host galaxy identiﬁcation for binary black hole mergers

MNRAS 474, 4385–4395 (2018) doi:10.1093/mnras/stx3077Advance Access publication 2017 November 29

Host galaxy identification for binary black hole mergers with longbaseline gravitational wave detectors

E. J. Howell,1‹ M. L. Chan,2 Q. Chu,1 D. H. Jones,3 I. S. Heng,2 H.-M. Lee,4 D. Blair,1

J. Degallaix,5 T. Regimbau,6 H. Miao,7 C. Zhao,1 M. Hendry,2 D. Coward,1

C. Messenger,2 L. Ju1 and Z.-H. Zhu8,9

1OzGrav-UWA, School of Physics and Astrophysics, University of Western Australia, Crawley WA 6009, Australia2SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK3English Language and Foundation Studies Centre, University of Newcastle, Callaghan NSW 2308, Australia4Seoul National University, Seoul 08826, Korea5Laboratoire des Materiaux Avances (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France6Artemis, Universite Cote d’Azur, Observatoire Cote d’Azur, CNRS, CS F-34229, F-06304 Nice Cedex 4, France7School of Physics and Astronomy, Institute of Gravitational Wave Astronomy, University of Birmingham, Birmingham B15 2TT, UK8Department of Astronomy, Beijing Normal University, Beijing 100875, China9School of Physics and Technology, Wuhan University, Wuhan 430072, China

Accepted 2017 November 24. Received 2017 November 24; in original form 2017 October 25

ABSTRACTThe detection of black hole binary coalescence events by Advanced LIGO allows the sciencebenefits of future detectors to be evaluated. In this paper, we report the science benefits of one ortwo 8 km arm length detectors based on the doubling of key parameters in an Advanced LIGO-type detector, combined with realizable enhancements. It is shown that the total detection ratefor sources similar to those already detected would increase to ∼ 103–105 per year. Within0.4 Gpc, we find that around 10 of these events would be localizable to within ∼10−1 deg2. Thisis sufficient to make unique associations or to rule out a direct association with the brightestgalaxies in optical surveys (at r-band magnitudes of 17 or above) or for deeper limits (downto r-band magnitudes of 20) yield statistically significant associations. The combination ofangular resolution and event rate would benefit precision testing of formation models, cosmicevolution, and cosmological studies.

Key words: black hole physics – gravitation – gravitational waves.

1 IN T RO D U C T I O N

The first gravitational wave (GW) observations of the coalescenceand merger of stellar mass binary black holes (BBHs) by Ad-vanced LIGO (aLIGO; Aasi et al. 2015) and Advanced Virgo (AdV;Acernese et al. 2015) prove the existence of a large cosmic popula-tion of these sources (Abbott et al. 2016b,c,e). Following these dis-coveries, the observation and localization to within 28 deg2 of a coa-lescing system of neutron stars (Abbott et al. 2017f), the associationwith a short-duration gamma-ray burst (Abbott et al. 2017c), and thesubsequent ground-breaking electromagnetic follow-up campaign(Abbott et al. 2017b) have firmly cemented the GW window intomainstream astronomy.

The observations of BBHs suggest that they could be the relics ofco-evolved binaries from the Pop III or Pop II era (as proposedby Lipunov, Postnov & Prokhorov 1997; Dominik et al. 2015;Belczynski et al. 2016), or could be dynamically formed in globu-

� E-mail: [email protected]

lar clusters (Bae, Kim & Lee 2014; Hong & Lee 2015; Rodriguezet al. 2015, 2016b; Rodriguez, Chatterjee & Rasio 2016a). The GWobservations of each event provide information on the masses andspins of the BBH system, and their location in a spatial volumeelement determined by the angular resolution and the luminositydistance error. However, as the intrinsic mass M is redshifted in theobserver frame by (1 + z), where z is the cosmological redshift, themeasured quantity of mass is the redshifted mass Mz = (1 + z)M.

To use the BBH population as a tool for distinguishing the for-mation mechanism, one requires a large population of such events(Stevenson, Ohme & Fairhurst 2015). Furthermore, to use GWs toinvestigate cosmology, it would be necessary to be able to iden-tify the host galaxies (Fan, Messenger & Heng 2014), and measuretheir redshift. Independent redshift measurements would also sig-nificantly improve the accuracy of measuring the mass parametersby breaking the mass–redshift degeneracy (Messenger et al. 2014;Ghosh, Del Pozzo & Ajith 2016).

Now that GW detectors have crossed the threshold from non-detection to detection, assuming only a roughly homogeneous dis-tribution of sources in the cosmos, we can estimate the number of

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4386 E. J. Howell et al.

detectable events as a function of detector sensitivity. This dependson the cosmic event rate density, integrated over the accessible vol-ume of the universe. At low redshift (z ≈ 0.2), the event rate scalesroughly as the cube of detector sensitivity so that the estimates ofimproved sensitivity can be made using limited assumptions. Forhigher redshifts, cosmic expansion and the distribution of coales-cence times influence the event number count.

The angular resolution of GW detector networks largely followsthe Rayleigh criterion, �� = (λ/D)ρ−1, where D is the detectorspacing, λ is the observed wavelength, and ρ is the signal-to-noiseratio (SNR), as discussed in detail below. Except for the lowestfrequencies, which to date have been difficult to access due totechnical noise, detector spacings are a few wavelengths (100 Hz ≈3000 km wavelength). There is a substantial advantage in measuringboth the relative phase and the amplitude of incoming signals todetermine their position in the sky. Maximum possible baselinesare always beneficial.

The current world array of detectors consist of aLIGO and AdV;KAGRA in Japan (Aso et al. 2013) is expected to be taking data by2020, and LIGO-India1 has been proposed for 2022. The detectornetwork noticeably omits a Southern hemisphere detector, eventhough such a detector would contribute long baselines to all thenorthern detectors (Wen & Chen 2010; Klimenko et al. 2011; Raffaiet al. 2013; Chu et al. 2016).

There have been several proposals for third-generation (3G)GW detectors (Punturo et al. 2010; Dwyer et al. 2015; Abbottet al. 2017d). Options include extending the arms from 4 kmto lengths of the order of 10–40 km (Dwyer et al. 2015; Ab-bott et al. 2017d), the use of cryogenics with silicon test masses(Punturo et al. 2010), and optics operating at about 2 μm wavelength(Abbott et al. 2017d). Such detectors are likely to come online inthe late 2020s, but necessarily depend on substantial research anddevelopment.

To bridge the gap between present second-generation (2G) andfuture 3G Interferometric GW Observatories (IFOs), an 8 km LIGO-type 2.5G detector has been proposed (Blair et al. 2015) that wouldbe constructed by scaling up currently proven technology. The 8 kmarm length was chosen as a safe length for which LIGO-type stain-less steel vacuum pipes could be used; pipe diameter is a major costdriver. As LIGO was initially designed to house up to three IFOs,doubling the arm length while maintaining the same pipe diameterallows implementation using the LIGO design.

The design also included doubling the fused silica suspension fi-bre length (to 1.5 m) and a doubling of the test masses to 80 kg.Two other enhancements match proposals for the enhancementof aLIGO: the use of Newtonian noise suppression (Coughlinet al. 2016) and squeezed light technology (Ligo Scientific Col-laboration et al. 2011). These technologies are already under de-velopment and could be tested and implemented in parallel withdetector construction.

In this paper, we analyse the angular resolution and source eventrate that could be expected if one or two 2.5G detectors were addedto the existing and planned worldwide array. We show that a detectorin China increases the event rate and also improves the angularresolution. However, an optimal arrangement is for this detectorto be complemented by a Southern hemisphere detector; we findthat if only one detector were to be installed, an Australia-basedinstrument is the optimal choice.

1 See https://dcc.ligo.org/LIGO-M1100296/public for Detailed Project Re-port.

We will show that of the order of ≈104 detections per year couldbe expected in the improved network corresponding to one eventevery hour. The strongest sources at about 0.4 Gpc have an SNR∼100, and can be localized sufficiently (both in direction and red-shift) that the brightest host galaxies of ≈1–10 sources per yearcould be directly identified without confusion. At larger ranges, theuncertainty value (measured in sky area × redshift interval) expandssteeply due to (a) the distance dependence of the linear size of theerror ellipse; (b) the increased angular error and luminosity distanceerror as the SNR decreases. This causes rapidly increasing sourceconfusion, and thus the number of candidate galaxies increases.

The detection prospects of other important GW sources, suchas stochastic backgrounds, binary neutron star coalescence, andcontinuous waves from rotating neutron stars, could be enhancedby 2.5G instruments; in this study, we choose to base our analysison only the known BBH sources that have crossed the detectionthreshold.

The structure of this paper is as follows: Section 2 presents aconceptual outline of an 8 km GW interferometric detector andSection 3 presents the angular resolution improvement obtained byadding such a detector to existing and proposed networks. The ex-pected event rates are calculated in Section 4 and the possibility forhost galaxy identification is assessed in Section 5. Finally, Section 6reviews the results and discusses the possibility of building 8 kmdetectors.

2 D E S I G N C O N C E P T F O R A N 8 K M A R ML E N G T H G W IN T E R F E RO M E T R I C D E T E C TO R

GW detectors must achieve an optimum balance of noise sourcesthat include quantum noise, thermal noise, residual gas noise, New-tonian noise, and seismic noise. The performance of LIGO andaLIGO has demonstrated a good current understanding of detectornoise, although at low frequency some noise sources are not fullyunderstood. Since GWs induce relative displacements that increaseproportional to the arm length, sensitivity should also increase pro-portional to arm length. Effectively, local noise sources associatedwith the test masses are diluted by increasing the arm length.

Further improvements can also be achieved by increasing thedimensions of the test mass system. First, by increasing the test masssize and mass, one can achieve improved averaging of the thermalnoise due to internal acoustic modes. Secondly, by lengtheningthe test mass suspension fibres, the pendulum frequency of thesuspension is reduced, which acts to reduce the pendulum modethermal noise.

The dominant noise budget and the total detector noise that re-sults from adopting these and other improvements are shown inFig. 1 (see also Blair et al. 2015). The lower panel shows a nearlyfourfold improvement factor. However, this is not a direct resultof the doubling of parameters, but a composite effect due to theaddition of thermal noise and quantum noise.

A key aspect of this proposed detector would be provision forupgrading from a 2.5G design to 3G technology (such as cryogenicdetectors with silicon test masses; Punturo et al. 2010) in the futurewhen these technologies are proven.

The specific parameters used to improve over aLIGO technologyand define the above results are (a) extending the arm length to8 km; (b) doubling the test mass weight to 80 kg; (c) extending thelast-stage test mass suspension to 1.5 m; (d) increasing the injectedlaser power to 250 W; (e) doubling the spot area; (f) implementingan 8 dB phase squeezed vacuum with a 100 m filter cavity to create

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Host galaxies of binary black hole mergers 4387

Figure 1. The noise budget of the 8 km GW detector described in this paperis shown in the top panel. The instrument has an 8 km arm length, 80 kgtest masses, and 250 W input laser power; the beam spot radii on input andend test masses are 11 and 12 cm, respectively. The detector incorporatesa 1.5 m test mass last-stage suspension and Newtonian noise cancellation.Frequency-dependent squeezed vacuum is generated by passing the 8 dBphase squeezed vacuum through a 100 m filter cavity. For reference, anaLIGO design sensitivity noise curve is shown. The lower panel shows thesensitivity improvement of the 8 km design over aLIGO.

frequency-dependent squeezed vacuum; (g) 2× Newtonian noisecancellation. We briefly address the feasibility of these proposedimprovements below.

The test masses forming the long arm cavities are the most criticaloptics of the interferometer. The arm cavity is the transducer thatimpinges the GW signal to the phase of the light, which can then bemeasured through interference. Any imperfection on the test massescan be absorbed or diffused by the light, thus creating excessiveoptical loss and ultimately reducing the sensitivity of the detector.

Due to the laser beam diffraction along its propagation over 8 km,the test masses must have a large diameter to be able to reflect all thelaser light. The cylindrical optics will have a diameter of 500 mmand weigh 80 kg. Since the mirrors can support a large laser beam, itpresents several advantages: the thermal noise can be lowered dueto improved averaging over the mirror surface and the decreasedlaser power density mitigates thermal effects induced by the opticalabsorption.

Test mass substrates would be made with the purest fused sil-ica: Heraeus Suprasil 3002. This material is available in large sizeand presents outstanding optical and mechanical properties at roomtemperature; hence, it is already used for current 2G interferometers(Mitrofanov et al. 2015; Pinard et al. 2016).

The polishing to shape the mirror profile would be specifiedat the nanometre level, using ion beam figuring. This technologyguarantees excellent surface accuracy and minimal roughness, thuslimiting the amount of scattered light (Pinard et al. 2016).

The test masses will have a high reflective side (inside the armcavity) whereas the second side will receive an antireflection coat-ing. Both treatments will be made with the ion beam sputteringtechnology to ensure very low optical loss and also low thermalnoise level (Pinard et al. 2016). It has been confirmed that the LMA‘Grand Coater’ machine in France is able to coat test masses to ourplanned dimensions.

As discussed earlier, the proposed implementation here is allbased on proven technologies and hence carries no substantial risk.As an example, a 550 mm diameter beamsplitter has already beenproduced and installed in the AdV interferometer.

To achieve a full factor of 4 strain sensitivity improvement overthe full aLIGO frequency band requires two additional technolo-gies. The first is quantum squeezing. This technology has alreadybeen demonstrated on GW detectors at high-frequency band (Godaet al. 2008; Aasi et al. 2013), but frequency-dependent squeezingis required to improve the quantum noise-limited sensitivity overthe full detection band to achieve the above design goal (Kimbleet al. 2001; Oelker et al. 2016). Two critical issues are the opti-cal losses in the interferometer input and output optical path, andthe optical loss of the filter cavity. Using the parameters of aLIGOupgrade (A+),2 Fig. 1 shows that the target sensitivity is achievable.

Finally, at the lowest frequencies, it is expected that Newtoniannoise associated with varying local gravitational forces acting onthe test masses could create additional noise. This noise can besuppressed by measuring the gravitational sources such as passinglow-frequency atmospheric or ground (seismic) waves and compen-sating by subtraction (Harms & Paik 2015; Coughlin et al. 2016;Harms & Venkateswara 2016). The design proposed for an 8 km de-tector assumes Newtonian noise suppression by two times, whichis a modest suppression factor compared to that proposed for otherdetector designs, such as LIGO Voyager.3

3 E V E N T R AT E S

The first detections of GWs from BBH mergers at z ≈ 0.1 firmlyplaced these events in the cosmological regime. For aLIGO, thehorizon volume in which a GW150914-type event could have beendetected during O1 extends out to z � 0.4 (Abbott et al. 2016a) andat design sensitivity extends to around z = 1; 3G detectors suchas Einstein telescope (ET) should routinely detect such events outto z ∼ 10 and beyond (Vitale 2016; Vitale & Evans 2017). Theranges accessible by an 8 km IFO, and indeed upgraded configu-rations of aLIGO, will extend far beyond the Euclidean regime.For these future instruments, projected estimations of the numbercounts of detected sources require a more rigorous treatment of cos-mic source rate evolution. Additionally, in comparison with lowermass systems that can be reasonably modelled by consideration ofonly the inspiral part of the signal, higher mass systems that merge atlower frequency and have fewer cycles in the detector band requiredetailed modelling of the inspiral and ringdown phases (Abbottet al. 2016b).

In the following sections, we will present a working frameworkto model the cosmic source rate evolution and to calculate the astro-physical reach of GW IFOs to BBH mergers. At the present earlystage of GW astronomy, there are many uncertainties in the detailsof the BBH populations, e.g. the mass distributions, the intrinsicevent rates, and their evolutionary pathways. We therefore pro-duce estimates based on confirmed events assuming two canonicalsources: 30–30 M� representing heavy events (such as GW150914and GW170104 with total masses 65 and 50 M�, respectively) and10–10 M� for lower mass systems (e.g. GW151226 with a totalsystem mass of 22 M�). We assume the same source rate evolutionand event rate ranges for both these canonical populations.

2 https://dcc.ligo.org/public/0113/T1400316/004/T1400316-v5.pdf3 See for example https://dcc.ligo.org/LIGO-G1501403.



3.1 The all sky event rate equation of BBH coalescence

To estimate the number of coalescing BBHs accessible by an 8 kmIFO, we first assume that their formation rate RBBH(z) tracks the starformation history of the Universe with a delay time td from forma-tion until final merger. As heavy BBH systems such as GW150914and GW170104 are predicted to form in low-metallicity stellar en-vironments (Abbott et al. 2016a), we include a model for cosmicmetallicity dependence.

For the star formation history of the Universe R�(z) (inM� yr−1 Mpc−3), we adopt the extinction-corrected cosmic star for-mation rate model of Madau & Dickinson (2014), which combinesmeasurements from sources observed at ultraviolet and far-infrared.

To estimate metallicity evolution, we adopt the model ofLanger & Norman (2006) that estimates the fraction �(z, ξ ) inredshift z of massive stars with metallicities less than some cut-offvalue ξ = Z/Z�. Following Abbott et al. (2016a,d), we adopt avalue of ξ = 0.5. A model of cosmic BBH formation rate includinga metallicity dependence is obtained by scaling the star formationhistory, R�(z), with the function �(z, ξ ):

RF(z) = �(z, ξ )R�(z) . (1)

To model the cosmic BBH merger rate RBBH(z), one must accountfor the delay time td between formation tf and the age of the Universeat the time of merger t(z) (Zhu et al. 2011). If zf and z represent theredshifts at which BBH systems form and merge, respectively, thedelay time for BBHs is given by

td =∫ zf

z

dz′

(1 + z′)H (z′). (2)

A BBH merger evolution model is calculated by convolving theBBH formation rate RF(z) with the delay time distribution P(td)(Regimbau & Hughes 2009):

RBBH(z) =∫ tmax

tmin

RF(zf )P (td)dtd. (3)

Following Abbott et al. (2016d), we take P(td) ∝ 1/td, for td > tmin,where tmin = 50 Myr is the minimum delay time for a BBH systemto evolve to merger and tmax is equal to the Hubble time. We nor-malize the BBH merger rate RBBH so that it corresponds at z = 0with the local event rate density (volumetric per unit time) of BBHmergers (Howell et al. 2014; Abbott et al. 2016d). The differentialBBH merger rate, dRBBH/dz, that describes the event rate within theredshift shell z to z + dz is then

dRBBH = dV

dz

RBBH(z)

1 + zdz . (4)

The (1 + z) factor accounts for time dilation of the observed ratethrough cosmic expansion, converting a source count to an eventrate. The comoving volume element:

dV

dz= 4πc

H0

d 2L (z)

(1 + z)2 h(z), (5)

describes how the number densities of non-evolving objects lockedinto Hubble flow are constant with redshift. The quantity dL(z) isthe luminosity distance (cf. Peebles 1993, p.332). For a ‘flat-’cosmology, we employ the cosmological parameters m = 0.31, = 0.69, and H0 = 67.8 km s−1 Mpc−1 (Planck CollaborationXIII 2016).

A cumulative event rate of BBH mergers throughout the Universeis estimated by integrating equation (4):

RBBH(z) =∫ z

0(dRBBH/dz)dz . (6)

Figure 2. The cumulative all sky rate of BBH coalescence based on therate estimates of Abbott et al. (2017a) for the four events: GW150914,LVT151012, GW151226, and GW170104. The solid and dashed curvesshow the median values determined using in-log uniform and power-lawdistributions of masses, respectively; the shaded region shows the combinedrate range. The plot shows that the universal rate of BBH mergers is of theorder of 10s/hour.

Fig. 2 shows the function RBBH(z) based on the rates given in Abbottet al. (2017a, updated from Abbott et al. 2016b) for the four events:GW150914, LVT151012, GW151226, and GW170104. The dashedand solid curves show the median values determined using a powerlaw (103+110

−63 Gpc−3 yr−1) and in-log uniform distribution (32+33−20

Gpc−3 yr−1) of masses, respectively; the shaded region shows thecombined rate range for the two distributions of 12–213 Gpc−3 yr−1.

The plot shows that the rate is asymptotic from about z = 3;this is due to a peak in the differential rate dRBBH/dz occurring ataround z ≈ 1.5. The universal rate of BBH mergers based on thisestimation is of the order of 10s/hour or approximately one eventevery 5 min. To estimate source counts, one must fold the functionRBBH(z) with a redshift-dependent detection efficiency function.We will first consider the optimal case, which is a horizon range foroptimally located and orientated sources.

3.2 The detection ranges for BBH coalescences

The horizon redshift, zH, is the maximum redshift for which anoptimally orientated and located source can be detected for somesensitivity threshold or SNR. To calculate this quantity, we useequation B11 of Ajith et al. (2008), which provides the optimalSNR ρopt as a function of distance for a non-spinning phenomeno-logical inspiral–merger–ringdown BBH waveform in the frequencydomain, for a given GW detector sensitivity noise curve. This equa-tion is parametrized in terms of the total mass M = m1 + m2 andreduced mass η = m1m2/M2 using a set of coefficients (see table 1in Ajith et al. 2008). The SNR is determined through the redshiftedquantities Mz = M(1 + z) and ηz = η(1 + z); values of zH arecalculated iteratively through z by determining the components Mz

and ηz required to produce a given ρopt.Fig. 3 illustrates the astronomical reach of an 8 km IFO for dif-

ferent BBH systems of equal-mass components and total redshiftedmasses Mz. The ranges zH are calculated using a value of ρopt =8, which following standard convention can act as a proxy for adetector network (Abadie et al. 2010; Stevenson et al. 2015; Abbott



Figure 3. The astrophysical reach for BBH mergers as a function of theobserved (redshifted) total system mass assuming non-spinning and equal-mass components. The solid lines show the maximum observable distances(in Gpc and cosmological redshift) for an 8 km (thick line) and an aLIGOIFO (thin line; this is consistent with fig. 2 of Ghosh et al. 2016). The thickdashed line shows an average distance assuming a 50 per cent probability ofdetection. The stars indicate the positions on each curve for a GW150914-type event.

et al. 2016a).4 For comparison, we also calculate the aLIGO rangesusing the zero-detuning design sensitivity noise curve.5

The plot illustrates the impressive astronomical reach obtained byan 8 km IFO for an optimally oriented and located GW150914-typesystem (in terms of the estimated intrinsic component masses); theplot shows that the horizon distance for such a system is zH = 8.9;the comparative estimate for aLIGO at design sensitivity is zH = 1.8.We note that although the definition of zH is a useful measure of adetector’s capabilities, observing optimally orientated and locatedevents will be rare; to provide more realistic detection rate estimates,in the next section we will model the detection efficiency as afunction of redshift.

3.3 The detector efficiency function for BBH inspirals

To estimate the fraction of sources that exceed a detection thresholdas a function of redshift, ε(z), we follow the approach of Belczynskiet al. (2014) and Dominik et al. (2015) who utilized the projectionparameter ω (Finn & Chernoff 1993). This quantity describes thedetector responses for different values of sky location, inclination,and polarization of a GW source; for an optimal face-on sourcedirectly above a GW detector, ω = 1 and conversely ω = 0 fora poorly located and orientated event. A cumulative distributionfunction of this quantity c(ω), which contains all the informationof single detector response, has been provided analytically by bothFinn (1996) and Dominik et al. (2015).

For a system described by the rest-frame quantities {M, η}and assuming an SNR threshold ρ th = 8, for each value of z thecorresponding ρopt can be calculated through the procedure outlinedin Section 3.2 for each corresponding {z, Mz} . The function ε(z)

4 To be 99 per cent confident that a GW has been detected, an SNR ∼8 isequivalent to a false alarm rate of 1 in 100 yr of observation (3 × 10−10 Hz).5 https://dcc.ligo.org/LIGO-T1200307

Figure 4. The detection efficiency functions for BBH mergers with totalsystem masses (assuming non-spinning and equal-mass components) equalto 30–30 M� (top) and 10–10 M� BBH mergers (bottom). Curves areshown for both 8 km IFOs and aLIGO at design sensitivity. The plot em-phasizes how lighter systems such as GW151226 (∼10–10 M�) will onlybe detected within smaller cosmological volumes than heavier GW150914(∼30–30 M�) type systems.

can then be constructed by mapping ω = ρ th/ρopt to the distributionc(ω) through

ε(z) = c(ω) = c(ρth/ρopt(Mz, ηz)), (7)

producing a set of efficiency curves as a function of redshift forBBH mergers of different component masses.

Fig. 4 shows the efficiency functions for GW signals from bothheavy 30–30 M� and less massive 10–10 M� type systems com-posed of non-spinning equal-mass components. It is quite evidentthat lighter systems such as GW151226 will only be detected withinsmaller cosmological volumes than heavier GW150914-type sys-tems. If one assumes that both types of sources are drawn fromthe same population, it is reasonable to expect that larger systems,accessible at greater cosmological volumes, will dominate the statis-tics.

As detections at the horizon will be rare, it is interesting to es-timate an average sensitive range for BBH systems;6 in this study,we define such a quantity as the value of z at which the detectionefficiency is equal to 50 per cent; for an 8 km IFO (aLIGO), the sen-sitive ranges are z = 2.8 (0.49) for 30–30 M� and z = 0.86 (0.18)for 10–10 M� type events.

As a crude verification of our efficiency calibrations, one can usethe recorded values of GW150914 with the sensitivity curves of thefirst aLIGO observing run (O17). Assuming that GW150914 wasof average orientation (there is posterior support for GW150914being face off; see Abbott et al. 2016b) and location, we constructequation (7) assuming a threshold SNR of ρ th = 23.7 equal tothat recorded for GW150914 and determine the redshift at whichε(z) ≈ 50 per cent. We find a value of z � 0.07 which is within thepublished range, z ∼ 0.09+0.03

−0.04 for this event (Abbott et al. 2016c).

6 In a Euclidean regime, the sensitive and horizon volumes obey the scalingVsensitive/Vhorizon ≈ (1/2.26)3; at cosmological volumes, this approximationis no longer valid.7 Using the ‘early’ curves of https://dcc.ligo.org/LIGO-T1200307.



Figure 5. The cumulative detection rate of BBH mergers as a function ofredshift based on our modelling for an 8 km IFO (bold curve) and an aLIGOIFO at design sensitivity (thin curve). The shaded area indicates the upperand lower limits on the detection rate of 30–30 M� mergers based on fouraLIGO observations. The detection number becomes asymptotic at aroundz = 3 for an 8 km IFO and z = 1 for aLIGO. The range on the intrinsicnumber of events (12–213 Gpc−3 yr−1) is bracketed by the dashed curves.

3.4 BBH coalescence source counts

To calculate the source counts for our two canonical populationsof BBH mergers: 30–30 M� representing heavy events (suchas GW150914 and GW170104) and 10–10 M� for lower masssystems (e.g. GW151226), we use the frameworks provided inSections 3.1–3.3. To calculate cumulative event rates, we usethe range estimates provided in Abbott et al. (2017a) of 12–213 Gpc−3 yr−1 for upper and lower limits on the total source dis-tribution.

We note that a more accurate estimation of source counts couldbe produced by, for example, convolving the function RBBH(z) withthe fraction of sources accessible at each z, estimated by integrat-ing over the detector accessible fraction of the chirp mass dis-tribution; however, until we accumulate a larger number of detec-tions, such a scheme would require many assumptions. We thereforeuse a simpler scheme based on present knowledge, using our twocanonical systems; we suggest that the results provided by the ap-proximations can provide reasonable upper and lower limits basedon high mass/upper rate [30–30 M�/213 Gpc−3 yr−1] and lowermass/lower rate [10–10 M�/12 Gpc−3 yr−1].

Fig. 5 shows the cumulative number of detections with redshift forboth an 8 km IFO and aLIGO assuming a population dominated bysources of 30–30 M�. The detection number becomes asymptoticat around z = 3 for an 8 km IFO and z = 1 for aLIGO; as thedifferential source rate peaks at around z ≈ 1.5, there is minimalcontribution beyond this range despite the fact that the averagereach (50 per cent detection efficiency) is around z ≈ 2.8 for an8 km instrument.

The curves show that if all BBH sources were made up of 30–30 M� systems, an 8 km IFO could detect nearly 104 to 200 000events each year. This is around 60 per cent of the intrinsic popula-tion shown by the dashed curves; comparing the intrinsic populationcurves with the efficiency curves of Fig. 4 shows how most of suchmassive systems are accessible to an 8 km IFO. For an aLIGO detec-tor at full sensitivity, the equivalent number of detections is around500–10 000 yr−1 (around 3 per cent of all such sources).

Fig. 6 shows the cumulative number of detections with redshiftassuming that 10–10 M� BBHs dominate the source population.

Figure 6. As for Fig. 5 but assuming less massive equal-mass BBH systemsof 10–10 M� similar to GW151226. In comparison with 30–30 M� typemergers, a smaller fraction of the population are detected due to a decreaseddetection efficiency (see Fig. 4).

In this case, the astronomical reach is not as impressive and so thenumber of detections decreases accordingly. However, assumingour adopted rate range, we see that we could still expect around3000–50 000 detections a year (around 15 per cent of the universalpopulation of 10–10 M� systems) using an 8 km IFO or of theorder of 30–500 yr−1 for aLIGO at full sensitivity.

To identify possible host galaxies, one requires detections withina small enough cosmological volume that optical surveys wouldhave a reasonable amount of completeness; additionally, to providesmaller angular error regions, closer events will have higher GWSNRs. However, the reach should be large enough that event ratesare sufficient. We choose a distance of 0.4 Gpc corresponding tothe first two confident detections, GW150914 and GW151226; atthis range, for an 8 km IFO, the signal SNR will be large enough toensure that the efficiencies will be close to maximum (see Fig. 4)and the angular resolutions will be sufficiently compact to minimizethe number of galaxies.

Assuming populations of both 30–30 M� BBHs and 10–10 M� BBHs, our calculations predict around 2–30 detectionsa year respectively within a range of 0.4 Gpc (z ∼ 0.09). Within0.4 Gpc, the detection efficiencies of aLIGO are high enough thatsimilar numbers could be expected; however, the smaller SNRsmean that the angular error regions will be much larger.

4 A N G U L A R R E S O L U T I O N O F D E T E C TO RN E T WO R K S

To obtain estimates of angular resolutions for BBH mergers, wehave followed the method provided in Wen & Chen (2010). Thismethod estimates unknown parameters using the Fisher informationmatrix and calculates a lower bound on the parameter estimatesthat is method independent. We assume that the GW waveform ofBBH signals is known, and only their locations are the unknownparameters. To generate sufficient statistics, we simulate 103 BBHsignals at a representative distance of 0.4 Gpc; as discussed in theprevious section, this distance approximately corresponds to thedistance of the first two confirmed GW events GW150914 andGW151226 and is also in the range of galaxy survey completenessfor follow-up of such GW sources (see Section 5).

We simulate two synthetic populations based on the two LIGOdetections assuming equal components of both 30 and 10M�. For



Figure 7. The localization capabilities of different GW interferometer net-works calculated for 1000 30–30 M� BBH mergers at 0.4 Gpc. The sourcelocations are randomly generated in right ascension and declination, andthe polarization and inclination angles are randomized. We denote the in-dividual detectors in the network as follows: L : aLIGO-Livingston, H :aLIGO-Hanford, V : AdV, J : KAGRA, I : LIGO-India, A : Australian 8 km,C : China 8 km.

Figure 8. As for Fig. 7 but for 1000 10–10 M� BBH mergers at 0.4 Gpc.

each simulated source, we randomize the polarization, inclination,and position in the sky. The sensitivity of aLIGO (L : aLIGO-Livingston, H : aLIGO-Hanford) and AdV (V) is assumed to beat their design sensitivity; for KAGRA (J) and LIGO-India (I) weassume aLIGO design sensitivity; we further model the Australian(A) and Chinese (C) detectors as 4× the sensitivity of aLIGO.

Figs 7 and 8 show the angular resolutions achievable by a rangeof GW detector networks for detections at 0.4 Gpc based on oursimulations; the results are shown for synthetic populations of 30–30 and 10–10 M� type sources, respectively. The plots show thecumulative distributions as a function of the 90 per cent credibleregions of the angular resolution error regions: that is the percentageof sources that can be constrained within a specified localizationerror region. Tables 1 and 2 summarize the main results shown inthese figures for both synthetic source populations. As has beenhighlighted in many other studies (Fairhurst 2011; Schutz 2011;Chu, Wen & Blair 2012; Nissanke, Kasliwal & Georgieva 2013a;Aasi et al. 2016; Chen & Holz 2016; Gaebel & Veitch 2017; Vitale

Table 1. The localization statistics obtained for the different GW detec-tor networks shown in the first column for 30–30 M� BBH mergers at adistance of 0.4 Gpc. Based on the 90 per cent credible regions of our simu-lations, we show the percentage of sources expected to be localized withindifferent size error regions from 0.1 to 10 deg2. The individual instrumentsare denoted as follows: L : aLIGO-Livingston, H : aLIGO-Hanford, V :AdV, J : KAGRA, I : LIGO-India, A : Australian 8 km, C : China 8 km.

Network Percentage of detections within credible region0.1 deg2 0.5 deg2 1 deg2 5 deg2 10 deg2

LHV 0.00 1.11 7.59 44.65 60.50LHVJ 0.00 16.44 37.59 82.45 91.59LHVI 0.00 8.26 28.93 80.74 91.30LHVA 1.05 45.30 71.48 96.07 98.55LHVC 0.63 32.26 54.02 89.71 95.86LHVJI 0.00 26.29 51.49 90.39 96.25LHVJIC 1.58 42.97 66.33 95.09 98.53LHVJIA 7.31 66.74 88.01 99.71 99.93LHVJIAC 25.06 81.06 94.63 99.90 100.00

Table 2. As Table 1 but for 10–10 M� BBH mergers at a distance of0.4 Gpc.

Network Percentage of detections within credible region0.1 deg2 0.5 deg2 1 deg2 5 deg2 10 deg2

LHV 0.00 0.00 0.00 8.36 21.63LHVJ 0.00 0.00 1.99 36.75 59.95LHVI 0.00 0.00 0.00 31.36 56.84LHVA 0.00 1.20 13.48 73.06 88.59LHVC 0.00 0.79 9.21 55.24 74.58LHVJI 0.00 0.00 4.57 51.64 73.49LHVJIC 0.00 1.90 14.37 67.48 83.24LHVJIA 0.00 7.74 32.27 88.37 96.24LHVJIAC 0.00 27.48 52.58 95.20 99.05

& Evans 2017), the improvement in angular resolution with eachnew addition to the worldwide network is quite apparent.

For a population of 30–30 M� type events, starting from an LHVnetwork we find 60 per cent of detections within 10 deg2 improvingto 1 deg2 with the inclusion of J and I. Adding in C and A indi-vidually improves the error regions to 1 and 0.6 deg2, respectively,for 50 per cent of the detections. For a full LHVKIAC network, theerror regions become of the order of 0.2 deg2 for 50 per cent of thesources and around 0.1 deg2 for nearly 30 per cent of the sources.

For a population of 10–10 M� type events, we find that50 per cent of detections of an LHV network would be within30 deg2 improving to 5 deg2 with the inclusion of J and I. Adding inC and A individually improves the error regions to 5 and 3 deg2, re-spectively, for 50 per cent of the detections. For a full LHVJIAC net-work, the error regions become of the order of 1 deg2 for 50 per centof the sources and less than 0.5 deg2 for 20 per cent of the sources.

It should be noted that the error region estimates presented heredo not include the effects of calibration uncertainty. Calibration un-certainties are typically 10 per cent in strain amplitude and 10 degin waveform phase for interferometric GW detectors (see Abbottet al. 2017e, for a recent example). Studies have shown that suchcalibration uncertainties will lead to systematic errors in sky local-ization estimates (e.g. Vitale et al. 2012).

We note that impact of calibration uncertainty is within thestatistical uncertainties for SNRs close to the detection threshold(SNR 10). However, for higher SNR signals, such as the loudest10 per cent of the detected signals discussed here, calibration un-certainties will be a significant limitation. Therefore, calibration



Figure 9. The integral number of galaxies at fixed distance of400 ± 120 Mpc per deg2 accessible at different survey magnitude lim-its. We assume an error of ±30 per cent in luminosity distance for the GWsource. For comparison, a Milky Way-sized galaxy would have an apparentR magnitude of around 17 at this distance, yielding ∼100 to 200 galaxiesper deg2.

of future-generation GW detectors must be improved to allow therequired level of precision.

5 ID E N T I F I C ATI O N O F H O S T G A L A X I E S

The possibility of host galaxy identification for BBH mergers de-pends on the ability to localize the source in three dimensions.Localization on the sky depends on the array properties and theSNR as discussed above. The depth of localization is determined bythe luminosity distance estimate that itself depends on the SNR. Foran advanced network of IFOs, Ghosh et al. (2016) have simulatedthe fractional errors in the luminosity distance for BBH mergers;their distributions peak at around 40 per cent. As the errors in lu-minosity distance are expected to be smaller for the higher SNRsources, we conservatively select a value of 30 per cent.8

We have seen above that for 30–30 M� BBH mergers at 0.4 Gpc,the angular resolution for around 30 per cent of the sources fallswithin 10−1 deg2. Given an uncertainty in luminosity distance of±30 per cent, we determine the fraction of galaxies in a volumedefined by sky location and distance uncertainty, ��d (see alsoChen & Holz 2016; Singer et al. 2016). Fig. 9 shows predictednumber counts (per deg2 of sky) for galaxies with distances in ourBBH detection range (dL = 400 ± 120 Mpc). Number counts werederived by integrating the r-band luminosity function of Lovedayet al. (2012) over those luminosities corresponding to typical ap-parent magnitudes’ detection limits (r = 14 to 24). The Lovedayet al. luminosity function is derived from the GAMA9 survey thatprobes similar redshifts (z ∼ 0.05–0.25) to those in our angularresolution calculation (Section 4). No redshift evolution is imple-mented and similar values are obtained using the lower redshift

8 For BH–NS sources, the simulations of Nissanke et al. (2013b) find dis-tance errors clustered around 15–25 per cent. However, we note that Gaebel& Veitch (2017) find uncertainties of the order of 50 per cent even for afive-detector network at design sensitivity for GW150914-like events.9 GAMA: Galaxy and Mass Assembly survey – for further details, seehttp://www.gama-survey.org/.

Figure 10. The localization capabilities of the largest GW interferometernetwork considered in this study (LHVJIAC) calculated for 103 30–30 M�BBH mergers at different distances. As previously, the source locations arerandomly generated in right ascension and declination, while the polarizationand inclination angles are randomized.

(z = 0.05) r-band luminosity function of the 6dF Galaxy Survey(Jones et al. 2006).

Fig. 9 shows that around 102 galaxies are observed per deg2

brighter than r = 17 (1 galaxy per 0.1 deg2). This corresponds todetecting a single Milky Way-sized galaxy at our canonical distanceof 0.4 Gpc (see discussion in Gehrels et al. 2016, on the benefitsof strategies that target the brightest galaxies). At deeper limits(r = 20), the number of galaxies in the same volume increases10-fold (103 per deg2).

Assuming a population of 30–30 M�, our estimates show thata full LHVKIAC network would localize around 30 per cent of thesources to within 0.1 deg2 (on average). Scaling this by the estimateddetection rate (Section 3.1) yields ∼1 to 10 events per year. In thisscenario, a handful of BBH mergers could be uniquely associatedwith r ≤ 17 bright galaxies in a single year of observation. However,for an r ≤ 20 survey, there are ∼10 galaxies per field per BBHmerger, meaning that a few years of observation would be necessaryfor statistical localization.

As shown elsewhere in this paper (e.g. Fig. 3), 8 km instrumentswill routinely detect BBH mergers out to significantly greater dis-tances than 0.4 Gpc. Fig. 10 shows how the angular resolution(roughly proportional to the SNR) increases with astronomical dis-tance. In the case of 30–30 M� BBH mergers at a distance of 0.8Gpc (z ∼ 0.17), 20 per cent of the events could be localized withinaround 0.4 deg2; this corresponds to ∼10 to 200 BBH events peryear.

To estimate the number of galaxies within a 0.4 deg2 field ofview at 0.8 Gpc, we repeat our galaxy number calculation. Thistime we determine the total number of galaxies within the range800 ± 240 Mpc (0.12 ≤ z < 0.21) per deg2 as a function oflimiting magnitude. As before, the distance range reflects the±30 per cent assumed luminosity distance uncertainty for the GWsource.

Fig. 11 shows the results of this calculation. At the limit r = 17,we expect around 100 bright galaxies in a 0.4 deg2 field around a0.8 Gpc distant BBH merger. As expected, the greater cosmologi-cal volumes make source confusion problematic. These issues are



Figure 11. We repeat the calculation of Fig. 9 within 800 ± 240 Mpc perdeg2.

compounded by the increased observational difficulty of confirminggalaxy redshifts at greater distances.

We suggest that although less frequent, the low-redshift eventswith high SNR are the most valuable in terms of assigning hostgalaxy associations. In practice, identification of host galaxies fornearby GW sources would provide a guideline in assigning likeli-hood rankings among the galaxies in the confused field for distantsources. For example, if the gravitational sources are predominantlyfound from nearby star-forming galaxies, galaxies with greater blueluminosity are more likely to be the hosts. In this way, we canprogressively widen the horizon.

6 A N 8 K M D E T E C TO R O P E R AT I N G AT L OWOPTICAL POWER

The analysis above considered the performance of an 8 km interfer-ometer operating with an arm cavity power of 1.4 MW. It is inter-esting to also consider the performance if the arm cavity power wasreduced to 200 kW, since high optical power is one of the greatesttechnical challenges. It is well known that high power introducesthermal aberrations (Zhao et al. 2006) and can cause parametricinstability (Zhao et al. 2005, 2015; Evans et al. 2015). The valueof 200 kW is chosen because it is comparable to the power levelsalready achieved in aLIGO.

Fig. 12 shows the sensitivity noise curve of an 8 km IFO operatingwith 200 kW arm cavity power. For comparison, it is compared to the1.4 MW configuration, aLIGO at design sensitivity, and a proposedconfiguration of the Einstein telescope, ET-B (Hild, Chelkowski &Freise 2008). We see that up to around 30 Hz there is no changeand up to around 270 Hz the performance is degraded by less thana factor of 2.

Table 3 shows a comparison of the horizon distance and eventrates for both 200 kW and at the nominal 1.4 MW arm cavity power;for reference, we show results based on the first two confirmedGW detections. The loss of performance is less than might be ex-pected because the events we are considering are dominated by low-frequency noise and thermal noise that are reduced in this design;this is particularly evident for heavier GW150914-type systems.For the heavier-type systems, the horizon redshifts are comparable;however, the average ranges (defined as the distance at which thedetection efficiency is 50 per cent) do vary. This can be explainedby Fig. 13, which compares the optimal SNR with redshift for

Figure 12. The sensitivity noise curve of an 8 km interferometer operat-ing with 200 kW arm cavity power (8 km–200 kW IFO) is compared tothe 1.4 MW configuration (8 km IFO), aLIGO at design sensitivity, and aproposed configuration of the Einstein telescope, ET-B.

Table 3. A comparison of the performance between 8 km interferometricdetectors operating with 1.4 MW and 200 kW arm cavity power. The averagereach is defined as the redshift range at which the detection efficiency is50 per cent.

GW150914-type GW151226-type1.4 MW 200 kW 1.4 MW 200 kW

Horizon redshift 8.8 8.7 4.3 2.5Average reach 2.7 1.9 0.9 0.6Detection rate (yr−1) 4100 3100 8300 3800

Figure 13. The optimal SNR with redshift for a GW150914-type system isshown for the nominal 8 km detector (1.4 MW optical cavity power) and foran 8 km detector with 200 kW optical cavity power. Both these instrumentsare compared with aLIGO and the ET-B 3G configuration. The SNR issimilar at high z (due to similar low-frequency performance) but differs byaround a factor of nearly 2 at around z ∼ 2.



the two 8 km configurations. The plot shows that due to similarlow-frequency performance, the SNR is comparable at high z butdiffers by around a factor of nearly 2 at the intermediate range ofaround z ∼ 2.

The loss of sensitivity at high frequency, which scales as thesquare root of the power ratio, would affect ability to detect blackhole quasi-normal modes at larger ranges, and also high-frequencysources such as binary neutron star mergers. We find that for theselatter sources the horizon distance decreases from 1.9 Gpc (z =0.36) to 1.4 Gpc (z = 0.27) if the arm cavity power is reduced to200 kW.

7 D ISCUSSION

For this study, we have based our modelling around the threeunambiguously identified signals: GW150914, GW151226, andGW170104 using two canonical GW signals, those from 30–30 M� and 10–10 M� BBH mergers. An alternative would havebeen to conduct an analysis based on a model mass distribution.However, given that there still exist many uncertainties in the BBHformation channels and the intrinsic event rate from only three(possibly four including LVT151012) observations, we have cho-sen the former option to present a case solely based on observations.Therefore, the two scenarios we consider span the possibility spacebased on present knowledge (heavy system/upper rate; lighter sys-tem/lower rate) to provide an estimate of the astrophysics that couldbe accessed by an 8 km detector.

For a population dominated by 30–30 M� type events, we findthe limit of the detection horizon of the order of z ∼ 8.8 and a50 per cent chance of detecting sources at z ∼ 2.8. One could con-servatively expect between 104 and 105 detections a year.

For the less massive 10–10 M� type events, we find of the orderof 3000–50 000 detections in one year of observation. The astro-nomical reach to these lighter events is still impressive; a horizondistance of z ∼ 4.26 and a 50 per cent probability of detection atz ∼ 0.9. Such an astronomical reach is sufficient to capture a largeproportion of events as the peak of the source distribution is aroundz ∼ 1.5–2.

Assuming a population of 30–30 M�, our estimates showthat a full LHVKIAC network would on average localize around30 per cent of the sources to within 0.1 deg2; we find that this cor-responds to around 1–10 BBH events per year. Our calculationssuggest that if one considers the brightest galaxies of a survey,greater than r = 17 in apparent magnitude, unique GW–galaxy as-sociations may be possible. At deeper magnitudes down to r = 20,one can expect 10 galaxies in a 0.1 deg2 field for each BBH mergerleading to data of useful statistical significance. At greater distancesthan 0.4 Gpc, although the number of detections will be greater, acombination of lower SNR and thus larger angular error regions,source confusion, and survey incompleteness suggests that for an8 km IFO, the optimal strategy to find host galaxies is to targetGW sources within 0.4 Gpc. One should note, however, that evenat closer distances, another factor that will reduce the number ofgalaxy localizations is the Galactic plane, which obstructs the viewof around 20 per cent of the extragalactic sky at visible wavelengths.

The prospect of host galaxy identification relies on the GW net-work’s ability to resolve sources to within 0.1 deg2. The ability toachieve the desired angular resolution is subject to the effects ofcalibration uncertainties that will limit the network’s sky localiza-tion capabilities. Therefore, the improved calibration techniques arerequired for future GW detectors.

We have also considered an alternative design in which the armcavity power is reduced from 1.4 MW to 200 kW, similar to thepower levels already achieved in aLIGO. Our motivation here is tocircumvent some of the difficulties encountered with high opticalpowers such as parametric instabilities. We find comparable perfor-mance levels in detecting heavier GW150914-type systems (partic-ularly for the more distant events with greater redshifted masses) butaround a factor of 2 less detections for GW151226-type systems.Therefore, an 8 km interferometric detector with reduced opticalpower can still provide an abundance of detections in the range1000–100 000 events per year.

8 C O N C L U S I O N

We have shown that a realistic design concept for one or two 8 kmlaser interferometer GW detectors could enable the detection of upto 3000–200 000 BBH mergers per year. For a small proportion(1–10), this could allow sources to be directly identified with brighthost galaxies. If such an association was proven, this would allowindependent redshift measurements as well as a detailed study ofthe BBH population with view to understanding their origins. Atdeeper magnitude limits, say r ∼ 20, some tens of galaxies wouldoccupy a ��d volume – such samples could enable host galaxyassociations to be probed statistically.

An array with such high angular resolution could also be veryimportant for mapping stochastic backgrounds, GW burst sources,and binary neutron stars, as well as being a powerful tool formulti-messenger astronomy. The individual high-sensitivity detec-tors would allow much deeper searches for continuous GWs fromspinning neutron stars.

Because the 8 km detector is not dependent on new technologiesfor initial operation, it could be brought online rapidly, therebyenabling greatly improved angular resolution and event rates inthe expanding worldwide network. It is important to note that inanalogy with very long baseline interferometry systems for highangular resolution radio astronomy, it is common for telescopes tohave varying performance. Thus, there would be no incompatibilityissues associated with the installation of a significantly improveddetector because noise contributes as the geometric mean.

AC K N OW L E D G E M E N T S

EJH acknowledges support from an Australian Research CouncilDECRA Fellowship (DE170100891). DC is supported by an Aus-tralian Research Council Future Fellowship (FT100100345). Z-HZwas supported by the National Basic Science Program (Project973) of China (Grant No. 2014CB845800), the National NaturalScience Foundation of China under Grants Nos. 11633001 and11373014, and the Strategic Priority Research Program of the Chi-nese Academy of Sciences, Grant No. XDB23000000. We thankM. Colless (Australian National University) for useful discussionsthat aided the analysis in Section 5.

R E F E R E N C E S

Aasi J. et al., 2013, Nat. Photonics, 7, 613Aasi J. et al., 2015, Class. Quantum Grav., 32, 074001Aasi J. et al., 2016, Living Rev. Relativ., 19, 1Abadie J. et al., 2010, Class. Quantum Grav., 27, 173001Abbott B. P. et al., 2016a, ApJ, 818, L22Abbott B. P. et al., 2016b, Phys. Rev. X, 6, 041015Abbott B. P. et al., 2016c, Phys. Rev. Lett., 116, 061102



Abbott B. P. et al., 2016d, Phys. Rev. Lett., 116, 131102Abbott B. P. et al., 2016e, Phys. Rev. Lett., 116, 241103Abbott B. P. et al., 2017a, Phys. Rev. Lett., 118, 221101Abbott B. P. et al., 2017b, ApJ, 848, L12Abbott B. P. et al., 2017c, ApJ, 848, L13Abbott B. P. et al., 2017d, Class. Quantum Grav., 34, 044001Abbott B. P. et al., 2017e, Phys. Rev. D, 95, 062003Abbott B. P. et al., 2017f, Phys. Rev. Lett., 119, 161101Acernese F. et al., 2015, Class. Quantum Grav., 32, 024001Ajith P. et al., 2008, Phys. Rev. D, 77, 104017Aso Y., Michimura Y., Somiya K., Ando M., Miyakawa O., Sekiguchi T.,

Tatsumi D., Yamamoto H., 2013, Phys. Rev. D, 88, 043007Bae Y.-B., Kim C., Lee H. M., 2014, MNRAS, 440, 2714Belczynski K., Buonanno A., Cantiello M., Fryer C. L., Holz D. E., Mandel

I., Miller M. C., Walczak M., 2014, ApJ, 789, 120Belczynski K., Holz D. E., Bulik T., O Shaughnessy R., 2016, Nature, 534,

512Blair D. et al., 2015, Sci. China Phys. Mech. Astron., 58, 5747Chen H.-Y., Holz D. E., 2016, preprint (arXiv:1612.01471)Chu Q., Wen L., Blair D., 2012, J. Phys.: Conf. Ser., 363, 012023Chu Q., Howell E. J., Rowlinson A., Gao H., Zhang B., Tingay S. J., Boer

M., Wen L., 2016, MNRAS, 459, 121Coughlin M., Mukund N., Harms J., Driggers J., Adhikari R., Mitra S.,

2016, Class. Quantum Grav., 33, 244001Dominik M. et al., 2015, ApJ, 806, 263Dwyer S., Sigg D., Ballmer S. W., Barsotti L., Mavalvala N., Evans M.,

2015, Phys. Rev. D, 91, 082001Evans M. et al., 2015, Phys. Rev. Lett., 114, 161102Fairhurst S., 2011, Class. Quantum Grav., 28, 105021Fan X., Messenger C., Heng I. S., 2014, ApJ, 795, 43Finn L. S., 1996, Phys. Rev. D, 53, 2878Finn L. S., Chernoff D. F., 1993, Phys. Rev. D, 47, 2198Gaebel S. M., Veitch J., 2017, Class. Quantum Grav., 34, 174003Gehrels N., Cannizzo J. K., Kanner J., Kasliwal M. M., Nissanke S., Singer

L. P., 2016, ApJ, 820, 136Ghosh A., Del Pozzo W., Ajith P., 2016, Phys. Rev. D, 94, 104070Goda K. et al., 2008, Nat. Phys., 4, 472Harms J., Paik H. J., 2015, Phys. Rev. D, 92, 022001Harms J., Venkateswara K., 2016, Class. Quantum Grav., 33, 234001Hild S., Chelkowski S., Freise A., 2008, preprint (arXiv:0810.0604)Hong J., Lee H. M., 2015, MNRAS, 448, 754Howell E. J., Coward D. M., Stratta G., Gendre B., Zhou H., 2014, MNRAS,

444, 15Jones D. H., Peterson B. A., Colless M., Saunders W., 2006, MNRAS, 369,

25Kimble H. J., Levin Y., Matsko A. B., Thorne K. S., Vyatchanin S. P., 2001,

Phys. Rev. D, 65, 022002

Klimenko S. et al., 2011, Phys. Rev. D, 83, 102001Langer N., Norman C. A., 2006, ApJ, 638, L63Lipunov V. M., Postnov K. A., Prokhorov M. E., 1997, New Astron., 2, 43Loveday J. et al., 2012, MNRAS, 420, 1239Ligo Scientific Collaboration et al., 2011, Nat. Phys., 7, 962Madau P., Dickinson M., 2014, ARA&A, 52, 415Messenger C., Takami K., Gossan S., Rezzolla L., Sathyaprakash B. S.,

2014, Phys. Rev. X, 4, 041004Mitrofanov V. P., Chao S., Pan H.-W., Kuo L.-C., Cole G., Degallaix J.,

Willke B., 2015, Sci. China Phys. Mech. Astron., 58, 120404Nissanke S., Kasliwal M., Georgieva A., 2013a, ApJ, 767, 124Nissanke S., Holz D. E., Dalal N., Hughes S. A., Sievers J. L., Hirata C. M.,

2013b, preprint (arXiv:1307.2638)Oelker E., Isogai T., Miller J., Tse M., Barsotti L., Mavalvala N., Evans M.,

2016, Phys. Rev. Lett., 116, 041102Peebles P. J. E., 1993, Principles of Physical Cosmology, 1st edn. Princeton

Univ. Press, Princeton, NJPinard L. et al., 2016, in Optical Interference Coatings 2016, The Mir-

rors Used in the LIGO Interferometers for the First-time Detection ofGravitational Waves. Optical Society of America, p. MB.3

Planck Collaboration XIII, 2016, A&A, 594, A13Punturo M. et al., 2010, Class. Quantum Grav., 27, 084007Raffai P., Gondan L., Heng I. S., Kelecsenyi N., Logue J., Marka Z., Marka

S., 2013, Class. Quantum Grav., 30, 155004Regimbau T., Hughes S. A., 2009, Phys. Rev. D, 79, 062002Rodriguez C. L., Morscher M., Pattabiraman B., Chatterjee S., Haster C.-J.,

Rasio F. A., 2015, Phys. Rev. Lett., 115, 051101Rodriguez C. L., Chatterjee S., Rasio F. A., 2016a, Phys. Rev. D, 93, 084029Rodriguez C. L., Haster C.-J., Chatterjee S., Kalogera V., Rasio F. A., 2016b,

ApJ, 824, L8Schutz B. F., 2011, Class. Quantum Grav., 28, 125023Singer L. P. et al., 2016, ApJ, 829, L15Stevenson S., Ohme F., Fairhurst S., 2015, ApJ, 810, 58Vitale S., 2016, Phys. Rev. D, 94, 121501Vitale S., Evans M., 2017, Phys. Rev. D, 95, 064052Vitale S., Del Pozzo W., Li T. G. F., Van Den Broeck C., Mandel I., Aylott

B., Veitch J., 2012, Phys. Rev. D, 85, 064034Wen L., Chen Y., 2010, Phys. Rev. D, 81, 082001Zhao C., Ju L., Degallaix J., Gras S., Blair D. G., 2005, Phys. Rev. Lett., 94,

121102Zhao C. et al., 2006, Phys. Rev. Lett., 96, 231101Zhao C., Ju L., Fang Q., Blair C., Qin J., Blair D., Degallaix J., Yamamoto

H., 2015, Phys. Rev. D, 91, 092001Zhu X.-J., Howell E., Regimbau T., Blair D., Zhu Z.-H., 2011, ApJ, 739, 86

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