The Properties of Massive Galaxies at Cosmic Noon: Evolutionary

Sydney Beth Sherman

2021 The Dissertation Committee for Sydney Beth Sherman Certiﬁes that this is the approved version of the following Dissertation:

Pathways and Implications for Physical Models of Galaxy Growth

Committee:

Shardha Jogee, Supervisor

Steven L. Finkelstein

Caitlin Casey

Volker Bromm

Neal Evans

Chris Conselice The Properties of Massive Galaxies at Cosmic Noon: Evolutionary

Pathways and Implications for Physical Models of Galaxy Growth

Sydney Beth Sherman

Dissertation

Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulﬁllment of the Requirements for the Degree of

Doctor of Philosophy

The University of Texas at Austin

May 2021 I have been lucky enough to be able to spend the last decade in my own little world studying galaxy evolution, of all things. This thesis is dedicated to all the people who made sure I didn’t make this journey alone. Acknowledgments

I would like to start by thanking my PhD thesis committee and the faculty and staff of the UT Astronomy department. You have all prepared me for life after my PhD in more ways than you will ever know and for that I am extremely grateful for this experience. To the grad students - thanks for the hallway chats, Fridays at Crown, and spending too much time at cookies. Grad school would have been pretty boring without all of you. I’d also like to thank two women who don’t know me but have made a huge impact on my time in grad school. Angela Duckworth and Liz Wiseman, your books were there when I truly needed them and helped me immensely in getting to this finish line. Sometimes you just need to multiply yourself. There are a few hobbies that have really helped me through grad school. Thanks to The Pond Hockey Club and Ro Fitness for the really hard but really fun workouts. I’d be remiss if I didn’t give a huge thanks to my Dad for emailing me dozens of articles about sourdough bread baking until I gave in, wasted tons of flour pretending I was a microbiologist, and finally brought Boris the sourdough starter to life! I’ll always be a firm believer that freezers exist to be filled with homemade bread and chocolatey baked goods. Finally, thank you to my family for always encouraging me to do the things I’m interested in and stick with it. Mom and Dad, you froze your toes off and schlepped me around the country to play hockey, sent me to summer at camp so I could learn how to live away from home, helped me to travel the world, and encouraged me to take all the science, math, and programming classes that I was interested in (even if I could get an A in English with much less effort!). All of these things (and more!) helped me become the person I am today. I love you very much.

v Abstract

The Properties of Massive Galaxies at Cosmic Noon: Evolutionary

Pathways and Implications for Physical Models of Galaxy Growth

Sydney Beth Sherman, Ph.D. The University of Texas at Austin, 2021

Supervisor: Shardha Jogee

The formation and evolution of massive galaxies in the first few billion years after the Big Bang remain important questions in extragalactic astronomy. Technological advancements allowing for multi-wavelength surveys that are both wide, covering large portions of the sky, and deep, pushing studies to higher redshifts, have opened the door for statistically significant studies of rare and important populations of galaxies at early times. Massive 11 galaxies (with stellar mass M? > 10 M ) provide an excellent testbed for theoretical models of galaxy evolution, however, because they have low number densities, large area surveys are required in order to locate uniformly-selected, statistically significant samples of these objects. In this thesis I detail the methods used to locate the largest samples to date of these massive galaxies, I investigate their number densities, quenched fractions, and specific star-formation rates, and I perform detailed comparisons of my empirical results with predictions from theoretical models. This work is a significant advancement as it mitigates uncertainties from Poisson statistics and cosmic variance, effects which have historically limited studies of the massive galaxy population at cosmic noon. Key results are summarized below. In Chapter 2 (Sherman et al. 2020a, MNRAS, 491, 3318) I present the high-mass end of the galaxy stellar mass function using a gri-selected sample of 5,352 star-forming galaxies 11 with M? > 10 M at cosmic noon, 1.5 < z < 3.5. This sample is uniformly selected across 17.2 deg2 (∼0.44 Gpc3 comoving volume from 1.5 < z < 3.5), mitigating the

vi effects of cosmic variance and encompassing a wide range of environments. This area, a factor of 10 larger than previous studies, provides robust statistics at the high-mass end. Using multi-wavelength data in the Spitzer/HETDEX Exploratory Large Area (SHELA) footprint I find that the SHELA footprint star-forming galaxy stellar mass function is steeply declining at the high-mass end probing values as high as ∼10−4 Mpc−3/dex and as low as −8 −3 ∼5×10 Mpc /dex across a stellar mass range of log(M?/M ) ∼ 11 - 12. I compare the empirical star-forming galaxy stellar mass function at the high mass end to three types of numerical models: hydrodynamical models from IllustrisTNG, abundance matching from the UniverseMachine, and three different semi-analytic models (SAMs; SAG, SAGE, GALACTICUS). At redshifts 1.5 < z < 3.5 I find that results from IllustrisTNG and abundance matching models agree within a factor of ∼2 to 10, however the three SAMs strongly underestimate (up to a factor of 1,000) the number density of massive galaxies. I discuss the implications of these results for our understanding of galaxy evolution. In Chapter 3 (Sherman et al. 2020b, MNRAS, 499, 4239) I explore the buildup of 11 quiescent galaxies using a Ks-selected sample of 28,469 massive (M? ≥ 10 M ) galaxies at redshifts 1.5 < z < 3.0, drawn from a 17.5 deg2 area (0.33 Gpc3 comoving volume at these redshifts). This allows for a robust study of the quiescent fraction as a function of mass at 1.5 < z < 3.0 with a sample ∼40 times larger at log(M?/M )≥ 11.5 than previous studies. I derive the quiescent fraction using three methods: specific star-formation rate, distance from the main sequence, and UVJ color-color selection. All three methods give similar values at 1.5 < z < 2.0, however the results differ by up to a factor of two at 2.0 < z < 3.0. At redshifts 1.5 < z < 3.0 the quiescent fraction increases as a function of stellar mass. By 11 z = 2, only 3.3 Gyr after the Big Bang, the universe has quenched ∼25% of M? = 10 M 12 galaxies and ∼45% of M? = 10 M galaxies. I discuss physical mechanisms across a range of epochs and environments that could explain these results. I compare these results with predictions from hydrodynamical simulations SIMBA and IllustrisTNG and semi-analytic models (SAMs) SAG, SAGE, and Galacticus. The quiescent fraction from IllustrisTNG is higher than our empirical result by a factor of 2 − 5, while those from SIMBA and the three SAMs are lower by a factor of 1.5 − 10 at 1.5 < z < 3.0. In Chapter 4 (Sherman et al. 2021) I present the main sequence for all galaxies and star- 11 forming galaxies for a sample of 28,469 massive (M? ≥ 10 M ) galaxies at cosmic noon (1.5 < z < 3.0), uniformly selected from a 17.5 deg2 area (0.33 Gpc3 comoving volume at these redshifts). This large sample allows for a novel approach to investigating the

vii galaxy main sequence that has not been accessible to previous studies. I measure the main sequence in small mass bins in the SFR-M? plane without assuming a functional form for the main sequence. With a large sample of galaxies in each mass bin, I isolate star-forming galaxies by locating the transition between the star-forming and green valley populations in the SFR-M? plane. This approach eliminates the need for arbitrarily defined fixed cutoffs when isolating the star-forming galaxy population, which often biases measurements of the scatter around the star-forming galaxy main sequence. I find that the main sequence for all galaxies becomes increasingly flat towards present day at the high-mass end, while the star-forming galaxy main sequence does not. I attribute this difference to the increasing fraction of the collective green valley and quiescent galaxy population from z = 3.0 to z = 1.5. Additionally, I measure the total scatter around the star-forming galaxy main sequence and find that it is ∼ 0.5 − 1.0 dex with little evolution as a function of mass or redshift. I discuss the implications that these results have for pinpointing the physical processes driving massive galaxy evolution. This thesis concludes (Chapter 5) with a discussion of the key results presented in Chapters 2, 3, and 4 and their impact on the understanding of massive galaxy evolution. I also discuss the future of extragalactic studies of massive galaxies and how this work can contribute to those studies.

viii Table of Contents

List of Tables...... xii

List of Figures ...... xiii

Chapter 1 Introduction...... 1 1.1 Massive Galaxy Evolution ...... 1 1.2 Practicalities of Studying Massive Galaxies...... 2 1.3 Properties of Massive Galaxies at z > 1 ...... 4 1.4 Thesis Overview...... 5 1.4.1 Reliably Finding the Biggest Pieces of Hay in the Haystack ...... 5 1.4.2 Signiﬁcantly Improved Statistics ...... 7 1.4.3 Detailed Comparisons with Various Types of Theoretical Models ..... 8

Chapter 2 Exploring the High-Mass End of the Stellar Mass Function of Star Forming Galaxies at Cosmic Noon ...... 10 2.1 Introduction ...... 10 2.2 Data ...... 12 2.3 Data Analysis And SED Fitting...... 15 2.3.1 Galaxy Properties From EAZY-py ...... 15 2.3.2 Testing EAZY-py With Mock Galaxies...... 23 2.4 Results...... 27 2.4.1 Massive Star-Forming Galaxies in the SHELA Footprint...... 27 2.4.2 Eddington Bias...... 30 2.4.3 Comparing SHELA Footprint SMF to Previous Observational Results 32 2.4.4 Comparing SHELA Footprint SMF to Theoretical Results ...... 36 2.5 Summary...... 42

Chapter 3 Investigating The Growing Population of Massive Quiescent Galaxies at Cosmic Noon ...... 45 3.1 Introduction ...... 45 3.2 Data ...... 48 3.3 Data Analysis & SED Fitting ...... 49

ix 3.3.1 Sample Selection...... 52 3.4 Empirical Results ...... 54 3.4.1 Empirical Quiescent Fraction As a Function of Mass...... 54 3.4.2 Estimating Contamination From DSFGs...... 60 3.4.3 Comparing the Empirical Quiescent Fraction to Previous Observations 61 3.4.4 Empirical Quiescent Fraction As a Function of Redshift ...... 63 3.4.5 Empirical Stellar Mass Function for Star-Forming, Quiescent, and All Galaxies...... 65 3.5 Discussion ...... 69 3.5.1 Quenching Mechanisms Across Diﬀerent Epochs and Environments. 70 3.5.2 Comparing the Empirical Quiescent Fraction As a Function of Mass to Theoretical Predictions...... 74 3.5.3 Comparing the Empirical Quiescent Fraction As a Function of Red- shift to Theoretical Predictions ...... 82 3.5.4 Comparing the Stellar Mass Function to Theoretical Predictions...... 84 3.6 Summary...... 86

Chapter 4 The Shape and Scatter of The Galaxy Main Sequence for Massive Galaxies at Cosmic Noon...... 89 4.1 Introduction ...... 89 4.2 Data and Analysis...... 92 4.3 Galaxy Main Sequence...... 95 4.3.1 Measuring the Main Sequence for All Galaxies ...... 95 4.3.2 Isolating Star-Forming Galaxies and Measuring the Main Sequence for Star-Forming Galaxies ...... 96 4.3.3 Implications of the Growing Green Valley and Quiescent Populations102 4.4 Scatter Around the Star-Forming Galaxy Main Sequence ...... 108 4.5 Comparison With Previous Observations ...... 111 4.5.1 Comparison of the Main Sequence for All Galaxies and Star-Forming Galaxies with Previous Observations...... 111 4.5.2 Comparison of the Scatter Around the Star-Forming Galaxy Main Sequence with Previous Observations ...... 114 4.6 Comparison With Theoretical Models ...... 115 4.7 Discussion ...... 118

x 4.8 Summary...... 120

Chapter 5 Summary and Future Work ...... 123 5.1 Key Results...... 123 5.1.1 What is the Shape of the Stellar Mass Function for Massive Galaxies?123 5.1.2 When Does the Massive Galaxy Population Become Predominantly Quiescent?...... 124 5.1.3 Which Physical Mechanisms Drive The Shift Towards Quiescence?.. 125 5.1.4 How Does the Shrinking Star-Forming Population Impact the Slope of the Main Sequence?...... 126 5.1.5 What Can be Learned From The Distribution of Star-Forming

Galaxies in the SFR-M? Plane?...... 127 5.1.6 Can Current Theoretical Models Correctly Recover the Observed Properties of Massive Galaxies? ...... 128 5.2 Future Work...... 131 5.2.1 Empirical Studies of Massive Galaxies ...... 131 5.2.2 Theoretical Studies of Massive Galaxies...... 135

Appendix A Appendix to Chapter 3...... 137 A.1 Testing the Impact of Photometric Redshift Error and Eddington Bias on the Empirical Quiescent Fraction ...... 137 A.2 Testing Diﬀerent Aperture Choices and Main Sequence Deﬁnitions in Illus- tris TNG ...... 137

Appendix B Appendix to Chapter 4...... 141

B.1 The Distribution of Galaxies in the SFR-M? Plane for Theoretical Models.... 141

Bibliography...... 144

xi List of Tables

1.1 The total number of galaxies with log(M?/M ) ≥ 11.5 for the Ks-selected sample used in Chapters 3 and 4 of this work and values from previous publications. The sample used in this work is more than a factor of ∼ 40 larger than those from previous works...... 8

2.1 SED template-based magnitude oﬀsets determined for each photometric band using low redshift galaxies in the SHELA footprint that have spectroscopic redshifts from SDSS. These oﬀsets are self-consistently computed

within EAZY-py and are applied to source photometry such that foﬀset =

Offset × fcatalog, where fcatalog is the flux density in the published catalog (Wold et al., 2019), “Offset" is the SED template-based magnitude offset

determined by EAZY-py, and foffset is the object’s flux after applying the magnitude offset...... 19 2.2 (1) Redshift bin for the full redshift range of our sample and divided into smaller bins of ∆z = 0.5. (2) Total number of star-forming massive galaxies, number per square degree, and number density of galaxies found in our sample split into smaller mass bins (3-5). When comparing the number of

galaxies found to have log(M?/M ) > 11.5 (columns 4 and 5) to the works of Muzzin et al. (2013), Ilbert et al. (2013), and Tomczak et al. (2014), we ﬁnd an order of magnitude more star-forming galaxies than these previous small-area studies. Errors represent Poisson uncertainties...... 31

xii List of Figures

2.1 The area in which an object with a given r-band magnitude can be detected in our survey footprint with S/N ≥ 5. The gray shaded region represents magnitudes fainter than the r = 24.8 AB mag 80% completeness limit found by Wold et al. (2019). Across all four adjoining tiles (B3, B4, B5, and B6) that comprise the SHELA footprint, the area does not vary as a function of magnitude for objects brighter than the r-band 80% completeness limit. Across all four tiles, objects can be detected with r-band S/N ≥ 5 in ∼17.2 deg2...... 14 2.2 Photometric redshift distribution for high-conﬁdence star-forming galaxies (see Section 2.3.1 for a description of sample selection) in the SHELA footprint. The photometric redshift shown here, and used throughout this paper, refers to the EAZY-py best-ﬁt redshift at which χ2 is minimized. The shaded region represents the redshift range of interest (1.5 < z < 3.5) in this paper. For z < 1 galaxies with spectroscopic redshifts from SDSS,

we find σNMAD = 0.0377. We discuss tests of photometric redshift recovery of 1.5 < z < 3.5 galaxies using a sample of mock galaxies in Section 2.3.2. Across all redshifts, we find 219,996 galaxies, of which, 14,910 have redshifts 1.5 < z < 3.5...... 16 2.3 Example SED fits, photometric redshift probability distributions, and pho- 11 tometry for two M? > 10 M 1.5 < z < 2.5 galaxies in our sample. Indicated in the inset box in the upper left panel are the object’s best-fitting 2 photometric redshift (zphot, the redshift at which χ is minimized), reduced 2 2 χ (χν ) , stellar mass, and star-formation rate. The upper left panel shows the best-fitting SED template (purple) to the object’s photometry (green points) with the set of templates (gray SED curves) added in non-negative linear combination to achieve the best-fitting SED. The upper right panel shows the photometric redshift probability distribution (purple curve), with the best-fitting redshift indicated by a vertical green line. Image cutouts show the photometry in all nine of our photometric bands. Each cutout is 1000 × 1000...... 17 11 2.4 Same as Figure 2.3 for two M? > 10 M 2.5 < z < 3.5 galaxies...... 18

xiii 2.5 Comparison of redshift (top panel), stellar mass (middle panel), and SFR (bottom panel) between EAZY-py output and the input values for 10,000 randomly selected mock galaxies. Error bars span the 68th percentile of the data in each bin, which corresponds to an average dispersion in redshift

of 0.19 ∆z/(1+zMock), average dispersion in stellar mass of 0.58 dex, and average dispersion in SFR of 0.69 dex. We ﬁnd that redshift recovery error

(σNMAD = 0.092) is higher than that found using a low redshift sample of SHELA footprint galaxies with SDSS spectroscopic redshifts, however this increased error is expected. On average, we ﬁnd that EAZY-py may over-predict stellar mass by ∼0.09 dex and under-predict SFR by ∼0.46 dex when comparing the output values from EAZY-py to those associated with the mock galaxies. There are no data points lying behind the caption boxes... 26 2.6 Map of the SHELA footprint (gray) with massive star-forming galaxies shown in color. The color and size of each point corresponds to the mass of the galaxy, with brighter, larger points representing more massive galaxies. Panels from top to bottom increase in redshift by ∆z = 0.5 from z = 1.5 to

z = 3.5. The lowest redshift bin (1.5 < z < 2) contains galaxies with M? 11 > 10 M , while the higher redshift bins (2 < z < 3.5) contain galaxies more massive than the 80% mass completeness limit determined for each redshift bin in Section 2.3.1. The minimum mass in each redshift bin and the number of galaxies above that mass threshold are shown in the upper left corner of each panel. Vertical lines represent the boundaries of the SHELA footprint tiles (B3, B4, B5, and B6) discussed in Section 2.2, and tile names are indicated in each panel. The number per unit area of massive galaxies 11 2 (M? > 10 M ) at 1.5 < z < 3.5 is quite low (∼310/deg ), emphasizing the beneﬁt of our large area SHELA footprint in providing a statistically 11 signiﬁcant sample (5,352 with M? > 10 M ) of massive star-forming galaxies. 28

xiv 2.7 The number of star-forming galaxies per square degree for 1.5 < z < 3.5 galaxies in the SHELA footprint. The dark solid lines correspond to the number of sources found at each mass, while the light purple regions represent Poisson errors. The gray shaded regions represent masses below the 80% mass completeness limit for each redshift bin. The total number of galaxies that we find in the high stellar mass regime are indicated in the inset box for each redshift bin...... 29 2.8 Purple points represent the star-forming galaxy stellar mass function for 1.5 < z < 3.5 galaxies in the SHELA footprint, where error bars represent Poisson errors. Gray lines are stellar mass functions generated from 100 realizations of the catalog in which photometric redshifts are drawn from each object’s photometric redshift probability distribution. These 100 realizations are used to estimate the effects of Eddington bias, as outlined in Section 2.4.2. The gray shaded regions represent masses below the 80% mass completeness limit for each redshift bin. We find that scatter is introduced to the stellar mass function when the catalog is perturbed, however results remain consistent with those from the original catalog...... 33 2.9 Galaxy stellar mass function for 1.5 < z < 3.5 star-forming galaxies in the SHELA footprint. Error bars represent Poisson errors. The gray shaded regions represent masses below the 80% mass completeness limit for each

redshift bin. The vertical dotted line indicates log(M?/M ) = 11.5, the mass above which we compare to previous studies from the literature, restricted to only their star-forming samples. Note that in our 2 < z < 3.5 redshift

bins the size of our sample of massive (log(M?/M ) ≥ 11.5) star-forming galaxies (as shown in the inset in each panel) is a over a factor of 10 larger than the samples from previously published studies. We ﬁnd that our star- forming galaxy stellar mass function shows fair agreement (within a factor of ∼ 2 to 4) with those from the literature...... 35

xv 2.10 Comparison of the empirical galaxy stellar mass function for 1.5 < z < 3.5 star-forming galaxies in the SHELA footprint to the stellar mass functions from three classes of theoretical models: hydrodynamical models from Il- lustrisTNG using rTNG300 (Pillepich et al., 2018b), abundance matching models from the UniverseMachine (Behroozi et al., 2019) populating dark matter halos from Bolshoi-Planck, and three diﬀerent semi-analytic models (SAMs), namely SAG (radio-mode AGN feedback, Cora et al. 2018), GALACTICUS (radio-mode AGN feedback, Benson 2012), and SAGE (quasar-mode AGN feedback, Croton et al. 2016) applied to the MDPL2 dark matter simulation. In our lowest redshift bin (1.5 < z < 2) results from all three model classes are in rough agreement with results from the SHELA footprint. In the 2 < z < 3 bins, results from IllustrisTNG hydrodynamical models, UniverseMachine abundance matching, and the SAG semi-analytic model are within a factor of ∼2 - 10 to those from the SHELA footprint. In this redshift bin, SAMs SAGE and GALACTICUS strongly underestimate the number density of massive galaxies by up to a factor of ∼100. In our highest redshift bin (3 < z < 3.5), the results from IllustrisTNG agree with those from the SHELA footprint within a factor of 2 - 3 and those from the UniverseMachine agree within a factor of 3 - 5. In this redshift bin all three SAMs underestimate the number density of massive galaxies by a factor of 10 - 1,000. We refer the reader to Section 2.4.4 for details. Error bars on SHELA footprint stellar mass function points represent Poisson errors, and the gray shaded region represents masses below the 80% mass completeness limit for our SHELA footprint star-forming galaxy sample. All results from simulations have had mass and volume measures computed using (or scaled to) h = 0.7, however no other aspects of the models have been scaled. The results from IllustrisTNG and the three SAMs have been convolved by the average stellar mass error for SHELA footprint galaxies in each redshift bin.. 39

xvi 3.1 The relationship between star-formation rate (SFR) and stellar mass (M?) for all galaxies in our sample. The main sequence is represented by dark pink circles, which are the average SFR in a given mass bin (see Section 3.4.1). Errors on the main sequence are determined using the bootstrap resampling procedure described in Section 3.4.1. The gold line represents the main sequence - 1 dex which is used in this work to identify quiescent galaxies. The dash-dot line represents the sSFR = 10−11yr−1 criterion also used for selecting quiescent galaxies. The main sequence - 1 dex criterion is more eﬀective at selecting green valley galaxies to be quiescent than the sSFR-selection method. Areas of parameter space where our study is not complete in mass are shaded in grey. Inset color bars indicate the number of galaxies in each two dimensional bin. Insets on the upper right of each 11 panel show the number (N11) of galaxies in our sample with M? ≥ 10 M . . 55 3.2 The UVJ color-color diagram for our sample, with the separation of quiescent and star-forming galaxies adopted from Muzzin et al. (2013). Galaxies in the upper left region of parameter space are quiescent, while those lying to the right of the boundary are dusty star-forming galaxies, and those below the boundary are star-forming galaxies. We see that the population of quiescent galaxies grows from high to low redshift. Inset color bars indicate the number of galaxies in each two dimensional bin. Insets on the lower

left of each panel show the number (N11) of galaxies in our sample with 11 M? ≥ 10 M ...... 56

xvii 3.3 Empirical quiescent fraction for our sample of 1.5 < z < 3.0 galaxies using the three selection methods described in Section 3.4.1: sSFR (pink circles), UVJ (purple squares), main sequence - 1 dex (gold pentagons). These three methods of determining the quiescent fraction produce similar trends showing that the quiescent fraction of galaxies increases with mass 11 12 from M? = 10 − 10 M in all three redshift bins over the range 1.5 < z < 3.0 and it also increases as a function of redshift in fixed mass bins. The quiescent fractions measured with these three methods are similar, particularly at 1.5 < z < 2.0, but differ by up to a factor of 2 at 2.0 < z < 3.0. It is remarkable that in only 3.3 Gyr (from the Big Bang to z = 2) the 11 Universe can build and quench more than 25% of massive (M? = 10 M ) galaxies. Our result is a significant improvement over previous observational studies which used smaller sample sizes (our sample is a factor of 40 larger

than that from Muzzin et al. (2013) for log(M?/M ) ≥ 11.5 galaxies at these redshifts). The gray shaded region indicates masses below our completeness

limit. Insets on the upper left of each panel show the number (N11) of 11 galaxies in our sample with M? ≥ 10 M ...... 59 3.4 Empirical UVJ-selected quiescent fraction (purple squares) compared with previous observational results from Muzzin et al. (2013) (green circles), Tomczak et al. (2016) (orange triangles), and Martis et al. (2016) (pink diamonds). Our work extends to higher masses and our larger sample size allows us to achieve smaller errors than previous works. Our sample of

galaxies with log(M?/M ) ≥ 11.5 is a factor of ∼40 larger than samples from previous works. The quiescent fraction measured from our sample is a factor of ∼ 2 − 3 larger than that from previous studies at 2.0 < z < 3.0 and we ﬁnd good agreement at 1.5 < z < 2.0, however the errors from previous studies are large. The gray shaded region indicates masses below our completeness limit. Insets on the upper left of each panel show the 11 number (N11) of galaxies in our sample with M? ≥ 10 M ...... 62

xviii 11 3.5 Quiescent fraction for galaxies in our sample with M? ≥ 10 M shown for our three redshift bins. We show our results using three different methods of computing the quiescent fraction and find that all three methods give a quiescent fraction that increases from high to low redshift. In our highest redshift bin (2.5 < z < 3.0), we find quiescent fractions that span from 13% (sSFR-based selection) to 26% (main sequence-based selection). In our lowest redshift bin (1.5 < z < 2.0) our empirical quiescent fractions span from 50% (sSFR and UVJ-based selection) to 55% (main sequence-based

selection). The inset on the lower left shows the number (N11) of galaxies 11 in our sample with M? ≥ 10 M across all three redshift bins spanning 1.5 < z < 3.0...... 64 11 3.6 Our empirical quiescent fraction for all massive (M? ≥ 10 M ) galaxies selected using the sSFR (left) and UVJ (right) methods as a function of redshift compared with previous observations. For the sSFR-based method, Kriek et al. (2006) ﬁnds the quiescent fraction at z ∼ 2.5 to be higher than our empirical result by a factor of ∼2. Our UVJ-based result is in good agreement with those from Muzzin et al. (2013) and Martis et al. (2016), however our empirical quiescent fraction is larger than that from Tomczak et al. (2016) by a factor of 2. Insets on the lower left of each panel show the 11 number (N11) of galaxies in our sample with M? ≥ 10 M across all three redshift bins spanning 1.5 < z < 3.0. Our sample is more than an order of magnitude larger than samples from previous studies, which allows for smaller Poisson errors...... 65

xix 3.7 The empirical galaxy stellar mass function for our sample of massive galaxies. In both the top and bottom rows, the purple line represents the galaxy stellar mass function for all galaxies in our sample. In the top row, the solid and dashed pink lines are the star-forming and quiescent galaxy stellar mass functions, respectively, where the quiescent galaxies were selected using the sSFR-based method. Similarly, in the bottom row the gold solid and dashed lines are the star-forming and quiescent galaxy stellar mass functions, respectively, with quiescent galaxies selected by the main sequence-based method. Poisson errors are indicated by the colored regions and are often smaller than the lines. The total, star-forming, and quiescent galaxy stellar mass functions are related through the quiescent fraction, as described in Equation 3.3. In each of our three redshift bins spanning 1.5 < z < 3.0, we ﬁnd the stellar mass function to be steeply declining at the high mass end. The gray shaded region indicates masses below our completeness limit.

Insets on the upper right of each panel show the number (N11) of galaxies 11 in our sample with M? ≥ 10 M ...... 67 3.8 The empirical galaxy stellar mass function for our total sample of massive galaxies (purple line) compared with the total galaxy stellar mass functions from previous works (Ilbert et al. 2013, Muzzin et al. 2013, and Tomczak et al. 2014). The gray shaded region indicates masses below our completeness limit. We ﬁnd fair agreement, within a factor of ∼ 2 − 3, with previous results in the two redshift bins spanning 2.0 < z < 3.0 (center and right panels). In the lowest redshift bin, our result is a factor of ∼ 3 lower at

log(M?/M ) < 11.2 than previous studies (see discussion in Section 3.4.5). Poisson errors for our empirical result are indicated by the light purple regions and are often smaller than the lines. Insets on the upper right of each panel show the number of galaxies in our sample and those we compare with

that have log(M?/M ) > 11.5. The dotted vertical line marks log(M?/M ) = 11.5. Our sample is more than a factor of 40 larger than samples from previous studies...... 68

xx 3.9 Empirical sSFR-selected quiescent fraction compared with sSFR-selected quiescent fractions from the hydrodynamical models SIMBA and Illus- trisTNG (left) and semi-analytic models SAG, SAGE, and Galacticus (right). We ﬁnd that results from the SIMBA model show a similar increase in quiescent fraction as a function of mass at 1.5 < z < 2.0 as is seen with our empirical result, although the error bars are quite large. The results from IllustrisTNG show a quiescent fraction that increases as a function of mass at 2.0 < z < 3.0, but decreases as a function of mass in the 1.5 < z < 2.0 bin. We note that the quiescent fraction results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). SAM SAG is able to reproduce the trend seen in our empirical result as a function of mass, but underestimates the quiescent fraction by up to a factor of ∼ 1.5 − 3 compared with our empirical result. SAM SAGE does not predict a quiescent fraction that increases as a function of mass and it underestimates the quiescent fraction at the high mass end compared with our result, while Galacticus predicts a quiescent fraction that increases steeply at the high mass end, but with large error bars. The gray shaded region indicates masses below our completeness limit. Insets on the upper

left of each panel show the number (N11) of galaxies in our sample with 11 M? ≥ 10 M ...... 75

xxi 3.10 Empirical main sequence-selected quiescent fraction compared with the main sequence-selected quiescent fraction from hydrodynamical models IllustrisTNG and SIMBA (left) and semi-analytic models SAG, SAGE, and Galacticus (right). SIMBA under-predicts the quiescent fraction by a factor of ∼ 1.5 − 4 at 1.5 < z < 3.0 compared with our empirical result, but with large error bars. The IllustrisTNG model over-predicts the quiescent fraction by a factor of ∼ 2 in the 2.0 < z < 3.0 redshift bins compared with our empirical result and increases as a function of mass. In the lowest redshift bin (1.5 < z < 2.0), however, the IllustrisTNG quiescent fraction decreases as a function of mass. We note that the quiescent fraction results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). The three SAMS under-predict the quiescent fraction at the high mass end by up to a factor of 10 compared with our empirical result. SAG is the only SAM that predicts an increase in the quiescent fraction as a function of stellar mass. The gray shaded region indicates masses below our completeness limit. Insets on the upper

left of each panel show the number (N11) of galaxies in our sample with 11 M? ≥ 10 M ...... 76 11 3.11 Empirical quiescent fraction for massive galaxies (M? ≥ 10 M ) in our sample, selected using the sSFR (left) and main sequence (right) methods, compared with those from theoretical models. Theoretical models SIMBA, SAG, SAGE, and Galacticus under-predict the quiescent fraction for all massive galaxies by up to a factor of ∼10, while IllustrisTNG over-predicts the quiescent fraction by up to a factor of 3 compared with our empirical result. We note that results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). Using both the sSFR- and main sequence-based methods, all models except for Galacticus and IllustrisTNG predict a quiescent fraction that increases as a function of redshift...... 79

xxii 3.12 Empirical galaxy stellar mass function for our observed sample compared with predictions from hydrodynamical models SIMBA and IllustrisTNG and semi-analytic models SAG, SAGE, and Galacticus. The top row shows results for all galaxies. The 2nd and 3rd rows from the top show the star- forming and quiescent galaxy stellar mass functions, respectively, split into these populations using the sSFR-based method. The 4th and 5th rows from the top are analogous to rows 2 and 3, but split the quiescent and star-forming populations using the main sequence-based method. Poisson errors are indicated by the colored regions and are often smaller than the lines. The gray shaded region indicates masses below our completeness limit. In the top row, insets on the upper left of each panel show the total 11 number (N11) of galaxies in our sample with M? ≥ 10 M . A detailed comparison of our empirical results with those from theoretical models is given in Section 3.5.4. Brieﬂy, we ﬁnd that hydrodynamical model SIMBA is in good agreement with our empirical total galaxy stellar mass function in our two redshift bins spanning 2.0 < z < 3.0, while predictions from IllustrisTNG are lower than our result by a factor of 15 at these redshifts. We note that results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). The three SAMs under-predict the number density of the total population of massive galaxies by up to a factor of 10,000 compared with our empirical result, with the discrepancy being lower for SAG and SAGE than Galacticus...... 83

xxiii 4.1 The SFR-M? relation (2D histogram) and main sequence (pink circles) for all galaxies in our sample. The main sequence is the average SFR in individual mass bins, while errors on the main sequence are computed using the bootstrap resampling procedure described in Section 4.3.1. The main 11 sequence for all galaxies shows a ﬂattening at the highest masses (M? = 10 12 to 10 M ), and this ﬂattening becomes more prominent as time progresses towards z = 1.5. Colorbars show the number of galaxies in each cell of the 2D histogram, and gray shaded regions represent masses below our 95% completeness limit. We emphasize that the results presented in this 11 12 work focus on the mass range M? = 10 to 10 M , and that results above 12 M? = 10 M (vertical dashed gray line) are unlikely to be robust. Insets

on the upper right of each panel show the total number (N11) of galaxies in 11 our sample with M? ≥ 10 M ...... 96

xxiv 4.2 An example schematic of our method used to locate the transition between the star-forming and green valley galaxy populations. The labeled steps are as follows and they correspond to the same numbered steps in Section 4.3.2. Step 1: For all galaxies in a given mass bin (in this example, the 11 M? = 10 M bin for 1.5 < z < 2.0 galaxies) construct a histogram of speciﬁc star-formation rate values. Step 2: Interpolate the shape of this histogram using a univariate spline. Step 3: Find the local maximum at log(sSFR)> −10.2 as a rough estimate of the ridge of the main sequence. Step 4: Step bin-by-bin from higher to lower sSFR. Step 5: Stop bin-by-bin stepping when the interpolated spline goes from decreasing to increasing, and deﬁne this local minimum as the transition between the star-forming and green valley populations. We remind the reader that for every galaxy in our sample, we obtain a measure of dust-corrected SFR from our SED

fitting procedure. The inset figure shows the SFR-M? plane in the 1.5 < z < 2.0 bin with the main sequence for all galaxies shown in pink and the dividing line (green with black outline) between the star-forming and green valley populations determined using the procedure described here and in Section 4.3.2. The results of implementing this procedure to isolate the star-forming population in all three redshift bins can be seen in Figure 4.4. In the inset figure, the gray shaded region represents masses below our 95% completeness limit, and the vertical dashed gray line represents 12 M? = 10 M , above which our results are unlikely to be robust...... 99

xxv 4.3 The quiescent fraction as a function of stellar mass determined using the transition between star-forming and green valley galaxies to separate star- forming systems from the collective green valley and quiescent populations (green triangles). Also plotted are the results from Sherman et al. (2020b) who determined the quiescent fraction in three ways: sSFR-selected (pink circles), main sequence - 1 dex selected (gold pentagons), and UVJ-selected (purple squares). The four measurements of the quiescent fraction give consistent results across our three redshift bins spanning 1.5 < z < 3.0. Gray shaded regions represent masses below our 95% completeness limit. Error bars represent Poisson errors. We emphasize that the results presented 11 12 in this work focus on the mass range M? = 10 to 10 M , and that results 12 above M? = 10 M (vertical dashed gray line) are unlikely to be robust.

Insets on the upper left of each panel show the total number (N11) of galaxies 11 in our sample with M? ≥ 10 M ...... 103

4.4 The SFR-M? relation (2D histogram) and main sequence (pink circles) for star-forming galaxies in our sample. Star-forming galaxies are selected by locating the transition between star-forming and green valley populations, then removing galaxies below this transition, as is described in Section 4.3.2. The star-forming main sequence is the average SFR in individual mass bins, while errors on the star-forming main sequence are computed using the bootstrap resampling procedure described in Section 4.3.1. Unlike the main sequence for all galaxies, the star-forming galaxy main sequence does not show a strong evolution in the high mass end slope from z = 3.0 to z = 1.5. Colorbars show the number of galaxies in each cell of the 2D histogram, and gray shaded regions represent masses below our 95% completeness limit. We emphasize that the results presented in this work 11 12 focus on the mass range M? = 10 to 10 M , and that results above 12 M? = 10 M (vertical dashed gray line) are unlikely to be robust. Insets

on the upper right of each panel show the number (N11) of star-forming 11 galaxies in our sample with M? ≥ 10 M ...... 104

xxvi 4.5 Speciﬁc star-formation rate distributions for individual mass bins in the

SFR-M? plane (purple histograms), with the splines used to interpolate these distributions (solid pink lines). The three vertical columns of panels are for each of our three redshift bins spanning z = 1.5 to z = 3.0. The

top row shows the log(M?/M ) = 11.2 bin, and the bottom row shows the

log(M?/M ) = 11.7 bin. In each panel, star-forming galaxies fall to the right of the vertical dashed green line, green valley galaxies are between the vertical dashed green line and the vertical dash-dot pink line, and quiescent galaxies lie to the left of the vertical dash-dot pink line. The procedure used to identify the location of the transition between star-forming and green valley galaxies and transition between green valley and quiescent galaxies are described in Sections 4.3.2 and 4.3.3, respectively. As we move from higher to lower redshift, the buildup of the populations of green valley and quiescent galaxies becomes prominent. We again note that our SED ﬁtting procedure provides a measure of dust-corrected SFR for every galaxy in our

Ks-selected sample...... 106 4.6 The main sequence for all galaxies (pink circles) and star-forming galaxies (purple squares) in our sample. Star-forming galaxies are selected by locating the transition between star-forming and green valley populations, then removing galaxies below this transition, as is described in Section 4.3.2. The (star-forming) main sequence is the average SFR in individual mass bins, while errors on the (star-forming) main sequence are computed using the bootstrap resampling procedure described in Section 4.3.1. We note that error bars are included, however they are often smaller than the symbol. At early epochs (z > 2) the star-forming galaxy main sequence is up to a factor of 1.5 higher than the main sequence for all galaxies, and at later epochs (1.5 < z < 2.0), the star-forming galaxy main sequence is a factor of 1.5 − 3 higher than the main sequence for all galaxies. Gray shaded regions represent masses below our 95% completeness limit. We emphasize that 11 the results presented in this work focus on the mass range M? = 10 to 12 12 10 M , and that results above M? = 10 M (vertical dashed gray line) are unlikely to be robust...... 107

xxvii 4.7 Top Row: The total scatter (blue shaded region) around the star-forming galaxy main sequence (pink) overlaid on the distribution of star-forming galaxies (2D histogram; colorbar indicates the number of galaxies in each

2D bin) in the SFR-M? plane. The upper (lower) bound of the blue shaded region is the 84th (16th) percentile of the SFR distribution in a given mass bin. Insets on the upper right of each panel in the top row show the

number (N11) of galaxies in the star-forming population in our sample with 11 M? ≥ 10 M . Bottom Row: The total (squares), upper (circles), and lower (pentagons) observed scatter around the star-forming galaxy main sequence. The total scatter shows a modest increase with increasing stellar mass (less 11 12 than a factor of three from M? = 10 to 10 M in each redshift bin), and the total scatter is fairly constant across our three redshift bins from z = 1.5 to z = 3.0. In every redshift bin, the lower scatter is larger than the upper scatter by up to a factor of 3. Gray shaded regions represent masses below our 95% completeness limit. We emphasize that the results presented in 11 12 this work focus on the mass range M? = 10 to 10 M , and that results 12 above M? = 10 M (vertical dashed gray line) are unlikely to be robust. .... 110 4.8 Our empirical main sequence for all galaxies (top row) and star-forming galaxies (bottom row) compared with results from previous observations. We ﬁnd similar results to those from Tomczak et al. (2016) for both the total (top row) and star-forming (bottom row) galaxy populations. The results from Whitaker et al. (2014) for both the total (top row) and star-forming (bottom row) galaxy populations are higher than our empirical results by a factor of ∼ 1.5 − 6.5. Gray shaded regions represent masses below our 95% completeness limit. Insets on the upper right of each panel show the

number (N11) of galaxies for the total population (top row) and star-forming 11 population (bottom row) in our sample with M? ≥ 10 M . We emphasize 11 that the results presented in this work focus on the mass range M? = 10 12 12 to 10 M , and that results above M? = 10 M (vertical dashed gray line) are unlikely to be robust...... 113

xxviii 4.9 Our empirical main sequence for all galaxies compared with results from hydrodynamical models SIMBA and IllustrisTNG and SAM SAG. The main sequence for all galaxies from SIMBA is within a factor of ∼ 1.5 of our empirical result and that from SAG is higher than our empirical result by up to a factor of ∼ 3. SIMBA does not show a ﬂattening at the highest masses by z = 1.5, while SAG begins to show a ﬂattening high-mass slope towards z = 1.5. The main sequence for all galaxies from IllustrisTNG is lower than our empirical result by up to a factor of ∼ 10 and shows a strong turnover at the highest masses at 2.0 < z < 3.0 that is not seen in our empirical result. Gray shaded regions represent masses below our 95% completeness limit. We emphasize that the results presented in this work focus on the 11 12 12 mass range M? = 10 to 10 M , and that results above M? = 10 M (vertical dashed gray line) are unlikely to be robust...... 117

A1 Results of the test in which we explore the impact of photometric redshift uncertainty and Eddington bias on our empirical quiescent fraction results. The three panels show the quiescent fraction measured using sSFR-selection (upper), UVJ-selection (center), and distance from the main sequence selection (lower). In each of the three panels, the quiescent fraction presented in Section 3.3 is shown as a colored line, and the results from the 100 catalog iterations are shown as grey lines. Our results are shown for each of the three redshift bins used throughout this work, which span 1.5 < z < 3.0 and the redshift bin is indicated in the upper left of each row of the three panels. Using all three methods of measuring the quiescent fraction, the results of the 100 catalog iterations are consistent with the results presented in Section 11 12 3.3 for M? = 10 − 10 M , our mass range of interest throughout this work.138

xxix A2 We compare the empirical quiescent fraction computed using the main sequence (left) and sSFR (right) methods with results from IllustrisTNG that are determined using diﬀerent aperture types and main sequence deﬁnitions.

Throughout this work we use the 2 × R1/2 aperture (light blue) and the main sequence described in Section 3.4.1 to compute the quiescent fraction for the IllustrisTNG model and ﬁnd that the IllustrisTNG main sequence- and sSFR-based quiescent fractions are higher than our empirical results. In contrast, when using masses and SFR measured for all particles bound to a subhalo (navy blue, the total “aperture"), and the main sequence described in Section 3.4.1, IllustrisTNG under-predicts the main sequence- and sSFR- based quiescent fractions compared to our empirical results. We also show the IllustrisTNG main sequence-based quiescent fraction from Donnari et al.

(2019) (black), which uses the 2 × R1/2 aperture and a main sequence that is extrapolated from lower to higher masses, rather than a main sequence computed in every mass bin. This method gives a main sequence-based quiescent fraction that is higher than our empirical result...... 140

A1 Top row: A reproduction of Figure 4.9 for ease of comparison. Second row: A reproduction of Figure 4.1 for ease of comparison. Third to ﬁfth row:

The distribution of galaxies in the SFR-M? plane for theoretical models IllustrisTNG, SIMBA, and SAG. In rows two through ﬁve, the inset box in the upper right corner identiﬁes the data used to generate the 2D histogram in that panel and colorbars show the number of galaxies in each cell of the 2D histogram. IllustrisTNG is more successful at reproducing the distribution

of massive galaxies in the SFR-M? plane seen in our empirical results than SIMBA and SAG, however IllustrisTNG over-predicts the fraction of galaxies in the collective green valley and quiescent populations (Sherman et al., 2020b). In all rows, the gray shaded regions represent masses below our 95% completeness limit. We emphasize that the results presented in 11 12 this work focus on the mass range M? = 10 to 10 M , and that results 12 above M? = 10 M (vertical dashed gray line) are unlikely to be robust...... 143

xxx Chapter 1: Introduction

1.1 Massive Galaxy Evolution

It is generally well established that galaxies form and evolve hierarchically (e.g., Cole et al. 2000) within the Λ Cold Dark Matter (ΛCDM; Blumenthal et al. 1984) cosmological model. In this model, small dark-matter halos form via gravitational instability, later merging with other small dark-matter halos to eﬀectively build dark-matter halos of increasing size over cosmic time. Baryons, which reside in these dark-matter halos, provide observational evidence of this hierarchical process. It naturally follows that low-mass systems should be found at early times, while high-mass systems should exclusively be found at late times. 11 Massive (M? > 10 M ) galaxies, however, are found at early times within the ﬁrst ∼ 2 Gyr after the Big Bang. Studies (e.g., Cowie et al. 1996, Bundy et al. (2006), Conselice et al. 2011, van der Wel et al. 2011. Weinzirl et al. 2011, Muzzin et al. 2013, van Dokkum et al. 2015, Martis et al. 2016, Tomczak et al. 2016) suggest that their growth timeline may have been accelerated, leading to rapid mass buildup and early quenching of these systems, compared with lower mass galaxies. Understanding the physical processes driving the evolution of the massive galaxy population is a key question in extragalactic astronomy. Cosmic noon (1.5 < z < 3.5, corresponding to ∼ 1.8 − 4.3 Gyr after the Big Bang) is an important epoch for the massive galaxy population. At this time, proto-clusters begin to collapse into bound clusters, and black hole accretion rate and star formation rate are at their peak (Madau & Dickinson, 2014). This is also the epoch over which the massive galaxy population begins transitioning from a population that is primarily star-forming to one that is predominantly quiescent. The physical processes that lead to this transition are complex and multi-faceted (see Chapter 3), including major and minor mergers (e.g., Mihos & Hernquist 1994, Mihos & Hernquist 1996, Jogee et al. 2009, Robaina et al. 2010, Hopkins et al. 2013), tidal interactions (e.g., Barnes & Hernquist 1992 and references therein, Gnedin 2003), spontaneously or tidally induced bars (e.g., Sakamoto et al. 1999, Jogee et al. 2005, Peschken & Łokas 2019) ram pressure stripping (e.g., Gunn & Gott 1972, Giovanelli & Haynes 1983, Cayatte et al. 1990, Koopmann & Kenney 2004, Crowl 2005, Singh et al. 2019), tidal stripping (Moore et al. 1996, Moore et al. 1998), starvation and strangulation (Larson, 1980), stellar feedback (e.g., Ceverino & Klypin 2009, Vogelsberger et al. 2013, Hopkins et al. 2016, Núñez et al. 2017) and AGN feedback (e.g., Hambrick et al. 2011,

1 Fabian 2012, Vogelsberger et al. 2013, Choi et al. 2015, Hopkins et al. 2016). Additionally, the observed properties of massive galaxies provide important benchmarks for theoretical models which employ hierarchical growth frameworks. Typically, models aim to implement physical processes that will reproduce the observed properties of typical 10 galaxies (M? ∼ 10 M ). These models are less successful at simultaneously reproducing the properties of both the low-mass and massive galaxy populations across cosmic times (e.g., Somerville & Primack 1999, Cole et al. 2000, Bower et al. 2006, Croton et al. 2006, Conselice et al. 2007, Somerville et al. 2008, Benson 2012, Somerville & Davé 2015 and references therein, Croton et al. 2016, Naab & Ostriker 2017 and references therein, Weinberger et al. 2017, Asquith et al. 2018, Cora et al. 2018, Knebe et al. 2018, Behroozi et al. 2019, Cora et al. 2019, Davé et al. 2019, Sherman et al. 2020a, Sherman et al. 2020b). In many ways, rectifying this mismatch has historically been limited by computational power, as well as challenges in understanding and implementing relevant physical processes. Full hydrodynamical simulations (e.g., IllustrisTNG (Pillepich et al. 2018b, Springel et al. 2018, Nelson et al. 2018, Naiman et al. 2018, Marinacci et al. 2018) and SIMBA (Davé et al., 2019)) are just now able to model volumes that are a few hundred Mpc on a side and, because of this, they remain limited by small numbers of massive galaxies in their models. Semi-analytic models (SAMs; e.g., SAG (Cora et al., 2018), SAGE (Croton et al., 2016), and Galacticus (Benson, 2012)) are much less computationally expensive than hydrodynamical models, and can therefore study larger volumes with increased statistics for massive galaxies, however the physics underlying galaxy evolution must be simplified in order to take this approach. Detailed empirical studies of statistically significant, uniformly selected samples of the massive galaxy population are imperative for understanding how the physics implemented in these models needs to be modified to better match the observed properties of massive galaxies.

1.2 Practicalities of Studying Massive Galaxies

The past century has seen significant advances in the understanding of extragalactic systems. This began with morphological classification of individual nearby galaxies by Edwin Hubble in the 1920’s (e.g., Hubble 1926) and has continually been a field pushing the limits of available technology. In the 21st century, technological advancements across every step of the scientific process (improved architecture allowing for enormous telescopes, innovative

2 CCD technology, automated image processing software, sophisticated spectral energy distribution modeling techniques, and high performance computing resources, among others) have significantly expanded the capabilities of extragalactic studies. Detailed studies of nearby galaxies continue today (e.g., York et al. 2000, Blanc et al. 2013, Ma et al. 2014, Eisenstein et al. 2011, Bundy et al. 2015, Blanton et al. (2017), Carrillo et al. 2020), where their high-resolution photometry and spectroscopy not only advance the understanding of these systems, but they also provide spectral energy distributions (SEDs) that can be used to model data obtained at higher redshifts, which is often much lower resolution. High-resolution data at high redshifts is typically difficult to obtain, particularly for unbiased studies, as it requires a large strain on already over-subscribed observing facilities. Extragalactic “legacy fields” (such as CANDELS (Grogin et al., 2011)) circumvent these restrictions by pooling resources to obtain extensive multi-wavelength photometric observations of small patches of sky, often less than 1 deg2, with spectroscopic followup of objects of interest. This approach has been successful for generating deep catalogs of extragalactic systems with highly constrained redshifts (both photometric and spectroscopic), stellar masses, and star-formation rates, among other properties of interest. It has also allowed for the studies of fundamental relations (stellar mass function, main sequence, etc.) 8 9 down to fairly low stellar masses (∼ 10 −10 M ). These small area studies face significant challenges from cosmic variance, however, which can be as high as 50 − 70% (Moster et al., 11 2011) for massive (M? > 10 M ) galaxies at 1.5 < z < 3.5. Massive galaxies, which are rare in number density, require large area studies in order to obtain robust measures of the population. While legacy fields may have 30 or more filters of multi-wavelength photometry, and spectroscopy for select galaxies, much larger area studies covering 15−20 deg2 typically have sparse multi-wavelength coverage (∼ 10 filters of SED coverage) and limited spectroscopy. Studying objects in this type of survey requires strong reliance on SED fitting techniques, validation of those results using mock galaxies, and high performance computing resources to manage large amounts of data. While this is challenging, the benefits of large area studies outweigh the limits of lower resolution. These studies allow for the discovery and exploration of statistically significant numbers of objects that are rare in number density, such as massive galaxies, reducing Poisson errors and rendering uncertainty from cosmic variance negligible. Additionally, with consistent multi-wavelength coverage across large

3 areas, rare objects can be uniformly selected, thereby providing measures of the population without biases due to pre-selection.

1.3 Properties of Massive Galaxies at z > 1

As mentioned in Section 1.2, previous studies of massive galaxies were typically done in deep legacy-type fields and often focused on obtaining detailed observations of small numbers of objects. These studies, which are typically targeted observations, suggests that massive galaxies are home to old stellar populations (Cowie et al. 1996, Fontana et al. 2009, Kajisawa et al. 2011, Greene et al. 2015, among others) that formed rapidly at early times, developing first as compact red nuggets (e.g., van der Wel et al. 2011, Weinzirl et al. 2011, van Dokkum et al. 2015) and building extended populations at later times through minor mergers, which are known to be frequent at z < 2 (e.g., Jogee et al. 2009, Lotz et al. 2011). 10.8 van der Wel et al. (2011) used a sample of 14 1.5 < z < 2.5 M? > 10 M galaxies observed with HST to show that massive galaxies at these redshifts have half light radii < 2kpc, which is roughly three times smaller than more local massive galaxies, and are 11 disk dominated. Weinzirl et al. (2011) took a targeted approach to study 82 M? > 10 M galaxies spanning 1 < z < 3 in the GOODS-NICMOS survey (Conselice et al., 2011) and similarly showed that these galaxies were largely compact and disky. van Dokkum et al. 10.6 (2015) explored a sample of 582 M? > 10 M galaxies in CANDELS/3D-HST spanning 2.0 < z < 2.5 and show that the progenitors of massive compact galaxies likely experienced inside-out growth and that massive galaxies have a steeper slope in the mass-size plane than less massive galaxies. The steepened relation between the size and mass of massive galaxies suggest that following their early compaction, their acquired outer regions are more diffuse and likely built through minor mergers (e.g., Newman et al. 2012, van Dokkum et al. 2015, de la Rosa et al. 2016). Studies at 1.5 < z < 3.5 of key relations, such as the stellar mass function (e.g., Muzzin et al. 2013, Ilbert et al. 2013, Tomczak et al. 2014, Grazian et al. 2015, Davidzon et al. 2017), main sequence (e.g., Daddi et al. 2007, Elbaz et al. 2007, Noeske et al. 2007, Karim et al. 2011, Rodighiero et al. 2011, Guo et al. 2013b, Speagle et al. 2014, Whitaker et al. 2014, Lee et al. 2015, Renzini & Peng 2015, Salmon et al. 2015, Schreiber et al. 2015, Tasca et al. 2015, Tomczak et al. 2016, Santini et al. 2017, Popesso et al. 2019), and the quiescent fraction (e.g., Kriek et al. 2006, Muzzin et al. 2013, Martis et al. 2016, Tomczak

4 et al. 2016) for the population of massive galaxies have been performed, but they suﬀer strongly at the highest masses from Poisson errors and cosmic variance since these studies were done using small area surveys. Generally, these studies show that the massive galaxy population has low number density, and that cosmic noon (1.5 < z < 3.5) is the epoch at which massive galaxies begin to become quiescent. These studies, however, have not been able to robustly constrain the number densities of massive galaxies, their quiescent fraction as a function of mass, or the slope of the high-mass end of the main sequence.

1.4 Thesis Overview

In this thesis, I leverage the statistical power of a multi-wavelength survey that is both 11 wide and deep to find the largest population to date of massive (M? > 10 M ) galaxies at cosmic noon (1.5 < z < 3.5), and use that sample to investigate their properties and evolutionary pathways. I show (1) the most massive end of the stellar mass function is steeply declining at the high mass end (Chapters 2 and 3), (2) within the massive galaxy population, more massive galaxies quench earlier and the massive galaxy population as a whole is predominantly quiescent by z = 1.5 (Chapters 3 and 4), (3) the slope of the main sequence for all galaxies is flattened at the high mass end by the buildup of the collective green valley and quiescent population whereas the star-forming galaxy main sequence is not flattened (Chapter 4), and (4) the distribution of star-forming galaxies around the star-forming galaxy main sequence is not Gaussian, indicating that massive star-forming galaxies spend more time with moderate SFR than they do with extreme SFR (Chapter 4). I also compare these empirical results with those from previous observational studies and state of the art theoretical models. I use the empirical results to provide feedback on the physical processes that may be implemented in future models to better match observed trends (Chapters 2, 3, and 4). These scientific results are made possible by several important advances made in this thesis, which are described below.

1.4.1 Reliably Finding the Biggest Pieces of Hay in the Haystack

The multi-wavelength data used in this work are taken across a ∼ 17.5 deg2 equatorial region (0.44 Gpc3 comoving volume from 1.5 < z < 3.5) within the Sloan Digital Sky Survey (SDSS; Eisenstein et al. 2011) Stripe 82. This particular patch of sky is rich in

5 low-redshift spectroscopy provided by SDSS, and higher-redshift spectroscopy is currently being obtained by the Hobby Eberly Telescope Dark Energy Experiment (HETDEX) (Hill et al., 2008) for 1.9 < z < 3.5 Lyman-α emitters. Although extensive data will be available from HETDEX in coming years, this work had access to limited early data releases for only small numbers of objects. Because of this, this work employed photometric data almost exclusively when investigating the massive galaxy population. For several decades now, spectral energy distribution (SED) fitting techniques (e.g., Ilbert et al. 2006. Brammer et al. 2008, da Cunha et al. 2008, Kriek et al. 2009, Noll et al. 2009, Ciesla et al. 2015, da Cunha et al. 2015, Leja et al. 2017, Yang et al. 2020) have been used to extract critical information such as redshift, stellar mass, and star-formation rate from multi-wavelength broadband photometry. Results of SED fitting are highly dependent on the underlying templates used for fitting, the choice of priors and whether to use those during fitting, as well as the underlying dust law and IMF. Systematic studies, such as that conducted by Mobasher et al. (2015), have investigated the uncertainty caused by these choices by asking many groups to use their SED fitting technique to recover the stellar mass for a fixed catalog. Mobasher et al. (2015) showed that differences in the underlying templates and whether or not they had nebular emission lines were large drivers of uncertainty (up to 0.2 dex and 0.3 dex, respectively). Although priors can can be useful for reducing contamination from interlopers, they are only useful when the priors can adequately represent all populations in a given empirical catalog. In the case of this study, priors constructed from pencil beam lightcones built from small volume simulations did not adequately represent the massive galaxy population, and therefore, priors were not used in this work. Additionally, the population of luminous AGN are not well fit by traditional SED fitting codes as they do not account for the AGN contribution to the SED template. Because of this, known luminous AGN are removed throughout this work. Those that are removed here are studied in detail by Florez et al. (2020) using the AGN-specific SED fitting code CIGALE (Noll et al. 2009, Ciesla et al. 2015, Yang et al. 2020). This work relies on the SED fitting accurately recovering the properties for all objects in our catalog of ∼ 3 million sources. Chapter 2 details the addition of a Monte Carlo procedure to the SED fitting code EAZY-py (Brammer et al., 2008), and how this addition provides measures of uncertainty for every object’s best-fit stellar mass, SFR, and other important galaxy parameters. Chapter 2 also describes validation of the SED fitting procedure using

6 a set of mock galaxies (V. Acquaviva, private communication). With limited spectroscopic coverage, it is imperative that photometric redshifts are shown to be robust. When available, comparisons are made with low-redshift galaxies from SDSS or small samples (less than 56 galaxies) with spectroscopic redshifts from HETDEX. When those are not available, I implement tests which investigate how the scientific results would be affected by incorrect redshifts (see Chapters 2 and 3 for details). These tests also serve as tests of the effects of Eddington Bias (Eddington, 1913), the phenomenon through which lower mass galaxies would be scattered to higher masses due to uncertainties in photometry and photometric redshifts. The uncertainty estimates, SED fitting validation, and testing the impact of photometric redshift errors described here are important advances which allow individual populations of galaxies, in this case massive galaxies, to be reliably located within large photometric catalogs. Anomalies in the imaging, which propagate to the photometric catalog, however, still require visual inspection to mitigate. In rare cases, light from a local star or nearby galaxy can contaminate the light measured for a distant object in some filters, but not others. When this happens, these objects are artificially brightened and can be fit by the SED fitting code to have extraordinarily high stellar masses. In Chapters 2 and 3 I describe the visual inspection performed to mitigate this type of contaminant and ensure a high-confidence sample of massive galaxies.

1.4.2 Signiﬁcantly Improved Statistics

A particular challenge faced by intermediate redshift studies of massive galaxies is that they often find only small numbers of these systems that are rare in number density. The sample of massive galaxies used in this thesis is more than a factor of ∼ 40 larger than those from previous works for log(M?/M ) ≥ 11.5 galaxies at 1.5 < z < 3.0 (Table 1.1). This significant advancement is enabled by the large area probed by this study (∼ 17.2 deg2) compared with previous works (up to ∼ 1 deg2). Increased number statistics lead to significantly reduced Poisson errors. Additionally, the study presented here uses multi-wavelength data that uniformly covers a contiguous 2 ∼ 17.2 deg area in all primary filters used in SED fitting (DECam ugriz, NEWFIRM Ks, and IRAC 3.6 and 4.6µm). Uniform coverage of this large area makes uncertainties due to cosmic variance negligible. Smaller area studies and those that use disparate smaller fields combined into a catalog may suffer strongly from the affects of cosmic variance, particularly

7 Table 1.1: The total number of galaxies with log(M?/M ) ≥ 11.5 for the Ks-selected sample used in Chapters 3 and 4 of this work and values from previous publications. The sample used in this work is more than a factor of ∼ 40 larger than those from previous works. Publication 1.5 < z < 2.0 2.0 < z < 2.5 2.5 < z < 3.0 This Work (Chapters 3 and 4) 1020 2506 1276 Tomczak et al. (2014) 28 22 10 Muzzin et al. (2013) 17 13 28 Ilbert et al. (2013) 24 29 21

at the massive end. Finally, the large sample of massive galaxies used in this study, the largest to date, allows for novel methods of studying this population. Historically, with few numbers of massive galaxies, assumptions needed to be made about the population or all galaxies with 11 M? ≥ 10 M were placed in the same bin. This thesis is able to break the population 11 into several small mass bins above M? ≥ 10 M (Chapters 2, 3, and 4). In this work, fundamental relations such as the stellar mass function (Chapter 2) and the main sequence for all massive galaxies and massive star-forming galaxies (Chapter 4) are investigated without assuming functional forms of those relations. I am also able to implement a new method which uses the stellar mass and SFR of galaxies in each mass bin to isolate the star-forming galaxy population in a meaningful way (Chapter 4).

1.4.3 Detailed Comparisons with Various Types of Theoretical Models

This work is able to provide measures of fundamental properties of massive galaxies with the best statistics available to date. Since robust constraints can be made on this population, it naturally follows to compare these results with the most recent theoretical models of galaxy evolution. Various types of theoretical models exist (e.g., hydrodynamical models, semi-analytic models, and abundance matching), each with unique beneﬁts and drawbacks. For example, hydrodynamical models (e.g., IllustrisTNG (Pillepich et al. 2018b, Springel et al. 2018, Nelson et al. 2018, Naiman et al. 2018, Marinacci et al. 2018) and SIMBA (Davé et al., 2019)) implement detailed physical processes to follow the evolution of galaxies from high to low redshifts. Although the results are quite detailed, due to the computational expense, these models are often run on smaller volumes than those probed by the empirical study used in this work. On the opposite end of the spectrum, semi-analytic models

8 (e.g., SAG (Cora et al., 2018), SAGE (Croton et al., 2016), and Galacticus (Benson, 2012)) implement physics to populate an underlying dark-matter-only simulation. This method is not prohibitively expensive, however it implements simplified physics which is calibrated to observed quantities. Chapters 2, 3, and 4 make detailed comparisons of the empirical results obtained in this work with different classes of theoretical models. This work also investigates how different implementations of physical processes in the models could improve agreement with empirical results. Finally, current limitations of the models in comparisons with large-area empirical results are explored.

9 Chapter 2: Exploring the High-Mass End of the Stellar Mass Function of Star Forming Galaxies at Cosmic Noon

2.1 Introduction

Massive galaxies present an excellent testbed of galaxy evolution and structure formation theories. Evidence suggests that massive galaxies are home to old stellar populations (Cowie et al. 1996, Fontanot et al. 2009, Fontana et al. 2009, Kajisawa et al. 2011, Greene et al. 2015, among others) that formed rapidly at early times, developing first as compact red nuggets (e.g., van der Wel et al. 2011, Weinzirl et al. 2011, van Dokkum et al. 2015) and building extended populations at later times through minor mergers, which are known to be frequent at z < 2 (e.g., Jogee et al. 2009, Lotz et al. 2011). Despite their importance, massive galaxies have proven challenging to study at high redshifts due to small-area surveys (e.g., Grogin et al. 2011, Koekemoer et al. 2011, Whitaker et al. 2011, Straatman et al. 2016) that find only a handful of these elusive objects. As a result, the assembly history of the most massive galaxies remains largely unclear. Measures of the number of galaxies at different epochs, typically in the form of the galaxy stellar mass function (Muzzin et al. 2013, Ilbert et al. 2013, Tomczak et al. 2014, Grazian et al. 2015, Davidzon et al. 2017, among others), have become benchmark tests for galaxy formation theory (e.g., Behroozi et al. 2010, Vogelsberger et al. 2014a, Somerville & Davé 2015, Pillepich et al. 2018b). Assembling galaxies at the high-mass end, in particular, requires efficient formation mechanisms such as major mergers and high star formation rates (SFRs) to build such massive systems by z ∼ 2. Therefore, the number density of high-mass galaxies places constraints on the merger history and star-formation efficiency of these systems, and can strongly inform theoretical models of galaxy evolution. On the theoretical front, different classes of numerical models, such as hydrodynamical

A signiﬁcant portion of this Chapter is accepted for publication in the Monthly Notices of the Royal Astronomical Society (Sherman et al. 2020a, MNRAS, 491, 3318). Sydney Sherman served as the ﬁrst author of this work and conducted the original research contained herein. Coauthors provided useful feedback and guidance that shaped the research and subsequent direction of this work. Coauthors are: Shardha Jogee, Jonathan Florez, Matthew L. Stevans, Lalitwadee Kawinwanichakij, Isak Wold, Steven L. Finkelstein, Casey Papovich, Viviana Acquaviva, Robin Ciardullo, Caryl Gronwall, and Zacharias Escalante.

10 simulations, semi-analytic models (SAMs), and abundance matching models are making increasingly sophisticated attempts to simulate massive galaxies from early cosmic times to today. Hydrodynamical simulations, such as IllustrisTNG (Pillepich et al. 2018b, Springel et al. 2018, Nelson et al. 2018, Naiman et al. 2018, Marinacci et al. 2018) are now covering larger volumes (IllustrisTNG simulation suite includes ∼503 Mpc3 to ∼3003 Mpc3 volumes) and including more sophisticated implementations of feedback processes (Weinberger et al., 2017). Multi-DarkPlanck2 and Bolshoi-Planck dark-matter-only simulations (e.g., Klypin et al. 2016, Rodríguez-Puebla et al. 2016, Knebe et al. 2018) simulate much larger volumes of 0.25h−1Gpc and 1.0 h−1Gpc, respectively, on a side with different resolutions. The properties they output for the dark-matter component can be combined with different implementations of baryonic physics in SAMs (e.g., Benson 2012, Somerville & Davé 2015, Croton et al. 2016, Cora et al. 2018) or in abundance matching models (e.g., Behroozi et al. 2010, Behroozi et al. 2019) to model galaxy evolution. Previous high redshift studies have focused on very deep, small-area surveys (e.g., Grogin et al. 2011, Koekemoer et al. 2011, Whitaker et al. 2011, Straatman et al. 2016) pushing constraints on the stellar mass function to the low mass end. Deep, small-area surveys, however, suffer from the effects of cosmic variance at the high-mass end (e.g., Driver & Robotham 2010, Moster et al. 2011) and find only small samples of high-redshift 11 galaxies with M? > 10 M (e.g., Conselice et al. 2011, Weinzirl et al. 2011, Wang et al. 2012, Muzzin et al. 2013, Ilbert et al. 2013, Tomczak et al. 2014). Works such as Muzzin et al. (2013), Ilbert et al. (2013), and Tomczak et al. (2014) closely examine evolution in the stellar mass function, finding that the quiescent population evolves rapidly since z ∼ 2, while there is little evolution in the star-forming population. In the local Universe, recent integral field spectroscopy (IFS) studies (e.g., Sánchez et al. 2012, Ma et al. 2014, Bundy et al. 2015) have confirmed that the most massive galaxies in the nearby Universe have old stellar populations indicative of early growth and rapid quenching at early times (e.g., Pérez et al. 2013, Greene et al. 2015). Deep, wide-area surveys (e.g., Jannuzi & Dey 1999, de Jong et al. 2015, Papovich et al. 2016, Wold et al. 2019) are necessary to compile large, statistically significant samples of rare systems, such as massive galaxies, overcome cosmic variance, and probe a wide range of environments. As massive galaxies present a challenge to the overall hierarchical structure formation expected in ΛCDM cosmology (e.g., Cowie et al. 1996, Fontanot et al. 2009), it is imperative that statistically significant samples of massive galaxies are constructed.

11 Here, we present an unprecedentedly large sample of massive star-forming galaxies 11 (5,352 galaxies with M? > 10 M ) in the Spitzer/HETDEX Exploratory Large Area (SHELA) footprint, a ∼17.2 deg2 region of SDSS Stripe 82 with extensive multi-wavelength coverage from the rest-frame UV through far-IR/submillimeter. Our study focuses on the peak in cosmic star formation rate density (1.5 < z < 3.5), a time when star formation and black hole accretion peaked, proto-clusters began to collapse, and galaxies underwent signiﬁcant growth. With such a large area survey and a uniformly selected sample, we are able to place some of the most robust constraints to date on the high-mass end of the star-forming galaxy stellar mass function with negligible uncertainties due to cosmic variance. This paper is organized as follows. In Section 2.2 we introduce the data available in the SHELA footprint and the data products used in this work. The analysis used to obtain photometric redshifts, galaxy properties, and selection of a galaxy sample is discussed in Section 2.3. We introduce the SHELA footprint star-forming galaxy stellar mass function in Section 2.4 where we compare this stellar mass function to previous results from observation and theory and discuss the implications of measuring the stellar mass function in large area surveys. Finally, we summarize our results in Section 2.5. Throughout this work we adopt

a ﬂat ΛCDM cosmology with h = 0.7, Ωm = 0.3, and ΩΛ = 0.7.

2.2 Data

This work utilizes a unique large-area, multi-wavelength survey conducted in the data- rich equatorial field SDSS Stripe 82 to study the significant epoch of 1.5 < z < 3.5. The SHELA/HETDEX survey footprint (Papovich et al. 2016, Wold et al. 2019), con- sists of five photometric data sets (Dark Energy Camera (DECam) u,g,r,i,z (Wold et al.,

2019), NEWFIRM Ks (PI Finkelstein; Stevans et al. in preparation), Spitzer-IRAC 3.6 and 4.5µm (PI Papovich; Papovich et al. 2016), Herschel-SPIRE (HerS, Viero et al. 2014) far-IR/submillimeter, as well as XMM-Newton and Chandra X-ray Observatory X-ray data from the Stripe 82X survey (LaMassa et al. 2013a, LaMassa et al. 2013b, Ananna et al. 2017)) and a future optical spectroscopic survey from the Hobby Eberly Telescope Dark

Energy Experiment (HETDEX, Hill et al. 2008). Additional J and Ks data from the VICS82 Survey (Geach et al., 2017) are used to supplement the near-IR data available in the SHELA region.

12 In this work, we utilize the DECam u,g,r,i,z, VICS82 J and Ks, and Spitzer-IRAC 3.6 and 4.5µm data in the SHELA footprint to obtain photometric redshifts and galaxy properties, such as stellar mass and star formation rate, for 1.5 < z < 3.5 galaxies. This redshift range probes the peak of the cosmic star formation rate density (Madau & Dickinson, 2014), and also contains the redshift range (1.9 < z < 3.5) over which the HETDEX project is expected to obtain Lyα-based spectroscopic redshifts for approximately one third of our sources (Hill et al., 2008). This rest-frame UV to rest-frame near-IR subset of the full data products within the SHELA footprint covers ∼17.2 deg2, corresponding to ∼0.44 Gpc3 from 1.5 < z < 3.5. This huge comoving volume mitigates the effects of cosmic variance and allows for the compilation of a statistically significant sample of massive galaxies (5,352 11 star-forming galaxies with M? > 10 M ) across diverse environments (e.g., group-like, proto-cluster, field). A complete description of the data reduction procedure for both the DECam and Spitzer- IRAC data can be found in Wold et al. (2019), and will very briefly be described here. The DECam u,g,r,i,z catalog is built from a stacked, PSF-matched r, i, z detection image using Source Extractor (SExtractor; Bertin & Arnouts 1996). By using r, i, z selection, our sample is biased towards star-forming galaxies, and we describe how any remaining quiescent galaxies are removed from our sample in Section 2.3.1. In this work, we utilize the MAG_AUTO values output by SExtractor. The DECam data reach a 5σ depth of r = 24.5 AB mag (Wold et al., 2019). IRAC photometry is extracted using The Tractor (Lang et al., 2016), which uses forced photometry to deblend the IRAC imaging with source positions from the higher resolution DECam catalog used as location priors. This procedure is necessary due to the low spatial resolution of IRAC (∼1.900) compared to that of DECam (∼1.200) and improves upon the default SExtractor deblending procedure that was used in the original SHELA Spitzer-IRAC catalog from Papovich et al. (2016). The IRAC data reach a 5σ depth of 22 AB mag in both IRAC bands. Additionally, we use SExtractor MAG_AUTO values in the J and Ks bands from the VICS82 Survey, which reach 5σ depths of 21.4 and 20.9 AB mag respectively (Geach et al., 2017). To determine the area of our survey footprint, we count the number of pixels in the DECam r-band image where an object with a particular r-band magnitude could be found with S/N ≥ 5. This is done using the r-band to conform to the r, i, z-based selection for the DECam catalog. The DECam imaging (Wold et al., 2019) is divided into four adjoining tiles denoted B3, B4, B5, and B6, and we compute the area separately for each tile. For

13 6

) 5 2 g

e 4 d (

e 3 r A

y 2 e

v B3 Tile r

u B4 Tile 1 S B5 Tile B6 Tile 0 20 21 22 23 24 25 26 27 28 r-band AB mag

Figure 2.1: The area in which an object with a given r-band magnitude can be detected in our survey footprint with S/N ≥ 5. The gray shaded region represents magnitudes fainter than the r = 24.8 AB mag 80% completeness limit found by Wold et al. (2019). Across all four adjoining tiles (B3, B4, B5, and B6) that comprise the SHELA footprint, the area does not vary as a function of magnitude for objects brighter than the r-band 80% completeness limit. Across all four tiles, objects can be detected with r-band S/N ≥ 5 in ∼17.2 deg2. r-band magnitudes spanning r = 20 - 28 AB mag with step size 0.1 mag, we determine the threshold noise in nJy required for a source with that magnitude to have S/N = 5. If a given pixel in the DECam rms map (containing values for the background noise associated with each pixel) has 5σ rms value larger than the S/N = 5 threshold for an object with a given r-band magnitude, then that pixel is not included in the calculated survey area for objects of that magnitude. We ﬁnd that the survey area within each tile (Figure 2.1) does not evolve as a function of magnitude for all objects brighter than the r = 24.8 AB mag 80% completeness limit reported by Wold et al. (2019). With all four tiles combined, objects above the r-band 80% completeness limit can be detected with S/N ≥ 5 across ∼17.2 deg2.

14 2.3 Data Analysis And SED Fitting

2.3.1 Galaxy Properties From EAZY-py

Photometric Redshifts and Error Estimates

Photometric redshifts were obtained using EAZY-py1, an updated Python-based version of the template-based code EAZY (Brammer et al., 2008). EAZY-py fits a set of twelve Flexible Stellar Population Synthesis (FSPS) templates (Conroy et al. 2009, Conroy & Gunn 2010) in non-negative linear combination. The twelve default FSPS models included with EAZY-py span a wide range of galaxy types (star-forming, quiescent, dusty), with different realistic star-formation histories (SFH; bursty and slowly rising). The best-fit combination of templates is determined through χ2 minimization. This method is preferable when fitting a diverse sample of low- and high-redshift galaxies as it mitigates the bias to low- redshift objects that may occur when using single templates based primarily on low-redshift galaxies. The redshift distribution of galaxies in the SHELA footprint is shown in Figure 2.2, and example spectral energy distribution (SED) fits and photometry of galaxies fit to 11 have M? > 10 M and 1.5 < z < 3.5 are shown in Figure 2.3 and Figure 2.4. Properties such as photometric redshift, stellar mass, and star formation rate from SED fitting procedures inherently carry some uncertainties. We test the reliability of the SED fits by comparing photometric and spectroscopic redshifts later in this section, as well as investigating how well we can recover the properties of mock galaxies with known redshift, stellar mass, and star formation rate (see Section 2.3.2). Even with the careful construction of the EAZY-py template set, which is meant to represent a wide range of galaxy SED templates spanning quiescent and star-forming populations with a simple set of twelve templates, there is still the potential that these templates (or any combination thereof) are not perfect representations of the real galaxies in the SHELA footprint. These discrepancies appear in output SEDs as systematically higher or lower flux densities extracted from the best-fitting SED in a particular band compared to observed source photometry in that band. To combat this potential discrepancy and account for systematic offsets in the template set, we utilize a sample of 4,951 galaxies in the SHELA footprint that have spectroscopic redshifts from SDSS. These spectroscopically confirmed galaxies are used to compute the SED template-based magnitude offsets in each

1https://github.com/gbrammer/eazy-py

15 105

104

103

2 Number 10

101

0 1 2 3 4 5 6 Redshift [zphot]

Figure 2.2: Photometric redshift distribution for high-confidence star-forming galaxies (see Section 2.3.1 for a description of sample selection) in the SHELA footprint. The photometric redshift shown here, and used throughout this paper, refers to the EAZY-py best-fit redshift at which χ2 is minimized. The shaded region represents the redshift range of interest (1.5 < z < 3.5) in this paper. For z < 1 galaxies with spectroscopic redshifts from SDSS, we find σNMAD = 0.0377. We discuss tests of photometric redshift recovery of 1.5 < z < 3.5 galaxies using a sample of mock galaxies in Section 2.3.2. Across all redshifts, we find 219,996 galaxies, of which, 14,910 have redshifts 1.5 < z < 3.5.

16 zphot = 1.66 3.0 2 106 = 0.50 log(M /M ) = 11.21 2.5 log(SFR/M /yr) = 2.17

] 2.0 y 4 J 10 n

[ 1.5

P(z) f 1.0 102

0.5

100 0.0 103 104 105 106 0 2 4 6 (Å) zphot 10"

u g r i z J Ks 3.6 m 4.5 m

zphot = 2.20 2 = 5.01 6 10 log(M /M ) = 12.07 3 log(SFR/M /yr) = 2.60 ] y J 104 n 2 [

P(z) f 102 1

100 0 103 104 105 106 0 2 4 6 (Å) zphot 10"

u g r i z J Ks 3.6 m 4.5 m

Figure 2.3: Example SED fits, photometric redshift probability distributions, and photom- 11 etry for two M? > 10 M 1.5 < z < 2.5 galaxies in our sample. Indicated in the inset box in the upper left panel are the object’s best-fitting photometric redshift (zphot, the redshift 2 2 2 at which χ is minimized), reduced χ (χν ) , stellar mass, and star-formation rate. The upper left panel shows the best-fitting SED template (purple) to the object’s photometry (green points) with the set of templates (gray SED curves) added in non-negative linear combination to achieve the best-fitting SED. The upper right panel shows the photometric redshift probability distribution (purple curve), with the best-fitting redshift indicated by a vertical green line. Image cutouts show the photometry in all nine of our photometric bands. Each cutout is 1000 × 1000.

17 z = 2.58 5 phot 10 2 = 6.77 2.0 log(M /M ) = 11.58 104 log(SFR/M /yr) = 0.92

] 1.5 y J 103 n [

P(z) 1.0 f 102 0.5 101

100 0.0 103 104 105 106 0 2 4 6 (Å) zphot 10"

u g r i z J Ks 3.6 m 4.5 m

z = 3.10 106 phot 1.50 2 = 2.87 5 log(M /M ) = 11.04 10 log(SFR/M /yr) = 2.13 1.25

] 4 y 10 1.00 J n

[ 3

10 P(z) 0.75 f 102 0.50

101 0.25

100 0.00 103 104 105 106 0 2 4 6 (Å) zphot 10"

u g r i z J Ks 3.6 m 4.5 m

11 Figure 2.4: Same as Figure 2.3 for two M? > 10 M 2.5 < z < 3.5 galaxies.

18 Table 2.1: SED template-based magnitude offsets determined for each photometric band using low redshift galaxies in the SHELA footprint that have spectroscopic redshifts from SDSS. These offsets are self-consistently computed within EAZY-py and are applied to source photometry such that foffset = Offset × fcatalog, where fcatalog is the flux density in the published catalog (Wold et al., 2019), “Offset" is the SED template-based magnitude offset determined by EAZY-py, and foffset is the object’s flux after applying the magnitude offset. Photometric Band Offset DECam u 0.9923 DECam g 0.9908 DECam r 1.0000 DECam i 0.9820 DECam z 0.9823 VICS82 J 0.9968 VICS82 Ks 0.9916 IRAC 3.6 µm 0.9987 IRAC 4.5 µm 0.9845

photometric band using the built-in EAZY-py magnitude offset function. For the sample of SDSS galaxies in the SHELA footprint (all z < 1), we find extremely small offsets in each band (Table 2.1), indicating that the EAZY-py method of fitting all templates in non- negative linear combination can produce SEDs that fit the observed population well without extensive adjustments. To quantify the photometric redshift error that results from the fits of SDSS-matched galaxies with EAZY-py, the normalized median absolute deviation (Brammer et al., 2008) is computed: ∆z − median(∆z) σNMAD = 1.48 × median . (2.1) 1 + zspec

With the previously computed magnitude offsets applied when fitting for photometric redshift, we find that σNMAD = 0.0377 for the z < 1 galaxies in our survey footprint that have spectroscopic redshifts from SDSS. This value of σNMAD is based on bright SDSS sources at low redshifts and may not be representative of the fainter and/or higher redshift galaxies in our sample2. We therefore complement this SDSS-based test of photometric

2Using a preliminary internal data release from the HETDEX spectroscopic survey, we perform this same test of photometric redshift accuracy on a small sample of 16 galaxies from our 1.5 < zphot < 3.5 sample

19 redshift recovery with a diﬀerent test based on the recovery of photometric redshifts for mock galaxies modeled at higher redshifts (see Section 2.3.2).

Stellar Mass

Stellar masses and other galaxy parameters, such as star-formation rate, for galaxies in the SHELA footprint are generated using EAZY-py. The FSPS templates (Conroy et al. 2009, Conroy & Gunn 2010) implemented in EAZY-py have gained popularity in recent years due to the options for implementing star-formation histories that are more realistic (e.g., bursty SFH, slowly rising and falling SFR) than the commonly used exponentially declining model (e.g., Reddy et al. 2012, Leja et al. 2017). We use the default EAZY-py FSPS models that are built with a Chabrier (2003) initial mass function, Kriek & Conroy (2013) dust law, and solar metallicity. In order to compute the errors on stellar mass and other galaxy parameters, we draw 100 SEDs for each source from the best-fitting SED’s template error function. This procedure ultimately gives 100 values of each galaxy parameter for every object. For each distribution of galaxy parameters, we assign the 50th percentile of the galaxy parameter distribution to be the median-fit value, and the 16th and 84th percentiles as the lower and upper error bars, respectively. The median-fit is adopted throughout this work. To estimate stellar mass completeness, we follow the procedure of Pozzetti et al. (2010) and Davidzon et al. (2013) in which mass completeness is determined using the galaxies found in our survey. The backbone of this method is the premise that the mass completeness limit of a survey is the mass of the least massive galaxy that can be detected in a given bandpass with a magnitude equal to the limiting magnitude of the survey in that bandpass.

At each redshift, we select the 20% faintest objects and scale their mass (log(M?,EAZY−py)) such that their AB magnitude (m) equals the magnitude limit (mlim) of the survey in a given bandpass:

log(M?,m=mlim ) = log(M?,EAZY−py) + 0.4(m − mlim). (2.2)

After scaling the mass of the 20% faintest objects, we ﬁnd the 80th percentile of the mass distribution and assign this value to be the 80% mass completeness limit in each redshift that have HETDEX spectroscopic redshifts. For this small sample we ﬁnd σNMAD = 0.168, indicating fair agreement between our photometric and spectroscopic redshifts.

20 bin. While mass completeness is usually estimated using a ﬁlter closest to the rest-frame

Ks-band (in our case, the IRAC 4.5µm band), we choose to estimate the mass-completeness using the r-band. While the r-band does not directly trace the stellar mass buildup of a galaxy, without a strong enough detection in the r-band, it is unlikely that a source will have significant detections in enough filters to obtain a successful SED fit, without which we don’t have redshift or stellar mass information. Using the r-band, with the 5σ 80% completeness of 24.8 AB mag reported by Wold et al. (2019), we find that at the bounds of

our redshift range of interest, z = 1.5 (3.5), the 80% mass completeness is log(M?/M ) = 10.89 (11.35). Regions of parameter space falling below the 80% mass completeness limits for individual redshift ranges are indicated by gray shaded regions throughout this paper. In selecting our sample, we require detections with S/N ≥ 5 in r-band and IRAC 3.6 and 4.5µm (see Section 2.3.1). With this in mind, we also performed this procedure using both IRAC bands with 5σ 80% completeness of 22.0 AB mag reported by Papovich et al. (2016) and found that in every redshift bin, the IRAC-based 80% mass completeness limit is less than that found using the r-band. At the bounds of our redshift range of interest z = 1.5

(3.5), the 80% mass completeness is log(M?/M ) = 10.41 (10.89) for the 3.6µm band and log(M?/M ) = 10.41 (10.81) for the 4.5µm band. In using the r-band, we therefore report the most conservative estimate of the 80% mass completeness limit for our sample.

Selecting A High-Conﬁdence Sample

The ultimate goal of this work is to compile a sample of the most massive star-forming galaxies from 1.5 < z < 3.5, however it is important to select a clean sample of galaxies at all masses in order to put the massive galaxy population into the overall context of galaxy evolution. In order to achieve this, we must select a sample of galaxies that are highly likely to be 1.5 < z < 3.5 and fit with accurate stellar mass and related stellar population parameters. We require that each source in our “high-confidence" sample meet several criteria in order to remain in the sample. At the most basic level, we require that the source is not identified as a star or AGN by SDSS. This requirement removes ∼2% of objects from our catalog at all redshifts. Known luminous AGN are removed due to the lack of specific fitting procedures to account for AGN components in EAZY-py. It has been shown (e.g., Salvato et al. 2011, Ananna et al. 2017, Florez et al. in preparation) that without specifically accounting for emission from the AGN and the dusty torus, photometric redshifts and other derived quantities (stellar

21 mass, star formation rate, dust extinction, etc.) are unreliable. With consideration to low luminosity AGN, we do not have a method for identifying these systems, however Salvato et al. (2011) showed that galaxies with low-luminosity AGN (defined in their study to have −15 F0.5−2keV < 8 × 10 cgs) were adequately fit by normal galaxy templates without the specific implementation of AGN templates. Therefore, while low-luminosity AGN are not removed from our sample, we believe that they are reasonably fit with the SED fitting procedure used for our whole catalog. Additionally, we remove all galaxies with SDSS spectroscopic redshifts (all zspec < 1) from our sample. Only one SDSS zspec < 1 galaxy was wrongly fit to have photometric redshift 1.5 < z < 3.5, and this one contaminant was removed. Sources in this high confidence sample must have an SED fit that is constrained by 2 six or more photometric bands and has χν < 20 for the best-fitting EAZY-py template combination. A particular band is used in the fit when fν > −90 nJy (the EAZY-py “not_obs_threshold", below which, a source is considered a non-detection) and there are no flags indicating a problem in that band. Specifically, we require that SExtractor external flags equal zero (no data quality issues), SExtractor internal flags are less than or equal to three (indicating a deblended source or source with no flags), and Tractor flags equal zero in each IRAC band (sources were successfully deblended). The requirement of six or more filters, which removes ∼15% of objects from 1.5 < z < 3.5, is chosen such that the SED fit is relatively well constrained. In cases where there are five or fewer filters, we found that 2 even though a “best-fit" template was fit by EAZY-py (sometimes with a low χν value), the same photometry could be reasonably fit by several different template combinations. Through visual inspection, we found that diffraction spikes and diffuse light from nearby stars or foreground galaxies can artificially inflate the IRAC flux for a given object, which is particularly troubling for our high-mass sample as these inflated IRAC fluxes result in unrealistically high stellar masses. In order to identify and remove these objects from 11 our sample, we perform visual inspection of all objects fit to have M? > 10 M . Visual inspection is conducted three times for each source using the Zooniverse3 interface. We ultimately find that the contamination fraction is ∼2% for log(M?/M ) < 11.5 and rapidly increases to 100% contamination at the highest masses (log(M?/M ) & 12.5) fit by EAZY- py, further emphasizing the importance of visual inspection in the high-mass galaxy regime. After flagging these contaminated sources, they are removed from our sample.

3zooniverse.org

22 These initial quality cuts leave us with a sample of 158,879 galaxies at 1.5 < z < 3.5 with robust photometric redshift measurements and obvious contaminants removed. In our redshift range of interest (1.5 < z < 3.5) it is imperative that objects have robust measurements in both IRAC ﬁlters in order to constrain the stellar mass. Over this entire

redshift range, the only filters consistently redward of the Balmer break are VICS82 Ks and IRAC 3.6 and 4.5µm (VICS82 J is initially redward, but moves blue of the Balmer break in our z = 2.5 bin). As the VICS82 data do not cover the entirety of our field, we only place constraints on the IRAC data. To remove galaxies with unreliable stellar mass, we impose a S/N ≥ 5 requirement for an object to remain in our “high confidence" sample. Following this cut (and previous quality cuts described above) we are left with a sample of 45,050 galaxies with robust measures of stellar mass at 1.5 < z < 3.5, of which 17,609 (60.9%) 11 have M? > 10 M . Our science case focuses on star-forming galaxies, and we must remove quiescent galaxies in order to achieve a clean sample. To do this we impose two cuts, the first of which is a S/N ≥ 5 requirement in the r-band which reduces our sample size to 5,510 galaxies 11 with M? > 10 M . Second, we require that galaxies in our sample have specific star formation rate sSFR > 10−11 yr−1, following Fontana et al. (2009) and Martis et al. (2016) 11 where sSFR =SFR/M?. This gives us a final sample of 5,352 massive (M? > 10 M ) star-forming galaxies at 1.5 < z < 3.5, the largest uniformly selected sample of these objects to date. Applying the selection for star-forming galaxies removed ∼69% of galaxies with 11 M? > 10 M , which is consistent with results from Fontana et al. (2009) and Martis et al. (2016) that find 50-70% of galaxies at the high mass end to be quiescent. Finally, we estimate the number of massive star-forming galaxies that we may be missing as a result of imposing the strict IRAC S/N ≥ 5 cut needed for robust estimates of stellar mass. If we take the stellar mass fit by EAZY-py at face value, we find that 511 galaxies with S/N < 5 in both IRAC filters have S/N ≥ 5 in the r-band and are fit to have M? > 11 10 M at 1.5 < z < 3.5. These 511 potentially real massive star-forming galaxies that were removed from our sample would constitute ∼9.5% of our final sample of massive star-forming galaxies at these redshifts.

2.3.2 Testing EAZY-py With Mock Galaxies

Due to the uncertainties that come with SED fitting, it is important to confirm that the SED fitting procedure and models used (in our case, EAZY-py with FSPS models) can

23 correctly recover galaxy redshifts and parameters for galaxies with our filter set. Testing redshift recovery is difficult at z > 1 due to the limited number of spectroscopic redshifts available. Galaxy spectroscopic redshifts in the SHELA field come solely from SDSS and are for z < 1 galaxies. Future optical spectroscopy from HETDEX will provide spectroscopic redshifts for Lyα emitters within 1.9 < z < 3.5, and these will provide a sample to test the accuracy of photometric redshift recovery at z > 1. Since these samples do not currently exist, we rely on our sample of mock galaxies to test our photometric redshift recovery for 1.5 < z < 3.5 galaxies. We begin by constructing a sample of mock galaxies (Acquaviva, V., Private Com- munication) built from an expanded version of GALAXEV (Bruzual & Charlot, 2003). 10 Several thousand z ∼ 0, M? ' 10 M models were generated to span several initial mass functions (IMF; Chabrier, Salpeter, and Kroupa), dust laws (Calzetti and Milky Way), and star formation histories (exponentially declining, delayed exponential, constant, and linearly increasing) for a large grid of age, e-folding time (τ), extinction, and metallicity values. This base set of models is then redshifted to z = 0.001 − 6 with ∆z = 0.2 and scaled in 10 10 11 11 12 mass to M? '[1 × 10 , 5 × 10 , 1 × 10 , 5 × 10 , 1 × 10 ]M . Ultimately, this passive model scaling leads to ∼ 2.4 million mock galaxies. Finally, from each full mock galaxy spectrum, we extract photometry in the filters available in the SHELA footprint (DECam ugriz, VICS82 J, Ks, and Spitzer-IRAC 3.6 and 4.5µm). Assigning errors to the extracted mock galaxy photometry is a three step process, completed separately for each photometric band of every mock galaxy. In the first step, we find an object in the SHELA footprint “high-confidence" sample (see Section 2.3.1) with similar magnitude (within ∆mag = 0.2) in a particular photometric band to the mock galaxy’s magnitude in that band. Using all of the SHELA footprint galaxies found to be in this magnitude bin, we construct a distribution of flux errors associated with those real SHELA footprint galaxies and an error value is drawn from that distribution. In the second step, the value of the flux for a given mock galaxy in a particular photometric band is scattered. This is done by constructing a Gaussian centered on the original mock galaxy’s flux with σ equal to the error value drawn in the first step of this process. The scattered flux in that photometric band is then drawn from the Gaussian. Scattering is done to re-create the random error associated with extracting photometry from images in the SHELA footprint. Finally, in the third step, we repeat the procedure of step one using the scattered mock galaxy magnitude found in step two as the magnitude around which we search for SHELA

24 footprint galaxies and select a new error bar. This three step procedure produces a scattered flux with realistic errors for each photometric band of every mock galaxy. It is important to note that this procedure of passively scaling mock galaxy spectra constructed in various ways and adding error bars is not akin to constructing a mock catalog, and therefore, does not represent a realistic distribution of galaxies. Rather, for this test we simply require a diverse set of mock galaxies with known properties (e.g., redshift, stellar mass, SFR) to test the ability of our SED fitting procedure to recover these properties. Our main interest for this work lies with galaxies at 1.5 < z < 3.5 and our comparison here will focus on mock galaxies falling in this redshift range. In order to test EAZY-py, we run a randomly selected sample of 10,000 mock galaxies through EAZY-py and compare their output redshift, stellar mass, and SFR to the “truth" associated with that mock galaxy. This random subset of mock galaxies contains models spanning the full range of IMFs, dust laws, SFHs, ages, e-folding times, extinction, and metallicity values used to construct our mock galaxy sample. The primary goal of this exercise of fitting mock galaxies is to determine if the SED fitting procedure used on real SHELA footprint galaxies can adequately recover the redshift, stellar mass, and star formation rate for the mock sources. Extreme discrepancies here in this somewhat idealized sample would be cause for concern with the use of EAZY-py to fit the sources in the SHELA footprint. We find that EAZY-py does a good job of recovering the redshift of the sources in the redshift range 1.5 < z < 3.5, with a redshift error of σNMAD = 0.092 and 11.2% 3σ outliers (top panel of Figure 2.5). Extreme outliers are generally mock galaxies with featureless SEDs or those fit to have highly multi-peaked photometric redshift distributions where there are several probable photometric redshift fits, but the redshift found by EAZY-py to have the lowest χ2 is not the true redshift for that object. Additionally, we find that EAZY-py, on average, slightly overestimates stellar mass by ∼0.09 dex and underestimates SFR by ∼0.46 dex (middle and bottom panels of Figure 2.5, respectively). Systematic offsets may be partially attributed to differences between the BC03 models used to construct the mock galaxies and the FSPS models used in the EAZY-py SED fitting. These systematic offsets may also have contributions from the non-negative linear combination fitting method used in EAZY-py. We emphasize that these tests on mock galaxies are simply meant to demonstrate that EAZY-py can adequately recover the redshift, stellar mass, and star formation rate for a set

25 ) +15 k NMAD = 0.092, N = 10000, 3 Outliers = 11.2% c

o +10 M z +5 + 1

( 0 /

z 5

1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 zMock 2

) 0 M ( 2 g o l 4 Average Offset = 0.085 dex

[EAZY-py - Mock] 6 1010 1011 1012 M , Mock [M ] 5.0 Average Offset = -0.464 dex

) 2.5 R F

S 0.0 ( g o l 2.5

[EAZY-py - Mock] 5.0 10 1 100 101 102 103 104 1 SFRMock [M yr ]

Figure 2.5: Comparison of redshift (top panel), stellar mass (middle panel), and SFR (bottom panel) between EAZY-py output and the input values for 10,000 randomly selected mock galaxies. Error bars span the 68th percentile of the data in each bin, which corresponds to an average dispersion in redshift of 0.19 ∆z/(1+zMock), average dispersion in stellar mass of 0.58 dex, and average dispersion in SFR of 0.69 dex. We ﬁnd that redshift recovery error (σNMAD = 0.092) is higher than that found using a low redshift sample of SHELA footprint galaxies with SDSS spectroscopic redshifts, however this increased error is expected. On average, we ﬁnd that EAZY-py may over-predict stellar mass by ∼0.09 dex and under-predict SFR by ∼0.46 dex when comparing the output values from EAZY-py to those associated with the mock galaxies. There are no data points lying behind the caption boxes.

26 of mock galaxies with widely different underlying SEDs. We do not to make any corrections to our data or theoretical models using the results of our mock galaxy tests because the sample of mock galaxies does not have the same relative distribution of different types of galaxies as our observational catalog. Instead, when needed, we use the average stellar mass error in each redshift bin based on SED fits performed on our galaxy sample (see Section 2.3.1 for details) as a measure of the uncertainty on the stellar mass.

2.4 Results

2.4.1 Massive Star-Forming Galaxies in the SHELA Footprint

We find that the sample of massive star-forming galaxies in the SHELA footprint is distributed across the entirety of the ∼17.2 deg2 area (Figure 2.6). While this is not unexpected, it further highlights the necessity of a large area survey with a uniformly selected sample when compiling statistically significant populations of sparse objects. With our large survey footprint, we can provide measures of the number of objects per square degree in specific mass and redshift bins, which may prove useful in the design of future surveys. The total number of star-forming galaxies, number per square degree, and number density found in several mass and redshift bins is detailed in Table 2.2, while Figure 2.7 shows the number per square degree as a function of mass in small redshift bins with ∆z = 0.5 from

z = 1.5 to z = 3.5. In all, we find 962 star-forming galaxies with log(M?/M ) > 11.5, the largest uniformly selected sample of these objects found to date from 1.5 < z < 3.5. Intuitively, one would expect that the number of extremely massive galaxies (for the full star-forming and quiescent population) would increase towards present day, such that there should be more massive galaxies in our 1.5 < z < 2 bin than there are in the 3 < z < 3.5 bin. From Figure 2.7 and Table 2.2, we find that the number of the most massive (M? > 12 10 M ) star-forming galaxies decreases toward our lowest redshift bin, as is expected for 11 star-forming massive galaxies at this epoch. For star-forming galaxies with 10 M < M? 12 < 10 M we find that the number of massive star-forming galaxies increases from z = 3.5 to z ∼ 2, and begins to decrease in the 1.5 < z < 2 bin. Previous studies (e.g., Fontana et al. 11 2009, Martis et al. 2016) have shown that 50 - 70% of massive (M? > 10 M ) galaxies are quiescent by z ∼ 1.5. The SHELA footprint star-forming galaxy stellar mass function is computed using the

1/Vmax method (Schmidt, 1968) following the procedure of Weigel et al. (2016). We begin

27 Figure 2.6: Map of the SHELA footprint (gray) with massive star-forming galaxies shown in color. The color and size of each point corresponds to the mass of the galaxy, with brighter, larger points representing more massive galaxies. Panels from top to bottom increase in redshift by ∆z = 0.5 from z = 1.5 to z = 3.5. The lowest redshift bin (1.5 < z < 2) contains 11 galaxies with M? > 10 M , while the higher redshift bins (2 < z < 3.5) contain galaxies more massive than the 80% mass completeness limit determined for each redshift bin in Section 2.3.1. The minimum mass in each redshift bin and the number of galaxies above that mass threshold are shown in the upper left corner of each panel. Vertical lines represent the boundaries of the SHELA footprint tiles (B3, B4, B5, and B6) discussed in Section 2.2, and tile names are indicated in each panel. The number per unit area of massive galaxies 11 2 (M? > 10 M ) at 1.5 < z < 3.5 is quite low (∼310/deg ), emphasizing the beneﬁt of our large area SHELA footprint in providing a statistically signiﬁcant sample (5,352 with M? 11 > 10 M ) of massive star-forming galaxies.

28 1.5 < z < 2 2 < z < 2.5 103 103 11 log(M /M ) < 11.5 = 964 11 log(M /M ) < 11.5 = 1792 11.5 log(M /M ) < 12 = 85 11.5 log(M /M ) < 12 = 275 log(M /M ) 12 = 2 log(M /M ) 12 = 13 x 2 x 102

e 10 e d d / / 2 2 1 g 1 g 10 e 10 e d d / / r r 0 e e 10 b 100 b m m

u u 1

N N 10 10 1 10 2 109 1010 1011 1012 1013 109 1010 1011 1012 1013 M [M ] M [M ] 2.5 < z < 3 3 < z < 3.5 103 103 11 log(M /M ) < 11.5 = 1181 11 log(M /M ) < 11.5 = 453 11.5 log(M /M ) < 12 = 346 11.5 log(M /M ) < 12 = 198 log(M /M ) 12 = 15 log(M /M ) 12 = 28 x 2 x 102

e 10 e d d / / 2 2 1 g 1 g 10 e 10 e d d / / r r 0 e e 10 b 100 b m m

u u 1

N N 10 10 1 10 2 109 1010 1011 1012 1013 109 1010 1011 1012 1013 M [M ] M [M ]

Figure 2.7: The number of star-forming galaxies per square degree for 1.5 < z < 3.5 galaxies in the SHELA footprint. The dark solid lines correspond to the number of sources found at each mass, while the light purple regions represent Poisson errors. The gray shaded regions represent masses below the 80% mass completeness limit for each redshift bin. The total number of galaxies that we ﬁnd in the high stellar mass regime are indicated in the inset box for each redshift bin.

29 by ﬁnding the 95% mass completeness limit as a function of redshift by repeating our mass completeness procedure described in Section 2.3.1 with the 95% r-band completeness limit of r = 23.5 AB mag from Wold et al. (2019). This allows us to determine the redshift at which our data are 95% complete for a given stellar mass. We bin our sample by photometric

redshift into four redshift bins from 1.5 < z < 3.5 with ∆zbin = 0.5 and further bin by stellar mass within these redshift bins. The 1/Vmax term is then determined for each mass bin based on the maximum redshift at which that mass bin is 95% complete (zmax). In the case that zmax is greater than the maximum redshift of a particular redshift bin, we assign

Vmax to equal the comoving volume of that redshift bin. If zmax lies within the redshift bin of

interest, then the Vmax term is simply the comoving volume between the minimum redshift

of that bin and zmax. Finally, if zmax is less than the minimum redshift of a particular redshift

bin we assign Vmax to be the minimum of the comoving volume from z = 0 to zmax and the comoving volume for our redshift bin of interest. Our empirical star-forming galaxy stellar mass function, shown in Figures 2.8, 2.9, and

2.10 as dark purple points, spans masses from log(M?/M ) ∼ 9 to log(M?/M ) ∼ 12.5. We ﬁnd that at the high mass end, our stellar mass function (Φ) is steeply declining, spanning values of Φ as large as ∼10−4 Mpc−3/dex and as small as ∼5×10−8 Mpc−3/dex. Errors on our empirical stellar mass function are entirely from Poisson errors as the large area of our survey renders errors from cosmic variance negligible. In Section 2.4.2, we estimate the eﬀect that Eddington bias (Eddington, 1913) has on our measured stellar mass function. In Section 2.4.3 we compare our empirical star-forming galaxy stellar mass function to previous observational results, and in Section 2.4.4 we compare with results from theoretical models.

2.4.2 Eddington Bias

Eddington bias is the phenomenon in which, due to photometric error and errors in estimating photometric redshift, lower mass galaxies may scatter into a higher mass bin (Eddington 1913). This is particularly important to consider at the high-mass end of the stellar mass function, where the steep slope and low number statistics compared to intermediate masses are easily inﬂuenced by a small number of low mass interlopers. In 11 our mass range of interest (M? > 10 M ), the primary error which causes a low-mass galaxy to be placed in a high-mass bin is ﬁtting a low redshift galaxy at a high redshift. Errors on stellar mass estimates can also contribute in the steeply declining portion of the stellar mass function (Kawinwanichakij et al. in preparation), however stellar mass errors

30 Table 2.2: (1) Redshift bin for the full redshift range of our sample and divided into smaller bins of ∆z = 0.5. (2) Total number of star-forming massive galaxies, number per square degree, and number density of galaxies found in our sample split into smaller mass bins (3-5). When comparing the number of galaxies found to have log(M?/M ) > 11.5 (columns 4 and 5) to the works of Muzzin et al. (2013), Ilbert et al. (2013), and Tomczak et al. (2014), we ﬁnd an order of magnitude more star-forming galaxies than these previous small-area studies. Errors represent Poisson uncertainties. ≤ M? < ≤ M? < M? ≥ Redshift Sample Statistic 11 log( M ) 11.5 11.5 log( M ) 12 log( M ) 12 (1) (2) (3) (4) (5) Total N 4390 ± 66.25 904 ± 30.07 58 ± 7.62 1.5 < z < 3.5 N/deg2 254.73 ± 3.84 52.46 ± 1.74 3.37 ± 0.44 N/Mpc3 1.01 × 10−5 ± 1.52 × 10−7 2.08 × 10−6 ± 6.91 × 10−8 1.33 × 10−7 ± 1.75 × 10−8

31 Total N 964 ± 31.05 85 ± 9.22 2 ± 1.41 1.5 < z < 2 N/deg2 55.94 ± 1.8 4.93 ± 0.53 0.12 ± 0.08 N/Mpc3 9.19 × 10−6 ± 2.96 × 10−7 8.10 × 10−7 ± 8.79 × 10−8 1.91 × 10−8 ± 1.35 × 10−8 Total N 1792 ± 42.33 275 ± 16.58 13 ± 3.61 2 < z < 2.5 N/deg2 103.98 ± 2.46 15.96 ± 0.95 0.75 ± 0.21 N/Mpc3 1.61 × 10−5 ± 3.81 × 10−7 2.48 × 10−6 ± 1.49 × 10−7 1.17 × 10−7 ± 3.25 × 10−8 Total N 1181 ± 34.37 346 ± 18.60 15 ± 3.87 2.5 < z < 3 N/deg2 68.53 ± 1.99 20.08 ± 1.08 0.87 ± 0.22 N/Mpc3 1.06 × 10−5 ± 3.09 × 10−7 3.11 × 10−6 ± 1.67 × 10−7 1.35 × 10−7 ± 3.49 × 10−8 Total N 453 ± 21.28 198 ± 14.07 28 ± 5.29 3 < z < 3.5 N/deg2 26.29 ± 1.24 11.49 ± 0.82 1.62 ± 0.31 N/Mpc3 4.19 × 10−6 ± 1.97 × 10−7 1.83 × 10−6 ± 1.30 × 10−7 2.59 × 10−7 ± 4.89 × 10−8 are incorporated into our SED fitting procedure as described in 2.3.1 and we do not further implement them here for the purposes of estimating Eddington Bias. To approximate the effects of Eddington bias on our results, we generate 100 realizations of our catalog in which we draw a new photometric redshift value from each object’s redshift probability distribution. We perform SED fitting at the selected photometric redshift to generate 100 realizations of our catalog. We note that this procedure is performed for objects in the catalog at all redshifts such that objects originally outside 1.5 < z < 3.5 may scatter into this range, while those originally inside this redshift range may scatter out. Finally, we construct stellar mass functions for each of the 100 realizations of the catalog (Figure 2.8). These stellar mass function realizations are constructed in the same manner as the “high-confidence" star-forming galaxy sample (see Section 2.3.1) used to construct our empirical stellar mass function (purple points on Figure 2.8). We find that these 100 realizations lead to a scatter in the high-mass end of the stellar mass function of 0.04 - 0.8 dex compared to the empirical SHELA footprint result. We discuss how Eddington bias affects comparisons of our empirical star-forming galaxy stellar mass function with previous stellar mass function results from the literature in Section 2.4.3 and from theoretical models in Section 2.4.4, however we do not make any corrections to our empirical stellar mass function based on the Eddington bias estimates.

2.4.3 Comparing SHELA Footprint SMF to Previous Observational Results

Over the past decade, three papers have risen to stand as the primary literature comparisons for intermediate redshift galaxy stellar mass functions. These are Tomczak et al. (2014) probing galaxies from 0.2 < z < 3 and Muzzin et al. (2013) and Ilbert et al. (2013) which both explore the galaxy stellar mass function from 0 < z < 4. In contrast to the SHELA survey, these works utilize small-area, deep surveys. The three works and their relation to the results in the SHELA footprint are described below and shown in Figure 2.9. Tomczaket al. (2014) utilizes data from the FourStar Galaxy Evolution Survey (ZFOURGE; Straatman et al. 2016) with additional data from the Cosmic Assembly near-IR Deep Ex- tragalactic Legacy Survey (CANDELS; Grogin et al. 2011, Koekemoer et al. 2011). These data span 316 arcmin2, a signiﬁcantly smaller area than the SHELA footprint, but are signif-

icantly deeper reaching an H160 limiting magnitude of 26.5 mag. The primary leverage of a

32 1.5 < z < 2 2 < z < 2.5 3 ) x

e 4 d / 3

c 5 p M / 6 ( g o l 7

8 2.5 < z < 3 3 < z < 3.5 3 ) x

e 4 d / 3

c 5 p M / 6 ( g o l 7

8 9 10 11 12 13 9 10 11 12 13 log(M /M ) log(M /M )

Figure 2.8: Purple points represent the star-forming galaxy stellar mass function for 1.5 < z < 3.5 galaxies in the SHELA footprint, where error bars represent Poisson errors. Gray lines are stellar mass functions generated from 100 realizations of the catalog in which photometric redshifts are drawn from each object’s photometric redshift probability distribution. These 100 realizations are used to estimate the eﬀects of Eddington bias, as outlined in Section 2.4.2. The gray shaded regions represent masses below the 80% mass completeness limit for each redshift bin. We ﬁnd that scatter is introduced to the stellar mass function when the catalog is perturbed, however results remain consistent with those from the original catalog.

33 survey of this type is to investigate the low-mass end of the galaxy stellar mass function. To increase the area surveyed, the authors add data from the NEWFIRM Medium Band Survey (NMBS; Whitaker et al. 2011) spanning 1300 arcmin2. Without the addition of larger area data, it would have been impossible for Tomczak et al. (2014) to place any constraints on the high-mass end of the stellar mass function. The larger 1.62 deg2 UltraVista survey used by Muzzin et al. (2013) and Ilbert et al. (2013) is better equipped to study the high-mass end of the galaxy stellar mass function. While both studies use UltraVista imaging, their catalog construction, source selection, and SED fitting procedure differ. Both studies perform SED fitting with ∼30 filters in order to obtain photometric redshifts and galaxy stellar masses. Similarly, Muzzin et al. (2013) and Ilbert et al. (2013) investigate the evolution of the stellar mass function with redshift and find that the quiescent population evolves much more rapidly than the star-forming galaxy population. While each of these surveys places constraints on the high-mass end of the stellar mass function, cosmic variance remains high. From Moster et al. (2011), the cosmic variance for 11 M? > 10 M galaxies in the Tomczak et al. (2014) study may be as much as 50-70% from 1.5 < z < 3.5, while Muzzin et al. (2013) and Ilbert et al. (2013) report cosmic variance to 11 be 10-30% for massive galaxies (M? > 10 M ) at these redshifts. We compare the high-mass end (above our 80% mass completeness limit) of the SHELA footprint star-forming galaxy stellar mass function to results from the literature (we scale the results from Muzzin et al. (2013) by a factor of 0.039 dex in stellar mass to convert from a Kroupa to Chabrier IMF) and find good agreement at all redshifts. Our results indicate that a significant population of massive star-forming galaxies is already in place at z = 3, −6 3 11 where we find ∼39 galaxies per square degree (∼6.28× 10 per Mpc ) with M? > 10 M . Our own study and those we compare with rely on SED fitting techniques to extract photometric redshifts and galaxy stellar masses, the results of which generally rely on the assumptions that are made. Agreement (disagreement) between results would then suggest a similarity (difference) in assumptions influencing the interpretation of the data. A detailed comparison of SED fitting codes and assumptions by Mobasher et al. (2015) showed that free parameters (such as redshift and star-formation history) can contribute a scatter in best-fit stellar mass of 0.136 dex across codes, while differences in model SED templates and the inclusion (or exclusion) of nebular emission lines can contribute a scatter of 0.2 dex and 0.3 dex, respectively. Our study utilizes FSPS templates with bursty SFHs for red

34 2 Number with Number with 1.5 < z < 2 log(M /M ) 11.5: 2 < z < 2.5 log(M /M ) 11.5: This Work = 87 This Work = 288

) 3 Tomczak+14 = 11 Tomczak+14 = 19

x Muzzin+13 = 9 Muzzin+13 = 10

e Ilbert+13 = 16 Ilbert+13 = 18 d

/ 4 3 c

p 5 M /

( 6 g o l 7

8 2 2.5 < z < 3 Number with This Work Number with log(M /M ) 11.5: Tomczak+14 log(M /M ) 11.5: This Work = 361 This Work = 226 Muzzin+13 ) 3 Tomczak+14 = 8 Muzzin+13 = 28 Ilbert+13 x Muzzin+13 = 26 Ilbert+13 = 14

e Ilbert+13 = 17 d

/ 4 3 c

p 5 M /

( 6 g o l 7 3 < z < 3.5 8 9 10 11 12 13 14 9 10 11 12 13 14 log(M /M ) log(M /M )

Figure 2.9: Galaxy stellar mass function for 1.5 < z < 3.5 star-forming galaxies in the SHELA footprint. Error bars represent Poisson errors. The gray shaded regions represent masses below the 80% mass completeness limit for each redshift bin. The vertical dotted line indicates log(M?/M ) = 11.5, the mass above which we compare to previous studies from the literature, restricted to only their star-forming samples. Note that in our 2 < z < 3.5 redshift bins the size of our sample of massive (log(M?/M ) ≥ 11.5) star-forming galaxies (as shown in the inset in each panel) is a over a factor of 10 larger than the samples from previously published studies. We ﬁnd that our star-forming galaxy stellar mass function shows fair agreement (within a factor of ∼ 2 to 4) with those from the literature.

35 galaxies and rising SFHs for blue galaxies. Additionally, our models implement nebular emission lines. Tomczak et al. (2014) and Muzzin et al. (2013) both employ EAZY to obtain photometric redshifts and FAST (Kriek et al., 2009) to fit for stellar masses using Bruzual & Charlot (2003) models without nebular emission lines and exponentially declining SFHs. Ilbert et al. (2013) implement Le Phare (Arnouts et al. 2002, Ilbert et al. 2006) to fit for both photometric redshifts and stellar masses with Bruzual & Charlot (2003) templates that include nebular emission lines, and exponentially declining SFHs. These differences in SED fitting methods lead to scatter in estimated stellar masses, which can lead to differences in the resulting galaxy stellar mass functions, particularly at the very steep high-mass end. As a result, it is challenging to disentangle discrepancies from fitting methods and differences in underlying physical processes contained in the implemented SED models when comparing observed stellar mass functions. An advantage of our large sample is that on average, we are more likely to uncover the true distribution of stellar masses of our galaxy population, while scatter increases with smaller sample sizes.

2.4.4 Comparing SHELA Footprint SMF to Theoretical Results

Hydrodynamical Simulations

In recent years, the Illustris Project (Vogelsberger et al. 2014a, Vogelsberger et al. 2014b, Genel et al. 2014) has emerged as a heavily relied upon hydrodynamical model tracing galaxy formation and evolution across cosmic time and on cosmological scales. The original Illustris Project utilized a ∼1003Mpc3 box with high resolution and reproduced observables such as the galaxy stellar mass function and cosmic star formation rate density. While this box size and model was the state-of-the-art for its time, the volume was simply too small to adequately study the mass assembly and properties of the most massive galaxies in the Universe. IllustrisTNG (Pillepich et al. 2018b, Springel et al. 2018, Nelson et al. 2018, Naiman et al. 2018, Marinacci et al. 2018), the newest rendition of the Illustris simulation, now includes a larger box size (TNG300 has ∼3003Mpc3) with updated physics. Such a large volume allows for the study of the most massive halos and the massive galaxies that live within them. Updated prescriptions for AGN feedback (Weinberger et al., 2017) generate signiﬁcantly more realistic massive galaxies with reasonable star formation rates, quenched fractions (Donnari et al., 2019), and gas fractions (Weinberger et al. 2017, Pillepich et al. 2018a).

36 Without proper implementations of AGN feedback (Weinberger et al., 2017), the number density of massive galaxies (Pillepich et al., 2018b) and their color distribution (Nelson et al., 2018) do not match observations. If massive galaxies grow too large, without having star formation regulated by AGN feedback, this would artificially increase the number density of these systems. The solution, however, is not simply to increase the strength of AGN feedback to suppress star-formation as this would decrease the gas fraction in rich environments which was found to be low in the original Illustris simulation (Weinberger et al., 2017). Therefore, modified prescriptions, such as the kinetic-mode feedback implemented in IllustrisTNG are necessary to suppress star-formation while preserving the gas fraction and matching other observational constraints. When comparing the results from IllustrisTNG to that of the SHELA footprint (Figure 2.10), we utilize stellar mass functions from the largest volume of the IllustrisTNG series, TNG300, following Pillepich et al. (2018b). Here, we adopt IllustrisTNG stellar masses measured within twice the half mass radius (2 × r1/2) to ensure a one-to-one comparison between the way in which SHELA galaxy stellar masses are measured and how masses are extracted from the IllustrisTNG simulation. Additionally, we use the rescaled results of the simulation, denoted rTNG300, which is corrected for the reduced resolution of the ∼3003Mpc3 run compared to that of the ∼1003Mpc3 run (Pillepich et al., 2018b). To further ensure a fair comparison with the SHELA footprint results, we convolve the results from IllustrisTNG with the average SHELA footprint stellar mass error in each redshift bin (∼0.16 dex), where this stellar mass error comes from our SED fitting procedure as described in Section 2.3.1. Finally, we adjust the total stellar mass function by the fraction of star-forming galaxies in each mass bin to obtain a star-forming galaxy stellar mass function. Quiescent galaxies are defined as those falling more than 1 dex below the galaxy main sequence, and those that don’t meet that criterion are designated as star-forming (Donnari et al., 2019). At 1.5 < z < 2 and 3 < z < 3.5, we find that the rTNG300 model is in rough agreement (within a factor of 2 to 3) with that found in the SHELA footprint. In the 2 < z < 3 bins the rTNG300 model agrees within a factor of 2 to 3 in the mass range 1011 - 5 × 1011, but the discrepancy rapidly increases to a factor of ∼10 at the highest masses. It is important to note that although the increase in simulation volume to ∼3003Mpc3 is a significant milestone, this volume is only a small fraction of that of the SHELA footprint. Because of this, the results from rTNG300 do not probe the highest masses that we find in our massive galaxy sample. As computational resources continue to improve in coming years,

37 large hydrodynamical simulation volumes will prove important in exploring the extreme 12 high-mass (M? & 10 M ) galaxy regime. It is important to note that discrepancies in number density estimates for a particular mass bin are not the only consideration when comparing the results from simulation and observation. At the smallest number densities probed by rTNG300 (∼3×10−5 Mpc3/dex), galaxies from the simulation in our three highest redshift bins (2 < z < 3.5) are less massive than those in the SHELA footprint by ∼0.3 - 0.4 dex. Therefore, discrepancies in stellar mass function results may also be due to the way in which mass is assigned in the simulation.

Abundance Matching

Typically, abundance matching assumes a direct relation between the size of a halo in a dark-matter only simulation and the stellar mass of a galaxy that would live in that halo (e.g., Conroy & Wechsler 2009, Behroozi et al. 2010, Moster et al. 2013). This method provides a direct link between simulated halo merger trees and observables. To improve upon this method, Behroozi et al. (2019) use a Monte Carlo based technique to probe the full range of observed quantities, such as the galaxy stellar mass function and cosmic star formation rate density to populate dark matter halos with realistic galaxies. Halos are populated ﬁrst by assigning a star formation rate to a given halo and computing a stellar mass based on the assembly history of that halo. This matching method, the UniverseMachine (Behroozi et al., 2019), populates halos from the Bolshoi-Planck and MultiDark-Planck2 (MDPL2) dark matter-only simulations (Klypin et al. 2016, Rodríguez-Puebla et al. 2016) with galaxies from 0 < z < 10. Bolshoi- Planck and MDPL2 simulate 0.25h−1Gpc and 1.0 h−1Gpc, respectively, on each side (Klypin et al., 2016). While the box size of MDPL2 is larger than that of Bolshoi-Planck, the mass 9 8 resolution of MDPL2 (1.5×10 M /h) is poorer than Bolshoi-Planck (1.6×10 M /h). The large box size of MDPL2 is used by Behroozi et al. (2019) primarily for probing the space of observed galaxy correlation functions, while Bolshoi-Planck, with higher resolution, is better suited to this reﬁned abundance matching method. The resulting galaxy stellar mass functions produced by the UniverseMachine are publicly available4 for 0 < z < 10. In Figure 2.10 we compare the empirical SHELA footprint star-forming galaxy stellar mass function with the UniverseMachine stellar mass function. We correct the UniverseMa- chine stellar mass function, which contains all galaxies, by a factor of (1 - Quiescent Fraction)

4https://bitbucket.org/pbehroozi/universemachine

38 1.5 < z < 2 2 < z < 2.5 3 ) x

e 4 d / 3

c 5 p M / 6 ( g o l 7

8 2.5 < z < 3 This Work MDPL2-SAG UniverseMachine MDPL2-GALACTICUS 3 Illustris rTNG300 MDPL2-SAGE ) x

e 4 d / 3

c 5 p M / 6 ( g o l 7 3 < z < 3.5 8 9 10 11 12 13 9 10 11 12 13 log(M /M ) log(M /M )

Figure 2.10: Comparison of the empirical galaxy stellar mass function for 1.5 < z < 3.5 star-forming galaxies in the SHELA footprint to the stellar mass functions from three classes of theoretical models: hydrodynamical models from IllustrisTNG using rTNG300 (Pillepich et al., 2018b), abundance matching models from the UniverseMachine (Behroozi et al., 2019) populating dark matter halos from Bolshoi-Planck, and three diﬀerent semi- analytic models (SAMs), namely SAG (radio-mode AGN feedback, Cora et al. 2018), GALACTICUS (radio-mode AGN feedback, Benson 2012), and SAGE (quasar-mode AGN feedback, Croton et al. 2016) applied to the MDPL2 dark matter simulation. In our lowest redshift bin (1.5 < z < 2) results from all three model classes are in rough agreement with results from the SHELA footprint. In the 2 < z < 3 bins, results from IllustrisTNG hydrodynamical models, UniverseMachine abundance matching, and the SAG semi-analytic model are within a factor of ∼2 - 10 to those from the SHELA footprint. In this redshift bin, SAMs SAGE and GALACTICUS strongly underestimate the number density of massive galaxies by up to a factor of ∼100. In our highest redshift bin (3 < z < 3.5), the results from IllustrisTNG agree with those from the SHELA footprint within a factor of 2 - 3 and those from the UniverseMachine agree within a factor of 3 - 5. In this redshift bin all three SAMs underestimate the number density of massive galaxies by a factor of 10 - 1,000. We refer the reader to Section 2.4.4 for details. Error bars on SHELA footprint stellar mass function points represent Poisson errors, and the gray shaded region represents masses below the 80% mass completeness limit for our SHELA footprint star-forming galaxy sample. All 39 results from simulations have had mass and volume measures computed using (or scaled to) h = 0.7, however no other aspects of the models have been scaled. The results from IllustrisTNG and the three SAMs have been convolved by the average stellar mass error for SHELA footprint galaxies in each redshift bin. in each mass bin to obtain a star-forming galaxy stellar mass function. The quiescent fraction as a function of redshift and mass bin is given in the UniverseMachine data release. We do not apply any correction for systematic stellar mass error as this is already accounted for in the UniverseMachine data release. We ﬁnd that in our lowest redshift bins (1.5 < z < 2.5) the UniverseMachine predicts number densities of massive galaxies within a factor of 2 to that found in the SHELA footprint. In the 2.5 < z < 3.5 bins, the UniverseMachine under-predicts the number density of massive galaxies by a factor of 3 to 5. As the method used by the UniverseMachine is heavily reliant on the available observations, this may be one explanation for this discrepancy. Additionally, discrepancies could point towards the relationship used by the UniverseMachine to relate baryonic properties to dark matter halos. Because the UniverseMachine calibrates results against small-area surveys, the strength of this abundance matching method is not at the high-mass end. With our study of massive galaxies across diverse environments at high redshifts, the results from the SHELA footprint may prove useful in calibrating abundance matching methods for massive galaxies.

Semi-Analytic Models

Knebe et al. (2018) also utilize the MDPL2 dark matter simulation, and model the physics of baryons within dark matter halos by implementing semi-analytic models (SAMs). SAMs are models of galaxy evolution that track overall properties such as gas temperature and feedback processes in order to follow the growth of galaxies across cosmic time (Somerville & Davé, 2015). In contrast to more detailed numerical simulations, such as hydrodynamic simulations, SAMs are much less computationally expensive and can relatively easily be scaled to large volumes. The flexible and inexpensive nature of SAMs allows for different physical models of galaxy evolution and prescriptions for their growth over time to be explored. With this in mind, Knebe et al. (2018) applied three SAMs to the dark matter halos and merger trees from MDPL2. The three SAMs, GALACTICUS (Benson, 2012), SAG (Cora et al., 2018), and SAGE (Croton et al., 2016) differ in their prescriptions for cooling, star-formation, and AGN feedback, among others. These differences are described in detail in Knebe et al. (2018), where they ultimately find that these differences lead to discrepancies between the SAMs in the number of massive galaxies produced by z = 0.1. GALACTICUS and SAG are found by Knebe et al. (2018) to over-predict the number of massive galaxies at z = 0.1

40 compared to SAGE, which produced a galaxy stellar mass function in agreement with results from SDSS at this redshift. They attribute these discrepancies to the differing treatment of AGN feedback among the models, which is implemented as radio-mode feedback in GALACTICUS and SAG and quasar-mode wind in SAGE. They also note that the differences seen in the stellar mass function may be attributed to different prescriptions for galaxy mergers and interactions, which become increasingly important in the rich environments where many massive galaxies reside, as well as differing prescriptions for the treatment of satellite galaxies. Results from applying the GALACTICUS, SAGE, and SAG SAMs to the MDPL2 dark matter halos are publicly available5, and we utilize results for the z ∼ 2, 2.5, 3, and 3.5 snapshots to compare with the results from galaxies in the SHELA footprint (Figure 2.10). Each galaxy in a snapshot has separate stellar masses and star formation rates published for the disk and spheroid components of the galaxy. We combine these two values to obtain a single stellar mass and star formation rate value for each galaxy. We further convolve this mass by the average stellar mass error of SHELA footprint galaxies (determined from our SED fitting procedure, see Section 2.3.1) in each redshift bin (∼ 0.16 dex) to provide a more realistic comparison with our empirical result (Kitzbichler & White, 2007). We compute the specific star formation rate for each object and keep only star-forming galaxies having sSFR > 10−11 yr−1, consistent with our selection of star-forming galaxies in the SHELA footprint. Stellar masses along with the box volume at each snapshot are used to compute the star-forming galaxy stellar mass function for each SAM following the method of Tomczak et al. (2014) where every galaxy in a particular redshift bin has the same comoving volume term. We find that in the 1.5 < z < 3.5 bin, all three SAMs are in good agreement with the results from the SHELA footprint. In the 2 < z < 3 redshift bins, SAG agrees with the results from the SHELA footprint to within a factor of 10, however at these redshifts SAGE and GALACTICUS under-estimate the number density of star-forming galaxies by a factor of 10 - 100. In the highest redshift bin (3 < z < 3.5), the three SAMs severely under-estimate the number density of massive star-forming galaxies by up to a factor of 1,000, with SAG showing less discrepancy than SAGE and GALACTICUS. This result is in agreement with Asquith et al. (2018), who find that SAGE and SAG underestimate the number density of massive galaxies when compared to intermediate redshift observations.

5http://www.skiesanduniverses.org

41 Asquith et al. (2018) perform their study using a different underlying dark matter model than that of Knebe et al. (2018), which points to the discrepancy lying with the SAMs themselves, rather than the dark-matter simulation. Similar discrepancies between SAM results and observations were found by Conselice et al. (2007), who showed a factor of 100 difference between massive galaxy number densities from the Millennium Run SAM (De Lucia et al., 2006) and observations in the Palomar/DEEP2 survey (e.g., Davis et al. 2003, Giavalisco et al. 2004, Bundy et al. 2005, Davis et al. 2007) at z ∼ 2. The discrepancies found between stellar mass functions from the SHELA footprint and those from the SAMs are not exclusively linked to the models under-predicting the number density of massive galaxies. An alternative is that the SAMs simply do not produce galaxies that are massive enough (they are under-massive by up to ∼1.5 dex at the lowest number densities) pointing to the implementation of baryonic physics as an underlying cause. We find that at 1.5 < z < 3.5, the results from GALACTICUS and SAGE are in agreement despite their implementation of quasar-mode and radio-mode AGN feedback respectively. SAG, which utilizes quasar-mode feedback, produces more massive galaxies in all redshift bins than both GALACTICUS and SAGE. This suggests that different implementations of baryonic physics, such as prescriptions for satellite treatment, cooling, and details of the particular AGN feedback mode may play an important role.

2.5 Summary

We present a comprehensive study of the high-mass end of the star-forming galaxy stellar mass function at cosmic noon (1.5 < z < 3.5), an important epoch in the growth of galaxies, and their constituent stars and black holes. The main strengths of this study are that the sample is drawn from a very large area (17.2 deg2, corresponding to a colossal comoving volume of ∼0.44 Gpc3 from 1.5 < z < 3.5) thereby limiting cosmic variance and encompassing a wide range of environments (ﬁelds, groups, and proto-clusters). The

resulting sample of massive star-forming galaxies (5,352 galaxies with log(M?/M ) > 11,

of which 962 have log(M?/M ) > 11.5) at 1.5 < z < 3.5 in this large volume is a factor of 10 larger than previous studies, thereby providing robust statistics in the high-mass galaxy regime. To further increase the strength of our results, we also test uncertainties in SED ﬁtting and characterize how well galaxy parameters can be recovered. Our results are summarized below.

42 • We ﬁnd that the star-forming galaxy stellar mass function in the SHELA footprint from 1.5 < z < 3.5 is steeply declining at the high-mass end and probes values as high as ∼10−4 Mpc−3/dex and as low as ∼5×10−8 Mpc−3/dex, across a stellar mass

range of log(M?/M ) ∼ 11 - 12. With our statistically signiﬁcant sample of high- mass star-forming galaxies and improved SED ﬁtting procedure, we place some of the strongest constraints to date on the high-mass end of the star-forming galaxy stellar mass function from 1.5 < z < 3.5.

• We compare our results to previous observational studies from Tomczak et al. (2014), Muzzin et al. (2013), and Ilbert et al. (2013). Our sample of massive star-forming

galaxies (962 galaxies with log(M?/M ) > 11.5) is more than a factor of 10 larger than the samples presented in these previous studies. Our results are therefore more statistically robust and suﬀer less from uncertainties due to cosmic variance. We ﬁnd that our results are in good agreement with those from the literature in all of our redshift bins.

• We compare our results to different numerical models of galaxy evolution, including hydrodynamical simulations from IllustrisTNG (Pillepich et al. 2018b, Springel et al. 2018, Nelson et al. 2018, Naiman et al. 2018, Marinacci et al. 2018), abundance matching from the UniverseMachine (Behroozi et al., 2019), and three SAMs (SAG (Cora et al., 2018), SAGE (Croton et al., 2016), and GALACTICUS (Benson, 2012)). In our lowest redshift bin (1.5 < z < 2) we find that all models are in rough agreement with the results from the SHELA footprint. For 2 < z < 3, we find that the IllustrisTNG hydrodynamical models, UniverseMachine abundance matching models, and SAG semi-analytic model results are within a factor of ∼ 2 to 10 of the SHELA footprint results at the high-mass end of the galaxy stellar mass function. In the highest redshift bin (3 < z < 3.5), results from IllustrisTNG and the UniverseMachine are within a factor of 2 to 5 to those from the SHELA footprint. At 2 < z < 3.5, SAMs SAGE and GALACTICUS severely underestimate the number density of galaxies by a factor of 10 - 1,000, and in the highest redshift bin (3 < z < 3.5), a factor of 100 discrepancy is also seen with SAG. These large discrepancies highlight the challenges that SAMs face in implementing baryonic physics that can reproduce observed galaxy

43 relations simultaneously at low- (z = 0), and high-redshifts (z = 2 − 4).

44 Chapter 3: Investigating The Growing Population of Massive Quiescent Galaxies at Cosmic Noon

3.1 Introduction

Understanding how galaxies are transformed from star-forming to quiescent is a key question in the study of galaxy evolution. The population of massive galaxies, with stellar 11 masses M? ≥ 10 M , is thought to grow rapidly at early times (e.g., Cowie et al. 1996, Bundy et al. 2006) compared to less massive galaxies. Theoretical models have shown the important role that feedback plays in galaxy evolution (e.g., Somerville & Primack 1999, Cole et al. 2000, Bower et al. 2006, Croton et al. 2006, Somerville et al. 2008, Benson 2012, Somerville & Davé 2015 and references therein, Croton et al. 2016, Naab & Ostriker 2017 and references therein, Weinberger et al. 2017, Cora et al. 2018, Knebe et al. 2018, Behroozi et al. 2019, Cora et al. 2019, Davé et al. 2019), and without these feedback mechanisms, galaxies at present day are too massive compared to the observed galaxy population (e.g., Weinberger et al. 2017, Pillepich et al. 2018b). Compiling statistically significant samples of these massive galaxies at cosmic noon (1.5 < z < 3.0), a time when galaxy assembly progressed rapidly, can help to uncover the physical processes, specifically as a function of mass, driving the shift from a predominantly star-forming massive galaxy population to one that is primarily quiescent. The number and properties of massive quiescent galaxies in place by z ∼ 2 (only 3.3 Gyr after the Big Bang) provide important tests of galaxy evolution models. Theoretical models need to implement physical processes that can reproduce the rapid formation and early quenching of massive galaxies in such a short time following the Big Bang, along with the wide range of sizes, structures, and specific star-formation rates (sSFR; sSFR = SFR/M?) (e.g., Conselice et al. 2011, van der Wel et al. 2011. Weinzirl et al. 2011, van Dokkum

A signiﬁcant portion of this Chapter is accepted for publication in the Monthly Notices of the Royal Astronomical Society (Sherman et al. 2020b, MNRAS, 499, 4239). Sydney Sherman served as the ﬁrst author of this work and conducted the original research contained herein. Coauthors provided useful feedback and guidance that shaped the research and subsequent direction of this work. Coauthors are: Shardha Jogee, Jonathan Florez, Matthew L. Stevans, Lalitwadee Kawinwanichakij, Isak Wold, Steven L. Finkelstein, Casey Papovich, Robin Ciardullo, Caryl Gronwall, Sofía A. Cora, Tomás Hough, and Cristian A. Vega-Martínez.

45 et al. 2015) seen in observational studies by z ∼ 2. Additionally, these models must simultaneously match the much slower growth of less massive systems. Cosmic noon (1.5 < z < 3.0) is a particularly important epoch to study galaxy evolution as this is a time when proto-clusters begin collapsing into the galaxy clusters seen at present day and the cosmic star-formation rate density and black hole accretion rate peak (e.g., Madau & Dickinson 2014). In the extragalactic community galaxies are typically defined to be “quiescent" if they have sufficiently low specific star-formation rate (e.g., Fontanot et al. 2009), lie a given distance below the main sequence (e.g., Fang et al. 2018, Donnari et al. 2019), or fall in a particular region of rest-frame color-color space (e.g., Labbé et al. 2005, Wuyts et al. 2007, Williams et al. 2009, Muzzin et al. 2013). It should be noted that these definitions of quiescence do not necessarily imply an abrupt cessation of star-formation. In the literature, a wide variety of mechanisms have been invoked for quenching star-formation in galaxies (e.g., Kawinwanichakij et al. 2017, Man & Belli 2018, Papovich et al. 2018), and they fall into two inter-related categories. The first involves processes that accelerate star-formation and the consumption of gas (e.g., Man & Belli 2018) by driving gas to the circumnuclear regions where the gas reaches high densities and fuels rapid star-formation. These processes include major and minor mergers (e.g., Mihos & Hernquist 1994, Mihos & Hernquist 1996, Jogee et al. 2009, Robaina et al. 2010, Hopkins et al. 2013), tidal interactions (e.g., Barnes & Hernquist 1992 and references therein, Gnedin 2003), and spontaneously or tidally induced bars (e.g., Sakamoto et al. 1999, Jogee et al. 2005, Peschken & Łokas 2019). The second category involves processes that suppress star-formation. This includes ram pressure stripping (e.g., Gunn & Gott 1972, Giovanelli & Haynes 1983, Cayatte et al. 1990, Koopmann & Kenney 2004, Crowl 2005, Singh et al. 2019) where the intra-cluster medium removes cold gas from a galaxy traveling within a cluster, tidal stripping (Moore et al. 1996, Moore et al. 1998), or starvation and strangulation (Larson, 1980). This second category also includes mechanisms such as stellar (e.g., Ceverino & Klypin 2009, Vogelsberger et al. 2013, Hopkins et al. 2016, Núñez et al. 2017) and AGN feedback (e.g., Hambrick et al. 2011, Fabian 2012, Vogelsberger et al. 2013, Choi et al. 2015, Hopkins et al. 2016) that heat, redistribute, and/or expel gas residing in a galaxy or gas accreting onto the galaxy. Previous observational studies (e.g., Kriek et al. 2006, Muzzin et al. 2013, Martis et al. 2016, Tomczak et al. 2016) have typically focused on the quiescent fraction as a function of redshift for large mass bins and have found that the quiescent fraction at the massive end

46 increases towards present day. A significant challenge faced by these studies is that their 11 small area provides small samples of massive (M? ≥ 10 M ) galaxies, which are rare in number density. Additionally, small area studies suffer from the effects of cosmic variance (e.g., Driver & Robotham 2010, Moster et al. 2011), which, in combination with small sample sizes leads to large errors in measures of the quiescent fraction of massive galaxies. Without many galaxies at the high mass end, large mass bins are typically used which leads to broad conclusions about the nature of the population of quenched massive galaxies. In this work, we present the quiescent fraction of massive galaxies measured three ways (specific star-formation rate, distance from the main sequence, and UVJ color-color 11 selection) using a sample of 28,469 massive (M? ≥ 10 M ) galaxies at 1.5 < z < 3.0 which are uniformly selected from a 17.5 deg2 area which probes a comoving volume of ∼0.33 Gpc3 at these redshifts. With this large sample of star-forming and quiescent galaxies selected over a large comoving volume we are able to significantly reduce the error due to Poisson statistics and cosmic variance. We are uniquely suited to split our results at the high mass end as a function of mass, which allows us to place constraints on the quenching mechanisms at play across a range of galaxy stellar masses. This is a significant improvement over previous works that used large mass bins (typically all galaxies with 11 M? ≥ 10 M in a single bin) due to small sample sizes. Our 1.5 < z < 3.0 sample is a factor of ∼40 larger at log(M?/M ) ≥ 11.5 than samples from previous studies. We discuss the physical processes which may contribute to the trends found in our empirical quiescent fraction as a function of mass. We also compare our empirical quiescent fraction with predictions from two types of theoretical models: hydrodynamical models from IllustrisTNG (Pillepich et al. 2018b, Springel et al. 2018, Nelson et al. 2018, Naiman et al. 2018, Marinacci et al. 2018) and SIMBA (Davé et al., 2019), and semi-analytic models (SAMs) SAG (Cora et al., 2018), SAGE (Croton et al., 2016), and Galacticus (Benson, 2012). To further constrain models of galaxy evolution, we also compute the galaxy stellar mass function for the total sample of galaxies, as well as the star-forming and quiescent galaxy populations. Comparisons of our empirical quiescent fraction and stellar mass function with predictions from theoretical models provides powerful constraints on the implementation of baryonic physics in these models (particularly star-formation and feedback models). This paper is organized as follows. In Section 3.2 we introduce the data used in this work and in Section 3.3 we detail the data analysis and SED fitting procedure. Our empirical

47 results are presented in Section 3.4, including the quiescent fraction as a function of mass (Section 3.4.1) and redshift (Section 3.4.4), and the empirical galaxy stellar mass function (Section 3.4.5). In Section 3.5 we discuss the physical mechanisms that may quench the galaxies in our sample (Section 3.5.1). In Sections 3.5.2, 3.5.3, and 3.5.4 we compare our empirical results on the quiescent fraction as a function of mass and redshift, and the galaxy stellar mass function with predictions from theoretical models. Finally, we summarize our results in Section 3.6. Throughout this work we adopt a ﬂat ΛCDM cosmology with

h = 0.7, Ωm = 0.3, and ΩΛ = 0.7.

3.2 Data

The data used in this work come from large area surveys, covering ∼17.5 deg2, in the Spitzer-HETDEX Exploratory Large Area (SHELA; Papovich et al. 2016, Wold et al. 2019) footprint. The ﬁve primary photometric data sets used in this study come from the

Dark Energy Camera (DECam) u,g,r,i,z (Wold et al., 2019), NEWFIRM Ks (PI Finkelstein; Stevans et al. submitted), Spitzer-IRAC 3.6 and 4.5µm (PI Papovich; Papovich et al. 2016), Herschel-SPIRE (HerS, Viero et al. 2014) far-IR/submillimeter, and XMM-Newton and Chandra X-ray Observatory X-ray data from the Stripe 82X survey (LaMassa et al. 2013a, LaMassa et al. 2013b, Ananna et al. 2017, the X-ray data cover ∼11.2 deg2). We gain

additional photometric coverage in the near-IR with J and Ks data from the VICS82 Survey (Geach et al., 2017). Optical spectroscopy in this region is being acquired by the Hobby Eberly Telescope Dark Energy Experiment (HETDEX, Hill et al. 2008).

In this work we utilize data from DECam u,g,r,i,z, NEWFIRM Ks, VICS82 J and Ks, and Spitzer-IRAC 3.6 and 4.5µm to perform spectral energy distribution (SED) ﬁtting of our sample (see Section 3.3). Our catalog (Stevans et al. Submitted) is Ks-selected by

implementing Source Extractor (SExtractor; Bertin & Arnouts 1996) on the NEWFIRM Ks imaging, which reach a 5σ depth of 22.4 AB mag. With object locations determined from

running SExtractor on the NEWFIRM Ks imaging, forced photometry is performed on the DECam u,g,r,i,z (r-band 5σ depth is r = 24.5 AB mag; Wold et al. (2019)) and Spitzer-IRAC 3.6 and 4.5µm imaging (with 5σ depth of 22 AB mag in both ﬁlters; Papovich et al. (2016)) using the Tractor (Lang et al., 2016). For a complete and detailed description of catalog construction, see Stevans et al. (submitted) and Kawinwanichakij et al. (2020), as well as Wold et al. (2019) who implement a similar procedure.

48 We note that the sample used in this paper is constructed in a similar way to that from Sherman et al. (2020a), however one key diﬀerence has allowed for the study contained 11 in this work. Sherman et al. (2020a) performed a study of massive (M? ≥ 10 M ) star-forming galaxies in the same footprint used here, but their analysis was limited to star-forming galaxies, as the catalog used (Wold et al., 2019) was riz-selected. Since that

publication, NEWFIRM Ks data have become available in the footrprint, which allows for the selection of both the star-forming and quiescent populations of massive galaxies.

3.3 Data Analysis & SED Fitting

SED fitting is performed using EAZY-py, a Python-based version of EAZY (Brammer et al., 2008), which fits a set of twelve Flexible Stellar Population Synthesis (FSPS; Conroy et al. 2009, Conroy & Gunn 2010) templates in non-negative linear combination. We utilize the default set of EAZY-py FSPS templates which are constructed using a Chabrier (2003) initial mass function (IMF), Kriek & Conroy (2013) dust law, solar metallicity, and realistic star-formation histories including bursty and slowly rising models. A full description of the fitting procedure used here and tests of EAZY-py on a set of mock galaxies are given in Sherman et al. (2020a) and will briefly be described here. For each galaxy in our sample, EAZY-py uses χ2 minimization to identify the best- fit combination of the twelve built-in templates at the redshift at which χ2 is minimized, which is the “best-fit" redshift used throughout this work. We estimate our photometric redshift accuracy using two samples of galaxies with spectroscopic redshifts. The first is a low redshift (z < 1) sample of galaxies from the Sloan Digital Sky Survey (SDSS) with spectroscopic redshifts. The second is an intermediate redshift (1.9 < z < 3.5) sample of galaxies from the second internal data release of the HETDEX survey (Hill et al., 2008). For each of these samples, we estimate the photometric redshift quality using the normalized median absolute deviation (Brammer et al., 2008): ∆z − median(∆z) σNMAD = 1.48 × median . (3.1) 1 + zspec

We ﬁnd that for the low redshift sample σNMAD = 0.053 and for the intermediate redshift sample σNMAD = 0.102. We note that the sample used to estimate intermediate redshift photometric redshift recovery is quite small (56 galaxies) and will grow substantially with

49 future data releases from the HETDEX project. Of this small sample from HETDEX, 3 (5.3%) of the 56 galaxies are catastrophic outliers, where EAZY-py ﬁts them to have

2.0 < zphot < 3.0 and preliminary spectra from HETDEX suggest that these objects are low-z (zspec < 0.5) galaxies. We note that visual inspection was performed for all HETDEX detections to verify the line identification made by the HETDEX pipeline. To estimate the stellar masses and star-formation rates for the galaxies in our sample, we implement an improved parameter estimate over that contained in the current EAZY-py procedure. We first use the built-in EAZY-py fitting procedure to find the best fit template combination at the redshift at which χ2 is minimized. Then, at this redshift we draw 100 SEDs from the best-fit SED’s template error distribution (Sherman et al., 2020a). Each of these SED draws gives a unique set of galaxy parameters such as stellar mass and SFR, and we construct distributions of these parameters from the 100 draws. When presenting galaxy parameter values throughout this work, we adopt the median of the parameter distribution as the "best-fit" and the 16th and 84th percentiles as the lower and upper error bars, respectively. From this procedure, we find that typical stellar mass and star-formation rate errors in our redshift range of interest (1.5 < z < 3.0) are ±0.08 dex and ±0.18 dex, respectively. We note that because the underlying parameters associated with each EAZY-py FSPS template are the intrinsic values for that template, our SFR values for given galaxy SED fits are the extinction corrected intrinsic SFR for that galaxy. To validate this SED fitting procedure for redshift and parameter recovery, Sherman et al. (2020a) performed extensive tests of EAZY-py by fitting a diverse sample of mock galaxies (V. Acquaviva, private communication). These mock galaxies were assigned realistic error bars using the SHELA footprint sample of galaxies. It was found that EAZY-py does a good job of recovering the underlying galaxy parameters (photometric redshift, stellar mass, and SFR) for this diverse set of mock galaxies, which includes systems with low sSFR. Specifically, for mock galaxies with redshifts 1.5 < z < 3.0 EAZY-py tends to underestimate the SFR, on average, by 0.46 dex and overestimates stellar mass, on average, by 0.085 dex. These offsets are likely due to systematic differences in the mock galaxy templates constructed from Bruzual & Charlot (2003) and the FSPS templates used for SED fitting. We note that an under-estimate of the SFR may lead to an over-estimate of the quiescent fraction, and we discuss tests to ensure this is not the case in Section 3.4.1. Finally, we perform a test of our SED fitting procedure to estimate both the impact of photometric redshift uncertainty and Eddington bias (Eddington, 1913) on our results.

50 Eddington bias describes the situation where uncertainties in both photometry and photometric redshifts can cause low-mass galaxies to scatter into high-mass bins. In our test (see also Sherman et al. 2020a), we generate 100 iterations of our catalog by drawing 100 new photometric redshifts for each galaxy from that galaxy’s photometric redshift probability distribution. We then re-fit galaxies at their drawn redshifts using the SED fitting procedure described above and perform the sample selection and analysis presented in Sections 3.3.1 12 and 3.4 of this work. We find that for M? < 10 M , the quiescent fractions and stellar mass functions for the 100 iterations are consistent with our empirical results presented in 12 Section 3.4. For M? > 10 M we see the effects of Eddington bias, and our results from the 100 catalog iterations differ from our original results by up to a factor of 2 − 5. This scatter at the highest masses is expected, and our results throughout this work focus on the 11 12 mass range M? = 10 − 10 M . The quiescent fractions from the 100 catalog iterations compared with the results presented in Section 3.4 can be found in Appendix A.1. This test ultimately shows that photometric redshift uncertainty does not dominate the error on results presented throughout this work. We estimate the mass completeness of our sample following the method from Pozzetti et al. (2010) (see also Davidzon et al. 2013 and Sherman et al. 2020a) which uses the science sample (see Section 3.3.1 for sample selection) to estimate completeness. With this method, we scale the mass of the 20% faintest sample galaxies in small redshift bins such that their

Ks-band magnitude equals the 95% completeness limit of our NEWFIRM Ks-band survey (22.4 AB mag at 5σ). The 95th percentile of the distribution of scaled galaxy masses in each redshift bin is adopted as the 95% mass completeness limit for our study for that

particular redshift bin. We find that the 95% mass completeness limits are log(M?/M ) = 10.69, 10.86, and 11.13 in our 1.5 < z < 2.0, 2.0 < z < 2.5, and 2.5 < z < 3.0 bins, respectively. We also performed this procedure using the IRAC 4.5µm band and found that the 95% mass completeness values are smaller in each redshift bin. We therefore report the most conservative mass completeness value by using the Ks-band. Estimating an SFR completeness is not as straightforward as estimating the mass completeness. The SFR values used throughout this work are the extinction-corrected values computed by performing SED fitting with EAZY-py. The SED fitting procedure uses all available data, including the rest-frame UV data (in our case, DECam u,g,r,i,z), and an underlying attenuation model to find a best-fit SED and extinction-corrected SFR. Here, we utilize a simplified method to compute a FUV-based SFR and SFR completeness from

51 observed FUV fluxes, which are not corrected for extinction. Following Florez et al. (2020) we use the g-band flux as a proxy for FUV-flux. Using a similar procedure to that used for estimating the mass completeness, we begin by identifying the 20% faintest g-band objects in each of our three redshift bins from redshift z = 1.5 to 3.0. We then approximate a FUV-based, dust-obscured SFR using the SFR conversion factor from Hao et al. (2011) which assumes a Kroupa IMF (Kroupa, 2001), 100 Myr timescale,

and a mass range of 0.1 − 100M . We then scale these FUV-based SFR values (SFRFUV) to

what the SFR would be (SFRlim) if that galaxy’s g-band magnitude (mgal) were the g-band

5σ completeness limit (mlim = 24.8 mag AB) found by Wold et al. (2019) using:

log(SFRlim) = log(SFRFUV) + 0.4(mgal − mlim). (3.2)

th After this scaling procedure, we find the 95 percentile of the distribution of SFRlim, and this value is the 95% SFR completeness limit for our sample. We find that the 95% −1 SFR completeness limits are SFR = 3.53, 6.06, and 9.46 M yr in our 1.5 < z < 2.0, 2.0 < z < 2.5, and 2.5 < z < 3.0 bins, respectively. We emphasize that the sample used in this work is Ks-selected, not g-band selected, so for every galaxy detected in the Ks-band our SED fitting procedure fits an extinction-corrected SFR. We do not impose any g-band (or any other rest-UV filter) S/N cut, and therefore, we are able to detect massive galaxies with SFR below the 95% completeness limit estimated here.

3.3.1 Sample Selection

Our primary science focus lies in understanding the population of massive quiescent galaxies at cosmic noon (1.5 < z < 3.0) in comparison to the total population of galaxies at these redshifts. To achieve this, we place several quality control cuts on our full sample to achieve a high-confidence, representative sample of galaxies. We begin by removing all objects identified by SDSS to be stars, spectroscopically confirmed low-z galaxies, and luminous AGN, as well as those identified to be luminous AGN by the Stripe82X survey. This initial cut removes ∼4% of objects from our catalog before SED fitting is performed. Luminous AGN are thought to play an important role in galaxy evolution, however we remove them here as our SED fitting technique inadequately accounts for the contribution from the luminous AGN (e.g., Salvato et al. 2011, Ananna et al. 2017, Florez et al. 2020). A detailed analysis of the properties of galaxies hosting

52 44 −1 X-ray luminous AGN (with LX > 10 erg s ) in our sample has been performed by Florez et al. (2020) using the CIGALE SED fitting code (Noll et al. 2009, Ciesla et al. 2015, Yang et al. 2020), which performs careful fitting of AGN emission. At 1.5 < z < 3.0 they find 44 X-ray luminous AGN above their completeness limits and as this sample is quite small compared to our massive galaxy sample, the exclusion of these objects does not significantly impact our results. Previous works (e.g., Salvato et al. 2011) have shown that −15 low luminosity AGN (those with F0.5−2keV < 8 × 10 cgs) are sufficiently well fit with SED templates that do not account for AGN contribution. We do not have a suitable method for identifying or removing low luminosity AGN from our sample, however we believe that they are fit well enough by our SED fitting procedure. 2 To ensure adequate SED fits, we require that the best-fit SED has reduced χν < 20 and that the fit is constrained by at least four filters, three of which are NEWFIRM Ks, IRAC 3.6 2 and 4.5µm. The requirement of four or more filters and χν < 20 removes ∼ 2% of objects from our sample of objects fit to have redshift 1.5 < z < 3.0. We further require that a galaxy has signal-to-noise S/N ≥ 5 in both IRAC 3.6 and 4.5µm filters. Our requirement of robust IRAC detections enables the selection of massive galaxies with constraints to their SED fit redward of the Balmer break. Wold et al. (2019) showed that beyond z ∼ 1, IRAC data are imperative for reducing photometric redshift error, which is extremely important in this work because we do not place S/N requirements on any other filters. The IRAC S/N requirement further removes ∼ 60% of objects from

our 1.5 < z < 3.0 sample, leaving 54,001 Ks-selected galaxies with robust SED fits and 11 photometric redshifts, of which 28,781 are fit to have M? ≥ 10 M . Of the galaxies with 11 12 IRAC S/N < 5 that are fit to have 1.5 < z < 3.0, only 7% are fit to have M? = 10 −10 M 12 (the primary mass range of interest in this work), and 9% are fit to have M? ≥ 10 M , which is unrealistic given their poor photometric quality. If we were to loosen the strict 11 IRAC S/N ≥ 5 criterion and only require IRAC S/N ≥ 2, our sample size of M? ≥ 10 M galaxies would increase to 32,542 galaxies. We choose, however, to use the stricter S/N ≥ 5 as this ensures high quality photometric redshift fits. Additionally, we note that employing the looser requirement of IRAC S/N ≥ 2 does not change the results presented in this work. Due to the low number densities of massive galaxies, a clean sample is important for making conclusions about their nature. At the highest masses (log(M?/M ) ≥ 11.5), the most common contaminants are objects fit to have high masses because their light is contaminated by that from a nearby star, typically a bright diffraction spike. To mitigate

53 this type of contaminant, we visually inspect every object ﬁt to have log(M?/M ) ≥ 11.5 three times using a custom Zooniverse1 interface. We also adopt visual inspection results for objects in our catalog that were found in the riz-selected catalog used by Sherman et al. 11 (2020a) who inspected galaxies ﬁt to have M? ≥ 10 M and found contamination of ∼2%

at log(M?/M ) < 11.5. Objects ﬂagged as contaminated by a nearby object are removed from our sample. Following this visual inspection (and adoption of previous inspection 11 results), we are left with a sample of 28,469 M? ≥ 10 M galaxies with robust masses, star-formation rates, and redshifts.

3.4 Empirical Results

3.4.1 Empirical Quiescent Fraction As a Function of Mass

When investigating the quiescent population of galaxies in our sample, we utilize three deﬁnitions of “quiescent" to enable fair comparisons with previously published results from observations and diﬀerent classes of theoretical models. These are:

1. sSFR-Selected: Galaxies are quiescent when their speciﬁc star-formation rate is sSFR ≤ 10−11 yr−1. Fontanot et al. (2009) implemented this sSFR cut to distinguish between star-forming and quiescent galaxies in a sample of galaxies out to z ∼ 4 using

the SFR-M? relation to motivate this choice. This deﬁnition is straightforward and is simple to compute using the output from SED ﬁtting codes or simulations. This method aims to select galaxies with little recent star-formation, however this threshold (sSFR ≤ 10−11 yr−1) does not change with redshift. Fixing the sSFR threshold does not account for the higher average star-formation rates of high redshift galaxies compared to local systems with a similar stellar mass.

2. Main Sequence-Selected: This selection method uses the sample of galaxies to deﬁne a main sequence (e.g., Tomczak et al. 2016), then identiﬁes any object lying more than 1 dex below that main sequence as quiescent (Fang et al. 2018, Donnari et al. 2019). This technique is similar to the sSFR-selection method, but allows the threshold for quiescence to vary with redshift and stellar mass.

1zooniverse.org

54 1.5 < z < 2.0 N11 = 8480 2.0 < z < 2.5 N11 = 15401 2.5 < z < 3.0 N11 = 4588 4

3 ] r y

/ 2 M

[ 1

) R

F 0 S

( 1

g r 1 11 y o l 10 = FR 2 sS 100 101 100 101 102 100 101 102 3

10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure 3.1: The relationship between star-formation rate (SFR) and stellar mass (M?) for all galaxies in our sample. The main sequence is represented by dark pink circles, which are the average SFR in a given mass bin (see Section 3.4.1). Errors on the main sequence are determined using the bootstrap resampling procedure described in Section 3.4.1. The gold line represents the main sequence - 1 dex which is used in this work to identify quiescent galaxies. The dash-dot line represents the sSFR = 10−11yr−1 criterion also used for selecting quiescent galaxies. The main sequence - 1 dex criterion is more eﬀective at selecting green valley galaxies to be quiescent than the sSFR-selection method. Areas of parameter space where our study is not complete in mass are shaded in grey. Inset color bars indicate the number of galaxies in each two dimensional bin. Insets on the upper right of each panel 11 show the number (N11) of galaxies in our sample with M? ≥ 10 M .

55 3.0 1.5 < z < 2.0 2.0 < z < 2.5 2.5 < z < 3.0

2.5

2.0

1.5

U - V 1.0

0.5

0.0 100 101 100 101 100 101

0.5 N11 = 8480 N11 = 15401 N11 = 4588

0 1 2 3 0 1 2 3 0 1 2 3 V- J V- J V- J

Figure 3.2: The UVJ color-color diagram for our sample, with the separation of quiescent and star-forming galaxies adopted from Muzzin et al. (2013). Galaxies in the upper left region of parameter space are quiescent, while those lying to the right of the boundary are dusty star-forming galaxies, and those below the boundary are star-forming galaxies. We see that the population of quiescent galaxies grows from high to low redshift. Inset color bars indicate the number of galaxies in each two dimensional bin. Insets on the lower left 11 of each panel show the number (N11) of galaxies in our sample with M? ≥ 10 M .

The main sequence for our sample of 1.5 < z < 3.0 galaxies is explored in detail in Sherman et al. (in preparation) and will briefly be described here. We define the main sequence using stellar masses and star-formation rates from our SED fitting analysis using EAZY-py (Fig. 3.1). The value of the main sequence is determined by computing the average SFR in individual mass bins. This method is consistent with the approach from other studies that use mass-complete samples of the total population of galaxies (e.g. Whitaker et al. 2014, Tomczak et al. 2016). By computing the main sequence in individual mass bins, we leverage our large sample of massive galaxies. We compute the errors on the main sequence by employing a bootstrap procedure. In each bootstrap draw, we select a random sample of galaxies in a given mass bin, where the size of the random sample is equal to the number of galaxies in that mass bin. This is done with replacement, so objects can be selected more than once in a single draw. The bootstrap procedure is repeated 1,000 times, each time computing the average SFR of the random sample to construct a distribution of average SFR values in each mass bin. Lower and upper error bars on the main sequence are the 16th and 84th percentiles of this distribution, respectively. The relationship between

56 SFR and stellar mass, as well as our main sequence is shown in Figure 3.1. The main sequence shown here is in good agreement with that presented by Tomczak et al. (2016). When determining the quiescent fraction, we bin our data into the same mass bins used to define the main sequence. In each mass bin, if an object falls 1 dex or more below the main sequence value defined in that bin, it is determined to be quiescent. We find that the value of the main sequence for our 1.5 < z < 3.0 sample decreases to lower average SFR towards present day (e.g. Whitaker et al. 2014, Tomczak et al. 2016), and therefore, the threshold for quiescence decreases towards present day. In addition to a quiescent threshold that varies with mass and redshift, this method is an improvement over the fixed sSFR threshold as it provides a more meaningful separation of the quiescent and star-forming galaxy populations. In our redshift range of interest (1.5 < z < 3.0), the fixed sSFR = 10−11 yr−1 threshold runs directly

through the so-called green valley (Wyder et al., 2007) in the SFR-M? plane. In contrast, the main sequence-based method effectively separates the main sequence population from the entire green valley population. We note that the quiescent fraction measured from the position relative to the main sequence is dependent on how the main sequence is defined and we take care throughout this work to use only the main sequence definition described here.

3. UVJ-Selected: With this selection, galaxy rest-frame U, V, and J colors are estimated in EAZY-py based on the shape of the best-ﬁt SED. If the resulting U - V and V - J colors fall in a particular region of parameter space (Fig. 3.2), then that galaxy is determined to be quiescent. In this work, we adopt the parameter space used by Muzzin et al. (2013) to select quiescent galaxies in the UVJ plane. The bimodality of star-forming and quiescent galaxy populations in the UVJ plane was initially established at high redshift using primarily photometric samples (e.g., Labbé et al. 2005, Wuyts et al. 2007) and was interpreted using evolutionary tracks from Bruzual & Charlot (2003) stellar population models. Williams et al. (2009) conﬁrmed the location of quiescent galaxies using a spectroscopically-selected sample of passive galaxies out to z ∼ 2 and implemented dividing lines based on their empirical data. Muzzin et al. (2013) used their sample to update the empirically-based division

57 between these populations. The boundary effectively separates red quiescent galaxies (located in the upper left region of the UVJ diagram) from dusty star-forming galaxies (located in the upper right region of the UVJ diagram) and blue star-forming galaxies (in the lower regions of the UVJ diagram). We note that although rest-frame colors are now standard outputs from SED fitting codes, a limitation of using color to identify quiescent galaxies is that these colors are highly dependent on the stellar population models and dust laws used to fit galaxy photometry.

We show the quiescent fraction of galaxies in our sample as determined using these three methods in Fig. 3.3. Qualitatively, we find that the quiescent fraction increases from low to high masses and the quiescent fraction increases in fixed mass bins from z = 3.0 to z = 1.5 regardless of the method used to determine the quiescent fraction. Results are similar in a given redshift bin using all three methods of determining the quiescent fraction with the most significant differences seen in the 2.0 < z < 2.5 bin where our three methods differ by up to a factor of 2. In Section 3.3 we noted that Sherman et al. (2020a) found that EAZY-py, the SED fitting code used in this work, may systematically under-estimate the SFR by 0.46 dex, on average, which would potentially lead to an over-estimate of the quiescent fraction. We do not believe this is the case as the sSFR-based quiescent fraction is the only one that would be affected by a systematic under-estimate of the SFR and it is in good agreement with the UVJ and main sequence-based quiescent fractions, which are not impacted by a systematic under-estimate of the SFR. The UVJ color-color method would not be affected as it uses the shape of the underlying SED to extract galaxy rest frame colors. The main sequence-based method separates star-forming and quiescent galaxies based on their relative distance from the main sequence (which is defined using the sample of galaxies) and would therefore not be affected. Of our three methods, the only one that would be impacted by a systematic under-estimate of the SFR is the sSFR-based method, which employs a fixed cutoff to separate star-forming and quiescent galaxies. We performed a test where we increase the SFR for all galaxies in our sample by 0.46 dex and recompute our sSFR-based quiescent fraction. With the systematic increase in the SFR, our sSFR-based quiescent fraction would decrease by less than a factor of 2, and we would still find that the quiescent fraction increases as a function of stellar mass. The results presented throughout this work would not differ significantly if we were, in fact, systematically under-estimating the SFR by 0.46 dex.

58 log(M /M ) 10.0 10.5 11.0 11.5 12.0 12.5 1.0 1.5 < z < 2.0 sSFR N = 8480 0.8 11 UVJ 0.6 MS - 1 dex 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.0 < z < 2.5 0.8 N11 = 15401 0.6 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.5 < z < 3.0 0.8 N11 = 4588 0.6 0.4

Fraction 0.2

Quiescent 0.0 10.0 10.5 11.0 11.5 12.0 12.5 log(M /M )

Figure 3.3: Empirical quiescent fraction for our sample of 1.5 < z < 3.0 galaxies using the three selection methods described in Section 3.4.1: sSFR (pink circles), UVJ (purple squares), main sequence - 1 dex (gold pentagons). These three methods of determining the quiescent fraction produce similar trends showing that the quiescent fraction of galaxies 11 12 increases with mass from M? = 10 − 10 M in all three redshift bins over the range 1.5 < z < 3.0 and it also increases as a function of redshift in fixed mass bins. The quiescent fractions measured with these three methods are similar, particularly at 1.5 < z < 2.0, but differ by up to a factor of 2 at 2.0 < z < 3.0. It is remarkable that in only 3.3 Gyr (from the Big Bang to z = 2) the Universe can build and quench more than 25% of 11 massive (M? = 10 M ) galaxies. Our result is a significant improvement over previous observational studies which used smaller sample sizes (our sample is a factor of 40 larger than that from Muzzin et al. (2013) for log(M?/M ) ≥ 11.5 galaxies at these redshifts). The gray shaded region indicates masses below our completeness limit. Insets on the upper left 11 of each panel show the number (N11) of galaxies in our sample with M? ≥ 10 M .

59 As an example of our quiescent fraction results, using the main-sequence based quiescent fraction we ﬁnd that at early epochs (2.5 < z < 3.0) the quiescent fraction increases from

13.5%±7.1% at log(M?/M ) = 11 to 39.6%±11.2% at log(M?/M ) = 11.75. At intermediate epochs (2.0 < z < 2.5) the quiescent fraction increases from 26.3% ± 2.5% at log(M?/M )

= 11 to 36.7% ± 9.1% at log(M?/M ) = 11.75. It is remarkable that by z = 2 (only 3.3 Gyr after the Big Bang) the universe has managed to quench more than 25% of massive 11 (M? = 10 M ) galaxies. At later epochs (1.5 < z < 2.0) the main sequence-based quiescent fraction is 51.9% ± 2.5% at log(M?/M ) = 11 and increases to 66.4% ± 13.1% at log(M?/M ) = 11.75. The two other methods by which we measure the quiescent fraction (sSFR- and UVJ-based) give similar results.

3.4.2 Estimating Contamination From DSFGs

Dusty star-forming galaxies (DSFGs) are a population of galaxies that require careful consideration because their star-formation is known to be highly obscured by dust (e.g., Papovich et al. 2006, Casey et al. 2014 and references therein, Escalante et al. 2020), particularly at z ∼ 2. Here, we explore the degree to which our sample of quiescent galaxies might be contaminated with DSFGs by using a subset of our sample that has available far-IR data. A robust way of identifying DSFGs is to use long-wavelength data, in our case Herschel- SPIRE (HerS, Viero et al. 2014) far-IR/submillimeter taken at 250, 350, and 500µm. These data are capable of breaking the degeneracy because a HerS detection indicates that photons produced during star-formation are absorbed by dust and reemitted in the far-IR. Although the HerS data has been taken across the majority of our survey footprint, the resolution is poor (the 250µm band has 1800 resolution) compared to our lower-wavelength data. Because of this, careful consideration must be taken for blended objects as it is difficult to disentangle the contribution from several nearby Ks-selected objects. To eliminate this issue, we only utilize isolated HerS objects in our contamination estimate. 11 To select a sample, we first identify all massive (M? ≥ 10 M ) Ks-selected objects fit to have 1.5 < z < 3.0 that are position matched to the HerS catalog and have positive flux values in all three HerS bands. There are 222 such objects in our catalog. Next, we match the Ks-selected objects that have HerS matches to the full Ks-selected catalog in the

SHELA footprint. If a Ks-selected object with HerS detections has another Ks-selected object within 900, then that object is discarded. After this procedure, we are left with 29

60 massive 1.5 < z < 3.0 Ks-selected galaxies with isolated HerS detections. We emphasize that the HerS data is not used in our SED fitting procedure because we are simply using the HerS data to classify these 29 galaxies as DSFGs. We do not aim to correct SED fits to get the obscured SFR. Because a HerS detection implies that a galaxy is a DSFG, if any of our three methods identify these galaxies to be quiescent, then they should be considered a contaminant to the quiescent sample. For the sSFR-based method, 6 (26%) of the isolated HerS sample are fit by EAZY-py to be quiescent. Using the UVJ-based method we find that 1 (3.5%) galaxy in our sample of HerS-identified DSFGs is placed into the quiescent population, and for the main sequence-based method 8 (38%) of our DSFGs are labeled as quiescent. With such a small sample of DSFGs, it is difficult to provide definitive estimates of the contamination due to DSFGs, however it is encouraging that the UVJ-based method of determining the quiescent fraction is largely uncontaminated and this method provides similar empirical quiescent fraction results to our other two methods.

3.4.3 Comparing the Empirical Quiescent Fraction to Previous Ob- servations

We compare our empirical quiescent fraction as a function of mass with quiescent fraction measures from several previous studies (Fig. 3.4; Muzzin et al. 2013, Martis et al. 2016, Tomczak et al. 2016) that use the UVJ-selection method. The previous works all implement similar boundaries between quiescent and star-forming populations to those adopted in our study from Muzzin et al. (2013). As outlined in Section 3.4.1, our study finds that the quiescent fraction of massive 11 galaxies (M? > 10 M ) measured in three ways increases as a function of mass from 11 12 M? = 10 − 10 M in all three redshift bins over the range 1.5 < z < 3.0 and it also increases as a function of redshift, towards present day, in fixed mass bins. Using the UVJ-based selection method, we find that at early epochs (2.5 < z < 3.0) the quiescent fraction is 9.7% ± 8.2% at log(M?/M ) = 11 and increases with mass to 40.4% ± 11.1% at log(M?/M ) = 11.75. At later epochs (1.5 < z < 2.0), we find that the UVJ-based method gives a quiescent fraction of 43.4% ± 2.7% at log(M?/M ) = 11, which increases with mass to 69.1% ± 12.9% at log(M?/M ) = 11.75. Our work significantly extends that from previous studies to higher stellar masses at

61 log(M /M ) 10.0 10.5 11.0 11.5 12.0 12.5

1.0 1.5 < z < 2.0 This Work: UVJ 0.8 N11 = 8480 Muzzin+13 0.6 Tomczak+16 Martis+16 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.0 < z < 2.5 0.8 N11 = 15401 0.6 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.5 < z < 3.0 0.8 N11 = 4588 0.6 0.4

Fraction 0.2

Quiescent 0.0 10.0 10.5 11.0 11.5 12.0 12.5 log(M /M )

Figure 3.4: Empirical UVJ-selected quiescent fraction (purple squares) compared with previous observational results from Muzzin et al. (2013) (green circles), Tomczak et al. (2016) (orange triangles), and Martis et al. (2016) (pink diamonds). Our work extends to higher masses and our larger sample size allows us to achieve smaller errors than previous works. Our sample of galaxies with log(M?/M ) ≥ 11.5 is a factor of ∼40 larger than samples from previous works. The quiescent fraction measured from our sample is a factor of ∼ 2 − 3 larger than that from previous studies at 2.0 < z < 3.0 and we ﬁnd good agreement at 1.5 < z < 2.0, however the errors from previous studies are large. The gray shaded region indicates masses below our completeness limit. Insets on the upper left of 11 each panel show the number (N11) of galaxies in our sample with M? ≥ 10 M .

62 1.5 < z < 3.0 due to the larger volume probed by our 17.5 deg2 study compared with Muzzin et al. (2013) (1.62 deg2), Martis et al. (2016) (1.62 deg2), and Tomczak et al. (2016) 2 (400 arcmin ). Our sample of galaxies with log(M?/M ) ≥ 11.5 is a factor of ∼40 larger than samples from Muzzin et al. (2013), Martis et al. (2016), and Tomczak et al. (2016). This larger sample size allows for significantly smaller error bars than previous studies and our larger volume renders errors from cosmic variance negligible in our work (cosmic 11 variance for redshift 1.5 < z < 3.0 M? ≥ 10 M galaxies is ∼ 10 − 30% for the samples from Muzzin et al. (2013) and Martis et al. (2016), and ∼ 50 − 70% for the sample from Tomczak et al. (2016)). Direct comparisons with previous results are challenging at the high mass end due to the small sample sizes and large error bars from previous works. We do, however, note some distinct trends. At redshifts 2.0 < z < 3.0 our empirical quiescent fraction is a factor 11 of ∼ 2 − 3 higher at M? > 10 M than the quiescent fraction found by earlier studies. In our lowest redshift bin (1.5 < z < 2.0) there is general agreement in the quiescent fraction at the high mass end, although the error bars from previous studies remain quite large. Differences in the measured quiescent fraction among observational studies are not only attributable to sample size, but also the stellar population models and dust laws used in SED fitting. Rest-frame colors are typically estimated by passing the best-fit SED from the SED fitting procedure through the U, V, and J filter transmission curves. Therefore, systematic differences in the stellar population models used for SED fitting can lead to systematic differences in the measured rest-frame UVJ colors and, subsequently, the quiescent fraction measured from these colors.

3.4.4 Empirical Quiescent Fraction As a Function of Redshift

In the previous sections, we focused on our results as a function of mass as that highlights the major strengths of our study (large, uniformly selected sample with a statistically signiﬁcant number of massive galaxies). Here, we show the quiescent fractions in our sample using the three methods presented throughout this work, as a function of redshift 11 for galaxies with M? ≥ 10 M (Fig. 3.5). Additionally, we present comparisons with previous observational results (Fig. 3.6). When we explore the quenched fraction (computed for all galaxies in our sample with 11 M? ≥ 10 M ) as a function of redshift, we ﬁnd that the sSFR-selection method produces the lowest quiescent fraction for all massive galaxies in every redshift bin. The UVJ-

63 0.7 sSFR < 1011yr 1 0.6 MS - 1dex UVJ 0.5

0.4

0.3

0.2

Quiescent Fraction 0.1 N11 = 28469 0.0 1.5 2.0 2.5 3.0 Redshift

11 Figure 3.5: Quiescent fraction for galaxies in our sample with M? ≥ 10 M shown for our three redshift bins. We show our results using three different methods of computing the quiescent fraction and find that all three methods give a quiescent fraction that increases from high to low redshift. In our highest redshift bin (2.5 < z < 3.0), we find quiescent fractions that span from 13% (sSFR-based selection) to 26% (main sequence-based selection). In our lowest redshift bin (1.5 < z < 2.0) our empirical quiescent fractions span from 50% (sSFR and UVJ-based selection) to 55% (main sequence-based selection). The inset on the 11 lower left shows the number (N11) of galaxies in our sample with M? ≥ 10 M across all three redshift bins spanning 1.5 < z < 3.0.

selection method produces the highest quiescent fraction for all massive galaxies in the 2.0 < z < 2.5 bin, while the main sequence-based technique gives the highest quiescent fraction for all massive galaxies in the 1.5 < z < 2.0 and 2.5 < z < 3.0 bins. Regardless of the method used to compute the quiescent fraction for all massive galaxies, we find that the quiescent fraction increases from high redshift (quiescent fraction spanning ∼ 13 - 26% across our three methods of estimating the quiescent fraction) to low redshift (quiescent fraction spanning ∼ 50 - 55% across our three methods of estimating the quiescent fraction). A key advantage of our study is that our statistically significant sample selected over a large area gives us small errors which are dominated by Poisson error (error from cosmic variance is negligible). Our large sample size allows us to robustly establish that the 11 quenched fraction for all galaxies with stellar masses M? ≥ 10 M increases from high to low redshift. As an example, we find that with the main-sequence based method the quiescent fraction at the massive end increases from 25.6% ± 3.3% at 2.5 < z < 3.0 to

64 1.0 This Work QF Selection: 1.0 This Work QF Selection: UVJ Kriek+06 sSFR < 1011yr 1 Muzzin+13 0.8 0.8 Martis+16 Tomczak+16 0.6 0.6

0.4 0.4

0.2 0.2 Quiescent Fraction Quiescent Fraction 0.0 N11 = 28469 0.0 N11 = 28469 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 Redshift Redshift

11 Figure 3.6: Our empirical quiescent fraction for all massive (M? ≥ 10 M ) galaxies selected using the sSFR (left) and UVJ (right) methods as a function of redshift compared with previous observations. For the sSFR-based method, Kriek et al. (2006) ﬁnds the quiescent fraction at z ∼ 2.5 to be higher than our empirical result by a factor of ∼2. Our UVJ-based result is in good agreement with those from Muzzin et al. (2013) and Martis et al. (2016), however our empirical quiescent fraction is larger than that from Tomczak et al. (2016) by a factor of 2. Insets on the lower left of each panel show the number 11 (N11) of galaxies in our sample with M? ≥ 10 M across all three redshift bins spanning 1.5 < z < 3.0. Our sample is more than an order of magnitude larger than samples from previous studies, which allows for smaller Poisson errors.

55.4% ± 1.8% at 1.5 < z < 2.0. Earlier studies (Muzzin et al. 2013, Martis et al. 2016, Tomczak et al. 2016) with much smaller samples found a similar trend with redshift (see Fig. 3.6), albeit with much larger error bars.

3.4.5 Empirical Stellar Mass Function for Star-Forming, Quiescent, and All Galaxies

Like the quiescent fraction of massive galaxies, the galaxy stellar mass function is an important tool in understanding the way in which massive galaxies evolve. While the quiescent fraction provides insights about the processes that quench star-formation in the massive galaxy population, the stellar mass function gives information about the buildup of the entire massive galaxy population per unit volume. The slope and normalization of the galaxy stellar mass function at the high mass end place important constraints on theoretical

65 models. Sherman et al. (2020a) explored the galaxy stellar mass function for a sample of star- forming galaxies and compared their results with those from previous observational studies and theoretical models. As was discussed earlier, the sample from Sherman et al. (2020a) was taken in the same footprint as the sample used in this work. However, since the previous

work was riz-selected the sample was biased towards star-forming galaxies. With the Ks- band selection used in this work, we are now able to explore the high mass end of the stellar mass function for all galaxies, those that are star-forming, and those that are quiescent.

Our stellar mass function is computed using the 1/Vmax method (Schmidt, 1968) following the procedure of Weigel et al. (2016) (see also Sherman et al. 2020a). We begin by using our procedure for estimating the 95% mass completeness (Section 3.3) to ﬁnd the redshift at which our study is 95% complete in a given mass bin. We then split our sample into three redshift bins (1.5 < z < 3.0, ∆z = 0.5) and further bin by mass. For each mass bin, the accessible volume is computed using the maximum redshift (zmax) at which our

study is 95% complete in that mass bin. If zmax is greater than the maximum redshift of a given redshift bin, then the comoving volume is set to be the volume of the redshift bin of interest. In the case that zmax lies within the redshift bin of interest, the comoving volume is measured to be the volume between the minimum redshift of that bin and zmax. In the event that zmax is less than the minimum redshift of a given bin (this only occurs for mass bins well below our 95% mass completeness limit), then the comoving volume is set to be the minimum of the comoving volume of the redshift bin of interest or the comoving volume from z = 0 to zmax. The procedure described here is used to compute the stellar mass function for our total sample of galaxies as well as star-forming and quiescent samples. Throughout this work we have used three methods to separate star-forming and quiescent galaxies: sSFR, distance from the main sequence, and UVJ. Our interest lies in later comparing our results with those from theoretical models (see Section 3.5.4), for which we only separate star-forming and quiescent galaxies using the sSFR-based and main sequence-based methods. Therefore, we employ only the sSFR and main sequence-based methods for separating star-forming and quiescent galaxies. These two methods of separating star-forming and quiescent galaxies give similar star-forming and quiescent galaxy stellar mass functions, which is not surprising since both of these methods give similar quiescent fractions as a function of mass. In Figure 3.7 we show the total stellar mass function and star-forming and quiescent

66 1.5 < z < 2.0 N11 = 8480 2.0 < z < 2.5 N11 = 15401 2.5 < z < 3.0 N11 = 4588 3 ) x

e 4 d / 3

c 5 p M / 6 (

g Total o l 7 QF Selection: SF 11 sSFR < 10 Q 8 10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

1.5 < z < 2.0 N11 = 8480 2.0 < z < 2.5 N11 = 15401 2.5 < z < 3.0 N11 = 4588 3 ) x

e 4 d / 3

c 5 p M / 6 (

g Total o l 7 QF Selection: SF MS - 1 dex Q 8 10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure 3.7: The empirical galaxy stellar mass function for our sample of massive galaxies. In both the top and bottom rows, the purple line represents the galaxy stellar mass function for all galaxies in our sample. In the top row, the solid and dashed pink lines are the star-forming and quiescent galaxy stellar mass functions, respectively, where the quiescent galaxies were selected using the sSFR-based method. Similarly, in the bottom row the gold solid and dashed lines are the star-forming and quiescent galaxy stellar mass functions, respectively, with quiescent galaxies selected by the main sequence-based method. Poisson errors are indicated by the colored regions and are often smaller than the lines. The total, star-forming, and quiescent galaxy stellar mass functions are related through the quiescent fraction, as described in Equation 3.3. In each of our three redshift bins spanning 1.5 < z < 3.0, we ﬁnd the stellar mass function to be steeply declining at the high mass end. The gray shaded region indicates masses below our completeness limit. Insets on the upper right of each 11 panel show the number (N11) of galaxies in our sample with M? ≥ 10 M .

67 2 Number with Number with Number with 1.5 < z < 2 log(M /M ) 11.5: 2 < z < 2.5 log(M /M ) 11.5: 2.5 < z < 3 log(M /M ) 11.5:

) This Work = 1020 This Work = 2506 This Work = 1276

x 3 Tomczak+14 = 28 Tomczak+14 = 22 Tomczak+14 = 10 Muzzin+13 = 17 Muzzin+13 = 13 Muzzin+13 = 28 e Ilbert+13 = 24 Ilbert+13 = 29 Ilbert+13 = 21 d / 4 3 c

p 5 M /

( 6 This Work g Tomczak+14 o l 7 Muzzin+13 Ilbert+13 8 10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure 3.8: The empirical galaxy stellar mass function for our total sample of massive galaxies (purple line) compared with the total galaxy stellar mass functions from previous works (Ilbert et al. 2013, Muzzin et al. 2013, and Tomczak et al. 2014). The gray shaded region indicates masses below our completeness limit. We ﬁnd fair agreement, within a factor of ∼ 2 − 3, with previous results in the two redshift bins spanning 2.0 < z < 3.0 (center and right panels). In the lowest redshift bin, our result is a factor of ∼ 3 lower at log(M?/M ) < 11.2 than previous studies (see discussion in Section 3.4.5). Poisson errors for our empirical result are indicated by the light purple regions and are often smaller than the lines. Insets on the upper right of each panel show the number of galaxies in our sample and those we compare with that have log(M?/M ) > 11.5. The dotted vertical line marks log(M?/M ) = 11.5. Our sample is more than a factor of 40 larger than samples from previous studies.

68 populations split using the sSFR-based method and the main-sequence based method (top

and bottom rows of Fig. 3.7, respectively). The total galaxy stellar mass function (Φtot) is related to the star-forming galaxy stellar mass function (ΦSF) and quiescent galaxy stellar mass function (ΦQ) through the quiescent fraction ( fQ; see Section 3.4.1 and Fig. 3.3) as follows:

Φtot = ΦQ + ΦSF = fQ × Φtot + ΦSF (3.3)

We find for the total, star-forming, and quiescent stellar mass functions that the stellar mass 11 function is steeply declining at the high mass (M? ≥ 10 M ) end. We also compare our total galaxy stellar mass functions with results from Ilbert et al. (2013), Muzzin et al. (2013), and Tomczak et al. (2014) (Fig. 3.8). Above our stellar mass completeness limit in the two higher redshift bins (2.0 < z < 2.5 and 2.5 < z < 3.0), our stellar mass function is in fair agreement, within a factor of ∼ 2 − 3 with previous studies, which have large error bars at high masses due to small number statistics. However, in the lowest redshift bin (1.5 < z < 2.0), our stellar mass function is lower by a factor of ∼ 3 than previous results at masses log(M?/M ) < 11.2. Our tests suggest that in this redshift bin, our filter coverage is not as sensitive to SED features (such as the Balmer break and UV slope), which may lead to the deficit of galaxies in this bin. We note, however, that cosmic variance significantly impacts the studies we compare with by 10 − 30% for Ilbert et al. (2013) and Muzzin et al. (2013) and 50 − 70% for Tomczak et al. (2014), while it is negligible for our study due to the large area covered by our data. The significant impact of cosmic variance on previous studies may drive the difference seen between our result and results from previous works, and we treat the stellar mass function in this lowest redshift bin with caution throughout this paper. We will compare our stellar mass function results to different classes of theoretical models in Section 3.5.4 to evaluate how well the models predict both the quenched fraction and the overall population of massive galaxies.

3.5 Discussion

In previous sections, we showed that the quiescent fraction of massive galaxies increases as a function of mass (Section 3.4.1) and redshift (Section 3.4.4). In Section 3.5.1, we discuss which physical processes may contribute to this ﬁnding across diﬀerent epochs and environments. We then compare our empirical quiescent fraction and stellar mass function

69 results with several classes of theoretical models in Sections 3.5.2, 3.5.3, and 3.5.4. These comparisons provide key benchmarks for these models and can be used to implement future improvements.

3.5.1 Quenching Mechanisms Across Diﬀerent Epochs and Environ- ments

Our study allows for one of the most robust investigations to date of the buildup of the 11 quiescent galaxy population as a function of mass at the highest masses (M? ≥ 10 M ) at cosmic noon (1.5 < z < 3.0). This is achieved due to our large sample size (28,469 galaxies 11 2 with M? ≥ 10 M ) selected over a 17.5 deg area, which gives small errors dominated by Poisson statistics and renders errors from cosmic variance negligible. We showed that the 11 quiescent fraction computed in three different ways rises with stellar mass from M? = 10 12 to 10 M in three redshift bins spanning 1.5 < z < 3.0 (Fig. 3.3). Additionally, we show that the quiescent fraction of massive galaxies increases towards present day (Fig. 3.3 and Fig. 3.5). To interpret these results, we first consider the population of massive galaxies at high redshifts (z ∼ 3). At early epochs (z = 3 is only 2.2 Gyr after the Big Bang) massive galaxies are believed to have stemmed from density fluctuations that grow hierarchically through gravitational instability (e.g., Springel et al. 2005). These overdensities may evolve into proto-clusters (e.g., Lotz et al. 2013, Overzier 2016, Chiang et al. 2017) and proto-groups (Diener et al., 2013), which are the likely progenitors of modern day clusters and groups. Galaxy interactions and mergers are common in these overdense environments, which are conducive to rapid growth and mass buildup. Chiang et al. (2017) used results from the Millennium Simulation (Springel et al. 2005, Guo et al. 2013a, Henriques et al. 2015) to show that these proto-clusters, while diffuse and rare in number density compared to their modern day descendants, are responsible for ∼30% of the cosmic star-formation rate density at z ∼ 3. They also report that the cores of these proto-clusters are home to only ∼30% of the mass and star-formation within the proto- cluster, indicating that massive galaxies residing in proto-clusters are not necessarily the central galaxy at early times. These results suggest that massive galaxies in proto-clusters at z ∼ 3 (and even to z ∼ 1) move with respect to the proto-cluster core and are subject to environmental effects, such as tidal interactions and major or minor mergers.

70 Galaxy-galaxy interactions are frequent in proto-cluster environments. Unlike in present day clusters, proto-cluster environments (which are similar environments to present-day groups) have high galaxy number densities and low velocity dispersions; conditions which often lead to mergers. Mergers are favored when the galaxy velocity dispersion within the group is smaller than the average stellar velocity within the interacting galaxies (Binney & Tremaine, 1987). Major and minor mergers generate large gas inflows to the central regions of the galaxy which increase central gas densities and enhance star-formation rates (e.g., Hernquist & Mihos 1995, Mihos & Hernquist 1996, Di Matteo et al. 2007, Jogee et al. 2009, Robaina et al. 2010). These high star-formation rates cause massive galaxies to use their gas supply faster and quench at early epochs. As major mergers trigger central starbursts and AGN activity (e.g., Springel et al. 2005, Jogee 2006 and references therein, Di Matteo et al. 2008, Capelo et al. 2015, Park et al. 2017), stellar and AGN feedback can heat, expel, and redistribute gas, which suppresses future star-formation. Therefore, at early epochs, frequent mergers coupled with stellar and AGN feedback can act as a powerful quenching mechanism, first accelerating, then suppressing star-formation. We note that without spectroscopic redshifts or high resolution imaging, we are unable to accurately determine a merger rate for our sample. As galaxies evolve, they accrete gas from the ionized intergalactic medium at all epochs. The gas is accreted through both the hot mode where gas is shock heated to the virial temperature of the halo, as well as the cold mode where gas is fed via cold, dense intergalactic filaments that penetrate the halo without shock heating (e.g., Birnboim & Dekel 2003, Katz et al. 2003, Kereš et al. 2005, Dekel & Birnboim 2006, Ocvirk et al. 2008, Kereš et al. 2009, Brooks et al. 2009, van de Voort et al. 2011). The dense filaments have a short cooling time and can thus deliver cold gas to the galaxy where it can rapidly form stars (e.g., Katz et al. 2003, Kereš et al. 2005, Faucher-Giguère & Kereš 2011). At high redshifts (z > 2) halos 12 with Mhalo . 10 M accrete primarily through the cold mode, while massive galaxies 12 residing in halos with Mhalo & 10 M have their accretion dominated by the hot mode and they host a higher fraction of hot gas than cold gas in their halo (Gabor & Davé, 2012). Therefore, the fractional supply of cold halo gas available for future star-formation is lower in more massive galaxies. Simulations further show that the star-formation rate per unit mass is lower in these more massive systems (Kereš et al., 2012). This accretion history naturally leads to less efficient star-formation and eventually a higher quenched fraction for galaxies with higher mass when the high fraction of hot gas is coupled with mechanisms,

71 such as feedback processes, that prevent cooling. At later epochs (z . 2), for galaxies residing in clusters, additional environmental quenching mechanisms such as ram pressure stripping, harassment, strangulation, and radio mode AGN feedback become important. Observational studies have found evidence of clusters with established intracluster media (ICM) as early as z = 2.5 (Wang et al., 2016) and z = 2.07 (Gobat et al., 2011). In such environments, as a massive galaxy falls towards the center of the cluster, ram pressure stripping can strip cold gas from its outer disk (e.g., Gunn & Gott 1972, Giovanelli & Haynes 1983, Cayatte et al. 1990, Koopmann & Kenney 2004, Crowl 2005, Singh et al. 2019) if the pressure exerted by the ICM exceeds the restorative gravitational pressure provided by the galaxy. In the simpliﬁed treatment of Gunn & Gott (1972), this happens when:

2 Σ Σ ρICMVinfall > 2π ? gas (3.4)

where ρICM is the density of the ICM, Vinfall is the component of the infalling galaxy’s velocity perpendicular to its outer disk, and Σ? and Σgas are the stellar and gas surface density in the disk of the infalling galaxy. Ram pressure stripping is particularly effective in stripping cold gas from the outer disk of galaxies where the gas and stellar surface densities are lower than in the central regions. This process is used to explain why the observed ratio of HI radius to optical radius is less than one for spiral galaxies in clusters while it is greater than one for field spirals (e.g., Giovanelli & Haynes 1983, van Gorkom 2011), as well as the existence of truncated star-forming disks (e.g., Cayatte et al. 1990, Koopmann & Kenney 2004, Crowl 2005). The effectiveness of ram pressure stripping depends on many factors including orientation, galaxy mass, gas density, and whether the stripped gas falls back to the disk and induces later star-formation (e.g., Dressler & Gunn 1983, Gavazzi 1993, Vollmer et al. 2001, Singh et al. 2019). In evolved clusters where galaxies have high velocity dispersions, harassment, the cumulative effect of many high speed tidal interactions (Moore et al. 1996, Moore et al. 1998) also becomes important. Harassment leads to gas inflows from the outer disk to the central regions via gravitational torques from induced bars and companions, causing high gas densities and high star-formation rates in the central regions of galaxies, at the expense of the outer disk. Cluster galaxies can also be starved of fuel for future episodes of star-formation through strangulation, the slow removal of a cluster galaxy’s hot gas reservoir through interactions

72 with the cluster potential (e.g., tidal stripping) and ram pressure stripping by the cluster ICM (e.g., Larson 1980, Balogh et al. 2008, van den Bosch et al. 2008). Starvation can lead to a slow decline of star-formation (Larson, 1980). Models that implement strangulation with delayed stripping (e.g., Font et al. 2008, Cora et al. 2018) rather than instantaneous stripping (e.g., Springel et al. 2001, Kauffmann et al. 1993) typically agree better with observational studies of the fraction of red and quiescent galaxies. An additional process that delays future star-formation in cluster galaxies is the radio mode of AGN feedback driven by powerful AGN jets (e.g., Fabian 2012, Heckman & Best 2014) which heat surrounding cluster gas. This AGN feedback mode is observed directly through X-ray observations of the central galaxies of cool core clusters in the form of bubbles in the hot surrounding medium (Fabian, 2012). In summary, a variety of mechanisms likely contribute to our empirical results which show that the quiescent fraction of massive galaxies increases as a function of stellar mass and that the quiescent fraction increases towards present day. Mergers, stellar and AGN feedback, and hot mode accretion play key roles across diverse environments, while mechanisms such as ram pressure stripping, harassment, strangulation, and radio mode AGN feedback become relevant at late times (z . 2) in cluster environments. In order to observationally test the prevalence and impact of these quenching mechanisms, we are collecting and analyzing additional data. From a statistical perspective, the large comoving volume (0.33 Gpc3 at 1.5 < z < 3.0) probed by our study is expected to host a large number of massive dark matter halos and proto-clusters at z < 3. In order to identify potential proto-clusters and perform clustering analyses, spectroscopic redshifts are needed. These will be available in our field once the ongoing HETDEX optical spectroscopic survey is completed over the next several years (see Section 3.2). In conjunction with the spectroscopic redshifts, our planned proposals to acquire deep high resolution space-based imaging will be able to reveal morphological signatures of tidal interactions and mergers (e.g., double nuclei, tails, arcs, ripples and other asymmetries), and will help to accurately estimate merger rates. We have also explored the relationship between AGN and star-formation activity in our field in Florez et al. (2020). Deeper X-ray data will allow for a comprehensive study of the connection between AGN and star-formation, and their important contributions to massive galaxy evolution.

73 3.5.2 Comparing the Empirical Quiescent Fraction As a Function of Mass to Theoretical Predictions

In Section 3.4.1 we showed that our empirical quiescent fraction increases as a function of mass in three redshift bins spanning 1.5 < z < 3.0 and in Section 3.4.4 we showed 11 that the quiescent fraction for all massive galaxies (M? ≥ 10 M ) increases as a function of redshift. Here, we compare our empirical results with two types of theoretical models: hydrodynamical models from IllustrisTNG (Pillepich et al. 2018b, Springel et al. 2018, Nelson et al. 2018, Naiman et al. 2018, Marinacci et al. 2018) and SIMBA (Davé et al., 2019), and semi-analytic models (SAMs) SAG (Cora et al., 2018), SAGE (Croton et al., 2016), and Galacticus (Benson, 2012). The goals of this comparison are to provide benchmarks to improve future implementations of theoretical models and to explore the implementations of physical processes (such as those discussed in Section 3.5.1, including mergers, stellar and AGN feedback, hot mode accretion, ram pressure stripping, and tidal stripping) that drive massive galaxy evolution and impact the quiescent fractions predicted by these models. For all of these models we compute the quiescent fraction for individual snapshots in the same way that we compute the quiescent fraction for our observed sample. These methods are described in detail in Section 3.4.1. We focus our comparison with theoretical models on two of the three popular methods for measuring the quiescent fraction: sSFR-based and main sequence-based. For the sSFR-based method we use the same sSFR < 10−11 yr−1 threshold used for our data. To compute the main sequence-based quiescent fraction we define a main sequence for each model in the same way as is done for the data (where the main sequence is defined to be the average SFR in individual mass bins). We choose not to use the UVJ-based method for theoretical models because the results are strongly influenced by the chosen SEDs and dust laws used to extract photometry from the model.

Hydrodynamical Models

IllustrisTNG is the latest generation of the Illustris hydrodynamical model that implements a variety of box sizes and improved feedback mechanisms. We utilize the largest 3 3 7 volume available, ∼300 Mpc (TNG300; mass resolution mbaryon = 1.1 × 10 M ) with masses and star-formation rates measured within twice the stellar half mass radius (the

2 × R1/2 aperture). We investigate how the choice of aperture impacts our comparison with IllustrisTNG quenched fractions in Appendix A.2. When the SFR is below the IllustrisTNG

74 log(M /M ) log(M /M ) 10.0 10.5 11.0 11.5 12.0 12.5 13.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0

1.0 1.5 < z < 2.0 This Work: sSFR 1.0 1.5 < z < 2.0 This Work: sSFR 0.8 N11 = 8480 SIMBA 0.8 N11 = 8480 SAG TNG300 SAGE 0.6 0.6 Galacticus 0.4 0.4

Fraction 0.2 Fraction 0.2 Quiescent Quiescent 0.0 0.0 1.0 2.0 < z < 2.5 1.0 2.0 < z < 2.5 0.8 N11 = 15401 0.8 N11 = 15401 0.6 0.6 0.4 0.4

Fraction 0.2 Fraction 0.2 Quiescent Quiescent 0.0 0.0 1.0 2.5 < z < 3.0 1.0 2.5 < z < 3.0 0.8 N11 = 4588 0.8 N11 = 4588 0.6 0.6 0.4 0.4

Fraction 0.2 Fraction 0.2 Quiescent Quiescent 0.0 0.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0 log(M /M ) log(M /M )

Figure 3.9: Empirical sSFR-selected quiescent fraction compared with sSFR-selected quiescent fractions from the hydrodynamical models SIMBA and IllustrisTNG (left) and semi- analytic models SAG, SAGE, and Galacticus (right). We ﬁnd that results from the SIMBA model show a similar increase in quiescent fraction as a function of mass at 1.5 < z < 2.0 as is seen with our empirical result, although the error bars are quite large. The results from IllustrisTNG show a quiescent fraction that increases as a function of mass at 2.0 < z < 3.0, but decreases as a function of mass in the 1.5 < z < 2.0 bin. We note that the quiescent fraction results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). SAM SAG is able to reproduce the trend seen in our empirical result as a function of mass, but underestimates the quiescent fraction by up to a factor of ∼ 1.5 − 3 compared with our empirical result. SAM SAGE does not predict a quiescent fraction that increases as a function of mass and it underestimates the quiescent fraction at the high mass end compared with our result, while Galacticus predicts a quiescent fraction that increases steeply at the high mass end, but with large error bars. The gray shaded region indicates masses below our completeness limit. Insets on the upper 11 left of each panel show the number (N11) of galaxies in our sample with M? ≥ 10 M .

75 log(M /M ) log(M /M ) 10.0 10.5 11.0 11.5 12.0 12.5 13.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0

1.0 1.5 < z < 2.0 This Work: MS - 1dex 1.0 1.5 < z < 2.0 This Work: MS - 1dex 0.8 N11 = 8480 SIMBA 0.8 N11 = 8480 SAG TNG300 SAGE 0.6 0.6 Galacticus 0.4 0.4

Fraction 0.2 Fraction 0.2 Quiescent Quiescent 0.0 0.0 1.0 2.0 < z < 2.5 1.0 2.0 < z < 2.5 0.8 N11 = 15401 0.8 N11 = 15401 0.6 0.6 0.4 0.4

Fraction 0.2 Fraction 0.2 Quiescent Quiescent 0.0 0.0 1.0 2.5 < z < 3.0 1.0 2.5 < z < 3.0 0.8 N11 = 4588 0.8 N11 = 4588 0.6 0.6 0.4 0.4

Fraction 0.2 Fraction 0.2 Quiescent Quiescent 0.0 0.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0 log(M /M ) log(M /M )

Figure 3.10: Empirical main sequence-selected quiescent fraction compared with the main sequence-selected quiescent fraction from hydrodynamical models IllustrisTNG and SIMBA (left) and semi-analytic models SAG, SAGE, and Galacticus (right). SIMBA under-predicts the quiescent fraction by a factor of ∼ 1.5 − 4 at 1.5 < z < 3.0 compared with our empirical result, but with large error bars. The IllustrisTNG model over-predicts the quiescent fraction by a factor of ∼ 2 in the 2.0 < z < 3.0 redshift bins compared with our empirical result and increases as a function of mass. In the lowest redshift bin (1.5 < z < 2.0), however, the IllustrisTNG quiescent fraction decreases as a function of mass. We note that the quiescent fraction results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). The three SAMS under-predict the quiescent fraction at the high mass end by up to a factor of 10 compared with our empirical result. SAG is the only SAM that predicts an increase in the quiescent fraction as a function of stellar mass. The gray shaded region indicates masses below our completeness limit. Insets on the upper left of each panel show the number (N11) 11 of galaxies in our sample with M? ≥ 10 M .

76 resolution limit, the group catalogs have this value set to be SFR = 0. Following Donnari et al. (2019), we reset this SFR to a random value between SFR = 10−5 and 10−4 before beginning our analysis to better represent the SFR for these objects. We note that the resulting quiescent fractions are the same whether we leave SFR = 0 or assign a random value between SFR = 10−5 and 10−4. The IllustrisTNG model implements both thermal-mode AGN feedback and kinetic- mode AGN feedback at high and low black hole accretion states, respectively (Weinberger et al. 2017, Pillepich et al. 2018a). The thermal-mode is a continuous injection of thermal energy into the gas surrounding the central black hole (heating the gas), while the kinetic- mode is a pulsed injection of kinetic energy to the regions near the black hole (acting as a wind). Stellar feedback is implemented through wind particles which are launched in random directions, where the strength of the wind is determined by the energy released from the supernova. We find that the IllustrisTNG model over-predicts the sSFR-based quiescent fraction by a factor of ∼ 2 − 5 and it over-predicts main sequence-based quiescent fractions by up to 11 a factor of ∼ 2 at the high mass end (M? ≥ 10 M ) compared to our empirical results (Fig. 3.9 and Fig. 3.10, respectively) at redshifts 1.5 < z < 3.0. In the 2.0 < z < 3.0 bins, the IllustrisTNG quiescent fractions increase as a function of mass, similarly to our empirical result. In the lowest redshift bin (1.5 < z < 2.0), however, the IllustrisTNG 11 quiescent fraction turns over at M? ' 10 M and begins to decrease at the highest masses, albeit with large error bars. At log(M?/M ) ≥ 11.5 in the 1.5 < z < 2.0 bin, IllustrisTNG under-predicts the quiescent fraction by up to a factor of ∼ 3 using both the sSFR- and main sequence-based methods compared with our empirical result. We note that the quiescent fraction results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture, and we show the results using different aperture choices in Appendix A.2. Donnari et al. (2019) also investigates the quenched fraction using the main sequence- based method and, using a different definition of the main sequence, they find a quiescent fraction that increases as a function of mass in all 1.5 < z < 3.0 bins and is a factor of ∼ 2 − 4 larger than our empirical result. The comparison between these results is described in detail in Appendix A.2 and brings to light the importance of using the same methods when comparing quiescent fractions from different studies. We also compare our empirical result with that from the SIMBA cosmological simulation (Davé et al., 2019) which implements meshless finite mass hydrodynamics in a 100 Mpc/h

77 7 box with mass resolution mgas = 1.82 × 10 M . We use the total stellar mass and SFR for galaxies in the SIMBA group catalog. The SIMBA model performs black hole feedback through both kinetic and X-ray modes. The kinetic-mode feedback is implemented as a bipolar wind (in the form of a collimated jet), and the X-ray mode injects energy into surrounding gas. We note that although SIMBA and IllustrisTNG both use the term “kinetic- mode" to describe AGN feedback, their implementations of this feedback are quite diﬀerent. Supernova feedback is implemented in SIMBA through a wind which carries hot and cold gas, as well as metals, away from star-forming regions. With the available SIMBA output (R. Davé, private communication) we are able to compute the quiescent fraction using the sSFR and main sequence-based methods for their massive galaxies. We note that the small box size of the SIMBA cosmological simulation compared with the volume probed by our empirical sample leads to greater uncertainty at the highest masses. The SIMBA model tends to under-predict the quiescent fraction of massive galaxies when using both the sSFR-based method (Fig. 3.9) and the main sequence-based method (Fig. 3.10) by a factor of ∼ 1.5 − 4 compared with our empirical result at 1.5 < z < 3.0. We note that at 2.0 < z < 3.0 the quiescent fraction predicted by SIMBA using both methods is largely ﬂat as a function of mass, but in the lowest redshift bin (1.5 < z < 2.0), the SIMBA model begins to predict a quiescent fraction that increases as a function of mass.

Semi-Analytic Models

The results from three SAMs (SAG, SAGE, and Galacticus) are compared with our sSFR-based quiescent fraction (Fig. 3.9) and main sequence-based (Fig. 3.10) empirical results. The benefit of using SAMs is that they are far less computationally expensive compared to hydrodynamical models and they provide a platform for exploring different analytical recipes for the physical processes underlying galaxy evolution. Additionally, SAMs efficiently model large volumes which allows for statistically significant samples of massive galaxies. The three SAMs we compare with, SAG (Cora et al., 2018), SAGE (Croton et al., 2016), and Galacticus (Benson, 2012) are described in detail in the aforementioned works, as well as Knebe et al. (2018), and will briefly be described here. The three SAMs implement their physical models to populate halos from the MultiDark-Planck2 (MDPL2) dark matter-only simulation, which has a box size of 1.0 h−1Gpc on a side. The version of SAG used here

78 1.0 This Work QF Selection: 1.0 QF Selection: This Work SAG sSFR < 1011yr 1 MS - 1 dex SIMBA 0.8 SAGE 0.8 TNG300 Galacticus

0.6 0.6

0.4 0.4

0.2 0.2 Quiescent Fraction Quiescent Fraction 0.0 0.0 1.5 2.0 2.5 3.0 1.5 2.0 2.5 3.0 Redshift Redshift

11 Figure 3.11: Empirical quiescent fraction for massive galaxies (M? ≥ 10 M ) in our sample, selected using the sSFR (left) and main sequence (right) methods, compared with those from theoretical models. Theoretical models SIMBA, SAG, SAGE, and Galacticus under-predict the quiescent fraction for all massive galaxies by up to a factor of ∼10, while IllustrisTNG over-predicts the quiescent fraction by up to a factor of 3 compared with our empirical result. We note that results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). Using both the sSFR- and main sequence-based methods, all models except for Galacticus and IllustrisTNG predict a quiescent fraction that increases as a function of redshift.

79 (S. Cora, private communication) is run on 9.4% of the full MDPL2 volume, while SAGE and Galacticus are run on the full 1.0 h−1Gpc box. We use the total stellar mass and SFR for galaxies in the group catalogs for every SAM. Each of the SAMs implement different physical processes that influence galaxy evolution and the resulting quiescent fraction. We discuss the key points of these models (AGN and stellar feedback, treatment of mergers, the interaction of galaxies with the cluster potential, and the redshift at which the model is calibrated to observational results) here, but direct the reader to the original SAM papers for more detailed discussion. SAG implements AGN feedback through a radio-mode feedback scheme in which energy is injected into the region surrounding the black hole, reducing hot gas cooling. Stellar feedback heats gas within the galaxy and the energy transfer is regulated by a virial velocity and redshift dependence. The parameter that regulates the redshift dependence has been modified to generate the galaxy catalog used in this work (S. Cora, private communication). This parameter was adjusted to better reproduce the evolution of the star-formation rate density at high redshifts (z > 1.5), and has also been shown to achieve a local quiescent fraction of galaxies that is in better agreement with observations from previous works (Cora et al., 2018). A fraction of the supernova ejecta is heated and removed from the halo. The ejected gas is reincorporated into the hot gas with a timescale that is inversely proportional to the corresponding (sub)halo virial mass. During major mergers, a starburst occurs in the bulge after stars and cold gas from the remnant are placed in the central regions. In a minor merger the stars of the less massive galaxy are transferred to the bulge of the more massive galaxy. A significant advantage of the SAG model is that it explicitly models ram pressure and tidal stripping for satellites falling into a group or cluster. Different stripping radii are used for the hot and cold gas components, as well as the disk and bulge stellar populations. The combined effects of ram pressure stripping (of gas) and tidal stripping (of stars and gas) are not instantaneous, rather the processes gradually remove the gas supply from a satellite. Calibration of SAG is performed considering observational constraints at z = 0, z = 0.15 and z = 2. SAGE models AGN feedback through both radio- and quasar-modes. Radio-mode feedback heats the gas surrounding the black hole and keeps a history of past feedback events by implementing a hot gas region around the black hole which is not allowed to cool in subsequent time steps. This region of hot gas is only allowed to grow with time. The quasar-mode ejects cold gas (and hot gas if energetic enough) into a gas reservoir. Stellar

80 winds from supernova feedback similarly eject gas into this reservoir. Gas in the reservoir is slowly incorporated back into the galaxy with the reincorporation regulated by the mass of the halo (higher mass halos receive more gas from the reservoir). In SAGE, a major merger results in the destruction of both disks and the stars are rearranged into a spheroid. Minor mergers simply move the satellite’s gas and stars to the bulge of the central. SAGE implements a gradual stripping of satellites which is proportional to the stripping of the subhalo’s dark matter, but it does not implement ram pressure stripping. The SAGE model is only calibrated to observational constraints at z = 0. The Galacticus model implements AGN feedback through radio-mode which is an ejection of energy via a jet regulated by the black hole spin, and a quasar-mode wind. Stellar feedback is implemented as a wind that removes cold gas from the disk and into the hot halo. During major mergers, the gas and stars in merging galaxies are rearranged to form a spheroid, while in minor mergers the smaller galaxy is absorbed into the bulge of the massive galaxy. Ram pressure stripping and tidal stripping are not included in the model, however there is strangulation in which the hot atmosphere of satellites is stripped. Galacticus is only calibrated to observational constraints at z = 0, and we note that the Galacticus model has not been calibrated to the MDPL2 dark matter simulation. We find that SAG does the best job of reproducing the trend of the sSFR-selected quiescent fraction that we find in our empirical results in all redshift bins where the quiescent fraction increases as a function of mass, however it under-predicts the quiescent fraction by up to a factor of ∼ 1.5−3 at the high mass end compared to our empirical result. In contrast, SAGE finds that the sSFR-selected quiescent fraction is ∼0% in the 2.5 < z < 3.0 bin and in the 2.0 < z < 2.5 bin it finds that the quiescent fraction decreases as a function of mass at the highest masses and under-predicts the quiescent fraction, compared with our empirical result, by a factor of ∼ 2 − 5. In the 1.5 < z < 2.0 bin SAGE finds an sSFR-based quiescent fraction that is flat as a function of stellar mass and the quiescent fraction is lower than our empirical result by a factor of ∼ 3. Galacticus finds that the sSFR-selected quiescent fraction in the 2.0 < z < 3.0 bins rises steeply as a function of mass, albeit with large error bars. In the 1.5 < z < 2.0 bin, Galacticus under-predicts the quiescent fraction by up to a factor of 10 compared with our empirical result. The three SAMs underestimate the quiescent fraction of massive galaxies by up to a factor of ∼10 using the main sequence-based selection method in all of our redshift bins compared with our empirical result, however we note that SAG is able to correctly predict

81 the increase in the quiescent fraction with increasing stellar mass. Galacticus predicts a quiescent fraction of ∼0% at the high mass end and does not achieve a main sequence-based quiescent fraction that increases with increasing stellar mass. SAGE predicts a quiescent fraction that is ﬂat in the 1.5 < z < 2.0 bin and decreases at the high mass end in the 2.0 < z < 3.0 bins.

3.5.3 Comparing the Empirical Quiescent Fraction As a Function of Redshift to Theoretical Predictions

When exploring the quiescent fraction as a function of mass in individual redshift bins for theoretical models (Section 3.5.2), results are indicative of individual snapshots of the 11 simulation. We can also compare the quiescent fraction for all galaxies with M? ≥ 10 M as a function of redshift from theoretical models (Fig. 3.11) to our empirical result (see Section 3.4.4) to gain insights into the evolution of the massive galaxy population across several snapshots in the theoretical models. We ﬁnd that hydrodynamical model SIMBA predicts quiescent fractions that increase from high- to low-redshift in a similar way to our empirical result for the sSFR-based method, however, SIMBA under-predicts the sSFR- and main sequence-based quiescent fractions 11 for all galaxies with M? ≥ 10 M by up to a factor of ∼ 2 compared with our empirical 11 result. The IllustrisTNG quiescent fraction for all galaxies with M? ≥ 10 M is largely ﬂat as a function of redshift and over-predicts the sSFR- and main sequence-based quiescent fractions by factors of ∼ 3 and ∼ 2, respectively, compared with our empirical result. We note, again, that the quiescent fraction results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). For both the sSFR-based and main sequence-based methods of identifying quenched

galaxies, the three SAMs under-predict the quiescent fraction for all galaxies with M? ≥ 11 10 M at 1.5 < z < 3.0 compared with our empirical result, with the disagreement being larger for the main sequence-based method. Using the sSFR- and main sequence- based methods, semi-analytic model Galacticus under-predicts the quiescent fraction for all 11 galaxies with M? ≥ 10 M by up to a factor of ∼10 compared with our empirical result and is ﬂat as a function of redshift. SAMs SAG and SAGE ﬁnd quiescent fractions for all massive galaxies that increase as a function of redshift similarly to our empirical result using both the sSFR-based and main sequence-based methods. With the sSFR-based method, SAG and

82 2 1.5 < z < 2.0 All Galaxies 2.0 < z < 2.5 All Galaxies 2.5 < z < 3.0 All Galaxies ) N11 = 8480 N11 = 15401 N11 = 4588 x

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p 5

M This Work / 6 TNG300

( SIMBA

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o 7 SAGE l Galacticus 8 2 1.5 < z < 2.0 SF, sSFR 2.0 < z < 2.5 SF, sSFR 2.5 < z < 3.0 SF, sSFR ) x

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o 7 l This Work 8 10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure 3.12: Empirical galaxy stellar mass function for our observed sample compared with predictions from hydrodynamical models SIMBA and IllustrisTNG and semi-analytic models SAG, SAGE, and Galacticus. The top row shows results for all galaxies. The 2nd and 3rd rows from the top show the star-forming and quiescent galaxy stellar mass functions, respectively, split into these populations using the sSFR-based method. The 4th and 5th rows from the top are analogous to rows 2 and 3, but split the quiescent and star-forming populations using the main sequence-based method. Poisson errors are indicated by the colored regions and are often smaller than the lines. The gray shaded region indicates masses below our completeness limit. In the top row, insets on the upper left of each panel 11 show the total number (N11) of galaxies in our sample with M? ≥ 10 M . A detailed comparison of our empirical results with those from theoretical models is given in Section 3.5.4. Briefly, we find that hydrodynamical model SIMBA is in good agreement with our empirical total galaxy stellar mass function in our two redshift bins spanning 2.0 < z < 3.0, while predictions from IllustrisTNG are lower than our result by a factor of 15 at these redshifts. We note that results from IllustrisTNG83 and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). The three SAMs under-predict the number density of the total population of massive galaxies by up to a factor of 10,000 compared with our empirical result, with the discrepancy being lower for SAG and SAGE than Galacticus. 11 SAGE under-predict the quiescent fraction for all galaxies with M? ≥ 10 M by a factor of ∼ 3 − 4 compared with our empirical result. Using the main sequence-based method, SAG and SAGE under-predict the quiescent fraction of massive galaxies by a factor of ∼5 compared with our empirical result. In order to better agree with our empirical result, theoretical models SIMBA, SAG, SAGE, and Galacticus might consider implementing physical processes that increase the fraction of quiescent galaxies in their massive galaxy population and reproduce the trend seen in our empirical result where the quiescent fraction increases as time progresses from z = 3.0 to z = 1.5. In contrast, IllustrisTNG may consider revisiting physical processes that decrease the quiescent fraction in their massive galaxy population in order to better agree with our empirical result. We note, again, that results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). SAM Galacticus and the hydrodynamical model from IllustrisTNG face particularly hard challenges as they both predict quiescent fractions which are flat as a function of redshift (Fig. 3.11).

3.5.4 Comparing the Stellar Mass Function to Theoretical Predictions

In Section 3.4.5 we showed the empirical galaxy stellar mass function for the total galaxy population, as well as the star-forming and quiescent galaxy populations. The total galaxy stellar mass function and quiescent galaxy stellar mass functions are connected through the quiescent fraction (see Eqn. 3.3) and, therefore, the stellar mass function provides important insights when interpreting the quiescent fraction of massive galaxies. Comparisons of our empirical galaxy stellar mass functions and those predicted by theoretical models place important constraints on the physical process implemented in the theoretical models. In Section 3.4.5 we compared our result with those from previous observational studies and showed that in the two higher redshift bins (2.0 < z < 2.5 and 2.5 < z < 3.0) our total stellar mass function is in fair agreement with previous studies, while in the lowest redshift bin

(1.5 < z < 2.0), we may have a deﬁcit of galaxies at masses log(M?/M ) < 11.2. Therefore, when comparing our empirical galaxy stellar mass function to theoretical models, we treat this lowest redshift bin with caution and do not draw any strong conclusions from it. The stellar mass functions from all theoretical models used in this work (hydrodynamical models from IllustrisTNG and SIMBA, SAMs SAG, SAGE, and Galacticus) are computed following the method of Tomczak et al. (2014) which is the same method used for our

84 observed sample, but without a 1/Vmax correction as this is not necessary for theoretical models. Instead, the volume term is simply the volume of the simulation box for a given model. Additionally, we convolve the stellar mass functions from theoretical models with the average stellar mass error for our observed sample (Kitzbichler & White, 2007), which is computed from SED ﬁtting (see Section 3.3). We ﬁnd that hydrodynamical model SIMBA is in agreement with the empirical number density of the total population of massive galaxies in the two redshift bins spanning 2.0 < z < 3.0, while the prediction from IllustrisTNG is lower than our empirical result by up to a factor of 15 at these redshifts (top row Fig. 3.12). In section 3.5.2 we showed that the SIMBA model under-predicts the quiescent fraction using both the sSFR and main-sequence methods by a factor of ∼ 1.5 − 4 at 1.5 < z < 3.0 compared with our empirical result, and the IllustrisTNG model over-predicts the quiescent fraction using both methods by a factor of ∼ 2 − 5 compared with our empirical result. We note, however, that results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). In order to bring both the predicted quiescent fraction and stellar mass function into better agreement with our empirical result, the SIMBA hydrodynamical model may consider revisiting their implementation of processes that can increase the quiescent fraction across all three redshift bins spanning 1.5 < z < 3.0, while maintaining the number density of the massive galaxy population at 2.0 < z < 3.0. These processes include stellar and AGN feedback, ram pressure stripping, tidal stripping, strangulation, and harassment at z < 2.0 when galaxy clusters are established. The IllustrisTNG model may consider implementing physical processes that will increase the number density of the massive galaxy population at early times (2.0 < z < 3.0). The SAMs SAG, SAGE, and Galacticus under-predict the number density of the total population of massive galaxies (top row Fig. 3.12) compared with our empirical result by up to a factor of ∼10,000 at the high mass end for our three redshift bins spanning 1.5 < z < 3.0, with the discrepancy being smaller for SAG and SAGE than it is for Galacticus. The discrepancy decreases towards later epochs (1.5 < z < 2.0). In Section 3.5.2 we showed that the three SAMs under-predict the quiescent fraction of massive galaxies by a factor of ∼ 1.5 − 10, compared with our empirical result, using both the main sequence-based and sSFR-based quiescent galaxy selection. The SAMs show a larger level of disagreement with the total stellar mass function than they do with the quiescent fraction. In order to achieve better agreement with our empirical results, the three

85 SAMs may consider improving the implementation of physical processes (see Section 3.5.1) that can simultaneously alleviate the large disagreement with the empirical total galaxy stellar mass function and the moderate disagreement with the empirical quiescent fraction. Processes that could help to dramatically increase the total number density of massive galaxies include higher merger rates, diﬀerent treatments of star-formation eﬃciency during mergers, and higher gas accretion. The models may be able to moderately increase their predicted quiescent fractions with the implementation of stronger ram pressure stripping, tidal stripping, strangulation, and stellar and AGN feedback.

3.6 Summary

Using multiwavelength data available in the 17.5 deg2 SHELA footprint, we explore the 11 buildup of the population of massive (M? ≥ 10 M ) quiescent galaxies at cosmic noon as a function of stellar mass. We perform careful SED ﬁtting to explore the growth and quenching of massive galaxies as a function of stellar mass at redshifts 1.5 < z < 3.0. Our study beneﬁts from the large area probed by our data which allows for small error bars dominated by Poisson statistics, as well as our uniform sample selection across large cosmic volumes giving an unbiased result. Our key results are summarized below.

1. We implement three common techniques for measuring the quiescent fraction of massive galaxies: sSFR-based, main sequence-based, and UVJ-based selection techniques (Fig. 3.3). Each of these three methods uses results from SED ﬁtting to classify galaxies as either star-forming or quiescent. These three methods produce results that show an increase in the quiescent fraction as a function of mass and they are in good agreement at 1.5 < z < 2.0 but diﬀer by up to a factor of 2 at

2.0 < z < 3.0. As the stellar mass varies from log(M?/M ) = 11 to 11.75 we ﬁnd that at 2.5 < z < 3.0 the main sequence-based quiescent fraction increases from 13.5% ± 7.1% to 39.6% ± 11.2%, while at 1.5 < z < 2.0 the quiescent fraction increases from 51.9% ± 2.5% to 66.4% ± 13.1%. It is remarkable that by z = 2, only 3.3 Gyr after the Big Bang, the universe has quenched more than 25% of massive 11 (M? = 10 M ) galaxies.

2. We compare our empirical result using the UVJ-based quiescent fraction method with those from previous observational studies (Fig. 3.4). Due to the larger volume

86 probed by our 17.5 deg2 study, our work at 1.5 < z < 3.0 extends to higher stellar

masses than earlier studies and our sample of galaxies with log(M?/M ) ≥ 11.5 is a factor of ∼40 larger than samples from Muzzin et al. (2013), Martis et al. (2016), and Tomczak et al. (2016). We ﬁnd a similar trend with redshift (Fig. 3.6), albeit with much smaller error bars and lower cosmic variance.

3. We explore several physical mechanisms that contribute to galaxy quenching across a range of environments and epochs (Section 3.5.1). Additionally, we address which of these mechanisms can lead to our results that the quenched fraction increases as a function of mass at the high mass end and that the quenched fraction of massive galaxies increases towards present day. Across diverse environments, mergers, stellar and AGN feedback, and hot mode accretion play an important role, while in cluster environments mechanisms such as ram pressure stripping, harassment, strangulation, and radio mode AGN feedback likely become increasingly relevant for quenching star-formation.

4. We also compare our empirical result with those from several classes of theoretical models (Fig. 3.9 and Fig 3.10). Hydrodynamical model IllustrisTNG over-predicts the main sequence-based quiescent fraction by a factor of 2 and the model over- predicts the sSFR-based quiescent fraction by a factor of 2 to 5 compared with our empirical result, however, the quiescent fraction results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (see Appendix A.2). The SIMBA cosmological simulation tends to under-predict the quiescent fraction, compared with our empirical result, when using both the sSFR and main- sequence based methods by a factor of ∼ 1.5−4, respectively, but in the lowest redshift bin (1.5 < z < 2.0) it starts to correctly predict the observed trend of rising quiescent fraction with stellar mass. Semi-analytic models SAG, SAGE, and Galacticus tend to under-predict the quiescent fraction of massive galaxies using both the sSFR and main sequence-based selection techniques by a factor of ∼ 1.5−10 compared with our empirical result, however we note that SAG does the best job of recovering the trend of increasing quiescent fraction with increasing stellar mass found in our empirical result.

87 Additionally, we compare these models to our empirical galaxy stellar mass function at the high-mass, steeply declining end (Fig. 3.12) for the total galaxy population, as well as the star-forming and quiescent populations. While the SAMs and the hydrodynamical model SIMBA under-predict the quiescent fraction of massive galaxies by a moderate factor of 1.5 to 10 at 1.5 < z < 3.0 compared with our empirical result, we ﬁnd that the SAMs drastically under-predict the number density of the total massive galaxy population by a factor of up to 10,000, while hydrodynamical models SIMBA and IllustrisTNG show only up to a factor of ∼15 disagreement (for IllustrisTNG, results and any associated conclusions are highly dependent on the choice of aperture; see Appendix A.2). We discuss physical processes that might be revisited in the theoretical models to produce better agreement with the empirical quiescent fraction and stellar mass function.

88 Chapter 4: The Shape and Scatter of The Galaxy Main Sequence for Massive Galaxies at Cosmic Noon

4.1 Introduction

The way in which massive galaxies build their stellar populations, and achieve this earlier than lower mass populations, remains an important question in the study of galaxy evolution. Theoretical models (e.g., Somerville & Primack 1999, Cole et al. 2000, Bower et al. 2006, Croton et al. 2006, Somerville et al. 2008, Benson 2012, Somerville & Davé 2015 and references therein, Croton et al. 2016, Naab & Ostriker 2017 and references therein, Weinberger et al. 2017, Cora et al. 2018, Knebe et al. 2018, Behroozi et al. 2019, Cora et al. 2019, Davé et al. 2019) struggle to implement physical processes that can simultaneously reproduce the observed properties of the massive and low mass galaxy populations at both high and low redshifts (e.g., Conselice et al. 2007, Asquith et al. 2018, Sherman et al. 2020a, Sherman et al. 2020b). Observations of large samples of massive galaxies at cosmic noon (1.5 < z < 3.0), a time when the massive galaxy population transitions from star-forming to quiescent (e.g., Conselice et al. 2011, van der Wel et al. 2011. Weinzirl et al. 2011, Muzzin et al. 2013, van Dokkum et al. 2015, Martis et al. 2016, Tomczak et al. 2016, Sherman et al. 2020b), can provide important constraints on the physical processes driving the early assembly of massive galaxies. The stellar masses and star-formation rates of galaxies at cosmic noon (1.5 < z < 3.0) are fundamental quantities that provide insights into this dynamic period in the history of the universe. At this epoch, proto-clusters began to collapse into the rich clusters seen at present day (e.g., Gobat et al. 2011, Lotz et al. 2013, Overzier 2016, Wang et al. 2016, Chiang et al. 2017), star-formation and black hole accretion peaked (e.g., Madau & Dickinson 2014), 11 and the massive (M? ≥ 10 M ) galaxy population transitioned from being predominantly

A signiﬁcant portion of this Chapter has been submitted for publication in the Monthly Notices of the Royal Astronomical Society. Sydney Sherman served as the ﬁrst author of this work and conducted the original research contained herein. Coauthors provided useful feedback and guidance that shaped the research and subsequent direction of this work. Coauthors are: Shardha Jogee, Jonathan Florez, Steven L. Finkelstein, Robin Ciardullo, Isak Wold, Matthew L. Stevans, Lalitwadee Kawinwanichakij, Casey Papovich, and Caryl Gronwall

89 star-forming to predominantly quiescent (e.g., Conselice et al. 2011, van der Wel et al. 2011. Weinzirl et al. 2011, Muzzin et al. 2013, van Dokkum et al. 2015, Martis et al. 2016, Tomczak et al. 2016, Sherman et al. 2020b). The relationship between star-formation rate and stellar mass, coined the “main sequence" by Noeske et al. (2007), provides key insights into the formation history of the massive galaxy population. Although a signiﬁcant number of studies (e.g., Daddi et al. 2007, Elbaz et al. 2007, Noeske et al. 2007, Karim et al. 2011, Rodighiero et al. 2011, Guo et al. 2013b, Speagle et al. 2014, Whitaker et al. 2014, Lee et al. 2015, Renzini & Peng 2015, Salmon et al. 2015, Schreiber et al. 2015, Tasca et al. 2015, Tomczak et al. 2016, Santini et al. 2017,

Popesso et al. 2019, among others) have investigated the nature of galaxies in the SFR-M? plane, a consensus has not yet been reached for a single definition of the “main sequence", specifically as it pertains to the star-forming galaxy main sequence. Some studies choose to pre-select for star-forming galaxies (e.g., Noeske et al. 2007, Daddi et al. 2007, Whitaker et al. 2014, Tomczak et al. 2016), typically via emission at 24µm. Others select a sample of star-forming galaxies from a sample containing all galaxies (e.g., Whitaker et al. 2014 and Tomczak et al. 2016 at intermediate redshifts), with techniques such as color-color selection. In this work, we investigate both the main sequence for all galaxies and for star-forming 11 galaxies using a sample of massive (M? ≥ 10 M ) galaxies that spans a wide range of specific star-formation rates in the star-forming, green valley (e.g., Martin et al. 2007, Salim et al. 2007, Wyder et al. 2007), and quiescent populations. Previous studies have focused on three key aspects of the main sequence: the slope, normalization, and scatter around the main sequence. The slope provides information about when galaxies of different masses begin to quench (the so-called “downsizing" scenario; Cowie et al. 1996). Out to z ∼ 6 the power-law slope is measured to be between ∼ 0 − 1 (e.g., Daddi et al. 2007, Elbaz et al. 2007, Noeske et al. 2007, Rodighiero et al. 2011, Guo et al. 2013b, Speagle et al. 2014, Whitaker et al. 2014, Renzini & Peng 2015, Tomczak et al. 2016, Santini et al. 2017, among others), with evidence that higher mass star-forming galaxies exhibit a shallower slope than lower mass star-forming galaxies (e.g., Whitaker et al. 2014, Lee et al. 2015, Tasca et al. 2015). The normalization of the main sequence has been shown to increase with increasing redshift, indicating that the specific star-formation rates of extreme galaxies found at late times were more typical specific star-formation rates at earlier times (e.g., Karim et al. 2011, Speagle et al. 2014, Whitaker et al. 2014, Tomczak et al. 2016, Santini et al. 2017). Finally, the star-forming galaxy main sequence relation

90 has been found to be quite tight with a rather constant scatter (typical scatter is measured to be 0.2 − 0.4 dex; e.g., Rodighiero et al. 2011, Speagle et al. 2014, Schreiber et al. 2015, Popesso et al. 2019) with the level of scatter often attributed to the level of stochasticity in the star-formation history of the population (e.g., Caplar & Tacchella 2019, Matthee & Schaye 2019). Typically, previous studies have focused on achieving deep observations taken over small 8 9 areas, often pushing constraints of the main sequence to fairly low masses (∼ 10 − 10 M ; e.g., Whitaker et al. 2014, Tomczak et al. 2016). Different methods taken by previous studies for measuring the main sequence (e.g., extrapolation from low to high masses, fitting single and double power laws, stacking analyses, etc.), as well as inconsistent (and often biased) methods of separating star-forming galaxies from the total population (e.g., color- color indicators, specific star-formation rate thresholds, distance below the main sequence, detection in particular filters, etc.) have led to measures of the main sequence that are not unbiased (Renzini & Peng, 2015). Furthermore, biased selection of star-forming galaxies has often forced previous works to make assumptions about the distribution of star-forming galaxies in the SFR-M? plane, which makes robust measures of the scatter around the star-forming galaxy main sequence, a strong tracer of the stochasticity of star-formation histories, quite difficult. In this work, we present the massive end of the galaxy main sequence for all galaxies and star-forming galaxies at cosmic noon (1.5 < z < 3.0) using a sample of 28,469 massive 11 (M? ≥ 10 M ) galaxies. Notably, we do not make any assumptions about the functional form of the galaxy main sequence nor do we make assumptions about the distribution of massive galaxies in the SFR-M? plane. This novel, unbiased approach is made possible by our large sample which is uniformly selected from a 17.5 deg2 area (∼ 0.33 Gpc3 comoving volume over 1.5 < z < 3.0), significantly reducing Poisson errors and rendering the effects of cosmic variance negligible. With this large sample, we are uniquely suited to separate star-forming galaxies from the collective green valley and quiescent galaxy populations by locating the transition between the star-forming and green valley populations in the SFR-M? plane in small mass bins, rather than using fixed cutoffs to define these populations. Finally, due to our meaningful separation of star-forming galaxies from the total population, we are able to perform an unbiased study of the scatter around the star-forming galaxy main sequence as a function of stellar mass. We also compare our empirical results with those from hydrodynamical models SIMBA

91 (Davé et al., 2019) and IllustrisTNG (Pillepich et al. 2018b, Springel et al. 2018, Nelson et al. 2018, Naiman et al. 2018, Marinacci et al. 2018), as well as the semi-analytic model SAG (Cora et al., 2018). Sherman et al. (2020b) showed that these models face significant 11 challenges in reproducing the observed quiescent fraction of massive (M? ≥ 10 M ) galaxies at 1.5 < z < 3.0, indicating that the implementation of the physical processes underlying massive galaxy evolution at these epochs may need to be revised. This paper is organized as follows. In Section 4.2 we detail the data used in this work, the SED fitting procedure, and sample selection. Section 4.3.1 presents our measurement of the main sequence for all galaxies, Section 4.3.2 presents the main sequence for star- forming galaxies, and in Section 4.3.3 we compare the resulting main sequences for all and star-forming galaxies. In Section 4.4 we measure the scatter around the star-forming galaxy main sequence. In Section 4.5 we present comparisons with previous observational studies, and in Section 4.6 we compare our empirical result with those from theoretical models. Finally, we discuss the implications of our results in Section 4.7 and summarize our results in Section 4.8. Throughout this work we adopt a flat ΛCDM cosmology with h = 0.7,

Ωm = 0.3, and ΩΛ = 0.7.

4.2 Data and Analysis

The data, SED fitting, sample selection, and stellar mass completeness estimates used in this work are the same as those used in Sherman et al. (2020b) and will briefly be described here. Our catalog is NEWFIRM Ks-selected (depth 22.4 AB mag at 5σ; PI Finkelstein, Stevans et al. 2021) and covers 17.5 deg2 in the SDSS Stripe 82 equatorial field. In addition to the NEWFIRM Ks data, we also utilize u, g, r, i, z photometry from the Dark Energy Camera (DECam) (Wold et al. 2019, Kawinwanichakij et al. 2020, Stevans et al. 2021; r- band 5σ depth is r = 24.5 AB mag), VICS82 J and Ks data (Geach et al. 2017; 5σ depth for J-band is 21.5 AB mag and for K-band is 20.9 AB mag), and Spitzer-IRAC 3.6 and 4.5µm photometry (PI Papovich; Papovich et al. 2016, Kawinwanichakij et al. (2020)); 5σ depth is 22 AB mag in both filters). Combined, these data provide up to 10 photometric data points with which we can use SED fitting techniques to estimate redshift, stellar mass, SFR, and other galaxy properties. Additional photometric data in this footprint (which are not used in SED fitting) come from Herschel-SPIRE (HerS, Viero et al. 2014) far-IR/submillimeter, and XMM-Newton and Chandra X-ray Observatory X-ray data from the Stripe 82X survey

92 (LaMassa et al. 2013a, LaMassa et al. 2013b, Ananna et al. 2017, the X-ray data cover ∼11.2 deg2). In this region, optical (3500 − 5500Å) spectroscopy is being obtained by the Hobby Eberly Telescope Dark Energy Experiment (HETDEX, Hill et al. 2008), and these data are only used to estimate the accuracy of photometric redshifts, when available (see below). SED fitting is performed using EAZY-py1, a python-based version of EAZY (Brammer et al., 2008), which simultaneously fits for photometric redshift, stellar mass, SFR, and other galaxy properties, with an implementation from Sherman et al. (2020a) and Sherman et al. (2020b) that also gives error estimates for these parameters (finding typical stellar mass and SFR errors of ±0.08 dex and ±0.18 dex, respectively for 1.5 < z < 3.0 galaxies above our estimated mass completeness limits, detailed below). EAZY-py performs SED fitting using twelve Flexible Stellar Population Synthesis (FSPS; Conroy et al. 2009, Conroy & Gunn 2010) templates in non-negative linear combination. Our SED fitting is performed using the default EAZY-py FSPS templates which are built with a Chabrier (2003) initial mass function (IMF), the Kriek & Conroy (2013) dust law, solar metallicity, and star-formation histories including bursty and slowly rising models. We note that recent studies (e.g., Carnall et al. 2019, Leja et al. 2019) have showed the strong influence that the chosen star-formation history has on the resultant SFR given by SED fitting. In our study, the EAZY-py fitting method constructs a best-fit SED from the non-negative linear combination of twelve templates, each with different star-formation histories. Because of this, the resultant best-fit SED is not restricted to a single underlying star-formation history. Additionally, Sherman et al. (2020a) used a diverse set of mock galaxies (V. Acquaviva, private communication) constructed with Bruzual & Charlot 12 (2003) templates and spanning stellar masses up to M? = 10 M to validate the SED fitting procedure described above. These models were constructed from various underlying dust laws, IMFs, and star-formation histories (including exponentially declining, delayed exponential, constant, and linearly increasing). Sherman et al. (2020a) found that for galaxies at 1.5 < z < 3.0, EAZY-py is able to adequately recover the redshift, stellar mass, and SFR for the mock galaxies. Photometric redshift accuracy is estimated using spectroscopic redshifts from SDSS (Eisenstein et al., 2011) at z < 1 and the second internal data release of the HETDEX survey

1The version of EAZY-py used in this work was downloaded in May 2018 from https://github.com/ gbrammer/eazy-py and was later modiﬁed by Sherman et al. (2020a) (also described in Sherman et al. 2020b) to add functions that provide uncertainties on measured galaxy parameters.

93 (Hill et al., 2008) at 1.9 < z < 3.5. For both samples, Sherman et al. (2020b) quantiﬁed

the photometric redshift recovery using the normalized median absolute deviation (σNMAD;

Brammer et al. 2008). Using the low-redshift sample from SDSS σNMAD = 0.053, and for the intermediate redshift galaxies from HETDEX σNMAD = 0.102. This intermediate redshift sample has only 56 galaxies, which are all visually inspected to confirm the spectroscopic redshift from the HETDEX pipeline, and this sample is expected to grow with future data releases. Three of the 56 intermediate redshift galaxies are catastrophic outliers (5.3%) where the HETDEX spectrum places them at (z < 0.5) but the best-fit photometric redshift is z > 2. We note that catastrophic outliers are not removed from the low or high redshift samples before computing σNMAD. Our science sample is the same as that from Sherman et al. (2020b), comprised of 11 54,001 galaxies at 1.5 < z < 3.0, of which, 28,469 are fit to have M? ≥ 10 M . The

95% stellar mass completeness limits for this sample are log(M?/M ) = 10.69, 10.86, and 11.13 in our 1.5 < z < 2.0, 2.0 < z < 2.5, and 2.5 < z < 3.0 bins, respectively. We refer the reader to Sherman et al. (2020b) for details regarding sample selection and mass completeness estimates.

For every galaxy in our Ks-selected sample, we obtain a measure of dust-corrected SFR, with an associated uncertainty, from our SED fitting procedure. The SED fitting procedure uses all available filters to find the best-fitting SED. Unlike the rather straightforward

connection between a galaxy’s Ks-band magnitude and that galaxy’s stellar mass, there is not a straightforward connection between the measured dust-corrected SFR and a particular band. To estimate an SFR completeness, however, we can use the g-band as a proxy for FUV ﬂux (see Sherman et al. 2020b and Florez et al. 2020) and obtain a g-band SFR completeness estimate. To achieve this, we take the 5σ g-band limiting magnitude for our

survey (mg,lim = 24.8 mag AB; computed by Wold et al. 2019) and, following Sherman et al. (2020b) and Florez et al. (2020), we apply the conversion factor from Hao et al. (2011)

to convert the 5σ g-band limiting magnitude into an estimate of SFRFUV. The Hao et al.

(2011) conversion assumes a Kroupa (2001) IMF, and we reduce the estimated SFRFUV by 0.046 dex to align the results with the Chabrier (2003) IMF used throughout this work. We estimate the g-band based SFR completeness limits to be SFR = 2.36, 4.39, and 7.16 −1 M yr in our 1.5 < z < 2.0, 2.0 < z < 2.5, and 2.5 < z < 3.0 bins, respectively. If we further apply a dust correction based on the median extinction measured by our SED ﬁtting procedure for galaxies within ±0.1 mag of the 5σ g-band completeness limit (this

94 value is ∼ 0.8 − 1.0Av across our three redshift bins), we find that the dust-corrected g-band −1 SFR completeness limits are SFR = 4.80, 8.89, and 17.56 M yr in our 1.5 < z < 2.0, 2.0 < z < 2.5, and 2.5 < z < 3.0 bins, respectively. Again, we emphasize that because our sample is Ks selected, not g-band selected, for every object in our science sample we have a measurement, from SED fitting, of the dust-corrected SFR with an associated uncertainty. This holds true even for those with SFR measured by our SED fitting procedure to be below the 5σ g-band based SFR completeness limit estimates.

4.3 Galaxy Main Sequence

In this Section we present the main sequence for all galaxies, which is computed in individual small mass bins at the high mass end, thereby eliminating the need for extrapolation or assumed functional forms. We also detail a novel method for isolating the star-forming galaxy population in an unbiased way, and we use this sample to explore the main sequence for star-forming galaxies. Finally we compare the main sequence for all galaxies with the main sequence for star-forming galaxies, and detail how the buildup of the collective green valley and quiescent galaxy populations inﬂuences the time evolution of the slope of the main sequences for all galaxies and star-forming galaxies.

4.3.1 Measuring the Main Sequence for All Galaxies

The main sequence in each of our three redshift bins spanning 1.5 < z < 3.0 is defined to be the average SFR in small mass bins in the SFR-M? plane. To compute the error on the main sequence, we employ a bootstrap resampling procedure (Sherman et al. 2020b, Florez et al. 2020) that is repeated 1000 times. During each bootstrap draw we select a random sample of galaxies from each mass bin, with replacement, where the sample size is equal to the number of galaxies in the bin. By taking the average SFR in each of the 1000 draws, we generate a distribution of average SFR (main sequence) values. The lower and upper error bars on the main sequence are the 16th and 84th percentiles of this distribution, respectively. 11 12 We find that at the high mass end (M? = 10 to 10 M ), the main sequence for all galaxies is flattened (Figure 4.1; compared to the often assumed slope of unity; e.g., Wuyts et al. 2011), and this flattening becomes more pronounced as redshift decreases toward z = 1.5. Although we do not assume any functional form of the main sequence,

95 1.5 < z < 2.0 N11 = 8480 2.0 < z < 2.5 N11 = 15401 2.5 < z < 3.0 N11 = 4588 4

3 ] r y

/ 2 M

[ 1

) R

F 0 S (

g 1 o l 2 100 101 100 101 102 100 101 102 3

10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure 4.1: The SFR-M? relation (2D histogram) and main sequence (pink circles) for all galaxies in our sample. The main sequence is the average SFR in individual mass bins, while errors on the main sequence are computed using the bootstrap resampling procedure described in Section 4.3.1. The main sequence for all galaxies shows a ﬂattening at the 11 12 highest masses (M? = 10 to 10 M ), and this ﬂattening becomes more prominent as time progresses towards z = 1.5. Colorbars show the number of galaxies in each cell of the 2D histogram, and gray shaded regions represent masses below our 95% completeness limit. 11 We emphasize that the results presented in this work focus on the mass range M? = 10 to 12 12 10 M , and that results above M? = 10 M (vertical dashed gray line) are unlikely to be robust. Insets on the upper right of each panel show the total number (N11) of galaxies in 11 our sample with M? ≥ 10 M .

11 using an ordinary least squares regression (ﬁt to main sequence values between M? = 10 12 to 10 M ), we can determine that the power law slope of the main sequence evolves from 0.30 ± 0.0005 at 2.5 < z < 3.0, to 0.24 ± 0.0008 at 2.0 < z < 2.5, and ﬁnally to −0.02 ± 0.0004 at 1.5 < z < 2.0. Further exploration of the implication of the shape of the main sequence for all galaxies will be discussed in Sections 4.3.3 and 4.7.

4.3.2 Isolating Star-Forming Galaxies and Measuring the Main Se- quence for Star-Forming Galaxies

To compute the star-forming galaxy main sequence, we ﬁrst need to isolate the star- forming galaxy population from the collective green valley and quiescent population (see Figure 4.1). To do this, we require a method that both utilizes the quantities of interest

96 in this study (stellar mass and star-formation rate) and does not place artiﬁcial limits on the width or scatter around the star-forming galaxy main sequence, as that would limit our ability to study the scatter around this relation later in this work (see Section 4.4). Sherman et al. (2020b) used three methods to separate the star-forming and quiescent

galaxy populations: a fixed specific star-formation rate (sSFR; sSFR = SFR/M?) threshold, a fixed distance below the main sequence, and UVJ color-color selection. All three methods give quiescent fractions as a function of mass that are consistent within a factor of two. The fixed sSFR and distance below the main sequence methods both place artificial limits on the scatter around the main sequence by using a fixed threshold separating star-forming and quiescent galaxies. In Sherman et al. (2020b) the sSFR threshold was set to be sSFR = 10−11yr−1 for all mass bins in our three redshift bins spanning 1.5 < z < 3.0. Using the distance from the main sequence method, Sherman et al. (2020b) computed the main sequence in the same way as described here and considered all galaxies lying 1 dex or more below the main sequence to be quiescent. This method was an improvement over the fixed sSFR threshold because the threshold varied with stellar mass and redshift bin, however it still set an artificial limit of 1dex on the scatter around the star-forming galaxy main sequence. Alternatively, the UVJ color-color method seeks to separate galaxies into star-forming and quiescent populations by using their position in color-color parameter space. These populations were initially interpreted using evolutionary tracks (e.g., Labbé et al. 2005, Wuyts et al. 2007), and a boundary was later placed between them using the empirically-based locations of the two populations (e.g., Williams et al. 2009, Muzzin et al. 2013). Although this method is a common way to separate star-forming and quiescent galaxies (e.g., Whitaker et al. 2014, Tomczak et al. 2016) it relies heavily on where the boundary between star-forming and quiescent galaxies is drawn and how rest-frame U, V, and J fluxes are estimated during the SED fitting procedure. An unbiased, meaningful way of isolating the star-forming galaxy population would be to employ the information provided by the SFR-M? plane itself. Our large sample size allows us to make this separation by locating the transition between star-forming galaxies and galaxies in the green valley (e.g., Martin et al. 2007, Salim et al. 2007, Wyder et al. 2007) in individual small mass bins. In this work, we consider green valley galaxies to be those lying in the region of the SFR-M? plane below the star-forming galaxy population and above the quenched galaxy population. We note that while some works select green valley galaxies in color space, we exclusively refer to this population as it relates to their location

97 in the SFR-M? plane. Previous works with significantly smaller samples than ours have studied the green valley population by separating transitional green valley galaxies from star-forming and quiescent populations in the SFR-M? plane. Pandya et al. (2017) made this separation at z = 0 − 3 by first finding the main sequence (where the normalization is determined using 9 9.5 the M? = 10 − 10 M population and the slope is assumed to be unity), then defining a region from 0.6 − 1.4 dex below the main sequence which contained the green valley population. Jian et al. (2020) first found the median relationships for all star-forming and quiescent galaxies (where the former is simply the star-forming main sequence and the latter is a linear fit to the quiescent galaxy sample, where these populations are found using an iterative approach) and defined the center of the green valley to be the average of these linear fits for a sample of galaxies at z = 0.2 − 1.1. They then adopted a fixed width for the green valley to define their transition galaxy population, and the upper limit of this region served as a fixed lower limit for the star-forming population. Both the methods from Pandya et al. (2017) and Jian et al. (2020) place artificial limits on the width of the star-forming

galaxy population in the SFR-M? plane, the same limitation encountered in Sherman et al. (2020b). A different, yet similarly limiting approach, is taken by Janowiecki et al. (2020) who define the star-forming population at z = 0.01 − 0.05 by fitting un-constrained Gaussians to the sSFR distributions of galaxies in small mass bins. This is first done at low masses where galaxies are predominantly star-forming, then the modes of these Gaussians are extrapolated to higher masses to define the main sequence around which one-sided Gaussians with fixed modes are then fit to galaxies with sSFR greater than the mode. The star-forming population is defined to be the Gaussian distribution of galaxies around the star-forming main sequence (extrapolated modes), and they define green valley galaxies to be those 1σ below the ridge of the main sequence. Because the width of the best-fitting Gaussian in a given mass bin is determined solely from fitting a one-sided Gaussian to galaxies lying above the extrapolated mean sSFR, the lower bound of the star-forming population is reliant on the distribution of highly star-forming galaxies and the underlying assumption that star-forming galaxies adhere to a Gaussian distribution in the SFR-M? plane. In this work, we avoid biasing the scatter around the star-forming galaxy main sequence and use the values of interest (stellar mass and star-formation rate) to isolate the star- forming galaxy population, by employing a method that locates the transition between

98 4 1

Figure 4.2: An example schematic of our method used to locate the transition between the star-forming and green valley galaxy populations. The labeled steps are as follows and they correspond to the same numbered steps in Section 4.3.2. Step 1: For all galaxies in a given 11 mass bin (in this example, the M? = 10 M bin for 1.5 < z < 2.0 galaxies) construct a histogram of specific star-formation rate values. Step 2: Interpolate the shape of this histogram using a univariate spline. Step 3: Find the local maximum at log(sSFR)> −10.2 as a rough estimate of the ridge of the main sequence. Step 4: Step bin-by-bin from higher to lower sSFR. Step 5: Stop bin-by-bin stepping when the interpolated spline goes from decreasing to increasing, and define this local minimum as the transition between the star-forming and green valley populations. We remind the reader that for every galaxy in our sample, we obtain a measure of dust-corrected SFR from our SED fitting procedure. The inset figure shows the SFR-M? plane in the 1.5 < z < 2.0 bin with the main sequence for all galaxies shown in pink and the dividing line (green with black outline) between the star-forming and green valley populations determined using the procedure described here and in Section 4.3.2. The results of implementing this procedure to isolate the star-forming population in all three redshift bins can be seen in Figure 4.4. In the inset figure, the gray shaded region represents masses below our 95% completeness limit, and the vertical dashed 12 gray line represents M? = 10 M , above which our results are unlikely to be robust.

99 the star-forming galaxy population and galaxies lying in the green valley. We locate this transition in each of our small mass bins (mass bins have 0.25 dex width) within our three redshift bins spanning 1.5 < z < 3.0 in order to isolate the star-forming galaxy population without using ﬁxed cutoﬀs. We are uniquely suited to take this approach because each of our small mass bins contains enough high mass galaxies to robustly locate the transition between the star-forming and green valley populations.

We note that the local minima seen in the SFR-M? plane (see Figure 4.1) are physically motivated, and they are not products of our SED fitting procedure. Our SED fitting method determines the best-fitting SED for each galaxy by combining a set of twelve SED templates in non-negative linear combination. There are no constraints placed on the contribution of each template, aside from requiring that the templates either provide a positive contribution or zero contribution to the final best-fitting SED. Therefore, since galaxies are fit to be in the transition regions between populations, these regions of parameter space are accessible to these template combinations. If galaxies are not fit to be in the transition regions between populations it is because those regions did not provide the best-fitting SED, not because those regions are inaccessible to the template SEDs. Locating the transition between the star-forming and green valley populations is a five step process (see Figure 4.2 for a schematic). First, in each of our small mass bins we construct a histogram of the sSFR of all galaxies in that bin. These histograms are binned using the Freedman-Diaconis Estimator (Freedman & Diaconis, 1981), which optimizes bin size based on sample size while being robust to outliers. This allows the bin size for each sSFR histogram in small mass bins to vary based on the number of galaxies in that small mass bin. Second, we interpolate over this histogram using a univariate spline with degree three (a cubic spline). This smoothed interpolation is robust to small amounts of bin-to-bin noise, and allows us to define the shape of the sSFR histogram in each small stellar mass bin. We note that the spline interpolation is based on the left edges of the sSFR histogram bins because we want all galaxies placed in an sSFR bin to have the same designation as star forming or green valley. If we were to place the separation between the star-forming and green valley populations at an sSFR in the center of an sSFR bin, then the galaxies in that bin would be placed into two separate categories. Third, we estimate the location of the ridge of the main sequence by finding the local maximum at log(sSFR)> −10.2, and fourth we step along our interpolated distribution from high to low sSFR values until the number of galaxies switches from decreasing to increasing. This switch occurs at the local

100 minimum between the star-forming population and the green valley population, and finally (step five), we define this local minimum to be the transition between star-forming galaxies and the collective green valley and quiescent galaxy population in each of our small mass bins. We note that the procedure described above is only implemented when there are more than 100 galaxies in a small mass bin and the transition between the star-forming and green valley populations can be clearly defined. This required number of galaxies was determined through trial and error. We found that when there were fewer than 100 galaxies in a given mass bin, the sSFR histogram was too sparsely populated to reliably locate the transition between star-forming and green valley galaxies, if any exists. In that case, the threshold between star-forming and quiescent galaxies was set to sSFR = 10−11yr−1. This only impacts mass bins well below our completeness limit or at the extreme high-mass end 12 11 12 (M? > 10 M ), and, because this work focuses on the mass range M? = 10 to 10 M , this requirement of 100 galaxies in a small mass bin does not impact our results. A potential source of uncertainty in isolating star-forming galaxies with this method arises from measurement uncertainty. Our method relies on accurately identifying the first inflection point leftward of the main sequence in the sSFR histogram in a given mass bin. If the true sSFR value for a galaxy is slightly different than the sSFR measured from our SED fitting procedure, the true inflection point in the sSFR histogram may be different than the one we measure. To investigate the impact of this type of uncertainty, we implement a procedure in which we draw a new sSFR (and associated stellar mass) for every galaxy in our science catalog using its parameter measurement errors given by our SED fitting procedure (see Sherman et al. 2020a for details of this error measurement). We then repeat the above procedure to re-compute the location of the inflection point in the sSFR histogram in each mass bin. This procedure is performed 1000 times, thereby giving 1000 values, in each mass bin, of the local minimum between the star-forming and green valley populations. We are then able to investigate how different inflection point locations impact our measurements of the main sequence for star-forming galaxies and the scatter around that relation. Through this procedure we find that the typical draw gives an sSFR inflection point within a factor of 11 12 ∼ 2 of our best-fit measurement for M? = 10 to 10 M . Because there are relatively few galaxies around the local minimum between the star-forming and green valley populations, we find that our measured main sequence for star-forming galaxies and the scatter around that relation are robust (within factors of ∼ 1.3 and ∼ 2, respectively) to small changes in

101 the value for the local minimum in the sSFR histogram. Although we allow galaxies to move between mass bins during this test, we note that our best-fit measurements of the (star- forming) galaxy main sequence and scatter around the star-forming galaxy main sequence, which are presented throughout this work, do not account for scatter between mass bins (we remind the reader that typical stellar mass errors are ±0.08 dex for 1.5 < z < 3.0 galaxies above our estimated mass completeness limits, which is significantly smaller than our 0.25 dex bin size). To confirm that our method separating star-forming galaxies from the collective population of green valley and quiescent galaxies is consistent with other methods of isolating star-forming galaxies, we compare our collective fraction of green valley and quiescent galaxies to the fractions determined by Sherman et al. (2020b), who used three methods (sSFR-selected, main sequence - 1 dex selected, and UVJ-selected quiescent fractions; Fig- ure 4.3). The agreement is strongest with the quiescent fraction computed using the main sequence - 1 dex method. This is expected as this method was most effective at separating star-forming galaxies from the collective green valley and quiescent galaxy populations in Sherman et al. (2020b). The method implemented in this work is an improvement over the main sequence - 1 dex method as it does not place an arbitrary distance below the main sequence as a criterion for isolating star-forming galaxies. With a population of star-forming galaxies identified, we are able to compute the star- forming galaxy main sequence (Figure 4.4), which is the average SFR in each mass bin, with error bars computed using the bootstrap resampling procedure described in Section 4.3.1. The star-forming galaxy main sequence does not show a significant flattening at the high 11 12 mass end (M? = 10 to 10 M ). Its power law slope, computed using an ordinary least 11 squares fit to the star-forming galaxy main sequence values over the mass range M? = 10 12 to 10 M , evolves mildly from 0.47 ± 0.0011 at 2.5 < z < 3.0, to 0.46 ± 0.0001 at 2.0 < z < 2.5 , and finally to 0.35 ± 0.0013 at 1.5 < z < 2.0.

4.3.3 Implications of the Growing Green Valley and Quiescent Popu- lations

As is seen in Figure 4.1, our large sample of galaxies in the SFR-M? plane shows three distinct populations of galaxies: star-forming, green valley, and quiescent. In Section 4.3.2 we described a novel method for using the transitions between these populations to

102 log(M /M ) 10.0 10.5 11.0 11.5 12.0 12.5 1.0 1.5 < z < 2.0 sSFR N = 8480 0.8 11 UVJ 0.6 MS - 1 dex 0.4 GV Trans.

Fraction 0.2

Quiescent 0.0 1.0 2.0 < z < 2.5 0.8 N11 = 15401 0.6 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.5 < z < 3.0 0.8 N11 = 4588 0.6 0.4

Fraction 0.2

Quiescent 0.0 10.0 10.5 11.0 11.5 12.0 12.5 log(M /M )

Figure 4.3: The quiescent fraction as a function of stellar mass determined using the transition between star-forming and green valley galaxies to separate star-forming systems from the collective green valley and quiescent populations (green triangles). Also plotted are the results from Sherman et al. (2020b) who determined the quiescent fraction in three ways: sSFR-selected (pink circles), main sequence - 1 dex selected (gold pentagons), and UVJ-selected (purple squares). The four measurements of the quiescent fraction give consistent results across our three redshift bins spanning 1.5 < z < 3.0. Gray shaded regions represent masses below our 95% completeness limit. Error bars represent Poisson errors. We emphasize that the results presented in this work focus on the mass range 11 12 12 M? = 10 to 10 M , and that results above M? = 10 M (vertical dashed gray line) are unlikely to be robust. Insets on the upper left of each panel show the total number (N11) of 11 galaxies in our sample with M? ≥ 10 M .

103 4 1.5 < z < 2.0 N11 = 3264 2.0 < z < 2.5 N11 = 10649 2.5 < z < 3.0 N11 = 3465 ] r

y 3 /

M 2 [

)

R 1 F S (

g 0 o l 100 101 100 101 102 100 101 1

10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure 4.4: The SFR-M? relation (2D histogram) and main sequence (pink circles) for star- forming galaxies in our sample. Star-forming galaxies are selected by locating the transition between star-forming and green valley populations, then removing galaxies below this transition, as is described in Section 4.3.2. The star-forming main sequence is the average SFR in individual mass bins, while errors on the star-forming main sequence are computed using the bootstrap resampling procedure described in Section 4.3.1. Unlike the main sequence for all galaxies, the star-forming galaxy main sequence does not show a strong evolution in the high mass end slope from z = 3.0 to z = 1.5. Colorbars show the number of galaxies in each cell of the 2D histogram, and gray shaded regions represent masses below our 95% completeness limit. We emphasize that the results presented in this work focus 11 12 12 on the mass range M? = 10 to 10 M , and that results above M? = 10 M (vertical dashed gray line) are unlikely to be robust. Insets on the upper right of each panel show the 11 number (N11) of star-forming galaxies in our sample with M? ≥ 10 M .

104 isolate the star-forming galaxy population. This procedure can also be used to find the local minimum in sSFR space between the green valley and quiescent populations. To locate this transition, we employ a version of the five step procedure described in Section 4.3.2, with a small modification to step three. Here, we (1) construct an sSFR histogram in each mass bin, (2) interpolate using a smoothed cubic spline, (3) find the local maximum of the green valley population (local maximum between log(sSFR)> −12.0 and the sSFR at which the local minimum occurs between the green valley and star-forming populations, as determined in Section 4.3.2), (4) step bin-by bin from high to low sSFR, and finally (5) stop stepping when a local minimum in the spline is found. This local minimum is the transition between the green valley and quiescent populations (Figure 4.5). In Figure 4.5, we show that the sSFR distributions in individual mass bins can provide more information about the buildup of the collective green valley and quiescent populations as time progresses and that higher mass bins have larger collective populations of quiescent and green valley galaxies than star-forming galaxies. This result is consistent with measures of the quiescent fraction from Sherman et al. (2020b), who showed that at these redshifts and stellar masses, the quiescent fraction increases from z = 3.0 to z = 1.5 at the highest 12 masses and that higher mass galaxies (M? = 10 M ) at a given redshift have a larger 11 quiescent fraction than lower mass systems (M? = 10 M ). The method used in this work to isolate star-forming galaxies by locating the transition between star-forming and green valley galaxies is an improvement over the main sequence - 1 dex technique used by Sherman et al. (2020b) as it more meaningfully isolates star-forming galaxies from the collective green valley and quiescent population without employing an ad hoc threshold below the main sequence. Our empirical main sequences measured for all galaxies (see Section 4.3.1) and star- forming galaxies (see Section 4.3.2) are compared in Figure 4.6. In our two highest redshift 11 bins (2.0 < z < 2.5 and 2.5 < z < 3.0), where only ∼ 20−40% of massive (M? ≥ 10 M ) galaxies are members of the collective green valley and quiescent population (Figure 4.3), the total galaxy main sequence is higher than the star-forming galaxy main sequence by up to a factor of 1.5. At lower redshifts (1.5 < z < 2.0) where the collective green valley and quiescent population are ∼ 40 − 70% of the total massive galaxy population (Figure 4.3), the star-forming galaxy main sequence is a factor of 1.5 − 3 higher than the main sequence for the total galaxy population. The significant buildup of the collective green valley and quiescent galaxy populations as a function of redshift and stellar mass leads to the flattening

105 700 1.5 < z < 2.0 700 2.0 < z < 2.5 2.5 < z < 3.0 Bin: log(M /M ) = 11.2 Bin: log(M /M ) = 11.2 175 Bin: log(M /M ) = 11.2 600 600 150 500 500 125 400 400 100

300 300 Number Number Number 75

200 200 50

100 100 25

0 0 0 13 12 11 10 9 8 13 12 11 10 9 8 13 12 11 10 9 8 log(sSFR) [M /yr] log(sSFR) [M /yr] log(sSFR) [M /yr]

1.5 < z < 2.0 2.0 < z < 2.5 2.5 < z < 3.0 Bin: log(M /M ) = 11.7 Bin: log(M /M ) = 11.7 200 Bin: log(M /M ) = 11.7 250 400 175

200 150 300 125 150 200 100 Number Number Number 100 75

100 50 50 25

0 0 0 13 12 11 10 9 8 13 12 11 10 9 8 13 12 11 10 9 8 log(sSFR) [M /yr] log(sSFR) [M /yr] log(sSFR) [M /yr]

Figure 4.5: Speciﬁc star-formation rate distributions for individual mass bins in the SFR-M? plane (purple histograms), with the splines used to interpolate these distributions (solid pink lines). The three vertical columns of panels are for each of our three redshift bins spanning z = 1.5 to z = 3.0. The top row shows the log(M?/M ) = 11.2 bin, and the bottom row shows the log(M?/M ) = 11.7 bin. In each panel, star-forming galaxies fall to the right of the vertical dashed green line, green valley galaxies are between the vertical dashed green line and the vertical dash-dot pink line, and quiescent galaxies lie to the left of the vertical dash-dot pink line. The procedure used to identify the location of the transition between star-forming and green valley galaxies and transition between green valley and quiescent galaxies are described in Sections 4.3.2 and 4.3.3, respectively. As we move from higher to lower redshift, the buildup of the populations of green valley and quiescent galaxies becomes prominent. We again note that our SED ﬁtting procedure provides a measure of dust-corrected SFR for every galaxy in our Ks-selected sample.

106 3 1.5 < z < 2.0 ] r y

/ 2 M [ log(SFR) 1

3 2.0 < z < 2.5 ] r y

/ 2 M [ log(SFR) 1

3 2.5 < z < 3.0 ] r y

/ 2

M All [ log(SFR) 1 Star-Forming

9.5 10.0 10.5 11.0 11.5 12.0 12.5 log(M /M )

Figure 4.6: The main sequence for all galaxies (pink circles) and star-forming galaxies (purple squares) in our sample. Star-forming galaxies are selected by locating the transition between star-forming and green valley populations, then removing galaxies below this transition, as is described in Section 4.3.2. The (star-forming) main sequence is the average SFR in individual mass bins, while errors on the (star-forming) main sequence are computed using the bootstrap resampling procedure described in Section 4.3.1. We note that error bars are included, however they are often smaller than the symbol. At early epochs (z > 2) the star-forming galaxy main sequence is up to a factor of 1.5 higher than the main sequence for all galaxies, and at later epochs (1.5 < z < 2.0), the star-forming galaxy main sequence is a factor of 1.5−3 higher than the main sequence for all galaxies. Gray shaded regions represent masses below our 95% completeness limit. We emphasize that the results presented in this 11 12 12 work focus on the mass range M? = 10 to 10 M , and that results above M? = 10 M (vertical dashed gray line) are unlikely to be robust. of the massive end slope of the main sequence for all galaxies as time progresses from z = 3.0 to z = 1.5. Our sample, which is used to study both the main sequence for all galaxies and star- 12 forming galaxies contains galaxies with M? > 10 M , particularly in the 2.0 < z < 2.5 and 2.5 < z < 3.0 bins where the comoving volume observed by our study is larger. For this extreme high-mass population, we see main sequence relations with steeper slopes 12 11 12 at M? > 10 M than are seen at stellar masses M? = 10 to 10 M . Individual 12 mass bins above M? = 10 M have fewer than 100 galaxies, making robust studies of this population challenging. Sherman et al. (2020b) also showed that the impact of uncertainties

107 in photometric redshifts and Eddington bias on results for this extreme population is likely to be large (see Sherman et al. 2020b and their Appendix Figure A1) and that some of this population may be low-redshift interlopers. In this work, we focus on galaxies 11 12 in the mass range M? = 10 to 10 M , and note that high-resolution imaging and spectroscopic followup of these extreme high-mass objects is necessary to better understand

their properties and behavior in the SFR-M? plane.

4.4 Scatter Around the Star-Forming Galaxy Main Sequence

In the absence of stochastic processes (e.g., mergers, gas accretion from the cosmic web, stellar and AGN feedback), the relationship between stellar mass and star-formation rate for star-forming galaxies should be relatively tight, with scatter around that relationship due only to measurement uncertainty (e.g., Caplar & Tacchella 2019, Matthee & Schaye 2019). Therefore, measures of the scatter around the star-forming galaxy main sequence provide insights into the importance of stochastic processes in driving galaxy evolution. Sherman et al. (2020b) outlined how different stochastic processes could play a key role in driving the evolution of the massive galaxy population, where mergers are likely drivers of early mass buildup and environmental processes (e.g., ram pressure stripping, tidal stripping, harassment) are likely to suppress star-formation at z < 2, when emerging clusters develop their intracluster medium (ICM). We measure the total scatter around the star-forming galaxy main sequence (Figure 4.7) without assuming either a functional form of the main sequence or a fixed criterion for isolating star-forming galaxies. This is a significant improvement over previous studies where the selection of the star-forming galaxy population was biased and measures of the

scatter often assumed an underlying distribution of galaxies in the SFR-M? plane (such as a Gaussian; see Section 4.5.2 for further comparison with previous empirical results). As is described in Section 4.3.2, our star-forming galaxy population is selected by locating the transition between the star-forming and green valley populations in small mass bins, and the star-forming galaxy main sequence is the average SFR of the star-forming galaxy population in each mass bin. This approach is made possible by our large sample of 28,469 11 massive (M? ≥ 10 M ) galaxies spanning 1.5 < z < 3.0. The total scatter around the star-forming galaxy main sequence measured in each of our small mass bins is simply the diﬀerence between the 84th and 16th percentile of the

108 distribution of SFR values for star-forming galaxies in each mass bin. We also compute the upper scatter (difference between 84th percentile of SFR and the star-forming galaxy main sequence value in a given mass bin) and lower scatter (difference between the star-forming galaxy main sequence value and 16th percentile of SFR in a given mass bin) to provide a closer comparison with previous works. Additionally, we can approximate the intrinsic scatter around the star-forming galaxy main sequence by accounting for the ±0.18 dex measurement uncertainty in SFR from our SED fitting procedure. Our SFR error estimates are determined by drawing 100 SEDs from the best-fit SED’s template error distribution (see Sherman et al. (2020a) for a detailed description of this procedure), and therefore, this error estimate takes into account uncertainties in other fundamental measurements, such as extinction. We do not find that the measurement uncertainty in SFR varies as a function of stellar mass, indicating that removing the scatter due to measurement uncertainty will not change the trends (or lack thereof) observed in the total, upper, and lower scatter as a function of mass and redshift. We measure the total observed scatter to be ∼ 0.5 − 1.0 dex (corresponding to ∼ 0.47 − 0.98 dex intrinsic scatter) and we find that the total observed scatter increases from 11 12 low to high masses (M? = 10 to 10 M ) by less than a factor of three in each of our three redshift bins. The scatter does not show significant evolution as a function of redshift across our three redshift bins spanning 1.5 < z < 3.0. In each of our redshift bins, the observed upward scatter is fairly constant as a function of mass and redshift, with a value of ∼ 0.3 dex (corresponding to ∼ 0.24 dex intrinsic scatter), consistent with values for the observed scatter found by previous studies (see Section 4.5.2). The lower scatter around the main sequence is larger than the upper scatter in all redshift bins. Our result shows that the often assumed symmetrical Gaussian distribution of star- forming galaxies around the star-forming galaxy main sequence does not hold true at these 11 redshifts (1.5 < z < 3.0) for massive (M? ≥ 10 M ) galaxies.

109 4 1.5 < z < 2.0 N11 = 3264 2.0 < z < 2.5 N11 = 10649 2.5 < z < 3.0 N11 = 3465 ] r

y 3 /

M 2 [

)

R 1 F S (

g 0 o l 100 101 100 101 102 100 101 1

2.0 Total Scatter [log(SFR84) - log(SFR16)] Upper Scatter [log(SFR84) - log(SFRMS)]

1.5 Lower Scatter [log(SFRMS) - log(SFR16)] 1.0 0.5

Scatter [dex] 0.0 10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure 4.7: Top Row: The total scatter (blue shaded region) around the star-forming galaxy main sequence (pink) overlaid on the distribution of star-forming galaxies (2D histogram; colorbar indicates the number of galaxies in each 2D bin) in the SFR-M? plane. The upper (lower) bound of the blue shaded region is the 84th (16th) percentile of the SFR distribution in a given mass bin. Insets on the upper right of each panel in the top row show the 11 number (N11) of galaxies in the star-forming population in our sample with M? ≥ 10 M . Bottom Row: The total (squares), upper (circles), and lower (pentagons) observed scatter around the star-forming galaxy main sequence. The total scatter shows a modest increase 11 12 with increasing stellar mass (less than a factor of three from M? = 10 to 10 M in each redshift bin), and the total scatter is fairly constant across our three redshift bins from z = 1.5 to z = 3.0. In every redshift bin, the lower scatter is larger than the upper scatter by up to a factor of 3. Gray shaded regions represent masses below our 95% completeness limit. 11 We emphasize that the results presented in this work focus on the mass range M? = 10 to 12 12 10 M , and that results above M? = 10 M (vertical dashed gray line) are unlikely to be robust.

110 4.5 Comparison With Previous Observations

4.5.1 Comparison of the Main Sequence for All Galaxies and Star- Forming Galaxies with Previous Observations

Since the first work referencing the galaxy main sequence by Noeske et al. (2007), many works have implemented different methods of measuring the main sequence for all galaxies and isolating star-forming galaxies to measure the star-forming galaxy main sequence. Rapid innovation in galaxy surveys over the past decade has produced a number of new methods, however this makes true one-to-one comparisons with previous works difficult. In this work we have leveraged our sample of massive galaxies, the largest uniformly selected set compiled to date, to measure the galaxy main sequence for the total population and star-forming galaxies in small mass bins at the high mass end. A significant benefit of our large sample is that we do not need to adopt a functional form of the main sequence, and we can isolate star-forming galaxies in a meaningful way without prior assumptions. Moreover, the large area probed by our study also renders errors due to cosmic variance negligible. The two works we compare with (Whitaker et al. 2014 and Tomczak et al. 2016) present the main sequence for both the total galaxy population and star-forming galaxy population. The study from Whitaker et al. (2014) focused on the low-mass end of the main sequence using galaxies in the CANDELS/3D-HST fields. Their main sequence values in individual mass bins were computed using stacked UV + IR luminosities (with LIR from Spitzer-MIPS 24µm photometry and assuming a Chabrier (2003) IMF), and they separated star-forming and quiescent galaxies using UVJ colors. Their work finds that the main sequence is best characterized by a broken power law fit, however for comparison with our empirical result (Figure 4.8), we utilize their average stacked SFR values in each stellar mass bin rather than the functional fit to those data. We find that the main sequence for all galaxies and star-forming galaxies from Whitaker et al. (2014) are factors of 1.5 − 4.5 and 1.7 − 3 higher than our empirical main sequences for all galaxies and star-forming galaxies, respectively 11 12 at 1.5 < z < 2.5 for M? = 10 to 10 M . The study from Whitaker et al. (2014) does not investigate the main sequence in our highest redshift bin (2.5 < z < 3.0). Tomczak et al. (2016) performed a similar study to that from Whitaker et al. (2014),

using a stacking analysis of UV + IR luminosities (also with LIR from Spitzer-MIPS 24µm photometry and using a Chabrier (2003) IMF) to derive the average SFR (main sequence

111 values) in small mass bins for galaxies in ZFOURGE. Similar to Whitaker et al. (2014), Tomczak et al. (2016) separated star-forming and quiescent galaxies using UVJ color. When comparing with our empirical result, we find that the results from Tomczak et al. (2016) are in general agreement, within a factor of ∼ 1.5, with our main sequence for all galaxies 11 and star-forming galaxies in our three redshift bins spanning 1.5 < z < 3.0 for M? = 10 12 to 10 M . We note that in the 2.5 < z < 3.0 bin, the highest masses probed by Tomczak et al. (2016) only reach our mass completeness limit. Therefore, comparisons between our empirical result and that from Tomczak et al. (2016) in the 2.5 < z < 3.0 bin are not informative. There are several important caveats to the comparisons presented above that must be noted. First, these studies both utilize data from similar legacy fields, often the same fields with updated photometry, spectroscopy, or different modeling techniques. The CANDELS/3D-HST fields (∼ 900 arcmin2) used by Whitaker et al. (2014) include AEGIS, COSMOS, GOODS-N, GOODS-S, and UDS. The ZFOURGE fields (∼ 400 arcmin2) used by Tomczak et al. (2016) include CDF-S, COSMOS, and UDS. Second, these legacy fields, while rich in spectroscopy and multi-wavelength photometry allowing for strongly constrained SEDs, are small area studies with small samples of galaxies at the highest masses. Across the three redshift bins spanning 1.5 < z < 3.0, the study from Tomczak et al. (2016) 11 has 81 M? ≥ 10 M galaxies in their total galaxy population. The publicly available CANDELS/3D-HST catalog (Brammer et al. 2012, Skelton et al. 2014) used by Whitaker 11 et al. (2014) has 533 M? ≥ 10 M total galaxies spanning 1.5 < z < 2.5, however Whitaker et al. (2014) may have only used a sub sample of these objects. Third, the small areas probed by these studies may be strongly impacted by the effects of cosmic variance. 11 For M? ≥ 10 M the cosmic variance is ∼ 50 − 70% for studies of this size (Moster et al., 2 11 2011). For comparison, our 17.5 deg study has 28,469 M? ≥ 10 M galaxies between 1.5 < z < 3.0. This effectively eliminates errors due to cosmic variance. Finally, the stacked 24µm-based SFR values used by Whitaker et al. (2014) and Tomczak et al. (2016) may be systematically different from our rest-frame UV-based SFR values determined for individual galaxies through SED fitting.

112 4 1.5 < z < 2.0 N11 = 8480 2.0 < z < 2.5 N11 = 15401 2.5 < z < 3.0 N11 = 4588

] All Galaxies All Galaxies All Galaxies r

y 3 / M [

) 2 R F S (

g 1 This Work o

l Whitaker+14 Tomczak+16 0 10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

4 1.5 < z < 2.0 N11 = 3264 2.0 < z < 2.5 N11 = 10649 2.5 < z < 3.0 N11 = 3465

] Star-Forming Galaxies Star-Forming Galaxies Star-Forming Galaxies r

y 3 / M [

) 2 R F S (

g 1 This Work o

l Whitaker+14 Tomczak+16 0 10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure 4.8: Our empirical main sequence for all galaxies (top row) and star-forming galaxies (bottom row) compared with results from previous observations. We ﬁnd similar results to those from Tomczak et al. (2016) for both the total (top row) and star-forming (bottom row) galaxy populations. The results from Whitaker et al. (2014) for both the total (top row) and star-forming (bottom row) galaxy populations are higher than our empirical results by a factor of ∼ 1.5 − 6.5. Gray shaded regions represent masses below our 95% completeness limit. Insets on the upper right of each panel show the number (N11) of galaxies for the total population (top row) and star-forming population (bottom row) in our sample with 11 M? ≥ 10 M . We emphasize that the results presented in this work focus on the mass 11 12 12 range M? = 10 to 10 M , and that results above M? = 10 M (vertical dashed gray line) are unlikely to be robust.

113 4.5.2 Comparison of the Scatter Around the Star-Forming Galaxy Main Sequence with Previous Observations

Using our method of isolating the star-forming galaxy population by locating the transition between the star-forming and green valley populations in the SFR-M? plane, we investigated the scatter around the star-forming galaxy main sequence in Section 4.4. Our result shows that the scatter around the star-forming galaxy main sequence does not evolve significantly either as a function of stellar mass or redshift over the stellar mass range 11 12 M? = 10 to 10 M and redshifts 1.5 < z < 3.0. Our method of isolating star-forming galaxies does not place artificial constraints on the lower boundary of this population, or on the underlying distribution of star-forming galaxies in the SFR-M? plane, and we find that that star-forming galaxies are not normally distributed around the star-forming galaxy main sequence. This is a significant finding as the distribution of star-forming galaxies in the SFR-M? plane is often assumed to be a Gaussian by previous works. Comparisons with previous results for the scatter around the star-forming galaxy main sequence are challenging as a consensus has not been reached by previous works when it comes to measuring the scatter. These measurements are further complicated by the different approaches to separating star-forming galaxies from the total population (e.g. different color indicators or fixed thresholds) and different ways of measuring the main sequence (e.g., stacking analyses, average SFR, median SFR, extrapolation from low to high masses, assumed functional forms). Schreiber et al. (2015) investigated the scatter of galaxies above the main sequence using individual Herschel-detected galaxies in the CANDELS-Herschel fields out to z = 4. They found the scatter above the main sequence to be 0.32 dex with little evolution as a function of mass or redshift. Rodighiero et al. (2011) used a sample of 1.5 < z < 2.5 BzK color-selected star-forming galaxies in COSMOS and found the scatter around the main sequence to be 0.24 dex, assuming a Gaussian distribution of galaxies around the star- forming galaxy main sequence. Popesso et al. (2019) took yet another approach, whereby they used an IR-selected sample of star-forming galaxies in the CANDELS+GOODS fields out to z = 2.5 and only fit for the normalization of the main sequence, adopting the slope from the local relation. They found that the scatter around the star-forming galaxy main sequence increases from ∼ 0.3 dex to ∼ 0.4 dex as a function of mass for 1.5 < z < 2.5 galaxies. Results from these previous studies are broadly consistent with our result, however

114 detailed comparisons are difficult due to the very different methods used. Additionally, as described above, our approach to measuring the scatter around the star-forming galaxy main sequence is a significant improvement over previous works as it does not rely on assumed functional forms of the star-forming galaxy main sequence, ad hoc cutoffs for selecting the star-forming galaxy population, or assuming a Gaussian distribution of star-forming galaxies in the SFR-M? plane.

4.6 Comparison With Theoretical Models

In this work, we have explored the main sequence for all galaxies (Section 4.3.1), used a novel approach to identify the star-forming galaxy population in the SFR-M? plane (Section 4.3.2), and investigated the scatter around the star-forming galaxy main sequence (Section 11 12 4.4) in an unbiased way, with our focus placed on the mass range M? = 10 to 10 M . Theoretical models, such as hydrodynamical simulations and semi-analytic models (SAMs), seek to implement physical processes that drive galaxy evolution and, therefore, insights from theoretical models may allow for interpretation of the physical processes driving observed trends. Large volume empirical studies, such as the study presented in this work, can likewise provide benchmarks for these models. Our comparison will focus on the hydrodynamical models SIMBA (Davé et al., 2019) and IllustrisTNG (Pillepich et al. 2018b, Springel et al. 2018, Nelson et al. 2018, Naiman et al. 2018, Marinacci et al. 2018), as well as the semi-analytic model SAG (Cora et al., 2018). Details about each model can be found in their respective publications, as well as in Sherman et al. (2020b), and the key points will brieﬂy be described here. SIMBA 7 has a 100 Mpc/h box with mass resolution mgas = 1.82 × 10 M and we utilize the total stellar mass and SFR for each galaxy in their group catalog. IllustrisTNG oﬀers several volumes, and we use the largest box that is ∼3003Mpc3 (TNG300) with mass resolution 7 mbaryon = 1.1 × 10 M and masses and SFR measured within twice the stellar half mass radius (the 2 × R1/2 aperture; see Sherman et al. 2020b for a detailed study of aperture types in IllustrisTNG). SAG populates halos in the MultiDark-Planck2 (MDPL2) dark matter-only simulation, and we utilize an updated version of the model (S. Cora, private communication) which has been run on 9.4% of the 1.0 h−1Gpc box available in MDPL2. For SAG, we use total masses and SFR for galaxies in their group catalog. The group catalogs for all three models hard code SFR = 0 when the SFR for an object falls below the resolution limit.

115 To account for this, following Donnari et al. (2019) and Sherman et al. (2020b), we assign −5 −4 −1 these objects a random SFR between SFR = 10 − 10 M yr before performing our analysis. The above models have significantly smaller volumes than our empirical study, leading 11 12 to significantly smaller numbers of galaxies with stellar masses M? = 10 to 10 M . Because of this, we will compare our empirical main sequence for all galaxies with the corresponding relation from the theoretical models, with a focus on galaxies with masses 11 12 spanning the range M? = 10 to 10 M . At this time, a fair and informative comparison cannot be done between our empirical star-forming galaxy main sequence and results from theoretical models, as the theoretical models do not have enough galaxies in small mass 11 12 bins spanning M? = 10 to 10 M across our redshift range of interest (1.5 < z < 3.0) to define the relation or study the scatter around it. The main sequence for all galaxies for each of the three theoretical models is computed in the same way as our empirical main sequence (see Section 4.3.1) We find that in all three of our redshift bins spanning 1.5 < z < 3.0, the hydrodynamical model SIMBA is in fair agreement, within a factor of ∼ 1.5, with our empirical main sequence for all galaxies, but does not show a flattening at the highest masses in the lowest redshift bin (1.5 < z < 2.0). The SAM SAG is up to a factor of ∼ 3 higher than our empirical result and starts to show a flattening slope at the highest masses in the 1.5 < z < 2.0 bin. The hydrodynamical model IllustrisTNG is below our empirical result by up to a factor of ∼ 10 and shows a strong turnover at the highest masses in the 2.0 < z < 3.0 bins, where our empirical result does not show this trend. These results are consistent with those from Sherman et al. (2020b) who showed that SIMBA and SAG under-estimate the fraction of the collective green valley and quiescent galaxy population compared with the star-forming galaxy population at the high-mass end, while the IllustrisTNG model was shown to over-predict the fraction of massive galaxies lying in the collective green valley and quiescent galaxy population. Further exploration of the implication of comparisons with results from theoretical models will be discussed in Section 4.7. We also recognize that a single line (in this case, the main sequence for all galaxies) is not an adequate representation of the full distribution of galaxies in the SFR-M? plane, and we refer the reader to Appendix B.1 for a comparison of our empirical data in the SFR-M? plane and those from the models.

116 ] 1.5 < z < 2.0 2.0 < z < 2.5 2.5 < z < 3.0 r 4 y / 3 M [

) 2 R

F 1 S (

g 0 This Work - All Galaxies SIMBA o

l TNG300 SAG 1 10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure 4.9: Our empirical main sequence for all galaxies compared with results from hydrodynamical models SIMBA and IllustrisTNG and SAM SAG. The main sequence for all galaxies from SIMBA is within a factor of ∼ 1.5 of our empirical result and that from SAG is higher than our empirical result by up to a factor of ∼ 3. SIMBA does not show a ﬂattening at the highest masses by z = 1.5, while SAG begins to show a ﬂattening high-mass slope towards z = 1.5. The main sequence for all galaxies from IllustrisTNG is lower than our empirical result by up to a factor of ∼ 10 and shows a strong turnover at the highest masses at 2.0 < z < 3.0 that is not seen in our empirical result. Gray shaded regions represent masses below our 95% completeness limit. We emphasize that the results 11 12 presented in this work focus on the mass range M? = 10 to 10 M , and that results above 12 M? = 10 M (vertical dashed gray line) are unlikely to be robust.

117 4.7 Discussion

In this work, we presented the main sequence for all galaxies (Section 4.3.1), the main sequence for star-forming galaxies (Section 4.3.2), and an unbiased measurement of the scatter around the star-forming galaxy main sequence (Section 4.4). Our large sample of 11 massive (M? ≥ 10 M ) galaxies has allowed us to separate star-forming galaxies from the green valley and quiescent populations in a natural way without any prior assumptions about the data. With our approach, we are able, for the first time, to present the star-forming galaxy main sequence and measure the scatter about the mean relation without making assumptions about the functional form of the main sequence or the distribution of star-forming galaxies in the SFR-M? plane. The slope of the main sequence for all galaxies at the high-mass end provides important information about the downsizing (Cowie et al., 1996) of the massive galaxy population. 11 Sherman et al. (2020b) showed that the massive (M? ≥ 10 M ) galaxy population becomes increasingly quiescent from z = 3.0 to z = 1.5, and that more massive galaxies (M? ∼ 12 11 10 M ) have a higher quiescent fraction than less massive (M? ∼ 10 M ) systems. The increased flattening of the high-mass end slope of the main sequence for all galaxies as time progresses from z = 3.0 to z = 1.5 traces the downsizing of the massive galaxy population (Figures 4.1 and 4.6). A further investigation of the buildup of the collective green valley and quiescent galaxy populations as a function of stellar mass and redshift can be seen in Figure 4.5, further supporting the downsizing scenario. In contrast to the main sequence for all galaxies, the massive end of the star-forming galaxy main sequence does not demonstrate a strong flattening as time progresses (Figure 4.6). We have measured that the slope of the massive star-forming galaxy main sequence is rather constant across 1.5 < z < 3.0, with the slope (and normalization) only beginning to decrease at 1.5 < z < 2.0. This suggests that, although there is a decrease in the fraction of massive galaxies that are star-forming, those that remain highly star-forming at 1.5 < z < 2.0 have fairly similar specific star-formation rates as massive star-forming galaxies at earlier epochs (2.0 < z < 3.0). Our finding that the total scatter around the star-forming galaxy main sequence remains relatively constant from z = 3.0 to z = 1.5 and as a function of stellar mass at the high-mass 11 12 end (M? = 10 to 10 M ) is in alignment with our result showing that the slope of the star-forming galaxy main sequence does not significantly flatten as time progresses towards z = 1.5. The total scatter around the star-forming galaxy main sequence is thought to trace

118 the stochasticity of processes driving star-forming galaxy evolution (e.g., Caplar & Tacchella 2019, Matthee & Schaye 2019). Additionally, with our unbiased approach to identifying the star-forming galaxy population, we ﬁnd that the distribution of massive star-forming

galaxies in the SFR-M? plane does not follow the often assumed Gaussian distribution. This non-Gaussian distribution around the star-forming galaxy main sequence, which is skewed towards galaxies with lower SFR, suggests that galaxies spend less time in the high SFR phase (above the star-forming galaxy main sequence) than they do in the more moderate SFR phase (below the main sequence). This aligns with studies of the molecular gas content of massive galaxies out to z ∼ 4 using ALMA (e.g., Tacconi et al. 2018, Franco et al. 2020), which showed that massive galaxies lying above the main sequence have shorter gas depletion timescales than those lying below the main sequence. They report that galaxies above the main sequence may deplete their gas supply in ∼ 102 Myr, while star-forming galaxies below the main sequence have depletion times closer to ∼ 103 Myr. A natural inquiry following the results presented in this work is the question of why the local minima appear in the SFR-M? plane between the three populations of interest (star-forming, green valley, and quiescent), and specifically why a peak appears in the green valley. Potential scenarios leading to this green valley peak are complex. Previous works (e.g., Pandya et al. 2017, Janowiecki et al. 2020) have shown that galaxies do not necessarily take a simple one way trip from the star-forming sequence to the quiescent population, and the way in which galaxies move through the SFR-M? plane, and specifically how they arrive in the green valley population, is dependent on several factors such as environment, available cold gas reservoir, and evolutionary history, among others. This is particularly true for massive galaxies which are likely to live in rich environments where environmental effects are common. Just as environmental mechanisms can remove galaxies from the star-forming population (e.g., AGN and stellar feedback, hot-mode accretion, ram-pressure stripping, tidal stripping, harassment; e.g., Man & Belli 2018, Sherman et al. 2020b), events such as mergers and gas accretion can rejuvenate a previously quenched (or partially quenched) galaxy. The peak seen in the green valley region of the SFR-M? plane may arise from the superposition of these massive galaxy populations with diverse evolutionary histories. Additionally, the peak in the green valley suggests that galaxies may spend a non-trivial amount of time in this regime. Pandya et al. (2017) estimate that the upper limit for the time galaxies spend in the green valley is ∼ 1.5 − 2 Gyr for 1.5 < z < 3. We note, how-

119 ever, that their model makes the simplifying, and unlikely, assumption that galaxies move uni-directionally from the star-forming to quiescent population through the green valley. Interestingly, they find that the population of galaxies in the green valley is rather stable, with more galaxies remaining in the population than moving in or out of the population between timesteps. Again, we emphasize that movement of massive galaxies through and within the green valley is complex and likely to be multi-directional. Although our comparisons with theoretical models (hydrodynamical models SIMBA and IllustrisTNG and SAM SAG) are limited to the main sequence for all galaxies due to the small volumes of these models (Section 4.6), we can use comparisons with these models to interpret the trends seen in our empirical result. The shape and slope of the main sequence for all galaxies, computed for the three theoretical models in the same way as is done for our empirical main sequence for all galaxies, provides information about the transition of the massive galaxy population from being predominantly star-forming to predominantly quiescent. We find in our comparison that the models are unable to simultaneously recover the average specific star-formation rates of massive galaxies found in our observed sample and the flattening of the high-mass end slope of the main sequence for all galaxies as time progresses from z = 3.0 to z = 1.5. This result indicates that the models do not adequately represent the observed trends, specifically the buildup of the collective green valley and quiescent populations, seen in our empirical results at these redshifts. Our findings support those from Sherman et al. (2020b) who showed that the SAG and SIMBA models under-estimate the fraction of massive galaxies in the collective green valley and quiescent population, while the IllustrisTNG model over-estimates the fraction of massive galaxies in the collective green valley and quiescent population.

4.8 Summary

11 Using a large sample of 28,469 massive (M? ≥ 10 M ) galaxies that are uniformly selected from data spanning 17.5 deg2, we investigate the nature of the main sequence for all galaxies and for star-forming galaxies. With our large sample, we are uniquely suited to conduct this study without assuming the functional shape of the main sequence or placing prior constraints on the distribution of galaxies in the SFR-M? plane. A summary of our key results is presented below.

1. Our large sample size allows us to compute the main sequence in small stellar mass

120 bins and isolate star-forming galaxies using the quantities of interest (SFR and stellar mass) by finding the local minimum between the star-forming and green valley populations in each mass bin (Fig. 4.2). A key advantage of this method is that it does not place artificial constraints on the distribution of galaxies around the star-forming galaxy main sequence. Following this approach, we show that the main sequence for all galaxies (Fig. 4.1) has a distinct flattening at the high-mass end, which becomes increasingly flat as time progresses from z = 3.0 to z = 1.5. We show that this flattening is due to the increasing fraction of the green valley and quiescent galaxy population from z = 3.0 to z = 1.5 (Fig. 4.5). The star-forming galaxy main sequence (Fig. 4.4) does not show this flattening (see also Fig. 4.6). This indicates that the average specific star-formation rate of the massive star-forming galaxy population does not evolve significantly over that epoch.

2. We measure the total scatter around the star-forming galaxy main sequence to be ∼ 0.5 − 1.0 dex and ﬁnd that there is little evolution in the scatter as a function of stellar mass or redshift (Fig. 4.7). With our meaningful isolation of star-forming galaxies, we avoid biasing our result by assuming an underlying distribution around the star-forming galaxy main sequence. We also quantify the scatter above (upper) and below (lower) the star-forming galaxy main sequence and ﬁnd the lower scatter is larger than the upper scatter by up to a factor of 3 in all three redshift bins spanning 1.5 < z < 3.0, indicating that the underlying distribution of galaxies around the star-forming galaxy main sequence is not the often assumed symmetrical Gaussian.

3. Additionally, we compare our empirical main sequence for all galaxies with results from theoretical models SIMBA, IllustrisTNG, and SAG. Results from SIMBA are within a factor of ∼ 1.5 of our empirical result but do not show a ﬂattening at the highest masses in our lowest redshift bin (1.5 < z < 2.0); those from SAG lie above our results but do show the ﬂattening at the high-mass end in the 1.5 < z < 2.0 bin. The main sequence for all galaxies from IllustrisTNG is below our empirical result and shows a strong turnover at the highest masses at 2.0 < z < 3.0, which is not seen in our empirical result. Interpretation of comparisons with theoretical models is not straightforward as the physical processes driving stellar mass buildup

121 and star-formation rates are highly inter-dependent in the models.

122 Chapter 5: Summary and Future Work

Understanding the evolutionary history of the massive galaxy population is important for understanding galaxy evolution as a whole. This thesis has made important advances in making robust measures of fundamental parameters for the massive galaxy population. These advancements have been made possible by the large area, multi-wavelength data used throughout this work, which have enabled the study of the massive galaxy population while minimizing Poisson errors and negating uncertainty due to cosmic variance. Key advances have also been made in the SED ﬁtting procedure and validation of those results, which give conﬁdence in the results presented in this thesis. In this Chapter, I will summarize the key results of this thesis (Section 5.1), and in Section 5.2 I describe the next steps that can be taken with the rich data set used in this work.

5.1 Key Results

5.1.1 What is the Shape of the Stellar Mass Function for Massive Galaxies?

The high-mass end of the galaxy stellar mass function is steeply declining for both the star-forming and total galaxy populations (e.g., Figures 2.9 and 3.7). The total galaxy stellar mass function is related to the star-forming galaxy stellar mass function through the quiescent fraction, and evolution in the massive galaxy quiescent fraction from 1.5 < z < 3.0 implies a similar evolution in the relationship between the total and star-forming galaxy stellar mass functions (see 5.1.2 below). This result remains robust regardless of the method used to isolate the star-forming galaxy population. In Chapter 2 the sample is biased towards star-forming galaxies as it is gri-selected. Chapter 3 uses three methods to identify the star- forming galaxy population (sSFR, main sequence - 1dex, and UVJ color-color selection) and shows that all methods give stellar mass functions that are steeply declining at the high mass end. Care is taken when measuring the stellar mass function to make corrections for mass

incompleteness (the 1/Vmax correction) and to test for the impact of Eddington Bias on the 11 results (Figure 2.8). The results presented in this thesis focus on the mass range M? = 10 12 12 to 10 M as the tests for Eddington Bias show that measurements at M? > 10 M may

123 not be robust. This work also does not rely on assumed functional forms (i.e., the Schechter function) to study the massive end of the stellar mass function. Robust measures of the high-mass end of the stellar mass function are important for placing constraints on the merger history and star-formation eﬃciency of the massive galaxy population. Because of this, they are often used as benchmarks for theoretical models. As this work produced the most robust measures to date of the high-mass end of the galaxy stellar mass function for both star-forming galaxies and the total galaxy population, it will contribute signiﬁcantly to the improvement of future theoretical models.

5.1.2 When Does the Massive Galaxy Population Become Predomi- nantly Quiescent?

Pinpointing the time when the massive galaxy population transitions from primarily star- forming to primarily quiescent is an important endeavor in extragalactic studies. Previous works (e.g., Muzzin et al. 2013, Martis et al. 2016, and Tomczak et al. 2016; Figure 3.4) showed that this generally occurs at cosmic noon, however their studies suffered from small number statistics and the extreme effects of cosmic variance. In Chapter 3, significant advancements are made in measuring the quiescent fraction of the massive galaxy population. Unlike previous studies, this thesis uses a large sample of massive galaxies, allowing the population to be split into small mass bins, each containing a statistically significant number of massive galaxies. This allows for the robust study of 11 the quiescent fraction for different masses above M? = 10 M , which had not been done for statistically significant samples of massive galaxies in previous works. With this, I am able to show that the quiescent fraction increases as a function of stellar mass from 11 12 M? = 10 M to M? = 10 M within a given redshift bin spanning 1.5 < z < 3.0 (Figure 3.3). Additionally, Chapter 3 details three methods for measuring the quiescent fraction, and Chapter 4 introduces yet another method. All four methods (sSFR, main sequence - 1 dex, UVJ color-color selection, and locating the top of the green valley) give quiescent fraction 11 12 results that are within a factor of two at all M? = 10 − 10 M for 1.5 < z < 3.0 (Figure 4.3). This is an important advancement as it (1) shows that measures of the quiescent fraction in this work are robust to the method used for measuring it, and (2) this allows for apples-to-apples comparisons with previous works and theoretical models (Figures 3.9 and

124 3.10).

A key conclusion from Chapter 3 is that as the stellar mass varies from log(M?/M ) = 11 to 11.75, at 2.5 < z < 3.0 the main sequence-based quiescent fraction increases from 13.5% ± 7.1% to 39.6% ± 11.2%, while at 1.5 < z < 2.0 the quiescent fraction increases from 51.9% ± 2.5% to 66.4% ± 13.1%. It is remarkable that by z = 2, only 3.3 Gyr after the 11 Big Bang, the universe has quenched more than 25% of massive (M? = 10 M ) galaxies, and that by z = 1.5 the massive galaxy population is more than 50% quiescent.

5.1.3 Which Physical Mechanisms Drive The Shift Towards Quies- cence?

The ∼ 2.2 Gyr spanning 1.5 < z < 3.0 is an extraordinarily important epoch in galaxy evolution. At this time, proto-clusters began to collapse into the rich clusters seen at present day. Additionally, SFR and black hole accretion rate peaked. Because of this, both internal and external quenching mechanisms are available to transform the massive galaxy population from primarily star-forming to primarily quiescent. Chapter 3 details the many mechanisms that could potentially quench massive galaxies and how the available mechanisms change from z = 3.0, a time before proto-clusters became clusters with established ICMs, to z = 1.5 when cluster dynamics come into play. These mechanisms are those that both accelerate and suppress star-formation. Those that accelerate star-formation and the consumption of gas (e.g., Man & Belli 2018) do so by driving gas to the circumnuclear regions where the gas reaches high densities and fuels rapid star-formation. These processes include major and minor mergers (e.g., Mihos & Hernquist 1994, Mihos & Hernquist 1996, Jogee et al. 2009, Robaina et al. 2010, Hopkins et al. 2013), tidal interactions (e.g., Barnes & Hernquist 1992 and references therein, Gnedin 2003), and spontaneously or tidally induced bars (e.g., Sakamoto et al. 1999, Jogee et al. 2005, Peschken & Łokas 2019). Those that suppress star-formation include ram pressure stripping (e.g., Gunn & Gott 1972, Giovanelli & Haynes 1983, Cayatte et al. 1990, Koopmann & Kenney 2004, Crowl 2005, Singh et al. 2019) where the intra-cluster medium removes cold gas from a galaxy traveling within a cluster, tidal stripping (Moore et al. 1996, Moore et al. 1998), or starvation and strangulation (Larson, 1980). Also included in processes that suppress star-formation are mechanisms such as stellar (e.g., Ceverino & Klypin 2009, Vogelsberger et al. 2013, Hopkins et al. 2016, Núñez et al. 2017) and AGN feedback (e.g.,

125 Hambrick et al. 2011, Fabian 2012, Vogelsberger et al. 2013, Choi et al. 2015, Hopkins et al. 2016) that heat, redistribute, and/or expel gas residing in a galaxy or gas accreting onto the galaxy. At early times (z > 2.5), when proto-clusters and proto-groups were in the early stages of their formation, quenching mechanisms which rely on interaction with an ICM are not available for quenching massive galaxies. Instead, at these times, proto-cluster and proto- group environments are home to frequent mergers, which accelerate star-formation. At later times (1.5 < z < 2.5), bound clusters have established ICMs and processes such as ram pressure stripping, harassment, strangulation, and radio-mode AGN feedback can contribute to the quenching of massive galaxies. Many of the processes described above are interconnected. This makes isolating any individual physical process as the mechanism moving massive galaxies from the star-forming to quiescent population diﬃcult, if not impossible. Additionally, it is unlikely that a single mechanism is responsible for this change. Instead, it is likely that a combination of physical processes, both internal and environmental, contribute to the suppression and cessation of star-formation in the massive galaxy population.

5.1.4 How Does the Shrinking Star-Forming Population Impact the Slope of the Main Sequence?

Chapter 3 introduces the main sequence for all galaxies (Figure 3.1) for the Ks-selected sample used in this work, and Chapter 4 details the main sequence for all galaxies (Figure 4.1) and the star-forming galaxy populations (Figure 4.4). As the massive galaxy populations shift from being predominantly star-forming at z ∼ 3 to primarily residing in the collective green valley and quiescent populations by z ∼ 1.5, the slope of the main sequence for all galaxies becomes flattened (Figure 4.6). Although this thesis does not assume any functional form of the main sequence, using 11 an ordinary least squares regression (fit to main sequence values between M? = 10 to 12 10 M ), I find that the power law slope of the main sequence evolves from 0.30 ± 0.0005 at 2.5 < z < 3.0, to 0.24 ± 0.0008 at 2.0 < z < 2.5, and finally to −0.02 ± 0.0004 at 1.5 < z < 2.0. This is in contrast to the main sequence for star-forming galaxies, which 11 12 does not show a significant flattening at the high mass end (M? = 10 to 10 M ). Its power law slope, computed using an ordinary least squares fit to the star-forming galaxy

126 11 12 main sequence values over the mass range M? = 10 to 10 M , evolves mildly from 0.47 ± 0.0011 at 2.5 < z < 3.0, to 0.46 ± 0.0001 at 2.0 < z < 2.5 , and ﬁnally to 0.35 ± 0.0013 at 1.5 < z < 2.0. The reduced slope of the main sequence for all galaxies at the high-mass end is directly tied to the increased buildup of the collective green valley and quiescent massive galaxy populations. This movement of massive galaxies out of the star-forming population can be linked to the “downsizing” (Cowie et al., 1996) scenario. The physical mechanisms driving this shift are explored in detail in Chapter 3 and again in Chapter 4.

5.1.5 What Can be Learned From The Distribution of Star-Forming

Galaxies in the SFR-M? Plane?

In order to accurately investigate the nature of star-forming galaxies in the SFR-M? plane, it is imperative to first identify the star-forming galaxy population in an unbiased way. Chapter 4 details a novel method for isolating the star-forming galaxy population by identifying the inflection point between the star-forming and green valley populations in the SFR-M? plane (Figure 4.2). This is done in small mass bins such that the transition is allowed to vary as a function of both mass and redshift. With a meaningfully-selected star-forming galaxy population in hand, this thesis shows in Chapter 4 (Figure 4.7) that the total observed scatter around the star-forming galaxy main sequence ∼ 0.5 − 1.0 dex (corresponding to ∼ 0.47 − 0.98 dex intrinsic scatter). It 11 is also found that the total observed scatter increases from low to high masses (M? = 10 12 to 10 M ) by less than a factor of three in the three redshift bins spanning 1.5 < z < 3.0 explored throughout this work. The scatter also does not show significant evolution as a function of redshift over 1.5 < z < 3.0. Additionally, with the meaningful, unbiased selection of star-forming galaxies in each mass and redshift bin, it can be shown in this thesis that the distribution of massive galaxies around the star-forming galaxy main sequence is not Gaussian, as it is often assumed to be. Instead, the lower scatter around the main sequence is larger than the upper scatter in all redshift bins. This result can be tied to the timescales that galaxies spend both above and below the star-forming galaxy main sequence, and it is in alignment with previous studies of the molecular gas content of massive galaxies out to z ∼ 4 using ALMA (e.g., Tacconi et al. 2018, Franco et al. 2020). These studies showed that massive galaxies lying above the

127 main sequence have larger molecular gas fractions and shorter gas depletion timescales than those lying below the main sequence, where galaxies above the main sequence may deplete their gas supply in ∼ 102 Myr, while star-forming galaxies below the main sequence have depletion times closer to ∼ 103 Myr. These results are consistent with scenarios in which mergers elevate galaxies above the main sequence by quickly accelerating star-formation and gas consumption. Subsequently, galaxies settle below the main sequence in the moderate star-forming, green valley, or quiescent populations depending on the level of gas depletion and suppression of star-formation following the merger.

5.1.6 Can Current Theoretical Models Correctly Recover the Ob- served Properties of Massive Galaxies?

In Chapters 2, 3, and 4 this thesis explores the extent to which diﬀerent classes of theoretical models (hydrodynamical models, semi-analytic models, and abundance matching) can recover empirical trends for massive galaxies (Figures 2.10, 3.9, 3.10, 3.11, 3.12, A2, 4.9). Some of the models explored here are more successful than others, however it is noted that none of the models compared with the empirical results in this work can recover all of the empirical massive galaxy relations that are explored. Throughout this work care is taken to ensure that the best-available apples-to-apples comparisons are used for comparing results from theoretical models with empirical results. This includes discussions with those building the theoretical models about aperture choices, how parameters are extracted, and limitations of the models (see, for example, detailed de- scriptions of the implementation of physical processes in the models used in Chapter 3). For all theoretical models used in this work, I use the group catalog data to compute their stellar mass functions, quiescent fractions, and main sequence relations in the same way as is done for the empirical data used in this thesis. Because the methodology for computing these relations is the same, comparisons are more meaningful. When a mismatch between the results from the models and those from my empirical study occurs, any potential uncertainties from the procedure used to determine the fundamental relations are removed. Therefore, the various levels of disagreement seen between models and empirical results throughout this thesis can be traced back to the models themselves, whether that be computational limitations, or limitations of the physics implemented in the models. The IllustrisTNG hydrodynamical model implements both thermal-mode AGN feedback

128 and kinetic-mode AGN feedback at high and low black hole accretion states, respectively (Weinberger et al. 2017, Pillepich et al. 2018a). The thermal-mode is a continuous injection of thermal energy into the gas surrounding the central black hole (heating the gas), while the kinetic-mode is a pulsed injection of kinetic energy to the regions near the black hole (acting as a wind). Stellar feedback is implemented through wind particles which are launched in random directions, where the strength of the wind is determined by the energy released from the supernova. The total galaxy stellar mass function from hydrodynamical model IllustrisTNG shows up to a factor of ∼ 15 disagreement with the empirical result presented in this thesis. The model also over-predicts the main sequence-based quiescent fraction by a factor of 2 and IllustrisTNG over-predicts the sSFR-based quiescent fraction by a factor of 2 to 5 compared with our empirical result. The main sequence for all galaxies from IllustrisTNG shows a strong turnover at the highest masses which is not seen in the empirical result. We note, however, that the quiescent fraction results from IllustrisTNG and any associated conclusions are highly dependent on the choice of aperture (Appendix A.2). The SIMBA cosmological simulation performs black hole feedback through both kinetic and X-ray modes. The kinetic-mode feedback is implemented as a bipolar wind (in the form of a collimated jet), and the X-ray mode injects energy into surrounding gas. We note that although SIMBA and IllustrisTNG both use the term “kinetic-mode" to describe AGN feedback, their implementations of this feedback are quite diﬀerent. Supernova feedback is implemented in SIMBA through a wind which carries hot and cold gas, as well as metals, away from star-forming regions. The SIMBA model shows good agreement with our empirical total galaxy stellar mass function at 2.0 < z < 3.0, but over-predicts the number density of massive galaxies in the 1.5 < z < 2 bin by up to a factor of ∼ 10. They also tend to under-predict the quiescent fraction, compared with our empirical result, when using both the sSFR and main sequence based methods by a factor of ∼ 1.5 − 4, respectively, but in the lowest redshift bin (1.5 < z < 2.0) it starts to correctly predict the observed trend of rising quiescent fraction with stellar mass. The normalization of the SIMBA main sequence for all galaxies is similar to our empirical result, but it does not show the ﬂattening at 1.5 < z < 2.0 that is seen in the empirical result. Of the three SAMs explored in this thesis, semi-analytic model SAG is most successful at recovering the trends seen in our empirical results. SAG implements AGN feedback through

129 a radio-mode feedback scheme in which energy is injected into the region surrounding the black hole, reducing hot gas cooling. Stellar feedback heats gas within the galaxy and the energy transfer is regulated by a virial velocity and redshift dependence. The parameter that regulates the redshift dependence has been modified to generate the galaxy catalog used in this work (S. Cora, private communication). This parameter was adjusted to better reproduce the evolution of the star-formation rate density at high redshifts (z > 1.5), and has also been shown to achieve a local quiescent fraction of galaxies that is in better agreement with observations from previous works (Cora et al., 2018). A fraction of the supernova ejecta is heated and removed from the halo. The ejected gas is reincorporated into the hot gas with a timescale that is inversely proportional to the corresponding (sub)halo virial mass. During major mergers, a starburst occurs in the bulge after stars and cold gas from the remnant are placed in the central regions. In a minor merger the stars of the less massive galaxy are transferred to the bulge of the more massive galaxy. A significant advantage of the SAG model is that it explicitly models ram pressure and tidal stripping for satellites falling into a group or cluster. Different stripping radii are used for the hot and cold gas components, as well as the disk and bulge stellar populations. The combined effects of ram pressure stripping (of gas) and tidal stripping (of stars and gas) are not instantaneous, rather the processes gradually remove the gas supply from a satellite. Calibration of SAG is performed considering observational constraints at z = 0, z = 0.15 and z = 2. At 2.0 < z < 3.0 SAG under-predicts the total galaxy stellar mass function by up to a factor of 10,000, but it is in general agreement with the empirical result at 1.5 < z < 2.0. While SAG under-predicts the quiescent fraction of massive galaxies using both the sSFR and main sequence-based selection techniques by a factor of ∼ 1.5 − 10 compared with our empirical result, it is able to recover the trend of increasing quiescent fraction with increasing stellar mass found in our empirical result. The main sequence for all galaxies from SAG is higher than our empirical result by up to a factor of ∼ 3, and it begins to show a flattening high-mass slope towards z = 1.5. Models must consider updating their implementations of physical processes to better reproduce the observed stellar mass function, main sequence, distribution of galaxies in the SFR-M? plane, and quiescent fractions of their massive galaxy populations. That may include adjusting the merger rate for massive galaxies in order to better match the empirical number density for these systems or altering the efficiency of AGN and stellar feedback to suppress or enhance star-formation in the massive galaxy population. As has been

130 discussed above, the physical processes driving massive galaxy evolution are multi-faceted and intertwined, indicating that the implementation of more than one physical process in the models may need to be modiﬁed to bring the models into better alignment with the observations.

5.2 Future Work

5.2.1 Empirical Studies of Massive Galaxies

Spectroscopic Followup

This thesis relied primarily on photometric data to obtain information about massive galaxies. A large portion of this work was focused on validating the results of SED fitting through testing with mock galaxies (see Chapter 2) and uncertainty testing (Chapters 2, 3, and 4). While these tests provide confidence in the results presented throughout this work, spectroscopy would provide a more precise view of properties such as redshift, stellar mass, and SFR for the massive galaxies studied here. A subset of the massive galaxy sample used in this work will have spectroscopy obtained from the HETDEX study (Hill et al., 2008) in coming years. HETDEX uses integral field spectrographs, and therefore obtains a spectrum for objects that fall on the fibers of the spectrograph units. This is incredibly beneficial as the footprint used in this work will have uniform spectroscopic coverage. A challenge, however, is that the wavelength range covered by HETDEX (3500−5500Å) is sensitive to the Lyman-α emission line at 1.9 < z < 3.5, and low-redshift (z < 0.5) [OII] emitters. At cosmic noon, therefore, only Lyman-α emitters (LAEs) will have emission line detections, and emission line-based spectroscopic redshifts, while other sources may have only continuum detections. Because HETDEX is biased to LAEs at 1.9 < z < 3.5, additional spectroscopic followup will be imperative for the massive galaxy population identified in this thesis. A significant benefit of this thesis is that the massive galaxies are uniformly selected across a large area, and it is important that this not be lost when performing spectroscopic followup. Spectroscopic followup will be most beneficial if a large sample of the massive galaxies identified through SED fitting are sampled across a significant portion of the survey area. This will allow studies to continue to minimize the impact of cosmic variance and reduce Poisson errors.

131 Photometric Followup

The work presented in this thesis performed SED fitting on a limited set of filters (a maximum of 10 filters were used in SED fitting). Increased coverage of the SED would be helpful in improving the SED fitting and give further information to eliminate interlopers to the 1.5 < z < 3.5 massive galaxy population. This additional coverage could be obtained in the near-IR using instruments on GMT and JWST, which would improve constraints of the rest-frame optical SED. Improvements would be made with deeper data taken in the current filter set. In our highest redshift bins (2.5 < z < 3.0 and 3.0 < z < 3.5), the studies presented in this 11 work are not mass complete down to M? = 10 M . The NEWFIRM instrument is currently decommissioned, however deeper data in the Ks-band would allow for lower mass completeness in these redshift bins. Although the region studied in this work is covered by Herschel-SPIRE (HerS, Viero et al. 2014) far-IR/submillimeter at 250, 250, and 500µm, the data are quite shallow and much lower resolution than the shorter wavelength data used in this work. To improve upon the far-IR/submillimeter coverage, observations with ALMA would be needed. ALMA can provide far-IR/submillimeter data that is comparable in resolution to the shorter wavelength data already in hand for this region. ALMA would be capable of unveiling the dust content of the massive galaxy sample and provide accurate measures of dust-corrected SFR. The structure of massive galaxies was not explored in this work as the available photometry did not have high enough resolution. High resolution photometry (obtained with HST or GMT) allowing for morphological studies of massive galaxies would be particularly interesting. With these in hand, it would be possible to look for signatures of recent interactions or other physical processes that may drive the evolution of the massive galaxy population. Possible signatures of interaction in the imaging could then be followed up spectroscopically to perform kinematic studies.

Advancements in SED Fitting

The SED fitting code used in this work, EAZY-py, was an improvement over the original code EAZY (Brammer et al., 2008). EAZY is a code which is primarily used to obtain photometric redshifts by fitting multiple galaxy templates in non-negative linear combination. Combining multiple templates into a single best-fit was a novel method, however the

132 utility of the code was limited in that it only provided photometric redshifts, and it could not give galaxy properties such as stellar mass and star-formation rate. EAZY-py, which is Python-based, continues to give best-fits which are non-negative linear combinations of multiple templates and it now provides both photometric redshifts and galaxy parameters. I further improved upon this code by adding functions that give error estimates for best-fit parameters (see Chapter 2). Many other SED fitting codes exist, each with benefits and drawbacks. For example, FAST (Kriek et al., 2009) requires previously known redshifts as input, it provides single- template best-fits, and, because it constructs templates from grids of input parameter ranges, it occasionally gets stuck in regions of parameter space that are unphysical (i.e. it sometimes −40 −1 gives galaxies best-fit SFR = 10 M yr ). MAGPHYS (da Cunha et al. 2008, da Cunha et al. 2015) is an energy-balance code which simultaneously fits the UV to near-IR SED and the FIR to submillimeter SED. It is an excellent tool for fitting full galaxy SEDs and constraining the contribution from dust-obscured star-formation. Until recently, it was not able to obtain photometric redshifts, and even with this new feature, it is quite slow compared to EAZY-py. Because of this, it would not be feasible to fit entire large-area catalogs using MAGPHYS. At this time, state of the art SED fitting models are exploring large areas of parameter space using MCMC procedures and non-parametric star-formation histories to fit broadband galaxy photometry. An example of this type of code is Prospector-α (Leja et al., 2017). At low redshifts, these codes have been show to accurately recover the redshift and parameters of galaxies. While Prospector-α provides significant improvements in SED fitting accuracy, it is currently unable to be used on large catalogs of galaxies. Even with high performance computing resources, individual objects can take several hours to fit. Currently, it may be feasible to followup specific objects of interest using Prospector-α, but future improvements to the code’s speed will be important for applying this important modeling technique to large samples of galaxies.

Further Understanding of Sub-Populations

Several important sub-populations of massive galaxies were mentioned in this work, but their populations were not explored in great detail. These include (1) massive galaxies with low luminosity AGN, (2) dusty star-forming galaxies, and (3) galaxies ﬁt to have 12 M? ≥ 10 M .

133 Known luminous AGN were removed because the SED fitting procedure used in this work could not properly account for the luminous AGN and, therefore, results from SED fitting for these objects was unreliable. Florez et al. (2020) explored the population of luminous AGN that was removed here. The sample of known luminous AGN in this region with 1.5 < z < 3.5 and stellar mass above the mass completeness limit is quite small (only 44 galaxies) indicating that removing these objects does not significantly impact the results prsented in this work. Deeper X-ray data in this region would allow for robust detection of both luminous and low-luminosity AGN, which could further improve the results obtained in this work. This is particularly important because AGN feedback may be a key contributor to massive galaxy evolution and quenching. X-ray data would likely need to be targeted as eRosita (Merloni et al., 2012), the latest space-based X-ray observatory performing an all- sky survey, will not achieve even the depth of the current luminous AGN surveys (LaMassa et al. 2013a, LaMassa et al. 2013b) available in the region studied in this work. Because the Herschel-SPIRE data available in this region is quite shallow and low resolution, it can only be used for isolated galaxies (those that don’t have nearby neighbors within the FWHM of the Herschel-SPIRE PSF). Throughout this work, tests were performed on this sample of isolated Herschel-SPIRE galaxies to see if these dusty star-forming galaxies were fit by the SED fitting procedure to be interlopers to the massive quiescent galaxy population. It was found (Chapter 3) that this was unlikely to be the case, however the test sample was quite small. Followup with ALMA would allow for a more detailed study of the dusty star-forming galaxies in our massive galaxy sample. Tests of the effects of Eddington Bias performed in Chapters 2 and 3 showed that results 12 for galaxies with M? ≥ 10 M may not be robust due to low mass and/or low redshift interlopers in this mass range. This population is quite interesting as it can only be studied in large area surveys such as the one presented in this thesis, however spectroscopic followup 12 is required for all objects fit to have M? ≥ 10 M . Without spectroscopic confirmation of their redshift and stellar mass, results for this extreme high-mass population will not be considered robust.

Environmental Studies

This work makes the general underlying assumption that most massive galaxies reside in proto-clusters at early times, which grow into rich clusters at late times. It is not a requirement, however, that these systems live in the most dense environments. A particularly

134 interesting followup study would be to split the results contained in this thesis as a function of environment. This type of study would require precise spectroscopic redshifts for not only the massive galaxies identified in this work, but the lower mass galaxies surrounding them. An additional measure that could be obtained with detailed spectroscopy is the merger fraction of the massive galaxy population. This could help to identify the role that major mergers have in building and driving the evolution of the massive galaxy population. Again, a study such as this will require precise measures of the spectroscopic redshift for both massive and lower-mass galaxies in the footprint studied in this thesis. In addition to the lack of high-redshift spectroscopy in this region, a significant limitation for environmental studies is the depth of the photometric data. Of the primary redshift bins 11 studied in this work, two of the three are estimated to be mass complete for M? ≥ 10 M (only 2.5 < z < 3.0 is not). This is not a significant issue when studying exclusively the massive galaxy population, however this becomes a limitation when interest arises in lower- mass galaxies. For example, when considering major mergers with mass ratios spanning 11 1:1 to 1:4, the sample of low mass companions to M? = 10 M galaxies at 2.5 < z < 3.0 is not mass complete. It follows that minor mergers with mass ratios down to 1:10 are also highly incomplete in stellar mass for the low-mass companions to massive galaxies. Therefore, it is imperative to obtain deeper photometric data in order to perform robust studies of the environment surrounding the massive galaxy population.

5.2.2 Theoretical Studies of Massive Galaxies

It has been shown throughout this thesis (Chapters 2, 3, and 4, and Section 5.1.6) that theoretical models, regardless of their class (e.g., hydrodynamical models, abundance matching, SAMs, etc.) face steep challenges when it comes to reproducing observed trends. This is particularly true when they are asked to simultaneously reproduce the evolutionary history and observed properties of rare populations, such as massive galaxies, and galaxies with more typical mass. At this time, the most detailed models (hydrodynamical models) are limited by computational power. This limits their resolution capabilities and requires certain prescriptions to drive galaxy evolution. Alternate methods, such as SAMs are able to use much larger box sizes, but they must use (often) simpliﬁed physical processes to populate dark matter halos with baryons and track their evolution through cosmic time. They also typically calibrate

135 their results to observed relations, and, many times, these relations come from small area studies. Moving forward, with the results of this thesis in hand, those building theoretical models can implement physical processes that will better represent the empirical relations for the massive galaxy population. These results not only provide benchmarks for all theoretical models, but they can also be used for higher-redshift calibrations of SAMs. This thesis also details speciﬁc physical processes that theoretical models can revisit (such as prescriptions for mergers, AGN and stellar feedback, and ram-pressure stripping) in order to have their models better represent the empirical results.

136 Appendix A: Appendix to Chapter 3

A.1 Testing the Impact of Photometric Redshift Error and Eddington Bias on the Empirical Quiescent Fraction

In Section 3.3 we described a test in which we generate 100 iterations of our catalog by forcing our SED procedure to fit each galaxy in our catalog at 100 redshift values that are drawn from each galaxy’s photometric redshift probability distribution. This test allows us to estimate the impact of photometric redshift uncertainty on our results and test the impact of Eddington bias (Eddington, 1913), the potential scattering of galaxies with low masses into a high mass bin. We find that our results from the 100 catalog iterations 12 are consistent with our empirical results presented in Section 3.4 for M? < 10 M . For 12 M? > 10 M we find scatter in the quiescent fraction (up to a factor of 2 − 5), which is expected at these extreme masses, and does not impact our results which focus on stellar 11 12 masses M? = 10 −10 M . The quiescent fraction for the 100 catalog iterations measured using the three methods employed throughout this work (sSFR, main sequence - 1 dex, and UVJ) are shown in Figure A1.

A.2 Testing Diﬀerent Aperture Choices and Main Sequence Deﬁni- tions in Illustris TNG

Throughout this work we have computed the main sequence-based quiescent fraction using the main sequence definition described in Section 3.4.1, where the main sequence is defined to be the average SFR in small mass bins and errors are computed using a bootstrap resampling procedure. We have also used the IllustrisTNG aperture where the stellar mass and SFR are measured within twice the stellar half mass radius (the 2 × R1/2 aperture). Here, in Figure A2, we show how the results differ if we use different aperture definitions or different definitions of the main sequence. We find that the IllustrisTNG main sequence-based (left panel Fig. A2) and the sSFR- based (right panel Fig. A2) quiescent fractions using masses and SFR measured within the 2 × R1/2 aperture are over-predicted compared with our empirical result, as is shown throughout this work (see Section 3.5.2). If, instead, the total galaxy mass and SFR (computed for all star particles bound to a subhalo) are used, the IllustrisTNG quiescent

137 log(M /M ) 10.0 10.5 11.0 11.5 12.0 12.5 1.0 1.5 < z < 2.0 sSFR 0.8 0.6 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.0 < z < 2.5 0.8 0.6 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.5 < z < 3.0 0.8 0.6 0.4

Fraction 0.2

Quiescent 0.0 10.0 10.5 11.0 11.5 12.0 12.5 log(M /M )

log(M /M ) 10.0 10.5 11.0 11.5 12.0 12.5 1.0 1.5 < z < 2.0 UVJ 0.8 0.6 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.0 < z < 2.5 0.8 0.6 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.5 < z < 3.0 0.8 0.6 0.4

Fraction 0.2

Quiescent 0.0 10.0 10.5 11.0 11.5 12.0 12.5 log(M /M )

log(M /M ) 10.0 10.5 11.0 11.5 12.0 12.5 1.0 1.5 < z < 2.0 MS - 1dex 0.8 0.6 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.0 < z < 2.5 0.8 0.6 0.4

Fraction 0.2

Quiescent 0.0 1.0 2.5 < z < 3.0 0.8 0.6 0.4

Fraction 0.2

Quiescent 0.0 10.0 10.5 11.0 11.5 12.0 12.5 log(M /M )

Figure A1: Results of the test in which we explore the impact of photometric redshift uncertainty and Eddington bias on our empirical quiescent fraction results. The three panels show the quiescent fraction measured using sSFR-selection (upper), UVJ-selection (center), and distance from the main sequence selection (lower). In each of the three panels, the quiescent fraction presented in Section 3.3 is shown as a colored line, and the results from the 100 catalog iterations are shown as grey lines. Our results are shown for each of the three redshift bins used throughout this work, which span 1.5 < z < 3.0 and the redshift bin is indicated in the upper left of each row138 of the three panels. Using all three methods of measuring the quiescent fraction, the results of the 100 catalog iterations are consistent 11 12 with the results presented in Section 3.3 for M? = 10 −10 M , our mass range of interest throughout this work. fraction is lower than our empirical result by a factor of ∼ 2 − 10. Note that in making these comparisons with the main sequence-based quiescent fraction, we use the same main sequence definition used throughout this work and described in Section 3.4.1. Donnari et al. (2019) investigated the quiescent fraction of galaxies in the IllustrisTNG model using the main sequence - 1 dex method out to z = 3 (M. Donnari and A. Pillepich, private communication) using a different method to define the main sequence. Their method recursively computed a median SFR and removed galaxies 1 dex below that median until the median value (the main sequence) converged. This recursive procedure was done for all 10.2 galaxies with stellar masses (measured using the 2 × R1/2 aperture) up to M? ≤ 10 M and was then linearly extrapolated to higher masses. With the extrapolated main sequence definition, Donnari et al. (2019) found a quiescent fraction that rises as a function of stellar mass and is a factor of ∼ 2 − 4 larger than our empirical quiescent fraction result in our three redshift bins spanning 1.5 < z < 3.0 (left panel of Fig. A2). The difference in quiescent fraction results that are computed using different aperture types and main sequence definitions highlight the extreme importance of comparing results achieved using the same methods.

139 log(M /M ) log(M /M ) 10.0 10.5 11.0 11.5 12.0 12.5 13.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0

1.0 1.5 < z < 2.0 Data: This Study (S20) 1.0 1.5 < z < 2.0 Data: This Study (S20) QF Selection: MS - 1 dex TNG: Total, MS def in S20 QF Selection: sSFR TNG: Total 0.8 0.8 TNG: 2 x R1/2, MS def in S20 TNG: 2 x R1/2 TNG: 2 x R , MS in Donnari+19 0.6 1/2 0.6

0.4 0.4 Fraction Fraction

Quiescent 0.2 Quiescent 0.2

0.0 0.0

1.0 2.0 < z < 3.0 1.0 2.0 < z < 2.5 QF Selection: MS - 1 dex QF Selection: sSFR 0.8 0.8

0.6 0.6

0.4 0.4 Fraction Fraction

Quiescent 0.2 Quiescent 0.2

0.0 0.0

1.0 2.5 < z < 3.0 1.0 2.5 < z < 3.0 QF Selection: MS - 1 dex QF Selection: sSFR 0.8 0.8

0.6 0.6

0.4 0.4 Fraction Fraction

Quiescent 0.2 Quiescent 0.2

0.0 0.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0 10.0 10.5 11.0 11.5 12.0 12.5 13.0 log(M /M ) log(M /M )

Figure A2: We compare the empirical quiescent fraction computed using the main sequence (left) and sSFR (right) methods with results from IllustrisTNG that are determined using different aperture types and main sequence definitions. Throughout this work we use the 2×R1/2 aperture (light blue) and the main sequence described in Section 3.4.1 to compute the quiescent fraction for the IllustrisTNG model and find that the IllustrisTNG main sequence- and sSFR-based quiescent fractions are higher than our empirical results. In contrast, when using masses and SFR measured for all particles bound to a subhalo (navy blue, the total “aperture"), and the main sequence described in Section 3.4.1, IllustrisTNG under-predicts the main sequence- and sSFR-based quiescent fractions compared to our empirical results. We also show the IllustrisTNG main sequence-based quiescent fraction from Donnari et al. (2019) (black), which uses the 2 × R1/2 aperture and a main sequence that is extrapolated from lower to higher masses, rather than a main sequence computed in every mass bin. This method gives a main sequence-based quiescent fraction that is higher than our empirical result.

140 Appendix B: Appendix to Chapter 4

B.1 The Distribution of Galaxies in the SFR-M? Plane for Theoretical Models

In the comparison of our empirical main sequence for all galaxies with those from theoretical models (see Section 4.6), we noted that the comparison of the main sequence relation alone does not provide all available information about discrepancies (or agreements) between observations and theoretical models. In this Appendix we show (Figure A1) the

full distribution of galaxies in the SFR-M? for our data (reproducing Figure 4.1 for ease of comparison) and the same distributions for the three theoretical models with which we perform comparisons (IllustrisTNG, SIMBA, and SAG). We remind the reader that for all three theoretical models, we compute their main sequence from their group catalog data with the same method used for our empirical data (see Section 4.3.1). The group catalogs for all three models hard code SFR = 0 when the SFR for an object falls below the resolution limit. To account for this, following Donnari et al. (2019) and Sherman et al. (2020b), we assign these objects a random SFR between −5 −4 −1 SFR = 10 − 10 M yr before performing our analysis. IllustrisTNG is the most successful at producing galaxies in the green valley and quiescent regions of parameter space, however Sherman et al. (2020b) showed that IllustrisTNG over-produces the collective fraction of green valley and quiescent galaxies at 1.5 < z < 3.0. This translates directly to the main sequence for all galaxies from the IllustrisTNG model having a lower normalization than that from the empirical data and the strong turnover seen at the highest masses in the 2.0 < z < 2.5 and 2.5 < z < 3.0 bins. Both SIMBA and SAG were shown by Sherman et al. (2020b) to under-predict the collective fraction of green valley and quiescent galaxies and this can be seen in Figure A1. We emphasize that the “success” of a model cannot be tied to a model matching a singular empirical relation well. Instead, several key relations (e.g., the stellar mass function (see Sherman et al. 2020b), main sequence, and quiescent fraction (see Sherman et al. 2020b)) must simultaneously be recovered. The models must also consider the implications that turning individual “dials” in the models may have on other measured parameters. Because of this, it is necessary for models to adjust processes that build the stellar populations of massive galaxies (such as mergers and star-formation eﬃciency), as well as processes that

141 suppress star-formation (such as stellar and AGN feedback and ram pressure stripping at late times).

142 1.5 < z < 2.0 2.0 < z < 2.5 2.5 < z < 3.0

] 4 r y / 3 M [ 2 ) R F 1 S ( g

o 0 l This Work - All Galaxies SIMBA TNG300 SAG 1 1.5 < z < 2.0 This Work 2.0 < z < 2.5 This Work 2.5 < z < 3.0 This Work 4 N11 = 8480 All Galaxies N11 = 15401 All Galaxies N11 = 4588 All Galaxies ] r y / 2 M [

)

R 0 F S ( g

o 2 0 1 0 1 2 0 1 2

l 10 10 10 10 10 10 10 10

4 1.5 < z < 2.0 TNG300 2.0 < z < 2.5 TNG300 2.5 < z < 3.0 TNG300 ] r

y 2 /

M 0 [

)

R 2 F S (

g 4

o 0 1 2 3 0 1 2 3 0 1 2 3

l 10 10 10 10 10 10 10 10 10 10 10 10 6

4 1.5 < z < 2.0 SIMBA 2.0 < z < 2.5 SIMBA 2.5 < z < 3.0 SIMBA ] r

y 2 /

M 0 [

)

R 2 F S (

g 4

o 0 1 2 3 0 1 2 3 0 1 2 3

l 10 10 10 10 10 10 10 10 10 10 10 10 6

4 1.5 < z < 2.0 SAG 2.0 < z < 2.5 SAG 2.5 < z < 3.0 SAG ] r

y 2 /

M 0 [

)

R 2 F S (

g 4

o 0 1 2 3 0 1 2 3 0 1 2 3

l 10 10 10 10 10 10 10 10 10 10 10 10 6

10 11 12 13 10 11 12 13 10 11 12 13 log(M /M ) log(M /M ) log(M /M )

Figure A1: Top row: A reproduction of Figure 4.9 for ease of comparison. Second row: A reproduction of Figure 4.1 for ease of comparison. Third to fifth row: The distribution of galaxies in the SFR-M? plane for theoretical models IllustrisTNG, SIMBA, and SAG. In rows two through five, the inset box in the upper right corner identifies the data used to generate the 2D histogram in that panel and colorbars show the number of galaxies in each cell of the 2D histogram. IllustrisTNG is more successful at reproducing the distribution of massive galaxies in the SFR-M? plane seen in our empirical results than SIMBA and SAG, however IllustrisTNG over-predicts the fraction of galaxies in the collective green valley and quiescent populations (Sherman et al., 2020b). In all rows, the gray shaded regions represent masses below our 95% completeness limit. We emphasize that the results 11 12 presented in this work focus on the mass range M? = 10 to 10 M , and that results above 12 M? = 10 M (vertical dashed gray line) are unlikely to be robust.

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