Multi-Element Abundances as Probes of Galaxy Growth Across Cosmic Time Citation Zhuang, Zhuyun (2026) Multi-Element Abundances as Probes of Galaxy Growth Across Cosmic Time. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5e14-b360. https://resolver.caltech.edu/CaltechTHESIS:08112025-205331711 Abstract This thesis presents a comprehensive study of multi-elemental abundances in galaxies across a wide range of stellar masses, star formation rates, and redshifts, aiming to better characterize mass-metallicity relations (MZRs) and to probe the physical processes that govern chemical enrichment in galaxies over cosmic time. Chapter 2 demonstrates that low- and high-mass stellar MZRs can be placed on a consistent absolute scale by comparing stellar metallicities from resolved and integrated-light spectroscopy in NGC 147, a Local Group dwarf galaxy. The two methods yield consistent [Fe/H] values, validating integrated-light techniques in measuring stellar metallicity in distant galaxies. In Chapter 3, I analyze deep Keck spectra of two gravitationally lensed, quiescent galaxies at z ~ 1. Both galaxies are metal-poor compared to local analogs but share comparable [Mg/Fe]. These results suggest that both galaxies experienced early, rapid star formation and strong outflows that depleted their gas reservoirs and drove early quenching. Chapter 4 introduces a new sample of 46 star-forming and 2 quiescent systems with M * = 10 8 –10 10 M ☉ at z ∼ 0, observed with the Keck Cosmic Web Imager (KCWI). Combining with SDSS data, I construct the first consistently derived Fe- and Mg-MZRs from 10 8 to 10 11.5 M * . I find that scatter in the stellar MZRs is driven by varying sSFR, with more active galaxies showing lower stellar abundances at fixed mass. This chapter also presents the first comparison of α elements (O and Mg) in stars and the ionized gas beyond the Local Group, revealing a tight [Mg/H] * –[O/H] g correlation. The finding that [O/H] g generally exceeds [Mg/H] * implies star formation is fueled by enriched, well-mixed interstellar medium rather than pristine gas inflows. Chapter 5 further explores spatially resolved nebular and stellar properties in the KCWI sample. Star-forming dwarfs exhibit clumpy star formation, diverse local ionization conditions, and smooth stellar mass profiles. Some show established gas-phase metallicity gradients, although diffuse ionized gas may bias gradient measurements. Together, these studies advance our understanding of how elemental abundances evolve across different galaxy masses and redshifts, offering new insights into the processes that regulate galaxy growth, enrichment, and quenching. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: galaxies; chemical abundances; stellar population; interstellar medium; dwarf galaxies; spectroscopy; mass-metallicity relation Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Astrophysics Thesis Availability: Public (worldwide access) Research Advisor(s): Steidel, Charles C. (advisor) Kirby, Evan N. (co-advisor) Group: Astronomy Department Thesis Committee: Ravi, Vikram (chair) Steidel, Charles C. Kirby, Evan N. Hopkins, Philip F. Martin, D. Christopher Kasliwal, Mansi M. Defense Date: 22 May 2025 Funders: Funding Agency Grant Number NASA FINESST Fellowship 80NSSC22K1755 NSF AST-1847909 Record Number: CaltechTHESIS:08112025-205331711 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08112025-205331711 DOI: 10.7907/5e14-b360 Related URLs: URL URL Type Description https://doi.org/10.3847/1538-4357/ac1340 DOI Article adapted for Ch. 2 https://doi.org/10.3847/1538-4357/acc79b DOI Article adapted for Ch. 3 https://doi.org/10.3847/1538-4357/ad5ff8 DOI Article adapted for Ch. 4 ORCID: Author ORCID Zhuang, Zhuyun 0000-0002-1945-2299 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17609 Collection: CaltechTHESIS Deposited By: Zhuyun Zhuang Deposited On: 21 Aug 2025 21:43 Last Modified: 28 Aug 2025 09:09 Thesis Files PDF - Final Version See Usage Policy. 25MB Repository Staff Only: item control page

Multi-Element Abundances as Probes of Galaxy Growth Across Cosmic Time Thesis by Zhuyun Zhuang In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2026 Defended May 22, 2025 ii © 2026 Zhuyun Zhuang ORCID: 0000-0002-1945-2299 All rights reserved iii To the brave little girl, who endured, who fought, who never gave up—this is the future you made possible. iv ACKNOWLEDGMENTS It has been nineteen years since I read my first book about astronomy, and more than a decade since I made up my mind to (at least try to) become an astronomer and earn a degree in astronomy from here. Even now, it feels almost surreal that this childhood dream is finally coming true. Along this long and winding journey, I have been extraordinarily fortunate to meet many wonderful people who have inspired, encouraged, and supported me through both hardship and triumph. This thesis is dedicated to all those incredible individuals, to whom I owe more thanks than words can express. First and foremost, to the best advisors I could have ever hoped for, Chuck Steidel and Evan Kirby. Evan has been a guiding light in my life since I joined his group in my first year. I am deeply grateful for his open-mindedness in allowing me to pursue the research directions I was genuinely passionate about, and for forgiving me for never being excited about r-process or s-process elements. He has always been patient, supportive, and generous with praise, even in moments when I struggled to believe in myself. Thank you, Evan, for listening to and tolerating my endless frustrations about research and life, and still encouraging me with unwavering belief. Being your student has been one of the greatest privileges of my graduate journey. My heartfelt thanks also go to Chuck, who generously took me in after Evan moved, and under whose mentorship I spent most of my PhD. I have been consistently inspired by Chuck’s brilliance, curiosity, and keen scientific insight. I’m especially grateful for him always being available for me, whether for research guidance or for last-minute feedback on paper drafts and proposals. Even though I sometimes complain that many of our two-hour conversations didn’t lead to definitive conclusions, I later find them incredibly enlightening and insightful, especially when I encounter new problems in my research or listen to other science talks at conferences. Those long conversations have truly shaped who I am as a researcher today. I am also grateful to both Evan and Chuck for their steadfast support in proposal writing and Keck observing runs, which have been among the most incredible and unforgettable experiences of my PhD. I extend my thanks as well to Rosalie McGurk and the Keck Observatory staff for their help during these observations. To the mentors and colleagues I’ve had the privilege of working with. Thank you to v Nicha Leethochawalit for patiently and repeatedly teaching me how to perform stellar population synthesis and full-spectrum fitting. I am grateful to Karl Glazebrook for introducing me to the world of lensed galaxies. Many thanks to Mia de los Reyes and Yuguang Chen for their invaluable guidance during my early years in graduate school, and to Allison Strom for inspiring conversations about chemical abundances and for always checking in on me whenever I stopped by CIERA. Special thanks to Nik Prusinski for his tremendous help with KCWI data reduction, and for the many soul-searching conversations that pulled me through difficult stretches of research. I am also deeply thankful to my undergraduate advisor, Yong Shi, the first astronomer I worked with and the one who introduced me to the world of observational extragalactic astronomy. To my thesis committee members — Chris Martin, Phil Hopkins, Mansi Kasliwal, and Vikram Ravi — and to the Caltech Astronomy faculty and staff, thank you for your thoughtful feedback on my thesis plan and for broadening my horizons in astronomy. I especially want to acknowledge Shri Kulkarni and Lin Yan for their early mentorship during my undergraduate research. To my friends at Caltech. Thank you, Yuhan, for your unwavering support and deep conversations over the years, and for always standing by me even after leaving Pasadena. Thank you, Samantha, Xiaoshan, and Mandy, for all the delicious food and boba, and for cheering me up in difficult times. Thank you, Yapeng, for listening with such patience to my worries, anxieties, and complaints, for the many late-night conversations, and for all the wonderful meals. To the rest of my cohort — Evan N., Yashvi, Viraj, Sarah, and Max — thank you for sharing the ups and downs of our first year, even amidst the challenges of the COVID lockdown. Thank you to Mia, Nik, Jerry, Jean, Ivey, Sam P., Zhihui, Yuanze, Isaac, and the rest of the incredible astrograd community for making my time at Caltech warmer and more vibrant. To my friends who have shaped different parts of my life. My deepest gratitude goes to Huanghao, one of my best friends since middle school and my roommate for most of my time at Caltech, who has incredibly shared eleven years of academic life with me. Thank you for inspiring me with your strength, brilliance, resilience, and optimism, for your unconditional support in my lowest moments and for sharing all the joys in this journey. I truly cannot imagine graduate school without you. I’m also deeply thankful to Yining for the countless deep conversations across the Pacific Ocean, and for the laughs and tears we’ve shared over the last decade. I’m so lucky we met on the very first day of college and have remained close ever since. vi Special thanks to Shihui and Yudan for accompanying me through the difficult years of my adolescence. My heartfelt gratitude also goes to Jiayi, my steadfast friend since before we could even walk. Thank you for always being there, and for being the person I can share absolutely everything with. To my loved ones. I owe everything to my mom Ying D., who has selflessly sacrificed so much for my education and my growth and supported me unconditionally, no matter what path I chose. Mom, you are the strongest, most resilient person in my life. None of this would have been possible without your seen and unseen love. Thank you, Guochao, for being my constant through every rise and fall. Thank you, truly, for everything. Lastly, to the little girl I once was, the one who dared to dream of the stars, even when the world around her felt dim. Her world was small, but her dreams were vast. Every step she took brought me here. Thank you for your courage, your persistence, and for believing in a future I now have the privilege to live. This PhD isn’t just mine; it’s yours, too. We made it. vii ABSTRACT This thesis presents a comprehensive study of multi-elemental abundances in galaxies across a wide range of stellar masses, star formation rates, and redshifts, aiming to better characterize mass–metallicity relations (MZRs) and to probe the physical processes that govern chemical enrichment in galaxies over cosmic time. Chapter 2 demonstrates that low- and high-mass stellar MZRs can be placed on a consistent absolute scale by comparing stellar metallicities from resolved and integrated-light spectroscopy in NGC 147, a Local Group dwarf galaxy. The two methods yield consistent [Fe/H]∗ values, validating integrated-light techniques in measuring stellar metallicity in distant galaxies. In Chapter 3, I analyze deep Keck spectra of two gravitationally lensed, quiescent galaxies at 𝑧 ≳ 1. Both galaxies are metal-poor compared to local analogs but share comparable [Mg/Fe]. These results suggest that both galaxies experienced early, rapid star formation and strong outflows that depleted their gas reservoirs and drove early quenching. Chapter 4 introduces a new sample of 46 star-forming and 2 quiescent systems with 𝑀∗ = 108 –1010 𝑀⊙ at 𝑧 ∼ 0, observed with the Keck Cosmic Web Imager (KCWI). Combining with SDSS data, I construct the first consistently derived Fe- and MgMZRs from 108 to 1011.5 𝑀⊙ . I find that scatter in the stellar MZRs is driven by varying sSFR, with more active galaxies showing lower stellar abundances at fixed mass. This chapter also presents the first comparison of 𝛼 elements (O and Mg) in stars and the ionized gas beyond the Local Group, revealing a tight [Mg/H]∗ –[O/H]g correlation. The finding that [O/H]g generally exceeds [Mg/H]∗ implies star formation is fueled by enriched, well-mixed interstellar medium rather than pristine gas inflows. Chapter 5 further explores spatially resolved nebular and stellar properties in the KCWI sample. Star-forming dwarfs exhibit clumpy star formation, diverse local ionization conditions, and smooth stellar mass profiles. Some show established gas-phase metallicity gradients, although diffuse ionized gas may bias gradient measurements. Together, these studies advance our understanding of how elemental abundances evolve across different galaxy masses and redshifts, offering new insights into the processes that regulate galaxy growth, enrichment, and quenching. viii PUBLISHED CONTENT AND CONTRIBUTIONS Zhuang, Z. et al. (Sept. 2024). “Metals in Star-forming Galaxies with KCWI. I. Methodology and First Results on the Abundances of Iron, Magnesium, and Oxygen”. In: ApJ 972.2, p. 182. doi: 10.3847/1538-4357/ad5ff8. Z.Z. participated in the conception of the project, obtained and analyzed the data, and wrote the bulk of the manuscript. Zhuang, Z. et al. (May 2023). “A Glimpse of the Stellar Populations and Elemental Abundances of Gravitationally Lensed, Quiescent Galaxies at z ≳ 1 with Keck Deep Spectroscopy”. In: ApJ 948.2, p. 132. doi: 10.3847/1538-4357/acc79b. Z.Z. participated in the conception of the project, obtained and analyzed the data, and wrote the bulk of the manuscript. Zhuang, Z. et al. (Oct. 2021). “NGC 147 Corroborates the Break in the Stellar Mass-Stellar Metallicity Relation for Galaxies”. In: ApJ 920.1, p. 63. doi: 10. 3847/1538-4357/ac1340. Z.Z. analyzed the data and wrote the bulk of the manuscript. ix TABLE OF CONTENTS Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Published Content and Contributions . . . . . . . . . . . . . . . . . . . . . . viii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Chapter I: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 The Role of Chemical Abundances in Galaxy Evolution . . . . . . . 1 1.2 Observational Approaches to Measuring Abundances . . . . . . . . 2 1.3 Open Questions in Chemical Evolution of Galaxies . . . . . . . . . . 6 1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Chapter II: Resolving the Discrepancy in the Stellar Mass–Metallicity Relation 16 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4 Global Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 Spatial Distributions of Stellar Population . . . . . . . . . . . . . . . 33 2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.8 Appendix: Comparison with CSP Models . . . . . . . . . . . . . . . 44 Chapter III: Stellar Abundances and Ages of Gravitationally Lensed, Quiescent Galaxies at 𝑧 ∼ 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2 Galaxy Sample and Data . . . . . . . . . . . . . . . . . . . . . . . . 51 3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Chapter IV: Metals in Star-Forming Galaxies with KCWI: Global Abundances 78 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.3 Emission-Line Measurements . . . . . . . . . . . . . . . . . . . . . 89 4.4 Stellar Abundance Determination . . . . . . . . . . . . . . . . . . . 94 4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4.8 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Chapter V: Metals in Star-Forming Galaxies with KCWI: Spatially Resolved Nebular and Stellar Population Properties . . . . . . . . . . . . . . . . . 131 x 5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 5.4 Appendix: KCWI Maps of the Entire Sample . . . . . . . . . . . . . 147 Chapter VI: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 6.2 Looking Forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 xi LIST OF ILLUSTRATIONS Number Page 1.1 Overview of stellar population synthesis . . . . . . . . . . . . . . . . 4 1.2 Example response functions of individual elements . . . . . . . . . . 5 1.3 Example MZR from the literature . . . . . . . . . . . . . . . . . . . 9 1.4 Physical processes shaping the MZR . . . . . . . . . . . . . . . . . . 10 2.1 DSS image of NGC 147 . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Example PCWI spectra and the best-fit models . . . . . . . . . . . . 27 2.3 Metallicity distribution for the resolved stars in NGC 147 . . . . . . 32 2.4 MZR measured from [Mg/H] at 𝑧 ∼ 0 . . . . . . . . . . . . . . . . . 33 2.5 Spatially resolved measurements of SSP parameters . . . . . . . . . 34 2.6 Metallicity gradient of NGC 147 . . . . . . . . . . . . . . . . . . . . 36 2.7 MZR measured from [Fe/H] at 𝑧 ∼ 0 . . . . . . . . . . . . . . . . . 41 2.8 Comparison between the measured [Fe/H] and stellar ages in different stellar population models . . . . . . . . . . . . . . . . . . . . . . . . 45 3.1 Color images of AGEL1323 and AGEL0014 . . . . . . . . . . . . . . . 52 3.2 HST/WFC3 color image of AGEL1323 . . . . . . . . . . . . . . . . . 55 3.3 Lens Modeling of AGEL1323 . . . . . . . . . . . . . . . . . . . . . . 56 3.4 Lens Modeling of AGEL0014 . . . . . . . . . . . . . . . . . . . . . . 57 3.5 Broadband SED fitting of AGEL1323 and AGEL0014 . . . . . . . . . 60 3.6 Observed spectrum and best-fit SSP model of AGEL1323 . . . . . . . 63 3.7 Observed spectrum and best-fit SSP model of AGEL0014 . . . . . . . 63 3.8 [Fe/H], [Mg/Fe] and [Mg/H] as a function of stellar mass for quiescent galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.9 Model spectra with different [Mg/Fe] near the Mg b triplet at ∼5170 Å 67 3.10 Dependence of [Fe/H], [Mg/Fe], and [Mg/H] on galaxy formation time 70 3.11 Mass-loading factor (𝜂) inferred from [Mg/H] as a function of stellar mass for quiescent galaxies . . . . . . . . . . . . . . . . . . . . . . . 72 4.1 SFR as a function of stellar mass of the star-forming and quiescent galaxies in the KCWI sample . . . . . . . . . . . . . . . . . . . . . 84 4.2 Example KCWI white-light image and the integrated spectrum . . . . 91 4.3 Illustration of the two-step approach . . . . . . . . . . . . . . . . . . 97 xii 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 5.1 5.2 5.3 5.4 Comparison of [Mg/Fe] for the massive SDSS quiescent galaxies measured from alf and from the two-step approach . . . . . . . . . 100 Comparison of [Fe/H] for the massive SDSS quiescent galaxies measured from alf and from the two-step approach . . . . . . . . . . . . 101 Comparison of stellar population ages for the massive SDSS quiescent galaxies measured from alf and from the two-step approach . . . . . 101 Comparison of gas-phase and stellar abundances . . . . . . . . . . . 104 Δ𝑍O,Fe as a function of different galaxy properties . . . . . . . . . . 106 Δ𝑍O,Mg as a function of different galaxy properties . . . . . . . . . . 107 MZRs of the KCWI sample . . . . . . . . . . . . . . . . . . . . . . 109 Stellar MZRs of dwarf and massive galaxies . . . . . . . . . . . . . 116 Fe-MZR of the KCWI sample measured from different apertures . . . 126 Mg-MZR of the KCWI sample measured from different apertures . . 127 Comparison of age derived from broadband SED and full-spectrum fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 SFR as a function of stellar mass of the KCWI and SDSS sample . . 129 O-MZR of the KCWI and SDSS sample . . . . . . . . . . . . . . . . 130 Comparison of an example sky-subtracted spectrum produced by the standard KCWI DRP and by KSkyWizard . . . . . . . . . . . . . . . 135 Comparison between the D4000 and light-weighted age for an example galaxy from the KCWI sample . . . . . . . . . . . . . . . . . . . 141 Example KCWI maps of physical properties . . . . . . . . . . . . . . 143 Example KCWI maps of emission line diagnostics . . . . . . . . . . 146 xiii LIST OF TABLES Number Page 2.1 PCWI Observations of NGC 147 . . . . . . . . . . . . . . . . . . . 20 2.2 Basic Properties of NGC 147 . . . . . . . . . . . . . . . . . . . . . 22 2.3 Metallicity Catalog for RGB Stars Observed with Keck/DEIMOS . . 25 2.4 Best-fit stellar population parameters for the stacked spectrum of NGC 147 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 Best-fit stellar population parameters for spatially resolved integrated spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.1 Spectroscopic and Photometric Observations of the Lensed Galaxies . 52 3.2 Stellar Population Properties of the Lensed Galaxies . . . . . . . . . 62 4.1 General Properties of the KCWI Galaxy Sample . . . . . . . . . . . 85 4.1 General Properties of the KCWI Galaxy Sample . . . . . . . . . . . 86 4.2 KCWI observations of the Galaxy Sample . . . . . . . . . . . . . . . 87 4.2 KCWI observations of the Galaxy Sample . . . . . . . . . . . . . . . 88 4.3 Emission-Line Parameters . . . . . . . . . . . . . . . . . . . . . . . 92 4.4 The Derived Properties of the KCWI Star-Forming Galaxies . . . . . 102 4.4 The Derived Properties of the KCWI Star-Forming Galaxies . . . . . 103 5.1 General Properties of the KCWI Galaxy Sample . . . . . . . . . . . 132 5.2 Emission-Line Parameters . . . . . . . . . . . . . . . . . . . . . . . 137 5.3 Definitions of Strong-line Ratios . . . . . . . . . . . . . . . . . . . . 139 1 Chapter 1 INTRODUCTION 1.1 The Role of Chemical Abundances in Galaxy Evolution One of the ultimate goals of science—and indeed of all intellectual pursuits—is to understand the existence of human beings as well as all other forms of life around us. As astronomers, one of the ways to answer this profound question is to decipher the universe’s remarkable ability to generate and distribute the elements heavier than hydrogen and helium—such as carbon, oxygen, magnesium, and iron—that are the building blocks of life. Unlike hydrogen and helium that were created within a few minutes after the Big Bang around 13.7 billion years ago, these heavy elements, often referred to as “metals” by astronomers, can only be created by stars. Stars act as cosmic furnaces where nuclear fusion converts hydrogen and helium into heavier elements up to iron. At the end of their life cycles, stars release metals into the interstellar medium (ISM) through supernova explosions or stellar winds, during which elements heavier than iron are produced. Some of these metals are recycled into the next generation of stars, some are expelled from galaxies by outflows driven by stellar feedback or galactic feedback, and others remain in the gas. Meanwhile, relatively pristine gas inflows consisting of little metals from the surrounding circumgalactic medium (CGM) can dilute the chemical abundances of the ISM while serving as fuel to sustain the continuing star formation. The dynamic processes of forming and redistributing these various heavy elements collectively result in an evolving chemical composition of stars and gas as star formation continues. That said, the chemical enrichment of a galaxy is shaped by the interplay among star formation, gas inflows and outflows, and feedback from supernovae and active galactic nuclei (AGN). By characterizing the elemental abundances in stars and gas of galaxies at different stages (i.e., described by their masses, ages, star formation rates, environments, etc.), we can reconstruct the overall galaxy assembly history, assess the efficiency of metal retainment and probe the timescales over which different enrichment processes operate. 1.1.1 Metals as Tracers of Galactic Evolution Different elements are synthesized in different types of stars and on varying timescales, making multi-element abundance measurements a powerful tool for constraining a 2 galaxy’s star formation and chemical enrichment history (see Nomoto, Kobayashi, and Tominaga, 2013, for a comprehensive review). Among the heavy elements, iron and oxygen are the most commonly measured. Iron is often used as a proxy for stellar metallicity due to the abundance of iron absorption features in stellar spectra, while oxygen serves as a tracer of gas-phase metallicity because it is the most abundant heavy element in the ISM and exhibits strong emission lines in the optical spectrum. When the signal-to-noise (S/N) in the stellar continuum is sufficiently high, magnesium abundances can also be measured, typically using the Mg b triplet near 5170 Å. Iron-peak elements are primarily produced by Type Ia supernovae, whose progenitors are usually low-mass stars or interacting binaries, with a characteristic delay timescale of ≳ 100 Myr, extending up to several Gyr (Maoz, Mannucci, and Brandt, 2012). On the other hand, massive stars with initial mass above 10𝑀⊙ end their short lives (∼ 10 Myr) as core-collapse supernovae, enriching the ISM with 𝛼 elements such as oxygen and magnesium. As a result, iron abundances tend to trace enrichment on longer timescales, while oxygen and magnesium reflect more recent chemical enrichment. Galaxies with extended star formation histories (SFH) typically exhibit lower [𝛼/Fe] or [Mg/Fe] ratios, because they have had sufficient time for iron enrichment from delayed Type Ia supernovae. 1.2 1.2.1 Observational Approaches to Measuring Abundances Stellar Abundances of Iron and Magnesium Stellar abundance measurements play an important role in understanding the chemical enrichment history of galaxies. There are two primary spectroscopic approaches for determining stellar chemical abundances: resolved stellar spectroscopy and integrated-light spectroscopy. Each approach has its own strengths and limitations, the choice between which largely depends on the distance of the target galaxy. In practice, it is typically not possible to apply both methods to the same system except in special cases, such as presented in Chapter 2. Resolved Stellar Spectroscopy In nearby galaxies, individual stars can be resolved and observed with mediumto high-resolution spectroscopy, enabling direct measurements of elemental abundances (such as iron and 𝛼 elements) in individual stars from absorption features in their stellar atmospheres. Large spectroscopic surveys like APOGEE (Majewski 3 et al., 2017), which use high-resolution infrared spectroscopy, have mapped multielement abundances across the Milky Way (Nidever et al., 2014; Hayden et al., 2015). Medium-resolution spectroscopy on large ground-based telescopes, such as the Keck telescopes, has also been used to determine the detailed abundances of red giant stars in dwarf satellite galaxies beyond the Milky Way (e.g., Kirby, Guhathakurta, and Sneden, 2008). Galactic metallicity is then determined as the luminosity-weighted value of metallicity distribution of individual stars. These resolved stellar abundance measurements reveal the metals locked into the stars formed at different epochs, providing the most detailed information on the chemical enrichment history of a galaxy. However, this method is limited to galaxies within the Local Group where most of the galaxies are dwarf satellites, as it is generally infeasible to resolve individual stars in more distant galaxies without gravitational lensing. Integrated-Light Spectroscopy For more massive and distant galaxies that cannot be resolved into individual stars, stellar metallicities must be inferred from integrated-light spectroscopy—that is, from the combined starlight of the entire stellar population. This method requires constructing spectral templates of galaxies (i.e., stellar population synthesis (SPS) models) to compare against observed spectra (Figure 1.1) and relies on many assumptions about the underlying stellar properties (see Conroy, 2013, for a comprehensive review). The simplest such model is the simple stellar population (SSP), which assumes that all stars formed at the same time with the same metallicity and abundance pattern. To construct SSPs across a range of ages and metallicities, one must adopt an initial mass function (IMF), choose stellar isochrones, and use either empirical or synthetic stellar spectral libraries. SSPs have been widely used to measure the ages and metallicities of quiescent galaxies (e.g., Choi et al., 2014; Kriek et al., 2016; Leethochawalit et al., 2018a), as their SFHs are relatively simple. Previous studies have shown that while SSP-based models tend to yield younger ages than those derived from more complex models (Choi et al., 2014), the inferred SSP metallicities are generally robust and consistent with the results measured with more realistic assumptions on the SFHs(Mentz et al., 2016; Leethochawalit et al., 2018a). For more complex systems like star-forming galaxies, which experience ongoing star 4 Figure 1.1: Overview of stellar population synthesis. (a) Ingredients used for constructing SSP models: an IMF, isochrones for a range of ages and metallicities, stellar spectra for of different spectral types. (b) Components needed for constructing CSP models: SFH and chemical evolution models, SSPs, and a model for dust attenuation and emission. Figure reproduced from Conroy (2013). 5 formation, composite stellar population (CSP) models are more appropriate. CSP is a linear combination of SSPs of different ages and metallicities, weighted according to an assumed SFH and chemical evolution history. Dust attenuation and emission can also be incorporated into these models to represent a more realistic galaxy. Because of the additional degrees of freedom, the derived ages and metallicities are more sensitive to the assumed SFH and chemical enrichment history. A common approach is to use either a parametric or non-parametric SFH while assuming a single metallicity for the population (e.g., Carnall et al., 2018; Leja et al., 2019), or to fit the observed spectra with a linear combination of SSPs spanning multiple ages and metallicities (e.g., Cid Fernandes et al., 2005; Cappellari, 2017). Both SSP and CSP models described above typically assume solar abundance patterns. To measure individual element abundances such as magnesium, models with variable abundance patterns must be constructed. This is commonly done using response functions, which quantify how the theoretical SSP spectrum changes with the enhancement or depletion of a given element relative to solar-scaled models (Conroy et al., 2018). Response functions for elements like Mg are computed at various ages and metallicities (Figure 1.2), and then applied to SSPs based on empirical stellar libraries. This hybrid approach enables more accurate modeling of observed spectra with non-solar abundance patterns, allowing for measurements of element ratios such as [Mg/Fe]. Figure 1.2: Response functions as a function of age and metallicity for Fe, Mg, and Ti. Each response function is defined as the ratio between two theoretical SSPs: one with a non-solar abundance of a single element, and the other with solar-scaled abundance ratios. Figure reproduced from Conroy et al. (2018). 6 1.2.2 Gas-Phase Oxygen Abundance Gas-phase oxygen abundance (i.e., gas-phase metallicity) is generally easier to measure than stellar abundances, as it can be inferred from nebular emission lines. Because oxygen is a primary coolant in photoionized gas, its abundance is closely tied to the electron temperature (𝑇𝑒 ): a more metal-rich ISM results in more efficient cooling and thus a lower electron temperature. The most and reliable method for measuring gas-phase metallicity is to use metal recombination lines (e.g., Esteban et al., 2014), but these lines too faint (∼ 10−4 of H𝛽) to be detected in a large statistical sample. The collision-excited auroral lines such as [O iii]𝜆4363 and [O ii]𝜆𝜆7320,7330 are much brighter than oxygen recombination lines, so they have been more widely used to measure the electron temperature of the high- and lowionization zones in H ii regions in order to infer the oxygen abundance (i.e., the direct 𝑇𝑒 method). However, these auroral lines are still much fainter than H𝛽 (∼ 10−1 − 10−2 of H𝛽) and become even weaker in high-metallicity environments where the gas is cooler, making them increasingly difficult to detect. As a result, obtaining 𝑇𝑒 -based metallicities for large samples of galaxies is observationally expensive, requiring long integration times on large telescopes. A more practical and widely used alternative is the strong-line method, which relies on brighter emission lines such as [O ii]𝜆𝜆3726,3729, [O iii]𝜆5007, [N ii]𝜆6585, and [S ii]𝜆𝜆6716,6731. The ratios between these metal lines and the Balmer lines are calibrated either empirically, using galaxies with direct 𝑇𝑒 -based measurements (e.g., McGaugh, 1991; Pettini and Pagel, 2004; Pilyugin and Thuan, 2005; Pilyugin and Grebel, 2016), or theoretically, through photoionization models (e.g., Tremonti et al., 2004). More recently, Bayesian frameworks have been developed to infer metallicities by comparing observed emission line fluxes directly to theoretical predictions of photoionization model grids (e.g., Blanc et al., 2015; Strom et al., 2022). Despite these advancements, different strong-line calibrations can yield oxygen abundances that differ by up to ∼0.7 dex (Kewley and Ellison, 2008), introducing significant systematic uncertainties in gas-phase metallicity estimates. 1.3 Open Questions in Chemical Evolution of Galaxies 1.3.1 Detailed Abundances Beyond the Local Group Over the past decade, significant progress has been made in measuring the detailed abundances of stars in dwarf satellite galaxies (e.g., Kirby et al., 2011b; de los Reyes et al., 2020) and in the ionized gas of individual H ii regions (e.g., Pilyugin and Thuan, 2005; Berg et al., 2020) within the Local Group, providing deeper 7 insights into the chemical evolution of nearby galaxies. However, compared to the detail with which we know the Local Group, we have only a surface understanding of the more distant field galaxies. The dearth of detailed abundance measurements results from the difficulty in determining the abundances of other elements precisely with integrated light spectra of distant galaxies. More recently, spectroscopic studies have turned to detailed abundances of galaxies beyond the Local Group using modern techniques such as full-spectrum fitting of the stellar continuum (e.g., Conroy et al., 2018), providing us with a deeper understanding of galactic chemical evolution. For instance, Leethochawalit et al. (2019) used the relation between stellar masses and [Mg/H] for quiescent galaxies to constrain the mass-loading factor of galactic outflows. Several works have also used [Mg/Fe] to probe the star formation timescale of quiescent galaxies at higher redshifts (e.g., Choi et al., 2014; Kriek et al., 2016). Some other studies on high𝑧 star-forming galaxies also use [O/Fe] as a stand-in for [𝛼/Fe] (e.g., Steidel et al., 2016), to constrain the star formation timescale because oxygen is also an 𝛼 element, when [Fe/H] of massive, young stars that just formed out of the ISM can be determined from the deep rest-frame UV spectroscopy1 . Apart from the detailed abundances of stellar populations at a given epoch, the connections between metals in the gas and stars can also reveal the chemical enrichment histories in star-forming galaxies. Gallazzi et al. (2005) measured the stellar metallicities and compared them with the gas metallicities for the same SDSS galaxies measured by Tremonti et al. (2004). They found that the stellar metallicities exhibit large scatter (at least 0.3 dex) at a fixed gas metallicities for SDSS galaxies. Because the residuals in stellar metallicities with respect to a simple linear fit of the median relation between stellar and gas metallicities show dependence on various galaxy properties (stellar mass, surface density, D4000, specific star formation rate, gas fraction and etc.), they attributed the large scatter observed should result from gas inflows and/or outflows rather than bias caused by the techniques used for stellar and gas metallicity estimates. Although we can indeed extract useful information from the comparison of stellar and gas metallicities, we should always proceed with caution. While the oxygen abundance represents the instantaneous metal enrichment of the ISM, the iron 1 [O/Fe] should not be used as a proxy of [𝛼/Fe] when [Fe/H] is determined from rest-optical spectrum. [Fe/H] measured in optical is sensitive to the metallicity of older, lower-mass stars, so [Fe/H] and [O/H] eventually trace chemical enrichment at different epochs. 8 abundance indicates the amount of metals locked inside the stars integrated over the past SFH. Because the two elements trace the metal content in different phases and formation timescales, it is dangerous to treat both Fe∗ to Ogas as an indicator of the same “metallicity” between galaxies of different SFHs. Fraser-McKelvie et al. (2022) introduced a new method to compare the metals in the two phases — converting the gas oxygen abundance into the iron-based metallicity using the scaling relations of Nicholls et al. (2017) based on the stellar abundance patterns in H ii regions of the Milky Way, Large Magellanic Cloud (LMC), and Small Magellanic Cloud — which they believe to be a better indicator as it removes the intrinsic discrepancies in the elemental abundances (Fe and O in their cases). However, they also admit that this method cannot fully remove the effects of SFH. Moreover, the scaling relations of Nicholls et al. (2017) between [O/H] and [Fe/H] are based on the abundance patterns of only three galaxies, so they still somewhat rely on the specific SFHs. A better way to connect metals in the stars and the ISM is to compare the stellarphase magnesium and the gas-phase oxygen. As they are both 𝛼 elements, their abundance ratio should be less affected by the SFHs than [O/Fe]. As Mg∗ and Ogas still represent the metals in different phases, they can inform us how the pristine inflows and/or enriched outflows can affect the metals in galaxies. In addition, comparing the [Mg/Fe]∗ and [O/Fe] for the same galaxies would allow us to know whether the commonly-used 𝛼-enhancement indicator [O/Fe] in the studies of starforming galaxies at all redshifts needs any systematic corrections. However, prior to this thesis, no studies had directly compared Mg∗ and Ogas in distant galaxies beyond the Local Group, because it is extremely challenging to measure Mg∗ in highly star-forming galaxies. Such measurements require new SPS models that account for non-solar abundance patterns at young ages, as well as the detection of Mg-sensitive absorption features, which are significantly fainter in young, star-forming stellar populations. In Chapter 4, I develop a novel method to characterize Mg∗ in actively star-forming galaxies, by applying the latest SPS models to a new high-quality dataset of low-mass star-forming dwarf galaxies, enabling the first-ever comparison of 𝛼 elements in the ionized gas and stars beyond the Local Group. 9 1.3.2 The Stellar Mass–Metallicity Relation (MZR) and Its Challenges The most direct way to link measured metallicity (either stellar or gas-phase) to a galaxy’s evolutionary history is by positioning the sample on the stellar mass– metallicity relation (MZR). In the past few decades, numerous studies have revealed the tight correlation between the stellar masses (luminosities) and the metallicities of galaxies, i.e., the MZR (e.g., Lequeux et al., 1979b; Tremonti et al., 2004; Gallazzi et al., 2005; Kirby et al., 2013; Leethochawalit et al., 2019). Figure 1.3: Example MZR from the literature. Left: Gas-phase MZR measured as the oxygen abundance in the ISM for the SDSS galaxies. Right: Stellar MZR measured as the iron abundance in the stellar population for the Local Group satellites and the SDSS galaxies. Figures reproduced from Tremonti et al. (2004) and Kirby et al. (2013). The observed MZR (Figure 1.3) indicates that more massive galaxies are more metalrich than less massive ones. The trend can be interpreted as a result of differences in metal retention, wherein high-mass galaxies with deep gravitational potential wells can resist galactic winds and retain more metals (Dekel and Silk, 1986). Recent works have argued that the interplay between accretion, outflow, and star formation may also shape the MZR (e.g., Finlator and Davé, 2008; Calura et al., 2009; Magrini et al., 2012). Figure 1.4 summarizes key physical processes shaping the MZR. The shape of the MZR, especially the slope, is particularly interesting because changes in the MZR slope indicate how the physical processes governing metal retention and the interaction with the surrounding environment vary as galaxies grow in mass. However, determining the exact shape of the MZR across the full range of galaxy mass is still challenging due to the diverse approaches used to measure stellar and gas-phase metallicity in different mass regimes (see Section 1.2 for more details). 10 Figure 1.4: A schematic diagram illustrating the key physical processes that shape the MZR. Star formation synthesizes heavy elements, increasing both stellar mass and metallicity. Metal-poor inflows initially dilute gas metallicity but also sustain star formation, ultimately contributing to chemical enrichment. Metal-enriched outflows can remove metals from the galaxy. Over time, the metallicity reaches equilibrium with supernova yields, preventing further enrichment despite continued star formation. Even if the gas-phase MZR is easier to measure from emission lines, the discrepancies between different metallicity calibrations used in different mass regimes (as discussed in Section 1.2.2) can significantly impact both the slope and normalization of the measured MZR. Most studies have found that the gas-phase MZR has a steep slope in the low-mass regime and flattens at the high-mass end in the local universe, regardless of the calibration used to measure metallicity (e.g., Tremonti et al., 2004; Andrews and Martini, 2013; Blanc et al., 2019). However, the transition in the slope of the gas MZR at ∼ 109 𝑀⊙ is controversial due to the large systematic errors in different techniques used to measure gas metallicity. While most previous work has revealed a smooth transition in the slope of gas MZR (e.g., Tremonti et al., 2004; Andrews and Martini, 2013), Blanc et al. (2019) found that the slope steepens significantly around 𝑀∗ ≃ 109.5−10.1 𝑀⊙ and flattens again at a higher stellar mass, suggesting a sharp transition in how galaxies retain their metals with increasing mass. Similarly, the stellar MZR at 𝑧 ∼ 0 derived from resolved stellar spectroscopy for satellites (𝑀∗ ≲ 108 𝑀⊙ ; Kirby et al., 2013) does not reconcile with that of the massive ellipticals derived from integrated-light spectroscopy (𝑀∗ ≳ 109.5 𝑀⊙ ; Leethochawalit et al., 2019), with the latter exhibiting a much flatter slope and higher 11 normalization. This discrepancy may reflect a real physical transition in the stellar MZR between low- and high-mass galaxies, possibly driven by changes in feedback processes that shape the relation (Finlator and Davé, 2008), or it may result from systematic differences between the two measurement techniques, similar to the wellknown calibration offsets in gas-phase metallicity indicators. Therefore, a direct comparison of stellar metallicities derived using both resolved and integrated-light approaches is needed to resolve this issue. Moreover, prior to this thesis, there were few precise measurements of the stellar MZR for individual intermediate-mass galaxies (108 < 𝑀∗ /𝑀⊙ < 109 ) in the local universe, making it difficult to determine the exact shape of the stellar MZR between low- and high-mass regimes. This gap largely originates from the challenge of measuring stellar metallicities in the highly star-forming galaxies that dominate this mass range (Tomczak et al., 2014). First, young, massive stars that contribute significantly to the integrated light of a galaxy lack prominent metal absorption lines useful for stellar abundance determination. Second, bright nebular emission lines originating from the ionized gas make it harder to measure the Balmer absorption lines precisely to determine the age of the stellar population. Therefore, deep spectroscopy of highly star-forming dwarfs and advanced SPS models are necessary to disentangle this problem. Another key question is whether the stellar MZR evolves with redshift, and if so, how. While the redshift evolution of the gas-phase MZR has been well established out to 𝑧 ∼ 2–3 (Sanders et al., 2021; Strom et al., 2022), the stellar MZR has only been studied in a large statiscal sample up to 𝑧 ∼ 0.7 (Leethochawalit et al., 2018a; Leethochawalit et al., 2019; Beverage et al., 2023). This dearth of data is largely due to the observational challenge of measuring stellar abundances in high-𝑧 quiescent galaxies, whose stellar absorption features are extremely faint. Obtaining spectra with sufficient S/N for abundance measurements typically requires 10-20 hours of integration time on large 8-10 m ground-based telescopes to analyze a single galaxy. Therefore, astronomers must either leverage the unprecedented capabilities of the James Webb Space Telescope (JWST), or combine innovative strategies like gravitational lensing with easier access to large ground-based facilities. Chapter 2 and Chapter 4 demonstrate the new progress made to better characterize the shape of the stellar MZR measured from different elements at 𝑧 ∼ 0 across the full range of galaxy masses. Chapter 3 presents new measurements of stellar abundances and abundance ratios of gravitationally lensed, quiescent galaxies at 12 𝑧 ≳ 1. 1.3.3 Spatial Distribution of Ionized Gas and Stellar Population in Dwarf Galaxies To fully understand how galaxies grow and evolve into the states we observe today, it is necessary not only to capture the global trends of galaxies across different evolutionary stages using large samples, but also to resolve the internal processes that shape their structures. The development of integral field unit (IFU) spectroscopy has provided a powerful tool for studying the physical mechanisms that drive galaxy evolution on local scales, offering spatially resolved views that connect global galaxy properties to their internal structures and kinematics. Over the past decade, large IFU surveys such as MaNGA (Bundy et al., 2015), SAMI (Croom et al., 2012), and CALIFA (Sánchez et al., 2012) have revolutionized our understanding of galaxy evolution by delivering resolved maps of stellar and nebular properties across thousands of galaxies in the low-redshift universe. These surveys have uncovered a number of general trends in galaxies with stellar masses above 109 𝑀⊙ . Many of the scaling relations first established on global scales through slit and fiber spectroscopy, such as the star-forming main sequence and the gas-phase MZR, have been shown to hold even at kpc scales (Sánchez et al., 2013). Radial gradients in stellar population age, stellar and gas-phase metallicity, and SFR have been reported in massive galaxies by multiple IFU surveys (e.g., González Delgado et al., 2016; Goddard et al., 2017; Belfiore et al., 2017; Lian et al., 2018a; Zibetti et al., 2020). Spatially resolved maps of nebular emission-line ratios also reveal that ionization conditions can vary significantly across different regions within a galaxy. Actively star-forming regions hosting massive OB stars exhibit distinct line ratios compared to regions dominated by diffuse ionized gas (DIG), where hot evolved stars are thought to be the primary ionizing sources (Belfiore et al., 2015; Zhang et al., 2017). As a result, contributions from the DIG can bias gas-phase metallicity measurements if not properly accounted for (Sanders et al., 2017; Vale Asari et al., 2019). Despite these advances, many published analyses group galaxies into bins—by stellar mass, SFR, morphology, or specific line ratios—and average all spaxels within a bin to improve S/N and extract robust population-wide trends. While this strategy successfully reveals general behaviors, it tends to obscure the rich internal diversity that can exist even among galaxies with similar global properties. In 13 particular, rare or unusual spatial trends, present only in a small fraction of galaxies, are often lost in the averaging process. This limitation becomes especially pronounced when studying dwarf galaxies. Their shallow gravitational potentials make them more susceptible to both internal feedback and external environmental effects. Hydrodynamical simulations predict that star formation in dwarf galaxies proceeds in a bursty, stochastic manner (Hopkins et al., 2023), disrupting the coherent radial gradients commonly observed in more massive galaxies. Therefore, the diversity among dwarf galaxies offers a valuable testbed for studying how feedback, chemical evolution, and environmental interactions affect galaxies on an individual basis. To answer this question, I have led an observational program to obtain IFU data for a sample of low-mass, star-forming galaxies at 𝑧 ∼ 0, using the Keck Cosmic Web Imager (KCWI)—an integral field spectrograph mounted on one of the world’s largest ground-based optical telescopes. In Chapter 5, I present the first results on the spatially resolved properties of ionized gas and stellar populations in these dwarf galaxies. 1.3.4 Stellar Populations and Chemical Abundances at 𝑧 ≳ 1 Not only can we learn the chemical evolution of nearby galaxies from the detailed abundances, but chemical constraints of high-𝑧 galaxies from deep spectroscopy also provide a unique opportunity to understand how and when galaxies form stars and quench in the early universe. The majority of stellar mass in the universe at 𝑧 = 0 resides in the “red sequence” (i.e., passive galaxies), but most of those galaxies were star-forming at 𝑧 > 1. Nonetheless, some of these galaxies were quenched at a lookback time over half of the age of the universe. A full understanding of the end phase of galaxy evolution requires that we examine the galaxies that ceased star formation relatively early. At high redshifts, most chemical studies have focused on the gas abundances of starforming galaxies measured from nebular emission lines, which trace the chemical compositions of the ISM at the time of observation and is affected by both star formation and gas inflows/outflows (e.g., Finlator and Davé, 2008; Strom et al., 2022). On the other hand, characterizing the stellar absorption lines and the overall continuum shape of high-𝑧 quiescent galaxies, which encode valuable information on the age, stellar abundances and SFH, is much more challenging and invariably requires much deeper spectroscopy due to the faintness of the stellar continuum. 14 Prior to the launch of JWST and the work presented in this thesis, only five quiescent galaxies at 𝑧 ≳ 1 had detailed abundance and age measurements (Kriek et al., 2016; Kriek et al., 2019; Jafariyazani et al., 2020), and all of them had especially large stellar masses: 𝑀∗ > 1010.6 𝑀⊙ . Gravitational lensing provides a powerful tool to obtain high-quality spectra of faint, high-𝑧 quiescent galaxies. By boosting both their apparent brightness and angular size, lensing enables detailed studies with imaging and spectroscopy that would otherwise be infeasible. With the advent of machine learning techniques, an increasing number of strongly lensed systems at high redshift have been identified in deep imaging surveys (e.g., Jacobs et al., 2019b). The time is now ripe to spectroscopically follow up these rare, lensed quiescent galaxies at 𝑧 ≳ 1 to deepen our understanding of galaxy formation and chemical enrichment in the early universe. In Chapter 3, I present a detailed spectral analysis of lensed, quiescent galaxies in the high-𝑧 universe to probe galaxy evolution in the early universe. 1.4 Thesis Outline This thesis is organized into four main science chapters, each addressing a key aspect of measuring and interpreting chemical abundances in galaxies using integratedlight spectroscopy. Chapter 2 investigates whether integrated-light spectroscopy can recover reliable stellar metallicities by comparing integrated and resolved measurements of NGC 147, a dwarf elliptical satellite of M31, offering insight into the stellar MZR at 𝑧 ∼ 0 across the full range of galaxy masses. Chapter 3 presents a detailed spectral analysis of two gravitationally lensed quiescent galaxies at 𝑧 ≳ 1 observed with the Keck telescopes. Using the integrated-light spectroscopy and full-spectrum fitting validated in Chapter 2, the analysis yields robust measurements of [Fe/H], [Mg/Fe], and stellar population ages, enabling a study of the redshift evolution of the stellar MZR and offering insights into the processes responsible for quenching galaxies in the early universe. Chapter 4 presents a new sample of star-forming dwarf galaxies observed with Keck/KCWI, to further investigate the shape of the stellar MZR in the intermediatemass regime between the Local Group satellites and massive field ellipticals at 𝑧 ∼ 0. Using a novel technique I developed to measure stellar iron and magnesium abundances in star-forming galaxies, this chapter also provides the first direct 15 comparison of 𝛼 elements (gas-phase O and stellar Mg) in both stars and the ISM beyond the Local Group. Chapter 5 extends the analysis of the KCWI sample presented in Chapter 4 to investigate the spatially resolved properties of ionized gas and stellar populations in star-forming dwarf galaxies at 𝑧 ∼ 0. Preliminary results show that these galaxies host short-lived, irregular, and clumpy star formation, accompanied by significant spatial variation in local ionization conditions. In contrast, the time-integrated stellar mass profiles appear much smoother, reflecting a more organized underlying structure. Finally, in Chapter 6, I summarize the main results of this thesis and discuss potential avenues for future research into the chemical evolution of galaxies and the interplay between ionized gas and stellar populations. 16 Chapter 2 RESOLVING THE DISCREPANCY IN THE STELLAR MASS–METALLICITY RELATION Zhuang, Z. et al. (Oct. 2021). “NGC 147 Corroborates the Break in the Stellar Mass-Stellar Metallicity Relation for Galaxies”. In: ApJ 920.1, p. 63. doi: 10. 3847/1538-4357/ac1340. Abstract The stellar mass-stellar metallicity relation (MZR) is an essential approach to probing the chemical evolution of galaxies. It reflects the balance between galactic feedback and gravitational potential as a function of stellar mass. However, the current MZR of local dwarf satellite galaxies (𝑀∗ ≲ 108 𝑀⊙ , measured from resolved stellar spectroscopy) may not be reconcilable with that of more massive galaxies (𝑀∗ ≳ 109.5 𝑀⊙ , measured from integrated-light spectroscopy). Such a discrepancy may result from a systematic difference between the two methods, or it may indicate a break in the MZR around 109 𝑀⊙ . To address this question, we measured the stellar metallicity of NGC 147 from integrated light using the Palomar Cosmic Web Imager. We compared the stellar metallicity estimates from integrated light with the measurements from resolved stellar spectroscopy and found them to be consistent within 0.1 dex. On the other hand, the high-mass MZR overpredicts the metallicity by 0.6 dex at the mass of NGC 147. Therefore, our results tentatively suggest that the discrepancy between the low-mass MZR and high-mass MZR should not be attributed to a systematic difference in techniques. Instead, real physical processes cause the transition in the MZR. In addition, we discovered a positive age gradient in the innermost region and a negative metallicity gradient from the resolved stars at larger radii, suggesting a possible outside-in formation of NGC 147. 2.1 Introduction In the past few decades, numerous works have revealed the tight correlation between the stellar masses (luminosities) and the metallicities of galaxies, i.e., the stellar mass-metallicity relation (MZR) (e.g., McClure and van den Bergh, 1968; Lequeux et al., 1979a; Tremonti et al., 2004; Lee et al., 2006; Kirby et al., 2013; Leethochawalit et al., 2018b). The observed MZR indicates that more massive 17 galaxies are more metal-rich than less massive ones. The trend can be interpreted as a result of metal retention, wherein high-mass galaxies with deep gravitational potential wells can resist galactic winds and retain more metals (Dekel and Silk, 1986). Recent works have argued the metallicity may also be regulated by star formation efficiency (e.g., Calura et al., 2009; Magrini et al., 2012) as well as by the interplay between inflow, outflow, and enrichment (Finlator and Davé, 2008). Generally, galactic metallicities are measured in two forms: gas-phase and stellarphase. While gas-phase metallicity reflects the metals in the interstellar medium (ISM) at the time of observation, stellar metallicity indicates the amount of metals incorporated into the stars at the time they formed, which is less susceptible to instantaneous fluctuations and represents the metal abundance averaged over the star formation history (SFH). Therefore, the stellar MZR is a more stable indicator of the chemical evolution of galaxies than the gas-phase MZR. The MZR1 at 𝑧 ∼ 0 can be measured from two independent techniques. Local dwarf galaxies can be resolved into stars, so their stellar metallicities are derived from spectroscopy of individual stars (e.g., Kirby et al., 2013). On the other hand, more massive galaxies are too far for us to resolve the stars. Therefore, metallicities are obtained from the integrated-light spectra of whole galaxies (e.g., Gallazzi et al., 2005; Zahid et al., 2013; Leethochawalit et al., 2018b; Leethochawalit et al., 2019). Although the low-mass and high-mass MZRs both indicate more massive galaxies are more metal-rich, they follow different forms of expression. Kirby et al. (2013, hereafter K13) used Geha et al.’s (2010) Keck/DEIMOS spectra to derive the low-mass MZR from resolved stellar spectroscopy in Local Group dwarf galaxies (𝑀∗ ≲ 108 𝑀⊙ )2 as [Fe/H] ∝ 𝑀∗0.30±0.02 , while Leethochawalit et al. (2019, hereafter L19) measured the high-mass MZR from integrated-light spectra of local massive quiescent galaxies (𝑀∗ ≳ 109.5 𝑀⊙ ) as [Fe/H] ∝ 𝑀∗0.11±0.02 . Choi et al. (2014) similarly observed a flat slope in the high-mass MZR, where the metallicities for massive quiescent galaxies (𝑀∗ ≥ 1010.6 𝑀⊙ ) in the local universe were measured from the stacked spectra in bins of stellar mass. Sybilska et al. (2017) estimated the stellar metallicities for 258 nearby massive quiescent galaxies (𝑀∗ ≳ 109.8 𝑀⊙ ) in the ATLAS3D survey (Cappellari et al., 2011) using spectrophotometric indices. They also recovered a high-mass MZR similar to that of L19. All these studies indicate a shallower slope and higher normalization in the high-mass MZR than in 1 In this paper, MZR refers to the stellar-phase MZR, if not otherwise specified. 2 K13 measured the stellar metallicities of both quiescent and star-forming dwarf galaxies, but they found no difference in the MZR between these two groups. 18 the low-mass MZR, such that an extrapolation of the high-mass MZR to low mass would predict much higher metallicities than are observed in low-mass galaxies. One possible explanation for the discrepancy is that there is a physical break in the MZR around 108 − 1010 𝑀⊙ . This behavior would mimic the gas-phase MZR, which follows a single power law at low to intermediate masses (106 𝑀⊙ ≲ 𝑀∗ ≲ 109.5 𝑀⊙ ), and flattens at the high-mass end (e.g., Blanc et al., 2019). The possible transition may result from different feedback mechanisms of the two mass ranges. Theoretically, it has been suggested that energy-driven winds dominate in lowmass galaxies (Murray, Quataert, and Thompson, 2005), while momentum-driven winds dominate in high-mass galaxies (Hopkins, Quataert, and Murray, 2012). Finlator and Davé (2008) also suggested that the observed gas-phase MZR at 𝑧 ∼ 2 for massive galaxies indicates the momentum-driven winds are dominant in the outflows of high-mass galaxies. Such a transition in the slope of the stellar MZR was seen by Sybilska et al. (2017), who found that the slope around 109.5 𝑀⊙ steepens significantly as compared to that at the lowest and highest masses. However, the stellar MZR derived by Sybilska et al. (2017) does not go below 109 𝑀⊙ , so it cannot fill the mass gap in the stellar MZR and capture the behavior of the MZR across the full range of galaxy masses. The existing measurements in the mass gap are too scarce to constrain the intermediate-mass stellar MZR. However, the discrepancy in the MZRs may also result from a systematic difference between the two techniques used to measure stellar metallicities. Previous works that tested the consistency between the stellar population parameters—including the metallicities—among various measurement methods have mainly focused on simple systems like globular clusters e.g., González Delgado and Cid Fernandes, 2010; Conroy, Graves, and van Dokkum, 2014; Conroy et al., 2018. So far, only Ruiz-Lara et al. (2018) have compared the metallicity of each SFH age bin obtained from the integrated-light spectrum of Leo A, a star-forming dwarf irregular (dIrr) galaxy with 𝑀∗ ∼ 3 × 106 𝑀⊙ , with that measured by Kirby et al. (2017) from individual stars. They found that the integrated-light [Fe/H] at all age bins is higher than the resolved-star [Fe/H]. The differences in [Fe/H] range from ∼ 0.25–1.5 dex. However, the differences here can be explained by other reasons, such as the inaccurate modeling of Balmer nebular emission lines, the incompleteness of metal-poor stars in the current stellar libraries, or a negative metallicity gradient, as suggested by Kirby et al. (2017). In this work, we focus on NGC 147, a dwarf elliptical (dE) satellite of M31 with 19 𝑀∗ ≃ 108 𝑀⊙ (K13). This galaxy is a good target to investigate possible systematic differences between different techniques of measuring stellar metallicities. First, the galaxy is near enough (712 kpc; Conn et al. 2012) to obtain individual stellar metallicities but also far enough to be observed in integrated light with an integral field unit (IFU). Second, no H i gas has been detected in NGC 147, so the spectrum is free from nebular emission line contamination. Third, NGC 147 is more metalrich than Leo A, so it will suffer less from the incompleteness of metal-poor stars in the current stellar libraries. The main goals of this paper are (1) to determine whether there is a systematic offset between integrated-light and resolved-star spectroscopic measurements of NGC 147’s stellar metallicity, (2) to use these measurements to bolster or diminish the evidence of a break in the stellar MZR, and (3) to leverage IFU data cubes to study the spatial distribution of the stellar population in the innermost region. We use both new IFU data cubes and archival resolved-star spectra (Section 2.2). We use a variety of full spectral fitting algorithms (Section 2.3) to estimate the global stellar metallicity and age from integrated light (Section 2.4). Section 2.4.2 specifically addresses goal (1) in determining the consistency between the two different metallicity techniques. We also present some interesting spatial trends of the stellar population that suggest that NGC 147 formed outside in (Section 2.5). We compare our work with the previous literature on the stellar metallicity determinations and discuss the subsequent implications for the MZR (goal 2) in Section 2.6. Finally, we summarize our findings in Section 2.7. 2.2 2.2.1 Observations Palomar Cosmic Web Imager Sample Observations and data reduction Observations for NGC 147 were performed with the Palomar Cosmic Web Imager (PCWI) on 2019 September 23 and 24. PCWI is a medium-resolution integral field spectrograph (IFS) mounted on the Cassegrain focus of the Palomar 200-inch Hale Telescope with a field of view of 60′′ × 40′′. It consists of 24 spatial slices with a width of ∼ 2.5′′ and an in-slice pixel scale of ∼ 0.5′′. The seeing was around 2′′ for two nights, so both the spatial axis along each slice and spectral 𝑧-axis are seeing-limited while the spatial axis across the slices was slit-limited. NGC 147 has an effective radius (𝑅eff ) of ∼ 6.7′, which means that a single PCWI pointing covers only a small portion of the galaxy. We observed the central regions of the galaxy 20 within 2′ with three pointings (Figure 2.1), as described in Table 2.1. Table 2.1: PCWI Observations of NGC 147 Central R.A. (J2000) 00 33 12.223 Decl. (J2000) +48 30 27.341 Surface Brightness𝑎 (g-band mag arcsec −2 ) 21.32 South 00 33 08.561 +48 29 14.526 21.59 North 00 33 15.570 +48 31 48.328 21.58 Pointing Central Wavelength (Å) 4300 5140 4300 5140 5140 Date 2019 Sep 23 2019 Sep 23 2019 Sep 23 2019 Sep 24 2019 Sep 24 Exposure Time (s) 6 × 900 6 × 900 4 × 900 5 × 900 6 × 900 Some observations lacked quality sufficient for this study. This table does not include those observations. a Derived from the best-fit surface brightness profile for diffuse light in Crnojević et al. (2014). The MEDREZ grating was used to provide the largest spectral range (∼ 900Å) that PCWI offers and a resolution of 𝑅 ≃ 1500. With two configurations centered at 4300 Å and 5140 Å, respectively, the spectra span from 3750 Å to 5550 Å, which is sufficient to measure age, metallicity, and Mg enhancement via full-spectrum fitting (Leethochawalit et al., 2018b; Leethochawalit et al., 2019). Figure 2.1: Digitized Sky Survey (DSS) image of NGC 147. The red rectangles show the three PCWI fields observed. The dashed circle indicates the circular effective radius. The pink circles show locations of the RGB star samples used in this study. Because the galaxy is larger than the field of view of PCWI, additional off-field blank-sky observations were taken adjacent to each science observation with the same exposure time for sky subtraction. The weather was cloudy with the Moon 21 up in the late half of the second night, leading to significant variance in the sky spectra. Therefore, we had to abandon all science frames of the blue side of the north pointing due to inaccurate sky subtraction. Table 2.1 lists all the observations used in this study. The raw data were reduced using the standard PCWI Data Reduction Pipeline (DRP)3 . This pipeline converts raw, 2D science frames into flux-calibrated, 3D cubes with spatial positions and wavelengths. PCWI is subject to gravitational flexure because it is mounted at the Cassegrain focus. Flexure induces minor changes in the spectrum, such as alteration of the wavelength solution. Flexure correction in the PCWI DRP relies on cross-correlation of a time series of data cubes. However, the spectral offsets were not completely eliminated after the flexure correction. We recalibrated the wavelength solution by cross-correlating the spatially collapsed spectra of each image with the sky spectrum taken nearest to the night calibration set. In this way, the wavelength solution was standardized to a common reference. We applied only a constant offset and ignored higher-order terms. The world coordinates of each cube were corrected with CWITools (O’Sullivan and Chen, 2020) via comparing the location of known foreground point sources with accurate R.A. and Decl. The sky frames were subtracted from the adjacent science frames directly to obtain the sky-subtracted cubes. The sky-subtracted cubes were coadded using CWITools, which calculates the footprint of each input pixel on the coadd frame and distributes flux onto the coadd grid. The instrumental resolution was measured by fitting the widths of arc lines as a function of wavelength. PCWI uses a ThAr lamp, which gives a dense spectrum of emission lines. As a result, some arc lines were blended. We restricted the arc line list to isolated arc lines in order to eliminate the bias introduced by blended lines. We identified isolated arc lines by setting thresholds on the first and second derivatives of the arc flux. First, we required that the first derivative must be close to zero and that the second derivative must be negative, in order to find the locations of the line peaks. Second, we required that the peak must be sharp rather than having a flat or broadened feature. This means that the first derivative must abruptly change from positive to negative, i.e., that the second derivative must be smaller than some threshold. We experimented with different combinations of the thresholds and visually inspected the result. We found that setting the first derivative of the spectrum to be smaller than 0.2 and the second derivative to be smaller than −0.01 3 PCWI DRP: https://github.com/scizen9/pderp 22 Table 2.2: Basic Properties of NGC 147 R.A. (J2000) 00 33 12.1 Decl. (J2000) +48 30 31 𝑀V (mag) -15.33 𝑚i,TRGB (mag) 20.82+0.08 −0.08 𝑑MW (kpc) 712+21 −19 𝑅eff (arcmin (kpc)) 6.70 (1.41) 𝜎𝑣 (km s −1 ) 16 ± 1 log( 𝑀∗ /𝑀⊙ ) (dex) 8.00 ± 0.05 [Fe/H] (dex) −0.83 ± 0.25 The columns show (1–2) the equatorial coordinates from NED for the galaxy center; (3-6) the absolute total 𝑉 magnitude, the apparent TRGB 𝑖 -band magnitude, the de-projected distance from the Milky Way (MW), and the effective radius taken from Crnojević et al. (2014); (7) the velocity dispersion measured from the resolved stars (Geha et al., 2010); and (8-9) the stellar mass and stellar metallicity obtained from the resolved RGB stars taken from K13. provides relatively clean isolated lines. The FWHMs of the isolated lines were then fitted into a quadratic polynomial to obtain the resolution (≃ 3.27 Å or 90 km s−1 ). However, there was still a slight offset between the blue and red spectra, as we only applied first-order correction. Instead of fitting for the higher-order terms, we transformed the observed wavelengths into the rest frame separately for both wavelength settings. The spatially collapsed spectra of each cube were extracted from the sky-subtracted cubes. We then cross-correlated them with a template galaxy spectrum that was smoothed to the PCWI resolution and re-sampled to the wavelength grid of our data using SpectRes (Carnall, 2017). A template with a simple stellar population (SSP) was generated from the Flexible Stellar Population Synthesis (FSPS) (Conroy, Gunn, and White, 2009; Conroy, White, and Gunn, 2010), based on the physical properties of NGC 147 listed in Table 2.2. Because NGC 147 has an extended SFH that ended ∼ 4 Gyr ago, we adopted a stellar population age of 8 Gyr, which approximately corresponds to the average age of the stellar population (Weisz et al., 2014). We conducted further analyses only on the rest-frame spectra. Foreground Star Masking As shown in Figure 2.1, some bright foreground stars are located in the field of PCWI. We masked them before the spectrum extraction to avoid contamination of the galaxy spectrum. The masking regions were determined from the white-light image. For NGC 147, the tip of the red giant branch has an 𝑖-band magnitude of ∼ 20.82 (Crnojević et al., 2014), so even the brightest star members would be too faint to be detected individually by PCWI. Therefore, any resolved stars in the field were considered foreground stars. We used the DSS image to identify the foreground stars. For each pointlike source on the DSS image within the PCWI field, we modeled its point spread function (PSF) on the white-light image assuming a 2D elliptical Gaussian profile. The point-source mask was determined as a circle centered at the fitted peak, with a radius of three times the fitted semi-major axis. Nevertheless, 23 some bright residuals, which may be related to scattered light, were still present in the field. We masked all the regions above 1.35 times the median. We also experimented with several thresholds, and it turned out that 1.35 times the median removed most of the bright extended features, which might have contaminated the spectra, while leaving most of the galaxy contribution. Spectrum Extraction IFS data are known to underestimate the variance due to the covariance between adjacent spaxels. This effect originates from the redistribution of the flux from the same pixel onto a new spatial grid when coadding or smoothing the data cubes. When we coadded the single-exposure cubes, the flux within the same slice with a width of ∼ 2.5 arcsec was redistributed again into the final coadded image with a pixel scale of 0.58 arcsec. Therefore, the signal-to-noise ratio (S/N) derived from the PCWI DRP was significantly overestimated. To estimate the true noise, we followed the procedures in O’Sullivan et al. (2020) for PCWI data. First, the variance for each cube was first rescaled by 1.5 to account for the covariance introduced by coadding. For the covariance added by spatially binning the neighboring spaxels, O’Sullivan et al. (2020) measured the true noise (𝜎adjusted ) in the binned data as 𝜎adjusted = [1 + 0.79 log (𝑁 𝑏 )]𝜎nocov , (2.1) where 𝜎nocov is the noise derived from error propagation and 𝑁 𝑏 is the number of spaxels in the binned spectrum. For large 𝑁 𝑏 ≫ 120, the signals in different spaxels are uncorrelated, so the scaling becomes 𝜎adjusted ≃ 2.6 𝜎nocov . We stacked the extracted spectra from all the coadded cubes into a single spectrum, which resembles the long-slit integrated-light spectra of more massive galaxies. To remove sensitivity to possibly imperfect flux calibration, we normalized the spectra by the median of the flux between 4400 Å and 4800 Å. We then scaled them according to the surface brightness profile measured by Crnojević et al. (2014) (Table 2.1) and summed them to obtain the global spectrum. In this case, the number of spaxels used for spectrum extraction is much larger than 120. Therefore, we scaled the weighted variance by 2.62 = 6.76. In addition, we extracted the spatially resolved spectra using the Voronoi binning algorithm of Cappellari and Copin (2003), which is one of the most commonly used binning methods in IFS data. It can adaptively combine the spectra in adjacent 24 pixels to reach a given minimum S/N, and it allows us to adjust the S/N using using Equation 2.1 when optimizing the binning strategy. We only included the central and south pointings for the spatially resolved studies because the north pointing lacks reliable spectral coverage below 4700 Å, which is important to determine the stellar population age. For the central and south pointings, the S/N was calculated from the wavelength range between 4400-4600 Å. We required each bin to have S/N > 20 pix−1 (26 Å−1 ) for the central pointing and S/N > 15 pix−1 (20 Å−1 ) for the south pointing. We made this choice because the south pointing has many fewer bins in the field due to its lower surface brightness. In the end, we have 17 and 4 bins for the central and south pointings, respectively (Figure 2.5). We further corrected the variance of the stacked spectrum and the spatially resolved spectra by comparing with the best-fit model in order to obtain accurate uncertainties of the stellar population parameters (see Section 2.3). 2.2.2 Keck/DEIMOS Sample We used archival Keck/DEIMOS (Faber et al., 2003) observations of four slitmasks along the major axis of NGC 147. These observations were originally obtained by Geha et al. (2010). We downloaded the raw data from the Keck Observatory Archive and reduced them with the spec2d software (Cooper et al., 2012; Newman et al., 2013). K13 already measured stellar metallicities from coadded spectra of red giants in NGC 147. However, one of the purposes of this paper is to determine whether individual stellar metallicities are consistent with integrated light. Spectral coaddition is a form of integrated light, which means that the existing measurements in K13 are not appropriate for our purpose. Therefore, we remeasured the stellar metallicities for individual stars. We measured metallicities by 𝜒2 fitting to a grid of synthetic spectra, as described by Kirby, Guhathakurta, and Sneden (2008), Kirby et al. (2009), and Kirby et al. (2010). This method uses photometric estimates of effective temperature and surface gravity to guide the fitting. We used photometry from the Pan-Andromeda Archaeological Survey (PAndAS, Martin et al., 2013), which took place at the Canada–France– Hawaii 3.6 m Telescope (CFHT). This photometry is different from that used by K13, which possibly had errors in its zero-points. Only the stars with uncertainties of [Fe/H] smaller than 0.5 dex were included in the further analysis. This cut gives us 317 stars in the sample. The updated measurements are listed in Table 2.3. 00 32 23.9 00 32 25.8 00 32 27.6 00 32 29.5 00 32 29.7 00 32 30.5 00 32 31.1 00 32 32.0 00 32 33.6 00 32 33.9 4456 4608 4778 4885 4894 4961 5026 5129 5324 5368 +48 19 53.8 +48 18 57.2 +48 18 13.8 +48 17 34.2 +48 19 03.8 +48 19 46.6 +48 18 04.2 +48 16 37.4 +48 16 36.3 +48 17 50.8 Decl. (J2000) 𝑔 𝑔 𝑔 𝑔 𝑔 𝑔 𝑔 𝑔 𝑔 𝑔 Filter 2 𝑖 𝑖 𝑖 𝑖 𝑖 𝑖 𝑖 𝑖 𝑖 𝑖 Magnitude 1𝑎 (mag) 23.065 ± 0.027 23.106 ± 0.028 22.715 ± 0.020 23.297 ± 0.032 23.239 ± 0.031 24.125 ± 0.066 22.977 ± 0.025 23.416 ± 0.035 23.099 ± 0.027 22.779 ± 0.021 20.921 ± 0.012 21.007 ± 0.013 21.117 ± 0.014 20.808 ± 0.011 21.424 ± 0.018 21.426 ± 0.018 21.163 ± 0.014 21.145 ± 0.014 21.238 ± 0.015 21.256 ± 0.016 Magnitude 2𝑎 (mag) 3744 ± 44 3770 ± 42 4126 ± 45 3592 ± 56 3929 ± 41 3528 ± 51 3936 ± 39 3748 ± 52 3923 ± 49 4232 ± 42 𝑇eff (K) ... Additional rows available in the online published version ... Filter 1 a PAndAS photometry corrected for extinction. R.A. (J2000) ID 0.26 ± 0.1 0.32 ± 0.1 0.62 ± 0.1 0.04 ± 0.1 0.64 ± 0.1 0.23 ± 0.1 0.53 ± 0.1 0.31 ± 0.1 0.54 ± 0.1 0.72 ± 0.1 log 𝑔 (cm s−2 ) Table 2.3: Metallicity Catalog for RGB Stars Observed with Keck/DEIMOS 2.08 2.07 2.00 2.13 1.99 2.09 2.02 2.07 2.02 1.97 𝜉 (km s−1 ) −1.12 ± 0.12 −0.49 ± 0.11 −1.10 ± 0.12 −3.03 ± 0.17 −0.81 ± 0.12 −3.21 ± 0.23 −0.85 ± 0.11 −2.23 ± 0.16 −1.08 ± 0.13 −1.36 ± 0.12 [Fe/H] (dex) 25 26 2.3 Methods We used full-spectrum fitting via stellar population synthesis (SPS) to measure the stellar population of NGC 147. Compared to spectrophotometric indices, full-spectrum fitting derives the stellar population properties using the information from the whole spectrum instead of portions with strong absorption lines, so high-precision measurements can be achieved. We adopted the fitting method of L19, from which the high-mass MZR was derived, and we refer the reader to that paper for a full description. We chose the same fitting algorithms to minimize the systematic difference caused by different full-spectrum fitting codes and different templates. In summary, L19 used the SSP models from FSPS (Conroy, Gunn, and White, 2009; Conroy, White, and Gunn, 2010) version 3.0 with the Kroupa (2001) initial mass function (IMF), Padova isochrones (Marigo and Girardi, 2007), and the MILES spectral library (Sánchez-Blázquez et al., 2006). The metallicities and ages of the templates range within −1.98 ≤ log 𝑍 ≤ 0.20 and 0.3 Myr–14 Gyr, respectively. We interpreted [Z/H] in the base models as [Fe/H]. In addition to the stellar metallicity [Fe/H], the enhancements of Mg and N were also included using the theoretical response functions from Conroy et al. (2018), which depend on age and metallicity. The templates were smoothed to match with the resolution of the observed data. We fit for the velocity dispersion, stellar population age, [Fe/H] and [Mg/Fe] by interpolating the SSP models. Therefore, the obtained ages and metallicities are SSP-equivalent. Leethochawalit et al. (2018b) tested the SSP assumption by fitting the mock composite stellar population (CSP) model spectra, which have exponentially declining SFHs, with the SSP models, and successfully recovered the true metallicity within 0.1 dex. This result indicates that SSP-equivalent metallicity agrees well with the light- or mass-weighted metallicity. We emphasize that the goal of this paper is to investigate whether the high-mass MZR measured in SSP-equivalent [Fe/H] has systematic offsets relative to the lowmass MZR. As demonstrated in Appendix 2.8, although the choice of SSP or CSP model will affect the stellar age estimates, the measured metallicity is much less affected. Therefore, adopting SSP models will not affect the major conclusion of this paper. We focus on the recovery of SSP-equivalent parameters in the following analyses. To avoid a possible mismatch in flux calibration between the blue and red spectra, we normalized the spectral continuum on both sides using a spline fit. L19 developed an algorithm to minimize any alteration to the template spectra. The algorithm applies 27 Figure 2.2: Two examples of the observed spectra (black), the corresponding best-fit models (red), and the model residuals (bottom panel of each spectrum). The gray regions are not included in the spectrum fitting. The top panel shows the stacked spectrum from the entire field, which has the highest S/N, while the bottom panel is an example of a spectrum at the lower end of S/N in one Voronoi cell. The S/N is estimated from the residual of the fits. a synthesized continuum to the observed continuum-normalized spectrum. In the first iteration, we fit the continuum-normalized observed spectrum with continuumnormalized model spectra, and generated a synthesized continuum by fitting a B-spline to the quotient of the continuum-normalized spectrum and the best-fit SSP model spectrum. Subsequent fits were performed on the corrected observed spectrum with unaltered model spectra. The method is described in full detail in L19. For each spectrum, we performed two separate fits. For the first fit, we only masked out the wavelength regions contaminated by the strong sky line residuals. The Ca ii H and K lines were also excluded because of the strong nonlocal thermodynamic equilibrium (NLTE) effects, which the current models poorly reproduce. After the first fit, we masked out the regions that were ⩾ 3𝜎 from the best-fit model. We visually inspected these newly masked regions to make sure they deviated from the model due to weak sky features rather than deficiencies in the fitting algorithm. Then, we rescaled the variance derived from Section 2.2.1 by the reduced 𝜒2 of the first fit to estimate the true noise. We then fit the spectrum with new masking regions and corrected variance again to measure the stellar population properties. To validate our measurements, we also compared our results with those derived from 28 Table 2.4: Best-fit stellar population parameters for the stacked spectrum of NGC 147 Row Quantity Units Best-fit value (1) (2) (3) (4) (5) (6) (7) (8) 𝜎SSP AgeSSP [Fe/H]SSP [Mg/Fe]SSP 𝜎alf Agealf [Fe/H]alf [Mg/Fe]alf km/s Gyr dex dex km/s Gyr dex dex 40.45 ± 1.85 8.11+0.74 −0.54 −1.069+0.029 −0.031 0.024+0.20 −0.20 23.59+3.35 −3.68 12.50+0.32 −0.31 −1.105+0.011 −0.010 0.090+0.017 −0.017 (1)-(4) are derived from L19’s method; (5)-(8) are obtained from the alf simple mode. alf (Conroy et al., 2018), which is another full-spectrum fitting algorithm capable of measuring detailed abundances using the Markov Chain Monte Carlo (MCMC) method of parameter estimation. We used the “simple” mode of alf, which also assumes SSPs. The [Fe/H] and [Mg/Fe] results from our own code are consistent with those obtained from alf within 2𝜎. Examples of the observed spectra and best-fit models at the highest and lowest ends of the S/N are shown in Figure 2.2. We summarize our results for the global spectrum in Table 2.4 and for the spatially resolved spectra in Table 2.5. 2.4 Global Properties In this section, we report the stellar population properties of NGC 147 from the global integrated-light spectrum and compare the best-fit SSP-equivalent results with the updated measurements of the resolved stars. 2.4.1 SSP Age The best-fit SSP age derived from our method is 8.11+0.74 Gyr, while alf obtains −0.54 an age of 12.50+0.32 −0.31 Gyr. We suspect the difference (∼ 0.14 dex) may be attributed to systematic discrepancies of the SSP models used in the fitting codes. First, alf uses the newer MIST isochrones (Dotter, 2016; Choi et al., 2016) with metallicity coverage larger than that of the Padova isochrones used in our method. Second, the intrinsic spectral resolution of the stellar libraries in alf is lower than the instrumental resolution of PCWI, so the observed spectra needed to be smoothed by 00 33 11.72 00 33 12.37 00 33 13.20 00 33 12.97 00 33 13.28 00 33 10.62 00 33 11.43 00 33 12.49 00 33 10.98 00 33 11.91 00 33 12.18 00 33 13.95 00 33 09.99 00 33 14.36 00 33 13.59 00 33 12.22 00 33 08.32 00 33 09.93 00 33 07.47 00 33 09.16 Central +48 30 33.8 +48 30 40.2 +48 30 35.8 +48 30 27.0 +48 30 48.2 +48 30 20.6 +48 30 42.2 +48 30 15.4 +48 30 08.6 +48 30 10.6 +48 30 53.6 +48 30 30.2 +48 30 11.7 +48 30 42.1 +48 30 21.7 +48 30 01.1 +48 29 22.1 +48 29 19.5 +48 29 04.0 +48 28 59.7 Decl. (J2000) 0.14 (0.03) 0.17 (0.04) 0.25 (0.05) 0.29 (0.06) 0.34 (0.07) 0.35 (0.07) 0.37 (0.08) 0.42 (0.09) 0.43 (0.09) 0.44 (0.09) 0.48 (0.10) 0.51 (0.11) 0.51 (0.11) 0.52 (0.11) 0.54 (0.11) 0.69 (0.14) 1.33 (0.28) 1.38 (0.29) 1.67 (0.35) 1.76 (0.37) 𝑅ellip (arcmin (kpc)) [Fe/H] SSP 𝑎 (dex) -1.11+0.03 −0.04 -1.11+0.04 −0.04 -1.09+0.04 −0.04 -1.05+0.04 −0.04 -1.08+0.04 −0.05 -1.15+0.04 −0.04 -1.11+0.04 −0.04 -1.14+0.05 −0.05 -1.03+0.03 −0.04 -1.10+0.04 −0.05 -1.07+0.04 −0.04 -1.11+0.04 −0.04 -1.11+0.05 −0.05 -1.06+0.04 −0.04 -1.10+0.04 −0.04 -1.07+0.04 −0.04 -1.05+0.03 −0.04 -1.07+0.04 −0.04 -1.10+0.04 −0.04 -1.08+0.04 −0.04 AgeSSP 𝑎 (Gyr) 7.08+0.69 −0.44 7.55+0.89 −0.55 7.43+0.89 −0.54 7.63+1.19 −0.68 7.85+1.55 −0.88 7.83+1.17 −0.71 7.62+0.85 −0.54 8.87+1.63 −1.12 7.03+0.69 −0.42 7.87+1.39 −0.88 7.79+1.42 −0.86 7.98+1.38 −0.92 8.00+1.50 −0.92 7.22+0.94 −0.58 7.72+1.26 −0.80 7.94+1.19 −0.73 8.92+1.57 −1.07 8.36+1.41 −0.92 8.73+1.72 −1.25 8.56+1.52 −0.95 b Signal-to-noise ratio of the spectra used for fitting. a Best-fit parameters for single stellar population (SSP) models. South R.A. (J2000) Pointing 0.13+0.24 −0.28 0.44+0.20 −0.25 -0.04+0.28 −0.29 -0.37+0.32 −0.31 -0.18+0.32 −0.33 -0.36+0.28 −0.28 0.09+0.25 −0.28 -0.33+0.32 −0.31 -0.42+0.32 −0.31 -0.09+0.30 −0.31 -0.05+0.30 −0.32 0.14+0.26 −0.29 -0.19+0.33 −0.32 -0.01+0.28 −0.30 -0.09+0.30 −0.30 -0.04+0.29 −0.30 -0.00+0.25 −0.29 -0.04+0.29 −0.31 -0.09+0.29 −0.32 0.05+0.26 −0.31 [Mg/Fe] SSP 𝑎 (dex) 7.86+0.34 −0.43 11.67+0.63 −0.52 9.35+0.57 −0.70 9.40+0.55 −0.39 12.14+0.81 −0.81 11.05+0.54 −0.41 12.01+0.65 −0.64 13.90+0.08 −0.35 7.17+0.34 −0.28 9.96+0.57 −0.56 10.87+0.70 −0.60 12.43+0.65 −0.70 12.60+0.76 −0.89 9.25+0.55 −0.47 12.90+0.61 −0.69 13.29+0.52 −0.78 13.93+0.05 −0.23 13.56+0.35 −0.68 13.46+0.42 −0.98 13.81+0.16 −0.56 Agealf (Gyr) -0.99+0.04 −0.03 -1.20+0.03 −0.03 -1.12+0.04 −0.04 -0.96+0.03 −0.03 -1.21+0.03 −0.03 -1.28+0.03 −0.03 -1.19+0.03 −0.03 -1.31+0.03 −0.04 -1.03+0.03 −0.03 -1.07+0.03 −0.03 -1.12+0.04 −0.04 -1.12+0.03 −0.03 -1.18+0.03 −0.03 -1.06+0.04 −0.03 -1.18+0.03 −0.03 -1.20+0.03 −0.03 -1.05+0.02 −0.02 -1.08+0.03 −0.03 -1.08+0.03 −0.03 -1.10+0.03 −0.03 [Fe/H] alf (dex) Table 2.5: Best-fit stellar population parameters for spatially resolved integrated spectra 0.14+0.05 −0.05 0.35+0.05 −0.05 0.09+0.06 −0.06 -0.11+0.05 −0.05 -0.03+0.06 −0.06 -0.10+0.05 −0.05 0.10+0.06 −0.06 0.01+0.06 −0.06 -0.02+0.04 −0.05 -0.05+0.06 −0.06 0.17+0.06 −0.06 0.05+0.06 −0.06 -0.06+0.06 −0.06 0.07+0.06 −0.06 0.02+0.06 −0.06 0.13+0.05 −0.05 0.03+0.05 −0.05 0.05+0.05 −0.04 0.05+0.05 −0.05 0.06+0.04 −0.04 [Mg/Fe] alf (dex) 40.6 39.9 38.4 42.1 36.0 44.1 39.6 36.3 39.7 36.1 35.1 39.1 34.4 36.9 37.2 42.6 38.7 39.9 38.2 40.0 S/N𝑏 (Å−1 ) 29 30 another 𝜎 =100 km s−1 before being input to alf. Third, even in the simple mode, alf includes six more elements than our code does. Degeneracy between the extra free parameters may also affect the posterior distributions and the final results. Ideally, we would compare the age of the stellar population measured from integrated light to the average ages of individual stars. Unfortunately, it is extremely challenging to measure the ages of individual RGB stars. Generally, the stellar age can only be indirectly estimated by comparing the observed data with stellar models (e.g., Soderblom, 2010). The most commonly used method is to place the observations on a color-magnitude diagram (CMD), and match them with isochrones in a Hertzsprung–Russell diagram. This method works best for main-sequence and subgiant stars and is less effective for old, metal-poor RGB stars. For example, the difference in color between a 9 Gyr and 12 Gyr red giant is on the order of the difference in color between isochrone sets modeling the same star. We therefore infer the accuracy of the SSP age by comparing it with the age measured from CMD fitting via Hubble Space Telescope (HST) photometry by Weisz et al. (2014). They obtained a mass-weighted age of 7.53 Gyr, more consistent with the SSP age derived from our algorithm than with that derived from alf. The agreement suggests that even though NGC 147 has an extended SFH with several stellar populations formed at distinct epochs, the SSP assumption may be valid to recover the mass-weighted age in some cases, though the recovered stellar age is highly model-dependent. Therefore, obtaining a more reliable and consistent measurement of stellar age for galaxies sometimes requires a model of the SFH more complex than an SSP. As suggested in Appendix 2.8, CSP models may be more appropriate to recover the stellar age of complicated systems, although this method would also require higher data quality. 2.4.2 Iron abundance Before comparing the metallicity determined from integrated light ([Fe/H]SSP ) to that of the resolved stars ([Fe/H]stars ), it is important to understand whether the method of averaging [Fe/H]stars would affect the final results. The median, mean, and the inverse variance-weighted mean of [Fe/H]stars are −1.047±0.044, −1.106±0.031 and −0.983 ± 0.024, respectively. As shown in Fig. 2.3, [Fe/H]SSP = −1.069+0.029 −0.031 from integrated light is consistent with the median and the mean of the [Fe/H]stars within 1𝜎. On the other hand, [Fe/H]SSP is slightly lower than the weighted mean, although the difference is smaller than 0.1 dex. 31 We calculated the uncertainties of [Fe/H]SSP according to the methods of L19, which assume perfect model spectra. This assumption is not true in reality. First, NGC 147 has multiple stellar populations, contrary to the model’s SSP assumption. Second, even for a simple system with an SSP, the synthetic spectra are generated from the empirical stellar libraries and the theoretical isochrones, none of which is perfect. Therefore, we attribute the small difference (≲ 0.1 dex) between the two techniques to systematic error that is not included in the uncertainties of the best-fit parameters. Still, it is appropriate to conclude that the metallicity measured from the resolved stellar spectroscopy is consistent with that derived from the integrated-light spectroscopy for NGC 147. In addition, the consistency between the two methods indicates that the SSP assumption is sufficient to recover the true metallicity of a galaxy with a complicated SFH. The agreement between the integrated-light and resolved stellar metallicities also implies that the metallicity measured from the center of NGC 147 (covered by PCWI) is representative of the much larger region covered by DEIMOS. Although NGC 147 has a slightly negative metallicity gradient (see Section 2.5), the two methods agree despite their drastically different spatial coverage. If this holds true for more distant galaxies, the limited spatial coverage of galaxy surveys with fiber spectrographs would have less impact on the measurement of the stellar metallicity for galaxies with metallicity gradients as shallow as those of NGC 147. A largesample study is essential to further investigating the limited-aperture effect on the stellar metallicity recovery but it is beyond the scope of this work. 2.4.3 Magnesium enhancement Ideally, we would compare Mg abundances measured from integrated light to those measured from resolved stars. It is possible to measure [Mg/Fe] from DEIMOS spectra of individual stars (e.g., Kirby et al., 2010). However, the spectral range of the DEIMOS configuration employed by the archival spectra used in this paper does not reach the Mg b triplet or other strong Mg lines. Instead, the available lines have relatively high excitation potential, and they are consequently weak. This makes it difficult to measure Mg in low-S/N spectra, including those of stars in galaxies as distant as NGC 147. The result of attempting to measure [Mg/Fe] in such galaxies is a bias toward high values of [Mg/Fe]4 because low values of [Mg/Fe] result in the Mg lines becoming lost in the noise. 4 See Figure 10 of Kirby et al. (2020) for a demonstration of this effect. 32 Figure 2.3: The metallicity distribution for the resolved stars analyzed in this sample. The value of [Fe/H]SSP (light blue region) is consistent with the mean (green dashed line), the median (red dashed line) and the inverse-variance weighted mean (blue dashed line) of [Fe/H]stars . An alternative way to validate the [Mg/Fe]SSP is to use the MZR for [Mg/H]. The low-mass MZR for [Mg/H] can be deduced from resolved stellar spectroscopy of MW satellite galaxies (Kirby et al., 2010), which are near enough to allow S/N that overcome the bias against low values of Mg abundances. The high-mass MZR can be measured from integrated-light spectroscopy of more distant galaxies (L19). The low-mass and high-mass MZRs for [Mg/H] predict different values at the mass of NGC 147, as is the case for [Fe/H] (see Section 2.6.2). If [Mg/H]SSP (the sum of the best-fit [Mg/Fe]SSP and [Fe/H]SSP ) falls on the low-mass MZR ([Mg/H]) for dwarf galaxies, then we have circumstantial evidence that the two methods give similar values of Mg abundance. We constructed the MZR for [Mg/H] from the measurements of eight MW dwarf spheroidal (dSph) satellites (Kirby et al., 2010). We excluded more distant galaxies due to the aforementioned weak Mg lines, and we excluded most ultrafaint dwarf galaxies due to small sample sizes. We constructed the MZR from an orthogonal, least-squares linear regression taking into account measurement uncertainties in both axes (Akritas and Bershady, 1996). The resulting MZR is ⟨[Mg/H]⟩ = −3.31 + 0.32 log(𝑀∗ /𝑀⊙ ). As seen in Fig. 2.4, the [Mg/H]SSP of NGC 147 is much more likely to fall on the lowmass MZR (Mg) of dwarf galaxies than on the high-mass one. Considering the lowmass MZR (Mg) was determined only from a few dwarf galaxies at 𝑀∗ < 108 𝑀⊙ , the small difference (< 0.2 dex) between the [Mg/H]SSP and the predicted value 33 might be attributed to an extrapolation error at the mass of NGC 147 or to intrinsic dispersion in the MZR. We therefore conclude that we have tentative evidence that [Mg/Fe]SSP is representative of the whole stellar population in the galaxy. Figure 2.4: The MZR measured from [Mg/H] at 𝑧 ∼ 0. The green dashed line shows the high-mass MZR for Mg determined from the integrated spectra of massive quiescent galaxies (green diamonds) by L19. The low-mass MZR for Mg is determined only from the MW dSph satellites (blue circles). The rms for the two best-fit lines are shown in the green and blue bands. The [Mg/H] of NGC 147 measured in this work (red star) is more likely to fall on the low-mass MZR rather than on the high-mass MZR. 2.5 Spatial Distributions of Stellar Population 2.5.1 Population Gradients Taking the advantage of IFS data, we were able to study the spatial distribution of the stellar population in the innermost region for the first time. We measured the stellar population in each Voronoi cell (Section 2.2.1). Because the north pointing lacks reliable blue spectra below 4700 Å, which are essential to determining the stellar population age, we excluded the north pointing for spatial distribution studies. Figure 2.5 shows the 2D maps and the radial trends for the SSP-equivalent stellar population age, [Fe/H] and [Mg/Fe]. As demonstrated by Koleva et al. (2011), the SSP-equivalent parameters are sufficient to recover the true population gradients. We calculated the galactocentric elliptical radius using the position angle and ellipticity in Crnojević et al. (2014). We fit a linear model to the gradients for age, [Fe/H], and [Mg/Fe], with the emcee MCMC sampler5 (Foreman-Mackey et al., 2013). The 5 For each gradient, the initial parameters were obtained from 𝜒 2 minimization. Broad, uniform 34 Figure 2.5: The spatially resolved measurements of SSP parameters for the central and south pointings. Left: The 2D maps of the best-fit stellar population age, [Fe/H], and [Mg/Fe]. The contours indicate the (projected) galactocentric elliptical radii with 0.1 kpc intervals. Right: The radial gradients of the stellar population. The dashed lines represent the best-fit lines from MCMC. The gray shaded region indicates the ranges between the 16th and 84th percentiles. 35 uncertainties of each parameter were taken to be the asymmetric 68% confidence level of the posteriors. In the PCWI field, we marginally detected a positive age gradient within 0.4 kpc as age
𝑚 age = Δ 𝑅 = 4.5 ± 2.5 Gyr kpc−1 . The south field is ∼ 1.5 Gyr older than the innermost bin. The positive age gradient may suggest that star formation persisted longer in the central region compared to that in more extended regions. However, no age gradient is present in the alf measurements. As shown in Table 2.5, around half of the best-fit results are very close to the upper limit of the stellar population age (i.e., the age of the universe), suggesting the age derived from alf is not well constrained. We suspect the factors discussed in Section 2.4.1 may also account for the difference. Meanwhile, the detected positive age gradient is consistent with previous literature. Han et al. (1997) also found that the younger stars in NGC 147 are more centrally concentrated than the majority of the old stars. Weisz et al. (2014) measured the SFH from HST/WFPC2 photometry in the central regions of NGC 147, which demonstrates that ∼ 20% of the stars were formed within the past 2.5 Gyr. On the other hand, the SFH determined from an HST/ACS field targeted at much larger radii suggests NGC 147 had formed 80% of its stars (6+2 −1 ) Gyr ago and its star formation ceased at least 3 Gyr ago (Geha et al., 2015). The different SFHs derived from HST data at different radii are qualitatively consistent with the positive age gradients we measured from integrated-light spectroscopy. The is relatively uniform in the PCWI fields, with a slope of 𝑚 [Fe/H] =   metallicity [Fe/H] = 0.08 ± 0.09 dex kpc−1 . On the other hand, we find a large scatter for Δ 𝑅   [Mg/Fe] [Mg/Fe], with a slope of 𝑚 [Mg/Fe] = Δ = −0.08+0.64 dex kpc−1 . The large 𝑅 −0.63 uncertainty on the [Mg/Fe] gradient precludes us from drawing conclusions about the relevance of this gradient to the galaxy’s SFH. Furthermore, the gradient was estimated from the very central region of the galaxy so it may not represent the whole stellar population. To investigate the population gradient at larger scales, we made use of the stellar metallicities of resolved RGB stars. As shown in Figure 2.6, the resolved metallicities for the innermost region (∼400 pc) show large scatter. There are only 17 stars within the outermost radius of the PCWI fields, so the resolved metallicities may not indicate the characteristic metallicity of the stellar population in this region. The integrated metallicities derived from PCWI data are between the lowest and highest priors were used. We ran 5000 steps with 32 walkers. Burn-in usually happened after around 40 steps, so the posteriors were well-constrained. 36 Figure 2.6: Metallicity gradient of NGC 147. Left: The metallicity map for the resolved stars (circles) and integrated light (triangles). The black contours demonstrate the galactocentric radii at 4, 8, 12 and 16 kpc, respectively. The inset shows the zoom-in map of the galaxy central part. The gray dashed ellipse is the maximum elliptical radius of the PCWI spatial coverage. The metallicities obtained from the integrated light are very close to those of the individual RGB stars. There is no prominent spatial variance of the stars’ metallicities. Right: The radial gradient of the metallicity. The best-fit linear gradient of the resolved stars’ metallicities is shown by the purple line. A negative slope of ∼ -0.13 dex kpc−1 is marginally detected. values of the resolved metallicities. The resolved study reveals a negative gradient ∼ −0.13 ± 0.03 dex kpc−1 , different from the flat metallicity profile of Δ <[Fe/H> 𝑅 revealed in the PCWI fields. Because the resolved study extends to a much larger radius, we believe that the negative metallicity gradient is more representative of the galaxy population. The negative metallicity gradient is inconsistent with the flat to positive gradient found by Crnojević et al. (2014) and Vargas, Geha, and Tollerud (2014). Crnojević et al. (2014) estimated the photometric metallicity gradient from the metallicity distribution functions (MDFs) in three radial bins from 2.5 to 6.4 kpc. Their sample consists of stars at much larger radii compared to ours and lacks measurements within 2.5 kpc. In addition, the authors suggested that their gradient may be biased because stars from tidal tails can contribute to the mean stellar metallicity in the outermost region. On the other hand, Vargas, Geha, and Tollerud (2014) measured spectroscopic metallicities from Keck/DEIMOS spectra. Similar to that in K13, the photometry used to estimate the effective temperature and surface gravity possibly had errors in its zero-points, leading to unreliable metallicity estimates. In fact, Vargas, Geha, and Tollerud (2014) reported a mean [Fe/H] for NGC 147 as ∼ −0.5 dex, which is around twice the values derived in other literature, including photometric 37 and spectroscopic estimates (Han et al., 1997; Davidge, 2005; Gonçalves et al., 2007; Geha et al., 2010; Crnojević et al., 2014). We recovered similarly high values of [Fe/H] when we used the questionable photometry. We conclude that we should not compare our gradient to that measured by Vargas, Geha, and Tollerud (2014). 2.5.2 Outside-in Formation of NGC 147? Stellar population gradients can provide us insight into the evolution of a galaxy. Observational studies have suggested that dSph6 galaxies in the Local Group generally have positive age gradients and negative metallicity gradients (e.g., Koleva et al., 2011; Kirby et al., 2011a). The observed gradients are usually explained as a result of outside-in formation(e.g., Benítez-Llambay et al., 2016; Revaz and Jablonka, 2018; Genina et al., 2019), where the metals accumulate at the center of the galaxy, and the star formation becomes more concentrated with time. In particular, Genina et al. (2019) identified that ram pressure—imposed by the massive host galaxy when the satellite galaxy falls in—can compress the gas at the center of the satellite galaxy while stripping the gas from the outskirts. Consequently, the star formation at the center can be reignited while the outer regions are quenched, giving rise to the gradients observed in the Local Group dSphs. The age and metallicity gradients of NGC 147 found in this work are in alignment with the outside-in scenario, if the age gradient detected in the PCWI field is real. As NGC 147 has no H i detection (Young and Lo, 1997), tidal stripping and ram pressure stripping are very likely to have played an important role in quenching the star formation and shaping the observed radial gradients in this galaxy. Crnojević et al. (2014) uncovered the presence of extended tidal tails in NGC 147. The tails indicate a strong tidal interaction with its host galaxy, M31. Geha et al. (2006) found kinematic evidence for tidal disruption in another M31 dE satellite, NGC 205. Mayer et al. (2006) showed that the combined effects of tides and ram pressure are significantly more successful at removing the gas from the dwarfs than tidal stripping alone. In addition, Kormendy (1985) and Kormendy and Bender (2012) also suggested that ram-pressure stripping would be one of the major quenching mechanisms for dSph galaxies in the Local Group. 6 Some studies call the fainter dwarf ellipticals spheroidal galaxies (Kormendy et al., 2009). 38 2.6 2.6.1 Discussion Comparison with previous work So far, most works investigating the validity of recovering the stellar population, especially the metallicity, from integrated-light spectroscopy have studied relatively simple systems like globular clusters (e.g., González Delgado and Cid Fernandes, 2010; Barber et al., 2014; Conroy et al., 2018), which tend to have formed stars at the same epoch. Very few attempts have been made to directly compare the stellar populations measured from integrated and resolved spectroscopic analyses for complex systems with multiple stellar populations. Ruiz-Lara et al. (2018) obtained an integrated spectrum of the central part of Leo A, one of the the Local Group’s star-forming dIrr galaxies with 𝑀∗ ∼ 3 × 106 𝑀⊙ . They derived the SFH and the metallicity of each age bin from the integrated spectrum. They found that while the SFH is consistent with that derived from CMD fitting, the derived metallicity at all age bins is higher than the average value of individual stars obtained by Kirby et al. (2017). The differences in metallicity range from ∼ 0.25 dex in the intermediate-age bins to > 1.0 dex in younger-age bins, in contrast to our results for NGC 147. However, such a discrepancy can be explained by factors other than the intrinsic systematic effects between the two techniques. First, Leo A is still star-forming and therefore has nebular emission. If the modeling of the Balmer emission lines from the ISM was not perfect, it could have affected the depths of the Balmer absorption lines, which heavily affect the measurement of the stellar population age. In turn, this could have affected the measured metallicity according to the age–metallicity degeneracy. As an old, quiescent galaxy, NGC 147 would not suffer the same source of uncertainty. Second, Leo A is metal poor ([Fe/H] ∼ −1.5). Most stellar libraries used in the modeling of integrated-light spectra do not contain enough stars with [Fe/H] < −1. If the incompleteness of the metal-poor stars in the stellar libraries causes the discrepancy found by Ruiz-Lara et al. (2018), it will not affect the existing metallcities of more massive and more metal-rich galaxies like NGC 147 derived from integrated light. In addition, Leo A exhibits a stronger metallicity gradient (∼ -0.33 dex/kpc; Kirby et al., 2017) than NGC 147, which may explain the discrepancy between Kirby et al. (2017) and Ruiz-Lara et al. (2018). Kirby et al. (2017) measured stars at larger radii (∼ 7′), whereas Ruiz-Lara et al. (2018) observed a total area of 19.2′′× 7′′ in the central region, corresponding to a region within a 0.15 half-light radius. 39 On the other hand, Boecker et al. (2020) recovered an age-metallicity distribution of M54 measured from integrated-light spectra that was consistent with the resolved stellar spectra obtained on MUSE. Unlike most other star clusters, M54 has known multiple stellar populations formed at different epochs (Siegel et al., 2007; AlfaroCuello et al., 2019). Boecker et al. fit for a linear combination of SSP models to account for the SFH rather than assuming an SSP, and they found excellent agreement between the mass-weighted age and metallicity. The mass-weighted metallicity of the integrated-light spectra is 0.2 dex lower than the mean for the resolved stars, whereas the difference in the light-weighted metallicity is as small as 0.1 dex. The results are similar to ours, suggesting that taking the SFH into account or not does not significantly affect the recovery of metallicity from the integrated spectra. However, their data set is slightly different from ours. First, a number of stars are resolved in the MUSE field of M54, so that the resolved stars would contribute greatly to the integrated-light spectra. Since the resolved stars are the brightest ones among the whole stellar population, one is more likely to obtain consistent light-weighted values from the integrated and resolved analyses even though systematic offsets are present. Second, both the integrated and resolved spectra are obtained on the same instrument; therefore, the instrumental effects would be minimized. Our work moves one step toward validating the comparability of integrated-light spectra of distant galaxies to resolved spectra of local galaxies because we directly compare the measurements from completely unresolved and completely resolved populations. 2.6.2 Implications for the MZR Measuring the MZR across the full range of galaxy mass is extremely important to unveil how the physical processes regulating metal retention and interaction with the surrounding environment vary as the galaxies grow in mass. However, possible systematic effects between different methods of determining the metallicity obfuscate the exact form of the MZR. Constructing the MZR from gas-phase metallicities has taught us an important lesson on understanding the role of systematic effects when measuring metallicities in different galaxy types and ages. Previous studies have found that different methods used to measure gas metallicity suffer from systematic offsets (e.g., Nagao, Maiolino, and Marconi, 2006; Kewley and Ellison, 2008; Andrews and Martini, 2013; Yates et al., 2020), and the discrepancy can be as large as 0.7 dex (Kewley and Ellison, 2008). These systematic effects can lead to quantitatively and qualitatively different shapes for the gas-phase MZR. For instance, most studies favor a continuous gas-phase 40 MZR that exhibits a single power law at low and intermediate mass, and gradually flattens at the high-mass end (e.g., Tremonti et al., 2004; Kewley and Ellison, 2008; Zahid et al., 2013), while Blanc et al. (2019) discovered a sharp transition in the gas-phase MZR, which has a much steeper slope at 109.5 −1010.5 𝑀⊙ . Therefore, it is extremely important to understand the systematic offsets between different methods before placing the MZRs on the same absolute scale. The literature discussion of systematic effects on galactic stellar metallicities is small relative to the extensive studies on the discrepancies of gas metallicity diagnostics. The different treatment exists partly because it is difficult to apply resolved stellar spectroscopy and integrated-light spectroscopy to the same galaxies. It is impossible to resolve RGB stars in massive galaxies beyond Andromeda, while most local dwarf galaxies are too large to fit in a long-slit spectrograph for integrated-light spectroscopy. So far, only Ruiz-Lara et al. (2018) have compared the stellar metallicity of Leo A determined from integrated light to that obtained from resolved stars. As discussed in Section 2.6.1, the large discrepancy may result from factors other than systematic offsets. The agreement we obtained between resolved stars and integrated light in NGC 147 is encouraging because we adopted the same fitting algorithm used to derive the high-mass MZR L19, which indicates relatively small systematic offsets in the stellar metallicity determination. As seen in Figure 2.7, the high-mass MZR predicts an [Fe/H] at the mass of NGC 147 that is higher by 0.6 dex relative to the low-mass MZR. Our consistent resolved and integrated metallicity estimates tentatively suggest that the discrepancy between the low-mass MZR and high-mass MZR cannot be attributed to systematic effects intrinsic to the two techniques. We also exclude the possibility that the consistency in the two approaches is biased due to the SSP assumption in Appendix 2.8.Instead, our results support a real break related to physical processes governing the metal content. If the systematic offsets of the resolved and integrated-light methods are indeed as low as what we obtained for NGC 147, it is possible that the stellar MZR may also have a sharp transition, like the gas-phase MZR derived by Blanc et al. (2019). This break in the stellar MZR was also observed by Gallazzi et al. (2005), who measured the stellar MZR from a single method (spectrophotometric indices) rather than comparing the MZRs measured from different methods in different mass ranges. However, the uncertainties of [Fe/H] below 1010 𝑀⊙ are too large to distinguish between the low-mass and high-mass MZRs. A break in the stellar MZR was also reported by Panter et al. (2008), who measured 41 Figure 2.7: The MZR measured from [Fe/H] at 𝑧 ∼ 0. This figure is the same as Fig. 2.4, except that the low-mass MZR is obtained from dIrrs in addition to dSphs/dEs. The purple region shows the MZR of local Sloan Digital Sky Survey (SDSS) galaxies using the spectrophotometric indices (Gallazzi et al., 2005). The weighted mean of the [Fe/H] of NGC 147 for resolved stars, which is highlighted by the purple star, is remeasured in this work using updated photometry (Section 2.2.2). The [Fe/H] of NGC 147 measured from integrated light (red star) falls on the low-mass MZR, indicating the systematic difference between the two techniques cannot explain the discrepancy in the MZRs between the two mass ranges. the stellar MZR for a large sample of local SDSS galaxies above 108 𝑀⊙ via fullspectrum fitting and discovered a steeper slope for galaxies between 108 − 1010 𝑀⊙ than observed at higher mass. They suggested that the steeper slope was an artificial bias introduced by the limited aperture of the SDSS fibers, which cannot observe the outer region of low-mass galaxies. However, Sybilska et al. (2017) measured the stellar metallicities for dwarf and giant quiescent galaxies from IFS data cubes obtained with the SAURON IFU, which suffers much less from aperture bias. A break was still present in their MZR in the same mass range, further suggesting that the break is very likely to be real. The two MZRs may indicate a change in the feedback mechanisms as the galaxies grow in mass. Hayward and Hopkins (2017) proposed an analytic model to explain how stellar feedback simultaneously regulates star formation and drives outflows in a turbulent ISM. They argued that the mass-loading factor could decrease dramatically for galaxies above ∼ 1010 𝑀⊙ , so that high-mass galaxies become much less efficient in expelling the metal-enriched ISM. Because the stellar metallicity represents the metals locked inside the stars from the surrounding ISM averaged 42 over the SFH, the feedback changes can also affect the shape of the stellar MZR indirectly. Unfortunately, the current stellar MZR (Fig. 2.7) has few individual precise measurements for intermediate-mass galaxies (108 < 𝑀∗ /𝑀⊙ < 1010 ), so we cannot determine how the shape of the stellar MZR would change across the full range of galaxy mass. Further studies focusing on the MZR of individual galaxies at intermediate mass are necessary to unveil the nature of the processes regulating the metal cycle and shaping the MZR. Nevertheless, the stellar MZRs of individual dwarf and massive galaxies can be a useful tool to help us understand the physical processes related to galactic chemical evolution. Our work presents the first evidence that it is reasonable to put the two MZRs on the same absolute scale to jointly constrain the shape of the stellar MZR. Our investigation of systematic effects focused on just one galaxy: NGC 147. It is possible that our result is fortuitous and that a larger ensemble of galaxies would reveal some systematic differences between resolved spectroscopy and integrated light. Nonetheless, our results for NGC 147 suggest that these systematic effects do not play an important role in causing the discrepancy observed between different mass ranges of the stellar MZR. We anticipate observing more galaxies in the future to retire once and for all the possibility that the difference in technique—rather than in astrophysics—is responsible for the discrepancy. 2.7 Conclusions We measured the stellar population age, [Fe/H], and [Mg/Fe] of the central region (≲400 pc, i.e., 2′) in NGC 147 from integrated-light spectra obtained with PCWI. We also provided updated metallicity estimates for 317 RGB stars in the sample of K13. We compared the mean metallicity of the resolved stars with the measurement from integrated light to investigate systematic effects between the two techniques. A summary of our findings is as follows: 1. We recovered the global SSP-equivalent stellar population from integrated spectra and measured the stellar population age= 8.11+0.74 Gyr, [Fe/H]= −0.54 +0.029 +0.20 −1.069−0.031 and [Mg/Fe]= 0.024−0.20 . The iron and magnesium abundances are consistent with the best-fit parameters obtained from alf’s simple mode. 2. The best-fit SSP age is only 0.03 dex higher than the mass-weighted age determined from the CMD fitting of Weisz et al. (2014). The difference between [Fe/H]SSP and the weighted mean of [Fe/H]stars is less than 0.1 dex, implying that the SSP assumption is valid to recover the mean stellar metallicity for a 43 complex system with multiple stellar populations. It also suggests that the SSP assumption may recover the stellar age in some cases, although it strongly depends on the choice of SSP templates. 3. Making use of the IFS cubes, we detected a marginally positive age gradient in the central regions. Combining this age gradient with the negative metallicity gradient in the resolved stars, it is possible that NGC 147 formed outside in. 4. The resolved and integrated metallicities of NGC 147 are consistent within 0.1 dex, suggesting that systematic effects cannot explain the ∼ 0.6 dex discrepancy between the low-mass (K13) and high-mass (L19) stellar MZRs. Therefore, we tentatively conclude that the break in the MZRs at different mass ranges implies some physical mechanism transitions at 108 𝑀⊙ < 𝑀∗ < 1010 𝑀⊙ . There is only one target in this work, so it is possible that such a small systematic offset (< 0.1 dex) is underestimated. Nevertheless, our analysis of NGC 147 is strong evidence that the systematic effects of different techniques of determining metallicity will not be the major cause of the discrepancy in the stellar MZRs. Future observations are necessary to expand this study to a larger sample in order to verify that the underlying astrophysical processes are ultimately responsible for the changing behavior of stellar MZR. Acknowledgments The authors acknowledge the constructive feedback from the anonymous referee, which helped us improve the manuscript. We thank Yuguang Chen, Donal O’Sullivan and James (Don) Neill for useful discussions on PCWI data reduction and covariance correction. We gratefully thank the staff at the Palomar Observatory, including support astronomers Carolyn Heffner and Kevin Rykoski, and telescope operator Kajsa Peffer, for assisting in the observations. This material is based on work supported by the National Science Foundation under Grant No. AST-1847909. E.N.K. gratefully acknowledges support from a Cottrell Scholar Award administered by the Research Corporation for Science Advancement. M.A.dl.R. acknowledges the financial support of the NSF Graduate Research Fellowship Program. We are grateful to the many people who have worked to make the Keck Telescope and its instruments a reality and to operate and maintain the Keck Observatory. 44 The authors wish to extend special thanks to those of Hawaiian ancestry, on whose sacred mountain we are privileged to be guests. Without their generous hospitality, none of the observations presented herein would have been possible. This research has made use of the Keck Observatory Archive, which is operated by the W. M. Keck Observatory and the NASA Exoplanet Science Institute, under a contract with the National Aeronautics and Space Administration. 2.8 Appendix: Comparison with CSP Models In this section, we investigate whether fitting the data with more complicated CSP models would affect our primary results. Because CSP models have more free parameters and thus require higher-quality data to achieve the same precision, we limit our analysis to the stacked spectrum, which has very high S/N (∼ 111 Å−1 ). Here we present the measured ages and [Fe/H] from three different full spectral fitting codes that fit for multicomponent stellar populations: L19’s method (Appendix 2.8.1), alf (Appendix 2.8.2), and pPXF (Cappellari, 2017, Appendix 2.8.3). As shown in Figure 2.8, the stellar metallicity estimates are not greatly affected by the choice of models, while the measured stellar ages are more strongly dependent on the assumed SFH. We find that taking the SFH into account leads to greater consistency between different methods and templates than assuming an SSP. Therefore, CSP models may be a more appropriate way to estimate the stellar age of complex systems when the data quality is good enough. 2.8.1 Comparison to the CSP models in L19’s fitting code To investigate whether adopting CSP models would affect the recovered metallicities, we fit for a multicomponent stellar population with ages and weights determined from the SFH measured from CMD fitting to HST photometry (Weisz et al., 2014). Instead of fitting for linear combinations of SSP models with different metallicities, we choose to unrealistically assume that all components have the same metallicity. This can reduce the degeneracy of free parameters and approximately estimate the mass-weighted metallicities to the greatest accuracy. +0.15 The best-fit metallicities are [Fe/H]CSP =−1.000+0.018 −0.014 and [Mg/Fe]CSP =0.096−0.37 . +0.20 Compared to [Fe/H]SSP = −1.069+0.029 −0.031 and [Mg/Fe]SSP = 0.024−0.20 , the bestfit metallicities derived from CSP models are higher and closer to the resolved metallicities, further diminishing the systematic offsets between the two techniques. The differences in the recovered [Fe/H] and [Mg/Fe] from SSP models and CSP models are within 0.1 dex; therefore, we conclude that the metallicity measurements 45 Figure 2.8: The comparison between the measured [Fe/H] (top panel) and stellar ages (bottom panel) in different stellar population models. Top: The blue dashed line and the shaded region indicate the [Fe/H] predicted by the low-mass MZR K13 at the mass of NGC 147 and the corresponding 1𝜎 confidence interval. The data points show the measured [Fe/H] (weighted mean for CSP models) via various methods discussed in this work, which are all consistent with the low-mass MZR. Bottom: the measured ages (weighted mean for CSP models) via different methods discussed in this work. Among them, only the SSP age derived from L19’s method is consistent with the mass-weighted age obtained from the CMD fitting in Weisz et al. (2014) (red dashed line). are not affected significantly by the choices of SSP and CSP models, consistent with the results of Mentz et al. (2016) and Leethochawalit et al. (2018b). 2.8.2 Comparison to the results from alf full mode In addition to the SSP models in simple mode, alf also provides a full mode that fits for two-component stellar populations with an older (>3 Gyr) and a younger population (<3 Gyr), which allows us to approximate the SFH of the galaxy. We fit the stacked spectrum in alf full mode. The mass-weighted age derived in full mode (CSP-equivalent) is ∼ 9.4 Gyr. Compared to the SSP-equivalent age (12.5 Gyr) derived in simple mode, the difference between the CSP age and the mass-weighted age from CMD fitting by Weisz et al. (2014) is smaller. The consistency suggests that more complicated stellar population 46 models are necessary to obtain more accurate stellar age measurements in galaxies. On the other hand, the best-fit results from alf full mode indicate that less than 0.5% of the stellar population was formed in the past 3 Gyr, while the SFH revealed by the CMD fitting in Weisz et al. (2014) suggests that ∼20% of stars were formed in the past 2.5 Gyr. We also notice that the CSP age is surprisingly younger than the SSP age, whereas Choi et al. (2014) found that SSP-equivalent ages are younger than both light- and mass-weighted ages derived in models with extended SFHs. The discrepancy may arise from the fact that alf assumes two independent starbursts at different epochs rather than extended SFHs. The disagreements above may also suggest that the recovered stellar age is sensitive to the adopted CSP models and their underlying assumptions on SFH, and thus future investigations are important to explore which CSP models are more suitable to measuring the stellar ages of galaxies. Unlike the large difference seen in ages, the metallicities derived in the two modes are very similar. [Mg/Fe]CSP =0.064+0.018 ) is consistent with [Mg/Fe]SSP within 1𝜎, −0.016 +0.015 while [Fe/H]CSP = −0.907−0.017 is slightly higher than [Fe/H]SSP . The difference between [Fe/H]CSP and [Fe/H]stars is still within 0.1 dex, which once again demonstrates that the metallicity measurements are less affected by the assumed stellar population models. 2.8.3 Comparisons to pPXF full spectral fitting code Apart from the two fitting methods discussed in the main text, we test our CSP measurements by running another independent code, pPXF (Cappellari, 2017), which fits for linear combinations of different SSPs to account for complex SFHs in galaxies. For simplicity, 𝛼-enhancement is not included. We use the SSP models from the E-MILES library (Vazdekis et al., 2016), generated from the BaSTI isochrones (Pietrinferni et al., 2004) and Kroupa (Kroupa, 2001) IMF. The metallicities and ages of the templates range from −2.27 to 0.4 dex and 0.03 to 14 Gyr, respectively. Because the SSP models assume solar-scaled abundances, the metallicity [M/H] can be interpreted as [Fe/H]. Regularization is used to address some of the deficiencies in pPXF: that it does not necessarily return unique solutions, and that it is very sensitive to the noise in data due to the vast parameter space explored in fitting. The mass- and light-weighted stellar population parameters can be computed from the weights of each SSP component returned by pPXF. The mass- and light-weighted [Fe/H] are −1.033 ± 0.079 and −1.026 ± 0.08, re- 47 spectively, consistent with the metallicities measured from other methods. The uncertainties are calculated as the weighted variance of the ages and metallicities of each SSP component. On the other hand, the mass- and light-weighted ages are both 9.96 ± 0.01 Gyr, higher than the SFH-based age measured by Weisz et al. (2014) but similar to the mass-weighted age derived in alf full mode, which also uses CSP models. The results suggest that stellar age estimates from integrated-light spectroscopy depend more heavily than metallicity estimates on the assumed SFH. 48 Chapter 3 STELLAR ABUNDANCES AND AGES OF GRAVITATIONALLY LENSED, QUIESCENT GALAXIES AT 𝑧 ∼ 1 Zhuang, Z. et al. (May 2023). “A Glimpse of the Stellar Populations and Elemental Abundances of Gravitationally Lensed, Quiescent Galaxies at z ≳ 1 with Keck Deep Spectroscopy”. In: ApJ 948.2, p. 132. doi: 10.3847/1538-4357/acc79b. Abstract Gravitational lenses can magnify distant galaxies, allowing us to discover and characterize the stellar populations of intrinsically faint, quiescent galaxies that are otherwise extremely difficult to directly observe at high redshift from ground-based telescopes. Here, we present the spectral analysis of two lensed, quiescent galaxies at 𝑧 ≳ 1 discovered by the ASTRO 3D Galaxy Evolution with Lenses survey: AGEL1323 (𝑀∗ ∼ 1011.1 𝑀⊙ , 𝑧 = 1.016, 𝜇 ∼ 14.6) and AGEL0014 (𝑀∗ ∼ 1011.5 𝑀⊙ , 𝑧 = 1.374, 𝜇 ∼ 4.3). We measured the age, [Fe/H], and [Mg/Fe] of the two lensed galaxies using deep, rest-frame-optical spectra (S/N ≳ 40 Å−1 ) obtained on the Keck I telescope. The ages of AGEL1323 and AGEL0014 are 5.6+0.8 −0.8 Gyr and 3.1+0.8 −0.3 Gyr, respectively, indicating that most of the stars in the galaxies were formed less than 2 Gyr after the Big Bang. Compared to nearby quiescent galaxies of similar masses, the lensed galaxies have lower [Fe/H] and [Mg/H]. Surprisingly, the two galaxies have comparable [Mg/Fe] to similar-mass galaxies at lower redshifts, despite their old ages. Using a simple analytic chemical evolution model connecting the instantaneously recycled element Mg with the mass-loading factors of outflows averaged over the entire star formation history, we found that the lensed galaxies may have experienced enhanced outflows during their star formation compared to lower-redshift galaxies, which may explain why they quenched early. 3.1 Introduction How galaxies form and evolve to the state we see today has been a long-standing question in modern astronomy. One way to unveil the evolutionary history of a galaxy is to constrain its chemical composition because the overall metal abundance of a galaxy reflects the interplay among the gravitational potential (e.g., Dekel and Silk, 1986), star formation efficiency (e.g., Calura et al., 2009; Magrini et al., 2012) 49 and galactic inflows/outflows (e.g., Finlator and Davé, 2008). The well-known mass–metallicity relation (MZR), a tight correlation between galaxy stellar mass and metallicity, has been widely used to investigate the metal retention of galaxies at different masses and redshifts (e.g., Tremonti et al., 2004; Gallazzi et al., 2005; Erb et al., 2006; Finlator and Davé, 2008; Kirby et al., 2013; Lu, Blanc, and Benson, 2015; Ma et al., 2016; Kacprzak et al., 2016; Leethochawalit et al., 2019; Zhuang et al., 2021). While the majority of previous studies have used metallicity (i.e., gas-phase oxygen abundance or stellar-phase iron abundance) to characterize the chemical abundances of galaxies that cannot be resolved into stars, spectroscopic studies have turned to detailed abundances of galaxies using modern techniques, such as full-spectrum fitting of the stellar continuum to determine stellar abundances (e.g., Conroy et al., 2018). Measuring the abundances of individual 𝛼 elements (including O, Mg, Si and Ca) in stellar populations is a more effective probe of galactic chemical evolution than measuring iron alone. While iron is primarily produced in Type Ia supernovae of low-mass stars with a delayed explosion timescale, 𝛼-elements are synthesized by core-collapse supernovae of massive stars. Because of the difference in their recycling time, bulk 𝛼 enhancement—[𝛼/Fe]—has been used to measure the duration of star formation historically (e.g., Thomas et al., 2005; Walcher et al., 2015; Kriek et al., 2016), if assuming a closed box where outflows and/or inflows are absent. In addition, 𝛼 elements can be approximated to be instantaneously recycled given the short lifetime of massive stars, so they can be used in some simple chemical evolution models. For instance, Leethochawalit et al. (2019) used the relation between stellar masses and [Mg/H] for quiescent galaxies derived from chemical evolution models to constrain the mass-loading factors of galactic outflows, when galaxies are assumed to be leaky boxes in this case. Whereas the stellar abundances of quiescent galaxies have been extensively studied out to 𝑧 ∼ 0.7 (Choi et al., 2014; Gallazzi et al., 2014; Leethochawalit et al., 2018a; Leethochawalit et al., 2019; Beverage et al., 2021), we still have limited knowledge about the chemical composition of stellar populations at 𝑧 > 1, especially 𝛼-enhancements. A more nuanced understanding of the chemical abundances of high-𝑧 galaxies is crucial to develop a full picture of the chemical evolution and enrichment of galaxies through cosmic time. Unlike measuring the gas-phase abundances for high-𝑧 star-forming galaxies, which relies on strong emission lines, constraining the stellar abundances for high-𝑧 quiescent galaxies requires deep spec- 50 troscopy to capture the faint stellar absorption lines. Consequently, the few available measurements at 𝑧 > 1 are either based on a stacked spectrum of quiescent galaxies at similar redshifts and masses (e.g., Onodera et al., 2015; Carnall et al., 2022) or ultra-deep spectroscopy, which typically requires tens of hours on large groundbased 8-10 m telescopes for a single galaxy (e.g., Toft et al., 2012; Lonoce et al., 2015; Kriek et al., 2016; Kriek et al., 2019). Several studies have also attempted to determine the stellar metallicity of high-𝑧 quiescent galaxies using low-resolution grism spectra obtained with the Hubble Space Telescope (HST) (e.g., Morishita et al., 2018; Estrada-Carpenter et al., 2019), but these studies primarily used the continuum shape. Consequently, they cannot characterize the detailed shapes of stellar absorption lines, leading to high degeneracy between stellar metallicity and other galaxy properties, such as age. Gravitational lensing is a promising way to revolutionize our understanding of faint, high-𝑧 quiescent galaxies because it magnifies both the flux and angular resolution of distant galaxies. The magnified flux of lensed galaxies enabled us to obtain comparable or even higher signal-to-noise (S/N) spectra with shorter integration times, allowing us to investigate the stellar population from the faint stellar continua more accurately (e.g., Newman et al., 2018; Jafariyazani et al., 2020; Man et al., 2021). The magnified, lensed galaxies are more extended, providing us an opportunity to resolve the galaxies that are much more compact in the source plane in exquisite detail. With the help of gravitational lensing, early studies were able to reveal unprecedented details of high-𝑧 galaxies, such as the metallicity gradient (e.g., Leethochawalit et al., 2016; Jafariyazani et al., 2020) and morphology (e.g., Newman et al., 2018; Man et al., 2021). In this work, we present the spectral analysis of two gravitationally lensed, quiescent galaxies at 𝑧 ≳ 1 discovered by the ASTRO 3D Galaxy Evolution with Lenses (AGEL) survey (Tran et al., 2022) in order to characterize their stellar populations, especially the stellar elemental abundances. In Section 3.2, we describe our sample and data used for analysis. We explain how we determine the stellar mass and stellar population properties in Section 3.3. We present our results (the measured stellar population age, [Fe/H] and [Mg/Fe]) in Section 3.4 and discuss their physical implications in Section 3.5. Finally, we summarize our findings in Section 3.6. Throughout this work we assume a flat ΛCDM cosmology with Ω𝑚 = 0.3, ΩΛ = 0.7 and 𝐻0 = 70 km s−1 Mpc−1 . 51 3.2 Galaxy Sample and Data 3.2.1 The Lensed Galaxies The two gravitationally lensed galaxies, AGEL132304+034319 (hereafter AGEL1323) at 𝑧 = 1.016 and AGEL001424+004145 (AGEL0014) at 𝑧 = 1.374, were identified as part of the AGEL survey (Tran et al., 2022). The AGEL survey performed spectroscopic observations on strong gravitational lenses selected from the Dark Energy Survey (DES; Abbott et al., 2018) and the Dark Energy Camera Legacy Survey (DECaLS; Dey et al., 2019) to measure their redshifts. These lensed galaxy candidates were discovered using convolutional neural networks (Jacobs et al., 2019b; Jacobs et al., 2019a) and were notable for their red arcs. AGEL1323 was also independently discovered by the COOL-LAMPS Surveys as COOL J1323+0343 (Sukay et al., 2022) in a visual search of the northern galactic cap portion of the southern DECaLS dataset. Neither galaxy displayed emission lines in the identification spectra from AGEL survey, indicating their quiescent nature. As shown in Figure 3.1, AGEL1323 is a five-image1 system lensed by a group of galaxies with three visible clumps, while AGEL0014 is an arc spanning at least 3′′ lensed by a foreground lens galaxy. The magnified flux of the lensed images make the two galaxies ideal for studying the detailed abundances and spatially resolved kinematics with deep spectroscopy. While this paper focuses on the chemical abundances of the lensed galaxies, Sweet et al. (in prep.) will present a high-resolution kinematic analysis of AGEL1323 in an upcoming paper. In 2021, we acquired deeper follow-up observations with Keck/LRIS and Keck/MOSFIRE for the galaxies to capture the portion of the rest-frame optical between 3600 Å and 5500 Å, which is sufficient to recover the ages and Fe and Mg abundances of the stellar population (Leethochawalit et al., 2018a; Leethochawalit et al., 2019; Zhuang et al., 2021). In this section, we describe the spectroscopic and photometric data used for the stellar population analyses (Table 3.1). 3.2.2 Spectroscopy Keck/LRIS We observed AGEL1323 with LRIS on the Keck I telescope with the D560 dichroic, 400/8500 grating and 1′′ slit width for the red side for a total of 6 hours. The seeing varied between ∼ 0.8′′ and ∼ 1.1′′ throughout the night. We determined a FWHM 1 Two of the lensed images are only visible in high resolution HST imaging (Figure 3.2). 52 Table 3.1: Spectroscopic and Photometric Observations of the Lensed Galaxies Object R.A. (J2000) Decl. (J2000) 𝑧spec AGEL1323 13h 23m 04s .1 +03d 43m 19s .4 1.016 Instrument Date Integration Time S/N𝑎 (Å −1 ) Keck/LRIS Keck/MOSFIRE-Y 2021-04-05 2021-04-17 2021-04-17 2021-04-17 2022-06-18 2022-06-18 2021-08-17 2021-08-17 2021-10-30 2021-10-30 6.0 h 5.0 h 786 s 105 s 600 s 598 s 1.5 h 1.5 h 1830 s 1668 s 60 50 50 40 - ∗ Keck/MOSFIRE-Y ∗ Keck/MOSFIRE-K 𝑠 ∗ HST/WFC3-F200LP ∗ HST/WFC3-F140W AGEL0014 00h 14m 24s .3 +00d 41m 45s .5 1.374 Keck/MOSFIRE-Y Keck/MOSFIRE-J ∗ Keck/MOSFIRE-J ∗ Keck/MOSFIRE-K 𝑠 a S/N of the stacked spectra, including all lensed images. The S/N was calculated as median ratio of the noise array to the flux array in the wavelength range of 4000–5500Å. For this purpose, the noise array was not augmented by 𝜒 2 . That augmentation applies only to the reported uncertainties on stellar population parameters (see Section 3.3.3). * Photometric observations. Figure 3.1: Color images of AGEL1323 (top) and AGEL0014 (bottom). The images were constructed using HSC 𝑟𝑖-band and MOSFIRE-K𝑠 imaging. The MOSFIRE (yellow) and LRIS (magenta) slits are overplotted. of 6.47 Å from the spectrum of the arc lamp, corresponding to 3.21 Å in the rest frame. The spectral energy distribution of AGEL1323 is such that the blue side of the LRIS spectrum had insufficient flux for a meaningful analysis. The data were reduced with PypeIt (Prochaska et al., 2020a; Prochaska et al., 2020b), a semi-automatic software that performs flat field correction, cosmic ray removal, wavelength calibration, flexure correction via sky lines, heliocentric corrections, sky subtraction and spectral extraction. Because we used HgNeArCdZn lamps, different from the archived arcs in PypeIt, we calibrated the wavelength solution by visually identifying the arc lines instead of using the automatic line detecting algorithms. The extracted 1D spectra of each image of AGEL1323 (A1, A2, and A3) were flux-calibrated and coadded separately after the main run of PypeIt. The telluric corrections were performed directly on the coadded science spectra, which 53 fits a fifth-order polynomial model representing the continuum of the galaxy and spectral regions sensitive to telluric absorption to a grid of telluric spectral templates. Readers are referred to PypeIt’s website2 for details. The coadded spectra for the three lensed images were stacked with inverse variation weighting to maximize the S/N in order to better characterize the stellar population properties. Keck/MOSFIRE We observed AGEL1323 with MOSFIRE Y-band on Keck I telescope MOSFIRE-Y using a slit width of 0.7′′ for the slit mask for 5 hours. The seeing was around 1′′, yielding a FWHM of ∼ 2.5 Å. On the second night, we observed AGEL0014 using a slit width of 1.0′′ for a total of 3 hours in Y and J band. The seeing was around 0.4′′ on the second night, providing a FHWM of ∼ 3.5 Å in the Y-band and ∼ 4.4 Å in the J-band. The raw data were reduced using the MOSFIRE DRP3 to generate a coadded 2D spectrum for the entire night. Generally, the MOSFIRE DRP expects that the data were taken with a standard dithering pattern of ABAB within the slits, which results in one positive and one negative trace in the differential image. However, we adopted a non-standard dither pattern for AGEL1323 because the small separations (∼ 7′′) between the three lensed images do not allow enough room to nod within the slits. We therefore required the telescope to nod across the slits. The mask was designed to have two pairs of slits separated by 23.94′′, corresponding to the length of three slits. Three traces of the three lensed images were present on the different slits at the two different telescope pointings. This strategy made the differential image consist of either a positive or a negative trace in one slit. We modified the DRP slightly to handle the sky subtraction to account for this nodding solution. In each slit of the differential image, the light profile was generated from the median of 2D spectrum. We then fit a Gaussian profile to the light profile and masked out the regions within 2𝜎 where most of the light is from the galaxy. We then estimated the sky background from the unmasked regions. We also experimented with a few choices of thresholds and found that 2𝜎 masking could give the cleanest background while keeping enough signal from the galaxy. One-dimensional (1D) spectra were extracted from the 2D spectrum produced by the DRP using MOSPEC (Strom et al., 2017). We used optimal extraction (Horne, 2 PypeIt: https://pypeit.readthedocs.io/en/release/index.html 3 MOSFIRE DRP: https://keck-datareductionpipelines.github.io/MosfireDRP/ 54 1986). The flux calibration was performed by comparing the observed spectrum of the standard star with the Vega spectrum scaled to its J-band magnitude. A B-spline was fitted to the ratio of the scaled spectrum to the observed spectrum to derive the response curve. We then applied the curve to other extracted science spectra to obtain the flux-calibrated, telluric-corrected spectrum of each science target. 3.2.3 Photometry Ground-based Imaging To construct the lens model, we obtained MOSFIRE images for AGEL1323 and AGEL0014 on 2021 Apr 5 and 2021 Oct 30, respectively. The sky was clear on both nights, with an average seeing of 0.82′′ on Apr 5 and 0.65′′ on Oct 30. We reduced the images by using the standard IRAF commands to perform dark subtraction, flat correction, and sky subtraction. The final images have a 5𝜎 limiting magnitude of 24.88 mag in the J-band and 24.38 mag in the K𝑠 -band for AGEL0014, and 23.93 mag in the Y-band and 23.14 mag in the K𝑠 -band for AGEL1323 on a pixel-to-pixel basis. We performed the flux calibration by comparing the instrumental magnitudes of 2MASS stars in the field obtained from SExtractor (Bertin and Arnouts, 1996) with the values in 2MASS Point Source Catalog (Skrutskie et al., 2006). In addition, the public images of AGEL1323 and AGEL0014 in the Hyper SuprimeCam (HSC) Subaru Strategic Program DR3 (Aihara et al., 2022) were used for lens modeling (Section 3.3.2). HST/WFC3 We used F140W and F200LP images from HST/WFC3 from program 16773 (PI Glazebrook). The target was observed in the IR/F140W filter for 3 exposures of 200 seconds, and in the UVIS/F200LP filter for 2 exposures of 300 seconds (Shajib et al., 2022a; Shajib et al., 2022b). The images were reduced using the STScI DrizzlePac software package to align the separate exposures, as well as correct for background distortion and remove flagged cosmic rays. Within the AstroDrizzle function, we customized the WCS for the final stacked output to rotate the filters in the same orientation. We set the final pixel size of “0.08 to match the F200LP filter with the scaling of filter F140W. To create the mock-RGB combined image in Figure 3.2, we used the Lupton et al. (2004) algorithm implemented in astropy’s make_lupton_rgb. 55 Figure 3.2: The HST/WFC3 color image of AGEL1323 constructed with F200LP and F140W imaging. The counter-image and the central image are marked by the green and red circle, respectively. 3.3 Methods 3.3.1 Lens Modeling To obtain a reliable mass estimate, a lens model is needed to calculate the magnification factor and yield the delensed stellar mass. We used the lens modeling software PyAutoLens4 (Nightingale and Dye, 2015; Nightingale, Dye, and Massey, 2018; Nightingale, Hayes, and Griffiths, 2021; Nightingale et al., 2021) to fit the observed images. Although Sukay et al. (2022) already constructed the lens model for AGEL1323 by fitting the Magellan/FourStar 𝐻-band image with LENSTOOL (Jullo et al., 2007) and derived a magnification factor of 𝜇 = 74+49 −28 , our HST data reveals a fifth image of the source that was not identified by Sukay et al. (2022). The counter-image is very close to one of the lens galaxies and marked by the green arrow in Figure 3.2. Our results differ from those of Sukay et al. because the counter-image is visible only with the high spatial resolution of our HST images. As a result, our lens model results in a significantly lower magnification. AGEL1323 is a group scale lens containing multiple lens galaxies. We fit the HST F200LP imaging data. We first subtract the light of the two brightest galaxies marked with black crosses in Figure 3.3, by fitting elliptical Sérsic light profiles. To this foreground subtracted data we apply a custom mask (drawn via a graphical 4 https://github.com/Jammy2211/PyAutoLens 56 Observed Image 8.6 8.6 600 Lens Subtracted Image 600 500 500 5.5 5.5 2.4 300 400 y (arcsec) y (arcsec) 400 2.4 300 200 -0.7 200 -0.7 100 -3.8 -6.1 8.6 -2.97 0.15 x (arcsec) 3.28 6.4 Model Lensed Source 100 0 -3.8 -6.1 600 8.6 -2.97 0.15 x (arcsec) 3.28 6.4 0 Residual Map 100 500 5.5 5.5 50 2.4 300 y (arcsec) y (arcsec) 400 2.4 0 200 -0.7 50 -0.7 100 100 -3.8 -6.1 -2.97 0.15 x (arcsec) 3.28 6.4 0 -3.8 -6.1 -2.97 0.15 x (arcsec) 3.28 6.4 Figure 3.3: The observed HST F200 image (upper left), observed image with a model for the foreground lensing galaxies subtracted (upper right), best-fit model lensed source (bottom left) and residual map (bottom right) of lens modeling performed with PyAutoLens. Cut-outs were extracted from the full HST F200 image shown in Figure 3.2. The white line plotted over the bottom left panel is the lens model’s tangential critical curve. In the lens-subtracted image, five distinct multiple images are seen, which are all reproduced by the lens model. The units of the colorbar are counts. 57 1000 800 -2.38 y (arcsec) 600 -0.81 0.76 -3.96 Lens Subtracted Image 1000 800 -2.38 600 -0.81 400 2.34 -2.52 -3.96 y (arcsec) Observed Image -3.96 0.76 200 -0.94 0.63 x (arcsec) 2.2 3.78 Model Lensed Source 0 2.34 -2.52 1000 -3.96 800 -2.38 400 200 -0.94 0.63 x (arcsec) 2.2 3.78 Residual Map 0 30 20 -2.38 y (arcsec) -0.81 y (arcsec) 10 600 -0.81 400 0 10 0.76 2.34 -2.52 200 -0.94 0.63 x (arcsec) 2.2 3.78 0 0.76 20 2.34 -2.52 -0.94 0.63 x (arcsec) 2.2 3.78 30 Figure 3.4: The observed MOSFIRE-K𝑠 image (upper left), observed image with a model for the foreground lensing galaxy subtracted (upper right), best-fit model lensed source (bottom left) and residual map (bottom right) of lens modeling performed with PyAutoLens. The units of the colorbar are counts. Cut-outs were extracted from the full MOSFIRE-K𝑠 image shown in Figure 3.1. The white line plotted over the bottom left panel is the lens model’s tangential critical curve. In the lens-subtracted image, a faint counter-image is seen around (𝑥 = 0.7′′, 𝑦 = −0.7′′), which is successfully recovered in the model lensed source. 58 user interface) which retains only the lensed source’s multiple images. We then fit a mass model where the mass of the two galaxies marked with black crosses in Figure 3.3 are singular isothermal ellipsoids, and the group’s host dark matter halo is modeled with a spherical NFW profile (Navarro, Frenk, and White, 1997). The NFW profile’s concentration is set to the mean of the mass-concentration relation of Ludlow et al. (2016). The source is again modeled by an elliptical Sérsic profile. We fit the mass and source profiles simultaneously. As shown in Figure 3.3, the best-fit model successfully reproduces all five images, including the central image. We define the magnification 𝜇 as the ratio of the total image-plane flux of the source divided by the total source-plane flux, and infer a value of 𝜇 = 14.55+0.55 −1.07 . For AGEL0014, we performed the fitting on the MOSFIRE-K𝑠 image. For the lens galaxy, we fit an elliptical Sérsic light profile for its light and singular isothermal ellipsoid for its mass. For the source, we fit an elliptical Sérsic light profile. We fit all three components simultaneously, using the nested sampling algorithm dynesty (Speagle, 2020). As shown in Figure 3.4, the best-fit model successfully detects a faint source counter image, which is offset ∼ 0.5” from the lens galaxy center and is not visible until after the lens light subtraction. For the magnification we infer a value of 𝜇 = 4.33+0.16 −0.11 . 3.3.2 Stellar Mass Estimates The lensed stellar masses were measured by fitting the broadband spectral energy distribution (SED). For AGEL1323 we used photometry from DECaLS 𝑔𝑟𝑧, HSC-𝑟𝑖, MOSFIRE-YK𝑠 and HST/WFC3-F140W. We adopted HSC-𝑔𝑟𝑖𝑧𝑦 and MOSFIRE-YK𝑠 for the photometry of AGEL0014. For each galaxy, we smoothed the high resolution images to match the point spread function (PSF) with the one that has lowest resolution and extracted the photometry from the reduced images with SExtractor (Bertin and Arnouts, 1996). We padded the photometric uncertainties to 0.1 mag if the formal errors are smaller than that to account for possible systematics originated from complicated morphologies of the lensing system. The photometry is corrected for Galactic reddening using the 𝐸 (𝐵 −𝑉) values measured by Schlafly and Finkbeiner (2011). We modeled the SED assuming an delayed exponentially declining (delayed-𝜏) SFH with BAGPIPES (Carnall et al., 2018; Carnall et al., 2019). We used the Calzetti et al. (2000) dust extinction law and required the attenuation in the 𝑉 band (𝐴𝑉 ) to be varied between 0 < 𝐴𝑉 < 2. The redshift for each galaxy has a Gaussian 59 prior centered at 𝑧 𝑠𝑝𝑒𝑐 in the AGEL catalog, with a standard deviation of 0.005. The other free parameters and their priors are stellar mass (9 < log (𝑀∗ /𝑀⊙ ) < 15), stellar metallicity (−2 < log (𝑍/𝑍 ⊙ ) < 0.4), time since the onset of star formation (30 Myr < 𝑇0 < 𝑡 𝑜𝑏𝑠 5 ), and the 𝑒-folding SFR timescale (30 Myr < 𝜏 < 10 Gyr). As shown in Figure 3.5, the SED models yield a lensed stellar mass of log (𝑀∗ /𝑀⊙ ) = 12.3 ± 0.1 and log (𝑀∗ /𝑀⊙ ) = 12.1 ± 0.1 for AGEL1323 and AGEL0014, respectively, which translates a delensed stellar mass of log (𝑀∗ /𝑀⊙ ) = 11.13 ± 0.10 and log (𝑀∗ /𝑀⊙ ) = 11.48 ± 0.09 when the magnification is corrected. To quantify the systematic uncertainties of stellar masses due to different assumptions on SFH, we also performed SED fitting with four other SFH models, including single burst, single exponentially declining, log-normal, and double-power-law SFHs. The root-mean-square (RMS) errors among the best-fit stellar masses6 of different models are used as estimates of the systematic uncertainties (0.02 dex for AGEL1323 and 0.08 dex for AGEL0014). In the end, we obtained a delensed stellar mass of log (𝑀∗ /𝑀⊙ ) = 11.13±0.10 for AGEL1323 and log (𝑀∗ /𝑀⊙ ) = 11.48±0.12 for AGEL0014. We also performed some robustness tests: experimenting with different detection and analysis thresholds for SExtractor, including spectroscopic data for SED fitting, and only fitting for the photometry reported by Sukay et al. (2022). All the results are consistent with our reported values within 1𝜎. For both galaxies, the delensed stellar masses of the two galaxies derived from the SED fitting and the velocity dispersion determined from the full-spectrum fitting (Section 3.3.3) are consistent with the stellar mass–velocity dispersion relation of quiescent galaxies at 𝑧 ∼ 1 (Belli, Newman, and Ellis, 2014; Mendel et al., 2020). 3.3.3 Stellar Population Fitting We analyzed the combined spectra using the full-spectrum fitting algorithm absorption line fitter (alf, Conroy and van Dokkum, 2012; Conroy et al., 2018) because of its capability of measuring detailed elemental abundances in addition to overall stellar metallicity, [Fe/H]. alf uses MIST isochrones (Choi et al., 2016) and empirical stellar spectra (Sánchez-Blázquez et al., 2006; Villaume et al., 2017), along with a theoretical response function covering a wide range of elemental abundances. This code operates on the continuum-normalized spectrum by fitting a high-order polynomial to the ratio of the model and data to avoid potential issues with imperfect flux calibration and dust attenuation. This functionality also allows alf to 5𝑡 𝑜𝑏𝑠 stands for the age of the universe at the observed redshift. 6 The best-fit stellar masses here mean the median value of the 1D posterior distribution. 60 Figure 3.5: Broadband SED fitting of AGEL1323 and AGEL0014. Left: The observed photometry and the SED model of AGEL1323 (top) and AGEL0014 (bottom) assuming delayed-𝜏 SFH derived by BAGPIPES (Carnall et al., 2018; Carnall et al., 2019). The observed and model photometry are shown by the navy and orange dots, respectively. For AGEL1323, the photometric data is from the DECaLS 𝑔𝑟𝑧-band, HSC 𝑟𝑖-band, MOSFIRE-YK𝑠 and HST/WFC3-F140W. For AGEL0014, the photometry is from HSC 𝑔𝑟𝑖𝑧𝑦-band and MOSFIRE-JK𝑠 . The orange regions show the 1𝜎 confidence interval of model spectra (light orange) and model photometry (dark orange). Right: The posterior distributions and covariances of the lensed stellar mass and the mass-weighted stellar age averaged over the SFH determined from BAGPIPES for AGEL1323 (top) and AGEL0014 (bottom). The contours represent the 1𝜎, 2𝜎 and 3𝜎 level. 61 fit multiple spectra of the same source taken on various instruments with different flux calibrations and instrumental resolutions. The fitting is accomplished with the ensemble Markov Chain Monte Carlo (MCMC) sampler emcee (Foreman-Mackey et al., 2013) to efficiently explore a large parameter space. We used alf’s simple mode, which assumes a simple stellar population (SSP) and a fixed Kroupa (2001) initial mass function (IMF). It simultaneously fits for the recession velocity, velocity dispersion, stellar age, stellar metallicity [Fe/H], and the abundances of C, N, O, Na, Mg, Si, Ca, and Ti. The resulting stellar population parameters are SSP-equivalent, which are similar to light-weighted age and abundances. Following Beverage et al. (2021), the default priors were used, except that of maximum age was set to be 1 Gyr older than the age of universe at the observed redshift to fully explore the parameter space and to avoid a truncated posterior distribution. The recovered parameters are consistent with the results when the maximum allowed age is the age of universe at the observed redshift. Although alf also has a full mode describing a double-component stellar population, Conroy et al. (2018) indicated that the simple mode is more reliable when only the blue optical spectrum is available. Zhuang et al. (2021) also found out that the abundances derived from the alf simple mode are more consistent with those obtained from resolved stellar spectroscopy. Therefore, the following analysis focuses on the results obtained from the simple mode. Given the quality and wavelength coverage of our data, we focused on the age, [Fe/H], and [Mg/Fe] derived from alf. We chose to measure Mg for two reasons. First, Mg is one of the 𝛼-elements that is mainly produced by core-collapse supernovae. Due to the short lifetime of massive stars, its recycling time can be approximated as instantaneous, for which magnesium is a good tracer of the overall galaxy evolution. For instance, Leethochawalit et al. (2019) used [Mg/H] of quiescent galaxies as a proxy to constrain the mass-loading factor of outflows averaged over the entire SFH. Second, the Mg 𝑏 triplet at 5170 Å, which minimally overlaps with absorption features of other elements, is available in our spectra, allowing us to determine the Mg abundance reliably. We excluded any regions below 4000 Å for the alf fitting because the difficulty of matching the continuum around the 4000 Å break may introduce some errors in the recovered abundances 7 . This also excluded the Ca ii H and K lines from the fitting, which is known to have strong non-local thermodynamic equilibrium (NLTE) effects 7 Private communication with Meng Gu. 62 Table 3.2: Stellar Population Properties of the Lensed Galaxies Row Quantity Unit AGEL1323 AGEL0014 (1) (2) (3) (4) (5) (6) (7) log 𝑀∗ 𝜎𝑣 𝑡SSP [Fe/H]SSP [Mg/Fe]SSP [Mg/H]SSP 2 /d.o.f 𝜒SSP 𝑀⊙ km s−1 Gyr dex dex dex - 11.13 ± 0.10 183+7 −8 5.6+0.8 −0.8 −0.30+0.08 −0.07 0.19+0.08 −0.09 −0.11+0.10 −0.11 3.88 11.48 ± 0.12 263+18 −16 3.1+0.8 −0.3 +0.10 −0.26−0.11 0.28+0.13 −0.13 0.02+0.13 −0.14 3.80 Rows show (1) the delensed stellar mass estimates; (27) the velocity dispersion, stellar ages, [Fe/H], [Mg/Fe], [Mg/H] and the reduced 𝜒2 determined from alf’s simple mode assuming an SSP. The errors here have been corrected for the systematic uncertainties originated from the imperfect models and underestimated noise from the pipelines (See Section 3.3.3). that the current models poorly reproduce (Conroy et al., 2018). For each spectrum, we ran two iterations to remove the sky line residuals. In the first iteration, we only masked out the regions where the telluric features cannot be corrected. After the first fit, the pixels with 4𝜎 deviations from the best-fit model were masked to reduce the contamination of bright sky lines to the fitting. We then re-fit the spectrum with the new pixel mask to determine the best-fit model and the corresponding stellar population parameters. The reduced 𝜒2 of each spectrum is greater than 1, which may result from either models imperfections or underestimated flux uncertainties from the data reduction pipeline. Therefore, the uncertainties reported in Table 3.2 are rescaled by the square root of the reduced 𝜒2 to incorporate the systematic errors that were not captured by the posterior distribution and the random errors. We experimented with different degrees of polynomials for continuum normalization and found out that all the measurements are consistent with each other. The observed spectra and best-fit models determined by alf’s simple mode, as well as the posterior distributions of the corresponding model parameters without the error correction, are shown in Figure 3.6 for AGEL1323 and Figure 3.7 for AGEL0014. We list all measured parameters in Table 3.2. 63 Figure 3.6: Left: The observed spectrum (black) and best-fit SSP model (red) used in this work for AGEL1323. The gray areas represent the 1𝜎 uncertainties of the observed spectrum. We masked out a small portion in the LRIS-red spectrum for AGEL1323 because of the telluric features that cannot be corrected. The green lines show the ratio of the model residuals over the uncertainties, with the 3𝜎 regions indicated by the shaded beige regions. Right: Corner plot showing the posterior distributions and covariances among velocity dispersion (𝜎), age, [Fe/H], and [Mg/Fe] of the best-fit model. The uncertainties shown here are the random errors obtained from the posterior distribution, without being corrected for the systematic errors (See Section 3.3.3). The contours demonstrate the 1𝜎, 2𝜎 and 3𝜎 levels. Figure 3.7: Same as Figure 3.6, but showing the results of AGEL0014. 64 3.4 3.4.1 Results Old Ages and Possible Rapid Star Formation +0.8 Gyr, The measured SSP ages of AGEL1323 and AGEL0014 are 5.6±0.3 Gyr and 3.1−0.3 respectively, both corresponding to a formation redshift of 𝑧form ≳ 4. Although the SSP assumption may be too simple compared to the true SFHs, the SSP age is still a good indicator of the time when most of stars were formed in a galaxy considering its bias towards the youngest population. In other words, our alf results suggest that the majority of the stellar populations in the two galaxies were formed less than 2 Gyr after the Big Bang, indicating that they must have experienced rapid star formation to reach the stellar masses we see today. 3.4.2 Chemical Abundances of the Lensed Galaxies In Figure 3.8, we show the measured [Fe/H], [Mg/Fe], [Mg/H] of the AGEL galaxies compared with other quiescent galaxies at different redshifts as a function of stellar mass. To minimize the systematic effects between various full-spectrum fitting algorithms based on different model assumptions, we limit our comparison to those derived using the alf simple mode. We compare our results with the LEGA-C sample at 𝑧 ∼ 0.7 (Beverage et al., 2021) and other quiescent galaxies at 𝑧 ≳ 1 (Kriek et al., 2016; Kriek et al., 2019; Carnall et al., 2022). We also plot a sample of local SDSS galaxies (𝑧 ∼ 0.05) as reference. The SDSS sample is taken from Leethochawalit et al. (2019), who randomly selected 152 quiescent galaxies from the Gallazzi et al. (2005) sample in the mass range 109 −1011.5 𝑀⊙ . We re-measured their abundances with alf using the same wavelength range as the spectra of the lensed galaxies for consistency. We excluded the galaxies for which posterior distributions hit the upper or lower limits of the priors, leaving a sample of 123 galaxies. The best-fit 𝑧 ∼ 0 MZRs of [Fe/H] [Fe/H], [Mg/Fe], and [Mg/H] for the updated alf measurements of nearby SDSS galaxies are: [Fe/H] = (−0.14 ± 0.01) + (0.14 ± 0.02)𝑀10 [Mg/H] = (0.06 ± 0.01) + (0.20 ± 0.02) 𝑀10 (3.1) [Mg/Fe] = (0.20 ± 0.01) + (0.06 ± 0.01) 𝑀10 , where 𝑀10 = log [𝑀∗ /1010 𝑀⊙ ]. These relations are shown in Figure 3.8 to show the evolution in the mass–metallicity relation for the samples at different redshifts. The lensed galaxies and most of the high-𝑧 galaxies are more metal-poor than their local counterparts with similar stellar masses, consistent with the redshift evolution of the MZR found by Choi et al. (2014) and Leethochawalit et al. (2019). However, 65 Figure 3.8: The [Fe/H] (top), [Mg/Fe] (middle) and [Mg/H] (bottom) as a function of stellar mass for quiescent galaxies. AGEL1323 at 𝑧 = 1.016 and AGEL0014 at 𝑧 = 1.37 are plotted as a filled square and a pentagon, respectively. The SDSS galaxies at 𝑧 ∼ 0.05 (open green triangles) are taken from Leethochawalit et al. (2019) but re-measured with alf for consistency. The open yellow stars show the measurements for the LEGA-C sample at 0.59 < 𝑧 < 0.75 by Beverage et al. (2021). The abundances of individual high-𝑧 quiescent galaxies measured by Kriek et al. (2016) (blue open down triangle) and Kriek et al. (2019) (black open circles) as well as that of a stacked spectrum at 𝑧 = 1.15 determined by Carnall et al. (2022) are plotted for comparison. The green solid lines and shaded regions represent the best-fit linear relations and intrinsic scatter of the 𝑧 ∼ 0.05 SDSS galaxies. 66 the [Fe/H] of the AGEL galaxies, along with other high-𝑧 galaxies, appear to be comparable to those of the LEGA-C 𝑧 ∼ 0.7 galaxies. This finding does not necessarily contradict the redshift evolution. Leethochawalit et al. (2019) estimated that the normalization of the MZR decreases 0.04 dex per observed Gyr, which translates to a decrease of 0.2 dex in [Fe/H] from 𝑧 ∼ 0 to 𝑧 ∼ 0.7, and roughly 0.1 dex from 𝑧 ∼ 0.7 to 𝑧 ∼ 1.4. If we assume the intrinsic scatter of the MZR ∼ 0.06 dex at 𝑧 ≲ 0.54, Leethochawalit et al., 2019 has negligible redshift evolution, the combined effects of the observed uncertainties and intrinsic scatter in [Fe/H] at a given stellar mass can account for why the AGEL galaxies have similar [Fe/H] as LEGA-C galaxies at lower redshifts. A larger sample would be necessary to further investigate the redshift evolution of the MZR at high-𝑧. Jafariyazani et al. (2020) found one quiescent galaxy at 𝑧 ∼ 2 to be more metalrich ([Fe/H] = 0.26) than most quiescent galaxies at any redshift. Because this measurement is a significant outlier in metallicity compared to most of the previous studies, which discovered more metal-poor quiescent galaxies at higher redshifts, we do not include the result by Jafariyazani et al. (2020) in our comparison. It is beyond the scope of this work to understand why that galaxy at 𝑧 ∼ 2 is significantly more metal-rich than other high-𝑧 quiescent galaxies. The measurements of [Mg/Fe] of the AGEL galaxies are comparable to those in the nearby universe at similar masses, although the scatter in the mass–[Mg/Fe] relations of LEGA-C galaxies makes it hard to know if there is any redshift evolution between 𝑧 ∼ 0 and 𝑧 ∼ 0.7. Typically, [Mg/Fe] can be used to probe the SFH. Because iron has a more delayed production timescale than magnesium, Kriek et al. (2016) and Kriek et al. (2019) used the measured [Mg/Fe] as a proxy for star formation duration when assuming a closed box model, suggesting that high-𝑧 quiescent galaxies with enhanced [Mg/Fe] should have shorter star formation timescales. Therefore, the redshift evolution in the mass–[Mg/Fe] relation may reveal whether high-𝑧 galaxies have SFHs distinct from those at lower redshifts. However, the existing studies of redshift evolution in the mass–[Mg/Fe] relation are quite controversial. Leethochawalit et al. (2019) found that [Mg/Fe] is smaller at higher redshifts at fixed stellar mass for cluster quiescent galaxies below 𝑧 ≲ 0.54, while Kriek et al. (2019) and Beverage et al. (2021) did not detect any significant redshift evolution for LEGA-C galaxies at 𝑧 ∼ 0.7 and three quiescent galaxies at 𝑧 ∼ 1.4. Given the current sample size, the mass–[Mg/Fe] relation appears to be similar at local and 𝑧 ≳ 1 and thus in favor of what Beverage et al. (2021) and 67 Kriek et al. (2019) found, but again a larger sample would be needed for stronger constraints. The absence of significant 𝛼-enhancement of the lensed galaxies is unexpected because we expect old, quiescent galaxies to have enhanced [𝛼/Fe] ratios. The unexpected result inspired us to consider carefully whether the measured [Mg/Fe] from alf might be underestimated due to imperfect flux calibrations. As a fullspectrum fitting algorithm, alf adopts the information from the whole spectrum, including the continuum and metal absorption lines, to constrain the Mg abundance. Conroy et al. (2018) indicated that the continuum between 4000 Å and 5300 Å is also sensitive to Mg abundance, for which any small mismatch between the continuum level of the model spectrum and that of the observed data due to imperfect flux calibrations over a wider wavelength range may bias the measurement of [Mg/Fe]. For each galaxy, we generated alf model spectra with different [Mg/Fe] but fixed all other parameters to the best-fit values returned by alf. Figure 3.9: The model spectra with different [Mg/Fe] vs. the observed spectra for AGEL1323 (top) and AGEL0014 (bottom) near the Mg b triplet at ∼5170 Å. In each plot, the upper panel shows the models corresponding to 68% confidence interval of the best-fit [Mg/Fe] by the red region. The model spectra at 2𝜎 deviation from the median of [Mg/Fe] are overplotted by the blue and green lines for comparison. The masked pixels are marked by the grey vertical regions. The 1𝜎 random errors of the observed spectra are indicated by the grey-shaded regions. The lower panel of each plot is the error spectrum, representing the sky background. The models with higher or lower [Mg/Fe] give poorer fits to the Mg b triplet, which validates our measured [Mg/Fe] from alf. Figure 3.9 shows model spectra with [Mg/Fe] varying within 2𝜎 of the best-fit value compared to the observed data near the Mg b triplet region for each galaxy. We chose the Mg b triplet because it is the most prominent Mg feature in the observed wavelength range. These narrow atomic features are less affected by the flux calibrations than wider Mg-bearing molecular bands nearby. We evaluate the 68 reduced 𝜒2 near the Mg b for model spectra with 2𝜎 higher or lower [Mg/Fe] than the best-fit value and compare them with that of the best-fit model. As shown in Figure 3.9, for both lensed galaxies, neither a more 𝛼-rich nor a more 𝛼-poor model can better describe Mg b triplet than the best-fit model does, which validates our measured [Mg/Fe] obtained from the full-spectrum fitting. We now scrutinize the expectation that [Mg/Fe] should be enhanced in old, quiescent galaxies. In fact, the shape of SFH, merger history, the delayed explosion time of Type Ia supernovae and the presence of outflows/inflows can all affect the final [Mg/Fe] at the time when the galaxies quenched. For this reason, a galaxy that rapidly built its mass (e.g., over ∼ 1 Gyr) does not necessarily have to be very 𝛼enhanced. We have seen such evidence in the Local Group. de los Reyes et al. (2022, among others) found that Sculptor, a dwarf spheroidal galaxy in the Local Group, finished forming stars within ∼0.9 Gyr, but has only a moderate 𝛼-enhancement of [Mg/Fe] ≈ 0.2, comparable to [Mg/Fe] of our lensed galaxies. In addition, [Mg/Fe] of the lensed galaxies appears to be positively correlated with stellar mass, consistent with the findings of Kriek et al. (2019). We believe future James Webb Space Telescope (JWST) observations would be able to yield more reliable measurements of [Mg/Fe] in order to constrain the mass–[Mg/Fe] relation in the high-𝑧 universe (Nanayakkara et al., 2022). With the new measurements of our lensed galaxies, a mass dependence of [Mg/H] emerges for quiescent galaxies at 𝑧 ≳ 1, suggesting that [Mg/H] is likely to be correlated with stellar mass in the high-𝑧 universe. The AGEL galaxies and other high-𝑧 galaxies appear to have lower [Mg/H] compared to local quiescent galaxies. This redshift evolution in the mass–[Mg/H] relation is contradictory to the results of Leethochawalit et al. (2019), who argued for universal relations for quiescent galaxies at 𝑧 ≲ 0.54. While the discrepancy may result from different full-spectrum fitting algorithms used to determine [Mg/H], it is more likely that galaxies observed at 𝑧 > 1, especially those that formed at 𝑧 > 3, may have experienced qualitatively different physical processes shaping the final [Mg/H]. We discuss one of the possible origins in Section 3.5.2. 3.5 3.5.1 Discussion Dependence of Abundances on Galaxy Formation Time As many literature studies have reported the evolution of the MZR with observed redshift for quiescent galaxies (e.g., Gallazzi et al., 2014; Choi et al., 2014; 69 Leethochawalit et al., 2019), it is natural to ask whether such evolution is driven by galaxies’ observed redshifts (age of the universe when galaxies were observed) or formation redshifts (age of the universe when galaxies formed). In other words, should we expect galaxies located at similar redshifts or those forming stars at similar time to have similar metal abundances? Leethochawalit et al. (2019) studied the evolution of the MZR below 𝑧 ≲ 0.54 and argued that evolution of metallicity is more fundamental with formation redshift when mass dependence is removed. Following Leethochawalit et al. (2019), we investigate the dependence of abundances on galaxy formation time here. We first examine the measured [Fe/H], [Mg/Fe] and [Mg/H] as a function of SSP age obtained from alf’s simple mode for quiescent galaxies at various redshifts. As shown in Figure 3.10, [Fe/H] of high-𝑧 quiescent galaxies are distinct from those of local SDSS quiescent galaxies at a given SSP age, while such significant difference is not seen in [Mg/H]. At a certain SSP age, high-𝑧 quiescent galaxies are relatively more metal-poor and more 𝛼-enhanced compared to local counterparts. This scenario is expected as high-𝑧 galaxies have less time for Type Ia supernova explosion for iron production. The lack of prominent [Mg/H] separation between local and high-𝑧 populations can be explained by the short recycling timescale of magnesium. The distributions of [Mg/Fe] for high-z and local populations are slightly different, as the production of iron and magnesium both affect this trend. If high-𝑧 galaxies evolve passively and remain quenched to 𝑧 ∼ 0, their stellar abundances would not change significantly due to the absence of new star formation. Because high-𝑧 quiescent galaxies are believed to be the progenitors of local quiescent galaxies, we expect the high-𝑧 populations to overlap with the local counterparts in age–abundance plots once the age differences are corrected. Here, we approach this problem in a reverse way. If we ignore the small metallicity change as galaxies evolve passively, we can correct the age differences between the high-𝑧 and local galaxies by tracing back the age of the universe at galaxy formation, which is the difference between the age of the universe at the observed redshift and the measured SSP age for each galaxy. As can be seen in the second column of Figure 3.10, the differences of [Fe/H] and [Mg/Fe] between high-𝑧 galaxies and local galaxies are attenuated when we compare them as a function of galaxy formation time rather than SSP age. We further remove the first-order mass dependence of abundances by subtracting the best-fit MZRs at 𝑧 ∼ 0 (Equation 3.1) from the observed abundances. The deviations 70 Figure 3.10: Dependence of [Fe/H], [Mg/Fe], and [Mg/H] on galaxy formation time. Left: Dependence of [Fe/H], [Mg/Fe], and [Mg/H] on the SSP age (first column) and galaxy formation time (second column). Right: Dependence of abundances on the galaxy formation time with the stellar mass dependence removed (see Section 3.5.1). The grey shaded regions show the 68% confidence interval for 𝑧 ∼ 0 SDSS galaxies. The symbols for galaxies at different redshifts are the same as in Figure 3.8. in the right panels of Figure 3.10 demonstrate how galaxy formation time affects the final abundances. At 𝑧 ∼ 0, the evolution in [Fe/H] and [Mg/Fe] with formation time is 0.024 ± 0.003 dex per Gyr and −0.013 ± 0.002 dex per Gyr, respectively. On the contrary, we do not detect a significant dependence of [Mg/H] on galaxy formation time for local galaxies, with the best-fit slope of 0.010±0.004 dex per formation Gyr. The weak evolution of [Mg/H] with formation age is in agreement with the short recycling timescale of magnesium. As can be seen in Figure 3.10, the LEGA-C and high-𝑧 galaxies exhibit similar evolution of abundances when the dependence on mass and observed redshift is removed. The tighter relations in [Fe/H] and [Mg/Fe] imply that at a fixed stellar mass, the galaxy formation time since the Big Bang plays more fundamentally determines stellar metallicity and 𝛼-enhancement than the observed redshift. Still, [Fe/H] and [Mg/H] of the LEGA-C galaxies and high-𝑧 galaxies are systematically lower than local galaxies when the dependence on mass and age is removed, although the differences are relatively small. The discrepancy for high-𝑧 galaxies implies that additional mechanisms are needed to explain the small offset. One possibility is that not all high-𝑧 quiescent galaxies evolve passively. There is a 71 chance that some of them may rejuvenate and form younger stars in a later epoch. Recent studies have suggested that accretion of satellite galaxies is important to explain the size growth of massive elliptical galaxies across cosmic time (e.g., Oser et al., 2010; Greene et al., 2013; Oyarzún et al., 2019, and references therein). Such mergers may trigger star formation in originally quenched galaxies. If some of these high-𝑧 quiescent galaxies were at the temporary quenching phase between two starbursts, they would have a higher [Fe/H] and a younger formation time when reaching 𝑧 ∼ 0. We believe this scenario may be necessary to explain the redshift evolution of the MZR in Figure 3.8. As high-𝑧 quiescent galaxies evolve to 𝑧 ∼ 0 passively, they would become less massive and slightly more metal-poor. It appears that the most massive galaxies cannot move to the local sequence unless they can get metal-enriched in the later epoch, which would require either new star formation or mergers with much more metal-rich systems. The latter is less likely to happen because massive galaxies tend to accrete more metal-poor satellite galaxies (Oser et al., 2010). With the few available measurements at 𝑧 ≳ 1, we conclude that galaxy formation time would still be the key factor determining the metal abundances in quiescent galaxies below 𝑧 ≲ 2. At the same time, it is possible that some of the high-𝑧 galaxies may re-start forming stars at a later epoch. A larger sample of quiescent galaxies at 𝑧 ≳ 1 would be necessary to confirm this possible rejuvenation in star formation. 3.5.2 Enhanced outflows during the star formation To understand why AGEL1323 and AGEL0014 quenched so early in the universe, we use the measured [Mg/H] to constrain the outflows of the lensed galaxies during their star formation. Leethochawalit et al. (2019) presented a simple analytic chemical evolution model for quiescent galaxies that connects instantaneously recycled metals to the time-averaged mass-loading factor, based on the work of Lu, Blanc, and Benson (2015). Readers are encouraged to read Leethochawalit et al. (2019) for the details of the model. To summarize, the mass-loading factor here is defined as the ratio of the mass outflow rate to the SFR, averaged over the entire SFH. They also assume that: 1. The interstellar medium (ISM) where star formation occurs is perfectly mixed. 2. Metals are instantaneously recycled. 72 Figure 3.11: The mass-loading factor (𝜂) inferred from the measured [Mg/H] as a function of stellar mass for quiescent galaxies. The sample and the symbols are the same as Figure 3.8. The two AGEL galaxies appear to have higher mass-loading factors than nearby galaxies at similar masses. 3. Outflows and inflows are permitted, but only the outflows can significantly affect the total metal budget in the ISM. Because magnesium is the product of core-collapse supernovae of short-lived stars, it can be approximated as an instantaneously recycled element and thus fit into the model above. If assuming that no or minimal amount of gas is left in the quiescent galaxies, the abundance of an instantaneously recycled element would be 𝑍∗,quiescent ≈ 𝑦 ⟨𝜂⟩ 1 + 1−𝑅 , (3.2) where 𝑦 is the supernova yield and 𝑅 is the return mass fraction defined to be the fraction of the mass of a stellar generation that returns to the interstellar medium from short-lived massive stars and stellar winds. 𝑍∗,quiescent can be substituted as the absolute Mg abundance of quiescent galaxies. Following Leethochawalit et al. (2019), we adopted the solar abundance of Mg from Asplund et al. (2009) and the yield as three times the solar Mg abundance (Nomoto et al., 2006) to calculate the absolute Mg abundance. The return fraction is set to 𝑅 = 0.46 (Lu, Blanc, and Benson, 2015) for all galaxies. In Figure 3.11, we show the mass-loading factors inferred from the measured [Mg/H] for quiescent galaxies at various redshifts. The AGEL galaxies—as well as other 73 high-𝑧 galaxies—appear to have higher mass-loading factors than nearby quiescent galaxies, implying that galaxies may have enhanced outflows when they were forming stars in the early universe. The strong outflows would naturally cause the two galaxies to lose gas quickly and thus can no longer sustain further star formation. The observational constraints on the mass-loading factors for high-𝑧 galaxies are qualitatively consistent with the FIRE simulations (Hayward and Hopkins, 2017), which predict that 𝜂 increases significantly as redshift increases at 𝑀∗ ≳ 1010 𝑀⊙ . Therefore, it will be essential to perform similar studies when a larger sample of high-𝑧 quiescent galaxies at 𝑧 > 1 is available in order to further investigate whether there is a redshift evolution in the mass-loading factor as suggested by the FIRE simulations. 3.5.3 Comparison with Sukay et al. (2022) Sukay et al. (2022) derived the stellar population properties of AGEL1323 via a joint fit of photometry and spectroscopy with Prospector (Johnson et al., 2021). They adopted a non-parametric SFH model with seven age bins to characterize the stellar population. In this work, we instead measure the stellar population via fullspectrum fitting algorithms alf assuming an SSP or two SSPs (i.e., one or two age bins). Sukay et al. (2022) used the spectrum obtained on Alhambra Faint Object Spectrograph and Camera (ALFOSC) at the 2.56 m Nordic Optical Telescope (NOT) with a total integration time of 80 minutes. The low-resolution spectrum (𝑅 = 590) covers the rest-frame wavelength between 2820 Å and 5030 Å and thus is unable to resolve most of the faint metal absorption lines which is important to robustly constrain the stellar metallicity. Our new Keck spectra therefore are much deeper and have a much higher resolution. The Keck spectra cover the rest-frame optical between 3600-5500 Å, which includes many more metal absorption lines essential to the determination of [Fe/H] and [Mg/Fe]. We prefer an SSP model over more complicated SFHs because its simplicity reduces the degeneracy among free parameters. Although we adopted a different SFH model, the SSP age in this work is still in qualitatively good agreement with the SFH derived by Sukay et al. (2022). We obtained an SSP age of 5.6 ± 0.8 Gyr, while the SFH derived by Sukay et al. (2022) indicates an absence of prominent star formation activity until ∼3 Gyr ago. Both results indicate that AGEL1323 is an old system that quenched very early in the universe. We measured elemental abundances of [Fe/H] = −0.30+0.08 −0.07 and [Mg/Fe] = 74 0.19+0.08 −0.09 . If we convert our measurements to total metallicity as [Z/H] = [Fe/H] + 0.94[Mg/Fe] (Thomas, Maraston, and Bender, 2003), the total metallicity is [Z/H] = −0.12 ± 0.11, which is consistent with Sukay et al.’s best-fit stellar metallicity, log(𝑍/𝑍 ⊙ ) = −0.19. 3.5.4 Comparison between the ages and metallicities derived from different approaches While we primarily focus on the ages and the metallicities derived from alf with full-spectrum fitting, we also measured the stellar populations with SED fitting to estimate the stellar masses (Section 3.3.2). Here we briefly discuss the differences in the measurements from the two approaches. Since we adopt the delayed-𝜏 model in the broadband SED fitting, we compare the mass-weighted stellar ages averaged over the SFHs with the SSP ages derived from alf. As shown in Figure 3.5, we obtained a mean stellar age of 3.6+0.8 −1.1 Gyr +0.7 for AGEL1323 and 2.3−0.9 Gyr for AGEL0014. Although the ages derived from broadband SED fitting are still consistent with the SSP ages within 2𝜎, they are systematically lower than the values measured with alf. The mean stellar ages vary slightly across different SFH models, but all of them predict ages younger than the SSP ages while remaining consistent with alf’s measurements within 2𝜎. Even if such age differences can be attenuated by conducting a joint fitting of photometry and spectroscopy with BAGPIPES, the measured ages of both galaxies are still lower than those measured from alf. +0.07 for As for the stellar metallicities, we determine the [Z/H]BAGPIPES = −0.20−0.08 +0.03 for AGEL0014 when the red spectrum AGEL1323 and [Z/H]BAGPIPES = −0.17−0.04 covering the Mg b triplet and Fe I lines is included for each galaxy. The delayed𝜏 SFH with a single metallicity is assumed. The stellar metallicities measured from the joint fitting of photometry and spectroscopy are therefore consistent with the [Fe/H] determined by alf within 1𝜎, although BAGPIPES still yields higher metallicity measurements. The BAGPIPES measurement of [Z/H] of AGEL1323 is also within 1𝜎 of the total metallicity when we convert the alf’s measurements of [Fe/H] and [Mg/Fe] into [Z/H] as [Z/H] = [Fe/H] + 0.94[Mg/Fe] (Thomas, Maraston, and Bender, 2003), for consistency with other recent work (e.g., Kriek et al., 2019; Carnall et al., 2019). However, the total metallicities of AGEL0014 are consistent between the two approaches within 2𝜎. Even though the stellar ages and metallicities measured from SED fitting with BAG- 75 PIPES and full-spectrum fitting with alf appear to be consistent with each other, SED fitting systematically recovers younger and more metal-rich populations than full-spectrum fitting does. Several factors may account for the potential systematic effects, such as different SSP templates and the choices of SFH models. The fitted wavelength region may also affect the results. BAGPIPES only allows one spectrum to be included in the fit while alf can analyze two spectra obtained on different instruments/gratings. SED fitting also spans a much wider spectral range than fullspectrum fitting. There is no doubt that different spectral regions are sensitive to stellar populations at different ages. With the current sample of only two galaxies, it is beyond the scope of this work to quantify the possible systematic differences in the stellar population parameters measured with different approaches. 3.6 Conclusions We presented the deep rest-frame optical spectra obtained on the Keck I telescope for two gravitationally lensed, massive quiescent galaxies at 𝑧 ≳ 1: AGEL1323 (log (𝑀∗ /𝑀⊙ ) ∼ 11.1) and AGEL0014 (log (𝑀∗ /𝑀⊙ ) ∼ 11.5). The high S/N of the spectra enabled us to robustly characterize the stellar population and elemental abundances of the lensed galaxies via full-spectrum fitting under the SSP assumption. A summary of our findings is as follows: 1. We determined the stellar metallicities as [Fe/H] = −0.30+0.08 −0.07 for AGEL1323 +0.10 (𝑧 = 1.016) and [Fe/H] = −0.26−0.11 for AGEL0014 (𝑧 = 1.374). Compared with low-𝑧 galaxies at similar masses, the lensed galaxies in our sample are more metal-poor, consistent with other stellar metallicity measurements of quiescent galaxies at similar redshift Kriek et al. (2019) and Carnall et al. (2019). This tentatively indicates that the redshift evolution of the stellar MZR should be in place at 𝑧 ≲ 1.4. When we remove the mass dependence of metallicity for quiescent galaxies at different redshifts, we find that galaxies of the same masses that formed at the same time have similar metallicities, regardless of their observed redshift. This result implies that the evolution of the stellar MZR is more fundamental with formation redshift than with observed redshift. 2. We also measured the 𝛼-enhancements for two lensed galaxies as [Mg/Fe] = 0.19+0.08 −0.09 for AGEL1323 and [Mg/Fe] = 0.28±0.13 for AGEL0014. The lensed galaxies have comparable [Mg/Fe] as their low-𝑧 counterparts, despite of their old ages. 76 3. We obtained SSP-equivalent ages of 5.6±0.8 Gyr for AGEL1323 and 3.1+0.8 −0.3 Gyr for AGEL0014. Considering the observed redshifts and stellar masses of the lensed galaxies, the old ages show that the majority of the stellar population formed very rapidly in the galaxies (less than 2 Gyr after the Big Bang). Using a simple chemical evolution (Leethochawalit et al., 2019), we inferred mass-loading factors of the galaxies from the measured [Mg/H]. The high mass-loading factors imply that the two galaxies both experienced enhanced outflows during their star formation, which may have led to their early quenching. This work has demonstrated how gravitational lensing can further our understanding of the chemical evolution of quiescent galaxies in the high-redshift universe. At the moment, there are still just a handful of robust stellar abundance measurements for quiescent galaxies at 𝑧 ≳ 1. Therefore, larger samples would be necessary to systematically investigate the relation between stellar mass, stellar abundances, and the inferred mass-loading factors of high-𝑧 quiescent galaxies. The early data from JWST have revealed numerous new lens candidates that may be quiescent galaxies from even higher redshifts than those presented in this work. The upcoming bounty of spectroscopic and imaging data will revolutionize our knowledge of chemical enrichment histories of quiescent galaxies in the early universe. Acknowledgments The authors acknowledge the insightful and constructive feedback from the anonymous referee, which helped us improve the manuscript. We would also like to thank Meng Gu for helpful advice on full-spectrum fitting with alf and Allison Strom for useful discussions on MOSFIRE data reduction and analysis with MOSPEC. We gratefully thank the staff at the W. M. Keck Observatory, including support astronomers Luca Rizzi, Carlos Alvarez and Jim Lyke, and telescope operators Arina Rostopchina, Julie Renauld-Kim, and Heather Hershey, for assisting in the observations. We are grateful to the many people who have worked to make the Keck Telescope and its instruments a reality and to operate and maintain the Keck Observatory. The authors wish to extend special thanks to those of Hawaiian ancestry, on whose sacred mountain we are privileged to be guests. Without their generous hospitality, none of the observations presented herein would have been possible. This material is based on work supported by the National Science Foundation under 77 Grant No. AST-2233781 (E.N.K.) and AST-2009278 (C.C.S.). Z.Z., E.N.K. and C.C.S. acknowledge financial support from National Aeronautics and Space Administration (NASA) through the FINESST program (No. 80NSSC22K1755). K.G., T.N. and C.J. acknowledge support from Australian Research Council (FL180100060). S.M.S. acknowledges funding from the Australian Research Council (DE220100003). T.J. and K.V.G.C. gratefully acknowledge financial support from NASA through grant HST-GO-16773, the Gordon and Betty Moore Foundation through Grant GBMF8549, and the National Science Foundation through grant AST-2108515. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. This work makes use of observations with the NASA/ESA Hubble Space Telescope obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. Support for Program number GO-16773 was provided through a grant from the STScI under NASA contract NAS5-26555. 78 Chapter 4 METALS IN STAR-FORMING GALAXIES WITH KCWI: GLOBAL ABUNDANCES Zhuang, Z. et al. (Sept. 2024). “Metals in Star-forming Galaxies with KCWI. I. Methodology and First Results on the Abundances of Iron, Magnesium, and Oxygen”. In: ApJ 972.2, p. 182. doi: 10.3847/1538-4357/ad5ff8. Abstract Understanding the chemical enrichment of different elements is crucial to gaining a complete picture of galaxy chemical evolution. In this study, we present a new sample of 46 low-redshift, low-mass star-forming galaxies at 𝑀∗ ∼ 108−10 𝑀⊙ along with two quiescent galaxies at 𝑀∗ ∼ 108.8 𝑀⊙ observed with the Keck Cosmic Web Imager (KCWI), aiming to investigate the chemical evolution of galaxies in the transition zone between Local Group satellites and massive field galaxies. We develop a novel method to simultaneously determine stellar abundances of iron and magnesium in star-forming galaxies. With the gas-phase oxygen abundance (O/H)g measured using the strong line method, we are able to make the first-ever apples-to-apples comparison of 𝛼 elements in the stars and the ISM. We find that the [Mg/H]∗ –[O/H]g relation is much tighter than the [Fe/H]∗ –[O/H]g relation, which can be explained by the similar production processes of 𝛼 elements. Most galaxies in our sample exhibit higher [O/H]g than [Fe/H]∗ and [Mg/H]∗ . In addition, we construct mass–metallicity relations (MZRs) measured as three different elements (Fe∗ , Mg∗ , Og ). Compared to the gas O-MZR, the stellar Fe- and Mg-MZRs show larger scatter driven by variations in specific star formation rates (sSFR), with star-forming galaxies exhibiting higher sSFR and lower stellar abundances at fixed mass. The excess of [O/H]g compared to stellar abundances as well as the anticorrelation between sSFR and stellar abundance suggests that galaxy quenching of intermediate-mass galaxies at 𝑀∗ ∼ 108−10 𝑀⊙ is primarily driven by starvation. 4.1 Introduction Heavy elements are invaluable tracers of the evolutionary history of galaxies. The amount of metals (i.e., metallicity) residing in the interstellar medium (ISM) and stellar population of a galaxy is governed by the interplay between the gravitational 79 potential well (e.g., Dekel and Silk, 1986), nucleosynthesis during star formation (e.g., Kobayashi, Karakas, and Lugaro, 2020), efficiency of gas mixing in the ISM (e.g., Veilleux, Cecil, and Bland-Hawthorn, 2005), galactic outflows driven by stellar and AGN feedback (e.g., Murray, Quataert, and Thompson, 2005; Faucher-Giguère, Quataert, and Hopkins, 2013; Hopkins et al., 2014), and pristine inflows from the circumgalactic and intergalactic medium (CGM and IGM) over cosmic time (e.g., Kereš et al., 2005). Over the past five decades, significant progress has been made in measuring metallicities in galaxies from the Local Group to the high-redshift universe. Using emission line diagnostics that trace gas metallicity of galaxies, Lequeux et al. (1979a) first discovered a correlation between stellar masses and gas metallicities of the ISM in star-forming galaxies, which is known as the mass–metallicity relation (MZR). Later, Tremonti et al. (2004) measured the gas metallicities of ∼ 53, 000 starforming galaxies in the Sloan Digital Sky Survey (SDSS) from emission lines and confirmed that the gas metallicity is strongly correlated with stellar mass in all SDSS star-forming galaxies. Gallazzi et al. (2005) also discovered a similar correlation between stellar mass and stellar metallicity measured from stellar absorption features for a sample of 44,254 galaxies drawn from the SDSS survey. The trend was later confirmed by other works using various methods to measure metallicities in the SDSS galaxies (e.g., Andrews and Martini, 2013; Zahid et al., 2017). Previous studies have also found that both the stellar MZR and the gas MZRs exist in the Local Group satellite galaxies (e.g., Lee et al., 2006; Berg et al., 2012; Kirby et al., 2013). More recently, astronomers have shown that the MZR exists at all different redshifts, establishing the stellar MZR of quiescent galaxies up to 𝑧 ∼ 2 (Choi et al., 2014; Kriek et al., 2019; Leethochawalit et al., 2019; Zhuang et al., 2023; Beverage et al., 2024) and the gas MZR of star-forming galaxies up to 𝑧 ∼ 10 (e.g., Erb et al., 2006; Steidel et al., 2014; Maiolino and Mannucci, 2019; Sanders et al., 2020; Strom et al., 2022; Curti et al., 2023). All these studies suggest that at fixed stellar mass, high-𝑧 galaxies tend to have lower metallicities than their local counterparts. These trends are also captured by large cosmological simulations (e.g., Ma et al., 2016; De Rossi et al., 2017; Torrey et al., 2019). Generally, measurements of the MZR are based on the abundance of a single element: iron abundance [Fe/H]∗ for stars and oxygen abundance [O/H]g for ionized gas in the ISM. The gas-phase MZR indicates the chemical enrichment in the current ISM as galaxies grow in mass, while the stellar MZR represents the metals locked in stars 80 averaged over the entire star formation history (SFH). While most work to date has focused on measuring either the stellar or the gas-phase MZR, usually for passively evolving (e.g., Leethochawalit et al., 2019) or star-forming galaxies (e.g., Curti et al., 2020) respectively, recent work has attempted to relate the gas metallicity measured from nebular emission lines to the stellar metallicity determined from the stellar continuum for nearby (e.g., Lian et al., 2018b; Fraser-McKelvie et al., 2022, from the rest-optical continuum) and high-𝑧 star-forming galaxies (e.g., Steidel et al., 2016; Topping et al., 2020; Strom et al., 2022, from the rest-FUV continuum to which young OB stars primarily contribute the observed features). Such work has found that the two abundance measurements do not yield the same “metallicity” for galaxies with significant ongoing star formation, where gas metallicity measured as oxygen abundance is significantly higher than stellar metallicity that uses iron abundance as a proxy. Moreover, these comparison studies have shown that gasphase and stellar metallicities scale with stellar masses differently, resulting in different shapes (slopes and normalizations) of the gas-phase and stellar MZRs in the nearby and high-𝑧 universe (e.g., Fraser-McKelvie et al., 2022; Strom et al., 2022). The mismatch between the stellar and gas-phase metallicity is likely to result from the different recycling times of iron and oxygen. Oxygen is an 𝛼 element produced primarily by core collapse supernovae (CCSNe) on characteristic timescales of < 10 Myr, while the production of Fe is dominated by Type Ia supernovae (SNe) with characteristic delay times ≳ 400 Myr (Burbidge et al., 1957; Tinsley, 1980; Chen, Hu, and Wang, 2021). If a galaxy has formed a substantial fraction of its stars in the relatively recent past, the abundance of 𝛼 elements relative to iron, [𝛼/Fe], will be much higher than the solar ratio. In addition, if [Fe/H]∗ is measured from the restframe optical instead of UV spectrum, the result reflects the chemical enrichment of relatively old, low-mass stars because the stellar photospheric features of young OB stars reside primarily in the rest-frame UV. The oxygen abundance measured from emission lines instead indicates the amount of metals that reside in the current ISM, which better represents the level of chemical enrichment of the youngest stars. The combined effects of the distinct recycling times of iron and oxygen and the stars at different ages to which stellar and gas-phase metallicity are sensitive make it less straightforward to interpret the relation between metallicities in different phases. A better way to approach this problem would be to relate two elements for which the abundance ratio is less sensitive to the short-timescale details of the SFH. Magne- 81 sium in the stars is useful here. Because oxygen and magnesium are both 𝛼 elements, their abundance ratio should be much less affected by the varying delayed timescale of Type Ia SNe than [O/Fe] derived from the optical spectrum. Comparing [Mg/H]∗ of the stellar population with [O/H]g can therefore inform us about the degree to which metal-poor gas accretion or metal-rich outflows have affected the overall galactic metallicity. Relating the abundances of gas-phase oxygen, stellar iron, and stellar magnesium allows us to correlate chemical enrichment at different timescales. In addition, [Mg/Fe]∗ provides unique insights on the chemical enrichment history of a galaxy. In this work, we present a novel technique to determine [Fe/H]∗ and [Mg/Fe]∗ of star-forming galaxies via full-spectrum fitting of the optical stellar continuum. We apply this technique to a new sample of low-redshift, low-mass star-forming galaxies between 108 𝑀⊙ and 1010 𝑀⊙ observed with the Keck Cosmic Web Imager (KCWI; Morrissey et al., 2018), yielding the first-ever apples-to-apples comparison of 𝛼 elements in different phases. The KCWI sample consists of star-forming galaxies in the transition zone between the Local Group dwarf satellite galaxies and massive field galaxies that have been well-studied by large spectroscopic surveys. The sample’s purpose is to fully understand the shape of the stellar MZRs across the full range of galaxy masses. A simple extrapolation of the stellar MZR of satellite galaxies in the Local Group (𝑀∗ ≲ 108 𝑀⊙ , Kirby et al., 2013) appears to disagree with measurements of more massive, quiescent galaxies in the field (𝑀∗ ≳ 109.5 𝑀⊙ , Leethochawalit et al., 2019). At 𝑀∗ ∼ 109 𝑀⊙ , the high-mass and low-mass MZRs are discrepant in [Fe/H]∗ by ∼ 0.6 dex, much larger than the scatter of either MZR (see Figure 7 in Zhuang et al. 2021). In our previous work (Zhuang et al., 2021), we ruled out the possibility that the large discrepancy originates from systematic differences in the techniques used to estimate [Fe/H]∗ of galaxies at different masses, and we suggested that there is a transition mass in the stellar MZR in the local universe. Constraining the shape of the MZR, especially the stellar one, in the transition mass is essential to unveil how the physical processes regulating metal retention and interaction with the surrounding environment vary as galaxies grow in mass. The main goals of this paper are (1) to compare stellar and gas-phase abundances of a new sample of low-mass star-forming galaxies observed with KCWI; (2) to construct the MZR of our sample measured from three different elements (Og , Fe∗ and Mg∗ ); and (3) to quantify the shape of the stellar MZR for galaxies beyond the 82 Local Group in order to put constraints on the chemical evolution of galaxies. The structure of this paper is as follows. We describe the basic properties of the sample, the observations, and data reductions in Section 4.2. In Section 4.3, we present the methods used for emission line measurements and gas-phase metallicity determination. In Section 4.4, we explain the new technique used in this work to measure [Fe/H]∗ and [Mg/Fe]∗ of star-forming galaxies. We present our measurements from the KCWI data in Section 4.5 and discuss their implications when combining the abundance measurements of more massive SDSS galaxies in Section 4.6. Finally, we summarize our findings in Section 4.7. Throughout this work we assume a flat ΛCDM cosmology with Ω𝑚 = 0.3, ΩΛ = 0.7 and 𝐻0 = 70 km s−1 Mpc−1 . 4.2 Data We use KCWI mounted at Nasmyth focus on the Keck II telescope to obtain the spectroscopic data for our analysis. We describe the sample selection in Section 4.2.1, global properties of galaxies estimated from broadband photometry in Section 4.2.2, and summarize the KCWI observations and data reduction in Section 4.2.3. 4.2.1 Target Selection Our sample consists of 46 star-forming galaxies at 𝑧 < 0.06 in a stellar mass range of 108 − 1010 𝑀⊙ (Table 4.1). We chose this mass range because it represents the transition from the Local Group dwarf galaxies to the well-studied massive galaxies in the Hubble flow. The weak stellar absorption features of heavily star-forming galaxies dominant in this mass range has prevented observers from obtaining reliable measurements of not only stellar metallicity but also [Mg/Fe]∗ of individual starforming dwarfs from large spectroscopic optical surveys. Aiming to measure stellar and gas-phase abundances simultaneously of the same star-forming galaxies, we acquired very high-quality integral field spectroscopic data for this small sample to reveal their faint stellar features. 19 galaxies were selected from the clumpy galaxy catalog compiled by Mehta et al. (2021) that made use of the classification provided by the citizen science-powered Galaxy Zoo based on the SDSS Stripe82 images, while the other 27 galaxies were selected from the SDSS MPA-JHU catalog (Brinchmann et al., 2004; Tremonti et al., 2004). All these targets were randomly selected from the parent catalogs based on their stellar masses. We restricted our sample to galaxies with sSFR between 10−9 −10−11 yr−1 based on the SDSS MPA-JHU catalog (galSpecLine, SDSS DR17; Brinchmann et al., 2004; Tremonti et al., 2004), a range that is representative of 83 typical SDSS star-forming galaxies. Additionally, two quiescent galaxies, 0241-0810 and 0125-0024 at log (𝑀∗ /𝑀⊙ ) ∼ 8.8, were added to the sample as filler targets to investigate whether low-mass quiescent galaxies exhibit stellar abundances distinct from star-forming galaxies at similar masses. 0241-0810 is in the vicinity of the massive elliptical galaxy NGC 1052 with a similar radial velocity. The dwarf galaxy likely belongs to a virialized group structure in the environment of NGC 1052 (Román, Castilla, and Pascual-Granado, 2021). However, 0125-0024 is identified as an isolated dwarf galaxy at least 1 Mpc away from the nearest massive galaxy (log (𝑀∗ /𝑀⊙ ) > 10) by Kado-Fong et al. (2020) from the SDSS. 4.2.2 Photometry, Broadband SED Fitting and Size Measurements Although the SDSS catalog provides stellar masses and SFRs measured from SDSS 𝑢𝑔𝑟𝑖𝑧 photometry, we performed our own spectral energy distribution (SED) fitting with BAGPIPES (Carnall et al., 2018; Carnall et al., 2019) using photometry from far-UV to mid-IR wavelengths to obtain more reliable estimates of galaxies’ global properties. We retrieved the publicly-available coadded science images from the Galaxy Evolution Explorer (GALEX; Martin et al., 2005), the Sloan Digital Sky Survey (SDSS; York et al., 2000), the Panoramic Survey Telescope and Rapid Response System (PS1; Flewelling et al., 2020), and the Wide-field Infrared Survey Explorer (WISE; Wright et al., 2010) through the unblurred coadds of the WISE imaging (unWISE) archive (Lang, 2014). For each galaxy, we first calculated the flux densities ( 𝑓 𝑘 ) in each band 𝑘 with the same elliptical aperture defined as the Kron (1980) radius of the PS1-𝑖 image. To account for the resolution mismatch in different filters, each PS1-𝑖 detection image was downgraded to the resolutions in other photometric ′ bands, from which we estimated the flux densities in the same aperture as 𝑓ps1−i,k . The final photometry 𝑓 𝑘,final in the band 𝑘 was calculated as: 𝑓 𝑘,final = ′ 𝑓ps1−i,k 𝑓ps1−i 𝑓𝑘 (4.1) All the photometry was then corrected for Galactic reddening using the 𝐸 (𝐵 − 𝑉) values measured by Schlafly and Finkbeiner (2011). The SFRs and stellar masses were derived from BAGPIPES, a Bayesian-SED fitting code. We assumed a delayed exponentially declining (delayed-𝜏) SFH for each galaxy. We fixed the redshifts at the values in the SDSS catalog and adopted the 84 Calzetti et al. (2000) dust attenuation relation with a uniform prior of 0 < 𝐴𝑉 < 2. Nebular emission models based on the CLOUDY photoionization code (Ferland et al., 2017) with a varying ionization parameter −4 < log 𝑈 < −2 were included to account for the contribution from emission lines and nebular continuum. The other free parameters and their priors were stellar mass formed (7 < log (𝑀∗ /𝑀⊙ ) < 12), stellar metallicity (−2 < log (𝑍/𝑍 ⊙ ) < 0.4), time since the onset of star formation (1 Myr < 𝑇0 < 14 Gyr), and the 𝑒-folding SFR timescale (1 Myr < 𝜏 < 100 Gyr). We assumed uniform priors on the logarithmic scale for all the free parameters. The best-fit SFRs and stellar masses were taken as the 50th percentile of the marginalized 1D posterior distribution. We experimented with four other SFHs: single exponentially declining, log-normal, double-power-law, and constant SFHs. The root-mean-square (RMS) errors of the best-fit values (i.e., the median of the posteriors) between different SFH models are quoted as the reported uncertainties. 2 sSFR = 10−8 yr−1 10−9 yr−1 10−10 yr−1 1 log SFR [M yr−1] 10−11 yr−1 0 −1 −2 −3 star-forming quiescent −4 −5 8 9 10 11 12 log M∗ [M ] Figure 4.1: SFR as a function of stellar mass of the star-forming (blue squares) and quiescent (red stars) galaxies in our sample. The contours show the SDSS SFMS at a similar redshift range (𝑧 < 0.06) taken from the GSWLC catalog (Salim et al., 2016) at 1-3 𝜎. The grey dots indicate all the GSWLC galaxies at the same redshift range as our sample. All star-forming galaxies in our sample have typical SFRs and stellar masses like those in the SDSS “star-forming main sequence” (SFMS), as shown in Figure 4.1, except for the two quiescent galaxies. For 38 out of 48 galaxies in our sample, SFR and mass measurements are available from the GALEX-SDSS-WISE Legacy Catalog (GSWLC) (Salim et al., 2016; Salim, Boquien, and Lee, 2018). For 26 of these galaxies, the stellar masses and the SFRs we measured are consistent with the GSWLC estimates within 2𝜎 uncertainties. However, we emphasize that the major conclusions in this work remain unchanged when using the mass and SFR 85 estimates from the GSWLC catalog. The derived masses and SFRs are listed in Table 4.1. The SED-based SFR estimates of two spectroscopically confirmed quiescent galaxies show large uncertainties due to their faint UV fluxes, so their best-fit SFRs are only a proxy of their quiescent nature and should be taken with caution. Table 4.1: General Properties of the KCWI Galaxy Sample Galaxy 2225−0046 0231−0043 0133−0109 2329+1552 2152−0110 0845+5145 2334+0029 0121−0853 0013−0956 0155−0037 0140−0012 0023−0939 0233+0038 0256−0010 2259−0019 2300−0832 0233−0819 0125−0024 0241−0810 2301+1451 0332−0600 2131−0613 0850+6145 0256−0707 0033+0012 2137+1243 0137−0942 0040−0017 0136+1356 2304−0933 0309−0041 RA (J2000) Dec (J2000) 𝑧𝑎 log M∗ b [M⊙ ] log SFR𝑏 [M⊙ yr −1 ] 𝑅𝑒 (kpc) 22 25 07.92 02 31 32.17 01 33 41.39 23 29 46.17 21 52 22.46 08 45 54.52 23 34 14.80 01 21 51.93 00 13 45.42 01 55 01.92 01 40 52.90 00 23 48.32 02 33 03.92 02 56 32.90 22 59 03.19 23 00 51.88 02 33 05.84 01 25 06.09 02 41 35.06 23 01 06.26 03 32 00.36 21 31 03.64 08 50 39.67 02 56 34.76 00 33 14.83 21 37 52.51 01 37 43.57 00 40 35.09 01 36 15.18 23 04 30.86 03 09 58.06 −00 46 06.03 −00 43 36.63 −01 09 29.76 +15 52 38.96 −01 10 15.95 +51 45 11.12 +00 29 07.28 −08 53 10.63 −09 56 03.67 −00 37 35.27 −00 12 49.52 −09 39 09.85 +00 38 41.59 −00 10 51.13 −00 19 45.82 −08 32 13.36 −08 19 08.79 −00 24 31.22 −08 10 24.52 +14 51 16.74 −06 00 42.77 −06 13 58.27 +61 45 44.42 −07 07 11.12 +00 12 03.66 +12 43 42.63 −09 42 36.36 −00 17 37.19 +13 56 43.26 −09 33 03.58 −00 41 39.58 0.016 0.009 0.016 0.009 0.016 0.014 0.024 0.018 0.013 0.023 0.018 0.020 0.024 0.029 0.016 0.025 0.019 0.016 0.005 0.024 0.018 0.025 0.024 0.017 0.014 0.031 0.019 0.019 0.024 0.032 0.037 8.09±0.10 8.09±0.10 8.11±0.14 8.23±0.10 8.40±0.10 8.42±0.10 8.42±0.10 8.43±0.10 8.51±0.10 8.56±0.10 8.59±0.10 8.59±0.10 8.67±0.10 8.69±0.10 8.71±0.10 8.75±0.10 8.77±0.10 8.78±0.10 8.79±0.10 8.81±0.11 8.82±0.10 8.82±0.10 8.88±0.10 8.96±0.10 8.97±0.10 8.98±0.11 9.02±0.10 9.02±0.10 9.03±0.10 9.04±0.10 9.05±0.10 −1.84 ± 0.08 −1.67 ± 0.08 −1.36 ± 0.13 −1.67 ± 0.08 −1.72 ± 0.13 −1.80 ± 0.14 −1.19 ± 0.07 −1.55 ± 0.10 −1.45 ± 0.21 −1.50 ± 0.12 −1.74 ± 0.16 −1.10 ± 0.06 −0.93 ± 0.08 −0.89 ± 0.08 −1.21 ± 0.09 −1.58 ± 0.15 −1.61 ± 0.17 −4.67𝑐 −2.77𝑐 −0.74 ± 0.12 −1.71 ± 0.17 −0.73 ± 0.10 −1.05 ± 0.14 −1.08 ± 0.12 −0.57 ± 0.09 −0.91 ± 0.12 −0.88 ± 0.12 −0.95 ± 0.12 −0.49 ± 0.20 −0.94 ± 0.12 −0.51 ± 0.09 0.76±0.01 1.05±0.02 1.07±0.02 0.53±0.01 0.97±0.01 0.69±0.01 1.31±0.03 0.85±0.01 0.83±0.01 1.32±0.03 1.19±0.03 1.03±0.01 1.20±0.01 2.04±0.01 1.32±0.01 1.26±0.06 1.08±0.01 1.24±0.03 0.79±0.01 1.73±0.12 1.17±0.03 1.84±0.01 1.23±0.01 1.84±0.04 2.04±0.02 1.75±0.01 2.49±0.01 2.39±0.05 1.88±0.05 1.85±0.01 3.57±0.10 continued 86 Table 4.1: General Properties of the KCWI Galaxy Sample Galaxy 0019−0004 0208+0048 0306−0033 0346+0023 0243+0032 2318+0105 2206−0041 2243+0040 0334+0106 0317−0004 2211+0006 0245−0045 0030−0042 2139+0019 0407−0634 0254+0103 0140−0013 RA (J2000) Dec (J2000) 𝑧𝑎 log M∗ b [M⊙ ] log SFR𝑏 [M⊙ yr −1 ] 𝑅𝑒 (kpc) 00 19 17.04 02 08 48.30 03 06 24.96 03 46 06.86 02 43 33.19 23 18 01.34 22 06 46.12 22 43 58.53 03 34 06.02 03 17 20.20 22 11 47.47 02 45 57.45 00 30 13.43 21 39 56.73 04 07 04.64 02 54 50.52 01 40 47.46 −00 04 11.50 +00 48 01.41 −00 33 04.38 +00 23 24.93 +00 32 45.29 +01 05 13.31 −00 41 17.40 +00 40 25.70 +01 06 15.19 −00 04 37.04 +00 06 49.79 −00 45 12.27 −00 42 28.45 +00 19 23.69 −06 34 02.15 +01 03 26.97 −00 13 05.74 0.040 0.020 0.025 0.031 0.028 0.030 0.029 0.039 0.049 0.022 0.057 0.054 0.041 0.050 0.038 0.043 0.058 9.15±0.10 9.15±0.10 9.16±0.10 9.18±0.10 9.34±0.10 9.35±0.10 9.37±0.16 9.37±0.10 9.44±0.10 9.46±0.10 9.58±0.10 9.60±0.10 9.63±0.10 9.72±0.10 9.88±0.10 9.90±0.10 10.02±0.10 −0.45 ± 0.08 −0.66 ± 0.05 −0.98 ± 0.15 −0.32 ± 0.08 −0.68 ± 0.13 −0.59 ± 0.11 −0.11 ± 0.14 −0.48 ± 0.11 −0.03 ± 0.09 −0.08 ± 0.10 −0.20 ± 0.06 0.04 ± 0.10 0.13 ± 0.10 0.23 ± 0.09 0.01 ± 0.06 0.43 ± 0.06 −0.02 ± 0.12 2.95±0.09 3.84±0.05 1.58±0.04 2.56±0.05 3.13±0.05 3.97±0.05 1.64±0.01 4.07±0.06 3.87±0.01 3.86±0.03 4.00±0.19 5.05±0.10 2.74±0.01 4.60±0.06 4.75±0.06 6.48±0.02 6.28±0.12 a Redshifts are taken from SDSS DR17 (Abdurro’uf et al., 2022). b The stellar masses and SFRs are derived from broadband SED fitting with BAGPIPES. c Galaxies 0125-0024 and 0241-0810 are quiescent. The SED-based SFRs may not reflect the true level of star formation activity and thus only serve as a proxy of their quiescent nature. We decided to re-measure the sizes of the galaxies in our sample in spite of the existing size measurements in the SDSS catalog, because some of them with multiple star-forming clumps are mis-labeled as several individual galaxies instead of one galaxy in the SDSS catalog. Because of their complex light profiles, we chose to fit the Petrosian (1976) half-light radius (𝑅𝑒 ) independent of the assumption on galaxy light profiles. We estimated the Petrosian half-light radii of our sample from the PS1-𝑖 image using the PetroFit package (Geda et al., 2022). The size measurements and the associated errors are listed in Table 4.1. 4.2.3 KCWI Observations The KCWI data were taken over the course of five nights in October 2021 and September to November 2023. The seeing varied between ∼ 1.0′′ and ∼ 2.0′′ throughout the five nights. Table 4.2 describes the observations of each galaxy. The total exposure time for each galaxy ranged from 5 minutes to 100 minutes. We used 87 the BL grating with the Medium Slicer centered at 4500 Å, which gives a field of view (FoV) of 16.5′′×20.4′′ and wavelength coverage of 3500–5600 Å1 . From the arc spectra, we determined a spectral resolution FWHM of 2.5 Å (𝜎 ∼ 70 km s−1 ) for both nights. We observed most of the galaxies at multiple position angles (the orientation of the KCWI slices on the sky) to maximize the spatial resolution and minimize covariance during stacking. To perform sky subtraction for the galaxies with their angular sizes comparable or even larger than the IFU FoV, we either placed multiple pointings on the target to obtain the in-field sky or took off-field sky frames adjacent to the science frames with half of the science exposure time. Table 4.2: KCWI observations of the Galaxy Sample Galaxy 2225 − 0046 0231 − 0043 0133 − 0109 2329+1552 2152 − 0110 0845+5145 2334+0029 0121 − 0853 0013 − 0956 0155 − 0037 0140 − 0012 0023 − 0939 0233+0038 0256 − 0010 2259 − 0019 2300 − 0832 0233 − 0819 0125 − 0024 0241 − 0810 2301+1451 0332 − 0600 2131 − 0613 0850+6145 0256 − 0707 0033+0012 2137+1243 0137 − 0942 0040 − 0017 0136+1356 2304 − 0933 0309 − 0041 0019 − 0004 0208+0048 0306 − 0033 0346+0023 𝑧 Exposure (s) Position Angles (deg) Date Airmass 0.016 0.009 0.016 0.009 0.016 0.014 0.024 0.018 0.013 0.023 0.018 0.02 0.024 0.029 0.016 0.025 0.019 0.016 0.005 0.024 0.018 0.025 0.024 0.017 0.014 0.031 0.019 0.019 0.024 0.032 0.037 0.04 0.02 0.025 0.031 2320 5160 4200 950 2710 1985 2350 2000 1265 1900 2000 1000 2000 2965 3670 2057 2000 2336 1000 2340 2000 2000 1000 2000 1200 2250 2000 2400 1547 2000 3900 4800 2700 2000 1800 0, 90 70, 160 50, 140 90 0,90 0, 90 0, 90 0, 90 0, 90 0, 90 0, 90 0 0, 90 0, 120, 240 30, 90, 150 0 0, 90 0, 90 0 0, 90 0, 90 0, 90 90 0, 90 45 0,90 80, 170 110 0, 90 0, 90 170 0 90 0, 90 70, 160 2023-09-23 2021-10-02 2021-10-02 2023-09-23 2023-09-23 2023-11-05 2023-10-13 2023-10-13 2023-09-23 2023-11-05 2023-10-13 2023-10-13 2023-11-05 2023-11-05 2023-09-23 2023-09-23 2023-11-05 2023-10-13 2023-11-05 2023-10-13 2023-11-05 2023-10-13 2023-11-05 2023-11-05 2021-10-02 2023-09-23 2023-09-23 2021-10-10 2023-10-13 2023-10-13 2021-10-10 2021-10-02 2021-10-10 2023-11-05 2021-10-02 1.12 1.07 1.16 1.04 1.14 1.22 1.06 1.15 1.21 1.27 1.18 1.15 1.24 1.07 1.10 1.14 1.22 1.07 1.15 1.12 1.24 1.15 1.35 1.13 1.14 1.15 1.16 1.11 1.04 1.16 1.24 1.43 1.06 1.14 1.06 Off-field Sky ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Equivalent Extraction Radius𝑎 ( 𝑅𝑒 ) 1.1 1.6 1.7 1.4 1.6 2.1 1.6 1.8 1.2 1.2 1.5 1.2 1.4 1.3 1.0 1.5 1.5 0.9 1.2 1.5 1.5 1.3 1.4 1.4 1.8 1.7 1.1 1.9 1.9 1.7 1.2 1.8 1.5 1.6 1.6 continued 1 For the galaxies observed in 2023, we also have KCWI red channel data covering a spectral range of 6300–9500 Å. For consistency between data taken in different nights, we consider only the KCWI blue spectra. We are preparing a separate article (Z. Zhuang et al. in prep.) that will discuss the red optical data. 88 Table 4.2: KCWI observations of the Galaxy Sample Galaxy 0243+0032 2318+0105 2206 − 0041 2243+0040 0334+0106 0317 − 0004 2211+0006 0245 − 0045 0030 − 0042 2139+0019 0407 − 0634 0254+0103 0140 − 0013 𝑧 Exposure (s) Position Angles (deg) Date Airmass Off-field Sky Equivalent Extraction Radius𝑎 ( 𝑅𝑒 ) 0.028 0.03 0.029 0.039 0.049 0.022 0.057 0.054 0.041 0.05 0.038 0.043 0.058 2400 3600 1200 3600 1985 600 2400 1800 1200 1200 2000 2400 2700 90 60, 150 0, 90 50 0, 90 140 0, 90 90 45 0, 90 0, 90 20, 110 80, 170 2021-10-10 2021-10-10 2021-10-02 2021-10-10 2023-11-05 2021-10-10 2021-10-10 2021-10-10 2021-10-02 2021-10-02 2023-11-05 2021-10-02 2021-10-02 1.07 1.11 1.13 1.18 1.28 1.14 1.24 1.14 1.19 1.13 1.39 1.20 1.07 ✓ ✓ 1.7 1.5 2.2 1.8 0.6 1.4 1.5 1.5 1.5 1.3 0.9 1.6 1.4 ✓ ✓ ✓ ✓ ✓ a Because we used an irregular aperture to extract the spectrum for each galaxy, we estimate the equivalent binning radius as the fraction of the effective radius using the square root of the ratio of the area used for KCWI spectrum extraction and the area within 1 𝑅𝑒 . Data Reduction We reduced the KCWI data using a modified version of the publicly available KCWI data reduction pipeline with the updates detailed in Prusinski et al. (in prep.)2 . This pipeline converts raw, 2D science frames into flux-calibrated, 3D data cubes with a spatial sampling of 0.29′′× 0.68′′ and a spectral dispersion of 1 Å per pixel. It also allows us to scale the off-field sky frames for sky subtraction. The reduced data cubes were aligned, stacked, and resampled to a new spatial grid with a spatial sampling of 0.3′′× 0.3′′ and a dispersion of 1 Å per spectral channel using the KCWIKit package3 (Chen et al., 2021; Prusinski and Chen, 2024). Binning and Covariance Correction In this work, we focus only on the spatially integrated properties of the entire galaxies; results from a spatially-resolved analysis will be presented in future work (Zhuang et al., in prep). The integrated spectra for each galaxy were obtained by summing the spectra of spaxels with S/N > 1 per spectral pixel in the stellar continuum between 4200 Å and 4400 Å. As listed in Table 4.2, the extraction regions are equivalent to the area within 0.6–2.2 𝑅𝑒 for the galaxies in our sample. We selected regions based the S/N threshold instead of adopting a uniform aperture for spectrum extraction in order to maximize the S/N from the galaxies. As we further demonstrate in Appendix 4.8.1, any aperture bias that results from the irregular extraction region affects our main results negligibly. 2 https://github.com/prusinski/KCWI_DRP 3 https://github.com/yuguangchen1/KcwiKit 89 The IFU data underestimate the variance of the spatially-binned data due to covariance between adjacent spaxels, so we need to correct the variance of the binned spectra. This issue originates from the redistribution of the flux in the same pixel onto the new spatial grid when stacking the data. If we adopted standard error propagation to calculate the variances of the stacked data cubes assuming the adjacent pixels are independent of each other, the variances would be underestimated. As suggested by O’Sullivan and Chen (2020) the error of a KCWI data cube can be corrected as 𝜎measured = 𝐶 [1 + 𝛼 log (𝑁 𝑏 )]𝜎nocov , (4.2) for 𝑁 𝑏 ≲ 𝑁thresh , and as 𝜎measured = 𝐶 [1 + 𝛼 log (𝑁thresh )]𝜎nocov , (4.3) for 𝑁 𝑏 > 𝑁thresh , where 𝑁thresh represents the kernels beyond which the pixels become uncorrelated. To measure the correction parameters 𝐶, 𝛼, and 𝑁thresh , we followed the method developed by de los Reyes et al. (2023). In brief, we first simulated mock sky cubes as Gaussian noise centered at zero with variances determined from the variance cubes of the science frames. The variance values of mock sky cubes are the same as those of science cubes. The data and variance cubes of the mock sky were passed through the same stacking procedures as the science cubes. The 𝜎measured were calculated as the standard deviation of the mock sky data, while the 𝜎nocov were estimated as the median of the variance for the stacked sky cube. We then fit the 𝜎measured and 𝜎nocov to Equation (4.2) and (4.3) to derive 𝛼 and 𝑁thresh . Finally, the covariance correction factor from Equation (4.2) and (4.3) was multiplied into the flux uncertainties of the stacked spectra, which we previously calculated from error propagation without accounting for covariance. 4.3 Emission-Line Measurements The following section details the spectral analysis for gas-phase abundance measurements. Prior to the spectral analysis, the spectra were first corrected for Galactic extinction using the Galactic reddening maps of Schlafly and Finkbeiner (2011). We adopted the Galactic extinction law by O’Donnell (1994) to calculate the dereddening correction. The spectra are converted to the rest frame using the spectroscopic redshifts in the SDSS DR17 catalog (Abdurro’uf et al., 2022). 90 4.3.1 Disentangling stellar continuum and emission lines The first step in the spectral analysis is to separate the stellar continuum and emission lines in order to measure properties of the stellar population and the nebular gas. To do this, we performed a simultaneous fit of the stellar continuum and emission lines of the integrated spectrum using the Penalized Pixel-Fitting method (pPXF; Cappellari and Emsellem, 2004; Cappellari, 2017; Cappellari, 2023), which is a 𝜒2 -minimization code that fits for a linear combination of simple stellar population (SSP) models at different ages and metallicities to account for complex SFHs of star-forming galaxies. For the stellar population synthesis (SPS) templates, we generated SSP models from the Flexible Stellar Population Synthesis code (FSPS; Conroy, Gunn, and White, 2009; Conroy and Gunn, 2010) version 3.2, assuming a Kroupa (2001) IMF, the MIST isochrones (Choi et al., 2016), and the MILES stellar spectral libraries (Sánchez-Blázquez et al., 2006). The SSP models accessed through the PYTHONFSPS bindings (Foreman-Mackey, Sick, and Johnson, 2014) have metallicities spanning the range [Fe/H] = −2.0 to +0.5 with an interval of 0.25 dex, corresponding to the grid of the MIST isochrones. The ages range from log(Age) [yr] = 5.0 to 10.2 with an interval of 0.2 dex. Given that the instrumental resolution of KCWI (∼ 2.5 Å in the observed frame) is slightly higher than that of the FSPS SSP templates (2.54 Å in the rest frame), the observed spectra were convolved with a Gaussian kernel to match the spectral resolution of the SSP templates. We also restricted the spectral analysis to rest-frame wavelengths between 3650 Å and 5500 Å. Inspired by the MaNGA data-analysis pipeline (Westfall et al., 2019), we ran two iterations of pPXF for each spectrum to better constrain the stellar kinematics and stellar continuum. In the first iteration, the spectral regions around potential emission lines (Table 4.3) in the velocity range of ±400 km s−1 were masked to determine the stellar kinematics. We included an eighth-order additive Legendre polynomial and an eighth-order multiplicative Legendre polynomial in the fit of the stellar continuum, motivated by the experience of the MaNGA team (Westfall et al., 2019; Belfiore et al., 2019) to improve the quality of kinematics results. The two polynomials allow the overall shape of the model spectra to better match that of the data, which may suffer from imperfect flux calibration and small inaccuracies in the dust extinction correction. Each fit ran pPXF twice. After the first run with the default emission-line mask, we used a moving boxcar with a wavelength width of 100 Å (∼ 91 7000 km s−1 ) to determine the local mean and standard deviation of the fit residual. We then re-ran the fit with the updated mask excluding the > 3𝜎 outliers. In the second iteration, we fixed the stellar kinematics to the values determined from the first iteration and performed a simultaneous fit of emission lines and stellar continuum. The emission lines and their constraints used in the fits are listed in Table 4.3. As suggested by Sarzi et al. (2006) and Oh et al. (2011), this approach is preferable to fitting the emission lines separately on a continuum-subtracted spectrum, which tends to overestimate the emission line fluxes and widths when a small mismatch exists between the stellar continuum and SPS models. Figure 4.2 shows an example of a best-fit model obtained with the joint fitting from the second iteration along with the observed spectrum. [NI]− [OIII]− Hβ− [OIII]− Hγ− observed spectrum best-fit gas model best-fit stellar cont fλ 0030-0042 −0◦ 420 2500 102 1 kpc 3500 0h 30m 13.8s 13.6s 13.4s 13.2s 13.0s 3750 4000 4250 3750 4000 4250 −Mgb − −Hβ −CH −Hγ −Hδ −Hζ −CaK −CaH 0.05 −H11 −Hθ −Hη 3000 ∆fλ/fλ Dec Hδ− H− 103 Surface Brightness (10−14 erg/s/cm2 /arcsec2 ) 1 2 3 4 5 Hη− [NeIII]− Hζ− 0 [OII]− This method provides measurements of integrated emission line fluxes that properly account for the stellar continuum. Additionally, we obtain a emission-free stellar continuum spectrum by subtracting the best-fit emission line model from the observed spectrum; we will use this stellar continuum spectrum in Section 4.4 to estimate stellar abundances. 4500 4750 5000 5250 4500 4750 5000 5250 0.00 −0.05 RA λrest(Å) Figure 4.2: Left: Example KCWI white-light image computed by integrating the spectrum in the wavelength direction for each spatial pixel. Right: Example integrated KCWI spectrum of the same galaxy (top) and the model residual (bottom). In the top panel, the observed integrated spectrum is shown in black, while the best-fit model of the stellar continuum and the emission lines are shown in cyan and red, respectively. The 𝑦-axis is on a logarithmic scale. Prominent emission lines (blue) and stellar absorption features (red) are marked in the top and middle panels. The full set of the emission lines included in the fit is listed in Table 4.3. 4.3.2 Gas-phase oxygen abundance The intrinsic dust attenuation of each galaxy was calculated from the Balmer decrement H𝛾/H𝛽, because the spectral range of the KCWI-blue data did not include H𝛼. Assuming Case B recombination, 𝑇𝑒 = 10, 000 K and 𝑛𝑒 = 100 cm−3 , the theoretical 92 Table 4.3: Emission-Line Parameters ID Line Name 𝑎 (Å) 𝜆rest Fixed Ratio 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 H16 H15 H14 [O ii]𝜆3726 [O ii]𝜆3729 H13 H12 H11 H𝜃 He i𝜆3820 H𝜂 [S iii]𝜆3856 [Ne iii]𝜆3869 He i𝜆3889 H𝜁 [Ne iii]𝜆3967 H𝜖 He i𝜆4026 [S ii]𝜆4069 [S ii]𝜆4076 H𝛿 H𝛾 [O iii]𝜆4363 He i𝜆4471 [Fe iii]𝜆4658 He ii𝜆4686 He i𝜆4713 H𝛽 He i𝜆4922 [O iii]𝜆4959 [Fe iii]𝜆4985 [Fe iii]𝜆4986 [O iii]𝜆5007 He i𝜆5016 [N i]𝜆5198 [N i]𝜆5200 3704.913 3713.034 3723.003 3727.092 3729.875 3735.436 3751.217 3771.701 3798.976 3820.691 3836.472 3857.111 3869.860 3889.749 3890.151 3968.590 3971.195 4027.328 4069.749 4077.500 4102.892 4341.684 4364.436 4472.734 4659.414 4687.015 4714.466 4862.683 4923.305 4960.295 4985.900 4987.200 5008.240 5017.077 5199.349 5201.705 ... ... ... ... 0.28–1.47 [O ii]𝜆3726𝑏 ... ... ... ... ... ... ... ... ... ... 0.31 [Ne iii]𝜆3869 ... ... ... 0.40 [S ii]𝜆4069 ... ... ... ... ... ... ... ... ... 0.34 [O iii]𝜆5007 ... ... ... ... ... 0.37 [N i]𝜆5198 a Ritz wavelengths in vacuum from the National Institute of Standards and Technology (NIST) Atomic Spectra database (https://physics.nist. gov/PhysRefData/ASD/lines_form.html). b The line ratio of [O ii]𝜆3726/[O ii]𝜆3729 is only allowed to vary in the range of 0.28–1.47, as required by atomic physics (Osterbrock and Ferland, 2006). 93 ratio of H𝛾/H𝛽 is 0.47 (Osterbrock and Ferland, 2006). The intrinsic 𝐸 (𝐵 − 𝑉), derived from the theoretical ratio of H𝛾/H𝛽 along with the Cardelli, Clayton, and Mathis (1989) dust extinction law, was applied to the emission-line measurements to yield the dereddened line fluxes for nebular oxygen abundance determination. Ideally, nebular oxygen abundances would be measured from the reliable direct 𝑇𝑒 method, which directly determines the electron temperature of ionized gas. However, the direct 𝑇𝑒 method relies on the detection of auroral lines, such as [O iii]𝜆4363, which are exceedingly faint, especially for relatively metal-rich systems. We detected [O iii]𝜆4363 in fewer than 1/3 of the sample. We therefore used an empirical strong-line calibration derived from 𝑇𝑒 -based measurements to estimate the gasphase oxygen abundance for constructing an unbiased MZR. We will discuss the gas-phase oxygen abundances derived from different approaches in more detail in future work focusing on the KCWI-red data (Zhuang et al., in prep.). For the present, we use the “𝑅 calibration” (Pilyugin and Grebel, 2016), defined as: (O/H) 𝑅,𝑈 = 8.589 + 0.022 log(𝑅3 /𝑅2 ) + 0.399 log 𝑁2 + (0.164 log(𝑅3 /𝑅2 ) + 0.589 log 𝑁2 − 0.137) (4.4) × log 𝑅2 , when log 𝑁2 ≥ −0.6; and (O/H) 𝑅,𝐿 = 7.932 + 0.944 log(𝑅3 /𝑅2 ) + 0.695 log 𝑁2 + (0.970 − 0.291 log(𝑅3 /𝑅2 ) − 0.019 log 𝑁2 ) (4.5) × log 𝑅2 , when log 𝑁2 < −0.6, where 𝑅2 = 𝐼 [O II]𝜆3727+𝜆3729 /𝐼H𝛽 , 𝑅3 = 𝐼 [O III]𝜆4959+𝜆5007 /𝐼H𝛽 , and 𝑁2 = 𝐼 [N II]𝜆6548+𝜆6584 /𝐼H𝛽 4 . Because our full sample of the KCWI data does not cover the spectral region of [N ii]𝜆𝜆6548,6584, we use the emission line fluxes of H𝛼 and [N ii] from the SDSS MPA-JHU catalog (galSpecLine, SDSS DR17; Brinchmann et al., 2004; Tremonti et al., 2004). Assuming Case B recombination at 𝑇𝑒 = 10, 000 K and 𝑛𝑒 = 100 cm−3 , the 𝑁2 ratio is calculated assuming that 4 The 𝑁 2 ratio defined by Pilyugin and Grebel (2016) is different from the commonly used “N2” index used by other strong line calibrations (e.g., Pettini and Pagel, 2004), where 𝑁2 = log ( [N II]𝜆6584/H𝛼) instead. 94 𝑁2 = 𝐼 [N II]𝜆6548+𝜆6584 /𝐼H𝛽 =𝐼 [N II]𝜆6548+𝜆6584 /𝐼H𝛼 × 2.86. (4.6) Combining 𝑅2 and 𝑅3 based on the KCWI measurements with the SDSS results for 𝑁2 , we derive the gas-phase oxygen abundance of each galaxy using Equations (4.4) and (4.5), with results listed in Table 4.4. The reported uncertainties are the square root of the quadrature sum of the systematic uncertainty of the 𝑅 calibration (0.1 dex, Pilyugin and Grebel, 2016; Pilyugin et al., 2018) and the random errors from the flux measurement uncertainties. Our measurements from KCWI+SDSS data are consistent within 1𝜎 of the values derived from using only the SDSS emission line fluxes. 4.4 Stellar Abundance Determination Stellar abundances of iron and magnesium can be measured from spectral indices of stellar absorption lines sensitive to the stellar population parameters (e.g., Thomas et al., 2005; Thomas et al., 2010), or full-spectrum fitting that utilizes the information from the entire spectrum (e.g., Choi et al., 2014; Conroy et al., 2018). In this work, we use the full-spectrum fitting method that relies on galaxy templates with variable [Mg/Fe] to constrain [Mg/Fe] in our star-forming galaxies. Existing models for measuring the detailed abundances of individual 𝛼 elements (alf, Conroy et al., 2018), can only be applied to quiescent galaxies because the models exist only for older populations, usually > 1 Gyr in age. In order to fit galaxies with a wide range of ages, we made use of the latest FSPS SSP models with variable [𝛼/Fe] (Park et al., in prep.), as detailed in Section 4.4.1, in order to estimate [Mg/Fe] in the star-forming galaxies. The updated model was designed to capture variation in [𝛼/Fe] over the full range of possible stellar ages, from 0.1 Myr to 20 Gyr. This was achieved by constructing a new set of stellar spectral libraries and isochrones (see Park et al., in prep., for details). Similar to existing SSP models with variable [𝛼/Fe] (Vazdekis et al., 2015; Knowles et al., 2023), our models assume that all 𝛼 elements (O, Ne, Mg, Si, S, Ca, and Ti) vary in lock-step (i.e., [Mg/Fe] = [𝛼/Fe]). One must be cautious when interpreting an inferred [𝛼/Fe] as identical to [Mg/Fe]; as addressed in Choi et al. (2014) and Beverage et al. (2023), individual 𝛼 elements may not track each other in quiescent galaxies when each 𝛼 element is fitted separately using alf. To mitigate this issue, 95 we developed our own fitting algorithm (Section 4.4.2) and show in Section 4.4.3 that our measured [𝛼/Fe] represents [Mg/Fe] consistent with the alf results in the sample galaxies. 4.4.1 SSP models with variable [𝛼/Fe] To construct SSP models with variable [𝛼/Fe], we followed the methodology described by Conroy and van Dokkum (2012) and Conroy et al. (2018). At a given age and metallicity, the SSP spectrum ( 𝑓 ) of arbitrary [𝛼/Fe] can be calculated as: 𝑓 ([𝛼/Fe]) = 𝑓base ([𝛼/Fe] lib ) 𝑓theo ([𝛼/Fe]) , 𝑓theo ([𝛼/Fe] lib ) (4.7) where 𝑓base is the base empirical SSP model and 𝑓theo is the synthetic SSP template with arbitrary abundance pattern from theoretical models. The ratio 𝑓theo ([𝛼/Fe])/ 𝑓theo ([𝛼/Fe] lib ) is the “response function” which indicates the relative change in the spectrum due to a change in [𝛼/Fe] from the base model. For the base empirical model, we adopted the FSPS SSP models generated using the MILES stellar libraries (hereafter FSPS-MILES SSPs) described in Section 4.3.1. Because all the available empirical SSP models including FSPS-MILES SSPs do not have 𝛼 variation, we have to resort to theoretical models. The theoretical SSP models (hereafter FSPS-C3K SSPs) were generated with FSPS using the Kroupa IMF (Kroupa, 2001), 𝛼-enhanced MIST isochrones (Dotter, et al., in prep), and the theoretical C3K stellar model grids (Park et al., in prep). The FSPS-C3K SSPs have the same grid in age and metallicity as the FSPS-MILES SSP models and span a wide range of [𝛼/Fe] ([-0.2, 0.0, 0.2, 0.4, 0.6]). Because our goal is to determine [Mg/Fe], we used the relation for [Mg/Fe] as a function of [Fe/H] for MILES stars reported by Milone, Sansom, and SánchezBlázquez (2011) as a proxy for [𝛼/Fe]lib at a given [Fe/H]. The theoretical SSP model at a given [𝛼/Fe]lib is derived from linear interpolation of two adjacent grids. We therefore obtain our new SSP models with variable age, [Fe/H], and [𝛼/Fe] using Equation 4.7. The final models have 27 grid steps in age (log(Age) [yr] = 5.0 to 10.2 at an interval of 0.2 dex), 11 grid steps in [Fe/H] ([Fe/H] = −2.0 to 0.5 at an interval of 0.25 dex), and 5 grid setps in [𝛼/Fe] ([𝛼/Fe] = −0.2 to 0.6 at an interval of 0.2 dex). 4.4.2 Model fitting We developed a two-step fitting approach to measure both [Fe/H] and [Mg/Fe] of the star-forming galaxies in our sample. 96 In the first step, we use pPXF to fit the full emission-free stellar continuum spectrum of each galaxy from 3650 to 5500 Å in the rest frame to infer the SFHs for each galaxy (the top panel of Figure 4.3). It fits for a linear combination of discrete SSPs at different ages, [Fe/H] and [𝛼/Fe], along with the stellar velocity dispersion and offset from the initial spectroscopic redshift in the SDSS catalog to the observed spectrum. The young galaxies in our sample could have SFHs that are more complex than can be described by simple parameterizations (i.e., an SSP). Therefore, the non-parametric approach of pPXF is appropriate for our case. In this paper, we use the SFHs only to derive average ages (described below). The full SFHs will be analyzed in the future. Appendix 4.8.2 gives a complete justification of our use of non-parametric SFH fits. Each SSP model is normalized over the spectral range 4800–5500 Å for “light-weighted” property estimates. Similar to the fits described in Section 4.3.1, we ran two iterations for each spectrum. The 3𝜎 outliers from the first iteration are masked in the second iteration to remove pixels affected by imperfect subtraction of emission lines. The error spectra are also scaled by the square root of the reduced 𝜒2 of the first iteration to yield more reasonable estimates of the stellar population uncertainties. Following Cappellari (2023), “regularization” was also employed in the fitting with regul = 30 to recover a relatively smooth SFH. We also included a ninth-order multiplicative Legendre polynomial as a “nuanced” parameter to account for internal dust extinction and/or imperfect flux calibration. Following Cappellari (2023), the light-weighted properties are derived according to Í ⟨log Age⟩ = 𝑖 𝑤 𝑖 × log Age𝑖 Í , (4.8a) , (4.8b) , (4.8c) 𝑖 𝑤𝑖 Í ⟨[Fe/H]⟩ = 𝑖 𝑤 𝑖 × [Fe/H] 𝑖 Í 𝑖 𝑤𝑖 Í ⟨[𝛼/Fe]⟩ = 𝑖 𝑤 𝑖 × [𝛼/Fe] 𝑖 Í 𝑖 𝑤𝑖 where 𝑤 𝑖 is the weight of the 𝑖 th SSP template returned by pPXF. In the second step, we re-fit the stellar continuum limited to the rest-frame spectral region 4800–5500 Å (the bottom panel of Figure 4.3). As we will demonstrate in Section 4.4.3, a second fit is necessary to recover a value closer to the [Mg/Fe] consistent with the alf measurements. In the real galaxy spectra, individual 𝛼 elements may not track each other (Thomas, Maraston, and Bender, 2003; Conroy, Graves, and van Dokkum, 2014; Choi et al., 2014; Beverage et al., 2023); the derived [𝛼/Fe] from the first iteration is sensitive not only to Mg but also to other 𝛼 97 elements, such as Ca. The spectral region 4800–5500 Å contains most of the Feand Mg- sensitive features (i.e., the Mg b triplet, Fe5270, Fe5335) as well as the age indicator H𝛽. For example, Vazdekis et al. (2015) found that they could reproduce values of [Mg/Fe] consistent with the literature for two massive ellipticals only if the fits were limited to the stellar continuum in the range 4800–5500 Å; the fits failed when they were performed using a larger spectral range. 1.25 fλ 1.00 0.75 First step ∆fλ/fλ 0.50 0.05 0.00 −0.05 3750 4000 4250 4500 4750 5000 5250 3750 4000 4250 4500 4750 5000 5250 fλ 1.25 1.00 0.75 ∆fλ/fλ Second step 0.05 0.00 −0.05 4800 4900 5000 4800 4900 5000 5100 5200 5300 5100 5200 5300 λrest(Å) Figure 4.3: Illustration of the two-step approach for the same star-forming galaxy in Figure 4.2. The flux densities are normalized to have median in the spectral region 4800-5500 Å. Note that the two panels cover different wavelength ranges of the same spectrum. Top: The emission-line-subtracted stellar spectrum (black), best-fit pPXF model spectrum (orange), and the model residual (green) in the first fitting step, which operates on the entire KCWI spectrum. The blue shaded regions indicate the masked pixels that are 3𝜎 outliers in the first iteration. The gray shaded region marks the spectral regions used in the second step. Bottom: the stellar continuum (black), best-fit model (red), and the model residual (pink) in the second fitting step of the same spectrum, which operates on the spectral region ∼ 4800 − 5500 Å. The blue shaded regions are the same masked pixels inherited from the first step. In this iteration, [Fe/H] and [Mg/Fe] are allowed to vary, but the SFH and the stellar kinematics are fixed to the values determined in the first step. To fit the spectral region 4800–5500 Å, we fixed the non-parametric SFHs and stellar kinematics to the values recovered in the first step. We retained the weights of each age bin returned by the first step, but allowed [Fe/H] and [𝛼/Fe] to vary within each bin in the second iteration. We followed the continuum correction approach of alf (Conroy et al., 2018) by including in the fitting process a fourth-order multiplicative polynomial in the form Í4 of 𝑝(𝜆) = 𝑖=0 𝑐𝑖 (𝜆 − 𝜇) 𝑖 , where 𝜇 is the mean wavelength of the region being fit. 98 The polynomial degree was determined by 𝑛 = (𝜆max − 𝜆 min )/200 Å so that the correction is flexible enough to account for any mismatch in the continuum shape due to imperfect flux calibration or dust attenuation, but not so flexible that it over-fits regions containing real broad absorption features. In each iteration, we calculated the ratio of the data and model, masked the spectral regions with strong stellar absorption features and gas emission lines, and performed a least-squares polynomial fit to the unmasked pixels. The data were then compared with the altered model multiplied by the best-fit polynomial to calculate the likelihood. We experimented with different polynomial orders, including 𝑛 = 0 and 𝑛 = (𝜆 max − 𝜆 min )/100 Å and found that the changes of the recovered abundances are within the reported uncertainties. The fits were accomplished using dynesty (Speagle, 2020), a Python package for dynamic nested sampling capable of estimating the Bayesian posterior distribution. For each age bin, we adopted a uniform prior for [Fe/H] in the range [−2.0, 0.5] and a uniform prior for [𝛼/Fe] in the range [−0.2, 0.6]. The SSP models at nongridpoint values of model parameters were calculated via linear interpolation. Using the posteriors of [Fe/H] and [𝛼/Fe] in each age bin from dynesty along with Equations (4.8b) and (4.8c), we obtained the posterior distributions of the lightweighted [Fe/H] and [𝛼/Fe] for each galaxy. All the galaxies have converged, single-peaked posteriors. The best-fit results are quoted as the median of the 1D marginalized posteriors. Because the maximum a posteriori (MAP) estimates for some galaxies fell outside the 1𝜎 (68%) confidence interval, but were always within the 2𝜎 interval, the quoted uncertainties are based on the 2𝜎 confidence interval (i.e., 2.5% and 97.5% percentiles). 4.4.3 Verification of Magnesium Abundance Measurement As mentioned above, one must be cautious when interpreting the measured [𝛼/Fe] as [Mg/Fe] if the SPS models used for analysis tie all the 𝛼 elements together (i.e., the case of our analysis). If 𝛼 elements do not track each other—for instance, [Ca/Fe] ∼ 0 when [Mg/Fe] > 0 (Choi et al., 2014; Beverage et al., 2023)—then the derived [𝛼/Fe] may not reflect [Mg/Fe]. In fact, Leethochawalit et al. (2019) showed in their Appendix A that [Mg/Fe] was underestimated by ∼ 0.1 − 0.2 dex when the SSP models were fit with the response functions of individual 𝛼 elements fixed to the same value. Therefore, it is essential to validate that our method recovers the correct [Mg/Fe] rather than an amalgam of different elements, i.e., [𝛼/Fe]. As a result, we seek to understand how to interpret the measured [𝛼/Fe], age, and 99 [Fe/H] via the two-step approach along with the new SPS models before applying the method to our KCWI sample. To validate the two-step method, we made use of the sample of 123 SDSS quiescent galaxies compiled by Leethochawalit et al. (2018b), which has existing measurements of individual [Mg/Fe], [Fe/H] and SSP age from alf by Zhuang et al. (2023). We re-measured their light-weighted age, [Fe/H] and [𝛼/Fe] using the two-step method described in Section 4.4.2 in order to compare them with the existing results obtained from alf. To illustrate the need for the two-step method, we also experimented with fits using only a single iteration of pPXF. We performed the fits with two different spectral regions: the spectral range of KCWI-blue overlapping with those of the empirical SSP models (∼ 3650 − 5500 Å), which is essentially the first step in the two-step method, and the spectral region 4800-5500 Å, which contains most of the Fe- and Mg- sensitive features present in the full spectrum. The pPXF setup was the same as the one described in Section 4.4.2. To estimate the uncertainties in the pPXF measurements, we adopted the “wild bootstrap method” (Davidson and Flachaire, 2008) following the example described by Cappellari (2023)5 . In summary, after running the first pPXF regularized fit with regul = 30, we bootstrapped the residuals and repeated the pPXF fit 100 times with no regularization. For each iteration, we calculated the light-weighted properties using Equation 4.8. The uncertainties were estimated as the standard deviations of the distributions for the light-weighted properties. Figure 4.4 compares [𝛼/Fe] measured from the two-step and one-step methods with [Mg/Fe] derived by alf (Zhuang et al., 2023); Figure 4.5 shows the same comparison for [Fe/H]. For each method, we calculated the reduced 𝜒2 between the alf results and our new measurements as: 𝑁 𝜒𝜈2 = 1 ∑︁ (𝑚𝑖,Alf − 𝑚𝑖,X ) 2 , 2 2 𝑁 𝑖 𝜎𝑖,Alf + 𝜎𝑖,X (4.9) where 𝑚𝑖,Alf and 𝜎𝑖,Alf indicate the measurements and the uncertainties from alf, while 𝑚𝑖,X and 𝜎𝑖,X represent those from the three methods illustrated above. As can be seen in the middle panels of Figure 4.4, [𝛼/Fe] derived using pPXF is significantly lower than [Mg/Fe] from alf for highly 𝛼-enhanced spectra when we fit the entire spectral range of KCWI (∼ 3650 − 5500 Å), with a 𝜒𝜈2 = 11.2. On the 5 https://github.com/micappe/ppxf_examples/blob/main/ppxf_example_ population_bootstrap.ipynb 100 [α/Fe] − [Mg/Fe]alf N 30 [α/Fe] − [Mg/Fe]alf 20 20 10 10 0 10 −0.3 −0.2 −0.1 0.0 0.1 0 χ2ν =1.01 [α/Fe] (this work) [α/Fe] − [Mg/Fe]alf 30 20 −0.3 −0.2 −0.1 0.0 0.1 0 χ2ν =11.23 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 Two-step Method 0.0 0.2 [Mg/Fe]alf 0.4 0.0 pPXF (3650-5500) 0.0 −0.2 −0.1 0.0 0.1 χ2ν =1.30 0.4 0.0 −0.3 0.2 [Mg/Fe]alf 0.4 0.0 pPXF (4800-5500) 0.0 0.2 0.4 [Mg/Fe]alf Figure 4.4: Comparison of [Mg/Fe] for the massive SDSS quiescent galaxies compiled by Leethochawalit et al. (2019) measured from alf by Zhuang et al. (2023) and from the methods presented in Section 4.4.3. Here we show the measurements of [𝛼/Fe] derived from the two-step method (purple stars) in the left column, those from fitting the entire spectra (∼ 3650 − 5500 Å) via pPXF (red squares) in the middle column, and those from fitting the spectral regions of ∼ 4800 − 5500 Å (green circles) in the right column. In each column, the top panel shows the difference between the new results and alf measurements, while the lower panel demonstrates the direct comparison between the measurements. The red dashed lines indicate equal values for both axes. The weighted RMS (𝜎) is also shown in each panel. other hand, the two-step method as well as the pPXF fit over a narrower region of 4800 − 5500 Å, give a much closer estimate of [Mg/Fe], with 𝜒𝜈2 = 1.01 and 1.30, respectively. It might seem that the single-step fit over a limited spectral range (4800 − 5500 Å) performs as well as the two-step approach. However, Figure 4.5 shows that fitting a narrower region between 4800 − 5500 Å overestimates [Fe/H] by ∼ 0.2 dex on average compared to alf. The difference can be up to 0.5 dex for the most metalpoor galaxy in the SDSS sample. On the contrary, the two-step method and the pPXF fit of the entire KCWI spectral coverage both give measurements of [Fe/H] consistent with alf yielding 𝜒𝜈2 = 0.85 and 0.94, respectively. The discrepancy can be explained by the fact that most of the spectral features sensitive to the stellar population age and SFH reside near the Balmer/4000 Å breaks, so ignoring them inhibits the breaking of the age–metallicity degeneracy. This effect can be seen in Figure 4.6, where we compare the light-weighted age derived from pPXF using two different regions with the SSP age determined by alf. The pPXF fit of the region between 4800 Å and 5500 Å significantly underestimates 101 ∆[Fe/H] ∆[Fe/H] ∆[Fe/H] 30 20 20 N 20 10 0 −0.2 0.0 0.2 0 0.4 χ2ν =0.85 0.2 [Fe/H] (this work) 10 10 0.2 −0.2 0.0 0.2 0 0.4 χ2ν =0.94 0.0 0.0 −0.2 −0.2 −0.2 −0.4 −0.4 −0.4 −0.6 Two-step Method −0.8 −0.6 −0.4 −0.2 0.0 −0.8 −0.6 0.2 [Fe/H]alf −0.6 pPXF (3650-5500) −0.4 −0.2 0.0 [Fe/H]alf 0.2 0.4 pPXF (4800-5500) −0.8 −0.6 0.2 0.0 χ2ν =1.33 0.2 0.0 −0.6 −0.2 −0.4 −0.2 0.0 0.2 [Fe/H]alf Figure 4.5: As for Figure 4.4, but comparing measurements of [Fe/H]. ∆ log Age ∆ log Age 20 N 20 10 10 0 −1.0 −0.6 −0.4 −0.2 0.0 0 −1.0 0.2 χ2ν =1.12 10.00 log AgepPXF [yr] −0.8 9.75 9.50 9.50 9.25 9.25 9.00 9.00 8.75 9.4 9.6 9.8 log Agealf [yr] 10.0 −0.4 8.75 pPXF (3650-5500) 9.2 −0.6 10.2 −0.2 0.0 0.2 χ2ν =3.34 10.00 9.75 −0.8 pPXF (4800-5500) 9.2 9.4 9.6 9.8 10.0 10.2 log Agealf [yr] Figure 4.6: As for Figure 4.4, but comparing measurements of stellar population age. the stellar population age, while the fit of the full KCWI spectrum recovers consistent age estimates even though pPXF and alf assume different forms for the SFH. The results of the pPXF fit over different regions are in agreement with the direction of the age–metallicity degeneracy: because the models predict younger stellar populations due to a lack of age constraints from NUV and bluer optical features, they have to compensate for the deeper absorption features from older stars by increasing [Fe/H]. The tests performed above use quiescent galaxies which still have deep H𝛽 absorption present to constrain stellar population age to some extent when we fit over a narrower range of 4800 − 5500 Å. This issue would be more severe in low-mass, star-forming galaxies in our KCWI sample because they host younger stellar populations with higher star formation activity. The shallower H𝛽 absorption and the 102 contamination of the H𝛽 from the ionized gas would prohibit the single-step fit over a limited range from yielding a reasonable age estimate. We therefore have to use the information from the full spectrum to minimize the age–metallicity degeneracy. We note that the 𝜒𝜈2 of the two-step method in the cases of [Fe/H] and [Mg/Fe] are both slightly smaller than that of the best pPXF fit, which may result from larger uncertainties in the two-step method. We emphasize that we adopted the two-step because it is a compromise to recover reasonable value of [Fe/H] and [Mg/Fe] of the star-forming galaxies in our sample. We do not imply that the two-step method is significantly better in measuring [Fe/H] or [Mg/Fe] alone for quiescent galaxies than running pPXF directly. To conclude, we have demonstrated above that our novel two-step approach can recover [Mg/Fe] and [Fe/H] consistent with the alf measurements, even using the SSP models that lock all the 𝛼 element variation together, while a single-step fit (over either the full KCWI spectral coverage or a portion of the spectrum (4800 − 5500 Å) carrying most of the Fe- and Mg- sensitive features) via pPXF would underestimate [Mg/Fe] or overestimate [Fe/H]. Our two-step method preserves the age constraints from the full spectrum while reducing the contamination from other 𝛼 elements that might not track Mg. Now, we apply the two-step approach to the KCWI starforming galaxies to constrain their stellar [Fe/H] and [Mg/Fe]6 . Table 4.4 lists the stellar abundance measurements derived from the two-step approach described in Section 4.4.2. Table 4.4 also reports the stellar velocity dispersion and the lightweighted age obtained from the first step of the two-step method, along with the uncertainties determined from 100 bootstraps of the residuals. Table 4.4: The Derived Properties of the KCWI Star-Forming Galaxies Galaxy 2225−0046 0231−0043 0133−0109 2329+1552 2152−0110 0845+5145 2334+0029 0121−0853 0013−0956 0155−0037 𝑧 log M∗ [𝑀⊙ ] 𝜎∗ km s −1 ⟨log Age⟩∗ [yr] [Fe/H]∗ dex [Mg/Fe]∗ dex 12 + log (O/H)g dex 0.016 0.009 0.016 0.009 0.016 0.014 0.024 0.018 0.013 0.023 8.09±0.10 8.09±0.10 8.11±0.14 8.23±0.10 8.40±0.10 8.42±0.10 8.42±0.10 8.43±0.10 8.51±0.10 8.56±0.10 54.8±3.5 56.7±3.1 61.7±3.4 42.3±2.2 49.4±4.6 64.5±2.5 56.9±4.6 51.0±2.8 44.7±3.0 69.0±3.3 8.96±0.05 8.81±0.05 8.56±0.08 9.07±0.04 9.13±0.07 8.89±0.06 8.70±0.06 8.85±0.05 9.00±0.04 8.93±0.05 −0.88+0.09 −0.11 −1.07+0.14 −0.15 −1.02+0.16 −0.16 −0.72+0.07 −0.08 −1.02+0.10 −0.11 −0.56+0.08 −0.10 −1.10+0.20 −0.17 −0.54+0.09 −0.08 −0.53+0.08 −0.10 −1.16+0.11 −0.11 0.09+0.06 −0.06 0.19+0.09 −0.09 0.16+0.08 −0.09 0.18+0.05 −0.05 0.14+0.08 −0.08 0.15+0.06 −0.05 0.10+0.07 −0.09 0.06+0.04 −0.05 0.22+0.06 −0.05 0.08+0.06 −0.07 7.90±0.11 7.74±0.10 7.90±0.10 8.24±0.10 8.20±0.10 8.27±0.10 7.97±0.10 8.10±0.10 8.22±0.11 7.92±0.10 continued 6 In the following analysis, we refer the [𝛼/Fe] measured from the two-step method as [Mg/Fe]. 103 Table 4.4: The Derived Properties of the KCWI Star-Forming Galaxies Galaxy 0140−0012 0023−0939 0233+0038 0256−0010 2259−0019 2300−0832 0233−0819 0125−0024 0241−0810 2301+1451 0332−0600 2131−0613 0850+6145 0256−0707 0033+0012 2137+1243 0137−0942 0040−0017 0136+1356 2304−0933 0309−0041 0019−0004 0208+0048 0306−0033 0346+0023 0243+0032 2318+0105 2206−0041 2243+0040 0334+0106 0317−0004 2211+0006 0245−0045 0030−0042 2139+0019 0407−0634 0254+0103 0140−0013 𝑧 log M∗ [𝑀⊙ ] 𝜎∗ km s −1 ⟨log Age⟩∗ [yr] [Fe/H]∗ dex [Mg/Fe]∗ dex 12 + log (O/H)g dex 0.018 0.02 0.024 0.029 0.016 0.025 0.019 0.016 0.005 0.024 0.018 0.025 0.024 0.017 0.014 0.031 0.019 0.019 0.024 0.032 0.037 0.04 0.02 0.025 0.031 0.028 0.03 0.029 0.039 0.049 0.022 0.057 0.054 0.041 0.05 0.038 0.043 0.058 8.59±0.10 8.59±0.10 8.67±0.10 8.69±0.10 8.71±0.10 8.75±0.10 8.77±0.10 8.78±0.10 8.79±0.10 8.81±0.11 8.82±0.10 8.82±0.10 8.88±0.10 8.96±0.10 8.97±0.10 8.98±0.11 9.02±0.10 9.02±0.10 9.03±0.10 9.04±0.10 9.05±0.10 9.15±0.10 9.15±0.10 9.16±0.10 9.18±0.10 9.34±0.10 9.35±0.10 9.37±0.16 9.37±0.10 9.44±0.10 9.46±0.10 9.58±0.10 9.60±0.10 9.63±0.10 9.72±0.10 9.88±0.10 9.90±0.10 10.02±0.10 58.0±2.8 55.2±3.9 51.7±3.3 65.0±3.7 49.2±3.0 47.6±3.1 53.7±2.1 50.5±1.9 54.7±1.8 47.9±3.5 52.7±2.4 57.8±3.9 64.6±4.8 60.3±2.5 61.5±2.3 56.5±4.4 60.3±2.2 50.1±2.7 58.0±3.3 60.0±2.4 66.9±3.9 69.9±3.9 46.0±3.1 49.0±2.6 64.2±3.5 49.4±2.9 65.4±3.0 65.9±2.6 57.7±4.8 77.4±4.7 55.4±2.3 50.3±4.6 55.9±3.5 63.8±2.2 66.3±3.6 59.9±3.6 71.2±3.3 76.4±2.5 8.85±0.05 8.87±0.06 8.92±0.06 8.84±0.06 9.14±0.06 9.05±0.05 8.95±0.04 9.74±0.04 9.79±0.03 8.87±0.06 9.04±0.06 8.78±0.07 9.06±0.08 8.93±0.04 8.72±0.04 8.95±0.07 8.71±0.04 8.72±0.04 8.60±0.05 8.84±0.05 8.72±0.06 8.74±0.05 8.93±0.05 9.04±0.04 8.81±0.06 8.75±0.06 8.82±0.05 8.43±0.06 8.76±0.05 8.13±0.07 8.62±0.05 8.43±0.09 8.49±0.06 8.63±0.04 8.58±0.08 9.13±0.07 8.61±0.06 8.57±0.04 −0.50+0.06 −0.08 −0.86+0.09 −0.10 −0.87+0.11 −0.11 −1.06+0.10 −0.11 −0.51+0.09 −0.11 −0.82+0.13 −0.06 −0.50+0.06 −0.09 −0.45+0.06 −0.08 −0.68+0.04 −0.03 −0.77+0.13 −0.13 −0.42+0.06 −0.07 −0.96+0.13 −0.13 −0.69+0.09 −0.11 −0.44+0.06 −0.07 −0.63+0.10 −0.10 −0.83+0.09 −0.11 −0.57+0.07 −0.10 −0.53+0.08 −0.08 −0.62+0.09 −0.11 −0.73+0.08 −0.09 −0.84+0.11 −0.12 −0.78+0.13 −0.13 −0.65+0.08 −0.08 −0.54+0.08 −0.10 −0.89+0.11 −0.12 −0.70+0.10 −0.10 −0.71+0.08 −0.08 −0.72+0.13 −0.13 −0.83+0.09 −0.10 −0.35+0.10 −0.12 −0.58+0.09 −0.09 −0.43+0.12 −0.11 −0.35+0.10 −0.10 −0.53+0.09 −0.09 −0.83+0.20 −0.21 −0.18+0.08 −0.09 −0.82+0.13 −0.13 −0.40+0.09 −0.10 0.10+0.05 −0.05 0.18+0.06 −0.06 0.14+0.07 −0.07 0.21+0.08 −0.08 0.10+0.05 −0.06 0.08+0.05 −0.07 0.09+0.04 −0.04 0.12+0.06 −0.07 0.13+0.05 −0.05 0.09+0.06 −0.07 0.09+0.04 −0.05 0.20+0.07 −0.07 0.10+0.06 −0.06 0.12+0.05 −0.05 0.17+0.06 −0.06 0.19+0.06 −0.07 0.10+0.05 −0.05 0.08+0.05 −0.05 0.09+0.06 −0.06 0.21+0.07 −0.06 0.12+0.06 −0.06 0.09+0.07 −0.07 0.15+0.05 −0.05 0.17+0.05 −0.05 0.21+0.07 −0.08 0.20+0.06 −0.06 0.22+0.06 −0.05 0.22+0.09 −0.09 0.13+0.06 −0.06 0.12+0.06 −0.05 0.15+0.05 −0.05 0.17+0.06 −0.06 0.13+0.06 −0.06 0.17+0.05 −0.05 0.18+0.09 −0.09 0.09+0.05 −0.05 0.20+0.08 −0.07 0.21+0.05 −0.05 8.12±0.10 8.15±0.10 8.25±0.10 8.13±0.10 8.39±0.10 8.16±0.11 8.12±0.11 -𝑎 -𝑎 8.19±0.10 8.20±0.12 8.20±0.10 8.35±0.11 8.29±0.10 8.26±0.10 8.26±0.11 8.14±0.10 8.19±0.10 8.26±0.10 8.29±0.10 8.28±0.10 8.37±0.10 8.36±0.10 8.46±0.10 8.31±0.10 8.34±0.10 8.36±0.11 8.34±0.10 8.25±0.10 8.32±0.10 8.32±0.10 8.47±0.10 8.38±0.10 8.56±0.10 8.51±0.10 8.46±0.11 8.45±0.10 8.48±0.10 The columns show (1) the galaxy ID; (2-3) the spectroscopic redshift and the spectroscopic redshift from Table 4.1; (4-5) the stellar velocity dispersion and light-weighted ages measured from the pPXF fit of the entire KCWI spectra (Sections 4.4.2 and 4.4.3); (6-7) the [Fe/H]∗ and [Mg/Fe]∗ estimated from the two-step method (Section 4.4.2); (8) the gas-phase oxygen abundance obtained from the 𝑅 calibration by Pilyugin and Grebel (2016) described in Section 4.3.2. a The absence of emission lines in the quiescent galaxies prevents us from determining their gas-phase metallicities. 104 4.5 4.5.1 Results Comparison between stellar and gas-phase abundances 0.0 0.0 −0.2 −0.2 −0.4 −0.4 [O/H]g [O/H]g We now compare the ionized gas-phase oxygen abundances with the stellar abundances of iron and magnesium for our sample. For a more direct comparison, we convert the gas-phase metallicity 12 + log (O/H) into [O/H]g using the solar oxygen abundance of 12 + log (O/H) ⊙ = 8.69 (Asplund et al., 2009). −0.6 −0.8 −0.8 r = 0.53 −1.0 −1.2 −0.6 −1.25 −1.00 −0.75 −0.50 [Fe/H]∗ −0.25 r = 0.61 −1.0 p = 1.48 × 10−4 0.00 −1.2 p = 5.60 × 10−6 −1.25 −1.00 −0.75 −0.50 [Mg/H]∗ −0.25 0.00 Figure 4.7: Comparison of [O/H]g with [Fe/H]∗ (left) and [Mg/H]∗ (right). The dashed-dotted lines indicate the one-to-one relation (i.e., [O/H] g = [X/H] ∗ ). The weighted Pearson coefficients 𝑟 and the 𝑝-values of the null hypothesis are shown in each panel. Figure 4.7 shows the comparison between the gas-phase oxygen abundance [O/H]g and the stellar iron abundance [Fe/H]∗ of our sample. We derive a inverse-variance weighted Pearson coefficient 𝑟 = 0.53 and the corresponding 𝑝-value 𝑝 = 1.48 × 10−4 , indicating that the [O/H]g and the [Fe/H]∗ are correlated at the ∼ 3.8𝜎 level. Four galaxies exhibit lower [O/H]g than [Fe/H]∗ , but at < 2𝜎 significance. The remaining galaxies in our sample exhibit higher [O/H]g than [Fe/H]∗ . On average, [O/H]g is higher than [Fe/H]∗ by 0.25 dex, in agreement with the results of Fraser-McKelvie et al. (2022) for a sample of more massive star-forming galaxies at 𝑀∗ > 109 𝑀⊙ observed by the SAMI Galaxy Survey. The discrepancy is not surprising, given that the two elemental abundances trace the chemical enrichment of different stellar populations. The [Fe/H]∗ presented here is measured from the rest-frame optical stellar continuum, so the measured [Fe/H]∗ indicates the chemical enrichment for older stellar populations. On the contrary, the [O/H]g is a proxy for the chemical enrichment in regions where the youngest OB stars have just formed out of the ISM. In addition, the different formation timescales of oxygen and iron can also contribute to the abundance offset. Iron is primarily formed by Type Ia SNe that explode ≳ 300 − 400 Myr after the initial starburst, while oxygen, an 𝛼 105 element, is produced by core-collapse SNe of massive stars a ∼ 10 Myr timescale. As a result, the chemical enrichment of iron is expected to lag behind that of oxygen, especially for galaxies that have formed the majority of their stars in the past Gyr before the Type Ia SNe began exploding, although the difference would be attenuated if galaxies have smoother and more sustained SFHs. The combined effects of the distinct stellar populations probed by oxygen and iron and the disparate formation timescales can naturally explain the lower [Fe/H]∗ in Figure 4.7. As mentioned above, it is complicated to interpret the relation between [Fe/H]∗ and [O/H]g because Fe is delayed relative to O. On the other hand, comparing the abundance of gas-phase oxygen and stellar magnesium is a more direct comparison between the metals in the gas and stars because magnesium is another 𝛼 element produced by the same mechanism as oxygen. [Mg/H]∗ traces the SFH-averaged stellar abundance and can be interpreted as an approximation of the gas-phase abundance averaged over the SFH of the galaxies. In the right panel of Figure 4.7, we compare [O/H]g and [Mg/H]∗ , which is the sum of the [Fe/H]∗ and [Mg/Fe]∗ derived in Section 4.4.2. [Mg/H]∗ is still lower than [O/H]g , but as expected, the differences between [O/H]g and [Mg/H]∗ (0.11 dex) are significantly smaller compared to [Fe/H]∗ (0.25 dex). The Pearson coefficient of the [O/H]g –[Mg/H]∗ relation (𝑟 = 0.61) is higher than that of the [O/H]g –[Fe/H]∗ with a 𝑝-value lower by two orders of magnitude, suggesting that [O/H]g is more linearly correlated with [Mg/H]∗ . Among 46 star-forming galaxies in our sample, 23 of them have consistent [O/H]g and [Mg/H]∗ within 1𝜎, whereas 19 galaxies have slightly higher [O/H]g than [Mg/H]∗ at the 1 − 3𝜎 level. We note that we measure [O/H]g using strong-line calibrations based on the 𝑇𝑒 metallicity scale, which is likely to underestimate the actual (O/H)gas due to temperature fluctuations in the H ii regions (García-Rojas and Esteban, 2007). If we convert the 𝑇𝑒 -based measurements to the abundance scale based on recombination lines and photoionization models by adding 0.24 dex to the measured [O/H]g (Esteban et al., 2014; Blanc et al., 2015; Steidel et al., 2016), all star-forming galaxies would have higher [O/H]g than [Mg/H]∗ . Most of (or all) galaxies in our sample therefore have higher [O/H]g because the youngest populations are more chemically enriched. Nevertheless, the reduced lag between [O/H]g and [Mg/H]∗ arises from the fact that the two elements are produced by the same process, rendering them less sensitive to the shapes of the SFHs. Even though we have demonstrated that stellar magnesium indeed tracks gas-phase oxygen more closely than stellar iron does, we emphasize that the [Mg/H]∗ and the 106 [O/H]g are not fully consistent for all galaxies in our sample as discussed above. One would always expect that [O/H]g is higher than [Mg/H]∗ unless star formation is occurring in metal-poor gas from external accretion. Therefore, one should be cautious when using [Og /Fe∗ ] as a substitute for [𝛼/Fe]∗ in star-forming galaxies if [Fe/H]∗ is determined from the rest-frame optical spectrum7 . In this case, using the difference of [O/H]g and [Fe/H]∗ as a proxy for [𝛼/Fe]∗ may overestimate [Mg/Fe]∗ . 4.5.2 The gas-to-stellar abundance ratio as a function of galaxy properties Aiming to understand the connection between metals in different phases, we explore how the gas-to-stellar abundance ratios (more accurately, their logarithmic difference), Δ𝑍O,Fe and Δ𝑍O,Mg depend on different galaxy properties in Figures 4.8 and 4.9, respectively. We define two gas-to-stellar abundance ratios as: Δ𝑍O,Fe = [O/H] gas − [Fe/H] ∗ (4.10a) Δ𝑍O,Mg = [O/H] gas − [Mg/H] ∗ . (4.10b) r = 0.13 0.8 r = 0.25 0.8 p = 0.40 0.2 0.4 0.2 0.0 0.0 −0.2 −0.2 −2.0 8.5 9.0 9.5 10.0 log M∗ [M ] r = −0.02 0.8 p = 0.91 0.4 0.2 0.0 −1.5 −1.0 −0.5 0.0 −0.2 −10.75 −10.50 −10.25 −10.00 0.5 log SFR [M yr−1] r = 0.03 p = 0.19 0.4 0.2 0.4 0.2 0.0 0.0 0.0 −0.2 −0.2 −0.2 8.2 8.4 8.6 8.8 log Age [yr] 9.0 9.2 −9.25 0.6 ∆ZO,Fe ∆ZO,Fe 0.2 −9.50 r = −0.20 0.8 0.6 0.4 −9.75 log sSFR [yr−1] p = 0.83 0.6 ∆ZO,Fe 0.6 ∆ZO,Fe 0.4 0.8 p = 0.0025 0.6 ∆ZO,Fe ∆ZO,Fe 0.6 8.0 r = 0.4349 0.8 p = 0.10 8.00 8.25 8.50 8.75 log Φ [M kpc−1] 9.00 9.25 7.8 8.0 8.2 8.4 8.6 8.8 9.0 log Σ [M kpc−2] Figure 4.8: The differences between [O/H]g and [Fe/H]∗ (Δ𝑍O,Fe ) as a function of different galaxy properties, including stellar mass (top left), SFR (top middle), sSFR (top right), light-weighted stellar population age (bottom left), log Φ (bottom middle) and log Σ (bottom right). The weighted Pearson coefficients (𝑟) and the 𝑝-values are shown in each panel. We explore the dependence of these quantities on six galaxy properties: (1) stellar mass, (2) SFR, (3) sSFR, (4) light-weighted age derived from the full-spectrum fitting, (5) log Φ = log (𝑀∗ /𝑅𝑒 ), a proxy for the gravitational potential well, and (6) 7 [Fe/H] determined from the FUV stellar continuum is sensitive mostly to young OB stars. ∗ [O/Fe] is commonly used in high-𝑧 galaxies when their rest-FUV stellar continuum can be easily obtained from ground- or space-based telescopes. 107 r = −0.08 r = 0.08 0.6 0.6 p = 0.58 0.2 0.2 0.0 0.0 −0.2 −0.2 −0.2 8.5 9.0 9.5 −2.0 10.0 log M∗ [M ] r = 0.03 0.6 p = 0.85 −1.0 −0.5 0.0 −10.6 −10.4 −10.2 −10.0 −9.8 0.5 log SFR [M yr−1] log sSFR [yr−1] r = −0.02 0.2 0.2 0.0 −0.2 −0.2 −0.2 8.6 8.8 log Age [yr] 9.0 9.2 8.8 9.0 −9.2 p = 0.14 0.2 0.0 8.4 −9.4 0.4 0.0 8.2 −9.6 r = −0.22 0.6 p = 0.89 0.4 ∆ZO,Mg 0.4 −1.5 ∆ZO,Mg 0.6 ∆ZO,Mg 0.2 0.0 8.0 p = 0.0056 0.4 ∆ZO,Mg 0.4 ∆ZO,Mg ∆ZO,Mg 0.4 r = 0.4018 0.6 p = 0.62 8.0 8.2 8.4 8.6 8.8 log Φ [M kpc−1] 9.0 9.2 7.8 8.0 8.2 8.4 8.6 log Σ [M kpc−2] Figure 4.9: Similar to Figure 4.8, but for the differences between [O/H]g and [Mg/H]∗ (Δ𝑍O,Mg ). log Σ = log (𝑀∗ /𝑅𝑒2 ), a proxy for stellar mass surface density. The properties are chosen because they are known to be correlated/anti-correlated either with stellar/gas abundances (e.g., Tremonti et al., 2004; Gallazzi et al., 2005; Mannucci et al., 2010), or with the gas-to-stellar abundance ratios for more massive star-forming galaxies (e.g., Fraser-McKelvie et al., 2022). To quantify whether these galaxy properties are correlated with Δ𝑍O,Fe and Δ𝑍O,Mg , we calculate inverse variance-weighted Pearson coefficients (𝑟) and corresponding 𝑝-values for each relation. Among all the relations investigated, we find that Δ𝑍O,Fe and Δ𝑍O,Mg are significantly correlated (i.e., 𝑝-value < 0.05) only with sSFR. A similar trend was also found by Fraser-McKelvie et al. (2022), who compared the stellar and gas-phase metallicity of the star-forming galaxies at log (𝑀∗ /𝑀⊙ ) ≳ 108.5 in the SAMI sample. Because Fraser-McKelvie et al. (2022) did not measure [Mg/H]∗ , they converted the measured gas-phase metallicity in the oxygen-based scale into the iron-based scale using the empirical abundances in the Milky Way, Large Magellanic Cloud (LMC), and Small Magellanic Cloud (SMC) by Nicholls et al. (2017). This conversion was intended to account for the difference in the recycling time of oxygen and iron. In contrast, our analysis allows for an apples-to-apples comparison of stellar and gas-phase abundances of 𝛼 elements, without relying on abundance patterns based on specific galaxies. One might expect that Δ𝑍O,Fe and Δ𝑍O,Mg would be correlated with sSFR. Δ𝑍O,Fe and Δ𝑍O,Mg reflect the differences in the level of chemical enrichment between that of the current ISM and that obtained when the bulk of the stars that dominate the current optical spectrum were forming, i.e., in the past, weighted roughly by light. 108 The measured stellar abundances are therefore a proxy for the ISM abundances around 600 − 700 Myr (the typical light-weighted age in this sample) ago. A galaxy with higher sSFR would have experienced a larger increase in ISM abundance over the same interval of time, leading to a larger value of Δ𝑍O,Fe and Δ𝑍O,Mg . While the correlation between Δ𝑍O,Fe and sSFR (𝑟 = 0.43) is slightly stronger than that between Δ𝑍O,Mg and sSFR (𝑟 = 0.40), the differences are not significant. Perhaps surprisingly, Δ𝑍O,Fe and Δ𝑍O,Mg lack a strong dependence on SFR (see Figures 4.8 and 4.9). It is well known that at a given stellar mass, galaxies with higher SFRs tend to have more metal-poor ISM (Mannucci et al., 2010) because their high gas fractions dilute the current gas-phase metallicity. However, [Fe/H]∗ and [Mg/H]∗ , the amount of metals locked in the stars averaged over the entire SFH, are expected to be much less influenced by the current SFR because they have only a weak dependence on the current star formation. If there is a universal “fundamental” MZR of galaxies, where the normalization of the gas MZR decreases as SFR goes up, Δ𝑍O,Fe and Δ𝑍O,Mg should be correlated with SFR. The absence of dependence on SFR here implies that the stellar MZR is not universal for galaxies at different SFRs, as we will further discuss in Section 4.5.3. We do not detect significant correlations of Δ𝑍O,Fe or Δ𝑍O,Mg with stellar mass, log Φ, or log Σ, while Fraser-McKelvie et al. (2022) found that the gas-to-stellar abundance ratio is anti-correlated with mass and log Φ and uncorrelated with log Σ after correcting the abundance scale offsets between iron and oxygen. The discrepancy may be attributed to the different mass range in the current sample as compared to that of Fraser-McKelvie et al. (2022) – the two anti-correlations found by FraserMcKelvie et al. (2022) are driven primarily by galaxies with log 𝑀∗ /𝑀⊙ ≳ 109.5 and log Φ ≳ 9.25 (their Figure 10), whereas our sample consists of much less massive galaxies. It could be that the trends with mass and log Φ have not yet been established in dwarf galaxies. Finally, we find that both Δ𝑍O,Fe and Δ𝑍O,Mg are uncorrelated with the light-weighted age. We suspect that this is because the star-forming galaxies in our sample are extremely young with light-weighted ages < 1 Gyr. It could be that the trends with age have not yet been established. 4.5.3 The Mass–Metallicity Relation The left column of Figure 4.10 shows the gas-phase O-MZg R, stellar Fe-MZ∗ R, and stellar Mg-MZ∗ R along with the mass–[Mg/Fe]∗ relation color-coded by their 109 (a) 8.6 Berg+12 8.4 8.2 r = 0.82 p = 3.18 × 10−12 8.0 log sSFR [yr−1 ] 7.8 −10.4 7.6 −0.2 8.0 8.5 (b) Kirby+13 −10.2 −10.0 9.0 −9.8 9.5 8.2 8.0 7.8 7.6 10.0 −0.2 (f) 8.25 8.50 8.75 r = 0.87 p = 1.78 × 10−15 9.00 9.25 9.50 [Fe/H]∗ [Fe/H]∗ r = 0.59 p = 1.48 × 10−5 −0.6 −0.8 −0.8 −1.0 −1.2 8.0 0.0 (c) −0.2 8.5 9.0 r = 0.46 p = 1.31 × 10−3 9.5 −1.0 star-forming quiescent −1.2 8.00 10.0 8.25 8.50 8.75 9.00 9.25 9.50 0.0 r = 0.52 p = 2.02 × 10−4 (g) −0.2 −0.4 [Mg/H]∗ [Mg/H]∗ −0.4 −0.6 −0.6 −0.8 −0.8 −1.0 star-forming quiescent 8.0 8.5 9.0 9.5 10.0 −1.0 −1.2 0.30 (d) 0.25 0.20 0.20 8.00 8.25 8.50 8.75 9.00 r = 0.65 p = 8.30 × 10−7 9.25 9.50 (h) [Mg/Fe]∗ [Mg/Fe]∗ 0.25 0.15 0.15 0.10 0.10 r = 0.23 p = 0.118 0.05 0.00 8.00 −0.4 −0.6 0.30 (e) 8.4 −9.6 −0.4 −1.2 12 + log(O/H)g 12 + log(O/H)g 8.6 8.0 8.5 9.0 log M∗ [M ] 9.5 r = 0.22 p = 0.142 0.05 10.0 0.00 8.00 8.25 8.50 8.75 9.00 9.25 9.50 log (M∗/Re) [M /kpc] Figure 4.10: MZRs of the KCWI sample. Left: The O-MZg R (a), Fe-MZ∗ R (b), Mg-MZ∗ R (c), and the mass-[Mg/Fe]∗ relation (d) of the KCWI sample. In panel (a), the magenta dashed-dotted line shows the O-MZg R of local dwarf galaxies derived from the direct method (Berg et al., 2012). In panel (b), the blue dashed-dotted line shows the Fe-MZ∗ R of Local Group satellites obtained from resolved stellar spectroscopy (Kirby et al., 2013). Right: The gas-phase (O/H)g (e), stellar [Fe/H]∗ (f), stellar [Mg/H]∗ (g), and [Mg/Fe]∗ (h) as a function of log Φ = log (𝑀∗ /𝑅𝑒 ) of the KCWI sample. In each panel, the star-forming galaxies (squares) are color-coded by their sSFRs. The two quiescent galaxies are shown by the dark red stars. The weighted Pearson coefficients 𝑟 and the 𝑝-values of the null hypothesis are listed in each panel. 110 sSFRs in panels (a) - (d), respectively. For each relation, we calculated the weighted Pearson coefficient and the 𝑝-value of the null hypothesis to quantify their linearity. Nevertheless, there is no theoretical reason to expect the MZRs should be linear across this mass range (e.g., Ma et al., 2016), as simple linear relation do not capture the flatness of the MZ∗ R as we later discuss in Section 4.6.1. We pick the Pearson coefficient only for its simplicity to describe this small data set. Overall, we recover significant correlations between stellar mass and abundances of three elements with 𝑝 < 0.05, but do not detect significant correlation between stellar mass and [Mg/Fe]∗ . Among the three MZRs, we find that the O-MZg R is the most linear relation with 𝑅 = 0.82. The Mg-MZ∗ R (𝑅 = 0.52) is more linear than Fe-MZ∗ R (𝑅 = 0.46). In panel (d), the dwarf quiescent galaxies as well as the star-forming galaxies with the lowest sSFRs in our sample have lower [Mg/Fe]∗ than the rest of our sample. The low [Mg/Fe]∗ in these galaxies that are already or almost quenched indicate that their past star formation may have lasted for a protracted period of time, as the star formation there would have to occur in gas whose ISM is already enriched in iron by Type Ia SNe. The [Mg/Fe]∗ of the star-forming galaxies with higher sSFRs show large variations in our sample. There is no reason to expect their [Mg/Fe]∗ to be related to stellar mass because these galaxies are still actively forming stars with evolving [Mg/Fe]∗ . We also compare our O-MZg R and Fe-MZ∗ R with the literature on the local dwarf galaxies in Figure 4.10. The O-MZg R of the star-forming galaxies in our KCWI sample in panel (a) exhibits a relatively tight linear relation and is consistent with the O-MZg R derived from the direct 𝑇𝑒 method by Berg et al. (2012) for local dwarf galaxies at 𝑀∗ ∼ 106−9.7 𝑀⊙ . Our Fe-MZ∗ R in panel (b), instead, does not completely fall on the extrapolation of the low-mass Fe-MZ∗ R of the Local Group satellites at 𝑀∗ ≲ 8.5𝑀⊙ (Kirby et al., 2013). Most of the star-forming galaxies with high sSFRs fall on the extrapolation of the low-mass MZ∗ R of Local Group dwarf satellite galaxies measured by Kirby et al. (2013), while most of the star-forming galaxies with higher [Fe/H]∗ at fixed mass that lie above the extrapolation of the low-mass MZ∗ R have lower sSFRs. The shape of the Mg-MZ∗ R in panel (c) is very similar to the Fe-MZ∗ R. The disagreement between our Fe-MZ∗ R and the relation of Kirby et al. (2013) is not surprising because many physical processes such as outflows are changing rapidly with galaxy mass. Furthermore, theoretical predictions do not necessarily predict linear MZRs (e.g., Ma et al., 2016). For instance, Davé, Finlator, and Oppenheimer (2012) suggested that the slope of the MZR strongly depends on the primary feedback processes regulating galaxy growth 111 and driving outflows. They found that the slope of the simulated MZR can be changed easily by altering the mass dependence of the mass-loading factor of the outflows alone. Because star-forming galaxies at 108 𝑀⊙ ≲ 𝑀∗ ≲ 1010 𝑀⊙ are likely to different feedback processes than that of the Local Group satellites, we do not expect Fe-MZ∗ Rs in this mass range to be consistent with the relation by Kirby et al. (2013). It has been controversial whether star-forming and quiescent galaxies should exhibit distinct MZ∗ Rs. For the dwarf satellite galaxies (log (𝑀∗ /𝑀⊙ ) ≲ 8.5) in the Local Group, Kirby et al. (2013) found that star-forming and quiescent dwarf galaxies in the Local Group fall on a universal MZ∗ R and have similar [Fe/H]∗ at a given mass. However, large spectroscopic surveys such as SDSS, MaNGA and SAMI of massive field galaxies (log (𝑀∗ /𝑀⊙ ) ≳ 9) suggest that star-forming galaxies generally have more metal-poor stars than quiescent galaxies at the same masses (e.g., Gallazzi et al., 2021; Neumann et al., 2021; Vaughan et al., 2022). When we look at the two quiescent galaxies in our sample on the Fe-MZ∗ Rs, we find that only one of them, the more metal-poor 0241-0810 has similar [Mg/H]∗ and [Fe/H]∗ as those of heavily star-forming galaxies at the same mass. The other quiescent galaxy 01250024 that is more metal-rich, instead, has comparable [Fe/H]∗ and [Mg/H]∗ to the KCWI star-forming galaxies with suppressed sSFRs (the yellow to orange squares in Figure 4.10). To confirm that the two quiescent galaxies indeed possess different metal content, we also measured their [Fe/H]∗ and [Mg/H]∗ using alf by Conroy et al. (2018), and we recovered the same results to within 1𝜎. The distinct [Fe/H]∗ and [Mg/H]∗ of the two quiescent galaxies may be explained by their different environments. 0241-0810 is located in the vicinity of the massive elliptical galaxy NGC 1052, and it has similar radial velocity to that of NGC 1052 (Román, Castilla, and Pascual-Granado, 2021). The projected distance between 0241-0810 and NGC 1052 is around ∼ 50-60 kpc, while the projected virial radius of NGC 1052 is 390 kpc (Forbes et al., 2019), suggesting that 0241-0810 is likely to be a satellite of NGC 1052. The overdense environment where 0241-0810 resides might explain why it is consistent with the low-mass MZ∗ R of the Local Group dwarfs. In particular, galaxies in dense environments can be rapidly quenched by external effects, like ram pressure stripping. Therefore, a galaxy that would have naturally evolved to a higher normalization on the MZ∗ R may have been prevented from doing so due to a sudden cessation of star formation. On the other hand, 0125-0024 is an isolated dwarf galaxy identified by Kado-Fong et al. (2020) with 112 no massive galaxies nearby. This galaxy does not fall on the Fe-MZ∗ R of the Local Group dwarfs, possibly because it evolved naturally without external causes for gas removal. Surprisingly, compared to the O-MZg R in panel (a), the Fe- and Mg-MZ∗ Rs in panels (b) and (c) show much larger scatters in Figure 4.10. The scatter in both MZ∗ Rs appears to be driven by different sSFRs (indicated with a color bar in Figure 4.10). Because the stellar abundances represent the metals averaged over a much longer timescale than the instantaneous metal content in the current ISM, [Fe/H]∗ and [Mg/H]∗ are expected to be less “stochastic" and have less reason to depend on SFR/sSFR. Instead, we see the opposite behavior here. It has been suggested that the scatter of the MZg R could be underestimated from the strong line estimators (see discussions in Section 7.3 of Andrews and Martini (2013) and Section 7.2 in Section of Steidel et al. (2014)). In brief, the empirical strong line calibrations used to infer 𝑍𝑔 are not perfect correlations between 𝑇𝑒 -based measurements and strong line ratios, and thus have their own calibration errors (e.g., 0.1 dex for the 𝑅 calibration used in this work). For example, if we accounted for the ∼ 0.1 dex scatter of the "R" index-based metallicities against direct 𝑇e measurements as a source of systematic uncertainty in our measures of oxygen abundances, the implied intrinsic scatter in the MZgR becomes uncomfortably small. Additionally, as shown in Steidel et al. (2014), the relative intensities of the strong emission lines used in these empirical calibrations are sensitive to the changes not only in (O/H)g but also the excitation parameter and the hardness of the stellar radiation field. These parameters are also strongly correlated with stellar mass and sSFR, and thus yield a tighter relation than the actual MZg R. Besides, the empirical relations are calibrated to the 𝑇𝑒 -based abundance measurements of local H ii regions that only span a limited parameter space in physical properties such as excitation parameter while distant galaxies have much more diverse physical conditions, so the 𝑍𝑔 obtained with the strong line methods may not capture the change in physical properties related to SFR as well as the direct method. Although the scatter of the MZg R of local dwarf galaxies measured from the direct 𝑇𝑒 method (0.15 dex, Berg et al., 2012) is comparable to the scatter of our O-MZg R in Figure 4.10, we believe it is not a fair comparison. There are only 11 galaxies in the sample of Berg et al. (2012) in the similar mass range of our KCWI sample, which span a narrower range of sSFR (based on the measurements of the same sample by Dale et al., 2023) than our sample. We might expect the scatter of the MZg R 113 inferred from the direct 𝑇𝑒 method to be larger for a larger sample of star-forming galaxies with more diverse sSFRs. Indeed, the MZg R of the SDSS stacked spectra8 measured by Andrews and Martini (2013) using the direct 𝑇𝑒 method has much greater scatter. At 𝑀∗ ∼ 108.5 𝑀⊙ , [O/H]g can differ by up to ∼ 0.6 dex between the most star-forming and quiescent galaxies. We therefore conclude that the scatter of our O-MZg R is likely to be underestimated due to the strong line method used in this work. The scatter in the MZ∗ R driven by sSFR/SFR has seldom been discussed in the literature. As shown in panels (b) and (c) of Figure 4.10, the Mg-MZ∗ R appears to be more linear than the Fe-MZ∗ R, as the Mg-MZ∗ R has a larger Pearson coefficient. This implies that the large scatter of the Fe-MZ∗ R can partially attributed to the varying delay time of Type Ia SNe in galaxies. It is unclear whether the O-MZg R is indeed tighter than the Mg-MZ∗ R, or whether the difference in scatter is driven by the aforementioned systematics due to the strong line method. The stellar measurements of star-forming galaxies could also suffer from systematics due to the limitations of the current SPS models and the age–metallicity degeneracy, as we further discuss in Section 4.6.4. However, we still believe that the large scatter in the Fe- and MgMZ∗ Rs as well as our stellar abundance measurements of the star-forming galaxies should be robust, because we see that the two quiescent galaxies (marked by stars in Figure 4.10) — which are expected to suffer much less from the age-metallicity degeneracy — have distinct [Fe/H]∗ and [Mg/H]∗ despite having similar stellar masses. We therefore conclude that the MZ∗ Rs of Fe and Mg in the mass range between the Local Group satellites and more massive field galaxies exhibit large scatter driven by their varying sSFRs and the host environments. They should not be described by a single relation, especially not a single power law, as we further discuss in Section 4.6.1. We also emphasize that our results do not directly imply the stellar MZRs are bimodal with a metallicity gap at log (𝑀∗ /𝑀⊙ ) ∼ 8.5. The gap is more likely to originate from the selection bias in the sample, as we see a similar gap in the log 𝑀∗ –log SFR plane in Figure 4.1. 8 The metallicity obtained from the stacked spectra may suffer from the contamination in diffuse ionized gas ionized by the evolved, hot stars and thus also has its own systematics as we further discuss in Appendix 4.8.3 114 4.5.4 Abundances and Abundance Ratio as a function of Gravitational Potential Recently, Vaughan et al. (2022) investigated the relation between stellar metallicity and log Φ = log (𝑀∗ /𝑅𝑒 ) for low-redshift galaxies from Data Release 3 of the SAMI galaxy survey (Croom et al., 2021), and found that star-forming and quiescent galaxies form a single sequence on the Φ–𝑍 plane, with an offset of Δ[Z/H] ≈ 0.1 dex. They argued that the Φ–𝑍 relation is more fundamental than the MZR, which they explained as a result of galaxies with deeper gravitational potentials (and thus larger Φ) retaining more metals from galactic outflows. To investigate, we constructed the Φ–𝑍 relation of (O/H)g , [Fe/H]∗ , and [Mg/H]∗ , as well as the Φ–[Mg/Fe]∗ relation for our sample in the right column of Figure 4.10. For each relation, we listed their weighted Pearson coefficient and the 𝑝-value of the null hypothesis to in each panel of Figure 4.10. Still, the scatter of the Φ–𝑍 relation for (O/H)g (panel (e) in Figure 4.10) is significantly smaller than that of the relations for [Fe/H]∗ (panel (f)) and [Mg/H]∗ (panel (g)). As discussed above, it is possible that the scatter in the Φ–𝑍g relation is underestimated due to the strong line method used here. By moving from the mass–metallicity plane to the Φ–metallicity plane, we see that the relations for (O/H)g , [Fe/H]∗ and [Mg/H]∗ all become tighter and more linearlycorrelated, as the Pearson coefficients (and the 𝑝-value) are significantly higher (smaller) in the Φ–𝑍 relations. In particular, the differences in stellar abundances between galaxies with different sSFRs become smaller. However, the dependence on sSFR is not completely eliminated when we switch to the Φ–𝑍 relations (panels (e)-(g) in Figure 4.10). At a given Φ, most star-forming galaxies with lower sSFRs still have higher [Fe/H]∗ and [Mg/H]∗ . The scatters in the stellar Φ–𝑍∗ relation measured from iron and magnesium are ∼ 0.5 dex and 0.4 dex, respectively, which are much larger than the ≈ 0.1 dex offset between quiescent and star-forming galaxies suggested by Vaughan et al. (2022) for the SAMI sample. The disagreement between our results and those of Vaughan et al. (2022) may be explained by the different SFHs of galaxies at different masses. Dwarf galaxies are known to have more bursty SFHs than massive galaxies (Emami et al., 2019). The diverse SFHs of the low-mass galaxies, coupled with the delayed timescale of Type Ia SNe, can result in a wide range of stellar abundances at a given mass or Φ compared to more massive galaxies. The larger scatter we observe may originate from the dominance of dwarf galaxies in our sample. The majority of the SAMI sample of 115 Vaughan et al. (2022) instead contains more massive galaxies at 𝑀∗ > 1010 𝑀⊙ . In fact, the scatter in the low-mass bins (𝑀∗ ≲ 109.5 𝑀⊙ ) of the SAMI sample (Figure 3 of Vaughan et al. 2022) are also > 0.3 − 0.5 dex even though the mean offset is nearly zero. Finally, when we plot [Mg/Fe]∗ as a function of Φ, we find that the scatter remains similar to that of the mass–[Mg/Fe]∗ relation. Star formation and SNe continue in the star-forming galaxies, so their [Mg/Fe]∗ continues to evolve. Therefore, there is no reason to expect them to be correlated with any general properties of galaxies, as we saw in the trends for massive quiescent galaxies (Choi et al., 2014; Leethochawalit et al., 2019; Zhuang et al., 2023). We conclude that both the stellar and gas-phase elemental abundances of the rapidly evolving low-mass galaxies are jointly shaped by stellar mass, sSFR (or SFH), size, and the host environment, while the gas-to-stellar abundance ratios of low-mass star-forming galaxies are more related to their sSFR (or SFH). 4.6 4.6.1 Discussion A Further Look at the Stellar MZR To further investigate the shape of the MZ∗ Rs across the full range of galaxy masses, we construct the MZRs of more massive galaxies drawn from SDSS. We focus the discussion on the shape of the MZ∗ Rs only, rather than the MZg R for the KCWI+SDSS sample because the strong line 𝑅 calibration employed in determining the oxygen abundance in the KCWI sample is more suitable for metal-poor, low-mass galaxies but inappropriate for more massive galaxies, as detailed in Appendix 4.8.3. Because different gas metallicity calibrations are known to have significant systematics and thus affect the shape of the MZg R, we decided not to construct the MZg R beyond the KCWI sample in this paper. As pointed out in our previous work (see Figure 7 in Zhuang et al. 2021), the linear extrapolation of the MZ∗ R of the Local Group satellite galaxies (𝑀∗ ≲ 108 𝑀⊙ , Kirby et al., 2013) appears to disagree with measurements of more massive, quiescent galaxies in the field (𝑀∗ ≳ 109.5 𝑀⊙ , Leethochawalit et al., 2019). At 𝑀∗ ∼ 109 𝑀⊙ , they predicted different [Fe/H]∗ by up to ∼ 0.6 dex. By comparing the stellar metallicity of NGC 147, a dwarf elliptical satellite of Andromeda, derived from resolved stellar spectroscopy and integrated-light spectroscopy, we ruled out the possibility that the apparent discrepancy originates from systematic differences in the methods used for stellar metallicity estimates. Instead, the consistent results 116 from the two approaches present the first evidence that it is reasonable to put the MZ∗ Rs measured from different approaches on the same scale. To give an unbiased comparison of the Fe-MZ∗ R of the Local Group dwarfs, the KCWI sample, and the SDSS galaxies, we re-measured the stellar abundances of the SDSS quiescent galaxy sample compiled by Leethochawalit et al. (2019) using the two-step method proposed in Section 4.4.2. We also selected a subsample of 124 star-forming galaxies from Gallazzi et al. (2005) using criteria similar to those of Leethochawalit et al. (2019). The selection criteria, the stellar mass estimates, and the abundance measurements are detailed in Appendix 4.8.3. 0.25 0.50 KCWI star-forming KCWI quiescent SDSS star-forming SDSS quiescent 0.25 0.00 −0.25 −0.25 [Fe/H]∗ −0.50 −9.50 −9.75 −10.00 −0.50 −0.75 −0.75 SF −1.00 QS Zahid+17 ([Z/H]) 8 9 10 log M∗ [M ] 11 SF −10.25 QS −1.00 Kirby+13 Gallazzi+05 ([Z/H]) −1.25 −1.50 −9.25 [Mg/H]∗ 0.00 KCWI star-forming KCWI quiescent SDSS star-forming SDSS quiescent 12 −10.50 SDSS stack of ETGs (Choi+14) −1.25 −1.50 log sSFR [yr−1] 0.50 Center of Local Massive ETGs (Gu+22) −10.75 NGC 147 (Zhuang+21) 8 9 10 11 12 −11.00 log M∗ [M ] Figure 4.11: The MZ∗ Rs of iron (left) and magnesium (right) for the KCWI sample (squares for the star-forming galaxies, and dark red stars for the quiescent galaxies) and the SDSS sample (triangles for the star-forming galaxies, red open circles for the quiescent galaxies). The typical measurement errors of the SDSS star-forming (SF) and quiescent (QS) galaxies are shown in each panel. The star-forming galaxies are color-coded by their SFRs. The local MZ∗ Rs measured in other works (Gallazzi et al., 2005; Kirby et al., 2013; Choi et al., 2014; Zahid et al., 2017) and the stellar abundance measurements of individual galaxies in the local universe (Zhuang et al., 2021; Gu et al., 2022) are shown. A detailed review of all references in the plot is in Section 4.6.1. The left panel of Figure 4.11 shows the Fe-MZ∗ Rs of the KCWI and the SDSS samples along with the extrapolation of that of the Local Group dwarfs (Kirby et al., 2013), as well as some measurements from the literature. First, our updated highmass Fe-MZ∗ R of the SDSS quiescent galaxies (red circles) is still inconsistent with the extrapolation of low-mass Fe-MZ∗ R of the Local Group dwarfs (red dashed line). They disagree by ≳ 0.5 dex in [Fe/H]∗ at log (𝑀∗ /𝑀⊙ ) ∼ 9, similar to the results in our previous work (Zhuang et al., 2021), which indicates that the Fe-MZ∗ R cannot be described a single power law across the full range of mass. Second, the Fe-MZ∗ R of the SDSS quiescent sample (red circles) agrees with the alf measurements of the [Fe/H]∗ of the stacked spectra of early-type galaxies (ETGs) by Choi et al. (2014) 117 (purple crosses) and those of the center of local ETGs in the MASSIVE survey (Gu et al., 2022) (green diamonds). The left panel of Figure 4.11 also compares our results with other existing highmass MZ∗ Rs measuring the total stellar metallicity [Z/H]∗ instead of distinguishing between [Fe/H]∗ and [Mg/H]∗ . We interpret the measured [Z/H]∗ in Gallazzi et al. (2005) (gray band) and Zahid et al. (2017) (black stars) as [Fe/H]∗ for the following reason. Gallazzi et al. (2005) used the spectrophotometric indices defined in the SPS models of Bruzual and Charlot (2003) to measure [Z/H]∗ . These indices in Bruzual and Charlot (2003) were chosen to be the ones that are not sensitive to the change in [𝛼/Fe]∗ and capable of recovering solar-scaled metallicity (i.e., [Fe/H]∗ =[Z/H]∗ ). Zahid et al. (2017) determined [Z/H]∗ using full-spectrum fitting technique with the FSPS models derived from the solar-scaled MIST isochrones (Choi et al., 2016) and the MILES stellar spectral libraries (Sánchez-Blázquez et al., 2006), similar to the FSPS-MILES SSPs models presented in Section 4.4.1. The metallicities of MILES stellar library were also measured in terms of [Fe/H]∗ . Therefore, the measured [Z/H]∗ by Zahid et al. (2017) should also best interpreted as [Fe/H]∗ instead of [Mg/H]∗ . The MZ∗ R of all SDSS galaxies in the MPA-JHU sample by Gallazzi et al. (2005), regardless of their quiescence or star-forming state, exhibits scatter larger than 1 dex at log (𝑀∗ /𝑀⊙ ) ∼ 9 and therefore is consistent with both the low-mass MZ∗ R of Kirby et al. (2013) and our high-mass MZ∗ R of the SDSS sample. The MZ∗ R measured from stacked spectra of SDSS star-forming galaxies in different mass bins by Zahid et al. (2017) did not quantify the scatter of the MZ∗ R of star-forming galaxies. Their relation has overall higher normalization than our high-mass MZ∗ R of the SDSS star-forming and quiescent sample, which might result from the different wavelength ranges, SPS models, and algorithms used in the full-spectrum fitting. The Fe-MZ∗ Rs of the KCWI and the SDSS samples are derived using the same approach. They are free from the systematic effects of different fitting methods and thus yield the most straightforward and interpretable relation of [Fe/H]∗ of galaxies at different masses. First, the SDSS star-forming galaxies exhibit large scatter in their [Fe/H]∗ compared to their quiescent counterparts, with the most heavily starforming examples lying well below the high-mass MZ∗ R of the quiescent galaxies. The trend is similar in the KCWI sample. The dwarf galaxies at the low mass end of the KCWI sample (log (𝑀∗ /𝑀⊙ ) ∼ 8) have comparable [Fe/H]∗ as that of NGC 147 derived from alf (Zhuang et al., 2021). The combined results of the KCWI 118 and SDSS samples suggest that the Fe-MZ∗ R at 𝑀∗ > 108 𝑀⊙ is not linear. Our result reveals that the transition in the MZ∗ R between the Local Group satellites and massive field galaxies in the SDSS is largely shaped by the change in star-formation activity indicated by sSFR and the environment. We also compare the Mg-MZ∗ R of the KCWI and SDSS samples in the right panel of Figure 4.11. Our updated Mg-MZ∗ R of the SDSS quiescent galaxies is consistent with the results measured from the stacked spectra of the SDSS ETGs by Choi et al. (2014) but lower than the [Mg/H]∗ of the center of local ETGs in the MASSIVE survey (Gu et al., 2022). The behavior of the Mg-MZ∗ R is similar to Fe-MZ∗ R, although the scatter of the Mg-MZ∗ R of the star-forming galaxies in the KCWI sample and the SDSS sample is slightly smaller. Still, we find that at 𝑀∗ ≳ 109 𝑀⊙ , more heavily star-forming galaxies have lower [Mg/H]∗ than the quiescent galaxies at similar masses. Although there is yet no measurement of the Mg-MZ∗ R of the Local Group satellites, we show that the dwarf elliptical galaxy NGC 147 (Zhuang et al., 2021) and the quiescent satellite candidate 0241-0810 have [Mg/H]∗ comparable to those of the more heavily star-forming galaxies in the KCWI sample. To conclude, Fe- and Mg-MZ∗ Rs beyond the Local Group do not appear to be linear and cannot be described by a relatively tight linear relation. The stellar abundances of the star-forming galaxies beyond ∼ 108 𝑀⊙ are much more diverse and exhibit larger scatter that probably depends on factors other than stellar mass. 4.6.2 The sSFR Dependence of Stellar Abundance Upon a closer look at Figure 4.11, we can tentatively see the dependence on sSFR of the Fe- and Mg-MZ∗ Rs of star-forming galaxies in both the dwarf galaxies (𝑀∗ ≲ 109 𝑀⊙ ) in the KCWI sample and the massive galaxies (𝑀∗ ≳ 1010 𝑀⊙ ) in the SDSS sample, whereas such dependence on sSFR is less obvious for galaxies at 𝑀∗ ∼ 109−10 𝑀⊙ . A similar behavior is seen in the MZg R, where galaxies with higher SFRs at fixed mass are generally more metal-poor (e.g., Mannucci et al., 2010), likely due to the higher gas fraction diluting the gas metallicity in the ISM. Recently, Looser et al. (2024) reported a smooth relation between stellar mass, SFR and the light-weighted stellar metallicity in their study of 7,323 MaNGA galaxies at log (𝑀∗ /𝑀⊙ ) > 9 and referred to the relation as stellar fundamental metallicity relation, suggesting a potential correlation between stellar metallicity and SFR/sSFR. Looser et al. divided the MaNGA sample into six groups based on their offsets from the SFMS (somewhat similar to sSFR) and constructed the stellar 119 MZR within each group. They found that at log (𝑀∗ /𝑀⊙ ) ≳ 9.5 the MZ∗ R of the galaxies below the SFMS (i.e., more quiescent) have a higher normalization than that of the galaxies above the SFMS (i.e., more starbursty). They argued that the sSFR dependence of the MZ∗ R suggests that the metal contents of galaxies are primarily governed by long-lasting inflow of metal-poor gas accretion from the IGM/CGM instead of short-lived “episodic” accretion that only affects the gas metallicity, consistent with the theoretical models of IGM/CGM accretion by (Forbes et al., 2014; Torrey et al., 2019). Although our sample size is much smaller than that of Looser et al. (2024), we pushed the stellar mass limit down to log (𝑀∗ /𝑀⊙ ) ∼ 8, bridging the gap between the Local Group satellites (in which the stellar metallicity dependence on their sSFR is absent) and the massive galaxies (where the dependence on the sSFR has already been established). In addition, the Mg-MZ∗ R of the sample presented in this work is a better analog of O-MZg R because the trend will be less disrupted by the delay time of Type Ia SNe. Additionally, Garcia et al. (2024) observed similar strong dependence of the normalization of the MZ∗ R on the sSFR from the hydrodynamic simulations Illustris, TNG, and EAGLE. This finding is similar to the observations in this work and that of Looser et al. (2024). Garcia et al. (2024) suggested that the similar sSFR dependence of the MZ∗ R and MZg R can be attributed to the tight correlation between stellar and gas-phase metallicities in the simulation suites, and thus the MZ∗ R inherits the shape of the MZg R. Nevertheless, they were also concerned that the sub-grid treatment of the ISM employed in these simulations can only produce smooth stellar feedback. Consequently, the SFR/sSFR dependence discovered in their work may break down if galaxies have very bursty SFHs which may significantly disrupt the processes that allows stellar metallicities to catch up to the gas-phase metallicities. 4.6.3 Implications for Galaxy Growth and Quenching The interplay between stellar and gas-phase abundances we measure from the KCWI sample, as well as the stellar abundance dependence on mass, SFR, and environment, may provide us a hint as to the chemical enrichment history of galaxies as they grow and quench. First, Figure 4.11 shows that dwarf quiescent galaxies in different environments can have distinct stellar abundances at similar masses. The dwarf satellite candidate 0241-0810 that is more metal-poor falls on the extrapolation of the low-mass MZ∗ R 120 of the Local Group satellites, implying that galaxies in the group environment would still evolve along the low-mass MZ∗ R established in the Local Group. It is possible that galaxy 0241-0810 was quenched through ram pressure stripping (first proposed by Gunn and Gott 1972) that efficiently removed all the cold gas and resulted in fast quenching, and thus may not have had enough time to leave the low-mass MZ∗ R before becoming quiescent (e.g., Mayer et al., 2006). The isolated dwarf quiescent galaxy 0125-0041 that is more metal-rich instead was less impacted by environmental effects during its star formation. It might have quenched more slowly than 0241-0810, so that it would have had more time to form more metal-rich stars before the cessation of star formation. The dwarf star-forming galaxies in our sample that are on their way to quiescence in Figure 4.11 could have experienced gas starvation (Peng, Maiolino, and Cochrane, 2015; Trussler et al., 2020). When the supply of metal-poor gas from the surrounding CGM/IGM lags behind the gas consumption of the star formation, star formation would continue in the progressively more metal-enriched ISM and form more metalrich stars, which can explain why these dwarf star-forming galaxies with low sSFRs have significantly higher stellar abundances than those that are still actively forming stars at the similar masses. The starvation scenario is also supported by the higher [O/H]g compared to the [Mg/H]∗ in most galaxies in our KCWI sample (Figure 4.7). If the metal-poor gas inflows were dominant in driving star formation in these galaxies, one would expect [O/H]g lower than the [Mg/H]∗ . Although gas metallicity calibrations are known to have many systematic effects (Kewley and Ellison, 2008) and the absolute oxygen abundance scale may be off, the 𝑅 calibration (Pilyugin and Grebel, 2016) adopted in this work is calibrated to the 𝑇𝑒 -based measurements, which are usually lower than the gas-phase metallicity measurements based on nebular recombination lines or photoionization models (Esteban et al., 2014; Blanc et al., 2015; Steidel et al., 2016; Strom et al., 2018). In other words, if we have underestimated the true [O/H]g , it only strengthens our conclusion about starvation. In addition, the prominent differences of the stellar abundances between the galaxies with enhanced and suppressed SFRs at similar masses might suggest that most of the chemical enrichment (at least for the elements that substantially affect the lightweighted stellar abundance) occurs when galaxies are approaching quiescence. This finding is consistent with Leung et al. (2024), who found that the post-starburst galaxies in the MaNGA survey significantly increased their stellar metallicity during the recent starbursts. 121 Once galaxies grow above above ∼ 1010 𝑀⊙ , the MZ∗ Rs of star-forming and quiescent galaxies both become flattened in Figure 4.11. Massive galaxies have deeper gravitational potential well that can retain an increasingly large fraction of their metals. Theoretically, it has been suggested that energy-driven winds that are more efficient in ejecting metals dominate in low-mass galaxies (e.g., Murray, Quataert, and Thompson, 2005), while momentum-driven winds that drive less intense outflows dominate in high-mass galaxies (e.g., Hopkins, Quataert, and Murray, 2012; Davé, Finlator, and Oppenheimer, 2012). Consequently, these massive galaxies retain more metals than low-mass galaxies. At this stage, massive galaxies tend to start being strongly affected by a combination of "starvation" and "cessation" of star formation due to the increasing prevalence of AGN feedback (e.g., Weinberger et al., 2018), and thus generate metals much less efficiently. Additionally, the ISM of the massive galaxies that have been significantly chemically enriched contains high level of metals deposited by stellar winds and SNe and are almost saturated, so they will not increase metallicity significantly even if star formation continues. All of these combined effects lead to the flattened slope we observe in Figure 4.11. The levels of scatter in the Fe- and Mg-MZ∗ Rs of the SDSS star-forming galaxies are still much larger than those of the quiescent galaxies, given that the SDSS star-forming galaxies still have very diverse sSFRs and would contribute to the distinct stellar abundances at fixed masses as we discuss above. 4.6.4 Limitations and Caveats of This Study We now discuss potential limitations and caveats of this study that may affect our results. First, our sample is restricted to the star-forming galaxies with sSFRs in the range of 10−9 –10−11 yr−1 , so our conclusions must be limited to galaxies with sSFRs in that range. We excluded starburst galaxies due to the difficulty in determining their stellar abundances from the weak stellar absorption features in the rest-frame optical. Assuming that the dependence of stellar abundance on sSFR would exist in galaxies at all different sSFRs, it is possible that the dwarf starburst galaxies would lie even below the extrapolation of the low-mass MZ∗ R of the Local Group satellites, resulting in even larger scatter in the Fe- and Mg-MZ∗ Rs than the ones in Figure 4.10. As shown in Figure 4.1, the sample is also not evenly distributed in the log 𝑀∗ –log SFR plane. The current sample lacks many star-forming galaxies with intermediate sSFRs at 𝑀∗ ∼ 108.5 𝑀⊙ , so the MZ∗ Rs in Figure 4.10 are slightly bimodal. We hypothesize that denser sampling would reveal a continuous change 122 in the normalization of MZ∗ R with increasing sSFR. The scatter in the MZg R may also increase if starburst galaxies are included because previous works have found significant correlation between sSFR and (O/H)g (e.g., Mannucci et al., 2010; Andrews and Martini, 2013). Second, our sample contains only two quiescent galaxies residing in distinct environments. A larger sample would be needed to take a census of the metal content of dwarf galaxies in different environments, in order to resolve whether environment is as important in shaping the MZ∗ R as we suspect from this work. Third, because 40% of the KCWI sample lacks the H𝛼+[N ii]𝜆𝜆6549, 6585 coverage9 , we determined the gas-phase oxygen abundances of our sample from a combination of line ratios measured from the KCWI spectra and SDSS spectra. Therefore, we had to assume that the [N ii]/H𝛼 ratio remains constant within galaxies because the KCWI FoV is much larger than the SDSS fiber aperture. We cannot construct the MZg R using direct 𝑇𝑒 measurements because we detected [O iii]𝜆4363 in less than 1/3 of the sample. The only strong line calibration that does not require the red optical line ratios is 𝑅23 (e.g., Pilyugin and Thuan, 2005) which is known as a double-branched calibration (see Figure 8 of Pilyugin and Grebel 2016 for an example)10 . In addition, any strong-line calibration onto the direct 𝑇𝑒 abundance scale (like the 𝑅 calibration used here) may underestimate the actual gas-phase O/H in galaxies, as discussed in Section 4.6.3. Finally, we acknowledge that the stellar abundances we measure from the two-step method might still suffer from systematic effects. Due to the lack of SPS models that directly quantify the variation in [Mg/Fe]∗ , we still have to rely on models that vary all 𝛼 elements together with respect to Fe. Although we validated the method for quiescent galaxies in Section 4.4.3, it is possible that the two-step method may be subject to different systematic errors in star-forming galaxies due to the combined effects of the age–metallicity degeneracy and the difficulty in recovering the age of young galaxies (Carnall et al., 2019). The most direct way to verify the twostep method is to apply it to a nearby star-forming galaxy where we can measure its [Mg/Fe]∗ from its resolved stellar population, similar to the recent work done in dwarf elliptical galaxies or globular clusters with multiple stellar populations 9 The red channel of the KCWI was not available until the summer of 2023, after some of our data were obtained. 10 The 𝑅 23 calibration is relatively insensitive to galaxies with oxygen abundances falling near turnover of the curve at 12 + log (O/H) ∼ 8.0–8.4, which coincides with the gas-phase metallicity of most galaxies in our sample. 123 (Ruiz-Lara et al., 2018; Boecker et al., 2020; Zhuang et al., 2021). 4.7 Summary In this work, we presented a sample of 46 star-forming and two quiescent galaxies with 𝑀∗ ∼ 108−10 𝑀⊙ observed with Keck/KCWI, with the aim of understanding the shape of the MZ∗ R in the relatively unexplored mass range between the Local Group dwarf satellite galaxies and massive field galaxies, as well as the connection between the metals in the stars and the ISM. Our findings are as follows: 1. Applying SPS models with variable [𝛼/Fe] directly to the stellar continuum with pPXF significantly underestimates [Mg/Fe]∗ or overestimates [Fe/H]∗ (Figures 4.4 and 4.5). To solve this problem, we developed a two-step method that is capable of recovering the [Fe/H]∗ and [Mg/Fe]∗ of the stellar population. 2. We determined the gas-phase oxygen abundances via the 𝑅 calibration (Pilyugin and Grebel, 2016) and the stellar iron and magnesium abundances via the two-step method within the same galaxies of our KCWI sample. For the first time, we can not only relate the stellar and gas-phase metallicity but also make an apples-to-apples comparison of 𝛼 elements within the same galaxies. The correlation between [O/H]g and [Mg/H]∗ is tighter than that of [O/H]g and [Fe/H]∗ . Furthermore, [O/H]g is higher than [Fe/H]∗ and [Mg/H]∗ in most galaxies, suggesting that new stars are forming in gas that has participated in the overall chemical enrichment of the ISM, and not in metal-poor gas that has recently been accreted. 3. The gas-to-stellar abundance ratios, Δ𝑍O,Fe and Δ𝑍O,Mg , are correlated with sSFR but do not depend on stellar mass, SFR, light-weighted age, log Φ (a proxy for the gravitational potential), or log Σ (the stellar mass surface density). 4. We constructed the ionized O-MZg R and the Fe-MZ∗ R and Mg-MZ∗ R of our KCWI sample, and we found that the scatters in the Fe- and Mg-MZ∗ Rs are significantly larger than that of the O-MZg R. Further work would be necessary to understand the origin of these scatters. The observed scatters in the MZ∗ Rs are primarily driven by varying sSFRs. At a given mass, star-forming galaxies with higher sSFRs exhibit lower [Fe/H]∗ and [Mg/H]∗ . The relations become tighter in the Φ–Z plane, but the dependence on sSFR is not eliminated. For 124 the two quiescent galaxies in our sample, the dwarf satellite candidate 02410810 is more metal poor, has comparable stellar abundances to the heavily star-forming galaxies at similar masses, while the isolated dwarf quiescent galaxy 0125-0041 is more metal-rich and exhibits abundances similar to the star-forming galaxies with low sSFRs. 5. We compared the Fe- and Mg-MZ∗ Rs of our KCWI sample with those of more massive SDSS galaxies and found that they could not be described by a single linear relation. At a fixed mass, heavily star-forming galaxies still tend to have lower [Fe/H]∗ and [Mg/H]∗ than quiescent galaxies. This suggests that the increasing scatter in the stellar abundances at a fixed 𝑀∗ exhibited by the KCWI dwarfs may be driven, at least in part, by the sSFR tracing the remaining gas supply. This trend also supports a physical scenario in which starvation is primarily responsible for quenching galaxies in the field. This work is the first paper in a series whose goal is to understand the chemical evolution of low-mass galaxies at low redshift, especially those that remain actively star-forming, over the mass range 𝑀∗ ∼ 108−10 𝑀⊙ based on IFU data cubes. While we are limited by the sample size, the high-quality data obtained with a 10 m telescope allows us to place unprecedented constraints on the chemical enrichment of galaxies in the mass range intermediate between Local Group satellites and massive galaxies that have been well-studied by large spectroscopic surveys. In the future, we will leverage the spatial information from the IFU data and investigate the spatially-resolved elemental abundances in the stellar and gas phases, which will provide unparalleled details to interpret the chemical evolution of star-forming dwarf galaxies. Acknowledgments The authors acknowledge the insightful and constructive feedback of the anonymous referee. We thank Yuguang Chen, Allison Strom, Adam Carnall, Claudia Maraston, and Ryan Sanders for useful discussions. We are grateful to the many people who have worked to make the Keck Telescopes and their instruments a reality and to operate and maintain the Keck Observatory, including support astronomers Greg Doppmann and Rosalie McGurk, and telescope operator Tony Connors. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the Native Hawaiian community. 125 We are most fortunate to have the opportunity to conduct observations from this mountain. This material is based on work supported by the National Aeronautics and Space Administration (NASA) under FINESST Grant No. 80NSSC22K1755 (Z.Z. and C.C.S.). E.N.K. acknowledges the support from the National Science Foundation (NSF) under CAREER Grant No. AST-2233781. C.C.S. has been supported in part by NSF grant No. AST-2009278. C.C. acknowledges support from NSFAST-131547. Most of the data presented herein were obtained at Keck Observatory, which is a private 501(c)3 non-profit organization operated as a scientific partnership among the California Institute of Technology, the University of California, and NASA. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. 4.8 4.8.1 Appendices Appendix A: Potential Aperture Effect The main analysis in this work made use of the spectra obtained from summing the spaxels with S/N > 1 in the stellar continuum. To explore whether this extraction approach would introduce any bias due to the potential metallicity radial gradients in these galaxies, we also extracted the spectra from four different circular apertures, with diameters ranging from 1′′ to 4′′, and measured their stellar abundances using the method described in Section 4.4.2. We did not measure the gas metallicity because the scatter in gas metallicity is more likely driven by the calibration method instead of an aperture effect, as detailed in Section 4.5.3. We show the Fe- and Mg-MZ∗ Rs of the KCWI sample extracted using different aperture sizes in Figure 4.12 and 4.13, respectively. Compared to the MZ∗ Rs obtained from the entire KCWI data cube (roughly around 6′′ to 20′′ in diameter; Figure 4.10), the overall shape and the scatter of the MZ∗ Rs remained largely unchanged when smaller aperture sizes are used, indicating that potential radial gradients and aperture effects are not responsible for driving the large scatter in the MZ∗ Rs. The dependence of the stellar abundances on sSFR remains present across all aperture sizes. 4.8.2 Appendix B: Comparison of stellar population age derived from different SFH models Here we discuss the light-weighted stellar population ages of the KCWI sample derived assuming different SFH models and fitting methods. Figure 4.14 com- 126 Aperture = 1” Aperture = 2” −0.4 −0.4 −0.6 −0.6 [Fe/H]∗ −0.2 [Fe/H]∗ −0.2 −0.8 −0.8 −1.0 −1.0 −10.4 −1.2 8.0 8.5 −10.2 log sSFR [yr−1 ] −10.0 9.0 9.5 −9.8 −9.6 KCWI star-forming KCWI quiescent −1.2 10.0 8.0 8.5 log M∗ [M ] 9.5 10.0 9.5 10.0 log M∗ [M ] Aperture = 3” Aperture = 4” −0.2 −0.2 −0.6 −0.6 [Fe/H]∗ −0.4 [Fe/H]∗ −0.4 −0.8 −0.8 −1.0 −1.0 −1.2 9.0 −1.2 8.0 8.5 9.0 log M∗ [M ] 9.5 10.0 8.0 8.5 9.0 log M∗ [M ] Figure 4.12: The Fe-MZ∗ R of the KCWI star-forming (squares) and quiescent (stars) sample, measured from the spectra extracted from different circular apertures (1′′ – 4′′). The star-forming galaxies are color-coded by their sSFRs. The overall shape and the scatter of the Fe-MZ∗ R remains largely unchanged across different sizes of aperture. pares the light-weighted ages derived using pPXF (i.e., the first step of the two-step method) assuming non-parametric SFHs with those derived from broadband SED fits using BAGPIPES assuming four different parametric SFHs: delayed exponential, log-normal, double-power-law, and constant. The light-weighted ages obtained from spectral analysis are broadly consistent with those obtained from SED fits, particularly for an assumed constant SFH. The consistency indicates that invoking a non-parametric SFH that allows star formation to occur at any time and to accommodate any possible shape of the SFH does not introduce any significant bias to the light-weighted age measurement. Given that broadband photometry is more sensitive to stellar populations formed at different epochs due to its wider spectral coverage than KCWI spectroscopy, Figure 4.14 shows that the light-weighted ages derived from pPXF spectral fits in the relatively narrow wavelength range 3650– 5500 Å are reasonable. 127 Aperture = 1” Aperture = 2” 0.0 0.0 −0.2 −0.2 −0.4 [Mg/H]∗ [Mg/H]∗ −0.4 −0.6 −0.6 −0.8 −0.8 −1.0 −10.4 8.0 8.5 −10.2 log sSFR [yr−1 ] −10.0 9.0 −9.8 9.5 −1.0 −9.6 KCWI star-forming KCWI quiescent 10.0 8.0 8.5 log M∗ [M ] 9.0 9.5 10.0 9.5 10.0 log M∗ [M ] Aperture = 3” Aperture = 4” 0.0 0.0 −0.4 −0.4 [Mg/H]∗ −0.2 [Mg/H]∗ −0.2 −0.6 −0.6 −0.8 −0.8 −1.0 −1.0 8.0 8.5 9.0 9.5 −1.2 10.0 8.0 8.5 log M∗ [M ] 9.0 log M∗ [M ] Figure 4.13: Similar to Figure 4.12, but comparing the Mg-MZ∗ R measured from different apertures. 10.00 10.00 9.75 BAGPIPES SFH: delayed exp 9.75 9.50 log Agebagpipes [yr] log Agebagpipes [yr] 9.50 9.25 9.00 8.75 9.25 9.00 8.75 8.50 8.50 KCWI star-forming KCWI quiescent 8.25 8.00 BAGPIPES SFH: log-normal 8.50 8.75 9.00 9.25 9.50 log Ageppxf [yr] 9.75 8.25 8.00 10.00 8.75 9.00 9.25 9.50 log Ageppxf [yr] 9.75 10.00 10.00 9.75 10.00 BAGPIPES SFH: constant BAGPIPES SFH: double-power-law 9.75 log Agebagpipes [yr] log Agebagpipes [yr] 9.50 9.25 9.00 8.75 9.50 9.25 9.00 8.75 8.50 8.50 8.25 8.25 8.00 8.5 9.0 log Ageppxf [yr] 9.5 10.0 8.00 8.5 9.0 9.5 log Ageppxf [yr] 10.0 Figure 4.14: Comparison of light-weighted stellar population age derived from SED fitting using BAGPIPES and from full-spectrum fitting using pPXF for the star-forming (blue squares) and quiescent (red stars) galaxies in our KCWI sample. In each panel, the one-to-one line is shown by the yellow dashed line. 128 4.8.3 Appendix C: The Selection and Abundance Measurements of the SDSS Sample We adopt the SDSS quiescent sample selected by Leethochawalit et al. (2018b). In summary, Leethochawalit et al. (2018b) selected a sample of 152 quiescent galaxies with H𝛼 EW < 1 Å from 44,254 SDSS spectra from Gallazzi et al. (2005). In each bin of 0.1 dex in stellar mass spanning from 109 to 1011.5 𝑀⊙ , they randomly selected at most eight quiescent galaxies, yielding a subsample of 152 quiescent galaxies. In this work, we selected the SDSS star-forming sample in a similar way to Leethochawalit et al. (2018b). We restricted the galaxies to the SFMS with sSFRs in the range of 10−11 and 10−9 yr−1 using the sSFRs from the SDSS MPA-JHU catalog (galSpecExtra, SDSS DR17; Kauffmann et al., 2003a; Brinchmann et al., 2004; Salim et al., 2007). Similarly, we randomly selected at most eight star-forming galaxies in each bin of 0.1 dex in the mass range of 109−11.5 𝑀⊙ . We cross-matched the subsamples with the GSWLC catalog to obtain stellar mass estimates for comparison with the KCWI sample. As the stellar masses of the KCWI sample were derived from BAGPIPES assuming the Kroupa (Kroupa, 2001) IMF, the Chabrier-based (Chabrier, 2003) stellar masses in the GSWLC catalog were adjusted to Kroupa-based values by applying an offset of +0.025 dex (Salim et al., 2007). To be consistent with the KCWI spectra, we limited the wavelength range of the SDSS spectra to 3650 − 5500 Å and measured the ages, [Fe/H]∗ , and [Mg/Fe]∗ in the same manner as Section 4.4. We excluded the galaxies with errors in [Fe/H]∗ > 0.15 dex to provide a clear trend, yielding 125 quiescent and 124 star-forming galaxies in the SDSS sample. The stellar masses and SFRs of the SDSS sample are shown in Figure 4.15. We do not discuss the best-fit O-MZg R of the SDSS star-forming galaxies in Section 4.6 because it becomes flat around log (𝑀∗ /𝑀⊙ ) ∼ 10.2 (Figure 4.16). It is unclear to us whether the flattening of the SDSS O-MZg R results from the underlying physical mechanisms governing the metal retention or originates from the systematics in the 𝑅 calibration, as Pilyugin and Grebel (2016) only validated the 𝑅 calibration to the 𝑇𝑒 -based measurements up to 12 + log (O/H) ≳ 8.7. Because the KCWI data cannot cover many nebular features sensitive to gas-phase metallicity in the red optical, we refrain from experimenting with other strong-line calibrators in this comparison. It is beyond the scope of this paper to investigate how the systematics of different gas metallicity indicators could affect the high-mass MZg R of the SDSS galaxies. 129 2 sSFR = 10−8 yr−1 10−9 yr−1 10−10 yr−1 1 log SFR [M yr−1] 10−11 yr−1 0 −1 −2 −3 KCWI star-forming KCWI quiescent SDSS quiescent SDSS star-forming −4 −5 8 9 10 11 12 log M∗ [M ] Figure 4.15: SFR as a function of stellar mass of the galaxies in our KCWI and SDSS samples. The blue squares and red stars represent the star-forming and the quiescent galaxies of the KCWI sample, while the cyan triangles and dark red dots indicate the star-forming and the quiescent galaxies described in Appendix 4.8.3. The contours show the SDSS SFMS at a similar redshift range (𝑧 < 0.06) taken from the GSWLC catalog (Salim et al., 2016) at 1-3 𝜎. The grey dots indicate all the GSWLC galaxies in the same redshift range as those in our sample. Nevertheless, we trust that the 𝑅 calibration is reliable for the low-mass galaxies in our KCWI sample, which all have 12 + log (O/H) < 8.6. The O-MZg R of the KCWI sample also agrees with that of the local dwarf galaxies measured by Berg et al. (2012) using the 𝑇𝑒 method. However, our gas-phase metallicities and those measured by Berg et al. (2012) are lower than the MZg R measured by Andrews and Martini (2013) for stacked SDSS spectra via the 𝑇𝑒 method. Andrews and Martini (2013) included a large sample of galaxies with galaxies at various sSFRs when they generated the stacked spectra. The emission from diffuse ionized gas (DIG) ionized by evolved, hot stars becomes increasingly important when the sSFR is low. As pointed out by Sanders et al. (2017), the contamination from DIG tends to affect the emission line fluxes from the low-ionization species and lower the electron temperature estimate in the low-ionization zone. Consequently, the gas metallicity derived from the stacked spectra with significant contribution from DIG would be overestimated. Although our sample also consists of star-forming galaxies with low sSFRs, we measured the gas metallicity for individual galaxies where DIG contribution should be much less significant. We therefore suspect that the contamination from DIG in the sample of Andrews and Martini (2013) may explain 130 8.8 −9.25 −9.50 8.4 −9.75 −10.00 8.2 −10.25 8.0 Berg+12 Andrews & Martini 13 SDSS star-forming KCWI star-forming 7.8 7.6 8 9 10 11 log sSFR [yr−1] 12 + log(O/H)g 8.6 −10.50 −10.75 −11.00 log M∗ [M ] Figure 4.16: The O-MZg R of the KCWI sample and the SDSS sample, colorcoded by the sSFRs. The O-MZR of the local dwarf galaxies (and the associated 1𝜎 confidence interval, Berg et al., 2012) and the stacked spectra of the SDSS galaxies (Andrews and Martini, 2013) derived from the direct 𝑇𝑒 method are shown by the purple dashed-dotted line (and shaded region) and the black dashed line, respectively. the discrepancy. 131 Chapter 5 METALS IN STAR-FORMING GALAXIES WITH KCWI: SPATIALLY RESOLVED NEBULAR AND STELLAR POPULATION PROPERTIES In this chapter, we extend our analysis of star-forming dwarf galaxies observed with KCWI, as introduced in Chapter 4 (Zhuang et al., 2024, hereafter Paper I), to explore their spatially resolved stellar and nebular properties in greater depth. While the previous analysis was based solely on KCWI-blue data, here we conduct a joint analysis combining both the blue and red channels of the KCWI. The observations and data reduction are described in Section 5.1. In Section 5.2, we present the methods used to determine the spatially resolved properties of ionized gas and stellar populations. We present the preliminary results on the spatially resolved properties in Section 5.3. 5.1 5.1.1 Data Sample In the previous chapter, we presented the first results of 46 star-forming galaxies in a mass range of 108 − 1010 𝑀⊙ observed on the KCWI in 2021B and 2023B. In this chapter, we focus on 27 galaxies of the sample observed in 2023B (Table 5.1) with the blue (KCWI) and red (KCRM) red coverage, 25 of which have stellar masses 𝑀∗ ≲ 109 𝑀⊙ and two of have stellar masses 109.5 ≲ 𝑀∗ ≲ 1010 𝑀⊙ , allowing us to better characterize spatially resolved nebular properties. All targets were randomly selected from the SDSS MPA-JHU catalog (Brinchmann et al., 2004; Tremonti et al., 2004) to have 108 𝑀⊙ ≲ 𝑀∗ ≲ 109 𝑀⊙ and specific star formation rates (sSFR) between 10−9 and 10−11 yr−1 . We re-measured the stellar masses and star formation rates (SFR) of our sample by fitting broadband photometry from FUV to mid-IR wavelengths with BAGPIPES (Carnall et al., 2018; Carnall et al., 2019) assuming an exponentially declining (delayed-𝜏) star formation history (SFH). We made use of the publicly available images from the Galaxy Evolution Explorer (GALEX; Martin et al., 2005), the Sloan Digital Sky Survey (SDSS; York et al., 2000), the Panoramic Survey Telescope and Rapid Response System (PS1; Flewelling et al., 2020), and the Wide-field Infrared Survey Explorer (WISE; Wright et al., 2010). The photometry and spectral energy 132 distribution (SED) fitting was described in full detail in Paper I. Table 5.1: General Properties of the KCWI Galaxy Sample log M∗ b log SFR𝑏 [M⊙ ] [M⊙ yr −1 ] 0.016 8.09±0.10 −1.84 ± 0.08 +15 52 38.96 0.009 8.23±0.10 −1.67 ± 0.08 21 52 22.46 −01 10 15.95 0.016 8.40±0.10 −1.72 ± 0.13 0845+5145 08 45 54.52 +51 45 11.12 0.014 8.42±0.10 −1.80 ± 0.14 2334+0029 23 34 14.80 +00 29 07.28 0.024 8.42±0.10 −1.19 ± 0.07 0121−0853 01 21 51.93 −08 53 10.63 0.018 8.43±0.10 −1.55 ± 0.10 0013−0956 00 13 45.42 −09 56 03.67 0.013 8.51±0.10 −1.45 ± 0.21 0155−0037 01 55 01.92 −00 37 35.27 0.023 8.56±0.10 −1.50 ± 0.12 0140−0012 01 40 52.90 −00 12 49.52 0.018 8.59±0.10 −1.74 ± 0.16 0023−0939 00 23 48.32 −09 39 09.85 0.020 8.59±0.10 −1.10 ± 0.06 0233+0038 02 33 03.92 +00 38 41.59 0.024 8.67±0.10 −0.93 ± 0.08 0256−0010 02 56 32.90 −00 10 51.13 0.029 8.69±0.10 −0.89 ± 0.08 2259−0019 22 59 03.19 −00 19 45.82 0.016 8.71±0.10 −1.21 ± 0.09 2300−0832 23 00 51.88 −08 32 13.36 0.025 8.75±0.10 −1.58 ± 0.15 0233−0819 02 33 05.84 −08 19 08.79 0.019 8.77±0.10 −1.61 ± 0.17 2301+1451 23 01 06.26 +14 51 16.74 0.024 8.81±0.11 −0.74 ± 0.12 0332−0600 03 32 00.36 −06 00 42.77 0.018 8.82±0.10 −1.71 ± 0.17 2131−0613 21 31 03.64 −06 13 58.27 0.025 8.82±0.10 −0.73 ± 0.10 0850+6145 08 50 39.67 +61 45 44.42 0.024 8.88±0.10 −1.05 ± 0.14 0256−0707 02 56 34.76 −07 07 11.12 0.017 8.96±0.10 −1.08 ± 0.12 2137+1243 21 37 52.51 +12 43 42.63 0.031 8.98±0.11 −0.91 ± 0.12 0137−0942 01 37 43.57 −09 42 36.36 0.019 9.02±0.10 −0.88 ± 0.12 0136+1356 01 36 15.18 +13 56 43.26 0.024 9.03±0.10 −0.49 ± 0.20 2304−0933 23 04 30.86 −09 33 03.58 0.032 9.04±0.10 −0.94 ± 0.12 0306−0033 03 06 24.96 −00 33 04.38 0.025 9.16±0.10 −0.98 ± 0.15 0334+0106 03 34 06.02 +01 06 15.19 0.049 9.44±0.10 −0.03 ± 0.09 0407−0634 04 07 04.64 −06 34 02.15 0.038 9.88±0.10 0.01 ± 0.06 Galaxy RA Dec (J2000) (J2000) 2225−0046 22 25 07.92 −00 46 06.03 2329+1552 23 29 46.17 2152−0110 𝑧𝑎 a Redshifts are taken from SDSS DR17 (Abdurro’uf et al., 2022). b The stellar masses and SFRs are derived from broadband SED fitting with BAGPIPES. 133 5.1.2 KCWI Observations The KCWI observations were conducted over three nights in the 2023B semester, with an average seeing of approximately ∼1′′. All targets were observed using the medium slicer, providing a field of view (FoV) of 16.5′′ × 20.4′′. For the blue channel, we used the BL grating centered at 4500 Å, yielding a spectral resolution FWHM of 2.5 Å and a wavelength coverage of 3500–5500 Å. For the red channel, we used the RL grating centered at 7800 Å, with a spectral resolution FWHM of 4 Å and a wavelength range of 6300–9500 Å. For most galaxies, we rotated the position angles (i.e., the orientation of the KCWI slices on the sky) in order to minimize covariance when stacking exposures. Each pointing included at least three five-minute exposures in the red channel to facilitate more effective cosmic ray (CR) removal, along with a single exposure in the blue channel matched in total integration time. The total exposure time per galaxy ranged from 15 to 60 minutes. For galaxies with angular sizes comparable to the KCWI FoV, we also obtained off-field sky frames adjacent to the science frames to enable accurate sky subtraction. We reduced the KCWI-blue data using a modified version of the publicly available KCWI data reduction pipeline (DRP), incorporating the updates described in Chen et al. (2021) and N. Prusinski et al. (in prep.)1 . This pipeline produces sky-subtracted, flux-calibrated 3D data cubes with a spatial sampling of 0.29′′× 0.68′′ and a spectral dispersion of 1 Å per pixel for individual exposures. We used the same pipeline to reduce the red channel data. To ensure spatial alignment between the two channels, we set the reference wavelength for differential atmospheric refraction (DAR) in the red channel to 4500 Å, matching the value used for the blue channel. However, the red data are affected by long-tailed cosmic rays that are not effectively removed by the default CR removal algorithm in the DRP, which uses the astroscrappy package (McCully et al., 2018). To address this, we created CR masks using the new kcrm_create_crmsk function in the KCWIKit package (Chen et al., 2021; Prusinski and Chen, 2024)2 . The algorithm compares each exposure with the median image of all exposures at a given pointing to identify outliers, and we found that 3𝜎 clipping was sufficient to mask CR-contaminated pixels. We did not perform CR removal for standard star observations, as their short integration times (less than one minute) make CR contamination much less 1 https://github.com/yuguangchen1/KCWI_DRP/tree/KCWIKit 2 https://github.com/yuguangchen1/KcwiKit 134 of a concern, and only the broad spectral shape is needed to estimate the inverse sensitivity function. We also skipped sky subtraction and flux calibration of the red-channel science frames and their associated sky frames (if available). The standard KCWI DRP uses a single master b-spline sky model across all slices for sky subtraction, which requires highly accurate flat-fielding, wavelength calibration, and a uniform line spread function (LSF) across all the slices. While this method has been shown to work well for the blue channel (e.g., Chen et al., 2021; de los Reyes et al., 2023; Zhuang et al., 2024), it can leave significant residuals in regions with dense sky lines, especially when science signals overlap with sky features (Figure 5.1). To overcome these limitations, we developed KSkyWizard3 , a standalone GUI-based Python tool for post-processing DRP-reduced red-channel cubes. KSkyWizard reads in non-sky-subtracted, DAR-corrected cubes (icubed files) and performs sky subtraction, flux calibration, and telluric correction4 . To account for imperfect flat-fielding and spatial variations in the LSF, we adopted the Zurich Atmosphere Purge (ZAP; Soto et al., 2016) package, an algorithm based on principal component analysis (PCA) to model the sky from blank regions of the cube or from the blank sky frame. ZAP uses continuum filtering to disentangle narrow sky lines from broader features in the science target and reconstructs the sky model in each spaxel independently, significantly reducing sky residuals while preserving the flux of the target. KSkyWizard serves as a GUI wrapper for ZAP, providing features such as wavelength cropping, white-light image generation (for science region masking), and sky model configuration. Users can apply ZAP either with in-field sky (using a mask) or with an adjacent sky frame, and choose between global PCA or segmented PCA in the multiple regions following Soto et al. (2016). Its interactive interface allows users to iteratively adjust masks and spectral segments until optimal results are achieved. KSkyWizard also performs flux calibration and telluric correction. The standard DRP estimates the inverse sensitivity function by fitting a polynomial to userdefined regions, which often fails if dense telluric regions are present, especially in the red end of the spectrum. KSkyWizard refines this by fitting a cubic-spline interpolation to the standard star spectrum using user-defined knots, improving the fit in telluric regions. The corrected spectrum of the standard star is then passed 3 https://github.com/zhuyunz/KSkyWizard 4 KSkyWizard can also refine the sky subtraction of already sky-subtracted cubes generated by the DRP. 135 to PypeIt (Prochaska et al., 2020a; Prochaska et al., 2020b) to generate a telluric model at the airmass of the standard star, which is then scaled to match the airmass of the science target and applied for telluric correction. Figure 5.1 compares a skysubtracted spectrum produced by KSkyWizard with that from the standard DRP. The KSkyWizard result shows significantly reduced sky residuals and improved correction of telluric absorption features. 4.0 DRP-subtracted spectrum KSkyWizard-subtracted spectrum Fλ (10−18 erg/s/cm2 /Å) 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 6500 7000 7500 8000 8500 9000 9500 Observed Wavelength (Å) Figure 5.1: Comparison of an example sky-subtracted spectrum produced by the standard KCWI DRP (red) and by KSkyWizard (blue). Both spectra were extracted from the same 2′′ diameter aperture centered on the target. Finally, the sky-subtracted, flux-calibrated data cubes from both channels of all pointings for a given target were aligned, stacked, and resampled to a common spatial grid with 0.3′′ × 0.3′′ spatial sampling and 1 Å spectral dispersion using the KCWIKit package5 (Chen et al., 2021; Prusinski and Chen, 2024). 5.2 Analysis 5.2.1 Summary of the Fitting Algorithms We developed our own custom Python pipeline to analyze the stacked KCWI data cubes to obtain high-level data products, including emission line maps and spatially resolved stellar population parameters, by following the general procedures of the MaNGA data-analysis pipeline (DAP) (Westfall et al., 2019). The main purpose of this pipeline is to extract the maps of nebular and stellar population properties separately for further measurements via the penalized pixel-fitting method (pPXF) by Cappellari (2017), a 𝜒2 minimization code that fits for a linear combination of simple stellar population (SSP) models at different ages and metallicities. 5 https://github.com/yuguangchen1/KcwiKit 136 We generated SSP models using the PYTHON-FSPS package (Foreman-Mackey, Sick, and Johnson, 2014), the Python wrapper of the Flexible Stellar Population Synthesis code (FSPS; Conroy, Gunn, and White, 2009; Conroy and Gunn, 2010) version 3.2, assuming a Kroupa (2001) IMF, the MIST isochrones (Choi et al., 2016), and the MILES stellar spectral libraries (Sánchez-Blázquez et al., 2006). The SSP models have metallicities spanning the range [Fe/H] = −2.0 to +0.5 with an interval of 0.25 dex, the same as the grid of the MIST isochrones, and ages ranging from log(Age) [yr] = 5.0 to 10.2 with an interval of 0.2 dex. Because the MILES stellar spectral library has a spectral coverage of 3525−7500 Å, we excluded the spectral regions beyond 7500 Å in the KCWI data for further analysis in this work. We save the very red end of the spectra for future analysis. The spectral regions below 3650 Å were also excluded from the analysis because strong nebular continuum in the highly star-forming regions blueward of the Balmer break might affect the estimation of stellar population properties obtained from the full-spectrum fitting (Byler et al., 2017; Miranda et al., 2025). All spaxels with an average signal-to-noise ratio (S/N) per wavelength channel, weighted by the SDSS-𝑔 band response function (i.e., S/N𝑔 ), greater than 0.5 are included in the spatially resolved analysis. We tested several S/N𝑔 thresholds and found that adopting a relatively loose criterion of S/N𝑔 > 0.5 allows us to retain spaxels in the outskirts—where only emission lines are typically detected—without introducing significant bias in the integrated stellar continuum within each spatial bin (see Section 5.2.2). Before continuing the spectral analysis, we corrected the spectra for Galactic extinction using the 𝐸 (𝐵 − 𝑉) value from Schlafly and Finkbeiner (2011). We adopt the Galactic extinction law by O’Donnell (1994) to calculate the de-reddening correction. 5.2.2 Stellar Kinematics We first measured the spatially resolved stellar kinematics using pPXF. Following the approach adopted by the MaNGA team (Westfall et al., 2019; Belfiore et al., 2019), we included both an eighth-order additive Legendre polynomial and an eighth-order multiplicative Legendre polynomial in the stellar continuum fit. These polynomials allow the model spectra to better match the overall shape of the observed spectra, which may suffer from imperfect flux calibrations and dust attenuation. To better determine stellar kinematics, we masked spectral regions within a velocity range of 137 ±400 km s−1 around potential emission lines (see Table 5.2). Table 5.2: Emission-Line Parameters ID Line Name 𝑎 (Å) 𝜆rest Fixed Ratio ID Line Name 𝑎 (Å) 𝜆rest Fixed Ratio 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 H16 H15 H14 [O ii]𝜆3726 [O ii]𝜆3729 H13 H12 H11 H𝜃 He i𝜆3820 H𝜂 [S iii]𝜆3856 [Ne iii]𝜆3869 He i𝜆3889 H𝜁 [Ne iii]𝜆3967 H𝜖 He i𝜆4026 [S ii]𝜆4069 [S ii]𝜆4076 H𝛿 H𝛾 [O iii]𝜆4363 He i𝜆4471 [Fe iii]𝜆4658 He ii𝜆4686 3704.9133 3713.0335 3723.0035 3727.092 3729.875 3735.4365 3751.2174 3771.7012 3798.9757 3820.691 3836.472 3857.111 3869.86 3889.749 3890.1506 3968.59 3971.1951 4027.328 4069.749 4077.5 4102.8922 4341.6837 4364.436 4472.734 4659.414 4687.015 ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 0.31 [Ne iii]𝜆3869 ... ... ... 0.40 [S ii]𝜆4069 ... ... ... ... ... ... 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 He i𝜆4713 H𝛽 He i𝜆4922 [O iii]𝜆4959 [Fe iii]𝜆4985 [Fe iii]𝜆4986 [O iii]𝜆5007 He i𝜆5016 [N i]𝜆5198 [N i]𝜆5200 [O i]𝜆6300 [S iii]𝜆6312 [O i]𝜆6364 [N ii]𝜆6548 H𝛼 [N ii]𝜆6583 He i𝜆6678 [S ii]𝜆6716 [S ii]𝜆6731 OI ]𝜆7002 He i𝜆7065 [A riii]𝜆7136 He i𝜆7281 [O ii]𝜆7320 [O ii]𝜆7330 4714.466 4862.683 4923.3051 4960.295 4985.9 4987.2 5008.24 5017.0769 5199.349 5201.705 6302.046 6313.8 6365.536 6549.86 6564.608 6585.27 6679.994 6718.295 6732.674 7004.161 7067.228 7137.75 7283.357 7321.687 7332.22 ... ... ... 0.34 [O iii]𝜆5007 ... ... ... ... ... 0.37 [N i]𝜆5198 ... ... 0.33 [O i]𝜆6300 0.33 [N ii]𝜆6583 ... ... ... ... ... ... ... ... ... ... ... a Ritz wavelengths in vacuum from the National Institute of Standards and Technology (NIST) Atomic Spectra database (https://physics.nist.gov/PhysRefData/ASD/lines_form.html). To obtain reliable kinematic measurements, we binned the spectra spatially to reach a minimum S/N threshold. We used the Voronoi binning algorithm of Cappellari and Copin (2003), a widely adopted method for IFU data, which adaptively groups neighboring spaxels to meet the target S/N. However, because resampling during the stacking process introduces covariance between adjacent pixels, the variance of the binned spectra tends to be underestimated. To correct for this effect, we applied the empirical correction formula from O’Sullivan and Chen (2020): 𝜎measured = 𝐶 [1 + 𝛼 log (𝑁 𝑏 )]𝜎nocov , (5.1) for 𝑁 𝑏 ≲ 𝑁thresh , and as 𝜎measured = 𝐶 [1 + 𝛼 log (𝑁thresh )]𝜎nocov , (5.2) for 𝑁 𝑏 > 𝑁thresh , where 𝑁 𝑏 is the number of spaxels in a bin, and 𝑁thresh is the threshold beyond which covariance becomes negligible. The parameters 𝐶, 𝛼, and 𝑁thresh were determined following the procedure outlined in Paper I and de los Reyes 138 et al. (2023). We adopted a target covariance-corrected S/N𝑔 of 20 for the Voronoi binning, which can give comparable precision to the S/N threshold used in MaNGA DAP (see Figure 19 in Westfall et al. (2019) for details). Within each spatial bin, we ran pPXF twice. After an initial fit using the default emission-line mask, we additionally masked > 3𝜎 outliers and repeated the fitting to refine the stellar kinematic measurements. 5.2.3 Simultaneous Fit of Gas and Stars Next, we adopted a hybrid binning scheme similar to that used by Belfiore et al. (2019) to optimize the spatially resolved measurement of emission lines. The stellar kinematics determined for each spatial bin were remapped back to the individual spaxels within that bin. We then performed a simultaneous fit of the emission lines and stellar continuum using pPXF, with the stellar kinematics fixed to the values obtained in the previous stage. As suggested by Sarzi et al. (2006) and Oh et al. (2011), this approach is preferred over fitting emission lines on a continuumsubtracted spectrum, as the latter way can lead to overestimates of line fluxes and widths in the presence of even small mismatches between the data and the stellar templates. In the joint fit, we included an eighth-order multiplicative Legendre polynomial to account for imperfect flux calibration and dust attenuation. We excluded additive polynomials, as they can artificially alter absorption line strengths and bias the recovery of stellar population parameters. The emission lines included in the fit are listed in Table 5.2, with doublet ratios fixed to their theoretical values based on atomic physics. All emission lines were tied to share the same velocity and velocity dispersion to improve constraints on weaker lines. In addition, we performed the same fitting procedure on the integrated spectra to estimate the global properties of each galaxy. For each object, we generated two types of integrated spectra: one by summing all spaxels used in the spatially resolved analysis (i.e., those with S/N𝑔 > 0.5), and another extracted from a 3′′ diameter circular aperture centered on the target, consistent with the SDSS fiber aperture. 5.2.4 Strong-Line Ratios and Gas-phase Abundances To ensure reliable measurements of the ionization parameter and gas-phase abundances in individual spaxels, we restricted our analysis to those with S/N > 3 in 139 [O ii]𝜆𝜆3726,3729, H𝛽, [O iii]𝜆5007, H𝛼, [N ii]𝜆6583, and [S ii]𝜆𝜆6716,6731. We then constructed spatially resolved maps of emission-line ratios sensitive to metallicity and/or ionization parameter for each galaxy. Throughout this chapter, we adopt the abbreviations listed in Table 5.3 to refer to the emission-line ratios used in the subsequent analysis. Unless otherwise noted, all line ratios have been corrected for dust attenuation using the Balmer decrement, H𝛼/H𝛽, assuming Case B recombination with 𝑇𝑒 = 10, 000 K and 𝑛𝑒 = 100 cm−3 , which yields a theoretical H𝛼/H𝛽 ratio of 2.86 (Osterbrock and Ferland, 2006). The observed Balmer decrement was compared to this theoretical value, and the extinction correction was applied to each emission-line map using the Cardelli, Clayton, and Mathis (1989) extinction law. Table 5.3: Definitions of Strong-line Ratios Notation Line Ratio R2 R3 N2 S2 R23 O32 O3N2 log ( [O ii]𝜆𝜆3726, 3729/H𝛽) log ([O iii]𝜆5007/H𝛽) log ( [N ii]𝜆6583/H𝛼) log ( [S ii]𝜆𝜆6716, 6731/H𝛼) log [([O ii]𝜆𝜆3726, 3729 + [O iii]𝜆𝜆4959, 5007) /H𝛽] log ( [O iii]𝜆𝜆4959, 5007/[O ii]𝜆𝜆3726, 3729) log ( [O iii]𝜆5007/H𝛽) − log ([N ii]𝜆6583/H𝛼) Note. The 𝜆𝜆 notation refers to the sum of both lines. The direct 𝑇𝑒 method, which estimates nebular abundances from the electron temperature of ionized gas, is considered the most reliable approach for determining gas-phase metallicity from the optical spectrum. However, it requires the detection of faint auroral lines such as [O iii]𝜆4363 or [O ii]𝜆𝜆7320,7330, which are typically much weaker than H𝛽 and become increasingly difficult to detect at higher metallicities. Even though our sample consists of low-metallicity dwarf galaxies, auroral lines were only detected in a few spaxels, predominantly in the cores of the most actively star-forming regions. Consequently, we adopted the empirical strong-line calibration known as the “R calibration” from Pilyugin and Grebel (2016) to derive the maps of nebular abundances as6 : 6 The 𝑁 , 𝑅 ratios defined by Pilyugin and Grebel (2016) are different from the commonly used 2 2 “N2” and “R3” indices defined in Table 5.3. 140 12 + log(O/H) 𝑅,𝑈 = 8.589 + 0.022 log(𝑅3 /𝑅2 ) + 0.399 log 𝑁2 + (0.164 log(𝑅3 /𝑅2 ) + 0.589 log 𝑁2 − 0.137) (5.3) × log 𝑅2 , when log 𝑁2 ≥ −0.6; and 12 + log(O/H) 𝑅,𝐿 = 7.932 + 0.944 log(𝑅3 /𝑅2 ) + 0.695 log 𝑁2 + (0.970 − 0.291 log(𝑅3 /𝑅2 ) − 0.019 log 𝑁2 ) (5.4) × log 𝑅2 , when log 𝑁2 < −0.6, where log 𝑅2 = 𝑅2, log 𝑅3 = log 𝐼 [O III]𝜆4959+𝜆5007 /𝐼H𝛽 = 𝑅3 + 0.127, and log 𝑁2 = log 𝐼 [N II]𝜆6548+𝜆6584 /𝐼H𝛽 = 𝑁2 + 0.58. In addition, we employed the strong-line calibration from Eq. 13 of Pilyugin and Grebel (2016), which uses the N2 and R2 ratios to infer the spatially resolved nitrogen abundance as: log(N/O) = − 0.657 − 0.201 log 𝑁2 + (0.742 − 0.075 log 𝑁2 ) × log(𝑁2 /𝑅2 ), (5.5) where log 𝑅2 = 𝑅2 and log 𝑁2 = 𝑁2 + 0.58. Given that DIG can enhance the strength of low-ionization emission lines and inflate ratios such as N2, O2, and S2 (Zhang et al., 2017), we also derived gas-phase metallicities using the O3N2 calibration from Pettini and Pagel (2004): 12 + log(O/H)O3N2 = 8.73 − 0.32 × O3N2. (5.6) The O3N2-based metallicity is expected to be less sensitive to DIG contamination because H ii regions and DIG tend to overlap in the [O iii]/H𝛽 versus [N ii]/H𝛼 diagnostic diagram (Zhang et al., 2017; Sanders et al., 2017). 5.2.5 Stellar Mass Density, Light-weighted Age and Star Formation Density Alongside the emission-line measurements, we also estimated the stellar mass surface density and light-weighted stellar age (normalized over the spectral range 3650–5500 Å) in each spaxel based on the joint fitting procedure described in Section 5.2.3. We did not attempt to derive spatially resolved stellar metallicities due 141 to the insufficient S/N in individual spaxels. However, we consider the recovered light-weighted ages to be reliable, as their spatial distribution closely follows that of the D4000 index (Figure 5.2). The D4000 index, defined as the ratio of the average flux density between 4000–4100 Å and 3850–3950 Å (Balogh et al., 1999), serves as a robust age-sensitive tracer of stellar populations, particularly in low S/N data. log Age [yr] 9.25 1.60 8 6 1.55 6 9.00 4 1.50 4 8.75 2 1.45 0 1.40 −2 1.35 −4 1.30 −4 1.25 −6 −6 −8 −7.5 1 kpc 1.20 −5.0 −2.5 0.0 2.5 ∆ RA (arcsec) 5.0 7.5 ∆ Dec (arcsec) ∆ Dec (arcsec) D4000 8 2 8.50 0 8.25 −2 −8 −7.5 8.00 7.75 1 kpc −5.0 −2.5 0.0 2.5 5.0 7.50 7.5 ∆ RA (arcsec) Figure 5.2: Comparison between the D4000 index (left) and light-weighted age (right) for an example galaxy from the KCWI sample. The D4000 index is defined following Balogh et al. (1999) as the ratio of the average flux density in the continuum bands 4000–4100 Å and 3850–3950 Å, after correcting for emission-line contributions. To estimate the SFR surface density ΣSFR , we converted the dust-corrected H𝛼 surface density, ΣH𝛼 , to ΣSFR using the calibration of Kennicutt (1998): ΣSFR (M⊙ yr−1 kpc−2 ) = 7.9 × 10−42 ΣH𝛼 (erg s−1 kpc−2 ). (5.7) The sSFR surface density, ΣsSFR , was then derived as ΣsSFR = ΣSFR − Σ∗ . 5.3 Results In Figure 5.3, we present example composite maps from the KCWI data cube for galaxy 2259-0019, including the continuum image (a) and emission line map (b). Panels (c) through (l) show ten additional maps of derived quantities based on the analysis described in Section 5.2: (c) gas velocity relative to the systemic redshift, (d) stellar surface density (Σ∗ ), (e) star formation rate surface density (ΣSFR ), (f) specific star formation rate surface density (ΣsSFR ), (g) light-weighted stellar population age, (h) O32 (used as a proxy for ionization parameter), (i) S2, (j) gas-phase metallicity based on the O3N2 calibration from Pettini and Pagel (2004), and (k–l) gas-phase oxygen and nitrogen abundances, respectively, derived using 142 the strong-line calibration of Pilyugin and Grebel (2016). Maps for the rest of the galaxy sample are provided in Appendix 5.4. 5.3.1 Star Formation Morphology and Clumpiness We find that 19 out of 27 galaxies host at least one off-center star-forming clump, while the remaining eight show more centrally concentrated or nuclear star formation. This implies the fraction of star-forming galaxies with off-center clumps ( 𝑓clumpy ) in our sample is around 70%. This is significantly higher than the 𝑓clumpy ∼ 3–4% reported for low-mass, star-forming galaxies (9 < log(𝑀∗ /𝑀⊙ ) < 9.8) at 𝑧 ∼ 0 (Shibuya et al., 2016; Adams et al., 2022). However, Shibuya et al. (2016) and Adams et al. (2022) adopted a much stricter criterion proposed by Guo et al. (2015) to identify clumpy galaxies, relying on luminosity thresholds rather than visual inspection. Specifically, they required that the ratio of clump to galaxy UV or SDSS-𝑢 luminosity exceed 8%. In contrast, we identify clumpy galaxies through visual inspection of ΣSFR . As a next step, we will estimate the ratio of clump to galaxy H𝛼 luminosity (as a proxy for UV luminosity) to replicate the selection method used by Shibuya et al. (2016) and Adams et al. (2022), allowing for a more stringent test of whether our sample indeed exhibits a significantly higher 𝑓clumpy . 5.3.2 Ionization and Excitation Structure The spatial distribution of O32, a proxy for the ionization parameter, is even more patchy than the star formation itself. Most off-center star-forming clumps show elevated O32 values, consistent with more ionizing photons from young, massive stars. However, the peaks in O32 do not always align with the highest ΣSFR regions. This mismatch could arise from multiple effects. First, O32 increases at low metallicity, so its enhancement in outer star-forming clumps may partly reflect metallicity gradients. Second, the ionization parameter decreases with increasing gas density. Thus, even regions with similar ionizing photons can show higher O32 if the gas density is lower. Unfortunately, we cannot precisely measure the local gas density, as the [O ii]𝜆3729/𝜆3726 and [S ii]𝜆6716/𝜆6731 ratios are in the low-density limit across most galaxies. When examining the S2 maps, we find a strong local-scale anti-correlation between O32 and S2 across all galaxies. Regions with higher excitation, indicated by elevated O32 values, consistently exhibit lower S2. This trend arises because S+ ions have a relatively low ionization potential, making them more abundant in low-ionization 143 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.51+0.09 −0.11 (a) [Mg/Fe] = 0.10+0.05 −0.06 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.5 8.0 8.5 −10 −10 10 −5 0 5 (g) 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 7.75 8.00 8.25 8.50 8.75 9.00 10 −0.6 9.25 −0.4 −0.2 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 −5 0 ∆ RA (arcsec) 5 10 (f) −10.0 −9.5 −9.0 −8.5 5 10 (i) −5 −0.7 −0.6 −0.5 −0.4 0 5 −0.3 −0.2 10 (l) log (N/O) −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 −1.05 8.50 −10 −10 15 10 S2 −10 10 5 8.10 5 0 −0.8 5 −10 10 −10 −10 10 −5 0.2 −10 −10 5 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.50 0 0 −10.5 5 −10 −5 −10 −10 10 log Age [yr] −5 −3.50 −3.25 −3.00 −2.75 −2.50 −2.25 −2.00 −1.75 9.0 −10 −10 5 7.0 (c) vgas (km/s) −15 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.71±0.10, logsSFR = -9.92±0.13 2259-0019 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 5 10 ∆ RA (arcsec) Figure 5.3: KCWI maps of 2259-0019. (a) A broadband image constructed using 𝑔 (blue), 𝑖 (green), and 𝑧 (red) filters, synthesized from the KCWI data cube of galaxy 2259-0019 by convolving each spaxel’s spectrum with the corresponding PS1 filter response; (b) a composite emission-line image combining [O iii] (blue), H𝛼 (green), and [N ii] (red) maps from the same data cube; (c) the gas velocity map; (d) the stellar mass surface density Σ∗ ; (e) the SFR surface density ΣSFR obtained from the dust-corrected ΣH𝛼 ; (f) the sSFR rate surface density; (g) the light-weighted stellar age map; (h) the O32 map, used as a proxy for the ionization parameter; (i) the S2 map; (j) the gas-phase metallicity map derived from the O3N2 diagnostic using the calibration of Pettini and Pagel (2004); and (k–l) gas-phase oxygen and nebular abundances derived using the calibrations from Pilyugin and Grebel (2016). 144 zones. In addition, the DIG that is likely ionized by hot, evolved stars rather than the young massive stars in H ii regions tends to show enhanced S2 (Zhang et al., 2017). These observations motivate further investigation into the underlying stellar populations in regions with varying S2 and O32 values, and the extent to which they influence line ratios that are sensitive to local ionization conditions. 5.3.3 Chemical Abundance Patterns The nebular abundances are relatively uniform and more homogeneous compared to star formation and local ionization. The nitrogen-to-oxygen ratio log(N/O) is much more uniform across most spaxels and typically stays below −1.0, consistent with primary nitrogen production. In contrast, gas-phase oxygen abundances exhibit more spatial variation. Most galaxies show flat or mildly negative radial gradients, with central regions being slightly more metal-rich. However, a handful of galaxies display inverted metallicity gradients, where the central regions have lower oxygen abundance than the outskirts. These galaxies also show intense central star formation and younger stellar populations in the core. The metallicity structure depends on the calibration method used. The O3N2-based maps (Pettini and Pagel, 2004) tend to follow O32 more closely, while the metallicity maps derived from the R-calibration of Pilyugin and Grebel (2016) show smoother distributions with less dependence on local excitation. As discussed further in Section 6.2.1, the presence of DIG may complicate this comparison, and measuring direct-𝑇𝑒 metallicities—even just in the core of the star-forming clumps and in the integrated spectra—would help resolve these ambiguities. 5.3.4 Stellar versus Nebular Morphologies Despite the clumpy and irregular appearance of ΣSFR and nebular properties, the stellar mass profiles (Σ∗ ) are generally smooth and regular. Even the most disturbed systems, such as 2131-0613 (hosting two infalling/accreted off-center star-forming complexes) and 2334+0029 (with a quenched tidal tail), maintain undisturbed stellar mass profiles. This is consistent with expectations from simulations, which predict that massive star-forming clumps are short-lived (≲ 500 Myr; Bournaud et al. 2014; Mandelker et al. 2014). While ionized gas and star formation can appear chaotic, the time-integrated stellar mass reflects the longer-term structural stability of the galaxy. In contrast, light-weighted age profiles are more strongly influenced by recent star- 145 bursts and appear less smooth than the stellar mass profiles. This is because the starlight is dominated by the brightest stellar populations, which are typically those formed most recently. 5.3.5 Gas Kinematics Of the 27 galaxies, five show no evidence for coherent rotation in their gas velocity maps. While the remaining 22 exhibit some rotation, only eight have clearly defined rotation axes. The other 14 systems display disturbed or asymmetric velocity fields, possibly due to ongoing mergers, accretion events, or turbulence driven by stellar feedback. A detailed dynamical modeling effort will be needed to disentangle these possibilities and assess whether the kinematic irregularities stem from internal or external processes. 5.3.6 Large Spread in Spatially Resolved Line Ratios The KCWI maps in Figures 5.3 and 5.5–5.30 reveal substantial spatial variations in emission-line ratios within individual dwarf galaxies. In Figure 5.4, we further discuss this phenomenon using one example galaxy, 2259−0019. Although we present only this case in detail, we emphasize that similar behavior is seen across our entire sample. In the [N ii]-BPT diagram (panel c of Figure 5.4), the dashed curve denotes the empirical demarcation line by Kauffmann et al. (2003b), which separates pure star-forming regions from composite systems, while the solid line represents the theoretical upper limit of pure star formation from photoionization models by Kewley et al. (2001), beyond which additional ionizing sources such as AGN are required to explain the line ratios. The spaxel measurements of 2259−0019 exhibit a clear gradient in this diagram. Compared to the off-center star-forming knots, the galaxy center shows higher [N ii]/H𝛼 (N2) and slightly lower [O iii]/H𝛽 (R3), leading to a ∼ 0.3 dex difference in N2 between the central SDSS-equivalent spectrum and the global spectrum. The full spread in N2 across the galaxy spans nearly ∼ 1 dex, significantly larger than the observational uncertainties of the global spectrum. Spaxels with enhanced N2 (yellow to red colors) show line ratios consistent with the locus of SDSS star-forming galaxies, while the bluer star-forming spaxels exhibit line ratios that more closely resemble individual H ii regions. In the [S ii]-BPT diagram (panel d), the solid line again shows the SF demarcation by Kewley et al. (2001), and the dashed line represents the empirical division between Seyfert and low-ionization narrow emission-line regions (LINERs) as defined by 146 10.0 10.0 7.5 7.5 2259-0019 1 kpc 2.5 0.0 −2.5 2.5 0.0 −2.5 −5.0 −5.0 −7.5 −7.5 (a) −10.0 −10 [OIII] −5 0 ∆ RA (arcsec) Hα [NII] 5 10 log [OIII]λ5007/Hβ 5.0 ∆ Dec (arcsec) 0.0 (b) −10.0 −10 1.5 −5 0.2 0.4 0.6 0 ∆ RA (arcsec) 0.8 1.0 Seyfert 0.0 SF Comp 5 −1.0 10 (c) −1.5 1.5 1.0 0.5 −0.5 ×10−17 1.2 1.4 −1.0 −0.5 0.0 log [NII]λ6585/Hα 0.5 0.5 1.0 0.0 0.5 0.5 O32 LINER SF 0.0 N2O2 ∆ Dec (arcsec) AGN 1.0 5.0 log [OIII]λ5007/Hβ 1.5 [OII]λλ7320,7330 −0.5 0.0 −1.0 −0.5 −1.0 −1.5 −0.5 (d) −1.5 (e) −1.0 −0.5 0.0 log [SII]λλ6716, 6731/Hα 0.5 −1.0 0.4 0.6 0.8 R23 1.0 1.2 −1 (f) 0 1 O3N2 2 3 Figure 5.4: Emission-line diagnostics for galaxy 2259−0019 in the KCWI sample. (a) Composite emission-line map combining [O iii] (blue), H𝛼 (green), and [N ii] (red), with the green circle showing the 3′′ SDSS fiber aperture. (b) Map of the [O ii]𝜆𝜆7320,7330 auroral lines where detected at > 3𝜎. Panels (c)–(f) show spatially resolved diagnostic diagrams: (c) the [N ii] BPT diagram, (d) the [S ii] BPT diagram, (e) the R23 vs. O32 diagram, and (f) the O3N2 vs. N2O2. Each point corresponds to a spaxel, color-coded as in panel (a). The yellow star represents the measurement of the global spectrum obtained from summing all spaxels with S/N𝑔 > 0.5; the green circle shows the measurement within the SDSS-equivalent 3′′ aperture. White contours in (c)-(f) show the distribution of SDSS star-forming galaxies from the MPA-JHU catalogs at 1–2𝜎 density. Gray crosses are the H ii regions compiled by Pilyugin and Thuan (2005). Demarcation lines in (c) and (d) follow Kauffmann et al. (2003b), Kewley et al. (2001), and Kewley et al. (2006) as described in the main text. Kewley et al. (2006). The spaxels span a similarly broad range in [S ii]/H𝛼 (S2), with a spread of ∼ 1 dex. Off-center star-forming knots show notably lower S2 than the central regions with less star formation, resulting in a ∼ 0.3 dex difference in S2 between the global and SDSS-equivalent spectra. The discrepancy between SDSS galaxies and individual H ii regions is even more pronounced in this diagram: most H ii regions lie outside the 2𝜎 SDSS contour, indicating the different ionization conditions. Spaxels from the bluest star-forming regions match the H ii region distribution, whereas the rest (with lower ΣSFR ) align with SDSS fiber-based measurements. 147 Panels (e) and (f) show additional diagnostic diagrams that are sensitive to gas-phase metallicity, nitrogen enrichment, and ionization parameters. The R23–O32 diagram (panel e) shows considerable variation in O32 (∼ 1 dex), while the R23 values display smaller dispersion. This is likely because the 𝑅23 ratios of most spaxels are near the saturation limit of ∼ 1, where R23 becomes relatively insensitive to changes in metallicity. In the O3N2–N2O2 diagram (f), we observe dispersions of ∼ 1.5 dex in O3N2 and ∼ 0.8 dex in N2O2, again exceeding typical measurement uncertainties and revealing the diversity in ionized gas conditions. Although strong nebular lines are detected throughout the galaxy, the auroral lines [O ii]𝜆𝜆7320,7330, which are essential for determining direct 𝑇𝑒 -based metallicities from KCWI red-channel data cubes, are only detected in a few spaxels located at the centers of the star-forming knots (panel b). However, we detect [O ii]𝜆𝜆7320,7330 in the global spectrum at a significance level of 6.7𝜎. Given that the strong nebular [O ii] and [O iii] lines are observed across all spaxels, it is likely that the 𝑇𝑒 metallicity derived from the global spectrum differs from that of the individual spaxels where the auroral lines are detected. A systematic comparison between 𝑇𝑒 metallicities derived from the global spectrum and from individual spaxels will be crucial for understanding how to reconcile empirical strong-line calibrations based on 𝑇𝑒 measurements of individual H ii regions (Pilyugin, Grebel, and Mattsson, 2012) with those inferred from stacked SDSS spectra (Curti et al., 2020). Taken together, these results demonstrate that line ratios measured from integrated spectra, whether using small, centered or larger, global apertures, can differ significantly from spatially resolved measurements. This reflects the complexity and heterogeneity of nebular conditions within galaxies and suggests that integrated diagnostics may overlook small-scale structures and gradients. Consequently, a systematic analysis of how line fluxes and derived quantities like metallicity vary with the choice of aperture is crucial. We also need to explore whether these biases depend on global galaxy properties such as stellar mass, size, and SFR to understand whether any corrections would be needed when only an integrated spectrum is available. 5.4 Appendix: KCWI Maps of the Entire Sample Below, I present the color images and spatially resolved properties for the remaining galaxies in my KCWI sample, following the format of Figure 5.3. 148 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.88+0.09 −0.11 (a) [Mg/Fe] = 0.09+0.06 −0.06 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.50 7.75 8.00 8.25 8.50 8.75 −10 −10 10 −5 0 5 (g) 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.00 8.25 8.50 8.75 9.00 9.25 10 −0.7 9.50 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.1 8.2 8.3 8.4 8.0 8.1 8.2 8.3 −5 0 ∆ RA (arcsec) 5 10 20 25 5 10 (f) −9.8 −9.6 −9.4 −9.2 0 5 10 (i) −5 0 5 10 (l) log (N/O) −1.50 −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 8.4 −10 −10 0 S2 −10 10 5 8.0 15 −0.65 −0.60 −0.55 −0.50 −0.45 −0.40 −0.35 −0.30 −0.25 5 −10 10 −10 −10 10 −5 0.1 −10 −10 5 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.75 0 −10.6 −10.4 −10.2 −10.0 5 −10 −5 −10 −10 10 log Age [yr] −5 −3.50 −3.25 −3.00 −2.75 −2.50 −2.25 −2.00 −1.75 −1.50 9.00 −10 −10 [NII] 5 7.25 (c) vgas (km/s) −15 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.09±0.10, logsSFR = -9.93±0.13 2225-0046 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.5: Same as Figure 5.3, but for galaxy 2225-0046. 5 10 149 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.72+0.07 −0.08 (a) [Mg/Fe] = 0.18+0.05 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 8.00 8.25 8.50 8.75 9.00 9.25 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.5 9.0 −0.6 9.5 10 −0.4 −0.2 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.15 8.20 8.25 8.30 8.35 8.40 8.45 −5 0 ∆ RA (arcsec) 5 10 (f) 5 10 (i) −5 −0.5 −0.4 −0.3 0 5 −0.2 −0.1 10 (l) log (N/O) −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 8.50 −10 −10 10 S2 −10 10 5 8.15 5 0 −0.6 5 −10 30 −10 −10 10 0 −5 0.2 −10 −10 20 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.0 10 −10.75−10.50−10.25−10.00 −9.75 −9.50 −9.25 −9.00 5 −10 0 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 9.50 −10 −10 [NII] 5 7.75 (c) vgas (km/s) −20 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.23±0.10, logsSFR = -9.89±0.13 2329+1552 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.6: Same as Figure 5.3, but for galaxy 2329+1552. 5 10 150 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −1.02+0.10 −0.11 (a) [Mg/Fe] = 0.14+0.08 −0.08 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα 5 [NII] −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.50 7.75 8.00 8.25 8.50 8.75 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.00 8.25 8.50 8.75 9.00 10 −0.6 9.25 −0.4 −0.2 0.0 0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.1 8.2 8.3 8.4 8.0 8.1 8.2 8.3 −5 0 ∆ RA (arcsec) 5 10 (f) −9.6 −9.4 −9.2 −9.0 −8.8 5 10 (i) −5 −0.8 −0.7 −0.6 −0.5 0 5 −0.4 10 (l) log (N/O) −1.5 8.4 −10 −10 10 S2 −10 10 5 8.0 5 0 −0.9 5 −10 30 −10 −10 10 −5 0.4 −10 −10 20 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.75 10 0 −10.4 −10.2 −10.0 −9.8 5 −10 0 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 9.00 −10 −10 5 7.25 (c) vgas (km/s) −20 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.40±0.10, logsSFR = -10.12±0.17 2152-0110 −1.4 −1.3 −1.2 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.7: Same as Figure 5.3, but for galaxy 2152-0110. 5 10 151 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.56+0.08 −0.10 (a) [Mg/Fe] = 0.15+0.06 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 8.0 8.2 8.4 8.6 8.8 9.0 −10 −10 10 −5 0 5 (g) 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.25 8.50 8.75 9.00 9.25 9.50 10 −0.6 9.75 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.15 8.20 8.25 8.30 8.35 8.40 8.45 −5 0 ∆ RA (arcsec) 5 10 (f) −9.6 −9.4 5 10 (i) −5 −0.4 −0.3 0 5 −0.2 −0.1 10 (l) log (N/O) −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 −1.05 8.50 −10 −10 10 10 S2 −10 10 5 8.15 5 5 0 −0.5 5 −10 0 −10 −10 10 0 −5 0.1 −10 −10 −5 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.00 −10 −10.8 −10.6 −10.4 −10.2 −10.0 −9.8 5 −10 −15 −10 −10 10 log Age [yr] −5 −3.75 −3.50 −3.25 −3.00 −2.75 −2.50 −2.25 −2.00 −1.75 9.2 −20 −10 5 7.8 (c) vgas (km/s) −25 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.42±0.10, logsSFR = -10.22±0.17 0845+5145 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.8: Same as Figure 5.3, but for galaxy 0845+5145. 5 10 152 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −1.10+0.20 −0.17 (a) [Mg/Fe] = 0.10+0.07 −0.09 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 6.75 7.00 7.25 7.50 7.75 8.00 8.25 −3.0 −2.5 −2.0 −1.5 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.0 8.5 9.0 10 −0.2 9.5 −0.1 0.0 0.1 0.2 0.3 0.4 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.10 8.15 8.20 8.25 8.30 8.35 8.05 8.10 8.15 8.20 8.25 8.30 −5 0 ∆ RA (arcsec) 5 10 (f) 5 10 (i) −5 −0.7 −0.6 −0.5 0 5 −0.4 −0.3 10 (l) log (N/O) −1.50 −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 8.35 −10 −10 30 10 S2 −10 10 5 8.05 5 0 −0.8 5 −10 20 −10 −10 10 0 −5 0.5 −10 −10 10 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.5 0 −10.50 −10.25 −10.00 −9.75 −9.50 −9.25 −9.00 −8.75 5 −10 −10 −10 −10 10 −5 −1.0 −10 −10 10 −3.5 8.50 −20 −10 5 6.50 (c) vgas (km/s) −30 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.42±0.10, logsSFR = -9.61±0.12 2334+0029 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.9: Same as Figure 5.3, but for galaxy 2334+0029. 5 10 153 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.54+0.09 −0.08 (a) [Mg/Fe] = 0.06+0.04 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.50 7.75 8.00 8.25 8.50 −3.5 8.75 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.4 8.6 8.8 9.0 9.2 9.4 9.6 10 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 9.8 0.0 0.1 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.10 8.15 8.20 8.25 8.30 8.35 8.40 −5 0 ∆ RA (arcsec) 5 10 10 (i) −5 −0.5 −0.4 −0.3 −0.2 0 5 −0.1 0.0 10 (l) log (N/O) −1.50 −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 8.45 −10 −10 5 S2 −10 10 5 8.10 10 (f) 0 −0.6 5 −10 5 −10 −10 10 0 −5 0.2 −10 −10 20 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.2 10 −11.0 −10.8 −10.6 −10.4 −10.2 −10.0 −9.8 −9.6 −9.4 5 −10 0 −10 −10 10 −5 −1.5 −10 −10 10 −3.0 −10 −10 5 7.25 (c) vgas (km/s) −20 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.43±0.10, logsSFR = -9.98±0.14 0121-0853 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.10: Same as Figure 5.3, but for galaxy 0121-0853. 5 10 154 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.53+0.08 −0.10 (a) [Mg/Fe] = 0.22+0.06 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 8.00 8.25 8.50 8.75 9.00 9.25 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.25 8.50 8.75 9.00 9.25 9.50 10 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 9.75 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 −5 0 ∆ RA (arcsec) 5 10 (f) 5 10 (i) −5 −0.5 −0.4 −0.3 −0.2 0 5 −0.1 0.0 10 (l) log (N/O) −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 8.50 −10 −10 30 10 S2 −10 10 5 8.10 5 0 −0.6 5 −10 20 −10 −10 10 0 −5 0.1 −10 −10 10 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.00 0 −10.75 −10.50 −10.25 −10.00 −9.75 −9.50 −9.25 −9.00 5 −10 −10 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 9.50 −20 −10 5 7.75 (c) vgas (km/s) −30 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.51±0.10, logsSFR = -9.96±0.23 0013-0956 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.11: Same as Figure 5.3, but for galaxy 0013-0956. 5 10 155 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −1.16+0.11 −0.11 (a) [Mg/Fe] = 0.08+0.06 −0.07 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα 5 [NII] −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.25 7.50 7.75 8.00 8.25 −3.0 −2.5 −2.0 −1.5 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.4 8.6 8.8 9.0 9.2 10 −0.6 9.4 −0.4 −0.2 0.0 0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.1 8.2 8.3 8.4 8.0 8.1 8.2 8.3 −5 0 ∆ RA (arcsec) 5 10 50 (f) 5 10 (i) −5 −0.6 −0.4 −0.2 0 5 0.0 10 (l) log (N/O) −1.6 8.4 −10 −10 40 10 S2 −10 10 5 8.0 5 0 −0.8 5 −10 30 −10 −10 10 0 −5 0.4 −10 −10 20 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.2 10 −10.50 −10.25 −10.00 −9.75 −9.50 −9.25 −9.00 −8.75 5 −10 0 −10 −10 10 −5 −1.0 −10 −10 10 −3.5 8.50 −10 −10 5 7.00 (c) vgas (km/s) −20 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.56±0.10, logsSFR = -10.05±0.16 0155-0037 −1.5 −1.4 −1.3 −1.2 −1.1 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.12: Same as Figure 5.3, but for galaxy 0155-0037. 5 10 156 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.50+0.06 −0.08 (a) [Mg/Fe] = 0.10+0.05 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.8 8.0 8.2 8.4 8.6 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.6 8.8 9.0 9.2 9.4 9.6 10 −0.5 9.8 −0.4 −0.3 −0.2 −0.1 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.20 8.25 8.30 8.35 8.40 8.45 8.15 8.20 8.25 8.30 8.35 8.40 −5 0 ∆ RA (arcsec) 5 10 (f) −9.6 −9.4 5 10 (i) −5 −0.4 −0.3 −0.2 −0.1 0.0 0 5 0.1 10 (l) log (N/O) −1.40 8.45 −10 −10 10 S2 −10 10 5 8.15 5 0 −0.5 5 −10 20 −10 −10 10 0 −5 0.1 −10 −10 10 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.4 0 −11.0 −10.8 −10.6 −10.4 −10.2 −10.0 −9.8 5 −10 −10 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 8.8 −20 −10 5 7.6 (c) vgas (km/s) −30 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.59±0.10, logsSFR = -10.33±0.19 0140-0012 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.13: Same as Figure 5.3, but for galaxy 0140-0012. 5 10 157 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.86+0.09 −0.10 (a) [Mg/Fe] = 0.18+0.06 −0.06 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.0 7.5 8.0 −3.5 8.5 −10 10 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 7.75 8.00 8.25 8.50 8.75 9.00 9.25 10 −0.8 9.50 −0.6 −0.4 −0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.10 8.15 8.20 8.25 8.30 8.35 8.40 −5 0 ∆ RA (arcsec) 5 10 5 10 (f) 0 5 10 (i) −5 −0.4 −0.2 0 5 0.0 10 (l) log (N/O) −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 8.45 −10 −10 30 S2 −10 10 5 8.10 0 −0.6 5 −10 20 −10 −10 10 −5 0.0 −10 −10 10 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.50 0 −10.50−10.25−10.00 −9.75 −9.50 −9.25 −9.00 −8.75 5 −10 −10 −10 −10 10 −5 −1.5 −10 −20 −10 5 6.5 (c) vgas (km/s) −30 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.59±0.10, logsSFR = -9.69±0.11 0023-0939 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.14: Same as Figure 5.3, but for galaxy 0023-0939. 5 10 158 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.87+0.11 −0.11 (a) [Mg/Fe] = 0.14+0.07 −0.07 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.25 7.50 7.75 8.00 8.25 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.2 8.4 8.6 8.8 9.0 9.2 10 −0.8 9.4 −0.6 −0.4 −0.2 0.0 0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.2 8.3 8.4 8.1 8.2 8.3 −5 0 ∆ RA (arcsec) 5 10 10 (f) 0 5 10 (i) −5 −0.6 −0.5 −0.4 0 5 −0.3 10 (l) log (N/O) −1.55 −1.50 −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 8.4 −10 −10 5 S2 −10 10 5 8.1 0 −0.7 5 −10 30 −10 −10 10 −5 0.4 −10 −10 20 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.0 10 −10.4 −10.2 −10.0 −9.8 −9.6 −9.4 −9.2 −9.0 −8.8 5 −10 0 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 8.50 −10 −10 5 7.00 (c) vgas (km/s) −20 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.67±0.10, logsSFR = -9.60±0.13 0233+0038 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.15: Same as Figure 5.3, but for galaxy 0233+0038. 5 10 159 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −1.06+0.10 −0.11 (a) [Mg/Fe] = 0.21+0.08 −0.08 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 6.75 7.00 7.25 7.50 7.75 8.00 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 7.50 7.75 8.00 8.25 8.50 8.75 9.00 10 −0.5 −0.4 −0.3 −0.2 −0.1 9.25 0.0 0.1 0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 −5 0 ∆ RA (arcsec) 5 10 (f) −9.5 −9.0 −8.5 5 10 (i) −5 −0.6 −0.5 −0.4 0 5 −0.3 −0.2 10 (l) log (N/O) −1.55 −1.50 −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 8.40 −10 −10 10 S2 −10 10 5 8.00 60 5 0 −0.7 5 −10 40 −10 −10 10 −5 0.3 −10 −10 20 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.25 0 −10.0 5 −10 0 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 8.25 −20 −10 5 6.50 (c) vgas (km/s) −40 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.69±0.10, logsSFR = -9.58±0.13 0256-0010 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.16: Same as Figure 5.3, but for galaxy 0256-0010. 5 10 160 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.82+0.13 −0.06 (a) [Mg/Fe] = 0.08+0.05 −0.07 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.25 7.50 7.75 8.00 8.25 8.50 −10 −10 10 −5 0 5 (g) 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.25 8.50 8.75 9.00 9.25 10 −0.6 9.50 −0.5 −0.4 −0.3 −0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 −5 0 ∆ RA (arcsec) 5 10 10 (f) −10.6 −10.4 −10.2 −10.0 −9.8 −9.6 5 10 (i) −5 −0.5 −0.4 −0.3 0 5 −0.2 −0.1 0.0 10 (l) log (N/O) −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 8.50 −10 −10 30 S2 −10 10 5 8.10 20 5 0 −0.6 5 −10 10 −10 −10 10 −10.8 −5 −0.1 −10 −10 0 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.00 −10 0 −11.0 5 −10 −20 −10 −10 10 log Age [yr] −5 −3.6 −3.4 −3.2 −3.0 −2.8 −2.6 −2.4 −2.2 −2.0 8.75 −30 −10 5 7.00 (c) vgas (km/s) −40 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.75±0.10, logsSFR = -10.34±0.18 2300-0832 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.17: Same as Figure 5.3, but for galaxy 2300-0832. 5 10 161 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.50+0.06 −0.09 (a) [Mg/Fe] = 0.09+0.04 −0.04 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.50 7.75 8.00 8.25 8.50 −4.0 8.75 −10 10 −3.5 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.6 8.8 9.0 9.2 9.4 10 −0.8 9.6 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.2 8.3 8.4 8.5 8.1 8.2 8.3 8.4 −5 0 ∆ RA (arcsec) 5 10 (f) −9.6 5 10 (i) −5 −0.4 −0.3 −0.2 −0.1 0.0 0 5 0.1 0.2 10 (l) log (N/O) −1.5 8.5 −10 −10 10 S2 −10 10 5 8.1 40 5 0 −0.5 5 −10 20 −10 −10 10 0 −5 −0.1 −10 −10 0 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.4 −20 −11.0 −10.8 −10.6 −10.4 −10.2 −10.0 −9.8 5 −10 −40 −10 −10 10 −5 −1.5 −10 −60 −10 5 7.25 (c) vgas (km/s) −80 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.77±0.10, logsSFR = -10.39±0.20 0233-0819 −1.4 −1.3 −1.2 −1.1 −1.0 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.18: Same as Figure 5.3, but for galaxy 0233-0819. 5 10 162 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.77+0.13 −0.13 (a) [Mg/Fe] = 0.09+0.06 −0.07 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.00 7.25 7.50 7.75 8.00 8.25 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.00 8.25 8.50 8.75 9.00 9.25 10 −0.6 9.50 −0.4 −0.2 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.45 −5 0 ∆ RA (arcsec) 5 10 (f) −10.0 −9.5 −9.0 −8.5 5 10 (i) −5 −0.5 −0.4 −0.3 −0.2 0 5 10 (l) log (N/O) −1.5 8.50 −10 −10 10 S2 −10 10 5 8.10 5 0 −0.6 5 −10 20 −10 −10 10 −5 0.2 −10 −10 10 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.75 0 0 −10.5 5 −10 −10 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 8.50 −20 −10 5 6.75 (c) vgas (km/s) −30 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.81±0.11, logsSFR = -9.55±0.16 2301+1451 −1.4 −1.3 −1.2 −1.1 −1.0 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.19: Same as Figure 5.3, but for galaxy 2301+1451. 5 10 163 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.42+0.06 −0.07 (a) [Mg/Fe] = 0.09+0.04 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.8 8.0 8.2 8.4 8.6 8.8 −10 −10 10 −5 0 5 (g) 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.4 8.6 8.8 9.0 9.2 9.4 10 −0.8 9.6 −0.6 −0.4 −0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.2 8.3 8.4 8.5 8.1 8.2 8.3 8.4 −5 0 ∆ RA (arcsec) 5 10 (f) −10.8 −10.6 −10.4 −10.2 −10.0 −9.8 −9.6 5 10 (i) −5 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 0 5 0.1 10 (l) log (N/O) −1.4 8.5 −10 −10 10 S2 −10 10 5 8.1 20 5 0 −0.6 5 −10 10 −10 −10 10 −5 0.0 −10 −10 0 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.2 0 −11.0 5 −10 −10 −10 −10 10 log Age [yr] −5 −3.75 −3.50 −3.25 −3.00 −2.75 −2.50 −2.25 −2.00 −1.75 9.0 −20 −10 5 7.6 (c) vgas (km/s) −30 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.82±0.10, logsSFR = -10.52±0.19 0332-0600 −1.3 −1.2 −1.1 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.20: Same as Figure 5.3, but for galaxy 0332-0600. 5 10 164 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.96+0.13 −0.13 (a) [Mg/Fe] = 0.20+0.07 −0.07 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.0 7.5 8.0 −3.0 −2.5 −2.0 −1.5 −1.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 7.5 8.0 8.5 10 −0.4 9.0 −0.2 0.0 0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.1 8.2 8.3 8.4 8.0 8.1 8.2 8.3 −5 0 ∆ RA (arcsec) 5 10 (f) −10.0 −9.5 −9.0 −8.5 −8.0 5 10 (i) −5 −0.7 −0.6 −0.5 −0.4 0 −0.3 −0.2 5 10 (l) log (N/O) −1.6 8.4 −10 −10 10 S2 −10 10 5 8.0 30 5 0 −0.8 5 −10 20 −10 −10 10 −5 0.4 −10 −10 10 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.0 0 −10.5 5 −10 0 −10 −10 10 −5 −0.5 −10 −10 10 −3.5 8.5 −10 −10 5 6.5 (c) vgas (km/s) −20 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.82±0.10, logsSFR = -9.55±0.14 2131-0613 −1.5 −1.4 −1.3 −1.2 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.21: Same as Figure 5.3, but for galaxy 2131-0613. 5 10 165 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.69+0.09 −0.11 (a) [Mg/Fe] = 0.10+0.06 −0.06 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα 5 [NII] −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.50 7.75 8.00 8.25 8.50 8.75 −10 −10 10 −5 0 5 (g) 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.00 8.25 8.50 8.75 9.00 9.25 10 −0.5 9.50 −0.4 −0.3 −0.2 −0.1 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.30 8.35 8.40 8.45 8.50 8.25 8.30 8.35 8.40 8.45 −5 0 ∆ RA (arcsec) 5 10 (f) 0 5 10 (i) −5 0 5 10 (l) log (N/O) −1.4 8.50 −10 −10 10 S2 −10 10 5 8.25 5 −0.55 −0.50 −0.45 −0.40 −0.35 −0.30 −0.25 5 −10 40 −10 −10 10 −5 0.0 −10 −10 0 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.75 20 −10.25 −10.00 −9.75 −9.50 −9.25 −9.00 −8.75 5 −10 0 −10 −10 10 log Age [yr] −5 −3.25 −3.00 −2.75 −2.50 −2.25 −2.00 −1.75 −1.50 9.00 −20 −10 5 7.25 (c) vgas (km/s) −40 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.88±0.10, logsSFR = -9.94±0.17 0850+6145 −1.3 −1.2 −1.1 −1.0 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.22: Same as Figure 5.3, but for galaxy 0850+6145. 5 10 166 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.44+0.06 −0.07 (a) [Mg/Fe] = 0.12+0.05 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.8 8.0 8.2 8.4 8.6 8.8 −3.00 −2.75 −2.50 −2.25 −2.00 −1.75 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.7 8.8 8.9 9.0 9.1 10 −0.8 9.2 −0.6 −0.4 −0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.15 8.20 8.25 8.30 8.35 8.40 8.45 −5 0 ∆ RA (arcsec) 5 10 (f) 5 10 (i) −5 −0.6 −0.5 0 5 −0.4 −0.3 10 (l) log (N/O) −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 8.50 −10 −10 10 S2 −10 10 5 8.15 5 0 −0.7 5 −10 40 −10 −10 10 −5 0.0 −10 −10 0 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.6 20 −10.25 −10.00 −9.75 −9.50 −9.25 −9.00 −8.75 5 −10 0 −10 −10 10 −5 −1.50 −10 −10 10 −3.25 9.0 −20 −10 5 7.6 (c) vgas (km/s) −40 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.96±0.10, logsSFR = -10.04±0.16 0256-0707 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.23: Same as Figure 5.3, but for galaxy 0256-0707. 5 10 167 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.83+0.09 −0.11 (a) [Mg/Fe] = 0.19+0.06 −0.07 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.00 7.25 7.50 7.75 8.00 8.25 −10 −10 10 −5 0 5 (g) 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 7.75 8.00 8.25 8.50 8.75 9.00 10 −0.6 9.25 −0.4 −0.2 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.10 8.15 8.20 8.25 8.30 8.35 8.40 −5 0 ∆ RA (arcsec) 5 10 30 (f) 5 10 (i) −5 −0.7 −0.6 −0.5 −0.4 0 −0.3 5 10 (l) log (N/O) −1.45 8.45 −10 −10 20 10 S2 −10 10 5 8.10 10 5 0 −0.8 5 −10 0 −10 −10 10 0 −5 0.2 −10 −10 −10 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.50 −20 −10.50 −10.25 −10.00 −9.75 −9.50 −9.25 −9.00 −8.75 5 −10 −30 −10 −10 10 log Age [yr] −5 −3.25 −3.00 −2.75 −2.50 −2.25 −2.00 −1.75 −1.50 −1.25 8.50 −40 −10 5 6.75 (c) vgas (km/s) −50 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 8.98±0.11, logsSFR = -9.89±0.16 2137+1243 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.24: Same as Figure 5.3, but for galaxy 2137+1243. 5 10 168 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.57+0.07 −0.10 (a) [Mg/Fe] = 0.10+0.05 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.4 7.6 7.8 8.0 8.2 8.4 8.6 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.2 8.4 8.6 8.8 9.0 9.2 10 −0.4 −0.3 −0.2 −0.1 9.4 0.0 0.1 0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.10 8.15 8.20 8.25 8.30 8.35 8.40 8.05 8.10 8.15 8.20 8.25 8.30 8.35 −5 0 ∆ RA (arcsec) 5 10 (f) −9.8 −9.6 −9.4 −9.2 −9.0 5 10 (i) −5 −0.6 −0.5 −0.4 −0.3 −0.2 0 5 10 (l) log (N/O) −1.50 8.40 −10 −10 10 S2 −10 10 5 8.05 5 0 −0.7 5 −10 40 −10 −10 10 −5 0.3 −10 −10 20 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.0 0 −10.4 −10.2 −10.0 5 −10 0 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 8.8 −20 −10 5 7.2 (c) vgas (km/s) −40 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 9.02±0.10, logsSFR = -9.90±0.15 0137-0942 −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.25: Same as Figure 5.3, but for galaxy 0137-0942. 5 10 169 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.62+0.09 −0.11 (a) [Mg/Fe] = 0.09+0.06 −0.06 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.25 7.50 7.75 8.00 8.25 8.50 −3.0 −2.5 −2.0 −1.5 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.00 8.25 8.50 8.75 9.00 10 −0.6 9.25 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.20 8.25 8.30 8.35 8.40 8.45 8.50 8.15 8.20 8.25 8.30 8.35 8.40 8.45 −5 0 ∆ RA (arcsec) 5 10 (f) 5 10 (i) −5 −0.5 −0.4 −0.3 0 5 −0.2 −0.1 10 (l) log (N/O) −1.50 −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 8.50 −10 −10 20 10 S2 −10 10 5 8.15 15 5 0 −0.6 5 −10 10 −10 −10 10 0 −5 0.1 −10 −10 5 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.75 0 −10.50−10.25−10.00 −9.75 −9.50 −9.25 −9.00 −8.75 −8.50 5 −10 −5 −10 −10 10 −5 −1.0 −10 −10 10 −3.5 8.75 −10 −10 5 7.00 (c) vgas (km/s) −15 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 9.03±0.10, logsSFR = -9.52±0.23 0136+1356 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.26: Same as Figure 5.3, but for galaxy 0136+1356. 5 10 170 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.73+0.08 −0.09 (a) [Mg/Fe] = 0.21+0.07 −0.06 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.00 7.25 7.50 7.75 8.00 8.25 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.0 8.2 8.4 8.6 8.8 9.0 10 −0.5 −0.4 −0.3 −0.2 −0.1 9.2 0.0 0.1 0.2 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.10 8.15 8.20 8.25 8.30 8.35 8.40 −5 0 ∆ RA (arcsec) 5 10 (f) −9.6 −9.4 −9.2 −9.0 5 10 (i) −5 −0.6 −0.5 −0.4 −0.3 −0.2 0 5 −0.1 0.0 10 (l) log (N/O) −1.50 −1.45 −1.40 −1.35 −1.30 −1.25 −1.20 −1.15 −1.10 8.45 −10 −10 10 S2 −10 10 5 8.10 5 0 −0.7 5 −10 40 −10 −10 10 −5 0.3 −10 −10 20 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.8 0 −10.6 −10.4 −10.2 −10.0 −9.8 5 −10 0 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 8.50 −20 −10 5 6.75 (c) vgas (km/s) −40 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 9.04±0.10, logsSFR = -9.98±0.16 2304-0933 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.27: Same as Figure 5.3, but for galaxy 2304-0933. 5 10 171 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.54+0.08 −0.10 (a) [Mg/Fe] = 0.17+0.05 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.6 7.8 8.0 8.2 8.4 8.6 −3.0 −2.5 −2.0 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.4 8.6 8.8 9.0 9.2 9.4 −0.9 9.6 10 −0.8 −0.7 −0.6 −0.5 −0.4 −0.3 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.45 8.50 8.55 8.60 8.65 8.70 8.40 8.45 8.50 8.55 8.60 8.65 −5 0 ∆ RA (arcsec) 5 10 (f) 5 10 (i) −5 −0.4 −0.3 −0.2 −0.1 0.0 0 5 10 (l) log (N/O) −1.2 8.70 −10 −10 10 S2 −10 10 5 8.40 5 0 −0.5 5 −10 40 −10 −10 10 −5 −0.2 −10 −10 0 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.2 20 −11.00 −10.75 −10.50 −10.25 −10.00 −9.75 −9.50 −9.25 5 −10 0 −10 −10 10 −5 −1.5 −10 −10 10 −3.5 8.8 −20 −10 5 7.4 (c) vgas (km/s) −40 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 9.16±0.10, logsSFR = -10.14±0.18 0306-0033 −1.1 −1.0 −0.9 −0.8 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.28: Same as Figure 5.3, but for galaxy 0306-0033. 5 10 172 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.35+0.10 −0.12 (a) [Mg/Fe] = 0.12+0.06 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα [NII] 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 6.50 6.75 7.00 7.25 7.50 7.75 −2.5 −2.0 −1.5 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 7.6 7.8 8.0 8.2 8.4 8.6 8.8 10 −0.6 9.0 −0.5 −0.4 −0.3 −0.2 −0.1 0.0 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.15 8.20 8.25 8.30 8.35 8.40 8.45 8.10 8.15 8.20 8.25 8.30 8.35 8.40 −5 0 ∆ RA (arcsec) 5 10 (f) −9.5 −9.0 −8.5 5 10 (i) −5 −0.5 −0.4 −0.3 0 −0.2 5 10 (l) log (N/O) −1.5 8.45 −10 −10 40 10 S2 −10 10 5 8.10 20 5 0 −0.6 5 −10 0 −10 −10 10 −5 0.1 −10 −10 −20 log ΣsSFR [yr−1 kpc−2] −10 10 5 7.4 −40 0 −10.0 5 −10 −60 −10 −10 10 −5 −1.0 −10 −10 10 −3.0 8.00 −80 −10 5 6.25 (c) vgas (km/s) −100 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 9.44±0.10, logsSFR = -9.47±0.13 0334+0106 −1.4 −1.3 −1.2 −1.1 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.29: Same as Figure 5.3, but for galaxy 0334+0106. 5 10 173 ∆ Dec (arcsec) 10 5 0 0 0 −5 −5 −5 10 [Fe/H] = −0.18+0.08 −0.09 (a) [Mg/Fe] = 0.09+0.05 −0.05 −5 0 5 (d) log Σ∗ [M kpc−2] −10 10 [OIII] 1 kpc −5 0 Hα 5 −10 10 (e) log ΣSFR [M yr−1 kpc−2] 10 5 5 0 0 0 −5 −5 −5 7.6 7.8 8.0 8.2 8.4 −2.50 −2.25 −2.00 −1.75 −1.50 −5 0 5 (g) log Age [yr] 10 −5 0 5 (h) O32 10 5 0 0 0 −5 −5 −5 8.7 8.8 8.9 9.0 9.1 9.2 −0.7 9.3 10 −0.6 −0.5 −0.4 −0.3 −5 0 5 (j) 12 + log (O/H)O3N2 10 −5 0 5 (k) 12 + log (O/H)R 10 5 0 0 0 −5 −5 −5 8.2 8.3 8.4 8.5 8.6 8.1 8.2 8.3 8.4 8.5 −5 0 ∆ RA (arcsec) 5 10 10 (f) 0 5 10 (i) −5 0 5 10 (l) log (N/O) −1.4 8.6 −10 −10 5 S2 −10 10 5 8.1 60 −0.60 −0.55 −0.50 −0.45 −0.40 −0.35 −0.30 −0.25 −0.20 5 −10 40 −10 −10 10 0 −5 −0.2 −10 −10 20 log ΣsSFR [yr−1 kpc−2] −10 10 5 8.6 0 −10.6 −10.4 −10.2 −10.0 −9.8 −9.6 −9.4 −9.2 −9.0 5 −10 −20 −10 −10 10 −5 −1.25 −10 −10 10 −2.75 8.6 −40 −10 [NII] 5 7.4 (c) vgas (km/s) −60 −10 10 −10 ∆ Dec (arcsec) 10 5 −10 ∆ Dec (arcsec) (b) 10 5 −10 ∆ Dec (arcsec) logM = 9.88±0.10, logsSFR = -9.87±0.12 0407-0634 −1.3 −1.2 −1.1 −1.0 −0.9 −10 −10 −5 0 ∆ RA (arcsec) 5 10 −10 −5 0 ∆ RA (arcsec) Figure 5.30: Same as Figure 5.3, but for galaxy 0407-0634. 5 10 174 Acknowledgments I acknowledge the use of ChatGPT (OpenAI, 2024) for assistance with improving English usage and grammar in this chapter. The prompts were phrased along the lines of “Please improve the language and clarity of the following sentences.” All outputs were carefully reviewed and edited by me to ensure that they accurately convey the original meaning. 175 Chapter 6 CONCLUSION 6.1 Summary In this thesis, I presented a series of spectroscopic studies examining multi-elemental abundances in galaxies across a range of masses and redshifts, with the goal of better characterizing the shapes of MZRs for different elements and probing the physical processes that govern chemical enrichment during galaxy assembly. In Chapter 2, I conducted one of the first direct comparisons between stellar metallicities derived from resolved stellar spectroscopy and those from integrated-light spectroscopy in galaxies with complex stellar populations. Focusing on NGC 147, a Local Group satellite suitable for both approaches, I measured [Fe/H]∗ using integrated-light spectra from the PCWI and found consistency with existing resolved stellar measurements (Kirby et al., 2013) to within 0.1 dex. While the recovered metallicity remained robust against the SSP assumptions, the inferred stellar age was more sensitive to those assumptions. This study provides the first evidence that it is reasonable to put the low-mass and high-mass MZRs measured from distinct approaches on the same absolute scale to jointly constrain the shape of the stellar MZR. In Chapter 4, I introduced a new sample of 46 low-redshift star-forming galaxies with 𝑀∗ ∼ 108−10 𝑀⊙ , along with two quiescent galaxies at 𝑀∗ ∼ 108.8 𝑀⊙ , observed with Keck/KCWI. I developed a novel technique to simultaneously measure [Fe/H]∗ and [Mg/H]∗ in star-forming galaxies. Combining this sample with SDSS spectra, I constructed the first Fe- and Mg-MZRs measured consistently across a stellar mass range spanning 108 to 1011.5 𝑀⊙ . I found that galaxies lying closer to the extrapolated high-mass MZRs tend to have lower sSFRs, indicating that variations in sSFR drive the transition in MZR shape at 𝑀∗ ∼ 109 𝑀⊙ . This suggests that galaxies approaching quiescence enrich efficiently and rapidly arrive on the highmass MZR, consistent with trends observed in post-starburst galaxies. The distinct stellar abundances of two quiescent galaxies at similar masses suggest that environmental factors also influence the transition: The metal-poor quiescent galaxy, likely a satellite, aligns with the extrapolation of the low-mass MZR of Local Group satellites, while the more metal-rich quiescent galaxy, likely an isolated dwarf, lies 176 above the extrapolated low-mass MZR. Chapter 4 also includes the first comparison of 𝛼 element in ionized gas and stars beyond the Local Group, through direct measurements of gas-phase oxygen and stellar magnesium in the KCWI sample. I found that [Mg/H]∗ tracks [O/H]g more closely than [Fe/H]∗ , and their ratio is less sensitive to sSFR, corroborating that Mg∗ is a better analog to Og in stellar–gas abundance comparisons. Most galaxies exhibit [O/H]g > [Mg/H]∗ , suggesting that current star formation is fueled by chemically enriched gas, rather than recently accreted, metal-poor inflows—indicating relatively well-mixed ISM. In Chapter 5, I performed a spatially resolved analysis of the nebular and stellar properties of the same KCWI sample. The preliminary results reveal that starforming dwarf galaxies host irregular, clumpy star formation and exhibit significant spatial variation in ionization conditions, whereas their stellar mass distributions are much smoother. Many systems show established gas-phase metallicity gradients, though these may be biased by contributions from DIG. In addition, I also discussed some possible next steps to further analyze and interpret the existing dataset. Finally, in Chapter 3, I extended my analysis to the high-redshift universe, studying the stellar abundances and SFHs of quiescent galaxies at 𝑧 ≳ 1. Leveraging gravitational lensing, I obtained deep rest-frame optical spectra of two quiescent galaxies at 𝑧 ≳ 1 using the Keck I telescope, and successfully measured their [Fe/H]∗ , [Mg/H]∗ , and stellar population ages. Like other quiescent galaxies at 𝑧 ∼ 1, they exhibit lower [Fe/H]∗ and [Mg/H]∗ than local ellipticals of similar mass. However, despite forming the majority of their stars within 2 Gyr of the Big Bang and quenching shortly thereafter, both galaxies have [Mg/Fe] ratios comparable to those of their local counterparts. Treating Mg as an instantaneously recycled element, I used a simple chemical evolution model to infer their mass-loading factors over time. The results show that quiescent galaxies at 𝑧 ∼ 1 formed much more rapidly and experienced enhanced outflows during star formation compared to most present-day ellipticals at similar masses, which may explain why they quenched early. In conclusion, this thesis has shown that chemical abundances derived from highquality spectroscopy are powerful tools for probing the assembly history of galaxies, both in the local universe and at high redshift. Integral field unit (IFU) spectroscopy and traditional slit spectroscopy complement each other in revealing physical processes operating at different spatial and temporal scales across cosmic time. Most importantly, the relationship between the gas and stellar components of galaxies is 177 far more complex than what can be captured by simple theoretical models. As such, detailed studies that explicitly focus on the connection between gas and stars are essential for uncovering the full picture of galaxy evolution. 6.2 Looking Forward In this section, I outline potential directions for future research related to the questions explored in this thesis. 6.2.1 Evolution in the Low-Redshift Star-Forming Dwarfs An Evolutionary Pathway from Chaos to Organization Preliminary KCWI maps of our sample reveal distinct spatial distributions between ionized gas and stellar populations within individual dwarf galaxies (Figure 5.3). Our findings are consistent with a recent IFU study of more massive galaxies (𝑀∗ > 109 , 𝑀⊙ ) from the CALIFA survey, which shows that ionized gas tends to be more extended and clumpier than the stellar component, especially in systems with high sSFR (Nersesian et al., 2023). A similar trend has been reported for lowmass star-forming galaxies (∼ 108−10 𝑀⊙ ) based on medium-band imaging from the Merian survey (Mintz et al., 2024). However, our results also seem to suggest an underlying order within this apparent chaos. On average, the spatial profiles of stellar population properties are smoother than those of nebular properties. Within the stellar component, the mass distribution is more spatially coherent than the distribution of the light-weighted age. Among the nebular properties, oxygen and nitrogen abundance profiles are less irregular than the patchy distributions of recent star formation, while ionization conditions display the most varied and complex morphologies. These observations indicate that a systematic morphological analysis of the spatially resolved properties within each galaxy will be essential to revealing how galaxies transition from irregular, clumpy structures to more organized systems, and how stochastic processes like local starbursts in a small region or minor mergers can perturb established gradients. As a next step, I will apply a nonparametric morphological analysis similar to that of Nersesian et al. (2023), using structural parameters such as the Gini–𝑀20 statistics (Abraham, van den Bergh, and Nair, 2003; Lotz, Primack, and Madau, 2004) and the concentration–asymmetry–smoothness (CAS) indices (Conselice, 2003). While Nersesian et al. (2023) focused on the morphology of the stellar continuum 178 and bright emission lines ([O iii]𝜆5007, H𝛼, and [N ii]𝜆6583), I will extend this framework to include line ratios and derived physical quantities. This will allow us to better characterize the spatial structure of both the ionized gas and the underlying stellar populations in star-forming dwarf galaxies. Possible Biases in Metallicity Measurement Due to the Presence of DIG As discussed in Section 5.3.6, star-forming dwarf galaxies exhibit significant spatial variations in observed emission-line ratios. The trends shown in Figure 5.4 likely arise from two main factors. First, galaxies can exhibit intrinsic metallicity gradients as a result of inside-out formation (Chiosi, 1980; Matteucci and Francois, 1989; Boissier and Prantzos, 1999; Chiappini, Matteucci, and Romano, 2001). All the line ratios discussed above are at least moderately sensitive to metallicity, so their spatial variations can be interpreted, in part, as reflecting such gradients. Second, DIG, which is thought to occupy the regions outside H ii regions, tends to exhibit enhanced strengths in low-ionization lines. This can systematically affect emissionline diagnostics such as R2, N2, and S2 (Zhang et al., 2017). Consequently, applying strong-line calibrations based on 𝑇𝑒 metallicities derived from H ii regions may lead to biased metallicity measurements in DIG-dominated regions. Indeed, using the criterion from Zhang et al. (2017) that defines DIG-dominated regions as those with ΣH𝛼 < 1039 erg s−1 kpc−2 , most spaxels located outside the star-forming knots in our sample appear to be DIG-dominated. To assess whether the spaxels with lower ΣSFR are truly dominated by DIG, I will measure the shape of the ionizing spectrum using Cue (Li et al., 2024), a Bayesian inference-based tool that estimates ionization parameter, ionizing spectrum shape, and elemental abundances by comparing to theoretical photoionization models. As suggested by Zhang et al. (2017), DIG is primarily ionized by hot, evolved stars that have a harder ionizing spectrum than massive OB stars. Therefore, accounting for variations in the ionizing spectrum when inferring nebular abundances will not only improve constraints on abundance measurements and their spatial gradients in star-forming dwarf galaxies, but also allow us to test whether regions identified as DIG-dominated indeed exhibit harder ionizing radiation. Spatially Resolved Stellar Abundances In the previous chapter, we compared the global stellar and gas-phase abundances of our KCWI sample and found that the gas-to-stellar abundance ratio correlates 179 with the global sSFR. In other words, galaxies with higher sSFRs tend to exhibit larger differences between gas-phase and stellar metallicities. A natural next step is to investigate whether this correlation persists on local scales within galaxies. However, accurately measuring spatially resolved stellar abundances is much more challenging due to the low signal-to-noise ratio (S/N) of the stellar continuum in individual spaxels. To overcome this limitation, spectral binning is necessary. Although Voronoi binning is widely used in IFU studies to increase the S/N of stellar continua (Cappellari and Copin, 2003), it does not account for the morphology of the ionized gas, which can exhibit spatially distinct chemical abundances as suggested by the KCWI maps shown in Figure 5.3. A promising solution to this issue was recently proposed by de Souza et al. (2024), who applied hierarchical clustering to classify spaxels into physically motivated substructures of the MaNGA sample, thereby boosting S/N while preserving meaningful spatial variation. In future work, I plan to explore a similar approach to simultaneously determine stellar and nebular abundances within each substructure. This will enable us to investigate metal recycling processes on small spatial scales in star-forming dwarf galaxies. 6.2.2 The Interplay Between Stellar Population and Ionized Gas beyond the Local Universe Distant high-𝑧 star-forming galaxies also provide a unique perspective for studying the interaction between massive stars and ionized gas. In contrast with low-redshift, star-forming galaxies, where stellar populations can be constrained using the optical absorption features, astronomers studying high-𝑧 galaxies at cosmic noon typically rely on rest-FUV spectroscopy (e.g., Steidel et al., 2016; Topping et al., 2020; Chartab et al., 2024). At this epoch, the light from star-forming galaxies is dominated by massive OB stars, which emit primarily in the UV. The stellar features of older stars residing in the rest-optical are outshined by these massive stars and have remained elusive even in the deepest observations from 10-meter ground-based telescopes Steidel et al., 2016. As a result, prior to JWST, rest-optical spectra of star-forming galaxies were used exclusively for nebular studies of high-𝑧 galaxies. With the incredible capabilities of JWST, it is now possible to probe the stellar populations of quiescent galaxies at 𝑧 ≳ 2 by fitting the rest-optical continuum (e.g., Carnall et al., 2023; Beverage et al., 2024). However, stellar properties derived from rest-optical and rest-FUV spectra reflect very different stellar populations: 180 FUV light traces high-mass stars forming “now,” while optical light captures lowermass stars accumulated over a galaxy’s lifetime. Consequently, stellar metallicities and SFHs inferred from these different approaches might not align, complicating comparisons between star-forming and quiescent galaxies at high redshift. The way forward is to look for faint optical absorption in the deepest JWST spectra of star-forming galaxies at cosmic noon. JWST has already delivered high-quality spectra at high redshifts (e.g., Strom et al., 2023), enabling the detection not only of nebular emission lines—including temperature-sensitive auroral lines—but also possible stellar continua through stacked spectra of galaxies with similar properties. Some JWST programs have obtained ultra-deep rest-frame FUV spectra, making it possible to directly compare the properties of massive stars (traced by FUV light) with those of older, lower-mass stars (traced by optical light). This combined dataset provides a powerful constraint on SFHs by probing stellar populations formed at different epochs. Such comparisons will also test the reliability of SFHs inferred from Bayesian spectral energy distribution (SED) fitting codes like Prospector (Leja et al., 2019) and BAGPIPES (Carnall et al., 2018). For example, it will be valuable to assess whether joint fitting of broadband photometry and rest-frame FUV spectra without access to rest-frame optical spectra can accurately recover SFHs. This is particularly important for interpreting the demographics of star-forming galaxies at 𝑧 ∼ 3 that will be observed by the Prime Focus Spectrograph (PFS) Galaxy Evolution Survey, which will lack rest-frame optical coverage. The PFS Galaxy Evolution Survey, a 130-night program on the Subaru Telescope that began in March 2025, will ultimately obtain high-quality spectra for approximately 14,000 galaxies at 𝑧 = 0.7–2.0 (the low-𝑧 deep sample, 𝐽 < 22.8 mag) and another ∼14,000 galaxies at 𝑧 = 2.1–3.5 (the high-𝑧 IGM sample, 𝑦 < 24.3 mag), each observed with ∼12 hours of integration time (Greene et al., 2022). Building on the tools and methods developed in this thesis and extending them in future work will place us in a strong position to interpret this unprecedented dataset. In particular, it will significantly improve our understanding of galaxy-wide chemical abundances in a mass-complete sample and the interplay between gas and stars in the early universe. 181 BIBLIOGRAPHY Abbott, T. M. C. et al. (Dec. 2018). “The Dark Energy Survey: Data Release 1”. In: ApJS 239.2, p. 18. doi: 10.3847/1538-4365/aae9f0. Abdurro’uf et al. (Apr. 2022). “The Seventeenth Data Release of the Sloan Digital Sky Surveys: Complete Release of MaNGA, MaStar, and APOGEE-2 Data”. In: ApJS 259.2, p. 35. doi: 10.3847/1538-4365/ac4414. Abraham, R. G., S. van den Bergh, and P. Nair (May 2003). “A New Approach to Galaxy Morphology. I. Analysis of the Sloan Digital Sky Survey Early Data Release”. In: ApJ 588.1, pp. 218–229. doi: 10.1086/373919. Adams, D. et al. (May 2022). “Galaxy Zoo: Clump Scout: Surveying the Local Universe for Giant Star-forming Clumps”. In: ApJ 931.1, p. 16. doi: 10.3847/ 1538-4357/ac6512. Aihara, H. et al. (Apr. 2022). “Third data release of the Hyper Suprime-Cam Subaru Strategic Program”. In: PASJ 74.2, pp. 247–272. doi: 10.1093/pasj/psab122. Akritas, M. G. and M. A. Bershady (Oct. 1996). “Linear Regression for Astronomical Data with Measurement Errors and Intrinsic Scatter”. In: ApJ 470, p. 706. doi: 10.1086/177901. Alfaro-Cuello, M. et al. (Nov. 2019). “A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. I. Data and Stellar Population Characterization”. In: ApJ 886.1, p. 57. doi: 10.3847/1538-4357/ab1b2c. Andrews, B. H. and P. Martini (Mar. 2013). “The Mass-Metallicity Relation with the Direct Method on Stacked Spectra of SDSS Galaxies”. In: ApJ 765.2, p. 140. doi: 10.1088/0004-637X/765/2/140. Asplund, M. et al. (Sept. 2009). “The Chemical Composition of the Sun”. In: ARA&A 47.1, pp. 481–522. doi: 10.1146/annurev.astro.46.060407.145222. Balogh, M. L. et al. (Dec. 1999). “Differential Galaxy Evolution in Cluster and Field Galaxies at z~0.3”. In: ApJ 527.1, pp. 54–79. doi: 10.1086/308056. Barber, C. et al. (June 2014). “Validation of optimized population synthesis through mock spectra and Galactic globular clusters”. In: MNRAS 440.4, pp. 2953–2968. doi: 10.1093/mnras/stu439. Belfiore, F. et al. (May 2015). “P-MaNGA Galaxies: emission-lines properties - gas ionization and chemical abundances from prototype observations”. In: MNRAS 449.1, pp. 867–900. doi: 10.1093/mnras/stv296. Belfiore, F. et al. (July 2017). “SDSS IV MaNGA - metallicity and nitrogen abundance gradients in local galaxies”. In: MNRAS 469.1, pp. 151–170. doi: 10 . 1093/mnras/stx789. 182 Belfiore, F. et al. (Oct. 2019). “The Data Analysis Pipeline for the SDSS-IV MaNGA IFU Galaxy Survey: Emission-line Modeling”. In: AJ 158.4, p. 160. doi: 10. 3847/1538-3881/ab3e4e. Belli, S., A. B. Newman, and R. S. Ellis (Mar. 2014). “Velocity Dispersions and Dynamical Masses for a Large Sample of Quiescent Galaxies at z > 1: Improved Measures of the Growth in Mass and Size”. In: ApJ 783.2, p. 117. doi: 10.1088/ 0004-637X/783/2/117. Benítez-Llambay, A. et al. (Feb. 2016). “Mergers and the outside-in formation of dwarf spheroidals”. In: MNRAS 456.2, pp. 1185–1194. doi: 10.1093/mnras/ stv2722. Berg, D. A. et al. (Aug. 2012). “Direct Oxygen Abundances for Low-luminosity LVL Galaxies”. In: ApJ 754.2, p. 98. doi: 10.1088/0004-637X/754/2/98. Berg, D. A. et al. (Apr. 2020). “CHAOS IV: Gas-phase Abundance Trends from the First Four CHAOS Galaxies”. In: ApJ 893.2, p. 96. doi: 10.3847/15384357/ab7eab. Bertin, E. and S. Arnouts (June 1996). “SExtractor: Software for source extraction.” In: A&AS 117, pp. 393–404. doi: 10.1051/aas:1996164. Beverage, A. G. et al. (Aug. 2021). “Elemental Abundances and Ages of z 0.7 Quiescent Galaxies on the Mass-Size Plane: Implication for Chemical Enrichment and Star Formation Quenching”. In: ApJL 917.1, p. L1. doi: 10.3847/20418213/ac12cd. Beverage, A. G. et al. (May 2023). “From Carbon to Cobalt: Chemical Compositions and Ages of z 0.7 Quiescent Galaxies”. In: ApJ 948.2, p. 140. doi: 10.3847/ 1538-4357/acc176. Beverage, A. G. et al. (May 2024). “The Heavy Metal Survey: The Evolution of Stellar Metallicities, Abundance Ratios, and Ages of Massive Quiescent Galaxies since z ∼ 2”. In: ApJ 966.2, p. 234. doi: 10.3847/1538-4357/ad372d. Blanc, G. A. et al. (Jan. 2015). “IZI: Inferring the Gas Phase Metallicity (Z) and Ionization Parameter (q) of Ionized Nebulae Using Bayesian Statistics”. In: ApJ 798.2, p. 99. doi: 10.1088/0004-637X/798/2/99. Blanc, G. A. et al. (May 2019). “A Characteristic Mass Scale in the Mass-Metallicity Relation of Galaxies”. In: ApJ 877.1, p. 6. doi: 10.3847/1538-4357/ab16ec. Boecker, A. et al. (June 2020). “Recovering Age-Metallicity Distributions from Integrated Spectra: Validation with MUSE Data of a Nearby Nuclear Star Cluster”. In: ApJ 896.1, p. 13. doi: 10.3847/1538-4357/ab919d. Boissier, S. and N. Prantzos (Aug. 1999). “Chemo-spectrophotometric evolution of spiral galaxies - I. The model and the Milky Way”. In: MNRAS 307.4, pp. 857– 876. doi: 10.1046/j.1365-8711.1999.02699.x. 183 Bournaud, F. et al. (Jan. 2014). “The Long Lives of Giant Clumps and the Birth of Outflows in Gas-rich Galaxies at High Redshift”. In: ApJ 780.1, p. 57. doi: 10.1088/0004-637X/780/1/57. Brinchmann, J. et al. (July 2004). “The physical properties of star-forming galaxies in the low-redshift Universe”. In: MNRAS 351.4, pp. 1151–1179. doi: 10.1111/ j.1365-2966.2004.07881.x. Bruzual, G. and S. Charlot (Oct. 2003). “Stellar population synthesis at the resolution of 2003”. In: MNRAS 344.4, pp. 1000–1028. doi: 10.1046/j.1365- 8711. 2003.06897.x. Bundy, K. et al. (Jan. 2015). “Overview of the SDSS-IV MaNGA Survey: Mapping nearby Galaxies at Apache Point Observatory”. In: ApJ 798.1, p. 7. doi: 10. 1088/0004-637X/798/1/7. Burbidge, E. M. et al. (Jan. 1957). “Synthesis of the Elements in Stars”. In: Reviews of Modern Physics 29.4, pp. 547–650. doi: 10.1103/RevModPhys.29.547. Byler, N. et al. (May 2017). “Nebular Continuum and Line Emission in Stellar Population Synthesis Models”. In: ApJ 840.1, p. 44. doi: 10 . 3847 / 1538 4357/aa6c66. Calura, F. et al. (Sept. 2009). “The evolution of the mass-metallicity relation in galaxies of different morphological types”. In: A&A 504.2, pp. 373–388. doi: 10.1051/0004-6361/200911756. Calzetti, D. et al. (Apr. 2000). “The Dust Content and Opacity of Actively Starforming Galaxies”. In: ApJ 533.2, pp. 682–695. doi: 10.1086/308692. Cappellari, M. (Apr. 2017). “Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions”. In: MNRAS 466.1, pp. 798–811. doi: 10.1093/mnras/stw3020. Cappellari, M. (Dec. 2023). “Full spectrum fitting with photometry in PPXF: stellar population versus dynamical masses, non-parametric star formation history and metallicity for 3200 LEGA-C galaxies at redshift z ≈ 0.8”. In: MNRAS 526.3, pp. 3273–3300. doi: 10.1093/mnras/stad2597. Cappellari, M. and Y. Copin (June 2003). “Adaptive spatial binning of integral-field spectroscopic data using Voronoi tessellations”. In: MNRAS 342.2, pp. 345–354. doi: 10.1046/j.1365-8711.2003.06541.x. Cappellari, M. and E. Emsellem (Feb. 2004). “Parametric Recovery of Line-of-Sight Velocity Distributions from Absorption-Line Spectra of Galaxies via Penalized Likelihood”. In: PASP 116.816, pp. 138–147. doi: 10.1086/381875. Cappellari, M. et al. (May 2011). “The ATLAS3𝐷 project - I. A volume-limited sample of 260 nearby early-type galaxies: science goals and selection criteria”. In: MNRAS 413.2, pp. 813–836. doi: 10.1111/j.1365-2966.2010.18174.x. 184 Cardelli, J. A., G. C. Clayton, and J. S. Mathis (Oct. 1989). “The Relationship between Infrared, Optical, and Ultraviolet Extinction”. In: ApJ 345, p. 245. doi: 10.1086/167900. Carnall, A. C. (May 2017). “SpectRes: A Fast Spectral Resampling Tool in Python”. In: arXiv e-prints, arXiv:1705.05165. Carnall, A. C. et al. (Nov. 2018). “Inferring the star formation histories of massive quiescent galaxies with BAGPIPES: evidence for multiple quenching mechanisms”. In: MNRAS 480.4, pp. 4379–4401. doi: 10.1093/mnras/sty2169. Carnall, A. C. et al. (Mar. 2019). “How to Measure Galaxy Star Formation Histories. I. Parametric Models”. In: ApJ 873.1, p. 44. doi: 10.3847/1538-4357/ab04a2. Carnall, A. C. et al. (Apr. 2022). “The Stellar Metallicities of Massive Quiescent Galaxies at 1.0 < z < 1.3 from KMOS + VANDELS”. In: ApJ 929.2, p. 131. doi: 10.3847/1538-4357/ac5b62. Carnall, A. C. et al. (July 2023). “A massive quiescent galaxy at redshift 4.658”. In: Nature 619.7971, pp. 716–719. doi: 10.1038/s41586-023-06158-6. Chabrier, G. (July 2003). “Galactic Stellar and Substellar Initial Mass Function”. In: PASP 115.809, pp. 763–795. doi: 10.1086/376392. Chartab, N. et al. (Jan. 2024). “LATIS: The Stellar Mass-Metallicity Relation of Star-forming Galaxies at z 2.5”. In: ApJ 960.1, p. 73. doi: 10 . 3847 / 1538 4357/ad0554. Chen, X., L. Hu, and L. Wang (Nov. 2021). “Constraining Type Ia Supernova Delay Time with Spatially Resolved Star Formation Histories”. In: ApJ 922.1, p. 15. doi: 10.3847/1538-4357/ac178d. Chen, Y. et al. (Nov. 2021). “The KBSS-KCWI survey: the connection between extended Ly 𝛼 haloes and galaxy azimuthal angle at z 2-3”. In: MNRAS 508.1, pp. 19–43. doi: 10.1093/mnras/stab2383. Chiappini, C., F. Matteucci, and D. Romano (June 2001). “Abundance Gradients and the Formation of the Milky Way”. In: ApJ 554.2, pp. 1044–1058. doi: 10. 1086/321427. Chiosi, C. (Mar. 1980). “Chemical evolution of the galactic disk: the inflow problem.” In: A&A 83, pp. 206–216. Choi, J. et al. (Sept. 2014). “The Assembly Histories of Quiescent Galaxies since z = 0.7 from Absorption Line Spectroscopy”. In: ApJ 792.2, p. 95. doi: 10.1088/ 0004-637X/792/2/95. Choi, J. et al. (June 2016). “Mesa Isochrones and Stellar Tracks (MIST). I. Solarscaled Models”. In: ApJ 823.2, p. 102. doi: 10.3847/0004-637X/823/2/102. Cid Fernandes, R. et al. (Apr. 2005). “Semi-empirical analysis of Sloan Digital Sky Survey galaxies - I. Spectral synthesis method”. In: MNRAS 358.2, pp. 363–378. doi: 10.1111/j.1365-2966.2005.08752.x. 185 Conn, A. R. et al. (Oct. 2012). “A Bayesian Approach to Locating the Red Giant Branch Tip Magnitude. II. Distances to the Satellites of M31”. In: ApJ 758.1, p. 11. doi: 10.1088/0004-637X/758/1/11. Conroy, C. (Aug. 2013). “Modeling the Panchromatic Spectral Energy Distributions of Galaxies”. In: ARA&A 51.1, pp. 393–455. doi: 10.1146/annurev-astro082812-141017. Conroy, C., G. J. Graves, and P. G. van Dokkum (Jan. 2014). “Early-type Galaxy Archeology: Ages, Abundance Ratios, and Effective Temperatures from Fullspectrum Fitting”. In: ApJ 780.1, p. 33. doi: 10.1088/0004-637X/780/1/33. Conroy, C. and J. E. Gunn (Apr. 2010). “The Propagation of Uncertainties in Stellar Population Synthesis Modeling. III. Model Calibration, Comparison, and Evaluation”. In: ApJ 712.2, pp. 833–857. doi: 10.1088/0004-637X/712/2/833. Conroy, C., J. E. Gunn, and M. White (July 2009). “The Propagation of Uncertainties in Stellar Population Synthesis Modeling. I. The Relevance of Uncertain Aspects of Stellar Evolution and the Initial Mass Function to the Derived Physical Properties of Galaxies”. In: ApJ 699.1, pp. 486–506. doi: 10.1088/0004637X/699/1/486. Conroy, C. and P. G. van Dokkum (Nov. 2012). “The Stellar Initial Mass Function in Early-type Galaxies From Absorption Line Spectroscopy. II. Results”. In: ApJ 760.1, p. 71. doi: 10.1088/0004-637X/760/1/71. Conroy, C., M. White, and J. E. Gunn (Jan. 2010). “The Propagation of Uncertainties in Stellar Population Synthesis Modeling. II. The Challenge of Comparing Galaxy Evolution Models to Observations”. In: ApJ 708.1, pp. 58–70. doi: 10.1088/ 0004-637X/708/1/58. Conroy, C. et al. (Feb. 2018). “Metal-rich, Metal-poor: Updated Stellar Population Models for Old Stellar Systems”. In: ApJ 854.2, p. 139. doi: 10.3847/15384357/aaab49. Conselice, C. J. (July 2003). “The Relationship between Stellar Light Distributions of Galaxies and Their Formation Histories”. In: ApJS 147.1, pp. 1–28. doi: 10.1086/375001. Cooper, M. C. et al. (Feb. 2012). “The DEEP3 Galaxy Redshift Survey: the impact of environment on the size evolution of massive early-type galaxies at intermediate redshift”. In: MNRAS 419.4, pp. 3018–3027. doi: 10.1111/j.1365- 2966. 2011.19938.x. Crnojević, D. et al. (Dec. 2014). “A PAndAS view of M31 dwarf elliptical satellites: NGC 147 and NGC 185”. In: MNRAS 445.4, pp. 3862–3877. doi: 10.1093/ mnras/stu2003. Croom, S. M. et al. (Mar. 2012). “The Sydney-AAO Multi-object Integral field spectrograph”. In: MNRAS 421.1, pp. 872–893. doi: 10.1111/j.1365-2966. 2011.20365.x. 186 Croom, S. M. et al. (July 2021). “The SAMI Galaxy Survey: the third and final data release”. In: MNRAS 505.1, pp. 991–1016. doi: 10.1093/mnras/stab229. Curti, M. et al. (Jan. 2020). “The mass-metallicity and the fundamental metallicity relation revisited on a fully T𝑒 -based abundance scale for galaxies”. In: MNRAS 491.1, pp. 944–964. doi: 10.1093/mnras/stz2910. Curti, M. et al. (Apr. 2023). “JADES: Insights on the low-mass end of the mass– metallicity–star-formation rate relation at 3 < 𝑧 < 10 from deep JWST/NIRSpec spectroscopy”. In: arXiv e-prints, arXiv:2304.08516. doi: 10.48550/arXiv. 2304.08516. Dale, D. A. et al. (June 2023). “Spectral Energy Distributions for 258 Local Volume Galaxies”. In: AJ 165.6, p. 260. doi: 10.3847/1538-3881/accffe. Davé, R., K. Finlator, and B. D. Oppenheimer (Mar. 2012). “An analytic model for the evolution of the stellar, gas and metal content of galaxies”. In: MNRAS 421.1, pp. 98–107. doi: 10.1111/j.1365-2966.2011.20148.x. Davidge, T. J. (Nov. 2005). “The Evolved Stellar Content of NGC 147, NGC 185, and NGC 205”. In: AJ 130.5, pp. 2087–2103. doi: 10.1086/491706. Davidson, R. and E. Flachaire (2008). “The wild bootstrap, tamed at last”. In: Journal of Econometrics 146.1, pp. 162–169. issn: 0304-4076. doi: https : //doi.org/10.1016/j.jeconom.2008.08.003. de los Reyes, M. A. C. et al. (Mar. 2020). “Manganese Indicates a Transition from Sub- to Near-Chandrasekhar Type Ia Supernovae in Dwarf Galaxies”. In: ApJ 891.1, p. 85. doi: 10.3847/1538-4357/ab736f. de los Reyes, M. A. C. et al. (Jan. 2022). “Simultaneous Constraints on the Star Formation History and Nucleosynthesis of Sculptor dSph”. In: ApJ 925.1, p. 66. doi: 10.3847/1538-4357/ac332b. de los Reyes, M. A. C. et al. (July 2023). “Dwarfs in Void Environments (DIVE): The Stellar Kinematics of Void Dwarf Galaxies Using the Keck Cosmic Web Imager”. In: ApJ 951.1, p. 52. doi: 10.3847/1538-4357/acd189. De Rossi, M. E. et al. (Dec. 2017). “Galaxy metallicity scaling relations in the EAGLE simulations”. In: MNRAS 472.3, pp. 3354–3377. doi: 10.1093/mnras/ stx2158. de Souza, R. S. et al. (Oct. 2024). “Capivara: A Spectral-based Segmentation Method for IFU Data Cubes”. In: arXiv e-prints, arXiv:2410.21962. doi: 10 . 48550 / arXiv.2410.21962. Dekel, A. and J. Silk (Apr. 1986). “The Origin of Dwarf Galaxies, Cold Dark Matter, and Biased Galaxy Formation”. In: ApJ 303, p. 39. doi: 10.1086/164050. Dey, A. et al. (May 2019). “Overview of the DESI Legacy Imaging Surveys”. In: AJ 157.5, p. 168. doi: 10.3847/1538-3881/ab089d. 187 Dotter, A. (Jan. 2016). “MESA Isochrones and Stellar Tracks (MIST) 0: Methods for the Construction of Stellar Isochrones”. In: ApJS 222.1, p. 8. doi: 10.3847/ 0067-0049/222/1/8. Emami, N. et al. (Aug. 2019). “A Closer Look at Bursty Star Formation with L 𝐻𝛼 and L 𝑈𝑉 Distributions”. In: ApJ 881.1, p. 71. doi: 10.3847/1538-4357/ab211a. Erb, D. K. et al. (June 2006). “The Mass-Metallicity Relation at z>~2”. In: ApJ 644.2, pp. 813–828. doi: 10.1086/503623. Esteban, C. et al. (Sept. 2014). “Carbon and oxygen abundances from recombination lines in low-metallicity star-forming galaxies. Implications for chemical evolution”. In: MNRAS 443.1, pp. 624–647. doi: 10.1093/mnras/stu1177. Estrada-Carpenter, V. et al. (Jan. 2019). “CLEAR. I. Ages and Metallicities of Quiescent Galaxies at 1.0 < z < 1.8 Derived from Deep Hubble Space Telescope Grism Data”. In: ApJ 870.2, p. 133. doi: 10.3847/1538-4357/aaf22e. Faber, S. M. et al. (Mar. 2003). “The DEIMOS spectrograph for the Keck II Telescope: integration and testing”. In: Instrument Design and Performance for Optical/Infrared Ground-based Telescopes. Ed. by M. Iye and A. F. M. Moorwood. Vol. 4841. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, pp. 1657–1669. doi: 10.1117/12.460346. Faucher-Giguère, C.-A., E. Quataert, and P. F. Hopkins (Aug. 2013). “Feedbackregulated star formation in molecular clouds and galactic discs”. In: MNRAS 433.3, pp. 1970–1990. doi: 10.1093/mnras/stt866. Ferland, G. J. et al. (Oct. 2017). “The 2017 Release Cloudy”. In: RMxAA 53, pp. 385– 438. doi: 10.48550/arXiv.1705.10877. Finlator, K. and R. Davé (Apr. 2008). “The origin of the galaxy mass-metallicity relation and implications for galactic outflows”. In: MNRAS 385.4, pp. 2181– 2204. doi: 10.1111/j.1365-2966.2008.12991.x. Flewelling, H. A. et al. (Nov. 2020). “The Pan-STARRS1 Database and Data Products”. In: ApJS 251.1, p. 7. doi: 10.3847/1538-4365/abb82d. Forbes, D. A. et al. (Nov. 2019). “Dark matter and no dark matter: on the halo mass of NGC 1052”. In: MNRAS 489.3, pp. 3665–3669. doi: 10.1093/mnras/stz2420. Forbes, J. C. et al. (Feb. 2014). “Balance among gravitational instability, star formation and accretion determines the structure and evolution of disc galaxies”. In: MNRAS 438.2, pp. 1552–1576. doi: 10.1093/mnras/stt2294. Foreman-Mackey, D., J. Sick, and B. Johnson (Oct. 2014). python-fsps: Python bindings to FSPS (v0.1.1). Zenodo. Version v0.1.1. doi: 10 . 5281 / zenodo . 12157. Foreman-Mackey, D. et al. (Mar. 2013). “emcee: The MCMC Hammer”. In: PASP 125.925, p. 306. doi: 10.1086/670067. 188 Fraser-McKelvie, A. et al. (Feb. 2022). “The SAMI Galaxy Survey: the drivers of gas and stellar metallicity differences in galaxies”. In: MNRAS 510.1, pp. 320–333. doi: 10.1093/mnras/stab3430. Gallazzi, A. et al. (Sept. 2005). “The ages and metallicities of galaxies in the local universe”. In: MNRAS 362.1, pp. 41–58. doi: 10.1111/j.1365-2966.2005. 09321.x. Gallazzi, A. et al. (June 2014). “Charting the Evolution of the Ages and Metallicities of Massive Galaxies since z = 0.7”. In: ApJ 788.1, p. 72. doi: 10.1088/0004637X/788/1/72. Gallazzi, A. R. et al. (Apr. 2021). “Galaxy evolution across environments as probed by the ages, stellar metallicities, and [𝛼 /Fe] of central and satellite galaxies”. In: MNRAS 502.3, pp. 4457–4478. doi: 10.1093/mnras/stab265. Garcia, A. M. et al. (Jan. 2024). “Interplay of Stellar and Gas-Phase Metallicities: Unveiling Insights for Stellar Feedback Modeling with Illustris, IllustrisTNG, and EAGLE”. In: arXiv e-prints, arXiv:2401.12310. doi: 10.48550/arXiv.2401. 12310. García-Rojas, J. and C. Esteban (Nov. 2007). “On the Abundance Discrepancy Problem in H II Regions”. In: ApJ 670.1, pp. 457–470. doi: 10.1086/521871. Geda, R. et al. (May 2022). “PetroFit: A Python Package for Computing Petrosian Radii and Fitting Galaxy Light Profiles”. In: AJ 163.5, p. 202. doi: 10.3847/ 1538-3881/ac5908. Geha, M. et al. (Jan. 2006). “Local Group Dwarf Elliptical Galaxies. I. Mapping the Dynamics of NGC 205 Beyond the Tidal Radius”. In: AJ 131.1, pp. 332–342. doi: 10.1086/498686. Geha, M. et al. (Mar. 2010). “Local Group Dwarf Elliptical Galaxies. II. Stellar Kinematics to Large Radii in NGC 147 and NGC 185”. In: ApJ 711.1, pp. 361– 373. doi: 10.1088/0004-637X/711/1/361. Geha, M. et al. (Oct. 2015). “HST/ACS Direct Ages of the Dwarf Elliptical Galaxies NGC 147 and NGC 185”. In: ApJ 811.2, p. 114. doi: 10.1088/0004- 637X/ 811/2/114. Genina, A. et al. (Sept. 2019). “The distinct stellar metallicity populations of simulated Local Group dwarfs”. In: MNRAS 488.2, pp. 2312–2331. doi: 10.1093/ mnras/stz1852. Goddard, D. et al. (Apr. 2017). “SDSS-IV MaNGA: Spatially resolved star formation histories in galaxies as a function of galaxy mass and type”. In: MNRAS 466.4, pp. 4731–4758. doi: 10.1093/mnras/stw3371. Gonçalves, D. R. et al. (Feb. 2007). “The chemical content of nearby galaxies from planetary nebulae: NGC 147”. In: MNRAS 375.2, pp. 715–724. doi: 10.1111/ j.1365-2966.2006.11339.x. 189 González Delgado, R. M. et al. (May 2016). “Star formation along the Hubble sequence. Radial structure of the star formation of CALIFA galaxies”. In: A&A 590, A44. doi: 10.1051/0004-6361/201628174. González Delgado, R. M. and R. Cid Fernandes (Apr. 2010). “Testing spectral models for stellar populations with star clusters - II. Results”. In: MNRAS 403.2, pp. 797–816. doi: 10.1111/j.1365-2966.2009.16152.x. Greene, J. et al. (June 2022). “The Prime Focus Spectrograph Galaxy Evolution Survey”. In: arXiv e-prints, arXiv:2206.14908. doi: 10.48550/arXiv.2206. 14908. Greene, J. E. et al. (Oct. 2013). “The Stellar Halos of Massive Elliptical Galaxies. II. Detailed Abundance Ratios at Large Radius”. In: ApJ 776.2, p. 64. doi: 10.1088/0004-637X/776/2/64. Gu, M. et al. (June 2022). “The MASSIVE Survey. XVI. The Stellar Initial Mass Function in the Center of MASSIVE Early-type Galaxies”. In: ApJ 932.2, p. 103. doi: 10.3847/1538-4357/ac69ea. Gunn, J. E. and I. Gott J. Richard (Aug. 1972). “On the Infall of Matter Into Clusters of Galaxies and Some Effects on Their Evolution”. In: ApJ 176, p. 1. doi: 10.1086/151605. Guo, Y. et al. (Feb. 2015). “Clumpy Galaxies in CANDELS. I. The Definition of UV Clumps and the Fraction of Clumpy Galaxies at 0.5 < z < 3”. In: ApJ 800.1, p. 39. doi: 10.1088/0004-637X/800/1/39. Han, M. et al. (Mar. 1997). “Stellar Populations in the Dwarf Elliptical Galaxy NGC 147”. In: AJ 113, p. 1001. doi: 10.1086/118316. Hayden, M. R. et al. (Aug. 2015). “Chemical Cartography with APOGEE: Metallicity Distribution Functions and the Chemical Structure of the Milky Way Disk”. In: ApJ 808.2, p. 132. doi: 10.1088/0004-637X/808/2/132. Hayward, C. C. and P. F. Hopkins (Feb. 2017). “How stellar feedback simultaneously regulates star formation and drives outflows”. In: MNRAS 465.2, pp. 1682–1698. doi: 10.1093/mnras/stw2888. Hopkins, P. F., E. Quataert, and N. Murray (Apr. 2012). “Stellar feedback in galaxies and the origin of galaxy-scale winds”. In: MNRAS 421.4, pp. 3522–3537. doi: 10.1111/j.1365-2966.2012.20593.x. Hopkins, P. F. et al. (Nov. 2014). “Galaxies on FIRE (Feedback In Realistic Environments): stellar feedback explains cosmologically inefficient star formation”. In: MNRAS 445.1, pp. 581–603. doi: 10.1093/mnras/stu1738. Hopkins, P. F. et al. (Oct. 2023). “What causes the formation of discs and end of bursty star formation?” In: MNRAS 525.2, pp. 2241–2286. doi: 10.1093/mnras/ stad1902. 190 Horne, K. (June 1986). “An optimal extraction algorithm for CCD spectroscopy.” In: PASP 98, pp. 609–617. doi: 10.1086/131801. Jacobs, C. et al. (July 2019). “An Extended Catalog of Galaxy-Galaxy Strong Gravitational Lenses Discovered in DES Using Convolutional Neural Networks”. In: ApJS 243.1, p. 17. doi: 10.3847/1538-4365/ab26b6. Jacobs, C. et al. (Apr. 2019). “Finding high-redshift strong lenses in DES using convolutional neural networks”. In: MNRAS 484.4, pp. 5330–5349. doi: 10 . 1093/mnras/stz272. Jafariyazani, M. et al. (July 2020). “Resolved Multi-element Stellar Chemical Abundances in the Brightest Quiescent Galaxy at z ∼ 2”. In: ApJL 897.2, p. L42. doi: 10.3847/2041-8213/aba11c. Johnson, B. D. et al. (June 2021). “Stellar Population Inference with Prospector”. In: ApJS 254.2, p. 22. doi: 10.3847/1538-4365/abef67. Jullo, E. et al. (Dec. 2007). “A Bayesian approach to strong lensing modelling of galaxy clusters”. In: New Journal of Physics 9.12, p. 447. doi: 10.1088/13672630/9/12/447. Kacprzak, G. G. et al. (July 2016). “Cold-mode Accretion: Driving the Fundamental Mass-Metallicity Relation at z ~2”. In: ApJL 826.1, p. L11. doi: 10.3847/20418205/826/1/L11. Kado-Fong, E. et al. (Mar. 2020). “Star Formation in Isolated Dwarf Galaxies Hosting Tidal Debris: Extending the Dwarf-Dwarf Merger Sequence”. In: AJ 159.3, p. 103. doi: 10.3847/1538-3881/ab6ef3. Kauffmann, G. et al. (May 2003). “Stellar masses and star formation histories for 105 galaxies from the Sloan Digital Sky Survey”. In: MNRAS 341.1, pp. 33–53. doi: 10.1046/j.1365-8711.2003.06291.x. Kauffmann, G. et al. (Dec. 2003). “The host galaxies of active galactic nuclei”. In: MNRAS 346.4, pp. 1055–1077. doi: 10.1111/j.1365-2966.2003.07154.x. Kennicutt Jr., R. C. (Jan. 1998). “Star Formation in Galaxies Along the Hubble Sequence”. In: ARA&A 36, pp. 189–232. doi: 10.1146/annurev.astro.36. 1.189. Kereš, D. et al. (Oct. 2005). “How do galaxies get their gas?” In: MNRAS 363.1, pp. 2–28. doi: 10.1111/j.1365-2966.2005.09451.x. Kewley, L. J. et al. (July 2001). “Theoretical Modeling of Starburst Galaxies”. In: ApJ 556.1, pp. 121–140. doi: 10.1086/321545. Kewley, L. J. and S. L. Ellison (July 2008). “Metallicity Calibrations and the MassMetallicity Relation for Star-forming Galaxies”. In: ApJ 681.2, pp. 1183–1204. doi: 10.1086/587500. 191 Kewley, L. J. et al. (Nov. 2006). “The host galaxies and classification of active galactic nuclei”. In: MNRAS 372.3, pp. 961–976. doi: 10 . 1111 / j . 1365 2966.2006.10859.x. Kirby, E. N., P. Guhathakurta, and C. Sneden (Aug. 2008). “Metallicity and AlphaElement Abundance Measurement in Red Giant Stars from Medium-Resolution Spectra”. In: ApJ 682.2, pp. 1217–1233. doi: 10.1086/589627. Kirby, E. N. et al. (Nov. 2009). “Multi-element Abundance Measurements from Medium-resolution Spectra. I. The Sculptor Dwarf Spheroidal Galaxy”. In: ApJ 705.1, pp. 328–346. doi: 10.1088/0004-637X/705/1/328. Kirby, E. N. et al. (Dec. 2010). “Multi-element Abundance Measurements from Medium-resolution Spectra. II. Catalog of Stars in Milky Way Dwarf Satellite Galaxies”. In: ApJS 191.2, pp. 352–375. doi: 10.1088/0067-0049/191/2/352. Kirby, E. N. et al. (Feb. 2011). “Multi-element Abundance Measurements from Medium-resolution Spectra. III. Metallicity Distributions of Milky Way Dwarf Satellite Galaxies”. In: ApJ 727.2, p. 78. doi: 10.1088/0004-637X/727/2/78. Kirby, E. N. et al. (Feb. 2011). “Multi-element Abundance Measurements from Medium-resolution Spectra. IV. Alpha Element Distributions in Milky Way Satellite Galaxies”. In: ApJ 727.2, p. 79. doi: 10.1088/0004-637X/727/2/79. Kirby, E. N. et al. (Dec. 2013). “The Universal Stellar Mass-Stellar Metallicity Relation for Dwarf Galaxies”. In: ApJ 779.2, p. 102. doi: 10 . 1088 / 0004 637X/779/2/102. Kirby, E. N. et al. (Jan. 2017). “Chemistry and Kinematics of the Late-forming Dwarf Irregular Galaxies Leo A, Aquarius, and Sagittarius DIG”. In: ApJ 834.1, p. 9. doi: 10.3847/1538-4357/834/1/9. Kirby, E. N. et al. (Feb. 2020). “Elemental Abundances in M31: The Kinematics and Chemical Evolution of Dwarf Spheroidal Satellite Galaxies”. In: AJ 159.2, p. 46. doi: 10.3847/1538-3881/ab5f0f. Knowles, A. T. et al. (Aug. 2023). “sMILES SSPs: a library of semi-empirical MILES stellar population models with variable [𝛼/Fe] abundances”. In: MNRAS 523.3, pp. 3450–3470. doi: 10.1093/mnras/stad1647. Kobayashi, C., A. I. Karakas, and M. Lugaro (Sept. 2020). “The Origin of Elements from Carbon to Uranium”. In: ApJ 900.2, p. 179. doi: 10.3847/1538-4357/ abae65. Koleva, M. et al. (Nov. 2011). “Age and metallicity gradients in early-type galaxies: a dwarf-to-giant sequence”. In: MNRAS 417.3, pp. 1643–1671. doi: 10.1111/ j.1365-2966.2011.19057.x. Kormendy, J. (Aug. 1985). “Families of ellipsoidal stellar systems and the formation of dwarf elliptical galaxies.” In: ApJ 295, pp. 73–79. doi: 10.1086/163350. 192 Kormendy, J. and R. Bender (Jan. 2012). “A Revised Parallel-sequence Morphological Classification of Galaxies: Structure and Formation of S0 and Spheroidal Galaxies”. In: ApJS 198.1, p. 2. doi: 10.1088/0067-0049/198/1/2. Kormendy, J. et al. (May 2009). “Structure and Formation of Elliptical and Spheroidal Galaxies”. In: ApJS 182.1, pp. 216–309. doi: 10 . 1088 / 0067 0049/182/1/216. Kriek, M. et al. (Dec. 2016). “A massive, quiescent, population II galaxy at a redshift of 2.1”. In: Nature 540.7632, pp. 248–251. doi: 10.1038/nature20570. Kriek, M. et al. (Aug. 2019). “Stellar Metallicities and Elemental Abundance Ratios of z ∼ 1.4 Massive Quiescent Galaxies”. In: ApJL 880.2, p. L31. doi: 10.3847/ 2041-8213/ab2e75. Kron, R. G. (June 1980). “Photometry of a complete sample of faint galaxies.” In: ApJS 43, pp. 305–325. doi: 10.1086/190669. Kroupa, P. (Apr. 2001). “On the variation of the initial mass function”. In: MNRAS 322.2, pp. 231–246. doi: 10.1046/j.1365-8711.2001.04022.x. Lang, D. (May 2014). “unWISE: Unblurred Coadds of the WISE Imaging”. In: AJ 147.5, p. 108. doi: 10.1088/0004-6256/147/5/108. Lee, H. et al. (Aug. 2006). “On Extending the Mass-Metallicity Relation of Galaxies by 2.5 Decades in Stellar Mass”. In: ApJ 647.2, pp. 970–983. doi: 10.1086/ 505573. Leethochawalit, N. et al. (Apr. 2016). “A Keck Adaptive Optics Survey of a Representative Sample of Gravitationally Lensed Star-forming Galaxies: High Spatial Resolution Studies of Kinematics and Metallicity Gradients”. In: ApJ 820.2, p. 84. doi: 10.3847/0004-637X/820/2/84. Leethochawalit, N. et al. (Mar. 2018). “Evolution of the Stellar Mass-Metallicity Relation. I. Galaxies in the z ∼ 0.4 Cluster Cl0024”. In: ApJ 856.1, p. 15. doi: 10.3847/1538-4357/aab26a. Leethochawalit, N. et al. (Mar. 2018). “Evolution of the Stellar Mass-Metallicity Relation. I. Galaxies in the z ∼ 0.4 Cluster Cl0024”. In: ApJ 856.1, p. 15. doi: 10.3847/1538-4357/aab26a. Leethochawalit, N. et al. (Nov. 2019). “Evolution of the Stellar Mass-Metallicity Relation. II. Constraints on Galactic Outflows from the Mg Abundances of Quiescent Galaxies”. In: ApJ 885.2, p. 100. doi: 10.3847/1538-4357/ab4809. Leja, J. et al. (May 2019). “How to Measure Galaxy Star Formation Histories. II. Nonparametric Models”. In: ApJ 876.1, p. 3. doi: 10.3847/1538- 4357/ ab133c. Lequeux, J. et al. (Dec. 1979). “Chemical Composition and Evolution of Irregular and Blue Compact Galaxies”. In: A&A 80, p. 155. 193 Lequeux, J. et al. (Dec. 1979). “Reprint of 1979A&A....80..155L. Chemical composition and evolution of irregular and blue compact galaxies.” In: A&A 500, pp. 145–156. Leung, H.-H. et al. (Mar. 2024). “Chemical evolution of local post-starburst galaxies: implications for the mass-metallicity relation”. In: MNRAS 528.3, pp. 4029–4052. doi: 10.1093/mnras/stae225. Li, Y. et al. (May 2024). “Cue: A Fast and Flexible Photoionization Emulator for Modeling Nebular Emission Powered By Almost Any Ionizing Source”. In: arXiv e-prints, arXiv:2405.04598. doi: 10.48550/arXiv.2405.04598. Lian, J. et al. (May 2018). “SDSS-IV MaNGA: modelling the metallicity gradients of gas and stars - radially dependent metal outflow versus IMF”. In: MNRAS 476.3, pp. 3883–3901. doi: 10.1093/mnras/sty425. Lian, J. et al. (Feb. 2018). “The mass-metallicity relations for gas and stars in star-forming galaxies: strong outflow versus variable IMF”. In: MNRAS 474.1, pp. 1143–1164. doi: 10.1093/mnras/stx2829. Lonoce, I. et al. (Dec. 2015). “Old age and supersolar metallicity in a massive z ∼ 1.4 early-type galaxy from VLT/X-Shooter spectroscopy”. In: MNRAS 454.4, pp. 3912–3919. doi: 10.1093/mnras/stv2150. Looser, T. J. et al. (Jan. 2024). “The stellar Fundamental Metallicity Relation: the correlation between stellar mass, star-formation rate and stellar metallicity”. In: arXiv e-prints, arXiv:2401.08769. doi: 10.48550/arXiv.2401.08769. Lotz, J. M., J. Primack, and P. Madau (July 2004). “A New Nonparametric Approach to Galaxy Morphological Classification”. In: AJ 128.1, pp. 163–182. doi: 10. 1086/421849. Lu, Y., G. A. Blanc, and A. Benson (Aug. 2015). “An Analytical Model for Galaxy Metallicity: What do Metallicity Relations Tell Us about Star Formation and Outflow?” In: ApJ 808.2, p. 129. doi: 10.1088/0004-637X/808/2/129. Ludlow, A. D. et al. (Aug. 2016). “The mass-concentration-redshift relation of cold and warm dark matter haloes”. In: MNRAS 460.2, pp. 1214–1232. doi: 10.1093/mnras/stw1046. Lupton, R. et al. (Feb. 2004). “Preparing Red-Green-Blue Images from CCD Data”. In: PASP 116.816, pp. 133–137. doi: 10.1086/382245. Ma, X. et al. (Feb. 2016). “The origin and evolution of the galaxy mass-metallicity relation”. In: MNRAS 456.2, pp. 2140–2156. doi: 10.1093/mnras/stv2659. Magrini, L. et al. (Dec. 2012). “Scaling relations of metallicity, stellar mass and star formation rate in metal-poor starbursts - II. Theoretical models”. In: MNRAS 427.2, pp. 1075–1088. doi: 10.1111/j.1365-2966.2012.22055.x. 194 Maiolino, R. and F. Mannucci (Feb. 2019). “De re metallica: the cosmic chemical evolution of galaxies”. In: A&A Rv 27.1, p. 3. doi: 10.1007/s00159- 0180112-2. Majewski, S. R. et al. (Sept. 2017). “The Apache Point Observatory Galactic Evolution Experiment (APOGEE)”. In: AJ 154.3, p. 94. doi: 10 . 3847 / 1538 3881/aa784d. Man, A. W. S. et al. (Sept. 2021). “An Exquisitely Deep View of Quenching Galaxies through the Gravitational Lens: Stellar Population, Morphology, and Ionized Gas”. In: ApJ 919.1, p. 20. doi: 10.3847/1538-4357/ac0ae3. Mandelker, N. et al. (Oct. 2014). “The population of giant clumps in simulated high-z galaxies: in situ and ex situ migration and survival”. In: MNRAS 443.4, pp. 3675–3702. doi: 10.1093/mnras/stu1340. Mannucci, F. et al. (Nov. 2010). “A fundamental relation between mass, star formation rate and metallicity in local and high-redshift galaxies”. In: MNRAS 408.4, pp. 2115–2127. doi: 10.1111/j.1365-2966.2010.17291.x. Maoz, D., F. Mannucci, and T. D. Brandt (Nov. 2012). “The delay-time distribution of Type Ia supernovae from Sloan II”. In: MNRAS 426.4, pp. 3282–3294. doi: 10.1111/j.1365-2966.2012.21871.x. Marigo, P. and L. Girardi (July 2007). “Evolution of asymptotic giant branch stars. I. Updated synthetic TP-AGB models and their basic calibration”. In: A&A 469.1, pp. 239–263. doi: 10.1051/0004-6361:20066772. Martin, D. C. et al. (Jan. 2005). “The Galaxy Evolution Explorer: A Space Ultraviolet Survey Mission”. In: ApJL 619.1, pp. L1–L6. doi: 10.1086/426387. Martin, N. F. et al. (Oct. 2013). “The PAndAS View of the Andromeda Satellite System. I. A Bayesian Search for Dwarf Galaxies Using Spatial and Color-Magnitude Information”. In: ApJ 776.2, p. 80. doi: 10.1088/0004-637X/776/2/80. Matteucci, F. and P. Francois (Aug. 1989). “Galactic chemical evolution : abundance gradients of individual elements.” In: MNRAS 239, pp. 885–904. doi: 10.1093/ mnras/239.3.885. Mayer, L. et al. (July 2006). “Simultaneous ram pressure and tidal stripping; how dwarf spheroidals lost their gas”. In: MNRAS 369.3, pp. 1021–1038. doi: 10. 1111/j.1365-2966.2006.10403.x. McClure, R. D. and S. van den Bergh (June 1968). “Five-color intermediate-band photometry of stars, clusters, and galaxies.” In: AJ 73, pp. 313–337. doi: 10. 1086/110634. McCully, C. et al. (Nov. 2018). astropy/astroscrappy: v1.0.5 Zenodo Release. Version v1.0.5. doi: 10.5281/zenodo.1482019. McGaugh, S. S. (Oct. 1991). “H II Region Abundances: Model Oxygen Line Ratios”. In: ApJ 380, p. 140. doi: 10.1086/170569. 195 Mehta, V. et al. (May 2021). “Investigating Clumpy Galaxies in the Sloan Digital Sky Survey Stripe 82 Using the Galaxy Zoo”. In: ApJ 912.1, p. 49. doi: 10. 3847/1538-4357/abed5b. Mendel, J. T. et al. (Aug. 2020). “The Kinematics of Massive Quiescent Galaxies at 1.4 < z < 2.1: Dark Matter Fractions, IMF Variation, and the Relation to Local Early-type Galaxies”. In: ApJ 899.1, p. 87. doi: 10.3847/1538-4357/ab9ffc. Mentz, J. J. et al. (Dec. 2016). “Abundance ratios and IMF slopes in the dwarf elliptical galaxy NGC 1396 with MUSE”. In: MNRAS 463.3, pp. 2819–2838. doi: 10.1093/mnras/stw2129. Milone, A. D. C., A. E. Sansom, and P. Sánchez-Blázquez (June 2011). “Element abundances in the stars of the MILES spectral library: the Mg/Fe ratio”. In: MNRAS 414.2, pp. 1227–1252. doi: 10.1111/j.1365-2966.2011.18457.x. Mintz, A. et al. (Oct. 2024). “A Nonparametric Morphological Analysis of H𝛼 Emission in Bright Dwarfs Using the Merian Survey”. In: ApJ 974.2, p. 273. doi: 10.3847/1538-4357/ad6861. Miranda, H. et al. (Feb. 2025). “Importance of modelling the nebular continuum in galaxy spectra”. In: A&A 694, A102. doi: 10.1051/0004-6361/202451648. Morishita, T. et al. (Mar. 2018). “Metal Deficiency in Two Massive Dead Galaxies at z ∼ 2”. In: ApJL 856.1, p. L4. doi: 10.3847/2041-8213/aab493. Morrissey, P. et al. (Sept. 2018). “The Keck Cosmic Web Imager Integral Field Spectrograph”. In: ApJ 864.1, p. 93. doi: 10.3847/1538-4357/aad597. Murray, N., E. Quataert, and T. A. Thompson (Jan. 2005). “On the Maximum Luminosity of Galaxies and Their Central Black Holes: Feedback from Momentumdriven Winds”. In: ApJ 618.2, pp. 569–585. doi: 10.1086/426067. Nagao, T., R. Maiolino, and A. Marconi (Nov. 2006). “Gas metallicity diagnostics in star-forming galaxies”. In: A&A 459.1, pp. 85–101. doi: 10.1051/0004-6361: 20065216. Nanayakkara, T. et al. (Jan. 2022). “Massive high-redshift quiescent galaxies with JWST”. In: PASA 39, e002. doi: 10.1017/pasa.2021.61. Navarro, J. F., C. S. Frenk, and S. D. M. White (Dec. 1997). “A Universal Density Profile from Hierarchical Clustering”. In: ApJ 490.2, pp. 493–508. doi: 10 . 1086/304888. Nersesian, A. et al. (May 2023). “Non-parametric galaxy morphology from stellar and nebular emission with the CALIFA sample”. In: A&A 673, A63. doi: 10. 1051/0004-6361/202345962. Neumann, J. et al. (Dec. 2021). “SDSS-IV MaNGA: drivers of stellar metallicity in nearby galaxies”. In: MNRAS 508.4, pp. 4844–4857. doi: 10.1093/mnras/ stab2868. 196 Newman, A. B. et al. (Aug. 2018). “Resolving Quiescent Galaxies at z ≳ 2. II. Direct Measures of Rotational Support”. In: ApJ 862.2, p. 126. doi: 10.3847/15384357/aacd4f. Newman, J. A. et al. (Sept. 2013). “The DEEP2 Galaxy Redshift Survey: Design, Observations, Data Reduction, and Redshifts”. In: ApJS 208.1, p. 5. doi: 10. 1088/0067-0049/208/1/5. Nicholls, D. C. et al. (Apr. 2017). “Abundance scaling in stars, nebulae and galaxies”. In: MNRAS 466.4, pp. 4403–4422. doi: 10.1093/mnras/stw3235. Nidever, D. L. et al. (Nov. 2014). “Tracing Chemical Evolution over the Extent of the Milky Way’s Disk with APOGEE Red Clump Stars”. In: ApJ 796.1, p. 38. doi: 10.1088/0004-637X/796/1/38. Nightingale, J. W. and S. Dye (Sept. 2015). “Adaptive semi-linear inversion of strong gravitational lens imaging”. In: MNRAS 452.3, pp. 2940–2959. doi: 10.1093/ mnras/stv1455. Nightingale, J. W., S. Dye, and R. J. Massey (2018). “AutoLens: Automated modeling of a strong lens’s light, mass, and source”. In: MNRAS 478.4, pp. 4738–4784. issn: 13652966. doi: 10.1093/mnras/sty1264. Nightingale, J. W., R. G. Hayes, and M. Griffiths (2021). “‘PyAutoFit‘: A Classy Probabilistic Programming Language for Model Composition and Fitting”. In: Journal of Open Source Software 6.58, p. 2550. doi: 10.21105/joss.02550. Nightingale, J. W. et al. (2021). “‘PyAutoLens‘: Open-Source Strong Gravitational Lensing”. In: Journal of Open Source Software 6.58, p. 2825. doi: 10.21105/ joss.02825. Nomoto, K., C. Kobayashi, and N. Tominaga (Aug. 2013). “Nucleosynthesis in Stars and the Chemical Enrichment of Galaxies”. In: ARA&A 51.1, pp. 457–509. doi: 10.1146/annurev-astro-082812-140956. Nomoto, K. et al. (Oct. 2006). “Nucleosynthesis yields of core-collapse supernovae and hypernovae, and galactic chemical evolution”. In: NuPhA 777, pp. 424–458. doi: 10.1016/j.nuclphysa.2006.05.008. O’Donnell, J. E. (Feb. 1994). “R v-dependent Optical and Near-Ultraviolet Extinction”. In: ApJ 422, p. 158. doi: 10.1086/173713. O’Sullivan, D. and Y. Chen (Nov. 2020). “CWITools: A Python3 Data Analysis Pipeline for the Cosmic Web Imager Instruments”. In: arXiv e-prints, arXiv:2011.05444. O’Sullivan, D. B. et al. (May 2020). “The FLASHES Survey. I. Integral Field Spectroscopy of the CGM around 48 z ≃ 2.3-3.1 QSOs”. In: ApJ 894.1, p. 3. doi: 10.3847/1538-4357/ab838c. 197 Oh, K. et al. (Aug. 2011). “Improved and Quality-assessed Emission and Absorption Line Measurements in Sloan Digital Sky Survey Galaxies”. In: ApJS 195.2, p. 13. doi: 10.1088/0067-0049/195/2/13. Onodera, M. et al. (Aug. 2015). “The Ages, Metallicities, and Element Abundance Ratios of Massive Quenched Galaxies at z ≈ 1.6”. In: ApJ 808.2, p. 161. doi: 10.1088/0004-637X/808/2/161. OpenAI (2024). “” In: ChatGPT-4o (May 13 version) [Large Language Model], https://chat.openai.com/chat. Oser, L. et al. (Dec. 2010). “The Two Phases of Galaxy Formation”. In: ApJ 725.2, pp. 2312–2323. doi: 10.1088/0004-637X/725/2/2312. Osterbrock, D. E. and G. J. Ferland (2006). Astrophysics of gaseous nebulae and active galactic nuclei. Oyarzún, G. A. et al. (Aug. 2019). “Signatures of Stellar Accretion in MaNGA Earlytype Galaxies”. In: ApJ 880.2, p. 111. doi: 10.3847/1538-4357/ab297c. Panter, B. et al. (Dec. 2008). “The cosmic evolution of metallicity from the SDSS fossil record”. In: MNRAS 391.3, pp. 1117–1126. doi: 10 . 1111 / j . 1365 2966.2008.13981.x. Peng, Y., R. Maiolino, and R. Cochrane (May 2015). “Strangulation as the primary mechanism for shutting down star formation in galaxies”. In: Nature 521.7551, pp. 192–195. doi: 10.1038/nature14439. Petrosian, V. (Dec. 1976). “Surface Brightness and Evolution of Galaxies”. In: ApJL 210, p. L53. doi: 10.1086/18230110.1086/182253. Pettini, M. and B. E. J. Pagel (Mar. 2004). “[OIII]/[NII] as an abundance indicator at high redshift”. In: MNRAS 348.3, pp. L59–L63. doi: 10 . 1111 / j . 1365 2966.2004.07591.x. Pietrinferni, A. et al. (Sept. 2004). “A Large Stellar Evolution Database for Population Synthesis Studies. I. Scaled Solar Models and Isochrones”. In: ApJ 612.1, pp. 168–190. doi: 10.1086/422498. Pilyugin, L. S. and E. K. Grebel (Apr. 2016). “New calibrations for abundance determinations in H II regions”. In: MNRAS 457.4, pp. 3678–3692. doi: 10 . 1093/mnras/stw238. Pilyugin, L. S., E. K. Grebel, and L. Mattsson (Aug. 2012). “’Counterpart’ method for abundance determinations in H II regions”. In: MNRAS 424.3, pp. 2316–2329. doi: 10.1111/j.1365-2966.2012.21398.x. Pilyugin, L. S. et al. (May 2018). “Validity of abundances derived from spaxel spectra of the MaNGA survey”. In: A&A 613, A1. doi: 10.1051/0004-6361/ 201732185. 198 Pilyugin, L. S. and T. X. Thuan (Sept. 2005). “Oxygen Abundance Determination in H II Regions: The Strong Line Intensities-Abundance Calibration Revisited”. In: ApJ 631.1, pp. 231–243. doi: 10.1086/432408. Prochaska, J. X. et al. (2020). “PypeIt: The Python Spectroscopic Data Reduction Pipeline”. In: Journal of Open Source Software 5.56, p. 2308. doi: 10.21105/ joss.02308. Prochaska, J. X. et al. (Apr. 2020). pypeit/PypeIt: Release 1.0.0. Version v1.0.0. doi: 10.5281/zenodo.3743493. Prusinski, N. Z. and Y. Chen (Apr. 2024). KCWIKit: KCWI Post-Processing and Improvements. Astrophysics Source Code Library, record ascl:2404.003. Revaz, Y. and P. Jablonka (Aug. 2018). “Pushing back the limits: detailed properties of dwarf galaxies in a ΛCDM universe”. In: A&A 616, A96. doi: 10.1051/00046361/201832669. Román, J., A. Castilla, and J. Pascual-Granado (Dec. 2021). “Discovery and analysis of low-surface-brightness galaxies in the environment of NGC 1052”. In: A&A 656, A44. doi: 10.1051/0004-6361/202142161. Ruiz-Lara, T. et al. (Sept. 2018). “Integrated-light analyses vs. colour-magnitude diagrams. II. Leo A: an extremely young dwarf in the Local Group”. In: A&A 617, A18. doi: 10.1051/0004-6361/201732398. Salim, S., M. Boquien, and J. C. Lee (May 2018). “Dust Attenuation Curves in the Local Universe: Demographics and New Laws for Star-forming Galaxies and High-redshift Analogs”. In: ApJ 859.1, p. 11. doi: 10 . 3847 / 1538 - 4357 / aabf3c. Salim, S. et al. (Dec. 2007). “UV Star Formation Rates in the Local Universe”. In: ApJS 173.2, pp. 267–292. doi: 10.1086/519218. Salim, S. et al. (Nov. 2016). “GALEX-SDSS-WISE Legacy Catalog (GSWLC): Star Formation Rates, Stellar Masses, and Dust Attenuations of 700,000 Low-redshift Galaxies”. In: ApJS 227.1, p. 2. doi: 10.3847/0067-0049/227/1/2. Sánchez, S. F. et al. (Feb. 2012). “CALIFA, the Calar Alto Legacy Integral Field Area survey. I. Survey presentation”. In: A&A 538, A8. doi: 10.1051/00046361/201117353. Sánchez, S. F. et al. (June 2013). “Mass-metallicity relation explored with CALIFA. I. Is there a dependence on the star-formation rate?” In: A&A 554, A58. doi: 10.1051/0004-6361/201220669. Sánchez-Blázquez, P. et al. (Sept. 2006). “Medium-resolution Isaac Newton Telescope library of empirical spectra”. In: MNRAS 371.2, pp. 703–718. doi: 10. 1111/j.1365-2966.2006.10699.x. 199 Sanders, R. L. et al. (Dec. 2017). “Biases in Metallicity Measurements from Global Galaxy Spectra: The Effects of Flux Weighting and Diffuse Ionized Gas Contamination”. In: ApJ 850.2, p. 136. doi: 10.3847/1538-4357/aa93e4. Sanders, R. L. et al. (Jan. 2020). “The MOSDEF survey: direct-method metallicities and ISM conditions at z ∼ 1.5-3.5”. In: MNRAS 491.1, pp. 1427–1455. doi: 10.1093/mnras/stz3032. Sanders, R. L. et al. (June 2021). “The MOSDEF Survey: The Evolution of the Mass-Metallicity Relation from z = 0 to z 3.3”. In: ApJ 914.1, p. 19. doi: 10. 3847/1538-4357/abf4c1. Sarzi, M. et al. (Mar. 2006). “The SAURON project - V. Integral-field emission-line kinematics of 48 elliptical and lenticular galaxies”. In: MNRAS 366.4, pp. 1151– 1200. doi: 10.1111/j.1365-2966.2005.09839.x. Schlafly, E. F. and D. P. Finkbeiner (Aug. 2011). “Measuring Reddening with Sloan Digital Sky Survey Stellar Spectra and Recalibrating SFD”. In: ApJ 737.2, p. 103. doi: 10.1088/0004-637X/737/2/103. Shajib, A. J. et al. (Oct. 2022). “LensingETC: A Tool to Optimize Multifilter Imaging Campaigns of Galaxy-scale Strong Lensing Systems”. In: ApJ 938.2, p. 141. doi: 10.3847/1538-4357/ac927b. Shajib, A. J. et al. (Oct. 2022). LensingETC: Lensing Exposure Time Calculator. Astrophysics Source Code Library, record ascl:2210.027. Shibuya, T. et al. (Apr. 2016). “Morphologies of ~190,000 Galaxies at z = 0-10 Revealed with HST Legacy Data. II. Evolution of Clumpy Galaxies”. In: ApJ 821.2, p. 72. doi: 10.3847/0004-637X/821/2/72. Siegel, M. H. et al. (Sept. 2007). “The ACS Survey of Galactic Globular Clusters: M54 and Young Populations in the Sagittarius Dwarf Spheroidal Galaxy”. In: ApJL 667.1, pp. L57–L60. doi: 10.1086/522003. Skrutskie, M. F. et al. (Feb. 2006). “The Two Micron All Sky Survey (2MASS)”. In: AJ 131.2, pp. 1163–1183. doi: 10.1086/498708. Soderblom, D. R. (Sept. 2010). “The Ages of Stars”. In: ARA&A 48, pp. 581–629. doi: 10.1146/annurev-astro-081309-130806. Soto, K. T. et al. (May 2016). “ZAP - enhanced PCA sky subtraction for integral field spectroscopy”. In: MNRAS 458.3, pp. 3210–3220. doi: 10.1093/mnras/ stw474. Speagle, J. S. (Apr. 2020). “DYNESTY: a dynamic nested sampling package for estimating Bayesian posteriors and evidences”. In: MNRAS 493.3, pp. 3132– 3158. doi: 10.1093/mnras/staa278. Steidel, C. C. et al. (Nov. 2014). “Strong Nebular Line Ratios in the Spectra of z ~2-3 Star Forming Galaxies: First Results from KBSS-MOSFIRE”. In: ApJ 795.2, p. 165. doi: 10.1088/0004-637X/795/2/165. 200 Steidel, C. C. et al. (Aug. 2016). “Reconciling the Stellar and Nebular Spectra of High-redshift Galaxies”. In: ApJ 826.2, p. 159. doi: 10.3847/0004-637X/826/ 2/159. Strom, A. L. et al. (Feb. 2017). “Nebular Emission Line Ratios in z ≃ 2-3 Starforming Galaxies with KBSS-MOSFIRE: Exploring the Impact of Ionization, Excitation, and Nitrogen-to-Oxygen Ratio”. In: ApJ 836.2, p. 164. doi: 10 . 3847/1538-4357/836/2/164. Strom, A. L. et al. (Dec. 2018). “Measuring the Physical Conditions in High-redshift Star-forming Galaxies: Insights from KBSS-MOSFIRE”. In: ApJ 868.2, p. 117. doi: 10.3847/1538-4357/aae1a5. Strom, A. L. et al. (Feb. 2022). “Chemical Abundance Scaling Relations for Multiple Elements in z ≃ 2-3 Star-forming Galaxies”. In: ApJ 925.2, p. 116. doi: 10.3847/ 1538-4357/ac38a3. Strom, A. L. et al. (Nov. 2023). “CECILIA: The Faint Emission Line Spectrum of z 2-3 Star-forming Galaxies”. In: ApJL 958.1, p. L11. doi: 10 . 3847 / 2041 8213/ad07dc. Sukay, E. et al. (Mar. 2022). “COOL-LAMPS II. Characterizing the Size and Star Formation History of a Bright Strongly Lensed Early-Type Galaxy at Redshift 1.02”. In: arXiv e-prints, arXiv:2203.11957. Sybilska, A. et al. (Sept. 2017). “The hELENa project - I. Stellar populations of early-type galaxies linked with local environment and galaxy mass”. In: MNRAS 470.1, pp. 815–838. doi: 10.1093/mnras/stx1138. Thomas, D., C. Maraston, and R. Bender (July 2003). “New clues on the calcium underabundance in early-type galaxies”. In: MNRAS 343.1, pp. 279–283. doi: 10.1046/j.1365-8711.2003.06659.x. Thomas, D. et al. (Mar. 2005). “The Epochs of Early-Type Galaxy Formation as a Function of Environment”. In: ApJ 621.2, pp. 673–694. doi: 10.1086/426932. Thomas, D. et al. (June 2010). “Environment and self-regulation in galaxy formation”. In: MNRAS 404.4, pp. 1775–1789. doi: 10.1111/j.1365-2966.2010. 16427.x. Tinsley, B. M. (Jan. 1980). “Evolution of the Stars and Gas in Galaxies”. In: FCPh 5, pp. 287–388. doi: 10.48550/arXiv.2203.02041. Toft, S. et al. (July 2012). “Deep Absorption Line Studies of Quiescent Galaxies at z ~2: The Dynamical-mass-Size Relation and First Constraints on the Fundamental Plane”. In: ApJ 754.1, p. 3. doi: 10.1088/0004-637X/754/1/3. Tomczak, A. R. et al. (Mar. 2014). “Galaxy Stellar Mass Functions from ZFOURGE/CANDELS: An Excess of Low-mass Galaxies since z = 2 and the Rapid Buildup of Quiescent Galaxies”. In: ApJ 783.2, p. 85. doi: 10.1088/0004637X/783/2/85. 201 Topping, M. W. et al. (July 2020). “The MOSDEF-LRIS Survey: the interplay between massive stars and ionized gas in high-redshift star-forming galaxies”. In: MNRAS 495.4, pp. 4430–4444. doi: 10.1093/mnras/staa1410. Torrey, P. et al. (Apr. 2019). “The evolution of the mass-metallicity relation and its scatter in IllustrisTNG”. In: MNRAS 484.4, pp. 5587–5607. doi: 10.1093/ mnras/stz243. Tran, K.-V. H. et al. (Oct. 2022). “The AGEL Survey: Spectroscopic Confirmation of Strong Gravitational Lenses in the DES and DECaLS Fields Selected Using Convolutional Neural Networks”. In: AJ 164.4, p. 148. doi: 10.3847/15383881/ac7da2. Tremonti, C. A. et al. (Oct. 2004). “The Origin of the Mass-Metallicity Relation: Insights from 53,000 Star-forming Galaxies in the Sloan Digital Sky Survey”. In: ApJ 613.2, pp. 898–913. doi: 10.1086/423264. Trussler, J. et al. (Feb. 2020). “Both starvation and outflows drive galaxy quenching”. In: MNRAS 491.4, pp. 5406–5434. doi: 10.1093/mnras/stz3286. Vale Asari, N. et al. (Nov. 2019). “Diffuse ionized gas and its effects on nebular metallicity estimates of star-forming galaxies”. In: MNRAS 489.4, pp. 4721–4733. doi: 10.1093/mnras/stz2470. Vargas, L. C., M. C. Geha, and E. J. Tollerud (July 2014). “The Distribution of Alpha Elements in Andromeda Dwarf Galaxies”. In: ApJ 790.1, p. 73. doi: 10.1088/0004-637X/790/1/73. Vaughan, S. P. et al. (Oct. 2022). “The SAMI galaxy survey: Galaxy size can explain the offset between star-forming and passive galaxies in the mass-metallicity relationship”. In: MNRAS 516.2, pp. 2971–2987. doi: 10.1093/mnras/stac2304. Vazdekis, A. et al. (May 2015). “Evolutionary stellar population synthesis with MILES - II. Scaled-solar and 𝛼-enhanced models”. In: MNRAS 449.2, pp. 1177– 1214. doi: 10.1093/mnras/stv151. Vazdekis, A. et al. (Dec. 2016). “UV-extended E-MILES stellar population models: young components in massive early-type galaxies”. In: MNRAS 463.4, pp. 3409– 3436. doi: 10.1093/mnras/stw2231. Veilleux, S., G. Cecil, and J. Bland-Hawthorn (Sept. 2005). “Galactic Winds”. In: ARA&A 43.1, pp. 769–826. doi: 10 . 1146 / annurev . astro . 43 . 072103 . 150610. Villaume, A. et al. (June 2017). “The Extended IRTF Spectral Library: Expanded Coverage in Metallicity, Temperature, and Surface Gravity”. In: ApJS 230.2, p. 23. doi: 10.3847/1538-4365/aa72ed. Walcher, C. J. et al. (Oct. 2015). “Abundance patterns in early-type galaxies: is there a “knee” in the [Fe/H] vs. [𝛼/Fe] relation?” In: A&A 582, A46. doi: 10.1051/ 0004-6361/201525924. 202 Weinberger, R. et al. (Sept. 2018). “Supermassive black holes and their feedback effects in the IllustrisTNG simulation”. In: MNRAS 479.3, pp. 4056–4072. doi: 10.1093/mnras/sty1733. Weisz, D. R. et al. (July 2014). “The Star Formation Histories of Local Group Dwarf Galaxies. I. Hubble Space Telescope/Wide Field Planetary Camera 2 Observations”. In: ApJ 789.2, p. 147. doi: 10.1088/0004-637X/789/2/147. Westfall, K. B. et al. (Dec. 2019). “The Data Analysis Pipeline for the SDSS-IV MaNGA IFU Galaxy Survey: Overview”. In: AJ 158.6, p. 231. doi: 10.3847/ 1538-3881/ab44a2. Wright, E. L. et al. (Dec. 2010). “The Wide-field Infrared Survey Explorer (WISE): Mission Description and Initial On-orbit Performance”. In: AJ 140.6, pp. 1868– 1881. doi: 10.1088/0004-6256/140/6/1868. Yates, R. M. et al. (Feb. 2020). “Present-day mass-metallicity relation for galaxies using a new electron temperature method”. In: A&A 634, A107. doi: 10.1051/ 0004-6361/201936506. York, D. G. et al. (Sept. 2000). “The Sloan Digital Sky Survey: Technical Summary”. In: AJ 120.3, pp. 1579–1587. doi: 10.1086/301513. Young, L. M. and K. Y. Lo (Feb. 1997). “The Neutral Interstellar Medium in Nearby Dwarf Galaxies. II. NGC 185, NGC 205, and NGC 147”. In: ApJ 476.1, pp. 127– 143. doi: 10.1086/303618. Zahid, H. J. et al. (July 2013). “The Chemical Evolution of Star-forming Galaxies over the Last 11 Billion Years”. In: ApJL 771.2, p. L19. doi: 10.1088/20418205/771/2/L19. Zahid, H. J. et al. (Sept. 2017). “Stellar Absorption Line Analysis of Local Starforming Galaxies: The Relation between Stellar Mass, Metallicity, Dust Attenuation, and Star Formation Rate”. In: ApJ 847.1, p. 18. doi: 10.3847/15384357/aa88ae. Zhang, K. et al. (Apr. 2017). “SDSS-IV MaNGA: the impact of diffuse ionized gas on emission-line ratios, interpretation of diagnostic diagrams and gas metallicity measurements”. In: MNRAS 466.3, pp. 3217–3243. doi: 10 . 1093 / mnras / stw3308. Zhuang, Z. et al. (Oct. 2021). “NGC 147 Corroborates the Break in the Stellar Mass-Stellar Metallicity Relation for Galaxies”. In: ApJ 920.1, p. 63. doi: 10. 3847/1538-4357/ac1340. Zhuang, Z. et al. (May 2023). “A Glimpse of the Stellar Populations and Elemental Abundances of Gravitationally Lensed, Quiescent Galaxies at z ≳ 1 with Keck Deep Spectroscopy”. In: ApJ 948.2, p. 132. doi: 10.3847/1538-4357/acc79b. Zhuang, Z. et al. (Sept. 2024). “Metals in Star-forming Galaxies with KCWI. I. Methodology and First Results on the Abundances of Iron, Magnesium, and Oxygen”. In: ApJ 972.2, p. 182. doi: 10.3847/1538-4357/ad5ff8. 203 Zibetti, S. et al. (Jan. 2020). “Insights into formation scenarios of massive earlytype galaxies from spatially resolved stellar population analysis in CALIFA”. In: MNRAS 491.3, pp. 3562–3585. doi: 10.1093/mnras/stz3205.