Search for Subsolar-Mass Ultracompact Binaries
in Advanced LIGO
’
s First Observing Run
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
and S. Shandera
(Received 15 August 2018; published 7 December 2018)
We present the first Advanced LIGO and Advanced Virgo search for ultracompact binary systems with
component masses between
0
.
2
M
⊙
–
1
.
0
M
⊙
using data taken between September 12, 2015 and January
19, 2016. We find no viable gravitational wave candidates. Our null result constrains the coalescence rate of
monochromatic (delta function) distributions of nonspinning (
0
.
2
M
⊙
,
0
.
2
M
⊙
) ultracompact binaries to be
less than
1
.
0
×
10
6
Gpc
−
3
yr
−
1
and the coalescence rate of a similar distribution of (
1
.
0
M
⊙
,
1
.
0
M
⊙
)
ultracompact binaries to be less than
1
.
9
×
10
4
Gpc
−
3
yr
−
1
(at 90% confidence). Neither black holes nor
neutron stars are expected to form below
∼
1
M
⊙
through conventional stellar evolution, though it has been
proposed that similarly low mass black holes could be formed primordially through density fluctuations in
the early Universe and contribute to the dark matter density. The interpretation of our constraints in the
primordial black hole dark matter paradigm is highly model dependent; however, under a particular
primordial black hole binary formation scenario we constrain monochromatic primordial black hole
populations of
0
.
2
M
⊙
to be less than 33% of the total dark matter density and monochromatic populations
of
1
.
0
M
⊙
to be less than 5% of the dark matter density. The latter strengthens the presently placed bounds
from microlensing surveys of massive compact halo objects (MACHOs) provided by the MACHO and
EROS Collaborations.
DOI:
10.1103/PhysRevLett.121.231103
Introduction.
—
The era of gravitational wave astronomy
began with the observation of the binary black hole merger
GW150914
[1]
. Since then, four additional binary black
hole mergers
[2
–
5]
and one binary neutron star merger
[6]
have been announced as of November 2017. Thus far,
Advanced LIGO and Advanced Virgo searches have tar-
geted binary systems with total masses from
2
–
600
M
⊙
[7,8]
, but the LIGO and Virgo detectors are also sensitive to
ultracompact binaries with components below
1
M
⊙
if
the compactness (mass to radius ratio) is close to that of
a black hole. White dwarf binaries, while often formed with
components below one solar mass, are not sufficiently
compact to be a LIGO/Virgo gravitational wave source.
Neutron stars or black holes are sufficiently compact as
would be other exotic compact objects. Previous gravita-
tional wave searches for sub-solar-mass ultracompact bina-
ries used data from initial LIGO observations from February
14, 2003
–
March 24, 2005
[9,10]
. Advanced LIGO
[11]
presently surveys a volume of space approximately 1000
times larger than the previous search for sub-solar-mass
ultracompact objects, therefore improving the chances of
detecting such a binary 1000-fold.
In conventional stellar evolution models, the lightest
ultracompact objects are formed when stellar remnants
exceed
∼
1
.
4
M
⊙
, the Chandrasekhar mass limit
[12,13]
.
Beyond the Chandrasekhar mass limit, electron degeneracy
pressure can no longer prevent the gravitational collapse of
a white dwarf. The lightest remnants that exceed the
Chandrasekhar mass limit form neutron stars
[14]
. When
even the neutron degeneracy pressure cannot prevent
collapse, heavier stellar remnants will collapse to black
holes. Some equations of state predict that neutron stars
remain stable down to
∼
0
.
1
M
⊙
[15]
; there is no widely
accepted model for forming neutron stars below
∼
1
M
⊙
,
though a recent measurement does not exclude the pos-
sibility of
0
.
92
M
⊙
neutron star
[16]
. This result may be
due to the low inclination of the system. The lowest
precisely measured neutron star mass is
1
.
174
M
⊙
[17]
.
Observationally, black holes appear to have a minimum
mass of
∼
5
M
⊙
with a gap between the heaviest observed
neutron star (
∼
2
M
⊙
) and black hole masses
[18
–
21]
.
Detecting ultracompact objects below one solar mass could
challenge our ideas about stellar evolution or possibly hint
at new, unconventional formation scenarios.
Beyond conventional stellar evolution, one of the most
prolific black hole formation models posits that primordial
black holes (PBHs) could have formed in the early
Universe through the collapse of highly overdense regions
*
Full author list given at end of the Letter.
PHYSICAL REVIEW LETTERS
121,
231103 (2018)
0031-9007
=
18
=
121(23)
=
231103(13)
231103-1
© 2018 American Physical Society
[22
–
26]
. It has been suggested that PBHs could constitute a
fraction of the missing dark matter
[23,26]
, though this
scenario has been constrained
[27]
. LIGO
’
s detections have
revived interest in black hole formation mechanisms and, in
particular, the formation of primordial black holes (PBHs)
[28
–
30]
. Though there are proposals on how to distinguish
a primordial black hole distribution from an astrophysical
one
[31
–
36]
, disentangling them is challenging when the
populations overlap in mass. Hence, detection of sub-solar-
mass ultracompact objects would provide the cleanest
signature for determining primordial formation. Still, recent
proposals for nonbaryonic dark matter models can produce
sub-solar-mass black holes either by allowing a lower
Chandrasekhar mass in the dark sector
[37]
, or by trigger-
ing neutron stars to collapse into
∼
1
M
⊙
black holes
[38]
.
This Letter describes a gravitational wave search for
ultracompact binary systems with component masses
between
0
.
2
M
⊙
and
1
.
0
M
⊙
using data from Advanced
LIGO
’
s first observing run. No viable gravitational wave
candidates were identified. We briefly describe the data
analyzed and the anticipated sensitivity to sub-solar-mass
ultracompact objects, as well as the search that was
conducted, which led to the null result. We then describe
how the null result constrains the merger rate of sub-solar-
mass binaries in the nearby universe. We consider the
merger rate constraints in the context of binary merger rate
estimates most recently given by Sasaki
et al.
[29]
thereby
constraining the fraction of dark matter density made up of
PBHs between
0
.
2
M
⊙
and
1
.
0
M
⊙
. Finally, we conclude
with a discussion of future work.
Search.
—
We report on data analyzed from Advanced
LIGO
’
s first observing run, taken from September 12,
2015
–
January 19, 2016 at the LIGO Hanford and LIGO
Livingston detectors. After taking into account data quality
cuts
[39]
and detector downtime, we analyzed a total of
48.16 days of Hanford-Livingston coincident data. The
data selection process was identical to that used in previous
searches
[40]
.
During Advanced LIGO
’
s first observing run, each
LIGO instrument was sensitive to sub-solar-mass ultra-
compact binaries at extra-galactic distances. Figure
1
shows
the maximum distance to which an equal-mass compact
binary merger with given component masses would be
visible at a signal-to-noise ratio of 8 in either LIGO
Hanford or LIGO Livingston.
The search was conducted using standard gravitational
wave analysis software
[41
–
46]
. Our search consisted of a
matched-filter stage that filtered a discrete bank of tem-
plates against the LIGO data. The peak SNR for each
template for each second was identified and recorded as a
trigger. Subsequently, a chi-squared test was performed that
checked the consistency of the trigger with a signal
[42]
.
The triggers from each LIGO detector and gravitational
wave template were combined and searched for coinci-
dences within 20 ms. Candidates that pass coincidence
were assigned a likelihood ratio
L
that accounts for the
relative probability that the candidates are signal versus
noise as a function of SNR, chi-squared, and time delay and
phase offset between detectors. Larger values of
L
were
deemed to be more signal-like. The rate at which noise
produced candidates with a given value of
L
was computed
via a Monte Carlo integral of the noise derived from
noncoincident triggers, which we define as the false alarm
rate of candidate signals.
Our discrete bank of 500332 template waveforms
[47]
conformed to the gravitational wave emission expected
from general relativity
[48,49]
. We use the 3.5 post-
Newtonian order TaylorF2 waveform to model the inspiral
portion of the binary evolution, which is constructed under
the stationary phase approximation
[49]
. The TaylorF2
waveform has been used in previous low-mass Advanced
LIGO and Advanced Virgo searches. The bank covered
component masses in the detector frame between
0
.
19
–
2
.
0
M
⊙
with 97% fidelity. While we restrict our
analysis of the search results to the subsolar region, we
have allowed for the possibility of high mass ratio systems.
Our template bank assumed that each binary component
has negligible spin. Relaxing that assumption is a direction
for future work, but is a computationally challenging
problem requiring resources well beyond those used for
this and previous LIGO analyses. We integrated the
template waveforms between 45
–
1024 Hz, with the longest
waveform lasting about 470 seconds. Advanced LIGO is
sensitive down to
∼
15
Hz, but integrating from that
frequency would have been too computationally burden-
some. Our choice to integrate from 45 to 1024 Hz
recovered 93.0% of the total possible SNR that integration
FIG. 1. Distance to which an optimally oriented and aligned
equal-mass ultracompact binary merger would produce at least
SNR 8 in each of the LIGO Livingston and LIGO Hanford
detectors as a function of component mass, based on the median
sensitivity obtained from our analyzed data.
PHYSICAL REVIEW LETTERS
121,
231103 (2018)
231103-2
over the full band would have provided. Additional details
are described in Ref.
[47]
.
No viable gravitational wave candidates were found. Our
loudest gravitational wave candidate was consistent with
noise and had a false alarm rate of 6.19 per year.
Constraint on binary merger rate.
—
We constrained the
binary merger rate in this mass region by considering nine
monochromatic mass distributions with equal component
masses and negligible spin. We constructed sets of simulated
signals with component masses
m
i
∈
f
0
.
2
;
0
.
3
;
...
;
1
.
0
g
M
⊙
distributed uniformly in distance and uniformly on the sky.
We injected 374480 simulated signals into the LIGO data
and conducted a gravitational wave search with the same
parameters as described earlier. We then calculated our
detection efficiency as a function of distance
ε
i
ð
r
Þ
. This
allowed us to compute the volume-time
h
VT
i
that was
accessible for our search via
h
VT
i
i
¼
T
Z
4
π
r
2
ε
i
ð
r
Þ
dr;
ð
1
Þ
where
T
is 48.16 days. We then used the loudest event
statistic formalism
[50]
to compute an upper limit on the
binary merger rate in each mass bin to 90% confidence,
R
90
;i
¼
2
.
3
h
VT
i
i
:
ð
2
Þ
We report the upper limits on the binary merger rate in Fig.
2
.
Several factors in our analysis could lead to uncertainty in
R
90
at the 25% level, including LIGO calibration errors and
Monte Carlo errors. However, these errors are far smaller
than potential systematic errors in the models we will be
considering in the next section, so we do not attempt to
further quantify them in this work.
Constraint on primordial black holes as dark matter.
—
For an assumed model of PBH binary formation, the
constraint on the binary merger rate places bounds on
the total fraction of dark matter made of primordial black
holes,
f
. These bounds are derived from the expected event
rate for a uniform distribution of monochromatic PBHs
with mass
m
i
as considered above. The limits on
f
are
sensitive to the model of binary formation. Motivated by
previous LIGO searches
[9]
we follow a method originally
proposed by Refs.
[51,52]
and recently used to constrain
∼
30
M
⊙
PBH mergers by Ref.
[29]
.
We assume an initial, early Universe, monochromatic
distribution of PBHs. As the Universe expands, the energy
density of a pair of black holes not too widely separated
becomes larger than the background energy density. The
pair decouples from the cosmic expansion and can be
prevented from prompt merger by the local tidal field,
determined primarily by a third black hole nearest the pair.
The initial separation of the pair and the relative location of
the primary perturber determine the parameters of the initial
binary. From those, the coalescence time can be deter-
mined. Assuming a spatially uniform initial distribution of
black holes, the distribution of coalescence times for those
black holes that form binaries is
dP
¼
8
>
>
<
>
>
:
3
f
37
8
58
h
f
−
29
8
ð
t
t
c
Þ
3
37
−
ð
t
t
c
Þ
3
8
i
dt
t
;t<t
c
3
f
37
8
58
h
f
−
29
8
ð
t
t
c
Þ
−
1
7
−
ð
t
t
c
Þ
3
8
dt
t
;t
≥
t
c
;
ð
3
Þ
where
t
c
is a function of the mass of the PBHs and the
fraction of the dark matter they comprise:
t
c
¼
3
170
c
5
ð
Gm
i
Þ
5
=
3
f
7
ð
1
þ
z
eq
Þ
4
8
π
3
H
2
0
Ω
DM
4
=
3
:
ð
4
Þ
This expression is evaluated at the time today
t
0
, then
multiplied by
n
BH
the current average number density of
PBHs, to get the model event rate
[29]
:
R
model
¼
n
BH
dP
dt
t
¼
t
0
:
ð
5
Þ
Given the measured event rate
R
90
;i
and a particular
mass, the above expression can be inverted to find a
constraint on the fraction of dark matter in PBHs at that
mass. The results of this calculation using the measured
upper limits on the merger rate are shown in Fig.
3
.A
discussion on how some assumptions of this model may
affect the constraints on
f
shown in Fig.
3
, are discussed in
FIG. 2. Constraints on the merger rate of equal-mass ultra-
compact binaries at the 9 masses considered. The gray region
represents an exclusion at 90% confidence on the binary merger
rate in units of Gpc
−
3
yr
−
1
. These limits are found using the
loudest event statistic formalism, as described inthe text andin
Ref.
[50]
. The bounds presented here are
∼
3
orders of magnitude
stricter than those found in the initial LIGO
’
s search for sub-solar-
mass ultracompact objects
[9,10]
.
PHYSICAL REVIEW LETTERS
121,
231103 (2018)
231103-3
Ref.
[47]
. The nondetection of a stochastic background
in the first observing run of Advanced LIGO
[53]
also
implies an upper limit on the merger rate and therefore
the PBH abundance. In particular, it is shown that the
nondetection of a stochastic background yields con-
straints that are about a factor of 2 weaker than the targeted
search
[54
–
57]
.
These results are sensitive to the model of binary
formation as well as the mass distribution of PBHs. The
effects of initial clustering of PBHs is a current area of
research, though it appears that for the expected narrow
mass distributions of PBHs this effect is small in the mass
range we consider
[64
–
66]
. While the results presented here
to not take into account other effects on the binary
parameters
[67]
, they provide a conservative estimate of
the bounds.
Conclusion.
—
We presented the first Advanced LIGO
and Advanced Virgo search for ultracompact binary merg-
ers with components below
1
M
⊙
. No viable gravitational
wave candidates were found. Therefore, we were able
to constrain the binary merger rate for monochromatic
mass functions spanning from
0
.
2
M
⊙
–
1
.
0
M
⊙
. Using a
well-studied model from the literature
[29,51,52]
,we
constrained the abundance of primordial black holes as a
fraction of the total dark matter for each of our nine
monochromatic mass functions considered.
This work was only the first step in constraints by
LIGO on new physics involving sub-solar-mass ultracom-
pact objects. The constraints presented in Fig.
2
(and,
consequently, those that arise from the model of binary
formation we consider shown in Fig.
3
) may not apply if the
ultracompact binary components have non-negligible spin
since the waveforms used for signal recovery were gen-
erated only for nonspinning binaries. Future work may
either quantify the extent to which the present search could
detect spinning components, or expand the template bank
to include systems with spin. Third, we should consider
more general distributions of primordial black hole masses;
extended mass functions allow for the possibility of
unequal mass binaries, and the effect of this imbalance
on the predicted merger rate has not been quantified. We
also stress that our present results do not rule out an
extended mass function that peaks below
0
.
2
M
⊙
and
extends all the way to LIGO
’
s currently detected systems
at or above
30
M
⊙
. Each model would have to be explicitly
checked by producing an expected binary merger rate
density that could be integrated against Advanced LIGO
and Advanced Virgo search results. Extensions to more
general distributions have already been considered in the
literature
[68]
.
The first two areas of future work are computational
challenges. Lowering the minimum mass and including
spin effects in the waveform models could easily increase
the computational cost of searching for sub-solar-mass
ultracompact objects by an order of magnitude each, which
would be beyond the capabilities of present LIGO data grid
resources.
Advanced LIGO and Advanced Virgo have not reached
their final design sensitivities. The distance to which
Advanced LIGO will be sensitive to the mergers of ultra-
compact binaries in this mass range should increase by a
factor of 3 over the next several years
[69]
. Furthermore, at
least a factor of 10 more data will be available than what
were analyzed in this work. These two facts combined
imply that the merger rate constraint should improve by
⪆
2
orders of magnitude in the coming years.
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
FIG. 3. Constraints on the fraction of dark matter composed
of primordial black holes for monochromatic distributions
(
f
¼
Ω
PBH
=
Ω
DM
). Shown in black are the results for the nine
mass bins considered in this search. For this model of primordial
black hole formation, LIGO finds constraints tighter than those of
the MACHO Collaboration
[58]
for all mass bins considered and
tighter than the EROS Collaboration
[59]
for
m
i
∈
ð
0
.
7
;
1
.
0
Þ
M
⊙
.
The limits presented here also improve upon other constraints at
this mass
[60]
. The curves shown in this figure are digitizations of
the original results from Refs.
[58,59,61,62]
. We use the Planck
“
TT
;
TE
;
EE
þ
lowP
þ
lensing
þ
ext
”
cosmology
[63]
.
PHYSICAL REVIEW LETTERS
121,
231103 (2018)
231103-4
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
RussianFoundationfor Basic Research,the RussianScience
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 (NKFI), the National Research
Foundation of Korea, Industry Canada and the Province of
OntariothroughtheMinistry ofEconomicDevelopmentand
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 support of the NSF,
STFC, MPS, INFN, CNRS and the State of Niedersachsen/
Germany for provision of computational resources. Funding
for this project was provided by the Charles E. Kaufman
Foundation of The Pittsburgh Foundation. Computing
resources and personnel for this project were provided by
the Pennsylvania State University. This Letter has been
assigned the document number LIGO-P1800158-v13.
[1] B. P. Abbott
et al.
, Observation of Gravitational Waves from
a Binary Black Hole Merger,
Phys. Rev. Lett.
116
, 061102
(2016)
.
[2] B. P. Abbott
et al.
, GW151226: Observation of Gravita-
tional Waves from a 22-Solar-Mass Binary Black Hole
Coalescence,
Phys. Rev. Lett.
116
, 241103 (2016)
.
[3] B. P. Abbott
et al.
, GW170104: Observation of a 50-Solar-
Mass Binary Black Hole Coalescence at Redshift 0.2,
Phys.
Rev. Lett.
118
, 221101 (2017)
.
[4] B. P. Abbott
et al.
, GW170608: Observation of a 19-solar-
mass Binary Black Hole Coalescence,
Astrophys. J.
851
,
L35 (2017)
.
[5] B. P. Abbott
et al.
, GW170814: A Three-Detector Obser-
vation of Gravitational Waves from a Binary Black Hole
Coalescence,
Phys. Rev. Lett.
119
, 141101 (2017)
.
[6] B. P. Abbott
et al.
, GW170817: Observation of Gravita-
tional Waves from a Binary Neutron Star Inspiral,
Phys.
Rev. Lett.
119
, 161101 (2017)
.
[7] B. P. Abbott
et al.
, Binary Black Hole Mergers in the First
Advanced LIGO Observing Run,
Phys. Rev. X
6
, 041015
(2016)
.
[8] B. P. Abbott
et al.
, Search for intermediate mass black hole
binaries in the first observing run of Advanced LIGO,
Phys.
Rev. D
96
, 022001 (2017)
.
[9] B. Abbott
et al.
, Search for gravitational waves from
primordial black hole binary coalescences in the galactic
halo,
Phys. Rev. D
72
, 082002 (2005)
.
[10] B. Abbott
et al.
, Search for gravitational waves from binary
inspirals in S3 and S4 LIGO data,
Phys. Rev. D
77
, 062002
(2008)
.
[11] J. Aasi
et al.
, Advanced LIGO,
Classical Quantum Gravity
32
, 115012 (2015)
.
[12] S. Chandrasekhar, The highly collapsed configurations of a
stellar mass (Second paper),
Mon. Not. R. Astron. Soc.
95
,
207 (1935)
.
[13] S. Chandrasekhar, The maximum mass of ideal white
dwarfs,
Astrophys. J.
74
, 81 (1931)
.
[14] N. K. Glendenning,
Compact Stars: Nuclear Physics,
Particle Physics and General Relativity
(Springer-Verlag,
New York, 2012).
[15] A. Y. Potekhin, A. F. Fantina, N. Chamel, J. M. Pearson, and
S. Goriely, Analytical representations of unified equations
of state for neutron-star matter,
Astron. Astrophys.
560
, A48
(2013)
.
[16] J. G. Martinez, K. Stovall, P. C. C. Freire, J. S. Deneva,
T. M. Tauris, A. Ridolfi, N. Wex, F. A. Jenet, M. A.
McLaughlin, and M. Bagchi, Pulsar J1411+2551: A
Low-mass Double Neutron Star System,
Astrophys. J.
851
, L29 (2017)
.
[17] J. G. Martinez, K. Stovall, P. C. C. Freire, J. S. Deneva, F. A.
Jenet, M. A. McLaughlin, M. Bagchi, S. D. Bates, and A.
Ridolfi, Pulsar J0453+1559: A double neutron star system
with a large mass asymmetry,
Astrophys. J.
812
, 143 (2015)
.
[18] J. M. Lattimer, The nuclear equation of state and neutron
star masses,
Annu. Rev. Nucl. Part. Sci.
62
, 485 (2012)
.
[19] F. Özel, D. Psaltis, R. Narayan, and J. E. McClintock, The
black hole mass distribution in the Galaxy,
Astrophys. J.
725
, 1918 (2010)
.
[20] W. M. Farr, N. Sravan, A. Cantrell, L. Kreidberg, C. D.
Bailyn, I. Mandel, and V. Kalogera, The mass distribution of
stellar-mass black holes,
Astrophys. J.
741
, 103 (2011)
.
[21] L. Kreidberg, C. D. Bailyn, W. M. Farr, and V. Kalogera,
Mass measurements of black holes in X-ray transients: Is
there a mass gap?,
Astrophys. J.
757
, 36 (2012)
.
[22] Y. B. Zeldovich and I. D. Novikov, The hypothesis of cores
retarded during expansion and the hot cosmological model,
Sov. Astron.
10
, 602 (1967).
[23] S. Hawking, Gravitationally collapsed objects of very low
mass,
Mon. Not. R. Astron. Soc.
152
, 75 (1971)
.
PHYSICAL REVIEW LETTERS
121,
231103 (2018)
231103-5
[24] B. J. Carr and S. W. Hawking, Black holes in the early
Universe,
Mon. Not. R. Astron. Soc.
168
, 399 (1974)
.
[25] P. M ́
eszáros, The behaviour of point masses in an expanding
cosmological substratum, Astron. Astrophys.
37
, 225 (1974).
[26] G. F. Chapline, Cosmological effects of primordial black
holes,
Nature (London)
253
, 251 (1975)
.
[27] B. Carr, F. Kühnel, and M. Sandstad, Primordial black holes
as dark matter,
Phys. Rev. D
94
, 083504 (2016)
.
[28] S. Bird, I. Cholis, J. B. Muñoz, Y. Ali-Haïmoud, M.
Kamionkowski, E. D. Kovetz, A. Raccanelli, and A. G.
Riess, Did LIGO Detect Dark Matter?,
Phys. Rev. Lett.
116
, 201301 (2016)
.
[29] M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama,
Primordial Black Hole Scenario for the Gravitational-Wave
Event GW150914,
Phys. Rev. Lett.
117
, 061101 (2016)
.
[30] S. Clesse and J. García-Bellido, The clustering of massive
primordial black holes as dark matter: Measuring their mass
distribution with Advanced LIGO,
Phys. Dark Universe
15
,
142 (2017)
.
[31] E. D. Kovetz, I. Cholis, P. C. Breysse, and M. Kamionkowski,
Black hole mass function from gravitational wave measure-
ments,
Phys. Rev. D
95
, 103010 (2017)
.
[32] A. Raccanelli, E. D. Kovetz, S. Bird, I. Cholis, and J. B.
Munoz, Determining the progenitors of merging black-hole
binaries,
Phys. Rev. D
94
, 023516 (2016)
.
[33] I. Cholis, E. D. Kovetz, Y. Ali-Haïmoud, S. Bird, M.
Kamionkowski, J. B. Muñoz, and A. Raccanelli, Orbital
eccentricities in primordial black hole binaries,
Phys. Rev. D
94
, 084013 (2016)
.
[34] A. Raccanelli, Gravitational wave astronomy with radio
galaxy surveys,
Mon. Not. R. Astron. Soc.
469
, 656 (2017)
.
[35] S. M. Koushiappas and A. Loeb, Maximum Redshift of
Gravitational Wave Merger Events,
Phys. Rev. Lett.
119
,
221104 (2017)
.
[36] H. Nishikawa, E. D. Kovetz, M. Kamionkowski, and J. Silk,
Primordial-black-hole mergers in dark-matter spikes,
arXiv:1708.08449.
[37] S. Shandera, D. Jeong, and H. S. G. Gebhardt, Gravitational
Waves from Binary Mergers of Subsolar Mass Dark Black
Holes,
Phys. Rev. Lett.
120
, 241102 (2018)
.
[38] C. Kouvaris, P. Tinyakov, and M. H. G. Tytgat, Non-
primordial solar mass black holes, .
[39] B. P. Abbott
et al.
, Effects of data quality vetoes on a search
for compact binary coalescences in Advanced LIGO
’
s first
observing run,
Classical Quantum Gravity
35
, 065010
(2018)
.
[40] B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F.
Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso,
R. X. Adhikari
et al.
, Binary Black Hole Mergers in the First
Advanced LIGO Observing Run,
Phys. Rev. X
6
, 041015
(2016)
.
[41] K. Cannon
et al.
, Toward early-warning detection of
gravitational waves from compact binary coalescence,
As-
trophys. J.
748
, 136 (2012)
.
[42] C. Messick
et al.
, Analysis framework for the prompt
discovery of compact binary mergers in gravitational-wave
data,
Phys. Rev. D
95
, 042001 (2017)
.
[43] GstLAL software,
git.ligo.org/lscsoft/gstlal
.
[44] Lal software,
git.ligo.org/lscsoft/lalsuite
.
[45] P. Ajith, N. Fotopoulos, S. Privitera, A. Neunzert, and A. J.
Weinstein, Effectual template bank for the detection of
gravitational waves from inspiralling compact binaries with
generic spins,
Phys. Rev. D
89
, 084041 (2014)
.
[46] C. Capano, I. Harry, S. Privitera, and A. Buonanno,
Implementing a search for gravitational waves from binary
black holes with nonprecessing spin,
Phys. Rev. D
93
,
124007 (2016)
.
[47] R. Magee, A.-S. Deutsch, P. McClincy, C. Hanna, C. Horst,
D. Meacher, C. Messick, S. Shandera, and M. Wade,
Methods for the detection of gravitational waves from
sub-solar mass ultracompact binaries,
arXiv:1808.04772.
[48] L. Blanchet, T. Damour, B. R. Iyer, C. M. Will, and A. G.
Wiseman, Gravitational-Radiation Damping of Compact
Binary Systems to Second Post-Newtonian Order,
Phys.
Rev. Lett.
74
, 3515 (1995)
.
[49] A. Buonanno, B. R. Iyer, E. Ochsner, Y. Pan, and B. S.
Sathyaprakash, Comparison of post-newtonian templates
for compact binary inspiral signals in gravitational-wave
detectors,
Phys. Rev. D
80
, 084043 (2009)
.
[50] R. Biswas, P. R. Brady, J. D. E. Creighton, and S. Fairhurst,
The Loudest event statistic: General formulation, properties
and applications,
Classical Quantum Gravity
26
, 175009
(2009)
; Erratum,
Classical Quantum Gravity,
30
, 079502(E)
(2013)
.
[51] T. Nakamura, M. Sasaki, T. Tanaka, and K. S. Thorne,
Gravitational waves from coalescing black hole MACHO
binaries,
Astrophys. J.
487
, L139 (1997)
.
[52] K. Ioka, T. Chiba, T. Tanaka, and T. Nakamura, Black hole
binary formation in the expanding Universe: Three body
problem approximation,
Phys. Rev. D
58
, 063003 (1998)
.
[53] B. P. Abbott
et al.
, Upper Limits on the Stochastic
Gravitational-Wave Background from Advanced LIGO
’
s
First Observing Run,
Phys. Rev. Lett.
118
, 121101 (2017)
;
Erratum,
Phys. Rev. Lett.
119
, 029901(E) (2017)
.
[54] V. Mandic, S. Bird, and I. Cholis, Stochastic Gravitational-
Wave Background due to Primordial Binary Black Hole
Mergers,
Phys. Rev. Lett.
117
, 201102 (2016)
.
[55] S. Wang, Y.-F. Wang, Q.-G. Huang, and T. G. F. Li,
Constraints on the Primordial Black Hole Abundance from
the First Advanced LIGO Observation Run Using the
Stochastic Gravitational-Wave Background,
Phys. Rev.
Lett.
120
, 191102 (2018)
.
[56] I. Cholis, On the gravitational wave background from black
hole binaries after the first LIGO detections,
J. Cosmology
Astropart. Phys. J. Cosmol. Astropart. Phys. 6 (2017) 037.
[57] M. Raidal, V. Vaskonen, and H. Veermäe, Gravitational
waves from primordial black hole mergers,
J. Cosmol.
Astropart. Phys. 9 (2017) 037.
[58] R. A. Allsman
et al.
, MACHO project limits on black hole
dark matter in the 1-30 solar mass range,
Astrophys. J.
550
,
L169 (2001)
.
[59] P. Tisserand
et al.
, Limits on the macho content of the
galactic halo from the EROS-2 survey of the magellanic
clouds,
Astron. Astrophys.
469
, 387 (2007)
.
[60] M. Zumalacarregui and U. Seljak, Limits on Stellar-Mass
Compact Objects as Dark Matter from Gravitational Lens-
ing of Type Ia Supernovae,
Phys. Rev. Lett.
121
, 141101
(2018)
.
PHYSICAL REVIEW LETTERS
121,
231103 (2018)
231103-6
[61] S. M. Koushiappas and A. Loeb, Dynamics of Dwarf
Galaxies Disfavor Stellar-Mass Black Holes as Dark Matter,
Phys. Rev. Lett.
119
, 041102 (2017)
.
[62] T. D. Brandt, Constraints on MACHO Dark matter from
compact stellar systems in ultra-faint dwarf galaxies,
As-
trophys. J.
824
, L31 (2016)
.
[63] P. A. R. Ade
et al.
, Planck 2015 results. XIII. Cosmological
parameters,
Astron. Astrophys.
594
, A13 (2016)
.
[64] V. Desjacques and A. Riotto, The spatial clustering of
primordial black holes,
arXiv:1806.10414.
[65] G. Ballesteros, P. D. Serpico, and M. Taoso, On the merger
rate of primordial black holes: Effects of nearest neighbours
distribution and clustering,
J. Cosmol. Astropart. Phys. 10
(2018) 043.
[66] Y. Ali-Haïmoud, Correlation Function of High-Threshold
Regions and Application to the Initial Small-Scale Clustering
of Primordial Black Holes,
Phys.Rev.Lett.
121
, 081304 (2018)
.
[67] Y. Ali-Haïmoud, E. D. Kovetz, and M. Kamionkowski,
Merger rate of primordial black-hole binaries,
Phys. Rev.
D
96
, 123523 (2017)
.
[68] N. Bellomo, J. L. Bernal, A. Raccanelli, and L. Verde,
Primordial black holes as dark matter: Converting
constraints from monochromatic to extended mass
distributions,
J. Cosmol. Astropart. Phys. 01 (2018) 004.
[69] B. P. Abbott
et al.
, Prospects for observing and localizing
gravitational-wave transients with advanced LIGO, ad-
vanced Virgo and KAGRA,
Living Rev. Relativity
21
,3
(2018)
;
19
, 1 (2016)
.
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
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
B. D. Cheeseboro,
40
H. Y. Chen,
92
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,
93
M. Cho,
76
J. H. Chow,
24
N. Christensen,
94,66
Q. Chu,
64
A. J. K. Chua,
47
S. Chua,
71
K. W. Chung,
95
S. Chung,
64
G. Ciani,
52,53,49
A. A. Ciobanu,
56
R. Ciolfi,
96,97
F. Cipriano,
66
C. E. Cirelli,
50
A. Cirone,
81,61
F. Clara,
46
J. A. Clark,
77
P. Clearwater,
98
F. Cleva,
66
C. Cocchieri,
86
E. Coccia,
16,17
P.-F. Cohadon,
71
D. Cohen,
27
A. Colla,
99,35
C. G. Collette,
100
C. Collins,
60
L. R. Cominsky,
101
M. Constancio Jr.,
15
L. Conti,
53
S. J. Cooper,
60
P. Corban,
6
T. R. Corbitt,
2
I. Cordero-Carrión,
102
K. R. Corley,
103
N. Cornish,
104
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,
103
P. Couvares,
1
P. B. Covas,
105
E. E. Cowan,
77
D. M. Coward,
64
M. J. Cowart,
6
D. C. Coyne,
1
R. Coyne,
106
J. D. E. Creighton,
20
T. D. Creighton,
107
J. Cripe,
2
S. G. Crowder,
108
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,
109
C. F. Da Silva Costa,
49
V. Dattilo,
30
I. Dave,
62
M. Davier,
27
D. Davis,
43
E. J. Daw,
110
B. Day,
77
D. DeBra,
50
M. Deenadayalan,
18
J. Degallaix,
25
M. De Laurentis,
79,4
PHYSICAL REVIEW LETTERS
121,
231103 (2018)
231103-7
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,
111
A. S. Deutsch,
88
O. de Varona,
9,10
S. Dhurandhar,
18
M. C. Díaz,
107
L. Di Fiore,
4
M. Di Giovanni,
112,97
T. Di Girolamo,
79,4
A. Di Lieto,
21,22
B. Ding,
100
S. Di Pace,
99,35
I. Di Palma,
99,35
F. Di Renzo,
21,22
A. Dmitriev,
60
Z. Doctor,
92
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,
110
M. C. Edwards,
94
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,
92
H. Estelles,
105
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,
113
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,
92
R. P. Fisher,
43
J. M. Fishner,
14
M. Fitz-Axen,
44
R. Flaminio,
7,114
M. Fletcher,
45
H. Fong,
115
J. A. Font,
23,116
P. W. F. Forsyth,
24
S. S. Forsyth,
77
J.-D. Fournier,
66
S. Frasca,
99,35
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,
105
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,
112,97
J. A. Giaime,
2,6
K. D. Giardina,
6
A. Giazotto,
22
,
†
K. Gill,
37
G. Giordano,
3,4
L. Glover,
111
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,
109
X. Guo,
83
A. Gupta,
88
M. K. Gupta,
109
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
O. A. Hannuksela,
95
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,
115
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,
92
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,
105
S. H. Huttner,
45
T. Huynh-Dinh,
6
A. Iess,
32,33
N. Indik,
9
C. Ingram,
56
R. Inta,
84
G. Intini,
99,35
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,
110
J. S. Key,
128
F. Y. Khalili,
63
B. Khamesra,
77
H. Khan,
28
I. Khan,
16,33
S. Khan,
9
Z. Khan,
109
E. A. Khazanov,
129
N. Kijbunchoo,
24
Chunglee Kim,
130
J. C. Kim,
131
K. Kim,
95
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
A. Królak,
134,135
G. Kuehn,
9,10
P. Kumar,
136
R. Kumar,
109
S. Kumar,
19
L. Kuo,
89
A. Kutynia,
134
S. Kwang,
20
B. D. Lackey,
38
K. H. Lai,
95
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,
99,35
S. Leavey,
9,10
C. H. Lee,
93
H. K. Lee,
138
H. M. Lee,
130
H. W. Lee,
131
K. Lee,
45
J. Lehmann,
9,10
A. Lenon,
40
M. Leonardi,
9,10,114
N. Leroy,
27
N. Letendre,
7
Y. Levin,
5
J. Li,
83
T. G. F. Li,
95
X. Li,
47
S. D. Linker,
111
T. B. Littenberg,
139
J. Liu,
64
X. Liu,
20
R. K. L. Lo,
95
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
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
V. Mangano,
45
G. L. Mansell,
24
M. Manske,
20,24
M. Mantovani,
30
F. Marchesoni,
51,42
F. Marion,
7
S. Márka,
103
Z. Márka,
103
C. Markakis,
11
A. S. Markosyan,
50
A. Markowitz,
1
E. Maros,
1
A. Marquina,
102
F. Martelli,
72,73
L. Martellini,
66
I. W. Martin,
45
R. M. Martin,
113
D. V. Martynov,
14
K. Mason,
14
E. Massera,
110
A. Masserot,
7
T. J. Massinger,
1
M. Masso-Reid,
45
S. Mastrogiovanni,
99,35
A. Matas,
44
F. Matichard,
1,14
L. Matone,
103
N. Mavalvala,
14
N. Mazumder,
69
J. J. McCann,
64
PHYSICAL REVIEW LETTERS
121,
231103 (2018)
231103-8
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,
98
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,
98
E. E. Mikhailov,
144
L. Milano,
79,4
A. L. Miller,
49
A. Miller,
99,35
B. B. Miller,
91
J. Miller,
14
M. Millhouse,
104
J. Mills,
36
M. C. Milovich-Goff,
111
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,
107
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,
99,35
R. K. Nayak,
149
J. Neilson,
111
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,
111
G. H. Ogin,
150
J. J. Oh,
132
S. H. Oh,
132
F. Ohme,
9
H. Ohta,
82
M. A. Okada,
15
M. Oliver,
105
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,
95
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,
112,97
L. M. Perri,
91
H. P. Pfeiffer,
115,38
M. Phelps,
45
K. S. Phukon,
18
O. J. Piccinni,
99,35
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,
105
V. Predoi,
36
T. Prestegard,
20
M. Principe,
8
S. Privitera,
38
G. A. Prodi,
112,97
L. G. Prokhorov,
63
O. Puncken,
9,10
M. Punturo,
42
P. Puppo,
35
M. Pürrer,
38
H. Qi,
20
V. Quetschke,
107
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,
107
K. E. Ramirez,
107
A. Ramos-Buades,
105
Javed Rana,
18
P. Rapagnani,
99,35
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,
99,35
P. M. Ricker,
11
K. Riles,
123
M. Rizzo,
59
N. A. Robertson,
1,45
R. Robie,
45
F. Robinet,
27
T. Robson,
104
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,
156,55
M. P. Ross,
157
S. Rowan,
45
A. Rüdiger,
9,10
P. Ruggi,
30
G. Rutins,
158
K. Ryan,
46
S. Sachdev,
1
T. Sadecki,
46
M. Sakellariadou,
159
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,
160
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,
111
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,
105
B. J. J. Slagmolen,
24
T. J. Slaven-Blair,
64
B. Smith,
6
J. R. Smith,
28
R. J. E. Smith,
5
S. Somala,
161
E. J. Son,
132
B. Sorazu,
45
F. Sorrentino,
61
T. Souradeep,
18
A. P. Spencer,
45
A. K. Srivastava,
109
K. Staats,
37
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,
107
D. J. Stops,
60
K. A. Strain,
45
G. Stratta,
72,73
S. E. Strigin,
63
A. Strunk,
46
R. Sturani,
162
A. L. Stuver,
163
T. Z. Summerscales,
164
L. Sun,
98
S. Sunil,
109
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
D. B. Tanner,
49
M. Tápai,
120
A. Taracchini,
38
J. D. Tasson,
94
J. A. Taylor,
139
R. Taylor,
1
S. V. Tewari,
153
T. Theeg,
9,10
F. Thies,
9,10
E. G. Thomas,
60
M. Thomas,
6
P. Thomas,
46
K. A. Thorne,
6
E. Thrane,
5
S. Tiwari,
16,97
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,
112,97
L. Trozzo,
165,22
K. W. Tsang,
13
M. Tse,
14
R. Tso,
47
D. Tsuna,
82
L. Tsukada,
82
D. Tuyenbayev,
107
K. Ueno,
20
D. Ugolini,
166
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,
13,167
D. C. Vander-Hyde,
43
L. van der Schaaf,
13
J. V. van Heijningen,
13
PHYSICAL REVIEW LETTERS
121,
231103 (2018)
231103-9