ICM-SHOX. I. Methodology Overview and Discovery of a Gas
–
Dark Matter Velocity
Decoupling in the MACS J0018.5
+
1626 Merger
Emily M. Silich
1
,
2
, Elena Bellomi
2
, Jack Sayers
1
, John ZuHone
2
, Urmila Chadayammuri
3
, Sunil Golwala
1
,
David Hughes
4
, Alfredo Montaña
4
, Tony Mroczkowski
5
, Daisuke Nagai
6
, David Sánchez-Argüelles
7
, S. A. Stanford
8
,
Grant Wilson
9
, Michael Zemcov
10
, and Adi Zitrin
11
1
Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA
2
Center for Astrophysics
|
Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA
3
Max Planck Institut für Astronomie, Königstuhl 17, 69121 Heidelberg, Germany
4
Instituto Nacional de Astrofísica, Óptica, y Electrónica
(
INAOE
)
, Aptdo. Postal 51 y 216, 7200, Puebla, Mexico
5
European Southern Observatory, Karl-Schwarzschild-Str. 2, D-85748, Garching, Germany
6
Physics Department, Yale University, New Haven, CT 06520, USA
7
Consejo Nacional de Ciencia y Tecn
ología-Instituto Nacional de Astrofísica, Óptica, y Electrónica
(
CONACyT-INAOE
)
, Luis Enrique Erro 1, 72840 Puebla, Mexico
8
Department of Physics and Astronomy, University of California, Davis, CA 95616, USA
9
University of Massachusetts, Amherst, MA 01003, USA
10
Rochester Institute of Technology, Rochester, NY 14623, USA
11
Ben-Gurion University of the Negev, P.O. Box 653, Be
’
er-Sheva 8410501, Israel;
esilich@caltech.edu
Received 2023 September 21; revised 2024 April 4; accepted 2024 April 4; published 2024 June 12
Abstract
Galaxy cluster mergers are rich sources of information to t
est cluster astrophysics and cosmology. However, cluster
mergers produce complex projected signals that are dif
fi
cult to interpret physically from
individual observational probes.
Multi-probe constraints on the gas and dark matter
(
DM
)
cluster components are necessary to infer merger parameters
that are otherwise degenerate. We present Improved Constraints on Mergers with SZ, Hydrodynamical simulations,
Optical, and X-ray
(
ICM-SHOX
)
, a systematic framework to jointly infer mu
ltiple merger parameters quantitatively via
a pipeline that directly compares a novel combination of m
ulti-probe observables to mo
ck observables derived from
hydrodynamical simulations. We report a
fi
rst application of the ICM-SHOX pipeline to MACS J0018.5
+
1626,
wherein we systematically examine simulated snapshots cha
racterized by a wide range of initial parameters to constrain
the MACS J0018.5
+
1626 merger geometry. We constrain the epoch of MACS J0018.5
+
1626 to the range 0
–
60 Myr
post-pericenter passage, and
the viewing angle is inclined
≈
27
°
–
40
°
from the merger axis. We obtain constraints for the
impact parameter
(
250 kpc
)
,massratio
(
≈
1.5
–
3.0
)
, and initial relative velocity wh
en the clusters are separated by
3Mpc
(
≈
1700
–
3000 km s
−
1
)
. The primary and secondary clusters initially
(
at 3 Mpc
)
have gas distributions that are
moderately and strongly disturbed, respectively.
We discover a velocity space decoupling of the DM and gas
distributions in MACS J0018.5
+
1626, traced by cluster-member galax
y velocities and the kinematic Sunyaev
–
Zel'dovich effect, respectively. Our sim
ulations indicate this decoupling is d
ependent on the different collisional
properties of the two distributions for particular merger epochs, geometries, and viewing angles.
Uni
fi
ed Astronomy Thesaurus concepts:
Galaxy clusters
(
584
)
;
Intracluster medium
(
858
)
;
Hydrodynamical
simulations
(
767
)
;
Observational cosmology
(
1146
)
;
X-ray astronomy
(
1810
)
;
Sunyaev-Zeldovich effect
(
1654
)
;
Galaxy spectroscopy
(
2171
)
;
Strong gravitational lensing
(
1643
)
Supporting material:
animations, machine-readable tables
1. Introduction
The standard
Λ
cold dark matter
(
Λ
CDM
)
cosmological model
predicts that structures in the universe form hierarchically
(
e.g.,
Springeletal.
2005
)
. In the early universe, weak positive
fl
uctuations in the cosmic density
fi
eld formed small overdensities,
which overcame cosmic expansion and collapsed via gravity. From
these density perturbations, larger structures form throughout
cosmic time by merging and smooth accretion. The current
(
z
∼
0
)
stage of cosmological structure formation in the universe is
the formation and growth of galaxy clusters.
12
With total
masses of
∼
10
14
–
10
15
M
e
, galaxy clusters comprise two main
mass components: dark matter
(
DM;
∼
80%
–
90% of the total
mass
)
and baryonic matter
(
∼
10%
–
20%
)
, which is dominated
by hot, diffuse plasma in the intracluster medium
(
ICM; see
Voit
2005
; Kravtsov & Borgani
2012
, for reviews
)
.
While some growth of galaxy clusters can be attributed to the
smooth accretion of streams of material from the cosmic web
and lower mass structures
(
e.g., galaxies
)
, the primary
hierarchical growth mechanism of clusters is major mergers
between similar mass systems
(
Muldrew et al.
2015
;Molnar
2016
)
. Such events can drive bulk motions and large-scale
turbulence in the ICM with velocities of
∼
10
3
km s
−
1
and heat
the gas up to temperatures of
∼
10
7
–
10
8
K
(
Markevitch &
Vikhlinin
2007
)
. Studies of galaxy clusters can, therefore, play
two key scienti
fi
c roles. First, because of the enormous scales of
distance
(
a few megaparsecs; Voit
2005
)
and energy
(
10
64
erg;
Molnar
2016
)
that clusters probe, generic physical processes like
turbulence, shocks, and accretion play out to an unprecedented
degree in mergers. Consequently, complementary observational
The Astrophysical Journal,
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)
, 2024 June 20
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/
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/
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/
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© 2024. The Author
(
s
)
. Published by the American Astronomical Society.
Original content from this work may be used under the terms
of the
Creative Commons Attribution 4.0 licence
. Any further
distribution of this work must maintain attribution to the author
(
s
)
and the title
of the work, journal citation and DOI.
12
As the expansion of the Universe continues to accelerate under the standard
Λ
CDM model, the largest expected virialized structures are only a few times
larger than the most massive clusters currently known
(
e.g., Araya-Melo et al.
2009
)
.
1
and simulation-based studies of major mergers are a powerful
means to further our understanding of these ubiquitous physical
phenomena and the role they play in cosmological structure
formation. Second, population statistics of major mergers
between massive clusters of galaxies are a sensitive diagnostic
of the underlying cosmological model
(
e.g., Lacey & Cole
1993
;
Fakhouri et al.
2010
; Thompson & Nagamine
2012
)
.For
example, major mergers trace the velocity distribution of halos at
the extreme end of the mass function, so observed velocities
from well-characterized samples can be compared to velocity
distribution predictions derived from cosmological simulations
in order to test various cosmological parameterizations
(
Mol-
nar
2016
)
. Exceptional mergers
(
e.g., the
“
Bullet Cluster
”
1E
0657-558; Markevitch et al.
2002
)
have the potential to provide
powerful tests of the
Λ
CDM paradigm, and much simulation
work has been undertaken to understand the cosmological
implications of these mergers
(
see Thompson et al.
2015
)
.
Observational diagnostics of galaxy cluster mergers have
included X-ray imaging and spectroscopy, gravitational lensing
(
GL
)
mass reconstructions, radio relics, thermal Sunyaev
–
Zel'dovich
(
tSZ
)
effect imaging, and positional offsets between
these observables
(
Clowe et al.
2006
; van Weeren et al.
2010
;
Molnar et al.
2012
; Molnar
2016
; Di Mascolo et al.
2021
;
Russell et al.
2022
)
, which can generally be reproduced by both
cosmological and idealized simulations
(
see ZuHone et al.
2018
)
. However, observational comparisons to simulations
have primarily been limited in two ways. Most analyses
involve only a single object because of the need for deep,
multi-probe data in order to characterize a merger adequately.
Furthermore, these analyses focus on mergers occurring in or
near the plane-of-sky
(
POS
)
, so that the morphological
signatures associated with the merger can be clearly identi
fi
ed,
thus making them more straightforward to interpret. To
overcome these limitations, one can also make use of line-of-
sight
(
LOS
)
velocity information, which expands the set of
mergers that can be analyzed and may also be critical to
obtaining conclusive results from comparisons to simulations
(
e.g., Chadayammuri et al.
2022
)
.
LOS velocity information in mergers has typically been
obtained from redshifts of cluster-member galaxies, which are
believed to reliably trace the DM distribution
(
Ma et al.
2009
;
Owers et al.
2011
; Boschin et al.
2013
)
. However, as mergers
evolve, the DM velocities are expected to decouple from the
ICM velocities, since the collisional ICM is affected by
hydrodynamical processes, while the DM is collisionless,
interacting only via gravity
(
Poole et al.
2006
)
. While the
existence of a velocity space difference between the ICM and
DM can be inferred from positional offsets of the two
components
(
e.g., Merten et al.
2011
)
, a direct measurement
of this velocity decoupling has not yet been achieved
observationally, since this requires spatially resolved measure-
ments of both the ICM and DM LOS velocities. In the X-ray
band, such observations can be carried out with microcalori-
meter instruments, as shown by the observations of bulk
velocities in the Perseus cluster with Hitomi
(
Hitomi
Collaboration et al.
2016
,
2018
)
. While this technique will be
made available by upcoming instruments on XRISM
(
XRISM
Science Team
2020
)
, Athena
(
Barret et al.
2020
)
, and LEM
(
Kraft et al.
2022
)
, it is not currently available. Recently, ICM
LOS velocities of individual clusters have been measured using
the kinematic Sunyaev
–
Zel'dovich
(
kSZ
)
effect
(
Sayers et al.
2013
; Adam et al.
2017
; Sayers et al.
2019
)
, which is a Doppler
shift of the cosmic microwave background
(
CMB
)
signal due
to the bulk motion of galaxy clusters
(
Sunyaev & Zeldo-
vich
1980
; see Mroczkowski et al.
2019
for a review
)
.By
incorporating LOS ICM velocities derived from current kSZ
measurements, it is now possible to directly probe both the
POS morphology and LOS velocity features of both mass
components
(
DM and ICM
)
in mergers.
In this paper, we introduce the Improved Constraints on
Mergers with SZ, Hydrodynamical simulations, Optical, and
X-ray
(
ICM-SHOX
)
sample, which comprises a set of deep,
multi-probe data for eight massive, intermediate-redshift galaxy
clusters. From these data, we are able to characterize the POS
morphology and LOS velocity structure of the constituent ICM
and DM components for the
fi
rst time in such a merger
analysis. ICM-SHOX contains four galaxy cluster mergers
likely occurring primarily along the LOS, three mergers likely
occurring in the POS, and one relaxed object as a control
(
see
Table
1
)
. The quality of these multi-probe data is relatively
uniform across each object in the sample. The ICM-SHOX
sample consists primarily of exceptional
(
e.g., high-mass,
actively merging
)
objects, which allows us to test for deviations
from
Λ
CDM in the most extreme regime of structure growth in
the universe.
In order to determine the geometry of these mergers and
obtain robust population statistics of cluster component masses,
gas pro
fi
les, initial impact parameters, initial relative velocities,
merger epochs, and viewing angles, we compare observables
derived from the multi-probe data to analogous mock
observables generated with tailored idealized hydrodynamical
binary galaxy cluster merger simulations. We have developed
an automated pipeline that enables us to reduce the observa-
tional data for each cluster, generate analogous mock
Table 1
Details of the Galaxy Clusters in ICM-SHOX
a
Cluster Name
R.A.
Decl.
zM
500
Dynamical State
(
10
14
M
e
)
A0697
08
h
42
m
57.
s
6
+
36
°
21
′
57
′′
0.28
17.1
Likely LOS merger
A1835
14
h
01
m
01.
s
9
+
02
°
52
′
40
′′
0.25
12.3
Relaxed
MACS J0018.5
+
1626
00
h
18
m
33.
s
4
+
16
°
26
′
13
′′
0.55
16.5
Likely LOS merger
MACS J0025.4-1222
00
h
25
m
29.
s
9
−
12
°
22
′
45
′′
0.58
7.6
Likely POS merger
MACS J0454.1-0300
04
h
54
m
11.
s
4
−
03
°
00
′
51
′′
0.54
11.5
Likely POS merger
MACS J0717.5
+
3745
07
h
17
m
32.
s
1
+
37
°
45
′
21
′′
0.55
24.9
Likely LOS merger
MACS J2129.4-0741
21
h
29
m
25.
s
7
−
07
°
41
′
31
′′
0.59
10.6
Likely LOS merger
RX J1347.5-1145
13
h
47
m
30.
s
8
−
11
°
45
′
09
′′
0.45
21.7
Likely POS merger
Note.
a
Summarized from Table 1 of Sayers et al.
(
2019
)
and references therein.
2
The Astrophysical Journal,
968:74
(
25pp
)
, 2024 June 20
Silich et al.
observables from simulations characterized by a vast array of
initial parameters, and directly compare the data sets. Our
framework then jointly infers the above merger parameters for
each cluster quantitatively via a frequentist statistical analysis.
In this study, we demonstrate the capabilities of this pipeline
applied to our novel combination of multi-probe data for one
member of ICM-SHOX, MACS J0018.5
+
1626.
In Section
2
, we describe the observational data for the full
ICM-SHOX sample and detail the data reduction and analysis
procedures for MACS J0018.5
+
1626. Section
3
contains an
overview of the hydrodynamical simulations we employ and
describes our process of generating mock observables for direct
comparison to the observational data. In Sections
4
and
5
,we
describe methods for constraining the MACS J0018.5
+
1626
merger parameters with the ICM-SHOX pipeline and the
resulting constraints, respectively. Section
6
contains a detailed
simulation-based exploration of the decoupling between the gas
and DM velocity structure observed in MACS J0018.5
+
1626.
We give conclusions and applications to the full ICM-SHOX
sample in Section
7
. We assume a spatially
fl
at
Λ
CDM
cosmology with
H
0
=
70 km s
−
1
Mpc
−
1
and
Ω
m
,0
=
0.3, unless
otherwise speci
fi
ed.
2. Observational Data
2.1. The ICM-SHOX Sample
For each object in the sample, we characterize the POS DM
morphology using projected total mass
(
Σ
)
maps from strong
GL models
fi
t to imaging data from the Hubble Space
Telescope
(
HST; e.g., Zitrin et al.
2011
,
2015
)
. The POS
ICM morphology is described by two observables. First, we
construct X-ray surface brightness
(
XSB
)
and temperature
(
kT
)
maps using observations taken with the Chandra X-ray
Observatory. Then, we obtain projected ICM density maps
using the SZ effect
(
Sayers et al.
2019
)
measured via a
combined analysis of data from Bolocam, AzTEC, and Planck.
The LOS DM velocity is traced using spectroscopic redshifts
(
z
spec
)
of cluster-member galaxies obtained primarily with the
DEIMOS instrument
(
Faber et al.
2003
)
at the Keck
Observatory. We characterize the LOS ICM velocity
(
ICM
v
pec
)
using projected ICM velocity maps from the SZ effect,
again based on an analysis of Bolocam, AzTEC, and Planck
observations
(
Sayers et al.
2019
)
.
Each data set probes
>
¢
3
from the center of the cluster, with
the exception of the GL maps
(
which are limited by the HST
fi
eld of view
)
and the
kT
maps
(
which are only constructed
within a central region where the cluster counts are comparable
to background counts; see Section
2.2
)
. At the redshift of the
ICM-SHOX sample, this angular extent corresponds to
∼
1 Mpc in the POS, which is typically large enough to capture
primary features of the merger
(
e.g., separate cluster mass
peaks and merger-driven shocks
)
. In this analysis, we focus on
one member of the ICM-SHOX sample, MACS J0018.5
+
1626, which is a massive, extensively studied cluster merger
(
see, e.g., Solovyeva et al.
2007
)
at
z
=
0.546
(
Ebeling et al.
2007
)
that is likely elongated along the LOS
(
Piffaretti et al.
2003
; Sayers et al.
2019
)
. We describe each observational data
set
(
see Figure
1
)
and corresponding data processing for MACS
J0018.5
+
1626 below.
2.2. X-Ray
The X-ray data reduction was performed with
CIAO
version
4.14
(
Fruscione et al.
2006
)
. MACS J0018.5
+
1626 observa-
tions correspond to Chandra ObsId 520, doi:
10.25574
/
00520
.
The raw ACIS-I data for ObsID 520 were calibrated using the
CalDB version 4.9.4 with
chandra
_
repro
. The data were
exposure-corrected with
fluximage
. Point sources were
identi
fi
ed using the
CIAO
implementation of a wavelet source
detection method
(
wavdetect
; Freeman et al.
2002
)
and
excluded from the exposure-corrected images. The light curve
was
fl
are-
fi
ltered with
deflare
to identify good time intervals
Figure 1.
MACS J0018.5
+
1626 multi-probe observations: top row, from left: LOS galaxy velocities
(
v
gal
)
, XSB, GL projected total mass
(
Σ
)
; bottom row, from left:
LOS ICM velocities
(
ICM
v
pec
)
, X-ray derived temperatures
(
kT
)
, LOS ICM electron optical depth
(
τ
)
.
3
The Astrophysical Journal,
968:74
(
25pp
)
, 2024 June 20
Silich et al.
(
GTI
)
, which were applied to the data. The total GTI after data
fi
ltering is 63.8 ks. We used the
flux
_
obs
tool to generate a
fi
ltered, exposure-corrected 0.5
–
7 keV XSB map free of point
sources, which, having 1.7
×
10
4
source counts, is suf
fi
ciently
deep to resolve morphological features.
The
blanksky
routine was used to construct blank-sky
background event
fi
les scaled and reprojected to match the
MACS J0018.5
+
1626 data. Since they are derived from deep,
point source-free observations averaged across large regions of
the sky, the background
fi
les nominally account for contribu-
tions from the particle-induced instrumental background
(
Bartalucci et al.
2014
)
, as well as astrophysical foreground
components
(
e.g., the Local Hot Bubble and the hot Galactic
halo
)
and background components
(
e.g., the contributions from
unresolved extragalactic point sources to the cosmic X-ray
background
)
.
In order to generate robust
kT
maps, we
fi
rst identi
fi
ed a
circular region centered on MACS J0018.5
+
1626, within
which the cluster source counts
(
N
cluster
)
are comparable to or
larger than the background counts within each pixel
(
N
BKG
)
.
We estimated
N
cluster
+
N
BKG
for each pixel in the 0.5
–
7 keV
fi
ltered events image
(
binned to a pixel size of 4
′′
to reduce
statistical variation between pixels
)
, and we derived
N
BKG
with
the analogously binned blank-sky background image. The
resulting circular region within which
N
source
∼
N
BKG
for
75% of the pixels has
r
=
1
8.
Then, the 0.5
–
7 keV
fi
ltered events image was contour
binned within the 1
8; circular region using the
contbin
algorithm
(
Sanders
2006
)
. The 0.5
–
7 keV blank-sky back-
ground image was speci
fi
ed for the signal-to-noise ratio
(
S
/
N
)
calculations used to determine the bin edges. We extracted
source spectra from the
fi
ltered event
fi
le and background
spectra from the blank-sky event
fi
le for each of the regions
de
fi
ned by the contour bins with
specextract
. We tailored
the contour binning algorithm input parameters so each cluster
bin has
∼
1000 counts after the blank-sky background
subtraction to maximize the
kT
map spatial resolution while
maintaining suf
fi
cient counts to obtain a high-quality spectral
fi
t. Each extracted spectrum was binned to have a minimum of
25 counts per spectral bin to allow the use of
χ
2
statistics in the
spectral
fi
tting.
All spectral
fi
tting was performed with
sherpa
over an
energy range of 0.5
–
7 keV. The blank-sky background-
subtracted cluster bins were
fi
t with a model for a single
collisionally ionized plasma modi
fi
ed by interstellar absorption
(
tbabs
×
apec
; Wilms et al.
2000
; Smith et al.
2001
)
with
fi
xed
n
H
=
4
×
10
20
cm
−
2
(
HI4PI Collaboration et al.
2016
)
,
z
=
0.546, and
Z
=
0.3
Z
e
using abundances from Anders &
Grevesse
(
1989
)
. The plasma temperature and normalization
were
fi
t as free parameters. For MACS J0018.5
+
1626, the
contour binning produces 14 spatial bins within
¢
1. 8
of the
cluster center, within which temperature enhancements due to
shocks produced in the merger are easily identi
fi
able.
We then inspected the MACS J0018.5
+
1626 XSB and
kT
maps for discontinuities associated with merger-driven shocks,
which, if present, could be used to help constrain the merger
geometry
(
e.g., Markevitch et al.
2002
)
and evolutionary state
(
e.g., Russell et al.
2012
)
.We
fi
rst applied a Gaussian gradient
magnitude
fi
lter
(
Sanders et al.
2016a
,
2016b
)
to the MACS
J0018.5
+
1626 XSB map and identi
fi
ed enhancements that
would be indicative of merger-driven shocks. For each of these
enhancements, we generated radial surface brightness pro
fi
les
and inspected them for evidence of surface brightness jumps. In
a study of the A2256 merger, Breuer et al.
(
2020
)
note that for
highly inclined mergers
(
occurring near the LOS
)
, temperature
jumps can be more reliable indicators of the presence of a
shock front. Therefore, in any regions that indicated the
possible presence of a radial surface brightness jump, we
fi
t
downstream and upstream plasma temperatures to photons
extracted from regions below and above the jump position,
respectively. We applied the Rankine
–
Hugoniot jump condi-
tions as a function of Mach number for the ratio of the
downstream and upstream plasma temperatures across a plane-
parallel shock
(
Landau & Lifshitz
1959
)
to each enhancement-
identi
fi
ed region of interest. Within uncertainties, all Mach
numbers were consistent with one
(
i.e., no shock
)
. Given our
relatively low S
/
N, we do not use the presence
(
or lack
)
of
clear shocks in the X-ray observables as a diagnostic of the
merger geometry.
2.3. GL
The projected total mass distribution of MACS J0018.5
+
1626 was modeled using the Light Traces Mass
(
LTM
)
GL
approach of Zitrin et al.
(
2015
)
applied to HST imaging. A full
description of the method is given in Zitrin et al.
(
2015
)
;in
short, the LTM model assumes that cluster-member galaxy
masses scale like their luminosities, and the total DM
distribution follows a similar shape, so that it can be
represented by a smoothed map of the cluster-member galaxies.
The model is constrained by minimizing the distances of
predicted multiple images from their actual observed locations
with a Markov Chain Monte Carlo
(
MCMC
)
minimization
utilizing a
χ
2
function.
A preliminary strong lensing model of MACS J0018.5
+
1626 based on older HST data was detailed in Zitrin et al.
(
2011
)
. Here, we use a revised model that incorporates publicly
available Very Large Telescope
/
MUSE data
(
Program ID
0103.A-0777
(
B
)
, PI: Edge
)
as well as dedicated Gemini
/
GNIRS data
(
Program ID: GN-2021B-Q-903, PI: Zitrin
)
for the
cluster. These data reveal UV and optical emission lines as well
as a
(
double-peaked
)
Ly
α
line at
z
=
3.21 for the main lensed
system
(
Furtak et al.
2022
)
. HST imaging data from the
RELICS survey
(
Coe
2016
; Coe et al.
2019
)
has yielded two
new multiple-image systems, which are also incorporated in the
revised version. In total, the current model, which is similar to
the one presented in Furtak et al.
(
2022
)
, has 10 free parameters
and uses six sets of multiple image constraints from
fi
ve
background galaxies up to redshift
z
∼
5 as constraints. The
fi
nal image reproduction rms of the model is 0
86. In the
resulting projected total mass distribution map, two primary
mass peaks are clearly identi
fi
able.
2.4. SZ Effect
Sayers et al.
(
2019
)
produced projected LOS ICM density
and velocity maps for each merger in our sample, including
MACS J0018.5
+
1626, using SZ effect observations from
Bolocam, AzTEC, and Planck. The data were used to generate
SZ effect maps at 140 and 270 GHz with a common point-
spread function with a full width at half-maximum
(
PSF
FWHM
)
of 70
′′
. The data from Planck were used solely to set the
absolute additive normalization of the SZ effect maps, since,
while the ground-based data provide much better angular
resolution than Planck, the data processing procedures required
4
The Astrophysical Journal,
968:74
(
25pp
)
, 2024 June 20
Silich et al.
to subtract atmospheric
fl
uctuations also remove the normal-
ization information. The 140 and 270 GHz data were combined
with an X-ray-derived
kT
map to produce the LOS ICM density
and velocity maps. We note that the
kT
map used in the SZ
analysis is derived from the same data as the MACS J0018.5
+
1626
kT
map generated in this work
(
see Section
2.2
)
but
was calculated with an older X-ray analysis procedure.
Differences between the X-ray reduction used by Sayers
et al.
(
2019
)
and that employed in the current work produce
negligible changes in the SZ-derived quantities relative to the
measurement noise. The S
/
N for the ICM density map is
∼
5
–
10, and the uncertainty within each 70
′′
resolution element
in the ICM
v
pec
map is
∼
1000 km s
−
1
.
2.5. Cluster-member Optical Spectroscopy
Previous studies have shown that averaging redshifts of
cluster-member galaxies is a useful measure of the bulk LOS
DM velocity structure in a galaxy cluster
(
e.g., Boschin et al.
2006
; Ma et al.
2009
; Dehghan et al.
2017
)
. Furthermore,
cosmological simulations have indicated that the bias between
the velocity dispersions of cluster-member galaxies and DM is
relatively low
(
Anbajagane et al.
2022
)
. Therefore, throughout
this work, we assume that the LOS cluster-member galaxy
velocities trace the LOS DM velocity structure.
We have combined both existing literature catalogs
(
Dressler
& Gunn
1992
; Ellingson et al.
1998
; Crawford et al.
2011
)
with
new DEIMOS observations obtained by our group to collect
156 cluster-member
z
spec
across the face of MACS J0018.5
+
1626 within a
¢ ́¢
6. 7 6. 7
region around the cluster center.
The DEIMOS data which were observed prior to 2021 August
were reduced with the
spec2d
DEIMOS data reduction
pipeline
(
Cooper et al.
2012
; Newman et al.
2013
)
, and those
observed from 2021 August onward were reduced with a
modern Python implementation of the DEIMOS data reduction
pipeline
(
PypeIt
; Prochaska et al.
2020
)
. We used
SpecPro
(
Masters & Capak
2011
)
to extract redshifts from the 1D
reduced cluster-member galaxy spectra by identifying either the
Ca
II
H
+
K absorption lines or the
[
O
II
]
3727
Å
doublet, with
some objects additionally showing the H
δ
-
and
G
-band
absorption lines. We provide tables of the MACS J0018.5
+
1626 literature cluster-member redshifts, as well as
(
non-
)
cluster-member redshifts that were observed in our Keck
program in Appendix
C
(
Tables
C1
–
C3
)
.
Next, we converted each redshift relative to the median
redshift of the cluster
(
0.546
)
to a velocity relative to the
average SZ-derived bulk ICM LOS velocity of MACS J0018.5
+
1626
(
v
bulk
;
−
100 km s
−
1
; Sayers et al.
2019
)
. In other
words, we de
fi
ne a cluster-member galaxy at
z
=
0.546 to be at
rest relative to the bulk ICM LOS velocity. We thus enforce
that the overall average observed bulk velocity of the ICM and
the DM are equal. Then, we applied the weighted Voronoi
tessellation
(
WVT
)
algorithm of Diehl & Statler
(
2006
)
to bin
the cluster-member velocities within the
¢ ́¢
6. 7 6. 7
region into
a high-
fi
delity spatial map. We use a publicly available Python
implementation of the WVT algorithm
(
XtraAstronomy
/
Pumpkin; Rhea et al.
2020
)
for the spatial binning, and we
apply estimators from Beers et al.
(
1990
)
to calculate the
velocity
(
v
gal
)
within each spatial bin. The MACS J0018.5
+
1626 LOS galaxy velocity map has 19 spatial bins across the
face of the cluster.
3. Hydrodynamical Binary Merger Simulations
3.1. Simulated Data Sets
We generate simulated observables analogous to the multi-
probe MACS J0018.5
+
1626 data by tailoring a suite of
idealized hydrodynamical galaxy cluster merger simulations,
after the manner of previous works
(
e.g., Ricker & Sara-
zin
2001
; Poole et al.
2006
; ZuHone
2011
; Chadayammuri
et al.
2022
)
. We use the GPU-accelerated code GAMER-2
(
Schive et al.
2018
)
to run the simulations, which solves the
equations of hydrodynamics,
N
-body interactions, and gravity
on an adaptive mesh re
fi
nement
(
AMR
)
grid. Each simulation
is initialized as a binary cluster merger for a given choice of
total mass, mass ratio
R
=
M
P
/
M
S
of the primary to the
secondary cluster
(
where both masses are de
fi
ned as the
enclosed mass within the cluster
’
s
r
200
c
)
, impact parameter
b
,
and relative velocity of the infalling galaxy clusters
v
i
.
We de
fi
ne the total MACS J0018.5
+
1626 mass derived
from the GL mass reconstruction map
(
M
500
=
1.1
×
10
15
M
e
)
in all simulations and use this to scale the masses of the two
clusters pre-merger. We note that this GL mass estimate is
lower than that derived from an X-ray scaling relation
(
see
Table
1
)
. However, we select the GL mass estimate for our
simulations since using the X-ray derived mass estimate results
in inconsistencies when comparing the total surface den-
sity maps.
The clusters are initially separated by a distance of 3 Mpc,
and
v
i
is de
fi
ned along the merger axis
(
x
ˆ
)
while
b
is de
fi
ned
along the orthogonal
y
ˆ
axis. A schematic of the merger
initialization is shown in Figure
2
. Whenever projections of a
simulation are taken, the viewing angle vector
(
L
)
represents
the position of the
observer
(
i.e., the vector whose perpend-
icular plane is the projection plane
)
. Each cluster is comprised
of DM and star particles and gas de
fi
ned on the grid distributed
by choices of total mass, gas, and stellar pro
fi
les; all assumed
to be spherically symmetric and in hydrostatic and virial
Figure 2.
Schematic of the merger geometry initial con
fi
guration
(
based on
Figure 1 of Chadayammuri et al.
2022
)
.
M
P
and
M
S
are the primary and
secondary cluster masses, respectively.
b
is the impact parameter
(
de
fi
ned
along the
y
ˆ
axis
)
.
v
i
,
p
and
v
i
,
s
are the primary and secondary cluster initial
velocities
(
de
fi
ned in the
x
ˆ
axis
)
, where
v
i
=
|
v
i
,
p
−
v
i
,
s
|
.
L
is the viewing angle
vector for simulation projections, de
fi
ned with components in
(
x
ˆ
,
y
ˆ
,
z
ˆ
)
.
5
The Astrophysical Journal,
968:74
(
25pp
)
, 2024 June 20
Silich et al.