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D
RAFT VERSION
O
CTOBER
17, 2017
Typeset using L
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preprint2
style in AASTeX61
A GRAVITATIONAL-WAVE STANDARD SIREN MEASUREMENT OF THE HUBBLE CONSTANT
T
HE
LIGO S
CIENTIFIC
C
OLLABORATION AND
T
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IRGO
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OLLABORATION
, T
HE
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OLLABORATION
,
T
HE
D
ARK
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NERGY
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AMERA
GW-EM C
OLLABORATION AND THE
DES C
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,
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OLLABORATION
, T
HE
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UMBRES
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BSERVATORY
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VINROUGE C
OLLABORATION
, T
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MASTER C
OLLABORATION
, et al.
ABSTRACT
The detection of GW170817 (Abbott et al. 2017a) in both gravitational waves and electromagnetic waves
heralds the age of gravitational-wave multi-messenger astronomy. On 17 August 2017 the Advanced Laser
Interferometer Gravitational-wave Observatory (LIGO) (LIGO Scientific Collaboration et al. 2015) and
Virgo (Acernese et al. 2015) detectors observed GW170817, a strong signal from the merger of a binary
neutron-star system. Less than 2 seconds after the merger, a gamma-ray burst (GRB 170817A) was detected
within a region of the sky consistent with the LIGO-Virgo-derived location of the gravitational-wave source
(Abbott et al. 2017b; Goldstein et al. 2017; Savchenko et al. 2017). This sky region was subsequently
observed by optical astronomy facilities (Abbott et al. 2017c), resulting in the identification of an optical
transient signal within
10
arcsec of the galaxy NGC 4993 (Coulter et al. 2017; Soares-Santos et al. 2017;
Valenti et al. 2017; Arcavi et al. 2017; Tanvir et al. 2017; Lipunov et al. 2017). These multi-messenger
observations allow us to use GW170817 as a standard siren (Schutz 1986; Holz & Hughes 2005; Dalal et al.
2006; Nissanke et al. 2010, 2013), the gravitational-wave analog of an astronomical standard candle, to mea-
sure the Hubble constant. This quantity, which represents the local expansion rate of the Universe, sets the
overall scale of the Universe and is of fundamental importance to cosmology. Our measurement combines
the distance to the source inferred purely from the gravitational-wave signal with the recession velocity
inferred from measurements of the redshift using electromagnetic data. This approach does not require
any form of cosmic “distance ladder” (Freedman et al. 2001); the gravitational-wave (GW) analysis can be
used to estimate the luminosity distance out to cosmological scales directly, without the use of intermedi-
ate astronomical distance measurements. We determine the Hubble constant to be
70
.
0
+12
.
0
8
.
0
km s
1
Mpc
1
(maximum a posteriori and 68% credible interval). This is consistent with existing measurements (Planck
Collaboration et al. 2016; Riess et al. 2016), while being completely independent of them. Additional
standard-siren measurements from future gravitational-wave sources will provide precision constraints of
this important cosmological parameter.
arXiv:1710.05835v1 [astro-ph.CO] 16 Oct 2017
2
The Hubble constant
H
0
measures the mean ex-
pansion rate of the Universe. At nearby distances
(
d
.
50
Mpc) it is well approximated by the ex-
pression
v
H
=
H
0
d,
(1)
where
v
H
is the local “Hubble flow” velocity of a
source, and
d
is the distance to the source. At such
distances all cosmological distance measures (such
as luminosity distance and comoving distance) dif-
fer at the order of
v
H
/c
where
c
is the speed of
light. As
v
H
/c
1%
for GW170817 we do not
distinguish between them. We are similarly insen-
sitive to the values of other cosmological parame-
ters, such as
m
and
Λ
.
To obtain the Hubble flow velocity at the posi-
tion of GW170817, we use the optical identifica-
tion of the host galaxy NGC 4993 (Abbott et al.
2017c). This identification is based solely on the
2-dimensional projected offset and is independent
of any assumed value of
H
0
. The position and red-
shift of this galaxy allow us to estimate the appro-
priate value of the Hubble flow velocity. Because
the source is relatively nearby the random relative
motions of galaxies, known as peculiar velocities,
need to be taken into account. The peculiar veloc-
ity is
10%
of the measured recessional velocity
(see Methods).
The original standard siren proposal (Schutz
1986) did not rely on the unique identification of
a host galaxy. By combining information from
100
independent GW detections, each with a set
of potential host galaxies, a
5%
estimate of
H
0
can be obtained even without the detection of any
transient optical counterparts (Del Pozzo 2012).
This is particularly relevant, as gravitational-wave
networks will detect many binary black hole merg-
ers over the coming years (Abbott et al. 2016a),
and these are not expected to be accompanied by
electromagnetic counterparts. Alternatively, if an
EM counterpart has been identified but the host
galaxy is unknown, the same statistical method
can be applied but using only those galaxies in
a narrow beam around the location of the opti-
cal counterpart. However, such statistical analyses
are sensitive to a number of complicating effects,
including the incompleteness of current galaxy cat-
alogs or the need for dedicated follow-up surveys,
as well as a range of selection effects (Messen-
ger & Veitch 2013). In what follows we exploit
the identification of NGC 4993 as the host galaxy
of GW170817 to perform a standard siren mea-
surement of the Hubble constant (Holz & Hughes
2005; Dalal et al. 2006; Nissanke et al. 2010,
2013).
Analysis of the GW data associated with GW170817
produces estimates for the parameters of the
source, under the assumption that general rela-
tivity is the correct model of gravity (Abbott et al.
2017a). We are most interested in the joint pos-
terior distribution on the luminosity distance and
binary orbital inclination angle. For the analysis in
this paper we fix the location of the GW source on
the sky to the identified location of the counterpart
(Coulter et al. 2017). See the Methods section for
details.
An analysis of the GW data alone finds that
GW170817 occurred at a distance
d
= 43
.
8
+2
.
9
6
.
9
Mpc
(all values are quoted as the maximum posterior
value with the minimal width
68
.
3%
credible inter-
val). We note that the distance quoted here differs
from that in other studies (Abbott et al. 2017a),
since here we assume that the optical counter-
part represents the true sky location of the GW
source instead of marginalizing over a range of
potential sky locations. The
15%
uncertainty
is due to a combination of statistical measurement
error from the noise in the detectors, instrumen-
tal calibration uncertainties (Abbott et al. 2017a),
and a geometrical factor dependent upon the cor-
relation of distance with inclination angle. The
GW measurement is consistent with the distance
to NGC 4993 measured using the Tully-Fisher re-
lation,
d
TF
= 41
.
1
±
5
.
8 Mpc
(Sakai et al. 2000;
Freedman et al. 2001).