of 18
All-sky search for short gravitational-wave bursts in the second Advanced LIGO and
Advanced Virgo run
The LIGO Scientific Collaboration and The Virgo Collaboration
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 search sensitivity for a variety of signal waveforms and report upper limits on the
source rate-density as function of the characteristic frequency of the signal. These upper limits are a
factor of three 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.
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 de-
tected from seven binary black hole 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 tran-
sients. 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 tran-
sients [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 tran-
sients. 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-
tion 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 III A,
we describe the three search algorithms used to look for
generic unmodeled GW transients and the results of those
searches. Second, in III B we discuss briefly some as-
pects regarding the detection of the known BBH signals.
In III C, we discuss the sensitivity of these searches and
give rate-density limits of 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 Section V, we discuss the results and impli-
cations 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
Livingston Advanced LIGO detectors were in observa-
tional mode. On August 1, 2017, Advanced Virgo joined
the detector network. During O2, the combined Hanford-
Livingston network sensitivity was slightly more sensi-
tive than it was in the first bserving run (O1), achiev-
ing a roughly 30% increase in binary-neutron-star (BNS)
range [21]. The Advanced Virgo detector was less sen-
sitive than the Advanced LIGO detectors, with a BNS
range that was roughly a factor of 2-3 lower [21]. As a re-
sult 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 livetime of the data col-
lected 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
approximately 118 days. Not all of this data is ultimately
analyzed though, as the data can sometimes be polluted
arXiv:1905.03457v1 [gr-qc] 9 May 2019
2
by instrumental 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 calibra-
tion 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 substract some
well identified sources of noise from the data are used, in-
creasing 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 sig-
nals 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 [30].
III. UNMODELED GW TRANSIENTS
We describe here the unmodeled search for short du-
ration 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 Hz to 4096
Hz. This covers a wide parameter space of sources, in-
cluding GWs from mergers of compact objects such as
neutron stars or black holes. While there exist more nar-
rowly 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 bi-
nary black hole (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 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 ev-
ery pipeline, and so the combination of the different ap-
proaches 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 resolu-
tions, 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 non-
stationary power-spectrum lines and a class of low fre-
quency, 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 [23]: non-
stationary 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 focus-
ing 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 re-
sults for a cWB dedicated search for chirping signals is
reported in [3]. The search in [3] differs from the one
presented here in both post-production thresholds and
selection of power excesses in time-frequency. The lat-
ter is performed in [3] favoring time-frequency patterns
with increasing frequency over time. This feature, in ad-
dition to dedicated thresholds, reduces the background
and increases the sensitivity to compact binary coales-
cence waveforms.
The high-frequency analysis uses data in the 1024 -
4096 Hz range and is also divided into two bins. The
first bin,
HF
1, contains triggers with central frequency
above 2048 Hz, and events with central frequency in the
band 1000 - 1150 Hz for the period of the run before
Jan 22nd, 2017. The second bin,
HF
2, contains the re-
maining 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 orig-
inating 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 livetime in an-
alyzable data because cWB requires at least 1200 sec-
3
onds 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
livetime, resulting in 21 chunks in total. The background
distribution of triggers for each individual chunk is cal-
culated 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 back-
ground data, which allows the search to reach the sta-
tistical 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 ac-
count fluctuating noise levels of the detectors over the
duration of the observing run.
The significance of each trigger found in the real coin-
cident data is then calculated by comparing the coherent
network signal-to-noise ratio
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 de-
tectors, referred to as an incoherent analysis. It then
follows up stretches of data that are potentially corre-
lated across the detector network, referred to as a coher-
ent analysis. The incoherent analysis (“Omicron”) [37]
flags stretches of coincident excess power. The coherent
follow-up (“LIB”) [38] models GW signals and noise tran-
sients with a single sine-Gaussian, and then produces two
different Bayes factors. Each of these Bayes factors is ex-
pressed 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 qual-
10
2
10
1
10
0
10
1
10
2
10
3
10
4
iFAR (years)
10
0
10
1
Cumulative number of events
GW170814
GW170104
GW170608
GW170823
GW170809
GW170729
32-1024 Hz
Predicted
Search results (No BBH)
Search results
1,2,3
σ
10
2
10
1
10
0
10
1
10
2
10
3
10
4
iFAR (years)
10
0
10
1
Cumulative number of events
1024-4096 Hz
Predicted
Search results
1,2,3
σ
FIG. 1.
Cumulative number of events versus inverse false
alarm rate (iFAR) found by the cWB search using all O2
data (circle points) and the cWB search where times around
all compact binary coalescence sources (see table I from [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.
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.
ity factor of the signal into high-Q and low-Q search bins
(see [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 re-
gion 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 cut off here is set to 1124 Hz in order
to reject a high number of glitches in the 1024-1124 Hz
4
frequency range which were described in 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 sensi-
tivity. 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 non-extreme SNR balance across the detector net-
work. Specifically, we require event candidates to satisfy
max
{
BSN
H1
/
BSN
L1
,
BSN
L1
/
BSN
H1
}
<
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 livetime. This
is slightly more than what was analyzed by cWB because
oLIB does not have the same requirement of 1200 sec-
onds of continuous data. Using the time-slide method,
oLIB collected 496 years worth of data to determine
the background 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 back-
ground distribution. Similar to the O1 analysis, we se-
lect single-detector events with SNR
>
5.0. The search
results are shown in Fig. 2. No coincident events sat-
isfy the cuts of the low-Q bin, and the event rate of the
high-frequency search matches the expected rate of ac-
cidental 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 5-threshold Event Stacking Test [39], the devi-
ation peaks in significance at the 5
th
-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 algorithm [40, 41] models non-
Gaussian features in GW detector data as the sum of
sine-Gaussian wavelets using a reversible jump Markov
10
2
10
1
10
0
10
1
10
2
10
3
10
4
iFAR (years)
10
0
10
1
Cumulative number of events
GW170104
GW170823
32-1024 Hz
Predicted
Search results (No BBH)
Search results
1,2,3
σ
10
2
10
1
10
0
10
1
10
2
10
3
10
4
iFAR (years)
10
0
10
1
Cumulative number of events
1024-2048 Hz
Predicted
Search results
1,2,3
σ
FIG. 2.
Cumulative number of events versus inverse false
alarm rate (iFAR) found by the oLIB search using all O2 data
(circle points) and the oLIB search where times around all
compact binary coalescence sources (see table I from [3]) have
been dropped out (triangular points). The solid line shows the
expected background, given the analysis time. The shaded re-
gions 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.
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 calcu-
lates 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
indi-
cates more evidence for a glitch, and a positive ln
B
sg
indicates more evidence for a signal. Beyond minor im-
provements to the algorithm, the most notable change
to BayesWave’s mode of operation between O1 and O2
5
10
2
10
1
10
0
10
1
10
2
10
3
10
4
iFAR (years)
10
0
10
1
Cumulative number of events
GW170104
GW170608
GW170809
GW170814
GW170823
Predicted
Search results (No BBH)
Search results
1,2,3
σ
FIG. 3.
Cumulative number of events versus inverse false
alarm rate (iFAR) found by the BW followup to the cWB
low-frequency search using all O2 data (circle points) and the
BW followup where times around all compact binary coales-
cence sources (see table I from [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.
is the prior on the number of wavelets (
N
w
) used in
the reconstruction. While O1 used a flat distribution
of
N
w
[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 signifi-
cant 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
= 20. This prior peaks
at
N
w
= 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 fre-
quency search, treating the
LF
1 and
LF
2 search bins as
a single bin, and using a threshold of
η
c
= 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.
1
The only known BBH signal detected by the cWB all-sky algo-
rithm that did not pass the
η
c
threshold was GW170729
B. Known BBH Signals
The LIGO and Virgo Collaboration recently released
the First GW Transient Catalog (GWTC-1) [3], which re-
ports all GWs detected by searches targeting compact bi-
nary signals in O1 and O2. GWTC-1 includes ten signals
from binary black hole (BBH) mergers, seven of which oc-
curred 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 num-
ber 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
followup. 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 [3] that identified GW170818 found it only had
an SNR of 4.1 in the Hanford detector. As the unmod-
eled 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 Section III A 1, the cWB results
reported in GWTC-1 are from a version of cWB with
settings for a dedicated for compact binary coalescence
search. GW170809 instead was not found by cWB in
GWTC-1 because that particular time-frequency selec-
tion included noise excesses. This decreases the coher-
ence 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.
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 sec-
ond 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 remain-
der 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 tar-
geted search pipelines.
6
C. Sensitivity
We measure the detection efficiency of the searches for
unmodeled transient events by adding simulated GW sig-
nals into real detector data, and using the unmodeled
analyses described in 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 po-
tential 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 in-
cludes 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 char-
acteristic parameters: SG waveforms are parameterized
by their central frequency (
f
0
) and quality factor (
Q
); GA
waveforms are parameterized by the duration (
τ
); and fi-
nally WNB waveforms are parameterized by their band-
width (∆
f
), lower frequency bound (
f
low
), and duration
in time (
τ
). Details about the specifics of these wave-
forms can be found in [19]. To fully test the pipelines
sensitivity to range of signals, these waveforms are in-
jected 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 us-
ing
Minke
[43], an open-source Python package devel-
oped during the O1 detector run. It produces data that
contains simulated transient GW signals using the sig-
nal generation provided by
LALSimulation
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, al-
though the centre time of each signal is shifted by a time
drawn from a uniform distribution, between -5 s and +5
s from each division of the timespan. The
h
rss
of each
signal was drawn from the distribution
r
+ 50
/r
, which is
uniform in the square of signal distance
r
2
, constructed
such that the minimum
h
rss
produced was 5
×
10
23
, and
the maximum 1
×
10
20
.
Signals are produced for each of the detectors, with the
sky location chosen by drawing from a uniform distribu-
tion across the sky, and a uniform distribution over wave-
form polarization; the waveform’s sky location is used to
calculate the injection time for each signal for each de-
tector. The remaining parameters of each waveform are
held fixed for each injection set.
Morphology
cWB
oLIB
BW
Gaussian pulses
τ
= 0
.
1 ms
8.4
6.2
N/A
τ
= 2
.
5 ms
11
5.3
N/A
sine-Gaussian wavelets
f
0
= 70 Hz,
Q
= 3
4.9
-
N/A
f
0
= 70 Hz,
Q
= 100
6.4
-
N/A
f
0
= 153 Hz,
Q
= 8
.
9
1.4
1.3
16
f
0
= 235 Hz,
Q
= 100
3.3
1.1
1.4
f
0
= 554 Hz,
Q
= 8
.
9
1.8
1.5
N/A
f
0
= 849 Hz,
Q
= 3
5.5
2.0
17
f
0
= 1304 Hz,
Q
= 9
3.3
2.8
-
f
0
= 1615 Hz,
Q
= 100
3.6
3.3
-
f
0
= 2000 Hz,
Q
= 3
5.4
5.3
-
f
0
= 2477 Hz,
Q
= 8
.
9
7.5
-
-
f
0
= 3067 Hz,
Q
= 3
9.7
-
-
White-Noise Bursts
f
low
= 100 Hz, ∆
f
= 100 Hz,
τ
= 0
.
1 s
1.4
3.0
3.0
f
low
= 250 Hz, ∆
f
= 100 Hz,
τ
= 0
.
1 s
1.4
3.8
3.8
f
0
= 750 Hz, ∆
f
= 100 Hz,
τ
= 0
.
1 s
1.8
3.7
4.2
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.
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 sig-
nal 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 bins instead of three. Consequently the thresh-
old value applied to
η
c
decreases at the same FAR. The
combination of the two effects leads to significant im-
provements 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