From Galaxy Clustering to Dark Matter Clustering DISSERTATION Presented in Partial Fulflllment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Jaiyul Yoo ***** The Ohio State University 2007 Dissertation Committee: Approved by Professor David H. Weinberg, Adviser Professor Andrew P. Gould Adviser Astronomy Graduate Program Professor Christopher S. Kochanek ABSTRACT Galaxy clustering measurement has been one of the leading tools in cosmology for estimating a more fundamental quantity, the clustering of the underlying dark matter distribution. With the recent advances in galaxy redshift surveys, and hence dramatic improvement in observational data, the main obstacle to achieving this goal has become the theoretical uncertainty of galaxy bias, the difierence between the galaxy and the matter distributions. The halo occupation distribution (HOD) program has emerged as a powerful tool to overcome the di–culty in inferring dark matter clustering by providing a theoretical framework that describes statistical properties of galaxy populations in individual dark matter halos. Moreover, gravitational lensing depends only on gravity, regardless of whether it is produced by dark or luminous matter, thus providing an observational method to break the degeneracy between the galaxy bias and underlying cosmology. In particular, weak gravitational lensing uses the subtle distortion of background galaxy shapes to measure how foreground lensing matter is statistically distributed, making its method well suited to the HOD description. ii In this thesis, I describe three methods to quantify dark matter clustering based on the HOD framework, making full use of precision measurements of galaxy clustering and weak lensing from recent galaxy redshift surveys. First, using galaxy clustering measurements on small scales, I infer the scale-dependent bias function, which makes it possible to extend the recovery of the primordial matter power spectrum over a large dynamic range, and thereby tighten constraints on cosmological parameters obtainable from the galaxy samples of the Sloan Digital Sky Survey. Second, I develop an analytic model for combining galaxy-galaxy lensing and galaxy clustering to constrain the matter density parameter › and m the matter (cid:176)uctuation amplitude (cid:190) . Finally, I present a novel method to constrain 8 dark energy models using cluster-galaxy weak lensing and apply our method to the planned Dark Energy Survey (DES), forecasting our ability to measure cosmological parameters. Comprehensive analysis of galaxy clustering measurements with these complementary approaches will provide a unique opportunity for a complete description of dark matter clustering. iii dedicated to my parents and little sister iv ACKNOWLEDGMENTS There are many people I would like to thank, and without their help and support I would not be in a position to complete this thesis. I hope that this short acknowledgment be able to describe at least a fraction of their help I have received over the past flve years. I thank Andy Gould. His intensive student-care system quickly led me to completion of several research projects that shaped the early stage of my research ability. I am more grateful to him for the personal conversations with him that helped me believe I can overcome any di–culty. Our collaboration was for one year but his help has never stopped. I thank Jordi Miralda-Escud¶e. He has always been easy to talk to about any kind of problems. His insight and detailed explanation greatly helped me build my ability to tackle any research problem. I am grateful to him for always replying with smiles to all of my questions. I thank Chris Kochanek. His witty and sardonic comments have greatly improved my research ability, and I still remember the time he says, \something is screwy" in my dream and also in reality. He has always welcomed me with incomprehensible and most importantly inaudible jokes, relieving my stress from v scientiflc and personal problems. I am grateful to him for his support and help. I also thank Bob Scherrer. The very flrst project in my graduate study provided me with a starting point for my future research and helped me become confldent in myself, when I was troubled and confused at the flrst year of my arrival at US. Even with a short period of collaboration, he has always been my supporter. I thank the person who has had the most in(cid:176)uence on my scientiflc career, has shown the path, and has believed in my potential from the day one; I would like to express my gratitude to my adviser, David Weinberg. He has been a great mentor who anyone wants to have, whose in(cid:176)uence is not limited to science. I have beneflted a lot over many years just from talking and working with him; his insight and clear explanation tremendously helped me understand research problems at hand. Of course, his active discussion at the Astro Cofiee makes a good example for myself and other students regarding what a good scientist ought to be. Especially, his emphasis on writing has vastly changed my attitude, though it really takes a while to fully appreciate his point as is true for everything he taught me. I am truly grateful to him for his encouragement and patience, which has been the source of my confldence and the nutrition of my research ability. Gerry Newsom showed how the department can operate so smoothly with no strings attached but his strong arm alone. Pat Osmer and Brad Peterson are the flgures of how the department chair should be. I am really grateful for their unique contribution to the department in which I can successfully flnish my degree. vi I would like to thank Scott Gaudi, Paul Martini, and Kris Stanek for the stimulating discussions and also the personal guidance arising from their own experience, which has been of signiflcant value to me. It has been a great pleasure to talk with my colleagues, Zheng Zheng, Jeremy Tinker, and Juna Kollmeier. I have beneflted a lot from discussing research projects and daily astro-ph with them. They also greatly helped me as a role model during my graduate years. I thank Deokkeun An for conversations on various topics that made my life less stressful, and I also thank my o–cemates, Misty Bentz, Kelly Denney, Stephan Frank, Linda Watson, and Matthias Dietrich for enjoyable discussions and stories. Finally, I would like to express my heartfelt gratitude to my parents and little sister for their everlasting support and belief, without which all my achievement would have not been possible and, more importantly, would have no meaning to me. vii VITA September 4, 1975 ............. Born { Seoul, Korea 1998 ........................... B.S. Astronomy, Seoul National University 2002 { 2003 .................... Graduate Fellow, The Ohio State University 2003 { 2006 .................... Graduate Teaching and Research Associate, The Ohio State University 2006 { 2007..................... Presidential Fellow, The Ohio State University PUBLICATIONS Research Publications 1. J. Yoo, H.-W. Lee, and S.-H. Ahn, \Proflles of the Resonance Doublets Formed in Bipolar Winds in Symbiotic Stars", MNRAS, 334, 974, (2002). 2. J. Yoo, J.-Y. Bak, and H.-W. Lee, \Polarization of the Broad Hfi Wing in Symbiotic Stars", MNRAS, 336, 467, (2002). 3. J. Yoo and R. J. Scherrer, \BBN and CMB Constraints on the Time Variation of the Higgs Vacuum Expectation Value", PRD, 67, 043517, (2003). 4. J. Yoo, J. Chanam¶e, and A. Gould, \The End of the MACHO Era: Limits on Halo Dark Matter from Stellar Halo Wide Binaries", ApJ, 601, 311, (2004). 5. J. Yoo, et al. (19 authors) \OGLE-2003-BLG-262: Finite-Source Efiects from a Point-Mass Lens", ApJ, 603, 139, (2004). viii 6. J. Yoo and J. Miralda-Escud¶e, \Formation of the Black Holes in the Highest Redshift Quasars", ApJ, 614, 25L, (2004). 7. J. Yoo, et al. (19 authors) \Constraints on Planetary Companions in the Magniflcation A=256 Microlensing Event: OGLE-2003-BLG-423", ApJ, 616, 1204, (2004). 8. J. Yoo, C. S. Kochanek, E. E. Falco, and B. A. McLeod, \The Lens Galaxy in PG1115+080 is an Ellipse", ApJ, 626, 51, (2005). 9. J. Yoo, C. S. Kochanek, E. E. Falco, and B. A. McLeod, \Halo Structures of Gravitational Lens Galaxies", ApJ, 642, 22, (2006). 10. J. Yoo, J. L. Tinker, D. H. Weinberg, Z. Zheng, N. Katz, and R. Dav¶e, \From Galaxy-Galaxy Lensing to Cosmological Parameters", ApJ, 652, 26, (2006). 11. M. Tegmark, (67 authors, incl. J. Yoo) \Cosmological Constraints from the SDSS Luminous Red Galaxies", PRD, 74, 123507, (2006). 12. J. Yoo, J. Miralda-Escud¶e, D. H. Weinberg, Z. Zheng, and C. W. Morgan, \The Most Massive Black Holes in the Universe: Efiects of Mergers in Massive Galaxy Clusters", ApJ, in press FIELDS OF STUDY Major Field: Astronomy ix Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Chapter 1 Galaxy Clustering and Dark Matter Clustering : : : : : : 1 1.1 Primordial Matter Power Spectrum . . . . . . . . . . . . . . . . . . . 4 1.2 Galaxy Clustering and Galaxy-Galaxy Lensing . . . . . . . . . . . . . 6 1.3 Dark Energy and Cluster-Galaxy Weak Lensing . . . . . . . . . . . . 7 Chapter 2 Extending Recovery of the Primordial Matter Power Spectrum : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Calculational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.1 Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2.2 Analytic Model . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.3 Redshift-Space Multipoles . . . . . . . . . . . . . . . . . . . . 22 2.3 Recovering the Real-Space Galaxy Power Spectrum . . . . . . . . . . 25 2.4 Recovering Linear Matter Power Spectrum . . . . . . . . . . . . . . . 30 x