Low-Latency Detection of Gravitational Waves for Electromagnetic Follow-up

PhD Thesis

Low-Latency Detection of Gravitational Waves for Electromagnetic Follow-up

Author: Shaun Hooper

Supervisors: Prof. David Blair A/Prof. Linqing Wen Prof. Yanbei Chen Dr Chad Hanna

This thesis is presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy of The University of Western Australia.

School of Physics 2013

Preface This section describes the author’s contribution to the work presented here, and a summary of the layout in its presentation. This thesis was undertaken between January 2009 and January 2013 at the University of Western Australia, which includes three months between March 2010 and June 2010 at the California Institute of Technology. This thesis describes the design, implementation and testing of a new search algorithm designed to detect the presence of gravitational waves from low-mass binary coalescence in advanced detector data in real-time and with near zero latency. The author is not solely responsible for all work that contributed to this thesis. Indeed, most gravitational wave scientists, including the author, are members of a large >800 author collaboration known as the LIGO scientific collaboration (LSC). For the introductory chapters of this thesis, particularly the background mathematical foundations of inspiral analysis in Chapter 2, the author has taken inspiration from similar theses such as [1] and [2] to introduce the reader to the details required to understand the development of the new lowlatency inspiral analysis pipeline presented in this thesis. Some descriptions of linearised gravity in Chapter 2 overlap information found in standard texts such as [3], where greater detail can be found. Chapter 3 describes the design of the new search algorithm. The original idea of using a summed IIR filter method for low-latency detection was introduced to the author through the work of Yanbei Chen, Linqing Wen and Jing Luan. Chapter 3 was published as a follow-up to a paper by Luan, et. al. 2012 [4] that describes the use of a summed IIR method to search for i

Newtonian waveforms. The author’s contribution to this chapter is, however, original in its description and implementation of the design for higher order waveforms. The author wrote this article, wrote the underlying experimental programs, and analysed the results, with input from co-authors. Chapter 5 is the result of an experiment that the author and Chad Hanna performed on the LIGO computer cluster. The experimental results were obtained from a computer application written by the author, but uses many sub-routines from the LIGO algorithm library (LAL), which is a software project contributed by many scientists. The author contributed significant key sub-routines necessary to run the experiment in Chapter 5, such as the IIR template bank construction, and the pipeline application itself (although the design borrows heavily from similar pipelines written by Kipp Cannon, Chad Hanna and Drew Keppel). The design and implementation of the experiment and presentation of the results are the author’s work, with advice and suggestions from the supervisors. Chapter 6 contains the results of the pipeline that was part of a major LIGO engineering run. The pipeline was similar to the one the author wrote in Chapter 5, however again, much of the infrastructure to execute the pipeline, such as the source of data, was supplied by the LSC. The design and implementation of the experiment and presentation of the results are the author’s work, with advice and suggestions from the supervisors.

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Abstract Existing ground-based gravitational wave detectors are currently being upgraded to their advanced configuration. When operational, the significant increase in sensitivity will likely guarantee detection of gravitational waves. With the imminent detection comes the question of what kind of electromagnetic counterparts gravitational wave sources will have. One example has the coalescence of neutron star binaries as a progenitor of short hard gamma-ray bursts. Observing the rapidly fading electromagnetic counterpart of such sources immediately after coalescence will provide information to verify astrophysical models and give greater insight to these highly energetic events. Observation of the prompt optical and radio emission of gamma ray bursts in real-time will require fast moving ground-based telescopes to respond to triggers generated from gravitational wave detector searches. This thesis describes the design, implementation and testing of a new search algorithm designed to detect the presence of gravitational waves from low-mass binary coalescence in advanced detector data in real-time and with near zero latency. An introduction to the field of gravitational waves is given in the first chapter, and specific gravitational wave data analysis techniques are described in explicit detail in the second. The new algorithm, based on the use of a bank of computationally efficient infinite impulse response filters to search for an approximation of the inspiral phase of the gravitational waveform, is presented in the third and fourth chapters. With a good choice of filter coefficients, the inspiral signals are shown to be approximated to greater than 99%. The method was implemented in LIGO’s data analysis software library, and made available to the greater community. The fifth chapter describes a search pipeline based on the new algorithm that was applied to real iii

detector data from LIGO’s fifth science run, both with and without simulated low-mass binary inspiral signals injected into the data. No significant loss in detection efficiency or parameter estimation using the new algorithm was found when compared to the theoretical limit. The sixth chapter demonstrates the ability of the algorithm to recover signals in real-time and with low-latency by searching for signals in LIGO’s second engineering run. The pipeline was able to search for approximately 5000 templates in real-time and report on multiple-detector coincident triggers for further follow-up with a typical latency of ∼30 seconds. A final chapter describes how the aim of the thesis was achieved, and outlines future work that can be developed from this research.

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Acknowledgements This thesis would not be possible without the help and guidance from all of my supervisors; Prof Linqing Wen, Prof David Blair, Prof Yanbei Chen and Chad Hanna. Throughout my candidature, there have been a number of fellow scientists that have contributed to the thesis. In particular, I owe a debt of gratitude to Chad Hanna for his continuous encouragement. Similarly, I would like to thank Kipp Cannon and Drew Keppel for their extensive help on all matters related to gravitational wave research. In 2010 I was fortunate enough to temporarily join the LIGO data analysis group at Caltech under the guidance of Prof Alan Weinstein. Help from graduate students Stephen Privitera, Leo Singer, Kari Hodge and Melissa Frei there was indispensable. Discussions with colleagues Shin Kee Chung, Yuan Liu, Qi Chu and Prof Zhihui Du have been very beneficial. In reviewing this thesis, I would like to thank Prof Ron Burman for his time and attention to detail. Throughout my thesis, I have received help from the many professional staff both at the UWA School of Physics, and the International Centre for Radio Astronomy Research. I would like to thank Ian McArthur, Paul Abbott, Jay Jay Jegathesan, Ruby Chan, Leanne Goodsell, Kathy Kok, Lee Triplett, Micah Foster, Jeff Pollard, Michael Eilon, Mark Boulton and David London for their professionalism. The PhD experience would not have been the same (or as fun) if not for my fellow students not already mentioned; Stefan Westerlund, Sunil Susmithan, Francis Torres, Zhu Xingjiang, Lucienne Dill, Timo Dill, Jacinta Delhaize, Scott Meyer, Lee Kelvin, Morag Scrimgeour, Giovanna Zanardo, Laura Hoppmann, Toby Potter, Mehmet Alpaslan, Florian Beutler, Rebecca Lange, Jurek Malarecki, Gemma Anderson, Gar-Wing Truong and Chris v

Perrella. Other scientists that I have gained great insight from are; Jean-Charles Dumas, Prof Ju Li, Eric Howell, Prof David Coward, Prof Gerhardt Meurer, Prof Richard Dodson and Prof Chris Power. Finally, I would like to thank the people of my personal life that have helped me getting through the sometimes difficult experience of being a postgraduate student. Although distant, I have counted on the support from my family in Melbourne and New Zealand. So too have I from Wiebe & Shanti Wilbers, whose friendship I consider close to family. Last but not least I thank my wife, Shannon, for her patience and continuing support and love.

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Contents Preface

i

Abstract

iv

Acknowledgements

v

Table of contents

x

List of figures

xii

List of tables

xiii

List of abbreviations

xv

Useful formula

xvii

1 Introduction

1

1.1

Background to gravitational waves . . . . . . . . . . . . . . .

2

1.2

Sources of gravitational waves . . . . . . . . . . . . . . . . . .

2

1.3

Indirect observation of gravitational waves . . . . . . . . . . .

6

1.4

Direct detection of gravitational waves . . . . . . . . . . . . .

7

1.5

Multi-messenger astronomy . . . . . . . . . . . . . . . . . . . 11 1.5.1

Gamma ray bursts . . . . . . . . . . . . . . . . . . . . 11

1.5.2

GRB triggered GW search . . . . . . . . . . . . . . . . 14

1.5.3

GW triggered EM search . . . . . . . . . . . . . . . . . 15

1.6

Motivation for low-latency GW detection method . . . . . . . 16

1.7

Goals of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 vii

1.8

Outline of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 Gravitational Waves 2.1

2.2

Linearised gravity . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.1

Plane wave solution . . . . . . . . . . . . . . . . . . . . 23

2.1.2

Transverse traceless gauge . . . . . . . . . . . . . . . . 23

Detection of gravitational waves . . . . . . . . . . . . . . . . . 24 2.2.1

2.3

2.4

2.6

Noises in interferometer . . . . . . . . . . . . . . . . . 28

Inspiral gravitational waves . . . . . . . . . . . . . . . . . . . 30 2.3.1

Geometry of binary system . . . . . . . . . . . . . . . . 31

2.3.2

Orientation of the binary relative to an observer . . . . 34

2.3.3

Orbital frequency as a function of time . . . . . . . . . 37

2.3.4

Higher order multipole corrections . . . . . . . . . . . . 38

Inspiral waveform . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4.1

2.5

21

Intrinsic and extrinsic parameters . . . . . . . . . . . . 43

Signal processing . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.5.1

Matched Filter . . . . . . . . . . . . . . . . . . . . . . 44

2.5.2

Inner product . . . . . . . . . . . . . . . . . . . . . . . 46

2.5.3

Template bank . . . . . . . . . . . . . . . . . . . . . . 47

2.5.4

Matched filter as a function of unknown time of coalescence . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.5.5

Matched filter of unknown phase . . . . . . . . . . . . 49

2.5.6

Signal to noise ratio

2.5.7

Discrete time domain filtering . . . . . . . . . . . . . . 51

2.5.8

Infinite Impulse Response Filter . . . . . . . . . . . . . 53

. . . . . . . . . . . . . . . . . . . 50

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3 Low-Latency GW Detection Method

57

3.0

Paper abstract

. . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.2

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2.1

The Inspiral Waveform . . . . . . . . . . . . . . . . . . 62

3.2.2

Two-Phase Matched Filter . . . . . . . . . . . . . . . . 65 viii

3.3

3.4

3.2.3

Discrete Time Domain Filtering . . . . . . . . . . . . . 67

3.2.4

Infinite Impulse Response Filter . . . . . . . . . . . . . 68

3.2.5

Approximation to an inspiral waveform . . . . . . . . . 69

3.2.6

Summed Parallel IIR filtering . . . . . . . . . . . . . . 72

Implementation for Performance Testing . . . . . . . . . . . . 72 3.3.1

IIR bank construction . . . . . . . . . . . . . . . . . . 72

3.3.2

Detector Data Simulation . . . . . . . . . . . . . . . . 73

3.3.3

Detection Efficiency . . . . . . . . . . . . . . . . . . . . 75

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.4.1

Inspiral Waveform Overlap . . . . . . . . . . . . . . . . 76

3.4.2

Ability to Recover SNR . . . . . . . . . . . . . . . . . 77

3.4.3

Detection Efficiency . . . . . . . . . . . . . . . . . . . . 78

3.5

Summary and Discussion . . . . . . . . . . . . . . . . . . . . . 80

3.6

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 81

3.7

Noise Spectral Density . . . . . . . . . . . . . . . . . . . . . . 82

4 Multi-rate SPIIR method

83

4.1

Multi-rate SPIIR filtering . . . . . . . . . . . . . . . . . . . . 83

4.2

Multiple templates . . . . . . . . . . . . . . . . . . . . . . . . 87

4.3

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5 Offline SPIIR pipeline 5.1

91

The SPIIR application . . . . . . . . . . . . . . . . . . . . . . 93 5.1.1

Internal structure of gstlal iir inspiral . . . . . . . 94

5.2

Data for offline run . . . . . . . . . . . . . . . . . . . . . . . . 98

5.3

IIR Bank generation . . . . . . . . . . . . . . . . . . . . . . . 100

5.4

Simulated inspiral signals . . . . . . . . . . . . . . . . . . . . . 103

5.5

Behaviour in non-Gaussian data . . . . . . . . . . . . . . . . . 105

5.6

Ranking triggers . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.7

The offline SPIIR pipeline . . . . . . . . . . . . . . . . . . . . 110

5.8

Confirmation of false alarm rate estimation . . . . . . . . . . . 112

5.9

Sensitivity of search . . . . . . . . . . . . . . . . . . . . . . . . 113

5.10 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . 117 ix

5.11 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6 Online SPIIR pipeline 6.1 SPIIR online pipeline . . . . . . 6.1.1 GraCEDb . . . . . . . . 6.2 LIGO’s second engineering run 6.3 Analysis setup . . . . . . . . . . 6.4 ER2 search parameter space . . 6.5 Results of search . . . . . . . . 6.6 Blind software injections . . . . 6.7 Discussion . . . . . . . . . . . .

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123 . 125 . 127 . 129 . 132 . 133 . 137 . 142 . 144

7 Conclusion 7.1 Thesis motivation . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Thesis aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . .

149 . 149 . 150 . 154

Bibliography

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157

x

List of Figures 1.1

Gravitational wave spectrum. . . . . . . . . . . . . . . . . . .

4

1.2

Operating schedule for GW detectors . . . . . . . . . . . . . .

9

1.3

Volume of space seen by LIGO . . . . . . . . . . . . . . . . . . 10

2.1

Schematic of GW detector interferometer . . . . . . . . . . . . 25

2.2

Sky coordinates of incoming GW relative to detector frame . . 26

2.3

Best strain sensitivities (ASD) for initial LIGO . . . . . . . . . 30

2.4

Binary coordinate system

2.5

Binary coordinate system with respect to an observer . . . . . 35

2.6

Trajectories of compact binary coalescence . . . . . . . . . . . 40

3.1

A schematic overview of the SPIIR method . . . . . . . . . . . 61

3.2

Flow chart of digital single-pole IIR filter . . . . . . . . . . . . 69

3.3

Illustrative diagram of summed sinusoids . . . . . . . . . . . . 71

3.4

Overlap as a function of number of sinusoids . . . . . . . . . . 76

3.5

Example SPIIR output . . . . . . . . . . . . . . . . . . . . . . 77

3.6

ROC curve of IIR method . . . . . . . . . . . . . . . . . . . . 79

4.1

Multirate SPIIR . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.2

Multirate multi-template SPIIR . . . . . . . . . . . . . . . . . 89

5.1

Flow of data through gstlal iir inspiral . . . . . . . . . . 95

5.2

Segments

5.3

IIR template bank generation . . . . . . . . . . . . . . . . . . 100

5.4

Parameter space . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.5

Offline IIR overlap . . . . . . . . . . . . . . . . . . . . . . . . 103

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xi

5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13

Chi-square-SNR distribution . . . . . Post-gstlal iir inspiral procedure Inverse FAR distribution . . . . . . . Detection efficiency . . . . . . . . . . Search Volume . . . . . . . . . . . . Search Range . . . . . . . . . . . . . Chirp mass accuracy . . . . . . . . . Time accuracy . . . . . . . . . . . . .

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107 111 113 115 116 117 119 120

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10

Flow of online pipeline . . Low-latency data transfer Online analysis DAG . . . ER2 Parameter space . . . Online IIR overlap . . . . Number of IIR filters . . . False alarm rate . . . . . . Event rate . . . . . . . . . Latency . . . . . . . . . . Latency histogram . . . .

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128 131 133 134 135 137 139 140 141 142

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xii

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List of Tables 1.1

List of known neutron star-neutron star systems . . . . . . . .

2.1 2.2

Intrinsic and extrinsic inspiral parameters . . . . . . . . . . . 43 Approximate template duration . . . . . . . . . . . . . . . . . 53

4.1

Computational cost of the multi-rate SPIIR method . . . . . . 87

6.1

Simulated injections . . . . . . . . . . . . . . . . . . . . . . . 144

xiii

7

xiv

List of abbreviations ASD amplitude spectral density EM

electromagnetic

ER2 Engineering Run 2 GraCEb Gravitational-wave Candidate Event Database GRB gamma-ray burst GW

gravitational waves

gwf

Gravitational wave frame (files)

ISCO innermost stable circular orbit LAL LIGO Algorithm Library LIGO Laser Interferometer Gravitational-wave Observatory LLOID Low-Latency On-line Inspiral Data MBTA Multi-Band Template Analysis NS

neutron star

PSD power spectral density SNR signal to noise

xv

xvi

Useful formulae Quantity Strain Geometrized solar mass Total mass Reduced mass Chirp mass Symmetric mass ratio ISCO frequency

Formula h = ∆L/L T = GM /c3 M = m1 + m2 µ = m1 m2 /M M = η 3/5 M η = m1 m2 /M 2√
fISCO = c3 / 6 6πGM

xvii

Unit unitless time mass mass mass unitless hertz

Chapter 1 Introduction

In this introduction chapter, I will describe why there is a scientific need for a new method to detect perturbations of space-time in real-time and with little delay — i.e low-latency. Firstly I will introduce the predictions of Einstein’s general theory of relativity, including the propagation of the perturbations, commonly known as gravitational waves (GWs). A discussion of potential sources will follow, noting that perhaps the most promising candidate for detection will be GWs from the inspiral phase of solar mass coalescing compact binaries. Detecting the inspiral phase of GWs produced by low-mass coalescing compact binaries with low-latency will be the focus of this thesis. The confidence of the existence of GWs will be described by detailing their indirect observation. The latest efforts to detect GWs directly will be outlined, with an emphasis on the next generation ground based laser interferometer detectors, which are expected to have an unprecedented level of sensitivity. The scientific benefit of directly detecting the presence of GWs in real-time and with a low-latency processing time will be demonstrated by describing the GW sources that may have transient electromagnetic counterparts. The goals of this thesis will be stated, and an overview of the rest of the thesis will be given, describing the lay-out of the research done. 1

2

1.1

CHAPTER 1. INTRODUCTION

Background to gravitational waves

Einstein’s general theory of relativity is a remarkable improvement to the Newtonian theory of gravitation. So far, general relativity has accounted for all the observations of both the special theory of relativity and Newton’s law of gravitation, and additionally explains observations that the Newtonian theory can’t. For example general relativity accurately accounts for the previously unexplained precession of the perihelion (closest approach to the Sun) of the planet Mercury. One of the early experimental confirmations of general relativity occurred during a solar eclipse in 1919 when Eddington observed the light from distant stars displaced by the Sun during a total eclipse [5]. It was known as early as 1801 that Newtonian gravity would predict a deflection, however this value was only half of that predicted by general relativity. Eddington’s observation was the definitive turning point in confirming general relativity. Since then there have been many experiments that have all verified general relativity to ever increasing accuracy [6]. Instead of describing gravity as an interaction between massive bodies at a distance, general relativity describes space-time itself as curved. The curvature is caused by the presence of matter, and can be specified by the Einstein field equations. Most of the observations verifying general relativity have been made where the curvature is slight, the so called weak field limit. One prediction of general relativity is that the motion of non-spherically symmetric bodies with a time-varying quadrupole moment will emit gravitational waves (GWs) — perturbations or ripples of space-time. Only in the strong field limit, where the curvature is the greatest are GWs likely to be detected.

1.2

Sources of gravitational waves

Gravitational radiation can be described (in an order of magnitude estimate) as an analog of electromagnetic (EM) radiation. For EM radiation, the power outputted is proportional to the second time derivative of the electric and magnetic multipole moments. The strongest EM moment is the electric dipole moment, followed by the magnetic dipole moment and the electric

1.2. SOURCES OF GRAVITATIONAL WAVES

3

quadrupole moment. In the gravitational analog, mass moments of inertia are analogous to the electric and magnetic moments. Hence the strongest source of gravitational radiation would be the second time derivative of the mass dipole, which is the change in total momentum. But this must vanish due to the conservation of momentum. The next strongest type of radiation is the gravitational analog of the magnetic moment, the total angular momentum. The second time derivative of this moment also vanishes due to the conservation of angular momentum. To produce any kind of GW, a source must have a time-varying mass quadrupole moment I, i.e., have a non-axisymmetric time-varying mass distribution. It can be shown that the power outputted ... by a GW is proportional to (G/c5 ) I 2 [3]. A very large quadrupole moment will be required to overcome the very small G/c5 ∼ 10−53 W−1 factor. Hence any terrestrial or laboratory generation of GWs is very unlikely (see Section 36.3 of [3] for a good example of why). However a large quadrupole moment comparable to c5 /G can be expected when studying astrophysical systems where the quadrupole moment is relativistic, i.e. v approaches c. As the GWs propagate outwards from their source they distort local space-time by alternately stretching and squeezing it. The frequency of the stretching and squeezing is known as the gravitational wave frequency, and the fractional distortion change the strain, commonly denoted by the symbol h. In general GW scientists classify four main types of astrophysical gravitational wave sources characterised by their expected GW signature, or gravitational waveform. Figure 1.1 shows the spectrum of expected gravitational wave sources and the sensitive bandwidths of proposed and existing GW detectors. Details of how ground-based GW detectors operate will be given in Section 2.2. As we will show, of the four different sources of GWs, those from solar mass coalescing compact binaries are perhaps the most promising source for detection since their gravitational waveform is known to high precision, and they have a GW frequency that enters the sensitive bandwidth of ground based GW detectors. Detection of GWs from the inspiral phase of compact binary coalescence will be the primary focus of this thesis. A thorough derivation of the inspiral gravitational waveform will be given in Section 2.3.

4

CHAPTER 1. INTRODUCTION

Figure 1.1: Gravitational wave spectrum. The amplitude spectral density (strain) of different sources of GWs are shown as a function of their frequency. The sensitivity limits of three different kinds of GW detectors: the radio telescope based Parkes Pulsar Timing Array (PPTA), the proposed satellite mission Laser Interferometer Space Antenna (LISA) and the ground based Laser Interferometer Gravitational-wave Observatory (LIGO) are shown. Credit: PPTA Collaboration [7]. For now, a qualitative description of the four main sources follows: Compact Binary Coalescence/Inspiral One example of transient source of GWs is that of two closely orbiting compact (dense) bodies. As the bodies orbit each other, there is a large time varying mass quadrupole moment, from which general relativity predicts that GWs will be emitted by the system. The GWs carry energy away from the binary system and, to obey the conservation of energy, the orbital separation of the two bodies decreases, as does the orbital period. The frequency of the

1.2. SOURCES OF GRAVITATIONAL WAVES

5

GW emitted is directly related to the orbital frequency, which is monotonically increasing in time as the orbital separation shrinks. This is known as the inspiral phase and the waveform predicted is sometimes called a chirping waveform. As the bodies coalesce, the amplitude of the gravitational strain h increases approximately as a power law with time. Given the intrinsic parameters of the system (e.g. component masses) the inspiral gravitational waveform can be modelled analytically with a high degree of accuracy using post-Newtonian methods [8, 9, 10]. The inspiral gravitational waveform will be derived in Section 2.3. It is predicted that beyond a boundary known as the innermost stable circular orbit, the bodies will plunge in toward each other and cataclysmically merge (the merger phase). Finally, the resulting mass will oscillate in the ringdown phase. The entire process is called compact binary coalescence. Examples of compact bodies are neutron stars (NS), black holes (BH) and white dwarfs. A typical NS has a mass roughly equivalent to our Sun, but a radius on the order of 10 kilometres. The masses of the bodies will dictate the particular signature of the inspiral phase (described in detail in Section 2.3). For NS-NS binaries (with component masses around 1 − 3 M ), the GW frequency near coalescence will be around 102 − 103 Hz. For BH-NS or BH-BH binaries, the GW frequency will be much lower. Burst Any other transient GW signal of short duration is called a GW burst event. Generally the morphology of the signal is highly uncertain. There are a variety of potential sources; for example the non-symmetric core collapse of a supernova or NS glitch (such as a starquake), or perhaps the merger phase of a compact binary coalescence event. See [11, and references therein] for a review on burst sources and how GW analysts search for them. Continuous wave Any source of GWs that produces a quasi-monochromatic gravitational waveform signal and is distinguishable from the background is called a continuous wave source. An example of a continuous

6

CHAPTER 1. INTRODUCTION source could be a rapidly rotating NS that has a slight non-spherical distortion. As NSs are compact objects that spin very fast, any slight non-axisymmetric symmetry would produce a very strong quadrupole radiation. For a full review of continuous wave sources see [12, and references therein].

Stochastic background As the EM spectrum has a background of unresolved sources, so one would expect something similar for the GW spectrum. This background could have originated from cosmological sources such as inflation, cosmic strings and pre-Big-Bang models. GWs from Galactic white-dwarf binaries or slow spinning Galactic pulsars could also account for a stochastic background. Searches to define this background are generally done by cross-correlating the strain data recorded from different GW detectors. See [13, 14, 15, 16] for important stochastic background searches.

1.3

Indirect observation of gravitational waves

The first observational evidence of the existence of GWs came from a double neutron star (NS-NS) system. The pulsar binary system PSR B1913+16 was discovered and observed by Russell Hulse and Joseph Taylor [17]. Radio observations of the pulsar indicated that it is in a binary system, where the companion body is another NS, and has an orbital period of 7.75 hr. Decades of observing the timing of the radio pulses showed that orbital period is slowing with a rate of decrease within 0.2% of the rate predicted by general relativity [18, 19]. This discovery earned Hulse and Taylor the 1993 Nobel Prize in Physics. Although this indirect detection of GWs is significant in verifying general relativity, indirect detection in this way relies solely on serendipity — to discover this system, at least one NS had to be a pulsar with its beaming angle passing the Earth. To date, there have been only six confirmed discoveries of NS-NS systems [20]. Table 1.1 gives details of them. Although the effect of period decrease can be attributed with high accuracy to that predicted by the

1.4. DIRECT DETECTION OF GRAVITATIONAL WAVES

7

Table 1.1: List of known neutron star-neutron star systems PSR

Year discovered B1913+16 1974 B1534+12 1991 B2127+11C 1991 J0737-3079 2003 J1756-2251 2005 J1906+0746 2006

Orbital Period ( hr) 7.75 10.1 8.05 2.45 7.67 3.98

m1 m2 Distance Reference ( M ) ( M ) ( kpc) 1.4398 1.3332 1.358 1.24 1.40 1.248

1.3886 1.3452 1.354 1.35 1.18 1.365

9.9 1.02 9.58 0.5-0.6 2.5 5

[18, 21] [22, 23] [24, 25] [26] [27] [28]

generation of GWs, the frequency of the signal is outside the bandwidth of ground based GW detectors. As will be shown in Section 2.3, the amplitude of the strain increases when the binary is close to coalescence. However none of the known NS-NS systems will coalesce for at least a few millions of years. There have been many studies into the actual coalescence rate of compact binaries (see [29, references therein]). Coalescence rates are usually quoted in either per Milky Way Equivalent Galaxy per Myr or per Mpc3 per Myr. There are significant uncertainties in the astrophysical rates of compact binary coalescence estimates owing to the small sample size of known galactic NS-NS binaries and poor constraints for population-synthesis models. At present, the latest estimate is 1 per Myr per Mpc3 [29, 30]. The actual detection rate will depend on the properties of the GW detection instrument(s) used. It must be noted that the uncertainties can amount to 1 or 2 orders of magnitude, hence making statements about the expected number of events observed highly variable.

1.4

Direct detection of gravitational waves

The trouble with measuring the strain is that for a category of sources in the nearby universe h ∼ 10−22 ! So far, there has been no direct detection of GWs by measuring the strain h. Despite the incredibly small strain h predicted by general relativity, there has been concerted worldwide effort to directly detect GWs over the last 50

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CHAPTER 1. INTRODUCTION

years. The first generation of GW detectors built in the 1960s and 1970s were solid metal cylindrical bars — so called bar detectors. First built by Joesph Weber [31], these bar detectors were isolated from the effects of the surrounding environment by using seismic isolation suspensions inside vacuum chambers to prevent acoustic interference. Piezoelectric transducers were glued to the surface of the bar designed to measure any vibrations induced in this driven harmonic oscillator by GWs (results in [31, 32]). Weber’s research spurred on much activity in this field, and soon several groups around the world built their own bar detectors. Later a different kind of technology was built to analyse the minute difference in length a GW causes. This was based on Michelson laser interferometers. This kind of GW detector is designed to measure the actual differential fractional change in arm length as opposed to the amplitude of oscillations induced in the bar detectors. More details on how interferometric GW detectors operate, and their sources of noise, will be given in Section 2.2. GW detectors built as interferometers are known as second generation. The first interferometer built for detection of GWs had arm lengths of one metre [33]. However this detector was too small to have a sensitivity that could measure typical GWs [34]. Several ground based kilometre scale GW interferometric detectors have been built in the US and Europe. The US effort, known as the Laser Interferometer Gravitational-wave Observatory (LIGO [35]) has built two 4 kilometre long Michelson interferometers in Hanford, Washington, and Livingston, Louisiana [36]. The French/Italian consortium Virgo [37] has built a 3 kilometre interferometer near Cascina, Italy [38]. There is also the smaller 300 metre TAMA300 detector based at the Tokyo Astronomical Observatory, Japan [39]. The sensitivity of this detector not as high as the larger LIGO/Virgo detectors, but aims to act as a test bed for developing advanced detector hardware. Similarly, there is also the 600 metre GEO600, built by the German/British and located outside of Hannover, Germany [40]. With arms on the kilometre scale, these type of detectors have a sensitive bandwidth in the 40 Hz–2000 Hz range. This is because they have been optimised for detecting GWs from compact binary coalescence events where

1.4. DIRECT DETECTION OF GRAVITATIONAL WAVES

9

the binary sources have masses in the range of 1 M –20 M (i.e. NS-NS and NS-BH binaries). The first configuration of the LIGO detectors, known as initial LIGO was built in the late 1990s/early 2000s. There have since been six science runs, known as S1, S2, etc. The inaugural S1 ran for 17 days in 2002, and data was collected from both LIGO detector sites [41]. Since then subsequent science runs with ever increasing sensitivities have taken place [42], some in coincidence with GEO600, TAMA300 and Virgo detectors. For an overview of the operating schedule, see Figure 1.2. For a complete list of publications by the LIGO Scientific Collaboration including observational results and conference proceedings, see [43] and the the LIGO document control center [44].

Figure 1.2: The operating schedule of the various ground-based GW detectors in the initial detector era. Credit: [45] Currently both the LIGO and Virgo detectors are offline, as they are undergoing a major hardware change to the advanced detector configuration. Both the Advanced LIGO[46] and Advanced Virgo [47] are expected to be operational from 2015. Once built, Advanced LIGO is expected to have a 10 fold sensitivity improvement compared to initial LIGO [48]. Hence in the era of advanced detectors GWs produced from compact binary coalescence events will be detectable within a volume of space one thousand times larger than that of initial LIGO, out to ∼200 Mpc–300 Mpc [49] (see Figure 1.3). With this increase in sensitivity the estimated detection rate for GWs from NS-NS binaries could be between 1 and 400 per year (see table 5 of [29] for

10

CHAPTER 1. INTRODUCTION

Figure 1.3: The volume of space that Advanced LIGO is sensitive to is expected to be ten times that of initial LIGO. Credit: [50, 51]

a full discussion on the difficulties of predicting detection rates). A number of other gravitational wave detection experiments are either underway or planned. A pulsar timing array measures the arrival time differences of pulses emitted from millisecond pulsars due to GWs (e.g. [52]). The sensitive bandwidth of this experiment is in the low frequency regime of 10−9 Hz–10−6 Hz. There are also proposals for a space based laser interferometer, for example the eLISA mission [53]. This experiment would have a sensitive bandwidth in the 10−4 Hz–10−1 Hz range.

1.5. MULTI-MESSENGER ASTRONOMY

1.5

11

Multi-messenger astronomy

With the imminent detection of GWs, scientists have begun to ask what sort of EM counterparts are coincident with a GW event [54]. Connecting the detection of a GW event with an EM counterpart will break the degeneracy of inferred binary parameters (for GWs from compact binary coalescence events). Observing GWs that originate from extra-Galactic host galaxies will give a measure of absolute distance, thereby allowing an independent measure of the Hubble constant [54, 55, 56, 57, 58, 59, 60, 61]. Perhaps one of the most promising EM counterparts of a compact binary coalescence event is that of gamma ray bursts (GRBs). So called “multi-messenger” astronomy, where both GW and EM information are collected, will give maximum insight to the physics of such highly energetic events.

1.5.1

Gamma ray bursts

In this section I briefly summarise the observations and basic underlying models that cause GRBs. For excellent reviews on the topic of GRBs, see [62] and [63]. Gamma ray bursts (GRBs) are intense flashes of γ-rays in the MeV band, that for a short time radiate in an otherwise empty γ-ray sky. The flash overwhelms any other γ-ray source, including the Sun. GRBs were first observed between 1969 and 1972 by the Vela military satellites designed to monitor violations of the nuclear test ban treaty [64]. However it was quickly discovered that the bursts were coming from not the Earth, but the opposite direction, the sky. Over the next decades, a series of satellites was launched to observe this new astrophysical phenomenon, and many theoretical models of GRBs were founded to explain the observations (see [62] for a complete history). However it was not until the 1991 launch of the Compton Gamma Ray Observatory [65] (see [66] for results) that greater insight was obtained. On board, the Burst and Transient Source Experiment detected more than 3000 isotropically distributed bursts, suggesting a cosmological rather than Galactic distribution. Later, in 1996 the Beppo-SAX [67] satellite was launched, and was able to localise the X-ray emission from some GRBs. It also dis-

12

CHAPTER 1. INTRODUCTION

covered the previously predicted “afterglow”, which appears as fading softer X-ray, optical and radio emissions [68]. This in turn allowed host galaxies to be identified, and redshifts to be observed. The High-Energy Transient Explorer (HETE-2) satellite [69] was launched in 2000, and continued providing afterglow positions. Further advances were made after the 2004 launch of the Swift satellite [70] due to its onboard array of multi-wavelength instrumentation, and greater sensitivity. Upon detecting a GRB, it is able to rapidly (within about 100 s) slew to the direction of the source, and record multi-wavelength spectra and light curves. The most recent GRB satellite to be launched was the Fermi [71] mission in 2008, which has provided the most powerful window into these high energy events. Other operating GRB satellites are the European space agency’s International Gamma-Ray Astrophysics Laboratory [72] launched 2002, and Astrorivelatore Gamma a Immagini Leggero [73] launched in 2007. Despite some recent classification issues [74], there is enough evidence to show that GRBs can be divided into two distributions based on their duration [75]. Those with burst durations longer than 2 seconds are characterised as long soft GRBs, and those with durations less than 2 seconds are characterised as short hard GRBs. The two populations are thought to have different progenitor models: Long GRB It has been thought that the core collapse of a rapidly rotating massive star could be the progenitor of long GRBs [62, 76, 77]. Short GRB Merging compact bodies (NS-NS or BH-NS) have been proposed as the progenitors of short GRBs (e.g. [63, 78, 79, 80, etc] amongst others). Following the coalescence of the binary system, where the characteristic inspiral GW signal is produced, the two bodies merge, and form an accretion disk around a central body (perhaps a black hole) (see [81] and references). The rapid accretion (