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The Connection Between Galaxy Stellar Masses and Dark Matter Halo Masses: Constraints from Semi-Analytic Modeling and Correlation Functions by Catherine E. White A dissertation submitted to The Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy. Baltimore, Maryland August, 2016 c Catherine E. White 2016 ⃝ All rights reserved Abstract One of the basic observations that galaxy formation models try to reproduce is the buildup of stellar mass in dark matter halos, generally characterized by the stellar mass-halo mass relation, M? (Mhalo). Models have difficulty matching the < 11 observed M? (Mhalo): modeled low mass galaxies (Mhalo 10 M ) form their stars ∼ ⊙ significantly earlier than observations suggest. Our goal in this thesis is twofold: first, work with a well-tested semi-analytic model of galaxy formation to explore the physics needed to match existing measurements of the M? (Mhalo) relation for low mass galaxies and second, use correlation functions to place additional constraints on M? (Mhalo). For the first project, we introduce idealized physical prescriptions into the semi-analytic model to test the effects of (1) more efficient supernova feedback with a higher mass-loading factor for low mass galaxies at higher redshifts, (2) less efficient star formation with longer star formation timescales at higher redshift, or (3) less efficient gas accretion with longer infall timescales for lower mass galaxies. In addition to M? (Mhalo), we examine cold gas fractions, star formation rates, and metallicities to characterize the secondary effects of these prescriptions. ii ABSTRACT The technique of abundance matching has been widely used to estimate M? (Mhalo) at high redshift, and in principle, clustering measurements provide a powerful inde- pendent means to derive this relation. Our second project is to measure the M? (Mhalo) relation from clustering in the CANDELS fields. We measure angular correlation func- 8 12 tions in bins of stellar mass over 10 M < M? < 10 M and photometric redshifts ⊙ ⊙ 1 < z < 6, then calculate the linear bias from power law fit coefficients. To validate the measurement technique, we perform a careful analysis of the power-law mass measurement on a dark-matter simulation and use this to calibrate the conversion between clustering amplitude and linear bias (and hence, halo mass). Our clustering M? (Mhalo) relation is in agreement with abundance matching results and the ten- sion between the fiducial semi-analytic model and our best estimates of M? (Mhalo) remains. Primary Reader: Harry Ferguson Secondary Reader: Colin Norman iii Acknowledgments I would like to begin by thanking my advisor, Harry Ferguson, without whom I would not have finished my doctorate. He has been an amazing mentor, challenging me, allowing me to puzzle through most things on my own, and gently guiding me back to the path when I was too far off in the weeds. Throughout, he has been kind and understanding and I could not have asked for a better advisor. I would also like to thank my husband, who has spent the last several years helping me stay sane, supplying me alternately with advice, comfort, and frozen yogurt. He has also been exceedingly understanding the past few months, picking up chores as I disappeared into my work and always being available for hugs when I needed them. Thanks to my parents, who have always guided me, supported me, and encouraged me in all of my endeavors. My father has often helped me work through problems, scientific and professional alike, and my mother has always being willing to listen, commiserate, and offer hugs and wonderful food. Many thanks to Colin Norman and my colleagues on the CANDELS team, in particular Peter Behroozi, Rachel Somerville, Jeff Newman, Eric Gawiser, and Soo iv ACKNOWLEDGMENTS Lee for their support, assistance, and enlightening discussions. Thanks to my friends for their support and encouragement, and particular thanks to Alireza Mortazavi whose revision has significantly improved this work. Lastly, thanks to my cats, Andromeda and Remy, who blessed this thesis with an abundance of cat hair and provided the occasional adorable distraction. v Dedication For my father, who inspired my curiosity about the world around me; for my mother, who has always been at my side to support me; and for my husband, who loves me no matter how much I complain about correlation functions. vi Contents Abstract ii Acknowledgments iv List of Tables xii List of Figures xiii 1 Introduction 1 1.1 Cosmological context . 2 1.2 Galaxy processes . 6 1.3 Observing galaxy properties . 9 1.4 Trends in galaxy properties . 12 1.4.1 Stellar and halo masses . 12 1.4.2 Clustering . 17 1.5 Galaxy models . 20 1.5.1 Abundance matching . 21 vii CONTENTS 1.5.2 Halo occupation distributions . 22 1.5.3 Semi-analytic models . 25 1.5.4 Hydrodynamic models . 28 1.6 The problem . 30 1.6.1 Modeling problems . 31 1.6.2 Observational problems . 33 2 Matching M? (Mhalo) with semi-analytic models 35 2.1 Introduction . 35 2.1.1 The Problem . 36 2.1.2 Previous work . 38 2.1.3 The goal of this project . 39 2.2 Summary of the model . 42 2.2.1 Gas handling . 43 2.2.2 Star formation . 45 2.2.3 Stellar feedback . 46 2.2.4 Main free parameters . 47 2.3 Properties of the fiducial model . 48 2.3.1 Stellar mass function and f? ................... 49 2.3.2 Cold gas fractions . 52 2.3.3 Specific star formation rates . 55 2.3.4 Metallicity . 56 viii CONTENTS 2.4 Exploration of existing parameter space . 58 2.4.1 Varying Veject or Σcrit ....................... 61 2.4.2 Varying ϵSN or αRH ........................ 61 2.4.3 Varying τ? ............................. 63 2.4.4 Varying χReIn ........................... 64 2.5 Results with Modified Recipes . 65 2.5.1 Preferential reheating: changing stellar feedback scalings . 66 2.5.2 Direct suppression: changing the star formation efficiency . 75 2.5.3 Parking lot: changing gas accretion rates . 84 2.6 Comparison with the results of Henriques et al. (2013) . 94 2.7 Conclusions . 101 3 Calculating correlation functions 109 3.1 Introduction . 109 3.1.1 What is a correlation function? . 110 3.1.2 General properties of correlation functions . 112 3.1.3 Correlation function ingredients . 115 3.2 The data . 116 3.2.1 CANDELS survey . 117 3.2.1.1 CANDELS Photometry . 117 3.2.1.2 CANDELS Redshifts . 119 3.2.1.3 CANDELS Stellar masses . 120 ix CONTENTS 3.2.2 SHAMs . 120 3.2.3 SAMs . 121 3.3 Estimators . 124 3.4 Randoms . 128 3.5 Error bars . 130 3.6 Theta binning . 134 3.7 Integral constraint . 136 3.8 Combining fields . 140 3.9 Summary . 142 4 Mass measurement from correlation functions 145 4.1 Introduction . 146 4.2 Theory . 149 4.2.1 Definition of bias . .150 4.2.2 Calculating bias from correlation functions . 155 4.2.3 Getting 3D fit parameters from 2D fits . .158 4.2.4 Caveats . 161 4.3 Fitting a power law to the angular CF . 162 4.3.1 Fitting procedure . 162 4.3.2 Effects of CF calculation choices . .169 4.3.3 Error estimation on fit parameters . 177 4.3.4 Methods we use . 181 x CONTENTS 4.4 Masses from fit parameters . 182 4.4.1 Fit parameters to bias . 184 4.4.2 Corrections to the derived bias . 190 4.4.3 Measured masses . 202 4.5 Discussion . 207 4.6 Conclusion . 213 5 Conclusions 216 Vita 234 xi List of Tables 3.1 Choices made for correlation functions . 144 4.1 Fit values for CANDELS fields . 184 4.2 Linear fits to ∆b (bobs) . 194 4.3 Biases for CANDELS fields . 202 4.4 Masses for CANDELS fields . 205 xii List of Figures 1.1 Illustration of the cosmic web from the Millennium XXL simulation . 5 1.2 Stellar mass function 0:3 < z < 3 .................... 13 1.3 Halo mass function . 15 1.4 M? (Mhalo) and f? (Mhalo) relations from Behroozi et al. (2013a) . 16 1.5 SDSS map of galaxies out to redshift z = 0:15 . 18 1.6 Example halo merger tree . 27 2.1 SAM fiducial model f? .......................... 50 2.2 SAM fiducial model stellar mass functions . 51 2.3 SAM fiducial model cold gas fractions . 54 2.4 SAM fiducial model specific star formation rates . 55 2.5 SAM fiducial model metallicity . 57 2.6 Effects of αRH, ϵSN, τ?, and χReIn on z = 0 galaxy properties . 59 2.7 Effects of αRH, ϵSN, τ?, and χReIn on galaxy properties over time . 60 2.8 Preferential reheating mass-loading factor . 66 2.9 Preferential reheating model f? ..................... 67 2.10 Preferential reheating model stellar mass functions . 68 2.11 Preferential reheating model cold gas fractions . 69 2.12 Preferential reheating model specific star formation rates . 70 2.13 Preferential reheating model metallicity . 71 2.14 Direct suppression model star formation timescale . 76 2.15 Direct suppression model f? ....................... 79 2.16 Direct suppression model stellar mass functions . 80 2.17 Direct suppression model cold gas fractions . 81 2.18 Direct suppression model specific star formation rates . 82 2.19 Direct suppression model gas phase metallicity . 83 2.20 Parking lot model re-infall timescale . 88 2.21 Parking lot model f? ........................... 89 2.22 Parking lot model stellar mass functions . 90 2.23 Parking lot model cold gas fractions . 91 xiii LIST OF FIGURES 2.24 Parking lot model specific star formation rates . 92 2.25 Parking lot model metallicity . 93 2.26 Henriques et al. 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