GW190412: Observation of a Binary-Black-Hole Coalescence with Asymmetric Masses

Abstract

We report the observation of gravitational waves from a binary-black-hole coalescence during the first two weeks of LIGO’s and Virgo’s third observing run. The signal was recorded on April 12, 2019 at 05∶30∶44 UTC with a network signal-to-noise ratio of 19. The binary is different from observations during the first two observing runs most notably due to its asymmetric masses: a ∼ 30 M ⊙ black hole merged with a ∼ 8 M ⊙ black hole companion. The more massive black hole rotated with a dimensionless spin magnitude between 0.22 and 0.60 (90% probability). Asymmetric systems are predicted to emit gravitational waves with stronger contributions from higher multipoles, and indeed we find strong evidence for gravitational radiation beyond the leading quadrupolar order in the observed signal. A suite of tests performed on GW190412 indicates consistency with Einstein’s general theory of relativity. While the mass ratio of this system differs from all previous detections, we show that it is consistent with the population model of stellar binary black holes inferred from the first two observing runs.

Published by the American Physical Society 2020

Full text

LIGO-P190412-v9
GW190412: Observation of a Binary-Black-Hole Coalescence with Asymmetric Masses
LIGO Scientific Collaboration and Virgo Collaboration
We report the observation of gravitational waves from a binary-black-hole coalescence during the
first two weeks of LIGO’s and Virgo’s third observing run. The signal was recorded on April 12, 2019
at 05:30:44 UTC with a network signal-to-noise ratio of 19. The binary is different from observations
during the first two observing runs most notably due to its asymmetric masses: a ∼30 Mblack
hole merged with a ∼8Mblack hole companion. The more massive black hole rotated with
a dimensionless spin magnitude between 0.17 and 0.59 (90% probability). Asymmetric systems
are predicted to emit gravitational waves with stronger contributions from higher multipoles, and
indeed we find strong evidence for gravitational radiation beyond the leading quadrupolar order in
the observed signal. A suite of tests performed on GW190412 indicates consistency with Einstein’s
general theory of relativity. While the mass ratio of this system differs from all previous detections,
we show that it is consistent with the population model of stellar binary black holes inferred from
the first two observing runs.
I. INTRODUCTION
The first detections [1–12] of gravitational-wave
(GW) signals by the Advanced Laser Interferometer
Gravitational-wave Observatory (LIGO) [13] and Ad-
vanced Virgo [14] detectors during their first two ob-
serving runs have begun to constrain the population of
astrophysical binary black holes (BBHs) [15]. Prior to
the start of the third observing run (O3) the Advanced
LIGO and Advanced Virgo detectors were upgraded to
increase the sensitivity of all three interferometers [16–
19]. This increase in sensitivity has broadened the detec-
tor network’s access to GW signals from the population
of merging BBH sources [20], allowing for the detection
of rarer systems.
To be able to characterize the full range of potential
systems, models of the gravitational radiation emitted
by BBHs are continuously being improved. In particu-
lar, physical effects associated with unequal masses and
misaligned spins have recently been extended in models
covering the inspiral, merger and ringdown of BBHs [21–
33]. For GW signals with sufficient signal-to-noise ra-
tio (SNR), the inclusion of these effects is important to
accurately infer the source parameters. In addition, im-
proved signal models allow for stronger tests of the va-
lidity of general relativity (GR) as the correct underlying
theory.
In this paper we report the detection of GWs from
a BBH whose properties make it distinct from all other
BBHs reported previously from the first two observing
runs. The event, called GW190412, was observed on
April 12, 2019 at 05:30:44 UTC by the Advanced Virgo
detector and both Advanced LIGO detectors. While
the inferred individual masses of the coalescing black
holes (BHs) are each within the range of masses that
have been observed before [7, 9–12], previously detected
binaries all had mass ratios q=m2/m1(with m1≥m2)
that were consistent with unity [34]. GW190412, how-
ever, is the first observation of GWs from a coalescing
binary with unequivocally unequal masses, q= 0.28+0.13
−0.06
(median and 90% symmetric credible interval). The mass
asymmetry of the system provides a second novelty of
GW190412: the GWs carry subtle, but for the first
time clearly measurable, imprints of radiation that os-
cillates not only at the binary’s dominant GW emission
frequency, but also at other frequencies with subdom-
inant contributions. We introduce the nature of these
corrections and present the source parameters inferred
for GW190412 using signal models that include higher
multipoles.
This paper is organized as follows: in Sec. II we report
details on the detection of GW190412. The source prop-
erties are discussed in Sec. III. Sec. IV presents a suite of
analyses illustrating that the observed data indeed con-
tain measurable imprints of higher multipoles. In Sec. V
we present tests of GR performed in this previously un-
explored region of the parameter space. Implications for
our understanding of the BBH population and formation
channels are discussed in Secs. VI and VII.
II. DETECTORS & DETECTION
The third observing run of LIGO [35] and Virgo [14]
began on 1 April 2019, and GW190412 occurred in the
second week of the run. At the time of the event, both
LIGO detectors and the Virgo detector were online and
operating stably for over 3.5 hours. Strain data from
around the time of GW190412 for all three detectors is
shown in Figure 1, with excess power consistent with the
observed signal present in all detectors. The relative sen-
sitivity of the LIGO and Virgo detectors accounts for the
difference in strength of the signal in the data.
LIGO and Virgo interferometers are calibrated using
electrostatic fields and radiation pressure from auxiliary
lasers at a known frequency and amplitude [36–38]. At
the time of the event, the maximum calibration error at
both LIGO sites is 7.0% in amplitude and 3.8◦in phase.
At Virgo, the errors are 5.0% in amplitude and 7.5◦in
phase.
Numerous noise sources that limit detector sensitivity
are measured and subtracted, including noise from cali-
bration lines and noise from the harmonics of the power
arXiv:2004.08342v2 [astro-ph.HE] 27 Apr 2020

2
100
50
500
LIGO Hanford
100
50
500
Frequency (Hz)
LIGO Livingston
−0.75 −0.50 −0.25 0.00 0.25
Time (seconds)
100
50
500
Virgo
0.0 2.5 5.0 7.5 10.0 12.5 15.0
Normalized energy
FIG. 1. Time-frequency representations [42] of the strain data
at the time of GW190412 in LIGO Hanford (top), LIGO Liv-
ingston (middle), and Virgo (bottom). Times are shown from
April 12, 2019, 05:30:44 UTC. Excess power, consistent with
the measured parameters of the event, is present in all three
detectors. The amplitude scale of each time-frequency tile is
normalized by the respective detector’s noise amplitude spec-
tral density. The lower frequency limit of 20 Hz is the same
as in analyses of the source properties of GW190412.
mains. Similar to procedures from the second observing
run [39, 40], these noise sources are linearly subtracted
from the data using auxiliary witness sensors. In O3,
this procedure was completed as a part of the calibration
pipeline [37], both in low latency and offline. Additional
noise contributions due to non-linear coupling of the 60
Hz power mains are subtracted for offline analyses using
coupling functions that rely on machine learning tech-
niques [41].
GW190412 was initially detected by the GstLAL [43],
SPIIR [44], cWB [45], MBTA [46], and PyCBC Live
[47] pipelines running in low-latency configuration, and
reported under the identifier S190412m. The GstLAL,
SPIIR,MBTA, and PyCBC Live pipelines identify
GW signals by matched-filtering [48–50] data using a
bank of filter waveforms that cover a wide range of source
parameters [51–57]. The coherent, unmodelled cWB
pipeline [45], identifies clusters of coherent excess power
with increasing frequency over time in data processed
with the wavelet transform [58].
All analysis pipelines running in low-latency identi-
fied GW190412 as a confident event. The observed SNR
from the GstLAL pipeline was 8.6 in LIGO Hanford,
15.6 in LIGO Livingston, and 3.7 in Virgo. GW190412
was identified with consistent SNR across all low-latency
pipelines.
A GCN alert [59] announcing the event was publicly
distributed 60 minutes after GW190412 and included an
initial sky localization computed using a rapid Bayesian
algorithm, BAYESTAR [60], applied to data from all
available detectors. This sky localization constrained the
position of the event to a 90% credible area of 156 deg2.
Additional offline analysis of the data from April 8 to
April 18 was completed by the GstLAL [61, 62] and Py-
CBC [63, 64] matched filtering pipelines, and the coher-
ent, template independent cWB pipeline [45]. The offline
analyses utilize an updated version of the calibration of
the LIGO data [37] and additional data quality vetoes
[65]. The GstLAL pipeline incorporates data from all
three detectors, while the PyCBC and cWB pipelines
only use data from the two LIGO detectors.
All three offline pipelines identified GW190412 as a
highly significant GW event. This event was assigned a
false-alarm rate (FAR) of <1 per 1 ×105years by the
GstLAL pipeline and <1 per 3 ×104years by the Py-
CBC pipeline. The template independent cWB pipeline
assigned this event a FAR of <1 per 1 ×103years. As
GW190412 was identified as more significant than any
event in the computed background, the FARs assigned
by all offline pipelines are upper bounds.
Validation procedures similar to those used to evaluate
previous events [7, 66] were used in the case of GW190412
to verify that instrumental artifacts do not affect the
analysis of the observed event. These procedures rely
upon sensor arrays at LIGO and Virgo to measure en-
vironmental disturbances that could potentially couple
into the interferometers [67]. For all three interferom-
eters, these procedures identified no evidence of excess
power from terrestrial sources that could impact detec-
tion or analysis of GW190412. Data from Virgo contains
instrumental artifacts from scattered light [68] that im-
pact data below 20 Hz within 4 seconds of the coalescence
time. As analyses of GW190412 source properties only
use data from above 20 Hz, no mitigation of these arti-
facts was required.
III. SOURCE PROPERTIES
A. On Radiative Multipoles and Source Properties
GW radiation is observed as a combination of two po-
larizations, h+and h×weighted with the detector re-

3
sponse functions [69]. For GW theory, it is efficient to
work with the complex valued quantity, h=h+−ih×.
From the perspective of the observer, hcan be expanded
into multipole moments using spherical polar coordinates
defined in a source centered frame [70]. Each multipole
moment encodes information about the gravitationally
radiating source. Interfacing GW theory with data anal-
ysis allows the connections between radiative multipole
moments and source properties to be decoded.
Starting with the pioneering work of Einstein, and later
refined by Newman, Penrose, Thorne and many others,
GWs have been known to be at least quadrupolar [70–72].
The −2 spin-weighted spherical harmonics −2Y`m(θ, φ)
have been found to be the simplest appropriate harmonic
basis. They are the orthonormal angular eigenfunctions
of gravitationally perturbed spherically symmetric space-
times and we refer to their beyond-quadrupolar multipole
moments in this basis as higher multipoles [72–77].
In this basis the multipolar decomposition is
h+−ih×=X
`≥2X
−`≤m≤`
h`m(t, λ
λ
λ)
DL−2Y`m(θ, φ),(1)
where (θ, φ) are respectively the polar and azimuthal an-
gles defining the direction of propagation from the source
to the observer, and DLthe luminosity distance from
the observer. The radiative multipoles, h`m , depend
on source properties (condensed in λ
λ
λ) such as the BH
masses, m1and m2, and their spins ~
S1and ~
S2.
When at least one of the BH spins is misaligned with
respect to the binary’s angular momentum, the orbital
plane and the spins precess around the direction of the
total angular momentum. We refer to these systems as
precessing. For non-precessing systems, reflection sym-
metry about a fixed orbital plane results in a complex
conjugate symmetry between moments of azimuthal in-
dex mand −m. Therefore, when we refer to a specific
(`, m) multipole, h`m, we always mean (`, ±m). For pre-
cessing systems and their non-fixed orbital plane, one
may define a co-precessing frame such that θis relative
to the direction of maximal radiation emission. In this
co-precessing frame h`m approximately take on features
of their non-precessing counterparts [78–82].
Long before merger, the instantaneous frequencies,
f`m, of each h`m are linked to the orbital frequency of the
binary forb by f`m 'mforb [74]. In the moments shortly
before the two BHs merge this simple scaling is broken,
but its imprint persists through the final stages of coa-
lescence [22]. Therefore, higher multipoles imply an ap-
proximately harmonic progression of frequencies within
GW signals from quasi-circularly coalescing BHs.
The source geometry depends on mass ratio and is
most prominently manifested in the relative contribution
of multipoles with odd or even m: for an exactly equal
mass binary with non-spinning components, only multi-
poles with even mrespect orbital symmetry and so are
present in the radiation [74]. In this and nearly equal
mass cases, the quadrupole, h22 , is by far the most dom-
inant, followed by other multipoles with even m. How-
ever, for sufficiently unequal mass ratios, numerical and
analytical studies have shown that the `=m= 3 and
subsequent multipoles with `=mgain increasing im-
portance [74, 75, 83–86]. In the context of source detec-
tion and characterization, analytical and numerical stud-
ies [76, 87–95] have shown that higher multipoles can
have increasing relative importance as system asymme-
try increases due to source properties such as unequal
masses, spin magnitudes and, in the case of precession,
spin directions.
Source orientation also contributes to higher multipole
content and can impact the inference of source param-
eters. Systems whose orbital planes point directly to-
wards the observer present signals which are generally
dominated by h22. In such instances the net dependence
on θand DLenter co-linearly as −2Y22(θ, φ)/DL. Thus
distance and inclination can be approximately degenerate
for each GW detector. However, for inclined systems, the
higher multipoles introduce other dependencies on θvia
their harmonics, −2Y`m(θ, φ). Consequently, higher mul-
tipoles may break the inclination-distance degeneracy,
thereby tightening constraints on inferred source inclina-
tion and luminosity distance. We show in Sec. III D how
signal models including higher multipoles can break this
degeneracy and improve our ability to infer the source
parameters of GW190412. When we refer to the incli-
nation of GW190412 below, we define it as the angle
between the system’s total angular momentum and the
direction of propagation from the source to the observer,
and denote it by θJN for clarity.
Importantly, GW signal models are used to map be-
tween radiative multipole content and source properties,
and for the robust estimation of source properties, ex-
perimental uncertainty requires GW signal models to be
used in conjunction with methods of statistical inference.
B. Method and Signal Models
We perform an inference of the properties of the binary
using a coherent Bayesian analysis of 8 seconds of data
around the time of the detection from the three detectors
(see e.g., [96]). Results presented here were mainly pro-
duced with a highly parallelized version of the code pack-
age Bilby [97, 98]. Additional analyses were performed
with the package LALInference [99]. RIFT [100, 101]
was also used to check consistency of the intrinsic pa-
rameters and for corroborating the Bayes factors that
are presented below. The power spectral density (PSD)
of the noise that enters the likelihood calculation is es-
timated from the data using BayesWave [102, 103]. The
low-frequency cutoff for the likelihood integration is set
to 20 Hz, and the prior distributions we use are described
in Appendix B.1 of [7]. We note that after initial anal-
yses with large prior intervals on the individual masses,
more restrictive prior boundaries were introduced to ac-
celerate further Bilby analyses. Those additional bound-

4
aries do not affect the posterior probabilities reported be-
low as the likelihood is insignificantly small outside the
allowed prior region. However, Kullback-Leibler diver-
gences [104] calculated between prior and posterior are
sensitive to this choice. Full prior specifications can be
found in the data accompanying this paper [105].
The signal models we use to sample the BBH pa-
rameter space are enhanced versions of the models that
have been used in past analyses (e.g., [7]). We em-
ploy models from the effective-one-body (EOB) [106–109]
family that are constructed by completing an analyti-
cal inspiral-merger-ringdown description which builds on
post-Newtonian (PN) [110–112] and black-hole perturba-
tion theory, with numerical-relativity information. The
phenomenological family [113, 114] on the other hand,
is based on a frequency-domain description of hybridized
EOB-inspiral and numerical-relativity merger. The latest
developments used here include the effects of higher mul-
tipoles in precessing models both in the EOBNR family
(SEOBNRv4PHM, [33, 115, 116]) and the phenomeno-
logical family (IMRPhenomPv3HM, [23, 24]).
All model variants that we use in the analysis of
GW190412 are detailed in Table I. In order to test for
imprints of spin-precession and higher multipoles in the
data, we also perform analyses using models without spin
precession and/or without higher multipoles. To verify
the robustness of our results against waveform system-
atics we also performed an analysis using the numerical-
relativity surrogate NRHybSur3dq8 [27] that includes the
effect of higher multipoles, but is limited to spins aligned
with the angular momentum. This surrogate model
is constructed from numerical-relativity waveforms ex-
tended with EOB-calibrated PN waveforms.
C. Masses
In Table II we summarize the inferred values of the
source parameters of GW190412. The statistical un-
certainty is quantified by the equal-tailed 90% credi-
ble intervals about the median of the marginalized one-
dimensional posterior distribution of each parameter. We
report the results obtained with the two most complete
signal models – those members of the EOBNR and Phe-
nom family that include both the effects of precession
and higher multipoles (see Table I). As a conservative
estimate, and because we do not favor one model over
the other, we combine the posteriors of each model with
equal weight, which is equivalent to marginalizing over a
discrete set of signal models with a uniform probability.
The resulting values are provided in the last column of
Table II, and we refer to those values in the text unless
explicitly stated otherwise.
The component masses for this system in the source
frame are m1= 29.7+5.0
−5.3Mand m2= 8.4+1.8
−1.0M. They
are consistent with the BH mass ranges of population
models inferred from the first two LIGO and Virgo ob-
serving runs [7]. However, GW190412 is particularly in-
FIG. 2. The posterior distribution for the mass ratio qand ef-
fective spin χeff of GW190412. We show the two-dimensional
marginalized distribution as well as the one-dimensional
marginalized distribution of each parameter along the axes
for two different signal models that each include the effects
of precessing spins and higher multipoles. The indicated two-
dimensional area as well as the horizontal and vertical lines
along the axes, respectively, indicate the 90% credible regions.
teresting for its measured mass ratio of q= 0.28+0.13
−0.06.
Figures 2 and 3 illustrate that the mass ratio inferred
for GW190412 strongly disfavors a system with compa-
rable masses. We exclude q > 0.5 with 99% probability.
In Section VI we show that the asymmetric component
mass measurement is robust when analyzed using a prior
informed by the already-observed BBH population.
The posteriors shown in Fig. 2 for the two precessing,
higher multipole models are largely overlapping, but dif-
ferences are visible. The EOBNR PHM model provides
tighter constraints than Phenom PHM, and the peak of
the posterior distributions are offset along a line of high
correlation in the q–χeff plane. This mass-ratio–spin de-
generacy arises because inspiral GW signals can partly
compensate the effect of a more asymmetric mass ra-
tio with a higher effective spin [125–129]. The effective
spin [108, 130, 131] is the mass-weighted sum of the indi-
vidual spin components ~
S1and ~
S2perpendicular to the
orbital plane, or equivalently projected along the direc-
tion of the Newtonian orbital angular momentum, ~
LN,
χeff =1
M ~
S1
m1
+~
S2
m2!·~
LN
k~
LNk,(2)
with M=m1+m2.
GW190412 is in a region of the parameter space that
has not been accessed through observations before; and

5
TABLE I. Waveform models used in this paper. We indicate which multipoles are included for each model. For precessing
models, the multipoles correspond to those in the co-precessing frame.
family short name full name precession multipoles (`, |m|)ref.
EOBNR
EOBNR SEOBNRv4 ROM ×(2, 2) [57]
EOBNR HM SEOBNRv4HM ROM ×(2, 2), (2,1), (3, 3), (4, 4), (5, 5) [26, 32]
EOBNR P SEOBNRv4P X(2, 2), (2, 1) [33, 115, 116]
EOBNR PHM SEOBNRv4PHM X(2, 2), (2, 1), (3, 3), (4, 4), (5, 5) [33, 115, 116]
Phenom
Phenom IMRPhenomD ×(2, 2) [117, 118]
Phenom HM IMRPhenomHM ×(2, 2), (2, 1), (3, 3), (3, 2), (4, 4), (4, 3) [22]
Phenom P IMRPhenomPv2/v3aX(2, 2) [23, 119]
Phenom PHM IMRPhenomPv3HM X(2, 2), (2, 1), (3, 3), (3, 2), (4, 4), (4, 3) [24]
NR surrogate NRSur HM NRHybSur3dq8 ×`≤4, (5, 5) but not (4, 0), (4, 1) [27]
aThe recently improved, precessing model IMRPhenomPv3 is used in Sec. IVA to calculate Bayes factors. For consistency with
previous analyses and computational reasons, the tests presented in Sec. V A use IMRPhenomPv2 instead.
FIG. 3. The one-dimensional posterior probability density
for the mass ratio qof GW190412, obtained with a suite of
different signal models. The vertical lines above the bottom
axes indicate the 90% credible bounds for each signal model.
we find that the two models give slightly different, yet
largely consistent results. However, this is the first
time that systematic model differences are not much
smaller than statistical uncertainties. We tested the ori-
gin of these differences by repeating the analysis with
an extended suite of signal models, as shown in Fig. 3.
The results indicate that the mass-ratio measurement
of GW190412 is robust against modeling systematics,
and the different treatments of higher multipoles in the
EOBNR and Phenom families may account for some of
the observed differences. We also see that the NRSur HM
model and the EOBNR HM model agree well with each
other, while the Phenom HM model deviates slightly.
This is consistent with the fact that the NRSur HM
and EOBNR HM models have some features in common.
In NRSur HM, the PN inspiral part of the waveform is
calibrated to EOB waveforms, and in EOBNR HM the
merger and ringdown part of the waveform is calibrated
to a subset of the numerical-relativity simulations used
in the construction of NRSur HM. Further studies will be
needed to fully understand the systematics visible here
and mitigate them as models improve.
D. Orientation and Spins
The contribution of higher multipoles in the gravita-
tional waveform is important for the parameter estima-
tion of systems with small mass ratios [132, 133]. In
Fig. 4 we show the marginalized two-dimensional pos-
terior distribution for luminosity distance and inclina-
tion obtained using signal models either without higher
multipoles, with higher multipoles, or with higher mul-
tipoles and spin-precession. The degeneracy between lu-
minosity distance and inclination angle that is present in
the results obtained without higher multipoles is broken
when higher multipoles are included. The inclusion of
precession effects helps to constrain the 90% credible re-
gion further. Results obtained with the Phenom family
show the same degeneracy breaking when higher multi-
poles are included, but the 90% credible region obtained
with Phenom PHM has some remaining small support
for θJN > π/2.
We constrain the spin parameter χeff of GW190412’s
source to be 0.25+0.08
−0.11. After GW151226 and
GW170729 [2, 7, 34], this is the third BH binary we
have identified whose GW signal shows imprints of at
least one nonzero spin component, although recently an-
other observation of a potentially spinning BH binary
was reported [11]. However, inferred spins are more sen-
sitive than other parameters (e.g., component masses)
to the choice of the prior. A re-analysis of GW events
with a population-informed spin prior recently suggested
that previous binary component spins measurements may

6
TABLE II. Inferred parameter values for GW190412 and their
90% credible intervals, obtained using precessing models in-
cluding higher multipoles.
parameteraEOBNR PHM Phenom PHM Combined
m1/M31.7+3.6
−3.527.5+4.6
−4.129.7+5.0
−5.3
m2/M8.0+0.9
−0.79.0+1.6
−1.18.4+1.8
−1.0
M/M39.7+3.0
−2.736.5+3.5
−2.738.1+4.0
−3.7
M/M13.3+0.3
−0.313.3+0.5
−0.413.3+0.4
−0.3
q0.25+0.06
−0.04 0.33+0.12
−0.08 0.28+0.13
−0.06
Mf/M38.6+3.1
−2.835.3+3.6
−2.837.0+4.1
−3.9
χf0.68+0.04
−0.04 0.66+0.06
−0.07 0.67+0.05
−0.07
mdet
1/M36.5+4.2
−4.231.5+5.5
−4.934.2+5.7
−6.5
mdet
2/M9.2+0.9
−0.710.3+1.7
−1.29.7+1.8
−1.1
Mdet/M45.7+3.5
−3.341.8+4.3
−3.343.9+4.6
−4.7
Mdet/M15.3+0.1
−0.215.2+0.3
−0.215.3+0.2
−0.2
χeff 0.28+0.06
−0.08 0.21+0.08
−0.10 0.25+0.08
−0.11
χp0.31+0.14
−0.15 0.29+0.25
−0.16 0.30+0.19
−0.15
χ10.46+0.12
−0.15 0.38+0.22
−0.29 0.43+0.16
−0.26
DL/Mpc 740+120
−130 730+150
−200 730+140
−170
z0.15+0.02
−0.02 0.15+0.03
−0.04 0.15+0.03
−0.03
ˆ
θJN 0.71+0.23
−0.21 0.76+0.39
−0.29 0.73+0.34
−0.24
ρH9.5+0.1
−0.29.5+0.2
−0.39.5+0.1
−0.3
ρL16.2+0.1
−0.216.1+0.2
−0.316.2+0.1
−0.3
ρV3.7+0.2
−0.53.5+0.4
−1.33.6+0.3
−1.0
ρHLV 19.1+0.2
−0.219.0+0.2
−0.319.1+0.1
−0.3
aSymbols: mi: individual mass; M=m1+m2;
M= (m1m2)3/5M−1/5; superscript “det” refers to the
detector-frame (redshifted) mass, while without subscript,
masses are source-frame masses, assuming a standard
cosmology [120] detailed in Appendix B of [7]; q=m2/m1;Mf,
χf: mass and dimensionless spin magnitude of the remnant BH,
obtained through numerical-relativity fits [121–124]; χeff,χp:
effective and precessing spin parameter; χ1: dimensionless spin
magnitude of more massive BH; DL: luminosity distance; z:
redshift; ˆ
θJN : inclination angle (folded to [0, π/2]); ρX
matched-filter SNRs for the Hanford, Livingston and Virgo
detectors, indicated by subscript. ρHLV: network SNR.
have been overestimated because of the use of an unin-
formative prior [134]. Collecting more observations will
enable us to make more confident statements on BH spins
in the future.
The parameter χeff only contains information about
the spin components perpendicular to the orbital plane.
The in-plane spin components cause the orbital plane to
precess [135], but this effect is difficult to observe, espe-
cially when the inclination angle is near 0 or π. Us-
ing models with higher multipoles, however, we con-
strain the inclination of GW190412 exceptionally well
and put stronger constraints on the effect of precession
than in previous binaries [7]. The strength of precession
is parameterized by an effective precession parameter,
FIG. 4. The posterior distribution for the luminosity dis-
tance, DL, and inclination, θJ N (angle between the line-of-
sight and total angular momentum), of GW190412. We il-
lustrate the 90% credible regions as in Fig. 2. By comparing
models that include either the dominant multipole (and no
precession), higher multipoles and no precession, or higher
multipoles and precession, we can see the great impact higher
multipoles have on constraining the inclination and distance.
All models shown here are part of the EOBNR family.
0≤χp<1, defined by [136]
χp= max (k~
S1⊥k
m2
1
, κ k~
S2⊥k
m2
2),(3)
where ~
Si⊥=~
Si−~
LN×(~
Si·~
LN)/k~
LNk2and κ=q(4q+
3)/(4 + 3q). Large values of χpcorrespond to strong
precession.
Fig. 5 shows that the marginalized one-dimensional
posterior of χpis different from its global prior distribu-
tion. The Kullback-Leibler divergence [104], DKL, for the
information gained from the global prior to the posterior
is 0.96+0.03
−0.03 bits and 0.52+0.02
−0.02 bits for the EOBNR PHM
and Phenom PHM model, respectively. Those values are
larger than what we found for any observation during
the first two observing runs (see Table V in Appendix B
of [7]). Since the prior we use introduces non-negligible
correlations between mass ratio, χeff and χp, we check if
the observed posterior is mainly derived from constraints
on χeff and q. We find that this is not the case, as a prior
restricted to the 90% credible bounds of qand χeff (also
included in Fig. 5) is still significantly different from the
posterior, with DKL = 0.97+0.03
−0.03 bits (0.54+0.02
−0.02 bits) for
the EOBNR PHM (Phenom PHM) model. We constrain
χp∈[0.15,0.49] at 90% probability, indicating that the
signal does not contain strong imprints of precession, but

7
FIG. 5. The posterior density of the precessing spin parame-
ter, χp, obtained with the two models that include both the
effects of precession and higher multipoles. In addition, we
show the prior probability of χpfor the global prior parame-
ter space, and restricted to the 90% credible intervals of χeff
and qas given in the “Combined” column of in Table II.
very small values of χp.0.1 are also disfavored. The
results obtained with the EOBNR PHM model are more
constraining than the Phenom PHM results. We return
to the question if GW190412 contains significant imprints
of precession below, and in the context of Bayes factors
in Sec. IV A.
The asymmetric masses of GW190412 means that the
spin of the more massive BH dominates contributions to
χeff and χp. Therefore, we obtain that the spin magni-
tude of the more massive BH is χ1= 0.43+0.16
−0.26, which
is the strongest constraint from GWs on the individual
spin magnitude of a BH in a binary so far [7]. The spin
magnitude of the less massive BH remains largely uncon-
strained.
To further explore the presence of precession in the
signal, we perform the following analysis. Gravitational
waveforms from precessing binaries can be decomposed
into an expansion in terms of the opening angle between
the total and orbital angular momenta [137, 138]. Con-
sidering only `= 2 modes, this expansion contains five
terms, each not showing the characteristic phase and am-
plitude modulations of a precessing signal. When the
spin component that lies in the binary’s orbital plane is
relatively small, the angle between the total angular mo-
mentum and the orbital angular momentum is small as
well [139], and higher-order contributions in this expan-
sion may be neglected. As a result, a precessing waveform
can be modeled by the sum of the leading two contribu-
tions, where the amplitude and phase modulations of a
precessing signal arise from the superposition of these
terms.
In order to identify precession, we therefore require be-
ing able to measure both of these terms. We quantify the
measurability of precession ρpby how much power there
012345678
ρ
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Probabilty Density
pχ2
2
Precession
33-mode
3σ
FIG. 6. The probability distribution of the precessing SNR,
ρp(blue) and the orthogonal optimal SNR, ρ, contained in the
strongest higher multipole, (`, m) = (3,3) (orange). We also
show the expected distribution from Gaussian noise (dotted
line) and the 3-σlevel (dashed line). The results indicate that
there is marginal support for precession, but the posterior
supports a clearly measurable higher multipole.
is in the sub-dominant contribution. The distribution of
ρpis shown in Fig. 6. In the absence of any precession in
the signal, we expect ρ2
pto follow a χ2-distribution with
two degrees of freedom. Using the inferred posterior dis-
tributions, our analysis shows that ρp= 2.86+3.43
−1.56. We
may interpret this as moderate support for precession as
the median exceeds the 90% confidence interval expected
from noise, but a non-negligible fraction of the ρpposte-
rior lies below. This calculation assumes a signal domi-
nated by the `= 2 multipole. However, we have verified
that the contribution of higher multipoles to the mea-
surement of spin-precession is subdominant by a factor
of ∼5.
IV. HIGHER MULTIPOLES
Signal models that include higher multipoles are
needed to infer the strongest constraints on GW190412’s
source properties. This is because if the data contain
significant imprints of higher multipoles, the appropriate
models can fit the data better than dominant-mode mod-
els, leading to a higher statistical likelihood. Conversely,
if the data would not contain imprints of higher multi-
poles, using more complex models allows us to disfavor
configurations in which clear imprints of higher multi-
poles are predicted [22, 132, 133].
In this section, we analyze how strong the imprints of
higher multipoles are in GW190412 and ask if their con-
tributions in the data are significantly stronger than ran-
dom noise fluctuations. We address this question using
four different approaches, each coming with its unique
set of strengths and caveats.

8
A. Bayes Factors and Matched-Filter SNR
We may first ask if higher-multipole models actually fit
the data better than dominant-multipole models. This
can be quantified by the matched-filter network SNR,
ρHLV, which is based on the sum of the squared inner
products between the instruments’ data and the signal
model. Thus the SNR quantifies the extent to which
a single signal model recovers coherent power between
detectors. For the EOBNR family, we find that ρHLV in-
creases from 18.1+0.2
−0.2for the dominant-multipole model
to 18.8+0.2
−0.3for the higher multipole model to 19.1+0.2
−0.2for
the most complete EOBNR PHM model. The precessing,
but dominant-multipole model yields ρHLV = 18.5+0.2
−0.3,
which is smaller than the value for the non-precessing,
higher-multipole model. A similar trend can be observed
for the Phenom family, where the dominant-multipole
model, the Phenom P model, Phenom HM and Phe-
nom PHM yield ρHLV = 18.2+0.2
−0.3, 18.3+0.2
−0.3, 18.9+0.2
−0.3, and
19.0+0.2
−0.3, respectively.
A more complete answer to the question of which
model describes the data best can be given in the
Bayesian framework. The ratio of marginalized like-
lihoods under two competing hypotheses is called the
Bayes factor, B[140]. Bayes factors may be used to
quantify support for one hypothesis over another. The
Bayes factor does not take into account our prior belief
in the hypotheses being tested. Within GR, every com-
pact binary coalescence signal includes higher multipoles
and the prior odds in favor of their presence in the signal
are infinite. We therefore focus on the Bayes factors and
do not discuss the odds ratio (which is the Bayes factor
multiplied by the prior odds).
Table III presents log10 Bfor various combinations of
two models within the same waveform family. To esti-
mate systematic uncertainties, we test the same hypothe-
ses using multiple model families and multiple codes to
calculate log10 B. Bilby [97, 98] and LALInference [99]
use variants of the nested sampling algorithm [141–144].
RIFT [100, 101] is based on interpolating the marginal-
ized likelihood over a grid covering only the intrinsic
source parameters. Table entries marked “–” have not
been calculated because of computational constraints
(LALInference analysis of precessing EOBNR models) or
because the NRSurrogate model does not allow precess-
ing spins.
We consistently find log10 B ≥ 3 in favor of higher mul-
tipoles. This indicates strong evidence that the observed
signal contains measurable imprints of higher multipoles,
assuming either precessing or non-precessing (aligned
spin) systems. Systematic differences between codes and
waveform models dominate the uncertainty in the num-
bers we report. We find larger differences between codes
when assuming precessing spins, because this is a more
complex analysis that requires exploring more degrees
of freedom in the parameter space than in the non-
precessing case. However, log10 Bis large enough across
all models and codes that a statement about higher mul-
tipoles can convincingly be made despite uncertainties of
up to the order unity.
It would be desirable to also compare the hypotheses
that the signal contains imprints of precession with as-
suming no precession. However, using the same codes
and models that were used in Table III, the Bayes fac-
tors we found ranged from no decisive support for ei-
ther hypothesis to indicating marginal support of pre-
cession. All values for log10 Bcomparing precession vs.
non-precessing models were smaller or comparable to the
systematic uncertainties of order unity. More extensive
studies will be needed to understand the origin of these
systematics better.
B. Optimal SNR
A complementary way to quantify the strength of
higher multipoles is to use parameter-estimation re-
sults from a signal model including higher-order multi-
poles [145, 146]. Each multipole is decomposed into parts
parallel and perpendicular to the dominant multipole by
calculating the noise-weighted inner product [125, 147]
(often referred to as overlap) between it and the dom-
inant multipole. Among the strongest multipoles that
are included in our models, the (`, m) = (3,3), (4,4)
and (4,3) multipoles of GW190412 are close to orthogo-
nal to the dominant (2,2) multipole within the band of
the detector. In contrast, the (3,2) and (2,1) multipoles
have non-negligible parallel components. To quantify the
strength of the higher multipoles we remove any parallel
components from the multipoles and calculate the or-
thogonal optimal SNR using IMRPhenomHM [22]. We
find (`, m) = (3,3) to be the strongest subdominant mul-
tipole.
The templates that include higher multipoles do not
allow the amplitude and phase of the (3,3) multipole to
be free parameters; they are determined by the proper-
ties of the system. An analysis of this event using only
the dominant (2,2) multipole recovers posteriors that are
consistent with a broad range of inclinations, coalescence
phases, and mass ratios, while the same analysis using
higher multipoles results in significantly more restricted
posteriors (see Fig. 4). This suggests that by changing
those parameters, our models can effectively treat the
amplitude and phase of the higher multipoles as tun-
able parameters that make their contributions more or
less pronounced. If the data only contained the domi-
nant quadrupole mode and Gaussian noise, the squared
orthogonal SNR in the subdominant multipole will be χ2-
distributed with two degrees of freedom [137, 138]. This
was verified by analysing an injection with parameters
close to GW190412.
This noise-only distribution is shown in Fig. 6, along
with the orthogonal optimal SNR in the (`, m) = (3,3)
mode. The peak of the SNR distribution is at the Gaus-
sian equivalent 3-σlevel for the noise-only distribution,
making this the most significant evidence for something

9
TABLE III. log10 Bcomputed between two hypotheses that assume either a signal model including higher multipoles (`≤5) or
a dominant-multipole model (`= 2). log10 B>0 indicates support for higher multipoles. Each entry is based on a comparison
between either precessing (first row) or nonprecessing, aligned-spin (second row) models of the same model family. See Table I
for full details of the models. For each family, we also indicate the code used for calculating log10 B.
Hypotheses EOBNR Phenom NRSurrogate
Bilby LALInference RIFT Bilby RIFT
higher vs dominant multipoles (precessing) 4.1 – 3.0 3.5 –
higher vs dominant multipoles (aligned) 3.5 3.3 3.6 3.7 3.4
other than the dominant multipole to date [148].
C. Time-frequency Tracks
An independent analysis was performed to detect the
presence of higher-order multipoles in the inspiral part of
the signal, using the time-frequency spectrum of the data.
Full details of the approach are described in [149], but
we summarize the main idea and results for GW190412
below.
The instantaneous frequency f`m(t) of the GW sig-
nal from an inspiraling compact binary is related to that
of the dominant (2,2) mode by f`m(t)'(m/2) f22(t).
We compute f22(t) from the dominant multipoles of the
EOBNR HM and Phenom HM models, using the max-
imum likelihood source parameters from the standard
analysis presented in Sec. III. Inspired by the above scal-
ing relation, we then look along the generalized tracks,
fα(t)'αf22(t), in a time-frequency representation that
is the absolute square of the continuous wavelet transfor-
mation (CWT) of the whitened on-source data, ˜
X(t, f ).
We have used Morlet wavelets to perform the CWT,
where the central frequency of the wavelet was chosen so
as to maximize the sum of pixel values along the f22(t)
curve. This wavelet transformation is shown in the top
panel of Fig. 7.
In order to quantify the energy along each track, we
define Y(α) to be the energy |˜
X(t, f )|2in all pixels con-
taining the track fα(t), where we discretize the data with
a pixel size of ∆t= 1/4096 s along the time-axis and
∆f= 1/5 Hz along the frequency axis. By doing so, we
can decouple the energy in individual multipoles of the
signal. Once f22(t) is defined, this is a computationally
efficient way to analyze which multipoles have sufficient
energy to be detectable in the data; no further model-
ing input is needed, although we do not require phase
coherence along each track.
The resulting Y(α) for GW190412 is shown in the bot-
tom panel of Fig. 7. It has a global peak at α= 1, corre-
sponding to the dominant (2,2) multipole, and a promi-
nent local peak at α= 1.5, corresponding to the m= 3
multipoles. We also calculate Y(α) from different seg-
ments surrounding, but not including GW190412, to cap-
ture the detector noise characteristics; in this case we call
the quantity N(α). The ensemble average µ(α) = hN(α)i
and standard deviation σ(α) of N(α) are also plotted for
reference and to highlight the relative strength of the GW
signal present in the on-source segment.
Instead of estimating the significance of the m= 3
multipoles from comparing Y(α) to its background at
α= 1.5, we perform a more powerful statistical analysis
in which we test the hypotheses that the data contain ei-
ther only noise (H0), or noise and a dominant-multipole
maximum likelihood signal (H1), or noise and a maxi-
mum likelihood signal that includes m= 2 and m= 3
multipoles (H2). By maximizing the likelihood of observ-
ing Y(α) given each hypothesis over a free amplitude pa-
rameter for each multipole, we obtain likelihood ratios for
H1and H2, and their difference is in turn incorporated
into a detection statistic β(see Eq. (7) in [149]).
From the on-source data segment taken from the LIGO
Livingston detector, we found the detection statistic β=
6.5 with a p-value of 6.4×10−4for EOBNR HM model;
and β= 6.6 with a p-value <6.4×10−4for Phenom HM
model, which strongly supports the presence of m= 3
modes in the signal. The full distribution of βfrom off-
source data segments from the LIGO Livingston detector
surrounding the trigger time of GW190412 is shown in
the inset of Fig. 7.
D. Signal Reconstructions
As an additional test of consistency, and an instruc-
tive visual representation of the observed GW signal, we
compare the results of two signal reconstruction methods.
One is derived from the parameter-estimation analysis
presented in Sec. III, the second uses the model-agnostic
wavelet-based burst analysis BayesWave [150] which was
also used to generate PSDs. A detailed discussion of such
signal comparisons for previous BBH observations can be
found in [151].
For GW190412, both signal reconstruction methods
agree reasonably well as illustrated in Fig. 8. To quantify
the agreement for each signal model from the Phenom
and EOB families, we compute the noise-weighted in-
ner product [125, 147] between 200 parameter-estimation
samples and the BayesWave median waveform. The
BayesWave waveform is constructed by computing the
median values at every time step across samples. Similar
comparison strategies have been used in [3, 5, 34, 152].

10
FIG. 7. Top Panel: Time-frequency spectrogram of data con-
taining GW190412, observed in the LIGO Livingston detec-
tor. The horizontal axis is time (in seconds) relative to the
trigger time (1239082262.17). The amplitude scale of the de-
tector output is normalized by the PSD of the noise. To il-
lustrate the method, the predicted track for the m= 3 multi-
poles is highlighted as a dashed line, above the track from the
m= 2 multipoles that are visible in the spectrogram. Bottom
Panel: The variation of Y(α), i.e., the energy in the pixels
of the top panel, along the track defined by fα(t) = αf22(t),
where f22(t) is computed from the Phenom HM analysis. Two
consecutive peaks at α= 1.0 and α= 1.5 (thin dashed line)
indicate the energy of the m= 2 and m= 3 multipoles, re-
spectively. Inset: The distribution of the detection statistic
βin noise, used to quantify p-values for the hypothesis that
the data contains m= 2 and m= 3 multipoles (red dashed
line).
For the models of the EOBNR family, we find that the
agreement with the unmodeled BayesWave reconstruc-
tion increases slightly from overlaps of 0.84+0.01
−0.02 for the
dominant-multipole, non-precessing model to 0.86+0.01
−0.02
when higher multipoles are included, to 0.88+0.01
−0.02 for the
most complete EOBNR PHM model (median overlap and
90% errors). Increasing overlaps are consistent with the
findings of the other methods presented in this section
that indicate that the extra physical effects included in
the higher-multipole precessing model match the data
better. The overlaps we find are also consistent with ex-
pectations from [151]. The Phenom family may suggest
a similar trend. The overlap for non-precessing dom-
inant multipole model is 0.84+0.02
−0.02, and it increases to
0.85+0.01
−0.02 for the non-prcessing higher multipoles model,
to 0.86+0.02
−0.03 for the precessing higher multipoles model
Phenom PHM.
V. TESTS OF GENERAL RELATIVITY
As the first detected BBH signal with a mass ratio
significantly different from unity, GW190412 provides
the opportunity to test GR in a previously unexplored
regime. Due to the mass asymmetry, this signal contains
information about the odd parity multipole moments.
Hence the tests of GR reported here are sensitive to po-
tential deviations of the multipolar structure away from
GR [153]. A violation from GR may arise from how the
signal is generated by the source; additionally, the form
of the signal described by GR may be tested by check-
ing the consistency of independently obtained estimates
of parameters between the inspiral and merger-ringdown
parts of the full BBH waveform. The following analy-
ses are done by using the LALInference library [99] to
generate posterior probability distributions on these pa-
rameters by using the nested sampling algorithm.
A. Constraints on gravitational wave generation
We check the consistency of this source with general
relativistic source dynamics by allowing for parameter-
ized deformations in each phasing coefficient in the bi-
nary’s waveform. They were first performed on inspiral-
only waveforms in [154, 155] and an extension to higher-
modes was studied in [156]. The current version of the
test using the phenomelogical waveform models rely on
extensions of the methods laid out in [157, 158]. Such
tests have been performed on all GW detections made
in O1 and O2 [159, 160] and have been updated re-
cently with the best constraints by combining all signif-
icant BBH detections made during O1 and O2 in [161].
We perform this analysis with the precessing, dominant-
multipole phenomenological model Phenom P, and, for
consistency with previous tests, with the aligned-spin
dominant-mode EOBNR model (see Table I).

11
FIG. 8. Reconstructions of the gravitational waveform of GW190412 in the LIGO Hanford, LIGO Livingston and Virgo
detectors (from left to right). We show detector data, whitened by an inverse amplitude-spectral-density filter computed using
BayesLine [102], together with the unmodeled BayesWave reconstruction that uses a wavelet bases, and the reconstruction
based on the precessing, higher multipole models from the EOBNR and Phenom families. The bands indicate the 90% credible
intervals at each time. We caution that some apparent amplitude fluctuations in this figure are an artifact of the whitening
procedure.
The inspiral regime of both waveforms is modeled us-
ing the PN approximation. The fractional deviation pa-
rameters δˆϕnare added to their respective PN coeffi-
cients ϕnat n/2-PN order. While the deviation coeffi-
cients are added differently in the two models, the differ-
ences are taken care of by effectively re-parameterizing
the coefficients added to the EOB-based model for con-
sistency in comparing bounds from the Phenom-based
model. The full set of parameters being tested are
{δˆϕ0, δ ˆϕ1, δ ˆϕ2, δ ˆϕ3, δ ˆϕ4, δ ˆϕ5l, δ ˆϕ6, δ ˆϕ6l, δ ˆϕ7}.Here, δˆϕ5l
and δˆϕ6lrefer to the fractional deviations added to the
log-dependent terms at 2.5PN and 3PN respectively.
Moreover, δˆϕ1is an absolute deviation as there is no
0.5PN term within GR. These parameters are tested by
varying only one δˆϕnat a time, and introducing these to
the parameter set of the full signal model. This increased
parameter space dimensionality makes it especially chal-
lenging to use the already computationally expensive
Phenom PHM waveform, and we restrict our analysis to
using the precessing Phenom P approximant. To check
for possible systematics introduced from analyzing this
signal with the dominant-mode Phenom P model, a sig-
nal similar to GW190412 was created with the Phenom
PHM waveform model and injected into data generated
using the BayesWave PSDs for the event. The recovery of
this signal, using Phenom P shows that the posteriors are
completely consistent with the injected values, suggest-
ing that for a GW190412-like signal with same SNR, the
inclusion of the higher multipoles does not significantly
bias results when those multipoles are not included.
The posterior distributions on the fractional deviation
parameters are always found to be consistent with the
GR prediction of δˆϕn= 0. Additionally, the EOB model
can test deviations in the −1PN dipole term, while the
phenomenological signal model can be used to test the in-
termediate and merger-ringdown parameters of the sig-
nal, which are consistent with their GR value. How-
−1 PN
0 PN
0.5 PN
1 PN
1.5 PN
2 PN
2.5 PN(l)
3 PN
3 PN(l)
3.5 PN
10−1
100
101
|δˆ
ϕn|
EOBNR
Phenom P
FIG. 9. 90% upper bounds obtained from parameterized de-
viations in PN coefficients.
ever, owing to the longer inspiral of this signal, the
bounds obtained from this event in the inspiral regime
are among the most constraining bounds obtained from
the analyses on individual BBH detections as reported
in [161]. We show the 90% upper bounds computed in
Fig. 9. The only BBH signals that give more robust or
comparable bounds above 0 PN order are those from
GW170608 (the lowest mass BBH to have been pub-
lished) and GW151226.
B. Inspiral-Merger-Ringdown Consistency
We check the consistency of signal parameters between
the low and high frequency parts of the signal [162, 163].

12
Estimates of the final mass Mfand final spin χfof
the remnant BH are found from the two parts of the
frequency domain signal and their fractional differences
are checked for consistency. For this source, the transi-
tion from the lower-frequency to higher-frequency part
(the Kerr innermost stable circular orbit) of the signal
is estimated from the median intrinsic source parame-
ters and the resulting prediction for Mfand χfto be
at f= 211 Hz [164]. We used the signal model Phe-
nom PHM, sampling on the BBH parameter set to ob-
tain posterior probability distributions on all parameters.
The component masses and spins are estimated directly
from the lower-frequency part of the signal, and, using
numerical relativity fit formulae [121–124], the posteri-
ors on Mfand χfare inferred. From the higher-frequency
part of the signal, estimates on component masses and
spins are obtained again using the same waveform model,
and the posteriors on Mfand χfare inferred using the
same fit formulae as above. From those two distributions,
a posterior distribution of the fractional differences, de-
noted by ∆Mf/¯
Mfand ∆χf/¯χfrespectively, is then com-
puted. Here, ¯
Mfand ¯χfdenote the mean values of the
distributions of Mfand χfrespectively. While we ex-
pect mass and spin differences of exactly (0,0) given a
pure signal obeying GR, the presence of detector noise
will generally yield a posterior with some non-zero spread
around (0,0).
Figure 10 shows the results of the posterior distribu-
tions on these fractional quantities. The 90% credible
regions of the quantities ∆Mf/¯
Mfand ∆χf/¯χfenclose
(0,0) as can be seen from both the one-dimensional pos-
teriors and the two-dimensional contours. GW190412 re-
sults are consistent with past observations of BBHs [161].
VI. IMPLICATIONS FOR BBH POPULATION
PROPERTIES
BBHs detected by the LIGO–Virgo network can be
used to constrain the uncertain physical processes inher-
ent to compact binary formation channels. As the first
observed BBH with definitively asymmetric masses, the
inclusion of GW190412 in the current catalog of BBHs
has a significant impact on inferred population proper-
ties. Here, we examine (i) how the addition of GW190412
to the catalog of BBHs from the first and second observ-
ing runs affects population statements; (ii) the robust-
ness of the component mass measurements of GW190412
when evaluated as part of the previously observed pop-
ulation; and (iii) whether this system’s mass ratio is a
significant outlier with respect to that population.
Using the ten significant BBH events in the catalog of
GWs from the first and second observing runs (GWTC-
1, [7]), we constrained the parameters of phenomenolog-
ical models that represent the underlying BBH popula-
tion [15]. In certain models, the mass-ratio distribution
is parameterized with a power law, p(m2|m1)∝qβq[165–
167], where βqis the spectral index of the mass ratio dis-
FIG. 10. Posteriors on fractional parameter differences of final
mass and final spin. The GR value of 0 for both the param-
eters is marked by “+”. The brown contour encloses 90%
probability and the yellow contour encloses 68% probability.
tribution. Since all 10 events from GWTC-1 are consis-
tent with symmetric masses, the posteriors for βqshowed
a preference for positive values [15], providing initial ev-
idence supporting equal-mass pairings over randomly-
drawn mass pairings [168]. However, the steepness of βq
was unconstrained, which limited our ability to determine
how prevalent equal-mass pairings are relative to their
asymmetric counterparts. The inclusion of GW190412
in the population provides a much stronger constraint
on the mass ratio spectral index, as shown in Figure 11.
Applying the population of significant events from the
first and second observing runs as well as GW190412 to
the simplest model that invokes a power-law spectrum to
the mass ratio distribution (Model B from [15]), we find
βq<2.7 (5.8) at the 90% (99%) credible level. This in-
dicates that though equal-mass pairings may still be pre-
ferred, there is significant support for asymmetric mass
pairings; the posterior population distribution [15, 169]
for this model indicates that &10% of merging BBHs
should have a mass ratio of q.0.40. In fact, the support
for βq≤0 in the recovered distribution indicates that the
true mass ratio distribution may be flat or even favor
unequal-mass pairings. This is not in tension with the
mass ratios of the already-observed population; though
all mass ratio posteriors from GWTC-1 are consistent
with q= 1, they also have significant support for lower
values. These constraints on βqare preliminary and fi-
nal results from O3 will only be obtained after analyzing
the population that includes all BBH events from this
observing run.

13
FIG. 11. Posterior on mass ratio spectral index βqwith (solid
lines) and without (dashed lines) the inclusion of GW190412.
We show inference using both the EOBNR and Phenom fam-
ilies; for the 10 events from GWTC-1 we use the publically-
available samples for both of these waveform families pre-
sented in [7], and for GW190412 we use the EOBNR PHM
and Phenom PHM posterior samples presented in this paper.
We also check whether the asymmetric mass ratio for
GW190412 is robust when the component mass posterior
distributions are reweighted using a population-informed
prior based on Model B from [15]. Since the major-
ity of observed systems are consistent with equal mass,
the mass ratio posterior for GW190412 pushes closer to-
wards equal mass when using a population-informed prior
rather than the standard uninformative priors used to
generate posterior samples. However, the mass ratio of
GW190412 is still constrained to be q < 0.43 (0.59) at the
90% (99%) credible level, compared to q < 0.38 (0.49)
using the standard priors from parameter estimation.
Using methods from [170], we test the consistency of
GW190412 with the population of BBHs inferred from
the first and second observing runs. We first construct
a population model (Model B) derived only from the
events in GWTC-1, following the prescription in [15], and
draw 11 observations from this model (representing the
10 significant BBHs from the first two observing runs
as well as GW190412). Examining the lowest mass ra-
tio drawn from each set of 107such realizations, we find
the population-weighted mass ratio posterior samples of
GW190412 lie at the 1.7+10.3
−1.3percentile of the cumulative
distribution of lowest mass ratios. This indicates that
given the BBH population properties inferred from the
first two observing runs, drawing a system with a mass
ratio analogous to GW190412 would be relatively rare.
The apparent extremity of GW190412 is likely driven by
the limited observational sample of BBHs and the lack
of constraining power on the mass ratio spectrum prior
to the observation of GW190412. Constructing a popula-
tion model that includes the observation of GW190412 in
the fit, we find GW190412 to lie at the 25+47
−17 percentile
of the cumulative distribution of lowest mass ratios, in-
dicating that GW190412 is a reasonable draw from the
updated population.
VII. ASTROPHYSICAL FORMATION
CHANNELS FOR GW190412
Multiple astrophysical channels are predicted to pro-
duce the merging BBHs identified by the LIGO–Virgo
network. The majority of these channels have mass ratio
distributions that peak near unity, but also often pre-
dict a broad tail in the distribution that extends to more
asymmetric masses. Though a wide array of formation
channels exist, each with distinct predictions for merger
rates and distributions of intrinsic BBH parameters, most
channels can be broadly categorized as the outcome of
either isolated binary stellar evolution or dynamical as-
sembly (for reviews, see [171, 172], respectively).
In the canonical isolated binary evolution scenario, by
which a compact binary progenitor achieves a tight or-
bital configuration via a common envelope phase [171,
173–178], BBH mergers with mass ratios of q.0.5
are typically found to be less common than their near-
equal-mass counterparts by an order of magnitude or
more [179–184], though certain population synthesis
modeling finds BBH mergers with asymmetric masses to
be more prevalent [185, 186]. However, even if the forma-
tion probability of asymmetric mass ratio systems is an
order of magnitude lower than the formation probabil-
ity of equal mass systems, the observation of one clearly
asymmetric mass system given the current observational
catalog is unsurprising. In contrast, the progenitor of
GW190412 is unlikely to have formed through chemically
homogeneous evolution, as this scenario typically can-
not form binaries with mass ratios below q < 0.5 [187–
189]. The asymmetric component masses of GW190412
may also suggest formation in an environment with lower
metallicity, as lower metallicities are predicted to produce
a higher rate of merging BBHs having mass ratios con-
sistent with GW190412 [178, 179, 183, 184], though this
prediction is not ubiquitous across population synthesis
models [190].
Dense stellar environments, such as globular clus-
ters [191–194], nuclear clusters [195], and young open
star clusters [196–200], are also predicted to facilitate
stellar-mass BBH mergers. Numerical modeling of dense
clusters suggests that significantly asymmetric compo-
nent masses are strongly disfavored for mergers involving
two first-generation BHs that have not undergone prior
BBH mergers (e.g., [201]). However, asymmetric com-
ponent masses may be attained by a first-generation BH
merging with a higher-generation BH that has already
undergone a prior merger or mergers [166, 202, 203]. For
formation environments such as globular clusters, this
would require low natal spins for the initial population
of BHs so that an appreciable number of merger products
can be retained in the shallow gravitational potential of
the cluster [203, 204]. Alternatively, BBH mergers with

14
asymmetric masses may be the result of massive-star col-
lisions in young star clusters, as these environments have
been shown to amplify unequal-mass BBH mergers rela-
tive to their isolated counterparts [199].
Other formation scenarios may also be efficient at gen-
erating BBH mergers with significantly asymmetric com-
ponent masses. BBHs in triple or quadruple systems can
undergo Lidov–Kozai oscillations [205, 206] that may ex-
pedite the GW inspiral of the binary. Such systems can
either exist in the galactic field with a stellar-mass outer
perturber [207–213] or in galactic nuclei with a supermas-
sive BH as the tertiary component [214–217]. Though
most modeling of hierarchical stellar systems do not in-
clude robust predictions for mass ratio distributions of
merging BBHs, certain models find galactic field triples
with asymmetric masses for the inner BBH to have a
merger fraction that is about twice as large as their equal-
mass counterparts [207]. In the context of hierarchical
triples in galactic nuclei, recent modeling predicts a sig-
nificant tail in the mass ratio distribution of merging
BBHs that extends out to mass ratios of ∼8:1 [217].
BBH mergers with significantly asymmetric component
masses are also predicted for systems formed in the disks
of active galactic nuclei [218–224]. The deep gravita-
tional potential near the vicinity of the supermassive BH
may allow for stellar-mass BHs to go through many suc-
cessive mergers without being ejected by the relativistic
recoil kick, leading to BBH mergers with highly asym-
metric masses [223, 224]. Though these channels may
not be dominant, they could explain a fraction of the
sources observed by the LIGO–Virgo network.
In summary, though the mass ratio of GW190412 is
the most extreme of any BBH observed to date, it is con-
sistent with the mass ratios predicted from a number of
proposed BBH formation channels. Many astrophysical
channels predict that near-equal-mass BBH mergers are
more common than mergers with significantly asymmet-
ric component masses. However, as the observational
sample of BBHs grows, it is not unexpected that we
would observe a system such as GW190412 that occu-
pies a less probable region of intrinsic parameter space.
Future detections of BBHs will enable tighter constraints
on the rate of GW190412-like systems.
VIII. CONCLUSIONS
Every observing run in the advanced GW detector era
has delivered new science. After the first observations
of BBHs in the first observing run, and the continued
observation of BBHs as well as the multimessenger ob-
servation of a binary neutron star in the second observing
run [6, 225], O3 has been digging deeper into the popu-
lations of compact binary mergers. The observation of a
likely second neutron-star binary in O3 has already been
published [8], and here we presented another GW obser-
vation with previously unobserved features.
GW190412 was a highly significant event, with a com-
bined SNR of 19 across all three GW detectors. It is the
first binary observed that consists of two BHs of signifi-
cantly asymmetric component masses. With 99% prob-
ability, the primary BH has more than twice the mass
of its lighter companion. The measurement of asym-
metric masses is also robust even when the properties of
GW190412 are inferred using a population-based prior.
This observation indicates that the astrophysical BBH
population includes unequal-mass systems.
GW190412 is also a rich source from a more fundamen-
tal point of view. GR dictates that gravitational radia-
tion from compact binaries is dominated by a quadrupo-
lar structure, but it also contains weaker contributions
from subdominant multipoles. Here we provided conclu-
sive evidence that at least the second most important
multipole – the (`, |m|) = (3,3) multipole – makes a sig-
nificant, measurable contribution to the observed data.
As a result, the orientation of the binary is more accu-
rately determined and tighter bounds are obtained on
relevant intrinsic source parameters such as the mass ra-
tio and spin of the system.
The asymmetric mass ratio of GW190412 allows the
primary spin to have a more measurable effect on the sig-
nal. We find the primary spin magnitude to be 0.43+0.16
−0.26,
which is the strongest constraint on the individual spin
magnitude of a BH using GWs so far. Though we only
find marginal statistical hints of precession in the data,
the results presented here illustrate that we confidently
disfavor strong precession (as would be characterized by
a large in-plane spin parameter).
GW190412 is a BBH that occupies a previously un-
observed region of parameter space. As we continue to
increase the sensitivity of our detectors and the time
spent observing, we will gain a more complete picture
of the BBH population. Future observations of similar
types of binaries, or even more extreme mass ratios, will
sharpen our understanding of their abundance and might
help constrain formation mechanisms for such systems.
GW190412 also shows that numerical and analytical ad-
vances in modeling coalescing binaries in previously un-
explored regimes remains crucial for the analysis of cur-
rent and future GW data. The most recent and most
complete signal models robustly identified GW190412’s
source properties and showed consistency with GR. Sys-
tematic differences are visible and will become more im-
portant when we observe stronger signals, pointing to the
necessity for future work in this area.
LIGO and Virgo data containing GW190412, and sam-
ples from a subset of the posterior probability distribu-
tions of the source parameters [105], are available from
the Gravitational Wave Open Science Center [226].
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support of the
United States National Science Foundation (NSF) for
the construction and operation of the LIGO Laboratory

15
and Advanced LIGO as well as the Science and Tech-
nology Facilities Council (STFC) of the United King-
dom, the Max-Planck-Society (MPS), and the State of
Niedersachsen/Germany for support of the construction
of Advanced LIGO and construction and operation of
the GEO600 detector. Additional support for Advanced
LIGO was provided by the Australian Research Council.
The authors gratefully acknowledge the Italian Istituto
Nazionale di Fisica Nucleare (INFN), the French Centre
National de la Recherche Scientifique (CNRS) and the
Foundation for Fundamental Research on Matter sup-
ported by the Netherlands Organisation for Scientific Re-
search, for the construction and operation of the Virgo
detector and the creation and support of the EGO consor-
tium. The authors also gratefully acknowledge research
support from these agencies as well as by the Council of
Scientific and Industrial Research of India, the Depart-
ment of Science and Technology, India, the Science & En-
gineering Research Board (SERB), India, the Ministry of
Human Resource Development, India, the Spanish Agen-
cia Estatal de Investigaci´on, the Vicepresid`encia i Consel-
leria d’Innovaci´o, Recerca i Turisme and the Conselleria
d’Educaci´o i Universitat del Govern de les Illes Balears,
the Conselleria d’Educaci´o, Investigaci´o, Cultura i Es-
port de la Generalitat Valenciana, the National Science
Centre of Poland, the Swiss National Science Foundation
(SNSF), the Russian Foundation for Basic Research, the
Russian Science Foundation, the European Commission,
the European Regional Development Funds (ERDF), the
Royal Society, the Scottish Funding Council, the Scot-
tish Universities Physics Alliance, the Hungarian Scien-
tific Research Fund (OTKA), the Lyon Institute of Ori-
gins (LIO), the Paris ˆ
Ile-de-France Region, the National
Research, Development and Innovation Office Hungary
(NKFIH), the National Research Foundation of Korea,
Industry Canada and the Province of Ontario through
the Ministry of Economic Development and Innovation,
the Natural Science and Engineering Research Council
Canada, the Canadian Institute for Advanced Research,
the Brazilian Ministry of Science, Technology, Innova-
tions, and Communications, the International Center for
Theoretical Physics South American Institute for Fun-
damental Research (ICTP-SAIFR), the Research Grants
Council of Hong Kong, the National Natural Science
Foundation of China (NSFC), the Leverhulme Trust, the
Research Corporation, the Ministry of Science and Tech-
nology (MOST), Taiwan and the Kavli Foundation. The
authors gratefully acknowledge the support of the NSF,
STFC, INFN and CNRS for provision of computational
resources.
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LIGO-P190412-v9
Authors
R. Abbott,1T. D. Abbott,2S. Abraham,3F. Acernese,4, 5 K. Ackley,6C. Adams,7R. X. Adhikari,1V. B. Adya,8
C. Affeldt,9, 10 M. Agathos,11, 12 K. Agatsuma,13 N. Aggarwal,14 O. D. Aguiar,15 A. Aich,16 L. Aiello,17, 18
A. Ain,3P. Ajith,19 S. Akcay,11 G. Allen,20 A. Allocca,21 P. A. Altin,8A. Amato,22 S. Anand,1A. Ananyeva,1
S. B. Anderson,1W. G. Anderson,23 S. V. Angelova,24 S. Ansoldi,25, 26 S. Antier,27 S. Appert,1K. Arai,1
M. C. Araya,1J. S. Areeda,28 M. Ar`ene,27 N. Arnaud,29, 30 S. M. Aronson,31 K. G. Arun,32 Y. Asali,33
S. Ascenzi,17, 34 G. Ashton,6S. M. Aston,7P. Astone,35 F. Aubin,36 P. Aufmuth,10 K. AultONeal,37 C. Austin,2
V. Avendano,38 S. Babak,27 P. Bacon,27 F. Badaracco,17, 18 M. K. M. Bader,39 S. Bae,40 A. M. Baer,41 J. Baird,27
F. Baldaccini,42, 43 G. Ballardin,30 S. W. Ballmer,44 A. Bals,37 A. Balsamo,41 G. Baltus,45 S. Banagiri,46
D. Bankar,3R. S. Bankar,3J. C. Barayoga,1C. Barbieri,47, 48 B. C. Barish,1D. Barker,49 K. Barkett,50
P. Barneo,51 F. Barone,52, 5 B. Barr,53 L. Barsotti,54 M. Barsuglia,27 D. Barta,55 J. Bartlett,49 I. Bartos,31
R. Bassiri,56 A. Basti,57, 21 M. Bawaj,58, 43 J. C. Bayley,53 M. Bazzan,59,60 B. B´ecsy,61 M. Bejger,62 I. Belahcene,29
A. S. Bell,53 D. Beniwal,63 M. G. Benjamin,37 R. Benkel,64 J. D. Bentley,13 F. Bergamin,9B. K. Berger,56
G. Bergmann,9, 10 S. Bernuzzi,11 C. P. L. Berry,14 D. Bersanetti,65 A. Bertolini,39 J. Betzwieser,7R. Bhandare,66
A. V. Bhandari,3J. Bidler,28 E. Biggs,23 I. A. Bilenko,67 G. Billingsley,1R. Birney,68 O. Birnholtz,69, 70
S. Biscans,1, 54 M. Bischi,71, 72 S. Biscoveanu,54 A. Bisht,10 G. Bissenbayeva,16 M. Bitossi,30, 21 M. A. Bizouard,73
J. K. Blackburn,1J. Blackman,50 C. D. Blair,7D. G. Blair,74 R. M. Blair,49 F. Bobba,75, 76 N. Bode,9, 10 M. Boer,73
Y. Boetzel,77 G. Bogaert,73 F. Bondu,78 E. Bonilla,56 R. Bonnand,36 P. Booker,9, 10 B. A. Boom,39 R. Bork,1
V. Boschi,21 S. Bose,3V. Bossilkov,74 J. Bosveld,74 Y. Bouffanais,59, 60 A. Bozzi,30 C. Bradaschia,21 P. R. Brady,23
A. Bramley,7M. Branchesi,17, 18 J. E. Brau,79 M. Breschi,11 T. Briant,80 J. H. Briggs,53 F. Brighenti,71, 72
A. Brillet,73 M. Brinkmann,9, 10 R. Brito,64 P. Brockill,23 A. F. Brooks,1J. Brooks,30 D. D. Brown,63 S. Brunett,1
G. Bruno,81 R. Bruntz,41 A. Buikema,54 T. Bulik,82 H. J. Bulten,83, 39 A. Buonanno,64, 84 D. Buskulic,36
R. L. Byer,56 M. Cabero,9, 10 L. Cadonati,85 G. Cagnoli,86 C. Cahillane,1J. Calder´on Bustillo,6J. D. Callaghan,53
T. A. Callister,1E. Calloni,87, 5 J. B. Camp,88 M. Canepa,89,65 K. C. Cannon,90 H. Cao,63 J. Cao,91
G. Carapella,75, 76 F. Carbognani,30 S. Caride,92 M. F. Carney,14 G. Carullo,57, 21 J. Casanueva Diaz,21
C. Casentini,93, 34 J. Casta˜neda,51 S. Caudill,39 M. Cavagli`a,94 F. Cavalier,29 R. Cavalieri,30 G. Cella,21
P. Cerd´a-Dur´an,95 E. Cesarini,96, 34 O. Chaibi,73 K. Chakravarti,3C. Chan,90 M. Chan,53 S. Chao,97 P. Charlton,98
E. A. Chase,14 E. Chassande-Mottin,27 D. Chatterjee,23 M. Chaturvedi,66 K. Chatziioannou,99, 100 H. Y. Chen,101
X. Chen,74 Y. Chen,50 H.-P. Cheng,31 C. K. Cheong,102 H. Y. Chia,31 F. Chiadini,103, 76 R. Chierici,104
A. Chincarini,65 A. Chiummo,30 G. Cho,105 H. S. Cho,106 M. Cho,84 N. Christensen,73 Q. Chu,74 S. Chua,80
K. W. Chung,102 S. Chung,74 G. Ciani,59, 60 P. Ciecielag,62 M. Cie´slar,62 A. A. Ciobanu,63 R. Ciolfi,107, 60
F. Cipriano,73 A. Cirone,89, 65 F. Clara,49 J. A. Clark,85 P. Clearwater,108 S. Clesse,81 F. Cleva,73 E. Coccia,17, 18
P.-F. Cohadon,80 D. Cohen,29 M. Colleoni,109 C. G. Collette,110 C. Collins,13 M. Colpi,47, 48 M. Constancio Jr.,15
L. Conti,60 S. J. Cooper,13 P. Corban,7T. R. Corbitt,2I. Cordero-Carri´on,111 S. Corezzi,42, 43 K. R. Corley,33
N. Cornish,61 D. Corre,29 A. Corsi,92 S. Cortese,30 C. A. Costa,15 R. Cotesta,64 M. W. Coughlin,1
S. B. Coughlin,112, 14 J.-P. Coulon,73 S. T. Countryman,33 P. Couvares,1P. B. Covas,109 D. M. Coward,74
M. J. Cowart,7D. C. Coyne,1R. Coyne,113 J. D. E. Creighton,23 T. D. Creighton,16 J. Cripe,2M. Croquette,80
S. G. Crowder,114 J.-R. Cudell,45 T. J. Cullen,2A. Cumming,53 R. Cummings,53 L. Cunningham,53 E. Cuoco,30
M. Curylo,82 T. Dal Canton,64 G. D´alya,115 A. Dana,56 L. M. Daneshgaran-Bajastani,116 B. D’Angelo,89, 65
S. L. Danilishin,9, 10 S. D’Antonio,34 K. Danzmann,10, 9 C. Darsow-Fromm,117 A. Dasgupta,118 L. E. H. Datrier,53
V. Dattilo,30 I. Dave,66 M. Davier,29 G. S. Davies,119 D. Davis,44 E. J. Daw,120 D. DeBra,56 M. Deenadayalan,3
J. Degallaix,22 M. De Laurentis,87, 5 S. Del´eglise,80 M. Delfavero,69 N. De Lillo,53 W. Del Pozzo,57,21
L. M. DeMarchi,14 V. D’Emilio,112 N. Demos,54 T. Dent,119 R. De Pietri,121, 122 R. De Rosa,87, 5 C. De Rossi,30
R. DeSalvo,123 O. de Varona,9, 10 S. Dhurandhar,3M. C. D´ıaz,16 M. Diaz-Ortiz Jr.,31 T. Dietrich,39 L. Di Fiore,5
C. Di Fronzo,13 C. Di Giorgio,75, 76 F. Di Giovanni,95 M. Di Giovanni,124, 125 T. Di Girolamo,87, 5 A. Di Lieto,57, 21
B. Ding,110 S. Di Pace,126, 35 I. Di Palma,126, 35 F. Di Renzo,57, 21 A. K. Divakarla,31 A. Dmitriev,13 Z. Doctor,101
F. Donovan,54 K. L. Dooley,112 S. Doravari,3I. Dorrington,112 T. P. Downes,23 M. Drago,17, 18 J. C. Driggers,49
Z. Du,91 J.-G. Ducoin,29 P. Dupej,53 O. Durante,75, 76 D. D’Urso,127, 128 S. E. Dwyer,49 P. J. Easter,6G. Eddolls,53
B. Edelman,79 T. B. Edo,120 O. Edy,129 A. Effler,7P. Ehrens,1J. Eichholz,8S. S. Eikenberry,31 M. Eisenmann,36
R. A. Eisenstein,54 A. Ejlli,112 L. Errico,87, 5 R. C. Essick,101 H. Estelles,109 D. Estevez,36 Z. B. Etienne,130
T. Etzel,1M. Evans,54 T. M. Evans,7B. E. Ewing,131 V. Fafone,93, 34, 17 S. Fairhurst,112 X. Fan,91 S. Farinon,65
B. Farr,79 W. M. Farr,99, 100 E. J. Fauchon-Jones,112 M. Favata,38 M. Fays,120 M. Fazio,132 J. Feicht,1M. M. Fejer,56
F. Feng,27 E. Fenyvesi,55,133 D. L. Ferguson,85 A. Fernandez-Galiana,54 I. Ferrante,57, 21 E. C. Ferreira,15

21
T. A. Ferreira,15 F. Fidecaro,57, 21 I. Fiori,30 D. Fiorucci,17, 18 M. Fishbach,101 R. P. Fisher,41 R. Fittipaldi,134, 76
M. Fitz-Axen,46 V. Fiumara,135, 76 R. Flaminio,36, 136 E. Floden,46 E. Flynn,28 H. Fong,90 J. A. Font,95, 137
P. W. F. Forsyth,8J.-D. Fournier,73 S. Frasca,126, 35 F. Frasconi,21 Z. Frei,115 A. Freise,13 R. Frey,79 V. Frey,29
P. Fritschel,54 V. V. Frolov,7G. Fronz`e,138 P. Fulda,31 M. Fyffe,7H. A. Gabbard,53 B. U. Gadre,64 S. M. Gaebel,13
J. R. Gair,64 S. Galaudage,6D. Ganapathy,54 A. Ganguly,19 S. G. Gaonkar,3C. Garc´ıa-Quir´os,109 F. Garufi,87, 5
B. Gateley,49 S. Gaudio,37 V. Gayathri,139 G. Gemme,65 E. Genin,30 A. Gennai,21 D. George,20 J. George,66
L. Gergely,140 S. Ghonge,85 Abhirup Ghosh,64 Archisman Ghosh,141, 142, 143, 39 S. Ghosh,23 B. Giacomazzo,124, 125
J. A. Giaime,2, 7 K. D. Giardina,7D. R. Gibson,68 C. Gier,24 K. Gill,33 J. Glanzer,2J. Gniesmer,117 P. Godwin,131
E. Goetz,2, 94 R. Goetz,31 N. Gohlke,9, 10 B. Goncharov,6G. Gonz´alez,2A. Gopakumar,144 S. E. Gossan,1
M. Gosselin,30, 57, 21 R. Gouaty,36 B. Grace,8A. Grado,145, 5 M. Granata,22 A. Grant,53 S. Gras,54 P. Grassia,1
C. Gray,49 R. Gray,53 G. Greco,71, 72 A. C. Green,31 R. Green,112 E. M. Gretarsson,37 H. L. Griggs,85
G. Grignani,42, 43 A. Grimaldi,124,125 S. J. Grimm,17, 18 H. Grote,112 S. Grunewald,64 P. Gruning,29
G. M. Guidi,71, 72 A. R. Guimaraes,2G. Guix´e,51 H. K. Gulati,118 Y. Guo,39 A. Gupta,131 Anchal Gupta,1
P. Gupta,39 E. K. Gustafson,1R. Gustafson,146 L. Haegel,109 O. Halim,18, 17 E. D. Hall,54 E. Z. Hamilton,112
G. Hammond,53 M. Haney,77 M. M. Hanke,9, 10 J. Hanks,49 C. Hanna,131 M. D. Hannam,112 O. A. Hannuksela,102
T. J. Hansen,37 J. Hanson,7T. Harder,73 T. Hardwick,2K. Haris,19 J. Harms,17, 18 G. M. Harry,147 I. W. Harry,129
R. K. Hasskew,7C.-J. Haster,54 K. Haughian,53 F. J. Hayes,53 J. Healy,69 A. Heidmann,80 M. C. Heintze,7
J. Heinze,9, 10 H. Heitmann,73 F. Hellman,148 P. Hello,29 G. Hemming,30 M. Hendry,53 I. S. Heng,53 E. Hennes,39
J. Hennig,9, 10 M. Heurs,9, 10 S. Hild,149, 53 T. Hinderer,143, 39, 141 S. Y. Hoback,28, 147 S. Hochheim,9,10 E. Hofgard,56
D. Hofman,22 A. M. Holgado,20 N. A. Holland,8K. Holt,7D. E. Holz,101 P. Hopkins,112 C. Horst,23 J. Hough,53
E. J. Howell,74 C. G. Hoy,112 Y. Huang,54 M. T. H¨ubner,6E. A. Huerta,20 D. Huet,29 B. Hughey,37 V. Hui,36
S. Husa,109 S. H. Huttner,53 R. Huxford,131 T. Huynh-Dinh,7B. Idzkowski,82 A. Iess,93, 34 H. Inchauspe,31
C. Ingram,63 G. Intini,126, 35 J.-M. Isac,80 M. Isi,54 B. R. Iyer,19 T. Jacqmin,80 S. J. Jadhav,150 S. P. Jadhav,3
A. L. James,112 K. Jani,85 N. N. Janthalur,150 P. Jaranowski,151 D. Jariwala,31 R. Jaume,109 A. C. Jenkins,152
J. Jiang,31 G. R. Johns,41 N. K. Johnson-McDaniel,12 A. W. Jones,13 D. I. Jones,153 J. D. Jones,49 P. Jones,13
R. Jones,53 R. J. G. Jonker,39 L. Ju,74 J. Junker,9, 10 C. V. Kalaghatgi,112 V. Kalogera,14 B. Kamai,1
S. Kandhasamy,3G. Kang,40 J. B. Kanner,1S. J. Kapadia,19 S. Karki,79 R. Kashyap,19 M. Kasprzack,1
W. Kastaun,9, 10 S. Katsanevas,30 E. Katsavounidis,54 W. Katzman,7S. Kaufer,10 K. Kawabe,49 F. K´ef´elian,73
D. Keitel,129 A. Keivani,33 R. Kennedy,120 J. S. Key,154 S. Khadka,56 F. Y. Khalili,67 I. Khan,17, 34 S. Khan,9, 10
Z. A. Khan,91 E. A. Khazanov,155 N. Khetan,17, 18 M. Khursheed,66 N. Kijbunchoo,8Chunglee Kim,156 G. J. Kim,85
J. C. Kim,157 K. Kim,102 W. Kim,63 W. S. Kim,158 Y.-M. Kim,159 C. Kimball,14 P. J. King,49 M. Kinley-Hanlon,53
R. Kirchhoff,9, 10 J. S. Kissel,49 L. Kleybolte,117 S. Klimenko,31 T. D. Knowles,130 E. Knyazev,54 P. Koch,9, 10
S. M. Koehlenbeck,9, 10 G. Koekoek,39, 149 S. Koley,39 V. Kondrashov,1A. Kontos,160 N. Koper,9, 10 M. Korobko,117
W. Z. Korth,1M. Kovalam,74 D. B. Kozak,1V. Kringel,9, 10 N. V. Krishnendu,9, 10 A. Kr´olak,161, 162 N. Krupinski,23
G. Kuehn,9, 10 A. Kumar,150 P. Kumar,163 Rahul Kumar,49 Rakesh Kumar,118 S. Kumar,19 L. Kuo,97
A. Kutynia,161 B. D. Lackey,64 D. Laghi,57, 21 E. Lalande,164 T. L. Lam,102 A. Lamberts,73, 165 M. Landry,49
B. B. Lane,54 R. N. Lang,166 J. Lange,69 B. Lantz,56 R. K. Lanza,54 I. La Rosa,36 A. Lartaux-Vollard,29
P. D. Lasky,6M. Laxen,7A. Lazzarini,1C. Lazzaro,60 P. Leaci,126, 35 S. Leavey,9, 10 Y. K. Lecoeuche,49
C. H. Lee,106 H. M. Lee,167 H. W. Lee,157 J. Lee,105 K. Lee,56 J. Lehmann,9, 10 N. Leroy,29 N. Letendre,36
Y. Levin,6A. K. Y. Li,102 J. Li,91 K. li,102 T. G. F. Li,102 X. Li,50 F. Linde,168, 39 S. D. Linker,116 J. N. Linley,53
T. B. Littenberg,169 J. Liu,9, 10 X. Liu,23 M. Llorens-Monteagudo,95 R. K. L. Lo,1A. Lockwood,170 L. T. London,54
A. Longo,171, 172 M. Lorenzini,17, 18 V. Loriette,173 M. Lormand,7G. Losurdo,21 J. D. Lough,9, 10 C. O. Lousto,69
G. Lovelace,28 H. L¨uck,10, 9 D. Lumaca,93, 34 A. P. Lundgren,129 Y. Ma,50 R. Macas,112 S. Macfoy,24 M. MacInnis,54
D. M. Macleod,112 I. A. O. MacMillan,147 A. Macquet,73 I. Maga˜na Hernandez,23 F. Maga˜na-Sandoval,31
R. M. Magee,131 E. Majorana,35 I. Maksimovic,173 A. Malik,66 N. Man,73 V. Mandic,46 V. Mangano,53, 126, 35
G. L. Mansell,49, 54 M. Manske,23 M. Mantovani,30 M. Mapelli,59, 60 F. Marchesoni,58, 43, 174 F. Marion,36
S. M´arka,33 Z. M´arka,33 C. Markakis,12 A. S. Markosyan,56 A. Markowitz,1E. Maros,1A. Marquina,111
S. Marsat,27 F. Martelli,71, 72 I. W. Martin,53 R. M. Martin,38 V. Martinez,86 D. V. Martynov,13 H. Masalehdan,117
K. Mason,54 E. Massera,120 A. Masserot,36 T. J. Massinger,54 M. Masso-Reid,53 S. Mastrogiovanni,27 A. Matas,64
F. Matichard,1, 54 N. Mavalvala,54 E. Maynard,2J. J. McCann,74 R. McCarthy,49 D. E. McClelland,8
S. McCormick,7L. McCuller,54 S. C. McGuire,175 C. McIsaac,129 J. McIver,1D. J. McManus,8T. McRae,8
S. T. McWilliams,130 D. Meacher,23 G. D. Meadors,6M. Mehmet,9, 10 A. K. Mehta,19 E. Mejuto Villa,123, 76
A. Melatos,108 G. Mendell,49 R. A. Mercer,23 L. Mereni,22 K. Merfeld,79 E. L. Merilh,49 J. D. Merritt,79

22
M. Merzougui,73 S. Meshkov,1C. Messenger,53 C. Messick,176 R. Metzdorff,80 P. M. Meyers,108 F. Meylahn,9, 10
A. Mhaske,3A. Miani,124, 125 H. Miao,13 I. Michaloliakos,31 C. Michel,22 H. Middleton,108 L. Milano,87, 5
A. L. Miller,31, 126, 35 S. Miller,1M. Millhouse,108 J. C. Mills,112 E. Milotti,177,26 M. C. Milovich-Goff,116
O. Minazzoli,73, 178 Y. Minenkov,34 A. Mishkin,31 C. Mishra,179 T. Mistry,120 S. Mitra,3V. P. Mitrofanov,67
G. Mitselmakher,31 R. Mittleman,54 G. Mo,54 K. Mogushi,94 S. R. P. Mohapatra,54 S. R. Mohite,23
M. Molina-Ruiz,148 M. Mondin,116 M. Montani,71, 72 C. J. Moore,13 D. Moraru,49 F. Morawski,62 G. Moreno,49
S. Morisaki,90 B. Mours,180 C. M. Mow-Lowry,13 S. Mozzon,129 F. Muciaccia,126, 35 Arunava Mukherjee,53
D. Mukherjee,131 S. Mukherjee,16 Subroto Mukherjee,118 N. Mukund,9, 10 A. Mullavey,7J. Munch,63
E. A. Mu˜niz,44 P. G. Murray,53 A. Nagar,96, 138, 181 I. Nardecchia,93, 34 L. Naticchioni,126, 35 R. K. Nayak,182
B. F. Neil,74 J. Neilson,123, 76 G. Nelemans,183, 39 T. J. N. Nelson,7M. Nery,9, 10 A. Neunzert,146 K. Y. Ng,54
S. Ng,63 C. Nguyen,27 P. Nguyen,79 D. Nichols,143, 39 S. A. Nichols,2S. Nissanke,143, 39 F. Nocera,30
M. Noh,54 C. North,112 D. Nothard,184 L. K. Nuttall,129 J. Oberling,49 B. D. O’Brien,31 G. Oganesyan,17, 18
G. H. Ogin,185 J. J. Oh,158 S. H. Oh,158 F. Ohme,9, 10 H. Ohta,90 M. A. Okada,15 M. Oliver,109 C. Olivetto,30
P. Oppermann,9, 10 Richard J. Oram,7B. O’Reilly,7R. G. Ormiston,46 L. F. Ortega,31 R. O’Shaughnessy,69
S. Ossokine,64 C. Osthelder,1D. J. Ottaway,63 H. Overmier,7B. J. Owen,92 A. E. Pace,131 G. Pagano,57, 21
M. A. Page,74 G. Pagliaroli,17, 18 A. Pai,139 S. A. Pai,66 J. R. Palamos,79 O. Palashov,155 C. Palomba,35
H. Pan,97 P. K. Panda,150 P. T. H. Pang,39 C. Pankow,14 F. Pannarale,126, 35 B. C. Pant,66 F. Paoletti,21
A. Paoli,30 A. Parida,3W. Parker,7, 175 D. Pascucci,53, 39 A. Pasqualetti,30 R. Passaquieti,57, 21 D. Passuello,21
B. Patricelli,57, 21 E. Payne,6B. L. Pearlstone,53 T. C. Pechsiri,31 A. J. Pedersen,44 M. Pedraza,1A. Pele,7
S. Penn,186 A. Perego,124, 125 C. J. Perez,49 C. P´erigois,36 A. Perreca,124, 125 S. Perri`es,104 J. Petermann,117
H. P. Pfeiffer,64 M. Phelps,9, 10 K. S. Phukon,3, 168, 39 O. J. Piccinni,126,35 M. Pichot,73 M. Piendibene,57, 21
F. Piergiovanni,71, 72 V. Pierro,123, 76 G. Pillant,30 L. Pinard,22 I. M. Pinto,123, 76, 96 K. Piotrzkowski,81 M. Pirello,49
M. Pitkin,187 W. Plastino,171, 172 R. Poggiani,57, 21 D. Y. T. Pong,102 S. Ponrathnam,3P. Popolizio,30
E. K. Porter,27 J. Powell,188 A. K. Prajapati,118 K. Prasai,56 R. Prasanna,150 G. Pratten,13 T. Prestegard,23
M. Principe,123, 96, 76 G. A. Prodi,124, 125 L. Prokhorov,13 M. Punturo,43 P. Puppo,35 M. P¨urrer,64 H. Qi,112
V. Quetschke,16 P. J. Quinonez,37 F. J. Raab,49 G. Raaijmakers,143, 39 H. Radkins,49 N. Radulesco,73 P. Raffai,115
H. Rafferty,189 S. Raja,66 C. Rajan,66 B. Rajbhandari,92 M. Rakhmanov,16 K. E. Ramirez,16 A. Ramos-Buades,109
Javed Rana,3K. Rao,14 P. Rapagnani,126, 35 V. Raymond,112 M. Razzano,57,21 J. Read,28 T. Regimbau,36
L. Rei,65 S. Reid,24 D. H. Reitze,1, 31 P. Rettegno,138, 190 F. Ricci,126, 35 C. J. Richardson,37 J. W. Richardson,1
P. M. Ricker,20 G. Riemenschneider,190, 138 K. Riles,146 M. Rizzo,14 N. A. Robertson,1, 53 F. Robinet,29 A. Rocchi,34
R. D. Rodriguez-Soto,37 L. Rolland,36 J. G. Rollins,1V. J. Roma,79 M. Romanelli,78 R. Romano,4, 5 C. L. Romel,49
I. M. Romero-Shaw,6J. H. Romie,7C. A. Rose,23 D. Rose,28 K. Rose,184 D. Rosi´nska,82 S. G. Rosofsky,20
M. P. Ross,170 S. Rowan,53 S. J. Rowlinson,13 P. K. Roy,16 Santosh Roy,3Soumen Roy,191 P. Ruggi,30 G. Rutins,68
K. Ryan,49 S. Sachdev,131 T. Sadecki,49 M. Sakellariadou,152 O. S. Salafia,192, 47, 48 L. Salconi,30 M. Saleem,32
A. Samajdar,39 E. J. Sanchez,1L. E. Sanchez,1N. Sanchis-Gual,193 J. R. Sanders,194 K. A. Santiago,38 E. Santos,73
N. Sarin,6B. Sassolas,22 B. S. Sathyaprakash,131, 112 O. Sauter,36 R. L. Savage,49 V. Savant,3D. Sawant,139
S. Sayah,22 D. Schaetzl,1P. Schale,79 M. Scheel,50 J. Scheuer,14 P. Schmidt,13 R. Schnabel,117 R. M. S. Schofield,79
A. Sch¨onbeck,117 E. Schreiber,9, 10 B. W. Schulte,9, 10 B. F. Schutz,112 O. Schwarm,185 E. Schwartz,7J. Scott,53
S. M. Scott,8E. Seidel,20 D. Sellers,7A. S. Sengupta,191 N. Sennett,64 D. Sentenac,30 V. Sequino,65
A. Sergeev,155 Y. Setyawati,9, 10 D. A. Shaddock,8T. Shaffer,49 M. S. Shahriar,14 A. Sharma,17, 18 P. Sharma,66
P. Shawhan,84 H. Shen,20 M. Shikauchi,90 R. Shink,164 D. H. Shoemaker,54 D. M. Shoemaker,85 K. Shukla,148
S. ShyamSundar,66 K. Siellez,85 M. Sieniawska,62 D. Sigg,49 L. P. Singer,88 D. Singh,131 N. Singh,82 A. Singha,53
A. Singhal,17, 35 A. M. Sintes,109 V. Sipala,127, 128 V. Skliris,112 B. J. J. Slagmolen,8T. J. Slaven-Blair,74
J. Smetana,13 J. R. Smith,28 R. J. E. Smith,6S. Somala,195 E. J. Son,158 S. Soni,2B. Sorazu,53 V. Sordini,104
F. Sorrentino,65 T. Souradeep,3E. Sowell,92 A. P. Spencer,53 M. Spera,59, 60 A. K. Srivastava,118 V. Srivastava,44
K. Staats,14 C. Stachie,73 M. Standke,9, 10 D. A. Steer,27 M. Steinke,9, 10 J. Steinlechner,117, 53 S. Steinlechner,117
D. Steinmeyer,9, 10 S. Stevenson,188 D. Stocks,56 D. J. Stops,13 M. Stover,184 K. A. Strain,53 G. Stratta,196, 72
A. Strunk,49 R. Sturani,197 A. L. Stuver,198 S. Sudhagar,3V. Sudhir,54 T. Z. Summerscales,199 L. Sun,1S. Sunil,118
A. Sur,62 J. Suresh,90 P. J. Sutton,112 B. L. Swinkels,39 M. J. Szczepa´nczyk,31 M. Tacca,39 S. C. Tait,53
C. Talbot,6A. J. Tanasijczuk,81 D. B. Tanner,31 D. Tao,1M. T´apai,140 A. Tapia,28 E. N. Tapia San Martin,39
J. D. Tasson,200 R. Taylor,1R. Tenorio,109 L. Terkowski,117 M. P. Thirugnanasambandam,3M. Thomas,7
P. Thomas,49 J. E. Thompson,112 S. R. Thondapu,66 K. A. Thorne,7E. Thrane,6C. L. Tinsman,6
T. R. Saravanan,3Shubhanshu Tiwari,77, 124, 125 S. Tiwari,144 V. Tiwari,112 K. Toland,53 M. Tonelli,57, 21

23
Z. Tornasi,53 A. Torres-Forn´e,64 C. I. Torrie,1I. Tosta e Melo,127, 128 D. T¨oyr¨a,8E. A. Trail,2F. Travasso,58, 43
G. Traylor,7M. C. Tringali,82 A. Tripathee,146 A. Trovato,27 R. J. Trudeau,1K. W. Tsang,39 M. Tse,54 R. Tso,50
L. Tsukada,90 D. Tsuna,90 T. Tsutsui,90 M. Turconi,73 A. S. Ubhi,13 R. Udall,85 K. Ueno,90 D. Ugolini,189
C. S. Unnikrishnan,144 A. L. Urban,2S. A. Usman,101 A. C. Utina,53 H. Vahlbruch,10 G. Vajente,1G. Valdes,2
M. Valentini,124, 125 N. van Bakel,39 M. van Beuzekom,39 J. F. J. van den Brand,83, 149, 39 C. Van Den Broeck,39,201
D. C. Vander-Hyde,44 L. van der Schaaf,39 J. V. Van Heijningen,74 A. A. van Veggel,53 M. Vardaro,168, 39
V. Varma,50 S. Vass,1M. Vas´uth,55 A. Vecchio,13 G. Vedovato,60 J. Veitch,53 P. J. Veitch,63 K. Venkateswara,170
G. Venugopalan,1D. Verkindt,36 D. Veske,33 F. Vetrano,71, 72 A. Vicer´e,71, 72 A. D. Viets,202 S. Vinciguerra,13
D. J. Vine,68 J.-Y. Vinet,73 S. Vitale,54 Francisco Hernandez Vivanco,6T. Vo,44 H. Vocca,42, 43 C. Vorvick,49
S. P. Vyatchanin,67 A. R. Wade,8L. E. Wade,184 M. Wade,184 R. Walet,39 M. Walker,28 G. S. Wallace,24
L. Wallace,1S. Walsh,23 J. Z. Wang,146 S. Wang,20 W. H. Wang,16 R. L. Ward,8Z. A. Warden,37
J. Warner,49 M. Was,36 J. Watchi,110 B. Weaver,49 L.-W. Wei,9, 10 M. Weinert,9,10 A. J. Weinstein,1
R. Weiss,54 F. Wellmann,9, 10 L. Wen,74 P. Weßels,9, 10 J. W. Westhouse,37 K. Wette,8J. T. Whelan,69
B. F. Whiting,31 C. Whittle,54 D. M. Wilken,9, 10 D. Williams,53 J. L. Willis,1B. Willke,10, 9 W. Winkler,9,10
C. C. Wipf,1H. Wittel,9, 10 G. Woan,53 J. Woehler,9, 10 J. K. Wofford,69 C. Wong,102 J. L. Wright,53
D. S. Wu,9, 10 D. M. Wysocki,69 L. Xiao,1H. Yamamoto,1L. Yang,132 Y. Yang,31 Z. Yang,46 M. J. Yap,8
M. Yazback,31 D. W. Yeeles,112 Hang Yu,54 Haocun Yu,54 S. H. R. Yuen,102 A. K. Zadro˙zny,16 A. Zadro˙zny,161
M. Zanolin,37 T. Zelenova,30 J.-P. Zendri,60 M. Zevin,14 J. Zhang,74 L. Zhang,1T. Zhang,53 C. Zhao,74
G. Zhao,110 M. Zhou,14 Z. Zhou,14 X. J. Zhu,6A. B. Zimmerman,176 M. E. Zucker,54, 1 and J. Zweizig1
(The LIGO Scientific Collaboration and the Virgo Collaboration)
1LIGO, California Institute of Technology, Pasadena, CA 91125, USA
2Louisiana State University, Baton Rouge, LA 70803, USA
3Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
4Dipartimento di Farmacia, Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy
5INFN, Sezione di Napoli, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
6OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia
7LIGO Livingston Observatory, Livingston, LA 70754, USA
8OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia
9Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany
10Leibniz Universit¨at Hannover, D-30167 Hannover, Germany
11Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit¨at Jena, D-07743 Jena, Germany
12University of Cambridge, Cambridge CB2 1TN, UK
13University of Birmingham, Birmingham B15 2TT, UK
14Center for Interdisciplinary Exploration & Research in Astrophysics (CIERA),
Northwestern University, Evanston, IL 60208, USA
15Instituto Nacional de Pesquisas Espaciais, 12227-010 S˜ao Jos´e dos Campos, S˜ao Paulo, Brazil
16The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA
17Gran Sasso Science Institute (GSSI), I-67100 L’Aquila, Italy
18INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy
19International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
20NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
21INFN, Sezione di Pisa, I-56127 Pisa, Italy
22Laboratoire des Mat´eriaux Avanc´es (LMA), IP2I - UMR 5822,
CNRS, Universit´e de Lyon, F-69622 Villeurbanne, France
23University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
24SUPA, University of Strathclyde, Glasgow G1 1XQ, UK
25Dipartimento di Matematica e Informatica, Universit`a di Udine, I-33100 Udine, Italy
26INFN, Sezione di Trieste, I-34127 Trieste, Italy
27APC, AstroParticule et Cosmologie, Universit´e Paris Diderot,
CNRS/IN2P3, CEA/Irfu, Observatoire de Paris,
Sorbonne Paris Cit´e, F-75205 Paris Cedex 13, France
28California State University Fullerton, Fullerton, CA 92831, USA
29LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, F-91898 Orsay, France
30European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
31University of Florida, Gainesvil le, FL 32611, USA
32Chennai Mathematical Institute, Chennai 603103, India
33Columbia University, New York, NY 10027, USA
34INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
35INFN, Sezione di Roma, I-00185 Roma, Italy

24
36Laboratoire d’Annecy de Physique des Particules (LAPP), Univ. Grenoble Alpes,
Universit´e Savoie Mont Blanc, CNRS/IN2P3, F-74941 Annecy, France
37Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA
38Montclair State University, Montclair, NJ 07043, USA
39Nikhef, Science Park 105, 1098 XG Amsterdam, The Netherlands
40Korea Institute of Science and Technology Information, Daejeon 34141, South Korea
41Christopher Newport University, Newport News, VA 23606, USA
42Universit`a di Perugia, I-06123 Perugia, Italy
43INFN, Sezione di Perugia, I-06123 Perugia, Italy
44Syracuse University, Syracuse, NY 13244, USA
45Universit´e de Li`ege, B-4000 Li`ege, Belgium
46University of Minnesota, Minneapolis, MN 55455, USA
47Universit`a degli Studi di Milano-Bicocca, I-20126 Milano, Italy
48INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy
49LIGO Hanford Observatory, Richland, WA 99352, USA
50Caltech CaRT, Pasadena, CA 91125, USA
51Departament de F´ısica Qu`antica i Astrof´ısica, Institut de Ci`encies del Cosmos (ICCUB),
Universitat de Barcelona (IEEC-UB), E-08028 Barcelona, Spain
52Dipartimento di Medicina, Chirurgia e Odontoiatria “Scuola Medica Salernitana,
” Universit`a di Salerno, I-84081 Baronissi, Salerno, Italy
53SUPA, University of Glasgow, Glasgow G12 8QQ, UK
54LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
55Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Mikl´os ´ut 29-33, Hungary
56Stanford University, Stanford, CA 94305, USA
57Universit`a di Pisa, I-56127 Pisa, Italy
58Universit`a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
59Universit`a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
60INFN, Sezione di Padova, I-35131 Padova, Italy
61Montana State University, Bozeman, MT 59717, USA
62Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland
63OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia
64Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany
65INFN, Sezione di Genova, I-16146 Genova, Italy
66RRCAT, Indore, Madhya Pradesh 452013, India
67Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
68SUPA, University of the West of Scotland, Paisley PA1 2BE, UK
69Rochester Institute of Technology, Rochester, NY 14623, USA
70Bar-Ilan University, Ramat Gan 5290002, Israel
71Universit`a degli Studi di Urbino “Carlo Bo,” I-61029 Urbino, Italy
72INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
73Artemis, Universit´e Cˆote d’Azur, Observatoire Cˆote d’Azur,
CNRS, CS 34229, F-06304 Nice Cedex 4, France
74OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia
75Dipartimento di Fisica “E.R. Caianiello,” Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy
76INFN, Sezione di Napoli, Gruppo Collegato di Salerno,
Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
77Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
78Univ Rennes, CNRS, Institut FOTON - UMR6082, F-3500 Rennes, France
79University of Oregon, Eugene, OR 97403, USA
80Laboratoire Kastler Brossel, Sorbonne Universit´e, CNRS,
ENS-Universit´e PSL, Coll`ege de France, F-75005 Paris, France
81Universit´e catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
82Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
83VU University Amsterdam, 1081 HV Amsterdam, The Netherlands
84University of Maryland, College Park, MD 20742, USA
85School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
86Universit´e de Lyon, Universit´e Claude Bernard Lyon 1,
CNRS, Institut Lumi`ere Mati`ere, F-69622 Villeurbanne, France
87Universit`a di Napoli “Federico II,” Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
88NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
89Dipartimento di Fisica, Universit`a degli Studi di Genova, I-16146 Genova, Italy
90RESCEU, University of Tokyo, Tokyo, 113-0033, Japan.
91Tsinghua University, Beijing 100084, China
92Texas Tech University, Lubbock, TX 79409, USA

25
93Universit`a di Roma Tor Vergata, I-00133 Roma, Italy
94Missouri University of Science and Technology, Rolla, MO 65409, USA
95Departamento de Astronom´ıa y Astrof´ısica, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain
96Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi,” I-00184 Roma, Italy
97National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
98Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
99Physics and Astronomy Department, Stony Brook University, Stony Brook, NY 11794, USA
100Center for Computational Astrophysics, Flatiron Institute, 162 5th Ave, New York, NY 10010, USA
101University of Chicago, Chicago, IL 60637, USA
102The Chinese University of Hong Kong, Shatin, NT, Hong Kong
103Dipartimento di Ingegneria Industriale (DIIN),
Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy
104Institut de Physique des 2 Infinis de Lyon (IP2I) - UMR 5822,
Universit´e de Lyon, Universit´e Claude Bernard, CNRS, F-69622 Villeurbanne, France
105Seoul National University, Seoul 08826, South Korea
106Pusan National University, Busan 46241, South Korea
107INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy
108OzGrav, University of Melbourne, Parkville, Victoria 3010, Australia
109Universitat de les Illes Balears, IAC3—IEEC, E-07122 Palma de Mallorca, Spain
110Universit´e Libre de Bruxelles, Brussels 1050, Belgium
111Departamento de Matem´aticas, Universitat de Val`encia, E-46100 Burjassot, Val`encia, Spain
112Cardiff University, Cardiff CF24 3AA, UK
113University of Rhode Island, Kingston, RI 02881, USA
114Bellevue College, Bellevue, WA 98007, USA
115MTA-ELTE Astrophysics Research Group, Institute of Physics, E¨otv¨os University, Budapest 1117, Hungary
116California State University, Los Angeles, 5151 State University Dr, Los Angeles, CA 90032, USA
117Universit¨at Hamburg, D-22761 Hamburg, Germany
118Institute for Plasma Research, Bhat, Gandhinagar 382428, India
119IGFAE, Campus Sur, Universidade de Santiago de Compostela, 15782 Spain
120The University of Sheffield, Sheffield S10 2TN, UK
121Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`a di Parma, I-43124 Parma, Italy
122INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy
123Dipartimento di Ingegneria, Universit`a del Sannio, I-82100 Benevento, Italy
124Universit`a di Trento, Dipartimento di Fisica, I-38123 Povo, Trento, Italy
125INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy
126Universit`a di Roma “La Sapienza,” I-00185 Roma, Italy
127Universit`a degli Studi di Sassari, I-07100 Sassari, Italy
128INFN, Laboratori Nazionali del Sud, I-95125 Catania, Italy
129University of Portsmouth, Portsmouth, PO1 3FX, UK
130West Virginia University, Morgantown, WV 26506, USA
131The Pennsylvania State University, University Park, PA 16802, USA
132Colorado State University, Fort Collins, CO 80523, USA
133Institute for Nuclear Research (Atomki), Hungarian Academy of Sciences, Bem t´er 18/c, H-4026 Debrecen, Hungary
134CNR-SPIN, c/o Universit`a di Salerno, I-84084 Fisciano, Salerno, Italy
135Scuola di Ingegneria, Universit`a della Basilicata, I-85100 Potenza, Italy
136National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
137Observatori Astron`omic, Universitat de Val`encia, E-46980 Paterna, Val`encia, Spain
138INFN Sezione di Torino, I-10125 Torino, Italy
139Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
140University of Szeged, D´om t´er 9, Szeged 6720, Hungary
141Delta Institute for Theoretical Physics, Science Park 904, 1090 GL Amsterdam, The Netherlands
142Lorentz Institute, Leiden University, PO Box 9506, Leiden 2300 RA, The Netherlands
143GRAPPA, Anton Pannekoek Institute for Astronomy and Institute for High-Energy Physics,
University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
144Tata Institute of Fundamental Research, Mumbai 400005, India
145INAF, Osservatorio Astronomico di Capodimonte, I-80131 Napoli, Italy
146University of Michigan, Ann Arbor, MI 48109, USA
147American University, Washington, D.C. 20016, USA
148University of California, Berkeley, CA 94720, USA
149Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands
150Directorate of Construction, Services & Estate Management, Mumbai 400094 India
151University of Bia lystok, 15-424 Bia lystok, Poland
152King’s College London, University of London, London WC2R 2LS, UK
153University of Southampton, Southampton SO17 1BJ, UK

26
154University of Washington Bothell, Bothell, WA 98011, USA
155Institute of Applied Physics, Nizhny Novgorod, 603950, Russia
156Ewha Womans University, Seoul 03760, South Korea
157Inje University Gimhae, South Gyeongsang 50834, South Korea
158National Institute for Mathematical Sciences, Daejeon 34047, South Korea
159Ulsan National Institute of Science and Technology, Ulsan 44919, South Korea
160Bard College, 30 Campus Rd, Annandale-On-Hudson, NY 12504, USA
161NCBJ, 05-400 ´
Swierk-Otwock, Poland
162Institute of Mathematics, Polish Academy of Sciences, 00656 Warsaw, Poland
163Cornell University, Ithaca, NY 14850, USA
164Universit´e de Montr´eal/Polytechnique, Montreal, Quebec H3T 1J4, Canada
165Lagrange, Universit´e Cˆote d’Azur, Observatoire Cˆote d’Azur,
CNRS, CS 34229, F-06304 Nice Cedex 4, France
166Hillsdale College, Hillsdale, MI 49242, USA
167Korea Astronomy and Space Science Institute, Daejeon 34055, South Korea
168Institute for High-Energy Physics, University of Amsterdam,
Science Park 904, 1098 XH Amsterdam, The Netherlands
169NASA Marshall Space Flight Center, Huntsville, AL 35811, USA
170University of Washington, Seattle, WA 98195, USA
171Dipartimento di Matematica e Fisica, Universit`a degli Studi Roma Tre, I-00146 Roma, Italy
172INFN, Sezione di Roma Tre, I-00146 Roma, Italy
173ESPCI, CNRS, F-75005 Paris, France
174Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering,
Tongji University, 200092 Shanghai, People’s Republic of China
175Southern University and A&M College, Baton Rouge, LA 70813, USA
176Department of Physics, University of Texas, Austin, TX 78712, USA
177Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy
178Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco
179Indian Institute of Technology Madras, Chennai 600036, India
180Universit´e de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France
181Institut des Hautes Etudes Scientifiques, F-91440 Bures-sur-Yvette, France
182IISER-Kolkata, Mohanpur, West Bengal 741252, India
183Department of Astrophysics/IMAPP, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
184Kenyon College, Gambier, OH 43022, USA
185Whitman College, 345 Boyer Avenue, Walla Walla, WA 99362 USA
186Hobart and William Smith Colleges, Geneva, NY 14456, USA
187Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
188OzGrav, Swinburne University of Technology, Hawthorn VIC 3122, Australia
189Trinity University, San Antonio, TX 78212, USA
190Dipartimento di Fisica, Universit`a degli Studi di Torino, I-10125 Torino, Italy
191Indian Institute of Technology, Gandhinagar Ahmedabad Gujarat 382424, India
192INAF, Osservatorio Astronomico di Brera sede di Merate, I-23807 Merate, Lecco, Italy
193Centro de Astrof´ısica e Gravita¸c˜ao (CENTRA),
Departamento de F´ısica, Instituto Superior T´ecnico,
Universidade de Lisboa, 1049-001 Lisboa, Portugal
194Marquette University, 11420 W. Clybourn St., Milwaukee, WI 53233, USA
195Indian Institute of Technology Hyderabad, Sangareddy, Khandi, Telangana 502285, India
196INAF, Osservatorio di Astrofisica e Scienza dello Spazio, I-40129 Bologna, Italy
197International Institute of Physics, Universidade Federal do Rio Grande do Norte, Natal RN 59078-970, Brazil
198Villanova University, 800 Lancaster Ave, Villanova, PA 19085, USA
199Andrews University, Berrien Springs, MI 49104, USA
200Carleton College, Northfield, MN 55057, USA
201Department of Physics, Utrecht University, 3584CC Utrecht, The Netherlands
202Concordia University Wisconsin, 2800 N Lake Shore Dr, Mequon, WI 53097, USA