studi di Milano, Via
Celoria 16, I-20133 Milano, Italy  INAF – OAS, Osservatorio di Astrofisica e
Scienza dello Spazio di Bologna, via Gobetti 93/3, I-40129 Bologna, Italy  Ana
Acebron Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria
16, I-20133 Milano, Italy  INAF – IASF Milano, via A. Corti 12, I-20133
Milano, Italy  Claudio Grillo Dipartimento di Fisica, Università degli Studi
di Milano, Via Celoria 16, I-20133 Milano, Italy  INAF – IASF Milano, via A.
Corti 12, I-20133 Milano, Italy  Piero Rosati Dipartimento di Fisica e Scienze
della Terra, Università degli Studi di Ferrara, via Saragat 1, I-44122
Ferrara, Italy  INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio
di Bologna, via Gobetti 93/3, I-40129 Bologna, Italy  Gabriel Bartosch Caminha
Technische Universität München, Physik-Department, James-Franck Str. 1, 85741
Garching, Germany  Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-
Str. 1, D-85748 Garching, Germany  Amata Mercurio Dipartimento di Fisica “E.R.
Caianiello”, Università Degli Studi di Salerno, Via Giovanni Paolo II, I–84084
Fisciano (SA), Italy  INAF – Osservatorio Astronomico di Capodimonte, Via
Moiariello 16, I-80131 Napoli, Italy  Eros Vanzella INAF – OAS, Osservatorio
di Astrofisica e Scienza dello Spazio di Bologna, via Gobetti 93/3, I-40129
Bologna, Italy  Charlotte Mason Cosmic Dawn Center (DAWN), Jagtvej 128, DK2200
Copenhagen N, Denmark  Niels Bohr Institute, University of Copenhagen, Jagtvej
128, København N, DK-2200, Denmark  Tommaso Treu Department of Physics and
Astronomy, University of California, Los Angeles, 430 Portola Plaza, Los
Angeles, CA 90095, USA  Giuseppe Angora Dipartimento di Fisica e Scienze della
Terra, Università degli Studi di Ferrara, via Saragat 1, I-44122 Ferrara,
Italy  INAF – Osservatorio Astronomico di Capodimonte, Via Moiariello 16,
I-80131 Napoli, Italy  Gabriel B. Brammer Cosmic Dawn Center (DAWN), Jagtvej
128, DK2200 Copenhagen N, Denmark  Niels Bohr Institute, University of
Copenhagen, Jagtvej 128, København N, DK-2200, Denmark  Massimo Meneghetti
INAF – OAS, Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, via
Gobetti 93/3, I-40129 Bologna, Italy  National Institute for Nuclear Physics,
viale Berti Pichat 6/2, I-40127 Bologna, Italy  Mario Nonino INAF –
Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, I-34131 Trieste,
Italy  Kristan Boyett School of Physics, University of Melbourne, Parkville
3010, VIC, Australia  ARC Centre of Excellence for All Sky Astrophysics in 3
Dimensions (ASTRO 3D), Australia  Maruša Bradač University of Ljubljana,
Department of Mathematics and Physics, Jadranska ulica 19, SI-1000 Ljubljana,
Slovenia  Department of Physics and Astronomy, University of California Davis,
1 Shields Avenue, Davis, CA 95616, USA  Marco Castellano INAF – Osservatorio
Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Rome, Italy
Adriano Fontana INAF – Osservatorio Astronomico di Roma, Via Frascati 33,
00078 Monteporzio Catone, Rome, Italy  Takahiro Morishita IPAC, California
Institute of Technology, MC 314-6, 1200 E. California Boulevard, Pasadena, CA
91125, USA  Diego Paris INAF – Osservatorio Astronomico di Roma, Via Frascati
33, 00078 Monteporzio Catone, Rome, Italy  Gonzalo Prieto-Lyon Cosmic Dawn
Center (DAWN), Jagtvej 128, DK2200 Copenhagen N, Denmark  Niels Bohr
Institute, University of Copenhagen, Jagtvej 128, København N, DK-2200,
Denmark  Guido Roberts-Borsani Department of Physics and Astronomy, University
of California, Los Angeles, 430 Portola Plaza, Los Angeles, CA 90095, USA
Namrata Roy Center for Astrophysical Sciences, Department of Physics &
Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA.  Paola Santini
INAF – Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio
Catone, Rome, Italy  Benedetta Vulcani INAF – Osservatorio astronomico di
Padova, Vicolo Osservatorio 5, I-35122 Padova, Italy  Xin Wang School of
Astronomy and Space Science, University of Chinese Academy of Sciences (UCAS),
Beijing 100049, China  National Astronomical Observatories, Chinese Academy of
Sciences, Beijing 100101, China  Institute for Frontiers in Astronomy and
Astrophysics, Beijing Normal University, Beijing 102206, China  Lilan Yang
Kavli Institute for the Physics and Mathematics of the Universe, The
University of Tokyo, Kashiwa, Japan 277-8583

###### Abstract

We present a new high-precision, JWST-based, strong lensing model for the
galaxy cluster Abell 2744 at $z=0.3072$. By combining the deep, high-
resolution JWST imaging from the GLASS-JWST and UNCOVER programs and a
Director’s Discretionary Time program, with newly obtained VLT/MUSE data, we
identify 32 multiple images from 11 background sources lensed by two external
sub-clusters at distances of $\sim 160\arcsec$ from the main cluster. The new
MUSE observations enable the first spectroscopic confirmation of a multiple
image system in the external clumps. Moreover, the re-analysis of the spectro-
photometric archival and JWST data yields 27 additional multiple images in the
main cluster. The new lens model is constrained by 149 multiple images ($\sim
66\%$ more than in our previous Bergamini et al. 2023a model) covering an
extended redshift range between 1.03 and 9.76. The subhalo mass component of
the cluster includes 177 member galaxies down to $m_{\rm F160W}=21$, 163 of
which are spectroscopically confirmed. Internal velocity dispersions are
measured for 85 members. The new lens model is characterized by a remarkably
low scatter between predicted and observed positions of the multiple images
($0.43\arcsec$). This precision is unprecedented given the large multiple
image sample, the complexity of the cluster mass distribution, and the large
modeled area. The improved accuracy and resolution of the cluster total mass
distribution provides a robust magnification map over a $\sim\\!45$ arcmin2
area, which is critical for inferring the intrinsic physical properties of the
highly magnified, high-$z$ sources. The lens model and the new MUSE redshift
catalog are released with this publication.

Galaxy Cluster (584) — Strong Gravitational Lensing (1643) — Dark Matter (353)

††facilities: JWST(NIRCam), JWST(NIRISS), VLT(MUSE), HST(ACS), HST(WFC3)

##  1 Introduction

The first JWST observations of massive galaxy clusters have revealed
exceptionally rich background patterns of strongly lensed galaxies, thanks to
a revolutionary combination of angular resolution, depth and near-and mid-
infrared coverage (e.g., Mahler et al., 2022; Pascale et al., 2022; Caminha et
al., 2022). Several JWST survey programs have targeted cluster fields to
exploit the gravitational lensing magnification, in the effort to unveil
primordial star-forming systems and study their physical properties (e.g.,
Treu et al., 2022; Bezanson et al., 2022; Willott et al., 2022; Windhorst et
al., 2023). While current studies are identifying an increasing number of
strongly lensed sources at $z\gtrsim 8$ based on JWST/NIRCam photometry (Hsiao
et al., 2022; Adams et al., 2023; Bradley et al., 2022), some have already
obtained spectroscopic confirmations in the range $z=9.5-10$ (Roberts-Borsani
et al., 2022a; Williams et al., 2022).

Compared to blank field surveys, observations of highly magnified regions of
clusters have the advantage of extending to low luminosities and stellar
masses our knowledge of the galaxy populations in the first billion years of
cosmic history, providing unique insights on their inner structure down to
parsec resolutions (e.g., Bouwens et al., 2021; Vanzella et al., 2022; Meštrić
et al., 2022; Vanzella et al., 2023; Welch et al., 2023). This progress,
however, comes with significant challenges. High-precision strong lensing
models are needed to produce reliable magnification maps which are, in turn,
critical to infer the intrinsic physical properties of the lensed sources
(luminosities, stellar masses, star formation rates, sizes), as well as the
effective survey volume at varying redshifts and therefore their space
densities (Castellano et al., 2022). The accuracy and precision of lens models
in predicting accurate magnification ($\mu$) values depend essentially on the
number of bona-fide multiple images with spectroscopic redshifts, spanning a
wide $z$-range, and a complete knowledge of the member galaxies contributing
to the cluster mass distribution. While independent models based on high-
quality spectro-photometric data tend to be robust in the low-magnification
regime ($\mu\lesssim 3$, see e.g., Meneghetti et al., 2017), such a
requirement becomes progressively more important near the critical lines, at
$\mu\gtrsim 10$. In the most extreme cases, for sources found within a
fraction of arcseconds of a critical line (e.g., Chen et al., 2022; Diego et
al., 2022; Welch et al., 2022; Meena et al., 2023), including caustic crossing
events (Kelly et al., 2018), magnification values can be of the order of
hundreds or more, implying that the interpretation on the nature of the source
relies heavily on the lens model accuracy.

JWST observations of galaxy clusters with exceptional lensing cross sections
offer an unprecedented opportunity to zoom into primordial star-forming
regions. On the one hand, they also provide a high number density of multiple
image systems, a factor of 2-3 higher than HST based studies, which improves
the accuracy of the lens models. On the other hand, spectroscopic redshifts of
a significant fraction of these lensed sources, that were beyond the reach of
previous technology, have now become attainable with JWST.

In this context, the massive galaxy cluster Abell 2744 (A2744 hereafer), at
$z=0.3072$, has been the target of several observational campaigns with the
Hubble Space Telescope (HST) obtaining deep, high-resolution and wide-field
coverage (Lotz et al., 2017; Steinhardt et al., 2020). Its combination with
extensive ground and space based spectroscopic follow-up observations (Braglia
et al., 2009; Owers et al., 2011; Treu et al., 2015; Richard et al., 2021) has
enabled a new generation of strong lensing models including a large number of
secure multiple images (Wang et al., 2015; Richard et al., 2021; Bergamini et
al., 2023a, B23 hereafter). In particular, the lens model presented by B23
prior to the JWST observations included 90 spectroscopically confirmed
multiple images (from 30 background sources), achieving an accuracy in
reproducing the observed positions of the multiple images a factor of $2$
better than previous lens models (see e.g., Wang et al., 2015; Mahler et al.,
2018; Richard et al., 2021). These pre-JWST lens models found that several
massive structures residing at large distances from the main cluster core had
a non-negligible impact in the total mass reconstruction of the cluster inner
regions. B23 found magnification to be significantly different from one well
beyond the innermost 500 kpc from the cluster center, suggesting that these
specific regions cannot effectively be considered as blank fields.

Figure 1: JWST/NIRCam and VLT/MUSE pointings observed for the galaxy cluster
A2744 and the projected total mass density distribution obtained from the
extended lens model presented in this work. Left: Magellan $r$-band image of
the galaxy cluster A2744. The footprints of the NIRCam pointings observed
during the GLASS-JWST ERS, UNCOVER, and DTT-2756 programs are shown in orange,
blue, and red, respectively. The footprints of the MUSE pointings are drawn in
green. The magenta squared region represents the $6.7\times 6.7$ arcmin2 area
covered by the extended lens model. Red dots show the 313 newly determined
secure redshifts from the MUSE DDT observations. Right: Projected total mass
density distribution of A2744 obtained from the extended lens model. The green
crosses mark the position of the spectroscopically confirmed cluster member
galaxies, corresponding to the light-gray histogram in Figure 2. We note that
163 spectroscopic cluster galaxies with $m_{\mathrm{F160W}}<21$, plus 14 non-
spectroscopically confirmed galaxies (white circles), are included in the lens
model. The 24 cluster galaxies included in the lens model with a new
spectroscopic confirmation from the MUSE DDT data are encircled in orange.
Figure 2: Redshift distribution of the spectroscopic cluster member galaxies
of A2744. The redshift distribution of all the spectroscopically confirmed
cluster galaxies within the redshift interval $0.28\leq z\leq 0.34$ is plotted
using the light gray histogram (669 galaxies). The dark gray histogram
corresponds to the distribution of the newly identified members, with secure
redshift values, measured from the DDT MUSE data (82 galaxies). The red
histogram shows the redshift distribution of the spectroscopically confirmed
cluster member galaxies brighter than $m_{\mathrm{F160W}}=21$ considered in
the lens model (163 galaxies, see also Figure 1). Figure 3: Redshift
distribution of all the sources with a secure spectroscopic redshift higher
than the A2744 cluster redshift. The redshift distribution of all the galaxies
with $z>0.34$ is plotted using the light gray histogram. The dark gray
histogram corresponds to the distribution of the background sources with
secure redshift values measured from the new DDT MUSE data. The red histogram
shows the redshift distribution of the spectroscopically confirmed multiple
images considered in the lens model. All of the 121 spectroscopic multiple
images, including the lensed galaxy substructures, are included in the plot
(see also Figure 5).

More recently, A2744 has been among the first targets of JWST (Treu et al.,
2022; Bezanson et al., 2022). By exploiting the deep JWST/NIRCam observations
gathered from both programs, Furtak et al. 2022a (F22 hereafter) have
presented a lens model, identifying, for the first time, a large number of
photometric multiple images around the external clumps. The F22 lens model
(optimized on the source plane) is constrained by the observed positions of
138 multiple images (from 48 background sources) and it is characterized by an
r.m.s residual scatter on the lens plane of $0.66\arcsec$ in the multiple
image positions, compared to $0.37\arcsec$ for the model by B23.

In this work, we exploit the new JWST/NIRCam imaging and Multi Unit
Spectroscopic Explorer (MUSE) spectroscopic observations, together with
archival spectro-photometric data including recent JWST/NIRISS and
JWST/NIRSpec redshifts, to build an improved lens model of A2744, that
includes the largest sample of multiple images used to date. In addition, the
new identification of several multiple image systems in the cluster core and
around the external clumps enables a more accurate and precise reconstruction
of the total mass distribution of the cluster. The lens model presented in
this work plays a fundamental role in studying the intrinsic properties of the
lensed high-redshift sources from current and future JWST observations of
A2744.

The paper is organized as follows. Section 2 describes the archival imaging
and spectroscopic data sets, as well as the new JWST and MUSE observations,
that are used to develop the lens model of A2744. In Section 3, we detail the
selection of the multiple images and cluster members, and the adopted
methodology for the extended strong lensing modeling of the cluster. Our
results are discussed in Section 4 and our main conclusions are summarized in
Section 5.

Throughout this work, we adopt a flat Lambda cold dark matter ($\Lambda$CDM)
cosmology with $\Omega_{m}=0.3$ and $H_{0}=70\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$.
Using this cosmology, a projected distance of $1\arcsec$ corresponds to a
physical scale of 4.528 kpc at the A2744 redshift of $z=0.3072$. All
magnitudes are given in the AB system.

##  2 Data

This section presents the datasets used to build the extended strong lensing
model of A2744, focusing in particular on the new spectro-photometric data
compared to those exploited by B23. In Section 2.1, we describe the archival
HST and Magellan imaging as well as the new JWST NIRCam imaging of this
cluster field. Section 2.2 summarizes the spectroscopic coverage of the
cluster field and the new MUSE DDT observations.

###  2.1 Imaging data

We use deep, ancillary Magellan g, r, i imaging of A2744 obtained with MegaCam
on the Magellan 2 Clay Telescope on 2018 September 7-8 (see Treu et al., 2022,
for an overview). The Magellan $i$-band imaging was used to anchor the NIRCam
images to the Gaia-DR3 astrometric solution (see Paris et al., 2023). All the
coordinates in our new lens model are therefore also aligned to this World
Coordinate System (WCS)111This corresponds to a difference of $\Delta({\rm
R.A.,Dec.})_{\rm HFF-JWST}=(0.02\arcsec,-0.07\arcsec)$.. The uniform Magellan
multi-band photometry over the entire field can also be used to check the
color consistency of a few cluster members lying outside the HST coverage.

In addition, A2744 is one of the cluster fields with the deepest high-
resolution observations obtained with HST thanks to the Hubble Frontier Fields
program222https://archive.stsci.edu/prepds/frontier/ (HFF, Proposal ID: 13495,
Lotz et al., 2017) and other ancillary data from previous HST observational
campaigns. The BUFFALO survey (Beyond Ultra-deep Frontier Fields And Legacy
Observations, Steinhardt et al., 2020) has since provided an extended but
shallower coverage of the cluster field. In this work, we make use of the HFF
and BUFFALO HST mosaics that are described by B23.

Finally, we exploit the new JWST NIRCam imaging of A2744 obtained within the
GLASS-JWST program ERS-1324 (P.I.: Treu, Treu et al., 2022), the UNCOVER
(Ultradeep NIRSpec and NIRCam ObserVations before the Epoch of Reionization)
Cycle 1 Treasury program (GO-2561, co-P.I.s: Labbé and Bezanson, Bezanson et
al., 2022), and the DDT program 2756 (P.I.: Chen). The footprints from these
three observational programs are shown in Figure 1 in orange, blue, and red,
respectively. The fields of view, the filters, and the data reduction are
detailed in Merlin et al. (2022) and Paris et al. (2023). Briefly, the
resulting JWST/NIRCam coverage of the cluster from the three programs includes
observations with eight different filters (F090W, F115W, F150W, F200W, F277W,
F356W, F410M, F444W), over an area of $\rm 46.5~{}arcmin^{2}$ with a
$0.031\arcsec$ pixel scale. The final $5\sigma$ magnitude limit of the images
ranges from $\sim 28.6$ AB to $\sim 30.2$ AB, depending on the location and
filters. The reduced NIRCam images and the associated multi-wavelength
catalogs are made publicly
available333https://glass.astro.ucla.edu/ers/external_data.html,444https://archive.stsci.edu/doi/resolve/resolve.html?doi=10.17909/kw3c-n857.
The photometric redshifts are computed by means of the Spectral Energy
Distribution (SED) fitting code zphot.exe (Fontana et al., 2000). Using the
same method and assumptions as in Merlin et al. (2021) and Santini et al.
(2023), we have built the stellar library by adopting the Bruzual & Charlot
(2003) models and including nebular emission lines according to Castellano et
al. (2014) and Schaerer & de Barros (2009).

###  2.2 Spectroscopic data

The A2744 cluster field counts with an extensive spectroscopic coverage
obtained with several ground and space-based facilities, see B23 for a
detailed overview. Briefly, A2744 was observed with the wide-field VIsible
Multi-Object Spectrograph (VIMOS) as part of the ESO Large Program 169.A-0595
(P.I.: Böhringer, Braglia et al., 2009), the AAOmega multi-object spectrograph
on the 3.9m Anglo-Australian Telescope (Owers et al., 2011), and the HST
WFC3/IR grism through the HST GO program
GLASS555archive.stsci.edu/prepds/glass/ (Treu et al., 2015; Schmidt et al.,
2014). The $\rm\sim 4~{}arcmin^{2}$ central region of the galaxy cluster
(green footprints in Figure 1) was then targeted with the MUSE integral field
spectrograph, mounted on the Very Large Telescope (VLT, Bacon et al., 2012),
within the GTO Program 094.A-0115 (P.I.: Richard). The data consists of five
MUSE pointings, each with total exposure times raging from 2 to 5 hours
(Mahler et al., 2018; Richard et al., 2021, B23), allowing for the
spectroscopic confirmation of a large number of multiple image systems and
cluster members.

Besides these archival data, additional VLT/MUSE spectroscopy within the
GLASS-JWST NIRCam fields was recently acquired through the ESO DDT program
109.24EZ.001 (co-P.I.s: Mason, Vanzella) on the nights of July 28 and August
20 2022 (see also Prieto-Lyon et al., 2022, for further details). The new data
comprise 5 pointings of $\rm\sim 1~{}arcmin^{2}$ each with a total exposure
time of 1 hour per pointing (see the green footprints in Figure 1). Four of
the MUSE pointings overlap with the NIRCam fields from the GLASS-JWST ERS
program while the fifth targets a prominent cluster sub-structure at a
distance between $\sim 600-775~{}\rm kpc$ from the core of A2744 (B23). The
extended HST imaging from the BUFFALO program revealed several strong lensing
features around two bright cluster members, subsequently confirmed by the new
JWST imaging (F22).

The MUSE data cubes have been reduced and analyzed following Caminha et al.
(2017a, b, 2019), using the standard reduction pipeline (version 2.8.5,
Weilbacher et al., 2020). The “autocalibration” method and the Zurich
Atmosphere Purge (ZAP, Soto et al., 2016) are then applied to improve the
overall data reduction. The five pointings have a mean full width at half
maximum (FWHM) value of $0.75\arcsec$, and the pointing covering the cluster
sub-structure has a value of FWHM$=0.86\arcsec$.

The one-dimensional spectra of all the HST detected objects are extracted
within a $0.8\arcsec$ radius circular aperture, whereas custom apertures are
considered for faint sources, based on their estimated morphology from the HST
imaging (see Section 2.1). For sources with no HST detection (i.e., HST-dark
objects) we visually inspect the continuum subtracted data-cubes to identify
emission lines. We exploit spectral templates, as well as the identification
of emission lines, to construct the new redshift catalogs. The reliability of
each redshift measurement is then quantified with the following quality flag
(QF) assignments (see also Balestra et al., 2016; Caminha et al., 2019):
“tentative” (QF = 1), “likely” (QF = 2), “secure” (QF = 3), and “based on a
single emission line” (QF = 9).

The full spectroscopic sample from the MUSE DDT program contains 313 reliable
(i.e., QF $\geq$ 2) redshift measurements, of which 12 are stars, 12 are
foreground galaxies ($z<0.28$), 82 are cluster members ($0.28\leq z\leq 0.34$)
and 207 are background objects ($z>0.34$). The redshift distributions of the
spectroscopic cluster members and background galaxies from the MUSE DDT
observations are shown in Figures 2 and 3, respectively. We note that 42 UV-
faint $z\sim 3-7$ galaxies have been published by Prieto-Lyon et al. (2022).
The full catalog is presented in Table LABEL:tab:ddtcatalog.

Figure 4: Cumulative distributions of the distances of the multiple images of
A2744 from the BCG-N. We show in solid red the distribution of the images used
as constraints in this work (149 multiple images in total), and in dotted red
the distribution of the 121 spectroscopic images. The distributions of the
spectroscopic (90 multiple images, coinciding with those used by B23 in
addition to the two images JD1A and JD1B in Table LABEL:tab:multiple_images)
and of the complete (138 multiple images) samples of multiple images used in
F22 are shown in black. The distances of the other bright galaxies in the
field (i.e., BCG-S, G1, G2, and G3) are indicated with vertical dashed blue
lines. Figure 5: JWST color image (R: F444W+F356W, G: F277W+F200W, B:
F150W+F115W) of the galaxy cluster A2744 showing the positions of the 149
multiple images, from 50 background sources, used to constrain the lens model.
The colored crosses show the positions of the 121 spectroscopically confirmed
multiple images, while the colored circles are the 28 non-spectroscopic
multiple images used in the lens model. Red, green, and blue colors highlight
the images concentrated around the cluster BCGs (117 multiple images from 39
background sources), the two bright galaxies G1 and G2 (29 multiple images
from 10 background sources), and the galaxy G3 (3 multiple images from a
single background source), respectively. The critical lines at $z_{s}=6$
obtained from the best-fit lens model are drawn in white, while those from the
previous model by B23 are shown in magenta as a comparison. Figure 6: MUSE
spectrum of the multiple image 600c (containing the multiply imaged
substructures 600.1c, 600.3c, 600.4c, and 600.5c) overlaid to a star-forming
template from Talia et al. (2012) (red line). This system is a face-on spiral
at $z=2.584$ marked as a solid green circle in the left panel (corresponding
to the white box in Figure 5 around G2). Three other images of the system
(600a,b,d) are indicated as dashed green circles; white dotted squares show
the multiple images 601.1a,b,c and 602.1a,b,c,d with no spectroscopic
redshifts (see Figure 10 and Table LABEL:tab:multiple_images).

##  3 Extended strong lensing model

In this section we describe the new strong lensing model of A2744 making use
of the new imaging and spectroscopic datasets presented in Section 2. In
particular, thanks to the deep JWST imaging and the MUSE DDT follow-up
observations, we are able to expand the samples of multiple images and
spectroscopic cluster members compared to the model presented by B23. We use
the publicly available strong lensing modeling pipeline
LensTool666https://projets.lam.fr/projects/lenstool/wiki (Kneib et al., 1996;
Jullo & Kneib, 2009) that reconstructs the total mass distribution of a galaxy
cluster implementing a Bayesian technique. We note that the lens model adopts
the new JWST astrometric grid, tied to Gaia DR3 (see Section 2.1).

###  3.1 Parameterization of the cluster total mass

Thanks to the identification of a large number of multiple images in the
external clumps (see Section 3.2), we are able to improve the characterization
of the total mass distribution of A2744 compared to our previous, HST-based
strong lensing model by B23. The total mass parameterization of the cluster
core is the same as the one adopted by B23. We thus refer the reader to that
publication for a detailed description and provide hereafter a brief summary.
Within the parametric LensTool software (Jullo et al., 2007), the total mass
of the lens is separated into several components, where the following mass
contributions are considered in this analysis:

$\phi_{tot}=\sum_{i=1}^{N_{h}}\phi_{i}^{halo}+\sum_{j=1}^{N_{BCG}}\phi_{j}^{BCG}+\sum_{k=1}^{N_{g}}\phi_{k}^{gal}+\sum_{l=1}^{N_{s}}\phi_{l}^{ENV}.$
(1)

The cluster and subhalo mass components ($\phi^{halo}$, $\phi^{BCG}$ and
$\phi^{gal}$) are parameterized using dual pseudo-isothermal elliptical mass
distributions (dPIEs, Limousin et al., 2005; Elíasdóttir et al., 2007;
Bergamini et al., 2019). The dPIE profile is defined by seven free parameters:
the position ($x$, $y$); the ellipticity (defined as
$e=\frac{a^{2}-b^{2}}{a^{2}+b^{2}}$, where $a$ and $b$ are the values of the
major and minor semiaxes, respectively); the position angle $\theta$, computed
counterclockwise from the west direction; the central velocity dispersion
$\sigma_{0}$777LensTool adopts a scaled version of this quantity, identified
as $\sigma_{LT}$, such that $\sigma_{LT}=\sigma_{0}\sqrt{2/3}$; the core
radius $r_{core}$; and the truncation radius $r_{cut}$.

The large-scale dark matter component, $\phi^{halo}$, consists of two non-
truncated elliptical dPIEs, which are initially centered on the two Brightest
Cluster Galaxies (BCGs; labeled BCG-N and BCG-S) but are free to move within a
small range around their positions (corresponding to square regions of sizes
of about $\rm 45\,kpc$ and $\rm 90\,kpc$ for the BCG-N and BCG-S,
respectively; see Table 1). As pointed out by B23, the observed positions of
several multiple image systems with small angular separation from the BCG-N
and BCG-S are better reproduced when the parameters describing their mass
contribution – $\phi^{BCG}$ and ellipticity – are optimized outside the
scaling relations adopted for the other cluster members, as discussed below.
BCGs are known to be uncommon galaxies and their independent modeling
highlights the importance of the two BCGs for an accurate lensing analysis.

Of the 177 cluster member galaxies (see Section 3.3), 172 are modeled using
circular dPIEs with a vanishing core radius and scaled with total mass-to-
light ratios increasing with their HST F160W luminosities, i.e., a relation
that is compatible with the so-called tilt of the Fundamental Plane (e.g.,
Faber et al., 1987; Bender et al., 1992), as done by B23 (see their Eq. 4).
The two free parameters in the lens model are then the values of the velocity
dispersion and truncation radius of a reference galaxy, corresponding to the
BCG-N. We report in Table 1 the values of the relevant parameters of the
scaling relations. B23 further exploited the MUSE datacube to measure the
line-of-sight stellar velocity dispersion for 85 member galaxies, down to
$m_{\rm F160W}\sim 22$, allowing for an independent calibration of the slopes
of the velocity dispersion and truncation radius scaling relations (see B23
for details).

As previously mentioned, the main difference with respect to the strong
lensing analysis presented by B23 is the modeling of the cluster infalling
regions, $\phi^{ENV}$. Due to the lack of secure multiple image systems around
the massive structures in the northwestern region of the cluster prior to the
JWST/NIRCam imaging, the B23 reference LM-model included a simple description
of the mass contribution from three external clumps, associated with the three
brightest galaxies (G1, G2, and G3), as singular isothermal sphere (SIS)
profiles. The identification of 29 (3) multiple images around the galaxies
G1-G2 (G3) allows now for a more accurate total mass reconstruction of these
infalling structures, $\phi^{ENV}$, which is decomposed into the following
mass contributions:

$\phi^{ENV}=\phi_{G1-G2}^{halo}+\phi_{G3}^{halo}+\phi_{G1}+\phi_{G2}+\phi_{G3}$
(2)

The first two terms correspond to the cluster component that is modeled as two
cluster-scale non-truncated elliptical dPIEs: one associated with the galaxies
G1 and G2 and allowed to move within a large square region containing the two
galaxies (see Table 1, corresponding to a region of about $\rm 270\,kpc\times
180\,kpc$), and a second one centered on the position of the galaxy G3. The
parameters describing the mass contribution (i.e., the velocity dispersion and
cut radius) of the three galaxies G1, G2 and G3 are individually optimized,
within large flat priors. In addition, the ellipticity parameters of G1 and G2
are left free to vary (see Table 1). As mentioned in Section 3.3, the
parametric description of the cluster outskirsts is further enhanced by the
inclusion of a sample of spectroscopic cluster members from the new MUSE/DDT
observations (see Figure 1 and Section 3.3).

Finally, the redshifts of the 8 photometric multiple image systems are also
optimized in the lens model within uninformative flat priors. We note that the
redshift value of all the images of Sys-200 (i.e., A200.1a,b, B200.2a,b, and
C200.3a,b) is imposed to be equal in the optimization of the lens model (and
therefore corresponding to a single free parameter).

The priors assumed for the values of the parameters of the mass profiles
included in our reference lens model are reported in the upper part of Table
1, while the optimized values are provided in the bottom panel. The best-
fitting values of the model parameters that describe the total mass
distribution of the lens are obtained by minimizing on the image plane the
distance between the observed and the model-predicted point-like positions of
the multiple images through a $\chi^{2}$ function (see Eq. 1 in B23).
Following B23, we assign an initial positional uncertainty to each image
depending on the value of the Positional Quality Flag (QP), that are given in
Table LABEL:tab:multiple_images. These values are then rescaled, prior to the
sampling of the posterior distributions, in order to obtain a $\chi^{2}$ value
close to the number of degrees of freedom (dof) in the model, defined as:
$\mathrm{dof}=2\times[N^{tot}_{im}-N_{fam}]-N_{freepar}=N_{con}-N_{freepar}$,
where $N^{tot}_{im}$ and $N_{fam}$ refer, respectively, to the total number of
multiple images and families included in the lens model. $N_{con}$ and
$N_{freepar}$ are the number of model constraints and free parameters,
respectively. The total mass model of A2744 has $N_{freepar}=50$ free
parameters, including the 8 optimized redshifts of the non-spectroscopic
systems, leading to 148 dof. This model represents an extension of that
presented by B23, and thus is labeled as such in the following (Extended Model
or EM).

Figure 7: Displacements, $\boldsymbol{\Delta}_{i}$, along the $x$ and $y$
directions between the observed and model predicted positions of the 149
multiple images (from 50 background sources) included in the lens model. The
lens model is characterized by a $\Delta^{\rm TOT}_{rms}=0.43\arcsec$
corresponding to the radius of the black dashed circle. The 117 multiple
images, from 39 background sources, concentrated around the two BCGs are
plotted in red and have a $\Delta_{rms}=0.46\arcsec$. Similarly, the 29
multiple images (from 10 background sources) forming around the two bright
galaxies G1 and G2 (with $\Delta_{rms}=0.20\arcsec$), and the 3 multiple
images (from a single background source) around the galaxy G3 (with
$\Delta_{rms}=0.73\arcsec$) are plotted in green and blue, respectively. The
gray histograms refer to the complete sample of multiple images. Table 1:
Input and output parameters of the extended lens model for the galaxy cluster
A2744 presented in this work.

|  Input parameter values and assumed priors
---|---
| $x\,\mathrm{[arcsec]}$ | $y\,\mathrm{[arcsec]}$ | $e$ | $\theta\ [^{\circ}]$ | $\sigma_{LT}\,\mathrm{[km\ s^{-1}]}$ | $r_{core}\,\mathrm{[arcsec]}$ | $r_{cut}\,\mathrm{[arcsec]}$
Cluster-scale halos |  $1^{st}$ Cluster Halo | $-5.0\,\div\,5.0$ | $-5.0\,\div\,5.0$ | $0.0\,\div\,0.9$ | $0.0\,\div\,180.0$ | $300\,\div\,1500$ | $0.0\,\div\,30.0$ | $2000.0$
$2^{nd}$ Cluster Halo | $-27.9\,\div\,-7.9$ | $-30.0\,\div\,-10.0$ | $0.0\,\div\,0.9$ | $0.0\,\div\,90.0$ | $300\,\div\,1500$ | $0.0\,\div\,30.0$ | $2000.0$
G1,G2 Halo | $90.0\,\div\,150.0$ | $80.0\,\div\,120.0$ | $0.0\,\div\,0.9$ | $0.0\,\div\,180.0$ | $300\,\div\,1500$ | $0.0\,\div\,30.0$ | $2000.0$
G3 Halo | $24.2$ | $155.8$ | $0.0\,\div\,0.9$ | $0.0\,\div\,180.0$ | $100\,\div\,1500$ | $0.0\,\div\,30.0$ | $2000.0$
Subhalos | BCG-N | $0.0$ | $0.0$ | $0.0\,\div\,0.9$ | $0.0\,\div\,180.0$ | $200\,\div\,400$ | $0.0001$ | $0.1\,\div\,50.0$
BCG-S | $-17.9$ | $-20.0$ | $0.0\,\div\,0.9$ | $0.0\,\div\,180.0$ | $200\,\div\,400$ | $0.0001$ | $0.1\,\div\,50.0$
G1 | $99.4$ | $85.9$ | $0.0\,\div\,0.9$ | $0.0\,\div\,180.0$ | $150\,\div\,350$ | $0.0001$ | $0.1\,\div\,50.0$
G2 | $138.3$ | $99.8$ | $0.0\,\div\,0.9$ | $0.0\,\div\,180.0$ | $150\,\div\,350$ | $0.0001$ | $0.1\,\div\,50.0$
G3 | $24.2$ | $155.8$ | $0.0$ | $0.0$ | $150\,\div\,400$ | $0.0001$ | $0.1\,\div\,50.0$
Scaling relations | $\boldsymbol{N_{gal}=}172$ | $\boldsymbol{m_{\mathrm{F160W}}^{ref}=}17.34$ | $\boldsymbol{\alpha=}0.40$ | $\boldsymbol{\sigma_{LT}^{ref}=}190\,\div\,300$ | $\boldsymbol{\beta_{cut}=}0.41$ | $\boldsymbol{r_{cut}^{ref}=}0.5\,\div\,10.0$ | $\boldsymbol{\gamma=}0.20$

|  Optimized output parameters
---|---
| $x\,\mathrm{[arcsec]}$ | $y\,\mathrm{[arcsec]}$ | $e$ | $\theta\ [^{\circ}]$ | $\sigma_{LT}\,\mathrm{[km\ s^{-1}]}$ | $r_{core}\,\mathrm{[arcsec]}$ | $r_{cut}\,\mathrm{[arcsec]}$
Cluster-scale halos |  $1^{st}$ Cluster Halo | $-1.8^{+0.6}_{-0.6}$ | $-3.5^{+1.4}_{-1.1}$ | $0.4^{+0.1}_{-0.1}$ | $79.0^{+5.3}_{-7.0}$ | $558^{+33}_{-35}$ | $9.3^{+1.1}_{-1.1}$ | $2000.0$
$2^{nd}$ Cluster Halo | $-18.7^{+0.5}_{-0.4}$ | $-16.3^{+0.5}_{-0.5}$ | $0.4^{+0.1}_{-0.1}$ | $55.2^{+2.8}_{-2.7}$ | $603^{+25}_{-25}$ | $8.1^{+0.6}_{-0.6}$ | $2000.0$
G1,G2 Halo | $130.2^{+2.2}_{-2.8}$ | $97.9^{+0.8}_{-1.1}$ | $0.7^{+0.1}_{-0.1}$ | $23.8^{+2.1}_{-1.9}$ | $781^{+35}_{-38}$ | $16.8^{+2.0}_{-2.0}$ | $2000.0$
G3 Halo | $24.2$ | $155.8$ | $0.1^{+0.2}_{-0.1}$ | $14.1^{+25.7}_{-67.1}$ | $799^{+40}_{-37}$ | $22.9^{+3.8}_{-4.4}$ | $2000.0$
Subhalos | BCG-N | $0.0$ | $0.0$ | $0.6^{+0.1}_{-0.2}$ | $87.5^{+5.8}_{-8.1}$ | $266^{+15}_{-12}$ | $0.0001$ | $31.8^{+11.6}_{-12.1}$
BCG-S | $-17.9$ | $-20.0$ | $0.7^{+0.1}_{-0.1}$ | $23.7^{+3.3}_{-3.3}$ | $296^{+12}_{-14}$ | $0.0001$ | $44.9^{+3.7}_{-7.1}$
G1 | $99.4$ | $85.9$ | $0.3^{+0.3}_{-0.2}$ | $17.3^{+21.5}_{-54.6}$ | $232^{+16}_{-18}$ | $0.0001$ | $29.0^{+11.0}_{-9.7}$
G2 | $138.3$ | $99.8$ | $0.4^{+0.2}_{-0.2}$ | $-14.0^{+14.7}_{-19.8}$ | $231^{+15}_{-16}$ | $0.0001$ | $23.3^{+13.2}_{-11.5}$
G3 | $24.2$ | $155.8$ | $0.0$ | $0.0$ | $332^{+38}_{-38}$ | $0.0001$ | $13.4^{+8.4}_{-6.3}$
Scaling relations | $\boldsymbol{N_{gal}=}172$ | $\boldsymbol{m_{\mathrm{F160W}}^{ref}=}17.34$ | $\boldsymbol{\alpha=}0.40$ | $\boldsymbol{\sigma_{LT}^{ref}=}246^{+9}_{-10}$ | $\boldsymbol{\beta_{cut}=}0.41$ | $\boldsymbol{r_{cut}^{ref}=}9.3^{+0.5}_{-1.0}$ | $\boldsymbol{\gamma=}0.20$

###  3.2 Multiple image catalog

This work extends the multiple image catalog presented by B23, which was based
on the deep HST imaging and MUSE observations of the cluster core. The B23
sample consisted of 90 multiple images from 30 background sources, spanning a
redshift range between $z=1.69$ and $z=5.73$. For further details, we refer
the reader to Table A.1 of B23. By exploiting the ancillary and the recently
obtained JWST/NIRCam imaging and new VLT/MUSE data, we identify additional
multiple images both in the cluster core and in the external clumps.

Our new strong lensing model includes 149 multiple images from 50 background
sources, of which 121 are spectroscopically confirmed and span an extended
redshift range between $z=1.03$ and $z=9.76$ (see Figure 3). This represents
an increase of $\sim 66\%$ compared to the B23 sample. The cumulative
distribution of the distances of both the spectroscopic and photometric
multiple images included in the lens model from the BCG-N is shown in Figure 4
(red solid line), and compared to the one used by F22 (black solid line). The
complete sample presented in this work includes 11 more multiple images than
that from F22, and thus represents the largest set of constraints included in
a lens model of A2744 to date. The set of spectroscopic images is especially
noteworthy. In more general terms, A2744 is the second cluster with the
largest sample of secure multiple images after the lens cluster MACS
J0416.1$-$2403, that currently counts 237 (Bergamini et al., 2023b). For
consistency, we present in Table LABEL:tab:multiple_images the properties (in
the JWST-based astrometry) of the complete sample of multiple images used as
constraints in this work, included those presented by B23. The multiple image
positions are shown in Figure 5, where the crosses (circles) denote the
spectroscopic (photometric) images. We briefly describe below the
identification of the new multiple images with respect to those from B23.

\- Cluster core: Following B23, we re-analyze the MUSE datacube, extracting
the spectra of sources predicted by the lens model and measuring the redshift
of several multiple images using faint emission lines and the cross-
correlation with different templates. We thus include 14 additional
spectroscopically confirmed multiple images in the cluster core, from 5
systems. These new images are flagged by a star symbol in Table
LABEL:tab:multiple_images.

Recent JWST observations have allowed for the spectroscopic confirmation of
two additional multiple images in the cluster core as part of the GLASS-JWST
ERS program (identified by an asterisk in Table LABEL:tab:multiple_images).
While image 3c is too faint for a secure redshift measurement with VLT/MUSE,
JWST/NIRISS spectroscopy enables the detection of [OII]$\lambda$3727,3729 at
the expected wavelength position of 1.856 $\rm\mu m$, and consistent with the
counterimages 3a and 3b (Vanzella et al., 2022; Lin et al., 2023). The
$z_{phot}=9.8$ triply lensed candidate system reported by Zitrin et al. (2014)
was observed with NIRSpec prism spectroscopy (DDT 2756; P.I.: Chen) resulting
in a spectroscopic redshift measurement of $9.756^{+0.017}_{-0.007}$ of the
image JD1B (Roberts-Borsani et al., 2022b). The other two images, JD1A and
JD1C, which are not yet spectroscopically confirmed, are considered at the
same redshift as JD1B, consistent with their photometric redshifts.

The list of multiple images is further enhanced in the cluster core by
including 3 photometric strongly lensed sources, with a total of 9 multiple
images, securely identified in the JWST/NIRISS and JWST/NIRCam imaging from
the GLASS-JWST-ERS program. In particular, Sys-53 consists of a triply imaged
active galactic nucleus (AGN) candidate analyzed in Furtak et al. (2022b). The
very peculiar color and compactness of the source make the association of the
three multiple images of the system particularly secure.

The final sample in the main cluster core includes 117 multiple images from 39
background sources, of which 108 are spectroscopically confirmed.

\- External clumps: The main improvement with respect to B23 is the
identification of a large number of multiple images around the galaxies G1 and
G2 in the northwestern external clump. While the ancillary shallow HST imaging
of the cluster outskirts hinted at the presence of strong lensing features,
the recent deep, high-resolution JWST/NIRCam data clinched the identification
of several photometric systems. We identify 29 multiple images from 10
background sources around the galaxies G1 and G2, and 3 multiple images from a
single background source around the galaxy G3. We also include multiply lensed
clumps within resolved extended sources which have shown to be particularly
efficient at constraining the position of the critical curves (e.g. Grillo et
al., 2016, B23). In particular, thanks to the MUSE DDT observations we are
able to measure the redshift of the lensed face-on spiral galaxy (ID 600)
around G2. Due to the light contamination by a star and by G2 of the images
600a and 600b, respectively, a secure spectroscopic confirmation is not
currently possible for those images. The MUSE spectrum of image 600c,
extracted within a circular aperture of $0.8\arcsec$ diameter, is shown in
Figure 6, yielding a redshift measurement of $2.584$. This secure redshift is
based on the cross-correlation of the MUSE spectrum with several spectral
templates of star-forming galaxies with appropriate rest frame UV coverage,
which consistently shows a significant peak at the quoted redshift with a
variation of $\Delta z=0.003$. This is, to date, the only multiple image
system spectroscopically confirmed in the northwestern external clump.

The observed image positions of the 149 multiple images are used as
constraints in the new lens model, providing in total $N_{con}=198$
constraints.

###  3.3 Selection of cluster galaxies

For the selection of the cluster galaxies used in the lens model to describe
the subhalo mass component, we follow the procedure of B23 taking advantage of
the enhanced spectroscopic coverage in the northwestern clump. Initially,
cluster members are selected as the galaxies with a spectroscopic redshift in
the range $0.28\leq z\leq 0.34$, corresponding approximately to an interval of
$\pm 6000$ km/s rest-frame velocities around the median cluster redshift
$z_{CL}=0.3072$, and magnitudes brighter than $m_{\mathrm{F160W}}=24$ (a
dedicated work on the properties of cluster members is presented by Vulcani et
al. 2023). The larger range in redshift is motivated by the complexity of the
total mass distribution of A2744, a multi-component merger (see e.g., Merten
et al., 2011; Owers et al., 2011). This is clearly shown in Figure 2, where
the velocity difference between the BCG-N and BCG-S is of about 4000 km/s. The
new MUSE DDT data add 82 members to the full spectroscopic sample (see Section
2.2) which now includes 669 cluster galaxies, mostly based on the MUSE
observations (Richard et al., 2021, B23). When compiling this catalog, we only
consider secure or probable/likely redshift measurements from different
sources (see Section 2.2). The redshift distribution of the cluster members
over the cluster area is shown in Figure 2, while their spatial distribution
is shown in the right panel of Figure 1. The spectroscopic sample is then
completed down to $m_{\mathrm{F160W}}=24$ by adding the photometric members
identified with the convolution neural network (CNN) technique described by
Angora et al. (2020). Performance tests generally show a cluster member
identification rate (completeness) of $\sim\\!90\%$ with a purity of
$\sim\\!95\%$, superior to those from traditional color selection methods
(Angora et al., 2020).

The large number of cluster galaxies makes the extended lens model presented
here computationally very expensive, owing to the calculation of the
deflection angle induced by each individual cluster member. With the aim of
limiting the computational time increase, we reduce the number of faint
cluster galaxies in the lens model and study how the positional rms value,
$\Delta_{rms}$, varies when considering different magnitude threshold values
for the cluster members in the F160W band. We find no significant variation in
$\Delta_{rms}$ when only including in the model the galaxies with magnitudes
$m_{\rm F160W}<21$ and thus, we limit the number of cluster galaxies to those
brighter than $m_{\rm F160W}=21$. A similar finding is presented by Raney et
al. (2021), which shows that considering different magnitude limits for the
selection of member galaxies in the lens models of two HFF clusters, between
21 and 26 in the F814W band, results in little variations in the values of
$\Delta_{rms}$ or other metrics (see their Figure 4).

With the new magnitude cut, $m_{\rm F160W}=21$, 163 spectroscopic members are
included in the lens model (see the red histogram in Figure 2), in addition to
14 non-spectroscopic galaxies, over an area of $\sim\\!45$ arcmin2. The new
spectroscopic cluster members are concentrated in the NW mass clumps, around
G1, G2, and G3 (see Figure 1). As a comparison, the B23 strong lensing model
included 225 members with a limit 3 magnitudes fainter.

Figure 8: Cumulative projected total mass profiles of the galaxy cluster A2744
as a function of the projected distance from the bright galaxies BCG-N (top
left), G1 (top right), G2 (bottom left), and G3 (bottom right). The mass
profiles obtained from the extended lens model (EM) are drawn in black. The
small vertical black and blue bars show the projected distances of the
observed multiple images and of the cluster member galaxies considered in the
model, respectively. We also highlight, using vertical dashed lines, the
positions of the bright cluster galaxies BCG-N, BCG-S, G1, G2, and G3. In red,
we plot the cumulative projected total mass profiles from the previous lens
model by B23. The projected distances of the multiple images constraining that
model are marked with small vertical red bars. At the bottom of each panel, we
show the ratio between the total mass profiles obtained from the B23 model and
the extended model presented here. Figure 9: Comparison between the
magnification factors, and related errors, obtained from the A2744 extended
lens model presented in this paper and the previous model by B23. The black
crosses indicate the observed positions of the 90 multiple images used in B23.
The white crosses indicate instead those for the 59 new multiple images from
this work. Left: Relative difference between the median magnification maps
(see Section 4) obtained from the extended and B23 lens models. Right: Ratio
between the relative errors on the magnification maps values estimated from
500 realizations of the lens models obtained by randomly extracting parameter
samples from the model MCMC chains. Figure 10: Probability density
distributions for the redshift values of the six non-spectroscopic systems of
multiple images included in the lens model. The gray histograms correspond to
the marginalized probability distributions obtained from the lens model
optimization. The orange, blue, green, and magenta distributions represent the
photometric redshift probability density distributions measured for the
multiple images of the same system. On the top of the histograms, we show
color cutouts centered on the corresponding multiple images; the green circles
have a radius of $1\arcsec$. The remaining two non-spectroscopic systems of
multiple images considered in the lens model have optimized redshift values of
$z_{\rm EM}(\mathrm{Sys}\mbox{-}200)=5.9^{+2.4}_{-2.3}$ and $z_{\rm
EM}(\mathrm{Sys}\mbox{-}301)=4.1^{+1.2}_{-1.2}$. None of their images have a
measured photometric redshift.

##  4 Results

The best-fit Extended Model is characterized by a precision of
$\boldsymbol{\Delta}_{rms}^{\mathrm{TOT}}=0.43\arcsec$ in reproducing the
observed positions of the 149 multiple images used as constraints in the lens
model (see Section 3.1). In Figure 7, we show for each multiple image the
displacement $\boldsymbol{\Delta}_{i}$ between its observed and model
predicted positions. To quantify the precision of the lens model around the
three main massive structures within the considered area (see Figure 1), we
adopt different colors to distinguish the multiple images forming around the
main cluster BCGs (red), the two bright galaxies G1 and G2 (green), and the
cluster galaxy G3 (blue). We note that the same color scheme is adopted in
Figure 5 to indicate the observed positions of the multiple images. The
positions of the 117 multiple images forming around the main cluster BCGs are
reproduced with a precision of
$\boldsymbol{\Delta}_{rms}^{\mathrm{BCGs}}=0.46\arcsec$. This is a remarkable
result considering that this value is just $0.09\arcsec$ larger than that
obtained using the previous model by B23, which included 27 fewer multiple
images in the same region. An even higher precision of
$\boldsymbol{\Delta}_{rms}^{\mathrm{G1,G2}}=0.20\arcsec$ is found in
reproducing the observed positions of the 29 multiple images forming around G1
and G2. In contrast, the $\mathrm{EM}$ precision decreases to
$\boldsymbol{\Delta}_{rms}^{\mathrm{G3}}=0.73\arcsec$ around galaxy G3. Here,
only three non-spectroscopic images (700.a, 700.b, and 700.c) of a single
background galaxy are included in the lens model. We notice that the
deflecting contribution of the massive clump surrounding G3 is mainly driven
by its influence on the many multiple images observed relatively far from its
center, i.e. in the cluster core. For this reason, the optimized values of the
parameters of this clump might not be able to reproduce as well as for the
other sources the three multiple images appearing close to its center.

A further confirmation of our previous results comes from the cumulative
projected total mass profiles, presented in Figure 8. These profiles and the
associated statistical errors are computed considering 500 realizations
obtained by randomly extracting parameter samples from the $\mathrm{EM}$ MCMC
chains. The black and red solid lines correspond to the median mass profiles,
while the colored shaded bands are limited by the 16th and 84th percentiles.
Thanks to the large number of spectroscopically confirmed multiple images
observed around the main cluster core, the total mass distribution of the
cluster is reconstructed robustly in this region (top-left panel of the
figure). This results in a cumulative projected total mass profile measured
with very small statistical errors (black band in the figure). By comparing
the results from this $\mathrm{EM}$ with those by B23, we find a remarkably
good agreement. In particular, the cumulative projected total mass profiles of
the two models differ by less than 3% close to the BCG-N core and less than 1%
at distances between 20 kpc and 310 kpc. Unsurprisingly, larger differences
are found in the regions surrounding the three external clumps. On the top-
right and bottom-left panels of Figure 8, we plot the cumulative projected
total mass profiles as a function of the distance from the G1 and G2 galaxies,
respectively. These profiles demonstrate that the inclusion in the
$\mathrm{EM}$ of the multiple images identified with JWST/NIRCam imaging
around G1 and G2 reduces significantly the statistical uncertainty in the
total mass estimates. This is evidenced by the smaller extension of the black
bands with respect to the red ones. While the total mass profile around G1 is
compatible with the previous result by B23, a clear difference between the
total mass profiles is found in the vicinity of G2. The newly identified
multiple images around G1 and G2 – especially the 13 lensed substructures of
the spectroscopically confirmed spiral galaxy at $z=2.584$ (see Figure 6) –
are thus key to precisely reconstructing the total mass distribution in this
region. Similarly, we remark a large discrepancy between the total mass
profiles obtained from the $\mathrm{EM}$ and the B23 model, as displayed in
the bottom-right panel of Figure 8. In this case, the three non-spectroscopic
multiple images, from a single background source, lying close to the galaxy G3
can only poorly constrain the total mass distribution of the G3 halo. This is
reflected into the black error band which is more extended than those in the
other panels. We remark that the new subhalo scaling relation is consistent
over more than 5 magnitudes with that measured by B23 with MUSE spectroscopy,
within the $1\sigma$ statistical uncertainties (see Table 1 and their Figure
4). This highlights the importance of an independent determination of the
scaling relation in reducing inherent model degeneracies between the cluster-
and subhalo mass components.

On the left panel of Figure 9, we show the relative difference between the
median magnification values derived from the $\mathrm{EM}$
($\overline{\mu}_{\mathrm{EX}}$) and B23 model
($\overline{\mu}_{\mathrm{B23}}$). The median magnification maps are obtained
by considering 500 random realizations of the lens models and computing the
median magnification value in each pixel. The right panel of Figure 9 shows
instead the ratio of the relative errors on the predicted magnification values
for the two models. In this case, the absolute errors
$\Delta\mu_{\mathrm{EM}}$ and $\Delta\mu_{\mathrm{B22}}$ are computed from the
16th and 84th percentiles of the magnification distributions in each pixel.

In the region surrounding the main cluster, the $\mathrm{EM}$ and B23 models
predict very similar magnification values and associated errors (see the
bottom-left region in the maps). This result is corroborated by the similarity
of the B23 (magenta) and $\mathrm{EM}$ (white) critical lines displayed in
Figure 5 for a source at $z_{s}=6$. Within the main cluster, non-negligible
differences between the predicted magnification are observed only at distances
beyond $\sim 28\arcsec$ North-West from the BCG-N, a region deprived of
observed multiple images. The main cluster critical line predicted by the
best-fit $\mathrm{EM}$ becomes resonant with the secondary critical lines
produced by two bright galaxies. The consistency between the B23 and the
$\mathrm{EM}$ models in the main cluster region demonstrates that the modeling
parameterization from B23 is well suited to robustly characterize its total
mass distribution. As expected, closer to the external clumps surrounding
galaxies G1, G2, and G3 (in the top and top-right regions of Figure 9) the
differences between the $\mathrm{EM}$ and B23 models are significant. In
particular, the magnification maps reach relative differences of more than
$\pm 100\%$ in addition to the significant discrepancy on the shape of the
critical lines. In fact, the critical lines obtained by the new $\mathrm{EM}$
are significantly more centrally concentrated with respect to the large
critical lines produced by the simplistic SIS mass distributions used by B23
to parameterize the external clumps, illustrating the importance of adding
strong lensing constraints in those regions. The right panel of Figure 9
demonstrates that the $\mathrm{EM}$ model is characterized by similar relative
errors to B23 in the main cluster region in predicting the magnification
values, whereas significantly smaller relative errors are found around the
external clumps compared to B23. Particular attention has to be paid to the
red ring-like and dark blue areas centered on the external clumps. These
regions wrap the critical lines of the B23 model and $\mathrm{EM}$ computed
for a source at $z_{s}=3$ (corresponding to the redshift of the magnification
maps). We note that the magnification values presented by Castellano et al.
(2022) for the $z\sim 10$ galaxies, based on B23, all in the low$-\mu$ regime
($\mu<3.8$), are well in agreement with the values computed with the new lens
model.

An additional way to demonstrate the robustness of the lens model is to
compare the model-predicted redshift values of the non-spectroscopic systems
with the photometric redshift estimates for their multiple images. In Figure
10, we show a comparison between the probability density distributions of the
redshift values obtained from the $\mathrm{EM}$ lens model (gray histogram)
and the photometric redshift estimated by exploiting the JWST and HST multi-
band data (see Section 2.1) as the colored histograms, for the six non-
spectroscopic multiple image systems included in the lens model. The remaining
two non-spectroscopic systems (i.e., Sys-301 and Sys-200) used in the model do
not have reliable photometric redshift measurements for any of their images,
due to their faintness and to light contamination from nearby objects and, for
that reason, are not included in the figure. The photometric Sys-7, Sys-28,
and Sys-53 are located in the main cluster field (around the cluster BCGs) and
have three multiple images each, corresponding to the nine red circles in
Figure 5. From the JWST and HST multi-band observations, we obtain consistent
photometric redshift estimates for two out of the three multiple images of
Sys-7 and Sys-28 (i.e., 7a, 7c, 28a, and 28b). While for Sys-28 the
photometric redshifts are in very good agreement with the $\mathrm{EM}$
predicted redshift, we find that the model-predicted redshift of Sys-7 is
slightly underestimated compared to the photometric estimates. Regarding
Sys-53, the photometric redshift probability distribution for image 53b peaks
at $z^{peak}_{ph}(53b)=1.575$, that is well below the photometric redshift
values inferred for the other two multiple images, 53a and 53c (yellow and
green histograms in the plot, respectively) and the model-predicted redshift.
The likely reason for this discrepancy is the light contamination produced by
a cluster galaxy (with $m_{\mathrm{F160W}}=22.05$) residing at a projected
distance of just $0.9\arcsec$ from the image 53b. Moreover, Furtak et al.
(2022b) have measured a photometric redshift of
$z_{ph}(\rm{Sys\mbox{-}53})\sim 7.7$, in very good agreement with our model-
predicted redshift and with the photometric redshifts of the images 53a and
53c from this work. Sys-601 and Sys-602 both reside around the bright galaxy
G2 and count three and four multiple images, respectively (these correspond to
the seven green circles around the galaxy G2 in Figure 5, see also the dashed
white squares in Figure 6). The multi-band photometric data allow for the
estimate of the photometric redshifts for all the multiple images of the
systems. These are found to be compatible among each other and with the lens
model-predicted redshift probability density distributions. We note that we
obtain identical redshift values for the two systems. Considering that the
Sys-601 and Sys-602 sources are just $2.1\arcsec$ apart (corresponding to 17.5
kpc at $z=2.3$), we can argue that these are likely two galaxies belonging to
the same gravitationally bound system. We also note that the positions of the
images of the Sys-601 and Sys-602 are extremely well reproduced by the
$\mathrm{EM}$ with values of
$\Delta_{rms}^{\mathrm{Sys\mbox{-}601}}=0.28\arcsec$ and
$\Delta_{rms}^{\mathrm{Sys\mbox{-}601}}=0.22\arcsec$. Finally, Sys-700
consists of three multiple images forming around the galaxy G3 (blue circles
in Figure 5). Also in this case, the lens model-predicted redshift is in very
good agreement with the photometric redshift estimated for the single image
700.1c.

##  5 Conclusions

We have presented a new high-precision strong lensing model of the galaxy
cluster Abell 2744 ($z=0.3072$) based on the deep, wide-field JWST/NIRCam
imaging (Treu et al., 2022; Bezanson et al., 2022; Paris et al., 2023) and new
MUSE DDT observations, together with extensive archival spectro-photometric
datasets including two recent spectroscopic redshifts with JWST/NIRISS and
JWST/NIRSpec (Vanzella et al., 2022; Lin et al., 2023; Roberts-Borsani et al.,
2022b). The model is constrained by 149 multiple images (121 of which are
spectroscopically confirmed) from 50 background sources, spanning a very wide
redshift range between $1.03$ and $9.76$. The multiple image catalog compiled
for this cluster is the largest to date (see Figure 4), and represents an
increase of about $66\%$ with respect to our previous, HST-based lens model
(B23). Specifically, we have included 27 additional multiple images in the
main cluster core (18 of which are spectroscopically confirmed) thanks to a
re-analysis of faint multiple images in the archival MUSE and the JWST/NIRISS
data. In addition, the deep, high-resolution JWST/NIRCam observations have
proved to be key in the identification of a large number of multiple image
systems around the external clumps, in particular those associated with the
bright galaxies G1 and G2 (see also F22), where we have considered 29 multiple
images from 10 background sources. By analyzing the new data from the MUSE DDT
program, we have presented the first spectroscopic redshift of a multiple
image system in the G1-G2 external clump, a face-on spiral galaxy at
$z=2.584$.

The model includes 177 cluster member galaxies, 163 of which are
spectroscopically confirmed (24 of them are newly confirmed with the new MUSE
data), and 14 are securely identified as cluster members with a CNN deep-
learning technique (Angora et al., 2020). The new subhalo scaling relation is
consistent, within the $1\sigma$ statistical uncertainties, with the measured
one shown by B23, demonstrating the accurate total mass modeling of the lens
cluster.

The total root-mean-square separation between the observed and model-predicted
positions of the 149 multiple images is
$\boldsymbol{\Delta}_{rms}^{\mathrm{TOT}}=0.43\arcsec$ on the image plane (see
Figure 7). The achieved precision is similar to that obtained by B23
($\boldsymbol{\Delta}_{rms}^{\mathrm{TOT}}=0.37\arcsec$), despite the
significantly larger number of multiple images considered in this work. We
note that the precision of our model is significantly better than that of the
JWST-based lens model presented by F22, who quote a
$\boldsymbol{\Delta}_{rms}^{\mathrm{TOT}}=0.66\arcsec$ on the lens plane. The
newly included multiple image systems around the external clumps represent a
leap forward in the lens modeling of Abell 2744 in terms of precision and
accuracy. While the cumulative projected total mass profiles and the
magnification maps obtained from our new model are highly consistent with
those obtained by B23 in the main cluster core, these quantities are robustly
reconstructed at larger radii with significantly smaller statistical
uncertainties (see Figures 8 and 9) thanks to the newly included constraints.
The robustness of the lens model is further demonstrated by the consistency
between the model-predicted and photometric redshift estimates of 6 non-
spectroscopic multiple image systems included in the model (see Figure 10).

Our new lens model holds a fundamental role in the study of the lensed high-
redshift sources that are being observed by the JWST in this cluster field
(e.g., Castellano et al., 2022; Prieto-Lyon et al., 2022; Morishita et al.,
2022), in particular in the high-magnification regime (e.g., Roberts-Borsani
et al., 2022b; Vanzella et al., 2022). Further improvements will be possible
when additional multiple image systems will be spectroscopically confirmed
with on-going JWST spectroscopic observations.

The lens model presented in this work will be made publicly available with the
publication of this paper through our recently developed Strong Lensing Online
Tool, SLOT (B23), allowing researchers to take full advantage of the
predictive and statistical results of our lens model through a user-friendly
graphical interface. The complete catalog of secure redshift measurements
(i.e., QF $\geq$ 2) from the new VLT/MUSE DDT observations (see Section 2.2)
will also be released upon publication.

Support for program JWST-ERS-1324 was provided by NASA through a grant from
the Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-03127.
The Hubble Frontier Field program (HFF) and the Beyond Ultra-deep Frontier
Fields And Legacy Observations (BUFFALO) are based on the data made with the
NASA/ESA Hubble Space Telescope. The Space Telescope Science Institute is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5-26555. ACS was developed under NASA Contract NAS
5-32864. Based also on observations collected at the European Southern
Observatory for Astronomical research in the Southern Hemisphere under ESO
programmes with IDs 094.A-0115 (PI: Richard). We acknowledge financial support
through grants PRIN-MIUR 2015W7KAWC, 2017WSCC32, and 2020SKSTHZ. AA has
received funding from the European Union’s Horizon 2020 research and
innovation programme under the Marie Skłodowska-Curie grant agreement No
101024195 — ROSEAU. GBC thanks the Max Planck Society for support through the
Max Planck Research Group for S. H. Suyu and the academic support from the
German Centre for Cosmological Lensing. MM acknowledges support from the
Italian Space Agency (ASI) through contract “Euclid - Phase D”. We acknowledge
funding from the INAF “main-stream” grants 1.05.01.86.20 and 1.05.01.86.31. We
acknowledge support from the INAF Large Grant 2022 “Extragalactic Surveys with
JWST” (PI: Pentericci). This research is supported in part by the Australian
Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions
(ASTRO 3D), through project number CE170100013. The GLASS-JWST data are
associated with DOI 10.17909/mrt6-wm89 (NIRCam) and 10.17909/9a2g-sj78
(NIRSpec). The UNCOVER NIRcam data are associated with DOI 10.17909/zn4s-0243.
The JWST data from the DDT program 2756 are associated with DOI
10.17909/te6f-cg91.

##  Appendix A Catalog of multiple images in Abell 2744

We present here the complete catalog of multiple images included in the new
lens model in the JWST WCS (see Section 2.1). For consistency, we also list
the multiple images presented in the B23 HST-based lens model (marked with a
dagger symbol, $\dagger$) that were anchored to the HFF WCS. The multiple
images identified with a star symbol, $\star$, indicate those newly
spectrocopically confirmed with the central MUSE datacube, while those with an
asterisk, $\ast$, have been spectroscopically confirmed with JWST/NIRISS
(Vanzella et al., 2022; Lin et al., 2023) and JWST/NIRSpec (Roberts-Borsani et
al., 2022b). Further details can be found in B23 and in Section 3.2.

Table 2: List of the multiple images used as constraints in the Extended Model we are presenting. The multiple images of the same background source share the same numerical part of the ID (first column). In the fourth column, we quote the redshifts of the sources. The ‘positional quality flag’, QP, quantifies the precision in determining the on-sky position of the multiple images. QP=1 corresponds to images with a compact HST or JWST emission. The positional error assumed on these images in the lens model is the lowest. QP=2 stands for a diffuse or elongated HST or JWST emission. An intermediate positional error is associated to these images. Images with QP=3 are only detected in the MUSE datacube or are characterized by a very diffuse emission. These have the largest positional errors. In the last column, we report the region of the cluster where the multiple images are located. These regions are identified using the name of the brightest galaxies they contain (see Figure 5). ID | R.A. | Dec. | QP | z | QF | Location
---|---|---|---|---|---|---
| [deg.] | [deg.] |  |  |  |
1.1a$\dagger$ | $3.597551$ | $-30.403906$ | 1 | 1.688 | 3 | BGCs
1.1b$\dagger$ | $3.595952$ | $-30.406787$ | 1 | 1.688 | 2 | BGCs
1.1c$\dagger$ | $3.586210$ | $-30.409963$ | 1 | 1.688 | 3 | BGCs
1.2a$\dagger$ | $3.597062$ | $-30.404703$ | 1 | 1.688 | 2 | BGCs
1.2b$\dagger$ | $3.596384$ | $-30.406123$ | 1 | 1.688 | 3 | BGCs
1.2c$\dagger$ | $3.585732$ | $-30.410077$ | 1 | 1.688 | 3 | BGCs
1.3a$\dagger$ | $3.597746$ | $-30.403511$ | 2 | 1.688 | 3 | BGCs
1.3b$\dagger$ | $3.595516$ | $-30.407178$ | 2 | 1.688 | 3 | BGCs
1.3c$\dagger$ | $3.586444$ | $-30.409849$ | 2 | 1.688 | 3 | BGCs
1.4a$\dagger$ | $3.598073$ | $-30.403961$ | 1 | 1.688 | 1 | BGCs
1.4b$\dagger$ | $3.595710$ | $-30.407526$ | 1 | 1.688 | 1 | BGCs
1.4c$\dagger$ | $3.587368$ | $-30.410130$ | 1 | 1.688 | 1 | BGCs
2.1a$\dagger$ | $3.583251$ | $-30.403317$ | 1 | 1.887 | 3 | BGCs
2.1b$\dagger$ | $3.597281$ | $-30.396694$ | 1 | 1.887 | 3 | BGCs
2.1c$\dagger$ | $3.585356$ | $-30.399856$ | 1 | 1.887 | 3 | BGCs
2.1d$\dagger$ | $3.586400$ | $-30.402106$ | 1 | 1.887 | 3 | BGCs
2.2a$\dagger$ | $3.583015$ | $-30.403167$ | 1 | 1.887 | 3 | BGCs
2.2b$\dagger$ | $3.597130$ | $-30.396620$ | 1 | 1.887 | 3 | BGCs
2.2c$\dagger$ | $3.585122$ | $-30.399647$ | 1 | 1.887 | 3 | BGCs
2.2d$\dagger$ | $3.586425$ | $-30.401849$ | 1 | 1.887 | 3 | BGCs
2.3a$\dagger$ | $3.582980$ | $-30.403028$ | 1 | 1.887 | 3 | BGCs
2.3b$\dagger$ | $3.597087$ | $-30.396561$ | 1 | 1.887 | 3 | BGCs
2.3c$\dagger$ | $3.585004$ | $-30.399603$ | 1 | 1.887 | 3 | BGCs
2.3d$\dagger$ | $3.586381$ | $-30.401744$ | 1 | 1.887 | 3 | BGCs
2.4a$\dagger$ | $3.582905$ | $-30.402908$ | 1 | 1.887 | 3 | BGCs
2.4b$\dagger$ | $3.597044$ | $-30.396509$ | 1 | 1.887 | 3 | BGCs
2.4c$\dagger$ | $3.584902$ | $-30.399559$ | 1 | 1.887 | 3 | BGCs
2.4d$\dagger$ | $3.586340$ | $-30.401611$ | 1 | 1.887 | 3 | BGCs
2.5a$\dagger$ | $3.582814$ | $-30.402771$ | 2 | 1.887 | 3 | BGCs
2.5b$\dagger$ | $3.596982$ | $-30.396451$ | 2 | 1.887 | 3 | BGCs
2.5c$\dagger$ | $3.584807$ | $-30.399495$ | 2 | 1.887 | 3 | BGCs
2.5d$\dagger$ | $3.586309$ | $-30.401469$ | 1 | 1.887 | 3 | BGCs
2.6a$\dagger$ | $3.582758$ | $-30.402661$ | 2 | 1.887 | 3 | BGCs
2.6b$\dagger$ | $3.596934$ | $-30.396403$ | 2 | 1.887 | 3 | BGCs
2.6c$\dagger$ | $3.584710$ | $-30.399442$ | 2 | 1.887 | 3 | BGCs
2.6d$\dagger$ | $3.586272$ | $-30.401331$ | 2 | 1.887 | 3 | BGCs
2.7a$\dagger$ | $3.582516$ | $-30.402291$ | 2 | 1.887 | 3 | BGCs
2.7b$\dagger$ | $3.596726$ | $-30.396273$ | 2 | 1.887 | 3 | BGCs
2.7c$\dagger$ | $3.584460$ | $-30.399268$ | 2 | 1.887 | 3 | BGCs
2.7d$\dagger$ | $3.586224$ | $-30.400848$ | 2 | 1.887 | 3 | BGCs
3.1a$\dagger$ | $3.589365$ | $-30.393837$ | 1 | 3.98 | 3 | BGCs
3.1b$\dagger$ | $3.588797$ | $-30.393777$ | 1 | 3.98 | 3 | BGCs
3.1c$\ast$ | $3.576622$ | $-30.401792$ | 3 | 3.98 | 1 | BGCs
3.2a$\dagger$ | $3.589212$ | $-30.393824$ | 1 | 3.98 | 3 | BGCs
3.2b$\dagger$ | $3.588955$ | $-30.393795$ | 1 | 3.98 | 3 | BGCs
3.3a$\dagger$ | $3.589477$ | $-30.393850$ | 1 | 3.98 | 3 | BGCs
3.3b$\dagger$ | $3.588629$ | $-30.393765$ | 1 | 3.98 | 3 | BGCs
4.1a$\dagger$ | $3.592115$ | $-30.402640$ | 1 | 3.577 | 3 | BGCs
4.1b$\dagger$ | $3.595664$ | $-30.401614$ | 1 | 3.577 | 3 | BGCs
4.1c$\dagger$ | $3.580437$ | $-30.408922$ | 2 | 3.577 | 3 | BGCs
4.1e$\dagger$ | $3.593640$ | $-30.405097$ | 3 | 3.577 | 3 | BGCs
4.2a$\dagger$ | $3.592087$ | $-30.402507$ | 1 | 3.577 | 3 | BGCs
4.2b$\dagger$ | $3.595557$ | $-30.401499$ | 1 | 3.577 | 3 | BGCs
6.1a$\dagger$ | $3.598532$ | $-30.401773$ | 1 | 2.017 | 3 | BGCs
6.1b$\dagger$ | $3.594046$ | $-30.407978$ | 1 | 2.017 | 3 | BGCs
6.1c$\dagger$ | $3.586418$ | $-30.409340$ | 1 | 2.017 | 3 | BGCs
8.1a$\dagger$ | $3.589702$ | $-30.394316$ | 2 | 3.977 | 2 | BGCs
8.1b$\dagger$ | $3.588821$ | $-30.394182$ | 2 | 3.977 | 2 | BGCs
10a$\star$ | $3.588386$ | $-30.405852$ | 1 | 2.657 | 2 | BGCs
10b$\star$ | $3.587369$ | $-30.406455$ | 1 | 2.657 | 3 | BGCs
18.1a$\dagger$ | $3.576110$ | $-30.404448$ | 1 | 5.662 | 3 | BGCs
18.1b$\dagger$ | $3.588367$ | $-30.395610$ | 1 | 5.662 | 3 | BGCs
18.1c$\dagger$ | $3.590720$ | $-30.395523$ | 1 | 5.662 | 3 | BGCs
22.1a$\dagger$ | $3.587908$ | $-30.411586$ | 2 | 5.284 | 3 | BGCs
22.1b$\dagger$ | $3.600039$ | $-30.404396$ | 2 | 5.284 | 3 | BGCs
22.1c$\dagger$ | $3.596580$ | $-30.408968$ | 2 | 5.284 | 3 | BGCs
24a$\star$ | $3.595886$ | $-30.404448$ | 1 | 1.044 | 3 | BGCs
24b$\star$ | $3.595112$ | $-30.405881$ | 1 | 1.044 | 9 | BGCs
24c$\star$ | $3.587311$ | $-30.409064$ | 1 | 1.044 | 1 | BGCs
26.1a$\dagger$ | $3.593885$ | $-30.409703$ | 1 | 3.054 | 3 | BGCs
26.1b$\dagger$ | $3.590339$ | $-30.410553$ | 1 | 3.054 | 3 | BGCs
26.1c$\dagger$ | $3.600103$ | $-30.402920$ | 2 | 3.054 | 9 | BGCs
26.2a$\dagger$ | $3.593979$ | $-30.409677$ | 1 | 3.054 | 3 | BGCs
26.2b$\dagger$ | $3.590257$ | $-30.410588$ | 1 | 3.054 | 3 | BGCs
26.3a$\dagger$ | $3.594018$ | $-30.409583$ | 3 | 3.054 | 2 | BGCs
26.3b$\dagger$ | $3.589954$ | $-30.410571$ | 3 | 3.054 | 2 | BGCs
30a$\star$ | $3.591005$ | $-30.397415$ | 1 | 1.026 | 2 | BGCs
30b$\star$ | $3.586672$ | $-30.398157$ | 1 | 1.026 | 9 | BGCs
30c$\star$ | $3.581915$ | $-30.401675$ | 1 | 1.026 | 1 | BGCs
31a$\star$ | $3.585930$ | $-30.403132$ | 1 | 4.757 | 3 | BGCs
31b$\star$ | $3.583708$ | $-30.404073$ | 1 | 4.757 | 3 | BGCs
33.1a$\dagger$ | $3.584699$ | $-30.403125$ | 1 | 5.726 | 3 | BGCs
33.1b$\dagger$ | $3.584383$ | $-30.403371$ | 1 | 5.726 | 3 | BGCs
34.1a$\dagger$ | $3.593414$ | $-30.410812$ | 1 | 3.784 | 2 | BGCs
34.1b$\dagger$ | $3.593798$ | $-30.410692$ | 1 | 3.784 | 3 | BGCs
34.1c$\dagger$ | $3.600574$ | $-30.404413$ | 1 | 3.784 | 2 | BGCs
41a$\star$ | $3.599143$ | $-30.399557$ | 1 | 4.91 | 9 | BGCs
41b$\star$ | $3.593505$ | $-30.407730$ | 1 | 4.91 | 9 | BGCs
41c$\star$ | $3.583441$ | $-30.408475$ | 1 | 4.91 | 9 | BGCs
41d$\star$ | $3.590685$ | $-30.404541$ | 3 | 4.91 | 2 | BGCs
42.1a$\dagger$ | $3.597304$ | $-30.400586$ | 1 | 3.692 | 3 | BGCs
42.1b$\dagger$ | $3.590944$ | $-30.403231$ | 1 | 3.692 | 3 | BGCs
42.1c$\dagger$ | $3.581575$ | $-30.408608$ | 1 | 3.692 | 3 | BGCs
42.1d$\dagger$ | $3.594233$ | $-30.406367$ | 1 | 3.692 | 3 | BGCs
42.1e$\dagger$ | $3.592403$ | $-30.405176$ | 3 | 3.692 | 1 | BGCs
61.1a$\dagger$ | $3.595511$ | $-30.403465$ | 1 | 2.951 | 1 | BGCs
61.1b$\dagger$ | $3.595127$ | $-30.404451$ | 1 | 2.951 | 3 | BGCs
62.1a$\dagger$ | $3.591315$ | $-30.398623$ | 3 | 4.194 | 3 | BGCs
62.1b$\dagger$ | $3.590571$ | $-30.398898$ | 3 | 4.194 | 3 | BGCs
63.1a$\dagger$ | $3.582199$ | $-30.407119$ | 1 | 5.662 | 3 | BGCs
63.1b$\dagger$ | $3.592823$ | $-30.407011$ | 2 | 5.662 | 3 | BGCs
63.1c$\dagger$ | $3.589141$ | $-30.403406$ | 2 | 5.662 | 3 | BGCs
63.1d$\dagger$ | $3.598822$ | $-30.398255$ | 2 | 5.662 | 3 | BGCs
64.1a$\dagger$ | $3.581190$ | $-30.398712$ | 2 | 3.409 | 3 | BGCs
64.1c$\dagger$ | $3.596412$ | $-30.394247$ | 2 | 3.409 | 3 | BGCs
JD1A$\ast$ | $3.592492$ | $-30.401458$ | 1 | 9.756 | 2 | BGCs
JD1B$\ast$ | $3.595004$ | $-30.400730$ | 1 | 9.756 | 2 | BGCs
JD1C$\ast$ | $3.577512$ | $-30.408667$ | 1 | 9.756 | 2 | BGCs
600.1a | $3.543063$ | $-30.368102$ | 1 | 2.58 | 2 | G1-G2
600.1b | $3.540339$ | $-30.372503$ | 1 | 2.58 | 2 | G1-G2
600.1c | $3.540449$ | $-30.375070$ | 1 | 2.58 | 2 | G1-G2
600.1d | $3.542075$ | $-30.372619$ | 1 | 2.58 | 2 | G1-G2
600.3a | $3.542649$ | $-30.368409$ | 1 | 2.58 | 2 | G1-G2
600.3b | $3.540129$ | $-30.372309$ | 1 | 2.58 | 2 | G1-G2
600.3c | $3.540147$ | $-30.375323$ | 1 | 2.58 | 2 | G1-G2
600.4a | $3.543199$ | $-30.367893$ | 1 | 2.58 | 2 | G1-G2
600.4b | $3.540398$ | $-30.372637$ | 1 | 2.58 | 2 | G1-G2
600.4c | $3.540540$ | $-30.374834$ | 1 | 2.58 | 2 | G1-G2
600.5a | $3.542933$ | $-30.367952$ | 1 | 2.58 | 2 | G1-G2
600.5b | $3.540186$ | $-30.372640$ | 1 | 2.58 | 2 | G1-G2
600.5c | $3.540297$ | $-30.374845$ | 1 | 2.58 | 2 | G1-G2
7a | $3.598254$ | $-30.402310$ | 1 | - | - | BGCs
7b | $3.595216$ | $-30.407384$ | 1 | - | - | BGCs
7c | $3.584596$ | $-30.409797$ | 1 | - | - | BGCs
28a | $3.580439$ | $-30.405018$ | 1 | - | - | BGCs
28b | $3.597824$ | $-30.395939$ | 1 | - | - | BGCs
28c | $3.585308$ | $-30.397926$ | 1 | - | - | BGCs
53a | $3.579837$ | $-30.401562$ | 1 | - | - | BGCs
53b | $3.583540$ | $-30.396673$ | 1 | - | - | BGCs
53c | $3.597214$ | $-30.394337$ | 1 | - | - | BGCs
A200.1a | $3.556366$ | $-30.376714$ | 1 | - | - | G1-G2
A200.1b | $3.556536$ | $-30.375809$ | 1 | - | - | G1-G2
B200.2a | $3.556331$ | $-30.376780$ | 1 | - | - | G1-G2
B200.2b | $3.556531$ | $-30.375736$ | 1 | - | - | G1-G2
C200.3a | $3.556468$ | $-30.376380$ | 1 | - | - | G1-G2
C200.3b | $3.556511$ | $-30.376159$ | 1 | - | - | G1-G2
301.1a | $3.554637$ | $-30.373839$ | 1 | - | - | G1-G2
301.1b | $3.553188$ | $-30.375998$ | 1 | - | - | G1-G2
301.1c | $3.552300$ | $-30.378605$ | 1 | - | - | G1-G2
601.1a | $3.544279$ | $-30.368064$ | 1 | - | - | G1-G2
601.1b | $3.542829$ | $-30.373490$ | 1 | - | - | G1-G2
601.1c | $3.542022$ | $-30.374625$ | 1 | - | - | G1-G2
602.1a | $3.543093$ | $-30.369106$ | 1 | - | - | G1-G2
602.1b | $3.540729$ | $-30.375868$ | 1 | - | - | G1-G2
602.1c | $3.542623$ | $-30.372453$ | 1 | - | - | G1-G2
602.1d | $3.540913$ | $-30.372220$ | 1 | - | - | G1-G2
700.1a | $3.579703$ | $-30.357717$ | 1 | - | - | G3
700.1b | $3.579165$ | $-30.357833$ | 1 | - | - | G3
700.1c | $3.574908$ | $-30.356075$ | 1 | - | - | G3

##  Appendix B Redshift catalog

In this section, we present an extract of the catalog of all the sources for
which we measure a secure redshift value (QF $\geq$ 2) from the new MUSE data
obtained during the ESO DDT program 109.24EZ.001 (see Section 2.2 and Figure
1). The full catalog will be released upon publication.

Table 3: Extract of the catalog of the sources with a reliable redshift measurementfrom the VLT/MUSE data obtained during the ESO DDT program 109.24EZ.001. The values of the QF are described in Section 2.2. ID | R.A. | Dec. | z | QF
---|---|---|---|---
| [deg.] | [deg.] |  |
70000123 | $3.520965$ | $-30.372848$ | 0.000 | 3
70004495 | $3.499187$ | $-30.323966$ | 0.000 | 3
70005368 | $3.482608$ | $-30.318157$ | 0.000 | 3
70001070 | $3.543078$ | $-30.367872$ | 0.000 | 3
70006188 | $3.479497$ | $-30.306998$ | 0.000 | 3
… | … | … | … | …

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