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Gravitational Waves

Gravitational Waves

Amber L StuverVillanova University, Pennsylvania, USA

IOP Publishing, Bristol, UK

ª IOP Publishing Ltd 2019

All rights reserved. No part of this publication may be reproduced, stored in a retrieval systemor transmitted in any form or by any means, electronic, mechanical, photocopying, recordingor otherwise, without the prior permission of the publisher, or as expressly permitted by law orunder terms agreed with the appropriate rights organization. Multiple copying is permitted inaccordance with the terms of licences issued by the Copyright Licensing Agency, the CopyrightClearance Centre and other reproduction rights organizations.

Permission to make use of IOP Publishing content other than as set out above may be soughtat permissions@iop.org.

Amber L Stuver has asserted her right to be identified as the author of this work in accordancewith sections 77 and 78 of the Copyright, Designs and Patents Act 1988.

ISBN 978-0-7503-1393-3 (ebook)

DOI 10.1088/978-0-7503-1393-3

Version: 20190101

Physics World DiscoveryISSN 2399-2891 (online)

British Library Cataloguing-in-Publication Data: A catalogue record for this book is availablefrom the British Library.

Published by IOP Publishing, wholly owned by The Institute of Physics, London

IOP Publishing, Temple Circus, Temple Way, Bristol, BS1 6HG, UK

US Office: IOP Publishing, Inc., 190 North Independence Mall West, Suite 601, Philadelphia,PA 19106, USA

For Derek.

Contents

Abstract viii

Acknowledgements ix

Author biography x

Gravitational Waves 1

1 Introduction 1

2 Background 3

2.1 Theory 3

2.2 Methods of gravitational wave detection 6

2.3 LIGO detector description 10

3 Current directions 13

3.1 Noise sources and strain sensitivity 13

3.2 Gravitational wave searches 17

3.3 Gravitational wave astronomy 21

4 Outlook 25

4.1 Ground-based detectors 25

4.2 A space-based detector 26

4.3 Prospects 26

Additional resources 27

vii

Abstract

The detection of gravitational waves has ushered in a new era of gravitational waveastronomy and added a new medium to multi-messenger astronomy. This bookexamines the theoretical foundation of gravitational waves and the state of the art ofgravitational wave detection including interferometric detectors and pulsar timingarrays. The design and sensitivity of the LIGO interferometers are examined. Thesource and data analysis method for each of the four main classes of gravitationalwaves (compact binary coalescence, burst, continuous, and stochastic) are described.A summary of the gravitational waves that have been detected as of January 2019 ispresented along with what gravitational wave astronomy has been extracted fromthese observations. Finally, what the future of gravitational wave exploration lookslike in terms of ground-based and space-based detectors is presented.

viii

Acknowledgements

The author acknowledges valuable feedback from Joey Key, Peter Saulson, JosephBetzwieser, and Thomas Dent. This eBook is approved for publication by the LIGOScientific Collaboration and has been assigned document number LIGO-P1700026.

ix

Author biography

Amber L Stuver

Amber L Stuver is an assistant professor of physics at VillanovaUniversity, and has been a member of the LIGO ScientificCollaboration (LSC) since 1999. Before joining Villanova, she spenta decade working at the LIGO Livingston Observatory: first as apostdoctoral scholar, then as a staff scientist on a dual appointmentteaching at the Louisiana State University. She earned her PhD(2006) and MEd (2001) in physics from the Pennsylvania State

University. Stuver specializes in the computational aspects of gravitational wavesearches, with experience in data analysis design, gravitational wave simulation, anddetector characterization work to minimize the impact of noise in the search forastrophysical signals. As a member of the LSC, she was the co-recipient of the 2016Special Breakthrough Prize in Fundamental Physics, the 2016 Gruber CosmologyPrize, and the 2017 Princess of Asturias Award in Technical and Scientific Research.

Besides teaching and research, Stuver is experienced in science communication,having given tours to thousands of visitors to the LIGO Livingston Observatory,speaking at many local venues, and writing content for outlets like TED-Ed.

x

Physics World Discovery

Gravitational Waves

Amber L Stuver

Gravitational Waves

1 IntroductionFor gravity, information on the distribution of mass is communicated throughoutthe Universe by the gravitational field. In Newtonian physics, any change in thisdistribution is propagated by a corresponding change in gravitational field every-where instantaneously. But Einstein’s theory of relativity limits the speed at whichanything, including information carried on fields, can travel to the speed of light.Therefore, a change in the position of a mass is communicated to the rest of theUniverse through a propagating change in the gravitational field traveling in everydirection at the speed of light. This is a gravitational wave.

Observing gravitational waves, and therefore the changes in the mass distributionthey represent, allows us to witness phenomena that have been otherwise unobserv-able; examples include being able to directly observe black hole binaries topotentially observing the behavior of matter during the core collapse of a star.Detectable sources of gravitational waves are rapidly accelerating, compact con-centrations of mass. Such systems produce some of the most energetic, and evenviolent, astrophysical events.

Since gravity is a tidal force, a gravitational wave will affect the space it passesthrough by stretching and compressing it. To take advantage of this effect, thecurrent state of the art for observing gravitational waves is the interferometricdetector. At its most basic, it splits a single light source into two parts and directseach part in perpendicular directions, reflects each part back to the origin of the split,and recombines the light into an interference pattern. If both path lengths are exactlythe same (or an integer wavelength different), the light will constructively interfere;any change in length of the path can be measured by the degree of destructiveinterference. This simple device is called a Michelson interferometer (see figure 1).Today’s detectors are more sophisticated than this basic description (and detailedlater), but the fundamental operating principle is the same.

doi:10.1088/978-0-7503-1393-3ch1 1 ª IOP Publishing Ltd 2018

There are several interferometric gravitational wave detectors in the world, eitherexisting or under construction.

Existing:• The largest are the two detectors operated in the US called the LaserInterferometer Gravitational Wave Observatory (LIGO); also calledAdvanced LIGO since 2015 after seven years of enhancements to the originaldetectors. Located in Livingston, Louisiana, and Hanford, Washington, eachdetector has two 4 km long arms. The project is funded by the NationalScience Foundation (NSF) and is jointly operated by the California Instituteof Technology and the Massachusetts Institute of Technology, which togetherwith the two detectors, form the LIGO Laboratory. Over 1000 scientists,engineers, and technicians working in more than 90 institutions from 15countries are members of the LIGO Scientific Collaboration.

• The Virgo detector located outside Pisa, Italy, has 3 km long arms and is fundedby an international collaboration between France, Italy, The Netherlands,Poland and Hungary. Virgo is operated by the European GravitationalObservatory (EGO) established by the CNRS (Centre national de la recherche

Figure 1. Configuration of a basic Michelson interferometer. Credit: Caltech/MIT/LIGO Laboratory.

Gravitational Waves

2

scientifique), France, and the INFN (Istituto Nazionale di Fisica Nucleare),Italy. The Virgo Collaboration is made up of about 20 institutions with 300members and has pooled its resources with LIGO since 2007.

• The GEO600 detector is located in Hannover, Germany, and is operated by acollaboration between Germany and the UK, specifically by the Center ofGravitational Physics of the Albert Einstein Institute (AEI), LeibnizUniversität Hannover, University of Glasgow, and Cardiff University.While this detector has the shortest (600 m long) arms, limiting its sensitivity,it is a test bed for advanced technologies and has been used (besides normaloperation alongside LIGO and Virgo) alone during breaks in other detectors’operation to maintain sensitivity to any extraordinary gravitational waveevents. GEO600 is a member of the LIGO Scientific Collaboration.

Under construction:• Kamioka Gravitational Wave Detector (KAGRA) is a detector with 3 kmlong arms being built underground in the Kamioka Observatory in Japan.This detector will be the first to keep its test masses at cryogenic temperatures.Operation is estimated to begin in 2020. Note that KAGRA was originallyknown as the Large Scale Cryogenic Gravitational Wave Telescope (LCGT).

On 14 September 2015, the LIGO detectors made the first direct detection ofgravitational waves; the event was labeled GW150914 (GW for ‘gravitational wave’and 150914 for the date in year, month, day format). Two stellar-mass black holes,36 M⊙ and 31 M⊙, respectively, about 1.3 billion light years away coalesced into afinal mass of about 63 M⊙. The mass difference of 3 M⊙ was radiated in gravita-tional waves, making it 50 times as luminous as all of the stars in the Universe duringthe 0.2 s signal (see figure 2 for the detected signal). But this is more than just the firstdetection of gravitational waves: it is the first direct observation of black holes andthe first observation of a binary black hole system.

2 Background2.1 Theory

The Introduction already expounded on how the gravitational force in Newton’sformulation implied an instantaneous change in gravitational field as the position ofa mass changes and how this is in conflict with Einstein’s relativity. In 1916, Einsteinpublished his work predicting the existence of gravitational waves. The fundamentalrelation in general relativity is the Einstein field equations:

π=μν μνG T8

where μνG is the Einstein tensor and μνT is the stress–energy tensor, using the standardconvention that the gravitational constant, G (gravitational constant) = c (speed oflight) = 1. This relation describes the curvature of spacetime due to the distributionof mass on the left-hand side of the equation, while the right describes the stress–energy. In other words, it relates gravity to matter and energy (the source of gravity).

Gravitational Waves

3

On face value the relation appears straightforward enough, but on further inspectionthis impression is deceptive because the relation’s inherent nonlinearity is concealed;

μνG is quadratic in the metric (which describes the characteristics of spacetime) andits first derivatives, the equations for the second derivatives of the metric arecoupled, and there is a dependence on the source’s 4-momentum which in turndepends on the metric for normalization.

However, if an observer is far away from the source in question, spacetime isapproximately flat and can be approximated by the Minkowski metric (describing aflat spacetime), ημν. A gravitational wave, μνh , can then be treated as a perturbationon the flat spacetime yielding the following metric:

η= +μν μν μνg h .

This linearization of the metric is known as the weak field approximation and is usedas an ansatz to solve the Einstein field equations.

Figure 2. First direct gravitational wave detection (GW150914) as seen in the LIGO Hanford detector (top)and LIGO Livingston detector (center). A comparison of the signal as seen in each detector (bottom) is alsoshown, with the LIGO Hanford data shifted to account for the time it took the gravitational wave to travelbetween detectors. The top two images also show the signal compared to the predicted gravitational wavesignal for this system. Credit: Caltech/MIT/LIGO Laboratory.

Gravitational Waves

4

In the Lorentz gauge, the linearized field equations simplify to

π− =αβ μμ

αβh T16,

where αβh is the trace-reversed metric perturbation

η≡ −αβ αβ μνh h h12

.

The Lorentz gauge is defined by the gauge choice of forcing a vanishing divergenceof αβh and still allows further gauge freedom. We exploit this to choose a coordinatesystem where the gravitational wave is orthogonal to an observer. This gauge isknown as the transverse-traceless (TT) gauge. For a wave traveling in this direction,the gravitational wave takes the form

=−μν

+ ×

× +h

h h

h h

0 00

0 00

00 0

00 0

TT

⎛

⎝

⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟

with the usual basis order of (t, x, y, z) and where h+ and h× are the two independentlinear polarizations. This can also be written in terms of the reduced quadrupolemoment of the source ( μνI ):

=μν μνhr t

I t2 d

d( )TT

2

2

where r is the distance between the source and the observer. Due to conservation ofmass and conservation of momentum, there is no monopole or dipole radiation,respectively. Therefore, only dynamic and spherically asymmetric systems willproduce gravitational waves.

To visualize the effect each polarization has on the space it passes through,consider a gravitational wave perpendicularly incident on a ring of freely fallingparticles centered on the origin, i.e. traveling on geodesics (see figure 3). During thefirst half period of a + (plus) polarization gravitational wave, the horizontal

Figure 3. Illustration of the + and × gravitational wave polarizations. Credit: www.johnstonsarchive.net/relativity/pictures.html.

Gravitational Waves

5

components of the particles’ vector location will be pulled towards the origin andtheir vertical component pushed away from the origin, and vice versa for the secondhalf of the period. A × (cross) polarization gravitational wave is described in the sameway after applying a 45° rotation to the components being pushed and pulled. Thestrongest gravitational waves are expected to produce a change in displacement ofabout 10−18 m at Earth in the LIGO detectors.

A powerful property of gravitational waves is that the Universe is essentiallytransparent to them. That is, there is no gravitational wave analog of refraction orreflection. (The path of a gravitational wave is affected by the gravity of othermasses through gravitational lensing and they are Doppler shifted by the expansionof the Universe and other gravitational effects.) This makes gravitational waves aunique messenger with which to observe the Universe; there is nothing that canblock the observation of a gravitational wave. We also do not have to rely on asource producing light and having a clear line of sight to make observations; sourceslike black holes that by their nature do not produce light will be clearly detectable togravitational wave detectors.

2.2 Methods of gravitational wave detection

Resonant mass detectorsResonant mass detectors (sometimes referred to as ‘bar detectors’ or ‘Weber bars’)were the first attempt to directly detect gravitational waves and were pioneered byJoseph Weber of the University of Maryland during the 1960s. His apparatusconsisted of high Q (quality factor) cylindrical aluminum bars fitted with quartzstrain gauges. When a gravitational wave was incident perpendicular to the long axisof the bar and had a frequency near the bar’s resonant frequency of about 1660 Hz,an acoustic wave would be generated causing vibrations in the mass that would bemonitored with the strain gauges. These detectors were well suited to the ‘chirp’signals of binary coalescences that cover a range of frequencies. When the signalfrequency matched that of the bar, it would set the bar vibrating similar tosympathetic resonance.

In December 1968, Weber claimed to have discovered the first significantgravitational wave events originating from the Galactic Center. The announcementcaused great excitement in the physics community. Over the next few years, the rateat which these gravitational wave events were taking place increased as Weber madeadjustments to his bar—from an event a day to several a day. However, energyconsiderations shed the first doubts on these detections. At the rate at which theseevents were happening, and if they were really taking place in the Galactic Center,then the Milky Way would be eating itself alive by converting roughly one solarmass into pure gravitational energy for every detection. The case against these eventsbeing true detections became stronger when other scientists throughout the world setup their own bars and did not detect anything of significance over long periods ofobservation. While Weber never recanted his detection claims, by mid-1974 thegeneral consensus in the scientific community was that he had not detectedgravitational waves.

Gravitational Waves

6

Even though Weber did not make the first direct detection of gravitational waves,he was the ignition needed to kindle scientific inquiry into how to push the frontiersof technology to accomplish it. Work continued on resonant mass detectors. Thisincluded making them from new aluminum alloys, cryogenic cooling to reduce thenoise from the bar’s thermal vibrations, introducing mechanical means to amplifythe vibration, and replacing piezoelectric crystals with even more sensitive motionsensors (e.g. superconducting quantum interface devices, SQUID). Different shapes(like spheres) have also been used to increase sensitivity to gravitational wavescoming from different directions on the sky.

Ultimately however, these detectors’ noises are so high that they are only sensitiveto the strongest gravitational waves. This detection method has therefore fallen outof favor.

Interferometric detectorsThe effects of a gravitational wave are similar to the effect of an alternating tidalforce: alternating compression and expansion at orthogonal angles (see figure 3). Totake advantage of this, a detector capable of measuring the change in lengths inperpendicular components is desirable. An interferometer is ideal for this purpose inthat it is able to measure strain (h):

= Δh

LL2

where L is the length of one of the interferometer arms and ΔL the change in lengthof that arm (the factor of 2 in the denominator reflects that ΔL of each arm in anorthogonal detector will be the same magnitude and therefore the overall effectdoubled). The 10−18 m ΔL of a strong gravitational wave will therefore produce astrain of 10−21 in the 4 km long LIGO detectors.

All of the current interferometric detectors, excepting GEO600, expand on thebasic Michelson interferometer design (discussed in the Introduction) to includeFabry–Pérot optical cavities (discussed further in section 2.3), which cause light toresonate between the end mirror (usually referred to as the end test mass) and anintermediate mirror (usually referred to as the intermediate test mass) that is placedbefore the beam splitter (BS); see figure 4. (GEO600 uses a non-resonant lightfolding technique to store light in its arms.) The intermediate mirror intercepts thelight and sends it back toward the end mirror while a small amount is transmittedthrough to the BS. It is the light that is transmitted through the intermediate mirror(thus leaving the Fabry–Pérot cavity) that recombines with the light from the otherarm at the BS. The Fabry–Pérot cavity allows longer light storage times (making thearms ‘appear’ longer to the light) and a longer time for a gravitational wave signal toaffect the detector. There are also additional modifications made to increase thestrength of the signal and lower the noise of the detector. Some of these are discussedin section 4.

In the TT gauge, coordinates are defined by the world lines of freely fallingmasses. Therefore, the test masses used in our interferometric detector need to befreely falling in order to respond to produce a strain. This is done by hanging the test

Gravitational Waves

7

masses (mirrors) as pendula that are ‘freely falling’ in the direction parallel to thelaser beam for the small distances being measured.

Because gravitational waves can travel through matter unaffected, an interfero-metric detector is sensitive to almost all of the sky at once, including the skyobscured by the Earth beneath the detector. The most sensitive sky locations are atthe zenith and nadir of the detector. There are four sky locations on the plane ofeach detector where there is no sensitivity to gravitational waves (due to the effect ofa gravitational wave being the same in each arm, resulting in zero strain): the pointin the direction of the bisecting line of the arms, the point opposite of this bisectingline, and the two points perpendicular to the bisecting line and the vertex of thedetector. The description of the detector’s sensitivity to each point on the sky iscalled its antenna pattern. The polarization averaged (over the response to + and ×polarizations) antenna pattern for the LIGO Livingston detector is given in figure 5.The LIGO Hanford detector has a similar antenna pattern.

Unlike the original bar detectors that are sensitive to a single gravitational wavefrequency, interferometric detectors are broadband detectors limited by their noisespectrum. Advanced LIGO is sensitive to gravitational waves between the frequen-cies of about 10–7000 Hz (see figure 7).

Figure 4. Configuration of a Michelson interferometer with arms containing Fabry–Pérot cavities. Credit:Caltech/MIT/LIGO Laboratory.

Gravitational Waves

8

Pulsar timingMillisecond pulsars produce pulses of light in extremely regular intervals and someare stable enough to be more accurate than atomic clocks. By studying ultra-precisemillisecond pulsars, highly accurate predictions of the arrival time of the next lightpulse can be made assuming that the spacetime between Earth and the pulsar is notchanging in time. If a gravitational wave passes between Earth and the pulsar, theeffective distance the light travels is changed so that we can measure a differencebetween the predicted time and the actual pulse arrival time, called a residual, on theorder of tens of nanoseconds. As gravitational waves pass through a set of pulsarsbeing analyzed for this purpose, known as a pulsar timing array (PTA), they willproduce correlations in the arrival time of a pair of pulsars even though the effectson the pulsars themselves are uncorrelated. Using this correlation informationincreases the sensitivity to gravitational waves beyond the observation of singlepulsars.

Because of the limited sources of noise and long observing times, PTAs aresensitive to gravitational waves with nanohertz frequencies which could be from astochastic background of merging supermassive black holes or objects falling intothem, or possibly cosmic strings and relic gravitational waves from the Big Bang (seesection 3.2). This is an excellent complement to current interferometric detectorswhose sensitivity begins around 10 Hz.

The International Pulsar Timing Array (IPTA) is made up of three collaborations:

Figure 5. Polarization averaged antenna pattern for the LIGO Livingston detector. The locations of the LIGOHanford detector, Virgo, GEO600, and KAGRA are each marked with a black ×.

Gravitational Waves

9

• The North American Nanohertz Observatory for Gravitational Waves(NANOGrav) that utilizes the Arecibo Observatory in Puerto Rico andGreen Bank Telescope in West Virginia, USA.

• The European Pulsar Timing Array (EPTA) that utilizes the Effelsberg RadioTelescope in Germany, Lovell Telescope in the UK, Nançay Radio Telescopein France, Sardinia Radio Telescope in Italy, and Westerbork SynthesisRadio Telescope in The Netherlands.

• The Australian-based Parkes Pulsar Timing Array (PPTA) that utilizes theParkes Radio Telescope in New South Wales.

2.3 LIGO detector description

The following description of the detector focuses on the optical path of the laser lightused to measure gravitational waves. However, there are many support, engineering,and computational systems not discussed here that make it possible for laser light tobe used in the detection of gravitational waves: vacuum systems, suspension systemsfor optics, thermal compensation of absorbed light in the optics, scattered lightcontrol, seismic isolation systems, control systems, calibration, physical environ-ment monitoring, and data acquisition systems.

Optical path

Optical cavities: Before talking about the optical path light takes through theinterferometer, it is useful to have a short discussion about optical cavities. These arecomprised of two or more mirrors arranged so that light reflected multiple timesbetween these mirrors forms standing waves through interference effects when thelengths of the paths are adjusted properly. The resonances that are produced arecalled modes. Some of Advanced LIGO’s optical cavities specifically filter outunwanted transverse electromagnetic (TEM) modes. The desirable mode is aGaussian beam (TEM00) that has a Gaussian intensity profile along the diametermeasured in any direction. Other optical cavities (e.g. Fabry–Pérot cavities) areuseful for increasing light storage time, i.e. effectively increasing the path length ofthe laser light. Feedback loops are used to maintain these cavities, and many othercomponents of the detector, but are not discussed here.

Vacuum envelope: Each LIGO interferometer has a pair of orthogonal 4 km longarms all contained within an ultra-high vacuum (UHV) at about 10−9 torr.Instrumentation is located only at the corner and each end of the arms.Connecting the corner station to the end stations are beam tubes that couple tovacuum chambers containing the instrumentation. Together, these constitute thevacuum envelope and contain more than 8500 m3 of volume to form one of thelargest sustained UHVs in the world.

Input optics: The continuous laser light source for Advanced LIGO is a Nd:YAGlaser that produces a wavelength of 1064 nm. While this wavelength is quite longcompared to the magnitude of the measurements it is used to make, it was chosenbecause this solid-state laser produces a more consistent wavelength of light

Gravitational Waves

10

compared to dye or gas lasers. The laser itself is composed of three stages: a non-planar ring oscillator made up of the Nd:YAG crystal, a medium power amplifier toboost the resulting power to 35 W, and a final high power oscillator (HPO) with amaximum output of 220 W (with a maximum power of 180 W as the laser systemoutput). The HPO can be bypassed for operation up to 35 W, as was done for thefirst few observing runs with Advanced LIGO.

Once the laser light has been produced, it must be stabilized in frequency,intensity, and beam direction. The pre-mode cleaner (PMC) is a bow-tie cavitydesigned to isolate the TEM00 mode, reduce beam jitter, and to low-pass filter radiofrequency (RF) intensity fluctuations. The PMC has a similar configuration to theoutput mode cleaner (OMC) described later and illustrated in figure 6. Everythingup to this point is part of the pre-stabilized laser (PSL, labeled ‘Laser’ in figure 6)system.

Next the light undergoes RF modulation on the beam (labeled ‘ϕm’ in figure 6).Three modulation frequencies are applied with small modulation depth: 24 MHzused by the input mode cleaner (IMC), 9 MHz and 45 MHz, both used for the maininterferometer sensing for feedback control loops. Everything after this point islocated within the system’s vacuum envelope.

FI

SRM

T=1.4%

ITM

ETM

Input Mode

Cleaner

OutputMode

Cleaner

PRM

BS

4 km

T= 3%

Laser m

PDGW readout

FI

ITM ETM125 W

5.2 kW 750 kW

CP

ERM

SR3

SR2

PR2

PR3 ERM

Figure 6. Optical configuration of Advanced LIGO. Reproduced with permission from The LIGO ScientificCollaboration 2015 Class. Quantum Grav. 32 074001.

Gravitational Waves

11

Once the laser is injected into the vacuum envelope it encounters the IMC: athree-mirror ring cavity to further stabilize the beam position, mode content, and toprovide a high-quality frequency reference.

Core optics: Each LIGO detector has a set of core optics all made of fused silicasubstrates:

• Two input test masses (ITM) and two end test masses (ETM) forming theFabry–Pérot arms.

• A 50/50 BS at the vertex of the interferometer.• Two compensation plates (CP) that serve as actuation reaction masses for theITM, and to which thermal compensation (not discussed) can be applied.

• Two actuation reaction masses (ERM) for the ETM.• Four reflective curved mirrors in the signal (SR2 and SR3) and powerrecycling (PR2 and PR3) cavities.

• Signal recycling (SRM) and power recycling (PRM) mirrors.

These substrates are each polished and coated. The surface polishing of the testmasses is especially important since the round-trip optical loss in the Fabry–Pérotcavities determines the amount of power that can be stored in the arms and thequantum noise level (see section 3.1). Finally, the substrates are coated with manyalternating layers of two dielectric coatings to build up constructive thin filminterference to the laser wavelength of 1064 nm. The coating materials are chosenfor their low optical absorption, scatter, and mechanical loss, the latter of which is ofparticular importance in reducing the test mass thermal noise (see section 3.1).

As the light enters the interferometer, it is split into two even parts, one sent toeach perpendicular arm. Each arm contains a Fabry–Pérot cavity that serves thepurpose of increasing the stored laser power in the arm and the light storage time.Increasing the light storage time increases the amount of time a gravitational wavehas to affect the path of any given photon or phase front of the continuous laserbeam. The main optics of this cavity are the ETM (with minimal transmission) andthe ITM (with 1.4% transmission). Each of these also has a reaction mass (CP for theITM and ERM for the ETM) that is pushed against when actuation forces areapplied. The finesse of each Fabry–Pérot cavity is 450, meaning that each photontravels the length of the arm 450 times on average, increasing the apparent length ofthe arms to photons from 4 km to about 1800 km.

Power and signal recycling: Once the light exits the Fabry–Pérot cavities, itrecombines at the BS where part of it is sent back towards the input optics. Theother portion of the light, directed toward the output, is minimal since theinterferometer is controlled to be very close to a dark fringe or fully destructiveinterference at the output; this is the light that carries gravitational wave informa-tion. The power recycling cavity on the input side of the BS creates a resonancebetween the light from the IMC and that coming from the BS. The light reflectedback to the BS provides a boost to the input laser power and the transmitted lightthat would go back to the laser is further reduced by a Faraday isolator, whichallows the transmission of light in only one direction.

Gravitational Waves

12

Signal recycling allows the detector to be tuned for a range of anticipatedgravitational wave frequencies by placing a partially reflecting mirror between theBS and the output photodetector (PD). In Advanced LIGO, it is selected to boostsignals from coalescing binary black holes and neutron stars. By feeding the signalthat can carry gravitational wave information back into the detector, the light isallowed to have more time in the detector, increasing the strength of the signal.

Output optics:Once the light is transmitted through the SRM, it enters the OMC. Thisis a bow-tie cavity (similar to the design of the PMC) and is designed to filter out theimposed RF modulation and any higher-order spatial modes from the light, meaningonly the light carrying gravitational wave information is then measured at the PD.

3 Current directions3.1 Noise sources and strain sensitivity

The noise floor—the limit to the strain sensitivity caused by the sum of detector noisesources—is dominated by quantum noise and Brownian noise from the test masscoatings. These will be treated here in detail while other less significant sources willbe touched upon.

Figure 7 illustrates the nominal Advanced LIGO noise terms, calculated using aninput power to the PRM of 125 W, SRM transmission of 20%, and with the signal

Figure 7. Principal noise terms for the nominal (high power, broadband) mode of operation of Advanced LIGO.Reproduced with permission from The LIGO Scientific Collaboration 2015 Class. Quantum Grav. 32 074001.

Gravitational Waves

13

recycling cavity having zero detuning. These parameters are the expected operatingconfiguration of Advanced LIGO once it reaches its design sensitivity. At thissensitivity, Advanced LIGO will be able to detect a strain of 1/10 000 the diameter ofa proton.

Quantum noiseThere are two related sources of quantum noise: shot noise and radiation pressurenoise. Both of these are a consequence of the uncertainty principle which states thatthe uncertainty in the position of the test masses times the uncertainty in theirmomentum must be greater than or equal to the reduced Planck constant. Theuncertainty in the position of the test masses manifests itself through shot noise and theuncertainty in momentum through radiation pressure noise. The separate treatment ofshot noise and radiation pressure noise below assumes a semi-classical approximation.

Shot noise: Relative changes in the position of the test masses are measured throughthe changing optical power at the output of the detector. Therefore, the detector’ssensitivity to gravitational waves is directly related to its sensitivity to optical power.This requires us to address the discrete nature of light as photons. The photons oflight made by the laser are produced randomly and are independent of each other.Such processes are subject to Poisson statistics (sometimes called ‘counting statis-tics’). Ultimately, we see large fluctuations in measurements with low photon arrivalrates. These fluctuations in optical power are directly related to apparent fluctua-tions in strain, and thus noise. Therefore, the key to lowering shot noise is to increasethe laser power.

For a simple Michelson interferometer, the shot-noise-limited strain noisedensity is

λπ

= ℏh f

LcP

( )1

2 in

where L is the length of one arm, ℏ is the reduced Planck constant, c is the speed oflight, λ is the wavelength of the laser, and Pin is the power incident on the BS.

Radiation pressure noise: Since photons have momentum, when they are reflected offof a test mass, there is corresponding recoil. The random arrival times of the photonsmean the test masses move in a noisy way that causes a fluctuating length differencebetween the arms and a noisy optical power at the output PD. For a simpleMichelson interferometer, the radiation pressure strain noise density is

π λ= ℏ

h fMLf

Pc

( )1

22in

3

where M is the mass of the test masses, L is the length of one arm, ℏ is the reducedPlanck constant, Pin is the power incident on the BS, λ is the wavelength of the laser,and c is the speed of light.

By comparing the expressions for shot noise with this expression for radiationpressure noise, we find that increasing the laser power will lower shot noise, whileincreasing radiation pressure noise. The mitigating solution is to design the test

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masses with increasing mass as the expected maximum power of the interferometerincreases. The mass of Advanced LIGO’s ITM and ETM is 40 kg, which is a nearlyfour-fold increase from Initial LIGO (11 kg).

Total quantum noise: The total quantum noise is a complicated relationshiprequiring a full quantum treatment beyond the semi-classical description givenabove. The quantum noise curve shown in figure 7 for Advanced LIGO is calculatedusing the formalism of Alessandra Buonanno and Yanbei Chen published in 2001.

Test mass thermal noiseUltimately, thermal noise is a measure of the degree a test mass can remain at rest.An understanding of Brownian motion leads to an understanding that anything witha temperature is not truly at rest internally. Since the measurement of gravitationalwaves requires position measurements orders of magnitude smaller than thesubatomic scale, the thermal motion of the mirror surfaces is not negligible.

Coating Brownian noise: This is the dominant cause of test mass thermal noise andoriginates in the ability of microscopic thermal energy to excite macroscopic degreesof freedom. That is, the same channels that dissipate mechanical energy into thermalenergy can allow thermal energy to create noisy mechanical energy. (The fused silicasubstrate of the test mass has much lower mechanical dissipation than the coatingmaterials. The noise from this is labeled ‘Substrate Brownian noise’ in figure 7.) Thebasic starting point for considering this kind of noise is the fluctuation–dissipationtheorem. For Brownian motion, a moving particle in a fluid experiences drag whichdissipates kinetic energy by turning it into heat. Conversely, a particle in a fluid isbombarded with collisions from the fluid’s atoms/molecules, thus turning thermalenergy into kinetic energy—the opposite of drag. Here we see that fluctuations anddissipation are connected; the fluctuation–dissipation theorem describes theirrelationship.

For a test mass in a gravitational wave interferometer, the strain noise density forthe Brownian motion fluctuations in the coating is computed by

πϕ=h f

Lk Td

fYw( )

1 4 B2 2

where L is the arm length, kB is Boltzmann’s constant, T is the temperature inKelvin, f is the frequency, d is the coating thickness, Y is Young’s modulus, w is thebeam width, and ϕ is the mechanical loss (a measure of the dissipation of mechanicalenergy). To reduce test mass thermal noise, the beam size on the test masses is madeas large as possible and mechanical loss of the coating is minimized. Loweringtemperature would also lower this noise if the properties of the substrate remainedindependent of temperature. However, in glass coatings and substrates (as currentlyused in Advanced LIGO), ϕ increases at substantially lower temperatures, negatingany beneficial effects. Low temperatures could lower this type of noise if the coatingsand substrates were replaced with crystalline materials.

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15

Thermo-optic noise: Another much less significant source of test mass thermal noiseis thermo-optic noise originating in thermal dissipation (‘Coating Thermo-opticnoise’ in figure 7). Fluctuations in the distribution of thermal energy result in theexpansion of the material or change in index of refraction due to temperaturechange, creating departures in the intended optical path of the laser.

Suspension thermal noiseA full treatment of this subject requires a discussion of materials physics, which isoutside the scope of this ebook. But we can understand the basics by considering thatany suspension material is not a pure, homogeneous substance. Instead, it has manypoint defects, domain walls, grain boundaries, etc. As such, there are many degreesof freedom, each having an equilibrium dependent on their individual stresses. Whena wire flexes due to an applied force, the internal degrees of freedom respond over aperiod of time through a process called relaxation, and produce a thermal noisespectrum. These random thermal fluctuations in the suspension material drive themechanical system and a random displacement results.

Besides being proportional to kBT like any thermal process, internal friction isalso proportional to the anelasticity of the material. This dimensionless quantity isabout 10−3–10−4 for most metals and 10−5–10−7 for low-loss materials like fusedsilica. During Initial LIGO, the test mass suspensions were hung from steel pianowire with an anelasticity of × −3 10 4. Advanced LIGO now uses fused silica wires tohang the test masses yielding a 100-fold reduction in suspension thermal noise.

Using pendula to suspend test masses also aids in suppressing suspension thermalnoise through a phenomenon called dissipation dilution. Most of the restoring forcefor a pendulum comes from lossless gravity via tension in the wires, not throughflexing of wires as described above. The gravitational restoring force reduces theeffect of loss through suspension thermal noise by a factor of 100–1000.

Gravity gradient noiseSeismic waves pass by the detectors on a regular basis; after any strong earthquake,the entire Earth vibrates similar to the way a bell rings after being struck. As thesurface waves (most importantly Rayleigh waves) pass beneath and near the testmasses, they cause local density fluctuations in the surrounding mass and result influctuating gravitational forces being exerted on the test masses. These fluctuationsin gravitational force on the test masses create gravity gradient noise and areseparate from the physical vibrations induced by seismic activity (q.v. seismic noise).

The gravity gradient noise shown in figure 7 has been estimated using a transferfunction formulation based on characteristic seismic modes that the geological strataat the LIGO sites support combined with a model for seismic motion at the sites.This estimate can be quite variable at times due to transient events local to thedetector.

Residual gas noiseStray gas in the beam tubes passes through the resonating cavity beam and causesfluctuations in the effective index of refraction along the path, resulting in optical

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16

path length noise. This is modeled by calculating the impulsive change in the cavityfield’s phase as a molecule moves through the beam, and then integrating over thevelocity distribution of a dominant residual gas component. For the noise curveshown in figure 7, hydrogen at a pressure of × −4 10 7 pascals is used.

Other noise sourcesSeismic noise: While there are active and passive seismic isolation systems in LIGO,they cannot filter out all seismic activity. However, due to the large mechanicalisolation of this noise source, it is negligible above 11 Hz.

Technical noises: There are also other sources of technical noises such as laserfrequency or amplitude noise, photodetector dark noise, actuator noise, etc. Theseare controlled so that the equivalent strain noise of each is no greater than 10% ofthe target strain sensitivity.

At of the end of the second LIGO observing run (O2), there were also increasedtechnical noises at low frequencies due to choices that allowed for greater detectorstability and, at LIGO Hanford, due to the effects of the 6 July 2017 earthquake inMontana, USA. Figure 8 shows the strain sensitivity of both LIGO detectors(Hanford and Livingston) and the Virgo detectors during the first gravitational wavedetection observed by all three observatories (GW170814; see section 3.3 for details).

3.2 Gravitational wave searches

The goal of collecting data from interferometric detectors is to observe the changinglight intensities from a strain induced in the arms by a gravitational wave. We havealready established that there are sources of noise that continuously produce a signal

Figure 8. Sum of noise sources in each detector, also known as strain sensitivity, using 4096 s around theGW170814 detection. Reproduced with permission from LIGO Scientific Collaboration and VirgoCollaboration 2017 Phys. Rev. Lett. 119 141101.

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at the output of the detector (see section 3.1) that can obscure a signal when present.In order to extract signals from noisy data, the gravitational wave community hasdeveloped a system of data analysis techniques targeted at different classes ofgravitational waves.

A common characteristic of these data analysis techniques is that a true gravita-tional wave signal must be coincident in more than one detector, i.e. appear withinthe maximum gravitational wave time of flight between detectors (plus some extratime to account for calibration errors that affect timing). The large distancesbetween detectors means that the environmental noise between them is uncorrelated;demanding coincident detection allows the exclusion of local disturbances thatcreate noise artifacts that ‘look’ like a gravitational wave. The two LIGO detectorsare 3000 km apart, creating a maximum time of flight at the speed of light of 10 ms.

Data quality must also be evaluated. To do this, the characteristics of the detectorare continually studied to increase the overall sensitivity of the detector (byidentifying and eliminating sources of noise) and to identify segments of data whereinstrumental or environmental artifacts are present. These segments are then vetoedby the data analysis methods, i.e. contaminated times are removed from the searchfor a gravitational wave signal.

Compact binary coalescencesSources: As two objects orbit each other, they gradually lose energy causing theirorbital radius and period to decrease. Eventually, the distance between the objects issmall enough that their surfaces make contact and merge into a single object. Whentwo dense objects undergo such a process, they radiate large amounts of energy inthe form of gravitational waves just before the merger phase. This class ofgravitational waves is called compact binary coalescences (CBC), sometimescolloquially referred to as ‘inspirals’. Examples of such detectable sources are apair of neutron stars, a pair of stellar-mass black holes, or a combination of these.

Because the system is well defined, the gravitational waves it produces can bepredicted. Long before the merger itself, the two objects are orbiting each other witha slowly increasing frequency (at this point in their evolution they are producingcontinuous gravitational waves, discussed later). As the orbital radius decays, thegravity of the system becomes strong enough that the weak field approximation is nolonger valid. Therefore, CBC signals are calculated using numerical relativitymethods.

Analysis technique: Since numerical simulations give us a priori knowledge ofgravitational wave signals from different systems, analysis techniques that correlatea known signal to noisy data can be used in order to determine if that signal ispresent in those data. This method, known as matched filtering, only works for onespecific signal, called a template, at a time. It is not possible to use the matchedfiltering technique for every possible mass combination of binary systems. Hence, atemplate bank is developed so that any signals within a range of masses will matchone of the templates within a small error. During the first observing run (O1) ofAdvanced LIGO, approximately 250 000 templates were used in CBC searches.

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18

Even with a template bank, matched filtering is a computationally expensivetechnique. To help reduce the need for resources, data are resampled from 16 384 Hzto 2048 Hz. The cross-correlation is then computed for each template against thedata, successively shifting it through each data point. This produces a set of signal-to-noise ratio (SNR) values from each cross-correlation calculation and only valuesabove a specified threshold are accepted for further consideration. These accepteddata points are called triggers. As the template is shifted in time through the data,multiple triggers will be created near a true match due to there being a highcorrelation between the template and a near match in the data. Only the highestSNR trigger from a cluster is kept to distinguish the best match between the templateand the data. This is repeated for the data streams from other detectors and theresulting sets of trigger times are compared; those that occur within the possiblegravitational wave time of flight between respective detectors (plus some time toaccount for calibration errors) produce candidate gravitational wave detections.

Burst gravitational wavesSources: Some sources of gravitational waves are difficult or impossible to modeleither because the initial conditions are unknown, the dynamics in the extremeenvironment are not understood, or the system is simply unanticipated. Consider thecollapse of a stellar core before a type II supernova: this is a large quantity of massmoving in what is expected to be an asymmetrical fashion. The full physics of thesystem as it collapses is not fully understood, although computational models haveprovided simulations of how the resulting gravitational waveforms may appear.Ultimately, the true signal of this expected source is still not known.

A real possibility for detections in this class of gravitational waves is that, byperforming a search that makes minimal assumptions about a signal, gravitationalwaves are found from unexpected sources. There is a long history in astronomy oflooking at the Universe in a novel way and finding something new (for example, thediscovery of the cosmic microwave background) and burst gravitational wavespresent such an opportunity.

Analysis technique: The challenge of searching for burst gravitational waves is thatwe have no a priori knowledge of the signal to look for except that the signal will beshort duration and uncorrelated with the detector noise. However, we do know thatwhen a signal is added to a background of noise, the statistics of the combined signaland noise change. We can use such statistical changes to our advantage by using anexcess power method.

First, the characteristics of the background data (noise) must be estimated. This isdone by time-shifting data from pairs of detectors and analyzing the result.Repeating this shifting many times eliminates the possibility that there is a truecoincident signal in the data (the time shifts are greater than the gravitational wavetravel time between detectors) and the resulting accidental triggers from noisefluctuations yield a background distribution as a function of noise strength. Thisallows analysis thresholds to be tuned in order to produce candidate events with adesired false alarm rate.

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19

Coherent searches use results of multiple streams of data from different detectorsto identify coincident candidate events. The data from each stream are studied inboth the time and frequency domains using a time-frequency representation, e.g.wavelet transform. The maximum possible energy in each time-frequency locationacross all of the detectors is calculated and used to produce the maximum likelihoodratio for that location taking into account the time delay induced from different skylocations and their corresponding antenna response. This is effectively a combina-tion of excess power and cross-correlation calculations. Time–frequency locationswith high enough significance are then detection candidates. This method has alsobeen proven effective at identifying strong CBC chirp signals.

Once a time–frequency location has been identified as a detection candidate,further analysis is done to reconstruct the most probable gravitational wave signalusing a Markov chain Monte Carlo (MCMC) method with a linear combination ofwavelets. This step is vital to being able to use detections for astronomicalobservation since there is no a priori knowledge of the waveform going into thedata analysis.

Continuous gravitational wavesSources: As long as a mass is accelerating spherically asymmetrically, it will producegravitational waves. The short duration CBC and burst gravitational waves areviolent and often destructive. However, long-lived sources can produce gravitationalwaves of consistent frequency.

Any rapidly spinning compact object with a non-axisymmetric deformation willproduce a continuous gravitational wave. Consider a spinning neutron star with a‘mountain’ on its side. Due to the nature of a neutron star’s composition and itsextreme density, neutron stars are expected to be nearly perfectly spherical.Deformations are estimated to be on the order of 10 cm for normal neutron starmaterial to 10 m for exotic material. Energy is radiated away from the neutron starin the form of gravitational waves causing the period of the star’s rotation to slowlyincrease over time; this is characterized by its frequency derivative, also known asthe ‘spindown rate’. Detecting the gravitational waves from neutron star deforma-tions will allow further probing of the neutron star equation of state. There are manystudied neutron stars in the Milky Way with rotation rates within LIGO’s sensitivegravitational wave bandwidth.

Analysis technique: Since the waveform of the gravitational wave can be easilymodeled for continuous gravitational waves, a matched filtering data analysisapproach is used. Here, the data are broken into segments (usually a few hours)and undergo a Fourier transform or Hough transform (a technique used fordetecting patterns in digital images). The transformed data are then correlatedwith the transformed simulated gravitational wave template. High correlationsindicate a possible detection.

While appearing relatively straightforward, this must be done for each frequencyof interest and for each spindown rate. There is also the complication that the sourceof a continuous gravitational wave undergoes diurnal motion, creating a Doppler

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20

shift unique to its sky location. (This effect was ignored for CBC and burstgravitational waves due to their short duration.) Now, the search must be donefor each frequency, spindown rate, and sky location. This is a computationallyexpensive search so it is often targeted at identified neutron stars with knownrotational periods.

Stochastic gravitational wavesSources: As the sensitivity of gravitational wave detectors increases, the distancefrom which a typical source can be detected also increases, resulting in a largereffective volume being searched. With the inclusion of potential sources from thatincreased volume, the likelihood that multiple events from different sources arrive atEarth simultaneously increases. Therefore, it is expected that Earth is beingcontinuously bombarded by a background of weak and unresolved gravitationalwaves from distant sources. Because of the random nature of these gravitationalwaves, they are classified as stochastic.

The most distant stochastic source is the Big Bang. Quantum vacuum fluctuationsfrom nearly the instant after the Big Bang (~10−36 s) may have been amplified by aperiod of exponential expansion called inflation. They have continued to be redshiftedby the persistent (much slower) expansion of the Universe, and may still be detectable.If these relic gravitational waves from the Big Bang can be detected, they will carryinformation from the earliest and otherwise inaccessible history of the Universe, andwill be strong evidence towards confirming inflationary theory. By comparison, thecosmic microwave background—the relic light from the Big Bang—is from therecombination epoch over 300 000 years after the Big Bang.

Regardless of the population comprising the stochastic gravitational wave back-ground, be it astronomical sources like many binary black hole mergers and super-novae or cosmological like the Big Bang, these are the weakest gravitational wavesand may require further advancements in detector sensitivity to realize a detection.

Analysis technique: Due to the random nature of a stochastic gravitational wave, itappears as excess noise in the collected data. However, this noise is a common noisebetween multiple detectors. To determine if a common noise is present, a cross-correlation method is employed. The result of this analysis is a statistical descriptionof the stochastic gravitational wave, not a recovery of the signal waveform.

The analysis is performed by transforming the data into the frequency domain.Then the frequency domain data from a pair of detectors are multiplied by a filter thatoptimizes SNR by enhancing frequencies at which the template gravitational wavespectrum is strong and suppresses frequencies where the detector noise is large. Theresult of this analysis is a measure of stochastic gravitational wave energy density.

3.3 Gravitational wave astronomy

Gravitational wave discoveriesAs of the date of publication of this ebook, there have been eleven confirmedgravitational wave detections (ten from binary stellar-mass black hole coalescence,

Gravitational Waves

21

BH–BH, and one from a binary neutron star coalescence, NS–NS). Each detection isnamed according to the UTC date on which it was observed (for example, GW170817is a gravitational wave that was observed on 17 August 2017). A summary of thesedetections is given in table 1.

Black holesAs exotic as black holes are, they can be simply and completely described by threequantities: mass, spin, and charge. Since it is believed that the charge of anastrophysical black hole is negligible, we can learn almost everything about a blackhole if we can extract information about its mass and spin from a detectedgravitational wave. We can also learn more about the formation mechanism forbinary black hole systems from this information.

Two prominent stellar evolution theories for binary stellar-mass black holes are:1) isolated binary evolution, where two stars located within a galaxy evolve and

collapse into black holes;2) dynamical assembly, where two independent black holes, likely in an

environment of dense stellar clusters or galactic centers, are gravitationallycaptured to form the binary.

Alternatively, black hole binaries may also form from primordial black holes.

Black hole mass: The component masses of a black hole binary are determined bythe frequency evolution of the gravitational wave signal. For high-mass systems, themerger and ringdown phases provide a measure of the total mass (sum of thecomponent masses) while the chirp mass,

=+

m m

m m

( )

( )c

1 2

1 2

35

15

M

Table 1: Summary of all gravitational wave detections from the first and second observing runs (O1 and O2).

Label SourcePrimarymass (M⊙)

Secondarymass (M⊙)

Finalmass (M⊙)

Radiatedenergy (M⊙c

2)Luminositydistance (Mpc)

GW150914 BH-BH −+35.6 3.0

4.8−+30.6 4.4

3.0−+63.1 3.0

3.3−+3.1 0.4

0.4−+430 170

150

GW151012 BH-BH −+23.3 5.5

14.0−+13.6 4.8

4.1−+35.7 3.8

9.9−+1.5 0.5

0.5−+1060 480

540

GW151226 BH-BH −+13.7 3.2

8.8−+7.7 2.6

2.2−+20.5 1.5

6.4−+1.0 0.2

0.1−+440 190

180

GW170104 BH-BH −+31.0 5.6

7.2−+20.1 4.5

4.9−+49.1 3.9

5.2−+2.2 0.5

0.5−+960 410

430

GW170608 BH-BH −+10.9 1.7

5.3−+7.6 2.1

1.3−+17.8 0.7

3.2−+0.9 0.1

0.0−+320 110

120

GW170729 BH-BH −+50.6 10.2

16.6−+34.3 10.1

9.1−+80.3 10.2

14.6−+4.8 1.7

1.7−+2750 1320

1350

GW170809 BH-BH −+35.2 6.0

8.3−+23.8 5.1

5.2−+56.4 3.7

5.2−+2.7 0.6

0.6−+990 380

320

GW170814 BH-BH −+30.7 3.0

5.7−+25.3 4.1

2.9−+53.4 2.4

3.2−+2.7 0.3

0.4−+580 210

160

GW170817 NS-NS −+1.46 0.10

0.12−+1.27 0.09

0.09 ⩽2.8 ⩾0.04 −+40 10

10

GW170818 BH-BH −+35.5 4.7

7.5−+26.8 5.2

4.3−+59.8 3.8

4.8−+2.7 0.5

0.5−+1020 360

430

GW170823 BH-BH −+39.6 6.6

10.0−+29.4 7.1

6.3−+65.6 6.6

9.4−+3.3 0.8

0.9−+1850 840

840

Gravitational Waves

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can be extracted from the inspiral phase of a low-mass system. The magnitude of thecomponent masses can hint at the progenitor stars in a formation process. Considerisolated binary evolution scenarios. As the component stars evolve, they arecontinuously losing mass through solar winds. In order to have sufficient mass toleave a black hole remnant, they must avoid excessive mass loss. High-metallicity(those containing elements other than hydrogen and helium on the order of a fewpercent) stars are believed to have stronger solar winds, driven by their ownradiation pressure, than low-metallicity stars. Therefore, it is expected that high-metallicity progenitors will leave less massive black hole remnants than low-metallicity progenitors. (However, low mass loss may also have been possible forthe higher metallicities of strongly magnetized stars.) Therefore, the progenitors ofthe component black holes observed in GW170608—the least massive black holebinary observed with gravitational waves so far—may have originally been high-metallicity stars. In contrast, the GW170729 black hole progenitors—the mostmassive black hole binary observed so far—are more likely to have been low-metallicity stars.

Black hole spin: The spin of a black hole provides further clues to the history of thebinary system. For example, if the formation mechanism for the black hole systemwas isolated binary evolution, then it is expected that the spin of the black holewould be aligned with the direction of the orbital angular momentum due to tidesand mass transfer, although misalignments can be caused by supernova explosionsor torques during collapse. Conversely, binaries formed through dynamical assem-bly (both through stellar evolution from primordial black holes) are expected toproduce random spin tilts with equal probability for positive or negative effect spin,χeff , with negative χeff indicating a spin–orbit misalignment of at least onecomponent.

The effective spin, χeff , is a combination of the two component spins along theorbital angular momentum:

χ θ θ=+

+m m

m a m a1

( cos cos )LS LSeff1 2

1 1 2 21 2

where m1 and m2 are the component masses, a1 and a2 are the dimensionless spinmagnitudes of the component masses, =a cS

Gmii

i2 , that each have a value between 0

and 1, and θLS is the tilt angle between the spin of the component mass, S, and theorbital angular momentum, L:

θ = ˆ∙ ˆ− L Scos ( )LS i1

i

The effective spin is the primary measure of a binary system’s spin since theorientation of individual spin evolves due to precession but χeff remains approx-imately constant during orbital evolution. It is measured from a gravitational wavesignal from its effect on the inspiral rate of the binary and influence on the merger.

As of the date of this publication (January 2019), most gravitational wave blackhole binary spin measurements cluster around χeff ~ 0 (∣χeff ∣ < 0.3 at 90% confidence

Gravitational Waves

23

level); this disfavors formation mechanisms involving ‘second-generation’ mergerswhere at least one component of the binary is a black hole formed through a previousmerger.

Rate of observations: While not related to measuring properties of a specific blackhole binary system, the frequency at which we observe binary black hole mergers canbe contrasted against current predictions based on formation mechanism. From allgravitational wave observations from the first and second observing runs (O1and O2), the combined range of merger rates from two population models is25.9–108.5 Gpc−3 yr−1. For the formation models discussed previously, the rates arepredicted to be on the order of ~1–10 Gpc−3 yr−1. This is lower than the lower boundon the rate from gravitational wave observations, suggesting that a combination ofmore than one formation mechanism may be needed to produce the observed rate.

Ultimately, there has not been sufficient evidence to rule out or favor oneformation mechanism over another for any binary black hole observation. However,as we catalog more observations, at around O(100) binary black hole detections itmay become possible to determine the relative proportions of binaries originatingfrom each mechanism.

Neutron starsThe first detection of a gravitational wave from a source other than a binary blackhole was that of a binary neutron star merger (GW170817) that was alsoaccompanied by the observation of electromagnetic waves in multiple differentbands. About 1.7 s after peak gravitational wave signal (indicating merger), theFermi Gamma-ray Burst Monitor detected a short gamma-ray burst(GRB170817A) whose sky localization area overlapped with the area estimatedby the LIGO detectors. The Virgo detector was also operational but did not see thegravitational wave signal, even though Virgo was sensitive enough to detect agravitational wave of that strength. This is because the gravitational wave originatednear one of the areas on the sky where Virgo has low sensitivity (see figure 5 for anillustration of LIGO Livingston’s antenna pattern which has similar properties toVirgo’s). This non-detection led to a reduction in the size of the LIGO source area.

Notices were sent out by both Fermi and LIGO indicating a possible coincidentobservation of the same signal. The first optical detection was made 10 h and 52 minlater, originating in the galaxy NGC 4993. In the hours and days following, lightfrom different bands was observed: 11 h and 36 min after the gravitational wavedetection the first infrared detection occurred, 15 h after UV light was first observed,9 days later x-rays were discovered, and 16 days later radio waves were firstobserved. No neutrinos were observed associated with the event. This set ofdetections represents the true birth of gravitational waves in multi-messengerastronomy.

The observation of a neutron star merger observed through gravitational wavesand a coincident short gamma-ray burst from the same area on the sky is the firstconclusive evidence that the long-hypothesized origin of this class of gamma-ray

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24

bursts can be a neutron star merger. The progression of electromagnetic observa-tions agreed with the formation of a kilonova (sometimes referred to as a macro-nova) resulting from the merger. Spectra taken from this event also show thenucleosynthesis of lanthanides through the rapid neutron-capture process, or ‘r-process’, which also supports the hypothesis that a large proportion of the heavyelements in our Universe were formed through neutron star mergers instead ofprimarily through supernovae.

This detection is the first of its class; more will be needed to observe trends likethose described for black holes. However, it also gives us our first glimpse into thestructure of a neutron star. The nature of the final merged remnant from this systemis not known as it lies in a mass gap between observed neutron stars and observedblack holes. Therefore, it is either the most massive neutron star or the least massiveblack hole ever found. With this event, we were also able to measure the expansionrate of the Universe with gravitational waves for the first time. While this result isconsistent with SHOES (Supernova H0 for the Equation of State) and Planck data,it is the first measurement of the Hubble constant independent of electromagneticobservations.

4 OutlookAdvanced LIGO and Virgo have been successful in making detections of gravita-tional waves that have ushered in the era of gravitational wave astronomy. Whilethese accomplishments are monumental, observing more gravitational waves indifferent ways will expand on the potential of the field. Efforts looking to the futureare well underway to do just that.

4.1 Ground-based detectors

LIGO-IndiaIn order to determine the location of a gravitational wave source on the sky, atriangulation-like method is employed utilizing the detection time differencebetween detectors. However, the existing gravitational wave detectors lie onapproximately the same plane on the Earth resulting in a reduced ability to resolvesource locations for gravitational waves incident around the equator. Adding adetector located south of the existing detectors will improve the network’s resolvingability.

Plans are being made to install a third LIGO interferometer in India. The US willprovide the instrumentation and India the facility and staff. The instrumentation hasalready been made; the development of the Indian infrastructure is being prepared.LIGO-India is expected to make its first observations circa 2025.

Einstein TelescopeA third-generation (the first generation being Initial LIGO and Virgo and the secondbeing the upgraded detectors) European detector called the Einstein Telescope is inthe planning phase and will potentially have 100 times the sensitivity of advanced

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25

detectors. The facility will be located underground (to reduce seismic and gravitygradient noise) and be cryogenically cooled (to reduce thermal noise). It will beconfigured as an equilateral triangle with each corner being the vertex for twodetectors (one for low frequency, 1–250 Hz, and the other for high frequency, 10 Hz–10 kHz, gravitational waves). The arms of all of the detectors will be 10 km long.

The goal of this design is to perform higher precision gravitational waveastronomy than existing detectors, and expected upgrades will be capable of testinggravity in strong field environments. A target operational date for this project hasnot been determined.

4.2 A space-based detector

LISAA limiting factor of ground-based detectors is that they are subject to vibrationsfrom Earth’s active environment. This is especially problematic at low frequencieswhere seismic noise is dominant. The obvious solution is to build a space-baseddetector.

The Laser Interferometer Space Antenna (LISA) mission is composed of aconstellation of three satellites arranged in an equilateral triangle with a distanceof 1 million km between each satellite. The constellation will orbit the Sun 20° behindthe Earth with each satellite on its own orbital path so that they also rotate oncearound the center of their configuration per orbit. Each satellite protects a freelyfalling test mass within it; the primary function of the satellite is to counter externalforces that would otherwise affect the mass. Gravitational waves will be detected bymeasuring the changing distance between these freely falling masses. LISA will besensitive to gravitational waves between the frequencies of 0.1–100 mHz. Thisfrequency range lies between that of pulsar timing techniques and interferometrictechniques. LISA has been selected by the European Space Agency for its L3mission, with launch expected in 2034.

4.3 Prospects

In the short term, the addition of LIGO-India to the existing network of ground-based detectors (LIGO, Virgo, GEO600, and KAGRA) will add to our ability toaccurately determine the sky location of gravitational waves, increase the duty cycleof at least two detectors online at the same time, allow for full polarization tests ofgeneral relativity, and more. We will be detecting more gravitational waves andextracting more science with each detection.

In addition to science in LIGO’s frequency range, the Einstein Telescope’sadvanced ground-based detector will increase both amplitude sensitivity andfrequency range, and the LISA space-based detector will extend gravitationalwave sensitivity to even lower frequencies. This provides us with an analog tomulti-wavelength electromagnetic astronomy in that we will be able to detect signalsfrom multiple ‘octaves’ of the gravitational wave symphony, providing a morecomplete composition of this view of the Universe.

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Additional resourcesGeneral relativity

• Paper: Price R 1982 General relativity primer Am. J Phys. 50 300.• Introductory text: Schutz B 2009 A First Course in General Relativity 2nd edn(Cambridge: Cambridge University Press).

• Advanced text: Carroll S 2003 Spacetime and Geometry: An Introduction toGeneral Relativity (London: Pearson).

Gravitational waves• Book: Creighton J and Anderson W 2011 Gravitational Wave Physics andAstronomy (Hoboken, NJ: Wiley).

• Paper: Riles K 2013 Gravitational waves: Sources, detectors and searchesProg. Part. Nucl. Phys. 68 1–54.

• Paper: Sathyaprakash B S and Schutz B F 2009 Physics, astrophysics andcosmology with gravitational waves” Living Rev. Relativ. 12 2.

• Course: Ph 237: Gravitational waves, Kip Thorne’s 2002 web-based course atCaltech, with video lectures and homework problems (http://astro-gr.org/online-course-gravitational-waves/).

Interferometric detectors• Book: Saulson P 2017 Fundamentals of Interferometric Gravitational WaveDetectors 2nd edn (Singapore: World Scientific).

• Paper: LIGO Scientific Collaboration 2015 Advanced LIGO Class. QuantumGrav. 32 074001.

• Paper: Virgo Collaboration 2015 Advanced Virgo Class. Quantum Grav. 32024001.

• Paper: Saulson P 1997 If light waves are stretched by gravitational waves,how can we use light as a ruler to detect gravitational waves? Am. J. Phys. 65501–5.

LIGO resourcesThe LIGO white papers describe the current status and priorities for the coming year.Current white papers can be found at: http://www.ligo.org/about/white_paper.php.

• LIGO Scientific Collaboration, ‘The LSC-Virgo White Paper onGravitational Wave Searches and Astrophysics’ updated yearly.

• LIGO Scientific Collaboration, ‘Instrument Science White Paper’ updatedyearly.

LIGO maintains a central repository for its documents (papers, presentations, etc)called the Document Control Center. Internal or unreviewed documents are accessibleby LIGO Scientific Collaboration members only, but there is a public version as well.The gateway to both of these versions is available at: https://dcc.ligo.org.

The LIGO Open Science Center is the clearinghouse of data releases and containstutorials on how to manipulate data and do basic analysis. The tutorials are geared

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toward a scientist learning the basics of data analysis and include scripts to replicatethe tutorials.

• Home: https://losc.ligo.org/.• Tutorials: https://losc.ligo.org/tutorials/.• Web Course (2018): https://www.gw-openscience.org/static/workshop1/course.html.

Gravitational wave detection papersAll publications announcing the discovery of a gravitational wave detection arepublished open access in their respective journals:

GW150914: LIGO Scientific Collaboration and Virgo Collaboration 2016 Phys.Rev. Lett. 116 061102.

GW151226: LIGO Scientific Collaboration and Virgo Collaboration 2016 Phys.Rev. Lett. 116 241103.

GW170104: LIGO Scientific Collaboration and Virgo Collaboration 2017 Phys.Rev. Lett. 118 221101.

GW170608: LIGO Scientific Collaboration and Virgo Collaboration 2017 ApJL851 L35.

GW170614: LIGO Scientific Collaboration and Virgo Collaboration 2017 Phys.Rev. Lett. 119 141101.

GW170617: LIGO Scientific Collaboration and Virgo Collaboration 2017 Phys.Rev. Lett. 119 161101.

Gravitational-Wave Transient Catalog (GWTC-1): The LIGO ScientificCollaboration and Virgo Collaboration 2018 arXiv:1811.12907.

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