Analysis of Gravitational-Wave Data

by Piotr Jaranowski , Andrzej Krolak

• ISBN13: 9780521864596
• ISBN10: 0521864593
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-09-28
• Publisher: Cambridge University Press

Summary

This series provides a broad range of high quality books, suitable for experimentalists and theorists, covering all aspects of particle physics, nuclear physics, cosmology, and the interfaces between them.

Table of Contents

Preface	p. vii
Notation and conventions	p. x
Overview of the theory of gravitational radiation	p. 1
Linearized general relativity	p. 2
Plane monochromatic gravitational waves	p. 7
Description in the TT coordinate system	p. 10
Description in the observer's proper reference frame	p. 13
Gravitational waves in the curved background	p. 17
Energy-momentum tensor for gravitational waves	p. 19
Generation of gravitational waves and radiation reaction	p. 20
Astrophysical sources of gravitational waves	p. 26
Burst sources	p. 27
Periodic sources	p. 28
Stochastic sources	p. 29
Case study: binary systems	p. 30
Case study: a rotating triaxial ellipsoid	p. 42
Case study: supernova explosion	p. 45
Case study: stochastic background	p. 47
Statistical theory of signal detection	p. 51
Random variables	p. 52
Stochastic processes	p. 56
Hypothesis testing	p. 62
The matched filter in Gaussian noise: deterministic signal	p. 71
Estimation of stochastic signals	p. 76
Estimation of parameters	p. 79
Non-stationary stochastic processes	p. 90
Time series analysis	p. 99
Sample mean and correlation function	p. 99
Power spectrum estimation	p. 101
Tests for periodicity	p. 107
Goodness-of-fit tests	p. 109
Higher-order spectra	p. 111
Responses of detectors to gravitational waves	p. 114
Detectors of gravitational waves	p. 114
Doppler shift between freely falling observers	p. 115
Long-wavelength approximation	p. 122
Responses of the solar-system-based detectors	p. 124
Maximum-likelihood detection in Gaussian noise	p. 131
Deterministic signals	p. 131
Case studies: deterministic signals	p. 150
Network of detectors	p. 167
Detection of stochastic signals	p. 184
Data analysis tools	p. 192
Linear signal model	p. 192
Grid of templates in the parameter space	p. 197
Numerical algorithms to calculate the F-statistic	p. 201
Analysis of the candidates	p. 208
The chirp waveform	p. 212
Proof of the Neyman-Pearson lemma	p. 218
Detector's beam-pattern functions	p. 221
LISA detector	p. 222
Earth-based detectors	p. 225
Response of the LISA detector to an almost monochromatic wave	p. 229
Amplitude parameters of periodic waves	p. 233
References	p. 235
Index	p. 249
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