All-sky search for long-duration gravitational-wave bursts
in the third Advanced LIGO and Advanced Virgo run
R. Abbott
etal.
*
(LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration)
(Received 30 July 2021; accepted 4 October 2021; published 11 November 2021)
After the detection of gravitational waves from compact binary coalescences, the search for transient
gravitational-wave signals with less well-defined waveforms for which matched filtering is not well suited
is one of the frontiers for gravitational-wave astronomy. Broadly classified into
“
short
”
≲
1
s and
“
long
”
≳
1
s duration signals, these signals are expected from a variety of astrophysical processes, including
non-axisymmetric deformations in magnetars or eccentric binary black hole coalescences. In this work, we
present a search for long-duration gravitational-wave transients from Advanced LIGO and Advanced
Virgo
’
s third observing run from April 2019 to March 2020. For this search, we use minimal assumptions
for the sky location, event time, waveform morphology, and duration of the source. The search covers the
range of 2
–
500 s in duration and a frequency band of 24
–
2048 Hz. We find no significant triggers within
this parameter space; we report sensitivity limits on the signal strength of gravitational waves characterized
by the root-sum-square amplitude
h
rss
as a function of waveform morphology. These
h
rss
limits improve
upon the results from the second observing run by an average factor of 1.8.
DOI:
10.1103/PhysRevD.104.102001
I. INTRODUCTION
The third observing run of the Advanced LIGO
[1]
and Advanced Virgo
[2]
detectors has revealed a large
number of new gravitational-wave (GW) signals from the
collision of compact objects. Many binary black hole
systems
[3]
have been identified. These include
GW190521
[4]
with the largest progenitor masses discov-
ered so far, and GW190814, a merger containing an object
in the
“
mass-gap
”
between neutron stars and black holes
[5]
. A second binary neutron star (BNS) system was
also discovered, GW190425
[6]
, following the first BNS
system GW170817
[7]
, which also produced GRB
170817A
[8]
and an optical transient, AT 2017gfo
[9]
.
In addition, two neutron star
–
black hole binary coalescen-
ces (GW200105_162426 and GW200115_042309) have
also been detected
[10]
.
Searches for
“
long
”
≳
1
s duration signals cover a variety
of astrophysical phenomena
[11]
. While well-modeled
compact binary coalescences can have similar durations
in the sensitive band of the interferometers and the methods
employed in this paper are also sensitive to them, this
search is not aimed at these systems as matched filtering is
much more sensitive. However, there are less well-defined
waveforms for which matched filtering is not well-suited.
Plausible processes include fallback accretion onto a
rapidly rotating black hole
[12]
or in newborn neutron
stars
[13
–
15]
. They also include nonaxisymmetric
deformations in magnetars
[16]
or accretion disk instabil-
ities and fragmentation of material spiraling into a black
hole
[17
–
19]
and in the central engine of superluminous
supernovae
[20,21]
. Figure
1
shows several different
realizations of the corresponding waveform morphologies.
In this paper, we present the results of unmodeled long-
duration transient searches from the third observing run,
updating the results from the first two observing runs
[24,25]
.
As in previous analyses
[24
–
27]
, three pipelines are used;
theirdifferentassumptionsanddatahandlingtechniquesyield
complementary coverage of the signal models.
The paper is organized as follows. The data used in the
analysis is described in Sec.
II
. The algorithms used to
analyze the data are outlined in Sec.
III
. The results of the
analysis and their implications are discussed in Sec.
IV
.
II. DATA
The third observing run (O3) of Advanced LIGO and
Advanced Virgo spanned April 1, 2019
–
March 27, 2020.
O3 was broken up into two segments, with O3a running
April 1, 2019
–
Oct 1, 2019 and O3b running November 1,
2019
–
March 27, 2020; together, these correspond to
330 days. It is customary to assess detector sensitivities
in terms of a binary neutron star inspiral range (BNS
range), which is the average distance to which these signals
could be detected
[28,29]
. Detector upgrades to the LIGO
detectors in Hanford, WA, and Livingston, LA, yielded
binary neutron star ranges of
∼
115
and 133 Mpc, respec-
tively, amounting to improvements of
∼
50%
with respect to
*
Full author list given at the end of the article.
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© 2021 American Physical Society
O2. Similarly, Advanced Virgo reached a binary neutron
star range of
∼
50
Mpc, a
∼
100%
improvement. In the
following, the algorithms employed require at least two
detectors to be available to process the data; therefore, only
data where both LIGO detectors are simultaneously avail-
able are used. Due to the significant difference in detector
alignment and sensitivities, the Virgo data in the analysis
would not improve the coincidence selection when the
other two detectors are active, while the high rate of non-
Gaussian noise would increase the overall false-alarm rate.
We plan to include Virgo in the analysis of the next
observing run.
A major challenge in searches for gravitational-wave
transients is non-Gaussian noise. Known sources of noise,
including nonlinear sources such as time-varying spectral
lines, from, e.g., machinery on site, sidebands from the
60 Hz power lines, can be witnessed and subtracted using
both linear Wiener filters
[30]
and machine learning
techniques
[31,32]
. The analyses that follow use data for
which some of the identified sources of noise that couple in
linearly to the detector have been subtracted. Beyond
spectral features, there are transient noise triggers known
as
glitches
, which have a variety of origins
[33]
, such as the
light reflected from surfaces such as the chamber walls and
scattered back into the main beam
[34]
. Glitch rejection
procedures rely on correlations with auxiliary channels
[35,36]
such as seismometers and magnetometers; yet,
noise transients not witnessed by auxiliary sensors remain
and reduce sensitivity of the searches
[37,38]
. Each pipe-
line, described in the next section, implements different
strategies to reduce the impact from glitches. Altogether,
during the third observing run, coincident data of sufficient
quality to be analyzed totaled 204.4 days. Since some time
segments are too short to be processed by search pipelines,
a small fraction (
<
2%
) of this coincident data is not
analyzed.
III. SEARCHES
Long-duration unmodeled searches are now briefly
reviewed, and we refer the reader to previous publications
for further detail
[24,25]
. Most unmodeled searches use
time-frequency spectrograms with statistics derived from
Fourier transforms or wavelet analysis performed on
consecutive time segments. Pattern-recognition algorithms
then are employed to search for gravitational waves in these
spectrograms. These algorithms can be classified as
“
seed-
based
”
[39,40]
, for which pixels above predetermined
thresholds are clustered, and
“
seedless
”
[41,42]
, for which
sequences of pixels are derived from generic models, such
as B ́
ezier curves
[41
–
45]
. Seedless clustering algorithms
are sensitive to narrowband signals at the price of sensi-
tivity to broadband sources, while seed-based algorithms
are generally more sensitive to more generic wave-
form morphologies. These algorithms identify candidate
gravitational-wave events known as
triggers
. To estimate
FIG. 1. Time-frequency spectrogram of the reference waveforms used in this search. We show examples of astrophysical waveforms
such as postmerger magnetars (Magnetar)
[22]
, black hole accretion disk instabilities (ADI)
[18]
, newly formed magnetar powering a
gamma-ray burst plateau (GRB plateau)
[16]
, eccentric inspiral-merger-ringdown compact binary coalescence waveforms (ECBC)
[23]
,
broadband chirps from innermost stable circular orbit waves around rotating black holes (ISCO chirp)
[12]
, and
“
ad hoc
”
waveforms,
band-limited white noise burst (WNB) and sine-Gaussian bursts (SG). The ISCO chirp waveforms have been shifted up in frequency by
50 Hz for readability. Durations range from 6 (ADI-B) to 470 s (GRB plateau).
R. ABBOTT
et al.
PHYS. REV. D
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the background, all pipelines use
“
time slides,
”
[46,47]
,
where detector data is shifted by nonphysical time delays
and reanalyzed; this procedure is repeated a sufficient
number of times such that at least 50 years of coincident
live time is analyzed, allowing for a false alarm rate of 1 per
50 years to be estimated.
Three pipelines are deployed in the analysis: two differ-
ent versions of the Stochastic Transient Analysis Multi-
detector Pipeline-all sky (STAMP-AS) pipeline
[11,40,45]
and the long-duration configuration of coherent WaveBurst
(cWB)
[48]
. The cWB pipeline is seed based while the two
STAMP-AS algorithms, Zebragard and Lonetrack, use
seed-based and seedless clustering algorithms, respectively.
Altogether, the analyses are sensitive to transients lasting
2
–
500 s and covering a frequency band of 24
–
2048 Hz.
Due to the short duration of binary black hole signals
and the weakness of the coalescences containing neutron
stars observed during O3
[6]
, we are not sensitive to and
therefore do not excise any time around known compact
binary coalescences. All false alarm rates reported are per
pipeline, with no combination of searches made outside of
reporting the most sensitive limit across the parameter
space below.
A. STAMP-AS
Spectrograms, with duration 500 s and frequency band
24
–
2048 Hz and a pixel size of
1
s×
1
Hz, are derived with
cross-power SNR as the statistic computed in the maps.
Nonstationary, high-amplitude spectral features are masked
to limit their effect on the search. Zebragard uses cuts on
the fraction of SNR per time bin (summing all pixels of the
same time index) and the ratio in SNR between detectors to
remove data transients
[24]
; Lonetrack does not require this
cut due to the narrowband assumption. During a short
period of time, a time segment veto that flags periods of
instabilities in the high-power laser at Hanford is applied on
Zebragard triggers
[38]
.
B. CWB
The algorithm used by cWB
[48]
is based on a maximum
likelihood approach applied to the multiresolution time-
frequency representation of the time series of the detectors
’
data. Candidate triggers are identified as a cluster if there
is a coherent excess power in the time-frequency pixel
representation over the network data. The search is per-
formed in the frequency range 24
–
2048 Hz. Selection
criteria are applied on the duration and on the coherence
of the trigger; the coherence coefficient, measuring the
degree of correlation between the detectors, must be larger
than 0.6
[48]
. Moreover, the trigger energy-weighted
duration, defined as
d
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
w
i
ð
t
−
t
Þ
2
P
w
i
s
;
where
t
is the central time of the pixel,
w
the energy of the
pixel,
t
the mean time and the sum is computed over the
selected pixels of the event in all the resolutions, is required
to be greater than 1.5 s. Since observed glitch excess in the
16
–
48 Hz band, associated with elevated anthropogenic
noise, is different between the first and second part of the
run, the acceptance criteria in the latter one have been
slightly modified. The triggers have an energy-weighted
duration larger than 0.5 s and a total duration greater than
5 s, this to ensure increased acceptance for the eccentric
compact binary waveforms family discussed in the next
section.
IV. RESULTS AND FUTURE PROSPECTS
The detection threshold is defined to be a false alarm rate
lower than
1
=
50
years (equivalent to
6
.
3
×
10
−
10
Hz).
None of the pipelines found triggers consistent with such
a false alarm rate; the most significant triggers, nonover-
lapping between the different pipelines and consistent with
the background, are listed in Table
I
. The most significant
event reported by the cWB algorithm (statistical signifi-
cance
∼
1
.
7
σ
,
p
value 0.088) shows a time-frequency map
composed of two separated excess power cluster pixels,
respectively, at 838 and 861 Hz mean frequency. This
trigger appears to be associated with a random (time)
coincidence of pixels belonging to two different nonsta-
tionary spectral lines of unknown origin, at 838 Hz (present
in H1 and L1) and 861 Hz (present in H1). The STAMP-AS
Zebragard and Lonetrack pipeline triggers are consistent
with typical events identified in the background.
To place these results in context, upper limits are derived
on the gravitational-wave strain amplitude using a set of
simulated waveforms added coherently into detector data.
Waveforms that span the parameter space in both frequency
and time, as well as a sampling of potential astrophysical
models, are used. For the astrophysical models, postmerger
magnetars (Magnetar)
[22]
, black hole ADI
[18]
,newly
formed magnetar powering a GRB plateau
[16]
, ECBC
waveforms
[23]
, and broadband chirps from ISCO waves
around rotating black holes
[12]
are used (see Ref.
[49]
for further developments). To include signal morphologies
TABLE I. Properties of the most significant coincident triggers
found by each of the long-duration transient search pipelines
during the third observing run. FAR stands for false alarm rate,
while the
p
value is the probability of observing at least 1 noise
trigger at higher significance than the most significant coincident
trigger.
Pipeline
FAR
[Hz]
p
value
Frequency
[Hz]
Duration
[s]
Time
[GPS]
cWB
1
.
0
×
10
−
8
0.088 838
–
861
16 1252808855
Zebragard
5
.
6
×
10
−
8
0.40 1650
–
1769 21 1244819393
Lonetrack
1
.
7
×
10
−
8
0.14 1510
–
1937 417 1253105020
ALL-SKY SEARCH FOR LONG-DURATION GRAVITATIONAL-
...
PHYS. REV. D
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otherwise not addressed by the astrophysical models,
“
ad hoc
”
waveforms, band-limited white noise burst and
sine-Gaussian bursts are also used. Their time-frequency
spectrograms are shown in Fig.
1
.
The upper limits on the gravitational-wave strain ampli-
tude are typically reported for unmodeled searches using
the root-sum-square gravitational-wave amplitude at the
Earth,
h
rss
,
h
rss
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Z
∞
−∞
ð
h
2
þ
ð
t
Þþ
h
2
×
ð
t
ÞÞ
d
t
s
;
ð
1
Þ
where
h
þ
and
h
×
are the two signal polarizations.
Simulations are varied with
h
rss
and injected uniformly
in time, sky location, polarization angle, and the cosine of
the inclination angle of the assumed source.
Upper limits on gravitational-wave strain versus mean
frequency for sources detected with 50% efficiency and a
false alarm rate of 1 event in 50 years are shown in Fig.
2
.
The strongest bounds obtained from the three pipelines are
shown on the plot. Because each pipeline uses a different
clustering algorithm, their relative sensitivities vary with
waveform morphology. Lonetrack, which uses seedless
clustering, performs best on magnetar signals (Magnetar
and GRB plateau) but is not sensitive to white noise bursts.
Zebragard and coherent WaveBurst give the most con-
straining values with similar sensitivities for most of
the remaining waveforms. On average, for all waveforms
considered in this paper, the
h
rss
sensitivity improved
by a factor of 1.8 upon the analysis from the second
observing run
[25]
.
For the eccentric binary waveforms, we determine
90% confidence level limits on the rate of events. We do
this using the
“
loudest event statistic
”
method, which
uses the candidate with the largest value to estimate rate
constraints
[50]
. Taking as an example the eccentric binary
waveforms, the 90% upper limits on the event rates as a
function of distance are highlighted in Fig.
3
. In addition,
Table
II
gives the upper limits
R
90%
at 90% confidence on
the rate of eccentric binary coalescences per unit volume.
Following
[51]
, and assuming an isotropic and uniform
distribution of sources,
R
90%
is given by
R
90%
¼
2
.
3
4
π
T
R
r
max
0
drr
2
ε
ð
r
Þ
;
ð
2
Þ
where
ε
ð
r
Þ
is the detection efficiency as a function of
distance, computed as the fraction of transients detectable
at a given distance
[51]
,
r
max
is the maximum detectable
distance, and
T
¼
204
.
4
days is the total observing
time. For 1.4
–
1.4 solar masses eccentric binaries, rate
upper limits are
∼
1
.
5
–
2
lower than the ones computed
in Ref.
[52]
for O2 data. Such improvement can
be explained by both the increased sensitivity of the
search and the increased livetime between O2 and O3.
For comparison, estimated merger rates from the
second LIGO-Virgo GW transient catalog
[53]
are
23
.
9
þ
14
.
3
−
8
.
6
Gpc
−
3
yr
−
1
and
340
þ
490
−
240
Gpc
−
3
yr
−
1
for binary
black holes and binary neutron stars, respectively. With
eccentric systems expected to be only a small fraction of the
total binary systems, the upper limits derived are compat-
ible with an absence of detection of such systems in this
search; for this reason, we do not constrain the fraction of
10
2
10
3
10
-24
10
-23
10
-22
10
-21
10
-20
10
-19
10
-18
ADI
GRB plateau
ISCO chirp
ECBC
Magnetar
WNB
SG
FIG. 2. The GW root-sum-square strain amplitude versus mean
frequency at 50% detection efficiency and a FAR of
1
=
50
years.
The red, green, and blue curves are the averaged amplitude
spectral noise densities for Hanford, Livingston, and Virgo
detectors to show that the search results follow the detectors
’
sensitivity frequency. We also show in dashed-dotted lines the
gravitational-wave amplitudes corresponding to the energy of
0
.
01
M
⊙
c
2
at various distances, with examples at 100 kpc, 1, 10,
and 100 Mpc shown.
10
0
10
1
10
2
10
0
10
1
10
2
10
3
ECBC_A
ECBC_B
ECBC_C
ECBC_D
ECBC_E
ECBC_F
ECBC_G
ECBC_H
ECBC_I
10
0
10
1
2
3
4
5
6
O2 vs O3 ratio
FIG. 3. Upper limits at 90% confidence level on the rate of
eccentric compact binary coalescences as a function of the
distance. Only the best result is shown for each waveform.
The inset shows the ratio of the rates with respect to O2 results
[25]
for ECBC_A to ECBC_F (see Table
II
for parameters).
R. ABBOTT
et al.
PHYS. REV. D
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