CHEMICAL AND THERMODYNAMIC PROPERTIES OF ACCEPT2.0 CLUSTERS By Dana Lindsey Koeppe A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Astrophysics and Astronomy – Doctor of Philosophy 2021 ABSTRACT CHEMICAL AND THERMODYNAMIC PROPERTIES OF ACCEPT2.0 CLUSTERS By Dana Lindsey Koeppe Clusters of galaxies offer tremendous insight into the formation and evolution of large scale structure in the Universe. While most of the total mass of a cluster is in the form of dark matter, the bulk of observable matter exists as a hot X-ray emitting gas called the intracluster medium (ICM). Studies of X-ray emission from the ICM reveal the thermodynamic and chemical processes that affect cluster formation and evolution. Additionally, measurements of emission lines in the X-ray spectra of clusters revealed that the ICM is polluted with heavy elements that originated in stars, mostly in galaxies. The radial distributions of those heavy elements show evidence of interplay between the ICM and the cluster core. In chapter 2, we describe the data reduction and spectral analysis of an archival sample of X-ray observations of clusters from the second catalog of the Archive of 𝐶ℎ𝑎𝑛𝑑𝑟𝑎 Cluster Entropy Profile Tables (ACCEPT2.0). These clusters are used throughout this thesis to show how cluster X-ray properties can be used to test and constrain our theories of structure growth in the Universe. We also find that our analysis for the 𝐿 𝑋 − 𝑇 relation is consistent with previous works. We explore an analysis application of the 𝐿 𝑋 − 𝑇 relation for ACCEPT2.0 data in chapter 3 by testing a recent claim that the expansion of the Universe is not uniform in all directions. If the expansion of the universe were isotropic, the luminosity and temperature should scale similarly for clusters in all directions. Using global core-excised luminosities and temperatures for 302 ACCEPT2.0 clusters, we found that our sample measurements support the assumption of isotropic expansion. Chapter 4 investigates how the amount of metals in clusters’ ICM changes with redshift. Previous works have shown varying results, which are more scattered when including core emission. We show that the core-excised abundances for 302 ACCEPT2.0 clusters are not statistically different between cool-core (CC) and non-cool core (NCC) clusters, and that the global metallicity content of the ICM does not change significantly as a function of luminosity or redshift. Furthermore, we explore the degree to which a small systematic bias arising from model uncertainties that affect hot and cool spectra can look like evolution if luminosity bias is not taken into account. Finally, chapter 5 describes the ongoing work of a data reduction pipeline for the SOAR Adaptive-Module Optical Spectrograph (𝑆 𝐴𝑀𝑂𝑆). 𝑆 𝐴𝑀𝑂𝑆 is a multi-object spectrograph which will be commissioned on the SOuthern Astrophysical Research Telescope (SOAR) in 2021. The current version of the pipeline is able to produce wavelength calibrated spectra from test data using SOAR 𝐺𝑜𝑜𝑑𝑚𝑎𝑛, and is in active development. To my sister, mom, and dad—Thank you for always supporting me. I love you forever. iv ACKNOWLEDGEMENTS The completion of this work is owed to the support and friendship of many colleagues over the years. I would like to thank my cat, Gus (the best work-from-home buddy and the best cat, no matter what anybody else says), Massimo Robberto, Rachel Frisbie, Mark Voit, Laura Chomiuk, Kim Crosslan, Sam Swihart, Danny Huizenga, Carl Fields, Jenn Ranta, Austin Edmister, Laura Shishkovsky, Kelsey Funkhouser, Jessica Maldonado, Thomas Connor, Dan Kelson, Michael McDonald. I owe many thanks to my committee members Brian O’Shea, Steve Zepf, Jay Strader, and Kirsten Tollefson. Finally, I am especially grateful for the encouragement and support of my advisor, Megan Donahue, without whom this dissertation would not have been possible. The financial support for this dissertation was provided by the following grants: NASA NNX13A141G (HST Treasury Program/CLASH), a Chandra program GO5-16132-x, an HST grant HST-GO-15661.002-A. The majority of the support came from an NSF/JHU subaward JHU- 2003349346 grant (SOAR Adaptive-optics Multi-Object Spectrograph, or SAMOS). The pipeline I designed in this project is described in Chapter 4. This dissertation work was also supported by the MSU College of Natural Science Continuation (Fall 2019) and Completion (Summer 2020) Fellowships. v TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix CHAPTER 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Cluster Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Cosmology vernacular . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 Anatomy of galaxy clusters . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 X-ray scaling relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Metals in the ICM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 This work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 CHAPTER 2 ACCEPT2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 Archive of Chandra Cluster Entropy Profile Tables (ACCEPT) . . . . . . . . . . . 15 2.2 ACCEPT2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 K-correction and bolometric correction . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Vetting of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Initial Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4.2 Radially weighted temperature and abundance . . . . . . . . . . . . . . . . 22 2.4.3 𝐿 𝑋 − 𝑇 relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 CHAPTER 3 LUMINOSITY-TEMPERATURE RELATION OF ACCEPT2.0 CLUSTERS 59 3.1 The Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.4.1 Core-excised vs. core included 𝐿 𝑋 . . . . . . . . . . . . . . . . . . . . . . 68 3.4.2 Different spectral energy bandpasses . . . . . . . . . . . . . . . . . . . . . 70 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 CHAPTER 4 GLOBAL METALLICITY EVOLUTION OF ACCEPT2.0 CLUSTERS . . . 88 4.1 The Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.3.1 Dependence on core status . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.3.2 Luminosity dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.3.3 Redshift Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.3.4 Multiple Linear Regression Analysis . . . . . . . . . . . . . . . . . . . . . 95 4.3.5 Comparison to Maughan et al. (2008) . . . . . . . . . . . . . . . . . . . . 97 4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4.4.1 Comparison to observations . . . . . . . . . . . . . . . . . . . . . . . . . 105 vi 4.4.2 Comparison to simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 106 4.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 CHAPTER 5 PIPELINE FOR THE REDUCTION OF DATA FROM THE SOAR ADAPTIVE- OPTICS MULTI-OBJECT SPECTROGRAPH (SAMOS) . . . . . . . . . . 120 5.1 Pipeline Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.2 Step 0: Pipeline Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.3 Step 1: CCD Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.4 Step 2: Slit tracing and extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.4.1 Note on spectral extraction and tracing . . . . . . . . . . . . . . . . . . . . 128 5.5 Step 3: Wavelength calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5.6 Remaining steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 APPENDIX A BOLOMETRIC AND K- CORRECTION PROCEDURE . . . . . . 135 APPENDIX B RADIAL ABUNDANCE PROFILES FOR ACCEPT2.0 CLUSTERS 139 APPENDIX C RADIAL TEMPERATURE PROFILES FOR ACCEPT2.0 CLUS- TERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 vii LIST OF TABLES Table 2.1: ACCEPT vs. ACCEPT2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Table 2.2: ACCEPT2.0 Redshift Updates. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Table 2.3: Global CE properties for 432 ACCEPT2.0 clusters . . . . . . . . . . . . . . . . 26 Table 2.4: Table of full cluster names and coordinates in ACCEPT2.0. . . . . . . . . . . . . 43 Table 3.1: Best fit 𝐿 𝑋 − 𝑇 using tied and separate models . . . . . . . . . . . . . . . . . . 68 Table 3.2: Difference in normalization of 𝐿 𝑋 − 𝑇. . . . . . . . . . . . . . . . . . . . . . . 69 Table 3.3: Global CE 𝐿 𝑋 − 𝑇 properties for clusters separated by sky region. . . . . . . . . 76 Table 4.1: Median global CE abundances of ACCEPT2.0 sub samples. . . . . . . . . . . . 96 Table 4.2: Best fit parameters to the 𝑍 (𝐿 𝑋 , 𝑧) model. . . . . . . . . . . . . . . . . . . . . . 96 Table 4.3: Median CE global abundances comparison for ACCEPT2.0 and M08 overlap. . . 100 Table 4.4: Global CE luminosities and metallicities M08 and ACCEPT2.0 overlap. . . . . . 100 Table 4.5: Global CE temperatures M08 and ACCEPT2.0 overlap. . . . . . . . . . . . . . 103 Table 4.6: Full global metallicity table for 302 ACCEPT2.0 clusters. . . . . . . . . . . . . . 108 Table 5.1: 𝑆 𝐴𝑀𝑂𝑆 reduction pipeline status. . . . . . . . . . . . . . . . . . . . . . . . . . 123 viii LIST OF FIGURES Figure 1.1: CC vs. NCC surface brightness profiles. . . . . . . . . . . . . . . . . . . . . . 7 Figure 1.2: CC vs. NCC radial temperature profiles. . . . . . . . . . . . . . . . . . . . . . 8 Figure 1.3: CC vs. NCC X-ray emission . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Figure 1.4: Simulated X-ray spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Figure 2.1: 𝐿 𝑋 − 𝑇 core-included and core-excised posterior distributions. . . . . . . . . . 24 Figure 2.2: 𝐿 𝑋 − 𝑇 core-included vs. core-excised. . . . . . . . . . . . . . . . . . . . . . . 25 Figure 3.1: ACCEPT2.0 all-sky map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Figure 3.2: Posterior 𝐿 𝑋 − 𝑇 distributions for RF, RB, and NR clusters. . . . . . . . . . . . 65 Figure 3.3: Posterior distributions for the tied 𝐿 𝑋 − 𝑇 model. . . . . . . . . . . . . . . . . 66 Figure 3.4: Best fit 𝐿 𝑋 − 𝑇 for NR clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Figure 3.5: Best fit 𝐿 𝑋 − 𝑇 for RB clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Figure 3.6: Best fit 𝐿 𝑋 − 𝑇 for RF clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Figure 3.7: Stacked tied and separate 𝐿 𝑋 − 𝑇 for NR, RF, and RB clusters. . . . . . . . . . 73 Figure 3.8: 𝐿 𝑋 − 𝑇 for bandpass vs. bolometric luminosities. . . . . . . . . . . . . . . . . 73 Figure 4.1: Global 𝑍 null model MCMC results. . . . . . . . . . . . . . . . . . . . . . . . 92 Figure 4.2: Redshift distribution of CC and NCC clusters in ACCEPT2.0. . . . . . . . . . . 93 Figure 4.3: Binned weighted mean metallicity profiles for CCs and NCCs. . . . . . . . . . 94 Figure 4.4: Stacked weighted median metallicity profiles for CC and NCC clusters. . . . . . 95 Figure 4.5: Metallicity differences between simulated clusters. . . . . . . . . . . . . . . . . 97 Figure 4.6: Best fit results global CE abundance as a function of 𝐿 𝑋 and 𝑍. . . . . . . . . . 98 Figure 4.7: Temperatures from M08 vs. ACCEPT2.0 . . . . . . . . . . . . . . . . . . . . . 99 ix Figure 5.1: Cartoon multi-object spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Figure 5.2: First CCD data reduction steps. . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Figure 5.3: Slit cutout diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Figure 5.4: Cartoon diffraction grating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Figure 5.5: Wavelength calibrated spectrum output for 𝑆 𝐴𝑀𝑂𝑆 pipeline. . . . . . . . . . . 131 Figure B.1: Radial metallicity profile for clusters A0013 through A0160. . . . . . . . . . . 140 Figure B.2: Radial metallicity profile for clusters 011502+002441 through A3094. . . . . . 141 Figure B.3: Radial metallicity profile for clusters A3128 through AS0463. . . . . . . . . . . 142 Figure B.4: Radial metallicity profile for clusters 04371+0043 through A3376. . . . . . . . 143 Figure B.5: Radial metallicity profile for clusters A3391 through A0611. . . . . . . . . . . 144 Figure B.6: Radial metallicity profile for clusters A0644 through HydraA. . . . . . . . . . . 145 Figure B.7: Radial metallicity profile for clusters 0947124+762313 through A1033. . . . . . 146 Figure B.8: Radial metallicity profile for clusters A1068 through A1423. . . . . . . . . . . 147 Figure B.9: Radial metallicity profile for clusters 4-33144 through A1664. . . . . . . . . . . 148 Figure B.10: Radial metallicity profile for clusters A1689 through LCDCS0829. . . . . . . . 149 Figure B.11: Radial metallicity profile for clusters A1835 through 145715+222009. . . . . . 150 Figure B.12: Radial metallicity profile for clusters AS0780 through 15328+3021. . . . . . . . 151 Figure B.13: Radial metallicity profile for clusters A2107 through A2204. . . . . . . . . . . 152 Figure B.14: Radial metallicity profile for clusters A2218 through 43072. . . . . . . . . . . . 153 Figure B.15: Radial metallicity profile for clusters A2261 through A2384. . . . . . . . . . . 154 Figure B.16: Radial metallicity profile for clusters A2390 through A3921. . . . . . . . . . . 155 Figure B.17: Radial metallicity profile for clusters A2537 through A4038. . . . . . . . . . . 156 Figure B.18: Radial metallicity profile for A2670. . . . . . . . . . . . . . . . . . . . . . . . 157 x Figure C.1: Radial temperature profile for clusters A0013 through A0160. . . . . . . . . . . 159 Figure C.2: Radial temperature profile for clusters 011502+002441 through A3094. . . . . . 160 Figure C.3: Radial temperature profile for clusters A3128 through AS0463. . . . . . . . . . 161 Figure C.4: Radial temperature profile for clusters 04371+0043 through A3376. . . . . . . . 162 Figure C.5: Radial temperature profile for clusters A3391 through A0611. . . . . . . . . . . 163 Figure C.6: Radial temperature profile for clusters A0644 through HydraA. . . . . . . . . . 164 Figure C.7: Radial temperature profile for clusters 0947124+762313 through A1033. . . . . 165 Figure C.8: Radial temperature profile for clusters A1068 through A1423. . . . . . . . . . . 166 Figure C.9: Radial temperature profile for clusters 4-33144 through A1664. . . . . . . . . . 167 Figure C.10: Radial temperature profile for clusters A1689 through LCDCS0829. . . . . . . 168 Figure C.11: Radial temperature profile for clusters A1835 through 145715+222009. . . . . . 169 Figure C.12: Radial temperature profile for clusters AS0780 through 15328+3021. . . . . . . 170 Figure C.13: Radial temperature profile for clusters A2107 through A2204. . . . . . . . . . . 171 Figure C.14: Radial temperature profile for clusters A2218 through 43072. . . . . . . . . . . 172 Figure C.15: Radial temperature profile for clusters A2261 through A2384. . . . . . . . . . . 173 Figure C.16: Radial temperature profile for clusters A2390 through A3921. . . . . . . . . . . 174 Figure C.17: Radial temperature profile for clusters A2537 through A4038. . . . . . . . . . . 175 Figure C.18: Radial temperature profile for A2670. . . . . . . . . . . . . . . . . . . . . . . . 176 xi CHAPTER 1 INTRODUCTION As their name suggests, galaxy clusters are made from many individual galaxies living together in a large gravitational potential. These structures are typically 1014 − 1015 𝑀 1 and contain anywhere from a few hundred to tens of thousands of galaxies which are visible to us. Zwicky (1933) made one of the first mass estimates of the Coma cluster from observations of galaxy velocity dispersions, and the application of the virial theorem. Zwicky (1933, 1937) showed that if clusters are long- lived structures, there must be 10-100 times more unobserved matter, or “dark matter,” than can be accounted for by the stars in the galaxies. This dark matter comprises 80-85% of the mass of a cluster, with the remainder in the form of observable baryons. Before X-ray telescopes, clusters were defined by their optical properties. For instance, one could estimate the size of a cluster by the luminosity of its brightest members, or its “optical richness”. Originally defined by Abell (1958), optical richness is the number of galaxies brighter than some magnitude limit, with the richest clusters containing over 300 such galaxies, and fewer than 100 in poor clusters. In the 1960s and ‘70s, extended X-ray emission from the nearby Virgo, Coma, and Perseus clusters (Bradt et al., 1967; Meekins et al., 1971; Gursky et al., 1971; Forman et al., 1972) revealed that most of a cluster’s baryonic mass is in the form of hot X-ray emitting plasma that permeates the intracluster medium (ICM). The ubiquity of this hot gas naturally has led us to questions about the origin of the ICM, and its relation to cluster formation and evolution. With larger sample sizes, we have been able to study clusters in a broader context, and better understand their general characteristics. However, many samples in the past have been a combina- tion of previously analyzed data from multiple works. Consequently, combining different catalogs necessitates the use of correction factors to account for systematic differences between samples. The second release of the Archive of Chandra Cluster Entropy Profile Tables (Donahue, Baldi, et al, in prep, hereafter, ACCEPT2.0) will be the largest publicly available catalog of uniformly derived 1𝑀 ≡1 solar mass ∼ 2 × 1030 kg. 1 X-ray properties from X-ray observations of clusters of galaxies available from the Chandra Data Archive. Its predecessor ACCEPT (Cavagnolo et al., 2009) produced radial profiles of density, gas temperature, and entropy, which are related to the thermal history of a cluster. ACCEPT2.0 is an expansion of ACCEPT, as it includes measurements for more X-ray observables and contains more than twice as many clusters. This dissertation will investigate the differences between the average global X-ray properties of clusters of galaxies at different cosmological epochs, and in different directions on the sky, using X-ray data from ACCEPT2.0. Section 1.1 of this introduction will describe the X-ray observables relevant to this dissertation. Section 1.2 defines the terms used throughout this work. Section 1.3 will give an overview of recent literature regarding scaling relations. Section 1.4 covers abundance measurements from X-ray spectra. Finally, Section 1.5 will present an overview of this dissertation. 1.1 Cluster Observables The obvious cluster observables come from optical properties such as cluster richness (number of galaxies within 2 magnitudes2 of the third brightest galaxy member) and compactness (number of galaxies within some characteristic radius of the cluster center) (Abell, 1958), but X-ray observables are most important for this research, as most of the baryons in a cluster are in the form of hot X-ray emitting gas. For reviews of galaxy clusters and how they relate to cosmology, see the review by Voit (2005). Reviews regarding X-ray emission from clusters are provided by Sarazin (1986) and Böhringer & Werner (2009). We study clusters of galaxies to understand the largest structures in the Universe. One aspect of the theory of gravitational assembly of cosmic structure is the prediction of the cluster mass function. The cluster mass function is the number density of clusters above a certain mass 𝑀 as a function of redshift, and shows how many clusters of mass 𝑀 exist a redshift. The cluster mass function would give insights into how large scale structures have grown over the history of the Universe. Unfortunately, mass is not a directly observable quantity, which 2 The astronomical magnitude system quantifies the measured flux of visible light with a loga- rithmic brightness scale in which a difference of +5 magnitudes corresponds to a 100 factor decrease in brightness or flux. So an increase of two magnitudes corresponds to a factor of 1002/5 = 6.3 fainter. 2 is where X-ray observations come in handy. Temperature 𝑇 and luminosity 𝐿 𝑋 are easily derived from X-ray spectra. The temperature is tightly correlated with the mass, while the luminosity is more affected by processes such as recent mergers or AGN activity. Due to the dynamics affecting cluster luminosity, the scaling of luminosity with temperature (𝐿 𝑋 − 𝑇) and mass (𝐿 𝑋 − 𝑀) are more scattered than the mass-temperature (𝑀 − 𝑇) scaling. Therefore, we can use temperature and (less directly) luminosity in lieu of direct mass measurements. Another spectral probe of the ICM comes in the form of emission lines. The ubiquitous presence of heavy elements such as iron in the spectra of clusters is evidence that the ICM is comprised of gas processed in stars and subsequently distributed throughout the cluster. The global metallicity content (amount of elements heavier than hydrogen or helium) of the clusters acts as a tracer for when stellar byproducts became part of the ICM, and spatially-resolved measurements give clues for how this enrichment occurs. 1.2 Terminology Before proceeding, it is important to define some terminology that will be used throughout this dissertation. 1.2.1 Cosmology vernacular An object’s redshift 𝑧 is a dimensionless distance estimate based on the Doppler effect which arises from the finite speed of light and the expanding Universe. Consequently, the rest-frame wavelength of light from an object is lengthened–or “redshifted”–as light travels through the expanding Universe. The wavelength of emitted light increases by a factor of 1 + 𝑧 i.e., 𝜆 obs = 𝜆 rest (1 + 𝑧). Nearly a century ago, Edwin Hubble noticed that the recession velocity of galaxies increased in proportion to their distance, so more distant objects are moving away from us more quickly than nearby objects. We now characterize this expansion of the Universe through the Hubble parameter 𝐻 (𝑧), where the present day Hubble constant 𝐻0 is related to an object’s recessional 3 velocity 𝑣 and its distance 𝑑,3 𝑣 = 𝐻0 × 𝑑. (1.1) Here, the expansion rate of the present day Universe is 𝐻0 . For this work, we assume single digit precision such that 𝐻0 = 70 km s−1 Mpc−1 , where 1 Mpc (mega-parsec) = 3.26×106 light-years = 3.086 × 1024 cm. We relate the Hubble constant as a function of redshift to the present day value via 𝐻 (𝑧) = 𝐻0 𝐸 (𝑧), (1.2) p where 𝐸 (𝑧) = Ω 𝑀 (1 + 𝑧) 3 + ΩΛ , and the cosmological parameters Ω𝑚 ' 0.3 and ΩΛ ' 0.7 refer to the matter and dark energy content of the local Universe where Ω 𝑋 = 𝜌 𝑋 /𝜌𝑐,0 (I will define 𝜌𝑐,0 soon.) and redshift 𝑧 serves as a distance measure. Objects that are moving outward along the line of sight experience a redshift due to the Doppler Effect, so 𝑧 is able to give a general idea of the distance to a source based on its recession velocity. For local systems, redshift is 𝑧 ∼ 0. The redshift of a cluster is important for estimating its properties because it tells us about the environment in which it formed. For a given redshift and Hubble parameter, there is some critical density 𝜌𝑐 (𝑧) at which the gravitational potential of material within some radius overcomes and slows the expansion of space. The critical density is the maximum average density a Universe without dark energy can have before it would continue to expand forever. For reference, the present day critical density is 3𝐻02 𝜌𝑐,0 = ≈ 10−29 g cm−3 , (1.3) 8𝜋𝐺 where 𝐺 = 6.67 × 10−8 cm3 g−1 s−2 is the gravitational constant. We relate the critical density at different cosmological epochs to the present day critical density 𝜌𝑐,0 via 𝜌𝑐 (𝑧) = 𝐸 (𝑧) 2 𝜌𝑐,0 . (1.4) 3 ∫ 𝑧 𝐻 (𝑧) ' 𝐻0 (constant) when 𝑧 << 1. For larger 𝑧, the co-moving radial distance is 𝑑 (𝑧) = 𝑐 0 𝑑𝑧/𝐻 (𝑧). For flat universes, the luminosity distance, used to relate bolometric flux and bolometric luminosity by the equation 𝐿 = 4𝜋𝑑 2𝐿 𝐹 is 𝑑 𝐿 = (1 + 𝑧)𝑑. 4 1.2.2 Anatomy of galaxy clusters Ideally, clusters are spherical virialized structures in which a sphere of gas is supported against further collapse by outward pressure provided by the kinetic energy of the particles. According to the virial theorem, the average kinetic energy (𝐸 𝐾 ) of gas in an idealized ICM model is related to its gravitational potential energy (𝐸 𝐺 ) by 1 𝐸 𝐾 = − 𝐸𝐺 . (1.5) 2 Based on a virialized sphere of gas with mass 𝑀𝑣 , the virial radius 𝑅𝑣 is often used as a reference point for the “edge” of a cluster. Assuming the gas has been heated solely by gravitational processes, 𝑅𝑣 is the radius inside which the temperature of the gas (i.e. the virial temperature, 𝑇𝑣 ) provides enough thermal pressure to support the ICM against further collapse. In simulations, 𝑅𝑣 turns out to be the radius at which the density of material is ∼180-200 times the critical density of the Universe at the epoch of interest (Voit, 2005). However, 𝑅𝑣 is out of the typical X-ray instrument field of view for most nearby systems, and X-ray observations have to be fairly sensitive to detect an X-ray cluster this far from its much brighter center, so we often use scaled radii 𝑅Δ to define our regions of interest for a cluster. 𝑅Δ refers to the radius at which the density is Δ times the critical density of the Universe at the redshift of the cluster. Similarly, we define characteristic mass 𝑀Δ and temperatures 𝑇Δ as the mass and temperature within the scaled radius. Two commonly used values of Δ are 2500 and 500. Keep in mind that a smaller 𝑅Δ refers to a region of lower density and is therefore at larger radial distances, with virial radius being ∼ 𝑅200 . The use of scaled radii is also important for comparing clusters at different epochs because, as shown in Equation 1.4, the critical density changes with redshift as 𝜌𝑐 (𝑧) ∼ (1 + 𝑧) 3 . Due to expansion, the Universe is less dense today than in the past. Therefore, the angular size of 𝑅Δ is larger for a cluster at low 𝑧 than for an identical such cluster at high 𝑧. Similarly, the angular size 𝑅Δ can differ between clusters of different masses at the same 𝑧. Scaled radii are therefore useful because they factor out the angular size differences of clusters and allow us to directly compare their properties within similarly defined regions. 5 An interesting distinction between clusters is their status as either cool-core (CC) or non-cool core (NCC). The term “cool-core” arises from the drop in temperature towards the center. Increased density towards the centers of CCs result in sharper peaks in surface brightness aligning with the drop in the temperature profile. NCCs, however, show less dramatic central luminosity peaks and flatter temperature profiles in their cores. Outside the core radius, their temperatures and X-ray surface brightness profiles are nearly indistinguishable when scaled by size. The stacked profiles of CC Abell 2390 and NCC Abell 2219 give good examples of differences in surface brightness (Figure 1.1) and radial temperature profiles (Figure 1.2) between CCs and NCCs. Choice of aperture is therefore crucial when characterizing clusters by global X-ray properties. With adequate spatial resolution, global X-ray properties can be estimated for clusters within a full aperture, or for a core-excised aperture. We use core-excised global properties because they minimize dependence on a cluster’s core status. The “core” is used to describe the region inside which the density is such that thermodynamics unrelated to gravity can affect the gas in times comparable to the Hubble time, and shorter timescales increase the scatter in observable properties (Vikhlinin et al., 2005; Pratt et al., 2006). For the clusters in this work, we define the core in terms of scale radius: 𝑅𝑐 = 0.3𝑅2500 . Inside this core radius, there is more variability in the X-ray emission between clusters, whereas cluster properties are less scattered in the region [0.3 − 1] 𝑅2500 . The radial profiles in Figures 1.1 and 1.2 show how clusters compare in these two regions, where 𝑅𝑐 and 𝑅2500 are plotted as vertical dashed lines. 1.3 X-ray scaling relations Early X-ray observations showed a strong correlation between luminosity and temperature, or 𝐿 𝑋 − 𝑇 (Mitchell & Culhane, 1977; Mushotzky, 1984). Scaling relations such as this one are used for comparison to expectations from theoretical models. It is easiest to model the ICM as a hydrostatic sphere which has collapsed under gravitational pressure and is supported against further collapse via thermal pressure. The gravitational potential of the system, and therefore the temperature, is set by the size of the initial overdensity from which it originated. Because gravity is scale-invariant, the simplified hydrostatic model of the ICM results in clusters which are identical 6 102 cnts/arcsec2 101 100 CC ABELL 2390 NCC ABELL 2219 0.01 0.10 1.00 r/r2500 Figure 1.1: CC vs. NCC surface brightness profiles. ACCEPT2.0 surface brightness profile and the 1𝜎 errors for cool-core cluster Abell 2390 (blue triangles) and non-cool core cluster (of similar mass) Abell 2219 (red circles). The dotted lines represent the core-excised region 0.3𝑅2500 < 𝑟 < 1𝑅2500 , where 𝑅2500 is the distance at which the mean density is 2500 times the background density. 7 20 15 kT [keV] 10 5 CC ABELL 2390 NCC ABELL 2219 0.03 0.10 0.30 1.00 r/r2500 Figure 1.2: CC vs. NCC radial temperature profiles. Projected radial temperature profiles and their 1𝜎 errors using the same labels as Figure 1.1. 8 when scaled by mass. This model leads to predictable, self-similar scaling relations between the observables and the mass (Kaiser, 1986). For this model, the mass enclosed within some scaled radius is, 4 3 𝑀Δ = Δ 𝜋𝑅Δ 𝜌𝑐 (𝑧) ∝ 𝐸 (𝑧) 2 𝑅Δ3. (1.6) 3 Remember that the Δ in equation 1.6 is a scalar number reflecting the factor of the overdensity compared to the critical density at the redshift of the cluster (i.e, 200, 500, 2500, etc.). The virial theorem states that bound particles in a spherical volume in hydrostatic equilibrium will have an average kinetic energy equal to half the total gravitational potential energy. According to the theorem, potential and kinetic energy of the particles are related by, 𝑀Δ ∝ 𝜎𝑣2 ∝ 𝑇 . (1.7) 𝑅Δ Temperature should therefore scale with mass as 𝑇 ∝ [𝐸 (𝑧) 𝑀] 2/3 . (1.8) For typical ICM temperatures of 107 -108 K, the ICM radiates primarily via thermal bremsstrahlung due to collisions between ions and electrons. Assuming the gas is isothermal, the bolometric luminosity is 𝐿 𝑋 ∝ 𝑟 3 𝑛2𝑒 Λ(𝑇), where the cooling function Λ(𝑇) ∝ 𝑇 1/2 e−𝐸/𝑘𝑇 for thermal bremsstrahlung. Observations of the Perseus cluster by Branduardi-Raymont et al. (1981) showed a strongly peaked surface brightness profile which deviated from the isothermal model inside of ∼10 kpc. The profile of the Coma cluster, which is recovering from a recent merger (White et al., 1993), was shown to be consistent with the expected model (Branduardi-Raymont et al., 1985; Briel et al., 1992; Jones & Forman, 1999). Other works which considered larger cluster samples showed that clusters could generally be separated into two categories: those with a discernible peak in the surface brightness and those with a flatter profile inside the core (Jones & Forman, 1984). CC clusters have been observed to have a steep decline in temperature and increased luminosity towards the center, as opposed to NCC clusters (Fabian, 1994; Arnaud et al., 2002; Maughan et al., 9 2012). Outside of the denser regions, clusters are more well-behaved because the cooling time for the gas there is longer than the Hubble time, and therefore tracks the results of cosmological processes with longer timescales. Scaling relations of luminosity and temperature with cluster mass are therefore often evaluated using both core-excised CE and core-included CI measurements, where excising the core has been found to significantly reduce the scatter in the 𝐿 𝑋 −𝑇 relation (e.g., Markevitch, 1998; Pratt et al., 2009; Maughan et al., 2012). These results suggests that clusters evolve self-similarly outside of the core region. Still, the outer regions of clusters have been shown to deviate from the self-similar model. In the absence of extra heating and cooling of the gas, numerical simulations based on analytic theory predict, 𝐿𝑋 ∝ [𝑀Δ 𝐸 (𝑧)] 4/3 ∝ 𝑇 2 . (1.9) 𝐸 (𝑧) However, early CI observations showed slopes closer to ∼3 instead of 2 (Mushotzky, 1984; Sarazin, 1988, and references therein; Edge & Stewart, 1991). Later generations of telescopes which were able to excise the core showed that the removing core emission only marginally reduces the slope of 𝐿 𝑋 − 𝑇 to just below 3 (Arnaud & Evrard, 1999; Ettori et al., 2004; Pratt et al., 2009; Mittal et al., 2011). Additionally, the observed 𝐿 𝑋 − 𝑇 relation may steepen even further for lower temperature systems (Maughan et al., 2012; Sun, 2012), although the increased scatter in the lower luminosity systems and the effects of selection bias makes this steepening challenging to verify. The deviation from the predictions of self-similarity models in the 𝐿 𝑋 − 𝑇 relation for all clusters and groups may be indicative of some source of non-gravitational processes such as AGN feedback, supernovae feedback, and radiative cooling. These processes may become more important compared to the energy per particle incurred from gravitational accretion for systems with shallower potential wells, such as groups of galaxies or individual galaxies. Heating/cooling of gas does not necessarily raise/lower the temperature of the gas so much as it decreases/increases the density, or, more specifically, increases/lowers the gas entropy. When heat is injected into the ICM, −2/3 the gas puffs up and decreases the luminosity. Gas entropy, here scaled as 𝐾 ∝ 𝑇 𝑛𝑒 , is useful 10 ABELL 2390 ABELL 2219 Declination Right Ascension Figure 1.3: CC vs. NCC X-ray emission. The core is much brighter and more concentrated in CC Abell 2390 (𝑙𝑒 𝑓 𝑡) than that of NCC cluster Abell 2219 has more diffuse X-ray emission (𝑟𝑖𝑔ℎ𝑡). because it is able to track changes in density with temperature when they are normally independent of each other (Ponman et al., 1999; Voit, 2005). Relaxed CC clusters with high central densities (and therefore strongly peaked surface brightness profiles, as discussed previously in Section 1.2.2) have low central entropy. Conversely, NCC clusters may have higher central entropies as a result of recent mergers or AGN outbursts. This difference in central entropy between CC and NCC clusters is well-demonstrated by the entropy profiles in ACCEPT. ACCEPT (Cavagnolo et al. (2009)), further described in Section 2.1, is a catalog of entropy profiles, and the corresponding radial data, for 239 clusters observed with 𝐶ℎ𝑎𝑛𝑑𝑟𝑎. 1.4 Metals in the ICM In addition to gas temperature, the X-ray spectrum is influenced by chemical abundance. Heavy, non-primordial4 elements can be detected and measured in a spectrum through the analysis of an X-ray spectrum that includes emission lines generated by radiative de-excitation of ions, following collisions between electrons and the various ion species in the ICM. Detection of iron in the X-ray 4 Primordial gas is hydrogen or helium that has never been in any star. All other elements are considered “heavy." 11 spectra of the Perseus, Virgo, Coma, and Centaurus clusters gave the first evidence that gas is not primordial in nature, but was contained heavy elements from stars in galaxies which had been ejected and distributed throughout the ICM (Mitchell et al., 1976; Mitchell & Culhane, 1977; Serlemitsos et al., 1977). The quantity of hot gas in clusters of galaxies far exceeds the mass in stars by at least a factor of 5, which means that most of this gas does contain primordial H and He, but it is polluted with heavier elements. This pollution is caused by stars and their end-states (particularly merging white dwarfs, merging neutron stars, and massive star supernovae) which are very good at making and heavy elements and then sharing them with their environments. Energy ranges available to the ROSAT and Einstein missions were limited to below ∼ 2 − 4 keV, where the brightest lines are part of a region called the iron-L complex, near 1 keV. With ASCA (Tanaka et al., 1994), astronomers were able to sample a much broader energy range to include more line features, including the Fe-K complex at ∼7 keV. For reviews of observations of ICM metallicity, see Werner et al. (2008) and Mernier et al. (2018). Metals are formed from stars and supernovae (mostly SNIa but also a little SNII, a little contribution from asymptotic giant branch stars, and very heavy elements like gold which are formed in neutron star mergers). Excellent spectral resolution is needed to measure individual elements, but the most important emission feature for a relatively hot ICM is the Fe-K complex. Figure 1.4 shows an example of how the spectrum changes with respect to temperature and metallicity. The abundance is estimated from the strength of the emission line in comparison to the continuum. At higher gas temperatures, the strength of the Fe-K lines are easier to discern than the Fe-L features at lower energies, while at lower temperatures the spectra become more dominated by emission lines as the hydrogen-helium bremsstrahlung continuum cuts off at lower energies (𝐸 ∼ 𝑘𝑇, because of the exponential cutoff). The difference in the spectra has to do with the ionization state of the gas at a given temperature and the atomic structure of the iron ions. Gas with hydrogen-like iron5 is hot enough to be stripped of its outer L-shell electrons, leaving mostly K-shell transitions. At cooler temperatures, the iron ions with bound electrons in the L-shell dominate. 5A “hydrogen-like” atom is one that can be ionized to have a single electron. Similarly, a helium-like atom is one where a nucleus is paired with two electrons. 12 Current Theoretical Model Current Theoretical Model a) kT = 3 keV b) kT = 3 keV 1 Z = 0.3 Zsun 1 Z = 0.8 Zsun Photons cm−2 s−1 keV−1 Photons cm−2 s−1 keV−1 0.1 0.1 0.01 0.01 0.1 1 10 0.1 1 10 Energy (keV) Energy (keV) Current Theoretical Model Current Theoretical Model c) kT = 20 keV d) kT = 20 keV DanaKoeppe 23−Jul−2020 18:13 DanaKoeppe 23−Jul−2020 18:13 1 Z = 0.3 Zsun 1 Z = 0.8 Zsun Photons cm−2 s−1 keV−1 Photons cm−2 s−1 keV−1 0.1 0.1 0.01 0.01 0.1 1 10 0.1 1 10 Energy (keV) Energy (keV) DanaKoeppe 23−Jul−2020 18:14 DanaKoeppe 23−Jul−2020 18:14 Figure 1.4: Simulated X-ray spectra. Simulated X-ray spectra for gases with varying temperatures and metallicities. a) Relatively cool (kT=3 keV) gas with Solar abundance (Z=0.3 𝑍 ). b) Cool gas with higher metallicity shows stronger emission lines. The spectra were generated using 𝑋𝑆𝑃𝐸𝐶𝑣12.11 (Arnaud, 1996). The presence of heavy elements in the ICM leads to questions of when and how the gas made it out of individual galaxies (where most of the stars are) and into the ICM. Spatially resolved observations showed characteristic differences in the radial distribution of metals which coincided with the differences in surface brightness and temperature profiles between CC and NCC clusters. CCs typically have stronger metallicity gradients which increase towards the core, whereas NCCs have flatter, although still peaked6, profiles (De Grandi & Molendi, 2001). Simulations have been able to replicate the metallicity profiles with AGN feedback models. At larger radii and outside of the reach of the AGN, the ICM of massive clusters appear to be independent of core status, which 6 Because metallicity is emission-weighted, metallicities of very low density environments are more difficult to measure because the amount of photons observed from the source is comparable to the amount of non-source photons. That is, observations of the ICM are subject to low signal- to-noise ratio (SNR). 13 agrees with the notion that the characteristics of gas in the outer regions evolve on cosmological timescales, and can therefore be used to track the metal distribution history of a cluster. Recently, larger cluster samples with wider redshift ranges seem to support a model for early enrichment (𝑧 & 1), which is supported by the CE global abundances in ACCEPT2.0 (described in Chapter 4). 1.5 This work This dissertations will use measurements from ACCEPT2.0 show how X-ray observations of galaxy clusters can be used to constrain our understanding of their thermodynamic and chemical properties, and how they relate to the formation and evolution of large-scale structure in the Universe. Chapter 2 describes the ACCEPT2.0 data used throughout this work. We will show that the global properties are able to reproduce previous observations of the 𝐿 𝑋 − 𝑇 relation described in Section 1.3. In Chapter 3, we continue our work with this scaling relation and use global core-excised temperatures and luminosities to test the standard assumption of the isotropic expansion of the Universe. Chapter 4 looks at the relationship between the heavy metal content of the ICM and other properties such as core status, luminosity, and cluster redshift. We also compare our results with those obtained from another sample which used different data reduction methods. Finally, Chapter 5 describes the active development of a data reduction pipeline for the 𝑆𝑂 𝐴𝑅 Adaptive-optics Multi-Object Spectrograph (𝑆 𝐴𝑀𝑂𝑆). 14 CHAPTER 2 ACCEPT2.0 2.1 Archive of Chandra Cluster Entropy Profile Tables (ACCEPT) The Archive of Chandra Cluster Entropy Profile Tables (ACCEPT) began as an analysis of entropy profiles for 239 clusters (Cavagnolo et al., 2009). The goal was to understand what X-ray observations of the intracluster medium (ICM) can teach us about how the core interacts with the rest of a cluster. Entropy, 𝐾 ∝ 𝑘𝑇 𝑛−2/3 , is associated with changes in gas density and temperature and is a well-known tracer for the thermal history of the ICM (Bower, 1997; Ponman et al., 1999; Pearce et al., 2000). Left alone, the ICM will convect until 𝑑𝐾/𝑑𝑟 ≥ 0 (i.e., 𝐾 (𝑟) ∝ 𝑟 𝛼 ) everywhere, or all the high density/low temperature (low entropy) gas is below the low density/high temperature (high entropy) gas. A “relaxed” cluster (no recent merger event) would likely have a dominant galaxy at the center, called the brightest cluster galaxy, or BCG. Entropy profiles are, for the most part, compatible with hierarchical formation models outside of the core, but have been shown to flatten inside of 𝑅𝑐 ∼ 100 kpc1 (Ponman et al., 2003; Donahue et al., 2006). With 239 entropy profiles in ACCEPT, Cavagnolo et al. (2009) showed that clusters generally follow model predictions and decrease in entropy from the outskirts, but flatten to a nearly constant central entropy 𝐾0 in the core. Later assessments of cluster entropy profiles showed that CC systems could also be modeled with the broken power law (equation 2.1), with a steeper outer component (∝ 𝑟 1.1 ) and a shallower inner slope (∝ 𝑟 0.67 ), where NCCs have even flatter core entropy profiles (Tozzi & Norman, 2001; Voit, 2005; Cavagnolo et al., 2009). The entropy profile is modeled as,  𝛼 𝑟 𝐾 (𝑟) = 𝐾0 + 𝐾100 , (2.1) 100 kpc at 100 kpc, where 𝐾0 is the entropy excess over a simple power law, 𝐾100 is the normalization constant, and 𝛼 is the slope of the entropy profile. The flattened profiles indicate that something 11 kpc = 3.26 ×103 ly = 3.086×1021 cm 15 Table 2.1: ACCEPT vs. ACCEPT2.0. Main differences between ACCEPT and ACCEPT2.0. Major updates for ACCEPT2.0 include spatially resolved temprature and metallicity profiles, global estimates for temperature, luminosity and metallicity, and morphological classifications. ACCEPT ACCEPT2.0 # of clusters 239 606 # of entropy profiles 239 348 # of 𝑘𝑇, 𝑍 profiles ··· 398 Global 𝑇, 𝐿 𝑋 , 𝑍 ··· X Morphology ··· X prevents gas from cooling and condensing past some limit by displacing large amounts of gas around the core. We now know this phenomenon is caused by a feedback relationship between a cluster’s active galactic nucleus (AGN) and its environment (Bower et al., 2006; McNamara & Nulsen, 2007). When turned on, the AGN puffs up the surrounding gas and raises the entropy. Consequently, the effects of feedback from AGN in addition to other thermodynamic processes such as radiative cooling and feedback from supernovae (SNe) are seen in other X-ray observables. Until now, ACCEPT was the largest publicly-available collection of uniformly-derived radial profiles of density, temperature, and entropy. ACCEPT2.0 (Donahue, Baldi, et al, in prep) adds more clusters and expands the suite of derived X-ray properties. In addition to more than doubling the number of targets in its predecessor, ACCEPT2.0 includes estimates for morphological properties, global X-ray observables for temperature, luminosity, and metallicity, as well as ∼400 radial temperature and metallicity profiles. The major differences between ACCEPT and ACCEPT2.0 are highlighted in Table 2.1. 2.2 ACCEPT2.0 In this section, I will describe the essential elements of the ACCEPT2.0 pipeline. The specific work described here is the (yet) unpublished work of Baldi, Donahue (the ACCEPT2.0 pipeline), and Frisbie (the classification of clusters by their core entropy profiles). The main ACCEPT2.0 data analysis was performed by Alessandro Baldi using CIAO v4.7 (Fruscione et al., 2006) and SHERPA (Freeman et al., 2001) with the 𝐶ℎ𝑎𝑛𝑑𝑟𝑎 calibration database CALDBv4.5. The pipeline initially ran an automated quick spectral analysis of all clusters available 16 in the 𝐶ℎ𝑎𝑛𝑑𝑟𝑎 archive in order to have a rough estimate of the temperature of each cluster. The temperature estimate was used to set a count threshold to decide whether to include a cluster in the sample. Based on simulations, Alessandro Baldi determined that a minimum number of counts in the 0.5-7 keV band of 𝑛𝑚𝑖𝑛,𝑟𝑒𝑠 = 1377 · 𝑘𝑇 − 537 (where kT is the temperature of the cluster in keV) is necessary to have a 20% error on the measure of the cluster temperature in at least three spatial bins, whereas 𝑛𝑚𝑖𝑛,𝑔𝑙𝑏 = (1377 · 𝑘𝑇 −537)/3 is necessary to have the same error on the temperature in a single spatial bin. The pipeline therefore enforces 𝑛𝑚𝑖𝑛,𝑔𝑙𝑏 and 𝑛𝑚𝑖𝑛,𝑟𝑒𝑠 as the minimum counts necessary to include a cluster in the total sample and in the spatially resolved sample, respectively. Images and exposure maps are created with a binning factor of 2, corresponding to a pixel size in the image of 0.984 arcsec. A likelihood function function based on cstat was minimized to fit the spectrum to models for both the source and the background. ACCEPT2.0 global properties were estimated for three spatial regions: the cluster with the core included (CI, 𝑟 < 𝑅Δ ), core of the cluster (C, 𝑟 < 𝑟 core ), and the cluster with the core excised (CE, 𝑟 core < 𝑟 < 𝑅Δ ), where Δ=2500 or 500. The core radius is usually taken to be some fraction of the scale radius. The quantities of interest to this dissertation are approximated for radius 𝑅2500 because the aperture extent is consistent across 535 ACCEPT2.0 objects and we define the core radius as 𝑟 core = 0.3 𝑅2500 . The fits to 𝑅2500 , and the relative average temperature, 𝑇2500 , were performed using the formula derived by Vikhlinin et al. (2006), 𝑇2500 0.55   𝑅2500 ℎ𝐸 (𝑧) = 0.501 Mpc, (2.2) 5 keV p where 𝐸 (𝑧) = Ω𝑚 (1 + 𝑧) 3 + ΩΛ and ℎ = 𝐻0 /(100) km s−1 Mpc−1 . The pipeline used an input value of 𝑇2500 = 5 keV to estimate the first-guess for 𝑅2500 and extracting the core-excised (0.3𝑅2500 < 𝑟 < 𝑅2500 ) region from the spectrum. The pipeline then iterated over values for 𝑇2500 and 𝑅2500 until the model achieves convergence to a stable temperature (Δ𝑇2500 ≤ 0.01 keV between two successive iterations). The three different global regions were used because gas inside the core region evolve on time scales shorter than the age of the Universe, which results in high variation between the X-ray observables for clusters of the same mass. Outside of this region, 17 clusters appear mostly self-similar (Maughan et al., 2012). The source spectra and background were fitted simultaneously using spectral models in 𝑆ℎ𝑒𝑟 𝑝𝑎. There are several different models useful for observations of the ICM because it involves numerous calculations for various atomic interactions. ACCEPT2.0 source emission was fit to a model for a hot diffuse gas called a 𝑚𝑒𝑘𝑎𝑙 model (Kaastra et al., 1996; Liedahl et al., 1995) with the following parameters: The ratio between the elements were fixed to the Solar value as in Anders & Grevesse (1989a). The pipeline considered line-of-sight absorption fixed at the Galactic value 𝑁 𝐻 (Stark et al., 1992), and an additional internal absorption component left free to vary (consistent with zero in the large majority of clusters). The free parameters in the 𝑚𝑒𝑘𝑎𝑙 model were the temperature 𝑘𝑇, the metal abundance 𝑍, and the normalization. The redshift 𝑧 has been fixed at the literature value for the cluster. The background model used was made by two power-law models, several fixed instrumental gaussian emission lines and an 𝑎 𝑝𝑒𝑐 thermal model at low temperature (𝑘𝑇 = 0.17 keV, to take into account the soft diffuse X-ray background). The slopes of the power-laws and the quantity, position and strength of the instrumental emission lines depend on the specific ACIS chips and they are adjusted accordingly. The shape of this spectrum is held fixed. The core entropy profiles and core excess 𝐾0 values in ACCEPT2.0 were calculated by Rachel Frisbie (Frisbie, MSU dissertation, October 2020). 2.3 K-correction and bolometric correction In this section, I return to describing work that is primarily my own. Spectra were fit by the pipeline tasks over the observed 0.5-8 keV band. The pipeline did not compute the bolometric and K-corrections2 of the observed fluxes and luminosities, so those calculations were done by this author to support further scientific use. We used bolometric corrections to convert the bandpass spectral energy distribution (SED) to a spectrum that covers the full range of energies, and the K-correction to account for cosmology. Because of expansion, 2 The “K” here is an arbitrary variable that Hubble adopted in 1936 (Hubble, 1936) for the “K” correction, in magnitudes, to a bandpass-limited flux estimate arising from the Doppler shift of a spectrum. 18 photons from distant objects become redshifted as they travel towards us. Thus, their observed energies are lower than those of the photons emitted in the rest-frame and require correction. We perform the bolometric and K-corrections by generating spectral shapes using the best-fit results for the thermal plasma (𝑘𝑇, 𝑍/𝑍 ) from the ACCEPT2.0 pipeline and the cluster redshift using XSPEC v12.11.0 (Arnaud, 1996). Then, we convert the observed fluxes and luminosities to rest-frame energies. This conversion is done by calculating the ratios of integrated luminosity in the rest-frame energy range [0.5-8.0] keV with the integrated luminosity in the observed energy range [0.5-8.0] keV via 𝐸 rest = (1 + 𝑧)𝐸 observed . We then extrapolate the best-fit spectrum to a very broad energy range for “bolometric”3 values, and calculate the ratio between the integrated luminosity over this broad energy range and the integrated luminosity of the canonical rest-frame energies. We compute the correction factors by simulating observations of each cluster based on the temperature, metallicity, and redshift. Each simulated cluster returned values for the observed flux (after correction for Galactic and internal absorption) and luminosity with their corresponding rest-frame and bolometric quantities. The ratios of rest-frame and bolometric values to those of the observer frame were used as the correction factors for the real data. The specific process and the code for the K-correction procedure is provided in Appendix A. 2.4 Vetting of the Data For nearby clusters and groups with strong temperature gradients, global temperature and (emission-weighted) abundance estimates have been shown as biased towards those of the core region when fit to an isothermal model, and may be better characterized by a multi-temperature model (Buote, 2000) because the line of sight passes through gas of different temperatures, even with a simple radial temperature gradient. However, as mentioned in Section 1.3, previous works have shown that after excising the core region, the ICM spectra extracted from within 𝑅2500 or 3 These are not true bolometric values, as that would imply integration over all energies and XSPEC does not formally allow extrapolation to infinitely high energy, but contributions from very high energies gets vanishingly small because of the exponential drop off (∝ 𝑒𝑥 𝑝(−𝐸/𝑘𝑇)). The maximum energy allowed by the tabulated models is typically XX keV rest frame. 19 𝑅500 fit well with a single temperature. One of the goals of ACCEPT2.0 was to assign uniformly measured global properties to each cluster. These measurements come from spectroscopic fits to a single temperature mekal model for spectra obtained by a single large aperture. We obtained global properties in two main types of aperture: core-excised (CE), core-included (CI). To verify that the CE spectra for clusters in ACCEPT2.0 are adequately characterized by a single-temperature model, we compared ACCEPT2.0 spatially resolved temperature profiles of 154 objects to their global spectral temperatures. In summary, we found that 91% of the spectrum- approximated CE temperatures are within 1 standard deviation of the radially averaged value. The CE global properties here refer to measurements obtained within the region [0.3-1]𝑅2500 . We do the same thing with the CI region defined as [0-1]𝑅2500 . 2.4.1 Initial Cuts Originally 536 ACCEPT2.0 objects have global spectra for the [0.3-1]𝑅2500 aperture, 68 of which were removed from further analysis for any of the following reasons (the total numbers of affected clusters are listed in parentheses): • Clusters with updated redshift measurements, Δ𝑧/𝑧 > 10%. (12) • Spectral fits did not achieve a reliable temperature convergence. (20) • Too much of the core-excised aperture was outside the field of view to produce reliable global estimates for the aperture. (35) There are 15 clusters (Table 2.2) that were found to have updated redshifts, but three of them had percent changes below 10%. For these clusters with small redshift updates, we refit the global temperatures and abundances for the CE 𝑅2500 spectra and they have been flagged. Formally, the apertures used to compute the luminosities for these clusters should have been updated, and therefore the luminosities based on fluxes from the original apertures from the pipeline are not 20 Table 2.2: ACCEPT2.0 Redshift Updates. There are 15 ACCEPT2.0 clusters that have had updated redshifts since their spectra were analyzed. These clusters were left out of any further analysis, except for clusters marked with a † which had their CE global temperatures and abundances refit (but were left out of the 𝐿 𝑋 − 𝑇 analysis). The references are as follows: Ah2012-Ahn et al. (2012), Al2015-Alam et al. (2015), AS2017-Andrade-Santos et al. (2017), B2015-Bleem et al. (2015), C2017-Caminha et al. (2017), D2002-Donahue et al. (2002), M2016-McDonald et al. (2016), P2011-Piffaretti et al. (2011), S2013-Sifón et al. (2013), R2016-Rykoff et al. (2016), Wb2013-Webb et al. (2013), Wn2012-Wen et al. (2012), Wn2015-Wen & Han (2015). ACCEPT2.0 Name 𝑧 𝑜𝑙𝑑 𝑧 𝑛𝑒𝑤 𝐶ℎ𝑎𝑛𝑑𝑟𝑎 Obs. ID Reference ABELL_3084 0.098 0.219 9413 P2011 ABELL_3140 0.062 0.173 9416 P2011 ACT-CL_J0235-5121 0.430 0.278 12262 S2013 ACT-CL_J0237-4939 0.400 0.334 12266 S2013 ACT-CL_J0304-4921 0.470 0.392 12265 S2013 †ACT-CL_J0616-5227 0.710 0.684 12261,1312 S2013 ACT-CL_J0707-5522 0.430 0.296 12271 S2013 G115.71+17.52 0.400 0.300 13383 AS2017 †MACS_J0416.1-2403 0.420 0.396 16237,1044 C2017 NSCS_J144726+082824 0.195 0.376 10481 Ah2012, Wb2013 OC06_J1119+2127 0.400 0.061 5790 D2002, P2011 RCS_J2327-0204 0.200 0.700 14361,7355 Wn2015 SPT-CL_J0102-4915 0.750 0.870 14022,1402 S2013, B2015, M2016 †SPT-CL_J2344-4243 0.620 0.596 13401 S2013 ZwCl_1309.1+2216 0.266 0.170 7898,14014 R2016 quite right, even if they are calculated using the correct luminosity distance. To be conservative, the luminosities for these clusters were therefore left out of the 𝐿 𝑋 − 𝑇 analysis in this work. There are therefore 468 objects with spectral analysis in the global CE aperture (0.3 . 𝑟/𝑅2500 . 1). Using the procedure described in the next section, we removed 21 non-spatially resolved objects with reduced chi-square 𝜒2 /d.o.f & 1.5. Below this value, we found general agreement between the global measurements and those calculated from the radially averaged pro- files, although for clusters with radial profiles, we replaced the X-ray properties measured from single-aperture spectral fits with weighted means. 21 2.4.2 Radially weighted temperature and abundance This section’s goal is to define a reasonable reduced 𝜒2 beyond which to cut global temperature and abundance approximations in the region [0.3-1]𝑅2500 for the non-spatially resolved objects in the sample. Objects lacking radial profiles that host multiphase gas in their ICM can lead to misleading results from the spectral fit. Measurements for high S/N systems with multi-temperature plasma can have misleading goodness-of-fits when applied to an isothermal model, despite having reliable parameter estimates. Here, we use a sub sample of spatially resolved ACCEPT2.0 clusters and compared their spectrum-derived temperature estimates to those computed via their radial profiles to test the reliability of ACCEPT2.0 global properties. There are ∼400 clusters in ACCEPT2.0 with spatially resolved data, 154 of which have at least 3 data points in the region of interest, 0.3 < 𝑟/𝑅2500 < 1. We used projected radial temperature profiles to calculate each cluster’s weighted mean ( 𝑋),¯ mean error (𝜎𝑤 ), and standard deviation (𝜎std ), defined as follows, Σ𝑤𝑖 𝑋𝑖 𝑋¯ 𝑤 = (2.3) Σ𝑤𝑖 s 1 𝜎𝑤 = (2.4) Σ𝑤𝑖 s Σ𝑤𝑖 (𝑋𝑖 − 𝑋¯ 𝑤 ) 2 𝜎std = , (2.5) Σ𝑤𝑖 where the weight on each radial data point is 𝑤𝑖 = 1/𝜎𝑖2 . If a cluster hosts a relatively flat temperature profile outside the core, then 𝜎std /𝜎𝑤 should be of order unity. We compute radially weighted abundances in the same manner as above, but use the temperatures in the vetting process. We found that ∼91% of the weighted means were well within their stated uncertainties, and global properties with suspicious reduced 𝜒2 (and therefore underestimated uncertainties) were limited to clusters with unresolved temperature structure in the ICM. 22 In general, the values obtained from the global spectral fits are good estimates for the global average, despite the occasional underestimation of the error bars due to poor 𝜒2 . In general, we found good agreement between global properties and the weighted average. When possible we replaced global temperatures, metallicities, and their respective errors with values from the radially weighted profiles. For good fits (𝜒2 /d.o.f.1.2), we found no difference between using the global and radially averaged values. Beyond that, the data uncertainties were more representative of the quality of spectral fit for 1.2 . 𝜒2 /d.o.f.1.5. Of the clusters without radial profiles, we removed only 21 global measurements for having poor (reduced) 𝜒2 . The radial metallicity profiles are in Appendix B, and the radial temperature profiles are shown in Appendix C. The global CE properties for the final 447 ACCEPT2.0 clusters and groups is provided in Table 2.3. We followed the same procedure for the CI global properties. This replacement procedure ensured that objects with resolved multi-temperature gas are represented by data points with error bars based on good fits. 2.4.3 𝐿 𝑋 − 𝑇 relation Here, we use the global CE and CI 𝐿 𝑋 and 𝑇 values for 301 clusters (with CE bolometric luminosities 𝐿 𝑋 & 4×1043 erg s−1 ) to illustrate that the global CE quantities do a good job of removing scatter in the relation caused by core emission. There is a noticeable separation between CC (blue triangles) and NCC (red circles) clusters in the upper panel of Figure 2.2. In the lower panel, this scatter is significantly reduced. As mentioned previously in Section 1.3, CCs typically have higher core densities (lower central excess 𝐾0 4) than NCCs, which makes them brighter. For our sample, CCs are defined as having excess entropies of 𝐾0 < 30 keV cm2 , and those with higher 𝐾0 are NCCs. Clusters with no core status are plotted as crosses. We use the package emcee (Foreman-Mackey et al., 2013) to fit5 both the CE and the CI values to the 𝐿 𝑋 − 𝑇 relation of the form, 4 Central entropies were calculated by Rachel Frisbie (Frisbie, MSU dissertation, October 2020). 5 More details of the fitting procedure for the 𝐿 𝑋 − 𝑇 relation are in Chapter 3. 23 +0.22 LX,CI0 = 6.73−0.22 +0.09 LX,CE0 = 3.65−0.09 +0.10 β = 2.79−0.10 +0.08 β = 2.86−0.08 σ β 3. 2 3. 0 β 0. 0. 0. int0. 0. 2. 2. 2. 3. 3. 2. 8 2. 6 +0.03 +0.02 2. 4 σint = 0.50−0.03 σint = 0.34−0.02 σ0 0 28 32 36 40 44 55 70 85 00 15 0. 0. 0. int 40 45 50 .55 .60 0 4 8 7. 2. 2. 2 6 4 6 4 3. 6 3. 8 3. 2. 2. 2. 4. 3. 0 55 70 85 00 6. 6. 6. 7. 2. 8 3.15 β σint 3. 3. 0 0. 0.28 β σint LX,CE0 0.402 0.32 36 LX,CI0 0. 0. 0. 0.45 50 55 60 0. 0.40 44 Figure 2.1: 𝑳 𝑿 − 𝑻 core-included and core-excised posterior distributions. The posterior probability distributions for the variables of the 𝐿 𝑋 −𝑇 relation for CI (left) and CE (right) clusters. 𝐿 𝑋 𝐸 (𝑧) −1 𝑘𝑇 ln = ln𝐿 𝑋,0 + 𝛽ln , (2.6) 1044 erg s−1 6 keV where normalization 𝐿 𝑋,0 , slope 𝛽, and intrinsic scatter 𝜎int , are assumed to have Gaussian data and errors. The results of the fit are shown in Figure 2.2, where the upper panel contains the best fit model for the CI measurements, and the lower panel shows the CE results. The model for the CI cluster properties have a higher normalization of 𝐿 CI 𝑋,0 = 6.728+0.223 −0.216 (due to higher luminosity measurements) compared to the CE normalization 𝐿 CE +0.092 , but the slopes are similar = 3.652−0.090 𝑋,0 for both (𝛽CI = 2.793 ± 0.099 and 𝛽CE = 2.864 ± 0.076). The errors on the variables represent the 16th and 84th percentiles from the probability distributions returned by the fit. As expected from the larger scatter between CCs and NCCs in the top panel of Figure 2.2 (and the lack thereof in the lower panel), the scatter 𝜎int in the relation is reduced when using CE CI = 0.500+0.027 and 𝜎 CE = 0.339+0.021 . These 𝐿 − 𝑇 results agree with measurements, with 𝜎int −0.025 int −0.020 𝑋 previous works (Pratt et al., 2009; Mittal et al., 2011; Maughan et al., 2012), and reassures us of the quality of the data in ACCEPT2.0. 24 +0.223 1046 LCI X, 0 = 6.728−0.216 β = 2.793+0.099 −0.099 σint = 0.500+0.027 −0.025 1045 LX E −1 (z) [erg s−1 ] Cool Core 1044 Non-Cool Core Unknown Core Status 3 +0.0924 5 6 7 8 9 10 15 1046 LCE X, 0 = 3.652−0.090 β = 2.864+0.076 −0.076 σint = 0.339+0.021 −0.020 1045 1044 3 4 5 6 7 8 9 10 15 CE kT (keV) Figure 2.2: 𝑳 𝑿 − 𝑻 core-included vs. core-excised. Best fit 𝐿 𝑋 − 𝑇 relation for 301 clusters with global CI ([0-1]𝑅2500 ) and CE [0.3-1]𝑅2500 quantities. The upper panel shows the relation with luminosities measured in the CI aperture, and the lower panel shows the CE luminosities (both use CE temperatures.). The errors on the data points and best fit parameters are 1𝜎. 25 Table 2.3: Global CE properties for 432 ACCEPT2.0 clusters. Full list of 432 ACCEPT2.0 clusters presented in this dissertation. This table includes the clusters that had their global temper- atures and abundances refit. The columns are as follows: col(1) is ACCEPT2.0 name, col(2) is the cluster redshift, col(3) is the 𝑅2500 radius in kpc, cols(4,5) and cols(6,7) are the [0.5-8 keV] energy bandpass and bolometric luminosities in units of 1044 erg s−1 , cols(8,9) is the temperature and error in keV, cols(10,11) is the metallicity in solar units 𝑍 , col(12) is the reduced chi-square value obtained from the X-ray spectral fit, and col(13) is checked if the temperatures and metallicities obtained from the spectral fit were replaced with their radially averaged values. Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 000619+105206 0.167 466 1.85 0.072 2.636 0.102 5.184 0.399 0.35 0.092 1.073 00088+5215 0.104 456 0.751 0.03 1.052 0.043 4.711 0.3 0.164 0.087 1.264 00117-1523 0.378 451 6.014 0.194 8.839 0.285 5.892 0.399 0.271 0.066 1.132 A0013 0.094 461 0.641 0.016 0.899 0.023 4.767 0.257 0.24 0.058 1.048 X A2744 0.308 640 13.17 0.165 23.686 0.296 10.245 0.77 0.299 0.102 1.234 X 0014-4952 0.752 388 5.112 0.336 7.853 0.517 6.88 0.966 0.406 0.162 1.096 Cl0016+16 0.541 557 16.147 0.355 28.163 0.619 9.727 0.745 0.198 0.063 0.964 00254-1222 0.584 470 8.852 0.347 14.205 0.557 7.817 0.597 0.256 0.06 1.134 00278+2616 0.367 477 3.049 0.194 4.615 0.294 6.438 0.978 0.039 0.082 1.086 30484-4142 0.41 559 7.488 0.269 13.102 0.47 9.797 1.232 0.15 0.096 1.17 00305+2618 0.5 286 1.158 0.254 1.513 0.332 2.853 0.494 0.669 0.358 1.074 00354-2015 0.364 509 10.772 0.355 16.792 0.554 7.187 0.645 0.338 0.09 1.146 A0068 0.255 618 5.993 0.281 10.429 0.489 9.717 1.436 0.662 0.21 1.27 A0085 0.055 543 2.609 0.019 3.925 0.028 6.17 0.588 0.358 0.15 2.29 X A2813 0.292 559 7.287 0.223 11.762 0.361 7.95 0.739 0.287 0.086 1.303 00408+2404 0.083 437 0.823 0.028 1.129 0.038 3.826 0.623 0.291 0.102 1.28 X A0098N 0.104 405 0.332 0.026 0.445 0.034 3.782 0.387 0.54 0.166 1.278 A98ss 0.129 331 0.209 0.028 0.277 0.037 2.639 0.402 0.465 0.272 1.163 351-021 0.057 228 0.027 0.004 0.037 0.006 1.28 0.054 0.417 0.098 1.169 X A0119 0.044 541 1.115 0.013 1.628 0.019 5.916 0.591 0.29 0.131 3.338 X 0058-6145 0.83 322 3.844 0.629 5.312 0.869 4.416 1.052 0.341 0.229 1.053 200428 0.274 420 2.509 0.217 3.514 0.304 4.643 0.809 0.115 0.133 1.254 26 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) A0141 0.23 525 3.05 0.122 4.635 0.186 6.576 0.772 0.184 0.12 1.383 0106-5943 0.348 426 3.107 0.249 4.416 0.354 5.114 0.725 0.326 0.158 1.192 01670077+0105926 0.254 419 2.126 0.07 2.961 0.098 4.565 0.271 0.217 0.074 1.028 X 01077+5408 0.107 634 3.881 0.057 6.191 0.092 6.642 1.385 0.184 0.136 1.257 X A0160 0.045 275 0.084 0.006 0.117 0.009 1.807 0.375 0.094 0.069 2.12 X 011502+002441 0.045 353 0.197 0.006 0.261 0.008 2.482 0.382 0.306 0.132 3.115 X A2895 0.227 594 4.742 0.143 7.809 0.236 8.394 0.858 0.301 0.107 1.471 UGC00842 0.045 265 0.038 0.003 0.054 0.004 1.669 0.085 0.226 0.049 1.095 X 0123-4821 0.62 340 2.711 0.3 3.751 0.415 4.551 0.743 0.464 0.195 1.07 A0193 0.049 407 0.398 0.011 0.536 0.015 3.645 0.138 0.342 0.054 1.191 X A0209 0.206 607 6.31 0.161 10.466 0.266 8.547 0.665 0.25 0.082 1.313 Abell222 0.211 404 1.664 0.067 2.287 0.092 4.137 0.274 0.216 0.07 1.032 Abell223 0.207 473 1.37 0.062 1.981 0.089 5.47 0.5 0.247 0.1 1.152 01400-0555 0.454 476 7.056 0.392 10.985 0.61 7.139 0.822 0.256 0.103 1.149 01420+2131 0.28 526 5.46 0.165 8.543 0.258 7.218 0.649 0.118 0.09 1.265 01502127-1005305 0.365 378 3.501 0.257 4.825 0.354 4.233 0.485 0.229 0.112 1.19 0151-5954 1.03 246 2.655 0.702 3.561 0.941 3.561 0.956 0.386 0.316 1.039 01525-2853 0.341 457 4.091 0.126 6.018 0.186 5.815 0.584 0.058 0.081 1.125 A0267 0.231 563 4.166 0.105 6.6 0.166 7.57 0.63 0.393 0.106 1.224 0156-5541 1.22 266 8.173 1.394 11.753 2.004 5.334 1.101 0.017 0.081 1.075 02209-3829 0.229 414 2.352 0.136 3.225 0.187 4.346 0.368 0.546 0.14 1.23 A3017 0.22 538 3.931 0.175 6.124 0.272 7.115 0.939 0.111 0.106 1.08 0228259+003202 0.414 373 0.286 0.174 0.394 0.239 2.425 1.333 0.018 0.373 1.006 MZ10451 0.061 179 0.01 0.002 0.016 0.004 0.733 0.041 0.158 0.167 1.073 0232-4421 0.284 541 8.792 0.304 13.995 0.485 7.636 0.811 0.218 0.095 1.259 0234-5831 0.415 556 4.706 0.41 8.628 0.752 10.958 3.63 0.244 0.314 1.12 A0368 0.22 497 3.443 0.181 5.101 0.268 6.08 0.768 0.305 0.138 1.276 4000237-5224 0.136 355 0.303 0.048 0.403 0.065 3.171 0.43 0.385 0.201 1.319 27 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) A0370 0.375 558 6.827 0.11 11.422 0.183 8.753 0.459 0.285 0.074 1.206 02426-2132 0.314 459 4.837 0.298 7.085 0.436 5.751 0.774 0.151 0.115 1.156 0243-5930 0.635 410 5.702 0.535 8.615 0.808 6.502 1.066 0.347 0.14 1.042 AS0295 0.3 529 9.202 0.31 14.464 0.487 7.348 0.706 0.214 0.076 1.2 X 4000245+0936 0.147 323 0.169 0.041 0.22 0.054 2.629 0.538 0.7 0.541 1.27 A0376 0.048 468 0.515 0.011 0.713 0.016 4.174 0.67 0.346 0.208 1.875 X A0383 0.187 470 2.012 0.064 2.881 0.092 5.438 0.297 0.338 0.11 1.239 X 0252-4824 0.421 453 2.527 0.249 3.793 0.373 6.352 1.45 0.313 0.191 1.072 NGC1132 0.023 211 0.012 0.001 0.018 0.002 1.045 0.023 0.245 0.032 1.211 0256-5617 0.58 410 4.804 0.41 7.044 0.602 5.82 1.006 0.241 0.136 1.096 A0402 0.322 552 4.452 0.19 7.293 0.311 8.228 1.236 0.045 0.085 1.175 A0399 0.072 574 2.554 0.021 3.926 0.032 6.857 0.581 0.243 0.136 3.135 X A0401 0.074 609 4.434 0.016 7.035 0.025 7.881 0.877 0.282 0.099 1.488 X 03016+0155 0.17 432 1.687 0.079 2.341 0.11 4.45 0.333 0.233 0.09 1.19 4000302-0423 0.35 410 3.657 0.341 5.08 0.473 4.755 0.748 0.617 0.241 1.096 03037-7752 0.274 630 6.901 0.197 11.84 0.338 9.344 0.891 0.318 0.085 1.143 A3088 0.253 576 5.317 0.193 8.344 0.302 7.316 0.762 0.236 0.099 1.279 0307-6225 0.579 341 1.857 0.297 2.54 0.406 4.325 1.059 0.616 0.361 1.036 0307-5042 0.55 400 4.468 0.408 6.486 0.592 5.538 0.936 0.173 0.127 1.1 03089+2645 0.324 603 10.682 0.298 18.58 0.518 9.656 1.047 0.159 0.085 1.285 0310-4647 0.709 360 3.699 0.296 5.329 0.427 5.37 0.927 0.206 0.189 1.154 A3094 0.068 371 0.242 0.013 0.323 0.017 3.029 0.092 0.272 0.103 1.421 X 4000318-0302 0.37 447 2.455 0.252 3.587 0.368 5.621 1.316 0.027 0.108 1.168 0324-6236 0.73 361 4.985 0.724 7.213 1.047 5.38 1.158 0.032 0.092 1.003 4000328-2140 0.59 404 3.038 0.308 4.494 0.456 6.033 0.995 0.262 0.168 1.137 A3126 0.086 476 1.212 0.037 1.707 0.052 4.994 0.309 0.47 0.083 1.203 A3128 0.06 373 0.316 0.015 0.423 0.02 2.86 0.484 0.269 0.111 1.502 X 03311-2100 0.188 495 2.604 0.104 3.827 0.153 5.859 0.528 0.204 0.092 1.38 28 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 0334-4659 0.485 427 3.884 0.379 5.702 0.556 5.822 1.133 0.182 0.147 1.145 3C089 0.139 439 0.464 0.02 0.647 0.028 4.528 0.333 0.166 0.096 1.164 03408-4542 0.07 338 0.189 0.02 0.251 0.027 2.419 0.42 0.298 0.184 1.756 X IIIZw054 0.029 335 0.169 0.007 0.229 0.009 2.255 0.217 0.196 0.11 3.292 X A3158 0.06 480 2.057 0.018 2.899 0.026 5.435 0.313 0.387 0.082 2.722 X 0346-5438 0.55 359 3.95 0.44 5.499 0.613 4.573 0.813 0.253 0.158 0.989 0352-5647 0.67 427 3.616 0.269 5.573 0.415 6.834 1.37 0.006 0.095 1.135 03529+1941 0.109 364 1.013 0.041 1.362 0.055 3.135 0.165 0.2 0.052 1.111 X 03588-2955 0.425 548 12.749 0.337 21.346 0.564 8.747 0.487 0.143 0.052 1.13 4000405-4100 0.686 362 2.769 0.287 4.0 0.415 5.318 1.079 0.012 0.076 1.088 A0478 0.088 598 5.866 0.038 9.322 0.06 7.609 0.166 0.259 0.022 1.116 X 04161-2403 0.42 550 9.072 0.326 15.127 0.544 8.664 0.734 0.214 0.071 1.13 0417-4748 0.62 396 9.277 0.832 13.66 1.225 5.91 0.897 0.205 0.123 1.077 04175-1154 0.44 624 21.55 0.366 40.079 0.68 11.324 0.499 0.197 0.044 1.108 X 04258-0833 0.04 379 0.384 0.016 0.514 0.022 3.088 0.125 0.256 0.073 3.255 X 0426-5455 0.63 358 2.94 0.473 4.245 0.683 5.347 1.715 0.066 0.141 1.051 AS0463 0.039 353 0.094 0.004 0.125 0.005 2.503 0.532 0.214 0.139 2.257 X 04296-0253 0.399 491 5.376 0.254 8.315 0.393 7.0 0.9 0.302 0.132 1.159 04371+0043 0.285 518 4.937 0.134 7.58 0.205 6.101 0.632 0.265 0.041 1.251 X 04390+0715 0.23 513 5.31 0.166 8.038 0.252 6.528 0.534 0.293 0.083 1.16 04390+0520 0.208 451 1.883 0.103 2.67 0.145 5.024 0.48 0.251 0.107 1.22 04431+0210 0.19 406 1.189 0.087 1.628 0.12 4.147 0.474 0.348 0.149 0.998 A0514 0.071 402 0.317 0.014 0.43 0.018 3.959 0.534 0.257 0.035 1.588 X A3292 0.172 416 1.775 0.082 2.441 0.112 4.204 0.297 0.271 0.098 1.41 04519+0006 0.43 443 5.882 0.364 8.608 0.533 5.844 0.829 0.411 0.206 1.101 04541-0300 0.55 576 15.974 0.296 28.925 0.536 10.644 0.768 0.206 0.082 1.309 552-020 0.031 316 0.074 0.004 0.099 0.006 2.455 0.267 0.536 0.173 4.796 X 04552+0657 0.425 478 6.452 0.414 9.878 0.634 6.845 0.998 0.571 0.226 1.135 29 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 0456-5116 0.562 419 3.322 0.29 4.981 0.435 6.352 1.188 0.376 0.176 1.079 0509-5342 0.463 565 4.295 0.208 7.291 0.353 9.069 1.716 0.145 0.164 1.176 A3322 0.2 544 3.793 0.142 5.786 0.216 6.649 0.599 0.146 0.092 1.104 05107-0801 0.22 552 8.412 0.212 13.101 0.33 7.152 0.434 0.28 0.06 1.082 A0539 0.028 362 0.269 0.007 0.359 0.01 2.909 0.272 0.251 0.095 4.717 X AS0520 0.295 573 6.561 0.201 10.757 0.33 8.269 0.732 0.14 0.076 1.167 05207-1328 0.34 515 5.821 0.181 9.131 0.284 7.335 0.692 0.345 0.111 1.265 052215-481816 0.296 458 1.036 0.106 1.504 0.154 5.616 1.217 0.319 0.274 1.249 A3343 0.191 513 3.027 0.089 4.563 0.135 6.429 0.528 0.269 0.099 1.175 05282-2942 0.158 434 1.634 0.086 2.245 0.119 4.607 0.499 0.564 0.197 1.327 X RBS0653 0.284 594 7.669 0.109 13.057 0.185 9.151 0.339 0.234 0.041 1.153 X 28658-3125 0.21 536 3.759 0.128 5.678 0.194 6.484 0.54 0.301 0.091 1.06 A0545 0.154 582 3.448 0.047 5.431 0.073 7.372 0.311 0.124 0.052 1.265 05329-3701 0.275 594 6.799 0.197 11.333 0.329 8.644 0.843 0.136 0.08 1.134 3060170- 0.036 352 0.18 0.007 0.238 0.01 2.569 0.426 0.304 0.175 2.696 X 0542-4100 0.64 410 3.762 0.216 5.691 0.327 6.455 0.885 0.108 0.125 1.168 05470-3904 0.21 457 0.974 0.06 1.398 0.086 5.186 0.699 0.046 0.106 1.352 A3364 0.148 571 3.151 0.079 4.925 0.124 7.194 0.546 0.126 0.081 1.411 A0548A 0.04 371 0.261 0.012 0.348 0.016 3.221 0.352 0.335 0.188 1.56 X 0551-5709 0.423 363 1.975 0.204 2.7 0.279 4.06 0.603 0.296 0.176 1.074 A0550 0.099 507 2.168 0.062 3.165 0.09 5.669 0.298 0.141 0.067 1.202 05534-3342 0.407 649 13.416 0.212 24.118 0.382 10.463 0.68 0.192 0.055 1.119 0559-5249 0.611 357 3.915 0.379 5.512 0.534 4.818 0.622 0.17 0.095 1.073 A3376 0.046 496 0.541 0.006 0.762 0.008 4.696 0.499 0.386 0.121 3.323 X A3378 0.141 453 3.198 0.099 4.474 0.139 4.78 0.273 0.36 0.088 1.16 06163-2156 0.171 557 2.994 0.067 4.678 0.105 7.236 0.511 0.313 0.086 1.178 AS0579 0.152 449 1.508 0.056 2.119 0.078 4.789 0.352 0.213 0.092 1.146 0616-5227 0.71 441 6.591 0.809 10.537 1.293 7.749 1.798 0.318 0.208 1.043 30 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 13959+2418 0.27 539 7.876 0.283 12.273 0.44 7.189 0.635 0.378 0.086 1.169 A3391 0.051 549 1.028 0.021 1.498 0.031 5.794 0.222 0.232 0.068 3.227 X A3399 0.203 542 3.297 0.073 5.045 0.111 6.759 0.453 0.276 0.084 1.084 16765+1764 0.174 517 4.844 0.111 7.219 0.165 6.176 0.412 0.229 0.08 1.14 AS0592 0.222 598 7.97 0.188 13.233 0.313 8.581 0.651 0.312 0.08 1.363 A3402 0.146 311 0.189 0.049 0.251 0.065 2.399 0.42 0.372 0.284 1.087 A3404 0.167 640 6.357 0.151 10.236 0.244 7.851 0.642 0.049 0.062 1.148 A0562 0.11 353 0.392 0.019 0.526 0.025 2.943 0.193 0.182 0.056 1.122 X Bullet 0.296 708 24.166 0.131 46.462 0.252 12.364 1.145 0.208 0.066 1.326 X 07123+5931 0.328 409 2.554 0.218 3.563 0.304 4.676 0.539 0.289 0.126 1.176 0717+3745 0.546 647 25.993 0.368 51.818 0.734 13.243 0.62 0.219 0.042 1.136 X 4000720+7108 0.231 320 0.245 0.029 0.325 0.038 2.801 0.309 0.408 0.161 1.181 A0578 0.087 331 0.149 0.012 0.197 0.016 2.641 0.148 0.417 0.067 1.408 X A0586 0.171 516 3.337 0.093 4.977 0.139 6.241 0.395 0.374 0.075 1.157 07357+7421 0.216 516 3.873 0.033 5.843 0.05 6.447 0.632 0.331 0.103 1.236 X 07449+3927 0.698 442 13.375 0.576 21.465 0.924 7.805 0.634 0.179 0.067 1.114 PKS0745-19 0.103 628 5.794 0.034 9.484 0.055 8.36 0.483 0.304 0.083 1.593 X WBL154 0.022 179 0.024 0.001 0.035 0.001 1.199 0.178 0.15 0.116 1.485 X A0598 0.189 457 1.695 0.085 2.417 0.121 5.052 0.538 0.068 0.091 1.291 A0611 0.288 571 4.697 0.124 7.783 0.205 8.546 0.731 0.377 0.103 1.017 X 08065+2822 0.3 552 1.869 0.191 2.874 0.293 6.806 1.897 0.071 0.21 1.211 43062 0.064 446 0.191 0.038 0.252 0.051 3.764 0.538 1.025 1.219 1.418 A0644 0.07 567 2.89 0.031 4.41 0.047 6.58 0.821 0.317 0.089 2.778 X 08196+6336 0.119 384 0.758 0.044 1.025 0.06 3.498 0.321 0.17 0.088 1.238 UGCl120 0.029 276 0.047 0.009 0.063 0.012 1.896 0.116 0.456 0.17 1.499 08232+0425 0.225 427 1.718 0.107 2.383 0.148 4.66 0.514 0.51 0.168 1.271 A0665 0.182 614 4.817 0.059 7.91 0.096 8.136 0.857 0.26 0.075 1.314 X 2MFGC06756 0.241 445 2.694 0.055 3.823 0.078 5.053 0.229 0.277 0.049 1.057 X 31 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 4000838+1948 0.123 334 0.166 0.043 0.219 0.056 2.815 0.673 0.534 0.424 1.314 A3411 0.169 519 2.842 0.053 4.247 0.079 6.249 0.307 0.275 0.054 1.119 X 084254+292723 0.194 505 1.485 0.048 2.174 0.07 5.89 0.439 0.486 0.136 1.052 X A0697 0.282 713 12.109 0.291 23.094 0.555 11.987 1.107 0.333 0.106 1.311 08488+4455 0.543 248 0.393 0.081 0.524 0.108 2.498 0.491 0.355 0.249 1.104 08485+3341 0.371 504 2.719 0.21 4.25 0.328 7.258 1.76 0.38 0.288 1.054 08579+2107 0.23 414 2.167 0.079 2.994 0.11 4.389 0.256 0.31 0.074 0.993 X A0744 0.073 316 0.15 0.014 0.203 0.019 2.331 0.226 0.215 0.081 1.418 +1373+110+018 0.18 475 2.688 0.078 3.869 0.112 5.382 0.311 0.274 0.073 1.14 X 09112+1746 0.505 460 5.371 0.324 8.253 0.497 6.808 0.894 0.133 0.102 1.124 HCG037 0.022 203 0.003 0.004 0.004 0.006 0.963 0.238 0.205 0.174 1.12 20913454+405628 0.442 457 4.631 0.189 6.963 0.284 6.416 0.59 0.406 0.092 1.152 A0773 0.217 581 5.866 0.132 9.528 0.214 7.63 0.833 0.272 0.081 1.237 X HydraA 0.055 431 1.145 0.005 1.566 0.006 3.951 0.219 0.289 0.046 1.219 X 0918343+295318 0.289 235 0.424 0.349 0.558 0.46 1.703 0.589 0.639 1.389 0.906 092017+303027 0.258 506 3.036 0.123 4.554 0.184 6.352 0.661 0.352 0.105 1.115 0922076+034558 0.28 596 1.787 0.209 2.951 0.345 8.434 3.353 0.165 0.354 1.204 A0795 0.136 466 1.863 0.048 2.645 0.068 5.002 0.3 0.164 0.062 1.275 4000926+1242 0.489 405 1.533 0.14 2.217 0.202 5.471 1.018 0.239 0.209 1.067 0938209+520243 0.36 477 5.414 0.181 8.169 0.274 6.417 0.504 0.165 0.073 1.081 A0853 0.166 430 0.861 0.054 1.194 0.075 4.441 0.481 0.236 0.129 1.146 A0868 0.153 432 2.61 0.086 3.615 0.119 4.414 0.222 0.252 0.07 1.137 0947124+762313 0.354 550 7.738 0.176 12.772 0.291 8.464 0.567 0.409 0.076 1.088 X 09498+1708 0.383 576 9.104 0.381 16.267 0.681 10.311 1.712 0.184 0.151 1.258 09496+5207 0.214 479 2.228 0.048 3.243 0.069 5.642 0.211 0.256 0.046 1.088 X 0954+1738 0.828 271 1.806 0.359 2.407 0.478 3.574 0.901 0.587 0.357 1.087 4000956+4107 0.587 357 2.522 0.289 3.542 0.406 4.894 0.859 0.424 0.196 1.114 A0907 0.153 504 2.833 0.056 4.152 0.083 5.772 0.537 0.335 0.142 1.381 X 32 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 26441+1948 0.24 567 3.615 0.128 5.726 0.203 7.503 0.702 0.09 0.077 1.126 10005+4409 0.154 367 1.065 0.07 1.437 0.095 3.278 0.268 0.183 0.095 1.243 10069+3200 0.359 638 4.249 0.342 6.562 0.528 6.89 1.667 0.045 0.114 1.209 10061+1201 0.221 488 2.803 0.071 4.111 0.105 5.861 0.328 0.313 0.062 1.133 X 10105-1239 0.301 494 4.06 0.084 6.139 0.127 6.484 0.395 0.222 0.062 1.108 A0963 0.206 527 4.534 0.076 6.861 0.115 6.364 0.782 0.226 0.113 1.259 X A0970 0.059 454 0.817 0.027 1.134 0.038 4.504 0.402 0.276 0.014 1.387 X 10220+3830 0.049 343 0.047 0.003 0.062 0.004 2.664 0.237 0.361 0.098 1.229 A0980 0.158 529 3.039 0.09 4.606 0.136 5.902 1.038 0.22 0.086 1.204 X 10236+04111 0.291 589 8.464 0.127 14.162 0.213 8.052 0.966 0.285 0.096 1.289 X 1023399+490838 0.144 533 3.321 0.111 5.034 0.168 6.513 0.589 0.156 0.083 1.099 A3444 0.253 552 7.473 0.123 12.037 0.197 7.915 0.451 0.338 0.06 0.974 1029+2623 0.584 397 3.401 0.23 5.0 0.338 5.809 0.958 0.074 0.099 1.136 A1033 0.126 501 1.475 0.025 2.143 0.037 5.886 0.583 0.266 0.038 1.207 X 08842 0.426 323 0.317 0.082 0.427 0.11 3.294 1.238 0.233 0.284 1.109 EAD2007188 0.072 351 0.269 0.02 0.359 0.027 2.84 0.221 0.275 0.095 1.157 A1068 0.138 463 1.884 0.042 2.664 0.06 4.963 0.253 0.25 0.057 1.078 X 3402 0.015 179 0.006 0.001 0.008 0.001 0.824 0.013 0.385 0.048 1.052 X 10537+5452 0.07 281 0.196 0.021 0.276 0.029 1.769 0.167 0.137 0.037 1.103 X 10569-03373 0.823 401 7.212 0.383 11.42 0.607 7.494 1.083 0.096 0.107 1.444 A1142 0.035 311 0.032 0.002 0.044 0.003 2.147 0.169 0.145 0.051 1.246 11057-1014 0.466 589 7.646 0.598 12.986 1.015 9.115 2.406 0.383 0.258 1.249 11089+0906 0.449 472 5.708 0.269 8.786 0.414 6.863 0.744 0.193 0.106 1.128 NGC3551 0.032 271 0.023 0.002 0.032 0.002 1.623 0.062 0.32 0.051 1.229 A1190 0.075 397 0.599 0.028 0.808 0.038 3.597 0.19 0.271 0.083 1.247 A1201 0.169 492 2.527 0.054 3.681 0.079 5.309 0.543 0.359 0.06 1.254 X 11130-2615 0.725 310 1.505 0.15 2.058 0.205 4.239 0.552 0.498 0.262 1.149 A1204 0.171 423 1.629 0.066 2.253 0.092 4.327 0.277 0.218 0.084 1.31 33 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 1115+5319 0.466 604 8.139 0.364 14.554 0.651 10.328 1.639 0.141 0.157 1.084 11158+0129 0.352 589 8.02 0.227 13.674 0.388 9.18 0.73 0.189 0.068 1.253 11201+4318 0.6 348 5.466 0.67 7.677 0.941 4.71 0.906 0.088 0.128 1.022 4001120+2326 0.562 355 2.181 0.169 3.024 0.234 4.457 0.577 0.279 0.159 1.152 HCG051 0.026 235 0.014 0.001 0.02 0.002 1.319 0.031 0.294 0.038 1.156 A1240 0.159 415 0.492 0.032 0.675 0.044 4.158 0.42 0.279 0.137 1.411 11300+3637 0.06 269 0.07 0.004 0.1 0.006 1.738 0.083 0.13 0.032 1.188 X A1285 0.106 496 2.267 0.042 3.281 0.06 5.361 0.617 0.314 0.026 1.219 X A1300 0.307 786 9.614 0.24 17.836 0.446 11.265 1.174 0.262 0.099 1.285 11375+6625 0.782 334 5.411 0.347 7.728 0.495 5.174 0.629 0.228 0.122 1.088 1142248+583205 0.311 609 7.812 0.182 13.142 0.306 8.855 0.679 0.127 0.073 1.166 4-33018 0.051 341 0.089 0.005 0.119 0.007 2.516 0.44 0.328 0.144 1.265 X A1413 0.143 578 4.175 0.044 6.581 0.07 7.35 0.558 0.231 0.089 1.459 X A1423 0.213 441 0.323 0.01 0.447 0.014 5.932 0.945 0.245 0.115 1.393 X 17981192+4979669 0.383 569 7.801 0.394 13.915 0.702 10.276 1.691 0.267 0.141 1.111 4-33144 0.081 269 0.077 0.005 0.106 0.007 1.766 0.077 0.247 0.051 1.001 X 29251+2198 0.3 606 5.929 0.172 9.902 0.287 8.702 0.784 0.233 0.076 1.104 A1446 0.104 390 0.707 0.019 0.95 0.025 3.526 0.117 0.354 0.048 1.123 X 4001202+5751 0.677 275 1.944 0.352 2.532 0.458 3.184 0.758 0.949 0.609 1.112 12062-0847 0.44 606 16.98 0.49 31.633 0.913 11.369 1.423 0.225 0.109 1.235 4104 0.028 279 0.02 0.001 0.029 0.002 1.696 0.236 0.118 0.055 1.249 X 12154-3900 0.119 494 1.605 0.038 2.315 0.055 5.505 0.361 0.429 0.11 1.167 121733+033929 0.077 576 2.565 0.05 3.947 0.077 6.694 0.647 0.292 0.17 2.787 X 121831+401236 0.32 475 4.257 0.182 6.32 0.271 6.09 0.651 0.21 0.116 1.216 4001221+4918 0.7 428 4.586 0.318 7.143 0.495 7.16 1.083 0.299 0.138 1.08 4325 0.025 202 0.018 0.001 0.027 0.002 0.976 0.018 0.263 0.026 1.141 X 122648+215157 0.37 407 1.608 0.082 2.259 0.115 4.785 0.474 0.191 0.095 1.082 12269+3332 0.89 539 11.315 0.521 22.466 1.035 13.126 1.968 0.193 0.189 1.117 34 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 12303+1339 0.975 325 4.4 0.455 6.5 0.671 6.0 1.033 0.244 0.154 1.126 A1553 0.165 568 3.879 0.113 6.048 0.176 7.238 0.587 0.518 0.105 1.136 12342+0947 0.229 421 1.747 0.111 2.439 0.154 4.552 0.485 0.134 0.112 1.255 A1569 0.074 315 0.261 0.02 0.348 0.027 2.223 0.326 0.239 0.089 1.575 X A1576 0.279 566 2.87 0.107 4.654 0.174 8.001 0.772 0.057 0.063 1.187 12525-3116 0.054 352 0.229 0.013 0.301 0.017 2.869 0.165 0.515 0.102 1.344 A1644 0.047 481 0.818 0.007 1.171 0.009 4.858 0.506 0.344 0.141 3.047 X A1650 0.084 514 2.247 0.018 3.278 0.026 5.726 0.524 0.286 0.106 1.737 X 1259334+600409 0.33 501 3.904 0.145 6.024 0.223 6.894 0.515 0.112 0.068 1.062 125947+312215 0.058 190 0.026 0.008 0.04 0.012 0.91 0.104 0.142 0.075 1.349 A1664 0.128 468 1.93 0.041 2.747 0.059 5.018 0.211 0.093 0.04 1.178 X A1668 0.063 383 0.304 0.019 0.409 0.026 3.326 0.291 0.245 0.094 1.442 1305589+263048 0.305 537 4.356 0.192 6.829 0.3 7.269 0.948 0.151 0.097 1.082 A1682 0.234 550 3.71 0.105 5.803 0.164 7.205 0.618 0.116 0.092 1.131 13110-0311 0.494 428 4.349 0.189 6.435 0.28 6.031 0.482 0.228 0.071 1.128 A1689 0.183 676 8.559 0.103 15.062 0.181 10.0 0.874 0.279 0.11 1.41 X 4001312+3900 0.404 390 1.239 0.146 1.725 0.204 4.481 1.148 0.138 0.235 1.106 1315052+514902 0.291 583 6.692 0.136 11.224 0.229 8.765 0.771 0.025 0.048 1.149 NGC5044 0.009 187 0.001 0.0 0.001 0.0 1.32 0.026 0.404 0.049 0.996 A1722 0.328 631 3.531 0.237 5.955 0.399 8.969 2.186 0.553 0.267 1.251 5098 0.037 213 0.024 0.001 0.037 0.002 1.134 0.06 0.188 0.066 1.257 X A1736 0.046 387 0.638 0.013 0.854 0.017 3.07 0.313 0.322 0.158 3.124 X SSGC081 0.05 398 0.418 0.015 0.565 0.02 3.207 0.393 0.282 0.087 2.178 X a1750ss 0.091 330 0.138 0.016 0.185 0.021 2.405 0.202 0.238 0.096 1.175 A1750C 0.068 450 0.445 0.017 0.617 0.024 3.861 0.768 0.263 0.095 1.31 X A1750N 0.084 397 0.458 0.022 0.621 0.029 3.586 0.23 0.165 0.07 1.35 213312961+1107566 0.079 155 0.008 0.004 0.012 0.006 0.64 0.042 0.206 0.173 1.022 SC1329-313 0.048 406 0.269 0.014 0.362 0.019 3.182 0.222 0.184 0.092 2.819 X 35 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) A3562 0.049 470 0.826 0.018 1.149 0.026 4.701 0.503 0.34 0.125 3.211 X A1763 0.223 555 6.919 0.18 11.013 0.286 7.669 0.593 0.388 0.084 1.252 A1767 0.07 495 1.188 0.037 1.703 0.053 5.301 0.29 0.293 0.081 1.412 4001340+4017 0.171 244 0.074 0.015 0.101 0.021 1.583 0.167 0.36 0.155 1.021 A1775 0.072 408 0.923 0.011 1.238 0.015 3.76 0.413 0.503 0.11 1.616 X LCDCS0829 0.451 718 20.538 0.248 41.656 0.503 13.75 0.532 0.225 0.034 1.16 X 1348502+491801 0.162 421 0.451 0.034 0.624 0.048 4.274 0.675 0.163 0.17 1.392 4001354-0221 0.546 351 1.525 0.239 2.111 0.331 4.417 1.07 0.275 0.231 1.025 13546+7715 0.397 467 4.673 0.251 7.024 0.378 6.384 0.815 0.314 0.119 1.103 1357168+623249 0.563 382 2.449 0.255 3.513 0.366 5.225 1.059 0.127 0.155 1.052 13592-1929 0.447 456 2.59 0.194 3.938 0.296 6.565 1.197 0.103 0.124 1.198 A1831 0.062 399 0.538 0.017 0.72 0.023 3.541 0.159 0.447 0.077 1.347 1359495+623047 0.322 509 4.018 0.121 6.184 0.186 6.859 0.59 0.199 0.084 1.468 A1835 0.253 646 12.004 0.17 21.457 0.303 9.175 1.354 0.348 0.157 1.213 X 3C295 0.464 246 3.038 0.462 4.172 0.634 2.115 0.261 0.16 0.096 1.144 11382+4435 0.226 495 2.62 0.128 3.891 0.189 6.017 0.68 0.004 0.053 1.037 A1882a 0.14 385 0.316 0.017 0.424 0.022 3.556 0.226 0.403 0.102 1.129 X 1416238+444528 0.386 345 1.653 0.149 2.195 0.197 3.649 0.283 0.75 0.269 1.1 LCDCS0954 0.67 213 1.323 0.599 1.794 0.812 2.017 0.679 0.295 0.377 0.932 21594948+2407846 0.543 462 6.151 0.118 9.624 0.185 7.262 0.364 0.302 0.067 1.0 X A1914 0.171 633 9.446 0.147 15.799 0.246 8.422 1.044 0.213 0.053 1.398 X 1427161+440730 0.498 601 6.679 0.271 11.975 0.486 10.403 1.424 0.236 0.142 1.328 14276-2521 0.318 410 2.061 0.095 2.865 0.132 4.689 0.34 0.443 0.114 1.186 A1930 0.131 440 0.951 0.038 1.311 0.053 4.366 0.629 0.587 0.028 1.235 X A1942 0.224 465 1.401 0.046 2.016 0.066 5.305 0.486 0.373 0.031 1.219 X WBL518 0.027 368 0.14 0.005 0.186 0.006 2.895 0.37 0.269 0.134 3.427 X A1991 0.059 346 0.329 0.01 0.438 0.013 2.766 0.059 0.316 0.038 1.106 X 145715+222009 0.258 452 3.947 0.081 5.65 0.115 5.266 0.216 0.299 0.044 1.135 X 36 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) AS0780 0.236 551 5.352 0.074 8.395 0.117 7.326 0.292 0.314 0.057 1.065 X A2009 0.153 543 3.537 0.097 5.386 0.148 6.695 0.309 0.443 0.071 1.392 X 150117+422152 0.292 483 2.468 0.193 3.686 0.289 6.182 1.276 0.111 0.149 1.26 1504075-024816 0.215 620 9.519 0.13 16.069 0.219 8.482 0.751 0.238 0.07 1.463 X A2034 0.113 595 2.975 0.031 4.685 0.049 7.555 0.875 0.303 0.108 1.568 X 15149-1523 0.223 616 5.561 0.09 9.372 0.151 8.899 0.481 0.141 0.048 1.105 A2061 0.078 457 1.171 0.022 1.631 0.031 4.619 0.136 0.284 0.042 1.083 X MKW03s 0.045 394 0.65 0.006 0.875 0.008 3.434 0.404 0.261 0.113 2.072 X A2069 0.116 525 1.793 0.032 2.675 0.048 5.936 0.646 0.301 0.128 1.712 X 15242-3154 0.103 444 1.365 0.019 1.9 0.026 4.426 0.719 0.362 0.129 1.326 X 15246+0957 0.516 338 2.21 0.156 2.988 0.21 4.02 0.378 0.61 0.2 1.079 15328+3021 0.345 522 6.57 0.112 10.388 0.177 7.486 0.413 0.203 0.048 1.141 X A2107 0.041 434 0.433 0.009 0.588 0.012 3.766 0.48 0.265 0.114 3.251 X A2111 0.229 567 3.754 0.081 5.996 0.129 7.7 0.575 0.186 0.085 1.146 A2104 0.153 565 3.731 0.049 5.815 0.077 7.2 1.018 0.245 0.153 1.354 X A2125 0.246 343 0.632 0.031 0.85 0.042 3.158 0.206 0.197 0.089 1.133 A2124 0.066 485 0.326 0.012 0.463 0.017 5.092 0.4 0.35 0.113 1.104 X A2142 0.091 626 4.832 0.043 7.887 0.069 7.675 0.57 0.276 0.08 3.074 X 15583-1410 0.097 483 2.001 0.021 2.85 0.029 5.018 0.356 0.371 0.106 1.33 X A2147 0.035 449 0.537 0.007 0.737 0.01 4.275 0.343 0.321 0.101 4.436 X A2151 0.037 358 0.183 0.023 0.243 0.031 2.794 0.342 0.268 0.174 3.062 X 161314+564930 0.871 392 6.243 0.566 9.876 0.895 7.485 1.895 0.161 0.205 1.09 A2163 0.203 795 20.636 0.14 42.292 0.288 13.183 1.347 0.24 0.045 1.603 X 16213+3810 0.465 482 4.964 0.186 7.763 0.291 7.226 0.58 0.199 0.066 1.167 16235+2634 0.426 449 3.854 0.228 5.798 0.342 6.365 0.908 0.201 0.124 1.005 A2187 0.184 554 2.384 0.1 3.644 0.152 6.709 0.765 0.183 0.122 1.389 A2204 0.152 654 6.25 0.044 10.792 0.077 8.269 1.172 0.319 0.143 1.623 X A2218 0.176 520 4.315 0.084 6.482 0.127 6.318 0.55 0.201 0.076 1.287 X 37 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) A2219 0.226 699 14.778 0.091 27.42 0.169 11.017 0.888 0.28 0.093 1.223 X 4001641+4001 0.464 346 1.098 0.149 1.488 0.203 3.941 0.826 0.423 0.285 1.103 HerculesA 0.155 419 1.836 0.034 2.531 0.047 3.653 1.309 0.181 0.097 1.224 X NGC6269 0.035 308 0.078 0.004 0.108 0.006 1.813 0.314 0.107 0.111 3.295 X 021701+6412 0.453 453 2.479 0.125 3.72 0.188 6.371 0.771 0.379 0.154 1.122 A2244 0.097 515 2.68 0.024 3.927 0.036 5.812 0.105 0.268 0.028 1.106 X A2256 0.058 586 3.438 0.033 5.363 0.052 6.782 0.465 0.381 0.135 1.886 X A2249 0.082 486 1.267 0.035 1.811 0.051 5.153 0.342 0.168 0.086 1.204 A2255 0.081 530 2.107 0.026 3.133 0.038 6.086 0.559 0.325 0.113 1.828 X NGC6338 0.027 336 0.106 0.003 0.144 0.004 2.233 0.328 0.186 0.091 4.791 X A2259 0.164 508 3.248 0.119 4.806 0.176 6.089 0.502 0.427 0.128 1.254 43072 0.164 560 4.348 0.075 6.753 0.116 7.066 0.427 0.413 0.059 1.371 X 17202+3536 0.391 530 6.766 0.206 10.872 0.331 7.87 0.653 0.367 0.08 1.279 A2261 0.224 593 7.182 0.156 11.669 0.253 7.714 1.178 0.349 0.077 1.276 X A2294 0.169 570 4.578 0.17 7.178 0.266 7.303 0.736 0.26 0.106 1.415 17316+2251 0.366 551 6.784 0.211 11.278 0.351 8.608 0.849 0.299 0.123 1.32 Abell2276 0.141 338 0.501 0.046 0.672 0.061 2.831 0.277 0.202 0.104 1.249 17421+3306 0.076 437 1.099 0.017 1.507 0.024 4.076 0.352 0.374 0.179 1.653 X 174715+451155 0.156 447 1.518 0.066 2.128 0.093 4.729 0.378 0.182 0.084 1.142 17502+3504 0.171 442 1.689 0.078 2.364 0.109 4.639 0.356 0.126 0.083 1.187 18044+1002 0.152 545 5.159 0.144 8.034 0.225 7.097 0.592 0.092 0.075 1.225 A2302 0.179 447 1.324 0.055 1.862 0.077 4.821 0.382 0.203 0.096 1.157 18243+4309 0.487 476 1.922 0.182 2.995 0.283 7.102 2.235 0.06 0.211 1.099 18290+6913 0.203 402 0.843 0.044 1.151 0.06 4.057 0.305 0.335 0.109 1.234 18521+5711 0.109 418 0.465 0.019 0.635 0.026 4.003 0.283 0.259 0.096 1.345 18539+6822 0.093 423 1.031 0.025 1.419 0.034 4.129 0.221 0.19 0.074 1.199 33709-2597 0.264 563 6.544 0.138 10.438 0.221 7.658 0.539 0.118 0.07 1.181 A2319 0.056 670 5.846 0.046 10.028 0.078 8.664 1.413 0.319 0.131 3.532 X 38 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 19318-2635 0.352 540 8.805 0.104 14.152 0.168 7.793 0.786 0.374 0.147 1.326 X AS0821 0.237 511 5.443 0.174 8.184 0.261 6.386 0.506 0.302 0.072 1.108 19383+5409 0.26 539 8.739 0.35 13.629 0.546 7.202 0.728 0.356 0.091 1.124 19473-7623 0.217 574 5.483 0.179 8.604 0.28 7.337 0.632 0.338 0.086 1.214 A3653 0.109 450 0.524 0.015 0.733 0.021 4.781 0.341 0.345 0.071 1.222 19582-3011 0.117 399 0.088 0.012 0.119 0.016 3.283 0.982 0.182 0.452 1.212 20035-2323 0.317 599 7.858 0.19 13.401 0.324 9.178 0.804 0.131 0.072 1.222 20113-5725 0.279 363 2.134 0.151 2.886 0.205 3.629 0.373 0.231 0.11 1.156 20148-2430 0.161 560 4.182 0.099 6.499 0.154 7.148 0.389 0.467 0.088 1.19 X 2023-5535 0.232 609 5.848 0.172 9.627 0.283 8.387 0.761 0.291 0.085 1.121 20318-4037 0.342 494 7.965 0.43 12.201 0.659 6.735 0.918 0.128 0.117 1.116 2034-5936 0.92 298 6.077 0.871 8.49 1.216 4.721 0.886 0.298 0.17 1.101 A3695 0.089 550 1.909 0.042 2.887 0.064 6.465 0.427 0.161 0.084 1.352 2043-5035 0.723 356 6.36 0.474 9.192 0.685 5.436 0.683 0.19 0.099 1.073 20460-3430 0.423 428 4.194 0.216 6.1 0.314 5.606 0.447 0.212 0.086 1.136 20499-3216 0.325 528 5.29 0.221 8.338 0.348 7.423 0.952 0.262 0.109 1.259 A3739 0.165 516 2.874 0.12 4.251 0.177 6.084 0.527 0.413 0.111 1.096 2106-5844 1.132 329 22.47 1.818 34.961 2.829 7.158 0.782 0.193 0.096 1.044 IC1365 0.049 429 0.574 0.025 0.781 0.034 3.966 0.438 0.509 0.083 2.48 X 2129-0741 0.589 479 12.133 0.669 19.708 1.086 8.117 0.943 0.454 0.126 1.13 2135-0102 0.325 557 4.768 0.219 7.826 0.36 8.365 1.066 0.58 0.154 1.246 A2355 0.124 586 1.465 0.045 2.29 0.071 7.24 0.69 0.289 0.118 1.276 2135-5726 0.427 477 3.586 0.199 5.541 0.307 6.922 1.301 0.108 0.157 1.099 WBL671 0.051 208 0.012 0.004 0.019 0.006 1.004 0.119 0.111 0.061 1.187 21402-2339 0.313 468 3.985 0.11 5.86 0.162 5.922 0.343 0.314 0.059 1.07 X 2145-5644 0.48 462 4.965 0.361 7.663 0.557 6.866 1.278 0.006 0.078 1.053 2146-4633 0.933 339 3.815 0.471 5.731 0.707 6.267 1.339 0.01 0.092 1.102 A3809 0.062 354 0.426 0.014 0.565 0.019 3.117 0.292 0.413 0.138 1.303 X 39 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) 2148-6116 0.571 436 3.484 0.229 5.327 0.351 6.735 1.175 0.272 0.195 1.039 A2384 0.094 516 1.119 0.018 1.628 0.026 5.246 0.839 0.39 0.162 2.33 X A2390 0.228 668 13.625 0.092 25.178 0.169 11.164 0.313 0.28 0.032 1.068 X 21538+3746 0.292 608 11.047 0.148 19.077 0.256 9.495 0.365 0.258 0.036 1.148 X A2409 0.148 510 4.281 0.134 6.289 0.197 5.955 0.382 0.462 0.093 1.292 A3827 0.098 585 3.243 0.032 5.08 0.05 7.338 0.789 0.339 0.144 1.302 X A2415 0.058 344 0.401 0.012 0.534 0.016 2.583 0.284 0.347 0.094 1.236 X 22117-0349 0.27 655 6.301 0.219 11.029 0.383 9.815 1.315 0.221 0.121 1.394 3C444 0.153 473 0.613 0.021 0.876 0.03 4.379 0.393 0.332 0.098 1.334 X A2426 0.098 522 1.671 0.053 2.451 0.077 5.825 0.389 0.251 0.1 1.305 2214-1359 0.483 530 10.888 0.419 18.292 0.705 8.833 0.989 0.194 0.093 1.12 A3854 0.149 472 2.281 0.081 3.256 0.116 5.181 0.394 0.258 0.092 1.197 22186-3853 0.138 499 3.292 0.092 4.789 0.134 5.604 0.33 0.2 0.075 1.24 2218-4519 0.65 398 3.405 0.277 4.965 0.405 5.831 1.117 0.619 0.292 1.132 A2445 0.166 414 1.718 0.057 2.34 0.077 4.162 0.215 0.545 0.086 1.19 A3880 0.058 356 0.341 0.018 0.453 0.023 2.897 0.277 0.305 0.143 2.28 X 22286+2036 0.412 550 10.081 0.348 16.485 0.569 8.249 0.824 0.352 0.116 1.176 22298-2756 0.324 464 4.07 0.19 5.967 0.279 5.882 0.562 0.397 0.108 1.233 514-050 0.017 241 0.003 0.0 0.005 0.0 1.231 0.043 0.225 0.029 1.337 2232-5959 0.594 394 4.175 0.545 5.792 0.756 4.53 1.074 0.33 0.218 1.104 2233-5339 0.48 466 4.392 0.264 6.75 0.406 6.791 1.168 0.075 0.121 1.089 A2457 0.059 414 0.55 0.015 0.744 0.021 3.595 0.099 0.326 0.059 1.352 X A2465 0.245 294 0.343 0.03 0.457 0.04 2.378 0.209 0.354 0.143 1.165 22428+5301 0.192 595 4.117 0.053 6.747 0.088 8.271 0.345 0.206 0.03 1.048 X 2243198-093530 0.432 488 14.006 0.52 21.842 0.811 7.179 0.672 0.267 0.085 1.214 2245-6206 0.58 416 4.606 0.55 6.897 0.823 6.221 1.324 0.077 0.121 1.051 22450+2637 0.304 499 4.48 0.241 6.835 0.368 6.71 0.933 0.33 0.146 1.224 A3911 0.096 544 2.198 0.061 3.262 0.09 6.106 0.393 0.285 0.081 1.183 40 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) A2485 0.247 511 2.703 0.119 4.043 0.178 6.25 0.714 0.231 0.129 1.247 AS1063 0.348 663 22.56 0.412 41.905 0.765 11.302 0.722 0.359 0.07 1.219 A3921 0.093 522 1.981 0.037 2.916 0.054 5.766 0.762 0.36 0.085 1.879 X A2507 0.196 414 1.003 0.065 1.377 0.089 4.309 0.433 0.426 0.154 1.069 2259-6057 0.75 411 4.949 0.246 7.715 0.384 7.265 1.064 0.694 0.215 1.2 23028+0843 0.722 407 1.736 0.111 2.667 0.17 6.818 1.234 0.169 0.18 1.139 A2537 0.295 506 4.65 0.104 7.083 0.158 6.649 0.368 0.243 0.054 1.157 X 23115+0338 0.3 598 7.26 0.281 12.544 0.486 9.518 1.005 0.334 0.103 1.333 A2550 0.123 276 0.216 0.015 0.297 0.02 1.929 0.124 0.231 0.049 1.077 X A2556 0.087 413 0.814 0.018 1.105 0.024 3.86 0.155 0.281 0.041 1.157 X AS1101 0.058 345 0.541 0.01 0.726 0.013 2.698 0.286 0.199 0.089 2.076 X 23185+0034 0.78 382 2.373 0.178 3.611 0.271 6.597 1.195 0.152 0.138 1.091 A2597 0.085 442 0.878 0.01 1.214 0.015 4.266 0.259 0.279 0.08 1.31 X 2331-5051 0.571 419 3.893 0.38 5.899 0.575 6.486 1.747 0.096 0.143 1.078 A2626 0.055 382 0.443 0.012 0.593 0.016 3.264 0.111 0.349 0.044 1.119 X A2627 0.126 601 0.319 0.036 0.581 0.065 10.85 4.147 0.736 0.77 1.287 2337-5942 0.781 435 15.389 1.279 25.287 2.101 8.326 1.621 0.186 0.161 1.065 A2631 0.273 580 7.191 0.246 11.658 0.398 8.024 0.961 0.169 0.1 1.254 A4023 0.193 507 1.996 0.082 2.984 0.123 6.256 0.635 0.268 0.117 1.216 2341-5119 0.998 384 7.073 0.735 11.579 1.203 8.27 1.573 0.336 0.195 1.085 A2645 0.251 512 3.698 0.171 5.582 0.258 6.47 0.782 0.297 0.119 1.118 23442-0422 0.079 450 1.473 0.038 2.031 0.052 4.501 0.143 0.406 0.261 1.422 X 2344-4243 0.62 529 21.473 1.351 37.864 2.383 9.981 1.819 0.114 0.134 1.096 A2657 0.04 403 0.583 0.016 0.785 0.021 3.567 0.307 0.302 0.165 3.162 X 2345-6405 0.94 379 5.516 0.406 8.901 0.656 7.9 1.51 0.072 0.128 1.095 HCG097 0.022 197 0.007 0.001 0.012 0.002 0.812 0.035 0.135 0.03 1.166 A4038 0.028 369 0.394 0.007 0.525 0.009 2.878 0.263 0.286 0.118 3.54 X AS1150 0.261 453 0.851 0.103 1.217 0.148 5.221 1.32 0.23 0.291 1.079 41 Table 2.3 (cont’d) Name 𝑧 𝑅2500 𝐿 𝑋 e_𝐿 𝑋 𝐿𝑋 e_𝐿 𝑋 𝑘𝑇 e_𝑘𝑇 𝑍 e_𝑍 𝜒2 WTD [0.5-7 keV] [bol] kpc (1044 erg s−1 ) (1044 erg s−1 ) (keV) (𝑍 ) (d.o.f) A2665 0.056 458 0.489 0.018 0.68 0.025 4.553 0.294 0.31 0.095 1.412 A2667 0.23 556 7.819 0.208 12.434 0.331 7.604 0.677 0.163 0.084 1.046 A2670 0.076 435 0.743 0.021 1.019 0.028 4.001 0.706 0.31 0.114 2.206 X 2355-5056 0.35 395 2.27 0.258 3.154 0.358 4.536 0.913 0.273 0.202 1.119 2359-5009 0.76 294 1.729 0.295 2.35 0.401 4.011 0.806 0.423 0.215 1.006 42 Table 2.4: Table of full cluster names and coordinates in ACCEPT2.0. This table contains the coordinates of ACCEPT2.0 clusters and defines the naming convention used throughout this dissertation. Col(1) is the truncated cluster name, col(2) is the full name in ACCEPT2.0, cols(3,4) are the RA and DEC (J2000) in degrees, and cols(5,6) are the entropy excess 𝐾0 and error, if available. Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) 000619+105206 NSCS_J000619+105206 1.5845 10.8643 58.428 11.089 00088+5215 ZwCl_0008.8+5215 2.8647 52.5265 170.494 40.772 00117-1523 MACS_J0011.7-1523 2.9286 -15.3892 A0013 ABELL_0013 3.4098 -19.5005 130.014 31.3 A2744 ABELL_2744 3.5807 -30.3909 0014-4952 SPT-CLJ0014-4952 3.7037 -49.8838 Cl0016+16 Cl_0016+16 4.6402 16.4359 165.464 19.834 00254-1222 MACS_J0025.4-1222 6.3737 -12.3761 149.815 20.362 00278+2616 MCXC_J0027.8+2616 6.9383 26.2756 30484-4142 PLCKESZ_G304.84-41.42 7.026 -75.6358 00305+2618 WARP_J0030.5+2618 7.6427 26.3027 00354-2015 MCXC_J0035.4-2015 8.8586 -20.2623 136.376 16.255 A0068 ABELL_0068 9.2775 9.1578 A0085 ABELL_0085 10.4599 -9.3029 A2813 ABELL_2813 10.8535 -20.6234 00408+2404 ZwCl_0040.8+2404 10.9678 24.4059 9.048 1.165 A0098N ABELL_0098N 11.6029 20.6218 10.598 5.928 A98ss A98ss 11.6516 20.2567 351-021 ESO_351-_G_021 13.7497 -35.3214 3.731 0.865 A0119 ABELL_0119 14.0755 -1.2422 0058-6145 SPT-CLJ0058-6145 14.588 -61.7679 200428 _SBV2004__RS_28 16.2302 0.0596 A0141 ABELL_0141 16.3979 -24.6301 158.783 28.161 0106-5943 SPT-CLJ0106-5943 16.6175 -59.7204 01670077+0105926 MaxBCG_J016.70077+01.05926 16.7062 1.0563 11.751 0.707 01077+5408 CIZA_J0107.7+5408 16.9381 54.1327 305.475 45.983 43 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) A0160 ABELL_0160 18.2737 15.5298 011502+002441 NSCS_J011502+002441 18.7658 0.4041 A2895 ABELL_2895 19.5469 -26.9653 168.687 33.931 UGC00842 UGC_00842 19.7235 -1.0021 0123-4821 SPT-CLJ0123-4821 20.7992 -48.3566 A0193 ABELL_0193 21.2802 8.7003 134.938 9.008 A0209 ABELL_0209 22.9701 -13.6114 86.644 24.724 Abell222 Abell_222 24.3946 -12.9931 148.849 21.545 Abell223 Abell_223 24.4835 -12.8198 01400-0555 MACS0140.0-0555 25.0065 -5.9191 01420+2131 MCXC_J0142.0+2131 25.5134 21.5212 01502127-1005305 SDSS_J015021.27-100530.5_GROUP 27.5885 -10.0915 2.481 6.357 0151-5954 SPT-CLJ0151-5954 27.8452 -59.9075 01525-2853 MCXC_J0152.5-2853 28.1437 -28.8937 A0267 ABELL_0267 28.1774 1.0123 148.399 16.487 0156-5541 SPT-CLJ0156-5541 29.0423 -55.6987 02209-3829 MCXC_J0220.9-3829 35.2357 -38.4804 A3017 ABELL_3017 36.4715 -41.9152 36.916 7.731 0228259+003202 WHL_J022825.9+003202 37.1072 0.5328 MZ10451 MZ_10451 37.4397 -29.6287 11.591 10.746 0232-4421 SPT-CL_J0232-4421 38.0777 -44.3462 0234-5831 SPT-CL_J0234-5831 38.6747 -58.5236 A0368 ABELL_0368 39.3652 -26.508 4000237-5224 400d_J0237-5224 39.5034 -52.4198 A0370 ABELL_0370 39.9707 -1.5793 256.699 27.693 02426-2132 MACS_J0242.6-2132 40.6495 -21.5406 9.402 1.573 0243-5930 SPT-CLJ0243-5930 40.863 -59.5172 AS0295 ABELL_S0295 41.3616 -53.03 165.939 21.589 4000245+0936 400d_J0245+0936 41.4538 9.6106 44 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) A0376 ABELL_0376 41.5164 36.9055 61.935 16.644 A0383 ABELL_0383 42.0141 -3.5293 10.28 1.047 0252-4824 SPT-CLJ0252-4824 43.2076 -48.4163 NGC1132 NGC_1132 43.2158 -1.2748 0256-5617 SPT-CLJ0256-5617 44.1056 -56.2982 A0402 ABELL_0402 44.4217 -22.1549 A0399 ABELL_0399 44.4726 13.0253 A0401 ABELL_0401 44.7438 13.5788 154.597 14.171 03016+0155 MCXC_J0301.6+0155 45.4092 1.9208 12.181 1.87 4000302-0423 400d_J0302-0423 45.588 -4.39 03037-7752 MCXC_J0303.7-7752 45.9413 -77.8792 187.074 34.239 A3088 ABELL_3088 46.7581 -28.6658 0307-6225 SPT-CLJ0307-6225 46.8203 -62.4458 0307-5042 SPT-CLJ0307-5042 46.9607 -50.7019 03089+2645 MACS_J0308.9+2645 47.2331 26.7611 144.011 31.449 0310-4647 SPT-CLJ0310-4647 47.6349 -46.7862 A3094 ABELL_3094 47.8989 -26.8985 31.063 66.818 4000318-0302 400d_J0318-0302 49.6437 -3.0509 0324-6236 SPT-CLJ0324-6236 51.0518 -62.5988 4000328-2140 400d_J0328-2140 52.1494 -21.6736 A3126 ABELL_3126 52.1494 -55.718 158.222 13.322 A3128 ABELL_3128 52.4609 -52.5804 12.128 60.726 03311-2100 MCXC_J0331.1-2100 52.775 -21.0089 11.718 1.574 0334-4659 SPT-CLJ0334-4659 53.546 -46.996 3C089 3C_089 53.5625 -1.1882 30.855 5.532 03408-4542 MCXC_J0340.8-4542 55.2241 -45.6768 189.419 55.692 IIIZw054 III_Zw_054 55.3153 15.4097 A3158 ABELL_3158 55.7139 -53.6297 0346-5438 ACT-CL_J0346-5438 56.7326 -54.6485 45 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) 0352-5647 SPT-CLJ0352-5647 58.2416 -56.7955 03529+1941 MCXC_J0352.9+1941 58.2457 19.683 7.106 0.38 03588-2955 MACS_J0358.8-2955 59.7263 -29.9259 26.151 14.956 4000405-4100 400d_J0405-4100 61.3517 -41.0054 A0478 ABELL_0478 63.355 10.4653 11.58 0.91 04161-2403 MACS_J0416.1-2403 64.0393 -24.0655 76.272 106.522 0417-4748 SPT-CL_J0417-4748 64.3465 -47.8134 04175-1154 MACS_J0417.5-1154 64.3926 -11.9096 23.919 8.332 04258-0833 MCXC_J0425.8-0833 66.4634 -8.5604 6.656 1.32 0426-5455 SPT-CLJ0426-5455 66.5191 -54.9116 AS0463 ABELL_S0463 67.1569 -53.8402 117.469 23.573 04296-0253 MACS_J0429.6-0253 67.4 -2.8854 12.169 3.11 04371+0043 MCXC_J0437.1+0043 69.2898 0.7322 39.939 4.172 04390+0715 MCXC_J0439.0+0715 69.7523 7.2684 57.207 11.956 04390+0520 MCXC_J0439.0+0520 69.759 5.3454 6.155 1.597 04431+0210 MCXC_J0443.1+0210 70.7914 2.172 A0514 ABELL_0514 72.007 -20.4478 A3292 ABELL_3292 72.483 -44.6731 108.116 10.191 04519+0006 MACS_J0451.9+0006 72.9766 0.1055 04541-0300 MCXC_J0454.1-0300 73.5471 -3.0159 552-020 ESO_552-_G_020 73.7181 -18.1154 04552+0657 MACS_J0455.2+0657 73.822 6.9634 0456-5116 SPT-CLJ0456-5116 74.1149 -51.2789 0509-5342 SPT-CL_J0509-5342 77.3385 -53.7035 A3322 ABELL_3322 77.5713 -45.3215 104.613 17.637 05107-0801 MCXC_J0510.7-0801 77.6985 -8.0275 122.172 51.636 A0539 ABELL_0539 79.1556 6.4406 AS0520 ABELL_S0520 79.1571 -54.5131 320.133 39.838 05207-1328 MCXC_J0520.7-1328 80.1751 -13.4803 46 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) 052215-481816 CXOU_J052215-481816 80.5635 -48.3045 A3343 ABELL_3343 81.4534 -47.2528 163.757 19.794 05282-2942 MCXC_J0528.2-2942 82.0607 -29.7219 88.463 18.81 RBS0653 RBS_0653 82.2209 -39.4705 27.862 4.749 28658-3125 PLCKESZ_G286.58-31.25 82.8695 -75.1768 149.127 62.571 A0545 ABELL_0545 83.1057 -11.5422 146.987 21.961 05329-3701 MCXC_J0532.9-3701 83.2314 -37.0264 98.106 24.012 3060170- ESO3060170-A 85.0278 -40.8366 0542-4100 RDCS_J0542-4100 85.7091 -40.9996 05470-3904 MCXC_J0547.0-3904 86.7563 -39.074 A3364 ABELL_3364 86.9065 -31.8712 205.019 17.037 A0548A ABELL_0548A 87.1596 -25.4779 23.658 10.142 0551-5709 SPT-CL_J0551-5709 87.8876 -57.1491 A0550 ABELL_0550 88.2159 -21.0536 120.247 24.385 05534-3342 MACS_J0553.4-3342 88.3574 -33.7085 106.577 46.574 0559-5249 SPT-CL_J0559-5249 89.9283 -52.8309 A3376 ABELL_3376 90.548 -39.9498 A3378 ABELL_3378 91.4749 -35.3022 8.528 3.136 06163-2156 CIZA_J0616.3-2156 94.1033 -21.9383 234.527 60.544 AS0579 ABELL_S0579 94.1339 -39.7968 129.966 24.011 0616-5227 ACT-CL_J0616-5227 94.1427 -52.4521 13959+2418 G139.59+24.18 95.4541 74.7014 32.801 8.952 A3391 ABELL_3391 96.5785 -53.6926 203.151 29.569 A3399 ABELL_3399 99.3088 -48.4719 59.435 16.441 16765+1764 PLCKESZ_G167.65+17.64 99.5162 47.7986 209.979 18.217 AS0592 ABELL_S0592 99.702 -53.9742 A3402 ABELL_3402 100.4229 -49.7947 A3404 ABELL_3404 101.37 -54.2284 95.055 18.879 A0562 ABELL_0562 103.3394 69.331 122.537 34.177 47 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) Bullet Bullet_Cluster 104.6276 -55.9388 07123+5931 MACS_J0712.3+5931 108.0864 59.5389 0717+3745 MACS_J0717+3745 109.3756 37.76 4000720+7108 400d_J0720+7108 110.2248 71.1497 A0578 ABELL_0578 111.223 66.9854 16.576 48.228 A0586 ABELL_0586 113.0847 31.6325 116.11 10.286 07357+7421 ZwCl_0735.7+7421 115.4346 74.244 16.14 0.906 07449+3927 MACS_J0744.9+3927 116.2201 39.4573 53.443 7.508 PKS0745-19 PKS_0745-19 116.8795 -19.2947 8.581 0.315 WBL154 WBL_154 117.8364 50.2339 A0598 ABELL_0598 117.855 17.5139 8.32 2.293 A0611 ABELL_0611 120.237 36.0566 08065+2822 ZwCl_0806.5+2822 122.4251 28.2023 43062 SDSS-C4_3062 122.5973 42.2739 46.651 12.194 A0644 ABELL_0644 124.3585 -7.5088 70.24 6.441 08196+6336 MCXC_J0819.6+6336 124.858 63.6238 UGCl120 UGCl_120 125.8402 4.3726 08232+0425 ZwCl_0823.2+0425 126.4913 4.2467 72.063 16.331 A0665 ABELL_0665 127.7468 65.8395 2MFGC06756 2MFGC_06756 128.7284 55.5722 4000838+1948 400d_J0838+1948 129.6288 19.8055 A3411 ABELL_3411 130.4664 -17.4627 194.021 24.317 084254+292723 NSC_J084254+292723 130.7329 29.4576 22.863 2.043 A0697 ABELL_0697 130.7399 36.3664 229.645 22.639 08488+4455 RX_J0848.8+4455 132.199 44.9378 08485+3341 ZwCl_0848.5+3341 132.9121 33.5188 08579+2107 ZwCl_0857.9+2107 135.1535 20.8944 A0744 ABELL_0744 136.8355 16.6517 +1373+110+018 SDSS_+137.3+11.0+0.18 137.3031 10.9748 88.2 16.425 48 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) 09112+1746 MACS_J0911.2+1746 137.7988 17.7757 HCG037 HCG_037 138.4146 29.9928 2.267 1.28 20913454+405628 2MASSi_J0913454+405628 138.4395 40.9413 23.534 2.754 A0773 ABELL_0773 139.4711 51.728 179.097 21.364 HydraA Hydra_A 139.5246 -12.0957 15.711 0.627 0918343+295318 WHL_J091834.3+295318 139.6502 29.8919 092017+303027 NSC_J092017+303027 140.1118 30.4927 128.487 76.673 0922076+034558 WHL_J092207.6+034558 140.5428 3.7775 A0795 ABELL_0795 141.0241 14.1739 27.927 3.477 4000926+1242 400d_J0926+1242 141.6531 12.7178 0938209+520243 WHL_J093820.9+520243 144.5847 52.0484 92.459 18.089 A0853 ABELL_0853 145.5609 15.3818 A0868 ABELL_0868 146.3589 -8.6568 192.942 14.459 0947124+762313 GALEX_J094712.4+762313 146.8027 76.3871 25.087 1.568 09498+1708 MACS_J0949.8+1708 147.4651 17.1187 09496+5207 ZwCl_0949.6+5207 148.2055 51.8842 0954+1738 XMMU_J0954+1738 148.5707 17.6349 4000956+4107 400d_J0956+4107 149.0114 41.1226 A0907 ABELL_0907 149.5917 -11.064 26441+1948 PLCKESZ_G264.41+19.48 150.0067 -30.2772 94.347 40.037 10005+4409 MCXC_J1000.5+4409 150.1307 44.1458 10069+3200 MACS_J1006.9+3200 151.728 32.0286 10061+1201 ZwCl_1006.1+1201 152.1981 11.7908 10105-1239 MCXC_J1010.5-1239 152.6355 -12.6633 A0963 ABELL_0963 154.2652 39.0471 A0970 ABELL_0970 154.3481 -10.6851 102.112 18.122 10220+3830 MCXC_J1022.0+3830 155.5416 38.523 A0980 ABELL_0980 155.6182 50.1061 150.124 21.661 10236+04111 BLOX_J1023.6+0411.1 155.9154 4.1863 8.947 0.96 49 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) 1023399+490838 WHL_J102339.9+490838 155.9162 49.1445 128.079 20.582 A3444 ABELL_3444 155.9592 -27.2564 20.762 1.805 1029+2623 SDSS_J1029+2623 157.3007 26.3931 A1033 ABELL_1033 157.9363 35.0407 122.945 16.451 08842 SDSSCGB_08842 159.6786 48.8224 EAD2007188 _EAD2007__188 159.9115 5.1757 A1068 ABELL_1068 160.1854 39.9534 6.283 0.705 3402 NGC_3402_GROUP 162.6086 -12.845 1.666 0.119 10537+5452 MCXC_J1053.7+5452 163.3842 54.8754 63.3 12.56 10569-03373 BLOX_J1056.9-0337.3 164.2327 -3.6272 126.798 36.945 A1142 ABELL_1142 165.1936 10.5478 11057-1014 MACS_J1105.7-1014 166.4435 -10.2438 11089+0906 MACS_J1108.9+0906 167.2304 9.0989 80.249 38.94 NGC3551 NGC_3551 167.4352 21.7591 A1190 ABELL_1190 167.9159 40.8402 213.612 19.437 A1201 ABELL_1201 168.2278 13.4339 63.6 8.173 11130-2615 WARP_J1113.0-2615 168.2717 -26.261 A1204 ABELL_1204 168.3351 17.5944 14.727 1.691 1115+5319 SDSS_J1115+5319_CLUSTER 168.8116 53.3333 11158+0129 MACS_J1115.8+0129 168.9661 1.499 22.147 2.422 11201+4318 WARP_J1120.1+4318 170.0296 43.3022 4001120+2326 400d_J1120+2326 170.2379 23.4419 HCG051 HCG_051 170.6098 24.2986 A1240 ABELL_1240 170.9073 43.0975 196.271 92.437 11300+3637 MCXC_J1130.0+3637 172.5131 36.637 A1285 ABELL_1285 172.5932 -14.5807 186.247 29.134 A1300 ABELL_1300 172.9775 -19.9291 65.709 26.357 11375+6625 ClG_1137.5+6625 175.0935 66.1376 1142248+583205 WHL_J114224.8+583205 175.598 58.5203 459.851 44.958 50 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) 4-33018 SDSS-C4-DR3_3018 176.8046 55.7291 130.902 37.892 A1413 ABELL_1413 178.8247 23.4057 57.42 5.077 A1423 ABELL_1423 179.3218 33.611 17981192+4979669 GMBCG_J179.81192+49.79669 179.8078 49.7943 4-33144 SDSS-C4-DR3_3144 179.9675 55.5348 3.097 0.714 29251+2198 PLCKESZ_G292.51+21.98 180.2724 -39.8745 A1446 ABELL_1446 180.5176 58.0332 4001202+5751 400d_J1202+5751 180.5777 57.8659 12062-0847 MACS_J1206.2-0847 181.5504 -8.8005 54.2 11.443 4104 NGC_4104_GROUP 181.6621 28.1742 0.021 0.396 12154-3900 MCXC_J1215.4-3900 183.853 -39.0355 275.446 63.7 121733+033929 NSC_J121733+033929 184.4215 3.6555 121831+401236 NSCS_J121831+401236 184.6202 40.2075 4001221+4918 400d_J1221+4918 185.3669 49.3067 4325 NGC_4325_GROUP 185.7776 10.6213 3.284 0.201 122648+215157 NSCS_J122648+215157 186.7123 21.8323 57.719 16.388 12269+3332 WARP_J1226.9+3332 186.7423 33.5463 12303+1339 XMMU_J1230.3+1339 187.5711 13.6519 A1553 ABELL_1553 187.697 10.554 180.396 25.875 12342+0947 MCXC_J1234.2+0947 188.6008 9.7876 194.608 65.368 A1569 ABELL_1569 189.1027 16.5398 136.449 21.463 A1576 ABELL_1576 189.2436 63.1868 103.88 22.109 12525-3116 MCXC_J1252.5-3116 193.1446 -31.2666 A1644 ABELL_1644 194.3015 -17.4092 21.222 1.461 A1650 ABELL_1650 194.6728 -1.762 1259334+600409 WHL_J125933.4+600409 194.8877 60.0706 327.114 56.118 125947+312215 NSC_J125947+312215 194.9665 31.352 A1664 ABELL_1664 195.9271 -24.2452 14.131 0.879 A1668 ABELL_1668 195.9442 19.2703 6.156 1.317 51 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) 1305589+263048 WHL_J130558.9+263048 196.4983 26.5157 A1682 ABELL_1682 196.708 46.5592 13110-0311 MACS_J1311.0-0311 197.7569 -3.1773 32.423 3.781 A1689 ABELL_1689 197.873 -1.3412 61.841 4.922 4001312+3900 400d_J1312+3900 198.083 39.0153 1315052+514902 WHL_J131505.2+514902 198.7682 51.8201 159.895 30.277 NGC5044 NGC_5044 198.8497 -16.3854 1.305 0.143 A1722 ABELL_1722 200.0351 70.0771 5098 NGC_5098_GROUP 200.061 33.1431 4.798 0.944 A1736 ABELL_1736 201.7204 -27.171 139.631 39.368 SSGC081 SSGC_081 202.449 -31.6069 44.512 20.29 a1750ss a1750ss 202.5397 -2.0986 34.901 69.701 A1750C ABELL_1750C 202.7107 -1.8618 159.868 10.761 A1750N ABELL_1750N 202.7956 -1.7282 93.06 22.131 213312961+1107566 2MASX_J13312961+1107566 202.8734 11.1325 4.504 1.406 SC1329-313 SC_1329-313 202.8808 -31.8245 167.33 16.567 A3562 ABELL_3562 203.4055 -31.6716 70.592 12.786 A1763 ABELL_1763 203.8333 41.0005 186.619 22.108 A1767 ABELL_1767 204.0343 59.2055 136.566 62.655 4001340+4017 400d_J1340+4017 205.1365 40.2942 A1775 ABELL_1775 205.4517 26.3709 56.894 3.877 LCDCS0829 LCDCS_0829 206.8776 -11.7524 1348502+491801 WHL_J134850.2+491801 207.2526 49.3115 4001354-0221 400d_J1354-0221 208.572 -2.3674 13546+7715 MACS_J1354.6+7715 208.6858 77.2551 1357168+623249 WHL_J135716.8+623249 209.3195 62.5472 13592-1929 MACS_J1359.2-1929 209.7926 -19.4903 19.013 3.628 A1831 ABELL_1831 209.8156 27.9753 77.354 12.848 1359495+623047 WHL_J135949.5+623047 209.9609 62.518 21.238 6.093 52 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) A1835 ABELL_1835 210.2581 2.8789 11.299 1.211 3C295 3C_295 212.835 52.2029 11382+4435 G113.82+44.35 213.4699 71.3009 A1882a A1882a 213.7785 -0.492 61.304 63.352 1416238+444528 WHL_J141623.8+444528 214.1161 44.7792 18.734 17.583 LCDCS0954 LCDCS_0954 215.118 -11.5705 21594948+2407846 GMBCG_J215.94948+24.07846 215.9495 24.0785 A1914 ABELL_1914 216.5132 37.8238 84.494 15.9 1427161+440730 WHL_J142716.1+440730 216.8172 44.1252 12.595 3.479 14276-2521 MACS_J1427.6-2521 216.9143 -25.3508 9.474 4.811 A1930 ABELL_1930 218.1582 31.6471 A1942 ABELL_1942_AND_CLUMP 219.5915 3.6702 WBL518 WBL_518 220.1649 3.471 A1991 ABELL_1991 223.6314 18.6445 145715+222009 NSCS_J145715+222009 224.3129 22.3425 12.779 1.247 AS0780 ABELL_S0780 224.8706 -18.1793 20.933 1.311 A2009 ABELL_2009 225.0816 21.3699 18.811 2.582 150117+422152 NSCS_J150117+422152 225.3442 42.3462 1504075-024816 WHL_J150407.5-024816 226.0311 -2.8045 9.077 0.494 A2034 ABELL_2034 227.556 33.5124 15149-1523 MCXC_J1514.9-1523 228.7621 -15.3895 356.147 108.545 A2061 ABELL_2061 230.2929 30.6115 224.737 24.178 MKW03s MKW_03s 230.466 7.7081 18.044 1.755 A2069 ABELL_2069 231.0356 29.8818 15242-3154 MCXC_J1524.2-3154 231.0535 -31.9064 5.444 0.428 15246+0957 WARP_J1524.6+0957 231.1614 9.9604 15328+3021 MACS_J1532.8+3021 233.2242 30.3497 13.365 0.901 A2107 ABELL_2107 234.9126 21.7827 10.155 3.138 A2111 ABELL_2111 234.9244 34.4162 189.915 27.115 53 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) A2104 ABELL_2104 235.034 -3.3038 159.142 31.845 A2125 ABELL_2125 235.3106 66.2659 171.248 17.883 A2124 ABELL_2124 236.2458 36.1091 91.073 24.555 A2142 ABELL_2142 239.5847 27.231 15583-1410 MCXC_J1558.3-1410 239.5913 -14.1658 28.469 1.712 A2147 ABELL_2147 240.5694 15.9768 163.008 18.556 A2151 ABELL_2151 241.1494 17.7215 6.426 3.102 161314+564930 SpARCS_J161314+564930 243.3121 56.8253 A2163 ABELL_2163 243.9412 -6.1491 16213+3810 MACS_J1621.3+3810 245.3537 38.1689 16235+2634 MCXC_J1623.5+2634 245.8973 26.5707 A2187 ABELL_2187 246.0585 41.24 91.556 19.021 A2204 ABELL_2204 248.1956 5.5755 7.763 0.351 A2218 ABELL_2218 248.9614 66.2101 A2219 ABELL_2219 250.0829 46.7119 258.49 19.763 4001641+4001 400d_J1641+4001 250.4731 40.0292 HerculesA Hercules_A 252.7842 4.9925 NGC6269 NGC_6269 254.4921 27.8543 1.305 1.932 021701+6412 OC02_J1701+6412 255.3482 64.2365 A2244 ABELL_2244 255.6778 34.0608 A2256 ABELL_2256 255.8096 78.649 111.092 33.408 A2249 ABELL_2249 257.4381 34.4552 A2255 ABELL_2255 258.1724 64.0728 NGC6338 NGC_6338 258.8454 57.4112 A2259 ABELL_2259 260.0317 27.6705 43072 SDSS-C4_3072 260.0416 26.6251 19.703 1.477 17202+3536 MACS_J1720.2+3536 260.0701 35.6073 12.312 2.523 A2261 ABELL_2261 260.6133 32.1328 41.818 9.759 A2294 ABELL_2294 261.0495 85.8863 54 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) 17316+2251 MCXC_J1731.6+2251 262.9159 22.8606 Abell2276 Abell_2276 263.7693 64.1017 24.173 11.035 17421+3306 ZwCl_1742.1+3306 266.0598 32.9911 174715+451155 NSC_J174715+451155 266.8113 45.1968 290.692 35.204 17502+3504 MCXC_J1750.2+3504 267.5704 35.0828 18044+1002 CIZA_J1804.4+1002 271.131 10.0571 26.268 48.513 A2302 ABELL_2302 274.9917 57.1561 190.544 77.382 18243+4309 MACS_J1824.3+4309 276.0792 43.1635 18290+6913 MACS_J1829.0+6913 277.2735 69.2353 36.357 4.091 18521+5711 MCXC_J1852.1+5711 283.0358 57.1949 18539+6822 MCXC_J1853.9+6822 283.5094 68.3827 76.431 14.615 33709-2597 PLCKESZ_G337.09-25.97 288.6564 -59.4722 78.316 8.85 A2319 ABELL_2319 290.2945 43.9516 19318-2635 MACS_J1931.8-2635 292.9569 -26.5759 20.746 1.385 AS0821 ABELL_S0821 293.7197 -50.8761 19383+5409 CIZA_J1938.3+5409 294.5768 54.1597 82.492 12.545 19473-7623 MCXC_J1947.3-7623 296.8121 -76.3958 17.503 8.752 A3653 ABELL_3653 298.2641 -52.0369 174.821 44.382 19582-3011 MCXC_J1958.2-3011 299.5623 -30.1866 20035-2323 MCXC_J2003.5-2323 300.8713 -23.3734 217.888 91.725 20113-5725 MCXC_J2011.3-5725 302.8622 -57.4199 39.441 8.622 20148-2430 MCXC_J2014.8-2430 303.7153 -24.5062 5.104 0.8 2023-5535 SPT-CL_J2023-5535 305.8388 -55.5967 186.127 83.939 20318-4037 MCXC_J2031.8-4037 307.9602 -40.6252 2034-5936 SPT-CLJ2034-5936 308.5382 -59.6052 A3695 ABELL_3695 308.6888 -35.812 307.183 36.618 2043-5035 SPT-CLJ2043-5035 310.8231 -50.5923 15.848 3.138 20460-3430 MACS_J2046.0-3430 311.5021 -34.5048 6.476 2.108 20499-3216 MCXC_J2049.9-3216 312.484 -32.2803 55 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) A3739 ABELL_3739 316.0787 -41.3446 81.936 38.149 2106-5844 SPT-CLJ2106-5844 316.5214 -58.7419 IC1365 IC_1365 318.4822 2.5652 160.833 19.732 2129-0741 MACS_J2129-0741 322.3606 -7.6908 2135-0102 MACS_J2135-0102 323.7959 -1.0484 A2355 ABELL_2355 323.8204 1.4185 393.293 86.869 2135-5726 SPT-CLJ2135-5726 323.9094 -57.441 WBL671 WBL_671 324.2849 0.4464 21402-2339 MACS_J2140.2-2339 325.0633 -23.6611 12.928 1.101 2145-5644 SPT-CLJ2145-5644 326.4669 -56.7477 2146-4633 SPT-CLJ2146-4633 326.6447 -46.5492 A3809 ABELL_3809 326.7462 -43.8987 10.277 3.844 2148-6116 SPT-CLJ2148-6116 327.1843 -61.2784 A2384 ABELL_2384 328.0888 -19.5474 25.359 2.675 A2390 ABELL_2390 328.4032 17.6954 14.26 1.929 21538+3746 ClG_2153.8+3746 328.9675 38.0068 55.189 6.284 A2409 ABELL_2409 330.2184 20.9687 A3827 ABELL_3827 330.4713 -59.9456 133.726 15.264 A2415 ABELL_2415 331.4105 -5.5925 2.83 0.781 22117-0349 MCXC_J2211.7-0349 332.9415 -3.83 96.79 15.187 3C444 3C_444 333.6066 -17.0267 0.958 1.15 A2426 ABELL_2426 333.6347 -10.3705 54.818 12.515 2214-1359 MACS_J2214-1359 333.739 -14.0038 150.198 23.601 A3854 ABELL_3854 334.441 -35.7244 103.513 18.154 22186-3853 MCXC_J2218.6-3853 334.6644 -38.9009 132.838 15.498 2218-4519 SPT-CLJ2218-4519 334.7479 -45.3158 A2445 ABELL_2445 336.7336 25.8351 69.915 11.294 A3880 ABELL_3880 336.9766 -30.577 22286+2036 MCXC_J2228.6+2036 337.1424 20.6206 56 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) 22298-2756 MACS_J2229.8-2756 337.4384 -27.9267 7.679 1.376 514-050 CGCG_514-050 337.8359 39.3581 0.932 2.217 2232-5959 SPT-CLJ2232-5959 338.1405 -59.998 2233-5339 SPT-CLJ2233-5339 338.3131 -53.6552 A2457 ABELL_2457 338.9221 1.4867 24.049 17.816 A2465 ABELL_2465 339.9125 -5.7242 22428+5301 CIZA_J2242.8+5301 340.6647 52.9958 2243198-093530 WHL_J224319.8-093530 340.8379 -9.5935 2245-6206 SPT-CLJ2245-6206 341.2621 -62.1167 22450+2637 MACS_J2245.0+2637 341.2692 26.6348 38.968 6.768 A3911 ABELL_3911 341.6117 -52.7398 338.381 36.851 A2485 ABELL_2485 342.1291 -16.1079 74.814 26.486 AS1063 ABELL_S1063 342.1835 -44.5304 78.785 19.913 A3921 ABELL_3921 342.4861 -64.4302 75.119 14.847 A2507 ABELL_2507 344.2194 5.5046 198.227 27.121 2259-6057 SPT-CLJ2259-6057 344.7541 -60.9603 23028+0843 WARP_J2302.8+0843 345.7006 8.7307 A2537 ABELL_2537 347.0929 -2.1916 78.806 12.795 23115+0338 MCXC_J2311.5+0338 347.8885 3.6353 85.303 14.556 A2550 ABELL_2550 347.8993 -21.7462 A2556 ABELL_2556 348.2556 -21.6344 12.041 1.363 AS1101 ABELL_S1101 348.4946 -42.7253 11.526 0.499 23185+0034 RCS_J2318.5+0034 349.6296 0.5674 A2597 ABELL_2597 351.3326 -12.1242 9.501 0.288 2331-5051 SPT-CL_J2331-5051 352.9632 -50.8649 A2626 ABELL_2626 354.1267 21.1468 13.528 2.257 A2627 ABELL_2627 354.1754 23.9248 2337-5942 SPT-CL_J2337-5942 354.3532 -59.7064 A2631 ABELL_2631 354.4082 0.2672 57 Table 2.4 (cont’d) Name Full ACCEPT2.0 Name RA DEC K_0 e_K0 (deg) (keV cm2 ) A4023 ABELL_4023 355.0288 -85.1974 2341-5119 SPT-CL_J2341-5119 355.302 -51.3287 A2645 ABELL_2645 355.3232 -9.0165 23442-0422 MCXC_J2344.2-0422 356.0769 -4.3816 108.571 13.251 2344-4243 SPT-CL_J2344-4243 356.1833 -42.7201 A2657 ABELL_2657 356.2389 9.1921 2345-6405 SPT-CLJ2345-6405 356.2485 -64.0963 HCG097 HCG_097 356.8459 -2.3005 A4038 ABELL_4038 356.9374 -28.1406 AS1150 ABELL_S1150 356.9555 -35.5867 A2665 ABELL_2665 357.7108 6.1503 A2667 ABELL_2667 357.9141 -26.0837 19.098 2.169 A2670 ABELL_2670 358.5571 -10.4192 30.012 4.629 2355-5056 SPT-CL_J2355-5056 358.9477 -50.9281 2359-5009 SPT-CL_J2359-5009 359.9283 -50.1688 58 CHAPTER 3 LUMINOSITY-TEMPERATURE RELATION OF ACCEPT2.0 CLUSTERS We characterize galaxy clusters through observations of the X-ray spectra of the intracluster medium (ICM). Observed correlations between X-ray observables like temperature 𝑇 and luminosity 𝐿 𝑋 (Mitchell et al., 1976; Cavaliere et al., 1997; Pratt et al., 2009; Maughan et al., 2012; Migkas et al., 2020) are known as scaling relations for clusters of galaxies. Such relations are effective tools for understanding large scale structure and its evolution. Simple models of the ICM lead to predictions for how cluster mass 𝑀 relates to 𝑇 and 𝐿 𝑋 and therefore, how 𝑇 and 𝐿 𝑋 should relate to each other. Observations connecting the cluster observable properties (such as 𝐿 𝑋 and 𝑇) to properties of clusters well-constrained by theory (such as cluster mass 𝑀) allow us to constrain our cosmological models and improve our understanding of how overdensities in the early Universe have grown and evolved over time (full review by Voit, 2005). We make predictions for cluster temperatures and luminosities by assuming the ICM is a self- gravitating sphere. The virial theorem states that the kinetic energy (𝐸 𝐾 ) is related to gravitational potential energy (𝐸 𝐺 ) by 𝐸 𝐾 = |𝐸 𝐺 /2|. The virial radius, 𝑅𝑣 , for a cluster at some redshift 𝑧 is the radius inside which the virial theorem for bound galaxies or particles is satisfied. In a simulation, 𝑅𝑣 can be estimated based on this condition because the simulator can know the exact positions and velocities of all the galaxies in their simulation. In the real Universe, 𝑅𝑣 is based on calibration by simulations. These simulations indicate that 𝑅𝑣 is the radius at which the average interior density is ∼200 times the critical density (𝜌𝑐 (𝑧)) at the redshift in question. Recall from from Section 1.2.1 that 𝜌𝑐 (𝑧) is the maximum average density and is defined as, 𝜌𝑐 (𝑧) = 𝐸 (𝑧) 2 𝜌𝑐,0 , (3.1) where 𝜌𝑐,0 = 𝜌𝑐 (𝑧 = 0) = 3𝐻02 /8𝜋𝐺 is the present day critical density, 𝐻 (𝑧) = 𝐻0 𝐸 (𝑧), with p 𝐻0 = 70 km s−1 Mpc−1 and 𝐸 (𝑧) = Ω 𝑀 (1 + 𝑧) 3 + ΩΛ where Ω 𝑀 = 0.3 and ΩΛ = 0.7 account for the matter and dark energy content of the Universe. 59 The virial radius is large and outside of the typical X-ray telescope’s instrumental field of view for most nearby systems, so we often characterize cluster properties for some radius 𝑅Δ within which the density is Δ times the critical density 𝜌𝑐 (𝑧). For a cluster with mass 𝑀Δ at scaled radius 𝑅Δ , 𝑀Δ ∝ 𝐸 (𝑧) 2 𝑅Δ 3. (3.2) The virial theorem assumes that the ICM temperature is due to heating from the gas as it falls into the gravitational potential, leading to the expected relation, 2/3 𝑇 ∝ [𝐸 (𝑧)𝑀Δ ], (3.3) where 𝑇 is isothermal throughout the cluster. The scaling of temperature and mass of a cluster through its luminosity is less straightforward, as it requires an assumption of the density structure and knowledge of radiative processes of the gas including bremsstrahlung (or free-free) emission, and collisionally-excited emission lines from iron K- and L- shell transitions, and transitions from other elements. At typical cluster temperatures, radiation emitted by the gas is dominated by bremsstrahlung emission wherein electrons are deflected by the Coulomb field of an ion. We are able to express the radiation from all processes in terms of a cooling function Λ(𝑇, 𝑍). The cooling function is integrated over all emission processes and then weighted by the energy of emitted photons (Peterson & Fabian, 2006). Recalling from section 1.3 that 𝐿 𝑋 ∝ 𝑛2𝑒 𝑟 3 Λ(𝑇) for an isothermal gas, and for thermal bremsstrahlung emission, Λ(𝑇) ∝ 𝑇 1/2 . When these relations are combined with Equations 3.2 and 3.3, it leads to the expectation that 𝐿 𝑋 ∝ 𝑇 2 . However, observations have shown steeper slopes and increased scatter among the lower temperature clusters and groups (Cavaliere et al., 1997; Arnaud & Evrard, 1999; Pratt et al., 2009; Maughan et al., 2012). The existence of a reliable 𝐿 𝑋 − 𝑇 relation for clusters of galaxies could, in principle, allow for their use as standard candles. However, they are not generally considered as “good” standard candles because the extended emission is by nature difficult to measure in an exact manner. Additionally, 60 their luminosities–particularly in the core–are affected by local astrophysics, adding scatter to the 𝐿 𝑋 −𝑇 relation. Although clusters are not great standard candles in practice, large sample sizes might lead to interesting tests of cosmology. For example, cosmology generally assumes homogeneous isotropic expansion. A test of this assumption was conducted recently by Migkas et al. (2020) (hereafter, M20), who used a sample of 313 clusters to investigate the 𝐿 𝑋 − 𝑇 relation towards different directions on the sky. Intriguingly, they found a significant difference in normalization factor when observing the 𝐿 𝑋 − 𝑇 relation from different regions of the sky. They found that clusters within a 60◦ radius of galactic coordinates (𝑙, 𝑏) ∼ (281◦ , −16◦ ) are systematically fainter than those towards (𝑙, 𝑏) ∼ (34◦ , +4◦ ) by up to a factor of 36%. They suggest that their results may be due to inconsistencies in the Hubble constant 𝐻0 , and thus caused by anisotropic expansion. We performed a followup analysis for 302 clusters from the second catalog of the Archive of Chandra Cluster Entropy Profile Tables (Donahue, Baldi, et al, in prep, hereafter, ACCEPT2.0) and do not find the same difference in normalizations. We surmise that the discrepancies between ours and the results of M20 can be attributed to differences in the X-ray cluster luminosity measurements (ACCEPT2.0 luminosities are based on a broader X-ray energy bandpass and exclude the cluster cores) and possibly underestimates of the systematics related to Galactic absorption, since the direction of the discrepancies are relatively close to the Galactic plane. The outline of this chapter is as follows: Section 3.1 describes the cluster sample from AC- CEPT2.0. Section 3.2 gives the 𝐿 𝑋 − 𝑇 model and fitting procedure, followed by the results in Section 3.3. We compare our results to M20 in Section 3.4 and discuss reasons for the discrepancy between results, and summarize our analysis in Section 3.5. We assume a ΛCDM cosmology throughout the paper with 𝐻0 =70 km s−1 Mpc−1 , Ω𝑚 =0.3, and ΩΛ =0.7. 3.1 The Sample The 𝐿 𝑋 − 𝑇 relation becomes more scattered with decreasing temperature (or equivalently, mass) (Maughan et al., 2012). For a sample with selection based on luminosity, an 𝐿 𝑋 − 𝑇 relation with higher scatter will be more affected by luminosity selection bias than a sample with low scatter in 𝐿 𝑋 − 𝑇. We aim to limit the effects of this selection bias by restricting the luminosities to a 61 range similar to M20. We selected a subsample of 302 clusters with global bolometric luminosity 𝐿 𝑋 >4×1043 erg s−1 (although for analysis, we used luminosities measured in the bandpass [0.5-8] keV. M20 used ROSAT luminosities in the energy range [0.1-2.5] keV). Scatter in the relation also arises from the differences between cool core (CC) and non-cool core (NCC) clusters. CCs have profiles with steep drops in temperature towards the center, whereas NCCs have comparatively flat temperature profiles and a less centrally concentrated density structure. The CC clusters can be classified most straight forwardly by using the central entropy 𝐾0 = 𝑘𝑇 𝑛−2/3 keV cm2 . Here, we follow the classification of Cavagnolo et al. (2009) and ACCEPT2.01, which defines 𝐾0 ' 30 keV cm2 as the threshold below which a cluster is considered a CC. There are 67 CCs (∼22%) and 135 (∼44%) NCCs in our sample, where the remaining 106 (∼34%) clusters are undetermined. The difference in temperature and density profiles for CC and NCC clusters can increase the scatter in the 𝐿 𝑋 − 𝑇 relation, the angular resolution of 𝐶ℎ𝑎𝑛𝑑𝑟𝑎 allows us to obtain global temperature and luminosity estimates for a core-excised aperture of [0.3-1]𝑅2500 . M20 however, used luminosities for the full aperture inside of 𝑅500 , because the angular resolution of ROSAT does not allow core-excised measurements. There are 46 and 41 ACCEPT2.0 clusters in the 60◦ radius surrounding the regions (𝑙, 𝑏) ∼ (281◦ , −16◦ ) and (𝑙, 𝑏) ∼ (34◦ , +4◦ ), respectively. Migkas et al. (2020) found that clusters towards (281◦ , −16◦ ) were fainter, while those of the comparison region tended to be brighter. Therefore, the samples in these two regions will be designated as RF and RB, and the sample of clusters lying outside either sky region will be called NR. The full sample covers a redshift range of 𝑧 ∼ [0.02 − 0.9]. The RF clusters cover a redshift range of 𝑧 ∼ [0.05 − 0.75], and RB clusters cover the range 𝑧 ∼ [0.04 − 0.47]. M20 uses a sample of local clusters with redshifts 𝑧 . 0.42. 1𝐾 0 estimates are from ACCEPT2.0 (Frisbie, MSU dissertation, October 2020) 2 We find no difference in our results when restricting our redshift range to be 𝑧 . 0.4, so for this work, we report the results of an analysis for the largest, unrestricted redshift sample. 62 90◦ 30◦ 120◦ 60◦ 0◦ 330◦ 270◦ 210◦ -30◦ Galactic -90◦ Figure 3.1: ACCEPT2.0 all-sky map. Distribution of ACCEPT2.0 clusters colored according to region or core status. Red pentagons are NCC clusters and blue triangles are CC clusters, while clusters with no core status are red or blue crosses. Clusters that do not belong to a region subset are plotted in green. Red crosses are part of the region centered on galactic coordinates (𝑙, 𝑏) ∼ (281◦ , −16◦ ) (RF), blue crosses are inside the region centered on (𝑙, 𝑏) ∼ (34◦ , +4◦ )(RB). Clusters within 10◦ of the galactic latitude 𝑏 = 0◦ were excluded from all subsamples. 3.2 Methods Starting with a standard power-law, 𝐿 𝑋 𝐸 (𝑧) −1 𝑘𝑇 𝛽   = 𝐿 𝑋,0 , (3.4) 1044 erg s−1 6 keV we scale the power-law relation to the following linear model–including intrinsic scatter 𝜎int – to be used an estimate for the underlying 𝐿 𝑋 − 𝑇 relation, 𝑙 = 𝑙0 + 𝛽𝑡, (3.5) 𝐿 𝐸 (𝑧) −1 p where 𝑙 ≡ ln 44 𝑋 , 𝐸 (𝑧) = Ω𝑚 (1 + 𝑧) 3 + ΩΛ accounts for the redshift evolution of the 10 erg s−1 relation, 𝑙0 ≡ ln𝐿 𝑋,0 is the normalization constant, and 𝑡 ≡ ln 6 𝑘𝑇 keV . We implemented an MCMC 63 algorithm to obtain independent normalization, slope, and intrinsic scatter estimates for each sample using a likelihood function that assumes the data and errors are Gaussian. " # 1 ¯2 (𝑙𝑖 − 𝑙) 2 + 𝜎 2 )) lnℒ = − Σ𝑖 + ln(2𝜋(𝜎int (3.6) 2 2 2 𝜎int + 𝜎𝑙,𝑖 𝑙,𝑖 We use flat priors, where each parameter was allowed to vary over a generous range of values. M20 found that the normalization is the biggest contributor to the difference of the 𝐿 𝑋 − 𝑇 relation towards different regions of the sky. They used a model similar to Equation 3.2 and fixed the slope to the value obtained from the full sample. We therefore performed a second fit of our data assuming that the slope (𝛽) and intrinsic scatter (𝜎int ) for all three samples are the same. However, instead of fixing these parameters in the analyses, we performed the regression over the three subsamples simultaneously and allowed only the normalization to vary between them. We chose a log-likelihood (Equation 3.6) which tied the three subsamples because, while M20 was able to show that fixing the slope did not significantly affect their results, that method does not take into account the uncertainty of the slope for the full sample. We fit the five parameters, NR 𝑙0 , RB 𝑙0 , RF 𝑙0 , 𝛽, and 𝜎int using the following log-likelihood: ! ( NR 𝑙𝑖 − ( NR 𝑙0 +NR 𝑡𝑖 𝛽)) 2 lnL = − 1 2 [ Õ ln( NR 𝜎𝑖2 + 𝜎int 2 )+ NR 𝜎 2 2 + 𝜎int 𝑖 𝑖 RF RF RB 𝑡 𝛽)) 2 RF 𝜎 2 + 𝜎 2 ) + ( 𝑙 𝑗 − ( 𝑙 0 + Õ© 𝑗 + ln( ª ­ 𝑗 int RF 𝜎 2 + 𝜎 2 ® 𝑗 « 𝑗 int ¬ ! ( RB 𝑙 ( RB 𝑙 +RB 𝛽)) 2 + Õ ln( RB 𝜎𝑘2 + 𝜎int2 )+ 𝑘 − RB 𝜎 2 0 2 + 𝜎int 𝑡𝑘 ] (3.7) 𝑘 𝑘 3.3 Results The posterior distributions for the parameters are shown in Figure 3.2 for individually fit regions, and Figure 3.3 for the tied model. 64 LX,0 = 2.35+0.17 −0.16 LX,0 = 2.34+0.19 −0.17 RF Clusters RB Clusters β = 2.56+0.23 −0.22 β = 2.65+0.24 −0.23 2 3. 2 3. 8 2. 8 β β 2. 4 2. 4 2. σint = 0.36+0.06 σint = 0.39+0.06 0 2. 0 −0.05 2. −0.05 6 0. 5 60 0. σint σint 0. 4 0. 45 0. 3 0. 30 0. 1. 8 1 2. 4 2. 7 2. 0 3. 0 2. 4 2. 2. 8 2 3. 3 0. 4 0. 5 0. 6 0. 1. 6 0 2. 4 2. 2.8 3. 2 0 2. 4 2. 8 2. 2 3. 30 45 60 0. 0. 0. LX,0 β σint LX,0 β σint LX,0 = 2.51+0.07 −0.07 NR Clusters β = 2.60+0.09 −0.08 2 2 2 40 . 55 . 70 . 85 β 2. σint = 0.32+0.02 −0.02 0 0 0 0 24 .28 .32 .36 .40 σint 0. 25 40 55 70 40 55 70 85 24 28 32 36 40 2. 2. 2. 2. 2. 2. 2. 2. 0. 0. 0. 0. 0. LX,0 β σint Figure 3.2: Posterior 𝑳 𝑿 − 𝑻 distributions for RF, RB, and NR clusters. The posterior probability distributions for the variables of the 𝐿 𝑋 − 𝑇 relation for RF (top left), RB (top right), and NR (bottom) clusters. The 1-, 2-, and 3𝜎 contour levels correspond to 39th, 86th, and 99th percentiles. 65 NR LX,0 = 2.52+0.08 −0.07 RF LX,0 = 2.34+0.16 −0.15 LX,0 RF 3. 1. 2. 2. 2. 3. RB LX,0 = 2.33+0.16 2 8 1 4 7 0 −0.15 LX,0 2. 8 4 RB 2. β = 2.59+0.08 2. 0 −0.08 0 2 2 2 2 2 40 .44 .25 .40 .55 .70 .85 β σint = 0.34+0.02 −0.02 0. σint 0. 36 32 0. 28 0. 2. 2. 2. 25 40 55 0 4 8 3 2. . 2 2. 2. 25 40 55 2. 2. 1. 2. 2. 2. 3. 70 85 8 1 4 7 2. 2. 2. 2. 2. 0. 0. 0. 0. 0. 70 85 28 32 36 40 0 44 NR LX,0 RF LX,0 RB LX,0 β σint Figure 3.3: Posterior distributions for the tied 𝑳 𝑿 − 𝑻 model. The posterior probability distributions for the variables of the multi-parameter 𝐿 𝑋 − 𝑇 fit. The contour levels are the same as in 3.2. 66 Results for the model parameters according to region are shown in table 3.1, with the errors reported as the 16th and 84th percentiles (i.e., 68% confidence intervals) of the output parameter chains. The upper panel shows parameter output using tied log-likelihood (Equation 3.7) for simultaneous fitting and the lower panel shows the results for the separate fits (Equation 3.6. The left panel of Figure 3.7 contains the over-plotted simultaneous fits, and the right panel shows the individual model fits, with the shaded regions representing the 1𝜎 uncertainty for the model. The differences between normalizations 𝐿 𝑋,0 are R1 R2 Δ𝐿 𝑋,0 ≡R1 𝐿 𝑋,0 −R2 𝐿 𝑋,0 , where the error on this value comes from adding in quadrature the uncertainties on 𝐿 𝑋,0 . Our best fit parameters show no significant difference between using the tied or separate fitting models for any one subsample. Tied model values for slope (𝛽 = 2.514 ± 0.076) and intrinsic scatter (𝜎int = 0.322+0.020 −0.019 ) were consistent with those of the individual fits, with the faint region RF having the smallest individually fit slope of 𝑅𝐹 𝛽 = 2.332+0.226 −0.223 . Upon comparison of results from the tied and untied models, we find no statistical difference in 𝛽 or 𝜎int between subsamples, which is consistent with Migkas et al. (2020). There was no statistical difference in 𝐿 𝑋,0 between RB and RF, with 𝑅𝐵 𝑅𝐹 Δ𝐿 𝑋,0 = −0.018±0.218 for the tied model, and 𝑅𝐵𝑅𝐹 Δ𝐿 𝑋,0 = −0.019 ± 0.238 for the separate model. For both the tied and separate fitting mechanisms, Δ𝐿 𝑋,0 was smaller between RB and RF than between NR and either RB or RF. For the simultaneous fits, 𝑁 𝑅 𝑁𝑅 𝑅𝐵 Δ𝐿 𝑋,0 = 0.269 ± 0.173 and 𝑅𝐹 Δ𝐿 𝑋,0 = 0.251 ± 0.170. For the individual fits, 𝑁 𝑅 𝑁𝑅 𝑅𝐵 Δ𝐿 𝑋,0 = 0.267 ± 0.190, and , 𝑅𝐹 Δ𝐿 𝑋,0 = 0.248 ± 0.176. 3.4 Discussion None of the differences in 𝐿 𝑋,0 between the regions are statistically significant, which is contrary to the result of M20. In fact, ACCEPT2.0 clusters towards the extreme bright region RB described by M20 appear marginally 𝑓 𝑎𝑖𝑛𝑡𝑒𝑟 (RB RF Δ𝐿 𝑋,0 = −0.017 ± 0.220 for the tied model and RB Δ𝐿 = −0.009 ± 0.238 for the separate model) than those towards the extreme faint region RF. RF 𝑋,0 The low significance in Δ𝐿 𝑋,0 across all three samples can be attributed to systematic differences in the data between ROSAT and Chandra. Possible reasons for the discrepancy between ours and M20’s results are described below. 67 Table 3.1: Best fit 𝑳 𝑿 −𝑻 using tied and separate models. Output parameters for the fit to Equation 3.2. The upper half refers to parameters fit using the tied log-likelihood model (Equation 3.7). Parameters in the bottom half were computed for each subsample using separate log-likelihoods (3.6). Model Subsample 𝐿 𝑋,0 𝛽 𝜎int NR 2.446+0.077 −0.074 Tied RB 2.177+0.162 −0.150 2.514+0.076 0.322+0.020 −0.076 −0.019 model RF 2.195+0.157 −0.148 NR 2.446+0.077 −0.074 2.517+0.085 −0.084 0.302+0.024 −0.023 Separate RB 2.174+0.185 +0.239 2.421−0.227 0.338+0.061 −0.166 −0.052 models RF 2.194+0.165 −0.156 2.332+0.226 −0.223 0.309+0.056 −0.048 3.4.1 Core-excised vs. core included 𝐿 𝑋 Both samples for this analysis use core-excised (CE) measurements within the region [0.3-1] 𝑅2500 . However, M20 uses luminosities from ROSAT because its large field of view allows for global parameters for apertures within 𝑅500 . Unfortunately, ROSAT’s low spatial resolution means their luminosity measurements are not (and cannot be) core-excised. Core excision is important because cores of “cool-core” (CC) clusters have higher gas densities than the cores of non-cool core clusters (NCC), and therefore radiate more efficiently which results in higher SNR data. Unfortunately, measurements including core emission are subject to a bias in the luminosity because of the brighter central regions of CCs compared to those of NCCs. Core contribution to 𝐿 𝑋 −𝑇, regardless of core status, is illustrated in section 2.4.3, where we fit the model using luminosity measurements from both the CE aperture and the CI (core-included) aperture. Similarly, we demonstrate how cores of 68 Table 3.2: Difference in normalization of 𝑳 𝑿 − 𝑻. Differences in normalization 𝐿 𝑋,0 between clusters towards different parts of the sky. Top half shows differences between normalization subsamples evaluated independently and the lower half shows the differences from the tied model with an extra column containing the results reported by Migkas et al. (2020) (M20) for comparison. M20 fit for each sample separately using the same fixed slope (𝛽 = 2.102 ± 0.064) obtained from the full sample and allowing only the normalization to vary. Model Subsample Δ𝐿 𝑋,0 Migkas et al. (2020)Δ𝐿 𝑋,0 [1044 ergs−1 ] [1044 ergs−1 ] (RB-RF) −0.018 ± 0.218 Tied (NR-RB) 0.269 ± 0.173 (NR-RF) 0.251 ± 0.170 (RB-RF) −0.019 ± 0.238 0.406±0.086 Separate (NR-RB) 0.267 ± 0.190 0.198±0.070 (NR-RF) 0.248 ± 0.176 0.208±0.084 CCs affect the 𝐿 𝑋 − 𝑇 relation by fitting the model as described in Section 3.2 to 135 NCC and 67 CC clusters using both CE and CI luminosities. We found that with CE luminosities, there is a slight difference in the relation between CC and NCC clusters, with normalizations of 𝐿 𝐶𝐶 +0.154 = 2.777−0.145 𝑋,0 for the CC sample and 𝐿 𝑁𝐶𝐶 𝑋,0 = 2.251+0.093 −0.089 for the NCC sample. These parameters correspond to a difference of 𝐶𝐶 𝑁𝐶𝐶 Δ𝐿 𝑋,0 = 0.526 ± 0.175. When using the CI luminosities, the normalization parameters are 𝐿 𝐶𝐶𝑋,0 = 7.587+0.592 −0.541 for the CC sample and 𝐿 𝑁𝐶𝐶𝑋 = 3.642+0.159 −0.151 for the NCC sample, with a nearly 7𝜎 difference of 𝐶𝐶 𝑁𝐶𝐶 Δ𝐿 𝑋,0 = 3.945 ± 0.587. Presumably, excess luminosity in CCs would not affect the results as much if both regions had equal distributions of CC and NCC clusters. This perfect mixing of CCs and NCCs is not the case for our samples, which can be seen in Figure 3.1. Out of 46 RF clusters, 29 have 𝐾0 estimates–5 CCs and 24 NCCs. For the 41 clusters in RB, 25 have 𝐾0 measurements and are more evenly split 69 NR clusters LX E(z)−1 [erg s−1] 1045 1044 +0.076 tied β = 2.514−0.076 +0.085 β = 2.517−0.084 3 4 5 6 7 8 9 10 15 kT CE (keV) Figure 3.4: Best fit 𝑳 𝑿 −𝑻 for NR clusters. Best fit models for the luminosity-temperature for 215 +0.077 NR clusters. The best fit parameters of normalization and intrinsic scatter are 𝐿 𝑋,0 = 2.446−0.074 +0.020 for the tied model, and 𝐿 and 𝜎int = 0.322−0.019 +0.074 +0.024 𝑋,0 = 2.442−0.072 and 𝜎int = 0.302−0.023 for the separate model. Filled circles represent clusters used for the fit. Gray crosses are the clusters which were left out of the fit to NR because they belong to either RB or RF. with 13 CCs and 12 NCCs. RF has a lower fraction of clusters with bright cores, which could bias the normalization parameter of the 𝐿 𝑋 − 𝑇 relation low for that region. Because the luminosities used in M20 are for the full 𝑟 . 𝑅500 aperture, a random excess or paucity of CCs in one region of the sky could affect 𝐿 𝑋,0 , particularly for core included luminosity estimates. 3.4.2 Different spectral energy bandpasses Contributions from different radiation processes affect X-ray emissivity over different bandpasses. Therefore, the spectral energy range over which luminosity is measured can affect the observed 𝐿 𝑋 −𝑇 relation. For instance, ROSAT is sensitive to soft X-rays in the bandpass [0.1-2.5] keV. Within 70 RB clusters LX E(z)−1 [erg s−1] 1045 1044 +0.076 tied β = 2.514−0.076 +0.239 β = 2.421−0.227 3 4 5 6 7 8 9 10 15 kT CE (keV) Figure 3.5: Best fit 𝑳 𝑿 − 𝑻 for RB clusters. Same plot as Figure 3.4 but for 41 RB clusters in the region surrounding RB = (𝑙, 𝑏) ∼ (34◦ , +4◦ ). The best fit parameters of normalization and intrinsic scatter are 𝐿 𝑋,0 = 2.177+0.162 −0.150 and 𝜎int = 0.322+0.020 −0.019 +0.185 for the tied model, and 𝐿 𝑋,0 = 2.174−0.166 and 𝜎int = 0.338+0.061 −0.052 for the separate model. this bandpass, the spectrum is less sensitive to the exponential cutoff at 𝐸 ∼ 𝑘𝑇, characteristic of radiation from thermal bremsstrahlung, and the soft X-ray luminosity is less dependent on temperature. The 𝐿 𝑋 −𝑇 relation will therefore be shallower for a bandpass-limited 𝐿 𝑋 , particularly when confined to the lower energy range [0.1-2] keV. This effect can be seen in Figure 3.8 which shows the best fit tied model for ACCEPT2.0 NR clusters using bolometric luminosities versus their values measured in the energy range [0.5-8] keV. The slope of the 𝐿 𝑋 − 𝑇 relation using bandpass luminosities is 𝛽 = 2.514+0.076 −0.76 and 𝛽 = 2.740+0.076 −0.077 for bolometric luminosities. For comparison, the slope of the relation for the full sample in M20 is 𝛽 = 2.102 ± 0.064 using bandpass luminosities in the energy range [0.1-2.5] keV. 71 RF clusters LX E(z)−1 [erg s−1] 1045 1044 +0.076 tied β = 2.514−0.076 +0.226 β = 2.332−0.223 3 4 5 6 7 8 9 10 15 kT CE (keV) Figure 3.6: Best fit 𝑳 𝑿 − 𝑻 for RF clusters. Same plot as Figures 3.4 and 3.5 but for 46 RF clusters in the region surrounding RF = (𝑙, 𝑏) ∼ (281◦ , −16◦ ). The best fit parameters of normalization and intrinsic scatter are 𝐿 𝑋,0 = 2.195+0.157 −0.148 and 𝜎int = 0.322+0.020 −0.019 for the tied +0.165 +0.056 model, and 𝐿 𝑋,0 = 2.194−0.156 and 𝜎int = 0.309−0.048 for the separate model. More importantly, below energies of 𝑘𝑇 ∼2 keV, X-ray observables are more subject to system- atics from Galactic absorption 𝑁 𝐻 . To correct for the total absorption due to neutral hydrogen and related metals, each cluster in ACCEPT2.0 was assigned a single line-of-sight absorption value for neutral hydrogen 𝑁 𝐻𝐼 given by Stark et al. (1992), whereas M20 reversed the 𝑁 𝐻𝐼 correction from the parent catalogs and applied a new correction to their 𝐿 𝑋 values based on total 𝑁 𝐻 (which includes atomic and molecular hydrogen) provided by Willingale et al. (2013). That correction is not the likely source of the differences, but the correction for Galactic absorption is important for estimating intrinsic X-ray luminosity, and higher gas column densities require larger corrections. However, X-ray column densities arise from absorption due to metals along the line of sight. Such 72 Tied model Separate models LX E(z)−1 [erg s−1] 1045 1044 NR clusters RB clusters RF clusters 3 4 5 6 7 8 9 10 15 3 4 5 6 7 8 9 10 15 CE kT (keV) Figure 3.7: Stacked tied and separate 𝑳 𝑿 − 𝑻 for NR, RF, and RB clusters. Best fit models for the luminosity-temperature for the tied parameter model (left) and independent models (right). +0.076 [0.5-8keV]LX ,β = 2.514−0.076 +0.076 LX E(z)−1 [erg s−1] [bol]LX ,β = 2.740−0.077 1045 1044 [0.5-8keV]LX [bol]LX 3 4 5 6 7 8 9 10 15 kT CE (keV) Figure 3.8: 𝑳 𝑿 − 𝑻 for bandpass vs. bolometric luminosities. Best fit models for NR clusters using bolometric and bandpass luminosities. Luminosity is less dependent on temperature for low energy ranges, which results in a weaker relation when using [0.5-8] keV luminosities. 73 metals are related to hydrogen, rather than being hydrogen itself. Therefore, the absorption cor- rection based on a neutral hydrogen column might not account for all the material along the line of sight with a scaling between neutral and X-ray absorbing materials, especially for objects near the Galactic plane. If the difference reported by M20 is real, the result should not change with a different bandpass or 𝑁 𝐻 treatment. The result in M20 was surprising because a statistical difference in the normalization of the 𝐿 𝑋 − 𝑇 relation would suggest that, when correcting for redshift, different regions of the sky are subject to different cosmologies. If clusters in RF are truly fainter, it would suggest that their redshift-corrected, or comoving distance 𝐷 𝐶 is larger towards that region, which would be a consequence of greater 𝐻0 . Luminosity 𝐿 𝑋 of an object with flux 𝑆 𝑋 at redshift 𝑧 is, 𝐿 𝑋 = 𝑆 𝑋 [(1 + 𝑧)𝐷 𝐶 ] 2 . (3.8) 𝐷 𝐶 is the comoving distance and relates to the Hubble constant 𝐻0 via, ∫ 𝑐 𝑑𝑧 𝐷𝐶 = , (3.9) 𝐻0 𝐸 (𝑧) p where 𝐸 (𝑧) = (1 + 𝑧) 3 Ω 𝑀 + ΩΛ . A true difference in luminosity would suggest that 𝐻0 differs depending on where one looks on the sky and that the Universe is not expanding uniformly in all directions. M20’s conclusion is also surprising because the 𝐿 𝑋 − 𝑇 relation is (as far as we know) the only standard candle to show anisotropic expansion. For instance, distance estimates can be extrapolated from observations of objects with known absolute magnitude. For instance, if the value of 𝐻0 were truly anisotropic, we would expect to see differences in type Ia supernovae (SNe Ia), which have well-defined peak magnitudes and predictable light curves (Colgate, 1979). At the highest redshifts, the Cosmic Microwave Background (CMB) should show large-scale temperature anisotropy that correlates with observed small fluctuations, but various tests have not yielded statistically significant results (Bennett et al., 2011). Instead, it is more likely that the result in M20 can be attributed to differences in systematics rather than differences in cosmology. 74 3.5 Conclusion We used global core-excised temperatures and luminosities for 302 ACCEPT2.0 clusters to investigate differences in the 𝐿 𝑋 − 𝑇 relation towards different regions of the sky based on the results reported by Migkas et al. (2020) (M20). They found that 78 clusters within a 60 degree cone towards galactic coordinates (34◦ , +4◦ ), or bright region (RB), were up to 36% brighter than 84 clusters belonging to a faint region (RF) towards (281◦ , −16◦ ). M20 fit their data to a linear model similar to that of Equation 3.2 and found that the difference in normalization parameter (𝐿 𝑋,0 ) between clusters in the bright and faint regions is RB RF Δ𝐿 0 = 0.406 ± 0.086, a significance of nearly 5𝜎. This difference is contrary to our findings which resulted from models where clusters in each region were fit simultaneously ( 𝑅𝐵 𝑅𝐵 𝑅𝐹 Δ𝐿 𝑋,0 = −0.018 ± 0.218) and separately ( 𝑅𝐹 Δ𝐿 𝑋,0 = -0.019 ± 0.238). The implication of an 𝐿 𝑋 − 𝑇 relation that changes depending on sky location is that expansion of the Universe is not the same in all directions, and it would require us to learn a new cosmological model and give different treatments of cluster samples depending on their distance and where they are on the sky. We performed a similar analysis for 302 ACCEPT2.0 clusters divided into 46 clusters towards the RF direction, 41 towards the RB direction, and 215 remaining clusters covering the rest of the sky (NR). We performed the fit for two different model assumptions: a separate model for which all the parameters are independent of sky location, and a tied model where each subset is fit simultaneously and only the normalizations are allowed to vary between the subsamples. We found no statistical difference in the 𝐿 𝑋 − 𝑇 relation in different directions on the sky for either model, suggesting that the more likely explanation for results found by M20 are due to systematic effects. 75 Table 3.3: Global CE 𝑳 𝑿 − 𝑻 properties for clusters separated by sky region. Full list of 302 ACCEPT2.0 global core-excised X-ray properties (in order of increasing RA) and their region ID on the sky, where RB refers to the region (𝑙, 𝑏) ∼ (34◦ , +4◦ ), RF refers to the region (𝑙, 𝑏) ∼ (281◦ , −16◦ ), and NR clusters belong to neither region. The columns are as follows: col(1) is ACCEPT2.0 name, col(2) is the cluster region ID, col(3) is redshift, cols(4,5) and cols(6,7) are the [0.5-8 keV] energy bandpass and bolometric luminosities in units of 1044 erg s−1 , cols(8,9) is the temperature and error in keV, cols(10,11) is the metallicity in solar units 𝑍 , col(12) is the reduced chi-square value obtained from the X-ray spectral fit. The full version of this table can be found at the end of chapter 2. Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f 000619+105206 NR 0.167 1.850 0.072 2.636 0.102 5.184 0.399 0.350 0.092 1.073 00088+5215 NR 0.104 0.751 0.030 1.052 0.043 4.711 0.300 0.164 0.087 1.264 00117-1523 NR 0.378 6.014 0.194 8.839 0.285 5.892 0.399 0.271 0.066 1.132 A0013 NR 0.094 0.641 0.016 0.899 0.023 5.032 0.635 0.209 0.124 1.048 A2744 NR 0.308 13.170 0.165 23.686 0.296 10.245 0.770 0.299 0.102 1.234 0014-4952 RF 0.752 5.112 0.336 7.853 0.517 6.880 0.966 0.406 0.162 1.096 Cl0016+16 NR 0.541 16.147 0.355 28.163 0.619 9.727 0.745 0.198 0.063 0.964 00254-1222 NR 0.584 8.852 0.347 14.205 0.557 7.817 0.597 0.256 0.060 1.134 00278+2616 NR 0.367 3.049 0.194 4.615 0.294 6.438 0.978 0.039 0.082 1.086 30484-4142 RF 0.410 7.488 0.269 13.102 0.470 9.797 1.232 0.150 0.096 1.170 00354-2015 NR 0.364 10.772 0.355 16.792 0.554 7.187 0.645 0.338 0.090 1.146 A0068 NR 0.255 5.993 0.281 10.429 0.489 9.717 1.436 0.662 0.210 1.270 A0085 NR 0.055 2.609 0.019 3.925 0.028 6.170 0.588 0.358 0.150 2.290 A2813 NR 0.292 7.287 0.223 11.762 0.361 7.950 0.739 0.287 0.086 1.303 00408+2404 NR 0.083 0.823 0.028 1.129 0.038 3.826 0.623 0.291 0.102 1.280 A0119 NR 0.044 1.115 0.013 1.628 0.019 5.916 0.591 0.290 0.131 3.338 A0141 NR 0.230 3.050 0.122 4.635 0.186 6.576 0.772 0.184 0.120 1.383 01077+5408 NR 0.107 3.881 0.057 6.191 0.092 6.642 1.385 0.184 0.136 1.257 A2895 NR 0.227 4.742 0.143 7.809 0.236 8.394 0.858 0.301 0.107 1.471 A0193 NR 0.049 0.398 0.011 0.536 0.015 3.725 0.483 0.307 0.115 1.191 A0209 NR 0.206 6.310 0.161 10.466 0.266 8.547 0.665 0.250 0.082 1.313 76 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f Abell222 NR 0.211 1.664 0.067 2.287 0.092 4.137 0.274 0.216 0.070 1.032 Abell223 NR 0.207 1.370 0.062 1.981 0.089 5.470 0.500 0.247 0.100 1.152 01400-0555 NR 0.454 7.056 0.392 10.985 0.610 7.139 0.822 0.256 0.103 1.149 01420+2131 NR 0.280 5.460 0.165 8.543 0.258 7.218 0.649 0.118 0.090 1.265 01525-2853 NR 0.341 4.091 0.126 6.018 0.186 5.815 0.584 0.058 0.081 1.125 A0267 NR 0.231 4.166 0.105 6.600 0.166 7.570 0.630 0.393 0.106 1.224 02209-3829 RF 0.229 2.352 0.136 3.225 0.187 4.346 0.368 0.546 0.140 1.230 A3017 RF 0.220 3.931 0.175 6.124 0.272 7.115 0.939 0.111 0.106 1.080 0232-4421 RF 0.284 8.792 0.304 13.995 0.485 7.636 0.811 0.218 0.095 1.259 A0368 NR 0.220 3.443 0.181 5.101 0.268 6.080 0.768 0.305 0.138 1.276 A0370 NR 0.375 6.827 0.110 11.422 0.183 8.753 0.459 0.285 0.074 1.206 02426-2132 NR 0.314 4.837 0.298 7.085 0.436 5.751 0.774 0.151 0.115 1.156 AS0295 RF 0.300 9.202 0.310 14.464 0.487 7.072 0.896 0.257 0.059 1.200 A0376 NR 0.048 0.515 0.011 0.713 0.016 4.174 0.670 0.346 0.208 1.875 A0383 NR 0.187 2.012 0.064 2.881 0.092 5.438 0.297 0.338 0.110 1.239 A0402 NR 0.322 4.452 0.190 7.293 0.311 8.228 1.236 0.045 0.085 1.175 A0399 NR 0.072 2.554 0.021 3.926 0.032 6.857 0.581 0.243 0.136 3.135 A0401 NR 0.074 4.434 0.016 7.035 0.025 7.881 0.877 0.282 0.099 1.488 03016+0155 NR 0.170 1.687 0.079 2.341 0.110 4.450 0.333 0.233 0.090 1.190 03037-7752 RF 0.274 6.901 0.197 11.840 0.338 9.344 0.891 0.318 0.085 1.143 A3088 NR 0.253 5.317 0.193 8.344 0.302 7.316 0.762 0.236 0.099 1.279 03089+2645 NR 0.324 10.682 0.298 18.580 0.518 9.656 1.047 0.159 0.085 1.285 A3126 RF 0.086 1.212 0.037 1.707 0.052 4.994 0.309 0.470 0.083 1.203 A3128 RF 0.060 0.316 0.015 0.423 0.020 2.860 0.484 0.269 0.111 1.502 03311-2100 NR 0.188 2.604 0.104 3.827 0.153 5.859 0.528 0.204 0.092 1.380 3C089 NR 0.139 0.464 0.020 0.647 0.028 4.528 0.333 0.166 0.096 1.164 A3158 RF 0.060 2.057 0.018 2.899 0.026 5.435 0.313 0.387 0.082 2.722 03529+1941 NR 0.109 1.013 0.041 1.362 0.055 3.085 0.533 0.263 0.124 1.111 77 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f 03588-2955 RF 0.425 12.749 0.337 21.346 0.564 8.747 0.487 0.143 0.052 1.130 A0478 NR 0.088 5.866 0.038 9.322 0.060 7.546 0.554 0.270 0.121 1.116 04175-1154 NR 0.440 21.550 0.366 40.079 0.680 10.945 0.936 0.211 0.093 1.108 04258-0833 NR 0.040 0.384 0.016 0.514 0.022 3.088 0.125 0.256 0.073 3.255 04296-0253 NR 0.399 5.376 0.254 8.315 0.393 7.000 0.900 0.302 0.132 1.159 04371+0043 NR 0.285 4.937 0.134 7.580 0.205 6.101 0.632 0.265 0.041 1.251 04390+0715 NR 0.230 5.310 0.166 8.038 0.252 6.528 0.534 0.293 0.083 1.160 04390+0520 NR 0.208 1.883 0.103 2.670 0.145 5.024 0.480 0.251 0.107 1.220 A0514 RF 0.071 0.317 0.014 0.430 0.018 3.959 0.534 0.257 0.035 1.588 A3292 RF 0.172 1.775 0.082 2.441 0.112 4.204 0.297 0.271 0.098 1.410 04519+0006 NR 0.430 5.882 0.364 8.608 0.533 5.844 0.829 0.411 0.206 1.101 04541-0300 NR 0.550 15.974 0.296 28.925 0.536 10.644 0.768 0.206 0.082 1.309 04552+0657 NR 0.425 6.452 0.414 9.878 0.634 6.845 0.998 0.571 0.226 1.135 0509-5342 RF 0.463 4.295 0.208 7.291 0.353 9.069 1.716 0.145 0.164 1.176 A3322 RF 0.200 3.793 0.142 5.786 0.216 6.649 0.599 0.146 0.092 1.104 05107-0801 NR 0.220 8.412 0.212 13.101 0.330 7.152 0.434 0.280 0.060 1.082 AS0520 RF 0.295 6.561 0.201 10.757 0.330 8.269 0.732 0.140 0.076 1.167 05207-1328 NR 0.340 5.821 0.181 9.131 0.284 7.335 0.692 0.345 0.111 1.265 A3343 RF 0.191 3.027 0.089 4.563 0.135 6.429 0.528 0.269 0.099 1.175 05282-2942 RF 0.158 1.634 0.086 2.245 0.119 4.607 0.499 0.564 0.197 1.327 RBS0653 RF 0.284 7.669 0.109 13.057 0.185 8.558 0.836 0.258 0.066 1.153 28658-3125 RF 0.210 3.759 0.128 5.678 0.194 6.484 0.540 0.301 0.091 1.060 A0545 NR 0.154 3.448 0.047 5.431 0.073 7.372 0.311 0.124 0.052 1.265 05329-3701 RF 0.275 6.799 0.197 11.333 0.329 8.644 0.843 0.136 0.080 1.134 0542-4100 RF 0.640 3.762 0.216 5.691 0.327 6.455 0.885 0.108 0.125 1.168 05470-3904 RF 0.210 0.974 0.060 1.398 0.086 5.186 0.699 0.046 0.106 1.352 A3364 RF 0.148 3.151 0.079 4.925 0.124 7.194 0.546 0.126 0.081 1.411 A0550 RF 0.099 2.168 0.062 3.165 0.090 5.669 0.298 0.141 0.067 1.202 78 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f 05534-3342 RF 0.407 13.416 0.212 24.118 0.382 10.463 0.680 0.192 0.055 1.119 A3376 RF 0.046 0.541 0.006 0.762 0.008 4.696 0.499 0.386 0.121 3.323 A3378 RF 0.141 3.198 0.099 4.474 0.139 4.780 0.273 0.360 0.088 1.160 06163-2156 RF 0.171 2.994 0.067 4.678 0.105 7.236 0.511 0.313 0.086 1.178 AS0579 RF 0.152 1.508 0.056 2.119 0.078 4.789 0.352 0.213 0.092 1.146 13959+2418 NR 0.270 7.876 0.283 12.273 0.440 7.189 0.635 0.378 0.086 1.169 A3391 RF 0.051 1.028 0.021 1.498 0.031 5.794 0.222 0.232 0.068 3.227 A3399 RF 0.203 3.297 0.073 5.045 0.111 6.759 0.453 0.276 0.084 1.084 16765+1764 NR 0.174 4.844 0.111 7.219 0.165 6.176 0.412 0.229 0.080 1.140 AS0592 RF 0.222 7.970 0.188 13.233 0.313 8.581 0.651 0.312 0.080 1.363 A3404 RF 0.167 6.357 0.151 10.236 0.244 7.851 0.642 0.049 0.062 1.148 A0562 NR 0.110 0.392 0.019 0.526 0.025 2.946 0.451 0.237 0.083 1.122 Bullet RF 0.296 24.166 0.131 46.462 0.252 12.364 1.145 0.208 0.066 1.326 0717+3745 NR 0.546 25.993 0.368 51.818 0.734 12.868 1.576 0.181 0.048 1.136 A0586 NR 0.171 3.337 0.093 4.977 0.139 6.241 0.395 0.374 0.075 1.157 07357+7421 NR 0.216 3.873 0.033 5.843 0.050 6.447 0.632 0.331 0.103 1.236 07449+3927 NR 0.698 13.375 0.576 21.465 0.924 7.805 0.634 0.179 0.067 1.114 PKS0745-19 NR 0.103 5.794 0.034 9.484 0.055 8.360 0.483 0.304 0.083 1.593 A0598 NR 0.189 1.695 0.085 2.417 0.121 5.052 0.538 0.068 0.091 1.291 A0611 NR 0.288 4.697 0.124 7.783 0.205 7.993 0.430 0.408 0.118 1.017 A0644 NR 0.070 2.890 0.031 4.410 0.047 6.580 0.821 0.317 0.089 2.778 08196+6336 NR 0.119 0.758 0.044 1.025 0.060 3.498 0.321 0.170 0.088 1.238 08232+0425 NR 0.225 1.718 0.107 2.383 0.148 4.660 0.514 0.510 0.168 1.271 A0665 NR 0.182 4.817 0.059 7.910 0.096 8.136 0.857 0.260 0.075 1.314 2MFGC06756 NR 0.241 2.694 0.055 3.823 0.078 5.082 0.508 0.287 0.098 1.057 A3411 NR 0.169 2.842 0.053 4.247 0.079 6.161 0.454 0.348 0.095 1.119 084254+292723 NR 0.194 1.485 0.048 2.174 0.070 5.023 0.901 0.519 0.181 1.052 A0697 NR 0.282 12.109 0.291 23.094 0.555 11.987 1.107 0.333 0.106 1.311 79 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f 08579+2107 NR 0.230 2.167 0.079 2.994 0.110 4.517 0.176 0.356 0.160 0.993 +1373+110+018 NR 0.180 2.688 0.078 3.869 0.112 5.605 0.799 0.248 0.072 1.140 09112+1746 NR 0.505 5.371 0.324 8.253 0.497 6.808 0.894 0.133 0.102 1.124 20913454+405628 NR 0.442 4.631 0.189 6.963 0.284 6.416 0.590 0.406 0.092 1.152 A0773 NR 0.217 5.866 0.132 9.528 0.214 7.630 0.833 0.272 0.081 1.237 HydraA NR 0.055 1.145 0.005 1.566 0.006 3.951 0.219 0.289 0.046 1.219 092017+303027 NR 0.258 3.036 0.123 4.554 0.184 6.352 0.661 0.352 0.105 1.115 A0795 NR 0.136 1.863 0.048 2.645 0.068 5.002 0.300 0.164 0.062 1.275 0938209+520243 NR 0.360 5.414 0.181 8.169 0.274 6.417 0.504 0.165 0.073 1.081 A0853 NR 0.166 0.861 0.054 1.194 0.075 4.441 0.481 0.236 0.129 1.146 A0868 NR 0.153 2.610 0.086 3.615 0.119 4.414 0.222 0.252 0.070 1.137 0947124+762313 NR 0.354 7.738 0.176 12.772 0.291 8.581 0.841 0.286 0.196 1.088 09498+1708 NR 0.383 9.104 0.381 16.267 0.681 10.311 1.712 0.184 0.151 1.258 09496+5207 NR 0.214 2.228 0.048 3.243 0.069 5.346 0.581 0.291 0.096 1.088 A0907 NR 0.153 2.833 0.056 4.152 0.083 5.772 0.537 0.335 0.142 1.381 26441+1948 NR 0.240 3.615 0.128 5.726 0.203 7.503 0.702 0.090 0.077 1.126 10005+4409 NR 0.154 1.065 0.070 1.437 0.095 3.278 0.268 0.183 0.095 1.243 10061+1201 NR 0.221 2.803 0.071 4.111 0.105 5.860 0.459 0.305 0.027 1.133 10105-1239 NR 0.301 4.060 0.084 6.139 0.127 6.484 0.395 0.222 0.062 1.108 A0963 NR 0.206 4.534 0.076 6.861 0.115 6.364 0.782 0.226 0.113 1.259 A0970 NR 0.059 0.817 0.027 1.134 0.038 4.504 0.402 0.276 0.014 1.387 A0980 NR 0.158 3.039 0.090 4.606 0.136 5.902 1.038 0.220 0.086 1.204 10236+04111 NR 0.291 8.464 0.127 14.162 0.213 8.052 0.966 0.285 0.096 1.289 1023399+490838 NR 0.144 3.321 0.111 5.034 0.168 6.513 0.589 0.156 0.083 1.099 A3444 NR 0.253 7.473 0.123 12.037 0.197 7.915 0.451 0.338 0.060 0.974 A1033 NR 0.126 1.475 0.025 2.143 0.037 5.886 0.583 0.266 0.038 1.207 A1068 NR 0.138 1.884 0.042 2.664 0.060 5.225 0.552 0.370 0.092 1.078 10569-03373 NR 0.823 7.212 0.383 11.420 0.607 7.494 1.083 0.096 0.107 1.444 80 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f 11089+0906 NR 0.449 5.708 0.269 8.786 0.414 6.863 0.744 0.193 0.106 1.128 A1190 NR 0.075 0.599 0.028 0.808 0.038 3.597 0.190 0.271 0.083 1.247 A1201 NR 0.169 2.527 0.054 3.681 0.079 5.309 0.543 0.359 0.060 1.254 A1204 NR 0.171 1.629 0.066 2.253 0.092 4.327 0.277 0.218 0.084 1.310 1115+5319 NR 0.466 8.139 0.364 14.554 0.651 10.328 1.639 0.141 0.157 1.084 11158+0129 NR 0.352 8.020 0.227 13.674 0.388 9.180 0.730 0.189 0.068 1.253 A1240 NR 0.159 0.492 0.032 0.675 0.044 4.158 0.420 0.279 0.137 1.411 A1285 NR 0.106 2.267 0.042 3.281 0.060 5.361 0.617 0.314 0.026 1.219 A1300 NR 0.307 9.614 0.240 17.836 0.446 11.265 1.174 0.262 0.099 1.285 11375+6625 NR 0.782 5.411 0.347 7.728 0.495 5.174 0.629 0.228 0.122 1.088 1142248+583205 NR 0.311 7.812 0.182 13.142 0.306 8.855 0.679 0.127 0.073 1.166 A1413 NR 0.143 4.175 0.044 6.581 0.070 7.350 0.558 0.231 0.089 1.459 17981192+4979669 NR 0.383 7.801 0.394 13.915 0.702 10.276 1.691 0.267 0.141 1.111 29251+2198 NR 0.300 5.929 0.172 9.902 0.287 8.702 0.784 0.233 0.076 1.104 A1446 NR 0.103 0.707 0.019 0.950 0.025 3.606 0.513 0.332 0.163 1.123 12062-0847 NR 0.440 16.980 0.490 31.633 0.913 11.369 1.423 0.225 0.109 1.235 12154-3900 NR 0.119 1.605 0.038 2.315 0.055 5.505 0.361 0.429 0.110 1.167 121733+033929 NR 0.077 2.565 0.050 3.947 0.077 6.694 0.647 0.292 0.170 2.787 121831+401236 NR 0.320 4.257 0.182 6.320 0.271 6.090 0.651 0.210 0.116 1.216 122648+215157 NR 0.370 1.608 0.082 2.259 0.115 4.785 0.474 0.191 0.095 1.082 12269+3332 NR 0.890 11.315 0.521 22.466 1.035 13.126 1.968 0.193 0.189 1.117 A1553 NR 0.165 3.879 0.113 6.048 0.176 7.238 0.587 0.518 0.105 1.136 12342+0947 NR 0.229 1.747 0.111 2.439 0.154 4.552 0.485 0.134 0.112 1.255 A1576 NR 0.279 2.870 0.107 4.654 0.174 8.001 0.772 0.057 0.063 1.187 A1644 NR 0.047 0.818 0.007 1.171 0.009 4.858 0.506 0.344 0.141 3.047 A1650 NR 0.084 2.247 0.018 3.278 0.026 5.726 0.524 0.286 0.106 1.737 1259334+600409 NR 0.330 3.904 0.145 6.024 0.223 6.894 0.515 0.112 0.068 1.062 A1664 NR 0.128 1.930 0.041 2.747 0.059 4.732 0.484 0.239 0.047 1.178 81 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f A1668 NR 0.063 0.304 0.019 0.409 0.026 3.326 0.291 0.245 0.094 1.442 1305589+263048 NR 0.305 4.356 0.192 6.829 0.300 7.269 0.948 0.151 0.097 1.082 A1682 NR 0.234 3.710 0.105 5.803 0.164 7.205 0.618 0.116 0.092 1.131 13110-0311 NR 0.494 4.349 0.189 6.435 0.280 6.031 0.482 0.228 0.071 1.128 A1689 NR 0.183 8.559 0.103 15.062 0.181 10.000 0.874 0.279 0.110 1.410 1315052+514902 NR 0.291 6.692 0.136 11.224 0.229 8.765 0.771 0.025 0.048 1.149 A1736 NR 0.046 0.638 0.013 0.854 0.017 3.070 0.313 0.322 0.158 3.124 SSGC081 NR 0.050 0.418 0.015 0.565 0.020 3.207 0.393 0.282 0.087 2.178 A1750C NR 0.068 0.445 0.017 0.617 0.024 3.861 0.768 0.263 0.095 1.310 A1750N NR 0.084 0.458 0.022 0.621 0.029 3.586 0.230 0.165 0.070 1.350 A3562 NR 0.049 0.826 0.018 1.149 0.026 4.701 0.503 0.340 0.125 3.211 A1763 NR 0.223 6.919 0.180 11.013 0.286 7.669 0.593 0.388 0.084 1.252 A1767 NR 0.070 1.188 0.037 1.703 0.053 5.301 0.290 0.293 0.081 1.412 A1775 NR 0.072 0.923 0.011 1.238 0.015 3.760 0.413 0.503 0.110 1.616 LCDCS0829 NR 0.451 20.538 0.248 41.656 0.503 13.426 2.267 0.213 0.073 1.160 13546+7715 NR 0.397 4.673 0.251 7.024 0.378 6.384 0.815 0.314 0.119 1.103 A1831 NR 0.061 0.538 0.017 0.720 0.023 3.541 0.159 0.447 0.077 1.347 1359495+623047 NR 0.322 4.018 0.121 6.184 0.186 6.859 0.590 0.199 0.084 1.468 A1835 NR 0.253 12.004 0.170 21.457 0.303 9.175 1.354 0.348 0.157 1.213 11382+4435 NR 0.226 2.620 0.128 3.891 0.189 6.017 0.680 0.004 0.053 1.037 A1882a NR 0.141 0.316 0.017 0.424 0.022 3.317 0.158 0.302 0.080 1.129 21594948+2407846 NR 0.543 6.151 0.118 9.624 0.185 6.887 0.360 0.327 0.029 1.000 A1914 NR 0.171 9.446 0.147 15.799 0.246 8.422 1.044 0.213 0.053 1.398 1427161+440730 NR 0.498 6.679 0.271 11.975 0.486 10.403 1.424 0.236 0.142 1.328 14276-2521 NR 0.318 2.061 0.095 2.865 0.132 4.689 0.340 0.443 0.114 1.186 A1930 NR 0.131 0.951 0.038 1.311 0.053 4.366 0.629 0.587 0.028 1.235 A1942 NR 0.224 1.401 0.046 2.016 0.066 5.305 0.486 0.373 0.031 1.219 A1991 RB 0.059 0.329 0.010 0.438 0.013 2.695 0.319 0.299 0.114 1.106 82 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f 145715+222009 RB 0.258 3.947 0.081 5.650 0.115 5.120 0.434 0.296 0.101 1.135 AS0780 RB 0.236 5.352 0.074 8.395 0.117 7.021 0.628 0.310 0.122 1.065 A2009 RB 0.153 3.537 0.097 5.386 0.148 6.695 0.309 0.443 0.071 1.392 1504075-024816 RB 0.215 9.519 0.130 16.069 0.219 8.482 0.751 0.238 0.070 1.463 A2034 RB 0.113 2.975 0.031 4.685 0.049 7.555 0.875 0.303 0.108 1.568 15149-1523 RB 0.223 5.561 0.090 9.372 0.151 8.899 0.481 0.141 0.048 1.105 A2061 RB 0.078 1.171 0.022 1.631 0.031 4.310 0.527 0.278 0.118 1.083 MKW03s RB 0.045 0.650 0.006 0.875 0.008 3.434 0.404 0.261 0.113 2.072 01670077 NR 0.254 2.126 0.070 2.961 0.098 4.059 0.412 0.267 0.111 1.028 A2069 RB 0.116 1.793 0.032 2.675 0.048 5.936 0.646 0.301 0.128 1.712 15242-3154 RB 0.103 1.365 0.019 1.900 0.026 4.426 0.719 0.362 0.129 1.326 15328+3021 RB 0.345 6.570 0.112 10.388 0.177 7.129 0.720 0.239 0.065 1.141 A2107 RB 0.041 0.433 0.009 0.588 0.012 3.766 0.480 0.265 0.114 3.251 A2111 RB 0.229 3.754 0.081 5.996 0.129 7.700 0.575 0.186 0.085 1.146 A2104 RB 0.153 3.731 0.049 5.815 0.077 7.200 1.018 0.245 0.153 1.354 A2125 NR 0.246 0.632 0.031 0.850 0.042 3.158 0.206 0.197 0.089 1.133 A2124 RB 0.066 0.326 0.012 0.463 0.017 4.839 0.219 0.354 0.091 1.104 A2142 RB 0.091 4.832 0.043 7.887 0.069 7.675 0.570 0.276 0.080 3.074 15583-1410 RB 0.097 2.001 0.021 2.850 0.029 5.018 0.356 0.371 0.106 1.330 A2147 RB 0.035 0.537 0.007 0.737 0.010 4.275 0.343 0.321 0.101 4.436 A2163 RB 0.203 20.636 0.140 42.292 0.288 13.183 1.347 0.240 0.045 1.603 16213+3810 RB 0.465 4.964 0.186 7.763 0.291 7.226 0.580 0.199 0.066 1.167 16235+2634 RB 0.426 3.854 0.228 5.798 0.342 6.365 0.908 0.201 0.124 1.005 A2187 RB 0.184 2.384 0.100 3.644 0.152 6.709 0.765 0.183 0.122 1.389 A2204 RB 0.152 6.250 0.044 10.792 0.077 8.269 1.172 0.319 0.143 1.623 A2218 NR 0.176 4.315 0.084 6.482 0.127 6.318 0.550 0.201 0.076 1.287 A2219 RB 0.226 14.778 0.091 27.420 0.169 11.017 0.888 0.280 0.093 1.223 HerculesA RB 0.155 1.836 0.034 2.531 0.047 3.653 1.309 0.181 0.097 1.224 83 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f 021701+6412 NR 0.453 2.479 0.125 3.720 0.188 6.371 0.771 0.379 0.154 1.122 A2244 RB 0.097 2.680 0.024 3.927 0.036 5.919 0.484 0.327 0.096 1.106 A2256 NR 0.058 3.438 0.033 5.363 0.052 6.782 0.465 0.381 0.135 1.886 A2249 RB 0.082 1.267 0.035 1.811 0.051 5.153 0.342 0.168 0.086 1.204 A2255 NR 0.081 2.107 0.026 3.133 0.038 6.086 0.559 0.325 0.113 1.828 A2259 RB 0.164 3.248 0.119 4.806 0.176 6.089 0.502 0.427 0.128 1.254 43072 RB 0.164 4.348 0.075 6.753 0.116 7.066 0.427 0.413 0.059 1.371 17202+3536 RB 0.391 6.766 0.206 10.872 0.331 7.870 0.653 0.367 0.080 1.279 A2261 RB 0.224 7.182 0.156 11.669 0.253 7.714 1.178 0.349 0.077 1.276 A2294 NR 0.169 4.578 0.170 7.178 0.266 7.303 0.736 0.260 0.106 1.415 17316+2251 RB 0.366 6.784 0.211 11.278 0.351 8.608 0.849 0.299 0.123 1.320 17421+3306 RB 0.076 1.099 0.017 1.507 0.024 4.076 0.352 0.374 0.179 1.653 174715+451155 RB 0.157 1.518 0.066 2.128 0.093 4.729 0.378 0.182 0.084 1.142 17502+3504 RB 0.171 1.689 0.078 2.364 0.109 4.639 0.356 0.126 0.083 1.187 18044+1002 RB 0.152 5.159 0.144 8.034 0.225 7.097 0.592 0.092 0.075 1.225 A2302 RB 0.179 1.324 0.055 1.862 0.077 4.821 0.382 0.203 0.096 1.157 18290+6913 NR 0.203 0.843 0.044 1.151 0.060 4.057 0.305 0.335 0.109 1.234 18521+5711 RB 0.109 0.465 0.019 0.635 0.026 4.003 0.283 0.259 0.096 1.345 18539+6822 NR 0.093 1.031 0.025 1.419 0.034 4.129 0.221 0.190 0.074 1.199 33709-2597 RF 0.264 6.544 0.138 10.438 0.221 7.658 0.539 0.118 0.070 1.181 A2319 RB 0.056 5.846 0.046 10.028 0.078 8.664 1.413 0.319 0.131 3.532 19318-2635 NR 0.352 8.805 0.104 14.152 0.168 7.793 0.786 0.374 0.147 1.326 AS0821 NR 0.237 5.443 0.174 8.184 0.261 6.386 0.506 0.302 0.072 1.108 19383+5409 RB 0.260 8.739 0.350 13.629 0.546 7.202 0.728 0.356 0.091 1.124 19473-7623 RF 0.217 5.483 0.179 8.604 0.280 7.337 0.632 0.338 0.086 1.214 A3653 NR 0.109 0.524 0.015 0.733 0.021 4.781 0.341 0.345 0.071 1.222 20035-2323 NR 0.317 7.858 0.190 13.401 0.324 9.178 0.804 0.131 0.072 1.222 20148-2430 NR 0.161 4.182 0.099 6.499 0.154 6.629 0.996 0.447 0.125 1.190 84 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f 2023-5535 RF 0.232 5.848 0.172 9.627 0.283 8.387 0.761 0.291 0.085 1.121 20318-4037 NR 0.342 7.965 0.430 12.201 0.659 6.735 0.918 0.128 0.117 1.116 A3695 NR 0.089 1.909 0.042 2.887 0.064 6.465 0.427 0.161 0.084 1.352 20460-3430 NR 0.423 4.194 0.216 6.100 0.314 5.606 0.447 0.212 0.086 1.136 20499-3216 NR 0.325 5.290 0.221 8.338 0.348 7.423 0.952 0.262 0.109 1.259 A3739 NR 0.165 2.874 0.120 4.251 0.177 6.084 0.527 0.413 0.111 1.096 IC1365 NR 0.049 0.574 0.025 0.781 0.034 3.966 0.438 0.509 0.083 2.480 2129-0741 NR 0.589 12.133 0.669 19.708 1.086 8.117 0.943 0.454 0.126 1.130 2135-0102 NR 0.325 4.768 0.219 7.826 0.360 8.365 1.066 0.580 0.154 1.246 A2355 NR 0.124 1.465 0.045 2.290 0.071 7.240 0.690 0.289 0.118 1.276 2135-5726 RF 0.427 3.586 0.199 5.541 0.307 6.922 1.301 0.108 0.157 1.099 21402-2339 NR 0.313 3.985 0.110 5.860 0.162 5.638 0.740 0.306 0.144 1.070 A3809 NR 0.062 0.426 0.014 0.565 0.019 3.117 0.292 0.413 0.138 1.303 2148-6116 RF 0.571 3.484 0.229 5.327 0.351 6.735 1.175 0.272 0.195 1.039 A2384 NR 0.094 1.119 0.018 1.628 0.026 5.246 0.839 0.390 0.162 2.330 A2390 NR 0.228 13.625 0.092 25.178 0.169 10.095 1.521 0.290 0.096 1.068 21538+3746 NR 0.292 11.047 0.148 19.077 0.256 8.940 1.321 0.240 0.103 1.148 A2409 NR 0.148 4.281 0.134 6.289 0.197 5.955 0.382 0.462 0.093 1.292 A3827 RF 0.098 3.243 0.032 5.080 0.050 7.338 0.789 0.339 0.144 1.302 A2415 NR 0.058 0.401 0.012 0.534 0.016 2.583 0.284 0.347 0.094 1.236 22117-0349 NR 0.270 6.301 0.219 11.029 0.383 9.815 1.315 0.221 0.121 1.394 3C444 NR 0.153 0.613 0.021 0.876 0.030 4.379 0.393 0.332 0.098 1.334 A2426 NR 0.098 1.671 0.053 2.451 0.077 5.825 0.389 0.251 0.100 1.305 2214-1359 NR 0.483 10.888 0.419 18.292 0.705 8.833 0.989 0.194 0.093 1.120 A3854 NR 0.149 2.281 0.081 3.256 0.116 5.181 0.394 0.258 0.092 1.197 22186-3853 NR 0.138 3.292 0.092 4.789 0.134 5.604 0.330 0.200 0.075 1.240 A2445 NR 0.166 1.718 0.057 2.340 0.077 4.162 0.215 0.545 0.086 1.190 A3880 NR 0.058 0.341 0.018 0.453 0.023 2.897 0.277 0.305 0.143 2.280 85 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f 22286+2036 NR 0.412 10.081 0.348 16.485 0.569 8.249 0.824 0.352 0.116 1.176 22298-2756 NR 0.324 4.070 0.190 5.967 0.279 5.882 0.562 0.397 0.108 1.233 2233-5339 RF 0.480 4.392 0.264 6.750 0.406 6.791 1.168 0.075 0.121 1.089 A2457 NR 0.059 0.550 0.015 0.744 0.021 3.595 0.099 0.326 0.059 1.352 22428+5301 NR 0.192 4.117 0.053 6.747 0.088 7.813 1.165 0.183 0.120 1.048 2243198-093530 NR 0.432 14.006 0.520 21.842 0.811 7.179 0.672 0.267 0.085 1.214 22450+2637 NR 0.304 4.480 0.241 6.835 0.368 6.710 0.933 0.330 0.146 1.224 A3911 RF 0.097 2.198 0.061 3.262 0.090 6.106 0.393 0.285 0.081 1.183 A2485 NR 0.247 2.703 0.119 4.043 0.178 6.250 0.714 0.231 0.129 1.247 AS1063 NR 0.347 22.560 0.412 41.905 0.765 11.302 0.722 0.359 0.070 1.219 A3921 RF 0.093 1.981 0.037 2.916 0.054 5.766 0.762 0.360 0.085 1.879 A2507 NR 0.196 1.003 0.065 1.377 0.089 4.309 0.433 0.426 0.154 1.069 2259-6057 RF 0.750 4.949 0.246 7.715 0.384 7.265 1.064 0.694 0.215 1.200 23028+0843 NR 0.722 1.736 0.111 2.667 0.170 6.818 1.234 0.169 0.180 1.139 A2537 NR 0.295 4.650 0.104 7.083 0.158 6.629 0.625 0.224 0.038 1.157 23115+0338 NR 0.300 7.260 0.281 12.544 0.486 9.518 1.005 0.334 0.103 1.333 A2556 NR 0.087 0.814 0.018 1.105 0.024 3.756 0.398 0.356 0.086 1.157 AS1101 NR 0.058 0.541 0.010 0.726 0.013 2.698 0.286 0.199 0.089 2.076 A2597 NR 0.085 0.878 0.010 1.214 0.015 4.266 0.259 0.279 0.080 1.310 A2626 NR 0.055 0.443 0.012 0.593 0.016 3.263 0.379 0.378 0.131 1.119 A2631 NR 0.273 7.191 0.246 11.658 0.398 8.024 0.961 0.169 0.100 1.254 A4023 RF 0.193 1.996 0.082 2.984 0.123 6.256 0.635 0.268 0.117 1.216 A2645 NR 0.251 3.698 0.171 5.582 0.258 6.470 0.782 0.297 0.119 1.118 23442-0422 NR 0.079 1.473 0.038 2.031 0.052 4.501 0.143 0.406 0.261 1.422 A2657 NR 0.040 0.583 0.016 0.785 0.021 3.567 0.307 0.302 0.165 3.162 A4038 NR 0.028 0.394 0.007 0.525 0.009 2.878 0.263 0.286 0.118 3.540 A2665 NR 0.056 0.489 0.018 0.680 0.025 4.553 0.294 0.310 0.095 1.412 A2667 NR 0.230 7.819 0.208 12.434 0.331 7.604 0.677 0.163 0.084 1.046 86 Table 3.3 (cont’d) Name ID z LX e_LX LX e_LX kT e_kT 𝑍 e_𝑍 𝜒2 [0.5-8 keV] [bol] 1044 erg s−1 1044 erg s−1 keV 𝑍 d.o.f A2670 NR 0.076 0.743 0.021 1.019 0.028 4.001 0.706 0.310 0.114 2.206 87 CHAPTER 4 GLOBAL METALLICITY EVOLUTION OF ACCEPT2.0 CLUSTERS The first detection of iron in the X-ray spectra of galaxy clusters was evidence that the intracluster medium (ICM) is enriched with heavy elements that have been made by stars in galaxies (Mitchell et al., 1976; Mushotzky et al., 1996; Renzini, 1997). Therefore, we can study the metallicity of the ICM over a wide range of redshifts to understand when enrichment occurs, and if enrichment processes are the same for most clusters. For clusters with high signal-to-noise data, we can map out the Fe/H distribution and figure out where heavy metals have ended up. Consequently, simulations of galaxy clusters began to implement feedback from stellar and AGN sources, together with the enrichment associated with stars, to reproduce the observed chemical properties of the ICM. Early spatially-resolved observations of the ICM by ASCA and BeppoSAX showed that certain clusters, now referred to as cool core (CC), exhibit a significant excess in metallicity towards their centers, and a comparatively uniform radial distribution in non-cool core (NCC) clusters (Fabian et al., 1994; Fukazawa et al., 1994; De Grandi & Molendi, 2001). CCs are characterized by a dramatic decrease in gas temperature towards the center in comparison to flatter temperature profiles of NCC clusters. Outside of their core radii, the ICM is similar for both CC and NCC clusters, suggesting that differences in the global abundance is localized to the region surrounding a brightest cluster galaxy (BCG) (De Grandi & Molendi, 2001; De Grandi et al., 2004; Baldi et al., 2012; Ettori et al., 2015; McDonald et al., 2016). Therefore, X-ray cluster astronomers often use measurements excluding the core regions of clusters when studying their global metallicity. Previous works, such as those by Baldi et al. (2012); Ettori et al. (2015), and McDonald et al. (2016), have not shown statistically significant evolution for metallicities measured within a single core-excised (CE) aperture. McDonald et al. (2016) analyzed X-ray data from 153 clusters and found no evidence for metallicity evolution outside the core. Mantz et al. (2017) had the largest data set to date with 245 cluster observations compiled from four separate catalogues. The analysis reported in this chapter uses a sample of global CE metallicities for 302 clusters 88 from ACCEPT2.0 (Chapter 2) to assess the abundance evolution of the ICM. In Section 4.1, we give an overview of the clusters used in this analysis. Section 4.2 goes over the methods. Section 4.3 details the dependence of our sample of global CE abundance on a cluster’s CC status (Section 4.3.1), luminosity (Section 4.3.2, and redshift (Section 4.3.3). Section 4.3.4 fits the data to a linear model with dependence on luminosity and redshift. Then we apply the methods to more targeted samples in section 4.3.5. 4.1 The Sample For this analysis, we selected 302 clusters from ACCEPT2.0 (introduced in Chapter 2) with SNR>15 and bolometric 𝐿 𝑋 & 4 × 1043 erg s−1 . We did not include low luminosity systems because their X-ray observables differ from those of clusters due to their shallower gravitational potential wells and because, for the coolest systems, the metallicity and the electron density (the parameter that affects the normalization of the X-ray spectrum) become increasingly difficult to disentangle. Because the difference in observations of the global metallicity content of the ICM can be biased depending on the choice of aperture (Mushotzky & Loewenstein, 1997; Balestra et al., 2006; Maughan et al., 2008; Leccardi & Molendi, 2008; Anderson et al., 2009), we use the CE global X-ray properties (within the aperture [0.3-1] 𝑅2500 ) from ACCEPT2.0 so we may treat CCs and NCCs in the same manner. Additionally, CE flux can be underestimated for nearby objects that are larger than the 𝐶ℎ𝑎𝑛𝑑𝑟𝑎 field of view. We found that systems above this threshold were massive and distant enough where most of their CE apertures fit within the ACIS CCDs. There are 16 clusters with global CE abundance measurements consistent with zero metallicity within the 1𝜎1 uncertainties, although we find no significant difference in our results when these clusters are excluded. These 16 clusters are plotted according to their 3𝜎 (99.7%) upper limits. The X-ray properties for 302 ACCEPT2.0 clusters used in this chapter are provided in table 4.6. As described in Chapter 2, the source models used for spectral analysis is a 𝑚𝑒𝑘𝑎𝑙 model (Kaastra et al., 1996; Liedahl et al., 1995) where ratio of elements is fixed to the Solar value as in Anders & 1 The measured data point is smaller than the error. 89 Grevesse (1989b). 4.2 Methods The methods described here were used to test the global abundance dependencies on core status, luminosity, and redshift. To summarize, we separated the data according to central entropy, 𝐾0 , CE luminosity, 𝐿 𝑋 , or cluster redshift, 𝑧. We then compared the medians of these sub samples, all of which are provided in Table 4.1. We chose to use the median global abundance so as to minimize √ contribution from outliers. The errors on the medians are 𝜎 = 𝜎std / 𝑁, with 𝜎std as the weighted standard deviation defined as, s Σ𝑤𝑖 (𝑋𝑖 − 𝑋¯ 𝑤 ) 2 𝜎std = , (4.1) Σ𝑤𝑖 where the weight on each radial data point is 𝑤𝑖 = 1/𝜎𝑖2 . We found that, when the sample is divided according to luminosity and redshift, difference in the median global CE metallicities, Δ 𝑍,e warrant further investigation at ∼ 3𝜎. We test the significance of Δ 𝑍e by simulating clusters based on a null-hypothesis model which assumes a constant metallicity with intrinsic scatter. The simulated points have the same uncer- tainties as the observed data, but each simulated value was drawn from two Gaussian distributions. The first draw was centered on the sample mean ( 𝑍) ¯ with an intrinsic dispersion (𝜎int ). This first draw is used as a mean for the second Gaussian which has width determined by the uncertainty of the simulated observation. Each simulated sample was divided at the median redshift or luminosity and compared statisti- cally in the same manner as the real data. We compared the halves of every new simulated sample to the preceding samples to generate a probability distribution of observed differences between them. The simulated clusters are modeled under the null assumption that the global CE metallic- ities have no dependence on luminosity or redshift. The only source of variation in the measured global abundance is therefore assumed to be due to statistical measurement errors and intrinsic scatter 𝜎int . We therefore approximate the values of 𝑍¯ and 𝜎int via likelihood maximization. The 90 log-likelihood function for data with intrinsic scatter is, " # 1 ¯ 2 (𝑍𝑖 − 𝑍) 2 + 𝜎 2 )) , lnℒ = − Σ𝑖 + ln(2𝜋(𝜎int (4.2) 2 2 2 𝜎int + 𝜎𝑍,𝑖 𝑍,𝑖 where 𝑍𝑖 is the global CE metallicity for a cluster and 𝜎𝑍,𝑖 is the corresponding measurement error. We perform the fit using the package emcee (Foreman-Mackey et al., 2013), which is based on algorithms described by Goodman & Weare (2010). The bounds for the parameters were 0≤ 𝑍¯ ≤2 for abundance, and −5 ≤ ln𝜎int ≤1 for intrinsic scatter. We run the sampler over 105 steps, with the first 104 steps being burn-ins. The output chain results in the best-fit parameters 𝑍=0.260 ¯ +0.007 𝑍 −0.006 and 𝜎int =0.068+0.006 −0.006 , where the values and uncertainties are based on the 50th , 16th and 84th percentiles of the output chain. The results of the fit can be seen in figure 4.1. These parameters are used to define a consistent null hypothesis model where no trend in either luminosity or redshift exists. That model then is used to simulate data with the underlying constant metallicity 𝑍¯ and variation from adding randomly selected points from normal distributions with mean zero and widths corresponding to 𝜎int and the original data error. The result is a simulated sample with constant metallicity and variation solely due to underlying intrinsic scatter and errors on our data. 4.3 Results 4.3.1 Dependence on core status We aim to determine whether the global abundances of clusters have changed significantly since redshift 𝑧 ∼1. As alluded to in Section 1.4, answering this question requires a general view of each cluster without bias from the inner regions of cool cores. We therefore use the temperature and abundance measurements excluding the region r<0.3 R2500 . The difference between CC clusters versus NCC clusters is evidenced by their radial abundance profiles in Figures 4.3 and 4.4. These figures show the median spatial distribution of metals for CC and NCC clusters, where each radial bin contains 100 data points, with the exception of the outermost bins, which contain 56 and 65 points for CC and NCC clusters, respectively. It should be noted, however, that the extent of the data inside 0.3 𝑅2500 differs between CCs and NCCs because 𝑍 is an emission-weighted measurement. 91 +0.01 Z = 0.26−0.01 +0.01 σint = 0.07−0.01 09 0 0. σint 0. 07 5 06 0 0. 04 5 0. 24 0 25 5 27 0 0. 0. 28 0. 5 04 06 5 0 0. 0. 0. 0. 0. 07 09 5 0 Z σint ¯ and intrinsic Figure 4.1: Global 𝒁 null model MCMC results. Resulting constant metallicity, 𝑍, scatter, 𝜎int , from the MCMC . The less dense environment in the cores of NCC clusters does not allow for as many radial bins to meet the count threshold required for spectral extraction. The error bars are centered on the median e with sizes corresponding to the mean error, 𝜎 = (Σ𝑤𝑖 ) −1/2 . The shaded region of metallicity, 𝑍, Figure 4.3 represents the standard deviations, 𝜎int , of each bin. The sizes of these shaded regions in comparison to the error bars is an indication that 𝜎int  𝜎𝑤 . This profile shows that while radial abundances can vary from cluster to cluster, the profiles as a whole follow a general trend, depending on their central entropy. The binned radial profiles are stacked in Figure 4.4 to better show the contrast in spatial distribution of metals between CC and NCCs. 92 Cool Core 30 Non-Cool Core N clusters 20 10 0 0.03 0.10 0.30 0.50 1.00 redshift Figure 4.2: Redshift distribution of CC and NCC clusters in ACCEPT2.0. Redshift distribution for 66 CC clusters (hatch blue) and 132 NCC clusters (red). The median global CE metallicity for 66 CCs is 𝑍=0.290±0.012𝑍 e , and 𝑍=0.265±0.009𝑍 e e = 0.025 ± 0.015, is consistent with for the 132 NCCs. The low significance of their difference, Δ 𝑍 recent works, which found that the state of the ICM at outer radii is virtually independent of core status (Neumann, 2005; Leccardi & Molendi, 2008; Eckert et al., 2011) and provides reassurance that the 0.3 < 𝑟 < 1 𝑅2500 aperture adequately excised the core. These results are summarized in Table 4.1. 4.3.2 Luminosity dependence ACCEPT2.0 contains clusters for which there were enough data to obtain a temperature estimate and radial profiles of the X-ray properties, which means that our sample lacks data from low-luminosity clusters at higher redshifts. If there is some correlation between luminosity and global abundance it would be present in the relation between redshift and abundance. We therefore need to check 93 CC standard deviation NCC standard deviation 0.90 CC median abundance and mean error NCC median abundance and mean error 0.75 Z (Z ) 0.60 0.45 0.30 0.15 0.01 0.10 0.30 1.00 0.01 0.10 0.30 1.00 R/R2500 Figure 4.3: Binned weighted mean metallicity profiles for CCs and NCCs. Binned weighted means for projected metallicity profiles for CC (left) and NCC (right) clusters. The innermost radial bin for the NCC clusters is larger because NCCs tend to have lower X-ray central surface brightness, and therefore fewer independent, spatially-resolved X-ray spectra for their cores. that metallicity is independent of luminosity. After dividing the full sample at the median bolometric luminosity 𝐿 𝑋 ' 5.4 × 1044 erg s−1 , the difference in median abundance between low- and high-luminosity clusters is Δ 𝑍 e = 0.033 ± 0.011 𝑍 . This difference is significant at slightly less than 3𝜎 (Figure 4.5, left) using only the standard deviation as an estimator of 1𝜎. After simulating the null model, we found 68% of the simulations had differences within the range (-0.017,+0.018), and a 3𝜎 upper limit of 0.052, which exceeds the observed difference. With a significance less than 3𝜎, we conclude that any dependence of global abundance on luminosity here is weak at best. 4.3.3 Redshift Dependence The difference in the median global CE metallicity for the low-𝑧 vs. high-𝑧 sub samples is e = 0.035 ± 0.012 𝑍 (Table 4.1). After comparing 10,000 𝑍 Δ𝑍 e pairs based on 100 simulated sets of data, we found that 68% of the simulated null models were in the range (-0.018,+0.019) (Figure 94 0.60 0.50 Z(Z ) 0.40 0.30 Non-Cool Core 0.25 Cool Core 0.01 0.10 0.30 1.00 R/R2500 Figure 4.4: Stacked weighted median metallicity profiles for CC and NCC clusters. Binned weighted median for projected metallicity profiles for CC (closed circles) and NCC (open diamonds) clusters. 4.5), with a 3𝜎 upper limit of 0.047. Because the observed difference is below 3𝜎, we conclude that any dependence on redshift is weak, although it does not appear to be as weak as the dependence on luminosity. 4.3.4 Multiple Linear Regression Analysis We investigated this further by fitting the data to the functional form, 𝐿𝑋 ln𝑍 (𝐿 𝑋 , 𝑧) = ln𝑍0 + 𝛼ln + 𝛽ln𝑧. (4.3) 𝐿 piv By allowing the function to vary with luminosity and redshift simultaneously, we are able to gauge which dependence is stronger. For the full sample, the model dependence on 𝐿 𝑋 is 𝛼 = 95 Table 4.1: Median global CE abundances of ACCEPT2.0 sub samples. Median core-excised (CE) global abundances for sub populations of ACCEPT2.0 clusters. Col(1) is the name of the sub sample, col(2) is the value of the parameter used to separate the data, col (3) is the size of the sub sample, cols(4,5) is the median and mean error of the sub sample, and cols(6,7) is the difference between the median abundances and error. Cols(8,9) show the 1𝜎 lower and upper bounds for the simulated differences. √ Sub sample Split Value N 𝑍 e[𝑍 ] 𝜎std / 𝑁 Δ 𝑍 e[𝑍 ] 𝜎 e 68% Δ 𝑍 esim 99.7% Δ𝑍 Cool Core 66 0.290 0.011 30 keV cm2 0.024 0.013 ··· ··· Non-Cool Core 132 0.266 0.008 Lo 𝐿 𝑋 151 0.289 0.105 5.4×1044 0.033 0.011 (-0.017,+0.018) 0.052 Hi 𝐿 𝑋 151 0.256 0.096 Lo 𝑧 152 0.286 0.104 0.21 0.035 0.012 (-0.018,+0.019) 0.047 Hi 𝑧 150 0.251 0.098 Table 4.2: Best fit parameters to the 𝒁(𝑳 𝑿 , 𝒛) model. Output parameters for the linear fit of the full sample to Equation 4.3. When metallicity is fit to both luminosity and redshift simultaneously, there is a greater dependence on 𝐿 𝑋 than 𝑧, but neither are statistically significant. 𝑍0 𝛼 𝛽 𝜎int [𝑍 ] 0.290+0.025 −0.023 -0.047+0.030 −0.030 -0.015+0.047 −0.047 0.164+0.021 −0.019 −0.047 ± 0.029, and on redshift is 𝛽 = −0.014 ± 0.046. Although the best fit model shows a slightly stronger reliance on the luminosity component, neither 𝛼 nor 𝛽 are significant. The results are summarized in Table 4.2. 96 1600 ∆ZeLX > 0.033 = 3.77% ∆Zez > 0.035 = 1.91% 1400 Number of ∆Ze pairs 1200 1000 800 600 400 200 0 −0.06−0.04−0.02 0.00 0.02 0.04 0.06 −0.06−0.04−0.02 0.00 0.02 0.04 0.06 ∆Ze = ZelosimL − Zehi sim L[Z ] ∆Ze = Zelosimz − Zehi sim z [Z ] Figure 4.5: Metallicity differences between simulated clusters. Distribution of differences between pairs of simulated data based on the null model. Sub sample pairs were separated by either luminosity (left) or redshift (right). 4.3.5 Comparison to Maughan et al. (2008) We compared the results of our above analysis to those by M08, which used 115 clusters observed with 𝐶ℎ𝑎𝑛𝑑𝑟𝑎 and uniformly reduced for two apertures ([0-1] 𝑅500 and [0.15-1] 𝑅500 ). Their model for constant metallicity was rejected at 99.9% for the core-included (CI) aperture, but this significance was not present when the CE values were used, in agreement with the results of Section 4.3.1. We found 64 clusters in our sample that we share with M08, so we were able to redo the M08 analysis using their metallicities and compare them to what we get using our own. We found that temperatures from M08 are on average lower than ours in ACCEPT2.0, with increasing disparity at higher ACCEPT2.0 temperatures. The higher temperatures in ACCEPT2.0 result in slightly lower abundances than M08 (Figure 4.7). Private communication from Maughan revealed that he finds his temperatures from Maughan et al. (2012) and presumably M08 may be overestimated by a factor of about 15% owing to difference in the statistical treatments and the energy binning scheme used. This 15% correction appears as the dashed line in Figure 4.7. 97 lnZ(LX , z) =lnZ0 + αln 5.2×10L44X[ergs−1] +βln 0.80 0.50 Z0 = 0 0.30 Z [Z ] α=− β=− 0.10 0.05 σint = 0.10 1.00 redshift Figure 4.6: Best fit results global CE abundance as a function of 𝑳 𝑿 and 𝒁. Results of the fit to the model. When ICM metallicity is allowed to vary as a function of luminosity and redshift, dependence on luminosity is stronger than the dependence on metallicity, but neither dependence is statistically significant. Table 4.5 shows the ACCEPT2.0 cluster temperatures in comparison to M08, and Table 4.4 shows the comparison between our luminosities and metallicities. We divided the overlapping M08 and ACCEPT2.0 clusters by luminosity and redshift, and found the difference in median metallicities for both subsets to be higher for the M08 clusters. When split by luminosity, the ACCEPT2.0 e = 0.015 ± 0.021 𝑍 , and the M08 clusters show Δ 𝑍 clusters have Δ 𝑍 e = 0.075 ± 0.026 𝑍 . e = 0.045 ± 0.020𝑍 and M08 clusters have When split by redshift, ACCEPT2.0 clusters have Δ 𝑍 98 e = 0.065 ± 0.027 𝑍 . When we simulate the clusters with no dependence on luminosity or Δ𝑍 redshift, the samples do still show the same lack of discernible dependence on luminosity and redshift. 16 Cool Core 14 Non-Cool Core Unknown Core Status 12 M08 kT [keV] 10 8 6 4 2 2 4 6 8 10 12 14 16 ACCEPT2.0 kT [keV] Figure 4.7: Temperatures from M08 vs. ACCEPT2.0. Comparison of ACCEPT2.0 global CE temperatures to those of M08. The solid line represents the 1:1 ratio and the dashed line shows the approximate relation between ACCEPT2.0 clusters and M08 clusters that have been reduced by 15%. 99 Table 4.3: Median CE global abundances comparison for ACCEPT2.0 and M08 overlap. Median CE global abundance for the subsets of ACCEPT2.0 (top half ) and M08 (bottom half ) clusters that overlap with M08. Columns are the same as in Table 4.1. √ Sample Split Value N𝑐𝑙𝑢𝑠𝑡𝑒𝑟 𝑠 𝑍e[𝑍 ] 𝜎 / 𝑁 Δ 𝑍 e[𝑍 ] 𝜎 esim 𝑁 sim ≥ Δ 𝑍 std e 68% Δ 𝑍 e Δ𝑍 ACCEPT2.0 Clusters Lo 𝐿 𝑋 32 0.260 0.097 8.176×1044 erg s−1 0.015 0.021 (-0.032,0.031) 6325 Hi 𝐿 𝑋 32 0.275 0.071 Lo 𝑧 32 0.279 0.081 0.265 0.045 0.020 (-0.030,0.031) 1522 Hi 𝑧 32 0.234 0.082 M08 Clusters Lo 𝐿 𝑋 32 0.325 0.104 9.250×1044 erg s−1 0.075 0.026 (-0.038,0.036) 333 Hi 𝐿 𝑋 32 0.400 0.102 Lo 𝑧 32 0.335 0.094 0.267 0.065 0.027 (-0.038,0.036) 716 Hi 𝑧 32 0.400 0.121 Table 4.4: Global CE luminosities and metallicities M08 and ACCEPT2.0 overlap. Lumi- nosities and metallicities for clusters in ACCEPT2.0 clusters that overlap with M08. ACCEPT2.0 observables are from the [0.3-1] 𝑅2500 aperture. Column(1) is the ACCEPT2.0 name, column(2) is the ACCEPT2.0 redshift, columns(3,4) are bolometric luminosities and error, columns(5,6) are abundances in solar units. Column(7) is the redshift used by M08. Columns(8,9) are M08 bolo- metric luminosities, and columns(10-12) are the metallicities measured by M08, where the last two columns are the positive and negative uncertainties on the abundance. ACCEPT2.0 Name redshift 𝐿 𝑋 e_𝐿 𝑋 𝑍 e_𝑍 M08 redshift 𝐿 𝑋 e_𝐿 𝑋 𝑍 E_𝑍 e_𝑍 1044 erg s−1 𝑍 1044 erg s−1 𝑍 A0068 0.255 10.429 0.489 0.662 0.210 0.255 9.300 0.500 0.460 0.220 0.210 A0209 0.206 10.466 0.266 0.250 0.082 0.206 12.200 0.300 0.290 0.100 0.090 A0267 0.231 6.600 0.166 0.393 0.106 0.230 7.000 0.500 0.640 0.270 0.240 A0383 0.187 2.881 0.092 0.338 0.110 0.187 3.600 0.100 0.350 0.120 0.110 A0402 0.322 7.293 0.311 0.045 0.085 0.322 8.100 0.300 0.170 0.170 0.170 A0586 0.171 4.977 0.139 0.374 0.075 0.171 6.500 0.300 0.840 0.230 0.210 A0665 0.182 7.910 0.096 0.260 0.075 0.182 15.200 0.200 0.340 0.060 0.050 100 Table 4.4 (cont’d) ACCEPT2.0 Name redshift 𝐿 𝑋 e_𝐿 𝑋 𝑍 e_𝑍 M08 redshift 𝐿 𝑋 e_𝐿 𝑋 𝑍 E_𝑍 e_𝑍 1044 erg s−1 𝑍 1044 erg s−1 𝑍 A0697 0.282 23.094 0.555 0.333 0.106 0.282 24.400 0.500 0.470 0.100 0.100 A0773 0.217 9.528 0.214 0.272 0.081 0.217 10.900 0.300 0.570 0.090 0.080 A0907 0.153 4.152 0.083 0.335 0.142 0.153 4.800 0.100 0.360 0.050 0.050 A1204 0.171 2.253 0.092 0.218 0.084 0.171 2.700 0.100 0.130 0.100 0.100 A1240 0.159 0.675 0.044 0.279 0.137 0.159 1.600 0.100 0.180 0.110 0.100 A1300 0.307 17.836 0.446 0.262 0.099 0.307 20.900 0.600 0.410 0.150 0.150 A1413 0.143 6.581 0.070 0.231 0.089 0.143 7.400 0.100 0.340 0.050 0.050 A1682 0.234 5.803 0.164 0.116 0.092 0.234 7.500 0.500 0.330 0.340 0.300 A1689 0.183 15.062 0.181 0.279 0.110 0.183 14.300 0.200 0.400 0.070 0.070 A1763 0.223 11.013 0.286 0.388 0.084 0.223 13.700 0.300 0.260 0.090 0.090 A1914 0.171 15.799 0.246 0.213 0.053 0.171 12.400 0.200 0.280 0.090 0.090 A2034 0.113 4.685 0.049 0.303 0.108 0.113 6.200 0.100 0.360 0.050 0.050 A2069 0.116 2.675 0.048 0.301 0.128 0.116 5.100 0.100 0.260 0.060 0.050 A2111 0.229 5.996 0.129 0.186 0.085 0.229 7.700 0.300 0.200 0.190 0.180 A2125 0.246 0.850 0.042 0.197 0.089 0.246 1.500 0.100 0.200 0.080 0.070 A2163 0.203 42.292 0.288 0.240 0.045 0.203 54.100 1.200 0.480 0.130 0.130 A2204 0.152 10.792 0.077 0.319 0.143 0.152 12.300 0.300 0.320 0.120 0.110 A2218 0.176 6.482 0.127 0.201 0.076 0.176 8.300 0.100 0.350 0.060 0.060 A2259 0.164 4.806 0.176 0.427 0.128 0.164 5.200 0.200 0.410 0.170 0.160 A2261 0.224 11.669 0.253 0.349 0.077 0.224 13.500 0.200 0.330 0.080 0.080 A2294 0.169 7.178 0.266 0.260 0.106 0.178 8.700 0.300 0.230 0.190 0.180 A2409 0.148 6.289 0.197 0.462 0.093 0.148 6.300 0.200 0.320 0.120 0.110 A2631 0.273 11.658 0.398 0.169 0.100 0.273 13.500 0.500 0.430 0.160 0.150 AS1063 0.347 41.905 0.765 0.359 0.070 0.252 16.400 0.400 0.130 0.130 0.130 10236+04111 0.291 14.162 0.213 0.285 0.096 0.291 15.600 0.300 0.220 0.080 0.080 11375+6625 0.782 7.728 0.495 0.228 0.122 0.782 7.100 0.400 0.200 0.220 0.200 Cl0016+16 0.541 28.163 0.619 0.198 0.063 0.541 34.500 0.600 0.240 0.070 0.070 0947124+762313 0.354 12.772 0.291 0.286 0.196 0.354 11.700 0.600 0.540 0.230 0.210 21594948+2407846 0.543 9.624 0.185 0.327 0.029 0.543 11.300 0.700 0.430 0.230 0.210 101 Table 4.4 (cont’d) ACCEPT2.0 Name redshift 𝐿 𝑋 e_𝐿 𝑋 𝑍 e_𝑍 M08 redshift 𝐿 𝑋 e_𝐿 𝑋 𝑍 E_𝑍 e_𝑍 1044 erg s−1 𝑍 1044 erg s−1 𝑍 LCDCS0829 0.451 41.656 0.503 0.213 0.073 0.451 38.300 0.800 0.480 0.100 0.100 02426-2132 0.314 7.085 0.436 0.151 0.115 0.314 7.900 0.400 0.080 0.180 0.080 04296-0253 0.399 8.315 0.393 0.302 0.132 0.399 9.200 0.400 0.390 0.180 0.180 04519+0006 0.430 8.608 0.533 0.411 0.206 0.430 10.900 0.800 0.440 0.320 0.280 0717+3745 0.546 51.818 0.734 0.181 0.048 0.546 57.100 0.800 0.320 0.060 0.060 07449+3927 0.698 21.465 0.924 0.179 0.067 0.697 26.300 1.000 0.310 0.090 0.090 09498+1708 0.383 16.267 0.681 0.184 0.151 0.384 17.200 0.600 0.270 0.150 0.150 13110-0311 0.494 6.435 0.280 0.228 0.071 0.494 6.700 0.200 0.270 0.140 0.140 15328+3021 0.345 10.388 0.177 0.239 0.065 0.345 12.300 0.600 0.420 0.190 0.180 16213+3810 0.465 7.763 0.291 0.199 0.066 0.463 8.700 0.500 0.260 0.120 0.120 17202+3536 0.391 10.872 0.331 0.367 0.080 0.387 11.200 0.500 0.440 0.200 0.180 19318-2635 0.352 14.152 0.168 0.374 0.147 0.352 15.300 0.500 0.110 0.100 0.100 2129-0741 0.589 19.708 1.086 0.454 0.126 0.594 21.000 1.000 0.400 0.220 0.210 22298-2756 0.324 5.967 0.279 0.397 0.108 0.324 6.900 0.300 0.250 0.180 0.170 22450+2637 0.304 6.835 0.368 0.330 0.146 0.301 6.900 0.400 0.620 0.230 0.210 04390+0520 0.208 2.670 0.145 0.251 0.107 0.208 3.000 0.300 0.350 0.260 0.220 04390+0715 0.230 8.038 0.252 0.293 0.083 0.230 8.700 0.200 0.280 0.110 0.100 04541-0300 0.550 28.925 0.536 0.206 0.082 0.550 28.800 1.200 0.330 0.160 0.150 16235+2634 0.426 5.798 0.342 0.201 0.124 0.426 7.800 0.400 0.540 0.200 0.190 22286+2036 0.412 16.485 0.569 0.352 0.116 0.412 20.800 0.600 0.410 0.130 0.130 145715+222009 0.258 5.650 0.115 0.296 0.101 0.258 6.300 0.100 0.400 0.060 0.060 021701+6412 0.453 3.720 0.188 0.379 0.154 0.453 5.300 0.300 0.540 0.260 0.230 43072 0.164 6.753 0.116 0.413 0.059 0.164 7.800 0.200 0.450 0.070 0.070 +1373+110+018 0.180 3.869 0.112 0.248 0.072 0.180 4.700 0.100 0.220 0.090 0.090 0232-4421 0.284 13.995 0.485 0.218 0.095 0.284 17.600 0.500 0.410 0.160 0.160 12269+3332 0.890 22.466 1.035 0.193 0.189 0.890 21.700 1.100 0.520 0.220 0.220 23028+0843 0.722 2.667 0.170 0.169 0.180 0.722 3.300 0.300 0.040 0.230 0.040 1504075-024816 0.215 16.069 0.219 0.238 0.070 0.215 14.300 0.400 0.350 0.140 0.130 102 Table 4.5: Global CE temperatures M08 and ACCEPT2.0 overlap. Temperatures for clusters in ACCEPT2.0 clusters that overlap with M08. ACCEPT2.0 observables are from the [0.3-1]𝑅2500 aperture. Column(1) is the ACCEPT2.0 name, columns(2,3) are the core-excised temperatures. Column(4) is the truncated cluster name from M08, and columns(5-7) are the temperatures from M08, where column(6) is the positive uncertainty and column(7) is the negative uncertainty. A2 Name 𝑘𝑇 e_𝑘𝑇 M08 Name 𝑘𝑇 E_𝑘𝑇 e_𝑘𝑇 keV keV A0068 9.717 1.436 A68 6.500 1.000 0.700 A0209 8.547 0.665 A209 7.300 0.500 0.500 A0267 7.570 0.630 A267 4.600 0.500 0.400 A0383 5.438 0.297 A383 4.200 0.400 0.200 A0402 8.228 1.236 MACS J0257.6-2209 6.900 1.100 0.700 A0586 6.241 0.395 A586 6.400 0.600 0.500 A0665 8.136 0.857 A665 7.500 0.300 0.300 A0697 11.987 1.107 A697 8.800 0.700 0.600 A0773 7.630 0.833 A773 7.000 0.400 0.400 A0907 5.772 0.537 A907 5.600 0.300 0.300 A1204 4.327 0.277 A1204 3.800 0.300 0.300 A1240 4.158 0.420 A1240 3.900 0.300 0.300 A1300 11.265 1.174 MACS J1131.8-1955 9.100 1.100 1.000 A1413 7.350 0.558 A1413 7.000 0.300 0.300 A1682 7.205 0.618 A1682 6.100 1.100 0.900 A1689 10.000 0.874 A1689 8.400 0.400 0.300 A1763 7.669 0.593 A1763 7.700 0.500 0.500 A1914 8.422 1.044 A1914 8.900 0.600 0.600 A2034 7.555 0.875 A2034 6.400 0.200 0.200 A2069 5.936 0.646 A2069 6.200 0.300 0.300 A2111 7.700 0.575 A2111 6.600 0.900 0.700 A2125 3.158 0.206 A2125 2.500 0.200 0.200 A2163 13.183 1.347 A2163 15.500 1.200 1.200 A2204 8.269 1.172 A2204 7.400 0.600 0.600 A2218 6.318 0.550 A2218 6.300 0.200 0.200 A2259 6.089 0.502 A2259 5.200 0.600 0.400 103 Table 4.5 (cont’d) A2 Name 𝑘𝑇 e_𝑘𝑇 M08 Name 𝑘𝑇 E_𝑘𝑇 e_𝑘𝑇 keV keV A2261 7.714 1.178 A2261 7.400 0.400 0.400 A2294 7.303 0.736 A2294 8.600 1.200 0.700 A2409 5.955 0.382 A2409 5.700 0.400 0.400 A2631 8.024 0.961 A2631 6.500 0.600 0.600 AS1063 11.302 0.722 AS 1063 10.400 1.400 0.900 10236+04111 8.052 0.966 Zw 3146 8.200 0.400 0.400 11375+6625 5.174 0.629 MS 1137.5+6625 5.500 1.000 0.600 Cl0016+16 9.727 0.745 MS 0015.9+1609 8.900 0.600 0.700 0947124+762313 8.581 0.841 RBS797 6.300 0.900 0.700 21594948+2407846 6.887 0.360 MACS J1423.8+2404 5.700 0.900 0.700 LCDCS0829 13.426 2.267 RX J1347.5-1145 11.700 1.100 1.100 02426-2132 5.751 0.774 MACS J0242.5-2132 5.900 0.900 0.700 04296-0253 7.000 0.900 MACS J0429.6-0253 6.800 1.100 0.600 04519+0006 5.844 0.829 MACS J0451.9+0006 4.800 1.000 0.700 0717+3745 12.868 1.576 MACS J0717.5+3745 10.100 0.500 0.500 07449+3927 7.805 0.634 MACS J0744.9+3927 7.700 0.600 0.600 09498+1708 10.311 1.712 MACS J0949.8+1708 7.700 0.900 0.900 13110-0311 6.031 0.482 MACS J1311.0-0310 6.200 0.700 0.700 15328+3021 7.129 0.720 RX J1532.9+3021 6.100 0.800 0.700 16213+3810 7.226 0.580 MACS J1621.3+3810 6.100 0.600 0.600 17202+3536 7.870 0.653 MACS J1720.2+3536 7.800 1.000 1.000 19318-2635 7.793 0.786 MACS J1931.8-2634 5.800 0.600 0.500 2129-0741 8.117 0.943 MACS J2129.4-0741 8.400 1.300 1.200 22298-2756 5.882 0.562 MACS J2229.7-2755 5.900 0.800 0.800 22450+2637 6.710 0.933 MACS J2245.0+2637 5.300 0.700 0.500 04390+0520 5.024 0.480 RX J0439+0520 3.800 0.500 0.400 04390+0715 6.528 0.534 RX J0439.0+0715 5.600 0.400 0.400 04541-0300 10.644 0.768 MS 0451.6-0305 6.600 0.700 0.600 16235+2634 6.365 0.908 MS 1621.5+2640 6.100 0.800 0.700 104 Table 4.5 (cont’d) A2 Name 𝑘𝑇 e_𝑘𝑇 M08 Name 𝑘𝑇 E_𝑘𝑇 e_𝑘𝑇 keV keV 22286+2036 8.249 0.824 MACS J2228.5+2036 7.500 0.800 0.700 145715+222009 5.120 0.434 MS 1455.0+2232 4.700 0.200 0.200 021701+6412 6.371 0.771 RX J1701+6414 6.000 1.000 0.900 43072 7.066 0.427 RX J1720.1+2638 7.200 0.400 0.400 +1373+110+018 5.605 0.799 MS 0906.5+1110 4.800 0.300 0.300 0232-4421 7.636 0.811 RX J0232.2-4420 9.200 1.100 1.000 12269+3332 13.126 1.968 CL J1226.9+3332 9.000 1.600 1.300 23028+0843 6.818 1.234 CL J2302.8+0844 4.900 1.400 1.000 1504075-024816 8.482 0.751 RX J1504-0248 8.300 0.800 0.700 4.4 Discussion Our results show no statistical dependence of CE metallicity with either redshift or luminosity. At first glance, there appears to be a marginal difference in median metallicity of Δ 𝑍e = 0.033 ± 0.011 𝑍 and Δ 𝑍 e = 0.035 ± 0.012 𝑍 between cluster samples when they are divided by redshift and luminosity, respectively. However, 10,000 simulated pairs of clusters gave 3𝜎 upper limits of ∼0.052 𝑍 for luminosity, and ∼ 0.047 𝑍 for redshift. When we fit the full set of data to a linear model with dependence on 𝐿 𝑋 and 𝑧 (Equation 4.3), we found no significant dependence of abundance on either variable (although the relationship between 𝑍 and 𝐿 𝑋 was marginally larger). 4.4.1 Comparison to observations The difference in radial abundance profiles between CC and NCC clusters in Section 4.3.1 has been observed previously, and we found that using CE abundance and luminosity measurements removes most of the core bias from the global abundance approximations, which is consistent with prior results (Buote, 2000; De Grandi et al., 2004; Maughan et al., 2008; Leccardi et al., 2010; 105 McDonald et al., 2016; Mernier et al., 2017). We also find a lack of statistical dependence of global abundance on both luminosity and redshift. We tested this with a subset of clusters that overlap with those of M08 and found that, while neither sample shows statistical differences in median metallicity according to 𝐿 𝑋 or 𝑧, the differences observed with M08 data were greater than for ACCEPT2.0 clusters. Although both sets used the same clusters, the difference in results can be attributed to systematic differences regarding data reduction, which is evidenced by Figure 4.7 where ACCEPT2.0 shows slightly higher temperature estimates than M08, with the discrepancy becoming larger for higher temperatures. The difference in temperatures can stem from a number of reasons including how background emission is accounted for and the model used to fit the X-ray spectrum. M08 extracted spectra from source-free regions of each observation, and from the same regions in the corresponding blank-sky background. This method uses the assumption that some of the field of view does not include cluster emission, which can lead to overestimation of the soft background emission. Additionally, M08 source emission was modeled as an absorbed APEC model in the 0.6-9 keV band, while ACCEPT2.0 emission was modeled as an absorbed MEKAL model and includes a robust fit to the background emission. Another difference is that M08 used chi-square and minimum counts per bin to estimate the temperatures, which can result in poor estimates in the low-SNR regime. Rather than subtraction, ACEPT2.0 statistical analysis used cstat background modeling, which does not require minimum count spectral binning (though in practice workers usually require a minimum of 1 count per energy bin). The way different spectral codes treat sources of X-ray emission introduces an extra level of systematic uncertainty, which can make global abundance approximations a little noisier, especially when combining cluster observables from different catalogs. 4.4.2 Comparison to simulations Incorporating heavy elements in simulations is a difficult task because it involves using stellar evolution models to create the metals and then various methods to distribute those metals throughout the ICM. In the past few decades, simulations have been able to reproduce the metallicity content 106 and distribution of the ICM by including contributions from stellar ejecta and AGN (Valdarnini, 2003; Ettori, 2005; Rasia et al., 2015; Biffi et al., 2017a). The radial distributions of CC and NCC clusters shown in Section 4.3.1 are in agreement with simulations which include AGN feedback (Borgani et al., 2008; Rasia et al., 2015; Biffi et al., 2017a). Our observations of both CC and NCC clusters show higher metallicity inside 𝑟 ∼ 0.3 𝑅2500 , with a steeper gradient in CC than in NCC clusters and both slopes flattening outside the core to little difference in enrichment outside the cores. Similar abundance profiles are produced by simulations which include a central AGN as the dominant source of metal distribution for massive clusters. However, AGN activity for present day clusters is not enough to enrich the outermost reaches of their gravitational potential wells. Instead, the nearly one-third Solar abundance in the outer ICM can be explained by AGN activity at earlier epochs, when the cluster halo volume was smaller (Biffi et al., 2017b; Biffi et al., 2018). The lack of present day AGN influence on the outer ICM is supported by observations of clusters from the 𝐼𝑙𝑙𝑢𝑠𝑡𝑟𝑖𝑠𝑇 𝑁𝐺 simulations, which show that abundances of the outer ICM have been relatively constant since redshift 𝑧 ∼ 2 (Vogelsberger et al., 2018). Given that we see no statistical evidence for evolution since redshift 𝑧 ∼ 0.89, the metallicity data we have analyzed in this chapter is consistent with the notion that the ICM was enriched at times earlier than at least 𝑧 ∼ 1. One way to test enrichment scenarios from simulations would be to obtain more iron abundance measurements for the ICM of clusters with 𝑧 & 1.5 − 2.5. 4.5 Summary and Conclusions Improvements in the spatial resolution of X-ray telescopes have allowed for more robust inves- tigations of global abundance trends in the ICM. Previous observations such as those of Balestra et al. (2007), which did not excise core emission, were able to detect some evolution in metallicity, but we later learned that peaks in central metallicity of CC clusters in comparison to NCCs could affect the results. However, at larger radii, the ICM appears to be oblivious to the mechanics of the core, and are thought to evolve on cosmological time scales, which makes the outer ICM a useful place for tracking the stellar evolution history of clusters with respect to redshift. We have used a sample of 302 global core-excised (CE) metallicity estimates from ACCEPT2.0 to test their depen- 107 dence on luminosity and redshift. First, we confirmed that the presence of CC and NCC clusters in our sample did not affect the global CE metallicity, which supports the idea that AGN activity is confined to the regions surrounding cluster cores. Outside the core, characteristics of the ICM are governed by processes that shape clusters over cosmological time scales. Recent attempts to quantify this evolution have found little evidence for change in recent times. Because ACCEPT2.0 is an archival sample, it is subject to selection biases which can introduce a spurious result for metallicity evolution if it is dependent on the luminosity or temperature of the ICM. We verify that there is a possible weak dependence of metallicity on luminosity or temperature, but if that (small) effect is accounted for, we see no statistically signification indication of redshift evolution in the CE metal abundances of the ICM of clusters of galaxies (with bolometric 𝐿 𝑋 & 4 × 1043 erg s−1 ). Additionally, we compared the results of an overlapping sub sample with an additional study and found differing results consistent with differences between analysis techniques, based on private communication with the original study authors. The statistical and systematic limitations of this sample and analysis indicate that outside of the cores, the global cluster abundance has changed by less than ∼ 15% between 0.02. 𝑧 .0.9. Table 4.6: Full global metallicity table for 302 ACCEPT2.0 clusters. Full sample of 302 clusters. Column(1) is the cluster name, column(2) is the redshift, column(3) is the cluster scaled radius 𝑅2500 , columns(4,5) and (6,7) are bandpass limited and bolometric luminosities and their errors, columns(8,9) are global temperature and error, columns(10,11) are global abundance and error, and column(12) is the goodness of fit for the global properties. (See Chapter 2 for details.) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f 000619+105206 0.167 466.0 1.850 0.072 2.636 0.102 5.184 0.399 0.350 0.092 1.073 00088+5215 0.104 456.0 0.751 0.030 1.052 0.043 4.711 0.300 0.164 0.087 1.264 00117-1523 0.378 451.0 6.014 0.194 8.839 0.285 5.892 0.399 0.271 0.066 1.132 A0013 0.094 461.0 0.641 0.016 0.899 0.023 5.032 0.635 0.209 0.124 1.048 A2744 0.308 640.0 13.170 0.165 23.686 0.296 10.245 0.770 0.299 0.102 1.234 0014-4952 0.752 388.0 5.112 0.336 7.853 0.517 6.880 0.966 0.406 0.162 1.096 108 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f Cl0016+16 0.541 557.0 16.147 0.355 28.163 0.619 9.727 0.745 0.198 0.063 0.964 00254-1222 0.584 470.0 8.852 0.347 14.205 0.557 7.817 0.597 0.256 0.060 1.134 00278+2616 0.367 477.0 3.049 0.194 4.615 0.294 6.438 0.978 0.039 0.082 1.086 30484-4142 0.410 559.0 7.488 0.269 13.102 0.470 9.797 1.232 0.150 0.096 1.170 00354-2015 0.364 509.0 10.772 0.355 16.792 0.554 7.187 0.645 0.338 0.090 1.146 A0068 0.255 618.0 5.993 0.281 10.429 0.489 9.717 1.436 0.662 0.210 1.270 A0085 0.055 543.0 2.609 0.019 3.925 0.028 6.170 0.588 0.358 0.150 2.290 A2813 0.292 559.0 7.287 0.223 11.762 0.361 7.950 0.739 0.287 0.086 1.303 00408+2404 0.083 437.0 0.823 0.028 1.129 0.038 3.826 0.623 0.291 0.102 1.280 A0119 0.044 541.0 1.115 0.013 1.628 0.019 5.916 0.591 0.290 0.131 3.338 A0141 0.230 525.0 3.050 0.122 4.635 0.186 6.576 0.772 0.184 0.120 1.383 01670077+0105926 0.254 419.0 2.126 0.070 2.961 0.098 4.059 0.412 0.267 0.111 1.028 01077+5408 0.107 634.0 3.881 0.057 6.191 0.092 6.642 1.385 0.184 0.136 1.257 A2895 0.227 594.0 4.742 0.143 7.809 0.236 8.394 0.858 0.301 0.107 1.471 A0193 0.049 407.0 0.398 0.011 0.536 0.015 3.725 0.483 0.307 0.115 1.191 A0209 0.206 607.0 6.310 0.161 10.466 0.266 8.547 0.665 0.250 0.082 1.313 Abell222 0.211 404.0 1.664 0.067 2.287 0.092 4.137 0.274 0.216 0.070 1.032 Abell223 0.207 473.0 1.370 0.062 1.981 0.089 5.470 0.500 0.247 0.100 1.152 01400-0555 0.454 476.0 7.056 0.392 10.985 0.610 7.139 0.822 0.256 0.103 1.149 01420+2131 0.280 526.0 5.460 0.165 8.543 0.258 7.218 0.649 0.118 0.090 1.265 01525-2853 0.341 457.0 4.091 0.126 6.018 0.186 5.815 0.584 0.058 0.081 1.125 A0267 0.231 563.0 4.166 0.105 6.600 0.166 7.570 0.630 0.393 0.106 1.224 02209-3829 0.229 414.0 2.352 0.136 3.225 0.187 4.346 0.368 0.546 0.140 1.230 A3017 0.220 538.0 3.931 0.175 6.124 0.272 7.115 0.939 0.111 0.106 1.080 0232-4421 0.284 541.0 8.792 0.304 13.995 0.485 7.636 0.811 0.218 0.095 1.259 A0368 0.220 497.0 3.443 0.181 5.101 0.268 6.080 0.768 0.305 0.138 1.276 A0370 0.375 558.0 6.827 0.110 11.422 0.183 8.753 0.459 0.285 0.074 1.206 02426-2132 0.314 459.0 4.837 0.298 7.085 0.436 5.751 0.774 0.151 0.115 1.156 109 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f AS0295 0.300 529.0 9.202 0.310 14.464 0.487 7.072 0.896 0.257 0.059 1.200 A0376 0.048 468.0 0.515 0.011 0.713 0.016 4.174 0.670 0.346 0.208 1.875 A0383 0.187 470.0 2.012 0.064 2.881 0.092 5.438 0.297 0.338 0.110 1.239 A0402 0.322 552.0 4.452 0.190 7.293 0.311 8.228 1.236 0.045 0.085 1.175 A0399 0.072 574.0 2.554 0.021 3.926 0.032 6.857 0.581 0.243 0.136 3.135 A0401 0.074 609.0 4.434 0.016 7.035 0.025 7.881 0.877 0.282 0.099 1.488 03016+0155 0.170 432.0 1.687 0.079 2.341 0.110 4.450 0.333 0.233 0.090 1.190 03037-7752 0.274 630.0 6.901 0.197 11.840 0.338 9.344 0.891 0.318 0.085 1.143 A3088 0.253 576.0 5.317 0.193 8.344 0.302 7.316 0.762 0.236 0.099 1.279 03089+2645 0.324 603.0 10.682 0.298 18.580 0.518 9.656 1.047 0.159 0.085 1.285 A3126 0.086 476.0 1.212 0.037 1.707 0.052 4.994 0.309 0.470 0.083 1.203 A3128 0.060 373.0 0.316 0.015 0.423 0.020 2.860 0.484 0.269 0.111 1.502 03311-2100 0.188 495.0 2.604 0.104 3.827 0.153 5.859 0.528 0.204 0.092 1.380 3C089 0.139 439.0 0.464 0.020 0.647 0.028 4.528 0.333 0.166 0.096 1.164 A3158 0.060 480.0 2.057 0.018 2.899 0.026 5.435 0.313 0.387 0.082 2.722 03529+1941 0.109 364.0 1.013 0.041 1.362 0.055 3.085 0.533 0.263 0.124 1.111 03588-2955 0.425 548.0 12.749 0.337 21.346 0.564 8.747 0.487 0.143 0.052 1.130 A0478 0.088 598.0 5.866 0.038 9.322 0.060 7.546 0.554 0.270 0.121 1.116 04175-1154 0.440 624.0 21.550 0.366 40.079 0.680 10.945 0.936 0.211 0.093 1.108 04258-0833 0.040 379.0 0.384 0.016 0.514 0.022 3.088 0.125 0.256 0.073 3.255 04296-0253 0.399 491.0 5.376 0.254 8.315 0.393 7.000 0.900 0.302 0.132 1.159 04371+0043 0.285 518.0 4.937 0.134 7.580 0.205 6.101 0.632 0.265 0.041 1.251 04390+0715 0.230 513.0 5.310 0.166 8.038 0.252 6.528 0.534 0.293 0.083 1.160 04390+0520 0.208 451.0 1.883 0.103 2.670 0.145 5.024 0.480 0.251 0.107 1.220 A0514 0.071 402.0 0.317 0.014 0.430 0.018 3.959 0.534 0.257 0.035 1.588 A3292 0.172 416.0 1.775 0.082 2.441 0.112 4.204 0.297 0.271 0.098 1.410 04519+0006 0.430 443.0 5.882 0.364 8.608 0.533 5.844 0.829 0.411 0.206 1.101 04541-0300 0.550 576.0 15.974 0.296 28.925 0.536 10.644 0.768 0.206 0.082 1.309 110 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f 04552+0657 0.425 478.0 6.452 0.414 9.878 0.634 6.845 0.998 0.571 0.226 1.135 0509-5342 0.463 565.0 4.295 0.208 7.291 0.353 9.069 1.716 0.145 0.164 1.176 A3322 0.200 544.0 3.793 0.142 5.786 0.216 6.649 0.599 0.146 0.092 1.104 05107-0801 0.220 552.0 8.412 0.212 13.101 0.330 7.152 0.434 0.280 0.060 1.082 AS0520 0.295 573.0 6.561 0.201 10.757 0.330 8.269 0.732 0.140 0.076 1.167 05207-1328 0.340 515.0 5.821 0.181 9.131 0.284 7.335 0.692 0.345 0.111 1.265 A3343 0.191 513.0 3.027 0.089 4.563 0.135 6.429 0.528 0.269 0.099 1.175 05282-2942 0.158 434.0 1.634 0.086 2.245 0.119 4.607 0.499 0.564 0.197 1.327 RBS0653 0.284 594.0 7.669 0.109 13.057 0.185 8.558 0.836 0.258 0.066 1.153 28658-3125 0.210 536.0 3.759 0.128 5.678 0.194 6.484 0.540 0.301 0.091 1.060 A0545 0.154 582.0 3.448 0.047 5.431 0.073 7.372 0.311 0.124 0.052 1.265 05329-3701 0.275 594.0 6.799 0.197 11.333 0.329 8.644 0.843 0.136 0.080 1.134 0542-4100 0.640 410.0 3.762 0.216 5.691 0.327 6.455 0.885 0.108 0.125 1.168 05470-3904 0.210 457.0 0.974 0.060 1.398 0.086 5.186 0.699 0.046 0.106 1.352 A3364 0.148 571.0 3.151 0.079 4.925 0.124 7.194 0.546 0.126 0.081 1.411 A0550 0.099 507.0 2.168 0.062 3.165 0.090 5.669 0.298 0.141 0.067 1.202 05534-3342 0.407 649.0 13.416 0.212 24.118 0.382 10.463 0.680 0.192 0.055 1.119 A3376 0.046 496.0 0.541 0.006 0.762 0.008 4.696 0.499 0.386 0.121 3.323 A3378 0.141 453.0 3.198 0.099 4.474 0.139 4.780 0.273 0.360 0.088 1.160 06163-2156 0.171 557.0 2.994 0.067 4.678 0.105 7.236 0.511 0.313 0.086 1.178 AS0579 0.152 449.0 1.508 0.056 2.119 0.078 4.789 0.352 0.213 0.092 1.146 13959+2418 0.270 539.0 7.876 0.283 12.273 0.440 7.189 0.635 0.378 0.086 1.169 A3391 0.051 549.0 1.028 0.021 1.498 0.031 5.794 0.222 0.232 0.068 3.227 A3399 0.203 542.0 3.297 0.073 5.045 0.111 6.759 0.453 0.276 0.084 1.084 16765+1764 0.174 517.0 4.844 0.111 7.219 0.165 6.176 0.412 0.229 0.080 1.140 AS0592 0.222 598.0 7.970 0.188 13.233 0.313 8.581 0.651 0.312 0.080 1.363 A3404 0.167 640.0 6.357 0.151 10.236 0.244 7.851 0.642 0.049 0.062 1.148 A0562 0.110 353.0 0.392 0.019 0.526 0.025 2.946 0.451 0.237 0.083 1.122 111 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f 0.296 708.0 24.166 0.131 46.462 0.252 12.364 1.145 0.208 0.066 1.326 0717+3745 0.546 647.0 25.993 0.368 51.818 0.734 12.868 1.576 0.181 0.048 1.136 A0586 0.171 516.0 3.337 0.093 4.977 0.139 6.241 0.395 0.374 0.075 1.157 07357+7421 0.216 516.0 3.873 0.033 5.843 0.050 6.447 0.632 0.331 0.103 1.236 07449+3927 0.698 442.0 13.375 0.576 21.465 0.924 7.805 0.634 0.179 0.067 1.114 PKS0745-19 0.103 628.0 5.794 0.034 9.484 0.055 8.360 0.483 0.304 0.083 1.593 A0598 0.189 457.0 1.695 0.085 2.417 0.121 5.052 0.538 0.068 0.091 1.291 A0611 0.288 571.0 4.697 0.124 7.783 0.205 7.993 0.430 0.408 0.118 1.017 A0644 0.070 567.0 2.890 0.031 4.410 0.047 6.580 0.821 0.317 0.089 2.778 08196+6336 0.119 384.0 0.758 0.044 1.025 0.060 3.498 0.321 0.170 0.088 1.238 08232+0425 0.225 427.0 1.718 0.107 2.383 0.148 4.660 0.514 0.510 0.168 1.271 A0665 0.182 614.0 4.817 0.059 7.910 0.096 8.136 0.857 0.260 0.075 1.314 2MFGC06756 0.241 445.0 2.694 0.055 3.823 0.078 5.082 0.508 0.287 0.098 1.057 A3411 0.169 519.0 2.842 0.053 4.247 0.079 6.161 0.454 0.348 0.095 1.119 084254+292723 0.194 505.0 1.485 0.048 2.174 0.070 5.023 0.901 0.519 0.181 1.052 A0697 0.282 713.0 12.109 0.291 23.094 0.555 11.987 1.107 0.333 0.106 1.311 08579+2107 0.230 414.0 2.167 0.079 2.994 0.110 4.517 0.176 0.356 0.160 0.993 +1373+110+018 0.180 475.0 2.688 0.078 3.869 0.112 5.605 0.799 0.248 0.072 1.140 09112+1746 0.505 460.0 5.371 0.324 8.253 0.497 6.808 0.894 0.133 0.102 1.124 20913454+405628 0.442 457.0 4.631 0.189 6.963 0.284 6.416 0.590 0.406 0.092 1.152 A0773 0.217 581.0 5.866 0.132 9.528 0.214 7.630 0.833 0.272 0.081 1.237 HydraA 0.055 431.0 1.145 0.005 1.566 0.006 3.951 0.219 0.289 0.046 1.219 092017+303027 0.258 506.0 3.036 0.123 4.554 0.184 6.352 0.661 0.352 0.105 1.115 A0795 0.136 466.0 1.863 0.048 2.645 0.068 5.002 0.300 0.164 0.062 1.275 0938209+520243 0.360 477.0 5.414 0.181 8.169 0.274 6.417 0.504 0.165 0.073 1.081 A0853 0.166 430.0 0.861 0.054 1.194 0.075 4.441 0.481 0.236 0.129 1.146 A0868 0.153 432.0 2.610 0.086 3.615 0.119 4.414 0.222 0.252 0.070 1.137 0947124+762313 0.354 550.0 7.738 0.176 12.772 0.291 8.581 0.841 0.286 0.196 1.088 112 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f 09498+1708 0.383 576.0 9.104 0.381 16.267 0.681 10.311 1.712 0.184 0.151 1.258 09496+5207 0.214 479.0 2.228 0.048 3.243 0.069 5.346 0.581 0.291 0.096 1.088 A0907 0.153 504.0 2.833 0.056 4.152 0.083 5.772 0.537 0.335 0.142 1.381 26441+1948 0.240 567.0 3.615 0.128 5.726 0.203 7.503 0.702 0.090 0.077 1.126 10005+4409 0.154 367.0 1.065 0.070 1.437 0.095 3.278 0.268 0.183 0.095 1.243 10061+1201 0.221 488.0 2.803 0.071 4.111 0.105 5.860 0.459 0.305 0.027 1.133 10105-1239 0.301 494.0 4.060 0.084 6.139 0.127 6.484 0.395 0.222 0.062 1.108 A0963 0.206 527.0 4.534 0.076 6.861 0.115 6.364 0.782 0.226 0.113 1.259 A0970 0.059 454.0 0.817 0.027 1.134 0.038 4.504 0.402 0.276 0.014 1.387 A0980 0.158 529.0 3.039 0.090 4.606 0.136 5.902 1.038 0.220 0.086 1.204 10236+04111 0.291 589.0 8.464 0.127 14.162 0.213 8.052 0.966 0.285 0.096 1.289 1023399+490838 0.144 533.0 3.321 0.111 5.034 0.168 6.513 0.589 0.156 0.083 1.099 A3444 0.253 552.0 7.473 0.123 12.037 0.197 7.915 0.451 0.338 0.060 0.974 A1033 0.126 501.0 1.475 0.025 2.143 0.037 5.886 0.583 0.266 0.038 1.207 A1068 0.138 463.0 1.884 0.042 2.664 0.060 5.225 0.552 0.370 0.092 1.078 10569-03373 0.823 401.0 7.212 0.383 11.420 0.607 7.494 1.083 0.096 0.107 1.444 11089+0906 0.449 472.0 5.708 0.269 8.786 0.414 6.863 0.744 0.193 0.106 1.128 A1190 0.075 397.0 0.599 0.028 0.808 0.038 3.597 0.190 0.271 0.083 1.247 A1201 0.169 492.0 2.527 0.054 3.681 0.079 5.309 0.543 0.359 0.060 1.254 A1204 0.171 423.0 1.629 0.066 2.253 0.092 4.327 0.277 0.218 0.084 1.310 1115+5319 0.466 604.0 8.139 0.364 14.554 0.651 10.328 1.639 0.141 0.157 1.084 11158+0129 0.352 589.0 8.020 0.227 13.674 0.388 9.180 0.730 0.189 0.068 1.253 A1240 0.159 415.0 0.492 0.032 0.675 0.044 4.158 0.420 0.279 0.137 1.411 A1285 0.106 496.0 2.267 0.042 3.281 0.060 5.361 0.617 0.314 0.026 1.219 A1300 0.307 786.0 9.614 0.240 17.836 0.446 11.265 1.174 0.262 0.099 1.285 11375+6625 0.782 334.0 5.411 0.347 7.728 0.495 5.174 0.629 0.228 0.122 1.088 1142248+583205 0.311 609.0 7.812 0.182 13.142 0.306 8.855 0.679 0.127 0.073 1.166 A1413 0.143 578.0 4.175 0.044 6.581 0.070 7.350 0.558 0.231 0.089 1.459 113 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f 17981192+4979669 0.383 569.0 7.801 0.394 13.915 0.702 10.276 1.691 0.267 0.141 1.111 29251+2198 0.300 606.0 5.929 0.172 9.902 0.287 8.702 0.784 0.233 0.076 1.104 A1446 0.103 390.0 0.707 0.019 0.950 0.025 3.606 0.513 0.332 0.163 1.123 12062-0847 0.440 606.0 16.980 0.490 31.633 0.913 11.369 1.423 0.225 0.109 1.235 12154-3900 0.119 494.0 1.605 0.038 2.315 0.055 5.505 0.361 0.429 0.110 1.167 121733+033929 0.077 576.0 2.565 0.050 3.947 0.077 6.694 0.647 0.292 0.170 2.787 121831+401236 0.320 475.0 4.257 0.182 6.320 0.271 6.090 0.651 0.210 0.116 1.216 122648+215157 0.370 407.0 1.608 0.082 2.259 0.115 4.785 0.474 0.191 0.095 1.082 12269+3332 0.890 539.0 11.315 0.521 22.466 1.035 13.126 1.968 0.193 0.189 1.117 A1553 0.165 568.0 3.879 0.113 6.048 0.176 7.238 0.587 0.518 0.105 1.136 12342+0947 0.229 421.0 1.747 0.111 2.439 0.154 4.552 0.485 0.134 0.112 1.255 A1576 0.279 566.0 2.870 0.107 4.654 0.174 8.001 0.772 0.057 0.063 1.187 A1644 0.047 481.0 0.818 0.007 1.171 0.009 4.858 0.506 0.344 0.141 3.047 A1650 0.084 514.0 2.247 0.018 3.278 0.026 5.726 0.524 0.286 0.106 1.737 1259334+600409 0.330 501.0 3.904 0.145 6.024 0.223 6.894 0.515 0.112 0.068 1.062 A1664 0.128 468.0 1.930 0.041 2.747 0.059 4.732 0.484 0.239 0.047 1.178 A1668 0.063 383.0 0.304 0.019 0.409 0.026 3.326 0.291 0.245 0.094 1.442 1305589+263048 0.305 537.0 4.356 0.192 6.829 0.300 7.269 0.948 0.151 0.097 1.082 A1682 0.234 550.0 3.710 0.105 5.803 0.164 7.205 0.618 0.116 0.092 1.131 13110-0311 0.494 428.0 4.349 0.189 6.435 0.280 6.031 0.482 0.228 0.071 1.128 A1689 0.183 676.0 8.559 0.103 15.062 0.181 10.000 0.874 0.279 0.110 1.410 1315052+514902 0.291 583.0 6.692 0.136 11.224 0.229 8.765 0.771 0.025 0.048 1.149 A1736 0.046 387.0 0.638 0.013 0.854 0.017 3.070 0.313 0.322 0.158 3.124 SSGC081 0.050 398.0 0.418 0.015 0.565 0.020 3.207 0.393 0.282 0.087 2.178 A1750C 0.068 450.0 0.445 0.017 0.617 0.024 3.861 0.768 0.263 0.095 1.310 A1750N 0.084 397.0 0.458 0.022 0.621 0.029 3.586 0.230 0.165 0.070 1.350 A3562 0.049 470.0 0.826 0.018 1.149 0.026 4.701 0.503 0.340 0.125 3.211 A1763 0.223 555.0 6.919 0.180 11.013 0.286 7.669 0.593 0.388 0.084 1.252 114 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f A1767 0.070 495.0 1.188 0.037 1.703 0.053 5.301 0.290 0.293 0.081 1.412 A1775 0.072 408.0 0.923 0.011 1.238 0.015 3.760 0.413 0.503 0.110 1.616 LCDCS0829 0.451 718.0 20.538 0.248 41.656 0.503 13.426 2.267 0.213 0.073 1.160 13546+7715 0.397 467.0 4.673 0.251 7.024 0.378 6.384 0.815 0.314 0.119 1.103 A1831 0.061 399.0 0.538 0.017 0.720 0.023 3.541 0.159 0.447 0.077 1.347 1359495+623047 0.322 509.0 4.018 0.121 6.184 0.186 6.859 0.590 0.199 0.084 1.468 A1835 0.253 646.0 12.004 0.170 21.457 0.303 9.175 1.354 0.348 0.157 1.213 11382+4435 0.226 495.0 2.620 0.128 3.891 0.189 6.017 0.680 0.004 0.053 1.037 A1882a 0.141 385.0 0.316 0.017 0.424 0.022 3.317 0.158 0.302 0.080 1.129 21594948+2407846 0.543 462.0 6.151 0.118 9.624 0.185 6.887 0.360 0.327 0.029 1.000 A1914 0.171 633.0 9.446 0.147 15.799 0.246 8.422 1.044 0.213 0.053 1.398 1427161+440730 0.498 601.0 6.679 0.271 11.975 0.486 10.403 1.424 0.236 0.142 1.328 14276-2521 0.318 410.0 2.061 0.095 2.865 0.132 4.689 0.340 0.443 0.114 1.186 A1930 0.131 440.0 0.951 0.038 1.311 0.053 4.366 0.629 0.587 0.028 1.235 1942 0.224 465.0 1.401 0.046 2.016 0.066 5.305 0.486 0.373 0.031 1.219 A1991 0.059 346.0 0.329 0.010 0.438 0.013 2.695 0.319 0.299 0.114 1.106 145715+222009 0.258 452.0 3.947 0.081 5.650 0.115 5.120 0.434 0.296 0.101 1.135 AS0780 0.236 551.0 5.352 0.074 8.395 0.117 7.021 0.628 0.310 0.122 1.065 A2009 0.153 543.0 3.537 0.097 5.386 0.148 6.695 0.309 0.443 0.071 1.392 1504075-024816 0.215 620.0 9.519 0.130 16.069 0.219 8.482 0.751 0.238 0.070 1.463 A2034 0.113 595.0 2.975 0.031 4.685 0.049 7.555 0.875 0.303 0.108 1.568 15149-1523 0.223 616.0 5.561 0.090 9.372 0.151 8.899 0.481 0.141 0.048 1.105 A2061 0.078 457.0 1.171 0.022 1.631 0.031 4.310 0.527 0.278 0.118 1.083 MKW03s 0.045 394.0 0.650 0.006 0.875 0.008 3.434 0.404 0.261 0.113 2.072 A2069 0.116 525.0 1.793 0.032 2.675 0.048 5.936 0.646 0.301 0.128 1.712 15242-3154 0.103 444.0 1.365 0.019 1.900 0.026 4.426 0.719 0.362 0.129 1.326 15328+3021 0.345 522.0 6.570 0.112 10.388 0.177 7.129 0.720 0.239 0.065 1.141 A2107 0.041 434.0 0.433 0.009 0.588 0.012 3.766 0.480 0.265 0.114 3.251 115 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f A2111 0.229 567.0 3.754 0.081 5.996 0.129 7.700 0.575 0.186 0.085 1.146 A2104 0.153 565.0 3.731 0.049 5.815 0.077 7.200 1.018 0.245 0.153 1.354 A2125 0.246 343.0 0.632 0.031 0.850 0.042 3.158 0.206 0.197 0.089 1.133 A2124 0.066 485.0 0.326 0.012 0.463 0.017 4.839 0.219 0.354 0.091 1.104 A2142 0.091 626.0 4.832 0.043 7.887 0.069 7.675 0.570 0.276 0.080 3.074 15583-1410 0.097 483.0 2.001 0.021 2.850 0.029 5.018 0.356 0.371 0.106 1.330 A2147 0.035 449.0 0.537 0.007 0.737 0.010 4.275 0.343 0.321 0.101 4.436 A2163 0.203 795.0 20.636 0.140 42.292 0.288 13.183 1.347 0.240 0.045 1.603 16213+3810 0.465 482.0 4.964 0.186 7.763 0.291 7.226 0.580 0.199 0.066 1.167 16235+2634 0.426 449.0 3.854 0.228 5.798 0.342 6.365 0.908 0.201 0.124 1.005 A2187 0.184 554.0 2.384 0.100 3.644 0.152 6.709 0.765 0.183 0.122 1.389 A2204 0.152 654.0 6.250 0.044 10.792 0.077 8.269 1.172 0.319 0.143 1.623 A2218 0.176 520.0 4.315 0.084 6.482 0.127 6.318 0.550 0.201 0.076 1.287 A2219 0.226 699.0 14.778 0.091 27.420 0.169 11.017 0.888 0.280 0.093 1.223 HerculesA 0.155 419.0 1.836 0.034 2.531 0.047 3.653 1.309 0.181 0.097 1.224 021701+6412 0.453 453.0 2.479 0.125 3.720 0.188 6.371 0.771 0.379 0.154 1.122 A2244 0.097 515.0 2.680 0.024 3.927 0.036 5.919 0.484 0.327 0.096 1.106 A2256 0.058 586.0 3.438 0.033 5.363 0.052 6.782 0.465 0.381 0.135 1.886 A2249 0.082 486.0 1.267 0.035 1.811 0.051 5.153 0.342 0.168 0.086 1.204 A2255 0.081 530.0 2.107 0.026 3.133 0.038 6.086 0.559 0.325 0.113 1.828 A2259 0.164 508.0 3.248 0.119 4.806 0.176 6.089 0.502 0.427 0.128 1.254 43072 0.164 560.0 4.348 0.075 6.753 0.116 7.066 0.427 0.413 0.059 1.371 17202+3536 0.391 530.0 6.766 0.206 10.872 0.331 7.870 0.653 0.367 0.080 1.279 A2261 0.224 593.0 7.182 0.156 11.669 0.253 7.714 1.178 0.349 0.077 1.276 A2294 0.169 570.0 4.578 0.170 7.178 0.266 7.303 0.736 0.260 0.106 1.415 17316+2251 0.366 551.0 6.784 0.211 11.278 0.351 8.608 0.849 0.299 0.123 1.320 17421+3306 0.076 437.0 1.099 0.017 1.507 0.024 4.076 0.352 0.374 0.179 1.653 174715+451155 0.157 447.0 1.518 0.066 2.128 0.093 4.729 0.378 0.182 0.084 1.142 116 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f 17502+3504 0.171 442.0 1.689 0.078 2.364 0.109 4.639 0.356 0.126 0.083 1.187 18044+1002 0.152 545.0 5.159 0.144 8.034 0.225 7.097 0.592 0.092 0.075 1.225 A2302 0.179 447.0 1.324 0.055 1.862 0.077 4.821 0.382 0.203 0.096 1.157 18290+6913 0.203 402.0 0.843 0.044 1.151 0.060 4.057 0.305 0.335 0.109 1.234 18521+5711 0.109 418.0 0.465 0.019 0.635 0.026 4.003 0.283 0.259 0.096 1.345 18539+6822 0.093 423.0 1.031 0.025 1.419 0.034 4.129 0.221 0.190 0.074 1.199 33709-2597 0.264 563.0 6.544 0.138 10.438 0.221 7.658 0.539 0.118 0.070 1.181 A2319 0.056 670.0 5.846 0.046 10.028 0.078 8.664 1.413 0.319 0.131 3.532 19318-2635 0.352 540.0 8.805 0.104 14.152 0.168 7.793 0.786 0.374 0.147 1.326 AS0821 0.237 511.0 5.443 0.174 8.184 0.261 6.386 0.506 0.302 0.072 1.108 19383+5409 0.260 539.0 8.739 0.350 13.629 0.546 7.202 0.728 0.356 0.091 1.124 19473-7623 0.217 574.0 5.483 0.179 8.604 0.280 7.337 0.632 0.338 0.086 1.214 A3653 0.109 450.0 0.524 0.015 0.733 0.021 4.781 0.341 0.345 0.071 1.222 20035-2323 0.317 599.0 7.858 0.190 13.401 0.324 9.178 0.804 0.131 0.072 1.222 20148-2430 0.161 560.0 4.182 0.099 6.499 0.154 6.629 0.996 0.447 0.125 1.190 2023-5535 0.232 609.0 5.848 0.172 9.627 0.283 8.387 0.761 0.291 0.085 1.121 20318-4037 0.342 494.0 7.965 0.430 12.201 0.659 6.735 0.918 0.128 0.117 1.116 A3695 0.089 550.0 1.909 0.042 2.887 0.064 6.465 0.427 0.161 0.084 1.352 20460-3430 0.423 428.0 4.194 0.216 6.100 0.314 5.606 0.447 0.212 0.086 1.136 20499-3216 0.325 528.0 5.290 0.221 8.338 0.348 7.423 0.952 0.262 0.109 1.259 A3739 0.165 516.0 2.874 0.120 4.251 0.177 6.084 0.527 0.413 0.111 1.096 IC1365 0.049 429.0 0.574 0.025 0.781 0.034 3.966 0.438 0.509 0.083 2.480 2129-0741 0.589 479.0 12.133 0.669 19.708 1.086 8.117 0.943 0.454 0.126 1.130 2135-0102 0.325 557.0 4.768 0.219 7.826 0.360 8.365 1.066 0.580 0.154 1.246 A2355 0.124 586.0 1.465 0.045 2.290 0.071 7.240 0.690 0.289 0.118 1.276 2135-5726 0.427 477.0 3.586 0.199 5.541 0.307 6.922 1.301 0.108 0.157 1.099 21402-2339 0.313 468.0 3.985 0.110 5.860 0.162 5.638 0.740 0.306 0.144 1.070 A3809 0.062 354.0 0.426 0.014 0.565 0.019 3.117 0.292 0.413 0.138 1.303 117 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f 2148-6116 0.571 436.0 3.484 0.229 5.327 0.351 6.735 1.175 0.272 0.195 1.039 A2384 0.094 516.0 1.119 0.018 1.628 0.026 5.246 0.839 0.390 0.162 2.330 A2390 0.228 668.0 13.625 0.092 25.178 0.169 10.095 1.521 0.290 0.096 1.068 21538+3746 0.292 608.0 11.047 0.148 19.077 0.256 8.940 1.321 0.240 0.103 1.148 A2409 0.148 510.0 4.281 0.134 6.289 0.197 5.955 0.382 0.462 0.093 1.292 A3827 0.098 585.0 3.243 0.032 5.080 0.050 7.338 0.789 0.339 0.144 1.302 A2415 0.058 344.0 0.401 0.012 0.534 0.016 2.583 0.284 0.347 0.094 1.236 22117-0349 0.270 655.0 6.301 0.219 11.029 0.383 9.815 1.315 0.221 0.121 1.394 3C444 0.153 473.0 0.613 0.021 0.876 0.030 4.379 0.393 0.332 0.098 1.334 A2426 0.098 522.0 1.671 0.053 2.451 0.077 5.825 0.389 0.251 0.100 1.305 2214-1359 0.483 530.0 10.888 0.419 18.292 0.705 8.833 0.989 0.194 0.093 1.120 A3854 0.149 472.0 2.281 0.081 3.256 0.116 5.181 0.394 0.258 0.092 1.197 22186-3853 0.138 499.0 3.292 0.092 4.789 0.134 5.604 0.330 0.200 0.075 1.240 A2445 0.166 414.0 1.718 0.057 2.340 0.077 4.162 0.215 0.545 0.086 1.190 A3880 0.058 356.0 0.341 0.018 0.453 0.023 2.897 0.277 0.305 0.143 2.280 22286+2036 0.412 550.0 10.081 0.348 16.485 0.569 8.249 0.824 0.352 0.116 1.176 22298-2756 0.324 464.0 4.070 0.190 5.967 0.279 5.882 0.562 0.397 0.108 1.233 2233-5339 0.480 466.0 4.392 0.264 6.750 0.406 6.791 1.168 0.075 0.121 1.089 A2457 0.059 414.0 0.550 0.015 0.744 0.021 3.595 0.099 0.326 0.059 1.352 22428+5301 0.192 595.0 4.117 0.053 6.747 0.088 7.813 1.165 0.183 0.120 1.048 2243198-093530 0.432 488.0 14.006 0.520 21.842 0.811 7.179 0.672 0.267 0.085 1.214 22450+2637 0.304 499.0 4.480 0.241 6.835 0.368 6.710 0.933 0.330 0.146 1.224 A3911 0.097 544.0 2.198 0.061 3.262 0.090 6.106 0.393 0.285 0.081 1.183 A2485 0.247 511.0 2.703 0.119 4.043 0.178 6.250 0.714 0.231 0.129 1.247 AS1063 0.347 663.0 22.560 0.412 41.905 0.765 11.302 0.722 0.359 0.070 1.219 A3921 0.093 522.0 1.981 0.037 2.916 0.054 5.766 0.762 0.360 0.085 1.879 A2507 0.196 414.0 1.003 0.065 1.377 0.089 4.309 0.433 0.426 0.154 1.069 2259-6057 0.750 411.0 4.949 0.246 7.715 0.384 7.265 1.064 0.694 0.215 1.200 118 Table 4.6 (cont’d) ACCEPT2.0 Name redshift R2500 LX e_LX LX e_LX Z e_Z kT e_kT 𝜒2 [0.5-8 keV] [bol] (kpc) (1044 erg s−1 ) (1044 erg s−1 ) (𝑍 ) (keV) d.o.f 23028+0843 0.722 407.0 1.736 0.111 2.667 0.170 6.818 1.234 0.169 0.180 1.139 A2537 0.295 506.0 4.650 0.104 7.083 0.158 6.629 0.625 0.224 0.038 1.157 23115+0338 0.300 598.0 7.260 0.281 12.544 0.486 9.518 1.005 0.334 0.103 1.333 A2556 0.087 413.0 0.814 0.018 1.105 0.024 3.756 0.398 0.356 0.086 1.157 AS1101 0.058 345.0 0.541 0.010 0.726 0.013 2.698 0.286 0.199 0.089 2.076 A2597 0.085 442.0 0.878 0.010 1.214 0.015 4.266 0.259 0.279 0.080 1.310 A2626 0.055 382.0 0.443 0.012 0.593 0.016 3.263 0.379 0.378 0.131 1.119 A2631 0.273 580.0 7.191 0.246 11.658 0.398 8.024 0.961 0.169 0.100 1.254 A4023 0.193 507.0 1.996 0.082 2.984 0.123 6.256 0.635 0.268 0.117 1.216 A2645 0.251 512.0 3.698 0.171 5.582 0.258 6.470 0.782 0.297 0.119 1.118 23442-0422 0.079 450.0 1.473 0.038 2.031 0.052 4.501 0.143 0.406 0.261 1.422 A2657 0.040 403.0 0.583 0.016 0.785 0.021 3.567 0.307 0.302 0.165 3.162 A4038 0.028 369.0 0.394 0.007 0.525 0.009 2.878 0.263 0.286 0.118 3.540 A2665 0.056 458.0 0.489 0.018 0.680 0.025 4.553 0.294 0.310 0.095 1.412 A2667 0.230 556.0 7.819 0.208 12.434 0.331 7.604 0.677 0.163 0.084 1.046 A2670 0.076 435.0 0.743 0.021 1.019 0.028 4.001 0.706 0.310 0.114 2.206 119 CHAPTER 5 PIPELINE FOR THE REDUCTION OF DATA FROM THE SOAR ADAPTIVE-OPTICS MULTI-OBJECT SPECTROGRAPH (SAMOS) The 𝑆 𝐴𝑀𝑂𝑆 instrument is a multi-object spectrograph which uses a Digital Micromirror Device (DMD) (Smee et al., 2018) to focus light towards either an imaging or spectroscopy channel. The DMD allows for multiple slit configurations in a single observing run. Multi-object capabilities of the Goodman High Throughput Spectrograph require slit masks to be made in advance, and are installed in the afternoon leading up to the observation. 𝑆 𝐴𝑀𝑂𝑆 has the unique feature of being able to create on-the-fly slit patterns, which will be saved in the 𝐹 𝐼𝑇 𝑆 headers. The instrument is not set to be commissioned until at least 2021, so the current version of the 𝑆 𝐴𝑀𝑂𝑆 data reduction pipeline (SRP) uses multi-object data from the SOAR Goodman Spectrograph. This SRP will provide the foundation for 𝑆 𝐴𝑀𝑂𝑆 data reduction upon its commissioning. The test data used for the SRP was taken by SOAR Goodman on March 19, 2014. Eventually, the pipeline will be used to reduce multi-object spectroscopy data taken with the SOAR Adaptive-Module Optical Spectrograph (SAMOS). There are two main parts to the SRP: basic image reduction and spectroscopic reduction. For optical spectroscopy, we use detectors called charge-coupled devices (CCDs) to detect and convert light to a digital signal. When sensors on the CCD are hit by incoming photons, they save the information and it gets read out to a two-dimensional pixel array after the exposure. The exposure is saved as a 𝐹 𝐼𝑇 𝑆 (Flexible Image Transport System) file, which is able to store both the image data and calibration information in a header. There are a couple important systematics at play during exposure and readout, an obvious one being that CCDs are not perfect photon detectors. This imperfection means that pixels can vary in sensitivity across the array. We correct for this variation by normalizing, or flattening, the data. Additionally, CCDs are not completely cleared of their information after readout, which means that each exposure starts with a certain amount of signal. This “pre-charge” is called the readout bias. 120 sky lines spectrum spatial axis overscan dispersion axis Figure 5.1: Cartoon multi-object spectra. Simplified depiction of multi-object spectra. Sky light is also dispersed and appears as emission lines on either side of the spectrum. The lines are the same in each spectrum, but shift depending on slit position. Sometimes a region of the CCD called the “overscan” is used to correct for this readout noise. A cartoon layout of a CCD is shown in Figure 5.1. When dispersed photons1 hit the detector, they are mapped to the 2-D array, the mapping of light intensity–i.e., location along the spectroscopic slit (1 dimension), and wavelength (orthogonal dimension to slit location)–is not perfectly aligned with the pixels. We usually correct for this distortion by fitting the continuum (track of illuminated pixels) of a standard star as a function of 1 Like a rainbow. 121 pixel location (Marsh, 1989; Horne, 1986). This spectrum trace, shapes measured at different slit positions, can be used to rectify the corresponding science images. Once the correction is applied to the 2-D spectrum, we collapse it to one dimension for wavelength calibration. Wavelength calibration involves converting pixel coordinates of the 1-D spectrum to wavelength coordinates based on characteristics of the spectrum grating. Because each instrument comes with its own systematics, image reduction is rarely a cookie- cutting exercise, and spectral tracing and wavelength calibration are particularly difficult and tedious. Thus far, the Image Reduction and Analysis Facility (IRAF) (Tody, 1986, 1993) has been the only reduction package with enough robustness and versatility to make it the go-to spectroscopic data reduction source for nearly 30 years. However, the command language (CL) in which IRAF is written has been unable to keep up with more versatile languages such as Python. IRAF’s imminent demise is a source of worry, and there have only been a few efforts made to start the transition to a new generic reduction package (Lucas et al., 2018; Price-Whelan et al., 2018). The goal of the SRP is to have a complete spectral reduction package for 𝑆 𝐴𝑀𝑂𝑆 data which is completely independent of IRAF. 5.1 Pipeline Organization The 𝑆 𝐴𝑀𝑂𝑆 reduction pipeline is meant to be run within a 𝐽𝑢 𝑝𝑦𝑡𝑒𝑟 notebook, as it allows for the user to track the reduction progress. Begin each new session with the execution of the SAMOSNight class. This class stores the data and information for a particular night (defined by some observation ID), which is updated with each step of the data reduction. The current capabilities of the 𝑆 𝐴𝑀𝑂𝑆 pipeline are summarized in table 5.1, and each step is further described in the sections below. Each section is prefaced by the code used to execute the step. The code represented in this chapter is from the tutorial jupyter_NBtutorial/SAMOS_tutorial. Major updates for this pipeline will occur when we obtain test data from the 𝑆 𝐴𝑀𝑂𝑆 instrument. It should therefore be noted that some parts of the pipeline in its current state employ more generic data reduction methods, with the plan that more sophisticated methods can be chosen and applied once the actual parameters of the operational system are better known. Until then, we have adapted 122 Table 5.1: 𝑺 𝑨𝑴𝑶𝑺 reduction pipeline status. Current status of the 𝑆 𝐴𝑀𝑂𝑆 reduction pipeline. Each row describes a step in the data reduction process, its current completion status, and the planned updates for accomodating 𝑆 𝐴𝑀𝑂𝑆 data. Each step’s current status is in reference to its processing of the Goodman test data. Reduction Step Step Description Current Sta- Planned Updates tus SAMOSNight(...) initialize pipeline and complete This will eventually in- organize raw data clude the ability to make SQL queries for 𝑆 𝐴𝑀𝑂𝑆 data stored on a separate server ImageProcessor(...) image trim, overscan, complete add bias level correction flat correction using bias frames SlitBuckets(...) trace and crop individ- complete slit tracing method will ual slits need to read 𝑆 𝐴𝑀𝑂𝑆 slit mask patterns from the 𝐹 𝐼𝑇 𝑆 headers WaveCalBuckets(...) fits wavelength solution complete linelists for first-guess using comparison lamp solutions will refer to data those obtained from cal- ibration lamps observed with SAMOS Spectral Extraction extract source spectrum in progress method will outline and from slit crop out main spectral source Sky Subtraction/Flux subtract sky contribu- in progress Calibration tion from spectrum some working assumptions about the performance of the spectrograph which may differ from its actual performance. For instance, the pipeline assumes that the spectrum will not perfectly co-align with the rows and columns of the detector, the data have an overscan region which can be used for bias calibrations, and that other calibrations such as arc lamp exposures can be taken in the afternoon or during the night. The methods used for 𝑆 𝐴𝑀𝑂𝑆 data anaysis are heavily influenced by the Goodman Spectroscopic Pipeline (Torres-Robledo & Briceño, 2019) and the Astropy image reduction package ccdproc (Craig et al., 2017). The working directory for SRP contains the following required files and directories: 123 • UNCOMP_GDMN_DATA/: directory containing Goodman observations. • SAMOS_DRP/: directory containing main pipeline modules. • comp_refs/: directory containing linelists and wavelength solutions for comparison lamps in every spectroscopic configuration. • slit_refs: text file containing manually selected slit edges used as a first-guess when cropping slit data. • SAMOSenv.yml: independent environment file which contains the packages necessary to run the pipeline. 5.2 Step 0: Pipeline Initialization from SAMOS_DRP . SAMOS_NIGHT i m p o r t SAMOSNight SAMOS_setup = SAMOSNight ( o b s i d = ’ ’ , raw_data_dir= ’ ’ , proc_dir=’ ’ , LOG_FILENAME= ’ ’ , i g n o r e _ f l a t s =False , i g n o r e _ b i a s =True ) The 𝑆 𝐴𝑀𝑂𝑆 pipeline is initialized when the user executes the code shown above, where obsid is the observation ID corresponding to the night on which the data were observed, raw_data_dir is the directory containing the raw observation data, proc_dir is the directory for storage of pipeline results, LOG_FILENAME is the name of the .log file (if a file of the same name exists it is overwritten), ignore_flats gives the option to apply a flat field correction, and ignore_bias tells the pipeline whether to include bias correction from a series of zero exposures in the absence of the overscan region. First, the pipeline makes a directory for the data products and checks the files in raw_data_dir. Data are stored as 𝐹 𝐼𝑇 𝑆 (Flexible Image Transport System) (Wells et al., 1981) files, which store digital information in the form of multi-dimensional arrays. 𝐹 𝐼𝑇 𝑆 is the “standard” archival data 124 format for astronomers because it is able to store (and transfer) astronomical data that is completely self-contained. A typical 𝐹 𝐼𝑇 𝑆 file has a primary header and data unit (𝐻𝐷𝑈) extension, which is split into two arrays. The first array contains the top-level meta data for the exposure and is called the primary header. The primary header stores the information about an image in the form of keywords (observation date, target coordinates, exposure time, etc.) The second array usually contains the main data, but may be empty in a new 𝐹 𝐼𝑇 𝑆 file. They may also contain multiple other extensions, where each extension shares the same primary header information, but the local header contains information specific to that extension’s data (more information on 𝐹 𝐼𝑇 𝑆 files can be found in Pence et al. (2010)). The pipeline sorts the observations depending on exposure type (e.g. BIAS,FLAT,OBJ) by reading the 𝐹 𝐼𝑇 𝑆 headers. Once the data is organized, the user can view the main information by executing SAMOS_setup.data_buckets, and check that the data has been sorted properly. Each subsequent reduction step inherits the attributes of the previous step. Whenever something is done to the data, a new 𝐹 𝐼𝑇 𝑆 file is created. To keep track of what procedures were already performed, the intermediate products have the same base file names as their raw data, but with a new letter based on the intermediate step (e.g. trimmed+bias-corrected ∼ to_fname.FITS). The code reads the 𝐹 𝐼𝑇 𝑆 headers and creates arrays which separate the data into flats, com- parison lamps, and science data. Information for a night of observations is organized into a pandas.DataFrame called a ‘night_bucket’. This bucket object is further divided into the follow- ing main data reduction buckets: • Bias frames: not currently implemented because bias in the Goodman test images is accounted for via the overscan region, but these frames also can be used to verify the gain setting and can verify that the 2-d bias is “quiet”. • Flats: quartz flats to characterize nonuniformity in CCD pixel sensitivity. • Comparison lamps: Arc lamp exposures for wavelength calibration. • Science/Comparison pairs: Object exposures and the corresponding comparison lamps. 125 5.3 Step 1: CCD Image Processing from SAMOS_DRP . I m a g e P r o c e s s o r i m p o r t I m a g e P r o c e s s o r SAMOS_ccd_proc = I m a g e P r o c e s s o r ( SAMOS_setup ) SAMOS_ccd_proc ( ) The first step in reducing CCD data is to account for systematic effects during data acquisition and readout. CCDs are made of pixels which are sensitive to specific photon energies. Electrons in the pixel become excited by incoming light, and that charge is read out by the CCD. Every observation contains a bias level due to a combination of the camera noise from the readout process and electric “pre-charge” on a CCD chip by the electronics. Bias-subtraction and flat correction is executed with the command shown at the beginning of this section. The pipeline parses the FITS data array into regions of bias and target data by reading the FITS headers BIASSEC and DATASEC respectively. The latter section trims the field mask to the correct size. The BIASSEC header gives the region of overscan, which is a series of detector pixels that are shielded from incoming light. An array of this overscan region is made by grabbing the rows and columns from the data array. The function then takes the median (or mean) of the overscan regions along the rows (axis=1), and subtracts these values from each data value in their respective data rows. ©1ª 𝑑 𝑑 𝑑 ... 𝑑 ­ ® © 11 12 13 1𝑚 ª ­ ® ©𝑐𝑟𝑜 𝑝 𝑝𝑒𝑑 𝑎𝑛𝑑 ª ­­ ® ­ 1® ® ­𝑑 ® ­ ® ­ ® ­ 21 22 𝑑 ... ... 𝑑 2𝑚 ® ®   ­ ® ®=­ − ⊗ ­ ­ 𝑏𝑖𝑎𝑠 ­ 𝑠𝑢𝑏𝑡𝑟𝑎𝑐𝑡𝑒𝑑 ® ­ ® [𝑏 1 ] [𝑏 2 ] [𝑏 3 ] [...] [𝑏 𝑛 ] ­ ...® ­ ® ­ ® ­ ... ... ... ... ... ®® ­ ® ­ ® 𝑑𝑎𝑡𝑎 𝑚𝑎𝑡𝑟𝑖𝑥 ­ ® ­ ...® « ¬ 𝑑 ... ... ... 𝑑 ­ ® « 𝑛1 𝑛𝑚 ¬ ­ ® 1 « ¬ (5.1) Flat field images are used to characterize the variation in pixel sensitivity across the detector. During this step, each flat is scaled by its median so that the average pixel correction is ∼1. This 126 Raw data Bias corrected Master flat Bias/Flat corrected 0 8 25 59 125 0 259 8 525 25 1054 59 2121 1254231 2598434 525 105 Figure 5.2: First CCD data reduction steps. Data output after initial pipeline steps for CCD reduction. The raw data is in the upper left. (make better image and caption) -7 13 53 132 290 608 -7 1237 13 2490 53 5019 132 10021 290 19980 608 1237 normalization allows the statistics of the image to be maintained without having to pass along the details of the flat. The data are then median-combined to create the master flat. Finally, the pipeline divides the master flat from the science images. Examples of output of the pipeline through the first few steps are shown in Figure 5.2. 5.4 Step 2: Slit tracing and extraction from SAMOS_DRP . S l i t B u c k e t s i m p o r t S l i t B u c k e t s SAMOS_slits = S l i t B u c k e t s ( SAMOS_ccd_proc ) SAMOS_slits ( ) SAMOS is designed with a large Digital Micromirror Device (DMD). The mirrors can be selected to direct light to a spectrograph arm or an imaging arm, with the slit configurations stored in the FITS headers for each exposure and accessible to the pipeline upon instantiation. The current version of this pipeline uses data acquired from Goodman using multi-slit masks made in advance 127 of the observation. The most exciting feature of 𝑆 𝐴𝑀𝑂𝑆 will be its ability to create slit patterns in real time and save them to the FITS header for easy retrieval by the pipeline. Therefore, the slit location procedure is somewhat brute force as it will be replaced for analysis of 𝑆 𝐴𝑀𝑂𝑆 data. The method for identifying and excising individual slits from the images uses a manually made text file of pixel locations. The mask reference file slit_refs contains the y-pixel values for the top middle edge of each slit, obtained by inspection from the master flat file2. These reference pixels provide a first guess for the pipeline to map out the slit edges by calculating peaks in the difference of pixel intensity. The mask template is used to crop and pair the individual slits for the science and calibration lamp exposures. The cropped images are stored in a new directory corresponding to each slit number. The output of this procedure is shown in Figure 5.3. 5.4.1 Note on spectral extraction and tracing As mentioned above, the development version of the pipeline does not deal with spectral extraction as robustly as it will in the future. Once each slit is cut out and saved as its own 𝐹 𝐼𝑇 𝑆 file, instead of fitting the spectrum to a function based on the (minor) tilt with respect to the spatial axis, the pipeline takes sections of the slit and aligns them for a quick look at the pipeline progress. The crop-and-move alignment is adequate for testing purposes, as the spectra from 𝐺𝑜𝑜𝑑𝑚𝑎𝑛 are relatively well-behaved with respect to more extreme spatial distortions. A one-dimensional spectrum is “extracted” by taking the middle few rows of a spectrum and using their median to collapse them to a single row. This spectral extraction is a very crude method and only for the purposes of testing. In the future, the SRP will fit a function to characterize the layout of the spectrum over pixel coordinates. More information about the spatial distortion of spectra can be found in Marsh (1989) and Horne (1986). 5.5 Step 3: Wavelength calibration 2 The master flat provides the greatest contrast between the illuminated and non-illuminated sections of the detector. The 𝑆 𝐴𝑀𝑂𝑆 instrument team is developing a calibration from DMD to detector that will be verified during engineering testing at SOAR. We hope it goes well and turns out to be robust. Otherwise, the code described here can implement it as a first-guess. 128 Trace slit edges with master flat Use trace map to cut out slits Figure 5.3: Slit cutout diagram. Simplified version of slit tracing and extraction. The master flat (top) is used to find the slit edges, then a map of the pixel coordinates is applied to the science exposures (lower left) exposures. Each slit is saved as a new 𝐹 𝐼𝑇 𝑆 image which is ready to be wavelength calibrated (lower right). from SAMOS_DRP . DoWavecal i m p o r t WaveCalBuckets SAMOS_wavecal = WaveCalBuckets ( SAMOS_slits ) SAMOS_wavecal ( ) Each science exposure is paired with a calibration lamp. Calibration lamps, or arc lamps, are comprised of gas with emission lines which have been measured in a laboratory setting. Calibration lamp exposures are taken during the observing night so that each science spectrum is calibrated to the correct grating/filter setting. Each slit in the mask is paired with its own set of arc lamp exposures. Therefore, we must choose an arc lamp that features emission lines that are also present in the science spectrum. The angular dispersion of a grating is the change in angle of diffraction per change in wavelength (Å/arcsec). The simple diagram in Figure 5.4 shows how a spectrum is produced. The main source of light passes through a slit and is dispersed by a diffraction grating, after which the spectrum is 129 incident light 𝛂 grating normal 𝛃 camera/ spectrum Figure 5.4: Cartoon diffraction grating. Simplified depiction of how source light is dispersed by a diffraction grating and becomes a spectrum. projected onto the CCD. The angular dispersion is related to linear dispersion by the plate scale (arcsec/pixel). Therefore, the solution requires us to compare the linear pixel distance between emission lines in the uncorrected arc lamp exposure to change in wavelength Δ𝜆. It should be noted that the wavelength calibration for the 𝑆 𝐴𝑀𝑂𝑆 pipeline is not original code and it performs the fit using procedures from the GSP (Torres-Robledo & Briceño, 2019). The 𝑆 𝐴𝑀𝑂𝑆 pipeline will be updated to work with real 𝑆 𝐴𝑀𝑂𝑆 data in the future, with the GSP code as a solid foundation. The GSP simplifies the wavelength calibration process with a library of reference lamps with wavelength solutions for multiple grating/filter configurations which have already been calibrated. The use of a pre-fitted calibration spectrum means that the lines only need to be identified once, and then applied to future spectra. For a given arc lamp, the pipeline steps along the dispersion axis and collects pixel locations for lines which meet a certain count threshold. We are fitting to a model that matches a linear pixel distance from a central point to a change in wavelength. However, the mapping between pixels and wavelength is not necessarily linear, and the linear approximation can break down if the spectrum 130 Figure 5.5: Wavelength calibrated spectrum output for 𝑺 𝑨𝑴𝑶𝑺 pipeline. Final wavelength calibrated spectrum for extracted slit. Spectrum does not include background subtraction or flux calibration. is distorted. Finding the coefficients for the non-linear model is made simpler with a low order first-guess solution from the reference arc exposure. The pre-fitted reference lamp contains a list of emission lines with their pixel and angstrom values, along with its best fit solution stored as the coefficients of a polynomial model3. With the approximate wavelength solution, the pipeline interpolates over the locations of the known lines to estimate wavelengths of the unknown features in the spectrum. Once we have a pixel-to-angstrom map, we can convert the dispersion axis in the science exposures from pixels to angstroms. An example of the final wavelength calibrated spectrum is provided in Figure 5.5. 5.6 Remaining steps While the pipeline is able to produce a wavelength calibrated spectrum for the test data, there is still much to be done before 𝑆 𝐴𝑀𝑂𝑆 is commissioned in 2021, and development of the pipeline 3 The current pipeline version is only able to handle a Chebyshev1D model from astropy.models, but will be expanded in the future. 131 is ongoing. The remaining high priority reduction steps are described below. • Flux calibration: The flux of an object is captured by the CCD in photon counts. Because CCDs have different sensitivities across their pixels, the pipeline will need to produce a fit to the sensitivity function and scale the photon counts to units of magnitude. Flux calibration will use the continuum emission for a standard star exposure. • Background subtraction: Spectra contain emission from the sky within the line of sight of an object. This background emission needs to be subtracted from the science spectra. One technique for sky subtraction is nod-and-shuffle, wherein the source is shuffled between the lower edge of a slit and the upper edge. By having spectrum cover different regions of the slit, the sky emission at the opposite end can be characterized to a higher degree of accuracy. • Tracing/Spectral extraction: As mentioned previously, spectra can be distorted with respect to the spatial axis. Currently, the SRP uses a crude method of spectral extraction which will be updated to include a routine that traces the distortion, and then extracts a spectrum based on that trace. In addition to the remaining data reduction procedures, the SRP will include a suite of settings such that user will be able to have more control over what data is reduced and how. Right now, the user only has the options to name the directory of the data output, and whether to include flat or bias correction. A future version will include options to choose specific types of exposures, places to pause and restart the pipeline, and other features that allow the user to customize their data reduction. Before 𝑆 𝐴𝑀𝑂𝑆 is taken to 𝑆𝑂 𝐴𝑅, we plan to test the pipeline using simulated data from SAMOS. The test data from 𝐺𝑜𝑜𝑑𝑚𝑎𝑛 will therefore be replaced with simulated data from SAMOS, which should make the transition from testing to science even easier. SAMOS will be an exciting addition to 𝑆𝑂 𝐴𝑅. As a multi-object spectrograph, it will allow an observer to take spectra of multiple targets within a single exposure, which is particularly useful for observations of galaxy clusters. 𝑆 𝐴𝑀𝑂𝑆 will be able to maximize its multi-object capabilities, as it will be able to create a number of slit mask patterns throughout the night. This key aspect 132 makes 𝑆 𝐴𝑀𝑂𝑆 a highly anticipated instrument, and it has received a no-cost extension and access to reserve funds to aid in completion by Summer, 2021. We have been able to build a strong foundation for the 𝑆 𝐴𝑀𝑂𝑆 pipeline using methods from the 𝐺𝑜𝑜𝑑𝑚𝑎𝑛 spectroscopic pipeline (Torres-Robledo & Briceño, 2019) and data reduction packages provided by Price-Whelan et al. (2018), and we are actively making progress towards completion. 133 APPENDICES 134 APPENDIX A BOLOMETRIC AND K- CORRECTION PROCEDURE The code below shows the procedure used for making corrections to bolometric and rest-frame fluxes and luminosities. The code reads in a .CSV file with the names, redshifts, temperatures, and metallicities of the clusters. Then it simulates observed fluxes for each cluster, along with the bolometric and rest-frame luminosities. The main procedure is described in Chapter 2.3. Below shows the 𝑋𝑆𝑃𝐸𝐶 code used to simulate the observed fluxes and luminosities used to compute the correction factors. # set cosmology to H0=70 q0=−0.55 Omega_Lambda=0.7 cosmo 70 −0.55 0.7 # set energy grid to cover a large range energies 0.05 100.0 10000 log set outfile [open outfile w+] set f [open nocore_lumcorr_input ] #read in cluster data from f i l e set lines [ split [read $f] ‘‘\n’’] close $f puts ‘‘$lines ’’ # make simulated spectra foreach row $lines { set line [ split $row ‘‘,’’] 135 set name [ lindex $line 0] puts ‘‘name is $name ’’ set z [ lindex $line 1] puts ‘‘redshift is $z ’’ set T [ lindex $line 2] set Zsol [ lindex $line 3] puts ‘‘kT , Zsol , z is $T , $Zsol , $z ’’ # set mekal model params kT , nH, Zsolar , redshift , Switch , Normalization model mekal $T #set temperature 1.0 $Zsol $z 1 1.e −4 # store the f i r s t number in the string from t c l o u t # into variables fluxout , lum05_70 , lum_bol flux 0.5 7.0 tclout flux set fluxout [ string range $xspec_tclout 0 [ string first ‘‘ ’’ $xspec_tclout ]] lum 0.5 7.0 $z tclout lum ; set lum05_70 [ string range $xspec_tclout 0 [ string first ‘‘ ’’ $xspec_tclout 136 ]] lum 0.1 100.0 $z tclout lum set lum_bol [ string range $xspec_tclout 0 [ string first ‘‘ ’’ $xspec_tclout ]] # save kT , Zsol , z , fluxout , lum05_70 , lumbol to f i l e # Luminosities are in units of 1e44 erg / s puts $outfile ‘‘$name ,$T ,$Zsol ,$z ,$fluxout ,$lum05_70 , $lum_bol ’’ ; # writes line to f i l e } close $outfile The simulated fluxes are read in from the 𝑋𝑆𝑃𝐸𝐶 results and used to compute an observed luminosity with 𝐿 ∝ 𝐹 ((1 + 𝑧)𝑑) 2 , where 𝐹 is the flux and 𝑑 is the co-moving or Hubble distance of the cluster (section 1.2.1). Then we create the correction factor for each cluster as the ratio of the corrected-to-observed luminosity (and correction type) in the simulated clusters. These correction factors were multiplied by the observed luminosities in the real data. Below shows the general code used to compute the corrected luminosity for each cluster. This version has been simplified to show the main parts. import numpy a s np import c o s m o c a l c a s cosmo i m p o r t p a n d a s a s pd H0 = 70 WM = 0 . 3 SIMdata = pd . r e a d _ c s v ( s i m _ f i l e ) A 2 d a t a = pd . r e a d _ c s v ( ACCEPT2 . 0 _ d a t a ) 137 cosmo = c o s m o c a l c ( A 2 d a t a [ ’ z ’ ] , H0 ,WM,1 −WM) DL = cosmo [ ’DL_cm ’ ] s i m _ f l x = SIMdata . l o c [ ’ f l u x o u t ’ ] # s i m u l a t e d f l u x s i m _ r e s t l u m = SIMdata [ ’ r e s t _ l u m ’ ] s i m _ b o l l u m = SIMdata [ ’ b o l _ l u m ’ ] sim_obsLum = ( s i m _ f l x ∗4∗ np . p i ∗DL∗ ∗ 2 ) / 1 e44 u n c o r r _ l u m = A 2 d a t a [ ’ Lx ’ ] # u n c o r r e c t e d l u m i n o s i t y and e r r o r f r o m ACCEPT2 . 0 u n c o r r _ l u m e r r = A 2 d a t a [ ’ Lxe ’ ] r _ c o r r = s i m _ r e s t l u m / ( obsLum ) # c o r r e c t i o n f a c t o r s f r o m s i m u l a t e d data b _ c o r r = s i m _ b o l l u m / ( obsLum ) newLx_rest , newLx_restErr = uncorr_lum ∗ r _ c o r r , u n c o r r _ l u m e r r ∗ r _ c o r r # m u l t i p l y by o b s e r v e d l u m i n o s i t i e s newLx_bol , n e w L x _ b o l E r r = u n c o r r _ l u m ∗ b _ c o r r , u n c o r r _ l u m e r r ∗ b _ c o r r 138 APPENDIX B RADIAL ABUNDANCE PROFILES FOR ACCEPT2.0 CLUSTERS Radial metallicity profiles for 154 ACCEPT2.0 clusters. (For a description, see Chapter 2.) 139 r[arcmin] 0.04 0.12 0.44 1.31 4.38 0.02 0.07 0.23 0.70 2.34 0.08 0.25 0.84 2.52 8.44 1.00 0.30 Z[Z ] 0.10 ABELL 0013 ABELL 2744 ABELL 0085 0.03 z = 0.09 z = 0.31 z = 0.06 R2500 = 461 kpc h−1 70 R2500 = 640 kpc h−1 70 R2500 = 543 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.04 0.14 0.46 1.40 4.66 0.03 0.09 0.33 1.02 3.43 0.10 0.31 1.03 3.10 10.35 1.00 0.30 Z[Z ] 0.10 ZwCl 0040.8 + 2404 ESO 351 − G 021 ABELL 0119 0.03 z = 0.08 z = 0.06 z = 0.04 R2500 = 437 kpc h−1 70 R2500 = 228 kpc h−1 70 R2500 = 541 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.02 0.05 0.17 0.52 1.76 0.05 0.16 0.54 1.62 5.40 0.04 0.15 0.51 1.55 5.21 1.00 0.30 Z[Z ] 0.10 M axBCG J016.70077 + 01.05926 CIZA J0107.7 + 5408 ABELL 0160 0.03 z = 0.25 z = 0.11 z = 0.04 R2500 = 419 kpc h−1 70 R2500 = 634 kpc h−1 70 R2500 = 275 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.1: Radial metallicity profile for clusters A0013 through A0160. Radial metallic- ity profiles for the following clusters: A0013, A2744, A0085, 00408+2404, 351-021, A0119, 01670077+0105926, 01077+5408, A0160. 140 r[arcmin] 0.06 0.19 0.66 1.98 6.67 0.04 0.13 0.49 1.48 4.96 0.07 0.21 0.70 2.13 7.12 1.00 0.30 Z[Z ] 0.10 N SCS J011502 + 002441 U GC 00842 ABELL 0193 0.03 z = 0.04 z = 0.05 z = 0.05 R2500 = 353 kpc h−1 70 R2500 = 265 kpc h−1 70 R2500 = 407 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.02 0.06 0.19 0.59 1.97 0.07 0.25 0.81 2.46 8.22 0.02 0.07 0.25 0.75 2.49 1.00 0.30 Z[Z ] 0.10 ABELL S0295 ABELL 0376 ABELL 0383 0.03 z = 0.30 z = 0.05 z = 0.19 R2500 = 529 kpc h−1 70 R2500 = 468 kpc h−1 70 R2500 = 470 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.06 0.21 0.69 2.09 6.98 0.07 0.21 0.71 2.16 7.23 0.04 0.14 0.48 1.43 4.76 1.00 0.30 Z[Z ] 0.10 ABELL 0399 ABELL 0401 ABELL 3094 0.03 z = 0.07 z = 0.07 z = 0.07 R2500 = 574 kpc h−1 70 R2500 = 609 kpc h−1 70 R2500 = 371 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.2: Radial metallicity profile for clusters 011502+002441 through A3094. Radial metallicity profiles for the following clusters: 011502+002441, UGC00842, A0193, AS0295, A0376, A0383, A0399, A0401, A3094. 141 r[arcmin] 0.04 0.16 0.53 1.60 5.36 0.04 0.12 0.41 1.26 4.22 0.09 0.29 0.95 2.87 9.60 1.00 0.30 Z[Z ] 0.10 ABELL 3128 M CXC J0340.8 − 4542 III Zw 054 0.03 z = 0.06 z = 0.07 z = 0.03 R2500 = 373 kpc h−1 70 R2500 = 338 kpc h−1 70 R2500 = 335 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.06 0.20 0.69 2.08 6.92 0.03 0.08 0.30 0.91 3.04 0.05 0.17 0.60 1.81 6.04 1.00 0.30 Z[Z ] 0.10 ABELL 3158 M CXC J0352.9 + 1941 ABELL 0478 0.03 z = 0.06 z = 0.11 z = 0.09 R2500 = 480 kpc h−1 70 R2500 = 364 kpc h−1 70 R2500 = 598 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.02 0.05 0.18 0.54 1.81 0.06 0.23 0.78 2.39 8.03 0.06 0.21 0.75 2.24 7.54 1.00 0.30 Z[Z ] 0.10 M ACS J0417.5 − 1154 M CXC J0425.8 − 0833 ABELL S0463 0.03 z = 0.44 z = 0.04 z = 0.04 R2500 = 624 kpc h−1 70 R2500 = 379 kpc h−1 70 R2500 = 353 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.3: Radial metallicity profile for clusters A3128 through AS0463. Radial metallicity profiles for the following clusters: A3128, 03408-4542, IIIZw054, A3158, 03529+1941, A0478, 04175-1154, 04258-0833, AS0463. 142 r[arcmin] 0.02 0.06 0.20 0.60 2.00 0.05 0.15 0.49 1.47 4.92 0.08 0.24 0.82 2.49 8.39 1.00 0.30 Z[Z ] 0.10 M CXC J0437.1 + 0043 ABELL 0514 ESO 552 − G 020 0.03 z = 0.28 z = 0.07 z = 0.03 R2500 = 518 kpc h−1 70 R2500 = 402 kpc h−1 70 R2500 = 316 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.09 0.29 1.05 3.16 10.58 0.02 0.08 0.26 0.79 2.64 0.02 0.07 0.23 0.69 2.30 1.00 0.30 Z[Z ] 0.10 ABELL 0539 M CXC J0528.2 − 2942 RBS 0653 0.03 z = 0.03 z = 0.16 z = 0.28 R2500 = 362 kpc h−1 70 R2500 = 434 kpc h−1 70 R2500 = 594 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.07 0.23 0.82 2.46 8.24 0.06 0.23 0.79 2.36 7.90 0.07 0.26 0.91 2.75 9.22 1.00 0.30 Z[Z ] 0.10 ESO3060170 − A ABELL 0548A ABELL 3376 0.03 z = 0.04 z = 0.04 z = 0.05 R2500 = 352 kpc h−1 70 R2500 = 371 kpc h−1 70 R2500 = 496 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.4: Radial metallicity profile for clusters 04371+0043 through A3376. Radial metal- licity profiles for the following clusters: 04371+0043, A0514, 552-020, A0539, 05282-2942, RBS0653, 3060170-, A0548A, A3376. 143 r[arcmin] 0.08 0.27 0.90 2.72 9.11 0.02 0.08 0.29 0.87 2.93 0.03 0.08 0.26 0.80 2.66 1.00 0.30 Z[Z ] 0.10 ABELL 3391 ABELL 0562 Bullet Cluster 0.03 z = 0.05 z = 0.11 z = 0.30 R2500 = 549 kpc h−1 70 R2500 = 353 kpc h−1 70 R2500 = 708 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.02 0.05 0.17 0.50 1.67 0.03 0.09 0.34 1.02 3.39 0.02 0.07 0.24 0.73 2.44 1.00 0.30 Z[Z ] 0.10 M ACS J0717 + 3745 ABELL 0578 ZwCl 0735.7 + 7421 0.03 z = 0.55 z = 0.09 z = 0.22 R2500 = 647 kpc h−1 70 R2500 = 331 kpc h−1 70 R2500 = 516 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.05 0.16 0.55 1.65 5.53 0.04 0.19 0.64 1.99 6.70 0.02 0.07 0.22 0.65 2.18 1.00 0.30 Z[Z ] 0.10 P KS 0745 − 19 W BL 154 ABELL 0611 0.03 z = 0.10 z = 0.02 z = 0.29 R2500 = 628 kpc h−1 70 R2500 = 179 kpc h−1 70 R2500 = 571 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.5: Radial metallicity profile for clusters A3391 through A0611. Radial metallicity profiles for the following clusters: A3391, A0562, , 0717+3745, A0578, 07357+7421, PKS0745- 19, WBL154, A0611. 144 r[arcmin] 0.06 0.21 0.69 2.11 7.02 0.03 0.10 0.33 1.00 3.33 0.02 0.06 0.19 0.58 1.94 1.00 0.30 Z[Z ] 0.10 ABELL 0644 ABELL 0665 2M F GC 06756 0.03 z = 0.07 z = 0.18 z = 0.24 R2500 = 567 kpc h−1 70 R2500 = 614 kpc h−1 70 R2500 = 445 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.03 0.09 0.29 0.89 2.99 0.03 0.08 0.26 0.78 2.60 0.02 0.05 0.19 0.56 1.87 1.00 0.30 Z[Z ] 0.10 ABELL 3411 N SC J084254 + 292723 ZwCl 0857.9 + 2107 0.03 z = 0.17 z = 0.19 z = 0.23 R2500 = 519 kpc h−1 70 R2500 = 505 kpc h−1 70 R2500 = 414 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.02 0.08 0.26 0.78 2.60 0.02 0.08 0.27 0.82 2.74 0.06 0.19 0.67 2.01 6.72 1.00 0.30 Z[Z ] 0.10 SDSS + 137.3 + 11.0 + 0.18 ABELL 0773 Hydra A 0.03 z = 0.18 z = 0.22 z = 0.05 R2500 = 475 kpc h−1 70 R2500 = 581 kpc h−1 70 R2500 = 431 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.6: Radial metallicity profile for clusters A0644 through HydraA. Radial metallic- ity profiles for the following clusters: A0644, A0665, 2MFGC06756, A3411, 084254+292723, 08579+2107, +1373+110+018, A0773, HydraA. 145 r[arcmin] 0.02 0.05 0.18 0.55 1.83 0.02 0.07 0.22 0.68 2.28 0.03 0.09 0.31 0.95 3.15 1.00 0.30 Z[Z ] 0.10 GALEX J094712.4 + 762313 ZwCl 0949.6 + 5207 ABELL 0907 0.03 z = 0.35 z = 0.21 z = 0.15 R2500 = 550 kpc h−1 70 R2500 = 479 kpc h−1 70 R2500 = 504 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.02 0.07 0.22 0.68 2.27 0.02 0.07 0.26 0.78 2.59 0.06 0.19 0.66 1.99 6.65 1.00 0.30 Z[Z ] 0.10 ZwCl 1006.1 + 1201 ABELL 0963 ABELL 0970 0.03 z = 0.22 z = 0.21 z = 0.06 R2500 = 488 kpc h−1 70 R2500 = 527 kpc h−1 70 R2500 = 454 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.03 0.09 0.32 0.96 3.22 0.02 0.06 0.22 0.67 2.24 0.04 0.11 0.37 1.11 3.69 1.00 0.30 Z[Z ] 0.10 ABELL 0980 BLOX J1023.6 + 0411.1 ABELL 1033 0.03 z = 0.16 z = 0.29 z = 0.13 R2500 = 529 kpc h−1 70 R2500 = 589 kpc h−1 70 R2500 = 501 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.7: Radial metallicity profile for clusters 0947124+762313 through A1033. Ra- dial metallicity profiles for the following clusters: 0947124+762313, 09496+5207, A0907, 10061+1201, A0963, A0970, A0980, 10236+04111, A1033. 146 r[arcmin] 0.03 0.09 0.31 0.94 3.17 0.05 0.27 0.90 2.81 9.50 0.02 0.10 0.35 1.04 3.48 1.00 0.30 Z[Z ] 0.10 ABELL 1068 N GC 3402 GROU P M CXC J1053.7 + 5452 0.03 z = 0.14 z = 0.02 z = 0.07 R2500 = 463 kpc h−1 70 R2500 = 179 kpc h−1 70 R2500 = 281 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.02 0.08 0.28 0.85 2.84 0.03 0.11 0.37 1.15 3.86 0.03 0.12 0.42 1.27 4.24 1.00 0.30 Z[Z ] 0.10 ABELL 1201 M CXC J1130.0 + 3637 ABELL 1285 0.03 z = 0.17 z = 0.06 z = 0.11 R2500 = 492 kpc h−1 70 R2500 = 269 kpc h−1 70 R2500 = 496 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.05 0.17 0.57 1.71 5.70 0.03 0.11 0.38 1.15 3.83 0.02 0.06 0.21 0.63 2.11 1.00 0.30 Z[Z ] 0.10 SDSS − C4 − DR3 3018 ABELL 1413 ABELL 1423 0.03 z = 0.05 z = 0.14 z = 0.21 R2500 = 341 kpc h−1 70 R2500 = 578 kpc h−1 70 R2500 = 441 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.8: Radial metallicity profile for clusters A1068 through A1423. Radial metallicity profiles for the following clusters: A1068, 3402, 10537+5452, A1201, 11300+3637, A1285, 4-33018, A1413, A1423. 147 r[arcmin] 0.02 0.09 0.28 0.87 2.93 0.03 0.10 0.34 1.02 3.41 0.06 0.23 0.79 2.43 8.18 1.00 0.30 Z[Z ] 0.10 SDSS − C4 − DR3 3144 ABELL 1446 N GC 4104 GROU P 0.03 z = 0.08 z = 0.10 z = 0.03 R2500 = 269 kpc h−1 70 R2500 = 390 kpc h−1 70 R2500 = 279 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.06 0.19 0.65 1.97 6.59 0.07 0.20 0.66 1.97 6.63 0.04 0.11 0.37 1.12 3.75 1.00 0.30 Z[Z ] 0.10 N SC J121733 + 033929 N GC 4325 GROU P ABELL 1569 0.03 z = 0.08 z = 0.03 z = 0.07 R2500 = 576 kpc h−1 70 R2500 = 202 kpc h−1 70 R2500 = 315 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.07 0.25 0.86 2.58 8.63 0.05 0.16 0.54 1.63 5.43 0.03 0.10 0.33 1.02 3.39 1.00 0.30 Z[Z ] 0.10 ABELL 1644 ABELL 1650 ABELL 1664 0.03 z = 0.05 z = 0.08 z = 0.13 R2500 = 481 kpc h−1 70 R2500 = 514 kpc h−1 70 R2500 = 468 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.9: Radial metallicity profile for clusters 4-33144 through A1664. Radial metallicity profiles for the following clusters: 4-33144, A1446, 4104, 121733+033929, 4325, A1569, A1644, A1650, A1664. 148 r[arcmin] 0.03 0.11 0.36 1.09 3.65 0.05 0.14 0.48 1.44 4.88 0.06 0.20 0.70 2.15 7.16 1.00 0.30 Z[Z ] 0.10 ABELL 1689 N GC 5098 GROU P ABELL 1736 0.03 z = 0.18 z = 0.04 z = 0.05 R2500 = 676 kpc h−1 70 R2500 = 213 kpc h−1 70 R2500 = 387 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.05 0.19 0.67 2.05 6.84 0.05 0.17 0.58 1.73 5.77 0.07 0.21 0.71 2.13 7.16 1.00 0.30 Z[Z ] 0.10 SSGC 081 ABELL 1750C SC 1329 − 313 0.03 z = 0.05 z = 0.07 z = 0.05 R2500 = 398 kpc h−1 70 R2500 = 450 kpc h−1 70 R2500 = 406 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.07 0.24 0.82 2.45 8.16 0.05 0.15 0.49 1.49 4.97 0.02 0.06 0.20 0.62 2.06 1.00 0.30 Z[Z ] 0.10 ABELL 3562 ABELL 1775 LCDCS 0829 0.03 z = 0.05 z = 0.07 z = 0.45 R2500 = 470 kpc h−1 70 R2500 = 408 kpc h−1 70 R2500 = 718 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.10: Radial metallicity profile for clusters A1689 through LCDCS0829. Radial metallicity profiles for the following clusters: A1689, 5098, A1736, SSGC081, A1750C, SC1329- 313, A3562, A1775, LCDCS0829. 149 r[arcmin] 0.03 0.08 0.27 0.81 2.71 0.02 0.07 0.26 0.77 2.58 0.01 0.03 0.12 0.36 1.19 1.00 0.30 Z[Z ] 0.10 ABELL 1835 A1882a GM BCG J215.94948 + 24.07846 0.03 z = 0.25 z = 0.14 z = 0.54 R2500 = 646 kpc h−1 70 R2500 = 385 kpc h−1 70 R2500 = 462 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.03 0.10 0.36 1.08 3.61 0.03 0.09 0.31 0.94 3.13 0.02 0.06 0.21 0.64 2.14 1.00 0.30 Z[Z ] 0.10 ABELL 1914 ABELL 1930 ABELL 1942 AN D CLU M P 0.03 z = 0.17 z = 0.13 z = 0.22 R2500 = 633 kpc h−1 70 R2500 = 440 kpc h−1 70 R2500 = 465 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.09 0.34 1.11 3.38 11.30 0.04 0.15 0.50 1.51 5.07 0.02 0.05 0.19 0.56 1.87 1.00 0.30 Z[Z ] 0.10 W BL 518 ABELL 1991 N SCS J145715 + 222009 0.03 z = 0.03 z = 0.06 z = 0.26 R2500 = 368 kpc h−1 70 R2500 = 346 kpc h−1 70 R2500 = 452 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.11: Radial metallicity profile for clusters A1835 through 145715+222009. Radial metallicity profiles for the following clusters: A1835, A1882a, 21594948+2407846, A1914, A1930, 1942, WBL518, A1991, 145715+222009. 150 r[arcmin] 0.02 0.07 0.24 0.73 2.44 0.03 0.10 0.34 1.01 3.39 0.03 0.09 0.29 0.88 2.94 1.00 0.30 Z[Z ] 0.10 ABELL S0780 ABELL 2009 W HL J150407.5 − 024816 0.03 z = 0.24 z = 0.15 z = 0.22 R2500 = 551 kpc h−1 70 R2500 = 543 kpc h−1 70 R2500 = 620 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.04 0.14 0.48 1.44 4.82 0.04 0.15 0.51 1.54 5.13 0.06 0.21 0.73 2.22 7.41 1.00 0.30 Z[Z ] 0.10 ABELL 2034 ABELL 2061 M KW 03s 0.03 z = 0.11 z = 0.08 z = 0.04 R2500 = 595 kpc h−1 70 R2500 = 457 kpc h−1 70 R2500 = 394 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.04 0.12 0.41 1.24 4.15 0.04 0.11 0.39 1.17 3.91 0.02 0.05 0.18 0.53 1.76 1.00 0.30 Z[Z ] 0.10 ABELL 2069 M CXC J1524.2 − 3154 M ACS J1532.8 + 3021 0.03 z = 0.12 z = 0.10 z = 0.34 R2500 = 525 kpc h−1 70 R2500 = 444 kpc h−1 70 R2500 = 522 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.12: Radial metallicity profile for clusters AS0780 through 15328+3021. Radial metallicity profiles for the following clusters: AS0780, A2009, 1504075-024816, A2034, A2061, MKW03s, A2069, 15242-3154, 15328+3021. 151 r[arcmin] 0.08 0.27 0.88 2.67 8.90 0.03 0.10 0.35 1.05 3.53 0.05 0.19 0.63 1.92 6.41 1.00 0.30 Z[Z ] 0.10 ABELL 2107 ABELL 2104 ABELL 2124 0.03 z = 0.04 z = 0.15 z = 0.07 R2500 = 434 kpc h−1 70 R2500 = 565 kpc h−1 70 R2500 = 485 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.06 0.18 0.61 1.84 6.15 0.04 0.13 0.44 1.33 4.47 0.10 0.31 1.05 3.20 10.73 1.00 0.30 Z[Z ] 0.10 ABELL 2142 M CXC J1558.3 − 1410 ABELL 2147 0.03 z = 0.09 z = 0.10 z = 0.04 R2500 = 626 kpc h−1 70 R2500 = 483 kpc h−1 70 R2500 = 449 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.07 0.23 0.80 2.45 8.20 0.03 0.11 0.39 1.18 3.95 0.04 0.12 0.41 1.23 4.11 1.00 0.30 Z[Z ] 0.10 ABELL 2151 ABELL 2163 ABELL 2204 0.03 z = 0.04 z = 0.20 z = 0.15 R2500 = 358 kpc h−1 70 R2500 = 795 kpc h−1 70 R2500 = 654 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.13: Radial metallicity profile for clusters A2107 through A2204. Radial metallicity profiles for the following clusters: A2107, A2104, A2124, A2142, 15583-1410, A2147, A2151, A2163, A2204. 152 r[arcmin] 0.03 0.08 0.29 0.87 2.90 0.03 0.09 0.32 0.96 3.20 0.02 0.07 0.25 0.77 2.59 1.00 0.30 Z[Z ] 0.10 ABELL 2218 ABELL 2219 Hercules A 0.03 z = 0.18 z = 0.23 z = 0.15 R2500 = 520 kpc h−1 70 R2500 = 699 kpc h−1 70 R2500 = 419 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.07 0.22 0.72 2.21 7.40 0.05 0.14 0.47 1.43 4.78 0.07 0.25 0.86 2.59 8.67 1.00 0.30 Z[Z ] 0.10 N GC 6269 ABELL 2244 ABELL 2256 0.03 z = 0.03 z = 0.10 z = 0.06 R2500 = 308 kpc h−1 70 R2500 = 515 kpc h−1 70 R2500 = 586 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.05 0.16 0.58 1.74 5.80 0.09 0.30 1.00 3.03 10.17 0.03 0.09 0.33 0.99 3.30 1.00 0.30 Z[Z ] 0.10 ABELL 2255 N GC 6338 SDSS − C4 3072 0.03 z = 0.08 z = 0.03 z = 0.16 R2500 = 530 kpc h−1 70 R2500 = 336 kpc h−1 70 R2500 = 560 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.14: Radial metallicity profile for clusters A2218 through 43072. Radial metallicity profiles for the following clusters: A2218, A2219, HerculesA, NGC6269, A2244, A2256, A2255, NGC6338, 43072. 153 r[arcmin] 0.02 0.08 0.27 0.82 2.73 0.05 0.15 0.50 1.52 5.06 0.09 0.31 1.03 3.09 10.31 1.00 0.30 Z[Z ] 0.10 ABELL 2261 ZwCl 1742.1 + 3306 ABELL 2319 0.03 z = 0.22 z = 0.08 z = 0.06 R2500 = 593 kpc h−1 70 R2500 = 437 kpc h−1 70 R2500 = 670 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.02 0.05 0.18 0.54 1.80 0.03 0.10 0.34 1.01 3.35 0.07 0.21 0.72 2.21 7.40 1.00 0.30 Z[Z ] 0.10 M ACS J1931.8 − 2635 M CXC J2014.8 − 2430 IC 1365 0.03 z = 0.35 z = 0.16 z = 0.05 R2500 = 540 kpc h−1 70 R2500 = 560 kpc h−1 70 R2500 = 429 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.01 0.05 0.17 0.51 1.69 0.04 0.14 0.49 1.47 4.91 0.05 0.14 0.48 1.46 4.90 1.00 0.30 Z[Z ] 0.10 M ACS J2140.2 − 2339 ABELL 3809 ABELL 2384 0.03 z = 0.31 z = 0.06 z = 0.09 R2500 = 468 kpc h−1 70 R2500 = 354 kpc h−1 70 R2500 = 516 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.15: Radial metallicity profile for clusters A2261 through A2384. Radial metallicity profiles for the following clusters: A2261, 17421+3306, A2319, 19318-2635, 20148-2430, IC1365, 21402-2339, A3809, A2384. 154 r[arcmin] 0.03 0.09 0.30 0.91 3.03 0.02 0.07 0.23 0.69 2.30 0.05 0.16 0.53 1.60 5.35 1.00 0.30 Z[Z ] 0.10 ABELL 2390 ClG 2153.8 + 3746 ABELL 3827 0.03 z = 0.23 z = 0.29 z = 0.10 R2500 = 668 kpc h−1 70 R2500 = 608 kpc h−1 70 R2500 = 585 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.04 0.15 0.50 1.52 5.09 0.02 0.09 0.29 0.88 2.96 0.04 0.15 0.52 1.56 5.24 1.00 0.30 Z[Z ] 0.10 ABELL 2415 3C 444 ABELL 3880 0.03 z = 0.06 z = 0.15 z = 0.06 R2500 = 344 kpc h−1 70 R2500 = 473 kpc h−1 70 R2500 = 356 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.06 0.17 0.59 1.80 6.00 0.03 0.09 0.31 0.92 3.09 0.05 0.14 0.50 1.50 5.03 1.00 0.30 Z[Z ] 0.10 ABELL 2457 CIZA J2242.8 + 5301 ABELL 3921 0.03 z = 0.06 z = 0.19 z = 0.09 R2500 = 414 kpc h−1 70 R2500 = 595 kpc h−1 70 R2500 = 522 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.16: Radial metallicity profile for clusters A2390 through A3921. Radial metallicity profiles for the following clusters: A2390, 21538+3746, A3827, A2415, 3C444, A3880, A2457, 22428+5301, A3921. 155 r[arcmin] 0.02 0.06 0.19 0.57 1.90 0.02 0.06 0.20 0.62 2.08 0.04 0.12 0.42 1.25 4.21 1.00 0.30 Z[Z ] 0.10 ABELL 2537 ABELL 2550 ABELL 2556 0.03 z = 0.29 z = 0.12 z = 0.09 R2500 = 506 kpc h−1 70 R2500 = 276 kpc h−1 70 R2500 = 413 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.04 0.15 0.50 1.53 5.11 0.04 0.14 0.46 1.37 4.60 0.05 0.17 0.59 1.77 5.92 1.00 0.30 Z[Z ] 0.10 ABELL S1101 ABELL 2597 ABELL 2626 0.03 z = 0.06 z = 0.09 z = 0.06 R2500 = 345 kpc h−1 70 R2500 = 442 kpc h−1 70 R2500 = 382 kpc h−1 70 0.01 r/r2500 r/r2500 r/r2500 0.04 0.15 0.50 1.51 5.04 0.08 0.25 0.84 2.51 8.44 0.09 0.32 1.06 3.24 10.86 1.00 0.30 Z[Z ] 0.10 M CXC J2344.2 − 0422 ABELL 2657 ABELL 4038 0.03 z = 0.08 z = 0.04 z = 0.03 R2500 = 450 kpc h−1 70 R2500 = 403 kpc h−1 70 R2500 = 369 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure B.17: Radial metallicity profile for clusters A2537 through A4038. Radial metallicity profiles for the following clusters: A2537, A2550, A2556, AS1101, A2597, A2626, 23442-0422, A2657, A4038. 156 r[arcmin] 0.05 0.15 0.50 1.50 5.01 1.00 0.30 Z[Z ] 0.10 ABELL 2670 0.03 z = 0.08 R2500 = 435 kpc h−1 70 0.01 0.01 0.03 0.10 0.30 1.00 r/r2500 Figure B.18: Radial metallicity profile for A2670. Radial metallicity profile for A2670. 157 APPENDIX C RADIAL TEMPERATURE PROFILES FOR ACCEPT2.0 CLUSTERS Radial temperature profiles for 154 ACCEPT2.0 clusters. (For a description, see Chapter 2.) 158 r[arcmin] 0.04 0.12 0.44 1.31 4.38 0.02 0.07 0.23 0.70 2.34 0.08 0.25 0.84 2.52 8.44 20 ABELL z = 0.09 0013 ABELL 0085 z = 0.06 R2500 = 461 kpc h−1 70 R2500 = 543 kpc h−1 70 10 kT [keV] 5 2 ABELL 2744 z = 0.31 R2500 = 640 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.04 0.14 0.46 1.40 4.66 0.03 0.09 0.33 1.02 3.43 0.10 0.31 1.03 3.10 10.35 20 ZwCl 0040.8 + 2404 ESO 351 − G 021 z = 0.08 z = 0.06 R2500 = 437 kpc h−1 70 R2500 = 228 kpc h−1 70 10 kT [keV] 5 2 ABELL 0119 z = 0.04 R2500 = 541 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.02 0.05 0.17 0.52 1.76 0.05 0.16 0.54 1.62 5.40 0.04 0.15 0.51 1.55 5.21 20 M axBCG J016.70077 + 01.05926 z = 0.25 ABELL 0160 z = 0.04 R2500 = 419 kpc h−1 70 R2500 = 275 kpc h−1 70 10 kT [keV] 5 2 CIZA J0107.7 + 5408 z = 0.11 R2500 = 634 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.1: Radial temperature profile for clusters A0013 through A0160. Radial temper- ature profiles for the following clusters: A0013, A2744, A0085, 00408+2404, 351-021, A0119, 01670077+0105926, 01077+5408, A0160. 159 r[arcmin] 0.06 0.19 0.66 1.98 6.67 0.04 0.13 0.49 1.48 4.96 0.07 0.21 0.70 2.13 7.12 20 N SCS J011502 + 002441 z = 0.04 U GC 00842 z = 0.05 ABELL 0193 z = 0.05 R2500 = 353 kpc h−1 70 R2500 = 265 kpc h−1 70 R2500 = 407 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.02 0.06 0.19 0.59 1.97 0.07 0.25 0.81 2.46 8.22 0.02 0.07 0.25 0.75 2.49 20 ABELL 0376 ABELL 0383 z = 0.05 z = 0.19 R2500 = 468 kpc h−1 70 R2500 = 470 kpc h−1 70 10 kT [keV] 5 2 ABELL S0295 z = 0.30 R2500 = 529 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.06 0.21 0.69 2.09 6.98 0.07 0.21 0.71 2.16 7.23 0.04 0.14 0.48 1.43 4.76 20 ABELL 3094 z = 0.07 R2500 = 371 kpc h−1 70 10 kT [keV] 5 2 ABELL 0399 ABELL 0401 z = 0.07 z = 0.07 R2500 = 574 kpc h−1 70 R2500 = 609 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.2: Radial temperature profile for clusters 011502+002441 through A3094. Radial temperature profiles for the following clusters: 011502+002441, UGC00842, A0193, AS0295, A0376, A0383, A0399, A0401, A3094. 160 r[arcmin] 0.04 0.16 0.53 1.60 5.36 0.04 0.12 0.41 1.26 4.22 0.09 0.29 0.95 2.87 9.60 20 ABELL 3128 M CXC J0340.8 − 4542 III Zw 054 z = 0.06 z = 0.07 z = 0.03 R2500 = 373 kpc h−1 70 R2500 = 338 kpc h−1 70 R2500 = 335 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.06 0.20 0.69 2.08 6.92 0.03 0.08 0.30 0.91 3.04 0.05 0.17 0.60 1.81 6.04 20 ABELL z = 0.06 3158 M CXC J0352.9 + 1941 z = 0.11 ABELL 0478 z = 0.09 R2500 = 480 kpc h−1 70 R2500 = 364 kpc h−1 70 R2500 = 598 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.02 0.05 0.18 0.54 1.81 0.06 0.23 0.78 2.39 8.03 0.06 0.21 0.75 2.24 7.54 20 M CXC J0425.8 − 0833 ABELL S0463 z = 0.04 z = 0.04 R2500 = 379 kpc h−1 70 R2500 = 353 kpc h−1 70 10 kT [keV] 5 2 M ACS J0417.5 − 1154 z = 0.44 R2500 = 624 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.3: Radial temperature profile for clusters A3128 through AS0463. Radial temperature profiles for the following clusters: A3128, 03408-4542, IIIZw054, A3158, 03529+1941, A0478, 04175-1154, 04258-0833, AS0463. 161 r[arcmin] 0.02 0.06 0.20 0.60 2.00 0.05 0.15 0.49 1.47 4.92 0.08 0.24 0.82 2.49 8.39 20 ABELL 0514 ESO 552 − G 020 z = 0.07 z = 0.03 R2500 = 402 kpc h−1 70 R2500 = 316 kpc h−1 70 10 kT [keV] 5 2 M CXC J0437.1 + 0043 z = 0.28 R2500 = 518 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.09 0.29 1.05 3.16 10.58 0.02 0.08 0.26 0.79 2.64 0.02 0.07 0.23 0.69 2.30 20 ABELL 0539 M CXC J0528.2 − 2942 z = 0.03 z = 0.16 R2500 = 362 kpc h−1 70 R2500 = 434 kpc h−1 70 10 kT [keV] 5 2 RBS 0653 z = 0.28 R2500 = 594 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.07 0.23 0.82 2.46 8.24 0.06 0.23 0.79 2.36 7.90 0.07 0.26 0.91 2.75 9.22 20 ESO3060170 −A ABELL 0548A ABELL 3376 z = 0.04 z = 0.04 z = 0.05 R2500 = 352 kpc h−1 70 R2500 = 371 kpc h−1 70 R2500 = 496 kpc h−1 70 10 kT [keV] 5 2 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.4: Radial temperature profile for clusters 04371+0043 through A3376. Radial temperature profiles for the following clusters: 04371+0043, A0514, 552-020, A0539, 05282- 2942, RBS0653, 3060170-, A0548A, A3376. 162 r[arcmin] 0.08 0.27 0.90 2.72 9.11 0.02 0.08 0.29 0.87 2.93 0.03 0.08 0.26 0.80 2.66 20 ABELL 0562 z = 0.11 R2500 = 353 kpc h−1 70 10 kT [keV] 5 2 ABELL 3391 Bullet Cluster z = 0.05 z = 0.30 R2500 = 549 kpc h−1 70 R2500 = 708 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.02 0.05 0.17 0.50 1.67 0.03 0.09 0.34 1.02 3.39 0.02 0.07 0.24 0.73 2.44 20 ABELL 0578 ZwCl 0735.7 + 7421 z = 0.09 z = 0.22 R2500 = 331 kpc h−1 70 R2500 = 516 kpc h−1 70 10 kT [keV] 5 2 M ACS J0717 + 3745 z = 0.55 R2500 = 647 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.05 0.16 0.55 1.65 5.53 0.04 0.19 0.64 1.99 6.70 0.02 0.07 0.22 0.65 2.18 20 P KS 0745 − 19 W BL 154 z = 0.10 z = 0.02 R2500 = 628 kpc h−1 70 R2500 = 179 kpc h−1 70 10 kT [keV] 5 2 ABELL 0611 z = 0.29 R2500 = 571 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.5: Radial temperature profile for clusters A3391 through A0611. Radial temperature profiles for the following clusters: A3391, A0562, , 0717+3745, A0578, 07357+7421, PKS0745- 19, WBL154, A0611. 163 r[arcmin] 0.06 0.21 0.69 2.11 7.02 0.03 0.10 0.33 1.00 3.33 0.02 0.06 0.19 0.58 1.94 20 2M F GC 06756 z = 0.24 R2500 = 445 kpc h−1 70 10 kT [keV] 5 2 ABELL 0644 ABELL 0665 z = 0.07 z = 0.18 R2500 = 567 kpc h−1 70 R2500 = 614 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.03 0.09 0.29 0.89 2.99 0.03 0.08 0.26 0.78 2.60 0.02 0.05 0.19 0.56 1.87 20 N SC J084254 + 292723 ZwCl 0857.9 + 2107 z = 0.19 z = 0.23 R2500 = 505 kpc h−1 70 R2500 = 414 kpc h−1 70 10 kT [keV] 5 2 ABELL 3411 z = 0.17 R2500 = 519 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.02 0.08 0.26 0.78 2.60 0.02 0.08 0.27 0.82 2.74 0.06 0.19 0.67 2.01 6.72 20 SDSS z = 0.18 + 137.3 + 11.0 + 0.18 Hydra A z = 0.05 R2500 = 475 kpc h−1 70 R2500 = 431 kpc h−1 70 10 kT [keV] 5 2 ABELL 0773 z = 0.22 R2500 = 581 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.6: Radial temperature profile for clusters A0644 through HydraA. Radial tempera- ture profiles for the following clusters: A0644, A0665, 2MFGC06756, A3411, 084254+292723, 08579+2107, +1373+110+018, A0773, HydraA. 164 r[arcmin] 0.02 0.05 0.18 0.55 1.83 0.02 0.07 0.22 0.68 2.28 0.03 0.09 0.31 0.95 3.15 20 ZwCl 0949.6 + 5207 ABELL 0907 z = 0.21 z = 0.15 R2500 = 479 kpc h−1 70 R2500 = 504 kpc h−1 70 10 kT [keV] 5 2 GALEX J094712.4 + 762313 z = 0.35 R2500 = 550 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.02 0.07 0.22 0.68 2.27 0.02 0.07 0.26 0.78 2.59 0.06 0.19 0.66 1.99 6.65 20 ZwCl 1006.1 + 1201 z = 0.22 ABELL 0970 z = 0.06 R2500 = 488 kpc h−1 70 R2500 = 454 kpc h−1 70 10 kT [keV] 5 2 ABELL 0963 z = 0.21 R2500 = 527 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.03 0.09 0.32 0.96 3.22 0.02 0.06 0.22 0.67 2.24 0.04 0.11 0.37 1.11 3.69 20 BLOX J1023.6 + 0411.1 ABELL 1033 z = 0.29 z = 0.13 R2500 = 589 kpc h−1 70 R2500 = 501 kpc h−1 70 10 kT [keV] 5 2 ABELL 0980 z = 0.16 R2500 = 529 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.7: Radial temperature profile for clusters 0947124+762313 through A1033. Ra- dial temperature profiles for the following clusters: 0947124+762313, 09496+5207, A0907, 10061+1201, A0963, A0970, A0980, 10236+04111, A1033. 165 r[arcmin] 0.03 0.09 0.31 0.94 3.17 0.05 0.27 0.90 2.81 9.50 0.02 0.10 0.35 1.04 3.48 20 ABELL z = 0.14 1068 N GC 3402 GROU P z = 0.02 M CXC J1053.7 + 5452 z = 0.07 R2500 = 463 kpc h−1 70 R2500 = 179 kpc h−1 70 R2500 = 281 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.02 0.08 0.28 0.85 2.84 0.03 0.11 0.37 1.15 3.86 0.03 0.12 0.42 1.27 4.24 20 ABELL z = 0.17 1201 M CXC J1130.0 + 3637 z = 0.06 ABELL 1285 z = 0.11 R2500 = 492 kpc h−1 70 R2500 = 269 kpc h−1 70 R2500 = 496 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.05 0.17 0.57 1.71 5.70 0.03 0.11 0.38 1.15 3.83 0.02 0.06 0.21 0.63 2.11 20 SDSS − C4 − DR3 3018 ABELL 1423 z = 0.05 z = 0.21 R2500 = 341 kpc h−1 70 R2500 = 441 kpc h−1 70 10 kT [keV] 5 2 ABELL 1413 z = 0.14 R2500 = 578 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.8: Radial temperature profile for clusters A1068 through A1423. Radial temperature profiles for the following clusters: A1068, 3402, 10537+5452, A1201, 11300+3637, A1285, 4-33018, A1413, A1423. 166 r[arcmin] 0.02 0.09 0.28 0.87 2.93 0.03 0.10 0.34 1.02 3.41 0.06 0.23 0.79 2.43 8.18 20 SDSS − C4 − DR3 3144 ABELL 1446 N GC 4104 GROU P z = 0.08 z = 0.10 z = 0.03 R2500 = 269 kpc h−1 70 R2500 = 390 kpc h−1 70 R2500 = 279 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.06 0.19 0.65 1.97 6.59 0.07 0.20 0.66 1.97 6.63 0.04 0.11 0.37 1.12 3.75 20 N GC 4325 GROU P ABELL 1569 z = 0.03 z = 0.07 R2500 = 202 kpc h−1 70 R2500 = 315 kpc h−1 70 10 kT [keV] 5 2 N SC J121733 + 033929 z = 0.08 R2500 = 576 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.07 0.25 0.86 2.58 8.63 0.05 0.16 0.54 1.63 5.43 0.03 0.10 0.33 1.02 3.39 20 ABELL z = 0.05 1644 ABELL 1650 z = 0.08 ABELL 1664 z = 0.13 R2500 = 481 kpc h−1 70 R2500 = 514 kpc h−1 70 R2500 = 468 kpc h−1 70 10 kT [keV] 5 2 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.9: Radial temperature profile for clusters 4-33144 through A1664. Radial temperature profiles for the following clusters: 4-33144, A1446, 4104, 121733+033929, 4325, A1569, A1644, A1650, A1664. 167 r[arcmin] 0.03 0.11 0.36 1.09 3.65 0.05 0.14 0.48 1.44 4.88 0.06 0.20 0.70 2.15 7.16 20 N GC 5098 GROU P ABELL 1736 z = 0.04 z = 0.05 R2500 = 213 kpc h−1 70 R2500 = 387 kpc h−1 70 10 kT [keV] 5 2 ABELL 1689 z = 0.18 R2500 = 676 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.05 0.19 0.67 2.05 6.84 0.05 0.17 0.58 1.73 5.77 0.07 0.21 0.71 2.13 7.16 20 SSGC 081 ABELL 1750C SC 1329 − 313 z = 0.05 z = 0.07 z = 0.05 R2500 = 398 kpc h−1 70 R2500 = 450 kpc h−1 70 R2500 = 406 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.07 0.24 0.82 2.45 8.16 0.05 0.15 0.49 1.49 4.97 0.02 0.06 0.20 0.62 2.06 20 ABELL z = 0.05 3562 ABELL 1775 z = 0.07 R2500 = 470 kpc h−1 70 R2500 = 408 kpc h−1 70 10 kT [keV] 5 2 LCDCS 0829 z = 0.45 R2500 = 718 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.10: Radial temperature profile for clusters A1689 through LCDCS0829. Radial temperature profiles for the following clusters: A1689, 5098, A1736, SSGC081, A1750C, SC1329- 313, A3562, A1775, LCDCS0829. 168 r[arcmin] 0.03 0.08 0.27 0.81 2.71 0.02 0.07 0.26 0.77 2.58 0.01 0.03 0.12 0.36 1.19 20 ABELL z = 0.25 1835 A1882a z = 0.14 GM BCG J215.94948 + 24.07846 z = 0.54 R2500 = 646 kpc h−1 70 R2500 = 385 kpc h−1 70 R2500 = 462 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.03 0.10 0.36 1.08 3.61 0.03 0.09 0.31 0.94 3.13 0.02 0.06 0.21 0.64 2.14 20 ABELL 1930 ABELL 1942 AN D CLU M P z = 0.13 z = 0.22 R2500 = 440 kpc h−1 70 R2500 = 465 kpc h−1 70 10 kT [keV] 5 2 ABELL 1914 z = 0.17 R2500 = 633 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.09 0.34 1.11 3.38 11.30 0.04 0.15 0.50 1.51 5.07 0.02 0.05 0.19 0.56 1.87 20 W BL 518 z = 0.03 ABELL 1991 z = 0.06 N SCS J145715 + 222009 z = 0.26 R2500 = 368 kpc h−1 70 R2500 = 346 kpc h−1 70 R2500 = 452 kpc h−1 70 10 kT [keV] 5 2 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.11: Radial temperature profile for clusters A1835 through 145715+222009. Radial temperature profiles for the following clusters: A1835, A1882a, 21594948+2407846, A1914, A1930, 1942, WBL518, A1991, 145715+222009. 169 r[arcmin] 0.02 0.07 0.24 0.73 2.44 0.03 0.10 0.34 1.01 3.39 0.03 0.09 0.29 0.88 2.94 20 ABELL S0780 ABELL 2009 W HL J150407.5 − 024816 z = 0.24 z = 0.15 z = 0.22 R2500 = 551 kpc h−1 70 R2500 = 543 kpc h−1 70 R2500 = 620 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.04 0.14 0.48 1.44 4.82 0.04 0.15 0.51 1.54 5.13 0.06 0.21 0.73 2.22 7.41 20 ABELL z = 0.11 2034 ABELL 2061 z = 0.08 M KW 03s z = 0.04 R2500 = 595 kpc h−1 70 R2500 = 457 kpc h−1 70 R2500 = 394 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.04 0.12 0.41 1.24 4.15 0.04 0.11 0.39 1.17 3.91 0.02 0.05 0.18 0.53 1.76 20 M CXC J1524.2 − 3154 M ACS J1532.8 + 3021 z = 0.10 z = 0.34 R2500 = 444 kpc h−1 70 R2500 = 522 kpc h−1 70 10 kT [keV] 5 2 ABELL 2069 z = 0.12 R2500 = 525 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.12: Radial temperature profile for clusters AS0780 through 15328+3021. Radial temperature profiles for the following clusters: AS0780, A2009, 1504075-024816, A2034, A2061, MKW03s, A2069, 15242-3154, 15328+3021. 170 r[arcmin] 0.08 0.27 0.88 2.67 8.90 0.03 0.10 0.35 1.05 3.53 0.05 0.19 0.63 1.92 6.41 20 ABELL z = 0.04 2107 ABELL 2124 z = 0.07 R2500 = 434 kpc h−1 70 R2500 = 485 kpc h−1 70 10 kT [keV] 5 2 ABELL 2104 z = 0.15 R2500 = 565 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.06 0.18 0.61 1.84 6.15 0.04 0.13 0.44 1.33 4.47 0.10 0.31 1.05 3.20 10.73 20 ABELL 2142 M CXC J1558.3 − 1410 ABELL 2147 z = 0.09 z = 0.10 z = 0.04 R2500 = 626 kpc h−1 70 R2500 = 483 kpc h−1 70 R2500 = 449 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.07 0.23 0.80 2.45 8.20 0.03 0.11 0.39 1.18 3.95 0.04 0.12 0.41 1.23 4.11 20 ABELL z = 0.04 2151 ABELL 2204 z = 0.15 R2500 = 358 kpc h−1 70 R2500 = 654 kpc h−1 70 10 kT [keV] 5 2 ABELL 2163 z = 0.20 R2500 = 795 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.13: Radial temperature profile for clusters A2107 through A2204. Radial temperature profiles for the following clusters: A2107, A2104, A2124, A2142, 15583-1410, A2147, A2151, A2163, A2204. 171 r[arcmin] 0.03 0.08 0.29 0.87 2.90 0.03 0.09 0.32 0.96 3.20 0.02 0.07 0.25 0.77 2.59 20 Hercules A z = 0.15 R2500 = 419 kpc h−1 70 10 kT [keV] 5 2 ABELL 2218 ABELL 2219 z = 0.18 z = 0.23 R2500 = 520 kpc h−1 70 R2500 = 699 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.07 0.22 0.72 2.21 7.40 0.05 0.14 0.47 1.43 4.78 0.07 0.25 0.86 2.59 8.67 20 N GC 6269 z = 0.03 R2500 = 308 kpc h−1 70 10 kT [keV] 5 2 ABELL 2244 ABELL 2256 z = 0.10 z = 0.06 R2500 = 515 kpc h−1 70 R2500 = 586 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.05 0.16 0.58 1.74 5.80 0.09 0.30 1.00 3.03 10.17 0.03 0.09 0.33 0.99 3.30 20 ABELL 2255 N GC 6338 SDSS − C4 3072 z = 0.08 z = 0.03 z = 0.16 R2500 = 530 kpc h−1 70 R2500 = 336 kpc h−1 70 R2500 = 560 kpc h−1 70 10 kT [keV] 5 2 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.14: Radial temperature profile for clusters A2218 through 43072. Radial temperature profiles for the following clusters: A2218, A2219, HerculesA, NGC6269, A2244, A2256, A2255, NGC6338, 43072. 172 r[arcmin] 0.02 0.08 0.27 0.82 2.73 0.05 0.15 0.50 1.52 5.06 0.09 0.31 1.03 3.09 10.31 20 ZwCl 1742.1 + 3306 z = 0.08 R2500 = 437 kpc h−1 70 10 kT [keV] 5 2 ABELL 2261 ABELL 2319 z = 0.22 z = 0.06 R2500 = 593 kpc h−1 70 R2500 = 670 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.02 0.05 0.18 0.54 1.80 0.03 0.10 0.34 1.01 3.35 0.07 0.21 0.72 2.21 7.40 20 M ACS J1931.8 − 2635 M CXC J2014.8 − 2430 IC 1365 z = 0.35 z = 0.16 z = 0.05 R2500 = 540 kpc h−1 70 R2500 = 560 kpc h−1 70 R2500 = 429 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.01 0.05 0.17 0.51 1.69 0.04 0.14 0.49 1.47 4.91 0.05 0.14 0.48 1.46 4.90 20 M ACS J2140.2 − 2339 ABELL 3809 ABELL 2384 z = 0.31 z = 0.06 z = 0.09 R2500 = 468 kpc h−1 70 R2500 = 354 kpc h−1 70 R2500 = 516 kpc h−1 70 10 kT [keV] 5 2 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.15: Radial temperature profile for clusters A2261 through A2384. Radial temperature profiles for the following clusters: A2261, 17421+3306, A2319, 19318-2635, 20148-2430, IC1365, 21402-2339, A3809, A2384. 173 r[arcmin] 0.03 0.09 0.30 0.91 3.03 0.02 0.07 0.23 0.69 2.30 0.05 0.16 0.53 1.60 5.35 20 ABELL z = 0.23 2390 R2500 = 668 kpc h−1 70 10 kT [keV] 5 2 ClG 2153.8 + 3746 ABELL 3827 z = 0.29 z = 0.10 R2500 = 608 kpc h−1 70 R2500 = 585 kpc h−1 70 1 r/r2500 r/r2500 r/r2500 0.04 0.15 0.50 1.52 5.09 0.02 0.09 0.29 0.88 2.96 0.04 0.15 0.52 1.56 5.24 20 ABELL z = 0.06 2415 3C 444 z = 0.15 ABELL 3880 z = 0.06 R2500 = 344 kpc h−1 70 R2500 = 473 kpc h−1 70 R2500 = 356 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.06 0.17 0.59 1.80 6.00 0.03 0.09 0.31 0.92 3.09 0.05 0.14 0.50 1.50 5.03 20 ABELL z = 0.06 2457 ABELL 3921 z = 0.09 R2500 = 414 kpc h−1 70 R2500 = 522 kpc h−1 70 10 kT [keV] 5 2 CIZA J2242.8 + 5301 z = 0.19 R2500 = 595 kpc h−1 70 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.16: Radial temperature profile for clusters A2390 through A3921. Radial temperature profiles for the following clusters: A2390, 21538+3746, A3827, A2415, 3C444, A3880, A2457, 22428+5301, A3921. 174 r[arcmin] 0.02 0.06 0.19 0.57 1.90 0.02 0.06 0.20 0.62 2.08 0.04 0.12 0.42 1.25 4.21 20 ABELL z = 0.29 2537 ABELL 2550 z = 0.12 ABELL 2556 z = 0.09 R2500 = 506 kpc h−1 70 R2500 = 276 kpc h−1 70 R2500 = 413 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.04 0.15 0.50 1.53 5.11 0.04 0.14 0.46 1.37 4.60 0.05 0.17 0.59 1.77 5.92 20 ABELL z = 0.06 S1101 ABELL 2597 z = 0.09 ABELL 2626 z = 0.06 R2500 = 345 kpc h−1 70 R2500 = 442 kpc h−1 70 R2500 = 382 kpc h−1 70 10 kT [keV] 5 2 1 r/r2500 r/r2500 r/r2500 0.04 0.15 0.50 1.51 5.04 0.08 0.25 0.84 2.51 8.44 0.09 0.32 1.06 3.24 10.86 20 M CXC J2344.2 − 0422 ABELL 2657 ABELL 4038 z = 0.08 z = 0.04 z = 0.03 R2500 = 450 kpc h−1 70 R2500 = 403 kpc h−1 70 R2500 = 369 kpc h−1 70 10 kT [keV] 5 2 1 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 0.01 0.03 0.10 0.30 1.00 r/r2500 r/r2500 r/r2500 Figure C.17: Radial temperature profile for clusters A2537 through A4038. Radial temperature profiles for the following clusters: A2537, A2550, A2556, AS1101, A2597, A2626, 23442-0422, A2657, A4038. 175 r[arcmin] 0.05 0.15 0.50 1.50 5.01 20 ABELL z = 0.08 2670 R2500 = 435 kpc h−1 70 10 kT [keV] 5 2 1 0.01 0.03 0.10 0.30 1.00 r/r2500 Figure C.18: Radial temperature profile for A2670. Radial temperature profile for A2670. 176 BIBLIOGRAPHY 177 BIBLIOGRAPHY Abell, G. O. 1958, The Astrophysical Journal Supplement Series, 3, 211 Ahn, C. P., Alexandroff, R., Allende Prieto, C., et al. 2012, The Astrophysical Journal Supplement Series, 203, 21 Alam, S., Albareti, F. D., Allende Prieto, C., et al. 2015, The Astrophysical Journal Supplement, 219, 12 Anders, E., & Grevesse, N. 1989a, Geochimica et Cosmochimica Acta, 53, 197 —. 1989b, Geochimica et Cosmochimica Acta, 53, 197 Anderson, M. E., Bregman, J. N., Butler, S. C., & Mullis, C. R. 2009, The Astrophysical Journal, 698, 317 Andrade-Santos, F., Jones, C., Forman, W. 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