The Formation and Survival of Disk Galaxies by James E. Taylor B.Sc., University of Toronto, 1993 M.Sc., University of Toronto, 1994 A Thesis submitted in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY in the DEPARTMENT OP PHYSICS AND ASTRONOMY We accept this thesis as conforming to the required standard Dr.^.^^hbul, Supervisor (Department of Physics and Astronomy) Dr. ujfUNavarro, Departmental Member (Department of Physics and Astronomy) Dr. ^fH ^w ick, Department Member (Department of Physics and Astronomy) Dr. T. Dingle, Outside Mem%r (Department of Chemistry) Dr. T. Quinn, External Examiner (Department of Astronomy, University of Washington) © James E. Taylor, August 20, 2001 UNIVERSITY OF VICTORIA All rights reserved. This thesis may not be reproduced in whole or in part, by photocopy or other means, without the permission of the author. 11 Supervisor: Dr. A. Babul Abstract The dynamical evolution of substructure within dark matter halos is of central importance in determining many aspects of galaxy formation and galaxy evolution in cold dark matter cosmologies. The overall sequence in which the different stellar components of galaxies are assembled, the survival of galactic disks, the number of dwarf satellites orbiting giant galaxies, and the nature of stellar material in galactic halos all depend on the dynamics of halo substructure. In this thesis, I develop an analytic description of the evolution of substructure within a dark matter halo, and use it to construct a semi-analytic model of the formation and evolution of disk galaxies. Substructure within an individual halo is modelled as a set of distinct sub­ halos, orbiting in a smooth background. These subhalos evolve through three main processes: dynamical friction, tidal mass loss, and tidal heat­ ing. By including analytic descriptions of these three processes explicitly in a simple orbital integration scheme, it is possible to reproduce the results of high-resolution numerical simulations at a fraction of the com­ putational expense. The properties of a subhalo can be estimated with an accuracy of 20%, until it has lost most of its mass or been disrupted. Using this description of satellite dynamics, I construct a semi-analytic model for the the evolution of a galaxy or cluster halo. I show that this model reproduces the basic features of numerical simulations, and use it to investigate two major problems in current galaxy formation scenarios: the prediction of excessive substructure in galaxy halos, and the survival of galactic disks in halos filled with substructure. Ill I show that the small number of dwarf galaxies observed in the Local Group can be explained by considering the eSects of reionisation on star formation in small halos. The stellar luminosities predicted in this case match the observed luminosities of local satellites. The predicted spatial distribution, sizes and characteristic velocities of dwarf galaxies are also consistent with those observed locally. Many of these satellite galaxies are disrupted by tidal stripping or encoun­ ters. I investigate the properties of their debris, and show that its total mass and spatial distribution are similar to those of the stellar halo of the Milky Way. Furthermore, the stars in this debris are mainly old, sat­ isfying another observational constraint on models of galaxy formation. Some satellites have been disrupted fairly recently, however, suggesting that coherent tidal streams may still be visible at the present day. Finally, I investigate the effects of encounters on the central disk within the main halo. I find that the rate of disruptive encounters drops off sharply after the galaxy is assembled, such that the typical disk has remained undisturbed for the past 8-10 billion years. Less disruptive encounters are more common, and disks are often heated as they re-form after their last disruption, producing components like the thick disk of the Milky Way. These results may resolve the long-standing uncertainty about disk ages in hierarchical, cold dark m atter cosmologies. It is less clear whether the bulge-to-disk mass ratios predicted by the model, for the currently favoured LCDM cosmology, are consistent with observations. The relative mass of the bulge in typical disk galaxies may place an upper limit on the age of their stellar contents. IV Examiners; Dr. A. DMi^oupervisor (Department of Physics and Astronomy) Dr. ji KNgyarfo^Departmental Member (Department of Physics and Astronomy) Dr. D. Hartwick, Departmental Member (Department of Physics and Astronomy) Dr. T. Dingle, Outside Member (Department of Chemistry) Dr. T. Quinn, External Examiner (Department of Astronomy, University of Washington) THE FORMATION AND SURVIVAL OF DiSK GALAXIES by James E. Taylor UNIVERSITY OF VICTORIA Table of Contents Abstract il Table of Contents v List of Tables x List of Figures xi Acknowledgements xiv Dedication xv Preface 1 Part I 16 1 Introduction 16 1.1 Hierarchical Galaxy Formation in a Universe Dominated by Cold Dark M a tte r............................................................................................................. 17 1.2 Current Models of Galaxy Formation ....................................................... 21 1.2.1 Numerical Models............................................................................. 21 1.2.2 Semi-analytic Models ....................................................................... 23 1.3 An Alternative Approach ............................................................................. 25 1.4 Outline of the Thesis .................................................................................... 27 2 Calculating Satellite Orbits 28 2.1 An Overview of the Numerical Simulations............................................. 29 VI 2.1.1 The Hayashi & Navarro Simulations ............................................. 30 2.1.2 The Velazquez & White Simulations ............................................. 31 2.2 Basic Orbital C alculations.......................................................................... 34 2.2.1 The Integration Scheme .................................................................. 34 2.2.2 Properties of Orbits in an Axisymmetric P o tential ..................... 36 2.2.3 Comparison with S im ulations ...................................................... 37 2.3 Dynamical F ric tio n ....................................................................................... 38 2.3.1 Chandrasekhar’s Formula ............................................................. 38 2.3.2 Calculating the Coulomb Logarithm ............................................. 42 2.4 Adding Friction to the Orbital Calculations .......................................... 45 2.4.1 Analytic Prescription ...................................................................... 45 2.4.2 Comparison with Numerical S im ulations................................... 47 2.5 Summary ....................................................................................................... 50 3 Mass Loss 52 3.1 Measuring Mass in Simulations................................................................. 53 3.2 The Tidal Limit Approximation ................................................................. 55 3.2.1 D erivation.......................................................................................... 55 3.2.2 Alternate Formulations................................................................... 56 3.2.3 Comparison with Numerical Mass-loss R a te s ............................. 59 3.3 The Impulse Approximation ........................................................................ 60 3.4 A General Model for Mass L o s s ................................................................. 63 3.5 Comparison with Simulations ....................... 65 3.6 Summary ........................................................................................................ 67 4 Tidal Heating 68 4.1 T h eo ry .............................................................................................................. 69 4.1.1 The First and Second-order Heating T erm s ................................ 69 vil 4.1.2 Adiabatic Corrections ................................................................... 71 4.2 A General Model for Tidal H e a tin g .......................................................... 72 4.2.1 The Discrete Heating Calculation ............................................... 72 4.2.2 Corrections to the Heating R a te ................................................... 73 4.2.3 Relating Heating and Mass L oss ................................................... 75 4.3 Comparison with Simulations .................................................................... 77 4.3.1 The VW Sim ulations...................................................................... 77 4.3.2 The HN S im u latio n s...................................................................... 78 4.4 Structural Changes........................................................................................ 82 4.5 Comparison with S im u latio n s .................................................................... 83 4.6 Summary of Part I ........................................................................................ 86 Part II 88 5 Constructing Merger Histories for Dark Matter Halos 88 5.1 Cosmological M odels ..................................................................................... 90 5.2 Gravitational Instability and Press-Schechter S ta