Binary Black Hole Mergers in the first Advanced LIGO Observing Run
The LIGO Scientific Collaboration and The Virgo Collaboration
a
(23 JUNE 2016)
The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016,
saw the first detections of gravitational waves from binary black hole mergers. In this paper we present full re-
sults from a search for binary black hole merger signals with total masses up to 100M
and detailed implications
from our observations of these systems. Our search, based on general-relativistic models of gravitational wave
signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226,
with a significance of greater than 5
σ
over the observing period. It also identified a third possible signal,
LVT151012, with substantially lower significance, which has a 87% probability of being of astrophysical ori-
gin. We provide detailed estimates of the parameters of the observed systems. Both GW150914 and GW151226
provide an unprecedented opportunity to study the two-body motion of a compact-object binary in the large ve-
locity, highly nonlinear regime. We do not observe any deviations from general relativity, and place improved
empirical bounds on several high-order post-Newtonian coefficients. From our observations we infer stellar-
mass binary black hole merger rates lying in the range 9–240 Gpc
−
3
yr
−
1
. These observations are beginning to
inform astrophysical predictions of binary black hole formation rates, and indicate that future observing runs of
the Advanced detector network will yield many more gravitational wave detections.
I. INTRODUCTION
The first observing run (O1) of the Advanced LIGO de-
tectors took place from September 12, 2015, to January 19,
2016. The detectors provided unprecedented sensitivity to
gravitational waves over a range of frequencies from 30 Hz
to several kHz [1], which covers the frequencies of gravita-
tional waves emitted during the late inspiral, merger and ring-
down of stellar-mass binary black holes (BBHs). In this pa-
per, we report the results of a matched-filter search using rel-
ativistic models of BBH waveforms during the whole of the
first Advanced LIGO observing run. The compact binary co-
alescence (CBC) 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 dimen-
sionless spins up to 0.99. Here we report on results of the
search for BBHs. The search was performed using two in-
dependently implemented analyses, referred to as PyCBC [2–
4] and GstLAL [5–7]. These analyses use a common set of
template waveforms [8–10], but differ in their implementa-
tions of matched filtering [11, 12], their use of detector data-
quality information [13], the techniques used to mitigate the
effect of non-Gaussian noise transients in the detector [5, 14],
and the methods for estimating the noise background of the
search [3, 15]. We obtain results that are consistent between
the two analyses.
The search identified two BBH mergers: GW150914, ob-
served on September 14, 2015 at 09:50:45 UTC [16], and
GW151226, observed on December 26, 2015 at 03:38:53
UTC [17]. Both of these signals were observed with a sig-
nificance greater than 5
σ
. In addition a third candidate event,
LVT151012, consistent with a BBH merger was observed on
October 12, 2015 at 09:54:43 UTC with a significance of
.
2
σ
. Although LVT151012 is not significant enough to
claim an unambiguous detection, it is more likely to have re-
a
Full author list given at the end of the article
sulted from a gravitational-wave signal than from an instru-
mental or environmental noise transient. The key parameters
of these events are summarized in Table I.
The properties of the sources can be inferred from the ob-
served gravitational waveforms. In particular, the binary evo-
lution, which is encoded in the phasing of the gravitational
wave signal, is governed by the masses and spins of the binary
components. The sky location of the source is primarily deter-
mined through time of arrival differences at the two Advanced
LIGO sites. The observed amplitudes and relative phase of
the signal in the two Advanced LIGO detectors can be used
to further restrict the sky location and infer the distance to
the source and the binary orientation. We provide a detailed
evaluation of the source properties and inferred parameters
of GW150914, GW151226 and LVT151012. We use models
of the waveform covering the inspiral, merger and ringdown
phases based on combining post-Newtonian (PN) theory [18–
23], the effective-one-body (EOB) formalism [24–28] and nu-
merical relativity simulations [29–35]. One model is restricted
to spins aligned with the orbital angular momentum [8, 9]
while the other allows for non-aligned orientation of the spins,
which can lead to precession of the orbital plane [36, 37]. The
parameters of GW150914 have been reported previously in
[38, 39]. We provide revised results which make use of up-
dated instrumental calibration.
The emitted signals depend upon the strong field dynamics
of general relativity; thus our observations provide an extraor-
dinary opportunity to test the predictions of general relativity
for binary coalescence waveforms. Several tests of general
relativity were performed using GW150914, as described in
[41]. One of these was a parametrized test for the consis-
tency of the observed waveform with a general relativity based
model. We perform a similar test on GW151226. Since this
source is of lower mass than GW150914, the observed wave-
form lasts for many more cycles in the detector data, allowing
us to better constrain the PN coefficients that describe the evo-
lution of the binary through the inspiral phase. In addition, we
combine the results from GW150914 and GW151226 to place
still tighter bounds on deviations from general relativity.
arXiv:1606.04856v2 [gr-qc] 22 Jun 2016
2
Event
GW150914
GW151226
LVT151012
Signal-to-noise ratio
ρ
23.7
13.0
9
.
7
False alarm rate
FAR
/
yr
−
1
<
6
.
0
×
10
−
7
<
6
.
0
×
10
−
7
0.37
p-value
7
.
5
×
10
−
8
7
.
5
×
10
−
8
0
.
045
Significance
>
5
.
3
σ
>
5
.
3
σ
1
.
7
σ
Primary mass
m
source
1
/
M
36
.
2
+
5
.
2
−
3
.
8
14
.
2
+
8
.
3
−
3
.
7
23
+
18
−
6
Secondary mass
m
source
2
/
M
29
.
1
+
3
.
7
−
4
.
4
7
.
5
+
2
.
3
−
2
.
3
13
+
4
−
5
Chirp mass
M
source
/
M
28
.
1
+
1
.
8
−
1
.
5
8
.
9
+
0
.
3
−
0
.
3
15
.
1
+
1
.
4
−
1
.
1
Total mass
M
source
/
M
65
.
3
+
4
.
1
−
3
.
4
21
.
8
+
5
.
9
−
1
.
7
37
+
13
−
4
Effective inspiral spin
χ
eff
−
0
.
06
+
0
.
14
−
0
.
14
0
.
21
+
0
.
20
−
0
.
10
0
.
0
+
0
.
3
−
0
.
2
Final mass
M
source
f
/
M
62
.
3
+
3
.
7
−
3
.
1
20
.
8
+
6
.
1
−
1
.
7
35
+
14
−
4
Final spin
a
f
0
.
68
+
0
.
05
−
0
.
06
0
.
74
+
0
.
06
−
0
.
06
0
.
66
+
0
.
09
−
0
.
10
Radiated energy
E
rad
/
(
M
c
2
)
3
.
0
+
0
.
5
−
0
.
4
1
.
0
+
0
.
1
−
0
.
2
1
.
5
+
0
.
3
−
0
.
4
Peak luminosity
`
peak
/
(
erg s
−
1
)
3
.
6
+
0
.
5
−
0
.
4
×
10
56
3
.
3
+
0
.
8
−
1
.
6
×
10
56
3
.
1
+
0
.
8
−
1
.
8
×
10
56
Luminosity distance
D
L
/
Mpc
420
+
150
−
180
440
+
180
−
190
1000
+
500
−
500
Source redshift
z
0
.
09
+
0
.
03
−
0
.
04
0
.
09
+
0
.
03
−
0
.
04
0
.
20
+
0
.
09
−
0
.
09
Sky localization
∆Ω
/
deg
2
230
850
1600
TABLE I. Details of the three most significant events. The false
alarm rate, p-value and significance are from the PyCBC analysis;
the GstLAL results are consistent with this. For source parameters,
we report median values with 90% credible intervals that include sta-
tistical errors, and systematic errors from averaging the results of
different waveform models. The uncertainty for the peak luminos-
ity includes an estimate of additional error from the fitting formula.
The sky localization is the area of the 90% credible area. Masses are
given in the source frame; to convert to the detector frame multiply
by
(
1
+
z
)
. The source redshift assumes standard cosmology [40].
The observed events begin to reveal a population of stellar-
mass black hole mergers. We use these signals to constrain the
rates of BBH mergers in the universe, and begin to probe the
mass distribution of black hole mergers. The inferred rates are
consistent with those derived from GW150914 [42]. We also
discuss the astrophysical implications of the observations and
the prospects for future Advanced LIGO and Virgo observing
runs.
The results presented here are restricted to BBH systems
with total masses less than 100 M
. Searches for more mas-
sive black holes, compact binary systems containing neutron
stars and unmodeled transient signals will be reported else-
where.
This paper is organized as follows: Sec. II provides an
overview of the Advanced LIGO detectors during the first ob-
serving run, and the data used in the search. Sec. III presents
the results of the search, details of the two gravitational wave
events, GW150914 and GW151226, and the candidate event
LVT151012. Sec. IV provides detailed parameter-estimation
results for the events. Sec. V presents results for the consis-
tency of the two events, GW150914 and GW151226, with the
predictions of general relativity. Sec. VI presents the inferred
rate of stellar-mass BBH mergers, and VII discusses the im-
plications of these observations and future prospects. We in-
clude appendices that provide additional technical details of
the methods used. Appendix A describes the CBC search,
with A 1 and A 2 presenting details of the construction and
tuning of the two independently implemented analyses used
in the search, highlighting differences from the methods de-
scribed in [43]. Appendix B provides a description of the
parameter-estimation analysis and includes a summary table
of results for all three events. Appendix C and Appendix D
provide details of the methods used to infer merger rates and
mass distributions respectively.
II. OVERVIEW OF THE INSTRUMENTS AND THE DATA
SET
The two Advanced LIGO detectors, one located in Han-
ford, Washington (H1) and one in Livingston, Louisiana (L1)
are modified Michelson interferometers with 4-km long arms.
The interferometer mirrors act as test masses, and the pas-
sage of a gravitational wave induces a differential arm length
change which is proportional to the gravitational-wave strain
amplitude. The Advanced LIGO detectors came on line in
September 2015 after a major upgrade targeting a 10-fold im-
provement in sensitivity over the initial LIGO detectors [44].
While not yet operating at design sensitivity, both detectors
reached an instrument noise 3 to 4 times lower than ever mea-
sured before in their most sensitive frequency band between
100 Hz and 300 Hz [1]. The corresponding observable vol-
ume of space for BBH mergers, in the mass range reported
in this paper, was
∼
30 times greater, enabling the successful
search reported here.
The typical instrument noise of the Advanced LIGO de-
tectors during O1 is described in detail in [46]. In the left
panel of Figure 1 we show the amplitude spectral density of
the total strain noise of both detectors (
√
S
(
f
)
), calibrated in
units of strain per
√
Hz [47]. Overlaid on the noise curves of
the detectors, the waveforms of GW150914, GW151226 and
LVT151012 are also shown. The expected SNR
ρ
of a signal,
h
(
t
)
, can be expressed as
ρ
2
=
∫
∞
0
(
2
|
̃
h
(
f
)
|
√
f
)
2
S
n
(
f
)
d ln
(
f
)
,
(1)
where
̃
h
(
f
)
is the Fourier transform of the signal. Writing it in
this form motivates the normalization of the waveform plotted
in Figure 1 as the area between the signal and noise curves is
indicative of the SNR of the events.
3
FIG. 1. Left: Amplitude spectral density of the total strain noise of the H1 and L1 detectors,
√
S
(
f
)
, in units of strain per
√
Hz, and the
recovered signals of GW150914, GW151226 and LVT151012 plotted so that the relative amplitudes can be related to the SNR of the signal
(as described in the text). Right: Time evolution of the waveforms from when they enter the detectors’ sensitive band at 30 Hz. All bands
show the 90% credible regions of the LIGO Hanford signal reconstructions from a coherent Bayesian analysis using a non-precessing spin
waveform model [45].
The gravitational-wave signal from a BBH merger takes the
form of a chirp, increasing in frequency and amplitude as the
black holes spiral inwards. The amplitude of the signal is
maximum at the merger, after which it decays rapidly as the fi-
nal black hole rings down to equilibrium. In the frequency do-
main, the amplitude decreases with frequency during inspiral,
as the signal spends a greater number of cycles at lower fre-
quencies. This is followed by a slower falloff during merger
and then a steep decrease during the ringdown. The amplitude
of GW150914 is significantly larger than the other two events
and at the time of the merger the gravitational-wave signal
lies well above the noise. GW151226 has lower amplitude but
sweeps across the whole detector’s sensitive band up to nearly
800 Hz. The corresponding time series of the three wave-
forms are plotted in the right panel of Figure 1 to better vi-
sualize the difference in duration within the Advanced LIGO
band: GW150914 lasts only a few cycles while LVT151012
and GW151226 have lower amplitude but last longer.
The analysis presented in this paper includes the total set of
O1 data from September 12, 2015 to January 19, 2016, which
contains a total coincident analysis time of 51.5 days accu-
mulated when both detectors were operating in their normal
state. As described in [13] with regard to the first 16 days
of O1 data, the output data of both detectors typically con-
tain non-stationary and non-Gaussian features, in the form of
transient noise artifacts of varying durations. Longer duration
artifacts, such as non-stationary behavior in the interferom-
eter noise, are not very detrimental to CBC searches as they
occur on a time-scale that is much longer than any CBC wave-
form. However, shorter duration artifacts can pollute the noise
background distribution of CBC searches. Many of these arti-
facts have distinct signatures [48] visible in the auxiliary data
channels from the large number of sensors used to monitor in-
strumental or environmental disturbances at each observatory
site [49]. When a significant noise source is identified, con-
taminated data are removed from the analysis data set. After
applying this data quality process, detailed in [50], the remain-
ing coincident analysis time in O1 is 48.6 days. The analyses
search only stretches of data longer than a minimum duration,
to ensure that the detectors are operating stably. The choice is
different in the two analyses and reduces the available data to
46
.
1 days for the PyCBC analysis and 48
.
3 days for the Gst-
LAL analysis.
III. SEARCH RESULTS
Two different, largely independent, analyses have been im-
plemented to search for stellar-mass BBH signals in the data
of O1: PyCBC [2–4] and GstLAL [5–7]. Both these analyses
employ matched filtering [51–59] with waveforms given by
models based on general relativity [8, 9] to search for gravi-
tational waves from binary neutron stars, BBHs, and neutron
star–black hole binaries. In this paper, we focus on the results
of the matched filter search for BBHs. Results of the searches
for binary neutron stars and neutron star–black hole binaries
will be reported elsewhere. These matched-filter searches are
complemented by generic transient searches which are sensi-
4
tive to BBH mergers with total mass
∼
30 M
or greater [60].
A bank of template waveforms is used to cover the parame-
ter space to be searched [53, 61–64]. The gravitational wave-
forms depend upon the masses
m
1
,
2
(using the convention that
m
1
≥
m
2
), and angular momenta
S
1
,
2
of the binary compo-
nents. We characterise the angular momentum in terms of the
dimensionless spin magnitude
a
1
,
2
=
c
Gm
2
1
,
2
|
S
1
,
2
|
,
(2)
and the component aligned with the direction of the orbital
angular momentum,
L
, of the binary [65, 66],
χ
1
,
2
=
c
Gm
2
1
,
2
S
1
,
2
·
ˆ
L
.
(3)
We restrict this template bank to systems for which the spin
of the systems is aligned (or anti-aligned) with the orbital an-
gular momentum of the binary. Consequently, the waveforms
depends primarily upon the chirp mass [67–69]
M
=
(
m
1
m
2
)
3
/
5
M
1
/
5
,
(4)
the mass ratio [18]
q
=
m
2
m
1
≤
1
,
(5)
and the effective spin parameter [70–73]
χ
eff
=
m
1
χ
1
+
m
2
χ
2
M
,
(6)
where
M
=
m
1
+
m
2
is the binary’s total mass. The chirp mass
and effective spin are combinations of masses and spin which
have significant impact on the evolution of the inspiral, and
are therefore accurately measured parameters for gravitational
waveforms [56, 74–77].
The minimum black hole mass is taken to be 2M
, con-
sistent with the largest known masses of neutron stars [78].
There is no known maximum black hole mass [79], however
we limit this template bank to binaries with a total mass less
than
M
≤
100 M
. For higher mass binaries, the Advanced
LIGO detectors are sensitive to only the final few cycles of in-
spiral plus merger, making the analysis more susceptible to
noise transients. The results of searches for more massive
BBH mergers will be reported in future publications. In prin-
ciple, black hole spins can lie anywhere in the range from
−
1
(maximal and anti-aligned) to
+
1 (maximal and aligned). We
limit the spin magnitude to less than 0
.
99, which is the re-
gion over which we are able to generate valid template wave-
forms [8]. The bank of templates used for the analysis is
shown in Figure 2.
Both analyses separately correlate the data from each de-
tector with template waveforms that model the expected sig-
nal. The analyses identify candidate events that are detected
at both the Hanford and Livingston observatories consistent
with the 10 ms inter-site propagation time. Additional sig-
nal consistency tests are performed to mitigate the effects of
10
0
10
1
10
2
m
1
[
M
]
10
0
10
1
m
2
[
M
]
|
χ
1
|
<
0
.
9895
,
|
χ
2
|
<
0
.
05
|
χ
1
,
2
|
<
0
.
05
|
χ
1
,
2
|
<
0
.
9895
GW150914
GW151226
LVT151012 (gstlal)
LVT151012 (PyCBC)
FIG. 2. 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 colours indicate mass regions
with different limits on the dimensionless spin parameters
χ
1
and
χ
2
. Symbols indicate the best matching templates for GW150914,
GW151226 and LVT151012. For GW150914, GW151226 the tem-
plate was the same in the PyCBC and GstLAL searches while for
LVT151012 they differed. The parameters of the best matching tem-
plates are not the same as the detector frame masses provided by the
detailed parameter estimation discussed in Section IV.
non-stationary transients in the data. Events are assigned a
detection-statistic value that ranks their likelihood of being a
gravitational-wave signal. For PyCBC,
ˆ
ρ
c
is the quadrature
sum of signal-consistency re-weighted SNRs in the two de-
tectors. For GstLAL, ln
L
is the log-likelihood ratio for the
signal and noise models. The detection statistics are compared
to the estimated detector noise background to determine, for
each candidate event, the probability that detector noise would
give rise to at least one equally significant event. Further de-
tails of the analysis methods are available in Appendix A.
The results for the two different analyses are presented
in Figure 3. The figure shows the observed distribution of
events, as well as the background distribution used to assess
significance. In both analyses, there are three events that
lie above the estimated background: GW150914, GW151226
and LVT151012. All three of these are consistent with being
BBH merger signals and are discussed in further detail be-
low. The templates producing the highest significance in the
two analyses are indicated in Figure 2, the gravitational wave-
forms are shown in Figure 1 and key parameters are summa-
rized in Table I. There were no other significant BBH trig-
gers in the first advanced LIGO observing run. All other ob-
served events are consistent with the noise background for the
search. Follow up of the coincident events
ˆ
ρ
c
≈
9 in the Py-
CBC analysis suggests that they are likely due to noise fluctu-
ations or poor data quality, rather than a population of weaker
gravitational-wave signals.
It is clear from Figure 3 that at high significance, the
background distribution is dominated by the presence of
GW150914 in the data. Consequently, once an event has