of 21
GW150914: First results from the search for binary black hole
coalescence with Advanced LIGO
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 9 March 2016; published 7 June 2016)
On September 14, 2015, at 09
50:45 UTC the two detectors of the Laser Interferometer Gravitational-
Wave Observatory (LIGO) simultaneously observed the binary black hole merger GW150914. We report
the results of a matched-filter search using relativistic models of compact-object binaries that recovered
GW150914 as the most significant event during the coincident observations between the two LIGO
detectors from September 12 to October 20, 2015 GW150914 was observed with a matched-filter signal-to-
noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203000 years, equivalent to a
significance greater than 5.1
σ
.
DOI:
10.1103/PhysRevD.93.122003
I. INTRODUCTION
On September 14, 2015, at 09
50:45 UTC the LIGO
Hanford, Washington, and Livingston, Louisiana, observa-
tories detected a signal from the binary black hole merger
GW150914
[1]
. The initial detection of the event was made
by low-latency searches for generic gravitational-wave
transients
[2]
. We report the results of a matched-filter search
using relativistic models of compact binary coalescence
waveformsthat recovered GW150914 asthe mostsignificant
event during the coincident observations between the two
LIGO detectors from September 12 to October 20, 2015.
This is a subset of the data from Advanced LIGO
s first
observational period that ended on January 12, 2016.
The binary coalescence search targets gravitational-wave
emission from compact-object binaries with individual
masses from
1
M
to
99
M
, total mass less than
100
M
and dimensionless spins up to 0.99. The search was per-
formed using two independently implemented analyses,
referred to as PyCBC
[3
5]
and GstLAL
[6
8]
.These
analyses use a common set of template waveforms
[9
11]
,
but differ in their implementations of matched filtering
[12,13]
, their use of detector data-quality information
[14]
,
the techniques used to mitigate the effect of non-Gaussian
noise transients in the detector
[6,15]
, and the methods for
estimating the noise background of the search
[4,16]
.
GW150914 was observed in both LIGO detectors
[17]
with a time-of-arrival difference of 7 ms, which is less than
the 10 ms intersite propagation time, and a combined
matched-filter signal-to-noise ratio (SNR) of 24. The search
reported a false alarm rate estimated to be less than 1 event
per 203000 years, equivalent to a significance greater than
5.1
σ
. The basic features of the GW150914 signal point to it
being produced by the coalescence of two black holes
[1]
.
The best-fit template parameters from the search are
consistent with detailed parameter estimation that identifies
GW150914 as a near-equal mass black hole binary system
with source-frame masses
36
þ
5
4
M
and
29
þ
4
4
M
at the
90% credible level
[18]
.
The second most significant candidate event in the
observation period (referred to as LVT151012) was
reported on October 12, 2015, at 09
54:43 UTC with a
combined matched-filter SNR of 9.6. The search reported a
false alarm rate of 1 per 2.3 years and a corresponding false
alarm probability of 0.02 for this candidate event. Detector
characterization studies have not identified an instrumental
or environmental artifact as causing this candidate event
[14]
. However, its false alarm probability is not sufficiently
low to confidently claim this candidate event as a signal
[19]
. Detailed waveform analysis of this candidate event
indicates that it is also a binary black hole merger with
source frame masses
23
þ
18
6
M
and
13
þ
4
5
M
,ifitisof
astrophysical origin.
This paper is organized as follows: Sec.
II
gives an
overview of the compact binary coalescence search and the
methods used. Sections
III
and
IV
describe the construction
and tuning of the two independently implemented analyses
used in the search. Section
V
presents the results of the
search, and follow-up of the two most significant candidate
events, GW150914 and LVT151012.
II. SEARCH DESCRIPTION
The binary coalescence search
[20
27]
reported here
targets gravitational waves from binary neutron stars,
binary black holes, and neutron star
black hole binaries,
using matched filtering
[28]
with waveforms predicted by
general relativity. Both the PyCBC and GstLAL analyses
correlate the detector data with template waveforms that
model the expected signal. The analyses identify candidate
events that are detected at both observatories consistent
*
Full author list given at the end of the article.
PHYSICAL REVIEW D
93,
122003 (2016)
2470-0010
=
2016
=
93(12)
=
122003(21)
122003-1
© 2016 American Physical Society
with the 10 ms intersite propagation time. Events are
assigned a detection-statistic value that ranks their like-
lihood of being a gravitational-wave signal. This detection
statistic is compared to the estimated detector noise back-
ground to determine the probability that a candidate event is
due to detector noise.
We report on a search using coincident observations
between the two Advanced LIGO detectors
[29]
in
Hanford, Washington (H1), and in Livingston, Louisiana
(L1), from September 12 to October 20, 2015. During these
38.6 days, the detectors were in coincident operation for a
total of 18.4 days. Unstable instrumental operation and
hardware failures affected 20.7 hours of these coincident
observations. These data are discarded and the remaining
17.5 days are used as input to the analyses
[14]
. The
analyses reduce this time further by imposing a minimum
length over which the detectors must be operating stably;
this is different between the two analyses (2064 s for
PyCBC and 512 s for GstLAL), as described in Secs.
III
and
IV
. After applying this cut, the PyCBC analysis
searched 16 days of coincident data and the GstLAL
analysis searched 17 days of coincident data. To prevent
bias in the results, the configuration and tuning of the
analyses were determined using data taken prior to
September 12, 2015.
A gravitational-wave signal incident on an interferom-
eter alters its arm lengths by
δ
L
x
and
δ
L
y
, such that
their measured difference is
Δ
L
ð
t
Þ¼
δ
L
x
δ
L
y
¼
h
ð
t
Þ
L
,
where
h
ð
t
Þ
is the gravitational-wave metric perturbation
projected onto the detector, and
L
is the unperturbed arm
length
[30]
. The strain is calibrated by measuring the
detector
s response to test mass motion induced by photon
pressure from a modulated calibration laser beam
[31]
.
Changes in the detector
s thermal and alignment state cause
small, time-dependent systematic errors in the calibration
[31]
. The calibration used for this search does not include
these time-dependent factors. Appendix
A
demonstrates
that neglecting the time-dependent calibration factors does
not affect the result of this search.
The gravitational waveform
h
ð
t
Þ
depends on the chirp
mass of the binary,
M
¼ð
m
1
m
2
Þ
3
=
5
=
ð
m
1
þ
m
2
Þ
1
=
5
[32,33]
;
the symmetric mass ratio
η
¼ð
m
1
m
2
Þ
=
ð
m
1
þ
m
2
Þ
2
[34]
;
and the angular momentum of the compact objects
χ
1
;
2
¼
c
S
1
;
2
=Gm
2
1
;
2
[35,36]
(the compact object
s dimensionless
spin), where
S
1
;
2
is the angular momentum of the compact
objects. The effect of spin on the waveform depends also on
the ratio between the component objects
masses
[37]
.
Parameters which affect the overall amplitude and phase of
the signal as observed in the detector are maximized over in
the matched-filter search, but can be recovered through full
parameter estimation analysis
[18]
. The search parameter
space is therefore defined by the limits placed on the
compact objects
masses and spins. The minimum compo-
nent masses of the search are determined by the lowest
expected neutron star mass, which we assume to be
1
M
[38]
. There is no known maximum black hole mass
[39]
;
however we limit this search to binaries with a total mass
less than
M
¼
m
1
þ
m
2
100
M
. The LIGO detectors
are sensitive to higher mass binaries, however; the results of
searches for binaries that lie outside this search space will
be reported in future publications.
The limit on the spins of the compact objects
χ
1
;
2
are
informed by radio and x-ray observations of compact-
object binaries. The shortest observed pulsar period in a
double neutron star system is 22 ms
[40]
, corresponding to
a spin of 0.02. Observations of x-ray binaries indicate that
astrophysical black holes may have near extremal spins
[41]
. In constructing the search, we assume that compact
objects with masses less than
2
M
are neutron stars and
we limit the magnitude of the component object
s spin to
0
χ
0
.
05
. For higher masses, the spin magnitude is
limited to
0
χ
0
.
9895
, with the upper limit set by our
ability to generate valid template waveforms at high spins
[9]
. At current detector sensitivity, limiting spins to
χ
1
;
2
0
.
05
for
m
1
;
2
2
M
does not reduce the search
sensitivity for sources containing neutron stars with spins
up to 0.4, the spin of the fastest-spinning millisecond pulsar
[42]
. Figure
1
shows the boundaries of the search parameter
space in the component-mass plane, with the boundaries on
the mass-dependent spin limits indicated.
Since the parameters of signals are not known in adva-
nce, each detector
s output is filtered against a discrete bank
of templates that span the search target space
[21,43
46]
.
The placement of templates depends on the shape of the
power spectrum of the detector noise. Both analyses use a
low-frequency cutoff of 30 Hz for the search. The average
FIG. 1. The four-dimensional search parameter space covered
by the template bank shown projected into the component-mass
plane, using the convention
m
1
>m
2
. The lines bound mass
regions with different limits on the dimensionless aligned-spin
parameters
χ
1
and
χ
2
. Each point indicates the position of a
template in the bank. The circle highlights the template that best
matches GW150914. This does not coincide with the best-fit
parameters due to the discrete nature of the template bank.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
93,
122003 (2016)
122003-2
noise power spectral density of the LIGO detectors was
measured over the period of September 12 to September 26,
2015. The harmonic mean of these noise spectra from the
two detectors was used to place a single template bank
that was used for the duration of the search
[4,47]
. The
templates are placed using a combination of geometric
and stochastic methods
[7,11,48,49]
such that the loss in
matched-filter SNR caused by its discrete nature is
3%
.
Approximately 250,000 template waveforms are used to
cover this parameter space, as shown in Fig.
1
.
The performance of the template bank is measured by
the fitting factor
[50]
; this is the fraction of the maximum
signal-to-noise ratio that can be recovered by the template
bank for a signal that lies within the region covered by
the bank. The fitting factor is measured numerically by
simulating a signal and determining the maximum recov-
ered matched-filter SNR over the template bank. Figure
2
shows the resulting distribution of fitting factors obtained
for the template bank over the observation period. The loss
in matched-filter SNR is less than 3% for more than 99% of
the
10
5
simulated signals.
The template bank assumes that the spins of the two
compact objects are aligned with the orbital angular
momentum. The resulting templates can nonetheless effec-
tively recover systems with misaligned spins in the param-
eter-space region of GW150914. To measure the effect
of neglecting precession in the template waveforms, we
compute the effective fitting factor which weights the
fraction of the matched-filter SNR recovered by the
amplitude of the signal
[51]
. When a signal with a poor
orientation is projected onto the detector, the amplitude of
the signal may be too small to detect even if there were no
mismatch between the signal and the template; the
weighting in the effective fitting accounts for this.
Figure
3
shows the effective fitting factor for simulated
signals from a population of simulated precessing binary
black holes that are uniform in comoving volume
[52,53]
.
The effective fitting factor is lowest at high mass ratios and
low total mass, where the effects of precession are more
pronounced. In the region close to the parameters of
GW150914 the aligned-spin template bank is sensitive
to a large fraction of precessing signals
[53]
.
In addition to possible gravitational-wave signals, the
detector strain contains a stationary noise background that
primarily arises from photon shot noise at high frequencies
and seismic noise at low frequencies. In the mid-frequency
range, detector commissioning has not yet reached the
point where test mass thermal noise dominates, and the
noise at mid frequencies is poorly understood
[14,17,54]
.
The detector strain data also exhibit nonstationarity and
non-Gaussian noise transients that arise from a variety of
instrumental or environmental mechanisms. The measured
strain
s
ð
t
Þ
is the sum of possible gravitational-wave signals
h
ð
t
Þ
and the different types of detector noise
n
ð
t
Þ
.
To monitor environmental disturbances and their influ-
ence on the detectors, each observatory site is equipped
with an array of sensors
[55]
. Auxiliary instrumental
channels also record the interferometer
s operating point
and the state of the detector
s control systems. Many noise
transients have distinct signatures, visible in environmental
or auxiliary data channels that are not sensitive to gravi-
tational waves. When a noise source with known physical
FIG. 2. Cumulative distribution of fitting factors obtained with
the template bank for a population of simulated aligned-spin
binary black hole signals. Less than 1% of the signals have a
matched-filter SNR loss greater than 3%, demonstrating that the
template bank has good coverage of the target search space.
FIG. 3. The effective fitting factor between simulated precess-
ing binary black hole signals and the template bank used for the
search as a function of detector-frame total mass and mass ratio,
averaged over each rectangular tile. The effective fitting factor
gives the volume-averaged reduction in the sensitive distance of
the search at fixed matched-filter SNR due to mismatch between
the template bank and signals. The cross shows the location of
GW150914. The high effective fitting factor near GW150914
demonstrates that the aligned-spin template bank used in this
search can effectively recover systems with misaligned spins and
similar masses to GW150914.
GW150914: FIRST RESULTS FROM THE SEARCH FOR
...
PHYSICAL REVIEW D
93,
122003 (2016)
122003-3
coupling between these channels and the detector strain
data is active, a data-quality veto is created that is used to
exclude these data from the search
[14]
. In the GstLAL
analysis, time intervals flagged by data quality vetoes are
removed prior to the filtering. In the PyCBC analysis, these
data quality vetoes are applied after filtering. A total of
2 hours is removed from the analysis by data quality vetoes.
Despite these detector characterization investigations, the
data still contain nonstationary and non-Gaussian noise
which can affect the astrophysical sensitivity of the search.
Both analyses implement methods to identify loud, short-
duration noise transients and remove them from the strain
data before filtering.
The PyCBC and GstLAL analyses calculate the
matched-filter SNR for each template and each detector
s
data
[12,56]
. In the PyCBC analysis, sources with total
mass less than
4
M
are modeled by computing the inspiral
waveform accurate to third-and-a-half post-Newtonian
order
[34,57,58]
. To model systems with total mass larger
than
4
M
, we use templates based on the effective-one-
body (EOB) formalism
[59]
, which combines results from
the post-Newtonian approach
[34,58]
with results from
black hole perturbation theory and numerical relativity
[9,60]
to model the complete inspiral, merger and ringdown
waveform. The waveform models used assume that the
spins of the merging objects are aligned with the orbital
angular momentum. The GstLAL analysis uses the
same waveform families, but the boundary between post-
Newtonian and EOB models is set at
M
¼
1
.
74
M
. Both
analyses identify maxima of the matched-filter SNR
(triggers) over the signal time of arrival.
To suppress large SNR values caused by non-Gaussian
detector noise, the two analyses calculate additional tests to
quantify the agreement between the data and the template.
The PyCBC analysis calculates a chi-squared statistic to
test whether the data in several different frequency bands
are consistent with the matching template
[15]
. The value of
the chi-squared statistic is used to compute a reweighted
SNR for each maxima. The GstLAL analysis computes a
goodness-of-fit between the measured and expected SNR
time series for each trigger. The matched-filter SNR and
goodness-of-fit values for each trigger are used as param-
eters in the GstLAL ranking statistic.
Both analyses enforce coincidence between detectors by
selecting trigger pairs that occur within a 15 ms window
and come from the same template. The 15 ms window is
determined by the 10 ms intersite propagation time plus
5 ms for uncertainty in arrival time of weak signals. The
PyCBC analysis discards any triggers that occur during the
time of data-quality vetoes prior to computing coincidence.
The remaining coincident events are ranked based on the
quadrature sum of the reweighted SNR from both detectors
[4]
. The GstLAL analysis ranks coincident events using
a likelihood ratio that quantifies the probability that a
particular set of coincident trigger parameters is due to a
signal versus the probability of obtaining the same set of
parameters from noise
[6]
.
The significance of a candidate event is determined by
the search background. This is the rate at which detector
noise produces events with a detection-statistic value equal
to or higher than the candidate event (the false alarm rate).
Estimating this background is challenging for two reasons:
the detector noise is nonstationary and non-Gaussian, so its
properties must be empirically determined; and it is not
possible to shield the detector from gravitational waves to
directly measure a signal-free background. The specific
procedure used to estimate the background is different for
the two analyses.
To measure the significance of candidate events, the
PyCBC analysis artificially shifts the timestamps of one
detector
s triggers by an offset that is large compared to the
intersite propagation time, and a new set of coincident
events is produced based on this time-shifted data set. For
instrumental noise that is uncorrelated between detectors
this is an effective way to estimate the background. To
account for the search background noise varying across the
target signal space, candidate and background events are
divided into three search classes based on template length.
To account for having searched multiple classes, the
measured significance is decreased by a trials factor equal
to the number of classes
[61]
.
The GstLAL analysis measures the noise background
using the distribution of triggers that are not coincident in
time. To account for the search background noise varying
across the target signal space, the analysis divides the
template bank into 248 bins. Signals are assumed to be
equally likely across all bins and it is assumed that noise
triggers are equally likely to produce a given SNR and
goodness-of-fit value in any of the templates within a single
bin. The estimated probability density function for the
likelihood statistic is marginalized over the template bins
and used to compute the probability of obtaining a noise
event with a likelihood value larger than that of a
candidate event.
The results of the independent analyses are two separate
lists of candidate events, with each candidate event
assigned a false alarm probability and false alarm rate.
These quantities are used to determine if a gravitational-
wave signal is present in the search. Simulated signals are
added to the input strain data to validate the analyses, as
described in Appendix
B
.
III. PYCBC ANALYSIS
The PyCBC analysis
[3
5]
uses fundamentally the same
methods
[12,15,62
72]
as those used to search for gravi-
tational waves from compact binaries in the Initial LIGO
and Virgo detector era
[73
84]
, with the improvements
described in Refs.
[3,4]
. In this section, we describe the
configuration and tuning of the PyCBC analysis used in
this search. To prevent bias in the search result, the
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
93,
122003 (2016)
122003-4
configuration of the analysis was determined using data
taken prior to the observation period searched. When
GW150914 was discovered by the low-latency transient
searches
[1]
, all tuning of the PyCBC analysis was frozen
to ensure that the reported false alarm probabilities are
unbiased. No information from the low-latency transient
search is used in this analysis.
Of the 17.5 days of data that are used as input to the
analysis, the PyCBC analysis discards times for which
either of the LIGO detectors was in its observation state
for less than 2064s; shorter intervals are considered to
be unstable detector operation by this analysis and are
removed from the observation time. After discarding time
removed by data-quality vetoes and periods when detector
operation is considered unstable the observation time
remaining is 16 days.
For each template
h
ð
t
Þ
and for the strain data from a
single detector
s
ð
t
Þ
, the analysis calculates the square of the
matched-filter SNR defined by
[12]
ρ
2
ð
t
Þ
1
h
h
j
h
i
jh
s
j
h
t
Þj
2
;
ð
1
Þ
where the correlation is defined by
h
s
j
h
t
Þ¼
4
Z
0
~
s
ð
f
Þ
~
h

ð
f
Þ
S
n
ð
f
Þ
e
2
π
ift
d
f;
ð
2
Þ
where
~
s
ð
f
Þ
is the Fourier transform of the time-domain
quantity
s
ð
t
Þ
given by
~
s
ð
f
Þ¼
Z
−∞
s
ð
t
Þ
e
2
π
ift
d
t:
ð
3
Þ
The quantity
S
n
ðj
f
is the one-sided average power
spectral density of the detector noise, which is recalculated
every 2048s (in contrast to the fixed spectrum used in
template bank construction). Calculation of the matched-
filter SNR in the frequency domain allows the use of the
computationally efficient fast Fourier transform
[85,86]
.
The square of the matched-filter SNR in Eq.
(1)
is
normalized by
h
h
j
h
4
Z
0
~
h
ð
f
Þ
~
h

ð
f
Þ
S
n
ð
f
Þ
d
f;
ð
4
Þ
so that its mean value is 2, if
s
ð
t
Þ
contains only stationary
noise
[87]
.
Non-Gaussian noise transients in the detector can pro-
duce extended periods of elevated matched-filter SNR
that increase the search background
[4]
. To mitigate this,
a time-frequency excess power (burst) search
[88]
is used
to identify high-amplitude, short-duration transients that
are not flagged by data-quality vetoes. If the burst search
generates a trigger with a burst SNR exceeding 300, the
PyCBC analysis vetoes these data by zeroing out 0.5s of
s
ð
t
Þ
centered on the time of the trigger. The data are
smoothly rolled off using a Tukey window during the 0.25 s
before and after the vetoed data. The threshold of 300 is
chosen to be significantly higher than the burst SNR
obtained from plausible binary signals. For comparison,
the burst SNR of GW150914 in the excess power search is
10
. A total of 450 burst-transient vetoes is produced in the
two detectors, resulting in 225 s of data removed from
the search. A time-frequency spectrogram of the data at the
time of each burst-transient veto was inspected to ensure
that none of these windows contained the signature of an
extremely loud binary coalescence.
The analysis places a threshold of 5.5 on the single-
detector matched-filter SNR and identifies maxima of
ρ
ð
t
Þ
with respect to the time of arrival of the signal. For each
maximum we calculate a chi-squared statistic to determine
whether the data in several different frequency bands are
consistent with the matching template
[15]
. Given a
specific number of frequency bands
p
, the value of the
reduced chi-squared is given by
χ
2
r
¼
p
2
p
2
1
h
h
j
h
i
X
p
i
¼
1




h
s
j
h
i
i
h
s
j
h
i
p




2
;
ð
5
Þ
where
h
i
is the subtemplate corresponding to the
i
th
frequency band. Values of
χ
2
r
near unity indicate that the
signal is consistent with a coalescence. To suppress triggers
from noise transients with large matched-filter SNR,
ρ
ð
t
Þ
is
reweighted by
[64,82]
ˆ
ρ
¼

ρ
=
½ð
1
þð
χ
2
r
Þ
3
Þ
=
2

1
6
;
if
χ
2
r
>
1
;
ρ
;
if
χ
2
r
1
.
ð
6
Þ
Triggers that have a reweighted SNR
ˆ
ρ
<
5
or that occur
during times subject to data-quality vetoes are discarded.
The template waveforms span a wide region of time-
frequency parameter space and the susceptibility of the
analysis to a particular type of noise transient can vary
across the search space. This is demonstrated in Fig.
4
which shows the cumulative number of noise triggers as a
function of reweighted SNR for Advanced LIGO engineer-
ing run data taken between September 2 and September 9,
2015. The response of the template bank to noise transients
is well characterized by the gravitational-wave frequency
at the template
s peak amplitude,
f
peak
. Waveforms with a
lower peak frequency have fewer cycles in the detector
s
most sensitive frequency band from 30
2000 Hz
[17,54]
,
and so are less easily distinguished from noise transients by
the reweighted SNR.
The number of bins in the chi-squared test is a tunable
parameter in the analysis
[4]
. Previous searches used a fixed
number of bins
[89]
with the most recent Initial LIGO and
Virgo searches using
p
¼
16
bins for all templates
[82,83]
.
Investigations on data from LIGO
s sixth science run
GW150914: FIRST RESULTS FROM THE SEARCH FOR
...
PHYSICAL REVIEW D
93,
122003 (2016)
122003-5
[83,90]
showed that better noise rejection is achieved with a
template-dependent number of bins. The left two panels of
Fig.
4
show the cumulative number of noise triggers with
p
¼
16
bins used in the chi-squared test. Empirically, we
find that choosing the number of bins according to
p
¼
0
.
4
ð
f
peak
=
Hz
Þ
2
=
3
ð
7
Þ
gives better suppression of noise transients in Advanced
LIGO data, as shown in the right panels of Fig.
4
.
The PyCBC analysis enforces signal coincidence
between detectors by selecting trigger pairs that occur
within a 15 ms window and come from the same template.
We rank coincident events based on the quadrature sum
ˆ
ρ
c
of the
ˆ
ρ
from both detectors
[4]
. The final step of the
analysis is to cluster the coincident events, by selecting
those with the largest value of
ˆ
ρ
c
in each time window of
10 s. Any other events in the same time window are
discarded. This ensures that a loud signal or transient noise
artifact gives rise to at most one candidate event
[4]
.
The significance of a candidate event is determined by
the rate at which detector noise produces events with a
detection-statistic value equal to or higher than that of the
candidate event. To measure this, the analysis creates a
background data set
by artificially shifting the time-
stamps of one detector
s triggers by many multiples of 0.1 s
and computing a new set of coincident events. Since the
time offset used is always larger than the time-coincidence
window, coincident signals do not contribute to this back-
ground. Under the assumption that noise is not correlated
between the detectors
[14]
, this method provides an
unbiased estimate of the noise background of the analysis.
To account for the noise background varying across the
target signal space, candidate and background events are
divided into different search classes based on template
length. Based on empirical tuning using Advanced LIGO
engineering run data taken between September 2 and
September 9, 2015, we divide the template space into three
classes according to (i)
M
<
1
.
74
M
, (ii)
M
1
.
74
M
and
f
peak
220
Hz, and (iii)
M
1
.
74
M
and
f
peak
<
220
Hz. The significance of candidate events is measured
against the background from the same class. For each candi-
date event, we compute the false alarm probability
F
.Thisis
the probability of finding one or more noise background
events in the observation time with a detection-statistic value
above that of the candidate event, given by
[4,91]
F
ð
ˆ
ρ
c
Þ
P
ð
1
noise event above
ˆ
ρ
c
j
T; T
b
Þ
¼
1
exp

T
1
þ
n
b
ð
ˆ
ρ
c
Þ
T
b

;
ð
8
Þ
where
T
is the observation time of the search,
T
b
is the
background time, and
n
b
ð
ˆ
ρ
c
Þ
is the number of noise back-
ground triggers above the candidate event
s reweighted
SNR
ˆ
ρ
c
.
Equation
(8)
is derived assuming Poisson statistics for
the counts of time-shifted background events, and for the
count of coincident noise events in the search
[4,91]
.This
assumption requires that different time-shifted analyses
(i.e. with different relative shifts between detectors) give
independent realizations of a counting experiment for
noise background events. We expect different time shifts
to yield independent event counts since the 0.1 s offset
time is greater than the 10 ms gravitational-wave travel
time between the sites plus the
1
ms autocorrelation
length of the templates. To test the independence of event
counts over different time shifts over this observation
FIG. 4. Distributions of noise triggers over reweighted SNR
ˆ
ρ
,
for Advanced LIGO engineering run data taken between
September 2 and September 9, 2015. Each line shows triggers
from templates within a given range of gravitational-wave
frequency at maximum strain amplitude,
f
peak
. Left: Triggers
obtained from H1, L1 data respectively, using a fixed number of
p
¼
16
frequency bands for the chi-squared test. Right: Triggers
obtained with the number of frequency bands determined by the
function
p
¼
0
.
4
ð
f
peak
=
Hz
Þ
2
=
3
. Note that while noise distri-
butions are suppressed over the whole template bank with the
optimized choice of
p
, the suppression is strongest for templates
with lower
f
peak
values. Templates that have a
f
peak
<
220
Hz
produce a large tail of noise triggers with high reweighted SNR
even with the improved chi-squared test tuning; thus we separate
these templates from the rest of the bank when calculating the
noise background.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
93,
122003 (2016)
122003-6
period, we compute the differences in the number of
background events having
ˆ
ρ
c
>
9
between consecutive
time shifts. Figure
5
shows that the measured differences
on these data follow the expected distribution for the
difference between two independent Poisson random
variables
[92]
, confirming the independence of time-
shifted event counts.
If a candidate event
s detection-statistic value is larger
than that of any noise background event, as is the case
for GW150914, then the PyCBC analysis places an upper
bound on the candidate
s false alarm probability. After
discarding time removed by data-quality vetoes and
periods when the detector is in stable operation for less
than 2064 seconds, the total observation time remaining is
T
¼
16
days. Repeating the time-shift procedure
10
7
times on these data produces a noise background analysis
time equivalent to
T
b
¼
608000
years. Thus, the smallest
false alarm probability that can be estimated in this analysis
is approximately
F
¼
7
×
10
8
. Since we treat the search
parameter space as three independent classes, each of
which may generate a false positive result, this value
should be multiplied by a trials factor or look-elsewhere
effect
[61]
of 3, resulting in a minimum measurable false
alarm probability of
F
¼
2
×
10
7
. The results of the
PyCBC analysis are described in Sec.
V
.
IV. GSTLAL ANALYSIS
The GstLAL
[93]
analysis implements a time-domain
matched-filter search
[6]
using techniques that were devel-
oped to perform the near real-time compact-object binary
searches
[7,8]
. To accomplish this, the data
s
ð
t
Þ
and
templates
h
ð
t
Þ
are each whitened in the frequency domain
by dividing them by an estimate of the power spectral
density of the detector noise. An estimate of the stationary
noise amplitude spectrum is obtained with a combined
median
geometric-mean modification of Welch
s method
[8]
. This procedure is applied piecewise on overlapping
Hann-windowed time-domain blocks that are subsequently
summed together to yield a continuous whitened time
series
s
w
ð
t
Þ
. The time-domain whitened template
h
w
ð
t
Þ
is
then convolved with the whitened data
s
w
ð
t
Þ
to obtain the
matched-filter SNR time series
ρ
ð
t
Þ
for each template.
By the convolution theorem,
ρ
ð
t
Þ
obtained in this manner is
the same as the
ρ
ð
t
Þ
obtained by the frequency domain
filtering in Eq.
(1)
.
Of the 17.5 days of data that are used as input to the
analysis, the GstLAL analysis discards times for which
either of the LIGO detectors is in its observation state for
less than 512 s in duration. Shorter intervals are considered
to be unstable detector operation by this analysis and are
removed from the observation time. After discarding time
removed by data-quality vetoes and periods when the
detector operation is considered unstable the observation
time remaining is 17 days. To remove loud, short-duration
noise transients, any excursions in the whitened data that
are greater than
50
σ
are removed with 0.25 s padding. The
intervals of
s
w
ð
t
Þ
vetoed in this way are replaced with zeros.
The cleaned whitened data are the input to the matched-
filtering stage.
Adjacent waveforms in the template bank are highly
correlated. The GstLAL analysis takes advantage of this to
reduce the computational cost of the time-domain corre-
lation. The templates are grouped by chirp mass and spin
into 248 bins of
1000
templates each. Within each bin, a
reduced set of orthonormal basis functions
ˆ
h
ð
t
Þ
is obtained
via a singular value decomposition of the whitened tem-
plates. We find that the ratio of the number of orthonormal
basis functions to the number of input waveforms is
0
.
01
0
.
10
, indicating a significant redundancy in each
bin. The set of
ˆ
h
ð
t
Þ
in each bin is convolved with the
whitened data; linear combinations of the resulting time
series are then used to reconstruct the matched-filter SNR
time series for each template. This decomposition allows
for computationally efficient time-domain filtering and
reproduces the frequency-domain matched filter
ρ
ð
t
Þ
to
within 0.1%
[6,56,94]
.
Peaks in the matched-filter SNR for each detector and
each template are identified over 1 s windows. If the peak is
above a matched-filter SNR of 4, it is recorded as a trigger.
For each trigger, the matched-filter SNR time series around
the trigger is checked for consistency with a signal by
comparing the template
s autocorrelation function
R
ð
t
Þ
to
the matched-filter SNR time series
ρ
ð
t
Þ
. The residual found
after subtracting the autocorrelation function forms a
goodness-of-fit test,
FIG. 5. The distribution of the differences in the number of
events between consecutive time shifts, where
C
i
denotes the
number of events in the
i
th time shift. The green line shows the
predicted distribution for independent Poisson processes with
means equal to the average event rate per time shift. The blue
histogram shows the distribution obtained from time-shifted
analyses. The variance of the time-shifted background distribu-
tion is 1.996, consistent with the predicted variance of 2. The
distribution of background event counts in adjacent time shifts is
well modeled by independent Poisson processes.
GW150914: FIRST RESULTS FROM THE SEARCH FOR
...
PHYSICAL REVIEW D
93,
122003 (2016)
122003-7
ξ
2
¼
1
μ
Z
t
p
þ
δ
t
t
p
δ
t
d
t
j
ρ
ð
t
p
Þ
R
ð
t
Þ
ρ
ð
t
Þj
2
;
ð
9
Þ
where
t
p
is the time at the peak matched-filter SNR
ρ
ð
t
p
Þ
,
and
δ
t
is a tunable parameter. A suitable value for
δ
t
was
found to be 85.45 ms (175 samples at a 2048 Hz sampling
rate). The quantity
μ
normalizes
ξ
2
such that a well-fit
signal has a mean value of 1 in Gaussian noise
[8]
. The
ξ
2
value is recorded with the trigger.
Each trigger is checked for time coincidence with
triggers from the same template in the other detector. If
two triggers occur from the same template within 15 ms in
both detectors, a coincident event is recorded. Coincident
events are ranked according to a multidimensional like-
lihood ratio
L
[16,95]
and then clustered in a

4
s time
window. The likelihood ratio ranks candidate events by the
ratio of the probability of observing matched-filter SNR
and
ξ
2
from signals (h) versus obtaining the same param-
eters from noise (n). Since the orthonormal filter decom-
position already groups templates into regions with high
overlap, we expect templates in each group to respond
similarly to noise. We use the template group
θ
i
as an
additional parameter in the likelihood ratio to account for
how different regions of the compact binary parameter
space are affected differently by noise processes. The
likelihood ratio is thus
L
¼
p
ð
x
H
;
x
L
;D
H
;D
L
j
θ
i
;
h
Þ
p
ð
x
H
j
θ
i
;
n
Þ
p
ð
x
L
j
θ
i
;
n
Þ
;
ð
10
Þ
where
x
d
¼f
ρ
d
;
ξ
2
d
g
are the matched-filter SNR and
ξ
2
in
each detector, and
D
is a parameter that measures the
distance sensitivity of the given detector during the time of
a trigger.
The numerator of the likelihood ratio is generated using
an astrophysical model of signals distributed isotropically
in the nearby Universe to calculate the joint SNR distri-
bution in the two detectors
[16]
. The
ξ
2
distribution for the
signal hypothesis assumes that the signal agrees to within
90%
of the template waveform and that the nearby noise
is Gaussian. We assume that all
θ
i
are equally likely for
signals.
The noise is assumed to be uncorrelated between
detectors. The denominator of the likelihood ratio therefore
factors into the product of the distribution of noise triggers
in each detector,
p
ð
x
d
j
θ
i
;
n
Þ
. We estimate these using a
two-dimensional kernel density estimation
[96]
constructed
from all of the single-detector triggers not found in
coincidence in a single bin.
The likelihood ratio
L
provides a ranking of events such
that larger values of
L
are associated with a higher
probability of the data containing a signal. The likelihood
ratio itself is not the probability that an event is a signal, nor
does it give the probability that an event was caused by
noise. Computing the probability that an event is a signal
requires additional prior assumptions. Instead, for each
candidate event, we compute the false alarm probability
F
.
This is the probability of finding one or more noise
background events with a likelihood-ratio value greater
than or equal to that of the candidate event. Assuming
Poisson statistics for the background, this is given by
F
ð
L
Þ
P
ð
L
j
T;
n
Þ¼
1
exp
½
λ
ð
L
j
T;
n
Þ
:
ð
11
Þ
Instead of using time shifts, the GstLAL analysis estimates
the Poisson rate of background events
λ
ð
L
j
T;
n
Þ
as
λ
ð
L
j
T;
n
Þ¼
M
ð
T
Þ
P
ð
L
j
n
Þ
;
ð
12
Þ
where
M
ð
T
Þ
is the number of coincident events found
above threshold in the analysis time
T
, and
P
ð
L
j
n
Þ
is the
probability of obtaining one or more events from noise
with a likelihood ratio
L
(the survival function). We find
this by estimating the survival function in each template
bin and then marginalize over the bins; i.e.,
P
ð
L
j
n
Þ¼
P
i
P
ð
L
j
θ
i
;
n
Þ
P
ð
θ
i
j
n
Þ
. In a single bin, the survival
function is
P
ð
L
j
θ
i
;
n
Þ¼
1
Z
S
ð
L
Þ
p
0
ð
x
H
j
θ
i
;
n
Þ
p
0
ð
x
L
j
θ
i
;
n
Þ
d
x
H
d
x
L
:
ð
13
Þ
Here,
p
0
ð
x
d
j
θ
i
;
n
Þ
are estimates of the distribution of
triggers in each detector including all of the single-detector
triggers, whereas the estimate of
p
ð
x
d
j
θ
i
;
n
Þ
includes only
those triggers which were not coincident. This is consistent
with the assumption that the false alarm probability is
computed assuming all events are noise.
The integration region
S
ð
L
Þ
is the volume of the four-
dimensional space of
x
d
for which the likelihood ratios
are less than
L
. We find this by Monte Carlo integration of
our estimates of the single-detector noise distributions
p
0
ð
x
d
j
θ
i
;
n
Þ
. This is approximately equal to the number of
coincidences that can be formed from the single-detector
triggers with likelihood ratios
L
divided by the total
number of possible coincidences. We therefore reach a
minimum possible estimate of the survival function, without
extrapolation, at the
L
for which
p
0
ð
x
H
j
θ
i
;
n
Þ
p
0
ð
x
L
j
θ
i
;
n
Þ
1
=N
H
ð
θ
i
Þ
N
L
ð
θ
i
Þ
, where
N
d
ð
θ
i
Þ
are the total number of
triggers in each detector in the
i
th bin.
GW150914 was more significant than any other combi-
nation of triggers. For that reason, we are interested in
knowing the minimum false alarm probability that can be
computed by the GstLAL analysis. All of the triggers in a
template bin, regardless of the template from which they
came, are used to construct the single-detector probability
density distributions
p
0
within that bin. The false alarm
probability estimated by the GstLAL analysis is the
probability that noise triggers occur within a

15
ms time
window
and
occur in the same template. Under the
assumption that triggers are uniformly distributed over
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
93,
122003 (2016)
122003-8
the bins, the minimum possible false alarm probability that
can be computed is
MN
bins
=
ð
N
H
N
L
Þ
, where
N
bins
is the
number of bins used,
N
H
is the total number of triggers in
H, and
N
L
is the total number of triggers in L. For the
present analysis,
M
1
×
10
9
,
N
H
N
L
1
×
10
11
, and
N
bins
is 248, yielding a minimum value of the false alarm
probability of
10
11
.
We cannot rule out the possibility that noise produced by
the detectors violates the assumption that it is uniformly
distributed among the templates within a bin. If we consider
a more conservative noise hypothesis that does not assume
that triggers are uniformly distributed within a bin and
instead considers each template as a separate
θ
i
bin, we can
evaluate the minimum upper bound on the false alarm
probability of GW150914. This assumption would produce
a larger minimum false alarm probability value by approx-
imately the ratio of the number of templates to the present
number of bins. Under this noise hypothesis, the minimum
value of the false alarm probability would be
10
8
, which
is consistent with the minimum false alarm probability
bound of the PyCBC analysis.
Figure
6
shows
p
ð
x
H
j
n
Þ
and
p
ð
x
L
j
n
Þ
in the warm
colormap. The cool colormap includes triggers that are
also found in coincidence, i.e.,
p
0
ð
x
H
j
n
Þ
and
p
0
ð
x
L
j
n
Þ
,
which is the probability density function used to estimate
P
ð
L
j
n
Þ
. It has been masked to only show regions which are
not consistent with
p
ð
x
H
j
n
Þ
and
p
ð
x
L
j
n
Þ
. In both cases
θ
i
has been marginalized over in order to show all the data on
a single figure. The positions of the two loudest events,
described in the next section, are shown. Figure
6
shows
that GW150914 falls in a region without any noncoincident
triggers from any bin.
V. SEARCH RESULTS
GW150914 was observed on September 14, 2015, at
09
50:45 UTC as the most significant event by both analyses.
The individual detector triggers from GW150914 occurred
within the 10 ms intersite propagation time with a combined
matched-filter SNR of 24. Both pipelines report the same
matched-filter SNR for the individual detector triggers in the
Hanford detector (
ρ
H
1
¼
20
) and the Livingston detector
(
ρ
L
1
¼
13
). GW150914 was found with the same template
in both analyses with component masses
47
.
9
M
and
36
.
6
M
. The effective spin of the best-matching template
is
χ
eff
¼ð
c=G
Þð
S
1
=m
1
þ
S
2
=m
2
Þ
·
ð
ˆ
L
=M
Þ¼
0
.
2
, where
S
1
;
2
are the spins of the compact objects and
ˆ
L
is the direction of
the binary
s orbital angular momentum. Due to the discrete
nature of the template bank, follow-up parameter estimation
is required to accurately determine the best-fit masses and
spins of the binary
s components
[18,97]
.
The frequency at peak amplitude of the best-matching
template is
f
peak
¼
144
Hz, placing it in noise-background
class (iii) of the PyCBC analysis. Figure
7
(left) shows the
result of the PyCBC analysis for this search class. In the
time-shift analysis used to create the noise background
estimate for the PyCBC analysis, a signal may contribute
events to the background through random coincidences of
the signal in one detector with noise in the other detector
[91]
. This can be seen in the background histogram shown
by the black line. The tail is due to coincidence between the
single-detector triggers from GW150914 and noise in the
other detector. If a loud signal is in fact present, these
random time-shifted coincidences contribute to an over-
estimate of the noise background and a more conservative
FIG. 6. Two projections of parameters in the multidimensional likelihood ratio ranking for GstLAL (left: H1, right: L1). The relative
positions of GW150914 (red cross) and LVT151012 (blue plus) are indicated in the
ξ
2
=
ρ
2
vs matched-filter SNR plane. The yellow-
black colormap shows the natural logarithm of the probability density function calculated using only coincident triggers that are not
coincident between the detectors. This is the background model used in the likelihood ratio calculation. The red-blue colormap shows
the natural logarithm of the probability density function calculated from both coincident events and triggers that are not coincident
between the detectors. The distribution showing both candidate events and noncoincident triggers has been masked to only show regions
which are not consistent with the background model. Rather than showing the
θ
i
bins in which GW150914 and LVT151012 were found,
θ
i
has been marginalized over to demonstrate that no background triggers from any bin had the parameters of GW150914.
GW150914: FIRST RESULTS FROM THE SEARCH FOR
...
PHYSICAL REVIEW D
93,
122003 (2016)
122003-9
assessment of the significance of an event. Figure
7
(left)
shows that GW150914 has a reweighted SNR
ˆ
ρ
c
¼
23
.
6
,
greater than all background events in its class. This value is
also greater than all background in the other two classes.
As a result, we can only place an upper bound on the
false alarm rate, as described in Sec.
III
. This bound is
equal to the number of classes divided by the background
time
T
b
. With three classes and
T
b
¼
608000
years, we
find the false alarm rate of GW150914 to be less than
5
×
10
6
yr
1
. With an observing time of 384 hr, the false
alarm probability is
F
<
2
×
10
7
. Converting this false
alarm probability to single-sided Gaussian standard devia-
tions according to
ffiffiffi
2
p
erf
1
½
1
2
ð
1
F
Þ
, where erf
1
is
the inverse error function, the PyCBC analysis measures
the significance of GW150914 as greater than 5.1
σ
.
The GstLAL analysis reported a detection-statistic value
for GW150914 of ln
L
¼
78
, as shown in the right panel of
Fig.
7
. The GstLAL analysis estimates the false alarm
probability assuming that noise triggers are equally likely
to occur in any of the templates within a background bin.
However, as stated in Sec.
IV
, if the distribution of noise
triggers is not uniform across templates, particularly in
the part of the bank where GW150914 is observed, the
minimum false alarm probability would be higher. For this
reason we quote the more conservative PyCBC bound on
the false alarm probability of GW150914 here and in
Ref.
[1]
. However, proceeding under the assumption that
the noise triggers are equally likely to occur in any of the
templates within a background bin, the GstLAL analysis
estimates the false alarm probability of GW150914 to be
1
.
4
×
10
11
. The significance of GW150914 measured by
GstLAL is consistent with the bound placed by the PyCBC
analysis and provides additional confidence in the discov-
ery of the signal.
The difference in time of arrival between the Livingston
and Hanford detectors from the individual triggers in
the PyCBC analysis is 7.1 ms, consistent with the time
delay of
6
.
9
þ
0
.
5
0
.
4
ms recovered by parameter estimation
[18]
. Figure
8
(left) shows the matched-filter SNR
ρ
, the
χ
2
r
-
statistic, and the reweighted SNR
ˆ
ρ
for the best-matching
template over a period of

5
ms around the time of
GW150914 (we take the PyCBC trigger time in L1 as a
reference). The matched-filter SNR peaks in both detectors
at the time of the event and the value of the reduced chi-
squared statistic is
χ
2
H
1
¼
1
and
χ
2
L
1
¼
0
.
7
at the time of the
event, indicating an excellent match between the template
and the data. The reweighted SNRs of the individual
detector triggers of
ˆ
ρ
H
1
¼
19
.
5
and
ˆ
ρ
L
1
¼
13
.
3
are larger
than that of any other single-detector triggers in the
analysis; therefore the significance measurement of
5
.
1
σ
set using the 0.1 s time shifts is a conservative bound on the
false alarm probability of GW150914.
FIG. 7. Left: Search results from the PyCBC analysis. The histogram shows the number of candidate events (orange) and the number
of background events due to noise in the search class where GW150914 was found (black) as a function of the search detection statistic
and with a bin width of
Δ
ˆ
ρ
c
¼
0
.
2
. The significance of GW150914 is greater than 5.1
σ
. The scales immediately above the histogram
give the significance of an event measured against the noise backgrounds in units of Gaussian standard deviations as a function of the
detection statistic. The black background histogram shows the result of the time-shift method to estimate the noise background in the
observation period. The tail in the black-line background of the binary coalescence search is due to random coincidences of GW150914
in one detector with noise in the other detector. The significance of GW150914 is measured against the upper gray scale. The purple
background histogram is the background excluding coincidences involving GW150914 and it is the background to be used to assess the
significance of the second loudest event; the significance of this event is measured against the upper purple scale. Right: Search results
from the GstLAL analysis. The histogram shows the observed candidate events (orange) as a function of the detection statistic ln
L
. The
black line indicates the expected background from noise where candidate events have been included in the noise background probability
density function. The purple line indicates the expected background from noise where candidate events have not been included in the
noise background probability density function. The independently implemented search methods and different background estimation
method confirm the discovery of GW150914.
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
93,
122003 (2016)
122003-10
Figure
8
(right) shows

5
ms of the GstLAL matched-
filter SNR time series from each detector around the event
time together with the predicted SNR time series computed
from the autocorrelation function of the best-fit template.
The difference between the autocorrelation and the
observed matched-filter SNR is used to perform the
GstLAL waveform-consistency test. The autocorrelation
matches the observed matched-filter SNR extremely well,
with consistency test values of
ξ
H
1
¼
1
and
ξ
L
1
¼
0
.
7
.
No other triggers with comparable matched-filter SNR had
such low values of the signal-consistency test during the
entire observation period.
Both analyses have shown that the probability that
GW150914 was formed by random coincidence of detector
noise is extremely small. We therefore conclude that
GW150914 is a gravitational-wave signal. To measure
the signal parameters, we use parameter estimation meth-
ods that assume the presence of a coherent coalescing
binary signal in the data from both detectors
[18,97]
.Two
waveform models were used which included inspiral,
merger and ring-down portions of the signal: one which
includes spin components aligned with orbital angular
momentum
[60,98]
and one which includes the dominant
modulation of the signal due to orbital precession caused
by misaligned spins
[99,100]
. The parameter estimates are
described by a continuous probability density function over
the source parameters. We conclude that GW150914 is a
nearly equal mass black hole binary system of source-frame
masses
36
þ
5
4
M
and
29
þ
4
4
M
(median and 90% credible
range). The spin magnitude of the primary black hole is
constrained to be less than 0.7 with 90% probability. The
most stringent constraint on the spins of the two black holes
is on the effective spin parameter
χ
eff
¼
0
.
07
þ
0
.
16
0
.
17
. The
parameters of the best-fit template are consistent with these
values, given the discrete nature of the template bank. We
estimate GW150914 to be at a luminosity distance of
410
þ
160
180
Mpc, which corresponds to a redshift
0
.
09
þ
0
.
03
0
.
04
.
Full details of the source parameters for GW150914 are
given in Ref.
[18]
and summarized in Table
I
.
FIG. 8. Left: PyCBC matched-filter SNR (blue), reweighted SNR (purple) and
χ
2
r
(green) versus time of the best-matching template at
the time of GW150914. The top plot shows the Hanford detector and the bottom, Livingston. Right: Observed matched-filter SNR (blue)
and expected matched-filter SNR (purple) versus time for the best-matching template at the time of GW150914, as reported by the
GstLAL analysis. The expected matched-filter SNR is based on the autocorrelation of the best-matching template. The dashed black
lines indicate the
1
σ
deviations expected in Gaussian noise.
TABLE I. Parameters of the two most significant events. The false alarm rate (FAR) and false alarm probability (
F
) given here were
determined by the PyCBC pipeline; the GstLAL results are consistent with this. The source-frame chirp mass
M
, component masses
m
1
;
2
, effective spin
χ
eff
, and luminosity distance
D
L
are determined using a parameter estimation method that assumes the presence of a
coherent compact binary coalescence signal starting at 20 Hz in the data
[97]
. The results are computed by averaging the posteriors for
two model waveforms. Quoted uncertainties are 90% credible intervals that include statistical errors and systematic errors from
averaging the results of different waveform models. Further parameter estimates of GW150914 are presented in Ref.
[18]
.
Event
Time (UTC)
FAR (yr
1
)
FM
ð
M
Þ
m
1
ð
M
Þ
m
2
ð
M
Þ
χ
eff
D
L
(Mpc)
GW150914 September 14, 2015, 09
50:45
<
5
×
10
6
<
2
×
10
7
ð
>
5
.
1
σ
Þ
28
þ
2
2
36
þ
5
4
29
þ
4
4
0
.
07
þ
0
.
16
0
.
17
410
þ
160
180
LVT151012 October 12, 2015, 09
54:43
0.44
0.02
ð
2
.
1
σ
Þ
15
þ
1
1
23
þ
18
6
13
þ
4
5
0
.
0
þ
0
.
3
0
.
2
1100
þ
500
500
GW150914: FIRST RESULTS FROM THE SEARCH FOR
...
PHYSICAL REVIEW D
93,
122003 (2016)
122003-11
When an event is confidently identified as a real
gravitational wave signal, as for GW150914, the back-
ground used to determine the significance of other events
is reestimated without the contribution of this event. This
is the background distribution shown as purple lines in
Fig.
7
. Both analyses reported a candidate event on
October 12, 2015, at 09
54:43 UTC as the second-loudest
event in the observation period, which we refer to as
LVT151012. This candidate event has a combined
matched-filter SNR of 9.6. The PyCBC analysis reported
a false alarm rate of 1 per 2.3 years and a corresponding
false alarm probability of 0.02 for this event. The GstLAL
analysis reported a false alarm rate of 1 per 1.1 years
and a false alarm probability of 0.05. These results are
consistent with expectations for candidate events with
low matched-filter SNR, since PyCBC and GstLAL use
different ranking statistics and background estimation
methods. Detector characterization studies have not iden-
tified an instrumental or environmental artifact as causing
this candidate event
[14]
; however its false alarm prob-
ability is not sufficiently low to confidently claim the
event as a signal. It is significant enough to warrant
follow-up, however. The results of signal parameter
estimation, shown in Table
I
, indicate that if LVT151012
is of astrophysical origin, then the source would be a
stellar-mass binary black hole system with source-
frame component masses
23
þ
18
6
M
and
13
þ
4
5
M
.The
effective spin would be
χ
eff
¼
0
.
0
þ
0
.
3
0
.
2
and the distance
1100
þ
500
500
Mpc.
VI. CONCLUSION
The LIGO detectors have observed gravitational waves
from the merger of two stellar-mass black holes. The binary
coalescence search detects GW150914 with a significance
greater than
5
.
1
σ
during the observations reported. This
result is confirmed by two independent matched-filter
analyses, providing confidence in the discovery. Detailed
parameter estimation for GW150914 is reported in
Ref.
[18]
, the implications for the rate of binary black hole
coalescences in Ref.
[101]
, and tests for consistency of the
signal with general relativity in Ref.
[102]
. Reference
[103]
discusses the astrophysical implications of this discovery.
Full results of the compact binary search in Advanced
LIGO
s first observing run will be reported in a future
publication.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support of the
United States National Science Foundation (NSF) for the
construction and operation of the LIGO Laboratory and
Advanced LIGO as well as the Science and Technology
Facilities Council (STFC) of the United Kingdom, the
Max-Planck-Society (MPS), and the State of Niedersachsen/
Germany for support of the construction of Advanced LIGO
and construction and operation of the GEO 600 detector.
Additional support for Advanced LIGO was provided by the
Australian Research Council. The authors gratefully
acknowledge the Italian Istituto Nazionale di Fisica
Nucleare (INFN), the French Centre National de la
Recherche Scientifique (CNRS) and the Foundation for
Fundamental Research on Matter supported by
the Netherlands Organisation for Scientific Research, for
the construction and operation of the Virgo detector and the
creation and support of the EGO consortium. The authors
also gratefully acknowledge research support from these
agencies as well as by the Council of Scientific and Industrial
Research of India, Department of Science and Technology,
India; Science & Engineering Research Board (SERB),
India; Ministry of Human Resource Development, India;
the Spanish Ministerio de Economía y Competitividad; the
Conselleria d
Economia i Competitivitat and Conselleria
d
Educació; Cultura i Universitats of the Govern de les Illes
Balears;theNationalScienceCentreofPoland;theEuropean
Commission; the Royal Society; the Scottish Funding
Council; the Scottish Universities Physics Alliance; the
Hungarian Scientific Research Fund (OTKA); the Lyon
Institute of Origins (LIO); the National Research
Foundation of Korea; Industry Canada and the Province
of Ontario through the Ministry of Economic Development
and Innovation; the National Science and Engineering
Research Council Canada; Canadian Institute for Advanced
Research;theBrazilianMinistryofScience,Technology,and
Innovation; Russian Foundation for Basic Research; the
Leverhulme Trust; the Research Corporation, Ministry of
Science and Technology (MOST), Taiwan; and the Kavli
Foundation. The authors gratefully acknowledge the support
of the NSF, STFC, MPS, INFN, CNRS and the State of
Niedersachsen/Germany for provision of computational
resources.
APPENDIX A: DETECTOR CALIBRATION
The LIGO detectors do not directly record the strain
signal; rather they sense power fluctuations in the light at
the interferometer
s readout port
[29]
.Thiserrorsignalis
used to generate a feedback signal to the detector
s
differential arm length to maintain destructive interference
of the light moving towards the readout port
[17]
.The
presence of this feedback signal suppresses the length
change from external sources; a combination of the error
and control signals is used to estimate the detector strain.
The strain is calibrated by measuring the detector
s
response to test mass motion induced by photon pressure
from a modulated calibration laser beam. Changes in the
detector
s thermal and alignment state cause small, time-
dependent systematic errors in the calibration. For more
details see Ref.
[31]
.
Errors in the calibrated strain data lead to mismatches
between waveform templates and the gravitational-wave
signal. This mismatch has been shown to decrease the
B. P. ABBOTT
et al.
PHYSICAL REVIEW D
93,
122003 (2016)
122003-12