of 12
GW170817: Implications for the Stochastic Gravitational-Wave
Background from Compact Binary Coalescences
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 16 October 2017; revised manuscript received 16 January 2018; published 28 February 2018)
The LIGO Scientific and Virgo Collaborations have announced the event GW170817, the first detection
of gravitational waves from the coalescence of two neutron stars. The merger rate of binary neutron stars
estimated from this event suggests that distant, unresolvable binary neutron stars create a significant
astrophysical stochastic gravitational-wave background. The binary neutron star component will add to the
contribution from binary black holes, increasing the amplitude of the total astrophysical background
relative to previous expectations. In the Advanced LIGO-Virgo frequency band most sensitive to
stochastic backgrounds (near 25 Hz), we predict a total astrophysical background with amplitude
Ω
GW
ð
f
¼
25
Hz
Þ¼
1
.
8
þ
2
.
7
1
.
3
×
10
9
with 90% confidence, compared with
Ω
GW
ð
f
¼
25
Hz
Þ¼
1
.
1
þ
1
.
2
0
.
7
×
10
9
from binary black holes alone. Assuming the most probable rate for compact binary mergers, we find that
the total background may be detectable with a signal-to-noise-ratio of 3 after 40 months of total observation
time, based on the expected timeline for Advanced LIGO and Virgo to reach their design sensitivity.
DOI:
10.1103/PhysRevLett.120.091101
Introduction.
On 17 August 2017, the Laser
Interferometer Gravitational-Wave Observatory (LIGO)
[1]
Scientific and Virgo
[2]
Collaborations detected a
new gravitational-wave source: the coalescence of two
neutron stars
[3]
. This event, GW170817, comes almost
two years after GW150914, the first direct detection of
gravitational waves from the merger of two black holes
[4]
.
In total, six high confidence events detections and one sub-
threshold candidate from binary black hole merger events
have been reported: GW150914
[4]
, GW151226
[5]
,
LVT151012
[6]
, GW170104
[7]
, GW170608
[8]
, and
GW170814
[9]
. The last of these events was reported as
a three-detector observation by the two Advanced LIGO
detectors located in Hanford, Washington, and Livingston,
Louisiana, in the United States and the Advanced Virgo
detector, located in Cascina, Italy.
In addition to loud and nearby events that are detectable as
individual sources, there is also a population of unresolved
events at greater distances. The superposition of these
sources will contribute an astrophysical stochastic back-
ground, which is discernible from detector noise by cross-
correlating the data streams from two or more detectors
[10,11]
. For a survey of the expected signature of astro-
physical backgrounds, see
[12
18]
. See also
[19]
for a recent
review of data analysis tools for stochastic backgrounds.
Following the first detection of gravitational waves from
GW150914, the LIGO and Virgo Collaborations calculated
the expected stochastic background from a binary black
hole (BBH) population with similar masses to the
components of GW150914
[20]
. These calculations were
updated at the end of the first Advanced LIGO observing
run (O1)
[21]
to take into account the two other black hole
merger events observed during the run: GW151226, a high-
confidence detection, and LVT151012, an event of lower
significance. The results indicated that the background
from black hole mergers would likely be detectable
by Advanced LIGO and Advanced Virgo after a few
years of their operation at design sensitivity. In the most
optimistic case, a detection is possible even before instru-
mental design sensitivity is reached.
In this Letter, we calculate the contribution to the
background from a binary neutron star (BNS) population
using the measured BNS merger rate derived from
GW170817
[3]
. We also update the previous predictions
of the stochastic background from BBH mergers taking
into account the most recent published statements about the
rate of events
[7]
. We find the contributions to the back-
ground from BBH and BNS mergers to be of similar
magnitude. As a consequence, an astrophysical background
(including contributions from BNS and BBH mergers) may
be detected earlier than previously anticipated.
Background from compact binary mergers.
The
energy-density spectrum of a gravitational wave back-
ground can be described by the dimensionless quantity
Ω
GW
ð
f
Þ¼
f
ρ
c
d
ρ
GW
df
;
ð
1
Þ
which represents the fractional contribution of gravitational
waves to the critical energy density of the Universe
[10]
.
Here
d
ρ
GW
is the energy density in the frequency interval
f
*
Full author list given at the end of the article.
PHYSICAL REVIEW LETTERS
120,
091101 (2018)
Editors' Suggestion
0031-9007
=
18
=
120(9)
=
091101(12)
091101-1
© 2018 American Physical Society
to
f
þ
df
,
ρ
c
¼
3
H
2
0
c
2
/
ð
8
π
G
Þ
is the critical energy
density of the Universe, and the Hubble parameter
H
0
¼
67
.
9

0
.
55
km s
1
Mpc
1
is taken from Planck
[22]
.
In order to model the background from all the binary
mergers in the Universe, we follow a similar approach
to
[20]
. A population of binary merger events may be
characterized by a set of average source parameters
θ
(such
as component masses or spins). If such a population merges
at a rate
R
m
ð
z
;
θ
Þ
per unit comoving volume per unit source
time at a given redshift
z
, then the total gravitational-wave
energy density spectrum from all the sources is given by
(see, e.g.
[12,20]
)
Ω
GW
ð
f;
θ
Þ¼
f
ρ
c
H
0
Z
z
max
0
dz
R
m
ð
z
;
θ
Þ
dE
GW
ð
f
s
;
θ
Þ
/
df
s
ð
1
þ
z
Þ
E
ð
Ω
M
;
Ω
Λ
;z
Þ
:
ð
2
Þ
Here
dE
GW
ð
f
s
;
θ
Þ
/
df
s
is the energy spectrum emitted
by a single source evaluated in terms of the source
frequency
f
s
¼ð
1
þ
z
Þ
f
. The function
E
ð
Ω
M
;
Ω
Λ
;z
Þ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Ω
M
ð
1
þ
z
Þ
3
þ
Ω
Λ
p
accounts for the dependence of
comoving volume on redshift assuming the best-fit cos-
mology from Planck
[22]
, where
Ω
M
¼
1
Ω
Λ
¼
0
.
3065
.
We choose to cut off the redshift integral at
z
max
¼
10
.
Redshifts larger than
z
¼
5
contribute little to the integral
because of the
½ð
1
þ
z
Þ
E
ð
z
Þ
1
factor in Eq.
(2)
, as well as
the small number of stars formed at such high redshift; see,
for example,
[12
18,23]
.
The energy spectrum
dE
GW
/
df
s
is determined from the
strain waveform of the binary system. The dominant
contribution to the background comes from the inspiral
phase of the binary merger, for which
dE
/
df
s
M
c
5/3
f
1/3
,
where
M
c
¼ð
m
1
m
2
Þ
3
/5
/
ð
m
1
þ
m
2
Þ
1/5
is the chirp mass for
a binary system with component masses
m
1
and
m
2
. In the
BNS case we only consider the inspiral phase, since
neutron stars merge at
2
kHz, well above the sensitive
band of stochastic searches. We introduce a frequency
cutoff at the innermost stable circular orbit. For BBH
events, we include the merger and ringdown phases
using the waveforms from
[13,24]
with the modifications
from
[25]
.
The merger rate
R
m
ð
z
;
θ
Þ
is given by
R
m
ð
z
;
θ
Þ¼
Z
t
max
t
min
R
f
ð
z
f
;
θ
Þ
p
ð
t
d
;
θ
Þ
dt
d
;
ð
3
Þ
where
t
d
is the time delay between formation and merger of
a binary,
p
ð
t
d
;
θ
Þ
is the time delay distribution given
parameters
θ
,
z
f
is the redshift at the formation time
t
f
¼
t
ð
z
Þ
t
d
, and
t
ð
z
Þ
is the age of the Universe at merger.
We assume that the binary formation rate
R
f
ð
z
f
;
θ
Þ
scales
with the star formation rate. For the BNS background, we
make similar assumptions to those used in
[20]
, which are
outlined in what follows below. We adopt the star formation
model of
[26]
, which produces very similar results as
compared to the model described by
[27]
. We assume a
time delay distribution
p
ð
t
d
Þ
1
/
t
d
, for
t
min
<t
d
<t
max
.
Here
t
min
is the minimum delay time between the binary
formation and merger. We assume
t
min
¼
20
Myr
[28]
. The
maximum time delay
t
max
is set to the Hubble time
[29
37]
.
We also need to consider the distribution of the component
masses to calculate
Ω
GW
. We assume that each mass is
drawn from uniform distribution ranging from 1 to
2
M
.
The value of
R
m
at
z
¼
0
is normalized to the median
BNS merger rate implied by GW170817, which is
1540
þ
3200
1220
Gpc
3
yr
1
[3]
. This rate is slightly higher than
the realistic BNS merger rate predictions of
[38]
, and those
adopted in previous studies (e.g.
[12,14]
), but is consistent
with optimistic predictions.
The calculation of the BBH background is similar, with
the following differences. We assume
t
min
¼
50
Myr for
the minimum time delay
[20,37]
. Massive black holes are
formed preferentially in low-metallicity environments.
For binary systems with at least one black hole more
massive than
30
M
, we therefore reweight the star
formation rate
R
f
ð
z
Þ
by the fraction of stars with metal-
licities
Z
Z
/2. Following
[20]
, we adopt the mean
metallicity-redshift relation of
[27]
, with appropriate
scalings to account for local observations
[26,39]
.Fora
consistent computation, a mass distribution needs to be
specified. We use a power-law distribution of the primary
(i.e., larger mass) component
p
ð
m
1
Þ
m
2
.
35
1
and a uni-
form distribution of the secondary
[6,7]
.Inaddition,we
require that the component masses take values in the range
5
95
M
with
m
1
þ
m
2
<
100
M
and
m
2
<m
1
,in
agreement with the observations of BBHs to date
[7]
.
For the rate of BBH mergers, we use the most recent
published result associated with the power-law mass
distribution
103
þ
110
63
Gpc
3
yr
1
[7,40]
.Asshownin
[21]
, using a flat-log mass distribution instead of the
power-law only affects
Ω
GW
ð
f
Þ
at frequencies above
100 Hz, which has very little impact on the detectability
of the stochastic background with LIGO and Virgo.
Frequencies below 100 Hz contribute to more than
99% of the sensitivity of the stochastic search
[21]
.
The choices affecting the mass distribution have a
minimal effect on the background energy density
Ω
GW
in the low frequency part of the spectrum. We estimate the
magnitude of the effect on the rate
R
using the approximate
scaling relationship
R
h
VT
i
1
h
M
5
/2
c
i
1
, where
VT
is
the sensitive spacetime volume of the instrument
[41,42]
.In
the BBH case, for example, imposing a mass cutoff of
m
1
,
m
2
<
50
M
to the power-law mass distribution reduces
the estimate by less than 15%. Similarly, using the same
scaling law, we estimate that replacing a uniform mass
distribution for BNS with a Gaussian mass distribution
centered around
1
.
4
M
leads to an increase of approx-
imately 10%. Both adjustments are well within the dom-
inant statistical Poisson uncertainty.
PHYSICAL REVIEW LETTERS
120,
091101 (2018)
091101-2