# Ray-tracing with quantum correlated photons to image a 3D scene

Yingwen Zhang  National Research Council of Canada, 100 Sussex Drive, Ottawa
ON Canada, K1A0R6  Antony Orth  National Research Council of Canada, 100
Sussex Drive, Ottawa ON Canada, K1A0R6  Duncan England  Duncan.England@nrc-
cnrc.gc.ca National Research Council of Canada, 100 Sussex Drive, Ottawa ON
Canada, K1A0R6  Benjamin Sussman  National Research Council of Canada, 100
Sussex Drive, Ottawa ON Canada, K1A0R6  Department of Physics, University of
Ottawa, Ottawa, Ontario, K1N 6N5, Canada

###### Abstract

To capture the 3D information of a scene, conventional techniques often
require multiple 2D images of the scene to be captured from different
perspectives. In this work we demonstrate the reconstruction of a scene’s 3D
information through ray-tracing using quantum correlated photon pairs. By
capturing the two photons in different image planes using time-tagging cameras
and taking advantage of the position, momentum and time correlation of the
photons, the photons’ propagation trajectory can be reconstructed. With this
information on every photon pair, we were able to demonstrate refocusing,
depth of field adjustment and parallax visualization of a 3D scene. With
future camera advancements, this technique could achieve a much higher
momentum resolution than conventional techniques thus giving larger depth of
field and more viewing angles. The high photon correlation and low photon flux
from a quantum source also makes the technique well suited for 3D imaging of
light sensitive samples.

In conventional optical imaging, only the 2D spatial distribution of light on
the camera/detector is recorded. By capturing multiple 2D images from
different perspectives, both position and angular information of the light
rays can be gained, thus, 3D information of the scene can be reconstructed.
This allows capabilities such as refocusing, depth of field adjustments and
parallax viewing of the scene to be performed, all in post-processing. One way
to achieve this is through a moving light source, such as in Fourier
Ptychography Zheng2011 ; Zheng2013 , whereby a sample is scanned at different
angles by light emitted from individual elements of a LED array.
Alternatively, with a fixed light source, cameras can be placed at different
locations/angles relative to the scene, such as in axially distributed sensing
Schulein2009 , where the camera is moved relative to the subject or vice
versa. An alternative technique that requires no moving parts, and only a
single camera, is known as plenoptic or light field imaging Aldelson1992 ;
raytrix . In this approach a microlens array is placed one focal length away
from a CCD sensor, each microlens illuminates a subset of the pixels in the
CCD. By knowing which lens the light ray enters, and onto which pixel it
subsequently focuses, one can obtain both position and angular information of
the light ray respectively. Plenoptic imaging is akin to imaging a scene
simultaneously with an array of cameras thus requires no scanning or moving
parts. This class of 3D imaging techniques of placing camera(s) at different
angles relative to the scene is also known as Integral imaging Xiao2013 ;
Martinez2018 . A multitude of research in applications using these techniques
has been performed in recent decades, to name a few, this includes target
recognition Matoba2001 ; Kishk2003 , microscopy Jang2004 ; Levoy2006 ;
Zheng2013 ; Prevedel2014 , particle tracking Fahringer2015 ; Hall2016 ,
wavefront sensing Lv2016 ; Wu2016 ; Wu20162 , and microendoscopy Orth2019 .

Due to the way these conventional techniques are performed, they tend to have
a relatively low angular resolution compared to their position resolution as a
result of the number of viewing angles limited by either the number of light
sources or camera placement locations. And in the case of Plenoptic imaging,
position resolution has to be sacrificed for angular resolution. To overcome
these limitations, the use of temporally and spatially correlated classical or
quantum light has been proposed DAngelo2016 ; Pepe2016 ; DiLena2018 . Where
one beam illuminates a scene to obtain position information, and the
momentum/angular information of the correlated partner beam is measured on a
separate sensor. In this way both position and momentum can be measured with
high resolution allowing larger depth of field and more parallax viewing
angles. This technique, termed Correlation Plenoptic Imaging, has been
demonstrated using weakly correlated thermal light Pepe2017 ; DiLena2020 , but
further advantages have been predicted using highly correlated quantum light
Pepe2016 . A similar approach using quantum correlated light has also been
used to demonstrate Fourier Ptychography for amplitude and phase imaging
Aidukas2019 .

Based on the proposal in Pepe2016 , here, we demonstrate the reconstruction of
a scene’s 3D information through ray-tracing using quantum correlated photon
pairs for which we term the technique Quantum Correlated Ray-Tracing Imaging
(QCRTI). As shall be seen, our technique shares similarities with both
Plenoptic imaging and Fourier Ptychography, but also has important
differences. QCRTI uses quantum correlated photon pairs generated through the
process of spontaneous parametric down conversion (SPDC) with the aid of a
time tagging camera, capable of time tagging every photon detection with
nanosecond precision. By imaging one photon in the crystal’s Fourier plane and
it’s partner photon in the crystal image plane, then taking advantage of the
strong time, position and momentum correlation properties of the SPDC photon
pairs, we were able to trace the propagation trajectory of all the detected
photon pairs. Just as in Plenoptic imaging, no scanning or moving parts are
required to measure the photon trajectories, though here, the position and
momentum measurement comes from the quantum correlation rather than through a
microlens array. QCRTI is also similar to Fourier Ptychography in the sense
that each photon is illuminating the scene from a different angle, but the
illumination randomly changes due to the stochastic nature of quantum light,
thus separate light sources are not required. In this proof-of-principle
demonstration, we show that QCRTI can achieve various 3D imaging capabilities,
such as refocusing, depth-of-field adjustments and parallax viewing of a scene
all at a very low photon flux of $\sim 1000$ photons per second per pixel (or
$5\times 10^{-11}$ W/cm2 on the sample).

Figure 1: (a) Schematic of the QCRTI setup. (b) Raw image, before any post
processing, captured on the TPX3CAM with the resolution target placed 4 mm off
focus.

Experimental Setup and Method \- The experimental setup is shown in Fig. 1. A
405 nm continuous wave (CW) laser is used to pump a 1 mm thick Type II ppKTP
crystal to produce 810 nm, orthogonally polarized photon pairs correlated in
time, position and momentum through the process of spontaneous parametric
down-conversion (SPDC). A longpass spectral filter placed directly after the
crystal is used to block out the 405 nm pump and let through the 810 nm SPDC
photons. As the SPDC photons are emitted from the crystal in a divergent
manner, a 100 mm lens is used to collimate the SPDC beam. Thereafter a
polarizing beamsplitter (PBS) is used to split the photon pairs into separate
paths, in which the sample to be imaged is placed in one of the path. The two
photon beams are then recombined, but slightly displaced, by a second PBS just
before the time tagging camera (TPX3CAM Nomerotski2019 ; ASI ) such that each
beam will be imaged onto different locations of the camera. In one path,
through two magnifying 4f imaging systems, the crystal plane is first imaged
onto the location at which the sample is to be placed and then onto the
camera, with the beam spot magnified by 5 times. In the other path, 3 lenses
are used such that the Fourier plane of the crystal is imaged onto the camera
with a slightly demagnified beam spot. Ideally, two cameras can be used, one
for each beam spot, to achieve higher position and momentum resolution.

A thin (1 mm) nonlinear crystal is used to reduce the uncertainty in the depth
at which the SPDC photons are generated inside the crystal, this will improve
the photon pair’s position correlation. Also, since the SPDC photon pairs’
wavelength are not necessary degenerate, uncertainties in their momentum
correlation will be introduced. To reduce this uncertainty and also to reduce
background light, a 810/3 nm spectral bandpass filter is placed just before
the camera.

The power of the UV laser has been attenuated down to 20 mW, generating a
total of approximately $1.3\times 10^{7}$ photon pairs per second or an
average photon flux of $\sim 1000$ photons per pixel per second (after
accounting for the system quantum efficiency of 4%). Increasing the pump beam
power will produce more SPDC photons thereby speeding up the data acquisition
process, however, at the cost of reduced spatio-temporal correlation between
the photons thereby introducing more noise in the images. This is due to the
increased likelihood of multi-photon pair production in the crystal during a
detection time window, thus causing the incorrect photons being identified as
a pair during time correlation analysis. Inversely, by reducing the pump
power, one can reduce the image noise but at the cost of longer data
acquisition time.

In post processing, a virtual circular aperture is placed around each beam in
the images in order to limit time correlation analysis to just the photons
within the two beams thus reducing noise. Time correlation analysis is then
performed on all photons detected between the two selected beam spots to
identify the SPDC photon pairs. Finally, by utilizing the property that the
photon pairs are perfectly correlated in position and anti-correlated in
momentum, and the fact that all the optical elements and distances between
them are known, we can make use of the Klyshko picture Klyshko1988  to
backtrack the propagation path of one photon from its near field to the far
field of the other or vice versa, treating the crystal as a mirror, and gain
both the position and momentum information of the photon pairs. Since the
system is still mostly paraxial (the maximum illumination angle on our sample
is $\sim 0.85$ deg), the trajectory of the photons can be determined through a
simple ray transfer matrix analysis

$\begin{bmatrix}\overrightarrow{r_{2}}\\\
\overrightarrow{\theta_{2}}\end{bmatrix}=\begin{bmatrix}A&B\\\
C&D\end{bmatrix}\begin{bmatrix}\overrightarrow{r_{1}}\\\
\overrightarrow{\theta_{1}}\end{bmatrix},$ (1)

where $\overrightarrow{r_{1}}$ and $\overrightarrow{r_{2}}$ are the positions
of each photon pair detected at the two camera image planes,
$\overrightarrow{\theta_{1}}$ and $\overrightarrow{\theta_{2}}$ are the angles
at which the photons hits each plane and the ray transfer (ABCD) matrix is
determined by the optical components placed between the two image planes.
Since $\overrightarrow{r_{1}}$ and $\overrightarrow{r_{2}}$ are known from the
raw image data taken by the two cameras and the ABCD matrix is also known,
$\overrightarrow{\theta_{1}}$ and $\overrightarrow{\theta_{2}}$ can be easily
determined from Eq. 1. Thus, the full propagation trajectory of every detected
photon pair is known, and with this information, one can perform in post-
processing, the refocusing, depth of field adjustments and parallax viewing of
the scene. More details on the camera and data processing can be found in the
supplementary materials.

Figure 2: Demonstration of image refocusing in QCRTI using a 1951 USAF
resolution test target placed at different distances from the focal plane of
the imaging lenses. The line sets has a spacing of $\sim 5$ line pairs per mm.
The images in the top row, from a1-a4, are the images obtained after
performing only time correlation measurements on the detected photons, with a1
the ground truth of the resolution test target when placed in focus. The
second row, from b1-b3, are images obtained after refocusing is performed in
post-processing on a2-a4 respectively. The third row, shows the cross-section
through the blue line in a1 (c1) and red lines in b1-b3 (c2-c4 respectively).
Each image is taken over a period of 60 seconds. The diameter of the virtual
aperture seen in the raw images a1-a4 is 130 pixels.

Experimental Results \- In Fig. 2, the refocusing capability of QCRTI is
demonstrated on images taken of a 1951 USAF resolution test target placed at
different distances from the focal plane of the imaging lenses. It can be seen
that when the target is placed 4 mm away from the focus, in a conventional
image (Fig. 2 a2) the lines in the resolution target can no longer be clearly
observed, however, through QCRTI they can be brought back into focus (Fig. 2
b1) with good image sharpness. Even at extreme distances, where features of
the resolution target can no longer be identified through conventional imaging
(Fig. 2 a4), QCRTI can still bring the image mostly back into focus (Fig. 2
b3). As can be seen, the sharpness of the refocusing deteriorates when the
target is placed further away from the focus, this may be due to a multitude
of factors such as limited position and momentum resolution, imperfect
position correlation caused by the finite thickness of the crystal introducing
uncertainties over the depth at which the photon pairs are generated, and
lastly, imperfect momentum anti-correlation caused by the photon pairs having
non-degenerate wavelength/energy and pump beam divergence at the crystal. The
affect these factors have on QCRTI will require further, more detailed
investigation in the future and are not within the scope of this work.

Figure 3: Images demonstrating the refocusing and depth reconstruction of 4
thin wires of 0.15 mm diameter placed at different distances from the focus.
(a) Raw image of the 4 wires after performing time correlation measurements
with the manually measured distance from focus shown on image. (b) All wires
brought to focus through post processing. (c) Depth map of the wires with the
histogram of the depth shown in (d).

In Fig. 3, we show the refocusing and a depth map of 4 thin wires of 0.15 mm
diameter placed at different depths within the beam. Fig. 3 a shows the
traditional image of the scene after time correlation, without momentum
filtering. Using the photon momentum information, this image is refocused into
a stack of images, each corresponding to a different focus plane. The depth
map in Fig. 3 c is obtained by choosing the sharpest refocused plane for each
pixel in the image Nayar1994 . Good agreement is achieved between the
reconstructed depth and the manually measured depth (Fig. 3 d). The slight
discrepancy is likely due to inaccuracies in manually measuring with a ruler,
the wire locations and the distances between the optical components (lenses,
mirrors etc.). This measurement inaccuracy however, does not affect the image
sharpness in refocusing, as any inaccuracies here is a global effect affecting
all photons in the same manner, thus, it will only introduce errors in
parameters such as the size and position of the sample. From this depth map,
an all-in-focus image is constructed in Fig. 3 b by modifying the refocus
position to the depth map value in Fig. 3 c on a per-pixel basis. More details
on how the depth mapping is performed can be found in the supplementary
material.

Figure 4: Images demonstrating parallax visualization and depth-of-field
enhancement on 4 thin wires placed at different depth from the focus. a1 and
a2 shows the raw images taken in the crystal plane and it’s Fourier plane
respectively after time correlation analysis. To demonstrate parallax viewing,
correlation events between the full crystal plane and 9 sub-regions of the
Fourier plane (as indicated in a2) were selected out. Each sub-region of a2
corresponds to a different viewing angle of the wires, these are displayed as
a set of 9 images, labeled 0-8, displayed on the right, each corresponding to
the 9 labeled sub-regions (illumination/viewing angles) in a2 respectively.
Due to the small diameter, i.e. small momentum spread, of each of the sub-
regions, an increase in the depth-of-field is also achieved. The diameter of
each sub-region is 20 pixels wide, with the diameter of the virtual aperture
around the full beam at 130 pixels. The raw image data was acquired over 8
minutes to ensure enough photons are accumulated within each sub-region.
Smaller sub-regions can potentially be used but will require substantially
longer data acquisition times.

The demonstration of depth-of-field enhancement and parallax visualization on
the 4 wires is shown in Fig. 4. By selecting coincidence events from a smaller
sub-region in the Fourier plane, we can limit the allowed photon momentum,
thus adjusting, in post-processing, the imaging depth-of-field in the
corresponding crystal image plane. Choosing small sub-regions off centre from
the optical axis results in the Fourier plane beam, results in viewing the
wires in the crystal image plane from different angles thus allowing parallax
visualization to be performed.

It is important to note that QCRTI does not necessarily require the sample to
be placed near the image plane of the crystal, one can have the sample placed
in the crystal’s Fourier plane and still perform QCRTI. As the beam is more
collimated and larger in the Fourier plane, it will be more suited for imaging
larger objects with more depth. Demonstration of this is shown in the
supplementary materials. Videos demonstrating the post-processing of
refocusing, depth of field adjustments and parallax viewing are also shown in
the supplementary materials.

Conclusion \- To conclude, in this proof of concept demonstration of QCRTI, we
have demonstrated some of the major capabilities of 3D imaging, including
refocusing, depth of field adjustments and parallax visualization of an
object/scene. QCRTI shares similarities with both Plenoptic imaging and
Fourier Ptychography. QCRTI requires no scanning or moving parts to capture
information on the photon trajectories, in which it shares similarity with
Plenoptic imaging. However, in the Klysko picture, where the photon trajectory
is backtracked from the crystal’s Fourier plane to the image plane, the
similarities lies with Fourier Ptychography in which each pixel of the Fourier
plane camera can be treated as a light source that randomly emits photons.

QCRTI exhibits conceptual advantages over conventional 3D imaging, and this
initial demonstration takes significant steps toward realising these
advantages. In particular the momentum/angle and position of the photon can
both be measured with high resolution. In conventional techniques, the
position is typically measured by a high resolution camera, but angular
resolution is limited either by the number of camera positions (integral
imaging), the number of light sources (Fourier Ptychography), or the pitch of
the microlens array (plenoptic imaging). In QCRTI, the momentum resolution is
only limited by the number of pixels in camera placed in the fourier plane and
the photons’ degree of momentum correlation, also, unlike in plenoptic
imaging, one does not need to sacrifice imaging pixels to measure angular
information. Here around $10^{4}$ pixels were used, but with new high-
resolution time-tagging cameras Morimoto2020  this could increase to $10^{6}$
in the near future. Therefore, with a single quantum light source, one could
effectively illuminate a 3D scene from millions of different angles, a goal
that is impractical with conventional techniques.

Since QCRTI is based on quantum photon correlations, it also gains some of the
advantages of quantum correlation imaging over classical correlation imaging
techniques. As a result of the sub-Poissonian photon statistics of the SPDC
photons giving a much higher second-order photon correlations compared to
classical sources, a much lower background noise can be theoretically obtained
using SPDC photons in correlation imaging under low illumination conditions
Berchera_2019 ; Moreau2019 . This makes QCRTI potentially well suited for
imaging light sensitive samples, and we expect other advantages afforded by
quantum enhancements Genovese2016  to manifest in improved imaging in future
work.

## Acknowledgements

The authors are grateful to Philip Bustard, Frédéric Bouchard, Khabat Heshami,
Denis Guay, and Doug Moffatt for technical support and stimulating discussion.
This work was partly supported by Defence Research and Development Canada.

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# Precision modeling of JWST’s first cluster lens SMACS J0723.3$-$7327111Based
on observations made with the NASA/ESA Hubble Space Telescope, obtained at the
Space Telescope Science Institute, which is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.
These observations are associated with programs GO-11103, GO-12166, GO-12884,
GO-1409; and on observations made with the NASA/ESA/CSA James Webb Space
Telescope, under NASA contract NAS 5-03127 for JWST. These observations are
associated with program #2736.

Guillaume Mahler Centre for Extragalactic Astronomy, Durham University, South
Road, Durham DH1 3LE, UK  Institute for Computational Cosmology, Durham
University, South Road, Durham DH1 3LE, UK  Mathilde Jauzac Centre for
Extragalactic Astronomy, Durham University, South Road, Durham DH1 3LE, UK
Institute for Computational Cosmology, Durham University, South Road, Durham
DH1 3LE, UK  Astrophysics Research Centre, University of KwaZulu-Natal,
Westville Campus, Durban 4041, South Africa  School of Mathematics, Statistics
& Computer Science, University of KwaZulu-Natal, Westville Campus, Durban
4041, South Africa  Johan Richard Univ Lyon, Univ Lyon1, Ens de Lyon, CNRS,
Centre de Recherche Astrophysique de Lyon UMR5574, 69230, Saint-Genis-Laval,
FR  Benjamin Beauchesne Institute of Physics, Laboratory of Astrophysics,
École Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny,
CH-1290 Versoix, Switzerland  European Southern Observatory, Alonso de Cordova
3107, Vitacura, Santiago, Chile  Harald Ebeling Institute for Astronomy,
University of Hawaii, 640 N Aohoku Pl, Hilo, HI 96720, USA  David Lagattuta
Centre for Extragalactic Astronomy, Durham University, South Road, Durham DH1
3LE, UK  Institute for Computational Cosmology, Durham University, South Road,
Durham DH1 3LE, UK  Priyamvada Natarajan Department of Astronomy, Yale
University, 52 Hillhouse Avenue, New Haven, CT 06520, USA  Department of
Physics, Yale University, P.O. Box 208121, New Haven, CT 06520, USA  Black
Hole Initiative, Harvard University, 20 Garden Street, Cambridge MA 02138, USA
Keren Sharon Department of Astronomy, University of Michigan, 1085 S.
University Ave, Ann Arbor, MI 48109, USA  Hakim Atek Institut d’astrophysique
de Paris, CNRS, Sorbonne Universite, 98bis Boulevrad Arago, 75014, Paris,
France  Adélaïde Claeyssens The Oskar Klein Centre, Department of Astronomy,
Stockholm University, AlbaNova, SE-10691 Stockholm, Sweden  Benjamin Clément
Institute of Physics, Laboratory of Astrophysics, École Polytechnique Fédérale
de Lausanne (EPFL), Observatoire de Sauverny, CH-1290 Versoix, Switzerland
Dominique Eckert Department of Astronomy, University of Geneva, ch. d’Ecogia
16, CH-1290 Versoix, Switzerland  Alastair Edge Centre for Extragalactic
Astronomy, Durham University, South Road, Durham DH1 3LE, UK  Jean-Paul Kneib
Institute of Physics, Laboratory of Astrophysics, École Polytechnique Fédérale
de Lausanne (EPFL), Observatoire de Sauverny, CH-1290 Versoix, Switzerland
Anna Niemiec Centre for Extragalactic Astronomy, Durham University, South
Road, Durham DH1 3LE, UK  Institute for Computational Cosmology, Durham
University, South Road, Durham DH1 3LE, UK

(Received xxx; Revised xxx; Accepted xxx)

###### Abstract

Exploiting the fundamentally achromatic nature of gravitational lensing, we
present a lens model for the massive galaxy cluster SMACS J0723.3$-$7323
(SMACS J0723, $z=0.388$) that significantly improves upon earlier work.
Building on strong-lensing constraints identified in prior Hubble Space
Telescope (HST) observations, the mass model utilizes 21 multiple-image
systems, 16 of which were newly discovered in Early Release Observation (ERO)
data from the James Webb Space Telescope (JWST). The resulting lens model maps
the cluster mass distribution to an RMS spatial precision of $1\farcs 08$ and
is publicly
available222https://www.dropbox.com/sh/3iatmz5k4hafzqf/AAAh0JvLgpBVoLp6qsxYZkFGa?dl=0.
Consistent with previous analyses, our study shows SMACS J0723.3$-$7323 to be
well described by a single large-scale component centered on the location of
the brightest cluster galaxy, however JWST data point to the need for two
additional diffuse components west of the cluster, which in turn accounts for
all the currently identified multiply imaged systems. A comparison of the
galaxy distribution, the mass distribution, and gas distribution in the core
of SMACS J0723 based on HST, JWST, and Chandra data reveals a fairly
concentrated regular elliptical profile along with with tell-tale signs of
recent merger activity, possibly proceeding aligned closely to our line of
sight. The exquisite sensitivity of JWST’s NIRCAM reveals in spectacular
fashion both the extended intra-cluster-light distribution and numerous star-
forming clumps in magnified background galaxies. The high-precision lens model
derived here for SMACS J0723$-$7323 demonstrates impressively the power of
combining HST and JWST data for unprecedented studies of structure formation
and evolution in the distant Universe.

##  1 Introduction

Clusters of galaxies grow and evolve through large-scale merging processes and
offer many valuable observables for astrophysical and cosmological studies of
our Universe. In statistically representative samples, they uniquely constrain
key parameters of complex physical processes, such as structure formation, but
also the cosmological parameters characterizing the underlying world model
(Jullo et al., 2010; Schwinn et al., 2017). By measuring the mass distribution
within clusters, we also gain insight into cluster-specific properties, such
as their dark-matter content, the spatial distribution and clustering of dark
matter, and the cluster’s merger geometry and history (e.g., Bradač et al.,
2008; Umetsu et al., 2009; Kneib & Natarajan, 2011; Ebeling et al., 2017).
Furthermore, offsets between the location of baryonic and dark-matter profiles
have been used to probe the nature of dark matter (e.g., its self-interaction
cross-section, Markevitch et al. 2004; Randall et al. 2008; Wittman et al.
2018; Harvey et al. 2019).

Strong gravitational lensing provides an observational measure of the enclosed
total mass of a cluster at a given radius and thus offers a powerful tool for
studying both dark and luminous matter. Lensing occurs when the presence of
mass generates a large enough curvature in space–time near the cluster center
to make different light paths from the same distant source converge within the
field of view of the observer. Since the first spectroscopic confirmation of a
giant gravitational arc in Abell 370 (Soucail et al., 1987), strong
gravitational lensing has evolved into a valuable and potent technique for
measuring the total mass of clusters over a wide range of evolutionary states
and redshifts (e.g., Limousin et al., 2007; Richard et al., 2011).

By refining the mass model of the lensing cluster through the identification
of strong-lensing features, it is possible to quantify the magnifying power of
the cluster for background sources at a given redshift, thereby calibrating
galaxy clusters as cosmic telescopes for studies of the high-redshift Universe
(e.g. Mahler et al. 2019; Fox et al. 2022). The correct identification of
multiply imaged background sources is crucial in this context, because these
are the principal features that permit precisely probing the mass distribution
in the cluster core. The high angular resolution of the Hubble Space Telescope
(HST) has proven crucial for such work to determine the source morphology and
to properly match lensed images as originating from the same source.

The most ambitious example of this quest to date was the Hubble Frontiers
Field initiative (HFF, Lotz et al., 2017) which comprised very deep HST
observations ($\sim$180 orbits per target) in seven optical and near-infrared
passbands. The HFF observed six massive clusters ($M\approx 10^{15}$ M⊙) at
$z=0.3-0.6$, selected for their lensing power, and, specifically, their
capability to strongly magnify very distant ($z>6$) galaxies. The resulting
deep images revealed a remarkable collection of hundreds of multiple images
and were showcased in numerous publications (e.g., Jauzac et al., 2014, 2016;
Mahler et al., 2018).

Figure 1: JWST / NIRCam image of a $2\times 2$ arcmin2 area centred on the
brightest cluster galaxy (BCG) of SMACS J0723. The overlaid white contours
show the X-ray surface brightness (adaptively smoothed to $3\sigma$
significance using the algorithm of Ebeling et al., 2006) as observed with
Chandra. Contours are spaced logarithmically by factors of 1.5, starting at
three times the background level. The astrometric alignment of the two
underlying images is accurate to about 1″.

Providing an order-of-magnitude improvement in sensitivity, the _James Webb
Space Telescope_ (JWST) represents another dramatic step forward in our
efforts to probe the distant Universe to ever larger depth with gravitational
lensing. The enormous promise of JWST is exemplified in the release of JWST’s
first deep cluster observation, SMACS J0723.3$-$7327 (hereafter SMACS J0723),
results from which are discussed and presented in this paper.

Our paper is structured as follows. After a brief introduction of the target
and the history of its discovery (Section 2), we summarize the most relevant
ground- and space-based observations of SMACS J0723 in Section 3. Section 4
provides an overview of the analysis and modeling techniques used, and Section
5 describes the results obtained. We present a summary and conclusions in
Section 6.

For the underlying cosmological model, we assume the $\Lambda$CDM concordance
cosmology ($\Omega_{\Lambda}=0.7$, $\Omega_{m}=0.3$) and $h=0.7$ throughout.
In this cosmology, 1″ corresponds to 5.3 kpc at the cluster redshift of
$z=0.3877$.

##  2 SMACS J0723

SMACS J0723 was discovered in the course of the southern extension of the
Massive Cluster Survey (MACS; Ebeling et al., 2001) and is included in the
partial release of the MACS sample by Repp & Ebeling (2018).

The system’s initial identification as a putative distant cluster was based on
the presence of an unidentified X-ray source, 1RXS J072319.7$-$732735,
comprising 64 photons detected in a 531 s exposure accumulated during the
ROSAT All-Sky Survey (RASS; Voges et al., 1999). The source’s high X-ray
hardness ratio of 0.95 (HR1 in RASS parlance), very high even at the
relatively high neutral-hydrogen density of more than $10^{21}$ cm-2 at the
source’s low Galactic latitude ($b=-23$ deg), its high likelihood of being
extended, as well as the absence of alternative plausible optical counterparts
in shallow, archival Digital Sky Survey images, rendered 1RXS
J072319.7$-$732735 a prime candidate for follow-up observations. Consequently,
SMACS J0723 was targeted in imaging and low-resolution spectroscopy
observations with the 3.5m New Technology Telescope at the European Southern
Observatory (ESO) in 2002 and 2003, respectively, which unambiguously
confirmed the system as a massive cluster and established its tentative
redshift as $z=0.404$ (see Section 5.1 for an improved measurement).

##  3 Observations and data reduction

###  3.1 Optical and NIR imaging

####  3.1.1 James Webb Space Telescope

SMACS J0723 was observed in early June 2022 with several instruments aboard
JWST as part of the observatory’s Early Release
Observations333https://www.stsci.edu/jwst/science-execution/approved-
programs/webb-first-image-observations. Specifically, deep imaging was
performed in the NIRCAM filters F090W, F150W, F200W, F277W, F356W, and F444W
(Figs. 1 and 2). The central field was also imaged with MIRI and NIRISS.

Our analysis combines pre-JWST observations (described below) with NIRCAM data
and NIRSpec spectroscopy.

####  3.1.2 Hubble Space Telescope

SMACS J0723 has been observed several times with multiple instruments aboard
the Hubble Space Telescope (HST): first in the optical regime with the Wide
Field and Planetary Camera 2 (WFPC2; in F606W and F814W filters) in 2008
(GO-11103, PI Ebeling); then with the Advanced Camera for Surveys (ACS) in
2011 for GO-12166 and in 2014 for GO-12884 (in the same two filters, F606W and
F814W, respectively; both PI Ebeling); and finally in 2017 with the Wide-Field
Camera 3 (WFC3) and ACS in the F453W, F606W, F814W, F105W, F125W, F140W, and
F160W passbands for the RELICS program (GO-14096, PI Coe). In all cases the
observing time ranged from about 1/2 to 1 orbit per filter. Additional
snapshot images in the F606W and F105W passbands were obtained with WFC3 in
2022 for GO-16729 (PI Kelly).

Figure 2: JWST / NIRCam image displayed at high contrast after median
filtering with a sliding box spanning $21\times 21$ arcseconds to enhance low-
surface-brightness features. Very faint, diffuse emission well beyond the BCG
halo is highlighted in the square west of the cluster core. This image also
shows smooth emission highlighted by the arrows

###  3.2 Spectroscopy

####  3.2.1 ESO

Shallow (3$\times$970 s) observations of the cluster were undertaken in March
2019 under moderate seeing conditions (0.72″) for Programme 0102.A-0718(A) (PI
Edge) with the MUSE integral field spectrograph on the ESO Very Large
Telescope. The observation covered a 1$\times$1 arcmin2 region centered on the
BCG of SMACS J0723 and yielded spectra in the range from 475 to 930 nm for
both lensing features and foreground / cluster galaxies.

The reduction of the MUSE data cube was performed using the official ESO
pipeline (Weilbacher et al., 2020), with a number of specific improvements
regarding self-calibration and sky subtraction specific to the crowded fields
of lensing clusters. These are extensively discussed in Lagattuta et al.
(2022) and Richard et al. (2021).

####  3.2.2 JWST

As part of the JWST’s Early Release Observations of SMACS J0723, the
observatory also acquired spectroscopic data with the Micro-Shutter-Array
(MSA) NIRSpec of 58 individual galaxies, as well as spectra of all objects in
the entire field with NIRISS in Wide-Field Slitless mode. The total on-source
exposure time ranged from 1.5 to 5 hrs. Our first analysis presented here uses
primarily NIRSpec MSA data of various multiple images in the form of reduced
2D spectra and 1D extracted spectra directly available in the data release.

###  3.3 X-ray imaging spectroscopy

SMACS J0723 was observed with the Advanced CCD Imaging Spectrometer (ACIS-I)
aboard the Chandra X-ray Observatory on April 14, 2014. The observations
(Sequence Number 801329; ObsID 15296; PI Murray) were performed in VFAINT mode
for a total duration of 19.8 ks. We performed a standard reduction of the data
using CIAO444https://cxc.cfa.harvard.edu/ciao/ $4.13$ (Fruscione et al., 2006)
and CALDB $4.9.6$ pipelines. We removed point sources automatically detected
by the wavedetect routine or by visual inspection. Background flares were
corrected by running the deflare tool in the 9.5–12 keV band and for the whole
energy range. We used the blank-sky background data associated with the
observation as provided by the standard pipeline.

##  4 Methods

###  4.1 Intra-cluster light

The intra-cluster light (ICL) represents an important component of the cluster
mass distribution and is a unique tracer of a system’s dynamical history and
its underlying dark-matter distribution as demonstrated in recent work (e.g.,
Montes & Trujillo 2014; Montes 2019, 2022; Gonzalez et al. 2021; Deason et al.
2021). While the ICL has proven extremely difficult to detect and study with
ground- and space-based telescopes so far, the exceptional sensitivity of
JWST’s detectors holds great promise for the detection of these extremely low-
surface-brightness features.

In order to enhance faint, diffuse emission, we apply a running median
filtering with with a 21$\times$21 pixel box size. The resulting image is
shown in Fig. 2.

###  4.2 Strong-lensing mass modeling

We compute a mass model of SMACS J0723 based on strong-lensing constraints
identified in the cluster core, using the publicly available mass modeling
algorithm Lenstool (Jullo et al., 2007). We provide a short summary of our
approach here and refer the reader to Kneib et al. (1996), Smith et al.
(2005), Verdugo et al. (2011) and Richard et al. (2011) for more details. The
cluster mass distribution is modeled as a series of dual pseudo-isothermal
ellipsoid (dPIE, Elíasdóttir et al. 2007) parametric mass halos with seven
free parameters: the position $\Delta\alpha$, $\Delta\delta$ relative to a
reference location; ellipticity $\epsilon$; position angle $\theta$;
normalization $\sigma_{0}$; truncation radius $r_{cut}$; and core radius
$r_{core}$. We use as input constraints the positions of prominent light peaks
in each lensed image, as well as their spectroscopic redshifts where available
(see Section 5.3). The Lenstool algorithm uses a Monte Carlo Markov Chain
(MCMC) formalism to explore the parameter space and identifies the best fit as
the set of parameters that minimizes the scatter between the observed and
predicted image-plane positions of the lensed features.

The lens plane is modeled as a combination of cluster-scale and galaxy-scale
dPIE halos. For the cluster-scale DM halos, we fix the truncation radius
($r_{cut}$) at 1500 kpc since it is too far beyond the strong-lensing region
to be constrained by multiple images. All other parameters are optimized
unless otherwise indicated.

Galaxy-scale halos represent the contribution to the lensing potential from
cluster member galaxies (e.g., Natarajan & Kneib, 1997; Jauzac et al., 2019;
Sharon et al., 2020). Their positional parameters ($\Delta\alpha$,
$\Delta\delta$; $\epsilon$; $\theta$) are fixed to their observed values as
measured with Source Extractor (Bertin & Arnouts, 1996). The cluster-member
catalog relies on HST photometry, as the two filters F606W and F814W (which
straddle the Balmer break at the cluster redshift) provide a color gradient
that allows us to isolate cluster member galaxies that form the so-called red
sequence (Gladders & Yee, 2000). To keep the number of model parameters
manageable in terms of computing time, the scale parameters of the galaxy-
scale potentials to their observed $i$-band luminosity with respect to L∗,
using a parameterized mass-luminosity scaling relation (see Natarajan & Kneib
1997; Limousin et al. 2007 and discussions therein on the validity of such
parameterization), leaving only the cut radius, $r_{cut}$, and the central
velocity dispersion, $\sigma_{0}$, free to vary. The BCG is modeled
separately, since extremely luminous central cluster galaxies often do no
follow the general scaling relation (Newman et al. 2013b, a).

The models we construct and present here are publicly
available555https://www.dropbox.com/sh/3iatmz5k4hafzqf/AAAh0JvLgpBVoLp6qsxYZkFGa?dl=0;
a website that will be constantly updated and refer to other repositories as
they become available666https://sites.google.com/view/guillaume-mahler-
astronomer/smacs0723-precise-lens-modelling.

###  4.3 X-ray analysis

To recover the properties of the gaseous intracluster medium (ICM) from the
existing short Chandra X-ray observation of SMACS J0723, we model the spectrum
of the emission with the Astrophysical Plasma Emission Code
(APEC)777http://atomdb.org/, adopting abundance ratios as provided by Asplund
et al. (2009). To account for foreground absorption, we complement this main
spectral component with a photoelectric-absorption
model888https://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/manual/XSmodelPhabs.html.
The contribution from background emission is incorporated by creating an
empirical model of the blank-sky background with B-spline functions whose
coefficients were obtained through a fit of the blank-sky spectrum for the
ACIS-I CCD on which the cluster is observed. We then keep the shape of the
background spectrum constant in the fitting procedure and allow only its
normalization to vary.

We perform all modeling within the Sherpa fitting environment (Freeman et al.,
2001) combined with the Python wrapper of the MultiNest nested sampling
package (Buchner et al., 2014; Feroz et al., 2019) to explore the parameter
spaces of our model in the $0.5$-$8.0$ keV energy band. As appropriate for the
mostly low photon statistics per bin, we use a Poisson likelihood similar to
cstat999https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/XSappendixStatistics.html.
Depending on the fit, not all emission model parameters are left free to vary.
We consider the background normalization a nuisance parameter and marginalize
over it in our best-fit estimates of all physical model parameters.

##  5 Results

###  5.1 Cluster galaxies

In order to obtain an independent assessment of the dynamical state of SMACS
J0723 as probed by the spatial and velocity distribution of the system’s
member galaxies, we examine the MUSE data cube and extract a catalogue of 26
spectroscopically confirmed cluster members (Table 1).

Using the ROSTAT package of Beers et al. (1990) we derive an improved cluster
redshift of $z=0.3877$ for SMACS J0723 and determine the cluster velocity
dispersion as $\sigma=1180_{-180}^{+160}$ km s-1. We show the corresponding
redshift histogram in Fig. 3. Within the statistical uncertainties set by the
small sample size, the radial-velocity distribution exhibits no significant
substructure indicative of an active merger along an axis that lies close to
our line of sight. We note, however, that the radial velocity of the BCG is
clearly offset from the centroid of the distribution; and the implied peculiar
velocity might reflect incomplete relaxation after a recent line-of-sight
merger.

R.A. (deg) | Decl. (deg) | $z$
---|---|---
110.80001 | -73.45269 | 0.3791
110.80062 | -73.44852 | 0.3936
110.80247 | -73.45867 | 0.3904
110.80451 | -73.45615 | 0.3862
110.81613 | -73.45119 | 0.3841
110.81726 | -73.44940 | 0.3930
110.81824 | -73.45462 | 0.3908
110.81841 | -73.44827 | 0.3936
110.81852 | -73.45524 | 0.3848
110.82437 | -73.45991 | 0.3809
110.82514 | -73.45454 | 0.3767
110.82571 | -73.45869 | 0.3885
110.82639 | -73.45499 | 0.3909
110.82688 | -73.45463 |  0.3912 (BCG)
110.83269 | -73.45691 | 0.3867
110.83683 | -73.45652 | 0.3981
110.83763 | -73.45617 | 0.3895
110.83780 | -73.45360 | 0.3864
110.84009 | -73.45587 | 0.3908
110.84564 | -73.45134 | 0.3845
110.84875 | -73.46031 | 0.3970
110.85310 | -73.45666 | 0.3838
110.85378 | -73.45006 | 0.3844
110.85506 | -73.45020 | 0.3864
110.85574 | -73.45574 | 0.3815
110.85626 | -73.45070 | 0.3872
Table 1: Right ascension and declination (J2000) as well as redshifts of the
26 cluster members identified in the MUSE observation of the core of SMACS
J0723. Figure 3: Histogram of the redshifts of the 26 cluster members
identified spectroscopically within the MUSE data cube. Overlaid is the best
Gaussian model which determines the cluster velocity dispersion. The vertical
dashed line marks the location of the BCG in redshift space, $z_{BCG}=0.3912$,
which is displaced from the systemic redshift of the cluster, $z=0.3877$ (see
Section 5.1).

###  5.2 ICL

We examine the filtered NIRCam image of SMACS J0723 shown in Fig. 2 in search
of unusual low-surface-brightness features and note diffuse excess emission
west of the cluster core but also past the far eastern extension of the ICL
halo of the BCG. Although the physical nature and origin of such excess ICL is
not immediately obvious, we mark these areas as potential locations of minor
mass concentrations within the cluster lens that are not associated with
either overdensities of cluster members or excess X-ray emission and are thus
not readily identifiable by other means.

###  5.3 Strong-lensing constraints

Figure 4: Color image of SMACS J0723 with multiple-image systems used in our
models marked in green. Also shown are the critical curves for a source at
redshift $z=9$; in cyan for the single-component lens model and in pink for
our final model that includes the two additional mass clumps marked by excess
ICL. The white square highlights the ’Beret’ galaxy, a highly stretched spiral
at $z=1.16$ that is only partially multiply imaged (Sect. 5.3).

The strong-lensing features that constrain our lens model are given by the
image-plane locations of multiple images of lensed sources, identified either
in previous HST images or in in the new JWST observations.

Golubchik et al. (2022) identify five arc candidates in the field of SMACS
J0723 and report three multiple-image systems that have spectroscopic
redshifts. We confirm all of these in our examination of all available data
and identify 16 additional multiple-image systems. Through careful inspection
of the MUSE datacube (Section 3.2), we also secure an additional spectroscopic
redshift for one of the systems photometrically identified by Golubchik et al.
(2022); System 3 ($z=1.9914$).

Initial inspection of the NIRSpec MSA spectroscopic data yields an additional
spectroscopic constraint by confirming a star-forming region in image 17.2 to
be at $z=5.1727$, the highest spectroscopically confirmed multiple image in
this cluster (Figure 5). We also confirm the redshift for the ’Beret’ galaxy
(Fig. 4), a highly stretched spiral galaxy that is only partially multiply
imaged, as $z=1.16$; we do not include this image as a modeling constraint.

Figure 5: Identified emission lines of image 17.2, as revealed in
NIRSpec/G395m observations. The combination of strong [OIII]5007Å and
H$\alpha$ lines, accompanied by weaker [OIII]4959Å and [NII] emission, makes
this redshift determination robust.

All individual images are marked in Figure 4, and Table 2 summarizes the
positions and spectroscopic redshifts where available. Although the
identification of systems without spectroscopic confirmation for all
individual images should in principle be considered tentative, we propose to
adopt Systems 1, 2, and 3 as secure identifications, in view of their unique
morphology, which is identical for all of their multiple images.

Table 2: Securely identified multiple-image systems, denoted by a "System.ID" nomenclature. "System" specifies the group of images originating from the same source galaxy, whereas "ID" refers to the name of the individual image. R.A. and Decl. are the right ascension and declination (J2000) of the image. $z$ is the measured spectroscopic redshift. $\mu$ is the magnification at the location of the image. Where errors are listed, the cited values are the best magnification and the 1$\sigma$ statistical uncertainty from the lens-model optimisation. Some arcs are produced in very close proximity to their critical curve, with no credible statistical upper limit on their magnification. Their uncertainty is marked with “ $\cdots$ ”.  Sys. | R.A. [deg] | Decl. [deg] | $z_{spec}$ | $\mu$
---|---|---|---|---
ID | J2000 | J2000 |  |
1.1 | 110.8404700 | -73.4509750 | 1.449 | 4.0 $\pm$ 0.1
1.2 | 110.8427000 | -73.4547469 | 1.449 | 8.2 $\pm$ 0.4
1.3 | 110.8387600 | -73.4586919 | 1.449 | 3.3 $\pm$ <0.1
2.1 | 110.8384158 | -73.4510136 | 1.3779 | 3.6 $\pm$ 0.1
2.2 | 110.8405796 | -73.4551389 | 1.3779 | 14.9 $\pm$ 0.8
2.3 | 110.8361008 | -73.4587836 | 1.3779 | 3.0 $\pm$ <0.1
3.1 | 110.8252662 | -73.4596951 | 1.9914 | 8.3 $\pm$ 0.2
3.2 | 110.8318272 | -73.4551207 | 1.9914 | 1.2 $\pm$ <0.1
3.3 | 110.8302941 | -73.4485580 | 1.9914 | 2.2 $\pm$ <0.1
3.4 | 110.8232158 | -73.4547636 | 1.9914 | 0.6 $\pm$ <0.1
4.1 | 110.8050400 | -73.4545361 |  $\cdots$ | 8.4 $\pm$ 0.3
4.2 | 110.8068100 | -73.4583581 |  $\cdots$ | 4.7 $\pm$ 0.1
4.3 | 110.8130600 | -73.4486939 |  $\cdots$ | 3.2 $\pm$ <0.1
5.1 | 110.8237229 | -73.4518119 | 1.425 | 7.7 $\pm$ 0.2
5.2 | 110.8221554 | -73.4527017 | 1.425 | 20.6 $\pm$ 1.0
5.3 | 110.8207298 | -73.4601281 | 1.425 | 2.3 $\pm$ <0.1
6.1 | 110.8321200 | -73.4543750 |  $\cdots$ | 1.0 $\pm$ <0.1
6.2 | 110.8217000 | -73.4541080 |  $\cdots$ | 1.2 $\pm$ <0.1
6.3 | 110.8294800 | -73.4489140 |  $\cdots$ | 2.7 $\pm$ <0.1
6.4 | 110.8228900 | -73.4616310 |  $\cdots$ | 2.3 $\pm$ <0.1
7.1 | 110.8356027 | -73.4517354 |  $\cdots$ | 6.9 $\pm$ 0.2
7.2 | 110.8365200 | -73.4530053 |  $\cdots$ | 10.2 $\pm$ 0.4
7.3 | 110.8302054 | -73.4607783 |  $\cdots$ | 2.3 $\pm$ <0.1
8.1 | 110.8229525 | -73.4557225 |  $\cdots$ | 4.1 $\pm$ 0.1
8.2 | 110.8237650 | -73.4574778 |  $\cdots$ | 8.9 $\pm$ 0.3
8.3 | 110.8296182 | -73.4473761 |  $\cdots$ | 2.0 $\pm$ <0.1
9.1 | 110.8213633 | -73.4505622 |  $\cdots$ | 3.5 $\pm$ 0.1
9.2 | 110.8166542 | -73.4536869 |  $\cdots$ | 3.8 $\pm$ 0.1
9.3 | 110.8177396 | -73.4589208 |  $\cdots$ | 2.6 $\pm$ <0.1
10.1 | 110.8206913 | -73.4506744 |  $\cdots$ | 3.8 $\pm$ 0.1
10.2 | 110.8162196 | -73.4534906 |  $\cdots$ | 4.3 $\pm$ 0.1
10.3 | 110.8171638 | -73.4589111 |  $\cdots$ | 2.6 $\pm$ <0.1
11.1 | 110.8205446 | -73.4525444 |  $\cdots$ | 427.7 $\pm$ $\cdots$
11.2 | 110.8203379 | -73.4527633 |  $\cdots$ | 27.3 $\pm$ 1.2
11.3 | 110.8204463 | -73.4596864 |  $\cdots$ | 2.3 $\pm$ <0.1
12.1 | 110.8021824 | -73.4601442 |  $\cdots$ | 3.2 $\pm$ <0.1
12.2 | 110.7993001 | -73.4552794 |  $\cdots$ | 8.5 $\pm$ 0.2
13.1 | 110.8125550 | -73.4480347 |  $\cdots$ | 3.0 $\pm$ <0.1
13.2 | 110.8027083 | -73.4548592 |  $\cdots$ | 10.3 $\pm$ 0.4
13.3 | 110.8048946 | -73.4588756 |  $\cdots$ | 5.7 $\pm$ 0.2
14.1 | 110.8219646 | -73.4490944 |  $\cdots$ | 2.7 $\pm$ <0.1
14.2 | 110.8112242 | -73.4545281 |  $\cdots$ | 2.9 $\pm$ 0.1
14.3 | 110.8137933 | -73.4589608 |  $\cdots$ | 3.0 $\pm$ <0.1
15.1 | 110.8257175 | -73.4501981 |  $\cdots$ | 3.2 $\pm$ 0.1
15.2 | 110.8200154 | -73.4538917 |  $\cdots$ | 3.6 $\pm$ 0.1
15.3 | 110.8212175 | -73.4601403 |  $\cdots$ | 2.6 $\pm$ <0.1
16.1 | 110.8083567 | -73.4493158 |  $\cdots$ | 7.3 $\pm$ 0.2
16.2 | 110.8017854 | -73.4525411 |  $\cdots$ | 11.6 $\pm$ 0.6
16.3 | 110.8057167 | -73.4595078 |  $\cdots$ | 3.1 $\pm$ <0.1
17.1 | 110.7954292 | -73.4485406 | 5.1727 | 18.0 $\pm$ 0.9
17.2 | 110.7945008 | -73.4490581 | 5.1727 | 18.0 $\pm$ 1.0
17.3 | 110.7993617 | -73.4470114 | 5.1727 | 5.0 $\pm$ 0.1
18.1 | 110.7925663 | -73.4483789 |  $\cdots$ | 28.4 $\pm$ 3.1
18.2 | 110.7935367 | -73.4481472 |  $\cdots$ | 7.1 $\pm$ 0.3
18.3 | 110.7962837 | -73.4468367 |  $\cdots$ | 5.0 $\pm$ 0.1
19.1 | 110.8106596 | -73.4569608 |  $\cdots$ | 15.1 $\pm$ 2.5
19.2 | 110.8100754 | -73.4561633 |  $\cdots$ | 11.4 $\pm$ 1.9
20.1 | 110.7915608 | -73.4565256 |  $\cdots$ | 158.8 $\pm$ $\cdots$
20.2 | 110.7913679 | -73.4558061 |  $\cdots$ | 134.1 $\pm$ 124.5
21.1 | 110.8030487 | -73.4582211 |  $\cdots$ | 9.3 $\pm$ 0.3
21.2 | 110.7945008 | -73.4490581 |  $\cdots$ | 7.8 $\pm$ 0.3
21.3 | 110.8134338 | -73.4494697 |  $\cdots$ | 4.2 $\pm$ 0.1

###  5.4 Mass distribution

Table 3: Candidate Lens Models and Best-Fit Parameters

Model name | Component | $\Delta\alpha^{\rm~{}a}$ | $\Delta\delta^{\rm~{}a}$ | $\varepsilon^{\rm~{}b}$ | $\theta$ | $\sigma_{0}$ | rcut | rcore
---|---|---|---|---|---|---|---|---
(Fit statistics) |  | (″) | (″) |  | ($\deg$) | (km s-1) | (kpc) | (kpc)
Fiducial model | DM | -1.4${}^{+0.1}_{-0.2}$ | 1.4${}^{+0.0}_{-0.0}$ | 0.8${}^{+0.0}_{-0.0}$ | 5.1${}^{+0.1}_{-0.2}$ | 930.4${}^{+9.9}_{-2.5}$ | [1500.0] | 17.2${}^{+0.5}_{-0.1}$
rms = $1\farcs 08$ | BCG | [-0.0] | [0.0] | [0.16] | [29.2] | 420.7${}^{+3.3}_{-4.6}$ | 5.3${}^{+0.5}_{-0.2}$ | 0.3${}^{+0.0}_{-0.0}$
$\chi^{2}/\nu$ = 27.8 | ICL 1 | 40.2${}^{+0.1}_{-0.0}$ | 11.3${}^{+0.4}_{-0.2}$ | 0.01${}^{+0.0}_{-0.0}$ | 21.5${}^{+1.3}_{-0.8}$ | 457.5${}^{+5.4}_{-18.7}$ | 78.8${}^{+0.4}_{-0.6}$ | 12.2${}^{+0.2}_{-1.3}$
$\log$($\mathcal{L}$) = -576 | ICL 2 | 42.2${}^{+0.2}_{-0.5}$ | -7.7${}^{+0.0}_{-0.1}$ | 0.77${}^{+0.06}_{-0.08}$ | 27.8${}^{+0.3}_{-1.5}$ | 265.5${}^{+9.9}_{-2.7}$ | 29.7${}^{+0.8}_{-1.0}$ | 7.1${}^{+0.5}_{-0.4}$
$\log$($\mathcal{E}$) = -653 |  $L^{*}$ Galaxy |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 198.8${}^{+0.0}_{-0.1}$ | 61.0${}^{+0.8}_{-2.5}$ | [0.15]
BIC = 1356 AICc = 1277 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
Comparison model | DM | -0.1${}^{+0.0}_{-0.0}$ | 0.5${}^{+0.0}_{-0.0}$ | 0.85${}^{+0.0}_{-0.0}$ | 6.1${}^{+0.1}_{-0.1}$ | 1008.2${}^{+2.4}_{-3.5}$ | [1500.0] | 13.2${}^{+0.2}_{-0.2}$
rms = 1.26″ | BCG | [-0.0] | [0.0] | [0.16] | [29.2] | 341.0${}^{+3.3}_{-2.8}$ | 5.2${}^{+0.1}_{-0.3}$ | 0.1${}^{+0.0}_{-0.0}$
$\chi^{2}/\nu$ = 22.4 | NorthWest Gal | 30.0${}^{+0.1}_{-0.1}$ | 21.1${}^{+0.2}_{-0.1}$ | 0.0${}^{+0.05}_{-0.0}$ | 1.9${}^{+0.1}_{-0.2}$ | 263.5${}^{+3.8}_{-2.6}$ | 9.2${}^{+0.8}_{-1.3}$ | 1.4${}^{+0.1}_{-0.2}$
$\log$($\mathcal{L}$) = -523 |  $L^{*}$ Galaxy |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ | 195.3${}^{+0.8}_{-0.9}$ | 15.0${}^{+0.9}_{-1.2}$ | [0.15]
$\log$($\mathcal{E}$) = -647 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
BIC = 1210 AICc = 1140 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$

a $\Delta\alpha$ and $\Delta\delta$ are measured relative to the reference
coordinate point: ($\alpha$ = 110.82675, $\delta$ = -73.454628)
b Ellipticity ($\varepsilon$) is defined to be $(a^{2}-b^{2})/(a^{2}+b^{2})$,
where $a$ and $b$ are the semi-major and semi-minor axes of the ellipse
c Quantities in brackets are fixed parameters

####  5.4.1 Excess mass

The presence of two bright galaxies north-west of the BCG motivate the
inclusion of an additional large-scale halo in our model to better accommodate
two nearby multiply imaged galaxies (Systems 17 and 18, see 5.3). Moreover,
while we see no significant substructure in the distribution of cluster
galaxies west and south-west of the BCG, we observe an extension of the ICL in
this direction. The presence of this excess of diffuse light (highlighted in
Fig. 2 and discussed in Sections 4.1 and 5.2) leads us to add a second large-
scale mass component which proves crucial to reproduce the lensing geometry of
System 20. Figure 4 shows the locations of both mass clumps, referred to as
ICL1 and ICL2 in Table 3.

To assess the importance of these additions, we run two models with parameters
as listed in Table 3: one with only a cluster-scale halo around the BCG
(Comparison Model in Table 3), and another one including the two additional
large-scale halos described above near the two observed peaks of intra-cluster
light (Fiducial Model in Table 3). Going further in the analysis, we only use
the most complex model since it is the only one that recovers the geometry of
System 20.

####  5.4.2 Comparison with previous work

We compare the results of our improved strong-lensing analysis with previous
findings for SMACS J0723. Two of these existing models are part of the public
release of RELICS (Coe et al., 2019) cluster models, derived with Lenstool and
GLAFIC lens mapping packages. In addition, we compare our results with those
from the recently published model of Golubchik et al. (2022), obtained using
the LTM software.

Table 4 lists and compares the masses from all existing lens models for SMACS
J0723 at three different radii: 128 kpc, 200 kpc, and 400 kpc. Here, 128 kpc
corresponds to the largest cluster-centric distance of the strong-lensing
constraints common to all models (this multiple-image system is labeled System
4 in our analysis). The masses within 200 kpc can be compared to the larger
study by Fox et al. (2022) on 74 different clusters, whereas the radius of 400
kpc is the largest radius shared by all mass maps. Golubchik et al. (2022)
also cite masses at two additional radii, corresponding to the Einstein radii
derived with their model for source redshifts of $z=1.45$ and $z=2$:
M${}_{{\rm Golubchik+22,\ 78\,kpc}}=(3.42\pm 0.47)\times$1013M⊙, and
M${}_{{\rm Golubchik+22,\ 90\,kpc}}=(4.15\pm 0.58)\times$1013M⊙ respectively.
Our model yields higher masses of M${}_{{\rm 78\,kpc}}=(3.79\pm
0.01)\times$1013M⊙, and M${}_{{\rm 90\,kpc}}=(4.69\pm 0.01)\times$1013M⊙. This
disagreement remains within the statistical uncertainties but may also reflect
different modeling assumptions and the addition of spectroscopic redshifts.

Table 4: Total enclosed cluster mass at different radii; in units of $10^{12}$ M⊙ Model | M${}_{\rm 128\,kpc}$ | M${}_{\rm 200\,kpc}$ | M${}_{\rm 400\,kpc}$
---|---|---|---
this work | $76.3\pm 0.2$ | $134.6^{+0.6}_{-0.4}$ | $287.9^{+1.8}_{-1.1}$
RELICS-Lenstool | $80.8\pm 0.7$ | $146.1\pm 2.1$ | $323^{+8}_{-6}$
RELICS-GLAFIC | $79.1^{+2.5}_{-1.6}$ | $144.1^{+6.5}_{-5.5}$ | $338^{+26}_{-25}$
LTM | $68.6^{+0.5}_{-0.7}$ | $117.3^{+1.1}_{-1.9}$ | $276.9^{+5.8}_{-5.6}$

The full profile shown in Fig. 6 highlights the differences between the
various mass profiles. The LTM mass density falls significantly below other
measurements at about 300 kpc.

We note that Golubchik et al. (2022) report a high RMS uncertainty of
2$\farcs$3, whereas the RELICS models’ RMS (private communication) of
0$\farcs$5 is typical for similar cluster lens models based on a fairly
limited number of multiple-image systems. By contrast, our new models which
employ many more strong-lensing constraints yield an RMS of $1\farcs 08$, a
value that falls near the high end of cluster mass models of similar
complexity. This trend is in line with the analysis of Johnson & Sharon
(2016), which shows from simulated lensing clusters that models with a large
number of spectroscopic constraints are more accurate in reproducing the
strong lensing magnification and mass, despite having a higher RMS than models
with a small number of constrains.

Figure 6: Left: Mass density profiles of SMACS J0723 obtained by our analysis
(red) and in previous work: RELICS-Lenstool (green), RELICS-GLAFIC (orange),
and LTM (blue). Right: Integrated mass profiles obtained for SMACS J0723. The
bottom panels of both panels show the respective uncertainties of the models.
We see model uncertainties pinch where strong lensing constraints exists.

####  5.4.3 Dynamical state of SMACS J0723

The distribution of cluster members in SMACS J0723 shows no significant
substructure, neither in velocity space (see Section 5.1) nor in projection
onto the plane of the sky, suggesting the adequacy of a single cluster-scale
component for the mass model. However, in order to recover the geometry of
multiple images newly discovered in the JWST observations (i.e., to minimize
the RMS of our model), we require a more sophisticated mass model that
incorporates two additional diffuse mass concentrations as discussed in
Section 5.4.1. These could be interpreted as remnant/tracers of past dynamical
activity in the cluster. This final mass model has an RMS of $1\farcs 08$, a
substantial improvement over the value of 1$\farcs$26 for a model which only
includes a single cluster-scale halo centered on the BCG.

As discussed in Sect. 5.1, the distribution of the radial velocities of the
cluster galaxies does not show compelling evidence of substructure along the
line of sight. However, the offset between the radial velocity of the BCG and
the centroid of the overall redshift distribution is indicative of the
incompletely relaxed state of SMACS J0723, an assessment that is supported by
the complex mass distribution required and obtained by our strong-lensing
analysis.

Additional evidence for dynamic activity and ongoing cluster evolution is
provided by the excess ICL shown in Fig. 2. As discussed in Section 5.4.1,
these ICL features play an important role for our lens modeling efforts:
Without the ICL evidence provided by the JWST ERO data, refinements to our
mass model in the west and south-west regions would have been driven solely by
statistics, i.e., the need to lower the RMS, rather than being supported and
motivated by physical evidence for the presence of mass in these regions of
SMACS J0723.

Table 5: Surface area $\sigma_{\mu}$ in the source plane with magnifications in excess of a given magnification $\mu$ for this work and previous models. We quote $\sigma_{\mu}(>\mu)$ for $\mu=3$, 5, and 10 for a source at redshift $z=9$.  Model | $\sigma_{\mu}(3)$ | $\sigma_{\mu}(5)$ | $\sigma_{\mu}(10)$
---|---|---|---
this work | 1.52 | 1.0 | 0.7
RELICS-Lenstool | 1.5 | 0.95 | 0.5

###  5.5 Magnification measurements

Thanks to the dramatically increased number of multiply imaged systems with
JWST, as well as the availability of partial spectroscopic coverage to anchor
the mass and shape of the cluster lens, we are able to derive magnification
maps for SMACS J0723 across the footprints of all of the JWST instruments.
Figure 7 shows the magnification map obtained for sources at redshift $z=9$.

Following the method presented by Wong et al. (2012) and subsequently applied
to HFF analyses (e.g. Jauzac et al., 2014, 2015; Lam et al., 2014; Wang et
al., 2015; Hoag et al., 2016), we use the surface area in the source plane,
$\sigma_{\mu}$, above a given magnification factor $\mu$ as a metric to
quantify the efficiency of the lens to magnify high-redshift background
galaxies, noting that $\sigma_{\mu}$ is directly proportional to the unlensed
comoving volume covered at high redshift at a given magnification $\mu$.

Figure 7: Magnification map obtained from our mass model for a source at
redshift $z=9$. Overlaid are the footprints of JWST’s instruments.

Figure 8 shows the evolution of $\sigma_{\mu}(>\mu)$ as a function of the
magnification obtained from our final mass model of SMACS J0723 for a source
at a redshift $z=9$. Our model yields $\sigma_{\mu}(\mu>3)=1.52$ arcmin2,
$\sigma_{\mu}(\mu>5)=1.0$ arcmin2, and $\sigma_{\mu}(\mu>10)=0.7$ arcmin2.
Table 5 compares these values with measurements obtained with the RELICS-
Lenstool, i.e., the same mass modeling algorithm. The pre-JWST RELICS-Lenstool
model used 7 unique systems as constraints, with no spectroscopic redshifts
(private communication). The pre-JWST model yielded smaller areas than found
from the model presented in this paper, especially at very high
magnifications, suggesting that SMACS J0723 is a more powerful cluster lens
than initially believed.

As a general caveat regarding magnification maps, we acknowledge a lack of
constraints at large cluster-centric distances as limiting at present. We
note, however, that the wide-angle X-ray observation performed with Chandra’s
ACIS-I detector (discussed in Sections 4.3 and 5.6) does not reveal any
further sources indicative of gravitationally collapsed mass concentrations in
the vicinity of SMACS J0723. We therefore consider our magnification maps (and
the associated error maps), made available to the community with this
analysis, the currently best estimate from all data released from the JWST ERO
of SMACS J0723.

Figure 8: Surface area in the source plane within a 300″ box centered on the
cluster at a magnification above a given threshold $\mu$. We here compare the
values obtained with our updated mass model with those from the RELICS-
Lenstool model.

###  5.6 Intra-cluster medium (ICM)

####  5.6.1 X-ray morphology

Figure 1 shows iso-intensity contours of the adaptively smoothed X-ray surface
brightness from SMACS J0723 overlaid on the JWST colour image of the cluster
core. We find the X-ray emission to feature a well defined, single peak at a
location that coincides perfectly with that of the BCG101010Although a direct
astrometric alignment of the JWST and Chandra images is precluded by the fact
that all X-ray point sources detected in the Chandra observations fall outside
the JWST field of view, a comparison with wide-field J-band imaging obtained
by the VISTA Hemisphere Survey (ESO Progamme 179.A-2010, PI McMahon) limits
the relative astrometric misalignment to about 1″.. While such alignment can
be viewed as a sign of a system in dynamic equilibrium, the clearly disturbed
X-ray morphology outside the very core region represents unambiguous evidence
of recent merger activity.

Figure 9: Regions of interest for our measurements of the ICM temperature
overlaid on the Chandra ACSI-I image of SMACS J0723 (left; 2″pixels, 0.5–7
keV, logarithmic intensity scaling) and on the JWST image of the system
(right). The dashed circles have radii of 100, 200, 400, and 1000 kpc,
respectively, at the cluster redshift. The cyan square marks the region shown
in Fig. 1.

####  5.6.2 ICM temperature

The spectral analysis summarized in Section 4.3 yields a global ICM
temperature (within 1 Mpc of the X-ray peak) of k$T=9.80^{+1.54}_{-1.37}$ keV,
a metallicity of $Z=0.38^{+0.12}_{-0.11}$ $Z_{\odot}$, and an equivalent
hydrogen column density of $n_{H}=1.94^{+0.03}_{-0.03}\times 10^{21}$ cm-2.
Fig. 10 shows the global spectrum as well as the best-fit spectral model with
$68$ per cent uncertainties (as represented by the associated subset of the
sampled parameter distributions). Our best-fit value for $n_{H}$ agrees to
better than $1\sigma$ with the total hydrogen (i.e., HI and HII) column
density of $2.21\times 10^{21}$ cm-2 measured by Willingale et al. (2013).

We attempt to constrain spatial variations in the ICM temperature by fitting
separate spectral models to the data in the regions marked in Fig. 9.
Acknowledging the reduced signal in these smaller regions, we adopt the
Galactic total $n_{\rm H}$ value; we also freeze the metallicity at $Z=0.3$
for these fits, in agreement with typical metal-abundance values observed for
non-relaxed clusters at similar redshift (Ettori et al., 2015). The results,
shown in Fig. 11, are consistent with a constant ICM temperature but suggest
(at less than 2$\sigma$ significance) a slight drop in k$T$ in the very core
of SMACS J0723.

Figure 10: Global spectrum of the observed ICM emission within 1 Mpc
(approximately r1000) of the X-ray peak. Overlaid in red is the best-fit APEC
model and the associated $68$ per cent confidence range. Figure 11: ICM
temperature measurements within the regions shown in Fig. 9; vertical bars
represent $1\sigma$ uncertainties, horizontal bars represent the width of the
respective annulus. The ambient ICM temperature in the combined regions beyond
$r=100$ kpc (i.e., within the annulus from 200 to 1000 kpc) with its $1\sigma$
error is shown as an orange rectangle.

####  5.6.3 Gas mass

We perform a multi-scale deprojection of the gas density and gas mass using
the pyproffit python package developed by Eckert et al. (2020). The analysis
uses counts and background maps in the $0.5$-$2.0$ keV energy band; an
associated monochromatic exposure map for an energy of $1.2$ keV, as well as
the values from our best-fit spectral model. The resulting profiles of the ICM
density and the cumulative gas mass are shown in Fig. 12 and place the total
gas mass of SMACS J0723 at almost $10^{14}$ M⊙. A comparison with the total
gravitational mass derived from our lens model (Fig. 6 and Table 4) yields a
gas-mass fraction of just under 10% for the cluster core, typical of massive
clusters in general. A more detailed investigation of, e.g., the baryon
fraction across the system would require a significantly deeper X-ray
observation and much more sophisticated spatial modeling of the ICM.

Figure 12: Profiles of the ICM density (left) and the cumulative gas mass
(right) as determined from a spherical deprojection analysis.

####  5.6.4 Global properties

For reference, we summarize all global cluster properties derived for SMACS
J0723 from the only existing, dedicated X-ray observation of the cluster in
Table 6. All values are computed from the emission within $r=1$ Mpc which is
very close to $r_{\rm 1000}$.

With a total X-ray luminosity well in excess of $10^{45}$ erg s-1 in the ROSAT
energy band (0.1–2.4 keV) in which the system was originally discovered (see
Section 2), the properties of SMACS J0723 established here are a testament to
the power of X-ray selection of clusters in general, and of the MACS project
in particular, to uncover exceptionally massive clusters that stand to advance
our understanding of a broad range of science topics, from cluster formation
and evolution to lensing-assisted, ever-deeper views of the distant Universe.

R.A. Decl. (J2000) | k$T$
---|---
07:23:18.0 $-$73:27:19 | $9.8^{+1.5}_{-1.4}$

energy band |  $f_{\rm X}$ ($10^{-13}$ erg s-1 cm-2) |  $L_{\rm X}$ ($10^{44}$ erg s-1)
---|---|---
0.1–2.4 keV | $32.1^{+1.2}_{-1.1}$ | $18.6^{+0.7}_{-0.6}$
0.5–2.0 keV | $23.2^{+0.9}_{-0.8}$ | $13.4\pm 0.5$
0.5–7.0 keV | $58.2\pm 1.3$ | $33.6\pm 0.8$
2–10 keV | $43.6^{+2.5}_{-2.6}$ | $25.2^{+1.4}_{-1.5}$
bolometric | $73.3\pm 2.3$ | $42.4^{+1.4}_{-1.3}$

Table 6: Global X-ray properties of SMACS J0723 computed within $r=r_{\rm
1000}$. Unabsorbed fluxes and total luminosities are both point-source
corrected.

##  6 Discussion and Conclusion

We create and make available to the scientific community a strong-lensing mass
model of the galaxy cluster SMACS J0723 at $z=0.39$, the first strong-lensing
cluster observed with JWST. Our model uses JWST ERO data, as well as archival,
multi-wavelength data of the cluster from optical to X-ray wavelengths and
combines both imaging and spectroscopic observations. We identify 16 new
multiple-image systems, increasing the total number of known strongly lensed
galaxies in this field to 21. Our best mass model contains only one large
cluster-scale halo but also includes two diffuse large-scale halos that
account for mass traced by the cluster ICL. As a result, our model is able to
reproduce the positions of strong-lensing features to within an RMS of
$1\farcs 08$.

The mentioned low surface-brightness features – which appear clearly on large
scales and are enhanced in the JWST imaging by median filtering – it is worth
noting that the excess stellar cluster light might well represent a potential
signature of a recent merger event. Indeed, the combined evidence from our
analysis of the overall mass distribution, radial velocities of cluster
galaxies, and ICM properties also suggests that SMACS J0723 recently underwent
a merger along an axis close to our line of sight but is well on its way to
relaxation, as reflected in the nearly perfect alignment of the X-ray peak
with the BCG and the overall mass distribution, as well as the increased ICM
cooling in an emerging compact gaseous cluster core.

By combining greatly increased sensitivity with broad spectral coverage and
spectacular spectroscopic capabilities, JWST’s observation of SMACS J0723
reveals exquisite panchromatic details that not only dramatically facilitate
the identification of multiple images of galaxies at redshift greater than 5
but also provide additional leverage to constrain the dynamical and merger
history of clusters.

## Acknowledgements

Based on observations made with the NASA/ESA Hubble Space Telescope, obtained
at the Space Telescope Science Institute, which is operated by the Association
of Universities for Research in Astronomy, Inc., under NASA contract NAS
5-26555. These observations are associated with programs GO-11103, GO-12166,
GO-12884, GO-14096.

This work is based on observations made with the NASA/ESA/CSA James Webb Space
Telescope. The data were obtained from the Mikulski Archive for Space
Telescopes at the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5-03127 for JWST. These observations are associated with program
#2736. We thank Ian Smail for insightful discussions. GM acknowledges funding
from the European Union’s Horizon 2020 research and innovation programme under
the Marie Skłodowska-Curie grant agreement No MARACHAS - DLV-896778. MJ is
supported by the United Kingdom Research and Innovation (UKRI) Future Leaders
Fellowship ‘Using Cosmic Beasts to uncover the Nature of Dark Matter’ (grant
number MR/S017216/1). HE gratefully acknowledges support from STScI grants
GO-12166 and GO-12884. Durham authors acknowledge STFC support through
ST/T000244/1. HA acknowledges support from CNES. PN acknowledges the Black
Hole Initiative (BHI) at Harvard University, which is supported by grants from
the Gordon and Betty Moore Foundation and the John Templeton Foundation, for
hosting her.

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