Interferometric. Gravitational Wav. Detectors. \p World Scientific. Fundamentals of. Peter R. Sawlson. Syracuse University, USA.

Transcription

1 SINGAPORE HONGKONG Fundamentals of Interferometric Gravitational Wav Detectors Second Edition Peter R. Sawlson Martin A. Pomerantz '37 Professor of Physics Syracuse University, USA \p World Scientific NEW JERSEY LONDON BEIJING SHANGHAI TAIPEI CHENNAI TOKYO

2 Contents Preface to the Second Edition xix Preface xxi 1. The Search for Gravitational Waves The Importance of the Search A Bit of History The Practice of Gravitational Wave Detection A Guide for the Reader 6 2. The Nature of Gravitational Waves Waves in General Relativity The Michelson-Morley Experiment A Schematic Detector of Gravitational Waves Description of Gravitational Waves in Terms of Force Sources of Gravitational Waves Physics of Gravitational Wave Generation In the Footsteps of Heinrich Hertz? Observation of Gravitational Wave Emission Astronomical Sources ofgravitational Waves Neutron star binaries Supernovae Pulsars "Wagoner stars" Black holes 44 v

3 vi ii Fundamentals of Interferometric GW Detectors (2nd Edn.) B Stochastic backgrounds Discussion Linear Systems, Signals and Noise Characterizing a Time Series The Fourier transform Cross-correlation and autocorrelation Convolution The power spectrum The Periodogram Interpretation of power spectra The amplitude spectral density Linear Systems Bode plots Frequency response example The Signal-to-Noise Ratio Noise statistics Matched templates and matched filters SNR rules of thumb The characteristic amplitude Optical Readout Noise Photon Shot Noise Radiation Pressure Noise Shot Noise in Classical and Quantum Mechanics The Remarkable Precision of Interferometry Folded Interferometer Arms Herriott Delay Line Beam Diameter and Mirror Diameter Fabry-Perot Cavities A Long Fabry-Perot Cavity Hermite-Gaussian Beams Scattered Light in Interferometers Comparison of Fabry-Perot Cavities with Delay Lines Optical Readout Noise in Folded Interferometers Transfer Function of a Folded Interferometer To Fold, or Not to Fold? Thermal Noise Brownian Motion 107

4 Contents vii 7.2 Brownian Motion of a Macroscopic Mass Suspended in a Dilute Gas The Fluctuation-Dissipation Theorem Remarks on the Fluctuation-Dissipation Theorem The Quality Factor, Thermal Noise in a Gas-Damped Pendulum Dissipation from Internal Friction in Materials Special Features of the Pendulum Thermal Noise of the Pendulum's Internal Modes Seismic Noise and Vibration Isolation Ambient Seismic Spectrum Seismometers Vibration Isolators Myths About Vibration Isolation Isolation in an Interferometer Stacks and Multiple Pendulums Q: High or Low? A Gravitational "Short Circuit" Around Vibration Isolators Beyond Passive Isolation Design Features oflarge Interferometers How Small Can We Make a Gravitational Wave Inteferometer? Noise from Residual Gas Simple model Exact result Implications for Interferometer Design The Space-Borne Alternative Null Instruments Some Virtues of Nullity Null hypotheses Null experiments Null instruments Null features of a gravitational wave interferometer Active null instruments The Advantages of Chopping The Necessity to Operate a Gravitational Wave Interferometer as an Active Null Instrument 162

5 viii Fundamentals of Interferometric GW Detectors (2nd Edn.) B The need to chop The need to actively null the output Feedback Control Systems The Loop Transfer Function The Closed Loop Transfer Function Designing the Loop Transfer Function Instability Causes of instability Stability tests The Compensation Filter Active Damping: A Servo Design Example Feedback to Reduce Seismic Noise Over a Broad Band Suspension point interferometer Active isolation An Interferometer as an Active Null Instrument Fringe-Lock in a Non-Resonant Interferometer Shot Noise in a Modulated Interferometer Rejection of Laser Output Power Noise Locking the Fringe Fringe Lock for a Fabry-Perot Cavity A Simple Interferometer with Fabry-Perot Arms Beyond the Basic Interferometer Power recycling Signal recycling Resonant sideband extraction Resonant Mass Gravitational Wave Detectors Does Form Follow Function? The Idea of Resonant Mass Detectors A Bar's Impulse Response and Transfer Function Resonant Transducers Thermal Noise in a Bar Bandwidth of Resonant Mass Detectors When are narrow bandwidths optimum? Interpreting narrow-band observations A Real Bar Quantum Mechanical Sensitivity "Limit" Beyond the Quantum "Limit"? 230

6 Contents ix 14. Detecting Gravitational Wave Signals The Signal Detection Problem Probability Distribution oftime Series Coincidence Detection Optimum Orientation Local Coincidences Searching for Periodic Gravitational Waves When is a spectral peak improbably strong? Signatures of periodic gravitational waves Frequency noise in the source and elsewhere Searching for a Stochastic Background Gravitational Wave Astronomy Gravitational Wave Source Positions Network figure of merit Why measure positions? Inferences from precise positions Temporal coincidence with non-gravitational observations Interpretation of Gravitational Waveforms Core collapse Binary coalescences A gravitational standard candle Recognizing signals from black holes Previous Gravitational Wave Searches Room temperature bars Cryogenic bars The Strange case of Supernova 1987A Gravitational wave searches with interferometers Other observational upper limits Prospects A Prototype Interferometer LIGO Proposed Features of 4 km Interferometers Epilogue Introduction Physics/Engineering Background (Chapters 4, 10, 11) Prehistory of Gravitational Wave Detection (Chapter 1) 286

7 x Fundamentals of Interferometric GW Detectors (2nd Edn.) M 11A Gravitational Waves and their Interactions with Detectors (Chapter 2) Sources of Gravitational Waves (Chapter 3) Quantum Measurement Noise (Chapter 5) Interferometer Configurations (Chapters 6 and 12) Thermal Noise (Chapter 7) Seismic Noise (Chapter 8 and Section ) Resonant Mass Detectors (Chapter 13) Large Interferometers (Chapters 9 and 16) Data Analysis (Chapter 14) Gravitational Wave Astronomy (Chapter 15) 297 References 301