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Part I Preliminaries
1 A Brief History of Cosmology and Galaxy Formation.............................................................................................. 5
1.1 Prehistory..................................................................................... 5
1.2 The Galaxies and the Structure of our Galaxy........................................................................................... 7
1.3 The Theory of the Expanding Universe...................................................................................... 13
1.4 The Big Bang............................................................................................ 16
1.5 Galaxy and Structure Formation................................................................................... 18
1.6 Hot and Cold Dark Matter......................................................................................... 21
1.7 The Very Early Universe...................................................................................... 24
2 The Large Scale Structure of the Universe.............................................................................................. 29
2.1 The Spectrum and Isotropy of the Cosmic Microwave Background Radiation............................................................. 29
2.1.1 The Spectrum of the Cosmic Microwave
Background Radiation........................................................................ 30
2.1.2 The Isotropy of the Cosmic Microwave
Background Radiation........................................................................ 32
2.2 The Large-scale Distribution of Galaxies...................................................................................... 36 2.2.1 Two-point correlation functions........................................................................ 37 2.2.2 Walls and voids in the distribution of galaxies on large scales 41 2.3 Hubble’s Law and the Expansion of the Universe...................................................................................... 47 2.4 Conclusion.................................................................................. 513 Galaxies............................................................................................... 53
3.1 Introduction............................................................................... 53
3.2 The Revised Hubble Sequence for Galaxies...................................................................................... 54
3.3 Peculiar and Interacting Galaxies...................................................................................... 61
3.4 The Light Distribution in Galaxies...................................................................................... 63
3.4.1 Elliptical Galaxies.......................................................................... 63
3.4.2 Spiral and Lenticular Galaxies.......................................................................... 65
3.4.3 Putting the Light Distributions Together........................ 66
3.5 The Masses of Galaxies............................................................... 67
3.5.1 The Virial Theorem for Clusters of Stars, Galaxies and
Clusters of Galaxies........................................................ 67
3.5.2 The Rotation Curves of Spiral Galaxies........................... 70 3.5.3 The Velocity Dispersions of Elliptical Galaxies................ 73 3.6 The Properties of Spiral and Elliptical Galaxies.......................... 74 3.6.1 The Faber–Jackson Relation and the Fundamental Plane............................................................................... 74 3.6.2 Ellipticals Galaxies as Triaxial Systems........................... 75 3.6.3 The Tully-Fisher Relation for Spiral Galaxies................... 77 3.6.4 Luminosity-Metallicity Relations.................................... 783.7 The Luminosity Function of Galaxies.......................................... 80
3.7.1 Aspects of the Luminosity Function of Galaxies............. 83
3.7.2 The Integrated Luminosity and the Mean Mass- to-Luminosity Ratio for Visible Matter in the
Universe.......................................................................... 87
3.8 The Properties of Galaxies – Correlations Along the Hubble
Sequence..................................................................................... 89
3.9 The Red and Blue Sequences...................................................... 93
3.9.1 Colour versus Absolute Magnitude................................ 93
3.9.2 Sérsic Index and Colour.................................................. 94
3.9.3 Mean Stellar Age and Concentration Index C................ 94
3.9.4 The Effect of the Galaxy Environment............................ 97
3.9.5 The New Perspective...................................................... 98
3.10 Concluding Remark..................................................................... 98
4 Clusters of Galaxies............................................................................. 99
4.1 The Large-scale Distribution of Clusters of Galaxies.................. 99
4.1.1 The Abell Catalogues of Rich Clusters of Galaxies........ 100
4.1.2 Comparison with Clusters Selected from the Sloan Digital
Sky Survey................................................................... 1034.1.3 Abell Clusters and the Large-scale Distribution of Galaxies . 104
4.2 The Distribution of Galaxies in Clusters of Galaxies................. 106
4.2.1 The Galaxy Content and Spatial Distribution of Galaxies
in Clusters..................................................................... 1064.2.2 Clusters of Galaxies and Isothermal Gas Spheres........ 107
4.2.3 The Luminosity Function for Cluster Galaxies.............. 113
4.2.4 Summary of the Properties of Rich Clusters of Galaxies......................................................................... 114
4.3 Dynamical Estimates of the Masses of Clusters of Galaxies..... 114
4.4 X-ray Observations of Hot Gas in Clusters of Galaxies.............. 119
4.5 The Sunyaev-Zeldovich Effect in Hot Intracluster Gas.............. 129
4.6 Gravitational Lensing by Galaxies and Clusters of Galaxies...... 131
4.6.1 Basic Theory of Gravitational Deflections.................... 131
4.6.2 Magnification of Images by Gravitational Lensing....... 135
4.6.3 Extended Deflectors..................................................... 137
4.6.4 Gravitational Lensing and the Astrophysics of Galaxies........................................................................ 142
4.7 Forms of Dark Matter....................................................................................... 143
4.7.1 Baryonic Dark Matter.......................................................................... 144
4.7.2 Non-baryonic Dark Matter.......................................................................... 147
4.7.3 Astrophysical and Experimental Limits............................................................................ 149
Part II The Basic Framework
5 The Theoretical Framework........................................................................................ 155
5.1 The Cosmological Principle.................................................................................... 155
5.2 Isotropic Curved Spaces....................................................................................... 156
5.3 The Space-time Metric for Isotropic Curved Spaces....................................................................................... 161
5.4 The Robertson-Walker Metric....................................................................................... 165
5.5 Observations in Cosmology................................................................................ 168
5.5.1 The Cosmological Redshift........................................................................ 168
5.5.2 Hubble’s Law................................................................................ 173
5.5.3 Angular Diameters..................................................................... 173
5.5.4 Apparent Intensities..................................................................... 174
5.5.5 Number Densities....................................................................... 177
5.5.6 The Age of the Universe....................................................................... 177
5.6 Summary................................................................................... 178
6 An Introduction to Relativistic Gravity............................................................................................... 179
6.1 The Principle of Equivalence.............................................................................. 179
6.2 The Gravitational Redshift.................................................................................... 182
6.3 The Bending of Light Rays........................................................................................... 185
6.4 Further Complications........................................................................... 187
6.5 The Route to General Relativity................................................................................... 190
6.5.1 Four-tensors in Relativity...................................................................... 190
6.5.2 What Einstein Did................................................................................ 193
6.6 Experimental and Observational Tests of General Relativity................................................................................... 195
6.6.1 The Four Tests of General Relativity...................................................................... 195
6.6.2 Pulsars and General Relativity...................................................................... 198
6.6.3 Parameterised Post-Newtonian Models.......................................................................... 201
6.6.4 Variation of the Gravitational Constant with Cosmic Epoch . 203 6.7 Summary 205
7 The Friedman World Models............................................................................................... 207
7.1 Einstein’s Field Equations................................................................................. 207 7.2 The Standard Friedman World Models with Λ=0............................................................................................ 2107.2.1 The Newtonian Analogue of the Friedman World Models.......................................................................... 210
7.2.2 The Critical Density and the Density Parameter..................................................................... 212
7.2.3 The Dynamics of the Friedman Models with Λ=0................................................................................ 2137.3 Friedman Models with Non-zero Cosmological Constant................................................................................... 216
7.3.1 The Cosmological Constant and the Vacuum Energy Density 216
7.3.2 Varying the Equation of State of the Vacuum Energy........................................................................... 219
7.3.3 The Dynamics of World Models with Λ≠ 0: General Considerations...................................... 220
7.4 Observations in Cosmology................................................................................ 225
7.4.1 The Deceleration Parameter..................................................................... 225
7.4.2 The Cosmic Time–Redshift Relation........................................................................ 225
7.4.3 Distance Measures as a Function of Redshift........................................................................ 227
7.4.4 Angular Diameter-Redshift Relations...................................................................... 232
7.4.5 Flux Density-Redshift Relations...................................................................... 232
7.4.6 The Comoving Volume Within Redshift z.................................................................................... 236
7.5 Angular Diameter Distances Between Any Two Redshifts................................................................................... 238
7.6 The Flatness Problem.................................................................................... 240
7.7 Inhomogeneous World Models...................................................................................... 241
A7 The Robertson-Walker Metric for an Empty Universe.................................................................................................... 247
8 The Determination of Cosmological Parameters........................................................................................ 251
8.1 The Cosmological Parameters............................................................................... 251
8.2 Testing the Friedman Models...................................................................................... 253
8.3 Hubble’s Constant H0.............................................................................................. 256
8.4 The Age of the Universe T0....................................................................................................................... 260
8.5 The Deceleration Parameter q0............................................................................................... 262
8.5.1 The Redshift-Magnitude Relation for the Brightest
Galaxies in Clusters......................................................................... 263
8.5.2 The Redshift-Magnitude Relation for Radio Galaxies........................................................................ 264
8.5.3 The Redshift-Magnitude Relation for Type 1a Supernovae.................................................................. 267
8.5.4 The Number Counts of Galaxies........................................................................ 270 8.5.5 The Angular Diameter-Redshift Test.................................................................................................... 2718.6 QA and the Statistics of Gravitational Lenses....................................................................................... 274
8.7 The Density Parameter Q0.............................................................................................. 277
8.8 Summary................................................................................... 280
9 The Thermal History of the Universe............................................................................................ 281
9.1 Radiation-Dominated Universes.................................................................................. 281
9.2 The Matter and Radiation Content of the Universe.................................................................................... 283
9.3 The Epoch of Recombination......................................................................... 287
9.4 The Radiation-Dominated Era............................................................................................. 291
9.5 The Speed of Sound as a Function of Cosmic Epoch........................................................................................ 294
9.6 Early Epochs...................................................................................... 296
10 Nucleosynthesis in the Early Universe............................................................................................ 299
10.1 Equilibrium Abundances in the Early Universe.................................................................................... 299
10.2 The Decoupling of Neutrinos and the Neutrino Barrier....................................................................................... 300
10.3 The Synthesis of the Light Elements................................................................................... 302
10.4 The Abundances of the Light Elements................................................................................... 305
10.4.1 Determinations of the Observed Abundances of the Light Elements............................................... 306
10.4.2 Comparison of Theory and Observations................................................................ 309
10.5 The Neutrino Background Temperature and the Value of x................................................................................................ 311
10.6 Baryon-symmetric Universes.................................................................................. 314
Part III The Development of Primordial Fluctuations under Gravity
11 The Evolution of Perturbations in the Standard Big Bang................................................................................................... 321
11.1 What The Theorists Are Trying to Do.............................................................................................. 321
11.1.1 Why This Programme Is Feasible........................................................................ 322
11.1.2 A Warning........................................................................ 323
11.2 The Non-relativistic Wave Equation for the Growth of Small Perturbations in the Expanding Universe............................................................ 323
11.3 The Jeans’ Instability.................................................................................. 327
11.4 The Jeans’ Instability in an Expanding Medium.................................................................................... 329
11.4.1 Small Perturbation Analysis........................................................................ 329
11.4.2 Perturbing the Friedman Solutions...................................................................... 331
11.4.3 Falling Poles............................................................................. 333
11.4.4 The General Solution........................................................................ 335
11.5 The Evolution of Peculiar Velocities in the Expanding Universe.................................................................................... 338
11.6 The Relativistic Case.......................................................................................... 340
11.7 The Basic Problem.................................................................................... 343
12 More Tools and Problems........................................................................................... 345
12.1 Horizons and the Horizon Problem.................................................................................... 345
12.2 Pedagogical Interlude – Space–time Diagrams for the Standard
World Models...................................................................................... 349
12.2.1 Distance and Times............................................................................ 349
12.2.2 The Past Light Cone............................................................................. 351
12.2.3 The Critical World Model Ω0 = 1, ΩΛ = 0.................................................................................... 352
12.2.4 The Reference World Model Ω 0 = 0.3, Ω Λ = 0.7................................................................................. 354
12.3 Superhorizon Scales........................................................................................ 357
12.4 The Adiabatic Baryonic Fluctuations in the Standard Big Bang.......................................................................................... 360
12.4.1 The Radiation-Dominated Era................................................................................. 362
12.4.2 The Matter-Dominated Era................................................................................. 363
12.5 Dissipation Processes in the Pre-recombination Era............................................................................................. 365
12.6 Isothermal Perturbations........................................................................... 367
12.7 Baryonic Theories of Galaxy Formation................................................................................. 371
12.7.1 The Adiabatic Scenario........................................................................ 371
12.7.2 The Isothermal Scenario........................................................................ 373
12.8 What Went Wrong? 374
13 Dark Matter and Galaxy Formation.......................................................................................... 377
13.1 Introduction............................................................................. 377
13.2 Forms of Non-Baryonic Dark Matter....................................................................................... 379
13.3 WIMPs as Dark Matter Particles.................................................................................... 380
13.4 Metric Perturbations and Hot and Cold Dark Matter....................................................................................... 384
13.5 Free Streaming and the Damping of Hot Dark Matter Perturbations . 386
13.6 Instabilities in the Presence of Dark Matter....................................................................................... 387
13.7 The Evolution of Hot and Cold Dark Matter Perturbations........................................................................... 390
13.7.1 Hot Dark Matter Scenario........................................................................ 390
13.7.2 Cold Dark Matter Scenario........................................................................ 391
13.8 Conclusion................................................................................ 394
14 Correlation Functions and the Spectrum of the Initial Fluctuations....................................................................................... 395
14.1 The Two-point Correlation Function for Galaxies.................................................................................... 395
14.2 The Perturbation Spectrum.................................................................................. 398
14.2.1
( )
14.3 The Evolution of the Initial Perturbation Spectrum – Transfer Functions........................................................... 403
14.3.1 Adiabatic Cold Dark Matter.......................................................................... 403
14.3.2 Adiabatic Hot Dark Matter.......................................................................... 406
14.3.3 Isocurvature Cold Dark Matter.......................................................................... 406
14.3.4 The Subsequent Evolution...................................................................... 409
14.4 Biasing...................................................................................... 412
14.5 Reconstructing the Processed Initial Power Spectrum.................................................................................. 415
14.5.1 Redshift biases............................................................................ 416
14.5.2 Non-linear development of the density perturbations............................................................... 418
14.5.3 The role of baryon perturbations............................................................... 419
14.6 The Acoustic Peaks in the Power Spectrum of Galaxies.................................................................................... 421
14.6.1 The 2dF Galaxy Redshift Survey........................................................................... 422
14.6.2 The Sloan Digital Sky Survey........................................................................... 424
14.7 Variations on a Theme of Cold Dark Matter....................................................................................... 425
15 Fluctuations in the Cosmic Microwave Background Radiation........................................................................................... 431
15.1 The Ionisation of the Intergalactic Gas Through the Epoch of Recombination.................................................. 432
15.2 The Physical and Angular Scales of the Fluctuations.............................................................................. 434
15.2.1 The Last Scattering Layer............................................................................. 435
15.2.2 The Silk Damping Scale.............................................................................. 436
15.2.3 The Sound Horizon at the Last Scattering Layer............................................................................. 436
15.2.4 The Particle Horizon Scales............................................................................ 439
15.2.5 Summary...................................................................... 440
15.3 The Power Spectrum of Fluctuations in the Cosmic Microwave Background Radiation........................................................... 441
15.3.1 The Statistical Description of the Temperature Fluctuations . 441
15.3.2 The Power-Spectrum of Fluctuations in the Intensity of the Cosmic Microwave Background Radiation............................................... 444
15.4 Large Angular Scales........................................................................................ 445
15.4.1 The Sachs-Wolfe Effect – Physical Arguments.................................................................... 447
15.4.2 The Integrated Sachs-Wolfe and Rees-Sciama Effects........................................................................... 450
15.4.3 Primordial Gravitational Waves............................................................................................... 451
15.5 Intermediate Angular Scales – the Acoustic Peaks......................................................................................... 453
15.6 Small Angular Scales........................................................................................ 459
15.6.1 Statistical and Silk Damping....................................................................... 459
15.6.2 The Sunyaev-Zeldovich Effect in Clusters of Galaxies........................................................................ 460
15.6.3 Confusion due to Discrete Sources......................................................................... 462
15.7 The Reionised Intergalactic Gas............................................................................................ 462
15.8 The Polarisation of the Cosmic Microwave Background Radiation.................................................................................. 464
15.8.1 The Polarisation Mechanism for the Cosmic Microwave Background Radiation............................................... 465
15.8.2 Polarisation from the Last Scattering Layer............................................................................. 466
15.8.3 Polarisation from the Epoch of Reionisation................................................................. 469
15.8.4 Primordial Gravitational Waves............................................................................................... 469
15.8.5 Weak Gravitational Lensing.......................................................................... 471
15.9 The Determination of Cosmological Parameters............................................................................... 474
15.10Other Sources of Primordial Fluctuations.............................................................................. 476
15.11Reflections................................................................................ 477
Part IV The Post-Recombination Universe
16 The Post-Recombination Era...................................................................................................... 481
16.1 The Non-linear Collapse of Density Perturbations........................................................................... 483
16.1.1 Isotropic Top-hat Collapse........................................................................ 483
16.1.2 The Zeldovich Approximation............................................................. 486
16.2 The Role of Dissipation................................................................................ 488
16.3 The Press-Schechter Mass Function.................................................................................... 492
16.3.1 Exposition – Elementary Theory.......................................................................... 492
16.3.2 Development and Recapitulation.............................................................. 495
17 The Evolution of Galaxies and Active Galaxies with Cosmic Epoch................................................................................................. 501
17.1 Introduction............................................................................. 501
17.2 Counts of Galaxies and Active Galaxies.................................................................................... 502
17.2.1 Euclidean Source Counts.......................................................................... 503
17.2.2 Source Counts for the Standard World Models.......................................................................... 504
17.2.3 Submillimetre Counts of Dusty Galaxies........................................................................ 511
17.2.4 Number Counts in Models with Finite QA.................................................................................. 511
17.2.5 Fluctuations in the Background Radiation due to Discrete Sources.................................................. 514 17.317.4 The Background Radiation.................................................................................. 520
17.4.1 The Background Radiation and the Source Counts.......................................................................... 520
17.4.2 Evaluating the Background due to Discrete Sources......................................................................... 521
17.4.3 The Effects of Evolution – the Case of the Radio
Background Emission....................................................................... 523
17.5 The Evolution of Active Galaxies with Cosmic Epoch........................................................................................ 524
17.5.1
/
17.5.2 Radio Quiet Quasars......................................................................... 529
17.5.3 X-ray Source Counts.......................................................................... 533
17.5.4 X-ray Clusters of Galaxies........................................................................ 540
17.6 Infrared and Submillimetre Number Counts...................................................................................... 541
17.7 Counts of Galaxies.................................................................................... 548
17.8 Clusters of Galaxies.................................................................................... 553
18 The Intergalactic Medium............................................................................................. 557
18.1 The Background Emission of and Absorption by the Intergalactic
Gas............................................................................................ 558
18.2 The Gunn–Peterson Test................................................................................................................... 559
18.3 The Lyman-a Absorption Clouds....................................................................................... 562
18.3.1 The Properties of the Lyman-a Absorption Clouds........................................................................... 56318.3.2 The Nature of the Clouds in the Lyman-a Forest............................................................................ 565
18.3.3 The Evolution of Lyman-a Absorption Clouds with
Cosmic Epoch............................................................................ 566
18.3.4 The Power-spectrum of the Lyman-a Forest............................................................................ 567
18.4 The Luke-warm Intergalactic Gas............................................................................................ 570
18.4.1 The X-ray Background and a Cosmic Conspiracy.................................................................... 571
18.4.2 The Collisional Excitation of the Intergalactic Gas................................................................................ 572
18.4.3 The Emission and Absorption of Diffuse Luke-warm Intergalactic Gas......................................................... 573
18.4.4 The Proximity Effect and the Diffuse Ultraviolet
Background Radiation at Large Redshifts....................................................................... 578
18.5 The Lyman Continuum Opacity of the Intergalactic Gas............................................................................................ 579
18.6 Modelling the Evolution of the Intergalactic Medium.................................................................................... 582
18.7 The Epoch of Reionisation............................................................................. 584
18.8 The Origin of Magnetic Fields......................................................................................... 587
19 Making Real Galaxies............................................................................................. 593
19.1 Star and Element Formation in Galaxies.................................................................................... 593
19.1.1 The Background Radiation and Element Formation..................................................................... 594
19.1.2 The Global Star Formation Rate from Optical and
Ultraviolet Observations of Star-forming Galaxies........................................................................ 598
19.1.3 The Lyman-break Galaxies........................................................................ 601
19.1.4 The Hubble Deep and Ultra Deep Fields............................................................................ 601
19.1.5 Submillimetre Determinations of Cosmic Star Formation
Rate............................................................................... 606
19.2 The Abundances of Elements in Lyman-a Absorption Systems..................................................................................... 610
19.3 The Equations of Cosmic Chemical Evolution.................................................................................. 614 19.4 The Old Red Galaxies.................................................................................... 617 19.5 The Origin of Rotation.............................................................. 621 19.6 Putting It All Together – Semi-Analytic Models of Galaxy Formation62320 The Very Early Universe.................................................................... 631
20.1 The Big Problems...................................................................... 631
20.1.1 The horizon problem.................................................... 631
20.1.2 The flatness problem.................................................... 632
20.1.3 The baryon-asymmetry problem................................. 632
20.1.4 The Primordial Fluctuation Problem............................ 633
20.1.5 The Values of the Cosmological Parameters................ 633
20.1.6 The Way Ahead............................................................. 634
20.2 The Limits of Observation......................................................... 635
20.3 The Anthropic Cosmological Principle...................................... 636
20.4 The Inflationary Universe – Historical Background.................. 636
20.5 The Origin of the Spectrum of Primordial Perturbations......... 640
20.5.1 The equation of state................................................... 641
20.5.2 The duration of the inflationary phase........................ 641
20.5.3 The shrinking Hubble sphere........................................ 641
20.5.4 Scalar Fields.................................................................. 644
20.5.5 The Quantised Harmonic Oscillator............................. 646
20.5.6 The Spectrum of Fluctuations in the Scalar Field......... 647
20.6 Baryogenesis............................................................................. 651
20.7 The Planck Era........................................................................... 652
Index.......................................................................................................... 655References............................................................................... 689
Malcolm Longair, CBE, FRS, FRSE is Jacksonian Professor Emeritus of Natural Philosophy and Director of Development, Cavendish Laboratory. He has held many highly respected positions within the fields of physics and astronomy. He was appointed the ninth Astronomer Royal of Scotland in 1980, as well as the Regius Professor of Astronomy, University of Edinburgh, and the Director of the Royal Observatory, Edinburgh. He was head of the Cavendish Laboratory, the Physics Department of Cambridge University, from 1997 to 2005. He has served on and chaired many international committees, boards and panels, working with both NASA, the European Space Agency and the ERC. He has received much recognition for his work over the years. His main research interests are in high energy astrophysics, astrophysical cosmology and the history of physics and astrophysics. He has chaired numerous committees for specific science projects, including the Planck and Euclid missions of ESA. His major books, in addition to the present volume, include Theoretical Concepts in Physics (3rd edition 2020), High Energy Astrophysics (3rd edition 2011), Quantum Concepts in Physics (2013), the Cosmic Century: A History of Astrophysics and Cosmology (2008) and Maxwell’s Enduring Legacy: A Scientific History of the Cavendish Laboratory (2016).
This third edition of Malcolm Longair’s highly acclaimed textbook, Galaxy Formation, is an up-to-date text on astrophysical cosmology expounding the structure of classical cosmological models from a contemporary viewpoint. This forms the background to a detailed study of the origin of structure and galaxies in the Universe. The derivations of many of the most important results are described using simple physical arguments which illuminate the results of more advanced treatments. A very wide range of recent observational data is brought to bear upon the problems, including the results from the Hubble Space Telescope, the Planck mission of the European Space Agency, galaxy surveys such as the Sloan Digital Sky Survey, the ALMA submillimetre observatory, studies of Type 1a supernovae and many other remarkable recent observations.
This book serves as an ideal text for graduate level courses on astrophysical cosmology and is also highly appreciated as a reference source for professional astrophysicist and cosmologists.
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