Dark Matter in Galaxy Clusters: Shape, Projection, and Environment A Thesis Submitted to the Faculty of Drexel University by Austen M. Groener in partial fulfillment of the requirements for the degree of Doctor of Philosophy September 2015 c Copyright 2015 Austen M. Groener. ii Dedications I dedicate this thesis to my family, and to my wife, who supported me unconditionally throughout my career as a scientist. iii Acknowledgments I have many people to thank for making this work a possibility. Firstly, I would like to thank my advisor, Dr. David Goldberg. His guidance, support, and most of all his patience provided the framework for which I was able to build my work from. I would also like to thank my dissertation committee members, Dr. Michael Vogeley, Dr. Gordon Richards, Dr. Luis Cruz, and Dr. Andrew Hicks, for their constructive criticism and support of my research. I would also like to acknowledge fellow graduate students for their assistance and support. A special thanks to Justin Bird, Markus Rexroth, Frank Jones, Crystal Moorman, and Vishal Kasliwal for allowing me to bounce ideas off of them, which was a truly important but time consuming process. iv Table of Contents List of Tables ........................................... vi List of Figures .......................................... vii Abstract .............................................. ix 1. Introduction .......................................... 1 1.1 The Radial Density Profile.................................. 2 1.2 Cluster Scaling Relations .................................. 5 1.3 Clusters and Environment.................................. 7 1.4 Outline ............................................ 11 2. Cluster Shape and Orientation .............................. 12 2.1 Introduction.......................................... 12 2.2 Triaxial Projections...................................... 14 2.3 Sample and Methods..................................... 15 2.3.1 Simulation Sample .................................... 15 2.3.2 Methods.......................................... 18 2.3.3 Non-Virialized Halos................................... 19 2.4 Results............................................. 21 2.5 Summary and Conclusions.................................. 28 2.6 Future Work ......................................... 37 3. The Observed c-M Relation ................................ 38 3.1 Introduction.......................................... 38 3.2 Reconstruction Techniques.................................. 41 3.2.1 Weak Lensing (WL) ................................... 41 3.2.2 Strong Lensing (SL) ................................... 42 3.2.3 Weak+Strong Lensing (WL+SL)............................ 43 v 3.2.4 X-ray............................................ 43 3.2.5 Line-of-sight Velocity Dispersion (LOSVD)....................... 44 3.2.6 The Caustic Method (CM)................................ 44 3.2.7 Hybrid Techniques .................................... 45 3.3 The Sample.......................................... 45 3.3.1 Normalization Procedure................................. 48 3.4 The Observed c-M Relation................................. 51 3.5 Projection and Shape .................................... 56 3.6 Conclusions And Discussions ................................ 61 4. Clusters And The LSS Environment ........................... 66 4.1 Introduction.......................................... 66 4.2 Data.............................................. 67 4.3 Galaxies Around Clusters .................................. 70 4.3.1 Quantifying Structure .................................. 71 4.4 Results And Future Work.................................. 74 5. Conclusions ........................................... 79 Bibliography ............................................ 82 Appendix A: Analytical Projection of Prolate Spheroidal Halos . 90 Appendix B: Lensing Cosmology Correction ....................... 92 Appendix C: Full Observational Dataset .......................... 94 Vita .................................................. 127 vi List of Tables 2.1 Prolate Spheroidal Geometry................................. 15 2.2 Cluster Halo Geometry .................................... 23 2.3 Concentration Enhancements................................. 30 3.1 Population Overview...................................... 47 3.2 Best-Fit Concentration-Mass Relation Parameters ..................... 54 C.1 Cluster concentrations and masses .............................. 96 C.2 A Summary of The References ................................ 123 vii List of Figures 1.1 X-ray Gas in Abell 383 .................................... 2 1.2 The NFW Profile........................................ 3 1.3 c-M Relations: Then and Now ................................ 8 1.4 Cluster Formation ....................................... 9 1.5 Bolshoi Simulation....................................... 10 2.1 Analytical concentration and shape relations......................... 16 2.2 The MultiDark MDR1 Mass Function............................. 17 2.3 Examples of Virialized and Non-Virialized Halos ...................... 20 2.4 The Virial β Parameter .................................... 22 2.5 Low Mass Shape Results.................................... 24 2.6 Medium Mass Shape Results ................................. 25 2.7 High Mass Shape Results ................................... 26 2.8 MDR1 Intrinsic Concentration Parameters.......................... 27 2.9 The Intrinsic MDR1 c-M Relation .............................. 29 2.10 Low Mass Concentration Enhancements........................... 31 2.11 Medium Mass Concentration Enhancements......................... 32 2.12 A Summary of The Change in Shape for the Low Mass Sample.............. 33 2.13 Low Mass Isodensity Alignment................................ 34 2.14 Medium Mass Isodensity Alignment ............................. 35 2.15 High Mass Isodensity Alignment ............................... 36 3.1 Cluster Population Overview ................................. 48 3.2 Concentration/Mass Cosmology Correction ......................... 49 3.3 The Normalized Data ..................................... 52 3.4 Observed c-M Fits....................................... 55 viii 3.5 CLASH Comparison...................................... 56 3.6 The Full c-M Relation..................................... 58 3.7 Lensing Relations and MDR1 Halos ............................. 59 3.8 Comparison of Theory with Observations .......................... 60 3.9 WL and WL+SL Cluster Measurements........................... 61 3.10 X-ray and WL Cluster Measurements ............................ 62 3.11 CM and LOSVD Cluster Measurements........................... 62 4.1 The SDSS DR10 Footprint .................................. 67 4.2 The Galaxy Sample Defined.................................. 68 4.3 Galaxy Clusters In SDSS ................................... 69 4.4 Selecting Galaxies Around Clusters.............................. 72 m 4.5 Mass - Al Correlation..................................... 76 m 4.6 Concentration - Al Correlation................................ 77 m 4.7 Redshift Scaled Concentration - Al Correlation ...................... 78 LIST OF FIGURES LIST OF FIGURES ix Abstract Dark Matter in Galaxy Clusters: Shape, Projection, and Environment Austen M. Groener Dr. David Goldberg We explore the intrinsic distribution of dark matter within galaxy clusters, by combining insights from the largest N-body simulations as well as the largest observational dataset of its kind. Firstly, we study the intrinsic shape and alignment of isodensities of galaxy cluster halos extracted from the MultiDark MDR1 cosmological simulation. We find that the simulated halos are extremely prolate on small scales and increasingly spherical on larger ones. Due to this trend, analytical projection along the line of sight produces an overestimate of the concentration index as a decreasing function of radius, which we quantify by using both the intrinsic distribution of 3D concentrations (c200) and isodensity shape on weak and strong lensing scales. We find this difference to be ∼ 18% (∼ 9%) for low (medium) mass cluster halos with intrinsically low concentrations (c200 = 1 − 3), while we find virtually no difference for halos with intrinsically high concentrations. Isodensities are found to be fairly well-aligned throughout the entirety of the radial scale of each halo population. However, major axes of individual halos have been found to deviate by as much as ∼ 30◦. We also present a value-added catalog of our analysis results, which we have made publicly available to download. Following that, we then turn to observational measurements galaxy clusters. Scaling relations of clusters have made them particularly important cosmological probes of structure formation. In this work, we present a comprehensive study of the relation between two profile observables, con- centration (cvir) and mass (Mvir). We have collected the largest known sample of measurements from the literature which make use of one or more of the following reconstruction techniques: Weak gravitational lensing (WL), strong gravitational lensing (SL), Weak+Strong Lensing (WL+SL), the Caustic Method (CM), Line-of-sight Velocity Dispersion (LOSVD), and X-ray. We find that the concentration-mass (c-M) relation is highly variable depending upon the reconstruction technique used. We also find concentrations derived from dark matter only simulations (at approximately 14 Mvir ∼ 10 M ) to be inconsistent with the WL and WL+SL relations at