# LoVoCCS - II. Weak Lensing Mass Distributions, Red-Sequence Galaxy
Distributions, and Their Alignment with the Brightest Cluster Galaxy in 58
Nearby X-ray-Luminous Galaxy Clusters

Shenming Fu NSF’s National Optical-Infrared Astronomy Research Laboratory, 950
North Cherry Avenue, Tucson, AZ 85719, USA  Ian Dell’Antonio Department of
Physics, Brown University, 182 Hope Street, Box 1843, Providence, RI 02912,
USA  Zacharias Escalante Department of Physics, Brown University, 182 Hope
Street, Box 1843, Providence, RI 02912, USA  Jessica Nelson Department of
Physics, Brown University, 182 Hope Street, Box 1843, Providence, RI 02912,
USA  Anthony Englert Department of Physics, Brown University, 182 Hope Street,
Box 1843, Providence, RI 02912, USA  Søren Helhoski Department of Physics,
Brown University, 182 Hope Street, Box 1843, Providence, RI 02912, USA  Rahul
Shinde Department of Physics, Brown University, 182 Hope Street, Box 1843,
Providence, RI 02912, USA  Julia Brockland  Department of Physics, Brown
University, 182 Hope Street, Box 1843, Providence, RI 02912, USA  Philip
LaDuca  Department of Physics, Brown University, 182 Hope Street, Box 1843,
Providence, RI 02912, USA  Christelyn Larkin  Department of Physics, Brown
University, 182 Hope Street, Box 1843, Providence, RI 02912, USA  Lucca Paris
Department of Physics, Brown University, 182 Hope Street, Box 1843,
Providence, RI 02912, USA  Shane Weiner  Department of Physics, Brown
University, 182 Hope Street, Box 1843, Providence, RI 02912, USA  William K.
Black Department of Physics and Astronomy, Brigham Young University, N283 ESC,
Provo, UT 84602, USA  Ranga-Ram Chary Infrared Processing and Analysis Center,
MC 314-6, Caltech, 1200 E. California Boulevard, Pasadena, CA 91125, USA
Douglas Clowe Department of Physics and Astronomy, Ohio University, 1 Ohio
University, Athens, OH 45701, USA  M. C. Cooper Department of Physics and
Astronomy, University of California, Irvine, Irvine CA, USA  Megan Donahue
Department of Physics and Astronomy, Michigan State University, East Lansing,
MI 48824, USA  August Evrard Department of Astronomy, University of Michigan,
Ann Arbor, MI 48109, USA  Department of Physics, University of Michigan, Ann
Arbor, MI 48109, USA  Mark Lacy National Radio Astronomy Observatory, 520
Edgemont Road, Charlottesville, VA 22903, USA  Tod Lauer NSF’s National
Optical-Infrared Astronomy Research Laboratory, 950 North Cherry Avenue,
Tucson, AZ 85719, USA  Binyang Liu Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210023, China  Jacqueline McCleary Department of
Physics, Northeastern University, 110 Forsyth St, Boston, MA 02115  Massimo
Meneghetti Osservatorio di Astrofisica e Scienza dello Spazio di Bologna,
Istituto Nazionale di Astrofisica Via Gobetti 93/3, I-40129, Bologna, Italy
National Institute for Nuclear Physics, viale Berti Pichat 6/2, I-40127
Bologna, Italy  Hironao Miyatake Kobayashi-Maskawa Institute for the Origin of
Particles and the Universe (KMI), Nagoya University, Nagoya, 464-8602, Japan
Division of Physics and Astrophysical Science, Graduate School of Science,
Nagoya University, Nagoya 464-8602, Japan  Kavli Institute for the Physics and
Mathematics of the Universe (WPI), The University of Tokyo Institutes for
Advanced Study (UTIAS), The University of Tokyo, Chiba 277-8583, Japan  Mireia
Montes Instituto de Astrofísica de Canarias, c/ Vía Láctea s/n, E-38205 - La
Laguna, Tenerife, Spain  Departamento de Astrofísica, Universidad de La
Laguna, E-38205 - La Laguna, Tenerife, Spain  Priyamvada Natarajan Department
of Astronomy, Yale University, 266 Whitney Avenue, New Haven, CT 06511, USA
Department of Physics, Yale University, 217 Prospect Street, New Haven, CT
06520, USA  Michelle Ntampaka Space Telescope Science Institute, Baltimore, MD
21218, USA  Department of Physics and Astronomy, Johns Hopkins University,
Baltimore, MD 21218, USA  Elena Pierpaoli University of Southern California,
Los Angeles, CA 90089, USA  Marc Postman Space Telescope Science Institute,
3700 San Martin Drive, Baltimore, MD 21218, USA  Jubee Sohn Astronomy Program,
Department of Physics and Astronomy, Seoul National University, 1 Gwanak-ro,
Gwanak-gu, Seoul 08826, Republic of Korea  SNU Astronomy Research Center,
Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of
Korea  David Turner Department of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  Keiichi Umetsu Academia Sinica
Institute of Astronomy and Astrophysics (ASIAA), No. 1, Section 4, Roosevelt
Road, Taipei 10617, Taiwan  Yousuke Utsumi Kavli Institute for Particle
Astrophysics and Cosmology (KIPAC), SLAC National Accelerator Laboratory,
Stanford University, 2575 Sand Hill Road, Menlo Park, CA 94025, USA  Gillian
Wilson Department of Physics, University of California Merced, 5200 Lake Road,
Merced, CA 95343, USA

###### Abstract

The Local Volume Complete Cluster Survey (LoVoCCS) is an on-going program to
observe nearly a hundred low-redshift X-ray-luminous galaxy clusters
(redshifts $0.03<z<0.12$ and X-ray luminosities in the 0.1-2.4 keV band
$L_{{\rm X500c}}>10^{44}$ erg/s) with the Dark Energy Camera (DECam),
capturing data in $u,g,r,i,z$ bands with a $5\sigma$ point source depth of
approximately 25-26th AB magnitudes. Here, we map the aperture masses in 58
galaxy cluster fields using weak gravitational lensing. These clusters span a
variety of dynamical states, from nearly relaxed to merging systems, and
approximately half of them have not been subject to detailed weak lensing
analysis before. In each cluster field, we analyze the alignment between the
2D mass distribution described by the aperture mass map, the 2D red-sequence
(RS) galaxy distribution, and the brightest cluster galaxy (BCG). We find that
the orientations of the BCG and the RS distribution are strongly aligned
throughout the interiors of the clusters: the median misalignment angle is 19
deg within 2 Mpc. We also observe the alignment between the orientations of
the RS distribution and the overall cluster mass distribution (by a median
difference of 32 deg within 1 Mpc), although this is constrained by galaxy
shape noise and the limitations of our cluster sample size. These types of
alignment suggest long-term dynamical evolution within the clusters over
cosmic timescales.

Weak gravitational lensing (1797) — Astronomy data analysis (1858) — Surveys
(1671) — Galaxy clusters (584) — Observational cosmology (1146) — Dark matter
(353)

††journal: ApJ††facilities:  CTIO:4m(Blanco/DECam), Astro Data Lab, Astro Data
Archive, IRSA ††software:  Astropy (Astropy Collaboration et al., 2013, 2018),
Astroquery (Ginsburg et al., 2019), LSST Science Pipelines (Jurić et al.,
2017; Bosch et al., 2019), Matplotlib (Hunter, 2007), Numpy (Harris et al.,
2020), Scipy (Virtanen et al., 2020), Source Extractor (Bertin & Arnouts,
1996)

##  1 Introduction

While clusters of galaxies are the largest gravitationally bound structures in
the Universe, connections and interactions still exist between close pairs of
clusters, traced by inter-cluster filaments that connect them. Although the
direct detection of filaments has been achieved in a small number of clusters
(Dietrich et al., 2012b; Jauzac et al., 2012), it is generally difficult to
detect them without stacking data (Zhang et al., 2013). Low-redshift massive
clusters provide opportunities to inspect and study filaments individually in
high resolution because of their proximity (Haines et al., 2018).

The different components of a cluster – the central galaxy (CG) or the
brightest cluster galaxy (BCG), the member galaxy distribution, the gas, and
the dark matter – may come to display similar orientations as the cluster
evolves. Such alignment in low- and medium-mass clusters has been analyzed
statistically to study cluster triaxiality (Shin et al., 2018). The alignment
is stronger in massive clusters and has been detected in individual clusters
at medium redshift ($0.1<z<0.9$) with ground-based telescopes (Oguri et al.,
2010; Herbonnet et al., 2019) or space telescopes (Donahue et al., 2016;
Umetsu et al., 2018), but in relatively small samples. In addition, cluster
pairs may show alignment between their matter distributions due to the large-
scale tidal field. Low-redshift (low-z; $z\lesssim 0.1$) massive clusters
would reveal those intra- or inter-cluster features individually and in more
detail, which can be observed by even ground-based telescopes. Low-redshift
clusters allow one to resolve halo substructures and facilitate studies of
e.g., the correlation between cluster substructure and galaxy
population/evolution (McCleary et al., 2015).

Nearby clusters are also useful for cosmological studies by providing a low-
redshift anchor for the scaling relations between the cluster mass and the
observables at the late Universe. The evolution of halo mass function is
sensitive to the cosmological parameters $\Omega_{\rm m}$ and $\sigma_{8}$ at
the high mass end, where galaxy clusters reside, and thus clusters provide a
key probe of dark energy (Albrecht et al., 2006; Allen et al., 2011; The LSST
Dark Energy Science Collaboration et al., 2018). Building mass functions
requires accurate mass measurements of clusters with unbiased selection. Most
clusters in the Universe are not massive enough to produce significant
gravitational lensing signals that overcome measurement noise, and their
individual masses are difficult to be directly measured. However, their masses
can be statistically inferred from scaling relations between the mass and the
observables, e.g., member galaxy richness and gas properties (X-ray emission
or the Sunyaev-Zel’dovich/SZ effect). Weak lensing (WL) on the other hand,
yields unbiased mass estimates over a large ensemble of clusters and thus
permits calibration of those scaling relations (McClintock et al., 2019;
Miyatake et al., 2019; Umetsu, 2020). To construct a scaling relation, the
cluster sample needs to be complete and span a wide range of dynamical states
to avoid biased cosmological inference (Kettula et al., 2015).

In the past, it was difficult to study clusters at very low redshift via WL,
because those clusters require high-quality PSF modeling over a large sky area
and very deep observations to reduce shape noise as their lensing signal
($\propto D_{ls}D_{l}$) is low compared to clusters at medium redshift.
However, nowadays nearby clusters can be well captured by recently developed
large aperture and large Field-of-View (FoV) instruments, e.g., the Dark
Energy Camera (DECam; FoV $2.2\deg$) mounted on the 4-meter Blanco Telescope
at the Cerro Tololo Inter-American Observatory (CTIO), and the future LSST
Camera (FoV $3.5\deg$) mounted on the 8.4-meter Simonyi Survey Telescope at
the Rubin Observatory. The large aperture enables fast and deep observations
of hundreds of thousands of galaxies at the same time. Meanwhile, recent tools
strengthen the PSF modeling over a large FoV which improves the shape
measurements for lensing analysis (Bosch et al., 2018). As a result, accurate
lensing measurements of nearby clusters have become easier to achieve than in
earlier years. DECam has already proved its excellent performance in the
recently completed Dark Energy Survey (DES; Dark Energy Survey Collaboration
et al., 2016), and as a comparison, the 10-year LSST (Ivezić et al., 2019)
will be $\sim 3$ magnitudes deeper over a $\sim 3$ times larger sky footprint.
In addition to optical observations, X-ray observations (e.g., Chandra,
XMM/Newton, eROSITA) and SZ observations (e.g., Planck) provide vast amount of
information about the hot gas in nearby clusters.

We proposed the Local Volume Complete Cluster Survey (LoVoCCS; Proposal ID:
2019A-0308; PI: Ian Dell’Antonio) to observe a volume-complete sample of 107
nearby X-ray luminous clusters ($0.03<z<0.12$; [0.1–2.4 keV] $L_{\rm
X500c}>10^{44}$ erg/s; $M_{\rm 500c}\gtrsim 2\times 10^{14}M_{\odot}$, $M_{\rm
200c}\gtrsim 3\times 10^{14}M_{\odot}$) in low Galactic extinction fields
using DECam $u,g,r,i,z$-bands. Here, the subscript 500c (200c) means the mass
within a radius where the average overdensity is 500 (200) times the critical
density at that redshift; the mass $M_{\rm 500c}$ is given by Piffaretti et
al. (2011) and we convert it to $M_{\rm 200c}$ using typical NFW halos
(Navarro et al., 1997; Child et al., 2018). The survey started in 2019 and is
expected to conclude by 2024. The deep co-added images of each cluster field
have reached LSST Year $1-2$ depth ($\sim 1$ mag deeper than DES; Appendix A)
more than two years prior to the LSST Y1 data release. Additionally, $\gtrsim
10$ northern LoVoCCS clusters will not be fully covered by LSST (especially
the ones outside the North Ecliptic Spur and at high Declination). These co-
added images can also serve as a zeroth-year template for LSST transient
studies.

We observed the cluster sample in uniform depth but prioritize clusters that
have higher X-ray luminosities. Although delayed by the pandemic and inclement
weather, we have finished the observation of 83 clusters (complete to the top
52 clusters in terms of X-ray luminosity) and obtained $87\%$ of the survey
data (including archival data), as of the submission of this paper (Figure 1).
In addition, we have been awarded further DECam time to survey a sample of
Planck SZ clusters near the LoVoCCS X-ray luminosity cut to increase the SZ
completeness (Proposal ID: 2022A-658443; PI: Ian Dell’Antonio), and Hyper
Suprime-Cam (HSC) time to observe northern clusters selected by the same
criteria aiming to improve the all-sky completeness (Proposal ID: S20A-127,
S23B-105, S24A-81; PI: Hironao Miyatake).

Figure 1:  Celestial distribution of LoVoCCS clusters with their ranks and
observation completeness (107 clusters in total). The black-edge circles
denote clusters that have finished observation (83 clusters). The gray-edge
squares denote clusters that were partially observed (22 clusters). The light-
gray-edge triangles denote clusters that have not been observed (2 clusters).
The marker face color shows the cluster rank. A higher rank corresponds to a
higher X-ray luminosity (a brighter color in the figure); high rank clusters
are generally more complete in observation. The purple and blue solid curves
represent the ecliptic plane and the Milky Way galactic plane respectively,
and the dashed curves show $\pm 15\deg$ from the planes.

We presented the survey background, pipeline, and early science results in our
first LoVoCCS paper (Fu et al., 2022, hereafter Paper I). In this second
paper, we study a sample of 58 clusters from LoVoCCS (Section 2), with a focus
on the mass distributions and galaxy distributions in these clusters. About
half of the cluster sample ($\gtrsim\textsc{24}~{}$ clusters) have not been
studied in detail via WL previously, and the rest provide comparisons of our
study with previously reported results. In this work, we analyze the
performance of the photometric redshift measurement and improve the quality
check procedure in our pipeline, and we extend the pipeline by adding steps to
construct the distribution of red-sequence (RS) galaxies and to study cluster
triaxiality by measuring the orientations and positions of the BCG, the RS
galaxy distribution, and the lensing mass distribution on the plane of sky
(Section 3). In Section 4, we present the optical image overlaid with the mass
map and RS distribution contours of each cluster (or cluster pair/group), and
we compare the orientations and locations of those cluster components (BCG,
galaxy distribution, and mass distribution) in individual clusters as a
function of cluster evolution stage. We then discuss our results in Section 5
and summarize the paper in Section 6.

Throughout this paper, we use the same cosmological parameters as Paper I:
flat $\Lambda$CDM $H_{0}=71$ km/s/Mpc, $\Omega_{\rm m}=0.2648$; switching
between commonly used values slightly changes the angular diameter distances
and luminosity distances in this work (by $\lesssim 2\%$).

##  2 Dataset

Our sample of 58 clusters covers a large variety of X-ray luminosities (and
therefore masses)111X-ray luminosity in the 0.1–2.4 keV band: $1.1\times
10^{44}$ erg/s $<L_{\rm X500c}<8.7\times 10^{44}$ erg/s; mass based on the
X-ray emission: $2.0\times 10^{14}M_{\odot}\lesssim M_{\rm 500c}\lesssim
7.3\times 10^{14}M_{\odot}$ (Piffaretti et al., 2011).
https://heasarc.gsfc.nasa.gov/W3Browse/rosat/mcxc.html, redshifts
($0.04<z<0.12$), and dynamical states (perturbed or nearly relaxed). We rank
all LoVoCCS clusters by X-ray luminosity (Piffaretti et al., 2011) from 1 to
107. The 13 highest ranked LoVoCCS clusters are included in this work, and the
lowest rank in the sample is 99 (A3825). These 58 clusters are exposure-time
complete in LoVoCCS and have high-quality processing results. We give a list
of public datasets used for co-addition in Appendix B. Each cluster is covered
by $\gtrsim 100$ exposures. As mentioned earlier, we summarize the $5\sigma$
co-added depth of these cluster fields in Appendix A; the median depth values
are $25-26$th PSF magnitudes for point objects in $u,g,r,i,z$ bands, and the
CModel magnitudes for extended objects are $\sim 0.3$ mag shallower. The point
and extended objects are separated by the LSP parameter extendedness in $r$
band, which is the band for our shape measurements for lensing analysis (we
require seeing $\lesssim 1^{\prime\prime}$), and we have used the LSP flags
base_PsfFlux_flag and modelfit_CModel_flag to select objects that have high-
quality photometric measurements. We include archival $Y$-band data in the
processing for photometric redshift measurements.

##  3 Methods

The LoVoCCS pipeline has been presented in Paper I. Here we briefly summarize
the pipeline (Section 3.1), and emphasize the steps that have been taken to
improve it in the remainder of this section. We describe the performance of
our photometric redshift measurements (Section 3.2) and mass map construction
(Section 3.3); the new steps taken in performing the red-sequence galaxy
analysis (Section 3.4) and cluster triaxiality analysis (Section 3.5); and the
improvements in our data quality checks (Section 3.6).

###  3.1 Pipeline Steps

We require a framework that allows us to consistently analyze the full
diversity of virialized and merging clusters in LoVoCCS. For this, we use the
LSST Science Pipelines (LSP) software222https://pipelines.lsst.io to first
process the raw data and then use our own pipeline to analyze the LSP data
products of each cluster uniformly. The LSP software enables us to use the
latest algorithms designed for the future LSST data. The output images and
catalogs are therefore be compatible with the LSST data products, which
simplifies and enables future synergies. The LSP software has the ability to
process the data from different instruments, including DECam, Subaru/HSC and
Canada–France–Hawaii Telescope (CFHT)/MegaCam, in a similar manner. The
details of LSP have been described by Bosch et al. (2018).

In each cluster field, we first download the public DECam data from the
NOIRLab Astro Data Archive.333https://astroarchive.noirlab.edu We use the LSP
to detrend the raw DECam exposures at individual CCDs. The astrometry and
photometry of each CCD are calibrated against external stellar catalogs – Gaia
(Gaia Collaboration et al., 2016, 2018; Gaia Collaboration, 2018) for
astrometric calibration, and Pan-STARRS1 (PS1; Chambers et al., 2016; STScI,
2022)444All the PS1 data used in this paper can be found in MAST:
http://dx.doi.org/10.17909/55E7-5X63 (catalog 10.17909/55E7-5X63). , SkyMapper
(Wolf et al., 2018; Onken et al., 2019; Australian National University, 2017,
2019), and Sloan Digital Sky Survey (SDSS; Alam et al., 2015) for photometric
calibration. We then select high-quality CCD exposures by the seeing measured
on the processed images: median ellipticity $<0.13$, FWHM
$<1^{\prime\prime}.16$ in $r$ band (for lensing analysis), and ellipticity
$<0.33$, FWHM $<1^{\prime\prime}.74$ in other bands. We improve the astrometry
and photometry of those exposures by calibrating their catalogs jointly. Next,
the exposures are mapped onto 4k$\times$4k-pixel patches ($0.3\times 0.3$ deg,
$0^{\prime\prime}.263$ per pixel), and adjacent patches have an additional 100
pixel overlap. The exposures are then stacked on each patch and in each band.
After stacking, the LSP detects, de-blends, measures objects on the co-added
images, and performs forced photometry among different bands on each object.
We use the shape information measured on the co-added $r$-band image for
lensing analysis, and we use the forced photometry to obtain the color
information of each object.

After the LSP steps, we correct for the Galactic extinction using the dust
reddening map (Schlegel et al., 1998; Schlafly & Finkbeiner, 2011; IRSA,
2022), and further calibrate the magnitude zero points in the coadd catalog
(measured from the co-added images) using the model color-terms and the color-
color stellar locus. We then measure photometric redshifts, build lensing mass
maps and shear profiles, derive lensing masses, and check the data product
quality. In this work, we also add steps to construct red-sequence galaxy
distributions and cluster triaxiality metrics.

We adjust the pipeline in some special cases. The default angular cut on the
CCD selection is $1.5\deg$ towards the cluster center, which results in
$12\times 12$ patches generally. In the field of A401 and A3558, we use larger
angular cuts ($1.8\deg$ and $2\deg$ respectively) to include the nearby
clusters that they are interacting with. For the A401/A399 field in the
northern sky, since there is no SDSS coverage for the $u$-band photometric
calibration, we build a synthetic reference catalog for the LSP based on the
empirical color transformations between PS1 (deep observations in $g$ and $r$)
and DECam ($u$) in other cluster fields, and we further calibrate the $u$-band
photometry in the coadd catalog using the model stellar locus of $g-r$ vs.
$u-g$ after the extinction correction; we find that this approach produces
reasonable photometric redshifts compared to the spectroscopic redshifts.

###  3.2 Photometric Redshifts

In this work, we continue using the Bayesian Photometric Redshift (BPZ;
Benítez, 2000; Coe et al., 2006) algorithm to estimate galaxy photometric
redshifts (photo-zs), and we compare the results with archival public
spectroscopic redshifts (spec-zs) obtained from NASA/IPAC Extragalactic
Database (NED; Helou et al., 1991; NED, 2019).

As mentioned in Paper I, the photo-z outliers at low (true) redshift are
mainly caused by the lack of archival $u$-band data on the periphery of
cluster fields, blended objects, or special galaxy types/colors. However, the
insufficiency of $u$-band data is rarely the case in the cluster central areas
we observe for lensing analysis. After visual inspection, we find that the
galaxy type assigned by BPZ is generally correct (we use a two-step
interpolation between consecutive templates), and we also find that the
spirals in clusters are more likely to have photo-z’s biased high because they
are redder than field galaxies due to quenching. The outliers also include
cluster dwarf galaxies, which are more common in galaxies with blue BPZ galaxy
types. Figure 2 shows an example of our photo-z quality: a comparison between
the spec-zs and photo-zs of a clean sample of galaxies selected by $z_{\rm
s}<1.5$, $\texttt{odds}>0.95$, $\chi^{2}_{\texttt{mod}}<1$, and covered by $u$
band; the photo-z uncertainty and the outlier rate are both at a few percent.
Here odds and $\chi^{2}_{\texttt{mod}}$ give the BPZ probability concentration
and closeness of fit, respectively. Note the archival spec-z datasets mostly
focus on cluster member galaxies for dynamical analysis.

In this work, we use a photo-z cut at the cluster redshift plus 0.1 to remove
foreground galaxies, instead of a fixed cut at 0.15 used in Paper I.
Therefore, the photo-z cut is different in different cluster fields. This
change improves the lensing map S/N of our higher-redshift clusters by
$\lesssim 10\%$. This change in mass map could be caused not only by the
reduction of foreground galaxy contamination, but also by the high sensitivity
to lensing signal of background galaxies at low redshift. Adding higher
photo-z cuts can remove both foreground and background galaxies because of the
photo-z noise – we seek to find a balance between the lensing signal and shape
noise. In Paper I, under the original photo-z cut, we estimated that photo-z
outliers could dilute the lensing signal by a few percent. As more foreground
galaxies are removed under the new photo-z cut, we estimate the bias of mass
maps in this work introduced by photo-z errors is even smaller ($\sim$ percent
level). We note that in Figure 2 there is a cloud of galaxies at $z_{\rm
s}\sim 0.2$ with $z_{\rm p}\sim 0.25$ (these are likely dusty/quenched),
however these galaxies are mainly behind our cluster sample ($z\lesssim 0.1$),
and thus we do not expect their presence to affect our mass maps
significantly. As in Paper I, we also remove sources at photo-z higher than
1.4 because their shape measurements can be noisier.

To further filter out foreground galaxies, we examined the inclusion of
archival photometry in other wavelength bands. Given the depth, footprint, and
seeing of archival data, we consider adding external near-infrared (NIR)
photometry to remove the member/low-z galaxies (instead of increasing the
wavelength coverage of background sources). Those foreground galaxies are
relatively larger and brighter than the background sources, and thus they are
unlikely affected by the seeing and depth of those external catalogs. We match
the LS+WISE forced photometry catalog from the DESI Legacy Imaging Surveys
(LS; Dey et al., 2019) and the VISTA Hemisphere Survey catalog (VHS; McMahon,
2011; McMahon et al., 2013)555We obtained the LS+WISE and VHS catalogs from
the NOIRLab Astro Data Lab. https://datalab.noirlab.edu/index.php with the
LoVoCCS catalog and the NED spec-z catalog. We find that in the color-color
space of e.g., $z-w_{1}$ vs. $w_{1}-w_{2}$, $Y-J$ vs. $J-K_{\rm s}$, no simple
cut can fully separate those foreground galaxies ($z_{\rm s}\lesssim 0.1$)
from the others. Also, when comparing the mass maps with and without cuts on
NIR colors, we find no significant difference. Therefore, in the following
analysis we only use the photometry from LoVoCCS. Another approach to the
removal of foreground galaxies is to use a machine learning (ML) photo-z
algorithm which takes the morphology and special colors of cluster members
into account – we will explore this in the future.

In fact, as it turns out, the mass map morphology is not very sensitive to the
photo-z selection as member galaxy shapes are randomly distributed in general;
they do exhibit intrinsic alignment (IA) caused by tidal fields, but we expect
this to be a secondary effect compared to the cluster lensing signal.
Similarly, we assume that the IA between background sources is a secondary
effect as well and thus do not consider it when constructing mass maps.
Additionally, we make cuts on the photo-z quality metrics
($\texttt{odds}>0.95$ and $\chi^{2}_{\texttt{mod}}<4$) before making mass maps
to ensure the photo-z quality and to be consistent with the mass fitting step.
The photo-z quality cuts reduce the median galaxy number density from $\sim
22$ arcmin-2 (shape and photometry cuts have been applied) to $\sim 8$
arcmin-2, and the photo-z value cut further reduces the source density to
$\sim 7$ arcmin-2. Our test shows that including more sources using wider
photo-z quality cuts does not significantly improve the S/N of mass maps, and
the reason could be that the sources outside our quality cuts have noisier
shape measurements.

Figure 2: Comparison between the photo-zs ($z_{\rm p}$) and spec-zs ($z_{\rm
s}$) in all cluster fields studied in this paper with metrics of the photo-z
error $\Delta z={(z_{\rm p}-z_{\rm s})}/{(1+z_{\rm s})}$. Left: The dotted,
dashed, and solid lines represent biases of $|\Delta z|=0.15,0.05,0$,
respectively. We use a step of 0.01 in BPZ. The normalized-median absolute
deviation ($1.48\times\texttt{median}\\{|\Delta z|\\}$; NMAD) shows an
estimation of the photo-z uncertainty, and the percentage of galaxies that
have $|\Delta z|>0.15$ gives the outlier rate $\eta$. Right: The blue solid
curve shows the distribution of $\Delta z$, which is nearly a Gaussian
$N(0,\texttt{NMAD}^{2})$, the orange dotted curve; the small bias is mainly
caused by the low-z galaxies (mostly cluster members) at $z_{\rm s}\lesssim
0.2$.

###  3.3 Aperture Mass S/N Map

As in Paper I, we make quality cuts and conduct shear calibration on the HSM
shapes (Hirata & Seljak, 2003; Mandelbaum et al., 2005, 2018a) on the co-added
catalog before analyzing the lensing signal. We then use the aperture mass
statistics (Schneider, 1996) to build lensing mass S/N maps via the Schirmer
filter (Schirmer et al., 2004; Hetterscheidt et al., 2005; von der Linden et
al., 2014). The aperture mass signal is a convolution between the convergence
map (normalized surface mass density) and a circular (radially symmetric)
weight function, and it is equivalent to a convolution between the tangential
shear and a circular filter function (the Schirmer filter in this case). We
approximate the tangential shear by the mean of per-galaxy reduced shear
estimates derived from galaxy shapes, and we compute the mean within
$100\times 100$ pixel bins to reduce shape noise. The noise in the aperture
mass mainly comes from the shape dispersion of source galaxies. Therefore,
both the signal and noise parts of the mass S/N map scale with the source
galaxy shapes. The possible remaining biases (usually multiplicative) in the
galaxy shapes caused by e.g., blending, photo-z bias, shape measurement, can
be mostly factored out in the signal-to-noise ratio, and we thus consider them
as secondary effects.

The S/N mass map shows how the underlying mass is concentrated. The Schirmer
filter produces the highest S/N at an aperture center when the characteristic
scale of the halo structure around that center is $\sim 1/10$ of the aperture
radius. Thus, we vary the aperture radius starting from 3k pixels with steps
of 1k pixels to determine the mass map that best captures the cluster-scale
structure. In general, we choose the aperture that maximizes the peak S/N in
the mass map; if the corresponding scale size is too small or large, we
consider a local maximum where the aperture corresponds to the size of a
normal cluster. Also, the morphology, in particular, the orientation of the
projected halo should not be strongly affected by the convolution during the
mass map construction, given the symmetry of the weight function. Using mock
lensing catalogs, we verified that the mass map algorithm recovered elliptical
halo orientations (Appendix C).

Most of our mass maps are built based on the catalogs of central $6\times 6$
patches (24k$\times$24k pixels; $1.8\times 1.8$ deg) divided by the LSP. For
the cluster A3558 we consider the catalog of the full $15\times 15$ patches to
study the nearby structure in the Shapley supercluster, but we only present
the central mass map to ensure the quality. The flat sky approximation is
still valid in these sky regions. In Section 4.1, we present only the (curl-
free) E-mode maps derived from the tangential shear towards aperture centers.
We find that reassuringly, the corresponding B-mode maps derived from the
cross component show no clear patterns especially near the cluster centers.

The large angular sizes of the low-z clusters in LoVoCCS occasionally
encompasses background clusters in the field, which may contaminate the
lensing signal of the cluster of interest. If we select only the source
galaxies that lie in between the foreground cluster and the background
cluster, it would severely penalize the S/N. Hence, we retain background
clusters when constructing the mass maps, rather than using cuts on source
galaxy redshifts, to obtain sufficient S/N. Moreover, these background
clusters usually span an angular region much smaller than the foreground one,
and thus we expect that they only affect cluster substructure detection in
general. However, if the background cluster is very close to the foreground
cluster center, we remove the background source galaxies closer to the
background cluster (e.g., in A3128), because the background cluster may
strongly affect the mass peak position and S/N of the cluster of interest. In
the future, we plan to use external cluster catalogs or run cluster finders
(based on optical concentration, red sequence, or X-ray/SZ) to locate
background clusters, which is important for accurately determining the
foreground cluster mass.

As mentioned earlier, we use LSP flags to select high-quality objects for
analysis. We find that those flags generally remove objects affected by
saturated stars and satellite trails, and the cluster central morphology does
not change greatly after new masks are added around bright stars; we give more
examples in Section 4.1 when we study individual clusters.

###  3.4 Red-Sequence Galaxy Distribution

Galaxy clusters contain a large population of red elliptical/early-type
galaxies formed by galaxy merging and quenching. In the color–magnitude
diagram (CMD), they exhibit a characteristic “red sequence” (RS), which
results from the unique features in their spectral energy distributions (SED),
especially the 4000Å break caused by old stars and metal absorption lines. The
RS galaxies tend to be redder and brighter near the cluster center because of
their dynamical (infalling/merging) processes and quenching history. These RS
galaxies trace the overall matter distributions in clusters, and they are
closely related to luminous red galaxies (LRGs). LRGs are common tracers of
the large-scale structure (LSS) and delineate the connections between
clusters.

In this work, we include a new pipeline step that builds a red-sequence galaxy
distribution in each cluster field based on its color–magnitude diagram. To
best locate the RS in CMD, one can use the colors of spectroscopically
confirmed cluster member galaxies. This method works well in those LoVoCCS
clusters with adequate spec-z data; though the archival spec-zs in the LoVoCCS
cluster fields are limited, most of them are member galaxy spec-zs. However,
those spec-zs are mainly from bright galaxies, and in some clusters, the
number of member spec-zs is not sufficient ($\lesssim 200$) to allow reliable
data fitting in the CMD. In addition, photo-z does not work very well at low
redshift and is not so useful for picking out cluster galaxies. Therefore, we
also use all galaxies with valid photometry to locate the RS in the CMD. We
provide more details of our algorithms below, and we use the CModel magnitudes
for galaxies. In Appendix D, we show examples of RS detection and selection.

First, the archival spec-zs are accessed from NED (Section 3.2 and Paper I)
and matched with the LoVoCCS galaxy photometric catalog. The cluster member
galaxies are selected by $|z_{\rm s}-z_{\rm cl}|<0.01$, where $z_{\rm cl}$ is
the cluster redshift. Then, we consider both colors $g-r$ and $r-i$ because of
their wavelength coverage and depth, and we find that making cuts on two
colors instead of one color gives better selection of RS galaxies. We use the
$i$-band magnitude as a luminosity proxy because of its depth and small
K-correction ($\lesssim 0.05$ mag based on model SEDs used in BPZ) which
simplifies the comparison between LoVoCCS clusters, and we thus skip the
K-correction in the following analysis.

Next, we detect the RS in the CMD of spectroscopically-selected cluster
members and fit the data. We divide the $i$-band magnitude from 13.5 to 19.5
with a step of 0.3 mag, the $g-r$ color from 0.65 to 1.0 mag with a step of
0.06 mag, and the $r-i$ color from 0.25 to 0.45 with a step of 0.04 mag; each
color step approximates to the corresponding RS scatter. We then go through
the $i$-band magnitude bins, and for each magnitude bin we generate a
histogram of the $g-r$ color and find the peak among the color bins; we skip
the magnitude bin if the number of galaxies inside is below 10. Then, the
$i$-band magnitude bins and their corresponding $g-r$ color peaks are fitted
by a straight line via scipy.optimize.least_squares, and we use a loss
function soft_l1 to reduce outliers. After fitting, we select galaxies that
are 0.09 mag around the fitted $g-r$ color of their $i$-band magnitudes, and
within those selected galaxies, we repeat the above steps but on the $r-i$
color to make another fit. We found that fitting the selected galaxies rather
than all galaxies resulted in better RS detection.

We repeat the same procedure on the whole galaxy photometric catalog and
increase the number limit of galaxies per magnitude bin to 15. Then the higher
quality of the spectroscopic and photometric fits is selected through
visualization and comparison; the former usually gives a better result when
the spec-z data is sufficient. However, only $\sim 1/4$ of the cluster sample
has enough spec-zs. On the other hand, those clusters provide a validation for
the performance of the photometric fit – the completeness/purity between the
RS selections (see the magnitude and color cuts below) based on the
spectroscopic fit and the photometric fit is $\gtrsim 90\%$. In some special
cases, we also adjust parameters, e.g., the step, the number limit per bin, or
the bright end of the $i$ magnitude, to improve the fit. The result shows that
in our cluster sample the typical RS fit slopes are $\sim-0.04$ and
$\sim-0.02$ in $g-r$ and $r-i$ vs. $i$, respectively, with no obvious
dependence on redshift. Additionally, the RS seems to be more clear and
concentrated (and thus easier to locate and fit) in the CMD of more relaxed
clusters, possibly resulting from the cluster evolution.

After we obtain the best RS fit, we make color and magnitude cuts on the whole
galaxy photometric catalog. We select galaxies which are $<0.09$ mag and
$<0.06$ mag around the fitted $g-r$ and $r-i$ colors, respectively; we use
those scatter cuts to deal with the RS noise. We also make an $i$ magnitude
cut changing with the cluster redshift, which leads to a fixed luminosity
limit and simplifies direct comparison among clusters. The fiducial cutoff is
$i=20$ for a cluster at redshift $z=0.08$ (approximately the median of our
cluster sample and LoVoCCS), and we vary the $i$-band cut based on the cluster
luminosity distance (the difference among clusters is $\lesssim 2.5$ mag, much
larger than the K-correction). This $i$-band limit corresponds to an absolute
magnitude limit at $M_{i}\sim-17.8$. We set this limit based on the spec-z
data depth for the RS fit, and also to remove faint background objects since
our clusters are at low redshift. We expect that the RS contamination from
background clusters is low given the color and magnitude cuts. In addition,
our method directly detects the RS in the CMD without any training sets.

We make a further cut on the galaxy sample (after the color and magnitude cuts
above) before building the RS density map: we use BPZ galaxy type t_b==1 to
select a sample of elliptical galaxies. After checking spec-zs and optical
images, we find that this cut removes foreground/background galaxies within
the color ranges and gives a clean sample of bright cluster member galaxies.
We note that varying the t_b cut from 1 (elliptical) to 2 (spiral Sbc) does
not strongly affect the RS galaxy distribution morphology especially near the
cluster center. After the selection, the RS magnitude distribution is close to
a Gaussian, and the (apparent) magnitude histogram peak (about 3 mag from the
magnitude cut; $M_{i}\sim-21$) changes with the cluster redshift.

Once we have a clean sample of RS galaxies, we compute their 2D distribution
by Kernel Density Estimation (KDE) to get the RS density map. Similar to the
construction of mass maps, we generally consider the field of central $6\times
6$ patches (24k$\times$24k pixels), and count the galaxy number in $100\times
100$ pixel bins to reduce noise. We also remove a foreground/background galaxy
number density estimated by the density within 2k pixels from the field edge
(half of a patch); this density is not high because of the previous selections
on the galaxy color and type.

To make the final RS galaxy distribution, the galaxy count grid is then
convolved with a 2D Gaussian with a standard deviation $\sigma$ of 200 kpc
(KDE). This smoothing length is chosen to estimate the RS distribution in the
cluster and is fixed so that the RS maps of clusters at different redshifts
are comparable. Note, our RS maps are derived from only the number density and
are not magnitude or flux weighted. The resulting RS map for each cluster is
presented in Section 4.1.

###  3.5 Triaxiality: Orientation and Centering Analysis

We study cluster triaxiality by analyzing the orientations and positions of
the 2D mass distribution, RS galaxy distribution, and BCG. The BCG and cluster
member galaxy distribution can trace the (non-spherical) dark matter
distribution and the total mass distribution – they tend to have similar
orientations (e.g., Herbonnet et al., 2019). For low and medium mass clusters,
stacking cluster profiles aligned with the BCG or member galaxy distribution
can reveal the cluster triaxiality (e.g., Shin et al., 2018; Fu et al., 2023).
For high mass clusters (like the LoVoCCS sample studied in this work), those
types of orientation alignment are less noisier in observations and may be
visible in individual cluster fields.

Measuring the cluster ellipticity is more difficult than measuring the
orientation angle on the plane of sky. For example, measuring the ellipticity
of the mass distribution can be affected by the shear bias or the convolution
in the mass map construction; the same measurement on the galaxy distribution
can be affected by the galaxy population; the measurement on the BCG can be
affected by the intra-cluster light (ICL). In addition, the ellipticity
measurement may also vary with the cluster radius. However, measuring their
orientations is less sensitive to these factors noted above. Therefore in this
work we only measure the orientation angles.

We also compare the BCG centroid and the map peaks. In relaxed clusters, it
has been claimed that the offset between the BCG and the mass center can
provide constraints on self-interacting dark matter (SIDM; Kim et al., 2017;
Harvey et al., 2019), while in perturbed clusters the offset may result
naturally from merging process or projection effects. The mass center can be
traced by e.g., the X-ray emission or statistically the lensing mass map.

We summarize our measured angles and centers of the 2D distributions and the
BCG of each cluster in Table 4, 5 (Appendix E), and we give details of our
measurement method below.

#### BCG

To carry out more flexible measurement than the LSP, we first crop a $\sim
0.4\times 0.4$ Mpc region around the BCG on the optical $r$-band co-added
image to reduce neighboring structures e.g., bright stars/galaxies or ICL.
Then we use Source Extractor (SExtractor; Bertin & Arnouts, 1996) with the
detection threshold from $6\sigma$ to $35\sigma$ and a step of $2\sigma$ to
detect and measure objects. We then pick the object with the largest area (as
the BCG) under each threshold and take its median values of the coordinates
(`X_IMAGE` and `Y_IMAGE`) and the angles (`THETA_IMAGE`). As those galaxies
have angular sizes much larger than the PSF, we expect the systematics caused
by PSF are minimal. After visual inspections, we find that this process
further reduces the effect of ICL and noise from blended objects but still
gives the BCG orientation near the galaxy outer envelope. Note if a cluster
has multiple bright central galaxies, we pick the brightest one with the
largest area.

#### Mass map

In Section 4.1, we present the best mass S/N map of each cluster, which is
under the aperture that maximizes the S/N of the cluster-scale structure.
Starting from that mass map, we first locate the mass map peak within
$0.2\deg$ of the BCG mentioned above. Then we consider radial distance cuts of
0.5, 1.0, 2.0 Mpc from that peak on the mass map; they give the properties
near the cluster center, within the cluster edge, and within the nearby LSS,
respectively. We skip the region further out, because the signal is low and
the contamination of (projected) neighboring structure is strong there, and it
is close to the observation field edge of clusters at very low redshift. Also,
in some cluster fields the map could be “rounder” at larger radii, which makes
the angle measurement difficult. At each radial cut, we make small
perturbations on the cut from -10% to 10% with a step of 2%, measure an angle
in individual cropped mass maps, and take their median to reduce noise. The
angle is computed by the second moments (similar to the SExtractor
algorithm666https://astromatic.github.io/sextractor/Position.html) – in Eq. 1,
2, 3, $i$ is the pixel index, $m_{i}$ is the mass map pixel value.

$M_{\alpha}=\Sigma_{i}m_{i}\alpha_{i}/\Sigma_{i}m_{i};~{}\alpha=x~{}{\rm
or}~{}y$ (1)

$M_{\alpha\beta}=\Sigma_{i}m_{i}\alpha_{i}\beta_{i}/\Sigma_{i}m_{i}-M_{\alpha}M_{\beta};~{}\alpha,\beta=x~{}{\rm
or}~{}y$ (2)

$\theta=\frac{1}{2}\arctan\left(\frac{2M_{xy}}{M_{xx}-M_{yy}}\right)$ (3)

#### RS galaxy map

The method for measuring the orientation angle and peak of the RS distribution
is similar to that used for the mass map above – we replace the mass map with
the RS galaxy map.

In Section 4.2 and 4.3, we compare the orientations and centers, respectively,
of the BCG, mass and RS distributions of each cluster in our sample and study
their statistics.

###  3.6 Data Product Quality Check

We use a “quality check” step in the pipeline to examine the quality of our
data products by analyzing the statistics of representative quantities. The
major improvement in our quality check step is evaluating the star-galaxy
shape correlation as a function of distance. In Paper I, we use shape
correlations between the stars used for the PSF modeling and the galaxies used
for the lensing analysis to estimate the PSF modeling error. In this work, we
improve the calculation of shape correlations by using
`TreeCorr`777https://github.com/rmjarvis/TreeCorr (Jarvis et al., 2004).
`TreeCorr` is implemented in `C++` and uses a tree structure to divide the
catalog into small cells. It takes the mean values in the cells that are
greatly separated to compute the correlation for that distance bin, instead of
using individual pairs of objects in that bin. It thus saves the computing
resources. Therefore, we can reach deeper magnitudes for galaxies ($r<26$),
and we find that the star-galaxy shape correlation is $\lesssim 10^{-4}$,
i.e., the PSF modeling error is $\lesssim 10\%$ of the reduced shear. We
present more details of assessing the performance of PSF modeling and shape
measurement using shape correlations in Discussion (Section 5.1).

##  4 Results

###  4.1 Maps

We present an $r$-band co-added image with the aperture mass S/N map and RS
galaxy distribution overlaid in each diagram, in Figure 3, 4, 5, 6, and 7 – in
total 54 diagrams for 58 clusters sorted by X-ray luminosity; among them 4
diagrams include multiple LoVoCCS clusters (A2029/A2033, A401/A399,
A3827/A3825, and A2556/A2554). If two LoVoCCS clusters are shown in one
diagram, we label it with the one that has the higher X-ray luminosity. Each
diagram shows the central $4\times 4$ patches (16k$\times$16k pixels;
$1.2\times 1.2$ deg) around the cluster except the cluster pairs above and
A3558 (the Shapley supercluster) to show the nearby structure. We use an
arcsinh scaling to display both faint and bright features on the co-added
image, and the local sky over-subtraction effect near bright and large objects
is thus visible. Since the over-subtraction mainly affects the neighboring
large-area and low-surface-brightness objects, we do not expect it to strongly
bias the analysis of weak lensing signal and the detection of red-sequence
galaxies – the lensing sources have small sizes and the selected RS galaxies
are bright.

In the following text, each paragraph is labeled by the LoVoCCS cluster(s) in
the corresponding diagram, although other nearby/projected clusters could be
included in the field as well. In each field, we compare the optical image
with the 2D mass and galaxy distributions to study the origin of clumps in
those distributions. The term “aperture size” refers to the Schirmer filter
radius. Note, the maximal S/N mentioned in the following text is for the mass
map peak within an aperture, and therefore it is lower than the detection S/N
of the whole cluster. Instead, the detection S/N can be estimated by the error
bar of the shear profile or the lensing mass of the cluster (e.g., the S/N of
lensing masses presented in Paper I). Also, we note that a few clusters have
previous lensing mass measurements but no reported mass maps. Compared to
these previous studies, our dataset has larger wavelength coverage for better
determination of galaxy types and redshifts, along with deeper observation and
larger FoV for lensing analysis.

Figure 3: Grid of maps (Part I). In each diagram, the background is the
inverted $r$-band co-added image; the blue contours stand for the aperture
mass S/N, while the red contours represent the red-sequence galaxy
distribution. The mass S/N contours extend from 2 to 6$\sigma$ with a step of
1, and we choose an aperture that maximizes the S/N of the cluster-scale
structure. The galaxy density contours extend from 0.024 to 0.12 per
$100\times 100$ pixels ($26.3^{\prime\prime}\times 26.3^{\prime\prime}$) with
a step of 0.024, and we use a smoothing length of 200 kpc ($\sigma$ of a 2D
Gaussian) in the Kernel Density Estimation. The redshift is from SIMBAD
(Wenger et al., 2000). The color schemes in all diagrams are the same; a
darker color means a higher value.  Figure 4: Grid of maps (Part II).  Figure
5: Grid of maps (Part III).  Figure 6: Grid of maps (Part IV).  Figure 7: Grid
of maps (Part V).

#### A2029/A2033

A2029 ($z=0.077$) and A2033 ($z=0.082$) have been widely studied using
spectroscopic and lensing measurements in optical windows (e.g., Sohn et al.,
2019; McCleary et al., 2020). Compared to the previous study of McCleary et
al. (2020), this work includes more exposures to improve the depth (by $\sim
1$ mag for shape measurements) and uses a different pipeline for image
processing and lensing analysis; our results are similar. The lensing effect
comes from both A2029 and neighboring structures. Here we use a large aperture
(15k pixels in radius) where the S/N of the central peak is maximized
($7.6\sigma$) in the mass map, but the signal of the Southern Infalling Group
(SIG) is smoothed out. The lensing signal of SIG reaches a maximum of
$1.8\sigma$ at a small aperture (5k pixels), and the RS density clearly shows
a concentration of galaxies at SIG. The RS map shows a density peak SE of
A2033, which is also shown in the member distribution described by Sohn et al.
(2019). We note that A2033 produces a stronger lensing effect than SIG, but
has lower galaxy density than SIG, which is consistent with Sohn et al. (2019)
as well. We show the central $6\times 6$ patches (24k$\times$24k pixels;
$1.8\times 1.8$ deg) to include both clusters and nearby structures.

#### A401/A399

Previous studies using X-ray and SZ observations show that A401 ($z=0.074$)
and A399 ($z=0.072$) form a pre-merging pair with a gas filament connecting
the two (e.g., Akamatsu et al., 2017; Bonjean et al., 2018; Hincks et al.,
2022). Because their redshift difference is small, it is difficult to separate
the RS of individual clusters, and thus we study their RS galaxy distributions
together. We find a clear bridge of RS galaxies connecting the two clusters,
which is consistent with the gas and previous galaxy analysis (Bonjean et al.,
2018). Also, we present the first high-resolution lensing mass map of this
cluster pair. We find that A401 has both stronger lensing signal and higher RS
galaxy density than A399, which is similar to the gas distribution. Although
we see no clear lensing signal from the filament, the mass contours of A399
(and the central galaxies of both clusters) roughly align with the direction
connecting the two clusters. We use an aperture of 7k pixels in radius that
maximizes the S/N peak of A401 ($6.7\sigma$) in the mass map, while the S/N
peak of A399 reaches the maximum at 3k pixels ($3.4\sigma$) – both lensing
peaks are well detected despite cirrus and relatively high extinction ($\sim
0.3$ mag in $r$ band) in this field. We present the central $5\times 5$
patches (20k$\times$20k pixels; $1.5\times 1.5$ deg) to show both clusters.

#### A85

A85 is a merging cluster and has been studied via WL by McCleary et al. (2020)
and in Paper I. Here we reanalyze it using the updated pipeline, and we also
present its RS galaxy distribution (same for A3921 and A3911 below). The new
mass map is consistent with the previous results, and our catalog is $\sim 1$
mag deeper than the analysis of McCleary et al. (2020). We note that A85 has
two central BCGs (NE and SW), and that the mass map S/N keeps increasing as
the aperture grows because of the substructures (two central clumps around
respective BCGs). The SW peak has slightly larger S/N than the NE one under
small apertures ($<8$k pixels), indicating that it has a smaller physical size
than the other, which also corresponds to a smaller BCG. We use an aperture
(13k pixels; S/N $\sim 6$) before the two peaks merge into one. On the other
hand, the RS distribution aligns with the orientations of two BCGs (NW-SE).

#### A3667

A3667 is known as a merging cluster. We find that the RS galaxy distribution
closely aligns (SE-NW) with the central galaxy, which also aligns with the gas
distribution and the merging direction (Knopp et al., 1996). The mass
distribution shows alignment with that direction only in the cluster periphery
(below $2\sigma$) and has a large offset from that direction near the cluster
center. Here we use an aperture radius of 14k pixels when the mass S/N peak
reaches a maximum ($4.4\sigma$). Our mass map is similar to the early result
of Joffre et al. (2000) for the cluster central region.

#### A3827/A3825

We present A3827 ($z=0.097$) and A3825 ($z=0.074$) in the same diagram because
of their proximity on the plane of sky. However, they probably do not interact
because of their large redshift difference ($\Delta z\sim 0.02$), while their
RS colors could be quite similar ($\Delta(g-r)\sim 0.04$, close to the scatter
of RS). We estimate the color based on the elliptical galaxy SED template
El_B2004a used in BPZ. In the diagram we use an aperture of 7k pixels when the
A3827 S/N peak reaches a maximum ($6.5\sigma$). A3825 S/N peak reaches its
maximum ($2.4\sigma$) at a small aperture of 3k pixels and is smoothed out in
larger apertures. The central galaxies of A3825 align with its galaxy
distribution. The central strong lensing feature of A3827 has been used to
test the nature of dark matter (e.g., Massey et al., 2018). We find a
$16^{\prime\prime}$ offset between the WL S/N peak and the BCG, which is below
the mass map resolution – we will further study this in the next section.

#### A3266

A3266 is a merging cluster. Our result shows a strong correlation between the
BCG orientation and the galaxy distribution (NE-SW); the mass distribution
tilts more towards the N-S direction, which is likely caused by a north group
(instead of background clusters after visual inspection). The orientations are
consistent with the merging direction determined by galaxy motion and gas
(Dehghan et al., 2017; Sanders et al., 2022). We present the first lensing map
of this cluster – the mass S/N peak reaches the maximum at an aperture radius
of 13k pixels ($7.6\sigma$).

#### A1651

A1651 exhibits similar morphology between the central galaxy, the galaxy
distribution, and the large-scale mass distribution. The mass contours extend
to the west. The SW lensing peak comes from a background cluster ($z\sim
0.2$). The central mass S/N peak reaches the maximum at 12k pixels
($5.1\sigma$). Sifón et al. (2015) showed that A1651 is a relaxed cluster
using spectroscopic measurements. This indicates that even nearly relaxed
clusters can have elongated shapes.

#### A754

A754 is a merging cluster. Both the galaxy density and the mass distribution
peak at the BCG, and they both align with the BCG orientation (SE-NW). Also,
the galaxy density shows another peak at an SE group inside the cluster. In
the mass map, a corresponding small clump is only shown in small apertures,
which indicates that the substructure has a small characteristic size. The
mass map peak gradually shifts to SE from NW as the aperture increases because
of the SE subclump. Our mass map is similar to the early result from Subaru
for the cluster central region (Okabe & Umetsu, 2008). In the diagram we use a
large aperture (14k pixels) that maximizes the S/N ($7.7\sigma$).

#### A3571

A3571 shows alignment between the BCG, the mass distribution, and the RS
galaxy distribution (N-S). These components also align with the gas
distribution of this relaxed cluster (Nevalainen et al., 2000). The galaxy
density value is relatively small because of the low redshift and the wide
angular range. The mass NW tip likely comes from a group of member galaxies.
Though we use the LSST pipeline flags to remove objects affected by
saturation, here we further mask out objects within $0.25$ deg of the SW
bright star (i Cen.) to reduce artifacts, and we find that the cluster mass
map does not change greatly after the cut; the residual SW clump could be
caused by some background structure. We use an aperture of 11k pixels when the
peak S/N reaches the maximum ($3.9\sigma$). This is the first reported WL map
of the low-z cluster A3571. It is also part of the Shapley supercluster – we
will present more members of this supercluster later in the text
(A3558/A3532/A3528).

#### A3112

In A3112, the mass distribution and the galaxy distribution roughly align with
the BCG along the N-S direction, and both of their peaks have small offsets
from the BCG. The mass peak has an offset towards south, which could be caused
by a cluster sub-clump or a background cluster. The NW lobe in the RS
distribution at large radii could come from a group of member galaxies; it is
extending towards A3109 (NW 0.5 deg from A3112) and thus could be influenced
by filaments inside the Horologium supercluster. We use an aperture of 11k
pixels to reach the maximum $4.4\sigma$ in the mass map. This is the first
high-resolution lensing map of A3112.

#### A2597

A2597 shows weaker lensing signal compared to the clusters that have similar
X-ray luminosities. We choose the aperture at 5k pixels to show a S/N maximum
($3.3\sigma$). The galaxy distribution aligns with the BCG at small radii (SE-
NW) and tilts more to the N-S direction at large radii due to a group of
member galaxies.

#### A1650

A1650 (SDSS-C41041) shows orientation alignment between the BCG, the mass
distribution and the RS galaxy distribution. The east mass clump could come
from a background cluster/group. For the mass map, we use an aperture of 14k
pixels that maximizes the peak S/N ($4.9\sigma$).

#### A3558

A3558 lies in the center of the Shapley supercluster. In the diagram we
present A3558 (center; $z=0.047$) and its neighboring clusters A3562 (east;
$z=0.049$) and A3556 (west; $z=0.048$). We find alignment between the central
galaxy, the mass distribution, and the galaxy distribution of A3558. Both the
mass distribution and the galaxy distribution peak at the BCG of A3558 and
extend SE towards A3562 – in between we notice low mass S/N detection ($\sim
1\sigma$) and a low-density stream of bright RS galaxies ($\sim 0.015$ per
$100\times 100$ pixels; $\sim 25$ per Mpc2), which indicates filaments
connecting A3558, A3562, and the central groups between the two. On the other
hand, we find no clear signal between A3558 and A3556 in both mass and galaxy
distributions. Here we use an aperture of 12k pixels that maximizes the S/N
($5.0\sigma$), and we show the central $11\times 5$ patches (44k$\times$20k
pixels; $3.2\times 1.5$ deg) to include all three clusters. The mass and
galaxy distributions are consistent with the gas distribution (Planck
Collaboration et al., 2014) and are similar to the previous results of Higuchi
et al. (2020), and our depth is $\sim 1.5$ mag deeper.

#### A3695

We find alignment in orientations between the BCG, the galaxy distribution,
and the mass distribution of A3695 at small radii, though these distributions
show distorted shapes at large radii, which could be caused by merging. The
central galaxy has two peaks (showing a “dumbbell” shape) along its major
axis, indicating a possible merging direction (NW-SE). We use the mass map
that has the highest S/N peak ($4.9\sigma$) at an aperture of 6k pixels.

#### A3921

A3921 is a merging cluster and has been studied via WL in Paper I. Here we use
a higher photo-z cut and obtain a similar mass map. We adopt an aperture of
11k pixels that maximizes the S/N ($3.3\sigma$). Also, we include an RS map,
which has two peaks – one corresponds to the BCG (SE) and the other
corresponds to a group (NW). These peaks also match the main and secondary
components of the merging cluster.

#### A2426

A2426 shows alignment between the orientations of the BCG and the RS galaxy
distribution (E-W), while the mass distribution is along the N-S direction.
There may be an infalling group in the NW corner of the cluster, which would
explain the mass distribution elongation. The mass concentration in the SE of
the diagram is likely caused by a background cluster/group. The RS clumps at
the NE corner of the diagram may come from a nearby/foreground group. For the
mass map, we use an aperture of 10k pixels when the peak S/N reaches a maximum
($4.2\sigma$).

#### A3158

A3158 is a merging cluster suggested by the X-ray emission and member galaxy
motion (Whelan et al., 2022). Similarly, the central galaxy shows two strong
peaks, which also align with the galaxy and gas distributions (NW-SE). The
mass distribution tilts more to the N-S direction near the cluster center.
This is the first high-resolution WL map of A3158 – here we use an aperture of
11k pixels that maximizes the S/N ($6.7\sigma$). A3158 is in the Horologium
supercluster close to A3128 (presented later; 2.2 deg away). After combining
their catalogs, we find no clear sign of filaments between the two clusters
except some isolated groups.

#### RXCJ1217.6+0339

The mass and galaxy distributions and the central galaxy of RXCJ1217.6+0339
(RBS1092/ZwCl1215+0400) show orientation alignment (NE-SW), and the offsets
between their peaks are small. We use an aperture of 7k pixels that maximizes
the peak S/N ($6.0\sigma$).

#### A2811

In A2811 the mass distribution orientation weakly aligns with the central
galaxy (NW-SE). The galaxy distribution roughly aligns with the E-W direction
at small radii and align with the central galaxy at large radii. The peak S/N
reaches the maximum ($5.3\sigma$) at an aperture of 6k pixels as shown in the
mass map. The galaxy overdensity at the SW corner of the diagram comes from
A2804 but without clear lensing signal, which is likely caused by its low mass
inferred from the X-ray emission (Obayashi et al., 1998; Sato et al., 2010).

#### A780

A780 (Hydra A) shows alignment between the orientations of the BCG and the
galaxy distribution (NW-SE); the RS galaxies extend more towards SE due to an
infalling group (around LEDA87445; $\sim 1$ Mpc SE of the cluster center),
which is consistent with previous studies on the X-ray and spectroscopic data
(Girardi et al., 2022). The mass distribution is approximately along the E-W
direction at small radii. Here we use an aperture of 6k pixels that reaches an
S/N maximum of $4.0\sigma$.

#### A2420

The BCG and the galaxy distribution at small radii have similar orientations
(NE-SW); at large radii the galaxy distribution is more disturbed due to
nearby groups. The mass distribution extends in the E-W direction generally;
we use an aperture of 7k pixels where the S/N reaches the maximum of
$4.9\sigma$.

#### A1285

The BCG(s) of A1285 is an interacting pair aligning with the NW-SE direction.
The mass and RS galaxy distributions also generally align in that direction.
Both the mass and RS maps indicate a nearby group to the east of the cluster,
and there could be a few infalling groups on the periphery of the cluster
suggested by the galaxy distribution. For the mass map, we use an aperture of
12k pixels when the peak S/N maximized at $6.1\sigma$. After mass fitting, we
note that A1285 seems to have a higher mass compared to clusters that have
similar X-ray luminosities.

#### A3911

A3911 has been analyzed via WL in Paper I. We further include the RS galaxy
distribution in this paper, which aligns with the BCG along the NW-SE
direction. The BCG shows signs of interaction and has two cores. The lensing
mass map is similar to the result in Paper I, after a higher photo-z cut on
the source galaxies implemented in this work. Here we use an aperture of 10k
pixels that maximizes the peak S/N at $4.9\sigma$. The galaxy group at the
north edge of the diagram may be related to a nearby cluster A3915 ($z=0.096$;
$\sim 0.7$ deg from A3911).

#### A2055

A2055 has no sign of a giant BCG but a group of bright ellipticals
concentrating at the cluster center and several RS galaxies spreading along
the NW-SE direction. The mass map shows a complex shape surrounding the
central galaxies, and the peak has a clear offset from those central galaxies,
which might indicate that the cluster is undergoing merger activity. We use an
aperture of 8k pixels – the mass S/N map peak reaches a maximum of
$3.1\sigma$, which is much lower than the clusters that have similar X-ray
luminosities and redshifts (and leads to a low lensing mass).

#### A1750

A1750 is a merging cluster that has three subclusters located at the north
(A1750N), center (A1750C), and south (A1750S). The galaxy distribution shows
peaks located at the BCG of each subcluster. The RS galaxy density has the
highest peak at A1750C, which is also true for the X-ray surface brightness
(Bulbul et al., 2016). Note there is another galaxy density peak at the SW
corner of the diagram corresponding to a nearby cluster – SDSS-C41191
($z=0.087$; likely low-mass). For the mass map, under a small aperture ($\leq
5$k pixels) the peak is at A1750C ($\leq 4.5\sigma$), but under a large
aperture ($\geq 6$k pixels) the peak is at A1750N. This suggests that A1750C
has a smaller characteristic size than A1750N, but we also note a background
cluster XCLASS468 ($z=0.56$) $\sim 3$ arcmin SW of A1750N, which could
partially contribute to the lensing signal around A1750N. In the diagram we
use an aperture of 10k pixels when the S/N is at a maximum of $5.4\sigma$ to
show the cluster-scale structure. A1750S has no clear lensing signal (maximum
$0.4\sigma$ at a small aperture of 4k pixels), and it produces weak X-ray
emission as well (Bulbul et al., 2016). The clump to the east of A1750 could
come from a background compact group SDSS-CGB7175. Our results are similar to
the previous Subaru study (Okabe & Umetsu, 2008), but we use a larger FoV and
thus are able to show the structure around A1750.

#### A3822

A3822 has two close BCGs and a few bright galaxies at the cluster center.
There is another BCG in the NE, and the mass and RS galaxy distributions
extend towards that direction (similar phenomenon has been found in the X-ray
emission; Lakhchaura & Singh, 2014), indicating a possible cluster merger. The
central BCGs align along the NE-SW direction as well. However, near the
cluster center the orientations of mass and RS distributions align more with
the E-W direction. In addition, there are signs of groups in the NW connecting
A3822 with a neighboring cluster A3806 ($z=0.075$; $\sim 1.1$ deg from A3822).
For the mass map, we use an aperture of 12k pixels where the S/N peak reaches
the maximum ($6.3\sigma$). This is the first reported lensing result of A3822.

#### A2941

The BCG(s) of A2941 has multiple cores showing signs of merging. The RS
distribution aligns with the BCG (E-W). The mass distribution near the center
is along the N-S direction and tilts more towards the NE-SW direction at large
radii. For the mass map we use an aperture of 9k pixels where the peak S/N
reaches the maximum ($4.4\sigma$). This is the first published lensing result
of A2941.

#### A2440

A2440 is a merging cluster that shows a chain of bright elliptical galaxies
along the NE-SW direction without clear sign of a single BCG. Nonetheless, the
orientations of those bright ellipticals seem to align with the RS galaxy
distribution, which is consistent with previous studies (Maurogordato et al.,
2011) and we use a larger FoV. The mass S/N map shows a complex shape – at
small radii, the mass distribution is roughly along the NW-SE direction. We
tested further masking a circular region with a radius of 0.05 $\deg$ around
the northern bright star (HD212427; within the mass contour) and found no
significant change on the mass map. A mass clump near the west edge of the
diagram could come from a background cluster (RMJ222223.6-014423.7). Here we
use an aperture of 7k pixels where the peak S/N reaches a maximum of
$4.1\sigma$.

#### A1644

A1644 is a merging cluster. The RS galaxy distribution shows two peaks – a
strong peak (A1644N) in the north corresponding to a group, and a weaker peak
(A1644S) near the BCG. The mass distribution peaks at the BCG and extends to
the south. In the mass map we use an aperture of 13k pixels where the peak S/N
reaches the maximum ($6.2\sigma$). We note that under small apertures there is
a small mass peak ($\sim 2\sigma$ at an aperture of 3k pixels) near the
northern group, but it could be caused by shape noise as well. The RS galaxy
distribution approximately aligns with the mass distribution (the N-S
direction). Our results are similar to the ones of Monteiro-Oliveira et al.
(2020), and we use deeper data and a different pipeline.

#### A1348

A1348 shows alignment between the orientations of the BCG, the mass and galaxy
distributions at small radii; both distributions extend to the south at large
radii. The RS density peak shows a small offset from the BCG. The galaxy
distribution has a complex shape at large radii, which could partially be
caused by the infalling of neighboring groups, or projection effects of the
nearby structure along the line of sight due to the red sequence scatter; a
more detailed study requires sufficient spectroscopic redshift measurements. A
foreground bright elliptical galaxy to the SW (2MASXJ11405929-1223536;
$z=0.074$) and its neighboring galaxies could contaminate the RS distribution
because of similar colors. For the mass map we use an aperture of 6k pixels
that gives the maximal S/N ($4.8\sigma$).

#### RBS1847

In RBS1847 (2MAXIJ2216-647) the central galaxy orientation is quite different
from the RS and mass distributions. The single BCG is generally along the E-W
direction. The mass distribution is along the NW-SE direction (at small
radii), while the galaxy distribution is along the NE-SW direction. The
misalignment between the three might be related to the cluster dynamical
history. We use an aperture of 10k pixels where the S/N peak reaches the
maximum ($4.2\sigma$). This is the first lensing mass map of RBS1847.

#### RXCJ1215.4-3900

In RXCJ1215.4-3900 the BCG mostly aligns with the E-W direction and is
slightly tilted NE-SW. However the cluster shows alignment between the mass
and galaxy distributions at large radii along the N-S direction, and the RS
distribution shows a southern group that could be infalling. We use an
aperture of 9k pixels where the S/N reaches the maximum ($4.8\sigma$). This is
the first lensing mass map of RXCJ1215.4-3900.

#### A2351

A2351 exhibits alignment between the orientations of the BCG, the mass and
galaxy distributions (NW-SE), especially near the cluster center. The BCG has
a dumbbell shape showing signs of interaction. We tested the effect of adding
masks (radius $0.05\deg$) around the central bright stars (V* AS Cap. and
HD205131) near the BCG, but this did not change the mass map greatly. Here we
use an aperture of 8k pixels where the S/N reaches a maximum of $4.0\sigma$.
This is the first lensing mass map of A2351.

#### RXCJ2218.2-0350

RXCJ2218.2-0350 is a merging cluster. Near the cluster center there is a
stream of bright ellipticals, and their orientations are generally aligned
with the galaxy and mass distributions (NE-SW). RXCJ2218.2-0350 can be divided
into two subclusters at NE and SW respectively – X-ray (Gu et al., 2019) and
RS peaks are both at the NE subcluster, but the mass map peak is at the SW
subcluster, which may have been affected by merging. A few nearby
groups/clusters (with low masses) are also shown in the RS galaxy
distribution. We show the mass map with an aperture of 5k pixels when the peak
S/N is maximized at $3.8\sigma$. This is the first mass map of
RXCJ2218.2-0350.

#### A2443

A2443 is a merging cluster. We find that the galaxy distribution is along the
NW-SE direction, which is consistent with the gas (Clarke et al., 2013) and
previous studies (Golovich et al., 2019). The mass distribution is oriented NS
and peaks at the BCG, while the RS density peak shifts to the north. We use an
aperture of 5k pixels that maximizes the S/N peak ($6.2\sigma$) of the mass
map in the diagram.

#### A2050

A2050 shows alignment between the orientations of the BCG, the galaxy
distribution, and (at small radii) the mass distribution along the NE-SW
direction, and the distributions stretch more to the south at large radii. We
show the mass map at an aperture of 4k pixels that maximizes the S/N peak at
$4.0\sigma$.

#### A1736

A1736 has multiple BCGs (e.g., IC4252, ESO509-8, ESO509-9; separated by $\sim
0.7$ Mpc). The central galaxy ESO509-9 has a close and bright companion
LEDA47075, and several bright ellipticals are scattered $\sim 0.5-1$ Mpc from
the cluster center, suggesting that A1736 is undergoing a merger. The RS
distribution aligns with the central BCG orientation (N-S) at small radii,
while the mass distribution shows the alignment approximately at large radii.
The mass distribution is along the NE-SW direction at small radii, and the
mass peak lies to the NE ($\sim 2^{\prime}\sim 0.1$ Mpc) of the central
galaxy. In the mass map we use an aperture of 11k pixels that maximizes the
S/N peak at $3.9\sigma$. This is the first reported WL mass map of A1736.

#### A2384

A2384 is a merging cluster. RXCJ2152.2-1942/A2384(B) is in the SW ($\sim 1$
Mpc) of A2384. The BCGs of both (sub-)clusters generally align with the
orientations of their combined mass and galaxy distributions (NE-SW) and the
gas as well (Parekh et al., 2020). Each cluster has a RS density peak – A2384
has higher density, and the density drops and rises along the line from A2384
to A2384(B), indicating the filaments connecting the two clusters (consistent
with Maurogordato et al. 2011). The mass map peak is close to the BCG of
A2384. In the diagram we use an aperture of 7k pixels that maximizes the S/N
peak of the mass map at $5.7\sigma$.

#### A4059

A4059 has low (angular) surface density in mass and galaxy number due to its
low redshift; the lensing signal is further decreased by its high critical
surface density at low redshift, which leads to low aperture mass S/N. Despite
that, A4059 shows alignment between the orientations of the BCG, the RS galaxy
distribution, and roughly the mass distribution (NW-SE), and the gas
distribution also has a similar orientation at large radii (Bartolini et al.,
2022). The mass peak is slightly shifted to the SW of the BCG, which could be
affected by shape noise because of the low lensing signal, but we note that
there is a concentration of gas in the SW of the BCG as well. In the diagram
we show a mass map using an aperture of 5k pixels that maximizes the peak S/N
at $2.8\sigma$. This is the first WL map of A4059.

#### A3836

In A3836, the RS distribution aligns with the BCG orientation (N-S), while the
mass distribution extends along the E-W direction. In the mass map we use an
aperture of 8k pixels when the S/N peak reaches a maximum ($4.9\sigma$). This
is the first reported lensing map of A3836. Near the diagram SW corner, the
mass and RS peaks may correspond to a nearby cluster Ser148-4.

#### A2533

A2533 exhibits alignment between the orientations of the BCG and the RS galaxy
distribution at small radii (NE-SW); at large radii the galaxy distribution is
more tilted to the N-S direction. The mass distribution is along the NW-SE
direction; the peak is slightly shifted to the east. We use an aperture of 8k
pixels that maximizes the S/N peak at $4.6\sigma$. This is the first lensing
mass map of A2533.

#### A2556/A2554

In the diagram we present A2556 (east; $z=0.087$) and A2554 (north;
$z=0.109$), together with A2550 (middle-south; $z=0.123$), which all show
concentrations of RS galaxies. The lensing signal and concentration of RS
galaxies at the bottom of the diagram come from A2555 (south; $z=0.111$).
Similar to A3827/A3825, A2554/A2556 likely have no interaction because of
their redshift difference ($\Delta z\sim 0.02$), but their RS colors are
similar ($\Delta(g-r)\sim 0.04$), and A2556 has no significant lensing signal
(maximum $\sim 2.8\sigma$ at an aperture of 3k pixels; smaller at larger
apertures). Likewise, A2550 does not show clear lensing signal (maximum $\sim
2.5\sigma$ at an aperture of 3k pixels), and its color difference compared to
A2556 is also small ($\Delta(g-r)\sim 0.06$). A2554 shows alignment between
the orientations of the BCG and the RS distribution (N-S), but the mass
distribution align with the E-W direction generally. The RS distribution also
aligns with the gas distribution, and the X-ray and spectroscopic observations
indicate that A2554 is a perturbed system (Erdim & Hudaverdi, 2019). For A2556
we find the directions of the BCG and the RS distribution approximately align.
In the diagram we use an aperture of 6k pixels where the peak S/N of A2554
reaches the maximum ($4.5\sigma$), but A2556 and A2550 are at $\sim
1.7\sigma$, indicating their small characteristic sizes.

#### A3126

In A3126, both the galaxy and mass distributions show circular shapes at small
radii, and the BCG is nearly circular as well (but shows signs of merging with
a member galaxy at NW). At large radii, the galaxy distribution stretches
along the NW-SE direction, while the mass distribution extends in the N-S
direction. On the mass map, we also notice clumps in the north, SE, and SW of
A3126, and they are shown in the DES Y3 mass map as well (Jeffrey et al.,
2021); these clumps could come from nearby/background groups. We use an
aperture of 6k pixels where the peak S/N reaches a maximum at $4.7\sigma$.

#### RXCJ0049.4-2931

RXCJ0049.4-2931 (ACOS84) shows orientation alignment between the the BCG and
the mass distribution (SE-NW), while the RS distribution is generally along
the N-S direction. In the mass map we use an aperture of 6k pixels when the
S/N peak reaches a maximum at $4.2\sigma$. This is the first lensing mass map
of RXCJ0049.4-2931.

#### A3395

A3395 is a merging cluster and has two components (A3395N and A3395S), each
with a BCG (ESO161-8 and LEDA19057, respectively). The lensing peak is close
to the southern BCG, and A3395S produces stronger X-ray emission than A3395N
(e.g., Reiprich et al., 2021). The RS peak is near the northern BCG, which is
also brighter and larger than the southern BCG. The RS distribution and the
northern BCG present similar orientations. We use an aperture of 10k pixels
for the mass map, where the S/N peak reaches the maximum ($4.4\sigma$). This
is the first reported WL map of A3395.

#### A1606

A1606 has been studied by McCleary et al. (2020) via WL. Here we re-analyze it
using deeper data ($\sim 2$ mag) and present the RS map as well. The
orientations of the RS distribution and the BCG are roughly aligned. In the
mass map we use an aperture of 6k pixels where the S/N peak reach the maximum
$3.9\sigma$.

#### A2670

In A2670, the BCG and the mass and galaxy distributions at small radii are
nearly circular. At large radii the mass distributions is roughly along the
NW-SE direction and the RS distribution is generally along the N-S direction.
In the diagram we show the mass map using an aperture of 10k pixels that
maximizes the peak S/N at $5.8\sigma$.

#### A3532

A3532 has a close companion A3530 that is below our X-ray luminosity cut (west
of A3532 in the diagram). The two clusters may just start to interact
(Lakhchaura et al., 2013). We note that under small apertures A3532 has a
higher aperture mass S/N than A3530, while under large apertures it is the
opposite. Therefore, we use an aperture of 8k pixels so that both peaks have
close S/N ($\sim 3$) to show the structure in both clusters. This is the first
WL mass map of A3532. A3532 has higher RS density than A3530, and both
clusters show orientation alignment between the BCG and the RS distribution.
A3532 also shows alignment between the BCG and the mass distribution. The BCGs
of both clusters have dumbbell shapes showing signs of merging.

#### RXCJ1139.4-3327

In RXCJ1139.4-3327, we find that the central galaxy has two cores, which are
both nearly circular near the center, but their merged galaxy envelope
extending to the ICL is along the N-S direction. Interestingly, both the
lensing mass and RS galaxies are generally distributed along the N-S direction
as well. The distribution peaks are slightly shifted from the BCG, which could
be physical or caused by noise. In the mass map we use an aperture of 8k
pixels when the peak S/N reaches the maximum at $4.0\sigma$. This is the first
lensing mass map of RXCJ1139.4-3327.

#### RXJ0820.9+0751

In RXJ0820.9+0751 (RXJ0821.0+0752), we find that the BCG and both the mass and
galaxy distributions at small radii are along the NW-SE direction. At large
radii, both distributions are more disturbed – there is a group of RS galaxies
to the south of the cluster ($\sim 1$ Mpc within the lowest contour of the
cluster), which could be an infalling group. Another RS density peak to the SW
of the cluster ($\sim 0.3$ deg) could come from a foreground group. For the
mass map we use an aperture of 8k pixels where the peak S/N reaches a maximum
at $3.1\sigma$. This is the first reported WL mass map of RXJ0820.9+0751.

#### A3128

A3128 is a merging cluster in the Holograms supercluster (see also the
paragraph for A3158 above). There are a few bright ellipticals at the cluster
center showing different orientations, and in the NE of the cluster ($\sim
0.5$ Mpc) there is a massive background cluster ACT-CLJ0330-5227/DESJ0330-5228
($z=0.44$; $M_{\rm 200c}\sim 10^{15}M_{\odot}$; McCleary et al. 2015; Nord et
al. 2016) which can contribute to the lensing signal, and thus we mask the
background sources within $r_{\rm 200c}$ of the background cluster. The final
mass map has two central peaks at NE and SW respectively (separated by $\sim
4^{\prime}\sim 0.3$ Mpc), which is similar to the previous lensing result of
McCleary et al. (2015), and we use deeper data (by $\sim 1$ mag in $u,g,z$
bands) and include $i,Y$ bands for photo-z measurements. We find that at large
radii the mass and galaxy distributions are both approximately aligned with
the N-S direction. Here we use an aperture of 11k pixels where the mass map
S/N peak reaches the maximum at $6.2\sigma$. Interestingly, the two mass map
peaks roughly match the X-ray emission peaks of A3128 (after removing the
background cluster emission; Werner et al. 2007).

#### A1023

In A1023, the BCG orientation generally aligns with the galaxy distribution
(NW-SE); the mass distribution aligns with that direction only at small radii,
and is more circular at large radii. The mass peak at the NW corner of the
diagram comes from a background cluster A1013. We use an aperture of 5k pixels
that maximizes the peak S/N at $4.4\sigma$. This is the first mass map of
A1023.

#### A3528

A3528 is a merging cluster that has two BCGs separated by $\sim 1$ Mpc at NW
and SE, corresponding to two subclusters A3528N and A3528S. The RS galaxies
gather near the northern BCG (ESO443-4) and their distribution aligns with the
orientation of the northern BCG at small radii (the N-S direction); at large
radii the galaxy distribution extends to SE and spreads out around the
southern BCG (ESO443-7). The gas distribution orientation also aligns with the
BCGs (Gastaldello et al., 2003). The mass map shows two central peaks
corresponding to the two BCGs under small apertures. When the aperture
expands, the mass S/N map peak reaches a local maximum of $5.0\sigma$ at an
aperture of 4k pixels; after that, the peak S/N keeps increasing as the
aperture expands because of the large separation between the two central
clumps, and the corresponding northern and southern peaks start to merge into
one central peak at an aperture of 8k pixels. In the diagram we thus use an
aperture of 7k pixels to show the two peaks. In addition, the NE clump in the
mass map probably comes from a background cluster SPT-CLJ1256-2851 ($z=0.36$),
but we expect that its contribution to the A3528 central lensing signal is
small because of the large angular separation between the two clusters. The
mass clump at the bottom of the diagram could come from nearby/background
groups. This is the first reported lensing mass distribution of A3528.

#### A761

In A761, the mass map peak is close to the BCG (PMNJ0910-1034), but the RS
distribution is slightly offset to the east (its peak is close to another
bright central galaxy LEDA976301). We use an aperture of 4k pixels for the
mass map, where the S/N peak reaches the maximum ($4.1\sigma$). This is the
first WL map of A761. The RS distribution shows alignment with the BCG
orientation.

###  4.2 Orientation Alignment between the Mass and Galaxy Distributions and
the Brightest Cluster Galaxy

The figures in Section 4.1 show striking similarities between the orientations
of the mass/RS distributions and the BCG, especially between the RS
distribution and the BCG, in individual clusters. Therefore, we use the method
described in Section 3.5 to quantify their orientation angles, and then we
study the difference between those angles as a function of cluster dynamical
state and radial distance range (Figure 8). When computing the difference
angle, we use its supplementary angle if it is larger than $90\deg$. Because
it is difficult to determine the cluster dynamical state without enough spec-z
data, we instead use the number of central galaxies (Number of CG = 1, 2, or
$\geq 3$) as a proxy – clusters with more bright central galaxies tend to be
more perturbed (Edwards & Patton, 2012; Mann & Ebeling, 2012; Furnell et al.,
2018). We require that the central galaxies being counted are sufficiently
larger and brighter than other member galaxies and clearly separate from
neighboring large member galaxies. In the future, we will also seek to use the
X-ray/SZ information to determine the cluster dynamical state.

In Figure 8, we find that, statistically, the RS galaxy distribution aligns
with the BCG orientation throughout the entire cluster region and the
alignment even extends to LSS, while the mass distribution and the RS galaxy
distribution show alignment between their orientations only inside the cluster
with a larger offset angle, and the mass distribution and the BCG align only
near the cluster center. This is similar to the results of Oguri et al. (2010)
and Chu et al. (2021), but their samples are in different redshift ranges than
ours and are studied using different instruments and methodologies. Also, we
note that all types of alignment seem not to strongly depend on the cluster
redshift and the dynamical state, however this observation could be limited by
the cluster sample size. The “significance” of the orientation alignment can
be estimated by Monte Carlo tests or analytically calculated by the cumulative
function of a binomial distribution (Appendix F). We find that the probability
of more than half of the cluster sample having the angle difference below 30
deg is $\sim 0.5\%$, which is significantly small, assuming the angle
difference is uniformly distributed between 0 and 90 deg. It indicates that
only random fluctuation can not account for the large number of cases where
the angle between the RS distribution and the BCG/mass distribution (within 1
Mpc) is below 30 deg.

The strong alignment between the orientations of the BCG and the RS
distribution may result from the long-term dynamical process that those low-z
massive clusters have undergone. The RS galaxies we have selected are
relatively bright, and therefore they are older and have remained in the
cluster longer than other members. The central galaxy and the RS galaxy
distribution tend to align because of the gravitational potential (Donahue et
al., 2016) or more specifically the filamentary accretion and the tidal field
(Huang et al., 2016). The cluster dwarf members and blue members can also
affect the galaxy distribution morphology, but their membership is difficult
to determine without spectroscopic data. For lensing mass distributions, shape
noise affects their orientations randomly. Thus, the effect of shape noise is
statistically reduced in a large cluster sample (like the sample in this work)
for deriving the median misalignment, and the larger sample size helps bolster
confidence in our results – we will revisit this analysis for the whole
LoVoCCS sample. Additionally, it is worth pointing out that previous studies
mostly focus on the clusters at higher redshift ($z>0.1$) which generally
experience shorter evolution time than this sample.

Figure 8: Orientation alignment between the BCG, the RS galaxy distribution,
and the lensing mass distribution in each cluster of our sample. The
histograms are stacked on top of each other. We consider the distributions
within radial distance cuts of 0.5, 1.0, 2.0 Mpc, respectively. The Y-axis
shows the fraction in the sample (the total fraction is 1). We give the
fractions within 15, 30, and 45 deg in the text box, together with the median
(the vertical dashed line) and the standard deviation of all clusters. The
angles are in degrees.

###  4.3 Distribution of Center Offset

The figures in Section 4.1 also show a rough consistency between the peaks of
the maps and the BCG position. Here we compare those positions by studying
their distances and relative position angles. The positions are measured by
the method in Section 3.5, and we convert their angular separations into
physical ones to simplify comparison.

The result is presented in Figure 9. We find that most positions are aligned
(median $\sim 0.1$ Mpc), but perturbed clusters tend to have larger
separations. Also, the position difference has no clear dependence on the
position angle suggesting no significant systematics. The distance
distribution is similar to previous results (e.g., Oguri et al., 2010; von der
Linden et al., 2014; Donahue et al., 2016).

We note that mass maps could be affected by background clusters, and RS maps
could be affected by photometry noise or nearby groups/LSS. However, when we
combine the results from a sample of clusters (as in this work), we can treat
the locations of interlopers as random, so that they contribute to noise
without systematic bias at the peak location.

Figure 9: Offsets between the centers of the BCG, the RS distribution, and the
mass distribution in each cluster of our sample. The top panel shows the
distance distribution, while the bottom panel shows the (relative azimuth)
angle distribution. Similar to Figure 8, the histograms are stacked for
visualization, and the vertical dashed line gives the median of all clusters
in the sample. For reference, the standard deviation of a uniform distribution
is $\sim 29\%$ of the range (here $\sim 104$ deg).

As the offset between the mass center and the BCG in relaxed clusters (the BCG
“wobbling”) may indicate SIDM, we further discuss the result in Section 5.3.

##  5 Discussion

###  5.1 Shape Correlation, PSF modeling, and Shape Measurement

As mentioned in Section 3.6, we use TreeCorr to compute shape correlations –
the cross-correlation between the shapes of stars and galaxies, and the auto-
correlation of stellar shapes. We use those correlations to estimate the PSF
modeling bias in the lensing shear measurements. The details are given below.

We consider the correlations in Eq. 4 and 5, where the superscripts
$\alpha,\beta$ are star (s) or galaxy (g), the subscripts $i,j$ are 1 or 2,
$e_{i}(\textbf{R})$ is $i$th component of the ellipticity/shape of an object
at coordinate R, r is a vector with length $r$ connecting two objects, and
$\hat{\textbf{r}}$ is the unit vector of r.

$C_{ij}^{\alpha\beta}(r)=\langle e_{i}^{\alpha}(\textbf{R})\cdot
e_{j}^{\beta}(\textbf{R+r})\rangle_{\textbf{R},\hat{\textbf{r}}}$ (4)

$C^{\alpha\beta}(r)=C_{11}^{\alpha\beta}(r)+C_{22}^{\alpha\beta}(r)$ (5)

To compute the correlations, we use the stars for PSF modeling in the central
$6\times 6$ patches, and we use their SDSS shapes derived from second moments
without PSF correction. For galaxies, we use the high-quality selection from
lensing analysis and utilize their PSF-corrected HSM shapes (Section 3.3;
$r$-band depth $\sim 26$ mag). The measured galaxy shape can be described as a
sum of three elements (in the first order expansion) – the intrinsic shape
(shape noise), the WL induced distortion (proportional to shear), and the PSF
residual (the PSF “leakage”). After cross-correlating the galaxy shapes with
the star shapes (equivalent to the PSF), we expect that the contributions from
shape noise and lensing in the galaxy shapes should be averaged out, as they
are random to PSF. If we assume that the PSF residual is proportional to the
PSF, then the proportionality factor can be estimated by the ratio between the
galaxy-star and star-star correlations ($C^{\rm sg}/C^{\rm ss}$). Here, we
consider the contributions from the 1-1 and 2-2 component correlations; our
test shows that the contributions from the 1-2 and 2-1 correlations are
smaller. Next, we can obtain an estimate of the PSF shape magnitude from the
star-star correlation ($\sqrt{C^{\rm ss}}$), and thereby estimate the
magnitude of the PSF residual by $C^{\rm sg}/\sqrt{C^{\rm ss}}$. Note, that
term must be divided by 2 when compared to the (reduced) shear $g$ since
$g_{i}\sim\langle e_{i}\rangle/(2\mathcal{R})$ in WL, and the typical shear
responsivity $\mathcal{R}$ is $\sim 1/1.2$ (Paper I) and can be treated as a
secondary factor here. Similar methods have been used in the studies of Jarvis
et al. (2016) and Mandelbaum et al. (2018b).

Figure 10 shows that the effect of PSF modeling bias on the shear measurement
– the $C^{\rm sg}/(2\sqrt{C^{\rm ss}})$ ratio – is at the level of $\sim
10^{-3}$. We tested and found that using the calibrated per-object shear
estimate instead can produce a similar result. Since the typical shear value
in the cluster region that we are interested in is $\sim 0.02$ (at $\sim
0.5r_{\rm 200c}$ for representative NFW halos; Section 5.3), we conclude that
the PSF modeling bias on shear measurements is $\lesssim 10\%$ (at percent
level on average). We also note that the clusters with larger ratio values
usually have larger masses, and thus their lensing shear signals are also
larger, which compensates for the higher biases.

Figure 10: Left: Star-galaxy shape correlations ($C^{\rm sg}$) and star-star
correlations ($C^{\rm ss}$) in absolute values. Right: The effect of PSF
modeling bias on the shear measurement. In both diagrams, the values in
individual cluster fields are shown with low opacity, and their median values
in each distance bin are shown in bold solid lines.

###  5.2 Mass Map

Some LoVoCCS clusters are covered by DES, and we compare our mass maps with
the recent DES Y3 WL mass maps (Jeffrey et al., 2021). We select the Wiener
map from the DES Y3 maps, which has the best performance among the methods
used in that study. The Wiener map maximizes the convergence posterior using a
Gaussian prior and gives better reconstruction of mass distribution for LSS
than clusters. While the DES Y3 maps used sources from different redshift
bins, we use the full redshift range that includes all galaxies at different
redshifts, since our clusters are at very low redshift $z\lesssim 0.1$.
Although the DES Y3 maps are posterior convergence maps instead of aperture
mass maps (as in this work), we expect the mass distribution morphologies
described by the two types of maps to be consistent (Section 3.2, 3.3). After
comparison, we find that in those cluster fields our maps are similar to the
DES Y3 maps, and that our maps have higher resolution resulting from depth.

###  5.3 Mass-BCG Center Offset

Following Section 4.3, here we further discuss the centroid offset between the
lensing mass distribution and the BCG in relaxed clusters as a possible tracer
of SIDM. We find that clusters with only one bright central galaxy show a
median offset $\sim 0.09$ Mpc ($\sim 1$ arcmin) between the centroids of the
2D mass distribution and the BCG. However, this offset may be limited by the
catalog-binning size, and some of those clusters may still be perturbed. Also,
shape noise may contribute to this offset (McCleary et al., 2020).

To test those effects, we first reduce the binning size to $20\times 20$
pixels and rebuild the mass maps in higher resolution. Since the smaller
binning leads to much longer computational time, we only produce maps in the
central $\sim 5-10\%$ region near the original peak and ensure the new central
peak is within the window. This reanalysis indicates that the bin size
reduction does not significantly change the trend between the aperture radius
and the peak S/N. Additionally, we remove the clusters that have reported
mergers (Section 4.1) or have clear signs of interaction at the BCG (e.g., a
dumbbell shape with double cores) by visual inspection. Then, we remake the
offset histogram and compare that with the previous result – the left panel of
Figure 11 shows that the offset drops (median $\sim 64$ kpc) when we use
smaller bins and more relaxed clusters.

Next, we study the contribution from shape noise by building mock shape
catalogs distorted by a typical cluster in our sample with representative
lensing sources. We consider a spherical NFW halo at redshift $z=0.08$ with
mass $M_{\rm 200c}=7\times 10^{14}M_{\odot}$, and we set the source galaxies
at redshift $z=0.7$ with per-component shape dispersion 0.4 and number density
7 per arcmin2 – those are approximately the median values in our final
catalogs for lensing analysis. Then, we bin the catalog by 100 pixels and 20
pixels, make mass maps respectively, and measure the distance between the mass
map central peak and the NFW halo center. The distributions of their offsets
derived from mock catalogs are shown in the right panel of Figure 11. For the
100-pixel binning, the median values in the real (nearly relaxed) and mock
observations are $\sim 90$ kpc and $\sim 52$ kpc, respectively. Taking the
square root of the difference between their squares (the intrinsic offset and
the shape noise are independent), we conclude that the intrinsic/net offset is
$\lesssim 73$ kpc. Similarly, under the 20-pixel binning, the median values in
the real and mock observations are $\sim 64$ kpc and $\sim 49$ kpc,
respectively, and we estimate a net offset $\lesssim 41$ kpc. Note, the true
value could still be smaller since some clusters might not be fully relaxed,
the sample size is limited, and there could be other contributing noise
factors. Nonetheless, our result sets an upper limit of the intrinsic offset,
which is still larger than the common values in SIDM tests ($\lesssim 10$ kpc,
e.g., Harvey et al., 2019). In the future, we will revisit this problem
through the entire LoVoCCS sample, utilize the gas centroid (obtained from
high-resolution X-ray observations) as a tracer of the mass peak, and use more
complete spectroscopic data to determine the dynamical state. We will further
test the effect of shape noise using mock catalogs derived from cosmological
simulations (e.g., Dietrich et al., 2012a). Another interesting follow-up
study might examine the relationship between the offset and the BCG
orientation.

Figure 11: Left: Histogram of mass-BCG center distance from observation. The
blue solid curve corresponds to the distribution in Figure 9. The orange
dashed curve shows the distribution of the same clusters under the 20-pixel
binning. The green dash-dot curve shows the distribution of selected clusters
with the 20-pixel binning. The vertical lines at the bottom gives the median
of each distribution. Right: Histogram of the distance between the NFW halo
center and the detected lensing peak derived from the mock data (600 runs).

##  6 Summary

In this work, we analyzed the complete DECam observations of 58 LoVoCCS
clusters spanning a wide range of dynamical states, redshifts, and X-ray
luminosities and produced their lensing mass and red-sequence galaxy maps. The
depth of observation is unprecedented for the majority of our clusters, and
for about half of the sample, the weak lensing maps presented in this work are
the first in the literature.

We present and inspect the mass and galaxy distributions, and compare them
with previous studies (Section 4.1). We also study the correlations between
their orientation angles and centroids (Section 4.2 and 4.3). Many clusters in
our sample exhibit alignment between the orientations and/or centroids of the
BCG and mass/galaxy distributions, without strong dependence on the dynamical
state, redshift, and mass. The orientation alignment is stronger near the
cluster center than the outer region, and it is stronger between the BCG and
the RS galaxy distribution. The BCG and the RS distribution have a median
misalignment angle of 19 deg within a radial cut of 2 Mpc; the median center
offset is 0.09 Mpc. The mass and RS distributions show a median misalignment
angle of 32 deg within 1 Mpc; the median center offset is 0.13 Mpc. Between
the mass distribution and the BCG, the median misalignment angle within 0.5
Mpc is 35 deg, and the median center offset is 0.09 Mpc. Our results are
comparable to recent studies of different samples (e.g., Umetsu et al., 2018).

We are actively acquiring additional spectroscopic redshifts of both
background source galaxies and cluster members. Combined with anticipated
contributions from the Dark Energy Spectroscopic Instrument (DESI) survey,
future observations are expected to significantly enhance the spec-z
completeness for LoVoCCS clusters, which will be instrumental in refining the
calibration of photometric redshifts. Improved spec-z measurements will also
enable more accurate determination of cluster galaxy membership and dynamical
state, sharpening our detection of red sequence and blue cloud galaxies and
providing valuable insights into the star formation histories of our cluster
sample. In parallel, alternative methods for distinguishing red and blue
cluster member galaxies are under study, such as the Gaussian mixture model-
based Red Dragon algorithm (Black & Evrard, 2022). The future scope of our
work includes broadening the alignment studies to test the intrinsic alignment
of cluster member galaxies, and to incorporate gas morphology via X-ray and
Sunyaev–Zel’dovich (SZ) observations. We intend to utilize the distributions
of mass, galaxies, and gas to explore splashback features in greater detail.
Finally, the results of parametric mass fitting for LoVoCCS clusters will be
detailed in an upcoming publication. Our data products including co-added
images and final catalogs will be made available to the research community,
and interested parties can obtain the mass and galaxy maps from the
corresponding author. The LoVoCCS DECam exposures are publicly available on
the NOIRLab Astro Data Archive website.888https://astroarchive.noirlab.edu

## Acknowledgments

We thank the LSST Data Management team and the CTIO observation support team.
We thank the comments/supports from Xiangchong Li, Chun-Hao To, Yuanyuan
Zhang, Thomas Matheson, Camille Avestruz. We thank the members of the
Observational Cosmology, Gravitational Lensing and Astrophysics Research Group
at Brown University for contributing to the tests of the LoVoCCS run_steps
pipeline on different galaxy clusters, especially previous/current students
and group members: Isabel Horst, Taylor Knapp, Derek Waleffe, Andrea Minot,
Claire Hawkins, Alexandra Ekstrom, Natalie Rugg, Nicholas Conroy, Miguel Ruiz
Granda, Liam Storan, Jessica Washington, Pei-Jun Huang, Francesco Serraino,
Richard Dong, Youngik Lee, Dani Romero Mejia, Tim Launders, Vini Amit
Rupchandani, Alexander Green.

I.D. and D.C. are thankful for support from the National Science Foundation
(No. AST-2108287; Collaborative Research; LoVoCCS: The Local Volume Complete
Cluster Survey). G.W. gratefully acknowledges support from the National
Science Foundation through grant AST-2205189 and from HST program number
GO-16300. M.D., D.T., and A.E. are grateful for support from the National
Aeronautics and Space Administration Astrophysics Data Analysis Program
(NASA-80NSSC22K0476). K.U. acknowledges support from the National Science and
Technology Council of Taiwan (grant NSTC 112-2112-M-001-027-MY3) and from the
Academia Sinica Investigator Award (AS-IA-112-M04). J.S. was supported by the
National Research Foundation of Korea (NRF) grant funded by the Korea
government (MSIT) (No. RS-2023-00210597). E.P. is supported by NASA grant
80NSSC23K0747. The work of S.F. and T.L. is supported by NOIRLab, which is
managed by the Association of Universities for Research in Astronomy (AURA)
under a cooperative agreement with the National Science Foundation.

This research was conducted using computational resources and services at the
Center for Computation and Visualization, Brown University.

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been
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Edinburgh, the Queen’s University Belfast, the Harvard-Smithsonian Center for
Astrophysics, the Las Cumbres Observatory Global Telescope Network
Incorporated, the National Central University of Taiwan, the Space Telescope
Science Institute, the National Aeronautics and Space Administration under
Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA
Science Mission Directorate, the National Science Foundation Grant No.
AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

The national facility capability for SkyMapper has been funded through ARC
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Funding was contributed by the FIRST program from the Japanese Cabinet Office,
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Tololo Inter-American Observatory, a programme of NOIRLab (NOIRLab Prop.
2012B-0001; PI J. Frieman).

The Legacy Surveys consist of three individual and complementary projects: the
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together include data obtained, respectively, at the Blanco telescope, Cerro
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key project of the Telescope Access Programme (TAP), which has been funded by
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This research uses services or data provided by the Astro Data Lab at NSF’s
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This research is based on data obtained from the Astro Data Archive at NSF’s
NOIRLab. These data are associated with the observing programs listed in Table
3.

##  Appendix A Survey Depth

We use Table 1, 2 to show the $5\sigma$ depth of the cluster fields ($\sim
2\deg$ in diameter) whose maps are presented in Section 4.1. Those LoVoCCS
clusters are observation-time complete. We consider an annular region from a
radial distance of 10 arcmin to 1 deg towards the cluster in each field to
reduce the contamination effect of cluster member galaxies, although some
fields include scattered cluster pairs/groups (e.g., A401/A399, A3827/A3825,
and A2556/A2554); as the background galaxies are much fainter and greatly
outnumber the foreground galaxies, we expect the statistical bias caused by
member galaxies is minimal.

Name | R.A. (deg) | Decl. (deg) | $u_{\rm p5}$ | $g_{\rm p5}$ | $r_{\rm p5}$ | $i_{\rm p5}$ | $z_{\rm p5}$ | $u_{\rm c5}$ | $g_{\rm c5}$ | $r_{\rm c5}$ | $i_{\rm c5}$ | $z_{\rm c5}$
---|---|---|---|---|---|---|---|---|---|---|---|---
A2029 | 227.73 | 5.82 | 24.9 | 26.7 | 26.3 | 25.5 | 25.0 | 24.6 | 26.4 | 25.9 | 25.1 | 24.6
A401 | 44.74 | 13.58 | 24.7 | 25.5 | 25.7 | 25.1 | 24.2 | 24.4 | 25.2 | 25.3 | 24.8 | 23.9
A85 | 10.40 | -9.33 | 25.3 | 25.8 | 26.0 | 25.1 | 23.4 | 25.0 | 25.5 | 25.7 | 24.8 | 23.1
A3667 | 303.14 | -56.84 | 25.3 | 26.2 | 26.3 | 25.8 | 25.2 | 25.1 | 25.8 | 25.9 | 25.2 | 24.7
A3266 | 67.80 | -61.41 | 25.3 | 26.3 | 26.1 | 25.6 | 24.8 | 25.0 | 26.0 | 25.8 | 25.2 | 24.5
A1651 | 194.84 | -4.20 | 25.2 | 25.5 | 26.0 | 25.5 | 24.5 | 24.9 | 25.3 | 25.7 | 25.1 | 24.2
A754 | 137.21 | -9.64 | 25.7 | 26.1 | 25.9 | 25.3 | 25.2 | 25.5 | 25.8 | 25.5 | 25.0 | 24.8
A3571 | 206.87 | -32.87 | 25.3 | 25.9 | 26.1 | 25.3 | 24.6 | 25.0 | 25.7 | 25.8 | 25.1 | 24.4
A3112 | 49.47 | -44.24 | 25.4 | 25.5 | 26.3 | 25.4 | 24.4 | 25.1 | 25.3 | 26.0 | 25.1 | 24.1
A2597 | 351.33 | -12.12 | 25.2 | 26.1 | 26.1 | 25.4 | 25.0 | 25.0 | 25.9 | 25.8 | 25.1 | 24.7
A1650 | 194.68 | -1.76 | 25.2 | 26.0 | 25.7 | 25.9 | 25.0 | 24.9 | 25.7 | 25.4 | 25.6 | 24.6
A3558 | 201.98 | -31.49 | 25.3 | 26.3 | 26.0 | 25.3 | 24.6 | 25.0 | 26.0 | 25.7 | 24.9 | 24.3
A3695 | 308.70 | -35.83 | 25.2 | 26.1 | 26.1 | 25.9 | 25.0 | 24.9 | 25.9 | 25.8 | 25.5 | 24.7
A3921 | 342.50 | -64.43 | 25.2 | 25.6 | 26.0 | 25.5 | 24.3 | 25.0 | 25.4 | 25.7 | 25.2 | 24.0
A2426 | 333.61 | -10.37 | 25.4 | 26.0 | 26.1 | 25.6 | 24.5 | 25.2 | 25.7 | 25.8 | 25.3 | 24.2
A3158 | 55.66 | -53.63 | 25.4 | 25.6 | 26.2 | 25.2 | 24.4 | 25.1 | 25.3 | 25.4 | 24.9 | 24.1
RXCJ1217.6+0339 | 184.43 | 3.65 | 25.0 | 24.8 | 25.8 | 26.1 | 23.6 | 24.8 | 24.5 | 25.4 | 25.8 | 23.3
A2811 | 10.54 | -28.54 | 25.6 | 26.2 | 26.1 | 25.5 | 24.9 | 25.3 | 25.9 | 25.8 | 25.1 | 24.6
A780 | 139.62 | -12.26 | 25.5 | 26.0 | 26.0 | 25.3 | 24.4 | 25.2 | 25.8 | 25.7 | 25.0 | 24.0
A2420 | 332.59 | -12.19 | 25.3 | 25.9 | 26.1 | 25.4 | 24.8 | 25.1 | 25.7 | 25.8 | 25.1 | 24.5
A1285 | 172.61 | -14.56 | 25.0 | 25.7 | 26.0 | 25.1 | 24.4 | 24.8 | 25.5 | 25.6 | 24.8 | 24.1
A3911 | 341.59 | -52.74 | 25.5 | 25.9 | 26.2 | 25.6 | 24.3 | 25.3 | 25.7 | 25.8 | 25.3 | 24.0
A2055 | 229.69 | 6.23 | 25.1 | 25.5 | 25.9 | 25.4 | 24.6 | 24.8 | 25.2 | 25.6 | 25.1 | 24.3
A1750 | 202.71 | -1.86 | 25.0 | 26.0 | 26.0 | 25.4 | 24.7 | 24.7 | 25.8 | 25.6 | 25.1 | 24.4
A3822 | 328.53 | -57.85 | 25.2 | 26.2 | 25.9 | 25.5 | 24.6 | 24.9 | 26.0 | 25.6 | 25.2 | 24.3
A2941 | 26.27 | -53.02 | 25.4 | 25.9 | 26.0 | 25.1 | 24.5 | 25.1 | 25.7 | 25.7 | 24.8 | 24.1
A2440 | 335.97 | -1.60 | 24.9 | 25.6 | 25.9 | 25.2 | 24.5 | 24.6 | 25.4 | 25.6 | 24.9 | 24.1
A1644 | 194.30 | -17.41 | 25.1 | 26.2 | 26.1 | 25.3 | 24.6 | 24.8 | 25.9 | 25.8 | 25.1 | 24.3
Table 1: Cluster field depth (Part I). We show the $5\sigma$ PSF magnitudes of point sources ($m_{\rm p5}$) and CModel magnitudes of extended sources ($m_{\rm c5}$), in DECam $u,g,r,i,z$ bands of individual cluster fields (sorted by X-ray luminosity/cluster rank) and their median values (Table 2). These are apparent AB magnitudes without Galactic extinction correction ($\lesssim 0.1$ mag in $r$ band). The magnitude zero points have been corrected for the color-terms between the reference catalogs (PS1/SkyMapper/SDSS) and DECam, and here we only consider the magnitude uncertainties reported in the LSST pipeline forced photometry of co-added images. The residual zero point offsets are $\lesssim 0.03$ mag in $g,r,i,z$ when compared with DES (if available) and $\lesssim 0.05$ mag in $u$ when compared with model stellar loci in the color-color space. The celestial coordinates come from SIMBAD (ICRS, J2000).  Name | R.A. (deg) | Decl. (deg) | $u_{\rm p5}$ | $g_{\rm p5}$ | $r_{\rm p5}$ | $i_{\rm p5}$ | $z_{\rm p5}$ | $u_{\rm c5}$ | $g_{\rm c5}$ | $r_{\rm c5}$ | $i_{\rm c5}$ | $z_{\rm c5}$
---|---|---|---|---|---|---|---|---|---|---|---|---
A1348 | 175.35 | -12.27 | 25.4 | 26.1 | 25.9 | 26.2 | 24.7 | 25.1 | 25.9 | 25.6 | 25.9 | 24.4
RBS1847 | 334.50 | -65.18 | 25.2 | 26.1 | 26.0 | 25.0 | 24.1 | 24.9 | 25.8 | 25.7 | 24.7 | 23.8
RXCJ1215.4-3900 | 183.89 | -38.99 | 25.4 | 25.7 | 25.6 | 25.0 | 24.6 | 25.0 | 25.4 | 25.3 | 24.7 | 24.2
A2351 | 323.60 | -13.39 | 25.3 | 25.8 | 26.1 | 25.2 | 24.3 | 25.0 | 25.6 | 25.8 | 24.9 | 24.0
RXCJ2218.2-0350 | 334.58 | -3.83 | 25.2 | 25.7 | 25.8 | 24.9 | 24.1 | 24.9 | 25.5 | 25.5 | 24.6 | 23.7
A2443 | 336.56 | 17.42 | 25.0 | 26.0 | 26.0 | 25.0 | 24.5 | 24.7 | 25.6 | 25.6 | 24.7 | 24.1
A2050 | 229.08 | 0.06 | 25.3 | 26.3 | 26.2 | 25.7 | 24.8 | 25.0 | 26.0 | 25.9 | 25.3 | 24.5
A1736 | 201.72 | -27.11 | 24.8 | 26.7 | 26.5 | 25.4 | 24.5 | 24.5 | 26.4 | 26.0 | 25.0 | 24.2
A2384 | 328.08 | -19.61 | 25.5 | 25.6 | 25.9 | 25.2 | 25.0 | 25.2 | 25.3 | 25.6 | 24.9 | 24.6
A4059 | 359.17 | -34.67 | 25.4 | 25.8 | 25.9 | 25.3 | 24.3 | 25.1 | 25.5 | 25.6 | 25.0 | 24.1
A3836 | 332.40 | -51.84 | 25.0 | 26.6 | 25.9 | 25.5 | 24.1 | 24.7 | 26.3 | 25.6 | 25.2 | 23.8
A2533 | 346.81 | -15.22 | 25.2 | 26.0 | 25.5 | 25.0 | 24.3 | 25.0 | 25.7 | 25.2 | 24.8 | 24.0
A2556 | 348.26 | -21.63 | 25.3 | 25.8 | 25.7 | 25.3 | 24.7 | 25.0 | 25.5 | 25.4 | 25.0 | 24.3
A3126 | 52.18 | -55.71 | 24.8 | 25.9 | 26.1 | 25.0 | 24.2 | 24.5 | 25.7 | 25.8 | 24.8 | 23.9
RXCJ0049.4-2931 | 12.35 | -29.53 | 25.1 | 25.7 | 26.0 | 25.3 | 24.6 | 24.9 | 25.5 | 25.7 | 25.0 | 24.3
A3395 | 96.88 | -54.40 | 25.4 | 26.2 | 26.3 | 25.7 | 25.1 | 25.0 | 25.9 | 25.9 | 25.2 | 24.6
A1606 | 191.15 | -11.99 | 24.4 | 26.1 | 26.1 | 25.8 | 24.6 | 24.1 | 25.8 | 25.7 | 25.5 | 24.4
A2670 | 358.54 | -10.39 | 24.9 | 24.8 | 25.9 | 25.3 | 24.6 | 24.7 | 24.6 | 25.5 | 25.0 | 24.4
A3532 | 194.33 | -30.37 | 25.4 | 26.3 | 25.9 | 25.0 | 24.3 | 25.1 | 26.0 | 25.6 | 24.8 | 24.0
RXCJ1139.4-3327 | 174.86 | -33.45 | 25.5 | 26.1 | 26.0 | 25.5 | 24.1 | 25.1 | 25.8 | 25.7 | 25.0 | 23.8
RXJ0820.9+0751 | 125.26 | 7.86 | 25.0 | 25.8 | 26.1 | 25.7 | 24.9 | 24.7 | 25.5 | 25.8 | 25.3 | 24.5
A3128 | 52.64 | -52.55 | 25.9 | 26.4 | 26.3 | 25.4 | 24.9 | 25.6 | 26.1 | 25.6 | 25.1 | 24.5
A1023 | 157.00 | -6.80 | 25.2 | 26.1 | 26.0 | 25.1 | 24.2 | 24.9 | 25.7 | 25.7 | 24.7 | 23.8
A3528 | 193.58 | -29.02 | 24.9 | 25.8 | 26.3 | 25.3 | 24.6 | 24.6 | 25.6 | 26.0 | 25.1 | 24.3
A761 | 137.65 | -10.58 | 25.5 | 26.2 | 26.0 | 25.3 | 24.6 | 25.2 | 25.9 | 25.7 | 25.0 | 24.3
A3825 | 329.59 | -60.39 | 25.3 | 26.1 | 26.1 | 25.8 | 24.0 | 25.0 | 25.8 | 25.3 | 25.3 | 23.7
Median | – | – | 25.3 | 26.0 | 26.0 | 25.3 | 24.6 | 25.0 | 25.7 | 25.7 | 25.1 | 24.2
Table 2: Cluster field depth (Part II).

##  Appendix B DECam Archival Data

In Table 3, we list the proposal IDs of the public exposures used in our co-
addition. We thank the researchers of those programs for their observations.

PROPID | PI | PROPID | PI | PROPID | PI | PROPID | PI
---|---|---|---|---|---|---|---
2012B-0001 | Frieman | 2014A-0270 | Grillmair | 2016A-0189 | Rest | 2018A-0911 | Forster
2012B-0003 | DES SV | 2014A-0306 | Dai | 2016A-0190 | Dey | 2018A-0913 | Zenteno
2012B-0569 | Allen | 2014A-0321 | Geha | 2016A-0366 | Bechtol | 2018A-0914 | Makler
2012B-3004 | Dell’Antonio | 2014A-0339 | Hargis | 2016A-0384 | McCleary | 2018B-0905 | Oh
2012B-3007 | Thorman | 2014A-0386 | Dell’Antonio | 2016A-0386 | Malhotra | 2019A-0205 | Goldstein
2012B-9999 | Engineering | 2014A-0390 | Bloom | 2016A-0397 | Zenteno | 2019A-0265 | Finkbeiner
2013A-0327 | Rest | 2014A-0412 | Rest | 2016A-0618 | Mackey | 2019A-0272 | Zenteno
2013A-0360 | von der Linden | 2014A-0415 | von der Linden | 2016A-0622 | Penny | 2019A-0305 | Drlica-Wagner
2013A-0400 | Bloom | 2014A-0608 | Forster | 2016A-0951 | Bechtol | 2019A-0308 | Dell’Antonio
2013A-0411 | Nidever | 2014A-0610 | Taylor | 2016B-0124 | Frieman | 2019A-0913 | Carballo-Bello
2013A-0455 | Sheppard | 2014A-0613 | Rodriquez | 2016B-0301 | Rest | 2019A-0917 | Lopes
2013A-0529 | Rich | 2014A-0621 | Mackey | 2016B-0905 | Jerjen | 2019B-0323 | Zenteno
2013A-0611 | Mackey | 2014A-0624 | Jerjen | 2016B-0909 | Navarete | 2019B-0372 | Soares-Santos
2013A-0612 | Sheen | 2014B-0146 | Sullivan | 2017A-0260 | Soares-Santos | 2019B-0403 | Martinez-Vazquez
2013A-0613 | Munoz | 2014B-0244 | von der Linden | 2017A-0388 | Zenteno | 2019B-1004 | Chaname
2013A-0704 | Wood | 2014B-0265 | Dell’Antonio | 2017A-0909 | Cooke | 2019B-1014 | Olivares
2013A-0717 | Dell’Antonio | 2014B-0404 | Schlegel | 2017A-0916 | Carballo-Bello | 2020A-0399 | Zenteno
2013A-0719 | Saha | 2014B-0608 | Jaffe | 2017A-0925 | Munoz | 2020A-0402 | Vivas
2013A-0724 | Allen | 2015A-0062 | French | 2017B-0103 | Barkhouse | 2020A-0908 | Olivares
2013A-0737 | Sheppard | 2015A-0110 | De Boer | 2017B-0110 | Frieman | 2020A-0909 | Arevalo
2013A-0741 | Schlegel | 2015A-0163 | Grillmair | 2017B-0253 | Carlin | 2020B-0053 | Shen
2013A-2101 | Walker | 2015A-0306 | Balbinot | 2017B-0279 | Rest | 2020B-0241 | Zenteno
2013A-9999 | Lee | 2015A-0397 | Walker | 2017B-0904 | Lopes | 2020B-0909 | Chaname