of 13
First Search for Nontensorial Gravitational Waves from Known Pulsars
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 12 October 2017; revised manuscript received 16 November 2017; published 19 January 2018)
We present results from the first directed search for nontensorial gravitational waves. While general
relativity allows for tensorial (plus and cross) modes only, a generic metric theory may, in principle, predict
waves with up to six different polarizations. This analysis is sensitive to continuous signals of scalar, vector,
or tensor polarizations, and does not rely on any specific theory of gravity. After searching data from the
first observation run of the advanced LIGO detectors for signals at twice the rotational frequency of 200
known pulsars, we find no evidence of gravitational waves of any polarization. We report the first upper
limits for scalar and vector strains, finding values comparable in magnitude to previously published limits
for tensor strain. Our results may be translated into constraints on specific alternative theories of gravity.
DOI:
10.1103/PhysRevLett.120.031104
Introduction.
The first gravitational waves detected by
the Advanced Laser Interferometer Gravitational-Wave
Observatory (aLIGO) and Virgo have already been used
to place some of the most stringent constraints on devia-
tions from the general theory of relativity (GR) in the
highly dynamical and strong-field regimes of gravity
[1
4]
.
However, even though some partial progress has been made
with the observation of GW170814
[5,6]
and in spite of the
wealth of new information provided by GW170817
[7,8]
,it
has not yet been possible to unambiguously confirm GR
s
prediction that the associated metric perturbations are of a
tensor nature (helicity

2
), rather than vector (helicity

1
),
or scalar (helicity 0)
[9]
. This is unfortunate, since the
presence of nontensorial modes is a key prediction of many
extensions to GR
[10
14]
. Most importantly, the detection
of a scalar or vector component, no matter how small,
would automatically point to physics beyond Einstein
s
theory
[12,13]
.
In orderto experimentallystudy gravitational-wave polar-
izations directly, one needs a local measurement of their
geometric effect (i.e., which directions are stretched and
squeezed) that breaks degeneracies between the five dis-
tinguishable (to differential-arm instruments) modes sup-
ported by a generic metric theory of gravity
[10,11]
.For
transient waves like those detected so far, this cannot be fully
achieved with the LIGO-Virgo network, as at least five non-
co-oriented differential-arm antennas are required to break
all
such degeneracies
[13,15]
. Constraints on the magnitude
of non-GR polarizations inferred from indirect measure-
ments, like the rate of orbital decay of binary pulsars, are
only meaningful in the context of specific theories (see, e.g.,
Refs.
[16,17]
or Refs.
[18,19]
for reviews).
Theory-independent polarization measurements could
instead be carried out with current detectors in the presence
of signals sufficiently long to probe the detector antenna
patterns, which are themselves polarization sensitive
[20
23]
. Such is the case, for instance, for the continuous,
almost-monochromatic waves expected from spinning neu-
tron stars with an asymmetric moment of inertia
[24]
.
Known galactic pulsars are one of the main candidates
for searches for such signals in data from ground-based
detectors, and analyses targeting them have already achieved
sensitivities that are comparable to, or even surpass, their
canonical spin-down limit (i.e., the strain that would be
producediftheobservedslowdowninthepulsar
s rotation
was completely due to gravitational radiation)
[25]
.
However, all previous targeted searches have been, by
design, restricted to tensorial gravitational polarizations
only
.
This leaves open the possibility that, due to a departure from
GR, the neutron stars targeted in previous searches may
indeed be emitting strong continuous waves with non-
tensorial content, in spite of the null results of standard
searches.
In this Letter, we present results from a search for
continuous gravitational waves in aLIGO data that makes
no assumptions about how the gravitational field transforms
under local spatial rotations, and is thus sensitive to any of
the five measurable polarizations allowed by a generic metric
theory of gravity. We targeted 200 known pulsars using data
from aLIGO
s first observation run (O1), and assuming
emission at twice the rotational frequency of the source.
Our data provide no evidence for the emission of
gravitational signals of tensorial or nontensorial polariza-
tion from any of the pulsars targeted. For sources in the
most sensitive band of our detectors, we constrain the strain
of the scalar and vector modes to be below
1
.
5
×
10
26
at 95% credibility. These are the first direct upper limits for
*
Full author list given at the end of this article.
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
0031-9007
=
18
=
120(3)
=
031104(13)
031104-1
© 2018 American Physical Society
scalar and vector strain, and may in principle be used to
constrain beyond-GR theories of gravity.
Analysis.
We search aLIGO O1 data from the Hanford
(H1) and Livingston (L1) detectors for continuous waves of
any polarization (tensor, scalar, or vector) by applying the
Bayesian time-domain method of Ref.
[26]
, generalized to
non-GR modes as described in Ref.
[21]
and summarized
below. Our analysis follows closely that of Ref.
[25]
, and
uses the exact same interferometric data.
Calibrated detector data are heterodyned and filtered
using the timing solutions obtained from electromagnetic
observations for each pulsar. The maximum calibration
uncertainties estimated over the whole run give a limit on
the combined H1 and L1 amplitude uncertainties of 14%
this is the conservative level of uncertainty on the strain
upper limits
[25,27]
.
The data streams start on 2015 Sep 11 at 01
25:03 UTC
for H1 and 18
29:03 UTC for L1, and finish on 2016 Jan 19
at 17
07:59 UTC at both sites. The pulsar timing solutions
used are also the same as in Ref.
[25]
and were obtained
from the 42-ft telescope and Lovell telescope at Jodrell
Bank (UK), the 26-m telescope at Hartebeesthoek (South
Africa), the Parkes radio telescope (Australia), the Nancay
Decimetric Radio Telescope (France), the Arecibo
Observatory (Puerto Rico), and the
Fermi
Large Area
Telescope (LAT).
As described in detail in Ref.
[21]
, we construct a
Bayesian hypothesis that captures signals of any polariza-
tion content (our
any-signal
hypothesis,
H
S
) by combining
the sub-hypotheses corresponding to the signal being
composed of tensor, vector, scalar modes, or any combi-
nation thereof. Each of these sub-hypotheses corresponds
to a different signal model; in particular, the least restrictive
template includes contributions from all polarizations and
can be written as
h
ð
t
Þ¼
X
p
F
p
ð
t
;
α
;
δ
;
ψ
Þ
h
p
ð
t
Þ
;
ð
1
Þ
where the sum is over the five independent polarizations:
plus (
þ
), cross (×), vector
x
(
x
), vector
y
(
y
), and scalar (
s
)
[11]
. The two scalar modes in the most common basis,
breathing and longitudinal, are degenerate for networks of
quadrupolar antennas
[13]
, so we do not make a distinction
between them.
Each term in Eq.
(1)
is the product of an antenna pattern
function
F
p
and an intrinsic strain function
h
p
. We define
the different polarizations in a wave frame such that the
z
axis points in the direction of propagation,
x
lies in the
plane of the sky along the line of nodes (here defined to be
the intersection of the equatorial plane of the source with
the plane of the sky), and
y
completes the right-handed
system, such that the polarization angle
ψ
is the angle
between the
y
axis and the projection of the celestial North
onto the plane of the sky (see, e.g., Ref.
[28]
). We can thus
write the
F
p
s as implicit functions of the source
s right
ascension
α
, declination
δ
, and polarization
ψ
. (For the
sources targeted here,
α
and
δ
are always known to high
accuracy, while
ψ
is usually unknown.) The antenna
patterns acquire their time dependence from the sidereal
rotation of Earth; explicit expressions for the
F
p
s are given
in Refs.
[20
22,29,30]
.
For a continuous wave, the polarizations take the simple
form
h
p
ð
t
Þ¼
a
p
cos
½
φ
ð
t
Þþ
φ
p

;
ð
2
Þ
where
a
p
is a time-independent strain amplitude,
φ
ð
t
Þ
is the
intrinsic phase evolution, and
φ
p
a phase offset for each
polarization. The nature of these three quantities depends
on the specifics of the underlying theory of gravity and the
associated emission mechanism (for different emission
mechanisms within GR, see, e.g., Refs.
[31
33]
). While
we treat
a
p
and
φ
p
as free parameters, we take
φ
ð
t
Þ
to be
the same as in the traditional GR analysis
[25]
:
φ
ð
t
Þ¼
2
π
X
N
j
¼
0
ð
j
Þ
t
f
GW
;
0
ð
j
þ
1
Þ
!
½
t
T
0
þ
δ
t
ð
t
Þ
ð
j
þ
1
Þ
;
ð
3
Þ
where
ð
j
Þ
t
f
GW
;
0
is the
j
th time derivative of
f
GW
;
0
, the
emission frequency measured at the fiducial time
T
0
;
δ
t
ð
t
Þ
is the time delay from the observatory to the solar system
barycenter (including the known Rømer, Shapiro and
Einstein delays), and can also include binary system
corrections to transform the time coordinate to a frame
approximately inertial with respect to the source;
N
is the
order of the series expansion (1 or 2 for most sources).
The gravitational-wave frequency
f
GW
is related to the
rotational frequency of the source
f
rot
, which is in turn
known from electromagnetic observations. Although arbi-
trary theories of gravity and emission mechanisms may
predict gravitational emission at any multiple of the rota-
tional frequency, here we assume
f
GW
¼
2
f
rot
, in accor-
dance with the most favored emission model in GR
[24]
.
This restriction arises from practical considerations affect-
ing our specific implementation, and will be relaxed in
future studies.
For convenience, we define
effective strain amplitudes
for tensor, vector, and scalar modes, respectively, by
h
t
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a
2
þ
þ
a
2
×
q
;
ð
4
Þ
h
v
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a
2
x
þ
a
2
y
q
;
ð
5
Þ
h
s
a
s
;
ð
6
Þ
in terms of the intrinsic
a
p
amplitudes of Eq.
(2)
. These
quantities may serve as proxy for the total power in each
polarization group.
One may recover the GR hypothesis considered in
previous analyses by setting
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
031104-2
a
þ
¼
h
0
ð
1
þ
cos
2
ι
Þ
=
2
;
φ
þ
¼
φ
0
;
ð
7
Þ
a
×
¼
h
0
cos
ι
;
φ
×
¼
φ
0
π
=
2
;
ð
8
Þ
a
x
¼
a
y
¼
a
s
¼
0
;
ð
9
Þ
where
ι
is the inclination (angle between the line of sight
and the spin axis of the source), and
h
0
,
φ
0
are free
parameters. (As with
ψ
,
ι
is unknown for most pulsars.)
This corresponds to the standard triaxial-star emission
mechanism (see, e.g., Ref.
[34]
). We use this parameter-
ization only when we wish to incorporate known orienta-
tion information as explained below; otherwise, we
parametrize the tensor polarizations directly in terms of
a
þ
,
a
×
,
φ
þ
and
φ
×
.
Templates of the form of Eq.
(1)
, together with appro-
priate priors, allow us to compute Bayes factors (margin-
alized-likelihood ratios) for the presence of signals in the
data vs Gaussian noise. We do this using an extension of
the nested sampling implementation presented in Ref.
[35]
(see Ref.
[21]
for details specific to non-GR polarizations).
The Bayes factors corresponding to each signal model may
be combined into the odds
O
S
N
that the data contain a
continuous signal of any polarization vs Gaussian noise:
O
S
N
¼
P
ð
H
S
j
B
Þ
=P
ð
H
N
j
B
Þ
;
ð
10
Þ
i.e., the ratio of the posterior probabilities that the data
B
contain a signal of any polarizations (
H
S
) vs just Gaussian
noise (
H
N
). We compute these odds by setting model priors
such that
P
ð
H
S
Þ¼
P
ð
H
N
Þ
; then, by Bayes
theorem,
O
S
N
¼
B
S
N
, with the Bayes factor
B
S
N
P
ð
B
j
H
S
Þ
=P
ð
B
j
H
N
Þ
:
ð
11
Þ
Built into the astrophysical signal hypothesis,
H
S
, is the
requirement of coherence across detectors, which must be
satisfied by a real gravitational wave. In order to make the
analysis more robust against non-Gaussian instrumental
features in the data, we also define an
instrumental feature
hypothesis,
H
I
, that identifies non-Gaussian noise artifacts
by their lack of coherence across detectors
[25,36]
.In
particular, we define
H
I
to capture Gaussian noise
or
a
detector-incoherent signal (i.e., a feature that mimics an
astrophysical signal in a single instrument, but is not
recovered consistently across the network) in each detector
[21]
. We may then compare this to
H
S
by means of the odds
O
S
I
.For
D
detectors, this is given by
log
O
S
I
¼
log
B
S
N
X
D
d
¼
1
log
ð
B
S
d
N
d
þ
1
Þ
;
ð
12
Þ
where
B
S
d
N
d
is the signal vs noise Bayes factor computed
only from data from the
d
th detector. This choice implicitly
assigns prior weight to the models such that
P
ð
H
S
Þ¼
P
ð
H
I
Þ
×
0
.
5
D
[21]
. For an in depth analysis of the behavior
of the different Bayesian hypotheses considered here, in
the presence and absence of simulated signals of all
polarizations, we again refer the reader to the methods
paper
[21]
.
We compute likelihoods by taking source location,
frequency, and frequency derivatives as known quantities.
In computing Bayes factors, we employ priors uniform in
the logarithm of amplitude parameters (
h
0
or
a
p
s), since
these are the least informative priors for scaling coefficients
[37]
; we bound these amplitudes to the
10
28
10
24
range
[38]
. On the other hand, flat amplitude priors are used to
compute upper limits, to facilitate comparison with pub-
lished GR results in Ref.
[25]
. In all cases, flat priors are
placed over all phase offsets (
φ
0
and all the
φ
p
s).
For those few cases in which some orientation informa-
tion exists (see Table
I
), we analyze the data a second time
using the triaxial parametrization of tensor modes, Eqs.
(7)
and
(8)
, taking that information into account by margin-
alizing over ranges of cos
ι
and
ψ
in agreement with
measurement uncertainties. Following previous work
[25]
, we only consider orientation constraints obtained
from pulsar wind nebulae. However, pulsar orientations can
also be inferred from other measurements, especially if the
object is in a binary (e.g., Refs.
[39
41]
). We will consider
incorporating such constraints in future searches.
Results.
We find no evidence of continuous-wave
signals of any polarization, tensorial or otherwise, from
any of the 200 pulsars analyzed. The main quantity of
interest is log
10
O
S
I
, defined in Eq.
(12)
, since it encodes the
probability that the data contain a signal vs just instru-
mental noise (Gaussian or otherwise). This quantity,
together with the log(odds) for signal vs Gaussian noise,
is presented as a function of assumed emission frequency
for each pulsar in Fig.
1
, and histogrammed in Fig.
2
.
Importantly, the outliers in Fig.
1
lose significance once
log
10
O
S
I
is taken into account; indeed, Figs.
1
and
2
reveal
the usefulness of log
10
O
S
I
in increasing the robustness of
the search against non-Gaussian instrumental artifacts.
Based on the intrinsic probabilistic meaning of log
10
O
S
I
in terms of betting odds, it is standard to demand at least
log
10
O
S
I
>
1
to conclude that the signal model is favored
(see, e.g., the table in Sec. 3.2 of Ref.
[46]
, or Jeffrey
s
original criteria in Ref.
[47]
or
[48]
). Since none of the odds
obtained meet this criterion, we conclude that there is no
evidence for signals from any of the pulsars targeted.
TABLE I. Existing orientation information for pulsars in our
band, obtained from observations of the pulsar wind nebulae (see
Table 3 in Ref.
[42]
, and Refs.
[43,44]
for measurement details).
ιψ
J
0534
þ
2200
62
°.
2

1
°.
935
°.
2

1
°.
5
J0537
6910
92
°.
8

0
°.
941
°.
0

2
°.
2
J0835
4510
63
°.
6

0
°.
640
°.
6

0
°.
1
J1833
1034
85
°.
4

0
°.
345
°

1
°
J
1952
þ
3252
11
°.
5

8
°.
6
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
031104-3
In most cases, log
10
O
S
I
<
0
and the noise model is clearly
favored; the single exception is J
1932
þ
17
, for which
log
10
O
S
I
0
, so that we can make no conclusive statement
about which hypothesis is preferred. (The presence of this
nonsignificant outlier is to be expected, as it was already
identified in Ref.
[25]
.)
The distribution of the odds corresponding to the
subhypotheses making up
H
S
are summarized in the box
plots of Fig.
3
. These correspond to tensor-only (
t
), scalar-
only (
s
), vector-only (
v
), scalar-vector (
sv
), scalar-tensor
(
st
), vector-tensor (
vt
), and scalar-vector-tensor (
stv
) mod-
els. The mean of these distributions decreases with the
number of degrees of freedom in the model, which is to be
expected from the associated Occam penalties
[21]
. The
rightmost panel in Fig.
3
shows the distribution of
log
10
O
S
N
, which results from the combination of all the
other odds; this is the same quantity histogrammed on the
abscissa of Fig.
2
.
In the absence of any discernible signals, we produce
upper limits for the magnitude of scalar, vector, and tensor
polarizations, with a 95% credibility. As usual in Bayesian
analyses, upper limits are obtained by integrating posterior
probability distributions for the relevant parameters up to
the desired credibility (see, e.g., Ref.
[21]
). Using the
effective amplitude definitions of Eqs.
(4)
(6)
, these
quantities are presented in Fig.
4
as a function of assumed
emission frequency, and the Supplemental Material
[45]
.
The plotted upper limits are computed under the
assumption of a signal model that includes all five
independent polarizations (
H
svt
); limits obtained assuming
other signal models may be found online in Ref.
[45]
.
Previous work has demonstrated that the presence or
absence of a GR component does not affect the non-GR
upper limits (Fig. 13 in Ref.
[21]
).
As expected, the upper limits presented here are com-
parable in magnitude to the upper limits on the GR strain
obtained by the traditional searches
[25]
. However, con-
straints on the scalar amplitude are, on average, around
20% less stringent than those on the vector or tensor
amplitudes. This is a consequence of the fact that, for most
source locations in the sky, the LIGO detectors are intrinsi-
cally less sensitive to continuous waves of scalar (breathing
or longitudinal) polarization
[21]
.
Technically, traditional all-sky searches for continuous
gravitational waves are also sensitive to nontensorial
modes, because they are generally designed to look for
any signal of sidereal and half-sidereal periodicities in
the data, without assuming knowledge of phase evolution
or source sky location
[49
53]
. However, as can be seen
by comparing the magnitude of all-sky upper limits
FIG. 1. Log(odds) vs emission frequency. Log(odds) compar-
ing the any-signal hypothesis to the instrumental (top) and
Gaussian noise (bottom) hypotheses, as a function of assumed
gravitational-wave frequency,
f
GW
¼
2
f
rot
, for each pulsar.
Looking at the top plot for log
10
O
S
I
, notice that the instrumental
noise hypothesis is clearly favored for all pulsars except one, for
which the analysis is inconclusive. (This is J
1932
þ
17
, the same
nonsignificant outlier identified in Ref.
[25]
.) These results were
obtained without incorporating any information on the source
orientation, and are tabulated in Table II in the Supplemental
Material
[45]
. Expressions for both odds are given in Eq.
(10)
and Eq.
(12)
.
FIG. 2. Log(odds) distributions. Distributions of log(odds)
comparing the any-signal hypothesis to the instrumental (ordinate
axis, right) and Gaussian noise (abscissa axis, top) hypotheses for
all pulsars. This plot contains the same information as Fig.
1
and
displays the same nonsignificant outlier. These results were
obtained without incorporating any information on the source
orientation, and are tabulated in Table II in the Supplemental
Material
[45]
. Expressions for both odds in this plot are given in
Eq.
(10)
and Eq.
(12)
. We underscore that, although this plot
looks similar to Fig. 2 in Ref.
[25]
, the signal hypothesis here
incorporates scalar, vector, and tensor modes, in all possible
combinations.
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
031104-4
(e.g., Fig. 9 in Ref.
[49]
) to those shown here in Fig.
4
, the
sensitivity of these searches would be substantially poorer
than that of a targeted search like this one
if only because
they are not targeted to a specific source. This is especially
true if the search is optimized for a given signal polarization
(e.g., circular combination of plus and cross).
Odds and 95%-credible upper limits are summarized
in the Supplemental Material: Table I, for pulsars with
measured orientations (using the triaxial parameterization
of tensor modes), and Table II, for all pulsars without
incorporating any orientation information (using the uncon-
strained parameterization of tensor modes)
[45]
. Odds
values are reported with an error of 5% at 90% confidence;
errors on the upper limits due to the use of finite samples in
estimating posterior probability distributions are at most
10% at 90% confidence, which is slightly less than the 15%
error expected from calibration uncertainties.
Conclusion.
We have presented the results of the first
direct search for nontensorial gravitational waves. This is
also the first search targeted at known pulsars that is
sensitive to any of the five measurable polarizations of
the gravitational perturbation allowed by a generic metric
theory of gravity. From the analysis of O1 data from both
aLIGO observatories, we have found no evidence of signals
from any of the 200 pulsars targeted.
In the absence of a clear signal, we have produced the
first direct upper limits for scalar and vector strains (Fig.
4
,
and tables in the Supplemental Material
[45]
). The values of
the 95%-credible upper limits are comparable in magnitude
to previously published GR constraints, reaching
h
1
.
5
×
10
26
for pulsars whose frequency is in the most sensitive
band of our instruments. This means that, to 95% credi-
bility, none of the pulsars in our set is emitting gravitational
waves (tensorial or otherwise) at the frequencies analyzed
with enough power for them to reach Earth with amplitudes
larger than our upper limits.
Our results have been obtained in a theory-independent
fashion. However, our upper limits on nontensorial strain
can be translated into model-dependent constraints on
beyond-GR theories by picking a specific alternative theory
and emission mechanism. To do so, one should use the
upper limits produced under the assumption of a signal
model that incorporates the same polarizations allowed by
the theory one wishes to constrain; these may not neces-
sarily be those in Fig.
4
(e.g., for limits on a scalar-tensor
theory, one needs upper limits from
H
st
). However, this
also requires nontrivial knowledge of the dynamics of
spinning neutron stars under the theory of interest.
While it is conventional to compare the sensitivity of
continuous wave searches to the canonical spin-down limit
for each pulsar, it is not possible to do so here without
committing to a specific theory of gravity. This is because
doing so would require specific knowledge of how each
polarization contributes to the effective gravitational-wave
stress energy, how matter couples to the gravitational field,
how the waves propagate (dispersion and dissipation), and
what the angular dependence of the emission pattern is.
However, analogs of the canonical spin-down limit for
specific theories may be obtained from the results presented
here by using the strain upper limits obtained assuming the
sub-hypotheses with polarizations corresponding to that
theory, as mentioned above.
We have demonstrated the robustness of searches for
generalized polarization states (tensor, vector, or scalar)
in gravitational waves from spinning neutron stars.
Furthermore, even in the absence of a detection, we were
able to obtain novel constraints on the strain amplitude of
nontensorial polarizations. In the future, once a signal is
detected, similar methods will allow us to characterize the
gravitational polarization content and, in so doing, perform
novel tests of general relativity. Although this search
assumed an emission frequency of twice the rotational
FIG. 3. Sub-hypothesis odds. Box plots for the distribution of the signal vs noise log(odds) for each of the sub-hypotheses considered,
for all of the pulsars analyzed. The sub-hypotheses are (
st
), vector-tensor (
tv
), scalar-vector-tensor tensor-only (
t
), scalar-only (
s
), vector-
only (
v
), scalar-vector (
sv
), scalar-tensor (
st
), vector-tensor (
vt
), and scalar-vector-tensor (
stv
); these are all combined into the signal
hypothesis (
S
). The quantity represented is log
10
B
m
N
, which is the same as log
10
O
m
N
if neither
H
m
nor
H
N
are favored
a priori
(hence, the
label on the ordinate axis). The horizontal red line marks the median of the distribution, while each gray box extends from the lower to
upper quartile, and the whiskers mark the full range of the distribution of log
10
O
m
N
for the 200 pulsars analyzed. These results were
produced without incorporating any information on the source orientation, and are tabulated in Table II in the Supplemental Material
[45]
.
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
031104-5
frequency of the source, this restriction will be relaxed in
future analyses.
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
FIG. 4. Non-GR upper limits vs emission frequency. Circles mark the 95%-credible upper limit on the scalar,
h
95%
s
(top), and the
effective vector,
h
95%
v
(middle), and tensor
h
95%
t
(bottom) strain amplitudes as a function of assumed gravitational-wave frequency for
each of the 200 pulsars in our set. The upper limits are obtained assuming a signal model including all five independent polarizations
(
H
stv
), and incorporating no information on the orientation of the source (Table II in the Supplemental Material
[45]
). The effective
amplitude spectral density (ASD) of the detector noise is also displayed for reference; this is the harmonic mean of the H1 and L1
spectra; the scaling is obtained from linear regression to the upper limits.
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
031104-6
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, Department of Science
and Technology, India, Science & Engineering Research
Board (SERB), India, Ministry of Human Resource
Development, India, the Spanish Ministerio de Economía
y Competitividad, the Conselleria d
Economia i
Competitivitat and Conselleria d
Educació, Cultura i
Universitats of the Govern de les Illes Balears, the
National Science Centre of Poland, the European
Commission, the Royal Society, the Scottish Funding
Council, the Scottish Universities Physics Alliance, the
Hungarian Scientific Research Fund (OTKA), the Lyon
Institute ofOrigins(LIO), theNational ResearchFoundation
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, Canadian Institute for
Advanced Research, the Brazilian Ministry of Science,
Technology, and Innovation, Fundaçao de Amparo `
a
Pesquisa do Estado de São Paulo (FAPESP), Russian
Foundation for Basic Research, the Leverhulme Trust, the
Research Corporation, Ministry of Science and Technology
(MOST), Taiwan, and the Kavli Foundation. The authors
gratefully acknowledge the supportof the NSF, STFC, MPS,
INFN, CNRS, and the State of Niedersachsen, Germany for
provision of computational resources.
This paper has been assigned LIGO Document Number
LIGO-P1700009.
[1] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. Lett.
116
, 061102 (2016)
.
[2] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. Lett.
116
, 241103 (2016)
.
[3] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. X
6
, 041015 (2016)
.
[4] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. Lett.
118
, 221101 (2017)
.
[5] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. Lett.
119
, 141101 (2017)
.
[6] M. Isi, Technical Note No. LIGO-P1700276, 2017,
https://
arxiv.org/abs/1710.03794
.
[7] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. Lett.
119
, 161101 (2017)
.
[8] B. P. Abbott
et al.
(LIGO Scientific Collaboration, Virgo
Collaboration, Fermi Gamma-ray Burst Monitor, and
INTEGRAL),
Astrophys. J.
848
, L13 (2017)
.
[9] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. Lett.
116
, 221101 (2016)
.
[10] D. M. Eardley, D. L. Lee, A. P. Lightman, R. V. Wagoner,
and C. M. Will,
Phys. Rev. Lett.
30
, 884 (1973)
.
[11] D. Eardley, D. Lee, and A. Lightman,
Phys. Rev. D
8
, 3308
(1973)
.
[12] C. M. Will,
Theory and Experiment in Gravitational Physics
(Cambridge University Press, Cambridge, England, 1993),
revised ed.
[13] C. M. Will,
Living Rev. Relativity
17
, 4 (2014)
.
[14] E. Berti, E. Barausse, V. Cardoso, L. Gua
ltieri, P. Pani, U.
Sperhake,L.C.Stein,N.Wex,K.Yagi,T.Baker,C.P.Burgess,
F. S. Coelho, D. Doneva, A. D. Felice, P. G. Ferreira, P. C. C.
Freire, J. Healy, C. Herdeiro, M. Horbatsch, B. Kleihaus,
et al.
,
Classical Quantum Gravity
32
, 243001 (2015)
.
[15] K. Chatziioannou, N. Yunes, and N. Cornish,
Phys. Rev. D
86
, 022004 (2012)
.
[16] J. M. Weisberg, D. J. Nice, and J. H. Taylor,
Astrophys. J.
722
, 1030 (2010)
.
[17] P. C. C. Freire, N. Wex, G. Esposito-Far`
ese, 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)
.
[18] I. H. Stairs,
Living Rev. Relativity
6
, 5 (2003)
.
[19] N. Wex,
arXiv:1402.5594.
[20] M. Isi, A. J. Weinstein, C. Mead, and M. Pitkin,
Phys. Rev.
D
91
, 082002 (2015)
.
[21] M. Isi, M. Pitkin, and A. J. Weinstein,
Phys. Rev. D
96
,
042001 (2017)
.
[22] A. Nishizawa, A. Taruya, K. Hayama, S. Kawamura, and
M.-a. Sakagami,
Phys. Rev. D
79
, 082002 (2009)
.
[23] 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)
.
[24] K. S. Thorne, in
Three Hundred Years of Gravitation
, edited
by S. W. Hawking and W. Israel (Cambridge University
Press, Cambridge, England, 1987), Chap. 9, pp. 330
458.
[25] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Astrophys. J.
839
, 12 (2017)
.
[26] R. J. Dupuis and G. Woan,
Phys. Rev. D
72
, 102002 (2005)
.
[27] B. P. Abbott
et al.
(LIGO Scientific Collaboration),
Phys.
Rev. D
95
, 062003 (2017)
.
[28] W. G. Anderson, P. R. Brady, J. D. E. Creighton, and É. E.
Flanagan,
Phys. Rev. D
63
, 042003 (2001)
.
[29] A. B
ł
aut,
Phys. Rev. D
85
, 043005 (2012)
.
[30] E. Poisson and C. M. Will,
Gravity: Newtonian, Post-
Newtonian, Relativistic
(Cambridge University Press,
Cambridge, England, 2014).
[31] M. Zimmermann and E. Szedenits,
Phys. Rev. D
20
,351
(1979)
.
[32] B. J. Owen, L. Lindblom, C. Cutler, B. F. Schutz, A. Vecchio,
and N. Andersson,
Phys. Rev. D
58
, 084020 (1998)
.
[33] R. Bondarescu, S. A. Teukolsky, and I. Wasserman,
Phys.
Rev. D
79
, 104003 (2009)
.
[34] D. I. Jones and N. Andersson,
Mon. Not. R. Astron. Soc.
331
, 203 (2002)
.
[35] M. Pitkin, C. Gill, J. Veitch, E. Macdonald, and G. Woan,
J. Phys. Conf. Ser.
363
, 012041 (2012)
.
[36] D. Keitel, R. Prix, M. A. Papa, P. Leaci, and M. Siddiqi,
Phys. Rev. D
89
, 064023 (2014)
.
[37] E. Jaynes,
IEEE Trans. Syst. Sci. Cybern.
4
, 227 (1968)
.
[38] The specific range chosen for the amplitude priors has
little effect on our results, as explained in Appendix B of
Ref.
[21]
.
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
031104-7
[39] R. D. Ferdman, I. H. Stairs, M. Kramer, R. P. Breton, M. A.
McLaughlin, P. C. C. Freire, A. Possenti, B. W. Stappers,
V. M. Kaspi, R. N. Manchester, and A. G. Lyne,
Astro-
phys. J.
767
, 85 (2013)
.
[40] B. J. Rickett, W. A. Coles, C. F. Nava, M. A. McLaughlin,
S. M. Ransom, F. Camilo, R. D. Ferdman, P. C. C. Freire, M.
Kramer, A. G. Lyne, and I. H. Stairs,
Astrophys. J.
787
, 161
(2014)
.
[41] W. W. Zhu, I. H. Stairs, P. B. Demorest, D. J. Nice, J. A.
Ellis, S. M. Ransom, Z. Arzoumanian, K. Crowter, T. Dolch,
R. D. Ferdman, E. Fonseca, M. E. Gonzalez, G. Jones, M. L.
Jones, M. T. Lam, L. Levin, M. A. McLaughlin, T. Pennucci,
K. Stovall, and J. Swiggum,
Astrophys. J.
809
,41(2015)
.
[42] J. Aasi
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Astrophys. J.
785
, 119 (2014)
.
[43] C. Ng and R. W. Romani,
Astrophys. J.
601
, 479 (2004)
.
[44] C. Ng and R. W. Romani,
Astrophys. J.
673
, 411 (2008)
.
[45] See Supplemental Material at
http://link.aps.org/
supplemental/10.1103/PhysRevLett.120.031104
for
expanded tables with odds and upper-limits for all non-
GR hypotheses.
[46] R. E. Kass and A. E. Raftery,
J. Am. Stat. Assoc.
90
, 773
(1995)
.
[47] H. Jeffreys,
Theory of Probability
, 3rd ed. (Clarendon Press,
Oxford, 1998).
[48] C. P. Robert, N. Chopin, and J. Rousseau,
Stat. Sci.
24
, 141
(2009)
.
[49] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. D
94
, 102002 (2016)
.
[50] B. P. Abbott, M. A. Papa, H.-B. Eggenstein, and S. Walsh
(LIGO Scientific Collaboration and Virgo Collaboration),
Phys. Rev. D
96
, 082003 (2017)
.
[51] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. D
94
, 042002 (2016)
.
[52] B. P. Abbott
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. D
96
, 062002 (2017)
.
[53] J. Aasi
et al.
(LIGO Scientific Collaboration and Virgo
Collaboration),
Phys. Rev. D
90
, 062010 (2014)
.
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
C. Affeldt,
9
M. Afrough,
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
G. Allen,
11
A. Allocca,
20,21
P. A. Altin,
22
A. Amato,
23
A. Ananyeva,
1
S. B. Anderson,
1
W. G. Anderson,
24
S. Antier,
25
S. Appert,
1
K. Arai,
1
M. C. Araya,
1
J. S. Areeda,
26
N. Arnaud,
25,27
K. G. Arun,
28
S. Ascenzi,
29,17
G. Ashton,
9
M. Ast,
30
S. M. Aston,
6
P. Astone,
31
P. Aufmuth,
32
C. Aulbert,
9
K. AultONeal,
33
A. Avila-Alvarez,
26
S. Babak,
34
P. Bacon,
35
M. K. M. Bader,
13
S. Bae,
36
P. T. Baker,
37,38
F. Baldaccini,
39,40
G. Ballardin,
27
S. W. Ballmer,
41
S. Banagiri,
42
J. C. Barayoga,
1
S. E. Barclay,
43
B. C. Barish,
1
D. Barker,
44
F. Barone,
3,4
B. Barr,
43
L. Barsotti,
14
M. Barsuglia,
35
D. Barta,
45
J. Bartlett,
44
I. Bartos,
46
R. Bassiri,
47
A. Basti,
20,21
J. C. Batch,
44
C. Baune,
9
M. Bawaj,
48,40
M. Bazzan,
49,50
B. B ́
ecsy,
51
C. Beer,
9
M. Bejger,
52
I. Belahcene,
25
A. S. Bell,
43
B. K. Berger,
1
G. Bergmann,
9
C. P. L. Berry,
53
D. Bersanetti,
54,55
A. Bertolini,
13
J. Betzwieser,
6
S. Bhagwat,
41
R. Bhandare,
56
I. A. Bilenko,
57
G. Billingsley,
1
C. R. Billman,
5
J. Birch,
6
R. Birney,
58
O. Birnholtz,
9
S. Biscans,
14
A. Bisht,
32
M. Bitossi,
27,21
C. Biwer,
41
M. A. Bizouard,
25
J. K. Blackburn,
1
J. Blackman,
59
C. D. Blair,
60
D. G. Blair,
60
R. M. Blair,
44
S. Bloemen,
61
O. Bock,
9
N. Bode,
9
M. Boer,
62
G. Bogaert,
62
A. Bohe,
34
F. Bondu,
63
R. Bonnand,
7
B. A. Boom,
13
R. Bork,
1
V. Boschi,
20,21
S. Bose,
64,18
Y. Bouffanais,
35
A. Bozzi,
27
C. Bradaschia,
21
P. R. Brady,
24
V. B. Braginsky,
57
,
M. Branchesi,
65,66
J. E. Brau,
67
T. Briant,
68
A. Brillet,
62
M. Brinkmann,
9
V. Brisson,
25
P. Brockill,
24
J. E. Broida,
69
A. F. Brooks,
1
D. A. Brown,
41
D. D. Brown,
53
N. M. Brown,
14
S. Brunett,
1
C. C. Buchanan,
2
A. Buikema,
14
T. Bulik,
70
H. J. Bulten,
71,13
A. Buonanno,
34,72
D. Buskulic,
7
C. Buy,
35
R. L. Byer,
47
M. Cabero,
9
L. Cadonati,
73
G. Cagnoli,
23,74
C. Cahillane,
1
J. Calderón Bustillo,
73
T. A. Callister,
1
E. Calloni,
75,4
J. B. Camp,
76
M. Canepa,
54,55
P. Canizares,
61
K. C. Cannon,
77
H. Cao,
78
J. Cao,
79
C. D. Capano,
9
E. Capocasa,
35
F. Carbognani,
27
S. Caride,
80
M. F. Carney,
81
J. Casanueva Diaz,
25
C. Casentini,
29,17
S. Caudill,
24
M. Cavagli`
a,
10
F. Cavalier,
25
R. Cavalieri,
27
G. Cella,
21
C. B. Cepeda,
1
L. Cerboni Baiardi,
65,66
G. Cerretani,
20,21
E. Cesarini,
29,17
S. J. Chamberlin,
82
M. Chan,
43
S. Chao,
83
P. Charlton,
84
E. Chassande-Mottin,
35
D. Chatterjee,
24
B. D. Cheeseboro,
37,38
H. Y. Chen,
85
Y. Chen,
59
H.-P. Cheng,
5
A. Chincarini,
55
A. Chiummo,
27
T. Chmiel,
81
H. S. Cho,
86
M. Cho,
72
J. H. Chow,
22
N. Christensen,
69,62
Q. Chu,
60
A. J. K. Chua,
12
S. Chua,
68
A. K. W. Chung,
87
S. Chung,
60
G. Ciani,
5
R. Ciolfi,
88,89
C. E. Cirelli,
47
A. Cirone,
54,55
F. Clara,
44
J. A. Clark,
73
F. Cleva,
62
C. Cocchieri,
10
E. Coccia,
16,17
P.-F. Cohadon,
68
A. Colla,
90,31
C. G. Collette,
91
L. R. Cominsky,
92
M. Constancio Jr.,
15
L. Conti,
50
S. J. Cooper,
53
P. Corban,
6
T. R. Corbitt,
2
K. R. Corley,
46
N. Cornish,
93
A. Corsi,
80
S. Cortese,
27
C. A. Costa,
15
M. W. Coughlin,
69
S. B. Coughlin,
94,95
J.-P. Coulon,
62
S. T. Countryman,
46
P. Couvares,
1
P. B. Covas,
96
E. E. Cowan,
73
D. M. Coward,
60
M. J. Cowart,
6
D. C. Coyne,
1
R. Coyne,
80
J. D. E. Creighton,
24
T. D. Creighton,
97
J. Cripe,
2
S. G. Crowder,
98
T. J. Cullen,
26
A. Cumming,
43
L. Cunningham,
43
E. Cuoco,
27
T. Dal Canton,
76
S. L. Danilishin,
32,9
S. D
Antonio,
17
K. Danzmann,
32,9
A. Dasgupta,
99
C. F. Da Silva Costa,
5
V. Dattilo,
27
I. Dave,
56
M. Davier,
25
D. Davis,
41
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
031104-8
E. J. Daw,
100
B. Day,
73
S. De,
41
D. DeBra,
47
J. Degallaix,
23
M. De Laurentis,
75,4
S. Del ́
eglise,
68
W. Del Pozzo,
53,20,21
T. Denker,
9
T. Dent,
9
V. Dergachev,
34
R. De Rosa,
75,4
R. T. DeRosa,
6
R. DeSalvo,
101
J. Devenson,
58
R. C. Devine,
37,38
S. Dhurandhar,
18
M. C. Díaz,
97
L. Di Fiore,
4
M. Di Giovanni,
102,89
T. Di Girolamo,
75,4,46
A. Di Lieto,
20,21
S. Di Pace,
90,31
I. Di Palma,
90,31
F. Di Renzo,
20,21
Z. Doctor,
85
V. Dolique,
23
F. Donovan,
14
K. L. Dooley,
10
S. Doravari,
9
I. Dorrington,
95
R. Douglas,
43
M. Dovale Álvarez,
53
T. P. Downes,
24
M. Drago,
9
R. W. P. Drever,
1
,
J. C. Driggers,
44
Z. Du,
79
M. Ducrot,
7
J. Duncan,
94
S. E. Dwyer,
44
T. B. Edo,
100
M. C. Edwards,
69
A. Effler,
6
H.-B. Eggenstein,
9
P. Ehrens,
1
J. Eichholz,
1
S. S. Eikenberry,
5
R. A. Eisenstein,
14
R. C. Essick,
14
Z. B. Etienne,
37,38
T. Etzel,
1
M. Evans,
14
T. M. Evans,
6
M. Factourovich,
46
V. Fafone,
29,17,16
H. Fair,
41
S. Fairhurst,
95
X. Fan,
79
S. Farinon,
55
B. Farr,
85
W. M. Farr,
53
E. J. Fauchon-Jones,
95
M. Favata,
103
M. Fays,
95
H. Fehrmann,
9
J. Feicht,
1
M. M. Fejer,
47
A. Fernandez-Galiana,
14
I. Ferrante,
20,21
E. C. Ferreira,
15
F. Ferrini,
27
F. Fidecaro,
20,21
I. Fiori,
27
D. Fiorucci,
35
R. P. Fisher,
41
R. Flaminio,
23,104
M. Fletcher,
43
H. Fong,
105
P. W. F. Forsyth,
22
S. S. Forsyth,
73
J.-D. Fournier,
62
S. Frasca,
90,31
F. Frasconi,
21
Z. Frei,
51
A. Freise,
53
R. Frey,
67
V. Frey,
25
E. M. Fries,
1
P. Fritschel,
14
V. V. Frolov,
6
P. Fulda,
5,76
M. Fyffe,
6
H. Gabbard,
9
M. Gabel,
106
B. U. Gadre,
18
S. M. Gaebel,
53
J. R. Gair,
107
L. Gammaitoni,
39
M. R. Ganija,
78
S. G. Gaonkar,
18
F. Garufi,
75,4
S. Gaudio,
33
G. Gaur,
108
V. Gayathri,
109
N. Gehrels,
76
,
G. Gemme,
55
E. Genin,
27
A. Gennai,
21
D. George,
11
J. George,
56
L. Gergely,
110
V. Germain,
7
S. Ghonge,
73
Abhirup Ghosh,
19
Archisman Ghosh,
19,13
S. Ghosh,
61,13
J. A. Giaime,
2,6
K. D. Giardina,
6
A. Giazotto,
21
K. Gill,
33
L. Glover,
101
E. Goetz,
9
R. Goetz,
5
S. Gomes,
95
G. González,
2
J. M. Gonzalez Castro,
20,21
A. Gopakumar,
111
M. L. Gorodetsky,
57
S. E. Gossan,
1
M. Gosselin,
27
R. Gouaty,
7
A. Grado,
112,4
C. Graef,
43
M. Granata,
23
A. Grant,
43
S. Gras,
14
C. Gray,
44
G. Greco,
65,66
A. C. Green,
53
P. Groot,
61
H. Grote,
9
S. Grunewald,
34
P. Gruning,
25
G. M. Guidi,
65,66
X. Guo,
79
A. Gupta,
82
M. K. Gupta,
99
K. E. Gushwa,
1
E. K. Gustafson,
1
R. Gustafson,
113
B. R. Hall,
64
E. D. Hall,
1
G. Hammond,
43
M. Haney,
111
M. M. Hanke,
9
J. Hanks,
44
C. Hanna,
82
O. A. Hannuksela,
87
J. Hanson,
6
T. Hardwick,
2
J. Harms,
65,66
G. M. Harry,
114
I. W. Harry,
34
M. J. Hart,
43
C.-J. Haster,
105
K. Haughian,
43
J. Healy,
115
A. Heidmann,
68
M. C. Heintze,
6
H. Heitmann,
62
P. Hello,
25
G. Hemming,
27
M. Hendry,
43
I. S. Heng,
43
J. Hennig,
43
J. Henry,
115
A. W. Heptonstall,
1
M. Heurs,
9,32
S. Hild,
43
D. Hoak,
27
D. Hofman,
23
K. Holt,
6
D. E. Holz,
85
P. Hopkins,
95
C. Horst,
24
J. Hough,
43
E. A. Houston,
43
E. J. Howell,
60
Y. M. Hu,
9
E. A. Huerta,
11
D. Huet,
25
B. Hughey,
33
S. Husa,
96
S. H. Huttner,
43
T. Huynh-Dinh,
6
N. Indik,
9
D. R. Ingram,
44
R. Inta,
80
G. Intini,
90,31
H. N. Isa,
43
J.-M. Isac,
68
M. Isi,
1
B. R. Iyer,
19
K. Izumi,
44
T. Jacqmin,
68
K. Jani,
73
P. Jaranowski,
116
S. Jawahar,
117
F. Jim ́
enez-Forteza,
96
W. W. Johnson,
2
D. I. Jones,
118
R. Jones,
43
R. J. G. Jonker,
13
L. Ju,
60
J. Junker,
9
C. V. Kalaghatgi,
95
V. Kalogera,
94
S. Kandhasamy,
6
G. Kang,
36
J. B. Kanner,
1
S. Karki,
67
K. S. Karvinen,
9
M. Kasprzack,
2
M. Katolik,
11
E. Katsavounidis,
14
W. Katzman,
6
S. Kaufer,
32
K. Kawabe,
44
F. K ́
ef ́
elian,
62
D. Keitel,
43
A. J. Kemball,
11
R. Kennedy,
100
C. Kent,
95
J. S. Key,
119
F. Y. Khalili,
57
I. Khan,
16,17
S. Khan,
9
Z. Khan,
99
E. A. Khazanov,
120
N. Kijbunchoo,
44
Chunglee Kim,
121
J. C. Kim,
122
W. Kim,
78
W. S. Kim,
123
Y.-M. Kim,
86,121
S. J. Kimbrell,
73
E. J. King,
78
P. J. King,
44
R. Kirchhoff,
9
J. S. Kissel,
44
L. Kleybolte,
30
S. Klimenko,
5
P. Koch,
9
S. M. Koehlenbeck,
9
S. Koley,
13
V. Kondrashov,
1
A. Kontos,
14
M. Korobko,
30
W. Z. Korth,
1
I. Kowalska,
70
D. B. Kozak,
1
C. Krämer,
9
V. Kringel,
9
B. Krishnan,
9
A. Królak,
124,125
G. Kuehn,
9
P. Kumar,
105
R. Kumar,
99
S. Kumar,
19
L. Kuo,
83
A. Kutynia,
124
S. Kwang,
24
B. D. Lackey,
34
K. H. Lai,
87
M. Landry,
44
R. N. Lang,
24
J. Lange,
115
B. Lantz,
47
R. K. Lanza,
14
A. Lartaux-Vollard,
25
P. D. Lasky,
126
M. Laxen,
6
A. Lazzarini,
1
C. Lazzaro,
50
P. Leaci,
90,31
S. Leavey,
43
C. H. Lee,
86
H. K. Lee,
127
H. M. Lee,
121
H. W. Lee,
122
K. Lee,
43
J. Lehmann,
9
A. Lenon,
37,38
M. Leonardi,
102,89
N. Leroy,
25
N. Letendre,
7
Y. Levin,
126
T. G. F. Li,
87
A. Libson,
14
T. B. Littenberg,
128
J. Liu,
60
R. K. L. Lo,
87
N. A. Lockerbie,
117
L. T. London,
95
J. E. Lord,
41
M. Lorenzini,
16,17
V. Loriette,
129
M. Lormand,
6
G. Losurdo,
21
J. D. Lough,
9,32
C. O. Lousto,
115
G. Lovelace,
26
H. Lück,
32,9
D. Lumaca,
29,17
A. P. Lundgren,
9
R. Lynch,
14
Y. Ma,
59
S. Macfoy,
58
B. Machenschalk,
9
M. MacInnis,
14
D. M. Macleod,
2
I. Magaña Hernandez,
87
F. Magaña-Sandoval,
41
L. Magaña Zertuche,
41
R. M. Magee,
82
E. Majorana,
31
I. Maksimovic,
129
N. Man,
62
V. Mandic,
42
V. Mangano,
43
G. L. Mansell,
22
M. Manske,
24
M. Mantovani,
27
F. Marchesoni,
48,40
F. Marion,
7
S. Márka,
46
Z. Márka,
46
C. Markakis,
11
A. S. Markosyan,
47
E. Maros,
1
F. Martelli,
65,66
L. Martellini,
62
I. W. Martin,
43
D. V. Martynov,
14
K. Mason,
14
A. Masserot,
7
T. J. Massinger,
1
M. Masso-Reid,
43
S. Mastrogiovanni,
90,31
A. Matas,
42
F. Matichard,
14
L. Matone,
46
N. Mavalvala,
14
N. Mazumder,
64
R. McCarthy,
44
D. E. McClelland,
22
S. McCormick,
6
L. McCuller,
14
S. C. McGuire,
130
G. McIntyre,
1
J. McIver,
1
D. J. McManus,
22
T. McRae,
22
S. T. McWilliams,
37,38
D. Meacher,
82
G. D. Meadors,
34,9
J. Meidam,
13
E. Mejuto-Villa,
8
A. Melatos,
131
G. Mendell,
44
R. A. Mercer,
24
E. L. Merilh,
44
M. Merzougui,
62
S. Meshkov,
1
C. Messenger,
43
C. Messick,
82
R. Metzdorff,
68
P. M. Meyers,
42
F. Mezzani,
31,90
H. Miao,
53
C. Michel,
23
H. Middleton,
53
E. E. Mikhailov,
132
L. Milano,
75,4
A. L. Miller,
5
A. Miller,
90,31
B. B. Miller,
94
J. Miller,
14
M. Millhouse,
93
O. Minazzoli,
62
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
031104-9
Y. Minenkov,
17
J. Ming,
34
C. Mishra,
133
S. Mitra,
18
V. P. Mitrofanov,
57
G. Mitselmakher,
5
R. Mittleman,
14
A. Moggi,
21
M. Mohan,
27
S. R. P. Mohapatra,
14
M. Montani,
65,66
B. C. Moore,
103
C. J. Moore,
12
D. Moraru,
44
G. Moreno,
44
S. R. Morriss,
97
B. Mours,
7
C. M. Mow-Lowry,
53
G. Mueller,
5
A. W. Muir,
95
Arunava Mukherjee,
9
D. Mukherjee,
24
S. Mukherjee,
97
N. Mukund,
18
A. Mullavey,
6
J. Munch,
78
E. A. M. Muniz,
41
P. G. Murray,
43
K. Napier,
73
I. Nardecchia,
29,17
L. Naticchioni,
90,31
R. K. Nayak,
134
G. Nelemans,
61,13
T. J. N. Nelson,
6
M. Neri,
54,55
M. Nery,
9
A. Neunzert,
113
J. M. Newport,
114
G. Newton,
43
,
K. K. Y. Ng,
87
T. T. Nguyen,
22
D. Nichols,
61
A. B. Nielsen,
9
S. Nissanke,
61,13
A. Nitz,
9
A. Noack,
9
F. Nocera,
27
D. Nolting,
6
M. E. N. Normandin,
97
L. K. Nuttall,
41
J. Oberling,
44
E. Ochsner,
24
E. Oelker,
14
G. H. Ogin,
106
J. J. Oh,
123
S. H. Oh,
123
F. Ohme,
9
M. Oliver,
96
P. Oppermann,
9
Richard J. Oram,
6
B. O
Reilly,
6
R. Ormiston,
42
L. F. Ortega,
5
R. O
Shaughnessy,
115
D. J. Ottaway,
78
H. Overmier,
6
B. J. Owen,
80
A. E. Pace,
82
J. Page,
128
M. A. Page,
60
A. Pai,
109
S. A. Pai,
56
J. R. Palamos,
67
O. Palashov,
120
C. Palomba,
31
A. Pal-Singh,
30
H. Pan,
83
B. Pang,
59
P. T. H. Pang,
87
C. Pankow,
94
F. Pannarale,
95
B. C. Pant,
56
F. Paoletti,
21
A. Paoli,
27
M. A. Papa,
34,24,9
H. R. Paris,
47
W. Parker,
6
D. Pascucci,
43
A. Pasqualetti,
27
R. Passaquieti,
20,21
D. Passuello,
21
B. Patricelli,
135,21
B. L. Pearlstone,
43
M. Pedraza,
1
R. Pedurand,
23,136
L. Pekowsky,
41
A. Pele,
6
S. Penn,
137
C. J. Perez,
44
A. Perreca,
1,102,89
L. M. Perri,
94
H. P. Pfeiffer,
105
M. Phelps,
43
O. J. Piccinni,
90,31
M. Pichot,
62
F. Piergiovanni,
65,66
V. Pierro,
8
G. Pillant,
27
L. Pinard,
23
I. M. Pinto,
8
M. Pitkin,
43
R. Poggiani,
20,21
P. Popolizio,
27
E. K. Porter,
35
A. Post,
9
J. Powell,
43
J. Prasad,
18
J. W. W. Pratt,
33
V. Predoi,
95
T. Prestegard,
24
M. Prijatelj,
9
M. Principe,
8
S. Privitera,
34
R. Prix,
9
G. A. Prodi,
102,89
L. G. Prokhorov,
57
O. Puncken,
9
M. Punturo,
40
P. Puppo,
31
M. Pürrer,
34
H. Qi,
24
J. Qin,
60
S. Qiu,
126
V. Quetschke,
97
E. A. Quintero,
1
R. Quitzow-James,
67
F. J. Raab,
44
D. S. Rabeling,
22
H. Radkins,
44
P. Raffai,
51
S. Raja,
56
C. Rajan,
56
M. Rakhmanov,
97
K. E. Ramirez,
97
P. Rapagnani,
90,31
V. Raymond,
34
M. Razzano,
20,21
J. Read,
26
T. Regimbau,
62
L. Rei,
55
S. Reid,
58
D. H. Reitze,
1,5
H. Rew,
132
S. D. Reyes,
41
F. Ricci,
90,31
P. M. Ricker,
11
S. Rieger,
9
K. Riles,
113
M. Rizzo,
115
N. A. Robertson,
1,43
R. Robie,
43
F. Robinet,
25
A. Rocchi,
17
L. Rolland,
7
J. G. Rollins,
1
V. J. Roma,
67
R. Romano,
3,4
C. L. Romel,
44
J. H. Romie,
6
D. Rosi
ń
ska,
138,52
M. P. Ross,
139
S. Rowan,
43
A. Rüdiger,
9
P. Ruggi,
27
K. Ryan,
44
S. Sachdev,
1
T. Sadecki,
44
L. Sadeghian,
24
M. Sakellariadou,
140
L. Salconi,
27
M. Saleem,
109
F. Salemi,
9
A. Samajdar,
134
L. Sammut,
126
L. M. Sampson,
94
E. J. Sanchez,
1
V. Sandberg,
44
B. Sandeen,
94
J. R. Sanders,
41
B. Sassolas,
23
B. S. Sathyaprakash,
82,95
P. R. Saulson,
41
O. Sauter,
113
R. L. Savage,
44
A. Sawadsky,
32
P. Schale,
67
J. Scheuer,
94
E. Schmidt,
33
J. Schmidt,
9
P. Schmidt,
1,61
R. Schnabel,
30
R. M. S. Schofield,
67
A. Schönbeck,
30
E. Schreiber,
9
D. Schuette,
9,32
B. W. Schulte,
9
B. F. Schutz,
95,9
S. G. Schwalbe,
33
J. Scott,
43
S. M. Scott,
22
E. Seidel,
11
D. Sellers,
6
A. S. Sengupta,
141
D. Sentenac,
27
V. Sequino,
29,17
A. Sergeev,
120
D. A. Shaddock,
22
T. J. Shaffer,
44
A. A. Shah,
128
M. S. Shahriar,
94
L. Shao,
34
B. Shapiro,
47
P. Shawhan,
72
A. Sheperd,
24
D. H. Shoemaker,
14
D. M. Shoemaker,
73
K. Siellez,
73
X. Siemens,
24
M. Sieniawska,
52
D. Sigg,
44
A. D. Silva,
15
A. Singer,
1
L. P. Singer,
76
A. Singh,
34,9,32
R. Singh,
2
A. Singhal,
16,31
A. M. Sintes,
96
B. J. J. Slagmolen,
22
B. Smith,
6
J. R. Smith,
26
R. J. E. Smith,
1
E. J. Son,
123
J. A. Sonnenberg,
24
B. Sorazu,
43
F. Sorrentino,
55
T. Souradeep,
18
A. P. Spencer,
43
A. K. Srivastava,
99
A. Staley,
46
M. Steinke,
9
J. Steinlechner,
43,30
S. Steinlechner,
30
D. Steinmeyer,
9,32
B. C. Stephens,
24
R. Stone,
97
K. A. Strain,
43
G. Stratta,
65,66
S. E. Strigin,
57
R. Sturani,
142
A. L. Stuver,
6
T. Z. Summerscales,
143
L. Sun,
131
S. Sunil,
99
P. J. Sutton,
95
B. L. Swinkels,
27
M. J. Szczepa
ń
czyk,
33
M. Tacca,
35
D. Talukder,
67
D. B. Tanner,
5
M. Tápai,
110
A. Taracchini,
34
J. A. Taylor,
128
R. Taylor,
1
T. Theeg,
9
E. G. Thomas,
53
M. Thomas,
6
P. Thomas,
44
K. A. Thorne,
6
K. S. Thorne,
59
E. Thrane,
126
S. Tiwari,
16,89
V. Tiwari,
95
K. V. Tokmakov,
117
K. Toland,
43
M. Tonelli,
20,21
Z. Tornasi,
43
C. I. Torrie,
1
D. Töyrä,
53
F. Travasso,
27,40
G. Traylor,
6
D. Trifirò,
10
J. Trinastic,
5
M. C. Tringali,
102,89
L. Trozzo,
144,21
K. W. Tsang,
13
M. Tse,
14
R. Tso,
1
D. Tuyenbayev,
97
K. Ueno,
24
D. Ugolini,
145
C. S. Unnikrishnan,
111
A. L. Urban,
1
S. A. Usman,
95
H. Vahlbruch,
32
G. Vajente,
1
G. Valdes,
97
M. Vallisneri,
59
N. van Bakel,
13
M. van Beuzekom,
13
J. F. J. van den Brand,
71,13
C. Van Den Broeck,
13
D. C. Vander-Hyde,
41
L. van der Schaaf,
13
J. V. van Heijningen,
13
A. A. van Veggel,
43
M. Vardaro,
49,50
V. Varma,
59
S. Vass,
1
M. Vasúth,
45
A. Vecchio,
53
G. Vedovato,
50
J. Veitch,
53
P. J. Veitch,
78
K. Venkateswara,
139
G. Venugopalan,
1
D. Verkindt,
7
F. Vetrano,
65,66
A. Vicer ́
e,
65,66
A. D. Viets,
24
S. Vinciguerra,
53
D. J. Vine,
58
J.-Y. Vinet,
62
S. Vitale,
14
T. Vo,
41
H. Vocca,
39,40
C. Vorvick,
44
D. V. Voss,
5
W. D. Vousden,
53
S. P. Vyatchanin,
57
A. R. Wade,
1
L. E. Wade,
81
M. Wade,
81
R. Walet,
13
M. Walker,
2
L. Wallace,
1
S. Walsh,
24
G. Wang,
16,66
H. Wang,
53
J. Z. Wang,
82
M. Wang,
53
Y.-F. Wang,
87
Y. Wang,
60
R. L. Ward,
22
J. Warner,
44
M. Was,
7
J. Watchi,
91
B. Weaver,
44
L.-W. Wei,
9,32
M. Weinert,
9
A. J. Weinstein,
1
R. Weiss,
14
L. Wen,
60
E. K. Wessel,
11
P. Weßels,
9
T. Westphal,
9
K. Wette,
9
J. T. Whelan,
115
B. F. Whiting,
5
C. Whittle,
126
D. Williams,
43
R. D. Williams,
1
A. R. Williamson,
115
J. L. Willis,
146
B. Willke,
32,9
M. H. Wimmer,
9,32
W. Winkler,
9
C. C. Wipf,
1
H. Wittel,
9,32
G. Woan,
43
J. Woehler,
9
J. Wofford,
115
K. W. K. Wong,
87
J. Worden,
44
J. L. Wright,
43
D. S. Wu,
9
G. Wu,
6
PHYSICAL REVIEW LETTERS
120,
031104 (2018)
031104-10