Studying the Building Blocks of the Universe: the faint, low-mass galaxies

A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY

Vihang Mehta

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy

Advisor: Claudia Scarlata

August, 2018 © Vihang Mehta 2018 ALL RIGHTS RESERVED Acknowledgements

This achievement has only been made possible by a number of people helping and supporting me behind the scene. First and foremost, I have to thank my advisor, Claudia Scarlata, for all her support and advice through the past six years. Thank you for sticking with me quirky self through the ups and downs through the years. This would not have been possible without you believing in me and constantly pushing me to be the best I could. I have the highest respect for you as a researcher as well as a teacher and am honored to have you as my advisor and collaborator. The work presented here would not have been possible without the UVUDF, SPLASH, and WISPS programs and their respective PIs, Harry Teplitz, Peter Capak, and Matt Malkan. In addition to the UVUVDF, SPLASH, and WISP collaborations, I am indebted to Marc Rafelski, Iary Davidzon, Ivano Baronchelli, and James Colbert for all their help in getting me familiarized with the various programs as well as helping me with all the subtle issues that I encountered while working with the data. Not only did they welcome me into their collaborations and gave me an opportunity to do science, but they were also highly supportive of my work and provided ample guidance towards making it a success and for this, I am grateful. MIfA has been my home since I was part way through my undergrad and I am thankful for all the support the department has provided through the years. In particular, special thanks to Michael Rutkowski, Hugh Dickinson, and Dinesh Shenoy for their invaluable help in getting me acquainted with the nuances of the field and getting me kick-started on the basics. I also would like to thank my committee members, Evan Skillman, Larry Rudnick, Lucy Fortson, and Vuk Mandic for their time, expertise and guidance. Last but definitely not the least, the grad student body – without whom I would have lost my sanity through the years. I am eternally grateful to them for always being there to socially and mentally ground myself in reality in midst of the whirlwind that is grad school. I cannot put in words my gratitude towards my officemates, Micaela Bagley, Karlen

i Shahinyan, and Melanie Beck for getting me through each day of grad school. Be it random silly questions about astronomy, coding, or day-to-day life, I have always been able to rely on you guys for aligning me in the right direction. I cannot thank you enough for all your support through the years. The research presented in this thesis was made possible by three major programs: the WFC3 Infrared Spectroscopic Parallel (WISP) survey, the UltraViolet Ultra Deep Field (UVUDF) program, and the Spitzer Large Area Survey with Hyper-Suprime-Cam (SPLASH) program. Their respective acknowledgments are below. WISP: Support for HST Programs GO-11696, 12283, 12568, 12902 was provided by NASA through grants from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5- 26555. UVUDF : Support for HST Program GO-12534 was provided by NASA through grants from the Space Telescope Science Institute, which is operated by the Association of Uni- versities for Research in Astronomy, Inc., under NASA contract NAS5-26555. SPLASH : VM acknowledges the support from Jet Propulsion Laboratory under the grant award #RSA-1516084. VM also acknowledges support from the University of Min- nesota Doctoral Dissertation Fellowship 2016-17. Based in part on data collected at the Subaru Telescope and retrieved from the HSC data archive system, which is operated by Subaru Telescope and Astronomy Data Center at National Astronomical Observatory of Japan. Based in part on observations made with the Spitzer Space Telescope, which is oper- ated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. The Hyper Suprime-Cam (HSC) collaboration includes the astronomical communities of Japan and Taiwan, and Princeton University. The HSC instrumentation and software were developed by the National Astronomical Observatory of Japan (NAOJ), the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), the University of Tokyo, the High Energy Accelerator Research Organization (KEK), the Academia Sinica Institute for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University. Funding was contributed by the FIRST program from Japanese Cabinet Office, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), the Japan Society for the Promotion of Science (JSPS), Japan Science and Technology Agency (JST), the Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton University.

ii This research makes use of software developed for the Large Synoptic Survey Telescope. We thank the LSST Project for making their code available as free software at http: //dm.lsst.org/. Based in part on observations obtained with MegaPrime and MegaCam, a joint project of CFHT and CEA/IRFU, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Science de l’Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at Terapix available at the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

iii Dedication

I dedicate this thesis to my mother, Firuzi Mehta, who has been the cornerstone of my life.

iv Abstract

Faint, low-mass galaxies are the next frontier in extending our understanding of how our universe evolved into its present-day state that we observe. As the ever-advancing tech- nological prowess brings about the next generation of cutting-edge observational facilities, the limit down to which we can observe galaxies is constantly pushed to fainter fluxes and consequently, lower masses. With this new population of galaxies coming into focus, it also serves as a new set of subjects to test our models and theory of galaxy formation. While the current galaxy formation models have been widely successful at reproducing the general trends in observed properties of typical galaxies, they struggle to do so for galaxies in low 11 mass halos (MH . 10 M ). In simulations, the growth of the galaxies traces the growth of their parent dark matter halos too closely, which manifests as an over-prediction of low- mass galaxies compared to the observations. Feedback from star-formation and central black hole activity is necessary to decouple the evolution of the galaxies (made of baryonic material) from that of the dark matter halos. This is particularly critical for low-mass galaxies because of their shallow gravitational potential wells. The goal of this thesis is to understand the star-formation properties of faint, low-mass galaxies and to assemble statistically significant samples of these objects that can ultimately be used to perform more detailed follow-up studies and refine the galaxy formation models. Using deep UV imaging data obtained as part of the Hubble UltraViolet Ultra Deep Field (UVUDF) program, we measure the rest-UV luminosity functions for star-forming galaxies during the cosmic high-noon – the peak of cosmic star-formation rate at 1.5 < z < 3. With samples of galaxies extending ∼2 magnitudes deeper than other direct imaging studies, we definitively pin the faint-end slope for the rest-UV luminosity function at 1.5 < z < 3. We compare the star-formation properties of z ∼ 2 galaxies from these UV observations with results from Hα and UV+IR observations to find a lack of high SFR sources in the UV luminosity function. This can be explained by a population of dusty star-forming galaxies that are not properly accounted for by the generic relations used for dust corrections. We compute a volume-averaged UV-to-Hα ratio by abundance matching the rest-UV and Hα luminosity functions and find the observed ratio to deviate from the expectation for constant 9 star-formation history for low-mass galaxies (M? . 5 × 10 M ). We conclude that this could be due to a larger contribution from starbursting galaxies compared to the high-mass end.

v We next focus on the low-mass, highly star-forming galaxies characterized by the pres- ence of strong (high EW) emission lines in their spectra and thought to be representative of the earliest galaxies in the universe. While abundant in the high redshift universe, these objects are rare at lower redshifts. In order to compile a statistically significant sam- ple of these, we use the Spitzer Large Area Survey with Hyper-Suprime-Cam (SPLASH) dataset, which covers 2.4 deg2 on the Subaru-XMM Deep Field (SXDF) with deep opti- cal, near-infrared and mid-infrared imaging. We homogenize all available imaging data on to a common astrometric reference frame to generate multi-wavelength catalog containing ∼ 800, 000 objects with photometry in 28 bands, reliable photometric redshifts, and stellar population properties. Using this multi-wavelength catalog and applying a broadband selection technique to identify galaxies with strong emission lines, we identify samples of extreme emission line galaxies and Lyα-emitters over 0.06 < z < 0.7 and 2.4 < z < 3.8, respectively. The low- redshift EELGs are similar to the “Green Pea” and “blueberry” galaxies found in SDSS, albeit being much fainter and lower mass. From an initial round of spectroscopic follow- up with MMT/Hectospec, we already find one highly interesting object at z = 0.069 that exhibits signatures of an exotic interstellar medium with a Balmer ratio significantly lower than the canonical Case B assumption and a particularly high O32 ratio. The EELGs in SPLASH have similar specific star-formation rates as the brighter “blueberry” galaxies from SDSS, possibly suggesting common physical processes governing their star-formation. The LAEs exhibit extreme Lyα EWs that can only be caused by very recent star-formation, top-heavy IMFs and/or extremely metal poor populations. Upcoming space-based surveys such as Euclid and WFIRST-AFTA plan to unveil the nature of dark energy by performing galaxy redshift surveys observing emission line galaxies via slitless spectroscopy. These surveys will assemble an unprecedented collection of star- forming galaxies over 0.9 < z < 2. As part of strategy optimization for these missions, we use the current generation HST-based slitless survey, the WFC3 Infrared Spectroscopic Parallel (WISP) survey, to estimate the number of emission line galaxies observable by these future surveys.

vi Contents

Acknowledgementsi

Dedication iv

Abstract v

List of Tables xi

List of Figures xiii

1 Introduction1 1.1 Galaxy Formation Theory: a brief overview...... 2 1.1.1 Observational Evidence...... 2 1.1.2 Theoretical Framework...... 5 1.1.3 Connecting the theory and observations...... 10 1.2 Star-formation indicators...... 12 1.2.1 UV light...... 14 1.2.2 Emission lines...... 14 1.2.3 Other indicators...... 15 1.2.4 Dust...... 15 1.3 Low-mass galaxies...... 17 1.4 Surveying star-forming, low-mass galaxies...... 18 1.4.1 Rest-frame UV selection...... 18 1.4.2 Emission line galaxies...... 19 1.5 Prospects for upcoming surveys...... 22

2 UVUDF: UV Luminosity Functions at the cosmic high-noon 24 2.1 Data and Sample Selection...... 26

vii 2.1.1 UVUDF Data...... 26 2.1.2 Dropouts Sample Selection...... 27 2.1.3 Photometric Redshift Sample Selection...... 29 2.2 Completeness...... 30 2.2.1 Completeness Simulations...... 30 2.2.2 Selection Functions...... 33 2.2.3 Redshift distribution of the Dropout Sample...... 35 2.3 Deriving the Luminosity Function parameters...... 36 2.4 Results...... 37 2.4.1 Rest-frame UV Luminosity functions at z ∼ 1.5 − 3...... 37 2.4.2 Cosmic Variance...... 40 2.4.3 UV Luminosity Density...... 41 2.5 Discussion...... 45 2.5.1 Dust Correction...... 47 2.5.2 Star Formation Histories...... 48 2.6 Conclusions...... 52 2.A Completeness Functions...... 55 2.B UV Dust correction...... 56 2.C Hα Dust correction...... 58

3 SPLASH-SXDF Multi-wavelength Photometric Catalog 62 3.1 Data...... 63 3.1.1 Optical and near-infrared data...... 64 3.1.2 Mid-Infrared data...... 66 3.2 Data Homogenization...... 67 3.2.1 Creating Mosaics...... 67 3.2.2 Astrometric Corrections...... 70 3.2.3 PSF Homogenization...... 71 3.3 Multi-wavelength Catalog...... 75 3.3.1 Source Extraction...... 75 3.3.2 IRAC Photometry...... 76 3.3.3 Photometric errors and magnitude upper limits...... 79 3.3.4 Ancillary Datasets...... 82 3.4 Photometric Redshifts and Physical properties...... 82 3.4.1 Photometric Redshifts...... 82

viii 3.4.2 Star/Galaxy Classification...... 90 3.4.3 Physical Properties...... 91 3.5 Summary...... 92 3.A Catalog description...... 93 3.B Correcting photometric errors...... 93

4 Extreme emission line galaxies in SPLASH-SXDF 97 4.1 Data and Sample Selection...... 99 4.1.1 Color-color selection...... 100 4.1.2 Cleaning the samples...... 103 4.2 MMT Hectospec follow-up...... 105 4.2.1 EELG targets...... 105 4.2.2 Comparing spectroscopic and photometric line fluxes...... 109 4.3 Analysis...... 109 4.3.1 Low-redshift EELGs...... 111 4.3.2 Lyα emitters...... 115 4.4 Conclusions...... 120

5 Predicting the z∼2 Hα luminosity function using [OIII] emission line galaxies 124 5.1 Data...... 126 5.2 Hα–[OIII] Trend...... 127 5.3 Parametrization of the Bivariate Line luminosity function...... 128 5.4 Fitting Procedure...... 130 5.4.1 Original MLE...... 131 5.4.2 Modified MLE...... 132 5.4.3 Setting up the Bivariate LLF...... 133 5.4.4 Survey Incompleteness...... 135 5.5 Fitting the Bivariate LLF at z ∼ 1...... 135 5.6 Estimating Hα from [OIII] at z ∼ 1...... 139 5.7 Estimating Hα from [OIII] at z ∼ 2...... 143 5.8 Hα Number counts...... 144 5.9 Summary and Conclusions...... 146 5.A 1–D Simulations to test the modified MLE...... 150

6 Summary 152

ix References 155

x List of Tables

2.1 UVUDF: Best-fit parameters for rest-frame 1500A˚ UV LFs...... 41 2.2 UVUDF: UV luminosity densitya ...... 42 2.3 UVUDF: Star Formation Rate Densitya...... 44 2.4 UVUDF: Fit parameters to the empirical UV-to-Hα relationa...... 53 a 2.5 UVUDF: Rest-frame 1500A˚ UV LFs measured via the Vmax estimator ... 60 a 2.5 UVUDF: Rest-frame 1500A˚ UV LFs measured via the Vmax estimator ... 61 3.1 SPLASH-SXDF Catalog: Summary of photometric bands included in the catalog...... 68 3.2 SPLASH-SXDF Catalog: PSF parameters from PSFEx for optical and NIR bands...... 74 3.3 SPLASH-SXDF Catalog: Systematic offsets between the measured 200 fluxes and library templates as computed by LePhare ...... 85 3.4 SPLASH-SXDF Catalog: Samples with spectroscopically confirmed redshifts 86 3.5 SPLASH-SXDF Catalog: SExtractor parameters used for Dual image mode χ2 detection and photometry...... 94 3.6 SPLASH-SXDF Catalog: Column Descriptions for the SPLASH-SXDF Cat- alog v1.5† ...... 95 3.7 SPLASH-SXDF Catalog: Correction factors for SExtractor photometric errors...... 96 4.1 SPLASH-SXDF EELGs: Spectroscopic summary of EELG candidates with follow-up MMT observations...... 122 4.2 SPLASH-SXDF EELGs: Summary of all detected emission lines in the z = 0.069 bright EELG...... 123 5.1 WISP: Best-fit parameters for the Hα–[OIII] bivariate LLF for 0.8 < z < 1.2 sample...... 136 5.2 WISP: Best-fit parameters for the [OIII] exclusive LLF fit for 0.8 < z < 1.2 sample...... 141

xi 5.3 WISP: Best-fit parameters for the [OIII] exclusive LLF fit for 1.85 < z < 2.2 sample...... 143 5.4 WISP: Cumulative Hα number counts (after applying [NII] correction)a .. 147 5.5 WISP: Cumulative Hα number counts (without applying [NII] correction)a . 148

xii List of Figures

1.1 Introduction: The cosmic star-formation history...... 5 1.2 Introduction: Comparing the DM HMF vs. local GSMF...... 11 1.3 Introduction: Issues with low-mass galaxies in simulations...... 13 1.4 Introduction: The IRX-β relation...... 16 2.1 UVUDF: Color-color plots for dropout sample selection...... 27 2.2 UVUDF: Sample selection functions for dropout and photometric redshift- selected samples...... 34 2.3 UVUDF: Redshift distribution of dropout-selected samples...... 35 2.4 UVUDF: Rest-frame 1500A˚ UV luminosity functions at z∼1.7,2.2,3.0.... 38 2.5 UVUDF: Redshift evolution of the UV luminosity density...... 43 2.6 UVUDF: UV and Hα star formation rate functions at z∼2...... 46 2.7 UVUDF: UV-to-Hα ratio as a function of galaxy age...... 50 2.8 UVUDF: The volume-averaged UV-to-Hα ratio at z∼2...... 54 2.9 UVUDF: Cmpleteness functions for UVUDF filters...... 57 2.10 UVUDF: Dust corrections for UV and Hα ...... 58 3.1 SPLASH-SXDF Catalog: Coverage maps...... 64 3.2 SPLASH-SXDF Catalog: Transmission curves for photometric bands.... 66 3.3 SPLASH-SXDF Catalog: Maps of the 5σ limiting magnitude for select filters 69 3.4 SPLASH-SXDF Catalog: 5σ limiting depth for all filters...... 70 3.5 SPLASH-SXDF Catalog: Average scatter in astrometry...... 71 3.6 SPLASH-SXDF Catalog: Curve of growth plot for PSFs in all filters.... 73 3.7 SPLASH-SXDF Catalog: Number counts of sources detected...... 76 3.8 SPLASH-SXDF Catalog: Galactic extinction...... 77 3.9 SPLASH-SXDF Catalog: Photometric errors before and after SWARP pro- cessing...... 80 3.10 SPLASH-SXDF Catalog: Positions and redshift-magnitude distribution of spectroscopic sample...... 86

xiii 3.11 SPLASH-SXDF Catalog: Performance of photometric redshifts...... 87 3.12 SPLASH-SXDF Catalog: Performance of photometric redshifts for different depths and coverage...... 88 3.13 SPLASH-SXDF Catalog: Performance of photometric redshifts as a function of magnitude...... 89 3.14 SPLASH-SXDF Catalog: Identifying stars using BzK color-color diagram. 91 3.15 SPLASH-SXDF Catalog: Stellar mass distribution as a function of redshift 92 4.1 SPLASH-SXDF EELGs: Color-color diagram for EELG galaxy templates. 101 4.2 SPLASH-SXDF EELGs: Color-color diagram for EELG selection...... 103 4.3 SPLASH-SXDF EELGs: Candidate examples for Zooniverse...... 104 4.4 SPLASH-SXDF EELGs: MMT spectra for EELG candidates...... 106 4.5 SPLASH-SXDF EELGs: MMT spectrum for a bright z = 0.069 EELG... 107 4.6 SPLASH-SXDF EELGs: Line fluxes expected from photometry compared with spectroscopic measurements...... 110 4.7 SPLASH-SXDF EELGs: Photometric redshift distribution of EELGs.... 111 4.8 SPLASH-SXDF EELGs: Observed properties of low redshift EELGs.... 113 4.9 SPLASH-SXDF EELGs: Rest-frame EW as a function of observed magnitude and luminosity for low redshift EELGs...... 114 4.10 SPLASH-SXDF EELGs: SFR as a function of stellar mass for low redshift EELGs...... 115 4.11 SPLASH-SXDF EELGs: Observed properties of LAEs...... 117 4.12 SPLASH-SXDF EELGs: Time evolution of Lyα EW for extremely metal- poor galaxy templates...... 118 4.13 SPLASH-SXDF EELGs: Rest-frame EW(Lyα) distributions of LAEs.... 119 4.14 SPLASH-SXDF EELGs: The Ando effect for LAEs...... 119 5.1 WISP: Observed Hα and [OIII] luminosities...... 129 5.2 WISP: Hα–[OIII] bivariate LLF at 0.8 < z < 1.2...... 137 5.3 WISP: Posterior and joint-posterior distributions for the bivariate LLF pa- rameters...... 138 5.4 WISP: Collapsed [OIII] LLF for z∼1 sample...... 139 5.5 WISP: Collapsed Hα LLF for z∼1 sample...... 140 5.6 WISP: Comparison of z∼1 [OIII] LLF with literature...... 141 5.7 WISP: Comparison of z∼1 Hα LLF with literature...... 142 5.8 WISP: [OIII] LLF for z∼2 galaxies...... 144 5.9 WISP: z∼2 Hα LLF and number counts...... 145

xiv 5.10 WISP: Estimated Hα number counts for 0.7 < z < 2.0...... 149 5.11 WISP: Results of simulations to test the modified MLE...... 151

xv Chapter 1

Introduction

Ever since Edwin Hubble established that galaxies were indeed objects external to our Milky Way in 1926, understanding how these galaxies form and evolve with time has been one of the key questions driving the active field of study in astrophysics and cosmology. Over the past couple decades, we have made significant headway towards answering this question. Constrained by a multitude of observational evidence, the Λ cold dark mat- ter (ΛCDM) scenario has emerged as the leading candidate for the model of the universe (Primack, 2003). ΛCDM assumes that the universe is primarily composed of (i) ordinary baryonic matter, (ii) non-relativistic cold dark matter, which only interacts gravitationally, and (iii) “dark energy”, which is reponsible for the acceleration in the universe’s expansion. One of the interpretations for dark energy assumes it to take the form of a constant vac- uum energy density, referred to as the cosmological constant (Λ). The ΛCDM cosmological model serves as a compelling backbone for galaxy formation theories, which have also been increasingly successful. The latest models have been able to reproduce the general trends in observed properties of galaxies, including their number counts, clustering properties, colors, morphologies, as well as time evolution (e.g., Bower et al., 2006; Somerville et al., 2008; Guo et al., 2011; Dav´eet al., 2011; Vogelsberger et al., 2014b; Schaye et al., 2015). However, one of the difficulties that still plagues these models has been reproducing the 11 properties of galaxies in low-mass halos (virial mass MH . 10 M ), where the simulated galaxies form their stars too early and too efficiently (Fontanot et al., 2009). Even though the baryonic matter only comprises ∼5% of the energy content of the universe (Planck Collaboration et al., 2016a), it is the baryonic physics that predominantly govern the growth of galaxies by regulating the conversion of gas into stars. Stars produce a variety of feedback effects that inhibit the inflow of gas and, in turn, reduce the efficiency of star-formation. The equilibrium between star-formation and its feedback effects is important for the evolution

1 Chapter 1. Introduction 2

of all galaxies, but critically so for the low-mass galaxies due to their shallow gravitational potential wells which are highly sensitive to changes in the rate at which gas falls in and is driven out of the galaxy. The focus of this thesis is on these galaxies that lie toward the low-mass end of the galaxy mass function. The goal is to further our understanding of the star-formation processes in the faint, low-mass galaxies and also assembling statistically significant samples of these objects that can ultimately be used to perform more detailed follow-up studies and refine the galaxy formation models. This chapter serves as a comprehensive introduction on our current knowledge about the low-mass galaxies in order to provide context and scope for the work presented in this thesis. Three of the chapters included in this dissertation are published articles that have been accepted by major astrophysical journals after going through the standard scientific peer review process. These articles are included in their entirety with the exception of a few minor editions. The remaining chapter presents ongoing work that will be submitted to the Astrophysical Journal shortly after the defense of this thesis.

1.1 Galaxy Formation Theory: a brief overview

The currently-favored ΛCDM model for the structure formation in the universe predicts that the collapse of the dark matter halos proceeds in a “hierarchical” fashion, with smaller structures forming first and later merging into larger systems. The galaxies we observe and study are contained within these dark matter halos. However, at least from the perspective of their stellar populations, the galaxies do not seem to share the same hierarchical evolu- tionary history as their dark matter halos. The most massive galaxies (e.g., large ellipticals in galaxy groups and clusters) held within massive dark matter halos are dominated by older stellar populations, whereas the isolated faint, low-mass galaxies residing in smaller halos outside of major galaxy groups appear to have formed their stars much more recently and are dominated by younger stellar populations. The growth and evolution of galaxies clearly appears to be distinct and more complex than that of the dark matter halos they reside within.

1.1.1 Observational Evidence

Wide-field surveys such as the Sloan Digital Sky Survey (SDSS, York et al., 2000) have collected samples of millions of nearby galaxies, spanning multiple orders of magnitude in galaxy mass as well as a large variety of galaxy types, morphologies, and environments Chapter 1. Introduction 3

(e.g., Bell et al., 2003; Kauffmann et al., 2003; Baldry et al., 2004; Brinchmann et al., 2004; Tremonti et al., 2004; Eisenstein et al., 2005; Salim et al., 2007; Kewley & Ellison, 2008). On the other hand, deep surveys undertaken with the Hubble Space Telescope (HST) have uncovered galaxies all the way out to z ∼ 11, when the universe was less than 500 Myr old (e.g., Coe et al., 2013; Ellis et al., 2013; McLure et al., 2013; Bouwens et al., 2015; Finkelstein et al., 2015; McLeod et al., 2015; Calvi et al., 2016; Oesch et al., 2016; Salmon et al., 2018). A large suite of ground- and space-based telescopes provide a panchromatic view in imaging and spectroscopy, spanning from gamma-rays all the way out to radio wavelengths. This has enabled detailed measurement of the Spectral Energy Distribution (SED) for large samples of galaxies, which further allows us to measure the redshifts, stellar masses, star-formation rates, dust content, metallicities, and star-formation histories using parametric stellar population synthesis models (Leitherer et al., 1999, 2014; Bruzual & Charlot, 2003; Conroy, 2013). We have at our hands an ever growing collection of galaxies along with their observed properties and certain trends have stood out. A full review of all of the signatures in the observed properties of galaxies is beyond the scope of this chapter, but highlighted below are some that are relevant in providing context for the topics covered in this thesis. One of the first results from SDSS was the bimodal color-luminosity distribution of galaxies (Baldry et al., 2004) – the star-forming galaxies populating the “blue cloud” due to their younger stellar populations and ongoing star-formation as opposed to the quies- cent galaxies with their older stellar populations occupying the “red” sequence (Kauffmann et al., 2003; Brinchmann et al., 2004; Salim et al., 2007; Schiminovich et al., 2007). Recent deep surveys have been able to show these two populations of galaxies (star-forming and quiescent) as being distinguishable out to z ∼ 4 (Brammer et al., 2011; Muzzin et al., 2013). The distribution of galaxies as a function of their luminosity (the luminosity function, LF) as well as their stellar masses (the galaxy stellar mass function, GSMF) have been quantified for both star-forming and quiescent galaxies in rest-frame optical and near-infrared (NIR) out to z ∼ 4 (e.g., McLure et al., 2009; Ilbert et al., 2010; Caputi et al., 2011; Santini et al., 2012; Ilbert et al., 2013; Muzzin et al., 2013; Tomczak et al., 2014; Davidzon et al., 2017). The star-forming galaxy LF has been measured further out to z ∼ 8 using rest-frame ultra-violet (e.g., Arnouts et al., 2005; Sawicki, 2012; Yoshida et al., 2006; Bouwens et al., 2007; Dahlen et al., 2007; Reddy & Steidel, 2009; Hathi et al., 2010; Oesch et al., 2010; van der Burg et al., 2010; Sawicki & Thompson, 2006; Alavi et al., 2014, 2016; Bouwens et al., 2014b,a, 2015; Finkelstein et al., 2015; Bernard et al., 2016; Parsa et al., 2016; Mehta Chapter 1. Introduction 4

et al., 2017). It is clear from these observations that galaxies are: 1) continuously build- ing up their mass over time consistent with the hierarchical paradigm, 2) massive galaxies formed and assembled their stars earlier than lower mass galaxies (Marchesini et al., 2009; Moustakas et al., 2013; Muzzin et al., 2013), and 3) low-mass galaxies form their stars later and over a longer timescale – an effect often called “mass assembly downsizing” (Cimatti et al., 2006). Moreover, while the number and mass density of the quiescent population has been increasing since z ∼ 2, those of the star-forming galaxies have stayed roughly constant over the same time period (Bell et al., 2004, 2007; Faber et al., 2007; Brammer et al., 2011; Muzzin et al., 2013). In order to grasp the global scope of how and when galaxies assemble their stellar masses, considerable effort has been invested into measuring the cosmic star-formation rate density using star-forming galaxies at all redshifts z . 8 (e.g., Oesch et al., 2010; Alavi et al., 2014, 2016; Bouwens et al., 2014b,a, 2015; Finkelstein et al., 2015; Parsa et al., 2016; Mehta et al., 2017). Madau & Dickinson(2014) summarize a range of complementary observational techniques and theoretical tools to find a consistent picture of the star-formation history of the universe. Combining two of the popular star-formation indicators, rest-frame UV (e.g., Wyder et al., 2005; Robotham & Driver, 2011; Schiminovich et al., 2005; Dahlen et al., 2007; Reddy & Steidel, 2009; Bouwens et al., 2012; Cucciati et al., 2012; Schenker et al., 2013) and IR (e.g., Sanders et al., 2003; Takeuchi et al., 2003; Magnelli et al., 2009, 2011, 2013; Gruppioni et al., 2013), they find that the cosmic star-formation density rises steadily from z∼8 to 3, reaches its peak around z∼1.5–2 (often called the “cosmic high-noon”) and then drops exponentially at z . 1. Roughly half of the stellar mass of the universe was assembled at the cosmic high-noon, with galaxies forming stars ∼10 times faster than the local, present-day galaxies. Across the various surveys, galaxies also seem to exhibit many correlations between their global properties. The often-called “star-forming main sequence” (SFMS, Noeske et al., 2007; Salim et al., 2007; Elbaz et al., 2007; Pannella et al., 2009; Daddi et al., 2010; Wuyts et al., 2011; Whitaker et al., 2012; Reddy et al., 2012; Speagle et al., 2014) is a strong correlation between the galaxy stellar mass and its star-formation rate amongst the star-forming galaxy population. Speagle et al.(2014, and references therein) show that the SFMS exists out to z ∼ 6 and is remarkably tight with a 1σ scatter of only ∼0.2 dex, which remains constant over cosmic time. The observed “mass-metallicity relation” (MZR) of galaxies is evidence for how the gas-phase oxygen abundance in galaxies is strongly correlated with the stellar mass in star-forming galaxies with a tight scatter of ∼0.1 dex 6−7 extending over three orders of magnitude in stellar mass down to ∼10 M (Tremonti Chapter 1. Introduction 5

Figure 1.1 The cosmic star formation history adapted from Madau & Dickinson(2014). The top right panel shows the cosmic star-formation rate density estimates from FUV surveys, the bottom right from IR surveys and the left panel shows the combination of the two. This shows the remarkable evidence from a collection of different surveys that highlights the rise of the cosmic star-formation rate from z∼8 to 3, reaching its peak around z∼1.5–2 (the “cosmic high-noon”), and the subsequent decline at z . 1.

et al., 2004; Savaglio et al., 2005; Erb et al., 2006; Lee et al., 2006; Berg et al., 2012; Zahid et al., 2013; Steidel et al., 2014; Wuyts et al., 2014). Some of these correlations may be indicative of second-parameter dependencies while others may point towards the fundamental physics governing the behavior of galaxies. Re- gardless, it is these observed properties that ultimately the galaxy formation theory and models strive to reproduce.

1.1.2 Theoretical Framework

Over the past decade, the science of simulating realistic galaxies has also seen significant progress. At its core, galaxy formation is a two step process – the large-scale structure of the universe is shaped by the DM halos via hierarchical growth followed by baryonic material collapsing and cooling within the gravitational potential wells created by the DM halos and forming galaxies (White & Rees, 1978). Dark matter only N-body simulations within ΛCDM have been successful at resolving the substructure (the “cosmic web”) as well as the individual dark matter halos (e.g., Ghigna et al., 1998; Klypin et al., 1999; Springel et al., 2005; Boylan-Kolchin et al., 2009). In the standard ΛCDM model, the dark matter particles only interact via gravity and hence, this is the only major physical process required Chapter 1. Introduction 6

in pure dark matter simulations. On the other hand, forming galaxies requires tracing the evolution of the baryons whose interactions are governed by many more physical processes, some of which (e.g., star formation, and feedback effects from the stars and central black hole) are complex and still poorly understood. Moreover, simultaneously resolving both the large-scale structure and environment (on scales of Mpc) alongside star-formation, central black hole interactions and their feedback effects (on sub-pc scales) is extremely computa- tionally expensive and not feasible with current infrastructure. Therefore, galaxy formation simulations have become reliant on combining analytic modeling, numerical simulations, and empirical relations to best produce the observations. Outlined here are some of the major physical processes that affect the evolution of baryons in the context of galaxy formation:

• Gravity: Gravity defines the backbone for galaxy formation. The DM halos in which galaxies ultimately reside are formed by gravitationally evolving the primordial density fluctuations. The power spectrum of the primordial density fluctuations and gravity determine the number of DM halos of any given mass that have collapsed at any given cosmic time. These two components also determine the growth rate of the DM halos through accretion and merging as well as their clustering properties. In the most basic assumption, one galaxy is assigned to one of these DM halos. Mergers of the DM halos cause their central galaxies to eventually merge after gravitational and dynamic friction has sufficiently decayed their orbits. Mergers can trigger bursts of star-formation as well as accretion onto the central black hole and thus, have significant impact on the galaxy.

• Hydrodynamics and Thermal evolution: As the DM halos collapse under gravity, the gas contained within gets heated by shocks. The subsequent evolution of this gas is strongly dependent on how efficiently it can cool and radiate away its energy. Two-body radiative processes are the predominant cooling method for gas relevant 7 to galaxy formation. At &10 K, gas is fully collisionally ionized and cools primarily via bremsstrahlung radiation (free-free emission). Gas with temperatures ranging 104 < T < 107 K cools via electrons recombining with ions (free-bound radiation) and collisionally ionized atoms decaying to their ground state. Below 104 K, gas cooling mainly occurs via collisional (de-)excitation of heavy elements (metal line cooling) and molecular cooling.

The accretion of gas on to the galaxy is an important component in determining the amount of fuel available in the galaxy for forming stars. Gas accretion can occur in Chapter 1. Introduction 7

two main ways: (i) “hot mode” accretion where the cooling timescales for the gas are longer than the dynamical time and the gas ends up forming a pressure-supported quasi-hydrostatic gaseous halo that gradually cools and eventually switches to support by angular momentum, and (ii) “cold mode” accretion where the cooling times are short compared to the dynamical time and the gas accretes directly on to the galaxy (Birnboim & Dekel, 2003; White & Frenk, 1991). The latter tends to occur when the gas flows in along relatively cold, dense cosmic filaments (Kereˇset al., 2005).

• Star formation: Forming stars is one of the most critical steps for galaxy formation as it is the light from these stars that we ultimately measure and use for making inferences of the galaxy properties. Once the gas has collapsed onto the galaxy and becomes dense enough, self-gravity of the gas takes over and can collapse it further. A full simulation of the process of forming a star is often requires resolution that is finer by many orders compared to the galaxy. Typically, empirical sub-grid recipes are implemented for forming stars in current generation of cosmological simulations.

• Stellar Feedback: The baryonic material we can observe in galaxies accounts for .10% of the total baryon budget of the universe (e.g., Fukugita et al., 1998; Fukugita & Peebles, 2004; Salucci & Persic, 1999). The current paradigm of galaxy formation where we assign one galaxy per DM halo would not be successful without introducing some sort of “feedback” that suppresses the cooling of gas and consequently, star formation on some scales. This “overcooling” problem has been recognized since the inception of ΛCDM and it has been suggested that star-formation can be made inefficient by the energy generated in supernova explosions, which could heat the gas and possibly drive it out of galaxies (Dekel & Silk, 1986; White & Frenk, 1991; White & Rees, 1978). We now know from observations in our own galaxy that there are many processes associated with massive stars and supernovae such as photo-heating, photo- ionization, winds and shocks that can drive large-scale outflows carrying baryonic material out of the galaxy (see Hopkins et al., 2012). These effects play a critical role in regulating the star-formation within the shallow potential wells of low-mass galaxies. These processes are also on the scale of stellar clusters and cosmological simulations lack the range of resolution to fully simulate these effects in detail and often sub-grid recipes based on empirical knowledge are relied upon when simulating galaxies.

• Central black hole formation and growth: There is strong observational evidence that most or perhaps all massive galaxies contain a supermassive black hole at their center Chapter 1. Introduction 8

(see Kormendy & Ho, 2013). Little is known about how these central black holes form initially and how they grow with time. Theoretical studies suggest that it is possible to create a “seed” black hole in the early universe via direct collapse of low angular momentum gas, as the remnant of a Pop III (metal free) stars, or via stellar dynamical processes (Volonteri, 2010) and they can grow by accreting gas with negligible angular momentum or via an accretion disk that reduces the gas angular momentum through viscous processes (Netzer, 2013). Both of these processes are critical for galaxy formation as the central black hole plays an important role in defining the gravitation potential for the galaxy. However, due to their small scales, these effects need to be modeled with sub-grid recipes in the current generation of simulations.

• Feedback due to central black hole: From simple calculations it can be shown that the growth of the central supermassive black hole in galaxies releases energy that is comparable to the gravitational binding energy of the galaxy, suggesting that it could have a significant impact on its evolution (Silk & Rees, 1998). There is observational evidence of jets and high-velocity winds associated with Active Galactic Nuclei (AGN) which may eject gas from galaxies as well as of hot bubbles generated by the jets which may prevent gas cooling and accretion on to the galaxy (see Fabian 2012 and Heckman & Best 2014 for reviews). The question of how efficiently this feedback energy from the central black hole can couple to the gas within and surrounding the galaxy is one of active debate. Regardless, the feedback effects from the central black hole (often called as AGN feedback) play a crucial role in determining the evolution of galaxies, particularly for massive galaxies. Sub-grid recipes need to be invoked again for accounting for the AGN feedback in current cosmological simulations.

• Stellar populations and chemical evolution: Galaxies consist of large populations of stars that span multiple generations. It is important to consider the history of star- formation episodes, the spectrum of stars generated in a given episode as well as the lifetimes of the variety of stars when making inferences from the observed composite stellar light from a galaxy. The popular approach for making direct comparisons between the models and observations has been to use combinations of simple stellar population models that provide the SED for a stellar population of a single age and metallicity (e.g., Leitherer et al., 1999; Bruzual & Charlot, 2003; Conroy & Gunn, 2010) and assuming a stellar Initial Mass Function (IMF). The process of taking single stellar population models and converting them into an SED for composite stellar Chapter 1. Introduction 9

populations has turned into its own sub-field (see Conroy 2013 for a detailed review).

Moreover, as the stars evolve and reach the end of their lifetimes, they pollute their surrounding gas with the heavy elements produced within the stars and their super- novae. This metal-enriched gas can be ejected from the galaxy and may even enrich the surrounding intergalactic medium. Tracing this chemical evolution is important for galaxy formation models as these metals greatly enhance the cooling rates at inter- mediate temperatures. The metal content also affects the rate of formation of future generation of stars as well as their luminosities and spectra. Lastly, the heavy ele- ments produce dust in the interstellar medium, which reddens all stellar light from the galaxy (see Section 1.2.4). The chemical evolution of the galaxy and its surrounding gas is included in most of the modern galaxy formation models.

• Radiative transfer: The radiation from stars and the accretion disk around the central black hole has a significant impact on the galaxy’s evolution. Apart from heating the surrounding gas, it can also modify the ionization state of the gas depending on the shape of the emitted spectrum, which in turn can affect the cooling rates, particularly for metal-enriched gas. Moreover, the interaction of the radiation with the gas and dust in the interstellar medium can greatly impact the observed luminosity, color as well as the observationally determined morphological and structural properties of galaxies, particularly in the rest-frame UV and optical. Self-consistent treatment of radiative transfer in galaxy simulations is often too computationally expensive; however, with sufficient resolution, the radiative transfer effects can be computed in post-processing to estimate the pan-chromatic properties of galaxies (e.g., Jonsson et al., 2010) and their emission lines (e.g., Narayanan et al., 2008).

A successful model of galaxy formation needs to account for all of these physical pro- cesses as they trace the evolution of the baryons within the DM halos, however this is a non-trivial accomplishment due to the computational limitations. The two main theo- retical approaches that have been widely adopted for galaxy formation modelling are: (i) gas-dynamical simulations that rely on hydrodynamics and thermodynamics to simulate the baryonic physics, and (ii) semi-analytical modeling which uses simplified mathematical descriptions, and physically and observationally motivated analytic recipes applied to the evolving DM halos from an N-body simulations. The gas-dynamical simulations introduce baryonic matter into the DM-only N-body simulations while accounting for the baryonic physical processes, using hydrodynamics to model the gas physics and thermodynamics to simulate the radiative processes. However, Chapter 1. Introduction 10 these simulations come with heavy computational demands which ultimately restricts the dynamic range that can be simulated explicitly. For simulating the small scale processes such as star-formation, black hole growth, and feedback processes, these type of simulations have to rely on somewhat arbitrary and uncertain sub-grid recipes (Cen & Ostriker, 1993; Dav´eet al., 2001; Springel & Hernquist, 2003; Springel, 2005; Kereˇset al., 2005; Nagamine et al., 2005; Schaye et al., 2010). “Semi-analytic” models (SAM) provide an alternate approach to simulating galaxy for- mation in a cosmological context (White & Frenk, 1991; Cole et al., 1994, 2000; Somerville & Primack, 1999; Somerville et al., 2008; Croton et al., 2006; Weinmann et al., 2009; Guo et al., 2010). Instead of explicitly solving the fundamental equations for each particle or grid cell, these use pre-calculated DM merger trees and follow the formation of galaxies with a set of simplified, physically and observationally motivated analytic recipe (see reviews by Baugh 2006 and Benson 2010). In recent literature, there have been a breath of galaxy simulations employing the SAM approach such as Lu et al.(2014), Henriques et al.(2013), Gonzalez-Perez et al.(2014), and Porter et al.(2014) as well as hydrodynamical simulations such as EAGLE (Schaye et al., 2015), ezw (Dav´eet al., 2013), FIRE (Hopkins et al., 2014), NIHAO (Tollet et al., 2016), and Illustris (Vogelsberger et al., 2014a). A full review of all the theoretical efforts in modeling galaxies is beyond the scope of this introduction and we refer the reader to recent reviews by Somerville & Dav´e(2015) and Naab & Ostriker(2017).

1.1.3 Connecting the theory and observations

The basic observable statistical signature of galaxies – the galaxy LF or GSMF – cannot be “naturally” reproduced from the DM halo mass function (HMF) in galaxy formation models. The faint end power-law slope of the DM HMF is αH = −2, whereas the observed

GSMF has a much shallower slope of αg = −1.3 in the local universe. Feedback effects due to star-formation activity have been suggested as responsible for the flattening of the slope at the low-mass end (Larson, 1974; Dekel & Silk, 1986; White & Frenk, 1991). The shallow 9−11 gravitational potential wells of these low-mass DM halos (Mhalo ∼ 10 M ) allows stellar feedback such as supernova, radiation pressure, and winds from massive stars to efficiently eject gas and dust from the galaxy. This reduces the availability of gas to fuel further episodes of star formation, thus lowering the star formation efficiency and abating stellar 9 mass growth. For the lowest mass halos (Mhalo . 10 M ), other processes such heating of the intergalactic medium via photoionization due to the UV background may also play an dominant important role in lowering the star formation efficiency (see Benson et al. 2002, Chapter 1. Introduction 11

Figure 1.2 The comparison between the DM halo mass function from ΛCDM (thick curve) with the observed galaxy stellar mass function of local galaxies (plotted as data points) adapted from Bullock & Boylan-Kolchin(2017). The dotted curve shows the HMF adjusted for the cosmic baryon fraction. The shaded region shows the range of faint-end slopes observed for the GSMF. While the functional forms of the DM HMF and the GSMF are similar, there is a distinct difference in their power-law slopes at the low-mass end as well as the exponential cutoff at the high-mass end. Feedback effects from star-formation (for low- mass halos) and central black hole (for high-mass halos) are the most plausible explanation in current galaxy formation models that decouples the evolution of the galaxies from their parent DM halos.

13 Wechsler & Tinker 2018 and references therein). At the high-mass extreme (Mhalo & 10 M ), even though the GSMF and HMF have similar functional form, ΛCDM predicts the exponential cut-off in the HMF to be at much larger masses than the observed GSMF cut- off. Here, strong feedback from the central black hole is believed to be the lead cause for quenching of star formation by preventing inflow of cool gas via jet-like outflows as well as heating up the surrounding gas via thermal feedback (e.g., Binney & Tabor, 1995; Ciotti & Ostriker, 2001; Novak et al., 2011; Sazonov et al., 2005; Croton et al., 2006). Recipes to account for these feedback effects have been introduced in the current state- of-the-art galaxy simulations and while the predictions from theoretical models and ob- servations are in agreement in a broad sense (Somerville & Dav´e, 2015), there are prob- lems with reproducing the low-mass end. Fontanot et al.(2009) showed that low-mass ? 10 (M . 10 M ) galaxies were being overproduced by a factor of ∼2–3 over the redshift range 0.5 . z . 4 in three independently developed SAMs. This overproduction of low-mass Chapter 1. Introduction 12 galaxies is also observed in hydrodynamical simulations as illustrated in the case of Illustris (Torrey et al., 2014). Observations suggest that high-mass galaxies form and assemble most of their stellar mass early (Marchesini et al., 2009; Moustakas et al., 2013; Muzzin et al., 2013), but low-mass galaxies form later on a more extended timescale (Cimatti et al., 2006; Noeske et al., 2007). The fact that the simulations overpredict the low-mass galaxies is a failure of the current models. The likely reason for this symptom is that the star-formation histories in the current simulations trace the DM mass accretion histories too closely. From the theoretical perspective, the low-mass halos have earlier formation times than the high- mass halo, however this is the opposite of the observed trend (Conroy & Wechsler, 2009). One of the solutions to this problem lies in modifying the sub-grid recipes that control the star-formation and/or stellar feedback. This has been attempted a few times already: Henriques et al.(2013) found an improvement in the low-mass galaxy number counts at z . 3 by making the stellar feedback stronger and modifying the timescale for re-accretion of ejected gas; White et al.(2014) found modifications to the outflow efficiency and accretion timescales to be most effective for reconciling the simulations with the observations; Torrey et al.(2014) reported that adjusting the coupling strength and velocity of stellar driven winds changed the normalization of the predicted GSMF at the low-mass end but cannot change the shape, which is required to solve the problem. This issue is in addition to the more well-known problems with ΛCDM: the cusp-core problem (Flores & Primack, 1994; Moore, 1994), the missing satellites problem (Klypin et al., 1999; Moore et al., 1999), and the recently proposed too-big-to-fail problem (Boylan- Kolchin et al., 2011), which may be a confluence of the first two (see Bullock & Boylan- Kolchin 2017 for a detailed review of these problems). These problems do not necessarily point to shortcomings of ΛCDM as a whole, but potentially toward a failure to properly account for the baryonic effects and furthermore, they may be the manifestation of a smaller set of issues with the galaxy formation model. ? 6 Most of these problems concern the faint (M ∼ 10 M ) galaxies and the DM halos that 10 have the appropriate abundance to host them (Mvir ∼ 10 M ; Garrison-Kimmel et al., 2014; Brook et al., 2014). It may be possible to naturally resolve these issues through a better understanding of the star formation and feedback effects in low-mass galaxies.

1.2 Star-formation indicators

Before tackling low-mass galaxies, we need to establish a means to probe the star-formation activity in galaxies. Fundamentally, measuring the star-formation activity requires inferring Chapter 1. Introduction 13

Figure 1.3 This figure adapted from Fontanot et al.(2009) shows the galaxy stellar mass function predicted from three independent semi-analytic models (shown as black curves) compared with observations. The galaxy formation models over-predict the number density of faint galaxy at high redshifts which may be indicative of an incomplete understanding of how galaxies form. mass from light within a given stellar population (see Kennicutt 1998, Kennicutt & Evans 2012, Madau & Dickinson 2014 for detailed review). This is further complicated by the fact that stars have finite lifetimes and their emitted spectrum evolve over time. Stellar population synthesis models (e.g., Leitherer et al., 1999; Bruzual & Charlot, 2003; Conroy & Gunn, 2010) have allowed for the inference of the rate of star-formation in galaxies and Chapter 1. Introduction 14 their integrated stellar masses from the observed emission. A variety of spectral features can be used to infer the star-formation rate such as rest-frame UV, IR, submillimeter, and radio emission as well as nebular emission lines (e.g., Hα). Each of these probes has its own advantages and shortcomings.

1.2.1 UV light

The rest-frame ultraviolet light in a galaxy spectrum (1500–2800A)˚ is largely dominated by contributions from massive stars (typically O- and B-type). These stars have a relatively short lifetime of ∼100 Myr after which the UV emission fades quickly. Thus, the UV light can be used as a tracer for recent star-formation activity of the galaxy. Dust in galaxies can substantially attenuate the UV light and this effect needs to be accounted for when inferring the star-formation rates (for further discussion see Section 1.2.4). The dust-corrected UV luminosity can be converted to a star-formation rate assuming a stellar −1 −43.35 −1 population – e.g., SFRUV [M yr ] = 10 × νLν,UV,corr [erg s ](Kennicutt & Evans, 2012) which assumes 100 Myr old stellar population with a constant star-formation history.

> Rest-frame UV has been the primary method for investigating star-formation at z ∼ 1, since it is redshifted into optical bands is easily accessible with the current observational facilities. Space-based HST with its superior resolution has revolutionized this field with a combination of deep surveys in blank and lensing cluster fields collecting substantial samples of galaxies in rest-UV out to z ∼ 8. This complemented with the large-area surveys from the ground gives us a well-defined view of star-forming galaxies over the history of the universe.

1.2.2 Emission lines

The UV radiation from the hot, young O and B stars ionizes the interstellar gas surrounding them and the emission from recombining hydrogen gas in these star-forming regions (also called H II regions) can be used as to estimate the rate of production of the ionizing photos and thus, the rate of star-formation. Recombination lines such as Hα,Hβ, and Paschen α are often used to measure star-formation rates. These emission lines also need to be corrected for dust attenuation. Additionally, gas in the interstellar medium can also be excited via AGN activity or shocks, which adds a level of complexity when inferring the star-formation activity from emission lines. Overall, Hα has been regarded as the gold-standard of star-formation indicators due to its reliability. Being in the NIR, Paschenα is less affected by dust compared to Hα and thus, a great probe for measuring star-formation rates in dusty galaxies, but is rather weak and only currently accessible at low redshifts. Emission lines from heavier elements Chapter 1. Introduction 15 such as [OII]λ3727A˚ and [OIII]λλ4959+5007A˚ doublet also have been used, albeit their interpretation is more complex due to dependence on ISM conditions such as metallicity and excitation.

1.2.3 Other indicators

Alternative ways to measure star-formation beyond the ones mentioned here also exist such as IR, submillimeter, and radio emission (see Madau & Dickinson 2014 for detailed review). One of the widely used indicators is infrared light from galaxies. Dust absorbs the UV emission from stars in galaxies and re-radiates it at far-infrared (FIR) wavelengths (8–1000µm) and consequently, it is possible to estimate the star-formation rate from this reprocessed FIR radiation. The combination of UV and IR serves as one of the more robust indicators of star-formation since it circumvents the need for applying dust corrections. However, IR surveys are restricted to the low-redshift universe (z . 2) due to flux limit constraints. Direct detection of individual sources at z > 2 is limited only to the most luminous objects.

1.2.4 Dust

The presence of dust in the interstellar medium complicates the interpretation of star- formation indicators by attenuating the stellar light we observe. Furthermore, the attenua- tion by dust grains is wavelength dependent, with shorter wavelengths getting more atten- uated than longer wavelengths. This wavelength-dependent extinction has been calibrated for our Milky Way (Cardelli et al., 1989), the SMC (Prevot et al., 1984), as well as local starburst galaxies (Calzetti et al., 2000). Currently, Calzetti et al.(2000) extinction curve is the most commonly adopted extinc- tion law for modeling the stellar populations of high-redshift galaxies. This wide-spread support is based on studies comparing different star-formation indicators. Reddy & Steidel (2004) find that the star-formation rates derived from rest-UV colors, assuming Calzetti et al.(2000) law, for star-forming galaxies at 1 .5 < z < 3 in GOODS-N field agreed with radio and X-ray estimates. Pannella et al.(2009) report the rest-UV star-formation rates corrected using Calzetti et al.(2000) to match the extinction-free radio-derived star- formation rates for z ∼ 2 star-forming galaxies in COSMOS. Similarly, Reddy et al.(2006, 2010) and Daddi et al.(2007) also conclude that the Calzetti et al.(2000) law is valid for majority of the systems at z ∼ 2. At high redshifts where rest-frame FIR observations are unavailable, one of the most common ways of quantifying the reddening of a galaxy spectrum due to dust attenuation Chapter 1. Introduction 16

β is by using the rest-UV continuum slope (β, where fλ ∝ λ ) parameterized as the ratio of the infrared to UV (at ∼1600A)˚ luminosities defined as IRX=LIR/LUV . This IRX-β relation was first measured for local starburst galaxies (Calzetti, 1997; Meurer et al., 1999; Overzier et al., 2011; Takeuchi et al., 2012). This relation implicitly assumes a dust law (typically Calzetti et al. 2000 or Prevot et al. 1984) and an intrinsic (unattenuated) rest-UV continuum slope (β0). Most commonly, the dust law is taken to be Calzetti et al.(2000) and constant star formation history is assumed which gives typical values of β0 ∼ −2.2 to −2.3.

Figure 1.4 The IRX-β relation shown for local galaxies (left panel) and for z > 0 galaxies adapted from Casey et al.(2014). The generic Meurer et al.(1999) relation is shown in dashed grey curves. While the typical galaxies follow the relation, a population for dusty highly star-forming galaxies can be seen deviating.

The IRX-β relation provides a convenient way for estimating dust using just the observed rest-UV continuum slope. Indeed, this relation has been widely adopted for high-redshift galaxies (e.g., Bouwens et al., 2011, 2015; Ellis et al., 2013; Oesch et al., 2014; McLeod et al., 2015) with observational support suggesting that the locally calibrated IRX-β relation is broadly appropriate for typical star-forming galaxies at z ∼ 2 − 4 (Reddy et al., 2008; Pannella et al., 2009; Reddy et al., 2010, 2012; Heinis et al., 2013; Coppin et al., 2015; Alvarez-M´arquezet´ al., 2016; Puglisi et al., 2016; Bourne et al., 2017; Fudamoto et al., 2017). However, there are cases where galaxies deviate from the norm. Ultra-luminous infrared galaxies (ULIRGs) in the local universe are highly star-forming (extremely young stellar populations and hence, an intrinsic β0 lower than the typically assumed value for constant star formation) and have high dust content (high IRX ratio), causing them to lie Chapter 1. Introduction 17 off the IRX-β relation (Goldader et al., 2002). These dusty star-forming galaxies have been observed to have bluer UV continuum slopes for a given IRX than the nominal value from the Meurer et al.(1999) relation both locally (Burgarella et al., 2005; Buat et al., 2005; Howell et al., 2010; Takeuchi et al., 2010) and at high redshifts (Reddy et al., 2010; Heinis et al., 2013; Oteo et al., 2013; Casey et al., 2014; Ivison et al., 2016; Bourne et al., 2017). On the other hand, Lyman-break galaxies at high redshifts (z ∼ 2 − 3) have been observed to have redder UV continuum slopes for a given IRX, bringing them to being more consistent with the SMC attenuation curve rather than the canonical IRX-β relation which assumes Calzetti et al.(2000) law (e.g., Siana et al., 2008, 2009; Reddy et al., 2012, 2018; Capak et al., 2015; Bouwens et al., 2016; Koprowski et al., 2016; Pope et al., 2017; Smit et al., 2017). Dust extinction plays a critical role in our inference of the physical properties of galaxies from observations. There still remain some concerns regarding extension of locally calibrated relations to the high-redshift universe.

1.3 Low-mass galaxies

Faint, low-mass galaxies play an important role in the evolution of the universe, particularly at high redshifts. More than 80% of the total cosmic star-formation occurs in galaxies with luminosities below the characteristic galaxy luminosity (L?) at z ∼ 2 (e.g., Reddy & Steidel, 2009; Oesch et al., 2010; Alavi et al., 2014, 2016; Madau & Dickinson, 2014; Parsa et al., 2016; Mehta et al., 2017) and the impact of these low luminosity systems is even more pronounced at earlier times (e.g., Bunker et al., 2010; Oesch et al., 2012; Bouwens et al., 2012; Schenker et al., 2013; McLure et al., 2013; Finkelstein et al., 2015). Additionally, these faint galaxies have attracted much of the spotlight recently due to a variety of reasons. In the nearby universe, these systems probe galaxy formation on the finest scales and may contain clues to the nature of dark matter (e.g., Menci et al., 2012, 2016; Nierenberg et al., 2013; Kennedy et al., 2014). These galaxies are excellent tests of feedback due to star formation (e.g., Benson et al., 2003; Lo Faro et al., 2009; Weinmann et al., 2012). In the high redshift universe (z ∼ 6 − 10), these low luminosity star-forming galaxies are currently favored as the sources responsible for reionizing the universe (e.g., Finkelstein et al., 2012; Robertson et al., 2013, 2015). Moreover, these include the likely progenitors of the typical galaxies in the local universe (Boylan-Kolchin et al., 2015). While considerable progress has been made in understanding the star-formation and feedback process in galaxies with typical luminosities (L? galaxies; see Shapley 2011 for Chapter 1. Introduction 18 a detailed review), much of the knowledge about the nature of low luminosity systems is currently lacking. From global population statistics, we know that these objects evolve differently than the typical galaxies (as discussed in Section 1.1.3). The efficiency of star formation is greatly reduced in low-mass halos likely due to a combination of strong stellar feedback and heating due to photo-ionization from the UV background (e.g., Larson, 1974; Dekel & Silk, 1986; Efstathiou, 1992; Benson et al., 2002; Murray et al., 2005). In presence of strong feedback, the star formation histories are predicted to be ‘bursty’ (e.g., Stinson et al., 2007; Shen et al., 2013; Teyssier et al., 2013; Hopkins et al., 2013; Dom´ınguezet al., 2015).

1.4 Surveying star-forming, low-mass galaxies

Efficient sample selection techniques are necessary for studying large modern observational datasets such as SDSS. Several techniques have been developed over the past couple decades to select star-forming galaxies at all redshifts from both imaging as well as spectroscopic surveys. While these methods are not exclusive to selecting only the low-mass population, they just as efficient in the low-mass regime. Here, we mention the ones relevant to this work.

1.4.1 Rest-frame UV selection

The “Lyman break technique” is one of the primer methods for identifying high-redshift star-forming galaxies. It is based on their rest-frame UV colors. This method exploits the combined effects of neutral hydrogen opacity within galaxies and in the intergalactic medium along the line-of-sight, which causes a pronounced spectral “break” at 912A˚ (the Lyman limit) in the galaxy’s rest-frame. The Lyα forest also contributes to absorbing the flux below 1216A˚ and this is the dominant effect at high redshift (z & 4). The Lyα break can be observationally identified using broadband colors of three adjacent filters that straddle the Lyman break. This technique has be vastly successful at selecting high-redshift star-forming galaxies (so-called Lyman break galaxies or LBGs) (e.g., Steidel et al., 1996, 1999; Giavalisco, 2002; Steidel et al., 2003; Adelberger et al., 2004; Bouwens et al., 2004, 2006, 2010, 2011; Bunker et al., 2004, 2010; Rafelski et al., 2009; Reddy & Steidel, 2009; Reddy et al., 2012; Oesch et al., 2010; Hathi et al., 2012). Using LBGs selected from ground- and space-based imaging surveys, a large amount of effort has been devoted into obtaining accurate measurements of the rest-frame UV LF at all redshifts z . 10 (e.g., Arnouts et al., 2005; Sawicki, 2012; Yoshida et al., 2006; Bouwens Chapter 1. Introduction 19 et al., 2007; Dahlen et al., 2007; Reddy & Steidel, 2009; Hathi et al., 2010; Oesch et al., 2010; van der Burg et al., 2010; Sawicki & Thompson, 2006; Alavi et al., 2014, 2016; Bouwens et al., 2014b,a, 2015; Finkelstein et al., 2015; Bernard et al., 2016; Parsa et al., 2016; Mehta et al., 2017). These observations show that the UV LF evolves considerably over time. The overall normalization of the rest-UV LF steadily increases with time, and the characteristic luminosity shifts to fainter magnitudes below z ∼ 2 (e.g., see Parsa et al., 2016). The cosmic luminosity density (and consequently, the star-formation rate density) increases steadily up to z ∼ 2 − 3, followed by a slight decline out to the highest redshifts probed so far (e.g., see Madau & Dickinson, 2014). The low-mass galaxies shape the faint-end slope (α) of the rest-UV LF. Given their important role in refining the details of galaxy formation models, it is not surprising that the faint-end slope has been the subject of much interest, and is highly debated in the current literature. From published results, α appears to evolve dramatically, going from α ∼ −1.2 at z ∼ 0 to α ∼ −2 by z ∼ 8, albeit with a rather large scatter. At z ∼ 2, faint-end slope estimates vary from considerably shallow values of α ∼ −1.3 (Hathi et al., 2010; Parsa et al., 2016) to very steep values of α = −1.72 (Alavi et al., 2014, 2016). The survey limits are the main challenge in accessing the faint galaxies needed to significantly constrain the value of α (e.g., Oesch et al., 2010). Strong gravitational lensing enables one to circumvent this limitation, although, it introduces additional systematics and complications, such as a non-trivial effective survey volume calculation (e.g., Alavi et al., 2014, 2016) and is vulnerable to systematic biases (e.g., Bouwens et al., 2017). We measure the rest-UV LF at the peak of cosmic star-formation activity (1 < z < 3) from the deepest UV direct imaging data available from the Hubble Ultra-Violet Ultra Deep Field (UVUDF, Teplitz et al., 2013). Comparison of rest-UV as a tracer for star- formation activity with other star-formation indicators has been used to shed insight on to the star-formation histories of galaxies in the local universe (e.g., Lee et al., 2009, 2011; Dom´ınguezet al., 2015; Weisz et al., 2012; Koyama et al., 2015) as well as at high-redshifts (e.g., Wuyts et al., 2008; Shivaei et al., 2016). Chapter2 describes the measurement of the rest-UV LFs and its implications on the star-formation histories of low-mass galaxies at the cosmic high-noon (z ∼ 2).

1.4.2 Emission line galaxies

As discussed in Section 1.2.2, one of the signatures of on-going star formation is the presence of strong emission lines in the galaxy’s spectrum, which can be used to identify star-forming galaxies (often called emission line galaxies or ELGs). Since emission lines in galaxy spectra Chapter 1. Introduction 20 can also be powered by AGN activity or shocks, these need to be ruled out using additional diagnostics such as line ratios (e.g., Baldwin et al., 1981; Kewley & Dopita, 2002). On the other hand, the strength of the emission lines is directly correlated with the star formation activity and hence, this technique is ideal for picking out low-mass star-forming galaxies. For z . 4 galaxies, most of the star-formation indicating emission lines such as Hα, Hβ, Lyα, [OIII]λλ4959+5007, and [OII]λ3727 fall into optical and NIR wavelength regimes and are highly accessible from ground-based observational facilities as well as HST. Above z ∼ 4, selection of ELGs relies on Lyα. A multitude of observation techniques have been implemented for selecting ELGs, each with its advantages and disadvantages. Narrowband imaging surveys tuned to narrow redshift windows have been widely used to select galaxies with emission lines (e.g., Bunker et al., 1995; Fujita et al., 2003; Glaze- brook et al., 2004; Ly et al., 2007; Villar et al., 2008; Geach et al., 2008; Sobral et al., 2013). However, these are subject to high cosmic variance due to the thin redshift slice probed. On the spectroscopy side, NIR multi-object spectrographs on ground-based facilities have been useful, albeit require target pre-selection, and suffer from slit-loss and atmospheric absorp- tion. Recently, integral field unit (IFU) instruments have opened an exciting new avenue for surveying emission line galaxies (e.g., Dom´ınguezS´anchez et al., 2012; Bacon et al., 2017). Slitless spectroscopy with HST has been vastly successful for surveying emission line galax- ies by being able to circumvent concerns regarding slit losses and the atmosphere. WFC3 Infrared Spectroscopic Parallel (WISP) survey (Atek et al., 2010) and 3D-HST (Brammer et al., 2012) are two of the major slitless surveys undertaken with HST. The Lyα emission is undoubtedly an important tool for identifying actively star-forming galaxies. Over the past couple decades, Lyα emitting galaxies (Lyman-alpha emitters or LAEs) at high redshifts have been found routinely using narrowband imaging as well as spectroscopic surveys (e.g., Hu et al., 1998; Rhoads et al., 2000; Ouchi et al., 2003; Guaita et al., 2010; Shibuya et al., 2012; Matthee et al., 2014; Bagley et al., 2017; Konno et al., 2018). These high-redshift LAEs are generally compact, young star forming galaxies that have low stellar masses, low dust content, low metallicity, and high specific star formation rates (e.g., Pirzkal et al., 2007; Finkelstein et al., 2008; Pentericci et al., 2009; Bond et al., 2010; Malhotra et al., 2012). At high redshifts, the LAEs are also found to have high Lyα equivalent widths, which has been suggested as a signature for the youngest, possibly first generation of stars (e.g., Malhotra et al., 2001; Schaerer, 2003).

> High redshift (z ∼ 6) LAEs are an excellent probe for reionization. The epoch of reioniza- tion (EoR) represents the latest major phase change our universe underwent, where all of its neutral hydrogen was ionized over a relatively short period of time (between 6.5 . z . 10). Chapter 1. Introduction 21

Current theoretical models based in observational evidence suggest that star-forming galax- ies were the dominant contributor of the ionizing flux responsible for the EoR (e.g., Fan et al., 2006; Finkelstein et al., 2012; Robertson & Ellis, 2012; Robertson et al., 2013, 2015; Madau & Haardt, 2015). However, the fundamental details of how the ionizing radiation escapes these galaxies still remains unclear and the Lyα emission from these galaxies may contain clues to this mystery (e.g., Shapley et al., 2003; Iwata et al., 2009; Nestor et al., 2013; Nakajima et al., 2013; Verhamme et al., 2015). Lyα being a resonant line is easily scattered and consequently, the escape of Lyα is heavily dependent on the properties of the galaxy and its ISM. To properly utilize Lyα as a probe for studying EoR, it is imperative to understand the details of Lyα escape. However, absorption by the intergalactic neutral hydrogen limits the reliability of measurements of the Lyα line. Alternatively, the process of Lyα escape can be studied at lower redshifts in galaxies with similar properties as the high redshift LAE sample (e.g., Giavalisco et al., 1996; Kunth et al., 1998; Hayes et al., 2005, 2014; Deharveng et al., 2008; Atek et al., 2009; Finkelstein et al., 2009; Ostlin¨ et al., 2009, 2014; Scarlata et al., 2009; Leitherer et al., 2011; Heckman et al., 2011; Cowie et al., 2011; Wofford et al., 2013; Rivera-Thorsen et al., 2015). These low-redshift LAEs typically have low Lyα escape fractions (e.g., Hayes et al., 2011), which seem to be controlled by the geometry and kinematics of the neutral ISM (e.g., Giavalisco et al., 1996; Thuan & Izotov, 1997; Kunth et al., 1998; Shapley et al., 2003; Kornei et al., 2010). Another exciting population of ELGs was serendipitously discovered in SDSS imaging data by volunteers of the citizen science project Galaxy Zoo (Lintott et al., 2008) – the “Green Peas” (Cardamone et al., 2009). These rare objects (only 251 found in SDSS) were compact, unresolved galaxies in the SDSS that appeared green in SDSS’s false-color gri- band images due to the presence of strong [OIII]λλ4959+5007 doublet in the r band. These 8−10 are all galaxies at 0.11 < z < 0.36 and have stellar masses of ∼ 10 M , high specific star formation rates, large [OIII]λ5007/[OII]λ3727 ratios, and strong emission line equivalent widths (EW(Hα) and EW([OIII]λ5007)) exceeding a few hundreds of A(˚ Cardamone et al., 2009; Amor´ınet al., 2009; Izotov et al., 2011), similar to those of the high-redshift LAEs. Thus, the green pea galaxies have been suggested as the best local analogs of high-redshift LAEs (e.g., Jaskot & Oey, 2014; Henry et al., 2015; Yang et al., 2016, 2017; Verhamme et al., 2017). Five green pea galaxies have also been confirmed as Lyman continuum leakers (Izotov et al., 2016b). Recently, the green pea galaxies have sparked interest in devising techniques to system- atically identify these extreme ELGs (EELGs) with strong emission line equivalent widths Chapter 1. Introduction 22 at low redshifts. The so-called “blueberry” galaxies (e.g., Yang et al., 2017) have been the product of these efforts. Yang et al.(2017) used ugri-based photometric color cuts to select a sample of EELGs from the SDSS DR12 catalog along with spectroscopic follow-up. These objects are extremely rare with only 51 found in the SDSS catalog and a number density of about 3×10−6 Mpc−3. The blueberry galaxies are similar to the green pea galax- ies but at a lower redshift (z . 0.05) with similarly strong emission lines but ∼10–100 times smaller stellar masses, star-formation rates and luminosities. The blueberry galaxies likely represent the faint end of the green peas and LAEs. Selection of ELGs using photometric bands allows us to fully get advantage of the large area covered by imaging surveys and identify these rare EELGs. We use the Hyper-Suprime Cam Subaru Strategic Program (HSC-SSP; Aihara et al., 2017b) to identify samples of EELGs, including the low-redshift [OIII] emitters as well as the high-redshift LAEs, over ∼ 2.4deg2 in the Subaru-XMM Newton Deep Field (SXDF). The imaging data processing and catalog creation process is described in Chapter3 and the discussion of EELGs found in SXDF is detailed in Chapter4.

1.5 Prospects for upcoming surveys

Star-forming galaxies with strong emission lines are the cornerstone for upcoming dark- energy surveys such as the ESA-led Euclid mission (Laureijs et al., 2011; Vavrek et al., 2016) and NASA’s Wide Field Infrared Survey Telescope (WFIRST; Dressler et al., 2012; Green et al., 2012; Spergel et al., 2015). The nature of dark energy, which accounts for ∼68% of the total energy density of the universe (Planck Collaboration et al., 2016b) and is responsible for observed accelerated expansion of the universe, still remains as one of the most prominent challenges of modern cosmology. The current set of observations support the existence of dark energy, however, the uncertainties are too large to conclusively rule out alternative theories (such as a modified general relativity). In order to distinguish between dark energy and alternative theories, high precision measurements of the expansion history of the universe and growth rate of cosmic large-scale structure are required (e.g., Albrecht et al., 2006; Guzzo et al., 2008; Wang, 2008a,b). Upcoming missions, Euclid and WFIRST are tailored to obtain their measurements and help uncover the mystery of dark energy. The goal of these surveys is to measure the baryonic acoustic oscillations (BAOs), which can be used as standard rulers to quantify the expansion history of the universe (Blake & Glazebrook, 2003; Seo & Eisenstein, 2003), and the large-scale redshift-space distortions, which constrains the growth history of the Chapter 1. Introduction 23 large-scale structure (Kaiser, 1987; Song & Percival, 2009). For this, these missions will perform wide-field slitless spectroscopy targeting tens of millions of emission line galaxies. The predominant targets for these surveys will be Hα emitting galaxies over approxi- mately 0.9 . z . 2. In addition, they will also detect [OIII] and possibly [OII] emitters up to higher redshifts. Euclid will cover 15,000 deg2 with a line flux limit of 2 − 3 × 10−16 ergs s−1 cm−2, and WFIRST will survey ∼2200 deg2 down to a fainter flux limit of 1 × 10−16 ergs s−1 cm−2. These missions will expand the database for emission line galaxies to an unprecedented size and enable us to fully quantify the nature of star-forming galaxies at the cosmic high-noon. As part of strategy optimization for these upcoming missions, we use the current gener- ation slitless survey, the HST-based WFC3 Infrared Spectroscopic Parallel (WISP) survey (Atek et al., 2010), to estimate the number of emission line galaxies observable by the future surveys in Chapter5. Chapter 2

UVUDF: UV Luminosity Functions at the cosmic high-noon

Note: This chapter originally appeared as a refereed publication in the Astrophysical Journal under Mehta, V., Scarlata, C., Rafelski, M., et al. 2017, ApJ, 838, 29 titled “UVUDF: UV Luminosity Functions at the Cosmic High Noon” and is presented here as is, albeit with some minor modifications.

The galaxy luminosity function is one of the key observables in astronomy, providing the number density of galaxies at a given luminosity and time. The luminosity function is instrumental in establishing the connection between the observable light and the underlying distribution of dark matter halos. The link between these two depends on the baryonic physics which ultimately regulate the conversion of gas into stars and the luminosity output at any given wavelength. In the rest–frame ultra violet (UV), the galaxy continuum is dominated by light coming from young stars, and is therefore a direct tracer of recent star formation activity. Con- sequently, the UV luminosity function can be used to describe the volume averaged star formation rate in the Universe and to study the in-situ build up of stellar mass in galaxies. Moreover, unlike other star formation indicators, the rest-frame UV is continuously accessi- ble to very high redshifts and hence is an invaluable diagnostic for mapping star formation out to very early times. A large amount of effort has been devoted into obtaining accurate measurements of the rest-frame UV luminosity function at all redshifts z . 10 (e.g., Arnouts et al., 2005; Sawicki, 2012; Yoshida et al., 2006; Bouwens et al., 2007; Dahlen et al., 2007; Reddy & Steidel, 2009;

24 Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 25

Hathi et al., 2010; Oesch et al., 2010; van der Burg et al., 2010; Sawicki & Thompson, 2006; Alavi et al., 2014, 2016; Bouwens et al., 2014b,a, 2015; Finkelstein et al., 2015; Bernard et al., 2016; Parsa et al., 2016). These observations show that the UV luminosity density increases steadily up to z ∼ 2 − 3, followed by a slight decline out to the highest redshifts probed so far (e.g., see Alavi et al., 2016). Recently, a significant amount of focus has been put on the very faint galaxies. These faint, low-mass galaxies are expected to be essential for reionization of the universe (Bouwens et al., 2012; Finkelstein et al., 2012; Jaacks et al., 2012; Robertson et al., 2013, 2015). They include the likely progenitors of the L? galaxies in the local Universe (e.g., Boylan-Kolchin et al., 2015) and also serve as excellent objects to test the effects of feedback due to star formation and reionization (e.g., Benson et al., 2003; Lo Faro et al., 2009; Weinmann et al., 2012). The evolution of the faint-end slope (α) of the UV luminosity function can therefore inform us on many crucial aspects of galaxy formation and evolution. It is not surprising then, that the value of α and its time evolution has been the subject of much research, and it is highly debated in the current literature. From published results, α appears to evolve dramatically, going from α ∼ −1.2 at z ∼ 0 to α ∼ −2 by z ∼ 8, albeit with a rather large scatter. At z ∼ 2, faint-end slope estimates vary from considerably shallow values of α ∼ −1.3 (Hathi et al., 2010; Parsa et al., 2016) to very steep values of α = −1.72 (Alavi et al., 2014, 2016). The survey limits are the main challenge in accessing the faint galaxies needed to significantly constrain the value of α (e.g., Oesch et al., 2010). Strong gravitational lensing enables one to circumvent this limitation, although, it introduces additional systematics and complications, such as a non-trivial effective survey volume calculation (e.g., Alavi et al., 2014, 2016). Deep, direct imaging still provides the most robust estimate for α. Complementary to the UV, the Hα recombination line is a gold–standard indicator for ongoing star formation. These two tracers, however, are sensitive to star formation occurring over different timescales1 (Kennicutt & Evans, 2012), and are affected differently by interstellar dust attenuation. In the local Universe, the two indicators are found to agree with each other, under the assumption that the star-formation has been constant over a long enough time to allow equilibrium (> 100Myr; e.g., Buat et al., 1987; Buat, 1992; Bell & Kennicutt, 2001; Iglesias-P´aramoet al., 2004; Salim et al., 2007; Lee et al., 2009; Barnes et al., 2011; Hermanowicz et al., 2013). The effect of dust attenuation in the rest-frame UV is usually corrected using locally-calibrated empirical relations between the slope of the UV

1 The Hα emission traces star formation over short time scales (∼ 10s of Myrs, typical of the hot, O- and B-type stars that power HII regions). On the other hand, the contribution to the rest-frame UV continuum comes from the longer lived B-A stars (∼100 Myrs). Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 26 continuum and the IR excess (IRX − β relation, Meurer et al., 1999). The Meurer et al. (1999) relation was calibrated for central starbursts in the nearby Universe. As a whole, star forming galaxies in the nearby Universe lie below this relation, as found by many studies (e.g., Mu˜noz-Mateoset al., 2009; Boquien et al., 2012; Grasha et al., 2013; Ye et al., 2016). At high redshifts, it has been suggested that star formation is dominated by more stochastic, intense bursts which may also be more important in low(er)–mass galaxies (e.g., Shen et al., 2013; Hopkins et al., 2014; Dom´ınguezet al., 2015). If this is true, the constant star formation history assumption implicit in all luminosity-to-star formation rate conver- sions breaks down. There are also indications that the Meurer et al.(1999) correction for dust may not be adequate at z & 1 (e.g. Buat et al., 2012; Dayal & Ferrara, 2012; Wilkins et al., 2012; de Barros et al., 2014; Castellano et al., 2014; Smit et al., 2016; Reddy et al., 2015; Talia et al., 2015; Alvarez-M´arquezet´ al., 2016). Until JWST comes online, the high- est possible redshift where a direct comparison of the two SFR indicators can be performed is z = 2.5. In this chapter, we use the UVUDF (Teplitz et al., 2013), which is amongst the deepest UV data ever obtained, to derive the rest frame UV luminosity function at z ∼ 1.7, 2.2, 3, and constrain its faint–end slope. In addition, we use Hα luminosity functions available from the literature to compare the volume averaged SFR derived with the two SFR indicators at z ∼ 2. This paper is organized as follows: Section 2.1 describes the UVUDF data used for this work as well as our sample selection; Section 2.2 describes the completeness simulations and presents the selection functions; Section 2.3 outlines the LF fitting procedure as well as our results; Section 2.4 presents our results; Section 2.5 discusses our results in context with recent literature and analyzes the implications; and Section 2.6 summarizes our conclusions.

2.1 Data and Sample Selection

2.1.1 UVUDF Data

The full UVUDF dataset is comprised of eleven photometric broadband filters covering the Hubble UDF (α(J2000) = 0.3h32m39s, δ(J2000) = −27◦47039.”1) spanning wavelengths from the NUV to NIR. The NUV coverage of the HUDF provided by the UVUDF obser- vations includes three WFC3-UVIS filters: F225W, F275W, F336W (Teplitz et al., 2013). The optical wavelengths are covered by four ACS filters: F435W, F606W, F775W, F850LP (Beckwith et al., 2006). The NIR is covered by four WFC3-IR filters: F105W, F125W, F140W, F160W obtained as part of the UDF09 and UDF12 programs (Oesch et al., 2010; Bouwens et al., 2011; Koekemoer et al., 2013; Ellis et al., 2013). Moreover, the entire field Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 27 is also covered in F105W, F125W, and F160W as part of the CANDELS GOODS-S obser- vations (Grogin et al., 2011; Koekemoer et al., 2011). The UVUDF field with coverage in all eleven filters covers an area of 7.3 arcmin2. The data reduction, photometry and source catalog generation for the UVUDF is fully developed and described in Rafelski et al.(2015). We use the final catalog provided by Rafelski et al.(2015) for this work. Before applying the sample selection cuts, we remove all sources that are flagged as stars in the UVUDF catalog. Furthermore, we flag bright, compact sources (z850 < 25.5 and half-light radii, r1/2 < 1”) with a SExtractor stellarity parameter > 0.8 as stars. This criterion is only reliable for bright sources and hence, we instead use a color-color cut based on the Pickles(1998) stellar library at fainter magnitudes to flag stars. At z850 > 25.5, we

flag compact sources (r1/2 < 1”) that have V − i vs. i − z colors consistent with the Pickles (1998) stellar sequence to within 0.15 mag as stars. Lastly, we confirm that no stars are left in the final samples by visual inspection.

2.1.2 Dropouts Sample Selection

4 4 4 F225W Dropouts F275W Dropouts F336W Dropouts (z~1.65) (z~2.2) (z~3)

3 3 3

2 2 2

1 1 1 F225W - F275W F275W - F336W F336W - F435W

0 0 0

1 1 1 0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.5 0.0 0.5 1.0 1.5 2.0 2.5 F275W - F336W F336W - F435W F435W - F606W

Figure 2.1 The color selection criteria for F225W, F275W, F336W LBG dropouts at z ∼ 1.7, 2.2, 3 respectively (from left to right). The shaded regions highlight the selection region in color-color space for the dropouts. The black points are all detected sources in UVUDF, while the red are the ones that make the selection cut. Note the objects selected by the dropout criteria are not only require to be in the shaded region, but also need to make the S/N cuts from Equations 2.1–2.3. All sources with fluxes below the 1σ limit in the dropout filter have been replaced with their corresponding 1σ upper limit. The orange points are stars from Pickles(1998), the green lines show the color tracks for low redshift (0 < z < 1) elliptical galaxies from Coleman et al.(1980), and the blue lines show color tracks for star-forming galaxies with different dust content, E(B − V ) = 0 (solid), 0.15 (dashed), 0.3 (dotted). The star-forming tracks are derived using Bruzual & Charlot(2003) template for constant star-formation rate, solar metallicity, age of 100 Myr and dust extinction defined by Calzetti et al.(2000) law. Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 28

The Lyman break feature in galaxy SEDs has been proven to be very efficient at selecting high-redshift galaxies (e.g., Steidel et al., 1996, 1999, 2003; Adelberger et al., 2004; Bouwens et al., 2004, 2006, 2010, 2011; Bunker et al., 2004, 2010; Rafelski et al., 2009; Reddy & Steidel, 2009; Reddy et al., 2012; Oesch et al., 2010; Hathi et al., 2012). Here, we use the NUV filters available in the UVUDF to identify the Lyman break galaxies (LBGs) in the redshift range of z ∼ 1.5 − 3.5. The LBG dropout selection criteria we use, are based on standard color-color and S/N cuts, similar to Hathi et al.(2010), Oesch et al.(2010) and Teplitz et al.(2013). However, we further optimize the S/N cuts using the mock galaxy sample generated for our completeness simulations (see Section 2.2). The color-color selection criteria are shown in Figure 2.1. Specifically, we select galaxies between z ∼ 1.4 − 1.9 as follows:

 F 225W − F 275W > 0.75   F 275W − F 336W > −0.5   F 275W − F 336W < 1.4 (2.1) F 225W − F 275W > [1.67 × (F 275W − F 336W )] − 0.42   F 336W − F 435W > −0.5   S/N(F 275W ) > 5 This results in a sample of 25 galaxies from the UVUDF catalog. Similarly, galaxies between z ∼ 1.8 − 2.6 are selected using the following criteria:

 F 275W − F 336W > 1.0   F 336W − F 435W > −0.2   F 336W − F 435W < 1.2 (2.2) F 275W − F 336W > [1.3 × (F 336W − F 435W )] + 0.35   S/N(F 336W ) > 5   S/N(F 225W ) < 1 Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 29 providing a sample of 60 galaxies. The galaxies between z ∼ 2.4 − 3.6 are selected as:

 F 336W − F 435W > 0.8   F 435W − F 606W > −0.2   F 435W − F 606W < 1.2 (2.3) F 336W − F 435W > [1.3 × (F 435W − F 606W )] + 0.35   S/N(F 435W ) > 5   S/N(F 275W ) < 1 which returns 228 galaxies. When applying these color selection criteria, all sources with magnitudes below the 1σ limit in the dropout filter are replaced with their corresponding 1σ upper limits, as determined from our completeness simulations (see Section 2.2).

2.1.3 Photometric Redshift Sample Selection

The inclusion of NUV data (in addition to the optical and NIR) enhances the photometric redshift accuracy, particularly at z < 0.5 and 2 < z < 4 (Rafelski et al., 2015). The UVUDF catalog includes photometric redshifts calculated using the eleven broadband photometry via Bayesian Photometric Redshift (BPZ) algorithm (Ben´ıtez, 2000; Ben´ıtezet al., 2004; Coe et al., 2006). The SED templates used for BPZ are based on those from PEGASE (Fioc & Rocca-Volmerange, 1997) recalibrated using redshift information from FIREWORKS (Wuyts et al., 2008). The quality of the photometric redshift is reported by two quantities, ODDS (measuring the spread in the probability distribution function, P (z)) and modified reduced χ2 (measuring the goodness of fit)2 . We require the photometric redshift sample to have ODDS> 0.9 and modified reduced χ2 < 1 to ensure selecting only sources with reliable photometric redshifts. Applying these cuts gives a sample of 234, 258 and 440 galaxies in the redshift ranges 1.4 < z < 1.9, 1.8 < z < 2.6 and 2.4 < z < 3.6, respectively. Using the photometric redshifts enables sample selection down to fainter magnitudes than the corresponding dropout criteria. The dropout selected samples require 5σ in the detection band to confirm the strength of the break. On the other hand, photometric redshift selected samples only require a 5σ detection in the rest-1500A˚ filter. At these redshifts, the dropout detection band (F275W for F225W dropouts, F336W for F275W dropouts, F435W for F336W dropouts) is not the same as the rest-1500A˚ filter (F435W for

2 The modified reduced χ2 reported by BPZ is similar to a normal reduced χ2, except it includes an additional uncertainty for the SED templates in addition to the uncertainty in the galaxy photometry Coe et al.(2006). The resultant χ2 is a more realistic measure of the quality of the fit (for more discussion, see Rafelski et al.(2009). Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 30 z < 2.2; F606W for z > 2.2). This is because the dropout detection band looks for flux immediately redward of the Lyα (1216A),˚ whereas the rest-frame UV flux is still redward at 1500A.˚ Since the optical data available are deeper than NUV, the photometric redshift samples select galaxies down to fainter rest-1500A˚ magnitudes. We fit luminosity functions for both the LBG samples as well as photometric redshift- selected galaxy samples in the same redshift ranges as the dropout criteria to validate the fit robustness. Moreover, the depth of the photometric redshift sample allows for better constraints on the faint-end slope.

2.2 Completeness

Survey incompleteness and sample selection effects greatly impact the effective surveyed volume of a sample, a quantity critical to computing luminosity functions. We need a precise estimate of the completeness for the UVUDF samples in order to properly and accurately correct the volume density. A common approach for completeness estimation in field galaxy studies (e.g., Oesch et al., 2010; Finkelstein et al., 2015) is to insert mock galaxies into real data, apply identical data reduction and sample selection, and analyze the fraction of recovered artificial galaxies as a function of galaxy properties such as magnitude, redshift, and galaxy size. We perform an extensive set of completeness simulations following a similar procedure in order to quantify the completeness for the UVUDF.

2.2.1 Completeness Simulations

We start by generating a set of mock galaxies with properties representative of the observed sample. These mock galaxies are then planted directly into the real science images, thus preserving the noise properties. Only 150 mock galaxies are inserted at a time to also preserve the crowding properties of the data. These images with artificial galaxies are then put through the same data reduction, analysis for source detection, photometry, photometric redshift, and sample selection as was performed for the real data. By keeping track of the fraction of recovered and selected mock sources compared to the total number of input sources, we can quantify the completeness. Our full set of simulations consists of repeating this process for a total of 45,000 mock galaxies over 300 separate iterations. To ensure that the mock galaxies used for our completeness simulations are consistent with the observed sample, we assign the absolute magnitudes for our mock galaxies accord- ing to existing prescriptions of the UV LFs from the literature. In particular, we use the Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 31 rest-frame UV LFs from Oesch et al.(2010) to randomly generate a set of rest-1500 A˚ ab- solute magnitudes for our mock sample. The initial redshift distribution for our simulated sources is taken to be flat, i.e., dN/dz is constant. The colors for our mock sample are assigned using spectral templates from Bruzual & Charlot(2003, BC2003) models. Each mock galaxy is given a set of model parameters: metallicity, age, exponential SFR τ, and dust extinction. The metallicity is chosen to

be random from Z/Z = 0.0001, 0.0004, 0.004, 0.008, 0.02 (preset BC2003 models). We use the distributions of age, exponential SFR τ, and dust extinction (E(B − V )) from observed galaxies in 3D-HST (Skelton et al., 2014) to randomly generate these parameters for our mock galaxies. We also include the contribution from nebular emission lines using line ratios from Anders & Fritze-v. Alvensleben(2003). We apply a Calzetti et al.(2000) dust extinction law as well as Inoue et al.(2014) IGM attenuation model to the SEDs to simulate the dust extinction and IGM absorption, respectively. After translating the SEDs to the appropriate redshift, the magnitudes for the rest of the filters are then obtained by computing the contribution of the SED in the particular filter according to its response curve. We generate the mock galaxies for our completeness simulations using the IRAF task, mkobjects. The sizes for the mock galaxies are defined by assigning a half-light radius

for each source. We use the observed distribution of B435-band sizes for all sources (no cuts applied) in the UVUDF to randomize the half-light radii for our mock galaxies. The distribution of simulated half-light radii is roughly representative of a log-normal with a peak at 2.7-pixel, with a tail towards larger radii giving an interquantile range of 2.5 − 4.9 pixel corresponding to a physical size of ∼ 0.6 − 1.3 kpc at z ∼ 2. The observed UVUDF catalog shows no significant size bias (in pixels) as a function of redshift for z < 4 and hence, we choose the size distribution of our mock galaxies to be uniform at all redshifts, in order to fully explore the parameter space. We choose B435–band since it is the closest filter in wavelength and has a similar resolution to the rest-frame UV, in addition to the deep coverage available as well as the relatively narrow point-spread function (PSF). To fully generate an artificial galaxy, mkobjects also requires a Sersic index (n), axial ratio, image position, and position angle. The mock galaxies are assigned a Sersic profile that either represents exponential disks (n = 1; good description of spiral galaxies) or de Vaucoleuers profile (n = 4; good description of elliptical galaxies). These represent the two extremes for light profiles for observed galaxies. We fix the probability for a mock galaxy to have n=1 or n=4 to be equal (50% each). While observed galaxies do not exhibit this distribution, completeness as a function of Sersic index is expected to be well-behaved Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 32 between the two extremes. Our choice is motivated by wanting to properly sample the two extremes. Furthermore, we verify the simulation output and confirm that the choice of this Sersic index distribution does not bias the completeness in any statistically significant manner. The ellipticities (axial ratios) for our mock sample are randomized using the distribution of observed B435–band axial ratios in the UVUDF, with a peak at 0.7 and long tail towards lower axial ratios. The position of the simulated sources is randomized within a 4000×4400 pixel (20 × 2.50) region that ensures UV coverage of the UDF. We further limit the positions of mock galaxies to avoid chip edges as well as the WFC3/UVIS chip gap, as is done for the real sample. By allowing for random positions, we can encapsulate any variations in the depth or noise properties across the imaging data. Lastly, the position angles are randomized between 0◦and 360◦. We determine the optimal number of galaxies to insert in one iteration in order to avoid crowding issues by planting a varying number of mock galaxies into the images. From this, we find that the scatter in the recovered photometry compared to the input does not increase significantly between 100-200 sources inserted per iteration. Thus, planting . 200 sources per iteration does not change the crowding properties of our field. Being conservative, we choose to insert 150 sources per iteration. This is similar to the treatment for completeness simulations done for CANDELS/GOODS fields by Finkelstein et al.(2015). We split the simulation into 100 separate iterations and, for each iteration, we insert 150 mock galaxies into the original images. The mock galaxies are simulated and inserted into the original image for each of the eleven filters using mkobjects. The newly generated images with simulated sources are then run through identical data reduction, photometry and catalog creation process as for the real data. Briefly, the process involves using ColorPro (Coe et al., 2006) to measure photometry in the images, which runs Source Extractor (Bertin & Arnouts, 1996) for all filters in dual-image mode. ColorPro also applies aperture corrections for the different aperture sizes as well as PSF corrections to account for variations in the PSF across filters. The detection image used is created from the 4 optical and 4 NIR filters to maximize depth and robustness of the aperture sizes. In order to properly recover both bright and faint sources in a crowded field, photometry is measured using two different detection thresholds and two different deblending thresholds, which is then merged into a single photometric catalog. For the smaller apertures needed for the NUV filters, F435W is used as the detection image, instead. The full methodology is described in detail in Rafelski et al.(2015). The UVUDF catalog includes aperture-matched PSF corrected photometry for a robust Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 33 measurement of flux across images with varying PSFs. This is done by measuring pho- tometry on high-resolution data and applying a PSF correction for the NIR filters, which have larger PSFs. The PSF correction is determined by degrading the I775 image (red- dest high-resolution image with a well-behaved PSF available) to each of the NIR filters using the IRAF task, psfmatch. Instead of convolving the entire image after mock galaxies are inserted (which is computationally expensive), we instead create 500×500px (1500×1500) stamps for the simulated sources using mkobjects and convolve them individually before adding to the PSF matched image. This saves considerable amount of computation time per iteration. Lastly, we generate a catalog using the images with mock galaxies following the same pipeline as used for the real UVUDF catalog (Rafelski et al., 2015) and compare it to the input catalog to determine the fraction of recovered objects. In order to be recovered, an object is required to be positionally matched within 3px (0.0900). Typically, incompleteness is computed as a function of magnitude and redshift; however, we also consider another key factor: galaxy size. Even at a constant magnitude and redshift, an extended galaxy may not be recovered due to the low surface brightness compared to a compact one. We correct the effective volumes for our sample according to the magnitude, redshift as well as the galaxy size using selection functions as described in Section 2.2.2. We also compute the completeness as a function of apparent magnitude and galaxy size, which is used to define the survey magnitude limits (see Appendix 2.A).

2.2.2 Selection Functions

The mock galaxy sample can be used to determine the probability of a galaxy to satisfy the LBG selection criteria as long as there are no biases in the recovered magnitudes and colors of the mock galaxies. We verify that our completeness simulations do not introduce any offsets or biases in the magnitudes and colors of recovered mock galaxies, before proceeding. We apply the LBG selection criteria to the input mock sample to quantify the relative efficiency of the criteria to select a galaxy with given redshift, rest-1500A˚ absolute magnitude and half-light radius. The top row in Figure 2.2 shows the selection function for the three dropout criteria from Section 2.1.2, marginalized over the all galaxy sizes. Similarly, the photometric redshift selection criteria are also applied to the mock catalog and the corresponding selection functions are derived for the photometric redshift samples. These are plotted in the bottom row of Figure 2.2, again marginalized over all galaxy sizes. These selection functions are used to compute the effective volumes when fitting the UV LF in Section 2.3. Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 34

F225W Dropout sample F275W Dropout sample F336W Dropout sample 1.0 1.0 1.0 MUV = -20 z~1.65 MUV = -20 z~2.2 MUV = -20 z~3 MUV = -19 MUV = -19 MUV = -19

0.8 MUV = -18 0.8 MUV = -18 0.8 MUV = -18

MUV = -17 MUV = -17

MUV = -16 0.6 0.6 0.6

0.4 0.4 0.4

Relative Efficiency 0.2 Relative Efficiency 0.2 Relative Efficiency 0.2

0.0 0.0 0.0

20 20 20

19 19 19

18 18 18

17 17 17

16 16 16

Absolute UV Magnitude [AB] 15 Absolute UV Magnitude [AB] 15 Absolute UV Magnitude [AB] 15 0.5 1.0 1.5 2.0 1.0 1.5 2.0 2.5 3.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Redshift Redshift Redshift

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Relative Efficiency Relative Efficiency Relative Efficiency

F225W Photoz sample F275W Photoz sample F336W Photoz sample 1.0 1.0 1.0 MUV = -20 1.4

0.8 MUV = -18 0.8 MUV = -18 0.8 MUV = -18

MUV = -17 MUV = -17 MUV = -17

MUV = -16 MUV = -16 MUV = -16 0.6 0.6 0.6

0.4 0.4 0.4

Relative Efficiency 0.2 Relative Efficiency 0.2 Relative Efficiency 0.2

0.0 0.0 0.0

20 20 20

19 19 19

18 18 18

17 17 17

16 16 16

Absolute UV Magnitude [AB] 15 Absolute UV Magnitude [AB] 15 Absolute UV Magnitude [AB] 15 0.5 1.0 1.5 2.0 1.0 1.5 2.0 2.5 3.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Redshift Redshift Redshift

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Relative Efficiency Relative Efficiency Relative Efficiency

Figure 2.2 (Top row) Selection functions for the F225W, F275W and F336W dropout criteria shown as a function of redshift (top panel) and as a function of both redshift and absolute rest-frame UV magnitude (bottom panel). This shows the redshift and absolute rest-frame UV magnitude distributions of galaxies selected by the dropout criteria. The relative efficiency is the fraction of sources that are selected from the full input sample after applying the selection cuts. (Bottom row) Selection functions for the photometric redshift samples corresponding to the redshift selected by dropout criteria. Requiring a 5σ detection in the observed rest-frame UV magnitude and applying the cuts to ensure good quality photometric redshifts (ODDS> 0.9 and modified reduced χ2 < 1.0) are the primary factors affecting the relative efficiency for these selection functions.

The selection functions plotted in Figure 2.2 have been marginalized over all galaxy sizes. However, the information in the size dimension is preserved and the effective volume for each source is computed according to its size. The overall effect of galaxy sizes on the Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 35 completeness can be visualized by Figure 2.9 in Appendix 2.A, which shows the survey incompleteness as a function of observed magnitude and galaxy size.

2.2.3 Redshift distribution of the Dropout Sample

The selection functions computed here, when marginalized over the magnitude and size dimensions, describe the redshift distribution of galaxies in the selected sample. As a validation check, we compare the selection functions from our simulations with redshifts measured from observations. Spectroscopic redshifts are available in the UVUDF catalog (Rafelski et al., 2015) for a small fraction of the sources in our sample, whereas photometric redshifts are available for all the sources in the UVUDF catalog. Figure 2.3 shows the distribution of spectroscopic (where available) as well as photometric (for all sources) red- shifts. The selection functions derived from our completeness simulations are over-plotted for comparison. As seen in the figure, the redshift distributions (shown as histograms) are in overall agreement with the selection functions (shown as curves). Note that the pho- tometric redshifts and simulations are not expected to agree one-to-one by construction, because the galaxy templates used to estimate the photometric redshifts (Section 2.1.3) are not the same as those used to generate the mock catalog for our simulations (Section 2.2).

20 1.0 25 1.0 50 1.0 Photo-z F225W Dropouts F275W Dropouts (z~2.2) F336W Dropouts mUV = 25

Grism-z (z~1.65) (z~3) mUV = 26 Spec-z 0.8 20 0.8 40 m = 27 0.8 15 UV mUV = 28 0.6 15 0.6 30 0.6 10 0.4 10 0.4 20 0.4 Number 5 0.2 5 0.2 10 0.2 Completeness

0 0.0 0 0.0 0 0.0 0.5 1.0 1.5 2.0 1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Redshift Redshift Redshift

Figure 2.3 The redshift distribution of the dropout-selected samples. The grey, blue and red histograms show the distribution of photometric, grism, and spectroscopic redshifts for the dropout samples, respectively. The curves show the completeness associated with the corresponding dropout criteria for a range of observed UV magnitudes, as computed from our completeness simulations (Section 2.2). The right-hand axis gives the scale for the completeness values. Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 36

2.3 Deriving the Luminosity Function parameters

The rest-frame 1500A˚ UV LF is one of the key diagnostics for establishing the link between galaxy luminosities, galaxy masses, and the cosmic star formation rate. Considerable effort has been put into characterizing the shape and evolution of the UV LF near the peak of cosmic star formation (z ∼ 1 − 3) (e.g., Reddy & Steidel, 2009; Hathi et al., 2010; Oesch et al., 2010; Sawicki & Thompson, 2006; Parsa et al., 2016; Alavi et al., 2014, 2016). Here, we fit UV LFs using the dropout as well as photometric redshift selected samples described in Section 2.1 corresponding to the three redshift ranges: z ∼ 1.7, 2.2, 3.0. Using the Schechter function (Schechter, 1976) as the parametric shape for the UV LF is well motivated, as it matches the observed Universe well:

? −0.4(M−M?) φ(M) = 0.4 ln (10) φ?10−0.4(M−M )(1+α)e−10 (2.4)

We perform a maximum likelihood analysis to fit the UV LFs. Specifically, we use the modified maximum likelihood estimator (MLE) developed and presented in Mehta et al. (2015), which accounts for the measurement errors in galaxies’ observed magnitude, allowing for a more robust fitting procedure. Following the procedure from Mehta et al.(2015), we define the probability for detecting a galaxy in the sample as:

ZZ Mlim(z) φ(M)·veff (M, z)· −∞

N(M|{Mi, σi})dMdz P (Mi) = (2.5) ZZ Mlim(z) φ(M) · veff (M, z) · dMdz −∞

Here, Mi is the absolute rest-1500A˚ (UV) magnitude of the galaxy, φ(M) is the luminos-

ity function from Equation 2.4, Mlim(z) represents the survey’s detection limit, veff (M, z) is

the effective differential comoving volume and N(M|{Mi, σi}) is the term that marginalizes over the measurement error in the galaxy’s magnitude. The effective differential comoving volume is defined as:

dV v (M, z) = comov (z) · S(M, z, r ) · Ω (2.6) eff dz dΩ 1/2 where S(M, z, r1/2) is the selection function, which defines the efficiency of the selection criterion at a given redshift z as a function of the absolute UV magnitude M for a given half-light radius r1/2 derived from the completeness simulations in Section 2.2, and Ω is the Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 37 solid angle surveyed. The measurement error associated with the absolute UV magnitude

(σM,i) is modelled as a Gaussian:

" 2 !# 1 (M − Mi) N(M|{Mi, σi}) = √ exp − 2 (2.7) 2πσi 2σM,i In the MLE formalism, the Schechter function normalization φ? is calculated after finding the best-fit values for α and M ?:

N φ? = (2.8) ZZ Mlim(z) φ(M) · veff (M, z) · dMdz −∞ PN We construct the log likelihood function, ln L = i=1 ln P (Mi), where the probability

for each source to be detected in the sample, P (Mi) is computed using Equation 2.5. We maximize the log likelihood function (alternatively, minimize the negative log likelihood function). Once the best fit values for slope α and characteristic magnitude M ? are obtained, the normalization φ? is calculated. Furthermore, in order to properly quantify the uncertainties on our best-fit parameters, we perform a Markov Chain Monte Carlo analysis (MCMC). We probe the full posterior distribution for the free parameters in LF fitting using the Python package emcee (Foreman- Mackey et al., 2013b). We implement the Affine-Invariant Ensemble Sampler in emcee, initialized at the best-fit parameters. The uncertainties on our LF parameters are obtained from the distribution of the Markov chain, after discarding the burn-in period.

2.4 Results

2.4.1 Rest-frame UV Luminosity functions at z ∼ 1.5 − 3

Using the modified MLE fitting procedure described in Section 2.3, we fit a rest-frame UV LF for the dropout as well as photometric redshift selected samples from Section 2.1. The photometric redshift samples selected over the same redshift ranges as those covered by the dropout samples allows us to verify the robustness of our LF fits. Ideally, one would use the full sample selected down to the faintest magnitudes possible within the survey capabilities. However, near the survey limit, the incompleteness rises significantly and the correction applied to the effective volumes tends towards considerably large values. In order to avoid using sources with corrections that are too large, we choose to truncate the sample where the effective volume correction rises above 75% of the correction Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 38

0 10 0.5 z~2.2 1.0 α 10-1 1.5 2.0 ] 1

− 21 20 19 g 10-2

a M m

3

− -3

c 10

p This work (F275W dropouts, z~2.2) M

[ This work (photo-z, 1.8

φ 10 Reddy & Steidel09 (1.9

1 1.50 1 1.75 − 21 20 − 22 21 20 g g 10-2

a M a M m m

-2 3 10 3

− − -3

c c 10

p p This work (F336W dropouts, z~3) M M

[ [ This work (photo-z, 2.4

φ This work (photo-z, 1.4

Figure 2.4 The rest-frame 1500A˚ UV luminosity functions at z ∼ 1.7 (bottom left), z ∼ 2.2 (top), and z ∼ 3 (bottom right) measured using UVUDF. The best-fits obtained using the dropout samples from UVUDF are shown in red, and the corresponding photometric redshift samples are shown in black. The best-fit parameters for all luminosity function fits are reported in Table 2.1. The insets show the 68% (thick) and 95% (thin) confidence regions for the free luminosity function parameters (α and M ?) obtained from MCMC analysis. The shaded regions denote the 1σ confidence regions for the UV luminosity function fits. We also plot the UV luminosity functions at similar redshifts from recent literature for comparison. All LFs have been plotted for the range of magnitudes covered by their samples. at the bright end, which further reduces our sample size. Table 2.1 reports the final sample sizes used to fit the LFs.

UV LF at 1.4 < z < 1.9

The F225W dropout selection criterion results in a sample of 23 galaxies from the UVUDF catalog. Due to the small sample size, we choose not to fit a LF for the F225W dropouts. The corresponding photometric redshift sample (1.4 < z < 1.9), however, consists of 202 Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 39 galaxies – sufficient to properly fit a LF. We use the F435W as the rest-1500A˚ magnitude and the effective volumes corrected using the selection functions from Section 2.2. The resulting best-fit parameters are reported in Table 2.1 and the LF is plotted in the bottom-left panel of Figure 2.4 along with the results from recent literature. The UV LFs available from the literature at this redshift already show a considerable spread in their parameters. Our best-fit UV LF expects a higher number density at the bright end compared to other LFs. This can be inferred from the high M ? value we find for our best-fit LF. However, it is important to point out that the area covered by the UVUDF survey is small (7.3 arc. min2), which leads to high cosmic variance. The bright end of the LF is particularly prone to this, given the small number statistics. The faint-end slope of our best-fit LF is also considerably shallow compared to other LFs at similar redshifts. It is important to note that a higher M ? value also contributes towards flattening the faint- end slope. Our α value still agrees with the F225W dropout LFs from Hathi et al.(2010) and Oesch et al.(2010) within their uncertainties. There is minimal tension between our best-fit and Parsa et al.(2016), as their value is within < 1.5σ of ours. However, there is a substantial discrepancy between our result and Alavi et al.(2016) value of α = 1.56 ± 0.04.

UV LF at 1.8 < z < 2.6

The F275W dropout criterion selects galaxies with 1.8 < z < 2.6, where the rest-1500A˚ magnitude is covered by F435W for z < 2.2 and F606W for z > 2.2. For the photometric redshift sample, we use the appropriate rest-1500A˚ filter identified using the photometric redshift. However, for the dropout sample, this is not possible due to the lack of individual- ized redshift information; instead, we use F435W as the rest-1500A˚ filter for the full sample, since it covers rest-1500A˚ for the majority of the redshift range (considering the longer tail towards lower redshift). We fit a rest-frame UV LF for the sample of 58 galaxies selected by the F275W dropout criterion, with effective volumes corrected according the corresponding selection function. We also fit a LF using the 1.8 < z < 2.6 photometric redshift sample consisting of 238 galaxies. The LF fit using the photometric redshift sample agrees with the dropout sample LF, within the 1σ uncertainties. Both z ∼ 2.2 rest-frame UV LF fits are plotted in the top panel of Figure 2.4 along with the 68% confidence regions on the free parameters (α and M ?) in the inset, and the best-fit parameters are reported in Table 2.1. The nature of the UVUDF observations highlights the ability to go to faint, albeit in a small area. Hence, one of the main goals of this work is to constrain the faint-end slope of the UV LF. At z ∼ 2.2, we use the UVUDF photometric redshift sample to fit a UV LF faint-end +0.10 slope of α = −1.32−0.14, which in good agreement with Parsa et al.(2016) and Sawicki & Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 40

Thompson(2006), given their uncertainties. On the other hand, our result is considerably shallower than the estimates from Oesch et al.(2010) and Alavi et al.(2016), who find α = −1.60 ± 0.51 (for their F275W dropout sample) and α = −1.73 ± 0.04, respectively. However, our sample goes ∼3 magnitudes deeper than Oesch et al.(2010), thus providing a tighter constraint on the faint-end slope. Alavi et al.(2016) derive their UV LF using lensed galaxies in the Abell 1689 cluster as well as Abell 2744 and MACSJ0717 clusters from in the Hubble Frontier Fields (HFF). Although, Alavi et al.(2016) go much deeper (down to

MUV = −13) than the blank field surveys, there is a possibility of significant systematics affecting their result. Bouwens et al.(2016) assess the impact of systematic errors in the fits of the LFs derived from lensed galaxy surveys. They find considerable systematic scatter for faint, high magnification sources (µ > 20) dependent on the lens model used, which in turn, has a significant impact on the recovered LF. Most dramatically, they find that the faint- end of the recovered LF is preferentially steeper than the real value, when the systematic uncertainties in µ are not accounted for. This systematic could help resolve the tension between our result and Alavi et al.(2016).

UV LF at 2.4 < z < 3.6

The F336W dropout sample has 201 galaxies and the corresponding photometric redshift sample consists of 412 galaxies. F606W covers rest-1500A˚ filter for the redshift range se- lected by F336W dropouts (2.4 < z < 3.6). Our best fit values for the Schechter parameters along with the uncertainties for all our fits are reported in Table 2.1. The bottom right panel of Figure 2.4 shows the UV LFs for this redshift range, for both dropout and photometric redshift samples, in comparison with the results from recent literature. Our best-fit rest-frame UV LF at z ∼ 3 is in excellent agreement with Parsa et al. +0.08 (2016). Our faint-end slope value of α = −1.39−0.12 is considerably shallower than the Reddy & Steidel(2009) and Oesch et al.(2010) value of α ∼ −1.73. Similar to the F225W and F275W dropouts, there is significant tension when comparing our result to the Alavi et al.(2016) value of α ∼ −1.94 ± 0.06 fit at a slightly lower redshift z ∼ 2.7.

2.4.2 Cosmic Variance

The errorbars shown in Figure 2.4 already account for the Poisson errors on the number counts. However, given the small field-of-view of the UVUDF, the number counts are also affected by cosmic variance. This would help explain the discrepancy at the bright end of the lowest redshift (z ∼ 1.65) LF compared to other surveys with large coverage. We Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 41

Table 2.1. UVUDF: Best-fit parameters for rest-frame 1500A˚ UV LFs

a ? ? Redshift Sample Selection Mlim,UV N α M log φ

LBG dropout samples z ∼ 1.65 F225W dropouts -18.46 23 sample size too small +0.32 +0.32 +0.18 z ∼ 2.2 F275W dropouts -17.97 58 −1.31−0.75 −19.66−1.67 −2.21−1.13 +0.07 +0.12 +0.12 z ∼ 3.0 F336W dropouts -17.37 201 −1.32−0.26 −20.61−0.92 −2.36−0.19 Photometric redshift samples +0.10 +0.25 +0.12 1.4 < z < 1.9 Photo-z -15.94 202 −1.20−0.13 −19.93−0.40 −2.12−0.19 +0.10 +0.24 +0.12 1.8 < z < 2.6 Photo-z -16.30 238 −1.32−0.14 −19.92−0.44 −2.30−0.23 +0.08 +0.19 +0.11 2.4 < z < 3.6 Photo-z -16.87 412 −1.39−0.12 −20.38−0.43 −2.42−0.21

aSample size after removing any sources with high effective volume correction. See Section 2.4.1 for details. estimate the cosmic variance for our sample using the Cosmic Variance Calculator v1.023 (Trenti & Stiavelli, 2008). For a field-of-view of 2.70 × 2.70, we estimate a fractional error of

0.21, 0.21, 0.18 on the number counts of bright (MUV < −20) sources in our 1.4 < z < 1.9, 1.8 < z < 2.6, 2.4 < z < 3.6 photometric redshift samples, respectively. Similarly, the F275W and F336W LBG dropout samples are affected by a fractional error of 0.22, 0.17 on

the number counts of MUV < −20 sources, respectively.

2.4.3 UV Luminosity Density

The faint-end slope of the UV LF determines the relative contribution of faint and bright galaxies to the total cosmic UV luminosity. We use the new estimates derived in Sec- tion 2.4.1 to compute the observed cosmic UV luminosity density (not corrected for dust) as:

Z ∞ Z Mlim ρUV = Lφ(L)dL = L(M)φ(M)dM (2.9) Llim −∞ Table 2.2 reports the UV luminosity density computed integrating down to a variety of luminosity limits. For this calculation, we use the LF fits derived using the photometric redshift samples, due to their smaller statistical uncertainties as well as coverage down to fainter luminosities. The evolution of the UV luminosity density (not corrected for dust) over redshift is shown in Figure 2.5. All points shown were integrated down to MUV = −13 according to Equation 2.9 in a consistent fashion, using the LF parameters from the cited references along with the reported uncertainties. From z = 0 to z = 2, the observed UV

3 http://casa.colorado.edu/~trenti/CosmicVariance.html Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 42

Table 2.2. UVUDF: UV luminosity densitya

UV Luminosity Densitya,b Redshift ? c M < −0.03MUV M < −13 M < −10

+0.42 +0.45 +0.48 z ∼ 1.65 3.37−0.20 3.57−0.20 3.60−0.17 +0.20 +0.29 +0.30 z ∼ 2.2 2.42−0.18 2.65−0.15 2.69−0.15 +0.33 +0.35 +0.40 z ∼ 3.0 2.99−0.12 3.38−0.09 3.43−0.09

anot corrected for dust bin units of ×1026 ergs/s/Hz/Mpc3 c ? The MUV value used is from our LF fits using the photometric redshift sample, as reported in Table 2.1.

luminosity density rises (Arnouts et al., 2005) and peaks around z ∼ 2 − 3, after which it slightly declines again (Finkelstein et al., 2015; Bouwens et al., 2015). Overall, where multiple estimates are available, there is a large scatter in the UV lumi- nosity density. Particularly in the z ∼ 1.5 to 3.5 range, this scatter is many times larger than the formal errors quoted by some of the surveys, indicating that systematic errors (possibly resulting from the different selection functions and cosmic variance) are not ac- counted for. Our estimates at z ∼ 2 − 3 are within 20% of the two surveys most similar to ours, Alavi et al.(2016) (using lensed galaxies in HFF and Abell 1689) and Parsa et al. (2016) (using HUDF without the additional NUV coverage). At the lower redshift z ∼ 1.7, our UV luminosity density estimate is a factor 2.5 and 1.3 higher than Alavi et al.(2016) and Parsa et al.(2016), respectively. This discrepancy is caused due to the high number density we find at the bright end compared to the other two LFs. However, we would like to reemphasize that the coverage area of UVUDF is very small and hence, our result is affected by high cosmic variance. Using the UV luminosity density, we now compute the cosmic star formation rate den- sity (SFRD) of the Universe. Two main assumptions enter this conversion: i) the correction applied to the UV luminosity to account for interstellar dust attenuation, and ii) the con- version between UV luminosity and SFR (which depends on, e.g., stellar age, star formation history, and initial mass function, IMF). We implement the widely used IRX −β relation (Meurer et al., 1999, hereafter M99) to derive the average UV extinction as a function of the observed UV luminosity. The average

β for our sample is derived as a function of UV luminosity using the β − MUV relation

for the appropriate redshift from Kurczynski et al.(2014). The resulting IRX − β − MUV Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 43

M < -13 1027 UV ] 3 c p M / z 1026 H / s / s g r Arnouts+05 Cucciati+12 e [

Sawicki & Thomson06 Sawicki12 V U Bouwens+07 Bouwens+15 ρ 1025 Dahlen+07 Finkelstein+15 Reddy & Steidel09 Alavi+16 Hathi+10 Parsa+16 Oesch+10 This work 1 2 3 4 5 6 7 8 9 10 12 (1+z)

Figure 2.5 Redshift evolution of the observed UV luminosity density (not corrected for dust). Our points are shown in black in comparison to various rest-frame UV LFs available in the literature at different redshifts. All the points are derived by integrating the rest- frame UV LFs down to MUV = −13 and the errors on the points are estimated using the uncertainties in the LF parameters as reported by the individual references.

relation quantifies the dust extinction at the observed UV luminosity. For full details on the applied UV dust correction see Appendix 2.B. The dust corrected UV luminosity is converted into a star formation rate using the transformations tabulated in Kennicutt & Evans(2012) (which quotes Murphy et al. 2011). The computed SFRDs are reported in Table 2.3 for the same luminosity ranges used in Table 2.2. At z ∼ 2, we compare our result to the total intrinsic SFRD computed from the UV −1 −3 and IR data in Madau & Dickinson(2014), ψUV +IR(z = 2.2) = 0.127 M yr Mpc . −1 −3 We measure a dust-corrected UV SFRD of ψUV = 0.103 M yr Mpc (here, we use the Kennicutt 1998 transformation in order to match the Madau & Dickinson 2014 analysis) ? ? for MUV < 0.03MUV , where MUV is the measurement from our rest-frame UV LF fit using the photometric redshift sample. We find that the derived ψUV is approximately a factor of ∼ 1.2 lower than the total intrinsic SFRD computed from the UV and IR data in Madau & Dickinson(2014). At face value, this result suggests that the correction for dust extinction that we apply is underestimated. We can independently check this result using the Hα LF. For this calculation, we use the Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 44

Table 2.3. UVUDF: Star Formation Rate Densitya

SFR Densitya,b,c Redshift M < 0.03M ?d M < −13 M < −10

Using Meurer et al.(1999) relation +0.017 +0.017 +0.017 z ∼ 1.65 0.094−0.008 0.097−0.008 0.098−0.008 +0.008 +0.010 +0.010 z ∼ 2.2 0.066−0.006 0.070−0.005 0.070−0.005 +0.013 +0.013 +0.012 z ∼ 3 0.086−0.005 0.092−0.003 0.093−0.004 Using Castellano et al.(2014) relation +0.036 +0.038 +0.036 z ∼ 1.65 0.212−0.020 0.219−0.020 0.220−0.017 +0.020 +0.020 +0.022 z ∼ 2.2 0.148−0.013 0.157−0.014 0.158−0.011 +0.026 +0.030 +0.030 z ∼ 3 0.194−0.010 0.208−0.009 0.210−0.010 Using Reddy et al.(2015) relation +0.022 +0.022 +0.023 z ∼ 1.65 0.120−0.010 0.125−0.009 0.125−0.010 +0.011 +0.011 +0.011 z ∼ 2.2 0.084−0.007 0.089−0.007 0.090−0.007 +0.016 +0.017 +0.018 z ∼ 3 0.110−0.004 0.118−0.005 0.119−0.005

adust corrected

b 3 in units of M /yr/Mpc cusing the Kennicutt & Evans(2012) transformations dThe M ? value used is from our LF fits using the photometric redshift sample, as reported in Table 2.1.

? Sobral et al.(2013) z ∼ 2.23 Hα LF, removing the AGN contribution using the LHα/LHα vs. AGN fraction relation presented in Sobral et al.(2016). To account for dust extinction, we use the luminosity dependent dust correction from Hopkins et al.(2001), updated for z ∼ 2 according to the Dom´ınguez et al.(2013) results. For full details on the applied H α dust correction, see Appendix 2.C. For a direct comparison, we compute the SFRD by integrating the Hα LF down to −1 an Hα luminosity corresponding to a SFR of ∼ 0.5 M yr (i.e., the SFR corresponding ? to 0.03MUV,z=2) and converting the Hα luminosity density into SFRD (using Kennicutt (1998) again, to match the Madau & Dickinson 2014 analysis). The resulting SFRD is −1 −3 ψHα = 0.116 M yr Mpc , more in agreement with the Madau & Dickinson(2014) UV + IR prediction, and thus, pointing to the dust correction as the main reason for the discrepancy between the SFRD computed from the UV LF alone, and that computed from the UV + IR. Hα and UV as star formation indicators have been compared using multi-wavelength studies, both locally (e.g., Lee et al., 2009, 2011; Dom´ınguezS´anchez et al., 2012; Weisz et al., 2012; Koyama et al., 2015) as well as at high redshifts (e.g., Wuyts et al., 2011; Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 45

Shivaei et al., 2016). Hα has been shown to be a non-biased SFR indicator that agrees well with the total star formation in normal star-forming galaxies. Whereas, UV as a star formation indicator by itself is affected with the problem of dust correction. While it is possible that cosmic variance can impact our UV LF, it is important to note that at the redshift we are considering the bright end of our LF is in very good agreement with other surveys covering large areas. The result, therefore, is not expected to change drastically due to cosmic variance.

2.5 Discussion

We further investigate the discrepancies in the volume averaged SFR at z ∼ 2 using the rest-frame UV LF derived in this work and comparing it to the Hα LFs available in the literature. We start by computing the star formation rate functions (SFRFs) from both the UV and Hα LFs. Similar to the LFs, a SFRF measures the number density of galaxies, but as a function of the star-formation rate, instead of luminosity. Converting the LFs to SFRFs requires transforming the luminosities into a star-formation rate. As before, we correct the UV LF according to typical dust prescription, the M99 IRX − β relation (expanded to a

IRX − β − MUV relation), and the Hα LF according the Hopkins et al.(2001) relation adjusted using Dom´ınguezet al.(2013) results. Both UV and H α dust-corrected LFs are then converted into SFRFs, using the transformation tabulated in Kennicutt & Evans(2012) (which quotes Murphy et al. 2011) 4 . Figure 2.6 shows the resulting z ∼ 2 SFRFs, with the SFRF calculated using M99 shown in red and the SFRF from Hα shown in black. The comparison between these two estimates −1 shows that most of the discrepancy originates at the bright end. For SFR >30 M yr , the Hα SFRF estimates for a factor of ∼2.5 more sources compared to the UV SFRF. There is clear tension between the rest-frame UV and Hα LFs at z ∼ 2, under typical assumptions. Hence, one or more of the assumptions made require additional scrutiny. Recalling the main assumptions that enter this analysis:

• Dust: The observed light (both UV and Hα) needs to be corrected for interstellar

4 Specifically, we use:

−43.35 SFRUV [M /yr] = 10 · νLν,UV,corr [erg/s] −28 = 0.893 × 10 · Lν,1500,corr [erg/s/Hz] −41.27 SFRHa [M /yr] = 10 · LHα,corr [erg/s] −42 = 5.37 × 10 · LHα,corr [erg/s] Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 46

dust absorption before the light can be converted to a star formation rate.

• Stellar Population Properties: The intrinsic amount of light emitted from a galaxy (star forming or not) depends on stellar population, age, metallicity, and IMF. Con- sequently, when interpreting the galaxy light as a star formation rate, one has to assume a stellar population model. This assumption can be broken into finer details: star formation history, stellar age, metallicity, and IMF.

It is a not straightforward to investigate all of these assumptions simultaneously with only one measurement each of two observables, rest-frame UV and Hα LFs, due to the var- ious degeneracies involved. Here, we individually examine the effects of the most important assumptions: dust and star formation histories.

10-1 ) R

F -2

S 10 ( g o l d

) -3 R 10 F M16 SFRF(UV) (M99 dust cor.) S ( M16 SFRF(UV) (C14 dust cor.) Φ M16 SFRF(UV) (R15 dust cor.) S13 SFRF(Hα) 10-4 100 101 102 1 Star Formation Rate [M yr− ] ¯

Figure 2.6 Star formation rate functions derived from the UV luminosity function (this work) with dust corrections applied using the generic Meurer et al.(1999) (in red) IRX −β relation as well as Castellano et al.(2014) (in blue) and Reddy et al.(2015) (in green) relations, which are calibrated at high redshifts (z ∼ 2 − 3). The Hα star formation rate function derived using the Sobral et al.(2013)H α LF and corrected using Hopkins et al. (2001) (updated for high-redshift using Dom´ınguezet al. 2013 observations) is plotted in black. The UV SFRF corrected using the M99 dust law shows large discrepancy with the Hα SFRF, particularly at the bright end. Note that the LFs have only been plotted down to the survey limits. See text for full details on the applied dust corrections. Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 47

2.5.1 Dust Correction

Correcting for dust is a key step in going from the observed luminosity to the star formation rate. The IRX − β relation in M99 was calibrated using local star-forming galaxies. How- ever, the stellar population properties of high-redshift galaxies may be different from local objects, e.g., they are expected to have lower metallicities and younger ages than their local counterparts. This may cause high-redshift galaxies to have intrinsically bluer UV slopes, and using the M99 relation could underestimate the dust content (Wilkins et al., 2012). Recently, amendments to the original M99 IRX − β relation have been suggested for high redshift galaxies (e.g., Heinis et al., 2013; Castellano et al., 2014; Reddy et al., 2015). Here, we test two of the recently suggested prescriptions for z ∼ 2 galaxies: Castellano et al. (2014) and Reddy et al.(2015). Using a sample of well studied z ∼ 3 Lyman break galaxies (LBGs), Castellano et al. (2014, hereafter, C14) recently pointed out a systematic offset between the SFR(UV) com- puted using M99 and those computed from SED fitting. They provide a modification to +0.41 the IRX − β relation by only correcting for the systematic offset: AUV = 5.32−0.37 + 1.99β, implying a larger correction for dust than using M99. Reddy et al.(2015, hereafter, R15) study a sample of z ∼ 2 star forming galaxies with deep optical spectroscopy and multi- wavelength photometry. They fit an IRX − β slope of AUV = 4.48 + 1.84β for their z ∼ 2 sample, which also implies a slightly higher correction for dust than M99. The difference between these two and the M99 relations is highlighted in Appendix 2.B. In Figure 2.6, we show the SFRFs computed from the UV LF, but assuming the C14 (blue curve) and the R15 (green curve) IRX − β relation. Both of these dust prescriptions reduce the tension at the highest SFR. The C14 relation, in fact, over-corrects the UV SFRF −1 and only agrees with the Hα SFRF at the high SFR end (SFR & 80 M yr ). This is not entirely surprising when considering that C14 only applied an overall offset to the IRX − β −1 relation, which they compute using a sample of high SFR galaxies (SFR ∼ 100 M yr ). Ideally, the C14 calibration is only valid for the bright end. The UV SFRF corrected using R15 relation also results in more high-SFR galaxies compared to M99; however, it is still unable to reproduce all of the high SFR galaxies that are recovered in the Hα SFRF. Thus, a simple tweaking of the dust prescription is not sufficient to solve the discrepancy, as this prescription only measures the average behavior of a galaxy population. The high-SFR end of the SFRF can be also altered artificially because of the intrinsic scatter in the IRX − β − MUV relation. This effect is partially accounted for in the dust extinction as calculated in Appendix 2.B, where the scatter between β and MUV is consid- 2 2 ered (by the 0.2 ln 10b σβ term in the AUV − β conversion). This correction assumes that Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 48 the scatter is constant with luminosity and symmetric with respect to the best-fit relation. However, studies have shown that in fact this is not the case, and the scatter increases to- wards fainter magnitudes, and the distribution around the best-fit becomes skewed, because of the dust–free limit on β (e.g., Bouwens et al., 2012; Alavi et al., 2014; Kurczynski et al., 2014). Because of this effect, some faint galaxies may in reality have large dust corrections. A few of these objects would be sufficient to affect the bright end of the SFRF, given its ex- ponential fall-off. A proper treatment of the scatter could then reduce the tension between the UV and Hα SFRFs. There is considerable evidence for the existence of a population of the so-called “Dusty SFGs” (DSFGs; dusty star-forming galaxies), both locally (Goldader et al., 2002; Burgarella et al., 2005; Buat et al., 2005; Howell et al., 2010; Takeuchi et al., 2010) and at high redshifts (Reddy et al., 2010; Heinis et al., 2013; Casey et al., 2014; Ivison et al., 2016). The DSFGs −1 are a population of galaxies that have high star-formation rates (SFR > 50 M yr ) and 11 high IR luminosities (LIR & few ×10 L ). However, due to their high dust content, they have a high IRX (LIR/LUV ) that is offset from the nominal IRX − β relation. These galaxies are faint in the UV not because they are intrinsically faint and have low dust content, but instead because they are intrinsically bright and are highly obscured by dust. A generic IRX − β relation would underestimate the dust content for these galaxies and −1 hence, would result in a deficit of high SFR sources (SFR > 50 M yr ). The shortage of sources in the UV SFRF at the high SFR end can plausibly be explained by these objects.

2.5.2 Star Formation Histories

The conversion between light (either Hα or UV) and SFR is another key step in the calcu- lation of the SFRFs, which depends critically on the age of the star-burst, and therefore on the specific star formation history. Until this point, we have assumed the conversion from Kennicutt & Evans(2012), which implicitly assumes that the SFR has been constant for at least 100 Myr. If this is not the case, however, the Kennicutt & Evans(2012) conversion is not justified, and we have to take into account the fact that the rest-frame UV and the Hα luminosities are sensitive to star formation occurring over different timescales. In particular, the rest-frame UV is sensitive to star formation occurring over ∼100s of Myrs, whereas the Hα is sensitive to star formation over ∼ 10s of Myrs. The brightness of a galaxy in the two indicators (i.e., Hα and FUV) depends on the recent star formation history. Figure 2.7 shows the evolution of the UV-to-Hα ratio for a variety of star formation histories. The Hα output from a galaxy drops on much shorter timescales, after the end of a burst, compared to the non-ionizing UV, which takes longer to react, because of the longer Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 49 lived B and A stars that still produce UV photons, but have very little ionizing output. For a constant star formation history, the rates at which massive stars are formed and die reach an equilibrium after approximately 100 Myr, and therefore the UV-to-Hα ratio tends to a constant value (log10[νLν(1500)/LHα] ∼ 2); whereas, a burst of star formation would cause the UV-to-Hα ratio to scatter towards higher values. Figure 2.7 shows how the UV-to-Hα ratio evolves for Bruzual & Charlot(2003) models with Salpeter(1955), Kroupa(2001) as well as Chabrier(2003) IMFs and metallicities of

Z/Z = 0.02, 0.2, 1 with three different star formation histories: single instantaneous burst (SSP), short bursts of star formation (10Myr and 100Myr), and constant star formation. The main impact of the different IMFs on the UV-to-Hα ratio is limited to the values of their slopes at the high-mass end, since both Hα and UV are sensitive to hot, massive stars. Moreover, this difference in IMF slopes at the high masses is small enough between Salpeter(1955, α = −2.35), Kroupa(2001, α = −2.3), and Chabrier(2003, α = −2.3) IMFs that the resulting variation in the UV-to-Hα ratio is within the linewidths of the curves in Figure 2.7. For models with constant star formation histories, we compute the range of expected UV-to-Hα ratios at an age of 100Myr (the generic assumption in SFR conversions, e.g., Kennicutt & Evans(2012)). The horizontal band in Figure 2.7 shows this expectation from the constant star formation history case. The effect of the star formation histories (SFHs) on the UV-to-Hα ratio has been studied both in simulations (Shen et al., 2013; Hopkins et al., 2014; Dom´ınguezet al., 2015) as well as observations (Boselli et al., 2009; Finkelstein et al., 2011; Lee et al., 2011, 2012; Weisz et al., 2012; Guo et al., 2016). Dom´ınguezet al.(2015) used SFHs derived from hydro- dynamical simulations to study the variation of the UV-to-Hα ratio, which they suggest is a useful observable to quantify the “burstiness” of a galaxy’s SFH. Using their simulated 9 galaxies they find that galaxies with low stellar masses (M? . 10 M ) are dominated by bursty SF, and have a higher mean value and scatter of the UV-to-Hα ratio compared to more massive galaxies. This is a result of energy feedback from star formation being more efficient in low–mass galaxies (Somerville & Dav´e, 2015). We can study the trend between the volume-averaged UV-to-Hα ratio and the stellar mass by comparing the dust-corrected UV and Hα LFs. To do so, we need to be able to associate a given luminosity (either Hα or UV) to its corresponding halo mass. We use a standard “abundance matching” technique (e.g., Conroy et al., 2006; Guo et al., 2010; Moster et al., 2010; Trenti et al., 2010; Tacchella et al., 2013; Mason et al., 2015) to associate galaxies with given number densities to their corresponding dark matter halos. The implicit assumption in this step is that there is only one galaxy per dark matter halo. In practice, Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 50 we find a relation between the halo mass (Mh) and the observed luminosity (e.g., LUV ) by solving the following equations:

Z ∞ Z ∞ 0 0 0 0 n(Mh, z = 2.2)dMh = φ(LUV )dLUV Mh LUV Z ∞ (2.10) 0 0 = φ(LHα)dLHα LHα where n(Mh, z) is the analytical dark–matter halo mass function from (Sheth et al., 2001) computed at z = 2, φ(LUV ) is the z ∼ 2 UV LF from this work, and φ(LHα) is the z = 2.23 Hα LF from Sobral et al.(2013). By solving Equation 2.10 we derive the UV and H α luminosities that correspond to a given dark matter halo mass, and thus the UV-to-Hα ratio that corresponds to that halo mass. We limit this analysis only to luminosities down to which our z ∼ 2 UV LF sample extends. This does involve extrapolating the Hα LF 1 dex below their observation limit. Also, note that in order to compare to intrinsic flux ratio, the observed luminosities still need to be corrected for dust. We explore two dust relations (M99 and R15) from the previous section.

7 ) SSP Z=0.02Z

d ¯

e 10Myr Burst Z=0.2Z

t ¯

c 6 100Myr Burst Z=Z ¯ e

r constant SFR r o c

5 t s u d

( 4

) α H L

/ 3 V U , ν L

ν 2 (

g o l 1 100 101 102 103 Age [Myr]

Figure 2.7 The UV-to-Hα ratio plotted as a function of age since the onset of star formation for a range of star formation histories (single stellar population, single bursts, rising, and constant star formation) computed using Bruzual & Charlot(2003) models. The shaded band shows the expected log10[νLν(1500)/LHα] value for constant star formation, after accounting for a range of metallicities as well as different IMFs. See text for description of the models. Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 51

Figure 2.8 shows the main result of this analysis. The horizontal hatched region from

Figure 2.7 is shown again to highlight the expected range of values for log10[νLν(1500)/LHα] assuming a constant SFH and a range of metallicities (Z/Z = 0.02−1) and different IMFs (Salpeter, 1955; Kroupa, 2001; Chabrier, 2003). The derived volume-averaged UV-to-Hα ratio is not observed to be constant as a function of halo mass, but rather it increases above the value expected for constant SFH, as one moves towards the lower halo-mass end 12 (Mh . 10 M ). As seen in Figure 2.7, the impact of variation in IMF and/or metallicities on the UV-to-Hα ratio is small compared to the variations in the SFH. At face value, the increased ratio at low masses indicates a larger contribution by starbursting objects to the average population of galaxies, as suggested by the larger scatter predicted by Dom´ınguez et al.(2015). The halo mass where this effect seems to be important is below ∼ 5 × 1011 9 M , which would correspond to a stellar mass of ∼ 5 × 10 M , assuming the stellar mass to halo mass relation from Behroozi et al.(2013). We also provide polynomial fits to the empirical UV-to-Hα relation in Table 2.4. It is important to note that the measured empirical UV-to-Hα ratio from abundance matching in Figure 2.8 is very sensitive to the applied dust relation. However, they all exhibit the elevated UV-to-Hα ratio. The abundance matching technique matches the cumulative UV and Hα LFs and hence, it is also sensitive to the systematic differences at the bright end. As noted in the previous section, there is a distinct possibility of the presence of DSFGs in the UVUDF sample that are not being corrected for dust properly by the applied IRX − β relation. This impacts the bright end more significantly than the faint-end, due to low number statistics. Changing the bright end of the dust-corrected UV LF would offset the UV-to-Hα curves in Figure 2.8 vertically by a significant amount, while changing the overall shape of the curves only minimally. Thus the upturn in the UV- 12 to-Hα ratio at Mh . 10 M is preserved, although the characteristic stellar mass where this becomes important is somewhat dependent on the specific dust correction used in the analysis. Figure 2.8 clearly shows that the observed trend in the UV-to-Hα ratio is not constant with the observed UV luminosity and is inconsistent with constant star formation rate at all luminosities, even after accounting for a range of metallicities as well as different canonical IMFs. We also considered the possibility of a non-universal IMF, as introduced by Weidner & Kroupa(2005); Pflamm-Altenburg et al.(2007, 2009); Weidner et al.(2011). Based on statistical arguments, Weidner & Kroupa(2005) produced an integrated galactic initial mass function (IGIMF) which steepens in galaxies with lower SFRs, which could then reproduce a trend similar to what is observed in Figure 2.8. However, the main impact of Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 52 the SFR-dependent IGIMF occurs at SFR much lower than those probed by the current −2 −1 analysis (. 10 M yr ; Pflamm-Altenburg et al., 2009). In the SFR range (& 0.3 M yr−1) probed here, the IGIMF is in fact constant with SFR, and thus cannot account for the observed trend in the UV-to-Hα empirical relation by itself. Lastly, the Hα extinction correction we use is rather uncertain and hence, we explore whether the observed trend can be explained uniquely with dust. If dust were the only cause, the required Hα extinction correction would have to be nearly constant with Hα luminosity (A(Hα) ∼ 0.5) and thus stellar mass. The latter constraint is, however, inconsistent with observational results. Using a compilation of results from the recent literature, Price et al. (2014) show that the dust extinction increases for brighter, higher-mass galaxies, consistent with earlier results by Garn & Best(2010).

2.6 Conclusions

NUV coverage of the Hubble UDF provided by the UVUDF enables for LBG dropout and photometric redshift selection of galaxies near the peak of cosmic star formation (z ∼ 2−3). Additionally, it also enables the study of their rest-frame UV properties and consequently, their star formation properties. Here, we present the rest-frame 1500A˚ UV LFs for F225W (z ∼ 1.65), F275W (z ∼ 2.2), and F336W (z ∼ 3) dropout galaxies in the UVUDF selected by the LBG dropout criteria as well as by their photometric redshifts. We develop and execute a suite of completeness simulations to properly correct the effective volumes when fitting the LFs. Overall, our best-fit rest-frame UV LFs are in good agreement with the recent results from Parsa et al.(2016). We measure faint-end slopes that are within the errors compared to other blank-field surveys (such as, Hathi et al., 2010; Oesch et al., 2010). There is a striking discrepancy between our results and those from the Alavi et al.(2016) analysis of lensed galaxies. However, the steep faint-end of the LF measured from lensed galaxies could be the result of systematic uncertainties in the lensing modeling. These systematics are particularly important for the most magnified, i.e., intrinsically faintest, sources – those that contribute most to the measurement of α (Bouwens et al., 2016). At z ∼ 2.2, using our F275W dropout sample which covers the absolute UV magnitude range from −22.00 to −17.97 AB (where the effective volume correction drops to 25% of +0.32 that are the bright end), we measure a faint-end slope of α = −1.31−0.75. This is well in agreement with the corresponding photometric redshift sample, which covers a range of −22.00 to −16.30 AB in absolute UV magnitude, going ∼ 1.5 magnitudes deeper. When Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 53 b σ a 0 a relation α 1 a 2 a d ) 3 c

a 20) M i 12 − X i 10 a AB / , h N =0 4 UV i M X a M ) = = ( = log ( Hα X X /L 5 a (1500) ν νL 6 a . UVUDF: Fit parameters to the empirical UV-to-H ) range = (11.05,14.3)

range = (-16.45,-22.60) /M Table 2.4 h AB , M scatter about the mean relation UV σ log ( 1 The empirical relation: log( M d c b a Reddy et al. ( 2015 ) 1.46e-04Reddy -1.19e-05 et al. ( 2015 ) -2.51e-03 -7.67e-03 -6.60e-03 5.66e-02 1.92e-03 -1.44e-01 1.46e-01 1.31e-01 2.06 5.28e-02 0.153 -3.10e-01 2.12 0.153 Meurer et al. ( 1999 ) 1.46e-04 -2.13e-05Meurer et al. ( 1999 ) -2.49e-03 -7.61e-03 -6.37e-03 5.58e-02 2.21e-03 -1.42e-01 1.41e-01 1.28e-01 1.95 5.19e-02 0.154 -2.99e-01 2.01 0.154 UV Dust correction Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 54

Stellar Mass, M [M ] 109 1010 1¯011 1.5 1011 ×

Halo Mass, Mh [M ] 1011 1012 ¯ 1013 1014 )

d 2.4 e t c e r r

o 2.2 c

t s u d

( 2.0

α H L / 0 0

5 1.8 1 , ν

L using M99 dust cor. ν using R15 dust cor. g 1.6 o

l constant SFR expectation from BC03 models 16 17 18 19 20 21 22 23 Absolute UV Magnitude [AB]

Figure 2.8 The observed volume-averaged UV-to-Hα ratio plotted as a function of the observed UV luminosity using the empirical relations derived from abundance matching the z ∼ 2 UV LF and Sobral et al.(2013)H α LF, using two UV dust prescriptions: Meurer et al. (1999)(red curve) and Reddy et al.(2015)( green curve). The horizontal band again shows the expected log10[νLν(1500)/LHα] value for constant star formation, including a variety of IMFs and metallicities (see text for details). The abundance-matched DM halo mass is plotted on the top axis. Corresponding stellar masses are computed using the z = 2.2 stellar mass-halo mass relation from Behroozi et al.(2013) and plotted on a parallel axis. The shaded regions show the 1σ confidence regions for the measured empirical relation. The darker shaded bands show the range where both UV and Hα LFs have observations; whereas, the lighter shaded bands show the range when UV LFs have observations, but the Hα LF has been extrapolated.

compared with results from the literature, we find good agreement with Parsa et al.(2016) as well as Oesch et al.(2010) and Sawicki & Thompson(2006), given the uncertainties on their result. At z ∼ 1.65, our best-fit LF estimates a higher number density at the bright end in comparison to other results from the literature. However, due to the small area covered by the UVUDF, this sample is affected by high cosmic variance. For both F275W and F336W dropouts, the LFs measured from the LBG samples agree with those measured Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 55 from their corresponding photometric redshift samples, within the uncertainties.

We find an observed UV luminosity density (at MUV < −13) that is consistent within 20% of both Alavi et al.(2016) and Parsa et al.(2016) at z ∼ 2 − 3. We apply the Meurer et al.(1999) dust relation to correct the UV luminosities and compute the star formation rate density (SFRD) and find a factor of 2 discrepancy when compared to the total intrinsic star formation rate from UV + IR observations (Madau & Dickinson, 2014). This discrepancy is absent when using a z ∼ 2 Hα LF (Sobral et al., 2013) to compute the SFRD; thus, pointing to the dust correction as the main reason for the discrepancy. We compute the SFRF from the rest-frame UV LF using the generic M99 dust correction. The SFRF corrected according to the M99 relation failed to recover a factor of ∼ 2.5 high −1 SFR (> 30 M yr ) sources compared to the Hα SFRF. We find that using the M99 dust correction, which is calibrated using local galaxies, underestimates the dust content in the high-redshift (z ∼ 2) star-forming galaxies. Using relations calibrated at high-redshift such as Castellano et al.(2014) and Reddy et al.(2015), reduces the tension. However, a straightforward tweaking of the IRX − β relation is not sufficient to fully resolve the tension. One possibility is the presence of very dusty SFGs, that would not be properly corrected by the IRX − β relation because of their offset from the average relation. Another factor affecting the differences between the UV and Hα LFs is the burstiness of star formation in galaxies. We use abundance matching of the rest-frame UV and Hα LFs to compute a volume-averaged UV-to-Hα ratio – an indicator of “burstiness” in galaxies. We find an increasing UV-to-Hα ratio towards low halo masses. We conclude that this trend could be due to a larger contribution from starbursting galaxies at lower masses compared to the high-mass end. This trend is consistent with the expectation from hydrodynamical simulations.

2.A Completeness Functions

From our simulations, the completeness functions are computed using the fraction of re- covered sources as a function of observed magnitude as well as galaxy size. We use the

B435 half-light radius as a proxy for the galaxy size. These completeness functions are marginalized over all sizes to obtain completeness just as a function of magnitude, which is used to define the survey magnitude limits. These functions are only used to set the survey magnitude limits when computing the colors of sources not detected in the dropout filter. The effective volumes for computing the LF are fully corrected using the selection functions. Figure 2.9 shows the completeness functions for the F275W, F336W, and F435W Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 56

filters. Note that the compact sources have a higher recovery fraction at fainter magnitudes compared to more extended sources.

2.B UV Dust correction

For correcting the observed UV magnitudes, we use the dependence of dust extinction

(AUV ) on the UV slope β, also known as the IRX − β relation. Through the analysis, we

implement the IRX − β relation (AUV = a + b · β). We use multiple published fits for this relation: (i) the original Meurer et al.(1999, ; M99) calibrated using local star-forming galaxies: [a, b] = [4.43, 1.99], (ii) the Castellano et al.(2014) calibration using high-SFR +0.41 LBGs at z ∼ 3: [a, b] = [5.32−0.37, 1.99], and (iii) the Reddy et al.(2015) calibration using z ∼ 2 star-forming galaxies: [a, b] = [4.48, 1.84]. Furthermore, the UV slope β parameters are estimated as a function of the observed absolute UV magnitudes with a β − MUV relation. The distribution of β for the z ∼ 2 galaxies as a function of the absolute UV magnitudes is assumed using a parametric form, following Trenti et al.(2015) and Mason et al.(2015):

 dβ  (z)[MUV −M0]   dMUV (βM0 (z) − c) exp − β (z)−c + c,  M0   ifM ≥ M < β >= UV 0  dβ  dM (z)[MUV − M0] + βM0 (z),  UV   if MUV < M0

where c is the dust-free β. This relation avoids the unphysical negative values of AUV , while also avoiding unphysical discontinuities near magnitudes where the relation approaches dust-

free β. The parameters M0, βM0 , dβ/dMUV and σβ define the MUV − β relation and are constrained observationally. We use the results from Kurczynski et al.(2014), who derive this relation for 1 < z < 8 galaxies using the UVUDF. For z ∼ 2, the applied values are

M0 = −19.5, βM0 = −1.71, dβ/dMUV = −0.09, and σβ = 0.36.

Moreover, assuming a Gaussian distribution of β with a dispersion σβ gives the average 2 2 extinction: < AUV >= a + 0.2 ln (10)b σβ + b < β >, where b is the slope of the IRX − β relation (Tacchella et al., 2013; Mason et al., 2015). Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 57

1.0 F275W F336W 0.8 SN>5.0 SN>5.0

0.6

0.4 Comp.

0.2

0.0 7 0.21

6 0.18

5 0.15

4 0.12

F435W HLR [px] 3 0.09 F435W HLR [arcsec] 25 26 27 28 29 30 25 26 27 28 29 30 F275W Magnitude [AB] F336W Magnitude [AB]

1.0

0.8

0.6

0.4 Comp.

0.2 F435W F606W SN>5.0 SN>5.0 0.0 7 0.21

6 0.18

5 0.15

4 0.12

F435W HLR [px] 3 0.09 F435W HLR [arcsec] 25 26 27 28 29 30 25 26 27 28 29 30 F435W Magnitude [AB] F606W Magnitude [AB]

0.0 0.2 0.4 0.6 0.8 1.0 Completeness

Figure 2.9 Completeness functions for F275W, F336W, and F435W filters (from left to right) for sources detected at > 5σ. The top panel shows the completeness as a function of magnitude only, where as in the bottom panel, completeness is plotted as a function of magnitude and galaxy size. The dashed lines show where the completeness drops to 50%. The F435W (B-band) half-light radius (HLR) is used as an proxy for galaxy size. From the bottom panels, it is evident that galaxy size has a significant impact on the completeness – extended sources are missed more often than the more compact ones, even when they have the same magnitude. Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 58

4.0 Castellano14 + Kurczynski14 Reddy15 + Kurczynski14 3.5 Heinis13 + Kurczynski14 V Meurer99 + Kurczynski14 U 3.0 A

,

n 2.5 o i t

c 2.0 n i t

x 1.5 E

V 1.0 U 0.5

0.0 14 16 18 20 22 24 UV Magnitude [AB]

3.0 log LHα offset: 1.37 8 β Hopkins01 (no offset) H Hopkins01 (w/ offset) 7 / α

α 2.5 Hopkins01 (w/ offset, H H

smoothed) , A

6 t , Dominguez13

2.0 n n e o i t 5 m c 1.5 e r n i c t e x d e

1.0

4 r α e H m

0.5 l a

3 B 0.0 39 40 41 42 43 44 45 log Hα Luminosity, LHα [ergs/s]

Figure 2.10 Applied dust extinction correction for our analysis. (Top panel) The dust extinction in rest-frame UV as a function of the observed UV absolute magnitude. The widely used (Meurer et al., 1999, M99) relation was calibrated using local star forming galaxies, where as the Castellano et al.(2014) modifies the M99 relation for higher redshift galaxies. (Bottom panel) The dust extinction in the Hα line as a function of the observed Hα luminosity. The Hopkins et al.(2001) relation for local galaxies is shown in dashed black, whereas the solid curves show the same relation updated for z ∼ 2 galaxies according to the Dom´ınguezet al.(2013) observations. See text for full details.

2.C Hα Dust correction

The observed Hα luminosities are corrected for dust extinction by applying the luminosity dependent dust extinction (AHα) reported by Hopkins et al.(2001). They derive a SFR dependent reddening using a composite of UV, Hα emission line and FIR data. Most importantly, their dust correction can be applied as a function of attenuated SFR (or light). This is crucial for the analysis here, since the goal is to correct the Hα LF for dust as a Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 59 function of the observed Hα luminosity. However, the Hopkins et al.(2001) relation is derived for local galaxies. In order to scale the relation to match the dust properties of galaxies at z ∼ 2, we apply a shift such that it matches the Dom´ınguezet al.(2013) observations at 0 .7 < z < 1.5. This is motivated by the fact that a single relation holds even at higher redshifts, provided that the overall increased star formation (at higher redshift) is accounted for (Sobral et al., 2012). This can be done by applying an offset in the observed luminosity for the AHα − LHα relation. This can also be interpreted as the typical dust extinction in Hα not depending on the absolute star formation rate, but rather a relative dependence – how bright (or star-forming) a source is relative to the rest of the galaxy. 1.37 Following this justification, we apply an offset of LHα = 10 to adjust the Hopkins et al.(2001) local relation to match the Balmer decrement observations of star-forming galaxies at 0.7 < z < 1.5 from Dom´ınguezet al.(2013). We also apply a smoothing of 0.5 mag to avoid any discontinuities, as these would in turn, create unphysical discontinuities in the SFRFs. The bottom panel of Figure 2.10 shows the dust correction applied to Hα luminosities for our analysis. Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 60

a Table 2.5. UVUDF: Rest-frame 1500A˚ UV LFs measured via the Vmax estimator

b −3 −3 −1 c Redshift M1500 N φ [×10 Mpc mag ]

LBG Dropout samples +4.158 −18.22 14 6.659−1.495 +2.428 −18.72 11 3.447−0.873 F275W +2.162 −19.22 15 3.636−0.778 dropouts +1.639 −19.72 11 2.364−0.589 z ∼ 2.2 +1.079 −20.22 5 1.049−0.388 +0.693 −20.72 2 0.426−0.249 +4.499 −17.62 29 10.461−1.618 +2.832 −18.12 28 6.492−1.018 +2.514 −18.62 36 6.526−0.904 +1.956 F336W −19.12 34 4.953−0.703 +1.666 dropouts −19.62 34 4.216−0.599 +1.060 z ∼ 3 −20.12 16 1.844−0.381 +0.971 −20.62 13 1.522−0.349 +0.768 −21.12 8 0.945−0.276 +0.474 −21.62 3 0.357−0.170 Photometric redshift samples +7.485 −16.19 22 14.897−2.692 +4.975 −16.69 26 10.961−1.789 +4.904 −17.19 32 12.028−1.764 +4.034 −17.69 30 9.588−1.451 +3.189 −18.19 23 6.649−1.147 +3.272 1.4 < z < 1.9 −18.69 25 7.112−1.177 +2.868 −19.19 20 5.579−1.032 +2.299 −19.69 13 3.606−0.827 +1.670 −20.19 7 1.921−0.600 +1.081 −20.69 3 0.814−0.389 +0.621 −21.19 1 0.270−0.223 +4.560 −16.55 28 10.051−1.640 +3.946 −17.05 44 11.191−1.419 +2.945 −17.55 42 8.255−1.059 +2.500 −18.05 40 6.873−0.899 +2.117 −18.55 29 4.958−0.761 1.8 < z < 2.6 +1.960 −19.05 24 4.173−0.705 +1.682 −19.55 18 3.101−0.605 +1.058 −20.05 7 1.217−0.380 Chapter 2. UVUDF: UV Luminosity Functions at the cosmic high-noon 61

Table 2.5

b −3 −3 −1 c Redshift M1500 N φ [×10 Mpc mag ]

+0.899 −20.55 5 0.874−0.323 +0.403 −21.05 1 0.175−0.145 +2.776 −17.12 70 9.580−0.998 +2.367 −17.62 87 9.451−0.851 +1.623 −18.12 59 5.413−0.584 +1.780 −18.62 70 6.472−0.640 +1.376 −19.12 48 4.142−0.495 2.4 < z < 3.6 +1.180 −19.62 38 3.162−0.424 +0.780 −20.12 17 1.399−0.280 +0.708 −20.62 14 1.152−0.254 +0.420 −21.12 5 0.408−0.151 +0.265 −21.62 2 0.163−0.095

aThe LF fitting is done using the modified MLE technique which does not require binning and consequently, does not use these numbers explicitly. These numbers are provided for ease of plotting of our data. bRaw number counts in the luminosity bins. cCompleteness corrected number densities in the luminos- ity bins. Chapter 3

SPLASH-SXDF Multi-wavelength Photometric Catalog

Note: This chapter originally appeared as a refereed publication in the Astrophysical Journal under Mehta, V., Scarlata, C., Capak, P., et al. 2018, ApJS, 235, 36 titled “SPLASH-SXDF Multi-wavelength Photometric Catalog” and is presented here as is, albeit with some minor modifications.

Large-area, multi-wavelength, photometric surveys over the past couple decades have revolutionized our knowledge of galaxy formation and evolution by making it possible to study statistically significant populations of galaxies over most of the history of the universe. Such surveys are particularly useful when studying rare objects – e.g., low-mass galaxies with high specific star-formation rates that could potentially be low-redshift analogs of the earliest galaxies. Chapter4 presents a in-depth study of these objects (that are characterized by their strong emission lines in their spectra and thus, often called “extreme emission line galaxies”) using the photometric catalog presented here. The Subaru-XMM Newton Deep Field (SXDF; α=02h18m00s, δ=−5◦0000000; Furusawa et al., 2008; Ueda et al., 2008) is one of the largest area multi-wavelength survey datasets, along with the Cosmic Evolution Survey field (COSMOS; Scoville et al., 2007). The SXDF has attracted a wealth of observational campaigns from multiple state-of-the-art ground- and space-based observatories. The SXDF boasts a remarkable combination of depth (∼25-28 mag) over a large wavelength range from the optical to near-infrared and large area covered 2 on the sky (&2 deg ). The SXDF is perfectly suited for the study of the co-evolution of the cosmic large scale structure, the assembly and growth of galaxies and accurate measurement

62 Chapter 3. SPLASH-SXDF Catalog 63 of the evolution of the global properties of galaxies through cosmic history without being significantly affected by cosmic variance. Recently, the Spitzer Large Area Survey with Hyper-Suprime-Cam (SPLASH1 ; Capak et al., in prep.) program obtained additional warm-Spitzer coverage (3.6µmand 4.5µm) for the SXDF to accompany the optical coverage from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP; Aihara et al., 2017a) which uses the Hyper Suprime-Cam on the Subaru 8m telescope on Mauna Kea, Hawaii (Miyazaki et al., 2017, PASJ, in press). The combination of deep optical, near-infrared (NIR), and mid-infrared (MIR) coverage significantly improves the photometric redshifts and stellar mass estimates for high-redshift galaxies. We generate a multi-wavelength catalog including these newly acquired data along with all available archival data on the SXDF. The primary goal of this paper is to homogenize and assemble all available multi-wavelength data on the SXDF on a common astrometric reference frame to measure photometry in a consistent fashion across the various bands. Furthermore, exploiting the multi-wavelength photometry, we measure the photometric redshifts as well as physical properties such as stellar mass, ages, star formation rates, and dust attenuation for all sources. This chapter is organized as follows: Section 3.1 describes the observations; Section 3.2 outlines the steps involved in homogenizing the data and assembling it on our common reference frame; the catalog creation process is detailed in Section 3.3; and measurement of photometric redshifts and physical properties are described in Section 3.4.

3.1 Data

For this photometric catalog, we use the optical HSC imaging and the MIR warm-Spitzer data combined with archival optical and NIR imaging available from a variety of instruments and surveys. In this paper, we limit to a total area of 4.2 deg2 centered at (α, δ)=(02h18m00s, −5◦0000000), matching the size of the IRAC mosaics available. Of this, an area of 2.4 deg2 has optical imaging available from HSC (hereafter, HSC-UD area). The HSC-UD area also represents the region with the deepest data as well as largest wavelength coverage. Outside the HSC-UD area, there is limited coverage available in the optical from CFHTLS and MIR from Spitzer/IRAC along with VIDEO NIR coverage on a fraction of the area. Descriptions of the various observations included in this paper are provided below and

1 http://splash.caltech.edu Chapter 3. SPLASH-SXDF Catalog 64

Figure 3.1 Coverage maps from the HSC, IRAC, Suprime Cam instruments as well as the UVISTA/UDS, VIDEO, MUSUBI, and CFHTLS surveys for the SXDF shown overplotted on the HSC y-band mosaic. In addition to the labeled instruments/surveys, coverage from CFHTLS is available over the full mosaic. their footprint on the SXDF is shown in Figure 3.1. The full list of the photometric band- passes available from the various instruments and surveys is provided in Table 3.1 and the transmission curves are shown in Figure 3.2. Figure 3.3 shows the 5σ magnitude limit maps for a selected filter from the various imaging data included in the catalog.

3.1.1 Optical and near-infrared data

HSC: The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP; Aihara et al., 2017b) covers the SXDF in the grizy filters (Kawanomoto et al., 2017, PASJ, subm.) using the Hyper Suprime-Cam (Miyazaki et al., 2012) on the Subaru 8m telescope on Mauna Kea, Hawaii. The UltraDeep layer of the HSC-SSP covers two fields, COSMOS and SXDF, in Chapter 3. SPLASH-SXDF Catalog 65 broad- and narrow-band filters. In this paper, we include the imaging data from the HSC- SSP first public data release2 (Aihara et al., 2017a). These data go to only part of the full planned depth as the HSC-SSP continues to collect deeper data on these fields over the coming year. The exposure times for the g, r, i, z and y-bands are 70, 70, 130, 130 and 210 minutes, respectively, covering an area of 2.4 deg2, with ∼0.600 seeing. The data are processed with hscPipe (Bosch et al., 2017). We refer the reader to Aihara et al.(2017a,b) for detailed description of the survey and data processing. The depth of the data is listed in Table 3.1, measured using the technique outlined in Section 3.3.3. UDS: The Ultra Deep Survey (UDS) includes NIR imaging in the JHK filters on the SXDF from the UKIRT Wide-Field Camera. We use the JHK mosaics from their Data Release 113 (DR11). The DR11 covers the UDS over the full 0.8 deg2 going down to ∼25.3 mag (5σ 200 aperture) in the JHK bands. The UDS is a part of the UKIDSS project, described in Lawrence et al.(2007). Further details on the UDS can be found in Almaini et al. (in prep). VIDEO: The VISTA Deep Extragalactic Observations (VIDEO) survey4 (Jarvis et al.,

2013) covers the SXDF in ZYJHKs filters using the VISTA Infrared Camera (VIRCAM). 00 It reaches a 5σ depth of ∼23.7 (25.3) mag in the Ks-(Z-) band in a 2 aperture with a typical seeing of ∼ 0.800. Suprime-Cam: Additional optical coverage is available from the Subaru/XMM-Newton

Deep Survey (SXDS; Furusawa et al., 2008), which includes BVRci’z’ filters from the Subaru Suprime-Cam covering 1.22 deg2 centered at (α, δ) = (34.5◦, −5.0◦) down to ∼27.5 mag (5σ; 200 aperture). MUSUBI: The ultra-deep CFHT u-band stack is provided by the program Megacam Ultra-deep Survey: U-Band Imaging (MUSUBI, Wang et al., in prep). The MUSUBI team acquired 41.8 hr of u-band integration between 2012 and 2016, using MegaCam on CFHT. The image stack also includes 18.7 hr of archived MegaCam u-band data within the SXDF. The final reduced map covers an area of 1.7 deg2. The central region that receives the full 60.5 hr of integration has an area of 0.64 deg2. The central region reaches a 5σ depth of 27.37 mag in a 200 aperture. CFHTLS: The CFHT Legacy Survey (CFHTLS) also covers the SXDF in ugriz filters using MegaCam on CFHT, as part of its wide field coverage. We use the stacked mosaics released in the Terapix CFHTLS T0007 release5 . The median exposure times for the

2 https://hsc-release.mtk.nao.ac.jp/doc/ 3 http://www.nottingham.ac.uk/astronomy/UDS/data/dr11.html 4 http://www-astro.physics.ox.ac.uk/~video/public/Home.html 5 http://www.cfht.hawaii.edu/Science/CFHTLS/ Chapter 3. SPLASH-SXDF Catalog 66

CFHTLS u, g, r, i and z bands are 250, 208, 133, 500, and 360 minutes, respectively. The seeing for these data varies for individual pointings, ranging from 0.8400±0.1100, 0.7700±0.1000, 0.7000 ± 0.0700, 0.6500 ± 0.0800, and 0.6900 ± 0.1300 for the u, g, r, i, z-bands, respectively. The CFHTLS coverage is available over a much larger area and thus, we only consider a ∼2×2 deg2 area centered at (α, δ)=(02h18m00s, −5◦0000000).

Figure 3.2 Transmission curves for the photometric bands included in the catalog. For clarity, all curves have been normalized to have a maximum throughput of one and thus, the relative efficiencies of the individual telescopes and detectors are not shown.

3.1.2 Mid-Infrared data

The primary Spitzer-IRAC coverage at 3.6µm and 4.5µm (channel 1/2) in this field comes from the Spitzer Large Area with Hyper-Suprime-Cam (SPLASH) program (PID: 10042, PI: Capak, Capak et al. in prep) which reached a depth of ∼6h per pixel over the Hyper Suprime-Cam field of view. Additional data from programs 90038, 80218 (S-CANDELS; Ashby et al., 2015), 80159, 80156, 70039, 61041 (SEDS; Ashby et al., 2013), and 60024 (SERVS; Mauduit et al., 2012) were also included. These only covered parts of the field, but notably SEDS reaches ∼12.5h per pixel, while S-CANDELS reaches ∼51h per pixel over small fractions of the field. The 5.4µm and 8.0µm (channel 3/4) data were obtained during Chapter 3. SPLASH-SXDF Catalog 67 the cryogenic mission primarily by program 40021 (SpUDS; Caputi et al., 2011) along with programs 3248, and 181 (SWIRE; Lonsdale et al., 2003). These cryogenic mission data also obtain some additional IRAC channel 1/2 data. The full details of the data processing are presented in a companion paper (Capak et al. in prep). In brief, data reduction started with the corrected Basic Calibrated Data (cBCD) frames. These cBCDs have the basic calibration steps (dark/bias subtraction, flat fielding, astrometric registration, photometric calibration ect.) applied and include a correction for most known artifacts including saturation, column pulldown, reflections from bright off-field stars, muxstriping, and muxbleed in the cryogenic mission data. An addition correction was applied for the residual “first frame effect” bias pattern and the column pulldown effect and bright stars were also subtracted. In the warm mission the image uncertainty does not account for the bias pedestal level and so the uncertainty images need to be adjusted for this effect. Finally, the background was subtracted from the images to match it at zero across the mosaic. The background subtracted frames were then combined with the MOPEX6 mosaic pipeline. The outlier and box-outlier modules were used to reject cosmic rays, transient, and moving objects. The data were then drizzled onto a pixel scale of 0.600/px using a “pixfrac” of 0.65 and combined with an exposure time weighting. Mean, median, coverage, uncertainty, standard deviation, and color term images were also created. The depth of the IRAC data are presented in Table 3.1.

3.2 Data Homogenization

3.2.1 Creating Mosaics

One of the main goals of this effort is to homogenize all data available over the SXDF area onto a single common reference frame. We create new mosaics by resampling the available imaging data from their respective sources adjusting for the image center, pixel scale, astrometry, and photometric zeropoint. All optical and NIR data are resampled onto a single 50000 × 50000px reference frame with 0.1500/px centered at (α, δ)=(02h18m00s, −5◦0000000) using the SWARP7 software (Bertin et al., 2002) with the LANCZOS3 kernel. We set the zeropoint for all mosaics at 23.93 mag, equivalent of having the image in units of µJy. Corresponding weight maps are available via the data releases for the respective surveys and are also processed through

6 http://irsa.ipac.caltech.edu/data/SPITZER/docs/dataanalysistools/tools/mopex/ 7 http://www.astromatic.net/software/swarp Chapter 3. SPLASH-SXDF Catalog 68

Table 3.1. SPLASH-SXDF Catalog: Summary of photometric bands included in the catalog

Instrument/ Filters Central λ FWHM 5σ depth a Area Survey [µm] [µm] [mag] [deg2] (200/300)

g 0.4816 0.1386 26.84 / 26.13 2.4 r 0.6234 0.1504 26.36 / 25.65 2.4 HSC i 0.7741 0.1552 26.11 / 25.43 2.4 z 0.8912 0.0773 25.52 / 24.84 2.4 y 0.9780 0.0783 24.79 / 24.09 2.4 B 0.4374 0.1083 27.40 / 26.63 1.2 V 0.5448 0.0994 27.04 / 26.28 1.2 SupCam Rc 0.6509 0.1176 26.85 / 26.10 1.2 i0 0.7676 0.1553 26.63 / 25.87 1.2 z0 0.9195 0.1403 25.87 / 25.17 1.2 J 1.2556 0.1581 25.58 / 25.09 0.8 UDS H 1.6496 0.2893 25.02 / 24.56 0.8 K 2.2356 0.3358 25.32 / 24.82 0.8 Z 0.8779 0.0979 25.31 / 24.57 1.7 Y 1.0211 0.0927 24.86 / 24.15 2.5 VIDEO J 1.2541 0.1725 24.34 / 23.74 2.5 H 1.6464 0.2917 24.01 / 23.38 2.5 Ks 2.1488 0.3091 23.68 / 23.07 2.5 MUSUBI u 0.3811 0.0654 27.38 / 26.70 1.7 u 0.3811 0.0654 25.72 / 25.20 4.2b g 0.4862 0.1434 26.05 / 25.50 4.2b CFHTLS r 0.6258 0.1219 25.45 / 24.88 4.2b i 0.7553 0.1571 24.96 / 24.33 4.2b z 0.8871 0.0935 23.82 / 23.06 4.2b ch.1 3.5573 0.7431 25.39 / −c 4.2 ch.2 4.5049 1.0097 25.13 / −c 4.2 IRAC ch.3 5.7386 1.3912 23.04 / −c 3.3 ch.4 7.9274 2.8312 22.90 / −c 3.3

a5σ depth in AB magnitudes is computed from measuring the sky vari- ation by placing apertures in empty regions on the original images. bThis denotes the area of the CFHTLS data considered for this catalog. cThe limiting magnitudes for the IRAC channels are computed from the rms maps output from IRACLEAN by placing circular apertures in areas with no sources. Chapter 3. SPLASH-SXDF Catalog 69

Figure 3.3 Maps showing the 5σ limiting magnitude for a 200 circular aperture for selected bands from different surveys included the SXDF multi-wavelength catalog. The HSC data are particuarly affected by photometric artifacts around bright sources and hence, a star mask specific to the HSC data is applied. Each of the panel uses the same grid as Figure 3.1.

SWARP, simultaneously with the science images. The HSC data processing pipeline also generates a map highlighting bright objects. We use this flag map to mask large, bright objects (stars). This star mask is taken into account when generating the HSC photometry to avoid photometric artifacts due to the bright stars in their vicinity. The mask is only applied to the HSC bands as it is only available and valid for the HSC data. For SuprimeCam and CFHTLS data, we combine multiple separate pointings to get the maximum coverage and resample onto our reference frame and pixel scale. In the case of CFHTLS, even for a given band, the individual tiles have considerably different seeing and hence, we pre-process them for homogenizing the variations in the point-spread function (PSF) within the various tiles for a given band (see Section 3.2.3 for details). For the UDS, VIDEO and MUSUBI-u data, mosaics are already available from their respective Chapter 3. SPLASH-SXDF Catalog 70

Figure 3.4 The 5σ limiting magnitude for a 200 circular aperture in each band in the SXDF multi-wavelength catalog. The limiting magnitudes are computed by measuring the sky variation in empty apertures. The galaxy template shown is a Bruzual & Charlot(2003) 10 single stellar population template with an age of 200Myr and stellar mass of 10 M at z = 4.

data releases and we just resample them onto our reference frame while adjusting their native pixel scales. The IRAC data do not need resampling since the photometry for the IRAC images is measured with a different technique that performs source fitting directly on the IRAC mosaic (with its native pixel scale of 0.600/px) using the optical and NIR detection as a prior (see Section 3.3.2 for details).

3.2.2 Astrometric Corrections

Slight astrometric deviations are expected for the observations from different instruments and surveys that are reduced and processed through different pipelines. In order to ensure a common World Coordinate System reference frame for all our imaging data, we compute an astrometric solution needed to register each image to the SDSS-DR8 catalog (Aihara et al., 2011) using SCAMP8 . The astrometric matching is done using a source catalog of reliable objects (S/N&7) generated by running SExtractor9 (Bertin & Arnouts, 1996) on the individual mosaics.

8 http://www.astromatic.net/software/scamp 9 http://www.astromatic.net/software/sextractor Chapter 3. SPLASH-SXDF Catalog 71

These catalogs are processed through SCAMP to match the astrometry to a user-defined reference frame. The astrometric solution is calculated by fitting a 2D polynomial (of degree 5). This allows us to remove structural offsets in the datasets as a function of RA and DEC 00 and reduce the overall scatter in both RA and DEC to . 0.15 (1px) for all datasets. Figure 3.5 shows the reduction in the average astrometric scatter for the different datasets. As output, SCAMP generates a FITS header with keywords (polynomial distortion parameters) containing the updated astrometric information. These parameters are com- patible with SWARP. When resampling the mosaics, SWARP reads in the SCAMP solution and adjusts the astrometry according to the FITS keywords.

Figure 3.5 The average scatter in RA (squares) and DEC (circles) shown before (open symbols) and after (filled symbols) applying the astrometric corrections using SCAMP.

3.2.3 PSF Homogenization

Ground-based data are subject to variation in the point-spread function (PSF) due to the atmospheric conditions at the time of the observations as well as the instrument capabilities. In order to extract accurate photometry, we homogenize the PSF across all optical and NIR bands (IRAC bands are not homogenized because their photometry is extracted using a source-fitting technique; see details in Section 3.3.2). The PSF homogenization process implemented here is adopted from Laigle et al.(2017). Here, we ignore the variation in the PSF across an individual mosaic for a given band for all optical and NIR data, except CFHTLS. The PSF is relatively stable across the mosaics and, more importantly, the variations across different bands is always the dominant factor Chapter 3. SPLASH-SXDF Catalog 72 compared to the variation within a single band. This has not been the case for the CFHTLS tiles, where the PSF varied considerably even for a given band. For CFHTLS observations, we specifically choose to homogenize the PSF on a tile-by-tile basis. We use PSFEx10 (Bertin, 2011) to measure the PSFs for each of our filters. First, we generate a source catalog of bright but not saturated objects by running SExtractor on the mosaics in single-image mode with a strict > 25σ detection threshold. Next, we generate a size-magnitude diagram of all detected objects. For a point source, the radius encompass- ing a fixed fraction of the total flux is independent of the source brightness. Consequently, point-like sources are easily identifiable on a fraction-of-light radius vs. magnitude plot, as they are confined to a tight vertical locus. We only select unsaturated, point-like sources for fitting the PSF. The PSF is modeled using Gauss-Laguerre functions, also known as the “polar shapelet” basis (Massey & Refregier, 2005). The components of the “polar shapelet” basis have explicit rotational symmetry which is useful for fitting PSFs. The global best-fit PSF for each filter is derived by χ2 minimization using the postage stamps of point-like sources extracted by SExtractor. Once the best-fit PSF is obtained for each filter, we pick a “target” PSF that represents the desired PSF for all bands after homogenization. We choose a target PSF that is an average of all PSFs so as to minimize the applied convolution (see Figure 3.6). The target PSF is represented using a Moffat profile (Moffat, 1969), as it models the inner and outer regions of the profile better than a simple Gaussian. The Moffat profile (M) is described with two parameters [θ, β] as:

2 −β Ir = I0[1 + (r/α) ] (3.1)

p 1/β 2 −1 where α = θ/2 2 − 1, I0 = (β − 1)(πα ) and θ is the FWHM. We choose the Mof- fat profile M(θ, β) = M(0.700, 2.8) as our target PSF, which is close to the average for all bands. The convolution kernels for homogenizing the PSFs are generated by PSFEx pro- vided the parameters for our target PSF. Using the kernels, we convolve the original images to create the PSF-homogenized set of mosaics. These are used for measuring photometry in Section 3.3.1. The choice of a target PSF that is an average of all bands, as opposed to choosing the largest PSF, does result in a deconvolution for some of the bands. However, we emphasize that the convolved images are only used for flux measurement in the apertures defined by the detection image, which is made using the original unconvolved images. As such, a

10 http://www.astromatic.net/software/psfex Chapter 3. SPLASH-SXDF Catalog 73

Figure 3.6 Curve of growth plot for the PSFs in each filter computed using PSFEx showing the ratio of flux within radius (r) to the target PSF. The top panel shows the curves of growth before PSF homogenization; the bottom panel after PSF homogenization. The dashed vertical line shows the 200 aperture. deconvolution is not expected to create any biases. Regardless, the differences in the PSFs are small (see Table 3.2) and the (de)convolution is not drastic. Figure 3.6 shows the curve-of-growth, i.e., the flux contained within given aperture for each PSF normalized by that of the target PSF, both before and after the homogenization. 00 After homogenization the variation across bands is reduced to . 5% for a 2 aperture. Table 3.2 provides the Moffat profile parameters as derived by PSFEx in each band. Chapter 3. SPLASH-SXDF Catalog 74

Table 3.2. SPLASH-SXDF Catalog: PSF parameters from PSFEx for optical and NIR bands

Instruments/ Before PSF matching After PSF matching Filters Surveys θ [00] β θ [00] β

g 0.63 2.57 0.71 2.98 r 0.55 2.07 0.73 2.92 HSC i 0.58 2.78 0.71 2.94 z 0.45 1.64 0.66 2.72 y 0.55 2.43 0.72 2.85 B 0.80 3.19 0.77 3.66 V 0.80 3.65 0.77 3.76 SupCam Rc 0.80 3.36 0.77 3.66 i0 0.80 3.18 0.76 3.38 z0 0.80 3.34 0.78 3.71 J 0.76 2.95 0.74 3.22 UDS H 0.77 3.00 0.75 3.30 K 0.71 3.02 0.72 3.28 Z 0.73 2.25 0.74 4.84 Y 0.75 2.40 0.76 5.14 VIDEO J 0.74 3.05 0.76 5.02 H 0.73 3.91 0.75 4.18 Ks 0.76 3.89 0.77 4.45 MUSUBI u 0.89 2.92 0.81 3.53 u ······ 0.75 3.25 g ······ 0.74 3.54 CFHTLS r ······ 0.74 3.31 i ······ 0.78 2.68 z ······ 0.76 2.95 Chapter 3. SPLASH-SXDF Catalog 75

3.3 Multi-wavelength Catalog

3.3.1 Source Extraction

The object detection and flux measurement are done using SExtractor. We run SEx- tractor in dual image mode with the detection image defined as a combination of HSC- grzy, UDS-JHK, VIDEO-Y JHKs, MUSUBI-u, and CFHTLS-ugri. We use a χ2 com- bination in SWARP to create the detection image, which combines the input images by taking the square root of the reduced χ2 of all pixel values with non-zero weights. The χ2 combination is optimal for panchromatic detection on images taken at different wavelengths (Szalay et al., 1999). The non-homogenized versions of the mosaics are used for making the detection image in order to preserve the original noise properties of the data. The u-band data are included to ensure the detection of even the bluest objects. We exclude the HSC-i band due to excessive satellite trails that are left over from the pipeline reduction. Mosaics for the same band from different surveys are included in the detection image because they have different depths and coverage areas. We detect ∼1.17 million objects over the full mosaic area (4.2 deg2), with ∼800,000 objects detected in the 2.4 deg2 HSC-UD area. Figure 3.7 shows the number counts of detected sources in each filter. The fluxes are measured on the PSF-homogenized mosaics. We optimize the SEx- tractor parameters to ensure that real faint sources are detected, particularly near bright sources. The parameters used for our SExtractor run are listed in Table 3.5. In ad- dition to the Kron(1980) aperture (AUTO) and isophotal (ISO) magnitudes, we extract fixed-aperture fluxes for 100, 200, 300, 400, and 500 circular apertures. We correct the fluxes for Galactic extinction using the Schlegel et al.(1998) dust maps 11 . The reddening E(B − V ) due to galactic dust is queried for each object position and

converted into an extinction (Aλ) in each band using the Cardelli et al.(1989) extinction law. Figure 3.8 shows the extinction applied across the SXDF. Since the SXDF is large, the

Galactic extinction varies by AV ∼ 0.034 over the field. The magnitudes and fluxes in the final catalog are corrected using these values and the Galactic reddening E(B − V ) values are also reported in the final catalog for each source.

11 Specifically, we use the Python implementation available at http://github.com/adrn/SFD to query the SFD dust maps. Chapter 3. SPLASH-SXDF Catalog 76

Figure 3.7 Number counts of sources detected using our multi-band detection image shown for each filter as a function of magnitude.

3.3.2 IRAC Photometry

The IRAC observations have a considerably larger PSF than the optical and NIR data. In order to properly extract photometry from the high-confusion, crowded, and low resolution IRAC data, proper deblending is necessary. We use the IRACLEAN code (Hsieh et al., 2012) as modified by Laigle et al.(2016) to measure the fluxes for the IRAC channels. IRACLEAN deblends objects and measures accurate fluxes in a low resolution image by using, as a prior, the positional and morphological properties of sources detected in a higher resolution image in a different wavelength bandpass. We use our detection image made using optical and NIR bands as the prior in IRACLEAN. For a detailed description of the various steps involved in IRACLEAN, we refer the reader to Hsieh et al.(2012). IRACLEAN operates without the restriction that the intrinsic morphology of the source Chapter 3. SPLASH-SXDF Catalog 77

Figure 3.8 Galactic extinction corrected for in the SPLASH-SXDS catalog. Top panel shows the variation in the V -band extinction across the field. The bottom panel shows the distribution of AV for all the sources in the catalog. be the same in the two bandpasses. This is critical in minimizing the effect of morphological k-corrections when the prior and measurement bandpasses are different. However, as noted in Hsieh et al.(2012), the flux measurement can be biased when two objects are separated by less than ∼1 FWHM – in such cases, the flux of the brighter object can be overestimated. The Laigle et al.(2016) modification weights each object by the surface brightness of the object in the prior image when measuring fluxes to avoid the potential bias. We refer the reader to Laigle et al.(2016) where this is described in detail. The PSF modelling is critical to deblend sources in IRACLEAN to measure accurate photometry. However, the PSF of IRAC is asymmetric and therefore the effective PSF shape depends on the rotation and depth of individual frames that are combined to a mosaic, hence it is expected to vary as a function of position. We, therefore, derive the effective PSF for Chapter 3. SPLASH-SXDF Catalog 78 each position on the final SDXF IRAC mosaic by combining all the changes to IRAC’s intrinsic point response function (PRF) caused by the mosaicing process. For this, we start with the intrinsic PRF (depending on the position of the detector) at a native scale of 1.2200 and oversample by a factor of 100. The PRFs are rotated by the position angle of their corresponding individual frames and then run through the mosaicing process to obtain the final, combined PSF at each pre-defined grid point on the final mosaic. Instead of using a static PSF across the full mosaic, IRACLEAN is modified to read in all the PSFs derived on a 3000 grid over the mosaic. When performing the deblending algorithm for individual sources, the routine looks up the nearest grid point to the object position and uses the PSF associated with it. This functionality allows IRACLEAN to fully account for the variations in the PSF as function of position on the large-area mosaic. The segmentation map created from the optical and NIR detection image (described in Section 3.3.1) is used as the prior for measuring IRAC photometry in IRACLEAN. The segmentation map is identical in size and dimensions to the detection image with pixels attributed to each detected object set to the object’s identification number. Since the segmentation map and the IRAC mosaics need to be on the same pixel scale for running IRACLEAN, we rebin the segmentation map to the resolution of the IRAC images (0.600/px). The rebinned segmentation map is created by taking the mode of all the sub-pixels entering the rebinned pixel. We take additional measures to preserve objects that would occupy less than a pixel in the rebinned segmentation map but do not have any other nearby overlapping sources. Specifically, if a rebinned pixel assigned as background (from the calculation of the mode) had a detected object in the original segmentation map, the rebinned pixel is instead assigned to the detected object. This is critical for preserving isolated objects that are compact in the optical/NIR detection image but could still be extended in the IRAC channels. With this prescription, the rebinned segmentation map could still potentially miss sources that are compact (less than 1 IRAC pixel) and adjacent to another bright object. Hence, these objects are not guaranteed to be recovered even though the IRAC mosaic has coverage at their positions. Only 0.2% (1474) of the objects from our optical and NIR de- tection image fall into this category. In order to distinguish between IRAC sources lost due to lack of IRAC coverage and those due to rebinning of the segmentation map, we specify a source extraction flag for the IRAC photometry in the catalog. Objects lost due to the rebinning of the segmentation map are assigned a flag of 1, whereas those not recovered due to a lack of coverage are given a flag of 2. Lastly, in order to save computation time, we parallelize the photometry measuring Chapter 3. SPLASH-SXDF Catalog 79 process by running IRACLEAN on cutouts of the full mosaic. The IRAC mosaic is split into 1000×1000px (6000×6000) tiles with an overlap of 9700.5 to avoid edge effects. IRACLEAN is run for each tile using the surface brightness weighting parameter of n=0.3 and an aperture size of 100.8×100.8 to measure the flux ratios between the sources and PSFs for the deblending procedure. The final photometric catalog includes the total fluxes and associated errors for each object present in the segmentation map as measured by IRACLEAN. For objects with fluxes below 1σ, their magnitudes are set to the corresponding 1σ upper limits.

3.3.3 Photometric errors and magnitude upper limits

Since the optical and NIR images undergo multiple processing steps, it is critical to ensure that the photometric errors are propagated correctly.

SWARP photometric errors

All optical and NIR images used for measuring photometry are resampled onto a common reference frame. This step involves adjusting the pixel scale of the original images to a common 0.1500/px. While SWARP is expected to scale the science images as well as the weight maps in a consistent fashion, we test the photometric error properties explicitly before and after processing through SWARP. For this test, source catalogs are generated in single-image mode from the original and SWARP-processed images using SExtractor with the same parameters. We first compare the measured fixed-aperture fluxes and find them to agree. We compare the errors on aperture photometry for bright sources and find the errors to be systematically offset as a function of the original pixel scale. The photometric errors are underestimated for cases in which the original pixel scale is finer than the final pixel scale, whereas they are overestimated for cases in which the original pixel scale is coarser. Figure 3.9 shows the correction factor in each band needed for the photometric errors to be consistent before and after the SWARP resampling process. The correction factor scales in almost the same way as the ratio of pixel scales (original:resampled). As the first step, we adjust the photometric errors in each band to correct for this systematic.

Sky noise properties and survey depth

A more appropriate description of the photometric errors is derived from the sky noise. While the weight maps account for errors arising from instrumental effects and observation strategies, measuring the sky variation has the added benefit of accounting for undetected Chapter 3. SPLASH-SXDF Catalog 80

Figure 3.9 Comparison of the photometric errors before and after resampling images through SWARP. The key adjustment made when resampling is changing the native pixel scale to match that of our reference frame (0.1500/px). The photometric errors are system- atically offset as a function of the ratio of native pixel scale to the resampled one. faint objects. The errors computed by SExtractor accounts for the provided weight maps. However, since we perform photometry on the PSF-homogenized images, the errors measured from SExtractor are not precise due to the additional unaccounted correlated noise. When convolving the mosaics with the homogenization kernel to match the PSFs, the sky noise properties are altered. In order to accurately measure the sky noise, we compute the flux variation in random empty sky apertures for each band from the unconvolved mosaics. The sky noise properties are dependent on two major factors: the aperture size and the image depth. We measure the sky noise in 100, 200, 300, 400, and 500 circular apertures to quantify the dependence on aperture size. We use the value of the weight maps as a proxy for image depth, since the mosaic’s exposure time information is encoded in the weight maps. Ultimately, the sky noise is computed as a function of the aperture size and image depth. We use the SExtractor segmentation map to avoid sources when placing the random sky apertures and measure Chapter 3. SPLASH-SXDF Catalog 81 their fluxes using PhotUtils12 (Bradley et al., 2016). The sky variation is measured by fitting a Gaussian to the distribution of fluxes in the sky apertures in bins of the value of the weight map at the location of the source. We explicitly only fit the half of the sky flux distribution that is below its peak. The sky variation represents the faintest flux level (magnitude) at which a source can be detected in the mosaic. Thus, we can use the computed sky noise to define a 1σ limiting magnitude for our filters. Figure 3.3 shows the 5σ limiting magnitude for a 200 circular aperture over the full mosaic for an example filter from each dataset included in this work. A representative 5σ depth for each filter is listed in Table 3.1 and shown in Figure 3.4. Only for the fixed-aperture magnitudes reported in the photometric catalog, if the object’s flux is below the correponding sky noise value for the given aperture and image depth at the object’s position, the magnitude of that object is set to the 1σ upper limit. The photometric redshift computation uses the measured fluxes and does not utilize the upper limits (which are only applied to the magnitudes).

Correcting photometric errors

We compute a correction factor for adjusting the SExtractor errors to match the sky variation. The correction factor is computed as the ratio between the sky variation measured from the random sky apertures and the median of the SExtractor errors. This factor is computed after applying the correction from Section 3.3.3. See Appendix 3.B for a brief discussion of this procedure. Although this correction factor can be computed for each object in each of the filters, there is no physical motivation to apply the correction on a source-by-source basis. All processes affecting the photometric errors (e.g., resampling, convolution, etc.) are performed on the full mosaic and hence, should not have different impacts on an individual object basis. Ideally, in order to correct for these effects, a single correction factor over the full mosaic should suffice. However, we expect that areas of the mosaics with different depths and hence, are affected differently. Considering that most of our filters have varying depths across the image due to stacking different pointings, we choose to compute a separate factor when the image depth changes significantly. The computed correction is uniform over 2 regions for 0 0 the SuprimeCam BVRci z and VIDEO J mosaics, and 3 regions for the MUSUBI u-band mosaic. We compute the correction factors for the fixed apertures (100,200,300,400,500). For AUTO

12 http://photutils.readthedocs.io/ Chapter 3. SPLASH-SXDF Catalog 82 and ISO fluxes, we calculate the correction factor by interpolating between the fixed- aperture sizes. We use the Kron(1980) radius and number of pixels in the isophotal aperture to estimate the size of the AUTO and ISO apertures, respectively. The errors on fluxes and magnitudes in the catalog have this correction already applied.

3.3.4 Ancillary Datasets

Simpson et al.(2006) covered the SXDF with the Very Large Array (VLA) to obtain radio imaging at 1.4 GHz. Their catalog lists radio sources covering 0.8 deg2 on the SXDF down to a peak flux density of 100 µJy beam−1. Their synthesized beam has a roughly elliptical shape characterized by ∼500×400. They identify optical counterparts to the radio 0 0 sources using the BVRci z SuprimeCam images from Furusawa et al.(2008). For detailed description of the process of identifying the optical counterparts, we refer the reader to Simpson et al.(2006). We use their identified optical counterparts and match them to our photometric catalog. The 1.4GHz fluxes from the radio catalog are included in our final photometric catalog. Akiyama et al.(2015) present a catalog of X-ray sources over 1.3 deg 2 centered on the SXDF using XMM-Newton. The full area is covered with one central 300 diameter, 100ks exposure along with six flanking fields with 50ks exposures. The details of the observations and data processing are described in Ueda et al.(2008). Akiyama et al.(2015) select counterparts to the X-ray sources in the SuprimeCam R-band, IRAC 3.6µm channel, Near- UV, and 24µm source catalog image using a likelihood ratio analysis. We refer the reader to Akiyama et al.(2015) for a detailed description of the counterpart-identifying procedure. Using the positional information of these optical counterparts, we match and add the X-ray information for their objects to our catalog.

3.4 Photometric Redshifts and Physical properties

3.4.1 Photometric Redshifts

We compute the photometric redshifts for all objects in the catalog using LePhare13 (Arnouts et al., 1999; Ilbert et al., 2006). Object fluxes are used for the calculation of photometric redshift rather than object magnitudes, allowing for a robust treatment of faint objects and objects undetected in one or more filters. For faint sources, even negative fluxes are physically meaningful when included with the appropriate errors; while working with

13 http://www.cfht.hawaii.edu/~arnouts/lephare.html Chapter 3. SPLASH-SXDF Catalog 83 magnitudes upper limits are needed, which require a modification in the χ2 minimization algorithm (Sawicki & Thompson, 2006). Photometric redshift estimates are more accurate when galaxy colors are computed using fixed-aperture photometry, rather than pseudo-total magnitudes like AUTO magni- tudes. The latter ones assume a Kron(1980) aperture, and may be much noisier, especially for the faintest objects, due to the variable nature of this profile (see Hildebrandt et al., 2012; Moutard et al., 2016). On the other hand, fixed-aperture magnitudes are more appro- priate for measuring colors of galaxies; however, these are affected by the variations in the PSF across different bands. In our case, the issue of band-to-band PSF variations is solved by the PSF homogenization (Section 3.2.3). We use the 200 aperture for measuring photo- metric redshifts because from our testing with available spectroscopic redshifts, we find it to perform the better than the 100, 300, 400, and 500 apertures at recovering the redshifts. Aperture photometry is available for the optical and NIR bands from SExtractor; however, for IRAC channels we only perform measurement of the total flux. IRAC total fluxes need to be scaled to match the aperture fluxes before performing SED fitting to mea- sure the photometric redshifts. In order to adjust the total IRAC fluxes, we compute an offset factor converts between the aperture and total magnitudes. Since the photometry is performed on PSF-homogenized images, the offset between the aperture and total magni- tudes is expected to be the same across all bands. We check that the computed photometric offsets do not depend on other galaxy properties. We find no correlation with respect to the galaxy colors or magnitudes. Using multiple bands for calculating the offset also makes it more robust than using a single band. Following the treatment from Moutard et al.(2016), we compute a single multiplicative offset between the AUTO and aperture fluxes for each object as:   1 X fAUT O,i o = P × · wi (3.2) wi fAP ER,i filter i filter i where the weights wi are defined as: 1 w = (3.3) i σ2 + σ2 fAUT O,i fAP ER,i The offsets for each object are provided in the final catalog. The template library used in LePhare for photometric redshift calculation is similar to that used for the COSMOS field (Ilbert et al., 2009, 2013; Laigle et al., 2016). The template set consists of 31 templates which includes 19 templates of spiral and elliptical galaxies from Polletta et al.(2007) and 12 templates of young blue-star forming galaxies from Bruzual & Charlot(2003) model (BC03). We also include two additional extinction-free BC03 Chapter 3. SPLASH-SXDF Catalog 84 templates with an exponentially declining SFH with a short timescale of τ = 0.3 Gyr and

metallicities (Z = 0.008 and Z = 0.02 = Z ). As detailed in Ilbert et al.(2013), these improve the photometric redshifts for passive galaxies at z > 1.5 (Onodera et al., 2012), which are not well represented in the Polletta et al.(2007) library. The two additional BC03 templates are sampled for 22 ages between 0.5 Gyr and 4 Gyr. Dust extinction is left as a free parameter and allowed to vary within 0 ≤ E(B−V ) ≤ 0.5. A variety of dust extinction laws are considered: Prevot et al.(1984), Calzetti et al.(2000), and a modified version of the Calzetti et al.(2000) law that includes contribution from the 2175A˚ bump (Fitzpatrick, 1986) as proposed by Massarotti et al.(2001). No extinction is added for templates of earlier types than S0. Also, since the Sa and Sb templates from Polletta et al.(2007) are empirical and already include dust, no extinction is allowed for these templates either. In addition to the galaxy templates, we also include stellar templates from Bixler et al. (1991), Pickles(1998), Chabrier et al.(2000) and Baraffe et al.(2015). In particular, we include a large number of low-mass stars of spectral classes M through T from Baraffe et al. (2015). These stellar templates extend out to λ > 2.5µm and thus help distinguish between distant galaxies and brown dwarf stars (Wilkins et al., 2014; Davidzon et al., 2017). Expected fluxes in each band for all the templates are computed on a grid of 0 < z < 6. Contribution from emission lines is accounted for in the flux computation using an empirical relation between the UV luminosity and the emission lines fluxes as described in Ilbert et al. (2009). The photometric redshifts (Z BEST) are derived by χ2 minimization. One of the critical steps in computing photometric redshifts is evaluating the systematic offsets between the template and observed fluxes (Ilbert et al., 2006). These systematic offsets can be measured using known spectroscopic redshifts. For this galaxy subsample, the redshift is fixed at the spectroscopic value and then LePhare performs the template fitting in an iterative fashion, adding systematic offsets to each band until χ2 minimization convergence is reached. The resulting offset (Table 3.3) are applied to the input catalog when computing the photometric redshifts. We exclude IRAC ch.3 and 4 when measuring the photometric redshifts due to their high systematic offsets (0.4 mag). These systematic offsets values are likely due to the limitations of the template library, specifically the lack of dust emission redward of rest-frame 2µm. A cross-check with external Spitzer catalogs confirms the photometric calibration in ch.3 and 4 is accurate to 2%. This issue will likely be resolved with future JWST data that will provide high SNR templates at these long wavelengths. Chapter 3. SPLASH-SXDF Catalog 85

Table 3.3. SPLASH-SXDF Catalog: Systematic offsets between the measured 200 fluxes and library templates as computed by LePhare

Instrument/ Systematic Filters Survey Offset (200) [mag]

g -0.065 r -0.041 HSC i -0.023 z -0.063 y -0.046 B -0.047 V -0.025 SupCam Rc -0.124 i0 0.041 z0 0.061 J 0.055 UDS H 0.023 K -0.003 Z -0.046 Y -0.035 VIDEO J 0.011 H 0.030 Ks -0.061 MUSUBI u 0.043 u 0.202 g 0.098 CFHTLS r 0.128 i 0.045 z 0.138 ch.1 0.100 ch.2 0.100 IRAC ch.3 − ch.4 − Chapter 3. SPLASH-SXDF Catalog 86

Table 3.4. SPLASH-SXDF Catalog: Samples with spectroscopically confirmed redshifts

Spectroscopic Survey / Number z i med z med Reference of spec-zrange [mag]

VIPERS 8434 0.67 [0.07,1.71] 20.9 UDSz 1486 1.09 [0.00,4.79] 23.1 C3R2 319 0.65 [0.04,3.24] 21.8 Subaru compilation 183 3.71 [2.56,6.21] 25.3 X-UDS compilation 2111 0.44 [0.00,4.84] 20.6

Comparing photometric and spectroscopic redshifts

Numerous spectroscopic surveys cover the SXDF and hence a large number of objects have spectroscopic redshifts available. Table 3.4 lists the properties of the various spectroscopic samples that are included in the catalog.

Figure 3.10 The positions (left panel) and the redshift-magnitude distribution (right panel) of the sources used to refine and verify the performance of the photometric redshifts. These galaxies have a robust spectroscopic redshift measurement available from the various surveys described in Section 3.4.1.

• The VIMOS Public Extragalactic Redshift Survey (VIPERS; Garilli et al., 2014; Guzzo et al., 2014; Scodeggio et al., 2016) covers the SXDF, and measures galaxy spectra using VIMOS on the VLT. We match the VIPERS catalog to our photomet- ric catalog and only retain objects with highly secure spectroscopic redshifts with confidence > 99% (quality flag >= 3). We exclude objects identified as AGN in the VIPERS catalog. The VIPERS catalog contributes spectroscopic redshifts for 8451 objects. Chapter 3. SPLASH-SXDF Catalog 87

Figure 3.11 Comparison of the performance of the photometric redshifts in the SXDF catalog for sources. We find a σNMAD=0.023 and an outlier fraction (η = |∆z|/(1+z) > 0.15) of 3.2%. The various colors indicate the different spectroscopic surveys that are included in the calibration sample (described in Section 3.4.1. The inset shows the distribution of the fractional differences between the photometric and spectroscopic redshifts. The dashed line in the bottom panel and in the inset shows the median value. The dotted lines show the outlier criterion: zphot = zspec ± 0.15(1 + zspec). Only objects covered within the HSC footprint are compared, since these have adequate optical and NIR coverage. Chapter 3. SPLASH-SXDF Catalog 88

Figure 3.12 Performance of the photometric redshifts in the SXDF catalog compared for sources inside and outside of the HSC-UD area. Since the coverage in depth as well as wave- length is limited outside the HSC-UD area, the performance of the photometric redshifts drops slightly to σNMAD = 0.037. The lower outlier fraction is mainly due to the limited redshift coverage of the calibration sample outside the HSC-UD area.

• The UKIDSS Ultra-Deep Survey (UDSz; Bradshaw et al., 2013; McLure et al., 2013) obtained spectra for over 3000 K-selected galaxies using VIMOS and FORS2 instru- ments on the VLT. These galaxies span 1.3 < z < 1.5 over a 0.6 deg2 on the UDS field (part of the SXDF) down to a limit of K=23. The UDSz catalog contributes spectroscopic redshifts for 1489 sources in our catalog.

• The Complete Calibration of the Color-Redshift relation survey (C3R2; Masters et al., 2017, in prep.) is obtaining spectroscopic redshifts for large sample of targeted sources in COSMOS, SXDF, and EGS using Keck (DEIMOS, LRIS and MOSFIRE), Chapter 3. SPLASH-SXDF Catalog 89

Figure 3.13 Comparison between the photometric and spectroscopic redshifts as a function of the i-band magnitude along with σNMAD and outlier fraction for each magnitude bin. The dotted lines show the outlier criterion: zphot = zspec ± 0.15(1 + zspec). Objects below the detection limit in the B-band are replaced with their 1σ upper limits in the figure.

the Gran Telescopio Canarias (GTC; OSIRIS), and the Very Large Telescope (VLT; FORS2 and KMOS). A sample of 320 galaxies in the SXDF from our catalog have secure spectroscopic redshifts (quality flag >= 3) available from the C3R2 survey.

• Subaru compilation: This sample contributes spectroscopic redshifts for 122 objects in the catalog. These are narrow- and broadband selected objects in the SXDF provided by Masami Ouchi (private comm.) obtained from the Subaru and Magellan telescopes. This includes objects from Ouchi et al.(2005, 2008, 2010), Saito et al.(2008), Curtis- Lake et al.(2012), Matsuoka et al.(2016), Momcheva et al.(2016), Wang et al.(2016), Ono et al.(2017), Pˆariset al.(2017), Shibuya et al.(2017), Higuchi et al. (in prep) and Harikane et al. (in prep).

• X-UDS compilation: This sample includes spectroscopic redshifts for 2094 catalog sources. The X-UDS compilation consolidated spectroscopic redshifts from Yamada Chapter 3. SPLASH-SXDF Catalog 90

et al.(2005), Simpson et al.(2006), Geach et al.(2007), van Breukelen et al.(2007), Finoguenov et al.(2010), Akiyama et al.(2015), Santini et al.(2015) as well as the NASA/IPAC Extragalactic Database (NED). The list provides the highest resolution and/or best quality spectroscopic redshift available from the references for a source.

We assemble a sample of 12,342 galaxies with reliable spectroscopic redshifts covering the full range of 0 < z < 6. Figure 3.10 shows the distribution in the sky as well as the redshift- magnitude distribution of the full sample of galaxies with spectroscopic redshifts. Of these, we select 8,647 galaxies that are within the HSC-UD area and have proper wavelength coverage (particularly in the NIR) to use as the calibration sample for the photometric redshifts. We quantify the performance of the photometric redshifts using two statistical 14 measures: the normalized median absolute deviation (σNMAD; Hoaglin et al., 1983) and the outlier fraction (η = |∆z|/(1 + z) > 0.15). Figure 3.11 shows the comparison of the photometric and spectroscopic redshifts for our sample. We find excellent agreement between the two over the full redshift range, with a computed σNMAD of 0.023 and an outlier fraction (η) of 3.2% for sources within the HSC-UD area. Outside the HSC-UD area where the coverage is limited, the performance of the photometric redshifts drops slightly (σNMAD = 0.037) as shown in Figure 3.12. The majority of the outliers are faint sources (mi > 24) as evident in Figure 3.13, which shows the comparison as a function of the i-band magnitude. The outlier fractions We find the median of the marginalized probability distribution function (Z MED) to perform better as the photometric redshift estimator than the overall best template fit (Z BEST). Moreover, the errors on Z MED as reported by the 68% confidence interval (Z MED L68 and Z MED U68) are more robust. Z MED is not estimated for sources where the marginalized probability distribution is not well behaved (these make up for < 2% of all the sources in the catalog).

3.4.2 Star/Galaxy Classification

When running LePhare for measuring the photometric redshifts, we allow for both stellar and galaxy libraries. Comparing the best-fit solutions from each library for an object allows 2 2 us to flag objects as stars. Particularly, we flag objects as stars if the χstar < χgal with a further restriction that the object is in the BzK stellar sequence (z−Ks < 0.3×(B−z)−0.2). We emphasize that since the B-band data from Subaru SuprimeCam do not cover the full area of our mosaic, this classification is not available for all the sources in the catalog. Only objects that are within the SuprimeCam footprint are classified.

14 ∆z − median(∆z) σNMAD = 1.48 × median 1 + zspec Chapter 3. SPLASH-SXDF Catalog 91

Figure 3.14 shows the BzK color-color diagram for all sources in the catalog color-coded according to their photometric redshift. As evident from the figure, the B-band dropouts occupying the top-left part of the distribution are predominantly high redshifts (z & 3) galaxies, while galaxies with bluer z − K colors are at lower redshifts. The 6,364 objects flagged as stars according to the criterion specified above are shown in black.

Figure 3.14 A color-color diagram showing the B − z vs. z − Ks for all sources color- coded according to their photometric redshift. Source flagged as stars from the star/galaxy classification are shown in black. The upper limits (arrows) are sources that are undetected in the B-band and have their magnitudes replaced with the corresponding 1σ upper limit.

3.4.3 Physical Properties

The physical properties for the objects in our catalog are computed using LePhare. Proper estimates of the stellar masses require computation using all the light from the source and hence, we use the AUTO magnitudes. The templates used for measuring the stellar physical properties include Bruzual & Charlot(2003) models with exponentially declining SFH with nine timescale values in the range τ = 0.1 − 30 Gyr and different metallicities (Z = 0.004, Z = 0.008 and Z = 0.02 =

Z ). All models assumed a Chabrier(2003) initial mass function (IMF). We consider 57 ages Chapter 3. SPLASH-SXDF Catalog 92 well sampled between 0.01 Gyr and 13.5 Gyr. As we did when computing the photometric redshifts, emission lines are added to the templates using the empirical relation between the UV luminosity and emission line fluxes, as described in Ilbert et al.(2009). Dust extinction is added to the templates as a free parameter ranging between 0 ≤ E(B − V ) ≤ 1.2. The Prevot et al.(1984) and Calzetti et al.(2000) extinction laws are considered. The physical properties are measured by running LePhare with the redshift fixed to the measured photometric redshift (Z MED from Section 3.4.1). For sources where Z MED is not estimated, we revert to Z BEST (redshift from the best-fit template). Estimates for the stellar mass, age, star formation rate, dust attenuation, and best extinction law are reported in the catalog. Figure 3.15 shows the stellar mass distribution as a function of redshift for the SXDF catalog.

Figure 3.15 The distribution of stellar masses as estimated from the best-fit template shown as a function of the photometric redshift.

3.5 Summary

We present a photometric catalog for the Subaru-XMM Deep survey field, one of the deep fields with the largest contiguous area covered over a wide wavelength range. We include imaging data in 28 photometric bandpasses spanning from the optical to the mid-infrared. Importantly, we homogenize and assemble all optical and near-infrared data from various instruments and surveys onto a common reference frame to minimize systematic effects. The Chapter 3. SPLASH-SXDF Catalog 93 catalog contains ∼ 1.17 million objects over an area of ∼4.2 deg2 with multi-wavelength pho- tometry performed using a multi-band detection image, including ∼ 800, 000 objects within the 2.4 deg2 HSC-UD area of higher depth and superior wavelength coverage. Exploiting the extensive multi-wavelength coverage, we measure accurate photometric redshifts for all sources. The photometric redshifts are calibrated using ∼10,000 reliable spectroscopic redshifts available from various surveys. The SPLASH-SXDF catalog is perfectly suited for studying galaxies in the early universe and tracing their evolution through cosmic time. The large area coverage also allows for investigations of the large-scale structure and environmental effects on galaxy evolution, without being significantly affected by cosmic variance.

3.A Catalog description

Since the coverage area for individual bands is different, we include a special flag (COV- ERAGE FLAG) in the final catalog to identify whether an object was covered in a given band. For the optical and NIR filters, this flag identifies whether imaging data is available at the source position in the given band. In the case of the HSC filters, an object may also not be covered due to the star mask, which is also included in the COVERAGE FLAG. Table 3.5 lists the parameters used for the extraction of photometry using SExtractor in dual image mode with the χ2 detection image. Table 3.6 describes all the columns available in the catalog. A compressed version of the catalog (in binary FITS table format) is available for download here: https://z.umn.edu/SXDF.

3.B Correcting photometric errors

In order to properly account for the photometric errors, we measure the variation in the sky noise and use it to correct the photometric errors computed from the weight maps by SExtractor. The motivation for this comes from the fact that the sky variation can properly account for undetected faint objects and correlated noise that the weight maps cannot. Moreover, no weight maps were available for the SuprimeCam data and we had to use a smoothed background rms map instead. With the proposed treatment, the photometric errors would be made consistent across all bands. For each source, we measure the average value of the weight map at its location in each band. Using the aperture size and weight value (proxy for image depth), we can compute the expected photometric error based on the results of the empty sky aperture Chapter 3. SPLASH-SXDF Catalog 94

Table 3.5. SPLASH-SXDF Catalog: SExtractor parameters used for Dual image mode χ2 detection and photometry

Parameter Name Value

DETECT TYPE CCD DETECT MINAREA 5 DETECT MAXAREA 100000 THRESH TYPE ABSOLUTE DETECT THRESH 0.51 ANALYSIS THRESH 0.5 FILTER Y FILTER NAME gauss 3.0 5×5.conv DEBLEND NTHRESH 32 DEBLEND MINCONT 0.00001 CLEAN Y CLEAN PARAM 1.0 MASK TYPE CORRECT WEIGHT GAIN N RESCALE WEIGHTS N PHOT APERTURES 6.67, 13.33, 20.00, 26.67, 33.33 PHOT AUTOPARAMS 2.5, 3.5 PHOT AUTOAPERS 10, 10 PHOT FLUXFRAC 0.2, 0.5, 0.8 MAG ZEROPOINT 23.93 GAIN 0.0 GAIN KEY DUMMY BACK SIZE 128 BACK FILTERSIZE 3 BACKPHOTO TYPE LOCAL BACKPHOTO THICK 30 Chapter 3. SPLASH-SXDF Catalog 95

Table 3.6. SPLASH-SXDF Catalog: Column Descriptions for the SPLASH-SXDF Catalog v1.5†

Column No. Column Title Description

General Information 1 ID Source Identification number 2 RA Right Ascension [deg] 3 DEC Declination [deg] 4 A Semi-major axis [deg] 5 B Semi-minor axis [deg] 6 THETA Position Angle [deg] 7 X IMAGE Object position along x [px] 8 Y IMAGE Object position along y [px] 9 A IMAGE Semi-major axis [px] 10 B IMAGE Semi-minor axis [px] ......

†Only the first 10 rows shown. For the full table, please refer to the published version or the readme available with the digital version of the catalog.

analysis (Section 3.3.3). We can then compute a median correction factor to adjust the SExtractor-measured photometric errors to the value determined from the sky noise. We only consider sources in the mid-50% of the magnitude distribution, avoiding potential biases from the faintest and brightest sources. This correction is expected to scale with the aperture size. Additionally, we find this factor to differ for regions of the mosaic with different depths. In order to account for both these effects, we compute a separate aperture size-dependent correction factor at different depths. This only affects the SuprimeCam 0 0 BVRci z images which are divided into 2 subregions and the MUSUBI-u mosaic which is divided into 3 subregions. Table 3.7 lists the correction factors for each band in 100, 200, 300, 400and 500 apertures. Chapter 3. SPLASH-SXDF Catalog 96

Table 3.7. SPLASH-SXDF Catalog: Correction factors for SExtractor photometric errors

Instrument/ Aperture Size Filters Survey 100 200 300 400 500

g 1.26 1.70 2.18 2.70 3.16 r 1.26 1.72 2.20 2.69 3.15 HSC i 1.29 1.82 2.31 2.87 3.38 z 1.19 1.57 1.96 2.36 2.76 y 1.19 1.60 2.02 2.47 2.91 B 2.11, 2.30 3.29, 3.69 4.41, 5.08 5.47, 6.36 6.40, 7.45 V 2.35, 2.64 3.69, 4.21 4.92, 5.63 5.99, 6.81 6.84, 7.72 SupCam Rc 2.19, 2.44 3.28, 3.78 4.27, 4.98 5.19, 5.98 5.90, 6.78 i0 2.64, 2.93 4.33, 5.09 5.83, 7.01 7.15, 8.68 8.22,10.08 z0 2.49, 2.61 3.46, 3.85 4.21, 4.84 4.97, 5.76 5.61, 6.55 J 0.96 1.07 1.12 1.17 1.21 UDS H 0.93 1.01 1.03 1.05 1.07 K 0.96 1.07 1.12 1.18 1.23 Z 2.86 4.32 5.68 7.09 8.51 Y 2.45 3.44 4.39 5.36 6.32 VIDEO J 2.21, 2.26 2.72, 2.99 3.14, 3.60 3.59, 4.26 4.03, 4.94 H 2.30 3.03 3.63 4.20 4.78 Ks 2.21 2.69 3.10 3.53 3.94 MUSUBI u 0.18, 0.21, 0.19 0.24, 0.31, 0.26 0.30, 0.39, 0.32 0.35, 0.48, 0.39 0.40, 0.56, 0.45 u 0.61 0.68 0.73 0.80 0.86 g 1.05 1.21 1.34 1.47 1.60 CFHTLS r 0.85 0.98 1.08 1.20 1.31 i 0.74 0.92 1.10 1.27 1.43 z 0.97 1.58 2.14 2.66 3.11 Chapter 4

Extreme emission line galaxies in SPLASH-SXDF

Star-forming, low-mass galaxies play an essential role in the evolution of the universe, particularly at high redshifts. From recent studies, these objects are now believed to be the leading candidates for being the dominant contributors to the total ionizing photon budget during the epoch of reionization (e.g., Finkelstein et al., 2012; Robertson et al., 2013, 2015; Bouwens et al., 2015) and thus, considerable effort has been invested into probing these earliest galaxies (e.g., Bowler et al., 2012; Bouwens et al., 2012, 2015; Tilvi et al., 2013; Coe et al., 2013; Ellis et al., 2013; McLure et al., 2013; Matthee et al., 2014; Finkelstein et al., 2015; McLeod et al., 2015; Calvi et al., 2016; Oesch et al., 2016; Bagley et al., 2017; Salmon et al., 2018; Shibuya et al., 2018; Konno et al., 2018). Emission lines in the optical spectra of galaxies are an excellent tool to discover star- forming galaxies at high-redshifts. The presence of emission lines is a signature of ionized gas excited by recent star-formation, AGN activity or shocks. In the case of star-formation, the strength of these emission lines is directly correlated with the magnitude of recent star- formation activity and thus, active star-forming galaxies can be easily identified by the emission lines in their spectra. The Lyα emission line has been widely successful at identifying large samples of star- forming galaxies in the early universe (e.g., Dey et al., 1998; Hu et al., 1998; Rhoads et al., 2000; Ouchi et al., 2003; Wang et al., 2009; Kashikawa et al., 2011; Erb et al., 2014; Matthee et al., 2014) and is a powerful probe of reionization (e.g., Malhotra & Rhoads, 2004; Ouchi et al., 2010; Hu et al., 2010; Kashikawa et al., 2011; Tilvi et al., 2014; Matthee et al., 2014; Zheng et al., 2017). Lyman-α emitters (LAEs) make up for a significant fraction of the star-forming population, up to 60% at z > 6 (Stark et al., 2011). However, studying large

97 Chapter 4. SPLASH-SXDF EELGs 98 populations of LAEs and faint star-forming galaxies at high-redshifts remains challenging until JWST launches, as it usually requires long exposure times and difficult near-infrared observations (e.g., McLinden et al., 2014; Trainor et al., 2015). A popular complementary approach has been to study low-redshift analogs of these high-redshift LAEs and faint star- forming galaxies. Currently, the best low-redshift analogs of the earliest star-forming galaxies we have are the “green pea” galaxies (Cardamone et al., 2009; Amor´ınet al., 2010; Jaskot & Oey, 2014; Henry et al., 2015; Verhamme et al., 2017). The green pea galaxies were serendipitously discovered in SDSS by Galaxy Zoo volunteers (Lintott et al., 2007; Cardamone et al., 2009). These are compact galaxies that appear green in the SDSS false-color gri-band images due to the presence of the [OIII]λλ4959+5007 doublet (EW([OIII]λ5007)∼300–2500A)˚ dominating the r-band flux. These objects share many similar properties to the high-redshift LAEs 8−10 – e.g., small sizes, low stellar masses (10 M ), low metallicities, high specific star- formation rates, and large [OIII]λ5007/[OII]λ3727 ratios (e.g., Cardamone et al., 2009; Amor´ınet al., 2010; Izotov et al., 2011). The [OIII] emission line strengths in these green pea galaxies is higher than the typical galaxy and thus, they are often classified under the more general group of extreme emission line galaxies (EELGs). The discovery of green peas has sparked a wave of effort to search for low-redshift analogs of the earliest star-forming galaxies, particularly characterized with their strong emission lines. At low-redshifts, the challenge in studying the EELGs primarily comes from their low number densities. Performing a comprehensive study requires a wide area coverage on the sky with well-defined selection criteria. Slitless spectroscopic surveys (e.g., the WISP survey, Atek et al., 2010) are ideal for identifying EELGs but cannot cover a large area yet. This will change when the future missions such as Euclid and WFIRST come online. Traditionally, the largest samples of EELGs have been found via narrow-band imaging surveys (e.g., Moorwood et al., 2000; Malhotra et al., 2005; Kashikawa et al., 2006; Geach et al., 2008; Shibuya et al., 2012; Sobral et al., 2013; Konno et al., 2018), when the redshifted emission line falls within the bandpass and can be selected by comparing their narrow- and broad-band colors. However, the redshift slices probed by these surveys are very thin (and thus smaller surveyed volume) and these surveys are only sensitive to equivalent widths higher than the FWHM of the narrow-band filter (few tens of A˚ in the rest-frame). An alternative approach has recently become popular – if the emission line is strong enough, it may contribute significantly to the broad-band fluxes and it would be possible to identify these EELGs using a broad-band color selection. This technique has been suc- cessfully applied to SDSS galaxies to select samples of EELGs at z . 0.05 (Yang et al., Chapter 4. SPLASH-SXDF EELGs 99

6.5−7.5 9−10 2017) and ∼ 0.5 (Li & Malkan, 2018) with stellar masses ranging 10 M and 10

M , respectively. Here, we aim to extend this technique to much fainter magnitudes and thus, lower masses by applying it to the Spitzer Large Area Survey with Hyper-Suprime- Cam (SPLASH1 ; Capak et al., in prep.) dataset and the photometric catalog (described in Chapter3). SPLASH covers a 2.4 deg 2 area on the sky with a 5σ magnitude limit of 25.5 − 27 in the ugriz bands – the combination of which expands the survey volume enough to obtain a statistically significant sample of EELGs. Moreover, the multi-wavelength cov- erage allows us to select EELGs at different redshifts with the combination of multiple optical bandpasses available in SPLASH. Here, we use the ugriz filters to identify EELG candidates with a color excess due to the presence of an emission line in the g, r, or i filters. The emission line contributing to the broad-band flux can be either Lyα Hβ+[OIII]λλ4959+5007 complex, or Hα depending on the bandpass and the redshift of the galaxy. In the case of Hβ+[OIII]λλ4959+5007 doublet, these objects would be equivalents of the green pea galaxies. In the case of Lyα, these objects could be highly star-forming Lyman-alpha emitters (LAEs) with large Lyα EW, which could be indicative of exotic system with low metallicity stellar populations (e.g., pop III stars; Schaerer, 2003). In the case of Hα, these objects are likely low-mass yet highly star-forming galaxies that lie above the star-forming main sequence. This chapter is organized as follows: Section 4.1 describes the data and the sample selection technique; Section 4.2 discusses the follow-up spectroscopy for some of the objects from our sample; Section 4.3 presents the summary properties for the full EELG sample; and Section 4.4 concludes with a summary of the results.

4.1 Data and Sample Selection

Presence of strong emission lines in galaxy spectra is reflected in its distinctive colors. Using color-based selection criteria has already been demonstrated as an effective method to select EELGs (e.g., Cardamone et al., 2009; Yang et al., 2017). This technique relies on isolating a region in color-color space based on three adjacent filters that identifies a color excess in the middle filter (hereafter, the “selection” filter) caused due to the presence of the strong emission line. Cardamone et al.(2009) and Yang et al.(2017) have applied this technique to select samples of EELGs at 0.14 < z < 0.36 and z . 0.5, respectively, in SDSS using their gri-colors. For this work, we apply this selection technique to identify EELGs in the SPLASH

1 http://splash.caltech.edu Chapter 4. SPLASH-SXDF EELGs 100 survey (Capak et al., in prep). Particularly, we use the photometric catalog from Mehta et al.(2018) which covers the Subaru-XMM Newton Deep survey field (SXDF) in near-UV to mid-IR wavelengths (also presented in Chapter3). To fully exploit the multi-wavelength coverage of SPLASH, we expand the color selection to use ugriz bands. The griz optical bands coverage from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP; Aihara et al., 2017a) which uses the Hyper Suprime-Cam on the Subaru 8m telescope on Mauna Kea, Hawaii (Miyazaki et al., 2017, PASJ, in press) and the u-band coverage from MUSUBI and CFHT-LS surveys (see Section3 for details on the catalog). Here, we implement EELG sample selection based on ugr, gri, and riz color-color space.

4.1.1 Color-color selection

We optimize the color criteria for the SPLASH ugriz filters using a set of model galaxy spectra of EELGs and trace their redshift evolution in the color-color space. A range of Bruzual & Charlot(2003) galaxy templates are considered. Since the EELGs are expected to be young and star-forming, we consider models with constant star-formation history, very young ages (3 and 10 Myr), Chabrier(2003) IMF, no dust and solar metallicity. In order mimic an EELG, nebular emission lines are added to these spectra. The full suite of models includes Hα covering a range in rest-frame EW(Hα) = [1000A,˚ 2000A,˚ 3000A]˚ while the other significant lines (Hβ, Lyα, [OIII]λλ4959+5007 doublet, and [OII]λ3727) are added using fixed line ratios w.r.t. the Hα line flux. Hβ and Lyα line ratios are taken to be their Case B values of Hα/2.86 and 7.59 × Hα, respectively, for an electron temperature 4 −3 Te = 10 K and low electron density (ne = 100 cm ). For adding the [OIII] lines, we choose a fixed [OIII]/Hα ratio of 2 – the typical value for the sample of observed green pea galaxies in Cardamone et al.(2009). EELG samples surveyed across various studies have been characterized by high [OIII]/[OII](O32) line ratios, reaching values of up to 60 in some galaxies (Nakajima & Ouchi, 2014; Nakajima et al., 2016; Stasi´nska et al., 2015; Izotov et al., 2016a,c, 2017; Yang et al., 2017). Such high

O32 ratios may be indicative of density-bounded H II regions (e.g., Jaskot & Oey, 2013; Nakajima & Ouchi, 2014; Nakajima et al., 2016) or may be caused by low metallicity, high ionization parameter, or hard ionizing radiation (e.g., Jaskot & Oey, 2013; Stasi´nska et al.,

2015). Both low and high redshift Lyα emitting galaxies exhibit a typical O32 ratio of ∼3 to ∼20. For the purposes of creating mock EELGs galaxy spectra for defining our color

criteria, we adopt a nominal value of O32 = 6. Figure 4.1 shows the redshift evolution tracks for the model EELG galaxies for the ugr, gri, and riz color-color spaces. The shaded boxes show the color selection criterion that best Chapter 4. SPLASH-SXDF EELGs 101

Figure 4.1 Color-color diagram showing the selection criteria for EELGs, similar to Fig- ure 4.2. Here, the evolution of the tracks is annotated with redshift information. Also shown, in the bottom panel, are the redshift windows where EELGs would be selected by the various criteria. isolates a sample of EELGs from the general population (also see Figure 4.2). The broad- band color selection only identifies the presence of an emission line in the selection band and is insensitive to the identity of the emission line causing the color excess. Hence, this selection identifies EELGs over different ranges of redshifts, depending on which emission line enters in the selection filter. The g-band color excess selection criterion is defined as a combination of color-color and S/N cuts:

 0 ≤ u − g ≤ 1.8    −5 ≤ g − r ≤ −0.5  S/N(g) > 5 (4.1)   S/N(r) > 3   g > 20 The S/N threshold ensures reliable photometry for these objects. Moreover, we also apply a magnitude cut to avoid any bright galactic or local contaminants. With the g-band selection, we isolate low-redshift (0.06 . z . 0.1) EELGs where the g-band excess is due to the presence of the Hβ+[OIII]λλ4959+5007 complex in the g-band, whereas it also selects Chapter 4. SPLASH-SXDF EELGs 102 high-redshift (2.4 . z . 3.1) LAEs when Lyα is the contributing emission line. Similarly, with the r-band color excess, we pick out low-redshift EELGs at 0.3 . z . 0.4 due to the Hβ+[OIII]λλ4959+5007 complex and high-redshift LAEs at 3.5 . z . 3.8. The selection criterion for EELGs with an emission line in the i-band is defined as:

 0 ≤ g − r ≤ 1.8    −5 ≤ r − i ≤ −0.5  S/N(r) > 5 (4.2)   S/N(i) > 3   r > 20 Finally, the selection of EELGs with r-band excess is done using:

 0 ≤ r − i ≤ 1.8   −5 ≤ i − z ≤ −0.5   r − i ≥ 2 × [i − z + 0.8] (4.3) S/N(i) > 5   S/N(z) > 3   i > 20

The i-band color excess selects 0.06 . z . 0.1 EELGs (similar to the ugr selec- tion) due to the Hα line being in the i-band. Additionally, when the contributing line is Hβ+[OIII]λλ4959+5007 complex, the i-band selection identifies EELGs at 0.42 . z . 0.7. > The Lyα enters i-band at z ∼ 4.75 and given the shallower depth of the z-band in SPLASH- 43 −1 SXDF, we only expect to select LAEs with LLyα & 5 × 10 ergs s , where the luminosity −5 −3 function drops considerably (. 10 Mpc ), and thus, we do not expect to pick up a significant population of high-redshift LAEs with the i-band selection within the SPLASH survey area. Overall, the combination of these selection criteria allows us to select strong [OIII] emitters almost continuously from 0.06 . z . 0.7, with a small gap between z = 0.1 − 0.2 where the Hα is still present in the broad-band immediately redward of the selection band. Similarly, we can select LAEs from 2.4 . z . 3.8. Figure 4.2 shows the color-color selection applied to the SPLASH-SXDF catalog. We select samples of 625, 882, and 1062 galaxies with g, r, and i-band color excess respectively. Chapter 4. SPLASH-SXDF EELGs 103

Figure 4.2 Color-color diagram showing the color selection for the EELG samples. The grey points and contours show the full SPLASH-SXDF catalog, whereas the shaded regions and points show the selection criterion and the selected galaxies, respectively. Note that not all galaxies that lie in the selection region are selected. Some of these objects may be removed due to photometric issues (see Section 4.1.2). The tracks show the evolution of model EELG templates. These galaxy templates are generated for constant star-formation history, 10 Myr (solid tracks) and 3 Myr (dashed tracks) ages, and a range of Hα EW. Other nebular lines (Hβ, Lyα, [OIII], [OII]) are added to the spectra using fixed line ratios w.r.t. Hα. See Section 4.3 for details.

4.1.2 Cleaning the samples

The HSC imaging data is marred with satellite trails leftover from the reduction pipeline. These are particularly problematic when selecting galaxies based on color excess in one band. Consequently, the samples need additional pruning to ensure that the color selection is not identifying a satellite trail contaminating the source photometry in the selection bandpass. For this, we make use of the Zooniverse2 framework. We setup a private “Panoptes” project to visually vet all EELG candidates selected in Section 4.1.1. In addition to identifying regular objects masquerading as EELGs due to the presence of satellite trails in the selection bandpass, this also allows us to look for other photometric artifacts and contamination. Figure 4.3 shows an example of a fake EELG candidate which slipped into the color selection criterion due to the aforementioned satellite trail issue. The candidates are classified by at least one expert before it is included in the final sample. After removing all objects with photometric issues, we are left with 404, 487, and 411 galaxies in the g, r, and i-band color excess selected samples respectively.

2 The Project Builder template facility can be found at www.zooniverse.org/lab Chapter 4. SPLASH-SXDF EELGs 104

Figure 4.3 Examples of EELG candidates that are vetted through the Zooniverse frame- work. Shown here is an example of a good (top panel) and a bad (bottom panel) candidate. The candidate in the bottom panel clearly has a satellite trail passing on top of the object in the selection band (highlighted in green) and needs to be rejected. Chapter 4. SPLASH-SXDF EELGs 105

4.2 MMT Hectospec follow-up

The first round of spectroscopic follow-up was performed for 16 of the ugr-selected EELG candidates using the Hectospec Multifiber Spectrograph with the 270 gpm grating (Fabri- cant et al., 2005; Mink et al., 2007) at the MMT 6.5m telescope. Hectospec is a 300 fiber spectrometer with 1◦ diameter field of view and the 270 gpm grating covers a wavelength range of 3650–9200A˚ with a 6A˚ resolution (1.2 A/pixel,˚ R=600–1500). Unfortunately, the total integration time was cut short to just 1/5th of the proposed time due to instrument- related problems with the Hectospec fiber positioner. The total integration time for our targets was 1.25 hrs taken in a single configuration mode on Sept. 26, 2017 with Hectospec running in queue mode. The data were reduced using the HSRED 2.03 pipeline. The HSRED pipeline performs bias, flatfield, illumination, and wavelength calibrations, background sky subtraction, and extracts one-dimensional spectra. The flux calibration is performed using 3 standard stars (BD+28-4211, HD-217086, HD-192281) observed on Oct. 1–3, 2017 along with a set of 4 stars with photometry from SPLASH-SXDF included in our observations. Additionally, the data were also treated for fiber loss, using the photometry available from the SPLASH- SXDF catalog.

4.2.1 EELG targets

Out of the 16 objects with MMT spectra, we detect emission lines in 7 objects – 6 with a single emission line (likely to be Lyα) and 1 object with multiple emission lines. The rest of the spectra do not contain any convincing spectral features at the depth of the spectra. For the single line emitters, we do not detect any continuum. Given that we only detect one line, these objects are likely to be LAEs at high redshift (z=2.4–2.8) and this is in agreement with their photometric redshift estimates from the multi-wavelength catalog. The line fluxes for these objects ranges about 10−60×10−17 erg s−1 cm−2 A˚−1 and assuming the line is Lyα, the Lyα line luminosities range from 5 × 1042 to 4 × 1043 erg s−1. The Lyα luminosity function at z ∼ 2.23 has a characteristic luminosity of ∼ 4 × 1042 erg s−1 (Sobral et al., 2017), implying that these objects are slightly brighter than the typical LAEs at these redshifts. Figure 4.4 shows the spectra for these objects with the best-fit values for the emission lines for these objects reported in Table 4.1. One of the targets observed was confirmed to be a z = 0.069 low-mass EELG with strong nebular emission lines. Its spectrum contains the Balmer series lines Hα,Hβ,Hγ up to H12

3 http://mmto.org/node/536 Chapter 4. SPLASH-SXDF EELGs 106

Figure 4.4 Spectra for 15 EELG candidates in SPLASH-SXDF obtained using MMT/Hectospec. We detect a single emission line for 6 of the candidates, like to be Lyα. The best fits for detected emission lines are shown in red and the numbers in parenthesis report the S/N at which they are detected. A summary of their photometric as well as emission line properties is reported in Table 4.1. along with [OIII]λ4959, [OIII]λ5007, [OIII]λ4363, [OII]λ3727, and [OI]λ6300. In addition to these, emission lines from He I, He II, S II, N II, Ar IV, and Ne III are also detected. Chapter 4. SPLASH-SXDF EELGs 107 from SED fitting) galaxy with a

M 7 ) which is higher than the typical SDSS 10 1 − ∼ yr 8 − 10 × 4.86 ∼ 069 EELG selected from the SPLASH-SXDF EELG sample. The . = 0 z ), giving a sSFR( α 5. The best-fits for the various detected emission lines are reported in Table 4.2 . . 0 (estimated from H 1 z < − yr

486 M The MMT/Hectospec spectrum for the . 0 ∼ star-forming galaxies at SFR of spectrum has a dearth of emission lines detected. This object is a low-mass ( Figure 4.5 Chapter 4. SPLASH-SXDF EELGs 108

Figure 4.5 shows the observed spectrum for this galaxy and the full list of detected lines is reported in Table 4.2. This object is very compact and unresolved in the 0.700 seeing ground-based images. Fitting an stellar population synthesis models to its SED suggests 7 a stellar mass of only ∼10 M . The Hα line flux suggests a star-formation rate of 0.486 −1 M yr (using Kennicutt & Evans 2012 transformation and assuming no dust), giving it a sSFR of ∼4.86×10−8 yr−1. This value is more than a factor of 100 higher than the sSFR of the typical z < 0.5 star-forming galaxies in SDSS (10−10 yr−1). Its spectrum also exhibits several similarities with those of the most metal poor galaxies currently known (e.g., Skillman et al., 2013; Izotov et al., 2017) as well as the Green Peas. The Balmer ratio (Hα/Hβ) for this galaxy is measured to be 2.583 ± 0.056, which is significantly smaller than the canonical value of the Balmer decrement in H II regions. Under the generic Case B assumption (electron temperature of 104K and electron density of 102cm−3), the Balmer ratio is expected to be 2.863 (Osterbrock, 1989). However, the gas in this galaxy is clearly under more extreme conditions. In fact, a low Hα/Hβ may be a common feature of EELGs: 32 out of 41 of the EELGs in the Yang et al.(2017) sample have a Hα/Hβ ratio smaller than the Case B expectation. This may be evidence indicating that Case B assumption does not apply to EELGs and consequently, most of the intrinsic physical properties determined for these galaxies are incorrect. Critically, the element abundance for the EELGs would be underestimated , while the intrinsic ionizing power may be overestimated (Ferland, 1999) which may be significant impact on our model of how the universe was reionized.

The O32 line ratio for this galaxy is particularly high ([OIII]/[OII]= 11.7 ± 0.6), which may indicate density-bounded H II regions (Jaskot & Oey, 2013; Nakajima & Ouchi, 2014; Nakajima et al., 2016; Izotov et al., 2016a,c) or may be caused by low metallicity, high ionization parameter, or hard ionizing radiation (e.g., Jaskot & Oey, 2013; Stasi´nska et al.,

2015). The O32 ratio has recently been claimed as a possible signature of galaxies that have

leaking LyC radiation (Izotov et al., 2016a,c). In fact, the value of O32 for this object is consistent with that of J1154+2443, a galaxy with measured ionizing escape fraction of 46% (Izotov et al., 2018). We are currently following up this object with HST to obtain a far UV spectrum along with UV imaging to fully characterize the properties of the H II region and the nature of the sources responsible for its ionization state. The full analysis of this peculiar object is beyond the scope of this work and we refer the reader to Scarlata et al. (in prep) for an in-depth discussion. Chapter 4. SPLASH-SXDF EELGs 109

4.2.2 Comparing spectroscopic and photometric line fluxes

As an exercise, we compare the observed fluxes measured from spectroscopy with those expected from the photometric measurements. From just photometry, we can estimate the line fluxes for the emission line contributing to the broadband flux by comparing the colors with the adjacent bands. The continuum around the line can be estimated by averaging the fluxes in the bands immediately blueward and redward of the selection filter (u and r in the case of ugr-selected sample). This along with the flux in the selection band can then be used to estimate the flux of the line contributing the excess in the selection filter. Furthermore, we can also estimate the EW of the line:

fλ,conti = (fλ,blue + fλ,red)/2

fline = (fλ,conti − fλ,sel) ∗ ∆λsel (4.4)

EWline = fline/fλ,conti where, fλ,blue and fλ,red are the flux densities in the filters immediately blueward and redward of the selection filter respectively, fλ,sel is the flux density in the selection filter,

∆λsel is the FWHM of the selection filter, fλ,conti is the estimated continuum level, fline is

the line flux, and EWline is the equivalent width. Figure 4.6 shows the comparison between the observed spectroscopic fluxes and those estimated from photometry and the values are also reported in Table 4.1. For objects with detected lines, the line fluxes are computed by fitting an emission line model to the spectra, whereas for the objects with no lines, we estimate the noise level in the spectra and estimate an upper limit on the line flux. Overall, there is a good agreement between the observed and expected line fluxes. For a few objects, we would have expected to detect a line given the estimated line flux from the photometry, but did not see one in the spectra. In these cases, the line fluxes limits are estimated from the spectra assuming a single unresolved line. However, it is possible that the emission line causing the color excess is a complex of line (particularly in the case of Hβ+[OIII]λλ4959+5007) and consequently, the line is broader than the instrumental resolution. It is also possible that the expected line flux from broadband photometry may be overestimated for these objects. This can be verified in the next round of follow-up observations where we plan to prioritize these objects.

4.3 Analysis

For the rest of this discussion, we expand the scope back to the full sample of EELG candidates selected from the SPLASH-SXDF catalog based on their photometric colors. In Chapter 4. SPLASH-SXDF EELGs 110

Figure 4.6 Comparison showing the line flux expected from the broadband photometry and that observed in spectra for the 16 galaxies observed with MMT/Hectospec. Objects where no emission line was detected are shown as upper limits. The number adjacent to the points reports the S/N at which the line was detected. order to help distinguish between the EELG and LAE populations at different redshifts, we use the photometric redshift information available in the SPLASH-SXDF catalog. We prefer the photometric redshift information over other photometric cuts (e.g., a “dropout” color cut using a blueward band) since the depth and coverage of the data vary significantly across the survey area. Moreover, the photometric redshift measurement leverages the information from all the photometric bands allowing for a more robust determination of the redshift (for details see Section 3.4). Figure 4.7 shows the photometric redshift distribution for the three color-excess selected samples. The measurement uncertainties in photometry contribute to the intrinsic scatter in the calculated photometric redshifts. This intrinsic scatter can be significant as we go to fainter objects (see Figure 3.13) and hence, we opt to not use the exact redshift cutoffs obtained from the template model simulation, rather we simply separate the samples into a low-redshift EELG and high-redshift LAE samples at Chapter 4. SPLASH-SXDF EELGs 111 a redshift value that best separate the two redshift selection windows (these are shown as dashed vertical lines in Figure 4.7).

Figure 4.7 Distribution of photometric redshifts for the g-, r-, and i-band selected samples. The photometric redshift information is from the SPLASH-SXDF multi-wavelength catalog. The dashed vertical lines denotes the redshift used to separate the samples into the low-z EELG and high-z LAE samples.

4.3.1 Low-redshift EELGs

We isolate the low-redshift population from the EELG sample by applying a redshift cut of zphot < 0.5 for the ugr-selected and zphot < 1.0 for the gri-selected samples. Since we do not expect any high-redshift LAEs in the riz-selected sample, no redshift cut is applied for this sample. Collectively, we select:

• 123 galaxies from the ugr-selected sample (0.06 . z . 0.1)

• 267 galaxies from the gri-selected sample (0.3 . z . 0.4)

• 411 galaxies from the riz-selected sample (0.42 . z . 0.7) Chapter 4. SPLASH-SXDF EELGs 112

The strong Hβ+[OIII] emission in these galaxies is the cause of their distinctive colors. These samples of galaxies are similar to the various EELGs found in SDSS such as the green pea galaxies (0.14 < z < 0.36; Cardamone et al., 2009) and the “blueberry” galaxies (z . 0.05; Yang et al., 2017). However, here we utilize the much deeper SPLASH data as well as exploit the multi-wavelength coverage to select EELG samples spanning a larger redshift range. Figure 4.8 shows a summary of these low-redshift EELG samples. One of the key advan- tages of the SPLASH dataset is the its depth – reaching down to m=26–26.5 in the selection band, which is several magnitudes deeper than SDSS. In Figure 4.9, we show a comparison between the EELG samples from SDSS identified in SDSS – the blueberry galaxies (z . 0.05; Yang et al., 2017), the green pea galaxies (0.14 < z < 0.36; Cardamone et al., 2009), and the [OIII] emitters (0.4 < z < 0.6; Li & Malkan, 2018). Here the EW for our sample is calculated for the total flux causing the color excess (as per Equation 4.4). In other words, at these redshifts, the EW computed is for the Hβ+[OIII]λλ4959+5007 complex. We also estimate the line luminosity of the complex for these objects using the photometric redshift

> available from the catalog. The expected rest-frame EW of these objects is ∼ 500A˚ for the majority of the sample, extending out to extreme values of few 1000A.˚ As evident from the figure, the SPLASH-SXDF samples are really probing a previous unexplored parameter space of EELGs. The rest-frame EW range of SPLASH-SXDF EELGs is similar to their SDSS counterparts despite being more than a factor of 10 fainter, possibly hinted towards a common physics at play. In order to illustrate how far these objects deviate from the typical galaxy popula- tion, we compare their stellar masses and star-formation rates with the regular z < 0.5 star-forming galaxies in SDSS (see Figure 4.10). The stellar mass for our sample is avail- able from the SPLASH-SXDF catalog measured by SED fitting the multi-wavelength data (see Section 3.4.3). The star-formation rates are computed from the estimated flux in the Hβ+[OIII]λλ4959+5007 complex (using Equation 4.4). We convert the measured line flux of the complex to an Hβ line flux assuming Case B conditions and a fixed [OIII]5007/Hα ratio of 2, typical for green pea-like galaxies (Cardamone et al., 2009; Amor´ınet al., 2010). The Hβ flux is then converted to a star-formation rate using using Kennicutt & Evans −1 −41.27 (2012) transformation (assuming Case B): SFR [M yr ] = 2.86 × 10 × LHβ [ergs sec−1]. The dust content of these galaxies is negligible (e.g., Cardamone et al., 2009; Yang et al., 2017) and hence, we do not apply any dust corrections. The EELG samples from the SDSS studies are included again for comparison along with the star-forming galaxy popu- lation at z < 0.5. The most striking feature of these objects is their extremely high specific Chapter 4. SPLASH-SXDF EELGs 113

Figure 4.8 Observed properties of the three low-redshift EELG samples. Shown from top- to-bottom and left-to-right are the selection band magnitude (200 aperture), the stellar mass (as obtained from SED fitting), the estimated line flux (from broadband photometry), the estimated line rest-frame EW (from broadband photometry), the estimated line luminosity, and the cumulative line luminosity distributions normalized by the effective survey volume (not corrected for survey incompleteness). star-formation rates (sSFR; ∼ 107−8 yr−1) compared to the normal star-forming popula- tion. Although the star-forming main sequence is unconstrained at the stellar masses of these objects, these objects definitely lie above the relation observed in the higher mass galaxies. The sSFR for SPLASH-SXDF EELG samples is in good agreement with the Chapter 4. SPLASH-SXDF EELGs 114

Figure 4.9 (Left) The observed selection-band magnitude as a function of the rest-frame EW for the three EELG samples from SPLASH-SXDF. For comparison, the SDSS EELG samples from literature are also shown – the Cardamone et al.(2009) green peas, Yang et al. (2017) blueberries, and Li & Malkan(2018) [O III] emitters. (Right) The line luminosity for the EELGs shown as a function of rest-frame EW. In both panels, for the SPLASH-SXDF samples, the EW and line luminosities plotted are those for the Hβ+[OIII]λλ4959+5007 complex (computed using the selection-band color excess), whereas for the SDSS samples, the EW and line luminosities shown as for [OIII]λ5007.

4 z < 0.5 blueberry galaxies even at extremely low masses (∼10 M ), roughly 100 times lower than the SDSS samples. This could possibly suggest that the physical processes gov- erning star-formation in these galaxies is unaffected by the galaxy’s stellar mass over this range. For the z∼0.3–0.6 samples, we find a population of low-mass galaxies (M?∼106−8.5 −7 −1 M ) with slightly higher sSFR (∼10 yr ) compared to the green peas and the [OIII] 9−10.5 emitters from SDSS at 10 M . This could be explained if the star-formation for these objects gets more vigorous at lower masses. It is also possible that the star-formation rates are over-estimated for our z ∼ 0.3 − 0.6 samples, due to uncertainties in the redshift. The three samples have different luminosities down to which they are complete due to the varying depth between the filters used in the color selection. However, we can compare the bright end of the three samples after accounting for the differences in the survey volume for the three samples. The bottom right panel of Figure 4.8 shows the cumulative distribution of the EELG samples selected at different redshifts normalized the effective volume probed by each sample. The effective volume is computed using the redshift ranges of the model galaxy templates expected to be selected by the color criteria (i.e., the tracks from Figure 4.1). At the faint end, the difference are mainly due to the survey incompleteness which have Chapter 4. SPLASH-SXDF EELGs 115

Figure 4.10 The star-formation rates shown as a function of the stellar mass for EELG samples from SPLASH-SXDF. Also, shown for comparison are the EELG samples from SDSS. The black contours shown the general star-forming population at z < 0.5 from SDSS. The black dashed lines represent constant specific star-formation rates. not corrected for. However, the differences seen at the bright end not due to selection or completeness effects. We observe a significant drop in the number of luminous [OIII] emitters as we go to lower redshifts. This is indicative of a strong evolution in the bright end of the EELG luminosity function as one goes to higher redshifts. This effect has also been observed in slitless spectroscopic surveys which show that the number density of EELGs

> with strong (EW ∼ 200A)˚ emission lines increases by a factor of ten or more at z ∼ 1.5 (Atek et al., 2011, 2014) and continues to increase out to z ∼ 2.4 (Maseda et al., 2018).

4.3.2 Lyα emitters

Complementary to the low redshift sample of EELGs, the Lyα emitters (LAEs) dominate the currently accessible ELG population at high redshift universe (z ∼ 2 − 4). Observed samples of LAEs now span to thousands of objects (e.g., Kashikawa et al., 2011; Erb et al., 2014; Matthee et al., 2014; Santos et al., 2016; Zheng et al., 2016; Bagley et al., 2017; Konno et al., 2018; Shibuya et al., 2018). The strong Lyα emission in LAEs is indicative of Chapter 4. SPLASH-SXDF EELGs 116 the presence of a strong ionizing radiation field typically associated with young, hot stars. Similar to the EELGs, strong Lyα line emitters can be isolated with broadband colors. The selection criteria from Section 4.1.1 allows us to select LAEs in 2.4 . z . 3.1 with the ugr-selection and 3.5 . z . 3.8 with the gri selection. Similar to the EELG selection, we use the photometric redshifts for separating the high-redshift LAE samples. Allowing for the uncertainties and degeneracies involved in the photometric redshift measurement, we

select everything with zphot > 0.5 for the ugr-selected and zphot > 1.0 for the gri-selected samples resulting in a sample of 281 and 220 LAEs, respectively. Figure 4.11 shows the magnitude and mass distributions of the two LAE samples. Al- though more massive than the EELGs, these galaxies are still below the typical characteristic ? 10.8 stellar mass of star-forming galaxies at z ∼ 3 (M ∼10 M ; Davidzon et al., 2017) with 7 10 masses ranging from ∼10 to ∼10 M . We make the same calculations from Equation 4.4 to estimate the line flux and EW of the Lyα emission line responsible for the color excess in the selection band. The normalized cumulative distributions of the line luminosities shown in the bottom right panel does not suggest significant evolution in the bright end of the Lyα luminosity function between z∼2.8 and 3.6. The Lyα rest-frame EW for the LAEs is >100A˚ for the majority of the sample reaching up to ∼1000A˚ for some objects. These Lyα EWs are extreme and may be indicative of exotic systems with extremely low metallicity stellar populations (Malhotra & Rhoads, 2002; Schaerer, 2003; Kashikawa et al., 2012). Figure 4.12 shows the time evolution of Lyα EW for a set of galaxy templates (Schaerer, 2003) including a variety of IMFs, star formation histories, and metallicities going down to Z = 0 (metal-free) which representative of Pop III stars. The observed distribution of Lyα EWs suggests that these objects are either:

• are extremely metal-poor – the models with the lowest metallicities have higher Lyα EW (see Figure 4.12),

• galaxies undergoing a very recent burst of star-formation – the models with an instan- taneous burst exhibit high Lyα EW for the first few Myr as shown in Figure 4.12,

• have peculiar, top-heavy IMF – the models with higher mass cutoffs (e.g., IMF C

which has a mass range of 50-500 M ) also have higher Lyα EWs compared to the

other cases (IMF A which has a mass range of 1-100 M and IMF B with a mass

range of 1-500 M ),

or any combination of these. Chapter 4. SPLASH-SXDF EELGs 117

Figure 4.11 Observed properties of the two high-redshift LAE samples. Shown from top- to-bottom and left-to-right are the selection band magnitude (200 aperture), the stellar mass (as obtained from SED fitting), the estimated line flux (from broadband photometry), the estimated line rest-frame EW (from broadband photometry), the estimated line luminosity, and the cumulative line luminosity distributions normalized by the effective survey volume (not corrected for survey incompleteness).

The EWs of the Lyα line in these objects is distinctly different from the generic star- forming galaxies observed in the present-day universe. To illustrate this, we plot the cumu- lative distribution of the EW(Lyα) for LAEs at z ∼ 0.3 from Cowie et al.(2011) alongside our z ∼2.8 and 3.6 samples in Figure 4.13. The majority of the high-redshift LAEs have Chapter 4. SPLASH-SXDF EELGs 118

Figure 4.12 (Left panel) The distribution of rest-frame EW for LAEs in the SPLASH- SXDF EELG samples. (Right panel) The evolution of Lyα EW as a function of age for a suite of models from Schaerer(2003). The models are colored according to their metallic- ities as indicated by the colorbar. Z = 0 is representative of metal-free (Pop III) stellar population. The IMF A, B, and C have a mass range of 1-100 M , 1-500 M , and 50-500 M , respectively. The curves represent the models with an instantaneous burst, whereas the points show the equilibrium values for constant star formation history (and are plotted at arbitrary ages).

EW(Lyα)>100A˚ compared to the EW(Lyα).20-50A˚ for the bulk of the low redshift popu- lation. There is a a significant evolution in the EW distribution going towards high redshifts with high EW LAEs becoming more common at high redshifts. Observations of high-redshift LAEs and star-forming galaxies have noted a relation between their absolute UV continuum magnitude (MUV ) and rest-frame Lyα EWs. As seen in Figure 4.14 for the SPLASH-SXDF LAE samples, there is a lack high-EW objects that are also UV-bright. This trend was first found by Ando et al.(2006) for z ∼ 5 − 6 star-forming galaxies and later confirmed in both LAEs and star-forming galaxies over z ∼ 3 − 7 (e.g., Shimasaku et al., 2006; Ouchi et al., 2008; Stark et al., 2010; Furusawa et al., 2016; Ota et al., 2017). Following its initial discovery, this trend is often referred to as the “Ando” effect. Ando et al.(2006) argue for a physical reason responsible the observed relation between the rest-EW(Lyα) and the absolute UV continuum magnitude and propose Chapter 4. SPLASH-SXDF EELGs 119

Figure 4.13 The cumulative distribution of rest-frame EW of Lyα for the LAE samples from SPLASH-SXDF. For comparison, the sample of z ∼ 0.3 LAEs from Cowie et al.(2011), z ∼ 2.8 sample from Zheng et al.(2013), the z ∼ 4.5 sample from Zheng et al.(2016) are also plotted.

Figure 4.14 The rest-EW(Lyα) as function of the UV continuum magnitude (the “Ando” effect) shown for the LAE samples from SPLASH-SXDF. The dashed curves show the EW(Lyα) for constant Lyα luminosities.

that the trend could potentially arise due to luminosity-dependent dust extinction, the age or star-formation history of a galaxy, or gas dynamics of the galaxy. On the other hand, Chapter 4. SPLASH-SXDF EELGs 120 some studies have argued for no dependence between the rest-EW(Lyα) and absolute UV magnitude claiming that the “Ando” effect is purely a consequence of number statistics (Nilsson et al., 2009) – UV-bright and high-EW(Lyα) galaxies both being rare naturally results in the lack object in high-EW, UV-bright parameter space. One way to test this claim is to probe down to fainter fluxes and see if the trend holds. As shown in Figure 4.14, the SPLASH-SXDF samples reach down to MUV ∼ −15 and the rest-EW(Lyα) distribution does not seem to evolve considerably below MUV ∼ −20. The range of rest-frame Lyα EW

for objects below MUV ∼ −9.5 does not change considerably. This lends support to the argument for independence between the rest-EW(Lyα) and UV luminosities of galaxies. It appears as though the observed sample is randomly generated from a constant rest- EW(Lyα) distribution and the lack of high-EW, UV-bright objects is merely a consequence of the rarity of bright Lyα objects.

4.4 Conclusions

We select a statistically significant sample of extreme emission line galaxies from the 2.4 deg2 SPLASH-SXDF dataset using broadband color selection cuts. After some initial pruning to remove objects with photometric issues, we assemble samples of 123, 267, and 411 EELGs with the Hβ+[OIII]λλ4959+5007 complex in the selection band over the redshift ranges 0.06 . z . 0.1, 0.3 . z . 0.4, and 0.42 . z . 0.7, respectively. With the same color selection, we also select samples of 281 and 220 LAEs over 2.4 . z . 3.1 and 3.5 . z . 3.8, respectively. These samples fully exploit the depth of the SPLASH dataset, going about a factor of ∼10 fainter than other studies using the SDSS. We obtain optical spectroscopy for 16 EELG candidates using Hectospec on MMT. Out of the 16, we detect emission lines in 7 objects (6 with Lyα and 1 with multiple optical emission lines). For objects with detected emission lines, the measured line fluxes from spectroscopy are in good agreement with the estimates from photometry. The Lyα emitters observed have redshifts of z ∼ 2.23 and luminosities ranging from 5×1042 to 4×1043 erg s−1, making them slightly brighter than the typical LAEs at z ∼ 2.23. We also find a z = 0.069 low-mass EELG with strong nebular lines. The broadband SED suggests a stellar mass of 7 only ∼ 10 M for this object. Moreover, its spectrum is indicative of its gas being under extreme conditions with a Balmer ratio that is significantly lower than the canonical Case

B assumption and a particularly high O32 ratio similar to those observed for LyC leaking galaxies. Chapter 4. SPLASH-SXDF EELGs 121

Our samples of EELGs selected in SPLASH-SXDF at z < 0.7 extend to several magni- tudes fainter and roughly a factor of 100 lower than the EELG samples found in SDSS. These 4−8 EELGs are extremely low-mass galaxies (∼ 10 M ) with high specific star-formation rates (∼ 10−7 − 10−8 yr−1), and extreme [OIII] EWs ranging from 500A˚ to a few 1000A˚ (rest-frame). While the SPLASH-SXDF samples extend lower in stellar mass, the specific star-formation rates of these objects are similar to the blueberry galaxies observed by Yang et al.(2017), possibly suggesting common physical processes governing star-formation in these objects. We also observe a strong evolution in the bright end of the EELG luminosity function from z ∼ 0.08 to z ∼ 0.7. The LAE samples at z ∼ 2.4−3.8 in SPLASH-SXDF consist of sub-M? galaxies spanning 7 9 10 M to 10 M in stellar mass. These objects exhibit extreme Lyα EWs ranging from 100A˚ up to 1000A,˚ indicative of exotic stellar populations. Lyα EWs this high can only be caused by very recent star-formation activity, top-heavy IMFs and/or extremely metal poor stellar populations. In conclusion, we present a sample of EELG candidates that spans a large range in red- shift. These objects are the closest analogs to the galaxies in the early universe. Moreover, these objects seem to defy most of the canonical assumptions and knowledge of present-day, massive galaxies we have. These are the prime candidates for spectroscopic follow-up in to further study their chemical composition and stellar populations. Chapter 4. SPLASH-SXDF EELGs 122 c obs S/N ] 1 − -band). 5.795.63 ... 5.61 ... 5.725.96 ... 5.685.68 ... 5.13 ... 5.55 ...... g 2.2811.868 10.79 3.218 7.54 3.023 6.47 3.39 7.1091.994 364.88 2.388 29.86 11.99 > > > > > > > > > ± ± ± ± ± ± ± erg s obs f 17 − 10 × spec z 0.069 2594.26 c 5.72 b ][ 228.02 2.861324.07406.73 2.846 59.55 ... 587.66453.47271.64 2.390 24.62 ... 349.25206.48 2.465 ... 232.31 20.84 300.10 ... 278.02 10.27 ... 252.13 ... 301.52 ...... 271.49 2.569786.65 2.865 28.65 14.09 ± 1 exp ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − ˚ A EW 1824.26 b ][ 1 − 3.35 659.76 6.67 4.88 1547.16 2.993.30 1680.86 1747.48 3.192.87 1766.24 5.18 1410.83 3.98 509.87 3.20 787.15 3.71 600.98 557.74 2.962.88 643.70 3.00 477.53 392.88 3.43 1336.93 3.40 2441.73 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± b erg s exp f 17 − 10 × [ a 0.35 7.71 0.000.11 2416.68 0.230.21 42.29 0.33 19.64 0.27 17.99 0.260.32 12.35 0.23 10.83 0.24 10.12 0.29 9.68 0.30 9.66 0.34 9.26 7.17 5.60 3.98 0.170.32 20.04 15.82 r ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± m a 0.12 26.79 0.000.05 21.39 25.37 0.070.09 26.44 26.28 0.130.11 26.83 0.09 26.72 0.12 26.17 0.09 26.62 0.09 26.40 26.37 0.110.11 26.72 0.14 26.75 26.91 0.07 26.03 0.12 26.74 g ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± m follow-up MMT observations a 0.109 26.11 0.0010.204 20.49 24.80 0.1110.203 25.67 25.79 0.3060.309 26.20 0.228 26.23 0.235 25.62 0.061 25.99 0.137 25.80 25.79 0.1190.086 26.17 0.139 26.21 26.42 0.157 25.53 0.508 26.07 u ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± m circular aperture. 00 . SPLASH-SXDF EELGs: Spectroscopic summary of EELG candidates with phot z Table 4.1 ID RA DEC These quantities are estimated using the broadband photometry and Equation 4.4 The magnitudes reported here are for a 2 There are multiple emission lines detected for this object. The numbers represent the total of all emission lines that fall within the selection band ( 460050541371 34.803580 34.973517 -4.504900300077 -4.256412997411 0.11 34.862946 2.53 34.231040 21.41 -4.962332441896 25.93 -4.603389445937 0.89 34.605043509251 2.84 34.579668 26.63 -4.552162465095 35.151349 27.30 -4.540815997468 2.72 35.051588 -4.352837512564 2.24 34.444325 27.43 -4.486889 1.90 34.513283 27.36 -4.603297366848 2.11 25.78 -4.343345369690 0.90 34.955555 26.36 446559 0.83 34.911681 26.01 -4.762013 34.555359 25.97 -4.754134 2.20 -4.538925 0.83 26.47 1.58 26.35 26.51 a b c 1006616 34.358743 -4.574319 0.90 26.32 1064827 34.324684 -4.3768651024948 2.39 34.309987 26.57 -4.515143 2.48 27.91 Chapter 4. SPLASH-SXDF EELGs 123

Table 4.2. SPLASH-SXDF EELGs: Summary of all detected emission lines in the z = 0.069 bright EELG

λ λ Line Flux σ Continuum Species rest obs [A]˚ [A]˚ [×10−17 erg s−1][A]˚ [×10−17 erg s−1]

HeI 7065.30 7554.64±1.42 11.25 ± 5.38 3.27±1.13 0.23 ± 0.10 SII 6730.80 7199.12±1.34 18.49 ± 8.16 3.24±1.32 0.54 ± 0.11 SII 6716.40 7183.21±0.91 16.57 ± 8.65 1.68±0.70 0.54 ± 0.11 HeI 6678.10 7141.77±1.59 7.09 ± 5.38 2.04±1.48 0.72 ± 0.13 NII 6548.10 7002.35±3.45 12.22 ± 6.74 5.71±3.70 0.54 ± 0.07 Hα 6562.80 7019.16±0.35 724.44 ± 283.85 2.05±0.22 0.54 ± 0.07 NII 6583.40 7038.70±2.81 13.26 ± 6.82 5.19±2.96 0.54 ± 0.07 SIII 6312.10 6751.91±1.88 7.27 ± 5.95 2.21±1.77 0.81 ± 0.17 OI 6300.30 6738.98±2.16 5.28 ± 5.35 2.03±2.10 0.81 ± 0.17 HeI 5875.60 6284.30±0.97 26.55 ± 13.33 2.12±0.80 0.98 ± 0.10 HeI 5015.68 5365.39±4.55 11.01 ± 14.30 2.85±4.12 1.39 ± 0.17 OIII 5006.80 5355.49±0.37 1936.54 ± 726.47 2.05±0.22 1.39 ± 0.17 OIII 4958.92 5304.23±0.41 645.64 ± 246.13 2.10±0.26 1.50 ± 0.18 Hβ 4861.33 5199.75±0.50 291.96 ± 113.32 2.14±0.35 1.59 ± 0.18 ArIV 4740.20 5069.92±3.01 7.79 ± 8.81 2.35±2.68 1.57 ± 0.16 ArIV+HeI 4712.00 5039.50±2.49 6.91 ± 8.22 1.79±2.07 1.57 ± 0.16 HeII 4685.94 5012.81±2.44 6.59 ± 7.85 1.83±2.27 1.57 ± 0.16 HeI 4471.48 4782.47±2.18 9.65 ± 10.70 1.75±1.81 1.94 ± 0.32 OIII 4363.21 4667.03±0.95 43.57 ± 21.76 2.06±0.78 1.71 ± 0.18 Hγ 4340.47 4642.75±0.61 139.91 ± 58.37 1.92±0.43 1.71 ± 0.18 Hδ 4101.74 4387.35±0.78 72.24 ± 34.92 1.77±0.57 2.17 ± 0.37 HeI 4026.19 4305.16±5.45 7.46 ± 13.62 2.91±5.23 2.27 ± 0.42 NeIII+H7 3968.00 4244.84±0.88 87.84 ± 38.83 2.02±0.61 2.01 ± 0.24 HeI+H8 3889.00 4159.52±0.94 52.35 ± 28.58 1.70±0.67 2.44 ± 0.38 NeIII 3868.76 4138.42±0.64 164.67 ± 69.48 2.01±0.48 2.44 ± 0.38 H9 3835.39 4102.15±1.73 14.30 ± 14.53 1.51±1.48 2.57 ± 0.51 H10 3797.90 4061.10±1.48 16.72 ± 14.71 1.60±1.28 2.26 ± 0.56 H11 3770.63 4032.95±1.54 15.24 ± 12.71 1.71±1.39 2.03 ± 0.24 H12 3750.15 4011.93±1.58 7.31 ± 9.05 1.12±1.45 2.03 ± 0.24 OII 3727.00 3987.18±0.81 169.85 ± 62.28 3.02±0.69 2.03 ± 0.24 Chapter 5

Predicting the z∼2 Hα luminosity function using [OIII] emission line galaxies

Note: This chapter originally appeared as a refereed publication in the Astrophysical Journal under Mehta, V., Scarlata, C., Colbert, J. W., et al. 2015, ApJ, 811, 141 titled “Predict- ing the Redshift 2 Hα Luminosity Function Using [OIII] Emission Line Galaxies” and is presented here as is, albeit with some minor modifications.

The upcoming missions ESA’s Euclid (Laureijs et al., 2012) and NASA’s WFIRST- AFTA (Green et al., 2012; Dressler et al., 2012; Spergel et al., 2015) aim to solve one of the biggest mysteries in modern cosmology – the nature of dark energy – by performing complementary galaxy redshift surveys of emission line galaxies to map the large-scale struc- ture and its evolution over a cosmic time covering the last 10 billion years. Dark energy, believed responsible for the accelerated expansion of the universe Riess et al.(1998); Perl- mutter et al.(1999), affects both the expansion history of the Universe as well as the growth of structures. Both of these effects can be observationally constrained through large galaxy redshift surveys, which enable the measurement of Baryon Acoustic Oscillations (BAOs; thus, constraining the cosmic expansion history) and large scale redshift-space distortions (thus, constraining the growth history of the large scale structure). The combination of these two measurements allows the differentiation between an unknown energy component and modification of general relativity as the cause of observed cosmic acceleration (Guzzo

124 Chapter 5. WISP Bivariate Hα-[OIII] LF 125 et al., 2008; Wang, 2008a,b). Both Euclid and WFIRST-AFTA will use the Hαλ6563 line and [OIII]λλ4959+5007

< < doublet to select emission line galaxies as tracers of the large scale structure at 0.7 ∼ z ∼ 2 (in

< < Hα) and 2 ∼ z ∼ 2.7 (in [OIII]). The performance of the planned missions can be quantified by a figure-of-merit, which describes their ability to measure the present value and time evolution of the dark energy equation of state. The figure-of-merit for a dark energy survey depends on the number density of tracer galaxies available at each redshift. It is therefore critical to have a reliable and sufficiently precise knowledge of the expected number of Hα and [OIII] galaxies in the survey volumes. Euclid and WFIRST-AFTA will both perform IR slitless spectroscopy of emission line galaxies, in a way similar (scaled by many orders of magnitude in area) to the IR spec- troscopic surveys that are being conducted with the Wide Field Camera 3 (WFC3) on- board the Hubble Space Telescope (HST). The WFC3 Infrared Spectroscopic Parallel Sur- vey (WISP; Atek et al., 2010) is an on-going pure-parallel near-infrared grism spectroscopic survey using the WFC3 camera. While covering a substantially smaller area, WISP is very similar in many respects to the planned dark–energy surveys, and thus, can be used to test number count predictions, redshift measurement accuracy, target selection function, as well as completeness for the planned surveys. Towards this goal, Colbert et al.(2013) predicted the number counts of Hα – emitting galaxies in the redshift range 0.3 < z < 1.5. In this paper we extend the work by Colbert et al.(2013) and estimate H α number counts out to z ∼ 2. Ground-based wide-field narrow-band surveys like HiZELS (Geach et al., 2010; Sobral et al., 2009, 2012, 2013) and NEWFIRM Hα Survey (Ly et al., 2011) have been able to

< < measure the Hα luminosity function in the redshift range of interest (0.7 ∼ z ∼ 2). However, while having the advantage of high sensitivity to emission lines and covering significant areas in the sky, these surveys can only map very narrow redshift ranges. Volume densities of galaxies can thus be strongly affected by the presence of large scale structures in the field. Moreover, samples selected with narrow band surveys, without an extensive spectroscopic followup, can suffer from contamination by emission lines at different redshifts (e.g., [OIII] and [OII]; Martin et al., 2008; Henry et al., 2012). Finally, even narrow-band surveys with multiple filters tuned to identify multiple emission lines at the same redshifts still rely on continuum detections and miss the lowest mass galaxies, to which WISP is very sensitive. WISP’s grism coverage includes Hα for the redshift range 0.3 < z < 1.5 and [OIII] for 0.7 < z < 2.3. Since Hα is not directly covered by WISP at z > 1.5, we cannot measure the Hα luminosity function up to z∼2 explicitly. However, we can use the [OIII] coverage to Chapter 5. WISP Bivariate Hα-[OIII] LF 126 estimate the Hα luminosity function and number counts. In order to do this, we compute the bivariate Hα–[OIII] line luminosity function in the redshift where both lines are visible, and use the resulting fit at higher redshifts, where only [OIII]-emitters are observable in the WISP data. We also introduce a modified Maximum Likelihood Estimator to obtain the best-fit model parameters, which accounts for measurement uncertainties in the line luminosity (which can substantially affect the shape of the bright end of the luminosity function). This chapter is organized as follows: in Section 5.1, we summarize the new WISP data that we use in this work; Section 5.2 discusses the observed Hα–[OIII] relation; and Sec- tion 5.3 describes the parametrization for the bivariate luminosity function. In Section 5.4, we discuss the Maximum Likelihood Estimator modified to account for uncertainties in the line flux, and the fitting procedure, which we use to derive the Hα–[OIII] bivariate lumi- nosity function at redshift z ∼ 1 and the result is discussed in Section 5.5. Further, in Section 5.6, we demonstrate the ability to recover the Hα luminosity function as well as number counts from fitting only the [OIII] data at redshift z ∼ 1. Lastly, we fit the [OIII] luminosity function and use it to derive the Hα luminosity function and number counts at redshift z ∼ 2 in Section 5.7, along with the final number count estimates for the upcoming dark-energy surveys.

5.1 Data

The WFC3 Infrared Spectroscopic Parallel Survey (WISP) is discussed in full detail in Atek et al.(2010). Briefly, WISP consists of HST WFC3 pure–parallel IR slitless spectroscopic observations and imaging of hundreds of uncorrelated high-latitude fields. The spectroscopy is performed using the G102 (0.8 − 1.15 µm, R ∼ 210) and G141 (1.15 − 1.65 µm, R ∼ 130) grisms, while the associated near-IR imaging is obtained with the F110W and F160W, filters. For this paper, we use data from 52 separate fields for which both G102 and G141 grism spectroscopy are available, covering a total of 182 arcmin2. These fields include 23 new WISP fields in addition to the ones used by Colbert et al.(2013). All data are processed with a combination of the WFC3 pipeline CALWF3 and custom scripts, to account for the lack of dithering of the pure parallel data (see Atek et al., 2010). The siltless extraction package aXe 2.0 (K¨ummelet al., 2009) is used to perform the spectral extraction. We perform a blind search for emission lines in all fields (both grisms) down to a typical 5σ line flux-limit of (3 − 5) × 10−17 erg s−1 cm−2 as explained in Ross et al. (2015, in prep). In order to remove the high contamination rate from false and/or spurious sources due to Chapter 5. WISP Bivariate Hα-[OIII] LF 127 the parallel, slitless nature of the WISP survey, every candidate emission line undergoes independent visual inspection by two team members. This process of visually confirming the emission lines is described in further detail in Colbert et al.(2013). In this work, we are interested in the Hα λ6563 line and [OIII] λλ4959+5007 doublet, which are covered by WISP survey over the redshift ranges: 0.3 < z < 0.7 (only Hα), 0.7 < z < 1.5 (both Hα+[OIII]), 1.5 < z < 2.3 (only [OIII]). We exclude all sources with any ambiguity in their redshift determination among multiple reviewers. Specifically, we only retain sources with a quality flag < 16, which implies consensus among the independent reviewers (Ross et al. 2015, in prep). Since Hα line and [NII] λλ6548+6584 doublet is not resolved in the WISP grisms, we apply a correction factor of 0.71 to the Hα luminosities to account for [NII] contamination, similar to Colbert et al.(2013). Although Villar et al. (2008) and Cowie et al.(2011) report decreasing [N II]/Hα ratio with increasing Hα equiva- lent width, this ratio is nearly constant up to Hα EW ∼200A,˚ above which the correlation steepens. The fraction of galaxies in our sample for which we may overestimate the [NII] contribution due to the assumed constant correction is only 10%. In what follows, we use the completeness analysis from Colbert et al.(2013), who per- formed extensive simulations to quantify the survey incompleteness as a function of line signal–to–noise ratio, equivalent width (EW), as well as galaxy size. The completeness sim- ulations followed the full line extraction process after adding artificial sources to the real data, spanning a range in redshifts, radii, brightnesses, equivalent widths (EWs), as well as using different empirical spectral templates from the Kinney-Calzetti Altas. These simula- tions show that slitless spectroscopic surveys display some level of incompleteness even at large EWs and line fluxes, primarily because of spectral overlap and line mis-identification.

5.2 Hα–[OIII] Trend

Figure 5.1 shows the observed Hα against [OIII] line luminosity, for the WISP galaxies in the redshift range 0.8 < z < 1.2. The red points in Figure 5.1 show line luminosities for a sample of 2141 star-forming galaxies in the Sloan Digital Sky Survey (Thomas et al., 2013), limited to the redshift range 0.2 < z < 0.3, in order to ensure that 300 spectroscopic aperture contains most of the galaxy flux (rather than just the central nucleus), and to avoid evolutionary effects. Despite the large scatter (on the order of 0.5 dex), the two line luminosities are broadly correlated, both in the SDSS as well as WISP samples. This is not surprising: both Hα and [OIII] are observed in the ionized gas in star-forming galaxies, although, while the Chapter 5. WISP Bivariate Hα-[OIII] LF 128

Hα luminosity scales directly with the ionizing fluxes of embedded young, hot stars, the [OIII] luminosity is more strongly dependent on variations in the oxygen excitation state, overall gas oxygen abundance, gas density, as well as dust reddening (e.g., Kennicutt, 1992; Moustakas & Kennicutt, 2006). Figure 5.1 also shows that the Hα–[OIII] relation does not evolve significantly in the ∼4.5 billion years elapsed between z ∼ 0.25 (SDSS galaxies) and z ∼ 1 (WISP galaxies). Although the gas oxygen abundance is observed to evolve with cosmic time, the similarity between the observed trends suggests that any evolution is masked by the large scatter introduced by the range of physical conditions present in galaxies. As we will show in Section 5.6, the observed broad correlation between Hα and [OIII] luminosity is sufficient for the goal of estimating the number of Hα emitters from the numbers of [OIII] emitters, as long as the scatter is appropriately taken into account. In computing the number of Hα emitters from [OIII] emitters at higher redshifts, we will assume that the trend between Hα and [OIII] does not change in the ∼2.2 billion years between z ∼ 1 and z ∼ 1.8.

5.3 Parametrization of the Bivariate Line luminosity func- tion

The goal of this work is to predict the Hα number counts at redshift z ∼ 2 using the WISP dataset. At this redshift, the WISP survey does not cover Hα directly, but it does cover the [OIII] λλ4959+5007 doublet. Hence, we estimate the Hα number counts from the available [OIII] number counts. In order to do this, we start by computing the Hα–[OIII] bivariate line luminosity function (LLF), which describes the volume density of sources as a function of both the Hα and [OIII] luminosities. The most widely used parametric form for galaxy luminosity functions is the Schechter function (Schechter, 1976), which is fully described by the parameters L? (characteristic luminosity), φ? (number of galaxies per unit volume at L?), and α (faint end slope). This function is found to reproduce the LLF of both [OIII] and Hα-selected WISP galaxies (Colbert et al., 2013). We define the bivariate LLF by combining a Schechter form (to describe the [OIII] LLF) with the conditional probability for finding an Hα source given an [OIII] luminosity1 .

1 In this definition, the marginalized function over all [OIII] luminosities is not an exact Schechter form – but very close to it. Chapter 5. WISP Bivariate Hα-[OIII] LF 129

Figure 5.1 A broad correlation is observed between Hα and [OIII] luminosity in the SDSS star-forming galaxies in 0.2 < z < 0.3 (red points) as well as our WISP sample in redshift range 0.8 < z < 1.2 (black points). The black and red lines are linear fits to the WISP and SDSS data, respectively and the shaded regions show the 1σ deviations from the linear fit (∼ 0.5 dex).

Thus, we parametrize the [OIII] LLF as:

L α  L  dL ψ(L ) dL = φ? OIII exp − OIII OIII (5.1) OIII OIII L? L? L? where LOIII is the [OIII] line luminosity. We adopt a log-normal distribution to describe the conditional probability that a galaxy with [OIII] luminosity in the range (LOIII,LOIII+dLOIII) Chapter 5. WISP Bivariate Hα-[OIII] LF 130 has Hα luminosity in the range (LHα,LHα+dLHα):

p(LHα|L[OIII]) dLHα = " 2 # (5.2) 1 ln (LHα/hLHαi) dLHα √ · exp − 2 2σ LHα σlnLHα 2π lnLHα

where hLHαi defines the mean expected Hα luminosity for a given [OIII], and σlnLHα is the scatter around the mean relation. hLHαi and LOIII are related through the ratio r, such that:

hL i L β Hα = r · OIII (5.3) L0 L0

The ratio r is defined as the expected LHα/L0 at a nominal luminosity L0, where we 40 −1 arbitrarily choose L0 = 10 ergs s . The LLF and conditional probability equations (Equations 5.1 and 5.2, respectively) can now be combined into the bivariate luminosity

function, expressed in terms of the Hα and [OIII] log10 luminosities, (x and y respectively) as:

10y α+1  10y  Ψ(x, y; P~ ) dx dy = ln10 · exp − · L? L? " # (5.4) ln10 −[x − hxi]2 √ · exp dx dy 2(σ /ln10)2 σlnLHα 2π lnLHα where hxi is defined by Equation 5.3 as,

hxi − log L0 = log r + β(y − log L0) (5.5)

The bivariate LLF, Ψ(x, y; P~ ), in Equation 5.4 can now be fully described by the set of ~ ? parameters P = [α, L , β, r, σlnLHα ]. The formulation for the bivariate luminosity function described here, has been partly inspired from the size-luminosity bivariate distribution from Huang et al.(2013).

5.4 Fitting Procedure

There are various parametric as well as non-parametric techniques used to derive the best fit

parameters of luminosity functions (LF); to name a few: the Vmax estimator by Trumpler & Weaver(1953), the C− method by Lynden-Bell(1971), the maximum likelihood estimator Chapter 5. WISP Bivariate Hα-[OIII] LF 131 by Sandage et al.(1979, hereafter STY), and the stepwise maximum likelihood estimator by Efstathiou et al.(1988). In this paper, we use the STY parametric maximum likelihood estimator (MLE), modified to account for uncertainties in the measurements of the line luminosity, as explained in Section 5.4.2. One of the major advantages of the MLE is that it allows us to fit the data without binning. Particularly for small samples, this technique reduces the biases introduced by the choice of bin-size or bin-center as well as any effects due to changing completeness and effective volume within the bin (e.g., Ma´ızApell´aniz& Ubeda´ , 2005). The modification of the method we introduce in Section 5.4.2 allows us to account for significant measurement uncertainties on the data. Large photometric uncertainties can impact the determination of the best fit parameters of the LLF, particularly at the bright end, where the number density of galaxies is a steep function of galaxy’s luminosity (Henry et al., 2012). In slitless spectroscopy, photometric uncertainties can be large even for bright galaxies (i.e., the noise is not only due to the sky background but also to the possible contamination of the line flux due to the continuum of overlapping spectra), so it is crucial to account for line luminosity uncertainty in the fitting process.

5.4.1 Original MLE

The original MLE is a parametric estimator, where the best fit parameters are obtained by maximizing the likelihood function (L) of observing the galaxy sample with respect to the parameters of the model. For a given LF parametric description Ψ(L), the probability for detecting a given galaxy with log luminosity L is given by:

Ψ(Li) · Veff (Li) P (Li) = ∞ (5.6) Z Ψ(L) · Veff (L) · dL

Llim where Veff (L) is the effective volume of the survey. The effective volume varies with the galaxy’s line luminosity and redshift, and can be written as:

zmax Z dV V (L ) = comov (z) · C (L , z) Ω(z) · dz (5.7) eff i dz · dΩ i zmin where [zmin, zmax] are the redshift range of the survey, dVcomov/dz · dΩ is the differential co- moving volume at redshift z, C(L, z) is the completeness function, and Ω(z) is the solid angle covered by the survey. The likelihood function for the full sample can then be computed as Chapter 5. WISP Bivariate Hα-[OIII] LF 132 the product of the individual probabilities for all galaxies in the sample:

N Y L = P (Li) (5.8) i=1 The best fit parameters of the LF can be found by maximizing the likelihood function with respect to the model parameters. It is mathematically and computationally simpler to maximize the log-likelihood function:

N X lnL = lnP (Li) (5.9) i=1 Because this method involves ratios between the differential and integrated luminosity functions, the normalization (φ?) cancels out and, hence, it cannot be determined by this likelihood maximization procedure. φ? can be computed following (e.g., Alavi et al., 2014):

? N φ = ∞ (5.10) Z Ψ(L) · Veff (L) · dL

Llim where N is the total number of sources in the sample and the survey incompleteness is accounted for by the effective volume.

5.4.2 Modified MLE

All astronomical observations have an associated measurement uncertainty. It is crucial to account for these uncertainties, particularly when fitting models that vary steeply as a function of the independent variable (e.g., at the bright end of the Schechter function). In such cases, the best fit-parameters can change significantly, if even a few sources are scattered toward or away from the bright end due to photometric uncertainties. This problem is particularly important for slitless spectroscopic data, where line flux uncertainties can be substantial even for bright line fluxes, due to the common overlapping of spectral traces. We modify the original prescription to account for observational uncertainties as follows. Instead of calculating the probability that a galaxy is exactly at a given luminosity, we marginalize the Schechter function over the luminosity error probability distribution function, assumed to have a Gaussian form, centred at Li, and with standard deviation given by the measurement uncertainty σi. In other words, the probability P (Li) that an object Chapter 5. WISP Bivariate Hα-[OIII] LF 133 has a luminosity Li, given the Schechter model, is evaluated by integrating with respect to

L the convolution of the luminosity function with the Gaussian function N(L|{Li, σi}):

∞ Z Ψ(Li) · Veff (Li) · N(L|{Li, σi})dL

Llim P (Li) = ∞ Z Ψ(L) · V (L) · dL eff (5.11) Llim with,   2  1 (L − Li) N(L|{Li, σi}) = √ exp − 2 2πσi 2σi where L is the log luminosity, Veff (L) is the effective volume from Equation 5.7 – which also accounts for the completeness and area coverage of the survey. In the limit where the uncertainties are very small, the Gaussian becomes a delta function and the probability approaches the value defined in the original MLE, thus, recovering the original expression. In order to test the performance of our modified MLE, we performed a set of simulations (described in Appendix 5.A) to reproduce single-line luminosity functions. When the sample includes a small number of bright sources with significant measurement uncertainties the original MLE is less robust than the modified MLE, which marginalizes the probabilities over the measurement uncertainties. For a more detailed discussion, see Appendix 5.A.

5.4.3 Setting up the Bivariate LLF

The modified MLE method described in the previous Sections can be extended to the bivariate LLF by replacing the single line LF with the bivariate LLF from Equation 5.4 and marginalizing over both the Hα and [OIII] luminosities. The probability for a galaxy with Hα log-luminosity (x, in the equations below) and [OIII] log-luminosity (y, in the equations Chapter 5. WISP Bivariate Hα-[OIII] LF 134 below) can then be written as:

P (xi, yi) = ∞ Z Ψ(x, y;P~ ) · N(x, y|{xi, σx,i}, {yi, σy,i})·

Llim(z) dV · comov (z) · C(x , z ) · Ω · dx dy dz dz · dΩ i i ∞ Z dV Ψ(x, y; P~ ) · comov (z) · C(x, z) · Ω · dx dy dz (5.12) dz · dΩ Llim(z) with,

N(x, y|{xi, σx,i}, {yi, σy,i}) = " 2 2 !# 1 (x − xi) (y − yi) exp − 2 + 2 2πσx,iσy,i 2σx,i 2σy,i where σx and σy are the measurement uncertainties in Hα and [OIII] log luminosities, Ψ is now the bivariate luminosity function from Equation 5.4, and C is the completeness function (further described in Section 5.4.4). The probability for each source is calculated according to Equation 5.12. We construct the log likelihood function as in Equation 5.9. The log likelihood function is maximized and the best fit parameters are obtained using scipy.optimize.fmin l bfgs b . Here, all 5 ~ ? free model parameters P = [α, L , β, r, σlnLHα ] that define the bivariate luminosity function are left free and determined by the maximizing likelihood function. The scipy.optimize.fmin l bfgs b is a SciPy package that uses a limited-memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm in order to find the minimum of a function within the parameter space. The BFGS algorithm approximates the iterative Newton’s method for finding solutions to functions. The L-BFGS algorithm modifies BFGS algorithm to reduce the amount of computer memory used and is well suited for optimizing functions with large number of variables. The version of the algorithm implemented here, L-BFGS-B (Zhu et al., 1997), was written by Ciyou Zhu, Richard Byrd, and Jorge Nocedal2 . ? Once the best fit parameters, [α, L , β, r, σlnLHα ], are obtained, the normalization factor

2 http://www.ece.northwestern.edu/$\sim$nocedal/lbfgsb.html Chapter 5. WISP Bivariate Hα-[OIII] LF 135

φ? can be computed as:

N φ? = (5.13) Z dV Ψ(x, y; P~ ) · comov (z) · C(x, z) · Ωdx dy dz dz · dΩ Llim(z) where the integration limit is taken to be the median flux limit for all fields, N is the number of sources detected in the survey, x and y are the Hα and [OIII] log luminosities respectively,

Ψ is the bivariate luminosity function, Ω is the solid angle surveyed, dVcomov/dz dΩ(z) is the differential comoving volume at redshift z, and C is the completeness function. We obtain accurate errors for our best-fit model parameters by performing a Markov Chain Monte Carlo (MCMC) analysis using the publicly available emcee Python package3 (Foreman-Mackey et al., 2013a). We use uninformative uniform priors for our parameters and the likelihood function is defined as Equation 5.9 with individual probabilities described by Equation 5.12.

5.4.4 Survey Incompleteness

Colbert et al.(2013) performed an extensive completeness simulation to quantify the survey incompleteness for WISP, which we adopt here. Their completeness is provided as a func- tion of equivalent width and signal-to-noise ratio. In order to implement the completeness function into our formulation, we have to re-parametrize it as a function of flux. The com- pleteness for our sample is given by the Hα luminosity (converted to signal-to-noise ratio using the survey limit) and marginalized over the equivalent width distribution for WISP sources, assuming that the equivalent width distribution is independent of the flux.

Z  L  C(L, z) = C EW, S/N = 2 d(EW) (5.14) flim · 4πdL(z) where L is the line luminosity, EW and S/N are the equivalent width and signal-to-noise of the line, flim is the flux limit, and dL(z) is the luminosity distance at redshift z.

5.5 Fitting the Bivariate LLF at z ∼ 1

In this section, we use WISP galaxies to derive the best fit parameters of the bivariate LLF at z ∼ 1, where both Hα and [OIII] emission lines can be detected in the wavelength range covered by the G102+G141 spectroscopy. We select the sample to include only galaxies in the redshift range 0.8 < z < 1.2 to allow for sufficient sample size while minimizing the

3 http://dan.iel.fm/emcee/ Chapter 5. WISP Bivariate Hα-[OIII] LF 136

Table 5.1. WISP: Best-fit parameters for the Hα–[OIII] bivariate LLF for 0.8 < z < 1.2 sample

Parameter Best-Fit Value

+0.5 α -1.5 −0.2 ? +0.1 log L 42.1 −0.2 ? +0.33 log φ -2.95 −0.18 +0.06 β 1.13 −0.26 +0.35 r 0.28 −0.20 a +0.08 σln LHα 0.92 −0.11

a σln Hα = σlog10 Hα×ln(10), where

σlog10 Hα is in dex

impact of an evolving luminosity function over the redshift range. We select 487 galaxies from the 52 WISP fields that satisfy the quality flag cut described in Section 5.1 and have Hα signal-to-noise (S/N) ratio > 5. Of this sample, 166 galaxies have detected [OIII] with S/N > 2. After applying a strict cut of >5σ in Hα, looking for the [OIII] line is no longer a blind search. This allows us to relax the S/N cut for the [OIII] line while maintaining a high quality, pristine sample. Moreover, we do properly account for the errors in the line luminosity during the fitting procedure (see Section 5.4.2). We fit the Hα–[OIII] bivariate LLF to the sample of 166 galaxies, following the procedure described in Section 5.4.3. The best-fit model parameters are reported in Table 5.1 and shown in Figure 5.2. We also perform the MCMC analysis for the model parameters and their posterior distributions are shown in Figure 5.3. In Figure 5.2, the black data points show the sample used to fit the bivariate LLF and the contours show the best-fit bivariate LLF. The density map shows the Kernel Density Estimate (KDE) of the data points (detected in both Hα and [OIII]) corrected for the survey incompleteness. Both the density map and the contours are plotted on the same color-scale. The grey shaded regions show the survey flux limits at z = 0.8 (darker) and z = 1.2 (lighter). With the best fit parameters for the bivariate LLF, we can derive the single-line lumi- nosity function by marginalizing over the nuisance dimension (e.g., the [OIII] luminosity function can be computed by integrating over the Hα nuisance dimension). In Figure 5.4, we compare the marginalized [OIII] luminosity function with the result of the LF of Colbert Chapter 5. WISP Bivariate Hα-[OIII] LF 137

Figure 5.2 WISP data sample for 0.8 < z < 1.2 plotted along with the bivariate LLF best fit shown by the contours. The completeness corrected Kernel Density Estimate (KDE) map is plotted in color. The grey shaded regions represent our survey limit at z = 0.8 (darker) and z = 1.2 (lighter). et al.(2013), computed for galaxies in the 0 .7 < z < 1.5 redshift range. Our new estimate of the marginalized [OIII] LF has a faint end slope consistent within the errors with the +0.5 ? slope derived by Colbert et al.(2013, −1.5−0.2 versus −1.4±0.15). The characteristic L[OIII] +0.1 luminosity is somewhat lower, although the results are within 2σ from each other (42.1−0.2 versus 42.34 ± 0.06). However, we note that the two analyses are not expected to provide the same best-fit parameters for various reasons: first the narrower redshift range used in our work minimizes the effect of the evolution of L? over the redshift interval, and second our fitting method is not affected by the arbitrary choice of bin size and centers, as well as it accounts for uncertainties in the line luminosities. Chapter 5. WISP Bivariate Hα-[OIII] LF 138

Figure 5.3 The posterior as well as joint-posterior distributions for the bivariate LLF model parameters obtained from MCMC analysis. The best-fit parameters as obtained by the MLE are shown by black dots, and for the joint-posterior distributions, the 68% (thicker) and 95% (thinner) confidence contours are shown.

Now, we can compute the Hα LF by integrating the bivariate LLF over the [OIII] di- mension and accounting for the [OIII] non-detection rate. For fitting the bivariate LLF, we only used sources detected in both Hα and [OIII]. However, there is a significant fraction of sources that are detected in Hα but not in [OIII] despite being within the wavelength coverage, due to the significant intrinsic scatter in the Hα–[OIII] relation as well as the sensitivity limits of our survey. Thus, the bivariate LLF parameters obtained above repro- duce the number density of galaxies detected in both lines, but underestimates the number density of Hα-emitters selected regardless of their [OIII] luminosity. With the goal of ob- taining Hα number counts from the [OIII] luminosity function, we compute a statistical correction that accounts for the fraction of Hα-emitters missed due to [OIII] non-detections as a function of the Hα luminosity. The non-detection correction term is then applied when collapsing the bivariate LLF to obtain the single-line Hα LF. We compute the non-detection correction term as the fraction of galaxies below the Chapter 5. WISP Bivariate Hα-[OIII] LF 139

Figure 5.4 The collapsed [OIII] LLF derived from the best-fit bivariate LLF from Figure 5.2 compared with the [OIII] luminosity function from Colbert et al.(2013). The shaded regions represent the 1σ deviations in the best-fit parameters. detection limit in [OIII], in bins of Hα luminosity. For this analysis we used all galaxies in the redshift range 0.7 < z < 1.5, where both emission lines are covered in the spectro- scopic observations. The non-detection correction ranges between 100% and ∼400%, for Hα luminosities between 1043 and 1041 ergs s−1, respectively. In Figure 5.5, we show the marginalized Hα LF without the non-detection correction (black solid line) and with the correction applied (red line), and compare the results with the Hα LF derived in Colbert et al. (2013). The marginalized Hα LF corrected for the [OIII] non-detection fraction is excel- lent agreement with the Colbert et al. (2013) Hα LF. We note that in our formulation, the Hα LF marginalized function over the [OIII] dimension is not exactly a Schechter function, but as Figure 5.5 shows, it is very close to it.

5.6 Estimating Hα from [OIII] at z ∼ 1

The main goal of this work is to estimate the Hα number counts at z ∼ 2, starting from the [OIII] LF at the same redshift. Here, we test how accurately the Hα number counts obtained with this approximation reproduce the known Hα number counts at z ∼ 1, obtained through direct integration of the Hα LF. To this aim we use the sample of 129 [OIII]-selected galaxies in the 0.8 < z < 1.2 redshift range and with [OIII] S/N > 5, along with the same quality flag cuts as described in Section 5.1. The [OIII] single line luminosity function is computed using the modified MLE and the completeness analysis from Colbert et al.(2013). The Chapter 5. WISP Bivariate Hα-[OIII] LF 140

Figure 5.5 The collapsed Hα LLF derived from the best-fit bivariate LLF from Figure 5.2 compared with the Hα luminosity function from Colbert et al.(2013). The uncorrected (in black) and non-detection corrected (in red) LFs are shown. The shaded regions represent the 1σ deviations in the best-fit parameters.

best-fit parameters for the [OIII] LF at z ∼ 1 are reported in Table 5.2. Figure 5.6 shows our best-fit [OIII] single line luminosity function as well as the results from the literature. As noted before, we find a good agreement between our and Colbert et al.(2013) measurements of the LF on the WISP datasets. The rise in the faint-end for Khostovan et al.(2015) and Sobral et al.(2015)H β+[OIII] LFs can be attributed to the Hβ emitters in their sample. However, we note that the variation among different measurements is still substantial, especially at the bright end – the number density of L? galaxies (i.e., ∼ 1042 ergs s−1) varies by almost an order of magnitude. This comparison clearly shows that the nominal errors typically quoted on the best-fit LF parameters generally do not provide an adequate measurement of the actual variation observed in LF determination. The source of this variation is most likely systematic (e.g., different selection techniques provide systematically brighter/fainter samples, galaxy clustering could systematically en- hance/suppress number counts in small-area fields, and so on), and need to be accounted for in predictions used to optimize large galaxy redshift surveys aiming to constrain dark energy. Using the best-fit Schechter parameters obtained for the [OIII] single line LF, we recon-

struct the bivariate LLF using the parameters β, r, and σlnHα from Table 5.1. As done in Section 5.5, we compute the Hα luminosity function by marginalizing over the [OIII] dimension. In Figure 5.7, we compare the Hα single-line luminosity function obtained from Chapter 5. WISP Bivariate Hα-[OIII] LF 141

Table 5.2. WISP: Best-fit parameters for the [OIII] exclusive LLF fit for 0.8 < z < 1.2 sample

Parameter Best-Fit Value

+0.23 α -1.42 −0.43 ? +0.22 log L 42.21 −0.18 ? +0.27 log φ -3.17 −0.39

Figure 5.6 The best-fit [OIII] LLF derived for 0.8 < z < 1.2 WISP dataset compared with the [OIII] luminosity function from Colbert et al.(2013) as well as other estimates from the literature. The shaded regions represent the 1σ deviations in the best-fit parameters. The inset shows the joint-posterior distribution of α and L? from MCMC analysis for our best-fit [OIII] LF. the [OIII] LF with the direct estimate from Colbert et al. (2013). Clearly, the two LF agree very well, as demonstrated also by the cumulative number counts shown in Figure 5.7, where we show the Hα number counts obtained both from the [OIII]–only fit and from the bivariate LLF fit from Section 5.5 (black solid and dashed line, respectively). The errors on the number counts account for the uncertainties in the best fit parameters in addition to the normal Poisson errors. Also note that the number counts are corrected for survey incom- pleteness. As evident from the figure, the recovered Hα number counts from the [OIII]-only fit agree extremely well with the bivariate version as well as from direct integration of the Hα LF. We add for completeness the number counts from Sobral et al. (2012) and Geach et al. (2010). The differences between the WISP dataset and these two works are discussed Chapter 5. WISP Bivariate Hα-[OIII] LF 142 in detail in Colbert et al. (2013).

Figure 5.7 Top: The collapsed Hα LLF for 0.8 < z < 1.2 derived using the best fit [OIII] LLF in Figure 5.6 and the best fit bivariate LLF parameters β, r, and σlnHα from Table 5.1. Bottom: The Hα number counts estimated for z ∼ 1 from our Hα LF, along with estimates from other groups in the literature. The errors on our estimate accounts for the uncertainties in the best-fit parameters in addition to the normal Poisson errors. All number counts are corrected for survey incompleteness. Chapter 5. WISP Bivariate Hα-[OIII] LF 143

Table 5.3. WISP: Best-fit parameters for the [OIII] exclusive LLF fit for 1.85 < z < 2.2 sample

Parameter Best-Fit Value

+0.28 α -1.57 −0.77 ? +0.28 log L 42.55 −0.19 ? +0.31 log φ -2.69 −0.51

5.7 Estimating Hα from [OIII] at z ∼ 2

Having demonstrated the feasibility of our procedure at z ∼ 1, we now apply it to the redshift 2 case. In Section 5.2, we compared the Hα–[OIII] correlation for SDSS (0.2 < z < 0.3) and WISP (0.8 < z < 1.2) data. There is little evidence for significant evolution of the Hα–[OIII] correlation between z ∼ 0.25 and z ∼ 1. Continuing with the assumption that the Hα–[OIII] correlation from z ∼ 1 also holds at z ∼ 2, we use the sample of WISP [OIII]–emitters at z ∼ 2 together with the Hα–[OIII] ratio parameters obtained at z ∼ 1 (see Section 5.5) to derive the z ∼ 2 Hα number counts. We follow the same steps as in Section 5.6. Namely, we first fit a Schechter model to the [OIII]-only line LF. Next, we

use the best-fit parameters together with r, σLlnHα , and β from Table 5.1 to construct the z ∼ 2 bivariate LLF. Finally, we compute the marginalized z ∼ 2 Hα LF, and integrate it to obtain the Hα number counts. The z ∼ 2 sample consists of 91 WISP [OIII]-emitting galaxies selected to be in the redshift range 1.85 < z < 2.2, to have [OIII] S/N > 5, and redshift quality flags < 16. The [OIII] single line luminosity function is fit using the modified MLE, accounting for the measurement uncertainties, and the completeness analysis from Colbert et al.(2013). An additional completeness factor is applied in order to account for the loss of high-z [OIII] emission lines, due to the inability to resolve the doublet, as discussed in Colbert et al. (2013). The best-fit parameters for the [OIII] LF at z ∼ 2 are reported in Table 5.3. Our best-fit z ∼ 2 [OIII] luminosity function is plotted in Figure 5.8, along with the result from Colbert et al.(2013) and other estimates from the literature. Our best fit LF shows a slightly steeper faint-end slope and a higher φ? than what was derived by Colbert et al. (2013) on a smaller sample. The errors in our previous work, however, were substantial, and the differences are not significant. Using the best-fit [OIII] single line luminosity function, the bivariate LLF is recon-

structed using the parameters β, r, and σlnHα from Table 5.1 and the Hα luminosity function Chapter 5. WISP Bivariate Hα-[OIII] LF 144

Figure 5.8 The best-fit [OIII] LLF at z ∼ 2 derived from WISP data plotted along with other estimates from the literature. The shaded regions represent the 1σ deviations in the best-fit parameters. The inset shows the joint-posterior distribution of α and L? from MCMC analysis for our best-fit [OIII] LF. is obtained by marginalizing over the [OIII] dimension. In Figure 5.9, our best-fit z ∼ 2 Hα single line luminosity function obtained from fitting just the [OIII] data is shown alongside other estimates from the literature. The variation among different determinations is large, probably because of systematic uncertainties due to different selection techniques, area cov- ered, and procedures used for the estimates of the Schechter parameters. As noted before, these systematic effects are typically not accounted for in the errors quoted alongside the best-fit estimates of the parameters. Thus, the shaded areas shown in Figure 5.9, are lower limits to the real variation of the volume density at each Hα luminosity.

5.8 Hα Number counts

We use the collapsed Hα luminosity function to compute the 1.85 < z < 2.2 Hα number counts down to the a range of limiting flux values expected to be reached by future dark energy surveys, and plot the results in Figure 5.9. For comparison, we have also plotted numbers from Geach et al.(2010), Sobral et al.(2013), and Lee et al.(2012). The numbers for Geach et al.(2010) are reduced by a factor of ln(10) to account for an error in the published article, resulting from improper conversion of Ψ(logL) luminosity functions to the standard Ψ(L) luminosity functions. In Figure 5.9, our number counts are higher than previous estimates at all flux limits, although below 5 × 10−16 ergs s−1 cm−2, Geach et al. (2010), Lee et al.(2012), and our work agree within the error bars. The Sobral et al.(2013) Chapter 5. WISP Bivariate Hα-[OIII] LF 145

Figure 5.9 Top: The collapsed Hα LLF at z ∼ 2 derived using the best fit [OIII] LLF and the best fit bivariate LLF parameters from Table 5.1. The shaded regions represent the 1σ deviations in the best-fit parameters. Bottom: The Hα number counts estimated for z ∼ 2 from our Hα LF, along with estimates from other groups in the literature. The errors on our estimate accounts for the uncertainties in the best-fit parameters in addition to the normal Poisson errors. All number counts are corrected for survey incompleteness. counts are still lower than any previous as well as our estimates. At brighter fluxes, the variation among the various estimates is very large. Number counts of bright rare galaxies, however, are strongly affected by sample variance. The WISP number counts suffer less from this effect, because of the observing strategy (52 independent fields scattered over the full sky). Chapter 5. WISP Bivariate Hα-[OIII] LF 146

Finally, we also provide number counts for the whole redshift range expected to be covered by the upcoming dark energy surveys. Figure 5.10 shows the expected Hα number counts as a function of survey flux limit for the redshift range 0.7 < z < 2. The redshift range is broken into two: 0.7 < z < 1.5, where the best-fit Hα LF from Section 5.5 is used, and 1.5 < z < 2, where the result from Section 5.7 is used to compute the number counts. For comparison, we again plot the Colbert et al.(2013) (for 0 .7 < z < 1.5) and Geach et al. (2010) (for 0.7 < z < 2.0) number count estimates. For the redshift range 0.7 < z < 2, we expect ∼3000 galaxies/deg2 for a flux limit of 3 × 10−16 ergs s−1 cm−2 (the proposed depth of Euclid galaxy redshift survey, see Laureijs et al.(2011)) and ∼20,000 galaxies/deg2 for a flux limit of ∼ 10−16 ergs s−1 cm−2 (the baseline depth of WFIRST galaxy redshift survey, see Spergel et al.(2015)), when probing with H α. Number counts for various redshift ranges and limiting fluxes are summarized in Table 5.4. These number counts have been corrected for survey incompleteness as well as for [NII] contamination as discussed in Section 5.1. The planned spectral resolution for the Euclid mission, at the time of writing, is R∼250 (Laureijs et al., 2011), which will not be able to resolve Hα+[NII]. Hence, we also provide the numbers counts that are not corrected for the [NII] contamination – these are summarized in Table 5.5. For the redshift range 0.7 < z < 2, we expect ∼5700 galaxies/deg2 for the Hα+[NII] flux limit of 3 × 10−16 ergs s−1 cm−2.

5.9 Summary and Conclusions

Upcoming space based missions will be performing galaxy redshift surveys with the aim of understanding the physical origin of dark energy. The constraints that a given mission will be able to place on the dark energy equation of state parameters depend on the surface density of the used tracers. Both Euclid and WFIRST-AFTA will be using Hα and [OIII] emitters as tracers of the galaxy population and will focus on the 0.7 < z < 2 redshift range. The precise redshift intervals, however, are still being tuned to maximize the scientific output of these missions. Here, we use the WISP survey to extend on our previous work (focused on Hα number counts up to z=1.5) and statistically estimate the number counts of Hα emission line galaxies in the full 0.7 < z < 2 redshift range. To this aim, we have measured the bivariate Hα–[OIII] LLF at z ∼ 1, and showed how, at this redshift, Hα number counts can be accurately predicted from the [OIII]-only line LF, if the relationship between the Hα and [OIII] luminosities is known. We find that these two luminosities are broadly correlated, admittedly with a large scatter, that is dominated by different oxygen excitation states and amount of galaxy dust extinction. The large scatter Chapter 5. WISP Bivariate Hα-[OIII] LF 147 0 . 2 2530 233 939 502 72 122 +1315 − +451 − +242 − +80 − +37 − +50 − a < z < 238 464 6353 3052 1113 7 19478 . 0 0 . correction) 2 942 492 2526 216 106 58 II] +60 − +66 − +983 − +23 − +14 − +10 − 91 < z < 440 179 2848 1282 5 9813 . 5 1 . 1 140 168 97 87 62 43 +873 − +447 − +233 − +77 − +49 − +36 − < z < 672 285 147 9665 3505 1769 7 . 2 0 . 2 99 1465 539 273 42 21 +25 − +111 − +91 − +68 − +14 − +10 − number counts (after applying [N < z < 52 25 α 136 976 420 3730 85 . 2 1 . 1 273 263 188 97 58 35 +485 − +249 − +159 − +98 − +61 − +34 − < z < . . Fluxes have been corrected for survey incompleteness. The errors account 2 2 8 . − 0 cm b 1 . WISP: Cumulative H − ergs s 16 1.02.0 5578 2015 3.0 1004 5.0 369 7.5 151 10.0 76 Table 5.4 − Line Flux Limit in 10 All counts are per deg α a b H for uncertainties in the best-fit parameters along with the normal Poisson errors. Chapter 5. WISP Bivariate Hα-[OIII] LF 148 0 . 2 1328 3239 841 456 234 140 +1116 − +5548 − +446 − +243 − +151 − +93 − a < z < 975 524 5690 2212 7 11282 31925 . 0 0 . 2 correction) 3175 815 1298 422 211 121 +5461 − +252 − +953 − +190 − +132 − +83 − II] < z < 908 384 202 2524 5 5365 16924 . 5 1 . 1 643 208 277 173 70 100 +982 − +369 − +580 − +151 − +42 − +72 − < z < 321 591 3166 5917 1303 7 15001 . 2 0 . 2 737 77 2137 392 169 43 +450 − +78 − +1261 − +211 − +140 − +52 − < z < 59 117 857 291 1922 6736 85 number counts (without applying [N . α 2 1 . 1 158 233 175 93 58 258 +112 − +292 − +823 − +67 − +37 − +95 − < z < 8 . 0 b . Fluxes have been corrected for survey incompleteness. The errors account for . 2 2 − cm . WISP: Cumulative H 1 − 3.05.0 1817 733 2.07.5 3417 323 1.0 8614 ergs s 10.0 171 Line Flux Limit Table 5.5 16 − II] +[N in 10 All counts are per deg α a b H uncertainties in the best-fit parameters along with the normal Poisson errors. Chapter 5. WISP Bivariate Hα-[OIII] LF 149

Figure 5.10 The Hα number counts estimated for 0.7 < z < 2.0 – relevant redshift range for future surveys to cover Hα. The redshift range for each estimate is reported in parenthesis in the legend. Our estimate solid black is split into two ranges: 0.7 < z < 1.5 (dashed black) and 1.5 < z < 2 (dotted black), which use the z ∼ 1 and z ∼ 2 Hα LFs, respectively. We also plot two estimates from Sobral et al.(2013): solid green line represents the Hα number counts estimated using the Hα LF derived at z = 1.47 and dashed green line represents the sum of number counts estimated over the redshift ranges 0.7–1.2, 1.2–1.85, 1.85–2.0 using Hα LFs derived at z=0.84, 1.47, 2.23, respectively. The errors on our estimate accounts for the uncertainties in the best-fit parameters in addition to the normal Poisson errors. All number counts are corrected for survey incompleteness. is observed both in the nearby sample (z ∼ 0.25, from SDSS observations) as well as at z ∼ 1. Moreover, we find no significant evolution in the best-fit [OIII]–Hα relation in the ∼4.5 billion years elapsed between these two epochs. We make the working assumption that the relation continues not to evolve significantly out to redshift z ∼ 2, or, in other words, that any evolution is masked by the large scatter observed in the relation. To fit the bivariate LLF model to the data, we introduced a modified Maximum Like- lihood Estimator that allows us to properly account for the uncertainties in the line flux measurement. This modification can change the estimate of the best-fit parameters, par- ticularly for models that vary steeply over small range of luminosities. Our simulations show that the modified MLE improves the accuracy of the recovered best-fit parameters – especially, when dealing with larger samples, where the measurement uncertainties are Chapter 5. WISP Bivariate Hα-[OIII] LF 150 more significant than the uncertainty introduces by small number statistics. We combined the direct measurement of the z ∼ 1 − 1.5 Hα LF with the z ∼ 2 Hα LF determined from the [OIII] LF and the bivariate LLF information to provide an estimate of the number of Hα emitters expected to be observed down to different line flux limits. Our number count estimates in the full 0.7 < z < 2 are approximately 40% lower than those of Geach et al.(2010) at the bright flux limits (i.e., for line fluxes above 3 .5 × 10−16 ergs s−1 cm−2 ), confirming, with twice as many fields and with the full redshift range, the result of Colbert et al (2013) based on the number of Hα emitters up to z ∼ 1.5. However, we note that the variation in the number counts obtained from different published works in the literature is substantial at these bright flux levels. This is due to a combination of effects, including the different sample selection techniques, fitting algorithms used to obtain the Schechter parameters, as well the different area/depth combinations of various surveys. The work and results presented in this paper give us a better understanding of the expected performance from future planned galaxy redshift surveys aiming at constraining the properties of dark energy. This is a significant step toward reducing the uncertainty of figure-of-merit for dark energy for both Euclid and WFIRST-AFTA. In order to further optimize these planned surveys, more homogenous data are needed.

5.A 1–D Simulations to test the modified MLE

Before applying the modified MLE to deriving the Hα–[OIII] bivariate LLF for our 0.8 < z < 1.2 WISP sample, we test the validity of our modifications to the MLE – results of which are expected to scale to the bivariate case. We generate 1000 samples of galaxies distributed according to a known luminosity func- tion. We run two sets of simulations for two different sample sizes: (i) small (200 sources per sample), roughly the number of sources in our sample, and (ii) large (2000 sources per sample), roughly the number of sources expected to be covered by the end of the WISP survey within the redshift range of interest. The simulated galaxies are assigned the typical uncertainties observed for WISP galaxies at similar luminosities are further randomized within that error-bar. We then fit the simulate samples with both the original and modified MLE techniques. Figure 5.11 shows the results for the single line LF simulations, for the two different sample sizes for both the original and modified MLE. The modified MLE recovers the true parameters with greater overall accuracy in both large and small sample size cases, even though the scatter is similar. Since measurement uncertainties are not properly treated Chapter 5. WISP Bivariate Hα-[OIII] LF 151 by the original MLE, a few bright sources with large uncertainties can skew the results significantly. The modified MLE is much less prone to this effect since it marginalizes over the uncertainty. The efficiency of the two estimators depends on what factor is dominating: the statistical randomness of the sample or the measurement uncertainties of the sample. Since WISP is a slitless grism spectroscopy survey, even the bright sources can have significant uncertainties due to crowding, contamination or other issues. For our sample, the modified MLE is expected to provide an improvement over the original MLE.

Figure 5.11 Results from the 1-D simulations for small (200 sources per sample; top row) and large (2000 sources per sample; bottom row) sample sizes comparing the original (left column) and modified (right column) MLEs. The solid black lines show the true parameters expected to be recovered by the fitting procedures. The contours are at 10%, 33%, 66%, and 95% confidence levels. Chapter 6

Summary

The goal of this thesis was to contribute toward our understanding of the star-formation processes in the faint, low-mass galaxies as well as to assemble statistically significant sam- ples of these objects, both of which can be ultimately used to refine the models for galaxy formation. We show that the star-formation histories of low-mass galaxies at the cosmic high-noon (z ∼ 2; when the cosmic star-formation density was at its peak) tend to be more bursty on average compared to their higher mass counterparts. This analysis is done using samples of star-forming Lyman-break galaxies selected from the deepest UV direct imaging data available from the Hubble UVUDF. We compare the rest-frame UV LF computed for the z ∼ 2 LBGs with the Hα LF at z ∼ 2 using abundance matching. Since both rest-frame UV and Hα are indicators for recent star-formation but are sensitive to a different timescales, the comparison allows us to infer the properties of their star-formation histories. For the z ∼ 2 star-forming populations, we find that the volume-averaged UV-to-Hα ratio – an indicator of “burstiness” in the star-formation activity of galaxies – that is different from the canonical constant star formation expectation. Instead, we find an increasing UV-to-Hα ratio which is indicative of a larger contribution from starbursting galaxies at lower masses compared to the high-mass end. This comparison between the rest-frame UV and Hα LF also sheds insights on to the validity of the commonly used dust relations at high redshifts. Usage of the IRX-β relation has been widely accepted for correcting UV luminosities for dust at high redshifts. While this treatment has been shown to be appropriate for the majority of the normal star- forming population, the locally calibrated relation may not be applicable to all high-redshift galaxies. The discrepancies we find between the rest-UV and Hα LFs suggests the generic dust corrections may be underestimating the dust content of some high-redshift star-forming

152 Chapter 6. Summary 153 galaxies. Redshift of ∼ 2 is the highest redshift where a comparison between the rest-UV and Hα is possible with current generation of observational facilities. When JWST launches, we will push this comparison to higher redshifts and probe the star-formation histories as well as dust properties for the earliest galaxies. Following the analysis of the bulk population of the star-forming galaxies at high-redshift using the rest-UV, we turn our attention to the extreme emission line galaxies that consti- tute galaxies such as the Lyman-α emitters as well as Green Pea and blueberry galaxies, which attracted considerable attention recently. At high-redshifts, the LAEs make up for a significant fraction of the star-forming population, while at low-redshifts, these EELGs are of high interest due to their high specific star-formation rates. While rare in the lo- cal universe, they are expected to be common in the early universe. Recent observations suggest that these EELGs may play a role in reionizing the universe. While observations of EELGs are fraught with challenges, we use the recently popularized technique of using broadband colors to select EELGs by identifying a color excess caused by the presence of a strong emission line one of the bands. A comprehensive study of EELGs required a wide area coverage such as the SPLASH survey on the SXDF. We homogenize and assemble all available optical and near-infrared data on the SXDF along with the deep optical HSC and mid-infrared Spitzer imaging from SPLASH onto a common reference frame and generate a photometric catalog with data in 28 photometric bandpasses, photometric redshifts and stellar population properties for ∼800,000 galaxies over ∼2.4 deg2. Using the SPLASH-SXDF dataset, we select samples of 123, 267, and 411 EELGs (with Hβ+[OIII]λλ4959+5007 complex in the selection band) over redshift ranges 0.06 . z . 0.1, 0.3 . z . 0.4, and 0.42 . z . 0.7, respectively. These EELGs are extremely low-mass 4−8 −7 −8 −1 galaxies (∼ 10 M ) with high specific star-formation rates (∼ 10 − 10 yr ), and extreme [OIII] EWs ranging from 500A˚ to a few 1000A˚ (rest-frame). While the SPLASH- SXDF samples extend a factor of ∼100 lower in stellar mass, the specific star-formation rates of these objects are similar to the blueberry galaxies observed by Yang et al.(2017), possibly suggesting common physical processes governing star-formation in these objects. The LAE samples selected at z ∼ 2.4 − 3.8 in SPLASH-SXDF have stellar masses of 107−9

M and extreme rest-frame Lyα EWs of 100–1000A.˚ The high Lyα EWs in these objects can only be caused by very recent star-formation, top-heavy IMFs and/or extremely metal poor stellar populations. From an initial round of spectroscopic follow up, we find one of 7 these EELGs to be a low redshift (z = 0.069) galaxy with a stellar mass of only ∼10 M Chapter 6. Summary 154 and its spectrum suggestive of its gas being under extreme conditions with a Balmer ratio that is significantly lower than the canonical Case B expectation and a particularly high

O32 ratio. The low-redshift EELGs and higher redshift LAEs may be part of the same type of galaxies but at different masses. These EELGs are arguably the closest analogs to the galaxies in the early universe and they seem to defy most of the canonical assumptions and knowledge of present-day, massive galaxies we have. We will be performing spectroscopic follow up for these objects to fully characterize the properties of their H II regions as well as the nature of the sources responsible for its ionization. Emission line galaxies are the cornerstone for upcoming dark energy surveys such as Euclid and WFIRST. While the primary goal of these surveys is to uncover the nature of dark energy, they will achieve this with slitless spectroscopic observations of emission line galaxies over the redshift range 0.9 . z . 2. These missions are planned to survey large areas (∼15,000 deg2 for Euclid and ∼2200 deg2 for WFIRST) with deeper coverage on a smaller subset of the total area. As part of optimizing the observation strategy, we estimated Euclid to be able to observe ∼5700 Hα emitters per square degree. This amounts to an unprecedented collection of emission line galaxies at the cosmic high-noon. We plan to fully explore these datasets to study the star-formation properties of EELGs from the local universe out to the peak of cosmic star-forming as well as their link to the earliest galaxies. References

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