THERMAL PROPERTIES OF THE GAS IN EARLY-TYPE GALAXIES AND GALAXY

CLUSTERS

By

Rachel L.S. Frisbie

A DISSERTATION

Michigan State University

in partial fulﬁllment of the requirements

Submitted to

for the degree of

Astrophysics and Astronomy – Doctor of Philosophy

2020

ABSTRACT

THERMAL PROPERTIES OF THE GAS IN EARLY-TYPE GALAXIES AND GALAXY

CLUSTERS

By

Rachel L.S. Frisbie

Most of the baryons, or “normal" matter, found in galaxies and galaxy clusters are found in the hot,
X-ray emitting gas known as the circumgalactic medium (CGM) or intracluster medium (ICM).
The hot gas traces the gravitational potential well and is aﬀected by both thermal and gravitational
processes, so we use observations of the hot gas to explore changes across the galaxy or cluster’s
radius. Heating and cooling in the central regions of galaxies and clusters is primarily driven by
feedback processes, including Active Galactic Nuclei (AGNs) and Type Ia supernovae. We can use
X-ray observations of the hot gas to understand its thermal history and how the various feedback
mechanisms aﬀect the gas at small and large radii. Furthermore, we use X-ray gas properties
(temperature, density, entropy, concentration, centroid shift, and power ratios) to characterize
galaxies and clusters, understand their evolution, and classify them in meaningful ways. The
combination of observations along with theoretical models and simulations explored in this thesis
provides key insight into understanding how feedback processes aﬀect the hot gas.

I begin by presenting gas property results for a uniformly reduced sample of 348 galaxy clusters
and show how those results can be used to characterize the sample and for further galaxy cluster
science. I will then turn my focus to early-type galaxies for the remainder of this work. I examine a
sample of 12 nearby early-type galaxies with powerful radio sources and ﬁnd that IC 4296 exhibits
unusually low central entropy as previously observed in NGC 4261. We also ﬁnd some evidence
that the minimum of the ratio between the cooling time and free-fall time, if it occurs at the galaxy
center, may indicate the presence of a powerful radio source. Finally, I examine the galactic
atmospheres of a sample of 49 early-type galaxies. I will show that the equilibrium pressure and
density radial proﬁles for single- and multiphase galaxies agree with the Voit et al. (2020) theoretical

model. I also ﬁnd evidence for a correlation between the central velocity dispersion and entropy
proﬁle slope of the galaxies in the sample that agrees with the theoretical model.

Copyright by
RACHEL L.S. FRISBIE
2020

For Dustin and Torrey

v

ACKNOWLEDGEMENTS

Defending my dissertation virtually and amidst a pandemic is not exactly how I envisioned closing
this chapter of my life, but here we are. I would not be presenting this work if not for the wonderful
people I have in my life, both personally and professionally.

First, I want to thank my advisor, Megan Donahue, and my committee, Mark Voit, Brian O’Shea,
Wolfgang Kerzendorf, and Tyce DeYoung for their scientiﬁc guidance and support throughout my
PhD. My collaborators, Thomas Connor, Yuan Li, Kiran Lakhchaura, Ming Sun, Norbert Werner,
Romana Grossova, and Lorenzo Lovisari were also instrumental in developing the work in this
thesis. I also want to thank Thomas Connor and the Carnegie Observatories for the opportunity to
manage an observing run on site at Las Campanas Observatory.

I want to thank the teachers and mentors who inspired me to become a scientist and educator
and encouraged me every step of the way. My middle and high school science teachers, Susan
Thackara, George Croll, and Suzanne Croll introduced me to science and taught me to ask questions
about the world around me. My undergraduate research advisor, mentor, and professor, Jeremy
Sepinsky, introduced me to astronomy research and supported my development as a scientist. I
would also like to thank the ISEE Professional Development Program, especially Devin Silvia,
Austin Barnes, Lisa Hunter, Rafael Palomino, and Philipp Grete for giving me the opportunity to
grow as an educator and providing me with a community when I needed it most.

I want to thank my family and friends. From our early days in undergraduate physics to now, my
husband Dustin has been my biggest supporter, best friend, and the best rubber duck. I also want
to thank our dog Freya for being the sweetest puppy and giving me all the snuggles I needed during
graduate school. To my wonderful nephew Tristan, for letting your Aunt Rachie read you endless
stories on video chat, thank you for being a wonderfully bright spot during the last several months
of my PhD. My older sister Torrey paved the way for me to become a scientist and has mentored
and supported me from the beginning. I also want to thank my parents for supporting me in all of
my endeavours. I am endlessly thankful to my fellow grad students, Dana Koeppe, Jennifer Ranta,

vi

Austin Edmister, Carl Fields, Forrest Glines, Jessica Maldonado, and Kathryn Bowen for bringing
much needed joy to graduate school. I also especially want to thank Kim Crosslan for her endless
patience and support throughout my time in graduate school. There are many more people who
have been part of my community for the past 27 years, and nowhere near enough space to list them.
Thank you all for being a part of my life and helping to shape me into the person I am today.

I acknowledge the support from Chandra grants SAO-AR7-18008X, GO5-16132-x, and GO1524X

as well as NASA ADAP-subaward (XMM Heritage) grant SAO-SV9-89010.

vii

TABLE OF CONTENTS

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CHAPTER 1

LIST OF TABLES .
LIST OF FIGURES .

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INTRODUCTION .

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xi
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Galaxy Clusters and Early-Type Galaxies . . . . . . . . . . . . . . . . . . . . . . .
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1.2 Cosmology Primer
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1.3 X-ray Observations .
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1.3.1 A Brief History of X-ray Astronomy . . . . . . . . . . . . . . . . . . . . .

1
1
5
8
8
1.3.1.1 Chandra X-ray Observatory . . . . . . . . . . . . . . . . . . . . 10
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.2 X-ray Observables
1.3.3 Deprojection as a Tool for X-ray Spectroscopy . . . . . . . . . . . . . . . . 11
1.3.4 Using Entropy to Understand X-ray Gas . . . . . . . . . . . . . . . . . . . 13
1.3.5 Morphology .
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1.4 The Gas in Clusters and Early-Type Galaxies . . . . . . . . . . . . . . . . . . . . . 14
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1.5 Structure of this Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
CHAPTER 2 ACCEPT 2.0 AND XMM HERITAGE . . . . . . . . . . . . . . . . . . . . 18
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2.2.1 Comparison to ACCEPT . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Morphology Calculations and K0 . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.2.1 Calculating Centroid Shift, Concentration, and Power Ratios . . . 25
. 29
2.3.1 Morphological Properties and K0 for Sample Comparisons . . . . . . . . . 30
2.3.2 ACCEPT 2.0 Comparison with REFLEX and XMM Heritage . . . . . . . . 32
. 36

2.3 Science with ACCEPT 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Introduction .

2.1
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2.2 Entropy Proﬁle Fitting .

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1.4.1 Multiphase Gas .
1.4.2

SNIa Feedback in Clusters vs. Galaxies

2.4 Summary .

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CHAPTER 3 PROPERTIES OF THE CGM IN EARLY-TYPE GALAXIES WITH

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Introduction .

POWERFUL RADIO SOURCES . . . . . . . . . . . . . . . . . . . . . . . 38
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3.1 Abstract
3.2
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3.3 Sample Selection and Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 42
. . . . . . . . . . . . . . . . . . . . . . . 42
3.3.1
3.3.2 Chandra data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.3
Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.4 Thermodynamic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Electron Density Proﬁles . . . . . . . . . . . . . . . . . . . . . . 47
Entropy and tcool/tﬀ Proﬁles . . . . . . . . . . . . . . . . . . . . 47

Sample Selection and Distances

3.3.4.1
3.3.4.2

viii

3.4 Discussion . .

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tcool/tﬀ Proﬁles and Multiphase Gas . . . . . . . . . . . . . . . . . . . . . 48
3.4.1
3.4.1.1 Comparison with Previous X-ray Analysis . . . . . . . . . . . . . 50
3.4.2 Radio Luminosity and tcool/tﬀ . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.3 Comparison to Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4.4 Metallicity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

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3.5 Conclusions .

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4.3.4

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CHAPTER 4 RELATIONSHIPS BETWEEN CENTRAL VELOCITY DISPERSIONS

4.4 Discussion .

4.1 Abstract
4.2
4.3 Methods .

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Introduction .
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4.3.1
4.3.2 Theoretical Model
4.3.3 Entropy Proﬁles .

AND ATMOSPHERES OF EARLY-TYPE GALAXIES . . . . . . . . . . . 58
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
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Sample Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
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4.3.3.1 Distribution of Central Entropy . . . . . . . . . . . . . . . . . . 66
Sub-Sample Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4.1 Low Central Entropy, Restricted σv, and the Analytical Prediction . . . . . 68
4.4.1.1
The Black-hole Feedback Valve Prediction . . . . . . . . . . . . 68
4.4.1.2 Comparison to the Analytic Prediction . . . . . . . . . . . . . . 68
4.4.2 Comparison to the Analytic Model and Numerical Integration Results . . . 71
4.4.3 Best ﬁt Entropy Proﬁle Slope, Multiphase gas extent, and min(tcool/tﬀ)
. . 72
4.4.4 Comments on Individual Galaxies . . . . . . . . . . . . . . . . . . . . . . 76
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.4.1 M87 .
. 76
4.4.4.2 NGC 4636 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 77
4.4.4.3 NGC 1521 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 77
4.4.4.4 NGC 4125 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 78
4.4.4.5 NGC 1404 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.4.6 NGC 533 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 78
Predictions for Equilibrium Pressure and Density Proﬁles . . . . . . . . . . 78
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
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APPENDIX A ACCEPT 2.0 PIPELINE DESCIPTION . . . . . . . . . . . . . . . . . 86
APPENDIX B ACCEPT 2.0 CENTRAL ENTROPY FITTING RESULTS . . . . . . . 91
APPENDIX C ACCEPT 2.0 RADIAL ENTROPY PROFILES . . . . . . . . . . . . . 104
APPENDIX D ACCEPT 2.0 MORPHOLOGICAL PROPERTIES . . . . . . . . . . . 154
APPENDIX E

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CHAPTER 5 SUMMARY .
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5.1 Summary .
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5.2 Future Work . .
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RADIAL PROFILES OF EARLY-TYPE GALAXIES WITH POW-
ERFUL RADIO SOURCES . . . . . . . . . . . . . . . . . . . . . . . 171

4.5 Conclusions . .

APPENDICES .

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4.4.5

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ix

APPENDIX F

RADIAL PROFILES FOR THE GALAXIES IN LAKHCHAURA
(2018)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

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BIBLIOGRAPHY .

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x

LIST OF TABLES

Table 2.1: ACCEPT vs. ACCEPT 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Table 2.2: Density Errata in ACCEPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Table 3.1: Chandra Observations of Early-type Galaxies . . . . . . . . . . . . . . . . . . . 43

Table 3.2: Sample of Radial Proﬁle Properties

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Table 4.1: Galaxy Parameters .

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Table 4.2: Entropy Proﬁle Slope and Velocity Dispersion Relationship Results

. . . . . . . 68

Table B.1: Fit parameters, redshift, and proﬁle center for ACCEPT 2.0 clusters

. . . . . . . 91

Table D.1: Morphological properties for ACCEPT 2.0 clusters . . . . . . . . . . . . . . . . 155

Table E.1: Radial proﬁles for early-type galaxies with powerful radio sources . . . . . . . . 171

Table F.1: Radial proﬁles for the HQ sample . . . . . . . . . . . . . . . . . . . . . . . . . 177

xi

LIST OF FIGURES

Figure 1.1: Hubble Deep Field .

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Figure 1.2: Hubble Tuning Fork .

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Figure 1.3: SDSS DR1 Cosmic Voids . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1.4: Virgo Cluster SDSS Optical . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Figure 1.5: Hubble H0 diagram .

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Figure 1.6: Deprojection .

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Figure 1.7: Composite Image of Hercules A . . . . . . . . . . . . . . . . . . . . . . . . . 15

Figure 2.1: MCMC ﬁt results

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Figure 2.2: Central Entropy for ACCEPT vs. ACCEPT 2.0 . . . . . . . . . . . . . . . . . . 25

Figure 2.3: Distribution of Central Entropy for clusters present in both ACCEPT and

ACCEPT 2.0 .

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Figure 2.4: Distribution of Central Entropy for clusters in ACCEPT with all clusters with

a measured Central Entropy in ACCEPT 2.0 . . . . . . . . . . . . . . . . . . . 27

Figure 2.5: Morphological Property Comparison for ACCEPT 2.0 . . . . . . . . . . . . .

. 31

Figure 2.6: Central Entropy vs. concentration for ACCEPT 2.0 . . . . . . . . . . . . . .

. 32

Figure 2.7: Morphological Property Comparison for the REFLEX sub-sample of AC-

CEPT 2.0 .

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Figure 2.8: Central Entropy vs. concentration for XMM Heritage and REFLEX sub-

samples of ACCEPT 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Figure 2.9: Morphological Property comparison for the XMM Heritage sub-sample of

ACCEPT 2.0 .

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Figure 3.1: Entropy Proﬁles for early-type galaxies with powerful radio sources . . . . . .
. 48
Figure 3.2: Radial proﬁles of tcool/tﬀ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

xii

Figure 3.3: Radio luminosity, min(tcool/tﬀ), and radius at min(tcool/tﬀ) . . . . . . . . . . . 52
. 53
Figure 3.4: Entropy proﬁles of NGC 4261 and IC 4296 compared to simulations . . . . .

Figure 3.5: Comparison of the inferred entropy proﬁles for NGC 4261 for diﬀerent as-

sumed values of abundance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 4.1: Stellar velocity dispersion vs. X-ray luminosity . . . . . . . . . . . . . . . . .

. 61

Figure 4.2: Distribution of K0 values for the HQ sample . . . . . . . . . . . . . . . . . . . 66

Figure 4.3: Stellar velocity dispersion vs. entropy proﬁle slope for the HQ sub-sample of

galaxies

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of galaxies .

Figure 4.4: Stellar velocity dispersion vs. entropy proﬁle slope for the low K0 sub-sample

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Figure 4.5: αK vs. min(tcool/tﬀ) for the main sample and αK by gas extent for the HQ sample 73
Figure 4.6: αK vs. min(tcool/tﬀ) and αK by gas extent for the low K0 sample . . . . . . . . 74
Figure 4.7: Equilibrium pressure vs. radius for single phase and multiphase galaxies in

the HQ sample . .

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Figure 4.8: Equilibrium electron density vs.

radius for single phase and multiphase

galaxies in the HQ sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Figure C.1: ACCEPT 2.0 Entropy Proﬁles and Fit Information . . . . . . . . . . . . . . . . 105

xiii

CHAPTER 1

INTRODUCTION

1.1 Galaxy Clusters and Early-Type Galaxies

The Hubble Deep Field image (Figure 1.1, Williams et al. (1996)) revealed that there are 3,000
galaxies visible in just one twenty-four-millionth of the sky, indicating that the universe is full of
galaxies. The masses, stellar populations, and shapes of galaxies vary widely, and astronomers still
often use the early Hubble classiﬁcations of galaxies to group them by their deﬁning characteristics.
Broadly, there are elliptical, spiral, and irregular galaxies. The Hubble “tuning fork” (see Figure
1.2) was developed because Hubble believed that elliptical galaxies would eventually evolve into
spiral galaxies. The belief that ellipticals evolved into spirals turned out to be incorrect, but the
naming convention of referring to generally elliptical shaped galaxies as “early-type” and spiral
shaped galaxies as “late-type” has prevailed and will appear in this dissertation. While the tuning
fork does not sort galaxies by evolutionary stage, it does sort them by their angular momentum with
spiral galaxies generally rotating faster than elliptical galaxies. Elliptical galaxies are generally red
in color, contain mostly older, low mass stars, have little active star formation, and are the most
massive galaxies. Spiral galaxies, like our own Milky Way, are generally blue in color, have all
types of stars, and are actively forming stars. Irregular galaxies have no speciﬁc shape, contain all
types of stars, are usually actively forming stars, and are typically the least massive of the three
types. Particularly low mass galaxies are known as dwarf galaxies, but they are beyond the scope
of this dissertation.

More recently, sky surveys of galaxies (the 2dF Galaxy survey (Colless et al., 2001) and the
Sloan Digital Digital Sky Survey (Stoughton et al., 2002)) revealed that galaxies are clumped
together along large scale ﬁlaments around large voids with diameters of ∼150 million light years
(see Figure 1.3) . The large scale ﬁlaments trace the distribution of dark matter in the universe.
Dark matter and dark energy are so named because we cannot directly observe them; we can only

1

Figure 1.1: Hubble Deep Field The Hubble Deep Field image shows the 3,000 galaxies found in
one twenty-four-millionth of the sky. The image was composed of data from the Hubble Space
Telescope taken over ten days in 1995 and published in 1996 (Williams et al., 1996).

2

Figure 1.2: Hubble Tuning Fork The original tuning fork diagram from Hubble’s 1936 book,
The Realm of the Nebulae (Hubble, 1936). Hubble developed the tuning fork to classify galaxies
by their “family traits” and thought that galaxies evolved along the tuning fork from ellipticals to
spirals. While we now know that the classiﬁcations are not evolutionary, but rather by angular
momentum, astronomers still classify galaxies in this way.

observe their gravitational inﬂuence on the universe. Dark matter and dark energy represent most
of the content of the universe, with dark energy comprising ∼ 70% and dark matter comprising
∼ 25% (Planck Collaboration et al., 2016). However, the focus of this dissertation is on the normal,
or “baryonic,” matter in the universe. Baryons make up the remaining ∼ 5% of the matter in the
universe. However, there are some baryons that can be diﬃcult to detect, leading to the “missing
baryon problem” in Cosmology.

The “missing baryon problem” refers to the disparity between the baryonic mass density inferred
from primordial nucleosynthesis via Cosmic Microwave Background (CMB) measurements and
the baryonic mass density of galaxies, where the baryonic mass from galaxies falls far short of
the baryonic mass from the CMB. The “Warm-Hot-Intergalactic-Medium” (WHIM) model was
proposed to account for the missing baryons (see Cen & Ostriker 1999; Bregman 2007). The
WHIM is characterized by a low-density, hot (105 − 106 K, Davé et al. (1999)) plasma which
produces a weak signal and would be challenging to detect. Bregman et al. (2018) showed that

3

Figure 1.3: SDSS DR1 Cosmic Voids The distribution of galaxies from the ﬁrst Sloan Digital Sky
Survey (SDSS) data release (Stoughton et al., 2002). The green galaxies are from the main SDSS
galaxy sample, and the red galaxies are from the luminous red galaxy sample (LRG).

baryon density estimates could be made, even with a weak signal, by stacking X-ray observations of
many early-type galaxies, scaled by their radii (R200). The stacked observations revealed that most,
if not all, of the “missing baryons” are hot and located beyond R200. While the source of missing
baryons for early-type galaxies can be accounted for with the stacked X-ray observations, Bregman
et al. (2018) also showed that the observed signal from early-type galaxies would be too high for
spiral galaxies. Therefore, the hot halos of spiral galaxies may be diﬀerent, and further constraints
on the hot gas content of early-type galaxies are needed from next generation X-ray observatories.
The large scale structure of the universe likely formed in a “bottom-up” fashion, meaning that

4

Figure 1.4: Virgo Cluster SDSS Optical Image of the Virgo Cluster assembled from SDSS DR15
optical data (Aguado et al., 2019). The Brightest Cluster Galaxy (BCG) is M87 (NGC 4486) and
is marked by the cross-hairs, and the 20’ scale corresponds to 100 kpc.

smaller scale structures merge and join together to create larger structures, along the distribution
of dark matter. The largest gravitationally bound structures in the universe are galaxy clusters,
composed of 100s-1000s of galaxies, all within a large clump of dark matter known as a dark
matter potential well (see Figure 1.4). Galaxy clusters can contain all types of galaxies, but the
majority of galaxy clusters are dominated by one galaxy called the Brightest Cluster Galaxy (BCG).
BCGs are usually the brightest, most massive galaxies in a cluster, are centrally located in the cluster,
and are usually elliptical galaxies. The BCG and the cluster evolve together, and understanding
how BCGs (and massive elliptical galaxies) work is crucial for understanding how galaxy clusters
evolve.
1.2 Cosmology Primer

Hubble (1929) observed a sample of galaxies and found that all galaxies are moving away
from our own, and their recessional velocities are proportional to their distance from our galaxies

5

Figure 1.5: Hubble H0 diagram Figure 1 from Hubble (1929) shows the distances and velocities
to the sample of galaxies Hubble used to show that the universe is expanding. The y-axis are the
radial velocities, corrected for solar motion, and the x-axis are the distances estimated from stars
and mean luminosities in the galaxies. The slope of this distance-velocity relationship is the Hubble
parameter, H0.

(see Figure 1.5). The velocity-distance relation, v = H0 r (Hubble’s Law), where H0 is referred
to as Hubble’s constant, shows that the universe is expanding uniformly. Hubble’s constant
characterizes the expansion of the universe and remains an active area of research. Type Ia
supernovae measurements give H0 = 73.8 ± 2.4 km s−1 Mpc−1 (Riess et al., 2011), while Cosmic
Microwave Background measurements give H0 = 67.4± 0.5 km s−1 Mpc−1 (Planck Collaboration
et al., 2018). In this dissertation, we will use the widely accepted value for a cold-dark matter
cosmology of H0 = 70 km s−1 Mpc−1. The eﬀect of choosing the Type Ia supernovae value
or Cosmic Microwave background value is much smaller than the statistical uncertainty for our
relevant measurements, so our choice to use single digit precision for H0 is negligible for this work.
Furthermore, for the work in Chapters 3 and 4, the galaxies are nearby enough to have distance
measurements independent of H0. In modern astronomy, when it became possible to obtain spectra

6

of galaxies, the distances to galaxies could be described more precisely with a quantity known as
redshift, z. Redshift is measured by the shift of the galaxy’s spectrum due to its motion away from
us in the the expanding universe. The shifting of a receding galaxy’s optical spectrum is similar to
how an ambulance’s siren appears to drop in pitch as it drives away. In the case of the ambulance,
the frequency of the receding siren is lowered and can be measured by the Doppler eﬀect for a
receding source. For a receding galaxy, the shift is observed in the optical (rather than sound)
spectrum, but the eﬀect is similar. The spectrum shifts to longer (redder) wavelengths the farther
the galaxy is from us because we know from Hubble’s Law that the farther a galaxy is from us, the
faster it is moving. The redshift, z of the galaxy’s spectrum is therefore

λobs − λrest

λrest

z =

(1.1)

where λobs is the observed wavelength, and λrest is the emitted wavelength. A small redshift
indicates that the galaxy is in the local universe, and a larger redshift indicates that the galaxy is far
away. Because higher redshifts correspond to larger distances, which in turn correspond to longer
light travel times, high redshift galaxies also provide us with an idea of how the universe looked
at earlier times. For context, the most distant conﬁrmed lensed quasars1 are around z ∼ 6.5 (Fan
et al., 2019). The largest spectroscopic redshift obtained from a galaxy (GN-z11) is at z = 11.1
(Oesch et al., 2016). However, the nearby galaxies in this dissertation range from z = 0.001 − 0.02
(corresponding to a luminosity distance, DL, of ∼ 4 − 90 Mpc), and the galaxy clusters extend to
z ∼ 1.5 (DL ∼ 104 Mpc).

The expansion of the universe provides insight into what sort of universe we live in, and key
cosmological parameters describe fundamental characteristics of that universe. As the quality of
observations has increased along with our theoretical understanding, our ability to describe the
universe with cosmological parameters has improved. Cosmic Microwave Background (CMB)
measurements showed that, in general, the universe is homogeneous and isotropic, and thus, H0
1“Quasi-stellar objects,” are extremely luminous Active Galactic Nuclei (AGN) found in the
centers of early galaxies. AGNs are compact regions at the centers of galaxies with higher than
normal luminosity and have spectra that indicate the excess luminosity is not from stars.

7

should be constant in all directions. However, because the expansion of the universe is accelerating
due to the presence of dark energy, H0 is dependent on redshift by:

where E(z) =(cid:112)

H(z) = H0 E(z),

(1.2)

ΩM(1 + z)3 + ΩΛ, and the cosmological parameters ΩM (cid:39) 0.3 and ΩΛ (cid:39) 0.7
refer to the matter and dark energy content of the universe, respectively. For this dissertation, we
will assume the stated values for ΩM and ΩΛ when determining distances and spatial properties
of galaxy clusters and early-type galaxies, except when redshift-independent distance measures are
available in the case of nearby galaxies (see Chapter 3). The eﬀect of using lower precision values
for ΩM and ΩΛ aﬀect E(z) by ∼ 2%, which is much lower than our statistical uncertainty, so we
are safe to make this assumption for this dissertation.
1.3 X-ray Observations

1.3.1 A Brief History of X-ray Astronomy

Much of the work in this dissertation builds on a long history of discoveries in the X-ray universe.
We can trace the historical context and motivation for my study of early-type galaxies and galaxy
clusters from the early days of X-ray astronomy to now.
In contrast to many other ﬁelds of
observational astronomy that date back hundreds to even thousands of years, the ∼ 70 year history
of X-ray astronomy is comparatively short. Because X-rays are almost entirely blocked by the
Earth’s atmosphere, the only way to observe the X-ray universe is from space. As a result,
observations of the X-ray universe were out of reach until detectors could be launched suﬃciently
high in the atmosphere. Giacconi et al. (1962) launched a rocket that detected Sco X-1, the ﬁrst
X-ray source besides the Sun (ﬁrst observed in the late 1940s (Burnight, 1949)), and detected an
isotropic X-ray background. The discovery of the ﬁrst X-ray source was monumental and inspired
further exploration of the X-ray universe.

The ﬁrst observations of extra-galactic X-ray sources were made with the Uhuru X-ray satellite
(Giacconi et al., 1971), launched in 1970. In a series of 4 letters (Giacconi et al. 1971; Tananbaum
et al. 1971; Gursky et al. 1971; Kellogg et al. 1971), presented observations from Uhuru that

8

conﬁrmed the existence of extra-galactic X-ray sources. Furthermore, they provided observations
of the spectral features and the variability of X-ray sources and the structure of X-ray emitting
regions at a resolution of 30(cid:48). The observations also led to the ﬁrst observations of extended
emission from galaxy clusters from the Perseus cluster (Forman et al., 1972). The results from the
Uhuru satellite planted the ﬁrst seeds for a great X-ray observatory that would eventually lead to
the launch of Chandra in 1999.

One major question X-ray astronomers sought to address when developing the successors to
Uhuru was whether the extended emission from extra-galactic X-ray sources was due to the inte-
grated contributions of several discrete X-ray point sources or from diﬀuse processes, particularly
in galaxies. To address the question of the nature of the extended emission, the Einstein X-ray
telescope (Giacconi et al., 1979b) was developed and launched in 1978 with signiﬁcantly increased
spatial resolution and sensitivity (∼ 106 more sensitive than the early X-ray detectors). Einstein
showed that many clusters of galaxies were “young” in dynamical age and involved in mergers
rather than “old” and dynamically relaxed (Jones et al. 1979; Jones & Forman 1984). Forman et al.
(1985) showed that early-type galaxies have hot gaseous coronae, a discovery that still inﬂuences
our exploration of the hot gas in early-type galaxies today. Einstein conﬁrmed the presence of
extended X-ray emission in galaxy clusters, but nearby, early-type galaxies remained an area of
debate (see Sarazin (1986) for a review). While observations of the emission from early-type galax-
ies from Einstein did contribute to understanding the extended emission from nearby early-type
galaxies (Giacconi et al., 1979a), the debate over its origin continued and would continue until
Chandra began collecting data and showed clear evidence for diﬀuse, extended, X-ray gas from the
Intracluster Medium (ICM) and Circumgalactic Medium (CGM).

In between the Einstein and the launch of ﬁner spatial resolution X-ray telescopes, the Roentgen
Satellite (ROSAT; Pfeﬀermann et al. (1987)) provided the ﬁrst spatially-resolved X-ray all-sky
survey. ROSAT was launched in 1990 and completed its all-sky survey in the ﬁrst 6 months and
continued to take pointed observations for the next nine years. The satellite was sensitive to the
“soft” X-rays between 0.1–2 keV, and contributed to mapping the diﬀuse galactic X-ray background

9

(Snowden et al., 1995) among many other discoveries. ROSAT remains the best X-ray all-sky
survey to this day, though it will soon be succeeded by eROSITA (Merloni et al., 2012) which
will complete an X-ray all sky survey by 2023 at similar angular resolution and ten times greater
sensitivity than ROSAT.

1.3.1.1 Chandra X-ray Observatory

NASA’s Chandra X-ray Observatory (Weisskopf et al., 2002) is a telescope specially designed to
detect X-ray emission from very hot regions of the universe such as exploded stars, clusters of
galaxies, and matter around black holes. The telescope orbits above the Earth’s atmosphere, up
to an altitude of 139,000 km, to capture the X-rays normally blocked by the atmosphere. The
telescope was launched on July 23, 1999 and has been providing unparalleled X-ray observations
for almost 20 years.

Chandra carries four precisely-constructed mirrors nested inside each other. Using data acquired
with X-ray CCD detectors, detailed spectroscopic images of the cosmic source can be made and
analyzed. Chandra has unparalleled spatial resolution and has provided countless insights for the
X-ray universe. One of the richest contributions of Chandra is the publicly available Chandra Data
Archive of observations, and the analysis software (CIAO) developed to reduce the data (Fruscione
et al., 2006). The Chandra X-ray observations used in this dissertation are entirely from the archive,
and this work would not be possible without the available data and the software tools to reduce and
analyze it.

1.3.2 X-ray Observables

In this dissertation, we are primarily concerned with the radial properties of extended X-ray
sources: galaxies and galaxy clusters. X-ray telescopes, like Chandra and XMM, obtain temporal,
spatial, and energy information about X-ray photons emitted from the hot gas in galaxy clusters
and early-type galaxies. The X-ray emission from the hot gas is primarily in the form of thermal
bremsstrahlung radiation, due to interactions where electrons pass close to ions and lose energy.

10

While the temperature of the hot gas in galaxy clusters is hotter than groups or individual galaxies,
they all exhibit extended X-ray emission, meaning that the X-ray emission is coming from diﬀuse,
hot gas, rather than point sources (see Sarazin (1986) for a review). In galaxies, the extended X-ray
gas is called the circumgalactic medium (CGM), and in galaxy clusters, it is called the intracluster
medium (ICM). The hot gas traces the gravitational potential well and is aﬀected by both thermal
and gravitational processes, so we use observations of the hot gas to explore changes across the
galaxy or cluster’s radius.

The temperature of the hot gas can be directly measured from X-ray observations, and the
density can be measured by modeling the hot gas properties (e.g. cooling, emissivity, metallicity)
and accounting for the hydrogen column density (NH). Because clusters and nearby early-type
galaxies are large enough to be spatially resolved by Chandra and XMM, we can break up the
images of extended sources into concentric annuli, usually centered on the peak or centroid of
the X-ray emission, to obtain independent X-ray spectra. Then we use the spectra to derive
radial proﬁles of temperature and density. The width of the annuli is usually set by a signal-to-
noise threshold based on the science goals for a particular analysis but must be larger than the
observatory’s point-spread-function (PSF) to avoid signiﬁcant corrections for light scattered from
outside the annuli or from other annuli. Proﬁles constructed from two-dimensional annuli are
known as “projected” radial proﬁles because the emission is assumed to be two-dimensional, and
the annuli are independent of each other. Projected proﬁles can be useful, particularly because of
their low computational cost, but they are limited in their ability to capture the three-dimensional
nature of the hot gas. Therefore, we rely on deprojection techniques to extract radial properties.

1.3.3 Deprojection as a Tool for X-ray Spectroscopy

If we can assume that the emissivity of the gas is constant and optically thin within a spherical shell,
we can use deprojection to obtain three-dimensional source properties from a two-dimensional
image. Figure 1.6 shows a geometric view of how deprojection works. The ICM/CGM are
approximately spherical, the gas is optically thin, and variations in the gas properties are small

11

Figure 1.6: Deprojection Geometric view of how deprojection works. The two-dimensional annuli
are converted to spherical shells to obtain two-dimensional source properties of a three-dimensional
object, in this case, a galaxy or galaxy cluster.
Image courtesy of deproject documentation
(https://deproject-test.readthedocs.io).

across annuli, so deprojection is well suited for obtaining radial proﬁles. Like projected proﬁles,
the image is broken up into annuli, centered approximately on the peak of the X-ray emission, based
on a signal-to-noise threshold for the annuli. However, rather than each annulus being independent,
the spectra of the annuli are ﬁt from the outermost annulus inwards, with each bin accounting for
the properties of the previous bins. The technique is often referred to as “onion-peeling” because it
treats the source as an onion where each annulus is representative of a spherical shell of emission,
so the emission in an annulus includes contributions from all external annuli, like a core sample
from an onion would contain contributions from all the layers.

Deprojection requires more computational time because of the iterative spectral ﬁtting process
and does not work as well for emission that is not centrally peaked or radii where the emission is close
to the contributions from the background. However, it does provide more accurate measurements
for temperature and density in the centers of galaxy clusters and early-type galaxies where we are
most interested in the radial gas properties. This dissertation contains multiple uses of deprojected

12

proﬁles to better understand the ICM and CGM at smaller radii.

1.3.4 Using Entropy to Understand X-ray Gas

The conventional deﬁnition of entropy, dS = dQ/T, is not easily determined from X-ray observa-
tions, so we must resort to a simpler surrogate for entropy, an adiabat. For an ideal monoatomic
5/3, where K is the adiabatic constant and ρ is the
gas, the adiabatic equation of state is P = K ρ
number density. Recasting that equation in terms of the X-ray observables temperature and electron
density, we get the quantity we call entropy:

K = kTkeV n−2/3

e

,

(1.3)

where kTkeV is the temperature of the gas in keV, and ne is the electron density. It is the preferred
physical quantity for capturing feedback in galaxies because the density and temperature of the
gas can change independently. Feedback processes such as thermal cooling, supernovae, or AGN
outbursts do not necessarily heat the gas, but they can change the rate at which it radiates energy
away which can change the time it takes the gas to cool. Entropy tracks gains and losses of energy
in the X-ray gas. The galaxy potential well serves as an entropy sorting device, with higher entropy
gas at outer radii and lower entropy gas at small radii. The lowest entropy gas is the densest and
brightest in the X-ray.

1.3.5 Morphology

In addition to determining the gas properties from X-ray observations, we can also quantify what
the galaxies and clusters “look” like, or their morphology. For a discussion of how to calculate
morphological properties, see Section 2.2.2.1, but here I will introduce the ways in which we
quantify the X-ray emission distribution qualitatively. We can describe how “peaked” the emission
is with a parameter referred to as concentration. Concentration is a ratio between the luminosity
interior to some inner radius to the total luminosity inside a larger radius. The value of the ratio is
between 0 and 1, where 1 indicates that all of the emission is within the inner radius and 0 indicates

13

that all of the emission would be outside the inner radius. X-ray luminosity is an observationally
easy measurement to make for most clusters, so determining how it relates to other properties of the
X-ray gas could allow us to make estimates for measurements that ordinarily require much longer
observations.

We can also determine how spherically symmetric, or “relaxed” the hot gas is by calculating
the centroid shift and power ratios. Full details of these calculations are provided in Section 2.2.2.
Centroid shift is measured by calculating the distance between the peak and centroid of the X-ray
emission and how that distance changes as the aperture for the measurement changes in size. Small
centroid shift indicates that the gas is more compact, and large centroid shift indicates that it is more
diﬀuse. For measurements of power ratios, any number of moments can be calculated for the hot
gas, but the most relevant are the 0th and 3rd moments because their ratio provides an indication
of asymmetries in the gas. The 0th moment is simply the total ﬂux, the 1st moment should be
near zero if the aperture is centered on the centroid, the 2nd moment estimates ellipticity, and the
3rd moment is sensitive to asymmetries in the surface brightness. If the 3rd moment is large in
comparison to the 0th moment, there is more substructure in the gas, meaning it is less symmetric
and less relaxed.
1.4 The Gas in Clusters and Early-Type Galaxies

In the center of (almost) every galaxy, there is a supermassive black hole that is tightly coupled
to the evolution of the galaxy (e.g. Kormendy & Richstone 1995; Haehnelt et al. 1998; Magorrian
et al. 1998; Ferrarese & Merritt 2000; Gebhardt et al. 2000; Kormendy & Ho 2013; Reines &
Volonteri 2015; Saglia et al. 2016; Ricarte et al. 2019). Many galaxies also have an Active Galactic
Nucleus (AGN) powered by accretion onto the black hole (Brandt & Hasinger, 2005). AGNs are
very small spatially in comparison to their host galaxy yet they are able to aﬀect the hot gas on
much larger scales (see Figure 1.7). How exactly the accretion fueling of the black hole is coupled
to the surrounding medium is still an unanswered question, but it may be through precipitation
driven feedback (e.g. Pizzolato & Soker 2005; McCourt et al. 2012; Voit et al. 2015b; Sharma et al.
2012; Voit et al. 2017). The precipitation model posits that feedback from the central black hole

14

Figure 1.7: Composite Image of Hercules A A composite image (X-ray (pink), optical, and radio
emission (blue)) for the nearby early-type galaxy Hercules A. The composite image illustrates the
importance of a multi-wavelength approach to studying the phenomena in galaxies and galaxy
clusters. NASA/CXC/SAO

holds the CGM in a state marginally unstable to condensation, so with the right conditions gas can
precipitate out. As gas cools and falls into the black hole, the AGN will turn on, heating the gas,
thus lengthening its cooling time and diminishing precipitation. In this dissertation, I will explore
how AGNs couple to the galactic atmosphere and aﬀect the gas entropy (see Chapters 3 and 4).

1.4.1 Multiphase Gas

Up to this point, I have focused on the hot X-ray emitting gas in galaxies and clusters, but I also
explored some of the other gas found in the ICM/CGM. At smaller radii in the ICM/CGM, we
ﬁnd multiphase gas: gas at diﬀerent temperatures and ionization states found in close proximity to
each other. The hot X-ray emitting gas is the volume-ﬁlling “ambient” phase of the atmosphere,

15

while the molecular gas is generally found towards the cluster/galaxy center. The presence of Hα
or CO emission usually indicates abundant molecular gas (Edge, 2001) and the potential for active
star formation. Some galaxies, particularly early-type or elliptical galaxies, have little to no active
star formation and thus have no extended multiphase gas, so we call these “single phase” galaxies.
Chapters 3 and 4 examine how the multiphase gas extent relates to other galaxy properties. We
also expect clusters to have multiphase gas if their gas entropy is low in the center.

1.4.2 SNIa Feedback in Clusters vs. Galaxies

In addition to feedback from AGN, this dissertation is also concerned with feedback from Type
Ia supernovae (SNIa), particularly with respect to its eﬀect on the hot atmospheres of early-type
galaxies (Voit et al., 2015b, 2020). Despite the generally older, low mass stellar populations of
elliptical galaxies, SNIa are found in early-type galaxies because SNIa progenitors are long-lived
white dwarf stars in binary systems. Unlike core-collapse supernovae, SNIa result from systems
where a two white dwarfs merge or a white dwarf accretes matter from a low-mass companion star
merge until oxygen fusion begins and the white dwarf explodes, rather than collapsing. Because
SNIa are found in older stellar populations, they can also be used as standard candles to measure
the expansion of the universe (see Section 1.2 and e.g. Riess et al. (2011)).

In galaxy clusters, the contributions to the sweeping of gas from inner radii via SNIa can usually
be neglected because the eﬀect is small in comparison to the inﬂuence of gravitational accretion
and AGN feedback processes. However, contributions from SNIa via stellar winds can be suﬃcient
to remove gas from the inner radii of an early-type galaxy. Chapter 4 discusses how stellar winds
from SNIa contribute to the balance of feedback and cooling in early-type galaxies.
1.5 Structure of this Dissertation

The structure of this dissertation is as follows. In Chapter 2, I will discuss the ACCEPT 2.0
entropy proﬁle and morphology measurements and present an early science application of the
ACCEPT 2.0 database. In Chapter 3, I will present the results of Frisbie et al. (2020) exploring
the thermal properties of the gas in a small sample of early-type galaxies with powerful radio

16

sources and compare them to simulations. In Chapter 4, I will present an observational test of
the black-hole feedback valve model for galactic atmospheres using early-type galaxies. Chapter 5
contains a summary of this dissertation as well as potential future projects.

17

CHAPTER 2

ACCEPT 2.0 AND XMM HERITAGE

2.1

Introduction

Most of the baryonic mass in a galaxy clusters is actually not in the galaxies but in the hot
(107−108 K) Intracluster Medium (ICM). The X-ray emission we observe comes from the radiation
of the ICM gas, and the baryons track the dark matter halo. In a galaxy cluster, the cooling of gas,
winds, and the heating of gas due to feedback from Active Galactic Nuclei (AGN) drive the cluster
cores away from hydrostatic equilibrium. To study the non-gravitational processes of the X-ray
gas, we primarily use the gas entropy (K) (see Section 1.3.4). Convection in the hot ICM, bound by
the gravitational potential of a cluster, causes high entropy gas to rise and low entropy gas to sink,
creating a positive entropy gradient across the cluster radius (dK/dr > 0). If the physics of the hot
ICM is dominated only by gravitational processes and gas accretion, the entropy should be a single
power law, so departures from power law entropy allow us to measure the eﬀect of feedback and
radiative cooling in the X-ray gas.

Cavagnolo et al. (2009) presented the ACCEPT (Archive of Chandra Cluster Entropy Proﬁle
Tables) project and showed that, generally, every galaxy cluster has an entropy excess near its center.
To quantify the entropy excess, they ﬁt a mathematical model of a power law with a core excess:

(cid:16)

(cid:17) α

K(r) = K0 + K100

r

100 kpc

,

(2.1)

where K0 is a characteristic central entropy, K100 is the best ﬁt entropy at a radius of 100 kpc,
and α is the best ﬁt power law slope. They measured K0 for a sample of 239 clusters and found
that, while the model to ﬁt the entropy proﬁles was a purely mathematical model, the distribution
of K0 values in the sample was bimodal with peaks at 15 keV cm2 and 150 keV cm2 and a
threshold entropy of 30 keV cm2. Furthermore, they found that clusters with “low” central entropy
(K0 < 30 keV cm2) generally also had multiphase gas present while clusters with “high” central
entropy (K0 > 30 keV cm2) never have multiphase gas. Therefore, central entropy serves as a

18

convenient way to sort galaxy clusters into those with BCGs that might have multi-phase gas and
those with BCGs that never have it.

The sorting of clusters by central entropy also fairly neatly separates clusters into cool core (CC)
and non-cool core (NCC). The division between cool-core and non-cool core arises from the radial
temperature proﬁles of clusters. Cool-core clusters have a drop in temperature towards the center
that aligns with a sharper peak in surface brightness and an increase in density. In non-cool core
clusters, however, the surface brightness peaks less dramatically, and their temperature proﬁles are
ﬂatter.

While the Chandra telescope remains the same, computational power and the number of clusters
observed have greatly increased since 2009. Therefore, the ACCEPT 2.0 project was established
in 2015. The X-ray data reduction was completed by Alessandro Baldi and full details of the
reduction pipeline can be found Section A.1. The morphological measurements were completed
with a pipeline written and run by Megan Donahue in 2018 (see Section 2.2.2.1). The main
improvements from ACCEPT to ACCEPT 2.0 are summarized in Table 2.1, but I will highlight the
most signiﬁcant for my thesis work here.

Table 2.1: ACCEPT vs. ACCEPT 2.0 Comparison between the data products of ACCEPT and
ACCEPT 2.0

# of Clusters
# of Proﬁles
Deprojected Density
Deprojected Temperature
Global T, L, Z
Morphology

ACCEPT ACCEPT 2.0

239
239
Yes
No
No
No

606
348
Yes
Yes
Yes
Yes

ACCEPT 2.0 contains entropy (and the associated temperature and density) proﬁles for 348
clusters and global measurements for up to 606 clusters. Deprojection is computationally intensive
because of the iterative ﬁtting process required, and in 2009, suﬃcient computational resources were
not available, so Cavagnolo et al. (2009) used projected temperature proﬁles instead. ACCEPT 2.0

19

uses deprojected proﬁles which provide a more accurate measure of the temperature and density
than projected temperatures. Rather than determining the temperature from two-dimensional
annulus, deprojected proﬁles use three-dimensional spherical annuli (see Section 1.3.3 for a full
description), accounting for the three-dimensional nature of galaxy clusters and providing more
accurate proﬁle measurements. In addition to more robust proﬁle measurements, ACCEPT 2.0
includes morphology (here referring to the shape and distribution of the X-ray gas) measurements
while ACCEPT did not. Finally, ACCEPT 2.0 contains global property measurements (temperature,
luminosity, and metallicity) for the sample while ACCEPT did not.
2.2 Entropy Proﬁle Fitting

The X-ray gas in clusters tends to be relatively spherically symmetric and centrally peaked
(usually on the BCG), so deprojection generally works well. However, deprojection does have its
limitations. The primary limitation that is relevant in this work is that when the diﬀerence between
the background and source emission is small, speciﬁcally in the outer edges of the cluster, the
contents of the deprojected bins can be over- or under- subtracted, resulting in a jagged proﬁle.
The jagged proﬁle results because one bin compensates for the estimated contents of an outer
bin. For that reason, direct deprojection is far more stable when the inner bins are far brighter
than the outer bins as in extended but centrally-peaked source distributions. Deprojection generally
assumes spherical or ellipsoidal symmetry, so clusters that have mergers, shocks, or other signiﬁcant
asymmetries in the X-ray gas will have more uncertain proﬁles. Finally, there is some covariance
in the radial proﬁle that would not be present in a projected proﬁle because projected annuli do not
attempt to consider contributions from other annuli as deprojection does, but it generally does not
need to be considered for my analysis.

Because entropy traces gains and losses of energy in the gas, we can use an entropy proﬁle
to gain an understanding of the thermal history of the cluster. The goal of ﬁtting entropy proﬁles
is to characterize the core excess of entropy because it provides a simple way of examining sub-
populations of galaxy clusters with similar characteristics. Speciﬁcally, Cavagnolo et al. (2009)
showed that there is some correlation between the presence of multiphase gas and cool-core clusters

20

and the absence of multiphase gas in non cool-core clusters. Furthermore, galaxy clusters with
low central entropy may have more peaked surface brightness proﬁles and may be more relaxed.
Therefore, central entropy measurements can provide additional ways to examine the morphological
properties of galaxy clusters, particularly with a sample as large as ACCEPT 2.0.

The entropy proﬁles are ﬁt with the functional form in Equation 2.1. While the functional form
describes the shape of the entropy proﬁle well, it is not a physically motivated model. Because the
data are not always smooth and not uniform across clusters, we elected to ﬁt the entropy proﬁles
Markov-Chain Monte Carlo ﬁtting, rather than simpler, less computationally expensive methods.
The best ﬁt parameters were determined using the emcee Python package. Because the best ﬁt
parameters for K0, K100, and α are not expected to have a particular a priori distribution, we
chose to initially limit parameter space broadly in log space for K0 and K100 (−102
< K0 < 103,
0 < K100 < 103) and linear space for α (0 < α < 2). To manage the computational time required,
we utilized 1000 parallel random walkers, each taking 1500 steps, to obtain a statistical distribution
for the best ﬁt parameters. See Figure 2.1 shows the results for one galaxy cluster (Abell 209).
Errors were determined from gaussian 1 σ contours in two dimensions (16-84%). The complete
results of these ﬁts are available in a table in Appendix B and radial entropy proﬁles are in Appendix
C.

For the purposes of classifying the clusters of ACCEPT 2.0 by central entropy, our priority was
to characterize the shape of the entropy proﬁles in the innermost regions of the galaxy clusters. In
80 of the clusters, to obtain a reasonable ﬁt in the central region, we restricted the radial range of
the ﬁt to the central radial bins (see Appendix C for radial ranges), rather than requiring a good ﬁt
to points at radii greater than ∼ 100 kpc. If restricting the radial range of the ﬁt did not improve the
statistical signiﬁcance of the ﬁt, or if there were insuﬃcient radial bins (less than 4) to ﬁt inside the
region of interest, we removed the proﬁle from the sample. Of the 606 galaxy clusters in ACCEPT
2.0, 348 had suﬃcient counts to ﬁt an entropy proﬁle. Of those 348 proﬁles, 39 were removed
from the sample because of insuﬃcient data resolution in the region of interest or the lack of a
statistically signiﬁcant ﬁt (reduced χ

> 1.1) in the region of interest.

2

21

Figure 2.1: MCMC ﬁt results Results of MCMC ﬁtting for the entropy proﬁles using emcee for
Abell 209. Abell 209 is used to represent the ﬁtting process because it has average data quality
for our sample and is present in both ACCEPT and ACCEPT 2.0 for validation purposes. Two
dimensional, marginal distributions of K0, K100, and α are given with respect to each other as
well as the distribution of each parameter independently with two dimensional gaussian 1σ errors,
represented by vertical dashed lines in one dimension and contours in two dimensions (lighter gray
in the center of the distributions).

22

2.2.1 Comparison to ACCEPT

As a ﬁrst validation of the ACCEPT 2.0 data reduction pipeline and central entropy ﬁtting and a test
of the conclusions from Cavagnolo et al. (2009), we compared the K0 results for clusters present
in both ACCEPT and ACCEPT 2.0 and the K0 results for all clusters in ACCEPT 2.0. While in
general the best ﬁt central entropies are slightly lower in ACCEPT 2.0 than in ACCEPT, there is
strong agreement between the clusters present in both samples, providing convincing validation
of both the entropy proﬁle ﬁtting procedure and the data reduction pipeline (see Figures 2.2 and
2.3). In Figure 2.4, we compare the best ﬁt K0 for all ACCEPT clusters with the best ﬁt K0 for all
ACCEPT 2.0 clusters. Cavagnolo et al. (2009) showed that the distribution of K0 was bimodal with
peaks at 15 keV cm2 and 150 keV cm2. They also showed that the characteristic central entropy,
K0 = 30 keV cm2, divides clusters into cool core and non-cool core clusters, and we recover that
same threshold entropy in the ACCEPT 2.0 cluster sample. Furthermore, ACCEPT showed that
K0 = 30 keV cm2 divides clusters into those with central radio sources and evidence for multiphase
gas (K0 < 30 keV cm2) and those without (K0 > 30 keV cm2), and we would expect the same
behavior from ACCEPT 2.0 clusters.

While it does not strongly aﬀect the agreement between ACCEPT and ACCEPT 2.0, there is a
small oﬀset between the results of ACCEPT and ACCEPT 2.0. Deprojected inner temperatures (as
we used in ACCEPT 2.0) are generally lower than projected temperatures (as we used in ACCEPT)
because deprojected temperatures are obtained by subtracting oﬀ the contribution of a spherical
shell rather than a two-dimensional annulus (as discussed in Section 2.2). Therefore, the slightly
lower characteristic central entropies in ACCEPT 2.0 are reasonable, and in fact expected. In my
comparison of ACCEPT to ACCEPT 2.0 proﬁles, I found that 21 (see Table 2.2 ACCEPT proﬁles
were systematically oﬀset from ACCEPT 2.0 as a result of an extraneous correction factor of ∼ 1.2
applied to the electron density computation in the ACCEPT proﬁles. However, the systematic
oﬀset in density was small relative to the uncertainty in temperature and the statistical uncertainty
in determining K0, so clusters with the oﬀset in ACCEPT remained in the comparison.

23

Table 2.2: Density Errata in ACCEPT Clusters listed in this table (by ACCEPT 2.0 name) are
clusters where the density provided by ACCEPT is systematically lower than the ACCEPT 2.0
density by a factor of ∼ 1.2.

ACCEPT 2.0 Name
MFGC_06756
Abell_223
ABELL_0402
ABELL_0611
ABELL_0963
ABELL_2069
ABELL_2813
ABELL_3088
ABELL_3444
ABELL_S0592
MACS_J2214-1359
MCXC_J0220.9-3829
MCXC_J0439.0+0520
MCXC_J0454.1-0300
MCXC_J0547.0-3904
MCXC_J1000.5+4409
MCXC_J1010.5-1239
MCXC_J1022.0+3830
MCXC_J1130.0+3637
ZwCl_0857.9+2107
ZwCl_0949.6+5207

2.2.2 Morphology Calculations and K0

Morphological measurements of galaxy clusters give us a way to characterize the shape and
distribution of the X-ray gas. The diﬀerent morphology measurements provide insight into the
history of galaxy clusters, including signiﬁcant mergers, star formation, and feedback processes.
We look at morphology measurements in relation to K0 for two primary reasons. First, because
K0 is a convenient way to divide a sample of galaxy clusters into groups with respect to the
presence of multiphase gas, we want to understand what correlations, if any, exist with respect to
the morphological properties (power ratio, P3/P0, centroid shift, w, and concentration, c). Second,
K0 is an observationally expensive measurement to make because it requires suﬃcient counts to

24

Figure 2.2: Central Entropy for ACCEPT vs. ACCEPT 2.0 K0 for ACCEPT vs. K0 for ACCEPT
2.0 to visualize consistency between the best ﬁt K0 values that overlap between the two samples.
Errors are 1-sigma. The blue line is a linear ﬁt to the data where the slope is the average of the ratio
between K0 for ACCEPT and K0 for ACCEPT 2.0, weighted by their statistical errors, and the red
line plots y = x (the results if the K0 values were perfectly consistent), for comparison.

construct a robust deprojected entropy proﬁle, and concentration requires far fewer counts, so we
want to determine if concentration could be used to sort cluster populations instead of K0.

2.2.2.1 Calculating Centroid Shift, Concentration, and Power Ratios

The morphological calculations were completed by Alessandro Baldi in 2015 (concentration) and
Megan Donahue in 2018 (centroid shift and power ratio) but the details are included here because
of their relevance to my thesis work. The full table of morphological properties can be found in
Appendix D.

25

101100101102103K0 (keVcm2) ACCEPT 101100101102103K0 (keVcm2) ACCEPT 2.0y=0.60xy=xFigure 2.3: Distribution of Central Entropy for clusters present in both ACCEPT and AC-
CEPT 2.0 Distribution of K0 for 164 clusters present in both ACCEPT and ACCEPT 2.0, with
statistically signiﬁcant ﬁts in ACCEPT 2.0. The ACCEPT clusters are in blue, and the ACCEPT
2.0 clusters are in yellow.

2.2.2.1.1 Centroid Shift

The centroid provides a measure of the center of gravity of the cluster and is calculated by:

cx =

(2.2)
where(xi, yj) are the coordinates of the pixels, and f(xi, yj) are the pixel values at those coordinates.
The dimensionless centroid shift, w, used in this work is based on the deﬁnition from Cassano et al.
(2010):

,

cy =

 yj f(xi, yj)
 xi f(xi, yj)
 f(xi, yj
 f(xi, yj
N − 1 Σ(∆i− < ∆ >)2(cid:105)1/2 1

Rmax

(cid:104)

1

w =

,

(2.3)

where the index i is for each sub-aperture (i runs from 1 to N, and in this case, N = 20), ∆i is the
distance between the X-ray peak within Rmax and the centroid of the i-th aperture, and < ∆ > is
the average of this separation for all the apertures. For this morphology analysis, Rmax = R2500
from the ACCEPT 2.0 core-excised global temperatures.

26

100101102103K0(keVcm2)05101520NACCEPTACCEPT2.0Figure 2.4: Distribution of Central Entropy for clusters in ACCEPT with all clusters with
a measured Central Entropy in ACCEPT 2.0 Distribution of K0 for 164 clusters in ACCEPT
with 348 clusters with a measured K0 in ACCEPT 2.0. The ACCEPT clusters are in blue, and the
ACCEPT 2.0 clusters are in yellow.

The centroid derived from the largest aperture was used for the power ratio estimations. The
ﬁrst moment, P1, is not particularly interesting but if it is close to zero, it veriﬁes that the centroid is
reasonable. The second moment, P2, gives the ellipticity and position angle, and the third moment,
P3, indicates asymmetries in the surface brightness. Following the treatment in Buote & Tsai
(1995), and noting that the surface brightness maps are in units of counts per image pixel (where
an image pixel for these maps was a double-binned physical pixel), Sx(x, y), is given as

Sint =

(cid:1),

2

< R2

max

Sx(cid:0)x2 + y
 Sx(x, y)x
 Sx(x, y)y

Sint

,

,

Sint

P1x =

P1y =

(2.4)

(2.5)

(2.6)

where x, y are deﬁned to be the horizontal and vertical oﬀset from the nominal centroid position.

27

100101102103K0(keVcm2)010203040NACCEPT2.0ACCEPTIf the centroid is correct, P1x ∼ P1y ∼ 0. We used this as an internal veriﬁcation for the
computation of centroids. The second moments lead to the computation of the ellipticity and
position angle inside 500 kpc or Rmax as allowed by the ﬁeld of view, similar to the procedure in
Donahue et al. (2014). We computed 3 terms,

Axx,yy,x y =

and then diagonalized the matrix,

 Sx(x, y) × (xx, yy, x y)
Axx Ax y

Ax y Ayy

,

(2.7)

(2.8)

Sint



to obtain the second moment. The morphological properties for ACCEPT 2.0 can be found in
Appendix D.

2.2.2.1.2 Concentration

Two surface brightness concentration parameters, c500 kpc and cR500, are computed to measure the
concentration of the X-ray-emission in the ACCEPT 2.0 clusters. Concentration has been deﬁned
in various ways in the literature. In this work, we adopt a common convention, that concentration
is a ratio, ranging from 0.0 to 1.0, between the total X-ray luminosity interior to an inner radius,
rinner, to the total luminosity inside a larger radius, router. If all the detected ﬂux is inside both
radii, then the concentration is close to 1.0, and if the source were somehow shaped like a donut,
with an empty center, the concentration would be zero. We have deﬁned two interpretations of
concentration: c500 kpc, where rinner = 100 kpc and router = 500 kpc (eg, Cassano et al. (2010)),
and cR500, where rinner = 0.1r500 and router = 0.5r500 (as in Rasia et al. (2012)).

2.2.2.1.3 Power Ratios

Power ratios (Buote & Tsai, 1995), mimic a multiple decomposition of the 2-D projected mass
distribution inside a certain aperture, Rap (R2500 for this analysis), but it is much simpler to apply
this decomposition to the X-ray surface brightness images S, instead of the mass. The m-th order

28

power ratio (m > 0) is deﬁned as Pm/P0 with
(a2
m + b2

Pm =

1

2m2R2m
ap

m); P0 = a0ln(Rap),

(2.9)

where a0 is the total intensity within the aperture radius, and am and bm are expressed in polar
coordinates (R and φ) and given by

am(r) =

and

R(cid:48)≤Rap

S(x(cid:48))(R(cid:48))mcos(mφ

(cid:48))d2x(cid:48)

,

(2.10)

Þ
Þ

bm(r) =

S(x(cid:48))(R(cid:48))msin(mφ

(cid:48))d2x(cid:48)

.

R(cid:48)≤Rap

(2.11)
The power ratio P2/P0 gives information about the cluster ellipticity and P3/P0 is an indicator
of bimodal distribution in the surface brightness and therefore is the most sensitive to detecting
asymmetries or substructures. P4/P0 is similar to P2/P0 but more sensitive to smaller scales. The
ACCEPT 2.0 pipeline computes all power ratios Pm/P0 with 1 ≤ m ≤ 6, but we will focus on
P3/P0 in this work because of its sensitivity to substructure and because it is less noisy than higher
order moments.
2.3 Science with ACCEPT 2.0

The primary goal of ACCEPT 2.0 was to provide a uniformly-reduced database of galaxy
clusters with as many X-ray observable properties as possible, given data reduction constraints.
While there are multiphase gas measurements for the clusters of ACCEPT, the sample in ACCEPT
2.0 can be used to further examine the presence or absence of multiphase gas and its correlation
with central entropy. The selection function of ACCEPT 2.0 is quite complicated because it is
a purely archival sample and therefore not only holds potential bias in mass, luminosity, and
other observables, but also in the selection of targets themselves. Future work could attempt to
characterize the selection function to answer scientiﬁc questions such as how common certain types
of clusters are and cosmological questions about the cluster mass function using the largest possible
sample. However, because ACCEPT 2.0 is a large, uniformly reduced sample, it is currently well
suited for drawing well-deﬁned sub-samples. As an example of this type of work, I have used

29

ACCEPT 2.0 data for an initial exploration of the sample of galaxy clusters observed through the
XMM Heritage project. The science uses for ACCEPT 2.0 discussed in this thesis represent just
a few of the countless projects that could use ACCEPT 2.0 to address key questions in cosmology
and cluster and galaxy evolution.

2.3.1 Morphological Properties and K0 for Sample Comparisons

Broadly, morphological properties describe what the galaxy clusters “look” like, including how the
X-ray gas is distributed (see Section 2.2.2.1 for details). Cassano et al. (2010) showed that, for a
small (32 clusters) sample, the power ratio P3/P0 is correlated with the centroid shift, w, and the
concentration, c; and concentration is correlated with centroid shift. Here, we will examine the
morphological properties for the ACCEPT 2.0 sample and two sub-samples; ROSAT-ESO Flux-
Limited X-ray (REFLEX) Galaxy Cluster Survey (Böhringer et al., 2004) and XMM Heritage.

In Figure 2.5, we show the results for correlation between P3/P0, w, and c500 for the entire
ACCEPT 2.0 sample. As in Cassano et al. (2010), we see correlation between P3/P0 and w, but the
correlation between P3/P0 and c500 is less clear. Overall, the clusters exhibit a correlation between
centroid shift and power ratio, and there are fewer clusters in the less relaxed, less symmetric
parameter space.

In Figure 2.6, we plot the central entropy ﬁt values and the concentration parameter. The hope
is that concentration could serve as a low-signal proxy for central entropy because we expect low
entropy clusters to be highly concentrated and high entropy clusters to not be as concentrated.
That is, if we know the concentration for a galaxy cluster with data quality insuﬃcient to get a
deprojected entropy proﬁle, we could make a prediction about the central entropy. While there is
weak correlation between c500 and K0, it is not strong enough to provide strong predictions for a
K0 measurement based on measured concentration. One weakness of c500 is that it is based on
r500, which may be too large a radius to be captured in the Chandra ﬁeld of view.

30

Figure 2.5: Morphological Property Comparison for ACCEPT 2.0 Power ratios compared to
centroid shift, w, and concentration, c500, colored by central entropy. Red points are clusters with
K0 > 30 keV cm2 and blue points are clusters with K0 < 30 keV cm2 for all of ACCEPT 2.0.

31

1011109107105P3/P0103102101100wK0<30keVcm2K0>30keVcm21010109108107106105P3/P0101c500K0<30keVcm2K0>30keVcm2Figure 2.6: Central Entropy vs. concentration for ACCEPT 2.0 Central entropy, K0, is plotted
with c500 for clusters in ACCEPT 2.0 to illustrate the potential for concentration to serve as a noisy
estimate of K0.

2.3.2 ACCEPT 2.0 Comparison with REFLEX and XMM Heritage

The XMM Heritage project seeks to create a signal to noise limited sample of deep observations
from XMM of 118 clusters from the Planck PSZ2 cosmological catalog. The targets include a
local sample at z < 0.2 with a mass range of 1014 M(cid:12) < M500 < 9 × 109M(cid:12) and the most
massive (M500 > 1014 M(cid:12)) clusters at z < 0.6. The ACCEPT 2.0 is an archival sample of
galaxy clusters observed by Chandra and is an expansion and analysis improvement of the ACCEPT
project (Cavagnolo et al., 2009). Here we combine our data products for clusters present in both
samples to gain insight into the properties of the X-ray gas in the XMM Heritage sample.

Bringing together the morphological properties and central entropies with the common clusters
between the two samples, we see that they exhibit a correlation between centroid shift and power
ratio, and the lower entropy clusters are not present at the less relaxed, less symmetric parameter
space (Figure 2.9). Shown in a diﬀerent way, we also ﬁnd that as in Bauer et al. (2005), cool core
clusters are more likely to be compact and symmetric.

32

Figure 2.7: Morphological Property Comparison for the REFLEX sub-sample of ACCEPT
2.0 Power ratios compared to centroid shift, w, and concentration, c500, colored by central entropy.
Red points are clusters with K0 > 30 keV cm2 and blue points are clusters with K0 < 30 keV cm2
for the REFLEX sub-sample of ACCEPT 2.0.

33

1011109107105P3/P0103102101100wK0<30keVcm2K0>30keVcm21010109108107106P3/P0101c500K0<30keVcm2K0>30keVcm2Figure 2.8: Central Entropy vs. concentration for XMM Heritage and REFLEX sub-samples
of ACCEPT 2.0 Central entropy, K0, is plotted with c500 for clusters in ACCEPT 2.0 and REFLEX
(left) and ACCEPT 2.0 and XMM Heritage (right).

Figure 2.7 shows the same plots as in Figure 2.9 but made for the common clusters between
ACCEPT 2.0 and the REFLEX sample (Böhringer et al., 2004). Between the two sub-samples
of ACCEPT 2.0, we see small diﬀerences in the plots for selection between X-ray ﬂux selected
(REFLEX) and high X-ray pressure selected (XMM Heritage/SZ) clusters. The pressure selected
sample that overlaps with ACCEPT 2.0 contains fewer cool core clusters and fewer symmetric,
relaxed clusters than the ﬂux selected sample overlapping with ACCEPT 2.0.

This work represents one of the early tests of the broad applications of the ACCEPT 2.0 project.
As more data for the XMM Heritage project are taken, we will be able to use the insights learned
from ACCEPT 2.0 to learn more about the thermal properties of the X-ray gas in these clusters. We
are also able to identify and conﬁrm Brightest Cluster Galaxy (BCG) coordinates for the overlapping
targets. Through our comparison of the XMM Heritage-ACCEPT 2.0 and REFLEX-ACCEPT 2.0
samples, we can begin to see the X-ray selection eﬀects for samples of galaxy clusters as well as
the value of archival data. The scientiﬁc applications for both ACCEPT 2.0 and the XMM Heritage
projects are widespread and extensive.

34

100101102K0 (keVcm2)0.050.100.150.200.250.300.35c500101102K0 (keVcm2)0.00.10.20.30.40.5c500Figure 2.9: Morphological Property comparison for the XMM Heritage sub-sample of AC-
CEPT 2.0 Power ratios compared to centroid shift, w, and concentration, c500, colored by cen-
tral entropy. Red points are clusters with K0 > 30keVcm2 and blue points are clusters with
K0 < 30keVcm2 for the XMM Heritage sub-sample of ACCEPT 2.0.

35

1011109107105P3/P0103102101100wK0<30keVcm2K0>30keVcm21010109108107106P3/P0101c500K0<30keVcm2K0>30keVcm22.4 Summary

ACCEPT 2.0 expands and improves upon the work done by Cavagnolo et al. (2009).

In
this chapter, I have presented the initial pipeline veriﬁcation via comparison to ACCEPT and a
few early science applications of the ACCEPT 2.0 data.
Initial veriﬁcation was accomplished
by comparing the deprojected temperature, density, and entropy proﬁles for the common clusters
between ACCEPT and ACCEPT 2.0 as well as comparing the overall sample characteristics of the
proﬁles and central entropy between ACCEPT and all ACCEPT 2.0 clusters. As in Cavagnolo et al.
(2009), I found that the distribution of central entropy was bimodal, with a break at 30 keV cm2
and peaks at ∼ 15 keV cm2 and ∼ 150 keV cm2. The distribution of central entropy suggests that
almost all galaxy clusters have a core excess of entropy, and that central entropy can approximately
divide galaxy clusters into cool core and non-cool core clusters, a classiﬁcation scheme that proves
to be useful when examining cluster properties for large samples.

We applied the classiﬁcation via central entropy to the XMM Heritage and comparison samples
to understand some of the selection characteristics, and we found that XMM Heritage has more
non-cool core clusters in the less relaxed, less symmetric parameters space compared to cool
core clusters. The distribution of clusters in the XMM Heritage sample by central entropy and
morphology may be the result of the sample being selected by X-ray pressure rather than X-
ray luminosity. Pressure selected samples are selected based on measurements of the Sunyaev-
Zeldovich eﬀect which is more signiﬁcant for less-relaxed clusters, like those that have undergone
recent mergers. We do ﬁnd that in the ACCEPT 2.0 sample, and more strongly in the XMM
Heritage sample, the power ratio and centroid shift do exhibit some correlation, supporting the
work of Cassano et al. (2010) on a smaller sample.

The ACCEPT 2.0 pipeline provides a large, uniformly reduced sample of galaxy cluster proper-
ties, and the measurements largely support claims about the distribution of galaxy cluster parameters
from previous works. Furthermore, ACCEPT 2.0 is an invaluable resource for comparisons to other
X-ray samples, particularly for understanding sample selection characteristics. We expect that AC-

36

CEPT 2.0 will provide a springboard for galaxy cluster studies for years to come.

37

CHAPTER 3

PROPERTIES OF THE CGM IN EARLY-TYPE GALAXIES WITH POWERFUL RADIO

SOURCES

This paper was published by the Astrophysical Journal Volume 899, number 2, in August 2020 (see
Frisbie et al. (2020)).
3.1 Abstract

We present an archival analysis of Chandra X-ray observations for 12 nearby early-type galaxies
hosting radio sources with radio power > 1023 W Hz−1 at 1.4 GHz, similar to the radio power of
the radio source in NGC 4261. Previously, in a similar analysis of eight nearby X-ray and optically
bright elliptical galaxies, Werner et al. (2012), found that NGC 4261 exhibited unusually low central
gas entropy compared to the full sample. In the central 0.3 kpc of NGC 4261, the ratio of cooling
time to freefall time (tcool/tﬀ) is less than 10, indicating that cold clouds may be precipitating out
of the hot ambient medium and providing fuel for accretion in the central region. NGC 4261 also
hosts the most powerful radio source in the original sample. Because NGC 4261 may represent an
important phase during which powerful feedback from a central active galactic nucleus (AGN) is
fueled by multiphase condensation in the central kiloparsec, we searched the Chandra archive for
analogs to NGC 4261. We present entropy proﬁles of those galaxies as well as proﬁles of tcool/tﬀ.
We ﬁnd that one of them, IC 4296, exhibits properties similar to NGC 4261, including the presence
of only single-phase gas outside of r ∼ 2 kpc and a similar central velocity dispersion. We compare
the properties of NGC 4261 and IC 4296 to hydrodynamic simulations of AGN feedback fueled by
precipitation. Over the course of those simulations, the single-phase galaxy has an entropy gradient
that remains similar to the entropy proﬁles inferred from our observations.
3.2

Introduction

Over the past two decades, Chandra has been used to observe the ambient medium of early-type
galaxies because of its high sensitivity in the soft X-ray band (0.5-2.0 keV) and its spatial resolution,

38

resulting in 2D spectroscopy of unprecedented quality (e.g. Kim et al. 2018; Diehl & Statler 2007,
2008a,b; Lakhchaura et al. 2018; Sun 2009). The hot atmospheres of those early-type galaxies
have provided key clues about the energetic processes known as “feedback” (McNamara & Nulsen,
2012; Soker, 2016; Fabian, 2012). X-ray signatures of feedback processes observed in the hot
atmospheres of nearby, early-type galaxies are also commonly and prominently observed in the
hot atmospheres of Brightest Cluster Galaxies (BCG), the brightest and most massive galaxies in
galaxy clusters. The supermassive black holes at the center of BCGs in clusters interact with the
surrounding medium, inﬂating bubbles of relativistic plasma (e.g. Boehringer et al. 1993; Churazov
et al. 2000; Fabian et al. 2003, 2006; Bîrzan et al. 2004; Dunn & Fabian 2006, 2008; Dunn et al.
2005; Forman et al. 2005, 2007; Raﬀerty et al. 2006; McNamara & Nulsen 2007). One insight
from studying feedback processes in galaxy clusters is that the activity state of the central Active
Galactic Nucleus (AGN) in a BCG is closely coupled to the thermodynamic state of the Intracluster
Medium (ICM) (e.g. Cavagnolo et al., 2008; Raﬀerty et al., 2008; Voit & Donahue, 2015; Voit
et al., 2015a). However, in individual early-type galaxies in groups, like those we discuss in this
work, the relationship may be a little more complex (Sun, 2009; Connor et al., 2014). Because
the gravitational potential depths are shallower for galaxies in groups than galaxies in clusters,
supernova explosions and galactic winds are energetically more important for galaxies than for
galaxy clusters. Furthermore, while nearly any reasonable amount of kinetic AGN output can be
contained in a cluster atmosphere, the question of whether or not a powerful AGN jet thermalizes
its energy output near or far from the AGN depends on the external gas pressure.
In turn, the
external gas pressure may depend on the large-scale structure the galaxy inhabits.

McNamara & Nulsen (2007, 2012) have summarized the evidence suggesting that black holes
suppress the star formation in massive galaxies, but how the accretion onto the black hole is aﬀected
by the surrounding hot gas is less clear. Precipitation-regulated feedback models hypothesize
that feedback suspends the ambient medium in a state that is marginally stable to multiphase
condensation. Feedback input aﬀects the thermodynamic state and susceptibility of the ambient gas
to condensation. Feedback output depends sensitively on the rate at which cold clouds precipitate

39

out of the hot medium (Pizzolato & Soker, 2005; Sharma et al., 2012; Gaspari et al., 2012, 2013,
2015, 2017; Voit et al., 2015b, 2017; Wang et al., 2019). Such a system is self-regulated, and ﬁnds
a balance at the marginally stable point.

Spatially resolved X-ray spectroscopy of the hot ambient medium provides insight into its
thermal evolution. The normalization and shape of an X-ray spectrum yields gas electron density
(ne), temperature (TX), and metallicity (Z). Broadly, for early-type galaxies, the temperature
of the hot gas is ∼1 keV with a nearly isothermal radial proﬁle, and the radial proﬁle of the
electron density approximately follows a power law. The temperature and density of the X-ray
gas, considered independently, do not reveal the thermal history because heating and cooling of
gravitationally conﬁned gas can cause it to expand or contract without much change in temperature.
However, combining these two X-ray observables to make the quantity K = kTXn−2/3
provides
us with more direct information about thermal history, because changes in kTXn−2/3
correspond
directly to changes in the speciﬁc entropy of the gas. Only gains and losses of heat energy in the gas
can change the entropy, so we can trace the thermal history of the ambient gas of a galaxy cluster
by observing the proﬁle K(r), which we will call an entropy proﬁle.

e

e

In addition to what we have learned from X-ray observations, numerical simulations show that
cool clouds can precipitate out of a galaxy’s hot gas atmosphere via thermal instability even if the
galaxy is in a state of global thermal balance, with heating approximately equal to cooling (Gaspari
et al., 2012; McCourt et al., 2012; Sharma et al., 2012). The critical criterion for precipitation is
the ratio between the cooling and freefall times of the gas. Here, the cooling time (tcool) is deﬁned
to be the time needed for a gas at temperature T to radiate an energy 3kT/2 per particle, and
the free fall time from a galactocentric radius r at the local gravitational acceleration g is deﬁned
to be tﬀ = (2r/g)1/2. We note that these models do not presume to claim that the gas must be
freely falling. The parameter tﬀ merely speciﬁes a useful dynamical timescale that characterizes
gravitationally driven motions. The freefall time does not assume anything about the turbulence,
viscosity, or other ﬂuid properties and is based on galaxy properties that can be inferred from
observations of the stellar light.

40

In both observations and in simulations (McCourt et al., 2012; Sharma et al., 2012; Gaspari
et al., 2012; Li & Bryan, 2014a), cooling appears to be fast enough for a fraction of the hot gas to
condense into cold clouds and precipitate out of the hot medium if tcool/tﬀ ∼ 10. Precipitation may
therefore play an essential role in maintaining the required state of global thermal balance if gas
cooled from the hot phase boosts the fuel supply for accretion (Pizzolato & Soker, 2010; Gaspari
et al., 2013, 2015; Li & Bryan, 2014a,b). In numerical simulations, accretion of precipitating clouds
can produce a black hole fueling rate two orders of magnitude greater than the Bondi accretion
rate of ambient gas. Such strong accretion then produces a feedback response that heats the gas,
bringing the system into approximate balance near tcool/tﬀ ≈ 10. Voit et al. (2015b) showed that
early-type galaxies do indeed have min(tcool/tﬀ) ≈ 10.

The hot atmosphere of an early-type galaxy can be broadly categorized as single-phase gas or
multiphase gas, depending on the extent of the Hα and [N 2] emission. Observationally, galaxies
with multiphase atmospheres have extended Hα and [N 2] emission present outside their centers
(central∼1 kpc), whereas galaxies with single-phase atmospheres have no evidence for extended Hα
emission outside of ∼ 2 kpc. X-ray observations of giant ellipticals from Werner et al. (2012, 2014)
showed that single- and multiphase galaxies are distinctly bimodal from 1–10 kpc. The entropy
proﬁles of single-phase galaxies scale as K ∝ r, while in multiphase galaxies the entropy scales
as K ∝ r2/3. However, both types exhibit excess entropy in the innermost kiloparsec equivalent to
∼ 2 keV cm2.

While Werner et al. (2012, 2014) showed that both single- and multiphase galaxies tend to have
entropy excesses relative to a power law in the central kiloparsec, one galaxy diﬀered from the
rest. X-ray observations of NGC 4261 from Werner et al. (2012) revealed that the entropy proﬁle
of NGC 4261 follows a single power law (K ∝ r), but instead of exhibiting an excess within the
central kpc, the power law continues into the central ∼0.5 kpc (∼4(cid:48)(cid:48)). The unusually low entropy in
the center (K ≈ 0.8 keV cm2) results in tcool/tﬀ < 10, putting it slightly below the limit at which
precipitation appears inevitable. NGC 4261’s radio luminosity is 2 orders of magnitude greater
than the rest of the Werner et al. (2012) sample, and the central jet power is 1044 erg s−1. Adopting

41

a central black hole mass of MBH = 5× 108M(cid:12) (Gaspari et al., 2013) would require an implausible
30% mass energy to jet power conversion eﬃciency for the radio source to be powered by Bondi
accretion alone (Voit et al., 2015b). Simulations from Gaspari et al. (2013, 2015) showed that a
transition to chaotic cold accretion could boost the jet power by up to 100 times over what Bondi
accretion of hot ambient gas could achieve and occurs when tcool/tﬀ ≈ 10.

Because this transitional regime has not been extensively investigated, we decided to explore
it by looking for other galaxies like NGC 4261. To that end, we analyzed an archival sample of
Chandra observations of 12 additional early-type galaxies with powerful radio sources.
In this
paper, we present a summary of our ﬁndings for this archival study, which yielded at least one
additional nearby analog, IC 4296, that similarly has both a steep entropy proﬁle with tcool/tﬀ < 10
at small radii and a powerful radio source.

The structure of our paper is as follows. Section 3.3 describes our sample selection, data analysis,
and our measurements of the thermodynamic properties. Section 3.4 presents a comparison of
tcool/tﬀ proﬁles to previous works, a comparison with simulations, and an analysis of the eﬀects
of metallicity assumptions on our measurements. Section 3.5 concludes by discussing how our
sample adds to the paradigm of precipitation-regulated feedback in massive galaxies. We assume
a ΛCDM cosmology with H0 = 70 km s−1 Mpc−1 and ΩM = 0.3 (ΩΛ = 0.7) throughout.
3.3 Sample Selection and Data Analysis

3.3.1 Sample Selection and Distances

NGC 4261 exhibits an unusually low central entropy, as well as tcool/tﬀ < 10 at r < 0.3 kpc (Voit
et al., 2015b). It also has a powerful radio source emitting 2.3× 1024 W Hz−1 in the 1.4 GHz band,
which may be powered by chaotic cold accretion onto the central supermassive black hole (Gaspari
et al., 2012, 2013, 2015) fed by precipitation of cold clouds out of the hot atmosphere (Voit et al.,
2015b).

In search of other systems similar to NGC 4261, we compiled a Chandra archival sample
of nearby (z < 0.02) massive early-type galaxies hosting radio sources with a power output

42

Table 3.1: Chandra Observations of Early-type Galaxies Column (1): galaxy name; Column (2):
redshift obtained from NEDa; Column (3): distance calculated from zspec with the exception of NGC
4374 and NGC 7626, for which we use redshift-independent distances from Tonry et al. (2001)
and Cantiello et al. (2007), respectively. Column (4): galactic neutral hydrogen column densities
from Kalberla et al. (2005) and HI4PI Collaboration et al. (2016); Column (5): radio ﬂuxes from
VLA or NVSS (Condon et al., 1998) except for NGC 4261 (PKS, Brown et al. 2011); Column (9)
whether there were suﬃcient counts to make deprojected temperature and density proﬁles for a
galaxy. Column (10): power-law entropy slope α determined by ﬁtting the relation K ∝ r α in the
1–10 kpc interval; Column (11): central velocity dispersion from Makarov et al. (2014); Column
(12): Hα+[N 2] morphology reported by Lakhchaura et al. (2018) from Connor (in preparation)
and Sun (in preparation), classiﬁed as follows: N: no cool gas emission; NE: Hα+[N 2] extent < 2
kpc; E: Hα+[N 2] extent ≥ 2 kpc; U: galaxies for which the presence/absence of Hα+[N 2] could
not be conﬁrmed with current observations.

1.4 GHz ObsID Exp Net CountsProﬁle

α

σv

(11)
197.6

(10)
−−
-
-
-

Hα+[N 2]
(Y/N) (1-10 kpc) (km s−1) Morphc,d
(12)
(9)
E
N
197.6±4.8
E
N
293.6±10.1
U
N
287.4±9.3
N
Y
Y 0.80±0.08 223.1±3.3
E
296.1±6.4
E
Y
191.8±16.6
-
N
252.8±11.3
-
N
Y 1.09±0.07 296.7±4.3
NE
Y 1.12±0.12 327.4±5.4
NEb
Y 0.75±0.05 277.6±2.4
NE
310.0±11.3 NE
Y
344.3±5.4
N
Y
266.6±3.7
Y
E

-
-
-

-
-
-

Galaxy

zspec D

NH,HI

(2)

(Mpc)(1020cm−2)(1024 W Hz−1)
(1)
(3)
NGC 193 0.01563.08
NGC 193 0.01563.08
NGC 315 0.01667.20
NGC 741 0.01875.42
NGC 13160.00625.51
IC 1459
0.00625.51
NGC 38010.01146.48
NGC 38940.01146.48
NGC 42610.00731.32
IC 4296
0.01250.64
NGC 43740.00318.37
NGC 47820.01563.08
NGC 54190.01458.94
NGC 76260.01158.34

(5)
0.468
0.468
0.973
0.327
9.75
0.1
0.296
0.125
2.58
5.52
0.125
3.33
0.146
0.222

(4)
2.46
2.46
5.88
4.24
1.99
0.94
1.99
1.83
1.61
3.95
2.90
3.10
5.40
4.59

(ks)
(6)
(7)
11389 93.13
11389 93.13
4156 53.84
17198 91.02
2022 29.86
2196 58.00
6843 59.20
10389 38.54
9569 100.34
3394 24.84
803 28.46
3220 49.33
5000 14.81
2074 26.54

per Bin

(8)
300
300
930
1500
450
300
330
300
1600
800
650
320
320
370

aThe NASA/IPAC Extragalactic Database (NED) is funded by the National Aeronautics and Space Administration and
operated by the California Institute of Technology.
bIC 4296 was identiﬁed as E in Lakhchaura et al. (2018). Since its multiphase gas is at < 2 kpc, we classify it here as
NE.
cBased on observations obtained at the Southern Astrophysical Research (SOAR) telescope, which is a joint project
of the Ministério da Ciência, Tecnologia, Inovações e Comunicações (MCTIC) do Brasil, the U.S. National Optical
Astronomy Observatory (NOAO), the University of North Carolina at Chapel Hill (UNC), and Michigan State University
(MSU)
dBased on observations obtained with the Apache Point Observatory 3.5-meter telescope, which is owned and operated
by the Astrophysical Research Consortium.

43

> 1023 W Hz−1 at 1.4 GHz (Condon et al., 1998, see Table 3.1). Other recent studies of Chandra
observations of early-type galaxies (e.g. Lakhchaura et al., 2018; Grossová et al., 2019; Juráňová
et al., 2019) include some of the same galaxies, but our sample emphasizes powerful radio sources
in order to identify galaxies similar to NGC 4261.

In our analysis, we used distances derived from the redshifts of the galaxies when calculating
the electron density, because the eﬀect of small uncertainties in distance on the inferred density,
entropy, and cooling time is small. However, for NGC 4374 and NGC 7626 we used the redshift-
independent measurements because the diﬀerences between the best redshift-independent distance
measurements and the redshift-dependent distances are large (20 − 30%; see Table 3.1).

In this work, we pay particular attention to NGC 4374 (M84), NGC 1316 (Fornax A), and
IC 4296 because Chandra observations of the central 10 kpc of those galaxies have the best signal-
to-noise ratios among those in our sample, and we are most interested in atmospheric properties
closest to the center. Each galaxy represents a diﬀerent manifestation of a powerful radio source.
M84 hosts an FR I radio jet1(Harris et al., 2002). Fornax A has a weak core in the radio (250 mJy),
but its radio lobes are some of the brightest radio sources in the sky (125,000 mJy, Ekers et al.,
1983). IC 4296 is the Brightest Group Galaxy (BGG) in a nearby galaxy group (Abell 3565), and
Hubble Space Telescope (HST) spectroscopy indicates a central black hole mass of ∼109M(cid:12) (Dalla
Bontà et al., 2009). Recent Very Large Array (VLA) D-conﬁguration observations show improved
mapping of the 160 kpc diameter radio lobes, ﬁrst discovered by Killeen et al. (1986), located over
230 kpc from the AGN host galaxy, as well as X-ray Multi-Mirror Mission (XMM) observations
that reveal a corresponding X-ray cavity (Grossová et al., 2019).

3.3.2 Chandra data reduction

All of the data used in this work are archival Chandra data taken between 2000 May and 2015
December. All observations were taken with the ACIS-S detector, except for NGC 5419 and
NGC 7626, which were obtained with the ACIS-I detector. We reprocessed the archival Chandra
1Deﬁned as a radio source in which the low-brightness regions of the jet are farther from the

galaxy than the high-brightness regions (Fanaroﬀ & Riley, 1974)

44

data listed in Table 3.1 using CIAO 4.9 and CALDB version 4.7.4. For simplicity, in the case of
targets with multiple observations, we chose to analyze the one with the longest net exposure time.
The time intervals containing data with anomalously high background were identiﬁed and
removed using the deflare script in CIAO. Bright point sources were identiﬁed and removed
using the wavdetect script (Freeman et al., 2002). We opted to account for the eﬀect of central
point sources in our spatially resolved spectral analysis. Background images and spectra were
derived from the blank-sky ﬁelds available from the Chandra X-ray Center. The background ﬁles
contain both particle and photon backgrounds and were ﬁltered and reprojected to match the target
observations. We rescaled the reprojected background rates to match the particle count rates,
gauged from the event rate between 10.0 and 12.0 keV (Hickox & Markevitch, 2006). Because our
analyses are based on regions of the galaxy where the signal is much higher than the background,
our results are insensitive to the details of the background scaling.

3.3.3 Spectral Analysis

We derived deprojected radial proﬁles of the X-ray gas properties: temperature, density, and gas
entropy. To prepare the spectra, we deﬁned radial annuli each containing at least 300 counts after
background subtraction (at temperatures around 0.7 − 1 keV, a minimum of ∼300 counts between
0.5 and 7 keV are required for a robust X-ray temperature estimate). We used the deﬁnitions of
these radial bins to extract radially binned X-ray event spectra for each galaxy and background
spectrum from the scaled and reprojected deep background data.

For each galaxy, we ﬁt all radial bins simultaneously with XSPEC v.12.9 (Arnaud, 1996) using
the projct model together with the X-ray thermal emission model apec and Galactic absorption
column model phabs. Because the spectral band above 2 keV is more likely to be dominated by
emission from X-ray background and unresolved point sources in typical X-ray spectra of early-type
galaxies, we restricted the energy range for the spectral ﬁts to 0.6 − 2.0 keV.

For each galaxy, the Galactic column density and redshift were ﬁxed to the values in Table 3.1,
and the gas metallicity was ﬁxed at a solar abundance. We will discuss the impact of this abundance

45

Table 3.2: Sample of Radial Proﬁle Properties A portion of this table is printed here for form
and content, Additional proﬁles can be found in Appendix E. Errors given for radius represent bin
widths; all other errors are 1σ. Column (1): galaxy name. Column (2): radial bin center. Column
(3): half-width of the radial bin. Column (4): grouping of temperature bins. Columns (5)-(6):
best-ﬁt temperatures and their errors. Column (7): electron density bin number. Columns (8)-(9):
in units of 10−2 cm−3 for compactness. Columns (10)-(11):
best-ﬁt densities and their errors.
calculated entropies and their errors.

Galaxy radius ∆r
(kpc) (kpc)
IC 4296 0.48 0.24
IC 4296 0.72 0.12
IC 4296 0.97 0.12
IC 4296 1.45 0.24
IC 4296 1.93 0.24
IC 4296 2.66 0.36
IC 4296 3.87 0.60
IC 4296 6.28 1.21
IC 4296 9.42 1.57
IC 4296 12.56 1.57
IC 4296 15.46 1.45
IC 4296 17.88 1.21

kT bin kT σkT ne bin
ID (keV) (keV)
1
0.75 0.02
0.75 0.02
1
0.78 0.03
2
0.78 0.03
2
3
0.84 0.03
0.84 0.03
3
0.89 0.05
4
4
0.89 0.05
2.10 1.07
5
2.10 1.07
5
1.29 0.21
6
6
1.29 0.21
· · ·
· · ·

K

σK

ID (10−2 cm−3) (10−2 cm−3) (keV cm2) (keV cm2)
1
2
3
4
5
6
7
8
9
10
11
12

0.09
0.16
0.33
0.41
0.63
0.86
1.98
2.73
59.92
79.11
18.74
22.83

2.48
3.44
5.29
7.23
9.82
16.08
30.82
36.60
116.60
152.23
91.31
91.62
· · ·

σne

0.57
0.53
0.39
0.20
0.18
0.06
0.03
0.03
0.03
0.03
0.03
0.05

ne

16.50
10.10
5.62
3.52
2.50
1.19
0.49
0.38
0.24
0.16
0.17
0.17
· · ·

assumption in Section 3.4.4. Because the X-ray temperature gradient across the radial range we
are interested in is small, we can produce better statistical ﬁts with deprojection by ﬁtting a single
temperature across multiple (two to ﬁve) adjacent annuli while allowing the spectral normalization
to be free in each annulus. The full tabulated results of these ﬁts including uncertainties are
provided in Table 3.2.

NGC 193, NGC 3801, and NGC 3894 were removed from our sample because there were
not enough counts to obtain a deprojected temperature proﬁle with three or more radial bins.
NGC 4782 had suﬃcient counts to extract a proﬁle but had a bright central point source resulting
in large uncertainties in the central bins. For NGC 1316 and IC 4296, we do not attempt to ﬁt the
central point sources because our primary goal is to assess the shape of the entropy proﬁle and the
data quality for future work. Therefore, the central 2(cid:48)(cid:48) from IC 4296 and NGC 1316, 0.25 and
0.12 kpc, respectively, were excluded from our deprojection analyses of these two galaxies.

46

3.3.4 Thermodynamic Properties

3.3.4.1 Electron Density Proﬁles

To estimate the electron density within a given concentric shell i, we use the best-ﬁt spectral
normalization from the deprojection model in XSPEC,

Þ

10−14

4πD2(1 + z)2

ηi =

ne,inp,idVi.

(3.1)

The projct model performs the projection from 3D to 2D and the total emission measure
within the extraction volume as shown in Equation 3.1, in which D is the angular diameter distance
to the galaxy in centimeters (Table 1), ne and np are the electron and proton number densities,
respectively, in cm−3, and Vi is the volume of the concentric shell in cm3. With this deﬁnition of
normalization, the expression

(cid:115) 4πη(shell)D2(1 + z)2

10−14(ne/np)V(shell)

ne(shell) =

(3.2)

gives us the deprojected radial electron density proﬁle for each galaxy.

3.3.4.2 Entropy and tcool/tﬀ Proﬁles

We plot the entropy proﬁles of the galaxies in our sample in Figure 3.1. Radial proﬁles of the
tcool/tﬀ ratio are shown in Figure 3.2, with tcool deﬁned by

tcool =

3
2

nkT

nenHΛ(T, Z)

(3.3)

where n is the total number density of particles, ne is the electron density, np is the hydrogen density
(where we assume np = ne/1.2), and Λ(T, Z) is the temperature-dependent cooling function for
plasma of metallicity Z. Our ﬁducial cooling function, from Schure et al. (2009), assumes a solar-
metallicity (Z(cid:12)) plasma. The freefall time is calculated assuming a singular isothermal sphere with
velocity dispersions found in Table 3.1. We calculated tcool/tﬀ for NGC 4261 and three additional
galaxies with the best data quality (NGC 1316, NGC 4374, and IC 4296).

47

Figure 3.1: Entropy Proﬁles for early-type galaxies with powerful radio sources Left panel:
entropy proﬁles for the galaxies in our sample with suﬃcient data counts to extract a deprojected
radial proﬁle but insuﬃcient data to isolate the central ∼0.5 kpc. Right panel: deprojected entropy
proﬁles of the four galaxies with the best data quality (NGC 4261, IC 4296, NGC 1316, NGC 4374).
For comparison, the gray dots are the data points from the galaxies in the left panel. Gray dashed
lines on both plots show power-law proﬁles with K ∝ r to illustrate that NGC 4261 and IC
4296 diﬀer from the other galaxies with comparable data quality (NGC 1316 and NGC 4374) by
approximately following a similar power law into the central kiloparsec, rather than exhibiting a
small excess like the other single-phase galaxies.

3.4 Discussion

3.4.1 tcool/tﬀ Proﬁles and Multiphase Gas
Figure 3.2 shows the tcool/tﬀ proﬁles for the four galaxies with entropy proﬁles that come closest to
probing the inner ∼0.5 kpc of the galaxy. The proﬁles of IC 4296 and NGC 4374 are of particular
interest. While the data are not of the resolution of NGC 4261, they still allow us to see the shape
of the tcool/tﬀ and entropy proﬁles near the central ∼ 0.5 kpc of the galaxy. We also note that while
the X-ray structure of NGC 315 is not resolved inside ∼1 kpc, its gas entropy proﬁle appears to
follow a single power law like IC 4296 and NGC 4261. Furthermore, from the spectra reported in
Ho et al. (1997, 1993), its multiphase gas appears to be conﬁned to the nucleus, making it another
promising candidate for a system in this powerful but possibly short-lived state.

48

101100101102r(kpc)100101102103K(keVcm2)NGC 315NGC 741NGC 4782NGC 5419NGC 7626IC 1459101100101102r(kpc)NGC 1316NGC 4261NGC 4374IC 4296tcool/tﬀ
Figure 3.2: Radial proﬁles of tcool/tﬀ
tcool/tﬀ Radial proﬁles of tcool/tﬀ for the four galaxies with the best
S/N. The shaded region (tcool/tﬀ = 5 − 20) represents the precipitation zone where multiphase gas
is found for r = 1 − 10 kpc. We ﬁnd that, like NGC 4261, IC 4296 reaches tcool/tﬀ < 10 in the
central ∼1 kpc while the other galaxies do not.

Voit et al. (2015b) showed that tcool/tﬀ in the central ∼ 1 kpc of both single- and multiphase
galaxies usually remains above the apparent precipitation limit at tcool/tﬀ ∼ 10. Farther out from
the center (1–10 kpc), galaxies with multiphase gas have tcool/tﬀ proﬁles that approximately track
this precipitation limit, whereas galaxies with single-phase gas generally lie above the precipitation
zone at tcool/tﬀ ∼ 5 − 20 (blue shaded region in Figure 3.2). Voit et al. (2015b) found that, in
a sample of morphologically relaxed, X-ray-bright galaxies (Werner et al., 2012), only the radial
proﬁle for NGC 4261 dipped below tcool/tﬀ ∼ 10 in the center.

In our sample, the tcool/tﬀ proﬁle for NGC 4374 remains above the precipitation zone, and NGC
1316 is consistent with the multiphase galaxy pattern from Voit et al. (2015b). However, IC 4296
goes down to tcool/tﬀ ∼ 10 near the center, as in NGC 4261, suggesting that the AGN feedback
occurring in IC 4296 has interesting similarities to that of NGC 4261. The data were suﬃcient to
probe the inner ∼ 0.5 kpc of NGC 4261, but in general the proﬁles more closely follow a single
power law than a power law with an excess inside the central kiloparsec.

The Hα emission in NGC 4261 is nuclear rather than extended (Ferrarese et al., 1996;

49

101100101r(kpc)101102tcool/tffNGC 1316NGC 4261NGC 4374IC 4296Lakhchaura et al., 2018), consistent with the picture of giant galaxies with single-phase gas having
entropy proﬁles that scale as K(r) ∝ r. Of our studied galaxies, IC 4296 most closely resembles
NGC 4261, and Grossová et al. (2019) reported that in narrowband images from the Hubble and
Southern Astrophysical Research (SOAR) telescopes, IC 4296 also has no Hα emission beyond
r ∼ 2 kpc.

3.4.1.1 Comparison with Previous X-ray Analysis

In an independent analysis, Lakhchaura et al. (2018) report entropy proﬁles for a sample of 49
elliptical galaxies, including eight of the galaxies analyzed in this paper: NGC 315, NGC 741,
NGC 1316, NGC 4261, NGC 4374, NGC 4782, IC 4296, and NGC 5419. While there are small
variations among bin sizes and radial ranges, we veriﬁed that our results are nevertheless mutually
consistent within the measurement uncertainties. However, the work of Lakhchaura et al. (2018)
treated gas metallicity diﬀerently, which we address in Section 3.4.4. In Section 3.4.2, we include
some of the results of Lakhchaura et al. (2018) in our discussion. Additionally, in Table 3.1, we
report the multiphase gas classiﬁcations from Lakhchaura et al. (2018) as well as additional results
from Connor (in preparation) and Sun (in preparation) that use observations carried out using the
SOAR optical Imager (SOI) and Goodman High Throughput Spectrograph of the 4.1m SOAR
telescope and the Apache Point Observatory (APO) Astrophysics Research Consortium (ARC)
3.5m telescope.

3.4.2 Radio Luminosity and tcool/tﬀ
Figure 3.3 shows the minimum values of tcool/tﬀ for NGC 4261, IC 4296, NGC 1316, and
NGC 4374, along with the giant ellipticals from Lakhchaura et al. (2018), plotted as a function of
the radius at which tcool/tﬀ reaches its minimum value. We have adjusted the min(tcool/tﬀ) values
reported by Lakhchaura et al. (2018) for uniform comparison with our work, using the correction
factor estimated in Section 3.4.4. The typical amplitude and direction of that correction are plotted
in Figure 3.3 in the form of a purple arrow. This adjustment typically decreased the tc/tﬀ estimates

50

from Lakhchaura et al. (2018) by a factor of 1.6. Points vary in size according to radio power in
the 1.4 GHz band.

Notice that NGC 4261, IC 4296, and NGC 1316 have a lower min(tcool/tﬀ) at a smaller radius
than most of the other giant elliptical galaxies in the Lakhchaura et al. (2018) sample. Furthermore,
the tcool/tﬀ proﬁles in NGC 4261 and IC 4296, reach their minimum values in the central radial bin,
raising the possibility that min(tcool/tﬀ) is overestimated in these galaxies because of limited spatial
resolution. However, it is also possible for those min(tcool/tﬀ) values to be slight underestimates. In
well-resolved galaxies that reach min(tcool/tﬀ) outside the central radial bin, statistical ﬂuctuations
tend to cause the measurement of min(tcool/tﬀ) to be biased low. Figure 3.2 shows why the
magnitude of that bias in the galaxies we are focusing on is likely to be small. In all four galaxies,
the second-lowest value of tcool/tﬀ is nearly identical to the minimum value, well within the 1-sigma
statistical uncertainties. Also, the tcool/tﬀ proﬁles of those four galaxies are not constant in the
1–10 kpc range but only within the central ∼ 1 kpc, where there are only a few radial bins, reducing
the likelihood of an unrepresentative statistical ﬂuctuation. Consequently, the fact that NGC 4261
and IC 4296 have unusually low min(tcool/tﬀ) and greater radio power than most other galaxies in
the sample suggests that there may be a correlation between high radio power and tcool/tﬀ < 10 at
small radii. In particular, the combination of low min(tcool/tﬀ) and a power-law entropy slope that
does not signiﬁcantly ﬂatten within the central kiloparsec is a unique feature of NGC 4261 and IC
4296. The other galaxies, in which the central entropy proﬁle is ﬂatter and min(tcool/tﬀ) occurs at
a larger radius, could be systems in which AGN feedback has recently elevated the entropy in the
central kiloparsec.

3.4.3 Comparison to Simulations

Voit et al. (2015b) showed that the presence of multiphase gas outside the central kiloparsec of an
early-type galaxy correlates with the slope of the entropy proﬁle. Galaxies with an entropy slope of
K ∝ r2/3 have multiphase gas present at r > 1 kpc, while galaxies with an entropy slope of K ∝ r
have only single-phase gas beyond r ∼ 1 kpc. In order to better understand this relationship, we

51

tcool/tﬀ
tcool/tﬀ
Figure 3.3: Radio luminosity, min(tcool/tﬀ
tcool/tﬀ), and radius at min(tcool/tﬀ
tcool/tﬀ) Radius where we
measured the minimum value of the tcool/tﬀ proﬁle is plotted against the minimum tcool/tﬀ for the
sample of Lakhchaura et al. (2018, gold) oﬀset to solar metallicity (see 3.4.4), with our four galaxies
of best data quality (red). The purple arrow represents the oﬀset between the adjusted values and
the 0.3 Z(cid:12) values from Lakhchaura et al. (2018). The relative size of the points represents their
radio power (in W Hz−1) in the 1.4 GHz band. NGC 4261, IC 4296, and NGC 1316 have a
small min(tcool/tﬀ) radius, a low min(tcool/tﬀ), and a greater radio power than most galaxies in the
sample.

have compared our observed entropy proﬁles with the proﬁles of simulated galaxies from Wang
et al. (2019). Figure 3.4 shows a comparison between our data for NGC 4261 and IC 4296 and
simulated elliptical galaxies with both single- and multiphase gas as well as the entropy proﬁles
for galaxies classiﬁed as having extended multiphase gas and no extended multiphase gas from
Lakhchaura et al. (2018). The initial conditions for the simulations are chosen to mimic X-ray
observations of NGC 5044 (multiphase) and NGC 4472 (single-phase), but the simulations were
designed to represent generic single- and multiphase galaxies. The simulations do not resolve the
gas proﬁles at < 1 kpc, meaning that our data have greater eﬀective physical resolution than the
simulations. However, we can still make comparisons in the 1 − 10 kpc range.

We begin by considering whether the simulated galaxies are appropriate comparisons for our

52

101100101radius (tcool/tff = min) (kpc)101102min (tcool/tff)Z/Z = 0.3  offset NGC 4261NGC 4374NGC 1316IC 4296NGC 4486NGC 47823C449Lakhchaura+2018This workRadio Power (W/Hz)102010231025Figure 3.4: Entropy proﬁles of NGC 4261 and IC 4296 compared to simulations Entropy proﬁles
of NGC 4261 and IC 4296 compared to simulations of somewhat lower mass giant elliptical galaxies
with single-phase gas (top) and multiphase gas (bottom) from Wang et al. (2019) along with the
single-phase (top) and extended multiphase (bottom) galaxies from Lakhchaura et al. (2018).
Simulated proﬁles are shown at intervals 150 Myr, with earlier snapshots being shown in lighter
red. The initial conditions are given by the black line and represent typical entropy proﬁles for
single-phase and multiphase galaxies, based on NGC 4472 and NGC 5044, respectively. Galaxies
classiﬁed as “N” (no extended multiphase gas) and “E” (extended multiphase gas) from Lakhchaura
et al. (2018) are included in gray with errors bars removed for clarity. The simulated galaxies have
lower velocity dispersions than the observed galaxies, but the simulations were designed to represent
the behavior over time of generic single- and multiphase galaxies, rather than simulating a speciﬁc
galaxy. The galaxies are referred to as MPG (multi phase galaxy) and SPG (single-phase galaxy)
instead of their names throughout Wang et al. (2019). Note that the simulations do not resolve the
gas proﬁles inside 1 kpc, and the ﬂattening of the proﬁles in the center is likely a numerical eﬀect
because the resolution limit of the simulations can result in the simulated AGN aﬀecting a larger
region of the galaxy than real jets (Wang et al., 2019). Therefore, we expect the entropy slopes of the
single-phase simulations to be the same as our observations, though the normalization can diﬀer.
The measured entropy gradients are consistent with those seen in single-phase gas simulations of
radio sources in early-type galaxies.

53

10−1100101102r(kpc)100101102103K(keVcm2)SinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationSinglePhasegalaxysimulationNGC4261(1.0Z(cid:12))IC4296(1.0Z(cid:12))singlephasegalaxies,Lakhchaura+201801503004506007509001050120013501500165018001950Myr10−1100101102r(kpc)100101102103K(keVcm2)MultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationMultiPhasegalaxysimulationNGC4261(1.0Z(cid:12))IC4296(1.0Z(cid:12))multiphasegalaxies,Lakhchaura+201801503004506007509001050120013501500165018001950Myrsample. From Makarov et al. (2014), the velocity dispersions of NGC 5044 and NGC 4472 are
224.9 ± 9.1 km s−1 and 282 ± 2.9 km s−1, respectively, while the velocity dispersions for IC
4296 and NGC 4261 are 327.4 ± 5.4 km s−1 and 296.7 ± 4.3 km s−1, respectively. Voit et al.
(2015b) introduced the idea that there may be a correlation between the presence of multiphase gas,
the velocity dispersion, and entropy proﬁle slope in early-type galaxies. In contrast, Lakhchaura
et al. (2018) found little correlation in entropy proﬁle slope and the presence of multiphase gas
when examining a larger sample. However, this is still an area of open study in both theory and
observations of early-type galaxies. We do not expect the simulated proﬁles to match our data
exactly because the velocity dispersions of the simulated galaxies are smaller than those of NGC
4261 and IC 4296. However, we can still make useful comparisons between the overall behavior
of the simulations and observations that account for how the entropy proﬁle slope correlates with
velocity dispersion and the presence or absence of multiphase gas (Voit et al., 2015b).

For the single- and multiphase initial conditions simulated by Wang et al. (2019), the entropy
proﬁles agree with the expectations of the simple physical models shown in Voit et al. (2015b). The
2/3
multiphase gas simulation has an entropy proﬁle of K(r) = 3.5 r
kpc keV cm2, which corresponds
to the hypothesized precipitation limit at tc/tﬀ ≈ 10. The steeper entropy proﬁle characteristic of
single-phase galaxies, K(r) = 5 rkpckeVcm2, is consistent with models in which heating by Type Ia
supernovae drives an outﬂow. The implication is that self-regulated AGN feedback can maintain
the observed properties of both the single- and multiphase galaxies, consistent with both idealized
analytical models (Voit et al., 2015b) and simulations (Wang et al., 2019).

When we compare the single-phase simulation to NGC 4261 and IC 4296, the simulated
galaxy does appear to maintain approximately the same entropy slope as our data. Furthermore,
the comparison shows that the slopes of the single-phase entropy proﬁles from Lakhchaura et al.
(2018) are diﬀerent from the slopes of the multiphase entropy proﬁles, and the multiphase data have
similar slopes to the multiphase simulations. The comparison between NGC 4261 and IC 4296,
the multiphase galaxy simulations, and the extended multiphase gas data show that our galaxies
are better represented by single-phase galaxies. The observed entropy proﬁle slopes between 1 and

54

Figure 3.5: Comparison of the inferred entropy proﬁles for NGC 4261 for diﬀerent assumed
values of abundance The points represent 1.0 Z(cid:12) (red), 0.5 Z(cid:12) (orange), and 0.3 Z(cid:12) (yellow).
For increasing values of metallicity, the amplitude of the entropy proﬁle increases. Therefore, if
a galaxy has a diﬀerent metallicity than we have assumed, and if we no longer assume that each
galaxy has uniform metallicity, the slope of the entropy proﬁle could change as well. However, we
would still expect the proﬁle to fall within the metallicity range illustrated in the ﬁgure.

10 kpc are consistent with the entropy proﬁle of a single-phase galaxy, which has a steeper slope
(α ∼ 1). For some time steps, the central entropy proﬁle of the simulated single-phase galaxy
ﬂattens out, which could represent epochs when the black hole in the simulations is particularly
active. However, it could also be a numerical eﬀect because the resolution limit of the simulations
can result in the simulated AGN aﬀecting a larger region of the galaxy than real jets (Wang et al.,
2019).

3.4.4 Metallicity Analysis

When ﬁtting entropy proﬁles, we assumed that each galaxy had a constant metallicity of 1.0 Z(cid:12)
across the proﬁle. The hot gas abundances of early-type galaxies are diﬃcult to obtain from low-
resolution X-ray data, so we ﬁxed the gas metallicities while ﬁtting our observations. Here we
quantify the sensitivity of our estimates of the X-ray densities and temperatures to the assumed
metallicities. In Figure 3.5, we show an example result of the impact of three diﬀerent metallicity
assumptions on the entropy proﬁles for NGC 4261: 0.3, 0.5, and 1.0 Z(cid:12). This range of abundances

55

101100101r (kpc)100101102K(keVcm2)1.0 Z0.5 Z0.3 Zspans those from various treatments of early-type galaxies in observations and simulations found
in the literature (Werner et al., 2012; Li & Bryan, 2014b; Wang et al., 2019). The amplitude of
the inferred entropy increases as assumed abundance increases, but the slope of the entropy proﬁle
shows little change. Therefore, abundance changes over the full range of expected gas abundances
from 0.3 to 1.0 solar would result in a change in amplitude of the inferred entropy proﬁle on the
order of 10 − 20% (see Figure 3.5).

In comparing our results with entropy proﬁles from previous work, we ﬁnd that diﬀerent
abundance assumptions indeed result in small diﬀerences in the inferred entropy proﬁles. However,
when the identical assumptions for abundances are used, the entropy proﬁle results for diﬀerent
authors are the same within the uncertainties. For example, for the giant ellipticals examined by
Werner et al. (2012), the assumed abundances in the central kiloparsec were Z ∼ 0.5 Z(cid:12) and match
our entropy proﬁle results for NGC 4261 for a metallicity of Z ∼ 0.5 Z(cid:12).

The relation between abundance and electron density for an apec model for a narrow range of

gas temperatures (0.5 − 1.2 keV) can be quantiﬁed approximately by

(cid:21)

(cid:20) ne(Z)

ne(Z(cid:12))

log

= −m log(Z/Z(cid:12))

(3.4)

where Z is metallicity assumed in the determination of ne and m is the power-law slope. We would
expect m ∼ 0.4 based on the dependence of Λ(T) on Z in this temperature range (approximately
Λ ∝ Z0.8) and form of the emission integral. To verify this estimate, we found the best-ﬁt ne
and TX for the four galaxies with the best data quality, sampling a range of assumed metallicities.
We determined that the best-ﬁt temperature was insensitive to the metallicity assumption, while
density and assumed metallicity were related as in Equation 3.4 with m = 0.43± 0.04 (NGC 1316),
m = 0.43±0.04 (NGC 4261), m = 0.39±0.11 (NGC 4374), and m = 0.29±0.18 (IC 4296), where
uncertainties on m are 1σ. These results are consistent with the expectations from X-ray plasma
emission model for kT ∼ 0.6− 1 keV. The inferred electron density is therefore inversely related to
the assumed abundance.

Furthermore, if the abundance is actually lower in the center than we assume, we have under-
estimated the central density and overestimated the central entropy. So if a galaxy’s gas is less

56

metal-rich in the center than we have assumed, its central entropy proﬁle could be slightly steeper
than shown (e.g. Lakhchaura et al., 2019). However, even if the central metallicity is lower than
we assumed, the minima of the tcool/tﬀ proﬁles are less than tcool/tﬀ = 20 for NGC 4261 and
IC 4296.
3.5 Conclusions

Our analysis of the entropy proﬁles for a sample of nearby early-type galaxies with powerful
radio sources shows that at least one other galaxy (IC 4296) is like NGC 4261 in having a powerful
AGN and tcool/tﬀ ∼ 10 at < 1 kpc. While the spatial resolution of the X-ray data for IC 4296 is not
as good as for NGC 4261, both of their entropy proﬁles appear to be single power laws, and neither
has extended multiphase gas greater than 2 kpc from their nuclei. To be certain of their similarity,
we will need additional Chandra observations of IC 4296 to match the data quality of NGC 4261.
We produced deprojected temperature and density proﬁles for the hot gas surrounding seven
additional early-type galaxies with powerful radio sources, but these observations lacked suﬃcient
data quality to quantify the slope in the central ∼ 0.5 kpc. Unfortunately, these galaxies are
likely not good candidates for further study at this time because the additional Chandra ACIS
observations needed to achieve comparable data quality to NGC 4261 are prohibitively long, given
the degradation of Chandra’s sensitivity to soft X-rays. We found that, in comparing independent
analyses of entropy proﬁles in early-type galaxies, the treatment of abundance aﬀects the amplitude
of the entropy proﬁle. Additionally, if the gas is not well mixed, it may have a metallicity gradient,
meaning that the slope of the proﬁle could be aﬀected as well. Finally, we compared IC 4296
and NGC 4261 to recent simulations (Wang et al., 2019) and found that they are consistent with a
single-phase gas model galaxy. The simulations agree well with our observational results, providing
positive evidence for their ability to robustly model the hot ambient medium in early-type galaxies.
In this work we were able to show excellent agreement between our observations, the theory of
Voit et al. (2015b), and the simulations of Wang et al. (2019).

57

CHAPTER 4

RELATIONSHIPS BETWEEN CENTRAL VELOCITY DISPERSIONS AND

ATMOSPHERES OF EARLY-TYPE GALAXIES

4.1 Abstract

The Voit et al. (2020) black-hole feedback valve analytic model predicts relationships between
stellar velocity dispersion and atmospheric structure for massive galaxies. In this work, we test
the analytic model using the Chandra archival sample of 49 early-type galaxies from Lakhchaura
et al. (2018). We consider the relationships between stellar velocity dispersion and entropy proﬁle
slope, multiphase gas extent, and ratio between cooling time and free-fall time simultaneously. We
classify sub-samples limited to observations of high data quality and by entropy proﬁle properties
to explore the potential relationships between parameters and test the analytic model predictions.
We ﬁnd evidence for agreement with the equilibrium radial proﬁles from the Voit et al. (2020)
model as well as agreement with the analytic model for the sample with low central entropy and
limited velocity dispersion.
4.2

Introduction

Early-type galaxies, encompassing both elliptical and lenticular galaxies, are characterized by
their elliptical shapes, older stellar populations, and lack of signiﬁcant active star formation. Star
formation in galaxies occurs when there is suﬃcient molecular gas to form stars and proceeds until
the molecular gas supply runs out, either through stars forming more rapidly than the molecular gas
can accumulate or the galaxy preventing further accumulation of molecular gas. It follows then,
because little star formation is observed in early-type galaxies, that the galaxy must be preventing
the molecular gas from accumulating. Molecular gas can accumulate in galaxies via cold streams
(e.g. Kereš et al. 2005, 2009; Dekel et al. 2009), cooling ﬂows (e.g. White & Frenk 1991; Fabian
1994; McNamara & Nulsen 2007, 2012; Werner et al. 2019), or stellar mass loss (e.g. Mathews &
Brighenti 2003; Leitner & Kravtsov 2011; Voit & Donahue 2011). Therefore, feedback processes

58

in early-type galaxies must act to prevent each of these sources.

2/3
e

Observationally, the eﬀect of feedback processes on the galactic atmosphere can be captured
via observations of the hot X-ray gas. Entropy, in terms of X-ray observables, K ≡ kTn
, where
kT is the X-ray temperature and ne is the electron density, is the preferred quantity for investigating
feedback processes in galaxies. Feedback can change the rate at which the gas radiates energy away,
aﬀecting the cooling time of the gas. Here, the cooling time (tcool) is deﬁned to be the time needed
for a gas at temperature T to radiate an energy 3kT/2 per particle, and the free fall time from a
galactocentric radius r at the local gravitational acceleration g is deﬁned to be tﬀ = (2r/g)1/2. If
the heating due to feedback is gradual compared to the time it takes for the heated gas to expand
within the gravitational potential, the temperature of the gas may not change while the gas density
lowers, lengthening the cooling time. We turn to entropy to capture gains and losses of energy in
the gas. The gas entropy across the radius of a galaxy provides insight into the thermal history of
the galactic atmosphere. In general, the galaxy potential well serves as an entropy sorting device,
where lower entropy gas sinks to small radii, and higher entropy gas rises to larger radii. The lowest
entropy gas is the densest and brightest gas in the galaxy, as observed in the X-ray. Voit et al.
(2015b) examined the properties of a sample of 14 massive elliptical galaxies previously studied by
Werner et al. (2012, 2014) and showed that the entropy proﬁle slopes of early-type galaxies and the
presence of multiphase gas are correlated. In the Werner et al. (2012) sample, inside ∼ 2 kpc, the
gas entropy levels of the galaxies are similar, but outside ∼ 2 kpc, the slopes of the entropy proﬁles
can diﬀer from galaxy to galaxy depending on what thermal processes dominate. Galaxies with
extended multiphase gas exhibit entropy proﬁles with K ∝ r2/3 from ∼1–10 kpc while galaxies
with no extended multiphase gas (hereafter referred to as single phase galaxies) exhibit steeper
entropy proﬁles, with K ∝ r from ∼1–10 kpc. The diﬀerence in the entropy proﬁle slopes for
galaxies with or without extended multiphase gas could be due to SNIa heating and sweeping gas
ejected by the old stellar population out of single phase galaxies into an extended gaseous halo
(Voit et al., 2015b). Voit et al. (2015b) also found that the velocity dispersions of the galaxies with
extended multiphase gas were σ ≤ 255 km s−1 while galaxies with no extended multiphase gas had

59

velocity dispersions of σ ≥ 263 km s−1, indicating that entropy proﬁle slope, velocity dispersion,
and multiphase gas extent may be correlated and related to how the black hole interacts with the
galactic atmosphere.

Lakhchaura et al. (2018) explored the relationship between entropy proﬁle slope and multiphase
gas extent for a larger archival sample (∼50 galaxies) and did not report evidence for a relationship.
However, Lakhchaura et al. (2018) did ﬁnd evidence that the average behavior of entropy proﬁles
and the ratio of the cooling time and free-fall time of the gas are related. Babyk et al. (2018) explored
the relationship between entropy proﬁle slope and velocity dispersion for an archival sample of 40
early-type galaxies (and 110 clusters). They also reported no evidence for a relationship between
entropy proﬁle slope and velocity dispersion, but they did ﬁnd some evidence for a relationship
between entropy proﬁle slope and temperature.

Voit et al. (2020) investigated the coupling between supernova sweeping of stellar ejecta, the
conﬁning circumgalactic medium (CGM) pressure, and bipolar kinetic feedback fueled by accretion
of cooling gas onto the central black hole, forming what they called a black hole feedback valve.
They proposed an analytic model, investigating this idea, that predicts a relationship between
the velocity dispersion and the entropy proﬁle slope, that determines the eﬀect of feedback on
the galactic atmosphere, and whether multiphase gas can form. The model is informed by both
numerical simulations and observations and analytically models feedback processes in massive
galaxies. The model predicts that the entropy proﬁle slope over the radial range where supernova
heating exceeds radiative cooling (∼ 1–10 kpc) is determined by the ratio of the speciﬁc thermal
energy of the ejected stellar gas to the depth of the galactic potential well, as long as the velocity
ﬁeld is subsonic.

The structure of this paper is as follows: Section 4.3 describes our sample selection and
data analysis processes, Section 4.4 discusses the connection between observations and theory,
and Section 4.5 concludes by discussing how this work adds to the current understanding of
precipitation-driven feedback in massive galaxies.

60

Figure 4.1: Stellar velocity dispersion vs. X-ray luminosity Stellar velocity dispersion, σv, is
plotted with the X-ray luminosity within 10 kpc for the subsample of galaxies from Lakhchaura
et al. (2018) with suﬃcient data to measure an accurate entropy proﬁle slope at 1-10 kpc. The points
are also classiﬁed by their multiphase gas extent from Lakhchaura et al. (2018). Blue triangles are
galaxies with extended multiphase gas, red crosses are galaxies with no extended multiphase gas,
green squares are galaxies with multiphase gas contained within 2 kpc, and black dots are galaxies
without a gas extent classiﬁcation. The vertical dashed line indicates the velocity dispersion (240
km s−1) that corresponds to the critical entropy proﬁle slope of αK = 2/3 (Voit et al., 2020).

4.3 Methods

4.3.1 Sample Description

Our primary goal in this work is to determine whether the observed relationship between the
velocity dispersion and entropy proﬁle slope is consistent with the analytic model predictions from
Voit et al. (2020). Making such a comparison requires suﬃcient resolution in the observations to
measure an entropy proﬁle slope, so we need to use a sample of early-type galaxies with accurate
entropy proﬁles and velocity dispersion measurements to test the analytic model’s predictions.

The main sample explored in this work is the sample of 49 nearby, X-ray and optically bright,

61

200220240260280300320340v(km/s)101100LX (1042 erg/s)NGC 4486 (M87)v=240 km/sunknownE (extended MPG)NE (MPG < r = 2 kpc)N (no extended MPG)elliptical galaxies with archival Chandra data from Lakhchaura et al. (2018). We use the derived
radial proﬁle measurements of electron density, ne, X-ray temperature, kT, entropy, K, and ratio
of cooling time to free-fall time, tc/tﬀ, as well as their multiphase gas classiﬁcation scheme1 and
X-ray luminosities. Full details of the galaxy parameters are found in Table 4.1.

Figure 4.1 shows the relationships between X-ray luminosity, stellar velocity dispersion, and
multiphase gas characteristics for galaxies with suﬃciently resolved entropy proﬁles (see Section
4.3.3 for details). Voit et al. (2020) showed that σv = 240km s−1 corresponds to αK = 2/3 and
represents a critical number for the analytic model. Extended multiphase gas appears to be more
common among galaxies with σv < 240km s−1 than among those with σv > 240km s−1 (Voit et al.,
2015b). In Figure 4.1, we also see that galaxies with mulitphase gas conﬁned to the inner ∼ 2 kpc
are represented across the range of velocity dispersion. The most notable exception to the division
between galaxies with extended multiphase gas and those with no extended multiphase gas is M87
(upper right of Figure 4.1) which resides in one of the most massive halos in the sample and has one
of the highest X-ray luminosities. The massive halo and high luminosity indicate that the galaxy
likely has high external gas pressure, and that its atmospheric characteristics are representative of
the entire massive halo rather than only this single galaxy. Apart from M87, the upper envelope of
the sample exhibits a decline in X-ray luminosity with increasing velocity dispersion. Voit et al.
2015b, 2020 also predicted that galaxies with higher velocity dispersion will have steeper entropy
proﬁle slopes. A steeper entropy proﬁle slope means that the electron density of the gas is lower at
10 kpc (the aperture for measuring LX) than it would be for shallower entropy proﬁles slopes.

The sample from Lakhchaura et al. (2018), after initial data quality limits are applied, is well-
In Section 4.3.4, we will

suited to test the analytic model predictions from Voit et al. (2020).
discuss further the ways in which we subdivide the sample in our test of the analytic model.

1Except for IC 4296 which is correctly identiﬁed as NE, rather than E, in Frisbie et al. (2020)

62

Table 4.1: Galaxy Parameters (1) Name; (2) redshift obtained from NED; (3) redshift independent
distance; (4) σv and error; (5) 0.5–7.0 keV intrinsic X-ray luminosities and their errors estimated
from a 10 kpc radius circular region around the X-ray peak (Lakhchaura et al., 2018); (6) Hα+[N 2]
morphology classiﬁed as follows: N: no cool gas emission, NE: Hα+[N 2] extent < 2 kpc, E:
Hα+[N 2] extent ≥ 2 kpc and U: galaxies for which the presence/absence of Hα+[N 2] could not
be conﬁrmed (Lakhchaura et al., 2018); (7) αK and error; (8) minimum ratio of cooling time to
free-fall time and error; (9) Fit central entropy and error.

Galaxy

z

αK

min

(tcool/tﬀ)

K0

keV/cm2

D
Mpc
(3)

σv
km/s
(4)

LX

1042erg/s

(5)

gas
extent
(6)

(8)

(9)

(7)

(1)

E
E

(2)
0.0229 95.75 259.8 ± 12.0 0.68 ± 0.050 NE 0.66 ± 0.24 18.42 ± 2.40 5.92 ± 0.97
IC1860
0.0124 47.31 327.4 ± 5.4 0.14 ± 0.003 NE 1.23 ± 0.11 11.63 ± 0.78 0.69 ± 0.20
IC4296
0.0150 59.52 278.4 ± 5.8 0.49 ± 0.050 NE 0.88 ± 0.22 11.01 ± 1.20 1.82 ± 0.72
IC4765
0.0164 56.01 293.6 ± 10.1 0.12 ± 0.010 U 0.83 ± 0.24 20.02 ± 4.65 0.91 ± 0.96
NGC315
0.0176 66.00 291.8 ± 5.4 0.35 ± 0.140 NE 0.76 ± 0.35 27.30 ± 5.22 4.93 ± 1.36
NGC410
0.0147 60.74 253.2 ± 6.7 0.41 ± 0.030 NE 0.74 ± 0.24 34.18 ± 3.19 6.90 ± 4.16
NGC499
0.0164 59.83 292.1 ± 5.9 0.23 ± 0.020 N 0.80 ± 0.34 30.15 ± 5.61 7.14 ± 3.38
NGC507
0.0184 61.58 271.9 ± 5.6 0.51 ± 0.030
0.88 ± 0.14 12.28 ± 3.75 1.74 ± 0.36
NGC533
0.0162 64.19 221.8 ± 7.8 0.88 ± 0.020
0.64 ± 0.06 12.04 ± 0.29 5.38 ± 0.15
NGC708
0.0186 64.39 287.4 ± 9.3 0.21 ± 0.010 N 0.93 ± 0.09 19.16 ± 0.73 2.57 ± 0.39
NGC741
0.0167 58.08 315.1 ± 5.6 0.60 ± 0.120 N 0.59 ± 0.24 24.11 ± 3.01 5.22 ± 1.01
NGC777
NGC1316 0.0059 19.25 223.1 ± 3.3 0.04 ± 0.002
0.72 ± 0.25 32.57 ± 6.72 0.58 ± 0.61
NGC1399 0.0048 17.75 332.2 ± 5.3 0.16 ± 0.004 N 0.94 ± 0.03 26.05 ± 0.40 0.89 ± 0.11
NGC1404 0.0065 19.18 229.7 ± 3.8 0.12 ± 0.001 N 0.80 ± 0.03 20.23 ± 0.51 0.70 ± 0.04
NGC1407 0.0060 23.27 265.6 ± 5.1 0.07 ± 0.003 N 0.83 ± 0.06 41.92 ± 1.67 4.13 ± 0.25
NGC1521 0.0140 50.93 233.6 ± 8.9 0.07 ± 0.010 NE 0.38 ± 0.39 20.90 ± 5.21 0.96 ± 0.83
NGC1600 0.0158 45.77 331.4 ± 7.0 0.07 ± 0.010 N 0.72 ± 0.18 42.60 ± 7.16 5.07 ± 0.39
NGC2300 0.0064 41.45 266.0 ± 5.6 0.10 ± 0.010 N 0.91 ± 0.13 26.09 ± 1.27 4.18 ± 0.43
NGC2305 0.0113 47.88 242.6 ± 13.4 0.19 ± 0.020 NE 0.70 ± 0.25 20.22 ± 3.36 1.54 ± 0.58
NGC3091 0.0122 48.32 311.0 ± 7.7 0.20 ± 0.020 N 0.40 ± 0.10 30.74 ± 4.16 3.48 ± 2.54
NGC3923 0.0058 20.97 245.6 ± 4.9 0.04 ± 0.001 N 0.92 ± 0.12 21.98 ± 1.41 1.34 ± 0.12

E

63

Table 4.1 (cont’d)
Galaxy

z

D
Mpc
(3)

σv
km/s
(4)

LX

1042erg/s

(5)

gas
extent
(6)

αK

min

(tcool/tﬀ)

K0

keV/cm2

(7)

(8)

(9)

(2)

(1)
NGC4073 0.0197 60.08 267.6 ± 6.3 1.05 ± 0.050 N 0.61 ± 0.20 32.22 ± 2.92 8.30 ± 1.18
NGC4125 0.0045 21.41 239.8 ± 6.9 0.02 ± 0.001 U 0.13 ± 0.45 28.22 ± 12.35 1.43 ± 1.40
NGC4261 0.0073 29.58 296.7 ± 4.3 0.06 ± 0.003 NE 1.16 ± 0.06 14.17 ± 1.47 0.52 ± 0.08
NGC4374 0.0033 16.68 277.6 ± 2.4 0.05 ± 0.002 NE 1.18 ± 0.14 25.04 ± 6.58 1.86 ± 0.19
NGC4406 0.0006 16.08 231.4 ± 2.6 0.10 ± 0.004
0.54 ± 0.14 26.28 ± 1.60 5.21 ± 3.26
NGC4472 0.0032 15.82 282.0 ± 2.9 0.16 ± 0.001 N 0.96 ± 0.02 26.80 ± 0.23 1.17 ± 0.05
NGC4486 0.0042 16.56 323.0 ± 4.3 2.16 ± 0.004
0.61 ± 0.01 22.73 ± 0.27 3.00 ± 0.10
NGC4552 0.0009 15.97 250.3 ± 2.9 0.03 ± 0.001 N 0.95 ± 0.09 11.35 ± 0.63 2.23 ± 0.11
NGC4636 0.0031 15.96 199.5 ± 2.7 0.20 ± 0.002 NE 1.00 ± 0.03 10.79 ± 0.36 1.89 ± 0.08
NGC4649 0.0034 16.55 330.5 ± 4.6 0.11 ± 0.002 N 1.00 ± 0.02 22.63 ± 0.35 1.49 ± 0.02
NGC4696 0.0098 37.48 242.9 ± 6.5 2.49 ± 0.010
2.24 ± 0.07
NGC4782 0.0133 48.63 310.0 ± 11.3 0.05 ± 0.010 NE 0.59 ± 0.26 18.94 ± 9.92 4.30 ± 2.62
NGC5044 0.0090 35.75 224.9 ± 9.1 1.29 ± 0.010
0.08 ± 0.12
NGC5419 0.0139 50.87 344.3 ± 5.4 0.24 ± 0.020 N 1.19 ± 0.28 17.30 ± 2.21 1.38 ± 0.70
0.51 ± 0.02 12.20 ± 0.26 3.44 ± 0.13
NGC5813 0.0064 29.23 236.0 ± 3.4 0.50 ± 0.003

0.69 ± 0.01

0.56 ± 0.03

5.75 ± 0.14

4.73 ± 0.03

E

E

E

E

E

4.3.2 Theoretical Model

Voit et al. (2020) presents a basic model for the relationship between the entropy proﬁle slope, αK,
and the stellar velocity dispersion, σv. The basic model assumes that the stellar mass distribution
can be approximated by a singular isothermal sphere with one-dimensional velocity dispersion,
σv = vc/√
2. The outﬂow driving by Type Ia supernova (SNIa) heating is assumed to be subsonic
and therefore close to hydrostatic equilibrium. Combining the contributions to the entropy proﬁle
from supernova energy, orbital energy, and gravitational potential energy then gives the following

64

relation between αK and σv:

αK ≈ 5
3

2
c

v

(cid:16) ∗

(cid:17)−1

,

− 1
4

(4.1)

where ∗ is the mean speciﬁc energy of the gas coming from stars. Therefore, the structure of the
galaxy’s atmosphere at 1 − 10 kpc depends strongly on the ratio of ∗/v
2
c. Given this relationship
between the entropy proﬁle slope and the stellar velocity dispersion, we will use the velocity
dispersions and entropy proﬁle slopes from observations to test the model.

Voit et al. (2020) also presented a more complex form of the basic model by instead assuming
that the galaxy’s halo has an NFW density proﬁle and the stellar mass density follows a modiﬁed
Einasto proﬁle. Numerical integration of the more complex model shows that the basic model over-
predicts the entropy proﬁle slope for σv > 300 km s−1, and we will compare that modiﬁcation of
the model with data in Section 4.4.1.2.

4.3.3 Entropy Proﬁles

Equation 4.1 is based on a pressure-bounded, subsonic outﬂow solution, heated only by SNIa,
and predicts a constant radial slope for the entropy proﬁle. Because we want to test that model’s
prediction for the relationship between the power-law slope of the entropy proﬁle and stellar velocity
dispersion, we limit the range over which we ﬁt the power-law slope to the radial range that is aﬀected
as little as possible by other heating processes. If the AGN is as powerful as NGC 4261 and IC4296
(see Frisbie et al. (2020)), it typically deposits its energy rather far from the center (r > 10 kpc) by
drilling through the hot gas via jet. In some systems, some fraction of the AGN energy output might
couple to gas closer to the AGN, resulting in ﬂattening or even inversion of the entropy proﬁle near
1 kpc. Therefore, we limit our gas slope measurements to 1-10 kpc to get a “clean” measure of the
gas slope where stellar processes are most likely to dominate.

While a few of the galaxies in our sample have entropy proﬁles that resemble a single power
law (Frisbie et al., 2020), most have an excess of entropy over a single power law in the central
∼kpc. Therefore, we have adapted the functional form from Donahue et al. 2005, 2006; Voit &

65

Figure 4.2: Distribution of K0K0K0 values for the HQ sample Histogram of K0 values for the sample
where K0 is ﬁt using Equation 4.2. The black dashed vertical line is at K0 = 3 keV cm2 and
represents the limit we applied to remove galaxies with elevated central entropy outside of 1 kpc.

Donahue 2005; Cavagnolo et al. 2009 to the radial range for galaxies instead of clusters,

(cid:16)

(cid:17) αK

K(r) = K0 + K10

r

10 kpc

,

(4.2)

where K0 is the best ﬁt central entropy, K10 is the best ﬁt entropy at a radius of 10 kpc, and αK is
the best ﬁt power law slope. We ﬁt over 1-10 kpc because as discussed in Section 4.3.4, that radial
range is where the potential eﬀect of SNIa on the entropy proﬁle is best measured. We calculate the
best ﬁt parameters using the python package emcee. We establish an initial broad expected range
for the parameters in log space with 0 < K0 < 102, 0 < K10 < 102, and 0 < αK < 2. Errors were
determined from MCMC contours in two dimensions (16 − 84%).

4.3.3.1 Distribution of Central Entropy

Our entropy proﬁle ﬁts suggest that approximately half of the overall sample is clustered near
K0 ∼ 1 − 2keV cm2, while the rest have K0 (cid:38) 3 keV cm2 (see Figure 4.2). In the group with
low K0, the entropy proﬁle at 1–10 kpc is close to a pure power law. This sub-sample is therefore

66

02468K0 (keV cm2)01234567Nmore suitable for testing the prediction represented in Equation 4.1. The subsample with greater
K0, on the other hand, clearly deviates from the pure power-law entropy proﬁle predicted by the
basic model for an outﬂow heated by only SNIa. In those galaxies, central heating by the AGN
may be producing an entropy ﬂoor at small radii, causing a break in the power-law proﬁle. The
best-ﬁtting values of αK in the high-K0 sample may still be representative of SNIa heating, but
the measurements of αK are not as clean because of greater degeneracy between K0 and αK in the
ﬁtting procedure.

4.3.4 Sub-Sample Selection

During our analysis, we subdivided the full sample so as to test the prediction in Equation 4.1 as
accurately as possible. Our smallest sub-sample with the most restrictive criteria represents the
cleanest case to test the model predictions, and the full sample with the least restrictive criteria
provides a more general lower limit on the value of αK associated with a given σv. Our analysis
requires a statistically signiﬁcant measurement of the slope parameter αK, so we only include those
galaxies from the sample with suﬃcient resolution (at least 4 radial bins of any size) from 1–10
kpc. There are 36 galaxies from the sample that ﬁt this criterion, hereafter referred to as the high
quality (HQ) sample.

We implement two further limits on our sample for the analysis: central entropy, K0, and
velocity dispersion, σv. Of the 36 galaxy proﬁles with suﬃcient data quality, we deﬁne a sample
of 22 proﬁles with low central gas entropy (hereafter referred to as the low K0 sub-sample). We
describe the rationale for that selection in Section 4.3.3.1. From that sample, we ﬁlter galaxies with
velocity dispersions of 210–310 km s−1 (hereafter referred to as the restricted σv sample), leaving
us with a sample of 16 galaxies. The velocity dispersion limit eliminates more high σv galaxies
than low σv galaxies. We discuss the rationale for that selection in Section 4.4.1.2.

67

Table 4.2: Entropy Proﬁle Slope and Velocity Dispersion Relationship Results Each sample is
a subset of the previously listed samples. Descriptions of the sample are in Section 4.3.4. The ﬁt is
an ordinary least-squares ﬁt to a linear model (αK = Aσ240 + B, σ240 ≡
240 km s−1 ) with intrinsic
scatter (Akritas & Bershady, 1996), and errors on the slope are 1σ. Column 1: Sample selection
criteria; Column 2: Slope of ordinary least squares ﬁt to the data; Column 3: Reduced chi squared
for the ﬁt; Column 3: Intrinsic scatter and error; Column 5: Number of galaxies included in the ﬁt.

σv

Slope

Sample
High Quality (HQ) 0.52 ± 0.24
0.80 ± 0.33
Low K0
1.80 ± 0.51
restricted σv

Reduced χ

1.03
1.05
1.08

2 Intrinsic Scatter Number

0.18 ± 0.02
0.22 ± 0.03
0.16 ± 0.02

36
22
16

4.4 Discussion

4.4.1 Low Central Entropy, Restricted σv, and the Analytical Prediction
4.4.1.1 The Black-hole Feedback Valve Prediction

The Voit et al. (2020) analytic model predicts a relationship for stellar velocity dispersion and
entropy proﬁle slope (Equation 4.1) in the radial range where SNIa heating is signiﬁcant (1–10
kpc). Elevated central entropy, K0, beyond 1 kpc, suggests that the central AGN is more strongly
coupled to the surrounding medium. Therefore, SNIa heating is not the dominant heating process,
and the model is not expected to apply. Because the model applies best to galaxies without elevated
central entropy, we will investigate the relationship between velocity dispersion and entropy proﬁle
slope for that particular sub-sample.

4.4.1.2 Comparison to the Analytic Prediction

With the criteria explained in Section 4.3, we examine the relationship between the stellar velocity
dispersion, σv, and the entropy proﬁle slope, αK. Table 4.2 summarizes the results for our
exploration of the relationship between velocity dispersion and entropy proﬁle slope for the three
samples. To quantify the potential relationship between αK and σv, we assume that the relationship
is approximately linear, αK = Aσ240 + B, with intrinsic scatter and determine the strength of the

68

relationship by ﬁtting a linear model with intrinsic scatter to the entropy proﬁle slope, αK, versus
the scaled velocity dispersion, σ240, with ordinary least squares (Akritas & Bershady, 1996). We
use the same process for each sub-sample of galaxies, limited via criteria discussed in 4.3.4.

We ﬁrst show that, with the requirement for radial resolution and ﬁtting entropy proﬁle slope
between 1-10 kpc (see Section 4.3.3 for the entropy proﬁle ﬁtting procedure), some relationship
emerges (see Figure 4.3). The slope of the relation is 0.53 ± 0.27, so while the slope is only about
2σ away from from 0, there is some evidence for relationship between σv and αK before any
additional limits were placed on the sample. Limiting the radial range of the entropy proﬁle ﬁt
and requiring suﬃcient data resolution over that radial range clearly reduces some of the ambiguity
found in previous work (e.g. Babyk et al. 2018; Lakhchaura et al. 2018).

The main sample generally contains massive elliptical galaxies, but there are some that are not
necessarily representative of the galaxies the Voit et al. (2020) model sets out to describe. Figure
4.4 shows the ﬁt for the the low K0 sub-sample determined by the criteria discussed in Section
4.3.3. The slope is 0.80 ± 0.33, so we see mildly stronger evidence for a relationship when the
sample is limited to those galaxies without elevated central entropy.

We determined our ﬁnal sub-sample, the restricted σv sample, shown in Figure 4.4 using the σv
limiting stated in Section 4.3.4. Galaxies with σv < 210 km s−1 may not yet have a well-developed
and suﬃciently hot circumgalactic medium, so there is no reason to believe that the analytic model
would apply. We limit σv < 310 km s−1 on the upper end for two reasons. (1) The Voit et al.
(2020) model assumes a singular isothermal sphere which simpliﬁes the mass proﬁle (see Section
4.3.2), resulting in the analytic model overpredicting the entropy proﬁle slope for galaxies with high
σv. (2) Some galaxies in the sample, like M87, are in galaxy groups or clusters, and thus are in a
potential well with a stellar velocity dispersion signiﬁcantly greater than that of the central galaxy,
resulting in a shallower entropy proﬁle slope than predicted for an isolated galaxy. Limiting the
velocity dispersion in this way limits the sample to galaxies most representative of the restricted σv
the analytic model describes.

For the restricted σv sample, we ﬁnd a slope of 1.80 ± 0.51, or ∼ 3σ away from a ﬂat line.

69

σv

Figure 4.3: Stellar velocity dispersion vs. entropy proﬁle slope for the HQ sub-sample of
galaxies Scaled stellar velocity dispersion, σ240 ≡
240 km s−1 , is plotted with the entropy proﬁle
slope, αK for the sub-sample of galaxies from Lakhchaura et al. (2018) with suﬃcient data between
1–10 kpc. The points are also classiﬁed by their multiphase gas extent from Lakhchaura et al.
(2018). Blue triangles are galaxies with extended multiphase gas, red crosses are galaxies with no
extended multiphase gas, green squares are galaxies with multiphase gas contained within 2 kpc,
and black dots are galaxies without a gas extent classiﬁcation. The black line is the ordinary least
squares ﬁt to the data, and the grey band is the 1σ error. The pink dashed lines represents the
steady ﬂow solutions for σv (cid:38) 300 km s−1.

The criteria we have applied limit the main sample to those galaxies that are most likely to follow
the analytic model, so it is not surprising that the evidence for a relationship is stronger when the
sample is limited to the galaxies to which the model is expected to apply: velocity dispersion-limited
galaxies with limited direct central coupling (r < 10 kpc) by the central AGN, as shown by lack of
central entropy elevations or inversions in the entropy proﬁle. However, the relationship between
entropy proﬁle slope and velocity dispersion may be stronger than indicated by previous works.

70

0.80.91.01.11.21.31.41.52400.00.20.40.60.81.01.21.4kanalytic modelHQ sample fitsteady flow solutionsunknownENENFigure 4.4: Stellar velocity dispersion vs. entropy proﬁle slope for the low K0 sub-sample of
galaxies Scaled stellar velocity dispersion, σ240 ≡
240 km s−1 , is plotted with the entropy proﬁle
slope, αK, for the subsample of galaxies with K0 < 3 keV cm2, and ordinary least squares ﬁts
are given for both the for low K0 subsample (K0 < 3 keV cm2) and the restricted σv subsample
(210 km s−1
< σv < 310 km s−1, K0 < 3 keV cm2). The blue dotted line is the ﬁt to the low K0
sample, and the black dashed line is the ﬁt to the σv limited sample. The maroon dash-dotted line
is the analytic solution from Voit et al. (2020). The pink dashed lines represents the steady ﬂow
solutions for σv (cid:38) 300 km s−1. The grey bands are 1σ errors.

σv

4.4.2 Comparison to the Analytic Model and Numerical Integration Results

Figure 4.4 also includes the analytic model plotted with the ﬁt to the K0 and σv limited sample.
We ﬁnd very good agreement over the range of the “best case” ﬁt. Furthermore, as discussed in
Section 4.3.2, the analytic model over-predicts the entropy proﬁle slopes for galaxies with higher
σv, so the numerical integration results may actually better represent the data for σv > 310 km s−1
than the analytic model.

The analytic prediction for the relation between σv and αK from Equation 6 of Voit et al.
< σv < 310 km s−1 interval.

(2020) is a good ﬁt when the data are restricted to the 210 km s−1

71

0.80.91.01.11.21.31.41.52400.00.20.40.60.81.01.21.4KLow K0Isolated ETGanalytic modelsteady flow solutionsunknownENENHowever, the 9 points at σv > 310 km s−1 all fall below the model prediction and the 1 point at
σv < 210 km s−1 (NGC 4636) is above it. A closer look at the modeling shows that Equation 6
overpredicts αK at σv < 300 km s−1, compared to the numerical steady ﬂow solutions, shown by
the pink dashed line in Figure 4.6.

4.4.3 Best ﬁt Entropy Proﬁle Slope, Multiphase gas extent, and min(tcool/tﬀ)
The free-fall time, tﬀ = (2r/g)1/2, where r is the galactocentric radius and g is the local gravitational
acceleration, provides a dynamical timescale to characterize the gravitationally-driven motions of
the gas and is based on observations of the stellar light from the galaxy. For our purposes, we will
use the equivalent form of tﬀ = r/σv. The cooling time is deﬁned as:

tcool ≡ 3
2

nkT

nenHΛ(T, Z),

(4.3)

where n is the total number density of particles, ne is the electron density, np is the hydrogen density
(where we assume nH = ne/1.2), and Λ(T, Z) is the temperature dependent cooling function for
plasma of metallicity Z. The ratio of the cooling time to the free-fall time (tcool/tﬀ) indicates
if precipitation occurs in the ambient gas. For tcool/tﬀ (cid:27) 5 − 20, the galaxy is said to be in the
precipitation zone, where multiphase gas is found (Voit et al., 2015b). Voit et al. (2015b) also
showed that from 1–10 kpc, galaxies with extended multiphase gas generally track the precipitation
zone whereas galaxies without extended multiphase gas generally remain above the precipitation
zone. The minimum value of tcool/tﬀ is anti-correlated with the presence of multiphase gas (Voit
& Donahue, 2015), so we expect galaxies with greater min(tcool/tﬀ) to have little to no multiphase
gas in their centers.

The expectation from theoretical models is that the entropy proﬁle slope should correlate with
multiphase gas extent, with galaxies with no extended multiphase gas having entropy proﬁle slopes
of K ∼ r and galaxies with extended multiphase gas having K ∼ r2/3. Furthermore, tcool/tﬀ is
coupled with the entropy proﬁle because K = T/n
and tcool ∝ T/neΛ(T), so entropy and cooling
time are approximately proportional to each other. Therefore, proﬁles with higher min(tcool/tﬀ)
have higher entropy gas with longer cooling times.

2/3
e

72

tcool/tﬀ
Figure 4.5: αKαKαK vs. min(tcool/tﬀ
tcool/tﬀ) for the main sample and αKαKαK by gas extent for the HQ sample
Top: αK vs. min(tcool/tﬀ) for the main sample Bottom: Gaussian Kernel Density Estimation of αK
by gas extent for the High Quality sample. Multiphase gas classiﬁcations are from Lakhchaura et al.
(2018). Blue triangles are galaxies with extended multiphase gas, green squares are galaxies with
extended multiphase gas that does not extended past 2 kpc, red crosses are galaxies with no extended
multiphase gas, and black dots are galaxies with no multiphase gas extent classiﬁcation. The colors
indicated each category of multiphase gas extent are the same in the bottom plot. Bandwidths used
for KDE were E: 0.115, NE: 0.192, and N: 0.152.

73

0.00.20.40.60.81.01.21.4k01020304050min(tc/tff)unknownENEN0.00.20.40.60.81.01.21.4K0.00.51.01.52.02.5NormalizedDensityENENtcool/tﬀ
Figure 4.6: αKαKαK vs. min(tcool/tﬀ
tcool/tﬀ) and αKαKαK by gas extent for the low K0K0K0 sample Top: αK vs.
min(tcool/tﬀ) Bottom: Gaussian Kernel Density Estimation of αK by gas extent for the low K0
sample. Blue triangles are galaxies with extended multiphase gas, green squares are galaxies with
extended multiphase gas that does not extended past 2 kpc, red crosses are galaxies with no extended
multiphase gas, and black dots are galaxies with no multiphase gas extent classiﬁcation. The colors
indicated each category of multiphase gas extent are the same in the bottom plot. Bandwidths used
for KDE were E: 0.132, NE: 0.278, and N: 0.110.

74

0.00.20.40.60.81.01.21.4k510152025303540min(tc/tff)unknownENEN0.00.20.40.60.81.01.21.4K0.00.51.01.52.02.53.0NormalizedDensityENENWe can expand our understanding of the relationships between galaxy parameters by exploring
min(tcool/tﬀ) for both the high quality sample and the sample limited to galaxies with K0 <
3 keV cm2, along with the multiphase gas extent and entropy proﬁle slope, αK. Figure 4.5
and Figure 4.6 summarize this relationship for the high quality sample and the low K0 sample,
respectively. For the analysis of the relationship between multiphase gas extent and αK, we employ
Kernel Density Estimation to capture the distribution of multiphase gas extent with αK. Kernel
Density Estimation (KDE) convolves the discrete data with a smooth kernel function, in this case,
a one-dimensional Gaussian with constant bandwidth. We choose to use KDE because it captures
the continuum behavior of the distribution as well as behavior of the distribution that could be
masked by choice of bin size in a histogram. The kernel is the function used to take the average of
neighboring points, thereby making the distribution continuous instead of discrete. We chose the
Gaussian kernel because the data are relatively simple and one-dimensional. The bandwidths were
determined for each multiphase gas extent category in each sub-sample by minimizing the mean
integrated square error. The bandwidth size is driven by minimizing the mean integrated square
error (MISE) by minimizing the integral:

Þ

MISE( ˆfkern) = E

[ ˆfkern(x) − f(x)]2dx,

(4.4)
where ˆfkern is the chosen kernel function, E represents the expected or mean value, and f(x) is the
underlying probability density function. For the KDE shown in the bottom panel of Figures 4.5 and
4.6, we used the KDE tools from the Python package sci-kit learn (Pedregosa et al., 2011).

In Figure 4.5, we consider the high quality sample, and we ﬁnd that galaxies with extended
multiphase gas (categorized as “E”) have entropy proﬁle slopes close to r2/3, but the galaxies with
no extended multiphase gas (categorized as “N”), that we would expect to have entropy proﬁles
slopes around r, extend down to lower entropy proﬁle slopes. However, when we examine the
low K0 sample in Figure 4.6, we ﬁnd that removing galaxies with elevated central entropy outside
1 kpc eﬀectively removes the galaxies with no multiphase gas and lower entropy proﬁle slopes.
Furthermore, we see that removing galaxies with elevated central entropy also removes many of
the galaxies with greater min(tcool/tﬀ), likely because the feedback increases the cooling time.

75

If we consider the high quality sample, we ﬁnd that the galaxies with high σv and no extended
multiphase gas extend down to lower entropy proﬁle slopes, Taken together, the two samples show
that elevated K0 outside 1 kpc and higher min(tc/tﬀ) can serve as ﬂags for galaxies that are not
representative of SN-heated outﬂows, but rather have been ﬂattened by feedback, allowing us to
better test the analytical model.

4.4.4 Comments on Individual Galaxies

In Figure 4.3, some galaxies stand out as not conforming to the model. Because of the simplicity
of the analytic model, we do not necessarily expect it to apply to all galaxies, particularly those
with more complex environments. In this section, we discuss those galaxies and what particular
characteristics of their environments may explain why they do not conform to the model. NGC
533 conforms to the analytical prediction by entropy proﬁle slope and velocity dispersion, but its
multiphase gas extent does not. Other galaxies (M87, NGC 4636, NGC 1521, NGC 1404, and
NGC 4125) do not conform to the analytical prediction. Here, we present possible explanations for
these notable exceptions to the model.

4.4.4.1 M87

M87 has high σv, but an entropy proﬁle near αK = 2/3. However, we do not expect M87 to
conform to the model because it is in a potential well with a velocity dispersion signiﬁcantly greater
than the stellar velocity dispersion of the central galaxy, though αK is consistent with a galaxy near
the precipitation limit.

4.4.4.2 NGC 4636

NGC 4636, has αK ∼ 1 but is classiﬁed as having multiphase gas present inside 2 kpc. The
entropy proﬁle is consistent with the precipitation limit from 0.5–8 kpc, but is also consistent with
a pure cooling ﬂow from 0–2 kpc (Voit et al., 2020). Voit et al. (2020) also states that at smaller
radii, the entropy proﬁle ﬂattens, relative to the the K ∝ r2/3 precipitation-limited proﬁle, but

76

reaches ∼ 1 keV cm2 inside of 100 pc, considerably below the level expected from ∼ 1042erg s−1
of intermittent kinetic feedback power. There are several possible explanations for this low central
entropy level: (1) time-averaged kinetic AGN power has been ∼ 1041erg s−1 for the last ∼ 100
Myr, (2) the AGN power has been highly collimated, as in NGC 4261, and has penetrated to (cid:29) 1
kpc without dissipating much power, (3) AGN power has been too weak to balance cooling for the
last ∼ 100 Myr. In this last case, a cooling catastrophe is imminent, as suggested by the entropy
proﬁle between 0.5 and 2 kpc, and will soon trigger a strong feedback episode.

4.4.4.3 NGC 1521

NGC 1521 does not conform to the model, most likely because of low spatial resolution. The
entropy proﬁle only has four radial bins between 1–10 kpc, and only one additional radial bin,
interior to 1 kpc. The best ﬁt entropy proﬁle slope has a large uncertainty, and the uncertainty does
overlap the analytic prediction. Therefore, improved spatial resolution is necessary to determine if
the galaxy conforms to the model.

4.4.4.4 NGC 4125

NGC 4125 does not conform to the analytic model, but like NGC 1521, may not conform due
to spatial resolution. However, the shape of the entropy proﬁle and the galaxy parameters are
a bit more interesting. The X-ray luminosity (measured inside 10 kpc) is the lowest in the HQ
sample (0.023 ± 0.001 × 1042 erg s−1). Between 1–10 kpc, the entropy proﬁle is almost ﬂat and
based on six radial bins, resulting in a low best ﬁt entropy proﬁle slope (and larger uncertainty).
However, interior to 1 kpc, the entropy proﬁle slope is much steeper, and Lakhchaura et al. (2018)
ﬁnd a power law component of the spectrum, indicating the presence of an AGN with luminosity
0.006 ± 0.001 × 1041erg/s. Wiklind et al. (1995) detected an upper limit for the molecular gas
content, but the measurement is uncertain due to high systematic errors. The combination of the
presence of an AGN, σv < 240 km s−1, and the ﬂattened entropy proﬁle at larger radii may
indicate that this is a galaxy where the steady ﬂow is cooling dominated at larger radii and prone to

77

developing entropy inversions (Voit et al., 2020).

4.4.4.5 NGC 1404

NGC 1404 is not far from the analytic prediction, but it has low σv for its αK because it has an
entropy proﬁle with a sharp increase in slope beyond 7 kpc. It is a satellite of NGC 1399, so the
sharp increase in the entropy proﬁle could potentially be a result of ram-pressure stripping by the
IGM around NGC 1399.

4.4.4.6 NGC 533
NGC 533 has σv = 272 km s−1 and αK = 0.9. The velocity dispersion of the surrounding galaxies
is ∼464 km s−1, according to Zabludoﬀ & Mulchaey (1998), so we would not expect the basic
model to apply.

4.4.5 Predictions for Equilibrium Pressure and Density Proﬁles

The analytic model of Voit et al. (2020) explores the behavior of the heating/cooling equality based
on the Black-hole feedback valve model. Here, we present an observational test of the derived
equilibrium proﬁles with the pressure and density proﬁles from Lakhchaura et al. (2018). An
entropy proﬁle slope of αK ≈ 2/3 is a critical slope for the analytic model, meaning that the
behavior of the galactic outﬂows should be fundamentally diﬀerent above and below αK ≈ 2/3.
Voit et al. (2020) shows that the ratio of stellar heating to radiative cooling decreases with radius
for galaxies with an entropy proﬁle slope below αK ≈ 2/3 and rises with radius for galaxies with
an entropy proﬁle slope above αK ≈ 2/3. Following from Equation 4.1, the velocity dispersion
corresponding to this critical entropy proﬁle slope is ≈ 240 km s−1.

When radiative cooling per unit volume equals stellar heating per unit volume, for a given
radius, they ﬁnd an equilibrium pressure proﬁle along which supernova heating equals radiative
cooling for a temperature, T (Equation 11 in Voit et al. (2020)):

78

Figure 4.7: Equilibrium pressure vs. radius for single phase and multiphase galaxies in the
HQ sample The equilibrium pressure at temperature T, for radius r (black dashed line), is plotted
with the extended multiphase (E, blue lines) and single-phase (N, red lines) galaxies in the HQ
sample. Errors bars are removed from the proﬁles for clarity. The blue line below the black dashed
line is NGC 1316, and the red line above the black dashed line is NGC 4073. See Section 4.4.5 for
a discussion of these two galaxies.

Peq(r) ≡(cid:104)(cid:16)

∗ +

3
2
2 σ
v

(cid:17)(cid:16) n2

(cid:17)

nenp

(cid:105)1/2

kT,

(4.5)

ρ∗
t∗Λ(T)

where np is the proton density, ρ∗ is the stellar mass density, t−1∗
is the speciﬁc stellar mass-
loss rate, and Λ(T) is the radiative cooling function. For the velocity dispersion and temperature
corresponding to the critical entropy proﬁle slope (σv ≈ 240 km s−1, kT ≈ 0.75 keV, αK ≈ 2/3),
the critical proﬁles are as follows (Equations 12 and 13 in Voit et al. (2020)):

Peq(r) ≈ (1.4 × 10−10erg cm−3) σ
ne,eq ≈ (0.06 cm−3) σ240r−1
kpc,

240r−1
3
kpc

(4.6)

(4.7)

79

Figure 4.8: Equilibrium electron density vs. radius for single phase and multiphase galaxies
in the HQ sample The equilibrium electron density at temperature T, for radius r (black dashed
line), is plotted with the extended multiphase (E, blue lines) and single-phase (N, red lines) galaxies
in the HQ sample. Errors bars are removed from the proﬁles for clarity. The blue line below the
black dashed line is NGC 1316, and the red line above the black dashed line is NGC 4073. See
Section 4.4.5 for a discussion of these two galaxies.

where rkpc ≡ r/1 kpc, σ240 ≡ σv/240 km s−1, ρ∗ = σv/2πGr2, the isothermal stellar mass
distribution, and the ﬁducial values µmp∗ ≈ 2 keV and t∗ ≈ 200 Gyr, if the weak dependence of
Λ(T) on σv is ignored.

Figures 4.7 and 4.8 show the comparison of the extended multiphase (E) and single-phase
(N) galaxies in our sample to the equilibrium pressure and density proﬁles. The galaxies with
multiphase gas conﬁned to the central 2 kpc have been removed for clarity. The model predicts
that the equilibrium proﬁles should divide the proﬁles of galaxies with extended multiphase gas
(αK (cid:46) 2/3) from the galaxies with no extended multiphase gas (generally higher αK (cid:38) 2/3).
We ﬁnd that overall, the equilibrium proﬁles for both Peq and ne,eq do indeed divide our sample
as predicted. However, there are a two notable exceptions; one each from the multiphase and

80

single-phase galaxies. The multiphase galaxy, NGC 1316, does conform to the analytic model
within uncertainty, but the entropy proﬁle exhibits an inversion at r ∼ 2.5 kpc, an entropy proﬁle
characteristic of massive elliptical galaxies with σv (cid:46) 240 km s−1 predicted by Voit et al. (2020).
NGC 1316 is also one of the lowest luminosity galaxies in the sample. The single-phase galaxy,
NGC 4073, has one of the highest luminosities and one of the highest temperatures in the sample. It
is classiﬁed as a single-phase galaxy but has αK ≈ 0.6 and σv ≈ 268 km s−1 and does not conform
to the analytic model within uncertainty.
4.5 Conclusions

In this work, we were able to show that not only is there evidence for a relationship between
the stellar velocity dispersion, σv, and the entropy proﬁle slope, αK, the relationship agrees with
the analytic model proposed in Voit et al. (2020). In contrast to previous analyses of this relation,
we applied limits to data quality of the archival observations as well as limits on the parameters
explored as informed by the data and the analytic model. While the results from the sample limited
by both K0 and σv are a more promising comparison to the analytic model, we still see evidence for
a relationship between αK and σv for the samples with fewer limits applied. Furthermore, results
from the numerical integration of the analytic model suggest that the data may agree with the model
for higher σv as well. For galaxies in groups with much lower entropy proﬁle slopes than predicted
for their velocity dispersion, Voit et al. (2020) proposes that the entropy proﬁle may have a slope
of αK = 2/3 that is more representative of a cool-core cluster with extended multiphase gas or
galaxies with 200 km s−1

< σv < 240 km s−1.

When we set out to characterize the sample by central entropy K0, we found that there were
two populations of galaxies that we could separate by applying a limit of K0 < 3 keV cm2. Those
galaxies with K0 > 3 keV cm2 that were removed from the sample are likely galaxies that have
experienced recent feedback, elevating their entropy out to larger radii. When we explored the
min(tcool/tﬀ), multiphase gas extent, and entropy proﬁles slopes of those galaxies as well, we found
that galaxies with no extended multiphase gas and lower entropy proﬁle slopes than expected also
typically had higher min(tcool/tﬀ), providing further evidence for recent feedback causing lower

81

αK. However, we also note that the galaxies with multiphase gas present but inside 2 kpc remain
spread across the range of αK, though more with lower αK were removed than with higher αK,
indicating that some entropy proﬁles may be ﬂattened due to feedback, but the eﬀect is less clear.
The analytic model requires the galaxies to be in equilibrium, so it is not surprising that galaxies
out of equilibrium do not follow it, but model does agree with galaxies close to equilibrium.

Our work shows that while the Voit et al. (2020) analytic model may be relatively simple,
it describes the relationship between key galaxy parameters well and can be used to further our
understanding of how feedback in massive galaxies works. The comparison of the model to the
data supports the notion that SNIa supernova feedback plays an important role in the thermal
evolution of massive galaxies. Furthermore, the relationship between entropy proﬁle slope and
velocity dispersion is highly dependent on the external gas pressure at larger radii. Current X-ray
observations are not able to resolve pressure measurements at large radii, but Athena and LYNX
may be able to. Taking the model predictions and existing observations, one could predict what the
gas pressure at large radii and then test that prediction with the next generation of X-ray telescopes.

82

CHAPTER 5

SUMMARY

5.1 Summary

This dissertation sought to add to our understanding of the thermal properties of galaxy clusters
and early-type galaxies. Chapter 2 introduced the ACCEPT 2.0 database, presented my analysis
of the entropy proﬁles for clusters with deprojected radial temperature and density proﬁles, and
provided an example of the science applications of the ACCEPT 2.0 data products including central
entropy and morphology measurements. I showed that ACCEPT 2.0 provides robust, uniformly
reduced, deprojected entropy proﬁles and central entropy classiﬁcations as well as morphology
measurements with great potential for scientiﬁc impact. The central entropy measurements I
obtained show that ACCEPT 2.0 reproduces the distribution of central entropy, K0 from ACCEPT
and that distribution holds when all of the new clusters with central entropy measurements in
ACCEPT 2.0 are introduced. Finally, ACCEPT 2.0 reproduces some of the early morphology work
from Cassano et al. (2010) and provides meaningful insights about sample selection for the XMM
Heritage sample.

In Chapter 3, I explored the properties of early-type galaxies with powerful radio sources. I
found that there are other galaxies, like NGC 4261, with powerful radio sources and single power
law entropy proﬁles, namely IC 4296 and potentially NGC 315. Furthermore, if the ratio of the
cooling time to the free-fall time is lowest in the central radial bin, it may indicate the presence of
a powerful radio source. Finally, when I compared the radial entropy proﬁles for NGC 4261 and
IC 4296, along with the radial entropy proﬁles from Lakhchaura et al. (2018), to the simulations of
Wang et al. (2019), I found good agreement in the general entropy proﬁle slope behavior between
observations and simulations for both single phase and multiphase galaxies.

In Chapter 4, I presented an observational test of the black-hole feedback valve model for galactic
atmospheres from Voit et al. (2020) using the sample of early-type galaxies from Lakhchaura et al.

83

(2018). I found that equilibrium pressure and density proﬁles support the model prediction that
galaxies above and below the critical values, α ∼ 2/3 and σv ∼ 240 km s−1, behave diﬀerently.
I also found that, when we select a sub-sample of galaxies from the original sample that the
analytic model would be expected to apply to, based on velocity dispersion and central entropy
measurements, there is a correlation between the entropy proﬁle slope and velocity dispersion.
The slope of the relation between velocity dispersion and entropy proﬁle slope for this sub-sample
is at the 3σ level and matches the analytic prediction well. When we broaden our analysis to
include all galaxies in the sample with suﬃcient data resolution to obtain an entropy proﬁle slope,
including those that may not be expected to follow the analytic model, we still ﬁnd some evidence
for correlation, although at closer to 2σ signiﬁcance.
5.2 Future Work

There are many possible avenues to explore from the work completed in this dissertation, both
in the realm of galaxies and galaxy clusters. With the release of the ACCEPT 2.0 data products, it
will be the largest uniformly reduced, publicly available database of cluster properties and thus can
be used to gain insight into the systematics of other X-ray samples. As shown in Chapter 3, X-ray
systematics are signiﬁcant enough to aﬀect conclusions made from data, so the uniform reduction
of ACCEPT 2.0 is helpful for exploring the characteristics of large samples of galaxy clusters.

With respect to early-type galaxies, we have obtained additional X-ray data for IC 4296 from
both Chandra and XMM that will hopefully allow us to better probe the inner ∼ kpc of the galaxy.
In the more distant future, improved spatial resolution from an X-ray observatory like LYNX would
allow us to examine the central kpc of the galaxies in our sample that would require prohibitively
long observations to achieve the resolution of NGC 4261 with current telescopes. Looking ahead to
Athena or LYNX, we could make predictions about the external gas pressure in early-type galaxies,
based on the black-hole feedback valve model for galactic atmospheres, that could be tested with
more sensitive X-ray telescopes.

84

APPENDICES

85

APPENDIX A

ACCEPT 2.0 PIPELINE DESCIPTION

A.1 ACCEPT 2.0 Pipeline Details

A.1.1 Sample Selection and Data Processing and Analysis

This Appendix is provided to document choices made within the ACCEPT 2.0 pipeline. This text
is heavily drawing on the text that the author team of the ACCEPT 2.0 data release paper, in draft,
will be publishing in an Astrophysical Journal Supplement Series.

The ACCEPT 2.0 cluster sample was selected from all Chandra archival observations available
as of July 2014. The automated pipeline (integrated with visual inspection of the products, when
necessary) was developed to select the sample and perform the data processing and analysis. Using
CIAO v4.7, CALDB 4.5, and SHERPA they ran an automated quick spectral analysis of all clusters
available in the archive in order to have a rough estimate of the temperature of each cluster. The
temperature estimate was used to set a count threshold to decide whether to include a cluster in
the sample. To establish a 20% error threshhold on the cluster temperature measurement from
at least three spatial bins, they determined from simulations that the minimum number of counts
required in the 0.5–7 keV band is given by nmin,res = 1377 · kT − 537, where kT is the cluster
temperature in keV. For a 20% error on the temperature in a single spatial bin, the number of counts
required in the 0.5–7 keV band is given by nmin,glb = (1377 · kT − 537)/3. They set nmin,glb
and nmin,res as the minimum counts necessary to include a cluster in our total sample and in the
spatially resolved sample, respectively. The total ACCEPT 2.0 sample consists of 606 clusters
of which 402 are suitable for a spatially resolved analysis in at least three spatial bins. Of the
clusters with spatially resolved analysis, 348 had suﬃcient counts for deprojection. Chandra data
reprocessing was performed in an automated fashion using CIAO task chandra_repro, which
applies the appropriate ACIS gain maps, the time-dependent ACIS gain correction, and the ACIS
charge transfer ineﬃciency correction. The background light curve during each observation was

86

used to detect and remove periods of anomalously high background following the recommendations
of Markevitch et al. (2003). The automated procedure to remove background ﬂares was followed
by a manual visual inspection of the light curves to check for undetected ﬂares or excessive ﬂare
cleaning.

A.1.1.1

Initial Pipeline Spatial Analysis

Once clean event ﬁles for each ObsID of a cluster are obtained, they used the CIAO tool merge_obs
to produce ﬂuxed images and exposure maps for each ObsID and for the sum of all ObsIDs. Images
and exposure maps are created with a binning factor of 2, corresponding to a pixel size in the image
of 0.984 arcsec. At this stage, point sources are detected in the merged image using CIAO tool
wavdetect in order to create a list of point sources that will be excluded from the spatial and spectral
analysis of the cluster and to create an image of the diﬀuse emission using CIAO tool dm f ilth. The
point source list is also visually inspected using DS9 in order to prevent false detections or excess
exclusion of undetected point sources.

As a default, the X-ray emission peak was used as the center of the radial proﬁles, however
the pipeline allowed manual inspection of the validity of this choice and to use the X-ray emission
centroid if necessary. They initially considered concentric annuli with a thickness of 5 arcsec. If
the cluster had at least 1500 counts in the 0.5-7 keV band, they grouped the annuli in the radial
proﬁle to have at least 300 counts per spatial bin prior to background subtraction. If the cluster
had less than 1500 total counts, the minimum number of counts required for each spatial bin was
lowered to one-ﬁfth of the total counts in the cluster. The radial proﬁles extend out until the number
of source counts in a given annulus reach 30% of the background counts in that annulus (or when
an annulus reaches the chip boundary, in very bright and extended clusters).

The pipeline then performs a ﬁt of the image from a 2-D Lorentz model with a varying power

law (also known as a 2-D β model) using Sherpa. The function ﬁtted to the image is:

f(x, y) = f(r) = A(1 + [r/r0]2)−α

(A.1)

87

(cid:113)[x2

new(1 − )2 + y

new]/(1 − ), xnew = (x − xo)cos(θ) + (y − yo)sin(θ), and
where r(x, y) =
2
ynew = (y − yo)cos(θ) − (x − xo)sin(θ). The most important parameters of this model are the
core radius r0, the power-law index α, the ellipticity , and the angle of ellipticity θ. The last
two parameters are used for a morphological analysis of the clusters in relation with other cluster
properties (see Section 2.2.2.1). This spatial analysis procedure was repeated for every single
cluster in the sample.

A.1.1.2 Global Spectral Extraction and Analysis

To analyze the global properties of each cluster, the pipeline performs a spectral extraction in three
diﬀerent spatial regions: the whole cluster (r < rcluster), the cluster core (r < rcore), and the cluster
with the core excised (rcore < r < rcluster). They used the CIAO tool specextract to generate the
spectra, appropriate redistribution matrix ﬁles (RMFs), and ancillary response ﬁles (ARFs). The
maximum cluster extension rcluster has been set to 500 h−1 kpc. If the maximum radius cannot
ﬁt in the S2 chip, the cluster was observed only with ACIS-S, or was observed in all four chips of
ACIS-I, if at least one of the observations was performed with ACIS-I, the largest radius that can ﬁt
in the ACIS ﬁeld of view is used. The core radius was set by default to 70 h−1 kpc, but if this radius
is larger than 0.3rcluster, the core radius is set to rcore = 0.3rcluster. Detected point sources are
excised from the spectra of the diﬀuse emission from the cluster. At this stage background spectra
and radial proﬁles are also built.

A.1.1.2.1 Background Subtraction

The pipeline used the blank-ﬁeld observations, processed identically to the cluster observations,
and reprojected onto the sky using the aspect information from the cluster pointings. The synthetic
backgrounds correspond to far longer exposure times (∼ 0.5 Msec) than the majority of the cluster
observations, giving a good estimate of the background. For clusters observed on ACIS-I, the
blank-ﬁeld background correction is renormalized to the background of the observation, using the
ACIS-S2 chip, in a region of the ACIS ﬁeld of view practically free from cluster emission. For

88

clusters observed with ACIS-S, the chip used for the renormalization is ACIS-S1. The energy band
from 9.5 to 12 keV (mostly dominated by charged particles) is used to perform the normalization.
Using the renormalized and reprojected background event ﬁles, the pipeline produces radial proﬁles
of background counts and surface brightness for use in the analysis of the cluster surface brightness
proﬁles.

A.1.1.2.2 Spectral Analysis

The spectra of the whole cluster, the cluster core, and the cluster with the core excised were analyzed
in an automatic fashion by the pipeline using the Python tools within Sherpa. The spectra were
analyzed in the 0.5-8 keV spectral band, and the source and background are ﬁtted simultaneously.
The source model used is a mekal model Kaastra et al. 1996; Liedahl et al. 1995 in which the ratio
between the elements is ﬁxed to the solar value as in Anders & Grevesse (1989). They considered
line of sight absorption ﬁxed at the Galactic value nH (Stark et al., 1992), and an additional internal
absorption component left free to vary (consistent with zero in the large majority of clusters). The
free parameters in the mekal model are temperature, kT, metal abundance, Z, and normalization,
η. The redshift, z, was ﬁxed at the literature value for the cluster. The background model used was
composed of two power-law models, several gaussian emission lines, and an apec thermal model at
low temperature (kT = 0.17 keV, to account for the soft, diﬀuse X-ray background). The power-law
slopes and the quantity, position, and strength of the emission lines depends on the speciﬁc ACIS
chip used and are adjusted accordingly. The shape of the spectrum is held ﬁxed.

A.1.1.3 Spatially Resolved Spectral Extraction and Analysis

For clusters with a suﬃcient number of counts and at least three spatial bins, a spatially-resolved
spectral analysis was performed. The cluster was divided into concentric annuli that are required to
contain at least nmin,res/3 counts per annulus for the projected spectral analysis and nmin,res counts
per annulus for the deprojected spectral analysis. In both analyses, the annuli have a minimum
thickness of 5 arcsec and extend out until the source counts reach 50% of the background counts.

89

CIAO tool specextract was then used to generate the spectra of each annular region and their
relative RMFs and ARFs.

The projected spectral analysis ﬁts each annular region spectrum independently from the others.
The X-ray band considered is 0.5-8 keV. Similarly to the global spectral analysis, source and
background spectra are ﬁtted simultaneously using the same models described in Section A.1.1.2.2.
If at least three spatial annuli exist, the pipeline uses the deproject module in Sherpa to extract
the deprojected temperature and density proﬁles (see Section 1.3.3 for a discussion of deprojection).

90

APPENDIX B

ACCEPT 2.0 CENTRAL ENTROPY FITTING RESULTS

Table B.1: Fit parameters, redshift, and proﬁle center for ACCEPT 2.0 clusters Column 1:
Cluster Name; Column 2: Proﬁle center RA; Column 3: Proﬁle Center DEC; Column 4: redshift;
Column 5-6: Best ﬁt K0 and associated 1σ error; Column 7-8: Best ﬁt K100 and associated 1σ
error; Column 9-10: Best ﬁt α and associated 1σ error;

Cluster Name

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

ABELL_2717
NSCS_J000619+105206
ZwCl_0008.8+5215
ABELL_2734_NED01
MACS_J0011.7-1523
ABELL_0013
ABELL_2744
Cl_0016+16
MACS_J0025.4-1222
PLCKESZ_G304.84-41.42
MCXC_J0035.4-2015
ABELL_2813
ZwCl_0040.8+2404
ABELL_0098N
ESO_351-_G_021
ABELL_0141
MaxBCG_J016.70077+01.05926 16.7042
CIZA_J0107.7+5408
IC_1633
ABELL_2895
UGC_00842

29.928
0.8040 -35.9334 0.0490
58.428
1.5845
10.8643 0.1670
52.5292 0.1040 170.494
2.8396
2.8401 -28.8540 0.0753
25.692
2.9290 -15.3891 0.3780
7.906
3.4078 -19.5025 0.0943 130.014
3.5814 -30.3917 0.3080 151.716
4.6396
16.4369 0.5410 165.464
6.3737 -12.3761 0.5843 149.815
7.0238 -75.6301 0.4100 -48.267
8.8607 -20.2628 0.3640 136.376
10.8537 -20.6236 0.2924 136.338
9.048
10.9678 24.4054 0.0830
11.6029 20.6221 0.1043
10.598
13.7493 -35.3209 0.0571
3.731
16.3933 -24.6330 0.2300 158.783
11.751
16.9381 54.1327 0.1066 305.475
17.4809 -45.9308 0.0243
2.846
19.5469 -26.9653 0.2270 168.687
19.7248 -1.0021 0.0452 -22.632

1.0538 0.2539

6.217
11.089
40.772
17.051
6.688
31.300
90.749
19.834
20.362
43.675
16.255
22.780
1.165
5.928
0.865
28.161
0.707
45.983
0.783
33.931
19.270

9.684 0.933 0.114
123.474
17.235 0.908 0.084
135.616
53.516 0.932 0.198
114.906
24.192 0.578 0.078
153.977
14.306 0.861 0.076
139.323
156.989
51.950 0.783 0.219
240.949 140.399 0.480 0.240
16.004 1.319 0.126
56.168
63.487
19.633 1.337 0.154
45.563 0.488 0.083
356.033
12.893 1.521 0.149
41.337
65.152
32.801 1.403 0.287
3.727 1.136 0.044
113.822
13.006 0.982 0.097
179.603
104.966
6.880 0.942 0.056
34.694 1.396 0.285
61.340
68.442
2.757 1.517 0.047
52.333 1.107 0.300
66.095
95.777 1.219 0.057
845.517
90.111
37.843 1.130 0.194
20.699 0.430 0.160
215.221

91

Table B.1 (cont’d)
Cluster Name

ABELL_0193
ABELL_0209
Abell_222
Abell_223
ABELL_0267
ABELL_0262
NGC_0741_GROUP
NGC_0766
GMBCG_J029.95560-08.83299
NGC_0777
ARP_318
MCXC_J0220.9-3829
ABELL_3017
MZ_10451
SPT-CL_J0232-4421
ABELL_0370
MACS_J0242.6-2132
ABELL_S0295
ABELL_0376
ABELL_0383
NGC_1132
ABELL_0402
ABELL_0400
ABELL_0401
MCXC_J0301.6+0155
MCXC_J0303.7-7752
IC_1880_GROUP
ABELL_3088
MACS_J0308.9+2645

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

8.6992 0.0486 134.938
21.2819
22.9690 -13.6108 0.2060
86.644
24.3940 -12.9930 0.2110 148.849
24.4832 -12.8196 0.2070 101.808
28.1761
1.0126 0.2310 148.399
3.562
28.1929 36.1533 0.0174
5.6272 0.0185
29.0876
1.343
29.6769
8.3471 0.0270
1.208
29.9560 -8.8336 0.3220 -10.805
30.0620 31.4294 0.0167
4.297
5.359
32.4095 -10.1459 0.0132
18.431
35.2358 -38.4809 0.2287
36.4712 -41.9179 0.2195
36.916
11.591
37.4404 -29.6300 0.0608
38.0782 -44.3463 0.2836
16.418
39.9715 -1.5769 0.3750 256.699
40.6496 -21.5406 0.3140
9.402
41.3602 -53.0297 0.3000 165.939
61.935
41.5164 36.9055 0.0484
42.0140 -3.5291 0.1871
10.280
43.2163 -1.2740 0.0231
-1.648
44.4209 -22.1531 0.3224 115.241
44.4234
86.201
44.7372 13.5707 0.0737 154.597
45.4092
12.181
45.9387 -77.8798 0.2742 187.074
4.003
46.6186 -9.7312 0.0338
46.7572 -28.6654 0.2534
20.390
47.2330 26.7606 0.3240 144.011

1.9205 0.1695

6.0243 0.0244

9.008
24.724
21.545
21.115
16.487
0.138
0.211
0.676
5.842
0.287
0.210
3.386
7.731
10.746
17.740
27.693
1.573
21.589
16.644
1.047
0.843
24.785
20.899
14.171
1.870
34.239
1.229
9.298
31.449

16.118 1.559 0.293
43.896
30.617 0.812 0.083
165.614
37.967 1.362 0.395
48.218
31.330 1.023 0.160
120.946
15.020 1.745 0.148
54.930
26.609 1.459 0.026
484.188
595.269
91.607 1.369 0.065
294.920 298.944 1.338 0.299
217.850
13.766 0.837 0.049
552.908 227.639 1.838 0.117
157.740 311.625 1.810 0.141
7.654 1.049 0.059
110.540
109.848
14.716 1.258 0.086
73.110
20.113 0.569 0.459
416.131 384.037 1.254 0.509
25.614 1.614 0.236
42.280
5.660 1.302 0.059
85.748
36.248
26.526 1.560 0.279
32.288 0.869 0.157
178.494
117.585
3.732 1.253 0.041
3.305 0.663 0.035
112.294
30.745 1.202 0.192
87.153
104.441
45.919 0.939 0.588
17.379 0.940 0.098
115.707
112.084
4.925 1.064 0.045
47.786 1.420 0.316
85.939
75.624 1.588 0.154
342.980
178.149
18.196 0.886 0.074
32.825 1.111 0.141
106.556

92

Table B.1 (cont’d)
Cluster Name

ABELL_3094
ABELL_3120
UGC_02748
ABELL_3126
MACS_J0329.6-0211
ABELL_3128
MCXC_J0331.1-2100
3C_089
ABELL_3140
Fornax_Cluster
MCXC_J0338.6+0958
MCXC_J0340.8-4542
MCXC_J0352.9+1941
MACS_J0358.8-2955
ABELL_0478
MACS_J0416.1-2403
MACS_J0417.5-1154
MCXC_J0425.8-0833
ABELL_S0463
MACS_J0429.6-0253
ABELL_0496
MCXC_J0437.1+0043
MCXC_J0439.0+0715
MCXC_J0439.0+0520
ABELL_3292
WEIN_051
MCXC_J0454.1-0300
ESO_552-_G_020
ABELL_3322

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

47.8995 -26.8988 0.0677
31.063
50.4853 -51.3265 0.0690
17.504
51.9752
2.5616 0.0302
5.953
52.1524 -55.7180 0.0856 158.222
52.4237 -2.1966 0.4500
4.991
12.128
52.4605 -52.5801 0.0599
11.718
52.7751 -21.0092 0.1880
53.5625 -1.1882 0.1386
30.855
91.667
54.0652 -40.6285 0.0620
54.6204 -35.4499 0.0046
0.346
54.6713
5.111
9.9669 0.0363
55.2241 -45.6765 0.0698 189.419
58.2437 19.6819 0.1090
7.106
26.151
59.7190 -29.9303 0.4250
63.3556 10.4653 0.0881
11.580
76.272
64.0393 -24.0669 0.4200
64.3945 -11.9091 0.4400
23.919
66.4636 -8.5601 0.0397
6.656
67.1559 -53.8418 0.0394 117.469
67.4004 -2.8858 0.3990
12.169
4.569
68.4085 -13.2610 0.0329
39.939
0.7322 0.2850
69.2898
69.7530
7.2688 0.2300
57.207
69.7592
6.155
5.3453 0.2080
72.4841 -44.6725 0.1723 108.116
72.5271 45.0510 0.0222
84.177
73.5458 -3.0145 0.5500 193.350
73.7180 -18.1157 0.0314
-6.756
77.5705 -45.3212 0.2000 104.613

83.173 0.399 0.169
225.536
66.818
153.473
12.136 0.982 0.122
5.900
329.791 103.667 1.659 0.212
1.207
14.489 1.725 0.167
50.469
13.322
118.081
5.828 1.095 0.042
2.268
72.740 0.341 0.215
200.471
60.726
5.396 1.252 0.053
114.991
1.574
214.297
11.182 1.347 0.077
5.532
16.033 1.808 0.124
194.228
6.967
274.257
7.900 0.918 0.011
0.066
0.925 1.395 0.011
106.901
0.100
132.705 0.633 0.750
68.974
55.692
56.749
2.013 1.494 0.061
0.380
22.122 0.687 0.062
167.420
14.956
216.321
33.585 1.549 0.130
0.910
106.522 245.717 116.894 0.421 0.225
14.094 0.935 0.061
8.332
1.320
3.695 0.924 0.042
44.890 1.076 0.411
23.573
3.110
8.616 1.166 0.071
1.605 0.984 0.014
0.330
8.153 1.301 0.079
4.172
11.956
17.768 0.946 0.095
5.101 1.067 0.044
1.597
10.191
10.662 1.694 0.168
94.348 0.420 0.258
55.153
20.322 1.387 0.197
20.561
7.226
10.816 0.609 0.081
21.058 1.196 0.147
17.637

159.396
122.571
100.204
109.873
146.262
88.447
116.269
118.345
35.724
196.260
49.053
206.197
77.060

93

Table B.1 (cont’d)
Cluster Name

MCXC_J0510.7-0801
ABELL_S0520
ABELL_3343
MCXC_J0528.2-2942
RBS_0653
PLCKESZ_G286.58-31.25
ABELL_0545
MCXC_J0532.9-3701
ESO3060170-A
MCXC_J0547.0-3904
ABELL_3364
ABELL_0548A
ABELL_0550
MACS_J0553.4-3342
ABELL_3378
SPT-CL_J0615-5746
CIZA_J0616.3-2156
ABELL_S0579
G139.59+24.18
ABELL_3391
ABELL_3395_SW
ABELL_3399
PLCKESZ_G167.65+17.64
ABELL_S0592
ABELL_3404
ABELL_0562
ABELL_0576
ABELL_0578
ABELL_0586

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

77.6985 -8.0275 0.2195 122.172
79.1571 -54.5131 0.2952 320.133
81.4530 -47.2528 0.1913 163.757
88.463
82.0613 -29.7208 0.1582
82.2210 -39.4710 0.2839
27.862
82.8684 -75.1793 0.2100 149.127
83.1054 -11.5424 0.1540 146.987
83.2314 -37.0264 0.2747
98.106
2.005
85.0279 -40.8369 0.0358
86.7566 -39.0745 0.2100
10.804
86.9071 -31.8732 0.1483 205.019
87.1596 -25.4779 0.0395
23.658
88.2147 -21.0536 0.0990 120.247
88.3653 -33.7104 0.4070 106.577
91.4749 -35.3022 0.1410
8.528
93.9661 -57.7794 0.9720
77.522
94.1033 -21.9383 0.1710 234.527
94.1339 -39.7968 0.1520 129.966
95.4541 74.7014 0.2700
32.801
96.5896 -53.6958 0.0514 203.151
96.7019 -54.5498 0.0510 190.118
99.3105 -48.4719 0.2026
59.435
99.5154 47.7983 0.1740 209.979
30.594
99.7025 -53.9740 0.2216
101.3709 -54.2286 0.1670
95.055
103.3397 69.3309 0.1100 122.537
63.842
110.3766 55.7616 0.0389
111.2230 66.9854 0.0866
16.576
113.0848 31.6329 0.1710 116.110

51.636
39.838
19.794
18.810
4.749
62.571
21.961
24.012
1.515
2.398
17.037
10.142
24.385
46.574
3.136
10.404
60.544
24.011
8.952
29.569
25.741
16.441
18.217
7.827
18.879
34.177
7.638
48.228
10.286

150.700
79.443 0.574 0.180
30.757
30.494 1.656 0.233
46.150
19.915 1.602 0.225
91.877
37.031 1.361 0.366
164.154
10.315 0.941 0.043
146.327
86.892 0.782 0.226
114.049
28.338 0.894 0.125
128.772
35.406 1.020 0.151
441.229 108.030 1.170 0.126
124.928
8.182 1.179 0.072
17.143 1.635 0.206
42.820
20.112 0.920 0.173
170.653
102.004
32.615 1.014 0.181
82.059 0.694 0.179
220.930
120.248
6.808 0.910 0.060
14.033 1.314 0.111
77.435
92.762 0.854 0.290
117.417
68.501
26.967 1.134 0.185
18.544 1.244 0.247
150.993
122.635
45.810 0.917 0.228
44.497 1.376 0.344
99.607
25.195 0.867 0.078
164.359
21.819
7.294 1.886 0.086
13.223 0.915 0.073
141.163
119.833
26.794 1.080 0.141
77.220 0.761 0.498
82.469
14.401 1.295 0.200
204.151
216.253
74.410 0.644 0.369
10.676 1.443 0.092
67.379

94

Table B.1 (cont’d)
Cluster Name

ZwCl_0735.7+7421
FBQS_J074417.4+375317
MACS_J0744.9+3927
PKS_0745-19
ABELL_0598
ABELL_0611
SDSS-C4_3062
ABELL_0644
MCXC_J0819.6+6336
NGC_2563_GROUP
UGCl_120
ZwCl_0823.2+0425
2MFGC_06756
ABELL_3411
NSC_J084254+292723
ABELL_0697
ZwCl_0857.9+2107
SDSS_+137.3+11.0+0.18
HCG_037
2MASSi_J0913454+405628
ABELL_0773
Hydra_A
NSC_J092017+303027
ABELL_0795
UGC_05088_GROUP
WHL_J093820.9+520243
ABELL_0868
GALEX_J094712.4+762313
ZwCl_0949.6+5207

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

115.4344 74.2440 0.2160
16.140
116.0724 37.8878 1.0686 -18.950
116.2200 39.4568 0.6976
53.443
8.581
116.8810 -19.2944 0.1028
117.8504 17.5147 0.1894
8.320
63.673
120.2368 36.0567 0.2880
46.651
122.5951 42.2739 0.0638
124.3551 -7.5111 0.0704
70.240
6.464
124.8584 63.6240 0.1190
125.1485 21.0679 0.0163
1.362
-2.576
125.8402 4.3726 0.0293
126.4910 4.2470 0.2248
72.063
128.7288 55.5725 0.2411
12.469
130.4664 -17.4627 0.1687 194.021
130.7332 29.4575 0.1940
22.863
130.7398 36.3660 0.2820 229.645
18.933
135.1535 20.8945 0.2300
137.3031 10.9756 0.1800
88.200
2.267
138.4130 29.9952 0.0223
138.4405 40.9416 0.4422
23.534
139.4690 51.7273 0.2170 179.097
139.5249 -12.0955 0.0549
15.711
140.1105 30.4938 0.2578 128.487
27.927
141.0241 14.1736 0.1359
143.3570 34.0481 0.0274
3.275
144.5847 52.0482 0.3605
92.459
146.3589 -8.6568 0.1530 192.942
146.8029 76.3871 0.3541
25.087
4.895
148.2049 51.8848 0.2140

0.906
10.380
7.508
0.315
2.293
8.437
12.194
6.441
14.100
0.679
2.074
16.331
1.187
24.317
2.043
22.639
2.344
16.425
1.280
2.754
21.364
0.627
76.673
3.477
3.277
18.089
14.459
1.568
8.399

121.650
2.649 1.155 0.022
163.806
19.684 0.802 0.094
86.734
11.754 1.151 0.086
118.197
1.029 1.167 0.012
144.903
7.307 1.134 0.082
112.999
14.631 1.241 0.111
160.145
27.816 1.264 0.264
114.365
8.615 1.049 0.047
160.309
26.200 0.695 0.134
930.543
51.355 1.318 0.037
238.187
25.844 0.979 0.094
90.869
25.862 1.267 0.215
95.625
3.373 1.177 0.034
76.514
25.816 1.275 0.179
100.849
6.189 1.546 0.106
54.663
16.890 1.620 0.148
81.093
5.949 1.716 0.129
99.194
23.788 1.015 0.165
503.351 339.928 1.180 0.198
96.232
5.776 1.162 0.046
17.288 1.388 0.130
64.053
142.639
19.031 1.462 0.111
206.504 111.689 0.593 0.193
6.809 1.085 0.059
115.745
104.321
8.406 0.788 0.142
40.973 1.255 0.546
60.018
6.529 1.866 0.099
14.989
75.232
4.847 1.915 0.059
12.195 1.070 0.097
129.424

95

Table B.1 (cont’d)
Cluster Name

PLCKESZ_G264.41+19.48
HCG_042
MCXC_J1000.5+4409
ZwCl_1006.1+1201
MCXC_J1010.5-1239
ABELL_0963
ABELL_0970
NGC_3209
MCXC_J1022.0+3830
ABELL_0980
BLOX_J1023.6+0411.1
WHL_J102339.9+490838
ABELL_3444
ABELL_1033
ABELL_1068
NGC_3402_GROUP
MCXC_J1053.7+5452
BLOX_J1056.9-0337.3
MACS_J1108.9+0906
NGC_3551
1RXS_J111039.6+284316
ABELL_1190
ABELL_1201
ABELL_1204
MACS_J1115.8+0129
HCG_051
ABELL_1240
MCXC_J1130.0+3637
ABELL_1285

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

150.0067 -30.2770 0.2400
94.347
150.0593 -19.6363 0.0133
1.714
150.1334 44.1444 0.1540
16.985
152.1978 11.7934 0.2210 122.660
152.6346 -12.6658 0.3010
22.531
154.2656 39.0470 0.2060
39.105
154.3476 -10.6859 0.0587 102.112
155.1602 25.5051 0.0209
3.265
155.5418 38.5232 0.0491
38.803
155.6182 50.1061 0.1582 150.124
155.9156 4.1856 0.2906
8.947
155.9162 49.1445 0.1440 128.079
155.9591 -27.2566 0.2533
20.762
157.9367 35.0396 0.1259 122.945
160.1855 39.9529 0.1375
6.283
1.666
162.6088 -12.8449 0.0154
163.3837 54.8792 0.0704
63.300
164.2330 -3.6277 0.8231 126.798
167.2304 9.0991 0.4490
80.249
167.4343 21.7594 0.0320 -21.019
167.6690 28.7138 0.0220
64.272
167.9159 40.8402 0.0751 213.612
168.2270 13.4358 0.1688
63.600
14.727
168.3351 17.5940 0.1706
168.9669 1.4990 0.3520
22.147
170.6101 24.2976 0.0258
-7.020
170.9098 43.0968 0.1590 196.271
172.5116 36.6356 0.0600
21.316
172.5932 -14.5807 0.1061 186.247

40.037
0.342
5.367
18.258
50.166
8.506
18.122
0.846
9.494
21.661
0.960
20.582
1.805
16.451
0.705
0.119
12.560
36.945
38.940
22.510
9.246
19.437
8.173
1.691
2.422
2.692
92.437
2.683
29.134

56.786 0.783 0.139
176.575
23.760 1.009 0.060
188.993
9.943 0.940 0.083
111.258
23.767 1.187 0.175
86.035
73.456 0.561 0.187
227.985
13.215 0.826 0.057
149.621
122.251
26.244 1.014 0.145
182.701 297.526 1.217 0.527
16.646 1.018 0.255
177.395
62.493
23.780 1.465 0.227
3.162 1.216 0.026
106.958
22.416 1.253 0.177
65.204
94.190
4.675 1.340 0.045
22.449 1.044 0.126
116.344
109.284
3.042 1.157 0.031
2.839 0.955 0.020
93.942
16.230 1.189 0.161
60.464
87.750
78.523 1.248 0.487
64.854 0.789 0.252
111.019
218.204
37.104 0.491 0.317
44.615 1.464 0.397
84.537
18.426 1.686 0.227
25.935
176.604
19.440 1.575 0.259
4.882 1.440 0.138
82.196
124.017
9.386 1.667 0.183
130.845
10.858 0.558 0.075
117.624 160.964 0.672 0.708
119.264
8.124 1.098 0.124
35.964 0.997 0.214
77.426

96

Table B.1 (cont’d)
Cluster Name

ABELL_1300
WHL_J114224.8+583205
ABELL_1361
SDSS-C4-DR3_3018
MACS_J1149.6+2223
ABELL_1413
ABELL_1423
SDSS-C4-DR3_3144
ABELL_1446
MKW_04
MACS_J1206.2-0847
NGC_4104_GROUP
MCXC_J1215.4-3900
NGC_4325_GROUP
NSCS_J122648+215157
ABELL_1553
MCXC_J1234.2+0947
MESSIER_089
ABELL_1569
ABELL_1576
NGC_4636
Centaurus_Cluster
NGC_4759_GROUP
ABELL_3528B
NGC_4782-3
ABELL_1644
ABELL_3532
NGC_4839
WHL_J125933.4+600409

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

172.9774 -19.9290 0.3072
65.709
175.6006 58.5331 0.3109 459.851
175.9151 46.3557 0.1171
18.048
176.8274 55.7400 0.0510 130.902
177.3994 22.3986 0.5444 267.540
57.420
178.8245 23.4061 0.1427
179.3219 33.6104 0.0761
36.915
179.9679 55.5349 0.0810
3.097
180.5156 58.0383 0.1035 157.742
181.1134 1.8952 0.0200
2.617
54.200
181.5512 -8.8007 0.4400
181.6624 28.1750 0.0283
0.021
183.8527 -39.0363 0.1190 275.446
3.284
185.7773 10.6222 0.0252
186.7123 21.8326 0.3700
57.719
187.6970 10.5540 0.1652 180.396
188.6014 9.7892 0.2290 194.608
188.9157 12.5567 0.0011
1.274
189.1084 16.5383 0.0735 136.449
189.2428 63.1872 0.2790 103.880
0.801
190.7077 2.6877 0.0031
0.873
192.2053 -41.3110 0.0114
193.2739 -9.2043 0.0147
2.485
15.261
193.5927 -29.0111 0.0530
193.6504 -12.5607 0.0154
3.197
194.2986 -17.4091 0.0473
21.222
194.3430 -30.3626 0.0554 150.770
194.3517 27.4977 0.0246 -26.397
194.8877 60.0706 0.3300 327.114

26.357
44.958
3.005
37.892
25.887
5.077
6.299
0.714
17.020
0.437
11.443
0.396
63.700
0.201
16.388
25.875
65.368
0.032
21.463
22.109
0.091
0.026
0.104
2.683
0.756
1.461
20.305
15.220
56.118

36.791 0.929 0.083
203.526
25.032 1.732 0.197
14.713
8.970 1.464 0.144
134.880
73.251 1.068 0.657
103.086
9.184 1.859 0.104
18.052
8.112 1.047 0.044
129.718
31.006 1.209 0.143
359.425
61.006 1.448 0.104
393.635
31.082 1.462 0.362
62.913
7.150 0.863 0.025
176.954
20.755 1.105 0.102
134.851
94.140 1.316 0.044
871.354
105.128 1.131 0.466
71.648
3.216 1.289 0.026
110.659
26.521 0.911 0.164
120.674
22.365 1.443 0.192
57.808
115.821 0.842 0.419
87.959
52.840 1.230 0.016
928.754
65.747 0.904 0.672
44.110
31.722 1.026 0.135
127.184
13.528 1.025 0.022
228.937
3.843 1.198 0.005
324.906
8.097 1.156 0.025
168.149
8.800 1.157 0.061
218.802
63.049 1.246 0.100
309.122
78.787 1.815 0.107
616.093
83.651
29.757 1.251 0.249
856.067 103.825 0.777 0.114
80.081 1.332 0.418
36.889

97

Table B.1 (cont’d)
Cluster Name

ABELL_1664
ABELL_1668
NGC4936-oﬀset2
MACS_J1311.0-0311
ABELL_1689
WHL_J131505.2+514902
NGC_5044
NGC_5098_GROUP
NGC_5129
ABELL_1736
ABELL_3558
NGC_5171
SSGC_081
a1750ss
ABELL_1750C
ABELL_1750N
SC_1329-313
2MASX_J13312961+1107566
ABELL_3560
ABELL_1758
ABELL_3562
ABELL_1763
ABELL_1767
ABELL_1775
ABELL_3571
LCDCS_0829
ABELL_1795
NSCS_J135021+094042
MACS_J1359.2-1929

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

14.131
195.9276 -24.2449 0.1283
6.156
195.9445 19.2705 0.0634
-0.354
196.0715 -30.5261 0.0103
32.423
197.7569 -3.1776 0.4940
61.841
197.8734 -1.3413 0.1832
198.7700 51.8193 0.2911 159.895
1.305
198.8498 -16.3854 0.0093
200.0610 33.1425 0.0366
4.798
201.0416 13.9755 0.0230
-0.457
201.7060 -27.1634 0.0458 139.631
49.877
201.9869 -31.4955 0.0480
41.304
202.3540 11.7626 0.0229
202.4490 -31.6065 0.0495
44.512
202.5424 -2.1044 0.0914
34.901
202.7093 -1.8629 0.0678 159.868
202.7956 -1.7282 0.0837
93.060
202.8650 -31.8213 0.0482 167.330
202.8737 11.1319 0.0790
4.504
203.1071 -33.1360 0.0489
40.383
203.2017 50.5424 0.2790 166.511
203.4075 -31.6700 0.0490
70.592
203.8248 40.9988 0.2230 186.619
204.0327 59.2044 0.0703 136.566
56.894
205.4527 26.3722 0.0717
206.8685 -32.8646 0.0391
59.964
3.460
206.8775 -11.7528 0.4510
15.172
207.2200 26.5899 0.0625
207.5913 9.6698 0.0900
-6.289
19.013
209.7926 -19.4903 0.4470

0.879
1.317
3.076
3.781
4.922
30.277
0.143
0.944
0.659
39.368
14.911
17.842
20.290
69.701
10.761
22.131
16.567
1.406
61.464
49.643
12.786
22.108
62.655
3.877
13.817
2.299
0.779
1.541
3.628

4.539 1.690 0.081
107.446
7.882 1.033 0.053
167.323
11.701 0.593 0.131
102.788
8.127 1.357 0.085
83.827
7.801 1.156 0.048
126.295
32.233 1.161 0.150
100.569
1.766 0.722 0.022
47.729
6.625 1.160 0.060
129.716
33.879 0.923 0.075
212.419
80.890 0.691 0.463
75.724
20.760 0.772 0.094
194.069
84.833 0.987 0.735
103.650
31.988 0.614 0.122
165.343
91.102 0.580 0.361
186.190
9.678 1.886 0.082
56.099
37.180 0.980 0.211
117.458
24.466 1.703 0.208
61.944
37.766 1.462 0.285
130.128
198.695
85.109 0.367 0.251
189.649 105.927 1.036 0.431
18.709 0.942 0.101
144.224
54.570
15.648 1.348 0.124
147.731 126.407 0.647 0.585
19.789 1.860 0.099
256.554
210.881
14.705 0.699 0.151
6.231 1.074 0.036
177.098
1.460 1.080 0.018
118.037
172.190
5.844 0.831 0.040
9.761 1.330 0.106
92.645

98

Table B.1 (cont’d)
Cluster Name

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

12.848
6.093
1.211
1.107
0.936
0.667
63.352
40.951
17.583
3.403
15.900
3.479
4.811
2.733
74.345
48.075
1.701
0.244
1.247
1.311
2.582
0.494

19.688 1.165 0.154
100.593
77.354
209.8159 27.9756 0.0615
ABELL_1831
13.843 1.179 0.131
181.636
21.238
209.9605 62.5179 0.3216
WHL_J135949.5+623047
4.227 1.323 0.034
105.985
11.299
210.2581 2.8787 0.2532
ABELL_1835
423.685
52.658 0.861 0.056
-1.973
210.9117 -33.9781 0.0138
NGC5419-oﬀset2
795.366 128.597 1.053 0.064
0.834
210.9119 -33.9783 0.0138
NGC5419-oﬀset1
51.951 1.380 0.150
183.191
8.670
211.8741 -27.0183 0.0230
ABELL_3581
97.281 0.529 0.356
189.657
213.7848 -0.4931 0.1405
61.304
A1882a
162.648
57.392 0.456 0.217
213.7954 36.2022 1.0300 -10.568
WARP_J1415.1+3612
37.534 0.900 0.233
104.876
18.734
WHL_J141623.8+444528
214.1164 44.7801 0.3859
132.581
7.921 1.167 0.105
GMBCG_J215.94948+24.07846 215.9490 24.0779 0.5431
5.560
22.462 0.853 0.081
139.103
84.494
216.5128 37.8244 0.1712
ABELL_1914
10.844 1.267 0.078
135.389
12.595
216.8172 44.1271 0.4981
WHL_J142716.1+440730
133.733
10.335 0.922 0.066
MACS_J1427.6-2521
216.9177 -25.3541 0.3180
9.474
182.246
6.827 0.823 0.042
-3.707
218.1579 31.6479 0.1313
ABELL_1930
229.305 101.357 0.466 0.200
ABELL_1942_AND_CLUMP
219.5912 3.6703 0.2240
67.023
94.679 0.405 0.307
144.171
89.363
220.1651 3.4704 0.0270
WBL_518
8.898 1.556 0.061
195.746
11.220
221.8610 8.4737 0.1954
NSCS_J144726+082824
122.804
2.375 0.996 0.017
ABELL_1991
223.6318 18.6449 0.0587
0.392
3.027 1.135 0.027
80.992
12.779
224.3129 22.3424 0.2578
NSCS_J145715+222009
114.084
10.975 1.817 0.128
ABELL_S0780
224.8701 -18.1787 0.2357
20.933
7.018 1.105 0.044
133.365
18.811
225.0816 21.3699 0.1532
ABELL_2009
226.0309 -2.8044 0.2153
WHL_J150407.5-024816
82.228
2.096 1.329 0.019
9.077
228.7606 -15.3892 0.2226 356.147 108.545 137.948 191.290 0.611 0.399
MCXC_J1514.9-1523
19.474 1.434 0.233
230.2923 30.6115 0.0784 224.737
ABELL_2061
38.185
MKW_03s
230.4664 7.7089 0.0450
18.044
2.724 0.910 0.029
117.220
46.812 0.963 0.212
231.0474 29.8720 0.1160 297.687
ABELL_2069
84.813
2.303 1.195 0.022
5.444
231.0535 -31.9045 0.1028
MCXC_J1524.2-3154
104.851
MACS_J1532.8+3021
233.2241 30.3496 0.3450
13.365
2.761 1.339 0.030
82.169
120.495 105.986 0.690 0.623
79.498
233.3234 31.1379 0.0669
ABELL_2092

24.178
1.755
41.573
0.428
0.901
62.076

99

Table B.1 (cont’d)
Cluster Name

ABELL_2107
ABELL_2111
ABELL_2104
ABELL_2125
ABELL_2124
ABELL_2146
MCXC_J1558.3-1410
ABELL_2147
ABELL_2151
AWM_4
MACS_J1621.3+3810
ABELL_2187
ABELL_2204
ABELL_2219
Hercules_A
NGC_6269
ABELL_2256
Ophiuchus_CLUSTER
SDSS-C4_3072
MACS_J1720.2+3536
ABELL_2261
ABELL_2294
Abell_2276
ZwCl_1742.1+3306
NSC_J174715+451155
MCXC_J1750.2+3504
NGC_6482
CIZA_J1804.4+1002
ABELL_2302

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

234.9130 21.7827 0.0411
10.155
234.9193 34.4244 0.2290 189.915
235.0339 -3.3042 0.1533 159.142
235.3090 66.2659 0.2465 171.248
236.2464 36.1095 0.0656
91.073
85.695
239.0512 66.3516 0.2343
239.5910 -14.1661 0.0970
28.469
240.5709 15.9745 0.0350 163.008
6.426
241.1495 17.7215 0.0366
241.2354 23.9340 0.0318
24.474
-2.413
245.3533 38.1691 0.4650
246.0584 41.2438 0.1836
91.556
248.1955 5.5758 0.1522
7.763
250.0838 46.7119 0.2256 258.490
252.7840 4.9923 0.1550
0.604
254.4921 27.8541 0.0348
1.305
255.9357 78.6365 0.0581 111.092
258.1155 -23.3685 0.0280 -22.281
19.703
260.0414 26.6248 0.1640
260.0706 35.6066 0.3913
12.312
41.818
260.6136 32.1329 0.2240
58.446
261.0423 85.8861 0.1694
263.7693 64.1017 0.1406
24.173
266.0605 32.9916 0.0757
12.335
266.8094 45.1960 0.1565 290.692
-1.787
267.5691 35.0828 0.1710
0.837
267.9531 23.0719 0.0131
271.1307 10.0568 0.1525
26.268
274.9918 57.1561 0.1790 190.544

3.138
27.115
31.845
17.883
24.555
4.204
1.712
18.556
3.102
5.366
5.626
19.021
0.351
19.763
2.871
1.932
33.408
1.747
1.477
2.523
9.759
48.431
11.035
1.209
35.204
2.580
0.243
48.513
77.382

32.782 0.923 0.086
327.958
27.655 1.189 0.156
88.337
43.602 0.820 0.178
127.169
19.667 1.588 0.272
25.368
38.843 0.814 0.173
196.375
6.028 1.891 0.078
66.396
4.612 1.496 0.102
115.116
36.313 1.411 0.378
78.332
5.699 0.791 0.056
150.802
6.625 0.655 0.094
108.464
12.893 0.917 0.058
168.760
26.700 1.194 0.163
108.736
3.209 1.509 0.028
144.831
17.930 1.458 0.189
49.427
20.461 1.072 0.127
211.799
47.558 0.892 0.100
279.709
57.048 0.764 0.272
159.118
2.600 0.513 0.013
259.384
4.069 1.308 0.030
104.101
7.489 1.122 0.048
131.324
14.832 0.899 0.070
139.288
77.184 0.724 0.174
216.653
18.928 0.818 0.125
132.597
4.566 1.256 0.064
120.830
16.426 1.751 0.186
11.492
7.589 0.886 0.042
163.642
9.968 0.826 0.057
75.095
70.702 0.494 0.134
220.224
121.021 139.110 0.764 0.418

100

Table B.1 (cont’d)
Cluster Name

_HB89__1821+643
MACS_J1829.0+6913
MCXC_J1852.1+5711
MCXC_J1853.9+6822
PLCKESZ_G337.09-25.97
MACS_J1931.8-2635
CIZA_J1938.3+5409
MCXC_J1947.3-7623
ABELL_3653
MCXC_J2003.5-2323
NGC_6868
MCXC_J2011.3-5725
MCXC_J2014.8-2430
SPT-CL_J2023-5535
ABELL_3695
SPT-CLJ2043-5035
MACS_J2046.0-3430
ABELL_3739
IC_1365
ABELL_2345
ABELL_2355
WBL_671
MACS_J2140.2-2339
ABELL_3809
ABELL_2384
ABELL_2390
ClG_2153.8+3746
ABELL_2409
ABELL_3827

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

7.264
4.091
7.763
14.615
8.850
1.385
12.545
8.752
44.382
91.725
0.554
8.622
0.800
83.939
36.618
3.138
2.108
38.149
19.732

182.036
12.223 0.976 0.051
275.4876 64.3438 0.2970 -27.371
99.984
8.250 1.328 0.094
36.357
277.2758 69.2356 0.2030
168.070
13.197 0.843 0.097
283.0367 57.1952 0.1094
9.598
198.874
33.895 1.402 0.384
76.431
283.5094 68.3827 0.0928
64.347
13.718 1.663 0.191
288.6564 -59.4722 0.2636
78.316
83.339
3.832 1.474 0.049
20.746
292.9569 -26.5761 0.3520
63.256
15.557 1.427 0.155
294.5768 54.1597 0.2600
82.492
179.217
16.098 0.824 0.059
296.8121 -76.3958 0.2170
17.503
172.274 103.031 1.184 0.517
298.2623 -52.0358 0.1089 174.821
134.248 149.277 0.877 0.468
300.8624 -23.3827 0.3171 217.888
564.773 228.792 1.219 0.119
0.698
302.4754 -48.3799 0.0095
64.575
15.583 1.194 0.206
302.8617 -57.4196 0.2786
39.441
116.626
3.757 1.208 0.035
303.7156 -24.5089 0.1612
5.104
142.241 160.670 0.758 0.646
305.8388 -55.5967 0.2320 186.127
41.785
35.309 1.562 0.278
308.6884 -35.8112 0.0894 307.183
8.551 1.242 0.089
82.653
15.848
310.8231 -50.5923 0.7230
6.179 1.145 0.061
103.510
311.5018 -34.5061 0.4230
6.476
150.954
60.833 0.824 0.202
316.0798 -41.3449 0.1651
81.936
318.4828 2.5638 0.0493 160.833
38.386 1.338 0.371
71.379
321.7897 -12.1748 0.1765 286.760 114.145 143.127 175.850 0.694 0.381
75.518
323.8195 1.4177 0.1244 393.293
152.817 1.183 0.529
254.081 101.207 0.702 0.395
324.2863 0.4459 0.0510 -10.889
325.0632 -23.6613 0.3130
12.928
91.533
3.478 1.350 0.041
8.319 0.867 0.059
132.956
10.277
326.7462 -43.8985 0.0623
328.0882 -19.5478 0.0943
25.359
139.689
6.597 1.271 0.056
5.093 1.070 0.030
151.843
14.260
328.4034 17.6957 0.2280
34.317 1.708 0.178
325.021
55.189
328.9678 38.0063 0.2920
330.2190 20.9685 0.1479
12.424
167.993
57.542 0.512 0.194
22.405 1.118 0.186
102.414
330.4717 -59.9453 0.0984 133.726

86.869
12.285
1.101
3.844
2.675
1.929
6.284
34.876
15.264

101

Table B.1 (cont’d)
Cluster Name

ABELL_2415
MCXC_J2211.7-0349
3C_444
ABELL_2426
MACS_J2214-1359
ABELL_3854
MCXC_J2218.6-3853
ABELL_2443
ABELL_2445
ABELL_3880
MACS_J2229.8-2756
CGCG_514-050
ABELL_2457
Stephans_Quintet
MACS_J2245.0+2637
ABELL_3911
ABELL_2485
ABELL_S1063
ABELL_3921
ABELL_2507
ABELL_2537
MCXC_J2311.5+0338
ABELL_2550
ABELL_2556
ABELL_S1101
UGC_12491
NGC_7618
ABELL_2597
RCS_J2327-0204

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

2.830
331.4108 -5.5916 0.0581
96.790
332.9411 -3.8270 0.2700
0.958
333.6124 -17.0256 0.1530
333.6347 -10.3705 0.0978
54.818
333.7394 -14.0026 0.4830 150.198
334.4406 -35.7241 0.1492 103.513
334.6651 -38.9017 0.1379 132.838
336.5270 17.3654 0.1080 164.262
69.915
336.7321 25.8362 0.1660
336.9773 -30.5763 0.0584
0.853
7.679
337.4390 -27.9273 0.3240
0.932
337.8355 39.3587 0.0171
338.9213 1.4862 0.0594
24.049
3.065
338.9996 33.9721 0.0215
341.2694 26.6343 0.3040
38.968
341.5639 -52.7242 0.0965 338.381
74.814
342.1291 -16.1079 0.2472
342.1846 -44.5301 0.3475
78.785
342.4910 -64.4284 0.0928
75.119
344.2191 5.5043 0.1960 198.227
78.806
347.0930 -2.1916 0.2950
85.303
347.8885 3.6356 0.2998
347.8963 -21.7449 0.1226
-0.845
12.041
348.2559 -21.6346 0.0871
348.4948 -42.7263 0.0580
11.526
6.963
349.6596 42.9581 0.0174
-2.042
349.9501 42.8532 0.0173
351.3324 -12.1243 0.0852
9.501
45.275
351.8647 -2.0775 0.2000

0.781
15.187
1.150
12.515
23.601
18.154
15.498
42.641
11.294
0.950
1.376
2.217
17.816
2.147
6.768
36.851
26.486
19.913
14.847
27.121
12.795
14.556
2.976
1.363
0.499
0.491
0.974
0.288
7.173

6.585 1.027 0.046
142.155
19.206 1.343 0.111
105.826
3.525 1.019 0.039
151.868
20.310 1.307 0.201
104.600
24.888 1.286 0.195
62.246
24.929 1.201 0.151
96.946
17.748 1.423 0.219
47.640
83.701 0.799 0.365
113.150
15.912 0.992 0.117
87.841
4.029 0.890 0.032
139.151
93.191
5.100 1.285 0.054
547.804 279.588 0.931 0.163
181.200
33.329 0.700 0.120
12.812 0.728 0.205
56.500
90.585
13.342 1.271 0.145
34.618 1.607 0.276
27.578
41.709 0.956 0.190
123.032
127.407
31.163 0.868 0.166
20.746 0.787 0.073
162.521
36.570
18.949 1.743 0.176
21.599 1.101 0.182
110.222
17.017 1.189 0.071
121.671
114.201
5.202 0.714 0.060
4.080 1.084 0.044
123.647
77.480
1.226 1.127 0.018
23.395 1.541 0.084
206.196
3.680 0.510 0.057
54.095
99.234
1.035 1.206 0.015
14.883 1.224 0.088
212.711

102

Table B.1 (cont’d)
Cluster Name

ABELL_2626
ABELL_2631
MCXC_J2344.2-0422
HCG_097
ABELL_2667
ABELL_2670

RA

deg

DEC

deg

z

K0

(keV cm2)

σK0

K100

(keV cm2)

σK100

α

σα

123.832

2.257
4.379 0.861 0.051
106.409 230.751 114.628 0.412 0.218
13.251
15.739 1.283 0.157
5.550 0.577 0.074
2.537
2.169
5.623 1.241 0.054
8.013 0.817 0.062
4.629

66.387
90.326
93.037
125.808

13.528
354.1269 21.1465 0.0553
354.4107 0.2681 0.2730
76.914
356.0772 -4.3813 0.0786 108.571
-2.965
356.8451 -2.2999 0.0218
357.9142 -26.0841 0.2300
19.098
30.012
358.5368 -10.4252 0.0762

103

APPENDIX C

ACCEPT 2.0 RADIAL ENTROPY PROFILES

Deprojected radial entropy proﬁles and ﬁts for the clusters from ACCEPT 2.0 with deprojected
proﬁles. Included on each plot are the best-ﬁt values for K0, K100, and α with their 1σ errors as
2 for the ﬁt and the radial range of the ﬁt. The RA and DEC of the proﬁle
well as the reduced χ
center are given in hh : mm : ss in the title of each plot.

104

Figure C.1 ACCEPT 2.0 Entropy Proﬁles and Fit Information

105

101102r(kpc)102K(keVcm2)ABELL_2717(0:03:12.967,-35:56:00.13)rmax for fit = 213.39 kpcreduced 2 = 1.03K0 = 29.93±6.22 keV cm2K100 = 123.47±9.68 keV cm2 = 0.93±0.11102r(kpc)102103K(keVcm2)NSCS_J000619+105206(0:06:20.290,10:51:51.46)rmax for fit = 714.08 kpcreduced 2 = 1.04K0 = 58.43±11.09 keV cm2K100 = 135.62±17.23 keV cm2 = 0.91±0.08102r(kpc)103K(keVcm2)ZwCl_0008.8+5215(0:11:21.498,52:31:45.15)rmax for fit = 711.21 kpcreduced 2 = 1.04K0 = 170.49±40.77 keV cm2K100 = 114.91±53.52 keV cm2 = 0.93±0.2101102r(kpc)102103K(keVcm2)ABELL_2734_NED01(0:11:21.624,-28:51:14.44)rmax for fit = 596.6 kpcreduced 2 = 1.02K0 = 25.69±17.05 keV cm2K100 = 153.98±24.19 keV cm2 = 0.58±0.08102r(kpc)102103K(keVcm2)MACS_J0011.7-1523(0:11:42.965,-15:23:20.80)rmax for fit = 713.38 kpcreduced 2 = 1.06K0 = 7.91±6.69 keV cm2K100 = 139.32±14.31 keV cm2 = 0.86±0.08101102r(kpc)2×1023×1024×1026×102K(keVcm2)ABELL_0013(0:13:37.884,-19:30:09.11)rmax for fit = 280.09 kpcreduced 2 = 1.04K0 = 130.01±31.3 keV cm2K100 = 156.99±51.95 keV cm2 = 0.78±0.22Figure C.1 (cont’d)

106

101102103r(kpc)103K(keVcm2)ABELL_2744(0:14:19.529,-30:23:30.23)rmax for fit = 532.94 kpcreduced 2 = 1.02K0 = 151.72±90.75 keV cm2K100 = 240.95±140.4 keV cm2 = 0.48±0.24102103r(kpc)103K(keVcm2)Cl_0016+16(0:18:33.504,16:26:12.98)rmax for fit = 1224.02 kpcreduced 2 = 1.04K0 = 165.46±19.83 keV cm2K100 = 56.17±16.0 keV cm2 = 1.32±0.13102103r(kpc)103K(keVcm2)MACS_J0025.4-1222(0:25:29.688,-12:22:33.87)rmax for fit = 808.81 kpcreduced 2 = 1.06K0 = 149.82±20.36 keV cm2K100 = 63.49±19.63 keV cm2 = 1.34±0.15102103r(kpc)102103K(keVcm2)PLCKESZ_G304.84-41.42(0:28:05.714,-75:37:48.38)rmax for fit = 886.21 kpcreduced 2 = 1.06K0 = 48.27±43.68 keV cm2K100 = 356.03±45.56 keV cm2 = 0.49±0.08102103r(kpc)103K(keVcm2)ABELL_2813(0:43:24.881,-20:37:25.07)rmax for fit = 798.52 kpcreduced 2 = 1.06K0 = 136.34±22.78 keV cm2K100 = 65.15±32.8 keV cm2 = 1.4±0.29101102r(kpc)101102K(keVcm2)ZwCl_0040.8+2404(0:43:52.269,24:24:19.27)rmax for fit = 273.19 kpcreduced 2 = 1.03K0 = 9.05±1.16 keV cm2K100 = 113.82±3.73 keV cm2 = 1.14±0.04Figure C.1 (cont’d)

107

101102r(kpc)102K(keVcm2)ABELL_0098N(0:46:24.685,20:37:19.62)rmax for fit = 267.98 kpcreduced 2 = 1.09K0 = 10.6±5.93 keV cm2K100 = 179.6±13.01 keV cm2 = 0.98±0.1101102r(kpc)101102K(keVcm2)ESO_351-_G_021(0:54:59.837,-35:19:15.23)rmax for fit = 127.3 kpcreduced 2 = 1.14K0 = 3.73±0.86 keV cm2K100 = 104.97±6.88 keV cm2 = 0.94±0.06102103r(kpc)103104K(keVcm2)ABELL_0141(1:05:34.385,-24:37:58.76)rmax for fit = 615.43 kpcreduced 2 = 1.05K0 = 158.78±28.16 keV cm2K100 = 61.34±34.69 keV cm2 = 1.4±0.29101102r(kpc)102K(keVcm2)MaxBCG_J016.70077+01.05926(1:06:49.016,1:03:13.70)rmax for fit = 464.68 kpcreduced 2 = 1.06K0 = 11.75±0.71 keV cm2K100 = 68.44±2.76 keV cm2 = 1.52±0.05102r(kpc)1033×1024×1026×102K(keVcm2)CIZA_J0107.7+5408(1:07:45.139,54:07:57.61)rmax for fit = 687.8 kpcreduced 2 = 1.02K0 = 305.48±45.98 keV cm2K100 = 66.1±52.33 keV cm2 = 1.11±0.3100101102r(kpc)101102103K(keVcm2)IC_1633(1:09:55.405,-45:55:50.79)rmax for fit = 63.68 kpcreduced 2 = 1.03K0 = 2.85±0.78 keV cm2K100 = 845.52±95.78 keV cm2 = 1.22±0.06Figure C.1 (cont’d)

108

102103r(kpc)103K(keVcm2)ABELL_2895(1:18:11.262,-26:57:54.93)rmax for fit = 982.24 kpcreduced 2 = 1.04K0 = 168.69±33.93 keV cm2K100 = 90.11±37.84 keV cm2 = 1.13±0.19101102r(kpc)102103K(keVcm2)UGC_00842(1:18:53.945,-1:00:07.52)rmax for fit = 88.87 kpcreduced 2 = 1.06K0 = 22.63±19.27 keV cm2K100 = 215.22±20.7 keV cm2 = 0.43±0.16101102r(kpc)102103K(keVcm2)ABELL_0193(1:25:07.661,8:41:57.08)rmax for fit = 218.89 kpcreduced 2 = 1.03K0 = 134.94±9.01 keV cm2K100 = 43.9±16.12 keV cm2 = 1.56±0.29102103r(kpc)103K(keVcm2)ABELL_0209(1:31:52.565,-13:36:38.81)rmax for fit = 1080.52 kpcreduced 2 = 1.03K0 = 86.64±24.72 keV cm2K100 = 165.61±30.62 keV cm2 = 0.81±0.08102r(kpc)2×1023×1024×1026×102K(keVcm2)Abell_222(1:37:34.562,-12:59:34.87)rmax for fit = 395.6 kpcreduced 2 = 1.06K0 = 148.85±21.55 keV cm2K100 = 48.22±37.97 keV cm2 = 1.36±0.4102r(kpc)102103K(keVcm2)Abell_223(1:37:55.963,-12:49:10.52)rmax for fit = 584.66 kpcreduced 2 = 1.06K0 = 101.81±21.11 keV cm2K100 = 120.95±31.33 keV cm2 = 1.02±0.16Figure C.1 (cont’d)

109

102r(kpc)103K(keVcm2)ABELL_0267(1:52:42.269,1:00:45.32)rmax for fit = 718.82 kpcreduced 2 = 1.06K0 = 148.4±16.49 keV cm2K100 = 54.93±15.02 keV cm2 = 1.75±0.15100101r(kpc)101102K(keVcm2)ABELL_0262(1:52:46.298,36:09:11.81)rmax for fit = 18.57 kpcreduced 2 = 1.03K0 = 3.56±0.14 keV cm2K100 = 484.19±26.61 keV cm2 = 1.46±0.03101102r(kpc)102K(keVcm2)MCXC_J0220.9-3829(2:20:56.582,-38:28:51.20)rmax for fit = 621.95 kpcreduced 2 = 1.08K0 = 18.43±3.39 keV cm2K100 = 110.54±7.65 keV cm2 = 1.05±0.06101r(kpc)3×1014×1016×101K(keVcm2)MZ_10451(2:29:45.684,-29:37:48.17)rmax for fit = 61.61 kpcreduced 2 = 2K0 = 11.59±10.75 keV cm2K100 = 73.11±20.11 keV cm2 = 0.57±0.46102r(kpc)1033×1024×1026×102K(keVcm2)ABELL_0370(2:39:53.170,-1:34:36.95)rmax for fit = 580.76 kpcreduced 2 = 1.04K0 = 256.7±27.69 keV cm2K100 = 42.28±25.61 keV cm2 = 1.61±0.24101102103r(kpc)102103K(keVcm2)MACS_J0242.6-2132(2:42:35.906,-21:32:26.30)rmax for fit = 746.81 kpcreduced 2 = 1.13K0 = 9.4±1.57 keV cm2K100 = 85.75±5.66 keV cm2 = 1.3±0.06Figure C.1 (cont’d)

110

102r(kpc)103K(keVcm2)ABELL_S0295(2:45:26.452,-53:01:46.85)rmax for fit = 734.94 kpcreduced 2 = 1.06K0 = 165.94±21.59 keV cm2K100 = 36.25±26.53 keV cm2 = 1.56±0.28101102r(kpc)102K(keVcm2)ABELL_0376(2:46:03.946,36:54:19.75)rmax for fit = 379.2 kpcreduced 2 = 1.04K0 = 61.94±16.64 keV cm2K100 = 178.49±32.29 keV cm2 = 0.87±0.16101102r(kpc)102103K(keVcm2)ABELL_0383(2:48:03.365,-3:31:44.69)rmax for fit = 305.21 kpcreduced 2 = 1.04K0 = 10.28±1.05 keV cm2K100 = 117.59±3.73 keV cm2 = 1.25±0.04100101r(kpc)101102K(keVcm2)NGC_1132(2:52:51.923,-1:16:26.46)rmax for fit = 72.28 kpcreduced 2 = 1.09K0 = 1.65±0.84 keV cm2K100 = 112.29±3.3 keV cm2 = 0.66±0.03102103r(kpc)102103K(keVcm2)ABELL_0402(2:57:41.023,-22:09:11.12)rmax for fit = 760.26 kpcreduced 2 = 1.08K0 = 115.24±24.79 keV cm2K100 = 87.15±30.74 keV cm2 = 1.2±0.19101102r(kpc)102103K(keVcm2)ABELL_0401(2:58:56.921,13:34:14.52)rmax for fit = 549.98 kpcreduced 2 = 1.01K0 = 154.6±14.17 keV cm2K100 = 115.71±17.38 keV cm2 = 0.94±0.1Figure C.1 (cont’d)

111

101102r(kpc)102K(keVcm2)MCXC_J0301.6+0155(3:01:38.211,1:55:13.76)rmax for fit = 527.63 kpcreduced 2 = 1.06K0 = 12.18±1.87 keV cm2K100 = 112.08±4.93 keV cm2 = 1.06±0.05102103r(kpc)103K(keVcm2)MCXC_J0303.7-7752(3:03:45.279,-77:52:47.16)rmax for fit = 428.57 kpcreduced 2 = 1.04K0 = 187.07±34.24 keV cm2K100 = 85.94±47.79 keV cm2 = 1.42±0.32102103r(kpc)103K(keVcm2)MACS_J0308.9+2645(3:08:55.927,26:45:38.34)rmax for fit = 1126.59 kpcreduced 2 = 1.04K0 = 144.01±31.45 keV cm2K100 = 106.56±32.83 keV cm2 = 1.11±0.14102r(kpc)2×1023×1024×1026×102K(keVcm2)ABELL_3094(3:11:35.879,-26:53:55.53)rmax for fit = 430.99 kpcreduced 2 = 1.04K0 = 31.06±66.82 keV cm2K100 = 225.54±83.17 keV cm2 = 0.4±0.17101102r(kpc)102K(keVcm2)ABELL_3120(3:21:56.465,-51:19:35.40)rmax for fit = 227.54 kpcreduced 2 = 1.09K0 = 17.5±5.9 keV cm2K100 = 153.47±12.14 keV cm2 = 0.98±0.12101r(kpc)101102K(keVcm2)UGC_02748(3:27:54.037,2:33:41.76)rmax for fit = 34.76 kpcreduced 2 = 1.06K0 = 5.95±1.21 keV cm2K100 = 329.79±103.67 keV cm2 = 1.66±0.21Figure C.1 (cont’d)

112

102r(kpc)1032×1023×1024×1026×102K(keVcm2)ABELL_3126(3:28:36.565,-55:43:04.78)rmax for fit = 489.56 kpcreduced 2 = 1.05K0 = 158.22±13.32 keV cm2K100 = 50.47±14.49 keV cm2 = 1.73±0.17101102r(kpc)102103K(keVcm2)ABELL_3128(3:29:50.514,-52:34:48.33)rmax for fit = 217.02 kpcreduced 2 = 1.08K0 = 12.13±60.73 keV cm2K100 = 200.47±72.74 keV cm2 = 0.34±0.22101102r(kpc)102103K(keVcm2)MCXC_J0331.1-2100(3:31:06.019,-21:00:32.94)rmax for fit = 683.45 kpcreduced 2 = 1.05K0 = 11.72±1.57 keV cm2K100 = 114.99±5.4 keV cm2 = 1.25±0.05101102r(kpc)102103K(keVcm2)3C_089(3:34:14.997,-1:11:17.39)rmax for fit = 354.77 kpcreduced 2 = 1.03K0 = 30.86±5.53 keV cm2K100 = 214.3±11.18 keV cm2 = 1.35±0.08101102r(kpc)102103K(keVcm2)ABELL_3140(3:36:15.636,-40:37:42.68)rmax for fit = 244.98 kpcreduced 2 = 1.05K0 = 91.67±6.97 keV cm2K100 = 194.23±16.03 keV cm2 = 1.81±0.12101102r(kpc)101102K(keVcm2)MCXC_J0338.6+0958(3:38:41.105,9:58:00.66)rmax for fit = 124.43 kpcreduced 2 = 1.02K0 = 5.11±0.1 keV cm2K100 = 106.9±0.93 keV cm2 = 1.39±0.01Figure C.1 (cont’d)

113

102r(kpc)2×1023×1024×102K(keVcm2)MCXC_J0340.8-4542(3:40:53.790,-45:40:35.31)rmax for fit = 366.61 kpcreduced 2 = 1.13K0 = 189.42±55.69 keV cm2K100 = 68.97±132.71 keV cm2 = 0.63±0.75101102r(kpc)101102K(keVcm2)MCXC_J0352.9+1941(3:52:58.482,19:40:54.76)rmax for fit = 193.99 kpcreduced 2 = 1.04K0 = 7.11±0.38 keV cm2K100 = 56.75±2.01 keV cm2 = 1.49±0.06102103r(kpc)102103K(keVcm2)MACS_J0358.8-2955(3:58:52.563,-29:55:49.10)rmax for fit = 1030.72 kpcreduced 2 = 1.04K0 = 26.15±14.96 keV cm2K100 = 167.42±22.12 keV cm2 = 0.69±0.06101102r(kpc)101102103K(keVcm2)ABELL_0478(4:13:25.344,10:27:55.15)rmax for fit = 45.3 kpcreduced 2 = 1.02K0 = 11.58±0.91 keV cm2K100 = 216.32±33.58 keV cm2 = 1.55±0.13102103r(kpc)1032×1023×1024×1026×102K(keVcm2)MACS_J0416.1-2403(4:16:09.444,-24:04:00.73)rmax for fit = 802.23 kpcreduced 2 = 1.05K0 = 76.27±106.52 keV cm2K100 = 245.72±116.89 keV cm2 = 0.42±0.22102103r(kpc)102103K(keVcm2)MACS_J0417.5-1154(4:17:34.687,-11:54:32.72)rmax for fit = 497.47 kpcreduced 2 = 1.03K0 = 23.92±8.33 keV cm2K100 = 159.4±14.09 keV cm2 = 0.94±0.06Figure C.1 (cont’d)

114

101102r(kpc)101102K(keVcm2)MCXC_J0425.8-0833(4:25:51.271,-8:33:36.43)rmax for fit = 265.17 kpcreduced 2 = 1.02K0 = 6.66±1.32 keV cm2K100 = 122.57±3.69 keV cm2 = 0.92±0.04101102r(kpc)2×1023×1024×1026×102K(keVcm2)ABELL_S0463(4:28:37.425,-53:50:30.50)rmax for fit = 214.51 kpcreduced 2 = 1.04K0 = 117.47±23.57 keV cm2K100 = 100.2±44.89 keV cm2 = 1.08±0.41102r(kpc)102K(keVcm2)MACS_J0429.6-0253(4:29:36.089,-2:53:09.02)rmax for fit = 549.87 kpcreduced 2 = 1.13K0 = 12.17±3.11 keV cm2K100 = 109.87±8.62 keV cm2 = 1.17±0.07101102r(kpc)101102K(keVcm2)ABELL_0496(4:33:38.038,-13:15:39.64)rmax for fit = 149.34 kpcreduced 2 = 1.02K0 = 4.57±0.33 keV cm2K100 = 146.26±1.6 keV cm2 = 0.98±0.01101102r(kpc)102103K(keVcm2)MCXC_J0437.1+0043(4:37:09.546,0:43:56.03)rmax for fit = 709.07 kpcreduced 2 = 1.05K0 = 39.94±4.17 keV cm2K100 = 88.45±8.15 keV cm2 = 1.3±0.08102103r(kpc)102103K(keVcm2)MCXC_J0439.0+0715(4:39:00.710,7:16:07.64)rmax for fit = 789.96 kpcreduced 2 = 1.05K0 = 57.21±11.96 keV cm2K100 = 116.27±17.77 keV cm2 = 0.95±0.1Figure C.1 (cont’d)

115

101102r(kpc)102103K(keVcm2)MCXC_J0439.0+0520(4:39:02.218,5:20:43.12)rmax for fit = 637.88 kpcreduced 2 = 1.06K0 = 6.15±1.6 keV cm2K100 = 118.35±5.1 keV cm2 = 1.07±0.04102r(kpc)102103K(keVcm2)ABELL_3292(4:49:56.189,-44:40:21.16)rmax for fit = 607.94 kpcreduced 2 = 1.06K0 = 108.12±10.19 keV cm2K100 = 35.72±10.66 keV cm2 = 1.69±0.17101102r(kpc)103K(keVcm2)WEIN_051(4:50:06.509,45:03:03.48)rmax for fit = 196.29 kpcreduced 2 = 1.02K0 = 84.18±55.15 keV cm2K100 = 196.26±94.35 keV cm2 = 0.42±0.26101102r(kpc)102K(keVcm2)ESO_552-_G_020(4:54:52.318,-18:06:56.52)rmax for fit = 208.68 kpcreduced 2 = 1.04K0 = 6.76±7.23 keV cm2K100 = 206.2±10.82 keV cm2 = 0.61±0.08102r(kpc)103K(keVcm2)ABELL_3322(5:10:16.916,-45:19:16.24)rmax for fit = 750.66 kpcreduced 2 = 1.06K0 = 104.61±17.64 keV cm2K100 = 77.06±21.06 keV cm2 = 1.2±0.15102103r(kpc)2×1023×1024×1026×102K(keVcm2)MCXC_J0510.7-0801(5:10:47.643,-8:01:39.10)rmax for fit = 815.59 kpcreduced 2 = 1.03K0 = 122.17±51.64 keV cm2K100 = 150.7±79.44 keV cm2 = 0.57±0.18Figure C.1 (cont’d)

116

102103r(kpc)103K(keVcm2)ABELL_S0520(5:16:37.711,-54:30:47.30)rmax for fit = 1189.24 kpcreduced 2 = 1.04K0 = 320.13±39.84 keV cm2K100 = 30.76±30.49 keV cm2 = 1.66±0.23102r(kpc)1032×1023×1024×1026×102K(keVcm2)ABELL_3343(5:25:48.712,-47:15:10.19)rmax for fit = 565.52 kpcreduced 2 = 1.06K0 = 163.76±19.79 keV cm2K100 = 46.15±19.91 keV cm2 = 1.6±0.23102r(kpc)102103K(keVcm2)MCXC_J0528.2-2942(5:28:14.723,-29:43:14.77)rmax for fit = 232.24 kpcreduced 2 = 1.07K0 = 88.46±18.81 keV cm2K100 = 91.88±37.03 keV cm2 = 1.36±0.37101102103r(kpc)102103K(keVcm2)RBS_0653(5:28:53.040,-39:28:15.53)rmax for fit = 1050.0 kpcreduced 2 = 1.02K0 = 27.86±4.75 keV cm2K100 = 164.15±10.32 keV cm2 = 0.94±0.04102103r(kpc)1032×1023×1024×1026×102K(keVcm2)PLCKESZ_G286.58-31.25(5:31:28.417,-75:10:45.50)rmax for fit = 754.02 kpcreduced 2 = 1.06K0 = 149.13±62.57 keV cm2K100 = 146.33±86.89 keV cm2 = 0.78±0.23102103r(kpc)103K(keVcm2)ABELL_0545(5:32:25.302,-11:32:32.72)rmax for fit = 701.45 kpcreduced 2 = 1.03K0 = 146.99±21.96 keV cm2K100 = 114.05±28.34 keV cm2 = 0.89±0.12Figure C.1 (cont’d)

117

102103r(kpc)102103K(keVcm2)MCXC_J0532.9-3701(5:32:55.534,-37:01:35.13)rmax for fit = 847.79 kpcreduced 2 = 1.05K0 = 98.11±24.01 keV cm2K100 = 128.77±35.41 keV cm2 = 1.02±0.15101102r(kpc)101102103K(keVcm2)ESO3060170-A(5:40:06.686,-40:50:12.80)rmax for fit = 19.57 kpcreduced 2 = 1.02K0 = 2.01±1.51 keV cm2K100 = 441.23±108.03 keV cm2 = 1.17±0.13101102r(kpc)102103K(keVcm2)MCXC_J0547.0-3904(5:47:01.582,-39:04:28.24)rmax for fit = 505.54 kpcreduced 2 = 1.11K0 = 10.8±2.4 keV cm2K100 = 124.93±8.18 keV cm2 = 1.18±0.07102r(kpc)103K(keVcm2)ABELL_3364(5:47:37.697,-31:52:23.63)rmax for fit = 634.46 kpcreduced 2 = 1.03K0 = 205.02±17.04 keV cm2K100 = 42.82±17.14 keV cm2 = 1.64±0.21101102r(kpc)102K(keVcm2)ABELL_0548A(5:48:38.315,-25:28:40.37)rmax for fit = 224.8 kpcreduced 2 = 1.08K0 = 23.66±10.14 keV cm2K100 = 170.65±20.11 keV cm2 = 0.92±0.17102r(kpc)2×1023×1024×1026×102K(keVcm2)ABELL_0550(5:52:51.539,-21:03:13.04)rmax for fit = 543.81 kpcreduced 2 = 1.05K0 = 120.25±24.38 keV cm2K100 = 102.0±32.61 keV cm2 = 1.01±0.18Figure C.1 (cont’d)

118

102103r(kpc)103K(keVcm2)MACS_J0553.4-3342(5:53:27.671,-33:42:37.56)rmax for fit = 447.94 kpcreduced 2 = 1.03K0 = 106.58±46.57 keV cm2K100 = 220.93±82.06 keV cm2 = 0.69±0.18101102r(kpc)102K(keVcm2)ABELL_3378(6:05:53.987,-35:18:08.09)rmax for fit = 366.15 kpcreduced 2 = 1.05K0 = 8.53±3.14 keV cm2K100 = 120.25±6.81 keV cm2 = 0.91±0.06102103r(kpc)1032×1023×1024×1026×102K(keVcm2)CIZA_J0616.3-2156(6:16:24.787,-21:56:17.90)rmax for fit = 844.45 kpcreduced 2 = 1.05K0 = 234.53±60.54 keV cm2K100 = 117.42±92.76 keV cm2 = 0.85±0.29102103r(kpc)1032×1023×1024×1026×102K(keVcm2)ABELL_S0579(6:16:32.139,-39:47:48.63)rmax for fit = 826.04 kpcreduced 2 = 1.06K0 = 129.97±24.01 keV cm2K100 = 68.5±26.97 keV cm2 = 1.13±0.18101102103r(kpc)102103K(keVcm2)G139.59+24.18(6:21:48.992,74:42:05.05)rmax for fit = 196.42 kpcreduced 2 = 1.06K0 = 32.8±8.95 keV cm2K100 = 150.99±18.54 keV cm2 = 1.24±0.25101102r(kpc)103K(keVcm2)ABELL_3391(6:26:21.511,-53:41:44.81)rmax for fit = 451.44 kpcreduced 2 = 1.01K0 = 203.15±29.57 keV cm2K100 = 122.63±45.81 keV cm2 = 0.92±0.23Figure C.1 (cont’d)

119

102r(kpc)103104K(keVcm2)ABELL_3395_SW(6:26:48.463,-54:32:59.21)rmax for fit = 480.5 kpcreduced 2 = 1.02K0 = 190.12±25.74 keV cm2K100 = 99.61±44.5 keV cm2 = 1.38±0.34102103r(kpc)102103K(keVcm2)ABELL_3399(6:37:14.511,-48:28:18.76)rmax for fit = 891.6 kpcreduced 2 = 1.05K0 = 59.43±16.44 keV cm2K100 = 164.36±25.2 keV cm2 = 0.87±0.08102103r(kpc)103K(keVcm2)PLCKESZ_G167.65+17.64(6:38:03.685,47:47:53.91)rmax for fit = 620.18 kpcreduced 2 = 1.05K0 = 209.98±18.22 keV cm2K100 = 21.82±7.29 keV cm2 = 1.89±0.09101102103r(kpc)102103K(keVcm2)ABELL_S0592(6:38:48.610,-53:58:26.33)rmax for fit = 866.19 kpcreduced 2 = 1.03K0 = 30.59±7.83 keV cm2K100 = 141.16±13.22 keV cm2 = 0.92±0.07102103r(kpc)102103K(keVcm2)ABELL_3404(6:45:29.015,-54:13:43.13)rmax for fit = 578.41 kpcreduced 2 = 1.04K0 = 95.06±18.88 keV cm2K100 = 119.83±26.79 keV cm2 = 1.08±0.14102r(kpc)2×1023×1024×1026×102K(keVcm2)ABELL_0562(6:53:21.523,69:19:51.20)rmax for fit = 340.96 kpcreduced 2 = 1.04K0 = 122.54±34.18 keV cm2K100 = 82.47±77.22 keV cm2 = 0.76±0.5Figure C.1 (cont’d)

120

101102r(kpc)102K(keVcm2)ABELL_0576(7:21:30.394,55:45:41.94)rmax for fit = 105.96 kpcreduced 2 = 1.02K0 = 63.84±7.64 keV cm2K100 = 204.15±14.4 keV cm2 = 1.3±0.2102r(kpc)1022×1023×1024×102K(keVcm2)ABELL_0578(7:24:53.510,66:59:07.42)rmax for fit = 198.7 kpcreduced 2 = 1.17K0 = 16.58±48.23 keV cm2K100 = 216.25±74.41 keV cm2 = 0.64±0.37102103r(kpc)102103K(keVcm2)ABELL_0586(7:32:20.340,31:37:58.58)rmax for fit = 808.05 kpcreduced 2 = 1.03K0 = 116.11±10.29 keV cm2K100 = 67.38±10.68 keV cm2 = 1.44±0.09101102r(kpc)102103K(keVcm2)ZwCl_0735.7+7421(7:41:44.244,74:14:38.22)rmax for fit = 534.15 kpcreduced 2 = 1.03K0 = 16.14±0.91 keV cm2K100 = 121.65±2.65 keV cm2 = 1.15±0.02102103r(kpc)102103K(keVcm2)MACS_J0744.9+3927(7:44:52.802,39:27:24.41)rmax for fit = 891.95 kpcreduced 2 = 1.07K0 = 53.44±7.51 keV cm2K100 = 86.73±11.75 keV cm2 = 1.15±0.09101102r(kpc)101102K(keVcm2)PKS_0745-19(7:47:31.435,-19:17:39.77)rmax for fit = 420.49 kpcreduced 2 = 1.02K0 = 8.58±0.31 keV cm2K100 = 118.2±1.03 keV cm2 = 1.17±0.01Figure C.1 (cont’d)

121

101102r(kpc)102K(keVcm2)ABELL_0598(7:51:24.101,17:30:53.00)rmax for fit = 205.46 kpcreduced 2 = 1.08K0 = 8.32±2.29 keV cm2K100 = 144.9±7.31 keV cm2 = 1.13±0.08101102r(kpc)102103K(keVcm2)ABELL_0611(8:00:56.832,36:03:24.08)rmax for fit = 638.56 kpcreduced 2 = 1.05K0 = 63.67±8.44 keV cm2K100 = 113.0±14.63 keV cm2 = 1.24±0.11102r(kpc)102K(keVcm2)SDSS-C4_3062(8:10:22.822,42:16:26.10)rmax for fit = 214.75 kpcreduced 2 = 1.25K0 = 46.65±12.19 keV cm2K100 = 160.15±27.82 keV cm2 = 1.26±0.26101102r(kpc)102103K(keVcm2)ABELL_0644(8:17:25.224,-7:30:40.03)rmax for fit = 655.03 kpcreduced 2 = 1.01K0 = 70.24±6.44 keV cm2K100 = 114.37±8.62 keV cm2 = 1.05±0.05101102r(kpc)102K(keVcm2)MCXC_J0819.6+6336(8:19:26.006,63:37:26.54)rmax for fit = 348.99 kpcreduced 2 = 1.1K0 = 6.46±14.1 keV cm2K100 = 160.31±26.2 keV cm2 = 0.7±0.13101102r(kpc)101102K(keVcm2)UGCl_120(8:23:21.642,4:22:21.33)rmax for fit = 101.28 kpcreduced 2 = 1.25K0 = 2.58±2.07 keV cm2K100 = 238.19±25.84 keV cm2 = 0.98±0.09Figure C.1 (cont’d)

122

102r(kpc)102103K(keVcm2)ZwCl_0823.2+0425(8:25:57.849,4:14:49.03)rmax for fit = 514.59 kpcreduced 2 = 1.14K0 = 72.06±16.33 keV cm2K100 = 90.87±25.86 keV cm2 = 1.27±0.22101102r(kpc)102103K(keVcm2)2MFGC_06756(8:34:54.924,55:34:21.14)rmax for fit = 637.57 kpcreduced 2 = 1.04K0 = 12.47±1.19 keV cm2K100 = 95.63±3.37 keV cm2 = 1.18±0.03102103r(kpc)103K(keVcm2)ABELL_3411(8:41:51.927,-17:27:45.62)rmax for fit = 712.8 kpcreduced 2 = 1.02K0 = 194.02±24.32 keV cm2K100 = 76.51±25.82 keV cm2 = 1.28±0.18101102r(kpc)102103K(keVcm2)NSC_J084254+292723(8:42:55.968,29:27:26.96)rmax for fit = 483.23 kpcreduced 2 = 1.06K0 = 22.86±2.04 keV cm2K100 = 100.85±6.19 keV cm2 = 1.55±0.11102103r(kpc)103K(keVcm2)ABELL_0697(8:42:57.550,36:21:57.64)rmax for fit = 1204.98 kpcreduced 2 = 1.03K0 = 229.65±22.64 keV cm2K100 = 54.66±16.89 keV cm2 = 1.62±0.15101102r(kpc)101102103K(keVcm2)ZwCl_0857.9+2107(9:00:36.835,20:53:40.34)rmax for fit = 248.01 kpcreduced 2 = 1.06K0 = 18.93±2.34 keV cm2K100 = 81.09±5.95 keV cm2 = 1.72±0.13Figure C.1 (cont’d)

123

102103r(kpc)102103K(keVcm2)SDSS_+137.3+11.0+0.18(9:09:12.754,10:58:32.02)rmax for fit = 956.03 kpcreduced 2 = 1.03K0 = 88.2±16.43 keV cm2K100 = 99.19±23.79 keV cm2 = 1.01±0.16102103r(kpc)102103K(keVcm2)2MASSi_J0913454+405628(9:13:45.729,40:56:29.64)rmax for fit = 783.99 kpcreduced 2 = 1.07K0 = 23.53±2.75 keV cm2K100 = 96.23±5.78 keV cm2 = 1.16±0.05102103r(kpc)103K(keVcm2)ABELL_0773(9:17:52.567,51:43:38.17)rmax for fit = 878.77 kpcreduced 2 = 1.03K0 = 179.1±21.36 keV cm2K100 = 64.05±17.29 keV cm2 = 1.39±0.13101102r(kpc)102K(keVcm2)Hydra_A(9:18:05.986,-12:05:43.94)rmax for fit = 45.35 kpcreduced 2 = 1.02K0 = 15.71±0.63 keV cm2K100 = 142.64±19.03 keV cm2 = 1.46±0.11102103r(kpc)1032×1023×1024×1026×102K(keVcm2)NSC_J092017+303027(9:20:26.515,30:29:37.70)rmax for fit = 979.77 kpcreduced 2 = 1.06K0 = 128.49±76.67 keV cm2K100 = 206.5±111.69 keV cm2 = 0.59±0.19101102r(kpc)102K(keVcm2)ABELL_0795(9:24:05.777,14:10:25.07)rmax for fit = 421.1 kpcreduced 2 = 1.03K0 = 27.93±3.48 keV cm2K100 = 115.74±6.81 keV cm2 = 1.09±0.06Figure C.1 (cont’d)

124

101r(kpc)1012×1013×1014×1016×101K(keVcm2)UGC_05088_GROUP(9:33:25.676,34:02:53.22)rmax for fit = 70.16 kpcreduced 2 = 1.33K0 = 3.27±3.28 keV cm2K100 = 104.32±8.41 keV cm2 = 0.79±0.14102r(kpc)1022×1023×1024×1026×102K(keVcm2)WHL_J093820.9+520243(9:38:20.332,52:02:53.41)rmax for fit = 163.63 kpcreduced 2 = 1.07K0 = 92.46±18.09 keV cm2K100 = 60.02±40.97 keV cm2 = 1.26±0.55102103r(kpc)103K(keVcm2)ABELL_0868(9:45:26.138,-8:39:24.44)rmax for fit = 823.91 kpcreduced 2 = 1.05K0 = 192.94±14.46 keV cm2K100 = 14.99±6.53 keV cm2 = 1.87±0.1102r(kpc)102103K(keVcm2)GALEX_J094712.4+762313(9:47:12.694,76:23:13.42)rmax for fit = 236.41 kpcreduced 2 = 1.05K0 = 25.09±1.57 keV cm2K100 = 75.23±4.85 keV cm2 = 1.92±0.06101102r(kpc)101102103K(keVcm2)ZwCl_0949.6+5207(9:52:49.183,51:53:05.28)rmax for fit = 339.07 kpcreduced 2 = 1.03K0 = 4.9±8.4 keV cm2K100 = 129.42±12.2 keV cm2 = 1.07±0.1102103r(kpc)103K(keVcm2)PLCKESZ_G264.41+19.48(10:00:01.616,-30:16:37.08)rmax for fit = 929.4 kpcreduced 2 = 1.05K0 = 94.35±40.04 keV cm2K100 = 176.57±56.79 keV cm2 = 0.78±0.14Figure C.1 (cont’d)

125

100101r(kpc)101K(keVcm2)HCG_042(10:00:14.234,-19:38:10.75)rmax for fit = 27.17 kpcreduced 2 = 1.1K0 = 1.71±0.34 keV cm2K100 = 188.99±23.76 keV cm2 = 1.01±0.06102r(kpc)102K(keVcm2)MCXC_J1000.5+4409(10:00:32.023,44:08:39.70)rmax for fit = 414.19 kpcreduced 2 = 1.09K0 = 16.98±5.37 keV cm2K100 = 111.26±9.94 keV cm2 = 0.94±0.08102103r(kpc)103K(keVcm2)ZwCl_1006.1+1201(10:08:47.462,11:47:36.31)rmax for fit = 490.13 kpcreduced 2 = 1.03K0 = 122.66±18.26 keV cm2K100 = 86.04±23.77 keV cm2 = 1.19±0.18102103r(kpc)102103K(keVcm2)MCXC_J1010.5-1239(10:10:32.311,-12:39:56.81)rmax for fit = 368.32 kpcreduced 2 = 1.05K0 = 22.53±50.17 keV cm2K100 = 227.98±73.46 keV cm2 = 0.56±0.19101102r(kpc)102103K(keVcm2)ABELL_0963(10:17:03.744,39:02:49.16)rmax for fit = 650.0 kpcreduced 2 = 1.03K0 = 39.1±8.51 keV cm2K100 = 149.62±13.21 keV cm2 = 0.83±0.06101102r(kpc)102K(keVcm2)MCXC_J1022.0+3830(10:22:10.034,38:31:23.56)rmax for fit = 120.11 kpcreduced 2 = 1.06K0 = 38.8±9.49 keV cm2K100 = 177.4±16.65 keV cm2 = 1.02±0.25Figure C.1 (cont’d)

126

102r(kpc)103K(keVcm2)ABELL_0980(10:22:28.375,50:06:21.85)rmax for fit = 573.78 kpcreduced 2 = 1.06K0 = 150.12±21.66 keV cm2K100 = 62.49±23.78 keV cm2 = 1.46±0.23101102103r(kpc)102103K(keVcm2)BLOX_J1023.6+0411.1(10:23:39.734,4:11:08.05)rmax for fit = 1034.69 kpcreduced 2 = 1.03K0 = 8.95±0.96 keV cm2K100 = 106.96±3.16 keV cm2 = 1.22±0.03101102r(kpc)102103K(keVcm2)ABELL_3444(10:23:50.196,-27:15:23.76)rmax for fit = 681.01 kpcreduced 2 = 1.04K0 = 20.76±1.81 keV cm2K100 = 94.19±4.67 keV cm2 = 1.34±0.04101102r(kpc)1032×1023×1024×1026×102K(keVcm2)ABELL_1033(10:31:44.799,35:02:22.41)rmax for fit = 479.07 kpcreduced 2 = 1.02K0 = 122.95±16.45 keV cm2K100 = 116.34±22.45 keV cm2 = 1.04±0.13101102r(kpc)101102K(keVcm2)ABELL_1068(10:40:44.520,39:57:10.30)rmax for fit = 449.59 kpcreduced 2 = 1.03K0 = 6.28±0.7 keV cm2K100 = 109.28±3.04 keV cm2 = 1.16±0.03100101r(kpc)101102K(keVcm2)NGC_3402_GROUP(10:50:26.124,-12:50:41.75)rmax for fit = 69.82 kpcreduced 2 = 1.03K0 = 1.67±0.12 keV cm2K100 = 93.94±2.84 keV cm2 = 0.95±0.02Figure C.1 (cont’d)

127

102r(kpc)103K(keVcm2)BLOX_J1056.9-0337.3(10:56:55.916,-3:37:39.85)rmax for fit = 322.13 kpcreduced 2 = 1.07K0 = 126.8±36.95 keV cm2K100 = 87.75±78.52 keV cm2 = 1.25±0.49102103r(kpc)1022×1023×1024×1026×102K(keVcm2)MACS_J1108.9+0906(11:08:55.287,9:05:56.91)rmax for fit = 747.75 kpcreduced 2 = 1.11K0 = 80.25±38.94 keV cm2K100 = 111.02±64.85 keV cm2 = 0.79±0.25101102r(kpc)102K(keVcm2)NGC_3551(11:09:44.233,21:45:33.74)rmax for fit = 38.35 kpcreduced 2 = 1.09K0 = 21.02±22.51 keV cm2K100 = 218.2±37.1 keV cm2 = 0.49±0.32101r(kpc)1026×101K(keVcm2)1RXS_J111039.6+284316(11:10:40.556,28:42:49.63)rmax for fit = 58.93 kpcreduced 2 = 1.13K0 = 64.27±9.25 keV cm2K100 = 84.54±44.61 keV cm2 = 1.46±0.4102r(kpc)2×1023×1024×1026×102K(keVcm2)ABELL_1190(11:11:39.815,40:50:24.70)rmax for fit = 392.02 kpcreduced 2 = 1.08K0 = 213.61±19.44 keV cm2K100 = 25.93±18.43 keV cm2 = 1.69±0.23101102r(kpc)102103K(keVcm2)ABELL_1201(11:12:54.490,13:26:08.77)rmax for fit = 122.46 kpcreduced 2 = 1.03K0 = 63.6±8.17 keV cm2K100 = 176.6±19.44 keV cm2 = 1.58±0.26Figure C.1 (cont’d)

128

101102r(kpc)102103K(keVcm2)ABELL_1204(11:13:20.419,17:35:38.44)rmax for fit = 138.05 kpcreduced 2 = 1.05K0 = 14.73±1.69 keV cm2K100 = 82.2±4.88 keV cm2 = 1.44±0.14101102103r(kpc)102103K(keVcm2)MACS_J1115.8+0129(11:15:52.049,1:29:56.54)rmax for fit = 334.66 kpcreduced 2 = 1.05K0 = 22.15±2.42 keV cm2K100 = 124.02±9.39 keV cm2 = 1.67±0.18101r(kpc)101102K(keVcm2)HCG_051(11:22:26.419,24:17:51.19)rmax for fit = 46.73 kpcreduced 2 = 1.1K0 = 7.02±2.69 keV cm2K100 = 130.84±10.86 keV cm2 = 0.56±0.07102r(kpc)1033×1024×1026×102K(keVcm2)ABELL_1240(11:23:38.357,43:05:48.34)rmax for fit = 288.08 kpcreduced 2 = 1.05K0 = 196.27±92.44 keV cm2K100 = 117.62±160.96 keV cm2 = 0.67±0.71101102r(kpc)102K(keVcm2)MCXC_J1130.0+3637(11:30:02.789,36:38:08.27)rmax for fit = 162.29 kpcreduced 2 = 1.05K0 = 21.32±2.68 keV cm2K100 = 119.26±8.12 keV cm2 = 1.1±0.12102r(kpc)1032×1023×1024×1026×102K(keVcm2)ABELL_1285(11:30:22.360,-14:34:50.57)rmax for fit = 680.1 kpcreduced 2 = 1.02K0 = 186.25±29.13 keV cm2K100 = 77.43±35.96 keV cm2 = 1.0±0.21Figure C.1 (cont’d)

129

102103r(kpc)102103K(keVcm2)ABELL_1300(11:31:54.581,-19:55:44.54)rmax for fit = 1131.89 kpcreduced 2 = 1.04K0 = 65.71±26.36 keV cm2K100 = 203.53±36.79 keV cm2 = 0.93±0.08102103r(kpc)1034×1026×1022×103K(keVcm2)WHL_J114224.8+583205(11:42:24.138,58:31:59.24)rmax for fit = 1015.66 kpcreduced 2 = 1.04K0 = 459.85±44.96 keV cm2K100 = 14.71±25.03 keV cm2 = 1.73±0.2101102r(kpc)102103K(keVcm2)ABELL_1361(11:43:39.636,46:21:20.41)rmax for fit = 333.57 kpcreduced 2 = 1.11K0 = 18.05±3.0 keV cm2K100 = 134.88±8.97 keV cm2 = 1.46±0.14102r(kpc)2×1023×1024×1026×102K(keVcm2)SDSS-C4-DR3_3018(11:47:18.571,55:44:24.05)rmax for fit = 117.01 kpcreduced 2 = 1.05K0 = 130.9±37.89 keV cm2K100 = 103.09±73.25 keV cm2 = 1.07±0.66101102r(kpc)102103K(keVcm2)ABELL_1413(11:55:17.892,23:24:21.85)rmax for fit = 639.41 kpcreduced 2 = 1.02K0 = 57.42±5.08 keV cm2K100 = 129.72±8.11 keV cm2 = 1.05±0.04101102r(kpc)102103K(keVcm2)ABELL_1423(11:57:17.263,33:36:37.44)rmax for fit = 97.39 kpcreduced 2 = 1.03K0 = 36.92±6.3 keV cm2K100 = 359.42±31.01 keV cm2 = 1.21±0.14Figure C.1 (cont’d)

130

101102r(kpc)101102103K(keVcm2)SDSS-C4-DR3_3144(11:59:52.296,55:32:05.60)rmax for fit = 57.26 kpcreduced 2 = 1.08K0 = 3.1±0.71 keV cm2K100 = 393.63±61.01 keV cm2 = 1.45±0.1101102r(kpc)2×1023×1024×102K(keVcm2)ABELL_1446(12:02:03.744,58:02:17.92)rmax for fit = 223.39 kpcreduced 2 = 1.03K0 = 157.74±17.02 keV cm2K100 = 62.91±31.08 keV cm2 = 1.46±0.36102103r(kpc)102103K(keVcm2)MACS_J1206.2-0847(12:06:12.276,-8:48:02.41)rmax for fit = 1066.01 kpcreduced 2 = 1.05K0 = 54.2±11.44 keV cm2K100 = 134.85±20.75 keV cm2 = 1.1±0.1102r(kpc)1033×1024×1026×102K(keVcm2)MCXC_J1215.4-3900(12:15:24.644,-39:02:10.69)rmax for fit = 676.5 kpcreduced 2 = 1.06K0 = 275.45±63.7 keV cm2K100 = 71.65±105.13 keV cm2 = 1.13±0.47101102r(kpc)101102K(keVcm2)NGC_4325_GROUP(12:23:06.550,10:37:19.80)rmax for fit = 82.46 kpcreduced 2 = 1.04K0 = 3.28±0.2 keV cm2K100 = 110.66±3.22 keV cm2 = 1.29±0.03102103r(kpc)102103K(keVcm2)NSCS_J122648+215157(12:26:50.962,21:49:57.35)rmax for fit = 486.29 kpcreduced 2 = 1.04K0 = 57.72±16.39 keV cm2K100 = 120.67±26.52 keV cm2 = 0.91±0.16Figure C.1 (cont’d)

131

102103r(kpc)103K(keVcm2)MCXC_J1234.2+0947(12:34:24.324,9:47:21.24)rmax for fit = 869.76 kpcreduced 2 = 1.07K0 = 194.61±65.37 keV cm2K100 = 87.96±115.82 keV cm2 = 0.84±0.42101100r(kpc)101K(keVcm2)MESSIER_089(12:35:39.773,12:33:23.97)rmax for fit = 0.74 kpcreduced 2 = 1.11K0 = 1.27±0.03 keV cm2K100 = 928.75±52.84 keV cm2 = 1.23±0.02102r(kpc)2×1023×1024×102K(keVcm2)ABELL_1569(12:36:26.016,16:32:17.81)rmax for fit = 321.48 kpcreduced 2 = 1.05K0 = 136.45±21.46 keV cm2K100 = 44.11±65.75 keV cm2 = 0.9±0.67102103r(kpc)103K(keVcm2)ABELL_1576(12:36:58.274,63:11:13.88)rmax for fit = 878.39 kpcreduced 2 = 1.04K0 = 103.88±22.11 keV cm2K100 = 127.18±31.72 keV cm2 = 1.03±0.13100101r(kpc)101102K(keVcm2)Centaurus_Cluster(12:48:49.267,-41:18:39.53)rmax for fit = 26.26 kpcreduced 2 = 1.03K0 = 0.87±0.03 keV cm2K100 = 324.91±3.84 keV cm2 = 1.2±0.01100101r(kpc)101102K(keVcm2)NGC_4759_GROUP(12:53:05.741,-9:12:15.62)rmax for fit = 48.72 kpcreduced 2 = 1.03K0 = 2.49±0.1 keV cm2K100 = 168.15±8.1 keV cm2 = 1.16±0.02Figure C.1 (cont’d)

132

101102r(kpc)102103K(keVcm2)ABELL_3528B(12:54:22.250,-29:00:39.82)rmax for fit = 400.08 kpcreduced 2 = 1.04K0 = 15.26±2.68 keV cm2K100 = 218.8±8.8 keV cm2 = 1.16±0.06100101r(kpc)101102K(keVcm2)NGC_4782-3(12:54:36.101,-12:33:38.68)rmax for fit = 37.66 kpcreduced 2 = 1.09K0 = 3.2±0.76 keV cm2K100 = 309.12±63.05 keV cm2 = 1.25±0.1101102r(kpc)102103K(keVcm2)ABELL_1644(12:57:11.664,-17:24:32.87)rmax for fit = 48.7 kpcreduced 2 = 1.02K0 = 21.22±1.46 keV cm2K100 = 616.09±78.79 keV cm2 = 1.82±0.11102r(kpc)1032×1023×1024×1026×102K(keVcm2)ABELL_3532(12:57:22.326,-30:21:45.30)rmax for fit = 414.32 kpcreduced 2 = 1.03K0 = 150.77±20.3 keV cm2K100 = 83.65±29.76 keV cm2 = 1.25±0.25102r(kpc)1033×1024×1026×102K(keVcm2)WHL_J125933.4+600409(12:59:33.039,60:04:14.14)rmax for fit = 807.85 kpcreduced 2 = 1.05K0 = 327.11±56.12 keV cm2K100 = 36.89±80.08 keV cm2 = 1.33±0.42101102r(kpc)102103K(keVcm2)ABELL_1664(13:03:42.622,-24:14:41.60)rmax for fit = 400.96 kpcreduced 2 = 1.03K0 = 14.13±0.88 keV cm2K100 = 107.45±4.54 keV cm2 = 1.69±0.08Figure C.1 (cont’d)

133

101102r(kpc)101102K(keVcm2)ABELL_1668(13:03:46.682,19:16:13.94)rmax for fit = 213.5 kpcreduced 2 = 1.06K0 = 6.16±1.32 keV cm2K100 = 167.32±7.88 keV cm2 = 1.03±0.05101102103r(kpc)102103K(keVcm2)ABELL_1689(13:11:29.611,-1:20:28.68)rmax for fit = 561.77 kpcreduced 2 = 1.02K0 = 61.84±4.92 keV cm2K100 = 126.29±7.8 keV cm2 = 1.16±0.05102103r(kpc)103K(keVcm2)WHL_J131505.2+514902(13:15:04.789,51:49:09.38)rmax for fit = 937.79 kpcreduced 2 = 1.05K0 = 159.9±30.28 keV cm2K100 = 100.57±32.23 keV cm2 = 1.16±0.15100101r(kpc)101K(keVcm2)NGC_5044(13:15:23.947,-16:23:07.62)rmax for fit = 22.43 kpcreduced 2 = 1.02K0 = 1.3±0.14 keV cm2K100 = 47.73±1.77 keV cm2 = 0.72±0.02101102r(kpc)101102K(keVcm2)NGC_5098_GROUP(13:20:14.650,33:08:33.07)rmax for fit = 121.78 kpcreduced 2 = 1.05K0 = 4.8±0.94 keV cm2K100 = 129.72±6.62 keV cm2 = 1.16±0.06100101r(kpc)101102K(keVcm2)NGC_5129(13:24:09.984,13:58:31.82)rmax for fit = 30.19 kpcreduced 2 = 1.09K0 = 0.46±0.66 keV cm2K100 = 212.42±33.88 keV cm2 = 0.92±0.07Figure C.1 (cont’d)

134

102r(kpc)103K(keVcm2)ABELL_1736(13:26:49.452,-27:09:48.13)rmax for fit = 404.93 kpcreduced 2 = 1.02K0 = 139.63±39.37 keV cm2K100 = 75.72±80.89 keV cm2 = 0.69±0.46101102r(kpc)102K(keVcm2)ABELL_3558(13:27:56.854,-31:29:43.76)rmax for fit = 237.51 kpcreduced 2 = 1.02K0 = 49.88±14.91 keV cm2K100 = 194.07±20.76 keV cm2 = 0.77±0.09101102r(kpc)102K(keVcm2)SSGC_081(13:29:47.748,-31:36:23.54)rmax for fit = 336.48 kpcreduced 2 = 1.03K0 = 44.51±20.29 keV cm2K100 = 165.34±31.99 keV cm2 = 0.61±0.12102r(kpc)1022×1023×1024×102K(keVcm2)a1750ss(13:30:10.187,-2:06:15.72)rmax for fit = 302.18 kpcreduced 2 = 1.17K0 = 34.9±69.7 keV cm2K100 = 186.19±91.1 keV cm2 = 0.58±0.36102r(kpc)103K(keVcm2)ABELL_1750C(13:30:50.232,-1:51:46.42)rmax for fit = 386.15 kpcreduced 2 = 1.05K0 = 159.87±10.76 keV cm2K100 = 56.1±9.68 keV cm2 = 1.89±0.08102r(kpc)102103K(keVcm2)ABELL_1750N(13:31:10.949,-1:43:41.52)rmax for fit = 503.35 kpcreduced 2 = 1.05K0 = 93.06±22.13 keV cm2K100 = 117.46±37.18 keV cm2 = 0.98±0.21Figure C.1 (cont’d)

135

102r(kpc)2×1023×1024×1026×102K(keVcm2)SC_1329-313(13:31:27.606,-31:49:16.52)rmax for fit = 304.54 kpcreduced 2 = 1.05K0 = 167.33±16.57 keV cm2K100 = 61.94±24.47 keV cm2 = 1.7±0.21101r(kpc)101K(keVcm2)2MASX_J13312961+1107566(13:31:29.686,11:07:54.95)rmax for fit = 55.98 kpcreduced 2 = infK0 = 4.5±1.41 keV cm2K100 = 130.13±37.77 keV cm2 = 1.46±0.29101102r(kpc)2×1023×1024×102K(keVcm2)ABELL_3560(13:32:25.714,-33:08:09.60)rmax for fit = 181.87 kpcreduced 2 = 1.04K0 = 40.38±61.46 keV cm2K100 = 198.7±85.11 keV cm2 = 0.37±0.25101102r(kpc)102103K(keVcm2)ABELL_3562(13:33:37.800,-31:40:12.04)rmax for fit = 376.44 kpcreduced 2 = 1.02K0 = 70.59±12.79 keV cm2K100 = 144.22±18.71 keV cm2 = 0.94±0.1102103r(kpc)103K(keVcm2)ABELL_1763(13:35:17.957,40:59:55.79)rmax for fit = 1139.55 kpcreduced 2 = 1.03K0 = 186.62±22.11 keV cm2K100 = 54.57±15.65 keV cm2 = 1.35±0.12101102r(kpc)102103K(keVcm2)ABELL_1775(13:41:48.637,26:22:20.10)rmax for fit = 92.23 kpcreduced 2 = 1.02K0 = 56.89±3.88 keV cm2K100 = 256.55±19.79 keV cm2 = 1.86±0.1Figure C.1 (cont’d)

136

101102r(kpc)1026×1012×1023×1024×102K(keVcm2)ABELL_3571(13:47:28.433,-32:51:52.45)rmax for fit = 149.07 kpcreduced 2 = 1.02K0 = 59.96±13.82 keV cm2K100 = 210.88±14.71 keV cm2 = 0.7±0.15102103r(kpc)102103K(keVcm2)LCDCS_0829(13:47:30.593,-11:45:10.04)rmax for fit = 562.23 kpcreduced 2 = 1.03K0 = 3.46±2.3 keV cm2K100 = 177.1±6.23 keV cm2 = 1.07±0.04101102r(kpc)102K(keVcm2)ABELL_1795(13:48:52.802,26:35:23.53)rmax for fit = 297.98 kpcreduced 2 = 1.02K0 = 15.17±0.78 keV cm2K100 = 118.04±1.46 keV cm2 = 1.08±0.02101102r(kpc)101102K(keVcm2)NSCS_J135021+094042(13:50:21.919,9:40:11.36)rmax for fit = 268.65 kpcreduced 2 = 1.05K0 = 6.29±1.54 keV cm2K100 = 172.19±5.84 keV cm2 = 0.83±0.04102r(kpc)102103K(keVcm2)MACS_J1359.2-1929(13:59:10.221,-19:29:25.09)rmax for fit = 487.66 kpcreduced 2 = 1.17K0 = 19.01±3.63 keV cm2K100 = 92.64±9.76 keV cm2 = 1.33±0.11101102r(kpc)102K(keVcm2)ABELL_1831(13:59:15.821,27:58:32.15)rmax for fit = 421.07 kpcreduced 2 = 1.04K0 = 77.35±12.85 keV cm2K100 = 100.59±19.69 keV cm2 = 1.16±0.15Figure C.1 (cont’d)

137

101102r(kpc)102103K(keVcm2)WHL_J135949.5+623047(13:59:50.525,62:31:04.58)rmax for fit = 747.31 kpcreduced 2 = 1.05K0 = 21.24±6.09 keV cm2K100 = 181.64±13.84 keV cm2 = 1.18±0.13101102103r(kpc)102103K(keVcm2)ABELL_1835(14:01:01.951,2:52:43.18)rmax for fit = 779.48 kpcreduced 2 = 1.03K0 = 11.3±1.21 keV cm2K100 = 105.98±4.23 keV cm2 = 1.32±0.03102r(kpc)103K(keVcm2)A1882a(14:15:08.352,-0:29:35.06)rmax for fit = 272.24 kpcreduced 2 = 1.07K0 = 61.3±63.35 keV cm2K100 = 189.66±97.28 keV cm2 = 0.53±0.36102r(kpc)102K(keVcm2)WHL_J141623.8+444528(14:16:27.945,44:46:48.20)rmax for fit = 446.72 kpcreduced 2 = 1.5K0 = 18.73±17.58 keV cm2K100 = 104.88±37.53 keV cm2 = 0.9±0.23102r(kpc)102103K(keVcm2)GMBCG_J215.94948+24.07846(14:23:47.760,24:04:40.44)rmax for fit = 238.91 kpcreduced 2 = 1.06K0 = 5.56±3.4 keV cm2K100 = 132.58±7.92 keV cm2 = 1.17±0.11101102103r(kpc)102103K(keVcm2)ABELL_1914(14:26:03.060,37:49:27.84)rmax for fit = 932.69 kpcreduced 2 = 1.02K0 = 84.49±15.9 keV cm2K100 = 139.1±22.46 keV cm2 = 0.85±0.08Figure C.1 (cont’d)

138

102r(kpc)102103K(keVcm2)WHL_J142716.1+440730(14:27:16.133,44:07:37.49)rmax for fit = 624.38 kpcreduced 2 = 1.1K0 = 12.59±3.48 keV cm2K100 = 135.39±10.84 keV cm2 = 1.27±0.08101102r(kpc)102K(keVcm2)MACS_J1427.6-2521(14:27:40.243,-25:21:14.75)rmax for fit = 463.54 kpcreduced 2 = 1.11K0 = 9.47±4.81 keV cm2K100 = 133.73±10.34 keV cm2 = 0.92±0.07101102r(kpc)102K(keVcm2)ABELL_1930(14:32:37.887,31:38:52.49)rmax for fit = 362.22 kpcreduced 2 = 1.04K0 = 3.71±2.73 keV cm2K100 = 182.25±6.83 keV cm2 = 0.82±0.04102103r(kpc)1032×1023×1024×1026×102K(keVcm2)ABELL_1942_AND_CLUMP(14:38:21.878,3:40:12.97)rmax for fit = 828.31 kpcreduced 2 = 1.04K0 = 67.02±74.34 keV cm2K100 = 229.31±101.36 keV cm2 = 0.47±0.2101102r(kpc)2×1023×1024×102K(keVcm2)WBL_518(14:40:39.634,3:28:13.62)rmax for fit = 199.38 kpcreduced 2 = 1.03K0 = 89.36±48.07 keV cm2K100 = 144.17±94.68 keV cm2 = 0.41±0.31101102r(kpc)102103K(keVcm2)NSCS_J144726+082824(14:47:26.634,8:28:25.31)rmax for fit = 437.38 kpcreduced 2 = 1.08K0 = 11.22±1.7 keV cm2K100 = 195.75±8.9 keV cm2 = 1.56±0.06Figure C.1 (cont’d)

139

101102r(kpc)101102K(keVcm2)ABELL_1991(14:54:31.620,18:38:41.50)rmax for fit = 215.81 kpcreduced 2 = 1.03K0 = 0.39±0.24 keV cm2K100 = 122.8±2.38 keV cm2 = 1.0±0.02101102103r(kpc)102103K(keVcm2)NSCS_J145715+222009(14:57:15.089,22:20:32.50)rmax for fit = 909.78 kpcreduced 2 = 1.03K0 = 12.78±1.25 keV cm2K100 = 80.99±3.03 keV cm2 = 1.14±0.03101102r(kpc)102103K(keVcm2)ABELL_S0780(14:59:28.817,-18:10:43.49)rmax for fit = 121.63 kpcreduced 2 = 1.04K0 = 20.93±1.31 keV cm2K100 = 114.08±10.97 keV cm2 = 1.82±0.13101102103r(kpc)102103K(keVcm2)ABELL_2009(15:00:19.576,21:22:11.56)rmax for fit = 778.24 kpcreduced 2 = 1.03K0 = 18.81±2.58 keV cm2K100 = 133.36±7.02 keV cm2 = 1.1±0.04101102103r(kpc)101102103K(keVcm2)WHL_J150407.5-024816(15:04:07.416,-2:48:15.70)rmax for fit = 1135.52 kpcreduced 2 = 1.02K0 = 9.08±0.49 keV cm2K100 = 82.23±2.1 keV cm2 = 1.33±0.02102103r(kpc)103104K(keVcm2)MCXC_J1514.9-1523(15:15:02.556,-15:23:21.09)rmax for fit = 905.01 kpcreduced 2 = 1.02K0 = 356.15±108.55 keV cm2K100 = 137.95±191.29 keV cm2 = 0.61±0.4Figure C.1 (cont’d)

140

101102r(kpc)102K(keVcm2)MKW_03s(15:21:51.929,7:42:31.97)rmax for fit = 356.2 kpcreduced 2 = 1.01K0 = 18.04±1.76 keV cm2K100 = 117.22±2.72 keV cm2 = 0.91±0.03102r(kpc)103K(keVcm2)ABELL_2069(15:24:11.376,29:52:19.02)rmax for fit = 766.73 kpcreduced 2 = 1.02K0 = 297.69±41.57 keV cm2K100 = 84.81±46.81 keV cm2 = 0.96±0.21101102r(kpc)101102K(keVcm2)MCXC_J1524.2-3154(15:24:12.831,-31:54:16.15)rmax for fit = 330.72 kpcreduced 2 = 1.03K0 = 5.44±0.43 keV cm2K100 = 104.85±2.3 keV cm2 = 1.19±0.02101102r(kpc)102103K(keVcm2)MACS_J1532.8+3021(15:32:53.782,30:20:58.70)rmax for fit = 672.86 kpcreduced 2 = 1.04K0 = 13.36±0.9 keV cm2K100 = 82.17±2.76 keV cm2 = 1.34±0.031024×1016×1012×102r(kpc)1022×1023×102K(keVcm2)ABELL_2092(15:33:17.614,31:08:16.49)rmax for fit = 211.55 kpcreduced 2 = 2K0 = 79.5±62.08 keV cm2K100 = 120.49±105.99 keV cm2 = 0.69±0.62101102r(kpc)102103K(keVcm2)ABELL_2107(15:39:39.113,21:46:57.65)rmax for fit = 71.05 kpcreduced 2 = 1.01K0 = 10.16±3.14 keV cm2K100 = 327.96±32.78 keV cm2 = 0.92±0.09Figure C.1 (cont’d)

141

102103r(kpc)103K(keVcm2)ABELL_2111(15:39:40.637,34:25:28.02)rmax for fit = 860.61 kpcreduced 2 = 1.04K0 = 189.92±27.12 keV cm2K100 = 88.34±27.66 keV cm2 = 1.19±0.16101102r(kpc)103K(keVcm2)ABELL_2104(15:40:08.131,-3:18:15.01)rmax for fit = 525.76 kpcreduced 2 = 1.03K0 = 159.14±31.84 keV cm2K100 = 127.17±43.6 keV cm2 = 0.82±0.18102r(kpc)2×1023×1024×1026×102K(keVcm2)ABELL_2125(15:41:14.155,66:15:57.20)rmax for fit = 570.75 kpcreduced 2 = 1.1K0 = 171.25±17.88 keV cm2K100 = 25.37±19.67 keV cm2 = 1.59±0.27101102r(kpc)1022×1023×1024×1026×102K(keVcm2)ABELL_2124(15:44:59.131,36:06:34.13)rmax for fit = 277.0 kpcreduced 2 = 1.03K0 = 91.07±24.56 keV cm2K100 = 196.37±38.84 keV cm2 = 0.81±0.17101102r(kpc)102103K(keVcm2)MCXC_J1558.3-1410(15:58:21.847,-14:09:57.86)rmax for fit = 130.15 kpcreduced 2 = 1.02K0 = 28.47±1.71 keV cm2K100 = 115.12±4.61 keV cm2 = 1.5±0.1101102r(kpc)103K(keVcm2)ABELL_2147(16:02:17.026,15:58:28.31)rmax for fit = 189.82 kpcreduced 2 = 1.02K0 = 163.01±18.56 keV cm2K100 = 78.33±36.31 keV cm2 = 1.41±0.38Figure C.1 (cont’d)

142

101102r(kpc)102K(keVcm2)ABELL_2151(16:04:35.887,17:43:17.36)rmax for fit = 261.73 kpcreduced 2 = 1.02K0 = 6.43±3.1 keV cm2K100 = 150.8±5.7 keV cm2 = 0.79±0.06101102r(kpc)1023×1014×1016×1012×102K(keVcm2)AWM_4(16:04:56.486,23:56:02.44)rmax for fit = 138.18 kpcreduced 2 = 1.03K0 = 24.47±5.37 keV cm2K100 = 108.46±6.62 keV cm2 = 0.65±0.09102r(kpc)102103K(keVcm2)MACS_J1621.3+3810(16:21:24.802,38:10:08.65)rmax for fit = 704.01 kpcreduced 2 = 1.06K0 = 2.41±5.63 keV cm2K100 = 168.76±12.89 keV cm2 = 0.92±0.06102r(kpc)102103K(keVcm2)ABELL_2187(16:24:14.018,41:14:37.54)rmax for fit = 570.46 kpcreduced 2 = 1.07K0 = 91.56±19.02 keV cm2K100 = 108.74±26.7 keV cm2 = 1.19±0.16101102103r(kpc)101102103K(keVcm2)ABELL_2204(16:32:46.920,5:34:32.84)rmax for fit = 205.08 kpcreduced 2 = 1.02K0 = 7.76±0.35 keV cm2K100 = 144.83±3.21 keV cm2 = 1.51±0.03101102103r(kpc)103K(keVcm2)ABELL_2219(16:40:20.112,46:42:42.84)rmax for fit = 624.6 kpcreduced 2 = 1.02K0 = 258.49±19.76 keV cm2K100 = 49.43±17.93 keV cm2 = 1.46±0.19Figure C.1 (cont’d)

143

101102r(kpc)101102103K(keVcm2)Hercules_A(16:51:08.160,4:59:32.42)rmax for fit = 73.88 kpcreduced 2 = 1.03K0 = 0.6±2.87 keV cm2K100 = 211.8±20.46 keV cm2 = 1.07±0.13101102r(kpc)101102K(keVcm2)NGC_6269(16:57:58.110,27:51:14.62)rmax for fit = 45.03 kpcreduced 2 = 1.03K0 = 1.31±1.93 keV cm2K100 = 279.71±47.56 keV cm2 = 0.89±0.1101102r(kpc)2×1023×1024×102K(keVcm2)ABELL_2256(17:03:44.568,78:38:11.51)rmax for fit = 199.69 kpcreduced 2 = 1.02K0 = 111.09±33.41 keV cm2K100 = 159.12±57.05 keV cm2 = 0.76±0.27101102103r(kpc)102103K(keVcm2)SDSS-C4_3072(17:20:09.941,26:37:29.10)rmax for fit = 879.48 kpcreduced 2 = 1.02K0 = 19.7±1.48 keV cm2K100 = 104.1±4.07 keV cm2 = 1.31±0.03102r(kpc)102103K(keVcm2)MACS_J1720.2+3536(17:20:16.954,35:36:23.62)rmax for fit = 702.37 kpcreduced 2 = 1.06K0 = 12.31±2.52 keV cm2K100 = 131.32±7.49 keV cm2 = 1.12±0.05101102103r(kpc)102103K(keVcm2)ABELL_2261(17:22:27.254,32:07:58.58)rmax for fit = 612.23 kpcreduced 2 = 1.03K0 = 41.82±9.76 keV cm2K100 = 139.29±14.83 keV cm2 = 0.9±0.07Figure C.1 (cont’d)

144

102103r(kpc)103K(keVcm2)ABELL_2294(17:24:10.150,85:53:09.78)rmax for fit = 744.11 kpcreduced 2 = 1.06K0 = 58.45±48.43 keV cm2K100 = 216.65±77.18 keV cm2 = 0.72±0.17102r(kpc)102K(keVcm2)Abell_2276(17:35:04.631,64:06:06.05)rmax for fit = 420.99 kpcreduced 2 = 1.07K0 = 24.17±11.03 keV cm2K100 = 132.6±18.93 keV cm2 = 0.82±0.12101102r(kpc)102K(keVcm2)ZwCl_1742.1+3306(17:44:14.515,32:59:29.69)rmax for fit = 140.0 kpcreduced 2 = 1.03K0 = 12.33±1.21 keV cm2K100 = 120.83±4.57 keV cm2 = 1.26±0.06102103r(kpc)1033×1024×1026×102K(keVcm2)NSC_J174715+451155(17:47:14.257,45:11:45.53)rmax for fit = 839.49 kpcreduced 2 = 1.06K0 = 290.69±35.2 keV cm2K100 = 11.49±16.43 keV cm2 = 1.75±0.19101102r(kpc)102103K(keVcm2)MCXC_J1750.2+3504(17:50:16.577,35:04:58.17)rmax for fit = 706.13 kpcreduced 2 = 1.05K0 = 1.79±2.58 keV cm2K100 = 163.64±7.59 keV cm2 = 0.89±0.04100101r(kpc)101K(keVcm2)NGC_6482(17:51:48.743,23:04:18.67)rmax for fit = 32.12 kpcreduced 2 = 1.1K0 = 0.84±0.24 keV cm2K100 = 75.09±9.97 keV cm2 = 0.83±0.06Figure C.1 (cont’d)

145

102103r(kpc)102103K(keVcm2)CIZA_J1804.4+1002(18:04:31.362,10:03:24.63)rmax for fit = 762.04 kpcreduced 2 = 1.04K0 = 26.27±48.51 keV cm2K100 = 220.22±70.7 keV cm2 = 0.49±0.13102r(kpc)1032×1023×1024×1026×102K(keVcm2)ABELL_2302(18:19:58.020,57:09:22.09)rmax for fit = 725.15 kpcreduced 2 = 1.07K0 = 190.54±77.38 keV cm2K100 = 121.02±139.11 keV cm2 = 0.76±0.42101102r(kpc)102103K(keVcm2)MACS_J1829.0+6913(18:29:06.200,69:14:08.04)rmax for fit = 484.04 kpcreduced 2 = 1.06K0 = 36.36±4.09 keV cm2K100 = 99.98±8.25 keV cm2 = 1.33±0.09101102r(kpc)102103K(keVcm2)MCXC_J1852.1+5711(18:52:08.815,57:11:42.61)rmax for fit = 309.39 kpcreduced 2 = 1.05K0 = 9.6±7.76 keV cm2K100 = 168.07±13.2 keV cm2 = 0.84±0.1102r(kpc)102103K(keVcm2)MCXC_J1853.9+6822(18:54:02.258,68:22:57.72)rmax for fit = 120.8 kpcreduced 2 = 1.06K0 = 76.43±14.62 keV cm2K100 = 198.87±33.89 keV cm2 = 1.4±0.38102103r(kpc)102103K(keVcm2)PLCKESZ_G337.09-25.97(19:14:37.530,-59:28:19.80)rmax for fit = 314.98 kpcreduced 2 = 1.05K0 = 78.32±8.85 keV cm2K100 = 64.35±13.72 keV cm2 = 1.66±0.19Figure C.1 (cont’d)

146

101102103r(kpc)102103K(keVcm2)MACS_J1931.8-2635(19:31:49.656,-26:34:34.00)rmax for fit = 409.03 kpcreduced 2 = 1.04K0 = 20.75±1.38 keV cm2K100 = 83.34±3.83 keV cm2 = 1.47±0.05102103r(kpc)102103K(keVcm2)CIZA_J1938.3+5409(19:38:18.424,54:09:34.85)rmax for fit = 754.48 kpcreduced 2 = 1.06K0 = 82.49±12.54 keV cm2K100 = 63.26±15.56 keV cm2 = 1.43±0.15101102r(kpc)102103K(keVcm2)MCXC_J1947.3-7623(19:47:14.904,-76:23:44.79)rmax for fit = 667.86 kpcreduced 2 = 1.05K0 = 17.5±8.75 keV cm2K100 = 179.22±16.1 keV cm2 = 0.82±0.06102r(kpc)2×1023×1024×1026×102K(keVcm2)ABELL_3653(19:53:02.960,-52:02:08.82)rmax for fit = 193.84 kpcreduced 2 = 1.25K0 = 174.82±44.38 keV cm2K100 = 172.27±103.03 keV cm2 = 1.18±0.52101102103r(kpc)102103K(keVcm2)MCXC_J2003.5-2323(20:03:26.970,-23:22:57.77)rmax for fit = 543.61 kpcreduced 2 = 1.02K0 = 217.89±91.72 keV cm2K100 = 134.25±149.28 keV cm2 = 0.88±0.47102r(kpc)102K(keVcm2)MCXC_J2011.3-5725(20:11:26.803,-57:25:10.72)rmax for fit = 401.74 kpcreduced 2 = 1.17K0 = 39.44±8.62 keV cm2K100 = 64.58±15.58 keV cm2 = 1.19±0.21Figure C.1 (cont’d)

147

101102r(kpc)101102103K(keVcm2)MCXC_J2014.8-2430(20:14:51.741,-24:30:32.21)rmax for fit = 416.23 kpcreduced 2 = 1.04K0 = 5.1±0.8 keV cm2K100 = 116.63±3.76 keV cm2 = 1.21±0.04102103r(kpc)1032×1023×1024×1026×102K(keVcm2)SPT-CL_J2023-5535(20:23:21.324,-55:35:48.28)rmax for fit = 314.36 kpcreduced 2 = 1.06K0 = 186.13±83.94 keV cm2K100 = 142.24±160.67 keV cm2 = 0.76±0.65102r(kpc)103K(keVcm2)ABELL_3695(20:34:45.220,-35:48:40.30)rmax for fit = 705.17 kpcreduced 2 = 1.03K0 = 307.18±36.62 keV cm2K100 = 41.78±35.31 keV cm2 = 1.56±0.28102r(kpc)102103K(keVcm2)SPT-CLJ2043-5035(20:43:17.535,-50:35:32.32)rmax for fit = 687.49 kpcreduced 2 = 1.14K0 = 15.85±3.14 keV cm2K100 = 82.65±8.55 keV cm2 = 1.24±0.09102r(kpc)102K(keVcm2)MACS_J2046.0-3430(20:46:00.425,-34:30:22.05)rmax for fit = 500.04 kpcreduced 2 = 1.12K0 = 6.48±2.11 keV cm2K100 = 103.51±6.18 keV cm2 = 1.15±0.06102r(kpc)102K(keVcm2)ABELL_3739(21:04:19.151,-41:20:41.53)rmax for fit = 615.47 kpcreduced 2 = 1.08K0 = 81.94±38.15 keV cm2K100 = 150.95±60.83 keV cm2 = 0.82±0.2Figure C.1 (cont’d)

148

102r(kpc)1032×1023×1024×1026×102K(keVcm2)IC_1365(21:13:55.867,2:33:49.64)rmax for fit = 356.9 kpcreduced 2 = 1.04K0 = 160.83±19.73 keV cm2K100 = 71.38±38.39 keV cm2 = 1.34±0.37102r(kpc)1034×1026×102K(keVcm2)ABELL_2355(21:35:16.690,1:25:03.60)rmax for fit = 596.9 kpcreduced 2 = 1.06K0 = 393.29±86.87 keV cm2K100 = 75.52±152.82 keV cm2 = 1.18±0.53101r(kpc)101102K(keVcm2)WBL_671(21:37:08.706,0:26:45.09)rmax for fit = 34.86 kpcreduced 2 = infK0 = 10.89±12.29 keV cm2K100 = 254.08±101.21 keV cm2 = 0.7±0.39101102r(kpc)102103K(keVcm2)MACS_J2140.2-2339(21:40:15.178,-23:39:40.72)rmax for fit = 481.51 kpcreduced 2 = 1.06K0 = 12.93±1.1 keV cm2K100 = 91.53±3.48 keV cm2 = 1.35±0.04101102r(kpc)102K(keVcm2)ABELL_3809(21:46:59.094,-43:53:54.49)rmax for fit = 471.16 kpcreduced 2 = 1.05K0 = 10.28±3.84 keV cm2K100 = 132.96±8.32 keV cm2 = 0.87±0.06101102r(kpc)102103K(keVcm2)ABELL_2384(21:52:21.178,-19:32:51.90)rmax for fit = 354.49 kpcreduced 2 = 1.02K0 = 25.36±2.68 keV cm2K100 = 139.69±6.6 keV cm2 = 1.27±0.06Figure C.1 (cont’d)

149

101102r(kpc)102103K(keVcm2)ABELL_2390(21:53:36.826,17:41:44.38)rmax for fit = 775.64 kpcreduced 2 = 1.03K0 = 14.26±1.93 keV cm2K100 = 151.84±5.09 keV cm2 = 1.07±0.03101102r(kpc)102103104K(keVcm2)ClG_2153.8+3746(21:55:52.284,38:00:22.66)rmax for fit = 142.07 kpcreduced 2 = 1.03K0 = 55.19±6.28 keV cm2K100 = 325.02±34.32 keV cm2 = 1.71±0.18102r(kpc)102103K(keVcm2)ABELL_2409(22:00:52.567,20:58:06.56)rmax for fit = 284.22 kpcreduced 2 = 1.04K0 = 12.42±34.88 keV cm2K100 = 167.99±57.54 keV cm2 = 0.51±0.19101102r(kpc)101102K(keVcm2)ABELL_2415(22:05:38.595,-5:35:29.92)rmax for fit = 205.32 kpcreduced 2 = 1.04K0 = 2.83±0.78 keV cm2K100 = 142.15±6.58 keV cm2 = 1.03±0.05101102r(kpc)101102K(keVcm2)3C_444(22:14:26.966,-17:01:32.33)rmax for fit = 299.0 kpcreduced 2 = 1.05K0 = 0.96±1.15 keV cm2K100 = 151.87±3.52 keV cm2 = 1.02±0.04101102r(kpc)102103K(keVcm2)ABELL_2426(22:14:32.332,-10:22:13.85)rmax for fit = 307.41 kpcreduced 2 = 1.03K0 = 54.82±12.51 keV cm2K100 = 104.6±20.31 keV cm2 = 1.31±0.2Figure C.1 (cont’d)

150

102103r(kpc)103K(keVcm2)MACS_J2214-1359(22:14:57.468,-14:00:09.36)rmax for fit = 928.62 kpcreduced 2 = 1.07K0 = 150.2±23.6 keV cm2K100 = 62.25±24.89 keV cm2 = 1.29±0.2102r(kpc)102103K(keVcm2)ABELL_3854(22:17:45.749,-35:43:26.81)rmax for fit = 702.74 kpcreduced 2 = 1.06K0 = 103.51±18.15 keV cm2K100 = 96.95±24.93 keV cm2 = 1.2±0.15102r(kpc)102103K(keVcm2)MCXC_J2218.6-3853(22:18:39.619,-38:54:06.19)rmax for fit = 590.78 kpcreduced 2 = 1.05K0 = 132.84±15.5 keV cm2K100 = 47.64±17.75 keV cm2 = 1.42±0.22102r(kpc)2×1023×1024×1026×102K(keVcm2)ABELL_2443(22:26:06.485,17:21:55.46)rmax for fit = 399.67 kpcreduced 2 = 1.03K0 = 164.26±42.64 keV cm2K100 = 113.15±83.7 keV cm2 = 0.8±0.37102r(kpc)102K(keVcm2)ABELL_2445(22:26:55.703,25:50:10.47)rmax for fit = 525.84 kpcreduced 2 = 1.05K0 = 69.91±11.29 keV cm2K100 = 87.84±15.91 keV cm2 = 0.99±0.12101102r(kpc)101102103K(keVcm2)ABELL_3880(22:27:54.559,-30:34:34.82)rmax for fit = 364.57 kpcreduced 2 = 1.03K0 = 0.85±0.95 keV cm2K100 = 139.15±4.03 keV cm2 = 0.89±0.03Figure C.1 (cont’d)

151

101102r(kpc)102103K(keVcm2)MACS_J2229.8-2756(22:29:45.358,-27:55:38.42)rmax for fit = 633.7 kpcreduced 2 = 1.08K0 = 7.68±1.38 keV cm2K100 = 93.19±5.1 keV cm2 = 1.29±0.05100101r(kpc)101102K(keVcm2)CGCG_514-050(22:31:20.527,39:21:31.26)rmax for fit = 11.3 kpcreduced 2 = 1.03K0 = 0.93±2.22 keV cm2K100 = 547.8±279.59 keV cm2 = 0.93±0.16101102r(kpc)102K(keVcm2)ABELL_2457(22:35:41.116,1:29:10.28)rmax for fit = 416.31 kpcreduced 2 = 1.06K0 = 24.05±17.82 keV cm2K100 = 181.2±33.33 keV cm2 = 0.7±0.12101102r(kpc)102103K(keVcm2)MACS_J2245.0+2637(22:45:04.656,26:38:03.44)rmax for fit = 561.89 kpcreduced 2 = 1.11K0 = 38.97±6.77 keV cm2K100 = 90.59±13.34 keV cm2 = 1.27±0.15102r(kpc)1034×1026×102K(keVcm2)ABELL_3911(22:46:15.331,-52:43:27.07)rmax for fit = 656.69 kpcreduced 2 = 1.04K0 = 338.38±36.85 keV cm2K100 = 27.58±34.62 keV cm2 = 1.61±0.28102r(kpc)102K(keVcm2)ABELL_2485(22:48:30.980,-16:06:28.26)rmax for fit = 591.34 kpcreduced 2 = 1.11K0 = 74.81±26.49 keV cm2K100 = 123.03±41.71 keV cm2 = 0.96±0.19Figure C.1 (cont’d)

152

101102103r(kpc)102103K(keVcm2)ABELL_S1063(22:48:44.294,-44:31:48.36)rmax for fit = 479.37 kpcreduced 2 = 1.03K0 = 78.78±19.91 keV cm2K100 = 127.41±31.16 keV cm2 = 0.87±0.17101102r(kpc)102103K(keVcm2)ABELL_3921(22:49:57.828,-64:25:42.17)rmax for fit = 642.83 kpcreduced 2 = 1.02K0 = 75.12±14.85 keV cm2K100 = 162.52±20.75 keV cm2 = 0.79±0.07102103r(kpc)103K(keVcm2)ABELL_2507(22:56:52.590,5:30:15.51)rmax for fit = 966.18 kpcreduced 2 = 1.05K0 = 198.23±27.12 keV cm2K100 = 36.57±18.95 keV cm2 = 1.74±0.18101102103r(kpc)102103K(keVcm2)ABELL_2537(23:08:22.313,-2:11:29.87)rmax for fit = 792.45 kpcreduced 2 = 1.04K0 = 78.81±12.8 keV cm2K100 = 110.22±21.6 keV cm2 = 1.1±0.18102103r(kpc)102103K(keVcm2)MCXC_J2311.5+0338(23:11:33.230,3:38:08.23)rmax for fit = 1268.86 kpcreduced 2 = 1.03K0 = 85.3±14.56 keV cm2K100 = 121.67±17.02 keV cm2 = 1.19±0.07101102r(kpc)102K(keVcm2)ABELL_2550(23:11:35.122,-21:44:41.53)rmax for fit = 253.41 kpcreduced 2 = 1.06K0 = 0.84±2.98 keV cm2K100 = 114.2±5.2 keV cm2 = 0.71±0.06Figure C.1 (cont’d)

153

101102r(kpc)102K(keVcm2)ABELL_2556(23:13:01.414,-21:38:04.45)rmax for fit = 317.93 kpcreduced 2 = 1.03K0 = 12.04±1.36 keV cm2K100 = 123.65±4.08 keV cm2 = 1.08±0.04101102r(kpc)101102K(keVcm2)ABELL_S1101(23:13:58.764,-42:43:34.72)rmax for fit = 429.63 kpcreduced 2 = 1.01K0 = 11.53±0.5 keV cm2K100 = 77.48±1.23 keV cm2 = 1.13±0.02100101r(kpc)101K(keVcm2)NGC_7618(23:19:48.021,42:51:11.68)rmax for fit = 47.48 kpcreduced 2 = 1.06K0 = 2.04±0.97 keV cm2K100 = 54.09±3.68 keV cm2 = 0.51±0.06101102r(kpc)101102K(keVcm2)ABELL_2597(23:25:19.778,-12:07:27.62)rmax for fit = 315.68 kpcreduced 2 = 1.03K0 = 9.5±0.29 keV cm2K100 = 99.23±1.04 keV cm2 = 1.21±0.01101102r(kpc)102103K(keVcm2)RCS_J2327-0204(23:27:27.523,-2:04:39.00)rmax for fit = 346.46 kpcreduced 2 = 1.06K0 = 45.27±7.17 keV cm2K100 = 212.71±14.88 keV cm2 = 1.22±0.09101102r(kpc)102K(keVcm2)ABELL_2626(23:36:30.451,21:08:47.36)rmax for fit = 220.24 kpcreduced 2 = 1.03K0 = 13.53±2.26 keV cm2K100 = 123.83±4.38 keV cm2 = 0.86±0.05APPENDIX D

ACCEPT 2.0 MORPHOLOGICAL PROPERTIES

154

Table D.1: Morphological properties for ACCEPT 2.0 clusters Morphological properties, global temperatures, and global
luminosities for ACCEPT 2.0 clusters with deprojected entropy proﬁles. Column 1: Cluster Name in ACCEPT 2.0; Column 2-3:
concentration and error using R500; Column 4-5: concentration and error with r = 500 kpc; Column 6: centroid shift calculated from
the data; Column 7: centroid shift from 100 bootstrapped versions of the original data; Column 8: dispersion in the centroid shift from
the simulated data; Column 9: power ratio P3/P0 calculated from the data; Column 10: power ratio from 100 bootstrapped versions of
the original data; Column 11: dispersion in the power ratio from the simulated data; Column 12-13: Best ﬁt global temperatures and
errors; Column 14-15: Best ﬁt global luminosity and errors.

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

21.100 21.200 1.170 5.85 0.39 0.20
0.521 5.18 0.40 1.85
1.000
0.506
0.421 4.71 0.30 0.74
0.448 4.61 0.63 0.07
3.610
0.202 5.89 0.40 6.23
0.351
6.410
0.779 4.77 0.26 0.63
0.394 10.48 0.43 14.30
2.200
0.373 9.73 0.74 18.40
0.559
1.370
0.743 7.82 0.60 9.83
1.890 9.80 1.23 8.31
8.750
0.264
0.402 7.95 0.74 7.71
0.087 4.24 0.23 0.81
0.134

1.160
0.692
3.550
0.387
6.650
2.230
0.735
1.550
8.920
0.494
0.161

LX
δLX
(1044erg s−1)
0.01
0.07
0.03
0.00
0.20
0.02
0.18
0.40
0.38
0.30
0.24
0.03

Cluster

ABELL_2717
NSCS_J000619+105206
ZwCl_0008.8+5215
ABELL_2734_NED01
MACS_J0011.7-1523
ABELL_0013
ABELL_2744
Cl_0016+16
MACS_J0025.4-1222
PLCKESZ_G304.84-41.42
ABELL_2813
ZwCl_0040.8+2404

0.103 0.007 0.219 0.007 0.116 0.116 0.001
0.163 0.013 0.397 0.025 0.009 0.010 0.001
0.098 0.017 NaN NaN 0.180 0.179 0.004
0.146 0.007 0.589 0.034 0.027 0.027 0.001
0.192 0.011 0.337 0.016 0.010 0.010 0.001
0.079 0.006 0.199 0.008 0.040 0.039 0.003
0.062 0.004 0.102 0.003 0.044 0.040 0.003
0.132 0.008 0.151 0.008 0.020 0.018 0.003
0.102 0.010 0.197 0.014 0.052 0.047 0.005
0.251 0.018 0.253 0.018 0.047 0.047 0.003
0.160 0.012 0.213 0.014 0.011 0.015 0.007
0.227 0.008 0.383 0.012 0.005 0.005 0.000

155

Table D.1 (cont’d)
Cluster

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

0.491
1.200

0.511 0.053 NaN NaN 0.010 0.011 0.002
ABELL_0098N
0.307 0.027 NaN NaN 0.016 0.016 0.002
ESO_351-_G_021
ABELL_0141
0.250 0.025 0.242 0.024 0.053 0.042 0.009
MaxBCG_J016.70077+01.05926 0.252 0.009 0.556 0.021 0.005 0.005 0.000
0.065 0.005 0.127 0.006 0.034 0.025 0.009
CIZA_J0107.7+5408
IC_1633
0.284 0.022 NaN NaN 0.073 0.074 0.002
0.209 0.015 0.209 0.015 0.068 0.065 0.004
ABELL_2895
0.303 0.037 NaN NaN 0.020 0.021 0.002
UGC_00842
ABELL_0193
0.067 0.006 0.139 0.005 0.023 0.021 0.002
0.140 0.008 0.171 0.009 0.027 0.025 0.002
ABELL_0209
Abell_222
0.064 0.012 0.265 0.020 0.080 0.073 0.005
0.156 0.013 0.444 0.036 0.019 0.019 0.002
Abell_223
0.181 0.013 0.256 0.016 0.031 0.027 0.004
ABELL_0267
ABELL_0262
0.066 0.004 0.191 0.002 0.047 0.047 0.000
0.038 0.001 0.702 0.250 0.005 0.009 0.003
NGC_0766
MCXC_J0220.9-3829
0.234 0.020 0.492 0.043 0.006 0.007 0.002
0.039 0.001 NaN NaN 0.040 0.037 0.007
MZ_10451
0.089 0.006 0.163 0.008 0.048 0.043 0.006
ABELL_0370
MACS_J0242.6-2132
0.388 0.025 0.429 0.027 0.002 0.002 0.001
0.122 0.011 0.189 0.014 0.159 0.158 0.003
ABELL_S0295

156

0.387 3.78 0.39 0.32
0.364
1.110
0.790 1.28 0.05 0.03
16.600 18.000 3.400 6.58 0.77 3.13
0.025
0.037 4.57 0.27 2.12
0.406 7.68 0.37 3.90
1.600
1.780
0.465 3.26 0.36 0.08
0.799 8.39 0.86 4.96
2.630
0.803 1.67 0.08 0.04
2.240
5.390
0.655 3.64 0.14 0.39
0.279 8.55 0.66 6.57
0.386
2.640
0.954 4.14 0.27 1.64
0.704 5.47 0.50 1.38
1.230
0.249 7.57 0.63 4.34
0.202
7.330
0.212 2.26 0.03 0.02
3.050 0.17 0.01 0.04
0.616
0.018
0.161 4.35 0.37 2.34
2.160 0.73 0.04 0.01
0.890
0.336 8.75 0.46 7.42
0.580
0.285
0.189 5.75 0.77 4.96
0.505 7.35 0.71 9.68
0.608

0.045
1.660
1.760
2.500
2.160
5.440
0.422
2.940
1.410
0.348
7.340
3.030
0.171
1.960
0.660
0.306
0.788

LX
δLX
(1044erg s−1)
0.02
0.00
0.13
0.07
0.06
0.00
0.15
0.00
0.01
0.17
0.07
0.06
0.11
0.00
0.06
0.14
0.00
0.12
0.31
0.33

Table D.1 (cont’d)
Cluster

ABELL_0376
ABELL_0383
NGC_1132
ABELL_0402
ABELL_0401
MCXC_J0301.6+0155
MCXC_J0303.7-7752
MACS_J0308.9+2645
ABELL_3094
ABELL_3120
UGC_02748
ABELL_3126
ABELL_3128
MCXC_J0331.1-2100
3C_089
ABELL_3140
MCXC_J0338.6+0958
MCXC_J0340.8-4542
MCXC_J0352.9+1941
MACS_J0358.8-2955

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

0.169 0.019 NaN NaN 0.038 0.038 0.003
0.216 0.008 0.409 0.012 0.004 0.004 0.001
0.223 0.043 0.350 0.029 0.046 0.046 0.003
0.358 0.026 0.313 0.023 0.012 0.012 0.002
0.046 0.002 0.184 0.001 0.015 0.011 0.003
0.222 0.014 0.446 0.026 0.008 0.008 0.001
0.272 0.015 0.193 0.012 0.025 0.025 0.003
0.239 0.013 0.215 0.012 0.014 0.013 0.003
0.073 0.013 NaN NaN 0.053 0.052 0.004
NaN NaN NaN NaN 0.009 0.009 0.002
0.386 0.039 NaN NaN 0.018 0.019 0.002
0.088 0.009 0.360 0.023 0.022 0.020 0.004
0.111 0.015 0.214 0.016 0.168 0.168 0.003
0.334 0.016 0.423 0.020 0.008 0.008 0.001
0.185 0.013 NaN NaN 0.040 0.039 0.002
NaN NaN 0.536 0.036 0.010 0.008 0.002
0.060 0.002 0.308 0.002 0.024 0.024 0.000
NaN NaN 0.014 0.001 0.100 0.099 0.005
0.221 0.008 0.505 0.018 0.004 0.004 0.000
0.133 0.008 0.242 0.011 0.069 0.069 0.001

0.651
0.560
5.070
1.970
0.883
0.166
0.915
0.350
0.153
0.534
0.041
0.320
5.490
0.043
0.161
0.466
0.037
0.018
0.034
1.740

0.781
0.575
5.580
2.040
0.878
0.240
1.160
0.464
0.302
0.671
0.161
0.362
5.420
0.098
0.269
0.503
0.038
0.304
0.062
1.890

157

LX
δLX
(1044erg s−1)
0.01
0.06
0.00
0.20
0.02
0.08
0.21
0.32
0.01
0.01
0.00
0.04
0.01
0.10
0.02
0.02
0.00
0.02
0.04
0.37

0.355 4.53 0.33 0.50
0.125 5.31 0.23 2.02
1.790 1.04 0.02 0.01
0.834 8.23 1.24 4.74
0.060 7.57 0.10 4.40
0.171 4.45 0.33 1.67
0.551 9.34 0.89 7.38
0.302 9.66 1.05 11.60
0.210 3.11 0.21 0.23
0.446 4.33 0.25 0.10
0.141 11.99 1.11 0.01
0.217 4.99 0.31 1.19
1.560 3.14 0.19 0.31
0.077 5.86 0.53 2.63
0.186 4.53 0.33 0.46
0.258 5.46 2.33 0.12
0.008 3.62 0.03 0.48
0.277 2.66 0.30 0.18
0.047 3.14 0.16 0.98
0.488 8.75 0.49 14.00

Table D.1 (cont’d)
Cluster

ABELL_0478
MACS_J0416.1-2403
MACS_J0417.5-1154
MCXC_J0425.8-0833
ABELL_S0463
MACS_J0429.6-0253
ABELL_0496
MCXC_J0437.1+0043
MCXC_J0439.0+0715
MCXC_J0439.0+0520
ABELL_3292
WEIN_051
ESO_552-_G_020
ABELL_3322
MCXC_J0510.7-0801
ABELL_S0520
ABELL_3343
MCXC_J0528.2-2942
RBS_0653
PLCKESZ_G286.58-31.25

0.135 0.002 0.268 0.002 0.004 0.004 0.000
0.158 0.013 0.193 0.015 0.071 0.070 0.005
0.219 0.008 0.272 0.009 0.037 0.037 0.001
0.186 0.010 0.473 0.023 0.022 0.022 0.001
0.439 0.136 NaN NaN 0.195 0.194 0.003
0.383 0.025 0.404 0.027 0.009 0.009 0.001
0.080 0.002 0.218 0.002 0.013 0.013 0.000
0.234 0.013 0.366 0.020 0.009 0.009 0.001
0.181 0.012 0.279 0.015 0.013 0.012 0.002
0.303 0.017 0.401 0.021 0.004 0.004 0.001
0.097 0.012 0.478 0.044 0.022 0.019 0.002
0.068 0.005 0.095 0.004 0.050 0.049 0.003
0.207 0.018 NaN NaN 0.031 0.031 0.002
0.217 0.017 0.272 0.019 0.017 0.015 0.002
0.112 0.010 0.166 0.010 0.048 0.047 0.005
0.099 0.011 0.118 0.012 0.075 0.067 0.008
0.167 0.014 0.301 0.021 0.009 0.008 0.002
0.099 0.014 0.655 0.092 0.027 0.026 0.003
0.160 0.008 0.264 0.009 0.071 0.075 0.001
0.104 0.011 0.219 0.018 0.023 0.018 0.006

0.017
1.690
6.830
5.320
1.080
0.361
0.810
0.229
2.930
0.045
1.090
0.596
0.039
0.022
0.480
0.630
0.772
0.262
0.583
0.227

0.017
1.980
7.160
5.430
1.130
0.477
0.805
0.251
3.060
0.090
1.180
0.614
0.148
0.242
0.661
1.050
0.926
0.505
0.600
0.465

158

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

LX
δLX
(1044erg s−1)
0.04
0.36
0.42
0.02
0.00
0.27
0.00
0.14
0.17
0.10
0.08
0.01
0.00
0.14
0.22
0.21
0.09
0.09
0.12
0.13

0.008 7.61 0.17 5.86
0.938 8.66 0.73 9.94
0.714 11.32 0.50 24.50
0.619 3.07 0.16 0.37
0.421 2.83 0.09 0.09
0.262 7.00 0.90 5.72
0.061 4.84 0.13 0.19
0.157 6.83 0.48 5.14
0.648 6.53 0.53 5.46
0.082 5.02 0.48 1.89
0.629 4.20 0.30 1.75
0.263 8.10 0.56 0.39
0.166 8.23 1.24 0.07
0.221 6.65 0.60 3.87
0.363 7.15 0.43 8.68
0.777 8.27 0.73 6.96
0.429 6.43 0.53 3.08
0.432 4.49 0.31 1.62
0.146 9.15 0.34 8.20
0.423 6.48 0.54 3.85

Table D.1 (cont’d)
Cluster

ABELL_0545
MCXC_J0532.9-3701
ESO3060170-A
MCXC_J0547.0-3904
ABELL_3364
ABELL_0548A
ABELL_0550
MACS_J0553.4-3342
ABELL_3378
CIZA_J0616.3-2156
ABELL_S0579
G139.59+24.18
ABELL_3391
ABELL_3395_SW
ABELL_3399
PLCKESZ_G167.65+17.64
ABELL_S0592
ABELL_3404
ABELL_0562
ABELL_0576

0.092 0.005 0.151 0.005 0.067 0.067 0.001
0.299 0.016 0.271 0.015 0.011 0.010 0.002
0.172 0.011 0.417 0.015 0.022 0.022 0.001
0.421 0.033 0.530 0.047 0.010 0.010 0.002
0.130 0.008 0.211 0.010 0.022 0.019 0.005
0.211 0.037 NaN NaN 0.031 0.031 0.002
0.080 0.011 0.226 0.014 0.052 0.050 0.004
0.126 0.006 0.132 0.006 0.042 0.041 0.002
0.201 0.015 0.377 0.020 0.021 0.021 0.002
0.109 0.012 0.220 0.017 0.034 0.033 0.003
0.096 0.014 0.337 0.030 0.042 0.040 0.003
0.281 0.017 0.314 0.018 0.036 0.035 0.002
0.079 0.006 0.318 0.014 0.017 0.017 0.001
0.076 0.008 NaN NaN 0.029 0.029 0.001
0.156 0.016 0.265 0.020 0.075 0.074 0.004
0.083 0.010 0.145 0.011 0.020 0.020 0.003
0.203 0.009 0.259 0.011 0.028 0.028 0.001
0.231 0.013 0.247 0.014 0.040 0.039 0.003
0.144 0.017 NaN NaN 0.025 0.025 0.003
0.072 0.005 0.141 0.004 0.037 0.037 0.002

159

5.990
1.160
0.117
1.850
0.214
0.644

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

4.960
0.219
0.049
0.383
0.416
0.697
0.508
3.130
0.366
0.352
2.420
7.960
1.300

0.457 7.37 0.31 3.50
5.000
0.173 8.64 0.84 7.20
0.112
0.040 2.67 0.10 0.17
0.021
0.295 5.19 0.70 0.98
0.243
0.237 7.19 0.55 3.19
0.341
0.518 3.07 0.16 0.25
0.571
0.304 5.67 0.30 2.15
0.390
0.656 10.46 0.68 15.00
2.960
0.224 4.78 0.27 3.17
0.296
0.287 7.24 0.51 3.06
0.100
0.986 4.79 0.35 1.50
1.880
1.520 7.19 0.64 8.23
7.790
1.230
0.323 8.55 0.66 1.01
30.100 30.100 1.490 2.26 0.03 0.61
1.510 6.76 0.45 3.38
5.720
0.983
0.715 6.18 0.41 4.90
0.087 8.58 0.65 8.34
0.055
0.643 7.85 0.64 6.50
1.570
0.133
0.183 2.94 0.19 0.38
0.203 4.40 0.15 0.21
0.638

LX
δLX
(1044erg s−1)
0.05
0.21
0.01
0.06
0.08
0.01
0.06
0.24
0.10
0.07
0.06
0.30
0.02
0.02
0.07
0.11
0.20
0.16
0.02
0.00

Table D.1 (cont’d)
Cluster

ABELL_0578
ABELL_0586
ZwCl_0735.7+7421
MACS_J0744.9+3927
PKS_0745-19
ABELL_0598
ABELL_0611
SDSS-C4_3062
ABELL_0644
MCXC_J0819.6+6336
UGCl_120
ZwCl_0823.2+0425
2MFGC_06756
ABELL_3411
NSC_J084254+292723
ABELL_0697
ZwCl_0857.9+2107
SDSS_+137.3+11.0+0.18
HCG_037
2MASSi_J0913454+405628

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

0.592 2.55 0.23 0.14
NaN NaN NaN NaN 0.083 0.083 0.007
0.304 6.24 0.40 3.38
0.125 0.008 0.305 0.013 0.005 0.006 0.002
0.070 6.47 0.11 3.97
0.114 0.004 0.328 0.004 0.005 0.005 0.000
0.775 7.80 0.63 15.00
0.285 0.017 0.342 0.020 0.024 0.024 0.002
0.021 8.55 0.73 5.82
0.142 0.001 0.333 0.002 0.009 0.009 0.000
0.274 5.05 0.54 1.69
0.294 0.019 0.489 0.034 0.029 0.029 0.001
0.181 8.55 0.73 5.00
0.264 0.011 0.324 0.013 0.006 0.006 0.001
0.615 3.76 0.54 0.19
NaN NaN NaN NaN 0.026 0.026 0.005
0.037 4.76 0.75 2.86
0.065 0.003 0.255 0.004 0.027 0.026 0.001
0.630 3.50 0.32 0.74
0.197 0.019 0.462 0.041 0.025 0.025 0.002
1.440 1.90 0.12 0.05
NaN NaN NaN NaN 0.023 0.023 0.004
0.787 4.66 0.51 1.72
0.188 0.022 0.943 0.507 0.006 0.007 0.002
0.033 5.05 0.23 2.71
0.193 0.006 0.439 0.011 0.005 0.005 0.000
0.164 6.25 0.31 2.87
0.065 0.008 0.241 0.015 0.146 0.143 0.005
0.115 5.89 0.44 1.51
0.300 0.014 0.470 0.022 0.005 0.005 0.001
0.387 11.99 1.11 13.20
0.293 0.013 0.155 0.009 0.010 0.009 0.003
0.269 0.010 0.531 0.020 0.002 0.002 0.000
0.064 4.39 0.26 2.15
0.097 0.008 0.298 0.013 0.312 0.310 0.003 141.000 140.000 5.900 5.38 0.31 2.70
0.007 0.001 0.585 0.214 0.012 0.015 0.005
9.790 0.96 0.24 0.00
0.034 6.42 0.59 4.90
0.372 0.015 0.492 0.021 0.002 0.002 0.000

0.740
0.792
0.449
2.810
0.435
0.600
0.308
0.525
0.143
1.060
2.410
1.400
0.062
0.197
0.181
0.534
0.111

0.632
0.733
0.450
2.700
0.438
0.482
0.291
0.007
0.143
0.816
1.810
1.140
0.055
0.105
0.114
0.361
0.093

LX
δLX
(1044erg s−1)
0.01
0.09
0.03
0.65
0.03
0.08
0.13
0.04
0.03
0.04
0.01
0.11
0.06
0.05
0.05
0.32
0.08
0.08
0.00
0.20

0.296
0.010

8.070
0.038

160

Table D.1 (cont’d)
Cluster

ABELL_0773
Hydra_A
NSC_J092017+303027
ABELL_0795
UGC_05088_GROUP
WHL_J093820.9+520243
ABELL_0868
GALEX_J094712.4+762313
ZwCl_0949.6+5207
PLCKESZ_G264.41+19.48
HCG_042
MCXC_J1000.5+4409
ZwCl_1006.1+1201
MCXC_J1010.5-1239
ABELL_0963
MCXC_J1022.0+3830
ABELL_0980
BLOX_J1023.6+0411.1
ABELL_3444
ABELL_1033

0.119 0.007 0.195 0.009 0.024 0.020 0.004
0.067 0.002 0.272 0.002 0.014 0.014 0.000
0.142 0.017 0.254 0.026 0.598 0.585 0.020
0.179 0.008 0.453 0.018 0.013 0.013 0.001
0.144 0.034 NaN NaN 0.047 0.047 0.004
0.158 0.015 0.316 0.023 0.098 0.098 0.002
0.060 0.013 0.218 0.016 0.043 0.035 0.006
0.351 0.011 0.424 0.013 0.001 0.002 0.000
0.135 0.005 0.467 0.013 0.029 0.029 0.001
0.204 0.016 0.263 0.020 0.007 0.008 0.001
0.196 0.020 0.480 0.040 0.017 0.016 0.002
0.206 0.020 0.551 0.052 0.067 0.067 0.003
0.097 0.008 0.301 0.015 0.086 0.079 0.005
0.127 0.012 0.236 0.015 0.098 0.098 0.002
0.130 0.005 0.292 0.008 0.015 0.015 0.001
NaN NaN NaN NaN 0.014 0.013 0.002
0.126 0.011 0.240 0.016 0.019 0.019 0.002
0.231 0.005 0.338 0.006 0.010 0.011 0.000
0.247 0.007 0.379 0.009 0.006 0.006 0.001
0.067 0.005 0.362 0.011 0.056 0.055 0.001

0.326
4.540
5.610
0.887
0.562
1.360
0.524
0.010
7.640
0.176
2.810
2.370
0.828
0.335
1.180
4.750
0.216
0.121
0.223
7.930

0.400
4.540
5.690
0.927
1.070
1.400
0.640
0.020
7.700
0.354
2.840
2.670
0.914
0.524
1.220
4.580
0.365
0.122
0.245
8.040

161

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

LX
δLX
(1044erg s−1)
0.14
0.00
0.13
0.05
0.00
0.19
0.09
0.19
0.05
0.13
0.00
0.07
0.07
0.09
0.08
0.00
0.09
0.14
0.13
0.03

0.240 8.10 0.56 6.11
0.063 4.08 0.03 1.12
1.810 6.35 0.66 3.13
0.275 5.00 0.30 1.85
0.979 2.33 0.23 0.01
0.673 6.42 0.50 5.66
0.403 4.41 0.22 2.58
0.015 8.46 0.57 8.35
0.440 5.64 0.21 2.26
0.347 7.50 0.70 3.76
0.888 0.82 0.05 0.00
0.948 3.28 0.27 1.03
0.328 5.86 0.33 2.85
0.347 6.48 0.40 4.22
0.237 6.49 0.32 4.63
1.300 2.66 0.24 0.05
0.316 6.54 0.53 3.07
0.041 8.75 0.37 9.03
0.090 7.92 0.45 7.84
0.738 5.61 0.18 1.47

Table D.1 (cont’d)
Cluster

ABELL_1068
NGC_3402_GROUP
BLOX_J1056.9-0337.3
MACS_J1108.9+0906
NGC_3551
1RXS_J111039.6+284316
ABELL_1190
ABELL_1201
ABELL_1204
MACS_J1115.8+0129
HCG_051
ABELL_1240
MCXC_J1130.0+3637
ABELL_1285
ABELL_1300
WHL_J114224.8+583205
ABELL_1361
SDSS-C4-DR3_3018
ABELL_1413
ABELL_1423

0.243 0.007 0.409 0.010 0.003 0.003 0.000
0.122 0.012 0.411 0.013 0.009 0.010 0.001
0.375 0.045 0.402 0.048 0.280 0.268 0.007
0.164 0.019 0.255 0.027 0.032 0.028 0.004
0.324 0.052 NaN NaN 0.017 0.018 0.004
NaN NaN NaN NaN 0.071 0.069 0.007
0.065 0.015 0.816 0.198 0.017 0.017 0.004
0.111 0.008 0.298 0.010 0.028 0.028 0.001
0.255 0.010 0.422 0.015 0.003 0.003 0.000
0.349 0.014 0.345 0.014 0.008 0.008 0.001
0.312 0.050 NaN NaN 0.050 0.050 0.004
NaN NaN NaN NaN 0.059 0.060 0.010
0.445 0.048 NaN NaN 0.016 0.016 0.002
0.061 0.009 0.212 0.010 0.035 0.030 0.005
0.544 0.037 0.204 0.013 0.066 0.064 0.002
0.079 0.008 0.096 0.008 0.080 0.080 0.006
0.382 0.023 0.396 0.030 0.005 0.006 0.001
0.019 0.002 0.020 0.001 0.036 0.037 0.005
0.092 0.003 0.239 0.003 0.007 0.007 0.000
0.172 0.012 0.307 0.016 0.015 0.015 0.002

162

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

0.019
0.075

0.014 4.96 0.25 1.87
0.011
0.040
0.056 0.82 0.01 0.01
11.000 11.600 2.890 7.49 1.08 8.11
0.220
0.567 6.86 0.74 6.09
0.361 1.62 0.06 0.02
0.286
4.840
1.580 1.29 0.09 0.01
0.573 3.60 0.19 0.58
0.690
0.622 5.69 0.21 2.54
5.040
0.159
0.082 4.33 0.28 1.61
0.060 9.18 0.73 8.71
0.042
1.510
0.860 1.32 0.03 0.01
3.170 4.16 0.42 0.48
10.200
0.634 1.74 0.08 0.07
1.760
0.723
0.290 5.52 0.21 2.25
0.781 11.26 1.17 10.50
2.060
1.800
1.020 8.86 0.68 8.37
0.221 17.00 10.00 0.68
0.252
0.523 2.64 0.17 0.09
1.470
0.557
0.077 7.41 0.17 4.23
0.190 4.33 0.26 0.32
0.445

0.574
0.424
5.060
0.951
4.900
0.171
0.081
1.760
9.950
1.950
0.846
2.160
2.160
0.363
1.540
0.565
0.496

LX
δLX
(1044erg s−1)
0.04
0.00
0.43
0.29
0.00
0.00
0.03
0.05
0.07
0.25
0.00
0.03
0.00
0.04
0.26
0.20
0.16
0.00
0.04
0.01

Table D.1 (cont’d)
Cluster

SDSS-C4-DR3_3144
ABELL_1446
MACS_J1206.2-0847
MCXC_J1215.4-3900
NGC_4325_GROUP
NSCS_J122648+215157
MCXC_J1234.2+0947
MESSIER_089
ABELL_1569
ABELL_1576
Centaurus_Cluster
NGC_4759_GROUP
ABELL_3528B
NGC_4782-3
ABELL_1644
ABELL_3532
WHL_J125933.4+600409
ABELL_1664
ABELL_1668
ABELL_1689

0.357 0.023 0.911 0.236 0.003 0.004 0.001
0.055 0.008 0.692 0.063 0.034 0.034 0.001
0.273 0.014 0.228 0.013 0.028 0.028 0.002
0.073 0.014 0.305 0.033 0.033 0.028 0.007
0.053 0.010 0.396 0.012 0.010 0.010 0.001
0.127 0.013 NaN NaN 0.214 0.212 0.004
0.172 0.038 NaN NaN 0.101 0.093 0.020
0.040 0.000 0.503 0.019 0.011 0.011 0.001
0.067 0.017 NaN NaN 0.020 0.021 0.002
0.207 0.013 0.283 0.017 0.016 0.015 0.002
0.109 0.002 0.204 0.001 0.023 0.023 0.000
0.082 0.005 0.484 0.010 0.019 0.019 0.001
0.344 0.022 NaN NaN 0.016 0.016 0.002
0.450 0.054 NaN NaN 0.039 0.039 0.002
0.111 0.007 0.157 0.003 0.032 0.032 0.001
0.100 0.009 0.889 0.246 0.045 0.044 0.003
0.080 0.014 0.160 0.017 0.094 0.089 0.006
0.166 0.006 0.404 0.011 0.009 0.009 0.001
0.283 0.016 0.367 0.020 0.033 0.033 0.002
0.125 0.002 0.294 0.003 0.004 0.004 0.000

0.056
0.566
2.640
2.610
0.355
9.120
4.680
1.050
1.810
1.530
0.336
0.003
1.790
5.200
5.210
3.160
3.430
0.568
1.190
0.030

0.252
0.603
2.660
2.960
0.371
9.760
4.570
1.080
1.770
1.610
0.339
0.009
1.880
5.560
5.190
3.190
3.780
0.585
1.310
0.033

163

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

LX
δLX
(1044erg s−1)
0.01
0.02
0.56
0.04
0.00
0.08
0.11
0.00
0.02
0.11
0.00
0.00
0.02
0.00
0.01
0.03
0.15
0.04
0.02
0.11

0.192 1.77 0.08 0.07
0.204 3.53 0.12 0.69
0.871 11.37 1.42 19.30
1.320 5.50 0.36 1.60
0.129 0.98 0.02 0.02
3.190 4.78 0.47 1.62
2.490 4.55 0.48 1.74
0.264 3.00 10.00 0.00
0.594 6.03 1.00 0.25
0.551 8.00 0.77 3.02
0.017 3.00 10.00 0.00
0.009 1.38 0.03 0.00
0.562 7.57 0.63 0.57
1.710 1.05 0.20 0.00
0.339 4.12 0.87 0.80
0.783 6.08 0.77 0.86
1.430 6.89 0.52 4.09
0.126 5.02 0.21 1.91
0.507 3.33 0.29 0.30
0.015 9.95 0.22 8.92

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

Table D.1 (cont’d)
Cluster

WHL_J131505.2+514902
NGC_5044
NGC_5098_GROUP
NGC_5129
ABELL_1736
ABELL_3558
SSGC_081
a1750ss
ABELL_1750C
ABELL_1750N
SC_1329-313
2MASX_J13312961+1107566
ABELL_3560
ABELL_3562
ABELL_1763
ABELL_1775
ABELL_3571
LCDCS_0829
ABELL_1795
NSCS_J135021+094042

0.155 0.011 0.196 0.013 0.010 0.011 0.004
0.054 0.009 0.206 0.002 0.024 0.024 0.000
0.187 0.026 NaN NaN 0.011 0.011 0.001
0.321 0.032 NaN NaN 0.012 0.012 0.003
0.059 0.018 0.195 0.010 0.039 0.040 0.008
0.089 0.004 0.122 0.003 0.036 0.036 0.001
0.099 0.012 0.296 0.015 0.034 0.034 0.002
NaN NaN 0.013 0.001 0.049 0.046 0.007
0.117 0.013 NaN NaN 0.028 0.028 0.002
0.182 0.027 NaN NaN 0.031 0.032 0.003
0.068 0.016 NaN NaN 0.050 0.047 0.007
0.219 0.077 NaN NaN 0.013 0.016 0.006
0.084 0.010 0.300 0.021 0.029 0.028 0.003
0.074 0.007 0.251 0.009 0.015 0.015 0.002
0.094 0.008 0.158 0.009 0.040 0.040 0.003
0.045 0.007 0.235 0.004 0.063 0.063 0.001
0.069 0.002 0.096 0.001 0.083 0.083 0.001
0.349 0.005 0.376 0.005 0.017 0.016 0.000
0.078 0.002 0.248 0.002 0.009 0.010 0.000
0.321 0.015 0.508 0.026 0.005 0.005 0.000

164

1.060
0.122
0.328
0.681
6.660
8.950
9.130
0.894
2.950
0.158
1.160

0.529 8.76 0.77 7.12
0.948
0.023 1.32 0.03 0.00
0.120
0.213 1.07 0.02 0.02
0.277
0.496 0.75 0.02 0.01
0.398
0.812 2.82 0.67 0.62
6.520
0.596 7.44 0.30 0.60
8.860
1.090 8.32 0.22 0.41
9.040
0.761 2.40 0.20 0.13
0.659
0.707 4.43 0.25 0.44
2.760
0.155 3.59 0.23 0.44
0.006
0.601 6.50 0.43 0.26
1.070
14.000 18.400 11.400 0.64 0.04 0.01
1.330 8.75 0.46 0.18
8.370
6.150
0.567 4.70 0.26 0.81
0.406 7.67 0.59 7.19
0.701
1.450
0.140 5.47 1.02 0.90
0.172 7.76 0.27 0.55
3.550
0.060 13.75 0.53 23.90
0.434
1.120
0.047 6.13 0.10 1.88
0.093 6.24 0.40 0.39
0.065

8.410
6.190
0.741
1.460
3.530
0.434
1.120
0.108

LX
δLX
(1044erg s−1)
0.14
0.00
0.00
0.00
0.01
0.01
0.01
0.02
0.02
0.02
0.01
0.00
0.00
0.02
0.19
0.01
0.01
0.29
0.01
0.02

Table D.1 (cont’d)
Cluster

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

0.490
0.689
0.452
0.132
0.468

0.802 0.155 0.685 0.091 0.013 0.013 0.002
MACS_J1359.2-1929
0.114 0.018 NaN NaN 0.012 0.014 0.003
ABELL_1831
0.255 0.013 0.358 0.017 0.011 0.011 0.001
WHL_J135949.5+623047
0.312 0.006 0.352 0.007 0.010 0.010 0.000
ABELL_1835
NaN NaN NaN NaN 0.022 0.021 0.003
A1882a
0.200 0.032 0.623 0.112 0.042 0.040 0.005
WHL_J141623.8+444528
GMBCG_J215.94948+24.07846 0.307 0.010 0.445 0.014 0.002 0.002 0.000
0.115 0.005 0.206 0.006 0.063 0.061 0.003
ABELL_1914
WHL_J142716.1+440730
0.683 0.069 0.425 0.029 0.010 0.010 0.001
0.256 0.020 0.557 0.049 0.004 0.005 0.001
MACS_J1427.6-2521
ABELL_1930
0.225 0.012 0.615 0.041 0.003 0.004 0.001
0.120 0.014 0.335 0.025 0.027 0.026 0.003
ABELL_1942_AND_CLUMP
0.083 0.009 NaN NaN 0.059 0.051 0.006
WBL_518
NSCS_J144726+082824
NaN NaN 0.526 0.027 0.002 0.002 0.001
0.150 0.006 0.338 0.007 0.011 0.011 0.000
ABELL_1991
NSCS_J145715+222009
0.176 0.005 0.419 0.009 0.006 0.006 0.000
0.251 0.009 0.409 0.012 0.015 0.015 0.001
ABELL_S0780
0.227 0.009 0.327 0.011 0.005 0.005 0.001
ABELL_2009
WHL_J150407.5-024816
0.265 0.004 0.434 0.008 0.004 0.004 0.000
0.056 0.007 0.087 0.005 0.062 0.052 0.010
MCXC_J1514.9-1523

165

0.419 6.56 1.20 2.74
0.362
0.324 3.54 0.16 0.52
0.655
0.289 6.86 0.59 4.20
0.319
0.043 10.33 0.62 12.80
0.118
0.226
0.411 3.56 0.23 0.31
83.100 80.800 18.400 3.65 0.28 1.61
0.064 7.26 0.36 6.71
0.049
0.190 8.74 0.46 9.73
0.775
1.190
0.519 10.40 1.42 7.62
0.368 4.69 0.34 2.07
0.541
0.168
0.123 4.51 0.26 0.94
0.998 5.39 0.36 1.42
2.500
0.334 8.14 0.36 0.14
0.888
0.055
0.072 19.22 7.76 1.71
0.085 2.77 0.06 0.32
0.307
0.071
0.031 5.27 0.22 4.00
0.130 7.33 0.29 5.56
0.321
0.108 6.70 0.44 3.58
0.207
0.033
0.013 8.96 0.38 9.96
0.467 8.90 0.48 5.82
0.596

0.080
0.784
1.240
0.678
0.202
2.610
0.911
0.095
0.312
0.081
0.362
0.266
0.035
0.816

LX
δLX
(1044erg s−1)
0.21
0.02
0.13
0.18
0.02
0.14
0.13
0.15
0.31
0.10
0.04
0.05
0.00
0.23
0.01
0.08
0.08
0.10
0.14
0.09

Table D.1 (cont’d)
Cluster

MKW_03s
ABELL_2069
MCXC_J1524.2-3154
MACS_J1532.8+3021
ABELL_2092
ABELL_2107
ABELL_2111
ABELL_2104
ABELL_2125
ABELL_2124
MCXC_J1558.3-1410
ABELL_2147
ABELL_2151
AWM_4
MACS_J1621.3+3810
ABELL_2187
ABELL_2204
ABELL_2219
Hercules_A
NGC_6269

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

0.064 0.003 0.307 0.003 0.011 0.011 0.000
0.063 0.007 0.152 0.006 0.201 0.198 0.012
0.175 0.005 0.417 0.008 0.003 0.003 0.000
0.240 0.005 0.430 0.009 0.002 0.002 0.000
0.218 0.074 NaN NaN 0.059 0.054 0.010
0.135 0.007 0.649 0.032 0.014 0.014 0.001
0.128 0.011 0.216 0.015 0.028 0.025 0.004
0.065 0.004 0.191 0.005 0.012 0.011 0.001
0.092 0.027 NaN NaN 0.083 0.080 0.006
0.181 0.010 0.245 0.012 0.021 0.020 0.002
0.104 0.004 0.353 0.006 0.007 0.007 0.000
0.052 0.009 0.153 0.006 0.044 0.043 0.003
0.144 0.013 0.483 0.026 0.011 0.011 0.001
0.094 0.005 0.345 0.008 0.005 0.005 0.001
0.309 0.013 0.447 0.020 0.008 0.008 0.001
0.300 0.024 0.357 0.029 0.043 0.043 0.003
0.283 0.003 0.340 0.003 0.006 0.006 0.000
0.059 0.003 0.140 0.002 0.037 0.036 0.001
0.184 0.008 0.392 0.008 0.003 0.004 0.000
0.293 0.025 NaN NaN 0.014 0.015 0.001

1.200
6.500
0.032
0.012
4.740
0.492
0.286
4.520
3.140
1.880
1.250
2.380
1.990
0.416
0.144
0.358
0.020
0.526
0.052
3.750

1.200
6.520
0.044
0.019
5.090
0.508
0.438
4.490
3.920
1.920
1.250
2.410
2.090
0.436
0.187
0.525
0.023
0.515
0.061
3.850

166

LX
δLX
(1044erg s−1)
0.01
0.03
0.02
0.12
0.02
0.01
0.08
0.05
0.03
0.01
0.02
0.01
0.02
0.00
0.20
0.10
0.05
0.10
0.03
0.00

0.076 5.67 0.30 0.63
1.030 4.46 0.58 1.79
0.027 4.47 0.12 1.34
0.017 7.49 0.41 6.98
2.790 2.86 0.44 0.12
0.124 3.18 0.76 0.42
0.348 7.70 0.57 3.90
0.414 7.17 0.25 3.79
1.500 3.16 0.21 0.61
0.479 5.09 0.40 0.32
0.143 5.18 0.12 1.98
0.430 7.16 1.08 0.52
0.455 4.48 1.15 0.18
0.110 2.74 0.09 0.06
0.109 7.23 0.58 5.35
0.337 6.71 0.76 2.43
0.011 4.42 1.07 6.43
0.074 11.27 0.20 15.70
0.031 4.26 0.10 1.81
0.886 2.94 0.19 0.08

Table D.1 (cont’d)
Cluster

ABELL_2256
SDSS-C4_3072
MACS_J1720.2+3536
ABELL_2261
ABELL_2294
Abell_2276
ZwCl_1742.1+3306
NSC_J174715+451155
MCXC_J1750.2+3504
NGC_6482
CIZA_J1804.4+1002
ABELL_2302
MACS_J1829.0+6913
MCXC_J1852.1+5711
MCXC_J1853.9+6822
PLCKESZ_G337.09-25.97
MACS_J1931.8-2635
CIZA_J1938.3+5409
MCXC_J1947.3-7623
ABELL_3653

0.046 0.004 0.073 0.002 0.140 0.136 0.006
0.189 0.005 0.333 0.006 0.004 0.004 0.000
0.310 0.014 0.353 0.016 0.016 0.015 0.001
0.223 0.009 0.283 0.010 0.009 0.009 0.001
0.181 0.014 0.216 0.015 0.028 0.026 0.003
0.233 0.021 NaN NaN 0.006 0.007 0.002
0.098 0.004 0.319 0.005 0.010 0.010 0.000
0.094 0.021 0.203 0.023 0.055 0.048 0.008
0.261 0.017 0.436 0.025 0.004 0.004 0.001
0.279 0.021 0.494 0.034 0.006 0.006 0.001
0.141 0.011 0.216 0.012 0.079 0.079 0.002
0.090 0.020 NaN NaN 0.092 0.085 0.008
0.188 0.014 NaN NaN 0.004 0.005 0.001
0.243 0.018 NaN NaN 0.005 0.005 0.001
0.098 0.015 0.807 0.147 0.046 0.043 0.002
0.183 0.011 0.288 0.015 0.032 0.031 0.002
0.270 0.007 0.393 0.009 0.002 0.002 0.000
0.195 0.013 0.271 0.016 0.022 0.021 0.002
0.300 0.017 0.309 0.017 0.027 0.027 0.001
NaN NaN NaN NaN 0.053 0.053 0.008

4.260
0.129
0.070
0.268
0.296
1.340
0.567
3.990
0.072
0.187
0.082
0.703
1.080
1.660
0.101
0.510
0.031
3.090
1.320
1.550

4.220
0.139
0.141
0.320
0.486
1.640
0.589
4.640
0.141
0.285
0.168
0.953
1.210
1.880
0.175
0.631
0.039
3.030
1.450
2.150

167

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

LX
δLX
(1044erg s−1)
0.03
0.08
0.22
0.16
0.17
0.04
0.02
0.07
0.08
0.00
0.15
0.05
0.04
0.02
0.02
0.14
0.11
0.36
0.18
0.01

0.360 3.56 0.23 3.40
0.040 7.11 0.27 4.43
0.110 7.87 0.65 7.30
0.137 8.10 0.59 7.49
0.378 7.30 0.74 4.67
0.638 2.83 0.28 0.48
0.083 5.00 0.30 1.08
1.670 4.73 0.38 1.51
0.123 4.64 0.36 1.67
0.258 0.48 0.04 0.00
0.130 7.10 0.59 5.23
0.638 4.82 0.38 1.32
0.492 4.06 0.30 0.83
0.685 4.00 0.28 0.45
0.169 4.13 0.22 1.01
0.345 7.66 0.54 6.85
0.028 7.87 0.33 9.42
0.766 7.20 0.73 9.11
0.601 7.34 0.63 5.67
1.190 4.78 0.34 0.52

Table D.1 (cont’d)
Cluster

MCXC_J2003.5-2323
MCXC_J2011.3-5725
MCXC_J2014.8-2430
SPT-CL_J2023-5535
ABELL_3695
SPT-CLJ2043-5035
MACS_J2046.0-3430
ABELL_3739
IC_1365
ABELL_2355
WBL_671
MACS_J2140.2-2339
ABELL_3809
ABELL_2384
ABELL_2390
ClG_2153.8+3746
ABELL_2409
ABELL_2415
3C_444
ABELL_2426

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

1.150
1.570
1.000
2.620
0.442
0.498
0.133
0.272

0.237 0.017 0.233 0.016 0.133 0.133 0.005
0.199 0.019 0.459 0.041 0.006 0.006 0.001
0.332 0.009 0.371 0.009 0.005 0.005 0.000
0.137 0.013 0.145 0.013 0.095 0.092 0.005
0.079 0.012 0.304 0.030 0.057 0.057 0.003
0.432 0.037 0.583 0.060 0.005 0.006 0.001
0.343 0.024 0.478 0.036 0.002 0.002 0.000
0.129 0.014 0.274 0.023 0.015 0.014 0.002
0.083 0.010 NaN NaN 0.356 0.356 0.003
0.229 0.030 0.441 0.065 0.031 0.034 0.005
0.037 0.001 NaN NaN 0.016 0.023 0.008
0.300 0.009 0.423 0.011 0.001 0.001 0.000
0.142 0.018 NaN NaN 0.013 0.013 0.002
0.149 0.008 0.339 0.011 0.056 0.056 0.002
0.165 0.003 0.258 0.003 0.013 0.013 0.000
0.180 0.007 0.260 0.007 0.069 0.069 0.001
0.111 0.010 0.207 0.012 0.032 0.031 0.002
0.194 0.018 NaN NaN 0.032 0.031 0.002
0.128 0.005 0.326 0.009 0.016 0.016 0.001
0.163 0.016 0.476 0.039 0.027 0.028 0.002

168

0.749 9.18 0.80 8.46
0.975
0.717 3.63 0.37 2.08
1.420
0.153 7.15 0.39 4.26
0.999
1.040 8.39 0.76 6.12
2.440
0.308 6.46 0.43 1.90
0.263
0.452 5.44 0.68 6.60
0.283
0.122 5.61 0.45 4.33
0.048
0.021
0.271 6.08 0.53 2.90
11.400 11.700 1.370 4.84 0.13 0.56
0.521 7.24 0.69 1.48
0.888
0.017
4.990 1.00 0.12 0.01
0.059 5.92 0.34 4.10
0.137
0.216 2.89 0.12 0.41
0.188
0.955
0.262 4.77 0.26 1.11
0.066 11.16 0.31 14.50
0.357
0.458
0.177 9.49 0.36 11.90
0.214 5.96 0.38 4.31
0.161
0.200 2.66 0.12 0.39
0.154
2.080
0.278 5.40 0.21 0.61
0.105 5.82 0.39 1.66
0.057

0.966
4.940
0.139
0.291
0.969
0.354
0.501
0.292
0.271
2.050
0.138

LX
δLX
(1044erg s−1)
0.20
0.15
0.10
0.18
0.04
0.49
0.22
0.12
0.02
0.05
0.00
0.11
0.01
0.02
0.10
0.16
0.14
0.01
0.02
0.05

Table D.1 (cont’d)
Cluster

MACS_J2214-1359
ABELL_3854
MCXC_J2218.6-3853
ABELL_2443
ABELL_2445
ABELL_3880
MACS_J2229.8-2756
CGCG_514-050
ABELL_2457
MACS_J2245.0+2637
ABELL_3911
ABELL_2485
ABELL_S1063
ABELL_3921
ABELL_2507
ABELL_2537
MCXC_J2311.5+0338
ABELL_2550
ABELL_2556
ABELL_S1101

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

0.224 0.016 0.228 0.016 0.011 0.011 0.003
0.152 0.015 0.329 0.024 0.009 0.009 0.002
0.082 0.009 0.252 0.015 0.018 0.018 0.003
0.085 0.007 0.348 0.019 0.052 0.051 0.003
0.081 0.010 0.488 0.034 0.013 0.013 0.002
0.198 0.011 0.644 0.041 0.023 0.022 0.000
0.364 0.018 0.435 0.022 0.001 0.002 0.001
0.391 0.039 NaN NaN 0.022 0.022 0.002
0.157 0.025 NaN NaN 0.015 0.016 0.003
0.346 0.025 0.368 0.027 0.008 0.008 0.001
0.063 0.009 0.149 0.013 0.600 0.599 0.004
0.292 0.029 0.526 0.063 0.005 0.007 0.002
0.181 0.007 0.208 0.007 0.043 0.042 0.002
0.085 0.006 0.236 0.007 0.012 0.012 0.001
0.253 0.040 NaN NaN 0.315 0.316 0.008
0.142 0.007 0.333 0.013 0.010 0.009 0.001
0.218 0.013 0.241 0.014 0.005 0.006 0.002
0.164 0.015 0.516 0.031 0.004 0.004 0.001
0.174 0.008 0.364 0.011 0.008 0.008 0.000
0.075 0.002 0.542 0.007 0.005 0.005 0.000

1.600
0.095
0.066
4.220
1.110
0.028
0.171
4.840
1.080
0.414
1.840
0.249
0.025
0.490
1.180
0.059
0.357
0.058
5.430
0.025

2.010
0.213
0.158
4.290
1.140
0.055
0.216
4.750
1.260
0.532
1.960
0.515
0.072
0.543
1.920
0.115
0.469
0.128
5.600
0.028

169

LX
δLX
(1044erg s−1)
0.47
0.08
0.09
0.05
0.06
0.02
0.20
0.00
0.02
0.25
0.06
0.12
0.46
0.04
0.06
0.11
0.30
0.01
0.02
0.01

0.942 8.83 0.99 12.10
0.196 5.18 0.39 2.27
0.112 5.60 0.33 3.29
0.681 9.72 1.44 1.70
0.359 4.16 0.22 1.70
0.044 5.31 0.23 0.33
0.135 5.88 0.56 4.20
0.778 1.23 0.04 0.00
0.539 3.81 0.22 0.54
0.365 6.71 0.93 4.67
0.644 6.11 0.39 2.18
0.415 6.25 0.71 2.77
0.066 11.30 0.72 25.00
0.178 6.92 0.41 1.96
1.330 4.31 0.43 0.99
0.093 6.65 0.37 4.84
0.338 9.52 1.00 7.83
0.098 1.93 0.12 0.20
0.554 3.86 0.16 0.79
0.010 7.57 0.10 0.52

Table D.1 (cont’d)
Cluster

NGC_7618
ABELL_2597
RCS_J2327-0204
ABELL_2626
ABELL_2631
MCXC_J2344.2-0422
HCG_097
ABELL_2667
ABELL_2670

LX
δLX
(1044erg s−1)
0.00
0.01
0.02
0.01
0.26
0.04
0.00
0.22
0.02

0.163 0.78 0.02 0.01
0.024 4.36 0.06 0.86
0.049 9.55 1.43 0.43
0.174 3.26 0.11 0.43
1.040 8.02 0.96 7.57
0.254 4.46 0.18 1.44
1.180 0.81 0.04 0.01
0.262 7.60 0.68 8.12
0.060 3.78 0.39 0.73

c500 δc500

c

δc wdata wsim δ wsim pdata
107

psim δ psim kT
(keV)

δkT

0.205 0.022 0.743 0.089 0.014 0.014 0.001
0.086 0.002 0.379 0.003 0.003 0.003 0.000
NaN NaN 0.569 0.030 0.005 0.004 0.001
0.126 0.006 0.255 0.007 0.012 0.012 0.001
0.212 0.018 0.185 0.016 0.047 0.038 0.006
0.063 0.010 0.591 0.064 0.034 0.033 0.002
NaN NaN NaN NaN 0.020 0.020 0.003
0.301 0.012 0.320 0.013 0.011 0.010 0.001
0.079 0.006 0.675 0.042 0.021 0.021 0.001

0.118
0.238
0.011
0.730
1.710
0.325
2.790
0.672
0.040

0.218
0.242
0.057
0.724
2.020
0.405
2.960
0.786
0.070

170

APPENDIX E

RADIAL PROFILES OF EARLY-TYPE GALAXIES WITH POWERFUL RADIO

SOURCES

Table E.1: Radial proﬁles for early-type galaxies with powerful radio sources Radial proﬁle
properties for each galaxy with suﬃcient counts for temperature deprojection. Errors given for
radius represent bin widths, all other errors are 1 sigma. Column 1: galaxy name; Column 2:
radial bin center; Column 3: half-width of the radial bin; Column 4: grouping of temperature
bins; Columns 5-6: best ﬁt temperatures and their errors; Column 7: electron density bin number;
Columns 8-9: best ﬁt densities and their errors; in units of 10−2 cm−3 for compactness; Columns
10-11: calculated entropies and their errors.

Galaxy

radius ∆r
(kpc)
(kpc)

NGC 315
NGC 315
NGC 315
NGC 315
NGC 315
NGC 741
NGC 741
NGC 741
NGC 741
NGC 741
NGC 741
NGC 741
NGC 741
NGC 741
NGC 741
NGC 741
NGC 741

1.12
0.56
1.60
0.24
2.24
0.32
3.05
0.40
4.49
0.72
2.52
1.26
5.04
1.26
8.10
1.53
11.69 1.80
16.37 2.34
26.80 5.22
37.24 5.22
46.23 4.50
54.15 3.96
61.52 3.69
68.72 3.60
75.74 3.51

kT bin kT σkT ne bin
ID (keV) (keV)

K

σK

ID (10−2 cm−3) (10−2 cm−3) (keV cm2) (keV cm2)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

3.99
5.69
8.17
11.77
15.35
12.23
18.98
30.07
46.21
86.63
110.53
193.51
228.92
205.20
470.97
242.57
219.04

0.26
0.37
0.42
0.58
0.52
0.24
0.46
0.79
2.20
2.53
4.08
24.86
32.23
33.25
55.73
202.78
30.52

σne

0.35
0.20
0.15
0.08
0.04
0.03
0.03
0.01
0.03
0.01
0.01
0.01
0.01
0.01
0.00
0.07
0.01

ne

7.36
4.33
2.90
1.68
1.08
1.74
0.90
0.45
0.44
0.17
0.12
0.08
0.07
0.08
0.02
0.06
0.06

1
1
2
2
3
1
1
1
2
2
2
3
3
3
4
4
4

0.70 0.04
0.70 0.04
0.77 0.03
0.77 0.03
0.75 0.02
0.82 0.01
0.82 0.01
0.82 0.01
1.24 0.03
1.24 0.03
1.24 0.03
1.74 0.21
1.74 0.21
1.74 0.21
1.64 0.16
1.64 0.16
1.64 0.16

171

Table E.1 (cont’d)
radius ∆r
Galaxy
(kpc)
(kpc)

NGC 1316 0.24
NGC 1316 0.37
NGC 1316 0.61
NGC 1316 0.85
NGC 1316 1.10
NGC 1316 1.46
NGC 1316 2.07
NGC 1316 2.92
NGC 1316 3.89
NGC 1316 4.99
NGC 1316 6.08
NGC 1316 6.94
NGC 1316 8.15
NGC 1316 9.61
NGC 4261 0.28
NGC 4261 0.43
NGC 4261 0.57
NGC 4261 0.71
NGC 4261 0.85
NGC 4261 0.99
NGC 4261 1.13
NGC 4261 1.28
NGC 4261 1.42
NGC 4261 1.56
NGC 4261 1.70
NGC 4261 1.84
NGC 4261 1.99
NGC 4261 2.27
NGC 4261 2.41

0.12
0.06
0.12
0.12
0.12
0.18
0.30
0.43
0.49
0.55
0.55
0.43
0.61
0.73
0.14
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.14
0.07

kT bin kT σkT ne bin
ID (keV) (keV)

ne

K

ID (10−2 cm−3) (10−2 cm−3) (keV cm2) (keV cm2)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

15.50
10.30
7.57
4.70
3.54
1.95
1.10
0.57
0.50
0.21
0.46
0.45
0.25
0.26
29.50
19.30
13.80
9.65
6.74
6.21
3.66
4.24
3.28
2.73
2.56
2.38
1.30
2.58
1.54

2.66
3.52
4.30
7.16
8.64
12.87
15.86
24.66
26.87
44.83
26.45
26.82
16.68
32.27
1.62
2.15
2.69
3.54
4.50
4.75
6.87
6.24
7.40
8.07
8.44
8.84
14.14
8.94
12.61

σne

1.14
0.82
0.35
0.23
0.25
0.09
0.05
0.03
0.05
0.01
0.14
0.03
0.01
0.02
0.90
0.40
0.38
0.33
0.31
0.42
0.22
0.57
0.28
0.31
0.35
0.32
0.18
0.44
0.13

σK

0.15
0.21
0.18
0.30
0.46
0.52
0.61
1.01
1.75
2.63
5.46
1.44
1.85
3.85
0.04
0.04
0.06
0.11
0.17
0.24
0.38
0.60
0.50
0.82
0.96
0.99
1.46
1.12
0.95

1
1
1
2
2
2
3
3
3
4
4
4
5
6
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5

0.77 0.02
0.77 0.02
0.77 0.02
0.93 0.02
0.93 0.02
0.93 0.02
0.79 0.02
0.79 0.02
0.79 0.02
0.73 0.03
0.73 0.03
0.73 0.03
0.31 0.03
0.61 0.07
0.72 0.01
0.72 0.01
0.72 0.01
0.74 0.02
0.74 0.02
0.74 0.02
0.76 0.03
0.76 0.03
0.76 0.03
0.73 0.05
0.73 0.05
0.73 0.05
0.78 0.04
0.78 0.04
0.78 0.04

172

Table E.1 (cont’d)
radius ∆r
Galaxy
(kpc)
(kpc)

NGC 4261 2.55
NGC 4261 2.84
NGC 4261 3.12
NGC 4261 3.40
NGC 4261 3.69
NGC 4261 4.11
NGC 4261 4.54
NGC 4261 4.96
NGC 4261 5.53
NGC 4261 6.38
NGC 4374 0.14
NGC 4374 0.28
NGC 4374 0.41
NGC 4374 0.55
NGC 4374 0.69
NGC 4374 0.83
NGC 4374 1.03
NGC 4374 1.17
NGC 4374 1.38
NGC 4374 1.59
NGC 4374 1.79
NGC 4374 2.00
NGC 4374 2.21
NGC 4374 2.55
NGC 4374 2.83
NGC 4374 3.17
NGC 4374 3.66
NGC 4374 4.21
NGC 4374 4.97

0.07
0.14
0.14
0.14
0.14
0.21
0.21
0.21
0.28
0.43
0.07
0.07
0.07
0.07
0.07
0.07
0.10
0.07
0.10
0.10
0.10
0.10
0.10
0.17
0.14
0.17
0.24
0.28
0.38

kT bin kT σkT ne bin
ID (keV) (keV)

ne

K

ID (10−2 cm−3) (10−2 cm−3) (keV cm2) (keV cm2)
16
17
18
19
20
21
22
23
24
25
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

1.09
1.22
1.14
0.76
0.75
0.53
0.58
0.44
0.48
0.31
16.30
9.75
6.68
4.04
5.24
3.20
1.74
2.61
2.23
1.67
1.33
1.78
0.96
1.02
0.91
0.77
0.62
0.37
0.32

14.58
13.51
14.16
21.79
22.13
27.99
29.05
34.86
32.96
60.35
2.62
3.68
4.74
6.63
5.57
6.09
9.12
6.97
7.74
9.40
13.13
10.84
16.32
15.74
16.92
24.02
27.81
38.95
43.51

σne

0.24
0.21
0.12
0.08
0.13
0.05
0.10
0.06
0.06
0.02
0.63
0.45
0.39
0.30
0.72
0.19
0.14
0.76
0.16
0.12
0.14
0.25
0.06
0.10
0.08
0.06
0.04
0.02
0.02

σK

2.38
1.87
1.42
1.85
2.89
2.42
3.78
3.47
3.32
3.29
0.09
0.14
0.21
0.35
0.53
0.31
0.56
1.36
0.45
0.55
0.97
1.03
0.76
1.07
1.01
1.27
1.20
1.59
2.31

6
6
6
7
7
7
8
8
8
9
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
4
4
4
4

0.72 0.05
0.72 0.05
0.72 0.05
0.85 0.05
0.85 0.05
0.85 0.05
0.94 0.05
0.94 0.05
0.94 0.05
1.29 0.03
0.78 0.02
0.78 0.02
0.78 0.02
0.78 0.02
0.78 0.02
0.61 0.02
0.61 0.02
0.61 0.02
0.61 0.02
0.61 0.02
0.74 0.02
0.74 0.02
0.74 0.02
0.74 0.02
0.74 0.02
0.94 0.02
0.94 0.02
0.94 0.02
0.94 0.02

173

Table E.1 (cont’d)
radius ∆r
Galaxy
(kpc)
(kpc)

0.45
NGC 4374 5.86
0.62
NGC 4782 7.10
1.05
NGC 4782 4.81
0.75
NGC 4782 6.32
0.75
NGC 4782 7.82
NGC 4782 9.03
0.60
NGC 4782 10.23 0.60
NGC 4782 11.13 0.45
NGC 4782 12.04 0.45
NGC 4782 13.24 0.60
NGC 4782 14.74 0.75
NGC 4782 17.45 1.35
NGC 4782 20.16 1.35
NGC 4782 22.57 1.20
NGC 4782 25.28 1.35
NGC 4782 28.29 1.50
NGC 4782 30.99 1.35
NGC 5419 0.28
0.14
0.42
NGC 5419 1.12
NGC 5419 3.09
0.98
NGC 5419 7.59
2.25
NGC 5419 12.65 2.53
NGC 5419 17.43 2.39
NGC 5419 22.50 2.53
NGC 5419 26.43 1.97
0.33
NGC 7626 0.67
0.67
NGC 7626 2.00
NGC 7626 3.77
0.89
1.44
NGC 7626 6.65

kT bin kT σkT ne bin
ID (keV) (keV)

ne

K

σK

ID (10−2 cm−3) (10−2 cm−3) (keV cm2) (keV cm2)
20
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
2
3
4
5
6
7
8
1
2
3
4

33.02
524.03
46.94
38.01
29.27
66.07
51.71
54.52
70.95
42.95
66.32
206.97
50.81
157.71
214.57
159.81
353.88
9.36
31.95
31.53
43.06
116.87
123.06
238.79
194.70
8.62
14.56
25.35
36.08

1.47
227.54
4.59
12.19
3.77
11.66
11.05
8.69
10.38
2.72
4.46
17.10
74.84
40.60
56.87
49.71
90.56
2.37
8.11
2.04
3.52
107.10
113.54
110.92
94.62
0.46
0.81
1.65
2.33

0.48
0.30
0.20
0.28
0.42
0.36
0.52
0.48
0.32
0.25
0.13
0.02
0.19
0.16
0.10
0.15
0.05
22.00
3.48
0.68
0.43
0.25
0.23
0.25
0.34
4.03
1.62
0.66
0.37

σne

0.03
0.06
0.03
0.13
0.08
0.07
0.14
0.08
0.04
0.02
0.01
0.00
0.42
0.02
0.02
0.04
0.01
0.57
0.14
0.03
0.04
0.03
0.05
0.09
0.15
0.16
0.06
0.03
0.02

4
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
1
1
2
2
3
3
4
4
1
2
3
4

0.94 0.02
10.89 4.50
0.76 0.03
0.76 0.03
0.76 0.03
1.55 0.18
1.55 0.18
1.55 0.18
1.55 0.18
0.78 0.03
0.78 0.03
0.78 0.03
0.78 0.03
2.13 0.52
2.13 0.52
2.13 0.52
2.13 0.52
3.41 0.86
3.41 0.86
1.13 0.06
1.13 0.06
2.17 1.98
2.17 1.98
4.37 1.70
4.37 1.70
1.01 0.05
0.93 0.05
0.89 0.05
0.86 0.05

174

Table E.1 (cont’d)
radius ∆r
Galaxy
(kpc)
(kpc)

NGC 7626 9.98
1.66
NGC 7626 13.53 1.77
NGC 7626 17.52 2.00
0.24
IC 1459
0.49
IC 1459
0.12
0.73
0.12
IC 1459
0.97
0.12
IC 1459
1.22
IC 1459
0.12
1.46
0.18
IC 1459
1.83
IC 1459
0.12
2.07
0.18
IC 1459
2.43
0.18
IC 1459
2.80
IC 1459
0.18
3.16
0.18
IC 1459
3.53
IC 1459
0.18
3.89
0.30
IC 1459
4.50
0.24
IC 1459
4.99
IC 1459
0.30
5.60
0.43
IC 1459
6.45
IC 1459
0.49
7.42
8.76
IC 1459
0.67
10.34 0.79
IC 1459
IC 1459
12.53 1.10
0.24
0.48
IC 4296
IC 4296
0.72
0.12
0.12
0.97
IC 4296
0.24
1.45
IC 4296
IC 4296
1.93
0.24
0.36
2.66
IC 4296

kT bin kT σkT ne bin
ID (keV) (keV)

ne

K

σK

ID (10−2 cm−3) (10−2 cm−3) (keV cm2) (keV cm2)
5
6
7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
2
3
4
5
6

0.27
0.18
0.28
5.14
2.70
1.92
1.67
1.09
0.98
0.96
0.69
0.46
0.59
0.36
0.38
0.32
0.27
0.19
0.19
0.09
0.10
0.08
0.11
16.50
10.10
5.62
3.52
2.50
1.19

4.62
6.20
5.54
0.23
0.45
0.89
1.12
2.05
2.21
2.45
2.68
63.42
55.20
76.24
74.18
3.92
5.04
6.09
6.45
6.63
13.60
8.98
5.92
0.09
0.16
0.33
0.41
0.63
0.86

49.64
62.74
43.40
6.78
10.41
13.08
14.34
7.81
8.38
8.53
10.59
55.32
47.01
65.09
63.09
26.94
30.16
38.20
38.17
80.01
75.13
82.70
69.92
2.48
3.44
5.29
7.23
9.82
16.08

σne

0.02
0.01
0.03
0.19
0.14
0.18
0.19
0.17
0.16
0.23
0.08
0.09
0.25
0.15
0.16
0.03
0.04
0.03
0.03
0.01
0.03
0.01
0.01
0.57
0.53
0.39
0.20
0.18
0.06

5
6
7
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
1
1
2
2
3
3

0.96 0.08
0.91 0.08
0.87 0.09
0.94 0.02
0.94 0.02
0.94 0.02
0.94 0.02
0.38 0.09
0.38 0.09
0.38 0.09
0.38 0.09
1.53 1.74
1.53 1.74
1.53 1.74
1.53 1.74
0.59 0.07
0.59 0.07
0.59 0.07
0.59 0.07
0.74 0.03
0.74 0.03
0.74 0.03
0.74 0.03
0.75 0.02
0.75 0.02
0.78 0.03
0.78 0.03
0.84 0.03
0.84 0.03

175

Table E.1 (cont’d)
radius ∆r
Galaxy
(kpc)
(kpc)

IC 4296
IC 4296
IC 4296
IC 4296
IC 4296
IC 4296

3.87
0.60
6.28
1.21
9.42
1.57
12.56 1.57
15.46 1.45
17.88 1.21

kT bin kT σkT ne bin
ID (keV) (keV)

K

σK

ID (10−2 cm−3) (10−2 cm−3) (keV cm2) (keV cm2)
7
8
9
10
11
12

30.82
36.60
116.60
152.23
91.31
91.62

1.98
2.73
59.92
79.11
18.74
22.83

σne

0.03
0.03
0.03
0.03
0.03
0.05

ne

0.49
0.38
0.24
0.16
0.17
0.17

4
4
5
5
6
6

0.89 0.05
0.89 0.05
2.10 1.07
2.10 1.07
1.29 0.21
1.29 0.21

176

APPENDIX F

RADIAL PROFILES FOR THE GALAXIES IN LAKHCHAURA (2018)

Table F.1: Radial proﬁles for the HQ sample Table of all the radial proﬁles in the HQ sample
from (Lakhchaura et al., 2018). Column 1: Galaxy name; Column 2-3: radius and half-bin
widths; Column 4-5: entropy and errors; Column 6-7: Ratio between the cooling time and
free=fall time, tc/tﬀ, and errors.

Galaxy

3C449
3C449
3C449
3C449
3C449
3C449
3C449
3C449
3C449
3C449
3C449
3C449
3C449
3C449
IC1860
IC1860
IC1860
IC1860
IC1860
IC1860
IC1860

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

2.64
8.79
15.82
22.85
30.21
38.13
46.00
53.26
60.27
67.18
73.76
80.24
86.90
93.73
2.28
5.25
6.62
7.99
9.48
11.31
13.25

2.64
3.51
3.51
3.51
3.85
4.06
3.80
3.46
3.55
3.37
3.20
3.29
3.37
3.46
2.28
0.69
0.69
0.69
0.80
1.03
0.91

11.20
61.72
66.22
69.14
72.70
98.98
119.66
110.53
132.54
138.31
118.02
117.18
141.59
96.52
8.03
11.85
16.01
20.49
22.30
25.98
29.95

177

σK

0.50
13.87
2.91
2.49
2.79
5.12
9.62
6.61
8.23
9.48
7.78
3.49
10.61
1.91
0.24
0.96
1.50
2.13
1.98
3.07
3.25

tc/t f f

δtc/t f f

13.46
131.46
105.62
78.87
62.81
81.67
96.02
64.78
116.22
108.28
65.52
56.10
75.67
28.30
18.42
19.99
22.65
32.70
32.29
33.96
34.22

1.26
48.20
9.78
5.85
5.15
9.70
17.63
9.03
15.84
16.48
9.65
5.22
13.72
2.32
2.40
3.30
4.20
7.84
6.80
7.54
8.40

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

IC1860
IC1860
IC1860
IC1860
IC1860
IC1860
IC1860
IC1860
IC4296
IC4296
IC4296
IC4296
IC4296
IC4296
IC4296
IC4765
IC4765
IC4765
IC4765
IC4765
IC4765
IC4765
NGC57
NGC57
NGC57
NGC315
NGC315
NGC315
NGC315

15.07
16.90
19.30
22.15
25.47
29.23
33.12
41.34
0.56
1.86
8.29
18.28
26.74
36.22
48.69
1.21
2.77
3.62
4.68
5.89
7.31
9.09
1.50
4.30
8.42
0.73
1.13
1.59
2.19

0.91
0.91
1.48
1.37
1.94
1.83
2.06
6.17
0.23
1.07
5.36
4.63
3.84
5.64
6.83
1.21
0.35
0.50
0.57
0.64
0.78
0.99
1.50
1.31
2.81
0.20
0.20
0.27
0.33

39.68
34.62
47.60
44.83
47.94
61.94
72.42
62.85
1.42
4.89
38.01
101.73
88.88
95.26
93.74
3.03
5.77
6.91
8.76
13.06
18.17
18.21
6.36
14.23
33.17
3.27
5.31
7.94
9.50

178

σK

6.48
3.60
5.59
4.31
3.09
6.41
5.83
1.59
0.07
0.17
1.83
12.11
5.21
7.23
4.18
0.23
0.63
0.63
0.75
1.73
3.24
1.65
0.34
1.28
2.49
0.32
0.45
0.74
0.63

tc/t f f

δtc/t f f

57.78
36.49
62.63
45.22
42.35
61.89
58.76
30.89
11.63
21.75
118.54
211.85
81.15
91.68
53.10
11.01
12.49
13.18
13.08
20.35
26.30
20.10
36.48
42.44
81.99
20.02
33.71
53.52
55.42

21.71
9.13
18.04
11.31
9.15
17.78
15.18
6.33
0.78
1.01
9.06
56.02
10.19
14.57
4.23
1.20
2.39
1.84
1.82
4.31
7.31
2.99
3.31
6.59
12.68
4.65
6.73
11.93
13.64

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC315
NGC315
NGC410
NGC410
NGC410
NGC499
NGC499
NGC499
NGC499
NGC499
NGC499
NGC499
NGC499
NGC499
NGC499
NGC499
NGC499
NGC499
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507

3.12
4.78
1.28
3.52
7.04
2.90
7.82
11.88
16.15
20.79
25.64
31.29
37.96
44.84
52.15
60.05
67.51
75.33
2.78
7.85
11.84
15.05
17.91
20.55
23.19
25.90
28.68
31.61
34.60

0.60
1.06
1.28
0.96
2.56
2.90
2.03
2.03
2.25
2.39
2.46
3.19
3.48
3.40
3.91
3.98
3.48
4.35
2.78
2.28
1.71
1.50
1.36
1.28
1.36
1.36
1.43
1.50
1.50

14.12
18.25
6.57
9.50
22.45
15.11
33.27
41.50
40.00
46.04
48.82
56.55
74.76
93.61
111.35
115.67
122.87
104.18
13.59
33.76
38.59
35.78
36.74
38.55
42.38
47.92
49.56
60.08
60.87

179

σK

0.91
0.73
0.79
1.11
1.48
0.52
1.99
2.62
2.52
1.53
1.72
1.91
2.88
4.44
6.12
6.23
6.57
2.20
0.42
3.27
5.35
4.36
3.44
3.07
2.21
4.65
3.56
4.98
3.34

tc/t f f

δtc/t f f

73.57
57.08
42.75
27.30
49.70
45.37
56.17
54.75
35.68
37.10
34.18
39.36
44.53
66.19
107.52
102.68
100.94
58.19
34.75
70.77
63.26
44.88
35.32
30.15
34.46
37.88
34.87
47.12
37.26

21.26
18.90
8.62
5.22
8.16
4.27
7.43
7.55
4.35
3.24
3.19
3.64
4.10
6.96
14.76
15.97
16.78
6.79
3.63
13.22
15.56
9.39
6.83
5.61
5.95
8.36
6.78
10.28
7.09

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC507
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533
NGC533

37.60
40.60
43.74
47.16
50.73
54.30
58.01
61.79
65.50
69.28
73.28
77.63
82.34
0.29
0.81
1.25
1.69
2.13
2.57
3.01
3.45
3.89
4.33
4.77
5.29
5.88
6.54
7.27
8.08

1.50
1.50
1.64
1.78
1.78
1.78
1.93
1.86
1.86
1.93
2.07
2.28
2.43
0.29
0.22
0.22
0.22
0.22
0.22
0.22
0.22
0.22
0.22
0.22
0.29
0.29
0.37
0.37
0.44

73.96
69.32
85.57
110.05
92.08
178.55
103.39
109.76
117.09
105.18
109.52
124.67
88.44
1.72
2.52
3.76
4.70
5.92
6.01
6.40
7.17
6.90
9.38
9.07
12.48
13.54
13.97
16.07
20.08

180

σK

6.31
4.61
7.26
14.22
8.08
68.20
10.78
11.44
12.33
8.21
6.80
9.18
1.90
0.24
0.24
0.54
0.44
0.46
0.69
0.73
0.72
0.56
1.47
0.51
1.31
1.14
0.93
1.33
1.68

tc/t f f

δtc/t f f

51.51
40.99
59.38
77.39
46.80
188.69
63.20
66.12
67.22
48.76
49.37
60.86
25.84
17.79
12.28
17.51
15.41
17.49
17.25
17.54
15.30
14.49
21.93
15.05
26.90
23.51
25.56
25.03
33.04

12.48
8.64
14.44
24.47
10.99
164.01
17.44
18.31
19.24
11.66
11.11
14.80
4.80
5.08
3.75
6.24
5.51
6.44
6.76
7.10
6.05
5.76
9.78
5.97
11.60
9.85
10.54
10.42
13.99

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC533
NGC533
NGC533
NGC533
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC708
NGC741
NGC741
NGC741
NGC741
NGC741
NGC741
NGC741

9.03
10.21
11.82
14.54
1.24
3.73
6.22
8.71
11.51
14.94
18.98
23.65
28.76
34.14
39.65
45.32
50.98
56.57
62.31
68.13
74.18
81.15
1.09
3.28
5.62
8.43
12.02
18.47
27.34

0.51
0.66
0.95
1.76
1.24
1.24
1.24
1.24
1.56
1.87
2.18
2.49
2.62
2.76
2.76
2.91
2.76
2.83
2.91
2.91
3.14
3.83
1.09
1.09
1.25
1.56
2.03
4.42
4.45

21.46
25.37
33.13
33.52
6.72
7.37
11.11
16.59
19.86
24.91
30.63
41.75
47.74
54.91
66.31
66.01
74.20
73.05
85.10
82.00
89.29
70.03
3.63
8.73
16.31
31.80
34.75
77.15
115.53

181

σK

1.50
2.04
2.54
0.56
0.22
0.07
0.08
0.18
0.10
0.19
0.19
0.76
0.97
0.42
0.63
0.52
0.80
0.71
1.09
1.00
0.75
0.47
0.11
0.31
0.35
2.75
1.33
3.94
15.81

tc/t f f

δtc/t f f

32.27
38.78
49.92
35.54
27.72
12.04
14.95
19.69
20.92
24.78
28.69
37.00
41.60
37.51
46.59
38.26
42.97
35.82
36.49
29.58
33.77
17.20
19.16
25.12
36.04
77.95
48.76
124.13
174.54

13.49
16.52
21.23
14.72
1.34
0.29
0.39
0.66
0.60
0.81
0.93
1.56
1.70
1.34
1.79
1.42
1.70
1.38
1.44
1.15
1.30
0.64
0.73
1.19
1.58
10.45
3.41
12.11
39.26

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC741
NGC741
NGC741
NGC741
NGC741
NGC741
NGC741
NGC741
NGC741
NGC777
NGC777
NGC777
NGC777
NGC777
NGC777
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132

35.63
42.85
49.38
55.60
61.67
67.81
74.18
80.56
86.93
1.73
4.50
6.58
9.07
12.19
17.45
2.73
9.23
16.25
22.43
28.10
33.34
38.26
43.19
48.12
52.84
57.45
62.17
66.99
71.81

3.84
3.38
3.15
3.07
2.99
3.15
3.23
3.15
3.23
1.73
1.04
1.04
1.45
1.66
3.60
2.73
3.77
3.25
2.94
2.73
2.52
2.41
2.52
2.41
2.31
2.31
2.41
2.41
2.41

173.52
165.06
163.43
195.82
225.48
192.79
242.59
226.06
169.45
6.91
11.17
13.70
19.75
19.39
25.56
9.68
37.08
53.59
65.36
61.24
109.38
65.53
94.64
91.03
99.82
84.29
124.78
95.26
114.65

182

σK

64.03
25.49
25.63
46.47
50.60
25.62
49.36
25.54
10.53
0.25
1.23
2.00
2.02
1.73
1.25
0.27
3.18
4.37
6.87
4.90
31.57
3.70
15.74
13.44
18.25
11.84
30.64
11.25
24.60

tc/t f f

δtc/t f f

202.01
139.44
123.46
163.88
153.69
108.60
155.94
117.48
74.82
37.38
30.25
29.98
34.10
24.11
26.15
33.23
80.44
64.72
80.77
50.29
146.24
37.79
70.47
56.61
59.44
40.61
84.23
41.16
55.30

92.20
25.86
23.88
63.75
48.76
18.33
39.75
18.79
7.02
2.36
4.57
5.81
5.31
3.01
2.17
1.47
11.76
9.54
17.85
8.02
94.86
4.66
22.89
15.87
19.51
9.67
44.69
8.90
20.21

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1132
NGC1316
NGC1316
NGC1316
NGC1316
NGC1316
NGC1316
NGC1316
NGC1316
NGC1399
NGC1399
NGC1399
NGC1399
NGC1399
NGC1399
NGC1399
NGC1399
NGC1399
NGC1399
NGC1399
NGC1404
NGC1404

76.63
81.46
86.28
93.30
100.33
105.25
110.49
116.36
0.23
0.41
0.62
0.87
1.17
1.65
2.61
4.42
0.47
1.86
4.17
6.84
9.32
11.65
13.91
16.09
18.21
20.37
23.04
0.18
0.55

2.41
2.41
2.41
4.61
2.41
2.52
2.73
3.14
0.09
0.09
0.11
0.14
0.16
0.32
0.64
1.17
0.47
0.93
1.38
1.29
1.19
1.14
1.12
1.06
1.06
1.10
1.57
0.18
0.18

151.87
123.46
128.80
160.85
117.01
159.05
157.93
110.23
2.56
3.26
4.42
5.97
7.03
11.26
20.57
17.17
2.48
8.26
22.11
36.16
39.80
44.08
53.32
50.90
60.99
59.74
54.88
1.28
2.21

183

σK

39.02
19.23
17.19
22.27
14.13
107.10
24.34
4.26
0.28
0.26
0.33
0.36
0.37
0.67
3.01
0.53
0.03
0.06
0.44
1.13
1.23
1.57
2.32
1.59
2.52
1.63
0.68
0.01
0.02

tc/t f f

δtc/t f f

83.15
47.75
51.51
75.79
34.15
87.58
56.95
23.52
32.57
38.76
51.38
68.14
61.97
94.06
169.46
55.60
26.05
43.02
90.46
110.21
84.91
76.49
89.24
59.57
73.97
56.89
38.89
20.73
20.23

45.79
14.48
14.66
22.47
7.60
83.60
19.72
2.00
6.72
5.82
7.43
11.05
10.22
17.26
43.63
12.24
0.40
0.60
2.99
6.62
5.04
5.10
7.77
3.76
6.47
3.44
1.02
0.42
0.51

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1404
NGC1407
NGC1407
NGC1407
NGC1407
NGC1407
NGC1407
NGC1407
NGC1407
NGC1407

0.96
1.49
2.20
3.13
4.30
5.63
7.00
8.51
10.23
11.99
13.66
15.19
16.61
17.96
19.29
20.59
21.87
23.20
24.60
25.99
0.69
1.91
3.41
5.30
7.80
10.79
13.87
16.90
20.03

0.23
0.30
0.41
0.53
0.64
0.69
0.69
0.82
0.89
0.87
0.80
0.73
0.69
0.66
0.66
0.64
0.64
0.69
0.71
0.69
0.53
0.69
0.80
1.08
1.42
1.58
1.50
1.53
1.61

3.25
4.45
5.70
6.86
8.27
11.61
13.38
20.09
33.96
48.40
70.55
65.86
95.69
95.67
100.91
93.39
93.53
89.64
146.84
63.66
4.67
8.57
12.78
22.75
44.32
75.03
81.63
144.82
104.88

184

σK

0.02
0.07
0.10
0.21
0.28
0.46
0.31
0.47
1.08
2.86
4.19
2.71
3.88
3.90
4.25
3.99
3.84
1.99
11.53
0.75
0.12
0.23
0.37
0.51
1.87
5.69
6.57
31.81
8.84

tc/t f f

δtc/t f f

21.72
23.16
24.59
24.82
23.63
30.10
26.85
41.34
83.59
124.43
171.97
122.90
143.38
125.45
125.25
98.56
89.24
75.46
207.38
28.79
47.66
44.98
41.92
63.10
128.12
221.54
182.53
478.53
178.53

0.58
0.75
0.86
1.14
1.17
1.71
1.13
1.74
4.67
11.56
21.36
9.66
11.46
10.10
10.52
7.76
6.62
4.15
36.95
1.01
1.71
1.79
1.67
2.41
9.47
31.42
28.17
230.97
28.08

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC1407
NGC1407
NGC1407
NGC1521
NGC1521
NGC1521
NGC1521
NGC1521
NGC1550
NGC1550
NGC1550
NGC1550
NGC1550
NGC1550
NGC1550
NGC1550
NGC1550
NGC1600
NGC1600
NGC1600
NGC1600
NGC1600
NGC1600
NGC1600
NGC2300
NGC2300
NGC2300
NGC2300
NGC2300

23.17
26.08
29.00
0.30
0.97
1.64
2.37
3.46
3.37
9.87
16.86
24.80
32.99
41.26
50.17
60.04
71.68
0.76
2.29
4.86
8.62
12.34
15.72
18.83
1.56
5.58
11.29
17.76
23.64

1.53
1.39
1.53
0.30
0.36
0.30
0.43
0.67
3.37
3.13
3.85
4.09
4.09
4.17
4.74
5.14
6.50
0.76
0.76
1.80
1.97
1.75
1.64
1.47
1.56
2.45
3.26
3.21
2.66

167.67
146.99
111.38
1.79
4.57
6.36
7.38
7.76
8.18
16.35
26.07
36.88
44.67
53.74
60.31
71.01
64.94
5.88
9.77
34.77
70.62
69.26
147.03
65.86
5.28
13.94
39.79
88.62
124.68

185

σK

34.72
20.32
6.55
0.28
0.55
0.69
0.94
0.43
0.16
0.43
0.80
0.98
1.48
1.32
1.77
2.48
1.33
0.23
0.39
3.14
11.27
8.91
74.08
5.56
0.19
0.56
2.48
9.28
17.55

tc/t f f

δtc/t f f

410.89
260.78
118.84
20.90
23.49
23.18
25.00
18.07
19.89
18.39
24.77
29.18
30.09
27.22
26.80
30.89
19.70
44.88
42.60
177.36
265.42
140.35
581.47
70.44
26.09
30.76
76.58
184.36
256.24

186.47
78.22
12.30
5.21
4.05
3.77
4.33
1.47
0.66
0.84
1.45
1.63
2.15
1.27
1.59
2.27
0.73
5.97
7.16
46.25
105.16
48.72
673.76
22.06
1.27
1.73
6.88
38.41
76.15

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC2300
NGC2300
NGC2300
NGC2300
NGC2300
NGC2300
NGC2305
NGC2305
NGC2305
NGC2305
NGC2305
NGC2305
NGC3091
NGC3091
NGC3091
NGC3091
NGC3091
NGC3091
NGC3923
NGC3923
NGC3923
NGC3923
NGC3923
NGC3923
NGC3923
NGC3923
NGC3923
NGC4073
NGC4073

28.46
32.65
36.58
40.47
44.53
48.38
0.30
0.84
1.48
2.47
3.86
5.98
1.38
3.46
4.78
5.99
7.43
9.16
0.20
0.58
1.03
1.75
2.93
4.45
6.08
7.70
9.20
1.86
4.37

2.16
2.03
1.90
1.99
2.07
1.78
0.30
0.25
0.40
0.59
0.79
1.33
1.38
0.69
0.63
0.58
0.86
0.86
0.20
0.18
0.28
0.45
0.73
0.80
0.83
0.80
0.70
1.86
0.64

91.95
118.68
121.46
127.58
129.14
85.24
2.36
2.98
4.38
7.88
13.37
11.11
8.35
12.93
16.90
15.79
22.39
17.56
1.70
2.37
3.58
5.43
9.14
14.77
17.34
30.91
24.90
10.88
16.45

186

σK

8.23
9.60
11.19
9.58
14.20
3.61
0.21
0.34
0.41
0.92
1.24
0.75
0.29
1.31
2.68
1.49
1.22
0.39
0.05
0.09
0.14
0.33
0.65
1.03
1.23
3.27
2.01
0.16
0.96

tc/t f f

δtc/t f f

97.13
112.37
99.41
95.08
105.19
36.37
41.58
20.22
21.28
31.43
42.83
21.51
53.15
41.98
49.59
30.74
43.43
18.47
24.64
21.98
26.99
31.16
40.15
54.93
45.51
89.41
39.50
32.22
36.79

16.45
17.57
18.43
13.45
25.30
2.76
5.38
3.36
2.77
4.91
6.20
2.01
3.13
5.99
11.19
4.16
5.29
0.93
1.53
1.41
2.11
3.15
4.62
7.21
6.06
18.07
5.27
2.92
4.46

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC4073
NGC4073
NGC4073
NGC4073
NGC4073
NGC4073
NGC4073
NGC4073
NGC4073
NGC4073
NGC4073
NGC4073
NGC4125
NGC4125
NGC4125
NGC4125
NGC4125
NGC4125
NGC4125
NGC4125
NGC4125
NGC4261
NGC4261
NGC4261
NGC4261
NGC4261
NGC4261
NGC4261
NGC4261

5.66
7.02
8.53
10.25
12.18
14.19
16.48
19.13
21.78
24.79
28.73
34.61
0.23
0.43
0.69
0.94
1.23
1.53
1.86
2.27
2.81
0.28
0.67
1.44
3.09
5.94
12.02
18.55
24.88

0.64
0.72
0.79
0.93
1.00
1.00
1.29
1.36
1.29
1.72
2.22
3.65
0.08
0.13
0.13
0.13
0.15
0.15
0.18
0.23
0.31
0.14
0.25
0.53
1.12
1.72
4.36
2.18
4.15

20.85
25.59
29.43
36.49
45.92
51.76
58.44
65.44
88.26
75.50
101.42
90.14
2.79
4.08
6.45
8.88
10.90
8.84
8.87
11.35
10.30
1.10
2.65
5.37
14.20
42.49
107.04
155.67
151.31

187

σK

1.88
4.44
3.38
4.56
5.86
7.29
6.06
6.40
16.27
10.83
7.59
3.79
0.52
0.63
0.54
0.88
1.24
0.96
0.73
0.96
0.59
0.02
0.04
0.14
0.30
1.49
12.62
21.64
11.96

tc/t f f

δtc/t f f

48.00
60.18
64.60
83.06
99.94
105.51
93.81
96.61
150.39
86.32
136.11
77.10
28.22
47.29
62.15
90.95
103.67
68.73
51.68
65.98
36.36
14.17
23.73
35.27
67.99
169.87
423.98
256.21
143.39

8.11
17.78
13.36
19.56
23.59
28.85
19.94
19.43
54.05
21.58
26.40
11.08
12.35
14.58
14.88
24.93
32.99
22.40
15.83
21.90
12.17
1.47
3.06
5.04
10.05
27.13
104.52
86.33
31.33

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC4261
NGC4374
NGC4374
NGC4374
NGC4374
NGC4374
NGC4374
NGC4374
NGC4374
NGC4374
NGC4374
NGC4374
NGC4374
NGC4406
NGC4406
NGC4406
NGC4406
NGC4406
NGC4406
NGC4406
NGC4406
NGC4406
NGC4406
NGC4406
NGC4406
NGC4472
NGC4472
NGC4472
NGC4472

31.77
0.41
0.99
1.70
2.57
3.78
5.60
7.95
10.29
12.45
14.55
16.52
18.37
1.61
4.37
6.41
8.09
9.68
11.24
12.85
14.56
16.22
17.80
19.33
20.85
0.32
0.96
1.74
2.79

2.74
0.24
0.34
0.38
0.49
0.71
1.11
1.25
1.09
1.07
1.03
0.95
0.89
1.61
1.15
0.88
0.81
0.79
0.77
0.84
0.86
0.81
0.77
0.77
0.75
0.32
0.32
0.45
0.60

113.86
2.29
3.69
5.73
8.74
15.22
27.25
49.78
52.64
88.41
100.51
139.13
80.61
10.87
26.62
22.78
23.33
31.29
26.31
36.03
41.99
48.19
45.89
53.74
35.32
2.38
4.34
7.56
13.36

188

σK

3.91
0.10
0.20
0.29
0.41
0.53
1.42
6.53
6.24
15.26
20.91
47.12
5.49
0.43
2.02
1.43
1.41
1.60
0.87
2.79
3.04
2.20
1.69
2.78
0.48
0.02
0.03
0.05
0.10

tc/t f f

δtc/t f f

66.51
26.32
25.04
27.13
34.74
54.98
109.44
220.69
159.97
234.34
228.15
314.58
73.56
52.64
75.24
40.44
32.98
46.93
26.28
37.36
42.70
48.56
38.67
49.64
17.54
35.65
26.80
36.00
57.55

11.23
7.29
6.58
6.77
8.40
13.26
28.74
73.07
54.33
103.59
119.14
260.58
27.31
2.85
8.69
3.63
2.84
5.00
1.60
4.16
4.82
5.09
3.30
5.88
0.67
0.31
0.23
0.31
0.60

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC4472
NGC4472
NGC4472
NGC4472
NGC4472
NGC4472
NGC4472
NGC4472
NGC4472
NGC4472
NGC4472
NGC4472
NGC4472
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486

4.02
5.24
6.47
7.71
8.98
10.28
11.62
13.00
14.41
15.86
17.39
19.09
21.13
0.79
1.93
2.78
3.64
4.61
5.65
6.76
7.88
8.96
10.01
11.03
12.08
13.14
14.22
15.33
16.45

0.62
0.60
0.62
0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.79
0.91
1.13
0.71
0.43
0.41
0.45
0.51
0.53
0.57
0.55
0.53
0.51
0.51
0.53
0.53
0.55
0.55
0.57

18.41
23.27
28.48
30.79
35.70
36.53
41.73
42.78
47.72
52.30
56.39
65.54
57.87
5.85
8.85
9.55
11.58
15.79
17.34
20.26
22.27
23.80
25.16
29.61
32.75
34.68
35.46
35.05
37.68

189

σK

0.14
0.27
0.32
0.32
0.44
0.49
0.42
0.64
0.59
0.85
1.07
1.31
0.41
0.02
0.03
0.07
0.06
0.04
0.07
0.08
0.11
0.11
0.09
0.10
0.12
0.13
0.17
0.14
0.17

tc/t f f

δtc/t f f

68.27
65.79
70.12
65.14
71.43
63.97
68.92
66.14
68.29
71.82
72.96
82.28
53.03
35.11
25.09
22.73
24.81
34.31
34.25
42.41
43.45
41.89
41.47
38.78
43.18
43.94
45.43
40.02
42.82

1.13
1.50
1.29
1.16
1.47
1.58
1.30
1.79
1.77
2.26
2.33
2.76
0.72
0.34
0.21
0.27
0.28
0.27
0.36
0.38
0.43
0.42
0.40
0.40
0.47
0.49
0.52
0.41
0.49

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4486
NGC4552
NGC4552
NGC4552
NGC4552
NGC4552
NGC4552
NGC4552
NGC4552
NGC4552
NGC4552
NGC4552
NGC4552
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636

17.61
18.81
20.09
21.47
22.93
24.49
26.12
27.80
29.51
0.21
0.49
0.76
1.02
1.44
2.12
3.04
4.21
6.22
9.71
13.66
16.92
0.38
1.01
1.56
2.21
2.87
3.50
4.09
4.68

0.59
0.61
0.67
0.71
0.75
0.81
0.83
0.85
0.87
0.13
0.15
0.11
0.15
0.27
0.42
0.49
0.68
1.33
2.16
1.78
1.48
0.38
0.25
0.30
0.34
0.32
0.30
0.29
0.30

40.95
42.03
45.76
49.27
52.68
57.37
56.33
74.52
47.13
2.21
3.14
3.58
3.79
5.34
7.32
8.65
12.27
25.35
42.84
66.67
110.80
1.84
2.88
4.03
5.61
6.83
7.37
9.15
10.52

190

σK

0.21
0.21
0.20
0.21
0.36
0.16
0.14
0.30
0.16
0.07
0.07
0.08
0.04
0.13
0.33
0.45
0.92
1.72
3.29
9.14
4.91
0.06
0.05
0.07
0.15
0.09
0.09
0.15
0.07

tc/t f f

δtc/t f f

45.24
43.85
44.67
48.17
50.12
54.30
47.66
67.70
22.21
11.35
29.71
30.87
24.97
42.30
50.44
37.89
47.33
93.05
116.47
108.97
55.62
11.53
10.79
15.23
22.73
22.67
20.35
20.36
22.00

0.50
0.48
0.47
0.52
0.60
0.57
0.48
0.76
0.22
0.63
1.33
1.31
0.61
1.54
3.61
2.51
4.18
9.31
15.27
18.49
4.20
0.61
0.36
0.51
0.99
0.89
0.80
0.83
0.85

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4636
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649
NGC4649

5.31
6.01
6.85
7.86
9.00
10.22
11.51
12.90
14.41
16.00
17.70
19.54
21.67
0.16
0.41
0.63
0.89
1.18
1.56
2.05
2.69
3.46
4.36
5.41
6.55
7.78
9.10
10.56
12.16

0.32
0.38
0.46
0.55
0.59
0.63
0.67
0.72
0.78
0.82
0.88
0.97
1.16
0.16
0.10
0.12
0.14
0.16
0.22
0.28
0.36
0.41
0.49
0.55
0.59
0.63
0.69
0.77
0.83

11.60
13.68
16.02
20.94
23.86
30.68
30.65
35.06
40.63
41.87
43.13
51.92
44.10
1.94
2.15
3.27
3.78
4.80
6.30
8.44
11.88
14.62
18.30
22.61
27.24
32.78
37.71
44.71
55.05

191

σK

0.10
0.18
0.22
0.23
0.26
0.57
0.54
0.63
0.80
0.65
0.63
0.42
0.24
0.01
0.02
0.02
0.02
0.05
0.07
0.05
0.07
0.08
0.13
0.28
0.42
0.43
0.51
0.64
1.09

tc/t f f

δtc/t f f

22.47
25.04
29.59
42.09
45.93
58.10
48.90
55.77
63.86
56.66
54.50
64.54
38.01
41.35
22.63
34.06
28.17
31.04
37.58
44.00
60.06
61.41
67.92
75.44
80.43
82.11
85.97
96.94
124.87

0.90
1.04
1.25
1.80
2.00
2.73
2.46
2.76
3.28
2.79
2.53
2.93
1.66
0.60
0.35
0.59
0.47
0.61
0.77
0.81
1.20
1.22
1.43
1.78
2.09
2.02
2.15
2.53
4.00

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC4649
NGC4649
NGC4649
NGC4649
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4696
NGC4778
NGC4778

13.86
15.56
17.22
20.81
1.34
3.53
5.14
6.71
8.32
10.06
11.98
14.04
16.23
18.51
20.83
23.16
25.48
27.85
30.31
32.90
35.76
38.85
42.07
45.55
49.71
54.85
61.47
1.56
4.24

0.87
0.83
0.83
2.76
1.34
0.85
0.76
0.80
0.80
0.94
0.98
1.07
1.12
1.16
1.16
1.16
1.16
1.21
1.25
1.34
1.52
1.56
1.65
1.83
2.32
2.82
3.80
1.56
1.13

72.12
87.41
109.43
110.16
4.60
9.31
10.25
13.92
15.46
19.34
22.60
28.72
35.10
40.86
43.92
47.73
49.99
52.32
54.33
61.77
76.92
85.48
90.99
92.99
111.19
138.93
122.94
5.64
8.68

192

σK

1.94
4.10
3.45
1.42
0.01
0.03
0.03
0.05
0.05
0.03
0.05
0.20
0.16
0.20
0.22
0.39
0.25
0.51
0.53
0.50
0.45
0.52
0.44
0.44
0.44
0.59
0.44
0.09
0.17

tc/t f f

δtc/t f f

177.98
232.40
295.42
216.18
4.73
9.98
10.61
14.35
15.63
20.27
24.63
30.41
37.86
44.91
46.48
47.27
48.21
45.66
44.14
46.99
63.02
70.96
68.23
63.64
78.21
110.93
70.47
19.99
15.02

7.48
15.59
20.67
5.71
0.03
0.06
0.06
0.07
0.09
0.08
0.10
0.40
0.23
0.29
0.31
0.44
0.33
0.49
0.47
0.42
0.48
0.57
0.47
0.41
0.47
0.77
0.35
3.95
2.54

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4778
NGC4782
NGC4782
NGC4782
NGC4782
NGC4782
NGC4782
NGC4782
NGC4936
NGC4936
NGC4936
NGC4936
NGC4936

6.65
9.26
12.09
15.27
19.38
24.61
30.34
36.28
42.36
48.44
54.52
60.46
66.19
71.99
78.71
86.91
96.74
0.75
2.15
4.06
5.80
7.31
10.49
15.91
2.99
8.53
13.39
17.69
21.50

1.27
1.34
1.49
1.70
2.40
2.83
2.90
3.04
3.04
3.04
3.04
2.90
2.83
2.97
3.75
4.46
5.37
0.41
0.99
0.93
0.81
0.70
2.48
2.95
2.99
2.54
2.32
1.98
1.83

13.36
17.32
21.82
26.51
41.99
60.55
71.67
92.59
112.56
125.81
165.52
172.03
155.83
158.50
192.48
376.99
183.69
5.50
15.51
35.57
41.77
31.66
72.69
78.48
12.45
33.59
47.46
48.95
48.71

193

σK

0.37
0.36
0.51
0.43
1.05
2.66
3.45
3.51
5.16
7.29
16.63
17.33
10.82
9.20
12.97
119.33
6.19
1.48
4.78
7.78
9.18
3.80
12.90
11.64
1.21
2.55
5.02
4.20
5.28

tc/t f f

δtc/t f f

21.79
22.67
27.70
26.28
51.95
69.48
73.01
89.51
108.76
114.13
174.48
162.30
111.77
100.89
142.79
547.61
90.45
18.94
60.42
60.68
56.43
26.26
113.93
70.41
29.89
56.79
63.84
55.72
43.94

3.58
3.72
4.70
4.60
9.70
14.28
15.86
19.96
25.71
28.61
54.92
51.99
31.07
26.95
40.02
411.43
23.03
9.92
35.43
26.70
24.84
8.03
47.16
21.24
12.12
23.32
29.86
28.13
23.41

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC4936
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5044
NGC5129
NGC5129
NGC5129

25.17
1.10
2.54
3.51
4.40
5.20
5.97
6.73
7.49
8.25
9.01
9.77
10.53
11.34
12.18
13.03
13.88
14.76
15.69
16.75
18.20
20.11
22.27
24.70
27.73
31.63
2.28
9.53
19.47

1.83
0.93
0.51
0.47
0.42
0.38
0.38
0.38
0.38
0.38
0.38
0.38
0.38
0.42
0.42
0.42
0.42
0.47
0.47
0.59
0.87
1.04
1.13
1.30
1.73
2.17
2.28
4.97
4.97

42.63
3.17
5.86
7.56
8.18
8.57
8.81
8.59
9.47
10.04
10.99
11.89
12.30
13.16
14.32
14.64
15.35
16.14
16.39
17.95
19.47
22.32
24.20
25.72
34.60
30.19
6.31
29.13
59.89

194

σK

2.06
0.05
0.10
0.14
0.13
0.20
0.20
0.14
0.17
0.14
0.13
0.15
0.07
0.07
0.08
0.08
0.08
0.09
0.08
0.14
0.15
0.14
0.13
0.11
0.16
0.06
0.16
1.00
4.74

tc/t f f

δtc/t f f

24.12
5.75
9.39
11.54
11.29
10.83
10.65
9.26
10.03
9.71
10.10
11.14
10.66
11.39
12.60
12.19
12.54
12.79
12.23
13.70
14.40
16.03
16.24
16.01
23.80
13.64
22.58
55.41
76.66

12.98
0.14
0.23
0.33
0.25
0.30
0.29
0.22
0.23
0.19
0.19
0.21
0.16
0.17
0.20
0.19
0.20
0.20
0.19
0.23
0.22
0.24
0.25
0.24
0.37
0.20
0.85
2.89
8.84

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC5129
NGC5129
NGC5129
NGC5129
NGC5129
NGC5129
NGC5129
NGC5129
NGC5419
NGC5419
NGC5419
NGC5419
NGC5419
NGC5419
NGC5419
NGC5419
NGC5419
NGC5419
NGC5419
NGC5419
NGC5813
NGC5813
NGC5813
NGC5813
NGC5813
NGC5813
NGC5813
NGC5813
NGC5813

28.80
36.98
44.33
51.17
57.69
64.01
70.23
76.24
0.74
1.52
6.25
14.62
22.21
28.76
34.46
39.56
44.47
49.14
53.15
56.85
1.00
2.04
2.93
3.86
4.79
5.65
6.48
7.27
8.03

4.35
3.83
3.52
3.31
3.21
3.11
3.11
2.90
0.25
0.54
4.19
4.19
3.40
3.15
2.55
2.55
2.37
2.31
1.70
2.00
0.59
0.45
0.45
0.48
0.45
0.41
0.41
0.38
0.38

67.05
77.18
96.76
79.98
93.98
77.60
91.52
59.99
2.72
5.59
34.25
112.67
130.20
227.11
120.04
138.21
124.60
162.76
115.08
98.25
4.30
4.61
5.78
7.04
8.38
7.53
9.59
10.12
11.53

195

σK

3.83
5.34
12.18
4.89
7.86
6.54
8.53
1.54
0.22
0.25
3.47
42.19
29.23
83.42
21.95
20.53
19.58
44.73
14.66
3.32
0.04
0.06
0.10
0.08
0.11
0.23
0.19
0.18
0.13

tc/t f f

δtc/t f f

61.04
56.21
75.95
39.75
47.58
36.60
46.06
15.71
17.30
27.59
137.55
269.90
167.59
396.10
107.06
119.27
87.61
137.41
47.57
30.10
15.90
12.20
15.01
17.24
19.33
14.27
17.10
15.61
15.48

6.20
7.59
21.18
5.11
8.65
6.91
9.63
0.88
2.21
2.04
22.11
127.33
51.70
286.55
34.07
25.03
18.42
75.48
13.62
2.28
0.33
0.26
0.39
0.41
0.55
0.60
0.56
0.49
0.41

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC5813
NGC5813
NGC5813
NGC5813
NGC5813
NGC5813
NGC5813
NGC5813
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846
NGC5846

8.79
9.58
10.44
11.44
12.68
14.23
16.26
18.95
0.78
2.23
3.66
5.15
6.67
8.19
9.64
11.07
12.49
13.91
15.31
16.66
18.06
19.54
21.13
22.81
24.56
26.34
28.15
29.93
31.71

0.38
0.41
0.45
0.55
0.69
0.86
1.17
1.52
0.78
0.68
0.74
0.74
0.78
0.74
0.71
0.71
0.71
0.71
0.68
0.68
0.71
0.78
0.81
0.87
0.87
0.91
0.91
0.87
0.91

11.70
13.02
14.10
14.84
16.95
19.05
24.84
20.56
3.58
5.39
7.70
8.82
12.08
14.13
16.14
19.05
22.39
22.30
23.86
26.16
30.41
37.67
39.17
50.80
63.26
68.29
76.42
81.23
76.60

196

σK

0.06
0.12
0.14
0.13
0.12
0.07
0.10
0.06
0.07
0.15
0.23
0.38
0.65
0.85
0.91
0.69
0.98
1.07
0.96
1.64
1.06
2.23
1.79
2.97
4.35
5.89
4.18
8.33
4.90

tc/t f f

δtc/t f f

13.87
15.15
15.28
15.42
17.99
19.77
29.16
14.12
24.27
16.49
19.06
17.71
21.72
22.07
22.33
24.36
26.67
25.24
23.23
26.31
26.03
37.80
37.19
49.44
65.45
74.94
78.23
85.34
72.61

0.32
0.38
0.38
0.38
0.44
0.49
0.74
0.35
2.61
2.27
2.81
2.75
3.56
3.67
3.74
3.98
4.44
4.30
3.86
4.62
4.29
6.63
6.26
8.79
11.97
18.25
13.87
18.46
14.39

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC5846
NGC5846
NGC6407
NGC6407
NGC6407
NGC6407
NGC6861
NGC6861
NGC6861
NGC6861
NGC6861
NGC6861
NGC6861
NGC6861
NGC6861
NGC6861
NGC6861
NGC6861
NGC6868
NGC6868
NGC6868
NGC6868
NGC6868
NGC6868
NGC6868
NGC6868
NGC7619
NGC7619
NGC7619

33.59
35.63
3.17
8.59
12.39
17.58
0.68
2.80
6.46
10.26
13.42
16.04
18.41
20.53
22.47
24.26
25.95
27.60
1.68
5.09
9.79
15.29
20.35
24.63
28.49
33.84
1.57
6.27
13.08

0.97
1.07
3.17
2.25
1.55
3.64
0.47
1.65
2.01
1.79
1.36
1.26
1.11
1.00
0.93
0.86
0.83
0.83
1.45
1.96
2.74
2.75
2.31
1.97
1.89
3.47
1.57
3.13
3.68

84.31
68.99
8.76
19.73
31.33
37.16
3.48
16.57
46.80
60.70
91.42
64.62
77.31
56.31
94.94
56.17
62.13
46.73
9.34
31.71
30.68
41.39
51.77
61.39
50.57
47.78
7.77
24.52
45.58

197

σK

5.29
1.81
0.88
3.10
9.25
4.60
0.14
1.01
6.57
6.22
23.97
6.61
18.72
5.50
37.13
5.45
7.54
2.12
0.47
2.34
1.98
1.52
2.44
4.81
2.44
1.69
0.16
0.68
1.53

tc/t f f

δtc/t f f

82.49
44.99
21.33
26.60
35.81
33.46
30.62
97.89
192.75
146.87
239.61
82.39
135.92
55.90
156.62
42.49
47.84
22.82
50.39
110.13
57.11
53.53
57.78
64.21
33.77
27.55
46.50
70.33
82.17

16.21
7.43
3.89
7.09
16.87
9.05
1.68
7.85
43.17
29.10
138.52
16.37
73.87
12.11
137.71
9.16
12.96
2.21
3.28
11.29
4.87
3.43
5.55
9.93
3.04
1.70
1.40
3.06
4.96

σK

4.73
7.93
13.10
12.44
24.55
13.70
10.56
26.14
4.09
0.48
3.97
2.82
9.61
11.90

tc/t f f

δtc/t f f

93.46
100.42
136.13
109.57
164.14
89.14
70.76
116.21
38.42
69.46
115.70
89.39
121.91
70.50

10.42
15.96
30.50
22.74
52.27
19.56
12.21
38.35
2.76
4.38
17.54
7.78
20.60
13.04

Table F.1 (cont’d)
Galaxy

radius
(kpc)

∆r
(kpc)

K

(keV cm2)

NGC7619
NGC7619
NGC7619
NGC7619
NGC7619
NGC7619
NGC7619
NGC7619
NGC7619
NGC7796
NGC7796
NGC7796
NGC7796
NGC7796

20.19
27.00
33.44
39.35
45.14
50.74
55.98
61.22
66.83
1.82
5.70
11.76
22.21
33.85

3.43
3.37
3.07
2.83
2.95
2.65
2.59
2.65
2.95
1.82
2.06
4.00
6.45
5.19

69.45
85.75
126.62
129.04
170.22
137.25
132.82
176.45
113.74
10.73
31.72
47.47
76.14
76.09

198

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