of 18
All-sky search for short gravitational-wave bursts in the second Advanced
LIGO and Advanced Virgo run
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 9 May 2019; published 11 July 2019)
We present the results of a search for short-duration gravitational-wave transients in the data from the
second observing run of Advanced LIGO and Advanced Virgo. We search for gravitational-wave transients
with a duration of milliseconds to approximately one second in the 32
4096 Hz frequency band with
minimal assumptions about the signal properties, thus targeting a wide variety of sources. We also perform
a matched-filter search for gravitational-wave transients from cosmic string cusps for which the waveform
is well modeled. The unmodeled search detected gravitational waves from several binary black hole
mergers which have been identified by previous analyses. No other significant events have been found by
either the unmodeled search or the cosmic string search. We thus present the search sensitivities for a
variety of signal waveforms and report upper limits on the source rate density as a function of the
characteristic frequency of the signal. These upper limits are a factor of 3 lower than the first observing run,
with a 50% detection probability for gravitational-wave emissions with energies of
10
9
M
c
2
at 153 Hz.
For the search dedicated to cosmic string cusps we consider several loop distribution models, and present
updated constraints from the same search done in the first observing run.
DOI:
10.1103/PhysRevD.100.024017
I. INTRODUCTION
The Advanced LIGO and Advanced Virgo detectors
[1,2]
have completed their second observing run (O2)
which lasted from November 30, 2016 to August 25, 2017.
During O2, gravitational waves (GWs) were detected from
seven binary black hole (BBH) mergers
[3]
, as well as the
first binary neutron star merger ever observed
[4]
. While
binary systems of compact objects such as black holes and/
or neutron stars are a main source of short-duration
transient GWs observable by LIGO and Virgo, there are
other predicted sources of GW transients. Some examples
include core-collapse supernovae
[5]
, pulsar glitches
[6]
,
neutron stars collapsing into black holes
[7]
, and cosmic
string cusps
[8
10]
. There also exists the possibility of new,
as-of-yet unpredicted GW sources.
In order to maximize our ability to detect any such GWs,
there exist a variety of so-called all-sky searches
those
with no prior assumption on the time of arrival of the GW
signal or its location in the sky. These searches fall broadly
into two categories: searches that target GWs from specific
sources, and those that look for GWs using minimal
assumptions about the source or signal morphology.
Targeted analyses include searches for merging stellar-
mass binary black holes and neutron stars
[3]
as well as
intermediate-mass black holes
[11]
, and searches for
cosmic string signals
[12
14]
. The more generic analyses
look for both long-duration GW transients
[15
17]
and
short-duration events
[18
20]
. In this paper, we report on
the results of two all-sky searches. The first is a generic
search for short-duration GW transients. The second is a
targeted search for cosmic string signals using the matched-
filtering method with template waveforms predicted from
past theoretical studies
[8
10]
.
The rest of this paper is organized as follows. In Sec.
II
we
review the data set used for these analyses. Section
III
is
dedicated to the search for unmodeled GW transients and is
divided into three parts. First, in Sec.
III A
, we describe the
three search algorithms used to look for generic unmodeled
GW transients and the results of those searches. Second, in
Sec.
III B
we discuss briefly some aspects regarding the
detectionoftheknown BBH signals.InSec.
III C
, wediscuss
the sensitivityofthesesearchesandgiverate-densitylimitsof
transient GW events, excluding known compact binary
sources. Section
IV
is dedicated to the modeled cosmic
string cusps search. We briefly outline the search algorithm
used for the analysis, and present our results and updated
parameter constraints. Finally, in Sec.
V
, we discuss the
results and implications from both the unmodeled GW
transients search and the modeled cosmic string cusp search.
II. O2: THE SECOND ADVANCED-DETECTOR
OBSERVING RUN
Our data set ranges from November 30, 2016 to August
25, 2017. Prior to August 2017, only the Hanford and
*
Deceased.
PHYSICAL REVIEW D
100,
024017 (2019)
2470-0010
=
2019
=
100(2)
=
024017(18)
024017-1
© 2019 American Physical Society
Livingston Advanced LIGO detectors were in observatio-
nal mode. On August 1, 2017, Advanced Virgo joined the
detector network. During O2, the combined Hanford-
Livingston network sensitivity was slightly more sensitive
than it was in the first observing run (O1), achieving a
roughly 30% increase in the binary-neutron-star (BNS)
range
[21]
. The Advanced Virgo detector was less sensitive
than the Advanced LIGO detectors, with a BNS range that
was roughly a factor of 2
3lower
[21]
. As a result of
this, including the Virgo data set did not improve the
sensitivity to the short-duration searches presented in this
paper. We thus present the analysis of only the Hanford-
Livingston data.
Over the course of O2, the live time of the data collected
by the two LIGO detectors was about 158 days for
Hanford, and about 154 days for Livingston. The amount
of coincident data between the two detectors is approx-
imately 118 days. Not all of this data is ultimately analyzed
though, as the data can sometimes be polluted by instru-
mental and environmental noise artifacts. In particular,
transient noise events known as
glitches
can potentially
mimic GW properties thereby lowering the sensitivity of
searches for short-duration GW bursts. To mitigate the
effect of instrumental and environmental noise, a large
number of auxiliary channels within the interferometer are
monitored in order to characterize the relation between
artifacts in these channels and the GW strain channel. This
auxiliary channel information is used to identify periods of
poor data quality, which is then excluded from the analysis
[22
25]
. The calibration uncertainties in O2 data for
Hanford and Livingston respectively are 2.6% and 3.9%
in amplitude, and 2.4 and 2.2 degrees in phase
[26,27]
.
Additionally, for the first time in Advanced LIGO data,
methods to subtract some well-identified sources of noise
from the data are used, increasing Hanford
s sensitivity by
10%
[28]
. While these methods remove many known
artifacts, not all glitches are removed. Thus, the pipelines
in this paper have been designed to confidently distinguish
between real GW signals and instrumental glitches.
The data used is this paper is part of the O1 Data Release
and O2 Data Release through the Gravitational Wave Open
Science Center
[29]
, and can be found at Ref.
[30]
.
III. UNMODELED GW TRANSIENTS
We describe here the unmodeled search for short-
duration transient signals. Given the uncertainty and the
wide spectrum of expected signals, the algorithms are
designed to use minimal assumptions on the expected
waveform and consider signals with a duration of a few
seconds or less in the frequency range of 32 to 4096 Hz.
This covers a wide parameter space of sources, including
GWs from mergers of compact objects such as neutron
stars or black holes. While there exist more narrowly
focused searches that target GWs from compact binary
systems which are naturally more sensitive to this type of
signal
[31
33]
, the unmodeled searches presented here are
sensitive to a wider variety of potential sources. In this
work, we identify and then remove the known BBH sources
in our analysis results, in order to focus on searching for
previously unidentified transients.
We use the same three unmodeled analyses that were
used in the O1 search
[20]
. By using multiple pipelines we
have the ability to independently verify search results.
Additionally, the regions of parameter space where these
algorithms are the most sensitive is not the same for
every pipeline, and so the combination of the different
approaches increases our ability to detect a wide range of
signals. Below we describe the three different algorithms
used to search for transient GW events.
A. Searches
1. Coherent WaveBurst
Coherent WaveBurst (cWB) is an algorithm based on
the maximum-likelihood-ratio statistic applied to power
excesses in the time-frequency domain
[34]
. This analysis
is done by using a wavelet transform at various resolutions,
as to adapt the time-frequency characterization to the signal
features. cWB has been used in the previous LIGO-Virgo
searches for transient signals
[18
20]
.
The cWB analysis is split into two frequency bands: low
and high frequency. The triggers are further divided into
search bins, similar to how it was done for the O1 analysis.
The low-frequency analysis covers the parameter space
ranging from 32
1024 Hz, and performs a down sampling
of the data. The triggers are divided into two different bins.
The first bin,
LF
1
, is polluted by nonstationary power-
spectrum lines and a class of low-frequency, short-duration
glitches known as
blip
glitches for which there is no
specific data quality veto
[22]
. These are selected using the
same criteria described in Ref.
[23]
: nonstationary lines
localize more than 80% of their energy in a frequency
bandwidth of less than 5 Hz; blip glitches are identified
according to their waveform properties so that their quality
factor (
Q
) is less than 3. The second bin,
LF
2
contains the
remaining low-frequency triggers. In the O1 analysis
[20]
there was a third class focusing on events with morphology
similar to compact object binaries
specifically events that
chirped up in frequency. This class is not considered in this
work, since the results for a cWB dedicated search for
chirping signals was reported in Ref.
[3]
. The search in
Ref.
[3]
differs from the one presented here in both post-
production thresholds and selection of power excesses in
time-frequency. The latter was performed in Ref.
[3]
favoring time-frequency patterns with increasing frequency
over time. This feature, in addition to dedicated thresholds,
reduces the background and increases the sensitivity to
compact binary coalescence waveforms.
The high-frequency analysis uses data in the 1024
4096 Hz range and is also divided into two bins. The first
B. P. ABBOTT
et al.
PHYS. REV. D
100,
024017 (2019)
024017-2
bin,
HF
1
, contains triggers with central frequencies above
2048 Hz, and events with central frequencies in the band
1000
1150 Hz for the period of the run before Jan 22,
2017. The second bin,
HF
2
, contains the remaining
triggers. The change in the bin definition pre
and post
Jan 22nd is due to an excess of glitches that were occurring
around 1100 Hz between October 2016 and January 2017.
These glitches were identified as originating from length
fluctuations in the Hanford detector
s output mode cleaner
optical cavity, and were successfully mitigated for the
remainder of O2
[35]
.
Periods of poor data quality were removed as described
in previous searches for short-duration GW events
[19,20,36]
. There is some additional loss of live time in
analyzable data because cWB requires at least 1200 seconds
of coincident data per analyzable segment. The final
amount of data analyzed by cWB was 113.9 days.
The cWB analysis is performed by dividing the run into
reduced periods of consecutive time epochs (called
chunks
). Each chunk is composed of about 5 days of
live time, resulting in 21 chunks in total. The background
distribution of triggers for each individual chunk is calcu-
lated by time shifting the data of one detector with respect
to the other detector by an amount that breaks any
correlation between detectors for a real signal. Each chunk
was time shifted to give about 500 years of background
data, which allows the search to reach the statistical
significance of
1
=
100
years while allowing for a trial factor
of 2 for each of the low- and high-frequency bands.
Performing the analyses in chunks takes into account
fluctuating noise levels of the detectors over the duration
of the observing run.
The significance of each trigger found in the real
coincident data is then calculated by comparing the
coherent network signal-to-noise ratio (SNR)
η
c
[20]
with
the background distribution of the chunk to which it
belongs.
The search results for the cWB low- and high-frequency
bands are shown in Fig.
1
. In the low-frequency search
band, cWB found six of the known BBH events with
inverse false-alarm rates (iFARs) ranging from 290 years
for GW170814 to 0.07 years for GW170729. The loudest
trigger in the high-frequency search band has an iFAR of
7 years, and it is related to some disturbances appearing
around 1600 Hz. To search for new events, we remove all
previously known GW signals. In this case, this means
removing the six BBH signals identified by the search. The
remaining events, shown as dashed curves in Fig.
1
, are all
consistent with expected noise events.
2. Omicron-LIB
Omicron-LIB (oLIB) is a hierarchical search algorithm.
oLIB first analyzes the data streams of individual detectors,
referred to as an incoherent analysis. It then follows up
stretches of data that are potentially correlated across the
detector network, referred to as a coherent analysis. The
incoherent analysis (
Omicron
)
[37]
flags stretches of
coincident excess power. The coherent follow-up (
LIB
)
[38]
models GW signals and noise transients with a single
sine-Gaussian, and then produces two different Bayes
factors. Each of these Bayes factors is expressed as the
natural logarithm of the evidence ratio of two hypotheses:
1) a GW signal versus Gaussian noise (BSN) and 2) a
coherent GW signal versus incoherent noise transients
(BCI). The joint likelihood ratio of these two Bayes factors,
Λ
, is used as a ranking statistic to assign a significance to
each event.
For this analysis, oLIB analyzes two frequency bands: a
low-frequency search band covering 32
1024 Hz, and a
high-frequency search band covering 1024
2048 Hz.
Similarly to how the analysis was done in O1, low-
frequency oLIB event candidates are divided by the quality
FIG. 1. Cumulative number of events versus inverse false-alarm
rate found by the cWB search using all O2 data (circle points) and
the cWB search where times around all compact binary coa-
lescence sources (see Table I from Ref.
[3]
) have been dropped
out (triangular points). The solid line shows the expected back-
ground, given the analysis time. The shaded regions show the 1,
2, and
3
σ
Poisson uncertainty regions. Top: Search results from
the cWB low-frequency (32
1024 Hz) band, with results grouped
considering all the bins, applying a trials factor equal to 2.
Bottom: Search results from the cWB high-frequency (1024
4096 Hz) band. No triggers associated with known BBH signals
were found in this search.
ALL-SKY SEARCH FOR SHORT GRAVITATIONAL-WAVE BURSTS
...
PHYS. REV. D
100,
024017 (2019)
024017-3
factor of the signal into high-
Q
and low-
Q
search bins (see
Ref.
[20]
). These bins are defined by slightly different cuts
than in O1, with the exact choices being made after the
background data is analyzed and prior to the analysis of real
coincident data. The low-
Q
bin contains only events whose
median quality factor
̃
Q
lies within the range of 0.2
1.2 and
whose median frequency
f
0
lies within the range of
32
1024 Hz. The high-
Q
bin contains only events whose
̃
Q
lies within the range 2
108 and whose
f
0
lies within the
range of 120
1024 Hz. The
Q
range of 1.2
2 is excluded
from the analysis
a priori
as that region of parameter space
is known to be populated by the blip glitches. The high-
frequency search band contains only events whose
̃
Q
lies
within the range of 2
108 and whose
f
0
lies within the
range of 1124
2048 Hz. The lower frequency cutoff here is
set to 1124 Hz in order to reject a high number of glitches in
the 1024
1124 Hz frequency range which were described
in Sec.
III A 1
. In all bins, event candidates are also required
to have positive Bayes factors, meaning the GW signal
model is favored over the noise models. A trials factor of 2
is applied to the low-frequency search to account for the
independent bins.
Two improvements are made to the O2 oLIB search,
as compared to the O1 search that increase the sensitivity.
The first is that log BSN is used as a search statistic
instead of BSN, which improves the accuracy of
oLIB
s kernel-density estimates of the signal and noise
likelihoods. Second, event candidates are required to have
nonextreme SNR balance across the detector network.
Specifically, we require event candidates to satisfy
max
f
BSN
H
1
=
BSN
L
1
;
BSN
L
1
=
BSN
H
1
g
<
9
, where BSN
i
is the BSN Bayes factor estimated using only the data
of detector
i
. This cut helps mitigate the contamination of
coincident non-Gaussian noise transients, which tend to
have much larger SNR imbalance than GW signals.
After removing the periods of poor data quality, oLIB
analyzed 114.7 days of coincident detector live time. This
is slightly more than what was analyzed by cWB because
oLIB does not have the same requirement of 1200 seconds
of continuous data. Using the time-slide method, oLIB
collected 496 years worth of data to determine the back-
ground distribution of glitches. The significance of triggers
found in the zero-lag data is calculated by comparing
oLIB
s ranking statistic to that of the background distri-
bution. Similar to the O1 analysis, we select single-detector
events with SNR
>
5
.
0
. The search results are shown in
Fig.
2
. No coincident events satisfy the cuts of the low-
Q
bin, and the event rate of the high-frequency search
matches the expected rate of accidental noise coincidences.
Two events in the high-
Q
bin are previously identified BBH
events (GW170823 and GW170104). Again, to search for
previously unidentified GW events, the previously known
events are removed. The results after removing these events
are shown as the dashed lines in Fig.
2
. We notice a small
deviation of the high-
Q
bin
s event rate from the expected
noise rate for the loudest event candidates, even after all
known BBH events are excised from the analysis. After
applying the trials factor of 2, the iFAR of our loudest
event candidate is about 1.4 years, which corresponds to a
p-value of 0.22. Using a five-threshold Event Stacking Test
[39]
, the deviation peaks in significance at the fifth-loudest
event, and the overall p-value of the test is 0.17. Both of
these p-values correspond to one-sided outliers that are less
than
1
σ
in units of Gaussian standard deviations, and
neither signifies a confident detection of GWs. Thus, we
conclude that the oLIB search did not find any new GW
events.
3. BayesWave follow-up
The BayesWave (BW) algorithm
[40,41]
models non-
Gaussian features in GW detector data as the sum of
FIG. 2. Cumulative number of events versus inverse false-alarm
rate found by the oLIB search using all O2 data (circle points) and
the oLIB search where times around all compact binary coa-
lescence sources (see Table I from Ref.
[3]
) have been dropped
out (triangular points). The solid line shows the expected back-
ground, given the analysis time. The shaded regions show the 1,
2, and
3
σ
Poisson uncertainty regions. Top: The results of the
low-frequency (32
1024 Hz) band. The low-frequency band
contains two search bins
a high-
Q
bin and a low-
Q
bin
but
as there were no foreground triggers in the low-
Q
bin, only the
high-
Q
bin is represented here. Bottom: The search results for the
high-frequency (1024
2048) band, which contains only a single
search bin.
B. P. ABBOTT
et al.
PHYS. REV. D
100,
024017 (2019)
024017-4
sine-Gaussian wavelets using a reversible jump Markov
chain Monte Carlo (RJMCMC), where the number of
wavelets used is not fixed
a priori
but determined via
the RJMCMC. BayesWave reconstructs the data in two
different models: the signal model which treats the data in
each interferometer as Gaussian noise plus a common
astrophysical signal, and the glitch model which treats the
data as Gaussian noise plus independent transient noise
artifacts in each detector. BayesWave then calculates the
natural log of the Bayesian evidence of each model.
The detection statistic used is the log signal-to-glitch
Bayes factor (ln
B
sg
), which is the difference between the
logarithm of the two evidences. A negative ln
B
sg
indicates
more evidence for a glitch, and a positive ln
B
sg
indicates
more evidence for a signal. Beyond minor improvements to
the algorithm, the most notable change to BayesWave
s
mode of operation between O1 and O2 is the prior on the
number of wavelets (
N
w
) used in the reconstruction. While
O1 used a flat distribution of
N
w
½
0
;
20

[40]
, for O2 a
prior based on the posterior distribution of
N
w
during O1
was implemented into the code. To construct the prior we
used the
maximum a posteriori
number of wavelets from a
sample of significant background events from O1 to infer
the distribution of wavelet dimension. This histogram was
then fit to a ratio of polynomials to predict the density at
model sizes larger than the O1 cutoff of
N
w
¼
20
. This
prior peaks at
N
w
¼
3
, and falls off for higher numbers of
wavelets.
In both O1 and O2 BayesWave was used as a follow-up
to the cWB pipeline, as adding this follow-up has been
shown to enhance confidence in GW detections
[42]
.For
O2, BayesWave followed up cWB events in the low-
frequency search, treating the
LF
1
and
LF
2
search bins
as a single bin, and using a threshold of
η
c
¼
9
. BayesWave
used the same approach used by cWB to divide the
113.9 days of analyzable data into chunks of approximately
5 days, and used the same background data set from time
slides.
There were nine cWB triggers which were above the
η
c
threshold, five of which are known BBH signals.
1
The
results of the BayesWave analysis is shown in Fig.
3
.
The five BBH events were the most significant triggers in
the BayesWave results, and after removing them as we did
for the cWB and oLIB analysis, all events are consistent
with accidental noise fluctuations.
B. Known BBH signals
The LIGO and Virgo Collaboration recently released the
First GW Transient Catalog (GWTC-1)
[3]
, which reports
all GWs detected by searches targeting compact binary
signals in O1 and O2. GWTC-1 includes ten signals from
BBH mergers, seven of which occurred during O2. These
BBHs tend to be short-duration signals that are within the
parameter space covered by the unmodeled searches
presented here. So while this search does not target
BBH signals, we still found a number of previously
identified BBH signals.
Of the seven BBH events in O2, six were identified by at
least one of the generic transient search algorithms. cWB
identified six of the BBH events found in O2. Of those six,
five were above the threshold used by the BW follow-up.
After applying the selection cuts described above, oLIB
identifies two of the BBH events: GW170104 and
GW170823. Two other BBH signals, GW170814 and
GW170608, are both excluded from the oLIB analysis
as a result of narrowly missing some of the data-quality cuts
chosen
a priori
for the analysis, but both become clear
detections if they are manually added back into the
analysis. One BBH event, GW170818, was not detected
by any of the unmodeled pipelines. The matched-filter
search in Ref.
[3]
that identified GW170818 found it only
had an SNR of 4.1 in the Hanford detector. As the
unmodeled analyses are less sensitive to quieter signals
like this one, it was missed by this search.
Two cases worth mentioning are GW170729 and
GW170809. GW170729 has a lower iFAR than the one
given in GWTC-1
[3]
(50 years). This is expected since, as
already explained in Sec.
III A 1
, the cWB results reported
in GWTC-1 are from a version of cWB with settings for a
dedicated search for compact binary coalescence.
GW170809 instead was not found by cWB in GWTC-1
because that particular time-frequency selection included
noise excesses. This decreases the coherence of this event
between the detectors, which means it did not pass one of
the post-production thresholds and thus was not assigned
any significance.
FIG. 3. Cumulative number of events versus inverse false-alarm
rate found by the BW follow-up to the cWB low-frequency
search using all O2 data (circle points) and the BW follow-up
where times around all compact binary coalescence sources (see
Table I from Ref.
[3]
) have been dropped out (triangular points).
The solid line shows the expected background, given the
analysis time. The shaded regions show the 1, 2, and
3
σ
Poisson
uncertainty regions.
1
The only known BBH signal detected by the cWB all-sky
algorithm that did not pass the
η
c
threshold was GW170729.
ALL-SKY SEARCH FOR SHORT GRAVITATIONAL-WAVE BURSTS
...
PHYS. REV. D
100,
024017 (2019)
024017-5
There was also one binary neutron star merger
(GW170817) detected in O2
[4]
. This was a longer signal
than the BBH events, appearing in the LIGO data for
almost 30 seconds. The unmodeled pipelines presented
here search for signals with a duration of about one second
or less, and so did not detect GW170817.
We defer discussion of the astrophysical properties and
implications of these events to GWTC-1. For the remainder
of this paper, we excise known BBH events from our results
and place upper limits on event rates from sources that have
not been previously identified by targeted search pipelines.
C. Sensitivity
We measure the detection efficiency of the searches for
unmodeled transient events by adding simulated GW
signals into real detector data, and using the unmodeled
analyses described in Sec.
III A
to search for these injected
signals. In this work, we use as a detection threshold an
iFAR of 100 years.
We do not have accurate waveforms for many of the
potential sources in the parameter space of the unmodeled
analyses described here. However, a variety of waveform
morphologies can be used to approximate physical sit-
uations that are likely to be generated by astrophysical
systems. We use these waveforms, distributed through a
wide range of amplitudes, durations, and characteristic
frequencies to test our unmodeled searches.
1. Injection data set
The set of injected signals used in this analysis includes
sine-Gaussian (SG), Gaussian (GA), and white-noise burst
(WNB) waveforms. These waveforms, which are not
derived from any particular astrophysical model, are the
standard in the testing and development of searches for
unmodeled GW signals
[19,20]
. Each of these injected
waveforms can be described by a few characteristic
parameters: SG waveforms are parametrized by their
central frequency (
f
0
) and quality factor (
Q
); GA wave-
forms are parametrized by the duration (
τ
); and finally
WNB waveforms are parametrized by their bandwidth
(
Δ
f
), lower frequency bound (
f
low
), and duration in time
(
τ
). Details about the specifics of these waveforms can be
found in Ref.
[19]
. To fully test the pipelines
sensitivity to
the range of signals, these waveforms are injected with a
range of amplitudes, which we measure as the root-mean-
square strain (
h
rss
) of the waveform at Earth.
The injected signal set for this work was produced using
M
INKE
[43]
, an open-source P
YTHON
package developed
during the O1 detector run. It produces data that contains
simulated transient GW signals using the signal generation
provided by LALS
IMULATION
routines as a part of the
LIGO Algorithm Library
[44]
.
For the signal set used in this analysis, signals were
produced at a rate of once every 50 seconds. These were
spaced evenly throughout the total time of the run, although
the center time of each signal is shifted by a time drawn
from a uniform distribution, between
5
s and
þ
5
s from
each division of the time span. The
h
rss
of each signal was
drawn from the distribution
r
þ
50
=r
, which is uniform in
the square of the signal distance
r
2
, constructed such that
the minimum
h
rss
produced was
5
×
10
23
, and the maxi-
mum was
1
×
10
20
.
Signals are produced for each of the detectors, with the
sky location chosen by drawing from a uniform distribution
across the sky, and a uniform distribution over waveform
polarization; the waveform
s sky location is used to
calculate the injection time for each signal for each detector.
The remaining parameters of each waveform are held fixed
for each injection set.
2. Results
Table
I
shows the specific parameters of all the wave-
forms analyzed here, and the
h
rss
value at which 50% of the
injections are detected by each pipeline for each signal
morphology. The O2 search is more sensitive than in O1.
This increase in efficiency can be attributed to both the
increase in detector sensitivity and the improvements made
to the algorithms to better deal with instrumental noise.
The introduction of analysis in chunks, for instance,
allows for adapting the threshold to the level of nearby
background noise. Moreover, cWB is now using two search
TABLE I. The
h
rss
values, in units of
10
22
Hz
1
=
2
, at which
50% detection efficiency is achieved at a FAR of 1 in 100 yr for
each of the algorithms, as a function of the injected signal
morphologies.
N/A
denotes that 50% detection efficiency was
not achieved.

denotes the waveform was not analyzed by
oLIB and BW because its characteristic frequency did not meet
the search cuts.
Morphology
cWB oLIB BW
Gaussian pulses
τ
¼
0
.
1
ms
8.4 6.2 N/A
τ
¼
2
.
5
ms
11
5.3 N/A
sine-Gaussian wavelets
f
0
¼
70
Hz,
Q
¼
3
4.9

N/A
f
0
¼
70
Hz,
Q
¼
100
6.4

N/A
f
0
¼
153
Hz,
Q
¼
8
.
9
1.4 1.3 16
f
0
¼
235
Hz,
Q
¼
100
3.3 1.1 1.4
f
0
¼
554
Hz,
Q
¼
8
.
9
1.8 1.5 N/A
f
0
¼
849
Hz,
Q
¼
3
5.5 2.0 17
f
0
¼
1304
Hz,
Q
¼
9
3.3 2.8

f
0
¼
1615
Hz,
Q
¼
100
3.6 3.3

f
0
¼
2000
Hz,
Q
¼
3
5.4 5.3

f
0
¼
2477
Hz,
Q
¼
8
.
9
7.5

f
0
¼
3067
Hz,
Q
¼
3
9.7

White-Noise Bursts
f
low
¼
100
Hz,
Δ
f
¼
100
Hz,
τ
¼
0
.
1
s 1.4 3.0 3.0
f
low
¼
250
Hz,
Δ
f
¼
100
Hz,
τ
¼
0
.
1
s 1.4 3.8 3.8
f
0
¼
750
Hz,
Δ
f
¼
100
Hz,
τ
¼
0
.
1
s
1.8 3.7 4.2
B. P. ABBOTT
et al.
PHYS. REV. D
100,
024017 (2019)
024017-6
bins instead of three. Consequently the threshold value
applied to
η
c
decreases at the same FAR. The combination
of the two effects leads to significant improvements in the
efficiency for waveforms belonging to the
LF
1
bin with
respect to O1 results.
oLIB cuts and tunings are especially beneficial for the
GA and WNB waveforms, as oLIB now achieves 50%
detection efficiency for all of these waveform morpholo-
gies, which it did not achieve in O1. Nevertheless, these
additional cuts do hurt the detection efficiency in some
regions of parameter space, such as the band below 120 Hz
in the high-
Q
bin. For example, the detection efficiency of
the SG waveform at 70 Hz is exactly 0 (although oLIB
s
detection efficiency for this morphology was also negli-
gible in O1 due to its long
1
.
5
s duration).
The BayesWave follow-up is the least sensitive to SG
signals, as shown in Ref.
[42]
. BayesWave
s detection
statistic, ln
B
sg
scales linearly with the number of sine-
Gaussian basis functions used in the signal reconstruction,
meaning for simple signals that can be accurately repre-
sented with a single sine-Gaussian it is harder to distinguish
between the signal and glitch models
[45]
. For signals with
more complicated structure in time-frequency space (such
as BBH signals which increase in frequency over time),
BayesWave is more efficient at distinguishing between the
signal and glitch models. Since the SG and GA waveforms
used here can be accurately modeled as single sine-
Gaussian wavelets, BayesWave is less sensitive to these
signals. One improvement made between O1 and O2 is the
addition of a jump proposal in the MCMC that helped with
the mixing of higher
Q
signals. This resulted in an
increased sensitivity to higher
Q
signals.
From the detection efficiencies given in Table
I
, we can
make a statement on the minimum amount of energy that
needs to be emitted by a GW in order to be detected. To do
this, we assume a standard candle source at a distance of
r
0
¼
10
kpc radiating GWs at a central frequency of
f
0
.
The amount of energy radiated is then
[19]
E
GW
¼
π
2
c
3
G
r
2
0
f
2
0
h
2
0
:
ð
1
Þ
We use the
h
rss
values of 50% detection efficiency given in
Table
I
to find the minimum amount of energy that needs to
be radiated by the GW source in order to be detected by at
least one of the unmodeled searches. These results are
shown in Fig.
4
, along with the results from the O1
unmodeled all-sky search
[20]
for comparison.
Given that the searches did not find any additional
detection results for GW sources beyond the known
BBH signals, we can update the upper limit of the rate
per unit volume of non-BBH standard-candle sources
[19,20]
, shown in Fig.
4
. For these upper limits, we use
the SG and WNB injection sets listed in Table
I
as
representative morphologies of non-BBH GW bursts.
The markers represent the upper limit at 90% confidence
for the rate density
[19]
, calculated assuming that no noise
events meet the detection threshold in our analysis data.
The results shown in Fig.
5
assume that
1
M
c
2
of GW
energy has been emitted from the source, but the upper
limits can be scaled to any emission energy
E
GW
by using
Eq.
(1)
to find that the rate density scales
E
3
2
GW
.
Compared to the rate-density upper limits placed in O1
[20]
using only the cWB analysis on SG injections, the
upper limits reported here for the O2 run are at least a factor
FIG. 4. The GW emitted energy in units of solar masses that
correspond to a 50% detection efficiency at an iFAR of 100 years,
for a source emitting at 10 kpc. The waveforms represented here
include all of the sine-Gaussian and white-noise burst injections
as give in Table
I
. We present the best sensitivity achieved by any
of the unmodeled search pipelines, for both the O1
[20]
and O2
searches.
FIG. 5. Upper limits on the 90% confidence intervals for the
GW rate density, as measured in O2 using the SG and WNB
waveforms listed in Table
I
. Here we show the strictest upper limit
achieved by any of the three unmodeled search pipelines. These
results can be scaled to any emission energy
E
GW
using the
rate density
E
3
=
2
GW
. We also show the results from the O1 all-
sky search
[20]
, which presented results from the cWB pipeline
for sine-Gaussian waveforms. Note that the O1 cWB search used
three bins, which mostly affected the efficiency for waveforms
belonging to
LF
1
(i.e., 70 and 235 Hz, shown here as blue dots).
ALL-SKY SEARCH FOR SHORT GRAVITATIONAL-WAVE BURSTS
...
PHYS. REV. D
100,
024017 (2019)
024017-7