of 15
UPPER LIMITS ON THE RATES OF BINARY NEUTRON STAR AND NEUTRON STAR
BLACK HOLE
MERGERS FROM ADVANCED LIGO
S FIRST OBSERVING RUN
LIGO Scienti
fi
c Collaboration and Virgo Collaboration
(
See the end matter for the full list of authors.
)
Received 2016 July 27; revised 2016 October 5; accepted 2016 October 8; published 2016 November 23
ABSTRACT
We report here the non-detection of gravitational waves from the merger of binary
neutron star systems and
neutron star
black hole systems during the
fi
rst observing run of the Advanced Laser Interferometer Gravitational-
wave Observatory
(
LIGO
)
. In particular, we searched for gravitational-wave signals from binary
neutron star
systems with component masses
Î
M
1, 3
[]
and component dimensionless spins
<
0.05. We also searched for
neutron star
black hole systems with the same neutron star parameters, black hole mass
Î
M
2, 99
[]
, and no
restriction on the black hole spin magnitude. We assess the sensitivity of the two LIGO detectors to these systems
and
fi
nd that they could have detected the merger of binary
neutron star systems with component mass
distributions of 1.35
±
0.13
M
e
at a volume-weighted average distance of
70 Mpc, and for neutron star
black
hole systems with neutron star masses of 1.4
M
e
and black hole masses of at least 5
M
e
, a volume-weighted
average distance of at least
110 Mpc. From this we constrain with 90% con
fi
dence the merger rate to be less than
12,600
Gpc
3
yr
1
for binary
neutron star systems and less than 3600
Gpc
3
yr
1
for neutron star
black hole
systems. We discuss the astrophysical implications of these results, which we
fi
nd to be in con
fl
ict with only the
most optimistic predictions. However, we
fi
nd that if no detection of neutron star
binary mergers is made in the
next two Advanced LIGO and Advanced Virgo observing runs we would place signi
fi
cant constraints on the
merger rates. Finally, assuming a rate of
-
+
10
7
20
Gpc
3
yr
1
, short gamma-ray bursts beamed toward the Earth, and
assuming that all short gamma-ray bursts have binary
neutron star
(
neutron star
black hole
)
progenitors, we can
use our 90% con
fi
dence rate upper limits to constrain the beaming angle of the gamma-ray burst to be greater than
-
+
2
.3
1.1
1.7
(
-
+
4
.3
1.9
3.1
)
.
Key words:
binaries: general
gamma-ray burst: general
gravitational waves
stars: black holes
stars: neutron
1. INTRODUCTION
Between 2015 September 12 and 2016 January 19 the two
advanced Laser Interferometer Gravitational-wave Observatory
(
LIGO
)
detectors conducted their
fi
rst observing period
(
O1
)
.
During O1, two high-mass binary black hole
(
BBH
)
events
were identi
fi
ed with high con
fi
dence
(
>
5
σ
)
: GW150914
(
Ab-
bott et al.
2016i
)
and GW151226
(
Abbott et al.
2016g
)
. A third
signal, LVT151012, was also identi
fi
ed with 1.7
σ
con
fi
den-
ce
(
Abbott et al.
2016c
,
2016f
)
In all three cases, the
component masses are con
fi
dently constrained to be above
the 3.2
M
e
upper mass limit of neutron stars
(
NSs
)
set by
theoretical considerations
(
Rhoades & Ruf
fi
ni
1974
; Abbott
et al.
2016j
)
. The details of these observations, investigations
about the properties of the observed BBH mergers, and the
astrophysical implications are explored in Abbott et al.
(
2016a
,
2016b
,
2016c
,
2016j
,
2016l
,
2016m
)
.
The search methods that successfully observed these BBH
mergers also target other types of compact binary coalescences
(
CBCs
)
, speci
fi
cally the inspiral and merger of neutron star
neutron star
(
BNS
)
systems and neutron star
black hole
(
NSBH
)
systems. Such systems were considered among the
most promising candidates for an observation in O1. For
example, a calculation prior to the start of O1 predicted
0.0005
4 detections of BNS signals during O1
(
Aasi
et al.
2016
)
. Some works, however, predicted that BBH
mergers would be the most promising candidates
(
Dominik
et al.
2015
; Belczynski et al.
2016
; Kinugawa et al.
2016
)
.
In this Letter, we report on the search for BNS and NSBH
mergers in O1. We have searched for BNS systems with
component masses
Î
M
1, 3
[]
, component dimensionless spins
<
0.05, and spin orientations aligned or anti-aligned with the
orbital angular momentum. We have searched for NSBH
systems with neutron star mass
Î
M
1, 3
[]
, black hole
(
BH
)
mass
Î
M
2, 99
[]
, neutron star dimensionless spin magnitude
<
0.05, BH dimensionless spin magnitude
<
0.99, and both
spins aligned or anti-aligned with the orbital angular momen-
tum. No observation of either BNS or NSBH mergers was
made in O1. We explore the astrophysical implications of this
result, placing upper limits on the rates of such merger events
in the local universe that are roughly an order of magnitude
smaller than those obtained with data from initial LIGO and
initial Virgo
(
Acernese et al.
2008
; Abbott et al.
2009
; Abadie
et al.
2012d
)
. We compare these updated rate limits to current
predictions of BNS and NSBH merger rates and explore how
the non-detection of BNS and NSBH systems in O1 can be
used to explore possible constraints of the opening angle of the
radiation cone of short gamma-ray bursts
(
GRBs
)
, assuming
that short GRB progenitors are BNS or NSBH mergers.
The layout of this Letter is as follows. In Section
2
,we
describe the motivation for our search parameter space. In
Section
3
, we brie
fl
y describe the search methodology, then
describe the results of the search in Section
4
. We then discuss
the constraints that can be placed on the rates of BNS and
NSBH mergers in Section
5
and the astrophysical implications
of the rates in Section
6
. Finally, we conclude in Section
7
.
2. SOURCE CONSIDERATIONS
There are currently thousands of known NSs, most detected
as pulsars
(
Manchester et al.
2005
; Hobbs et al.
2016
)
.Of
these,
70 are found in binary systems and allow estimates of
The Astrophysical Journal Letters,
832:L21
(
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)
, 2016 December 1
doi:10.3847
/
2041-8205
/
832
/
2
/
L21
© 2016. The American Astronomical Society. All rights reserved.
1
the NS mass
(
Lattimer
2012
; Antoniadis et al.
2016
; Ott et al.
2016
; Ozel & Freire
2016
)
. Published mass estimates range
from 1.0
±
0.17
M
e
(
Falanga et al.
2015
)
to 2.74
±
0.21
M
e
(
Freire et al.
2008
)
. Considering only precise mass measure-
ments from these observations one can set a lower bound on the
maximum possible neutron star mass of 2.01
±
0.04
M
e
(
Antoniadis et al.
2013
)
and theoretical considerations set an
upper bound on the maximum possible neutron star mass of
2.9
3.2
M
e
(
Rhoades & Ruf
fi
ni
1974
; Kalogera & Baym
1996
)
.
The standard formation scenario of core-collapse supernovae
restricts the birth masses of neutron stars to be above 1.1
M
e
(
Lattimer
2012
; Ozel et al.
2012
; Kiziltan et al.
2013
)
.
Several candidate BNS systems allow mass measurements
for individual components, giving a much narrower mass
distribution
(
Lorimer
2008
)
. Masses are reported between
1.0
M
e
and 1.56
M
e
(
Martinez et al.
2015
; Ott et al.
2016
;
Ozel & Freire
2016
)
and are consistent with an underlying
mass distribution of
M
1.35 0.13
(
)
(
Kiziltan et al.
2010
)
.
These observational measurements assume masses are greater
than 0.9
M
e
.
The fastest spinning pulsar observed so far rotates with a
frequency of 716 Hz
(
Hessels et al.
2006
)
. This corresponds to
a dimensionless spin
c
=
S
cGm
2
∣∣
of roughly 0.4, where
m
is
the object
ʼ
s mass and
S
is the angular momentum.
141
Such
rapid rotation rates likely require the NS to have been spun up
through mass transfer from its companion. The fastest spinning
pulsar in a con
fi
rmed BNS system has a spin frequency of
44 Hz
(
Kramer & Wex
2009
)
, implying that dimensionless
spins for NS in BNS systems are
„
0.04
(
Brown et al.
2012
)
.
However, recycled NS can have larger spins, and the potential
BNS pulsar J1807-2500B
(
Lynch et al.
2012
)
has a spin of
4.19 ms, giving a dimensionless spin of up to
0.2.
142
Given these considerations, we search for BNS systems with
both masses
Î
M
1, 3
[]
and component dimensionless aligned
spins
<
0.05. We note that some BNS systems with component
spins
>
0.05 are not recovered well when searching only for
systems with spins
<
0.05, as explored in Brown et al.
(
2012
)
.
However, increasing the search space to include BNS systems
with larger spins also increases the rate of false alarms. It was
found in Nitz
(
2015
)
that the overall search sensitivity for BNS
systems with spins
<
0.4 is larger when the search space
includes only systems with spins restricted to
<
0.05 than when
the search space is expanded to include spins
<
0.4.
143
NSBH systems are thought to be ef
fi
ciently formed in one of
two ways: either through the stellar evolution of
fi
eld binaries
or through dynamical capture of an NS by a BH
(
Grindlay
et al.
2006
; Sadowski et al.
2008
; Lee et al.
2010
; Benacquista
& Downing
2013
)
. Though no NSBH systems are known to
exist, likely progenitors have been observed, Cyg
X-3
(
Belczynski et al.
2013
; Casares et al.
2014
; Grudzinska
et al.
2015
)
.
Measurements of galactic stellar-mass BHs in X-ray binaries
yield BH masses 5
„
M
BH
/
M
e
„
24
(
Merloni
2008
; Ozel
et al.
2010
; Farr et al.
2011
; Wiktorowicz et al.
2013
; also see
the table in Wiktorowicz & Belcynski
2016
, for a full list of
citations for BH mass measurements
)
. Extragalactic high-mass
X-ray binaries, such as IC10 X-1 and NGC300 X-1 suggest BH
masses of 20
30
M
e
. Advanced LIGO has observed two
de
fi
nitive BBH systems and constrained the masses of the four
component BHs to
-
+
-
+
-
+
3
6 , 29 , 14
4
5
4
4
4
8
and
-
+
M
7
.5
2.3
2.3
, respec-
tively, and the masses of the two resulting BHs to
-
+
62
4
4
and
-
+
M
2
1
2
6
. In addition, if one assumes that the candidate BBH
merger LVT151012 was of astrophysical origin, then its
component BHs had masses constrained to
-
+
2
3
6
1
6
and
-
+
13
5
4
with
a resulting BH mass of
-
+
3
5
4
14
. There is an apparent gap of BHs
in the mass range 3
5
M
e
, which has been ascribed to the
supernova explosion mechanism
(
Belczynski et al.
2012
; Fryer
et al.
2012
)
. However, BHs formed from stellar evolution may
exist with masses down to 2
M
e
, especially if they are formed
from matter accreted onto neutron stars
(
O
Shaughnessy
et al.
2005a
)
. Depending on the amount of mass lost in stellar
winds, isolated and binary star evolution models typically
allow for stellar-mass BH up to
80
100
M
e
(
see, e.g.,
Woosley et al.
2002
; Heger et al.
2003
; Belczynski et al.
2010
;
Dominik et al.
2012
; Fryer et al.
2012
and references therein
)
;
stellar BHs with mass above 100
M
e
are also conceivable
(
Belczynski et al.
2014
; de Mink & Belczynski
2015
)
, possibly
separated from the low-mass region due to the effects of pair-
instability supernovae
(
Woosley et al.
2002
; Chen et al.
2014
;
Marchant et al.
2016
)
.
X-ray observations of accreting BHs indicate a broad
distribution of BH spin
(
Li et al.
2005
; Davis et al.
2006
;
McClintock et al.
2006
; Shafee et al.
2006
; Liu et al.
2008
; Gou
et al.
2009
; Miller et al.
2009
; Miller & Miller
2014
)
. Some
BHs observed in X-ray binaries have very large dimensionless
spins
(
e.g Cygnus X-1 at
>
0.95; Gou et al.
2011
; Fabian et al.
2012
)
, while others could have much lower spins
(
0.1;
McClintock et al.
2011
)
. Measured BH spins in high-mass
X-ray binary systems tend to have large values
(
>
0.85
)
, and
these systems are more likely to be progenitors of NSBH
binaries
(
McClintock et al.
2014
)
. Isolated BH spins are only
constrained by the relativistic Kerr bound
χ
„
1
(
Misner et al.
1973
)
. LIGO
ʼ
s observations of merging binary BH systems
yield weak constraints on component spins
(
Abbott et al.
2016c
,
2016g
,
2016j
)
. The microquasar XTE J1550-564
(
Stei-
ner & McClintock
2012
)
and population synthesis models
(
Fragos et al.
2010
)
indicate small spin
orbit misalignment in
fi
eld binaries. Dynamically formed NSBH systems, in contrast,
are expected to have no correlation between the spins and the
orbit.
We search for NSBH systems with NS mass
Î
M
1, 3
[]
,
NS dimensionless spins
<
0.05, BH mass
Î
M
2, 99
[]
,and
BH spin magnitude
<
0.99. Current search techniques are
restricted to waveform models where the spins are
(
anti-
)
aligned with the orbit
(
Usman et al.
2016
; Messick et al.
2016
)
, although methods to extend this to generic spins are
being explored
(
Harry et al.
2016
)
. Nevertheless, aligned-
spin searches have been shown to have good sensitivity to
systems with generic spin orientations in O1
(
Dal Canton
et al.
2015
; Harry et al.
2016
)
. An additional search for BBH
systems with total mass greater than 100
M
e
is also being
performed, the results of whic
hwillbereportedinafuture
publication.
141
Assuming a mass of 1.4
M
e
and a moment of inertia
=
J
/
Ω
of 1.5
×
10
45
gcm
2
; the exact moment of inertia is dependent on the unknown NS equation
of state
(
Lattimer
2012
)
.
142
Calculated with a pulsar mass of 1.37
M
e
and a high moment of inertia,
2
×
10
45
gcm
2
.
143
This assumes an isotropic distribution of spins on both bodies. The systems
that are not recovered well using search space where the dimensionless aligned
spins are
<
0.05 are those systems where both spins are large, are aligned with
the orbital plane, and point in the same direction. Such systems are quite rare
when considering an isotropic distribution of spins.
2
The Astrophysical Journal Letters,
832:L21
(
15pp
)
, 2016 December 1
Abbott et al.
3. SEARCH DESCRIPTION
To observe CBCs in data taken from Advanced LIGO we
use matched-
fi
ltering against models of compact binary merger
gravitational-wave
(
GW
)
signals
(
Wainstein & Zubakov
1962
)
.
Matched-
fi
ltering has long been the primary tool for modeled
GW searches
(
Abbott et al.
2004
; Abadie et al.
2012d
)
. As the
emitted GW signal varies signi
fi
cantly over the range of masses
and spins in the BNS and NSBH parameter space, the matched-
fi
ltering process must be repeated over a large set of
fi
lter
waveforms, or
template bank
(
Owen & Sathyaprakash
1999
)
.
The ranges of masses considered in the searches are shown in
Figure
1
. The matched-
fi
lter process is conducted indepen-
dently for each of the two LIGO observatories before searching
for any potential GW signals observed at both observatories
with the same masses and spins and within the expected light
travel time delay. A summary statistic is then assigned to each
coincident event based on the estimated rate of false alarms
produced by the search background that would be more
signi
fi
cant than the event.
BNS and NSBH mergers are prime candidates not only for
observation with GW facilities, but also for coincident
observation with electromagnetic
(
EM
)
observatories
(
Eichler
et al.
1989
; Narayan et al.
1992
; Li & Paczynski
1998
; Hansen
& Lyutikov
2001
; Nakar
2007
; Nakar & Piran
2011
; Metzger
& Berger
2012
; Berger
2014
; Zhang
2014
; Fong et al.
2015
)
.
We have a long history of working with the
Fermi
,
Swift
, and
IPN GRB teams to perform sub-threshold searches of GW data
in a narrow window around the time of observed GRBs
(
Ab-
bott et al.
2005
,
2008
; Abadie et al.
2012b
,
2012c
)
. Such a
search is currently being performed on O1 data and will be
reported in a forthcoming publication. In O1 we also aimed to
rapidly alert EM partners if a GW observation was made
(
Ab-
bott et al.
2016h
)
. Therefore, it was critical for us to rapidly
search for compact coalescences in our data to identify
potential BNS or NSBH mergers within a timescale of minutes
after the data is taken, thereby giving EM partners the best
chance to perform a coincident observation. We refer to this as
our
online
search.
Nevertheless, analyses running with minute latency do not
have access to full data-characterization studies, which can take
weeks to perform, or to data with the most complete knowledge
about calibration and associated uncertainties. Additionally, in
rare instances, online analyses may fail to analyze stretches of
data due to computational failure. Therefore, it is also
important to have an
of
fl
ine
search, which performs the
most sensitive search possible for BNS and NSBH sources. We
give here a brief description of both the of
fl
ine and online
searches, referring to other works to give more details when
relevant.
3.1. Of
fl
ine Search
The of
fl
ine CBC search of the O1 data set consists of two
independently implemented matched-
fi
lter analyses:
GstLAL
(
Messick et al.
2016
)
and
PyCBC
(
Usman et al.
2016
)
.For
detailed descriptions of these analyses and associated methods
we refer the reader to Allen
(
2005
)
, Allen et al.
(
2012
)
,Babak
et al.
(
2013
)
, Dal Canton et al.
(
2014
)
,andUsmanetal.
(
2016
)
for
PyCBC
and Cannon et al.
(
2012
,
2013
)
, Privitera et al.
(
2014
)
, and Messick et al.
(
2016
)
for
GstLAL
. We also refer the
reader to Abbott et al.
(
2016c
,
2016f
)
for a detailed description
of the of
fl
ine search of the O1 data set; here, we give only a brief
overview.
In contrast to the online search, the of
fl
ine search uses data
produced with smaller calibration errors
(
Abbott et al.
2016d
)
,
uses complete information about the instrumental data
quality
(
Abbott et al.
2016e
)
, and ensures that all available
data is analyzed. The of
fl
ine search in O1 forms a single search
targeting BNS, NSBH, and BBH systems. The waveform
fi
lters
cover systems with individual component masses ranging from
1to99
M
e
, total mass constrained to less than 100
M
e
(
see
Figure
1
)
, and component dimensionless spins up to
±
0.05 for
components with mass less than 2
M
e
and
±
0.99 otherwi-
se
(
Abbott et al.
2016c
; Capano et al.
2016
)
. Waveform
fi
lters
with total mass less than 4
M
e
(
chirp mass less than
1.73
M
e
144
)
for
PyCBC
(
GstLAL
)
are modeled with the
inspiral-only, post-Newtonian, frequency-domain approximant
TaylorF2
(
Arun et al.
2009
; Bohé et al.
2013
,
2015
;
Blanchet
2014
; Mishra et al.
2016
)
. At larger masses, it
becomes important to also include the merger and ringdown
components of the waveform. There a reduced-order model of
the effective-one-body waveform calibrated against numerical
relativity is used
(
Taracchini et al.
2014
; Pürrer
2016
)
.
3.2. Online Search
The online compact binary coalescence
(
CBC
)
search of the
O1 data also consisted of two analyses; an online version of
GstLAL
(
Messick et al.
2016
)
and
mbta
(
Adams et al.
2016
)
.
For detailed descriptions of the
mbta
analysis we refer the
reader to Beauville et al.
(
2008
)
, Abadie et al.
(
2012a
)
, and
Adams et al.
(
2016
)
. The bank of waveform
fi
lters used by
GstLAL
up to 2015 December 23
and by
mbta
for the
duration of O1
targeted systems that contained at least one
NS. Such systems are most likely to have an EM counterpart,
which would be powered by the material from a disrupted NS.
Figure 1.
Range of template mass parameters considered for the three different
template banks used in the search. The of
fl
ine analyses and online
GstLAL
after 2015 December 23 used the largest bank up to total masses of 100
M
e
.
The online
mbta
bank covered primary masses below 12
M
e
and chirp masses
(
see footnote 143
)
below 5
M
e
. The early online
GstLAL
bank up to 2015
December 23 covered primary masses up to 16
M
e
and secondary masses up to
2.8
M
e
. The spin ranges are not shown here but are discussed in the text.
144
The
chirp mass
is the combination of the two component masses that
LIGO is most sensitive to, given by
=+
-
mm m m
12
35
12
15
()(
)
, where
m
i
denotes the two component masses.
3
The Astrophysical Journal Letters,
832:L21
(
15pp
)
, 2016 December 1
Abbott et al.
These sets of waveform
fi
lters were constructed using methods
described in Brown et al.
(
2012
)
, Harry et al.
(
2014
)
, and
Pannarale & Ohme
(
2014
)
.
GstLAL
chose to cover systems
with component masses of
ÎÎ

mMm M
1, 16 ;
1, 2.8
12
[]
[ ]
and
mbta
covered
Î
mm
M
,1,12
12
[]
with a limit on chirp
mass
<
5M
(
see Figure
1
)
.In
GstLAL,
component
spins were limited to
χ
i
<
0.05 for
m
i
<
2.8
M
e
and
χ
i
<
1
otherwise, for
mbta
χ
i
<
0.05 for
m
i
<
2
M
e
and
χ
i
<
1
otherwise.
GstLAL
also chose to limit the template bank to
include only systems for which it is possible for an NS to have
disrupted during the late inspiral using constraints described in
Pannarale & Ohme
(
2014
)
. For the
mbta
search the waveform
fi
lters were modeled using the
TaylorT4
time-domain, post-
Newtonian inspiral approximant
(
Buonanno et al.
2009
)
. For
GstLAL
the TaylorF2 frequency-domain, post-Newtonian
waveform approximant was used
(
Arun et al.
2009
; Bohé
et al.
2013
,
2015
; Blanchet
2014
; Mishra et al.
2016
)
. All
waveform models used in this paper are publicly available in
the
lalsimulation
repository
(
Mercer et al.
2016
)
.
145
After 2015 December 23, and triggered by the discovery of
GW150914, the
GstLAL
analysis was extended to cover the
same search space
using the same set of waveform
fi
lters
as
the of
fl
ine search
(
Abbott et al.
2016c
; Capano et al.
2016
)
.
3.3. Data Set
Advanced LIGO
ʼ
s
fi
rst observing run occurred between
2015 September 12 and 2016 January 19 and consists of data
from the two LIGO observatories in Hanford, WA, and
Livingston, LA. The LIGO detectors were running stably with
roughly 40% coincident operation and had been commissioned
to roughly one-third of the design sensitivity by the time of the
start of O1
(
Martynov et al.
2016
)
. During this observing run,
the
fi
nal of
fl
ine data set consisted of 76.7 days of data from the
Hanford observatory and 65.8 days of data from the Livingston
observatory. We analyze only times during which
both
observatories took data, which is 49.0 days. Characterization
studies of the data set found 0.5 days of coincident data during
which time there was some identi
fi
ed instrumental problem
known to introduce excess noise
in at least one of the
interferometers
(
Abbott et al.
2016e
)
. These times are removed
before assessing the signi
fi
cance of events in the remaining
analysis time. Some additional time is not analyzed because of
restrictions on the minimal length of data segments and because
of data lost at the start and end of those segments
(
Abbott et al.
2016c
,
2016f
)
. These requirements are slightly different
between the two of
fl
ine analyses, and
PyCBC
analyzed 46.1
days of data while
GstLAL
analyzed 48.3 days of data.
The data available to the online analyses are not exactly the
same as that available to the of
fl
ine analyses. Some data were
not available online due to
(
for example
)
software failures and
can later be made available for of
fl
ine analysis. In contrast,
some data identi
fi
ed as analyzable for the online codes may
later be identi
fi
ed as invalid as the result of updated data-
characterization studies or because of problems in the
calibration of the data. During O1, a total of 52.2 days of
coincident data was made available for online analysis. Of this
coincident online data,
mbta
analyzed 50.5 days
(
96.6%
)
and
GstLAL
analyzed 49.4 days
(
94.6%
)
. A total of 52.0 days
(
99.5%
)
of data was analyzed by at least one of the online
analyses.
4. SEARCH RESULTS
The of
fl
ine search, targeting BBH as well as BNS and NSBH
mergers, found three signi
fi
cant events during O1. Two signals
were recovered with
>
5
σ
con
fi
dence
(
Abbott et al.
2016g
,
2016i
)
and a third signal was found with 1.7
σ
con
fi
dence
(
Abbott et al.
2016c
,
2016f
)
. Subsequent parameter inference
on all three of these events has determined that, to very high
con
fi
dence, they were not produced by a BNS or NSBH
merger
(
Abbott et al.
2016c
,
2016j
)
. No other events are
signi
fi
cant with respect to the noise background in the of
fl
ine
search
(
Abbott et al.
2016c
)
, and we therefore state that no
BNS or NSBH mergers were observed.
The online search identi
fi
ed a total of eight unique GW
candidate events with a false-alarm rate
(
FAR
)
less than 6 yr
1
.
Events with an FAR less than this are sent to electromagnetic
partners if they pass event validation. Six of the events were
rejected during the event validation as they were associated
with known non-Gaussian behavior in one of the observatories.
Of the remaining events, one was the BBH merger GW151226
reported in Abbott et al.
(
2016g
)
. The second event identi
fi
ed
by
GstLAL
was only narrowly below the FAR threshold, with
an FAR of 3.1 yr
1
. This event was also detected by
mbta
with a higher FAR of 35 yr
1
. This is consistent with noise in
the online searches and the candidate event was later identi
fi
ed
to have a false-alarm rate of 190 yr
1
in the of
fl
ine
GstLAL
analysis. Nevertheless, the event passed all event validation and
was released for EM follow-up observations, which showed no
signi
fi
cant counterpart. The results of the EM follow-up
program are discussed in more detail in Abbott et al.
(
2016h
)
.
All events identi
fi
ed by the
GstLAL
or
mbta
online
analyses with a false-alarm rate of less than 3200 yr
1
are
uploaded to an internal database known as the gravitational-
wave candidate event database
(
GraCEDb; Moe et al.
2016
)
.In
total, 486 events were uploaded from
mbta
and 868 from
GstLAL
. We can measure the latency of the online pipelines
from the time between the inferred arrival time of each event at
the Earth and the time at which the event is uploaded to
GraCEDb. This latency is illustrated in Figure
2
, where it can
be seen that both online pipelines achieved median latencies on
the order of one minute. We note that
GstLAL
uploaded twice
as many events as
mbta
because of a difference in how the
FAR was de
fi
ned. The FAR reported by
mbta
was de
fi
ned
relative to the rate of coincident data such that an event with an
FAR of 1 yr
1
is expected to occur once in a year of coincident
data. The FAR reported by
GstLAL
was de
fi
ned relative to
wall-clock time such that an event with an FAR of 1 yr
1
is
expected to occur once in a calendar year. In the following
section, we use the
mbta
de
fi
nition of FAR when computing
rate upper limits.
5. RATES
5.1. Calculating Upper Limits
Given no evidence for BNS or NSBH coalescences during
O1, we seek to place an upper limit on the astrophysical rate of
such events. The expected number of observed events
Λ
in a
145
The internal
lalsimulation
names for the waveforms used as
fi
lters
described in this work are
TaylorF2
for the frequency-domain, post-
Newtonian approximant,
SpinTaylorT4
for the time-domain approximant
used by
mbta,
and
SEOBNRv2_ROM_DoubleSpin
for the aligned-spin
effective-one-body waveform. In addition, for calculation of rate estimates
describe in Section
5
, the
SpinTaylorT4
model is used to simulate BNS
signals and
SEOBNRv3
is used to simulate NSBH signals.
4
The Astrophysical Journal Letters,
832:L21
(
15pp
)
, 2016 December 1
Abbott et al.
given analysis can be related to the astrophysical rate of
coalescences for a given source
R
by
L= á ñ
RVT
.1
()
Here,
á
ñ
VT
is the spacetime volume that the detectors are
sensitive to
averaged over space, observation time, and the
parameters of the source population of interest, which we
describe in detail later in this section. The likelihood for
fi
nding
zero observations in the data
s
follows the Poisson distribution
for zero events
L=
-L
ps e
(∣ )
. Bayes
theorem then gives the
posterior for
Λ
LμL
-L
ps pe
,2
(∣)
()
()
where
p
(
Λ
)
is the prior on
Λ
.
Searches of initial LIGO and initial Virgo data used a
uniform prior on
Λ
(
Abadie et al.
2012d
)
but included prior
information from previous searches. For the O1 BBH search,
however, a Jeffreys prior of
Lμ L
p
1
()
for the Poisson
likelihood was used
(
Farr et al.
2015
; Abbott et al.
2016c
,
2016m
)
. A Jeffreys prior has the convenient property that the
resulting posterior is invariant under a change in parameteriza-
tion. However, for consistency with past BNS and NSBH
results we will primarily use a uniform prior. In a Poisson
posterior, a prior
LμL
a
-
p
()
produces a posterior mean that is
a
á
Lñ = + -
N
1
obs
, where
N
obs
is the number of observed
events
(
zero in our case
)
. Common choices for
α
are
α
=
0
(
fl
at; as we use here
)
,
α
=
1
/
2
(
Jeffreys; as used in Abbott
et al.
2016c
,
2016m
)
, and
α
=
1
(
fl
at in
L
log ;
this prior
produces an improper posterior for our situation of zero
observations, and therefore is not appropriate here
)
. The choice
of
α
involves a trade off between formal unbiasedness
(
á
Lñ =
N
ob
s
)
, achieved by the
α
=
1 prior, and applicability
in the
N
obs
=
0 case.
We do not include additional prior information from past
observations because the sensitive
á
ñ
VT
from all previous runs
is an order of magnitude smaller than that of O1. We estimate
á
ñ
VT
by adding a large number of simulated waveforms
sampled from an astrophysical population into the data. These
simulated signals are recovered with an estimate of the FAR
using the of
fl
ine analyses. Monte Carlo integration methods are
then utilized to estimate the sensitive volume to which the
detectors can recover gravitational-wave signals below a
chosen FAR threshold, which in this Letter we choose to be
0.01 yr
1
. This threshold is low enough that only signals that
are likely to be true events are counted as found, and we note
that varying this threshold in the range 0.0001
1
yr
1
only
changes the calculated
á
ñ
VT
by about
±
20%.
Calibration uncertainties lead to a difference between the
amplitude of simulated waveforms and the amplitude of real
waveforms with the same luminosity distance
d
L
. During O1,
the 1
σ
uncertainty in the strain amplitude was 6%, resulting in
an 18% uncertainty in the measured
á
ñ
VT
. Results presented
here also assume that injected waveforms are accurate
representations of astrophysical sources. We use a time-
domain, aligned-spin, post-Newtonian point-particle approx-
imant to model BNS injections
(
Buonanno et al.
2009
)
, and a
time-domain, effective-one-body waveform calibrated against
numerical relativity to model NSBH injections
(
Pan et al.
2014
;
Taracchini et al.
2014
)
. Waveform differences between these
models and the of
fl
ine search templates are therefore including
in the calculated
á
ñ
VT
. The injected NSBH waveform model is
not calibrated at high mass ratios
(
m
1
/
m
2
>
8
)
, so there is
some additional modeling uncertainty for large-mass NSBH
systems. The true sensitive volume
á
ñ
VT
will also be smaller if
the effect of tides in BNS or NSBH mergers is extreme.
However, for most scenarios the effects of waveform modeling
will be smaller than the effects of calibration errors and the
choice of prior discussed above.
The posterior on
Λ
(
Equation
(
2
))
can be reexpressed as a
joint posterior on the astrophysical rate
R
and the sensitive
volume
á
ñ
VT
áñμ áñ
-á ñ
pR VT s pR VT e
,,.3
RVT
(∣)()
()
The new prior can be expanded as
áñ
=
pR VT
,
()
áñáñ
pR VT p VT
(∣
) (
)
. For
áñ
pR VT
(∣
)
, we will either use a
uniform prior on
R
or a prior proportional to the Jeffreys prior
áñ
RVT
1
. As with Abbott et al.
(
2016c
,
2016k
,
2016m
)
,we
use a log-normal prior on
á
ñ
VT
ms
áñ=
pVT
ln
, ,
4
2
()
( )
()
where
μ
is the calculated value of
áñ
VT
ln
and
σ
represents the
fractional uncertainty in
á
ñ
VT
. Below, we will use an
uncertainty of
σ
=
18% due mainly to calibration errors.
Finally, a posterior for the rate is obtained by marginalizing
over
á
ñ
VT
,
ò
=áñ áñ
pRs dVTpR VT s
,.
5
(∣)
(
∣)
()
The upper limit
R
c
on the rate with con
fi
dence
c
is then given
by the solution to
ò
=
dR p R s c
.6
R
0
c
(∣)
()
For reference, we note that in the limit of zero uncertainty in
á
ñ
VT
, the uniform prior for
áñ
pR VT
(∣
)
gives a rate upper limit
of
=
--
áñ
R
c
VT
ln 1
,7
c
()
()
Figure 2.
Latency of the online searches during O1. The latency is measured as
the time between the event arriving at Earth and time at which the event is
uploaded to GraCEDb.
5
The Astrophysical Journal Letters,
832:L21
(
15pp
)
, 2016 December 1
Abbott et al.
corresponding to
=áñ
R
VT
2.303
90%
for a 90% con
fi
dence
upper limit
(
Biswas et al.
2009
)
. For a Jeffreys prior on
áñ
pR VT
(∣
)
, this upper limit is
=
áñ
-
R
c
VT
erf
,8
c
12
[()]
()
corresponding to
=áñ
R
VT
1.353
90%
for a 90% con
fi
dence
upper limit.
5.2. BNS Rate Limits
Motivated by considerations in Section
2
, we begin by
considering a population of BNS sources with a narrow range
of component masses sampled from the normal distribution

MM
1.35 , 0.13
2
(()
)
and truncated to remove samples
outside the range
[
1, 3
]
M
e
. We consider both a
low spin
BNS population, where spins are distributed with uniform
dimensionless spin magnitude
Î
0, 0.05
[
]
and isotropic direc-
tion, and a
high spin
BNS population with a uniform
dimensionless spin magnitude
Î
0, 0.4
[]
and isotropic direction.
Our population uses an isotropic distribution of sky location
and source orientation and chooses distances assuming a
uniform distribution in volume. These simulations are modeled
using a post-Newtonian waveform model, expanded using the
TaylorT4
formalism
(
Buonanno et al.
2009
)
. From this
population we compute the spacetime volume that Advanced
LIGO was sensitive to during the O1 observing run. Results are
shown for the measured
á
ñ
VT
in Table
1
using a detection
threshold of FAR
=
0.01 yr
1
. Because the template bank for
the searches use only aligned-spin BNS templates with
component spins up to 0.05, the
PyCBC
(
GstLAL
)
pipelines
are 4%
(
6%
)
more sensitive to the low-spin population than to
the high-spin population. The difference in
á
ñ
VT
between the
two analyses is no larger than 6%, which is consistent with the
difference in time analyzed in the two analyses. In addition, the
calculated
á
ñ
VT
has a Monte Carlo integration uncertainty of
1.5% due to the
fi
nite number of injection samples.
Using the measured
á
ñ
VT
, the rate posterior and upper limit
can be calculated from Equations
(
5
)
and
(
6
)
, respectively. The
posterior and upper limits are shown in Figure
3
and depend
sensitively on the choice of uniform versus Jeffreys prior for
L= á ñ
RVT
. However, they depend only weakly on the spin
distribution of the BNS population and on the width
σ
of the
uncertainty in
á
ñ
VT
. For the conservative uniform prior on
Λ
and an uncertainty in
á
ñ
VT
due to calibration errors of 18%, we
fi
nd the 90% con
fi
dence upper limit on the rate of BNS mergers
to be 12,100
Gpc
3
yr
1
for low spin and 12,600
Gpc
3
yr
1
for high spin using the values of
á
ñ
VT
calculated with
PyCBC
;
results for
GstLAL
are also shown in Table
1
. These numbers
can be compared to the upper limit computed from analysis of
Initial LIGO and Initial Virgo data
(
Abadie et al.
2012d
)
. There,
the upper limit for 1.35
1.35
M
e
non-spinning BNS mergers is
given as 130,000 Gpc
3
yr
1
. The O1 upper limit is more than
an order of magnitude lower than this previous upper limit.
To allow for uncertainties in the mass distribution of BNS
systems we also derive 90% con
fi
dence upper limits as a
function of the NS component masses. To do this, we construct a
population of software injections with component masses
sampled uniformly in the range
[
1, 3
]
M
e
and an isotropic
distribution of component spins with magnitudes uniformly
distributed in
[
0, 0.05
]
. We then bin the BNS injections by mass
and calculate
á
ñ
VT
and the associated 90% con
fi
dence rate upper
limit for each bin. The 90% rate upper limit for the conservative
uniform prior on
Λ
as a function of component masses is shown
in Figure
4
for
PyCBC
. The fractional difference between the
PyCBC
and
GstLAL
results ranges from 1% to 16%.
5.3. NSBH Rate Limits
Given the absence of known NSBH systems and uncertainty
in the BH mass, we evaluate the rate upper limit for a range of
BH masses. We use three masses that span the likely range of
BH masses: 5
M
e
,10
M
e
, and 30
M
e
. For the NS mass, we use
the canonical value of 1.4
M
e
. We assume a distribution of BH
spin magnitudes uniform in
[
0, 1
]
and NS spin magnitudes
uniform in
[
0, 0.04
]
. For these three mass pairs, we compute
upper limits for an isotropic spin distribution on both bodies,
Table 1
Sensitive Spacetime Volume
á
ñ
VT
and 90% Con
fi
dence Upper Limit
R
90%
for BNS Systems
Injection
Range of Spin
á
ñ
VT
(
Gpc
3
yr
)
Range
(
Mpc
)
R
90%
(
Gpc
3
yr
1
)
Set
Magnitudes
PyCBC GstLAL PyCBC GstLAL PyCBC GstLAL
Isotropic low spin
[
0, 0.05
]
2.09
×
10
4
2.21
×
10
4
73.2
73.6
12,100
11,400
Isotropic high spin
[
0, 0.4
]
2.00
×
10
4
2.08
×
10
4
72.1
72.1
12,600
12,100
Note.
Component masses are sampled from a normal distribution

MM
1.35 , 0.13
2
(()
)
with samples outside the range
[
1, 3
]
M
e
removed. Values are shown for
both the
pycbc
and
gstlal
pipelines.
á
ñ
VT
is calculated using an FAR threshold of 0.01 yr
1
. The rate upper limit is calculated using a uniform prior on
L= á ñ
RVT
and an 18% uncertainty in
á
ñ
VT
from calibration errors.
Figure 3.
Posterior density on the rate of BNS mergers calculated using the
PyCBC
analysis. Blue curves represent a uniform prior on the Poisson
parameter
L= á ñ
RVT
, while green curves represent a Jeffreys prior on
Λ
. The
solid
(
low spin population
)
and dotted
(
high spin population
)
posteriors almost
overlap. The vertical dashed and solid lines represent the 50% and 90%
con
fi
dence upper limits, respectively, for each choice of prior on
Λ
. For each
pair of vertical lines, the left line is the upper limit for the low spin population
and the right line is the upper limit for the high spin population. Also shown are
the realistic
R
re
and high-end
R
high
of the expected BNS merger rates identi
fi
ed
in Abadie et al.
(
2010
)
.
6
The Astrophysical Journal Letters,
832:L21
(
15pp
)
, 2016 December 1
Abbott et al.
and for a case where both spins are aligned or anti-aligned with
the orbital angular momentum
(
with equal probability of aligned
versus anti-aligned
)
. Our NSBH population uses an isotropic
distribution of sky location and source orientation and chooses
distances assuming a uniform distribution in volume. Wave-
forms are modeled using the spin-precessing, effective-one-
body model calibrated against numerical relativity waveforms
described in Taracchini et al.
(
2014
)
and Babak et al.
(
2016
)
.
The measured
á
ñ
VT
for an FAR threshold of 0.01 yr
1
is
given in Table
2
for
PyCBC
and
GstLAL
. The uncertainty in
the Monte Carlo integration of
á
ñ
VT
is 1.5%
2%. The
corresponding 90% con
fi
dence upper limits are also given
using the conservative uniform prior on
Λ
and an 18%
uncertainty in
á
ñ
VT
. Analysis-speci
fi
c differences in the limits
range from 1% to 20%, comparable or less than other
uncertainties such as calibration. These results can be compared
to the upper limits found for initial LIGO and Virgo for a
population of 1.35
M
e
5
M
e
NSBH binaries with isotropic
spin of 36,000 Gpc
3
yr
1
at 90% con
fi
dence
(
Abadie
et al.
2012d
)
. As with the BNS case, this is an improvement
in the upper limit of over an order of magnitude.
We also plot the 50% and 90% con
fi
dence upper limits from
PyCBC
and
GstLAL
as a function of mass in Figure
5
for the
uniform prior. The search is less sensitive to isotropic spins
than to
(
anti-
)
aligned spins due to two factors. First, the
volume-averaged signal power is larger for a population of
(
anti-
)
aligned-spin systems than for isotropic spin systems.
Second, the search uses a template bank of
(
anti-
)
aligned-spin
systems, and thus loses sensitivity when searching for systems
with signi
fi
cantly misaligned spins. As a result, the rate upper
limits are less constraining for the isotropic spin distribution
than for the
(
anti-
)
aligned-spin case.
6. ASTROPHYSICAL INTERPRETATION
We can compare our upper limits with rate predictions for
compact object mergers involving NSs, shown for BNS in
Figure
6
and for NSBH in Figure
7
. A wide range of predictions
derived from population synthesis and from binary pulsar
observations were reviewed in 2010 to produce rate estimates
for canonical 1.4
M
e
NSs and 10
M
e
BHs
(
Abadie et al.
2010
)
.
We additionally include some more recent estimates from
population synthesis for both NSBH and BNS
(
de Mink &
Belczynski
2015
; Dominik et al.
2015
; Belczynski et al.
2016
;
keeping in mind these calculations do not simultaneously and
widely explore all uncertainties in binary evolution, hence
underestimating the underlying uncertainties; cf. O
Shaughnessy
et al.
2005b
,
2008
,
2010
, and references therein
)
and binary
pulsar observations for BNS
(
Kim et al.
2015
)
. Finally, to give a
sense of scale to the results shown in Figures
6
and
7
, we note
that the core-collapse supernova rate, in these units, is
10
5
Gpc
3
yr
1
(
Cappellaro et al.
2015
and references therein
)
.
We also compare our upper limits for NSBH and BNS
systems to beaming-corrected estimates of short GRB rates in
the local universe. Short GRBs are considered likely to be
produced by the merger of compact binaries that include NSs,
i.e., BNS or NSBH systems
(
Berger
2014
)
. The rate of short
GRBs can predict the rate of progenitor mergers
(
Coward
et al.
2012
; Petrillo et al.
2013
; Siellez et al.
2014
; Fong
et al.
2015
)
. For NSBH, systems with small BH masses are
considered more likely to be able to produce short GRBs
(
e.g.
Duez
2010
; Giacomazzo et al.
2013
; Pannarale
et al.
2015
)
, so we compare to our 5
M
e
1.4
M
e
NSBH rate
constraint. The observation of a kilonova is also considered to
be an indicator of a binary merger
(
Metzger & Berger
2012
)
,
Figure 4.
90% con
fi
dence upper limit on the BNS merger rate as a function of
the two component masses using the
PyCBC
analysis. Here, the upper limit for
each bin is obtained assuming a BNS population with masses distributed
uniformly within the limits of each bin, considering isotropic spin direction and
dimensionless spin magnitudes uniformly distributed in
[
0, 0.05
]
.
Table 2
Sensitive Spacetime Volume
á
ñ
VT
and 90% Con
fi
dence Upper Limit
R
90%
for NSBH Systems with Isotropic and Aligned-spin Distributions
NS mass
BH mass
Spin
á
ñ
VT
(
Gpc
3
yr
)
Range
(
Mpc
)
R
90%
(
Gpc
3
yr
1
)
(
M
e
)(
M
e
)
distribution
PyCBC GstLAL PyCBC GstLAL PyCBC GstLAL
1.4
5
Isotropic
7.01
×
10
4
7.75
×
10
4
110
112
3600
3260
1.4
5
Aligned
7.87
×
10
4
9.01
×
10
4
114
118
3210
2800
1.4
10
Isotropic
1.00
×
10
3
1.02
×
10
3
123
122
2530
2480
1.4
10
Aligned
1.36
×
10
3
1.53
×
10
3
137
140
1850
1650
1.4
30
Isotropic
1.10
×
10
3
9.12
×
10
4
127
118
2300
2770
1.4
30
Aligned
1.98
×
10
3
2.01
×
10
3
155
154
1280
1260
Note.
The NS spin magnitudes are in the range
[
0, 0.04
]
and the BH spin magnitudes are in the range
[
0, 1
]
. Values are shown for both the
pycbc
and
gstlal
pipelines.
á
ñ
VT
is calculated using an FAR threshold of 0.01
yr
1
. The rate upper limit is calculated using a uniform prior on
L= á ñ
RVT
and an 18% uncertainty in
á
ñ
VT
from calibration errors.
7
The Astrophysical Journal Letters,
832:L21
(
15pp
)
, 2016 December 1
Abbott et al.
and an estimated kilonova rate gives an additional lower bound
on compact binary mergers
(
Jin et al.
2015
)
.
Finally, some recent work has used the idea that mergers
involving NSs are the primary astrophysical source of r-process
elements
(
Lattimer & Schramm
1974
;Qian&Wasserburg
2007
)
to constrain the rate of such mergers from nucleosynthesis
(
Bauswein et al.
2014
; Vangioni et al.
2016
)
, and we include rates
from Vangioni et al.
(
2016
)
for comparison.
While limits from O1 are not yet in con
fl
ict with astrophysical
models, scaling our results to curr
ent expectations for advanced
LIGO
ʼ
s next two observing runs, O2 and O3
(
Aasi et al.
2016
)
,
suggests that signi
fi
cant constraints or observations of BNS or
NSBH mergers are possible in the next two years.
Assuming that short GRBs are produced by BNS or NSBH,
but without using beaming angle estimates, we can constrain
the beaming angle of the jet of gamma rays emitted from these
GRBs by comparing the rates of BNS
/
NSBH mergers and the
rates of short GRBs
(
Chen & Holz
2013
)
. For simplicity, we
assume here that all short GRBs are associated with BNS or
NSBH mergers; the true fraction will depend on the emission
mechanism. The short GRB rate
R
GRB
, the merger rate
R
merger
,
and the beaming angle
θ
j
are then related by
q
=-
R
R
cos
1
.
9
j
GRB
merger
()
We take
=
-
+
R
10
GRB
7
20
Gpc
3
yr
1
(
Nakar et al.
2006
;Coward
et al.
2012
)
. Figure
8
shows the resulting GRB beaming lower
limits for the 90% BNS and NSBH rate upper limits. With our
assumption that all short GRBs are produced by a single
progenitor class, the constraint is tighter for NSBH with larger
BH mass. Observed GRB beaming angles are in the range of 3
°
25
°
(
Fox et al.
2005
; Grupe et al.
2006
; Soderberg et al.
2006
;
Nicuesa Guelbenzu et al.
2011
;Marguttietal.
2012
; Sakamoto
et al.
2013
; Fong et al.
2015
)
. Compared to the lower limit
derived from our non-detection, these GRB beaming observa-
tions start to con
fi
ne the fraction of GRBs that can be produced
by higher-mass NSBH as progenitor systems. Future constraints
could also come from GRB and BNS or NSBH joint
detections
(
Dietz
2011
; Clark et al.
2015
; Regimbau et al.
2015
)
.
Figure 5.
50% and 90% upper limits on the NSBH merger rate as a function of
the BH mass using the more conservative uniform prior for the counts
Λ
. Blue
curves represent the
PyCBC
analysis, and red curves represent the
GstLAL
analysis. The NS mass is assumed to be 1.4
M
e
. The spin magnitudes were
sampled uniformly in the range
[
0, 0.04
]
for NSs and
[
0, 1
]
for BHs. For the
aligned-spin injection set, the spins of both the NS and BH are aligned
(
or anti-
aligned
)
with the orbital angular momentum. For the isotropic spin injection
set, the orientation for the spins of both the NS and BH are sampled
isotropically. The isotropic spin distribution results in a larger upper limit. Also
shown are the realistic
R
re
and high-end
R
high
of the expected NSBH merger
rates identi
fi
ed in Abadie et al.
(
2010
)
.
Figure 6.
Comparison of the O1 90% upper limit on the BNS merger rate to
other rates discussed in the text
(
Abadie et al.
2010
; Coward et al.
2012
; Petrillo
et al.
2013
; Siellez et al.
2014
; de Mink & Belczynski
2015
; Dominik et al.
2015
; Fong et al.
2015
; Jin et al.
2015
; Kim et al.
2015
; Vangioni et al.
2016
)
.
The region excluded by the low-spin BNS rate limit is shaded in blue.
Continued non-detection in O2
(
slash
)
and O3
(
dot
)
with higher sensitivities and
longer operation time would imply stronger upper limits. The O2 and O3 BNS
ranges are assumed to be 1
1.9 and 1.9
2.7 times larger than O1. The operation
times are assumed to be 6 and 9 months
(
Aasi et al.
2016
)
with a duty cycle
equal to that of O1
(
40%
)
. For comparison the core-collapse supernova rate in
these units is
10
5
Gpc
3
yr
1
(
Cappellaro et al.
2015
and references therein
)
.
Figure 7.
Comparison of the O1 90% upper limit on the NSBH merger rate to
other rates discussed in the text
(
Abadie et al.
2010
; Coward et al.
2012
;
Petrillo et al.
2013
; Dominik et al.
2015
; de Mink & Belczynski
2015
; Fong
et al.
2015
; Jin et al.
2015
; Vangioni et al.
2016
)
. The dark blue region assumes
an NSBH population with masses 5
1.4
M
e
, and the light blue region assumes
an NSBH population with masses 10
1.4
M
e
. Both assume an isotropic spin
distribution. Continued non-detection in O2
(
slash
)
and O3
(
dot
)
with higher
sensitivities and longer operation time would imply stronger upper limits
(
shown for 10
1.4
M
e
NSBH systems
)
. The O2 and O3 ranges are assumed to
be 1
1.9 and 1.9
2.7 times larger than O1. The operation times are assumed to
be 6 and 9 months
(
Aasi et al.
2016
)
with a duty cycle equal to that of O1
(
40%
)
. For comparison the core-collapse supernova rate in these units is
10
5
Gpc
3
yr
1
(
Cappellaro et al.
2015
and references therein
)
.
8
The Astrophysical Journal Letters,
832:L21
(
15pp
)
, 2016 December 1
Abbott et al.
7. CONCLUSION
We report the non-detection of BNS and NSBH mergers in
advanced LIGO
ʼ
s
fi
rst observing run. Given the sensitive
volume of Advanced LIGO to such systems we are able to
place 90% con
fi
dence upper limits on the rates of BNS and
NSBH mergers, improving upon limits obtained from initial
LIGO and initial Virgo by roughly an order of magnitude.
Speci
fi
cally we constrain the merger rate of BNS systems with
component masses of 1.35
±
0.13
M
e
to be less than
12,600
Gpc
3
yr
1
. We also constrain the rate of NSBH
systems with NS masses of 1.4
M
e
and BH masses of at least
5
M
e
to be less than 3210
Gpc
3
yr
1
if one considers a
population where the component spins are
(
anti-
)
aligned with
the orbit, and less than 3600
Gpc
3
yr
1
if one considers an
isotropic distribution of component spin directions.
We compare these upper limits with existing astrophysical
rate models and
fi
nd that the current upper limits are in con
fl
ict
with only the most optimistic models of the merger rate.
However, we expect that during the next two observing runs,
O2 and O3, we will either make observations of BNS and
NSBH mergers or start placing signi
fi
cant constraints on
current astrophysical rates. Finally, we have explored the
implications of this non-detection on the beaming angle of
short GRBs. We
fi
nd that if one assumes that all GRBs are
produced by BNS mergers, then the opening angle of gamma-
ray radiation must be larger than
-
+
2
.3
1.1
1.7
, or larger than
-
+
4
.3
1.9
3.1
if one assumes all GRBs are produced by NSBH mergers.
The authors gratefully acknowledge the support of the United
States National Science Foundation
(
NSF
)
for the construction
andoperationoftheLIGOLaboratoryandAdvancedLIGOas
well as the Science and Technology Facilities Council
(
STFC
)
of
the United Kingdom, the Max-Planck-Society
(
MPS
)
,andthe
State of Niedersachsen
/
Germany for support of the construction
of Advanced LIGO and construction and operation of the
GEO600 detector. Additional support for Advanced LIGO was
provided by the Australian Research Council. The authors
gratefully acknowledge the Italia
n Istituto Nazionale di Fisica
Nucleare
(
INFN
)
, the French Centre National de la Recherche
Scienti
fi
que
(
CNRS
)
and the Foundation for Fundamental
Research on Matter supported by the Netherlands Organisation
for Scienti
fi
c 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 Scienti
fi
c
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 Competitivita
t and Conselleria d
Edu-
cació Cultura i Universitats of the G
overn de les Illes Balears, the
National Science Centre of Poland, the European Commission,
the Royal Society, the Scottish Funding Council, the Scottish
Universities Physics Alliance, the Hungarian Scienti
fi
c 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 Natural Science and Engineering Research
Council Canada, Canad
ian Institute for Advanced Research, the
Brazilian Ministry of Science
, Technology, and Innovation,
Fundação de Amparo à Pesquisa do Estado de São Paulo
(
FAPESP
)
, Russian Foundation for Basic Research, the Lever-
hulme 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.
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Figure 8.
Lower limit on the beaming angle of short GRBs, as a function of the
mass of the primary BH or NS,
m
1
. We take the appropriate 90% rate upper
limit from this Letter, assume all short GRBs are produced by each case in turn,
and assume all have the same beaming angle
θ
j
. The limit is calculated using an
observed short GRB rate of
-
+
1
0
7
20
Gpc
3
yr
1
, and the ranges shown on the
plot re
fl
ect the uncertainty in this observed rate. For BNS,
m
2
comes from a
Gaussian distribution centered on 1.35
M
e
, and for NSBH, it is
fi
xed
to 1.4
M
e
.
9
The Astrophysical Journal Letters,
832:L21
(
15pp
)
, 2016 December 1
Abbott et al.