# Beyond MACS: Physical properties of extremely X-ray luminous clusters at _z_
> 0.5

H. Ebeling1, J. Richard2, B. Beauchesne3, Q. Basto2, A.C. Edge4 & I. Smail4

1 Institute for Astronomy, University of Hawaii, 640 N. Aohoku Place, Hilo, HI
96720, USA
2 Univ Lyon, Univ Lyon1, Ens de Lyon, CNRS, Centre de Recherche Astrophysique
de Lyon UMR5574, F-69230, Saint-Genis-Laval, France
3 Institute of Physics, Laboratory of Astrophysics, École Polytechnique
Fédérale de Lausanne, Observatoire de Sauverny, CH-1290 Versoix, Switzerland
4 Centre for Extragalactic Astronomy, Department of Physics, Durham
University, South Road, Durham DH1 3LE, UK E-mail<EMAIL_ADDRESS>
(Accepted —. Received —; in original form —)

###### Abstract

We present a sample of over 100 highly X-ray luminous galaxy clusters at
$z\approx 0.5$–$0.9$, discovered by the extended Massive Cluster Survey
(eMACS) in ROSAT All-Sky Survey (RASS) data. Follow-up observations of a
subset at higher resolution and greater depth with the Chandra X-ray
Observatory are used to map the gaseous intra-cluster medium, while strong-
gravitational-lensing features identified in Hubble Space Telescope imaging
allow us to constrain the total mass distribution. We present evidence of the
exceptional gravitational-lensing power of these massive systems, search for
substructure along the line of sight by mapping the radial velocities of
cluster members obtained through extensive ground-based spectroscopy, and
identify dramatic cases of galaxy evolution in high-density cluster
environments. The available observations of the eMACS sample presented here
provide a wealth of insights into the properties of very massive clusters
($\gtrsim 10^{15}$ M⊙) at $z>0.5$, which act as powerful lenses to study
galaxies in the very distant Universe. We also discuss the evolutionary state,
galaxy population, and large-scale environment of eMACS clusters and release
to the community all data and science products to further the understanding of
the first generation of truly massive clusters to have formed in the Universe.

###### keywords:

gravitational lensing: strong – galaxies: clusters: general

††pubyear: 2024††pagerange: Beyond MACS: Physical properties of extremely
X-ray luminous clusters at _z_ > 0.5–23

##  1 Introduction

Occupying the top spot in the mass-ranked hierarchy of gravitationally
collapsed structures in the Universe, massive galaxy clusters play a unique
role in numerous areas of astrophysical and cosmological research: they allow
us to study the evolution and interaction of baryonic and non-baryonic matter
across a wide range of environments and redshifts (e.g., Vikhlinin et al.,
2001; Markevitch et al., 2002; Harvey et al., 2015; Ebeling et al., 2017; van
Weeren et al., 2019), act as powerful gravitational telescopes that magnify
faint background sources out to the very highest redshifts (e.g., Kneib &
Natarajan, 2011, and references therein), and provide independent constraints
on fundamental cosmological parameters (e.g., Vikhlinin et al., 2009; Allen et
al., 2011; Planck Collaboration et al., 2014; Mantz et al., 2015; Bocquet et
al., 2019). Importantly, they also provide valuable opportunities to observe
and understand the evolution of galaxies in high-density environments, from
ram-pressure stripping of infalling galaxies (e.g., Gunn & Gott, 1972; Vollmer
et al., 2001; Cortese et al., 2007; Ebeling et al., 2014; Boselli et al.,
2022) to the mechanisms driving the growth of central cluster galaxies (e.g.,
Oemler, 1976; Merritt, 1985; Dubinski, 1998; De Lucia & Blaizot, 2007;
McDonald et al., 2016).

The ability to quantify changes in the ensemble properties of the population
of massive clusters with lookback time is crucial for many of the
aforementioned science applications. However, attempts to constrain the
physical properties of massive clusters, primarily their mass and relaxation
state, at ever-increasing redshifts face the obvious challenge that the most
massive clusters ($M\gtrsim 10^{15}$ M⊙) have not had time to form in
significant numbers beyond their typical redshift of formation, commonly
thought to be $z\sim 1$. As a result, observational studies of such systems
beyond the local Universe have, so far, been limited to extreme clusters at
the median redshift of $z\sim 0.45$ probed by the X-ray-based111An X-ray
luminosity of $10^{45}$ erg s-1 (0.1–2.4 keV) corresponds to a cluster mass of
$10^{15}$ M⊙ (e.g. Lovisari et al., 2020, and references therein). Massive
Cluster Survey (MACS; Ebeling et al., 2001; Ebeling et al., 2007, 2010; Mann &
Ebeling, 2012; Repp & Ebeling, 2018). At significantly higher redshifts,
studies frequently use the term “massive cluster” loosely, sampling systems of
average mass ($\sim 10^{14}$ M⊙), such as those detected in surveys exploiting
the Sunyaev-Zel’dovich (SZ; Sunyaev & Zeldovich, 1980) effect (Bleem et al.,
2020; Hilton et al., 2021) or in all-sky infrared surveys (Gonzalez et al.,
2019), or targeting the precursors of today’s massive clusters (in their
infancy) at redshifts well beyond unity (e.g., Steidel et al., 1998; Papovich
et al., 2010; Gobat et al., 2011; Newman et al., 2014; Wang et al., 2016;
Morishita et al., 2023).

The extended Massive Cluster Survey (eMACS; Ebeling et al., 2013), described
below, was designed to push X-ray searches for very massive clusters to the
highest possible redshifts without lowering the absolute mass threshold of
$\sim 10^{15}$ M⊙ set at $z>0.3$ by MACS (Applegate et al., 2014). We here
present the eMACS sample as it stands, including an overview of optical,
radio, and X-ray follow-up observations of eMACS clusters performed to date.
Based on the available data, we give first assessments of the physical
properties (mass, evolutionary state, large-scale environment etc) of all
eMACS clusters for which sufficient high-quality data, from both ground- and
space-based follow-up observations, are in hand.

This paper is structured as follows. After this brief introduction, we provide
an overview of the eMACS project in Section 2, summarize follow-up
observations in Section 3, and describe the methods used to analyze the
reduced data in Section 4. Section 5 presents the results obtained for the
physical properties of eMACS clusters, followed by our conclusions in Section
6. More technical details about the compilation of the eMACS sample from X-ray
and optical survey data can be found in Appendix A, while Appendix B serves as
a repository for summaries of key observational findings for each cluster.

We assume the $\Lambda$CDM concordance cosmology, i.e., $\Omega_{m}=0.3$,
$\Omega_{\Lambda}=0.7$, and $H_{0}=100h$ km s-1 Mpc-1, with $h=0.7$.

##  2 eMACS

The distant clusters presented and discussed here were all discovered (or, in
a few cases, re-discovered) in the course of the extended Massive Cluster
Survey, eMACS. An X-ray selected cluster survey based on ROSAT All-Sky Survey
data (RASS; Voges et al., 1999) within a solid angle of over 20,000 deg2,
defined by $|b|>20^{\circ}$, $\delta>-30^{\circ}$, eMACS extends similar work
at lower redshifts (e.g., Ebeling et al., 1997; De Grandi et al., 1999;
Ebeling et al., 2000; Ebeling et al., 2001; Reiprich, 2001; Ebeling et al.,
2002; Böhringer et al., 2004; Ebeling et al., 2007, 2010; Ebeling et al.,
2013; Böhringer et al., 2013) to $z>0.5$ in an attempt to find the first
generation of truly massive clusters out to redshifts approaching unity.

Figure 1: Left: Distribution of X-ray luminosity vs redshift for cluster
samples compiled from RASS data, as well as for SZ-selected samples. Right:
Mass estimates versus redshift for galaxy clusters from SZ and and X-ray
selected samples (adapted from Bleem et al., 2015). eMACS complements existing
surveys by focusing on the high-mass, high-redshift regime. Although total
masses are not available for all clusters shown in the left-hand plot, the
equivalence of an X-ray luminosity of $10^{45}$ erg s-1 (0.1–2.4 keV) and a
total mass of $10^{15}$ M⊙ is well established for galaxy clusters (e.g.,
Applegate et al., 2014).

Fig. 1 shows the X-ray luminosity, mass, and redshift regime explored by eMACS
in comparison with other cluster surveys. The RASS flux limits of the eBCS
(Ebeling et al., 2000), MACS, and eMACS surveys are $3\times 10^{-12}$,
$10^{-12}$, and $0.5\times 10^{-12}$ erg cm-2 s-1 (0.1–2.4 keV), respectively.
By design, eMACS finds clusters that are as X-ray luminous as the most extreme
systems discovered in the eBCS and MACS surveys, but at yet higher redshift.
Solid angle is crucial in this context; while the South Pole Telescope (SPT;
Carlstrom et al., 2011), a facility designed for the detection of the SZ
effect in clusters, is capable of detecting clusters with constant efficiency
at all redshifts, the much smaller solid angle covered by the SPT surveys
prevents it from finding exceptionally massive clusters in significant
numbers. The commonalities and differences between SZ- and X-ray cluster
surveys in mass-redshift space are summarized in Fig. 1 which also shows the
cluster samples compiled by the SPT, the Atacama Cosmology Telescope (ACT;
Swetz et al., 2011), and the Planck satellite. Although Planck covered the
entire sky, the mission’s limited angular resolution results in a selection
that is biased against clusters even at modest redshift (Malte Schäfer &
Bartelmann, 2007; Bleem et al., 2015), creating a strongly redshift-dependent
selection function more similar to that of RASS-based cluster samples at
moderate redshifts than those of high-resolution SZ surveys such as those
conducted with the SPT and ACT. As illustrated in Fig. 1, eMACS does not
compete with, but instead complements, SZ cluster surveys.

In a nutshell, the eMACS sample was compiled as follows. Candidates were
selected from the RASS source catalogue222Note that eMACS, unlike MACS, draws
not only from the RASS Bright Source Catalogue but also from the Faint Source
Catalogue. based on very few, simple X-ray selection criteria (beyond the
mentioned cuts in Galactic and equatorial latitude, cuts in the spectral X-ray
hardness ratio and in the RASS flux in the 0.1–2.4 keV band were applied; see
Appendix A for details). Next, visual inspection of optical images covering a
$5^{\prime}\times 5^{\prime}$ area around each source in the publicly
available data obtained by the PanSTARRS (PS) facility (Kaiser et al., 2002),
specifically the PS1 3$\pi$ survey (Chambers et al., 2016), was used to
identify plausible clusters as either overdensities of faint galaxies of
similar colour or fields that appear blank to the depth of the PS 3$\pi$ data.
We refer the reader to Appendix A for more details. As a final step,
spectroscopic follow-up observations of this tentative cluster sample were
conducted to limit the sample to clusters at a redshift of $z>0.5$. Results
from an eMACS pilot project were presented in Ebeling et al. (2013), and an
assessment of the lensing power of eMACS clusters is provided by Zalesky &
Ebeling (2020).

References to the “current” eMACS sample are motivated by the sample’s
incompleteness, both with regard to the optical screening of all cluster
candidates identified in the X-ray selection process described in Appendix A
and with regard to the spectroscopic confirmation of these candidates.
However, in light of the progress made in the compilation of cluster samples
from the RASS’ successor, the next-generation X-ray all-sky survey eROSITA
(e.g., Chiu et al., 2023), we opt for releasing the current eMACS sample
(together with all supporting follow-up data) to prevent unnecessary
investments of observing time into the confirmation and characterization of
eROSITA detections that merely duplicate prior eMACS discoveries and results.

Table 1 lists all 111 entries in the current eMACS sample and provides an
overview of selected follow-up observations performed to date (see Sections
3.2 and 3.4 for details). Fig. 2 shows the location of all clusters on the sky
and demonstrates that the incompleteness of the sample presented here is not a
strong function of celestial position, either in Galactic or equatorial
coordinates.

name | z | $n_{z}$ |  tACIS-I | JVLA | HST passbands
---|---|---|---|---|---
|  |  | (ks) | observed |
eMACSJ0014.9$-$0056 | 0.5330 | 18 | 30 | Y |  | F606W |  |  | F110W |  | F140W |
MACSJ0018.5$+$1626 | 0.5473 | - | 67 | Y | F435W | F606W | F814W | F105W |  | F125W | F140W | F160W
MACSJ0025.4$-$1222 | 0.5848 | - | 158 | Y | F435W |  | F814W | F105W |  | F125W | F140W | F160W
eMACSJ0026.2$+$0120 | 0.6357 | 22 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0027.0$+$1252 | 0.6063 | 22 |  | - |  |  |  |  | F110W |  | F140W |
eMACSJ0030.5$+$2618 | 0.4970 | 20 | 18 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0031.2$+$1907 | 0.5304 | 20 |  | - |  | F606W |  |  | F110W |  | F140W |
eMACSJ0042.5$-$1103 | 0.5701 | 13 | 12 | - |  |  | F814W |  | F110W |  | F140W |
eMACSJ0043.1$-$1129 | 0.7282 | 19 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0045.2$-$0151 | 0.5471 | 15 | 49 | Y |  |  |  |  | F110W |  | F140W |
eMACSJ0101.1$+$1831 | 0.6533 | 23 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0121.4$+$2143 | 0.6011 | 17 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0122.7$+$1454 | 0.5469 | 15 |  | - |  |  |  |  | F110W |  | F140W |
eMACSJ0124.0$+$0430 | 0.5363 | 14 |  | - |  | F606W |  |  |  |  |  |
eMACSJ0127.5$-$0606 | 0.5055 | 14 |  | - |  |  |  |  | F110W |  | F140W |
eMACSJ0135.2$+$0847 | 0.6185 | 38 | 12 | Y |  |  |  |  | F110W |  | F140W |
eMACSJ0153.4$+$1722 | 0.5464 | 21 |  | - |  | F606W |  |  |  |  |  |
eMACSJ0200.3$-$2454 | 0.7126 | 25 |  | - |  |  |  |  |  |  |  |
eMACSJ0224.5$-$1615 | 0.6223 | 15 |  | - |  |  |  |  | F110W |  | F140W |
eMACSJ0241.0$+$2557 | 0.5752 | 22 |  | - |  | F606W |  |  | F110W |  | F140W |
eMACSJ0248.2$+$0237 | 0.5561 | 19 | 45 | - |  |  |  |  | F110W |  | F140W |
eMACSJ0252.4$-$2100 | 0.7017 | 26 |  | - |  |  |  |  | F110W |  |  |
eMACSJ0256.7$-$1623 | 0.8621 | 18 | 33 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0256.9$-$1631 | 0.8670 | 17 | 33 | Y |  | F606W | F814W |  | F110W |  | F140W |
MACSJ0257.1$-$2325 | 0.5056 | - | 38 | Y | F435W | F606W | F814W | F105W |  | F125W | F140W | F160W
eMACSJ0324.0$+$2421 | 0.9023 | 26 | 31 | - | F435W | F606W | F814W | F105W |  | F125W | F140W | F160W
eMACSJ0325.4$-$0359 | 0.5721 | 12 |  | - |  |  |  |  | F110W |  | F140W |
eMACSJ0403.6$+$1544 | 0.5275 | 20 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0429.0$-$1011 | 0.5418 | 10 |  | - |  |  |  |  | F110W |  | F140W |
MACSJ0454.1$-$0300 | 0.5376 | - | 14 | Y |  |  | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ0502.9$-$2902 | 0.6028 | 23 | 49 | - |  | F606W | F814W |  | F110W |  | F140W |
MACSJ0647.7$+$7015 | 0.5922 | - | 39 | Y | F435W | F606W | F814W | F105W | F110W | F125W | F140W | F160W
MACSJ0717.5$+$3745 | 0.5454 | - | 243 | Y | F435W | F606W | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ0742.9$+$5001 | 0.6013 | 15 |  | - |  | F606W | F814W |  | F110W |  | F140W |
MACSJ0744.8$+$3927 | 0.6976 | - | 90 | Y | F435W | F606W | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ0747.0$+$6937 | 0.5696 | 13 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0804.6$+$5325 | 0.5786 | 20 | 4 | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0834.2$+$4524 | 0.6606 | 32 | 33 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0840.2$+$4421 | 0.6377 | 39 | 32 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0841.8$-$0429 | 0.5359 | 11 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0850.2$-$0611 | 0.5744 | 22 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0910.8$+$3850 | 0.5618 | 19 |  | - |  | F606W | F814W |  | F110W |  | F140W |
MACSJ0911.2$+$1746 | 0.5051 | - | 42 | Y | F435W |  | F814W | F105W |  | F125W | F140W | F160W
eMACSJ0921.6$-$0621 | 0.6842 | 15 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0934.6$+$0540 | 0.5627 | 15 |  | - |  | F606W |  |  | F110W |  | F140W |
eMACSJ0935.1$+$0614 | 0.7787 | 21 | 30 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ0943.3$-$1842 | 0.5687 | 12 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1025.0$-$1354 | 0.6196 | 13 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1027.2$+$0345 | 0.7482 | 10 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
Table 1: The eMACS sample at the time of publication; we list the cluster redshift, the number of spectroscopic redshifts measured, and the HST passbands in which imaging data were obtained. We also indicate which clusters were observed with the JVLA at 5 GHz to date. The 12 eMACS clusters released earlier as part of the MACS sample (Ebeling et al., 2007) are listed for completeness’ sake ($n_{z}$ entries are deliberately omitted for these 12 clusters). name | z | $n_{z}$ |  tACIS-I | JVLA | HST passbands
---|---|---|---|---|---
|  |  | (ks) | observed |
eMACSJ1030.5$+$5132 | 0.5182 | 23 | 20 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1050.6$+$3548 | 0.5077 | 39 |  | Y |  | F606W | F814W |  |  |  |  |
eMACSJ1057.5$+$5759 | 0.6027 | 12 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1131.1$+$3553 | 0.5159 | 12 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1136.8$+$0005 | 0.5968 | 26 | 4 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1144.2$-$2836 | 0.5070 | 30 | 31 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1148.0$+$5116 | 0.5834 | 28 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
MACSJ1149.5$+$2223 | 0.5445 | - | 366 | Y | F435W | F606W | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ1157.9$-$1046 | 0.5570 | 25 | 156 | - | F435W |  | F814W |  | F110W |  | F140W |
eMACSJ1209.4$+$2640 | 0.5553 | 22 | 16 | Y |  |  |  | F105W | F110W |  | F140W | F160W
eMACSJ1212.5$-$1216 | 0.6786 | 28 |  | Y |  |  | F814W |  | F110W |  | F140W |
eMACSJ1222.3$+$2418 | 0.5085 | 14 |  | Y |  | F606W |  |  | F110W |  | F140W |
eMACSJ1248.2$+$0743 | 0.5733 | 15 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1251.3$+$3131 | 0.5069 | 16 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1257.3$+$3654 | 0.5253 | 14 |  | - |  | F606W |  |  | F110W |  | F140W |
eMACSJ1341.9$-$2442 | 0.8339 | 26 | 34 | Y |  | F606W | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ1350.7$-$1055 | 0.8247 | 12 | 33 | Y |  |  |  |  |  |  |  |
eMACSJ1353.7$+$4329 | 0.7364 | 31 | 40 | Y | F435W | F606W | F814W | F105W |  | F125W | F140W | F160W
eMACSJ1407.0$-$0015 | 0.5520 | 14 | 4 | Y |  | F606W | F814W |  |  |  |  |
eMACSJ1414.7$+$5446 | 0.6121 | 26 | 33 | - |  | F606W | F814W |  | F110W | F125W | F140W | F160W
eMACSJ1419.1$-$0624 | 0.5432 | 22 |  | Y |  |  | F814W |  | F110W |  | F140W |
eMACSJ1419.2$+$5326 | 0.6384 | 32 |  | - |  |  | F814W |  | F110W |  | F140W |
MACSJ1423.8$+$2404 | 0.5434 | - | 19 | Y | F435W | F606W | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ1430.0$+$4127 | 0.6646 | 13 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1437.8$+$0616 | 0.5350 | 19 |  | - |  | F606W |  |  | F110W |  | F140W |
eMACSJ1443.2$+$0102 | 0.5284 | 23 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1508.1$+$5755 | 0.5421 | 48 | 49 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1518.3$+$2927 | 0.6050 | 33 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1523.1$+$1329 | 0.5010 | 18 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1527.6$+$2044 | 0.6967 | 28 | 25 | Y | F435W | F606W | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ1621.2$-$0231 | 0.5014 | 9 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1621.4$+$7232 | 0.5863 | 34 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1631.1$+$1528 | 0.5087 | 11 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1709.5$+$4731 | 0.5527 | 40 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1732.4$+$1934 | 0.5406 | 41 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1756.8$+$4008 | 0.5743 | 117 | 89 | Y | F435W | F606W | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ1757.5$+$3045 | 0.6105 | 32 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1823.1$+$7822 | 0.6754 | 20 | 22 | Y | F435W | F606W | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ1831.1$+$6214 | 0.8207 | 25 | 23 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1831.9$+$5746 | 0.7072 | 15 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ1852.0$+$4900 | 0.6035 | 32 | 20 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2018.3$-$2242 | 0.5302 | 20 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2020.1$-$1432 | 0.5653 | 22 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2025.5$-$2313 | 0.7098 | 19 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2026.7$-$1920 | 0.6219 | 40 | 32 | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2037.1$-$2534 | 0.5263 | 36 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2045.8$-$2438 | 0.5917 | 20 |  | - |  |  | F814W |  | F110W |  | F140W |
eMACSJ2100.4$+$0724 | 0.5742 | 13 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2114.4$+$0427 | 0.5898 | 20 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
MACSJ2129.4$-$0741 | 0.5879 | - | 40 | Y | F435W | F606W | F814W | F105W | F110W | F125W | F140W | F160W
eMACSJ2137.2$-$2232 | 0.6131 | 23 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2201.9$+$0711 | 0.5633 | 11 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2207.5$-$0302 | 0.5304 | 21 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
MACSJ2214.9$-$1359 | 0.5022 | - | 38 | Y |  |  | F814W | F105W |  | F125W |  | F160W
eMACSJ2220.3$-$1211 | 0.5292 | 35 | 12 | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2229.9$-$0808 | 0.6214 | 65 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2236.0$+$3451 | 0.7287 | 25 |  | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2315.3$-$2128 | 0.5400 | 43 | 31 | - |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2316.6$+$1246 | 0.5258 | 32 |  | Y |  | F606W | F814W |  | F110W |  | F140W |
eMACSJ2320.9$+$2912 | 0.4960 | 45 | 10 | - |  |  | F814W |  | F110W |  | F140W |
eMACSJ2327.4$-$0204 | 0.7055 | 24 | 146 | Y | F435W | F606W | F814W |  |  | F125W |  | F160W
eMACSJ2351.6$-$2818 | 0.5679 | 18 |  | - |  | F606W |  |  | F110W |  | F140W |
Table 1: continued. Figure 2: The distribution of eMACS clusters in the
equatorial sky. The 12 clusters also included in the MACS sample and presented
previously in Ebeling et al. (2007) are shown as open symbols. Solid lines
delineate the 40-deg wide exclusion zone around the Galactic plane. While the
statistical completeness of eMACS has not been quantified, the distribution of
clusters across the surveyed solid angle is approximately isotropic.

##  3 Observations and data reduction

###  3.1 Groundbased imaging

By design, all eMACS clusters are covered in five optical passbands
($g^{\prime}r^{\prime}i^{\prime}z^{\prime}y^{\prime}$) in the PS1 3$\pi$
survey (Chambers et al., 2016). Although crucial for the identification of
clusters among the many faint X-ray sources in the RASS, the PS1 3$\pi$
imaging data are too shallow to serve more ambitious purposes.

Consequently, we obtained short ($\sim$300s) observations of all eMACS
clusters to a limiting magnitude of approximately 23 (AB) through the
$g^{\prime},r^{\prime}$, and $i^{\prime}$ filters333For a small number of
clusters, imaging with GMOS was also obtained in the $z^{\prime}$ passband.
with the GMOS imaging spectrograph on the 8m Gemini-North telescope on
Maunakea. Extending to over 1 Mpc in radius from the centre of a cluster at
$z>0.5$, the 5.5′ field of view of GMOS offers a comprehensive view of the
projected spatial distribution of likely cluster galaxies (as identified from
their characteristic red-sequence colours) and allowed the efficient selection
of targets for the spectroscopic follow-up observations described in Section
3.3. A more detailed description of the GMOS imaging survey of eMACS clusters,
as well as of the associated data reduction techniques, is provided in the
context of the mass-traces-light algorithm AStroLens that provided a first
assessment of the gravitational-lensing strength of eMACS clusters (Zalesky &
Ebeling, 2020).

###  3.2 _HST_ imaging

Optical and near-infrared imaging with high angular resolution and low sky
background is critical for several key science goals of the eMACS project,
most notably the detection of strong-gravitational-lensing features, as well
as dust and star formation in brightest cluster galaxies (BCGs), and ram-
pressure stripping of “jellyfish” galaxies.

To achieve these objectives, eMACS clusters were observed with the Advanced
Camera for Surveys (ACS) and the Wide-Field Camera 3 (WFC3) aboard the Hubble
Space Telescope (HST) in four SNAPshot programs (GO-13671, GO-14098, GO-15132,
and GO-15843). In addition, eMACS clusters of special interest were targeted
by us in dedicated HST imaging campaigns (GO-15466, GO-15608, GO-15844,
GO-16428) that added either depth or area on the sky to existing SNAPshot
data. A number of eMACS clusters were also observed independently by other
teams.

The listed SNAPshot programmes requested imaging observations in four
passbands: F606W and F814W (ACS; 1200s each), as well as F110W and F140W
(WFC3; 700s each), although the random nature of SNAPshot surveys meant that
not all clusters were observed in all passbands. Imaging was also performed in
the F435W passband of ACS, as well as the WFC3 near-infrared filters F105W,
F125W, and F160W, in targeted GO observation awarded to us or other teams. An
overview of the available HST data in these eight passbands is provided in
Table 1. Except for eMACSJ0200.3 which has no HST imaging, all eMACS clusters
were observed in at least one passband444Scheduled HST observations of
eMACSJ1350.7 were canceled by the proposers after CXO observations of the
field failed to detect diffuse X-ray emission, thereby ruling out the presence
of a galaxy cluster (see Section 5.1.2).,

All HST data were reduced using standard procedures. Specifically, all
available HST images for a given field were corrected for geometric
distortions and mapped to a common coordinate frame tied to the Gaia
astrometric reference frame, using the TweakReg and AstroDrizzle packages
(Fruchter & et al., 2010). False-colour RGB images555Whenever possible (see
Table 1), we use the F606W, F814W, and F110W images to populate the B, G, and
R channels, respectively. were then created using the same colour table,
scaling, and limits for all fields. We used SExtractor (Bertin & Arnouts,
1996) to generate source catalogues and to obtain photometry in the three
chosen passbands. Cluster members were tentatively identified as members of
the red sequence (e.g., Visvanathan & Sandage, 1977; Bower et al., 1992) based
on colour-magnitude diagrams. We refer the reader to Basto et al. (in
preparation) for additional details.

We note that, since the vast majority of the HST images were obtained in
randomly selected SNAPshot observations, the resulting HST imaging dataset can
be considered unbiased and representative of the eMACS sample as a whole. A
mild bias is introduced, however, by our efforts to secure multi-passband
coverage (or greater observational depth) for clusters showing exceptional
strong-lensing features in the SNAPshot observations.

###  3.3 Optical and near-infrared spectroscopy

Extensive spectroscopic follow-up observations were conducted to target
presumed cluster members, potential strong-lensing features, and likely
counterparts of X-ray point sources (detected in the CXO observations
described in Section 3.4) in the eMACS cluster fields. These observations were
performed with the DEep Imaging Multi-Object Spectrograph (DEIMOS; Faber et
al., 2003), the Low-Resolution Imaging Spectrometer (LRIS; Oke et al., 1995),
and the Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE; McLean
et al., 2010, 2012) on the Keck-1 and -2 10m telescopes on Maunakea, Hawai’i.
The individual multi-object spectroscopy targets were selected from HST, GMOS,
PS1/3$\pi$, and CXO observations. Whenever possible (i.e., depending on the
availability and quality of HST and CXO data), priority was given to redshifts
measurements of likely strong-lensing features and X-ray point sources, with
the remainder of the mask being used to target probable cluster members
(selected by their colours). In the following we briefly summarize the
instrumental setup for the three spectrographs used.

DEIMOS:

1″ slit width; 600 line mm-1 grating; GG455 order-blocking filter; central
wavelength 6300Å; 1.2Å pixel-1 sampling;

LRIS:

1″ slit width; D680 dichroic; 300/5000 grism (8.8Å FWHM resolution, red arm);
600/7500 grating and central wavelength 8100Å (4.7Å resolution, blue arm);

MOSFIRE:

0.7″ slit width; $I$, $J$, $K$, and / or $H$ band, depending on the expected
wavelength of emission-line features; ABBA dither pattern with (typically)
1.5″ offset; 2.8Å pixel-1 sampling.

Exposure times ranged from approximately 1800s to several hours, depending on
atmospheric conditions, airmass, and the faintness of the primary targets on a
given MOS mask. We typically observed all targets first in the optical window
and then added near-infrared spectroscopy with MOSFIRE only for strong-lensing
features for which no identifiable features were detected in prior
observations with LRIS or DEIMOS.

Most of the DEIMOS spectra were reduced using a modified version of the DEEP2
pipeline (Cooper et al., 2012; Newman et al., 2013), with more recently
acquired data having been processed with the PypeIt package (Prochaska et al.,
2020). An early version of PypeIt was also used to reduce the LRIS data, while
the MOSFIRE data reduction was mostly performed with the pipeline designed by
the MOSFIRE commissioning team and written by Nick Konidaris with extensive
checking and feedback from Chuck Steidel and other MOSFIRE team members
(Steidel et al., 2014) .

Although we aimed at obtaining, for each eMACS cluster, at least 20
spectroscopic redshifts of cluster members as well as spectroscopic
confirmation of at least one gravitational-lensing feature, weather patterns
on Maunakea and the vagaries of the telescope-time allocation process
introduced seasonal biases. We also deliberately devoted extra resources to
the spectroscopic follow up of eMACS clusters of particular interest, e.g.,
the most distant ones, the most obvious and most spectacular gravitational
lenses, or the most extreme mergers. As a result, the spectroscopic coverage
of the sample presented here is uneven, as is apparent from the number of
redshifts obtained for each cluster listed in Table 1.

###  3.4 X-ray imaging spectroscopy

We searched the public archive CHASER666https://cda.harvard.edu/chaser/ for
data collected for eMACS clusters with the Advanced CCD Imaging Spectrometer
(ACIS) aboard the Chandra X-ray Observatory (CXO); for consistency, we
retrieved and analyzed only observations performed with the instrument’s
ACIS-I array in VFAINT mode. Of the resulting list of 47 eMACS clusters
observed (see Table 1), the majority were targeted by the eMACS team (PI
Ebeling), with most of the remainder having been selected as part of follow-up
observations of detections of the Sunyaev-Zeldovich effect. Excluding the 12
systems at $z>0.5$ discovered previously by the MACS project (Ebeling et al.,
2007) and discussed extensively in the literature (e.g., LaRoque et al., 2003;
Ebeling et al., 2007; Bradač et al., 2008; Zitrin et al., 2011; Limousin et
al., 2012; Ogrean et al., 2016; Wilber et al., 2018; Jauzac et al., 2018), we
are left with 35 new systems. For each cluster we reduce and then merge all
available observational datasets.

We emphasize that the resulting subset of eMACS clusters with CXO/ACIS-I data
is not representative of the full sample but reflects the scientific interests
and target selection criteria put forward by the authors of the underlying CXO
proposals. As a result, biases in favour of the most X-ray luminous, the most
distant, and the most disturbed clusters are introduced; additional biases may
be present but remain unknown to us.

Our data reduction extensively uses routines from the CIAO software
environment (Fruscione et al., 2006) and largely follows established
procedures, beginning with the reprocessing and reprojecting of the archival
data, before removing time intervals affected by background flares (we first
examine the high-energy 9–12 keV band, then the entire ACIS-I passband). We
subsequently identify X-ray point sources as detected by the wavdetect source-
detection algorithm (Freeman et al., 2002) but employ a visual check to ensure
the validity of all point sources in the automatically generated source list.

Since our analysis is similar to the process described in detail in the
literature (e.g., Mahler et al., 2023; Beauchesne et al., 2024); we here
provide only a brief summary. For each observation, we retrieve the associated
ACIS-I blank-sky background from the public archive and compute the response
of the instruments within a circle of radius $1$ Mpc, initially centred on the
cluster position in the RASS source catalogue. To model the background
emission (both instrumental and sky backgrounds), we use an empirical model
consisting of B-spline functions. For each observation, we build this model by
first fitting the blank-sky spectrum for each CCD in the 0.1–13 keV band. We
then use a linear combination of these models to define a background model per
observation as a linear combination of the CCD models. This linear combination
is optimised on the blank-sky spectrum of the chosen cluster region by keeping
all coefficients frozen for the spectral fit of the cluster and optimizing
only one global amplitude per observation. This procedure allows us to
estimate the scaling between the science and the blank-sky observations
without relying on the observing time or the particle background. More details
about the background estimation can be found in Appendix A of Beauchesne et
al. (2024).

###  3.5 Radio observations

The majority of the clusters presented here (see Table 1) were observed with
the Jansky VLA in B-array at 5 GHz in 2016 as part of a larger campaign to
observe MACS and eMACS clusters to search for activity in the BCG and other
cluster members (PI Edge, 16A-167). All targets were observed in two visits of
300s each, separated by 60–80 mins, with an associated, nearby phase
calibrator. These observations reach a consistent noise level of $\sim 30\
\mu$Jy per beam and a resolution of $\sim$2.0′′ that depends weakly on
declination.

##  4 Analysis

###  4.1 Galaxy spectroscopy

Redshifts were measured and corrected to the heliocentric frame using an
adaptation of the SpecPro package (Masters & Capak, 2011). We determined
cluster velocity dispersions with the ROSTAT software developed by Beers et
al. (1990).

###  4.2 X-ray imaging spectroscopy

To determine fundamental physical parameters of the ICM emission recorded with
CXO, we proceed as follows. The overall spectral model is the combination of
the previously defined empirical background with a physical model of the
cluster emission; we adopt a single-temperature plasma, represented by a
single APEC model (Astrophysical Plasma Emission Code, xsapec) with solar
abundance ratios from Asplund et al. (2009) and photoelectric absorption
parameterized by the column density of neutral hydrogen ($n_{\rm H}$) along
the line of sight (xsphabs). We fit the combined spectrum to the data in the
0.5–7 keV range using the nested-sampling algorithm provided in the Multinest
package (Feroz et al., 2019) through its Python wrapper (Buchner et al.,
2014). During this fit, the density, temperature (k$T$), and metallicity ($Z$)
of the intracluster medium (ICM) are allowed to vary, in addition to the
background normalisation. Since $n_{\rm H}$ is poorly constrained for most
clusters, we set it to the Galactic value provided by the HI4PI project (HI4PI
Collaboration et al., 2016).

We perform the spectral fitting within a circular area that is determined
iteratively. We start by fitting the data within a circle of radius $1$ Mpc
around the RASS position of each eMACS cluster. From the posterior
distribution of the ICM temperature and the cluster redshift, we derive the
distributions of $r_{\rm 1000}$ and $M_{\rm 1000}$ using the relation provided
in Arnaud et al. (2002). We also compute the centroid of the X-ray emission
within the initial fitting area of $1$ Mpc with the python package pyproffit
(Eckert et al., 2020) and then define a new extraction region around this
centroid position, with a radius given by the median of the $r_{\rm 1000}$
distribution. We repeat this process until the new $r_{\rm 1000}$ median is
included in the median-centred interval of $68$ per cent of the previous
distribution, and the associated emission centroids are similar. We do not
quantitatively monitor the convergence of the centre position, but require the
previous centre position to be within $6$ arcsec of the new one. In most
cases, the differences in the location of the centroid between fits are of the
order of $1$ arcsec or less. The resulting values of $r_{\rm 1000}$ range
approximately from $500$ to $1000$ kpc for our sample.

The spatial distribution of the X-ray emission from eMACS clusters observed
with CXO is, in all figures in this paper, represented by the isointensity
contours of the X-ray surface brightness after adaptive smoothing to $3\sigma$
significance with the asmooth algorithm (Ebeling et al., 2006).

###  4.3 Strong gravitational lensing

We use the multi-band high-resolution images obtained with HST (all but four
eMACS clusters were observed with HST in at least two passbands; see Section
3.2 and Table 1) to identify potential strongly lensed images based on their
similarity in colours and morphologies. The corresponding sources were given
high priority for the spectroscopic follow-up observations described in
Section 3.3. For the strong-lensing analysis described below we consider the
subset of 25 eMACS clusters with at least one multiple-image system confirmed
by spectroscopic redshifts.

We use the Lenstool software (Jullo et al., 2007) to create lens models by
parameterising the mass distribution of each cluster as a combination of
double Pseudo Isothermal Elliptical (dPIE) mass profiles at both large
(cluster) and small (galaxy) scales. Following similar work on large cluster
samples (e.g., Richard et al., 2010, 2021), we optimise the set of parameters
of large-scale dPIE components to best reproduce the locations of the
confirmed multiple-image systems in each cluster. To account for the mass in
small-scale components, we include each cluster member (selected from the red
sequence) as a galaxy-scale perturber of the overall mass distribution. We fix
these galaxies’ geometric parameters (centre, ellipticity, position angle) at
the values in the HST photometric catalogue, while the remaining parameters of
these small-scale dPIEs (velocity dispersion, cut and core radii) are assumed
to follow a light-traces-mass relation with their luminosity.

##  5 Results and Discussion

In the following we present our findings on the gravitational-lensing strength
(as estimated from our strong-lensing analysis), the properties of the ICM,
and the galaxy population of eMACS clusters.

We stress again that the eMACS sample presented here is not statistically
complete; in addition, the sample’s coverage in follow-up observations (be it
galaxy spectroscopy, HST imaging, or X-ray imaging spectroscopy with CXO) is
currently inhomogeneous. Given these limitations, the goal of this paper is
not a comprehensive characterization of the population of X-ray luminous
clusters at $z>0.5$. Rather, we aim to highlight subsets of the sample as well
as individual systems that were found to be exceptional, warrant further
study, or yield insights into the selection biases of cluster samples compiled
at different wavelengths and using different survey techniques.

The statistical completeness (or lack thereof) of eMACS and any eMACS
subsample is strongly affected by both statistical and systematic
uncertainties in the RASS data from which cluster candidates were selected
(see Section 2 and Appendix A for details). The most important contributors
are shot noise (some RASS detections of eMACS clusters are comprised of a
dozen or fewer net X-ray photons) and contamination by X-ray point sources, a
systematic issue that we describe and assess in the following section.

###  5.1 _CXO_ versus RASS

Since ROSAT’s effective point-spread function (PSF) is significantly broadened
during the RASS compared to the on-axis PSF of the system (and can not be
easily modeled, De Grandi et al., 1997), the standard source-detection
algorithms used in the RASS reliably recognize only relatively nearby and
X-ray bright clusters as intrinsically extended sources (Ebeling et al.,
1996). Moreover, the RASS X-ray fluxes and luminosities of clusters even at
$z<0.3$ are prone to contamination from unresolved X-ray point sources, be
they embedded in the cluster or physically unrelated fore- or background
sources. At the far higher redshifts and dramatically poorer photon statistics
probed by eMACS, the impact of X-ray point sources on our RASS-selected sample
is a priori unquantifiable but can be measured through follow-up observations
with CXO that allow point sources to be resolved and removed.

Fig. 3 demonstrates that eMACS delivers on the promise of Fig. 1 by showing a
comparison of the cluster luminosities as observed in the RASS and in the
dedicated follow-up observations performed with CXO of selected eMACS
clusters. Here, we have removed all point sources from the CXO data prior to
measuring the luminosity of the diffuse ICM emission, whereas (by necessity)
no such correction was applied to the RASS luminosities. We find that, in
general, contamination from X-ray point sources is a minor effect777For the
sample presented here, the median flux from point sources within the RASS
detect cell is less than $5\times 10^{-15}$ erg cm-2 s-1 (0.1–2.4 keV)., as no
significant offset from the identity relation (shown as a dotted line in Fig.
3) is seen in the correlation, and the scatter about it is largely consistent
with the statistical uncertainties in the RASS-based measurements, with the
exception of the four systems labeled in Fig. 3 and discussed below.

Figure 3: Comparison of eMACS cluster luminosities in the 0.1–2.4 keV band, as
derived from RASS and CXO observations. The most extreme outliers are labelled
and discussed in Section 5.1.1. Two CXO non-detections (see Section 5.1.2) are
plotted as upper limits at fiducial CXO luminosities of $1.2\times 10^{44}$
erg s-1. The distribution in RASS X-ray luminosity of the eMACS clusters
without CXO/ACIS-I data is shown as a histogram. Note that X-ray point sources
were removed before measuring cluster luminosities in the high-resolution CXO
data, whereas the luminosities observed in the RASS include X-ray point
sources (where present).

####  5.1.1 Flux contamination

We highlight in Fig. 3 two clusters (eMACSJ1144.2 and eMACSJ2315.3) for which
the point-source corrected X-ray luminosity as measured from CXO observations
falls below the RASS estimate by over a factor of five. Even for such
outliers, however, the cause of the discrepancy is not always readily
apparent. As shown in Figs. B20 and B43, several X-ray point sources
contribute to the X-ray flux measured for these two clusters at the low
angular resolution of the RASS; however, the total flux from all X-ray point
sources out to 2′ radius from the peak of the ICM emission amounts to less
than 10% of the reported RASS fluxes in Fig. 3. Then again, since many types
of X-ray point sources are time variable, any of the point sources apparent in
Figs. B20 and B43 could have been substantially brighter in the early 1990s
when the RASS was conducted.

The degree of point-source contamination in X-ray selected cluster surveys may
also depend on the mass and evolutionary state of the systems under study.
Low-mass clusters and groups of galaxies are less dense and dynamically
younger; as a result, late-type galaxies tend to be more prevalent and nuclear
activity (in cluster members as well as in galaxies in the cluster
environment) may be stronger and more common. Anecdotally, the point source
contamination appears indeed to be more pronounced in the RASS-selected MACS
and BCS cluster samples which, probing lower redshifts, sample a broader range
of cluster masses than eMACS (e.g., Ebeling et al., 2010).

####  5.1.2 Misidentifications

While the relative flux contributions from the diffuse ICM and from related or
unrelated point sources can be difficult to disentangle for individual
clusters (but does not invalidate the presence and discovery of the respective
cluster), a total absence of ICM emission renders the respective entry in our
catalogue a plain misidentification.

Based on the current CXO follow-up observations, we are aware of two such
cases: as noted in Fig. 3, eMACSJ0256.9 ($z=0.8670$) and eMACSJ1350.7
($z=0.8247$) show no significant extended X-ray emission in 33ks observations
with CXO. We show the HST image of the former (an already awarded HST
observation of the latter was cancelled by us after the CXO observation failed
to detect ICM emission) as well as the histogram of radial velocities of
galaxies in this region in Fig. B6. Note the absence of ICM emission from
eMACSJ0256.9 (Fig. B6) in spite of an obvious overdensity of galaxies at the
catalogued RASS source position and the high velocity dispersion of
1170${}^{+140}_{-240}$ km s-1 measured for the structure (based on 17
concordant redshifts). eMACSJ0256.9 thus underlines the critical importance of
moderately deep follow-up observations with a high-resolution X-ray facility
like CXO to identify non-clusters: as is apparent from Fig. B6, the X-ray flux
detected in the RASS is in fact generated by several X-ray point sources, the
brightest of which was spectroscopically identified by us as a QSO at
$z=0.8562$, i.e., at the same redshift of the purported cluster. We discuss
eMACSJ0256.9 further in Section 5.5.2 in the context of large-scale structure.

###  5.2 Strong lensing

Given the size of the eMACS sample (and the wealth of strong-lensing features
present), a comprehensive strong-lensing study of all eMACS clusters not only
requires significant observational and analytical resources but also faces
systematic challenges. Although compelling signs of strong gravitational
lensing are found in the majority of eMACS clusters for which the prerequisite
HST imaging is available (Fig. 6), the limitations of the data available for
some clusters (e.g., no colour information; no spectroscopic redshifts;
clipping of the strong-lensing area by the WFC3 aperture) hampers the secure
identification of the most powerful lensing constraints: multiple-image
systems. Nevertheless, for clusters with at least one spectroscopically
confirmed multiple-image system, we are able to create tentative lens models
as described in Section 4.3.

####  5.2.1 Lensed sources

Strong lensing by massive galaxy clusters offers unique insights into the
properties of background galaxies in two complementary ways: by probing the
background population in a statistical manner, thereby providing valuable
constraints on, for instance, the galaxy luminosity function at redshifts that
are not observationally accessible in other ways (e.g., Bouwens et al. 2022),
and by enabling detailed studies of the physical properties of individual,
intrinsically faint background objects at more modest redshifts (e.g., Alavi
et al. 2014). If quantitative insights are aimed for, both of these avenues of
research require credible models of the mass distribution within the cluster
lenses, and hence the identification of unambiguous strong-lensing features to
constrain these lens models (see Sect. 4.3). While exploiting the former,
statistical goal requires much deeper follow-up observations (such as those of
the Frontier Fields project Lotz et al. 2017, or the JWST UNCOVER program
Bezanson et al. 2022) than have been performed for eMACS to date, first steps
toward the latter goal can be taken with the data at hand.

For 106 eMACS clusters existing multi-band HST imaging enables us to visually
survey the core regions of the clusters for potential strongly lensed
background sources, identifiable as highly sheared images (arcs and giant
arcs) and multiply imaged sources. Many of these systems are cusp arcs,
producing three images, the brightest two of which display mirror symmetry
(e.g., eMACSJ0121.4 and eMACSJ1222.3 in Fig. 6). However, higher multiplicity
and more complex configurations are seen, such as quads (e.g., eMACSJ1027.2 in
Fig. 6) or rare hyperbolic umbilical lensing events as in eMACSJ1248.2 (System
2 in Fig.4; see also Fig. B25). The significance of such exotic lenses is
discussed, e.g., by Lagattuta et al. (2023).

Figure 4: HST image of the core of eMACSJ1248.2 at $z=0.573$ ($40\arcsec\times
30\arcsec$, see also Fig. B25). The components of three multiple-image systems
are marked, among them a rare hyperbolic-umbilical configuration (System 2,
with four images: 2.1–2.4), although unfortunately this currently lacks a
spectroscopic redshift. Figure 5: HST image of the core of eMACSJ1437.8 at
$z=0.535$ ($50\arcsec\times 50\arcsec$, see also Fig. B30), revealing a group
of background galaxies at $z=2.55$ gravitationally lensed by the foreground
cluster. The components of three multiple-image systems (two of them, Systems
1 and 2, spectroscopically confirmed at $z=2.546$ and $z=2.556$) are marked.

The colours and morphologies of the strongly lensed features showcase the
diversity of high-redshift sources seen through the cores of massive clusters
at $z>0.5$ and, in rare cases, can even reveal extended background structures,
such as the galaxy group at $z=2.55$ lensed by eMACSJ1437.8 (Figs. 5 and B30).
For background sources at modest redshifts, typically at $z\leq 2$, the larger
apparent sizes and in general brighter magnitudes allow complex internal
structures of the sources to be readily apparent through the mirror symmetry
and image shear that result from strong gravitational lensing; examples are
the spiral galaxy at $z=1.195$ behind eMACSJ1212.5 (Figs. 6 and B23), or the
quiescent galaxy at $z=1.594$ behind eMACSJ1341.9 (discussed in Ebeling et al.
2018; see also Figs. 6 and B26), although resolved galaxy features can be seen
out to higher redshifts (e.g., The Scream at $z=3.375$ behind eMACSJ222.9,
Figs. 6 and B42). At higher redshifts, the combination of strong image shear
and increasingly compact sources sizes (particularly in the restframe UV at
$z\gtrsim 2$), as well as surface-brightness dimming, contribute to the
apparent narrowness of some lensed features, such as the complex “straight
arc” at $z=2.03$ in eMACSJ1756.8 (Figs. 6 and B35), or highly sheared examples
like the giant arc in eMACSJ2327.4 at $z=2.983$ (Sharon et al., 2015, see also
Figs. 6 and B45).

Figure 6: Examples of strong-lensing features in HST images of eMACS clusters.
We use a shorthand notation for the cluster names.

####  5.2.2 Einstein radii and systematic effects

As a first indicator of central lensing strength, we list in Table 2 the
Einstein radius, $R_{\rm E}$888Following, e.g., Meneghetti et al. (2023), we
compute the equivalent Einstein radius $R_{\rm E}$ as the radius of the
circular aperture enclosing the same area as the tangential critical line at
this redshift., of the 25 eMACS clusters modeled to date with Lenstool,
estimated for a fiducial source at $z=2$; in addition, we also list the total
projected gravitational mass within that radius. Both quantities exhibit a
large spread for reasons that include true diversity in the clusters’ physical
characteristics999Including the cluster environment, as strong lensing is
sensitive to the total projected mass along the line of sight. as well as
uncertainties in the model assumptions for cluster lenses currently
constrained by only a single multiple-image system.

Name | $R_{\rm E,PM}$ | $M(r<R_{\rm E,PM})$ | $N_{\rm mi}$ | $N_{\rm mi,z}$
---|---|---|---|---
| (arcsec) | ($10^{12}$ M⊙) |  |
eMACSJ0030.5$+$2618 |  $9\pm 2$ |  16 | 4 | 4
eMACSJ0121.4$+$2143 | $12\pm 1$ |  40 | 3 | 3
eMACSJ0252.4$-$2100 | $15\pm 2$ |  72 | 12 | 12
eMACSJ0256.7$-$1623 | $11\pm 1$ |  49 | 12 | 12
eMACSJ0324.0$+$2421 | $11\pm 2$ |  51 | 3 | 3
eMACSJ0502.9$-$2902 | $25\pm 3$ | 164 | 20 | 9
eMACSJ0834.2$+$4524 | $32\pm 4$ | 324 | 9 | 9
eMACSJ0840.2$+$4421 | $14\pm 1$ |  58 | 8 | 8
eNACSJ0934.6$+$0540 | $16\pm 2$ |  60 | 10 | 7
eMACSJ0943.3$-$1842 | $>12$ | $>37$ | 3 | 3
eMACSJ1057.5$+$5759 | $20\pm 10$ | 119 | 4 | 2
eMACSJ1157.9$-$1046 | $>15$ | $>44$ | 9 | 3
eMACSJ1209.4$+$2640 | $22\pm 2$ | 131 | 19 | 7
eMACSJ1212.5$-$1216 | $40\pm 4$ | 542 | 3 | 3
eMACSJ1248.2$+$0743 | $17\pm 2$ |  69 | 11 | 3
eMACSJ1341.9$-$2442 | $16\pm 2$ |  79 | 5 | 5
eMACSJ1353.7$+$4329 | $38\pm 5$ | 525 | 13 | 4
eMACSJ1437.8$+$0616 | $14\pm 1$ |  47 | 11 | 8
eMACSJ1527.6$+$2044 | $21\pm 2$ | 136 | 7 | 2
eMACSJ1756.8$+$4008 | $>19$ | $>79$ | 7 | 7
eMACSJ1831.1$+$6214 | $>18$ | $>133$ | 5 | 5
eMACSJ1852.0$+$4900 | $15\pm 2$ |  54 | 5 | 5
eMACSJ2229.9$-$0808 | $>11$ | $>27$ | 9 | 6
eMACSJ2316.6$+$1246 | $22\pm 3$ | 114 | 9 | 9
eMACSJ2327.4$-$0204 | $35\pm 4$ | 420 | 12 | 12
Table 2: Einstein radii at $z_{\rm source}=2$ and enclosed masses from our
strong-lensing analysis of all eMACS clusters with spectroscopically confirmed
multiple-image systems (PM = Parametric Model). We show entries as lower
limits where an obviously present second mass component is not included in our
lens model due to a lack of strong-lensing constraints. Also listed is $N_{\rm
mi}$, the number of multiple images used to constrain each model, and $N_{\rm
mi,z}$, the number of such images belonging to spectroscopically confirmed
multiple-image systems.

The impact of modeling uncertainties (specifically fixing the core radius of
cluster-scale mass components) on the Einstein radii derived for eMACS
clusters with few strong-lensing constraints is particularly strong for models
based on a single multiple-image system with a redshift much lower or higher
than our fiducial redshift of $z=2$.

That both real physical cluster characteristics and the lens-modeling
methodology affect the derived Einstein radii becomes apparent also when the
Einstein radii from our Lenstool analysis are compared to those obtained in a
previous strong-lensing analysis of almost the entire eMACS cluster sample
with the AStroLens package (Zalesky & Ebeling, 2020). Unlike Lenstool,
AStroLens uses a light-traces-mass approach that, although calibrated using a
small number of clusters with spectroscopically confirmed strong-lensing
features, relies entirely on the spatial distribution of light from the
cluster galaxies (as measured from ground-based imaging) to derive mass models
for eMACS clusters. As such, AStroLens provides an estimate of the global
lensing power on scales determined by the extent of the distribution of
cluster galaxies. Lenstool, by contrast, models the mass distribution in much
greater detail from actual strong-lensing features – but only within the
strong-lensing regime, i.e., the cluster core.

Figure 7: Comparison of Einstein radii estimated for a fiducial background
source at $z=2$ for 25 eMACS cluster using the parametric-modeling software
Lenstool ($R_{\rm E,PM}$) and the light-traces-mass package AStroLens ($R_{\rm
E,LTM}$). The dotted line marks the identity relation; the five most extreme
outliers, labelled in this graph, are discussed in Section 5.2. The blue error
bar in the upper left indicates the approximate statistical uncertainty of 25%
of the $R_{\rm E,LTM}$ values. Note that all AStroLens measurements shown in
this graph were scaled by a factor of 0.8 to remove a systematic bias relative
to the Lenstool results.

Comparing the Einstein radii estimated by the two methods for the eMACS
subsample listed in Table 2, we find a systematic offset between the results
from the two methods, in the sense that AStroLens on average overestimates the
Einstein radius by a factor of 1.26$\pm$0.12. Once this bias is
removed101010We note that the subsample of Table 2 includes nine of the ten
eMACS clusters that were used in the calibration of AStroLens (the tenth one
being eMACSJ0850.2, Fig. B12), and that discrepancies for this subset were, in
part, apparent and acknowledged in Zalesky & Ebeling (2020). , the results
show an overall correlation that is reassuring, given the differences in the
methodologies of the two analyses and in the underlying observational data
(Fig. 7). The scatter about the identity line (characterized by $R_{\rm
E,LTM}/R_{\rm E,PM}=1.00\pm 0.28$, where $R_{\rm E,LTM}$ denotes the rescaled
Einstein radii obtained with AStroLens) is substantial though and indicative
of small-scale structure in the majority of eMACS clusters, as expected for a
population of clusters that are actively growing through mergers and accretion
(see Sections 5.3 and 5.4). The comparison of AStroLens and Lenstool results
also highlights dramatically different Einstein radii measured by the two
algorithms for three clusters, labelled in Fig. 7 and reviewed in more detail
below. The more sophisticated strong-lensing analysis of eMACS clusters
presented in Basto et al. (in preparation) will improve upon the lens models
used here and allow a more robust investigation of systematic effects.

While the Einstein radii determined by the two methods are in good agreement
once the mentioned systematic bias is removed, Fig. 7 reveals a handful of
extreme outliers that warrant discussion. The most extreme one is
eMACSJ1212.5, the cause being mostly the Lenstool assumption of a core radius
of 200 kpc and the significant extrapolation from the measured redshift of
$z=1.2$ of the multiple-image system to the fiducial value of $z=2$, as
illustrated in Fig. 8. In addition, for compact clusters whose light
distribution is dominated by only one or two galaxies with little contribution
from other cluster members, the Einstein radius obtained with AStroLens
depends sensitively on the assumed scaling relations for the BCG. Hence, while
Lenstool likely overestimates the lensing strength of eMACSJ1212.5, the same
quantity is likely to have been underestimated by AStroLens.

Figure 8: The core of eMACSJ1212.5 (cf. Fig. B23) with tangential critical
lines for strong gravitational lensing of a background source at $z=1.195$
(the redshift of the observed multiple-image system) and $z=2$ overlaid in
cyan and yellow, respectively. For each source redshift, the critical line is
shown for cluster core radii of 60, 100, and 200 kpc. By design, the critical
lines for $z_{\rm src}=1.195$ satisfy the strong-lensing constraints for any
core radius.

A different systematic effect is likely responsible for two slightly less
extreme outliers in Fig. 7, eMACSJ0834.2 (Fig. B10) and eMACSJ1353.7 (Fig.
B27). Both systems are small-separation double clusters and active mergers
with very high velocity dispersions of $1590^{+140}_{-200}$ km s-1 and
$1600^{+110}_{-160}$ km s-1, respectively; both are also extremely X-ray
luminous (see Section 5.4). In addition, the lens models of both clusters are
constrained by robust strong-lensing constraints at 100-200 kpc, i.e., at much
larger radial distances than eMACSJ1212.5, and the redshifts of the lensed
sources are closer to our fiducial value of $z=2$ than in the case of
eMACSJ1212.5. As a result, the required extrapolations are much more modest,
and the large Einstein radii presented in Table 2 and Fig. 7 are not only less
uncertain but also consistent with all other known physical properties of
these clusters. The outlier status of eMACSJ0834.2 and eMACSJ1353.7 in Fig. 7
is thus likely to be due to AStroLens underestimating the lensing power of
line-of-sight mergers whose galaxy distribution (and hence light distribution)
is by necessity much less extended than that of similarly massive systems
colliding along an axis that is closer to the plane of the sky.

The cause of the discrepancy in the $R_{\rm E}$ values of the remaining two
clusters labeled in Fig. 7, eMACSJ1157.9 (Fig B21) and eMACSJ1756.8 (Fig. B35)
is less speculative and already hinted at by them being flagged as lower
limits in Table 2. The reason for the small Einstein radius of eMACSJ1157.9, a
system that is included in the list of the ten most powerful cluster lenses in
the analysis by Zalesky & Ebeling (2020), is simply the lack of spectroscopic
redshifts for several multiple-image systems readily identified in the HST
images, which cause the western cluster component to be completely absent from
the current, tentative Lenstool model (Fig. B21). Future spectroscopic follow-
up observations are bound to secure additional redshifts for strong-lensing
features in this area and help recover the full extent of the cluster mass
distribution. An even more dramatic outlier (in the same sense as
eMACSJ1157.9) is eMACSJ1756.8, shown in Fig. B35). Again at least half of the
mass distribution of this highly elongated system is missing from the
parametric lens model. However, in this case the reason is not a lack of
redshifts but an actual lack of strong-lensing features in the eastern half of
the cluster. The cause of this cluster’s outlier status in Fig. 7 thus appears
to be a physical property of the system, namely an unusually flat mass profile
that dramatically reduces the probability for strong gravitational lensing
around the eastern cluster core. A weak-lensing analysis is needed to test
this hypothesis and establish a robust total mass for this extreme merger.
Weak-lensing follow-up studies might also benefit other eMACS clusters that
appear to contain additional cluster-scale components that lack suitable
strong-lensing features, such as eMACSJ0943.3 (Fig. B15), eMACSJ1831.1 (Fig.
B38), or eMACSJ2229.9 (Fig. B42).

While the short list of eMACS clusters with Lenstool models presented here
contains several exceptional gravitational lenses, many other eMACS clusters
exhibit strong-lensing features that make them promising candidates for in-
depth follow-up studies. Among the systems with existing HST images, such
noteworthy clusters are eMACSJ0014.9 (Fig. B1), eMACSJ0031.2 (Fig. B3),
eMACSJ0121.4 (Fig. B4), eMACSJ0747.0 (Fig. B9), eMACSJ0850.2 (Fig. B12),
eMACSJ0934.6 (Fig. B13), eMACSJ1027.2 (Fig. B16), eMACSJ1131.1 (Fig. B19),
eMACSJ1144.2 (Fig. B20), eMACSJ1222.3 (Fig. B24), eMACSJ1414.7 (Fig. B28),
eMACSJ1419.2 (Fig. B29), eMACSJ1508.1 (Fig. B31), eMACSJ1732.4 (Fig. B34), and
eMACSJ1823.1 (Fig. B37).

###  5.3 ICM properties and relaxation state

An overview of the key cluster properties derived from the X-ray follow-up
observations described in Section 3.4 is given in Table 3. Since most of the
underlying CXO observations were obtained with the explicit (and modest) goal
of establishing point-source-subtracted cluster luminosities and assessing the
large-scale morphology of the ICM, the chosen ACIS-I exposure times are
relatively short for such faint targets.

Name | $z$ | $n_{\rm H}$ | $L_{\rm X,RASS}$ | $t_{\rm ACIS-I}$ | $r_{\rm 1000}$ | $f_{\rm X,CXO}$ | $L_{\rm X,CXO}$ |  k$T_{\rm X,CXO}$ | $M_{\rm X,CXO}(<r_{\rm 1000})$ | Morph.
---|---|---|---|---|---|---|---|---|---|---
|  |  ($10^{20}$ cm-2) | [0.1–2.4 keV] | (ks) | (kpc) | [0.5–7 keV] | [0.5–7 keV] | (keV) |  ($10^{14}$ M☉) | class
eMACSJ0014.9$-$0056 | 0.5330 | 2.95 |  6.2$\pm$1.9 | 29.3 |  884${}^{+77}_{-60}$ |  11.6${}^{+0.6}_{-0.5}$ |  13.0${}^{+0.6}_{-0.6}$ |  10.2${}^{+1.7}_{-1.4}$ |  7.0${}^{+2.0}_{-1.4}$ | 2
eMACSJ0030.5$+$2618 | 0.4970 | 3.47 |  4.6$\pm$1.7 | 15.6 |  626${}^{+78}_{-61}$ |  3.7${}^{+0.4}_{-0.4}$ |  3.5${}^{+0.4}_{-0.4}$ |  4.9${}^{+1.3}_{-0.9}$ |  2.4${}^{+1.0}_{-0.6}$ | 2
eMACSJ0042.5$-$1103 | 0.5701 | 2.54 |  6.9$\pm$2.0 | 11.9 |  865${}^{+248}_{-193}$ |  4.6${}^{+0.6}_{-0.6}$ |  6.0${}^{+0.8}_{-0.8}$ |  10.1${}^{+6.7}_{-3.9}$ |  6.9${}^{+7.8}_{-3.7}$ | 4
eMACSJ0045.2$-$0151 | 0.5471 | 2.71 |  5.2$\pm$2.0 | 49.4 |  613${}^{+38}_{-35}$ |  5.9${}^{+0.3}_{-0.3}$ |  7.1${}^{+0.3}_{-0.4}$ |  5.0${}^{+0.6}_{-0.6}$ |  2.4${}^{+0.5}_{-0.4}$ | 3
eMACSJ0135.2$+$0847 | 0.6185 | 4.87 |  7.9$\pm$2.5 | 11.5 |  582${}^{+82}_{-60}$ |  6.3${}^{+0.6}_{-0.5}$ |  10.1${}^{+0.9}_{-0.9}$ |  4.9${}^{+1.5}_{-1.0}$ |  2.2${}^{+1.1}_{-0.6}$ | 4
eMACSJ0248.2$+$0237 | 0.5561 | 5.09 |  6.6$\pm$3.0 | 44.5 |  621${}^{+45}_{-38}$ |  5.6${}^{+0.3}_{-0.3}$ |  6.9${}^{+0.4}_{-0.3}$ |  5.2${}^{+0.8}_{-0.6}$ |  2.5${}^{+0.6}_{-0.4}$ | 4
eMACSJ0256.7$-$1623 | 0.8621 | 4.29 |  19.6$\pm$6.9 | 32.2 |  546${}^{+127}_{-94}$ |  3.3${}^{+0.5}_{-0.4}$ |  11.9${}^{+1.9}_{-1.5}$ |  5.7${}^{+3.0}_{-1.8}$ |  2.5${}^{+2.1}_{-1.1}$ | 3
eMACSJ0256.9$-$1631 | 0.8670 | 4.32 |  18.3$\pm$6.6 | 32.1 |  56${}^{+13}_{-16}$ |  0.0${}^{+0.0}_{-0.0}$ |  0.0${}^{+0.1}_{-0.0}$ |  0.1${}^{+0.0}_{-0.0}$ |  0.0${}^{+0.0}_{-0.0}$ | $-$
eMACSJ0324.0$+$2421 | 0.9023 | 8.48 |  14.4$\pm$5.3 | 30.8 |  787${}^{+99}_{-94}$ |  6.0${}^{+0.4}_{-0.4}$ |  24.3${}^{+1.8}_{-1.6}$ |  12.5${}^{+3.4}_{-2.9}$ |  7.7${}^{+3.3}_{-2.4}$ | 3
eMACSJ0502.9$-$2902 | 0.6028 | 1.25 |  6.7$\pm$1.9 | 47.5 |  753${}^{+46}_{-43}$ |  9.9${}^{+0.4}_{-0.4}$ |  14.9${}^{+0.6}_{-0.6}$ |  8.0${}^{+1.0}_{-0.9}$ |  4.7${}^{+0.9}_{-0.8}$ | 3
eMACSJ0804.6$+$5325 | 0.5786 | 3.81 |  5.8$\pm$2.1 | 3.9 |  888${}^{+256}_{-174}$ |  9.3${}^{+1.2}_{-1.2}$ |  12.7${}^{+1.6}_{-1.7}$ |  10.8${}^{+7.0}_{-3.8}$ |  7.5${}^{+8.6}_{-3.6}$ | 4
eMACSJ0834.2$+$4524 | 0.6606 | 2.80 |  10.0$\pm$2.8 | 32.6 |  643${}^{+32}_{-30}$ |  14.6${}^{+0.5}_{-0.5}$ |  27.5${}^{+0.9}_{-1.0}$ |  6.2${}^{+0.7}_{-0.6}$ |  3.2${}^{+0.5}_{-0.4}$ | 4
eMACSJ0840.2$+$4421 | 0.6377 | 2.42 |  14.4$\pm$4.3 | 31.4 |  715${}^{+28}_{-30}$ |  8.8${}^{+0.4}_{-0.3}$ |  15.2${}^{+0.7}_{-0.5}$ |  7.5${}^{+0.7}_{-0.6}$ |  4.2${}^{+0.5}_{-0.5}$ | 2
eMACSJ0935.1$+$0614 | 0.7787 | 3.55 |  15.2$\pm$4.8 | 29.9 |  681${}^{+59}_{-47}$ |  9.3${}^{+0.5}_{-0.5}$ |  26.3${}^{+1.3}_{-1.4}$ |  8.1${}^{+1.5}_{-1.1}$ |  4.3${}^{+1.2}_{-0.8}$ | 3
eMACSJ1030.5$+$5132 | 0.5182 | 1.28 |  6.7$\pm$1.4 | 19.7 |  578${}^{+22}_{-21}$ |  12.7${}^{+0.4}_{-0.4}$ |  13.3${}^{+0.5}_{-0.5}$ |  4.3${}^{+0.4}_{-0.3}$ |  1.9${}^{+0.2}_{-0.2}$ | 1
eMACSJ1136.8$+$0005 | 0.5968 | 2.10 |  5.7$\pm$2.0 | 3.9 |  844${}^{+261}_{-174}$ |  7.0${}^{+0.9}_{-0.8}$ |  10.3${}^{+1.4}_{-1.2}$ |  10.0${}^{+7.2}_{-3.7}$ |  6.6${}^{+8.2}_{-3.3}$ | 4
eMACSJ1144.2$-$2836 | 0.5070 | 5.52 |  16.5$\pm$5.2 | 30.8 |  675${}^{+75}_{-63}$ |  4.7${}^{+0.4}_{-0.4}$ |  4.6${}^{+0.4}_{-0.4}$ |  5.7${}^{+1.3}_{-1.1}$ |  3.0${}^{+1.1}_{-0.8}$ | 4
eMACSJ1157.9$-$1046 | 0.5570 | 2.91 |  7.6$\pm$3.4 | 125.3 |  558${}^{+17}_{-17}$ |  10.3${}^{+0.3}_{-0.3}$ |  12.9${}^{+0.3}_{-0.4}$ |  4.2${}^{+0.3}_{-0.3}$ |  1.8${}^{+0.2}_{-0.2}$ | 4
eMACSJ1209.4$+$2640 | 0.5553 | 1.48 |  6.1$\pm$1.7 | 15.9 |  712${}^{+67}_{-50}$ |  11.2${}^{+0.7}_{-0.6}$ |  13.9${}^{+0.8}_{-0.8}$ |  6.8${}^{+1.3}_{-0.9}$ |  3.8${}^{+1.2}_{-0.7}$ | 3
eMACSJ1341.9$-$2442 | 0.8339 | 6.01 |  16.2$\pm$6.2 | 32.8 |  546${}^{+69}_{-53}$ |  3.3${}^{+0.3}_{-0.3}$ |  11.0${}^{+0.9}_{-0.9}$ |  5.6${}^{+1.5}_{-1.1}$ |  2.4${}^{+1.0}_{-0.6}$ | 4
eMACSJ1350.7$-$1055 | 0.8247 | 3.42 |  12.0$\pm$4.7 | 31.9 |  62${}^{+10}_{-18}$ |  0.0${}^{+0.1}_{-0.0}$ |  0.0${}^{+0.3}_{-0.0}$ |  0.1${}^{+0.0}_{-0.0}$ |  0.0${}^{+0.0}_{-0.0}$ | $-$
eMACSJ1353.7$+$4329 | 0.7364 | 1.14 |  9.0$\pm$2.5 | 40.1 |  694${}^{+51}_{-51}$ |  7.3${}^{+0.4}_{-0.4}$ |  18.0${}^{+0.9}_{-0.9}$ |  7.9${}^{+1.2}_{-1.1}$ |  4.3${}^{+1.0}_{-0.9}$ | 4
eMACSJ1407.0$-$0015 | 0.5520 | 3.57 |  6.0$\pm$2.0 | 3.9 |  849${}^{+409}_{-291}$ |  5.6${}^{+1.2}_{-1.4}$ |  6.8${}^{+1.5}_{-1.7}$ |  10.0${}^{+11.1}_{-5.8}$ |  6.4${}^{+14.4}_{-4.6}$ | 3
eMACSJ1414.7$+$5446 | 0.6121 | 1.41 |  10.2$\pm$0.6 | 32.6 |  846${}^{+60}_{-52}$ |  10.9${}^{+0.5}_{-0.5}$ |  17.1${}^{+0.8}_{-0.7}$ |  10.2${}^{+1.5}_{-1.2}$ |  6.8${}^{+1.5}_{-1.2}$ | 3
eMACSJ1508.1$+$5755 | 0.5421 | 1.60 |  7.3$\pm$1.5 | 47.3 |  797${}^{+52}_{-55}$ |  7.7${}^{+0.3}_{-0.3}$ |  9.0${}^{+0.4}_{-0.4}$ |  8.3${}^{+1.2}_{-1.1}$ |  5.2${}^{+1.1}_{-1.0}$ | 4
eMACSJ1527.6$+$2044 | 0.6967 | 4.55 |  8.0$\pm$3.6 | 24.5 |  741${}^{+78}_{-59}$ |  9.4${}^{+0.6}_{-0.5}$ |  20.2${}^{+1.3}_{-1.1}$ |  8.7${}^{+1.9}_{-1.3}$ |  5.0${}^{+1.8}_{-1.1}$ | 3
eMACSJ1756.8$+$4008 | 0.5743 | 3.28 |  8.6$\pm$1.8 | 126.1 |  799${}^{+18}_{-17}$ |  18.2${}^{+0.2}_{-0.2}$ |  24.4${}^{+0.3}_{-0.2}$ |  8.7${}^{+0.4}_{-0.4}$ |  5.4${}^{+0.4}_{-0.3}$ | 4
eMACSJ1823.1$+$7822-NE | 0.6803 | 3.02 |  †12.7$\pm$1.9 | 22.1 |  496${}^{+41}_{-33}$ |  5.0${}^{+0.3}_{-0.3}$ |  9.9${}^{+0.7}_{-0.6}$ |  3.8${}^{+0.6}_{-0.5}$ |  1.5${}^{+0.4}_{-0.3}$ | 1
eMACSJ1823.1$+$7822-SW | 0.6784 | 3.02 |  †12.7$\pm$1.9 | 22.1 |  534${}^{+62}_{-50}$ |  2.4${}^{+0.2}_{-0.3}$ |  4.8${}^{+0.5}_{-0.5}$ |  4.2${}^{+1.0}_{-0.7}$ |  1.8${}^{+0.7}_{-0.5}$ | 3
eMACSJ1831.1$+$6214 | 0.8207 | 4.15 |  18.8$\pm$2.2 | 22.0 |  718${}^{+61}_{-59}$ |  11.4${}^{+0.6}_{-0.6}$ |  36.7${}^{+1.9}_{-2.1}$ |  9.5${}^{+1.7}_{-1.5}$ |  5.3${}^{+1.5}_{-1.2}$ | 4
eMACSJ1852.0$+$4900 | 0.6035 | 3.90 |  6.3$\pm$1.7 | 19.8 |  596${}^{+64}_{-59}$ |  8.4${}^{+0.6}_{-0.7}$ |  12.7${}^{+1.0}_{-1.1}$ |  5.0${}^{+1.1}_{-0.9}$ |  2.3${}^{+0.8}_{-0.6}$ | 4
eMACSJ2026.7$-$1920 | 0.6219 | 4.14 |  10.3$\pm$3.4 | 31.8 |  541${}^{+31}_{-27}$ |  6.1${}^{+0.3}_{-0.3}$ |  9.9${}^{+0.5}_{-0.5}$ |  4.2${}^{+0.5}_{-0.4}$ |  1.8${}^{+0.3}_{-0.3}$ | 1
eMACSJ2220.3$-$1211 | 0.5292 | 3.78 |  5.2$\pm$2.0 | 12.4 |  934${}^{+228}_{-136}$ |  10.0${}^{+1.0}_{-0.9}$ |  11.0${}^{+1.1}_{-1.0}$ |  11.3${}^{+6.2}_{-3.1}$ |  8.2${}^{+7.7}_{-3.1}$ | 2
eMACSJ2315.3$-$2128 | 0.5400 | 1.72 |  13.8$\pm$5.4 | 30.8 |  952${}^{+276}_{-183}$ |  3.1${}^{+0.4}_{-0.4}$ |  3.6${}^{+0.4}_{-0.4}$ |  11.9${}^{+7.9}_{-4.1}$ |  8.9${}^{+10.2}_{-4.2}$ | 3
eMACSJ2320.9$+$2912 | 0.4960 | 7.35 |  5.5$\pm$1.6 | 9.6 |  709${}^{+115}_{-88}$ |  14.6${}^{+1.3}_{-1.5}$ |  13.8${}^{+1.3}_{-1.4}$ |  6.2${}^{+2.2}_{-1.5}$ |  3.5${}^{+2.0}_{-1.1}$ | 3
eMACSJ2327.4$-$0204 | 0.7055 | 4.62 |  14.0$\pm$4.1 | 138.9 |  679${}^{+16}_{-16}$ |  17.8${}^{+0.3}_{-0.4}$ |  39.4${}^{+0.8}_{-0.8}$ |  7.3${}^{+0.4}_{-0.4}$ |  3.9${}^{+0.3}_{-0.3}$ | 2
Table 3: Global physical characteristics of eMACS clusters from CXO/ACIS-I
data available at the time of publication; $n_{\rm H}$ values represent the
Galactic neutral-hydrogen column density (HI4PI Collaboration et al., 2016);
all X-ray fluxes (unabsorbed) and luminosities are listed in units of
$10^{-13}$ erg s-1 cm-2 and $10^{44}$ erg s-1, respectively. Errors correspond
to $1\sigma$ confidence. We list the properties of the two components of the
double cluster eMACSJ1823 separately; note, however, that the listed RASS flux
(marged with a †symbol) is the same and duplicated for both entries, since
this source is not resolved in the RASS. See Ebeling et al. (2007) for a
description of the morphological classification listed in the final column. An
estimate of the total cluster mass within $r_{\rm 200}$ can be obtained by
doubling $M_{\rm 1000}=M(<{\rm r_{1000}})$ (see Section 5.3).

####  5.3.1 ICM temperature and luminosity; cluster mass

Although the global cluster luminosities and ICM temperatures presented here
should be considered tentative (our analysis is unable to account for low-
surface-brightness emission from the cluster outskirts, or for cool cores,
shock-heated gas, and any other temperature variations), the results are in
good agreement with the $L_{\rm X}$-k$T$ relation established for other X-ray
selected cluster samples. As shown in Fig. 9, eMACS extends the $L_{\rm
X}$-k$T$ relation for galaxy clusters to higher luminosities and higher ICM
temperatures than probed by existing X-ray selected cluster samples at
$z>0.5$.

The results of our X-ray analysis summarized in Table 3 also unambiguously
confirm that eMACS achieved its goal of probing both the redshift-X-ray
luminosity and the redshift-mass regime highlighted in Fig. 1. As shown in
Figs. 3 and 9, the point-source corrected X-ray luminosities of eMACS clusters
are of the order of $10^{45}$ erg s-1, consistent with the eMACS target range
shown in Fig. 1 (left). The same holds for the cluster masses. Although the
existing CXO observations allow direct measurements of the cluster mass (under
the assumption of hydrostatic equilibrium) only to a radius of $r_{\rm 1000}$,
$M_{\rm 200}$ can be estimated through extrapolation of the universal cluster
mass profile to $r_{\rm 200}$ which approximately doubles these values (e.g.,
Pointecouteau et al., 2005; Ettori et al., 2019), yielding total masses in
excess of $10^{15}$ M⊙ for over one third of the subset for which CXO data are
currently available (Fig 10). We note that this extrapolation assumes the NFW
profile found to describe the mass distribution in relaxed clusters (Navarro
et al., 1997); for disturbed systems (of which eMACS found many; see below),
the increase in the enclosed mass from $r_{\rm 1000}$ to $r_{\rm 200}$ would
be even higher. Since our follow-up observations with CXO targeted
preferentially the most distant and most X-ray luminous clusters, the mass
distribution shown in Fig 10 should, however, not be taken as representative
of the eMACS sample as a whole.

Figure 9: Bolometric luminosities and global ICM temperatures measured by us
for the subsample of 35 eMACS clusters observed with CXO, overlaid on the
$L_{\rm X}$–k$T$ relation determined by Takey et al. (2013) for a sample of
345 clusters detected with XMM-Newton (reproduced from Takey et al., 2013).
Note that, unlike Takey and collaborators, we measured both quantities within
$r_{\rm 1000}$. Figure 10: Distribution of total cluster masses ($M_{\rm
200}$) for the 33 eMACS clusters observed with CXO/ACIS-I to date (see Table
1). $M_{\rm 200}$ is estimated from $M_{\rm 1000}$ (Table 3) by extrapolating
the universal cluster mass profile (e.g., Pointecouteau et al., 2005; Ettori
et al., 2019) from $r_{\rm 1000}$ to $r_{\rm 1000}$. The vertical line marks
the mass of $10^{15}$ M⊙ referred to in Section 1 and highlighted as
characteristic for the eMACS target regime in mass-redshift space (Fig. 1,
right).

####  5.3.2 Relaxation state

We show in Fig. 11 the X-ray surface brightness for all eMACS clusters with
CXO/ACIS-I data. Note the wide range of morphologies, from almost perfectly
circular and strongly peaked (e.g., eMACSJ1030.5, eMACSJ2026.7) to extremely
disturbed (e.g., eMACSJ1157.9, eMACSJ1508.1, eMACSJ1756.8). Also noteworthy
are two fields which show no diffuse ICM emission at all, eMACSJ0256.9 and
eMACSJ1350.7; we discussed these eMACS misidentification earlier in Section
5.1.2 within the larger context of contamination from X-ray point sources.

Recognizing the futility of a sophisticated ICM substructure analysis based on
(typically) a few thousand photons, we adopt the simple but robust visual
classification scheme of Ebeling et al. (2007) and assign each cluster a
morphological classification from 1 (fully relaxed) through 4 (highly
disturbed), based on X-ray and optical appearance, as well as X-ray/optical
alignment. The resulting classification is indicated both in Fig. 11 and in
Table 3.

Figure 11: Contours of the adaptively smoothed X-ray surface brightness in the
0.5–7 keV band from the CXO observations described in Section 3.4. Contours in
this and all subsequent figures are logarithmically spaced by factors of 1.2,
starting at three times the background level. The 12 clusters previously
discovered in the MACS project (Ebeling et al., 2007) are included only for
completeness’ sake and shown in gray. The morphological class assigned to each
cluster is shown in the upper right corner of each panel. (Note that we again
exclude the 12 MACS clusters that, by design, are also part of the eMACS
sample.)

The low fraction of fully relaxed systems (morphological class 1) is
immediately apparent, indicating that massive clusters at $z>0.5$ are
undergoing vigorous growth through the accretion of surrounding structures. At
face value, the dominance of disturbed systems seems to contradict claims that
X-ray selected clusters samples suffer from a strong “cool-core bias” in favor
of relaxed clusters at higher redshift (Rossetti et al., 2017; Andrade-Santos
et al., 2017). This claim is disputed though, as it may attribute erroneously
to X-ray selection what is in fact caused by Malmquist bias: indeed, volume-
complete (as opposed to flux limited) samples of X-ray selected clusters were
found to be dominated not by cool-core clusters but by dynamically active,
disturbed systems (Chon & Böhringer, 2017). As is, the data shown in Fig. 11
cannot be used to assess the validity of either claim, since eMACS is not
volume complete and since the subset of eMACS clusters with existing CXO data
is biased in favour of disturbed systems simply as a result of the scientific
goals of the underlying CXO proposals. A subset with (almost) complete CXO
coverage can, however, be defined by considering only the most X-ray luminous
eMACS clusters. As shown in Fig. 12, only one of the 12 clusters in the almost
volume-complete subsample of eMACS clusters with $L_{\rm X,RASS}>1.1\times
10^{45}$ erg s-1 is classified as fully relaxed (morphological class 1). Of
the two systems without CXO data (both visible at $z\sim 0.7$ in Fig. 12), one
(eMACSJ0252.4, shown in Fig. 13) can be safely assumed to be highly relaxed
(morphology class 1 or, at most, 2), based on the analysis of Ebeling et al.
(2021) and the strong optical emission lines from its BCG, while the other
(eMACSJ2025.5) is a very improbable candidate for the same classification,
based on its optical appearance (see Fig. B41).

Figure 12: As Fig, 1 (left) but focusing solely on eMACS and highlighting the
subset of eMACS clusters observed with CXO/ACIS-I (coloured symbols). The 19
clusters with $L_{\rm X,RASS}>1.1\times 10^{45}$ erg s-1 (an additional two,
shown as open circles, are the misidentifications discussed in Section 5.1.2),
form an almost complete subsample of which only two are lacking CXO data. The
12 MACS clusters at $z>0.5$ are shown as stars. Very few of the most X-ray
luminous eMACS clusters exhibit a relaxed X-ray morphology. Figure 13: The
core of eMACSJ0252.4$-$2100, as viewed with HST; overlaid is the critical line
(for a source at $z=3.46$) from a lens model constrained by the two marked
multiple-image systems (figure reproduced from Ebeling et al., 2021). Although
no CXO data are available for eMACSJ0252 at present, the optical appearance
and extreme dominance of the BCG suggest this system is very likely to have a
morphological class of 1.

A conservative conclusion is thus that the fraction of cool-core clusters does
not significantly exceed 10% among the most X-ray luminous clusters at $z>0.5$
(2 of 19), in agreement with the findings of Mann & Ebeling (2012). A decrease
in the fraction of relaxed systems as we approach the redshift of formation
for massive clusters is not only plausible on evolutionary grounds, but also
firmly expected from the impact of mergers in the rapidly evolving exponential
tail of the most massive clusters. Such events boost, temporarily but
dramatically, both the X-ray luminosity and the ICM temperature of the
respective systems (Randall et al., 2002), thereby creating the opposite of a
“cool-core bias” (Fedeli & Bartelmann, 2007).

###  5.4 The most X-ray luminous eMACS clusters

We here provide a brief overview highlighting the ten most X-ray luminous
systems111111These systems fall precisely into the extreme regime of the
$L_{\rm X}$-$z$ parameter space targeted by the eMACS project and highlighted
in Fig. 1. with $L_{\rm X,CXO}\geq 1.5\times 10^{45}$ erg s-1, several of
which were previously highlighted in Zalesky & Ebeling (2020), but note that
an eleventh cluster, the massive merger eMACSJ0502.9 (Fig. B8), makes the same
luminosity cut, too. A visual summary of this subsample is shown in Fig. 14;
additional details for each cluster can be found in Appendix B. A more
comprehensive analysis and discussion of the properties of the most X-ray
luminous eMACS clusters121212Note that the subset of the most X-ray luminous
eMACS clusters selected from RASS data and highlighted in Fig. 12 differs from
the one drawn from the CXO-based X-ray luminosities listed in Table 3 and
considered here and by Basto and collaborators. Although the X-ray fluxes
recorded in the RASS and those derived from follow-up CXO observations are
correlated, both photon noise and contamination from (possibly time variable)
X-ray point sources introduce substantial scatter, as shown in Fig. 3.
Interestingly, the subset of the most X-ray luminous eMACS clusters drawn from
RASS data (Fig. 12) includes not only both of the eMACS misidentifications but
also both of the most dramatic outliers from the mentioned correlation (see
Fig. 3). is given by Basto et al. (in preparation).

Figure 14: HST images of the ten most X-ray luminous eMACS clusters (based on
point-source corrected fluxes measured from CXO observations). Overlaid in
gray and yellow are isointensity contours of the adaptively smoothed X-ray
emission and the critical line for gravitational lensing of a source at a
fiducial redshift of $z=2$, respectively.

####  5.4.1 eMACSJ0324.0$+$2421

eMACSJ0324.0 deserves special mention for being the only galaxy cluster at
$z>0.9$ not merely detected, but in fact discovered in the RASS. Fig. B7
summarizes the observational evidence for this system (see also Fig. 14). Two
almost equally luminous BCG candidates, a disturbed ICM morphology that
nonetheless features only a single X-ray peak, a very high global gas
temperature of $(13\pm 3)$ keV, a very large Einstein radius and very high
enclosed mass of $M(<240\,{\rm kpc})=4.6\times 10^{14}$ M⊙ derived from a lens
model constrained by two spectroscopically confirmed multiple-image systems
(see Section 5.2), and an exceptionally high velocity dispersion of
$1520^{+150}_{-220}$ km s-1 all suggest that eMACSJ0324.0 is an actively
growing, massive cluster, observed in the post-collision phase (but still
close to core passage) of a merger that proceeds largely along our line of
sight.

####  5.4.2 eMACSJ0834.2$+$4524

The appearance of eMACSJ0834.2 (Fig. B10, see also Fig. 14 and Section 5.2)
provides ample and unambiguous evidence of an ongoing collision of two
components of comparable mass. Although our strong-lensing mass model is
unable to resolve multiple cluster-scale components, two well separated peaks
are observed in the X-ray surface brightness. The offsets of these peaks in
the ICM density from the BCGs of the two subclusters are indicative of a
collision axis that lies at least partly in the plane of the sky. A line-of-
sight component of the merger-induced peculiar velocities is, however, also
likely, given the very high velocity dispersion of $1590^{+140}_{-200}$ km
s-1. We note the quite modest ICM gas temperature of ($6.2\pm 0.7$) keV; such
a low global temperature could be indicative of the presence of cool cores
(the eastern component of e0834 exhibits a noticeably compact X-ray peak) and
points to the absence of large amounts of shock-heated gas. We thus speculate
that we either observe the merger well before first core passage or that the
collision involves a large impact parameter, thereby leaving the cluster cores
relatively unperturbed, even after several core passages.

Owing to the system’s highly disturbed morphology, our best-fitting lens model
is characterized by a large Einstein radius and a high enclosed mass of
$M(<220\,{\rm kpc})=3.2\times 10^{14}$ M⊙.

####  5.4.3 eMACSJ0840.2$+$4421

While not fully relaxed (note the absence of a pronounced X-ray peak and the
non-circular geometry apparent in Fig. B11 and Fig. 14), eMACSJ0840.2 is one
of the least disturbed clusters in this subset of the most X-ray luminous
eMACS clusters. Both the excellent X-ray/optical alignment and the substantial
but (for a cluster of this size) modest ICM temperature of $(7.5\pm 0.7)$ keV
suggest that eMACSJ0840.2 is observed well past its most recent merger event.
Two spectroscopically confirmed multiple-image systems constrain the mass in
the cluster core to $M(<80\,{\rm kpc})=4\times 10^{13}$ M⊙. Since the velocity
dispersion of $(1320\pm 120)$ km $s^{-1}$ (based on 39 redshifts) of
eMACSJ0840.2 is unlikely to be inflated by ongoing merging activity along the
line of sight, we can use the virial scaling relation to compute an estimate
of the dynamical mass of the system (Evrard et al., 2008; Saro et al., 2013).
The result, $M_{\rm dyn}=(2.6\pm 0.1)\times 10^{15}$ M⊙, places eMACSJ0840.2
in the top tier of massive clusters at any redshift (see Fig 1).

####  5.4.4 eMACSJ0935.1$+$0614

Exceptionally X-ray luminous, in particular given its high redshift of
$z=0.78$, eMACSJ0935.1 is one of two eMACS clusters in our Top Ten list that
do not currently have a lens model. The CXO data for this system show neither
a compact core nor pronounced substructure in the ICM (Fig. 14); however,
markedly elliptical X-ray surface-brightness contours, as well as a clear
offset of the X-ray peak from the BCG, still identify eMACSJ0935.1 as a
dynamically disturbed cluster (Fig. B14). The cluster core features neither an
extremely luminous BCG nor signs of strong gravitational lensing, suggesting a
shallow mass profile that may be the result of mergers of several clusters of
moderate mass.

####  5.4.5 eMACSJ1353.7$+$4329

eMACSJ1353.7, previously discussed in Section 5.2, has one of the highest
velocity dispersions of any eMACS cluster (see Section 5.5.1); however, closer
inspection of all available data (Fig. B27) suggests that the measured value
of $1600^{+110}_{-160}$ km s-1 is inflated by an infalling group. The cluster
exhibits the textbook signature (a single X-ray peak between two BCGs, Fig.
14) of what is probably a late-stage merger close to the plane of the sky. The
two BCGs are at essentially the same redshift ($z=0.736$ and $z=0.739$); the
looser group of galaxies to the East, however, features redshifts close to
$z=0.75$, adding a pronounced and narrow peak to the radial-velocity histogram
that we interpret as evidence of infall of a foreground group of galaxies. The
lens model for eMACSJ1353.7, well constrained by three multiple-image systems,
one of which is spectroscopically confirmed, yields a very high enclosed mass
of $M(<250\,{\rm kpc})=4.3\times 10^{14}$ M⊙ for this powerful gravitational
lens. The not exceptionally high ICM temperature of ($7.9\pm 1.2$) kev
measured by us suggests that this ongoing merger is observed well after the
temporary temperature boost triggered by the initial collision.

####  5.4.6 eMACSJ1414.7$+$5446

Like for eMACSJ1353.7, the extreme velocity dispersion measured for
eMACSJ1414.7 ($1700^{+180}_{-210}$ km s-1) is likely inflated by peculiar
velocities from an ongoing merger proceeding along an axis that lies close to
our line of sight. Although strong-lensing features are clearly discernible
near the cluster core (Fig. B28), we currently have no spectroscopically
confirmed multiple-image system that could anchor a lens model for
eMACSJ1414.7 The fact that the X-ray peak of eMACSJ1414.7 is offset to the
West of the BCG (Fig. 14), with no obvious second cluster core apparent in
this direction in the galaxy distribution, might indicate a collision at a
significant impact parameter. The gap in the radial-velocity histogram and the
high global ICM temperature of 10 keV suggest that the eMACSJ1414.7 merger is
either observed shortly after the first core passage or prior to a second
collision with an infalling group of galaxies.

####  5.4.7 eMACSJ1527.6$+$2044

eMACSJ1527.6 is another eMACS cluster with an exceptionally high velocity
dispersion, $1580^{+190}_{-230}$ km s-1, but, in contrast to eMACSJ1353.7 and
eMACSJ1414.7, without clear signs of line-of-sight substructure in the radial-
velocity histogram (Fig. B32). Since the ICM temperature of
($8.7^{+1.9}_{-1.3}$) keV is above average, even for massive clusters, we
tentatively conclude that eMACSJ1527.6 is an active merger observed during or
shortly after first core passage. Although we cannot rule out that the absence
of multiple peaks in the X-ray surface brightness distribution (Fig. 14) is
primarily the result of the very short CXO/ACIS-I exposure time of only 25 ks,
the presence of several BCG candidates in close proximity in the cluster core
suggests, in conjunction with the very velocity dispersion, that the merging
clusters are on trajectories that would make them difficult to separate even
in a much deeper X-ray observation. Strong-lensing constraints from three
multiple-image systems (one of them spectroscopically confirmed) yield a lens
model of eMACSJ1527.6 that is markedly more elongated than the ICM
distribution (Fig. B32). A discrepancy between the collisonal and
collisionless mass components of this kind is a textbook characteristic of
ongoing merger activity.

####  5.4.8 eMACSJ1756.8$+$4008

eMACSJ1756.8 is an obvious large-separation merger and the most powerful
cluster lens in the eMACS sample according to AStroLens. Although we invested
substantial resources into spectroscopic follow-up observations of the strong-
lensing features identified in this system (Figs. 6 and B35), the lack of
multiple-image systems near the eastern cluster core prevents us from
constraining the mass in the presumably dominant part of this highly extended
system (see also Section 5.2. As a result, the Einstein radius and enclosed
mass listed for eMACSJ1756.8 in Table 2 should be considered firm lower
limits. A very high total mass is expected also from the X-ray estimate of
$5.4\times 10^{14}$ M⊙ for the total cluster mass (Table 3) and the very high
velocity dispersion of $1400^{+80}_{-90}$ km s-1, which is based on 117
spectroscopic redshifts, the largest number available for any eMACS cluster.
The wide (optical) separation of the three cluster cores in the plane of the
sky (800 kpc altogether), the location of the X-ray peak between two of them,
and the high ICM temperature of ($8.7\pm 0.4$) keV identify eMACSJ1756.8
unambiguously as a linear, post-collision merger of as many as three galaxy
clusters.

####  5.4.9 eMACSJ1831.1$+$6214

Although narrowly beaten to the title of “most X-ray luminous eMACS cluster”
by eMACSJ2327.4 (see below), eMACSJ1831.1 ($L_{\rm X,CXO}=(3.7\pm 0.2)\times
10^{45}$ erg s-1) stands out as one of only a handful exceptionally massive
clusters known at $z>0.8$. As is apparent from Fig. B38 eMACSJ1831.1 (not to
be confused with eMACSJ1831.9, Fig. B39) is a highly complex system that
consists of at least two components, as evinced by its very disturbed X-ray
morphology and the presence of several optical cluster cores (Fig. 14). Both
X-ray peaks are shallow and far from the closest BCG candidate, indicative of
a pronounced segregation of collisional and non-collisional matter that is
only observed in active mergers. Like eMACSJ1756.8 (Sections 5.2 and 5.4.8),
eMACSJ1831.1 lacks prominent strong-lensing features near two of its apparent
optical cores, causing the associated cluster-scale mass concentrations to be
missing from the Lenstool model (the respective Lenstool results are marked as
lower limits in Table 2). Spectroscopic confirmation of a faint straight arc
that appears to mark a saddle point in the potential close to the NE X-ray
peak (cf. Fig. B38) would greatly improve the current, incomplete lens model
of this exceptional system. The complexity of eMACSJ1831.1 ($z=0.8207$) is
reflected also in redshift space, where the discovery of a superimposed
background cluster at $z=0.858$ suggests that the system is part of an even
more extended large-scale structure.

####  5.4.10 eMACSJ2327.4$-$0204

The most X-ray luminous eMACS cluster, eMACSJ2327.4 (Fig. B45), was known
previously and published as RCS2 J2327 by Gilbank et al. (2011). For
completeness’ sake we show in Fig. 14 (and in Fig. B45) the archival CXO data
and a simple lens model based on the multiple-image systems at $z=1.42$ and
$z=2.98$ (Fig. 6) identified by Sharon et al. (2015). Since RCS2 J2327 is a
well known powerful gravitational lens, we refer the reader to the literature
for details of its physical properties.

###  5.5 Cluster galaxy properties

The spectroscopic follow-up observations of galaxies in the fields of eMACS
(candidate) clusters (see Section 3.3) served multiple purposes, the most
fundamental of which was the confirmation of the cluster ID and the
establishment of a cluster redshift above the $z=0.5$ threshold set for eMACS.
Subsequent spectroscopic observations targeted not only the clusters’ galaxy
population in general (to measure velocity dispersions and search for
substructure along the line of sight) but also specific galaxies of interest,
such as the brightest cluster galaxies (BCGs); possible cases of ongoing ram-
pressure stripping of infalling galaxies; potential AGN within (or
superimposed onto) the cluster flagged as X-ray point sources; and of course
strong-lensing features (i.e., highly amplified background galaxies) whose
redshifts are crucial to constrain the cluster mass distribution (Section 4.3)

Although an exhaustive discussion of the findings of all these studies is
beyond the scope of this paper, we present brief summaries and highlights in
the following sections.

####  5.5.1 Velocity dispersion and line-of-sight substructure

Figure 15: Histograms of the radial velocities for eMACS clusters with at
least 30 spectroscopic redshifts. We list for each cluster the velocity
dispersion in units of km s-1 and, in the upper left corner of each panel, the
probability of the redshift histogram within $\delta z=\pm 0.02$ of the
systemic cluster redshift being drawn from a Gaussian distribution, as well as
the morphological class of each cluster from Fig. 11, where available.

While a robust systemic cluster redshift can be derived from a handful of
concordant redshifts, a credible velocity dispersion requires much better
statistics and should ideally also be computed from a stellar-mass-limited and
spatially complete sample, in order to avoid biases introduced by an over-
representation of galaxies near the cluster core or, conversely, the cluster
outskirts. Since our selection of galaxies for spectroscopic follow-up was
largely driven by technical constraints (spectrograph characteristics) and our
desire to maximize efficiency by simultaneously advancing all science goals
served by these observations, the set of cluster galaxies with spectroscopic
redshifts is statistically not well defined. Specifically, in clusters with
few spectroscopic redshifts (fewer than 20) the dense cluster cores are likely
to be undersampled, leading to potentially systematically low velocity
dispersions.

We show in Fig. 15 the radial-velocity histograms of the 24 eMACS clusters for
which at least 30 spectroscopic redshifts have been secured. At present
eMACSJ2229.9 is the only eMACS cluster for which multiple components along the
line of sight can be clearly resolved with the radial-velocity data in hand.
Fig. B42 summarizes our knowledge of this system, a superposition of two
clusters at $z=0.595$ and $z=0.625$. No CXO data have been obtained for this
system to date; however, the presence of RASS 6135 (Villforth et al., 2017), a
luminous QSO that is in fact a member of the $z=0.625$ component of this
double cluster, suggests a significant point-source contribution to the X-ray
luminosity recorded in the RASS. A prominent fold arc at $z=3.375$ (dubbed
“The Scream” by us, in homage to Edvard Munch’s famous painting) with an
obvious counterimage to the north, together with a second triple image at
$z=5.166$, constrain a highly elongated Lenstool model131313Our strong-lensing
analysis supersedes the one presented by Griffiths et al. (2021) which is
based on an erroneous redshift for The Scream. that, however, does not fully
reflect the mass distribution of both cluster components acting in projection
along our line of sight (Section 5.2 and Table 2).

While the statistics of the radial-velocity data shown in Fig. 15 are too poor
to clearly reveal line-of-sight substructure in any other eMACS cluster, the
probability (as estimated by the Shapiro-Wilk statistic; Shapiro & Wilk, 1965)
of the observed set of redshifts having been drawn from a normal distribution
is a useful diagnostic to complement the morphological classification based on
a cluster’s optical and X-ray appearance in projection on the sky (Section 5.3
and Fig. 11). As can be seen in Fig. 15, a disturbed morphology in the plane
of the sky is not strongly correlated with significant substructure also along
the line of sight: of the nine eMACS clusters in morphological class 3 or 4,
only three have radial-velocity distributions that fail the Shapiro-Wilk
normality test at greater than 95% confidence ($p_{\rm N}<0.05$). Conversely,
however, all eMACS clusters that fail the test and have been observed with CXO
(eMACSJ1353.7, eMACSJ1508.1, and eMACSJ2320.9) are classified as heavily
disturbed based on the X-ray / optical apperance, and the remaining two with
$p_{\rm N}<0.05$ that have no CXO data as of yet (eMACSJ1709.5, Fig. B33, and
eMACSJ1732.4, Fig. B34) show the same highly complex galaxy distribution
associated with a morphological classification of 3 or 4. We tentatively
conclude that the collisions in progress in these systems proceed along axes
that are oblique with respect to both our line of sight and the plane of the
sky. For the remaining eMACS clusters in morphology class 3 and 4, the good
statistical agreement of the observed radial-velocity distributions with a
Gaussian suggests that the respective merger activity occurs predominantly in
the plane of the sky. These numbers are roughly consistent with isotropy in
the orientation of the merger axis. Interestingly, the complementary (if
small) subsample of the five eMACS clusters with at least 30 spectroscopically
confirmed cluster members and a relaxed or only mildly disturbed morphology
(morphology class 1 or 2) passes the Shapiro-Wilk normality test without
exception.

Although encouraging, our insights into line-of-sight substructure remain
qualitative even for the small subset of eMACS clusters targeted most heavily
in our spectroscopic follow-up observations. Much more extensive redshift
surveys of almost all eMACS clusters and their surroundings will be required
to map the environment in which eMACS clusters are embedded and the pathways
along which they accrete the matter that fuels their growth.

####  5.5.2 Large-scale structure

On much larger scales than typically probed by our spectroscopic follow-up
observations of individual clusters (see Section 3.3), a glimpse of the cosmic
web (Bond et al., 1996) is ironically provided with assistance from one of the
non-clusters in the eMACS sample, eMACSJ0256.9. Although no diffuse X-ray
emission is detected from eMACSJ0256.9 in our CXO follow-up observation (see
Section 5.1.2), an overdensity of galaxies is clearly discernible both in our
HST images and in the histogram of radial velocities of galaxies in this field
(Fig. B6). We conclude that eMACSJ0256.9 is likely a filamentary structure
aligned with our line of sight that masquerades as a three-dimensional
overdensity only in this projection. Although eMACSJ0256.9 is thus not a
three-dimensionally collapsed mass concentration, it appears to be a cluster
in the process of formation, as indicated by the high velocity dispersion of
$1170^{+140}_{-240}$ km s-1 measured for galaxies in this structure. The
presence of an actively evolving filament is of interest in the context of
interconnected large-scale structure since eMACSJ0256.9$-$1631 ($z=0.867$) is
only 6 Mpc (13′) away in projection from eMACSJ0256.7$-$1623 ($z=0.862$), an
intrinsically massive cluster (Fig. B5). This separation amounts to only about
three times the virial radius of eMACSJ0256.7, rendering matter overdensities
within the putative massive filament candidates for accretion onto the node of
the cosmic web marked by eMACSJ0256.7 within the next few Gyr.

While (after evaluation of the CXO data) eMACSJ0256.9$-$1631 and
eMACSJ0256.7$-$1623 remain a pair in the eMACS catalogue only by virtue of the
commonality of a high velocity dispersion, eMACSJ1823.1 ($z=0.680$, Fig. B37)
is a true cluster pair, and the only obvious pre-collision double cluster in
our sample. Separated by 865 kpc in projection, both components appear
dynamically relaxed, with the dominant north-eastern cluster exhibiting
evidence of a cool core. Although the radial-velocity histograms show no sign
of substructure along the line of sight (Fig. B37), the very high velocity
dispersion of the NE component ($\sigma>1500$ km s-1) suggests peculiar
velocities (bulk motions) along the line of sight, a notion that is supported
by the presence of a nearby foreground structure at $z=0.65$. eMACSJ1823.1
thus marks a node of the cosmic web that might be actively accreting matter
from orthogonal directions.

Figure 16: Close-up view (100 kpc on a side) of notable eMACS BCGs, as seen
with HST. Evidence of dust obscuration is found in the majority of these
galaxies. eMACSJ1057.5 and eMACSJ1148.0 show extended blue filaments to the
north-east and south of the BCG, respectively, comparable to systems at lower
redshift (O’Dea et al., 2010). All are detected in either our JVLA radio
observations or VLASS data.

####  5.5.3 Brightest Cluster Galaxies

All X-ray selected samples of galaxy clusters contain clusters dominated by a
BCG, these frequently display strong optical emission lines, star formation,
and an associated reservoir of cold molecular gas (e.g., Crawford et al.,
1999; Green et al., 2016). As demonstrated in the MUSE study of eMACSJ0252.4
(Ebeling et al., 2021, Fig. 13), such “active” BCGs are seen out to $z\sim
0.7$ and stand out in the optical regime as bluer than the expected colour of
an evolved stellar population.

Our spectroscopic follow-up covers all BCGs in eMACS apart from those in
eMACSJ0934.6, which has a published SDSS spectrum, and eMACSJ1852.0 which at
present has no publicly available spectrum. For 17 of the 110 BCGs in the
sample these spectra show significant [Oii]$\lambda$3727 line emission,
indicating star formation comparable to that seen in the most active BCGs at
lower redshifts (Green et al., 2016), where H$\alpha$ line emission is
typically used to gauge this activity. If we take the presence of an active
BCG as an indicator of cluster relaxation, this spectroscopic estimate of the
fraction of cool-core clusters of (15$\pm$4)% is consistent with the
percentage estimated from X-ray imaging (approximately 10%) in Section 5.3.
While the fraction of cool-core clusters is often found to be higher at lower
redshifts, these more local studies benefit from both the accessibility of the
H$\alpha$ line and more extensive X-ray observations.

Radio emission from 28 BCGs in our sample is detected at $>5\sigma$ or
150$\mu$Jy in the JVLA observations at 5 GHz. With 66 systems having been
observed, this number corresponds to a detection rate of (42$\pm$8)%,
comparable to the detection rate at the same observed frequency reported by
Hogan et al. (2015a) for the most X-ray luminous clusters at $z<0.3$. The
range in radio spectral index and the mean radio spectral index of
$\alpha=-0.95$, computed using available RACS, VLASS, TGSS, and LOFAR data for
the detected sources, are also comparable to those found in previous studies.
Of the remaining 45 clusters without a JVLA observation, 11 (i.e., 24%) have a
VLASS detection at 3 GHz at the higher flux density limit of 0.5 mJy reached
in that all-sky survey, suggesting a comparable radio-power distribution for
the sample as a whole.

Several BCGs in the eMACS sample in addition to eMACSJ0252.4 (Ebeling et al.,
2021, Fig. 13) are notable in their optical morphology. Specifically,
eMACS1030.5 (Figs. 16, B17 harbors a spectacular case of an active BCG and is
the brightest radio source in the eMACS sample, with properties comparable to
those of compact, core-dominated sources such as 4C$+$55.16 (Hogan et al.,
2015b; Rose et al., 2022; Timmerman et al., 2022) and MACSJ0242.5 (Allingham
et al., 2023). Signs of active star formation, dust or multiple cores are
discernible in the HST images of other eMACS BCGs, demonstrating that “active”
BCGs are common at $z>0.5$; Fig. 16 shows 100 kpc $\times$ 100 kpc cutouts
from our HST images for several examples.

####  5.5.4 Ram-pressure Stripping

In addition to being prime targets for investigations of phenomena and physics
operating on scales of hundreds of kpc, massive galaxy clusters provide a
high-density environment that shapes the evolution of the constituent galaxies
on kpc scales. Two areas of galaxy evolution that are of particular interest
are the interactions of BCGs and their active nuclei with the surrounding ICM
(see Section 5.5.3) and the potential rapid morphological transformation of
late-type field galaxies into early-type cluster members through ram-pressure
stripping by the ICM (Gunn & Gott, 1972).

While the textbook “jellyfish” appearance of galaxies undergoing ram-pressure
stripping (e.g., Cortese et al., 2007; Owers et al., 2012; Ebeling et al.,
2014) is less readily discernible at the high redshifts of eMACS clusters, the
superb angular resolution of HST reveals many promising cases in the eMACS
sample. We show in Fig. 17 examples of spectroscopically confirmed cluster
members likely experiencing ram-pressure stripping. Note that we include
spirals with an almost undisturbed morphology since, in the environment
encountered within massive clusters, essentially all late-type galaxies are
expected to be undergoing ram-pressure stripping to some degree and will
ultimately be stripped of the majority of their atomic and molecular gas. Many
other late-type galaxies with similarly intriguing morphology are found in HST
images of eMACS clusters and await spectroscopic follow-up observations to
establish cluster membership.

Although their faintness and small angular size renders these galaxies
challenging targets for in-depth follow-up studies of their internal dynamics,
the excitation state of the intragalactic medium, or the effects of ram-
pressure stripping on central black holes (all topics at the focus of
“jellyfish” studies in the more nearby Universe out to about $z=0.3$: Kalita &
Ebeling, 2019, and references therein), the mere detection of debris trails or
ICM-induced deformations of the galactic disk can provide valuable constraints
on the direction of motion in the plane of the sky. The potential of ram-
pressure stripping as a diagnostic of peculiar motions perpendicular to our
line of sight was pointed out by Ebeling & Kalita (2019) and, in the eMACS
sample, is exemplified by eMACSJ1757.5 (Fig. B36) which illustrates that the
tell-tale morphology of “jellyfish” galaxies can indeed reveal dominant axes
of galaxy infall even at $z>0.5$.

Figure 17: HST images (50 kpc on the side) of spectroscopically confirmed
cluster members showing evidence of ram-pressure stripping by the ICM.
Shortened names in the upper left corner of each panel indicate the respective
host cluster.

##  6 Conclusions

Based on RASS detections comprising as few as 6 photons, the extended Massive
Cluster Survey (eMACS) has compiled a sample of over 100 very X-ray luminous
galaxy clusters after searching over 20,000 square degrees of extragalactic
sky. Limited to clusters at $z>0.5$, eMACS probes a population that was
hitherto barely explored: the first generation of truly massive clusters
($M\gtrsim 10^{15}$ M⊙). Extensive follow-up observations of eMACS cluster
candidates with ground- and space-based observatories, crucial to overcome the
poor photon statistics of the underlying RASS detections, confirmed the
presence of clusters in the vast majority of the targeted systems but, so far,
have also shown two to be non-clusters. As importantly, follow-up work from
radio to X-ray wavelengths yielded valuable insights into the physical
properties of many of these systems and allowed us to constrain their
gravitational-lensing strength, evolutionary state, and ICM gas temperature.
In addition, these observations revealed examples of highly active BCGs,
powerful QSOs, and late-type galaxies undergoing ram-pressure stripping during
their high-velocity passage through the dense ICM.

The sample presented here includes the most distant galaxy cluster ever
discovered in the RASS (eMACSJ0324.0 at $z=0.90$, Fig. B7), extremely powerful
gravitational lenses (e.g., eMACSJ1212.5, Fig. B23; eMACSJ1341.9, Fig. B26 and
Ebeling et al. 2018; or eMACSJ1353.7, Fig. B27), a newly discovered “exotic”
hyperbolic umbilical lens (eMACSJ1248.2, Fig. 5), exceptionally X-ray luminous
cluster collisions in various phases of the merging process (e.g.,
eMACSJ1756.8, Fig. B35; eMACSJ1831.1, Fig. B38), extraordinarily “active”
BCGs, e.g., in eMACSJ0252.4 (Ebeling et al., 2021, Fig. 13) and eMACSJ1030.5
(Fig. 16), and numerous systems whose potentially remarkable physical
properties are only hinted at by the existing data (e.g., eMACSJ1144.2,
eMACSJ1508.1, eMACSJ1757.5).

We highlight in particular the potential importance of the massive clusters at
$z>0.5$ presented in this work as powerful gravitational telescopes to study
faint sources in the very distant Universe (as already demonstrated, for
example with the lensed sources at $z=3.375$ and $z=5.166$ in eMACSJ2229.9).
The main benefits of selected eMACS clusters as probes for James Webb Space
Telescope (JWST) surveys of the very distant Universe, $z\gg 10$, are their
high masses and high redshifts, which also yield a corresponding reduction in
contamination from intracluster light, allowing faint lensed features to be
more easily identified in the high-amplification regions near the cluster
centres. We anticipate that JWST surveys of these clusters will be as
productive as the current exploitation of the MACS sample for studying faint
galaxies and individual stars in the high-redshift Universe (e.g., Abdurro’uf
et al., 2023; Atek et al., 2023; Diego et al., 2023; Asada et al., 2024;
Fujimoto et al., 2024).

While the current eMACS sample is not statistically complete, tentative
conclusions about the physical properties of the population of very massive
clusters at $z>0.5$ can be drawn from better defined subsets. Specifically,
the morphology of the ICM of eMACS clusters in high-resolution imaging X-ray
observations and the optical properties of eMACS BCGS from both imaging and
spectroscopic follow-up work suggest that the cool-core fraction lies at or
below $\sim$15%, consistent with the findings of Mann & Ebeling (2012) and
expectations for a sample that approaches the redshift of cluster formation at
$z\sim 1$. The analysis of all existing CXO/ACIS-I data for eMACS clusters
shows that the power-law model of the $L_{\rm X}$–k$T$ relation established
for less massive clusters at lower redshifts (e.g., Takey et al., 2013)
extends to the regime probed by eMACS (Fig. 9). For the majority of eMACS
clusters, velocity dispersions are very high, reaching and exceeding 1500 km
s-1 for several systems (Fig. 15). While clear signs of line-of-sight
substructure are not detectable at the current statistics, the highest
velocity dispersions exceed reasonable virial estimates and suggest that
inflation from peculiar (bulk) velocities from ongoing cluster growth is
common in this cluster population.

As, over three decades after its completion, the RASS is being succeeded by
eRASS1 (Merloni et al., 2024), the second all-sky survey ever conducted with
an imaging X-ray telescope, the samples of the most X-ray luminous clusters at
$z>0.3$ compiled by the MACS and eMACS projects are being complemented by a
wealth of discoveries down the mass and luminosity scale, all the way to
groups of galaxies, protoclusters, and dense filaments. In addition, eROSITA’s
much greater sensitivity will yield vastly better photon statistics, and at
least estimated ICM temperatures, for all eMACS clusters that, as of yet, have
not been targeted in dedicated follow-up observations with CXO.

Although neither the compilation of the eMACS sample nor the analysis of the
physical properties of all eMACS clusters are complete at this point, we here
release all data and data products obtained and derived by us in the course of
this program to avoid duplication and unnecessary investments of precious
observing resources by the extragalactic community (Zaznobin et al., 2023).

## Acknowledgements

We thank Lukas Zalesky for permission to use unpublished AStroLens results in
Section 5.2.2. of this paper. HE gratefully acknowledges financial support
from grants administered by STScI and CXC. Specifically, support for programs
GO-13671, -14098, -15132, -15466, -15608, -15843, -15844, and -16428 was
provided by NASA through a grant from the Space Telescope Science Institute,
which is operated by the Associations of Universities for Research in
Astronomy, Incorporated, under NASA contract NAS5-26555. Support for this work
was also provided by the National Aeronautics and Space Administration through
CXO Award Number GO9-20120X, GO0-21125X, GO1-22119X, and GO2-23119X, issued by
the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical
Observatory for and on behalf of the National Aeronautics Space Administration
under contract NAS8-03060. Durham authors acknowledge support from STFC
(ST/T000244/1, ST/X001075/1). This research has made use of data obtained from
the Chandra Data Archive and the Chandra Source Catalogue, and software
provided by the Chandra X-ray Center (CXC) in the application packages CIAO
and Sherpa.

## Data Availability

The data underlying this article are available in the MAST, CXO, and Keck data
archives.

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##  Appendix A The compilation of cluster candidates from the RASS

The eMACS project was launched in 2010, almost a decade before the launch of
eROSITA, and was motivated by the realization that the RASS, the only existing
all-sky survey with an imaging X-ray telescope, had not been fully exploited