Galaxy Formation / Edition 2

Galaxy Formation / Edition 2

by Malcolm S. Longair
ISBN-10:
3540734775
ISBN-13:
9783540734772
Pub. Date:
01/08/2008
Publisher:
Springer Berlin Heidelberg
ISBN-10:
3540734775
ISBN-13:
9783540734772
Pub. Date:
01/08/2008
Publisher:
Springer Berlin Heidelberg
Galaxy Formation / Edition 2

Galaxy Formation / Edition 2

by Malcolm S. Longair
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Overview

Delineating the huge strides taken in cosmology in the past ten years, this much-anticipated second edition of Malcolm Longair's highly appreciated textbook has been extensively and thoroughly updated. Quite simply, it tells the story of modern astrophysical cosmology.


Product Details

ISBN-13: 9783540734772
Publisher: Springer Berlin Heidelberg
Publication date: 01/08/2008
Series: Astronomy and Astrophysics Library
Edition description: 2nd ed. 2008
Pages: 737
Product dimensions: 6.10(w) x 9.25(h) x 0.05(d)

About the Author

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).

Table of Contents

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.................................................................................. 51

3 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.................................... 78

3.7 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................................................................... 103

4.1.3 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..................................................................... 106

4.2.2 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............................................................................................ 210

7.2.1 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................................................................................ 213

7.3 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.................................................................................................... 271

8.6 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

( )

The Relation Between ξ r and the Power Spectrum of the Fluctuations.......................................... 398

14.2.2 The Initial Power-Spectrum...................................................................... 400

14.2.3 The Harrison–Zeldovich Power Spectrum...................................................................... 401

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

17.3


/

The V Vmax or Luminosity-Volume Test................................................................................................................... 517

17.4 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

/

Number Counts and V Vmax Tests for Extragalactic Radio Sources.................................................. 524

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........................................................................... 563

18.3.2 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 Formation623

20 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.......................................................................................................... 655

References............................................................................... 689

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