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ﬂ LIBRARY
2008 Michigan State
University

This is to certify that the
dissertation entitled

Investigating Feedback and Relaxation in Clusters of Galaxies
with the Chandra X-ray Observatory

presented by

Kenneth W. Cavagnolo

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Astronomy & Astrophysics

 

 

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Date

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PLACE IN RETURN BOX to remove this checkout from your record.
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INVESTIGATING FEEDBACK AND RELAXATION IN CLUSTERS OF
GALAXIES WITH THE CHANDRA X—RAY OBSERVATORY

By

Kenneth W. Cavagnolo

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Astronomy and Astrophysics

2008

ABSTRACT

INVESTIGATING FEEDBACK AND RELAXATION IN CLUSTERS OF
GALAXIES WITH THE CHANDRA X-RAY OBSERVATORY

By

Kenneth W. Cavagnolo

Presented in this dissertation is an analysis of the X-ray emission from the intracluster
medium (ICM) in clusters of galaxies observed with the Chandra X-ray Observatory.
The cluster dynamic state is investigated via ICM temperature inhomogeneity, and

ICM entropy is used to evaluate the thermodynamics of cluster cores.

If the hot ICM is nearly isothermal in the projected region of interest, the X—ray
temperature inferred from a broadband (0.7—7.0 keV) spectrum should be identical to
the X—ray temperature inferred from a hard-band (2.0-7.0 keV) spectrum. However, if
unresolved cool lumps of gas are contributing soft X-ray emission, the temperature of
a best-ﬁt single-component thermal model will be cooler for the broadband spectrum
than for the hard-band spectrum. Using this difference as a diagnostic, the ratio
of best-ﬁtting hard-band and broadband temperatures may indicate the presence of
cooler gas even when the X-ray spectrum itself may not have sufﬁcient signal-to—noise

ratio (S / N ) to resolve multiple temperature components.

In Chapter 2 we explore this band dependence of the inferred X-ray temperature
of the ICM for 192 well-observed galaxy clusters selected from the Chandra X-ray Ob-
servatory’s Data Archive. We extract X—ray spectra from core-excised annular regions
for each cluster in the archival sample. We compare the X-ray temperatures inferred
from single-temperature ﬁts when the energy range of the ﬁt is 0.7-7.0 keV (broad)
and when the energy range is 2.0 / (1+z)-7.0 keV (hard). We ﬁnd that the hard-band

temperature is signiﬁcantly higher, on average, than the broadband temperature.

On further exploration, we ﬁnd this temperature ratio is enhanced preferentially for
clusters which are known merging systems. In addition, cool-core clusters tend to
have best-ﬁt hard-band temperatures that are in closer agreement with their best-ﬁt
broadband temperatures.

ICM entropy is of great interest because it dictates ICM global properties and
records the thermal history of a cluster. Entropy is therefore a useful quantity for
studying the effects of feedback on the cluster environment and investigating the
breakdown of cluster self-similarity. Radial entropy proﬁles of the ICM for a collec-
tion of 233 clusters taken from the Chandra X-ray Observatory’s Data Archive are
presented in Chapter 3. We ﬁnd that most ICM entropy proﬁles are well-ﬁt by a
model which is a power-law at large radii and approaches a constant value at small
radii: K (r) = K0 + K100(r/ 100 kpc)“, where K0 quantiﬁes the typical excess of core
entropy above the best ﬁtting power-law found at larger radii. We also show that the
K0 distributions of both the full archival sample and the primary HIF L U GCS’ sample
of Reiprich (2001) are bimodal with a distinct gap centered at K0 z 40 keV cm2 and
population peaks at K0 ~ 15 keV cm2 and K0 ~ 150 keV cm2.

Utilizing the results of the the Chandra X-ray Observatory archival study of in-
tracluster entropy presented in Chapter 3, we show in Chapter 4 that Ha and radio
emission from the brightest cluster galaxy are much more pronounced when the clus-
ter’s core gas entropy is S, 30 keV cm2. The prevalence of Ha emission below this
threshold indicates that it marks a dichotomy between clusters that can harbor mul-
tiphase gas and star formation in their cores and those that cannot. The fact that
strong central radio emission also appears below this boundary suggests that feedback
from an active galactic nucleus (AGN) turns on when the ICM starts to condense,
strengthening the case for AGN feedback as the mechanism that limits star formation

in the Universe’s most luminous galaxies.

Copyright by
KENNETH W. CAVAGNOLO
2008

Dedicated to my mother: Miss Lorna Lorraine Cox.

ACKNOWLEDGMENTS

Thanks to Christopher Waters for the LATEX class used to format this thesis.

My deepest thanks to Megan Donahue and Mark Voit for their guidance, wisdom,
patience, and without whom I would be in quantum computing. I can only say,
“Thank you, Megan” for giving me the time and space to ﬁnd my bearings after my
mother’s passing, words are insufﬁcient to express my gratitude. Ming Sun always
listened, always had time for a question, and was never wrong. Jack Baldwin nutured
my painfully slow development as a research assistant, a more calming voice there
has never been. On behalf of everyone that has never said so, “We love you, Shawna
Prater. MSU Astronomy and Astrophysics cannot do business without you.” And of
course, Debbie Simmons, without whom I would have been dropped from all courses
and locked out of the building.

Many dissertations across many disciplines acknowledge many religious ﬁgures and
a multitude of gods; but what about the Sun? Every time I feel the startling warmth
of the Sun on my skin, it is an invigorating experience. To be bathed in photons
millions of years old from an inconceivably large nuclear power plant over a hundred
million kilometers away makes me feel connected to the Universe in a way that is
surreal. To feel purposely cared for by an absentee whose existence and operation are
fundamentally devoid of purpose is quite profound. Unknowingly, the Sun gave rise
to a species of sentient dissidents. For that I say, “Thank you, Sun!”

To my wife: Our vows were foretelling, I will indeed require the course of an
entire life to express my appreciation for the tenderness, care, love, and humor you

gave during completion of this dissertation. You are, and always will be, my beloved.

PREFACE

Our Universe is predominantly an untold story. Within a larger, nested framework of
complex mechanisms, humans evolved with minimal impact on the systems which sup-
port and nurture our existance. Yet, during the short era of global industrialization,
we have compromised the effectiveness and function of the systems which formed the
biodiversity which makes our planet such a wonderful place. As an acknowledgement
of the appreciation our species has for the Earth, and as a show of our understanding
for humanity’s fleeting presence in the Earth’s lifecycle, let us strive to utilize the
pursuit of knowledge, through application of reason and logic, so that our actions
beneﬁt “all the children, of all species, for all of time” (McDonough & Braungart,
2002). Let us all exert effort such that the Earth and the Universe will be enriched
by humanity, and that our actions — local, global, and possibly interplanetary - will

leave the places we inhabit and visit nourished from our presence.

TABLE OF CONTENTS

viii

List of Tables ........................................................ xi
ListofFigures.................. ..................................... xii
List of Symbols ...................................................... xiv
1 Introduction ...................................................... 1
1.1 Clusters of Galaxies ........................ 1
1.2 The Intracluster Medium ..................... 6
1.2.1 X-ray Emission ......................... 8
1.2.2 Entropy ............................. 14
1.3 The Incomplete Picture of Clusters ................ 16
1.3.1 Breaking of Self-Similarity ................... 16
1.3.2 The Cooling Flow Problem .................. 21
1.4 Chandra X-Ray Observatory ................... 26
1.4.1 Telescope and Instruments ................... 26
1.4.2 X-ray Background and Calibration .............. 32
Bandpass Dependence of X-ray Temperatures in Galaxy Clusters . 37
2.1 Introduction ............................ 37
2.2 Sample Selection .......................... 40
2.3 Chandra Data ........................... 43
2.3.1 Reprocessing and Reduction .................. 43
2.3.2 X-ray Background ....................... 45
2.4 Spectral Extraction ........................ 48
2.5 Spectral Analysis .......................... 49
2.5.1 Fitting ............................. 49
2.5.2 Simulated Spectra ....................... 51
2.6 Results and Discussion ....................... 55
2.6.1 Temperature Ratios ...................... 55
2.6.2 Systematics ........................... 56
2.6.3 Using TH B R as a Test of Relaxation ............. 63
2.7 Summary and Conclusions .................... 69
2.8 Acknowledgments ......................... 71

3 Intracluster Medium Entropy Proﬁles For A Chandra Archival Sam-
ple of Galaxy Clusters ............................................ 74
3.1 Introduction ............................ 74
3.2 Data Collection ........................... 79
3.3 Data Analysis ........................... 81
3.3.1 Temperature Proﬁles ...................... 82
3.3.2 Deprojected Electron Density Proﬁles ............ 85
3.3.3 ﬁ-model Fits .......................... 86

3.3.4 Entropy Proﬁles ........................ 87

3.3.5 Exclusion of Central Sources ................. 91
3.4 Systematics ............................. 93
3.4.1 PSF Effects ........................... 93
3.4.2 Angular Resolution Effects .................. 94
3.4.3 Proﬁle Curvature and Number of Bins ............ 97
3.4.4 Power-law Proﬁles ....................... 98
3.5 Results and Discussion ....................... 99
3.5.1 Non-Zero Core Entropy .................... 100
3.5.2 Bimodality of Core Entropy Distribution ........... 102
3.5.3 The HIFL UGCS Sub—Sample ................. 105
3.5.4 Distribution of Core Cooling Times .............. 107
3.5.5 Slope and Normalization of Power-law Components ..... 110
3.6 Summary and Conclusions .................... 112
3.7 Acknowledgements ......................... 114
3.8 Supplemental Cluster Notes .................... 115
An Entropy Threshold for Strong Ha and Radio Emission in the
Cores of Galaxy Clusters ......................................... 121
4.1 Introduction ............................ 121
4.2 Data Analysis ........................... 123
4.2.1 X-ray .............................. 123
4.2.2 Ha ................................ 124
4.2.3 Radio .............................. 125
4.3 Ha Emission and Central EntrOpy ................ 127
4.4 Radio Sources and Central Entropy ............... 128
4.5 Summary .............................. 132
4.6 Acknowledgements ......................... 132
Summary ........................................................ 133
5.1 Energy Band Dependence of X-ray Temperatures ........ 133
5.2 Chandra Archival Sample of Intracluster Entropy Proﬁles . . . 134
5.3 An Entropy Threshold for Strong Ha and Radio Emission in the
Cores of Galaxy Clusters ..................... 135
Tables cited in Chapter 2 ......................................... 138
B Tables cited in Chapter 3 ......................................... 167
C Chandra Observations Reduction Pipeline (CORP) ............... 219
CI Copyright .............................. 219
C2 Introduction to CORP ....................... 220
C3 Initial Reprocessing ........................ 222
C.3.1 Retrieving Data ........................ 222
C32 Create New Level-2 Events File ................ 226
C33 ' Remove Point Sources and Identify Cluster Center ..... 228
C4 Intermediate Analysis ....................... 232

ix

C.5 Final Analysis ........................... 234

C51 Spectral Adjustments and Fitting ............... 234
C52 Generating Entropy Proﬁles .................. 236
References ....................................................... 238

2.1

2.2

A.1
A2
A3
A4

B.1
B2
B3
B4

B.5

LIST OF TABLES

Summary of two—component simulations .................. 55
Weighted averages for various apertures .................. 56
Summary of sample for energy band dependance study .......... 140
Clusters with T H B R > 1.1 with 90% conﬁdence ............... 150
Summary of Excised R2500 Spectral Fits .................. 152
Summary of Excised R5000 Spectral Fits .................. 159
General properties of clusters in entropy proﬁle study ............ 169
Summary of B—Model Fits .......................... 181
M. Donahue’s Ha Observations ........................ 182
Statistics of Best-Fit Parameters ...................... 183
Summary of best-ﬁt entropy proﬁle models ................. 184

xi

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

3.1

3.2

3.3

LIST OF FIGURES

Hubble image of Abell 1689 .1 ........................ 2
Composite image of the Bullet Cluster ................... 4
Synthetic spectral model of kTX = 2.0 keV gas. .............. 11
Synthetic spectral model of kTX = 8.0 keV gas. .............. 11
Figures illustrating of large scale structure formation ............ l8
Chandra X-ray Observatory spacecraft .................... 29
ACIS focal plane during observation. .................... 30
Spectrum of Abell 1795. ........................... 31
Chandra effective area as a function of energy ................ 35
Redshift distribution of bolometric luminosities for TH B R sample . . . . 42
Histogram of hard-particle count rate ratios for TH B R sample ...... 47
TH B R vs. broadband temperature for TH B R sample ........... 57
Plot of several possible systematics for R2500—CORE apertures ....... 60
Plot of several possible systematics for R5000_CORE apertures ....... 61
TH B R vs. best-ﬁt metallicity ........................ 62
Number of cool and non-cool clusters as a function of TH B R ....... 65
Plot of TH B R vs. broadband temperatures color-coded for different cluster

types .................................... 68
Ratio of best-ﬁt K0 for temperature interpolation schemes ......... 89
Best-ﬁt K0 versus redshift ........................... 96
Montage of entropy proﬁles for varying cuts in cluster temperature. . . . 101

xii

3.4

Histogram and cumulative distribution of best-ﬁt K0 for full ACCEPT

sample .................................... 103
3.5 Histogram and cumulative distribution of best-ﬁt K0 for primary HI-

FL UGCS sample .............................. 108
3.6 Histograms and cumulative distributions of cooling times. ........ 111
3.7 Surface brightness proﬁles and best-ﬁt ﬁ-models. ............. 115
4.1 Ha luminosity versus core entropy ..................... 129
4.2 BCG radio power versus core entropy .................... 131
C.1 Example of strong X—ray ﬂare in Chandra data .............. 229

Images in this dissertation are presented in color.

 

xiii

LIST OF SYMBOLS

Mpc Megaparsec: A unit of length representing one million parsecs. The parsec
(pc) is a historical unit for measuring parallax and equals 3.0857 x 1013
km ......................................

z Dimensionless redshift: As is common in most of astronomy, I adopt
the deﬁnition of redshift using a dimensionless ratio of wavelengths,
z = (Aobserved/Arest) — 1, where the wavelength shift occurs because of
cosmic expansion ..............................

H0 Hubble constant: The current ratio of recessional velocity arising from
expansion of the Universe to an object’s distance from the observer,
v = HOD. H0 is assumed here to be ~ 70 km s“1 Mpc—1 . Inverted,
the Hubble constant yields the present age of the Universe, H61 m
13.7 billion years. H (2) denotes the Hubble constant at a particular
redshift, z ..................................

pc Critical density: The density necessary for a universe which has spatially
ﬂat geometry and in which the expansion rate of spacetime balances
gravitational attraction and prevents recollapse. In terms of relevant
quantities pc = 3H (.2)2 /87rG, with units g cm—3. ...........

(2 A Cosmological constant energy density of the Universe: The ratio of energy
density due to a cosmological constant to the critical density. Q A is
assumed here to be ~ 0.7. ........................

O M Matter density of the Universe: The ratio of total matter density to the
critical density. OM is currently measured to be ~ 0.3. ........

MG Mass of the Sun: One solar mass equals 1.9891 x 1030 kg ........

Z9 Metal abundance of the Sun: Individual elemental abundances can be
found in Anders & Grevesse (1989) ....................

N H Neutral hydrogen column density: The Galaxy is rich with metals such
as C, N, O, S, and Si which absorb incoming extragalactic soft X-ray
radiation. The density of neutral hydrogen is assumed to be a surrogate
for the density of metals. Photoelectric absorption models are used to
quantify the attenuation of soft X-rays, and typically take as input the
column density ( cm‘z) of neutral hydrogen in a particular direction.
NH is related to the number density, n H ( cm‘3), along the line of
sight, dl, as NH = andl. ........................

xiv

11

Cooling function: A function describing plasma emissivity for a given
temperature and metal composition, and typically given in units of

ergs cm3 s‘1 ................................

Comoving distance: The distance which would be measured between two
objects today if those two points were moving away from each other
with the expansion of the Universe. ...................

Angular diameter distance: The ratio of an object’s true transverse size to
its angular size. For a nearly flat universe, D A is a good approximation
of the comoving distance, D A z DC / (1 + z) ...............

Solid angle: For a sphere of a given radius, for example the distance to
an object Do, the area of that object, A, on the sphere subtends an
angle equal to {25 = A/Dg. This is the solid angle. ..........

Curvature of the Universe: For a spatially ﬁat universe, such as our own,
Qk z 0. ..................................

Comoving volume: The volume in which the number density of slowly
evolving objects locked into the local Hubble ﬂow, like galaxy clusters,
is constant with redshift. The comoving volume element for redshift
element dz and solid angle element dQS element is dVC = Dc [D A(1 +

z)12[nM(1 + z)3 + nk(1+ z)2 + nArl/Z dQS dz. ...........

XV

13

17

17

17

 

CHAPTER 1:
INTRODUCTION

 

1.1 CLUSTERS OF GALAXIES

Of the luminous matter in the Universe, stars and galaxies are often the most familiar
to a sky gazer. Aside from the Moon and the occasional bright planet, stars are the
most abundantly obvious patrons of the night sky. Viewed from a sufﬁciently dark lo-
cation, the stars form a band of light interspersed with dust and gaseous clouds which
deﬁne the Milky Way, our home galaxy. The Milky Way is only one of more than 30
galaxies in a gravitationally bound group of galaxies, named the Local Group, which
includes the well-known, nearby galaxy Andromeda. But in cosmological terms, the
Local Group is very small in comparison to immense structures containing thousands
of galaxies. In a turn of wit, these structures are appropriately named clusters of
galaxies, and are the focus of this dissertation.

Galaxy clusters are the most massive gravitationally bound structures to have yet
formed in the Universe. As where galaxy groups have roughly 10-50 galaxies, galaxy
clusters have hundreds to thousands of galaxies. When viewed through a telescope,
a galaxy cluster appears as a tight distribution of mostly elliptical and SO spiral
galaxies within a radius of ~ 1 — 5 Mpc1 of each other. Rich galaxy clusters are
truly spectacular objects, as can be seen in Figure 1.1 which shows the Hubble Space

Telescope’s close-up of the strong lensing cluster Abell 1689.

 

1Throughout this dissertation, a ﬂat ACDM cosmology of Ho = 70 km s‘1 Mpc"l , (M = 0.7,
and OM = 0.3 is assumed. These values are taken from Spergel et a1. (2007).

 

Figure 1.1 Optical image of the galaxy cluster Abell 1689 as observed with the ACS
instrument on—board the Hubble Space Telescope. The fuzzy yellowish spheres are
giant elliptical (gE) galaxies in the cluster, with the gE nearest the center of the
image being the brightest cluster galaxy — ostensibly, the cluster “center”. Image
taken from NASA’s Hubblesitecrg. Image Credits: NASA, N. Benitez (JHU), T.
Broadhurst (The Hebrew University), H. Ford (JHU), M. Clampin(STScI), G. Hartig
(STScI), G. Illingworth (UCO/ Lick Observatory), the ACS Science Team and BSA.

Galaxy clusters are deceptively named. As with most objects in the Universe, one
of the most revealing characteristics of an object is its mass, and the mass of clusters
of galaxies is not dominated by galaxies. A cluster of galaxies massis dominated
( 2, 85%) by dark matter with most ( ,Z 80%) of the baryonic mass2 in the form of
a hot (kT z 2 — 15 keV; 10—100 million degrees K), luminous (1043—46 ergs 5‘1),
diffuse (10‘1 — 10—4 cm-3) intracluster medium (ICM) which is co—spatial with the
galaxies but dwarfs them in mass (Blumenthal et al., 1984; David et al., 1990). For
comparison, the ICM in the core region of a galaxy cluster is, on average, 1020 times
less dense than typical Earth air, 105 times denser than the mean cosmic density,
more than 2000 times hotter than the surface of the Sun, and shines as bright as 1035
100 watt light bulbs.

Because of the ICM’s extreme temperature, the gas is mostly ionized, making
it a plasma. For the temperature range of clusters, the ICM is most luminous at
X—ray wavelengths of the electromagnetic spectrum. This makes observing galaxy
clusters with X-ray telescopes, like NASA’s Chandra X-ray Observatory, a natural
choice. Clusters have masses ranging over 1014—15 MG with velocity dispersions of
500 - 1500 km 3.1. The ICM has also been enriched with metals3 to an average value
of ~ 0.3 solar abundance. Shown in Figure 1.2 is an optical, X-ray, and gravitational
lensing composite image of the galaxy cluster 1E0657-56. This cluster is undergoing
an especially spectacular and rare merger in the plane of the sky which allows for the
separate dominant components of a cluster — dark matter, the ICM, and galaxies —
to be “seen” distinctly.

As knowing the characteristics of galaxy clusters is a small part of the discovery
process, we must also wonder, why study clusters of galaxies? Galaxy clusters have

two very important roles in the current research paradigm:

 

2Baryonic is a convenient term used to describe ordinary matter like atoms or molecules, while
non-baryonic matter is more exotic like free electrons or dark matter particles.

3It is common practice in astronomy to classify “metals” as any element with more than two
protons.

 

Figure 1.2 The galaxy cluster 1E0657-56, aka. the Bullet Cluster. All of the pri—
mary components of a galaxy cluster can be seen in this image: the X-ray ICM (pink),
dark matter (blue), and galaxies. The brilliant white object with diffraction spikes is
a star. This cluster has become very famous as the merger dynamics provide direct
evidence for the existence of dark matter (Clowe et al., 2006). Image taken from
NASA Press Release 06-297. Image credits: NASA/CXC/CfA/Markevitch et al.
(2002) (X—ray); NASA/STScI/l\/Iagellan/U.Arizona/Clowe et al. (2006) (Optical);
NASA/STScI/ESO VVFI/Magellan/U.Arizona/Clowe et al. (2006) (Lansing).

1. Galaxy clusters represent a unique source of information about the Universe’s
underlying cosmological parameters, including the nature of dark matter and
the dark energy equation of state. Large-scale structure growth is exponentially
sensitive to some of these parameters, and by counting the number of clusters
found in a comoving volume of space, speciﬁcally above a given mass threshold,

clusters may be very useful in cosmological studies (Voit, 2005).

2. The cluster gravitational potential well is deep enough to retain all the matter
which has fallen in over the age of the Universe. This slowly evolving “sealed
box” therefore contains a comprehensive history of all the physical processes
involved in galaxy formation and evolution, such as: stellar evolution, super-
novae feedback, black hole activity in the form of active galactic nuclei, galaxy
mergers, ram pressure stripping of in—falling galaxies and groups, et cetera. The
time required for the ICM in the outskirts of a cluster to radiate away its ther-
mal energy is longer than the age of the Universe, hence the ICM acts as a
record-keeper ‘of all the aforementioned activity. Therefore, by studying the
ICM’s physical properties, the thermal history of the cluster can be partially
recovered and utilized in developing a better understanding of cluster formation

and evolution.

In this dissertation I touch upon both these points by studying the emergent X-ray
emission of the ICM as observed with the Chandra X-ray Observatory.

While clusters have their speciﬁc uses in particular areas of astrophysics research,
they also are interesting objects in their own right. A rich suite of physics is brought to
bear when studying galaxy clusters. A full-blown, theoretical construction of a galaxy
cluster requires, to name just a few: gravitation, ﬂuid mechanics, thermodynamics,
hydrodynamics, magnetohydrodynamics, and high-energy/ particle/ nuclear physics.
Multiwavelength observations of galaxy clusters provide excellent datasets for testing

the theoretical predictions from other areas of physics, and clusters are also a unique

5

laboratory for empirically establishing how different areas of physics interconnect.
Just this aspect of clusters puts them in a special place among the objects in our
Universe worth intense, time-consuming, (and sometimes expensive) scrutiny. At a
minimum, galaxy clusters are most deﬁnitely worthy of being the focus of a humble
dissertation from a ﬂedgling astrophysicist.

As this is a dissertation focused around observational work, in Section §1.2 I pro-
vide a brief primer on the X—ray observable properties of clusters which are important
to understanding this dissertation. Section §1.2.2 provides discussion of gas entropy,
a physical property of the ICM which may be unfamiliar to many readers and is uti-
lized heavily in Chapters 3 and 4. In Section §1.3, I more thoroughly discuss reasons
for studying clusters of galaxies which are speciﬁc to this dissertation. Presented in
Section §1.3.1 is a discussion of why clusters of different masses are not simply scaled
versions of one another, and in Section §1.3.2 the unresolved “cooling ﬂow problem”
is brieﬂy summarized. The current chapter concludes with a brief description of the
Chandra X-ray Observatory (CXO) and its instruments in Section §1.4. Chandra is
the space-based telesc0pe with which all of the data presented in this dissertation was

collected.

1.2 THE INTRACLUSTER MEDIUM

In Section §1.1, the ICM was presented as a mostly ionized, hot, diffuse plasma which
dominates the baryonic mass content of clusters. But where did it come from and
what is the composition of this pervasive ICM? What are the mechanisms that result
in the ICM’s X-ray luminescence? How do observations of the ICM get converted
into physical properties of a cluster? In this section I brieﬂy cover the answers to
these questions in order to give the reader a better understanding of the ICM.
Galaxy clusters are built-up during the process of hierarchical merger of dark

matter halos and the baryons gravitationally coupled to those halos (White & Rees,

1978). Owing to the inefﬁciency of galaxy formation and the processes of galactic
mass ejection and ram pressure stripping, many of the baryons in these dark mat-
ter halos are in the form of diffuse gas and not locked up in galaxies. During the
merger of dark matter halos, gravitational potential energy is converted to thermal
energy and the diffuse gas is heated to the virial temperature of the cluster potential
through processes like adiabatic compression and accretion shocks. The cluster virial
temperature is calculated by equating the average kinetic energy of a gas particle to

its thermal energy,

I 3
§Hm<02> = EkTvirial (1-1)
2
um (I
Tvirial = —_3<?'—> (1'2)

where a is the mean molecular weight, k is the Boltzmann constant, Tvirial is the virial
temperature, m is the mass of a test particle, and (a) is the average velocity of the test
particle. In this equation, (a) can be replaced with the line-of-sight galaxy velocity
dispersion (a cluster observable) because all objects within the cluster potential (stars,
galaxies, protons, etc.) are subject to the same dynamics and hence have comparable
thermal and kinetic energies.

Galaxy clusters are the most massive objects presently in the Universe. The
enormous mass means deep gravitational potential wells and hence very high virial
temperatures. Most cluster virial temperatures are in the range kTvirial = 1 — 15 keV.
At these energy scales, gases are collisionally ionized plasmas and will emit X-rays
via thermal bremsstrahlung (discussed in Section §1.2.1). The ICM is not a pure
ionized hydrogen gas, as a result, atomic line emission from heavy elements with
bound electrons will also occur. The ICM is also optically thin at X—ray wavelengths,
e. g. the ICM optical depth to X—rays is much smaller than unity, r)‘ < 1, and hence

the X-rays emitted from clusters stream freely into the Universe. In the next section I

brieﬂy cover the processes which give rise to ICM X—ray emission and the observables
which result. For a magniﬁcently detailed treatise of this topic, see Sarazin (1986)4

and references therein.

1.2. 1 X-RAY EMISSION

Detailed study of clusters proceeds mainly through spatial and spectral analysis of
the ICM. By directly measuring the X-ray emission of the ICM, quantities such as
temperature, density, and luminosity per unit volume can be inferred. Having this
knowledge about the ICM provides an observational tool for indirectly measuring ICM
dynamics, composition, and mass. In this way a complete picture of a cluster can be
built up and other processes, such as brightest cluster galaxy (BCG) star formation,
AGN feedback activity, or using ICM temperature inhomogeneity to probe cluster
dynamic state, can be investigated. In this section, I brieﬂy cover how X-ray emission
is produced in the ICM and how basic physical properties are then measured.

The main mode of interaction in a fully ionized plasma is the scattering of free
electrons off heavy ions. During this process, charged particles are accelerated and
thus emit radiation. The mechanism is known as ‘free-free’ emission (ff), or by the
tongue-twisting thermal bremsstrahlung (German for “braking radiation”). It is also
called bremsstrahlung cooling since the X-ray emission carries away large amounts
of energy. The timescale for protons, ions, and electrons to reach equipartition is
typically shorter than the age of a cluster (Sarazin, 2003), thus the gas particles pop-
ulating the emitting plasma can be approximated as being at a uniform temperature

with a Maxwell-Boltzmann velocity distribution,

 

 

.. 3/2 ~ _ *2
f(v) = 4n (27:27,) 112 exp [ 27:; ] (1.3)

where m is mass, T is temperature, It is the Boltzmann constant, and velocity, 27, is

 

4Also available at http: / / nedwww.ipac.caltech.edu / 1eve15 / March02 / Sarazin / TOC .html

8

 

deﬁned as 27 = v3, + '03 + 223. The power emitted per cubic centimeter per second

1

(erg s‘ cm’3) from this plasma can be written in the compact form

eff 51.4 x 10—27T1/2nen,22g3 (1.4)

where 1.4 x 10‘27 is in cgs and is the condensed form of the physical constants and
geometric factors associated with integrating over the power per unit area per unit
frequency, n6 and n,- are the electron and ion densities, Z is the number of protons of
the bending charge, g B is the frequency averaged Gaunt factor (of order unity), and
T is the global temperature determined from the spectral cut-off frequency (Rybicki
& Lightman, 1986). Above the cut-off frequency, Vc = kT/h, few photons are created
because the energy supplied by charge acceleration is less than the minimum energy
required for creation of a photon. Worth noting is that free-free emission is a two—
body process and hence the emission goes as the gas density squared while having a
weak dependence on the thermal energy, 6 oc p2T1/2 for T Z, 107 K when the gas has
solar abundances.

Superimposed on the thermal emission of the plasma are emission lines of heavy
element contaminants such as C, Fe, Mg, N, Ne, O, S, and Si. The widths and
relative strengths of these spectral lines are used to constrain the metallicity of the
ICM, which is typically quantiﬁed using units relative to solar abundance, Z9 . On
average, the ICM has a metallicity of ~ 0.3 Z9, which is mostly stellar detritus
(Mushotzky & Loewenstein, 1997; Allen & Fabian, 1998b; Fukazawa et al., 1998).
In collisionally ionized plasmas with temperatures and metallicities comparable to
the ICM, the dominant ion species is that of the ‘closed—shell’ helium-like ground
state (K and L—shells) (Peterson & Fabian, 2006). The K and L shell transitions
are extremely sensitive to temperature and electron densities, therefore providing an
excellent diagnostic for constraining both of these quantities. The strongest K-shell

transition of the ICM can be seen from iron at [CT ~ 6.7 keV. If signal-to—noise of the

9

spectrum is of high enough quality, measuring a shift in the energy of this spectral
line can be used to conﬁrm or deduce the approximate redshift, and hence distance,
of a cluster. The rich series of iron L-shell transitions occur between 0.2 ,S T ,S 2.0
keV and are the best diagnostic for measuring metallicity. For the present generation
of X-ray instruments, the L—shell lines are seen as a blend with a peak around ~ 1
keV.

Shown in Figs. 1.3 and 1.4 are the unredshifted synthetic spectral models gener-
ated with XSPEC (Arnaud, 1996) of a 2 keV and 8 keV gas. Both spectral models
have a component added to mimic absorption by gas in the Milky Way, which is seen
as attenuation of ﬂux at E ,E, 0.4 keV. For both spectral models the metal abundance
is 0.3 Z9. These two spectral models differ by only a factor of four in temperature but
note the extreme sensitivity of both the thermal bremsstrahlung exponential cut-off
and emission line strengths to temperature.

Equation 1.4 says that observations of ICM X—ray emission will yield two quan-
tities: temperature and density. The gas density can be inferred from the emission
integral,

E1 = /nenp dV (1.5)

where ne is the electron density, np is the density of hydrogen-like ions, and dV is the
gas volume within a differential element. The emission integral is essentially the sum
of the square of gas density for all the gas parcels in a deﬁned region. Thus, the gas
density within a projected volume can be obtained from the spectral analysis, but it
can also be obtained from spatial analysis of the cluster emission, for example from
cluster surface brightness.

The number of photons detected per unit area (projected on the plane of the
sky) per second is given the name surface brightness. Assuming spherical symmetry,
2-dimensional surface brightness can be converted to 3-dimensional emission density.

By dividing a cluster observation into concentric annuli originating from the cluster

10

 

0.1

Flux[photonslcmzskeV]
001
llLuJi l lllll

 

 

 

 

 

' a E
a .
g I l l l l l J l l l l L 1 L 1 L 4 LL
" 0.1 1 10

Energy [keV]

Figure 1.3 Synthetic absorbed thermal spectral model of a N H =
1020 cm-z, kTX = 2.0 keV, Z/ZQ = 0.3, and zero redshift gas.
Notice that the strength of the iron L—shell emission lines is much
greater than the iron K-shell lines for this model.

O

'1'! 1 U l UUUUU I v ITTITr
‘- I I I

 

0.1

I'IIT'T' YTUTUW‘I' I II

 

Flux [photons/err!2 3 keV]
O 01

10“5
Tu"

  

 

 

ll I l L llll4l l L 1 ALA—LII

0.1 1 10
Energy [keV]

Figure 1.4 Same as Fig. 1.3 except for a kTX = 8.0 keV gas. Notice
that for this spectral model the iron L-shell emission lines are much
weaker and the iron K-shell lines are much stronger than in the
kTX = 2.0 keV model. Also note that the exponential cut-off of this
model occurs at a higher energy (E > 10 keV) than in the model
shown in Figure 1.3.

 

10"

11

center and subtracting off cluster emission at larger radii from emission at smaller
radii, the amount of emission from a spherical shell can be reconstructed from the
emission in an annular ring. For the spherical shell deﬁned by radii r,- and ”+1, Kriss
et al. (1983) shows the relation between the emission density, Cu“, to the observed
surface brightness, Sm.m+1, of the ring with radii rm and rm+1, is
m
b
Sm,m+l = A__ : Ci,z'+1 [(Vi,m+1 — Vi+l,m+1) — (Vim — Vi+1,m)l- (1-6)

m.m+l i—l

where b is the solid angle subtended on the sky by the object, Am,m+1 is the area
of the ring, and the V terms are the volumes of various shells. This method of
reconstructing the cluster emission is called deprojection. While assuming spherical
symmetry is clearly imperfect, it is not baseless. The purpose of such an assumption is
to attain angular averages of the volume density at various radii from an azimuthally
averaged surface density. Systematic uncertainties associated with deprojection are
discussed in Section §3.3.2.

In this dissertation the spectral model MEKAL (Mewe et al., 1985, 1986; Liedahl
et al., 1995) is used for all of the spectral analysis. The MEKAL model normalization,

r}, is deﬁned as
10—14
_ 47rD§,(1+ z)2

 

77 E] (1.7)

where z is cluster redshift, D A is the angular diameter distance, and E1 is the emission
integral from eqn. 1.5. Recognizing that the count rate, f (r), per volume is equivalent
to the emission density, Ci,z'+1 = f (r) / f dV, where dV can be a shell (deprojected)
or the sheath of a round column seen edge-on (projected), combining eqns. 1.6 and
3.1 yields an expression for the electron gas density which is a function of direct

observables,

 

 

ne(7‘) = \/1.2C(r)n(r)47r[DA(1+ z)]2 (1.8)

f(r)10‘14

12

where the factor of 1.2 comes from the ionization ratio ne=1.2np, C (r) is the radial
emission density derived from eqn. 1.6, n is the spectral normalization from eqn.
3.1, D A is the angular diameter distance, 2 is the cluster redshift, and f (r) is the
spectroscopic count rate.

Simply by measuring surface brightness and analyzing spectra, the cluster tem-
perature, metallicity, and density can be inferred. These quantities can then be used
to derive pressure, P = nkT, where n z 2%. The total gas mass can be inferred
using gas density as Mgas = f(4/3)7rr3nedr. By further assuming the ICM is in

hydrostatic equilibrium, the total cluster mass within radius r is

_ kT(r)r d(log ne(r)) d(log T(r))

MU) _ umHG d(log r) d(log r)

 

(1.9)

where all variables have their typical deﬁnitions. The rate at which the ICM is cooling
can also be expressed in simple terms of density and temperature. Given a cooling
function, A , which is sensitive to temperature and metal abundance (for the ICM
A(T, Z) ~ 10‘23 ergs cm3 3*), the cooling rate is given by Tcool = n2A(T, Z). For
some volume, V, the cooling time is then simply the time required for a gas parcel to

radiate away its thermal energy,

tcoolvrcool = VNkT (1'10)
'ynkT
t = —— 1.11

where 'y is a constant speciﬁc to the type of cooling process (e. g. 3/ 2 for isochoric
and 5 / 2 for isobaric). The cooling time of the ICM can be anywhere between 107‘10
yrs. Cooling time is a very important descriptor of the ICM because processes such
as the formation of stars and line-emitting nebulae are sensitive to cooling time.

By “simply” pointing a high-resolution X-ray telescope, like Chandra, at a cluster

and exposing long enough to attain good signal-to—noise, it is possible to derive a roster

13

of fundamental cluster properties: temperature, density, pressure, mass, cooling time,
and even entropy. Entropy is a very interesting quantity which can be calculated
using gas temperature and density and is most likely fundamentally connected to
processes like AGN feedback and star formation (discussed in Chapters 3 and 4). In
the following section I discuss how gas entropy is derived, why it is a useful quantity

for understanding clusters, and how it will be utilized later in this dissertation.

1 .2.2 ENTROPY

Entropy has both a macroscopic deﬁnition (the measure of available energy) and mi-
croscopic deﬁnition (the measure of randomness), with each being useful in many
areas of science. Study of the ICM is a macro-scale endeavor, so the deﬁnition of
entropy pertinent to discussion of the ICM is as a measure of the thermodynamic
processes involving heat transfer. But the conventional macroscopic deﬁnition of en-
tropy, d3 = dQ / T , is not the quantity which is most useful in the context of studying
astrophysical Objects. Thus we must resort to a simpler, measurable surrogate for
entropy, like the adiabat. The adiabatic equation of state for an ideal monatomic
gas is P = K p7 where K is the adiabatic constant and '7 is the ratio of speciﬁc heat
capacities and has the value Of 5 / 3 for a monatomic gas. Setting P = ka/ um H and
solving for K one ﬁnds
kT

K = ————. (1.12)
ume2/3

where a is the mean molecular weight of the gas and mg is the mass of the Hy-
drogen atom. The true thermodynamic speciﬁc entropy using this formulation is
s = kln K 3/ 2 + so, so neglecting constants and scaling K shall be called entropy in

this dissertation. A further simpliﬁcation can be made to recast eqn. 1.12 using the

14

observables electron density, ne, and X—ray temperature, TX (in keV):

TX

K = —.
.2/3

(1.13)

Equation 1.13 is the deﬁnition of entrOpy used throughout this dissertation. With a
simple functional form, “entrOpy” can be derived directly from X-ray observations.
But why study the ICM in terms of entropy?

ICM temperature and density alone primarily reﬂect the shape and depth of the
cluster dark matter potential (Voit et al., 2002). But it is the speciﬁc entropy of a gas
parcel, s = cv1n(T/p7_1), which governs the density at a given pressure. In addition,
the ICM is convectively stable when ds/dr 2 0, thus, without perturbation, the ICM
will convect until the lowest entropy gas is near the core and high entropy gas has
buoyantly risen to large radii. ICM entropy can also only be changed by addition or
subtraction of heat, thus the entropy of the ICM reﬂects most of the cluster thermal
history. Therefore, properties of the ICM can be viewed as a manifestation of the
dark matter potential and cluster thermal history - which is encoded in the entropy
structure. It is for these reasons that the study of ICM entropy has been the focus of
both theoretical and observational study (David et al., 1996; Bower, 1997; Ponman
et al., 1999; Lloyd-Davies et al., 2000; Tozzi & Norman, 2001; Voit et al., 2002;
Ponman et al., 2003; Piffaretti et al., 2005; Pratt et al., 2006; Donahue et al., 2005,
2006; Morandi & Ettori, 2007; McCarthy et al., 2008).

Hierarchical accretion of the ICM should produce an entropy distribution which
is a power-law across most radii with the only departure occurring at radii smaller
than 10% of the virial radius (Voit et al., 2005). Hence deviations away from a
power-law entropy proﬁle are indicative of prior heating and cooling and can be
exploited to reveal the nature of, for example, AGN feedback. The implication of
the” intimate connection between entropy and non-gravitational processes being that

both the breaking of self-similarity and the cooling ﬂow problem (both discussed in

15

Section §1.3) can be studied with ICM entrOpy.

In Chapter 3 and Chapter 4 I present the results of an exhaustive study of galaxy
cluster entropy proﬁles for a sample of over 230 galaxy clusters taken from the Chandra
Data Archive. Analysis of these proﬁles has yielded important results which can be
used to constrain models of cluster feedback, understand truncation of the high—
mass end of the galaxy luminosity function, and what effect these processes have on
the global properties of clusters. The size and scope of the entropy proﬁle library
presented in this dissertation is unprecedented in the current scientiﬁc literature, and
we hope our library, while having provided immediate results, will have a long-lasting
and broad utility for the research community. To this end, we have made all data

and results available to the public via a project web site5.

1.3 THE INCOMPLETE PICTURE OF CLUSTERS

The literature on galaxy clusters is extensive. There has been a great deal already
written about clusters (with much more eloquence), and I strongly suggest read-
ing Mushotzky (1984); Kaiser (1986); Evrard (1990); Kaiser (1991); Sarazin (1986);
Fabian (1994); Voit (2005); Peterson & Fabian (2006); Markevitch & Vikhlinin (2007);
McNamara & Nulsen (2007), and references therein for a comprehensive review of
the concepts and topics to be covered in this dissertation. The discussion of Sections
§1.3.1 and §1.3.2 focuses on a few unresolved mysteries involving galaxy clusters: the
breaking of self-similarity in relation to using clusters in cosmological studies and the

cooling ﬂow problem as it relates to galaxy formation.

1.3.1 BREAKING OF SELF-SIMILARITY

We now know the evolution of, and structure within, the Universe are a direct re-

sult of the inﬂuence from dark energy and dark matter. An all pervading repulsive

 

5http: / / www.pa.msu.edu/ astro/ MC2/ accept /

16

dark energy has been posited to be responsible for the accelerating expansion of the
Universe (Riess et al., 1998; Perlmutter et al., 1999; Riess et al., 2007). Dark matter
is an unknown form of matter which interacts with itself and ordinary matter (both
baryonic and non-baryonic) through gravitational forces. Up until the last ~ 5 billion
years (Riess et al., 1998; Perlmutter et al., 1999; Riess et al., 2007), the inﬂuence of
dark matter on the Universe has been greater than that of dark energy. The early
dominance of dark matter is evident from the existence of large-scale structure like
galaxy clusters.

An end result of the gravitational attraction between amalgamations of dark mat-
ter particles, called dark matter halos, is the merger of small halos into ever larger
halos. Since dark matter far outweighs baryonic matter in the Universe, the baryons
are coupled to the dark matter halos via gravity, and hence are dragged along during
the halo merger process. Like raindrops falling in a pond that drains into a river
which flows into the ocean, the process of smaller units merging to create larger units
is found ad inﬁnitum in the Universe and is given the name hierarchical structure
formation. A useful visualization of the hierarchical structure formation process is
shown in Fig. 1.5. Hierarchical formation begins with small objects like the ﬁrst
stars, continues on to galaxies, and culminates in the largest present Objects, clusters
of galaxies.

In an oversimpliﬁed summary, one can say dark energy is attempting to push
space apart while dark matter is attempting to pull matter together within that
space. Were the balance and evolution of dark energy and dark matter weighted
heavily toward one or the other it becomes clear that the amount of structure and
its distribution will be different. Thus, the nature of dark matter and dark energy
ultimately inﬂuence the number of clusters found at any given redshift (e.g. White
et al., 1993) and hence cluster number counts are immensely powerful in determining

cosmological parameters (e.g. Borgani et al., 2001).

17

{lurk Clint“
1" H1 f i;\f>:r< m

Inllation

Quantum '
ruclmnons '

 

Figure 1.5 Top panel: Illustration of hierarchical structure formation. Bottom panel:
Snapshots from the simulation of a galaxy cluster forming. Each pane is 10 Mpc
on a side. Color coding represents gas density along the line of sight (deep red is
highest, dark blue is lowest). Each snapshot is numbered on the illustration at the
approximate epoch each stage of cluster collapse occurs. Notice that, at ﬁrst (1-
2), very small objects like the ﬁrst stars and protogalaxies collapse and then these
smaller objects slowly merge into much larger halos (3—5). The hierarchical merging
process ultimately results in a massive galaxy cluster (6) which continues to grow as
sub—clusters near the box edge creep toward the cluster main body. Illustration taken
from NASA/WMAP Science Team and modiﬁed by author. Simulation snapshots
taken from images distributed to the public by the Virgo Consortium on behalf of
Dr. Craig Booth: http://www.virg0.dur.ac.uk

18

Individual clusters do not yield the information necessary to study the underlying
cosmogony. However, the number density of clusters above a given mass threshold
within a comoving volume element, 2'.e. the cluster mass function, is a useful quantity
(Voit, 2005). But the cluster mass function is a powerful cosmological tool only if
cluster masses can be accurately measured. With no direct method of measuring
cluster mass, easily observable properties of clusters must be used as proxies to infer
mass.

Reliable mass proxies, such as cluster temperature and luminosity, arise natu-
rally from the theory that clusters are scaled versions of each other. This property
is commonly referred to as self-similarity of mass-observables. More precisely, self-
similarity presumes that when cluster-scale gravitational potential wells are scaled by
the cluster-speciﬁc virial radius, the full cluster population has potential wells which
are simply scaled versions of one another (Navarro et al., 1995, 1997). Self-similarity
is also expected to yield low-scatter scaling relations between cluster properties such
as luminosity and temperature (Kaiser, 1986, 1991; Evrard & Henry, 1991; Navarro
et al., 1995, 1997; Eke et al., 1998; Frenk et al., 1999). Consequently, mass-observable
relations, such as mass-temperature and mass-luminosity, derive from the fact that
most clusters are virialized, meaning the cluster’s energy is shared such that the virial
theorem, —2(T) = (V) where (T) is average kinetic energy and (V) is average po-
tential energy, is a valid approximation. Both theoretical (Evrard et al., 1996; Bryan
&. Norman, 1998; Mohr et al., 1999; Bialek et al., 2001; Borgani et al., 2002) and
observational (Mushotzky, 1984; Edge 8: Stewart, 1991; White et al., 1997; Allen &
Fabian, 1998a; Markevitch et al., 1998; Amaud & Evrard, 1999; Finoguenov et al.,
2001) studies have shown cluster mass correlates well with X-ray temperature and
luminosity, but that there is much larger (z 20 — 30%) scatter and different SIOpes
for these relations than expected. The breaking of self-similarity is attributed to non-

gravitational processes such as ongoing mergers (eg Randall et al., 2002), heating via

19

feedback (eg Cavaliere et al., 1999; Bower et al., 2001), or radiative cooling in the
cluster core (eg Voit & Bryan, 2001; Voit et al., 2002).

To reduce the scatter in mass scaling-relations and to increase their utility for
weighing clusters, how secondary processes alter temperature and luminosity must
ﬁrst be quantiﬁed. It was predicted that clusters with a high degree of spatial uni-
formity and symmetry (e.g. clusters with the least substructure in their dark matter
and gas distributions) would be the most relaxed and have the smallest deviations
from mean mass-observable relations. The utility of substructure in quantifying re-
laxation is prevalent in many natural systems, such as a placid lake or spherical
gas cloud of uniform density and temperature. Structural analysis of cluster simula—
tions, take for example the recent work of Jeltema et al. (2007) or Ventimiglia et al.
(2008), have shown measures of substructure correlate well with cluster dynamical
state. But spatial analysis is at the mercy of perspective. If equally robust aspect-
independent measures of dynamical state could be found, then quantifying deviation
from mean mass-scaling relations would be improved and the uncertainty of inferred
cluster masses could be further reduced. Scatter reduction ultimately would lead to
a more accurate cluster mass function, and by extension, the constraints on theories
explaining dark matter and dark energy could grow tighter.

In Chapter 2, I present work investigating ICM temperature inhomogeneity, a
feature of the ICM which has been proposed as a method for better understanding the
dynamical state of a cluster (Mathiesen & Evrard, 2001). Temperature inhomogeneity
has the advantage of being a spectroscopic quantity and therefore falls into the class
of aspect-independent metrics which may be useful for reducing scatter in mass-
observable relations. In a much larger context, this dissertation may contribute to

the improvement of our understanding of the Universe’s make-up and evolution.

20

1.3.2 THE COOLING FLOW PROBLEM

For 50% - 66% of galaxy clusters, the densest and coolest (kTX E, Tvirial / 2) ICM
gas is found in the central ~ 10% of the cluster gravitational potential well (Stewart
et al., 1984; Edge et al., 1992; White et al., 1997; Peres et al., 1998; Bauer et al.,
2005). For the temperature regime of the ICM, radiative cooling time, two; (see eqn.
3.7), is more strongly dependent on density than temperature, two; oc Tg1 / 2p2, where
T9 is gas temperature and p is gas density. The energy lost via radiative cooling is
seen as diffuse thermal X-ray emission from the ICM (Gursky et al., 1971; Mitchell
et al., 1976; Serlemitsos et al., 1977). When thermal energy is radiated away from
the ICM, the gas density must increase while gas temperature and internal pressure
respond by decreasing. The cluster core gas densities ultimately reached through the
cooling process are large enough such that the cooling time required for the gas to
radiate away its thermal energy is much shorter than both the age of the Universe,
e. 9. two; << H61, and the age of the cluster (Cowie & Binney, 1977; Fabian & Nulsen,
1977). Without compensatory heating, it thus follows that the ICM in some cluster
cores should cool and condense.

Gas within the cooling radius, rcool, (deﬁned as the radius at which two, = H0— 1)
is underpressured and cannot provide sufﬁcient pressure support to prevent overly-
ing gas layers from forming a subsonic ﬂow of gas toward the bottom of the cluster
gravitational potential. However, if when the ﬂowing gas enters the central galaxy
it has cooled to the point where the gas temperature equals the central galaxy virial
temperature, then adiabatic compression6 from the galaxy’s gravitational potential
well can balance heat losses from radiative cooling. But, if the central galaxy’s gravi-
tational potential is ﬂat, then the gas energy gained via gravitational effects can also
be radiated away and catastrophic cooling can proceed.

The sequence of events described above was given the name “cooling ﬂow” (Fabian

 

6As the name indicates, no heat is exchanged during adiabatic compression; but gas temperature
rises because the internal gas energy increases due to external work being done on the system.

21

& Nulsen, 1977; Cowie & Binney, 1977; Mathews & Bregman, 1978) and is the most
simplistic explanation of what happens to the ICM when it is continuously cool-
ing, spherically symmetric, and homogeneous (see Fabian, 1994; Peterson & Fabian,
2006; Donahue & Voit, 2004, for reviews of cool gas in cluster cores). The the-
oretical existence of cooling ﬂows comes directly from X-ray observations, yet the
strongest observational evidence for the existence of cooling ﬂows will be seen when
the gas cools below X—ray emitting temperatures and forms stars, molecular clouds,
and emission line nebulae. Unfortunately, cooling ﬂow models were ﬁrst presented
at a time when no direct, complementary observational evidence for cooling ﬂows
existed, highlighting the difﬁculty of confronting the models. Undeterred, the X-ray
astrophysics community began referring to all clusters which had cores meeting the
criterion two; < H51 as “cooling ﬂow clusters,” a tragic twist of nomenclature fate
which has plagued many scientiﬁc talks.

A mass deposition rate, M, can be inferred for cooling ﬂows based on X—ray obser—
vations: M o< L X(r < rcool)(kTX)‘1, where L X(r < Tcool) is the X-ray luminosity
within the cooling region, kTX is the X-ray gas temperature, and M typically has
units of Mg yr‘l. The quantity M is useful in getting a handle on how much gas
mass is expected to be ﬂowing into a cluster core. Mass deposition rates have been
estimated for many clusters and found to be in the range 100— 1000 MG yr"l (Fabian
et al., 1984; White et al., 1997; Peres et al., 1998). Mass deposition rates can also be
estimated using emission from individual spectral lines: M oc L X(r < rcool)ef(T),
where L X(r < Tcool) is the X-ray luminosity within the cooling region and ef(T)
is the emissivity fraction attributable to a particular emission line. The ICM soft
X—ray emission lines of Fe XVII, 0 VIII, and Ne X at E < 1.5 keV for example, are
especially useful in evaluating the properties of cooling ﬂows. Early low-resolution
spectrosc0py found mass deposition rates consistent with those from X-ray observa-

tions (e.g. Canizares et al., 1982).

22

Not surprisingly, the largest, brightest, and most massive galaxy in a cluster, the
BCG, typically resides at the bottom of the cluster potential, right at the center of
where a cooling flow would terminate. Real cooling ﬂows were not expected to be
symmetric, continuous, or in thermodynamic equilibrium with the ambient medium.
Under these conditions, gas parcels at lower temperatures and pressures experience
thermal instability and are expected to rapidly develop and collapse to form gaseous
molecular clouds and stars. The stellar and gaseous components of some BCGs clearly
indicate some amount of cooling and mass deposition has occurred. But are the
properties of the BCG population consistent with cooling ﬂow model predictions?
For example, BCGs should be supremely luminous and continually replenished with
young, blue stellar populations since the epoch of a BCG’s formation. One should
then expect the cores of clusters suspected of hosting a cooling flow to have very
bright, blue BCGs bathed in clouds of emission line nebulae. However, observations of
cooling flow clusters reveal the true nature of the core to not match these expectations
of extremely high star formation rates, at least not at the rate of > 100 MG yr—l.

The optical properties of massive galaxies and BCGs are well known and neither
population are as blue or bright as would be expected from the extended periods of
growth via cooling ﬂows (Madau et al., 1996; Shaver et al., 1996; Cowie et al., 1996;
Crawford et al., 1999). While attempts were made in the past to selectively channel
the unobserved cool gas into optically dark objects, such as in low-mass, distributed
star formation (e. g. Prestwich & Joy, 1991), methodical searches in the optical, in-
frared, UV, radio, and soft X-ray wavelengths (kTX ,S, 2.0 keV) have revealed that
the total mass of cooler gas associated with cooling ﬂows is much less than expected
(Hu et al., 1985; Heckman et al., 1989; McNamara et al., 1990; O’Dea et al., 1994b,a;
Antonucci & Barvainis, 1994; McNamara & Jaffe, 1994; Voit & Donahue, 1995; Jaffe
& Bremer, 1997; Falcke et al., 1998; Donahue et al., 2000; Edge & Prayer, 2003).

Conﬁrming the suspicion that cooling ﬂows are not cooling as advertised, high-

23

resolution XMM-Newton RGS X-ray spectroscOpy Of clusters expected to host very
massive cooling ﬂows deﬁnitively proved that the ICM was not cooling to tempera-
tures less than 1 / 3 of the cluster virial temperature (Peterson et al., 2001; Tamura
et al., 2001; Peterson et al., 2003). A cooling X-ray medium which has emission
discontinuities at soft energies is not predicted by the simplest single-phase cooling
ﬂow models, and a troubling amount of ﬁne-tuning (e. g. minimum temperatures, hid—
den soft emission) must be added to agree with observations. Modiﬁcations such as
preferential absorption of soft X-rays in the core region (e.g. Allen et al., 1993) or
turbulent mixing of a multi-phase cooling ﬂow (e. g. Fabian et al., 2002) have been
successful in matching observations, but these models lack the universality needed to
explain why all cooling ﬂows are not as massive as expected.

All of the observational evidence has resulted in a two-component “cooling ﬂow
problem”: (1) spectroscopy of soft X-ray emission from cooling ﬂow clusters is in-
consistent with theoretical predictions, and (2) multiwavelength observations reveal a
lack of cooled gas mass or stars to account for the enormous theoretical mass deposi-
tion rates implied by simple cooling ﬂow models. So why and how is the cooling of gas
below T virial / 3 suppressed? As is the case with most questions, the best answer thus
far is simple: the cooling ﬂow rates were wrong, with many researchers suggesting the
ICM has been intermittently heated. But what feedback mechanisms are responsible
for hindering cooling in cluster cores? How do these mechanisms operate? What
observational constraints can we ﬁnd to determine which combination of feedback
mechanism hypotheses are correct? The answers to these questions have implications
for both cluster evolution and massive galaxy formation.

The cores of clusters are active places, so ﬁnding heating mechanisms is not too
difﬁcult. The prime suspect, and best prOposed solution to the cooling ﬂow problem
thus far, invokes some combination of supernovae and outbursts from the active galac-

tic nucleus .(AGN) in the BCG (Binney 8:: Tabor, 1995; Bower, 1997; Loewenstein,

24

2000; Voit & Bryan, 2001; Churazov et al., 2002; Briiggen & Kaiser, 2002; Briiggen
et al., 2002; Nath & Rcychowdhury, 2002; Ruszkowski & Begelman, 2002; Alexander,
2002; Omma et al., 2004; McCarthy et al., 2004; Roychowdhury et al., 2004; Hoeft
& Briiggen, 2004; Dalla Vecchia et al., 2004; Soker & Pizzolato, 2005; Pizzolato &
Soker, 2005; Voit & Donahue, 2005; Brighenti & Mathews, 2006; Mathews et al.,
2006). However, there are some big problems: (1) AGN tend to deposit their energy
along preferred axes, while cooling in clusters proceeds in a nearly spherically sym-
metric distribution in the core; (2) depositing AGN outburst energy at radii nearest
the AGN is difﬁcult and how this mechanism works is not understood; (3) there is
a serious scale mismatch in heating and cooling processes which has hampered the
development of a self-regulating feedback loop involving AGN. Radiative cooling pro-
ceeds as the square of gas density, whereas heating is proportional to volume. Hence,
modeling feedback with a small source object, r ~ 1 pc, that is capable of compensat-
ing for radiative cooling losses over an x 106 kpc3 volume, where the radial density
can change by four orders of magnitude, is quite diﬂicult. Dr. Donahue once framed
this problem as, “trying to heat the whole Of Europe with something the size of a
button.”

The basic model of how AGN feedback works is that ﬁrst gas accretes onto a
supermassive black hole at the center of the BCG, resulting in the acceleration and
ejection of very high energy particles back into the cluster environment. The energy
released in an AGN outburst is of order 1058—61 ergs. Under the right conditions,
and via poorly understood mechanisms, energy output by the AGN is transferred to
the ICM and thermalized, thereby heating the gas. The details of how this process
operates is beyond the scope of this dissertation (see McNamara & Nulsen, 2007,
for a recent review). However, in this dissertation I do investigate some observable
properties of clusters which are directly impacted by feedback mechanisms.

Utilizing the quantity ICM entropy, I present results in Chapter 3 which show

25

that radial ICM entropy distributions for a large sample of clusters have been altered
in ways which are consistent with AGN feedback models. Entropy and its connection
to AGN feedback is discussed in Subsection 1.2.2 of this chapter. In Chapter 4 I
also present observational results which support the hypothesis of Voit et al. (2008)
that electron thermal conduction may be an important mechanism in distributing
AGN feedback energy. Hence, this dissertation, in small part, seeks to add to the
understanding of how feedback functions in clusters, and thus how to resolve the
cooling ﬂow problem — the resolution of which will lead to better models of galaxy

formation and cluster evolution.

1.4 CHANDRA X-RAY OBSERVATORY

In this section I brieﬂy describe what makes the Chandra X-ray Observatory (Chandra
or CXO for short) a ground-breaking and unique telescope ideally suited for the work
carried out in this dissertation. In depth details of the telescope, instruments, and
spacecraft can be found at the CXO web sites7’8 or in Weisskopf et al. (2000). Much
of what is discussed in the following sections can also be found with more detail in
“The Chandra Proposers’ Observatory Guide.”9 All ﬁgures cited in this section are

presented at the end of the corresponding subsection.

1.4.1 TELESCOPE AND INSTRUMENTS

The mean free path of an X-ray photon in a gas with the density of the Earth’s atmo-
sphere is very short. Oxygen and nitrogen in the atmosphere photoelectrically absorb
X—ray photons resulting in 100% attenuation and make X—ray astronomy impossible
from the Earth’s surface. Many long-standing theories in astrophysics predict a wide

variety of astronomical objects as X-ray emitters. Therefore, astronomers and engi-

 

7http: //chandra.harvard.edu/
8http://cxc.harvard.edu/
9http: / / cxc.harvard.edu / proposer / POG /

26

neers have been sending X—ray telescopes into the upper atmosphere and space for
over 30 years now.

The most recent American X-ray mission to ﬂy is the Chandra X—ray Obser-
vatory. It is one of NASA’s Great Observatories along with Compton ('y-rays),
Hubble (primarily Optical), and Spitzer (infrared). Chandra was built by Northrop-
Grumman and is operated by the National Aeronautics and Space Agency. Chandra
was launched in July 1999 and resides in a highly elliptical orbit with an apogee of
~ 140, 000 km and a perigee of ~ 16, 000 km. One orbit takes z 64 hours to complete.
The teleSCOpe has four nested iridium—coated paraboloid-hyperboloid mirrors with a
focal length of ~ 10 In. An illustration of the Chandra spacecraft is shown in Figure
1.6.

All data presented in this dissertation was collected with the Advanced CCD
Imaging Spectrometer (ACIS) instrumentm. ACIS is quite an amazing and unique
instrument in that it is an imager and medium-resolution spectrometer at the same
time. When an observation is taken with ACIS, the data collected contains spatial and
spectral information Since the location and energy of incoming photons are recorded.
The dual nature of ACIS allows the data to be analyzed by spatially dividing up
a cluster image and then extracting spectra for these subregions of the image, a
technique which is used heavily in this dissertation.

The observing elements of ACIS are 10 1024 x 1024 CCDs: six linearly arranged
CCDs (ACIS-S array) and four CCDs arranged in a 2 x 2 mosaic (ACIS-I array).
The ACIS focal plane is currently kept at a temperature of ~ -120 °C. During
an observation, the ACIS instrument is dithered along a Lissajous curve so parts of
the sky which fall in the chip gaps are also observed. Dithering also ensures pixel
variations of the CCD response are removed.

The high spatial and energy resolution of Chandra and its instruments are ideal for

 

10http://acis.mit.edu/acis

27

studying clusters of galaxies. The telescope on-board Chandra achieves on-axis spatial
resolutions of ,S, 0.5’ ' / pixel but it is the pixel size of the ACIS instrument (~ 0.492”)
which sets the resolution limit for observations. ACIS also has an extraordinary
energy resolution of AE / E ~ 100. Below energies of ~ 0.3 keV and above energies
of ~ 10 keV the ACIS effective area is ostensibly zero. The ACIS effective area also
peaks in the energy range E ~ 0.7 — 2.0 keV. As shown in Figs. 1.3 and 1.4, a
sizeable portion of galaxy cluster emission occurs in the same energy range where
the ACIS effective area peaks. The energy resolution of ACIS also allows individual
emission line blends to be resolved in cluster spectra. These aspects make Chandra a
perfect choice for studying clusters and the ICM in detail. Shown in Fig. 1.7 are raw
observations of Abell 1795 with the aim-points on ACIS-I (top panel) and ACIS-S
(bottom panel). In Fig. 1.8 is a spectrum for the entire cluster extracted from the

ACIS-I observation.

28

50L: Array (2) Sunshade Door

   

Aspect Caner:
Stray Light Shade

Pﬁh Resolution
Camera

Instrument
Module
(ISM)

Transmission Thruster: (4) (mm)
Gratlngs l2) hosts.)

CCD imaging Low Geh
Spectrometer Month (2)

 
 

Figure 1.6 An artist’s rendition of the Chandra spacecraft. Chandra is the largest
(~ 17 m long; ~ 4 m wide) and most massive (~ 23K kg) payload ever taken into
space by NASA’s Space Shuttle Program. The planned lifetime of the mission was 5
years, and the 10 year anniversary party is already planned. Illustration taken from
Chandra X—ray Center.

29

ACIS Focal Plane
During Observation

e..—-: ~

ACIS-S

 

Figure 1.7 In both panels celestial North is indicated by the blue arrow. Top panel:
ACIS—I aimed observation of Abell 1795. The image has been binned by a factor of
four so the whole ﬁeld could be shown. Bottom panel: ACIS-S aimed observation
of Abell 1795. Again, the image is binned by a factor of four to show the whole
ﬁeld. For reference, the green boxes mark the ACIS-I chips which were off during this
observation.

30

 

 

 

 

 

 

 

‘- r f f
+ H, <
+ I
. ,+
- +
I
5'
g .
3. o' :- 1,, | -
E L liltlﬂ'.
8 1 ‘ 'Ji
g r
E
Z l
l
S _ .
i
1 A l l 1 l I l l 1
0.5 1 2 5

Energy [keV]

Figure 1.8 Global spectrum of the cluster Abell 1795 with the best-ﬁt single-
component absorbed thermal spectral model overplotted (solid line). Comparing this
spectrum with those of Figs. 1.3 and 1.4, the effects of ﬁnite energy resolution and
convolving the spectral model with instrument responses are apparent. Individual
spectral lines are now blends, and the spectral shape for E < 1.0 keV has changed
because of diminishing effective area.

31

1.4.2 X-RAY BACKGROUND AND CALIBRATION

Chandra is a magniﬁcent piece of engineering, but it is not perfect: observations are
contaminated by background, the instruments do not operate at full capacity, and
the observatory has a ﬁnite lifetime. In this section I brieﬂy discuss these areas and

how they might affect past, current, and future scientiﬁc study with Chandra.

COSMIC X-RAY BACKGROUND (CXB)

Chandra is in a very high Earth orbit and is constantly bathed in high-energy, charged
particles originating from the cosmos which interact with the CCDS (the eyes) and
the materials housing the instruments (the skull). The CXB is composed of a soft
(E < 2 keV) component attributable to extragalactic emission, local discrete sources,
and spatially varying diffuse Galactic emission. There are also small contributions
from the the “local bubble” (Snowden, 2004) and charge exchange within the solar
system (Wargelin et al., 2004). The possibility of emission from unresolved point
sources and other unknown CXB components also exists. In most parts of the sky
the soft CXB is not a large contributor to the total background and can be modeled
using a combination of power-law and thermal Spectral models and then subtracted
out of the data.

The CXB also has a hard (E > 2 keV) component which arises from mostly
extragalactic sources such as quasars and is well modeled as a power-law. The spectral
shape of the hard particle background has been quite stable (up until mid-2005)
and thus subtracting off the emission by normalizing between observed and expected
count rates in a carefully chosen energy band makes removal of the hard component
straightforward.

Occasionally there are also very strong X—ray ﬂares. These ﬂares are quite easy
to detect in observations because, for a judiciously chosen energy band/time bin

combination, the count rate as a function of observation time exhibits a dramatic

32

spike during ﬂaring. The time intervals containing ﬂare episodes can be excluded
from the analysis rendering them harmless. Harmless that is provided the ﬂare was

not too long and some of the observing time allotment is usable.

INSTRUMENTAL EFFECTS AND SOURCES OF UNCERTAINTY

There are a number of instrumental effects which must be considered when analyzing
data taken with Chandra. The geometric area of the telescope’s mirrors does not
represent the “usable” area of the mirrors. The true effective area of Chandra has been
deﬁned by the Chandra X—ray Center (CXC) as the product of mirror geometric area,
reﬂectivity, off-axis vignetting, quantum efficiency of the detectors, energy resolution
of the detectors, and grating efﬁciency (gratings were not in use during any of the
observations used in this dissertation). To varying degrees, all of these components
depend on energy and a few of them also have a spatial dependence. Discussion of
the effective area is a lengthy and involved topic. A more concise understanding of
the effective area can be attained from visualization, hence the effective area as a
function of energy is shown in Figure 1.9.

The ACIS instrument is also subject to dead/ bad pixels, damage done by inter-
action with very high-energy cosmic rays, imperfect read-out as a function of CCD
location, and a hydrocarbon contaminate which has been building up Since launch
(Marshall et al., 2004).

Observations are also at the mercy of uncertainty sources. The data reduction
software provided by the CXC (CIAO) and our own reduction pipeline (CORP,

discussed in Appendix C) takes into consideration:
1. Instrumental effects and calibration
2. z 3% error in absolute ACIS ﬂux calibration

3. Statistical errors in the Sky and background count rates

33

4. Errors due to uncertainty in the background normalization

5. Error due to the z 2% systematic uncertainty in the background spectral shape
6. Cosmic variance of X-ray background sources

7. Unresolved source intensity

8. Scattering of source ﬂux

The list provided above is not comprehensive, but highlights the largest sources
of uncertainty: counting statistics, instrument calibration, and background. In each
section of this dissertation where data analysis is discussed, the uncertainty and error
analysis is discussed in the context of the science objectives.

The Chandra mission was scheduled for a minimum ﬁve year mission with the
expectation that it would go longer. Nearing the ten year anniversary of launch,
it is therefore useful to wonder how Chandra might be operating in years to come
and what the future holds for collecting data with Chandra ﬁve and even ten years
from now. The “life expectancy” of Chandra can be broken down into the categories:
spacecraft health, orbit stability, instrument performance, and Observation constraint
evolution. Given the continued progress of understanding Chandra’s calibration, the
relative stability of the X-ray background, and the overall health of the telescope as
of last review, it has been suggested that Chandra will survive at least a 15 year

mission, e. g. a decommissioning ~ 2014 (Bucher, 2007, 2008).

34

Wovelen th A
20 910[]

 

 

 

 

 

100 50 5 2

1000_ I I F I I I _

— l

l _
E
.2.
U
9.’

< 100 — _

Q) _ ..

.2 *- 1

s . , I

_ '1 ACIS-$3 (Bl) — '-._

ACIS-'3 (Fl) """""" '.

l

10 I I.’ 1 I l I l l 1 l I I l I I I
0.1 1.0 10.0

Energy [keV]

Figure 1.9 Chandra effective area as a function of energy. The effective area results
from the product of mirror geometric area, reﬂectivity, off-axis vignetting, quantum
efﬁciency of the detectors, energy resolution of the detectors, and grating efﬁciency.
Note the ACIS peak sensitivity is in the energy range where the majority of the ICM
emission occurs, E = 0.1 — 2.0 keV. Figure taken from the CXC.

35

Chapter Two

Cavagnolo, Kenneth W., Donahue, Megan, Voit, G. Mark, Sun, Ming
(2008). Bandpass Dependence of X—ray Temperatures in Galaxy Clusters.
The Astrophysical Journal. 682:821-830.

 

36

 

CHAPTER 2:

BANDPASS DEPENDENCE OF X-RAY
TEMPERATURES IN GALAXY
CLUSTERS

 

2.1 INTRODUCTION

The normalization, shape, and evolution of the cluster mass function are useful for
measuring cosmological parameters (e. g. Evrard, 1989; Wang & Steinhardt, 1998;
Haiman et al., 2001; Wang et al., 2004b). In particular, the evolution of large scale
structure formation provides a complementary and distinct constraint on cosmological
parameters to those tests which constrain them geometrically, such as supernovae
(Riess et al., 1998, 2007) and baryon acoustic oscillations (Eisenstein et al., 2005).
However, clusters are a useful cosmological tool only if we can infer cluster masses from
observable properties such as X—ray luminosity, X-ray temperature, lensing shear,
optical luminosity, or galaxy velocity dispersion. Empirically, the correlation of mass
to these observable properties is well-established (see Voit, 2005, for a review). But,
there is non-negligible scatter in mass-observable scaling relations which must be
accounted for if clusters are to serve as high-precision mass proxies necessary for
using clusters to study cosmological parameters such as the dark energy equation
of state. However, if we could identify a “second parameter” — possibly reﬂecting
the degree of relaxation in the cluster — we could improve the utility of clusters as

cosmological probes by parameterizing and reducing the scatter in mass-observable

37

scaling relations.

Toward this end, we desire to quantify the dynamical state of a cluster beyond
simply identifying which clusters appear relaxed and those which do not. Most clus-
ters are likely to have a dynamical state which is somewhere in between (O’Hara
et al., 2006; Kravtsov et al., 2006; Ventimiglia et al., 2008). The degree to which a
cluster is virialized must ﬁrst be quantiﬁed within simulations that correctly predict
the observable properties of the cluster. Then, predictions for quantifying cluster
virialization may be tested, and possibly calibrated, with observations of an unbiased
sample of clusters (e. g.R.EXCESS sample Of BOhringer et al., 2007).

One study that examined how relaxation might affect the observable properties
of clusters was conducted by (Mathiesen & Evrard, 2001, hereafter ME01) using the
ensemble of simulations by Mohr & Evrard (1997). ME01 found that most clusters
which had experienced a recent merger were cooler than the cluster mass-observable
scaling relations predicted. They attributed this to the presence of cool, spectroscop-
ically unresolved accreting subclusters which introduce energy into the ICM and have
a long timescale for dissipation. The consequence was an under-prediction of cluster
binding masses of 15 — 30% (Mathiesen & Evrard, 2001). It is important to note
that the simulations of Mohr & Evrard (1997) included only gravitational processes.
The intervening years have proven that radiative cooling is tremendously important
in shaping the global properties of clusters (e. g. McCarthy et al., 2004; Poole et al.,
2006; N agai et al., 2007). Therefore, the magnitude of the effect seen by ME01 could
be somewhat different if radiative processes are included.

One empirical observational method of quantifying the degree of cluster relaxation
involves using ICM substructure and employs the power in ratios of X—ray surface
brightness moments (Buote & Tsai, 1995, 1996; Jeltema et al., 2005). Although an
excellent tool, power ratios suffer from being aspect-dependent (Jeltema et al., 2007;

Ventimiglia et al., 2008). The work of ME01 suggested a complementary measure

38

of substructure which does not depend on projected perspective. In their analysis,
they found hard-band (2.0-9.0 keV) temperatures were ~ 20% hotter than broadband
(0.5-9.0 keV) temperatures. Their interpretation was that the cooler broadband tem—
perature is the result of unresolved accreting cool subclusters which are contributing
Signiﬁcant amounts of line emission to the soft band (E < 2 keV). This effect has
been studied and conﬁrmed by Mazzotta et al. (2004) and Vikhlinin (2006) using
simulated Chandra and XMM-Newton spectra.

ME01 suggested that this temperature skewing, and consequently the ﬁngerprint
of mergers, could be detected utilizing the energy resolution and soft-band sensitiv-
ity of Chandra. They proposed selecting a large sample of clusters covering a broad
dynamical range, ﬁtting a single-component temperature to the hard-band and broad-
band, and then checking for a net skew above unity in the hard-band to broadband
temperature ratio. In this chapter we present the ﬁndings of just such a temperature—
ratio test using Chandra archival data. We ﬁnd the hard-band temperature exceeds
the broadband temperature, on average, by ~ 16% in multiple ﬂux-limited samples
of X-ray clusters from the Chandra archive. This mean excess is weaker than the
20% predicted by ME01, but is signiﬁcant at the 120 level nonetheless. Hereafter,
we refer to the hard-band to broadband temperature ratio as TH B R- We also ﬁnd
that non-cool core systems and mergers tend to have higher values of TH B R- Our
ﬁndings suggest that TH B R is an indicator of a cluster’s temporal proximity to the
most recent merger event.

This chapter proceeds in the following manner: In §2.2 we outline sample-selection
criteria and Chandra observations selected under these criteria. Data reduction and
handling of the X—ray background is discussed in §2.3. Spectral extraction is discussed
in §2.4, while ﬁtting and simulated spectra are discussed in §2.5. Results and discus-
sion of our analysis are presented in §2.6. A summary of our work is presented in §2.7.

For this work we have assumed a ﬂat ACDM Universe with cosmology (2 M = 0.3,

39

Q A = 0.7, and H0 = 70 km S_1 Mpc-1. All quoted uncertainties are at the 1.60 level
(90% conﬁdence).

2.2 SAMPLE SELECTION

Our sample was selected from Observations publicly available in the Chandra X-ray
Telescope’s Data Archive (CDA). Our initial selection pass came from the ROSAT
Brightest Cluster Sample (Ebeling et al., 1998), RBC Extended Sample (Ebeling
et al., 2000), and ROSAT Brightest 55 Sample (Edge et al., 1990; Peres et al., 1998).
The portion of our sample at z ,2 0.4 can also be found in a combination of the
Einstein Extended Medium Sensitivity Survey (Gioia et al., 1990), North Ecliptic
Pole Survey (Henry et al., 2006), ROSAT Deep Cluster Survey (Rosati et al., 1995),
ROSAT Serendipitous Survey (Vikhlinin et al., 1998), and Massive Cluster Survey
(Ebeling et al., 2001). We later extended our sample to include clusters found in
the REFLEX Survey (BOhringer et al., 2004). Once we had a master list of possible
targets, we cross-referenced this list with the CDA and gathered observations where
a minimum of R5000 (deﬁned below) is fully within the CCD ﬁeld of view.

RA, is deﬁned as the radius at which the average cluster density is Ac times the
critical density of the Universe, pa = 3H (2)2 / 87rG. For our calculations of RA; we

adopt the relation from Arnaudl et a1. (2002):

 

1 2 —1 2 _ kT ”2
RAG = 2.71 Mpc a]! A, / (1+2) W2<iﬁf7> (2.1)
AcQM
A =
z 187r2flz
3
92 QM(1+2)

 

[QM(1+ Zl3l + [(1 - QM - 9100+ Z)2l + QA

where RA; is in units of hi}, Ac is the assumed density contrast of the cluster at R Ac’

and HT is a numerically determined, cosmology-independent (S :l:20%) normalization

40

for the virial relation GM / 2R 2 BTkTvirial- We use ﬁT = 1.05 taken from Evrard
et al. (1996).

The result of our CDA search was a total of 374 observations of which we used
244 for 202 clusters. The clusters making up our sample cover a redshift range of
z = 0.045 — 1.24, a temperature range of TX = 2.6 — 19.2 keV, and bolometric
luminosities of Lbol = 0.12 — 100.4 X 104’4 ergs s’l. The bolometric (E = 0.1 —- 100
keV) luminosities for our sample clusters plotted as a function of redshift are shown
in Figure 2.1. These Lboj values are calculated from our best-ﬁt Spectral models and
are limited to the region of the spectral extraction (from R = 70 kpc to R = R2500,
or R5000 in the cases in which no R2500 ﬁt was possible). Basic properties of our
sample are listed in Table A.1.

For the sole purpose of deﬁning extraction regions based on ﬁxed overdensities as
discussed in §2.4, ﬁducial temperatures (measured with ASCA) and redshifts were
taken from Homer (2001) (all redshifts conﬁrmed with N EDI). We Show below that
the ASCA temperatures are sufﬁciently close to the Chandra temperatures such that
RAC is reliably estimated to within 20%. Note that RAc is proportional to Tl/z, so
that a 20% error in the temperature leads to only a 10% error in RAG, which in turn
has no detectable effect on our ﬁnal results. For clusters not listed in Homer (2001) ,
we used a literature search to ﬁnd previously measured temperatures. If no published
value could be located, we measured the global temperature by recursively extracting
a spectrum in the region 0.1 < r < 0.2R500 ﬁtting a temperature and recalculating
R500. This process was repeated until three consecutive iterations produced R500
values which differed by S 10. This method of temperature determination has been
employed in other studies, see Sanderson et al. (2006) and Henry et al. (2006) as

examples.

 

1 http: //nedwww.ipac.caltech.edu/

41

 

100.0

 

 

 

- . n." C . :
.- .. i ”,3 -
l- ‘ i F" i
9' - . ' i l
' :- 5" 3 ‘- "1131'“ :I 1
100 * "lli'uua'tq" g i i f
._ - 7* ' -:
a, :3??? :1 g? :
f; t 3'". xi. ' iii” I l l H :
~ «A; s l
3 1.0 51... ﬂ' l I E
5‘ °.' ° I; 5
0.1%.":R 1
' 1' J J n l n n n I n n n L-". n n I n n 1 I 1
0.2 0.4 0.6 0.8 1 .0 1 .2
Redshift

Figure 2.1 Bolometric luminosity (E = 0.1 — 100 keV) plotted as a function of redshift
for the 202 clusters which make up the initial sample. Lbol values are limited to the re—
gion of spectral extraction, R = R2500—CORE- For clusters without R2500—CORE ﬁts,
R = RSOOO-CORE ﬁts were used and are denoted in the ﬁgure by empty stars. Dotted
lines represent constant ﬂuxes of 3.0 X10-15, 10-14, 10—13, and 10"12 ergs s’l cm_2.

42

2.3 Chandra DATA

2.3.1 REPROCESSING AND REDUCTION

All data sets were reduced using the Chandra} Interactive Analysis of Observations
package (CIAO) and accompanying Calibration Database (CALDB). Using CIAO
3.3.0.1 and CALDB 3.2.2, standard data analysis was followed for each observation
to apply the most up-to-date time-dependent gain correction and when appropriate,
charge transfer inefficiency correction (Townsley et al., 2000).

Point sources were identiﬁed in an exposure-corrected events ﬁle using the adap-
tive wavelet tool WAVDETECT (Freeman et al., 2002). A 20 region surrounding
each point source was automatically output by WAVDETECT to deﬁne an exclusion
mask. All point sources were then visually conﬁrmed and we added regions for point
sources which were missed by WAVDETECT and deleted regions for spuriously de-
tected “sources.” Spurious sources are typically faint CCD features (chip gaps and
chip edges) not fully removed after dividing by the exposure map. This process
resulted in an events ﬁle (at “level 2”) that has been cleaned of point sources.

To check for contamination from background ﬂares or periods of excessively high
background, light curve analysis was performed using Maxim Markevitch’s contributed
CIAO script LC-CLEAN.SL2. Periods with count rates 2 30 and/or a factor 2 1.2
of the mean background level of the observation were removed from the good time
interval ﬁle. As prescribed by Markevitch’s cookbook3, ACIS front-illuminated (FI)
chips were analyzed in the 0.3 — 12.0 keV range, and the 2.5 — 7.0 keV energy range
for the ACIS back-illuminated (BI) chips.

When a FI and BI chip were both active during an observation, we compared light
curves from both chips to detect long duration, soft-ﬂares which can go undetected

on the FI chips but Show up on the BI chips. While rare, this class of ﬂare must

 

2http: / / cxc.harvard.edu / contrib/ maxim / acisbg /
3http: / / cxc.harvard.edu/ contrib/ maxim / acisbg/ COOKBOOK

43

be ﬁltered out of the data, as it introduces a spectral component which artiﬁcially
increases the best-ﬁt temperature via a high energy tail. We ﬁnd evidence for a long
duration soft ﬂare in the observations of Abell 1758 (David & Kempner, 2004), CL
J2302.8+O844, and IRAS 09104+4109. These ﬂares were handled by removing the
time period of the ﬂare from the GTI ﬁle.

Deﬁning the cluster “center” is essential for the later purpose of excluding cool
cores from our spectral analysis (see §2.4). To determine the cluster center, we cal-
culated the centroid of the ﬂare cleaned, point-source free level-2 events ﬁle ﬁltered
to include only photons in the 0.7 — 7 .0 keV range. Before centroiding, the events
ﬁle was exposure-corrected and “holes” created by excluding point sources were ﬁlled
using interpolated values taken from a narrow annular region just outside the hole
(holes are not ﬁlled during spectral extraction discussed in §2.4). Prior to centroiding,
we deﬁned the emission peak by heavily binning the image, ﬁnding the peak value
within a circular region extending from the peak to the chip edge (deﬁned by the ra-
dius Rm”), reducing Rm“ by 5%, reducing the binning by a factor of 2, and ﬁnding
the peak again. This process was repeated until the image was unbinned (binning
factor of 1). We then returned to an unbinned image with an aperture centered on
the emission peak with a radius Rmax and found the centroid using CIAO’s DMSTAT.
The centroid, (:rc, ye), for a distribution of N good pixels with coordinates (sci, yj)

and values f(xi,yj) is deﬁned as:

 

 

N
Q = Zﬂxayi) (2-2)
i,j=1
229:1182' ' f(l‘z', yr)
:rc =
Q
Zin=1yi ° f(ivz'Iyz')
yo = .
Q

If the centroid was within 70 kpc of the emission peak, the emission peak was

44

selected as the center, otherwise the centroid was used as the center. This selection
was made to ensure all “peaky” cool cores coincided with the cluster center, thus
maximizing their exclusion later in our analysis. All cluster centers were additionally

veriﬁed by eye.

2.3.2 X-RAY BACKGROUND

Because we measured a global cluster temperature, speciﬁcally looking for a tem-
perature ratio shift in energy bands which can be contaminated by the high-energy
particle background or the soft local background, it was important to carefully ana—
lyze the background and subtract it from our source Spectra. Below we outline three
steps taken in handling the background: customization of blank-sky backgrounds,
renormalization of these backgrounds for variation of hard-particle count rates, and
ﬁtting of soft background residuals.

We used the blank-Sky observations of the X-ray background from Markevitch
et al. (2001) and supplied within the CXC CALDB. First, we compared the ﬂux from
the diffuse soft X-ray background of the ROSAT All-Sky Survey (RASS') combined
bands R12, R45, and R67 to the 0.7-2.0 keV ﬂux in each extraction aperture for
each observation. RASS combined bands give ﬂuxes for energy ranges of 0.12-0.28,
0.47-1.21, and 0.76-2.04 keV respectively corresponding to R12, R45, and R67. For
the purpose of simplifying subsequent analysis, we discarded observations with an
R45 ﬂux 2 10% of the total cluster X-ray ﬂux.

The appropriate blank-sky dataset for each observation was selected from the
CALDB, reprocessed exactly as the observation was, and then reprojected using
the aspect solutions provided with each observation. For observations on the ACIS-
I array, we reprojected blank-Sky backgrounds for chips 1013 plus chips S2 and/or
S3. For ACIS-S observations, we created blank-sky backgrounds for the target chip,

plus chips I2 and/ or I3. The additional off aim-point chips were included only if

45

they were active during the Observation and had available blank-sky data sets for
the observation time period. Off aim-point chips were cleaned for point sources and
diffuse sources using the method outlined in §2.3.1.

The additional off aim-point chips were included in data reduction since they
contain data which is farther from the cluster center and are therefore more useful
in analyzing the observation background. For observations which did not have a
matching off aim-point blank-sky background, a source-free region of the active chips
is located and used for background normalization. To normalize the hard particle
component we measured ﬂuxes for identical regions in the blank-sky ﬁeld and target
ﬁeld in the 9.5-12.0 keV range. The effective area of the ACIS arrays above 9.5 keV
is approximately zero, and thus the collected photons there are exclusively from the
particle background.

A histogram of the ratios of the 9.5-12.0 keV count rate from an observation’s off
aim-point chip to that of the observation speciﬁc blank-sky background are presented
in Figure 2.2. The majority of the observations are in agreement to S, 20% of the
blank-sky background rate, which is small enough to not affect our analysis. Even
so, we re-normalized all blank-sky backgrounds to match the observed background.

Normalization brings the observation background and blank-sky background into
agreement for E > 2 keV, but even after normalization, typically, there may exist
a soft excess/ deﬁcit associated with the Spatially varying soft Galactic background.
Following the technique detailed in Vikhlinin et a1. (2005), we constructed and ﬁt soft
residuals for this component. For each observation we subtracted a spectrum of the
blank-sky ﬁeld from a spectrum of the off aim-point ﬁeld to create a soft residual.
The residual was ﬁt with a solar abundance, zero-redshift MEKAL model (Mewe
et al., 1985, 1986; Liedahl et al., 1995) in which the normalization was allowed to be
negative. The resulting best-ﬁt temperatures for all of the soft residuals identiﬁed

here were between 0.2-1.0 keV, which is in agreement with results of Vikhlinin et al.

46

 

 

 

 

 

 

 

50: I T I 1 I r Y 1 V:
I ' ' 2

: I I :

: ' ' :

. I I -
40.— I I '2
: I I I

I I I Z

Z l I :

: ' ' :
2530:- | I 1
h - I I -
a Z I I 2
E : I I I
r : ' =
- '_ l .2
02°: ' 1
- I ..

I I .1

I I :1

I I :
10;- l 1
: ' ' 1

: ' ' :

- I I .

I I I I

0- l 1 l l l l l L I l l l L 4 l 1 -
0.8 1.0 1.2 1.4 1.6 1.8

9.5-12 keV count rate ratio for Target/Blank-Sky

Figure 2.2 Ratio of target ﬁeld and blank-sky ﬁeld count rates in the 9.5-12.0 keV
band for all 244 observations in our initial sample. Vertical dashed lines represent
:l:20% of unity. Despite the good agreement between the blank-sky background and
observation count rates for most observations, all backgrounds are normalized.

47

(2005). The model normalization of this background component was then scaled to
the cluster sky area. The re-scaled component was included as a ﬁxed background

component during ﬁtting of a cluster’s spectra.

2.4 SPECTRAL EXTRACTION

The simulated spectra calculated by ME01 were analyzed in a broad energy band of
0.5 — 9.0 keV and a hard energy band of 2-0rest — 9.0 keV, but to make a reliable
comparison with Chandra data we used narrower energy ranges of 0.7-7.0 keV for the
broad energy band and 2.0rest — 7 .0 keV for the hard energy band. We excluded data
below 0.7 keV to avoid the effective area and quantum efﬁciency variations of the
ACIS detectors, and excluded energies above 7.0 keV in which diffuse source emission
is dominated by the background and where Chandra’s effective area is small. We also
accounted for cosmic redshift by Shifting the lower energy boundary of the hard-band
from 2.0 keV to 2.0/ (1 + 2) keV (henceforth, the 2.0 keV cut is in the rest frame).
ME01 calculated the relation between T0,5_9_0 and T2,0_9,0 using apertures of
R200 and R500 in size. While it is trivial to calculate a temperature out to R200 or
R500 for a simulation, such a measurement at these scales is extremely difﬁcult with
Chandra Observations (see Vikhlinin et al. (2005) for a detailed example). Thus, we
chose to extract spectra from regions with radius R5000, and R2500 when possible.
Clusters analyzed only within R5000 are denoted in Table A.1 by a double dagger (i).
The cores of some clusters are dominated by gas at S, Tvirz‘al / 2 which can greatly
affect the global best-ﬁt temperature; therefore, we excised the central 70 kpc of each
aperture. These excised apertures are denoted by “-CORE” in the text. Recent
work by Maughan (2007) has shown excising 0.15 R500 rather than a static 70 kpc
reduces scatter in mass-observable scaling relations. However, our smaller excised
region seems sufﬁcient for this investigation because for cool core clusters the average

radial temperature at r > 70 kpc is approximately isothermal (Vikhlinin et al., 2005).

48

Indeed, we ﬁnd that cool core clusters have smaller than average TH B R when the 70
kpc region has been excised (§2.6.3).

Although some clusters are not circular in projection, but rather are elliptical or
asymmetric, we found that assuming spherical symmetry and extracting spectra from
a circular annulus did not Signiﬁcantly change the best-ﬁt values. For another such
example see Bauer et al. (2005).

After deﬁning annular apertures, we extracted source spectra from the target
cluster and background Spectra from the corresponding normalized blank-sky dataset.
By standard CIAO means we created weighted effective area functions (WARFs)
and redistribution matrices (WRMFS) for each cluster using a ﬂux-weighted map
(WMAP) across the entire extraction region. The WMAP was calculated over the
energy range 0.3-2.0 keV to weight calibrations that vary as a function of position on
the chip. The CCD characteristics which affect the analysis of extended sources, such
as energy dependent vignetting, are contained within these ﬁles. Each spectrum was

then binned to contain a minimum of 25 counts per channel.

2.5 SPECTRAL ANALYSIS

2.5. 1 FITTING

Spectra were ﬁt with XSPEC 11.3.2ag (Arnaud, 1996) using a Single-temperature
MEKAL model in combination with the photoelectric absorption model WABS (Mor-
rison & McCammon, 1983) to account for Galactic absorption. Galactic absorption
values, N H, are taken from Dickey & Lockman (1990). The potentially free param-
eters of the absorbed thermal model are N H, X—ray temperature (TX), metal abun-
dance normalized to solar (elemental ratios taken from Anders & Grevesse, 1989),
and a normalization proportional to the integrated emission measure of the cluster.

Results from the ﬁtting are presented in Tables A3 and A4. No systematic error

49

is added during ﬁtting, and thus all quoted errors are statistical only. The statistic
used during ﬁtting was x2 (XSPEC statistics package CHI). Every cluster analyzed
was found to have greater than 1500 background-subtracted source counts in the
Spectrum.

For some clusters, more than one observation was available in the archive. We
utilized the power of the combined exposure time by ﬁrst extracting independent
spectra, WARFS, WRMFS, normalized background Spectra, and soft residuals for each
observation. Then, these independent spectra were read into XSPEC simultaneously
and ﬁt with one spectral model which had all parameters, except normalization, tied
among the spectra. The simultaneous ﬁt is what is reported for these clusters, denoted
by a star (11:), in Tables A3 and A.4.

Additional statistical error was introduced into the ﬁts because of uncertainty as-
sociated with the soft local background component discussed in §2.3.2. To estimate
the sensitivity of our best-ﬁt temperatures to this uncertainty, we used the differences
between TX for a model using the best-ﬁt soft background normalization and TX for
models using :tlo of the soft background normalization. The statistical uncertainty
of the original ﬁt and the additional uncertainty inferred from the range of normal-
izations to the soft X-ray background component were then added in quadrature to
produce a ﬁnal error. In all cases this additional background error on the tempera-
ture was less than 10% Of the total statistical error, and therefore represents a minor
inﬂation of the error budget.

When comparing ﬁts with ﬁxed Galactic column density with those where it was
a free parameter, we found that neither the goodness of ﬁt per free parameter nor
the best-ﬁt TX were signiﬁcantly different. Thus, N H was ﬁxed at the Galactic value
with the exception of three cases: Abell 399 (Sakelliou 85 Ponman, 2004), Abell 520,
and Hercules A. For these three clusters N H is a free parameter. In all ﬁts, the metal

abundance was a free parameter.

50

After ﬁtting we rejected several data sets as their best-ﬁt T2,0_7,0 had no upper
bound in the 90% conﬁdence interval and thus were insufficient for our analysis. All
ﬁts for the clusters Abell 781, Abell 1682, CL J1213+0253, CL J1641+4001, IRAS
09104+4109, Lynx E, MACS J1824.3+4309, MS 0302.7+1658, and RX J1053+5735
were rejected. We also removed Abell 2550 from our sample after ﬁnding it to be an
anomalously cool (TX ~ 2 keV) “cluster”. In fact, Abell 2550 is a line-of-sight set of
groups, as discussed by Martini et al. (2004). After these rejections, we are left with

a ﬁnal sample of 192 clusters which have R2500—CORE ﬁts and 166 clusters which

have R5000—CORE ﬁts.

2.5.2 SIMULATED SPECTRA

To quantify the effect a second, cooler gas component would have on the ﬁt of a
single-component spectral model, we created an ensemble of simulated spectra for
each real spectrum in our entire sample using XSPEC. With these simulated spectra
we sought to answer the question: Given the count level in each observation of our
sample, how bright must a second temperature component be for it to affect the
observed temperature ratio? Put another way, we asked at what ﬂux ratio a second
gas phase produces a temperature ratio, TH B R, of greater than unity with 90%
conﬁdence.

We began by adding the observation-speciﬁc background to a convolved, absorbed
thermal model with two temperature components observed for a time period equal
to the actual observation’s exposure time and adding Poisson noise. For each real-
ization of an observation’s Simulated spectrum, we deﬁned the primary component
to have the best-ﬁt temperature and metallicity of the R2500—CORE 0.7-7.0 keV ﬁt,
or R5000—CORE if no R2500—CORE ﬁt was performed. We then incremented the sec-
ondary component temperature over the values 0.5, 0.75, 1.0, 2.0, and 3.0 keV. The

metallicity of the secondary component was ﬁxed and set equal to the metallicity of

51

the primary component.

We adjusted the normalization of the simulated two-component spectra to achieve
equivalent count rates to those in the real spectra. The sum of normalizations can
be expressed as N = N1 + 6N2. We set the secondary component normalization to
N2 = {Nbﬁ where Nbf is the best-ﬁt normalization of the appropriate 0.7-7.0 keV
ﬁt and g is a preset factor taking the values 0.4, 0.3, 0.2, 0.15, 0.1, and 0.05. The
primary component normalization, N1, was determined through an iterative process
to make real and simulated spectral count rates match. The parameter 5 therefore
represents the fractional contribution of the cooler component to the overall count
rate.

There are many systematics at work in the full ensemble of observation speciﬁc
simulated spectra, such as redshift, column density, and metal abundance. Thus as a
further check of spectral sensitivity to the presence of a second gas phase, we simulated
additional spectra for the case of an idealized observation. We followed a similar
procedure to that outlined above, but in this instance we used a ﬁner temperature
and § grid of T2 = 0.5 —> 3.0 in steps of 0.25 keV, and 6 = 0.02 -+ 0.4 in steps of
0.02. The input spectral model was N H = 3.0 x 1020 cm‘2, T1 = 5 keV, Z /Z@ = 0.3
and z = 0.1. We also varied the exposure times such that the total number of counts
in the 0.7-7.0 keV band was 15K, 30K, 60K, or 120K. For these spectra we used the
on-axis sample response ﬁles provided to Cycle 10 proposers“. Poisson noise is added,
but no background is considered.

We also simulated a control sample Of single-temperature models. The control
sample is simply a simulated version of the best-ﬁt model. This control provides us
with a statistical test of how often the actual hard-component temperature might
differ from a broadband temperature ﬁt if calibration effects are under control. Fits

for the control sample are Shown in the far right panels of Figure 2.3.

 

4http: / / cxc.harvard.edu / caldb / prop..plan / imaging / index.html

52

For each Observation, we have 65 total simulated spectra: 35 single-temperature
control spectra and 30 two-component simulated spectra (5 secondary temperatures,
each with Six different 1;”). Our resulting ensemble of simulated Spectra contains 12,765
spectra. After generating all the spectra we followed the same ﬁtting routine detailed
in §2.5.1.

With the ensemble of simulated spectra we then asked the question: for each T 2
and ATX (deﬁned as the difference between the primary and secondary temperature
components) what is the minimum value of IE , called 5mm, that produces TH B R 2 1.1
at 90% conﬁdence? From our analysis of these simulated spectra we have found these

important results:

1. In the control sample, a Single-temperature model rarely (~ 2% of the time)
gives a signiﬁcantly different T0,7_7_0 and T2,0_7_0. The weighted average (Fig.
2.3, right panels) for the control sample is 1.002 i 0.001 and the standard
deviation is :t:0.044. The TH B R distribution for the control sample appears to
have an intrinsic width which is likely associated with statistical noise of ﬁtting
in XSPEC (Dupke, private communication). This result indicates that our
remaining set of observations is statistically sound, e. 9. our ﬁnding that TH B R

signiﬁcantly differs from 1.0 cannot result from statistical ﬂuctuations alone.

2. Shown in Table 2.1 are the contributions a second cooler component must make
in the case of the idealized spectra in order to produce TH B R 2 1.1 at 90%
conﬁdence. In general, the contribution of cooler gas must be > 10% for T2 < 2
keV to produce TH B R as large as 1.1. The increase in percentages at T2 <
1.0 keV is owing to the energy band we consider (0.7-7.0 keV) as gas cooler
than 0.7 keV must be brighter than at 1.0 keV in order to make an equivalent

contribution to the soft end of the spectrum at 0.7 keV.

3. In the full ensemble of observation-speciﬁc simulated spectra, we ﬁnd a great

53

deal of statistical scatter in 5min at any given ATX. This was expected as
the full ensemble is a superposition of spectra with a broad range of total
counts, N H, redshifts, abundance, and backgrounds. But using the idealized
simulated spectra as a guide, we ﬁnd for those spectra with Ncounts 2, 15000,
producing TH B R 2 1.1 at 90% conﬁdence again requires the cooler gas to be
contributing > 10% of the emission. These results are also summarized in Ta-
ble 2.1. The good agreement between the idealized and observation-speciﬁc
Simulated spectra indicates that while many more factors are in play for the
observation-speciﬁc spectra, they do not degrade our ability to reliably measure
T H B R > 1.1. The trend here of a common soft component sufﬁcient to change
the temperature measurement in a single-temperature model is statistical, a re-

sult that comes from an aggregate view of the sample rather than any individual

ﬁt.

. As redshift increases, gas cooler than 1.0 keV is slowly redshifted out of the
observable X-ray band. As expected, we ﬁnd from our Simulated spectra that
for z 2 0.6, TH B R is no longer statistically distinguishable from unity. In
addition, the T2_0_7,0 lower boundary nears convergence with the T0,7_7_0 lower
boundary as 2 increases, and for z = 0.6, the hard-band lower limit is 1.25 keV,
while at the highest redshift considered, 2 = 1.2, the hard-band lower limit
is only 0.91 keV. For the 14 clusters with z 2 0.6 in our real sample we are
most likely underestimating the actual amount of temperature inhomogeneity.

We have tested the effect of excluding these clusters on our results, and ﬁnd a

negligible change in the overall skew of TH BR to greater than unity.

54

Table 2.1: Summary of two-component Simulations

 

 

Idealized Spectra Observation-Speciﬁc Spectra
T2 {min T2 5min
keV keV

0.50 2 12% :f: 4% 0.50 2 14.5% :1: 0.1%
0.75 2 12% 2t 4% 0.75 2 11.7% :t 0.1%
1.00 2 8% :l: 3% 1.00 2 11.6% :1: 0.1%
1.25 _>_ 17% :l: 3% - -

1.50 2 23% :l: 5% - -

1.75 2 28% i 4% - -
2.00 none 2.00 2 25.5% :t 0.1%
3.00 none 3.00 2 28.9% :1: 0.1%

 

 

 

Table 2.1 summarizes the results Of the two temperature component spectra simu-
lations for the ideal and observation-speciﬁc cases (see §2.5.2 for details). The param-
eter 5min represents the minimum fractional contribution of the cooler component,
T2, to the overall count rate in order to produce TH B R 2 1.1 at 90% conﬁdence. The

results for the Observation-Speciﬁc spectra are for spectra with Ncounts > 15, 000.

2.6 RESULTS AND DISCUSSION

2.6.1 TEMPERATURE RATIOS

For each cluster we have measured a ratio of the hard-band to broadband temper-
ature deﬁned as TH B R = T2_0_7.0/T0_7_7_0. We ﬁnd that the mean TH B R for our
entire sample is greater than unity at more than 120 signiﬁcance. The weighted
mean values for our sample are shown in Table 2.2. Quoted errors in Table 2.2 are
standard deviation of the mean calculated using an unbiased estimator for weighted
samples. Simulated sample has been culled to include only T2=0.75 keV. Presented
in Figure 2.3 are the binned weighted means and raw TH B R values for R2500—CORE,
R5OOO—CORE: and the Simulated control sample. The peculiar points with TH B R <

1 are all statistically consistent with unity. The presence of clusters with TH B R =

55

1 suggests that systematic calibration uncertainties are not the sole reason for devi—
ations of TH B R from 1. We also ﬁnd that the temperature ratio does not depend
on the best-ﬁt broadband temperature, and that the observed dispersion of TH B R is
greater than the predicted dispersion arising from systematic uncertainties.

The uncertainty associated with each value of TH B R is dominated by the larger
error in T2,0_7_0, and on average, AT2,0_7_0 z 2.3AT0,7_7,0. This error interval
discrepancy naturally results from excluding the bulk of a cluster’s emission which
occurs below 2 keV. While choosing a temperature-sensitive cut-off energy for the
hard-band (other than 2.0 keV) might maintain a more consistent error budget across
our sample, we do not ﬁnd any systematic trend in TH B R or the associated errors

with cluster temperature.

Table 2.2: Weighted averages for various apertures

 

 

............. Without Core............. ...........With Core
[0.7-7.0] [2.0-7.0] THBR [0.7-7.0] [2.0-7.0] THBR
Aperture keV keV keV keV

 

R2500 4.93i0.03 6.24:1:0.07 1.16i0.01 4.47i0.02 5.45i0.05 1.13:1:0.01

R5000 4.75:1:0.02 5.97i0.07 1.14i0.01 4.27:l:0.02 5.29:1:0.05 1.14:t0.01
Simulated 3.853:f:0.004 4.457:t0.009 1.131 i0.002 - - -
Control 4.208:t:0.003 4.468:t0.006 1.002:t0.001 - - -

 

2.6.2 SYSTEMATICS

In this study we have found the average value of TH B R is signiﬁcantly greater than
one and that 0H B R > demand, with the latter result being robust against system-
atic uncertainties. AS predicted by ME01, both of these results are expected to arise
naturally from the hierarchical formation of clusters. But systematic uncertainty
related to Chandra instrumentation or other sources could shift the average value
of TH B R one would get from “perfect” data. In this section we consider some ad-

ditional sources of uncertainty. 5A First, the disagreement between XMM-Newton

56

 

1.25:" '
1.20,-

 

1.10}

 

 

 

 

1.05L

 

1.00 E
0.95 i
2.0 1

 

THBR = T2.0-7.0’To.7-7.o

1.5L

1.0 '

 

 

 

 

 

 

Tar-7.0 [keV]

Figure 2.3 Best-ﬁt temperatures for the hard-band, T2_0_7.0, divided by the broad-
band, T0_7_7_0, and plotted against the broadband temperature. For binned data,
each bin contains 25 clusters, with the exception of the highest temperature bins
which contain 16 and 17 for 122500-001“; and RSOOO—CORE: respectively. The sim-
ulated data bins contain 1000 clusters with the last bin having 780 clusters. The
line of equality is Shown as a dashed line and the weighted mean for the full sample
is shown as a dashed-dotted line. Error bars are omitted in the unbinned data for
clarity. Note the net skewing of TH B R to greater than unity for both apertures with
no such trend existing in the simulated data. The dispersion of TH B R for the real
data is also much larger than the dispersion of the simulated data.

57

and Chandra cluster temperatures has been noted in several independent studies, i.e.
Vikhlinin et al. (2005) and Snowden et a1. (2008). But the source of this discrepancy is
not well understood and efforts to perform cross-calibration between XMM-Newton
and Chandra have thus far not been conclusive. One possible explanation is poor
calibration of Chandra at soft X-ray energies which may arise from a hydrocarbon
contaminant on the High Resolution Mirror Assembly (HRMA) similar in nature to
the contaminant on the ACIS detectors (Marshall et al., 2004). We have assessed this
possibility by looking for systematic trends in TH B R with time or temperature, as
such a contaminant would most likely have a temperature and / or time dependence.

AS noted in §2.6.1 and seen in Figure 2.3, we ﬁnd no systematic trend with tem-
perature either for the full sample or for a sub-sample of single-observation clusters
with > 75% of the observed ﬂux attributable to the source (higher S / N observations
will be more affected by calibration uncertainty). Plotted in the lower-left pane of
Figures 2.4 and 2.5 is TH B R versus time for single observation clusters (clusters with
multiple observations are ﬁt simultaneously and any time effect would be washed out)
where the spectral ﬂux is > 75% from the source. We ﬁnd no signiﬁcant systematic
trend in T H B R with time, which suggests that if TH B R is affected by any contami—
nation of Chandra’s HRMA, then the contaminant is most likely not changing with
time. Our conclusion on this matter is that the soft calibration uncertainty is not
playing a dominant role in our results.

Aside from instrumental and calibration effects, some other possible sources of
systematic error are S/ N, redshift selection, Galactic absorption, and metallicity.
Also presented in Figures 2.4 and 2.5 are three of these parameters versus TH B R
for R2500—CORE and RSOOO—COREa respectively. The trend in TH B R with redshift
is expected as the 2.0/(1+2) keV hard-band lower boundary nears convergence with
the 0.7 keV broadband lower boundary at z z 1.85. We ﬁnd no systematic trends

of TH B R with S/ N or Galactic absorption, which might occur if the skew in TH B R

58

were a consequence of poor count statistics, inaccurate Galactic absorption, or very
poor calibration. In addition, the ratio of TH B R for R2500—CORE to RSOOO—CORE for
every cluster in our sample does not signiﬁcantly deviate from unity. Our results are
robust to changes in aperture size.

Also shown in Figures 2.4 and 2.5 are the ratios of ASCA temperatures taken
from Homer (2001) to Chandra temperatures derived in this work. The spurious
point below 0.5 with very large error bars is MS 2053.7-0449, which has a poorly
constrained ASCA temperature of 10.03':§:gg. Our value of ~ 3.5 keV for this cluster
is in agreement with the recent work of Maughan et al. (2008). Not all our sample
clusters have an ASCA temperature, but a sufﬁcient number (53) are available to
make this comparison reliable. Apertures used in the extraction of ASCA spectra
had no core region removed and were substantially larger than R2500. AS CA spectra
were also ﬁt over a broader energy range (0.6-10 keV) than we use here. Nonetheless,
our temperatures are in good agreement with those from ASCA, but we do note a
trend of comparatively hotter Chandra temperatures for TChandra > 10 keV. For
both apertures, the clusters with TChandra > 10 keV are Abell 1758, Abell 2163,
Abell 2255, and RX J1347.5—1145. Based on this trend, we test excluding the hottest
clusters (TChandra > 10 keV where ASCA and Chandra disagree) from our sample.
The mean temperature ratio for R2500—CORE remains 1.16 and the error Of the mean
increases from :l:0.014 to :l:0.015, while for R5000-CORE TH B R increases by a negli-
gible 0.9% to 1.15 :I: 0.014. Our results are not being inﬂuenced by the inclusion of
hot clusters.

The temperature range of the clusters we have analyzed (TX ~ 3 - 20 keV) is
broad enough that the effect of metal abundance on the inferred spectral temperature
is clearly not negligible. In Figure 2.6 we have plotted TH B R versus abundance in
solar units. Despite covering a factor of seven in temperature and metal abundances

ranging from Z /Z® z 0 to solar, we ﬁnd no trend in TH BR with metallicity. The

59

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 2.4 A few possible sources of systematic uncertainty vs. TH B R calculated for
the R2500—CORE apertures (192 clusters). Error bars have been omitted in several
plots for clarity. The line Of equality is shown as a dashed line in all panels. ( Top left: )
TH B R vs. redshift for the entire sample. The trend in TH B R with redshift is expected
as the T2_0_7,0 lower boundary nears convergence with the T0,7_7_0 lower boundary
at z z 1.85. Weighted values of TH B R are consistent with unity starting at 2 ~ 0.6.
( Top right: ) TH B R vs. percentage of spectrum ﬂux which is attributed to the source.
We ﬁnd no trend with signal-to—noise which suggests calibration uncertainty not is
playing a major role in our results. ( Middle left: ) TH B R vs. Galactic column density.
We ﬁnd no trend in absorption which would result if N H values are inaccurate or if we
had improperly accounted for local soft contamination. ( Middle right: ) TH B R vs. the
deviation from unity in units of measurement uncertainty. Recall that we have used
90% conﬁdence (1.60) for our analysis. (Bottom left: ) TH B R plotted vs. observation
start date. The plotted points are culled from the full sample and represent only
clusters which have a single observation and where the spectral ﬂux is > 75% from
the source. We note no systematic trend with time. ( Bottom right: ) Ratio of Chandra
temperatures derived in this work to ASCA temperatures taken from Homer (2001).
We note a trend of comparatively hotter Chandra temperatures for clusters > 10 keV,
otherwise our derived temperatures are in good agreement with those of ASCA.

60

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 2.5 Same as Fig. 2.4 except using the R5000—CORE apertures (166 clusters).

61

 

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Figure 2.6 TH 3 R as a function of metal abundance for R2500—CORE: RSOOO—CORE;
and the control sample (see discussion of control sample in §2.5.2). Error bars are
omitted for clarity. The dashed-line represents the linear best-ﬁt using the bivariate
correlated error and intrinsic scatter (BCES) method of Akritas & Bershady (1996)
which takes into consideration errors on both TH B R and abundance when performing
the ﬁt. We note no trend in TH B R with metallicity (the apparent trend in the top
panel is not signiﬁcant) and also note the low dispersion in the control sample relative
to the Observations. The striation of abundance arises from our use of two decimal
places in recording the best-ﬁt values from XSPEC.

62

slight trend in the R2500—CORE aperture (Fig. 2.6, top) is insigniﬁcant, while there

is no trend at all in the control sample or R5000—CORE aperture.

2.6.3 USING THBR AS A TEST OF RELAXATION
COOL CORE VERSUS NON-COOL CORE

As discussed in 2.1, ME01 gives us reason to believe the Observed skewing of TH B R
to greater than unity is related to the dynamical state of a cluster. It has also been
suggested that the process of cluster formation and relaxation may robustly result
in the formation Of a cool core (Ota et al., 2006; Burns et al., 2008). Depending
on classiﬁcation criteria, completeness, and possible selection biases, studies of ﬂux-
limited surveys have placed the prevalence of cool cores at 34% - 60% (White et al.,
1997; Peres et al., 1998; Bauer et al., 2005; Chen et al., 2007). It has thus become
rather common to divide up the cluster population into two distinct classes,’cool core
(CC) and non-cool core (NCC), for the purpose of discussing their different formation
or merger histories. We thus sought to identify which clusters in our sample have cool
cores, which do not, and if the presence or absence of a cool core is correlated with
TH B R- It is very important to recall that we excluded the core during spectral
extraction and analysis.

T0 classin the core of each cluster, we extracted a Spectrum for the 50 kpc region

surrounding the cluster center and then deﬁned a temperature decrement,

Tdec = T50/Tcluster (23)

where T50 is the temperature of the inner 50 kpc and T cluster is either the R2500—CORE
or R5000—CORE temperature. If Tdec was 20 less than unity, we deﬁned the cluster
as having a CC, otherwise the cluster was deﬁned as NCC. We ﬁnd CCS in 35% of

our sample and when we lessen the Signiﬁcance needed for CC classiﬁcation from 20

63

to 10, we ﬁnd 46% Of our sample clusters have CCS. It is important to note that
the frequency of CCS in our study is consistent with other more detailed studies of
CC/NCC pOpulations.

When ﬁtting for T50, we altered the method outlined in [6,251 to use the XSPEC
modiﬁed Cash statistic (Cash, 1979), CSTAT, on ungrouped spectra. This choice was
made because the distribution of counts per bin in low count spectra is not Gaussian
but instead Poisson. As a result, the best-ﬁt temperature using x2 is typically cooler
(Nousek & Shue, 1989; Balestra et al., 2007). We have explored this systematic in all
of our ﬁts and found it to be signiﬁcant only in the lowest count spectra of the inner
50 kpc apertures discussed here. But, for consistency, we ﬁt all inner 50 kpc spectra
using the modiﬁed Cash statistic.

With each cluster core classiﬁed, we then took cuts in T H B R and asked how many
CC and NCC clusters were above these cuts. Figure 2.7 shows the normalized number
of CC and NCC clusters as a function of cuts in THBR' If TH B R were insensitive
to the state of the cluster core, we expect, for normally distributed TH B R values,
to see the number of CC and N CC clusters decreasing in the same way. However,
the number of CC clusters falls off more rapidly than the number of NCC clusters.
If the presence of a CC is indicative of a cluster’s advancement towards complete
virialization, then the signiﬁcantly steeper decline in the percent of CC clusters versus
NCC as a function of increasing TH B R indicates higher values of TH B R are associated
with a less relaxed state. This result is insensitive to our choice of signiﬁcance level in
the core classiﬁcation, i.e. the result is the same whether using 10 or 20 signiﬁcance
when considering Tdec-

Because of the CC/NCC deﬁnition we selected, our identiﬁcation of CCS and
NCCS was only as robust as the errors on T50 allowed. One can thus ask the question,
did our deﬁnition bias us towards ﬁnding more NCCS than CCS? To explore this

question we simulated 20 spectra for each observation following the method outlined

64

 

 

 

 

 

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THBR.CUI

Figure 2.7 Normalized number of CC and NCC clusters as a function of cuts in TH B R-
There are 192 clusters plotted in the top panel and 166 in the bottom panel. We have
deﬁned a cluster as having a CC when the temperature for the 50 kpc region around
the cluster center divided by the temperature for R2500—CORE: or RSOOO—CORE: was
less than one at the 20 level. We then take cuts in TH B R at the 10 level and ask how
many CC and NCC clusters are above these cuts. The number of CC clusters falls off
more rapidly than NCC clusters in this classiﬁcation scheme suggesting higher values
of TH E R prefer less relaxed systems which do not have cool cores. This result is
insensitive to our choice of signiﬁcance level in both the core classiﬁcation and TH B R
cuts.

65

in §2.5.2 for the control sample but using the inner 50 kpc spectral best-ﬁt values
as input. For each simulated spectrum, we calculated a temperature decrement (eq.
2.3) and re—classiﬁed the cluster as having a CC or NCC. Using the new set of mock
classiﬁcations we assigned a reliability factor, w, to each real classiﬁcation, which is
simply the fraction of mock classiﬁcations which agree with the real classiﬁcation. A
value of w = 1.0 indicates complete agreement, with «p = 0.0 indicating no agreement.
When we removed clusters with «p < 0.9 and repeated the analysis above, we found
no signiﬁcant change in the trend of a steeper decrease in the relative number of CC
versus N CC clusters as a function of TH B R-

Recall that the coolest ICM gas is being redshifted out of the observable band as 2
increases and becomes a signiﬁcant effect at z 2 0.6 (§2.5.2). Thus, we are likely not
detecting “weak” CCs in the highest redshift clusters of our sample and consequently
these cores are classiﬁed as NCCS and are artiﬁcially increasing the N CC population.
When we excluded the 14 clusters at z 2 0.6 from this portion of our analysis and

repeated the calculations, we found no signiﬁcant change in the results.

MERGERS VERSUS N ONMERGERS

Looking for a correlation between cluster relaxation and a skewing in TH B R was
the primary catalyst of this work. The result that increasing values of TH B R are
more likely to be associated with clusters harboring non-cool cores gives weight to
that hypothesis. But, the simplest relation to investigate is if TH B R is preferentially
higher in merger systems. Thus, we now discuss clusters with the highest signiﬁcant
values of TH B R and attempt to establish, via literature based results, the dynamic
state of these systems.

The subsample of clusters on which we focus have 3 TH B R > 1.1 at 90% conﬁdence
for both their R2500—CORE and RSOOO—CORE apertures. These clusters are listed in

Table A.2 and are sorted by the lower limit of TH B R- Shown in Figure 2.8 is a plot

66

of TH B R versus Tog--730 for all the clusters in our sample. The clusters discussed in
this section are shown as green triangles and black stars. The clusters with only a
R5000-CORE analysis are listed separately at the bottom of the table. All 33 clusters
listed have a core classiﬁcation of 1,0 > 0.9 (see §2.6.3). The choice of the TH B R > 1.1
threshold was arbitrary and intended to limit the number of clusters to which we pay
individual attention, but which is still representative of mid— to high-TH B R values.
Only two clusters -— Abell 697 and MACS J 2049.9-3217 — do not have a TH B R > 1.1
in one aperture and not the other. In both cases although, this was the result of
the lower boundary narrowly missing the cut, but both clusters still have TH B R
signiﬁcantly greater than unity.

For those clusters which have been individually studied, they are listed as mergers
based on the conclusions of the literature authors (cited in Table A2). Many different
techniques were used to determine if a system is a merger: bimodal galaxy velocity
distributions, morphologies, highly asymmetric temperature distributions, ICM sub—
structure correlated with subclusters, or disagreement of X—ray and lensing masses.
From Table A.2 we can see clusters exhibiting the highest signiﬁcant values of TH B R
tend to be ongoing or recent mergers. At the 20 level, we ﬁnd increasing values of
TH B R favor merger systems with NCCS over relaxed, CC clusters. It appears merg-
ers have left a spectroscopic imprint on the ICM which was predicted by ME01 and
which we observe in our sample.

Of the 33 clusters with TH B R Signiﬁcantly > 1.1, only 7 have CCS. Three of those
— MKWBS, 3C 28.0, and RX J1720.1+2638 — have their apertures centered on the
bright, dense cores in conﬁrmed mergers. Two more clusters — Abell 2384 and RX
J1525+0958 — while not conﬁrmed mergers, have morphologies which are consistent
with powerful ongoing mergers. Abell 2384 has a long gas tail extending toward a
gaseous clump which we assume has recently passed through the cluster. RXJ 1525

has a core shaped like a rounded arrowhead and is reminiscent of the bow shock

67

 

 

 

 

 

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10

To.7-7.o [keV]

Figure 2.8 THBR plotted against T0‘7__7_0 for the R2500—CORE and RSOOO—CORE
apertures. Note that the vertical scales for both panels are not the same. The top
and bottom panels contain 192 and 166 clusters, respectively. Only two clusters —
Abell 697 and MACS J2049.9—3217 — do not have a TH B R > 1.1 in one aperture and
not the other. In both cases however, it was a result of narrowly missing the cut.
The dashed lines are the lines of equivalence. Symbols and color coding are based
on two criteria: (1) the presence of a CC and (2) the value of TH B R- Black stars
(6 in the top panel; 7 in the bottom) are clusters with a CC and TH BR signiﬁcantly
greater than 1.1. Green upright—triangles (21 in the top; 27 in the bottom) are NCC
clusters with TH B R signiﬁcantly greater than 1.1. Blue down—facing triangles (49 top;
60 bottom) are CC clusters and red squares (90 top; 98 bottom) are NCC clusters.
We have found most, if not all, of the clusters with TH B R 2, 1.1 are merger systems.
Note that the cut at TH B R > 1.1 is arbitrary and there are more merger systems in
our sample then just those highlighted in this ﬁgure. However it is rather suggestive
that clusters with the highest values of TH B R appear to be merging systems.

68

seen in 1E0657-56. Abell 907 has no Signs of being a merger system, but the highly
compressed surface brightness contours to the west of the core are indicative of a
prominent cold front, a tell-tale signature of a subcluster merger event (Markevitch
& Vikhlinin, 2007). Abell 2029 presents a very interesting and curious case because
of its seemingly high state of relaxation and prominent cool core. There are no
complementary indications it has experienced a merger event. Yet its core hosts
a wide-angle tail radio source. It has been suggested that such sources might be
attributable to cluster merger activity (Sakelliou & Merriﬁeld, 2000). Moreover, the
X-ray isophotes to the west of the bright, peaked core are slightly more compressed
and may be an indication of past gas sloshing resulting from the merger of a small
subcluster. Both of these features'have been noted previously, speciﬁcally by Clarke
et al. (2004, 2005). We suggest the elevated TH B R value for this cluster lends more
weight to the argument that A2029 has indeed experienced a merger recently, but
how long ago we do not know.

The remaining systems we could not verify as mergers — RX J0439.0+0715, MACS
J2243.3-0935, MACS J0547.0—3904, Zwicky 1215, MACS J2311+0338, Abell 267, and
NGC 6338 -— have N CCS and X-ray morphologies consistent with an ongoing or post-
merger scenario. Abell 1204 shows no Signs of recent or ongoing merger activity;
however, it resides at the bottom of the arbitrary TH B R cut, and as evidenced by Abell
401 and Abell 1689, exceptional spherical symmetry is no guarantee of relaxation. Our
analysis here is partially at the mercy of morphological assessment, and only a more
stringent study of a carefully selected subsample or analysis of simulated clusters can

better determine how closely correlated TH B R is with the timeline of merger events.

2.7 SUMMARY AND CONCLUSIONS

We have explored the band dependence of the inferred X-ray temperature of the ICM

for 166 well-observed (Ncounts > 1500) clusters of galaxies selected from the Chandra

69

Data Archive.

We extracted spectra from the annulus between R = 70 kpc and R = R2500, R5000
for each cluster. We compared the X—ray temperatures inferred for single-component
ﬁts to global spectra when the energy range of the ﬁt was 0.7-7.0 keV (broad) and
when the energy range was 2.0/ (1 + z)-7.0 keV (hard). We found that, on average,
the hard-band temperature is signiﬁcantly higher than the broadband temperature.
For the R2500—CORE aperture we measured a weighted average of TH B R = 1.16 with
a = i010 and amean = i001 for the R5000—CORE aperture, and THBR = 1.14
with a = :l:0.12 and amean = :l:0.01. We also found no systematic trends in the
value of TH B R, or the dispersion of TH B R, with S / N, redshift, Galactic absorption,
metallicity, observation date, or broadband temperature.

In addition, we simulated an ensemble of 12,765 spectra which contained observation-
speciﬁc and idealized two-temperature component models, plus a control sample of
single-temperature models. From analysis of these simulations we found the statistical
ﬂuctuations for a single temperature model are inadequate to explain the Signiﬁcantly
different T0,7_7,0 and T2_0_7.0 we measure in our sample. We also found that the ob-
served scatter, 0H B R: is consistent with the presence of unresolved cool (TX < 2.0
keV) gas contributing a minimum of > 10% of the total emission. The simulations
also show the measured observational scatter in TH B R is greater than the statistical
scatter, amtml. These results are consistent with the process of hierarchical cluster
formation.

Upon further exploration, we found that TH B R is enhanced preferentially for
clusters which are known merger systems and for clusters without cool cores. Clusters
with temperature decrements in their cores (known as cool-core clusters) tend to
have best-ﬁt hard-band temperatures that are consistently closer to their best-ﬁt
broadband temperatures. The correlation of TH B R with the type of cluster core is

insensitive to our choice of classiﬁcation scheme and is robust against redshift effects.

70

Our results qualitatively support the ﬁnding by ME01 that the temperature ratio,
TH B R, might therefore be useful for statistically quantifying the degree of cluster
relaxation / virialization.

An additional robust test of the ME01 ﬁnding Should be made with simulations
by tracking TH B R during hierarchical assembly of a cluster. If TH B R is tightly
correlated with a cluster’s degree of relaxation, then it, along with other methods of
substructure measure, may provide a powerful metric for predicting (and therefore
reducing) a cluster’s deviation from mean mass-scaling relations. The task of reducing
scatter in scaling relations will be very important if we are to reliably and accurately

measure the mass of clusters.

2.8 ACKNOWLEDGMENTS

K. W. C. was supported in this work by the National Aeronautics and Space Ad-
ministration through Chandra X-Ray Observatory Archive grants AR—6016X and
AR—4017A, with additional support from a start-up grant for Megan Donahue from
Michigan State University. M. D. and Michigan State University acknowledge sup—
port from the NASA LTSA program NNG-05GD82G. G. M. V. thanks NASA for
support through theory grant NNG-04GI89G. The Chandra X-ray Observatory Cen-
ter is operated by the Smithsonian Astrophysical Observatory for and on behalf of
the National Aeronautics Space Administration under contract NAS8-03060. This re-
search has made use of software provided by the Chandra X—ray Center (CXC) in the
application packages CIAO, CHIPS, and SHERPA. We thank Alexey Vikhlinin for
helpful insight and expert advice. K. W. C. also thanks attendees of the “Eight Years
of Science with Chandra Calibration Workshop” for stimulating discussion regarding
XMM- Chandra cross-calibration. K. W. C. especially thanks Keith Arnaud for per—
sonally providing support and advice for mastering XSPEC. This research has made
use of the NASA/IPAC Extragalactic Database (NED), which is operated by the

71

Jet Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration. This research has also made
use of NASA’s Astrophysics Data System. ROSAT data and software were obtained
from the High Energy Astrophysics Science Archive Research Center (HEASARC),
provided by NASA’S Goddard Space Flight Center.

72

 

 

Chapter Three

Cavagnolo, Kenneth W., Donahue, Megan, Voit, G. Mark, Sun, Ming (2008). Intra-
cluster Medium Entropy Proﬁles For A Chandra Archival Sample of Galaxy Clusters.
The Astrophysical Journal Supplement Series. 0:000—000.

NB: The text of this chapter has been submitted for publication, but has
not been assigned a bibliographic code as of printing.

 

73

 

CHAPTER 3:

INTRACLUSTER MEDIUM ENTROPY
PROFILES FOR A CHANDRA
ARCHIVAL SAMPLE OF GALAXY
CLUSTERS

 

3.1 INTRODUCTION

The general process of galaxy cluster formation through hierarchical merging is well
understood, but many details, such as the impact of feedback sources on the cluster
environment and radiative cooling in the cluster core, are not. The nature of feedback
operating within clusters is of great interest because of the implications regarding the
formation of massive galaxies and for the cluster mass-observable scaling relations
used in cosmological studies. Early models of structure formation which included
only gravitation predicted self-similarity among the galaxy cluster population. These
self-Similar models made Speciﬁc predictions for how the physical properties of galaxy
clusters, such as temperature and luminosity, should scale with cluster redshift and
mass (Kaiser, 1986, 1991; Evrard & Henry, 1991; Navarro et al., 1995, 1997; Evrard
et al., 1996; Evrard, 1997; Teyssier et al., 1997; Eke et al., 1998; Bryan & Norman,
1998). However, numerous observational studies have shown clusters do not follow
the predicted Simple mass-observable scaling relations (Edge & Stewart, 1991; Allen
& Fabian, 1998a; Markevitch, 1998; Arnaud & Evrard, 1999; Horner et al., 1999;

Nevalainen et al., 2000; Finoguenov et al., 2001). To reconcile observation with theory,

74

it was realized non-gravitational effects, such as heating and radiative cooling in
cluster cores, could not be neglected if models were to accurately replicate the process
of cluster formation (e.g. Kaiser, 1991; Evrard & Henry, 1991; Loewenstein, 2000;
Borgani et al., 2002).

As a consequence of radiative coOling, best—ﬁt total cluster temperature decreases
while total cluster luminosity increases. In addition, feedback sources such as ac-
tive galactic nuclei (AGN) and supernovae can drive cluster cores (where most of
the cluster ﬂux originates) away from hydrostatic equilibrium. Thus, at a given
mass scale, radiative cooling and feedback conspire to create dispersion in otherwise
tight mass-observable correlations like mass-luminosity and mass-temperature. While
considerable progress has been made both observationally and theoretically in the ar-
eas of understanding, quantifying, and reducing scatter in cluster scaling-relations
(Buote 85 Tsai, 1996; Jeltema et al., 2005; Kravtsov et al., 2006; Nagai et al., 2007;
Ventimiglia et al., 2008), it is still important to understand how, taken as a whole,
non-gravitational processes affect cluster formation and evolution.

A related issue to the departure of clusters from self-similarity is that of cool-
ing ﬂows in cluster cores. The core cooling time in 50%-66% of clusters is much
Shorter than both the Hubble time and cluster age (Stewart et al., 1984; Edge et al.,
1992; White et al., 1997; Peres et al., 1998; Bauer et al., 2005). For such clusters
(and without compensatory heating), radiative cooling will result in the formation
a cooling ﬂow (see Fabian, 1994, for a review). Early estimates put the mass depo-
sition rates from cooling flows in the range of 100 — 1000 MG yr‘l, (e.g. Jones &
Forman, 1984). However, cooling flow mass deposition rates inferred from soft X-ray
spectroscopy were found to be signiﬁcantly less than predicted, with the ICM never
reaching temperatures lower than Tm-m-al / 3 (Tamura et al., 2001; Peterson et al., 2001,
2003; Kaastra et al., 2004). Irrespective of system mass, the massive torrents of cool

gas turned out to be more like cooling trickles.

75

In addition to the lack of soft X—ray line emission from cooling ﬂows, prior method-
ical searches for the end products of cooling ﬂows (2'. 6. molecular gas and emission line
nebulae) revealed far less mass is locked-up in by-products than expected (Heckman
et al., 1989; McNamara et al., 1990; O’Dea et al., 1994b; Voit &, Donahue, 1995).
The disconnects between observatiOn and theory have been termed “the cooling ﬂow
problem” and raise the question, “Where has all the cool gas gone?” The substantial
amount of observational evidence suggests some combination of energetic feedback
sources has heated the ICM to selectively remove gas with a short cooling time and
establish quasi-stable thermal balance of the ICM.

Both the breakdown of self-Similarity and the cooling ﬂow problem point toward
the need for a better understanding of cluster feedback and radiative cooling. Recent
revisions to models of how clusters form and evolve by including feedback sources has
led to better agreement between observation and theory (Bower et al., 2006; Croton
et al., 2006; Sam at al., 2006). The current paradigm regarding the cluster feedback
process holds that AGN are the primary heat delivery mechanism and that an AGN
outburst deposits the requisite energy into the ICM to retard, and in some cases
quench, cooling (see McNamara & Nulsen, 2007, for a review). How the feedback
loop functions is still the topic of much debate, but that AGN are interacting with
the hot atmospheres of clusters is no longer in doubt as evidenced by the prevalence
of bubbles in clusters (Birzan et al., 2004).

One robust observable which has proven useful in studying the effect of non-
gravitational processes is ICM entropy. Taken individually, ICM temperature and
density do not fully reveal a cluster’s thermal history. Gas temperature reﬂects the
depth of the potential well, while density reﬂects the capacity of the well to compress
the gas. However, at constant pressure the density of a gas is determined by its Speciﬁc
entropy. Rewriting the expression for the adiabatic index, K oc Pp-5/3, in terms of

2/3

9

temperature and electron density, one can deﬁne a new quantity, K = kTXne—

76

where T X is temperature and ne is electron gas density (Ponman et al., 1999; Lloyd-
Davies et al., 2000). This new quantity, K, captures the thermal history of the gas
because only gains and losses of heat energy can change K. This quantity is commonly
referred to as entropy in the X—ray cluster literature, but in actuality the classic
thermodynamic Speciﬁc entropy for a monatomic ideal gas is S = In K 3/ 2 + constant.

One important prOperty of gas entropy is that a gas cloud is convectively sta-
ble when dK/dr Z 0. Thus, gravitational potential wells are giant entropy sorting
devices: low entropy gas sinks to the bottom of the potential well, while high en-
tropy gas buoyantly rises to a radius at which the ambient gas has equal entropy. If
cluster evolution proceeded under the inﬂuence of gravitation only, then the radial
entropy distribution of clusters would exhibit power-law behavior for r > 0.1r200 with
a constant, low entropy core at small radii (Voit et al., 2005). Thus, large-scale depar-
tures of the radial entropy distribution from a power-law can be used to measure the
effect of processes such as AGN heating and radiative cooling. Several studies have
found that the radial ICM entropy distribution in some clusters ﬂattens inside 0.1r500
(David et al., 1996; Ponman et al., 1999; Lloyd-Davies et al., 2000; Ponman et al.,
2003; Piffaretti et al., 2005; Donahue et al., 2005, 2006; Morandi & Ettori, 2007).
These previous studies utilized smaller, focused samples and we have undertaken a
much larger study utilizing the Chandra Data Archive.

In this Chapter we present the data and results from a Chandra archival project
in which we studied the ICM entropy distribution for 233 galaxy clusters. We have
named this project the “Archive of Chandra Cluster Entropy Proﬁle Tablas,” or
ACCEPT for short. In contrast to the sample of nine classic cooling ﬂow clusters
studied in Donahue et al. (2006, hereafter D06), ACCEPT covers a broader range of
luminosities, temperatures, and morphologies, focusing on more than just cooling ﬂow
clusters. One of our primary objectives for this project was to provide the research

community with an additional resource to study cluster evolution and confront current

77

models with a comprehensive set of entropy proﬁles.

We have found that the departure of entropy proﬁles from a power-law at small
radii is a feature of most clusters, and given high enough angular resolution, possibly
all clusters. We also ﬁnd that the core entropy distribution of both the full ACCEPT
collection and the Highest X-Ray Flux Galaxy Cluster Sample (HIFL U G CS, Reiprich
2001; Reiprich & BOhringer 2002) are bimodal. In Chapter 4, we present results that
Show indicators of feedback - radio sources assumed to be associated with AGN and
Ha emission assumed to be the result of thermal instability formation - are strongly
correlated with core entropy.

A key aspect of this project is the dissemination of all data and results to the
public. We have created a searchable, interactive web site1 which hosts all of our re-
sults. The ACCEPT web Site will be continually updated as new Chandra cluster and
group observations are archived and analyzed. The web site provides all data tables,
plots, spectra, reduced Chandra data products, reduction scripts, and more. Given
the large number of clusters in our sample, ﬁgures, ﬁts, and tables showing/ listing
results for individual clusters have been omitted from this Chapter and are available
at the ACCEPT web site.

The structure of this Chapter is as follows: In §3.2 we outline initial sample
selection criteria and information about the Chandra observations selected under
these criteria. Data reduction is discussed in §3.3. Spectral extraction and analysis
are discussed in §3.3.1, while our method for deriving deprojected electron density
proﬁles is outlined in §3.3.2. A few possible sources of systematics are discussed in
§3.4. Results and discussion are presented in §3.5. A brief summary is given in §3.6.
For this work we have assumed a ﬂat ACDM Universe with cosmology QM = 0.3,
Q A = 0.7, and H0 = 70 km s‘1 Mpc—1. All quoted uncertainties are 90% conﬁdence
(1.6a).

 

lhttp: / / www.pa.msu.edu/ astro/ MC2 / accept

78

3.2 DATA COLLECTION

Our sample was initially collected from observations publicly available in the Chandra
Data Archive (CDA) as of June 2006. We ﬁrst assembled a list of targets from
multiple ﬂux-limited surveys: the ROSAT Brightest Cluster Sample (Ebeling et al.,
1998), RBCS Extended Sample (Ebeling et al., 2000), ROSAT Brightest 55 Sample
(Edge et al., 1990; Peres et al., 1998), Einstein Extended Medium Sensitivity Survey
(Gioia et al., 1990), North Ecliptic Pole Survey (Henry et al., 2006), ROSAT Deep
Cluster Survey (Rosati et al., 1995), ROSAT Serendipitous Survey (Vikhlinin et al.,
1998), Massive Cluster Survey (Ebeling et al., 2001), and REFLEX Survey (BOhringer
et al., 2004). After the ﬁrst round of data analysis concluded, we continued to expand
our collection by adding new archival data listed under the CDA Science Categories

”

“clusters of galaxies” or “active galaxies. AS of submission, we have inspected all
CDA clusters of galaxies observations and analyzed 510 of those observations (14.16
Msec). The Coma and Fornax clusters have been intentionally left out of our sample
because they are very well studied nearby clusters which require a more intensive
analysis than we undertook in this project.

The available data for some clusters limited our ability to derive an entropy proﬁle.
Calculation of entropy proﬁles require measurement of the radial gas temperature
and density structure (discussed further in §3.3). To infer a temperature which is
reasonably well constrained (AkTX z $1.0 keV) we imposed a minimum requirement
of three temperature bins containing 2500 counts each. A post-analysis check shows
our TX minimum criterion resulted in a mean AkTX = 0.87 keV for the ﬁnal sample.

In section 3.5.4 we cull the HIFL U CCS primary sample (Reiprich, 2001; Reiprich
& BOhringer, 2002) from our full archival collection. The groups M49, NGC 507, NGC
4636, NGC 5044, NGC 5813, and NGC 5846 are part of the HIFL UGCS primary

sample but were not members of our initial archival sample. In order to take full

advantage Of the HIFL U CCS primary sample, we analyzed observations of these

79

6 groups. Note, however, that none of these 6 groups are included in the general
discussion of ACCEPT.

We were unable to analyze some clusters for this study because of complica-
tions other than not meeting our minimum requirements for analysis. These clus-
ters were: 2PIGG J0311.8—2655, 3C 129, A168, A514, A753, A1367, A2634, A2670,
A2877, A3074, A3128, A3627, ASO463, APMCC 0421, MACS J2243.3-0935, MS
J1621.5+2640, RX J1109.7+2145, RX J1206.6+2811, RX J1423.8+2404, 'Ifiangu-
lum Australis, SDSS J198.070267—00.984433, and Zw5247.

After applying the T X constraint, adding the 6 HIFL U G CS groups, and remov-
ing troublesome observations the ﬁnal sample presented here contains 310 observa-
tions of 233 clusters with a total exposure time of 9.66 Msec. The sample cov-
erS the temperatures range kTX ~ 1 - 20 keV, a bolometric luminosity range of
Lbol ~ 1042‘46 ergs S_1, and redshifts of z ~ 0.05 - 0.89. Table A.1 lists the general
properties for each cluster in ACCEPT.

We also report previously unpublished Ha observations taken by M. Donahue
while a Carnegie Fellow. Thase observations were not utilized in this Chapter but are
used in Chapter 4. The new [N I I] / Ha ratios and Ha ﬂuxes are listed in Table B3.
The upper-limits listed in Table 33 are 30 Signiﬁcance. The observations were taken
with either the 5 m Hale Telescope at the Palomar Observatory, USA, or the DuPont
2.5 m telescope at the Las Campanas Observatory, Chile. All observations were made
with a 2” slit centered on the brightest cluster galaxy (BCG) using two position angles:
one along the semi-major axis and one along the semi-minor axis of the galaxy. The
overlap area was 10 pixels2. The red light (555-798 nm) setup on the Hale Double
Spectrograph used a 316 lineS/ mm grating with a dispersion of 0.31 nm/ pixel and an
effective resolution of 0.7-0.8 nm. The DuPont Modular Spectrograph setup included
a 1200 lines/ mm grating with a dispersion of 0.12 nm / pixel and an effective resolution

of 0.3 nm. The statistical and calibration uncertainties for the observations are both

80

~ 10%. The statistical uncertainty arises primarily from variability of the spectral

continuum and hence imperfect background subtraction.

3.3 DATA ANALYSIS

Measuring radial ICM entropy ﬁrst requires measurement of radial ICM tempera-
ture and density. The radial temperature structure of each cluster was measured by
ﬁtting a Single-temperature thermal model to spectra extracted from concentric an-
nuli centered on the cluster X-ray “center”. As discussed in Cavagnolo et al. (2008),
the ICM X—ray peak of the point-source cleaned, exposure-corrected cluster image
was used as the cluster center, unless the iteratively determined X-ray centroid was
more than 70 kpc away from the X-ray peak, in which case the centroid was used as
the radial analysis zero-point. To derive the gas density proﬁle, we ﬁrst deprojected
an exposure-corrected, background-subtracted, point source clean surface brightness
proﬁle extracted in the 0.7-2.0 keV energy range to attain a volume emission den-
sity. This emission density, along with spectroscopic information (count rate and
normalization in each annulus), was then used to calculate gas density. The resulting
entropy proﬁles were then ﬁt with two models: a Simple model consisting of only a
radial power-law, and a model which is the sum of a constant core entropy term, K0
and the radial power-law.

In this Chapter we cover the basics of deriving gas entropy from X—ray observables,
and direct interested readers to D06 for in—depth discussion of our data reprocessing
and reduction, and Cavagnolo et al. (2008) for details regarding determination of each
cluster’s “center” and how the X-ray background was handled. The only difference
between the analysis presented in this Chapter and that of D06 and Cavagnolo et al.
(2008), is that we have used newer versions Of the CXC issued data reduction software

(CIAO 3.4.1 and CALDB 3.4.0).

81

3.3.1 TEMPERATURE PROFILES

One of the two components needed to derive a gas entropy proﬁle is the temperature
as a function of radius. We therefore constructed radial temperature proﬁles for each
cluster in our collection. To reliably constrain a temperature, and allow for the de-
tection of temperature structure beyond isothermality, we required each temperature
proﬁle to have a minimum of three annuli containing 2500 counts each. The annuli for
each cluster were generated by ﬁrst extracting a background-subtracted cumulative
counts proﬁle using 1 pixel width annular bins originating from the cluster center and
extending to the detector edge. Temperature proﬁles, however, were truncated at the
radius bounded by the detector edge, or 05ng0, whichever was smaller. Trunca-
tion occured at 05ng0 as we are most interested in the radial entropy behavior of
cluster core regions (r f, 100 kpc) and 0.5R180 is the approximate radius where tem-
perature proﬁles begin to turnover (Vikhlinin et al., 2005). Additionally, analysis of
diffuse gas temperature structure at large radii, which spectroscopically is dominated
by background, requires a time consuming, Observation-Speciﬁc analysis of the X—ray
background (see Sun et al., 2008, for a detailed discussion on this point).
Cumulative counts proﬁles were divided into annuli containing at least 2500 counts.
For well resolved clusters, the number of counts per annulus was increased to reduce
the resulting uncertainty of ‘kTX and, for simplicity, to keep the number of annuli
less than 50. The method we use to derive entropy proﬁles is most sensitive to the
surface brightness radial bin size and not the resolution or uncertainties of the temper-
ature proﬁle. Thus, the loss of resolution in the temperature proﬁle from increasing
the number of counts per bin, and thereby reducing the number of annuli, has an
insigniﬁcant effect on the ﬁnal entropy proﬁles and best-ﬁt entropy models.
Background analysis was performed using the blank-sky datasets provided in the
CALDB. Backgrounds were reprocessed and reprojected to match each observation.

Off-axis chips were used to normalize for variations of the hard-particle background

82

by comparing blank-sky and Observation 9.5-12 keV count rates. Soft residuals were
also created and ﬁtted for each observation to account for the spatially-varying soft
Galactic background. This component was added as an additional, ﬁxed background
component during Spectral ﬁtting. Errors associated with the soft background are
estimated and added in quadrature to the ﬁnal error.

For each radial annular region, source and background spectra were extracted
from the target cluster and corresponding normalized blank-Sky dataset. Following
standard CIAO techniques2 we created weighted response ﬁles (WARF) and redis-
tribution matrices (WRMF) for each cluster using a ﬂux-weighted map (WMAP)
across the entire extraction region. These ﬁles quantify the effective area, quantum
efﬁciency, and imperfect resolution of the Chandra instrumentation as a function of
chip position. Each Spectrum was binned to contain a minimum of 25 counts per
energy bin.

Spectra were ﬁtted with XSPEC 11.3.2ag (Arnaud, 1996) using an absorbed,
single-temperature MEKAL model (Mewe et al., 1985, 1986) over the energy range
0.7-7.0 keV. Neutral hydrogen column densities, NH, were taken from Dickey &
Lockman (1990). A comparison between the NH values of Dickey & Lockman (1990)
and the higher-resolution LAB Survey (Kalberla et al., 2005) revealed that the two
surveys agree to within i20% for 80% of the clusters in our sample. For the other
20% of the sample, using the LAB value, or allowing NH to be free, did not result
in best-ﬁt temperatures or metallicities which differ signiﬁcantly from ﬁts using the
Dickey 82. Lockman (1990) values.

The potentially free parameters of the absorbed thermal model are NH, X—ray tem-
perature, metal abundance normalized to solar (Anders & Grevesse, 1989, elemental

ratios taken from), and a normalization proportional to the integrated emission mea-

 

2http://cxc.harvard.edu/ciao/guides/esa.html

83

sure within the extraction region,

10—14
= dV, 3.1
’7 4nDi(1+z)2/nenp ( )

 

where D A is the angular diameter distance, z is cluster redshift, he and np are the
electron and proton densities respectively, and V is the volume of the emission region.
In all ﬁts the metal abundance in each annulus was a free parameter and NH was
ﬁxed to the Galactic value. No systematic error is added during ﬁtting and thus all
quoted errors are statistical only. The statistic used during ﬁtting was x2 (XSPEC
statistics package CHI). All uncertainties were calculated using 90% conﬁdence.

For some clusters, more than one observation was available in the archive. We
utilized the combined exposure time by ﬁrst extracting independent spectra, WARFS,
WRMFS, normalized background Spectra, and soft residuals for each observation.
These independent spectra were then read into XSPEC simultaneously and ﬁt with
the same spectral model which had all parameters, except normalization, tied among
the spectra.

In D06 we studied a sample of nine “classic” cooling ﬂow clusters, all of which have
steep temperature gradients. Deprojection of temperature Should result in slightly
lower temperatures in the central bins of only the clusters with the steepest temper-
ature gradients. For these clusters, the end result would be a lowering of the entropy
for the central-most bins. Our analysis in D06 showed that spectral deprojection did
not result in Signiﬁcant differences between entropy proﬁles derived using projected
or deprojected quantities. Thus, for this work, we quote projected temperatures only.
We stress that spectral deprojection does not signiﬁcantly change the shape of the

entropy proﬁles nor the best-ﬁt K 0 values.

84

3.3.2 DEPROJECTED ELECTRON DENSITY PROFILES

For predominantly free-free emission, emissivity strongly depends on density and
only weakly on temperature, 6 oc p2T1/2. Therefore the ﬂux measured in a narrow
temperature range is an good diagnostic of ICM density. To reconstruct the relevant
gas density as a function of physical radius we deprojected the cluster emission from
high-resolution surface brightness proﬁles and converted to electron density using
normalizations and count rates taken from the spectral analysis.

We extracted surface brightness proﬁles from the 0.7-2.0 keV energy range using
concentric annular bins of size 5” originating from the cluster center. Each surface
brightness proﬁle was corrected with an observation speciﬁc, normalized radial ex-
posure proﬁle to remove the effects of vignetting and exposure time ﬂuctuations.
Following the recommendation in the CIAO guide for analyzing extended sources,
exposure maps were created using the monoenergetic value associated with the ob-
served count rate peak. The more sophisticated method of creating exposure maps
using Spectral weights calculated for an incident spectrum with the temperature and
metallicity of the Observed cluster was also tested. For the narrow energy band we
consider, the chip response is relatively ﬂat and we ﬁnd no signiﬁcant differences
between the two methods. For all clusters the monoenergetic value used in creating
exposure maps was between 0.8 — 1.7 keV.

The 0.7-2.0 keV Spectroscopic count rate and spectral normalization were interpo-
lated from the radial temperature proﬁle grid to match the surface brightness radial
grid. Utilizing the deprojection technique of Kriss et al. (1983), the interpolated
spectral parameters were used to convert observed surface brightness to deprojected

electron density. Radial electron density written in terms of relevant quantities is,

 

 

_ Tam 47TlDA(1+ z)l2 C(r) 77(7‘)
ne(T) — \/ 10_14 f(r) (3'2)

85

where rim is an ionization ratio (ne = 1.2np), C(r) is the radial emission density
derived from eqn. A1 in Kriss et al. (1983), 17 is the interpolated spectral normaliza-
tion from eqn. 3.1, D A is the angular diameter distance, z is cluster redshift, and
f (r) is the interpolated spectroscopic count rate. Cosmic dimming of source surface
brightness is accounted for by the D30 + z)2 term. This method of deprojection
takes into account temperature and metallicity ﬂuctuations which affect observed
gas emissivity. Errors for the gas density proﬁle were estimated using 5000 Monte
Carlo Simulations of the original surface brightness proﬁle. The Kriss et al. (1983)
deprojection technique assumes Spherical symmetry, but it was shown in D06 such

an assumption has little effect on ﬁnal entropy proﬁles.

3.3.3 ﬁ-MODEL FITS

Noisy surface brightness proﬁles, or proﬁles with irregularities such as inversions or
extended ﬂat cores, result in unstable, unphysical quantities when using the “onion”
deprojection technique like that of Kriss et al. (1983). For cases where deprojection
of the raw data was problematic, we resorted to ﬁtting the surface brightness proﬁle
with a ,B-model (Cavaliere & Fusco-Femiano, 197 8). It is well known that the B—model
does not precisely represent all the features of the ICM for clusters of high central
surface brightness (Ettori, 2000; Loken et al., 2002; Hallman et al., 2007). However,
for the proﬁles which required a ﬁt, the ﬂ-model was a suitable approximation, and
the model’s use was only a means for creating a smooth function which was easily

deprojected. The single (N = 1) and double (N = 2) ﬂ-models were used in ﬁtting,

—3/3+§

5;, = Z [1 + (32] . (3.3)

86

The models were ﬁtted using Craig Markwardt’s robust non-linear least squares min-
imization IDL routines3. The data inpUt to the ﬁtting routines were weighted using
the inverse square of the Observational errors. Using this weighting scheme rasulted
in residuals which were near unity for, on average, the inner 80% of the radial range
considered. Accuracy of errors output from the ﬁtting routine were checked against
a bootstrap Monte Carlo analysis of 1000 surface brightness realizations. Both the
single- and double—B models were ﬁt to each proﬁle and using the F—test functionality
of SHERPA4 we determined if the addition of extra model components was justiﬁed
given the degrees of freedom and X2 values of each ﬁt. If the signiﬁcance was less
than 0.05, the extra components were justiﬁed and the double-ﬂ model was used.

A best-ﬁt ﬁ-model was used in place of the data when deriving electron density
for the clusters listed in Table B.2. These clusters are also ﬂagged in Table A.1
with the note letter ‘a’. The best-ﬁt ﬂ-models and background-subtracted, exposure-
corrected surface brightness proﬁles are shown in Figure 3.7. See Section §3.8 for
notes discussing individual clusters. The disagreement between the best-ﬁt ﬁ-model
and the surface brightness in the central regions for some clusters is also discussed
in Section §3.8. In Short, the discrepancy arises from the presence of compact X-ray
sourcas, a topic which is addressed in §3.3.5. All clusters requiring a ﬂ-model ﬁt have

core entropy > 95 keV cm2 and the mean best-ﬁt parameters are listed in Table 8.4.

3.3.4 ENTROPY PROFILES

Radial entropy proﬁles were calculated using the widely adopted formulation K (r) =
ka(r)ne(r)"2/3. To create the radial entropy proﬁles, the temperature and density
proﬁles must be on the same radial grid. This was accomplished by interpolating the
temperature proﬁle across the higher-resolution radial grid of the deprojected electron

density proﬁle. Because, in general, density proﬁles have higher radial resolution, the

 

3http: //cow.physics.wisc.edu/ craigm/idl/
4http://cxc.harvard.edu/ciao3.4/ahelp/ftest.html

87

central bin of the temperature proﬁle spans several of the innermost bins of the
density proﬁle. Since we are most interested in the behavior of the entropy proﬁles
in the central regions, how the interpolation was performed for the inner regions.
Thus, temperature interpolation over the region of the density proﬁle where a single
central temperature bin encompasses several density proﬁle bins was applied in two
ways: (1) as a linear gradient consistent with the slope of the temperature proﬁle
at radii larger than the central TX bin (ATcenter aé 0; ’extr’ in Table B5), and
(2) as a constant (ATcenter = 0; ’ﬂat’ in Table B.5). Shown in Figure 3.1 is the
ratio of best-ﬁt core entropy, K0, using the above two methods. The ﬁve points
lying below the line of equality are clusters which are best-ﬁt by a power-law or have
K0 statistically consistent with zero. It is worth noting that both schemes yield
statistically consistent values for K0 except for the clusters marked by black squares
which have a ratio signiﬁcantly different from unity.

The clusters for which the two methods give K0 values that signiﬁcantly differ all
have steep temperature gradients with the maximum and minimum radial tempera-
tures differing by a factor of 1.3-5.0. Extrapolation of a steep temperature gradient
as r —r 0 results in very low central temperatures (typically TX 3 Tm-m-al / 3) which
are inconsistent with observations, most notably Peterson et al. (2003). Most impor-
tant however, is that the ﬂattening of entropy we observe in the cores of our sample
(discussed in §3.5.1) is not a rasult of the method chosen for interpolating the tem-
perature proﬁle. For this Chapter we therefore focus on the results derived assuming
a constant temperature across the central-most bins.

Uncertainty in K (r) arising from using a single-component temperature model
for each annulus during spectral analysis contributes negligibly to our ﬁnal ﬁts and
is discussed in detail in the Appendix of D06. Brieﬂy summarizing D06: we have
primarily measured the entropy of the lowest entropy gas because it is the most lu-

minous gas. For the best-ﬁt entropy values to be signiﬁcantly changed, the volume

88

 

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KNEW—0) / I‘d/ATM)
2
IUIIIIIIIIIIIII1IIUIIIUIjIIIIIII

.0
01

 

 

 

 

III I l I l l 1L1 77 l l I ll Ll

1 10 100
KO(AT 0,0,;0) [keV cm 2]

 

Figure 3.1 Ratio of best-ﬁt K0 for the two treatments of central temperature interpo-
lation (see §3.3.1): (1) temperature is free to decline across the central density bins
(ATcenter 75 0), and (2) the temperature across the central density bins is isothermal
(ATcenter = 0). Black squares are clusters for which the K0 ratio is inconsistent with
unity, however, all of these clusters have steep temperature gradients which result in

unsubstantiated cool temperatures in their cores when kTX is extrapolated to small
radii.

89

ﬁlling fraction of a higher-entropy component must be non-trivial (> 50%). As dis-
cussed in D06, our results are robust to the presence Of multiple, low luminosity gas
phases and mostly insensitive to X—ray surface brightness decrements, such as X—ray
cavities and bubbles, although in extreme cases their inﬂuence on an entropy proﬁle
can be detected (for an example, seelthe cluster A2052).

Each entropy proﬁle was ﬁt with two models: a Simple model which is a power-law
at large radii and approaches a constant value at small radii (eqn. 3.4), and a model
which is a power-law only (eqn. 3.5). The models were ﬁtted using Craig Markwardt’s
IDL routines in the package MPFIT. The output best-ﬁt parameters and associated
errors were checked against a bootstrap Monte Carlo analysis of 5000 entropy proﬁle

realizations to independently conﬁrm their accuracy.

 

 

a
,.
K(r) — K0+K100 (100 kpc) (3-4)
7, a

In our entropy models, K0 is what we call core entropy, K100 is a normalization for
entropy at 100 kpc, and a is the power-law index. Note, however, that K0 does not
necessarily represent the minimum core entropy or the entropy at r = 0. Nor does K0
capture the gas entropy which would be measured immediately around an AGN or in
a BCG X—ray corona. Instead, K0 represents the typical excess of core entropy above
the best ﬁtting power-law at larger radii. Fits were truncated at a maximum radius
(determined by-eye) to avoid the inﬂuence of noisy bins at large radii which result
from instability of our deprojection method. A listing of all the best-ﬁt parameters
for each cluster are listed in Table BS. The mean best-ﬁt parameters for the full
ACCEPT sample are given in Table B.4. Also given in Table B4 are the mean best-
ﬁt parameters for clusters below and above K0 = 50 keV cm2. We Show in §3.5.2

that the cut at K0 = 50 keV cm2 is not completely arbitrary as it approximately

90

demarcates the division between two distinct populations in the K0 distribution.
Some clusters have a surface brightness proﬁle which is comparable to a double
ﬁ-model. Our models for the behavior of K (r) are intentionally simplistic and are
not intended to fully describe all the features of K (r). Thus, for the small number
of clusters with discernible double-B behavior, ﬁtting of the entropy proﬁles was
restricted to the innermost of the two ,B-like features. These clusters have been
ﬂagged in Table A.1 with the note letter ‘b’. The best-ﬁt power-law index is typically
much steeper for these clusters, but the outer regions, which we do not discuss here,

have power-law indices which are typical of the rest of the sample, i.e. (1 ~ 1.2.

3.3.5 EXCLUSION OF CENTRAL SOURCES

For many clusters in our sample the ICM X—ray peak, ICM X—ray centroid, BCG
optical emission, and BCG infrared emission are coincident or well within 70 kpc
of one another. This made identiﬁcation of the cluster center robust and trivia].
However, in some clusters, there is an X-ray point source or compact X—ray source
(r ,S 5 kpc) found very near (r < 10 kpc) the cluster center and always associated
with a BCG. We identiﬁed 37 clusters with central sources and have ﬂagged them in
Table B.1 with the note letter ‘d’ for AGN and ‘e’ for compact but resolved sources.
The mean best-ﬁt parameters for these clusters are given in Table B.4 under the
sample name ’CSE’ for ’central source excluded.’ These clusters cover the redshift
range 2 = 0.0044 — 0.4641 with mean 2 = 0.1196 :l: 0.1234, and temperature range
kTX = l — 12 keV with mean kTX = 4.43 d: 2.53 keV. For some clusters — such as
3C 295, A2052, A426, Cygnus A, Hydra A, or M87 - the source is an AGN and there
was no question the source must be removed.

However, determining how to handle the compact X-ray sources was not so straight-
forward. These compact sources are larger than the PSF, fainter than an AGN, but

typically have'signiﬁcantly higher surface brightness than the surrounding ICM such

91

that the compact source’s extent was distinguishable from the ICM. These sources
are most prominent, and thus the most troublesome, in non—cool core clusters (i.e.
clusters which are approximately isothermal). They are troublesome because the
compact source is typically much cooler and denser than the surrounding ICM and
hence has an entropy much lower than the ambient ICM. We consider most of these
compact sources are X-ray coronae associated with the BCG (Sun et al., 2007).

Without removing the compact sources, we derived radial entropy proﬁles and
found, for all cases, that K (r) abruptly changes at the outer edge of the compact
source. Including the compact sources results in the central cluster region(s) appear-
ing overdense, and at a given temperature the region will have a much lower entropy
than if the source were excluded. Such a discontinuity in K (r) results in our simple
models Of K (r) not being a good description of the proﬁles. Aside from produc-
ing poor ﬁts, a signiﬁcantly lower entropy inﬂuences the value of best-ﬁt parameters
because the shape of K (r) is drastically changed. Obviously, two solutions are avail-
able: exclude or keep the compact sources during analysis. Deciding what to do with
these sources depends upon what cluster properties we are Speciﬁcally interested in
quantifying.

The compact X-ray sources discussed in this section are not representative of the
cluster’s core entropy; these sources are representative of the entropy within and
immediately surrounding peculiar BCGS. Our focus for the ACCEPT project was to
quantify the entropy structure of the cluster core region and surrounding “pristine”
ICM, not to determine the minimum entropy of cluster cores or to quantify the entropy
of peculiar core objects such as BCG coronae. Thus, we opted to exclude these
compact sources during our analysis. For a few extraordinary sources, it was simpler
to ignore the central bin of the surface brightness proﬁle during analysis because of
imperfect exclusion of a compact source’s extended emission. These clusters have

been ﬂagged in Table B.1 with the note letter ‘f’.

92

It is worth noting that when any source is excluded from the data, the empty
pixels where the source once was were not included in the calculation of the sur-
face brightness (counts and pixels are both excluded). Thus, the decrease in surface
brightness of a bin where a source has been removed is not a result of the count to

area ratio being artiﬁcially reduced.

3.4 SYSTEMATICS

Our models for K (r) were designed SO that the best-ﬁt K0 values are a good measure
of the entropy proﬁle ﬂattening at small radii. This ﬂattening could potentially be al—
tered through the effects of systematics such as PSF smearing and surface brightness
proﬁle angular resolution. To quantify the extent to which our K0 values are being
affected by these systematics, we have analyzed mock Chandra observations created
using the ray-tracing program MARX5, and also by analyzing degraded entropy pro-
ﬁles generated from artiﬁcially redshifting well-resolved clusters. In the analysis below
we Show that the lack of cluster with K0 ,3 10 keV cm2 at z 2, 0.1 is attributable to
resolution effects, but that deviation of an entropy proﬁle from a power-law, even if
only in the centralmost bin, cannot be accounted for by PSF effects. We also discuss
the number of proﬁles which are reasonably well-represented by the power-law only
proﬁle, and establish that no more than ~ 10% of the entropy proﬁles in ACCEPT

are consistent with a power-law.

3.4.1 PSF EFFECTS

To assess the effect of PSF smearing on our entropy proﬁles, we have updated the
analysis presented in §4.1 of D06 to use MARX Simulations. In the D06 analysis, we
assumed the density and temperature structure of the cluster core obeyed power-laws

with n8 oc r51 and TX oc r1/3. This results in a power-law entropy proﬁle with

 

5http://space.mit.edu/CXC/MARX/

93

K or r. Further assuming the main emission mechanism is thermal bremsstrahlung,
i.e. e X or Ti/z, yields a surface brightness proﬁle which has the form S X oc r-5/6.
A source image consistent with these parameters was created in IDL and then input
to MARX to create the mock Chandra Observations.

The MARX Simulations were performed using the spectrum of a 4.0 keV, 0.329
abundance MEKAL model. We have tested using input spectra with kTX = 2 — 10
keV with varying abundances and ﬁnd the effect of temperature and metallicity on
the distribution of photons in MARX to be insigniﬁcant for our discussion here. We
have neglected the X-ray background in this analysis as it is overwhelmed by cluster
emission in the core and is only important at large radii. Observations for both
ACIS-S and ACIS-I instruments were simulated using an exposure time of 40 ksec.
A surface brightness proﬁle was then extracted from the mock observations using the
same 5" bins used on the real data.

For 5” bins, we ﬁnd the difference between the central bins of the input surface
brightness and the output MARX observations to be less than the statistical uncer-
tainty. One should expect this result, as the on-axis Chandra PSF is ,5 1” and the
surface brightness bins we have used on the data are ﬁve times this size. What is
most interesting and important though, is that our analysis using MARX suggests
any deviation of the surface brightness — and consequently the entropy proﬁle — from
a power-law, even if only in the central bin, is real and cannot be attributed to
PSF effects. Even for the most poorly resolved clusters, the deviation away from a
power-law we observe in a large majority of our entropy proﬁles is not a result of our

deprojection technique or systematics.

3.4.2 ANGULAR RESOLUTION EFFECTS

Another possible limitation on evaluating K0 is the effect of using ﬁxed angular Size

bins for extracting surface brightness proﬁles. This choice may introduce a redshift-

94

dependence into the best-ﬁt K0 values because as redshift increases, a ﬁxed angular
Size encompasses a larger physical volume and the value of K 0 may increase if the bin
includes a broad range of gas entropy. Shown in Figure 3.2 is a plot of the best-ﬁt
K0 values for our entire sample versus redshift. At low redshift (z < 0.02), there
are a few objects with K0 < 10 keV cm2 and only one at higher redshift (A1991 —
K0 = 1.53i0.32, z = 0.0587 — which is a very peculiar cluster (Sharma et al., 2004)).
This raises the question: can the lack of clusters with K0 ,3 10 keV cm2 at z > 0.02
be completely explained by resolution effects?

To answer this question we tested the effect redshift has on our measurements
of K0 by selecting all clusters with K0 3 10 keV cm2 and z s 0.1 and degrading
their surface brightness proﬁles to mimic the effect of increasing the cluster redshift.
Our test is best illustrated using an example: consider a cluster at z = 0.1. For this
cluster, 5” z 9 kpc. Were the cluster at z = 0.2, 5” would equal % 16 kpc. To
mimic moving this example cluster from 2 = 0.1 —+ 0.2, we can extract a new surface
brightness proﬁle using a bin Size of 16 kpc instead of 5”. This will result in a new
surface brightness proﬁle which has the angular resolution for a cluster at a higher
redshift.

We used the preceding procedure to degrade the proﬁles of our subsample. New
surface brightness bin sizes were calculated for each cluster over an evenly distributed
grid of redshifts in the range 2 = 0.1 — 0.4 using step sizes of 0.02. The temperature
proﬁles for each cluster were also degraded by starting at the innermost temperature
proﬁle annulus and moving outward pairing-up neighboring annuli. New spectra
were extracted for these enlarged regions and analyzed following the same procedure
detailed in {3,331.

The ensemble of artiﬁcially redshifted clusters were analyzed using the procedure
outlined in §3.3.4. The notable effects on the entropy proﬁles arising from lower

angular resolution are: (1) less information about proﬁle Shape, and (2) increased

95

 

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redshift

Figure 3.2 Best-ﬁt K0 versus redshift. Some clusters have K 0 error bars smaller than
the point. The clusters with upper-limits (black points with downward arrows) are:
A2151, ASO405, MS 01163-0115, and RX J1347.5-1145. The numerically labeled
clusters are: (1) M87, (2) Centaurus Cluster, (3) RES 533, (4) HCG 42, (5) HCG
62, (6) SSZB153, (7) A1991, (8) MACSO744.8+3927, and (9) CL J1226.9+3332. For
CLJ1226, Maughan et 3.1. (2007) found best-ﬁt K0 = 132 i 24 keV cm2 which is
not signiﬁcantly different from our value of K0 = 166 :l: 45 keV cm2. The lack of
K0 < 10 keV cm2 clusters at z > 0.1 is most likely the result of insufﬁcient angular
resolution (see §3.4.2).

96

entropy of the centralmost bins. Obviously, as redshift increases, the number of radial
bins decreases. Fewer radial bins translates into a less detailed sampling of an entropy
proﬁle’s curvature, e.g. the proﬁles become less “curvy.” On its own this effect should
lead to lower best-ﬁt K0 values, but, while proﬁle curvature is reduced, the entropy
of the central—most bins is increasing because the bins encompass a broader range
of entropy. Horn z = 0.1 — 0.3 this last effect dominates, resulting in an increase
of (K6 — K0)/K0 = 2.72 :i: 1.84 where K0 is the original best-ﬁt value and K6 is
the best-ﬁt value of the degraded proﬁles However, at z > 0.3, the loss of radial
resolution dominates and the degraded proﬁles begin to resemble power-laws except
for the innermost bin which still lies above the power-law (the uncertainty of the
best-ﬁt K0 also increases). The result of a power-law proﬁle with a discrepant central
bin is that the degraded K0 values are only slightly larger than the best-ﬁt K0 of the
un-degraded data, (K6 — K0)/K0 = 0.71 i 0.57.

Our analysis of the degraded entropy proﬁles suggests that K0 is more sensitive
to the value of K (r) in the central bins than it is to the shape of the proﬁle or the
number of radial bins (systematics we explore further in §3.4.3). Most importantly
however, is that low-redshift clusters with K0 3 10 keV cm2 look like they have
K0 2: 10 — 30 keV cm2 if they are placed at z > 0.1. Thus we conclude that the lack

of K0 < 10 keV cm2 clusters at z 2, 0.1 can be attributed to resolution effects.

3.4.3 PROFILE CURVATURE AND NUMBER or BINS

From our analysis of the degraded entropy proﬁles in §3.4.2 we found: (1) that the
best-ﬁt K0 is sensitive to the curvature of the entropy proﬁle, and (2) that the number
of radial bins may also affect the best-ﬁt K0. This raises the possibility of two
troubling systematics in our analysis. To check for a possible correlation between
best-ﬁt K0 and proﬁle curvature we ﬁrst calculated average proﬁle curvatures, RA.

For each proﬁle, n A was calculated using the standard formulation for curvature of a

97

function, I»; = HyHII/(l + 31,2)3/2, where we set y = K(r) = K0 + K100(r/100 kpc)“.

This derivation yields,

a- 2”

dr

 

=fj W100 (—O 1)QK1001‘
[1+(100'0‘aK100ra 1)2]3F~’

fdr

 

(3.6)

where a and K100 are the best-ﬁt parameters unique to each entropy proﬁle. The
integral over all space ensures we evaluate the curvature of each proﬁle in the limit
where the proﬁles have asymptotically approached a constant at small radii and a
power law at large radii. We ﬁnd that at any value of K0, a large range of curvatures
are covered and that there is no systematic trend in KO associated with nA.

In §3.4.2 we also found that proﬁles with fewer radial bins tend toward lower
best-ﬁt K0 values. After examining ﬁgures of the number of bins ﬁt in each entropy
proﬁle versus best-ﬁt K0 we ﬁnd only scatter and no trends.

We do not ﬁnd any systematic trends with proﬁle shape or number of ﬁt bins
which would signiﬁcantly affect our best-ﬁt K0 values. Thus we conclude that the
K0 values presented in the following sections are an adequate measure of the core
entropy and any undetected dependence on proﬁle shape or radial resolution affect

our results at signiﬁcance levels much smaller than the measured uncertainties.

3.4.4 POWER-LAW PROFILES

Equation 3.4 is a special case of eqn. 3.5 with K0 = 0, e.g. the models we ﬁt to K (r)
are nested. In addition, the added parameter has an acceptable best-ﬁt value, K0 = O,
which lies on the boundary of the parameter space. While under these conditions X2,
associated p—values, and F-tests are not useful in determining which model is the
“best” description of K (7‘), comparison of the X2 values for each ﬁt imply, even if
only qualitatively, which model shows more agreement with the data. In addition, for

each ﬁt in Table B.5 we show the number of 0K0 the best-ﬁt K0 values are from zero.

98

We also show in Table 34 the number of clusters with K0 statistically consistent
with zero at various conﬁdence levels for a variety of sub-groups. From Table B.4
we see at 30 signiﬁcance, only ~ 10% of the full ACCEPT sample has a best-ﬁt K0
value which is consistent with zero.

Of the 233 clusters in ACCEPT, only four clusters have a K0 value which is
statistically consistent with zero (at 10), or are better ﬁt by the power-law only model
(based on comparison of reduced X2): A2151, ASO405, MS 0116.3-0115, and NGC
507 (part of HIFL U CCS analysis only). Two additional clusters, A1991 and A4059,
are better ﬁt by the power-law model only when interpolation of the temperature
proﬁle in the core is not constant (see §3.3.1). We ﬁnd that the entropy model which
approaches a constant core entropy at small radii appears to be a better descriptor
of the radial entropy distribution for most ACCEPT clusters. However, we cannot
rule out the power-law only model, but do point out that ~ 90% of clusters have
best—ﬁt K0 values greater than zero at > 30 signiﬁcance. Moreover, that there is a
systematic trend for a single power-law to be a poor ﬁt mainly at the smallest radii

suggests non-zero K0 is not random.

3.5 RESULTS AND DISCUSSION

Presented in Figure 3.3 is a montage of ACCEPT entropy proﬁles for different tem-
perature ranges. These ﬁgures highlight the cornerstone result of ACCEPT: a uni-
formly analyzed collection of entropy proﬁles covering a broad range of core entropy.
Each proﬁle is color-coded to represent the global cluster temperature. Plotted in
each panel of Fig. 3.3 are the mean proﬁles representing K0 3 50 keV cm2 clusters
(dashed-line) and K0 > 50 keV cm2 clusters (dashed-dotted line), in addition to the
pure-cooling model of Voit et a1. (2002) (solid black line). The theoretical pure-cooling
curve represents the entropy proﬁle of a 5 keV cluster simulated with radiative cooling

but no feedback and gives us a useful baseline against which to compare ACCEPT

99

proﬁles.

In the following sections we discuss results gleaned from analysis of our library of
entropy proﬁles. These results include the departure of most entropy proﬁles from
a simple radial power-law proﬁle, the bimodal distribution of core entropy, and the
asymptotic convergence of the entropy proﬁles to the self-similar K (r) o< 7'” power-

law at r 2 100 kpc.

3.5.1 NON-ZERO CORE ENTROPY

Arguably the most striking feature of Figure 3.3 is the departure of most proﬁles from
a simple power-law. Core flattening of surface brightness proﬁles (and consequently
density proﬁles) is a well known feature of clusters (e.g. Jones & Forman 1984, Mohr
et al. 1999 and Xue & Wu 2000). What is notable in our work however is that, based
on comparison of reduced X2 and signiﬁcance of K0 very few of the clusters in our
sample have an entropy distribution which is best-ﬁt by the power-law only model
(eqn. 3.5), rather they are sufﬁciently well-described by the model which ﬂattens in
the core (eqn. 3.4).

For the six clusters discussed in §3.4.4 which are more consistent with a power-
law, it may be the case that the ICM entropy departs from a power-law at a radial
scale smaller than the 5” bins we used for extracting surface brightness proﬁles. After
extracting new surface brightness proﬁles for these six clusters using 2.5” bins and
repeating the analysis, we ﬁnd that the proﬁles for A4059 and AS0405 do ﬂatten.
This leaves A1919, A2151, MS 0116.3-0115, and NGC 507 as the only clusters in
ACCEPT for which the power-law model cannot be reasonably argued against.

For clusters with central cooling times Shorter than the age of the cluster, non-
zero core entropy is an expected consequence of episodic heating of the ICM (Voit &

Donahue, 2005), with AGN as one possible heating source (Bower, 1997; Loewenstein,

100

 

 

 

 

 

 

 

 

 

 
  

4.0 < T,K < 8.0
1 I0

 

100 1000

Figure 3.3 Composite plots of entropy proﬁles for varying cluster temperature ranges.
Proﬁles are color-coded based on average cluster temperature. Units of the color bars
are keV. The solid—line is the pure-cooling model of Voit et al. (2002), the dashed-line
is the mean proﬁle for clusters with K0 3 50 keV cm2, and the dashed-dotted line is
the mean proﬁle for clusters with Ko > 50 keV cm2. Top left: This panel contains all
the entropy proﬁles in our study. Top right: Clusters with kTX < 4 keV. Bottom left:
Clusters with 4 keV < kTX < 8 keV. Bottom right: Clusters with kTX > 8 keV.
Note that while the dispersion of core entropy for each temperature range is large, as
the kTX range increases so to does the mean core entropy.

101

2000; Voit & Bryan, 2001; Soker et al., 2001; Churazov et al., 2002; Briiggen & Kaiser,
2002; Briiggen et al., 2002; Nath & Roychowdhury, 2002; Ruszkowski & Begelman,
2002; Alexander, 2002; Omma et al., 2004; McCarthy et al., 2004; Roychowdhury
et al., 2004; Hoeft & Briiggen, 2004; Dalla Vecchia et al., 2004; Soker & Pizzolato,
2005; Pizzolato & Soker, 2005; Brighenti & Mathews, 2006; Mathews et al., 2006).
Clusters with cooling times of order the age of the Universe, however, require other
mechanisms to generate their core entropy, for example via mergers or extremely
energetic AGN outbursts. For the very highest K0 values, K0 > 100 keV cm2, the
mechanism by which the core entropy came to be so large is not well understood as it
is difﬁcult to boost the entropy of a gas parcel to > 100 keV cm2 via merger shocks
(McCarthy et al., 2008) and would require AGN outburst energies which have never
been observed. We are providing the data and results of ACCEPT to the public
with the hope that the research community ﬁnds it a useful new resource to further

understand the processes which result in non-zero cluster core entropy.

3.5.2 BIMODALITY OF CORE ENTROPY DISTRIBUTION

The time required for a gas parcel to radiate away its thermal energy is a function
of the gas entropy. Low entropy gas radiates profusely and is thus subject to rapid
cooling and vice versa for high entropy gas. Hence, the distribution of K0 is of par-
ticular interest because it is an approximate indicator of the cooling timescale in the
cluster core. The K0 distribution is also interesting because it may be useful in bet-
ter understanding the physical processes operating in cluster cores. For example, if
processes such as thermal conduction and AGN feedback are important in establish-
ing the entropy state of cluster cores, then models which properly incorporate these
processes should approximately reproduce the observed K0 distribution.

In the top panel of Figure 3.4 is plotted the logarithmically binned distribution of

K0. In the bottom panel of Figure 3.4 is plotted the cumulative distribution of KO.

102

One can immediately see from these distributions that there are at least two distinct
populations separated by a small number of clusters with K0 z 30 — 60 keV cm2. If
the distinct bimodality of the K 0 distribution seen in the binned histogram were an
artifact of binning, then the cumulative distribution should be relatively smooth. But
there are clearly plateaus in the cumulative distribution, with one of these plateaus

coincident with the division between the two populations at K0 z 30 — 60 keV cm2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 3.4 Top panel: Histogram of best-ﬁt K0 for all the clusters in ACCEPT. Bin
widths are 0.15 in log space. Bottom panel: Cumulative distribution of K0 values for
the full sample. The distinct bimodality in K0 is present in both distributions, which
would not be seen if it were an artifact of the histogram binning. A KMM test ﬁnds
the K0 distribution cannot arise from a simple unimodal Gaussian.

TO further test for the presence of a bimodal population we utilized the KMM test
of Ashman et al. (1994). The KMM test estimates the probability that a set of data

points is better described by the sum of multiple Gaussians than by a single Gaussian.

103

We tested the unimodal case versus the bimodal case, with the assumption that the
dispersion of the two Gaussian components are not the same. We have used the
updated KMM code of Waters et a1. (2008) which incorporates bootstrap resampling
to determine uncertainties for all parameters. A post-analysis comparison of ﬁts
assuming the populations have the Same and different dispersions conﬁrms our initial
guess that the dispersions are different is a better model.

The KMM test, as with any statistical test, is very speciﬁc. At zeroth order, the
KMM test Simply determines if a population is unimodal or not, and ﬁnds the means
of these populations. However, the dispersions of these populations are subject to
the quality of sampling and the presence of outliers (e.g. KMM must assign all data
points to a population). The outputs of the KMM test are the best-ﬁt populations
to the data, not necessarily the best-ﬁt populations of the underlying distribution
(hence no goodness of ﬁt is output). However, the KMM test does output a P-value,
p, and with the assumption that X2 describes the distribution of the likelihood ratio
statistic, 1 — p is the conﬁdence interval for the null hypothesis.

There are a small number of clusters with K0 3 4 keV cm2 that when included
in the KMM test signiﬁcantly change the results. Thus we conducted tests including
and excluding K0 3 4 keV cm2 clusters and provide two sets of best-ﬁt parameters.
The results of the KMM test neglecting K0 3 4 keV cm2 clusters were two statis-
tically distinct peaks at K1 = 17.8 :1: 6.6 keV cm2 and K2 = 154 :l: 52 keV cm2.
121 clusters were assigned to the ﬁrst distribution, while 106 were assigned to the
second. Including K0 3 4 keV cm2 clusters, the KMM test found populations at
K1 = 15.0 :i: 5.0 keV cm2 (89 clusters) and K2 = 129 u: 45 keV cm2 (131 clusters).
The KMM test neglecting K0 5 4 keV cm2 clusters returned p = 1.16 x 10‘7, while
the test including all clusters returned p = 1.90 x 10‘”. These tiny p-values indicate
the unimodal distribution is signiﬁcantly rejected as the parent distribution of the

observed K0 distribution.

104

One possible explanation for a bimodal core entropy distribution is that it arises
from the effects of episodic AGN feedback and electron thermal conduction in the
cluster core. Voit & Donahue (2005) outlined a model of AGN feedback whereby

outbursts of ~ 1045 1

ergs s‘ occurring every ~ 108 yrs can maintain a quasi-steady
core entropy of z 10 — 30 keV cm2.‘ In addition, very energetic and infrequent AGN
outbursts of 1061 ergs can increase the core entropy into the z 30—50 keV cm2 range.
This model satisfactorily explains the distribution of K0 5 50 keV cm2, but depletion
of the K0 = 30 — 60 keV cm2 region and populating K0 > 60 keV cm2 requires more
physics. Voit et al. (2008) have recently suggested that the dramatic fall-off of clusters
beginning at K0 3 30 keV cm2 may be the result of electron thermal conduction.
After K0 has exceeded K0 z 30 keV cm2, conduction could severely slow, if not halt,
a cluster’s core from appreciably cooling and returning to a core entrOpy state with
K0 < 30 keV cm2. This model is supported by results presented in Chapter 4, Guo
et al. (2008), and Rafferty et al. (2008) which ﬁnd that the formation of thermal
instabilities are extremely sensitive to the core entropy state of a cluster.

We acknowledge that ACCEPT is not a complete, uniformly selected sample of
clusters. This raises the possibility that our sample is biased towards clusters that
have historically drawn the attention of observers, such as cooling ﬂows or mergers.
If that were the case, then one reasonable explanation of the K0 bimodality is that

K0 = 30 — 60 keV cm2 clusters are “boring” and thus go unobserved. However, as

we Show in §3.5.4, the unbiased ﬂux-limited HIFL U CCS sample is also bimodal.

3.5.3 THE HIFLUGCS SUB-SAMPLE

ACCEPT is not a ﬂux-limited or volume—limited sample. TO ensure our results are
not affected by an unknown selection bias, we culled the HIFL U CCS sample from
ACCEPT for separate analysis. HIFL UCCS is a ﬂux-limited sample ( f X 2 2 x
10"11 ergs s“1 cm'2) selected from the REFLEX sample (BOhringer et al., 2004)

105

with no consideration of morphology. Thus, at any given luminosity in HIF L U CCS
there is a good sampling of different morphologies, i.e. the bias toward cool-cores or
mergers has been removed. The sample also covers most of the Sky with holes near
Virgo and the Large and Small Magellanic Clouds, and has no known incompleteness
(Chen et al., 2007). There are a total of 106 objects in HIFL U C CS : 63 in the primary
sample and 43 in the extended sample. Of these 106 objects, no public Chandra
observations were available for 16 objects (A548e, A548w, A1775, A1800, A3528n,
A3530, A3532, A3560, A3695, A3827, A3888, ASO636, HCG 94, IC 1365, NGC 499,
RXCJ 23442-0422), 6 objects did not meet our minimum analysis requirements and
were thus insufﬁcient for study (3C 129, A1367, A2634, A2877, A3627, Triangulum
Australis), and as discussed in §3.2, Coma and Fornax were intentionally ignored.
This left a total of 82 HIFL UGCS Objects which we analyzed, 59 from the primary
sample (~ 94% complete) and 23 from the extended sample (~ 50% complete). The
primary sample is the more complete of the two, thus we focus our following discussion
on the primary sample only.

The clusters missing from the primary HIFL UGCS sample are A1367, A2634,
Coma, and Fornax. The extent to which these 4 clusters can change our analysis of
the K0 distribution for HIFL U CCS is limited. To alter or wash-out bimodality, all 4
clusters would need to fall in the range K0 = 20 - 40 keV cm2, which is certainly not
the case for any of these clusters. A1367 has been studied by Donnelly et al. (1998)
and Sun 85 Murray (2002), with both ﬁnding that two sub-clusters are merging in
the cluster. The merger process, and the potential for associated shock formation, is
known to create large increases of gas entropy (McCarthy et al., 2007). Given the
combination of low surface brightness, moderate temperatures (kTX = 3.5 — 5.0 keV),
lack of a temperature gradient, ongoing merger, and presence of a shock, it is unlikely
A1367 has a core entropy ,S, 40 keV cm2. A2634 is a very low surface brightness

cluster with the bright radio source 3C 465 at the center of an X—ray coronae (Sun

106

et al., 2007). Clusters with comparable properties to A2634 are not found to have
K0 ,5 40 keV cm2. Coma and Fornax are known to have core entropy > 40 keV cm2
(Rafferty et al., 2008, C. Scharf, private communication).

Shown in Figure 3.5 are the log—binned (top panel) and cumulative (bottom panel)
K0 distributions Of the HIFL UCCS primary sample. The bimodality seen in the
full ACCEPT collection is also present in the HIFL U CCS sub-sample. Mean best-
ﬁt parameters are given in Table 34. We again performed two KMM tests: one
test with, and another test without, clusters having K0 3 4 keV cm2. For the test
including K 0 S 4 keV cm2 clusters we ﬁnd populations at K1 = 9.7:l:3.5 keV cm2 (28
clusters) and K2 = 131 :l: 46 keV cm2 (31 clusters) with p = 3.34 x 10'3. Excluding
clusters with K0 3 4 keV cm2 we ﬁnd peaks at K1 = 10.5 :1: 3.4 keV cm2 and K2 =
116:1:42 keV cm2, each having 21 and 34 clusters, respectively. The probability these
populations are best described by a unimodal distribution is p = 1.55 x 10‘5.

Hudson & Reiprich (2007) note a similar core entropy bimodality to the one we
ﬁnd here. Hudson & Reiprich (2007) discuss two distinct groupings of Objects in a
plot of average cluster temperature versus core entropy, with the dividing point being
K z 40 keV cmz. Our results agree with the ﬁndings of Hudson & Reiprich (2007 )
with the gap in KO occurring at K0 z 40 keV cm2. While the gaps of ACCEPT
and HIFL UCCS do not cover the same K0 range, it is interesting that both gaps are
the deepest around K0 z 30 keV cm2. That bimodality is present in both ACCEPT
and the unbiased HIFL U CCS sub-sample suggests bimodality cannot be the result

of simple archival bias.

3.5.4 DISTRIBUTION OF CORE COOLING TIMES

In the X—ray regime, cooling time and entropy are related in that decreasing gas
entropy also means shorter cooling time. Thus, if the K0 distribution is bimodal, the

distribution of cooling times should also be bimodal. We have calculated cooling time

107

 

l

0.20

 

0.15

 

 

0.10

 

 

 

 

 

 

 

 

 

0.05

 

 

 

 

IIII'IIIIIIIIIIIFIF

 

 

 

 

 

 

 

Fractional number of clusters

.0
8
,__1
l
r—-
r

l

 

 

1.0

0.8

0.6

0.4

0.2

ITIIII'IIIIIII'IIIIIH

Fractional number of clusters

 

I U I
D II 1
D U 1
t (l (
’lllllllllllllLlllll I ' ll'llllllllllllll‘

 

 

U1 -A“”1o E-UA 100
Ko[kchm2]

 

Figure 3.5 Top panel: Histogram of best-ﬁt K0 values for the primary HIFL UGCS
sample. Bin widths are 0.15 in log space. Bottom panel: Cumulative distribution of
best-ﬁt K0 values. The distinct bimodality seen in the full ACCEPT sample (Fig.
3.4) is also present in the HIFL U CCS subsample and shares the same gap starting
at K0 z 30 keV cm2. That bimodality is present in both samples is strong evidence
it is not a result of an unknown archival bias.

108

proﬁles from the Spectral analysis using the relation

t _ 371ka
C001 _ 2nenHA(T, Z)

 

(3.7)

where n is the total ion number (x 2.3nH for a fully ionized plasma), ne and mi
are the electron and proton densities respectively, A(T, Z) is the cooling function for
a given temperature and metal abundance, and 3/2 is a constant associated with
isochoric cooling. The values of the cooling function for each temperature proﬁle bin
were calculated in XSPEC using the ﬂux of the best-ﬁt spectral model. Following
the procedure discussed in §3.3.4, A and kTX were interpolated across the radial grid
of the electron density proﬁle. The cooling time proﬁles were then ﬁt with a simple

model analogous to that used for ﬁtting K (r):

 

(3.8)

04
T

where tag is core cooling time and 15100 is a normalization at 100 kpc.

The K0 distribution can also be used to explore the distribution of core cooling
times. Assuming free-free interactions are the dominant gas cooling mechanism (i.e.
6 oc T1/2), Donahue et al. (2005) Show that for free-free emission, entropy is related

to cooling time via the formulation:

t K m 1 8 -——- -— . .
CO( 0) 0 yrs (10 keV cmz) (5 keV (3 9)

Shown in Figure 3.6 is the logarithmically binned and cumulative distributions of
best-ﬁt core cooling times from eqn. 3.8 (top panel) and core cooling times calculated
using eqn. 3.9 (bottom panel). The bin widths in both histograms are 0.20 in log-
space. The pile-up of cluster core cooling times below 1 Gyr is well known, e. g. (Hu

et al., 1985) and more recently Dunn & Fabian (2008), and the cooling times we

109

calculate are consistent with the results of other cooling time studies, e.g. Peres et al.
(1998) and Rafferty et al. (2008).

Most important about Fig. 3.6 is that the distinct bimodality of the K0 distri-
bution is also present in best-ﬁt core cooling time, tcO- A KMM bimodality test of
tea found peaks at tel = 0.60 :l: 0.24 Gyr and tag = 6.23 :l: 2.19 Gyr with 130 and 97
in each respective population. The probability that the unimodal distribution is a
better ﬁt is once again exceedingly small, p = 8.77 x 10—7.

If entropy is more closely related to the physical processes which cause bimodality
than is cooling time, then that the cooling time distribution does not present with
the sharp, deep bimodality seen in KO suggests entropy is the fundamental quantity
related to bimodality. But, since cooling time proﬁles are more sensitive to the
resolution of the temperature proﬁles than are the entropy proﬁles, it may be that
resolution effects are limiting the quantiﬁcation of the true cooling time of the core.
For example, if our temperature interpolation scheme is too coarse, or averaging over
many small-scale temperature ﬂuctuations signiﬁcantly increases tco, then tco would
not be the best approximation of true core cooling time. In which case, the core
cooling times might be lower and the sharpness and offsets of the distributions gaps

may signiﬁcantly change.

3.5.5 SLOPE AND NORMALIZATION OF POWER—LAW COMPONENTS

Beyond r a: 100 kpc the entropy proﬁles Show a striking similarity in the slope of the
power-law component which is independent Of K 0. For the full sample, the mean value
of a = 1.21 :l: 0.39. For clusters with K0 < 50 keV cm2, the mean a = 1.20 :l: 0.38,
and for clusters with K0 2 50 keV cm2, the mean a = 1.23 :l: 0.40. Our mean slope
of a z 1.2 is not statistically different from the theoretical value of a = 1.1 found
by Tozzi & Norman (2001) and oz = 1.2 found by Voit et al. (2005). For the full

sample, the mean value of K100 = 126 :l: 45 keV cm2. Again distinguishing between

110

 

l
a

0.15

0.10

0.05

IIIIIIIIIII

I
llllllllllllll

Fractional number of clusters

9
8
l

I

 

 

.0 P .o 7‘
«5 0’ a: C)
TVUIIIIIIIIIITIIIIIII

.0
to

 

 

’lllllllilllljllllll ll

Fractional number of clusters

    

 

10

 

l
l

0.12
0.10

0.08
0.06

 

0.04

0.02

0.00
1 .0

Fractional number of clusters

 

0.8

0.6

0.4

IUIIUIIIIIIIII'I W'IIIIIIIIUIIIIIIIIII

0.2

lllllllllLlllllllllll llllllllllllllllllllllJJ

Fractional number at clusters

 

 

 

10

tcc(Kc) [Myr]

Figure 3.6 Top panel: Log-binned histogram and cumulative distribution of best-ﬁt
core cooling times, toO (eqn. 3.8), for all the clusters in ACCEPT. Histogram bin
widths are 0.2 in log space. Bottom panel: Log-binned histogram and cumulative
distribution of core cooling times calculated from best-ﬁt K0 values, tcO(K0) (eqn.
3.9), for all the clusters in ACCEPT. Histogram bin widths are 0.2 in log Space. The
bimodality we observe in the K0 distribution is also present in best-ﬁt tco. However,
the gaps between the two populations of tcO and tcO(K0) differ by ~ 0.3 Gyrs with
scaled-entropy having the more pronounced gap with a shorter cooling time.

111

clusters below and above K0 = 50 keV cm2, we ﬁnd K100 = 150 :l: 50 keV cm2 and
K100 = 107 :l: 39 keV cmz, respectively. Scaling each entropy proﬁle by the cluster
virial temperature and virial radius considerably reduces the dispersion in K100, but

we reserve detailed discussion Of scaling relations for a future paper.

3.6 SUMMARY AND CONCLUSIONS

We have presented intracluster medium entropy proﬁles for a sample of 233 galaxy
clusters (9.66 Msec) taken from the Chandra Data Archive. We have named this
project ACCEPT for “Archive of Chandra Cluster Entropy Proﬁle Tables.” Our
analysis software, reduced data products, data tables, ﬁgures, cluster images, and
results of our analysis for all clusters and Observations are freely available at the
ACCEPT web site: http: / /www.pa.msu.edu/ astro/ MC2/ accept. We encourage Ob-
servers and theorists to utilize this library of entropy proﬁles in their own work.

We created radial temperature proﬁles using spectra extracted from a minimum of
three concentric annuli containing 2500 counts each and extending to either the chip
edge or 05ng0, whichever was smaller. We deprojected surface brightness proﬁles
extracted from 5” bins over the energy range 0.7—2.0 keV to obtain the electron gas
density as a function of radius. Entropy proﬁles were calculated from the density
and temperature proﬁles as K (r) = T(r)n(r)—2/3. Two models for the entropy
distribution were then ﬁt to each proﬁle: a power-law only model (eqn. 3.5) and a
power-law which approaches a constant value at small radii (eqn. 3.4).

We have demonstrated that the entropy proﬁles for the majority Of ACCEPT
clusters are well-represented by the model which approaches a constant entropy, K0,
in the core. The entropy proﬁles of ACCEPT are also remarkably Similar at radii
greater than 100 kpc, and asymptotically approach the self-similar pure-cooling curve
(r or 1.1) with a slope of a = 1.21 :l: 0.39 (the dispersion here is in the sample, not

in the uncertainty of the measurement). We also ﬁnd that the distribution of K0 for

112

the full archival sample is bimodal with the two populations separated by a poorly
populated region at K0 x 30—60 keV cmz. After culling out the primary HIFL U C CS
sub—sample of Reiprich (2001), we ﬁnd the K 0 distribution of this complete sub-sample
to be bimodal, refuting the possibility of archival bias.

Two core cooling times were derived for each cluster: (1) cooling time proﬁles were
calculated using eqn. 3.7 and each cooling time proﬁle was then ﬁt with eqn. 3.8
returning a best-ﬁt core cooling time, tcO; (2) Using best-ﬁt K0 values, entropy was
converted to a core cooling time, tcO(K0) using eqn. 3.9. We ﬁnd the distributions
of both core cooling times to be bimodal. Comparison of the core cooling times from
method (1) and (2) reveals that the gap in the bimodal cooling time distributions
occur over different timescales, ~ 2 — 3 Gyrs for tcO, and ~ 0.7 — 1 for tcO(K0).

After analyzing an ensemble of artiﬁcially redshifted entropy proﬁles, we ﬁnd the
lack of K0 ,3 10 keV cm2 clusters at z > 0.1 is most likely a result of resolution ef-
fects. Investigation of possible systematics affecting best-ﬁt K0 values, such as proﬁle
curvature and number Of proﬁle bins, revealed no trends which would signiﬁcantly
affect our results. We come to the conclusion that K0 is an acceptable measure of
average core entropy and is not overly inﬂuenced by proﬁle Shape or radial resolution.
We also ﬁnd that ~ 90% Of the sample clusters have a best—ﬁt K0 more than 30 away
from zero.

Our results regarding non-zero core entropy and K 0 bimodality support the sharp-
ening picture of how feedback and radiative cooling in clusters alter global clus-
ter properties and affect massive galaxy formation. Among the many models of
AGN feedback, Voit & Donahue (2005) outlined a model which Speciﬁcally addresses
how AGN outbursts generate and sustain non-zero core entropy in the regime of
K0 ,3 30 keV cm2 (see also Kaiser & Binney, 2003). In addition, if electron thermal
conduction is an important process in clusters, then there exists a critical entropy

threshold below which conduction is no longer efﬁcient at wiping out thermal insta-

113

bilities, the consequences Of which should be a bimodal core entropy distribution and
a sensitivity of cooling by—product formation (like star formation and AGN activity)
to this entropy threshold (Voit et al., 2008; Guo et al., 2008). We Show in Chapter 4
that indicators of feedback like Ha and radio emission are extremely sensitive to the
lower-bound of the bimodal gap at K0 2 30 keV cm2.

However, many details are still missing from this emerging picture, and there are
many Open questions regarding the evolution of the ICM and formation of thermal
instabilities in cluster cores: How are clusters with K0 > 100 keV cm2 produced? Is
an early episode of preheating necessary? What are the role of MHD instabilities, e. g.
MTI (Balbus, 2000; Quataert, 2008) and HBI (Parrish & Quataert, 2008), in shaping
the ICM? Are the compact X—ray sources we ﬁnd at the cores Of some BCGS truly
coronae? If so, are their properties consistent with the sample studied by Sun et al.
(2007)? Can BCG corona properties be used to constrain the effects of conduction?

We hope ACCEPT will be a useful resource in answering these questions.

3. 7 ACKNOWLEDGEMENTS

K. W. C. thanks Chris Waters for supplying and supporting his new KMM bimodal-
ity code. K. W. C. was supported in this work through Chandra X-ray Observa-
tory Archive grants AR—6016X and AR—4017A. M. D. acknowledges support from the
NASA LTSA program NNG-05GD82G. The Chandra X-ray Observatory Center is
Operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA
under contract NAS8-03060. This research has made use of software provided by
the Chandra X—ray Center in the application packages CIAO, CHIPS, and SHERPA.
This research has made use of the NASA/IPAC Extragalactic Database which is op-
erated by the Jet Propulsion Laboratory, California Institute of Technology, under
contract with NASA. This research has also made use of NASA’S Astrophysics Data

System. Some software was obtained from the High Energy Astrophysics Science

114

Archive Research Center, provided by NASA’S Goddard Space Flight Center.

3.8 SUPPLEMENTAL CLUSTER NOTES

NB: In this section we abbreviate Surface brightness as SB.

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

"J 10‘ .
10‘1- - 10"-
10‘- l t ‘ 10‘- .
10’s . 10‘-
Abe|l119 Abell160 Abell193
H 10" '1 10"'- " ’0‘“
T P 10‘- ‘ °
0) 10‘» v 4 § . ion
N o 0 1o"-
.8 10‘ ‘0‘ 1g:-
4 1 '-
‘° ’ Abell400 ‘ l|1060 10‘" Abe||1240 ‘
8 1 '°" ‘ *3? -
1. 10‘ 4 < 10*: o I
m ‘ ﬁgr- _‘ 0‘
a, ‘° 1 +11 . 1er ‘ ‘ 1
8 L "7; 10‘)- -
1—1 104 Abell 1736 . :3, Abell 2125 0‘ Abell 2255
r- ‘l 1 P d
8 10‘» ° - - lg? A - 3" "
0:) 10‘» - l§‘: :
4-1 10‘- - 10‘- . m1: 3
c 0‘ Io‘p _‘ .7: :
a) ' r Abell 2319 * w’- Abell 2462 - lli: Abell 2631 3
.c 10"- ‘ ‘0'," " "p— d
m . 1
10 - ‘ 10‘s ‘
0 . .0 r- -1
o 10"- '1 10". .1
m 10‘1- a
t 10’» Abell 3376 . 10‘-
‘?) 10"- + . . :32- .
10" . " ‘04,. .
10‘1- . -1 ‘0‘.
l.
'°“ MKW oa ‘ ‘°‘ RBS461
10‘ . 10‘»
_n 10"
1 10 100 1000 1 10 100 1000

 

led [arcsec]

Figure 3.7 Surface brightness proﬁles for clusters requiring a B—model ﬁt. The best-ﬁt
ﬂ-model for each cluster is overplotted as a dashed line. The discrepancy between
the data and best-ﬁt model for some clusters results from the presence of a compact
X-ray source at the center of the cluster. These cases are discussed below.

Abell 119 (z = 0.0442): This is a highly diffuse cluster without a prominent cool
core. The large core region and Slowly varying SB made deprojection highly
unstable. We have excluded a small source at the very center of the BCG. The
exclusion region for the source is z 2.2” in radius which at the redshift of the

cluster is ~ 2 kpc. This cluster required a double ﬁ-model.

115

Abell 160 (z = 0.0447): The highly asymmetric, low SB Of this cluster resulted in
a noisy surface brightness proﬁle that could not be deprojected. This cluster
required a double ﬁ-model. The BCG hosts a compact X-ray source. The
exclusion region for the compact source has a radius of ~ 5” or ~ 4.3 kpc. The
BCG for this cluster is not coincident with the X-ray centroid and hence is not

at the zero-point of our radial analysis.

Abell 193 (z = 0.0485): This cluster has an azimuthally symmetric and a very dif-
fuse ICM centered on a BCG which is interacting with a companion galaxy. In
Fig. 3.7 one can see that the central three bins of this cluster’s SB proﬁle are
highly discrepant from the best-ﬁt ,B-model. This is a result of the BCG being
coincident with a bright, compact X-ray source. AS we have concluded in 3.3.5,
compact X-ray sources are excluded from our analysis as they are not the focus
of our study here. Hence we have used the best-ﬁt ﬁ-model in deriving K (r)

instead Of the raw SB.

Abell 400 (z = 0.0240): The two ellipticals at the center Of this cluster have com-
pact X-ray sources which are excluded during analysis. The core entropy we
derive for this cluster is in agreement with that found by Hudson et al. (2006)

which supports the accuracy of the ﬁ-model we have used.

Abell 1060 (2 = 0.0125): There is a distinct compact source associated with the
BCG in this cluster. The ICM is also very faint and uniform in surface brightness
making the compact source that much more obvious. Deprojection was unstable

because of imperfect exclusion of the source.

Abell 1240 (2 = 0.1590): The SB of this cluster is well-modeled by a B-model.
There is nothing peculiar worth noting about the BCG or the core of this

cluster.

116

Abell 1736 (2 = 0.0338): Another “boring” cluster with a. very diffuse low SB ICM,
no peaky core, and no signs Of merger activity in the X—ray. The noisy SB proﬁle
necessitated the use of a double ﬁ-model. The BCG is coincident with a very
compact X-ray source, but the BCG is Offset from the X-ray centroid and thus
the central bins are not adversely affected. The radius of the exclusion region

for the compact source is z 2.3” or 1.5 kpc.

Abell 2125 (2 = 0.2465): Although the ICM of this cluster is very Similar to the
other clusters listed here (i.e. diffuse, large cores), A2125 is one of the more
compact clusters. The presence of several merging sub-clusters (Wang et al.,
1997, 2004a) to the NW Of the main cluster form a diffuse mass which cannot
rightly be excluded. This complication yields inversions of the deprojected SB

proﬁle if a double ﬁ-model is not used.

Abell 2255 (z = 0.0805): This is a very well studied merger cluster (Burns et al.,
1995; Feretti et al., 1997a). The core of this cluster is very large (r > 200 kpc).
Such large extended cores cannot be deprojected using our methods because
if too many neighboring bins have approximately the same SB, deprojection
results in bins with negative or zero value. The SB for this cluster is well

modeled as a [3 function.

Abell 2319 (z = 0.0562): A2319 is another well studied merger cluster (Feretti et al.,
1997b; Molendi et al., 1999) with a very large core region (r > 100 kpc) and a
prominent cold front (O’Hara et al., 2004). Once again, the SB proﬁle is well-ﬁt
by a ﬂ-model.

Abell 2462 (2 = 0.0737): This cluster is very Similar in appearance to A193: highly
symmetric ICM with a bright, compact X-ray source embedded at the center of
an extended diffuse ICM. The central compact source has been excluded from

our analysis with a region of radius a: 1.5” or ~ 3 kpc. The central bin Of the

117

SB proﬁle is most likely boosted above the best-ﬁt double B-model because of

faint extended emission from the compact source which cannot be discerned

from the ambient ICM.

Abell 2631 (2 = 0.2779): The SB proﬁle for this cluster is rather regular, but be-
cause the cluster has a large core it suffers from the same unstable deprojection
as A2255 and A2319. The ICM is symmetric about the BCG and is incredibly
uniform in the core region. We did not detect or exclude a source at the center
of this cluster, but under heavy binning the cluster image appears to have a
source coincident with the BCG, and the Slightly higher ﬂux in central bin of

the SB proﬁle may be a result of an unresolved source.

Abell 3376 (2: = 0.0456): The large core Of this cluster (r > 120 kpc) makes depro—

jection unstable and a ﬂ-model must be used.

Abell 3391 (2 = 0.0560): The BCG is coincident with a compact X-ray source. The
source is excluded using a region with radius % 2” or ~ 2 kpc. The large uniform

core region made deprojection unstable and thus required a ﬁ-model ﬁt.

Abell 3395 (2 = 0.0510): The SB proﬁle for this cluster is noisy resulting in depro-
jection inversions and requiring a B—model ﬁt. The BCG Of this cluster has a
compact X-ray source and this source was excluded using a region with radius

z 1.9” or ~ 2 kpc.

MKW 08 (z = 0.0270): MKW 08 is a nearby large group / poor cluster with a pair
of interacting elliptical galaxies in the core. The BCG falls directly in the middle
of the ACIS-I detector gap. However, despite the lack of proper exposure, CCD
dithering reveals that a very bright X-ray source is associated with the BCG. A
double ﬂ-model was necessary for this cluster because the low SB Of the ICM

is noisy and deprojection is unstable.

118

RES 461 (z = 0.0290): This is another nearby large group/poor cluster with an
extended, diffuse, axisymmetric, featureless ICM centered on the BCG. The
BCG is coincident with a compact source with size r z 1.7 kpc. This source

was excluded during reduction. The ﬁ-model is a good ﬁt to the SB proﬁle.

119

Chapter Four

Cavagnolo, Kenneth W., Donahue, Megan, Voit, G. Mark, Sun, Ming (2008). An
Entropy Threshold for Strong Ha and Radio Emission in the Cores of Galaxy
Clusters. The Astrophysical Journal Letters. 683:115—118.

 

120

 

CHAPTER 4:

AN ENTROPY THRESHOLD FOR
STRONG Ha AND RADIO
EMISSION IN THE CORES OF
GALAXY CLUSTERS

 

4.1 INTRODUCTION

In recent years the “cooling ﬂow problem” has been the focus of intense scrutiny as
the solutions have broad impact on existing theories Of galaxy formation (see Peterson
& Fabian, 2006, for a review). Current models predict that the most massive galaxies
in the Universe — brightest cluster galaxies (BCGS) — should be bluer and more
luminous than observations ﬁnd, unless AGN feedback intervenes to stop late-time
star formation (Bower et al., 2006; Croton et al., 2006; Sam et al., 2006). X—ray
observations of galaxy clusters have given this hypothesis considerable traction. From
the prOpertieS of X—ray cavities in the intracluster medium (ICM), Birzan et al. (2004)
concluded that AGN feedback provides the necessary energy to retard cooling in the
cores of clusters (see McNamara & Nulsen, 2007, for a review). This result suggests
that, under the right conditions, AGN are capable of quenching star formation by
heating the surrounding ICM.

If AGN feedback is indeed responsible for regulating star formation in cluster cores,
then the radio and star-forming properties of galaxy clusters should be related to the

distribution. Of ICM speciﬁc entropy. In previous observational work (see Donahue

121

et al., 2005, 2006, and Chapter 3), we have focused on ICM entropy as a means
for understanding the cooling and heating processes in clusters because it is a more
fundamental property of the ICM than temperature or density alone (Voit et al.,
2002; Voit, 2005). ICM temperature mainly reﬂects the depth and shape Of the dark
matter potential well, while entropy depends more directly on the history of heating
and cooling within the cluster and determines the density distribution of gas within
that potential.

We have therefore undertaken a large Chandra archival project to study how
the entropy structure of clusters correlates with other cluster properties. Chapter 3
presents the radial entropy proﬁles we have measured for a sample of 233 clusters
taken from the Chandra Data Archive. We have named this project the Archive
of Chandra Cluster Entropy Proﬁle Tables, or ACCEPT for short. TO characterize
the ICM entropy distributions of the clusters, we ﬁt the equation K (r) = K0 +
K100(r/ 100 kpc)“ to each entrOpy proﬁle. In this equation, K100 is the normalization
of the power-law component at 100 kpc and we refer to K0 as the central entropy.
Bear in mind, however, that K 0 is not necessarily the minimum core entropy or the
entropy at r = 0, nor is it the gas entropy that would be measured immediately
around the AGN or in a BCG X-ray corona. Instead, K0 represents the typical
excess of core entropy above the best-ﬁtting power law found at larger radii. Chapter
3 Shows that K0 is non-zero for almost all clusters in our sample.

In this chapter we present the results of exploring the relationship between the
expected by-products of cooling, e.g. Ha emission, star formation, and AGN activity,
and the K 0 values of clusters in our survey. To determine the activity level of feedback
in cluster cores, we selected two readily available observables: Ha and radio emission.
We have found that there is a critical entropy level below which Ha and radio emission
are often present, while above this threshold these emission sources are much fainter

and in most cases undetected. Our results suggest that the formation of thermal

122

instabilities in the ICM and initiation of processes such as star formation and AGN
activity are closely connected to core entropy, and we suspect that the Sharp entropy
threshold we have found arises from thermal conduction (see Voit et al., 2008, for
discussion Of this point).

This chapter proceeds in the following manner: In §4.2 we cover the basics of our
data analysis. The entropy-Ha relationship is discussed in §4.3, while the entropy-
radiO relationship is discussed in §4.4. A brief summary is provided in §4.5. For
this chapter we have assumed a ﬂat ACDM Universe with cosmogony QM = 0.3,
Q A = 0.7, and H0 = 70 km S—1 Mpc-1. All uncertainties are at the 90% conﬁdence

level.

4.2 DATA ANALYSIS

This section brieﬂy describes our data reduction and methods for producing entropy
proﬁles. More thorough explanations are given in Donahue et al. (2006), Chapter 2,
and Chapter 3.

4.2.1 X-RAY

X-ray data were taken from publicly available observations in the Chandra Data
Archive. Following standard CIAO reduction techniques,1 data were reprocessed
using CIAO version 3.4.1 and CALDB version 3.4.0, resulting in point-source and
ﬂare-clean events ﬁles at level-2. Entropy proﬁles were derived from the radial ICM
temperature and electron density proﬁles.

Radial temperature proﬁles were created by dividing each cluster into concentric
annuli with the requirement of at least three annuli containing a minimum of 2500
counts each. Source Spectra were extracted from these annuli, while corresponding

background Spectra were extracted from blank-sky backgrounds tailored to match

 

1 http: / / cxc.harvard.edu / ciao / guides /

123

each observation. Each blank-Sky background was corrected to account for variation
of the hard-particle background, while spatial variation of the soft-galactic back-
ground was accounted for through the addition Of a ﬁxed background component
during Spectral ﬁtting. Weighted (responses that account for Spatial variations of the
CCD calibration were also created for each Observation. Spectra were then ﬁtted over
the energy range 0.7-7.0 keV in XSPEC version 11.3.2ag (Arnaud, 1996) using a
Single-component absorbed thermal model.

Radial electron density proﬁles were created using surface brightness proﬁles and
spectroscopic information. Exposure-corrected, background-subtracted, point-source-
clean surface brightness proﬁles were extracted from 5” concentric annular bins over
the energy range 0.7-2.0 keV. In conjunction with the spectroscopic normalization and
0.7-2.0 keV count rate, surface brightness was converted to electron density using the
deprojection technique of Kriss et al. (1983). Errors were estimated using 5000 Monte
Carlo realizations of the surface brightness proﬁle.

A radial entropy proﬁle for each cluster was then produced from the temperature
and electron density proﬁles. The entropy proﬁles were ﬁtted with a simple model
that is a power-law at large radii and approaches a constant value, K0, at small radii

(see §4.1 for the equation). We deﬁne central entrOpy as K0 from the best-ﬁt model.

4.2.2 Ha

One goal of our project was to determine if ICM entropy is connected to processes such
as star formation. Here we do not directly measure star formation but instead use Ha,
which is usually a strong indicator of ongoing star formation in galaxies (Kennicutt,
1983). It is possible that some of the Ha emission from BCGS is not produced by
star formation (Begelman & Fabian, 1990; Sparks et al., 2004; Ruszkowski et al.,
2008; Ferland et al., 2008). Nevertheless, Ha emission unambiguously indicates the

presence of ~ 104 K gas in the cluster core and therefore the presence of a multiphase

124

intracluster medium that could potentially form stars.

Our Ha values have been gathered from several sources, most notably Crawford
et al. (1999). Additional sources of data are M. Donahue’s Observations taken at Las
Campanas and Palomar (see Table B.3), Heckman et al. (1989), Donahue et al. (1992),
Lawrence et al. (1996), Valluri & Anupama (1996), White et al. (1997), Crawford et al.
(2005), and Quillen et al. (2008). We have recalculated the Ha luminosities from these
sources using our assumed ACDM cosmological model. However, the observations
were made with a variety of apertures and in many cases may not reﬂect the full Ha
luminosity of the BCG. The exact levels of LHa are not important for the purposes
of this chapter and we use the LHa values here as a binary indicator of multiphase

gas: either Ha emission and cool gas are present or they are not.

4.2.3 RADIO

Another goal of this work was to explore the relationship between ICM entropy and
AGN activity. It has long been known that BCGS are more likely to host radio-loud
AGN than other cluster galaxies (Burns et al., 1981; Valentijn & Bijleveld, 1983;
Burns, 1990). Thus, we chose to interpret radio emission from the BCG of each
ACCEPT cluster as a Sign of AGN activity.

To make the radio measurements, we have taken advantage Of the nearly all-Sky
ﬂux-limited coverage Of the NRAO VLA Sky Survey (NVSS, Condon et al., 1998) and
Sydney University Molonglo Sky Survey (SUMSS, Bock et al., 1999; Mauch et al.,
2003). NVSS is a continuum survey at 1.4 GHz of the entire Sky north Of 6 = —40°,
while SUMSS is a continuum survey at 843 MHz of the entire sky south of 6 = —30°.
The completeness limit of NVSS is z 2.5 mJy and for SUMSS it is z 10 mJy when
6 > —50° or z 6 mJy when 6 S —50°. The NVSS positional uncertainty for both
right ascension and declination is ,S 1” for sources brighter than 15 mJy and z 7”

at the survey detection limit (Condon et al., 1998). At 7. = 0.2, these uncertainties

125

represent distances on the Sky Of ~ 3— 20 kpc. For SUMSS, the positional uncertainty
is ,S 2” for sources brighter than 20 mJy and is always less than 10” (Bock et al., 1999;
Mauch et al., 2003). The distance at z = 0.2 associated with these uncertainties is
~ 6 — 30 kpc. We calculate the radio power for each radio source using the standard
relation VLy = 471'.D%Syf0, where 3,, is the 1.4 GHz or 843 MHz ﬂux from NVSS
or SUMSS, D L is the luminosity distance, and f0 is the central beam frequency of
the observations. Our calculated radio powers are Simply an approximation of the
bolometric radio luminosity.

Radio sources were found using two methods. The ﬁrst method was to search for
sources within a ﬁxed angular distance of 20” around the cluster X-ray peak. The
probability of randomly ﬁnding a radio source within an aperture of 20” is exceedingly
low (< 0.004 for NVSS). Thus, in 233 total ﬁeld searches, we expect to ﬁnd no more
than one spurious source. The second method involved searching for sources within
20 projected kpc of the cluster X-ray peak. At z m 0.051, 1” equals 1 kpc, thus
for clusters at z 2, 0.05, the 20 kpc aperture is smaller than the 20” aperture, and
the likelihood of ﬁnding a spurious source gets smaller. Both methods produce nearly
identical lists of radio sources with the differences arising from the very large, extended
lobes Of low-redshift radio sources such as Hydra A.

To make a spatial and morphological assessment of the radio emission’s origins, 2'. e.
determining if the radio emission is associated with the BCG, high angular resolution
is necessary. However, NVSS and SUMSS are low-resolution surveys with FWHM of
z 45”. We therefore cannot distinguish between ghost cavities/ relics, extended lobes,
point sources, or reaccelerated regions or if the emission is coming from a galaxy
very near the BCG. We have handled this complication by visually inspecting each
radio source in relation to the Optical (using DSS I / II)2 and infrared (using 2MASS)3

emission of the BCG. We have used this method to establish that the radio emission

2http: //archive.stsci.edu/dss/
3http: //www.ipac.caltech.edu/2mass/

 

126

is most likely coming from the BCG. When available, high resolution data from VLA
FIRST4 were added to the visual inspection. VLA FIRST is a 10,000 deg2 high-
resolution (5”) survey at 20 cm of the north and south Galactic caps (Becker et al.,
1995). FIRST is also more sensitive than either NVSS or SUMSS with a detection
threshold of 1 mJy. I

4.3 Ha EMISSION AND CENTRAL ENTROPY

Of the 233 clusters in ACCEPT, we located Ha Observations from the literature for
110 clusters. Of those 110, Hoz was detected in 46, while the remaining 64 have
upper limits. The mean central entropy for clusters with detections is K0 = 13.9 :1:
4.9 keV cm2, and for clusters with only upper-limits K0 = 130 i 55 keV cm2.

In Figure 4.1 central entropy is plotted versus Ha luminosity. One can immediately
see the dichotomy between clusters with and without Ha emission. If a cluster has
a central entropy ,S 30 keV cm2, then Ha emission is usually “on,” while above this
threshold the emission is predominantly “off.” For brevity we refer to this threshold as
Kthresh hereafter. The cluster above Kthresh that has Ha emission (blue square with
inset orange circle) is Zw 2701 (K0 = 39.7 i 3.9 keV cm2). There are also clusters
below Kthresh without Ha emission (blue squares with red stars): A2029, A2107,
EXO 0422-086, and RBS 533. A2151 also lies below Kthresh and has no detected
Ha emission, but the best-ﬁt K0 for A2151 is statistically consistent with zero and
this cluster is plotted using the 20 upper-limit of K0 (Fig. 4.1, green triangle).
These ﬁve clusters are clearly exceptions to the much larger trend. The mean and
dispersion of the redshifts for clusters with and without Ha are not signiﬁcantly
different, z = 0.124 :1: 0.106 and z = 0.132 :1: 0.084 respectively, and applying a
redshift cut (i.e. z = 0—0.15 or z = 0.15—0.3) does not change the KO-Ha dichotomy.

Most important to note is that changes in the HO luminosities because of aperture

 

4http://sundog.stsci.edu

127

effects will move points up or down in Figure 4.1, while mobility along the K0 axis is
minimal. Qualitatively, the correlation between low central entropy and the presence
of HO emission is very robust.

The clusters with Ha detections are typically between 10 and 30 keV cm2, have
short central cooling times (< 1 Gyr), and under older nomenclature would be clas-
siﬁed as “cooling ﬂow” clusters. ' It has long been known that star formation and
associated Ha nebulosity appear only in cluster cores with cooling times less than a
Hubble time (Hu et al., 1985; Johnstone et al., 1987; McNamara & O’Connell, 1989;
Voit & Donahue, 1997; Cardiel et al., 1998). However, our results suggest that the
central cooling time must be at least a factor of 10 smaller than a Hubble time for
these manifestations Of cooling and star formation to appear. It is also very interest-
ing that the characteristic entropy threshold for strong Ha emission is so sharp. Voit
et al. (2008) have recently proposed that electron thermal conduction may be respon-
sible for setting this threshold. This hypothesis has received further support from the
theoretical work of Guo et al. (2008) showing that thermal conduction can stabilize
non-cool core clusters against the formation of thermal instabilities, and that AGN

feedback may be required to limit star formation when conduction is insufﬁcient.

4.4 RADIO SOURCES AND CENTRAL ENTROPY

Of the 233 clusters in ACCEPT, 100 have radio-source detections with a mean K0
of 23.3 :i: 9.4 keV cm2, while the other 122 clusters with only upper limits have a
mean K0 of 134 :l: 52 keV cmz. NVSS and SUMSS are low-resolution surveys with
FWHM at z 45”, which at z = 0.2 is z 150 kpc. This scale is larger than the size
of a typical cluster cooling region and makes it difﬁcult to determine absolutely that
the radio emission is associated with the BCG. We therefore focus only on clusters at
z < 0.2. After the redshift cut, 135 clusters remain — 64 with radio detections (mean

K0 = 18.3 i 7.7 keV cm?) and 71 without (mean K0 = 112 :l: 45 keV cm2).

128

 

103 III I I I IfIIil I‘TﬁIIIIII I I I II
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...

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102

101

 

10°

LHa [1O40 ergs 3"]

+
41 s-‘l’
“O
":5
6+6.
é—O
st:
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10‘1

r 4.
10'2E- 3 3 i t

....u.-?-. ....
10° 101 102
K0 [keV cmz]

I IIIIIW
O—O—

 

 

I l Illllll I

Figure 4.1 Central entropy vs. Ha luminosity. Orange circles represent Ha detections,
black circles are non-detection upper limits, and blue squares with inset red stars or
orange circles are peculiar clusters that do not adhere to the observed trend (see text).
A2151 is plotted using the 20 upper-limit of the best-ﬁt K0 and is denoted by a green
triangle. The vertical dashed line marks K0 = 30 keV cm2. Note the presence of a
sharp Ha detection dichotomy beginning at K0 5, 30 keV cm2.

129

In Figure 4.2 we have plotted radio power versus K0. The Obvious dichotomy
seen in the Ha measures and characterized by Kthreshis also present in the radio.
Clusters with V14, 2‘, 1040 ergs 8"1 generally have K0 ,3 Kthroﬁh. This trend was ﬁrst
evident in Donahue et al. (2005) and suggests that AGN activity in BCGS, while
not exclusively limited to clusters with low core entropy, is much more likely to be
found in clusters that have a core entropy less than Kthresh- That star formation and
AGN activity are subject to the same entropy threshold suggests that the mechanism
that promotes or initiates one is also involved in the activation Of the other. If the
entropy Of the hot gas in the vicinity of the AGN is correlated with K0, then the lack
Of correlation between radio power and K0 below the 30 keV cm2 threshold suggests
that cold-mode accretion (Pizzolato & Soker, 2005; Hardcastle et al., 2007) may be
the dominant method of fueling AGN in BCGS.

We have again highlighted exceptions to the general trend seen in Figure 4.2:
clusters below Kthresh without a radio source (blue squares with inset red stars) and
clusters above K thresh with a radio source (blue squares with inset orange circles). The
peculiar clusters below Kthresh are A133, A539, A1204, A2107, A2556, AWM7, ESO
5520200, MKW4, MS J0440.5+0204, and MS J1157.3+5531. The peculiar clusters
above Kthresh are 2PIGG J0011.5-2850, A193, A586, A2063, A2147, A2244, A3558,
A4038, and RBS 461. In addition, there are three clusters, A2151, AS405, and MS
01163-0115, that have best-ﬁt K0 statistically consistent with zero and are plotted
in Figure 4.2 using the 20 upper-limit of K0 (green triangles). All three clusters have
detected radio sources.

Finding a few clusters in our sample without radio sources where we expect to
ﬁnd them is not surprising given that AGN feedback could be episodic. However,
the clusters above Kthresh with a central radio source are interesting, and may be
special cases Of BCGS with embedded coronae. Sun et al. (2007) extensively studied

coronae and found that they are like “mini cooling cores” with low temperatures

130

 

    

 

  

    
        

 
 
 
 

 

 

4.... . ...”... “Inn”, .
1O ' " I z<0.20 '
|
. I .
. l
IQI
.— 102- e ' -
'70, '0'—O-l
(I) 0|- . |
2’ - e + o- s e -
0’ O -O-|
s I "
.9 0.. I * h ..
H 10 N 1|
_f —e— g I ‘ 1.
> L e ' If a§3°lﬁa_ 1:%
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10 "' I.
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... I
...I . . ......I . 1......1 . . ....1
100 101 102
K0[kchm2]

Figure 4.2 BCG radio power vs.

K0 for clusters with z < 0.2. Orange symbols
represent radio detections and black symbols are non-detection upper-limits. Circles
are for NVSS observations and squares are for SUMSS Observations. The blue squares
with inset red stars or orange circles are peculiar clusters that do not adhere to the
observed trend (see text). Green triangles denote clusters plotted using the 20‘ upper-
limit of the best-ﬁt K0. The vertical dashed line marks K0 = 30 keV cm2. The radio

sources Show the same trend as Ha: bright radio emission is preferentially “on

K0 ,3 30 keV cm2.

131

and high densities. Coronae are a low—entropy environment isolated from the high-
entropy ICM and may provide the conditions necessary for gas cooling to proceed.
And indeed, 2PIGG 0011, A193, A2151, A2244, A3558, A4038, and RBS 461 Show
indications that a very compact (r S, 5 kpc) X-ray source is associated with the BCG

(see Section 3.3.5).

4.5 SUMMARY

We have presented a comparison Of ICM central entropy values and measures of BCG
Ha and radio emission for a Chandra archival sample of galaxy clusters. We ﬁnd
that below a characteristic central entropy threshold of K0 z 30 keV cm2, Ha and
bright radio emission are more likely to be detected, while above this threshold Ha
is not detected and radio emission, if detected at all, is signiﬁcantly fainter. The
mean K0 for clusters with and without Ha detections are K0 = 13.9 :1: 4.9 keV cm2
and K0 = 130 :l: 55 keV cm2, respectively. For clusters at z < 0.2 with BCG radio
emission the mean K0 = 18.3 2!: 7.7 keV cm2, while for BCGS with only upper limits,
the mean K0 = 112 :t 45 keV cm2. While other mechanisms can produce Ha or radio
emission besides star formation and AGN, if one assumes that the Ha and radio
emission are coming from these two feedback sources, then our results suggest that
the development of multiphase gas in cluster cores (which can fuel both star formation

and AGN) is strongly coupled to ICM entropy.

4.6 ACKNOWLEDGEMENTS

We were supported in this work through Chandra SAO grants AR—4017A, AR—6016X,
and G05—6131X and NASA/LTSA grant NNG-05GD82G. The CXC is operated by
the SAO for and on behalf of NASA under contract NASS—03060.

132

 

CHAPTER 5:
SUMMARY

 

5.1 ENERGY BAND DEPENDENCE OF X-RAY TEMPER-

ATURES

Using a sample of 192 galaxy clusters we explored the band dependence of inferred X-
ray temperatures for the ICM. Utilizing core-excised global cluster Spectra extracted
from the regions encircled by R2500 and R5000, we inferred X-ray temperatures for a
single-component absorbed thermal model in a broadband (0.7-7.0 keV) and a hard-
band (2.0-7.0 keV). On average, we found that the hard-band temperatures were
greater, with the ratio of the temperatures, TH B R, having a mean value 1.16 :t 0.01
(where the error is of the mean) for the R2500 apertures, and 1.14 :l: 0.01 for the
R5000 apertures. No systematic trends were found, in either the values or dispersions,
with S / N , redshift, Galactic absorption, metallicity, Observation date, or broadband
temperature. Analysis of a simulated ensemble of 12,765 Observation-speciﬁc two-
component Spectra revealed statistical ﬂuctuations could not account for the skewing
measured in TH B R- The simulations also helped establish a lower limit on the ﬂux
contribution from a cooler gas component (TX < 2.0 keV) necessary to generate
TH B R as large as those found in the data. A second-cool gas phase must be con-
tributing 2, 10% of the total emission. The Simulations also reveal the Observational
scatter is larger than the statistical scatter, a result one should expect if an underlying

physical process is responsible for creating dispersion in TH B R-

133

The a priori motivation for studying temperature inhomogeneity comes from the
prediction of Mathiesen & Evrard (2001) that TH B R may be related to the process of
hierarchical structure formation. After assuming that the establishment and promi-
nence of a cool core in a cluster is an indicator of relaxation, we compared TH E R
values with the “strength” of the cool core based on the temperature decrement be-
tween the core and the cluster atmosphere. The result was a Signiﬁcant correlation
between clusters having higher values of TH B R being less likely to host a cool core.
A search of the scientiﬁc literature involving the clusters with the highest signiﬁcant
values Of TH B R (TH B R > 1.1) revealed that most, if not all, of these clusters are un-
dergoing, or have recently undergone, a merger event. With two strong connections
between TH B R and cluster dynamical state established, we conclude that temper-
ature inhomogeneity is most likely related to the process of cluster relaxation, and
that it may be useful as a metric to further quantify the degree to which a cluster is

relaxed, thus addressing point (1) brought up in Section §1.3.l.

5.2 CHANDRA ARCHIVAL SAMPLE OF INTRACLUSTER

ENTROPY PROFILES

A library of ICM entropy proﬁles was created for 233 galaxy clusters taken from the
Chandra Data Archive to better understand the role Of feedback and cooling in Shap-
ing global cluster properties. Radial gas density, ne(r), and gas temperature, kT$(r),
proﬁles were measured for each cluster. Radial entropy was calculated from the re-
lation K (r) = kTX(r)ne(r)_2/3. The uncertainties for each proﬁle were calculated
using 5000 Monte Carlo realizations of the Observed surface brightness proﬁle. Each
proﬁle was then ﬁt with two models: one which is a power-law at all radii (3.5), and
another (eqn. 3.5) which is a power-law at large radii but approaches a constant K 0

value at small radii. The K0 term is deﬁned as the core entropy.

134

Comparison of p-values, x2, and the Signiﬁcance of K0 above zero for the best-
ﬁt models revealed that for 90% of the 233 sample, the model with a constant core
entropy is a better description of the data. Systematics such as PSF smearing, angular
resolution, proﬁle curvature, and number of radial bins proved not to be important
in setting or changing best-ﬁt Ki). The Slope of the power-law component was also
found to be remarkably similar among the proﬁles with a mean value of 1.21 :l: 0.39
which is not Signiﬁcantly different from the value of ~ 1.1 expected from hierarchical
structure formation.

The distribution Of K0 for both the ACCEPT and HIFL U CCS samples was found
to be bimodal. The populations comprising the bimodality are strikingly similar be-
tween the two samples with peaks at K0 ~ 15 keV cm2 and K0 ~ 150 keV cm2. The
KMM test (Ashman et al., 1994; Waters et al., 2008) was applied and it determined,
for both ACCEPT and HIFL U CCS, that the populations were statistically distinct
and that a unimodal distribution was ruled out. The poorly populated region between
the populations for both samples occurred at K0 z 30 — 60 keV cm2. The measured
entropy proﬁle shapes and distribution of K0 were consistent with existing models
of AGN feedback which predict non-zero core entropy. All of the results and data
for ACCEPT were made available to the public with the intent that theorists and
observers might ﬁnd utility for ACCEPT in their own work. The work presented in
Chapter 3 directly addressed point (2) of Section §1.3.2.

5.3 AN ENTROPY THRESHOLD FOR STRONG Ha AND
RADIO EMISSION IN THE CORES OF GALAXY CLUS-

TERS

To study a suspected connection between low entropy gas in cluster cores and the

by-products Of cooling, namely AGN activity and formation of thermal instabilities,

135

the best-ﬁt K0 values from clusters in ACCEPT were compared against radio power
and Ha luminosity, both strong indicators of run-away cooling. A search Of the
research literature turned-up Ha observations for 110 clusters in ACCEPT. The NVSS
and SUMSS all-sky radio surveys were queried for each cluster to attain VLV, either
detections or upper-limits. New luminosities were then calculated using the preferred
cosmology assumed in this dissertation to place all observations on equal footing.

A comparison of HO luminosities and best-ﬁt K0 values showed a strong relation
between when Ha emission is detected and when it is not. Below an entropy threshold
Of K 0 f, 30 keV cm2 Ha emission is predominantly on, while above this threshold it is
always Off sans the exception of one cluster very near the K 0 = 30 keV cm2 boundary.
A very similar correlation was found between VLV and K0 for clusters at z < 0.2. A
redshift cut was applied because of the low resolution of NVSS and SUMSS. The en-
tropy threshold for 11L;l also occurs at K0 z 30 keV cm2 but with a larger fraction of
low power radio sources above K 0 z 30 keV cm2 than the fraction which was found in
Ha. However, it was found that powerful radio sources (VLV > 104‘0 ergs S_1 cm‘2)
were only found in clusters with K0 ,6 30 keV cm2 adding strength to the argument
that entropy sets a scale for development of a multiphase medium in cluster cores.
While the discussion is not presented in this dissertation, Voit et al. (2008) propose
that it is electron thermal conduction which gives rise to the entropy threshold Ob-

served in our study. The work presented in Chapter 4 is an extension of point (2) in

§1.3.2.

136

APPENDICES

137

 

APPENDIX A:
TABLES CITED IN CHAPTER 2

 

Table A.1 Notes

A (1) indicates a cluster analyzed within R5000 only. Italicized cluster names indicate
a. cluster which was excluded from our analysis (discussed in §2.5.1). For clusters with
multiple Observations, the X-ray centers differ by < 0.5 kpc. Col. (1) Cluster name;
col. (2) CDA observation identiﬁcation number; col. (3) RA. of cluster center; col.
(4) Dec. of cluster center; col. (5) nominal exposure time; col. (6) observing mode;

col. (7) CCD location Of centroid; col. (8) redshift; col. (9) bolometric luminosity.
Table A.2 Notes

Clusters ordered by lower limit of TH B R- Listed TH B R values are for the R2500—CORE
aperture, with the exception of the “R5000—CORE Only” clusters listed at the end
of the table. Excluding the “R5000—CORE Only” clusters, all clusters listed here
had TH B R signiﬁcantly greater than 1.1 and the same core classiﬁcation for both
the stoo-CORE and RSOOO—CORE apertures. Numbered references given in table:
[1] Gioia & Luppino (1994), [2] Kempner et al. (2003), [3] Yuan et a1. (2005), [4]
Markevitch et al. (1998), [5] Bagchi et al. (2006), [6] Teague et al. (1990), [7] Andersson
81. Madejski (2004), [8] Burns et al. (1995), [9] Feretti et al. (1997a), [10] Girardi et al.
(1997), [11] Dahle et al. (2002), [12] Smith et al. (2005), [13] Gioia et al. (1982), [14]
Hallman &, Markevitch (2004), [15] Yang et al. (2004), [16] Mercurio et al. (2003),
[17] Gémez et al. (2000), [18] Tucker et al. (1998), [19] Krempec—Krygier & Krygier

138

(1999), [20] Mazzotta et al. (2001), [21] Govoni et al. (2001), [22] Bliton et al. (1998),
[23] Gutierrez & Krawczynski (2005), [24] Markevitch et al. (1996), [25] Ohta et al.
(2001), [26] Molendi et a1. (2000), [27] Clarke et al. (2004), [28] Clarke et al. (2005),
[29] this work.

Table A.3 Notes

Note: “77” refers to 0.7-7.0 keV band and “27” refers to 2.0-7.0 keV band. Col.
(1) Cluster name; col. (2) size of excluded core region in kpc, (3) R2500 in kpc;
col. (4) absorbing Galactic neutral hydrogen column density; col. (5,6) best-ﬁt
MEKAL temperatures; col. (7) T0,7_7.0/T2,0_7,0 also called THBR; col. (8) best-ﬁt
77 MEKAL abundance; col. (9,10) respective reduced X2 statistics, and (11) percent
of emission attributable to source. A star (*) indicates a cluster which has multiple
Observations. Each Observation has an independent spectrum extracted along with
an associated WARF, WRMF, normalized background Spectrum, and soft residual.
Each independent Spectrum is then ﬁt Simultaneously with the same spectral model

to produce the ﬁnal ﬁt.
Table A.4 Notes

Note: “77” refers to 0.7-7.0 keV band and “27” refers to 2.0-7.0 keV band. Col.
(1) Cluster name; col. (2) size of excluded core region in kpc, (3) R5000 in kpc;
col. (4) absorbing Galactic neutral hydrogen column density; col. (5,6) best-ﬁt
MEKAL temperatures; col. (7) T0,7_7,0/T2,0_7,0 also called THBR; col. (8) best-ﬁt
77 MEKAL abundance; col. (9,10) respective reduced X2 statistics, and (11) percent
of emission attributable to source. A star (at) indicates a cluster which has multiple
observations. Each observation has an independent spectrum extracted along with
an associated WARF, WRMF, normalized background spectrum, and soft residual.
Each independent spectrum is then ﬁt simultaneously with the same Spectral model

to produce the ﬁnal ﬁt.

139

 

 

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APPENDIX B: -
TABLES CITED IN CHAPTER 3

 

Table B.1 Notes

Col. (1) Cluster name; col. (2) CXC CDA Observation Identiﬁcation Number; col.
(3) RA. of cluster center; col. (4) Dec]. of cluster center; col. (5) exposure time; col.
(6) observing mode; col. (7) CCD location of cluster center; col. (8) redshift; col. (9)
average cluster temperature; col. (10) core entropy measured in this work; col. (11)
cluster bolometric luminosity; and col. (12) notes are as follows: (a) - cluster analyzed
using the best-ﬁt ﬁ-model for the surface brightness proﬁles (discussed in §3.3.2); (b)
- clusters with complex surface brightness of which only the central regions were
used in ﬁtting K (1'); (c) - cluster only used during analysis of the HIFL U GCS sub-
sample (discussed in §3.5.4); (d) - cluster with central AGN removed during analysis
(discussed in §3.3.5); (e) - cluster with central compact source removed during analysis
(discussed in §3.3.5); and (f) - cluster with central bin ignored during ﬁtting (discussed
in §3.3.5).

Table B.2 Notes

Col. (1) Cluster name; col. (2) central surface brightness of ﬁrst component; col.
(3) core radius of ﬁrst component; col. (4) ﬂ parameter of ﬁrst component; col.
(5) central surface brightness of second component; col. (6) core radius of second
component; col. (7) ﬂ parameter of second component; col. (8) model degrees of

freedom; and col. (9) reduced chi-squared statistic for best-ﬁt model.

167

Table B.4 Notes

Listed here are the mean best-ﬁt parameters of the model K (r) = K0+K 100(1' / 100 kpc)“
for various sub-groups of the full ACCEPT sample. The ’CSE’ sample are the clusters
with a central source excluded (discussed in §3.3.5). The K12 values represent the
entropy at 12 kpc and are calculated from the best-ﬁt models. Col. (1) Sample being
considered; col. (2) number of objects in the sub-group; col. (3) fraction of objects
with p > 0.05 for power-law only model (eqn. 3.5); col. (4) fraction of objects with
p > 0.05 for power-law with constant core entropy model (eqn. 3.4); col. (5) frac-
tion of objects which do not meet p > 0.05 criterion for either model; col. (6) mean
best-ﬁt K0; col. (7) mean entropy at 12 kpc; col. (8) mean best-ﬁt K100; and col.
(9) mean best-ﬁt power-law index; and cols. (10,11,12) number of clusters consistent
with K0 = 0 keV cm2 at 10, 20, and 3a signiﬁcance, respectively. Percentage of the

sub-group represented by each is also listed.
Table B.5 Notes

Col. (1) Cluster name; col. (2) CDA observation identiﬁcation number; col. (3)
method of TX interpolation (discussed in §3.3.4); col. (4) maximum radius for ﬁt;
col. (5) number of radial bins included in ﬁt; col. (6) best-ﬁt core entropy; col. (7)
number of sigma K0 is away from zero; col. (9) best-ﬁt entropy at 100 kpc; col. (10)
best-ﬁt power-law index; col. (11) degrees of freedom in ﬁt; col. (12) x2 statistic of

best-ﬁt model; and col. (13) probability of worse ﬁt given X2 and degrees of freedom.

168

 

 

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171

 

 

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172

 

 

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173

 

 

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Agsﬂanoov Sega omega ~38?» E magma? mo ammﬁweoa 3.880 ”em 38¢.

174

 

 

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175

 

 

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176

 

 

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177

 

 

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3253:0an Scam mica maobg E Egg—o mo mmmﬁoaoa 3.850 "ﬁm Each.

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I omém ee.w 386 2 mdm ohmﬁwvnmo- Biponvoumﬁ mag wvmoééomg Km
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I cod- ww.n 33d mm 93 359833; vmodmnoonoﬁ Hmvm 8$+vdoog Km
I NH; nwd amid mm m.: mmémﬁmnmw+ boodmumﬁwc mam ommciwmﬁwoa Km
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179

 

 

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Table B.3 Comments
The abbreviation “PO” denotes observations taken on the 5 m Hale Telescope at the

Palomar Observatory, USA, while “LC” are observations taken on the DuPont 2.5 m
telescope at the Las Campanas Observatory, Chile. Upperlimits for Ha ﬂuxes are 30.

Table B.3: M. Donahue’s Ha Observations.

 

 

 

Cluster Telescope z [N I I ]/ Ha Ha Flux
10“15 ergs/s/cm2

Abell 85 PO 0.0558 2.67 0.581
Abell 119 LC 0.0442 — <0.036
Abell 133 LC 0.0558 — 0.88
Abell 496 LC 0.0328 2.50 2.90
Abell 1644 LC 0.0471 — 1.00
Abell 1650 LC 0.0843 - <0.029
Abell 1689 LC 0.1843 — <0.029
Abell 1736 LC 0.0338 - <0.026
Abell 2597 PO 0.0854 0.85 29.7
Abell 3112 LC 0.0720 2.22 2.66
Abell 3158 LC 0.0586 — <0.036
Abell 3266 LC 0.0590 1.62 <0.027
Abell 4059 LC 0.0475 3.60 2.22
Cygnus A PO 0.0561 1.85 28.4
EXO 0422-086 LC 0.0397 — <0.031
Hydra A LC 0.0522 0.85 13.4
PKS 0745-191 LC 0.1028 1.02 10.4

 

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Avmsﬁﬁoov $280888 850.888 830.888 5.885 .80 Sam ”Wm 83.88

190

 

 

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8088883888 88280888 080.888 830.8888 3.88885 .80 Edam ”Wm 83.88

191

 

 

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3888883883 88380888 830.888 830.8888 85-8828 .3 55m and 03.88

192

 

 

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Avgﬁaaovv 8835888 880.888 830.588 5.8888 .80 Sam 8nd @588

193

 

 

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32885888 £3808: 28:80.5 830.5888. 85.8885 .80 Edam 8nd @388

194

 

 

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ﬁgsﬁanoov 888880888 @505 839588 3-8885 .6 humanism ”Wm 83889

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Agsﬁuaoov 888608 850.888 830.8888 5.88.83 .80 Eagm 89m @389

196

 

 

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APPENDIX C: ~
CHANDRA OBSERVATIONS REDUCTION
PIPELINE (CORP)

 

This appendix has been written as a tutorial for the ﬁrst-time analyzer of Chandra
data (e.g. the “you” role in the text). “When your CIAO-E1 is good, only then will
you utilize the stowed backgrounds of the CALDB.”

C. 1 COPYRIGHT

As a formality, I have blanketed CORP with the GNU General Public License. Below
is the copyright and license agreement for all scripts in CORP:

Kenneth W. Cavagnolo’s Chandra Observations Reduction Pipeline (CORP)
COpyright © 2008 Kenneth W. Cavagnolo, kencavagnolocgmail.com

These programs are free software; you can redistribute them and/ or modify them
under the terms of the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any later version.
These programs are distributed in the hope that they will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details. You should have received a copy of the GNU General Public License
along with these programs; if not, write to the Free Software Foundation, Inc., 51

Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

219

C.2 INTRODUCTION To CORP

The reduction and analysis of Chandra data is given in exquisite detail in the CIAO
threads on the CXC’s web sitel. There is very little which is not discussed in the
CIAO and HelpDesk threads at the CXC web site. However, to streamline the lengthy
reduction and analysis process of extended X—ray sources, such as galaxy clusters and
groups, I have written several PERL and IDL scripts which make-up my own Chan-
dra Observations Reduction Pipeline (CORP, pronounced “core”). The purpose of
this pipeline software is to condense CIAO’s tedious prompts and command line
intensive steps into an easily executable series of scripts which require minimal inter-
action and produce science-ready data products. A pipeline also ensures that a large
sample of observations are reduced the same way, and a pipeline also eases the pain
of analyzing several hundred observations.

There is a critical caveat to the use of CORP and analyzing Chandra data in
general: no two Chandra observations are the same! CORP has allowances
for many different tool settings and instrument setups, but these options are ﬁnite,
and no amount of automation can replace human interactivity. It is an absolute
**necessity** that users of CORP view, scrutinize, and double check the output of
every reduction/ analysis step. This can be time consuming, but not nearly as time
consuming as ﬁnding and correcting errors embedded in on-going, or goodness forbid,
published work.

As of writing this dissertation, all CORP scripts properly interact with CIAO
3.4.1 and CALDB 3.4. The CXC software versions matter because the CXC pro-
grammers (whom are great people!) have a tendency to reinvent the wheel every so
often. This may result in a change to output filenames, extensions, header keywords,
data types, et cetera and can cause a script to err. Errors are not guaranteed however,

so it is important to be mindful of how CIAO or the CALDB have changed as a

 

1 http: / / cxc.harvard.edu/ ciao / threads / index.html

220

result of an update (release notes are always provided with an update: read them!)
There are some pretty great updates to CIAO included in the full, ﬁnal 4.0 version,
so I highly recommend CORP users email me to request new scripts when CIAO 4.0
is fully deployed.

Now for a few notes about me, the author and programmer:

1. I use plenty of analysis and X—ray “jargon” in this Appendix. If you come across
nomenclature which is unfamiliar, consult the CXC web site, there is absolutely
nothing you could want to know about Chandra that is not there. CORP is my
method for automating most of the logic trees which are in the CXC threads,

but this does not mean CORP’s operation will always be transparent to a user.

2. I am not a computer programmer. In fact, I only knew pseudo-code when I
entered graduate school. Hence, my style of programming is best described
as inelegant and brutish. Computer resources are cheap and abundant, so I
use lots of inefﬁcient code, but the overhead and time consumption are low, so
writing efﬁcient code does nothing to accelerate my work. The scripts of CORP
use no command line options besides input, and sometimes output, ﬁlenames.
Everything the script is being commanded to do is controlled by opening the
code and editing the “Options” section near the beginning of the program. Do

not worry, it’s as simple as editing a Word document.

3. As of now, the scripts are available via a tarball which I will email you. Someday
distribution of the code will be handled through a public CVS server. The tar-
ball contains all the scripts, a README ﬁle (which is a copy of this appendix),
and a folder of example data. Descriptions of what each script does, how it is
called, what it takes as input, and what is generated as output are all listed in

the header of each program.

4. I am not a debugger. Each script is written to run a very speciﬁc set of tasks.

221

Given the proper input, the scripts return the expected output. However, while
I wish the scripts were magic, alas, they are not. If you plan on giving the
programs non-standard input and there is some Operation you are not sure the
script will perform, then ﬁnd out ﬁrst by dissecting the code. I may have coded

a script to handle your odd data, but I may not. Find out ﬁrst!

C.3 INITIAL REPROOESSING

C3. 1 RETRIEVING DATA

Getting Chandra data from the CDA is not complicated. There are three methods
to get data: (1) run the stand-alone Chaser program, (2) use the web-based version
of Chaser, named WebChaserz, or (3) run my script query-cda.p1. The ﬁrst thing
to do is determine which ObsIDs need to be downloaded. This is accomplished by
searching the CDA via WebChaser. The WebChaser form is self-explanatory: search
via object name, sky coordinates, or using any set of other listed methods and options.
After searching the CDA, a list of archived observations will be returned. VERY
IMPORTANT: Now is the time to make a one column ﬁle where each line lists one
of the ObsIDs to be downloaded:

#Obsid
2419
791

etc .

This ﬁle is needed to download data and build the reference ﬁle used by every script
in CORP.
Open the script query_cda.p1 with an editor (like emacs or xemacs). Within the

script are three vital options that need to be set: $get_nh, $get_z, and $get_data.

 

2http://cda.harvard.edu/chaser/

222

When set to ’yes’, these options tell the script to: (1) ﬁnd the Galactic absorbing
column density (NH) using the LAB survey (Kalberla et al., 2005), (2) acquire a red-
shift from NED3, and (3) download data from the CDA. The $get_nh is trustworthy,
so set it to ’yes’. However, the $get_z option is not robust. The NED query returns
a list of galaxy clusters nearest the aimpoint of the Chandra observation, but the
proper redshift is not always returned. I typically leave this Option set to ’yes’ and
conﬁrm redshifts by manually querying NED (hey, it’s less typing).

The $get_data option will cause the script to download data and create a directory
for each ObsID and place both into the directory speciﬁed by the variable $dest. The
CDA is large, so a pre—compiled listing of where every ObsID is stored is provided
in the ﬁle cdaftp.dat (this ﬁle is part of the CORP tarball). The variable $ftpdat
needs to point to where this ﬁle is stored. The CDA is continually updated, so you

will need to update cdaftp. dat from time to time. This is accomplished by running:
[linux]% perl build_cdaftp.pl <output_filename>

Now, run the query script. WARNING: If there is an existing newref . list in

the working directory, it will be overwritten.
[linux]% perl query_cda.p1 <my_list_of_obsids>

The download time is completely dependent on download speed, so if there are many

ObsIDs to download, work on something else for a while. The script tells the user what

NH and redshift it has found and for what object. The script also informs the user how

many of the input ObsIDs were successfully found in the CDA and the total exposure

time of observations in the query. You will now have new directories which bear the

names of the downloaded ObsIDs (for example, <hard_drive>/<my_root_datadir>/<obsid>).
There should also be a new ﬁle named newref . list. Each column within newref . list

is described below:

3http: //nedwww.ipac.caltech.edu/

 

223

Name: This is the name of the TARGET object listed for the observation. This is
not necessarily the name you’d like to give the object, so feel free to change it.

ObsID: Obviously this is the ObsID. Most of the ﬁle naming convention in CORP
involves the ObsID since it is a unique identiﬁer. This may seem clumsy and awkward
(especially for the clusters that have multiple ObsIDs) but in the battle of clarity and
brevity, clarity wins in my book.

RA: The right ascension of the observation target object. The default output
format is decimal degrees, but this can be changed to sexigesimal by changing the
query_cda.p1 variable $outcrdunit from ’decimal’ to ’sexigesimal’.

Dec: The declination of the observation target object in decimal degrees.

Rmax: The maximum observation radius. This is the radius from the cluster
center to the nearest detector edge. Rmax needs to be speciﬁed by the user for each
observation. A script which automatically ﬁnds Rmax is forthcoming.

MinCts: The minimum number of counts per temperature annulus. The default
is 2500 but this number should be increased for observations with sufﬁcient counts or
adjusted depending on scientiﬁc goals.

z: The redshift of the target object. Even if the script has automatically queried
NED for this value, it is best to double-check. A batch query via NED is simple4.

N h20: The galactic absorbing neutral hydrogen column density, NH, in 1020 cm‘2.
These values are acquired from the nh tool which uses the LAB. Survey results
(Kalberla et al., 2005).

Tx: The global/virial cluster temperature. There are a number of ways to mea-
sure to a cluster temperature, it is best to keep a detailed record of how you made
this measurement or where you looked-up the temperature (e. g. KEEP CITATION S
you’ll want them later). If no temperature can be found in the literature, the script

$find_tx.p1 should be used to determine the cluster temperature. This script iter-

 

4 http:/ / nedwww.ipac.caltech.edu / help / batch. html

224

atively determines temperature in core-excised annuli using a user-speciﬁed fraction
of the virial radius as the outer radius. When to run the script after removing is
speciﬁed later.

Fe: The global cluster metallicity. The value listed in the reference ﬁle is used only
as a starting point for most spectral ﬁts, so the value listed is not all that important.
I’d go as far to say this is a deprecated entry. Again, if this value if looked-up in the
literature, keep a citation record.

Lbol: The cluster bolometric luminosity. Chandra has a small ﬁeld of view, so if
this is a value best taken from the literature, for example from Homer (2001).

Chip: The CCD on which the cluster center is located. The default is to list the
array on which the observation is taken (I or S), but specifying which chip_id (i.e.
S3 or IO) is left to the user.

E_obs, Diff, Robs: These are deprecated columns which have been left-in be-
cause most scripts were written before they were no longer needed. Forthcoming
versions of CORP will not need these columns.

Location: Sometimes data is stored across multiple volumes, hence this column
speciﬁes the path to each ObsID. For example if one ObsID is stored on /mnt/HD1
and another is on /media/USBI. This allows a single instance of a script to be run
on distributed data.

Great! The data is now out of the archive and into your hands. What are all these
different ﬁles? The answer to that question is lengthy and of fundamental importance
in honing your CIAO-Fu. Read the documentation on data products5’6.

Included in the CORP tarball is a script named d89_viewreg.pl. The script is
very useful for viewing observations quickly and has been invaluable throughout the

years. The program performs a multitude of tasks and relies on the functionality of

 

5 http: / / cxc.harvard.edu / ciao / data / basics.html
6http: / / cxc. harvard.edu / ciao / threads / intro_data /

225

D897. The script header completely explains all the variables and how to use the pro-
gram. Before starting the bulk of data reduction I recommend using d89_viewreg. p1
to determine the Chip and Rmax values for each ObsID and then entering them into

the newref . list ﬁle.

C.3.2 CREATE NEW LEVEL-2 EVENTS FILE

Before completing any true analysis, such as ﬁnding the cluster center or identifying
point sources, the CIAO threads recommend creating a new events ﬁle. Removing
bad grades, time intervals with flares, bad pixels, et cetera ensures that analysis
further downstream is more robust. The initial reprocessing step described here
requires running the script reprocess.p1 with some, but not all, of the internal
switches set to “yes”. Descriptions for the internal switches of this program are in
the code header. The program reprocess.p1 performs multiple tasks and will be
used more than once: In the ﬁrst pass, reprocess .p1 will perform the tasks outlined
below, later it will be used to exclude point sources. For more detail on any of the
steps below, read the CIAO documentation8’9.

First, edit the script so all the options are “yes” and only $exc1ude is equal to
“no”. To run the script, simply call it with PERL giving the reference ﬁle as input
(if you do not want an ObsID analyzed, simply comment it out of the reference ﬁle

by placing a “#” at the front of the line):
[linux]% perl reprocess.p1 reference.1ist

There is no speciﬁc version of PERL required to run CORP. For each ObsID in the
reference ﬁle, a new reprocessed subdirectory has been created and all new ﬁles
have been placed in that directory. The output ﬁles are listed at the end of the script

header. The reduction steps performed by reprocess.pl are: remove the ACIS

 

7http: / / hea-www.harvard.edu / RD / dsQ /
8http: / / cxc.harvard.edu/ ciao / guides / acis.data.html
9http: / / cxc.harva.rd.edu/ ciao/ threads / createL2 /

226

afterglow, create a new bad pixel ﬁle, set ardlib.par, update time—dependent gain
(TGAIN), apply charge transfer inefﬁciency (CTI) correction (if appropriate), ﬁlter
on event grade, ﬁlter on good time intervals (GTIs), destreak, remove background
ﬂares and/ or periods of excessively high background, make blank-Sky background
ﬁle, and make off-axis blank-sky background ﬁle.

Cleaning for ﬂares is a detailed step and is best understood by reading the CIAO
documentation. The main steps in extracting and ﬁltering a light curve are removing
bright sources, setting the time bin size speciﬁc to front or back illuminated CCDS,
setting the energy window for the speciﬁc CCD type, analyzing the light curve using
the contributed routine 1c-c1ean.sl, and ﬁltering out the time periods from the
GTIs which contain high background. All of these steps are handled automatically
by the script, however 1c_c1ean. 31 DOES NOT always ﬁnd the proper background
count rate mean. This results in the beginning or end of ﬂare not being excluded from
the GTIs, while perfectly good intervals are excluded (see Figure C.1 as an example).
The solution to this problem is very simple.

After reprocessing you should examine each light curve anyway, so ﬁnding these

cases will be easy. Run
[linux]% perl view_prof.pl reference.list

with the internal switches set to view lightcurves. If the lightcurve cleaning failed then
there will be no lightcurve to view, in which case run the following script for only
those clusters which experienced a failure (logged in errors.log) by commenting
out all the clusters in reference.list (placing a # at the beginning of the line in

reference. list) which did not fail, then running:

[linux]% idl

IDL) load_ltcrv, ’reference.list’

When you ﬁnd a case where a ﬂare has been improperly removed, estimate the

mean background count rate by ﬁnding the peak in the count rate distribution in

227

the bottom pane of the ﬁgure. Now we’ll create a new ASCII ﬁle which contains

information about this OBSID and it’s ﬂare. The ﬁle should have the format:

#0bsid Mean Rate
2419 1.300

791 0.175

Save this ﬁle, set the $f1arefile keyword in reprocess.p1 to point to this new
ﬁle, and now re—run reprocess.p1 with all other options set to “no” except the
$c1ean_events option which should be “yes”. Examine the new lightcurve and repeat
this process if the mean is not exactly where you think it should be.

Making blank-sky backgrounds is easily the most involved step in reprocess .p1
and to fully understand what is being done, reading Maxim Markevitch’s Cookbook10
in conjunction with the background thread11 are a must.

After reprocess.p1 has ﬁnished running, it is wise to Spend the time examining
all of the output ﬁles. This entails steps such as viewing the evt1, evt2, bgevt,
and clean ﬁles; checking the light curves for missed or improperly excluded ﬂares;
verifying the background ﬁle have the proper exposure times in the headers. If the

data is trustworthy, then move along.

C.3.3 REMOVE POINT SOURCES AND IDENTIFY CLUSTER CENTER

Determining the cluster center and identifying points sources for exclusion is a crucial
step in extended source analysis as these steps signiﬁcantly affect the ﬁnal results.
Reliably determine the cluster center and ﬁnding point sources ﬁrst requires an ex-
posure map. An exposure map is a replication of the optical system’s characteristics
(e.g. CCD quantum efﬁciency, CCD non-uniformitios vignetting, bad pixels, etc.)

dithered and exposed exactly as the observation. The exposure map is used to re-

 

10http: / / cxc.harvard.edu / contrib/ maxim / acisbg /
1 1 http: / / cxc.harvard.edu / ciao/ threads / acisbackground /

228

Lightcurve: 897-1c.fits

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Background Rate (/s)

Figure 0.1 Shown here is an example light curve output by 1c_clean. 31 which is
called when reprocess .pl is run. Top panel: Plot of background count rate versus
time in the observation. Green points mark those time intervals within i20% of the
mean rate. Zero rate bins at the beginning and end of an observation are intentional
dead times. The ﬂares can easily be identiﬁed in this example. Also note that the
automated mean detection did not remove the wings at ~ 5 ksec and ~ 9 ksec of
the weaker ﬂare. Bottom panel: Histogram of the light curve shown in the top panel.
The green line is again for the intervals within :l:20% of the mean rate.

229

move instrumental features, like chip gaps, which will be erroneously detected as point
sources or skew the calculation of the cluster center.

There are two ways of calculating an exposure map: using a monoenergetic in-
cident spectrum or a more speciﬁc spectral model. The script for making exposure
maps can do both, and it is up to the user to determine if one or the other is pre-
ferred for their analysis. For all of the clusters I have analyzed, the monoenergetic
assumption does not give signiﬁcantly different results from the more elegant spectral
model method.

There are many options for making an exposure map and they are explained in

the script header. To make an exposure map, run the script exp_map.p1:
[linux]% perl exp_map.p1 reference.list

The output will be an instrument map, aspect histogram, exposure map, and a nor-
malized image of the cluster (in ﬂux units). The normalized image is what will be
used to ﬁnd point sources and ﬁnd the cluster center. By default, the script makes
a full resolution (binning=1) exposure map. This has the drawback of being time
consuming, but the advantage of more accuracy in spatial analysis. If you are sim-
ply experimenting data, then increase the binning factor to four or eight. I do not
recommend using such highly binned data for analysis unless the cluster center is es-
pecially obvious (i.e. in highly peaked clusters) or you plan on remaking point source
exclusion regions by hand.

Now that you have an exposure map, edit the options in the script cent-emi.p1

and run the script.

[linux]% perl cent_emi.pl reference.list
or

[linux]% perl dub_centroid.pl dub_reference.list

This program will ﬁnd the cluster centroid and peak using the CIAO tool dmstat.

If these two quantities differ by less than 70 kpc, the peak will be returned as the

230

cluster center. The script also outputs a new reference ﬁle with the cluster center in
the RA and Dec columns. Now is the moment to be a researcher: view the clusters
with the center marked, does this solution look right?

After determining if the cluster center ﬁnder worked properly, the next step is
to identify and exclude point sources. The script which does this is find_pt_src .pl
which calls the CIAO tool wavdetect. The primary script output is an ASCII ﬁle

listing the exclusion regions.
[linux]% perl find_pt_src.p1 reference.list

It is very important at this stage to view the observation with the exclusion regions
overlaid. The wavdetect algorithm is very SOphisticated, however it will miss sources
(e.g. sources very close together), detect spurious sources (e.g. chip gaps and edges),
detect sources which are bright, diffuse cluster emission (e.g. the core of a bright,
peaky cluster), and miss sources in regions of high background (6. g. point sources in
or near bright cluster core).

While viewing the observation and regions with d89-viewreg.p1, it is straight
forward to delete, add, and alter regions. After doing so, go to the ’Regions’ menu,
’File Format’ tab, and click ’Ciao’. Then under the ’Regions’ menu click ’Save re-

3

gions... and simply overwrite the loaded <obsid>_exc1ude.reg region ﬁle. That is
all it takes to edit the exclusion regions in a quick, by-eye batch session. Now edit
the script reprocess.p1 so that all options are “no” except for the $exc1ude option
which should be “yes”. Running reprocess.p1 will now remove all the regions you

just saw/ speciﬁed in DSQ.
[linux12 perl reprocess.pl reference.list

The output from this ﬁnal step is the ﬁle <obsid>.exc1ude . fits which is the crown
jewel of CORP: an up-to—date, ﬂare-clean, point source-clean, events ﬁle at level-2. As
usual, you should view this ﬁle and make sure the point source exclusion functioned

as expected. The initial reprocessing steps are now complete, congrats.

231

0.4 INTERMEDIATE ANALYSIS

If at this point you still do not have a temperature for some number of clusters, run

the following script to ﬁnd one:
[linux]% perl find_tx.pl reference.list

This script can also be used to determine redshifts and metallicities. Read the script
header for more detailed instructions on use.

The intermediate analysis steps involve extracting radial proﬁles and spectra from
the observations. These radial proﬁles form the basis for the ﬁnal analysis steps of
the next section. One script, make_profile.p1, extracts both a cumulative counts
proﬁle and a surface brightness proﬁle. In the options section of the script you specify
the size of the annular bins used to extract the proﬁles. For the cumulative counts
proﬁle I recommend 2 pixel width bins, and either 5 pixel or 10 pixel width bins for
the surface brightness proﬁles. For the surface brightness proﬁles you also need to
specify the energy range for the extraction. There are many other options for this

script which are detailed in the program header.

[linux]% perl make_profile.pl reference.1ist
or

[linux]% perl make_mu1tiprof.p1 dub_reference.list

Depending on the number of counts in the observation, this step can take a few
minutes or a few hours. The script also outputs plots of the two proﬁles which should
be viewed to ensure everything ran correctly.

Now run the script exp_corr . p1 which extracts a radial proﬁle from the exposure
map and will be used for exposure correcting radial proﬁles later on. As usual, set
the options in the header, speciﬁcally the bin size of the proﬁle to extract. The bin
size needs to match that of the surface brightness proﬁle just extracted. It is possible

to extract multiple exposure proﬁles since the bin size is amended to the output ﬁle

232

name. This step is fast, so extracting proﬁle for bin sizes of 5, 10, or 20 pixels does

not take long.

[linux]% perl exp_corr.pl reference.1ist

OI‘

[linux12 perl multiexp_corr.p1 dub_reference.1ist

With the cumulative proﬁle, it is now possible to create annuli for the temperature
proﬁle. The script make_annuli_reg. pro is used to make the annuli. The cumulative
proﬁle is divided up into annular bins containing a minimum number of counts and
then these bins are output as region ﬁles later used to extract spectra. The entries
in the ’Mincts’ column of the reference ﬁle are used to set the minimum number of
counts. I typically run the script with all options set to “no” (meaning only mock
regions are produced) and view the output plot to ensure the number and spacing
of the bins is appropriate for the cluster in question. What is appropriate? Well,
too many closely spaced annuli for a symmetric peaked cluster is redundant, and too
few widely spaced annuli for a complex cluster is insufﬁcient, unless of course there
are not enough counts to produce more bins. After ensuring the number of annuli
produced is agreeable, run the script with the options set to “yes”. WARNING:
by default, the script deletes all annuli and associated spectral ﬁles. If you run this
script after having extracted spectra, be sure to set mkbackup to “yes” AND provide
the path to a valid, existing back-up directory, bkdir, this will save those existing

spectra.

[linux]% idl
IDL> make_annuli_reg, ’reference.1ist’
or

IDL> make-mu1tiannuli_reg, ’reference.list’

A whole ensemble of individual region ﬁles with the speciﬁed name will be output

by this script. With these region ﬁles extracting spectra is straightforward, simply

233

run the script extractspectrapl. This script has a number of important options

which are detailed in the script header.
[linux]% perl extract_spectra.p1 reference.list

If there have been no errors, then you should have radial proﬁles and spectra for

each ObsID in the reference ﬁle, congratulations.

(3.5 FINAL ANALYSIS

The ﬁnal steps in the analysis process are normalizing the background spectra for dif-
ferences between the blank-sky background and observation background hard-particle
count rates, extracting and ﬁtting residual spectra for the local soft background, ﬁt-
ting the cluster Spectra, and running the master IDL routine that produces entropy
proﬁles. An explanation of why and how background adjustments are made is pre-

sented in Chapter 2.

C.5.1 SPECTRAL ADJUSTMENTS AND FITTING

The hard-particle background is changing as a function of time. Thus, the strength
of this background component for the epoch in which the blank-sky backgrounds
were taken will be different from when the observations were taken. The ﬁrst step
in accounting for this difference involves running the script bgd_ratio.p1 which will

output the ratio of observation to blank-sky 9.5-12.0 keV count rates.
[linux]% perl bgd_ratio.p1 reference list

The script outputs a ﬁle containing these ratios. Keep this ﬁle someplace which is
easily accessible as a later script will be querying this list to normalize the spectra.
To account for the spatially varying Galactic soft-component you must extract

soft-residuals. Soft-residuals are the leftovers of subtracting a blank-sky spectrum

234

from an observation spectrum both extracted from the same part of the sky and far
from the cluster emission. The ﬁrst step is to clean-up the off-axis observation chips
of all point and diffuse sources. This step can be performed blind because if too many

sources are removed it does not matter.
[linux]% perl addbg_rm_pt_src.pl reference.list

The soft-residual spectra are output from this script.
Prior to ﬁtting any spectra all background spectra need to be normalized. This
is done quickly by specifying the names of the spectra to be normalized in the script

adj _backsca1.p1 and then running it.
[linux]% perl adj_backscal.pl reference.list

Normalization is applied by adjusting the header keyword BACKSCAL in the spectrum.
The BACKSCAL keyword is related to the ﬁnal background subtracted spectrum of an

observation by

SRCcts _ BGDcts . 1
SRCemp BGDexp BGDscal . SRCSCGI

 

 

where the abbreviations ‘SRC’ —-+ source, ‘BGD’ —-> background, ‘ctr’ —I count rate,
‘cts’ —> counts, ‘exp’ —> exposure time, and ‘scal’ —> BACKSCAL. The BACKSCAL keyword
is deﬁned as the detector area over which the spectrum was extracted, divided by the
total detector area. Adjustment of the blank—sky background BACKSCAL value follows
directly from the above equation by multiplying the existing value of BACKSCAL by a
correction factor, n, which is related to the ratio of the count rate in the 9.5-12.0 keV

range of the observation to the blank-Sky background by

’7 “ BGDct. '

235

Each background spectrum is copied into a new ﬁle before this correction is applied
so that reversal at a later date is possible.

Now that the spectra are all adjusted, the ﬁtting can begin. There are a large
number of options in spectral ﬁtting and these are detailed in the individual script’s
header. In addition, interpreting the results of the ﬁtting requires more discussion
than is useful here. The order in which ﬁtting is done is important since the master

spectral ﬁtting routines need output from the ﬁtting of the soft-residuals.

[linux]% perl fit_sofex.p1 reference.list (spectral model>
[linux]% perl fit_projected.p1 reference.1ist <spectral model>
or

[linuxJX perl fit_simu1ta.pl dub_reference.list <spectra1 model>

The output of these scripts are data tables with the spectral ﬁts for each annulus asso-
ciated with each ObsID. With radial proﬁles in-hand and spectral analysis complete,

it is now possible to calculate many more physical properties of a cluster.

0.5.2 GENERATING ENTROPY PROFILES

So here it is, the end of a long journey. Your CIAO-Fu is good, congratulations.
The master program which performs the deprojection, derives electron gas density,
pressure, entropy, mass (not to be trusted), and cooling time is kfitter.pro. This
program has a handler program run_kf it .pro which makes batch analysis simpler.
These programs have their own README ﬁles which have not been duplicated here.
After running kfitter.pro you will have a suite of data tables and plots for each
cluster which are publication ready. If desired, I have a whole suite of IDL programs
to offer which perform additional analysis, output many more plots, and handle odds-

n-ends type tasks like making web pages.

236

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237

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