Galaxy Formation

Preface
The Need for a New Approach?
The Aims and Scope of the Book
Acknowledgements
References
Contents
Part I Preliminaries
1 A Very Brief History of Cosmology and Galaxy Formation
1.1 Introduction
1.2 Early History of Cosmology
1.3 The Galaxies and the Structure of Our Galaxy
1.4 The Theory of the Expanding Universe
1.5 The Big Bang
1.6 Galaxy and Structure Formation
1.7 Hot and Cold Dark Matter
1.8 The Values of the Cosmological Parameters
1.9 The Very Early Universe
1.10 The Agenda
References
2 The Large Scale Structure of the Universe
2.1 The Isotropy and Spectrum of the Cosmic Microwave Background Radiation
2.1.1 The Isotropy of the Cosmic Microwave Background Radiation
2.1.2 The Spectrum of the Cosmic Microwave Background Radiation
2.2 The Large-Scale Distribution of Galaxies
2.2.1 Two-Point Correlation Functions
2.2.2 Walls and Voids in the Distribution of Galaxies on Large Scales
2.2.3 The Topology of the Galaxy Distribution on the Large Scale
2.3 Hubble's Law and the Expansion of the Universe
2.3.1 The Velocity-Distance Relation for Galaxies and Counts of Galaxies
2.3.2 The Expansion of the Universe
2.4 Conclusion
References
3 Galaxies
3.1 Introduction
3.2 The Hubble-de Vaucouleurs Sequence for Galaxies
3.3 Peculiar, Interacting, Starburst and Active Galaxies
3.3.1 Peculiar and Interacting Galaxies
3.3.2 Starburst Galaxies
3.3.3 Active Galaxies
3.4 Correlations Among the Populations of Galaxies: Broadband Properties
3.4.1 The Red and Blue Sequences
3.4.2 Colour Versus Absolute Magnitude
3.4.3 The Light Distribution in Galaxies and the Sérsic Index
3.5 Correlations Among the Populations of Galaxies: Spectroscopic and Gaseous Properties
3.5.1 Mean Stellar Age and Concentration C
3.5.2 The Faber–Jackson Relation and the Fundamental Plane
3.5.3 Luminosity-Metallicity Relations
3.5.4 The Tully-Fisher Relation for Spiral Galaxies
3.5.5 Neutral and Ionised Gas Along the Hubble Sequence
3.6 The Masses of Galaxies
3.6.1 The Virial Theorem for Clusters of Stars, Galaxies and Clusters of Galaxies
3.6.2 The Rotation Curves of Spiral Galaxies
3.6.3 The Velocity Dispersions of Elliptical Galaxies
3.7 The Luminosity Function of Galaxies
3.7.1 Is L* a Standard Candle?
3.7.2 The Brightest Galaxies in Clusters
3.8 The Effect of the Galaxy Environment
3.9 The Mean Mass-to-Luminosity Ratio for Visible Matter in the Universe
3.10 Concluding Remark
References
4 Clusters of Galaxies
4.1 The Demography of Clusters of Galaxies
4.1.1 The Abell Catalogues of Rich Clusters of Galaxies
4.1.2 Comparison with Clusters Selected from the Sloan Digital Sky Survey
4.1.3 Superclustering and the Large-Scale Distribution of Clusters of Galaxies
4.2 The Populations and Spatial Distribution of Galaxies in Clusters
4.3 Isothermal Gas Spheres
4.3.1 The Luminosity Function for Cluster Galaxies
4.3.2 Summary of the Properties of Rich Clusters of Galaxies
4.4 Dynamical Estimates of the Masses of Clusters of Galaxies
4.5 X-Ray Observations of Hot Gas in Clusters of Galaxies
4.5.1 Determining the Gravitational Potential
4.5.2 Scaling Relations
4.5.3 Cooling Flows
4.6 The Sunyaev-Zeldovich Effect in Hot Intracluster Gas
4.7 Gravitational Lensing by Galaxies and Clusters of Galaxies
4.7.1 Basic Theory of Gravitational Deflections
4.7.2 Magnification of Images by Gravitational Lensing
4.7.3 Extended Deflectors
4.7.4 Gravitational Lensing, Astrophysics and Cosmology
4.8 Forms of Dark Matter
4.8.1 Baryonic Dark Matter
4.8.2 Neutrinos with Finite Rest Mass
4.8.3 Astrophysical Constraints
4.9 Reflections
References
Part II The Basic Framework
5 The Theoretical Framework
5.1 The Cosmological Principle
5.2 Isotropic Curved Spaces
5.2.1 Isotropic 2-Dimensional Spherical Geometries
5.2.2 General Solution for Isotropic 2-spaces
5.3 The Space-Time Metric for Isotropic Curved Spaces
5.4 The Robertson-Walker Metric
5.5 Observations in Cosmology
5.5.1 The Cosmological Redshift
5.5.2 Hubble's Law
5.5.3 Angular Diameters
5.5.4 Apparent Intensities
5.5.5 Number Densities
5.5.6 The Age of the Universe
5.6 Summary
References
6 An Introduction to Relativistic Gravity
6.1 The Principle of Equivalence
6.2 The Gravitational Redshift
6.3 The Bending of Light Rays
6.4 Further Complications
6.5 The Route to General Relativity
6.5.1 Four-Tensors in Relativity
6.5.2 What Einstein Did
6.6 Experimental and Observational Tests of General Relativity
6.6.1 Parameterised Post-Newtonian Models
6.6.2 The Four Tests of General Relativity
6.6.2.1 The Gravitational Redshift
6.6.2.2 The Perihelion Shift of Mercury
6.6.2.3 The Gravitational Deflection of Electromagnetic Waves
6.6.2.4 The Shapiro Time-Delay Text
6.6.3 Pulsars and General Relativity
6.6.4 Variation of the Gravitational Constant with Cosmic Epoch
6.7 Summary
References
7 The Friedman World Models
7.1 Einstein's Field Equations
7.2 The Standard Friedman World Models with = 0
7.2.1 The Newtonian Analogue of the Friedman World Models
7.2.2 The Critical Density and the Density Parameter
7.2.3 The Dynamics of the Friedman Models with Λ= 0
7.2.4 Pedagogical digression: The Robertson-Walker Metric for an Empty Universe
7.3 Friedman Models with Non-zero Cosmological Constant
7.3.1 The Cosmological Constant and the Vacuum Energy Density
7.3.2 Varying the Equation of State of the Vacuum Energy
7.3.3 The Dynamics of World Models with =0: General Considerations
7.4 Observations in Cosmology
7.4.1 The Deceleration Parameter
7.4.2 The Cosmic Time–Redshift Relation
7.4.2.1 Models with Ω = 0
7.4.2.2 Models with Ω ≠0
7.4.3 Distance Measures as a Function of Redshift
7.4.3.1 Models with Ω = 0
7.4.3.2 Models with Ω ≠0
7.4.4 Angular Diameter-Redshift Relations
Models with Ω = 0
7.4.4.1 Models with Ω ≠0
7.4.5 Flux Density-Redshift Relations
7.4.5.1 Models with Ω= 0 and Ω ≠0
7.4.5.2 Ghost Images
7.4.6 The Comoving Volume Within Redshift z
7.4.6.1 Models with Ω = 0
7.4.6.2 Models with Ω ≠0
7.5 Angular Diameter Distances Between Any Two Redshifts
7.5.1 Models with Ω = 0
7.5.2 Models with Ω ≠0
7.6 The Flatness Problem
7.7 Inhomogeneous World Models
References
8 The Determination of Cosmological Parameters
8.1 The Cosmological Parameters
8.2 Testing the Friedman Models
8.3 Hubble's Constant H0
8.4 The Age of the Universe T0
8.5 The Deceleration Parameter q0
8.5.1 The Redshift-Magnitude Relation for the Brightest Galaxies in Clusters
8.5.2 The Redshift: K Magnitude Relation for Radio Galaxies—A Cautionary Tale
8.5.3 The Redshift-Magnitude Relation for Type 1a Supernovae
8.5.4 The Number Counts of Galaxies
8.5.5 The Angular Diameter-Redshift Test
8.6 Ω and the Statistics of Gravitational Lenses
8.7 The Density Parameter Ω0
8.8 Summary
References
9 The Thermal History of the Universe
9.1 Radiation-Dominated Universes
9.2 The Matter and Radiation Content of the Universe
9.3 The Epoch of Recombination
9.4 The Radiation-Dominated Era
9.5 The Speed of Sound as a Function of Cosmic Epoch
9.6 Early Epochs
References
10 Nucleosynthesis in the Early Universe
10.1 Equilibrium Abundances in the Early Universe
10.2 The Decoupling of Neutrinos and the Neutrino Barrier
10.3 The Synthesis of the Light Elements
10.4 The Abundances of the Light Elements
10.4.1 Determinations of the Observed Abundances of the Light Elements
10.4.2 Comparison of Theory and Observations
10.5 The Neutrino Background Temperature and the Value of χ
10.6 Baryon-Symmetric Universes
References
Part III The Development of Primordial Fluctuations Under Gravity
11 The Evolution of Density Perturbations in the Standard Big Bang
11.1 The Object of the Exercise
11.1.1 Preliminary Considerations
11.1.2 A Warning
11.2 The Non-relativistic Wave Equation for the Growth of Small Perturbations in the Expanding Universe
11.3 The Jeans' Instability
11.4 The Jeans' Instability in an Expanding Medium
11.4.1 Small Perturbation Analysis
11.4.2 Perturbing the Friedman Solutions
11.4.3 Falling Poles
11.4.4 The General Solution
11.5 The Evolution of Peculiar Velocities in the Expanding Universe
11.6 The Relativistic Case
11.7 The Basic Problem
References
12 More Tools and Problems
12.1 Horizons and the Horizon Problem
12.2 Pedagogical Interlude: Space–Time Diagrams for the Standard World Models
12.2.1 Distance and Times
12.2.2 The Past Light Cone
12.2.3 The Critical World Model Ω0 = 1, Ω = 0
12.2.4 The Reference World Model Ω0 = 0.3, Ω = 0.7
12.3 Superhorizon Scales
12.4 The Adiabatic Baryonic Fluctuations in the Standard Big Bang
12.4.1 The Radiation-Dominated Era
12.4.2 The Matter-Dominated Era
12.5 Dissipation Processes in the Pre-Recombination Era
12.6 Isothermal Perturbations
12.7 Baryonic Theories of Galaxy Formation
12.7.1 The Adiabatic Scenario
12.7.2 The Isothermal Scenario
12.8 What Went Wrong?
References
13 Dark Matter and Galaxy Formation
13.1 Introduction
13.2 Forms of Non-Baryonic Dark Matter
13.2.1 Axions
13.2.2 Neutrinos
13.3 WIMPs as Dark Matter Particles
13.3.1 Suppression Mechanism for WIMPs
13.3.2 Experimental Limits
13.4 Metric Perturbations and Hot and Cold Dark Matter
13.5 Free Streaming and the Damping of Hot Dark Matter Perturbations
13.6 Gravitational Instabilities in the Presence of Dark Matter
13.7 The Evolution of Hot and Cold Dark Matter Perturbations
13.7.1 Hot Dark Matter Scenario
13.7.2 Cold Dark Matter Scenario
13.8 Conclusion
References
14 Correlation Functions and the Spectrum of the Initial Fluctuations
14.1 The Two-Point Correlation Function for Galaxies
14.2 The Perturbation Spectrum
14.2.1 The Relation Between ξ(r) and the Power Spectrum of the Fluctuations
14.2.2 Power Spectra of Power-Law Form
14.2.3 The Harrison–Zeldovich Power Spectrum
14.3 The Evolution of the Initial Perturbation Spectrum: Transfer Functions
14.3.1 Adiabatic Cold Dark Matter
14.3.2 Adiabatic Hot Dark Matter
14.3.3 Isocurvature Cold Dark Matter
14.3.4 The Subsequent Evolution
14.4 Biasing
14.5 Reconstructing the Processed Initial Power Spectrum
14.5.1 Redshift Biases
14.5.2 Non-Linear Development of the Density Perturbations
14.5.3 The Role of Baryon Perturbations
14.6 Baryon Acoustic Oscillations in the Power Spectrum of Galaxies
14.6.1 The 2dF Galaxy Redshift Survey
14.6.2 The Sloan Digital Sky Survey
14.6.3 Putting it All Together
14.7 Variations on a Theme of Cold Dark Matter
References
15 The Cosmic Microwave Background Radiation
15.1 The Ionisation of the Intergalactic Gas Through the Epoch of Recombination
15.2 The Physical and Angular Scales of the Fluctuations
15.2.1 The Last Scattering Layer
15.2.2 The Silk Damping Scale
15.2.3 Particle and Sound Horizon Scales on the Last Scattering Surface
15.2.4 The Horizon Scale at the Epoch of Equality of Matter and Radiation Energy Densities
15.2.5 Summary
15.3 The Power Spectrum of Spatial Fluctuations in the Cosmic Microwave Background Radiation
15.3.1 The Statistical Description of the Temperature Fluctuations
15.3.2 The Power-Spectrum of Fluctuations in the Intensity of the Cosmic Microwave Background Radiation
15.4 Large Angular Scales
15.4.1 The Sachs-Wolfe Effect: Physical Arguments
15.4.2 The Integrated Sachs-Wolfe and Rees-Sciama Effects
15.4.3 Primordial Gravitational Waves
15.5 Intermediate Angular Scales: The Acoustic Peaks
15.6 Small Angular Scales
15.6.1 Statistical and Silk Damping
15.6.2 The Sunyaev-Zeldovich Effect in Clusters of Galaxies
15.6.3 Confusion Due to Discrete Sources
15.7 The Reionised Intergalactic Gas
15.8 The Polarisation of the Cosmic Microwave Background Radiation
15.8.1 The Polarisation Mechanism for the Cosmic Microwave Background Radiation
15.8.2 Polarisation from the Last Scattering Layer at the Epoch of Recombination
15.8.3 Polarisation from the Epoch of Reionisation
15.8.4 Primordial Gravitational Waves
15.8.5 Weak Gravitational Lensing
15.9 The Determination of Cosmological Parameters
15.10 Dark Energy Survey
15.11 Other Sources of Primordial Fluctuations
15.12 Reflections
References
Part IV The Post-recombination Universe
16 The Post-recombination Era
16.1 Introduction
16.2 The Non-linear Collapse of Density Perturbations
16.2.1 Isotropic Top-Hat Collapse
16.2.2 The Zeldovich Approximation
16.3 The Role of Dissipation
16.4 The Press-Schechter Mass Function
16.4.1 Elementary Theory
16.4.2 Evaluation
References
17 The Evolution of Galaxies and Active Galaxies with Cosmic Epoch
17.1 Introduction
17.2 Counts of Galaxies and Active Galaxies
17.2.1 Euclidean Source Counts
17.2.2 Source Counts for the Standard World Models
17.2.3 Submillimetre Counts of Dusty Galaxies
17.2.4 Number Counts in Models with Finite Ω
17.2.5 Fluctuations in the Background Radiation Due to Discrete Sources
17.3 The V/Vmax or Luminosity-Volume Test
17.4 The Background Radiation
17.4.1 The Background Radiation and the Source Counts
17.4.2 Evaluating the Background Due to Discrete Sources
17.4.3 The Effects of Evolution: The Case of the Radio Background Emission
17.5 The Evolution of Active Galaxies with Cosmic Epoch
17.5.1 Number Counts and V/Vmax Tests for Extragalactic Radio Sources
17.5.2 Radio Quiet Quasars
17.5.3 X-Ray Source Counts
17.5.4 X-Ray Clusters of Galaxies
17.6 Infrared and Submillimetre Number Counts
17.7 Counts of Galaxies
17.8 Clusters of Galaxies
References
18 The Intergalactic Medium
18.1 The Background Emission and Absorption of the Intergalactic Gas
18.2 The Gunn–Peterson Test
18.3 The Lyman-α Absorption Clouds
18.3.1 The Properties of the Lyman-α Absorption Clouds
18.3.2 The Nature of the Clouds in the Lyman-α Forest
18.3.3 The Evolution of Lyman-α Absorption Clouds with Cosmic Epoch
18.3.4 The Power-Spectrum of the Lyman-α Forest
18.4 The Luke-Warm Intergalactic Gas
18.4.1 A Salutary Tale: The X-Ray Background as a Cosmic Conspiracy
18.4.2 The Collisional Excitation of the Intergalactic Gas
18.4.3 The Lyman Continuum Opacity of the Intergalactic Gas
18.4.4 The Proximity Effect and the Diffuse Ultraviolet Background Radiation at Large Redshifts
18.5 The Post-reionisation Evolution of the Intergalactic Medium
18.6 The Epoch of Reionisation
18.7 The Origin of Magnetic Fields
18.7.1 The Biermann Battery
18.7.2 Turbulent Amplification of Magnetic Fields
18.7.3 Large-Scale Magnetic Fields from Extragalactic Radio Sources
References
19 Making Real Galaxies
19.1 Star and Element Formation in Galaxies
19.1.1 The Background Radiation and Element Formation
19.1.2 The Global Star Formation Rate from Optical and Ultraviolet Observations of Star-Forming Galaxies
19.1.3 The Lyman-Break Galaxies
19.1.4 The Hubble Deep and Ultra Deep Fields
19.2 The Cosmic Star Formation Rate
19.3 The Equations of Cosmic Chemical Evolution
19.4 The Abundances of Elements in Lyman-α Absorption Systems
19.5 The Old Red Galaxies
19.6 The Origin of Rotation
19.7 Putting It All Together: Semi-Analytic Models of Galaxy Formation
References
20 The Very Early Universe
20.1 The Big Problems
20.1.1 The Horizon Problem
20.1.2 The Flatness Problem
20.1.3 The Baryon-Asymmetry Problem
20.1.4 The Primordial Fluctuation Problem
20.1.5 The Values of the Cosmological Parameters
20.1.6 The Way Ahead
20.2 The Limits of Observation
20.3 The Anthropic Cosmological Principle
20.4 The Inflationary Paradigm: Historical Background
20.5 The Origin of the Spectrum of Primordial Perturbations
20.5.1 The Equation of State
20.5.2 The Duration of the Inflationary Phase
20.5.3 The Shrinking Hubble Sphere
20.5.4 Scalar Fields
20.5.5 The Quantised Harmonic Oscillator
20.5.6 The Spectrum of Fluctuations in the Scalar Field
20.6 Baryogenesis
20.7 The Planck Era
References
Main Index
Author Index