of 15
Tests of General Relativity with GW170817
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 20 November 2018; revised manuscript received 21 March 2019; published 1 July 2019)
The recent discovery by Advanced LIGO and Advanced Virgo of a gravitational wave signal from a binary
neutron star inspiral has enabled tests of general relativity (GR) with this new type of source. This source, for
the first time, permits tests of strong-field dynamics of compact binaries in the presence of matter. In this
Letter, we place constraints on the dipole radiation and possible deviations from GR in the post-Newtonian
coefficients that govern the inspiral regime. Bounds on modified dispersion of gravitational waves are
obtained; in combination with information from the observed electromagnetic counterpart we can also
constrain effects due to large extra dimensions. Finally, the polarization content of the gravitational wave
signal is studied. The results of all tests performed here show good agreement with GR.
DOI:
10.1103/PhysRevLett.123.011102
Introduction.
On August 17, 2017 at 12
41:04 UTC,
the Advanced LIGO and Advanced Virgo gravitational-
wave (GW) detectors made their first observation of a
binary neutron star inspiral signal, called GW170817
[1]
.
Associated with this event, a gamma ray burst
[2]
was
independently observed, and an optical counterpart was
later discovered
[3]
. In terms of fundamental physics, these
coincident observations led to a stringent constraint on the
difference between the speed of gravity and the speed of
light, allowed new bounds to be placed on local Lorentz
invariance violations, and enabled a new test of the
equivalence principle by constraining the Shapiro delay
between gravitational and electromagnetic radiation
[2]
.
These bounds, in turn, helped to strongly constrain the
allowed parameter space of alternative theories of gravity
that offered gravitational explanations for the origin of dark
energy
[4
10]
or dark matter
[11]
.
In this paper we present a range of tests of general
relativity (GR) that have not yet been done with
GW170817. Some of these are extensions of tests per-
formed with previously discovered binary black hole
coalescences
[12
18]
, an important difference being that
the neutron stars
tidal deformabilities need to be taken into
account in the waveform models. The parameter estimation
settings for this analysis broadly match with those of
Refs.
[19,20]
, which reported the properties of the source
GW170817. Our approach here is theory-agnostic where,
using GW170817, we constrain generic features in the
gravitational waveform that may arise from a breakdown of
GR. For a detailed discussion about specific alternative
theories that predict one or more of the physical effects
discussed here see, for instance, Sec. 5 of Ref.
[21]
and
Sec. 2 of Ref.
[22]
.
Three types of tests are presented. First, we study the
general-relativistic dynamics of the source, in particular
constraining dipole radiation in the strong-field and radi-
ative regime and checking for possible deviations in the
post-Newtonian (PN) description of binary inspiral by
studying the phase evolution of the signal. Next, we focus
on the way gravitational waves propagate over large
distances. Here we look for anomalous dispersion, which
enables complementary bounds on violations of local
Lorentz invariance to those of
[2]
; constraints on large
extra spatial dimensions are obtained by comparing the
distance inferred from the GW signal with the one inferred
from the electromagnetic counterpart. Finally, constraints
are placed on alternative polarization states, where this time
the position of the source on the sky can be used, again
because of the availability of an electromagnetic counter-
part. We end with a summary and conclusions.
Constraints on deviations from the general-relativistic
dynamics of the source.
Testing GR via the dynamics of a
binary system involves constructing a waveform model that
allows for parametrized deformations away from the
predictions of GR and then constraining the associated
parameters that govern those deviations
[13,15,16,23
28]
.
For previous observations of coalescing binary black holes
[13,15]
, these tests relied on the frequency domain
IMRPhenomPv2
waveform model of Refs.
[29
31]
,
which describes the inspiral, merger, and ringdown of
vacuum black holes, and provides an effective description
of spin precession, making the best use of the results from
analytical and numerical relativity
[32
39]
. The phase
evolution of this waveform is governed by a set of
coefficients
p
n
that depend on the component masses
and spins. These coefficients include post-Newtonian
(PN) parameters and phenomenological constants that
are calibrated against numerical relativity waveforms to
describe the intermediate regime between inspiral and
*
Full author list given at the end of the article.
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
Editors' Suggestion
0031-9007
=
19
=
123(1)
=
011102(15)
011102-1
© 2019 American Physical Society
merger, as well as the merger and ringdown. To test GR, the
waveform model is generalized to allow for relative
deviations in each of the coefficients in turn, i.e., by
replacing
p
n
ð
1
þ
δ
ˆ
p
n
Þ
p
n
, where the
δ
ˆ
p
n
are zero in
GR. The
δ
ˆ
p
n
are then varied along with all the parameters
that are also present in the case of GR (masses, spins, and
extrinsic parameters), and posterior density functions
(PDFs) are obtained using
LALInference
[40]
.For
GR to be correct, the value
δ
ˆ
p
n
¼
0
should fall within
the support of each of the PDFs. Note that although one
could also let
all
of the testing parameters vary at the same
time, this will tend to lead to uninformative posteriors
(see, e.g., Ref.
[13]
). Fortunately, as demonstrated in
Refs.
[27,28,41,42]
, checking for a deviation from zero
in a single testing parameter is an efficient way to uncover
GR violations that occur at multiple PN orders, and one can
even find violations at powers of frequency that are distinct
from the one that the testing parameter is associated with
[27,28,42]
. Thus, such analyses are well suited to search for
generic departures from GR. There is a limitation though:
Should a GR violation be present, then the measured values
of the
δ
ˆ
p
i
will not necessarily reflect the predictions of
whichever alternative theory happens to be the correct one.
To reliably constrain theory-specific quantities such as
coupling constants or extra charges, one should utilize full
inspiral waveform models from specific modified gravity
theories, including modifications to the phase at all the
orders where they appear. Unfortunately, in most cases only
leading-order modifications are available at the present
time
[43]
. However, in this section the focus is mostly on
model-independent tests of general relativity itself.
In this work, we modify this approach in two ways. First,
we use waveform models more suitable for binary neutron
stars. Second, whereas the infrastructure
[27]
used to test
GR with binary black holes observations
[13,15]
was
restricted to waveform models that depend directly on
the coefficients
p
n
, we also introduce a new procedure that
can include deviations to the phase evolution parametrized
by
δ
ˆ
p
n
to any frequency domain waveform model. We
conduct independent tests of GR using inspiral-merger-
ringdown models that incorporate deviations from GR
using each of these two prescriptions; by comparing
these analyses, we are able to estimate the magnitude of
systematic modeling uncertainty in our results.
The merger and ringdown regimes of binary neutron
stars differ from those of binary black holes, and tidal
effects not present in binary black holes need to be included
in the description of the inspiral. Significant work has been
done to understand and model the dynamics of binary
neutron stars analytically using the PN approximation to
general relativity
[44]
. This includes modeling the non-
spinning
[32,33]
and spinning radiative (or inspiral)
dynamics
[34
39]
as well as finite size effects
[45
47]
for binary neutron star systems. Frequency domain wave-
forms based on the stationary phase approximation
[48]
have been developed incorporating the above-mentioned
effects
[49
51]
and have been successfully employed for the
data analysis of compact binaries. A combination of these
analytical results with the results from numerical relativity
simulations of binary neutron star mergers (see Ref.
[52]
for
a review) have led to the development of efficient waveform
models which account for tidal effects
[53
55]
.
We employ the
NRTidal
models introduced in
Refs.
[55,56]
as the basis of our binary neutron star
waveforms: frequency domain waveform models for binary
black holes are converted into waveforms for inspiraling
neutron stars that undergo tidal deformations by adding to
the phase an appropriate expression
φ
T
ð
f
Þ
and windowing
the amplitude such that the merger and ringdown are
smoothly removed from the model; see Ref.
[56]
for
details. The closed-form expression for
φ
T
ð
f
Þ
is built by
combining PN information, the tidal effective-one-body
(EOB) model of Ref.
[53]
, and input from numerical
relativity (NR). We consider two waveform models that
use this description of tidal effects. One of these models
IMRPhenomPNRT
, detailed below
describes a binary
neutron star with precessing spins. Though the form of
φ
T
ð
f
Þ
was originally obtained in a setting where the
neutron stars were irrotational or had their spins aligned
to the angular momentum, tides can be included in this
waveform model by first applying
φ
T
ð
f
Þ
to an aligned-spin
waveform, and then performing the twisting-up procedure
that introduces spin precession
[57]
.
The first binary neutron star model we consider is con-
structed by applying this procedure to
IMRPhenomPv2
waveforms. Following the nomenclature of Ref.
[19]
,we
refer to the resulting waveform model as
PhenomPNRT
.
Parametrized deformations
δ
ˆ
p
n
are then introduced as shifts in
parameters describing the phase in precisely the same way as
was done for binary black holes. This will allow us to naturally
combine PDFs for the
δ
ˆ
p
n
from measurements on binary
black holes and binary neutron stars, arriving at increasingly
sharper results in the future. Because of the unknown merger-
ringdown behavior in the case of binary neutron stars, which in
any case gets removed from the waveform model, in practice
only deviations
δ
ˆ
φ
n
in the PN parameters
φ
n
can be bounded.
The set of possible testing parameters is taken to be
f
δ
ˆ
φ
2
;
δ
ˆ
φ
0
;
δ
ˆ
φ
1
;
δ
ˆ
φ
2
;
δ
ˆ
φ
3
;
δ
ˆ
φ
4
;
δ
ˆ
φ
ð
l
Þ
5
;
δ
ˆ
φ
6
;
δ
ˆ
φ
ð
l
Þ
6
;
δ
ˆ
φ
7
g
;
ð
1
Þ
where the
δ
ˆ
φ
n
are associated with powers of frequency
f
ð
5
þ
n
Þ
=
3
,and
δ
ˆ
φ
ð
l
Þ
5
and
δ
ˆ
φ
ð
l
Þ
6
with functions log
ð
f
Þ
and
log
ð
f
Þ
f
1
=
3
,respectively;
δ
ˆ
φ
5
would becompletelydegenerate
with some reference phase
φ
c
and hence is not included in
the list. In addition to corrections to the positive PN order
coefficients, deviations at
1
PN are included because they
offer the possibility to constrain the presence of dipole
radiation during the inspiral (discussed below).
δ
ˆ
φ
2
and
δ
ˆ
φ
1
represent absolute rather than relative deviations, as both
are identically zero in GR.
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-2
We also employ the
SEOBNRv4
waveform model, which
is constructed from an aligned-spin EOB model for binary
black holes augmented with information from NR simula-
tions
[58]
. Using the methods of Ref.
[59]
,thismodelis
evaluated in the frequency domain, and then we add the tidal
correction
φ
T
ð
f
Þ
as described above; we refer to the resulting
waveform model as
SEOBNRT
. Unlike
PhenomPNRT
,
the
SEOBNRT
model is not constructed explicitly in terms
of PN coefficients
φ
n
. Instead, we model the effect of a
relative shift
δ
ˆ
φ
n
by adding to the frequency domain phase a
term
δ
ˆ
φ
n
φ
n
f
ð
5
þ
n
Þ
=
3
or
δ
ˆ
φ
ð
l
Þ
n
φ
ð
l
Þ
n
f
ð
5
þ
n
Þ
=
3
log
ð
f
Þ
, as appli-
cable.These corrections are thentaperedtozeroatthemerger
frequency.
Figure
1
depicts the PDFs on
δ
ˆ
φ
n
recovered when only
variations at that particular PN order are allowed. We find
that the phase evolution of GW170817 is consistent with
the GR prediction. The 90% credible region for each
parameter contains the GR value of
δ
ˆ
φ
n
¼
0
at all orders
other than 3PN and 3.5PN. [Using
PhenomPNRT
(
SEOBNRT
), the GR value lies at the 6.8th (4.4th) percen-
tile of the PDF for the 3PN parameter and at the 95.0th
(96.7th) percentile for the 3.5PN parameter.] For the
pipeline used to perform parametrized tests with binary
black holes, it has been shown in Ref.
[28]
through
extensive simulations that no noticeable systematics are
present. In the case of binary neutron stars such a study is
computationally demanding because of the long signals,
and a similar study will be published at a later date. At
present we have no reason to believe that the offsets seen
here at 3PN and 3.5PN have anything other than a statistical
origin. In any case, we note that the value of zero is in the
support of the posterior density function for all testing
parameters. The bounds on the positive-PN parameters
(
n
0
) obtained with GW170817 alone are comparable to
those obtained by combining the binary black hole signals
GW150914, GW151226, and GW170104 in Ref.
[16]
using the
IMRPhenomPv2
waveform model. For conven-
ience we also separately give 90% upper bounds on
deviations in PN coefficients; see Fig.
2
.
The PDFs shown in Fig.
1
were constructed using the
same choice of prior distribution outlined in Ref.
[19]
with
the following modifications. We use uniform priors on
δ
ˆ
φ
n
that are broad enough to fully contain the plotted PDFs.
Because of the degeneracy between
δ
ˆ
φ
0
and the chirp mass,
a broader prior distribution was chosen for the latter as
compared to Ref.
[19]
for runs in which
δ
ˆ
φ
0
was allowed to
vary. All inference was done assuming the prior
j
χ
i
j
0
.
99
,
where
χ
i
¼
c
S
i
=
ð
Gm
2
i
Þ
is the dimensionless spin of each
body. This conservative spin prior was chosen to allow the
constraints on
δ
ˆ
φ
n
to be directly compared with those from
binary black hole observations, which used the same prior
[13,15]
. Nevertheless, throughout this Letter we assume
the two objects to be neutron stars, and following Ref.
[19]
we limit our prior on the component tidal parameters to
Λ
i
5000
. (For a precise definition of the
Λ
i
, see Ref.
[1]
and references therein.) This choice was motivated by
reasonable astrophysical assumptions regarding the
expected ranges for neutron star masses and equations of
state
[46,60,61]
; higher values of
Λ
are possible for some
equations of state if the neutron star masses are small
(
0
.
9
M
). The extra freedom introduced by including
δ
ˆ
φ
n
leads to a loss in sensitivity in the measurement of tidal
parameters; in particular, the tail of the PDF for the tidal
deformation of the less massive body
Λ
2
touches the prior
FIG. 1. Posterior density functions on deviations of PN coefficients
δ
ˆ
φ
n
obtained using two different waveform models
(
PhenomPNRT
and
SEOBNRT
); see the main text for details. The
1
PN and 0.5PN corrections correspond to absolute deviations,
whereas all others represent fractional deviations from the PN coefficient in GR. The horizontal bars indicate 90% credible regions.
FIG. 2. 90% upper bounds on deviations
j
δ
ˆ
φ
n
j
in the PN
coefficients following from the posterior density functions shown
in Fig.
1
.
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-3
upper bound in many of the tests. The correlation between
δ
ˆ
φ
n
and
Λ
2
means that the upper bounds for
j
δ
ˆ
φ
n
j
would be
weaker if we did not impose our neutron star prior
of
Λ
i
5000
.
Certain differences are present between the
PhenomPNRT
and
SEOBNRT
waveform models and the
way they are used. First,
PhenomPNRT
allows for pre-
cessing spin configurations, whereas the
SEOBNRT
is
restricted to systems with spins aligned with the orbital
angular momentum. Second, continuity conditions
enforced in the construction of
PhenomPNRT
waveforms
cause deviations from GR in the inspiral to affect the
behavior of later phases of the signal, whereas the tapering
of deviations in
SEOBNRT
ensures that the merger-ring-
down of the underlying waveform is exactly reproduced.
However, this discrepancy is not expected to affect mea-
surements of
δ
ˆ
φ
n
significantly because the signal is
dominated by the inspiral and both waveform models
are amplitude tapered near merger. Third, the spin-induced
quadrupole moment
[62]
, which enters the phase
at 2PN through quadrupole-monopole couplings, is com-
puted using neutron-star universal relations
[63]
in
PhenomPNRT
and is assumed to take the black-hole value
in
SEOBNRT
. Finally, in the
PhenomPNRT
model, frac-
tional deviations are applied only to nonspinning terms in
the PN expansion of the phase; i.e., terms dependent on the
bodies
spins retain their GR values (There is no funda-
mental reason for this choice; we follow the convention
used in previous publications on parametrized tests of
GR
[13,15,16,27,64]
.). In
SEOBNRT
, fractional deviations
are applied to all terms at a given post-Newtonian order.
One can convert between these two parametrizations
post
hoc
by requiring that the total phase correction be the same
with either choice; the results shown in Figs.
1
and
2
correspond to the parametrization used by
PhenomPNRT
.
Nevertheless, the different treatment of the spin terms may
still explain the discrepancy seen at 1.5PN, where spin
effects first enter. (In the
SEOBNRT
parametrization, the
PDF for
δ
ˆ
φ
7
touches the prior bounds. After mapping to the
PhenomPNRT
parametrization, these tails of the distribu-
tion are down weighted, so our final results are a good
approximation to the complete PDF.) Either parametriza-
tion offers a reasonable phenomenological description of
deviations from GR; the generally close correspondence at
most PN orders between results from the two models
indicates that the quantities measured can be interpreted in
similar ways. For more details on each waveform model we
use, see Table I of Ref.
[19]
.
The long inspiral observed in GW170817 (relative to
previous binary black hole signals) allows us to place the
first stringent constraints on
δ
ˆ
φ
2
. This parameter is of
particular interest due to its association with dipole radia-
tion, i.e., radiation sourced by a time-varying dipole moment
of the binary. Dipole radiation is forbidden in pure GR;
however, adding other long-range fields to theory
either in
thegravitational sector(e.g., masslessscalar-tensortheories)
or nongravitational sector (e.g., electromagnetism)
ena-
bles this new dissipative channel. The additional energy flux
induces a negative
1
PN order correction to the phase
evolution, provided that dipole radiation only contributes a
smallcorrectionto thetotalflux predictedinGR. Theprecise
nature of the additional long-range fields determines the
dependence of this
1
PN correction on the various other
parameters describing the binary (e.g., masses, spins, etc); in
line with the theory-agnostic approach pursued here, we
assume no
a priori
correlation between dipole radiation and
the other binary parameters by using a uniform prior
on
δ
ˆ
φ
2
.
Writing the total energy flux as
F
GW
¼
F
GR
ð
1
þ
Bc
2
=v
2
Þ
,
the leading-order modification to the phase due to
theory-agnostic effects of dipole radiation is given by
δ
ˆ
φ
2
¼
4
B=
7
[65,66]
. Combining the PDFs shown in
Fig.
1
obtained with the
PhenomPNRT
and
SEOBNRT
waveforms, converting to a PDF on
B
using the previous
relation, and restricting to the physical parameter space
B
0
corresponding to positive outgoing flux, the presence
of dipole radiation in GW170817 can be constrained to
B
1
.
2
×
10
5
. For comparison, precise timing of radio
pulses from the double pulsar PSR J0737-3039 offers some
of the best current theory-agnostic constraints
j
B
j
10
7
[66
70]
. (Neutron star-white dwarf binaries offer stronger
constraints than the double pulsar on certain
specific
alter-
native theories of gravity
[71
73]
, but provide comparable
theory-agnostic constraints.) This much stronger constraint
arises, in part, because of the much longer observation time
over which the inspirals of binary pulsars are tracked.
Though our bound on the dipole parameter
B
is weaker
than existing constraints, it is the first that comes directly
from the nonlinear and dynamical regime of gravity
achieved during compact binary coalescences. In this
regard, we note that for general scalar-tensor theories there
are regions of parameter space where constraints from both
Solar System and binary pulsar observations are satisfied,
and yet new effects not present in GR appear in the
frequency range of GW detectors, such as spontaneous
scalarization
[74,75]
or resonant excitation
[76,77]
of a
massive field, or dynamical scalarization
[72,78
81]
.
Constraints from gravitational wave propagation.
The
propagation of GWs may differ in theories beyond GR, and
the deviations depend on the distance that the GWs travel.
The search for such deviations provides unique tests of
relativity, particularly when the distance inferred through
GWs can be compared with an accurate, independent
distance measurement from EM observations. In GR,
GWs propagate nondispersively at the speed of light with
an amplitude inversely proportional to the distance trav-
eled. Using GW170817, we carry out two different types of
analyses to study the propagation of GWs, looking for
possible deviations from GR
s predictions. The first
method implements a generic modification to the GW
dispersion relation, adding terms that correct for a massive
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-4
graviton, and momentum dependent dispersion that could
be apparent in Lorentz violating models
[82,83]
. The
second modifies the distance relation GWs follow in GR
by adding correcting factors accounting for the GW
s
gravitational leakage into the large extra dimensions of
higher-dimensional theories of gravity
[84,85]
.
In GR, gravitational waves propagate at the speed of
light and are nondispersive, leading to a dispersion relation
E
2
¼
p
2
c
2
. An alternative theory may generically modify
this as
E
2
¼
p
2
c
2
þ
Ap
α
c
α
, where
A
is the coefficient
of modified dispersion corresponding to the exponent
denoted by
α
[82,83]
. When
α
¼
0
, a modification with
A>
0
may be interpreted as due to a nonzero graviton
mass (
A
¼
m
2
g
c
4
)
[83]
. It can be shown that such modified
dispersion relations would lead to corrections to the GW
phasing, thereby allowing us to constrain any dispersion of
GWs
[83]
. This method, implemented in a Bayesian frame-
work, placed bounds on
A
corresponding to different
α
using binary black hole detections
[16]
. We apply the above
method to constrain dispersion of GWs in the case of the
binary neutron star merger GW170817
[1]
. We find that
GW170817 places weaker bounds on dispersion of GWs
than the binary black holes. For instance, the bound on
the graviton mass
m
g
we obtain from GW170817 is
9
.
51
×
10
22
eV
=c
2
, which is weaker compared to the bounds
reported in Ref.
[16]
. This is not surprising as GW170817
is the closest source detected so far, and for the same SNR
propagation-based tests such as this are more effective
when the sources are farther away. This method comple-
mentstheboundsonnondispersivestandardmodelextension
coefficients
[86]
reported in Ref.
[2]
from GW170817.
In higher-dimensional theories of gravity the scaling
between the GW strain and the luminosity distance of the
source is expected to be modified, suggesting a damping of
the waveform due to gravitational leakage into large extra
dimensions. This deviation from the GR scaling
h
GR
d
1
L
depends on the number of dimensions
D>
4
and would
result in a systematic overestimation of the source lumi-
nosity distance inferred from GW observations
[84,85]
.A
comparison of distance measurements from GW and EM
observations of GW170817 allows us to constrain the
presence of large additional spacetime dimensions. We
assume, as is the case in many extra-dimensional models,
that light and matter propagate in four spacetime dimen-
sions only, thus allowing us to infer the EM luminosity
distance
d
EM
L
. In the absence of a complete, unique GW
model in higher-dimensional gravity, we use a phenom-
enological ansatz for the GWamplitude scaling and neglect
all other effects of modified gravity in the GW phase and
amplitude. This approach requires that gravity be asymp-
totically GR in the strong-field regime, while modifications
due to leakage into extra dimensions start to appear at large
distances from the source. We therefore consider gravity
modifications with a screening mechanism, i.e., a phenom-
enological model with a characteristic length scale
R
c
beyond which the propagating GWs start to leak into higher
dimensions. In this model, the strain scales as
h
1
d
GW
L
¼
1
d
EM
L

1
þ

d
EM
L
R
c

n

ð
D
4
Þ
=
ð
2
n
Þ
;
ð
2
Þ
where
D
denotes the number of spacetime dimensions,
and where
R
c
and
n
are the distance scale of the screening
and the transition steepness, respectively. Equation
(2)
reduces to the standard GR scaling at distances much
shorter than
R
c
, and the model is consistent with tests of
GR performed in the Solar System or with binary pulsars.
Unlike the scaling relation considered in Refs.
[84,85]
,
notice that Eq.
(2)
reduces to the GR limit for
D
¼
4
spacetime dimensions. An independent measurement of
the source luminosity distance from EM observations of
GW170817 allows us to infer the number of spacetime
dimensions from a comparison of the GW and EM
distance estimates, for given values of model parameters
R
c
and
n
. Constraints on the number of spacetime
dimensions are derived in a framework of Bayesian
analysis, from the joint posterior probability for
D
,
d
GW
L
,and
d
EM
L
, given the two statistically independent
measurements of EM data
x
EM
and GW data
x
GW
.The
posterior for
D
is then given by
p
ð
D
j
x
GW
;x
EM
Þ¼
Z
p
ð
d
GW
L
j
x
GW
Þ
p
ð
d
EM
L
j
x
EM
Þ
×
δ
½
D
D
ð
d
GW
L
;d
EM
L
;R
c
;n
Þ
dd
GW
L
dd
EM
L
:
ð
3
Þ
As in Ref.
[19]
, we use a measurement of the surface
brightness fluctuation distance to the host galaxy NGC 4993
from Ref.
[87]
to constrain the EM distance, assuming
a Gaussian distribution for the posterior probability
p
ð
d
EM
L
j
x
EM
Þ
, with the mean value and standard deviation
given by
40
.
7

2
.
4
Mpc
[87]
. Contrary to Ref.
[85]
,our
analysis relies on a direct measurement of
d
EM
L
and is
independent of prior information on
H
0
or any other
cosmological parameter. For the measurement of the GW
distance, the posterior distribution
p
ð
d
GW
L
j
x
GW
Þ
was inferred
from the GW data assuming general relativity and fixing the
sky position to the optical counterpart while marginalizing
over all other waveform parameters
[19]
.Ouranalysis
imposes a prior on the GW luminosity distance that is
consistent with a four-dimensional universe, but we have
checked that other reasonable prior choices do not signifi-
cantly modify the results. We invert the scaling relation in
Eq.
(2)
to compute
D
ð
d
GW
L
;d
EM
L
;R
c
;n
Þ
in Eq.
(3)
. Figure
3
shows the 90% upper bounds on the number of dimensions
D
, for theories with a certain transition steepness
n
and
distance scale
R
c
. Shading indicates the excluded regions of
parameter space. Our results are consistent with the GR
prediction of
D
¼
4
.
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-5
Additionally, the data allow us to infer constraints on the
characteristic distance scale
R
c
of higher-dimensional
theories with a screening mechanism, while fixing
D
to
5, 6, or 7. The posterior for
p
ð
R
c
j
x
GW
;x
EM
Þ
is obtained
from the joint posterior probability of
R
c
,
d
GW
L
, and
d
EM
L
,
given by a function that is formally the same as Eq.
(3)
,
but with
D
and
R
c
switching places. We fix the model
parameters
D
and
n
and compute
R
c
ð
d
GW
L
;d
EM
L
;D;n
Þ
by
inverting the scaling relation in Eq.
(2)
. Since we consider
higher-dimensional models that allow only for a relative
damping of the GW signal, we select posterior samples
with
d
GW
L
>d
EM
L
, leading to an additional step function
θ
ð
d
GW
L
d
EM
L
Þ
in
p
ð
R
c
j
x
GW
;x
EM
Þ
. In Fig.
4
, we show 10%
lower bounds on the screening radius
R
c
, for theories with a
certain fixed transition steepness
n
and number of dimen-
sions
D>
4
. Shading indicates the excluded regions of
parameter space. For higher-dimensional theories of gravity
with a characteristic length scale
R
c
of the order of
the Hubble radius
R
H
4
Gpc, such as the well-known
Dvali-Gabadadze-Porrati (DGP) models of dark energy
[88,89]
, small transition steepnesses [
n
O
ð
0
.
1
Þ
] are
excluded by the data. Our analysis cannot conclusively
rule out DGP models that provide a sufficiently steep
transition (
n>
1
) between GR and the onset of gravitational
leakage. Future LIGO-Virgo observations of binary neutron
star mergers, especially at higher redshifts, have the potential
to place stronger constraints on higher-dimensional gravity.
Constraints on the polarization of gravitational
waves.
Generic metric theories of gravity predict up to
six polarization modes for metric perturbations: two tensor
(helicity

2
), two vector (helicity

1
), and two scalar
(helicity 0) modes
[90,91]
. GWs in GR, however, have only
the two tensor modes regardless of the source properties;
any detection of a nontensor mode would be an unam-
biguous indication of physics beyond GR. The GW strain
measured by a detector can be written in general as
h
ð
t
Þ¼
F
A
h
A
, where
h
A
are the 6 independent polarization
modes and
F
A
represent the detector responses to the
different modes
A
¼ðþ
;
×
;x;y;b;l
Þ
. The antenna response
functions depend only on the detector orientation and GW
helicity; i.e., they are independent of the intrinsic properties
of the source. We can therefore place bounds on the
polarization content of GW170817 by studying which
combination of response functions is consistent with the
signal observed
[92
96]
.
The first test on the polarization of GWs was performed
for GW150914
[13]
. The number of GR polarization
modes expected was equal to the number of detectors in
the network that observed GW150914, rendering this test
inconclusive. The addition of Virgo to the network of GW
detectors allowed for the first informative test of polariza-
tion for GW170814
[17]
. This analysis established that
the GW data were better described by pure tensor modes
than pure vector or pure scalar modes, with Bayes factors
in favor of tensor modes of more than 200 and 1000,
respectively.
We here carry out a test similar to Ref.
[17]
by performing
a coherent Bayesian analysis of the signal properties with the
three interferometer outputs, using either the tensor or the
vector or the scalar response functions. (Note that although
the SNR in Virgo was significantly lower than in the two
LIGO detectors, the Virgo data stream still carries informa-
tion about the signal.) We assume that the phase evolution
of the GW can be described by GR templates, but the
polarization content can vary
[97]
. The phase evolution is
modeled with the GR waveform model
IMRPhenomPv2
and the analysis is carried out with
LALInference
[40]
.
Tidal effects are not included in this waveform model, but
this is not expected to affect the results presented here, since
the polarization test is sensitive to the antenna pattern
functions of the detectors and not the phase evolution of
the signal, as argued. The analysis described tests for the
presence of pure tensor, vector, or scalar modes. We leave
the analysis of mixed-mode content to future work.
FIG. 3. 90% upper bounds on the number of spacetime
dimensions
D
, assuming fixed transition steepness
n
and distance
scale
R
c
. Shading indicates the regions of parameter space
excluded by the data.
FIG. 4. 10% lower limits on the distance scale
R
c
(in Mpc),
assuming fixed transition steepness
n
and number of spacetime
dimensions
D
. Shading indicates the regions of parameter space
excluded by the data.
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-6
If the sky location of GW170817 is constrained to NGC
4993, we find overwhelming evidence in favor of pure
tensor polarization modes in comparison to pure vector and
pure scalar modes with a (base ten) logarithm of the Bayes
factor of
þ
20
.
81

0
.
08
and
þ
23
.
09

0
.
08
, respectively.
This result is many orders of magnitude stronger than
the GW170814 case both due to the sky position of
GW170817 relative to the detectors and the fact that the
sky position is determined precisely by electromagnetic
observations. Indeed if the sky location is unconstrained we
find evidence against scalar modes with
þ
5
.
84

0
.
09
,
while the test is inconclusive for vector modes with
þ
0
.
72

0
.
09
.
Conclusions.
Using the binary neutron star coalescence
signal GW170817, and in some cases also its associated
electromagnetic counterpart, we have subjected general
relativity to a range of tests related to the dynamics of the
source (putting bounds on deviations of PN coefficients),
the propagation of gravitational waves (constraining local
Lorentz invariance violations, as well as large extra
dimensions), and the polarization content of gravitational
waves. In all cases we find agreement with the predictions
of GR.
The upcoming observing runs of the LIGO and Virgo
detectors are expected to result in more detections of binary
neutron star coalescences
[98]
. Along with electromagnetic
observations, combining information from gravitational
wave events (including binary black hole mergers) will
lead to increasingly more stringent constraints on devia-
tions from general relativity
[27,28]
, or conceivably poten-
tial evidence of the theory
s shortcomings.
The authors gratefully acknowledge the support of the
United States National Science Foundation (NSF) for
the construction and operation of the LIGO Laboratory
and Advanced LIGO as well as the Science and Technology
Facilities Council (STFC) of the United Kingdom,
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 supported
by the Netherlands Organisation for Scientific Research,
for the construction and operation of the Virgo detector and
the creation and support of the EGO consortium. The
authors also gratefully acknowledge research support from
these agencies as well as by the Council of Scientific and
Industrial Research of India, the Department of Science
and Technology, India, the Science & Engineering
Research Board (SERB), India, the Ministry of Human
Resource Development, India, the Spanish Agencia Estatal
de Investigación, the Vicepresid`
encia i Conselleria
d
Innovació, Recerca i Turisme and the Conselleria
d
Educació i Universitat del Govern de les Illes Balears,
the Conselleria d
Educació, Investigació, Cultura i Esport
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 Scottish
Universities Physics Alliance, the Hungarian Scientific
Research Fund (OTKA), the Lyon Institute of Origins
(LIO), the Paris Île-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, Innovations,
and Communications, the International Center for
Theoretical Physics South American Institute for
Fundamental 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 Technology (MOST), Taiwan and the Kavli
Foundation. The authors gratefully acknowledge the sup-
port of the NSF, STFC, MPS, INFN, CNRS, and the State
of Niedersachsen/Germany for provision of computational
resources.
[1] B. Abbott
et al.
(Virgo and LIGO Scientific Collaborations),
Phys. Rev. Lett.
119
, 161101 (2017)
.
[2] B. P. Abbott
et al.
(Virgo, Fermi-GBM, INTEGRAL, and
LIGO Scientific Collaborations),
Astrophys. J.
848
, L13
(2017)
.
[3] B. P. Abbott
et al.
,
Astrophys. J.
848
, L12 (2017)
.
[4] T. Baker, E. Bellini, P. G. Ferreira, M. Lagos, J. Noller, and
I. Sawicki,
Phys. Rev. Lett.
119
, 251301 (2017)
.
[5] P. Creminelli and F. Vernizzi,
Phys. Rev. Lett.
119
, 251302
(2017)
.
[6] J. Sakstein and B. Jain,
Phys. Rev. Lett.
119
, 251303 (2017)
.
[7] J. M. Ezquiaga and M. Zumalacárregui,
Phys. Rev. Lett.
119
, 251304 (2017)
.
[8] D. Langlois, R. Saito, D. Yamauchi, and K. Noui,
Phys.
Rev. D
97
, 061501(R) (2018)
.
[9] A. Dima and F. Vernizzi,
Phys. Rev. D
97
, 101302(R)
(2018)
.
[10] C. de Rham and S. Melville,
Phys. Rev. Lett.
121
, 221101
(2018)
.
[11] S. Boran, S. Desai, E. O. Kahya, and R. P. Woodard,
Phys.
Rev. D
97
, 041501(R) (2018)
.
[12] B. P. Abbott
et al.
(Virgo and LIGO Scientific Collabora-
tions),
Phys. Rev. Lett.
116
, 061102 (2016)
.
[13] B. P. Abbott
et al.
(Virgo and LIGO Scientific Collabora-
tions),
Phys. Rev. Lett.
116
, 221101 (2016)
.
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-7
[14] B. P. Abbott
et al.
(Virgo and LIGO Scientific Collabora-
tions),
Phys. Rev. Lett.
116
, 241103 (2016)
.
[15] B. P. Abbott
et al.
(Virgo and LIGO Scientific Collabora-
tions),
Phys. Rev. X
6
, 041015 (2016)
.
[16] B. P. Abbott
et al.
(Virgo and LIGO Scientific Collabora-
tions),
Phys. Rev. Lett.
118
, 221101 (2017)
.
[17] B. P. Abbott
et al.
(Virgo and LIGO Scientific Collabora-
tions),
Phys. Rev. Lett.
119
, 141101 (2017)
.
[18] B. P. Abbott
et al.
(Virgo and LIGO Scientific Collabora-
tions),
Astrophys. J.
851
, L35 (2017)
.
[19] B. P. Abbott
et al.
(LIGO Scientific and Virgo Collabora-
tions),
Phys. Rev. X
9
, 011001 (2019)
.
[20] B. P. Abbott
et al.
(LIGO Scientific and Virgo Collabora-
tions),
Phys. Rev. Lett.
121
, 161101 (2018)
.
[21] J. R. Gair, M. Vallisneri, S. L. Larson, and J. G. Baker,
Living Rev. Relativity
16
, 7 (2013)
.
[22] N. Yunes and X. Siemens,
Living Rev. Relativity
16
,9
(2013)
.
[23] L. Blanchet and B. S. Sathyaprakash,
Phys. Rev. Lett.
74
,
1067 (1995)
.
[24] K. G. Arun, B. R. Iyer, M. S. S. Qusailah, and B. S.
Sathyaprakash,
Phys. Rev. D
74
, 024006 (2006)
.
[25] N. Yunes and F. Pretorius,
Phys. Rev. D
80
, 122003 (2009)
.
[26] C. K.Mishra, K. G. Arun, B. R. Iyer, and B. S. Sathyaprakash,
Phys. Rev. D
82
, 064010 (2010)
.
[27] T. G. F. Li, W. Del Pozzo, S. Vitale, C. Van Den Broeck, M.
Agathos, J. Veitch, K. Grover, T. Sidery, R. Sturani, and A.
Vecchio,
Phys. Rev. D
85
, 082003 (2012)
.
[28] J. Meidam
et al.
,
Phys. Rev. D
97
, 044033 (2018)
.
[29] S. Husa, S. Khan, M. Hannam, M. Pürrer, F. Ohme, X. J.
Forteza, and A. Boh ́
e,
Phys. Rev. D
93
, 044006 (2016)
.
[30] S. Khan, S. Husa, M. Hannam, F. Ohme, M. Pürrer, X. J.
Forteza, and A. Boh ́
e,
Phys. Rev. D
93
, 044007 (2016)
.
[31] M. Hannam, P. Schmidt, A. Boh ́
e, L. Haegel, S. Husa, F.
Ohme, G. Pratten, and M. Pürrer,
Phys. Rev. Lett.
113
,
151101 (2014)
.
[32] L. Blanchet, T. Damour, B. R. Iyer, C. M. Will, and A. G.
Wiseman,
Phys. Rev. Lett.
74
, 3515 (1995)
.
[33] L. Blanchet, T. Damour, G. Esposito-Farese, and B. R. Iyer,
Phys. Rev. Lett.
93
, 091101 (2004)
.
[34] L. E. Kidder,
Phys. Rev. D
52
, 821 (1995)
.
[35] L. Blanchet, A. Buonanno, and G. Faye,
Phys. Rev. D
74
,
104034 (2006)
;
81
, 089901(E) (2010)
.
[36] L. Blanchet, A. Buonanno, and G. Faye,
Phys. Rev. D
84
,
064041 (2011)
.
[37] B. Mikoczi, M. Vasuth, and L. A. Gergely,
Phys. Rev. D
71
,
124043 (2005)
.
[38] A. Boh ́
e, G. Faye, S. Marsat, and E. K. Porter,
Classical
Quantum Gravity
32
, 195010 (2015)
.
[39] S. Marsat,
Classical Quantum Gravity
32
, 085008 (2015)
.
[40] J. Veitch
et al.
,
Phys. Rev. D
91
, 042003 (2015)
.
[41] L. Sampson, N. Cornish, and N. Yunes,
Phys. Rev. D
87
,
102001 (2013)
.
[42] T. G. F. Li, W. Del Pozzo, S. Vitale, C. Van Den Broeck, M.
Agathos, J. Veitch, K. Grover, T. Sidery, R. Sturani, and A.
Vecchio,
J. Phys. Conf. Ser.
363
, 012028 (2012)
.
[43] N. Yunes, K. Yagi, and F. Pretorius,
Phys. Rev. D
94
,
084002 (2016)
.
[44] L. Blanchet,
Living Rev. Relativity
17
, 2 (2014)
.
[45] E. E. Flanagan and T. Hinderer,
Phys. Rev. D
77
, 021502(R)
(2008)
.
[46] T. Hinderer, B. D. Lackey, R. N. Lang, and J. S. Read,
Phys.
Rev. D
81
, 123016 (2010)
.
[47] J. Vines, E. E. Flanagan, and T. Hinderer,
Phys. Rev. D
83
,
084051 (2011)
.
[48] B. S. Sathyaprakash and S. V. Dhurandhar,
Phys. Rev. D
44
,
3819 (1991)
.
[49] A. Buonanno, B. R. Iyer, E. Ochsner, Y. Pan, and B. S.
Sathyaprakash,
Phys. Rev. D
80
, 084043 (2009)
.
[50] K. G. Arun, A. Buonanno, G. Faye, and E. Ochsner,
Phys.
Rev. D
79
, 104023 (2009)
;
Phys. Rev. D
84
, 049901(E)
(2011)
.
[51] C. K. Mishra, A. Kela, K. G. Arun, and G. Faye,
Phys. Rev.
D
93
, 084054 (2016)
.
[52] J. A. Faber and F. A. Rasio,
Living Rev. Relativity
15
,8
(2012)
.
[53] S. Bernuzzi, A. Nagar, T. Dietrich, and T. Damour,
Phys.
Rev. Lett.
114
, 161103 (2015)
.
[54] T. Hinderer
et al.
,
Phys. Rev. Lett.
116
, 181101 (2016)
.
[55] T. Dietrich, S. Bernuzzi, and W. Tichy,
Phys. Rev. D
96
,
121501(R) (2017)
.
[56] T. Dietrich
et al.
,
Phys. Rev. D
99
, 024029 (2019)
.
[57] P. Schmidt, M. Hannam, and S. Husa,
Phys. Rev. D
86
,
104063 (2012)
.
[58] A. Boh ́
e
et al.
,
Phys. Rev. D
95
, 044028 (2017)
.
[59] M. Pürrer,
Classical Quantum Gravity
31
, 195010 (2014)
.
[60] J. M. Lattimer,
Annu. Rev. Nucl. Part. Sci.
62
, 485 (2012)
.
[61] Y. Suwa, T. Yoshida, M. Shibata, H. Umeda, and K.
Takahashi,
Mon. Not. R. Astron. Soc.
481
, 3305 (2018)
.
[62] E. Poisson,
Phys. Rev. D
57
, 5287 (1998)
.
[63] K. Yagi and N. Yunes,
Science
341
, 365 (2013)
.
[64] B. P. Abbott
et al.
(LIGO Scientific and Virgo Collabora-
tions),
arXiv:1903.04467
.
[65] K. G. Arun,
Classical Quantum Gravity
29
, 075011 (2012)
.
[66] E. Barausse, N. Yunes, and K. Chamberlain,
Phys. Rev.
Lett.
116
, 241104 (2016)
.
[67] A. G. Lyne
et al.
,
Science
303
, 1153 (2004)
.
[68] M. Kramer
et al.
,
Science
314
, 97 (2006)
.
[69] N. Yunes and S. A. Hughes,
Phys. Rev. D
82
, 082002
(2010)
.
[70] M. Kramer,
Int. J. Mod. Phys. D
25
, 1630029 (2016)
.
[71] P. C. C. Freire, N. Wex, G. Esposito-Farese, J. P. W.
Verbiest, M. Bailes, B. A. Jacoby, M. Kramer, I. H. Stairs,
J. Antoniadis, and G. H. Janssen,
Mon. Not. R. Astron. Soc.
423
, 3328 (2012)
.
[72] L. Shao, N. Sennett, A. Buonanno, M. Kramer, and N. Wex,
Phys. Rev. X
7
, 041025 (2017)
.
[73] D. Anderson, P. Freire, and N. Yunes,
arXiv:1901.00938
.
[74] T. Damour and G. Esposito-Farese,
Phys. Rev. Lett.
70
,
2220 (1993)
.
[75] F. M. Ramazano
ğ
lu and F. Pretorius,
Phys. Rev. D
93
,
064005 (2016)
.
[76] V. Cardoso, S. Chakrabarti, P. Pani, E. Berti, and L.
Gualtieri,
Phys. Rev. Lett.
107
, 241101 (2011)
.
[77] L. Sampson, N. Cornish, and N. Yunes,
Phys. Rev. D
89
,
064037 (2014)
.
[78] E. Barausse, C. Palenzuela, M. Ponce, and L. Lehner,
Phys.
Rev. D
87
, 081506(R) (2013)
.
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-8
[79] M. Shibata, K. Taniguchi, H. Okawa, and A. Buonanno,
Phys. Rev. D
89
, 084005 (2014)
.
[80] C. Palenzuela, E. Barausse, M. Ponce, and L. Lehner,
Phys.
Rev. D
89
, 044024 (2014)
.
[81] L. Sampson, N. Yunes, N. Cornish, M. Ponce, E. Barausse,
A. Klein, C. Palenzuela, and L. Lehner,
Phys. Rev. D
90
,
124091 (2014)
.
[82] C. M. Will,
Phys. Rev. D
57
, 2061 (1998)
.
[83] S. Mirshekari, N. Yunes, and C. M. Will,
Phys. Rev. D
85
,
024041 (2012)
.
[84] C. Deffayet and K. Menou,
Astrophys. J.
668
, L143 (2007)
.
[85] K. Pardo, M. Fishbach, D. E. Holz, and D. N. Spergel,
J. Cosmol. Astropart. Phys. 07 (
2018
) 048.
[86] V. A. Kostelecky and N. Russell,
Rev. Mod. Phys.
83
,11
(2011)
.
[87] M. Cantiello
et al.
,
Astrophys. J.
854
, L31 (2018)
.
[88] G. R. Dvali, G. Gabadadze, and M. Porrati,
Phys. Lett. B
485
, 208 (2000)
.
[89] A. Lue,
Phys. Rep.
423
, 1 (2006)
.
[90] D. M. Eardley, D. L. Lee, and A. P. Lightman,
Phys. Rev. D
8
, 3308 (1973)
.
[91] C. M. Will,
Living Rev. Relativity
17
, 4 (2014)
.
[92] K. Chatziioannou, N. Yunes, and N. Cornish,
Phys. Rev. D
86
, 022004 (2012)
.
[93] M. Isi, M. Pitkin, and A. J. Weinstein,
Phys. Rev. D
96
,
042001 (2017)
.
[94] T. Callister, A. S. Biscoveanu, N. Christensen, M. Isi, A.
Matas, O. Minazzoli, T. Regimbau, M. Sakellariadou, J.
Tasson, and E. Thrane,
Phys. Rev. X
7
, 041058 (2017)
.
[95] B. P. Abbott
et al.
(Virgo and LIGO Scientific Collabora-
tions),
Phys. Rev. Lett.
120
, 201102 (2018)
.
[96] B. P. Abbott
et al.
(Virgo and LIGO Scientific Collabora-
tions),
Phys. Rev. Lett.
120
, 031104 (2018)
.
[97] M. Isi and A. J. Weinstein,
arXiv:1710.03794
.
[98] B. P. Abbott
et al.
(LIGO Scientific, Virgo, and KAGRA
Collaborations),
Living Rev. Relativity
21
, 3 (2018)
.
B. P. Abbott,
1
R. Abbott,
1
T. D. Abbott,
2
F. Acernese,
3,4
K. Ackley,
5
C. Adams,
6
T. Adams,
7
P. Addesso,
8
R. X. Adhikari,
1
V. B. Adya,
9,10
C. Affeldt,
9,10
B. Agarwal,
11
M. Agathos,
12
K. Agatsuma,
13
N. Aggarwal,
14
O. D. Aguiar,
15
L. Aiello,
16,17
A. Ain,
18
P. Ajith,
19
B. Allen,
9,20,10
G. Allen,
11
A. Allocca,
21,22
M. A. Aloy,
23
P. A. Altin,
24
A. Amato,
25
A. Ananyeva,
1
S. B. Anderson,
1
W. G. Anderson,
20
S. V. Angelova,
26
S. Antier,
27
S. Appert,
1
K. Arai,
1
M. C. Araya,
1
J. S. Areeda,
28
M. Ar`
ene,
29
N. Arnaud,
27,30
K. G. Arun,
31
S. Ascenzi,
32,33
G. Ashton,
5
M. Ast,
34
S. M. Aston,
6
P. Astone,
35
D. V. Atallah,
36
F. Aubin,
7
P. Aufmuth,
10
C. Aulbert,
9
K. AultONeal,
37
C. Austin,
2
A. Avila-Alvarez,
28
S. Babak,
38,29
P. Bacon,
29
F. Badaracco,
16,17
M. K. M. Bader,
13
S. Bae,
39
P. T. Baker,
40
F. Baldaccini,
41,42
G. Ballardin,
30
S. W. Ballmer,
43
S. Banagiri,
44
J. C. Barayoga,
1
S. E. Barclay,
45
B. C. Barish,
1
D. Barker,
46
K. Barkett,
47
S. Barnum,
14
F. Barone,
3,4
B. Barr,
45
L. Barsotti,
14
M. Barsuglia,
29
D. Barta,
48
J. Bartlett,
46
I. Bartos,
49
R. Bassiri,
50
A. Basti,
21,22
J. C. Batch,
46
M. Bawaj,
51,42
J. C. Bayley,
45
M. Bazzan,
52,53
B. B ́
ecsy,
54
C. Beer,
9
M. Bejger,
55
I. Belahcene,
27
A. S. Bell,
45
D. Beniwal,
56
M. Bensch,
9,10
B. K. Berger,
1
G. Bergmann,
9,10
S. Bernuzzi,
57,58
J. J. Bero,
59
C. P. L. Berry,
60
D. Bersanetti,
61
A. Bertolini,
13
J. Betzwieser,
6
R. Bhandare,
62
I. A. Bilenko,
63
S. A. Bilgili,
40
G. Billingsley,
1
C. R. Billman,
49
J. Birch,
6
R. Birney,
26
O. Birnholtz,
59
S. Biscans,
1,14
S. Biscoveanu,
5
A. Bisht,
9,10
M. Bitossi,
30,22
M. A. Bizouard,
27
J. K. Blackburn,
1
J. Blackman,
47
C. D. Blair,
6
D. G. Blair,
64
R. M. Blair,
46
S. Bloemen,
65
O. Bock,
9
N. Bode,
9,10
M. Boer,
66
Y. Boetzel,
67
G. Bogaert,
66
A. Bohe,
38
F. Bondu,
68
E. Bonilla,
50
R. Bonnand,
7
P. Booker,
9,10
B. A. Boom,
13
C. D. Booth,
36
R. Bork,
1
V. Boschi,
30
S. Bose,
69,18
K. Bossie,
6
V. Bossilkov,
64
J. Bosveld,
64
Y. Bouffanais,
29
A. Bozzi,
30
C. Bradaschia,
22
P. R. Brady,
20
A. Bramley,
6
M. Branchesi,
16,17
J. E. Brau,
70
T. Briant,
71
F. Brighenti,
72,73
A. Brillet,
66
M. Brinkmann,
9,10
V. Brisson,
27
,
P. Brockill,
20
A. F. Brooks,
1
D. D. Brown,
56
S. Brunett,
1
C. C. Buchanan,
2
A. Buikema,
14
T. Bulik,
74
H. J. Bulten,
75,13
A. Buonanno,
38,76
D. Buskulic,
7
C. Buy,
29
R. L. Byer,
50
M. Cabero,
9
L. Cadonati,
77
G. Cagnoli,
25,78
C. Cahillane,
1
J. Calderón Bustillo,
77
T. A. Callister,
1
E. Calloni,
79,4
J. B. Camp,
80
M. Canepa,
81,61
P. Canizares,
65
K. C. Cannon,
82
H. Cao,
56
J. Cao,
83
C. D. Capano,
9
E. Capocasa,
29
F. Carbognani,
30
S. Caride,
84
M. F. Carney,
85
G. Carullo,
21
J. Casanueva Diaz,
22
C. Casentini,
32,33
S. Caudill,
13,20
M. Cavagli`
a,
86
F. Cavalier,
27
R. Cavalieri,
30
G. Cella,
22
C. B. Cepeda,
1
P. Cerdá-Durán,
23
G. Cerretani,
21,22
E. Cesarini,
87,33
O. Chaibi,
66
S. J. Chamberlin,
88
M. Chan,
45
S. Chao,
89
P. Charlton,
90
E. Chase,
91
E. Chassande-Mottin,
29
D. Chatterjee,
20
K. Chatziioannou,
92
B. D. Cheeseboro,
40
H. Y. Chen,
93
X. Chen,
64
Y. Chen,
47
H.-P. Cheng,
49
H. Y. Chia,
49
A. Chincarini,
61
A. Chiummo,
30
T. Chmiel,
85
H. S. Cho,
94
M. Cho,
76
J. H. Chow,
24
N. Christensen,
95,66
Q. Chu,
64
A. J. K. Chua,
47
S. Chua,
71
K. W. Chung,
96
S. Chung,
64
G. Ciani,
52,53,49
A. A. Ciobanu,
56
R. Ciolfi,
97,98
F. Cipriano,
66
C. E. Cirelli,
50
A. Cirone,
81,61
F. Clara,
46
J. A. Clark,
77
P. Clearwater,
99
F. Cleva,
66
C. Cocchieri,
86
E. Coccia,
16,17
P.-F. Cohadon,
71
D. Cohen,
27
A. Colla,
100,35
C. G. Collette,
101
C. Collins,
60
L. R. Cominsky,
102
M. Constancio Jr.,
15
L. Conti,
53
S. J. Cooper,
60
P. Corban,
6
T. R. Corbitt,
2
I. Cordero-Carrión,
103
K. R. Corley,
104
N. Cornish,
105
A. Corsi,
84
S. Cortese,
30
C. A. Costa,
15
R. Cotesta,
38
M. W. Coughlin,
1
S. B. Coughlin,
36,91
J.-P. Coulon,
66
S. T. Countryman,
104
P. Couvares,
1
P. B. Covas,
106
E. E. Cowan,
77
D. M. Coward,
64
M. J. Cowart,
6
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-9
D. C. Coyne,
1
R. Coyne,
107
J. D. E. Creighton,
20
T. D. Creighton,
108
J. Cripe,
2
S. G. Crowder,
109
T. J. Cullen,
2
A. Cumming,
45
L. Cunningham,
45
E. Cuoco,
30
T. Dal Canton,
80
G. Dálya,
54
S. L. Danilishin,
10,9
S. D
Antonio,
33
K. Danzmann,
9,10
A. Dasgupta,
110
C. F. Da Silva Costa,
49
V. Dattilo,
30
I. Dave,
62
M. Davier,
27
D. Davis,
43
E. J. Daw,
111
B. Day,
77
D. DeBra,
50
M. Deenadayalan,
18
J. Degallaix,
25
M. De Laurentis,
79,4
S. Del ́
eglise,
71
W. Del Pozzo,
21,22
N. Demos,
14
T. Denker,
9,10
T. Dent,
9
R. De Pietri,
57,58
J. Derby,
28
V. Dergachev,
9
R. De Rosa,
79,4
C. De Rossi,
25,30
R. DeSalvo,
112
O. de Varona,
9,10
S. Dhurandhar,
18
M. C. Díaz,
108
T. Dietrich,
13
L. Di Fiore,
4
M. Di Giovanni,
113,98
T. Di Girolamo,
79,4
A. Di Lieto,
21,22
B. Ding,
101
S. Di Pace,
100,35
I. Di Palma,
100,35
F. Di Renzo,
21,22
A. Dmitriev,
60
Z. Doctor,
93
V. Dolique,
25
F. Donovan,
14
K. L. Dooley,
36,86
S. Doravari,
9,10
I. Dorrington,
36
M. Dovale Álvarez,
60
T. P. Downes,
20
M. Drago,
9,16,17
C. Dreissigacker,
9,10
J. C. Driggers,
46
Z. Du,
83
P. Dupej,
45
S. E. Dwyer,
46
P. J. Easter,
5
T. B. Edo,
111
M. C. Edwards,
95
A. Effler,
6
H.-B. Eggenstein,
9,10
P. Ehrens,
1
J. Eichholz,
1
S. S. Eikenberry,
49
M. Eisenmann,
7
R. A. Eisenstein,
14
R. C. Essick,
93
H. Estelles,
106
D. Estevez,
7
Z. B. Etienne,
40
T. Etzel,
1
M. Evans,
14
T. M. Evans,
6
V. Fafone,
32,33,16
H. Fair,
43
S. Fairhurst,
36
X. Fan,
83
S. Farinon,
61
B. Farr,
70
W. M. Farr,
60
E. J. Fauchon-Jones,
36
M. Favata,
114
M. Fays,
36
C. Fee,
85
H. Fehrmann,
9
J. Feicht,
1
M. M. Fejer,
50
F. Feng,
29
A. Fernandez-Galiana,
14
I. Ferrante,
21,22
E. C. Ferreira,
15
F. Ferrini,
30
F. Fidecaro,
21,22
I. Fiori,
30
D. Fiorucci,
29
M. Fishbach,
93
R. P. Fisher,
43
J. M. Fishner,
14
M. Fitz-Axen,
44
R. Flaminio,
7,115
M. Fletcher,
45
H. Fong,
92
J. A. Font,
23,116
P. W. F. Forsyth,
24
S. S. Forsyth,
77
J.-D. Fournier,
66
S. Frasca,
100,35
F. Frasconi,
22
Z. Frei,
54
A. Freise,
60
R. Frey,
70
V. Frey,
27
P. Fritschel,
14
V. V. Frolov,
6
P. Fulda,
49
M. Fyffe,
6
H. A. Gabbard,
45
B. U. Gadre,
18
S. M. Gaebel,
60
J. R. Gair,
117
L. Gammaitoni,
41
M. R. Ganija,
56
S. G. Gaonkar,
18
A. Garcia,
28
C. García-Quirós,
106
F. Garufi,
79,4
B. Gateley,
46
S. Gaudio,
37
G. Gaur,
118
V. Gayathri,
119
G. Gemme,
61
E. Genin,
30
A. Gennai,
22
D. George,
11
J. George,
62
L. Gergely,
120
V. Germain,
7
S. Ghonge,
77
Abhirup Ghosh,
19
Archisman Ghosh,
13
S. Ghosh,
20
B. Giacomazzo,
113,98
J. A. Giaime,
2,6
K. D. Giardina,
6
A. Giazotto,
22
,
K. Gill,
37
G. Giordano,
3,4
L. Glover,
112
E. Goetz,
46
R. Goetz,
49
B. Goncharov,
5
G. González,
2
J. M. Gonzalez Castro,
21,22
A. Gopakumar,
121
M. L. Gorodetsky,
63
S. E. Gossan,
1
M. Gosselin,
30
R. Gouaty,
7
A. Grado,
122,4
C. Graef,
45
M. Granata,
25
A. Grant,
45
S. Gras,
14
C. Gray,
46
G. Greco,
72,73
A. C. Green,
60
R. Green,
36
E. M. Gretarsson,
37
P. Groot,
65
H. Grote,
36
S. Grunewald,
38
P. Gruning,
27
G. M. Guidi,
72,73
H. K. Gulati,
110
X. Guo,
83
A. Gupta,
88
M. K. Gupta,
110
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
123
O. Halim,
17,16
B. R. Hall,
69
E. D. Hall,
14
E. Z. Hamilton,
36
H. F. Hamilton,
124
G. Hammond,
45
M. Haney,
67
M. M. Hanke,
9,10
J. Hanks,
46
C. Hanna,
88
M. D. Hannam,
36
O. A. Hannuksela,
96
J. Hanson,
6
T. Hardwick,
2
J. Harms,
16,17
G. M. Harry,
125
I. W. Harry,
38
M. J. Hart,
45
C.-J. Haster,
92
K. Haughian,
45
J. Healy,
59
A. Heidmann,
71
M. C. Heintze,
6
H. Heitmann,
66
P. Hello,
27
G. Hemming,
30
M. Hendry,
45
I. S. Heng,
45
J. Hennig,
45
A. W. Heptonstall,
1
F. J. Hernandez,
5
M. Heurs,
9,10
S. Hild,
45
T. Hinderer,
65
D. Hoak,
30
S. Hochheim,
9,10
D. Hofman,
25
N. A. Holland,
24
K. Holt,
6
D. E. Holz,
93
P. Hopkins,
36
C. Horst,
20
J. Hough,
45
E. A. Houston,
45
E. J. Howell,
64
A. Hreibi,
66
E. A. Huerta,
11
D. Huet,
27
B. Hughey,
37
M. Hulko,
1
S. Husa,
106
S. H. Huttner,
45
T. Huynh-Dinh,
6
A. Iess,
32,33
N. Indik,
9
C. Ingram,
56
R. Inta,
84
G. Intini,
100,35
H. N. Isa,
45
J.-M. Isac,
71
M. Isi,
1
B. R. Iyer,
19
K. Izumi,
46
T. Jacqmin,
71
K. Jani,
77
P. Jaranowski,
126
D. S. Johnson,
11
W. W. Johnson,
2
D. I. Jones,
127
R. Jones,
45
R. J. G. Jonker,
13
L. Ju,
64
J. Junker,
9,10
C. V. Kalaghatgi,
36
V. Kalogera,
91
B. Kamai,
1
S. Kandhasamy,
6
G. Kang,
39
J. B. Kanner,
1
S. J. Kapadia,
20
S. Karki,
70
K. S. Karvinen,
9,10
M. Kasprzack,
2
M. Katolik,
11
S. Katsanevas,
30
E. Katsavounidis,
14
W. Katzman,
6
S. Kaufer,
9,10
K. Kawabe,
46
N. V. Keerthana,
18
F. K ́
ef ́
elian,
66
D. Keitel,
45
A. J. Kemball,
11
R. Kennedy,
111
J. S. Key,
128
F. Y. Khalili,
63
B. Khamesra,
77
H. Khan,
28
I. Khan,
16,33
S. Khan,
9
Z. Khan,
110
E. A. Khazanov,
129
N. Kijbunchoo,
24
Chunglee Kim,
130
J. C. Kim,
131
K. Kim,
96
W. Kim,
56
W. S. Kim,
132
Y.-M. Kim,
133
E. J. King,
56
P. J. King,
46
M. Kinley-Hanlon,
125
R. Kirchhoff,
9,10
J. S. Kissel,
46
L. Kleybolte,
34
S. Klimenko,
49
T. D. Knowles,
40
P. Koch,
9,10
S. M. Koehlenbeck,
9,10
S. Koley,
13
V. Kondrashov,
1
A. Kontos,
14
M. Korobko,
34
W. Z. Korth,
1
I. Kowalska,
74
D. B. Kozak,
1
C. Krämer,
9
V. Kringel,
9,10
B. Krishnan,
9
A. Królak,
134,135
G. Kuehn,
9,10
P. Kumar,
136
R. Kumar,
110
S. Kumar,
19
L. Kuo,
89
A. Kutynia,
134
S. Kwang,
20
B. D. Lackey,
38
K. H. Lai,
96
M. Landry,
46
R. N. Lang,
137
J. Lange,
59
B. Lantz,
50
R. K. Lanza,
14
A. Lartaux-Vollard,
27
P. D. Lasky,
5
M. Laxen,
6
A. Lazzarini,
1
C. Lazzaro,
53
P. Leaci,
100,35
S. Leavey,
9,10
C. H. Lee,
94
H. K. Lee,
138
H. M. Lee,
130
H. W. Lee,
131
K. Lee,
45
J. Lehmann,
9,10
A. Lenon,
40
M. Leonardi,
9,10,115
N. Leroy,
27
N. Letendre,
7
Y. Levin,
5
J. Li,
83
T. G. F. Li,
96
X. Li,
47
S. D. Linker,
112
T. B. Littenberg,
139
J. Liu,
64
X. Liu,
20
R. K. L. Lo,
96
N. A. Lockerbie,
26
L. T. London,
36
A. Longo,
140,141
M. Lorenzini,
16,17
V. Loriette,
142
M. Lormand,
6
G. Losurdo,
22
J. D. Lough,
9,10
C. O. Lousto,
59
G. Lovelace,
28
H. Lück,
9,10
D. Lumaca,
32,33
A. P. Lundgren,
9
R. Lynch,
14
Y. Ma,
47
R. Macas,
36
S. Macfoy,
26
B. Machenschalk,
9
M. MacInnis,
14
D. M. Macleod,
36
I. Magaña Hernandez,
20
F. Magaña-Sandoval,
43
L. Magaña Zertuche,
86
R. M. Magee,
88
E. Majorana,
35
I. Maksimovic,
142
N. Man,
66
V. Mandic,
44
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-10
V. Mangano,
45
G. L. Mansell,
24
M. Manske,
20,24
M. Mantovani,
30
F. Marchesoni,
51,42
F. Marion,
7
S. Márka,
104
Z. Márka,
104
C. Markakis,
11
A. S. Markosyan,
50
A. Markowitz,
1
E. Maros,
1
A. Marquina,
103
S. Marsat,
38
F. Martelli,
72,73
L. Martellini,
66
I. W. Martin,
45
R. M. Martin,
114
D. V. Martynov,
14
K. Mason,
14
E. Massera,
111
A. Masserot,
7
T. J. Massinger,
1
M. Masso-Reid,
45
S. Mastrogiovanni,
100,35
A. Matas,
44
F. Matichard,
1,14
L. Matone,
104
N. Mavalvala,
14
N. Mazumder,
69
J. J. McCann,
64
R. McCarthy,
46
D. E. McClelland,
24
S. McCormick,
6
L. McCuller,
14
S. C. McGuire,
143
J. McIver,
1
D. J. McManus,
24
T. McRae,
24
S. T. McWilliams,
40
D. Meacher,
88
G. D. Meadors,
5
M. Mehmet,
9,10
J. Meidam,
13
E. Mejuto-Villa,
8
A. Melatos,
99
G. Mendell,
46
D. Mendoza-Gandara,
9,10
R. A. Mercer,
20
L. Mereni,
25
E. L. Merilh,
46
M. Merzougui,
66
S. Meshkov,
1
C. Messenger,
45
C. Messick,
88
R. Metzdorff,
71
P. M. Meyers,
44
H. Miao,
60
C. Michel,
25
H. Middleton,
99
E. E. Mikhailov,
144
L. Milano,
79,4
A. L. Miller,
49
A. Miller,
100,35
B. B. Miller,
91
J. Miller,
14
M. Millhouse,
105
J. Mills,
36
M. C. Milovich-Goff,
112
O. Minazzoli,
66,145
Y. Minenkov,
33
J. Ming,
9,10
C. Mishra,
146
S. Mitra,
18
V. P. Mitrofanov,
63
G. Mitselmakher,
49
R. Mittleman,
14
D. Moffa,
85
K. Mogushi,
86
M. Mohan,
30
S. R. P. Mohapatra,
14
M. Montani,
72,73
C. J. Moore,
12
D. Moraru,
46
G. Moreno,
46
S. Morisaki,
82
B. Mours,
7
C. M. Mow-Lowry,
60
G. Mueller,
49
A. W. Muir,
36
Arunava Mukherjee,
9,10
D. Mukherjee,
20
S. Mukherjee,
108
N. Mukund,
18
A. Mullavey,
6
J. Munch,
56
E. A. Muñiz,
43
M. Muratore,
37
P. G. Murray,
45
A. Nagar,
87,147,148
K. Napier,
77
I. Nardecchia,
32,33
L. Naticchioni,
100,35
R. K. Nayak,
149
J. Neilson,
112
G. Nelemans,
65,13
T. J. N. Nelson,
6
M. Nery,
9,10
A. Neunzert,
123
L. Nevin,
1
J. M. Newport,
125
K. Y. Ng,
14
S. Ng,
56
P. Nguyen,
70
T. T. Nguyen,
24
D. Nichols,
65
A. B. Nielsen,
9
S. Nissanke,
65,13
A. Nitz,
9
F. Nocera,
30
D. Nolting,
6
C. North,
36
L. K. Nuttall,
36
M. Obergaulinger,
23
J. Oberling,
46
B. D. O
Brien,
49
G. D. O
Dea,
112
G. H. Ogin,
150
J. J. Oh,
132
S. H. Oh,
132
F. Ohme,
9
H. Ohta,
82
M. A. Okada,
15
M. Oliver,
106
P. Oppermann,
9,10
Richard J. Oram,
6
B. O
Reilly,
6
R. Ormiston,
44
L. F. Ortega,
49
R. O
Shaughnessy,
59
S. Ossokine,
38
D. J. Ottaway,
56
H. Overmier,
6
B. J. Owen,
84
A. E. Pace,
88
G. Pagano,
21,22
J. Page,
139
M. A. Page,
64
A. Pai,
119
S. A. Pai,
62
J. R. Palamos,
70
O. Palashov,
129
C. Palomba,
35
A. Pal-Singh,
34
Howard Pan,
89
Huang-Wei Pan,
89
B. Pang,
47
P. T. H. Pang,
96
C. Pankow,
91
F. Pannarale,
36
B. C. Pant,
62
F. Paoletti,
22
A. Paoli,
30
M. A. Papa,
9,20,10
A. Parida,
18
W. Parker,
6
D. Pascucci,
45
A. Pasqualetti,
30
R. Passaquieti,
21,22
D. Passuello,
22
M. Patil,
135
B. Patricelli,
151,22
B. L. Pearlstone,
45
C. Pedersen,
36
M. Pedraza,
1
R. Pedurand,
25,152
L. Pekowsky,
43
A. Pele,
6
S. Penn,
153
C. J. Perez,
46
A. Perreca,
113,98
L. M. Perri,
91
H. P. Pfeiffer,
92,38
M. Phelps,
45
K. S. Phukon,
18
O. J. Piccinni,
100,35
M. Pichot,
66
F. Piergiovanni,
72,73
V. Pierro,
8
G. Pillant,
30
L. Pinard,
25
I. M. Pinto,
8
M. Pirello,
46
M. Pitkin,
45
R. Poggiani,
21,22
P. Popolizio,
30
E. K. Porter,
29
L. Possenti,
154,73
A. Post,
9
J. Powell,
155
J. Prasad,
18
J. W. W. Pratt,
37
G. Pratten,
106
V. Predoi,
36
T. Prestegard,
20
M. Principe,
8
S. Privitera,
38
G. A. Prodi,
113,98
L. G. Prokhorov,
63
O. Puncken,
9,10
M. Punturo,
42
P. Puppo,
35
M. Pürrer,
38
H. Qi,
20
V. Quetschke,
108
E. A. Quintero,
1
R. Quitzow-James,
70
F. J. Raab,
46
D. S. Rabeling,
24
H. Radkins,
46
P. Raffai,
54
S. Raja,
62
C. Rajan,
62
B. Rajbhandari,
84
M. Rakhmanov,
108
K. E. Ramirez,
108
A. Ramos-Buades,
106
Javed Rana,
18
P. Rapagnani,
100,35
V. Raymond,
36
M. Razzano,
21,22
J. Read,
28
T. Regimbau,
66,7
L. Rei,
61
S. Reid,
26
D. H. Reitze,
1,49
W. Ren,
11
F. Ricci,
100,35
P. M. Ricker,
11
G. M. Riemenschneider,
147,156
K. Riles,
123
M. Rizzo,
59
N. A. Robertson,
1,45
R. Robie,
45
F. Robinet,
27
T. Robson,
105
A. Rocchi,
33
L. Rolland,
7
J. G. Rollins,
1
V. J. Roma,
70
R. Romano,
3,4
C. L. Romel,
46
J. H. Romie,
6
D. Rosi
ń
ska,
157,55
M. P. Ross,
158
S. Rowan,
45
A. Rüdiger,
9,10
P. Ruggi,
30
G. Rutins,
159
K. Ryan,
46
S. Sachdev,
1
T. Sadecki,
46
M. Sakellariadou,
160
L. Salconi,
30
M. Saleem,
119
F. Salemi,
9
A. Samajdar,
149,13
L. Sammut,
5
L. M. Sampson,
91
E. J. Sanchez,
1
L. E. Sanchez,
1
N. Sanchis-Gual,
23
V. Sandberg,
46
J. R. Sanders,
43
N. Sarin,
5
B. Sassolas,
25
B. S. Sathyaprakash,
88,36
P. R. Saulson,
43
O. Sauter,
123
R. L. Savage,
46
A. Sawadsky,
34
P. Schale,
70
M. Scheel,
47
J. Scheuer,
91
P. Schmidt,
65
R. Schnabel,
34
R. M. S. Schofield,
70
A. Schönbeck,
34
E. Schreiber,
9,10
D. Schuette,
9,10
B. W. Schulte,
9,10
B. F. Schutz,
36,9
S. G. Schwalbe,
37
J. Scott,
45
S. M. Scott,
24
E. Seidel,
11
D. Sellers,
6
A. S. Sengupta,
161
N. Sennett,
38
D. Sentenac,
30
V. Sequino,
32,33,16
A. Sergeev,
129
Y. Setyawati,
9
D. A. Shaddock,
24
T. J. Shaffer,
46
A. A. Shah,
139
M. S. Shahriar,
91
M. B. Shaner,
112
L. Shao,
38
B. Shapiro,
50
P. Shawhan,
76
H. Shen,
11
D. H. Shoemaker,
14
D. M. Shoemaker,
77
K. Siellez,
77
X. Siemens,
20
M. Sieniawska,
55
D. Sigg,
46
A. D. Silva,
15
L. P. Singer,
80
A. Singh,
9,10
A. Singhal,
16,35
A. M. Sintes,
106
B. J. J. Slagmolen,
24
T. J. Slaven-Blair,
64
B. Smith,
6
J. R. Smith,
28
R. J. E. Smith,
5
S. Somala,
162
E. J. Son,
132
B. Sorazu,
45
F. Sorrentino,
61
T. Souradeep,
18
A. P. Spencer,
45
A. K. Srivastava,
110
K. Staats,
37
D. A. Steer,
29
M. Steinke,
9,10
J. Steinlechner,
34,45
S. Steinlechner,
34
D. Steinmeyer,
9,10
B. Steltner,
9,10
S. P. Stevenson,
155
D. Stocks,
50
R. Stone,
108
D. J. Stops,
60
K. A. Strain,
45
G. Stratta,
72,73
S. E. Strigin,
63
A. Strunk,
46
R. Sturani,
163
A. L. Stuver,
164
T. Z. Summerscales,
165
L. Sun,
99
S. Sunil,
110
J. Suresh,
18
P. J. Sutton,
36
B. L. Swinkels,
13
M. J. Szczepa
ń
czyk,
37
M. Tacca,
13
S. C. Tait,
45
C. Talbot,
5
D. Talukder,
70
N. Tamanini,
38
D. B. Tanner,
49
M. Tápai,
120
A. Taracchini,
38
J. D. Tasson,
95
J. A. Taylor,
139
R. Taylor,
1
S. V. Tewari,
153
T. Theeg,
9,10
F. Thies,
9,10
E. G. Thomas,
60
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-11
M. Thomas,
6
P. Thomas,
46
K. A. Thorne,
6
E. Thrane,
5
S. Tiwari,
16,98
V. Tiwari,
36
K. V. Tokmakov,
26
K. Toland,
45
M. Tonelli,
21,22
Z. Tornasi,
45
A. Torres-Forn ́
e,
23
C. I. Torrie,
1
D. Töyrä,
60
F. Travasso,
30,42
G. Traylor,
6
J. Trinastic,
49
M. C. Tringali,
113,98
L. Trozzo,
166,22
K. W. Tsang,
13
M. Tse,
14
R. Tso,
47
L. Tsukada,
82
D. Tsuna,
82
D. Tuyenbayev,
108
K. Ueno,
20
D. Ugolini,
167
A. L. Urban,
1
S. A. Usman,
36
H. Vahlbruch,
9,10
G. Vajente,
1
G. Valdes,
2
N. van Bakel,
13
M. van Beuzekom,
13
J. F. J. van den Brand,
75,13
C. Van Den Broeck,
13,168
D. C. Vander-Hyde,
43
L. van der Schaaf,
13
J. V. van Heijningen,
13
A. A. van Veggel,
45
M. Vardaro,
52,53
V. Varma,
47
S. Vass,
1
M. Vasúth,
48
A. Vecchio,
60
G. Vedovato,
53
J. Veitch,
45
P. J. Veitch,
56
K. Venkateswara,
158
G. Venugopalan,
1
D. Verkindt,
7
F. Vetrano,
72,73
A. Vicer ́
e,
72,73
A. D. Viets,
20
S. Vinciguerra,
60
D. J. Vine,
159
J.-Y. Vinet,
66
S. Vitale,
14
T. Vo,
43
H. Vocca,
41,42
C. Vorvick,
46
S. P. Vyatchanin,
63
A. R. Wade,
1
L. E. Wade,
85
M. Wade,
85
R. Walet,
13
M. Walker,
28
L. Wallace,
1
S. Walsh,
20,9
G. Wang,
16,22
H. Wang,
60
J. Z. Wang,
123
W. H. Wang,
108
Y. F. Wang,
96
R. L. Ward,
24
J. Warner,
46
M. Was,
7
J. Watchi,
101
B. Weaver,
46
L.-W. Wei,
9,10
M. Weinert,
9,10
A. J. Weinstein,
1
R. Weiss,
14
F. Wellmann,
9,10
L. Wen,
64
E. K. Wessel,
11
P. Weßels,
9,10
J. Westerweck,
9
K. Wette,
24
J. T. Whelan,
59
B. F. Whiting,
49
C. Whittle,
14
D. Wilken,
9,10
D. Williams,
45
R. D. Williams,
1
A. R. Williamson,
59,65
J. L. Willis,
1,124
B. Willke,
9,10
M. H. Wimmer,
9,10
W. Winkler,
9,10
C. C. Wipf,
1
H. Wittel,
9,10
G. Woan,
45
J. Woehler,
9,10
J. K. Wofford,
59
W. K. Wong,
96
J. Worden,
46
J. L. Wright,
45
D. S. Wu,
9,10
D. M. Wysocki,
59
S. Xiao,
1
W. Yam,
14
H. Yamamoto,
1
C. C. Yancey,
76
L. Yang,
169
M. J. Yap,
24
M. Yazback,
49
Hang Yu,
14
Haocun Yu,
14
M. Yvert,
7
A. Zadro
ż
ny,
134
M. Zanolin,
37
T. Zelenova,
30
J.-P. Zendri,
53
M. Zevin,
91
J. Zhang,
64
L. Zhang,
1
M. Zhang,
144
T. Zhang,
45
Y.-H. Zhang,
9,10
C. Zhao,
64
M. Zhou,
91
Z. Zhou,
91
S. J. Zhu,
9,10
X. J. Zhu,
5
A. B. Zimmerman,
170,92
M. E. Zucker,
1,14
and J. Zweizig
1
(LIGO Scientific Collaboration and Virgo Collaboration)
1
LIGO, California Institute of Technology, Pasadena, California 91125, USA
2
Louisiana State University, Baton Rouge, Louisiana 70803, USA
3
Universit`
a di Salerno, Fisciano, I-84084 Salerno, Italy
4
INFN, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
5
OzGrav, School of Physics & Astronomy, Monash University, Clayton 3800, Victoria, Australia
6
LIGO Livingston Observatory, Livingston, Louisiana 70754, USA
7
Laboratoire d
Annecy de Physique des Particules (LAPP), Univ. Grenoble Alpes, Universit ́
e Savoie Mont Blanc,
CNRS/IN2P3, F-74941 Annecy, France
8
University of Sannio at Benevento, I-82100 Benevento, Italy and INFN, Sezione di Napoli, I-80100 Napoli, Italy
9
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-30167 Hannover, Germany
10
Leibniz Universität Hannover, D-30167 Hannover, Germany
11
NCSA, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
12
University of Cambridge, Cambridge CB2 1TN, United Kingdom
13
Nikhef, Science Park 105, 1098 XG Amsterdam, Netherlands
14
LIGO, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
15
Instituto Nacional de Pesquisas Espaciais, 12227-010 São Jos ́
e dos Campos, São Paulo, Brazil
16
Gran Sasso Science Institute (GSSI), I-67100 L
Aquila, Italy
17
INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy
18
Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India
19
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
20
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, USA
21
Universit`
a di Pisa, I-56127 Pisa, Italy
22
INFN, Sezione di Pisa, I-56127 Pisa, Italy
23
Departamento de Astronomía y Astrofísica, Universitat de Val`
encia, E-46100 Burjassot, Val`
encia, Spain
24
OzGrav, Australian National University, Canberra, Australian Capital Territory 0200, Australia
25
Laboratoire des Mat ́
eriaux Avanc ́
es (LMA), CNRS/IN2P3, F-69622 Villeurbanne, France
26
SUPA, University of Strathclyde, Glasgow G1 1XQ, United Kingdom
27
LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit ́
e Paris-Saclay, F-91898 Orsay, France
28
California State University Fullerton, Fullerton, California 92831, USA
29
APC, AstroParticule et Cosmologie, Universit ́
e Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris,
Sorbonne Paris Cit ́
e, F-75205 Paris Cedex 13, France
30
European Gravitational Observatory (EGO), I-56021 Cascina, Pisa, Italy
31
Chennai Mathematical Institute, Chennai 603103, India
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-12
32
Universit`
a di Roma Tor Vergata, I-00133 Roma, Italy
33
INFN, Sezione di Roma Tor Vergata, I-00133 Roma, Italy
34
Universität Hamburg, D-22761 Hamburg, Germany
35
INFN, Sezione di Roma, I-00185 Roma, Italy
36
Cardiff University, Cardiff CF24 3AA, United Kingdom
37
Embry-Riddle Aeronautical University, Prescott, Arizona 86301, USA
38
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany
39
Korea Institute of Science and Technology Information, Daejeon 34141, Korea
40
West Virginia University, Morgantown, West Virginia 26506, USA
41
Universit`
a di Perugia, I-06123 Perugia, Italy
42
INFN, Sezione di Perugia, I-06123 Perugia, Italy
43
Syracuse University, Syracuse, New York 13244, USA
44
University of Minnesota, Minneapolis, Minnesota 55455, USA
45
SUPA, University of Glasgow, Glasgow G12 8QQ, United Kingdom
46
LIGO Hanford Observatory, Richland, Washington 99352, USA
47
Caltech CaRT, Pasadena, California 91125, USA
48
Wigner RCP, RMKI, H-1121 Budapest, Konkoly Thege Miklós út 29-33, Hungary
49
University of Florida, Gainesville, Florida 32611, USA
50
Stanford University, Stanford, California 94305, USA
51
Universit`
a di Camerino, Dipartimento di Fisica, I-62032 Camerino, Italy
52
Universit`
a di Padova, Dipartimento di Fisica e Astronomia, I-35131 Padova, Italy
53
INFN, Sezione di Padova, I-35131 Padova, Italy
54
MTA-ELTE Astrophysics Research Group, Institute of Physics, Eötvös University, Budapest 1117, Hungary
55
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, 00-716, Warsaw, Poland
56
OzGrav, University of Adelaide, Adelaide, South Australia 5005, Australia
57
Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Universit`
a di Parma, I-43124 Parma, Italy
58
INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy
59
Rochester Institute of Technology, Rochester, New York 14623, USA
60
University of Birmingham, Birmingham B15 2TT, United Kingdom
61
INFN, Sezione di Genova, I-16146 Genova, Italy
62
RRCAT, Indore, Madhya Pradesh 452013, India
63
Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
64
OzGrav, University of Western Australia, Crawley, Western Australia 6009, Australia
65
Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, Netherlands
66
Artemis, Universit ́
e Côte d
Azur, Observatoire Côte d
Azur, CNRS, CS 34229, F-06304 Nice Cedex 4, France
67
Physik-Institut, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
68
Univ Rennes, CNRS, Institut FOTON
UMR6082, F-3500 Rennes, France
69
Washington State University, Pullman, Washington 99164, USA
70
University of Oregon, Eugene, Oregon 97403, USA
71
Laboratoire Kastler Brossel, Sorbonne Universit ́
e, CNRS, ENS-Universit ́
e PSL, Coll`
ege de France, F-75005 Paris, France
72
Universit`
a degli Studi di Urbino
Carlo Bo
, I-61029 Urbino, Italy
73
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy
74
Astronomical Observatory Warsaw University, 00-478 Warsaw, Poland
75
VU University Amsterdam, 1081 HV Amsterdam, Netherlands
76
University of Maryland, College Park, Maryland 20742, USA
77
School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
78
Universit ́
e Claude Bernard Lyon 1, F-69622 Villeurbanne, France
79
Universit`
a di Napoli
Federico II
, Complesso Universitario di Monte S.Angelo, I-80126 Napoli, Italy
80
NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
81
Dipartimento di Fisica, Universit`
a degli Studi di Genova, I-16146 Genova, Italy
82
RESCEU, University of Tokyo, Tokyo, 113-0033, Japan
83
Tsinghua University, Beijing 100084, China
84
Texas Tech University, Lubbock, Texas 79409, USA
85
Kenyon College, Gambier, Ohio 43022, USA
86
The University of Mississippi, University, Mississippi 38677, USA
87
Museo Storico della Fisica e Centro Studi e Ricerche
Enrico Fermi
, I-00184 Roma, Italyrico Fermi, I-00184 Roma, Italy
88
The Pennsylvania State University, University Park, Pennsylvania 16802, USA
89
National Tsing Hua University, Hsinchu City, 30013 Taiwan, Republic of China
90
Charles Sturt University, Wagga Wagga, New South Wales 2678, Australia
PHYSICAL REVIEW LETTERS
123,
011102 (2019)
011102-13