of 14
GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary
Black Hole Coalescence
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 31 May 2016; published 15 June 2016)
We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-mass
black holes. The signal, GW151226, was observed by the twin detectors of the Laser Interferometer
Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initially
identified within 70 s by an online matched-filter search targeting binary coalescences. Subsequent off-line
analyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than
5
σ
. The signal persisted in the LIGO frequency band for approximately 1 s, increasing in frequency and
amplitude over about 55 cycles from 35 to 450 Hz, and reached a peak gravitational strain of
3
.
4
þ
0
.
7
0
.
9
×
10
22
. The inferred source-frame initial black hole masses are
14
.
2
þ
8
.
3
3
.
7
M
and
7
.
5
þ
2
.
3
2
.
3
M
,
and the final black hole mass is
20
.
8
þ
6
.
1
1
.
7
M
. We find that at least one of the component black holes has spin
greater than 0.2. This source is located at a luminosity distance of
440
þ
180
190
Mpc corresponding to a redshift
of
0
.
09
þ
0
.
03
0
.
04
. All uncertainties define a 90% credible interval. This second gravitational-wave observation
provides improved constraints on stellar populations and on deviations from general relativity.
DOI:
10.1103/PhysRevLett.116.241103
I. INTRODUCTION
A century after Einstein predicted the existence of
gravitational waves
[1]
, the Laser Interferometer
Gravitational-Wave Observatory (LIGO)
[2,3]
observed
the first gravitational-wave signal GW150914 from a
binary black hole merger
[4]
. In this Letter, we report
the observation of a second coincident signal GW151226,
also from the coalescence of two black holes. An analysis
of GW150914 and GW151226 as a population is described
in
[5]
. LVT151012, the third most significant binary black
hole candidate, is also included in this analysis (see Fig.
2
below). No other significant binary black hole candidates in
the total mass range
4
100
M
were found during
Advanced LIGO
s first observing period, September 12,
2015 to January 19, 2016.
Matched filtering
[6
12]
was essential to the detection of
GW151226 since the signal has a smaller strain amplitude
and the detectable signal energy is spread over a longer
time interval than GW150914. Detection
[13
18]
and
parameter estimation
[19
21]
rely on understanding the
sources of detector noise
[22,23]
and on precise waveform
models of compact binary coalescence. Waveforms have
been developed combining various techniques to model
the two-body dynamics and gravitational waves, notably
post-Newtonian theory
[24
28]
, the effective-one-body
formalism
[29
33]
, and numerical relativity
[34
39]
.
Matched filtering correlates a waveform model with the
data over the detectors
sensitive band, which enabled
GW151226 to be extracted from the detector noise.
II. OBSERVATION
On December 26, 2015, the gravitational-wave candidate
GW151226 was identified within 70 s by an online
matched-filter search
[17]
. The candidate had an inferred
coalescence time of 03:38:53.647 UTC at LIGO Livingston
and
1
.
1
þ
0
.
3
0
.
3
ms later at LIGO Hanford. False alarms more
significant than GW151226 would, in principle, be pro-
duced by the online search at a rate of approximately 1 per
1000 yr. The candidate signal thus passed the threshold for
generating an alert to electromagnetic partners
[40]
. The
source was localized to
1400
deg
2
on the sky (90%
credible level) within 3 min of the initial observation
[41]
.
Coarse sky localization is due to the limited information
afforded by only two sensitive detectors in observing mode.
The initial identification of this signal was confirmed by
performing two independent off-line matched-filter
searches
[14,17,18]
that used the waveform models in
Refs.
[42,43]
. Both searches identified GW151226 as a
highly significant event. Because of the signal
s smaller
strain amplitude and time-frequency morphology, the
generic transient searches that initially identified
GW150914
[44]
did not detect GW151226.
Based on current waveform modeling, we find that
GW151226 passed through LIGO
s sensitive band in
1 s, increasing in frequency over approximately 55 cycles
*
Full author list given at end of the article.
Published by the American Physical Society under the terms of
the
Creative Commons Attribution 3.0 License
. Further distri-
bution of this work must maintain attribution to the author(s) and
the published article
s title, journal citation, and DOI.
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=
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=
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=
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Published by the American Physical Society
from 35 Hz to a peak amplitude at 450 Hz. The signal-to-
noise ratio (SNR) accumulates equally in the early inspiral
(
45
cycles from 35 to 100 Hz) and late inspiral to merger
(
10
cycles from 100 to 450 Hz). This is different from the
more massive GW150914 binary for which only the last 10
cycles, comprising inspiral and merger, dominated the
SNR. As a consequence, the parameters characterizing
GW151226 have different precision than those of
GW150914. The chirp mass
[26,45]
, which controls the
binary
s evolution during the early inspiral, is determined
very precisely. The individual masses, which rely on
information from the late inspiral and merger, are measured
far less precisely.
Figure
1
illustrates that the amplitude of the signal is less
than the level of the detector noise, wherethe maximum strain
of the signal is
3
.
4
þ
0
.
7
0
.
9
×
10
22
and
3
.
4
þ
0
.
8
0
.
9
×
10
22
in LIGO
Hanford and Livingston, respectively. The time-frequency
representation of the detector data shows that the signal is not
easily visible. The signal is more apparent in LIGO Hanford
where the SNR is larger. The SNR difference is predomi-
nantly due to the different sensitivities of the detectors at the
time. Only with the accumulated SNR from matched filtering
does the signal become apparent in both detectors.
III. DETECTORS
The LIGO detectors measure gravitational-wave strain
using two modified Michelson interferometers located in
Hanford, WA and Livingston, LA
[2,3,46]
. The two
orthogonal arms of each interferometer are 4 km in length,
each with an optical cavity formed by two mirrors acting as
test masses. A passing gravitational wave alters the
FIG. 1. GW151226 observed by the LIGO Hanford (left column) and Livingston (right column) detectors, where times are relative to
December 26, 2015 at 03:38:53.648 UTC.
First row:
Strain data from the two detectors, where the data are filtered with a 30
600-Hz
bandpass filter to suppress large fluctuations outside this range and band-reject filters to remove strong instrumental spectral lines
[46]
.
Also shown (black) is the best-match template from a nonprecessing spin waveform model reconstructed using a Bayesian analysis
[21]
with the same filtering applied. As a result, modulations in the waveform are present due to this conditioning and not due to precession
effects. The thickness of the line indicates the 90% credible region. See Fig.
5
for a reconstruction of the best-match template with no
filtering applied.
Second row:
The accumulated peak signal-to-noise ratio (SNR
p
) as a function of time when integrating from the start of
the best-match template, corresponding to a gravitational-wave frequency of 30 Hz, up to its merger time. The total accumulated SNR
p
corresponds to the peak in the next row.
Third row:
Signal-to-noise ratio (SNR) time series produced by time shifting the best-match
template waveform and computing the integrated SNR at each point in time. The peak of the SNR time series gives the merger time of
the best-match template for which the highest overlap with the data is achieved. The single-detector SNRs in LIGO Hanford and
Livingston are 10.5 and 7.9, respectively, primarily because of the detectors
differing sensitivities.
Fourth row:
Time-frequency
representation
[47]
of the strain data around the time of GW151226. In contrast to GW150914
[4]
, the signal is not easily visible.
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differential arm length so that the measured difference is
Δ
L
ð
t
Þ¼
δ
L
x
δ
L
y
¼
h
ð
t
Þ
L
, where
L
¼
L
x
¼
L
y
and
h
is
the gravitational-wave strain amplitude projected onto the
detector. Calibration of the interferometers is performed by
inducing test mass motion using photon pressure from a
modulated calibration laser. Employing methods as
described in
[48]
, the calibration uncertainty (
1
σ
) in both
detectors at the time of the signal is better than 8% in
amplitude and 5 deg in phase.
At the time of GW151226, both LIGO detectors were
operating with a sensitivity typical of that exhibited
throughout the observing period
[46]
. Investigations similar
to the detection validation procedures for GW150914 found
no evidence that instrumental or environmental disturb-
ances contributed to GW151226
[4,23]
. Tests quantifying
the detectors
susceptibility to external environmental
disturbances, such as electromagnetic fields
[49]
, indicated
that any disturbance strong enough to account for the signal
would be clearly detected by the array of environmental
sensors. All environmental fluctuations recorded during
GW151226 were too small to account for more than 6% of
its peak strain amplitude. Furthermore, none of the envi-
ronmental sensors recorded any disturbances that evolved
in time and frequency like GW151226.
IV. SEARCHES
Two matched-filter searches
[18]
used coincident obser-
vations between the two LIGO detectors from September 12,
2015 to January 19, 2016 to estimate the significance of
GW151226
[5]
. Oneof these searches was theoff-lineversion
of the online search discussed previously
[17]
. The off-line
searches benefit from improved calibration and refined data
quality information not available to online searches
[5,23]
.
Each search identifies coincident events that are found in
both LIGO detectors with the same template and within
15 ms
[18]
. The 15-ms window is determined by the 10-ms
intersite propagation time plus a 5-ms allowance for uncer-
tainty in the arrival time of weak signals. Both searches use a
discrete bank of waveform templates
[7,50
55]
which target
gravitational waves from binary black hole systems with a
total mass of less than
100
M
and dimensionless spins
aligned with the orbital angular momentum. Details of this
bank are given in
[18]
. Identification by these two indepen-
dent searches increases our confidence in the robustness and
reliability of the detection.
The two searches employ different methods of ranking
gravitational-wave candidates and techniques for estimat-
ing the noise background
[14,17,18]
. Each search defines a
unique detection statistic to rank the likelihood of a
candidate being a signal. The significance of a candidate
event is estimated by comparing it with the noise back-
ground. This background is created using individual noise
events produced in each detector
s data. Since GW150914
had already been confirmed as a real gravitational-wave
signal
[4]
, it was removed from the data when estimating
the noise background.
FIG. 2. Search results from the two binary coalescence searches using their respective detection statistics
ˆ
ρ
c
(a combined matched
filtering signal-to-noise ratio, defined precisely in
[14]
; left) and ln
L
(the log of a likelihood ratio, defined precisely in
[17]
; right). The
event GW150914 is removed in all cases since it had already been confirmed as a real gravitational-wave signal. Both plots show the
number of candidate events (search results) as a function of detection statistic with orange square markers. The mean number of
background events as a function of the detection statistic is estimated using independent methods
[18]
. The background estimates are
found using two methods: excluding all candidate events which are shown as orange square markers (purple lines) or including all
candidate events except GW150914 (black lines). The scales along the top give the significance of an event in Gaussian standard
deviations based on the corresponding noise background. The raised tail in the black-line background (left) is due to random
coincidences of GW151226 in one detector with noise in the other detector and (right) due to the inclusion of GW151226 in the
distribution of noise events in each detector. GW151226 is found with high significance in both searches. LVT151012
[5,18]
, visible in
the search results at
2
.
0
σ
, is the third most significant binary black hole candidate event in the observing period.
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GW151226 was detected with a network matched-filter
SNR of 13 by both searches. Figure
2
shows the detection
statistic values assigned to GW151226 by the two searches
and their respective noise background distributions. At the
detection statistic value assigned to GW151226, the
searches estimate a false alarm probability of
<
10
7
(
>
5
σ
)
[14]
and
3
.
5
×
10
6
(
4
.
5
σ
)
[17]
when including
candidate events in the background calculation. This
procedure strictly limits the probability of obtaining a false
positive outcome in the absence of signals
[56]
. The
estimates from the two searches are consistent with expect-
ations for a compact binary coalescence signal, given the
differences in methods of data selection and candidate
event ranking. When excluding search candidate events
from the background calculation, a procedure that yields a
mean-unbiased estimate of the distribution of noise events,
the significance is found to be greater than
5
σ
in both
searches. Further details of the noise background and
significance estimation methods for each search are given
in
[18]
and discussions specific to GW151226 are in
[5]
.
V. SOURCE DISCUSSION
To estimate the source parameters, a coherent Bayesian
analysis
[21,57]
of the data was performed using two
families of waveform models. Both models are calibrated to
numerical simulations of binary black holes in general
relativity. One waveform model includes spin-induced
precession of the binary orbital plane
[58]
, created by
rotating the model described in
[59]
. The other waveform
model restricts the component black hole spins to be
aligned with the binary orbital angular momentum
[42,43]
. Both are publicly available
[60]
. Table
I
shows
source parameters for GW151226 including the initial and
final masses of the system. The parameter uncertainties
include statistical and systematic errors from averaging
posterior probability samples over the two waveform
models, in addition to calibration uncertainties. Here, we
report the median and 90% credible intervals.
The initial binary was composed of two stellar-mass black
holes with a source-frame primary mass
m
1
¼
14
.
2
þ
8
.
3
3
.
7
M
,
secondary mass
m
2
¼
7
.
5
þ
2
.
3
2
.
3
M
, and a total mass of
21
.
8
þ
5
.
9
1
.
7
M
. The binary merged into a black hole of mass
20
.
8
þ
6
.
1
1
.
7
M
, radiating
1
.
0
þ
0
.
1
0
.
2
M
c
2
in gravitational waves
with a peak luminosity of
3
.
3
þ
0
.
8
1
.
6
×
10
56
erg
=
s. These
estimates of the mass and spin of the final black hole, the
total energy radiated in gravitational waves, and the peak
gravitational-wave luminosity are derived from fits to
numerical simulations
[39,63
65]
. The source localization
is refined to
850
deg
2
, owing to the different methods used
[21]
, and refined calibration.
The long inspiral phase of GW151226 allows accurate
estimates of lower-order post-Newtonian expansion param-
eters, such as the chirp mass
[26,45]
. However, only loose
constraints can be placed on the total mass and mass ratio
(
m
2
=m
1
) because the merger and ringdown occur at
frequencies where the detectors are less sensitive.
Figure
3
shows the constraints on the component masses
of the initial black hole binary. The component masses
TABLE I. Source parameters for GW151226. We report median
values with 90% credible intervals that include statistical and
systematic errors from averaging results of the precessing and
nonprecessing spin waveform models. The errors also take into
account calibration uncertainties. Masses are given in the source
frame;toconverttothedetectorframe multiplyby(
1
þ
z
)
[61]
.The
spinsoftheprimaryandsecondaryblackholesareconstrained tobe
positive. The source redshift assumes standard cosmology
[62]
.
Further parameters of GW151226 are discussed in
[5]
.
Primary black hole mass
14
.
2
þ
8
.
3
3
.
7
M
Secondary black hole mass
7
.
5
þ
2
.
3
2
.
3
M
Chirp mass
8
.
9
þ
0
.
3
0
.
3
M
Total black hole mass
21
.
8
þ
5
.
9
1
.
7
M
Final black hole mass
20
.
8
þ
6
.
1
1
.
7
M
Radiated gravitational-wave energy
1
.
0
þ
0
.
1
0
.
2
M
c
2
Peak luminosity
3
.
3
þ
0
.
8
1
.
6
×
10
56
erg
=
s
Final black hole spin
0
.
74
þ
0
.
06
0
.
06
Luminosity distance
440
þ
180
190
Mpc
Source redshift
z
0
.
09
þ
0
.
03
0
.
04
FIG. 3. Posterior density function for the source-frame masses
m
source
1
(primary) and
m
source
2
(secondary). The one-dimensional
marginalized distributions include the posterior density functions
for the precessing (blue) and nonprecessing (red) spin waveform
models where average (black) represents the mean of the two
models. The dashed lines mark the 90% credible interval for the
average posterior density function. The two-dimensional plot
shows the contours of the 50% and 90% credible regions plotted
over a color-coded posterior density function.
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follow a line of constant chirp mass
8
.
9
þ
0
.
3
0
.
3
M
, and
constrain the mass ratio to be greater than 0.28. The
posterior distribution is not consistent with component
masses below
4
.
5
M
(99% credible level). This is above
the theoretical maximum mass of a neutron star for
common equations of state
[66,67]
. Thus, both components
are identified as black holes.
Compact binary coalescences act as standard sirens
[68,69]
. Their luminosity distance can be extracted from
the amplitude of an observed signal provided the orienta-
tion of the orbital plane can be determined. Information
about whether the orbit is face-on, edge-on, or in between is
encoded in the two polarizations of the gravitational wave.
However, the two LIGO detectors are nearly coaligned and
the source of GW151226 is likely to be located close to the
maxima of the directional responses of both detectors
[3]
.
Consequently, it is difficult to extract the polarization
content, and therefore the orientation of the orbital plane.
As a result, the luminosity distance is only weakly con-
strained to be
440
þ
180
190
Mpc, corresponding to a redshift of
0
.
09
þ
0
.
03
0
.
04
assuming a flat
Λ
CDM cosmology
[62]
.
Component spins affect the relativistic motion of the
binary but often have only subtle effects on the gravita-
tional waveform. Therefore, we can only extract limited
information about the spins. Figure
4
(left) shows the
probability density functions of the mass-weighted combi-
nations of orbit-aligned spins
χ
eff
[70,71]
and in-plane
spins
χ
p
[72]
for the precessing spin waveform model. The
same figure (right) shows the individual spins of the
component black holes. The posterior density functions
inferred from the precessing and nonprecessing spin wave-
form models indicate that
χ
eff
is positive at greater than the
99% credible level; therefore, at least one of the black holes
has nonzero spin. We find that at least one black hole has a
spin magnitude greater than 0.2 at the 99% credible level.
Only weak constraints can be placed on
χ
p
, suggesting that
the data are not informative regarding spin-precession
effects
[5]
.
To test whether GW151226 is consistent with general
relativity, we allow the coefficients that describe the
waveform (which are derived as functions of the source
parameters from the post-Newtonian approximation
[26
28]
and from fits to numerical relativity simulations)
to deviate from their nominal values, and check whether
the resulting waveforms are consistent with the data
[73]
.
The posterior probability densities of the coefficients
are found to center on their general relativity values.
Additionally, both the offsets and widths of the posteriors
for the post-Newtonian inspiral coefficients decrease sig-
nificantly when analyzing GW150914 and GW151226
jointly, in some cases to the 10% level, as discussed in
[5]
.
The waveform models used are consistent with general
relativity simulations. Figure
5
shows GW151226
s wave-
form reconstruction (90% credible region as in
[57]
) using
the nonprecessing spin templates employed to find the
signal and extract parameters, plotted during the time
interval with the most significant SNR. Also shown is a
direct numerical solution of Einstein
s equations
[38,74,75]
for a binary black hole with parameters near the peak of the
parameter estimation posterior.
FIG. 4.
Left:
Posterior density function for the
χ
p
and
χ
eff
spin parameters (measured at 20 Hz) compared to their prior distributions.
The one-dimensional plot shows probability contours of the prior (green) and marginalized posterior density function (black)
[58,59]
.
The two-dimensional plot shows the contours of the 50% and 90% credible regions plotted over a color-coded posterior density
function. The dashed lines mark the 90% credible interval.
Right:
Posterior density function for the dimensionless component spins,
c
S
1
=
ð
Gm
2
1
Þ
and
c
S
2
=
ð
Gm
2
2
Þ
, relative to the normal of the orbital plane
ˆ
L
.
S
i
and
m
i
are the spin angular momenta and masses of the
primary (
i
¼
1
) and secondary (
i
¼
2
) black holes,
c
is the speed of light and
G
is the gravitational constant. The posterior density
functions are marginalized over the azimuthal angles. The bins are designed to have equal prior probability; they are constructed linearly
in spin magnitudes and the cosine of the tilt angles cos
1
ð
ˆ
S
i
·
ˆ
L
Þ
.
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VI. ASTROPHYSICAL IMPLICATIONS
The inferred black hole masses are within the range of
dynamically measured masses of black holes found in x-ray
binaries
[76
80]
, unlike GW150914. For the secondary
black hole, there is a probability of 4% that it lies in the
posited
3
5
M
gap between observed neutron star and
black hole masses
[76,77]
, and there is no support for the
primary black hole to have a mass in this range.
Binary black hole formation has been predicted through a
range of different channels involving either isolated binaries
or dynamical processes in dense stellar systems
[81]
.At
present all types of formation channels predict binary black
hole merger rates and black hole masses consistent with the
observational constraints from GW150914
[82
84]
.Both
classical isolated binary evolution through the common
envelope phase and dynamical formation are also consistent
with GW151226, whose formation time and time delay to
merger cannot be determined from the merger observation.
Given our current understanding of massive-star evolution,
the measured black hole masses are also consistent with any
metallicity for the stellar progenitors and a broad range of
progenitor masses
[85,86]
.
The spin distribution of the black holes in stellar-mass
binary black holes is unknown; the measurement of a spin
magnitude for at least one companion greater than 0.2 is an
important first step in constraining this distribution.
Predictions of mass ratios and spin tilts with respect to
the orbital angular momentum differ significantly for
different channels. However, our current constraints on
these properties are limited; implications for the
evolutionary history of the observed black hole mergers
are further discussed in
[5]
.
The first observing period of Advanced LIGO provides
evidence for a population of stellar-mass binary black holes
contributing to a stochastic background that could be
higher than previously expected
[87]
. Additionally, we
find the rate estimate of stellar-mass binary black hole
mergers in the local Universe to be consistent with the
ranges presented in
[88]
. An updated discussion of the rate
estimates can be found in
[5]
.
A comprehensive discussion of inferred source param-
eters, astrophysical implications, mass distributions, rate
estimations, and tests of general relativity for the binary
black hole mergers detected during Advanced LIGO
s first
observing period may be found in
[5]
.
VII. CONCLUSION
LIGO has detected a second gravitational-wave signal
from the coalescence of two stellar-mass black holes with
lower masses than those measured for GW150914. Public
data associated with GW151226 are available at
[89]
.The
inferred component masses are consistent with values
dynamically measured in x-ray binaries, but are obtained
through the independent measurement process of gravita-
tional-wave detection. Although it is challenging to constrain
the spins of the initial black holes, we can conclude that at
least one black hole had spin greater than 0.2. These recent
detections in Advanced LIGO
s first observing period have
revealed a population of binary black holes that heralds the
opening of the field of gravitational-wave astronomy.
FIG. 5. Estimated gravitational-wave strain from GW151226 projected onto the LIGO Livingston detector with times relative to
December 26, 2015 at 03:38:53.648 UTC. This shows the full bandwidth, without the filtering used for Fig.
1
.
Top:
The 90% credible
region (as in
[57]
) for a nonprecessing spin waveform-model reconstruction (gray) and a direct, nonprecessing numerical solution of
Einstein
s equations (red) with parameters consistent with the 90% credible region.
Bottom:
The gravitational-wave frequency
f
(left
axis) computed from the numerical-relativity waveform. The cross denotes the location of the maximum of the waveform amplitude,
approximately coincident with the merger of the two black holes. During the inspiral,
f
can be related to an effective relative velocity
(right axis) given by the post-Newtonian parameter
v=c
¼ð
GM
π
f=c
3
Þ
1
=
3
, where
M
is the total mass.
PRL
116,
241103 (2016)
PHYSICAL REVIEW LETTERS
week ending
17 JUNE 2016
241103-6