# Weak-Lensing Characterization of the Dark Matter in 29 Merging Clusters that
Exhibit Radio Relics

Kyle Finner IPAC, California Institute of Technology, 1200 E California Blvd.,
Pasadena, CA 91125, USA  Department of Astronomy, Yonsei University, 50
Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea  M. James Jee
Department of Astronomy, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul
03722, Republic of Korea  Department of Physics and Astronomy, University of
California, Davis, One Shields Avenue, Davis, CA 95616, USA  Hyejeon Cho
Department of Astronomy, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul
03722, Republic of Korea  Center for Galaxy Evolution Research, Yonsei
Univesity, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea  Kim
HyeongHan Department of Astronomy, Yonsei University, 50 Yonsei-ro, Seodaemun-
gu, Seoul 03722, Republic of Korea  Wonki Lee Department of Astronomy, Yonsei
University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea
Reinout J. van Weeren Leiden Observatory, Leiden University, P.O. Box 9513,
2300 RA Leiden, The Netherlands  David Wittman Department of Physics and
Astronomy, University of California, Davis, One Shields Avenue, Davis, CA
95616, USA  Mijin Yoon Leiden Observatory, Leiden University, P.O. Box 9513,
2300 RA Leiden, The Netherlands

###### Abstract

We present a multiwavelength analysis of 29 merging galaxy clusters that
exhibit radio relics. For each merging system, we perform a weak-lensing
analysis on Subaru optical imaging. We generate high-resolution mass maps of
the dark matter distributions, which are critical for discerning the merging
constituents. Combining the weak-lensing detections with X-ray emission, radio
emission, and galaxy redshifts, we discuss the formation of radio relics from
the past collision. For each subcluster, we obtain mass estimates by fitting a
multi-component NFW model with and without a concentration-mass relation.
Comparing the two mass estimate techniques, we find that the concentration-
mass relation underestimates (overestimates) the mass relative to fitting both
parameters for high- (low-) mass subclusters. We compare the mass estimates of
each subcluster to their velocity dispersion measurements and find that they
preferentially lie below the expected velocity dispersion scaling relation,
especially at the low-mass end ($\scriptstyle\sim$$10^{14}\ M_{\odot}$). We
show that the majority of the clusters that exhibit radio relics are in major
mergers with a mass ratio below 1:4. We investigate the position of the mass
peak relative to the galaxy luminosity peak, number density peak, and BCG
locations and find that the BCG tends to better trace the mass peak position.
Finally, we update a golden sample of 8 galaxy clusters that have the simplest
geometries and can provide the cleanest picture of the past merger, which we
recommend for further investigation to constrain the nature of dark matter and
the acceleration process that leads to radio relics.

Galaxy clusters(584) - Optical astronomy(1776) - Weak gravitational
lensing(1797) - Extragalactic radio sources(508)

††software: Astropy (Astropy Collaboration et al., 2022), Matplotlib (Hunter,
2007), Scikit-learn (Pedregosa et al., 2011), IRAF (Tody, 1986), SDFRED1 (Yagi
et al., 2002), SDFRED2 (Ouchi et al., 2004), SExtractor (Bertin & Arnouts,
1996), SCAMP (Bertin, 2006), SWarp (Bertin et al., 2002), CIAO (Fruscione et
al., 2006)

##  1 Introduction

On large scales of the universe, dark matter, gas, and stars are organized
into galaxy clusters that are connected by filaments: the cosmic web (Peebles,
1980; Bond et al., 1996). Galaxy clusters grow through the hierarchical
buildup of mass where low-mass structures form and merge to produce more
massive structures. Major growth events occur when galaxy clusters merge.

Merging galaxy clusters provide an extreme environment to study the universe
in regions where the most energetic events since the Big Bang occur (Sarazin,
2002). The merging of galaxy clusters is driven by the gravitational force. It
begins with clusters detaching from the cosmic expansion and starting a Gyrs
plunge toward each other. As the outskirts of the galaxy clusters come in
contact (a few virial radii separated), the intracluster medium (ICM), able to
undergo electromagnetic interactions, feels a ram pressure as gas particles
collide (see for example Eckert et al., 2012, for gas density profiles of
clusters). The relative velocity of the galaxy clusters increases as they
approach pericenter and particle interactions become more frequent. The
clusters begin moving at supersonic velocities with Mach numbers in the range
of 1 to 5 (Gabici & Blasi, 2003). At these velocities, ram pressure becomes an
important perturber of the ICM causing a significant momentum exchange between
the gas of the two clusters and consequently a deceleration. Unlike the ICM,
galaxies, being sparse in the cluster environment, are effectively
collisionless and follow a path that gravity defines. This leads to the open
and alluring question as to the nature of dark matter, the most massive
component of galaxy clusters. The Bullet cluster (1E 0657-56) is a prime
example of a cluster that is valuable to understanding the nature of dark
matter. The cluster demonstrates a clear spatial separation of the ICM from
the dark matter and galaxies (Markevitch et al., 2004; Clowe et al., 2006).
This configuration provides a laboratory to study the nature of dark matter
(e.g., Randall et al., 2008).

A result of clusters colliding at supersonic velocities is the formation of
shocks. These shocks can be classified as equatorial shocks that propagate
perpendicular to the merger axis and bow (or axial) shocks that propagate
along the merger axis (Ha et al., 2018). Shocks are visible in X-ray
observations as an abrupt surface brightness drop but one must take care to
not confuse them with contact discontinuities (e.g., Markevitch & Vikhlinin,
2007). Shocks are also sometimes visible in radio observations as radio relics
(also known as cluster radio shocks), which in some of the best cases appear
as giant (up to a few Mpc) arc-shaped radio emission (see van Weeren et al.,
2019, for a review).

Radio relics are extended synchrotron emission from charged particles that are
accelerated by the magnetic fields of merger-induced shocks. It is postulated
that diffusive shock acceleration (DSA) is the primary acceleration mechanism.
However, the inefficiency of DSA to accelerate electrons from a thermal
distribution to energies that are sufficient to see the observed radio relic
brightness has been an issue given the low Mach number of these shocks
(Brunetti & Lazarian, 2007; Kang et al., 2012a; Botteon et al., 2020a). The
re-acceleration of previously energized electrons is the favored scenario with
evidence compounding (Bonafede et al., 2014a; van Weeren et al., 2017; Lee et
al., 2022). The rarity of radio relics, with not all merging clusters hosting
them, remains another unresolved issue. Simulations have shown that projection
may be somewhat to blame for the rarity of radio relics and the interpretation
of radio emission (Vazza et al., 2012; Skillman et al., 2013; Lee et al.,
2024). Furthermore, if re-acceleration is required, then a pre-existing
population of suprathermal electrons should be present for the passing shock
to accelerate.

Merging clusters are an ideal laboratory to study the nature of dark matter,
high-energy astrophysics, and the evolution of the large-scale structure of
the universe. However, observations provide only a single snapshot into the
Gyrs-long process. Therefore, to gain an understanding of the progression of
the merger, multiwavelength observations and a large sample of cluster mergers
are needed. X-ray and radio observations provide insight into the ICM. Optical
and IR observations track the galaxies. Dark matter, which by definition does
not emit light, can be detected through its gravitational potential via the
gravitational lensing effect.

Weak gravitational lensing (WL hereafter) is a statistical analysis of galaxy
shapes. WL analysis permits the detection of the total mass distribution of
galaxy clusters (for a review see Umetsu et al., 2020). It provides valuable
information on the centroid and morphology of the dark matter. It can discern
substructures and detect the connection to the large-scale structure (Eckert
et al., 2015; HyeongHan et al., 2024a), which is critical to understanding the
formation and evolution of clusters. Additionally, it can be used to estimate
the masses of the substructures. By combining the WL results with
multiwavelength observations of the ICM and stars, the past collision of
merging clusters can be reconstructed.

This work entails a WL analysis of galaxy clusters that exhibit radio relics.
The primary goal of the work is to identify and characterize the substructures
that are merging using the WL effect. In Section 2, observations, data
reduction, and photometry are described. Section 3 presents an overview of the
WL pipeline, which covers WL formalism, point-spread function (PSF) modeling,
source selection, lensing efficiency, convergence mapping, substructure
identification, and mass estimation. Results for each cluster are described in
Section 4 and the clusters are put into the context of the multi-wavelength
literature. Section 5 discusses the sample of clusters as a whole and presents
a statistical analysis of the cluster masses. We summarize our conclusions in
Section 6.

All magnitudes are presented in the AB magnitude system. In all calculations
and presentations, a flat $\Lambda$CDM cosmology is assumed with $H_{0}$=70 km
s-1 Mpc-1, $\Omega_{m}=0.3$ and $\Omega_{\Lambda}$=0.7. Masses are defined as
the mass within a sphere of radius $R_{\Delta}$, where $R_{\Delta}$ is the
radius at which the average density within is $\Delta$ times the critical
density of the universe at the redshift of the cluster.

###  1.1 Radio Relic Sample

The sample of clusters that are analyzed in this work exhibits megaparsec-
scale radio emission. The identification of the radio relics was done in past
radio studies such as van Weeren et al. (2011b) and Feretti et al. (2012).
Some of the clusters have bow-shaped radio emission that clearly resembles a
spherical shock. However, some have patchy radio emission that may have arisen
from other particle acceleration phenomena. The study of radio relics is a
very active field of astronomy and new insights into the nature of the radio
relics are occurring daily. We include the most up-to-date information of the
radio relics in our interpretations of the mergers.

By design, the galaxy clusters studied in this work are merging systems. This
selection should be considered when making conclusions. The detection of these
clusters is dependent on the brightness of the radio emission, and therefore
the sample is probing bright radio sources. Furthermore, the existence of the
radio relics is an indication that the clusters are likely post-pericenter
systems (Vazza et al., 2012; Skillman et al., 2013; Lee et al., 2024).
Conclusions in this work are made with the understanding that the clusters
belong to a small subset of galaxy clusters and may not be representative of
all merging clusters.

Table 1 lists the radio relic merging clusters that are studied here. The
sample of radio relic clusters range in redshift from 0.07 to 0.54. This range
of redshifts is ideal for ground-based WL due to the dependence of the lensing
signal on the distances of the lens and background galaxies. Golovich et al.
(2019a, hereafter G19) performed a thorough dynamical analysis of the clusters
utilizing a vast catalog of spectroscopic redshifts. Their study identified
subclusters using Gaussian mixture modeling (GMM) and derived velocity
dispersions. Combining X-ray and radio observations with the GMM-defined
subclusters, they developed merger scenarios for each of the systems. A key
finding of their study is that the majority of these clusters are merging near
the plane of the sky. Wittman et al. (2018) provide quantitative constraints
on the viewing angle of some of the clusters.

Table 1: Overview of 29 merging cluster sample

Cluster | Short name | R.A. | Decl. | Redshift | Discovery Band
---|---|---|---|---|---
1RXS J0603.3+4212 | 1RXSJ0603 | 06:03:13.4 | +42:12:31 | 0.226 | Radio
Abell 115 | A115 | 00:55:59.5 | +26:19:14 | 0.193 | Optical
Abell 521 | A521 | 04:54:08.6 | -10:14:39 | 0.247 | Optical
Abell 523 | A523 | 04:59:01.0 | +08:46:30 | 0.104 | Optical
Abell 746 | A746 | 09:09:37.0 | +51:32:48 | 0.214 | Optical
Abell 781 | A781 | 09:20:23.2 | +30:26:15 | 0.297 | Optical
Abell 1240 | A1240 | 11:23:31.9 | +43:06:29 | 0.195 | Optical
Abell 1300 | A1300 | 11:32:00.7 | -19:53:34 | 0.306 | Optical
Abell 1612 | A1612 | 12:47:43.2 | -02:47:32 | 0.182 | Optical
Abell 2034 | A2034 | 15:10:10.8 | +33:30:22 | 0.114 | Optical
Abell 2061 | A2061 | 15:21:20.6 | +30:40:15 | 0.078 | Optical
Abell 2163 | A2163 | 16:15:34.1 | -06:07:26 | 0.201 | Optical
Abell 2255 | A2255 | 17:12:50.0 | +64:03:11 | 0.080 | Optical
Abell 2345 | A2345 | 21:27:09.8 | -12:09:59 | 0.179 | Optical
Abell 2443 | A2443 | 22:26:02.6 | +17:22:41 | 0.110 | Optical
Abell 2744 | A2744 | 00:14:18.9 | -30:23:22 | 0.306 | Optical
Abell 3365 | A3365 | 05:48:12.0 | -21:56:06 | 0.093 | Optical
Abell 3411 | A3411 | 08:41:54.7 | -17:29:05 | 0.163 | Optical
CIZA J2242.8+5301 | CIZAJ2242 | 22:42:51.0 | +53:01:24 | 0.189 | X-ray
MACS J1149.5+2223 | MACSJ1149 | 11:49:35.8 | +22:23:55 | 0.544 | X-ray
MACS J1752.0+4440 | MACSJ1752 | 17:52:01.6 | +44:40:46 | 0.365 | X-ray
PLCK G287.0+32.9 | PLCKG287 | 11:50:49.2 | -28:04:37 | 0.383 | SZ
PSZ1 G108.18-11.53 | PSZ1G108 | 23:22:29.7 | +48:46:30 | 0.335 | SZ
RXC J1053.7+5452 | RXCJ1053 | 10:53:44.4 | +54:52:21 | 0.072 | X-ray
RXC J1314.4-2515 | RXCJ1314 | 13:14:23.7 | -25:15:21 | 0.247 | X-ray
ZwCl 0008.8+5215 | ZwCl0008 | 00:11:25.6 | +52:31:41 | 0.104 | Optical
ZwCl 1447+2619 | ZwCl1447 | 14:49:28.2 | +26:07:57 | 0.376 | Optical
ZwCl 1856.8+6616 | ZwCl1856 | 18:56:41.3 | +66:21:56 | 0.304 | Optical
ZwCl 2341+0000 | ZwCl2341 | 23:43:39.7 | +00:16:39 | 0.270 | Optical

Source: Golovich et al. (2019b)

##  2 OBSERVATIONS AND DATA REDUCTION

Our analysis combines WL with X-ray, radio, and optical observations to
provide a multi-wavelength insight into past cluster-cluster merger events
that resulted in radio relics. In this section, we describe the multi-
wavelength observations that we utilize in our analysis.

###  2.1 Subaru Observations

The observations used in this study to make WL measurements were obtained with
the Subaru telescope. The Subaru telescope has a primary mirror diameter of
8.2 m and is an optical/infrared telescope located at the top of Mauna Kea on
Hawaii. The optical observations used in this study come from two instruments:
Suprime-Cam (Miyazaki et al., 2002) and Hyper Suprime-Cam (HSC; Miyazaki et
al., 2018; Komiyama et al., 2018; Kawanomoto et al., 2018; Furusawa et al.,
2018). The Suprime-Cam is a $5\times 2$ array of $4\mathrm{k}\times
2\mathrm{k}$ Hamamatsu CCDs with a $34\arcmin\times 27\arcmin$ field of view.
In 2017, the Suprime-Cam was decommissioned and the HSC became the primary
imager. The HSC is a 116 CCD instrument (104 science detectors) with a 1.5
degree diameter field of view.

The imaging presented in this work are summarized in Table 2. For about 1/3 of
the clusters, archival imaging is available. For those that lack Subaru
imaging, additional observations were gathered by PI: D. Wittman and more
recently by PI: H. Cho. These observations were performed with WL analysis in
mind. A dithering and rotation technique was executed to minimize degradation
of the images from the diffraction spikes caused by bright stars, bad columns,
cosmic rays, and bleeding trails. This imaging technique has been shown to
increase the number of usable galaxies available for WL studies (Jee et al.,
2015, 2016).

WL analysis requires a careful modeling of the PSF because it mimics the
lensing effect. For ground-based observations, the PSF is predominately
affected by the atmospheric seeing. Subaru observations were obtained in some
of the best seeing conditions with typically sub-arcsecond seeing achieved
(Table 2). For each cluster, we selected the filter for WL analysis by
carefully balancing exposure time (maximize) and seeing (minimize) with a
preference given to the redder filter when the choice was close. Redder
filters are preferred in WL analysis because the redder light from galaxies
tends to be less clumpy than the blue, star-forming light and is thus better
fit with a smooth model (Lee et al., 2018). The filter selected for WL is
highlighted in bold font in Table 2.

###  2.2 Subaru Data Reduction

Data reduction requires special care to produce a WL quality image. Subaru
SDFRED 1 (pre 2009) and 2 (post 2009)
packages111http://subarutelescope.org/Observing/Instruments/SCam/sdfred were
used for the basic reduction steps of overscan subtraction, bias correction,
flat-fielding, and distortion correction for the Suprime-Cam images.
SExtractor (Bertin & Arnouts, 1996) was run on each frame to prepare a catalog
of objects for SCAMP (Bertin, 2006). SCAMP was applied to correct for residual
distortions and to refine the World Coordinate System (WCS) for each frame. We
used the Pan-STARRS photometric catalog (Chambers et al., 2016) as a reference
in SCAMP to compute the astrometry. For the HSC images, the LSST Science
Pipelines (Bosch et al., 2018, 2019; Jenness et al., 2022) were used for
overscan/bias/dark subtraction, flat fielding, astrometric correction, etc.

The final step in creating a WL-quality image is to co-add the frames into a
mosaic image. The best $S/N$ mosaic is created by mean averaging the frames.
However, the frames are prone to cosmic rays, saturation trails, and other
detector effects. For this reason, a two-step process was used to co-add the
frames. First, SWarp (Bertin et al., 2002) was applied to the frames to
generate a median-stacked mosaic image. In preparation for co-addition, SWarp
translates, rotates, and distortion corrects the frames. These individual
RESAMP frames are critical to our PSF modeling (Section 3.2) and were stored
for later use. After resampling, the frames were carefully aligned using the
WCS solution from SCAMP and co-added by SWarp into a median-stacked mosaic
image. The median-stacking process outputs a weight file for each component
frame. We utilized the weight files to remove the aforementioned spurious
signals. The median-stacked mosaic image was compared to the RESAMP frames and
pixels from the RESAMP frames that deviated more than 3 times from the root
mean square (rms) of the median-stacked image were set to zero in the
corresponding weight file. A second pass of SWarp was done by weight-averaging
the input frames, and a mean-stacked mosaic image was created. This process
was performed on the filter with the longest exposure time first, and then the
header information was applied to the remaining filters to ensure the same
alignment and footprint.

Figure 1 presents a color version of the co-added mosaic of A2061. The three
channels of the RGB image are $i$, $r$, and $g$, respectively. The rotation
and dithering technique is noticeable around the edges of the mosaic and the
benefit of the technique is apparent by comparing the bright star in the
center to the stars near the edge. The Suprime-Cam’s large field of view
provides ample coverage to perform a WL analysis of a galaxy cluster
($\scriptstyle\sim$4 Mpc diameter field of view at z=0.1).

Figure 1: The Subaru color image of the galaxy cluster A2061 provides an
example of the quality of the imaging (blue=g-band, green=r-band, red=i-band).
The rotation and dithering technique of the observations is noticeable at the
perimeter of the image and is beneficial to WL analysis because it minimizes
the diffraction spikes caused by stars and allows a better sampling of the
PSF.  Table 2: Subaru imaging

Cluster | Filters | Dates | Seeing | Exposure | Source Density | $\left<\beta\right>$
---|---|---|---|---|---|---
|  |  | [arcsec] | [s] | [arcmin-2] |
1RXSJ0603 | g, r | 2014/02/25, 2014/02/25 | 0.57, 0.57 | 720, 2800 | 31 | 0.66
A115 |  V, i | 2003/09/25, 2005/10/03 |  0.58, 0.65 |  1530, 2100 | 24 | 0.54
A521 | V, R, i | 2001/10/14, 2001/10/15 | 0.59, 0.65, 0.59 | 1800, 1620, 2040 | 44 | 0.63
A523 | g, r | 2014/02/26 | 1.00, 0.78 | 720, 2880 | 19 | 0.81
A746 | g, r2 | 2023/01/16,20,22 | 1.26, 0.75 | 3480, 4320 | 24 | 0.63
A781 | V, i | 2010/03/14, 2010/03/15 | 0.90, 0.80 | 3360, 2160 | 28 | 0.55
A1240 | g, r | 2014/02/25 | 0.67, 0.58 | 720, 2880 | 43 | 0.73
A1300 | g, r | 2014/02/26 | 0.89, 0.88 | 720, 2913 | 23 | 0.55
A1612 | g, i | 2014/02/25, 2010/04/11 | 0.62, 0.65 | 2880, 1920 | 19 | 0.70
A2034 | g, R | 2005/04/11, 2007/06/19 | 0.82, 0.90 | 720, 12880 | 35 | 0.82
A2061 | g, r, i | 2013/07/13, 2014/02/26 | 0.68, 0.67, 0.65 | 720, 2550, 4120 | 44 | 0.87
A2163 | V, R | 2009/04/30, 2008/04/07 | 0.70, 0.75 | 2100, 4500 | 27 | 0.69
A2255 | B, R, i | 2007/08/14, 2008/07/30 | 0.98, 1.00, 0.64 | 1260, 2520, 1200 | 26 | 0.86
A2345 | V, i | 2010/06/10, 2010/11/10, 2005/10/03 | 0.70, 0.72 | 3600, 2100 | 17 | 0.68
A2443 | $-$ | $-$ | $-$ | $-$ | $-$ | $-$
A2744 | B, R, z | 2013/07/15, 2013/07/16 | 1.00, 1.14, 0.79 | 2100, 3120, 3600 | 25 | 0.52
A3365 | g, r, i | 2014/02/25 | 0.97, 0.71, 0.62 | 720, 720, 2880 | 20 | 0.81
A3411 | g, r, i | 2014/02/25 | 0.8, 0.82, 0.77 | 1000, 720, 2880 | 13 | 0.69
CIZAJ2242 | g, i | 2013/07/13 | 0.63, 0.55 | 720, 2880 | 14 | 0.62
MACSJ1149 | V, R | 2003/04/5, 2005/03/05, 2010/03/18 | 0.90, 0.86 | 2520, 5490 | 26 | 0.40
MACSJ1752 | g, r, i | 2013/07/13 | 0.62, 0.64, 0.73 | 2520, 720, 4400 | 26 | 0.62
PLCKG287 | g, r | 2014/02/26 | 0.81, 0.97 | 720, 2880 | 27 | 0.55
PSZ1G108 | g, i2 | 2017/08/20, 2017/08/19 | 0.65, 0.72 | 1440, 2880 | 15 | 0.48
RXCJ1053 | g, r | 2014/02/26 | 0.83, 0.92 | 720, 2910 | $-$ | $-$
RXCJ1314 | g, r | 2014/02/25 | 0.86, 0.71 | 720, 2880 | 18 | 0.64
ZwCl0008 | g, r | 2013/07/13 | 0.52, 0.57 | 720, 2880 | 24 | 0.81
ZwCl1447 | g, r, i | 2014/02/26 | 0.91, 0.76, 0.55 | 720, 2880, 720 | 44 | 0.52
ZwCl1856 | g, r | 2015/09/12 | 0.70, 0.65 | 720, 2520 | 31 | 0.55
ZwCl2341 | g, r | 2013/07/13 | 0.49, 0.50 | 720, 2880 | 20 | 0.69

The filter used for WL is in bold font.

###  2.3 Keck/DEIMOS Observations

Throughout this study, we utilize redshifts that were measured from Keck DEep
Imaging Multi-Object Spectrograph (DEIMOS) observations. The survey and data
reduction of the observations are thoroughly described in Golovich et al.
(2019b). In G19, they performed an analysis of the spectroscopic redshifts and
identified subclusters utilizing a GMM method.

###  2.4 MMT Hectospec Observations and Data Reduction

Some of the clusters in the G19 work have insufficient numbers of
spectroscopic redshifts to discern substructures. We collected MMT/Hectospec
(Fabricant et al., 2005) fiber observations (PI: K.Finner) at the 6.5 m
monolithic-mirrored MMT telescope on Mount Hopkins, Arizona. Cluster targets
were selected based on the scarcity of their spectroscopic coverage and on the
prospect of them having detectable large scale filaments. The MMT/Hectospec is
an efficient instrument for simultaneously achieving these two scientific
goals because it has a one-degree diameter field of view and 300 fibers.
However, fibers collide at distances of about $20\arcsec$, which limits how
densely the cores of clusters can be sampled, especially for those at higher
redshifts.

We observed A521, A746, A1240, and A2443 with approximately 1.5 hours of
exposure time each. Two configurations of the Hectospec instrument were
designed for each galaxy cluster utilizing the 270 grating (spectral range
3650 - 9200 Å). The goal of the observations was to securely measure redshifts
for galaxies that reside in the clusters. We plotted color-magnitude diagrams
(CMDs) from Subaru imaging for A521, A746, and A1240 and SDSS imaging for
A2443. The spectroscopically confirmed cluster galaxies in the CMD form a red
sequence. We fit a line to the red sequence to select cluster member
candidates that fall within a color range of $g-r\pm 0.1$ with the $r$-band
brightness limit set to $21.5$.

Raw spectra were processed with the hs_pipeline_wrap command in HSRED
2.1222https://github.com/MMTObservatory/hsred to produce sky-subtracted and
variance-weighted spectra. The IRAF add-on RVSAO (Kurtz & Mink, 1998) was used
to cross-correlate a set of template spectra and estimate redshifts. To select
robust redshift estimates, we only retained estimates with a cross-correlation
$r$-value $>4$. The MMT/Hectospec redshift catalogs are published in Yoon et
al. (2020) for A521, Cho et al. (2022) for A1240, HyeongHan et al. (2024b) for
A746, and Kim et al. in prep. for A2443.

###  2.5 Archival Radio and X-ray Observations

In this study, we rely on archival radio and X-ray observations to investigate
the relation of dark matter and ICM. Table LABEL:table:xray_radio summarizes
the sources of the radio and X-ray data. Radio images were kindly provided by
the authors listed in the Radio References column. X-ray data were retrieved
from the respective archive and processed.

Chandra observations were downloaded from the
Chaser333https://cda.harvard.edu/chaser/ archive. Utilizing the Python version
of the CIAO444https://cxc.cfa.harvard.edu/ciao/ package, the multiple visits
for each cluster were reprocessed and combined into a broad flux image
containing emission from 0.5-7 keV. For this reduction, we followed the
Diffuse Emission tutorial.

XMM-Newton images were downloaded from the XMM-Newton science
archive555http://nxsa.esac.esa.int/nxsa-web/. The images were reduced and
combined with the SAS pipeline following the procedures for diffuse extended
sources described in the XMM-ESAS
Cookbook666http://heasarc.gsfc.nasa.gov/docs/xmm/esas/cookbook/. The final
combined images have an energy range of 0.5-7 keV.

Unless otherwise stated, the X-ray imaging processed through these methods are
used purely for qualitative analysis.

Table 3: Archival radio and X-ray imaging utilized in this study.

Cluster | Radio Image | Radio References | X-ray Telescope | Exposure (ks)
---|---|---|---|---
1RXSJ0603 | GMRT 610 MHz | van Weeren et al. (2012b) | Chandra | 250
A115 | LOFAR 150 MHz | Botteon et al. (2022) | Chandra | 360
A521 | MeerKAT 1.3 GHz | Knowles et al. (2022) | Chandra | 170
A523 | VLA 1.4 GHz | van Weeren et al. (2011b) | Chandra | 30
A746 | LOFAR 150 MHz | Botteon et al. (2022) | XMM-Newton | 184
A781 | LOFAR 150 MHz | Botteon et al. (2022) | Chandra | 48
A1240 | LOFAR 150 MHz | Botteon et al. (2022) | Chandra | 52
A1300 | GMRT 325 MHz | Venturi et al. (2013) | Chandra | 100
A1612 | GMRT 325 MHz | van Weeren et al. (2011b) | Chandra | 31
A2034 | LOFAR 150 MHz | Botteon et al. (2022) | Chandra | 261
A2061 | LOFAR 150 MHz | Botteon et al. (2022) | Chandra | 32
A2163 | VLA 1.4 GHz | Feretti et al. (2001) | Chandra | 90
A2255 | WSRT 350 MHz | Pizzo & de Bruyn (2009) | XMM-Newton | 42
A2345 | VLA 1.4 GHz | Bonafede et al. (2009a) | XMM-Newton | 93
A2443 | VLA 325 MHz | Cohen & Clarke (2011) | Chandra | 116
A2744 | MeerKAT 1.3 GHz | Knowles et al. (2022) | Chandra | 132
A3365 | VLA 1.4 GHz | van Weeren et al. (2011b) | XMM-Newton | 161
A3411 | GMRT 325 MHz | van Weeren et al. (2017) | Chandra | 215
CIZAJ2242 | WSRT 1382 MHz | van Weeren et al. (2010) | Chandra | 206
MACSJ1149 | LOFAR 150 MHz | Bruno et al. (2021) | Chandra | 372
MACSJ1752 | LOFAR 150 GHz | Botteon et al. (2022) | XMM-Newton | 13
PLCKG287 | GMRT 325 MHz | Bonafede et al. (2014b) | Chandra | 200
PSZ1G108 | GMRT 323 MHz | de Gasperin et al. (2015) | Chandra | 27
RXCJ1053 | WSRT 1382 MHz | van Weeren et al. (2011b) | Chandra | 31
RXCJ1314 | MeerKAT 1.3 GHz | Knowles et al. (2022) | XMM-Newton | 110
ZwCl0008 | WSRT 1382 MHz | van Weeren et al. (2011c) | Chandra | 411
ZwCl1447 | GMRT 700 MHz | Lee et al. (2022) | Chandra | 30
ZwCl1856 | LOFAR 150 MHz | Jones et al. (2021) | XMM-Newton | 12
ZwCl2341 | GMRT 610 MHz | van Weeren et al. (2009) | Chandra | 227

###  2.6 Object Detection and Photometry

The detection of the WL signal requires a statistical analysis of galaxy
shapes. A main source of noise that contributes to a WL analysis is shape
noise, which is caused by the dispersion of the intrinsic ellipticity of
galaxies. To reduce the contribution from shape noise, a large number of
galaxies is needed. Therefore, we optimize our object detection method to
robustly detect as many galaxies as possible.

We performed photometry with SExtractor (Bertin & Arnouts, 1996) in dual-image
mode. As the name implies, dual-image mode uses two images. The detection
image is kept constant while the measurement image is varied between runs to
ensure that the resulting filter-specific catalogs have the same objects. For
each cluster, we created a detection image by weight-averaging all available
filters together. When running SExtractor, a weight image for the detection
image was provided that was created by weight-averaging the SWarp weight
images together. Measurements were taken on the measurement image (one for
each filter) with an rms image provided for weighting. The rms image was
created by multiplying the weight image of the filter by the background rms of
its mosaic and masking spurious pixels. Our configuration of SExtractor set
DETECT_MINAREA to 5 pixels and DETECT_THRESH to 2. The settings for deblending
were set to DEBLEND_NTHRESH of 32 and DEBLEND_MINCOUNT of $10^{-4}$ to
maximize detection of overlapping objects.

The Subaru photometric zero-point was calibrated by matching stars to an
external star catalog. The first choice was the SDSS DR14 photometric catalog
but when not available the Pan-STARRS DR1 catalog was used. In all cases, the
difference in filter throughput was accounted for by performing synthetic
photometry (Sirianni et al., 2005). To derive the correct photometric
zeropoint, the magnitude of stars from the reference catalog were compared to
the SExtractor MAG_AUTO measurements. The left panel of Figure 2 displays the
magnitude difference as a function of magnitude for the stars in the A2061
$r$-band image. Instead of relying on the full population of stars, we
selected unsaturated stars from the stellar locus as shown in the right panel.
The magnitude difference follows a linear relation over the region shown and
in most cases has a slope close to 0. We repeated this method for each filter
and applied the linear calibration to the Subaru magnitudes.

Figure 2: Photometric zeropoint calibration of A2061 (left panel). The SDSS
catalog is used as a reference. Stars (red circles) are selected from the
size-magnitude plot (right panel) and matched with stars in the reference
catalog. The magnitude offset as a function of SDSS $r$-band magnitude is
plotted and a linear fit to the stars is made to determine the zeropoint. The
same stars are utilized in PSF modeling.

##  3 WL THEORY AND METHODOLOGY

###  3.1 Gravitational Lensing Formalism

Bartelmann & Schneider (2001), Hoekstra (2013), and Meneghetti (2022) provide
comprehensive reviews of gravitational lensing theory. For brevity, we state
the critical ideas and nomenclature that are required to understand our
analysis.

The gravitational lensing effect is caused by the deflection of light by a
gravitational potential. The deflection of light leads to a shift in the
apparent position of the light source, a galaxy in our case. The relation
between the true source position $\boldsymbol{\eta}$ and the observed position
$\mathbf{x}$ is

$\boldsymbol{\eta}=\mathbf{x}-\boldsymbol{\alpha}(\mathbf{x}),$ (1)

where

$\boldsymbol{\alpha}(\mathbf{x})=\frac{1}{\pi}\int\kappa(\mathbf{x^{\prime}})\frac{\mathbf{x}-\mathbf{x^{\prime}}}{|\mathbf{x}-\mathbf{x^{\prime}}|^{2}}d^{2}\mathbf{x}$
(2)

is the scaled deflection angle. The scaling depends on the convergence

$\kappa(\mathbf{x})=\frac{\Sigma(\mathbf{x})}{\Sigma_{c}},$ (3)

which is a dimensionless quantity of the projected mass density divided by the
lensing critical density. The lensing critical density is

$\Sigma_{c}=\frac{c^{2}D_{s}}{4\pi GD_{l}D_{ls}},$ (4)

where $D_{l}$ is the angular diameter distance to the lens, $D_{s}$ is the
angular diameter distance to the source, $D_{ls}$ is the angular diameter
distance from lens to source, $c$ is the speed of light, and $G$ is the
gravitational constant. The ratio $\beta=D_{ls}/D_{s}$ is referred to as the
lensing efficiency.

The tidal gravitational field causes an anisotropic distortion, called the
shear ($\gamma$), that stretches galaxy images tangential to the local
gravitational potential gradient. When the gravitational lensing effect is in
the weak regime ($\kappa\ll 1$, $\gamma\ll 1$), single galaxy images appear
and the distortions are small. Kaiser & Squires (1993) show that the shear and
convergence are related by the convolutions

$\kappa(\mathbf{x})=\frac{1}{\pi}\int
D^{*}(\mathbf{x}-\mathbf{x^{\prime}})\gamma(\mathbf{x^{\prime}})d^{2}\mathbf{x^{\prime}},$
(5)

$\gamma(\mathbf{x})=\frac{1}{\pi}\int
D(\mathbf{x}-\mathbf{x^{\prime}})\kappa(\mathbf{x^{\prime}})d^{2}\mathbf{x^{\prime}},$
(6)

where $D(\mathbf{x})=-1/(x_{1}-ix_{2})^{2}$ is the convolution kernel.

Observationally, we detect the reduced shear

$g=\frac{\gamma}{1-\kappa},$ (7)

which is the combination of the convergence and the shear. The distortions
caused by WL may be expressed by the Jacobian matrix

$A=(1-\kappa)\begin{bmatrix}1-g_{1}&-g_{2}\\\ -g_{2}&1+g_{1}\end{bmatrix}.$
(8)

The reduced shear is encoded as a complex term ($g=g_{1}+ig_{2}$) where
positive (negative) values of $g_{1}$ distort galaxy images along the $x$
($y$) directions and positive (negative) values of $g_{2}$ distort images
along the $x=y$ ($x=-y$) directions. In this work, we define the ellipticity
(shape) of galaxies as $e=(a-b)/(a+b)$, where $a$ and $b$ are the semi-major
and semi-minor axes, respectively. Each observed galaxy has a measured
ellipticity that includes its intrinsic shape and the local shear

$e\approx e_{\mathrm{intrinsic}}+g.$ (9)

Under the assumption that galaxy images have random orientations, the averaged
ellipticity of galaxy images is the reduced shear

$\langle e\rangle\approx g.$ (10)

###  3.2 Point Spread Function Modeling

WL requires the careful measurement of galaxy shapes. However, the turbulent
atmosphere and the diffraction of light through the telescope causes a
significant anisotropic blurring of the galaxy images. It is critical for a WL
analysis to properly model and remove the effect of the PSF. For our analysis,
we utilize a principal component analysis (PCA) approach to deriving a spatial
and temporal PSF model. Jee et al. (2007) showed that the PCA approach
accounts for small and large scale structures of the PSF. PCA is also
beneficial because it derives the basis functions from the data set itself and
requires few components. The PCA technique that is used in this work has been
applied to a variety of space- and ground-based observations (Finner et al.,
2017, 2020; HyeongHan et al., 2020; Finner et al., 2023c, b; HyeongHan et al.,
2024a) including the James Webb Space Telescope (JWST) in Finner et al.
(2023a).

The dynamic atmosphere causes the PSF of Subaru to vary temporally and
spatially. Furthermore, both the Suprime-Cam and the HSC have a large field of
view, which leads to a complex PSF across the full mosaic that is difficult to
interpolate and suffers from discontinuities at CCD boundaries (in similar
fashion to that shown in the Deep Lens Survey; Jee et al., 2013). To resolve
these issues, we create PSF models on a frame-by-frame basis and then stack
them into a final PSF model that is usable for measurement from the coadded
mosaic.

For brevity, we will list the steps of the PSF pipeline. For an in-depth
explanation of the pipeline, we refer the reader to Finner et al. (2017).
First, a PCA is performed on stars that best represent the PSF (isolated,
bright but not saturated, etc.).

  * •

Select stars for each frame based on size and magnitude. The right panel of
Figure 2 illustrates the selection process for one cluster. Create 21 pixel by
21 pixel postage stamps of each selected star and shift them to be centered on
the cutout.

  * •

Store the mean star and a residual array (N stars by 441 pixels) that is
created by subtracting the mean star from each individual star.

  * •

Perform a PCA of the residual and keep the 21 components with the highest
variance. The choice for keeping 21 components was found empirically by
evaluating the PSF residuals as presented later in this section.

The PCA and the mean star can be utilized to generate a PSF at any position in
the frame, which can then be stacked into PSF models for the coadded mosaic as
follows.

  * •

Fit the PCA result with a third order polynomial.

  * •

Add the fitted PCA result onto the mean star.

  * •

Repeat for all objects of interest in the frame.

  * •

For each object in the mosaic image, determine which frames compose the mosaic
and stack the PSF models for those frames to a coadded PSF model.

Figure 3 compares the ellipticity of stars (top) in A2061 to the corresponding
PSF models (bottom). In most cases, the PSF models trace the magnitude and
direction of the ellipticity of stars. Figure 4 displays the statistics of the
correction made by the PSF model. The red circles are the ellipticity of stars
in the mosaic. By subtracting the ellipticity of the PSF model for each star,
we get the residual (black circles). There are two desired effects that are
important to see when comparing the measured ellipticity of stars and the
residual. First, the distribution should shift toward 0 if the average
ellipticity is being corrected. Second, the distribution should tighten if the
spatial variation of the ellipticity is being corrected. We see that both
effects are being corrected for. A2061 demonstrates the typical residual for
our PSF models with a mean ellipticity residual of order $10^{-4}$ and
standard deviation of $10^{-3}$. This level of accuracy is sufficient for WL
analysis of galaxy clusters.

Figure 3: A2061 PSF distortion. Top: Measured ellipticity of a selection of
stars from the mosaic coadded image. The lines represent the direction and
magnitude of the ellipticity of stars. Outliers have not been removed and
clearly do not follow the general trend of the PSF. Bottom: Ellipticity of the
model PSFs at each star location. Models are designed in each component frame
and stacked to a coadded PSF. Comparing the top and bottom panels shows that
the measured stellar shape is well reproduced by the PSF model. Figure 4:
A2061 PSF model correction. Red circles denote the observed ellipticity of
stars. Black circles are the corrected ellipticities where the PSF model
ellipticities have been subtracted from the observed ellipticities of their
respective stars. The figure demonstrates that the ellipticity is being
corrected. The goal is to tighten the dispersion and shift the centroid to
zero. As the legend shows, the dispersion is decreased by about two and the
centroid is corrected to the $10^{-4}$ level.

###  3.3 Galaxy Shape Measurement with PSF Correction

Detection of the WL effect requires a statistical analysis of the shapes of
distorted galaxy images. We employed a model-fitting technique to measure the
shapes of galaxies. For each cluster, we follow the same recipe for measuring
galaxy shapes.

To measure the shape of a single galaxy, we cut out a postage stamp image of
the galaxy from the mosaic image. A corresponding rms noise postage stamp
$\sigma_{\mathrm{rms}}$ was also cut out from the rms mosaic image. It is
important to consider the size of the postage stamp image. A large postage
stamp image will contain the light from nearby objects, which may
significantly alter the shape measurement. However, a small postage stamp may
prematurely truncate the galaxy light profile and lead to truncation bias
(Mandelbaum, 2018). We chose to cut large postage stamp images that are eight
times the size of the half-light radius as measured by SExtractor (Bertin &
Arnouts, 1996), with a 10 pixel floor for very small objects. Making use of
the SExtractor segmentation map, we masked any nearby bright objects that
could influence the shape measurement by setting the relevant pixels in the
rms noise postage stamp to $10^{6}$.

We fit an elliptical Gaussian function, $G$, to the postage stamp image, $I$,
while forward-modeling the corresponding PSF model, $P$, as follows:

$\chi^{2}=\sum\left(\frac{I-G\circledast
P}{\sigma_{\mathrm{rms}}}\right)^{2},$ (11)

where the summation is over the pixels of the postage stamp. The elliptical
Gaussian function has seven free parameters: background, amplitude, position
($x$ and $y$), semi-major axis ($a$), semi-minor axis ($b$), and orientation
angle ($\phi$). To fit the galaxies, we utilized a Python version of the
Levenburg-Marquardt least-squares fitting code MPFIT. Uncertainties returned
by MPFIT are determined from the Hessian matrix and assume a Gaussian
distribution. We fixed the background, $x$, and $y$ to the SExtractor values
of BACKGROUND, XWIN_IMAGE, and YWIN_IMAGE while fitting the remaining four
parameters. Complex ellipticities were determined from the fitted values of
$a$, $b$, and $\phi$ as

$\begin{split}e_{1}&=\frac{a-b}{a+b}\cos 2\phi,\\\ e_{2}&=\frac{a-b}{a+b}\sin
2\phi.\end{split}$ (12)

Galaxy shape measurement techniques suffer from biases that must be corrected
for. The biases are typically encoded into a linear correction factor with a
multiplicative and additive bias. We derived a calibration factor from
simulations of our pipeline to correct for multiplicative bias. Following the
technique called SFIT (Jee et al., 2013), which was the best performing
technique in the GREAT3 challenge (Mandelbaum et al., 2015), we processed
simulated images with our Subaru WL pipeline and compared the input shear to
the measured shear. We found that a multiplicative calibration factor of 1.15
was necessary to correct the biases of our pipeline and that additive biases
were low ($<10^{-4}$).

For each cluster, galaxy shape measurements were made in the WL image (see
Table 2) and shape catalogs were compiled. The shape catalogs created through
this procedure will be further culled in the following sections to a
background source catalog that ideally contains only lensed galaxies.

###  3.4 Source Selection

The ideal catalog for a WL analysis contains only galaxies that are at a
greater distance than the lens (cluster) from the observer. Having distance
measurements for each galaxy would make source selection trivial. However,
gathering spectroscopic redshifts for all background galaxies is an immense
undertaking. Photometric redshifts are a second option but a reliable redshift
requires vast multiband imaging, which is not readily available for our sample
of galaxy clusters. We instead rely on colors and magnitudes to separate
foreground, cluster, and background galaxies.

There are multiple properties of galaxies that are useful for placing galaxies
into these three categories. Galaxies residing in a cluster environment tend
to have lower star formation rates, an overall older population of stars, and
a large amount of dust compared to field galaxies (Dressler, 1984). In
addition, an accumulation of metals that are deposited by past star formation
leads to a prominent feature in the spectral energy distribution (SED) of
evolved cluster galaxies called the 4000 Å break. The 4000 Å break manifests a
red-sequence relation in a CMD when observed with two filters that bracket the
feature. In the redshift range of our sample (0.07-0.54), the 4000 Å break is
well bracketed by the $g$ and $r$ or $g$ and $i$ filters. Figure 5 presents
the CMD of A2061. The red sequence is clearly marked by the red circles of
spectroscopically confirmed cluster galaxies. However, it can also be seen
extending to fainter magnitudes within the green, dashed rectangle. We make a
photometric selection of cluster galaxy candidates (dashed, green rectangle)
by extending the red sequence to an $r$-band magnitude of 21. We opt to select
galaxies that are within 0.1 in $g-r$ color to the linear fit, which
encapsulates the majority of red-sequence galaxies. Following this recipe, we
create a catalog of cluster galaxies that are used to plot galaxy luminosity
and number density maps in Section 4.

The color and magnitude properties of galaxies are also useful for selecting
background galaxies. Galaxies behind the cluster are on average fainter than
the cluster members as apparent brightness is proportional to inverse-squared
distance. Identifying background galaxies based on color is more complicated.
The cosmological expansion of space redshifts galaxy emission. However, there
is the competing evolutionary effect where galaxies at greater distances
appear on average to be younger than nearby galaxies. When viewed through the
color of $g-r$ or $g-i$, the evolutionary effect tends to be stronger than the
redshift effect beyond a redshift of 0.5, which leads to background galaxies
being bluer than cluster and foreground galaxies (see Schrabback et al., 2018,
for an example). Therefore, we select galaxies that are bluer than the red
sequence for clusters that are above redshift of 0.2. Below a redshift of 0.2,
limiting the background galaxy catalog to only sources that are bluer than the
red sequence leads to a low source density. Therefore, in these cases, we
include both red and blue galaxies in our source catalog but reject the
galaxies that exist in the color space that follows the red sequence. The CMD
for A2061 in Figure 5 shows this selection technique. In all cases, we set a
brightness limit for the source catalog of 22nd magnitude because the
likelihood of such bright galaxies being foreground or cluster galaxies is
high.

In addition to these magnitude and color selection criteria, we constrain the
background source catalog by our ability to measure their shapes. We ensure
that spurious objects that are too small to be lensed galaxies are removed by
constraining the semi-minor axis to be greater than 0.3 pixels. Highly
elongated objects are rejected by forcing the measured ellipticity to be less
than 0.9. We require the ellipticity error to be less than 0.3. Finally, only
“well fit” objects from the MPFIT fitter are kept (MPFIT status of 1).

These constraints lead to a robust source catalog that carefully balances the
purity and number density of the source (lensed) galaxy catalog. The source
densities for each cluster are summarized in Table 2. The average source
density is 25 arcmin-2.

Figure 5: CMD for A2061 with $g-r$ [MAG_ISO] color and $r$ [MAG_AUTO] from
SExtractor. Red circles represent the spectroscopically confirmed cluster
member galaxies within $z\pm 0.03$ of the cluster redshift. The green dashed
box highlights the photometrically selected sample of cluster member
candidates based on a linear fit to the red sequence. Background galaxies
(blue circles) are selected following the criteria described in section 3.4. A
red selection of source galaxies is included for A2061 because of its low
redshift ($z=0.08$).

###  3.5 Redshift Estimation

In a WL analysis, each source galaxy provides a probe of the projected galaxy
cluster potential. As is apparent in Equation 3, the effectiveness of the
gravitational lens varies on a source-by-source basis with the lensing
efficiency ratio, $\beta$. Unfortunately, distances to each of the source
galaxies in our sample are unavailable. To remedy this, we rely on the
photometric redshift catalog (Dahlen et al., 2010) of the GOODS-S field as a
reference for our source galaxy catalog. A version of the GOODS-S catalog that
is modeled to represent the source catalog is used to quantify the effective
redshift of the source catalog by the method described below. This technique
is common in WL studies that do not have the luxury of redshifts for each
source galaxy (to name a few, Jee et al., 2011; Okabe & Smith, 2016;
Schrabback et al., 2018).

The GOODS-S reference catalog is constrained with the same color and magnitude
criteria that are applied when selecting the source galaxies. Figure 6
compares the galaxy number density of the constrained GOODS-S catalog to the
A2061 source catalog. The GOODS-S observations are much deeper than the Subaru
observations and probe to much fainter magnitudes. To alleviate the difference
in depth, the constrained GOODS-S catalog is weighted by the number density
ratio for each bin. An effective $\beta$ for the source galaxies of the Subaru
imaging is then inferred from the constrained and weighted GOODS-S catalog
ensuring that any galaxy that is foreground is assigned a $\beta=0$ following

$\left<\beta\right>=\left<max\left(0,\frac{D_{ls}}{D_{s}}\right)\right>.$ (13)

The $\left<\beta\right>$ values for each cluster are tabulated in Table 2.
Since the source galaxies are represented by a single $\left<\beta\right>$, a
first-order correction (Seitz & Schneider, 1997)

$g^{\prime}=\left[1+\left(\frac{\left<\beta^{2}\right>}{\left<\beta\right>^{2}}-1\right)\kappa\right]g.$
(14)

is applied to the reduced shear to take the width of the distribution into
consideration. Foregoing this correction can lead to an overestimation of
cluster masses (e.g., Hoekstra et al., 2000).

Figure 6: Galaxy number density by magnitude for the constrained (by color)
GOODS-S reference catalog and A2061 source galaxy catalog. The GOODS-S
observations are much deeper, which gives rise to the large difference in
source density at faint magnitudes. To make up for the difference in depth,
the GOODS-S catalog is weighted by the ratio of the bins when used as a
reference catalog.

###  3.6 Convergence Reconstruction

In Section 3.1, the basic inversion method for convergence reconstruction was
introduced. The simplest method to recover the convergence is to average
galaxy shapes in spatial bins across the field of view of the cluster. The
spatial averaging of galaxy shapes produces a map of the reduced shear. Then,
by the convolution of Equation 5, the convergence distribution can be
recovered. This convolution method is prone to edge effects that can
artificially increase the lensing signal near the edge of the image. In this
work, we utilize a code called FIATMAP (Wittman et al., 2006) that performs
the convolution in real-space rather than in the Fourier domain.

###  3.7 Substructure Identification

One of the goals of this study is to identify the merging subclusters that may
be responsible for the formation of radio relics. For all of the clusters in
this study, multiple peaks in the WL maps are expected. However, not all of
these peaks should be taken as merging subclusters (substructures).

In order to identify the real WL peaks from the false detections, we utilize
the multiwavelength data. Significant subclusters are expected to be massive
enough to emit brightly in X-rays. Furthermore, they are expected to have
bright cluster galaxies in the vicinity of their WL peaks. Therefore, we will
identify subclusters as those with significant WL peaks ($S/N>3$) and nearby
galaxy overdensities or X-ray brightness peaks.

###  3.8 Mass Estimation

There are multiple methods to estimate the mass of a galaxy cluster. One
method is to use a proxy for the mass and calibrate it with a robust mass
estimate. These methods are called mass-scaling relations and rely on the
emission from the gas and stars as a tracer of the cluster potential. One of
the common scaling relations is the mass-richness relation, which positively
correlates the number of cluster galaxies to the total mass of the system
(e.g. Murata et al., 2019). Other scaling relations utilize the X-ray emission
or the Sunyaev Zel’dovich (SZ; Sunyaev & Zeldovich, 1972) effect from the gas
to estimate the mass (e.g. Ge et al., 2019). The galaxies and gas can also
provide a mass estimate directly by assuming that they are in hydrostatic
equilibrium (HSE). With that assumption, the gravitational potential can be
equated to the outward pressure force of the gas. In this work, we derive mass
from the galaxy velocity dispersion measurements presented in G19 by applying
the scaling relation from Evrard et al. (2008):

$M_{200}=\left(\frac{\sigma_{DM}}{\sigma_{DM,15}}\right)^{1/\alpha}10^{15}\
\mathrm{M}_{\odot},$ (15)

where $\sigma_{DM,15}=1082\pm 4$ km s-1 and $\alpha=0.3361\pm 0.0026$ are
derived from cosmological simulations.

The validity of applying HSE when estimating the mass of a galaxy cluster has
been questioned. Suto et al. (2013), and more recently Biffi et al. (2016),
found that the HSE assumption for clusters in cosmological simulations had
mass estimates that departed from the true cluster mass by as much as $30\%$.
As expected, these studies find that the disturbed systems show the largest
deviations from HSE.

Mass estimates based on the WL signal from galaxy clusters do not require an
HSE assumption. Furthermore, the WL signal is caused by the complete mass
(gravitational potential) of the cluster, which is predominantly dark matter.
Thus, WL should be a more accurate probe of the mass of merging systems.
However, there are recent investigations into the bias of fitting Navarro-
Frenk-White (NFW; Navarro et al., 1997) models to the WL signal of merging
galaxy clusters that suggests that mass estimates may be biased at certain
stages of the cluster merger process (Lee et al., 2023).

####  3.8.1 Multiple Halo Mass Estimation

The clusters that are being analyzed in this paper contain multiple
substructures. Hence, it would be improper to model them as a single object.
Instead, we fit a multi-halo NFW model to the observed data to estimate the
masses of each subcluster simultaneously. The fit is accomplished by
predicting the reduced shear at every source galaxy position and then
calculating the $\chi^{2}$ between the observed galaxy ellipticity and modeled
shear

$\chi^{2}=\sum_{i,j}\left(\frac{e_{i,j}-g_{i,j}}{\sigma_{i,j}}\right)^{2}$
(16)

where $i$ is summed over each galaxy and $j$ is summed over the two components
of the shear (ellipticity). In this equation, $\sigma_{i,j}=(\delta
e_{i,j}^{2}+\sigma_{SN}^{2})^{-0.5}$ is the ellipticity measurement
uncertainty $\delta e_{i,j}$ and the shape noise $\sigma_{SN}^{2}$ added in
quadrature. We fix the shape noise to $\sigma_{SN}=0.25$. The reduced shear is
predicted following the NFW equations from Wright & Brainerd (2000).

In this analysis, we use two different methods to constrain the mass with the
NFW profile. The first method utilizes a concentration-mass ($c-M$) relation.
The $\chi^{2}$ in Equation 16 is passed into the optimization package of
MPFIT, which typically converges on the order of 10 iterations. Relations for
$c-M$ are developed from cosmological simulations that cover a wide range of
redshifts and cluster masses. One of the more common $c-M$ relations that is
applied in WL studies is that of Duffy et al. (2008). Their $c-M$ relation is
derived from Gadget2 simulations with a box size of 400 Mpc and is as follows:

$M_{200}=2\left(1+z\right)^{-B/A}\left(\frac{c}{5.71\pm
0.12}\right)^{1/A}10^{14}\ \mathrm{M}_{\odot},$ (17)

where $A=-0.084\pm 0.006$ and $B=-0.47\pm 0.04$ for clusters in a redshift
range of $0<z<2$. However, $c-M$ relations that are derived from simulations
are subject to the limitations of the simulations. For instance, the limited
box size and cosmology imprinted on the initial conditions affect the $c-M$
relation. This is manifested in the variety of $c-M$ relations that have been
derived from various simulations (e.g. Duffy et al., 2008; Dutton & Macciò,
2014; Diemer & Joyce, 2019). We elect to use the Duffy et al. (2008) relation
in this work because it has been commonly applied in past WL studies and will
ease comparison.

An alternative to using a $c-M$ relation is to fit both concentration and
mass. However, there is a degeneracy between the concentration and mass that
prevents this technique from converging for clusters that have low WL signal
(Finner et al., 2017). Therefore, we sample the $c-M$ parameter space with
Markov Chain Monte Carlo (MCMC). We confine the MCMC to uniform priors that
sufficiently cover the typical range of the mass ($10^{13}$
M${}_{\odot}<M_{200}<10^{16}\ M_{\odot}$) and concentration ($1<c<9$) for
galaxy clusters. Masses are determined from the highest likelihood returned
from Equation 16 and uncertainties on the mass are calculated by marginalizing
over the concentration. We will refer to this method as 2PNFW (for 2
parameter) from here on.

In both of these methods, multiple halos are simultaneously fit to the WL
signal. We choose to fix each halo to its mass peak’s corresponding BCG. The
BCG is not necessarily the center of the cluster, but on average it is a good
tracer of the cluster potential centroid (Zitrin et al., 2012) and is well
defined. Another good choice is the WL derived mass peak, but there is a large
positional uncertainty associated with it for low $S/N$ WL results. Sommer et
al. (2022) investigated the impact of miscentering on WL mass estimates and
showed that it tends to lead to underestimates of the mass. In many of these
merging cluster cases, the X-ray peak would be a poor choice for the center
because it departs significantly from the dark matter density peak.

Table 4: WL Subcluster Mass Estimates

Cluster | Ind. |  Duffy $M_{200}$ |  2PNFW $M_{200}$ | $\sigma_{v}$
---|---|---|---|---
|  |  $10^{14}\ $M⊙ |  $10^{14}\ $M⊙ |  km s-1
1RXSJ0603 N | A | $6.2\pm 1.2$ | $12.9^{+3.3}_{-3.1}$ | $925\pm 51$
1RXSJ0603 S | A | $2.8\pm 0.8$ | $1.9^{+1.0}_{-0.6}$ | $763\pm 100$
A115 N | B | $1.4\pm 0.5$ | $1.0^{+0.5}_{-0.3}$ | $1056\pm 60$
A115 S | B | $3.0\pm 0.8$ | $3.3^{+1.4}_{-1.0}$ | $1108\pm 70$
A521 C | C | $3.5\pm 0.9$ | $5.9^{+2.4}_{-1.9}$ | $990\pm 85$
A521 NW | C | $1.1\pm 0.5$ | $0.5^{+0.6}_{-0.2}$ | $-$
A521 SE | C | $2.5\pm 0.7$ | $1.9^{+1.2}_{-0.8}$ | $735\pm 67$
A523 N | D | $2.7\pm 0.9$ | $2.2^{+1.7}_{-1.0}$ | $814\pm 60$
A523 S | D | $1.6\pm 0.7$ | $1.8^{+1.8}_{-0.9}$ | $673\pm 53$
A746 S | E | $6.3\pm 1.5$ | $6.6^{+2.7}_{-1.9}$ | $1094\pm 95$
A781a East | F | $3.3\pm 0.8$ | $2.8^{+1.6}_{-1.0}$ | $-$
A781 Middle | F | $4.2\pm 0.9$ | $5.0^{+2.9}_{-1.8}$ | $821\pm 65$
A781 Main | F | $3.5\pm 0.8$ | $4.0^{+2.0}_{-1.4}$ | $830\pm 54$
A781a North | F | $1.7\pm 0.6$ | $1.5^{+1.2}_{-0.6}$ | $-$
A1240 N | G | $2.6\pm 0.6$ | $3.3^{+0.9}_{-1.1}$ | $706\pm 52$
A1240 S | G | $1.1\pm 0.4$ | $0.8^{+0.5}_{-0.5}$ | $727\pm 68$
A1300 S | H | $11.0\pm 1.8$ | $12.8^{+2.7}_{-1.3}$ | $1205\pm 51$
A1612 E | I | $4.0\pm 1.0$ | $6.6^{+2.9}_{-2.0}$ | $826\pm 83$
A1612 W | I | $1.8\pm 0.7$ | $1.0^{+0.8}_{-0.5}$ | $662\pm 118$
A2034 N | J | $0.9\pm 0.4$ | $0.6^{+0.4}_{-0.2}$ | $815\pm 94$
A2034 S | J | $3.6\pm 0.7$ | $4.7^{+1.8}_{-1.3}$ | $726\pm 57$
A2061 N | K | $2.0\pm 0.6$ | $3.1^{+1.8}_{-1.3}$ | $841\pm 54$
A2061 S | K | $1.6\pm 0.5$ | $1.1^{+0.6}_{-0.4}$ | $-$
A2163a N | L | $1.1\pm 0.7$ | $0.8^{+0.6}_{-0.5}$ | $952\pm 92$
A2163 E | L | $9.2\pm 1.8$ | $9.0^{+2.3}_{-2.8}$ | $1389\pm 75$
A2163 W | L | $0.8\pm 0.6$ | $0.5^{+0.5}_{-0.3}$ | $741\pm 75$
A2255 E | M | $1.3\pm 0.6$ | $1.1^{+0.8}_{-0.5}$ | $-$
A2255 W | M | $4.7\pm 1.1$ | $5.1^{+3.2}_{-1.9}$ | $988\pm 36$
A2345a E | N | $4.7\pm 1.2$ | $5.0^{+1.3}_{-1.0}$ | $1065\pm 67$
A2345 C | N | $3.2\pm 1.0$ | $3.3^{+2.3}_{-1.5}$ | $1065\pm 67$
A2345 W | N | $2.1\pm 0.8$ | $1.6^{+1.6}_{-0.8}$ | $-$
A2744 E | O | $7.2\pm 1.8$ | $8.5^{+2.5}_{-2.5}$ | $772\pm 52$
A2744 W | O | $6.6\pm 2.3$ | $3.2^{+2.2}_{-1.5}$ | $678\pm 82$
A2744 N | O | $1.0\pm 0.8$ | $1.9^{+1.9}_{-1.0}$ | $1154\pm 70$
A2744 S | O | $0.6\pm 0.6$ | $0.8^{+0.6}_{-0.5}$ | $666\pm 52$
A3411 W | P | $2.3\pm 1.0$ | $3.9^{+3.9}_{-1.9}$ | $1204\pm 84$
A3411 E | P | $1.8\pm 1.0$ | $1.0^{+1.3}_{-0.6}$ | $-$
A3412a | P | $1.1\pm 0.8$ | $0.8^{+1.2}_{-0.5}$ | $1199\pm 82$

$68\%$ uncertainties reported
a denotes subclusters that are not involved in the merger

Table 4: WL Subcluster Mass Estimates continued

Cluster | Ind. | Duffy $M_{200}$ | 2PNFW $M_{200}$ | $\sigma_{v}$
---|---|---|---|---
|  |  $10^{14}\ $M⊙ |  $10^{14}\ $M⊙ | km s-1
CIZAJ2242 N | Q | $8.2\pm 1.8$ | $12.3^{+3.9}_{-3.0}$ | $1102\pm 69$
CIZAJ2242 S | Q | $9.3\pm 1.8$ | $15.8^{+4.6}_{-3.5}$ | $1146\pm 88$
MACSJ1149 C | R | $16.4\pm 3.1$ | $13.5^{+3.5}_{-2.8}$ | $1295\pm 62$
MACSJ1752 NE | S | $5.6\pm 1.8$ | $5.5^{+1.9}_{-1.4}$ | $1006\pm 68$
MACSJ1752 SW | S | $5.6\pm 1.7$ | $5.1^{+2.0}_{-1.5}$ | $1038\pm 77$
PLCKG287 SE | T | $1.7\pm 0.7$ | $1.0^{+0.7}_{-0.6}$ | $680\pm 87$
PLCKG287 C | T | $20.4\pm 1.9$ | $20.0^{+2.4}_{-2.2}$ | $1373\pm 72$
PLCKG287 NW | T | $1.4\pm 0.7$ | $1.0^{+0.7}_{-0.5}$ | $-$
PSZ1G108 M | U | $6.9\pm 2.1$ | $7.6^{+2.5}_{-2.5}$ | $873\pm 90$
PSZ1G108 NE | U | $1.5\pm 1.2$ | $1.4^{+1.2}_{-0.8}$ | $-$
RXCJ1314 E | V | $2.3\pm 1.0$ | $3.9^{+2.1}_{-1.9}$ | $799\pm 73$
RXCJ1314 W | V | $4.2\pm 1.3$ | $2.5^{+1.2}_{-0.8}$ | $845\pm 99$
ZwCl0008 E | W | $2.9\pm 0.8$ | $2.8^{+1.5}_{-1.0}$ | $757\pm 62$
ZwCl0008 W | W | $2.7\pm 0.8$ | $2.8^{+1.5}_{-1.0}$ | $681\pm 66$
ZwCl1447 N | X | $2.7\pm 0.8$ | $2.0^{+1.8}_{-0.9}$ | $1147\pm 63$
ZwCl1447 S | X | $1.0\pm 0.5$ | $1.2^{+2.2}_{-0.8}$ | $-$
ZwCl1447a X | 24 | $2.2\pm 0.7$ | $1.7^{+1.0}_{-0.6}$ | $-$
ZwCl1856 N | Y | $1.6\pm 0.8$ | $1.2^{+0.5}_{-0.5}$ | $934\pm 117$
ZwCl1856 S | Y | $1.5\pm 0.7$ | $1.0^{+0.4}_{-0.7}$ | $862\pm 133$
ZwCl2341 NW | Z | $0.8\pm 0.6$ | $0.6^{+0.7}_{-0.3}$ | $359\pm 39$
ZwCl2341 C | Z | $3.1\pm 1.2$ | $3.0^{+2.3}_{-1.3}$ | $-$
ZwCl2341 S | Z | $1.3\pm 0.7$ | $1.1^{+1.4}_{-0.6}$ | $801\pm 46$

$68\%$ uncertainties reported
a denotes subclusters that are not involved in the merger

##  4 WEAK LENSING MASS DISTRIBUTIONS

In this section, the WL analysis of 29 radio relic merging galaxy clusters are
presented and discussed. A summary of the literature on these merging clusters
is presented in G19. For this reason, we will try not to repeat the work of
G19 but will describe the relevant merging features, summarize previous WL
results, and present/compare our new WL results. Our goal is to provide new
insight into the merging systems with the mapping of the dark matter.

For each cluster, we present a four-panel figure. The top left panel is the WL
mass map $S/N$ contours plotted over the Subaru color image. Contours start at
$2\sigma$ and increase in intervals of $1\sigma$ unless otherwise noted in the
figure caption. These WL mass maps are available upon request to the authors.
We indicate each of the significant subclusters ($S/N>3$) with a blue, dashed
circle that is centered on the BCG that we have assigned to the subcluster.
The radius of the circles are chosen to be $R_{3000}$ because it fits
elegantly into the field of view, where $\Delta=3000$ is the density contrast.
Each $R_{3000}$ is derived from the mass estimates following the masses of the
$c-M$ relation fits in Table 4. The top right panel shows the WL contours over
the X-ray imaging with radio contours (green). The bottom-left and bottom-
right panels have the WL contours plotted over the galaxy luminosity and
number density maps, respectively, where these galaxies were selected
following the method in Section 3.4.

Table 4 contains the mass estimates for all the subclusters that we identified
as securely detected. As mentioned, WL mass estimates are done via the 2PNFW
method with $c$ and $M$ as free parameters and via the $c-M$ relation of Duffy
et al. (2008). In addition, the velocity dispersion measurements from G19 are
included in the table. The velocity dispersion measurements are matched to the
WL measurements by their projected separation from the location of the WL mass
peak.

Figure 7: 1RXSJ0603. A dissociative merger with an extremely large radio
relic.  Top-left: WL mass map (white contours) of the Toothbrush cluster over
Subaru color image. Top-right: WL mass over X-ray emission with radio relic
plotted as green contours. Bottom-left: WL over galaxy luminosity density.
Bottom-right: WL over galaxy number density.

###  4.1 1RXS J0603.3+4212 ($z=0.226$)

1RXSJ0603, also known as the Toothbrush cluster, is a well-studied merging
cluster because of its 2 Mpc radio relic that resembles a toothbrush (van
Weeren et al., 2012b; Stroe et al., 2016a; van Weeren et al., 2016; Rajpurohit
et al., 2018, 2020; de Gasperin et al., 2020). The morphology of the relic was
reproduced in hydrodynamic simulations (Brüggen et al., 2012). van Weeren et
al. (2016) suggested that re-acceleration is occurring at the Toothbrush relic
and simulations agreed that re-acceleration is likely (Kang, 2016a; Kang et
al., 2017). Radio measured Mach numbers for the Toothbrush relic range from
2.8 to 4.6 (van Weeren et al., 2012b, 2016; Rajpurohit et al., 2018).

The X-ray emission has an elongated morphology that stretches approximately
1.5 Mpc in a north-south direction with the radio relic lying to its north.
The southern region of the X-ray emission has sharp edges that resemble ram-
pressure stripping from a bullet-like core. Ogrean et al. (2013b) identified
two distinct subclusters in the X-ray emission and provided evidence for three
shocks with Mach numbers less than 2. Itahana et al. (2015) measured the Mach
number in the north shock to be $\scriptstyle\sim$1.5.

A WL analysis of Subaru and HST imaging is presented in Jee et al. (2016).
Their study detected four substructures of which two were deemed significant
and referred to as subclusters. These two subclusters are located at the BCGs
in the north and south and are likely the subclusters that collided to create
the radio relic. G19 identified four subclusters from galaxy redshifts with
the two with the largest velocity dispersion corresponding to the largest WL
signal detections. Jee et al. (2016) assumed the Duffy et al. (2008) $c-M$
relation and estimated the mass of the north (south) subclusters as
$M_{200}=6.3^{+2.2}_{-1.6}\times 10^{14}\ M_{\odot}$
($M_{200}=2.0^{+1.2}_{-0.7}\times 10^{14}\ M_{\odot}$).

WL result: Our WL analysis is done on solely the Subaru imaging (Figure 7). We
detect the two primary subclusters that are presented in Jee et al. (2016). In
addition, two other substructures from Jee et al. (2016) are detected as an
elongation from the northern mass peak and a separate peak directly to its
south. We estimate the mass of the north (south) subclusters to be
$M_{200}=6.2\pm 1.2\times 10^{14}\ M_{\odot}$ ($M_{200}=2.8\pm 0.8\times
10^{14}\ M_{\odot}$), which are consistent with the Jee et al. (2016) result.

Figure 8: A115. A merger with peculiar ram-pressure stripped gas that suggests
a large impact parameter. WL contours increase in steps of $0.5\sigma$.

Merger insight: As is apparent from the offset between the mass peak (or BCG)
and the X-ray emission in the south of the cluster, the Toothbrush cluster is
a dissociative merger. The alignment of the radio relic and the elongated
X-ray and WL distributions suggest that the N and S subclusters collided to
form the shock. The ram-pressure stripped morphology of the X-ray emission is
expected when the impact parameter is small. The Toothbrush cluster is a
strong candidate to constrain the properties of dark matter because of the
large separation of the mass peak from the X-ray peak but the cluster may be
too complex.

###  4.2 A115 ($z=0.193$)

A115 is a single radio relic cluster with double X-ray peaks (Beers et al.,
1983; Feretti et al., 1984). It stands out from the rest of the merging
clusters because both subclusters appear to have ram-pressure stripped gas
trailing behind cool cores, but the stripped gas does not align with the axis
that the radio relic (shock) is moving. Since the cluster has a unique X-ray
distribution, it has been the subject of quite a few studies. Shibata et al.
(1999) presented evidence that A115 is a merging cluster with temperature
variations measured by the Advanced Satellite for Cosmology and Astrophysics
(ASCA). The dynamical analysis of Barrena et al. (2007) identified two
structures in the galaxy distribution. Botteon et al. (2016) detected a shock
in Chandra observations that is co-spatial with the radio relic and determined
the Mach number to be $1.7\pm 0.1$. A hot region was found between the
subclusters in the X-ray temperature analysis of Hallman et al. (2018). From
VLA and GMRT observations, they calculated the radio Mach number to be 2.1.

Okabe et al. (2010) included A115 in their WL analysis of 30 galaxy clusters,
LoCuSS. Their WL mass map revealed two peaks. However, a $\scriptstyle\sim$300
kpc offset of the mass peak from the BCG was found in the northern cluster,
which is an expected signature of an exotic dark matter model (ie. SIDM).

Figure 9: A521. A three subcluster system with a cool core, a radio halo, and
two radio relics. The NW radio relic is faint and marked with a green
crescent. WL contours increase in steps of $0.5\sigma$.

WL result: Our WL analysis (Figure 8), published in Kim et al. (2019),
characterized the cluster as a bimodal merger with the northern cluster of
mass $M_{200}=1.5\pm 0.5\times 10^{14}\ M_{\odot}$ and southern cluster mass
$M_{200}=3.0\pm 0.8\times 10^{14}\ M_{\odot}$. As Figure 8 shows, both WL mass
peaks are consistent with their X-ray peak and BCG counterparts, which is in
contrast to the WL peak positions in Okabe et al. (2010).

Merger insight: The BCG, X-ray brightness peaks, and mass peaks are co-spatial
for each of the subclusters. The biggest mystery in A115 is reconciling the
ram-pressure stripped tails seen in X-ray with the position of the radio
relic. If one assumes that the tails are signifying the past direction of
motion for the subclusters, it does not agree with an axial shock origin for
the radio relic. Utilizing the WL measurements of Kim et al. (2019), idealized
RAMSES simulations of a two-cluster collision with a relatively large impact
parameter by Lee et al. (2020) concluded that the ram-pressure stripped tails
could be slingshot tails that have rotated relative to the original collision
axis. Their simulations also reproduced the radio relic in the observed
location. The large impact parameter of A115 sets it as unique merger that
exhibits a radio relic.

###  4.3 A521 ($z=0.247$)

Arnaud et al. (2000) showed that the X-ray emission of A521 has an irregular
morphology with two peaks that are separated by about 500 kpc. Maurogordato et
al. (2000) measured the radial velocities of 41 cluster galaxies and
calculated a velocity dispersion of $1386^{+206}_{-139}$ km s-1. Ferrari et
al. (2003) provided evidence for a merging system by showing that the line-of-
sight (LOS) velocity of the galaxies departs from a single Gaussian
distribution. The X-ray emission detected by Chandra is elongated in a NW to
SE direction with two major components (Ferrari et al., 2006). The radio relic
is situated to the east of the cluster and elongates north to south
(Giacintucci et al., 2006; Dallacasa et al., 2009). The cluster has a distinct
cool core that is co-spatial with the BCG and is compressed on its southern
side (Bourdin et al., 2013). Bourdin et al. (2013) highlighted a bullet-like
shape extending from the cool core, which may be further evidence of the
ongoing merger. They detected a shock at the location of the radio relic in
the XMM-Newton X-ray observation and found the Mach number to be 2.4. MeerKAT
observations from the cluster legacy survey (Knowles et al., 2022) are
presented in Figure 9. A second radio relic is found in the NW of the cluster
that may be a counter relic to the bright relic in the east (artificially
placed arc in Figure 9). The nature of the diffuse radio emission is
investigated further in Santra et al. (2023).

G19 mention that the galaxies of the cluster can be divided into three
subclusters with the primary in the center, one to the northwest, and one to
the southeast. However, their GMM does not separate the northwest from the
central subcluster and results in two components.

WL result: Our work on A521 was published in Yoon et al. (2020). The WL signal
has three peaks (Figure 9). The most significant peak is consistent with the
BCG and X-ray peak. In addition, WL peaks are found at the NW BCG (2nd) and
the SE overdense galaxy region. Our mass estimates for the subclusters are
$3.5\pm 0.9$, $1.1\pm 0.5$, and $2.5\pm 0.7\times 10^{14}\ M_{\odot}$ for the
C, NW, and SE subclusters, respectively.

Merger insight: The elongation of the mass distribution is slightly rotated
with respect to the X-ray emission, which gives it a better agreement with the
morphology of the radio relics than the X-ray emission has. The separation of
the two subclusters from the central subcluster does not provide clear
evidence to which subclusters collided to form the radio relics. Utilizing the
wealth of information gained from the multiwavelength data, Yoon et al. (2020)
tested merger scenarios with idealized simulations. Each tested merger
scenario had its agreeing and disagreeing features with the observed features.
The simulation showed that the subcluster that is now in the SE could have
approached from the north and collided with the central cluster with a large
impact parameter to form the shock that is observed at the SE radio relic
position. That collision may have also caused the formation of the NW radio
relic. Alternatively, the radio relics could originate from two different
collisions.

Figure 10: A523. A collision between two subclusters with radio emission in
the middle. WL contours increase in steps of $0.5\sigma$.

###  4.4 A523 ($z=0.104$)

A523 is a dissociative merger with the north ICM separated from the mass peak.
Girardi et al. (2016) specified that there are two BCGs with the brightest in
the north and second brightest in the south. They found a galaxy overdensity
directly west of the northern BCG and showed that two background structures
straddle the cluster on the east and west. Cova et al. (2019) investigated the
X-ray emission of the cluster with XMM-Newton and NuSTAR and detected the
X-ray emission from the west component. The radio emission in A523 is not
clearly a merger-induced bow shock and it is positioned between the BCGs (mass
peaks) of the subclusters. Vacca et al. (2022) analyzed LOFAR and VLA
observations of A523 and showed that the radio features are quite complex.

WL result: This is the first WL analysis of this cluster (Figure 10). Three
mass clumps are detected from the Subaru imaging. The most significant
detection is the north subcluster. The peak of the north subcluster is
elongated north to south and encapsulates two bright cluster galaxies, of
which the northern is brighter and elliptical and the southern is bluer and
disky. The southern mass peak is situated to the south of the X-ray brightness
peak and slightly north of the southern BCG. Our WL analysis also detects the
northwest subcluster that was suggested in literature (Girardi et al., 2016;
Cova et al., 2019). The NW subcluster is likely not involved in the collision
because the BCG associated with it is at a higher redshift of 0.13 (G19) and
thus the mass peak has been omitted from the analysis. A two-halo NFW fit with
peaks in the north and south give masses of $2.7\pm 0.9$ and $1.6\pm 0.7\times
10^{14}\ M_{\odot}$, respectively.

Merger insight: Since the X-ray emission is elongated in the N-S direction and
the radio emission is perpendicular to that, we predict that a collision
occurred between the north and south subclusters. The mass estimate shows that
the clusters that collided have a mass ratio of 3:1. It is interesting that
the more massive cluster is in the north with the BCG but the X-ray emission
peak is closer to the southern subcluster. The luminosity and number density
maps also show an inversion with the northern cluster being brighter but the
southern having more galaxies.

Figure 11: A746. A complex cluster merger with 4 diffuse radio sources.

###  4.5 A746 ($z=0.214$)

A746 is a complex system with double relics, two isolated relics, a candidate
radio halo, and many X-ray features (Rajpurohit et al., 2024). The X-ray and
radio analysis of Rajpurohit et al. (2024) detected three merger-driven shock
fronts. They estimated that the southern region of the cluster has an average
temperature of $\scriptstyle\sim$9 keV and the northern has
$\scriptstyle\sim$4 keV. They show that the giant radio relic in the west has
a filamentary emission.

WL result: The Subaru Suprime-Cam observations of A746 suffer from prominent
ghosts from a nearby bright star. Subaru HSC observations were collected (PI:
H. Cho) in 2022B with a careful planning to keep the bright star centered in
the HSC field of view (for symmetry reasons) and with shorter exposure times
per integration. The newly acquired HSC observations enabled a WL analysis
that is presented in HyeongHan et al. (2024b). The WL analysis (Figure 11)
shows a similar complexity to that found in the X-ray and radio emission. A
dominant mass peak is found that coincides with the BCG and two less
significant mass peaks are found to the west and north. The total mass of the
cluster is $M_{200}=6.3\pm 1.5\times 10^{14}$ $M_{\odot}$.

Merger insight: The complex features of A746 make it a difficult cluster to
disentangle. The double relics suggest a merger in the west but X-ray emission
and WL do not discern the two merger constituents. WL analysis with a
telescope that can achieve a much higher number density of galaxies (i.e.,
HST, JWST, Euclid, or Roman) may provide details into this complex merging
system.

Figure 12: A781. A large-scale structure of clusters comprised of Main,
Middle, and North. East is at a higher redshift. WL contours increase in steps
of $0.5\sigma$.

###  4.6 A781 ($z=0.297$)

A781 spans a large projected size on the sky (Figure 12). Here, we follow the
naming scheme for clusters that was presented in Sehgal et al. (2008) and
Wittman et al. (2014). The field of view contains 2 subclusters that are at
$z\raise 0.81805pt\hbox{$\scriptstyle\sim$}0.3$ (named Main and Middle), which
are flanked by subclusters at $z\raise 0.81805pt\hbox{$\scriptstyle\sim$}0.43$
called East and West (West is not shown in the figure). The candidate radio
relic is situated between the Main and Middle subclusters (Venturi et al.,
2008, 2011; Govoni et al., 2011). Botteon et al. (2019) performed an in-depth
analysis of X-ray and radio observations and suggested that the radio relic
may be a combination of a radio galaxy and a shock. However, the polarimetric
study of Hugo et al. (2023) concluded that it is likely not a radio relic.

The cluster is within the field of view of the Deep Lens Survey (DLS; Wittman
et al., 2002) and has a WL result (Wittman et al., 2014). The DLS analysis
detected the 4 subclusters and determined their masses. Cook & Dell’Antonio
(2012) also performed a WL analysis and detected the East, Main, and Middle
subclusters but were unable to detect the West subcluster, which hosts a
strong-lensing arc. G19 separated the cluster galaxies into 4 subclusters but
not the same subclusters as the previous WL results. Instead, they detected
the Middle subcluster and then separated the Main subcluster into 3 additional
subclusters.

WL result: Our WL result detects five subclusters: Main, Middle, East, West
(not shown in the Figure), and one to the North. The Main subcluster coincides
with the brightest X-ray emission and the BCG. The Main WL distribution is
elongated in a east-west direction and has extensions to the west and north.
These extensions are in agreement with the 3 substructures detected by G19.
Both the Middle and East subclusters have X-ray emission counterparts. We
remind the reader that the East subcluster is at a redshift of $z=0.43$. The
North detection is coincident with a galaxy overdensity ($z\raise
0.81805pt\hbox{$\scriptstyle\sim$}0.3$) and has X-ray emission as shown in
Botteon et al. (2019). Although it is not discussed, this North mass peak is
also detected in the DLS analysis (Wittman et al., 2014). We fit a four-halo
model to the mass distribution and find masses of $3.5\pm 0.8$, $4.2\pm 0.9$,
$3.3\pm 0.8$, and $1.7\pm 0.6$ $\times 10^{14}\ M_{\odot}$ for the Main,
Middle, East, and North subclusters, respectively.

Merger insight: The location of the candidate radio relic and the X-ray
emission hint that the merger-induced shock originated within the Main
cluster. The elongation of the X-ray emission and the mass map agrees with
this scenario. However, the resolution that is achievable with ground-based WL
is insufficient to discern substructures in the Main subcluster and prevents
us from constraining the mass of the collision that may have formed the relic.

Figure 13: A1240. A head-on collision, dissociative merger with double radio
relics.

###  4.7 A1240 ($z=0.195$)

A1240 is a double relic cluster with relics situated at opposing ends of the
ICM distribution (Bonafede et al., 2009b; Hoang et al., 2018). From the radio
spectral indices, Hoang et al. (2018) derived Mach numbers of 2.4 and 2.3 for
the north and south shocks, respectively. The X-ray emission spans the region
between the radio relics and shows gas dissociation. Barrena et al. (2009)
detected two X-ray emission peaks in the Chandra observation and estimated the
global temperature of the ICM to be 6 keV. Sarkar et al. (2024) detected X-ray
shocks at the locations of both radio relics and found them to have lower Mach
numbers than radio ($M_{S}=1.5$ and $M_{N}=1.4$), which they suggested may be
a sign of re-acceleration. G19 found that a two-halo model for the galaxy
distribution was favored with a 1:1 mass ratio. A second cluster, A1237
($z=0.194$), is located about 1.5 Mpc to the south of A1240.

WL result: This WL analysis was presented in Cho et al. (2022). The WL signal
of A1240 (Figure 13) shows the characteristic two peaks that are expected in
bimodal mergers. The mass distribution is elongated along the merger axis that
is represented by the X-ray and radio emission. The mass peak in the south is
directly on the BCG, whereas the northern mass peak shows an offset but is
statistically consistent with the BCG based on our bootstrapping. The signal
from A1237 is also detected. We determine the masses to be approximately equal
for the A1240 merger with $M_{200}=2.6\pm 0.6\times 10^{14}$ $M_{\odot}$ and
$M_{200}=1.1\pm 0.4\times 10^{14}$ $M_{\odot}$ for the North and South
subclusters, respectively. A bridge in the WL signal is found that runs
between the A1240 and A1237 but at low significance.

Merger insight: A1240 is a bimodal merger between nearly equal-mass
subclusters. Cho et al. (2022) utilized the projected separation of the radio
relics and the Monte Carlo Merger Analysis Code (MCMAC; Dawson, 2013) to find
that a merger phase that is returning from apocenter is favored with a time
since collision of $1.7\pm 0.2$ Gyr. Cho et al. (2022) show that the
A1240/1237 system is embedded in an $\scriptstyle\sim$80 Mpc long filament as
defined from SDSS galaxy positions. Further investigation of the connection of
the merger to the filament would be interesting. The extreme dissociation of
the gas for A1240 makes it a great candidate for further study of the nature
of dark matter.

Figure 14: A1300. A complex cluster with an offset of the mass peak from the
X-ray emission peak. An extension in the mass map traces an extension in the
X-ray map to the north.

###  4.8 A1300 ($z=0.306$)

Reid et al. (1999) detected two diffuse radio sources in A1300, a radio halo
and relic (both confirmed by Giacintucci, 2011). Pierre et al. (1997)
performed a dynamical analysis and found that the velocity dispersion of the
cluster galaxies had no significant departure from a Gaussian distribution.
However, Lemonon et al. (1997) highlighted the merging nature of A1300 from
the structures seen in X-ray emission. Ziparo et al. (2012) analyzed XMM-
Newton X-ray observations and showed that there are three primary ICM
features: a bright peak in the south that elongates towards the southwest, a
fainter peak about 250 kpc to the north, and an extension, possibly a
filament, further north. The BCG lies directly on top of the bright X-ray peak
in the south and has a semi-major axis along the same direction as the
elongation of the X-ray emission. Terni de Gregory et al. (2021) presented the
radio relic in the 1.3 GHz MeerKAT observation and noted that it has the
morphology expected for radio emission from merger-induced shocks. G19 were
unable to separate the cluster galaxies into multiple structures.

WL result: The WL map of A1300 (Figure 14) does not follow our expectations
based on the X-ray emission. Three features of the mass distribution stand
out: a triangular-shaped clump in the center, a subcluster detached to the
southeast, and a long extension to the north. The main clump has a primary
peak that resides between the BCG and a bright galaxy immediately to its
north. This peak is also offset from the X-ray brightness peak. The eastern
vertex of the triangle has a nearby bright cluster galaxy and so does the
northern vertex. It is likely that the complexity of the cluster is beyond the
capabilities of the Subaru imaging. The extension to the north roughly follows
cluster galaxies as can be seen in the luminosity and number density panels.
It also follows the X-ray emission. The subcluster detected
$\scriptstyle\sim$1 Mpc to the southeast coincides with a bright galaxy and a
faint X-ray detection. The agreement between the overall mass map and the
X-ray emission is mixed. Since there is a lack of consistency between the WL
substructures and the luminous tracers, we fit a single halo NFW model
centered at the BCG and find the mass of the cluster to be $M_{200}=1.1\pm
0.2\times 10^{15}$ $M_{\odot}$.

Merger insight: The X-ray morphology is complicated and does not provide a
clear feature that matches the position of the radio relic. The core of the
X-ray emission has a bullet shape, which is sometimes a good indicator of the
merger axis. However, like A115, it is hard to reconcile the bullet and the
position of the radio relic. Perhaps, this is another case of a large impact
parameter merger. The WL result seems to further complicate the interpretation
because it is offset from the X-ray peak. However, the elongation of the core
of the WL result does align with the radio relic. Similar to A746, the
complexity of the merger seems to be beyond the ground-based Subaru imaging
and may require higher resolution to discern the merging subclusters.

Figure 15: A1612. A merger between two equal-mass subclusters with a radio
relic that is misaligned with the WL and X-ray elongated distributions. WL
contours increase in steps of $0.5\sigma$.

###  4.9 A1612 ($z=0.182$)

A1612 has a single radio relic (van Weeren et al., 2011b) that is offset from
the axis defined by the elongated X-ray emission. The X-ray emission does not
show significant features, mostly because of the lack of X-ray photon counts.
The X-ray emission spans the region between the east and west BCGs. There is
also X-ray emission detected to the north and a cavity (maybe due to low
counts). G19 found two subclusters of galaxies that are each centered on the
two BCGs.

WL result: The WL signal from A1612 shows 2 peaks separated by
$\scriptstyle\sim$1 Mpc (Figure 15). The east mass peak is coincident with the
BCG and has a weaker S/N companion mass peak that is centered on the equally
bright galaxy to its immediate south. The western peak is near the third BCG.
The peaks are found at the ends of the elongated X-ray distribution. The
$i$-band observations are shallow for this cluster and the WL signal is poor,
even though the subclusters are resolved. A two-halo fit centered at the east
and west BCGs finds masses of $4.0\pm 1.0$ and $1.8\pm 0.7\times 10^{14}\
M_{\odot}$ for the E and W subclusters, respectively.

Merger insight: A1612 is a good candidate for a simple merger with a nearly
equal mass ratio. However, the cluster has not garnered enough attention and
lacks suffice multiwavelength observations to make strong conclusions about
the collision. The radio relic is not in line with the elongation of the X-ray
emission or the mass distribution, which may indicate a non-zero impact
parameter of the collision. The eastern mass peak and its BCG do not have
bright X-ray emission and thus A1612 may be a case of a dissociative merger.

Figure 16: A2034. A dissociative merger with a bullet shape.

###  4.10 A2034 ($z=0.114$)

A2034 is a dissociative merger with a bullet-shaped morphology in the X-ray
emission. A cold front was found in the Chandra observation and a candidate
radio relic (Kempner & Sarazin, 2001; Kempner et al., 2003). A shock ahead of
the northern cold front was detected in Owers et al. (2014) with a Mach number
of $1.6\pm 0.1$. For an in-depth discussion of the radio emission see the
LOFAR work by Shimwell et al. (2016), which discussed two additional radio
relic candidates. Okabe & Umetsu (2008) performed a WL analysis of the cluster
and detected 6 significant peaks, of which 3 are slightly background to the
cluster redshift. They suggested that these peaks may comprise a large-scale
filament. Monteiro-Oliveira et al. (2018) also presented a WL analysis of the
cluster. Their mass map detected two significant peaks (with additional
subpeaks) that are considered as the counterparts to the BCGs. In their work,
the southern and strongest peak is situated to the south of the BCG and the
northern peak is slightly offset to the east of the northern BCG. They
estimate the masses of the clusters to be $2.4\pm 1.0$ ($1.1\pm 0.6$) $\times
10^{14}\ M_{\odot}$ for the south (north). Moura et al. (2021) simulated the
cluster with N-body hydrodynamical simulations using the measured properties
from Monteiro-Oliveira et al. (2018) as initial conditions. They concluded
that the merger is near the plane of the sky with a low impact parameter and
about 0.26 Gyr after collision. G19 found three galaxy overdensities that are
centered in the north, south, and southwest regions. Their velocity dispersion
measurements show that the north and south subclusters are comparable in mass
and the southwest subcluster is minor.

WL result: Our mass map (Figure 16) portrays a binary merger between the N and
S subclusters. This is in agreement with the two previous WL studies of Okabe
et al. (2010) and Monteiro-Oliveira et al. (2018) and the dynamical analysis
of G19. The mass peak in the south is coincident with the BCG. The mass peak
in the north is offset to the east of its BCG but within the WL statistical
uncertainty. An extension is detected to the southwest that lies on top of the
third BCG with a weakly detected peak nearby. Our mass estimates are $3.6\pm
0.7$ ($0.9\pm 0.4$) $\times 10^{14}\ M_{\odot}$ for the south (north)
subclusters.

Merger insight: A2034 appears to be the most head-on merger in the sample. It
has a large gas dissociation and thus is an ideal cluster for studying dark
matter properties. There are some interesting features of this cluster that
may warrant further investigation. The published WL analyses of this cluster
show a consistent offset of the N mass peak to the east of its BCG. Is this a
systematic of the data or an offset caused by the collision? The southern BCG
is highly elongated along the merger axis. Is this a signature of the recent
pericenter passage?

Figure 17: A2061. A dissociative merger with a radio relic that is very
distant from the X-ray brightness peak. WL contours increase in steps of
$0.5\sigma$.

###  4.11 A2061 ($z=0.078$)

A2061 is the lowest redshift cluster in the sample. It is part of the Corona
Borealis supercluster (Postman et al., 1988; Pearson et al., 2014). The X-ray
emission peaks between the two BCGs suggesting that it is also a dissociative
merger. Northeast of the cluster is a blob of X-ray emitting gas that may have
been ejected from the main cluster (Sarazin et al., 2014). The radio relic is
approximately 2 Mpc southwest of the X-ray emission peak of the cluster
(Kempner & Sarazin, 2001; van Weeren et al., 2011b). G19 found that the
cluster galaxies follow a single-Gaussian distribution with mass from velocity
dispersion being $5.5\pm 0.2\times 10^{14}\ M_{\odot}$.

WL result: The WL map of A2061 shows a bimodal distribution with mass peaks
that lie directly on top of the BCGs (Figure 17). The elongation of the mass
map is slightly rotated from the elongation of the X-ray emission. Our two-
halo fit estimates masses of $1.6\pm 0.5$ ($2.0\pm 0.6$) $\times 10^{14}\
M_{\odot}$ for the south (north), which suggests a 1:1 mass ratio merger of
low total mass. The total mass found from lensing is in agreement with that of
velocity dispersion.

Merger insight: The different orientations of elongation for the mass map and
the X-ray emission is a possible signature of the impact parameter of the
collision. The radio relic of A2061 is one of the farthest from the cluster
when compared to the rest of this radio relic sample. The distance of the
radio relic could be a hint that A2061 is an old merger. The galaxy
distributions of A2061 show a group to the northeast and the WL signal has a
slight elongation toward the direction of the group. It is unclear if this
group was involved in the merger or is currently falling into the primary
cluster. A2061 is a cluster that warrants further investigation to understand
its dissociative nature and extreme distance to its radio relic.

Figure 18: A2163. A low-mass subcluster (W) colliding with a massive primary
cluster (E).

###  4.12 A2163 ($z=0.201$)

With a global temperature of $T=15$ keV (Arnaud et al., 1992), A2163 is one of
the hottest clusters in the sample. It is listed as the most massive cluster
in the Planck Collaboration et al. (2016) catalog. The X-ray emission from
A2163 is very extended, spanning approximately 2 Mpc in diameter in the south
with an additional X-ray emitting subcluster in the north. A dynamical
analysis by Maurogordato et al. (2008) showed that the southern cluster is
elongated in the east-west direction. G19 found that A2163 is composed of
three structures with two located in the southern X-ray emission and one in
the north. Based on their velocity dispersion estimates, the SE BCG is in the
dominant subcluster and the SW is subordinate. Previous WL analyses have been
consistent in detecting two mass peaks in the south and one in the north
(Radovich et al., 2008; Okabe et al., 2011; Soucail, 2012). The radio relic
candidate in A2163 (Feretti et al., 2004) is found to the NE. Shweta et al.
(2020) provided evidence for a radio relic found in the center of the cluster.
Thölken et al. (2018) detected 3 shocks in Suzaku observations. One of the
shocks is to the NE and coincides with the radio relic and the other two are
found in the SW.

WL result: Our WL analysis (Figure 18) detects the signal from both the north
and the south clusters. The mass distribution of the southern cluster has a
peak directly on the BCG (labeled as the E halo in Figure 18). The mass
distribution stretches to the west where it has a subordinate peak near the W
BCG. The southern mass distribution also stretches to the south somewhat
following the galaxy luminosity distribution, as shown in the bottom left
panel. The northern cluster is detected with the mass peak slightly offset
from the X-ray emission and the galaxy distributions. This offset is likely
from noise. We fit a three-halo model and find that the masses are $9.2\pm
1.8$, $0.8\pm 0.6$, and $1.1\pm 0.7\times 10^{14}\ M_{\odot}$ for the E, W,
and N subclusters, respectively. The mass estimate of the E subcluster agrees
with that of Soucail (2012).

Merger insight: A2163 is a complex cluster with many substructures.
Maurogordato et al. (2008) describe the many substructures of the cluster of
A2613 found in galaxy overdensities. The detection of the mass distribution
can provide support to some of the substructures. The cluster appears to be
elongated east-west, which does not exactly agree with the position of the
radio relic. However, the galaxy luminosity distribution shows an elongation
extending from the BCG along the NE-SW axis that aligns with the position of
the radio relic. The WL mass map also extends from the BCG along this axis but
at low significance. A past collision between the main cluster and a
subcluster directly to its southwest may be the cause of the radio relic.

Figure 19: A2255. A relaxed-appearing X-ray emission with WL substructures.

###  4.13 A2255 ($z=0.08$)

A2255 has an X-ray morphology that is slightly elliptical with the major axis
running east-west. The BCG is located near the western X-ray peak and there
are bright galaxies related to the eastern X-ray emission. G19 was unable to
resolve two subclusters in their dynamical analysis but did find a
$\scriptstyle\sim$2000 km s-1 difference in LOS velocity for the two BCGs in
the west. Botteon et al. (2020b) described the “beautiful mess” of radio
sources in A2255 and highlighted the NE radio relic. Akamatsu et al. (2017)
detected an X-ray shock at the location of the radio relic.

WL result: The WL map provides far more context to the merging system than the
X-ray emission (Figure 19). The mass distribution traces the bright cluster
galaxies and is elongated along the east-west axis. A mass peak is coincident
with the W BCG and an equally significant mass peak is detected about 100 kpc
to its southwest. The WL signal extends to the east and is coincident with the
eastern BCG. The proximity of the two western peaks prevent a three-halo model
from being robustly fit. Our two-halo model gives masses of $4.7\pm 1.1\times
10^{14}\ M_{\odot}$ and $1.3\pm 0.6\times 10^{14}\ M_{\odot}$ for west and
east, respectively.

Merger insight: There is great agreement between the WL mass map and the
galaxy positions in A2255. The X-ray brightness peak is offset from the BCG
and the mass peak, which makes this cluster a dissociative merger candidate.
The mass map provides critical information that can explain the location of
the radio relic. Rather than a merger between the E and W subclusters, it is
more likely that a collision between the two substructures in the west led to
the formation of the radio relic. Extending a line from the two substructures
in the west bisects the radio relic. If these are the two subclusters that
collided to form the radio relic, then their very small projected separation
($\scriptstyle\sim$200 kpc) relative to the distance to the radio relic
($\scriptstyle\sim$1 Mpc) is intriguing. It could indicate that the
subclusters have had time to reach apocenter and begin their return to a
second pericenter passage. Also, the large LOS velocity difference of the 2
BCGs in the west may indicate that projection may be important. This is an
interesting case for the potential of a merger with a LOS component to the
merger and a radio relic.

Figure 20: A2345. A chain of three subclusters in a merging system with two
relics. WL contours increase in steps of $0.5\sigma$.

###  4.14 A2345 ($z=0.179$)

A2345 is a rare double relic cluster (Bonafede et al., 2009a). Stuardi et al.
(2021) described additional merger features in the X-ray and radio emission.
The eastern relic is greater than one megaparsec in size and has the standard
arc shape of a shock. The BCG is located in the east and is coincident with
the X-ray brightness peak. The second brightest galaxy is 2 Mpc to the west of
the BCG. The X-ray emission spans about 2 Mpc by 2 Mpc in projection. G19 were
unable to separate subclusters in their analysis but they did present three
peaks in the galaxy light distribution. The X-ray emission includes a
subcluster that is located to the northwest of the second brightest galaxy.
Dahle et al. (2002) presented a WL result of A2345 that has three peaks with
the eastern peak offset from the BCG by $\scriptstyle\sim$1$\farcs$5 toward
the east.

WL result: Our WL distribution of A2345 (Figure 20) is tri-peaked in a chain
that aligns with the axis connecting the radio relics. The distances between
the central peak and the two other peaks are similar. As in Dahle et al.
(2002), the eastern mass peak is offset from the BCG toward the eastern radio
relic. The east mass peak is also detached from the bright X-ray emission
indicating a potential dissociative merger. No bright galaxies are found in
the region that the central peak is located but there is a galaxy overdensity.
This detection is reminiscent of the dark core in A520, the Trainwreck cluster
(Mahdavi et al., 2007; Jee et al., 2012). The western peak is centered on the
second BCG and the X-ray brightness peak in the region. Mass estimates for the
three subclusters are $4.7\pm 1.1$, $3.2\pm 1.0$, and $2.1\pm 0.8$ $\times
10^{14}\ M_{\odot}$ for east, central, and west, respectively.

Merger insight: Utilizing the information from the mass map, it is likely that
the radio relics were formed by a merger between the east and central
subclusters. These two mass peaks are approximately equal distance from the
respective radio relics. The western mass peak is external to the radio relic.
However, Stuardi et al. (2021) describe a bullet feature that is coincident
with this WL peak and has a tail to the east. This evidence would suggest that
the W subcluster is moving westward, further complicating the merging
scenario. For this subcluster to have formed the W relic and be positioned
further westward it would have to overrun it. Assuming a collision between the
E and C subclusters formed the radio relics, the remaining issue is
understanding the central mass peak and its lack of BCG.

Figure 21: A2744. A well-studied, complex system of four subclusters.

###  4.15 A2744 ($z=0.306$)

A2744 (Pandora’s cluster) is one of the most studied clusters in the sample.
Many WL and SL analyses have been accomplished for this cluster. Medezinski et
al. (2016) analyzed the Subaru observations that are used in this paper with
WL and were able to detect four substructures that roughly trace the galaxies
in the cluster. The joint SL-WL analysis (Jauzac et al., 2016) traced the
substructure of the cluster at high precision and discerned the substructures
in the core. More recently, the joint SL-WL analysis of Cha et al. (2024) used
JWST to provide tight constraints on mass peaks that agree with their
respective BCGs (see Harvey & Massey, 2024, for another JWST WL analysis).
Abriola et al. (2024) performed a WL analysis with Magellan observations and
estimated the total mass of the cluster to be $M_{200}=2.56\pm 0.26\times
10^{14}\ M_{\odot}$. The X-ray emission from A2744 has two peaks with the
brighter near the BCG and the fainter to the northwest. Giovannini et al.
(1999) detected a radio halo and the NE radio relic in the NRAO VLA Sky
Survey. Pearce et al. (2017) identified three more radio relics in VLA
observations. The radio features have been further analyzed by Rajpurohit et
al. (2021) and Knowles et al. (2022).

WL result: Our WL analysis detects four peaks (Figure 21). The most
significant peak is found on the E BCG. The second most significant peak is at
the location of the W BCG. This peak and the BCG are offset eastward from the
western X-ray emission peak. The two other mass-peak detections are in the
north and south and are coincident with cluster galaxy populations. Our four-
halo model results in mass estimates of $M_{200}=7.2\pm 1.8$, $6.6\pm 2.3$,
$1.0\pm 0.8$, and $0.6\pm 0.6\times 10^{14}\ M_{\odot}$ for the E, W, N, S
subclusters, respectively.

Merger insight: The position of the SE radio relic is easy to relate to the
two bright X-ray peaks and the significant WL peaks of E and W. However, the
NE and brighter relic is harder to reconcile with the detected substructures.
It may be that one of the less significant subclusters passed through the
system to form the NE radio relic. Both N and S mass peaks have better
agreement with the morphology and position of the radio relic. Another
scenario for the formation of the NE radio relic (but not the SE radio relic)
could be that the more massive subclusters merged with a large impact
parameter. The location of the BCG and the western mass peak inside the west
X-ray brightness peak is perplexing and goes against the expectation of ram-
pressure stripping for a dissociative merger. This configuration may occur at
a later stage of merging while the subcluster is returning from apocenter.
Merten et al. (2011) discuss a scenario in which a “ram-pressure slingshot”
effect has lead to the observed configuration of the X-ray emission and dark
matter halo.

Figure 22: A3411. A merging system with a cool core and a connection between a
radio galaxy and radio relic. WL contours increase in steps of $0.5\sigma$.

###  4.16 A3411 ($z=0.163$)

A3411 has a notable radio relic that was first detected in Giovannini et al.
(2013) and van Weeren et al. (2013). The relic is notable because it is
connected by a radio bridge to a nearby radio galaxy (van Weeren et al.,
2017). The bridge has a spectral index that steepens away from the radio
galaxy and then flattens along the radio relic, which they suggest is evidence
for shock re-acceleration of the non-thermal population of charged particles
that are seeded by the radio jet. Andrade-Santos et al. (2019) detected the
shock at the relic location in deep Chandra observations and calculated a Mach
number of $\lesssim 1.15$. They estimated the mass of the cluster from X-ray
observations to be $M_{500}=7.1\pm 0.7\times 10^{14}M_{\odot}$. Zhang et al.
(2020) analyzed deep XMM-Newton and Suzaku X-ray imaging and detected shocks
in the southern edge and across the radio relic. Their X-ray temperature
measurement of $T\raise 0.81805pt\hbox{$\scriptstyle\sim$}5$ keV gives a mass
of $M_{500}=5.1\times 10^{14}M_{\odot}$. G19 found that the galaxy
distribution shows two populations with one centered on the BCG in the NW and
the other at A3412. The subclusters were found to have equally high velocity
dispersion of$\raise 0.81805pt\hbox{$\scriptstyle\sim$}1200$ km s-1.

WL result: The mass distribution of A3411 is marginally detected with
$S/N\gtrsim 3$ (Figure 22). The mass distribution in the north peaks at the
BCG and is elongated in the same direction as the X-ray distribution and
toward the radio relic. Our WL analysis also detects A3412 but with low
significance. The A3412 WL detection is offset from the position that G19
detected the galaxy overdensity but the offset is not statistically
significant. Our mass estimates show that the W, E, and A3412 subclusters are
$M_{200}=2.3\pm 1.0$, $1.8\pm 1.0$, and $1.1\pm 0.8\times 10^{14}\ M_{\odot}$,
respectively.

Merger insight: The WL result presented in this work provides weak evidence
for the subclusters that collided to create the shock presented in van Weeren
et al. (2017). A merger between the E and W subclusters are the likely
culprits. We do not expect A3412 to be the cause of the radio relic because of
its position. New HSC observations (PI: H. Cho) have recently been completed
and may provide an updated WL view of the massive structures in this galaxy
cluster.

Figure 23: CIZAJ2242 (The Sausage Cluster). A system with a textbook, arc-
shaped radio relic, complex X-ray emission, and a bimodal mass distribution.

###  4.17 CIZA J2242.8+5301 ($z=0.189$)

CIZAJ2242 (The Sausage Cluster) contains the textbook example of a radio relic
(van Weeren et al., 2010) as well as radio relics to the south and east (see
van Weeren et al., 2011a; Stroe et al., 2013, 2014b, 2014a, 2016b; Hoang et
al., 2017; Loi et al., 2017; Di Gennaro et al., 2018). The X-ray emission is
elongated in the N-S direction with two peaks and an extension that stretches
to the north. Shocks have been detected in X-ray at the location of the
northern and southern radio relics as well as to the east (Ogrean et al.,
2013a, 2014a; Akamatsu et al., 2015). The archetypal relic in the north has
spurred many simulations to attempt to recreate its properties as well as
other ICM properties and features (van Weeren et al., 2011a; Matsukiyo et al.,
2011; Kang et al., 2012b; Kang & Ryu, 2015; Fujita et al., 2015; Kang, 2016b;
Fujita et al., 2016; Donnert et al., 2016; Molnar & Broadhurst, 2017; Donnert
et al., 2017). In addition, from SZ observations, Rumsey et al. (2017) found a
high pressure region that stretches perpendicular to the elongated X-ray
emission. Dawson et al. (2015) found the cluster galaxies to follow a bimodal
distribution with close to equal velocity dispersion, which suggests equal
mass subclusters.

Two previous WL analyses have been performed on CIZA2242. Okabe et al. (2015)
and Jee et al. (2015) both mapped the WL signal of the Sausage cluster and
found it to be bimodal. Both authors also found nearly 1:1 mass ratios (2:1
for Okabe et al. (2015)) when simultaneously fitting the subclusters with
Duffy et al. (2008) $c-M$ models. However, the total mass in Jee et al. (2015)
is almost two times higher.

WL result: We utilize the Jee et al. (2015) shape catalog for our analysis and
unsurprisingly result in a similar mass map (Figure 23) to Jee et al. (2015).
Fitting two NFW halos, we estimate a mass of $M_{200}=8.2\pm 1.8\ (9.3\pm
1.8)\times 10^{14}\ M_{\odot}$ for the north (south) subclusters, which are
consistent with Jee et al. (2015).

Merger insight: The morphology and features of the X-ray emission from
CIZA2242 are not as expected for a 1:1 mass ratio merger of two massive
clusters, as pointed out by Ogrean et al. (2013a). The brightest X-ray
emission is located near the BCG in the south. A second brightness peak is
located approximately 0.5 Mpc to the north and then an extension snakes a Mpc
further to the north. The complexity of the features suggests that additional
subclusters are likely to exist. CIZAJ2242 is a dissociative merger with
similarity to MACSJ1752 and ZwCl1856. An additional mystery is that the mass
peaks in the north and south show offsets from their respective BCGs. The
mystery may arise because ground-based WL cannot resolve such substructures
and provide a poor constraint on the mass peaks because of the high extinction
and stellar density of the zone of avoidance. High-resolution imaging is
required to achieve the number density of source galaxies that is needed to
constrain the mass peak positions and to resolve substructures.

Figure 24: MACSJ1149. A high-z cluster with a N-S elongation in the mass and
X-ray distributions. WL contours increase in steps of $0.5\sigma$.

###  4.18 MACS J1149.5+2223 ($z=0.544$)

MACSJ1149 is the highest redshift cluster in the sample. Bonafede et al.
(2012a) pointed out two radio relic candidates in the system but one was shown
to be a radio galaxy (Giovannini et al., 2020; Bruno et al., 2021). It is one
of the most X-ray luminous and hottest ($T=10.73^{+0.62}_{-0.43}$ keV)
clusters known (Ogrean et al., 2016). G19 found the cluster to have an extreme
velocity dispersion of $1668$ km s-1. The WL analysis by Umetsu et al. (2014)
showed an elongated signal that runs southeast from the BCG and the joint SL-
WL analysis of Finney et al. (2018) presented an elongated distribution that
runs from the BCG to the north. The disparity is likely caused by the
inclusion of strong lensing and the limited field of view of the HST
observations used in Finney et al. (2018).

WL result: Our WL mass reconstruction (Figure 24) has a peak directly on the
BCG. The WL mass is elongated to the north from the BCG and encompasses the
second BCG in similar fashion to the WL-SL analysis of Finney et al. (2018).
There is a hint of an extension toward the southeast from the BCG (as is found
in Umetsu et al. (2014)) but it has no clear peak. We also get a detection in
the northwest of the cluster that has a weak agreement with galaxy luminosity.
Since no clear subclusters are detected, we fit a single NFW halo and find the
mass to be $M_{200}=16.4\pm 3.1\times 10^{14}\ M_{\odot}$.

Merger insight: The low-significance substructures that are detected in our WL
analysis do not provide additional evidence to the origin of the radio relic.
As Bruno et al. (2021) pointed out, the orientation of the relic and the mass
distribution are difficult to reconcile.

Figure 25: MACSJ1752. An equal-mass merger with ram-pressure stripped tails in
the X-ray emission and double radio relics.

###  4.19 MACS J1752.0+4440 ($z=0.365$)

A multi-wavelength analysis of MACSJ1752 is presented in Finner et al. (2021).
MACSJ1752 contains two bright and extended radio relics (van Weeren et al.,
2012a; Bonafede et al., 2012b). The radio relics are arc-shaped and on
opposing ends of the elongated X-ray distribution. de Gasperin et al. (2015)
pointed out the extreme luminosity of the radio relics in MACSJ1752. The X-ray
emission is double peaked with a bridge running between the peaks. Finner et
al. (2021) showed that these two X-ray brightness peaks are the sites of cold
fronts. The elongated shape of the X-ray distribution resembles an “S” and is
evidence of a small impact parameter collision. As a textbook example of a
galaxy cluster merger, the cluster has been utilized in simulations to test
the mass bias of WL (Lee et al., 2023) and cosmic ray acceleration (Vazza et
al., 2016).

WL result: In Finner et al. (2021), our WL detection (Figure 25) revealed two
mass peaks that coincide with the BCGs and X-ray peaks. In addition, we found
a third substructure between the peaks that coincides with the third brightest
galaxy and an X-ray peak. Our mass estimates show that the NE and SW
subclusters have masses of $5.6\pm 1.8\times 10^{14}\ M_{\odot}$ and $5.6\pm
1.7\times 10^{14}\ M_{\odot}$ and the central substructure is
$0.3^{+0.4}_{-0.1}\times 10^{14}\ M_{\odot}$. MACSJ1752 is among the most
massive binary mergers in the sample.

Merger Scenario: The merger scenario of MACSJ1752 is straightforward. As shown
in many idealized cluster simulations, a low impact parameter merger between
equal-mass subclusters can recreate the observed X-ray morphology features
such as the “S” shape and cold fronts. The radio relics are not perfectly
symmetric but are among the cleanest example of double relics. An intriguing
connection between a galaxy and the southern radio relic is noted in the WSRT
observation in Finner et al. (2021) but further spectral analysis is needed to
see if it supports the re-acceleration mechanism.

Figure 26: PLCKG287. A centrally dominant, massive cluster with low-mass
subclusters and double radio relics at asymmetric projected separation.

###  4.20 PLCK G287.0+32.9 ($z=0.385$)

PLCKG287 is one of the more unusual clusters in the sample. The cluster has an
X-ray distribution that contains only a single peak and is somewhat relaxed in
appearance with a hint of an extension toward the southeast. The global
temperature of the cluster is 13 keV and it is the second most massive cluster
($26\pm 1.0\times 10^{14}\ M_{\odot}$) in the Plank catalog (Planck
Collaboration et al., 2016). There are a few tens of strong-lensing arcs found
around the BCG and the cluster is one of the largest strong lenses in the
universe that has been detected to date. G19 found the velocity dispersion of
the cluster to be $1756$ km s-1, the highest in this radio relic sample. Their
analysis of the cluster galaxies separated the cluster into a massive primary
with a secondary $\scriptstyle\sim$2.5 Mpc to the south. It has two radio
relics that are vastly different distances from the X-ray peak (Bagchi et al.,
2011; Bonafede et al., 2014b) and separated by about 3 Mpc. Bonafede et al.
(2014a) showed that the galaxy distribution follows a NW-SE layout and is
likely a filament that is feeding the massive cluster.

WL result: Published in Finner et al. (2017), the WL signal of PLCKG287 is
dominated by a central cluster with a mass peak that has excellent agreement
with the BCG and the X-ray brightness peak (Figure 26). Two additional
subclusters are detected that lie along a NW - SE axis. A 3-halo fit to the
mass distribution finds $20.4\pm 1.9\times 10^{14}\ M_{\odot}$, $1.7\pm
0.7\times 10^{14}\ M_{\odot}$, and $1.4\pm 0.7\times 10^{14}\ M_{\odot}$ for
the C, SE, and NW subclusters, respectively.

Merger insight: It is expected that either one of the substructures merged to
form both relics on two passages or that each of the two substructures were
responsible for a relic. Bonafede et al. (2014a) estimates the time since
collision (pericenter) for each of the relics to be approximately 0.7 and 0.1
Gyrs for the south and north radio relics, respectively. The BCG in the
cluster has a nearly equally bright, nearby companion that may be valuable in
interpreting the merger. It is also worth noting that the 3rd brightest
cluster galaxy, that is $\scriptstyle\sim$1 Mpc to the south east of the BCG,
does not have a WL peak.

Figure 27: PSZ1G108. A centrally dominant cluster with large separation double
radio relics. WL contours increase in steps of $0.5\sigma$.

###  4.21 PSZ1 G108.2-11.53 ($z=0.335$)

PSZG108 is a double radio relic cluster with a very large relic separation
($\scriptstyle\sim$3.5 Mpc). G19 identified two galaxy populations that are
near the central point between the relics. However, only 40 galaxies had
available redshifts and their GMM did not separate the galaxies into two
subclusters. The X-ray emission in PSZG108 peaks near the BCG and is elongated
along the axis that connects the radio relics. The second brightest galaxy is
$\scriptstyle\sim$1.5 Mpc to the northeast of the BCG and is coincident with
the northern radio relic. The radio relics of PSZG108 are two of the most
powerful found to date (de Gasperin et al., 2015).

WL result: We analyzed the Subaru HSC observations of PSZG108. Our WL mass
reconstruction (Figure 27) detects the signal with a main peak that is
coincident with the BCG. The WL signal elongates toward the NE following a
similar distribution to the X-ray emission. The significant WL signal
terminates at a galaxy overdensity that we consider the NE subcluster. We note
that the second BCG is further to the NE. The WL signal also extends slightly
to the SW where many of the bright clusters galaxies reside. We fit a two-halo
NFW model and find the subcluster masses to be $6.9\pm 2.1\times 10^{14}\
M_{\odot}$ and $1.5\pm 1.2\times 10^{14}\ M_{\odot}$ for the main and NE
subclusters.

Merger insight: The double-relic nature of PSZG108 can be used to constrain
the merger axis to be approximately northeast to southwest. The X-ray emission
and WL signal are elongated in the same direction. One scenario for the
formation of the radio relics is a collision between the two subclusters that
are detected in WL, which would have a mass ratio $\gtrsim$1:4. The large
separation of the radio relics suggests a long time has passed since the
collision if the shocks propagate at a constant velocity (Ha et al., 2018).
Close analysis of the HSC observations reveal that the BCG has many bright
companion cluster galaxies (as is apparent from the luminosity and number
density maps). An alternative scenario is that the collision that formed the
radio relics occurred far enough in the past that the two subclusters are both
situated in the BCG region. WL analysis would require a higher number density
of galaxies to resolve subclusters in this region. Follow up observations with
the HST or JWST would be valuable for SL-WL analysis of the cluster. There are
large blue arcs at the core of the cluster that are likely strong-lensing
images.

Figure 28: RXCJ1314. A merging system with a possibly large viewing angle and
radio relics at asymmetric projected separation. WL contours increase in steps
of $0.5\sigma$.

###  4.22 RXC J1314.4-2515 ($z=0.247$)

RXCJ1314 is the second example of a two radio relic cluster that has a
distinct difference in the distance of the radio relics from the barycenter of
the subclusters (like PLCKG287). The imbalanced radio relic distribution could
be caused by two merging events or it could also be a projection effect (for
recent radio work see Stuardi et al., 2019). A shock was detected in XMM-
Newton observations at the location of the western relic (Mazzotta et al.,
2011). G19 concluded that the member galaxies follow two Gaussian
distributions with a $\scriptstyle\sim$1500 km s-1 LOS velocity difference.
Therefore, projection effects are important to consider for RXCJ1314. Stuardi
et al. (2019) came to a similar conclusion from vastly different rotation
measures from the two radio relics and found that simulations suggest a 70
degree departure from the plane of sky. Nevertheless, the axis connecting the
radio relics agrees with the elongated X-ray emission and defines a probable
merging axis. The cluster was also recently observed with MeerKAT (Knowles et
al., 2022), which is presented in Figure 28.

WL result: The WL mass map (Figure 28) is elongated along the projected merger
axis. The W mass peak is dominant and coincides with the BCG. The E mass peak
is spatially consistent with the second BCG and a third mass clump is detected
to the south. It is unclear whether this 3rd mass peak is at the redshift of
the cluster or is background. Our two-halo fit finds a 2:1 mass ratio with
masses of $4.2\pm 1.3$ and $2.3\pm 1.0\times 10^{14}\ M_{\odot}$ for the E and
W subclusters, respectively.

Merger insight: The X-ray emission, galaxies, and WL signal offer a simple
merger geometry between the east and west subclusters. Similar to PLCKG287, it
could be that two different mergers have occurred that created the two radio
relics. However, our WL analysis does not detect an additional subcluster that
may have been involved in the merger.

Figure 29: ZwCl0008. A dissociative merger of equal mass subclusters. WL
contours increase in steps of $0.5\sigma$.

###  4.23 ZwCl 0008.9+5215 ($z=0.104$)

ZwCl0008 is another merging cluster with double radio relics (van Weeren et
al., 2011c). The double relics are quite different from each other with the
largest linear size of the east relic three times bigger than the west. A
similar discrepancy is found in the Sausage relics. ZwCl0008 exhibits a
bullet-shaped morphology in the ICM (Golovich et al., 2017). It also has a
very short radio relic standoff distance (for a discussion of the standoff
distance see Zhang et al., 2019). These two features are signs of a recent
merger. A WL analysis of the cluster was done with HST and Subaru imaging in
Golovich et al. (2017) and found that the eastern subcluster is four times
more massive than the western subcluster. The spectroscopic observations of
G19 suggest a cluster merger closer to a 1:1 mass ratio. From Chandra and
Suzaku observations, Di Gennaro et al. (2019) detected a shock at the western
radio relic and measured a Mach number of $1.5\pm 0.5$. They found no shock at
the location of the eastern relic. Kang et al. (2012c) simulated the collision
and showed that the radio relic agrees with the combination of DSA and re-
acceleration. Molnar & Broadhurst (2018) predicted that the cluster merger is
an off-axis binary merger that is viewed shortly after first core passage.

WL result: Our WL analysis on solely the Subaru imaging detects the two
subclusters (Figure 29). Using our multiple NFW halo fitting technique, we
find that the mass ratio is close to 1:1 with the eastern (western) subcluster
mass being $M_{200}=2.9\pm 0.8\ (2.7\pm 0.8)\times 10^{14}\ M_{\odot}$. This
is in agreement with the velocity dispersion values in G19. In addition to the
detection of the two subclusters, an elongation of the WL signal from the
western subcluster towards the south is found. This detection is coincident
with another bright cluster galaxy. Comparing the WL signal to the galaxy
luminosity and number density distributions shows that there is likely another
substructure.

Merger Insight: The merger scenario for ZwCl0008 is straightforward with a
collision between the two components of a mass distribution that is dominated
by two subclusters. The X-ray emission shows morphological features that
suggest a small impact parameter. The short standoff distance of the radio
relics is expected for a system that is observed shortly after collision.
ZwCl0008 is a great candidate for constraining the properties of dark matter.

Figure 30: ZwCl1447. A merging system with double radio relics. WL contours
increase in steps of $0.5\sigma$ and start at $3\sigma$.

###  4.24 ZwCl 1447+2619 ($z=0.376$)

ZwCl1447 is a Butcher & Oemler (1984) galaxy cluster that has a poorly defined
red sequence. Recent Chandra observations revealed a double clump ICM
distribution with a small ($\scriptstyle\sim$500 kpc) separation between the
subclusters (Lee et al., 2022). Giovannini et al. (2009) analyzed VLA 1.4 Ghz
data and discovered a radio relic to the south of the cluster. They also found
a radio relic candidate in the north but were undecided on whether it is a
relic or halo. However, recent GMRT observations by Lee et al. (2022) have
highlighted that the diffuse radio emission in the north is indeed a radio
relic. They showed that the relic in the south is a textbook example of a bow
shock (like the Sausage relic). In addition, they ruled out radio halo
emission. G19 were unable to divide the spectroscopically confirmed cluster
member galaxies into multiple distributions.

WL result: The WL analysis (Figure 30) for this cluster was first presented in
Lee et al. (2022). We find that the WL signal consists of three distinct
peaks. Two of the peaks are coincident with the X-ray brightness peaks. A
third peak is located about 1 Mpc to the SE of the BCG and is associated with
the second brightest galaxy in the region. As shown in Figure 30, there is
good agreement between galaxies and mass distribution in this cluster. The SE
mass peak that is coincident with the second brightest galaxy in the field has
no X-ray detection. One reason may be from the chip gap of the Chandra
detector. A second reason may be that the gas has been stripped from a past
merger with the primary cluster. Better planned X-ray observations would be
useful for understanding the nature of the SE substructure. Our three-halo fit
to the distribution gives masses of $2.7\pm 0.8$, $1.0\pm 0.5$, and $2.2\pm
0.7\times 10^{14}\ M_{\odot}$ for the N, S, and SE subclusters, respectively.

Merger Scenario: The alignment of the two subclusters in the north is in great
agreement with the radio relics. We suggest that these are the subclusters
that merged to form the shocks. Furthermore, the radio relic in the south has
a very uniform arc shape that may be indicating a head-on collision. The
location of the SE mass peak suggests that it has not been involved in the
merger, especially since it lies ahead of the radio relic. However, it is
peculiar to not detect any X-ray emission from it. For detailed simulations of
the cluster merger, see Lee et al. (2022).

Figure 31: ZwCl1856. An equal-mass merger with low total mass and double radio
relics. WL contours increase in steps of $0.5\sigma$.

###  4.25 ZwCl 1856.8+6616 ($z=0.334$)

ZwCl1856 is a pristine example of double radio relics that are nearly equal in
shape, size, distance from the center, and orientation. The relics were first
presented in de Gasperin et al. (2014a) and further analyzed in Jones et al.