Fundamentals Of Interferometric Gravitational Wave Detectors (Second Edition)

Fundamentals Of Interferometric Gravitational Wave Detectors (Second Edition)

by Peter R Saulson

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Overview

LIGO's recent discovery of gravitational waves was headline news around the world. Many people will want to understand more about what a gravitational wave is, how LIGO works, and how LIGO functions as a detector of gravitational waves.This book aims to communicate the basic logic of interferometric gravitational wave detectors to students who are new to the field. It assumes that the reader has a basic knowledge of physics, but no special familiarity with gravitational waves, with general relativity, or with the special techniques of experimental physics. All of the necessary ideas are developed in the book.The first edition was published in 1994. Since the book is aimed at explaining the physical ideas behind the design of LIGO, it stands the test of time. For the second edition, an Epilogue has been added; it brings the treatment of technical details up to date, and provides references that would allow a student to become proficient with today's designs.

Product Details

ISBN-13: 9789813143074
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 04/19/2017
Pages: 336
Product dimensions: 6.20(w) x 9.00(h) x 0.90(d)

Table of Contents

Preface to the Second Edition xix

Preface xxi

1 The Search for Gravitational Waves 1

1.1 The Importance of the Search 2

1.2 A Bit of History 3

1.3 The Practice of Gravitational Wave Detection 5

1.4 A Guide for the Reader 6

2 The Nature of Gravitational Waves 9

2.1 Waves in General Relativity 9

2.2 The Michelson-Morley Experiment 12

2.3 A Schematic Detector of Gravitational Waves 18

2.4 Description of Gravitational Waves in Terms of Force 25

3 Sources of Gravitational Waves 27

3.1 Physics of Gravitational Wave Generation 27

3.2 In the Footsteps of Heinrich Hertz? 31

3.3 Observation of Gravitational Wave Emission 34

3.4 Astronomical Sources of Gravitational Waves 37

3.4.1 Neutron star binaries 38

3.4.2 Super novae 39

3.4.3 Pulsars 42

3.4.4 "Wagoner stars" 43

3.4.5 Black holes 44

3.4.6 Stochastic backgrounds 45

3.4.7 Discussion 46

4 Linear Systems, Signals and Noise 49

4.1 Characterizing a Time Series 49

4.1.1 The Fourier transform 50

4.1.2 Cross-correlation and autocorrelation 50

4.1.3 Convolution 52

4.1.4 The power spectrum 52

4.1.5 The Periodogram 53

4.1.6 Interpretation of power spectra 54

4.1.7 The amplitude spectral density 55

4.2 Linear Systems 56

4.2.1 Bode plots 61

4.2.2 Frequency response example 61

4.3 The Signal-to-Noise Ratio 62

4.3.1 Noise statistics 63

4.3.2 Matched templates and matched filters 65

4.3.3 SNR rules of thumb 67

4.3.4 The characteristic amplitude 68

5 Optical Readout Noise 71

5.1 Photon Shot Noise 72

5.2 Radiation Pressure Noise 75

5.3 Shot Noise in Classical and Quantum Mechanics 80

5.4 The Remarkable Precision of Interferometry 83

6 Folded Interferometer Arms 85

6.1 Herriott Delay Line 86

6.2 Beam Diameter and Mirror Diameter 88

6.3 Fabry-Perot Cavities 91

6.4 A Long Fabry-Perot Cavity 97

6.5 Hermite-Gaussian Beams 97

6.6 Scattered Light in Interferometers 99

6.7 Comparison of Fabry-Perot Cavities with Delay Lines 101

6.8 Optical Readout Noise in Folded Interferometers 101

6.9 Transfer Function of a Folded Interferometer 103

6.10 To Fold, or Not to Fold? 105

7 Thermal Noise 107

7.1 Brownian Motion 107

7.2 Brownian Motion of a Macroscopic Mass Suspended in a Dilute Gas 108

7.3 The Fluctuation-Dissipation Theorem 110

7.4 Remarks on the Fluctuation-Dissipation Theorem 112

7.5 The Quality Factor, Q 114

7.6 Thermal Noise in a Gas-Damped Pendulum 115

7.7 Dissipation from Internal Friction in Materials 117

7.8 Special Features of the Pendulum 121

7.9 Thermal Noise of the Pendulum's Internal Modes 123

8 Seismic Noise and Vibration Isolation 127

8.1 Ambient Seismic Spectrum 127

8.2 Seismometers 129

8.3 Vibration Isolators 130

8.4 Myths About Vibration Isolation 131

8.5 Isolation in an Interferometer 132

8.6 Stacks and Multiple Pendulums 135

8.7 Q: High or Low? 138

8.8 A Gravitational "Short Circuit1' Around Vibration Isolators 140

8.9 Beyond Passive Isolation 141

9 Design Features of Large Interferometers 143

9.1 How Small Can We Make a Gravitational Wave Inteferometer? 143

9.2 Noise from Residual Gas 146

9.2.1 Simple model 147

9.2.2 Exact result 148

9.2.3 Implications for Interferometer Design 149

9.3 The Space-Borne Alternative 149

10 Null Instruments 151

10.1 Some Virtues of Nullity 152

10.1.1 Null hypotheses 152

10.1.2 Null experiments 152

10.1.3 Null instruments 155

10.1.4 Null features of a gravitational wave interferometer 157

10.1.5 Active null instruments 158

10.2 The Advantages of Chopping 161

10.3 The Necessity to Operate a Gravitational Wave Interferometer as an Active Null Instrument 162

10.3.1 The need to chop 163

10.3.2 The need to actively null the output 164

11 Feedback Control Systems 167

11.1 The Loop Transfer Function 169

11.2 The Closed Loop Transfer Function 170

11.3 Designing the Loop Transfer Function 172

11.4 Instability 174

11.4.1 Causes of instability 175

11.4.2 Stability-tests 176

11.5 The Compensation Filter 177

11.6 Active Damping: A Servo Design Example 179

11.7 Feedback to Reduce Seismic Noise Over a Broad Band 186

11.7.1 Suspension point interferometer 186

11.7.2 Active isolation 187

12 An Interferometer as an Active Null Instrument 189

12.1 Fringe-Lock in a Non-Resonant Interferometer 189

12.2 Shot Noise in a Modulated Interferometer 195

12.3 Rejection of Laser Output Power Noise 197

12.4 Locking the Fringe 198

12.5 Fringe Lock for a Fabry-Perot Cavity 200

12.6 A Simple Interferometer with Fabry-Perot Arms 204

12.7 Beyond the Basic Interferometer 206

12.7.1 Power recycling 206

12.7.2 Signal recycling 208

12.7.3 Resonant sideband extraction 208

13 Resonant Mass Gravitational Wave Detectors 211

13.1 Does Form Follow Function? 211

13.2 The Idea of Resonant Mass Detectors 212

13.3 A Bar's Impulse Response and Transfer Function 213

13.4 Resonant Transducers 216

13.5 Thermal Noise in a Bar 219

13.6 Bandwidth of Resonant Mass Detectors 222

13.6.1 When are narrow bandwidths optimum? 222

13.6.2 Interpreting narrow-band observations 224

13.7 A Real Bar 226

13.8 Quantum Mechanical Sensitivity "Limit" 227

13.9 Beyond the Quantum "Limit"? 230

14 Detecting Gravitational Wave Signals 233

14.1 The Signal Detection Problem 233

14.2 Probability Distribution of Time Series 234

14.3 Coincidence Detection 239

14.4 Optimum Orientation 241

14.5 Local Coincidences 242

14.6 Searching for Periodic Gravitational Waves 243

14.6.1 When is a spectral peak improbably strong? 243

14.6.2 Signatures of periodic gravitational waves 244

14.6.3 Frequency noise in the source and elsewhere 248

14.7 Searching for a Stochastic Background 248

15 Gravitational Wave Astronomy 253

15.1 Gravitational Wave Source Positions 253

15.1.1 Network figure of merit 255

15.1.2 Why measure positions? 257

15.1.3 Inferences from precise positions 260

15.1.4 Temporal coincidence with non-gravitational observations 261

15.2 Interpretation of Gravitational Waveforms 262

15.2.1 Core collapse 263

15.2.2 Binary coalescences 264

15.2.3 A gravitational standard candle 265

15.2.4 Recognizing signals from black holes 266

15.3 Previous Gravitational Wave Searches 267

15.3.1 Room temperature bars 267

15.32 Cryogenic bars 268

15.3.3 The Strange case of Supernova 1987A 270

15.3.4 Gravitational wave searches with interferometers 272

15.3.5 Other observational upper limits 273

16 Prospects 277

16.1 A Prototype Interferometer 277

16.2 LIGO 278

16.3 Proposed Features of 4 km Interferometers 279

17 Epilogue 283

17.1 Introduction 283

17.2 Physics/Engineering Background (Chapters 4, 10, 11) 285

17.3 Prehistory of Gravitational Wave Detection (Chapter 1) 286

17.4 Gravitational Waves and their Interactions with Detectors (Chapter 2) 287

17.5 Sources of Gravitational Waves (Chapter 3) 287

17.6 Quantum Measurement Noise (Chapter 5) 288

17.7 Interferometer Configurations (Chapters 6 and 12) 289

17.8 Thermal Noise (Chapter 7) 289

17.9 Seismic Noise (Chapter 8 and Section 11.7.2) 291

17.10 Resonant Mass Detectors (Chapter 13) 294

17.11 Large Interferometers (Chapters 9 and 16) 295

17.12 Data Analysis (Chapter 14) 296

17.13 Gravitational Wave Astronomy (Chapter 15) 297

References 301

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