GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed
by LIGO and Virgo during the First and Second Observing Runs
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 14 December 2018; revised manuscript received 27 March 2019; published 4 September 2019)
We present the results from three gravitational-wave searches for coalescing compact binaries with
component masses above
1
M
⊙
during the first and second observing runs of the advanced gravitational-
wave detector network. During the first observing run (
O
1
), from September 12, 2015 to January 19, 2016,
gravitational waves from three binary black hole mergers were detected. The second observing run (
O
2
),
which ran from November 30, 2016 to August 25, 2017, saw the first detection of gravitational waves from
a binary neutron star inspiral, in addition to the observation of gravitational waves from a total of seven
binary black hole mergers, four of which we report here for the first time: GW170729, GW170809,
GW170818, and GW170823. For all significant gravitational-wave events, we provide estimates of the
source properties. The detected binary black holes have total masses between
18
.
6
þ
3
.
2
−
0
.
7
M
⊙
and
84
.
4
þ
15
.
8
−
11
.
1
M
⊙
and range in distance between
320
þ
120
−
110
and
2840
þ
1400
−
1360
Mpc. No neutron star
–
black hole
mergers were detected. In addition to highly significant gravitational-wave events, we also provide a list
of marginal event candidates with an estimated false-alarm rate less than 1 per 30 days. From these results
over the first two observing runs, which include approximately one gravitational-wave detection per
15 days of data searched, we infer merger rates at the 90% confidence intervals of
110
−
3840
Gpc
−
3
y
−
1
for binary neutron stars and
9
.
7
−
101
Gpc
−
3
y
−
1
for binary black holes assuming fixed population
distributions and determine a neutron star
–
black hole merger rate 90% upper limit of
610
Gpc
−
3
y
−
1
.
DOI:
10.1103/PhysRevX.9.031040
Subject Areas: Astrophysics, Gravitation
I. INTRODUCTION
The first observing run (
O
1
) of Advanced LIGO, which
took place from September 12, 2015 until January 19,
2016, saw the first detections of gravitational waves (GWs)
from stellar-mass binary black holes (BBHs)
[1
–
4]
. After
an upgrade and commissioning period, the second observ-
ing run (
O
2
) of the Advanced LIGO detectors
[5]
com-
menced on November 30, 2016 and ended on August 25,
2017. On August 1, 2017, the Advanced Virgo detector
[6]
joined the observing run, enabling the first three-detector
observations of GWs. This network of ground-based
interferometric detectors is sensitive to GWs from the
inspiral, merger, and ringdown of compact binary coales-
cences (CBCs), covering a frequency range from about
15 Hz up to a few kilohertz (see Fig.
1
). In this catalog, we
report 11 confident detections of GWs from compact binary
mergers as well as a selection of less significant triggers
from both observing runs. The observations reported here
and future GW detections will shed light on binary
formation channels, enable precision tests of general
relativity (GR) in its strong-field regime, and open up
new avenues of astronomy research.
The events presented here are obtained from a total of
three searches: two matched-filter searches, PyCBC
[7,8]
and GstLAL
[9,10]
, using relativistic models of GWs from
CBCs, as well as one unmodeled search for short-duration
transient signals or bursts, coherent WaveBurst (cWB)
[11]
.
The two matched-filter searches target GWs from com-
pact binaries with a redshifted total mass
M
ð
1
þ
z
Þ
of
2
–
500
M
⊙
for PyCBC and
2
–
400
M
⊙
for GstLAL, where
z
is the cosmological redshift of the source binary
[12]
, and
with maximal dimensionless spins of 0.998 for black holes
(BHs) and 0.05 for neutron stars (NSs). The results of a
matched-filter search for sub-solar-mass compact objects in
O
1
can be found in Ref.
[13]
; the results for
O
2
will be
discussed elsewhere. The burst search cWB does not use
waveform models to compare against the data but instead
identifies regions of excess power in the time-frequency
representation of the gravitational strain. We report results
from a cWB analysis that is optimized for the detection
of compact binaries with a total mass less than
100
M
⊙
.
A different tuning of the cWB analysis is used for a search
for intermediate-mass BBHs with total masses greater than
100
M
⊙
; the results of that analysis are discussed else-
where. The three searches reported here use different
methodologies to identify GWs from compact binaries
*
Full author list given at the end of the article.
Published by the American Physical Society under the terms of
the
Creative Commons Attribution 4.0 International
license.
Further distribution of this work must maintain attribution to
the author(s) and the published article
’
s title, journal citation,
and DOI.
PHYSICAL REVIEW X
9,
031040 (2019)
2160-3308
=
19
=
9(3)
=
031040(49)
031040-1
Published by the American Physical Society
in an overlapping but not identical search space, thus
providing three largely independent analyses that allow
for important cross-checks and yield consistent results.
All searches have undergone improvements since
O
1
,
making it scientifically valuable to reanalyze the
O
1
data
in order to reevaluate the significance of previously
identified GW events and to potentially discover new ones.
The searches identified a total of ten BBH mergers and
one binary neutron star (BNS) signal. The GW events
GW150914, GW151012
[14]
, GW151226, GW170104,
GW170608, GW170814, and GW170817 have been
reported previously
[4,15
–
18]
. In this catalog, we announce
four previously unpublished BBH mergers observed
during
O
2
: GW170729, GW170809, GW170818, and
GW170823. We estimate the total mass of GW170729
to be
84
.
4
þ
15
.
8
−
11
.
1
M
⊙
, making it the highest-mass BBH
observed to date. GW170818 is the second BBH observed
in triple coincidence between the two LIGO observatories
and Virgo after GW170814
[16]
. As the sky location is
primarily determined by the differences in the times of
arrival of the GW signal at the different detector sites,
LIGO-Virgo coincident events have a vastly improved
sky localization, which is crucial for electromagnetic
follow-up campaigns
[19
–
22]
. The reanalysis of the
O
1
data did not result in the discovery of any new GW events,
but GW151012 is now detected with increased signifi-
cance. In addition, we list 14 GW candidate events that
have an estimated false-alarm rate (FAR) less than 1 per
30 days in either of the two matched-filter analyses but
whose astrophysical origin cannot be established nor
excluded unambiguously (Sec.
VII
).
Gravitational waves from compact binaries carry infor-
mation about the properties of the source such as the masses
and spins. These can be extracted via Bayesian inference by
using theoretical models of the GW signal that describe the
inspiral, merger, and ringdown of the final object for BBH
[23
–
30]
andtheinspiral(andmerger)forBNS
[31
–
33]
.Such
models are built by combining post-Newtonian calculations
[34
–
38]
, the effective-one-body formalism
[39
–
44]
, and
numerical relativity
[45
–
50]
. Based on a variety of theoreti-
cal models, we provide key source properties of all confident
GW detections. For previously reported detections, we
provide updated parameter estimates which exploit refined
instrumental calibration, noise subtraction (for
O
2
data)
[51,52]
, and updated amplitude power spectral density
estimates
[53,54]
.
The observation of these GW events allows us to place
constraints on the rates of stellar-mass BBH and BNS
mergers in the Universe and probe their mass and spin
distributions, putting them into astrophysical context. The
nonobservation of GWs from a neutron star
–
black hole
binary (NSBH) yields a stronger 90% upper limit on the
rate. The details of the astrophysical implications of our
observations are discussed in Ref.
[55]
.
This paper is organized as follows: In Sec.
II
,we
provide an overview of the operating detectors during
O
2
,
as well as the data used in the searches and parameter
estimation. Section
III
briefly summarizes the three
different searches, before we define the event selection
criteria and present the results in Sec.
IV
.Tables
I
and
II
summarize some key search parameters for the clear GW
detections and the marginal events. Details about the
source properties of the GW events are given in Sec.
V
,
and the values of some important parameters obtained
from Bayesian inference are listed in Table
III
. We do not
provide parameter estimation results for marginal
events. An independent consistency analysis between
the waveform-based results and the data is performed
in Sec.
VI
.InSec.
VII
, we describe how the probability of
astrophysical origin is calculated and give its value for
each significant and marginal event in Table
IV
.We
provide an updated estimate of binary merger rates in this
10
100
1000
Frequency [Hz]
10
−
23
10
−
22
10
−
21
10
−
20
Strain noise [1/
√
Hz]
FIG. 1. Left: BNS range for each instrument during
O
2
. The break at week 3 is for the 2016 end-of-year holidays. There is an
additional break in the run at week 23 to make improvements to instrument sensitivity. The Montana earthquake
’
s impact on the LHO
instrument sensitivity can be seen at week 31. Virgo joins
O
2
in week 34. Right: Amplitude spectral density of the total strain noise of
the Virgo, LHO, and LLO detectors. The curves are representative of the best performance of each detector during
O
2
.
B. P. ABBOTT
et al.
PHYS. REV. X
9,
031040 (2019)
031040-2
section before concluding in Sec.
VIII
.Wealsoprovide
the Appendixes containing additional technical details.
A variety of additional information on each event, data
products including strain data and posterior samples, and
postprocessing tools can be obtained from the accompany-
ing data release
[56]
hosted by the Gravitational Wave
Open Science Center
[57]
.
II. INSTRUMENTAL OVERVIEW AND DATA
A. LIGO instruments
The Advanced LIGO detectors
[58,59]
began scientific
operations in September, 2015 and almost immediately
detected the first gravitational waves from the BBH merger
GW150914.
Between
O
1
and
O
2
, improvements were made to both
LIGO instruments. At LIGO-Livingston (LLO), a mal-
functioning temperature sensor
[60]
was replaced immedi-
ately after
O
1
, contributing to an increase in the BNS
range from approximately 60 Mpc to approximately
80 Mpc
[61]
. Other major changes included adding passive
tuned mass dampers on the end test mass suspensions to
reduce ringing up of mechanical modes, installing a new
output Faraday isolator, adding a new in-vacuum array of
photodiodes for stabilizing the laser intensity, installing
TABLE I. Search results for the 11 GW events. We report a false-alarm rate for each search that found a given event; otherwise, we
display
. The network SNR for the two matched-filter searches is that of the template ranked highest by that search, which is not
necessarily the template with the highest SNR. Moreover, the network SNR is the quadrature sum of the detectors coincident in the
highest-ranked trigger; in some cases, only two detectors contribute, even if all three are operating nominally at the time of that event.
FAR
½
y
−
1
Network SNR
Event
UTC time
PyCBC
GstLAL
cWB
PyCBC
GstLAL
cWB
GW150914
09
∶
50
∶
45
.
4
<
1
.
53
×
10
−
5
<
1
.
00
×
10
−
7
<
1
.
63
×
10
−
4
23.6
24.4
25.2
GW151012
09
∶
54
∶
43
.
4
0.17
7
.
92
×
10
−
3
9.5
10.0
GW151226
03
∶
38
∶
53
.
6
<
1
.
69
×
10
−
5
<
1
.
00
×
10
−
7
0.02
13.1
13.1
11.9
GW170104
10
∶
11
∶
58
.
6
<
1
.
37
×
10
−
5
<
1
.
00
×
10
−
7
2
.
91
×
10
−
4
13.0
13.0
13.0
GW170608
02
∶
01
∶
16
.
5
<
3
.
09
×
10
−
4
<
1
.
00
×
10
−
7
1
.
44
×
10
−
4
15.4
14.9
14.1
GW170729
18
∶
56
∶
29
.
3
1.36
0.18
0.02
9.8
10.8
10.2
GW170809
08
∶
28
∶
21
.
81
.
45
×
10
−
4
<
1
.
00
×
10
−
7
12.2
12.4
GW170814
10
∶
30
∶
43
.
5
<
1
.
25
×
10
−
5
<
1
.
00
×
10
−
7
<
2
.
08
×
10
−
4
16.3
15.9
17.2
GW170817
12
∶
41
∶
04
.
4
<
1
.
25
×
10
−
5
<
1
.
00
×
10
−
7
30.9
33.0
GW170818
02
∶
25
∶
09
.
1
4
.
20
×
10
−
5
11.3
GW170823
13
∶
13
∶
58
.
5
<
3
.
29
×
10
−
5
<
1
.
00
×
10
−
7
2
.
14
×
10
−
3
11.1
11.5
10.8
TABLE II. Marginal triggers from the two matched-filter CBC searches. To distinguish events occurring on the same UTC day, we
extend the YYMMDD label by decimal fractions of a day as needed, always rounding down (truncating) the decimal. The search that
identifies each trigger is given, and the false alarm and network SNR. This network SNR is the quadrature sum of the individual detector
SNRs for all detectors involved in the reported trigger; that can be fewer than the number of nominally operational detectors at the time,
depending on the ranking algorithm of each pipeline. The detector chirp mass reported is that of the most significant template of the
search. The concentration of our marginal triggers at low chirp masses is consistent with expectations for noise triggers, because search
template waveforms are much more densely packed at low masses. The final column indicates whether there are any detector
characterization concerns with the trigger; for an explanation and more details, see the text.
Date
UTC
Search
FAR
½
y
−
1
Network SNR
M
det
½
M
⊙
Data quality
151008
14
∶
09
∶
17
.
5
PyCBC
10.17
8.8
5.12
No artifacts
151012.2
06
∶
30
∶
45
.
2
GstLAL
8.56
9.6
2.01
Artifacts present
151116
22
∶
41
∶
48
.
7
PyCBC
4.77
9.0
1.24
No artifacts
161202
03
∶
53
∶
44
.
9
GstLAL
6.00
10.5
1.54
Artifacts possibly caused
161217
07
∶
16
∶
24
.
4
GstLAL
10.12
10.7
7.86
Artifacts possibly caused
170208
10
∶
39
∶
25
.
8
GstLAL
11.18
10.0
7.39
Artifacts present
170219
14
∶
04
∶
09
.
0
GstLAL
6.26
9.6
1.53
No artifacts
170405
11
∶
04
∶
52
.
7
GstLAL
4.55
9.3
1.44
Artifacts present
170412
15
∶
56
∶
39
.
0
GstLAL
8.22
9.7
4.36
Artifacts possibly caused
170423
12
∶
10
∶
45
.
0
GstLAL
6.47
8.9
1.17
No artifacts
170616
19
∶
47
∶
20
.
8
PyCBC
1.94
9.1
2.75
Artifacts present
170630
16
∶
17
∶
07
.
8
GstLAL
10.46
9.7
0.90
Artifacts present
170705
08
∶
45
∶
16
.
3
GstLAL
10.97
9.3
3.40
No artifacts
170720
22
∶
44
∶
31
.
8
GstLAL
10.75
13.0
5.96
Artifacts possibly caused
GWTC-1: A GRAVITATIONAL-WAVE TRANSIENT CATALOG
...
PHYS. REV. X
9,
031040 (2019)
031040-3
higher quantum-efficiency photodiodes at the output port,
and replacing the compensation plate on the input test mass
suspension for the
Y
arm. An attempt to upgrade the LLO
laser to provide higher input power was not successful.
During
O
2
, improvements to the detector sensitivity con-
tinued, and sources of scattered light noise were mitigated.
As a result, the sensitivity of the LLO instrument rose from
a BNS range of 80 Mpc at the beginning of
O
2
to greater
than 100 Mpc by the run
’
s end.
The LIGO-Hanford (LHO) detector had a range of
approximately 80 Mpc as
O
1
ended, and it was decided
to concentrate on increasing the input laser power and forgo
any incursions into the vacuum system. Increasing the input
laser power to 50 W was successful, but since this increase
did not result in an improvement in sensitivity, the LHO
detector operated with 30 W input power during
O
2
.Itwas
eventually discovered that there was a point absorber on
one of the input test mass optics, which we speculate led to
increased coupling of input
“
jitter
”
noise from the laser
table into the interferometer. By use of appropriate witness
sensors, it was possible to perform an offline noise
subtraction on the data, leading to an increase in the
BNS range at LHO by an average of about 20% over all
of
O
2
[51,52]
.
On July 6, 2017, LHO was severely affected by a 5.8
magnitude earthquake in Montana. Postearthquake, the
sensitivity of the detector dropped by approximately
10 Mpc and remained in this condition until the end of
the run on August 25, 2017.
B. Virgo instrument
Advanced Virgo
[6]
aims to increase the sensitivity of the
Virgo interferometer by one order of magnitude, and
several upgrades were performed after the decommission-
ing of the first-generation detector in 2011. The main
modifications include a new optical design, heavier mir-
rors, and suspended optical benches, including photodiodes
in a vacuum. Special care was also taken to improve the
decoupling of the instrument from environmental disturb-
ances. One of the main limiting noise sources below 100 Hz
is the thermal Brownian excitation of the wires used for
suspending the mirrors. A first test performed on the Virgo
configuration showed that silica fibers would reduce this
contribution. A vacuum contamination issue, which has
since been corrected, led to failures of these silica suspen-
sion fibers, so metal wires were used to avoid delaying
Virgo
’
s participation in
O
2
. Unlike the LIGO instruments,
Virgo has not yet implemented signal recycling, which will
be installed in a later upgrade of the instrument.
After several months of commissioning, Virgo joined
O
2
on August 1, 2017 with a BNS range of approximately
25 Mpc. The performance experienced a temporary deg-
radation on August 11 and 12, when the microseismic
activity on site was highly elevated and it was difficult to
keep the interferometer in its low-noise operating mode.
C. Data
Figure
1
shows the BNS ranges of the LIGO and Virgo
instruments over the course of
O
2
and the representative
amplitude spectral density plots of the total strain noise for
each detector.
We subtract several independent contributions to the
instrumental noise from the data at both LIGO detectors
[51]
. For all of
O
2
, the average increase in the BNS range
from this noise subtraction process at LHO is approxi-
mately 20%
[51]
. At LLO, the noise-subtraction process
targeted narrow line features, resulting in a negligible
increase in the BNS range.
Calibrated strain data from each interferometer are
produced online for use in low-latency searches. Following
the run, a final frequency-dependent calibration is gener-
ated for each interferometer.
For the LIGO instruments, this final calibration benefits
from the use of postrun measurements and the removal of
instrumental lines. The calibration uncertainties are 3.8% in
amplitude and 2.1° in phase for LLO and 2.6% in amplitude
and 2.4° in phase for LHO. The results cited in this paper
use the full frequency-dependent calibration uncertainties
described in Refs.
[64,65]
. The LIGO timing uncertainty of
<
1
μ
s
[66]
is included in the phase correction factor.
The calibration of strain data produced online by Virgo
has large uncertainties due to the short time available for
measurements. The data are reprocessed to reduce the
errors by taking into account better calibration models
obtained from postrun measurements and the subtraction of
frequency noise. The reprocessing includes a time depend-
ence for the noise subtraction and for the determination of
the finesse of the cavities. The final uncertainties are 5.1%
in amplitude and 2.3° in phase
[67]
. The Virgo calibration
has an additional uncertainty of
20
μ
s originating from the
time stamping of the data.
During
O
2
, the individual LIGO detectors had duty
factors of approximately 60% with a LIGO network duty
factor of about 45%. Times with significant instrumental
disturbances are flagged and removed, resulting in about
118 days of data suitable for coincident analysis
[68]
.Of
these data, about 15 days are collected in coincident
operation with Virgo, which after joining
O
2
operated with
a duty factor of about 80%. Times with excess instrumental
noise, which is not expected to render the data unusable, are
also flagged
[68]
. Individual searches may then decide to
include or not include such times in their final results.
III. SEARCHES
The search results presented in the next section are
obtained by two different, largely independent matched-
filter searches, PyCBC and GstLAL, and the burst search
cWB. Because of the sensitivity imbalance between the
Advanced Virgo detector as compared to the two Advanced
LIGO detectors, neither PyCBC nor cWB elect to analyze
B. P. ABBOTT
et al.
PHYS. REV. X
9,
031040 (2019)
031040-4
data from Virgo. GstLAL, however, includes Virgo into its
search during the month of August. The two matched-filter
searches assume sources that can be modeled by general
relativity and, in particular, quasicircular binaries whose
spin angular momenta are either aligned or antialigned with
their orbital angular momenta. They are still capable,
however, of detecting many systems that exhibit precession
[69]
. In contrast, the cWB search relies on no specific
physical models of the source waveform, though in results
presented here it does impose a restriction that signals are
“
chirping
”
in the time-frequency plane. We therefore refer
to it as
weakly modeled
. In the remainder of this section,
we present a brief description of each of these searches,
summarizing both the parameter space searched and
improvements made since their use in
O
1
[4]
.
A. The PyCBC search
A pipeline to search for GWs from CBCs is constructed
using the PyCBC software package
[7,8]
. This analysis
performs direct matched filtering of the data against a bank
of template waveforms to calculate the signal-to-noise ratio
(SNR) for each combination of detector, template wave-
form, and coalescence time
[70]
. Whenever the local
maximum of this SNR time series is larger than a threshold
of 5.5, the pipeline produces a single-detector trigger
associated with the detector, the parameters of the template,
and the coalescence time. In order to suppress triggers
caused by high-amplitude noise transients (
“
glitches
”
), two
signal-based vetoes may be calculated
[71,72]
. Using the
SNR, the results of these two vetoes, and a fitting and
smoothing procedure designed to ensure that the rate of
single-detector triggers is approximately constant across
the search parameter space, a single-detector rank
ρ
is
calculated for each single-detector trigger
[73]
.
After generating triggers in the Hanford and Livingston
detectors as described above, PyCBC finds two-detector
coincidences by requiring a trigger from each detector
associated with the same template and with coalescence
times within 15 ms of each other. This time window
accounts for the maximum light-travel time between
LHO and LLO as well as the uncertainty in the inferred
coalescence time at each detector. Coincident triggers are
assigned a ranking statistic that approximates the relative
likelihood of obtaining the event
’
s measured trigger param-
eters in the presence of a GW signal versus in the presence
of noise alone
[73]
. The detailed construction of this
network statistic, as well as the single-detector rank
ρ
,is
improved from the corresponding statistics used in
O
1
,
partially motivating the reanalysis of
O
1
by this pipeline.
Finally, the statistical significances of coincident triggers
are quantified by their inverse false-alarm rate (IFAR). This
rate is estimated by applying the same coincidence pro-
cedure after repeatedly time shifting the triggers from one
detector and using the resulting coincidences as a back-
ground sample. Each foreground coincident trigger is
assigned a false-alarm rate (FAR) given by the number
of background triggers with an equal or larger ranking,
divided by the total time searched for time-shifted coinci-
dences. For an event with a given IFAR observed in the data
of duration
T
, the probability of obtaining one or more
equally highly ranked events due to noise is
p
¼
1
−
e
−
T=
IFAR
:
ð
1
Þ
In the analysis of this paper, the data are divided into
analysis periods that allow at least 5.2 days of coincident
data between the two LIGO detectors
[74]
. Though
previous publications performed time shifting across larger
amounts of time
[1,2,4]
, the results here consider only time
shifts within a given analysis period, which is done because
the noise characteristics of the detector vary significantly
from the beginning of
O
1
through the end of
O
2
, so this
restriction more accurately reflects the variation in detector
performance. This restriction means, however, that the
minimum bound on the false-alarm rate of candidates that
have a higher ranking statistic than any trigger in the
background sample is larger than it would be if longer
periods of data are used for the time-shift analysis.
For the PyCBC analysis presented here, the template bank
described in Ref.
[75]
is used. This bank covers binary
systems with a total mass between 2 and
500
M
⊙
and mass
ratios down to
1
=
98
. Components of the binary with a mass
below
2
M
⊙
are assumed to be neutron stars and have a
maximum spin magnitude of 0.05; otherwise, the maximum
magnitude is 0.998. The high-mass boundary of the search
space is determined by the requirement that the waveform
duration be at least 0.15 s, which reduces the number of
false-alarm triggers from short instrumental glitches. The
waveform models used are a reduced-order-model (ROM)
[29,76
–
78]
of SEOBNRv4
[29]
for systems with a total mass
greater than
4
M
⊙
and TaylorF2
[38,80]
otherwise.
B. The GstLAL search
A largely independent matched-filter pipeline based
on the GstLAL library
[9,10]
(henceforth GstLAL) also
performs a matched-filter search for CBC signals. GstLAL
produces triggers for each template waveform and each
detector by maximizing the matched-filter SNR
ρ
over one-
second windows and requiring that it exceed a threshold
of 4 for the two LIGO detectors and 3.5 for Virgo. The
relatively lower Virgo SNR threshold is an
ad hoc
choice
designed to improve the network sensitivity of the search
given Virgo
’
s smaller horizon distance. For the search
described here, candidates are formed by requiring a
temporal coincidence between triggers from the same
template but from different detectors, with the coincidence
window set by the light-travel time between detectors plus
5ms
[81]
. GstLAL ranks candidates using the logarithm of
the likelihood ratio,
L
, a measure of how likely it is to
observe that candidate if a signal is present compared to if
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only noise is present
[9,82,83]
. The noise model is
constructed, in part, from single-detector triggers that are
not found in coincidence, so as to minimize the possibility
of contamination by real signals. In the search presented
here, the likelihood ratio is a function of
ρ
, a signal-
consistency test, the differences in time and phase between
the coincident triggers, the detectors that contribute triggers
to the candidate, the sensitivity of the detectors to signals at
the time of the candidate, and the rate of triggers in each of
the detectors at the time of the candidate
[9]
. This function
is an expansion of the parameters used to model the
likelihood ratio in earlier versions of GstLAL and improves
the sensitivity of the pipeline used for this search over that
used in
O
1
.
The GstLAL search uses Monte Carlo methods and the
likelihood ratio
’
s noise model to determine the probability
of observing a candidate with a log likelihood ratio greater
than or equal to log
L
,
P
ð
log
L
≥
log
L
j
noise
Þ
. The
expected number of candidates from noise with log
likelihood ratios at least as high as log
L
is then
NP
ð
log
L
≥
log
L
j
noise
Þ
, where
N
is the number of
observed candidates. The FAR is then the total number
of expected candidates from noise divided by the live time
of the experiment,
T
, and the
p
value is obtained by
assuming the noise is a Poisson process:
FAR
¼
NP
ð
log
L
≥
log
L
j
noise
Þ
T
;
ð
2
Þ
p
¼
1
−
e
−
NP
ð
log
L
≥
log
L
j
noise
Þ
:
ð
3
Þ
For the analysis in this paper, GstLAL analyzes the same
periods of data as PyCBC. However, FARs are assigned
using the distribution of likelihood ratios in noise computed
from marginalizing
P
ð
log
L
≥
log
L
j
noise
;
period
Þ
over
all analysis periods; thus, all of
O
1
and
O
2
are used to
inform the noise model for FAR assignment. The only
exception is GW170608. The analysis period used to
estimate the significance of GW170608 is unique from
the other ones
[17]
, and thus its FAR is assigned using only
its local background statistics.
For this search, GstLAL uses a bank of templates with a
total mass between 2 and
400
M
⊙
and a mass ratio between
1
=
98
and 1. Components with a mass less than
2
M
⊙
have
a maximum spin magnitude of 0.05 (as for PyCBC);
otherwise, the spin magnitude is less than 0.999. The
TaylorF2 waveform approximant is used to generate
templates for systems with a chirp mass [see Eq.
(5)
] less
than 1.73, and the reduced-order model of the SEOBNRv4
approximant is used elsewhere. More details on the bank
construction can be found in Ref.
[84]
.
C. Coherent WaveBurst
Coherent WaveBurst (cWB) is an analysis algorithm
used in searches for weakly modeled (or unmodeled)
transient signals with networks of GW detectors. Designed
to operate without a specific waveform model, cWB
identifies coincident excess power in the multiresolution
time-frequency representations of the detector strain data
[85]
, for signal frequencies up to 1 kHz and durations up to
a few seconds. The search identifies events that are
coherent in multiple detectors and reconstructs the source
sky location and signal waveforms by using the constrained
maximum likelihood method
[11]
. The cWB detection
statistic is based on the coherent energy
E
c
obtained by
cross-correlating the signal waveforms reconstructed in the
two detectors. It is proportional to the coherent network
SNR and used to rank each cWB candidate event. For an
estimation of its statistical significance, each candidate
event is ranked against a sample of background triggers
obtained by repeating the analysis on time-shifted data,
similar to the background estimation in the PyCBC search.
To exclude astrophysical events from the background
sample, the time shifts are selected to be much larger than
the expected signal delay between the detectors. Each cWB
event is assigned a FAR given by the rate of background
triggers with a larger coherent network SNR.
To increase robustness against nonstationary detector
noise, cWB uses signal-independent vetoes, which reduce
the high rate of the initial excess power triggers. The
primary veto cut is on the network correlation coefficient
c
c
¼
E
c
=
ð
E
c
þ
E
n
Þ
, where
E
n
is the residual noise energy
estimated after the reconstructed signal is subtracted from
the data. Typically, for a GW signal
c
c
≈
1
, and for
instrumental glitches
c
c
≪
1
. Therefore, candidate events
with
c
c
<
0
.
7
are rejected as potential glitches.
Finally, to improve the detection efficiency for a specific
class of stellar-mass BBH sources and further reduce the
number of false alarms, cWB selects a subset of detected
events for which the frequency is increasing with time, i.e.,
events with a chirping time-frequency pattern. Such a time-
frequency pattern captures the phenomenological behavior of
most CBC sources. This flexibility allows cWB to potentially
identify CBC sources with features such as higher-order
modes, high mass ratios, misaligned spins, and eccentric
orbits; it complements the existing templated algorithms by
searching fornew andpossibly unexpected CBCpopulations.
For events that passed the signal-independent vetoes
and chirp cut, the detection significance is characterized
by a FAR computed as described above; otherwise, cWB
provides only the reconstructed waveforms (see Sec.
VI
).
IV. SEARCH RESULTS
A. Selection criteria
In this section, we motivate and describe the selection of
gravitational-wave events for presentation in this paper. We
include
any
candidate event that can be identified with a
nontrivial probability of association to an astrophysical
binary merger event, as opposed to instrumental noise
[86]
.
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The matched-filter and cWB search pipelines produce large
numbers of candidate events, but the majority of these are
of very low significance and have a correspondingly low
probability of being of astrophysical origin.
We desire to identify all events that are confidently
astrophysical in origin and additionally provide a manage-
able set of marginal triggers that may include some true
signals but certainly also includes noise triggers. To do this
identification, we establish an initial threshold on estimated
FAR of 1 per 30 days (about 12.2 per year), excluding any
event that does not have a FAR less than this threshold in at
least one of the two matched-filter analyses (see Sec.
III
).
The cWB search results are not used in the event selection
process. At this FAR threshold, if each pipeline produces
independent noise events, we would expect on average two
such noise events (false alarms) per month of analyzed
coincident time. During these first two observing runs, we
also empirically observe approximately two likely signal
events per month of analyzed time. Thus, for
O
1
and
O
2
,
any sample of events all of whose measured FARs are
greater
than 1 per 30 days is expected to consist of at least
50% noise triggers. Individual triggers within such a
sample are then considered to be of little astrophysical
interest. Since the number of triggers with a FAR less than
1 per 30 days is manageable, restricting our attention to
triggers with lower FAR captures all confident detections
while also probing noise triggers.
Within the sample of triggers with a FAR less than the
ceiling of 1 per 30 days in at least one of the matched-filter
searches, we assign the
“
GW
”
designation to any event for
which the probability of astrophysical origin from either
matched-filter search is greater than 50% (for the exact
definition and calculation of the astrophysical probability,
see Sec.
VII
). We list these events in Table
I
.
For the remaining events in the sample that pass the
initial FAR threshold, neither matched-filter search finds a
greater than 50% probability of astrophysical origin. These
are considered
marginal
events and are listed in Table
II
.
The astrophysical probabilities of all events, confident and
marginal, are given in Table
IV
.
B. Gravitational-wave events
Results from the two matched-filter searches are shown
in Fig.
2
and that of the unmodeled burst search in Fig.
3
.In
each plot, we show the observed distribution of events as a
function of the inverse false-alarm rate, as well as the
expected background for the analysis time, with Poisson
uncertainty bands. The foreground distributions clearly
stand out from the background, even though we show
only rightward-pointing arrows for any event with a
measured or bounded IFAR greater than 3000 y.
We present more quantitative details below on the 11
gravitational events, as selected by the criteria in Sec.
IVA
,
in Table
I
. Of these 11 events, seven have been previously
reported: the three gravitational-wave events from
O
1
[1
–
4]
and, from
O
2
, the binary neutron star merger GW170817
[18]
and the binary black hole events GW170104
[15]
,
GW170608
[17]
, and GW170814
[16]
. The updated results
we report here supersede those previously published. Four
new gravitational-wave events are reported here for the
first time: GW170729, GW170809, GW170818, and
GW170823. All four are binary black hole events.
As noted in Sec.
III
, data from
O
1
are reanalyzed
because of improvements in the search pipelines and the
FIG. 2. Cumulative histograms of search results for the matched-filter searches, plotted versus inverse false-alarm rate. The dashed
lines show the expected background, given the analysis time. Shaded regions denote sigma uncertainty bounds for Poisson uncertainty.
The blue dots are the named gravitational-wave events found by each respective search. Any events with a measured or bounded inverse
false-alarm rate greater than 3000 y are shown with an arrow pointing right. Left: PyCBC results. Right: GstLAL results.
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expansion of the parameter space searched. For the
O
2
events already published, our reanalysis is motivated by
updates to the data itself. The noise subtraction procedure
[52]
that is available for parameter estimation of three of the
published
O
2
events was not initially applied to the entire
O
2
dataset and, therefore, could not be used by searches.
Following the procedures of Ref.
[51]
, this noise subtrac-
tion is applied to all of
O
2
and is reflected in Table
I
for the
four previously published
O
2
GW events, as well as the
four events presented here for the first time.
For both PyCBC and cWB, the time-shift method of
background estimation may result in only an upper bound
on the false-alarm rate, if an event has a larger value of the
ranking statistic than any trigger in the time-shifted back-
ground; this result is indicated in Table
I
. For GW150914
and GW151226, the bound that PyCBC places on the FAR
in these updated results is in fact higher than that previously
published
[1,2,4]
, because, as noted in Sec.
III A
, this
search elects to use shorter periods of time shifting to better
capture the variation in the detectors
’
sensitivities. For
GstLAL, the FAR is reported in Table
I
as an upper bound
of
1
.
00
×
10
−
7
whenever a smaller number is obtained,
which reflects a more conservative noise hypothesis within
the GstLAL analysis and follows the procedures and
motivations detailed in Sec. IV in Ref.
[3]
.
Five of the GW events reported here occurred during
August 2017, which comprises approximately 10% of the
total observation time. There are ten nonoverlapping periods
of similar duration, with an average event rate of 1.1 per
period. The probability that a Poisson process would
produce five events or more in at least one of those periods
is 5.3%. Thus, seeing five events in one month is statistically
consistent with expectations. For more details, see Ref.
[87]
.
For the remainder of this section, we briefly discuss each of
the gravitational-wave events, highlighting interesting fea-
tures from the perspectives of the three searches. A discussion
of the properties of these sources may be found in Sec.
V
.
Though the results presented are from the final, offline
analysis of each search, for the four new GW events, we
also indicate whether the event is found in a low-latency
search and an alert sentto electromagnetic observing partners.
Where this process did occur, we mention in this paper only
the low-latency versions of the three searches with offline
results presented here; in some cases, additional low-latency
pipelinesalsofoundevents.Amorethoroughdiscussionofall
of thelow-latencyanalysesandthe electromagnetic follow-up
of
O
2
events may be found in Ref.
[22]
.
1. GW150914, GW151012, and GW151226
During
O
1
, two confident detections of binary black
holes were made: GW150914
[1]
and GW151226
[2]
.
Additionally, a third trigger was noted in the
O
1
catalog of
binary black holes
[3,4]
and labeled LVT151012. That label
is a consequence of the higher FAR of that trigger, though
detector characterization studies show no instrumental or
environmental artifact, and the results of parameter esti-
mation are consistent with an astrophysical BBH source.
Even with the significance that is measured with the
O
1
search pipelines
[4]
, this event meets the criteria of
Sec.
IVA
for a gravitational-wave event, and we henceforth
relabel this event as GW151012.
The improved
O
2
pipelines substantially reduce the FAR
assigned to GW151012: It is now
0
.
17
y
−
1
in the PyCBC
search (previously,
0
.
37
y
−
1
) and
7
.
92
×
10
−
3
y
−
1
in the
GstLAL search (previously,
0
.
17
y
−
1
). These improved
FAR measurements for GW151012 are the most salient
result of the reanalysis of
O
1
with the
O
2
pipelines; no new
gravitational-wave events were discovered. The first binary
black hole observation, GW150914, remains the highest
SNR event in
O
1
and the second highest in the combined
O
1
and
O
2
datasets, behind only the binary neutron star
inspiral GW170817.
Recently, Ref.
[88]
appeared. That catalog also presents
search results from the PyCBC pipeline for
O
1
and also
finds GW150914, GW151012, and GW151226 as the
only confident gravitational-wave events in
O
1
, with iden-
tical bounds on FAR to the PyCBC results in Table
I
for
GW150914 and GW151226. The measured FAR for
GW151012 is not identical but is consistent with the
results we present in Table
I
.
2. GW170104, GW170608, and GW170814
Three binary black hole events from
O
2
have already
been published: GW170104
[15]
, GW170608
[17]
,and
FIG. 3. Cumulative histograms of search results for the cWB
search, plotted versus the inverse false-alarm rate. The dashed
lines show the expected background, given the analysis time.
Shaded regions denote sigma uncertainty bounds for Poisson
uncertainty. The blue dots are the named gravitational-wave
events found by each respective search. Any events with a
measured or bounded inverse false-alarm rate greater than
3000 y are shown with an arrow pointing right.
B. P. ABBOTT
et al.
PHYS. REV. X
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031040-8
GW170814
[16]
. Updated search results for these events
are presented in Table
I
.Asnotedintheoriginal
publication for GW170608
[17]
, the Hanford detector
was undergoing a procedure to stabilize angular noise at
the time of the event; the Livingston detector was
operating in a nominal configuration. For this reason, a
specialized analysis time when both LIGO detectors were
operating in that same configuration is identified,
between June 7, 2017 and June 9, 2017. This period
that was used to analyze GW170608 in the initial
publication is again used for the results in Table
I
, though
with the noise subtraction applied.
In the reanalysis of
O
2
data, GW170814 is identified
as a double-coincident event between LLO and LHO by
GstLAL. This results from the noise subtraction in the
LIGO data and updated calibration of the Virgo data.
Because of the noise subtraction in the LIGO data, under
GstLAL
’
s ranking of multiple triggers
[9]
, a new template
generates the highest ranked trigger as double coincident,
with a Hanford SNR of 9.1 (the previous highest ranked
trigger, a triple, had 7.3). Though this highest ranked
event is a double-coincident trigger, the pipeline does
identify other highly significant triggers, some double
coincident and some triple coincident. As the search uses
a discrete template bank, peaks from the SNR time series
of the individual detectors, and clustering of several
coincident triggers over the bank, it is difficult in this
case to tell from the search results alone whether the
event is truly a triple-coincident detection. For a definitive
answer, we perform a fully Bayesian analysis with and
without the Virgo data, similar to the results in Ref.
[16]
.
Comparing the evidence, this Bayesian analysis
—
which
enforces coherence and therefore more fully exploits
consistency among detected amplitudes, phases, and
times of arrival than the search pipelines
—
finds that a
triple-coincident detection is strongly favored over a
double-coincident detection, by a factor of approximately
60. Thus, the updated results are consistent with those
that were previously published.
3. GW170817
Across the entirety of
O
1
and
O
2
, the binary neutron
star inspiral GW170817 remains the event with the highest
network SNR and is accordingly assigned the most
stringent possible bound on its FAR by PyCBC and the
highest value of
L
(the logarithm of the likelihood ratio) of
any event in the combined
O
1
and
O
2
dataset by GstLAL.
As explained in detail in the original detection paper
[18]
,
a loud glitch occurs near the end of this signal in LLO. For
the matched-filter searches, this glitch is excised via time-
domain gating (and that gating is applied consistently to
all such glitches throughout
O
2
). Because the cWB
pipeline is designed to detect short signals, it does not
use that gating technique, and it rejects this event because
of the glitch.
4. GW170729
We turn now to gravitational-wave events not previously
announced. The first of these is GW170729, observed at
18
∶
56
∶
29
.
3
UTC on July 29, 2017. The PyCBC pipeline
assigns it a FAR of
1
.
36
y
−
1
, the GstLAL pipeline a FAR of
0
.
18
y
−
1
, and the cWB pipeline a FAR of
0
.
02
y
−
1
.Asitis
identified with the highest significance among all three
search pipelines by the weakly modeled pipeline, it is worth
investigating whether this event is unusual in some way,
exhibiting effects (for instance, precession or higher-order
modes) not adequately modeled by the templates used in
the matched-filter searches. As a relatively simple way of
investigating this question, a comparison study is done
between the PyCBC pipeline and cWB, using software
injections with parameters drawn from the SEOBNRv4
ROM parameter estimation of this event. That waveform
does
not
incorporate precession or higher-order modes, but,
by using these samples as inputs to both searches, we can
probe how often we see comparable results. It is found that
approximately 4% of these SEOBNRv4 ROM samples are
recovered by both the PyCBC and cWB pipelines with
FAR
≥
1
y
−
1
and FAR
≤
0
.
02
y
−
1
, respectively. Thus, the
observed difference in FARs between the two pipelines is
not exceptionally unlikely and is consistent with a noise
fluctuation which happens to decrease the significance of
the event as seen by PyCBC and increase it for cWB. The
detailed CBC parameter estimation studies in Sec.
V
also
indicate no significant evidence for observationally impor-
tant precession or higher-order modes. This event was
identified only in the offline analyses, so no alert was sent
to electromagnetic partners.
5. GW170809
GW170809 was observed on August 9, 2017 at
08
∶
28
∶
21
.
8
UTC with a FAR of
1
.
45
×
10
−
4
y
−
1
by
PyCBC and
<
1
.
00
×
10
−
7
y
−
1
by GstLAL. This event
was identified in low latency by both the GstLAL and cWB
pipelines, and an alert was sent to electromagnetic observ-
ing partners. In the final offline cWB analysis with updated
calibration and noise subtracted from LIGO data, this
event did not pass one of the signal-independent vetoes
(Sec.
III C
) and was therefore not assigned a FAR.
6. GW170818
GW170818 was observed at
02
∶
25
∶
09
.
1
UTC on August
18, 2017, by GstLAL with a FAR of
4
.
20
×
10
−
5
y
−
1
;itwas
not observed by either the PyCBC or cWB pipelines. It is
observed as a triple-coincident event by GstLAL, with an
SNR in Virgo of 4.2, a Hanford SNR of 4.1, and a Livingston
SNR of 9.7. In the PyCBC search, a trigger is seen in the
Livingston detector with a comparable SNR and is noted as a
“
chirplike
”
single-detector trigger. When the Hanford and
Virgo data are analyzed with modified settings around the
time of that event, there are triggers with a similar SNR to
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