# COOL-LAMPS III: Discovery of a 25$\farcs$9 Separation Quasar Lensed by a
Merging Galaxy Cluster 111This paper includes data gathered with the 6.5m
Magellan Telescopes located at Las Campanas Observatory, Chile, and the 2.5m
Nordic Optical Telescope located at Rocque de los Muchachos Observatory, La
Palma.

Michael N. Martinez Current affiliation: Department of Physics, University of
Wisconsin, Madison, 1150 University Avenue, Madison, WI 53706, USA  Department
of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue,
Chicago, IL 60637, USA  Kate A. Napier Department of Astronomy, University of
Michigan, 1085 S. University Ave, Ann Arbor, MI 48109, USA  Aidan P. Cloonan
Department of Astronomy and Astrophysics, University of Chicago, 5640 South
Ellis Avenue, Chicago, IL 60637, USA  Ezra Sukay Department of Astronomy and
Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL
60637, USA  Katya Gozman Department of Astronomy and Astrophysics, University
of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Kaiya Merz
Department of Astronomy and Astrophysics, University of Chicago, 5640 South
Ellis Avenue, Chicago, IL 60637, USA  Gourav Khullar Department of Astronomy
and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL
60637, USA  Kavli Institute for Cosmological Physics, University of Chicago,
5640 South Ellis Avenue, Chicago, IL 60637, USA  Department of Physics and
Astronomy and PITT PACC, University of Pittsburgh, Pittsburgh, PA 15260, USA
Jason J. Lin Department of Astronomy and Astrophysics, University of Chicago,
5640 South Ellis Avenue, Chicago, IL 60637, USA  Owen S. Matthews Acuña
Department of Astronomy and Astrophysics, University of Chicago, 5640 South
Ellis Avenue, Chicago, IL 60637, USA  Elisabeth Medina  Department of
Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue,
Chicago, IL 60637, USA  Jorge A. Sanchez Department of Astronomy and
Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL
60637, USA  Emily E. Sisco Department of Astronomy and Astrophysics,
University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Daniel
J. Kavin Stein Department of Astronomy and Astrophysics, University of
Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA  Kiyan Tavangar
Department of Astronomy and Astrophysics, University of Chicago, 5640 South
Ellis Avenue, Chicago, IL 60637, USA  Juan Remolina Gonzàlez Department of
Astronomy, University of Michigan, 1085 S. University Ave, Ann Arbor, MI
48109, USA  Guillaume Mahler Department of Astronomy, University of Michigan,
1085 S. University Ave, Ann Arbor, MI 48109, USA  Department of Physics,
Durham University, South Road, Durham DH1 3LE  Keren Sharon Department of
Astronomy, University of Michigan, 1085 S. University Ave, Ann Arbor, MI
48109, USA  Håkon Dahle Institute of Theoretical Astrophysics, University of
Oslo, P.O. Box 1029, Blindern, NO-0315 Oslo, Norway  Michael D. Gladders
Department of Astronomy and Astrophysics, University of Chicago, 5640 South
Ellis Avenue, Chicago, IL 60637, USA  Kavli Institute for Cosmological
Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637,
USA

###### Abstract

In the third paper from the COOL-LAMPS Collaboration, we report the discovery
of COOL J0542-2125, a gravitationally lensed quasar at $z=1.84$, observed as
three images due to an intervening massive galaxy cluster at $z=0.61$. The
lensed quasar images were identified in a search for lens systems in recent
public optical imaging data and have separations on the sky up to 25$\farcs$9,
wider than any previously known lensed quasar. The galaxy cluster acting as a
strong lens appears to be in the process of merging, with two sub-clusters
separated by $\sim 1$ Mpc in the plane of the sky, and their central galaxies
showing a radial velocity difference of $\sim 1000$ km/s. Both cluster cores
show strongly lensed images of an assortment of background sources, as does
the region between them. A preliminary strong lens model implies masses of
$M(<250\ \rm{kpc})=1.79^{+0.16}_{-0.01}\times 10^{14}M_{\odot}$ and $M(<250\
\rm{kpc})=1.48^{+0.04}_{-0.10}\times 10^{14}M_{\odot}$ for the East and West
sub-clusters, respectively. This line of sight is also coincident with a ROSAT
ALL-sky Survey source, centered between the two confirmed cluster halos
reminiscent of other major cluster-scale mergers. Archival and new follow-up
imaging show flux variability in the quasar images of up to 0.4 magnitudes
within $\sim 1$ year, and new multi-color imaging data reveal a $2\sigma$
detection of the underlying quasar host. A lens system with this configuration
offers rare opportunities for a range of future studies of both the lensed
quasar and its host and the foreground cluster merger causing the lensing.

quasars: general; clusters: general; gravitational lensing: strong; galaxies:
evolution; quasars: supermassive black holes; cosmology: cosmological
parameters

††journal: ApJ††facilities: CTIO/4m Blanco Telescope, Magellan Telescopes 6.5m
(Clay/LDSS3C), NOT (ALFOSC), Pan-STARRS1 Telescope††software: NumPy (Harris et
al., 2020), matplotlib (Hunter, 2007), astropy (Astropy Collaboration et al.,
2013), Prospector (Johnson et al., 2021), SourceExtractor (Bertin & Arnouts,
1996b), Lenstool (Jullo et al., 2007), GALFIT (Peng et al., 2010), Aperture
Photometry Tool (Laher et al., 2012)

##  1 Introduction

Since the initial discovery of a gravitationally lensed quasar by Walsh et al.
(1979), more than 300 quasars have been found to be strongly lensed by an
intervening mass along the line of sight (Lemon et al., 2019, 2022). In the
vast majority of these cases, the object acting as a lens is an individual
galaxy, producing typical image separations of 1-2″. Only five cases with
image separations larger than 10″, corresponding to a cluster-scale lens mass
M${}_{200}\gtrsim 10^{14}\,M_{\sun}$, have so far been reported in the
literature (Inada et al., 2003, 2006; Dahle et al., 2013; Shu et al., 2018,
2019). These five cases have maximum image separations in the range 14″- 22″.
Numerical simulations (Hilbert et al., 2009; Robertson et al., 2020) predict a
significantly higher abundance of cluster-mass lenses than seen in the current
sample of lensed quasars. Robertson et al. (2020) found that for a typical
quasar source redshift of $z_{s}=2$, gravitational lens masses of
M${}_{200}>10^{14}\,M_{\sun}$ will contribute 25% of the total lensing cross
section. This implies that the current sample is biased towards galaxy-scale
lens masses and that the true fraction of quasars lensed by cluster-scale
masses could be an order of magnitude larger than suggested by the currently
known lensed quasars.

Figure 1: Selected images from the search process. Top Left: A perturbed
color-color diagram of known stars and known quasars, from the SDSS dataset.
Quasar images are shown, as well as the false-positive in-cluster AGN seen in
the bottom right panel. Top Right: Map of early-type galaxy (ETG) number
density in a range of redshift slices and prospective Einstein radii. Bottom
Left: On-sky map showing the ETG’s and circles representing Einstein radii
from the previous panel. Bottom Right: DECaLS image of the area around COOL
J0542-2125, with objects identified as possible lensed quasar images circled.
Note the cluster-redshift AGN contaminant at the left of the image (unlabeled
circle).

The quasars lensed by clusters constitute a distinct population of lens
systems that make them particularly advantageous for studies of both the
source quasar and its host galaxy, as well as the lensing cluster and
potentially cosmology. The large-separation images probe the source from
multiple viewing angles that differ enough to reveal the 3D structure of
quasar outflows (Misawa et al., 2013, 2014, 2016). The high magnification and
wide image separation from the foreground lens optimizes conditions for
resolved studies of the quasar host galaxy, as the host can be disentangled
from the bright quasar by the lensing effect (Bayliss et al., 2017). Wide-
separation lensed quasars can also be excellent targets for precise
measurements of the quasar’s supermassive black hole mass through
reverberation mapping, as demonstrated by Williams et al. (2021a, b).
Measurements of the time delays between the different quasar images constrains
a different derivative of the lensing potential than the image positions or
the combination of positions and magnification provide. Together with
redshifts and positions of other multiply lensed background sources, this
constrains the mass distribution of the cluster (Sharon et al., 2017; Oguri et
al., 2013).

Measurements of time delays between the different quasar images lensed by a
cluster (Fohlmeister et al., 2007, 2008, 2013; Dahle et al., 2015; Muñoz et
al., 2022) can in principle also provide constraints on the Hubble parameter
$H_{0}$ using the method of Refsdal (1964). Through its dependence on the
lensing mass distribution in the dark matter dominated regime, the use of
clusters for such studies largely avoids issues with systematic uncertanties
produced by the baryonic mass component which are difficult to resolve
observationally for galaxy-scale lenses (Kochanek, 2021; Van de Vyvere et al.,
2022). Nevertheless, the extant literature on $H_{0}$ measurements from strong
lensing time-delays on cluster scales consists of one measurement of a lensed
quasar (Rathna Kumar et al., 2015) and one cluster-scale lensed supernova
(Vega-Ferrero et al., 2018). A larger sample of quasars lensed by clusters
could be used to constrain $H_{0}$ through time-delays, as well as models for
cosmology and structure formation through their overall abundance and the
distribution of different lensing multiplicities and image configurations.

In this paper we present a new discovery from a catalog-based search of the
Dark Energy Camera Legacy Survey (DECaLS) (Dey et al., 2019). The search
algorithm is described in Section 2. We describe follow-up spectroscopy that
confirms this candidate as a gravitationally lensed quasar in Section 2.1. In
Section 3 we show that the lensing cluster is one of two sub-clusters
comprising a merging system. Using photometry based on archival and new
imaging data, we detect significant intrinsic variability in the lensed
source, leading to an initial constraint on the time delay between the two
brightest quasar images. We use these ground-based data to model the mass
distribution of both sub-clusters and detect the quasar host-galaxy in the two
brighter lensed images. We summarize and report on further opportunities for
study in Section 4. For all geometry and cosmology calculations we assume a
flat $\Lambda$CDM cosmology with $\Omega_{\Lambda}$ = 0.7, $\Omega_{m}$ = 0.3,
and H0 = 70 km s-1 Mpc-1. Magnitudes are reported in the AB system.

Figure 2: LDSS3 spectra of the three images of COOL J0542$-$2125\. Data were
smoothed with a moving average filter and normalized according to r-band
magnitude. The spectra of Images A and B were shifted by a constant (see
legend) to improve readability, and all wavelengths have been corrected to
vacuum.

##  2 Discovery

COOL J0542$-$2125 was discovered as part of the ChicagO Optically-selected
strong Lenses - Located At the Margins of Public Surveys (COOL-LAMPS)
collaboration, in a search for wide-separation lensed quasars utilizing
archival data from DECaLS Data Release 8 (DR8).

Unlike other lens-finding efforts by this collaboration (Khullar et al., 2021)
the search for wide-separation lensed quasars was primarily catalog-based,
with imaging data only examined at a late stage in the process. We began by
limiting our search area to regions near luminous red galaxies (LRGs) which we
selected using galaxy color-magnitude cuts. LRGs are often found in clusters
and are markers of large dark matter halos (Gladders & Yee, 2000) and so are
an obvious choice when searching for cluster-scale lenses. To save
computational time when analyzing the multi-million-object DR8 catalog, the
redshift of these galaxies and their orientation relative to candidate quasars
was not taken into account at this stage. We assumed any lensed quasar would
be cataloged in DECaLS as a point source, and therefore selected any well-
measured point source in the aforementioned fields as a candidate. To select
the subset of point sources most likely to be quasars, we adopted a
probabilistic approach applied in color-color space. For each candidate point
source, we considered its colors against two samples: a set of
spectroscopically confirmed quasars from the Sloan Digital Sky Survey (SDSS),
and bright but unsaturated DECaLS point sources, the vast majority of which
are stars. We perturbed the magnitudes of our quasar and star test points by
the uncertainty of the candidate DECaLS source, and then counted the number of
stars and quasars that fell within a small circle around the candidate point
source in $g$-$r$ and $r$-$z$ color-color space. The proportion of quasar to
stellar test points gives a relative likelihood of that source being a quasar
rather than a star. This probability is not absolute, since no absolute
density of stars and quasars is used. An example color-color diagram with the
perturbed points is shown in the top left panel of Figure 1. After the initial
photometric analysis, we matched all high-likelihood point pairs on the sky,
with a maximum image separation for a match set at 30”, which was 7.5” wider
than the published widest known quasar lens, SDSS J1029$+$2623 (Inada et al.,
2003).

We further analyzed the photometry of these pairs to increase the likelihood
that a given on-sky pair of quasar candidates was indeed two images of the
same object. Quasars vary significantly in color and brightness over time
(Schmidt et al., 2012), and time delays inherent in gravitational lensing
imply real differences in quasar image colors at a given observation epoch.
Thus, a strict match of colors or magnitudes within a possible quasar pair
would be unsuitable for a search. Taking this into consideration, we examined
the known sample of cluster-scale lensed quasars and used their color
differences in DECaLS to create a conservative cut to object pairs with
drastically different colors. We considered a candidate quasar pair more
likely to be lensed if its components were within 1 magnitude of each other in
$grz$-space. Altogether, this catalog-focused analysis produced hundreds of
thousands of candidates, which, while an improvement from the half-billion
point sources in DECaLS, was still far too many to inspect visually.

To further refine our search for gravitationally lensed quasars, we utilized a
geometric approach modeling each image in a candidate pair as lying on a
common Einstein Ring. While there are an infinite number of circles that share
these two points, we selected only ten - five on each side of the candidate
quasar pair - with radii ranging from half of the distance between pair
members to 1 arcminute. An example of this circle selection process is
illustrated in the bottom left panel of Figure 1.

Red-sequence galaxies are excellent markers of cluster- and group-scale dark
matter halos (Gladders & Yee, 2000). While the first stage of the search used
an LRG catalog to select search areas via a simple sky coordinate match, the
reduced size of the candidate quasar pair dataset allowed for a more detailed
analysis in tandem with the Einstein Ring approach. Using DECaLS DR8 catalog
data, we calculated number densities of red-sequence galaxies at a range of
redshifts within each chosen circle. This produces an overdensity ‘map’ in
redshift and radius, an example of which can be seen in the top right panel of
Figure 1. A spatial example showing the circles (but not accounting for
redshift) is displayed in the bottom left panel. We compared these density
maps to those produced by a background of randomly spaced pairs of points on
the sky, and selected pairs with higher density at a given radius and redshift
than that background, resulting in a few thousand final lensed quasar
candidates.

These were visually inspected by two co-authors and given a score on a scale
of 0 to 3, with 3 being a definite lensed quasar in the scorer’s opinion. High
scoring candidates were gathered and examined further, utilizing other
archival surveys such as unWISE (Lang, 2014) and GALEX (Murthy, 2014), to
create a high-priority candidate list for spectroscopic follow-up, of which
DECALS J0542-2125 was one.

Figure 3: Background: Map of the surrounding galactic structure around COOL J0542$-$2125 at the lens redshift and in the foreground. Contour lines correspond to the equivalent of Gaussian 1$\sigma$, 2$\sigma$, and 3$\sigma$ significance levels. Insets: Multiband imaging and spectra of objects observed with the LDSS3 spectrograph. Spectra are rest-frame and smoothed with a moving-average filter, with recognized lines marked. Color $grz$ images were taken with LDSS3 and were created using the Lupton et al. (2004) intensity rescaling method. ID | R.A. (deg) | Decl (deg) | z
---|---|---|---
Image A | 85.7392 | -21.4261 | $1.83833\pm 0.00086$
Image B | 85.7385 | -21.4260 | $1.83833\pm 0.00086$
Image C | 85.7419 | -21.4325 | $1.83833\pm 0.00086$
A1 | 85.7393 | -21.4274 | $0.6093\pm 0.0005$
A2 | 85.7394 | -21.4282 | $0.6133\pm 0.001$
A3 | 85.7451 | -21.4285 | $0.611\pm 0.002$
B1 | 85.6957 | -21.4286 | $0.6137\pm 0.0007$
B2 | 85.6969 | -21.4264 | $0.6158\pm 0.0006$
C1 | 85.7180 | -21.4563 | $0.10044\pm 0.0005$
C2 | 85.7130 | -21.4552 | $0.09681\pm 0.00015$
C3 | 85.7083 | -21.4546 | $0.09641\pm 0.00012$
Table 1:  Coordinates and redshifts of the sources targeted for spectroscopy
with LDSS3 and shown in Figures 2 and 3.

###  2.1 Follow-Up Observations

Two images of COOL J0542$-$2125, labeled as A & B in Figure 1, were observed
spectroscopically on October 21, 2020 using the LDSS3C spectrograph on the
Magellan 2 Clay telescope.The total integration time was 600 seconds, in
photometric conditions, using a 1$\farcs$25 wide longslit, dispersed by the
VPH-ALL grism; this yields a spectral resolution of $R\sim 500$ for an
unresolved source filling the slit. However, the seeing at the time of
observation was 0$\farcs$55, and so the effective resolution of the resulting
spectrum is somewhat finer, i.e. $R\sim 1200$. These initial spectra confirmed
images A&B as two images of the same background quasar. A further
spectroscopic observation, totaling 1200 seconds and using the same setup on
October 22, 2020, targeted the suspected third image (image C in Figure 1)
under similar conditions.This latter slit placement also targeted image A, and
contains sufficient flux to deduce a redshift for the two bright cluster
galaxies between images A and C. One final spectroscopic observation totaling
240 seconds was taken in twilight on the same night, targeting the three other
bright blue point sources - including one tagged by our analysis as a likely
AGN (See Figure 1) - near the lensing cluster center. Imaging of COOL
J0542$-$2125 was also acquired on this second night of observing, totaling 450
seconds in the $z$ filter, and 540 seconds in each of the $g$ and $r$ filters,
in $\sim$0$\farcs$5 seeing conditions.

Initial analysis of the DECaLS images and photometry indicated a complex mass
field (see §3.1 below) and motivated additional spectroscopy and imaging.
Three further longslit positions were observed on the nights of November 13
and 14, 2020. Two of these were placed to measure other mass structures near
the lensed quasar images, and the third was a re-observation of images A&B
using an order separating filter to cross check the identification of several
faint features in the initial spectrum as second-order lines from the extreme
blue. The observing setup was otherwise the same as the initial observations
described above. COOL J0542$-$2125 was also imaged for a total of 720 second
in each of the $grz$ filters on November 13, 2020, again in $\sim$0$\farcs$5
conditions.

##  3 Analysis

###  3.1 Galaxy Clusters in the COOL J0542–2125 Field

The DECaLS $grz$ color image (Dey et al., 2019) of the area surrounding COOL
J0542$-$2125 shows two obvious large-scale mass structures near the lens,
highlighted by early-type galaxies with colors consistent with expectations
for red-sequence galaxies. The first is a foreground cluster with redshift
$z\sim 0.1$, while the latter is the COOL J0542$-$2125 lensing cluster itself
and a neighboring cluster at the same redshift. Figure 3 displays a map of
these overdensities, estimated with a Gaussian kernel weighted by galaxy flux,
and with a kernel FWHM of 650 kpc at the two redshifts shown. The two peaks of
the $z=0.61$ density map are separated on the sky by an angular distance of
2.37 arcmin (0.948 Mpc), and the two BCGs are separated by 2.42 arcmin (0.968
Mpc).

###  3.2 Single-Epoch Images

Using archival single-epoch imaging from the DECaLS and PAN-STARRS surveys, as
well as that from the October 2020 observations, we constructed light curves
for the three confirmed images of COOL J0542$-$2125, as can be seen in Figure
4. This figure also includes 4 epochs of follow-up photometry using the
Alhambra Faint Object Spectrograph and Camera (ALFOSC) at the 2.56 m Nordic
Optical Telescope. This limited light curve is insufficient to measure a time
delay for the lensed system, but does establish the quasar’s high variability,
indicating such a study is achievable with more observations. Our limited
time-series data does show a tight correlation between images A and B,
suggesting a short time delay between those two images - as would be expected
for their small ($\sim 2.4"$) separation. The recent measurement of a 6-year
time delay for a similarly wide-separation quasar lens, SDSS J1004$+$4112
(Muñoz et al., 2022), suggests the delay between the close images and image C
could be on the order of several years.

Figure 4: Single-epoch photometry of the three images of COOL J0542$-$2125 in
the $g$ band. Blue, orange, and pink represent images A, B, and C
respectively. Diamonds represent archival PAN-STARRS photometry, and circles
DECaLS DR9. Triangles represent Magellan 2 Clay LDSS3 photometry, and x’s
represent Nordic Optical Telescope ALFOSC photometry. The data indicate that
the quasar shows high variability, and is suitable for time delay and
reverberation studies.

###  3.3 Lens Modeling

We construct a preliminary strong lensing model for the foreground structure
lens of COOL J0542$-$2125 from the existing ground-based imaging and
spectroscopy. Strong lens modeling requires observational constraints in the
form of sets of multiple images of the same background sources. The three
images of the lensed quasar, which we spectroscopically confirmed as multiple
images of the same source (section 2.1), are used as lensing constraints. We
identify several other lensed background sources in the field as described
below. We estimate their photometric redshifts using the Markov Chain Monte
Carlo (MCMC)-based stellar population synthesis (SPS) and parameter inference
code, Prospector (Johnson et al., 2021). Prospector is based on the Python-
FSPS framework, with the MILES stellar spectral library and the MIST set of
isochrones (Conroy & Gunn, 2010; Leja et al., 2017; Foreman-Mackey et al.,
2013; Falcón-Barroso et al., 2011; Choi et al., 2016). We use a single burst
star formation history model (corresponding to a unique formation episode of
simple stellar populations in this galaxy at burst age tage). This model also
used as free parameters the redshift, total stellar mass formed ($M_{\star}$)
and metallicity log$(Z/Z_{\odot})$. With suitable priors corresponding to a
quiescent galaxy, we sample posterior distributions using MCMC.

We identify a set of three images with similar color in the East sub-cluster,
with an estimated photometric redshift of $z=1.7\pm 0.1$ (triangles pointing
to three red sources in the top-left panel of Figure 5). In the West sub-
cluster, we identify a set of three images of a background galaxy with
distinctive green color in the $grz$ image (top-right panel of Figure 5). Its
estimated photometric redshift is $z=4.3\pm 0.1$. In the space between the two
sub-clusters, we identify two families of multiple images. We use the
aforementioned images as constraints. Their positions and spectroscopic or
photometric redshifts are listed in Table 2.

We compute the strong lensing model using the public software Lenstool (Jullo
et al., 2007). Lenstool uses a parametric modeling algorithm which describes
the mass distribution as a combination of halos, each defined by a set of
parameters. Lenstool utilizes MCMC sampling of the parameter space and
identifies the best-fit model as the one that minimizes the scatter between
the observed and model-predicted image locations in the image plane.

We model the lens plane with three mass halos representing the dark matter
mass distribution of the sub-clusters and correlated large scale structure,
supplemented with mass halos assigned to individual cluster-member galaxies.
Both the cluster-scale and galaxy-scale potentials are modeled as a pseudo-
isothermal ellipsoidal mass distribution (PIEMD, also known as dPIE; Jullo et
al. (2007); Elíasdóttir et al. (2007)) described by seven parameters: position
x, y; ellipticity, e = (a2-b2)/(a2+b2), where a and b are the semi-major and
semi-minor axes, respectively; position angle $\theta$, measured north of
west; core radius rcore; cut radius rcut; and effective velocity dispersion
$\sigma_{0}$. For the cluster-scale halos, we allow all of the parameters to
vary, except for rcut, which is fixed at 1500 kpc. This is because, for a
typical cluster, the cut radius extends further than the radius at which
lensing evidence is found, prohibiting it from being constrained by the model.
The galaxy scale halos’ normalization and radii parameters are scaled to their
observed luminosity (a description of the scaling relations can be found in
Limousin et al. (2005)). The positional parameters ($x$, $y$, $e$, $\theta$)
are measured with SourceExtractor (Bertin & Arnouts, 1996a) and fixed.

To select cluster member galaxies, we generated photometric catalogs of all
non-stellar objects in the field in grz from LDSS3 using SourceExtractor with
a detection threshold of 5$\sigma$ and a deblend parameter of 0.001 in dual-
image mode. Galaxies were identified in the z-band and colors measured in the
r\- and g\- bands within the same aperture. Cluster members were selected by
their color relative to the red sequence in a color-magnitude diagram (r-z vs.
z) (Gladders & Yee, 2000). The z-band mag_auto magnitude and the shape
parameters (a, b, $\theta$) were used in our galaxy catalog as the z-band best
samples the stellar mass at the cluster redshift.

The critical curves of the best-fit lens model are overplotted on the $grz$
LDSS3 image of the field in Figure 5. To guide the eye to the relevant lensing
configuration in each sub-cluster, we plot the critical curve for a source at
the quasar redshift in the East half of the field, and for a source at $z=4.3$
in the West. The preliminary lens model is somewhat under-constrained
considering the complexity of the lens plane. Significant improvement can be
made once space-based imaging is obtained, which will enable multiplexing the
constraints in the current lensed images by using the currently unresolved
substructure; confirming candidate lensed feature to be used as constraints;
and identifying additional lensed galaxies.

We use the best fit lens model to measure the projected mass density enclosed
within 250 kpc from the BCG of each of the sub-clusters, and find
$M(<250\,kpc)=1.79^{+0.16}_{-0.01}\times 10^{14}M_{\odot}$ and
$M(<250\,kpc)=1.48^{+0.04}_{-0.10}\times 10^{14}M_{\odot}$ for the East and
West sub-clusters, respectively. Uncertainties are derived from a suite of 100
random models from the MCMC sampling of the parameter space, and the errors
represent $1-\sigma$.

ID | R.A. (J2000) | Decl. (J2000) | z
---|---|---|---
1.1 | 85.73924927 | -21.42612745 | 1.84
1.2 | 85.73851675 | -21.42600703 | 1.84
1.3 | 85.74191404 | -21.43245443 | 1.84
2.1 | 85.7356128 | -21.4260133 | $1.7\pm 0.1$
2.2 | 85.7376021 | -21.4295212 | $1.7\pm 0.1$
2.3 | 85.7399502 | -21.4325734 | $1.7\pm 0.1$
3.1 | 85.6980251 | -21.4399683 | $4.3\pm 0.1$
3.2 | 85.6940618 | -21.4383539 | $4.3\pm 0.1$
3.3 | 85.6933073 | -21.4333820 | $4.3\pm 0.1$
4.1 | 85.7232636 | -21.4360147 |  $\cdots$
4.2 | 85.7236361 | -21.4391366 |  $\cdots$
4.3 | 85.7231149 | -21.4381354 |  $\cdots$
5.1 | 85.7232337 | -21.4356442 |  $\cdots$
5.2 | 85.7231199 | -21.4367619 |  $\cdots$
Table 2:  Images used as constraints in lens model. All redshifts shown are photo-z’s besides objects 1.x, the spectroscopically confirmed quasar images. Figure 5: COOL J0542$-$2125 and its surroundings, with zoomed-in views of the main subclusters in the top panels. Lensing critical curves are shown in white. The quasar lensing “East” cluster is visible on the left, with the three quasar images marked by arrows. Another object used to constrain the model, at a photometric redshift of $z\sim 1.7$, is marked with triangles. The critical curves shown correspond to the quasar redshift at $z=1.84$. On the right, the “West” cluster is shown. Critical curves are drawn at $z=4.3$, corresponding to the green $z\sim 4.3$ object used to constrain the model and marked with arrows. In the bottom center of the wide-field view, a third lens system of unknown source redshift is visible between the two main subclusters, with critical curves drawn at the quasar redshift of 1.84. Components of the arc used to constrain the model are labeled. Images are $grz$ and were taken with LDSS3 and rendered using the Lupton et al. (2004) intensity rescaling method. ID | Lens Redshift | Source Redshift | Number of Images | Max Image Separation (”) | Brightest Image (DECam $g$) | Discovery Reference
---|---|---|---|---|---|---
COOL J0542$-$2125 | 0.61 | 1.84 | 3 | 25.9 | 20.7 | This work
SDSS J1029$+$2623 | 0.584 | 2.199 | 3 | 22.54 | 18.5 | Inada et al. (2006)
SDSS J1326$+$4806 | 0.396 | 2.078 | 2 | 21.1 | 20.2 | Shu et al. (2019)
SDSS J2222$+$2745 | 0.49 | 2.82 | 6 | 15.1 | 20.4 | Dahle et al. (2013)
SDSS J1004$+$4112 | 0.68 | 1.74 | 5 | 14.72 | 19.7 | Inada et al. (2003)
SDSS J0909$+$4449 | 0.9 | 2.788 | 3 | 14.0 | 21.5 | Shu et al. (2018)
Table 3:  Currently published cluster-scale lensed quasars, ordered by maximum
image separation (shown in arcseconds).

##  4 Discussion and Future Work

The COOL J0542$-$2125 lensed quasar system, as well as the greater galactic
structure around it, present a remarkable opportunity for further study.

###  4.1 Time-Domain Observations

As mentioned in Section 3.2, COOL J0542$-$2125 displays significant
variability in brightness across the three confirmed quasar images. An exact
time delay for each lensed image is beyond the scope of this paper and the
data utilized in it, but from the image separation this delay could be
multiple years, requiring extensive follow-up observations that are already
underway. Additionally, COOL J0542$-$2125 is the only published cluster-scale
lens that lies in the Vera Rubin Observatory’s Legacy Survey of Space and Time
Wide-Fast-Deep “main survey” footprint (Bianco et al., 2022), and as such will
be observed frequently over the course of that program. These time delays can
be used to further constrain the lens model, and have the potential to be used
in constraining cosmological parameters such as the Hubble constant (Vega-
Ferrero et al., 2018; Napier, 2023, in preparation).

###  4.2 Host Galaxy

Lensed quasars in principal provide the best view of quasar host galaxies
currently possible at redshifts greater than 1 (e.g., Oguri et al., 2013;
Sharon et al., 2017; Bayliss et al., 2017). This is because the emission from
the very small region of the quasar’s engine, which usually dominates the
observed flux at most wavelengths, remains a point source when lensed, while
the host galaxy is typically distorted into spatially extended arc-like
images. Moreover, wide-separation lensed quasars are a particularly attractive
target for such studies, as the magnified host galaxy images are unlikely to
be conflated with light from the foreground lens (unlike in galaxy-scale
lensed quasars), and existing wide-separation systems tend to have higher
magnifications than galaxy-scale systems (Oguri et al., 2013; Sharon et al.,
2017; Lemon et al., 2020).

We have attempted to extract a detection of the host galaxy in this system.
The $grz$ images were each fit with a GALFIT (Peng et al., 2010) model in the
region of the two brightest images (A&B), with a point spread function
computed from nearby point sources of similar color, and foreground lens
galaxies and other point sources included in the model as needed and indicated
by the modeling residuals. We first fit each quasar image location with a
single point source and no component for host galaxy light. In this model, the
$z$-band residual indicated possibly significant flux between the two quasar
images. No residual flux was seen in the bluer bands. To attempt to measure
the host galaxy light in the $z$-band, we added to the model a single Sérsic
component constrained to sit near the midpoint between the two quasar images;
the likely image configuration for an extended source is two partial and
merging images, and so we expect host flux to be most prominent between the
two quasar images. The $z$-band image region used and the two residual images
from this process (one without and one with the additional Sérsic component)
are shown in Figure 6.

To measure an uncertainty for the notionally fitted host galaxy light, and to
establish whether the detection is significant, we added the fitted GALFIT
model image to realizations of the noise, and refit the GALFIT model to the
resulting image. The noise image was estimated from the RMS of the initial
model residual smoothed by a kernel of approximately the same size as the
image PSF, with each instance of the noise consisting of that image multiplied
by a unitary random Gaussian field. We computed 1000 instances of these model
realizations for two cases. In the first case we included the notional fitted
host galaxy light in the input model image, and in the second we excluded it.
In both cases that Sérsic component was included in the fitted model. If the
notional detection is significant, we would expect that the resulting
magnitude distribution of the host galaxy component for the first case
(notional host light included) would tend brighter than the second case. In a
set of random comparisons between instances of the two cases above, this
occurred 93.8% of the time, implying that our host galaxy detection is
significant at approximately the $2\sigma$ level. Given these analyses, we
measure a $z$-band magnitude of $23.17_{-0.27}^{+0.41}$ for the COOL
J0542$-$2125 host galaxy. Deeper and sharper imaging will be required to
refine our understanding of the host galaxy further.

Figure 6: Left to right: 1) LDSS3 $z$-band image of quasar images A and B. 2)
Residual from a GALFIT model of this field, using only PSF components at the
quasar images. 3) Residual image from a GALFIT model which includes a Sérsic
component located between images A and B.

###  4.3 Cluster Merger

The two cluster cores in the direct vicinity of COOL J0542$-$2125 are likely
merging (e.g., Korkidis et al., 2020) \- assuming both clusters are moving
only with the Hubble flow implies a radial separation of $10\pm 5$ Mpc (with
the range driven by the redshift uncertainties of the two cores) and the
tangential separation is much smaller at only 1 Mpc. Furthermore, publicly
available data from the ROSAT (Boller et al., 2016) satellite suggest X-ray
emission in the West cluster’s vicinity, but offset from the cluster center
and BCG toward the East cluster. Such an offset is often present in cluster
mergers, such as “El Gordo” (Menanteau et al., 2012), the “Bullet Cluster”
(Tucker et al., 1998), and the “Baby Bullet” (Bradač et al., 2008), and has
been used to constrain dark matter and alternative cosmologies (Clowe et al.,
2006). Further X-ray observation would be required to confirm the East and
West clusters as one of these mergers.

Another avenue of use for the structure surrounding COOL J0542$-$2125 is
presented by the “Moving Lens Effect” (Birkinshaw & Gull, 1983), where a
transversely-moving potential well induces a small frequency shift in passing
photons, from which the transverse velocity can be recovered. Though
originally introduced as a higher-order perturbation in the CMB similar to the
Rees-Sciama and kinetic Sunyaev-Zeldovich effects (Hotinli et al., 2021), the
effect has been theorized to be observable in closer targets which are lensed
by high-transverse-velocity objects. Molnar et al. (2013) demonstrated that
frequency shifts on the order of 1 kms-̂1 in lensed images behind the Bullet
Cluster could be observed, and that lensed quasars are the optimal systems for
such a measurement.

The initial measurements presented above will be significantly enhanced by
scheduled Chandra X-ray and Hubble observations (Program ID: 24800144; PI:
Napier), and ongoing efforts to measure the time delays of all three lensed
quasar images.

We would like to express gratitude towards the staff and workers at the 6.5m
Magellan Telescopes at the Las Campanas Observatory, Chile for their valuable
labor, and in particular for their care and efforts during a global pandemic,
during which all of the data in this paper were gathered. This paper is based
on data gathered with the 6.5 m Magellan Telescopes located at Las Campanas
Observatory, Chile. Magellan observing time for this program was granted by
the time allocation committees of the University of Chicago and the University
of Michigan. This paper is partially based on observations made with the
Nordic Optical Telescope, owned in collaboration by the University of Turku
and Aarhus University, and operated jointly by Aarhus University, the
University of Turku and the University of Oslo, representing Denmark, Finland
and Norway, the University of Iceland and Stockholm University at the
Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de
Astrofisica de Canarias. The data presented here were obtained in part with
ALFOSC, which is provided by the Instituto de Astrofisica de Andalucia (IAA)
under a joint agreement with the University of Copenhagen and NOT. This work
is supported by The College Undergraduate program at the University of
Chicago, and the Department of Astronomy and Astrophysics at the University of
Chicago. The Legacy Surveys consist of three individual and complementary
projects: the Dark Energy Camera Legacy Survey (DECaLS; Proposal ID
2014B-0404; PIs: David Schlegel and Arjun Dey), the Beijing-Arizona Sky Survey
(BASS; NOAO Prop. ID 2015A-0801; PIs: Zhou Xu and Xiaohui Fan), and the Mayall
z-band Legacy Survey (MzLS; Prop. ID 2016A-0453; PI: Arjun Dey). DECaLS, BASS
and MzLS together include data obtained, respectively, at the Blanco
telescope, Cerro Tololo Inter-American Observatory, NSF’s NOIRLab; the Bok
telescope, Steward Observatory, University of Arizona; and the Mayall
telescope, Kitt Peak National Observatory, NOIRLab. The Legacy Surveys project
is honored to be permitted to conduct astronomical research on Iolkam Du’ag
(Kitt Peak), a mountain with particular significance to the Tohono O’odham
Nation. NOIRLab is operated by the Association of Universities for Research in
Astronomy (AURA) under a cooperative agreement with the National Science
Foundation. This project used data obtained with the Dark Energy Camera
(DECam), which was constructed by the Dark Energy Survey (DES) collaboration.
Funding for the DES Projects has been provided by the U.S. Department of
Energy, the U.S. National Science Foundation, the Ministry of Science and
Education of Spain, the Science and Technology Facilities Council of the
United Kingdom, the Higher Education Funding Council for England, the National
Center for Supercomputing Applications at the University of Illinois at
Urbana-Champaign, the Kavli Institute of Cosmological Physics at the
University of Chicago, Center for Cosmology and Astro-Particle Physics at the
Ohio State University, the Mitchell Institute for Fundamental Physics and
Astronomy at Texas A&M University, Financiadora de Estudos e Projetos,
Fundacao Carlos Chagas Filho de Amparo, Financiadora de Estudos e Projetos,
Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro,
Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and the
Ministerio da Ciencia, Tecnologia e Inovacao, the Deutsche
Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy
Survey. The Collaborating Institutions are Argonne National Laboratory, the
University of California at Santa Cruz, the University of Cambridge, Centro de
Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, the
University of Chicago, University College London, the DES-Brazil Consortium,
the University of Edinburgh, the Eidgenossische Technische Hochschule (ETH)
Zurich, Fermi National Accelerator Laboratory, the University of Illinois at
Urbana-Champaign, the Institut de Ciencies de l’Espai (IEEC/CSIC), the
Institut de Fisica d’Altes Energies, Lawrence Berkeley National Laboratory,
the Ludwig Maximilians Universitat Munchen and the associated Excellence
Cluster Universe, the University of Michigan, NSF’s NOIRLab, the University of
Nottingham, the Ohio State University, the University of Pennsylvania, the
University of Portsmouth, SLAC National Accelerator Laboratory, Stanford
University, the University of Sussex, and Texas A&M University. The Legacy
Surveys imaging of the DESI footprint is supported by the Director, Office of
Science, Office of High Energy Physics of the U.S. Department of Energy under
Contract No. DE-AC02- 05CH1123, by the National Energy Research Scientific
Computing Center, a DOE Office of Science User Facility under the same
contract; and by the U.S. National Science Foundation, Division of
Astronomical Sciences under Contract No. AST-0950945 to NOIRLab. The Pan-
STARRS1 Surveys (PS1) and the PS1 public science archive have been made
possible through contributions by the Institute for Astronomy, the University
of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its
participating institutes, the Max Planck Institute for Astronomy, Heidelberg
and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns
Hopkins University, Durham University, the University of Edinburgh, the
Queen’s University Belfast, the Harvard-Smithsonian Center for Astrophysics,
the Las Cumbres Observatory Global Telescope Network Incorporated, the
National Central University of Taiwan, the Space Telescope Science Institute,
the National Aeronautics and Space Administration under Grant No. NNX08AR22G
issued through the Planetary Science Division of the NASA Science Mission
Directorate, the National Science Foundation Grant No. AST-1238877, the
University of Maryland, Eotvos Lorand University (ELTE), the Los Alamos
National Laboratory, and the Gordon and Betty Moore Foundation. This research
is based on observations made with the Galaxy Evolution Explorer, obtained
from the MAST data archive 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.

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