UNLV Retrospective Theses & Dissertations
1-1-1998
A study of x-ray substructure in rich clusters of galaxies
Philip Leroy Rogers University of Nevada, Las Vegas
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Repository Citation Rogers, Philip Leroy, "A study of x-ray substructure in rich clusters of galaxies" (1998). UNLV Retrospective Theses & Dissertations. 895. http://dx.doi.org/10.25669/8q3w-3m3y
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A STUDY OF X-RAY SUBSTRUCTURE
IN RICH CLUSTERS OF
GALAXIES
bv
Philip L. Rogers, Jr.
Bachelor of Science University o f Nevada, Reno 1993
A thesis submitted in partial fulfillment of the requirements for the degree of
Master o f Science
in
Physics
Department of Physics University of Nevada, Las Vegas August 1998
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UNiy Thesis Approval UNiy The Graduate College University of Nevada, Las Vegas
Ju ly 24
The Thesis prepared by P h ilip L. R ogers, J r.
Entitled A Strudy of X-Ray Substructure in Rich Clusters of Galaxies
is approved in partial fulfillment of the requirements for the degree of
Master of Science in Physics
Examination Committee Chair
Dean oftheC raluate College /
Exanunation Camintitee MenMember
Graduate College Faculty Representative
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT
A Study of X-tay Substructure in Rich Clusters of Galaxies
by
Philip L. Rogers, Jr.
Dr. George Rhee, Examination Committee Chair Professor of Physics University of Nevada, Las Vegas
comparison of three tests to determine substructure in rich Abell clusters of galaxies was
preformed and the results are presented in this paper. The data used are ROSAT PSPC X-ray
images of a sample of 21 clusters drawn from the ACO catalog, and a subset of the ESO
Nearby Abell Cluster Survey done by Katgert et. aL The three methods used are: the ‘center
shift* method developed by Mohr et aL, the ‘moment* method developed by Buote & Tsai, and
a wavelet analysis developed by Starck et aL. Models were then created to check the
significance of our findings. The conclusions reached were that substructure and cooling flows
are present in at least 50% of our sample. In addition, although it is possible to get a generally
accurate result using only one of the above methods, the use of a multi-pronged analysis
approach to achieve maximum accuracy is desirable.
u
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS
ABSTRACT...... ü
UST OF FIGURES...... iv
ACKNOWLEDGMENTS...... v
CHAPTER 1 INTRODUCTION...... 1
CHAPTER 2 TH E DATA...... 6
CHAPTER 3 TFIE METHODS...... 11 3.1 Moment Method ...... 11 3.2 Center Shift M ethod ...... 13 3.3 Wavelet Transform Method ...... 15
CHAPTER 4 TH E MODELS...... 17
CHAPTER 5 THE RESULTS...... 20 5.1 Abell 133 Results...... 20 5.2 Abell 514 Results...... 21 5.3 Abell 2052 Results...... 22
CHAPTER 6 CONCLUSIONS...... 25
APPENDIX A TABLES...... 30
APPENDIX B FIGURES...... 35
BIBLIOGRAPHY...... 183
VITA...... 185
m
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES
Figure 1. Cluster Classification Chart...... 4 Figure 2. Energy Spectrum for Coma Cluster ...... 8 Figure 3. Cleaned Image for Abell 85 ...... 36 Figure 4. Contour Map for Abell 85 ...... 37 Figure 5. Wavelet Transform Images for Abell 85 ...... 38 Figure 6. Histogram for P3 Moments for Abell 85 Models ...... 39 Figure 7. Histogram for P4 Moments for Abell 85 Models ...... 40 Figure 8. Sigma Significance Plot for Abell 85 ...... 41 Figure 9. Total Shift Plot for Abell 85 ...... 42 Figure 10. Cleaned Image for Abell 119 ...... 43 Figure 11. Contour Map for Abell 119 ...... 44 Figure 12. Wavelet Transform Images for Abell 119 ...... 45 Figure 13. Histogram for P3 Moments for Abell 119 Models ...... 46 Figure 14. Histogram for P4 Moments for Abell 119 Models ...... 47 Figure 15. Sigma Significance Plot for Abell 119 ...... 48 Figure 16. Total Shift Plot for Abell 119 ...... 49 Figure 17. Cleaned Image for Abell 133 ...... 50 Figure 18. Contour Map for Abell 133 ...... 51 Figure 19. Wavelet Transform Images for Abell 133 ...... 52 Figure 20. Histogram for P3 Moments for Abell 133 Models ...... 53 Figure 21. Histogram for P4 Moments for Abell 133 Models ...... 54 Figure 22. Sigma Significance Plot for Abell 133 ...... 55 Figure 23. Total Shift Plot for Abell 133 ...... 56 Figure 24. Cleaned Image for Abell 496...... 57 Figure 25. Contour Map for Abell 496 ...... 58 Figure 26. Wavelet Transform Images for Abell 496 ...... 59 Figure 27. Histogram for P3 Moments for Abell 496 Models ...... 60 Figure 28. Histogram for P4 Moments for Abell 496 Models ...... 61 Figure 29. Sigma Significance Plot for Abell 496 ...... 62 Figure 30. Total Shift Plot for Abell 496 ...... 63 Figure 31. Cleaned Image for Abell 500 ...... 64 Figure 32. Contour Map for Abell 500 ...... 65 Figure 33. Wavelet Transform Images for Abell 500 ...... 66 Figure 34. Histogram for P3 Moments for Abell 500 Models ...... 67 Figure 35. Histogram for P4 Moments for Abell 500 Models ...... 68 Figure 36. Sigma Significance Plot for Abell 500 ...... 69 Figure 37. Total Shift Plot for Abell 500 ...... 70
IV
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 38. Cleaned Image for Abell 514 ...... 71 Figure 39. Contour Map for Abell 514 ...... 72 Figure 40. Wavelet Transform Images for Abell 514 ...... 73 Figure 41. Histogram for P3 Moments for Abell 514 Models ...... 74 Figure 42. Histogram for P4 Moments for Abell 514 Models ...... 75 Figure 43. Sigma Significance Plot for Abell 514 ...... 76 Figure 44. Total Shift Plot for Abell 514 ...... 77 Figure 45. Cleaned Image for Abell 754 ...... 78 Figure 46. Contour Map for Abell 754 ...... 79 Figure 47. Wavelet Transform Images for Abell 754 ...... 80 Figure 48. Histogram for P3 Moments for Abell 754 Models ...... 81 Figure 49. Histogram for P4 Moments for Abell 754 Models ...... 82 Figure 50. Sigma Significance Plot for Abell 754 ...... 83 Figure 51. Total Shift Plot for Abell 754 ...... 84 Figure 52. Cleaned Image for Abell 2052 ...... 85 Figure 53. Contour Map for Abell 2052 ...... 86 Figure 54. Wavelet Transform Images for Abell 2052 ...... 87 Figure 55. Histogram for P3 Moments for Abell 2052 Models ...... 88 Figure 56. Histogram for P4 Moments for Abell 2052 Models ...... 89 Figure 57. Sigma Significance Plot for Abell 2052 ...... 90 Figure 58. Total Shift Plot for AbeU 2052 ...... 91 Figure 59. Cleaned Image for Abell 2382 ...... 92 Figure 60. Contour Map for Abell 2382 ...... 93 Figure 61. Wavelet Transform Images for Abell 2382 ...... 94 Figure 62. Histogram for P3 Moments for Abell 2382 Models ...... 95 Figure 63. Histogram for P4 Moments for Abell 2382 Models ...... 96 Figure 64. Sigma Significance Plot for Abell 2382 ...... 97 Figure 65. Total Shift Plot for Abell 2382 ...... 98 Figure 66. Cleaned Image for Abell 2717 ...... 99 Figure 67. Contour Map for Abell 2717 ...... 100 Figure 68. Wavelet Transform Images for Abell 2717 ...... 101 Figure 69. Histogram for P3 Moments for Abell 2717 Models ...... 102 Figure 70. Histogram for P4 Moments for Abell 2717 Models ...... 103 Figure 71. Sigma Significance Plot for Abell 2717 ...... 104 Figure 72. Total Shift Plot for Abell 2717 ...... 105 Figure 73. Cleaned Image for Abell 2734 ...... 106 Figure 74. Contour Map for Abell 2734 ...... 107 Figure 75. Wavelet Transform Images for Abell 2734 ...... 108 Figure 76. Histogram for P3 Moments for Abell 2734 Models ...... 109 Figure 77. Histogram for P4 Moments for Abell 2734 Models ...... 110 Figure 78. Sigma Significance Plot for Abell 2734 ...... 111 Figure 79. Total Shift Plot for Abell 2734 ...... 112 Figure 80. Cleaned Image for Abell 3111 ...... 113 Figure 81. Contour Map for Abell 3111 ...... 114 Figure 82. Wavelet Transform Images for Abell 3111 ...... 115 Figure 83. Histogram for P3 Moments for Abell 3111 Models ...... 116 Figure 84. Histogram for P4 Moments for Abell 3111 Models ...... 117
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VI
Figure 85. Sigma Significance Plot for Abell 3111 ...... 118 Figure 86. Total Shift Plot for Abell 3111 ...... 119 Figure 87. Cleaned Image for Abell 3112 ...... 120 Figure 88. Contour Map for Abell 3112 ...... 121 Figure 89. Wavelet Transform Images for AbeU 3112 ...... 122 Figure 90. Histogram for P3 Moments for Abell 3112 Models ...... 123 Figure 91. Histogram for P4 Moments for Abell 3112 Models ...... 124 Figure 92. Sigma Significance Plot for Abell 3112 ...... 125 Figure 93. Total Shift Plot for AbeU 3112 ...... 126 Figure 94. Cleaned Image for AbeU 3158 ...... 127 Figure 95. Contour Map for AbeU 3158 ...... 128 Figure 96. Wavelet Transform Im ^es for AbeU 3158 ...... 129 Figure 97. Histogram for P3 Moments for AbeU 3158 Models ...... 130 Figure 98. Histogram for P4 Moments for AbeU 3158 Models ...... 131 Figure 99. Sigma Significance Plot for AbeU 3158 ...... 132 Figure 00. Total Shift Plot for AbeU 3158 ...... 133 Figure 01. Cleaned Image for AbeU 3266 ...... 134 Figure 02. Contour Map for AbeU 3266 ...... 135 Figure 03. Wavelet Transform Images for AbeU 3266 ...... 136 Figure 04. Histogram for P3 Moments for AbeU 3266 Models ...... 137 Figure 05. Flistogram for P4 Moments for AbeU 3266 Models ...... 138 Figure 06. Sigma Significance Plot for AbeU 3266 ...... 139 Figure 07. Total Shift Plot for AbeU 3266 ...... 140 Figure 08. Cleaned Image for AbeU 3558 ...... 141 Figure 09. Contour Map for AbeU 3558 ...... 142 Figure 10. Wavelet Transform Images for AbeU 3558 ...... 143 Figure 11. Flistogram for P3 Moments for AbeU 3558 Models ...... 144 Figure 12. Histogram for P4 Moments for AbeU 3558 Models ...... 145 Figure 13. Sigma Significance Plot for AbeU 3558 ...... 146 Figure 14. Total Shift Plot for AbeU 3558 ...... 147 Figure 15. Cleaned Image for AbeU 3562 ...... 148 Figure 16. Contour Map for AbeU 3562 ...... 149 Figure 17. Wavelet Transform Images for AbeU 3562 ...... 150 Figure 18. Histogram for P3 Moments for AbeU 3562 Models ...... 151 Figure 19. Histogram for P4 Moments for AbeU 3562 Models ...... 152 Figure 20. Sigma Significance Plot for AbeU 3562 ...... 153 Figure 21. Total Shift Plot for AbeU 3562 ...... 154 Figure 22. Cleaned Image for AbeU 3667 ...... 155 Figure 23. Contour Map for AbeU 3667 ...... 156 Figure 24. Wavelet Transform Images for AbeU 3667 ...... 157 Figure 25. Histogram for P3 Moments for AbeU 3667 Models ...... 158 Figure 26. Histogram for P4 Moments for AbeU 3667 Models ...... 159 Figure 27. Sigma Significance Plot for AbeU 3667 ...... 160 Figure 28. Total Shift Plot for AbeU 3667 ...... 161 Figure 29. Cleaned Image for AbeU 3897 ...... 162 Figure 30. Contour Map for AbeU 3897 ...... 163 Figure 31. Wavelet Transform Images for AbeU 3897 ...... 164
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vu
Figure 132. Histogram .for P3 Moments for AbeU 3897 Models ...... 165 Figure 133. Histogram .for P4 Moments for AbeU 3897 Models ...... 166 Figure 134. Sigma Significance Plot for AbeU 3897 ...... 167 Figure 135. Total Shift Plot for AbeU 3897...... 168 Figure 136. Cleaned Image for AbeU 4038 ...... 169 Figure 137. Contour Map for AbeU 4038 ...... 170 Figure 138. Wavelet Transform Images for AbeU 4038 ...... 171 Figure 139. Histogram for P3 Moments for AbeU 4038 Models ...... 172 Figure 140. Histogram for P4 Moments for AbeU 4038 Models ...... 173 Figure 141. Sigma Significance Plot for AbeU 4038 ...... 174 Figure 142. Total Shift Plot for AbeU 4038...... 175 Figure 143. Cleaned Image for AbeU 4059 ...... 176 Figure 144. Contour Map for AbeU 4059 ...... 177 Figure 145. Wavelet Transform Images for AbeU 4059 ...... 178 Figure 146. Histogram for P3 Moments for AbeU 4059 Models ...... 179 Figure 147. Histogram for P4 Moments for AbeU 4059 Models ...... 180 Figure 148. Sigma Significance Plot for AbeU 4059 ...... 181 Figure 149. Total Shift Plot for AbeU 4059...... 182
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS
I would like to rhank NASA for partially supporting this research through the Nevada
Space Grant Consortium.
I would like to thank Dr. George Rhee, whose guidance, knowledge and enthusiasm have
made this project both educational and enjoyable. It is also a pleasure to thank S. Lepp, L.
Spight, and D. Weistrop for their insightful suggestions and support during this project.
I would like to express my gratitude to my fiiends and compatriots S. Cruzen, D. Eggers, J.
Kilburg, D. Carrol, T. Rennie, J. Opfer, K. Eddy, G. Budai, T. Colegrove, M. Rodrigue, and S.
Mitchell. I have found their patience and sometimes not so subtle hints to be invaluable.
Lastly and most importantly, I want to thank my wife, Alison, and my parents, Philip Sr.
and Bessie, to whom 1 dedicate this work. Without their love and guidance, I would be a much
lesser person.
viu
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 1
INTRODUCTION
One of the greatest quests in cosmology is the search for the value of Q , known as the
cosmological density parameter. O is defined as the ratio of p ^ the observed or measured
density of the universe, to p ^ , the critical density of the universe, so called because it is the
density needed to make the universe just closed. The knowledge of its value holds the key to
the mystery of the ultimate fate o f the cosmos. A value o f Q less than 1 would indicate that
the observed density of the universe is less than the critical density, meaning that there is not
enough matter in the universe to overcome the current acceleration. This would lead to an
open universe, which would continue to expand forever. O n the other hand, if the value of Q
were greater than 1 the observed density of imiverse would be more than the critical density.
This would indicate that there is enough matter in the universe to overcome the its current
acceleration, making the universe closed. In this case the universe would eventually begin to
contract and continue to do so until it reached a singularity of infinite density. Many methods
can be used to determine the limits of Q . One of these is the smdy of substructure in rich
clusters o f galaxies. The reasoning is that we currendy believe galaxy clusters form by a process
known as “violent relaxation”, a process that tends to erase substructure by dynamical
evolution. If we take this as given, then the observation o f substructure in galaxy clusters may
indicate that the clusters are still in the early stages of vinalizadon. This is an idea we can use to
probe the value of Q . 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. It has been held for many years that the ftequency of substructure in galaxy clusters can
lead to determining the lower limit o f Q (Richstone, Loeb & Turner 1992; Kaufftnann &
White 1993; Lacey & Cole 1993). To make sense of this statement we need to look a little
closer at the scenario. Imagine the value o f Q is low. If this is so then large structures such as
rich galaxy clusters must form early in time, before expansion could overcome the local
gravitational attraction. This being the case we would expect to find most clusters in a
virialized or relaxed state because the universe is sufficiently old for m ost o f the matter on the
cluster size scale to have smoothed out. O n the other hand, if the value of Q is high, than the
density o f the universe is sufficient to allow galaxy cluster formation into the present era. In
other words, on the large scale there is still enough matter close together to interact and form
clusters. If we accept the latter as the case, we would expect to see some substructure in at
least a few still forming galaxy clusters. In fact, recent observations support the latter view,
suggesting 30% - 50% of galaxy clusters show at least some evidence o f substructure either
optically or in their plasma distributions (Geller & Beers 1982; Dressier & Shectman 1988;
Mohr, Frabticant & Geller 1993; Salvador-Sole, Sanroma & Gonzalez-Casado 1993; Bird 1994;
Escalera et aL 1994; West et al. 1994).
Rich galaxy clusters are typically groups of hundreds or thousands of galaxies bound
together by their mutual gravitation. O n average they have a diameter o f about 3 Mpc. Using
the virial theorem and independent velocity dispersions it has been found that they can contain
upwards of several times 10'^ solar masses. Given the current interpretation o f general
relativity, each cluster contains three components of mass. Firstly, there is the mass associated
with the emitted light we see firom the individual galaxies, which amounts to less than 10% of
the total mass. Secondly, there is the mass associated with the hot intracluster plasma, which
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. amounts to perhaps 20% of the total mass. Lastly, there is the component associated with the
remaining bulk of the mass which is, non-luminous, and referred to as “Dark Matter”.
In general, clusters are characterized by their redshifts, velocity dispersions and apparent
morphologies. There is a wide range of accepted morphological classification schemes.
However for brevity we shall adopt two for this work. The Bautz and Morgan(1970) system
will be used for all the clusters, as well as the revised Rood-Sastry(1971) system from Struble
and Rood(1982) for the southern clusters and those clusters far enough north to have been
classified in this scheme.
The Bautz-Morgan system uses three main classifications or types and adds two other
categories that are merely combinations of the three main types. The types are defined as
follows:
Type I : Clusters dominated by a single bright central cD galaxy.
Type II: Clusters whose brightest galaxies are intermediate between cD and giant ellipticals.
Type III: Clusters that have no dominating cluster galaxies.
Type I - II and II - III: are clusters that are intermediates.
The Rood-Sastry system is defined as follows:
cD: the cluster is dominated by a central cD or cluster dominant galaxy.
B: binary — the cluster is dominated by a pair of luminous galaxies.
L: line - at least three o f the brightest galaxies appear to be in a straight line.
C: core - four or more of the ten brightest galaxies form a cluster core, with comparable separations.
F: flat — the brightest galaxies form a flattened distribution on the sky.
I: irregular — the distribution of brightest galaxies is irregular with no obvious center or core.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Cluster Classifications
•ü-.-.'
cD
Figure 1. Revised R.S. Cluster classifications firom Struble and Rood(1982).
The Rood-Sastry classifications are not the easiest to visualize so figure 1 is supplied for
clarification.
For our purposes the intracluster plasma is the prime concern, so lets look at it in more
detail. This plasma ranges in temperature from 10^ K to about 10® K, with a density of % 10^
atoms/cm^. It is comprised mosdy of hydrogen and helium but also contains traces of iron
and other heavy elements that have been stripped from the constituent galaxies by ram
pressure due to dynamical faction. This hot gas gives off emissions in the X-ray spectrum due
to bremsstrahlung. This is caused by relativistic electrons emitting “breaking radiation” due to
changes in the magnitudes of their acceleration when they interact with other ions. Because a
plasma consists of ions, its emission is proportional to the density squared. The firee-firee
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. etnissivity o f a plasma with an electron temperature a frequency V and an ion charge of Z
can be expressed as follows
1/2 2 ^ T js ^ ( 2 k ^ hu er. = Z=n,n,g,.(z,7-,,u)xr;''=exp 3m^c
Here n,, and n, are the number densities of electrons and ions, and (Z, , u) is the gaunt
factor. This factor corrects for quantum mechanical effects and distant collisions. This reliance
on the density squared makes the clusters stand out from the background radiation more
prominently than clusters in the optical range. Thus it is possible to see the plasma
distributions of many more clusters at greater distances using X-rays than it is to see the galaxy
distributions of the same clusters in optical wavelengths. Obviously, this advantage can be used
to produce a larger and more complete cluster sample, which is exactly the type of sample we
want in order to give us a more accurate measure of substructure in the universe.
With the above in m ind this project was taken on with the intent of answering three
important questions.
1) How do the three analysis programs used in this survey compare?
2) What is the prevalence of substructure in rich clusters of galaxies?
3) What are the implications of this result concerning the value of Q ?
In chapter 2 ,1 discuss the data selection and processing. In chapter 3, the three methods of
analysis are covered. Chapter 4 contains the details of the models used to calculate errors and
significance. Chapter 5 contains a detailed description of the results for 3 of the 21 clusters.
Finally, in chapter 6, there is a discussion of the general results and their relevance to our
search.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 2
TH E DATA
The sample of clusters was drawn from the ESO Nearby Abell Cluster Survey, or ENACS
for short, (Katgert et al 1994). This sample was chosen because the ENACS group’s
motivation was to compile a more complete redshift database for Abell clusters with richness
greater than 1 out to a redshift of approximately 0.1 than was previously available. The Abell
catalog was chosen because it uses a more stringent cluster definition than the other major
catalogs. To be defined as a rich cluster in the Abell or ACO (Abell, Corwin & Olowin 1989)
catalog, a cluster has to have > 50 galaxies within 2 magnitudes of the 3“* brightest galaxy lying
within 3 Mpc of the observed cluster center. The importance of using rich clusters of galaxies
is that due to their size and mass they have long been known to be objects that ran provide
data on the physics of large-scale structure formation. The ESO survey was done for all
clusters meeting the above criteria in a solid angle of 2.55 sr about the South Galactic Pole,
resulting in a database containing 107 clusters. In short, this should provided us with a
complete and unbiased database of rich Abell clusters from which to draw our sample.
It then had to be decided which X-ray satellite archive to use, ROSAT or the Einstein
Observatory. The ROSAT PSPC (Position Sensitive Proportional Counter) has a field of
view of 2° and an energy resolution of 43% at 0.93 KeV with an on-axis resolution of
about 25” at IKev out to 20’ from the center. This distance of 20’ is sufficient to include
the entire cluster X-ray morphology for all our data fram es. The Einstein Observatory’s
6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7
IPC (Image Proportional Counter) has a field of view of about 1 ° and a spatial resolution
of only 1.7’at Full Width Half Maximum. It was concluded that for the purposes of
observing subde changes in the cluster plasma the ROSAT PSPC was the best instrument
to use.
X-ray photons are of such high energy that they cannot be collected in the same fashion as
are photons in optical wavelengths. These photons have a distinct tendency to be absorbed
rather than reflected. In order to reflect target photons the X-ray telescope aboard ROSAT
uses a method of collection called grazing incidence. At energies < 2 KeV the incoming x-ray
photons can be reflected off composite metal surfeces when their angle of incidence
approaches unity. The X-ray telescope uses just such optics in an arrangement called a Wolter
t)^pe I telescope, which uses a combination o f annular sections of parabolic mirrors as grazing
incidence reflectors. Several of these systems are arranged concentrically in a nested
configuration to increase the sensitivity of the system A position sensitive detector is then
placed at the focal plane to produce high resolution images limited only by irregularities in the
mirrors. The drawback of this type of apparatus is that it only allows observations o f cluster
plasmas with temperatures less rhan 2.4 keV. We know from cluster dynamics that cluster
plasma temperatures can reach upwards of 30 keV in some cases. To convince ourselves that
the 2.4 keV limit will still suit our needs let us look at the above figure 2. Taking into account
that the Coma cluster is one of the better studied clusters and assuming it as an average cluster
representative it can be clearly seen the predominant emissions are due to temperatures in the
2-5 keV range, with the 2-3 keV range making up most of the photon counts in this area of the
curve. Thus for our purposes, the 2.4 keV limit is a sufficient range to detect substructure.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Energy Spectrum for the Coma Cluster
-0
-2
uI s OJI uE -3 cn z I XQ. -4
-5
1 2 3 4 5 6 9 10 12 16 20 30 40 50 60 80 100 14 18 ENERGY (keV)
Figure 2. HF.AO-1 A-2 low resolution X-ray spectrum of the Coma cluster. The plot gives
the number flux of X-ray photons per cm^-sec-keV versus photon energy in keV(Henriksen
and Mushotzky, 1986).
The ROSAT archive was scanned for all the observed and archived Abell clusters that
were common to both lists. In all, 44 clusters were found in the ROSAT archive that were
also in the ENACS survey. For each cluster there are three data frames available. A soft
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. band image from 0.07 — 0.4 keV, a hard band image from 0.4 - 2.4 keV and a total band
image which is comprised of both images together. It was decided to download only the
hardband (0.4 - 2.4 KeV) images of the clusters because this energy range is high enough
to minimise distortions due to the point spread function from the PSPC. It also reduces
the contamination effects from the X-ray background known to occur in the lower end of
the X-ray spectrum. After an initial examination of the data, 23 of the frames had to be
discarded. Seven of the frames were discarded due to misalignment of the instrument. This
misalignment either caused the clusters to appear at the edge of the frame, where the
distortions of the detector are greatest, or under the support structure, where it was
unobservable. The other sixteen frames were unusable because the exposure times were
too short to show any subde plasma structure, thus m aking it impossible to tun our
substructure analysis programs. This left us with a total of 21 usable cluster data frames
(Table 1 page 39).
These rem aining data frames were processed in the following manner. Firsdy, they were
divided by their exposure maps, which were also provided by the ROSAT archive. This
was done to correct for exposure variations and instrument vignetting. Secondly, they
were multiplied by their exposure times so that the final image was in the form of counts.
Thirdly, they were filtered using a program supplied by Starck et al. that uses a bspline
wavelet transform to reduce overall image noise, essentially smoothing the image. Lastiy,
they were cleaned of point sources. Each image was visually inspected for “obvious” point
source contamination that occurred outside the central plasma source. The sources were
checked to see if their FWHM was comparable to that of point sources imaged by the
PSPC. Unresolved sources were removed using the imedit program in the TV package of
IRAF. Briefly, what imedit does is replace what is in a user defined circle with the average
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10
counts contained in an annulus placed at a specific radius which is also defined by the user.
We identified point sources by eye because automated methods tended to identify and
correct “point sources” inside the central plasma structure. Although this is a plausible
place to find point source contamination, the automated corrections caused distortions in
the portion of the plasma structure in which we hoped to find subde changes. Point
sources near or in the center of the cluster cores were deleted using the fixpix program in
the PROTO package of IRAF. This gave substantially better results than the imedit
program that was used for the oudying point sources.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTERS
THE NETHODS
In this section, I discuss the three methods that were used to analyze the data, the
‘Center shift’ method, the ‘moment’ method, and the wavelet transform method. These
three very different methods were chosen in the hope that they would complement each
other and give a more complete picture of the amount and type of substructure in Abell
clusters.
3.1 Moment Method
The first method that will be discussed is what I refer to as the ‘moment’ method
developed and supplied by Buote and Tsai (1995). The main idea of this method is to be
able to quantitatively classify cluster morphologies in direct relation to their dynamical
state as indicated by the gravitational potential (Buote and Tsai 1995). The most natural
way to accomplish this is to use a two-dimensional muldpole expansion of the projected
gravitational potential. If we let Z(/2,^) be the two dimensional projection of the mass
density then we can write the two dimensional potential 4^(1?, ^) , as:
V^^{R,) = A7 cGL{R,(I>)
with G being the gravitational constant.. Using Green’s functions it can be shown that the
potential due to the material interior to R is given by:
'P(i?,^) = -2G qq In — - 2 G ^ cosm
11
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where a„, and b„, are the “Moments” of interest. They can be expressed in the following
wav:
c o sm ÿ 'j x'
b.= L,nx'XR')-smm^’d^x'
with x ’ = . 'P does not represent the total gravitational potential since the equation
fails to account for the mass exterior to R. However we are only concerned with the
gravitational effects of the mass interior to R.
It is clear from the above equations that we can consider as many moments as we like.
For our purposes we only concern ourselves with m =l, 2, 3, and 4, as higher order terms
reflect smaller scales which are dynamically less significant It is also clear that R is as yet
undefined. The fact that our clusters are centrally positioned on our data frames leaves
very little distance between their apparent edge and the ROSAT support spider. For this
reason we limited R to a single value of 1 Mpc referred to as R,p our radius aperture. This
places our boundary of interest just inside the support structure, leaving plenty of room to
search for substructure but ignoring the area underneath and around the support structure
where any source information can be either screened or distorted.
Another small problem to be dealt with is that the m >l terms of the equation for
vanish when integrated over (ft. This forces us to consider only the magnitude of
the terms for each order integrated over <(>. If we let 'Pm be the m'*' term of the multipole
expansion for 4* we can define the following quantity:
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Such that only terms for m= m ' are non-vanishing. This means P„ = measures the
‘power’ interior to for the terms of order m. If we ignore the factors of 2G, these
values are given by, Pq = [ûg InG/ ^ap)Ÿ for m=0 and p»» _ n 1 2 n 2m / ' ; m + ft M m / for values
of m>0. The total ‘power’ of all the moments would then be given by p - p . « «0
Therefore, the ratio of P„, to P reflects the contribution of the m* moment to the ‘power’
of the total potential interior to R^. Knowing that the gravitational potential is precisely
related to the dynamical state of the cluster, the P^’s are the substructure measures we are
looking for.
This can be put in a graphical sense in the following way. Let’s look at the T‘ moment,
which would look something like an 8 or oo. If this pattern is placed over the center of the
cluster and we add up the counts in each ear and subtract one from the other, any value
greater than 0 indicates the presence of substructure. The higher the number, the greater
the power of the substructure! This thought analysis can be extended to any of the
moments by simply adding another figure 8 overlapped at the center for each additional
moment.
3.2 Center Shift Method
The second method is the ‘center shift’ method developed and supplied by Mohr et
al.(1993). This program is also based on measuring the low order moments of a cluster.
However with this method we find the 1“ moment M,(r ), axial ratio and ellipsoidal
orientation angle 0i{r) at several different radii for each cluster. To make the
measurements we need to choose an initial radius and width for our annulus and find the
proper place to locate it on our data frame. For our purposes, we chose an initial radius o f
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2 pixels and an annulus of 2 pixels with each pixel having a value of 15”. We next Founer
expand the section of the image I{6,F) that lies within the annulus so that we can
determine the coefficient C ,, defined in the following expansion as
?C„(F) cos [/w0 - ot 0„(F)] m=0
with m ^ being the highest calculated harmonic. Next the location of the annulus on the
data frame is varied. This is repeated until we minimize C, . By minimizing C, we can find
the center of the image. However in order to save cpu time, the center values obtained
from the ‘moment’ method were used as starting values. With this done, the Founer
expansion of the photon distribution, defined by the centered location of the annulus is
now computed. We can use the expansion parameters to find the 1 ” moment A/, = (%, J '),
the ellipsoidal orientation angle , and the axial ratio 77 .
2 C :(r) r{d C Jd r)\,
Where, {dC^ / dr) |j; is the radial gradient of the surface brightness evaluated at r . Finally
we increase the radius of the annulus by 2 pixels per iteration and repeat the above steps
until the radius extends past the area of the X-ray image we are investigating.
Let us once again look at this in a graphical manner. Imagine a series of hula-hoops
having different radii but possessing the same thickness. Now let us place our hula-hoops
over the top of a symmetric anthill one at a time starting with the smallest one first. If we
look down on our system firom an overhead position, we notice that all the hoops share
the same center. Now imagine our anthill has some inhomogeneous asymmetry. In other
words, it may look symmetric at its apex but as we look farther down the base, it bulges to
one side or the other. Now start again by placing the hoops on the anthill one at a time
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with the smallest one first. As the radii of our hoops increase we notice that the centers of
our hoops are moving in the direction of our conic distortions. This ‘center shiff is caused
by the asymmetry of the anthill! As we begin to place larger and larger hoops over the
structure we begin to pick up the changes in the structure. In the case of X-ray clusters it is
the substructure that will be picked up by these ‘center shifts’.
3.3 Wavelet Transform Method
The third method is the wavelet transform method developed and supplied by Starck et
al. (1995), also see Slezak et al. (1994). This method is considerably m ore visual than either
of the previously described methods. First, it is necessary to think of the X-ray data as a
superposition of different valued scales. Now let f(^x) be the complete data function. Its
1-dimensional wavelet transform can now be written as
C (a, é) = T £ ./(A:)g- (— )*
where “a” is the scale, “b” is the location, and g is the complex conjugate of the analyzing
wavelet. Consider C(a,6) which is the wavelet transform of We can restore f{x)
with the following formula
— j j - ^ ^ a , o ) g — — — C g 0 -00 'V ÛT \ ^
where:
|2
^ 0 V
O f course, this is only true if Cg is defined. This is generally so as long as g(0) = 0. In
other words the mean value of the interrogating wavelet must be zero. It is the ability to
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vary the scale of the interrogating wavelet that makes this method a truly multi-resolution
approach. In our case, the scale of the wavelets ranges &om 1 to 8 pixels in order to
provide a more complete range to look for substructure.
Once again, let us look at the graphical implications. Imagine that we are going to look
for structure on an anthill This time instead of using hoops or figure eights we are going
to use calipers set to different sizes to measure the 2-D projected surface of the anthill.
The object is to use the calipers, set at differing widths, to trace the projection in order to
search for the different scale anomalies. First, let us assume that the anthill is on the order
of 1 meter in size and contains several polymorphic anomalies. Let us then imagine that we
start with the calipers set to a very small diameter, say 1 fjm . Next, we slide the calipers
along the outer surface or projection of the anthill in a tracing fashion. After doing this we
see that we can only measure variations that happen to occur between the caliper edges, in
this case on the order of 1 jjm . As the diameter of the caliper setting is increased to larger
sizes and the anthill is traced each time, larger variations in the structure can be measured
with each pass. Of course, if we add up all the measured variations at all the different
scales we can reconstruct our anthill in all its glory. It was hoped that the variability of this
method could be used as a visual check to see at which resolution level or levels the other
two methods were detecting substructure.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 4
THE MODELS
In order to calculate our errors and discern the significance of our results, cluster models
were created.
We began by parameterizing the cluster plasma distribution using the standard King (1966)
model, which appears as follows:
- 2 2 ' 112-ip X I(x,y) = /q 1 + + y / c . .n r - c .
where I(x, y) is the x-ray intensity as a function of x and y, L is the intensity at the center of the
cluster, X and y are the cluster image coordinates, r^ is the radius of the core, T] is the axial
ratio, and P is the power-law index. Each cluster was inspected and a model was created using
the te s t fit’ method. D u rin g this process it was discovered that the central regions for nearly
Vi of our clusters could not be fitted using the standard King model This standard King
model describes the central regions of clusters as being somewhat flattened, meaning that
these areas are, for the most part, isothermal To the contrary, we found that some of our
clusters had central regions better characterized by sharp intensity spikes. We believe that this
is due to cluster cooling flows.
A cluster cooling flow occurs when the gas at the center o f a cluster, where the temperature
and density are highest, cools through bremsstrahlung and line emission in a time less than the
cluster lifetime. As the temperature drops due to cooling, the pressure in the cluster central 17
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region also drops. In order to m ain fain the pressure the central density has to rise. This
happens with an inward flow of gas, resulting in an excess of luminosity at the cluster centers.
With the advent of newer X-ray satellites such as ASCA, better resolution is possible, which
enables more accurate observations of cluster cooling flows. These more accurate observations
in combination with the data presented in this paper and recent analysis of ROSAT PSPC
observations (Sarazin, 1998), indicates that perhaps as many as 50% of clusters exhibit cooling
flows.
As knowledge of cooling flows is still in its infancy, it was decided to ignore the cooling
flow process in our models. This should not effect the results because the p rim ary concern is
substructure that resides in the areas surrounding the central regions which is adequately
described by the King model The Taest fit’ models were then used to create 500 Monte Carlo
simulations for each cluster in which a random amount (between 1 and 5 counts) of Poisson
noise was added to each iteration. In order to fuHy emulate the real data fully, each simulation
was divided by the appropriate exposure map and multiplied by the image live-time.
To save CPU time, the models were centered at 256, 256 o f the 512, 512 image firame. The
fact that only the total ‘center shift’ and ‘moment’ numbers are important in this paper and
these values are independent of the models position on the image firame makes this short cut
possible. Each analysis program was allowed to run on the 500 models for each cluster. The
results for the 500 models for each cluster were sent to separate files and Fortran programs
were used to extract the pertinent data firom each file. Although it is possible to plot the results
in a myriad of ways, it was decided that the results for the ‘center shift’ method would be in
respect to the data to create the plots. The ‘moment’ model results were plotted as histograms where the number of models having a particular moment value were binned. These plotting Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 criteria made it possible to compare the data to the models, find the significance o f our results, and calculate our error bars. There was no reason to compare the models to the wavelet transform method for the following reason. If we know the type of noise in advance we ran tailor the wavelet transform method to account for this. In our case we input Poisson noise into the program. The wavelet transform method calculates the mean and standard deviation for the noise in each resolution range and only the signal above a user defined clipping level, 3 sigma for this study, is sent to the output image. The result of this, in theory at least, is that all the structures we see in the wavelet transform images are considered significant. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTERS THE RESULTS In all, 21 clusters were analyzed u sin g all three data analysis programs the results of which are presented in figures 3-149. For each cluster we present the smoothed image and contour plot, the histogram plots for the moment model results for Pj and P 4, and finally the 133, Abell 514, and Abell 2052 will be discussed in detail here. I believe that these three clusters portray the variety of cluster morphologies that were encountered in our sample and thus are a good representation of the results that our analysis programs produced. In addition, the general results firom all the 21 clusters will be used to compare and contrast the various methods. 5.1 Abell 133 Results Abell 133 is a cD cluster by the Rood-Sastry designation system and has a redshift o f .0566 (see Table 1). Visually this cluster appears to quite relaxed and symmetric (Figures 17 & 18). This is also how the cluster appears after inspection of the wavelet images (Figure 19). Each wavelet transformed image shows only a central regularly shaped circular image that seems to rem ain homogeneous as the wavelet scales get larger, which is exactly what one would expect for a relaxed cluster with little or no detectable substructure. The results for the ‘moment* program run on this data firame for Pj and P 4 (see Table 3 & Figures 20 & 21) are within 3 sigma of the model values, m ak in g them statistically insignificant, which also agrees with a 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 regular relaxed cluster. The total shift in RA and DEC (Figure 23) as reported by the ‘center shift* method shows that there is variation in shift of less than 0.5 arc minutes over most of the 13 arc minute search radius. There appears to be a somewhat larger shift of about 1 arc minute in the outer 3 arc minutes of rbis radius. However, changes of even a single count can make the results seem much larger out here where the counts in general are very low. It can be seen from the graph of / cr^„ (Figure 22) that the mean value (see Table 2) is about .73 with a calculated standard deviation value of .21 placing m a n y of the values near umty. This indicates that there is m inim al difference between the two values and therefore littie or no substructure detected by the ‘center shift* method. 5.2 Abell 514 Results Abell 514 has a R.S. designation of F, a Bautz-Morgan type of II-III, and a velocity dispersion of 874 km/sec with a red shift of 0.0713 (see Table 1). Abell 514 is perhaps the most visually interesting cluster of the sample. The cluster (Figures 38 & 39) appears as an irregu lar cloud that is surrounded by diffuse plasma forming an elongated kidney-shaped object. The wavelet transform images (Figure 40) show substructure on a progressive scale. In the 2 pixel scale several small knots of plasma can be seen with very littie diffuse plasma present. In the 3 pixel scale more of the diffuse plasma can be seen. This diffuse plasma appears as an irregular and elongated foot-Hke extension that appears to be coimecting several of the more prominent plasma knots. By the tim e the 4 pixel scale is reached virtually all the knots are no longer individually visible and in the 5 pixel scale the cluster looks like a single elongated blob of diffuse plasma with a brightened end. The ‘moment* program (see Table 3 & Figures 41 & 42) tun on the data yields a value o f Pj that is 37 sigma above the mean model values! The value for P 4 is surprisingly sm all given the extremely large Pj value. A data value o f Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 4.5 sigma above the mean model values indicates only a moderate significance. The ‘center shift* analysis method (Table 2 & Figure 44) shows a shift of almost 6 arc minutes. This proves to be very significant when compared to the plot (Figure 43), which has a mean value of .11 with only a .03 standard deviation value. This indicates that only about 10% of the models have a center shift that is on the order of the center shift o f the cluster. 53 Abell 2052 Results The third cluster is Abell 2052 which has a R.S. designation of cD and a B.M. designation of I II (see Table 1). It is known to possess a large cooling flow and has a redshift of .0348. By observing the contour plot (Figures 52 & 53) of this cluster it is possible to see that it appears slighdy irregular, possessing a mostly off center oval shape. If the wavelet transforms (Figure 54) are observed it is possible to see only a sm all portion of this apparent offset. For the most part the wavelet data shows nothing particularly irregular on any scale. The significance observed when the ‘moment* program is run on the data in the 2™^ moment (see Table 3) which would pick up this apparent elongation cannot be computed because our models were made to emulate this type o f feature. The value of Pj (see Table 3 & Figure 55) appears to be marginally significant at best, possessing a value only 4.5 sigma above the mean model values. The cluster value for P^ (Figure 56) is completely insignificant, on the order of 1.5 sigma above the average model value. The ‘center shift* method (Figure 58) shows only a very small (<.5 arc min.) overall shift inside the first 9.75 arc minutes of a 15 arc minute search radius. Outside this radius, extending through to the outer edge, we see a total shift of about 1.5 arc minutes. This shift is relatively small but appears quite significant when thecTn^,/ / 57) is viewed. This plot has a mean value of .38 with a standard deviation of .11. (see Table 2). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 This significance ran best be explained if the off-center characteristics of the cluster plasma are taken into account The above three described clusters were picked to be representative o f several types of cluster morphologies: a regular relaxed cluster with litde or no substructure at any level, a cluster that is very irreg u la r and shows substructure at many different levels, and finally a cluster that is somewhat regular on some scales but shows substructure at others. I believe that these clusters clearly show the sensitivity ranges of the three an aly sis programs. For instance, Abell 133 appears to be ‘regular* on virtually all scales to all three programs. If the results of each program are inspected individually it would not be misleading to say that this cluster appears to be a regular relaxed system. For Abell 514 each program shows substructure on different levels. The wavelet transform program shows substmcture in the intermediate and small levels while still showing the overall shape and form of the cluster. However, with no quantitative numbers it is difficult to classify the cluster or compare it to other clusters. The ‘moment* method*s large Pj value indicates that the shape is somewhat triangular, which can be seen if one imagines a narrow elongated triangle lying on its side. The elevated P^ value indicates that there is at least some amount of surroimding substructure. These structures are indeed observed in the cluster, and with the quantitative n u m b e rs it is possible compare it to other clusters. However the program doesn*t present a very visual picture of the cluster. The ‘center shift* results shown on the total shift plot for Abell 514 shows very strong indications for substructure. This method does not tell us exactly what kind of substructure there is, but it can indicate how “strong” the substructure is. It can also tell us how that substructure is oriented in relation to the m a in stmcture and image orientation. This method also provides the quantitative means necessary to compare one cluster to another direcdy. The results for Abell 2052 show the clear differences between the programs. The wavelet transform program shows Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 little or no irregularity. Due to the feet our models were made to emulate the clusters’ overall oval shape, we are not able to tell the significance of the 'moment* method ?2 results. However, if the Pj result is compared to the other clusters P; values, it does not appear very large at all. In fact it rums out to be one of the smallest! On the other hand the center shift method shows a clearly significant result, indicaring that at least for this example it is capable of detecting very subde changes. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 6 CONCLUSIONS Great care was taken to find and collect a non-biased group o f rich galaxy clusters, run three different types of analysis programs on each of them, and create cluster models in order to determine the significance o f our results. We are now in a position to ask ourselves, what conclusions, if any can be drawn firom this experience? In fact, there are several interesting conclusions that can be drawn firom our research. Let us recall the three main questions proposed in the introduction and attempt to answer them one at a time. 1) How do the three analysis methods used in this survey compare? It has already been seen firom the detailed examples that the three methods appear to be in agreement for the most obvious substructure cases. In order to get a better picture of the overall agreement between the two analytical methods we can look at the comparison chart on Table 4. Before any comparisons can be made it must be stated that in order to stay on the conservative side a 6 sigma cut-off for the ‘moment* method is used. For the ‘center shift* method a value of (mean + sigma >0.7) is taken as the approximate cut-off. Using these criteria and taking m arginal results as positive, it can be seen that there is agreement between the methods for all but 5 of the clusters. As can be seen firom the comments section of the chart, one of the disagreements for the Abell 3111 can be attributed to the cluster observation having counts that are possibly too low to work with. Two clusters, Abell 2052 and 3112, have predominantly off-set oval structures not accounted for in the ‘moment* values of Pj and P^. 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 As our models were made with this type of substructure we can ignore this apparent discrepancy. For Abell 3266 and 3562 it is possible that the substructure configurations are neither triangular nor cross like. These are the approximate shapes that the Pj and P^ moments would pick up. The type of substructure observed in these clusters might be more accurately detected in higher moments. As far as individual program performance is concerned, there is a general trend observable. The wavelet tr a n s fo rm method allows us to attain a strong visual sense for the cluster structure. However, th is is attained without clear quantitative means of comparing one cluster to another. The ‘moment* program supplies us with the quantitative means of comparison as well as giving us a general sense of the overall cluster morphology. The weakness of this program seems to be that it is fairly insensitive to sm all changes in intensity at or near the cluster centers or at their extremities. The ‘center shift* method by its nature is more sensitive to sm all changes at any position on the image. It is possible to use the results of this program to produce RA and DEC shift plots (not shown in this paper) for each cluster, making it possible to get a rough picture of how substructure is placed throughout the cluster. This data, however, only indicates substructure placement, giving little or no idea what that the intricacies of the substructure actually look like. Clearly, taking the above observations into account, it is possible using only one of the above methods to get a fairly clear picture of substructure, given a particular sample. If we were to ignore the clusters with low counts and the fact that our models were designed to account for elongated substructure, we would find only two major discrepancies between the methods. As has already been stated, the last two may be due to our use of only low moment values. O f course, it is always desirable to have the most complete picture attainable. This is true especially when attempting to expound on an issue as sensitive and controversial as the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 value of Q . It must also be taken into consideration the idea that all substructure may not be created equal! There may be m a n y explanations for the presence of substructure in galaxy clusters. For instance, if we wished to know if clusters are still forming we would look for evidence of large amounts of substructure at or near the centers of a clusters, which might indicate that the clusters were still undergoing dynamic relaxation. Suppose all that was found were fairly spherical cluster cores with some sm all oudying substructure blobs. This finding might indicate that these clusters are mature relaxed systems that happen to have recently swallowed some nearby matter, indicating that they are not young at alL With this in mind it becomes quite clear that searches o f this type must be conducted with great care. 2) What is the prevalence of substructure in rich clusters of galaxies? Recall that we started with the most unbiased cluster sample possible. Unfortunately, because not all clusters in this sample were observed by ROSAT or some observations were miss-pointed, our data set is only a subset of the original sample. We do, however, believe that this data set is still an unbiased representation. To convince ourselves of this the abstract for each observation proposal was searched. It was found that only 1 (Abell 3266) of the 21 cluster observations was done for the express purpose of a substructure search. Three others (Abell 3111, 3112, 3158) were observed for evidence of cluster-cluster or cluster-supercluster interactions. Generally this interaction leads to cluster elongation, a shape we do not consider substructure in our survey. However, to be conservative we take this as possible evidence for substructure and therefore possible sample biasing. Seven clusters (Abell, 85, 119, 133, 754, 3562, 3667, and 3897) were observed to help probe their cluster mass functions and help determine binding mass and dark matter distributions. Four clusters (Abell 496, 2052, 4038, and 4059) were observed to investigate cooling flow clusters. The remaining six were observed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 for a variety of reasons ran g in g from measuring the brightness gradients of clusters inside super clusters to measuring the X-ray emissions o f clusters near WAT (Wide-Angle-Tailed) radio sources. With this in m in d and again accepting m atinal results as positives, the ‘center shift* method found 13 of 21, or 62% of clusters showing evidence of substmcture. The ‘moment* method found that 11 of 21 clusters, or about 52% of the sample, exhibits defimtive evidence for significant substmcture. If our sample is indeed non-biased, then this is clear evidence that galaxy clusters are still forming. 3) What implications does this result have on the current accepted value of Q ? Recall, that if galaxy clusters are still fo rm in g , this implies we must accept an increased value of Q . At least larger than the currendy held value o f Q < 0.2. 4) Bonus Question: What is the percentage of rich galaxy clusters with cooling flows? As ftequendy happens in scientific endeavors o f this type, an unexpected but important observation was made. During the m o d elin g phase of our research it was found that almost 50% of our sample exhibited very high counts at their cluster cores, indicating cooling flow activity. Until very recendy it was unknown what the cooling flow percentage of galaxy clusters was or even if the phenomena was real This was due to the inability to resolve the clusters central regions finely enough. In the last two years instruments such as A.S.CA. and others have given us the resolution necessary to begin a comprehensive search for cooling flows in galaxy clusters. The most recent information has led to the finding that as many as Vi o f all galaxy clusters exhibit some cooling flow mechanics (Sarazin et al 1998). With these types of clusters occupying a greater percentage of the total it is imperative that our models become more sophisticated. We ra n only know the significance of our data if we properly and accurately model the physical phenomena we are probing. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 It is hoped that our results, along with further research in this area, will lead to the construction of a more reliable database, one that can not only be used to help answer the questions of today but one that is also sufficiently detailed to answer the questions of tomorrow. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX A TABLES 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 Table 1: General Cluster Information Abell RA. DEC. Rood- Bautz- Cluster z a-y 0 2 0 0 0 ) 0 2 0 0 0 ) Sastry Morgan Type Type 85 .0556 853 00 41 49 -09 17 51 CDI 119 .0440 740 00 56 14 -01 15 58 C n-iii 133 .0566 — 01 02 38 -21 47 53 CD — 496 .0327 682 04 22 38 -1315 40 CD I: 500 .0666 — 04 38 52 -22 06 38 I m 514 .0731 874 04 47 40 -20 25 44 F n-in : 754 .0534 — 09 08 35 -09 37 28 CD I-H: 2052 .0348 — 13 33 31 -31 40 22 CD I-II 2382 .0648 — 21 52 01 -15 39 53 L II - III 2717 .0498 512 00 03 15 -35 57 18 — I-II 2734 .0618 581 0 0 11 20 -28 52 18 — III 3111 .0775 770 03 17 47 -45 44 05 — I-II 3112 .0751 950 03 17 56 -44 14 06 — I 3158 .0590 1005 03 44 35 -53 28 27 — I-II 3266 .0594 1 1 2 2 04 31 09 -61 26 39 — I-II 3558 .0478 — 13 27 59 -31 30 31 — I 3562 .0499 — 13 33 31 -31 40 22 — I 3667 .0530 1059 20 12 29 -56 48 59 — I-II 3897 .0733 548 22 3917 -17 23 21 — II 4038 .0283 839 23 47 53 -28 09 19 — III 4059 .0478 536 23 57 01 -34 45 36 — I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 Table 2: Center shift data AbeU 119 .29 .07 0 133 .73 .21 54 496 .94 .26 175 500 .31 .12 0 514 .11 .03 0 754 .21 .06 0 2052 .38 .11 0 2382 .65 .20 24 2717 .41 .15 0 2734 .26 .10 0 3111 .30 .10 0 3112 .42 .17 0 3158 .54 .18 11 3266 .35 .09 0 3558 .15 .04 0 3562 .24 .06 0 3667 .1 0 .03 0 3897 .89 .33 184 4038 .57 .25 35 4059 .63 .23 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 Table 3: Moment data -\BELL Po P./Po P2 /P 0 P1 /P0 D a a P4 /P 0 Data CLUSTER distance distance from from models in models in sigma. 85 0.739E+11 0.330E+01 0.109E+02 0.578E+00 24 0.194E+00 14 119 0.500E+11 0.137E+01 0.165E+01 0.263E+01 50 OJ73E+0O 11 133 0.326E+11 0.297E+00 0.495E+01 0.166E+00 Z2 0J41E4)1 .89 496 0.849E+11 0.120E+01 0.698E+00 0.109E+00 IZ 0.262E411 .67 500 0.264E+10 0.311E+00 0.262E+00 0.288E+01 20 0.445E+00 6.9 514 0.242E+10 0.439E+01 0.147E+03 0.S85E+O1 37 0.485E+00 43 754 0 165E+11 0.503E+04 0.932E+02 0.588E+01 50Z 0.182E+01 8.2 2052 0.398E+11 0.832E+00 0.120E+01 0.165E+00 4.5 0j09EO l I j 2382 0.345E+10 0Z52E+01 0Z69E+O2 O.U2E+01 7 j 0.311E+00 4.6 2717 0.316E+10 0.160E+01 0.957E+01 0.127E+01 8.1 0J04E+00 7.5 2734 0.145E+10 0.108E+01 0.751E+01 0.121E+01 14 0.519E4)1 1.4 3111 0.940E+08 0.144E+01 0.171E+02 0.500E+01 5.7 0.239E+01 5.8 3112 0.118E+10 0.495E+01 0.345E+01 0.804E-01 .44 0.273E4)1 .20 3158 0.160E+10 0.459E+01 0.212E+02 0.621E+00 3.1 0.113E+00 .91 3266 0.217E+11 0.486E+01 0.170E+02 0.140E+00 21 0.169E411 .62 3558 0.527E+13 0.772E+00 0.468E+02 0.250E+01 312 0.681E+00 32 3562 0.503E+11 0.196E+01 0.184E+02 0.133E+00 1.7 0.145E+00 3.8 3667 0.782E+11 0.218E+01 0.522E+02 0.184E+01 71 0.574E+00 22 3897 0.474E+08 0.654E+00 0.203E+01 0.242E+01 24 0.524E+00 1.0 4038 0342E+10 0.306E+01 0.149E+02 0.570E411 .05 0.172E+00 1.4 4059 0.577E+10 0.114E+01 OJ05E+01 O.I68E4)l .16 0.795E4)1 1.4 - Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 Table 4; Comparison Table A b d l Center M oment Moment Agreement Comments Cluster Shift P, ?4 Detectiofl Detection Detection 85 yes yes yes 119 ves ves yes yes 133 yes 496 no no ves 500 yes yes yes 514 yes yes yes 754 yes ves yes yes 2052 yes no no Offset oval shape not accounted for in P, or P4 values 2382 yes no Possibly due to low counts. 271 - ves ves yes yes 2734 ves yes no yes 3111 ves marginal m arginal m a r g i n a l Possibly due to very low counts 3112 ves no no Offset oval shape not accounted for in P3 or P4 values 3158 no no yes 3266 yes no Substructure doesn’t fit P) or P4 shapes. 3558 yes yes yes yes 3562 yes Substructure doesn’t fit P3 or P4 shapes. 3667 yes yes yes yes 3897 no no yes 4038 no no yes 4059 no no yes Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX B FIGURES 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 ABELL 85 Figure 3. Cleaned and filtered image o f Abell 85. Scale is approximately 2 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■DCD Q.O C g Q. ■D CD A B E U . 85 C/) C/) A85 a 85 h c d .fits l2 0 5 :3 3 0 .175 = 320] 8 Fieid Center' ■D D"41"'39.25» -09^20'14.99 Scile' 13.49"/mih CD X/1 R atio : 1.00 Contour Levais: 3"3. 379.4716 CD 299.2349 235.9636 ■DCD O 106.0706 Q. 146.7272 C a 115.7027 3O 91.2301 "O 71.9464 o 56.7338 a 44.7378 CD Q. 35.2703 27.6189 21.9368 17.2994 ■D 13.6408 CD 10.7565 8.4821 C/) C/) 6.6806 -9°35* 5.2744 4.1591 3.2797 0^2"'00“ 40" 0^4 rOO" 40® 2.5862 Figure 4. Contour plot for Abell 85. Contour lines are in counts. Scale is approximately 2 Mpc per side. 38 ABELL 85 Figure 5. Wavelet transform images for Abell 85. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 in O - in LT) 00 en I 01 < 3 0 LD oc 5 I m i sa < I i in 1 o 1 E 2 X sd u o w o o o, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 o o m 30 CD in a 01 00 a 3 r-4 =3 < D a < o 0 OJ "O o 1 T CL 1 I &r o w v2 i I X o u Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 in S I •H 2 "U s i I lO 00 < in 1 1X3i I 00 u o o o ÜL, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 If) 00 CD y c l a u I < L CD I 3 •H £ ■Q if) IQ 00 01 =3 a < .S 1 I I c\ u o (M o Reprocjucecj with permission of the copyright owner. Further reproctuction prohibitect without permission. 43 ABELL 119 Figure 10. Cleaned and filtered image map of Abell 119. Scale is approximately 2 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. "OCD O Q. C g Q. "O CD C/) C/î A119 a11% cd.fits[l70:330.172 = 3401 F leid Cent«r' 8 & DhS6"23.3[P "O -01*15 07.50 -roo‘ Scale: 15.61"/,* X/ï Ratio: 1.00 CD Contour Levais: 14.8799 3"3. 11.3590 CD 8.6712 6.6194 "OCD O 5.0531 Q. 3.8575 C a 2.9447 3O 2.2479 "O 1.7160 O 1.3100 1.0000 CD Q. e "O CD C/) C/) 30^ 0^57"00= 30® û'^56’00® 30® Figure 11. Contour map of Abell 119. Scale is approximately 2 Mpc per side. Contour levels given in counts. 45 ABELL 119 Figure 12. Wavelet transform images for Abell 119. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 tn w OJ o c\ in o i 2 5 en u O O O tM i S z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 _ 0) C\ u < V4M O us i 1 o CL i 1 2 JS z U O OO O O Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 in v4 3 l .-S b üJ en ! Jc\ < in u o < 4 I o o o C/D i n u U. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 (0 c u c. M < à 1 et: 2 O lO IT) o NO U Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 ABELL 133 Figure 17. Cleaned and filtered image map of Abell 133. Scale is approximately 1.5 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. "OCD O Q. C g Q. "O CD C/) A B E U . 133 C/) Al 33 a 133hcd.f i t s [200:300.190 i 305) 8 FI eid Cen ber « "O O lW 47.â1® -21*5502.99 45' Sc&le: 10.71"/mm X/Tf Rabio: 1.00 Contour Levais^ 3"3. 440.8237 CD 50' 334.2497 "OCD 253.4412 O 192.1690 Q. C 145.7101 a 110.4830 3O "O 55' 83.7726 O 63.5196 48.1631 36.5191 CD Q. 27.6902 22* 0 0 ' 20.9958 15.9198 "O 12.0710 CD 9.1527 6.9400 C/) C/) 05' 5.2621 3.9900 3.0253 2.2939 1.7394 1^^D3'"GQ® 40= 1 ^0 2 * 0 0 = 1.3188 Figure 18. Contour map of Abell 133. Scale is approximately 1.5 Mpc per side. Contour levels are given in counts. cn 52 ABELL 133 Figure 19. Wavelet transform images for Abell 133. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 T O n o tn - u co < m m 3 O pH ID > 3 CM CQ I < TJ O n Q. f cT J o 1 s .2 I in in in o CM Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 (N O ID 2 £ (U o o o o w ^ o Z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 2 e u I in i en u < 3 m "g m b i ai i < s 1 ’ë 2 I I C/3 5 P o o o i 2 z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 in en en (0 M c < en m u c. i 2 d C/D en o es m in o 1 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 ABELL 496 Figure 24. Cleaned and filtered image map of Abell 496. Scale is approximately 1.1 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. "OCD O Q. C g Q. "O CD C/) C/) A496 a496hcd.fits[195:320.190:3201 8 -13°00' F leid Center' "O 04"33"37.37® -13*15 58.50- 05' S c ile : 12.1D"/m* X/ï Ratio: 1.00 CD Contour Levais: 3. 310.2136 3" 10 ' CD 239.0030 184.1392 CD "O 141.8694 O Q. 109.3029 C a 15' 04.2121 3O 64.6609 "O 49.9673 O 38.5126 29.6719 2 0 ' CD 22.8606 Q. 17.6129 13.5698 10.4546 25' "O 8.0549 CD 6.2058 4.7813 C/) C/) 3.6837 30’ 2.8381 2.1866 1.6847 40® 20® 444™00" 40® 20® 4^33"00® 40® 1.2979 Figure 25. Contour map of Abell 496. Scale is approximately 1.1 Mpc per side. Contour levels are piven in counts. Un 00 59 ABELL 496 Figure 26. Wavelet transform images for Abell 496. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 "I I I r I I I I f I I I I I I I I 1“ «0 o NO Qj n 2 2 CM »»«"■««»»»»* » J- ^ ' « «- o in in ÜU CM tH Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61. n o KÛ O o> =3 < Lw CM O o O 0) 013 î É fü £Q > < m "O o T CL O o o o o n CNi ^i "^ 3 z "o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 in a NO - a o a < I o 1 I CO o o o o o Ü. I ^ Z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 1 0) i : C 2 o u (D 3 NO *o m (T 'u M < ■â « "3 m U CMCO o II Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 ABELL 500 Figure 31. Cleaned and filtered image map of Abell 500. Scale is approximately 1.6 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■DCD O Q. C g Q. ■D CD C/) C/) ABELL 500 a500hcd.fits[215:310.195:2901 Flijd Center’ - 22° 0 0 ’ 04*’38*4B.72“ -22*09 29.99 ■D8 Scile! 7.70'/nm X/T Ratio: 1.00 Contour Levels: 05' 18.9637 14.1296 10.5270 7.0442 3"3. CD 5.0446 4.3547 CD 3.2447 ■D 10 ' O 2.4176 Q. C 1.0013 a I .3421 3O I.0000 "O o 15' CD Q. ■D CD r39'00® 4^8*00’ C/) C/) Figure 32. Contour map of Abell 500. Scale is approximately 1.6 Mpc per side. Contour levels are given in counts. ON in 66 ABELL 500 Figure 33. Wavelet transform images for Abell 500. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 •o o 8m J3 < "o o ino I Ë a in S < o o o o o co OJ I S Z "o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 o o o in IT) rn 1 < vm 0 §U-) 1 4 5 CNJ CQ < o o o o o kO CVJ il i 2 Z "o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 B § o o oIfl I 'ü I XI SQ < < .c 1 I c/3 >o u o o o o o o b 00 ID C\l Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 tn E o.I is I o u : SQi L < ’■5 o m in " =s _o < in Q, I r*^ cO u in in o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 A BELL 514 Figure 38. Cleaned and filtered image map o f Abell 514. Scale is approximately 1.3 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 ^ 8 a. È en oo in I CD CM s I C\] c/3 M- CNJ in OQ JD < <4^ m O s- d un ^I Ë CÜ V rsi «o co CM fNI CM ro co co II & a CM I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 ABELL 514 Figure 40. Wavelet transform images for Abell 514. Clockwise from upper left in 2,3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 0 0 o in 1 < O KO m I > 01 T3 A O < n i pT I CVJ 2 S - o U o o o J2 in II Z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 KO o in T|- a t 2 S o o o o o Ü3 OJ ÜL, ^ - 8 I ^ Z *0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 tn If) a 3 -3 b I in ■i o I c/3 9 o o o o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 2 o. (k a If) (D C § fflI u < c. 0) 3 *o u rü q : < 1 «t: I $ o kD Cvi O It Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 ABELL 754 Figure 45. Cleaned and filtered image o f Abell 754. Scale is approximately 1.9 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■DCD O Q. C g Q. ■D CD C/) A754 3o" O a754hcd.fits[215-.345,180:3351 - 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 111 11 11 1 - F leld C enter « 8 0i)"09'”57.765 3 2 5 ’ -O m i 0B.95 ci' - - Scile: 14.4r/«* X/ï R atio: 1.0G 30' - V - Contour Levels: 17.6227 3. 3" / 11.6967 CD 35’ 7.7634 CD ! ■D 5.1528 O 3.4200 - Q. ^\ C 40’ 2.2700 a Ï 1.5066 O rum 3 ^\\SS - 1.0000 ■D E O 45’ F - - CD Q. » 50’ -- ■D CD C/) 55’ C/) - - 10°00 ? h o W 40® 20® 9^09™00® 40® 20® 9^08'"00® Figure 46. Contour map of Abell 754. Scale is approximately 1.9 Mpc per side. Contour levels are given in counts. 80 ABELL 754 Figure 47. Wavelet transform images for Abell 754. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 iTi CO o =3 < KD m o I 3a < ■o (N O O O O OO O I S z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 tn -O . m 01 I m % > 01 a T3 < O i TT eC Û. à S2 1 o o o CNJ MI "o^ Z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 2 o. Æ I a -8 m b ï I < 1 I c/2 ino o o o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 in is 12 IT) (D r~- c § u CQ < in I1 I m P o m CM o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 ABELL 2052 Figure 52. Cleaned and filtered image o f Abell 2052. Scale is approximately 1.0 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■DCD O Q. C g Q. ■D CD C/) C/) a2052hcd.fîts[200:300,200:300] Fieid Center' 16h38"OO.OD5 +249 30 00.03 ■D8 280. Scile: 1945.43"/mm m Ratio: 1.00 Contour Levais' 260.9629 164.6564 3. 103.8912 3" 260. CD 65.5509 41.3598 ■DCD O 26.0963 Q. 16.4656 C 10.3891 Oa 3 6.5551 "O 240. 4.1360 O 2.6096 CD Q. 220. ■D CD C/) C/) 220. 240. 260. 280. Figure 53. Contour map of Abell 2052. Scale is approximately 1.0 Mpc per side. Contour levels ate given in counts. 87 ABELL 2052 Figure 54. Wavelet transform images for Abell 2052. Clockwise &om upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 OJ inOJ o OJ u OJ JQ < I 1 cs to .O R > g É a < I n cT 1 2 i£ in If) 32 • 5o^ o o o OJ I 2 Z "o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 CM 1) in CM < I CD 301 .o (D > a *o01 CQ o ! < &T xr 0_ in o i 2 X mso a • O O O o o M CM Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 rH I 12 I es in cs i n R 'u 13 < < "È I C/3 C/3 If) a o ooo o o J2 I ^ Z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 in II (D s c I cu in cu0 3 rS ad IT) OJ in in o 12 < n 1 y Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 ABELL 2382 Figure 59. Cleaned and filtered image of Abell 2382. Scale is approximately 1 .6 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■DCD O Q. C g Q. ■D CD WC/) 3o' O ABELL 2382 3 CD a2382hcd.fits[190=320,180:320] 8 Fleid Center' ■D 21"51"59.15» (O' 25 ' -15®39'25.5D O Scile: 13.02711» X/1 Rat 10: 1.00 30 ' Contour Levels' 3. 10.9755 3" CD 8.6374 6.7974 CD 35 ' ■D 5.3493 O Q. 4.2097 C 3.3129 Oa 2.6072 3 2.0518 ■D O 1.6147 1.2707 I .0000 CD 4 5' Q. ■D 5 0 ' CD (/) Figure 60. Contour map of Abell 2382. Scale is approximately 1.6 Mpc per side. Contour levels are given in counts. 94 ABELL 2382 Figure 61. Wavelet transform images for Abell 2382. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 u JO < ■§ (0 01 .0 CM 3 QO ro > "OQJ CO O I < n o_ ■i. s a • | « o in in OJ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 O O J • M0 0 u —OJ < I i a 1 < Q. !2 1 O 2 X 2 a • | s o O o o O O bu 5 m OJ w V i ^ Z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 in I S I S m 8 R É SQ < I < •i in o I co Tf vO o o o & CM U V i ^ z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 i îts I S J3 < i. 3 lO NO U o in in o o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 A BELL 2717 Figure 6 6 . Cleaned and filtered image o f Abell 2717. Scale is approximately 1.3 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■DCD O Q. C g Q. ■D CD WC/) 3o" O 3 A2717 CD ■D8 a2717hcd.f its (200:300,200*300] Fleid Center' (O' 0"03*27.44® O 50' - 35*58 39. 9 8 ' Scile: 8.11"/na X/t Ratio: 1.00 3. Contour Lovais: 3" CD 47.6118 55' 30.0410 CD ■D 18.9546 O Q. 11.9595 C 7.5460 Oa 4.7612 3 3.0041 ■D I .8955 O 1.1960 0.7546 CD 0.4761 Q. 05' ■D CD (/) 40* Figure 67. Contour map of Abell 2717. Scale is approximately 1.3 Mpc per side. Contour levels are given in counts. 101 ABELL 2717 Figure 6 8 . Wavelet transform images for Abell 2717. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 t lO m 1 i a < g •ia B X ÇU Cl, e g Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 u x> < " n 1 Î CM Z (C a 4 o r- -JT' I— tt, CS o Oo o O CM •Si ^ o Z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 in tH i. I I 3 j -a r- o R 1 < I < t in S o on r- u o oo o \û OJ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 105 in 2 & i g; H I a a < r- s "O =s J3 < in U te 3 f2 p! o KD o oo Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 ABELL 2734 Figure 73. Cleaned and filtered image of Abell 2734. Scale is approximately 1.5 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■DCD O Q. C g Q. ■D CD WC/) 3o " O ESO 409 G-25 3 CD a2734hcd.f i t s [200^300,200^300] 8 FleJd Center' [Tll'29.21» ci' -2B®53'15.9B O Scile: 8.11'Vni X/ï Ratio: 1.00 Contour Levais' 3. 14.0767 3" 9.6478 CD 50' 6.6124 ■DCD 4.5320 O 3.1061 Q. 2.1288 C a 1.4591 O 1.0000 3 ■D 55' O CD Q. ■D CD C/) C/) 20= Figure 74. Contour map of Abell 2734. Scale is approximately 1.5 Mpc per side. Contour levels are given in counts. 5 108 ABELL 2734 Figure 75. Wavelet transform images for Abell 2734. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 rn N V OJ < Th I .0 ÎQI < I cT a 1 S £ NO Sû fn oo o o k cs cfl to OJ WU 'M O II Z ‘o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 tn o CM ,rnN CM o .a I in 1 0) Ql3 > Ol y •o I CÛ o < T. V CL <2 S2 1 in o o 2 X rr~. - • Sr1^ tu K o o o \D o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ill tn II § 3 -H ^ b g; 1 I < i in y o I c/3 (Q G/] r-00 o o o ^i ^ "B z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 2 a. en I CQ 'u < in 1 « I C\r- CO kD CNJ o w Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 A BELL 3111 Figure 80. Cleaned and filtered image o f Abell 3111. Scale is approximately 1.9 Mpc in X and 2.5 Mpc in Y. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 18 .3 u __!» LfiCM C3^ m in X .3 U I" - C\ h )) W tia o '/( ; 1 \ CO V i CO m § • n Lr.i & OJ T I CM O I C O \q I < = & R R rë: V P o I I/ (C /Î % CO : ^ 'l O ( K)\I q --- % en rq . q C CO A /o \ 10 s I! III#, >1 r r v: s Ü»! 5b I i u "3 II 1.3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 ABELL 3111 Figure 82. Wavelet transform images for Abell 3111. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 in n I i n 3 Vm >m QJ *o O ! eT CM n Q. i 2 £ S3 o o o o Ci< PI Z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 in CM •n CM I I en ag I < frT V Û. i in o 2 2 & rn oo o o KÛ CM Mi I z Z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 118 Ii i B b en =3 I < •i in y o la c/3 - o O o O o o (g o GO I ^ Z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 2 CL a 0) c u i c CQ < m 3 fo "O =3 QC < 1 ctS •3 e2 S o CNJn o t t . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 ABELL 3112 Figure 87. Cleaned and filtered image o f Abell 3112. Scale is approximately 1.8 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. "OCD O Q. C g Q. "O CD C/) 3o" O 8 FIELD A-1 "O a3112hcd.fitsI200*300,200:300] (O' 1 1 1 1 r i 1 1 1 1 ' 1 "1 l"I"“ 3" 05' 1 1 1 1 1 1 Flejd Ctnt«r> 03"17*40.2B» i -4i®15-25,47 3 CD Scâleî 8.11"/ni "n c m Ritio: 1.00 3. 3" lo CD Contour Lovais* 120.9246 CD "O - - 74.8623 O 46.3460 Q. C 28.6920 17.7627 Oa [ ( I m 1 3 is- 10.9966 "O 6.8078 O 4.2146 - - 2.6092 1.6153 CD Q. I .0000 2 0 - "O CD - - (/) -44°25" 1 1 l l 1 1 1 1 1 1 1 1 11 1 i i___L_.-I___i_j___L_, 1 1 1 1 1 1- 40® 20* 3h8"00* 40® 20® ahz'oo® 40® Figure 8 8 . Contour map of Abell 3112. Scale is approximately 1.8 Mpc per side. Contour levels are given in counts. 122 ABELL 3112 Figure 89. Wavelet transform images for Abell 3112. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 123 u < -§ kO 0) .0 4 S3 1 < I Ia. S .23 I § Eb ^ m rn Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 124 .a < CN (D 1 013 m > CO < TT a. i2 CL 2 X o Ü . 3 CN in o in tH tH U4 U -9 0 Z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 125 CLI I I CVJ 2 -3 cn b s =3 CO < < I 1 \n I c/5 c\o i u oo o o KD ja CNJ 1 2 Z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 126 in 2 eu (N H I < (N î < 1 <ü "3 .0 fO C\ o o Ci, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 127 ABELL 3158 Figure 94. Cleaned and filtered image o f Abell 3158. Scale is approximately 1.8 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 128 Z.&V r\jm CM ^ I ^c»9inoor^CT*'^f«^*^o‘a ^ o ^ ^ ^ t o o T-' ^ ^ c_ tv. o CM V o~ lo M ry — I cc O'^ 0 ‘in CNI CM .a LU 5 i u_ m00 fO co I<4-1 O ro CL uîi8 « gS m •S CN (U I b i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 129 ABELL 3158 Figure 96. Wavelet transform images for Abell 3158. Clockwise &om upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 130 V •û < 1 lO00 KO (D m 3 i a 1 CN 3Sd °o & PO Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 131 V < i 00 m (0 013 ru ü] > CQ < 01 T3 I O TT Û. .0 i 2 I 00 ON 3 ®o ÎIn PO Z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132 in T4 en s § 00 in m00 a < ! 1r < 1 in o I in c< c\ u - o o o en o o ^ "§ I s z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 133 in I (D 30 c If) § H u in ■£ I 3 H s in o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 134 ABELL 3266 Figure 101. Cleaned and filtered image of Abell 3266. Scale is approximately 1.8 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■DCD O Q. C g Q. ■D CD WC/) 3o " 0 SER 40/6 3 CD a3266hcd.fitsl190i320,200=320] 8 ■D 10' Field Center! 04"31"27.13» (O'3" -61®23'43.50" 1 Scileî 10.51"/#* 3 CD 15' X/1 Ratio: 1.00 Contour Levais: 3. 21.9312 3" CD 16.1048 2 0 ' 11 .8263 ■DCD 8.6845 O 6.3773 Q. C 4.6831 3.4389 Oa 3 25' 2.5253 ■D 1.8544 O I.361B I.0000 CD Q. 30' ■D CD (/) Figure 102. Contour map of Abell 3266. Scale is approximately 1.8 Mpc pet side. Contour levels are given in counts. w cn 136 ABELL 3266 Figure 103. Wavelet transform images for Abell 3266. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 137 u M < n o - to 1 tu3 m > O 01 T3O î cC M Q. â i O I s ga vo • o o o o o j i n I ^ z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 138 M < I VO cn( V | pa < ! &T J 4 1 2 32 vo . o o o o o t l s CO lO CM u XiI "o^ Z "o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 139 in I v4 I >o B § I I b ^2 o. in I o c/5 a oo o o o o JS 00 CNJ u T3u .ay O g s (4-, z 0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 140 0) c u c. i (A *3 o M CNJ o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141 ABELL 3558 Figure 108. Cleaned and filtered image o f Abell 3558. Scale is approximately 1.8 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. "OCD O Q. C g Q. "O CD (AC/) 3o " 0 3 A3558 CD 8 a3558hcd.fits[190=320,200=320] "O 1 1 1 1 1 1 L * ^ ! 1 1 1 ? «0 1 1 15" . V *■-» F leld Cenl«r< (O' 13P27"57.16» 3" ♦ ♦ ♦ ♦ 0 * ’ -# Û -31*28 34.00- 1 i . 0 » \ o 3 CD ♦ Scile: 10.51"/** A* c f 0 ♦ 2 0 ' X/ï Ritio: 1.00 "n / o ^ S < ^ o ' 3.c • ( o / ? \ J . Contour Lovels-' 3" ♦ r 0 . ^ » 959.3879 CD 352.9499 □ CD 25' ' J 222.6963 "O > , \ j f W o O -♦ *? ♦ r y 140.5119 Q. r 0 ^ \ y ^ 88.6570 C I O J f O V . / 7 < a ^ - a ' / < K 65.93B8 O • Û ♦ - 35.2950 3 f t ' \ % 7 ( y ^ ♦ 22.2696 "O 30' o f . t <5 14.0512 O r r /t 8.8657 L V — 1 ( 9 / ^ / / o J y ^ ^ o CD r 1% ____: Q. o 35' 5 / ^ 1 > .< v X ♦ "O » ' * CD : -31“40' « % (/) ««>**, » 1 1 __ 1___1 c \ iQ 1 ♦ 1 1 1 1 13*’29*QÛ‘ 30" 13^28*00® 30* 1347"00® Figure 109. Contour map of Abell 3558. Scale is approximately 1.8 Mpc pet side. Contour levels are given in counts. 143 ABELL 3558 0 Figure 110. Wavelet tra n s fo rm images for Abell 3558. Clockwise from upper left in 2 , 3 , 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 144 in o inCO in n o 3 o < n tn 00 Of I m a m ,o >ID â 01 a T) < O I o fed SnUl o o o o o o tt. in CO CO \D CM I ^ Z "o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 145 in o • COm in —n o 4 n m I o I > 01 T3O I Oi Z (C °z a i I § 0 0 &5 U") o o o o iu iP KD CM I ’B 1 S 2 "o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 146 I a § 00 t o cOlO 00 B ■ë =3 o < A < I u in I c/3 r o oo o o o o U. tn tf) o i n i n CM tH !■ § I s Z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 147 I I m00 m o I 3 CO 00 < m (A *o 1 I I in in o ‘T o J l i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 148 ABELL 3562 Figure 115. Cleaned and filtered image of Abell 3562. Scale is approximately 1.8 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. "OCD O Q. C g Q. "O CD en en A3562 CD 8 a3562hcd.fitsI190i320,200i320] "O FleJd Center' CQ- 13"33"40.16» -31*39 19.50" Scile: 10.51711 X/1 Ratio: 1.00 Contour Levels-' 3. 61.94B4 3" CD 41.0041 27.1409 "OCD 17.9647 O 11.8910 Q. C 7.8707 a 5.2097 3O 3.4483 "O 2.2825 O 1.5108 1.0000 CD Q. "O CD -31*50' en en 13^34"00= 30® I3^33*00“ Figure 116. Contour map of Abell 3562. Scale is approximately 1.8 Mpc per side. Contour levels are given in counts. 150 ABELL 3562 Figure 117. Wavelet transform images for Abell 3562. Clockwise firom upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 151 u SI < 2 CD 1 in Ql 3 m i > CQ < QJ i (sT I o 2 2 od o Isa • o o o o tu % Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 152 in n - CN (0 I NO Qj m 3 m > 01 < "O o ! V (L in a ■ I s o o o & Jo CM iI - g^ Z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 153 S i § s in B en -ë Ü I I Ü i . 6 tn o c/3 o o o o o in tH I ^ Z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 154 l I CD S C fOto I u £. in 1 I I S (U o n o U h II U Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 155 ABELL 3667 Figure 122. Cleaned and filtered image of Abell 3667. Scale is approximately 1.8 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CD "D O Q. C g Q. "O CD C/) C/) CD A3667 8 "D a3667hc d .f i t s1160 > 360,175:3501 Fleid Center' CQ' 2[ri2"24.81» -56*47 41.99" Scaleî 16.13'/** X/ï Ratio: 1.00 3"3. Contour Lovais' CD 32.6155 20.5790 ■DCD à 12.9844 O 8.1926 Q. C 5.1692 Oa 3.2615 3 2.0579 "O Z 1.2984 O 0.0193 0.5169 CD 0.3262 Q. -5 7 °0 0 ’ ■D CD C/) C/) 20^15" Figure 123. Contour map of Abell 3667. Scale is approximately 1.8 Mpc per side. Contour levels are given in counts. Ln ON 157 ABELL 3667 Figure 124. Wavelet transform images for Abell 3667. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 158 in O XIu < n 1 o 0) so 301 ro y > 01 < T] O I £ eT m CL in o 1 I s U-) (S a • o o o n I s z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 159 in KÛ n < r4 O (D 1 SO 013 (Q > CQ < QJ T3O ! (C TT in Û. o 1 2 s a . o o o t i s CM ^I -Bs Z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 160 in tH \os I en ' b I CQ < 1 in i o C/3 N o o o O O O CM tH i l ■ i ^ z 'o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 161 in CL So IT) CL e s u Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 162 ABELL 3897 Figure 129. Cleaned and filtered image of Abell 3897. Scale is approximately 1.8 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ■DCD O Q. C g Q. ■D CD C/) 3o " O Abell 3897 8 a3897hcd.f its [200^300,2001300] ■D T } 1 1 r !— 1— 1— — 1 ! 1 1 ^ y I y I Field Center' CQ- 22"3<1«1B.91® -O' -17*22'01.49 Scale: S.II'Vni 15' X/1 R atio: 1.00 Contour Levais' 3. 7.7233 3" - CD t 4.8731 3.0747 CD ■D 2 0 ' 1.9400 O I \\ I .2241 Q. \\ C 0.7723 - ii\r a 0.4873 O 0.3075 3 V) ■D 0.1940 O Û.I224 25' i 0.0772 CD L// Q. - ■D -11*30' CD (\ j C/) O C/) 1 1 — 1___ 1___ 1___ 1______1___ 1___ L___ 1 1 1 1 1 1 22*’40"0D” 40* 20* 22"'39"00* 40* Figure 130. Contour map of Abell 3897. Scale is approximately 1.8 Mpc per side. Contour levels are given in counts. a 164 ABELL 3897 Figure 131. Wavelet transform images for Abell 3897. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 165 .o < I gen CQ < I 2 ,o i 1 2 S a . o o O c i s n CM tH Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 166 < n m 1 r- 01 Os00 3 tn m > 1 Of a "O < o I a. I 2 2 (f) 2 o o o o in (Mo o II Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 167 in § r- § § I u b < a U CQ .0 < I b Q- ID O c/3 ÇU - O o O o o a r*i CM .a "o 1 ^ 2 o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 168 oa . 0) I g c o z u i CQg: a VÜ < r- s S "O u m JO (T < o. I ui O in o 1 1 , Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 169 ABELL 4038 Figure 136. Cleaned and filtered image of Abell 4038. Scale is approximately 1.8 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. "OCD O Q. C g Q. "O CD C/) C/) CD A 4038 8 "O a4038hcd.f it s [200=300,200=3001 CQ- FleAd Ctnb«r< 2 y ’47"53.06® -28“ 00' -28*00 27.99- Scile: 8.11"/nm X/î R»tlo: 1.00 3. 3" Contour Lovais-' CD 43.2715 CD 29.6880 "O O 20.3686 Q. 13.9747 C 9.5878 a 6.67B1 3O "O 4.5132 O 3.0964 2.1244 1.4575 CD Q. I.0000 "O CD C/) C/) 23''4B™00® 40* 20* 23*'47"D0* Figure 137. Contour map of Abell 4038. Scale is approximately 1.8 Mpc per side. Contour levels are given in counts. 171 A BELL 4038 Figure 138. Wavelet transform images for Abell 4038. Clockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 172 tn o co m o < n i00 I a A < î eT j 4 I C\ tn 00 o o o n u. ’i 1 s 2 "o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 173 IT) O - OOn < 0 ■ X I 00 1 Iy < ! pT 4 2 2 ? # 0 0 o o o o tii CM w u ^ "o I ^ Z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 174 in I I 00 00 S i -3 H b u 3 CQ < < I •i s in LO o CO oo ? o o O r\i ^i -S 8 Z "o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 175 l i < "K I I Su o TT (M O, a | II Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 176 ABELL 4059 Figure 143. Cleaned and filtered image o f Abell 4059. Scale is approximately 1.8 Mpc per side. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. "OCD O Q. C g Q. "O CD WC/) 3o " 0 3 CD A 4059 "O8 a4059hc d.f i t s[200 = 300,200 1 300] Fteid Center! CQ'3" 2y’57*0B.11® - 3 4 0 4 7 15.98" 1 3 CD 40' Scile: 8.11 "/mm X/1 R atio: 1.00 "n 3.c Contour Lovais: 3" 56.0450 CD 35.3620 "OCD 22.3119 O 45' 14.0779 Q. C 8.8825 a 5.6045 O 3.5362 3 "O 2.2312 O 1.4078 50' 0.8883 0.5605 CD Q. "O CD C/) C/) Figure 144. Contour map of Abell 4059. Scale is approximately 1.8 Mpc per side. Contour levels are given in counts. 178 A BELL 4059 Figure 145. Wavelet transform images for Abell 4059. Qockwise from upper left in 2, 3, 4, and 5 pixel scales. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 179 \û m o ■ (0 01 1 m > CQ < 01 T3O £ g m a. v2 CNJ o 4 I U o o o o n t r ? Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 180 in o m • in o o " JD 1 O ! pT Q. 4 2 ï O S) o o o o O in n Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 181 in I S § c\ S I s ■H O a < CQ < I 1 8 in o ^— L • C/] 00 V O o o O \û TT CNJ i s z o Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 182 i I S ? s pa es < m I • i en I o CL. ^ ' i tn ^ 1 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY Abell, George. O., Corwin, Harold, G., Jr., Olowin, Ronald, P., 1989, ApJS, 70, lA Bautz, LP. & Moi^an, W. W., 1970, ApJ, 162,149 Bird, C., 1994, AAS, 185.5304 Buote, D. A. & Tsai, J. C., 1995, ApJ, 452, 522 Buote, D. A. & Tsai, J. C., 1996, ApJ, 458, 27 Dressier, A. & Shectman, S. A., 1988, AJ, 95, 985 Escalera, E., et al, 1994, ApJ, 423, 539 GeUer, M. J. & Beers, T. C., 1982, PASP 94, 421 Henriksen, M. J., Mushotzky, R. P., 1986, ApJ, 302,287 Katgert, P., Mazure, A., Perea, J., et aL, 1996, A&A, 310, 8 King, I. R., 1962, A.J., 67,471 King, I. R., 1966, A.J., 71, 64 Kauffrnann, G., & White, S. D. M., 1993, MNRAS, 261,921 Lacey, C. & Cole, S., 1993, MNRAS, 262, 627 Mazure, A , Ka%ert, P., den Hartog, R., et aL, 1996, A&A, 310, 31 Mohr, J. J., Fabricant, D. G. & Geller, M. J., 1993, ApJ, 413, 492 Mohr, J. J., Fabricant, D. G. & Geller, M. J., 1993, egtejiasa, 285 Pislar, V., Durret, F., Gerbal, D., et aL, 1997, A&A, 322, 53 PownaU, H. R., 1997, Ph.D Thesis, University of Leichester 183 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 184 Rhee, G., 1989, Ph.D Thesis, University o f Leiden Rhee, G., Bums, J. B. & Kowalski, M. P., 1994, AJ, 108,1137 Richstone, D., Loeb, A. & Turner, E. L., 1992, ApJ, 393,477 Rood, H. J., Sastry, G. N., 1971, PASP, 83, 313 Salvador-Sole, E., Sanroma, M. & Gonzalez-Casado, G., 1993, ApJ, 402, 398 Sarazin, C. L , 1998, Private Communication Sarazin, C. L., 1988, X-ray Emissions From Clusters o f Galaxies (Cambridge University Press) Starck, J. L., Murtagh, F. & Bijaoui, A., 1995, adass, 4, 279 Starck, J. L., Murtagh, F. & Bijaoui, A., 1995, GM&IP, 57,420 Struble, M. F. & Rood, H. J., 1984, ApJS, 63, 543 Struble, M. F. & Rood, H. J., 1982, AJ, 87, 7 West, M. J., Jones, C. & Forman, W., 1995, ApJ, 451, 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VTTA Graduate Collie University o f Nevada, Las V eg is Philip L. Rogers, Jr. Local Address: 2649 Heritage Dr. Las Vegas, Nevada 89121 Degrees: Bachelor of Science, Physics, 1993 University of Nevada, Reno Thesis Title: A Study o f X-ray Substructure in Rich Clusters of Galaxies Thesis Examination Committee: Chairperson, Dr. George Rhee, Ph.D. Committee Member, Dr. Lon Spight, Ph.D. Committee Member, Dr. Donna Weistrop, Ph.D. Committee Member, Dr. Stephen Lepp, Ph.D. Graduate Faculty Representative, Dr. Jean Cline, Ph.D. 185 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IMAGE EVALUATION TEST TARGET (Q A -3 ) 1.0 I g i a y â - ^ 2.2 ïï L 6 It 2.0 l.l iJ= 1.25 mil 1.4 1.6 150mm /APPLIED ^ IIVMGE . Inc 1653 East Main street ^ Rochester, NY 14609 USA Phone: 716/482-0300 Fax: 716/288-5989 0 1993, Applied Image, Inc.. All Rights Reserved Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.