Observing gravitational-wave transient GW150914
with minimal assumptions
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 25 February 2016; published 7 June 2016)
The gravitational-wave signal GW150914 was first identified on September 14, 2015, by searches for
short-duration gravitational-wave transients. These searches identify time-correlated transients in multiple
detectors with minimal assumptions about the signal morphology, allowing them to be sensitive to
gravitational waves emitted by a wide range of sources including binary black hole mergers. Over the
observational period from September 12 to October 20, 2015, these transient searches were sensitive to
binary black hole mergers similar to GW150914 to an average distance of
∼
600
Mpc. In this paper, we
describe the analyses that first detected GW150914 as well as the parameter estimation and waveform
reconstruction techniques that initially identified GW150914 as the merger of two black holes. We find that
the reconstructed waveform is consistent with the signal from a binary black hole merger with a chirp mass
of
∼
30
M
⊙
and a total mass before merger of
∼
70
M
⊙
in the detector frame.
DOI:
10.1103/PhysRevD.93.122004
I. INTRODUCTION
The newly upgraded Advanced LIGO observatories
[1,2]
, with sites near Hanford, Washington (H1), and
Livingston, Louisiana (L1), host the most sensitive
gravitational-wave detectors ever built. The observatories
use kilometer-scale Michelson interferometers that are
designed to detect small, traveling perturbations in
space-time predicted by Einstein
[3,4]
, and thought to
radiate from a variety of astrophysical processes. Advanced
LIGO recently completed its first observing period, from
September 2015 to January 2016. Advanced LIGO is
among a generation of planned instruments that includes
GEO 600, Advanced Virgo, and KAGRA; the capabilities
of this global gravitational-wave network should quickly
grow over the next few years
[5
–
8]
.
An important class of sources for gravitational-wave
detectors are short duration transients, known collectively
as gravitational-wave bursts
[9]
. To search broadly for a
wide range of astrophysical phenomena, we employ
unmodeled searches for gravitational-wave bursts of dura-
tions
∼
10
−
3
−
10
s, with minimal assumptions about the
expected signal waveform. Bursts may originate from a
range of astrophysical sources, including core-collapse
supernovae of massive stars
[10]
and cosmic string cusps
[11]
. An important source of gravitational-wave transients
are the mergers of binary black holes (BBH)
[12
–
14]
. Burst
searches in data from the initial generation of interferom-
eter detectors were sensitive to distant BBH signals from
mergers with total masses in the range
∼
20
–
400
M
⊙
[15,16]
. Since burst methods do not require precise
waveform models, the unmodeled search space may
include BBH mergers with misaligned spins, large mass
ratios, or eccentric orbits. A number of all-sky, all-time
burst searches have been performed on data from initial
LIGO and Virgo
[17
–
19]
. Recent work has focussed on
improving detection confidence in unmodeled searches,
and the last year has seen several improvements in the
ability to distinguish astrophysical signals from noise
transients
[20
–
24]
. As a result, burst searches are now
able to make high confidence detections across a wide
parameter space.
On September 14, 2015, an online burst search
[25]
reported a transient that clearly stood above the expected
background from detector noise
[26]
. The alert came only
3 min after the event
’
s time stamp of
09
∶
50
∶
45
UTC. A
second online burst search independently identified the
event with a latency of a few hours, providing a rapid
confirmation of the signal
[23]
. The initial waveform
reconstruction showed a frequency evolution that rises in
time, suggesting binary coalescence as the likely progen-
itor, and a best fit model provided a chirp mass around
28
M
⊙
, indicating the presence of a BBH signal. Within
days of the event, many follow-up investigations began,
including detailed checks of the observatory state to check
for any possible anomalies
[27]
. Two days after the signal
was found, a notice with the estimated source position was
sent to a consortium of astronomers to search for possible
counterparts
[28]
. Investigations continued over the next
several months to validate the observation, estimate its
statistical significance, and characterize the astrophysical
source
[29,30]
.
In this article, we present details of the burst searches that
made the first detection of the gravitational-wave transient,
*
Full author list given at the end of the article.
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=
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=
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=
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© 2016 American Physical Society
GW150914, announced in
[26]
. We describe results
reported in this announcement that are based on the
coherent Waveburst algorithm, along with those obtained
by two other analyses using omicron-LALInference-Bursts
and BayesWave
[23,25,31]
. In Sec.
II
, we present a brief
overview of the quality of the acquired data and detector
performance, before moving on, in Sec.
III
, to present the
three analyses employed. Using each pipeline, we assess
the statistical significance of the event. Section
IV
char-
acterizes each search sensitivity using simulated signals
from BBH mergers. In Sec.
V
, we demonstrate how a range
of source properties may be estimated using these same
tools
—
including sky position and masses of the black
holes. The reconstructed signal waveform is directly
compared to results from numerical relativity (NR) simu-
lations, giving further evidence that this signal is consistent
with expectations from general relativity. Finally, the paper
concludes with a discussion about the implications of
this work.
II. DATA QUALITY AND
BACKGROUND ESTIMATION
We identify 39 calendar days of Advanced LIGO data,
from September 12 to October 20, 2015, as a data set to
measure the sensitivity of the searches and the impact of
background noise events, known as glitches.
As in previous LIGO, Virgo and GEO transient searches
[17
–
19]
, a range of monitors tracking environmental noise
and the state of the instruments are used to discard periods
of poor quality data. Numerous studies have been per-
formed to identify efficient veto criteria to remove non-
Gaussian noise features, while having the smallest possible
impact on detector live time
[27]
.
However, it is not possible to remove all noise glitches
based on monitors. This leaves a background residual that
has to be estimated from the data. To calculate the back-
ground rate of noise events arising from glitches occurring
simultaneously at the two LIGO sites by chance
[17
–
19]
,
the analyses are repeated on
O
ð
10
6
Þ
independent time-
shifted data sets. Those data sets are generated by trans-
lating the time of data in one interferometer by a delay of
some integer number of seconds, much larger than the
maximum GW travel time
≃
10
ms between the Livingston
and Hanford facilities. By considering the whole coincident
live time resulting from each artificial time shift, we obtain
thousands of years of effective background based on the
available data. With this approach, we estimate a false
alarm rate (FAR) expected from background for each
pipeline.
The
“
time-shift
”
method is effective to estimate the
background due to uncorrelated noise sources at the two
LIGO sites. For the time immediately around GW150914,
we also examined potential sources of correlated noise
between the detectors, and concluded that all possible
sources were too weak to have produced the observed
signal
[27]
.
III. SEARCHES FOR
GRAVITATIONAL-WAVE BURSTS
Strain data are searched by gravitational-wave burst
search algorithms without assuming any particular signal
morphology, origin, direction or time. Burst searches are
performed in two operational modes: online and off-line.
Online, low-latency searches provide alerts within
minutes of a GW signal passing the detectors to facilitate
follow-up analyses such as searching for electromagnetic
counterparts. In the days and weeks following the data
collection, burst analyses are refined using updated infor-
mation on the data quality and detector calibration to
perform off-line searches. These off-line searches provide
improved detection confidence estimates for GW candi-
dates, measure search sensitivity, and add to waveform
reconstruction and astrophysical interpretation. For short-
duration, narrowband signals, coherent burst searches
have sensitivities approaching those of optimal matched
filters
[16,32]
.
In the following subsections, we describe the burst
analysis of GW150914. This includes two independent
end-to-end pipelines, coherent Waveburst (cWB) and
omicron-LALInference-Bursts (oLIB), and BayesWave,
which performed a follow-up analysis at trigger times
identified by cWB. These three algorithms employ different
strategies (and implementations) to search for unmodeled
GW transients; hence, they could perform quite differently
for specific classes of GW signals. Given the very broad
character of burst signals, the use of multiple search
algorithms is then beneficial, both to validate results and
to improve coverage of the wide signal parameter space.
A summary of the results from cWB has been presented
in
[26]
. Here, we provide more details regarding the cWB
search pertaining the discovery of GW150914 and present
its results with respect to the other burst searches. In this
paper, we focus our characterizations of our pipelines on
BBH sources only.
A. Coherent WaveBurst
The cWB algorithm has been used to perform all-sky
searches for gravitational-wave transients in LIGO, Virgo
and GEO data since 2004. The most recent cWB results
from the initial detectors are
[17,19,33]
. The cWB algo-
rithm has since been upgraded to conduct transient searches
with the advanced detectors
[24]
. The cWB pipeline was
used in the low-latency transient search that initially
detected GW150914, reporting the event 3 min after the
data were collected. This search aims at rapid alerts for the
LIGO/Virgo electromagnetic follow-up program
[28]
and
provides a first estimation of the event parameters and sky
location. A slightly different configuration of the same
B. P. ABBOTT
et al.
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pipeline was used in the off-line search to measure the
statistical significance of the GW150914 event, which was
reported in
[26]
. The low-latency search was performed in
the frequency range of 16
–
2048 Hz, while the off-line
search covered the band of the best detector sensitivity
between 16 and 1024 Hz.
1. cWB pipeline overview
The cWB pipeline searches for a broad range of
gravitational-wave transients in the LIGO frequency band
without prior knowledge of the signal waveforms
[25]
. The
pipeline identifies coincident events in data from the two
LIGO detectors and reconstructs the gravitational-wave
signal associated with these events using a likelihood
analysis.
First, the data are whitened and converted to the time-
frequency domain using the Wilson-Daubechies-Meyer
wavelet transform
[34]
. Data from both detectors are then
combined to obtain a time-frequency power map. A transient
event is identified as a cluster of time-frequency data samples
with power above the baseline detector noise. To obtain a
good time-frequency coverage for a broad range of signal
morphologies, the analysis is repeated with seven frequency
resolutions
Δ
f
ranging from 1 to 64 Hz in steps of powers of
2, corresponding to time resolutions
Δ
t
¼
1
=
ð
2
Δ
f
Þ
from
500 to 7.8 ms. The clusters at different resolutions over-
lapping in time and frequency are combined into a trigger
that provides a multiresolution representation of the excess
power event recorded by the detectors.
The data associated with each trigger are analyzed
coherently
[24]
to estimate the signal waveforms, the wave
polarization, and the source sky location. The signal wave-
forms in both detectors are reconstructed with the con-
strained likelihood method
[35]
. The constraint used in this
analysis is model independent and requires the reconstructed
waveforms to be similar in both detectors, as expected from
the close alignment of the H1 and L1 detector arms.
The waveforms are reconstructed over a uniform grid of
sky locations with
0
.
4
°×
0
.
4
° resolution. We select the best
fit waveforms that correspond to the maximum of the
likelihood statistic
L
¼
c
c
E
s
, where
E
s
is the total energy
of the reconstructed waveforms
1
and
c
c
measures the
similarity of the waveforms in the two detectors. The
coefficient
c
c
is defined as
c
c
¼
E
c
=
ð
E
c
þ
E
n
Þ
, where
E
c
is
the normalized coherent energy and
E
n
is the normalized
energy of the residual noise after the reconstructed signal is
subtracted from the data. The coherent energy
E
c
is
proportional to the cross-correlation between the recon-
structed signal waveforms in H1 and L1 detectors.
Typically, gravitational-wave signals are coherent and have
small residual energy, i.e.,
E
c
≫
E
n
and therefore
c
c
∼
1
.
On the other hand, spurious noise events (glitches) are often
not coherent, and have large residual energy because the
reconstructed waveforms do not fit the data well, i.e.,
E
c
≪
E
n
and therefore
c
c
≪
1
. The ranking statistic is defined as
η
c
¼ð
2
c
c
E
c
Þ
1
=
2
. By construction, it favors gravitational-
wave signals correlated in both detectors and suppresses
uncorrelated glitches.
2. Classification of cWB events
Events produced by the cWB pipeline with
c
c
>
0
.
7
are
selected and divided into three search classes
C
1
,
C
2
, and
C
3
according to their time-frequency morphology. The
purpose of this event classification is to account for
the non-Gaussian noise that occurs nonuniformly across
the parameter space searched by the pipeline.
The classes are determined by three algorithmic tests
and additional selection cuts. The first algorithmic test
addresses a specific type of noise transient referred to as
“
blip glitches
”
[27]
. During the run, both detectors expe-
rienced noise transients of unknown origin consisting of a
few cycles around 100 Hz. These blip glitches have a very
characteristic time-symmetric waveform with no clear
frequency evolution. Previous work has shown that
down-weighting signals with simple time-frequency struc-
ture can enhance pipeline performance
[21]
. To implement
this here, we apply a test that uses waveform properties to
identify, in the time domain, blip glitches occurring at both
detectors. The second algorithmic test identifies glitches
due to nonstationary narrow-band features, such as power
and mechanical resonance lines. This test selects candidates
which have most of their energy (greater than 80%)
localized in a frequency bandwidth less than 5 Hz. A
cWB event is placed in the search class
C
1
, if it passes
either of the aforementioned tests. In addition, due to the
elevated nonstationary noise around and below the
Advanced LIGO mechanical resonances at 41 Hz, events
with central frequency lower than 48 Hz were also placed
in the
C
1
class.
The third algorithmic test is used to identify events with a
frequency increasing with time. The reconstructed time-
frequency patterns can be characterized by an
ad hoc
parameter
M
following Eq.
(1)
in Sec.
VD
. For coalescing
binary signals
M
corresponds to the chirp mass of the
binary
[36]
. For signals that do not originate from coa-
lescing binaries and glitches,
M
takes on unphysical
values. In the unmodeled cWB analysis, the parameter
M
is used to distinguish between events with different
time-frequency evolution. By selecting events with
M
>
1
M
⊙
we identify a broad class of events with a
chirping time-frequency signature, which includes a sub-
class of coalescing binary signals. The events selected by
this test that also have a residual energy
E
n
consistent with
Gaussian noise are placed in the search class
C
3
. All other
events, not included in the
C
1
or
C
3
class, are placed in the
search class
C
2
. The union of all three independent search
classes covers the full parameter space accessible to the
unmodeled cWB search.
1
ffiffiffiffiffi
E
s
p
is the network signal-to-noise ratio
[24]
.
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3. False alarm rate
To establish the distribution of background events, we
use the time-shift procedure discussed in Sec.
II
, using all
the data available for each detector. The effective back-
ground live time for this analysis is 67 400 years, obtained
by analyzing more than
1
.
6
×
10
6
time-shifted instances
of 16 days of the observation time. Figure
1
reports the
cumulative false alarm rate distributions as a function of the
detection statistic
η
c
for the three defined search classes.
The significance of a candidate event is measured against
the background of its class. As shown in the plot, the
C
1
search class is affected by a tail of blip glitches with
the false alarm rate of approximately
0
.
01
y
−
1
. Confining
glitches in the
C
1
class enhances the search sensitivity to
gravitational-wave signals falling in the
C
2
and
C
3
classes. In fact, the tail is reduced by more than two
orders of magnitude in the
C
2
search class. The
background rates in the
C
3
search class are almost ten
times lower than in
C
2
, with no prominent tail of loud
events, indicating that it is highly unlikely for detectors to
produce coherent background events with a chirping
time-frequency evolution.
To check the homogeneity and stability of background
rates shown in Fig.
1
, these distributions have been
compared between instances of background data, generated
with different time shifts between the detectors, finding no
evidence for any dependence on the time-shift interval or
on the time period of data collection.
4. Significance of GW150914 event
GW150914 was detected with
η
c
¼
20
and belongs
to the
C
3
class. Its
η
c
value is larger than the detection
statistic of all observed cWB candidates. Also Fig.
2
(left)
shows that the GW150914
η
c
value is larger than the
detection statistic of any background event in its search
class in 67 400 years of the equivalent observation time.
All other observed event candidates (orange squares) are
consistent with the background.
The GW150914 significance is defined by its false
alarm rate measured against the background in the
C
3
class. Assuming that all search classes are statistically
independent, this false alarm rate should be increased by a
conservative trials factor equal to the number of classes.
By taking into account the trials factor of 3, the estimated
GW150914 false alarm rate is less than one event in
22 500 years. The probability that the 16 days of data
would yield a noise event with this false alarm rate is less
than
16
=
ð
365
×
22 500
Þ¼
2
×
10
−
6
.
The union of the
C
2
and
C
3
search classes represents a
transient search with no assumptions on the signal time-
frequency evolution. The result of such analysis with just
two search classes
C
1
and
C
2
þ
C
3
is shown in Fig.
2
FIG. 1. Cumulative rate distribution of background events as a
function of the detection statistic
η
c
for the three cWB search
classes. Vertical dashed line shows the value of the detection
statistic for the GW150914 event.
FIG. 2. Search results (in orange) and expected number of background events (black) in 16 days of the observation time as a function
of the cWB detection statistic (bin size 0.2) for the
C
3
search class (left) and
C
2
þ
C
3
search class (right). The black curve shows the
total number of background events found in 67 400 years of data, rescaled to 16 days of observation time. The orange star represents
GW150914, found in the
C
3
search class.
B. P. ABBOTT
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(right). In this case there are four events louder than
GW150914 in the
C
2
þ
C
3
class. With the trials factor
of 2, the false alarm rate is one event in 8 400 years. The
four loud events are produced by a random coincidence
of multiple blip glitches: two nearby blip glitches in one
detector and a single blip glitch in the second detector.
The algorithmic test that identifies blip glitches was not
designed to capture multiple ones and, therefore, missed
these events.
B. oLIB
The oLIB search
[23]
is a search pipeline for
gravitational-wave bursts designed to operate in low
latency, with results typically produced in around
30 min. However, the pipeline can operate in two modes,
online and off-line. The online version identified
GW150914 independently of cWB. The off-line version
is used here to establish the significance of GW150914.
1. oLIB pipeline overview
The oLIB pipeline follows a hierarchical scheme, first
performing a coincident event down selection followed
by a fully coherent Markov chain Monte Carlo Bayesian
analysis.
In the first step of the pipeline, a time-frequency map of
the single-interferometer strain data from all detectors is
produced using the Q-transform
[37]
implemented in
Omicron
[38]
. Stretches of excess power are flagged as
triggers. Neighboring triggers that occur within 100 ms,
with an identical central frequency
f
0
and quality factor
Q
,
are clustered together. After applying data quality vetoes as
described in Sec.
II
, a list of triggers that fall within a 10 ms
coincidence window (compatible with the speed-of-light
baseline separation of the detectors) is then compiled.
In the second step of the pipeline, all coincident triggers
identified in the first step are analyzed using LIB, a
Bayesian parameter estimation and model selection algo-
rithm that coherently explores the signal parameter space
with the nested sampling algorithm
[39]
available in the
LALInference software library
[40]
.
LIB models signals and glitches by a single sine-
Gaussian wavelet. Signals have a coherent phase across
detectors, while glitches do not. Using this model, LIB
calculates two Bayes factors, each of which represents an
evidence ratio between two hypotheses: coherent signal vs
Gaussian noise (BSN) and coherent signal vs incoherent
glitch (BCI). These two Bayes factors are then combined
into a scalar likelihood ratio
Λ
for the signal vs noise
(Gaussian or glitch) problem. More precisely,
Λ
is obtained
from the ratio of the probability distributions for the Bayes
factors BSN and BCI estimated empirically from
“
training
”
sets of events. Those sets consists of
≃
4000
simulated
gravitational-wave signals from a uniform-in-volume
source distribution and
≃
150
background triggers obtained
from time-shifted data for the signal and noise cases,
respectively.
The final ranking statistic
Λ
is evaluated for a different
set of background triggers from time-shifted data in order to
map a given value of the likelihood ratio into a FAR.
2. oLIB analysis of GW150914
For the purpose of this analysis, Omicron runs over the
32
–
1024 Hz bandwidth and selects triggers that exceed a
SNR threshold of 6.5. LIB uses the following priors:
uniform in sky location, uniform in central frequency
f
0
in the selected bandwidth, and uniform in quality factor
Q
from 0.1
–
110. Events with BSN or BCI
≤
0
are
discarded. We retain events with
48
≤
~
f
0
≤
1020
Hz and
2
≤
~
Q
≤
109
, where
~
f
0
and
~
Q
are median values computed
from the posterior distributions delivered by LIB. The
selection cut on
~
Q
is analogous to those used by cWB to
reject blip glitches and narrow-band features. The ranking
statistic
Λ
and its background distribution from which
the FAR is deduced are computed from the training and
background sets after applying all those cuts.
Because oLIB is able to run on short data segments
(
≳
3
s), this search analyzed nearly all available data, which
amounted to 17.4 days, i.e.,
∼
10%
more coincident data
than cWB. The data were time-shifted in 1-sec intervals to
produce the equivalent of 106 000 years of background
data. The background distribution is plotted as a function of
log
Λ
in Fig.
3
. As shown in the same figure GW150914
has a ranking statistic of log
Λ
¼
0
.
80
, corresponding to a
FAR of roughly 1 in 27 000 years. It is the only event in the
search results satisfying the selection cuts.
C. BayesWave follow-up
The BayesWave pipeline is a Bayesian algorithm
designed to robustly distinguish GW signals from glitches
in the detectors
[31,41]
. In this search, BayesWave is run as
FIG. 3. Cumulative rate distribution of background events as a
function of oLIB ranking statistic log
Λ
. GW150914 is the only
event in the search results to pass all thresholds. Its statistic
value log
Λ
¼
0
.
80
corresponds to a background FAR of
≃
1
in
27 000 years.
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a follow-up analysis to triggers identified by cWB. For each
candidate event, BayesWave compares the marginalized
likelihood, or evidence, among three hypotheses: the data
contain only Gaussian noise, the data contain Gaussian
noise and noise transients (glitches), or the data contain
Gaussian noise and an astrophysical signal.
The BayesWave algorithm models signals and glitches
using a linear combination of sine-Gaussian wavelets.
The number of wavelets needed in the glitch or signal
model is not fixed
a priori
, but instead is optimized using a
reversible jump Markov chain Monte Carlo. The glitch
model fits the data separately in each interferometer with an
independent linear combination of wavelets. The signal
model reconstructs the candidate event at some fiducial
location (the center of the Earth), taking into account the
response of each detector in the network to that signal.
BayesWave uses a parametrized phenomenological model,
BayesLine, for the instrument noise spectrum, simultane-
ously characterizing the Gaussian noise and instrument/
astrophysical transients
[41]
.
BayesWave produces posterior distributions for the
parameters of each model under consideration. For the
signal model, this includes the waveform, as constructed
from sums of sine-Gaussian wavelets, and the source
position. Waveform reconstructions are used to produce
posterior distributions for characteristics such as the
duration, central frequency, and bandwidth of the signal,
which are used to compare the data to theoretical models.
The marginalized posterior (evidence) for each model is
calculated by marginalizing over the different dimension
waveform reconstructions, and then is used to rank the
competing hypotheses.
BayesWave is used as a follow-up analysis for candidate
events first identified by cWB. The combined cWB
þ
BayesWave data analysis pipeline has been shown to allow
high-confidence detections across a range of waveform
morphologies
[21,22]
. The cWB
þ
BayesWave pipeline
uses the Bayes factor, comparing the signal and glitch
models (
B
SG
) as its detection statistic. Bayes factors are
reported on a natural logarithmic scale ln
B
SG
, which
scales with
N
ln SNR, where
N
is the number of wavelets
used in the reconstruction
[22]
. The consequence is that
BayesWave assigns a higher detection statistic to signals
with nontrivial time-frequency structure. Though Bayes
factors used by Bayeswave and oLIB methods both
produce a measure of coherence between the signal
morphologies observed in multiple detectors, the above
calculation indicates that BayesWave,
B
SG
, also includes a
measure of the signal complexity.
The
“
off-line
”
BayesWave pipeline analyzes all cWB
zero-lag and background events with a detection statistic
η
c
>
11
.
3
and correlation coefficient
c
c
>
0
.
7
. The thresh-
old on
η
for event follow-up is a compromise between
computational cost and in-depth analysis of cWB events.
The BayesWave computation is performed over a 4-sec
segment of data
2
centered on the event time reported by
cWB. We use 1 sec of data around the event time for model
comparison, while the remainder of the segment is used for
spectral estimation. We perform the analysis in the Fourier
domain over the frequency range of
32
<f<
1024
Hz
though, for cWB candidates with central frequency
f
cWB
<
200
Hz (including GW150914), BayesWave used a maxi-
mum frequency of 512 Hz to reduce the computational cost
of the analysis. Both the signal and the glitch model require
at least one wavelet (to make them disjoint from one
another and the Gaussian noise model) and have a
maximum of 20 wavelets allowed in the linear combina-
tion. Most of the priors used in the analysis are as described
in
[31]
and
[22]
, with the following changes. The prior on
the
“
quality factor
”
of the wavelets
Q
has been extended to
include lower values, so that it is uniform over the interval
[0.1,40]. The low
Q
values allow blip glitches to be
correctly characterized with a small number of wavelets.
Also, the functional form of the glitch amplitude prior has
been modified to scale as a power law rather than an
exponential in the large SNR limit. The new prior better
reflects the belief that very loud events (SNR
>
100
) are
more likely to be glitches than signals.
Figure
4
shows the cumulative rate distribution of back-
ground events as a function of the cWB
þ
BayesWave
detection statistic ln
B
SG
. The cWB
þ
BayesWave pipeline
considers the triggers from all cWB search classes together
(all curves in Fig.
1
) as a single search. The explicit glitch
model used by BayesWave reduces the tail in the back-
ground distribution
[22]
, so that loud background events are
down-weighted rather than grouped into different classes. In
FIG. 4. Cumulative rate distribution of background events as a
function of the cWB
þ
BayesWave detection statistic ln
B
SG
. The
cWB
þ
BayesWave pipeline considers all cWB candidates with
η
c
>
11
.
3
(combining all three curves in Fig.
1
). In the equivalent
of 67 400 years of data, GW150914 was the only zero-lag event
to pass all thresholds. Only one noise coincidence is ranked
higher than GW150914.
2
The 4 sec segment length was shown in testing to be the
minimum amount of data needed to estimate the power spectral
density.
B. P. ABBOTT
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the equivalent of 67 400 years of O1 data, 2374 cWB events
warranted a BayesWave follow-up and only one noise
coincidence (ln
B
SG
¼
53
.
1
3
.
4
) was ranked higher than
GW150914 (ln
B
SG
¼
49
.
4
0
.
8
). GW150914 is the only
zero-lag event to pass all thresholds. Investigations of the
highest ranking background events have revealed remark-
ably similar glitches in the two detectors which, were it not
for the large, unphysical time shifts applied to the data,
would be indistinguishable from a GW signal. However, the
waveform morphology of the most significant background
events is in no way similar to a BBH merger signal. Treating
all cWB candidates as coming from the same search,
BayesWave estimates a FAR for GW150914 of 1 in
67400 years.
IV. SEARCH SENSITIVITY
In this section, we demonstrate the ability of transient
searches to detect GWs from BBH mergers. We use
simulated gravitational waveforms that cover all three
phases of BBH coalescence, i.e., inspiral, merger and
ringdown. The analysis is performed by adding simu-
lated BBH waveforms to the detector data, and recov-
ering them using the three burst pipelines described in
Sec.
III
.
A. Simulation data set
BBH systems are characterized by the masses
m
1
and
m
2
, dimensionless spin vectors
a
1
and
a
2
of the two
component black holes, the source distance
D
, its
sky-location coordinates, and the inclination of the BBH
orbital momentum vector relative to the line of sight to
Earth. The black hole spins are obtained from the dimen-
sionless spin vectors by
S
i
¼
m
2
i
a
i
, where
j
a
i
j
≤
1
.
The simulation includes binaries that are isotropically
located on the sky and isotropically oriented, with total
masses
M
¼
m
1
þ
m
2
uniformly distributed between
30 and
150
M
⊙
, that is within a factor of
∼
2
of the
estimated total mass for GW150914
[29]
. We generate
three separate sets, each with a fixed mass ratio
q
¼
m
2
=m
1
∈
f
0
.
25
;
0
.
5
;
1
.
0
g
. We assume that the black
hole spins are aligned with the binary orbital angular
momentum, with a spin magnitude uniformly distributed
across
j
a
1
;
2
j
∈
½
0
;
0
.
99
. The distances are drawn from
distributions within 3.4 Gpc such that we get good
sampling for a range of SNR values around the detection
threshold. The simulation does not include redshift cor-
rections, which introduces small systematic errors for the
more distant sources. The signals are distributed uniformly
in time with a gap of 100 sec between them.
The BBH waveforms analyzed in this study have been
generated using the
SEOBNRv2
model in the
LAL
software
library
[42,43]
. This model only accounts for the dominant
l
¼
2
,
m
¼
2
GW radiated modes. The waveforms are
generated with an initial frequency of 15 Hz. The data sets
are summarized in Table
I
.
B. Results
To quantify the results of the study, we use the sensitive
radius which is the radius of the sphere with volume
V
¼
R
4
π
r
2
ε
ð
r
Þ
dr
, where
ε
ð
r
Þ
is the averaged search
efficiency for sources at distance
r
with random sky
position and orientation
[16]
. For each pipeline, we
calculate the sensitive radius as a function of FAR. The
results are shown in Fig.
5
. For example, at a FAR of 1 per
thousand years, the three searches show similar perfor-
mance, with each detecting the simulated equal-mass BBH
population to a sensitive distance in the range 700 to
TABLE I. Summary of the BBH simulations used for estimat-
ing search efficiency.
Total mass
M
¼
m
1
þ
m
2
30
–
150
M
⊙
Mass ratio,
q
¼
m
2
=m
1
0.25, 0.5, 1.0
Spin magnitude
j
a
1
;
2
j
0
–
0.99
Waveform model
SEOBNRv2
FIG. 5. Sensitive radius for the different search pipelines for simulated BBH waveforms with different mass ratios
q
. The sensitive
radius measures the average distance to which the search detects with a given FAR threshold. The cWB results include all three search
classes, with a corresponding trials factor.
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800 Mpc. To the far left side of the plots (very low FAR),
the differences between pipelines are dominated by the
loudest few background events; the cWB
C
3
search class
selection for chirping events allows many BBH signals to
be recovered with very low FAR.
The effect of intrinsic BBH parameters (component
masses and spins) on the sensitive radius of the three
pipelines is summarized in Fig.
6
. The three panels of the
figure correspond to three bins of effective spin. Effective
spin is defined as in
[29]
:
χ
eff
¼ð
S
1
m
1
þ
S
2
m
2
Þ
·
ˆ
L
M
, with
ˆ
L
the
direction of orbital angular momentum. Depending on the
mass and spin of the binary, the sensitive radius can vary
from about 250 Mpc up to over 1 Gpc. Over this range,
larger masses are detectable to further distances. Spins
which are aligned with the orbital angular momentum tend
to increase the sensitive radius, while antialigned spins
make the systems more difficult to detect. For the mass/spin
bin most like GW150914, 60
–
90 M
⊙
, the sensitive radius
of the searches is between 400 and 600 Mpc.
V. SOURCE CHARACTERIZATION
In
[29]
, we present estimates for the parameters of the
binary black hole model that best describes GW150914.
These parameters include the masses and spins of the
binary components, and their posterior distributions re-
present our most complete description of the astrophysical
source. In this work, we take a complementary approach,
by using the outputs of the burst pipelines described in
Sec.
III
to characterize the event. Many of the burst pipeline
outputs are available in low latency, so this approach can
inform follow-up studies in a timely fashion. For example,
the cWB estimate of the GW150914 chirp mass was
available within minutes, and provided the first evidence
that this signal originated from merging black holes.
Likewise, low-latency position estimates are used for
counterpart searches
[28]
.
Burst analyses are also able to estimate the time evolution
of observed waveforms, a process we refer to as waveform
reconstruction. Burst waveform reconstruction algorithms
do not rely on astrophysical models. Instead, estimates of the
coherent gravitational-wave power observed by the detector
network are used to reconstruct the signal. These waveform
reconstructions are valuable: they provide an unbiased view
of the signal most consistent with the observatory data. Such
reconstructed signals can be used to classify the source type,
compare with models, and potentially identify unexpected
features. In this section, we present how the outputs of the
burst pipelines were used to estimate the source position,
reconstruct the waveform, and characterize the BBH source.
We also compare the reconstructed waveforms with a set of
numerical relativity waveforms, in order to check the
consistency of our results against the most precise class
of models available.
A. Source localization
Three burst algorithms (cWB, BayesWave, and LIB)
produce localization estimates for the GW event. These
“
skymaps
”
can be interpreted as the posterior probability
distribution of the source
’
s right ascension (
α
) and decli-
nation (
δ
) given the observed data. cWB produces skymaps
during its detection process by maximizing a constrained
likelihood on a grid over the sky; these are available
within minutes of the candidate
’
s detection. LIB and
BayesWave perform more computationally expensive
analyses, and so produce results with higher latency.
LIB uses a space of single sine-Gaussian waveforms as
its waveform model, and produces skymaps after 1 to 2 h,
whereas BayesWave maps can take as long as several days
to be produced, since it explores a larger parameter space of
superpositions of sine-Gaussian waveforms. Each algo-
rithm makes different and somewhat complementary
assumptions about the signal, and these assumptions affect
their localization estimates. By localizing signals with
multiple algorithms, we can cross-check and validate the
localization estimate and identify any systematic difference
between the algorithms
[44]
.
An overview of the skymaps used by astronomers to
search for counterparts to GW150914 may be found in
[28]
, including the cWB and LIB skymaps. Here, we
FIG. 6. Dependence of sensitive radius on spins of BBH. To
investigate the effect of spins of black holes on the detection of
BBH systems, we show the search radius
R
for each pipeline for
varying effective spins with mass ratio
q
¼
1
at FAR
¼
10
−
3
1
=
yr. The total mass range is varied from
30
–
150
M
⊙
,
while the effective spin is distributed into three bins: aligned spins
(
χ
eff
∈
½
0
.
33
;
1
), antialigned (
χ
eff
∈
½
−
1
;
−
0
.
33
) and nonspin-
ning (
χ
eff
∈
½
−
0
.
33
;
0
.
33
). The error bars represent the statistical
uncertainty of the sample. The cWB results include all three
search classes, with a corresponding trials factor.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
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122004-8
compare cWB, LIB, and BayesWave skymaps in addition
to the map produced by LALInference with binary coa-
lescence templates, which samples the posterior distribu-
tion of all signal parameters using signal waveforms that
cover the inspiral, merger and ringdown phase
[40]
.For
GW150914, we expect the LALInference map to yield a
relatively precise localization, because it assumes a wave-
form from a compact binary coalescence, instead of the
broad waveform classes used by the burst pipelines. Burst
localization algorithms produce systematically larger sky-
maps than template-based algorithms because they make
fewer assumptions about the waveform. However, the
LALInference map reported here also includes the effects
of calibration uncertainty within the detectors, which
significantly widen the uncertainty of this reconstruction
[45]
. In principle, calibration effects could also be included
in the burst skymaps, but what is shown here represents the
information that was available at the time electromagnetic
astronomy observations began
[28]
.
Figure
7
shows Mollweide projections in (
α
,
δ
) of all
skymaps considered, as well as overlays of the 50% and
90% contours in a rotated frame of reference. Figure
8
shows the marginal distributions for the polar angle from
the line-of-sight between the two LIGO detectors. This
FIG. 7. All-sky projections of several skymaps produced for GW150914. Above, each map is shown by itself in celestial coordinates.
Below, a rotated coordinate system shows contours defining the 50% and 90% confidence regions for four reconstructions.
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