THE UNIVERSITY OF CHICAGO DARK MATTER HALOS AND THEIR ENVIRONMENTS A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ASTRONOMY & ASTROPHYSICS BY PHILIP MANSFIELD CHICAGO, ILLINOIS AUGUST 2020 Copyright c 2020 by Philip Mansfield All Rights Reserved Dedicated to the 2016-2017 students of the KICP Space Explorers program: the greatest scientists I have ever met. \To turn around that close to the summit...," Hall mused with a shake of his head on May 6 as Kropp plodded past Camp Two on his way down the mountain. \That showed incredibly good judgment on young G¨oran's part. I'm impressed - considerably more impressed than if he'd continued climbing and made the top." | Jon Krakauer, Into Thin Air, pp. 190 TABLE OF CONTENTS LIST OF FIGURES . viii LIST OF TABLES . ix ACKNOWLEDGMENTS . x ABSTRACT . xii 1 PROLOGUE . 1 2 AN INTERGALACTIC MURDER MYSTERY: WHY DO DARK MATTER HALOS DIE TOGETHER? . 7 2.1 The Setting: Galaxies and Dark Matter Halos . 7 2.1.1 Galaxies, Satellite Galaxies, and Distances . 7 2.1.2 Dark Matter . 10 2.1.3 Dark Matter Halos and Dark Matter Subhalos . 14 2.1.4 The Cosmic Web and Large Scale Structure . 19 2.2 The Crime: Assembly Bias . 22 2.3 The Suspects: Tides, Heating, and Misadventure . 25 2.4 The Plan: The Structure of This Thesis . 28 3 TECHNICAL BACKGROUND . 31 3.1 Simulations . 31 3.1.1 Force Softening . 34 3.2 Halo Finding and Halo Properties . 36 4 SPLASHBACK SHELLS OF COLD DARK MATTER HALOS . 43 4.1 Introduction . 43 4.2 Methods . 47 4.2.1 Simulations . 47 4.2.2 Algorithm Description . 48 4.2.3 Definitions of Basic Splashback Shell Properties . 55 4.2.4 Summary of the Algorithm Parameters . 56 4.3 Tests . 58 4.3.1 Comparison to Particle Trajectories . 62 4.4 Results . 63 4.4.1 Sample Selection . 63 4.4.2 Comparison With Stacked Radial Density Profiles . 65 4.4.3 Angular Median Density Profiles of Halos . 68 4.4.4 The Relationship Between Mass, Accretion Rate, and Splashback Radius 73 4.4.5 Splashback Shell Masses . 77 4.4.6 Splashback Shell Overdensities . 79 4.4.7 Splashback Shell Shapes . 79 v 4.5 Summary and Conclusions . 82 4.6 Appendices . 85 4.6.1 An Algorithm for Fast Line of Sight Density Estimates . 85 4.6.2 Splashback Candidate Filtering Algorithm . 88 4.6.3 Parameter-Specific Convergence Tests . 90 4.6.4 Setting Rkernel .............................. 91 4.6.5 Setting Nplanes .............................. 92 4.6.6 Computing Moment of Inertia-Equivalent Ellipsoidal Shell Axes . 94 5 HOW BIASED ARE COSMOLOGICAL SIMULATIONS? . 96 5.1 Introduction . 96 5.2 Methods . 99 5.2.1 Simulations and Halo Finding . 99 5.2.2 Halo Properties . 102 5.2.3 Finding Empirical \Convergence Limits" . 102 5.3 The Empirical Nvir Convergence Limits of Simulations . 111 5.3.1 Typical Convergence Limits . 111 5.3.2 Variation in Limits Between Simulations . 115 5.3.3 Differences Between Multidark and Illustris-TNG . 117 5.4 The Dependence of Halo Properties on Force Softening Scale . 119 5.4.1 Dependence of the Subhalo Mass Function on . 122 5.5 Estimating the Impact of Large on Vmax . 124 5.6 Discussion . 129 5.6.1 Timestepping as an Additional Source of Biases . 129 5.6.2 What is the \Optimal" ? . 135 5.7 Conclusion . 136 5.8 Appendices . 138 5.8.1 Recalibrating the Plummer-Equivalence Scale . 138 5.8.2 Fitting Parameters For Mean Halo Property Relations . 143 6 THE THREE CAUSES OF LOW-MASS ASSEMBLY BIAS . 145 6.1 Introduction . 145 6.2 Methods . 151 6.2.1 Simulations and codes . 151 6.2.2 Basic halo properties . 151 6.2.3 Definition of Halo Boundaries and Subhalos . 153 6.2.4 Halo Sample . 157 6.2.5 Measuring Tidal Force Strength . 158 6.2.6 Measuring Gravitational Heating . 161 6.2.7 Assembly Bias Statistics . 162 6.2.8 Measuring the Connection Between Assembly Bias and Other Variables163 6.3 Analysis . 167 6.3.1 Splashback Subhalos and Assembly Bias . 167 6.3.2 Contribution of Tidal Truncation and Gravitational Heating to As- sembly Bias . 169 vi 6.3.3 The Spatial and Concentration Distributions of the Halos Responsible for Assembly Bias . 173 6.3.4 Time and Mass Dependence of Assembly Bias . 178 6.3.5 Sensitivity to Splashback Subhalo Identification Method . 179 6.3.6 Comparison of the Bolshoi and BolshoiP Simulations . 180 6.4 Discussion . 181 6.4.1 Issues Associated with Proxy Definitions . 181 6.4.2 Sensitivity of Results to Definitional Choices . 181 6.4.3 Comparison with Previous Work . 184 6.4.4 Directions for Future Work . 188 6.5 Summary and Conclusions . 189 6.6 Appendices . 191 6.6.1 Effects of Halo Definition on Concentration in the Rockstar Halo Finder191 6.6.2 Fast Halo Containment Checks . 194 6.6.3 Tidal Force Errors . 195 6.6.4 Identifying Bound Particles in Halo Outskirts . 200 vii LIST OF FIGURES 2.1 Simulated image of a dark matter halo . 16 2.2 Simulated image of the cosmic web . 20 2.3 Qualitative illustration of assembly bias . 23 4.1 Overview of the Shellfish algorithm . 49 4.2 Shellfish surfaces compared against the density fields of several halos . 57 4.3 Convergence tests for various splashback surface properties . 59 4.4 A rare example of the Shellfish algorithm failing catastrophically . 61 4.5 Comparison between Shellfish surfaces and particle trajectories . 64 4.6 Disparity between Rsp measured by Shellfish and by stacked density profiles . 66 4.7 Demonstrations that spherically averaged profiles lead to biased Rsp: . 69 4.8 Agreement between Rsp measured by Shellfish and the median profile method 72 4.9 Fit to the Rsp(ΓDK14; ν200m; z) distribution . 74 4.10 Fit to the Msp(ΓDK14; ν200m; z) distribution . 75 4.11 Illustration of the scatter in the Msp fit. 75 4.12 Fit to the ∆sp(ΓDK14; ν200m; z) distribution . 80 4.13 The asphericity and ellipticity of splashback surfaces . 81 4.14 The alignment between the major axes of halos and their splashback surfaces . 81 4.15 Illustration of the Shellfish ray-tracing algorithm . 84 4.16 Convergence tests for Shellfish nuisance parameters . 93 5.1 Illustration of procedure for finding convergence limits . 103 5.2 The variation in Vmax convergence limits between simulations . 112 5.3 The convergence behavior of Vmax=Vvir and c=a as functions of Mvir . 113 5.4 Disagreement between Multidarkh and IllustrisTNG-Darki h i . 117 5.5 The dependence of various halo properties on force softening scale . 121 5.6 The dependence of subhalo abundances on force softening scale . 122 5.7 Analytic estimates of halo bias due to large . 130 5.8 Impact of analytic bias estimates on the full simulation suite. 131 5.9 Impact of force softening on gravitational fields and rotation curves . 139 6.1 Age-dependent clustering with and without splashback subhalos . 149 6.2 The impact of removing different halo populations on assembly bias . 167 6.3 How efficiently different cuts remove assembly bias from the entire halo population168 6.4 The distribution of different halo groups throughout the entire simulation box . 174 6.5 The distribution of different halo groups around a single dense filament . 175 6.6 The distribution of concentrations for different halo groups . 176 6.7 The mass and redshift dependence of assembly bias for different halo groups . 177 6.8 The impact of tracing age with a1=2 on assembly bias measurements . 182 6.9 The influence of Rockstar parameters on concentration measurements . 193 6.10 Tests of the errors associated with approximations of the tidal field around halos 196 viii LIST OF TABLES 3.1 Simulation parameters . ..