of 18
Search for intermediate mass black hole binaries in the first and second
observing runs of the Advanced LIGO and Virgo network
B. P. Abbott
etal.
*
(LIGO Scientific Collaboration and Virgo Collaboration)
(Received 4 July 2019; published 30 September 2019)
Gravitational-wave astronomy has been firmly established with the detection of gravitational waves
from the merger of ten stellar-mass binary black holes and a neutron star binary. This paper reports on the
all-sky search for gravitational waves from intermediate mass black hole binaries in the first and second
observing runs of the Advanced LIGO and Virgo network. The search uses three independent algorithms:
two based on matched filtering of the data with waveform templates of gravitational-wave signals
from compact binaries, and a third, model-independent algorithm that employs no signal model for the
incoming signal. No intermediate mass black hole binary event is detected in this search. Consequently, we
place upper limits on the merger rate density for a family of intermediate mass black hole binaries. In
particular, we choose sources with total masses
M
¼
m
1
þ
m
2
½
120
;
800

M
and mass ratios
q
¼
m
2
=m
1
½
0
.
1
;
1
.
0

. For the first time, this calculation is done using numerical relativity waveforms
(which include higher modes) as models of the real emitted signal. We place a most stringent upper limit of
0
.
20
Gpc
3
yr
1
(in comoving units at the 90% confidence level) for equal-mass binaries with individual
masses
m
1
;
2
¼
100
M
and dimensionless spins
χ
1
;
2
¼
0
.
8
aligned with the orbital angular momentum of
the binary. This improves by a factor of
5
that reported after Advanced LIGO
s first observing run.
DOI:
10.1103/PhysRevD.100.064064
I. INTRODUCTION
The first two observing runs of Advanced LIGO and
Virgo (O1 and O2 respectively) have significantly
enhanced our understanding of black hole (BH) binaries
in the Universe. Gravitational waves (GWs) from ten binary
black hole mergers with total mass between
18
.
6
þ
3
.
1
0
.
7
and
85
.
1
þ
15
.
6
10
.
9
M
weredetectedduring thesetwoobservingruns
[1
8]
. These observations have revealed a new population
of heavy stellar-mass BH components of up to
50
M
,
for which we had no earlier electromagnetic observational
evidence
[8,9]
. This finding limit is consistent with the
formation of heavier BHs from core collapse being
prevented by a mechanism known as
pulsational pair-
instability supernovae
[10
13]
. According to this idea, stars
with helium core mass in the range
32
64
M
undergo
pulsational pair instability leaving behind remnants of
65
M
. Stars with helium core mass in the range
64
135
M
undergo pair instability and leave no remnant,
while stars with helium mass
135
M
are thought to
directly collapse to intermediate mass black holes.
Intermediate mass black holes (IMBHs) are BHs heavier
than stellar-mass BHs but lighter than supermassive black
holes (SMBHs), which places them roughly in the range of
10
2
10
5
M
[14,15]
. Currently there is only indirect
observational evidence. Observations include probing the
mass of the central BH in galaxies as well as massive star
clusters with direct kinematical measurements which has
led to recent claims for the presence of IMBHs
[16
18]
.
Other observations come from the extrapolation of several
scaling relations between the mass of the central SMBH
and their host galaxies
[19]
to the mass range of globular
clusters
[20,21]
. In this way, several clusters have been
found to be good candidates for having IMBHs in their
centers
[22
24]
. If present, IMBHs would heat up the cores
of these clusters, strongly influencing the distribution of the
stars in the cluster and their dynamics, leaving a character-
istic imprint in the surface brightness profile, as well as in
the mass-to-light ratio
[25]
. Controversy exists regarding
the interpretation of these observations, as some of them
can also be explained by a high concentration of stellar-
mass BHs or the presence of binaries
[22
24,26]
. Empirical
mass scaling relations of quasiperiodic oscillations
[27]
in
luminous x-ray sources have also provided evidence for
IMBHs
[28]
. Finally, IMBHs have been proposed as
candidates to explain ultraluminous x-ray sources in nearby
galaxies, which are brighter than the accreting x-ray
sources with stellar-mass BHs
[29,30]
. However, neutron
stars or stellar-mass black holes emitting above their
Eddington luminosity could also account for such obser-
vations. In summary, no definitive evidence of IMBHs has
yet been obtained.
The possible astrophysical formation channels of IMBHs
remain uncertain. Proposed channels include the direct
*
Full author list given at the end of the article.
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collapse of massive first-generation, low metallicity
Population III stars
[31
34]
and mergers of stellar-mass
BHs in globular clusters
[35]
and multiple collisions of
stars in dense young star clusters
[18,36
39]
, among others
[40]
. Further, some astrophysical scenarios
[14]
indicate
that SMBHs in galactic centers might be formed from
hierarchical mergers of IMBHs
[15,41]
. The direct obser-
vation of IMBHs with gravitational waves could strengthen
the possible evolutionary link between stellar-mass BHs
and SMBHs. Finally, observing an IMBH population
would help to understand details of the pulsational pair-
instability supernovae mechanism.
The GW observation of a coalescing binary consisting of
at least one IMBH component or resulting in an IMBH
remnant, which we will term an IMBHB, could provide the
first definitive confirmation of the existence of IMBHs. In
fact, IMBHBs are the sources that would emit the most
gravitational-wave energy in the LIGO-Virgo frequency
band, potentially making them detectable to distances (and
redshifts) beyond that of any other LIGO-Virgo source
[42]
.
Even in the absence of a detection, a search for IMBHBs
provides stringent constraints on their merger rate density,
which has implications for potential IMBHB and SMBH
formation channels.
IMBHs are not only interesting from an astrophysical
point of view, they are also excellent laboratories to test
general relativity in the strong field regime
[43
46]
.
Their large masses would lead to strong merger and
ringdown signals in the Advanced LIGO-Virgo frequency
band. Therefore, higher modes might be visible in IMBHB
signals because those modes are especially strong in
the merger and ringdown stages. The observation of
multimodal merger and ringdown signals is paramount
to understanding fundamental properties of general rela-
tivity, such as the no-hair theorem
[47
50]
and BH kick
measurements
[51
53]
.
The first search for GWs from IMBHBs was carried out
in the data from initial LIGO and initial Virgo (2005
2010)
[54,55]
. Owing to the large masses of IMBHBs, such
systems are expected to merge at low frequencies where the
initial detectors were less sensitive due to the presence of
several noise sources, such as suspension noise, thermal
noise, and optical cavity control noise. As a result, those
detectors were sensitive to only the merger and ringdown
phases of the IMBHB systems. Initial IMBHB analyses
applied either the model-independent time-frequency
searches
[56]
or ringdown searches. No IMBHB merger
was detected in these searches.
Because of the improved low-frequency sensitivities of
the Advanced LIGO and Advanced Virgo detectors
[57,58]
, IMBHB signals are visible in band for a longer
period of time, which increases the effectiveness of
modeled searches that use more than just the ringdown
portion of an IMBHB
s waveform. Reference
[42]
reports
results from a combined search for IMBHBs that used two
independent search algorithms: a matched-filter analysis
called
G
st
LAL
[59
61]
, which uses the inspiral, merger, and
ringdown portions of the IMBHB waveform and the model-
independent analysis
coherent
W
ave
B
urst
(cWB)
[56]
.No
IMBHBs were found by these searches, and upper limits
on the merger rate density for 12 targeted IMBHB sources
with total mass between 120 and
600
M
and mass ratios
down to
1
=
10
were obtained. The most stringent upper limit
on the merger rate density from this combined analysis was
0
.
93
Gpc
3
yr
1
for binaries consisting of two
100
M
BHs with dimensionless spin magnitude 0.8 aligned with
the system
s orbital angular momentum.
All upper limits on the IMBHB merger rate reported in
past searches
[42,54,55]
were obtained using models for
the GW signal that include only the dominant radiating
mode, namely
ð
l
;m
Þ¼ð
2
;

2
Þ
, of the GW emission
[62]
.
However, it has been shown that higher modes contribute
more substantially to signals emitted by heavy binaries.
This impact increases as the system becomes more asym-
metric in mass
[63,64]
, as the spin of the BHs becomes
more negative
[65,66]
, and as the precession in the binary
becomes stronger
[67]
. As a consequence, the omission of
higher modes leads in general to more conservative upper
limits on the IMBHB merger rate
[68]
. In this work, we
improve on past studies in two distinct ways. We use
numerical relativity (NR) simulations with higher modes to
model GW signals from IMBHBs for computing upper
limit estimates. Additionally, our combined analysis now
includes the matched-filter search
P
y
CBC
[69,70]
in addition
to
G
st
LAL
and cWB. Because of these novelties, we have, in
addition to analyzing the O2 dataset, reanalyzed the O1
dataset and report here combined upper limits for the O1
and O2 observing runs. In this paper, we report upper limits
on the merger rate density of 17 targeted (nonprecessing)
IMBHB sources. Our most stringent upper limit is
0
.
20
Gpc
3
yr
1
for equal-mass binaries with component
spins aligned with the orbital angular momentum of the
system and dimensionless magnitudes
χ
1
;
2
¼
0
.
8
.
The rest of this paper is organized as follows. In Sec.
II
we describe the dataset, outline the individual search
algorithms that make up the combined search, and report
our search
s null detection of IMBHBs. In Sec.
III
we
describe the NR simulations that we use to compute the
upper limits on the IMBHB merger rates and report these
for the case of 17 IMBHB sources. We draw final
conclusions in Sec.
IV
.
II. IMBHB SEARCH IN O1 AND O2 DATA
A. Data summary
This analysis was carried out using O1 and O2 datasets
from the two LIGO (Livingston and Hanford) detectors and
Virgo. We have used the final calibration, which was
produced after the conclusion of the run, including com-
pensation for frequency-dependent fluctuations in the
B. P. ABBOTT
et al.
PHYS. REV. D
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calibration
[71
73]
. Well-identified sources of noise have
also been subtracted from the strain data as explained in
Refs.
[73,74]
. The maximum calibration uncertainty across
the frequency band of [10
5,000] Hz for the two LIGO
detectors is
10%
in amplitude and
5
deg in phase for
O1 and
4%
in amplitude and
3
deg in phase for O2
[7,71]
. For Virgo we consider an uncertainty of 5.1% in
amplitude and 2.3 deg in phase
[73]
. After removing data
with significant instrumental disturbance, we use 48.6 days
and 118.0 days of joint Hanford-Livingston data from the
O1 and O2 observing runs respectively. The Virgo detector
joined the LIGO detectors during the last
15
days of O2,
which provided 4.0 days of coincident data (Hanford-Virgo
or Livingston-Virgo) in addition to Livingston-Hanford
coincident data. The data from O1 and O2 were divided
into nine and 21 blocks respectively with coincident time
ranging from 4.7
7.0 days. For more details, see Ref.
[8]
.
B. Search algorithms
We combine the two matched-filter searches, namely
G
st
LAL
[59
61,75]
and
P
y
CBC
[69,70]
, and one model-
independent analysis, cWB
[76]
, into a single IMBHB
search. The two model-based matched-filtering analyses
use a bank of templates made of precomputed compact
binary merger GW waveforms. Matched-filter-based analy-
ses are optimal to extract known signals from stationary,
Gaussian noise
[77]
. However, the templates we use are
limited to noneccentric, aligned-spin systems. They contain
only the dominant waveform mode of the GWemission and
omit higher modes
[64,78]
. Additionally, Advanced LIGO
and Virgo data are known to contain a large number of short
noise transients
[79]
, which can mimic short GW signals
like those emitted by IMBHBs. While matched-filter
searches use several techniques to discriminate between
noisy transients and real GW events
[61,80,81]
, they are
known to lose significant efficiency when looking for short
signals like those from IMBHBs. Therefore, the IMBHB
search is carried out jointly with an analysis that can
identify short-duration GW signals without a model for the
morphology of the GW waveform. In this search, all three
analyses use O1 and O2 Advanced LIGO data. However,
because of the incomparable sensitivities between the
Advanced LIGO detector and Advanced Virgo detector,
only the
G
st
LAL
analysis uses Virgo data, as is done
in Ref.
[8]
.
1. Modeled analyses
The matched-filter analyses
G
st
LAL
and
P
y
CBC
use
templates that span the parameter space of neutron stars,
stellar-mass BHs, and IMBHs. In this study, we use the
same two searches reported in Ref.
[8]
to calculate upper
limits on the merger rate density of IMBHBs.
The matched-filter signal-to-noise ratio (SNR) time
series is computed for every template. Triggers are pro-
duced when the SNR time series surpasses a predetermined
threshold, where clusters of triggers are trimmed by
maximizing the SNR within small time windows. In
addition, a signal consistency veto
[61,81,82]
is calculated
for each trigger. A list of GW candidates is constructed
from triggers generated by common templates that are
coincident in time across more than one detector, where the
coincidence window takes into account the travel time
between detectors. Next, a ranking statistic is calculated for
each candidate that estimates a likelihood ratio that the
candidate would be observed in the presence of a GW
compared to a pure-noise expectation. Finally, a
p
-value
1
P
is determined by comparing the value of its ranking statistic
to that of triggers coming from background noise in the
data. A detailed description of the
G
st
LAL
and
P
y
CBC
pipelines can be found in Refs.
[59
61,75]
and
[69,70]
,
respectively; additionally, details outlining how candidates
are ranked across observing runs can be found in Ref.
[8]
.
The
G
st
LAL
analysis uses the template bank described in
Ref.
[83]
. The region of this bank that overlaps the IMBHB
parameter space, which starts at a total mass of
100
M
,
reaches up to a total mass of
400
M
in the detector frame,
and covers mass ratios in the range of
1
=
98
<q<
1
. The
waveforms used are a reduced-order model of the
SEOBNR
v4
approximant
[84]
. The spins of these templates
are either aligned or antialigned with the orbital angular
momentum of the system with dimensionless magnitudes
less than 0.999.
The
P
y
CBC
analysis uses the template bank described in
Ref.
[85]
. The region of this bank that overlaps the IMBHB
parameter space reaches up to a total mass of
500
M
in the
detector frame, excluding templates with duration below
0.15 s, and covers the range of
1
=
98
<q<
1
. The wave-
forms used are also a reduced-order model of the
SEOBNR
v4
approximant, and the aligned or antialigned dimensionless
spin magnitudes are less than 0.998.
2. Unmodeled analysis
cWB is the GW transient detection algorithm designed to
look for unmodeled short-duration GW transients in the
multidetector data from interferometric GW detector net-
works. Designed to operate without a specific waveform
model, cWB identifies coincident excess power in the
wavelet time-frequency representations of the detector
strain data
[86]
, for signal frequencies up to 1 kHz and
durations up to a few seconds. The search identifies events
that are coherent in multiple detectors and reconstructs the
source sky location and signal waveforms by using the
constrained maximum likelihood method
[76]
. The cWB
detection statistic is based on the coherent energy
E
c
obtained by cross-correlating the signal waveforms recon-
structed in multiple detectors. It is proportional to the
network SNR and used to rank the events found by cWB.
1
The probability that noise would produce a trigger at least as
significant as the observed candidate.
SEARCH FOR INTERMEDIATE MASS BLACK HOLE BINARIES
...
PHYS. REV. D
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To improve the robustness of the algorithm against
nonstationary detector noise, cWB uses signal-independent
vetoes, which reduce the high rate of the initial excess
power triggers. The primary veto cut is on the network
correlation coefficient
c
c
¼
E
c
=
ð
E
c
þ
E
n
Þ
, where
E
n
is the
residual noise energy estimated after the reconstructed
signal is subtracted from the data. Typically, for a GW
signal
c
c
1
and for instrumental glitches
c
c
1
.
Therefore, candidate events with
c
c
<
0
.
7
are rejected as
potential glitches.
To improve the detection efficiency of IMBHBs as well
as to reduce the false alarm rates (FARs), the cWB analysis
employs additional selection cuts based on the nature of
IMBHB signals. IMBHB signals have two distinct features
in the time-frequency representation. First, the signal
frequencies lie below 250 Hz. We use this to exclude all
the non-IMBHB events in the search, including noise
events. Secondly, the inspiral signal duration in the detector
band is relatively short, which leads to relatively low SNR
in the inspiral phase as compared to the merger and
ringdown phases. In the cWB framework, chirp mass
[
M
¼ð
m
1
m
2
Þ
3
=
5
M
1
=
5
] is estimated using the frequency
evolution of a signal
s inspiral. However, in the case of low
SNRs, we cannot accurately estimate the chirp mass of the
binary
[87]
; still, we use this framework to introduce
additional cuts on the estimated chirp mass to reject
non-IMBHB signals. The simulation studies show that
IMBHB signals are recovered with
j
M
j
>
10
M
which
we use in this search.
2
We apply this selection cut to reduce
the noise background when producing the candidate events.
For estimation of the statistical significance of the
candidate event, each event is ranked against a sample
of background triggers obtained by repeating the analysis
on time-shifted data
[1]
. To exclude astrophysical events
from the background sample, the time shifts are selected to
be much longer (1 s or more) than the expected signal time
delay between the detectors. By using different time shifts,
a sample of background events equivalent to approximately
500 years of background data is accumulated for each of
the 30 blocks of data. The cWB candidate events that
survived the cWB selection criteria are assigned a FAR
given by the rate of the corresponding background events
with the coherent network SNR value larger than that of the
candidate event.
C. Combined search
Each of our three algorithms produces its own list of GW
candidates characterized by GPS time, FAR, and associated
p
-value
P
. These three lists are then combined into a
common single list of candidates. To avoid counting
candidates more than once, candidates within a time
window of 100 ms across different lists are assumed to
be the same. To account for the use of three search
algorithms, we apply a conservative trials factor of 3
and assign each candidate a new
p
value given by
̄
P
¼
1
ð
1
P
min
Þ
3
;
ð
1
Þ
where
P
min
denotes the minimum
p
value reported across
the pipelines. This is equivalent to assuming that the three
searches produce independent lists of candidates.
3
We note
that while this choice of trials factor affects the significance
of individual triggers, it will not change the numerical value
of our upper limits. See Appendix
B
for a more detailed
discussion.
D. Search results
Here we report results from the combined cWB-
G
st
LAL
-
P
y
CBC
IMBHB search on full O1-O2 data. The top 21 most
significant events from the combined search include the
11 GWevents published in Ref.
[8]
, namely GW150914
[1]
,
GW151012, GW151226
[2]
, GW170104
[3]
, GW170608
[4]
, GW170729, GW170809, GW170814
[6]
, GW170817
[5]
, GW170818, and GW170823, and ten events tabulated
in Table
I
. All the events in Table
I
have a FAR much larger
than any of the GWs reported in Ref.
[8]
; no event in this list
was found with enough significance to claim an IMBHB
detection.
The top-ranked event
4
from Table
I
was observed by cWB
inO2 dataon May2,2017at 04
08:44UTC with acombined
SNR of 11.6 in the two Advanced LIGO detectors and a
significance of
P
cWB
¼
P
min
¼
0
.
14
. Applying Eq.
(1)
, this
event has a combined
p
value of
̄
P
¼
0
.
36
, too low to claim
it as a gravitational-wave detection.
Despite the low significance of this trigger, its character-
istics were consistent with those of an IMBHB, and we
decided to perform detailed data quality and parameter
estimation follow-ups.
5
In order to check for the presence
of environmental or instrumental noise, this event was
vetted with the same procedure applied to triggers of
marginal significance found in previous searches
[8]
in
O1-O2 data. These checks identified a correlation between
the trigger time and the glitching of optical lever lasers at
the end of one arm of the Hanford detector. This is a known
instrumental artifact previously observed to impact GW
searches
[88,89]
. The time of this trigger was not discarded
by the pretuned data quality veto designed to mitigate the
effects of these optical lever laser glitches. However, these
2
Negative
M
values correspond to frequencies decreasing
with time, which could be due to the pixels corresponding to the
ringdown part.
3
In general, correlations between searches would lead to a
trials factor less than 3. However, at the time, we are not able to
quantify this, and we choose to adopt the most conservative
approach.
4
We note that the most significant event in the O1 search
reported in Ref.
[42]
is the third event in this table.
5
See Appendix
D
for further details regarding the parameter
estimation investigations of this candidate.
B. P. ABBOTT
et al.
PHYS. REV. D
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vetoes are tuned for high efficiency and minimal impact on
analyzable time rather than exhaustively removing all non-
Gaussian features in the data. Further follow-up indicates
that this instrumental artifact is likely contributing power to
the gravitational-wave strain channel at the time and
frequency of the trigger. Given the SNR of the purported
signal in the Hanford detector and the relatively low
significance of the reported false alarm rate, we conclude
that this trigger is likely explained by detector noise.
III. UPPER LIMITS ON MERGER RATES
Given that no IMBHB signal was detected by our search,
we proceed to place upper limits on the coalescence rate
of these objects. This is done by estimating the sensitivity
of our search to an astrophysically motivated population of
simulated IMBHB signals that we inject in our detector
data. However, given the absence of well-motivated pop-
ulation estimates of IMBHBs, we opt for sampling the
parameter space in a discrete manner (for details, please see
Appendix
C
). As a consequence, in this section we estimate
the sensitive distance reach as well as the upper limit on
merger rate density for 17 selected fiducial IMBHB sources
tabulated in Table
II
of Appendix
C
using the loudest event
method
[90]
, following the procedure outlined in Ref.
[42]
and described again in Appendix
A
. For a given IMBHB
source, gravitational waveforms from simulated systems
scattered through space are injected into the data and
recovered by each of the three analyses. In this section,
we describe our simulation set and present our findings.
A. Injection set
Reference
[42]
reports upper limits on the merger rate
density for 12 IMBHB systems in its Table
I
. The waveform
simulations used to compute upper limits in that study
contain only the dominant quadrupolar mode of the GW
emission. In this work, we use highly accurate NR
simulations computed by the
SXS
[91]
,
RIT
[92]
, and
G
eorgia
t
ech
[93]
codes, which include higher modes. Since
higher modes are particularly important for large asymme-
tries in mass and for high total mass binaries, in this study
we extend our parameter space to mass ratios as low as
q
¼
1
=
10
and total masses as high as
M
¼
800
M
(see
Appendix
C
Table
II
for a detailed list). In general, NR
simulations can include modes of arbitrary
ð
l
;m
Þ
for a
given set of masses in the parameter space. However, weak
modes are sometimes dominated by numerical noise and do
not agree when compared across different numerical codes.
In fact, we disregard numerical modes with
l
5
, because
these have comparatively small amplitudes. The
l
5
modes with
m
¼
l
have also particularly short wave-
lengths, which makes it more challenging for numerical
relativity codes to resolve the propagation of these modes
away from the binary. In order to assess the accuracy of the
remaining modes, we only choose IMBHB simulations for
which higher modes have been computed by at least two
different NR codes. We select only those higher modes that
agree to an overlap of at least 0.97 across all available NR
codes for each of 17 the selected simulations.
6
The higher modes that passed this criteria and were
included in our analysis were the following:
ð
l
;m
Þ¼
2
;

1
Þ
;
ð
2
;

2
Þ
;
ð
3
;

2
Þ
;
ð
3
;

3
Þ
;
ð
4
;

2
Þ
;
ð
4
;

3
Þ
;
ð
4
;

4
Þg
.
Notably, the (2,2) mode agrees across NR codes to an
overlap
>
0
.
995
for every IMBHB source considered in
this study; the two modes closest to the 0.97 overlap
threshold were the (4,4) and (4,3) modes. We note that,
similar to what was described in Ref.
[68]
, omission of
l
>
4
modes may lead to an underestimation of the power
within the detector band radiated by the largest mass
binary BHs.
Of the 17 selected sources, we include three cases with
spins aligned or antialigned with the total angular momen-
tum of the binary with dimensionless spin magnitudes
j
χ
1
;
2
0
.
8
. The IMBHB injections are uniformly distrib-
uted in the binary orientation parameters [
φ
,cos
ð
ι
Þ
]
TABLE I. Details of the ten most significant events (excluding all published lower mass events). We report the date, UTC time,
observing pipeline (individual analysis that observed the event with the highest significance), FAR, SNR, and
P
min
for each event. The
combined
p
-value
̄
P
of each event is calculated using Eq.
(1)
. In the table, the events are tabulated in increasing value of
P
min
.
No
Date
UTC time
Pipeline
FAR (yr
1
)
SNR
P
min
1
2017-05-02
04
08
44.9
cWB
0.34
11.6
0.14
2
2017-06-16
19
47
20.8
P
y
CBC
1.94
9.1
0.59
3
2015-11-26
04
11
02.7
cWB
2.56
7.5
0.68
4
2017-06-08
23
50
52.3
cWB
3.57
10.0
0.79
5
2017-04-05
11
04
52.7
G
st
LAL
4.55
9.3
0.88
6
2015-11-16
22
41
48.7
P
y
CBC
4.77
9.0
0.88
7
2016-12-02
03
53
44.9
G
st
LAL
6.00
10.5
0.94
8
2017-02-19
14
04
09.0
G
st
LAL
6.26
9.6
0.95
9
2017-04-23
12
10
45.0
G
st
LAL
6.47
8.9
0.95
10
2017-04-12
15
56
39.0
G
st
LAL
8.22
9.7
0.98
6
We did allow for overlaps below 0.97 if the mode
s con-
tribution to the waveform was negligible.
SEARCH FOR INTERMEDIATE MASS BLACK HOLE BINARIES
...
PHYS. REV. D
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064064 (2019)
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uniformly distributed in comoving volume up to redshift
z
1
(luminosity distance of 6.7 Gpc) using the TT
þ
lowP
þ
lensing
þ
ext cosmological parameters given in
Table IVof Ref.
[94]
, and individually redshifted according
to this cosmological model. The overall effect of cosmo-
logical redshift is to shift each GW signal to lower
frequencies. At a given redshift, the mass of the injection
in the detector frame is
ð
1
þ
z
Þ
times larger than the source-
frame mass, and the luminosity distance is
ð
1
þ
z
Þ
times the
comoving distance. At redshifts of
z
¼
1
, this results in a
decrease in SNR ranging from
20%
for an equal-mass
M
¼
100
M
face-on system to
50%
for an equal-mass
M
¼
200
M
face-on system. The injections are spaced
roughly uniformly in time with an interval of at least 80 s
over the
T
0
¼
413
.
71
days of O1-O2 observing time,
and each injection set covers a total space-time volume
h
VT
i
tot
¼
110
.
68
Gpc
3
yr.
B. Sensitive distance reach and merger
rate density estimate
We use the loudest event method
[90]
to calculate the
sensitive distance reach of our search and to place upper
limits on the merger rate density of IMBHBs (see
Appendix
C
for a detailed description of our procedure).
The results of our combined search are reported using a
combined
p
value of
̄
P
¼
0
.
36
given by that of our loudest
event in Table
I
.
The left panel of Fig.
1
shows the sensitive distance reach
of our combined search toward our 17 targeted IMBHB
sources represented in the
m
1
m
2
plane (see Table
II
in Appendix
C
for a more detailed description). We find an
across-the-board improvement in the sensitive distance of
our combined search compared to the 12 targeted sources
reported in Ref.
[42]
. In particular, we find that the
combined search is most sensitive to the
ð
100
þ
100
Þ
M
aligned-spin source, which can be observed up
to 1.8 Gpc and is an increase of more than 10% compared
to the 1.6 Gpc obtained in Ref.
[42]
. These improvements
are the result of better detector sensitivity, the inclusion of
higher modes in our injections, and significant improve-
ments to the cWB search algorithm. As a general trend, our
reach decreases for increasing mass ratio and for increasing
total mass once this surpasses
200
M
. There are several
reasons for this behavior. First, the intrinsic amplitude of
the IMBHB signal decreases as the mass ratio decreases for
a fixed total mass. Second, sources with small
q
have a
significant fraction of their power contained in their
higher modes. Consequently, they are not well matched
by our search templates, which only include the dominant
quadrupole mode. Last, although the intrinsic luminosity
of IMBHBs rises with total mass, the merger frequency
decreases, and so signals persist in the detector sensitive
frequency band for a very short duration. This makes
it difficult to distinguish them from noise transients.
This effect is evident from the roughly equivalent sensitive
distances obtained for the (
60
þ
60
) and
ð
100
þ
100
Þ
M
sources despite the significantly larger total mass of the
latter.
The right panel of Fig.
1
shows the upper limits on the
merger rate density of our 17 targeted IMBHB sources,
which improve on those reported after O1 in Ref.
[42]
.We
set our most stringent upper limit at
0
.
20
Gpc
3
yr
1
for
equal-mass spin-aligned IMBHBs with component masses
of
100
M
and aligned dimensionless spins of 0.8. By
assuming a redshift-independent globular cluster (GC)
density of
3
GC Mpc
3
[95]
, we find that this upper limit
is equivalent to
0
.
07
GC
1
Gyr
1
, an improvement of a
factor of
5
over the
0
.
31
GC
1
Gyr
1
that was reported in
Ref.
[42]
. We also observe that for all equal-mass ratio
IMBHB sources, the merger rate density upper limits are
also improved. The sources with unequal masses show
larger improvement in the merger rate density as compared
to the previous result.
FIG. 1. The sensitive distance reach (
D
h
VT
i
sen
) in Gpc (left panel) and 90% upper limit on merger rate density (
R
90%
) in Gpc
3
yr
1
(right panel) for the 17 targeted IMBHB sources in the
m
1
m
2
plane. Each circle corresponds to one class of IMBHBs in the source
frame with a number in the circle indicating
D
h
VT
i
sen
(left panel) or
R
90%
(right panel). Spinning injection sets are labeled and shown as
displaced circles. The blue and light blue shaded regions mark the template space encompassed by the
G
st
LAL
(
M<
400
M
) and
P
y
CBC
(
M<
500
M
) template banks respectively.
B. P. ABBOTT
et al.
PHYS. REV. D
100,
064064 (2019)
064064-6
IV. CONCLUSIONS
We conducted a search for IMBHBs in the data collected
in the two observing runs of the Advanced LIGO and Virgo
detectors. This search combined three analysis pipelines:
two matched-filter algorithms
G
st
LAL
and
P
y
CBC
and the
model-independent algorithm cWB. The
P
y
CBC
and cWB
analyses used data from the Advanced LIGO detectors, and
G
st
LAL
used data from the Advanced LIGO and Advanced
Virgo detectors. No IMBHB detections were made in this
search. The loudest candidate event was found with a
marginal
p
-value
̄
P
¼
0
.
36
in our combined search. A
detailed detector characterization study of this event sug-
gested that it is likely explained by the detector noise.
Given the null detection, we placed upper limits on the
merger rate density for 17 IMBHB systems. For estimation
of the rate upper limits, we used NR waveforms provided
by the
SXS
,
RIT
, and
G
eorgia
t
ech
groups that include higher
modes in the gravitational-wave emission. The reported
rate limits are significantly more stringent than the previous
result reported in Ref.
[42]
. In particular, the most stringent
rate limit of
0
.
20
Gpc
3
yr
1
placed on
ð
100
þ
100
Þ
M
aligned-spin IMBHB systems is an improvement of a factor
of
5
. This improvement is due to the combination of three
factors: the increased sensitivity of our detector network,
the improvements in the cWB search algorithm, and the
incorporation of higher modes into our models for IMBHB
signals.
Anticipated increases of the network sensitivity in future
runs, particularly at low frequency, and further improve-
ment of the search algorithms will place more stringent
upper limits on the merger rate density of IMBHBs and
may even result in the first definitive detection of an IMBH.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the support of the
United States National Science Foundation (NSF) for the
construction and operation of the LIGO Laboratory and
Advanced LIGO as well as the Science and Technology
Facilities Council (STFC) of the United Kingdom, the Max-
Planck-Society (MPS), and the 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 Italian Istituto Nazionale di
Fisica Nucleare (INFN), the French Centre National de la
Recherche Scientifique (CNRS), and the Foundation
for Fundamental Research on Matter supported by the
Netherlands Organisation for Scientific 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 Scientific and
Industrial Research of India, the Department of Science and
Technology, India, the Science & Engineering Research
Board, India, the Ministry of Human Resource Develop-
ment, India, the Spanish Agencia Estatal de Investigación,
the Vicepresid`
encia i Conselleria d
Innovació, Recerca i
Turisme and the Conselleria d
Educació i Universitat del
Govern de les Illes Balears, the Conselleria d
Educació,
Investigació, Cultura i Esport de la Generalitat Valenciana,
the National Science Centre of Poland, the Swiss National
Science Foundation, the Russian Foundation for Basic
Research, the Russian Science Foundation, the European
Commission, the European Regional Development Funds,
the Royal Society, the Scottish Funding Council, the
Scottish Universities Physics Alliance, the Hungarian
Scientific Research Fund, the Lyon Institute of Origins,
the Paris Île-de-France Region, the National Research,
Development and Innovation Office Hungary, 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, the
Canadian Institute for Advanced Research, the Brazilian
Ministry of Science, Technology, Innovations, and
Communications, the International Center for Theoretical
Physics South American Institute for Fundamental
Research, the Research Grants Council of Hong Kong,
the National Natural Science Foundation of China, the
Leverhulme Trust, the Research Corporation, the Ministry
of Science and Technology, Taiwan, and the Kavli
Foundation.Theauthorsgratefully acknowledgethe support
of the NSF, STFC, MPS, INFN, CNRS, and the State of
Niedersachsen/Germany for provision of computational
resources.
APPENDIX A: SENSITIVE DISTANCE REACH
AND MERGER RATE
In this appendix we provide further details on our method
to compute the averaged space-time volume observed by a
search and its corresponding sensitive distance at a given
significance threshold. In general, the averaged space-time
volume to which our searches are sensitive is given by
[96,97]
h
VT
i
sen
¼
T
0
Z
dzd
θ
dV
c
dz
1
1
þ
z
s
ð
θ
Þ
f
ð
z;
θ
Þ
:
ð
A1
Þ
Here,
T
0
is the length of the observation in the detector
frame, and
V
c
ð
z
Þ
is the comoving volume spanned by a
sphere of redshift
z
. The function
s
ð
θ
Þ
is the distribution of
binary parameters
θ
, and
0
f
ð
z;
θ
Þ
1
, where
f
ð
z;
θ
Þ
denotes the fraction of injections with parameters
θ
detected
at a redshift
z
.
In this determination of sensitivity we have two main
limitations. First, the true population of IMBHBs in the
Universe is unknown, so it prevents us from choosing a
particular function
s
ð
θ
Þ
. Second, numerical relativity
SEARCH FOR INTERMEDIATE MASS BLACK HOLE BINARIES
...
PHYS. REV. D
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waveforms cover a discrete parameter space in
θ
. For this
reason, our study is focused on probing a discrete set of
IMBHB classes with parameters
f
θ
i
g
described in Table
II
.
Then the averaged space-time volume sensitivity of
Eq.
(A1)
can be approximated using a Monte Carlo
technique via
h
VT
i
sen
N
rec
N
tot
h
VT
i
tot
:
ð
A2
Þ
Here,
N
tot
is the total number of injections in a given set,
which are distributed in redshift and source orientations as
indicated in Sec.
III A
.
h
VT
i
tot
is the total space-time
volume into which injections were distributed.
N
rec
is the
number of recovered injections by the search, i.e., the
number of injections assigned a value
̄
P
̄
P
0
, where
̄
P
0
is
in general some arbitrary threshold. In our case, we set
̄
P
0
¼
0
.
36
, which is the
̄
P
of our most significant event in
our combined search.
The corresponding sensitive distance reach is computed
as
D
h
VT
i
sen
¼

3
h
VT
i
sen
4
π
T
a

1
=
3
;
ð
A3
Þ
where
T
a
is the amount of time analyzed by the search. We
estimated the 90% confidence upper limit in the merger rate
density for selected simulated signal classes as given by
R
90%
¼
ln
ð
0
.
1
Þ
h
VT
i
sen
;
ð
A4
Þ
where
h
VT
i
sen
is estimated using the loudest event method
and Eq.
(A2)
.
APPENDIX B: DETERMINING THE
p
VALUE OF THE COMBINED SEARCH
In general, the
p
value of the triggers of our combined
search is given by
̄
P
¼
1
ð
1
P
min
Þ
m
;
ð
B1
Þ
where
P
min
is the minimum
p
value reported by any of our
three searches, and
m
½
1
;
3

is the trials factor. The trials
factor is
m
¼
1
if the three searches are fully correlated (for
instance, if they are the same search) and 3 if they are fully
independent. In this work we adopt a conservative
approach and choose
m
¼
3
, omitting possible correlations
between the three analysis pipelines. Indeed, excluding the
11 detected GWs mentioned in Sec.
II D
, none of the 123
events with FAR
<
100
=
yr was common across the three
pipelines.
We note that while the significance of individual triggers
depends on our particular choice for the trials factor
m
applied in Eq.
(B1)
(which we set to
m
¼
3
),
N
rec
is
independent of this choice. This is because every GW
candidate output by the three analyses, including our
loudest event, will have the same trials factor applied
when combined into a single list, so that their relative
ranking will remain unchanged (see Sec.
II C
). Therefore,
the numerical value of our upper limit is unaffected by our
conservative choice of
m
¼
3
, since any choice would yield
the same
N
rec
and
h
VT
i
sen
.
As pointed out, since our choice of the trials factor
affects the significance of individual triggers, our
conservative approach may overly diminish the signifi-
cance of prospective louder IMBHB triggers, and it may
become important to make more accurate estimates of
m
in
the future. Since the lowest
p
value reported by any of our
individual analyses was
P
¼
0
.
14
, we conclude that our
choice of
m
does not impact our conclusion that no
IMBHBs have been observed.
APPENDIX C: SENSITIVE DISTANCE REACH
FOR INDIVIDUAL SEARCH ALGORITHMS
In this appendix, we report and compare the sensitive
distance reach of the three individual searches and the
combined search at their respective loudest event thresholds
(see Table
II
). For the case of the individual searches, this
threshold is set to
̄
P
0
¼
0
.
14
, equal to the loudest (most
significant) event found by cWB; for the combined search,
this is set to
̄
P
0
¼
0
.
36
. We control for differences in the
amount of analyzed time by only considering common
observing times in Table
II
, which allows for a more direct
comparison between the searches.
Table
II
shows that cWB reports the largest sensitive
distance reach to every IMBHB source considered. This is
expected for sources with
M
tot
>
500
M
, since the
G
st
LAL
and
P
y
CBC
template banks are bounded by a total
mass 40 and
500
M
, respectively. Additionally, since
cWB is not limited by constraints on waveform morphol-
ogy, it significantly outperforms matched-filter analyses in
the large mass and small mass ratio regions of the
parameter space that are covered by our analyses
template
banks. This finding is consistent with Ref.
[68]
,sincein
that region of parameter space, signals are shorter and
higher modes are more important. Reference
[68]
also
found that matched-filter searches outperform cWB in the
low mass end of our parameter space. Since then, however,
cWB has undergone major improvements that have led to a
sensitivity comparable to that of matched-filter searches
even for the lightest equal-mass systems considered in this
analysis.
G
st
LAL
reports sensitive distance reaches that are lower
than those found in Ref.
[42]
. This is the result of using a
large bank here that was not specifically tuned and targeted
for IMBHBs. Future searches will benefit from investiga-
tions into optimal template placement and binning as well
as a return to a dedicated IMBH bank.
B. P. ABBOTT
et al.
PHYS. REV. D
100,
064064 (2019)
064064-8
APPENDIX D: LOUDEST EVENT PARAMETER
ESTIMATION
Despite the low significance of our loudest event, two
characteristics motivated a detailed follow-up analysis. On
the one hand, initial parameter estimation put this trigger in
the IMBHB region of the parameter space. On the other,
this trigger was observed by our matched-filter analyses
with a SNR of only
6
, much lower than that recovered by
cWB. If this were a real GW, this difference might be
indicative that the signal contained physics that our search
templates omit (such as precession and higher modes),
which would lead to a reduction of its SNR and
significance.
To explore this possibility, we ran standard parameter
estimation on this event using the same approximants used
in Ref.
[8]
, namely
SEOBNR
v4
[84]
and
IMRP
henom
P
v2
[98]
.
Note that the latter approximant includes the effects of
precession that our search templates omit. For the precess-
ing
IMRP
henom
P
run, we assumed a spin magnitude prior
uniform between 0 and 0.99, and spin orientations were
isotropically distributed on the sphere; for the spin-aligned
SEOBNR
waveforms, we used a spin prior such that the
components of the spin aligned with the orbital angular
momentum matched the prior used for the
IMRP
henom
P
analysis. Remarkably, the two analyses not only report
broadly consistent parameter posterior distributions but
they also report consistent SNRs of
6
, in agreement with
that reported by our matched-filter searches. The latter
indicates that the low SNR obtained by our matched-filter
searches is not likely due to lack of precession in our
templates. Assuming this event is a compact binary, we
recover a source-frame chirp mass of
70
þ
24
20
M
, a source-
frame total mass of
171
þ
68
48
M
, an effective inspiral spin of
0
.
19
þ
0
.
44
0
.
46
, and a luminosity distance of
7
.
0
þ
8
.
0
4
.
2
Gpc. We
also note that, given the lack of information about the spins,
spin results are sensitive to the choice of prior. Further
parameter estimation was performed using the new
SEOBNR
v4
HM
[99]
approximant, which includes the impact
of higher order modes. This analysis reported parameter
posterior distributions and SNR consistent with the pre-
vious ones, suggesting that the low SNR obtained by our
matched-filter searches is not due to the lack of higher
modes in the search templates.
We further conducted parameter estimation of this
trigger by directly using numerical relativity waveforms
of generic spin configurations and higher modes with the
RIFT
algorithm
[100,101]
, which reported results consistent
with those obtained by our waveform approximants. In
addition, the event was also reconstructed using the model
agnostic algorithm
B
ayes
W
ave
[102,103]
, which reported a
SNR consistent with those obtained by our templates.
In summary, detailed follow-up of this event suggests
that, in the most optimistic scenario, this trigger would be
the combination of a weak IMBHB signal plus a noise
TABLE II. The sensitive distance reach and the merger rate density calculated for the 17 targeted IMBHB sources considered in this
study, whose intrinsic parameters are indicated in the first four columns. The fifth column indicates the numerical simulations used for
each case, following the naming conventions of the corresponding NR groups. The next three columns report the sensitive distance reach
for each of the individual analyses (cWB,
G
st
LAL
, and
P
y
CBC
), where we use the loudest event threshold of
P
¼
0
.
14
for each analysis for
comparison purposes. The last column gives the sensitive distance reach from the combined search. To control for differences in the
amount of analyzed time between individual analyses, we consider only common observed time across the three pipelines time, which
yields
T
a
¼
0
.
428
yr.
D
h
VT
i
sen
(Gpc)
m
1
M
m
2
M
Spin
χ
1
;
2
MM
NR simulation
cWB
G
st
LAL P
y
CBC
Combined
60
60
0
120 SXS:BBH:0180, RIT:BBH:0198:n140, GT:0905 1.2
1.2
1.2
1.3
60
60
0.8
120 SXS:BBH:0230, RIT:BBH:0063:n100, GT:0424 1.6
1.0
1.5
1.6
100
20
0
120
SXS:BBH:0056, RIT:BBH0120:n140, GT:0906 0.72 0.69
0.70
0.76
100
50
0
150 SXS:BBH:0169, RIT:BBH:0117:n140, GT:0446 1.2
0.79
1.1
1.2
100
100
0
.
8
200
SXS:BBH:0154, RIT:BBH:0068:n100
1.1
1.0
0.99
1.2
100
100
0
200
SXS:BBH:0180, RIT:BBH:0198:n140,GT:0905 1.4
0.90
1.3
1.4
100
100
0.8
200 SXS:BBH:0230, RIT:BBH:0063:n100, GT:0424 1.8
1.2
1.7
1.8
200
20
0
220
RIT:BBH:Q10:n173, GT:0568
0.48 0.30
0.36
0.49
200
50
0
250 SXS:BBH:0182, RIT:BBH:0119:n140, GT:0454 0.85 0.48
0.67
0.87
200
100
0
300 SXS:BBH:0169, RIT:BBH:0117:n140, GT:0446 1.1
0.59
0.86
1.1
300
50
0
350 SXS:BBH:0181, RIT:BBH:0121:n140, GT:0604 0.55 0.18
0.27
0.56
200
200
0
400 SXS:BBH:0180, RIT:BBH:0198:n140, GT:0905 1.0
0.47
0.72
1.0
300
100
0
400 SXS:BBH:0030, RIT:BBH:0102:n140, GT:0453 0.78 0.23
0.34
0.78
400
40
0
440
RIT:BBH:Q10:n173, GT:0568
0.35 0.10
0.16
0.35
300
200
0
500
RIT:BBH:0115:n140, GT:0477
0.79 0.16
0.14
0.79
300
300
0
600 SXS:BBH:0180, RIT:BBH:0198:n140, GT:0905 0.61 0.09
0.18
0.61
400
400
0
800 SXS:BBH:0180, RIT:BBH:0198:n140, GT:0905 0.31 0.10
0.23
0.31
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PHYS. REV. D
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transient with power detected by cWB (see Sec.
II D
),
raising the significance of the underlying IMBHB signal.
Since the resulting event has a marginal significance, the
underlying IMBHB trigger would be even less significant.
Hence, we conclude that this event is best explained by
detector noise.
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