Nanohertz Gravitational Wave Astronomy

Description

Nanohertz Gravitational Wave Astronomy explores the exciting hunt for low frequency gravitational waves by using the extraordinary timing precision of pulsars. The book takes the reader on a tour across the expansive gravitational-wave landscape, from LIGO detections to the search for polarization patterns in the Cosmic Microwave Background, then hones in on the band of nanohertz frequencies that Pulsar Timing Arrays (PTAs) are sensitive to. Within this band may lie many pairs of the most massive black holes in the entire Universe, all radiating in chorus to produce a background of gravitational waves. The book shows how such extra-Galactic gravitational waves can alter the arrival times of radio pulses emanating from monitored Galactic pulsars, and how we can use the pattern of correlated timing deviations from many pulsars to tease out the elusive signal. The book takes a pragmatic approach to data analysis, explaining how it is performed in practice within classical and Bayesian statistics, as well as the numerous strategies one can use to optimize numerical Bayesian searches in PTA analyses. It closes with a complete discussion of the data model for nanohertz gravitational wave searches, and an overview of the past achievements, present efforts, and future prospects for PTAs. The book is accessible to upper division undergraduate students and graduate students of astronomy, and also serves as a useful desk reference for experts in the field. Key features: Contains a complete derivation of the pulsar timing response to gravitational waves, and the overlap reduction function for PTAs. Presents a comprehensive overview of source astrophysics, and the dynamical influences that shape the gravitational wave signals that PTAs are sensitive to. Serves as a detailed primer on gravitational-wave data analysis and numerical Bayesian techniques for PTAs. Cover Half Title Title Page Copyright Page Contents Preface About the Author Chapter 1: A Window onto the Warped Universe Chapter 2: Gravity & Gravitational Waves 2.1. GRAVITY BEFORE AND AFTER EINSTEIN 2.1.1. Standing on the Shoulders of Giants 2.1.2. The Happiest Thought 2.2. GRAVITATIONAL WAVES 2.2.1. A Brief History of Doubt 2.2.2. Waves from Geometry 2.2.2.1. The Quadrupole Formula 2.3. STOCHASTIC GRAVITATIONAL WAVE BACKGROUNDS 2.3.1. The Energy Density of a SGWB 2.3.2. Characteristic Strain 2.3.3. Spectrum of the Strain Signal 2.3.4. Overlap Reduction Function 2.4. THE GRAVITATIONAL WAVE SPECTRUM 2.4.1. Ground-based Detectors 2.4.2. Space-borne Detectors Chapter 3: Pulsar Timing 3.1. PULSARS 3.2. PRECISION PULSAR TIMING 3.3. TIMING RESPONSE TO GRAVITATIONAL WAVES 3.4. OVERLAP REDUCTION FUNCTION FOR A BACKGROUND OF GRAVITATIONAL WAVES Chapter 4: Sources & Signals 4.1. SUPERMASSIVE BINARY BLACK HOLES 4.1.1. Characteristic Strain Spectrum 4.1.2. Binary Dynamical Evolution 4.1.2.1. Dynamical Friction 4.1.2.2. Stellar Loss-cone Scattering 4.1.2.3. Viscous Circumbinary Disk Interaction 4.1.2.4. Gravitational-wave Inspiral 4.1.3. Signal from an Individual Binary 4.1.4. Gravitational-wave Memory Burst 4.2. EXOTIC GRAVITATIONAL WAVE SOURCES 4.2.1. Relic GWs 4.2.2. Cosmological Phase Transitions 4.2.3. Cosmic strings 4.3. NON-GW SOURCES OF CORRELATED TIMING DELAYS 4.3.1. Clock errors 4.3.2. Solar-system Ephemeris Errors 4.3.3. Dark Matter 4.3.3.1. Cold dark Matter Substructure 4.3.3.2. Fuzzy Dark Matter Chapter 5: Data Analysis 5.1. STATISTICAL INFERENCE 5.2. FREQUENTIST INFERENCE 5.2.1. Significance 5.2.2. Type I & II Errors 5.2.3. Upper Limits 5.3. BAYESIAN INFERENCE 5.3.1. Parameter Estimation 5.3.2. Upper Limits 5.3.3. Model Selection 5.3.3.1. In-sample Model Selection 5.3.3.2. Out-of-Sample Model Selection Chapter 6: Numerical Bayesian Techniques 6.1. METROPOLIS ALGORITHMS 6.1.1. How Long to Sample? 6.1.2. How to Propose New Parameters? 6.1.2.1. Adaptive Metropolis 6.1.2.2. Single Component Adaptive Metropolis 6.1.2.3. Differential Evolution 6.1.2.4. The Full Proposal Cocktail 6.2. GIBBS SAMPLING 6.3. EVIDENCE EVALUATION AND MODEL SELECTION 6.3.1. Harmonic Mean Estimator 6.3.2. Information Criterion Proxies 6.3.2.1. Bayesian Information Criterion 6.3.2.2. Akaike Information Criterion 6.3.3. Thermodynamic Integration 6.3.4. Nested sampling 6.3.5. Savage-Dickey density ratio 6.3.6. Product Space Sampling Chapter 7: The PTA Likelihood 7.1. THE PULSAR-TIMING DATA MODEL 7.1.1. Timing Ephemeris 7.1.2. Achromatic Low-frequency Processes 7.1.3. Chromatic Low-frequency Processes 7.1.4. White Noise 7.2. THE LIKELIHOOD 7.2.1. Full hierarchical Likelihood 7.2.2. Marginalized Likelihood 7.2.3. Modeling Deterministic Signals 7.3. LIKELIHOOD-BASED STATISTICS 7.3.1. GWB Statistics 7.3.1.1. Optimal Statistic 7.3.1.2. Bridging the Bayesian Odds Ratio and the Frequentist Optimal statistic 7.3.2. Individual Binary Statistics 7.3.2.1. Fe Statistic 7.3.2.2. Fp Statistic Chapter 8: The Past, Present, and Future of PTAs Index