DARK MATTER IN UNIVERSE n d edited by John Bahcall Institute for Advanced Study, Princeton, USA Tsvi Piran The Hebrew University, Israel Steven Weinberg University of Texas, Austin, USA TECHNiSCHE INFORMATIONSBIBLIOTHEK UNIVERSITATSBIBLIOTHEK HANNOVER World Scientific
CONTENTS Foreword to the First Edition v Chapter 1. Introduction 1 John N. Bahcall Chapter 2. Distribution of Dark Matter in the Spiral Galaxy NGC 3198 7 T. S. van Albada, K. Begeman, R. Sanscisi and J. N. Bahcall 1 Introduction 7 2 Distribution of Light 11 3 Rotation Curve 12 4 Mass Models 14 4.1 Choice of Components 14 4.2 Fits with Exponential Disk and Halo 14 4.3 An Upper Limit for the Mass of the Spheroidal Component 18 5 Discussion 19 Appendix: Dark Matter and the Tully-Fisher Relation 21 References 22 Chapter 3. Some Possible Regularities in Missing Mass 25 John N. Bahcall and Stefano Casertano 1 Introduction 25 2 The Simplicity 25 3 The Numerical Characteristics 27 4 The Local Missing Mass 30 5 Implications 30 References 32
viii Contents Chapter 4. Evolution of Globular Clusters and the Globular Cluster System - I 35 J. P. Ostriker and C. Thompson 1 Globular Clusters 35 2 Basic Properties of Globular Clusters 36 3 Equilibrium Structure of Globular Clusters 37 4 Methods of Computing the Evolution of a Globular Cluster 42 5 Early Evolution of an Isolated Globular Cluster 42 6 Effects of Finite Stellar Size: Heating and Core Bounce 44 7 External Effects on the Evolution of a Globular Cluster 49 8 Evolution of the Globular Cluster System: Destruction of Clusters... 51 9 Outstanding Issues 52 10 Nature of the Dark Halo of Our Galaxy 53 References 55 Chapter 5. Positive Energy Perturbations in Cosmology - II 57 J. P. Ostriker and C. Thompson 1 Hydrodynamics in a Cosmological Setting 57 2 Various Self-Similar Solutions for Blast Waves 60 3 Shell Structure 64 4 Equation of Motion of a Thin Shell 65 5 Gravitational Instability in a Shell 68 6 Interactions between Cosmological Blasts 69 References 70 Chapter 6. Dark Matter in Galaxies and Galaxy Systems 71 Scott Tremaine and Hyung Mok Lee 1 Introduction 71 1.1 Virial Theorem 72 1.2 History of Dark Matter 73 1.3 A Quick Review of Cosmology 75 1.4 Mass-to-light Ratio in the Solar Neighbourhood 78 1.5 Classification Scheme of Dark Matter 78 2 Theory of Stellar Dynamics 79 2.1 Collisionless Boltzmann Equation 79 2.2 The Jeans Theorem 82 2.3 Examples of Distribution Functions 83 2.3.1 Plummer model 83 2.3.2 Isothermal sphere 84
Contents ix 2.4 Moments of the Collisionless Boltzmann Equation 85 3 Elliptical Cores and Dwarf Spheroidal Galaxies 86 4 The Extent of the Galactic Halo 90 4.1 Local Escape Speed 90 4.2 Magellanic Stream 91 4.3 Local Group Timing 91 4.4 Kinematics of Satellite Galaxies 92 4.5 Summary 95 5 Binary Galaxies 95 6 Masses of Groups and Clusters of Galaxies 97 6.1 Groups of Galaxies 97 6.2 Rich Clusters: Coma Cluster 98 7 Summary 100 References 101 Chapter 7. Gravitational Lenses 103 Roger D. Blandford and Christopher S. Kochanek 1 Introduction 103 1.1 History 103 1.2 Simple Estimates 104 1.3 Uses 107 1.4 Organization of Lectures 107 References 108 2 The Optics of Gravitational Lenses 108 2.1 Vector Formalism 109 2.1.1 The lens equation 109 2.1.2 Image amplification and parity 110 2.1.3 Distance measures Ill 2.2 Scalar Formalism: Fermat's Principle 112 2.3 Propagation Formalism: The Optical Scalar Equations 115 References 116 3 Gravitational Potential Wells 117 3.1 Uniform Sheet 117 3.2 Point Mass (Black Hole) 117 3.3 Singular Isothermal Sphere 118 3.4 Isothermal Sphere with Finite Core 118 3.5 Elliptical Potentials 121 3.6 Irregular Potentials 122 3.7 Cosmic Strings 122 References 124
Contents Generic Features of Images 124 4.1 Arrival Time Surfaces 124 4.2 Caustics and Catastrophes 127 4.2.1 Structural stability of images 127 4.2.2 Isolated image 128 4.2.3 Fold catastrophe 129 4.2.4 Cusp catastrophe 130 4.2.5 Higher order catastrophes 131 4.3 Caustics as Conjugate Points of Ray Congruences 132 References 133 Microlensing 133 5.1 Order of Magnitude Estimates 133 5.2 The Character of Microimages: Low Optical Depth 135 5.3 The Character of Microimages: Moderate Optical Depth 135 5.4 The Character of Microimages: Large Optical Depth 137 References 137 Compound Lenses 138 References 140 The Observational Position 141 7.1 A Reprise of Existing Candidates 141 7.1.1 The double QSO: 0957 + 561 141 7.1.2 PG 1115 + 080 141 7.1.3 2016 + 112 142 7.1.4 2237 + 0305 142 7.1.5 3C324 143 7.1.6 1042 +178 143 7.1.7 The dark matter lenses: 2345 + 007, 1635 + 267, and 0023 +171 143 7.1.8 1146+111 144 7.2 Space Density of Sources Quasars, Galaxies, and Radio Sources 145 7.3 Space Density of Lenses Galaxies and Clusters 145 7.4 Amplification Bias 146 7.5 Surveys and Future Prospects 146 References 147 Lenses as Probes of the Universe 152 8.1 The Hubble Constant 152 8.2 Galactic Masses 153 8.3 Lensing by Dark Matter 155 References 156 Concluding Remarks 157
Contents xi Chapter 8. An Introduction to Inflation 159 William H. Press and David N. Spergel 1 Review of Big Bang Cosmology 159 2 Inflation 162 3 Additional Topics Not Covered Here 165 References 167 Chapter 9. Wimps in the Sun and in the Lab 169 William H. Press and David N. Spergel 1 WIMPS and the Solar Neutrino Problem 169 2 Detecting WIMPS in the Lab 176 References 179 Chapter 10. An Introduction to Cosmic Strings 183 William H. Press and David N. Spergel 1 Birth of Cosmic Strings 183 2 The Motion of a Cosmic String Loop 186 3 Cosmic Strings and the Formation of Galaxies 189 3.1 Spherical Accretion Model 190 3.2 Competition between Loops 192 3.3 Galaxy Morphology 193 4 Observing Cosmic Strings 194 References 194 Chapter 11. A Departure from Newtonian Dynamics at Low Accelerations as an Explanation of the Mass- Discrepancy in Galactic Systems 197 Mordehai Milgrom 1 Introduction 198 2 Dynamics at Low Accelerations 200 3 A Nonrelativistic Formulation 203 4 Effects of an Ambient Field 205 5 Observational Consequences 207 5.1 Disc Galaxies 208 5.2 Elliptical Galaxies 211 5.3 The General Expression for the "Dark Matter" Density 213 5.4 The Sign of the Phantom Density Negative "Dark Matter"... 214 5.5 Phantom Matter in Galactic Discs 214 References 215
xii Contents Chapter 12. Dark Matter in Cosmology 217 Anthony Aguirre 1 Introduction 217 2 Dark Matter and Structure Formation 218 2.1 Initial Conditions and the Standard Cosmological Model 218 2.2 Evolution of Perturbations 219 3 Tests and Constraints from the Microwave Background 223 4 Tests and Constraints from the Ly-a Forest and Distribution of Galaxies 225 5 Dark Matter and Galaxy Formation 226 5.1 Halo Formation 226 5.2 The Halo Mass Function 227 5.3 Halo Profiles 228 5.4 Angular Momentum 228 5.5 From a Dark Halo to a Galaxy 229 5.6 Current Status of Galaxy Formation Theory 229 5.7 Outstanding Problems, and Alternatives to (Cold) Dark Matter.. 230 Conclusions 232 References 232