Tracer Populations in the Local Group This dissertation is submitted for the degree of Doctor of Philosophy by Laura Louise Watkins Institute of Astronomy & Gonville and Caius College University of Cambridge January 31st 2011 For Mum and Dad, who gave me wings so I could fly and a nest to come home to Contents Declaration ix Acknowledgments xi Summary xiii 1 Introduction 1 1.1 Structure formation..................................................3 1.1.1 Dark matter...................................................3 1.1.2 Overview of current structure formation theory.........................4 1.1.3 Overmerging and the missing satellite problem.........................6 1.1.4 Dominance and survivability of structure.............................7 1.2 The Milky Way......................................................8 1.2.1 The bulge....................................................8 1.2.2 The thin disk..................................................9 1.2.3 The thick disk................................................. 10 1.2.4 The halo..................................................... 11 1.3 The Andromeda galaxy................................................ 18 1.4 Dwarf spheroidal galaxies.............................................. 22 1.4.1 Milky Way dwarfs............................................... 22 1.4.2 M31 dwarfs................................................... 23 1.4.3 Comparison with star clusters...................................... 24 1.4.4 Dwarf properties............................................... 26 1.5 Tracer Populations in the Local Group..................................... 28 2 Variable stars in SDSS Stripe 82 31 2.1 The Sloan Digital Sky Survey............................................ 32 2.1.1 SDSS Stripe 82................................................. 34 2.2 Variable Stars in Stripe 82.............................................. 35 2.2.1 Variable Selection............................................... 35 2.2.2 Variable Properties.............................................. 37 2.2.3 The Proper Motions............................................. 38 2.3 Comparison with other variability surveys in Stripe 82......................... 39 2.4 Summary.......................................................... 40 v Contents 3 Substructure revealed by RR Lyraes in SDSS Stripe 82 43 3.1 Overview of RR Lyraes................................................. 43 3.2 Selection of the RR Lyrae sample......................................... 45 3.2.1 Identification of RR Lyraes........................................ 45 3.2.2 RR Lyrae Periods............................................... 46 3.2.3 RR Lyrae Classification........................................... 48 3.2.4 The RRab types................................................ 50 3.2.5 The RRc types................................................. 51 3.3 Substructure revealed by the RR Lyraes.................................... 52 3.3.1 RR Lyrae Distances.............................................. 52 3.3.2 The Sagittarius Stream, the Hercules-Aquila Cloud and the Pisces Overdensity.. 53 3.4 Summary.......................................................... 60 4 Masses of the Milky Way and Andromeda Galaxies 63 4.1 Mass estimators..................................................... 64 4.1.1 Tracer Mass Estimator........................................... 65 4.1.2 A Family of Estimators........................................... 68 4.2 Checks with Monte Carlo Simulations..................................... 70 4.3 Mass Estimates for Andromeda and the Milky Way............................ 72 4.3.1 Choice of Power-Law Index Parameters............................... 72 4.3.2 Radial Velocity Datasets.......................................... 75 4.3.3 Simultaneous Solution for Mass and Anisotropy........................ 81 4.3.4 Radial and Proper Motion Datasets.................................. 82 4.4 Discussion......................................................... 85 4.5 Summary.......................................................... 86 5 Application of the Timing Argument to host-satellite systems 89 5.1 Timing Argument.................................................... 91 5.2 The Data.......................................................... 93 5.3 M31 mass and orbit parameters.......................................... 94 5.3.1 M31 - And XII orbit.............................................. 94 5.3.2 M31 - And XIV orbit............................................. 97 5.4 Modelling.......................................................... 98 5.5 The Milky Way...................................................... 102 5.5.1 MW - Leo I orbit................................................ 102 5.6 Discussion......................................................... 103 6 Discussion & Conclusions 107 6.1 Chapter Summaries.................................................. 107 6.1.1 Variable stars in SDSS Stripe 82..................................... 107 6.1.2 Substructure revealed by RR Lyraes in SDSS Stripe 82..................... 108 6.1.3 Masses of the Milky Way and Andromeda Galaxies....................... 109 6.1.4 Application of the Timing Argument to host-satellite systems............... 111 vi Contents 6.2 Prospects for the Future............................................... 112 6.2.1 The Pisces Overdensity........................................... 112 6.2.2 Surveys...................................................... 113 A Coordinate and velocity calculations 117 A.1 Converting from equatorial to Galactic coordinates........................... 117 A.2 Galactocentric spatial velocities.......................................... 118 A.3 M31-centric spatial velocities........................................... 119 Bibliography 131 Nomenclature 134 List of tables 135 List of figures 138 vii Declaration I hereby declare that my thesis entitled Tracer Populations in the Local Group is not substantially the same as any that I have submitted for a degree or diploma or other qualification at any other University. I further state that no part of my thesis has already been or is being concurrently submitted for any such degree, diploma or other qualification. This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text. Those parts of this thesis which have been published or accepted for publication are as follows: The work presented in Chapters2 and3 has been completed in collaboration with N. W. Evans • and V. Belokurov and is published as: Watkins, L.L. et al (2009) ‘Substructure revealed by RR Lyraes in SDSS Stripe 82’, Monthly Notices of the Royal Astronomical Society, 398, 1757-1770. The work presented in Chapter4 has been completed in collaboration with N. W. Evans and J. • An and is published as: Watkins, L.L., Evans, N.W. & An, J. (2010) ‘The masses of the Milky Way and the Andromeda galaxies’, Monthly Notices of the Royal Astronomical Society, 406, 264-278. This thesis contains fewer than 60,000 words. Laura L. Watkins Cambridge, January 31st 2011 ix Acknowledgments There are so many people to whom I owe my thanks. Firstly, to my supervisors, Wyn Evans and Vasily Belokurov for their support, guidance and pa- tience throughout the course of my PhD - I could not have done any of this without them. To Helen and Sarah, for being the best flatmates I could ever have hoped for. To Martin, for sharing an office with me for four years and for keeping me company in the bur- rito queue. And to Richard, Berkeley, Sarah, Marcus, Shoko and Richard: for their friendship, their company over coffee and numerous pub trips and for making my time at the IoA so special. To everyone in the CDC for giving me the opportunity to dance; especially everyone in CUDT who made my final year so fantastic. And most of all, thank you, Ben, for dancing with me. To Tash, my best friend, for always being there. And last, but my no means least, I would like to thank my family; their unfailing love and support has put me where I am today and I would be nothing without them. Laura L. Watkins Cambridge, January 31st 2011 xi Summary Tracer Populations in the Local Group Laura L. Watkins So often in astronomy, an object is not considered for its individual merits, but for what we may learn from its properties regarding some larger population. The existence of dark matter is a prime example of this; we cannot see it directly but we can infer its presence by noting its effects on the stars orbiting within its potential. This thesis describes how various sets of tracer populations can be used to probe the properties of a variety of galaxies in the Local Group. I begin by describing the extraction of a variable catalogue from the Sloan Digital Sky Survey Stripe 82 dataset and then use the catalogue to select a high-quality set of RR Lyrae stars. Analysing the distribution of the RR Lyraes reveals three significant substructures in the Milky Way halo: the Hercules-Aquila Cloud and the Sagittarius Stream, which were already known to exist, and the Pisces Overdensity, which was previously undetected. It is a faint, extended structure found at 80 kpc ∼ and is of unknown origin. Altogether, I find that nearly 80% of the RR Lyraes are associated with substructures, consistent with the theory that galaxy halos are predominantly, or even entirely, made up from disrupted satellites. I also investigate the density distribution of RR Lyraes in the halo, finding that it is best