Galaxy Formation and Evolution PDF

This page intentionally left blank  G A L A X Y F O R M AT I O N A N D E VO L U T I O N The rapidly expanding field of galaxy formation lies at the interfaces of astronomy, particle physics, and cosmology. Covering diverse topics from these disciplines, all of which are needed to un...

This page intentionally left blank  G A L A X Y F O R M AT I O N A N D E VO L U T I O N The rapidly expanding field of galaxy formation lies at the interfaces of astronomy, particle physics, and cosmology. Covering diverse topics from these disciplines, all of which are needed to understand how galaxies form and evolve, this book is ideal for researchers entering the field. Individual chapters explore the evolution of the Universe as a whole and its particle and radi- ation content; linear and nonlinear growth of cosmic structures; processes affecting the gaseous and dark matter components of galaxies and their stellar populations; the formation of spiral and elliptical galaxies; central supermassive black holes and the activity associated with them; galaxy interactions; and the intergalactic medium. Emphasizing both observational and theoretical aspects, this book provides a coherent intro- duction for astronomers, cosmologists, and astroparticle physicists to the broad range of science underlying the formation and evolution of galaxies. H O U J U N M O is Professor of Astrophysics at the University of Massachusetts. He is known for his work on the formation and clustering of galaxies and their dark matter halos. F R A N K VA N D E N B O S C H is Assistant Professor at Yale University, and is known for his studies of the formation, dynamics, and clustering of galaxies. S I M O N W H I T E is Director at the Max Planck Institute for Astrophysics in Garching. He is one of the originators of the modern theory of galaxy formation and has received numerous international prizes and honors. Jointly and separately the authors have published almost 500 papers in the refereed professional literature, most of them on topics related to the subject of this book. GALA XY F O RMAT ION AND EVOLUTION HOUJUN MO University of Massachusetts F R A N K VA N D E N B O S C H Yale University SIMON WH ITE Max Planch Institute for Astrophysics CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Dubai, Tokyo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521857932 © H. Mo, F. van den Bosch & S. White 2010 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2010 ISBN-13 978-0-511-72962-1 eBook (NetLibrary) ISBN-13 978-0-521-85793-2 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.  Contents Preface page xvii 1 Introduction 1 1.1 The Diversity of the Galaxy Population 2 1.2 Basic Elements of Galaxy Formation 5 1.2.1 The Standard Model of Cosmology 6 1.2.2 Initial Conditions 6 1.2.3 Gravitational Instability and Structure Formation 7 1.2.4 Gas Cooling 8 1.2.5 Star Formation 8 1.2.6 Feedback Processes 9 1.2.7 Mergers 10 1.2.8 Dynamical Evolution 12 1.2.9 Chemical Evolution 12 1.2.10 Stellar Population Synthesis 13 1.2.11 The Intergalactic Medium 13 1.3 Time Scales 14 1.4 A Brief History of Galaxy Formation 15 1.4.1 Galaxies as Extragalactic Objects 15 1.4.2 Cosmology 16 1.4.3 Structure Formation 18 1.4.4 The Emergence of the Cold Dark Matter Paradigm 20 1.4.5 Galaxy Formation 22 2 Observational Facts 25 2.1 Astronomical Observations 25 2.1.1 Fluxes and Magnitudes 26 2.1.2 Spectroscopy 29 2.1.3 Distance Measurements 32 2.2 Stars 34 2.3 Galaxies 37 2.3.1 The Classification of Galaxies 38 2.3.2 Elliptical Galaxies 41 2.3.3 Disk Galaxies 49 v vi Contents 2.3.4 The Milky Way 55 2.3.5 Dwarf Galaxies 57 2.3.6 Nuclear Star Clusters 59 2.3.7 Starbursts 60 2.3.8 Active Galactic Nuclei 60 2.4 Statistical Properties of the Galaxy Population 61 2.4.1 Luminosity Function 62 2.4.2 Size Distribution 63 2.4.3 Color Distribution 64 2.4.4 The Mass–Metallicity Relation 65 2.4.5 Environment Dependence 65 2.5 Clusters and Groups of Galaxies 67 2.5.1 Clusters of Galaxies 67 2.5.2 Groups of Galaxies 71 2.6 Galaxies at High Redshifts 72 2.6.1 Galaxy Counts 73 2.6.2 Photometric Redshifts 75 2.6.3 Galaxy Redshift Surveys at z ∼ 1 75 2.6.4 Lyman-Break Galaxies 77 2.6.5 Lyα Emitters 78 2.6.6 Submillimeter Sources 78 2.6.7 Extremely Red Objects and Distant Red Galaxies 79 2.6.8 The Cosmic Star-Formation History 80 2.7 Large-Scale Structure 81 2.7.1 Two-Point Correlation Functions 82 2.7.2 Probing the Matter Field via Weak Lensing 84 2.8 The Intergalactic Medium 85 2.8.1 The Gunn–Peterson Test 85 2.8.2 Quasar Absorption Line Systems 86 2.9 The Cosmic Microwave Background 89 2.10 The Homogeneous and Isotropic Universe 92 2.10.1 The Determination of Cosmological Parameters 94 2.10.2 The Mass and Energy Content of the Universe 95 3 Cosmological Background 100 3.1 The Cosmological Principle and the Robertson–Walker Metric 102 3.1.1 The Cosmological Principle and its Consequences 102 3.1.2 Robertson–Walker Metric 104 3.1.3 Redshift 106 3.1.4 Peculiar Velocities 107 3.1.5 Thermodynamics and the Equation of State 108 3.1.6 Angular-Diameter and Luminosity Distances 110 3.2 Relativistic Cosmology 112 3.2.1 Friedmann Equation 113 3.2.2 The Densities at the Present Time 114  Contents vii 3.2.3 Explicit Solutions of the Friedmann Equation 115 3.2.4 Horizons 119 3.2.5 The Age of the Universe 119 3.2.6 Cosmological Distances and Volumes 121 3.3 The Production and Survival of Particles 124 3.3.1 The Chronology of the Hot Big Bang 125 3.3.2 Particles in Thermal Equilibrium 127 3.3.3 Entropy 129 3.3.4 Distribution Functions of Decoupled Particle Species 132 3.3.5 The Freeze-Out of Stable Particles 133 3.3.6 Decaying Particles 137 3.4 Primordial Nucleosynthesis 139 3.4.1 Initial Conditions 139 3.4.2 Nuclear Reactions 140 3.4.3 Model Predictions 142 3.4.4 Observational Results 144 3.5 Recombination and Decoupling 146 3.5.1 Recombination 146 3.5.2 Decoupling and the Origin of the CMB 148 3.5.3 Compton Scattering 150 3.5.4 Energy Thermalization 151 3.6 Inflation 152 3.6.1 The Problems of the Standard Model 152 3.6.2 The Concept of Inflation 154 3.6.3 Realization of Inflation 156 3.6.4 Models of Inflation 158 4 Cosmological Perturbations 162 4.1 Newtonian Theory of Small Perturbations 162 4.1.1 Ideal Fluid 162 4.1.2 Isentropic and Isocurvature Initial Conditions 166 4.1.3 Gravitational Instability 166 4.1.4 Collisionless Gas 168 4.1.5 Free-Streaming Damping 171 4.1.6 Specific Solutions 172 4.1.7 Higher-Order Perturbation Theory 176 4.1.8 The Zel’dovich Approximation 177 4.2 Relativistic Theory of Small Perturbations 178 4.2.1 Gauge Freedom 179 4.2.2 Classification of Perturbations 181 4.2.3 Specific Examples of Gauge Choices 183 4.2.4 Basic Equations 185 4.2.5 Coupling between Baryons and Radiation 189 4.2.6 Perturbation Evolution 191 4.3 Linear Transfer Functions 196 4.3.1 Adiabatic Baryon Models 198 viii Contents 4.3.2 Adiabatic Cold Dark Matter Models 200 4.3.3 Adiabatic Hot Dark Matter Models 201 4.3.4 Isocurvature Cold Dark Matter Models 202 4.4 Statistical Properties 202 4.4.1 General Discussion 202 4.4.2 Gaussian Random Fields 204 4.4.3 Simple Non-Gaussian Models 205 4.4.4 Linear Perturbation Spectrum 206 4.5 The Origin of Cosmological Perturbations 209 4.5.1 Perturbations from Inflation 209 4.5.2 Perturbations from Topological Defects 213 5 Gravitational Collapse and Collisionless Dynamics 215 5.1 Spherical Collapse Models 215 5.1.1 Spherical Collapse in a Λ = 0 Universe 215 5.1.2 Spherical Collapse in a Flat Universe with Λ > 0 218 5.1.3 Spherical Collapse with Shell Crossing 219 5.2 Similarity Solutions for Spherical Collapse 220 5.2.1 Models with Radial Orbits 220 5.2.2 Models Including Non-Radial Orbits 224 5.3 Collapse of Homogeneous Ellipsoids 226 5.4 Collisionless Dynamics 230 5.4.1 Time Scales for Collisions 230 5.4.2 Basic Dynamics 232 5.4.3 The Jeans Equations 233 5.4.4 The Virial Theorem 234 5.4.5 Orbit Theory 236 5.4.6 The Jeans Theorem 240 5.4.7 Spherical Equilibrium Models 240 5.4.8 Axisymmetric Equilibrium Models 244 5.4.9 Triaxial Equilibrium Models 247 5.5 Collisionless Relaxation 248 5.5.1 Phase Mixing 249 5.5.2 Chaotic Mixing 250 5.5.3 Violent Relaxation 251 5.5.4 Landau Damping 253 5.5.5 The End State of Relaxation 254 5.6 Gravitational Collapse of the Cosmic Density Field 257 5.6.1 Hierarchical Clustering 257 5.6.2 Results from Numerical Simulations 258 6 Probing the Cosmic Density Field 262 6.1 Large-Scale Mass Distribution 262 6.1.1 Correlation Functions 262 6.1.2 Particle Sampling and Bias 264 6.1.3 Mass Moments 266  Contents ix 6.2 Large-Scale Velocity Field 270 6.2.1 Bulk Motions and Velocity Correlation Functions 270 6.2.2 Mass Density Reconstruction from the Velocity Field 271 6.3 Clustering in Real Space and Redshift Space 273 6.3.1 Redshift Distortions 273 6.3.2 Real-Space Correlation Functions 276 6.4 Clustering Evolution 278 6.4.1 Dynamics of Statistics 278 6.4.2 Self-Similar Gravitational Clustering 280 6.4.3 Development of Non-Gaussian Features 282 6.5 Galaxy Clustering 283 6.5.1 Correlation Analyses 284 6.5.2 Power Spectrum Analysis 288 6.5.3 Angular Correlation Function and Power Spectrum 290 6.6 Gravitational Lensing 292 6.6.1 Basic Equations 292 6.6.2 Lensing by a Point Mass 295 6.6.3 Lensing by an Extended Object 297 6.6.4 Cosmic Shear 300 6.7 Fluctuations in the Cosmic Microwave Background 302 6.7.1 Observational Quantities 302 6.7.2 Theoretical Expectations of Temperature Anisotropy 304 6.7.3 Thomson Scattering and Polarization of the Microwave Background 311 6.7.4 Interaction between CMB Photons and Matter 314 6.7.5 Constraints on Cosmological Parameters 316 7 Formation and Structure of Dark Matter Halos 319 7.1 Density Peaks 321 7.1.1 Peak Number Density 321 7.1.2 Spatial Modulation of the Peak Number Density 323 7.1.3 Correlation Function 324 7.1.4 Shapes of Density Peaks 325 7.2 Halo Mass Function 326 7.2.1 Press–Schechter Formalism 327 7.2.2 Excursion Set Derivation of the Press–Schechter Formula 328 7.2.3 Spherical versus Ellipsoidal Dynamics 331 7.2.4 Tests of the Press–Schechter Formalism 333 7.2.5 Number Density of Galaxy Clusters 334 7.3 Progenitor Distributions and Merger Trees 336 7.3.1 Progenitors of Dark Matter Halos 336 7.3.2 Halo Merger Trees 336 7.3.3 Main Progenitor Histories 339 7.3.4 Halo Assembly and Formation Times 340 7.3.5 Halo Merger Rates 342 7.3.6 Halo Survival Times 343 x Contents 7.4 Spatial Clustering and Bias 345 7.4.1 Linear Bias and Correlation Function 345 7.4.2 Assembly Bias 348 7.4.3 Nonlinear and Stochastic Bias 348 7.5 Internal Structure of Dark Matter Halos 351 7.5.1 Halo Density Profiles 351 7.5.2 Halo Shapes 354 7.5.3 Halo Substructure 355 7.5.4 Angular Momentum 358 7.6 The Halo Model of Dark Matter Clustering 362 8 Formation and Evolution of Gaseous Halos 366 8.1 Basic Fluid Dynamics and Radiative Processes 366 8.1.1 Basic Equations 366 8.1.2 Compton Cooling 367 8.1.3 Radiative Cooling 367 8.1.4 Photoionization Heating 369 8.2 Hydrostatic Equilibrium 371 8.2.1 Gas Density Profile 371 8.2.2 Convective Instability 373 8.2.3 Virial Theorem Applied to a Gaseous Halo 374 8.3 The Formation of Hot Gaseous Halos 376 8.3.1 Accretion Shocks 376 8.3.2 Self-Similar Collapse of Collisional Gas 379 8.3.3 The Impact of a Collisionless Component 383 8.3.4 More General Models of Spherical Collapse 384 8.4 Radiative Cooling in Gaseous Halos 385 8.4.1 Radiative Cooling Time Scales for Uniform Clouds 385 8.4.2 Evolution of the Cooling Radius 387 8.4.3 Self-Similar Cooling Waves 388 8.4.4 Spherical Collapse with Cooling 390 8.5 Thermal and Hydrodynamical Instabilities of Cooling Gas 393 8.5.1 Thermal Instability 393 8.5.2 Hydrodynamical Instabilities 396 8.5.3 Heat Conduction 397 8.6 Evolution of Gaseous Halos with Energy Sources 398 8.6.1 Blast Waves 399 8.6.2 Winds and Wind-Driven Bubbles 404 8.6.3 Supernova Feedback and Galaxy Formation 406 8.7 Results from Numerical Simulations 408 8.7.1 Three-Dimensional Collapse without Radiative Cooling 408 8.7.2 Three-Dimensional Collapse with Radiative Cooling 409  Contents xi 8.8 Observational Tests 410 8.8.1 X-ray Clusters and Groups 410 8.8.2 Gaseous Halos around Elliptical Galaxies 414 8.8.3 Gaseous Halos around Spiral Galaxies 416 9 Star Formation in Galaxies 417 9.1 Giant Molecular Clouds: The Sites of Star Formation 418 9.1.1 Observed Properties 418 9.1.2 Dynamical State 419 9.2 The Formation of Giant Molecular Clouds 421 9.2.1 The Formation of Molecular Hydrogen 421 9.2.2 Cloud Formation 422 9.3 What Controls the Star-Formation Efficiency 425 9.3.1 Magnetic Fields 425 9.3.2 Supersonic Turbulence 426 9.3.3 Self-Regulation 428 9.4 The Formation of Individual Stars 429 9.4.1 The Formation of Low-Mass Stars 429 9.4.2 The Formation of Massive Stars 432 9.5 Empirical Star-Formation Laws 433 9.5.1 The Kennicutt–Schmidt Law 434 9.5.2 Local Star-Formation Laws 436 9.5.3 Star-Formation Thresholds 438 9.6 The Initial Mass Function 440 9.6.1 Observational Constraints 441 9.6.2 Theoretical Models 443 9.7 The Formation of Population III Stars 446 10 Stellar Populations and Chemical Evolution 449 10.1 The Basic Concepts of Stellar Evolution 449 10.1.1 Basic Equations of Stellar Structure 450 10.1.2 Stellar Evolution 453 10.1.3 Equation of State, Opacity, and Energy Production 453 10.1.4 Scaling Relations 460 10.1.5 Main-Sequence Lifetimes 462 10.2 Stellar Evolutionary Tracks 463 10.2.1 Pre-Main-Sequence Evolution 463 10.2.2 Post-Main-Sequence Evolution 464 10.2.3 Supernova Progenitors and Rates 468 10.3 Stellar Population Synthesis 470 10.3.1 Stellar Spectra 470 10.3.2 Spectral Synthesis 471 10.3.3 Passive Evolution 472 10.3.4 Spectral Features 474 10.3.5 Age–Metallicity Degeneracy 475 xii Contents 10.3.6 K and E Corrections 475 10.3.7 Emission and Absorption by the Interstellar Medium 476 10.3.8 Star-Formation Diagnostics 482 10.3.9 Estimating Stellar Masses and Star-Formation Histories of Galaxies 484 10.4 Chemical Evolution of Galaxies 486 10.4.1 Stellar Chemical Production 486 10.4.2 The Closed-Box Model 488 10.4.3 Models with Inflow and Outflow 490 10.4.4 Abundance Ratios 491 10.5 Stellar Energetic Feedback 492 10.5.1 Mass-Loaded Kinetic Energy from Stars 492 10.5.2 Gas Dynamics Including Stellar Feedback 493 11 Disk Galaxies 495 11.1 Mass Components and Angular Momentum 495 11.1.1 Disk Models 496 11.1.2 Rotation Curves 498 11.1.3 Adiabatic Contraction 501 11.1.4 Disk Angular Momentum 502 11.1.5 Orbits in Disk Galaxies 503 11.2 The Formation of Disk Galaxies 505 11.2.1 General Discussion 505 11.2.2 Non-Self-Gravitating Disks in Isothermal Spheres 505 11.2.3 Self-Gravitating Disks in Halos with Realistic Profiles 507 11.2.4 Including a Bulge Component 509 11.2.5 Disk Assembly 509 11.2.6 Numerical Simulations of Disk Formation 511 11.3 The Origin of Disk Galaxy Scaling Relations 512 11.4 The Origin of Exponential Disks 515 11.4.1 Disks from Relic Angular Momentum Distribution 515 11.4.2 Viscous Disks 517 11.4.3 The Vertical Structure of Disk Galaxies 518 11.5 Disk Instabilities 521 11.5.1 Basic Equations 521 11.5.2 Local Instability 523 11.5.3 Global Instability 525 11.5.4 Secular Evolution 528 11.6 The Formation of Spiral Arms 531 11.7 Stellar Population Properties 534 11.7.1 Global Trends 535 11.7.2 Color Gradients 537 11.8 Chemical Evolution of Disk Galaxies 538 11.8.1 The Solar Neighborhood 538 11.8.2 Global Relations 540  Contents xiii 12 Galaxy Interactions and Transformations 544 12.1 High-Speed Encounters 545 12.2 Tidal Stripping 548 12.2.1 Tidal Radius 548 12.2.2 Tidal Streams and Tails 549 12.3 Dynamical Friction 553 12.3.1 Orbital Decay 556 12.3.2 The Validity of Chandrasekhar’s Formula 559 12.4 Galaxy Merging 561 12.4.1 Criterion for Mergers 561 12.4.2 Merger Demographics 563 12.4.3 The Connection between Mergers, Starbursts and AGN 564 12.4.4 Minor Mergers and Disk Heating 565 12.5 Transformation of Galaxies in Clusters 568 12.5.1 Galaxy Harassment 569 12.5.2 Galactic Cannibalism 570 12.5.3 Ram-Pressure Stripping 571 12.5.4 Strangulation 572 13 Elliptical Galaxies 574 13.1 Structure and Dynamics 574 13.1.1 Observables 575 13.1.2 Photometric Properties 576 13.1.3 Kinematic Properties 577 13.1.4 Dynamical Modeling 579 13.1.5 Evidence for Dark Halos 581 13.1.6 Evidence for Supermassive Black Holes 582 13.1.7 Shapes 584 13.2 The Formation of Elliptical Galaxies 587 13.2.1 The Monolithic Collapse Scenario 588 13.2.2 The Merger Scenario 590 13.2.3 Hierarchical Merging and the Elliptical Population 593 13.3 Observational Tests and Constraints 594 13.3.1 Evolution of the Number Density of Ellipticals 594 13.3.2 The Sizes of Elliptical Galaxies 595 13.3.3 Phase-Space Density Constraints 598 13.3.4 The Specific Frequency of Globular Clusters 599 13.3.5 Merging Signatures 600 13.3.6 Merger Rates 601 13.4 The Fundamental Plane of Elliptical Galaxies 602 13.4.1 The Fundamental Plane in the Merger Scenario 604 13.4.2 Projections and Rotations of the Fundamental Plane 604 13.5 Stellar Population Properties 606 13.5.1 Archaeological Records 606 13.5.2 Evolutionary Probes 609 xiv Contents 13.5.3 Color and Metallicity Gradients 610 13.5.4 Implications for the Formation of Elliptical Galaxies 610 13.6 Bulges, Dwarf Ellipticals and Dwarf Spheroidals 613 13.6.1 The Formation of Galactic Bulges 614 13.6.2 The Formation of Dwarf Ellipticals 616 14 Active Galaxies 618 14.1 The Population of Active Galactic Nuclei 619 14.2 The Supermassive Black Hole Paradigm 623 14.2.1 The Central Engine 623 14.2.2 Accretion Disks 624 14.2.3 Continuum Emission 626 14.2.4 Emission Lines 631 14.2.5 Jets, Superluminal Motion and Beaming 633 14.2.6 Emission-Line Regions and Obscuring Torus 637 14.2.7 The Idea of Unification 638 14.2.8 Observational Tests for Supermassive Black Holes 639 14.3 The Formation and Evolution of AGN 640 14.3.1 The Growth of Supermassive Black Holes and the Fueling of AGN 640 14.3.2 AGN Demographics 644 14.3.3 Outstanding Questions 647 14.4 AGN and Galaxy Formation 648 14.4.1 Radiative Feedback 649 14.4.2 Mechanical Feedback 650 15 Statistical Properties of the Galaxy Population 652 15.1 Preamble 652 15.2 Galaxy Luminosities and Stellar Masses 654 15.2.1 Galaxy Luminosity Functions 654 15.2.2 Galaxy Counts 658 15.2.3 Extragalactic Background Light 660 15.3 Linking Halo Mass to Galaxy Luminosity 663 15.3.1 Simple Considerations 663 15.3.2 The Luminosity Function of Central Galaxies 665 15.3.3 The Luminosity Function of Satellite Galaxies 666 15.3.4 Satellite Fractions 668 15.3.5 Discussion 669 15.4 Linking Halo Mass to Star-Formation History 670 15.4.1 The Color Distribution of Galaxies 670 15.4.2 Origin of the Cosmic Star-Formation History 673 15.5 Environmental Dependence 674 15.5.1 Effects within Dark Matter Halos 675 15.5.2 Effects on Large Scales 677 15.6 Spatial Clustering and Galaxy Bias 679 15.6.1 Application to High-Redshift Galaxies 683  Contents xv 15.7 Putting it All Together 684 15.7.1 Semi-Analytical Models 684 15.7.2 Hydrodynamical Simulations 686 16 The Intergalactic Medium 689 16.1 The Ionization State of the Intergalactic Medium 690 16.1.1 Physical Conditions after Recombination 690 16.1.2 The Mean Optical Depth of the IGM 690 16.1.3 The Gunn–Peterson Test 692 16.1.4 Constraints from the Cosmic Microwave Background 694 16.2 Ionizing Sources 695 16.2.1 Photoionization versus Collisional Ionization 695 16.2.2 Emissivity from Quasars and Young Galaxies 697 16.2.3 Attenuation by Intervening Absorbers 699 16.2.4 Observational Constraints on the UV Background 701 16.3 The Evolution of the Intergalactic Medium 702 16.3.1 Thermal Evolution 702 16.3.2 Ionization Evolution 704 16.3.3 The Epoch of Re-ionization 705 16.3.4 Probing Re-ionization with 21-cm Emission and Absorption 707 16.4 General Properties of Absorption Lines 709 16.4.1 Distribution Function 709 16.4.2 Thermal Broadening 710 16.4.3 Natural Broadening and Voigt Profiles 711 16.4.4 Equivalent Width and Column Density 712 16.4.5 Common QSO Absorption Line Systems 714 16.4.6 Photoionization Models 714 16.5 The Lyman α Forest 714 16.5.1 Redshift Evolution 715 16.5.2 Column Density Distribution 716 16.5.3 Doppler Parameter 717 16.5.4 Sizes of Absorbers 718 16.5.5 Metallicity 719 16.5.6 Clustering 720 16.5.7 Lyman α Forests at Low Redshift 721 16.5.8 The Helium Lyman α Forest 722 16.6 Models of the Lyman α Forest 723 16.6.1 Early Models 723 16.6.2 Lyman α Forest in Hierarchical Models 724 16.6.3 Lyman α Forest in Hydrodynamical Simulations 731 16.7 Lyman-Limit Systems 732 16.8 Damped Lyman α Systems 733 16.8.1 Column Density Distribution 734 16.8.2 Redshift Evolution 734 16.8.3 Metallicities 736 16.8.4 Kinematics 738 xvi Contents 16.9 Metal Absorption Line Systems 738 16.9.1 MgII Systems 739 16.9.2 CIV and OVI Systems 740 A Basics of General Relativity 741 A1.1 Space-time Geometry 741 A1.2 The Equivalence Principle 743 A1.3 Geodesic Equations 744 A1.4 Energy–Momentum Tensor 746 A1.5 Newtonian Limit 747 A1.6 Einstein’s Field Equation 747 B Gas and Radiative Processes 748 B1.1 Ideal Gas 748 B1.2 Basic Equations 749 B1.3 Radiative Processes 751 B1.3.1 Einstein Coefficients and Milne Relation 752 B1.3.2 Photoionization and Photo-excitation 755 B1.3.3 Recombination 756 B1.3.4 Collisional Ionization and Collisional Excitation 757 B1.3.5 Bremsstrahlung 758 B1.3.6 Compton Scattering 759 B1.4 Radiative Cooling 760 C Numerical Simulations 764 C1.1 N-Body Simulations 764 C1.1.1 Force Calculations 766 C1.1.2 Issues Related to Numerical Accuracy 767 C1.1.3 Boundary Conditions 769 C1.1.4 Initial Conditions 769 C1.2 Hydrodynamical Simulations 770 C1.2.1 Smoothed-Particle Hydrodynamics (SPH) 770 C1.2.2 Grid-Based Algorithms 772 D Frequently Used Abbreviations 775 E Useful Numbers 776 References 777 Index 806  Preface The vast ocean of space is full of starry islands called galaxies. These objects, extraordinar- ily beautiful and diverse in their own right, not only are the localities within which stars form and evolve, but also act as the lighthouses that allow us to explore our Universe over cosmo- logical scales. Understanding the majesty and variety of galaxies in a cosmological context is therefore an important, yet daunting task. Particularly mind-boggling is the fact that, in the cur- rent paradigm, galaxies only represent the tip of the iceberg in a Universe dominated by some unknown ‘dark matter’ and an even more elusive form of ‘dark energy’. How do galaxies come into existence in this dark Universe, and how do they evolve? What is the relation of galaxies to the dark components? What shapes the properties of different galaxies? How are different properties of galaxies correlated with each other and what physics underlies these correlations? How do stars form and evolve in different galaxies? The quest for the answers to these questions, among others, constitutes an important part of modern cosmology, the study of the structure and evolution of the Universe as a whole, and drives the active and rapidly evolving research field of extragalactic astronomy and astrophysics. The aim of this book is to provide a self-contained description of the physical processes and the astronomical observations which underlie our present understanding of the formation and evolution of galaxies in a Universe dominated by dark matter and dark energy. Any book on this subject must take into account that this is a rapidly developing field; there is a danger that material may rapidly become outdated. We hope that this can be avoided if the book is appropri- ately structured. Our premises are the following. In the first place, although observational data are continually updated, forcing revision of the theoretical models used to interpret them, the general principles involved in building such models do not change as rapidly. It is these prin- ciples, rather than the details of specific observations or models, that are the main focus of this book. Secondly, galaxies are complex systems, and the study of their formation and evolution is an applied and synthetic science. The interest of the subject is precisely that there are so many unsolved problems, and that the study of these problems requires techniques from many branches of physics and astrophysics – the formation of stars, the origin and dispersal of the elements, the link between galaxies and their central black holes, the nature of dark matter and dark energy, the origin and evolution of cosmic structure, and the size and age of our Universe. A firm grasp of the basic principles and the main outstanding issues across this full breadth of topics is needed by anyone preparing to carry out her/his own research, and this we hope to provide. These considerations dictated both our selection of material and our style of presentation. Throughout the book, we emphasize the principles and the important issues rather than the details of observational results and theoretical models. In particular, special attention is paid to bringing out the physical connections between different parts of the problem, so that the reader will not lose the big picture while working on details. To this end, we start in each chapter with an introduction describing the material to be presented and its position in the overall scenario. In a field as broad as galaxy formation and evolution, it is clearly impossible to include all relevant xvii xviii Preface material. The selection of the material presented in this book is therefore unavoidably biased by our prejudice, taste, and limited knowledge of the literature, and we apologize to anyone whose important work is not properly covered. This book can be divided into several parts according to the material contained. Chapter 1 is an introduction, which sketches our current ideas about galaxies and their formation processes. Chapter 2 is an overview of the observational facts related to galaxy formation and evolution. Chapter 3 describes the cosmological framework within which galaxy formation and evolution must be studied. Chapters 4–8 contain material about the nature and evolution of the cosmo- logical density field, both in collisionless dark matter and in collisional gas. Chapters 9 and 10 deal with topics related to star formation and stellar evolution in galaxies. Chapters 11–15 are concerned with the structure, formation, and evolution of individual galaxies and with the statis- tical properties of the galaxy population, and Chapter 16 gives an overview of the intergalactic medium. In addition, we provide appendixes to describe the general concepts of general relativity (Appendix A), basic hydrodynamic and radiative processes (Appendix B), and some commonly used techniques of N-body and hydrodynamical simulations (Appendix C). The different parts are largely self-contained, and can be used separately for courses or sem- inars on specific topics. Chapters 1 and 2 are particularly geared towards novices to the field of extragalactic astronomy. Chapter 3, combined with parts of Chapters 4 and 5, could make up a course on cosmology, while a more advanced course on structure formation might be constructed around the material presented in Chapters 4–8. Chapter 2 and Chapters 11–15 contain material suited for a course on galaxy formation. Chapters 9, 10 and 16 contain special topics related to the formation and evolution of galaxies, and could be combined with Chapters 11–15 to form an extended course on galaxy formation and evolution. They could also be used independently for short courses on star formation and stellar evolution (Chapters 9 and 10), and on the intergalactic medium (Chapter 16). Throughout the book, we have adopted a number of abbreviations that are commonly used by galaxy-formation practitioners. In order to avoid confusion, these abbreviations are listed in Appendix D along with their definitions. Some important physical constants and units are listed in Appendix E. References are provided at the end of the book. Although long, the reference list is by no means complete, and we apologize once more to anyone whose relevant papers are overlooked. The number of references citing our own work clearly overrates our own contribution to the field. This is again a consequence of our limited knowledge of the existing literature, which is expanding at such a dramatic pace that it is impossible to cite all the relevant papers. The references given are mainly intended to serve as a starting point for readers interested in a more detailed literature study. We hope, by looking for the papers cited by our listed references, one can find relevant papers published in the past, and by looking for the papers citing the listed references, one can find relevant papers published later. Nowadays this is relatively easy to do with the use of the search engines provided by The SAO/NASA Astrophysics Data System1 and the arXiv e-print server.2 We would not have been able to write this book without the help of many people. We benefit- ted greatly from discussions with and comments by many of our colleagues, including E. Bell, A. Berlind, G. Börner, A. Coil, J. Dalcanton, A. Dekel, M. Hähnelt, M. Heyer, W. Hu, Y. Jing, N. Katz, R. Larson, M. Longair, M. Mac Low, C.-P. Ma, S. Mao, E. Neistein, A. Pasquali, J. Peacock, M. Rees, H.-W. Rix, J. Sellwood, E. Sheldon, R. Sheth, R. Somerville, V. Springel, R. Sunyaev, A. van der Wel, R. Wechsler, M. Weinberg, and X. Yang. We are also deeply indebted to our many students and collaborators who made it possible for us to continue to publish 1 http://adsabs.harvard.edu/abstract service.html 2 http://arxiv.org/  Preface xix scientific papers while working on the book, and who gave us many new ideas and insights, some of which are presented in this book. Many thanks to the following people who provided us with figures and data used in the book: M. Bartelmann, F. Bigiel, M. Boylan-Kolchin, S. Charlot, S. Courteau, J. Dalcanton, A. Dutton, K. Gebhardt, A. Graham, P. Hewett, G. Kauffmann, Y. Lu, L. McArthur, A. Pasquali, R. Saglia, S. Shen, Y. Wang, and X. Yang. We thankfully acknowledge the (almost) inexhaustible amount of patience of the people at Cambridge University Press, in particular our editor, Vince Higgs. We also thank the following institutions for providing support and hospitality to us during the writing of this book: the University of Massachusetts, Amherst; the Max-Planck Institute for Astronomy, Heidelberg; the Max-Planck Institute for Astrophysics, Garching; the Swiss Federal Institute of Technology, Zürich; the University of Utah; Shanghai Observatory; the Aspen Center for Physics; and the Kavli Institute of Theoretical Physics, Santa Barbara. Last but not least we wish to thank our loved ones, whose continuous support has been abso- lutely essential for the completion of this book. HM would like to thank his wife, Ling, and son, Ye, for their support and understanding during the years when the book was drafted. FB grate- fully acknowledges the love and support of Anna and Daka, and apologizes for the times they felt neglected because of ‘the book’. May 2009 Houjun Mo Frank van den Bosch Simon White  1 Introduction This book is concerned with the physical processes related to the formation and evolution of galaxies. Simply put, a galaxy is a dynamically bound system that consists of many stars. A typical bright galaxy, such as our own Milky Way, contains a few times 1010 stars and has a diameter (∼ 20 kpc) that is several hundred times smaller than the mean separation between bright galaxies. Since most of the visible stars in the Universe belong to a galaxy, the number density of stars within a galaxy is about 107 times higher than the mean number density of stars in the Universe as a whole. In this sense, galaxies are well-defined, astronomical identities. They are also extraordinarily beautiful and diverse objects whose nature, structure and origin have intrigued astronomers ever since the first galaxy images were taken in the mid-nineteenth century. The goal of this book is to show how physical principles can be used to understand the for- mation and evolution of galaxies. Viewed as a physical process, galaxy formation and evolution involve two different aspects: (i) initial and boundary conditions; and (ii) physical processes which drive evolution. Thus, in very broad terms, our study will consist of the following parts: Cosmology: Since we are dealing with events on cosmological time and length scales, we need to understand the space-time structure on large scales. One can think of the cosmological framework as the stage on which galaxy formation and evolution take place. Initial conditions: These were set by physical processes in the early Universe which are beyond our direct view, and which took place under conditions far different from those we can reproduce in Earth-bound laboratories. Physical processes: As we will show in this book, the basic physics required to study galaxy formation and evolution includes general relativity, hydrodynamics, dynamics of collision- less systems, plasma physics, thermodynamics, electrodynamics, atomic, nuclear and particle physics, and the theory of radiation processes. In a sense, galaxy formation and evolution can therefore be thought of as an application of (rela- tively) well-known physics with cosmological initial and boundary conditions. As in many other branches of applied physics, the phenomena to be studied are diverse and interact in many differ- ent ways. Furthermore, the physical processes involved in galaxy formation cover some 23 orders of magnitude in physical size, from the scale of the Universe itself down to the scale of individual stars, and about four orders of magnitude in time scales, from the age of the Universe to that of the lifetime of individual, massive stars. Put together, it makes the formation and evolution of galaxies a subject of great complexity. From an empirical point of view, the study of galaxy formation and evolution is very different from most other areas of experimental physics. This is due mainly to the fact that even the shortest time scales involved are much longer than that of a human being. Consequently, we cannot witness the actual evolution of individual galaxies. However, because the speed of light is finite, looking at galaxies at larger distances from us is equivalent to looking at galaxies when 1 2 Introduction the Universe was younger. Therefore, we may hope to infer how galaxies form and evolve by comparing their properties, in a statistical sense, at different epochs. In addition, at each epoch we can try to identify regularities and correspondences among the galaxy population. Although galaxies span a wide range in masses, sizes, and morphologies, to the extent that no two galaxies are alike, the structural parameters of galaxies also obey various scaling relations, some of which are remarkably tight. These relations must hold important information regarding the physical processes that underlie them, and any successful theory of galaxy formation has to be able to explain their origin. Galaxies are not only interesting in their own right, they also play a pivotal role in our study of the structure and evolution of the Universe. They are bright, long-lived and abundant, and so can be observed in large numbers over cosmological distances and time scales. This makes them unique tracers of the evolution of the Universe as a whole, and detailed studies of their large scale distribution can provide important constraints on cosmological parameters. In this book we therefore also describe the large scale distribution of galaxies, and discuss how it can be used to test cosmological models. In Chapter 2 we start by describing the observational properties of stars, galaxies and the large scale structure of the Universe as a whole. Chapters 3 through 10 describe the various physical ingredients needed for a self-consistent model of galaxy formation, ranging from the cosmolog- ical framework to the formation and evolution of individual stars. Finally, in Chapters 11–16 we combine these physical ingredients to examine how galaxies form and evolve in a cosmological context, using the observational data as constraints. The purpose of this introductory chapter is to sketch our current ideas about galaxies and their formation process, without going into any detail. After a brief overview of some observed properties of galaxies, we list the various physical processes that play a role in galaxy formation and outline how they are connected. We also give a brief historical overview of how our current views of galaxy formation have been shaped. 1.1 The Diversity of the Galaxy Population Galaxies are a diverse class of objects. This means that a large number of parameters is required in order to characterize any given galaxy. One of the main goals of any theory of galaxy formation is to explain the full probability distribution function of all these parameters. In particular, as we will see in Chapter 2, many of these parameters are correlated with each other, a fact which any successful theory of galaxy formation should also be able to reproduce. Here we list briefly the most salient parameters that characterize a galaxy. This overview is necessarily brief and certainly not complete. However, it serves to stress the diversity of the galaxy population, and to highlight some of the most important observational aspects that galaxy formation theories need to address. A more thorough description of the observational properties of galaxies is given in Chapter 2. (a) Morphology One of the most noticeable properties of the galaxy population is the existence of two basic galaxy types: spirals and ellipticals. Elliptical galaxies are mildly flattened, ellip- soidal systems that are mainly supported by the random motions of their stars. Spiral galaxies, on the other hand, have highly flattened disks that are mainly supported by rotation. Consequently, they are also often referred to as disk galaxies. The name ‘spiral’ comes from the fact that the gas and stars in the disk often reveal a clear spiral pattern. Finally, for historical reasons, ellipticals and spirals are also called early- and late-type galaxies, respectively. Most galaxies, however, are neither a perfect ellipsoid nor a perfect disk, but rather a combi- nation of both. When the disk is the dominant component, its ellipsoidal component is generally  1.1 The Diversity of the Galaxy Population 3 called the bulge. In the opposite case, of a large ellipsoidal system with a small disk, one typically talks about a disky elliptical. One of the earliest classification schemes for galaxies, which is still heavily used, is the Hubble sequence. Roughly speaking, the Hubble sequence is a sequence in the admixture of the disk and ellipsoidal components in a galaxy, which ranges from early- type ellipticals that are pure ellipsoids to late-type spirals that are pure disks. As we will see in Chapter 2, the important aspect of the Hubble sequence is that many intrinsic properties of galaxies, such as luminosity, color, and gas content, change systematically along this sequence. In addition, disks and ellipsoids most likely have very different formation mechanisms. There- fore, the morphology of a galaxy, or its location along the Hubble sequence, is directly related to its formation history. For completeness, we stress that not all galaxies fall in this spiral vs. elliptical classification. The faintest galaxies, called dwarf galaxies, typically do not fall on the Hubble sequence. Dwarf galaxies with significant amounts of gas and ongoing star formation typically have a very irreg- ular structure, and are consequently called (dwarf) irregulars. Dwarf galaxies without gas and young stars are often very diffuse, and are called dwarf spheroidals. In addition to these dwarf galaxies, there is also a class of brighter galaxies whose morphology neither resembles a disk nor a smooth ellipsoid. These are called peculiar galaxies and include, among others, galaxies with double or multiple subcomponents linked by filamentary structure and highly distorted galax- ies with extended tails. As we will see, they are usually associated with recent mergers or tidal interactions. Although peculiar galaxies only constitute a small fraction of the entire galaxy pop- ulation, their existence conveys important information about how galaxies may have changed their morphologies during their evolutionary history. (b) Luminosity and Stellar Mass Galaxies span a wide range in luminosity. The brightest galaxies have luminosities of ∼ 1012 L , where L indicates the luminosity of the Sun. The exact lower limit of the luminosity distribution is less well defined, and is subject to regular changes, as fainter and fainter galaxies are constantly being discovered. In 2007 the faintest galaxy known was a newly discovered dwarf spheroidal Willman I, with a total luminosity somewhat below 1000 L. Obviously, the total luminosity of a galaxy is related to its total number of stars, and thus to its total stellar mass. However, the relation between luminosity and stellar mass reveals a significant amount of scatter, because different galaxies have different stellar populations. As we will see in Chapter 10, galaxies with a younger stellar population have a higher luminosity per unit stellar mass than galaxies with an older stellar population. An important statistic of the galaxy population is its luminosity probability distribution func- tion, also known as the luminosity function. As we will see in Chapter 2, there are many more faint galaxies than bright galaxies, so that the faint ones clearly dominate the number density. However, in terms of the contribution to the total luminosity density, neither the faintest nor the brightest galaxies dominate. Instead, it is the galaxies with a characteristic luminosity similar to that of our Milky Way that contribute most to the total luminosity density in the present-day Universe. This indicates that there is a characteristic scale in galaxy formation, which is accen- tuated by the fact that most galaxies that are brighter than this characteristic scale are ellipticals, while those that are fainter are mainly spirals (at the very faint end dwarf irregulars and dwarf spheroidals dominate). Understanding the physical origin of this characteristic scale has turned out to be one of the most challenging problems in contemporary galaxy formation modeling. (c) Size and Surface Brightness As we will see in Chapter 2, galaxies do not have well-defined boundaries. Consequently, several different definitions for the size of a galaxy can be found in the literature. One measure often used is the radius enclosing a certain fraction (e.g. half) of the total luminosity. In general, as one might expect, brighter galaxies are bigger. However, even for 4 Introduction a fixed luminosity, there is a considerable scatter in sizes, or in surface brightness, defined as the luminosity per unit area. The size of a galaxy has an important physical meaning. In disk galaxies, which are rotation supported, the sizes are a measure of their specific angular momenta (see Chapter 11). In the case of elliptical galaxies, which are supported by random motions, the sizes are a measure of the amount of dissipation during their formation (see Chapter 13). Therefore, the observed distribution of galaxy sizes is an important constraint for galaxy formation models. (d) Gas Mass Fraction Another useful parameter to describe galaxies is their cold gas mass fraction, defined as fgas = Mcold /[Mcold + M ], with Mcold and M the masses of cold gas and stars, respectively. This ratio expresses the efficiency with which cold gas has been turned into stars. Typically, the gas mass fractions of ellipticals are negligibly small, while those of disk galaxies increase systematically with decreasing surface brightness. Indeed, the lowest surface brightness disk galaxies can have gas mass fractions in excess of 90 percent, in contrast to our Milky Way which has fgas ∼ 0.1. (e) Color Galaxies also come in different colors. The color of a galaxy reflects the ratio of its luminosity in two photometric passbands. A galaxy is said to be red if its luminosity in the redder passband is relatively high compared to that in the bluer passband. Ellipticals and dwarf spheroidals generally have redder colors than spirals and dwarf irregulars. As we will see in Chapter 10, the color of a galaxy is related to the characteristic age and metallicity of its stellar population. In general, redder galaxies are either older or more metal rich (or both). Therefore, the color of a galaxy holds important information regarding its stellar population. However, extinc- tion by dust, either in the galaxy itself, or along the line-of-sight between the source and the observer, also tends to make a galaxy appear red. As we will see, separating age, metallicity and dust effects is one of the most daunting tasks in observational astronomy. (f) Environment As we will see in §§2.5–2.7, galaxies are not randomly distributed throughout space, but show a variety of structures. Some galaxies are located in high-density clusters con- taining several hundreds of galaxies, some in smaller groups containing a few to tens of galaxies, while yet others are distributed in low-density filamentary or sheet-like structures. Many of these structures are gravitationally bound, and may have played an important role in the formation and evolution of the galaxies. This is evident from the fact that elliptical galaxies seem to prefer cluster environments, whereas spiral galaxies are mainly found in relative isolation (sometimes called the field). As briefly discussed in §1.2.8 below, it is believed that this morphology–density relation reflects enhanced dynamical interaction in denser environments, although we still lack a detailed understanding of its origin. (g) Nuclear Activity For the majority of galaxies, the observed light is consistent with what we expect from a collection of stars and gas. However, a small fraction of all galaxies, called active galaxies, show an additional non-stellar component in their spectral energy distribution. As we will see in Chapter 14, this emission originates from a small region in the centers of these galaxies, called the active galactic nucleus (AGN), and is associated with matter accretion onto a supermassive black hole. According to the relative importance of such non-stellar emission, one can separate active galaxies from normal (or non-active) galaxies. (h) Redshift Because of the expansion of the Universe, an object that is farther away will have a larger receding velocity, and thus a larger redshift. Since the light from high-redshift galaxies was emitted when the Universe was younger, we can study galaxy evolution by observing the galaxy population at different redshifts. In fact, in a statistical sense the high-redshift galaxies are the progenitors of present-day galaxies, and any changes in the number density or intrinsic properties of galaxies with redshift give us a direct window on the formation and evolution of the galaxy  1.2 Basic Elements of Galaxy Formation 5 population. With modern, large telescopes we can now observe galaxies out to redshifts beyond six, making it possible for us to probe the galaxy population back to a time when the Universe was only about 10 percent of its current age. 1.2 Basic Elements of Galaxy Formation Before diving into details, it is useful to have an overview of the basic theoretical framework within which our current ideas about galaxy formation and evolution have been developed. In this section we give a brief overview of the various physical processes that play a role dur- ing the formation and evolution of galaxies. The goal is to provide the reader with a picture of the relationships among the various aspects of galaxy formation to be addressed in greater detail in the chapters to come. To guide the reader, Fig. 1.1 shows a flow chart of galaxy for- mation, which illustrates how the various processes to be discussed below are intertwined. It is important to stress, though, that this particular flow chart reflects our current, undoubtedly incomplete view of galaxy formation. Future improvements in our understanding of galaxy for- mation and evolution may add new links to the flow chart, or may render some of the links shown obsolete. Fig. 1.1. A logic flow chart for galaxy formation. In the standard scenario, the initial and boundary con- ditions for galaxy formation are set by the cosmological framework. The paths leading to the formation of various galaxies are shown along with the relevant physical processes. Note, however, that processes do not separate as neatly as this figure suggests. For example, cold gas may not have the time to settle into a gaseous disk before a major merger takes place. 6 Introduction 1.2.1 The Standard Model of Cosmology Since galaxies are observed over cosmological length and time scales, the description of their formation and evolution must involve cosmology, the study of the properties of space-time on large scales. Modern cosmology is based upon the cosmological principle, the hypothesis that the Universe is spatially homogeneous and isotropic, and Einstein’s theory of general relativity, according to which the structure of space-time is determined by the mass distribution in the Universe. As we will see in Chapter 3, these two assumptions together lead to a cosmology (the standard model) that is completely specified by the curvature of the Universe, K, and the scale factor, a(t), describing the change of the length scale of the Universe with time. One of the basic tasks in cosmology is to determine the value of K and the form of a(t) (hence the space-time geometry of the Universe on large scales), and to show how observables are related to physical quantities in such a universe. Modern cosmology not only specifies the large-scale geometry of the Universe, but also has the potential to predict its thermal history and matter content. Because the Universe is expanding and filled with microwave photons at the present time, it must have been smaller, denser and hotter at earlier times. The hot and dense medium in the early Universe provides conditions under which various reactions among elementary particles, nuclei and atoms occur. Therefore, the application of particle, nuclear and atomic physics to the thermal history of the Universe in principle allows us to predict the abundances of all species of elementary particles, nuclei and atoms at different epochs. Clearly, this is an important part of the problem to be addressed in this book, because the formation of galaxies depends crucially on the matter/energy content of the Universe. In currently popular cosmologies we usually consider a universe consisting of three main com- ponents. In addition to the ‘baryonic’ matter, the protons, neutrons and electrons1 that make up the visible Universe, astronomers have found various indications for the presence of dark matter and dark energy (see Chapter 2 for a detailed discussion of the observational evidence). Although the nature of both dark matter and dark energy is still unknown, we believe that they are respon- sible for more than 95 percent of the energy density of the Universe. Different cosmological models differ mainly in (i) the relative contributions of baryonic matter, dark matter, and dark energy, and (ii) the nature of dark matter and dark energy. At the time of writing, the most pop- ular model is the so-called ΛCDM model, a flat universe in which ∼ 75 percent of the energy density is due to a cosmological constant, ∼ 21 percent is due to ‘cold’ dark matter (CDM), and the remaining 4 percent is due to the baryonic matter out of which stars and galaxies are made. Chapter 3 gives a detailed description of these various components, and describes how they influence the expansion history of the Universe. 1.2.2 Initial Conditions If the cosmological principle held perfectly and the distribution of matter in the Universe were perfectly uniform and isotropic, there would be no structure formation. In order to explain the presence of structure, in particular galaxies, we clearly need some deviations from perfect uni- formity. Unfortunately, the standard cosmology does not in itself provide us with an explanation for the origin of these perturbations. We have to go beyond it to search for an answer. A classical, general relativistic description of cosmology is expected to break down at very early times when the Universe is so dense that quantum effects are expected to be important. As we will see in §3.6, the standard cosmology has a number of conceptual problems when applied to the early Universe, and the solutions to these problems require an extension of the standard 1 Although an electron is a lepton, and not a baryon, in cosmology it is standard practice to include electrons when talking of baryonic matter  1.2 Basic Elements of Galaxy Formation 7 cosmology to incorporate quantum processes. One generic consequence of such an extension is the generation of density perturbations by quantum fluctuations at early times. It is believed that these perturbations are responsible for the formation of the structures observed in today’s Universe. As we will see in §3.6, one particularly successful extension of the standard cosmology is the inflationary theory, in which the Universe is assumed to have gone through a phase of rapid, exponential expansion (called inflation) driven by the vacuum energy of one or more quantum fields. In many, but not all, inflationary models, quantum fluctuations in this vacuum energy can produce density perturbations with properties consistent with the observed large scale structure. Inflation thus offers a promising explanation for the physical origin of the initial perturbations. Unfortunately, our understanding of the very early Universe is still far from complete, and we are currently unable to predict the initial conditions for structure formation entirely from first prin- ciples. Consequently, even this part of galaxy formation theory is still partly phenomenological: typically initial conditions are specified by a set of parameters that are constrained by observa- tional data, such as the pattern of fluctuations in the microwave background or the present-day abundance of galaxy clusters. 1.2.3 Gravitational Instability and Structure Formation Having specified the initial conditions and the cosmological framework, one can compute how small perturbations in the density field evolve. As we will see in Chapter 4, in an expand- ing universe dominated by non-relativistic matter, perturbations grow with time. This is easy to understand. A region whose initial density is slightly higher than the mean will attract its surroundings slightly more strongly than average. Consequently, over-dense regions pull matter towards them and become even more over-dense. On the other hand, under-dense regions become even more rarefied as matter flows away from them. This amplification of density perturbations is referred to as gravitational instability and plays an important role in modern theories of structure formation. In a static universe, the amplification is a run-away process, and the density contrast δ ρ /ρ grows exponentially with time. In an expanding universe, however, the cosmic expansion damps accretion flows, and the growth rate is usually a power law of time, δ ρ /ρ ∝ t α , with α > 0. As we will see in Chapter 4, the exact rate at which the perturbations grow depends on the cosmological model. At early times, when the perturbations are still in what we call the linear regime (δ ρ /ρ  1), the physical size of an over-dense region increases with time due to the overall expansion of the universe. Once the perturbation reaches over-density δ ρ /ρ ∼ 1, it breaks away from the expansion and starts to collapse. This moment of ‘turn-around’, when the physical size of the perturbation is at its maximum, signals the transition from the mildly nonlinear regime to the strongly nonlinear regime. The outcome of the subsequent nonlinear, gravitational collapse depends on the matter con- tent of the perturbation. If the perturbation consists of ordinary baryonic gas, the collapse creates strong shocks that raise the entropy of the material. If radiative cooling is inefficient, the sys- tem relaxes to hydrostatic equilibrium, with its self-gravity balanced by pressure gradients. If the perturbation consists of collisionless matter (e.g. cold dark matter), no shocks develop, but the system still relaxes to a quasi-equilibrium state with a more-or-less universal structure. This pro- cess is called violent relaxation and will be discussed in Chapter 5. Nonlinear, quasi-equilibrium dark matter objects are called dark matter halos. Their predicted structure has been thoroughly explored using numerical simulations, and they play a pivotal role in modern theories of galaxy formation. Chapter 7 therefore presents a detailed discussion of the structure and formation of dark matter halos. As we shall see, halo density profiles, shapes, spins and internal substructure 8 Introduction all depend very weakly on mass and on cosmology, but the abundance and characteristic density of halos depend sensitively on both of these. In cosmologies with both dark matter and baryonic matter, such as the currently favored CDM models, each initial perturbation contains baryonic gas and collisionless dark matter in roughly their universal proportions. When an object collapses, the dark matter relaxes violently to form a dark matter halo, while the gas shocks to the virial temperature, Tvir (see §8.2.3 for a definition) and may settle into hydrostatic equilibrium in the potential well of the dark matter halo if cooling is slow. 1.2.4 Gas Cooling Cooling is a crucial ingredient of galaxy formation. Depending on temperature and density, a variety of cooling processes can affect gas. In massive halos, where the virial temperature Tvir > 7 ∼ 10 K, gas is fully collisionally ionized and cools mainly through bremsstrahlung emission from free electrons. In the temperature range 104 K < Tvir < 106 K, a number of excitation and de-excitation mechanisms can play a role. Electrons can recombine with ions, emitting a pho- ton, or atoms (neutral or partially ionized) can be excited by a collision with another particle, thereafter decaying radiatively to the ground state. Since different atomic species have different excitation energies, the cooling rates depend strongly on the chemical composition of the gas. In halos with Tvir < 104 K, gas is predicted to be almost completely neutral. This strongly sup- presses the cooling processes mentioned above. However, if heavy elements and/or molecules are present, cooling is still possible through the collisional excitation/de-excitation of fine and hyper- fine structure lines (for heavy elements) or rotational and/or vibrational lines (for molecules). Finally, at high redshifts (z >∼ 6), inverse Compton scattering of cosmic microwave background photons by electrons in hot halo gas can also be an effective cooling channel. Chapter 8 will discuss these cooling processes in more detail. Except for inverse Compton scattering, all these cooling mechanisms involve two particles. Consequently, cooling is generally more effective in higher density regions. After nonlinear grav- itational collapse, the shocked gas in virialized halos may be dense enough for cooling to be effective. If cooling times are short, the gas never comes to hydrostatic equilibrium, but rather accretes directly onto the central protogalaxy. Even if cooling is slow enough for a hydrostatic atmosphere to develop, it may still cause the denser inner regions of the atmosphere to lose pres- sure support and to flow onto the central object. The net effect of cooling is thus that the baryonic material segregates from the dark matter, and accumulates as dense, cold gas in a protogalaxy at the center of the dark matter halo. As we will see in Chapter 7, dark matter halos, as well as the baryonic material associated with them, typically have a small amount of angular momentum. If this angular momentum is conserved during cooling, the gas will spin up as it flows inwards, settling in a cold disk in centrifugal equilibrium at the center of the halo. This is the standard paradigm for the formation of disk galaxies, which we will discuss in detail in Chapter 11. 1.2.5 Star Formation As the gas in a dark matter halo cools and flows inwards, its self-gravity will eventually dominate over the gravity of the dark matter. Thereafter it collapses under its own gravity, and in the presence of effective cooling, this collapse becomes catastrophic. Collapse increases the density and temperature of the gas, which generally reduces the cooling time more rapidly than it reduces the collapse time. During such runaway collapse the gas cloud may fragment into small, high- density cores that may eventually form stars (see Chapter 9), thus giving rise to a visible galaxy.  1.2 Basic Elements of Galaxy Formation 9 Unfortunately, many details of these processes are still unclear. In particular, we are still unable to predict the mass fraction of, and the time scale for, a self-gravitating cloud to be transformed into stars. Another important and yet poorly understood issue is concerned with the mass dis- tribution with which stars are formed, i.e. the initial mass function (IMF). As we will see in Chapter 10, the evolution of a star, in particular its luminosity as function of time and its eventual fate, is largely determined by its mass at birth. Predictions of observable quantities for model galaxies thus require not only the birth rate of stars as a function of time, but also their IMF. In principle, it should be possible to derive the IMF from first principles, but the theory of star formation has not yet matured to this level. At present one has to assume an IMF ad hoc and check its validity by comparing model predictions to observations. Based on observations, we will often distinguish two modes of star formation: quiescent star formation in rotationally supported gas disks, and starbursts. The latter are characterized by much higher star-formation rates, and are typically confined to relatively small regions (often the nucleus) of galaxies. Starbursts require the accumulation of large amounts of gas in a small volume, and appear to be triggered by strong dynamical interactions or instabilities. These pro- cesses will be discussed in more detail in §1.2.8 below and in Chapter 12. At the moment, there are still many open questions related to these different modes of star formation. What fraction of stars formed in the quiescent mode? Do both modes produce stellar populations with the same IMF? How does the relative importance of starbursts scale with time? As we will see, these and related questions play an important role in contemporary models of galaxy formation. 1.2.6 Feedback Processes When astronomers began to develop the first dynamical models for galaxy formation in a CDM dominated universe, it immediately became clear that most baryonic material is predicted to cool and form stars. This is because in these ‘hierarchical’ structure formation models, small dense halos form at high redshift and cooling within them is predicted to be very efficient. This disagrees badly with observations, which show that only a relatively small fraction of all baryons are in cold gas or stars (see Chapter 2). Apparently, some physical process must either prevent the gas from cooling, or reheat it after it has become cold. Even the very first models suggested that the solution to this problem might lie in feedback from supernovae, a class of exploding stars that can produce enormous amounts of energy (see §10.5). The radiation and the blast waves from these supernovae may heat (or reheat) surrounding gas, blowing it out of the galaxy in what is called a galactic wind. These processes are described in more detail in §§8.6 and 10.5. Another important feedback source for galaxy formation is provided by active galactic nuclei (AGN), the active accretion phase of supermassive black holes (SMBH) lurking at the centers of almost all massive galaxies (see Chapter 14). This process releases vast amounts of energy – this is why AGN are bright and can be seen out to large distances, which can be tapped by surrounding gas. Although only a relatively small fraction of present-day galaxies contain an AGN, obser- vations indicate that virtually all massive spheroids contain a nuclear SMBH (see Chapter 2). Therefore, it is believed that virtually all galaxies with a significant spheroidal component have gone through one or more AGN phases during their life. Although it has become clear over the years that feedback processes play an important role in galaxy formation, we are still far from understanding which processes dominate, and when and how exactly they operate. Furthermore, to make accurate predictions for their effects, one also needs to know how often they occur. For supernovae this requires a prior understanding of the star-formation rates and the IMF. For AGN it requires understanding how, when and where supermassive black holes form, and how they accrete mass. 10 Introduction inflow AGN accretion gas cooling star formation stars SMBH hot gas cold gas (evolving) feedback of energy, mass and metals outflow Fig. 1.2. A flow chart of the evolution of an individual galaxy. The galaxy is represented by the dashed box which contains hot gas, cold gas, stars and a supermassive black hole (SMBH). Gas cooling converts hot gas into cold gas, star formation converts cold gas into stars, and dying stars inject energy, metals and gas into the gas components. In addition, the SMBH can accrete gas (both hot and cold) as well as stars, producing AGN activity which can release vast amounts of energy which affect primarily the gaseous components of the galaxy. Note that in general the box will not be closed: gas can be added to the system through accretion from the intergalactic medium and can escape the galaxy through outflows driven by feedback from the stars and/or the SMBH. Finally, a galaxy may merge or interact with another galaxy, causing a significant boost or suppression of all these processes. It should be clear from the above discussion that galaxy formation is a subject of great com- plexity, involving many strongly intertwined processes. This is illustrated in Fig. 1.2, which shows the relations between the four main baryonic components of a galaxy: hot gas, cold gas, stars, and a supermassive black hole. Cooling, star formation, AGN accretion, and feedback processes can all shift baryons from one of these components to another, thereby altering the efficiency of all the processes. For example, increased cooling of hot gas will produce more cold gas. This in turn will increases the star-formation rate, hence the supernova rate. The addi- tional energy injection from supernovae can reheat cold gas, thereby suppressing further star formation (negative feedback). On the other hand, supernova blast waves may also compress the surrounding cold gas, so as to boost the star-formation rate (positive feedback). Understanding these various feedback loops is one of the most important and intractable issues in contemporary models for the formation and evolution of galaxies. 1.2.7 Mergers So far we have considered what happens to a single, isolated system of dark matter, gas and stars. However, galaxies and dark matter halos are not isolated. For example, as illustrated in Fig. 1.2, systems can accrete new material (both dark and baryonic matter) from the intergalactic medium, and can lose material through outflows driven by feedback from stars and/or AGN. In addition, two (or more) systems may merge to form a new system with very different properties from its progenitors. In the currently popular CDM cosmologies, the initial density fluctuations  1.2 Basic Elements of Galaxy Formation 11 t1 t2 t3 t4 Fig. 1.3. A schematic merger tree, illustrating the merger history of a dark matter halo. It shows, at three different epochs, the progenitor halos that at time t4 have merged to form a single halo. The size of each circle represents the mass of the halo. Merger histories of dark matter halos play an important role in hierarchical theories of galaxy formation. have larger amplitudes on smaller scales. Consequently, dark matter halos grow hierarchically, in the sense that larger halos are formed by the coalescence (merging) of smaller progenitors. Such a formation process is usually called a hierarchical or ‘bottom-up’ scenario. The formation history of a dark matter halo can be described by a ‘merger tree’ that traces all its progenitors, as illustrated in Fig. 1.3. Such merger trees play an important role in modern galaxy formation theory. Note, however, that illustrations such as Fig. 1.3 can be misleading. In CDM models part of the growth of a massive halo is due to merging with a large number of much smaller halos, and to a good approximation, such mergers can be thought of as smooth accretion. When two similar mass dark matter halos merge, violent relaxation rapidly transforms the orbital energy of the progenitors into the internal binding energy of the quasi-equilibrium remnant. Any hot gas associated with the progenitors is shock-heated during the merger and settles back into hydrostatic equilibrium in the new halo. If the progenitor halos contained central galaxies, the galaxies also merge as part of the violent relaxation process, producing a new central galaxy in the final system. Such a merger may be accompanied by strong star formation or AGN activity if the merging galaxies contained significant amounts of cold gas. If two merging halos have very different mass, the dynamical processes are less violent. The smaller system orbits within the main halo for an extended period of time during which two processes compete to determine its eventual fate. Dynamical friction transfers energy from its orbit to the main halo, causing it to spiral inwards, while tidal effects remove mass from its outer regions and may eventually dissolve it completely (see Chapter 12). Dynamical friction is more effective for more massive satellites, but if the mass ratio of the initial halos is large enough, the smaller object (and any galaxy associated with it) can maintain its identity for a long time. This is the process for the build-up of clusters of galaxies: a cluster may be considered as a massive dark matter halo hosting a relatively massive galaxy near its center and many satellites that have not yet dissolved or merged with the central galaxy. 12 Introduction As we will see in Chapters 12 and 13, numerical simulations show that the merger of two galaxies of roughly equal mass produces an object reminiscent of an elliptical galaxy, and the result is largely independent of whether the progenitors are spirals or ellipticals. Indeed, current hierarchical models of galaxy formation assume that most, if not all, elliptical galaxies are merger remnants. If gas cools onto this merger remnant with significant angular momentum, a new disk may form, producing a disk–bulge system like that in an early-type spiral galaxy. It should be obvious from the above discussion that mergers play a crucial role in galaxy formation. Detailed descriptions of halo mergers and galaxy mergers are presented in Chapter 7 and Chapter 12, respectively. 1.2.8 Dynamical Evolution When satellite galaxies orbit within dark matter halos, they experience tidal forces due to the central galaxy, due to other satellite galaxies, and due to the potential of the halo itself. These tidal interactions can remove dark matter, gas and stars from the galaxy, a process called tidal stripping (see §12.2), and may also perturb its structure. In addition, if the halo contains a hot gas component, any gas associated with the satellite galaxy will experience a drag force due to the relative motion of the two fluids. If the drag force exceeds the restoring force due to the satellite’s own gravity, its gas will be ablated, a process called ram-pressure stripping. These dynamical processes are thought to play an important role in driving galaxy evolution within clusters and groups of galaxies. In particular, they are thought to be partially responsible for the observed environmental dependence of galaxy morphology (see Chapter 15). Internal dynamical effects can also reshape galaxies. For example, a galaxy may form in a configuration which becomes unstable at some later time. Large scale instabilities may then redistribute mass and angular momentum within the galaxy, thereby changing its morphology. A well-known and important example is the bar-instability within disk galaxies. As we shall see in §11.5, a thin disk with too high a surface density is susceptible to a non-axisymmetric instability, which produces a bar-like structure similar to that seen in barred spiral galaxies. These bars may then buckle out of the disk to produce a central ellipsoidal component, a so-called ‘pseudo- bulge’. Instabilities may also be triggered in otherwise stable galaxies by interactions. Thus, an important question is whether the sizes and morphologies of galaxies were set at formation, or are the result of later dynamical process (‘secular evolution’, as it is termed). Bulges are particularly interesting in this context. They may be a remnant of the first stage of galaxy formation, or, as mentioned in §1.2.7, may reflect an early merger which has grown a new disk, or may result from buckling of a bar. It is likely that all these processes are important for at least some bulges. 1.2.9 Chemical Evolution In astronomy, all chemical elements heavier than helium are collectively termed ‘metals’. The mass fraction of a baryonic component (e.g. hot gas, cold gas, stars) in metals is then referred to as its metallicity. As we will see in §3.4, the nuclear reactions during the first three minutes of the Universe (the epoch of primordial nucleosynthesis) produced primarily hydrogen (∼ 75%) and helium (∼ 25%), with a very small admixture of metals dominated by lithium. All other metals in the Universe were formed at later times as a consequence of nuclear reactions in stars. When stars expel mass in stellar winds, or in supernova explosions, they enrich the interstellar medium (ISM) with newly synthesized metals. Evolution of the chemical composition of the gas and stars in galaxies is important for several reasons. First of all, the luminosity and color of a stellar population depend not only on its age and IMF, but also on the metallicity of the stars (see Chapter 10). Secondly, the cooling efficiency of gas depends strongly on its metallicity, in the sense that more metal-enriched gas cools faster  1.2 Basic Elements of Galaxy Formation 13 (see §8.1). Thirdly, small particles of heavy elements known as dust grains, which are mixed with the interstellar gas in galaxies, can absorb significant amounts of the starlight and reradiate it in infrared wavelengths. Depending on the amount of the dust in the ISM, which scales roughly linearly with its metallicity (see §10.3.7), this interstellar extinction can significantly reduce the brightness of a galaxy. As we will see in Chapter 10, the mass and detailed chemical composition of the material ejected by a stellar population as it evolves depend both on the IMF and on its initial metallicity. In principle, observations of the metallicity and abundance ratios of a galaxy can therefore be used to constrain its star-formation history and IMF. In practice, however, the interpretation of the observations is complicated by the fact that galaxies can accrete new material of different metallicity, that feedback processes can blow out gas, perhaps preferentially metals, and that mergers can mix the chemical compositions of different systems. 1.2.10 Stellar Population Synthesis The light we receive from a given galaxy is emitted by a large number of stars that may have different masses, ages, and metallicities. In order to interpret the observed spectral energy dis- tribution, we need to predict how each of these stars contributes to the total spectrum. Unlike many of the ingredients in galaxy formation, the theory of stellar evolution, to be discussed in Chapter 10, is reasonably well understood. This allows us to compute not only the evolution of the luminosity, color and spectrum of a star of given initial mass and chemical composition, but also the rates at which it ejects mass, energy and metals into the interstellar medium. If we know the star-formation history (i.e. the star-formation rate as a function of time) and IMF of a galaxy, we can then synthesize its spectrum at any given time by adding together the spectra of all the stars, after evolving each to the time under consideration. In addition, this also yields the rates at which mass, energy and metals are ejected into the interstellar medium, providing important ingredients for modeling the chemical evolution of galaxies. Most of the energy of a stellar population is emitted in the optical, or, if the stellar population is very young (< ∼ 10 Myr), in the ultraviolet (see §10.3