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