STELLAR MULTIPLICITY ANALYSIS WITH TIME-RESOLVED SPECTROSCOPY AND MARKOV CHAIN MONTE CARLO SIMULATIONS By Thomas Barrett Hettinger A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Astrophysics and Astronomy | Doctor of Philosophy 2015 ABSTRACT STELLAR MULTIPLICITY ANALYSIS WITH TIME-RESOLVED SPECTROSCOPY AND MARKOV CHAIN MONTE CARLO SIMULATIONS By Thomas Barrett Hettinger This dissertation examines the multiplicity properties of stars in the Milky Way and their relationship with metallicity. We present methods and techniques for data mining individual, raw, sub-exposure information from spectroscopic surveys as a statistical approach to per- forming scientific analyses in this era of Big Data. We also describe how Bayesian inference and Markov Chain Monte Carlo simulations work in conjunction with these sub-exposure spectroscopy techniques. Binary interactions play a key role in many astrophysical processes, from altering surfaces abundances, to producing supernova. In Chapter 1, we give a brief introduction to stellar multiplicity, beginning with a description of the star formation process and possible scenarios for binary star formation. We discuss how binary stars interact through Roche-lobe overflow, and how binary systems lead to various astrophysical phenomena. We conclude the chapter with a look at our current understanding of multiplicity properties of stars in the Milky Way as determined empirically from observations and surveys, and with a discussion for the future outlook of multiplicity studies. In Chapter 2 we describe a methodology for measuring radial velocity variations in stellar sources using sub-exposure spectra from multi-fiber spectroscopic surveys. In particular, we describe a cross-correlation technique used on spectra that were observed as part of the SDSS survey. In Chapter 3 we give a brief introduction to Bayesian inference and the use of the MCMC python package emcee. We describe the methods used for detecting binarity in stellar sources from sparsely sampled radial velocity curves. Chapter 4 contains the peer-reviewed article Hettinger et al. (2015) published in the Astrophysical Journal Letters. In this Letter, we employ the sub-exposure radial velocity measurement techniques and the MCMC methods outlined in this dissertation to examine a population of F-type dwarf stars in the Milky Way. The sample was divided into three groups by metallicity, with the goal of investigating the metallicity dependence on multiplic- ity properties. We find a higher fraction of short-period binaries for the metal-rich disk stars than the metal-poor halo stars. Finally, in Chapter 5, we extend the work of Hettinger et al. (2015) to investigate possible constraints on the separation distribution of binaries in the F-dwarf population. For my mother, Rita Murray. iv ACKNOWLEDGMENTS Firstly, I would like to express my sincere gratitude to my advisors and collaborators, Carles Badenes, Jay Strader, Timothy Beers, and Steven Bickerton, for their continuous support, motivation, and immense knowledge. I especially thank Carles for taking me on as his own student, and committing to work with me remotely across universities. His guidance was invaluable, and I am thankful to have had him as my advisor. To my wife, Mengling Hettinger, I am deeply grateful. As a colleague, she provided me with direction, focus, and confidence. Her tutoring in my course work and her support were crucial to my success. I could not have chosen a better partner to share the rest of my life experiences with. I love you Mengling. I would like to thank my senior graduate students, Charles Kuehn, Chris Richardson, Carolyn Peruta, and Aaron Hoffer for their advice; my office mates Alex Deibel, Brian Crosby, Tom Connor, and Ryan Connolly for their help with brainstorming and for my addiction to coffee; and I would like to thank coffee. For their work in outreach and community service, I thank John French, Shane Horvatin, and Dave Batch at the Abrams Planetarium, as well as Horace Smith and Laura Chomiuk for their work with public events at the telescope. I am grateful to the NSF, NASA, and the DoE for funding the majority of all astrophysics research. Astronomy is the least applicable of the sciences, but it asks the biggest questions. We are fortunate enough to have the capacity to ask these questions, therefore we must. I thank all my family and friends for their continuing support and encouragement. Finally, I want to thank Jason Linehan for introducing me to the night sky, without whom I would never have pursued astronomy. v TABLE OF CONTENTS LIST OF TABLES .................................... viii LIST OF FIGURES ................................... ix Chapter 1 A Brief Introduction to Stellar Multiplicity ............ 1 1.1 Introduction . 1 1.2 Star Formation and the Origin of Binary Stars . 2 1.2.1 Physical Principles . 2 1.2.2 Possible Binary Formation Mechanisms . 6 1.2.2.1 Capture . 6 1.2.2.2 Prompt Fragmentation . 6 1.2.2.3 Delayed Break-up . 7 1.2.3 Questions and Future Investigation . 8 1.3 Binary Evolution and Interactions . 10 1.3.1 Principles of the Evolution of Binary Systems . 10 1.3.2 Binary Interaction in Astrophysical Phenomena . 12 1.3.2.1 Hot Subdwarfs . 13 1.3.2.2 Chemically Peculiar Stars . 13 1.3.2.3 Symbiotic Binaries . 14 1.3.2.4 Blue Stragglers . 14 1.3.2.5 Thermonuclear Supernovae . 15 1.3.2.6 Core Collapse Supernovae . 15 1.4 Empirically Derived Multiplicity Properties . 16 1.4.1 Multiplicity Properties and Survey Methodology . 16 1.4.2 Trends and Characteristics of Multiple-Star Systems . 18 1.4.2.1 Multiplicity and Mass . 18 1.4.2.2 Multiplicity and Age . 22 1.4.3 Discussion . 23 1.5 Conclusion . 26 Chapter 2 Time-Resolved Spectroscopy ..................... 28 2.1 Introduction . 28 2.2 The Sloan Digital Sky Survey . 30 2.2.1 Sub-Exposures . 31 2.2.2 SEGUE Stellar Parameter Pipeline And Sample Selection . 32 2.2.3 Plate Systematics . 34 2.3 Radial Velocities . 41 2.3.1 Continuum Normalization . 41 2.3.2 Spectral Template . 44 vi 2.3.3 Cross-Correlations . 45 2.4 Empirical Uncertainties . 48 2.5 e=i Variability . 53 2.6 Discussion . 53 Chapter 3 Markov Chain Monte Carlo ...................... 55 3.1 Introduction . 55 3.2 Bayesian Inference and MCMC . 56 3.3 emcee: The MCMC Hammer . 57 3.3.1 An Affine-Invariant Ensemble Sampler . 57 3.3.2 Using emcee ................................ 58 3.4 Correcting Systematics in SDSS Spectra . 63 3.5 Modeling Multiplicity With Radial Velocity Curves . 64 3.5.1 Examples . 68 Chapter 4 Statistical Time-Resolved Spectroscopy: A Higher Fraction of Short-Period Binaries for Metal-Rich F-type Dwarfs in SDSS 77 4.1 Abstract . 77 4.2 Introduction . 78 4.3 Measurements . 80 4.3.1 SDSS Observations and Sample Selection . 80 4.3.2 Radial Velocities . 82 4.3.3 Uncertainties . 83 4.4 Multiplicity . 84 4.5 Discussion . 89 Chapter 5 Binary Fractions and Separation Distributions .......... 92 5.1 Introduction . 92 5.2 MCMC and Population-Wide Monte Carlo . 93 5.3 Discussion . 100 REFERENCES ...................................... 103 vii LIST OF TABLES Table 2.1 Suspect Plates in SDSS . 39 Table 2.2 Absorption Features in F-dwarfs . 42 Table 3.1 Prior Limits for Hettinger et al. (2015) MCMC . 67 viii LIST OF FIGURES Figure 1.1 Dependency of multiplicity fraction with primary mass for main se- quence stars and VLM objects. Values used from the review by Duch^ene& Kraus (2013). 21 Figure 1.2 Left: Orbital period distribution in the solar neighborhood from Raghavan et al. (2010). The limit for RLOF in the MS is indicated by the black vertical dashed line, and the range corresponding to pre-CE systems is shaded in gray. The best-fit log-normal function is shown in black. The dashed red plot represents a modified function that also fits the data. Right: Comparing the number of systems in the best-fit log-normal distribution (solid black) and the modified model (dashed red). The period ranges corresponding to low-mass X- ray binary progenitors, stable habitable planets around binary stars, and SN Ia progenitors are shown with horizontal rulers. The yellow dash-dotted line marks the pre-outburst period of V1309 Sco. 25 Figure 2.1 Distribution of the number of sub-exposures (top) and the time lags (bottom) for the F-dwarf stars from the Hettinger et al. (2015) sam- ple. Metallicity cutoff values are [Fe=H] = −1:43 and [Fe=H] = −0:66. 33 Figure 2.2 Distribution of stellar parameters for the F-dwarf stars from the Het- tinger et al. (2015) sample, including metallicity (top), effective tem- perature (middle), and surface gravity (bottom). Metallicity cutoff values are [Fe=H] = −1:43 and [Fe=H] = −0:66. 35 Figure 2.3 Scatter plot showing the distribution of metallicity and surface grav- ity for F-type stars in the SSPP DR9. The bimodal distribution of [Fe=H] traces the Halo and Disk components of the Milky Way. 36 Figure 2.4 RVs for F-dwarf stars located on plate plugging 2085-53379 before and after correcting the plate for systematic sub-exposure offsets. Red points are sub-exposures that have low SNR. Fiber IDs are given for each fiber on the right axis. Sub-exposures in the plate are ordered chronologically. Corrections to systematic offsets are successful on this plate. 38 Figure 2.5 Distribution of 10,264 systematic RV offsets estimated for all plate sub-exposures in the F-dwarf sample. 39 ix Figure 2.6 Same as Figure 2.4 for plate plugging 3002-54844. The left column of each subfigure shows RVs before correcting the plate for systematic offsets, and the right column shows RVs after correcting for offsets.