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Inferring the Milky Way Mass Profile Using Galactic Satellites And Lights in Dark Places: Inferring the Milky Way Mass Profile using Galactic Satellites and Hierarchical Bayes LIGHTS IN DARK PLACES: INFERRING THE MILKY WAY MASS PROFILE USING GALACTIC SATELLITES AND HIERARCHICAL BAYES BY GWENDOLYN M. EADIE M.Sc., Queen's University (Kingston, ON) B.Sc., Simon Fraser University (Burnaby, BC) a thesis submitted to the department of physics & astronomy and the school of graduate studies of mcmaster university in partial fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY c Copyright by Gwendolyn M. Eadie, August 2017 All Rights Reserved Ph.D. Thesis - Gwendolyn M. Eadie McMaster University - Physics & Astronomy Doctor of Philosophy (2017) McMaster University (Physics & Astronomy) Hamilton, Ontario, Canada TITLE: Lights in Dark Places: Inferring the Milky Way Mass Profile using Galactic Satellites and Hierarchical Bayes AUTHOR: Gwendolyn M. Eadie SUPERVISOR: Dr. William Harris NUMBER OF PAGES: xx, 265 ii Dedicated to my parents Ph.D. Thesis - Gwendolyn M. Eadie McMaster University - Physics & Astronomy iv Ph.D. Thesis - Gwendolyn M. Eadie McMaster University - Physics & Astronomy Abstract Despite valiant effort by astronomers, the mass of the Milky Way (MW) Galaxy is poorly constrained, with estimates varying by a factor of two. A range of techniques have been developed and different types of data have been used to estimate the MW's mass. One of the most promising and popular techniques is to use the velocity and position information of satellite objects orbiting the Galaxy to infer the gravitational potential, and thus the total mass. Using these satellites, or Galactic tracers, presents a number of challenges: 1) much of the tracer velocity data are incomplete (i.e. only line-of-sight velocities have been measured), 2) our position in the Galaxy complicates how we quantify measurement uncertainties of mass estimates, and 3) the amount of available tracer data at large distances, where the dark matter halo dominates, is small. The latter challenge will improve with current and upcoming observational programs such as Gaia and the Large Synoptic Survey Telescope (LSST ), but to properly prepare for these data sets we must overcome the former two. In this thesis work, we have created a hierarchical Bayesian framework to estimate the Galactic mass profile. The method includes incomplete and complete data simultaneously, and incorporates measurement uncertainties through a mea- surement model. The physical model relies on a distribution function for the tracers that allows the tracer and dark matter to have different spatial density v Ph.D. Thesis - Gwendolyn M. Eadie McMaster University - Physics & Astronomy profiles. When the hierarchical Bayesian model is confronted with the kine- matic data from satellites, a posterior distribution is acquired and used to infer the mass and mass profile of the Galaxy. This thesis walks through the incremental steps that led to the development of the hierarchical Bayesian method, and presents MW mass estimates when the method is applied to the MW's globular cluster population. Our best 12 estimate of the MW's virial mass is Mvir = 0:87 (0:67; 1:09)×10 M . We also present preliminary results from a blind test on hydrodynamical, cosmological computer-simulated MW-type galaxies from the McMaster Unbiased Galaxy Simulations. These results suggest our method may be able to reliably recover the virial mass of the Galaxy. vi Ph.D. Thesis - Gwendolyn M. Eadie McMaster University - Physics & Astronomy Co-Authorship Chapters 2, 3, 4, and 5 of this thesis are original research completed and written by myself, Gwendolyn Marie Eadie. The first three of these chapters have been published as peer-reviewed journal articles in The Astrophysical Journal (ApJ), and have been reformatted to meet the McMaster thesis criteria. Chapter 6 is original research by me, in preparation for submission to ApJ. The reference to Chapter 2 is Eadie, G., Harris, W., & Widrow, L. 2015, ApJ, 806, 54, DOI: 10:1088=0004 − 637X=806=1=54. The second and third authors on this publication are my PhD supervisor Dr. William Harris and my MSc supervisor Dr. Lawrence Widrow, respectively. The method that I developed during my MSc degree laid the groundwork for this study, and thus substantial parts of the introduction and theory (Sections 2.1 to 2.2.7) overlap with content in my Masters thesis (Eadie, G. M. 2013, Master's thesis, Queen's University, Kingston, Ontario, Canada). The analysis and results in this paper, including substantial improvements to the method, are original research completed during the first year of my PhD program. The reference for Chapter 3 is Eadie, G., & Harris, W. 2016, ApJ, 829, 108, DOI: 10:3847=0004 − 637X=829=2=108. The second author on this paper is my PhD supervisor Dr. William Harris. The reference for Chapter 4 is Eadie, G. M., Springford, A., & Harris, vii Ph.D. Thesis - Gwendolyn M. Eadie McMaster University - Physics & Astronomy W. E. 2017, ApJ, 835, 167, DOI: 10:3847=1538 − 4357=835=2=167. The sec- ond author on this paper is PhD candidate Aaron Springford from Queen's University, and the third author is my PhD supervisor Dr. William Harris. Aaron Springford helped develop the mathematical and statistical basis for the hierarchical Bayesian method. After publication of this paper, I found a mistake in my interpretation of the globular cluster data, fixed this mistake, re-ran the analysis, and published an erratum Eadie, G. M., Springford, A., & Harris, W. E. 2017, ApJ, 835, 167, DOI: 10:3847=1538 − 4357=aa64db, which is shown in shown in the Appendix. Chapter 5 will have co-authors Dr. Benjamin Keller and Dr. William Harris when it is submitted as an article to ApJ. Academic peer-reviewed papers require context in their introductions, and thus parts of the introductions to the articles may overlap in some content (Chapters 2, 3, and 4). viii Ph.D. Thesis - Gwendolyn M. Eadie McMaster University - Physics & Astronomy Acknowledgements I first want to acknowledge the entire Physics & Astronomy Department| the combined effort of everyone is what makes the department such a positive, inclusive, lively, and responsive place. A sincere thanks to Tina, Cheryl, Rose- mary, and Mara, whose availability, commitment, and kindness are always, deep, and true. The astronomy faculty are also an all-star team; thank you for instilling in me values of hard-work, critical thinking, kindness, humbleness, professionalism, and work-life balance. In particular, thank you Laura, James, and Allison for providing me with valuable guidance and advice these past four years. Bill Harris, you have been an exemplary and excellent PhD supervisor. Thank you for the consistent weekly meetings that kept me on track, for teaching me how to publish papers, for taking a keen interest in my career, for sending me to conferences all over the world, for giving me the freedom to fit figure skating into my schedule, and for generally caring about my well-being. I could not have asked for a better supervisor. (And Gretchen, thank you too!) To my academic siblings, the fellow graduate students with whom I have shared an equivalent experience in both space and time, you have been essential in creating a feeling of community. Thank you. I have been extremely lucky to share this four-year experience alongside so many cool people. I can't start listing names, lest I leave someone out. But I will single you out Gandhali, my officemate for the past four years! You have become a dear friend, and I think I'm going to miss you the most come September. ix Ph.D. Thesis - Gwendolyn M. Eadie McMaster University - Physics & Astronomy Family is not an important thing, it's everything. - Michael J. Fox Thank you Mom and Dad, two strong, well-rounded, interesting, and loving people. Your resilience in life motivates me to be resilient too. Thank you for all the phone chats that cheered me up, and for encouraging my curious mind from a very early age. John, thanks for being an inspiring big brother. If I can be half the astronomer that you are a cellist, then I think I'll have a shot at a Nobel Prize. Colin, you are easily the smartest of the three Eadie kids, and I know a game of chess with you will do damage to my ego. You are always ready to challenge my ideas and perceptions of the physical (and metaphysical?) world, and I thank you for that. Colleen, Doug, Mark, Dianna, and Patrick, (and newest editions to the Springford clan, Stephanie, Harrison, and John), I hope you know how much your love and support has helped me (and Aaron) through graduate school. Aaron, I can't thank you enough for all of your love, support, commitment, advice, and encouragement through graduate school. Thank you for moving to Hamilton so I could pursue a PhD too. You have always encouraged me to do what I want with my life, to choose to be happy, and to not care about what other people think (within reason, haha). Not only are you my husband, my best friend, my personal comedian, and my skating partner, but you are also a chef, a statistician, an academic collaborator, an award-winning homebrewer, and a soon-to-be Doctor of Philosophy. Your wide range of talents leaves me perplexed, and I sure cannot wait to see what you do next. But your love and companionship mean the most to me, it's true, and this thesis would not be complete without me thanking you. THANK YOU ~ x Ph.D. Thesis - Gwendolyn M. Eadie McMaster University - Physics & Astronomy Notation and abbreviations ABC Approximate Bayesian Compuation AJ The Astronomical Journal ApJ The Astrophysical Journal ApJL The Astrophysical Journal Letters ASA American Statistical Association CASCA Canadian Astronomical Society Decl.
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