Draft version June 10, 2021
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COSMOLOGICAL MHD SIMULATIONS OF GALAXY CLUSTER RADIO RELICS: INSIGHTS AND
WARNINGS FOR OBSERVATIONS
Samuel W. Skillman
1,2
, Hao Xu
3
, Eric J. Hallman
1,4,5
, Brian W. O’Shea
6,7
, Jack O. Burns
1,4
, Hui Li
3
, David C.
Collins
3
, Michael L. Norman
8
Draft version June 10, 2021
ABSTRACT
Non-thermal radio emission from cosmic ray electrons in the vicinity of merging galaxy clusters is
an important tracer of cluster merger activity, and is the result of complex physical processes that in-
volve magnetic fields, particle acceleration, gas dynamics, and radiation. In particular, objects known
as radio relics are thought to be the result of shock-accelerated electrons that, when embedded in a
magnetic field, emit synchrotron radiation in the radio wavelengths. In order to properly model this
emission, we utilize the adaptive mesh refinement simulation of the magnetohydrodynamic evolution
of a galaxy cluster from cosmological initial conditions. We locate shock fronts and apply models of
cosmic ray electron acceleration that are then input into radio emission models. We have determined
the thermodynamic properties of this radio-emitting plasma and constructed synthetic radio obser-
vations to compare to observed galaxy clusters. We find a significant dependence of the observed
morphology and radio relic properties on the viewing angle of the cluster, raising concerns regarding
the interpretation of observed radio features in clusters. We also find that a given shock should not
be characterized by a single Mach number. We find that the bulk of the radio emission comes from
gas with T > 5 × 10
7
K, ρ ∼ 10
−28
− 10
−27
g/cm
3
, with magnetic field strengths of 0.1 − 1.0µG and
shock Mach numbers of M ∼ 3 − 6. We present an analysis of the radio spectral index which suggests
that the spatial variation of the spectral index can mimic synchrotron aging. Finally, we examine the
polarization fraction and position angle of the simulated radio features, and compare to observations.
Subject headings: cosmology: theory — magnetohydrodynamics — methods: numerical — cosmic
rays — radiation mechanisms: nonthermal
1. INTRODUCTION
Galaxy clusters are hosts to a variety of thermal and
non-thermal phenomena, many of which are the result
of cosmological structure formation. The study of rela-
tivistic particles in galaxy cluster environments was mo-
tivated by the observation of the radio halo in the Coma
cluster by Large et al. (1959), and has since grown into
an industry of observations, theory, and simulation. For
a review on current radio observations of galaxy clusters
see Ferrari et al. (2008); Feretti et al. (2012), and for
a review on the non-thermal processes see Dolag et al.
(2008). Here we review the basic characteristics of galaxy
cluster radio “halos” and giant radio “relics,” to use the
classification in Ferrari et al. (2008). Radio halos are
usually ∼ Mpc−sized features in galaxy clusters, closely
following the X-ray morphology in the central regions
of the cluster. They are generally characterized by very
samuel.skillman@colorado.edu
1
Center for Astrophysics and Space Astronomy, Department
of Astrophysical & Planetary Science, University of Colorado,
Boulder, CO 80309
2
DOE Computational Science Graduate Fellow
3
Theoretical Division, Los Alamos National Laboratory, Los
Alamos, NM 87544
4
Lunar University Network for Astrophysics Research (LU-
NAR), NASA Lunar Science Institute, NASA Ames Research
Center, Moffet Field, CA, 94089
5
Tech-X Corporation, Boulder, CO 80303
6
Department of Physics & Astronomy, Michigan State Uni-
versity, East Lansing, MI, 48824
7
Lyman Briggs College and Institute for Cyber-Enabled Re-
search, Michigan State University, East Lansing, MI, 48824
8
Center for Astrophysics and Space Sciences, University of
California at San Diego, La Jolla, CA 92093, USA
low (< few percent) linear polarization fractions, and are
found in galaxy clusters with disturbed morphology and
no evidence for a cool core (Ferrari et al. 2008; Giovan-
nini et al. 2009; Feretti et al. 2012). The origin of the
emission is thought to be from relativistic (γ ∼ 10
4
) elec-
trons emitting synchrotron radiation. The source of the
energy in these electrons, however, is debated. It may
originate from the decay of pions (the “secondary” or
“hadronic” model), created by interactions between cos-
mic ray protons and the thermal population (Dennison
1980; Dolag & Enßlin 2000; Miniati et al. 2001), which
would be strengthened by the observation of gamma-
ray emission in cluster cores. However, initial studies
of many galaxy clusters using the FERMI satellite (Ack-
ermann et al. 2010), as well as for fewer objects with
other instruments (e.g. MAGIC observations of Perseus
Aleksi´c et al. 2010, 2012), combined with radio data (Jel-
tema & Profumo 2011; Brunetti et al. 2012) constrain
the energy in cosmic rays to be very low ( 10%) of
the thermal energy in most cases. Others believe that
the electrons are turbulently accelerated either from the
thermal population or from aging populations of elec-
trons either from shock acceleration or AGN/supernova
injection (Brunetti & Lazarian 2011).
Radio relics, on the other hand, are thought to be ac-
celerated by first-order Fermi acceleration through the
process of Diffusive Shock Acceleration (DSA) (Bland-
ford & Ostriker 1978). They have a relatively steep radio,
and therefore inferred electron, spectrum where S ∝ ν
−α
with α ≈ 1 − 2. These radio sources are not associated
with any of the cluster galaxies or AGN bubbles. They
arXiv:1211.3122v1 [astro-ph.CO] 13 Nov 2012
2
are also not associated with any point sources in other
wavelengths, and are usually found in the outskirts of
clusters. Their location can be up to ∼ 2 Mpc from the
cluster core, and can be extended up to ∼ 1.5 Mpc in
length (van Weeren et al. 2010, 2011c, 2012). In some
cases these radio features are coincident with X-ray sur-
face brightness and temperature jumps, potentially indi-
cating the presence of a shock front (Finoguenov et al.
2010; Akamatsu et al. 2012). While more rare, double
radio relics are observed in several systems. Double ra-
dio relics are unique in that they provide tighter con-
straints on the geometry and kinematics of the merging
clusters(van Weeren et al. 2011a). Upcoming radio tele-
scopes such as LOFAR, the Jansky VLA, and eventually
the SKA will provide an increase in sensitivity and res-
olution (both spectral and spatial) that will allow for
discoveries in blind surveys. Because of this, we are at
an important time to use simulation and theory to pre-
dict the number and the properties of relics in cosmo-
logical samples. Past simulations have focused on both
single clusters (Roettiger et al. 1999; Pfrommer et al.
2008; Battaglia et al. 2009) as well as ensembles of clus-
ters (Hoeft et al. 2008; Skillman et al. 2011; Vazza et al.
2012; Nuza et al. 2012). Both are needed in order to
constrain the plasma physics and how varying environ-
ments lead to observational quantities such as luminosity
functions.
In this paper we investigate the origins, properties, and
observational implications of a merging galaxy cluster us-
ing a numerical simulation. For the first time, we start
from cosmological initial conditions and self-consistently
evolve the cluster magnetic field from an AGN source the
equations of magnetohydrodynamics rather than assum-
ing a magnetic field strength and topology. This allows
us to explore one scenario in which the magnetic field
forms, evolves, and interacts with the radio relic emis-
sion. We describe, in detail, the plasma environment of
the radio-emitting regions.
After investigating the properties of the cluster gas,
we analyzed the resulting radio emission using novel ap-
proaches to explore systematic effects present in current
radio observations. We used a new tool to view this Eu-
lerian grid simulation from arbitrary directions in order
to demonstrate the effect of viewing angle on the derived
properties. We then developed the capability to inte-
grate the polarized radio emission along the line of sight
to provide the closest comparison to observations. We
then use this technique to produce polarization fraction
and position angle maps from our MHD AMR simula-
tion, and provide comments on the relevance of our re-
sults to current observations of radio features in galaxy
clusters. Finally, we discuss the impact of using previous
assumptions about the magnetic field compared to the
values that are self-consistently evolved from an AGN
source. We use this to provide insight into observational
results.
2. METHODS
2.1. Simulations
Our simulation was run using a modified version of the
Enzo cosmology code (Bryan & Norman 1997a,b; Nor-
man & Bryan 1999; O’Shea et al. 2004). Enzo uses block-
structured adaptive mesh refinement (AMR; Berger &
Colella 1989) as a base upon which it couples an Eulerian
hydrodynamic solver for the gas with an N-Body parti-
cle mesh (PM) solver (Efstathiou et al. 1985; Hockney
& Eastwood 1988) for the dark matter. In this work we
utilize the MHD solver described in Collins et al. (2010).
The solver employed here is spatially second order, while
the PPM solver (Colella & Woodward 1984) commonly
used in Enzo is spatially 3rd order. The net effect on
the shock-finding algorithm will be to broaden a single
shock by a small amount. However it will be impossi-
ble to disentangle this effect from the changes in shock
structure due to the addition of magnetic forces in the
evolution. None of the results we present here will be
sensitive to these small differences. We have extended
this version of Enzo to include temperature-jump based
shock-finding as described in Skillman et al. (2008) and
used in Skillman et al. (2011).
The galaxy cluster studied in this work is the same
as cluster U1 in Xu et al. (2011). In this work, clus-
ters were formed from cosmological initial conditions,
and magnetic fields were injected by the most massive
galaxy at a variety of stages in the cluster evolution. It
was found that different injection parameters of magnetic
fields have little impact on the cluster formation history.
This simulation models the evolution of dark matter,
baryonic matter, and magnetic fields self-consistently.
The simulation uses an adiabatic equation of state for
gas, with the ratio of specific heat being 5/3, and does
not include heating or cooling physics or chemical re-
actions. While studies have been done including these
physical models and their role in characterizing shocks
(Kang et al. 2007; Pfrommer et al. 2007), we chose to
ignore them due to both computational cost as well as
possible confusion between structure formation shocks
and those arising from star/galaxy feedback. Addition-
ally, Kang et al. (2007) found little effect on the overall
kinetic energy dissipation between simulations with adi-
abatic gas physics and those including cooling and feed-
back, and while Pfrommer et al. (2007) show changes at
high Mach number, as we will see these have little con-
sequence for the shocks involved with producing radio
relics.
The initial conditions of the simulation are generated
at redshift z = 30 from an Eisenstein & Hu (1999) power
spectrum of density fluctuations in a ΛCDM universe
with parameters h = 0.73, Ω
m
= 0.27, Ω
b
= 0.044,
Ω
Λ
= 0.73, σ
8
= 0.77, and n
s
= 0.96. These parame-
ters are close to the values from WMAP3 observations
(Spergel et al. 2003). While these parameters differ from
the latest constraints, it is largely irrelevant for this par-
ticular project. The simulated volume is (256 h
−1
Mpc)
3
,
and it uses a 128
3
root grid and 2 nested static grids
in the Lagrangian region where the cluster forms. This
gives an effective root grid resolution of 512
3
cells (∼
0.69 Mpc) and dark matter particle mass resolution of
1.07 × 10
10
M
. During the course of the simulation,
8 levels of refinements are allowed beyond the root grid,
for a maximum spatial resolution of 7.8125 h
−1
kpc. The
AMR is applied only in a region of (∼ 43 Mpc)
3
where
the galaxy cluster forms near the center of the simula-
tion domain. The AMR criteria in this simulation are
the same as in Xu et al. (2011). During the cluster for-
mation but before the magnetic fields are injected, the
3
refinement is only controlled by baryon and dark matter
density, refining on overdensities of 8 for each additional
level. After magnetic field injections, in addition to the
density refinement, all the regions where magnetic field
strengths are higher than 5 × 10
−8
G are refined to the
highest level. The importance of using this magnetic
field refinement criterion in cluster MHD simulations is
discussed in Xu et al. (2010).
The magnetic field initialization used is the same
method in Xu et al. (2008, 2009) as the original mag-
netic tower model proposed by Li et al. (2006), and as-
sumes the magnetic fields are from the outburst of AGN.
The magnetic fields are injected at redshift z = 3 in two
proto-clusters, which belong to two sub-clusters. The in-
jection locations are the same locations in simulations
U1a and U1b in Xu et al. (2011). There is ∼ 6 × 10
59
erg of magnetic energy placed into the ICM from each
injection, assuming that ∼ 1 percent of the AGN out-
burst energy of a several 10
8
M
SMBH is in magnetic
fields. Previous studies (Xu et al. 2010) have shown that
the injection redshifts and magnetic energy have limited
impact on the distributions of the ICM magnetic fields
at low redshifts.
The simulated cluster is a massive cluster with its basic
properties at redshift z = 0 as follows: R
virial
= 2.5
Mpc, M
virial
(total) = 1.9 × 10
15
M
, M
virial
(gas) =
2.7 × 10
14
M
, and T
virial
= 10.3 keV. This cluster
is in an unrelaxed dynamical state at z = 0 with its
two magnetized sub-clusters of similar size undergoing a
merger. The total magnetic energy in the simulation at
z = 0 is 9.6 × 10
60
erg, nearly all of which is within
the cluster virial radius. The details about the cluster
formation are described in Xu et al. (2011).
2.2. Synchrotron Emission
We use the same technique as was presented in Skill-
man et al. (2011) and based on Hoeft & Br¨uggen (2007),
except we no longer rely on the assumption that the mag-
netic field is a simple function of density and instead use
the magnetic field from the simulation. This method as-
sumes that a fraction of the incoming kinetic energy of
the gas is accelerated by the shock up to a power-law dis-
tribution in energy, which extends from the thermal dis-
tribution. This distribution is that predicted by diffusive
shock acceleration theory in the test-particle limit (Drury
1983; Bell 1978; Malkov & O’C Drury 2001; Achterberg
& Wiersma 2007; Blandford & Ostriker 1978; O’C. Drury
2012). At the high energy end, it also assumes that there
is an exponential cutoff determined by the balance of ac-
celeration and cooling. The total radio power from a
shock wave of area A, frequency ν
obs
, magnetic field B,
electron acceleration efficiency ξ
e
, electron power-law in-
dex s (n
e
∝ E
−s
), post-shock electron density n
e
and
temperature T
2
is (Hoeft & Br¨uggen 2007)
dP (ν
obs
)
dν
= 6.4 × 10
34
erg s
−1
Hz
−1
A
Mpc
2
n
e
10
−4
cm
−3
ξ
e
0.05
(
ν
obs
1.4GHz
)
−s/2
× (
T
2
7keV
)
3/2
(B/µG)
1+(s/2)
(B
CM B
/µG)
2
+ (B/µG)
2
Ψ(M).(1)
where Ψ(M) is a dimensionless shape function that rises
steeply above M ∼ 2.5 and plateaus to 1 above M ∼ 10.
In all work presented we use a fiducial value of ξ
e
= 0.005,
as suggested in Hoeft et al. (2008), and the same as used
in Skillman et al. (2011).
There are several important things to notice about this
model, which will help guide our interpretations of the
results throughout this paper. First, the emission scales
linearly with the downstream electron density, and with
the downstream temperature to the 3/2 power. Addi-
tionally, in regions where the magnetic field is less than
the equivalent magnetic field strength from the CMB en-
ergy density, B
CM B
, the emission scales with B
1+s/2
,
where s ∼ 3 for most relic situations.
2.3. Analysis Tools
In this work we relied heavily on the data analysis and
visualization toolkit, yt (Turk et al. 2011), to produce
the derived data products presented. Here we describe
the tools used specifically in our analysis, and leave fur-
ther description to the yt documentation
9
. Derived
Quantities
10
, such as WeightedAverageQuantity and To-
talQuantity, are used to calculate weighted averages and
totals of fluid quantities. For example, we use Weighte-
dAverageQuantity to calculate the average temperature,
weighted by cell mass. To analyze properties such as the
radio and X-ray emission from our simulations, we use
Derived Fields
11
to define the functional form of our new
fields, which is then calculated on a grid-by-grid basis as
needed. To calculate distribution functions, either as a
function of position or fluid quantity, we utilize 1-D Pro-
files and 2-D Phase Plots
12
. By specifying a binning field,
we are then able to calculate either the total of another
quantity or the average (along with the standard devia-
tion). These are used to create radial profiles as well as
characterize quantities such as the average magnetic field
strength as a function of density and temperature. We
also take advantage of adaptive slices and projections.
Slices
13
sample the data at the highest resolution data
available, and return an adaptive 2D image that can then
be re-sampled into fixed resolution images. Similarly, we
use weighted and unweighted projections
14
of quantities
to provide average or total quantities integrated along
the line of sight. Again, these adaptive 2D data objects
can then be re-sampled to create images at various res-
olutions. We also utilize and extend off-axis projections
for use in integrating the polarization vectors of radio
emission, to be described further in Section 2.4. Finally,
we use the spectral frequency integrator to calculate the
X-ray emission based on the Cloudy code, as was done
in Skillman et al. (2011) and Hallman & Jeltema (2011),
and was described in detail in Smith et al. (2008).
2.4. Polarization
In addition to calculating the synchrotron emission, in
this paper we investigate the polarization fraction and
position angles of the emission. In order to compare our
simulations to observations, we have developed several
9
http://yt-project.org/doc
10
http://yt-project.org/doc/analyzing/objects.html#derived-
quantities
11
http://yt-project.org/doc/analyzing/creating derived fields.html
12
http://yt-project.org/doc/visualizing/plots.html#d-profiles
13
http://yt-project.org/doc/visualizing/plots.html#slices
14
http://yt-project.org/doc/visualizing/plots.html#projections
4
new tools, including the ability to calculate the polariza-
tion properties of the radio emission. In this section, we
describe how we calculate Stokes I, Q, and U parameters
from any viewing angle of our simulation. For a review
of these topics, see Burn (1966); Longair (1994); Heiles
(2002). While previous analyses of polarized emission
were capable of viewing along the coordinate directions,
to our knowledge, this is the first presentation of
off-axis polarized radio emission from AMR sim-
ulations
15
. This capability presents several challenges.
Whereas the total radio emission is calculated as a direct
sum of the emission multiplied with the path length, the
calculation of the polarized emission requires simultane-
ous integration of each polarized component along the
line of sight due to their mixing through Faraday rota-
tion.
We have built this capability on top of the analysis
package yt. We began with the “off-axis projection”
16
operation, which is an off-axis ray-casting mechanism. It
operates by creating a fixed-resolution image plane for
which each pixel is then integrated through the simula-
tion volume. To do this correctly, first the AMR hier-
archy is homogenized into single-resolution bricks that
uniquely tile the domain. This ensures that only the
highest resolution data is used for a given point in space.
These bricks are ordered and traversed by the image
plane. The result of this is that we are able to inte-
grate along the line of sight through the AMR hierarchy
sampling only the highest-resolution cells for that given
point in space.
We have furthermore modified this framework such
that the RGB channels of the image act as the total
emission, I, and polarized emission along the x, I
x
, and
y, I
y
, axes. I
x
and I
y
can be thought of as the emission-
weighted electric field. The details of this calculation can
be found in Appendix A. We first create derived fields
that correspond to the magnetic field projected onto the
unit vectors ~v
x
, ~v
y
and ~v
||
, where ~v
x
and ~v
y
are defined
with respect to east and north vectors defined by the
viewing direction, ~v
||
. We label these magnetic fields as
B
x
, B
y
, and B
||
, respectively. We then define the po-
larization angle χ of the electric field as the angle made
between B
x
and B
y
rotated by π/2. Finally, we define
a Faraday rotation field ∆φ = 2.62 × 10
−17
× λ
2
n
e
B
||
dl,
where all variables are in cgs units. Using a similar no-
tation to Otmianowska-Mazur et al. (2009), we then in-
tegrate along the line of sight the I, I
x
, and I
y
values
using the following discrete step:
"
I
i+1
I
x,i+1
I
y,i+1
#
=
dl 0 0
dl f
p
( ~v
x
·
~
E) cos(∆φ) −sin(∆φ)
dl f
p
( ~v
y
·
~
E) sin(∆φ) cos(∆φ)
"
i
I
x,i
I
y,i
#
(2)
where ∆φ is the Faraday rotation, ~v
x
and ~v
y
are the
image plane coordinate vectors, f
p
is the fractional po-
larization of the synchrotron radiation of a given power-
law slope of electrons, dl is the ray segment length be-
tween the incoming and outgoing face of each cell, and
~
B is the magnetic field. Once integrated through the
15
Hoeft et al. (2008) studied the view dependence on the total
radio emission
16
http://yt-project.org/doc/cookbook/index.html#cookbook-
offaxis-projection
volume, we are then able to create intensity, polariza-
tion fraction, and polarization direction maps. This ca-
pability is available to download using the changeset
with hash fc3acb747162 here: https://bitbucket.org/
samskillman/yt-stokes.
3. RADIO RELIC PROPERTIES
In this section we describe the general properties of the
simulated galaxy cluster. We begin by comparing the
morphological similarities between our simulated cluster
and several observed clusters. We then move on to de-
scribe the other gas properties in an effort to constrain
the properties of the radio-emitting plasma. Finally, we
will look at the time evolution of these quantities in order
to understand their coupling during the merger process.
3.1. Simulated Radio & X-ray
We begin by comparing the radio and X-ray emis-
sion from our simulation with the radio relics present
in A3376 (see Figure 1a. in Bagchi et al. (2006)) and
CIZA J2242.8+5301 (see Figure 1 in van Weeren et al.
(2010)). In this work we calculate the X-ray emission
using Cloudy to integrate the emission from 0.5− 12 keV
assuming a metallicity of Z/Z
solar
= 0.3. The resulting
1.4 GHz radio and 0.5−12 keV X-ray emission is overlaid
in Figure 1. The X-ray is shown in color with a dynamic
range of 100. The radio flux is calculated by placing the
simulated cluster at a distance of 100Mpc/h. We then
mask the radio emission such that 10
−3
− 10
1
mJy is vis-
ible. The total integrated flux for the left and right relics
are 9.67×10
24
and 3.11×10
24
W/Hz at 1.4GHz, which is
similar to many of the observed single and double radio
relics (Feretti et al. 2012).
There are a few specific details that we highlight here
due to their similarities to many observed radio relics.
First, we note that this appears as a double radio relic.
These are relatively rare compared to their single-sided
counterparts. This snapshot is following a major merger
roughly 300 Myr after core passage. The primary cluster
is moving to the lower-left, with the secondary moving
primarily to the right. After core passage, a merger shock
develops, moving both to the lower left and upper right,
and as will be seen in later figures, aligns with strong
jumps in temperature and density. The two relic features
are aligned with the direction of the merger as well as the
shape of the X-ray emission. This alignment of the X-ray
morphology and radio emission is characteristic of double
radio relics (see Skillman et al. (2011)), as well as many
single relics (e.g. van Weeren et al. 2011b; Bonafede et al.
2012).
The second key feature to this simulated double relic
is the apparent aspect ratio of the radio emission. The
length of the left relic (if we connect the two pieces that
are separated by a short distance) is more than 2 Mpc/h,
while the right-moving relic is 1.5 − 2.0 Mpc/h. While
these relics are quite elongated, they are very thin. In
many regions it is at most 100 − 200 kpc/h wide, even
in projection. We note here, however, that this width is
most likely underestimated since we are not tracking the
aged populations of electrons that would exist for some
amount of time behind the shock front.
Comparing to A3376 (Bagchi et al. 2006), we see many
striking resemblances, including the complex morphology
5
Fig. 1.— Simulated X-ray and radio emission. The X-ray in the central regions shows a dynamic range of 100. The radio emission is
calculated by placing the simulated cluster at 100Mpc/h, and masked to show a dynamic range of 10
4
.
of the Eastern portion of the relic as well as the ring-
like structure to the outline of the radio emission. This,
at the very least, suggests that the radio-emitting elec-
trons are indeed related to the shock structures formed
in merging galaxy clusters. We see a similar structure in
CIZA J2242.8+5301 (van Weeren et al. 2010), where the
elongation of the X-ray emission points in the direction of
the merger, aligning with the double radio relic. We also
note the resemblance here with our simulation in terms
of the very thin region of radio emission along the relic.
This suggests that the cooling times of the relativistic
electrons must be short.
Figure 2 shows the fundamental quantities such as
density, temperature, Mach number, and magnetic field
strength, along with observable quantities such as the
1.4 GHz radio and temperature fluctuations in the CMB
due to the thermal Sunyaev-Zel’dovich effect. The ra-
dio flux assumes a distance to the simulated cluster of
100 Mpc/h. Each panel shows the same field-of-view
and depth of 4.0 Mpc/h at z=0. In all panels except
for the radio and Mach number maps, we have over-
plotted the radio emission to help guide the reader’s eye
in determining the location of the emission relative to
the underlying plasma. The top left panel shows the
density-weighted temperature. Here the correlation be-
tween the radio emission and the temperature structure
is very strong, as the outward moving shocks are heating
the gas to several ×10
8
K. Note that the sharp edges in
the temperature structure, as well as the maximum in
the temperature distribution, occurs 1.5 − 2Mpc/h away
from the center of the cluster. This highlights the unre-
laxed nature of this merging cluster.
The bottom-left panel shows the density-weighted den-
sity, and has a similar structure to the X-ray image shown
in Figure 1, as is expected since the X-ray emission is a
strong function of gas density. We note that unlike the
temperature, the density is strongly peaked towards the
center of the cluster, though the unrelaxed nature is ev-
