Astronomy & Astrophysics
manuscript no. o3imbh
©ESO 2021
June 1, 2021
Search for intermediate mass black hole binaries in the third
observing run of Advanced LIGO and Advanced Virgo
The LVK Collaboration (full author list in Appendix C)
1
June 1, 2021
ABSTRACT
Intermediate-mass black holes (IMBHs) span the approximate mass range
100
–
10
5
M
, between black holes (BHs) formed by stellar
collapse and the supermassive BHs at the centers of galaxies. Mergers of IMBH binaries are the most energetic gravitational-wave
sources accessible by the terrestrial detector network. Searches of the first two observing runs of Advanced LIGO and Advanced
Virgo did not yield any significant IMBH binary signals. In the third observing run (O3), the increased network sensitivity enabled the
detection of GW190521, a signal consistent with a binary merger of mass
∼
150 M
providing direct evidence of IMBH formation.
Here we report on a dedicated search of O3 data for further IMBH binary mergers, combining both modelled (matched filter) and
model independent search methods. We find some marginal candidates, but none are sufficiently significant to indicate detection of
further IMBH mergers. We quantify the sensitivity of the individual search methods and of the combined search using a suite of IMBH
binary signals obtained via numerical relativity, including the effects of spins misaligned with the binary orbital axis, and present the
resulting upper limits on astrophysical merger rates. Our most stringent limit is for equal mass and aligned spin BH binary of total
mass
200M
and effective aligned spin 0.8 at
0
.
056 Gpc
−
3
yr
−
1
(90% confidence), a factor of 3.5 more constraining than previous
LIGO-Virgo limits. We also update the estimated rate of mergers similar to GW190521 to
0
.
08 Gpc
−
3
yr
−
1
.
Use \titlerunning to supply a shorter title and/or \authorrunning to supply a shorter list of authors.
1. Introduction
Black holes are classified according to their masses: stellar-mass black holes (BHs) are those with mass below
∼
100 M
, formed
by stellar collapse, while supermassive BHs (Ferrarese & Ford 2005) at the centers of galaxies have masses above
10
5
M
. Between
stellar-mass and supermassive BHs is the realm of intermediate mass black holes (IMBHs) – BHs with masses in the range
100
−
10
5
M
(van der Marel 2004; Miller & Colbert 2004; Ebisuzaki et al. 2001; Koliopanos 2017; Inayoshi et al. 2020).
Stellar evolution models suggest that BHs with mass up to
∼
65 M
are the result of core-collapse of massive stars (Woosley
2017; Giacobbo et al. 2018; Woosley 2019; Farmer et al. 2019; Mapelli et al. 2020; Farmer et al. 2020). The final fate of the star is
determined by the mass of the helium core alone. Stars with helium core mass in the range
∼
32
−
64 M
undergo pulsational pair-
instability leaving behind remnant BHs of mass below
∼
65 M
(Fowler & Hoyle 1964; Barkat et al. 1967). When the helium core
mass is in the range
∼
64
−
135 M
, pair-instability drives the supernova explosion and leaves no remnant; while stars with helium
core mass greater than
∼
135 M
are expected to directly collapse to intermediate-mass BHs. Thus, pair-instability (PI) prevents the
formation of heavier BHs from core-collapse, and suggests a mass gap between
∼
65
−
120 M
in the BH population known as PI
supernova (PISN) mass gap (Bond et al. 1984; Woosley et al. 2007; Woosley & Heger 2021). Possible IMBH formation channels
also include the direct collapse of massive first-generation, low-metallicity Population III stars (Fryer et al. 2001; Heger et al. 2003;
Spera & Mapelli 2017; Madau & Rees 2001; Heger & Woosley 2002), and multiple, hierarchical collisions of stars in dense young
star clusters (Miller & Hamilton 2002; O’Leary et al. 2006; Giersz et al. 2015; Mapelli 2016), among others. It is not currently
known how supermassive black holes form. Hierarchical merger of IMBH systems in a dense environment is among the putative
formation channels for supermassive BHs (King & Dehnen 2005; Volonteri 2010; Mezcua 2017; Koliopanos 2017).
Several IMBH candidates are suggested by electromagnetic observations, but lack conclusive confirmation (Greene et al. 2020).
Observations include direct kinematical measurement of the mass of the central BH in massive star clusters and galaxies (Mezcua
2017; Miller & Hamilton 2002; Atakan Gurkan et al. 2004; Anderson & van der Marel 2010; Baumgardt et al. 2003; Pasham et al.
2015; Vitral & Mamon 2021). Other possible evidence for IMBH includes extrapolation of scaling relations between the masses
of host galaxies and their central supermassive BH to the mass range of globular clusters (Graham 2012; Graham & Scott 2013;
Kormendy & Ho 2013). In addition, observations of characteristic imprints on the surface brightness, mass-to-light ratio and/or line-
of-sight velocities also suggest that dense globular clusters harbour IMBHs (van den Bosch et al. 2006; Gebhardt et al. 2005; Noyola
et al. 2008; Lützgendorf et al. 2011; Kızıltan et al. 2017). 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 (Baumgardt et al. 2003;
Anderson & van der Marel 2010; Lanzoni et al. 2013). Empirical mass scaling relations of quasi-periodic oscillations in luminous
X-ray sources have also provided evidence for IMBHs (Remillard & McClintock 2006). Ultraluminous X-ray sources exceed the
Eddington luminosity of an accreting stellar-mass BH (Kaaret et al. 2017; Farrell et al. 2009). An accreting IMBH is a favored
explanation in several cases (Kaaret et al. 2001; Miller & Colbert 2004). However, neutron stars or stellar-mass black holes emitting
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arXiv:2105.15120v1 [astro-ph.HE] 31 May 2021
A&A proofs:
manuscript no. o3imbh
above their Eddington luminosity could also account for such observations (Bachetti et al. 2014; Israel et al. 2017). The strongest
IMBH candidate amongst them is HLX-1, an hyper-luminous X-ray source indicating an IMBH mass of
∼
0
.
3
−
30
×
10
4
M
(Farrell
et al. 2009; Godet et al. 2009; Servillat et al. 2011; Webb et al. 2012; Cseh et al. 2015; Soria et al. 2012). In Lin et al. (2018), an
intermediate-mass black hole candidate was found in a tidal disruption event in a massive star cluster. More recently, in Paynter
et al. (2021), there was a claim of an IMBH detection through a gravitationally lensed gamma ray burst.
The Advanced LIGO (Aasi et al. 2015) and Advanced Virgo (Acernese et al. 2015) interferometric gravitational wave (GW)
detectors have completed three observing runs between September 2015 and March 2020. The third observing run of Advanced
LIGO and Advanced Virgo, O3, extended from April 1st, 2019, 15:00 UTC to March 27th, 2020 17:00 UTC. The recently released
second gravitational-wave transient catalog provided a comprehensive summary of significant compact binary coalescence events
observed up to October 1st, 2019 (Abbott et al. 2020c), reporting a total of 50 events. The corresponding binary black hole (BBH)
population analysis of Abbott et al. (2020d) indicates that
99%
of primary BH masses lie below
m
99%
∼
60 M
: thus, the large
majority of merging BH have masses below a limit of
∼
65 M
consistent with expectations from PI.
Near the beginning of O3, the first intermediate-mass black hole coalescence event, GW190521 (Abbott et al. 2020b), was
observed. This GW signal was consistent with a coalescence of black holes of
85
+
21
−
14
M
, and
66
+
17
−
18
M
which resulted in a remnant
black hole of
142
+
28
−
16
M
falling in the mass range of intermediate-mass black holes. GW190521 provided the first conclusive evi-
dence for the formation of an IMBH below
10
3
M
. It is a massive binary black hole system with an IMBH remnant and a primary
BH in the PISN mass gap with high confidence (Abbott et al. 2020e) although, see Fishbach & Holz (2020); Nitz & Capano (2021)
for an alternative interpretation. The discovery triggered a variety of investigations regarding the evolution models and the subse-
quent mass gap in the BH population. It also suggested a possibility of the formation of massive BHs (>
100 M
) via hierarchical
merger scenario in a dense environment (Abbott et al. 2020e; Kimball et al. 2020).
The Advanced LIGO - Advanced Virgo detectors are sensitive to the lower end of the IMBH binary mass range, potentially
making IMBHs detectable out to cosmological distances, as is evident from GW190521. Observation of IMBH binary systems
are not only interesting for massive BH formation channels, but they act as a perfect laboratory to test general relativity (Abbott
et al. 2016b; Yunes et al. 2016; Yunes & Siemens 2013; Gair et al. 2013). Massive BH coalescences produce louder mergers
and ringdown signals in the sensitive band of the advanced GW detectors. Furthermore, these can display prominent higher-order
modes that confer GWs a more complex morphology that can significantly deviate from a canonical chirp (Calderon Bustillo et al.
2020). Observations of higher-order modes help to test general relativity and fundamental properties of BHs such as the no-hair
theorem (Kamaretsos et al. 2012; Meidam et al. 2014; Thrane et al. 2017; Carullo et al. 2018) and BH kick measurements (Gonzalez
et al. 2007; Campanelli et al. 2007; Calderón Bustillo et al. 2018). These IMBHs might be multi-band events observable by both
LIGO/Virgo and
LISA
(Amaro-Seoane et al. 2017), and could provide novel probes of cosmology and contribute to the stochastic
background (Fregeau et al. 2006; Miller 2009; Jani et al. 2020; Ezquiaga & Holz 2021).
The GW signal from a massive BBH coalescence is evident as a short-duration waveform with little inspiral and mostly merger-
ringdown signal, falling in the low-frequency region of the advanced detectors. With initial GW detectors (Abadie et al. 2012b; Aasi
et al. 2014), the IMBH binary searches were restricted to probe the merger-ringdown phase of the coalescing BBH system, using
the model waveform independent coherent WaveBurst (cWB) (Klimenko & Mitselmakher 2004; Klimenko et al. 2005, 2006), and
a ringdown templated search (Aasi et al. 2014). Improvement in the detector sensitivity at low frequencies in the advanced era made
IMBH binaries a target for a matched filtering search that would probe the short inspiral phase. In Abbott et al. (2017b), we used a
combined search with the matched filtering GstLAL (Messick et al. 2017; Hanna et al. 2020; Sachdev et al. 2019) search and model
independent cWB (Klimenko et al. 2011, 2016). This combined search was further extended with an additional matched filtering
PyCBC search (Usman et al. 2016; Allen 2005; Dal Canton et al. 2014; Nitz et al. 2017) in Abbott et al. (2019) using the data from
the first two observing runs. No significant IMBH binary event was found in these searches.
While all the previous matched filtering searches were generic BBH searches, the improvements in the detector sensitivity at
low frequencies and the IMBH merger signals’ short duration nature motivated us to use matched filter searches targeted to the
IMBH mass-spin parameter space. Here, we carry out an IMBH binary search using the entire year-long third observing run, O3,
of the Advanced LIGO and Advanced Virgo detector network with a combined search using three search algorithms: two matched-
filtering based focused IMBH binary searches, using the PyCBC and GstLAL libraries, and the minimally modelled time-frequency
based cWB search. We search for massive binary systems with at least one component above the expected PISN mass gap limit of
65 M
, and with an IMBH remnant. GW190521 remains as the most significant candidate in the combined search; no other event
is comparably significant. We provide the results from the combined search with the next most significant events and follow up
investigations to assess their origin.
The increased sensitivity of the O3 run allows us to set more stringent bounds on the binary merger rate density. The lack of a
confirmed IMBH population as well as possible formation channels of IMBH distinct from those of stellar-mass BHs preclude us
from using an overall mass model for the IMBH population. Thus, we confine all the upper limit studies to a suite of discrete points
in the IMBH parameter space. We incorporate more detailed physics in selecting the suite of IMBH binary waveforms as compared
to earlier upper limit studies. In Abbott et al. (2017b) we simulated a limited set of discrete mass and aligned-spin binary waveforms
in the first advanced detector observation data to obtain upper limits on merger rate. The study with the first two observation runs
used the most realistic numerical relativity (NR) simulation set with aligned spins for the upper limit study (Abbott et al. 2019).
The most recent stringent merger rate upper limit is
0
.
2 Gpc
−
3
yr
−
1
, for the equal mass binary system with a component mass of
100 M
and component spins of dimensionless magnitude
0
.
8
aligned with the binary orbital angular momentum. Recently, Chandra
et al. (2020) used IMBH binary systems with generically spinning BHs with total mass between
210
−
500 M
and obtained a most
stringent upper limit of
0
.
28 Gpc
−
3
yr
−
1
for equal-mass binaries with total mass of 210
M
.
Here, we use a suite of NR simulations of GW emission from IMBH binary system with generically spinning BHs in order to
estimate our search sensitivity over the O3 data. We place the most stringent 90% merger rate upper limit on equal mass and aligned
Article number, page 2 of 27
The LVK Collaboration (full author list in Appendix C): Search for intermediate mass black hole binaries in the third observing run of Advanced
LIGO and Advanced Virgo
spin BH binary of total mass
200 M
and with individual BH spins of
0
.
8
as
0
.
056 Gpc
−
3
yr
−
1
. The revised limit is a factor
∼
3
.
5
more stringent than that obtained with the first two observing runs. We also update the merger rate for systems compatible with the
source parameters of GW190521, first estimated in Abbott et al. (2020e), to
0
.
08
+
0
.
19
−
0
.
07
Gpc
−
3
yr
−
1
, using the combined search method
applied to simulated signals injected over the entire O3 data.
The paper organization is as follows: Sect. 2 summarizes the data being used for the search. Sect. 3 summarizes the combined
search approach from the results from three distinct IMBH binary search algorithms. Sect. 4 discusses the search results and
followup of the most significant candidate events. Sect. 5 provides a detailed discussion about the NR GW injection set used and
the rate upper limits study including the updated rate on the most significant GW190521-like systems.
2. Data Summary
We carry out the analysis using O3 data from both LIGO detectors (LHO-LIGO Hanford Observatory and LLO-LIGO Livingston
Observatory) and the Virgo detector. We condition the data in multiple steps before performing our search (Abbott et al. 2020a). The
strain data, recorded from each detector, are calibrated in near real-time to produce an online data set (Viets et al. 2018; Acernese
et al. 2018). A higher-latency offline calibration stage provides identification of systematic errors and calibration configuration
changes (Sun et al. 2020; Estevez et al. 2020). The analyses presented here use the offline recalibrated data from the LIGO detectors,
and the Virgo detector’s online data. For this search, we consider 246.2 days, 254.1 days, and 250.8 days of observing-mode data
from the Hanford, Livingston, and Virgo detector respectively. The joint observation time for the full network of three detectors is
156.4 days.
We then linearly subtract spectral features of known instrumental origin using auxiliary witness sensors, i.e., sensors that indicate
the presence of noise causing these features. The subtraction removes calibration lines in all detectors, as well as 60 Hz harmonics
produced by power mains coupling in the LIGO detectors (Driggers et al. 2019; Davis et al. 2019). Low-frequency modulation of
the power mains coupling also results in sidebands around the 60 Hz line; we apply an additional non-linear noise subtraction to
remove these sidebands (Vajente et al. 2020).
Periods of poor data quality are marked using data quality flags separated into three categories (Abbott et al. 2020a; Fisher et al.
2020; Davis et al. 2021), which are used to exclude time segments from different searches, as described below. Category 1 flags
indicate times when a detector is not operating or recording data in its nominal state; these periods are not analyzed by any search.
Category 2 flags indicate periods of excess noise that are highly likely to be caused by known instrumental effects. The cWB and
PyCBC searches use different sets of category 2 flags. The GstLAL search does not use category 2 flags, as discussed in Sect. 3.
Category 3 flags are based on statistical correlations with auxiliary sensors. Of the analyses presented here, only the cWB search
uses category 3 flags.
The candidate events in this paper are vetted in the same way as past GW events (Abbott et al. 2016a, 2020c). This validation
procedure identifies data quality issues such as non-stationary noise or glitches of instrumental origin appearing in the strain data.
Auxiliary sensors that monitor the detectors and environmental noise are used to check for artifacts that may either have accounted
for, or contaminated the candidate signal (Nguyen et al. 2021). For candidate events that coincide with glitches, subtraction of the
glitches from the strain data is performed if possible (Cornish & Littenberg 2015; Littenberg et al. 2016; Pankow et al. 2018); oth-
erwise recommendations are made to exclude the relevant time or frequency ranges from parameter estimation analyses. Validation
assessments for individual candidate events are provided in Sect.4 and Appendix A.
3. Search methods
In this section, we describe the analysis methods algorithms (pipelines) used to search the LIGO-Virgo data from O3 for IMBH
binary merger signals. Such signals have short durations in the detectors’ sensitive frequency band, typically less than 1 s. Thus,
methods for detection of generic short transient GW events (bursts) may be competitive compared to search methods which use
parameterized models of the expected signals (templates) from binary coalescences (e.g. Chandra et al. 2020). As in the IMBH
binary search of O1 and O2 (Abbott et al. 2017b, 2019), we employ both generic transient search methods and modelled template
searches. We first describe the generic transient pipeline, cWB, in the configuration used here, and then the two templated pipelines,
GstLAL and PyCBC, which have been adapted to maximize sensitivity to IMBH binary mergers. We then summarize the method
used to combine the search outputs into a single candidate list, and finally discuss selection criteria to distinguish IMBH binary
candidates from the known heavy stellar-mass BBH population (Abbott et al. 2020c,d).
The output of a transient search algorithm or pipeline is a set of candidate events, each with an estimated time of peak strain at
the participating detector(s).
1
Each event is also assigned a ranking statistic value, and its significance is quantified by estimating
the corresponding false alarm rate (FAR), which is the expected number per time of events caused by detector noise that have an
equal or higher ranking statistic value.
The sensitivity of a search to a population of IMBH mergers can be evaluated by adding simulated signals (injections) to real GW
detector strain data and analyzing the resulting data streams, to output the ranking statistic and estimated FAR that each simulated
signal would be assigned if present in an actual search. Specific simulation campaigns will be described in detail in Sect. 5 and
sensitivity estimates from individual search pipelines are included in a public data release.
1
For black hole binary mergers, this peak strain time is close to the formation of a common horizon.
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3.1. cWB model waveform independent search for IMBH binaries
cWB (Klimenko & Mitselmakher 2004; Klimenko et al. 2005, 2006, 2011, 2016; Drago et al. 2020) is a GW search that uses
minimal assumptions on signal morphology to detect and reconstruct GW transients. The search identifies coincident energy across
the network of detectors to classify GW signals. The cWB search has been participating in the search for IMBH signals since
Initial LIGO’s fifth science run (Abadie et al. 2012a). The algorithm uses a multi-resolution wavelet transform, known as the
Wilson Daubechies Meyer wavelet transform (Necula et al. 2012), to map the multi-detector data into the time-frequency domain,
as blocks of a fixed time-frequency area known as pixels. The algorithm selects pixels with excess energy above the expected noise
fluctuation and groups them into clusters, referred to as candidate events. The collection and clustering of pixels differ based on the
target source (Klimenko et al. 2016). Each candidate event is ranked according to its coherent signal-to-noise ratio (SNR) statistic
(Klimenko et al. 2016), which incorporates the estimated coherent energy and residual noise energy. An additional threshold is
applied to the network correlation which provides the measure on the event correlation across multiple detectors in the network.
The cWB algorithm reconstructs the source sky location and whitened signal waveforms using the constrained maximum likelihood
method (Klimenko et al. 2016).
We estimate the FAR of a search event with time lag analysis: data from one or more detectors are time-shifted by more than 1 s
with respect to other detectors in the network, then cWB identifies events in this time-shifted data. Since the time-shift is greater than
the GW time of flight between detectors, this analysis estimates the rate and distribution of false alarms. The analysis is repeated
many times with different time-shifts, yielding a total analyzed background time
T
bkg
. For a given search event, the FAR value is
estimated as the number of background events with coherent SNR greater than the value assigned to the event, divided by
T
bkg
.
The model independent nature of cWB search makes it susceptible to incorrectly classifying noise artifacts. We apply a series
of signal-dependent vetoes based on the time-frequency morphology and energy distribution properties to remove spurious noisy
transients. We tune the veto values based on the extensive simulation of IMBH binary signals (see Appendix A of Gayathri et al.
2019). We divide the cWB search for quasi-circular BBH signals into two separate configurations: high-mass search and low-mass
search, depending on the central frequency
f
c
of the GW signal. For a compact binary merger signal,
f
c
is inversely proportional
to the redshifted total mass
M
z
=
(1
+
z
)
M
, where
M
is the source frame total mass and
z
is the source redshift. We then optimize
the low-mass search sensitivity for signals with
f
c
>
80
Hz (the BBH regime), and the high-mass search sensitivity for signals with
f
c
<
80
Hz (the IMBH regime). In practice, a cut
f
c
>
60
Hz is imposed in the low-mass search and
f
c
<
100
Hz in the high-mass
search, resulting in an overlap region covering
60
−
100
Hz. In the O3 search, we combine the two searches by applying a trials
factor of
2
to the estimated FAR for events in the overlap region. This improves the overall search sensitivity to borderline IMBH
events (
?
).
The cWB search analyzes data from all three detectors in low latency. However, the follow up offline cWB analysis does not
improve detection efficiency with the inclusion of Virgo. This is primarily due to the additional noise in the Virgo detector. Thus,
at a given time, the cWB search uses the best available (most sensitive) two detector network configuration. This ensures that the
cWB search does not analyze the same data with multiple detector configurations. In case, if any event shows high significance in
low latency cWB analysis with the three-detector network and low significance in offline cWB analysis with the best two-detector
configuration, we re-analyze that observing time with both the LLO-LHO-Virgo and LLO-LHO networks and apply a trials factor
of
2
to the minimum FAR over the two networks for the final significance.
In the special case where an event shows high significance in low latency cWB analysis with the three-detector network and
low significance in offline cWB analysis with the best two-detector configuration, we re-analyze the event with both the LLO-
LHO-Virgo and LLO-LHO networks and apply a trials factor of
2
to the minimum FAR over the two networks to establish its final
significance.
3.2. Templated searches for IMBH mergers
For GW signals whose forms are known or can be theoretically predicted, search sensitivity is optimized by the use of matched
filter templates that suppress noise realizations inconsistent with the predicted signals. Since the binary parameters are
a priori
unknown, a discrete set (bank) of templates is used in order to cover signal parameter values within a predetermined range with a
specified minimum waveform accuracy (Sathyaprakash & Dhurandhar 1991; Owen 1996). General binary black hole coalescence
signals bear the imprint of component spins misaligned with the orbital axis, causing orbital precession, and potentially also of
orbital eccentricity. It is a so far unsolved problem to implement an optimal search over such a complex space of signals.
Instead, the searches presented here restrict the signal model to the dominant mode of GW emission from quasi-circular, non-
precessing binaries (Ajith et al. 2011), i.e. with component spins perpendicular to the orbital plane. Both the GstLAL and PyCBC
searches use the SEOBNRv4 waveform approximant (Bohé et al. 2017) as template waveforms, implemented as a reduced-order
model (Pürrer 2016) for computational speed. These templates may still have high matches to signals from precessing or eccentric
binaries, however in general, sensitivity to such signals will be reduced due to lower matches with template waveforms.
Each detector’s strain time series is then correlated with each template to produce a matched filter time series. Single-detector
candidates are generated by identifying maxima of the matched filter SNR above a predetermined threshold value. However, during
times of known disturbances in detector operation, or during very high amplitude non-Gaussian excursions in the strain data,
candidates are either not produced or are discarded, since such high-SNR maxima are very likely to be artifacts. Signal consistency
checks such as chi-squared (Allen 2005) are also calculated and single-detector candidates may also be discarded for excessive
deviation from the expected range of values.
If two or more detectors are operating, their single-detector candidates are compared in order to identify multi-detector candidate
events which are consistent in the template parameters, time of arrival, amplitude, and waveform phase over the detector network.
The resulting multi-detector events are then ranked via a statistic which depends on the properties of single-detector candidates
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The LVK Collaboration (full author list in Appendix C): Search for intermediate mass black hole binaries in the third observing run of Advanced
LIGO and Advanced Virgo
and their consistency over the network. Finally, the statistical significance of each multi-detector event is obtained by comparing its
statistic value to the distribution expected for noise events, resulting in an estimate of its FAR.
In what follows we briefly summarize the methods specific to each of the matched filter pipelines.
3.2.1. GstLAL search
The search for IMBH mergers executed by the matched filter based GstLAL pipeline (Messick et al. 2017; Hanna et al. 2020;
Sachdev et al. 2019) uses a template bank covering a parameter space of binaries with (redshifted) total masses in the range [50,
600]
M
. The mass ratios,
q
=
m
2
/
m
1
, of the binary systems covered lie between 1 and
1
/
10
, while their spins are either aligned
or anti-aligned with the total angular momentum of the system, with the dimensionless spin magnitude less than 0.98. The analysis
starts at a frequency of 10 Hz.
The SNR threshold applied for single-detector triggers is 4 for the Hanford and Livingston detectors and 3.5 for the Virgo
detector. The GstLAL search pipeline applies a signal-consistency test based on the template’s autocorrelation over time. The
search also uses a signal model to describe the prior probability of a binary from a given source population being detected by each
template: the signal model used for this search is uniform in the log of the reduced mass of the binary.
The ranking statistic applied to candidate events is an estimate of the relative probability of the event’s parameters being caused
by a GW signal as compared to noise, i.e. the likelihood ratio. In addition to events formed from triggers from multiple detectors,
triggers found in a single detector are also included in the search, albeit with a penalty applied to their ranking to account for the
higher probability of noise origin.
The GstLAL search does not use data quality based vetoes of category 2 and above. Instead, the search uses data quality
information known as iDQ (Essick et al. 2020; Godwin et al. 2020), from auxiliary channels monitoring the detector to compute a
penalty term in the denominator of the ranking statistic. This has been computed for both single-detector and multi-detector triggers
found by the search. The non-coincident and noise-like triggers are then used to estimate the background noise probability density,
which is sampled to find the estimated FAR, corresponding to the likelihood ratio for a candidate (Messick et al. 2017; Sachdev
et al. 2019).
3.2.2. PyCBC search
The PyCBC-IMBH search used here (Chandra et al. 2021) covers a target space of redshifted total masses between
100
and
600
M
,
with component masses greater than
40
M
and mass ratio between
1
/
1
and
1
/
10
. The components have dimensionless spins
projected onto the orbital axis between
−
0
.
998
and
0
.
998
. To reduce false alarms arising from short-duration noise transients (Cabero
et al. 2019), we discard any templates with a duration less than
0
.
07
s, measured from the fixed starting frequency of
15
Hz.
The analysis pre-processes the data from each detector by windowing out very high amplitude excursions (
>
50
σ
deviation
from Gaussian noise) in the whitened strain time-series (Usman et al. 2016). This gating step significantly suppresses the noise
background. The SNR threshold for trigger generation is chosen as
4
; any triggers in time marked by category-2 data quality veto
are discarded. We also remove LIGO triggers within
(
−
1
,
+
2
.
5)
s of the centre of a gating window, since empirically such times
contain many lower-amplitude noise transients correlated with the central high amplitude glitch (Chandra et al. 2021).
Signal-consistency
χ
2
r
and sine-Gaussian discriminant tests are applied to the remaining triggers (Allen 2005; Nitz 2018). The
single detector SNRs are corrected for short-term variation in the detector power spectral density (PSD) (Nitz et al. 2019; Mozzon
et al. 2020), and a penalty is applied to triggers with a short-term PSD measure over
10
times the expectation from stationary
noise (Chandra et al. 2021). The analysis also penalizes triggers with
χ
2
r
values above
10
, where the expectation for a well-matched
signal is unity. These vetoes significantly reduce the background.
The search identifies candidates by checking the consistency between triggers in 2 or 3 detectors. The resulting candidates are
ranked by using the expected distribution of astrophysical signal SNRs, phases and times over multiple detectors, as well as models
of the non-Gaussian noise distribution in each template and detector (Nitz et al. 2017; Davies et al. 2020). A FAR is assigned to
each candidate event by simulating the background noise distribution using time-shifted analyses (Usman et al. 2016), similar to
cWB. The FARs for events involving different detector combinations are finally combined as in (Davies et al. 2020).
Other PyCBC-based searches overlapping the IMBH parameter region were recently presented in Nitz et al. (2019); Abbott
et al. (2020c) using two strategies: a broad parameter space search covering compact binaries from binary neutron star (BNS) up to
IMBH, and a “focused” search for binary black hole (BBH) covering a restricted range of masses and with strict cuts to suppress
noise artifacts. The sensitivity of the present IMBH search, at a FAR threshold of
0
.
01 yr
−
1
, to a set of simulated generically spinning
binary merger signals is increased relative to the broad (BBH) PyCBC searches of Abbott et al. (2020c) by a factor of
∼
1
.
5
(
∼
1
.
1
)
in volume time (VT) for redshifted total mass
M
z
∈
[100
−
200] M
, up to a factor
∼
2
.
8
(
∼
12
.
6
) for
M
z
∈
[450
,
600] M
(Chandra
et al. 2021).
3.3. Combined search
Each of our three targeted searches produces its list of candidates characterized by GPS times and FAR values. The p-value for each
candidate in a given search, defined as the probability of observing one or more events from the noise alone with a detection statistic
as high as that of the candidate is then
p
=
1
−
e
−
T
·
FAR
,
(1)
where
T
is the total duration of data analyzed by the search. We combine these lists to form a single list of candidates by first
checking whether any events from different searches fall within a 0.1s time window of each other, and if so, selecting only the event
Article number, page 5 of 27
A&A proofs:
manuscript no. o3imbh
with the lowest p-value
p
min
. The resulting clustered events are ranked by a combined p-value,
̄
p
≡
1
−
(1
−
p
min
)
m
,
(2)
where
m
denotes the trials factor (look-elsewhere) factor (Abbott et al. 2017b, 2019). We take
m
=
3
under the assumption that
the noise backgrounds of our searches are independent of one another. If there is any correlation between these backgrounds, the
effective trials factor will be lower, which makes
m
=
3
a conservative choice.
3.4. Selection of Intermediate Mass Black hole Binaries
As noted in Abbott et al. (2020c,d), LIGO-Virgo observations include a population of black hole binaries with component masses
extending up to 60
M
or above, and remnant masses extending up to
∼
100 M
; thus, there is
a priori
no clear separation between
such heavy BBH systems and the lightest IMBH binaries. We also expect search pipelines tuned for sensitivity to IMBH mergers
to be capable of detecting such heavy stellar-mass BBH, since the overlap of their GW signals with those of IMBH binaries may be
large. We find indeed that many such BBH systems occurring within O3a are recovered with high significance by our search.
The complete catalog of such heavy BBH systems over the O3 run will be provided in a subsequent publication, as an update
to GWTC-2. Here, we select only those events for which, under the assumption that the signals were produced by a quasi-circular
binary black hole merger, we have clear evidence that the remnant is an IMBH of mass above 100
M
, and at least the primary black
hole has a mass greater than the lower bound of the pair-instability mass gap. Strong evidence that this is the case for the primary
component of GW190521 was presented in Abbott et al. (2020b,e).
The selection criteria are evaluated as follows. We begin by defining the hypothesis
H
according to which the detector output
time series
d
(
t
)
is given by
d
(
t
)
=
n
(
t
)
+
h
(
t
;
θ
)
(3)
where
n
(
t
)
is the noise time series, taken as a realisation of a zero-mean wide-sense stationary stochastic process, and
h
(
t
;
θ
)
is the
gravitational wave signal model dependent on a set of parameters
θ
. We estimate the parameters
θ
by computing their posterior
probability distribution
p
(
θ
|
d
,
H
)
using Bayes theorem:
p
(
θ
|
d
,
H
)
=
p
(
θ
|
H
)
p
(
d
|
θ,
H
)
p
(
d
|
H
)
(4)
where
p
(
θ
|
H
)
is the prior probability distribution,
p
(
d
|
θ,
H
)
is the likelihood function – taken as Normal distribution in the frequency
domain with variance given by the power spectral density of the data
d
(
t
)
thanks to the wide-sense stationarity assumption – and
p
(
d
|
H
)
=
∫
d
θ
p
(
θ
|
H
)
p
(
d
|
θ,
H
)
(5)
is the
evidence
for the hypothesis
H
. The latter quantity is particularly useful in the context of model selection. We can, in fact,
compare the evidence for the signal hypothesis
H
with the evidence for the hypothesis
N
according to which no signal is present to
assess their relative likelihoods by computing the (
log
10
) Bayes factor
log
10
B
SN
=
log
10
p
(
d
|
H
)
p
(
d
|
N
)
.
(6)
Each potential candidate is followed up with a coherent Bayesian parameter estimation analysis (Veitch et al. 2015; Lange et al.
2017; Wysocki et al. 2019). In these analyses, we model the GW signal as represented by precessing quasi-circular waveforms from
three different families:
NRSur7dq4
(Varma et al. 2019),
SEOBNRv4PHM
(Ossokine et al. 2020) and
IMRPhenomXPHM
(Pratten
et al. 2020). All considered models include the effects of higher-order multipole moments as well as orbital precession due to mis-
aligned BH spins. Details of the analysis configuration follow previously published ones (Abbott et al. 2020c) and are documented
in a separate paper (Abbott et al. 2021). In particular, we consider uniform priors on the redshifted component masses, the individual
spin magnitudes, and the luminosity distance proportional to its square modulus. For the source orientation and spin vectors, we
employ isotropic priors.
As a quantitative criterion to select a GW event as an IMBH binary, we consider the support of the joint posterior distributions
for the primary mass
m
1
and of the remnant mass
M
f
. For reference values
M
∗
=
100M
and
m
∗
1
=
65M
, we label a candidate an
intermediate-mass black hole binary if
∫
+
∞
M
∗
∫
+
∞
m
∗
1
dm
1
dM
f
p
(
M
f
,
m
1
|
D
,
H
)
≥
p
∗
,
(7)
where
p
∗
is a reference probability threshold, chosen to be
p
∗
=
0
.
9
. To perform the integral in Eq. (7), we construct a Gaussian
kernel density estimate to interpolate the posterior
p
(
M
f
,
m
1
|
D
,
H
)
which we use to perform the integral on a grid.
Thus, the main list of candidates presented in the following section does not correspond to the complete set of events recovered
by the searches, but only to those relevant to a potential astrophysical IMBH population. However, for comparison with earlier
results (Abbott et al. 2020c), we also report a full list of events detected by the combined IMBH search in O3a data, including BBH
events that do not fall into the IMBH region: see Sect. 4.2.
Article number, page 6 of 27
The LVK Collaboration (full author list in Appendix C): Search for intermediate mass black hole binaries in the third observing run of Advanced
LIGO and Advanced Virgo
Events
GPS Time
cWB FAR (yr
−
1
)
PyCBC FAR (yr
−
1
)
GstLAL FAR (yr
−
1
)
̄
p
GW190521
1242442967.5
2
.
0
×
10
−
4
1
.
4
×
10
−
3
1
.
9
×
10
−
3
4
.
5
×
10
−
4
200114_020818
†
1263002916.2
5
.
8
×
10
−
2
8
.
6
×
10
+
2
3
.
6
×
10
+
4
1
.
2
×
10
−
1
200214_224526
1265755544.5
1
.
3
×
10
−
1
-
-
2
.
5
×
10
−
1
Table 1.
Events from the combined search for intermediate mass black hole binary mergers in O3 data, sorted by their combined p-value
̄
p
.
†
200114_020818 was recovered by the cWB search using LHO-LLO data with a FAR of 15.87 yr
−
1
and by a followup search using LHO-LLO-
Virgo data with a FAR of 0.029 yr
−
1
; the FAR quoted in the table for cWB is derived from the LHO-LLO-Virgo search with a trials factor of
2.
The data for some events may not be consistent with the quasi-circular BBH signal plus Gaussian noise model, either because
they contain a signal which deviates significantly from this standard BBH model, or are affected by detector noise artefacts that
cannot be removed or mitigated. In such cases the values of
p
(
M
f
|
D
,
H
)
and
p
(
m
1
|
D
,
H
)
extracted from the Bayesian analysis may
either be inaccurate or indeed meaningless, for events arising from instrumental noise or even from a putative astrophysical source
that is not a compact binary merger. Such events will
not
be excluded from results presented here: they will be individually discussed
in the following sections.
4. Search results
4.1. Candidate IMBH events
The individual searches are applied on the full O3 data with the analysis time of 0.734 yr, 0.747 yr and 0.874 yr for cWB, PyCBC-
IMBH and GstLAL-IMBH search respectively. Table 1 summarises the results from the combined cWB-GstLAL-PyCBC IMBH
search on full O3 data detailed in Sect.3. These events have a combined p-value less than 0.26 (a threshold determined by the
loudest noise event in the combined search, 200214_224526 and satisfy the criteria for potential IMBH binary sources of Sect. 3.4.
For completeness, we have also listed marginal triggers found by our combined search in Appendix A.
The top-ranked event is GW190521 and it has a highly significant combined p-value of
4
.
5
×
10
−
4
. If this signal is from a
quasi-circular merger, then the signal is found to be consistent with the merger of two black holes in a mildly precessing orbit, with
component masses of
85
+
21
−
14
M
and
66
+
17
−
18
M
and a remnant black hole of
142
+
28
−
16
M
falling in the mass range of intermediate-mass
black holes. A full description of GW190521 and its implications can be found in Abbott et al. (2020b,e).
The second-ranked candidate, 200114_020818, was observed on 14th January 2020 at 02:08:18 UTC and identified by the low
latency cWB search in the LHO-LLO-Virgo detector network configuration, with a FAR of
<
0
.
04 yr
−
1
. The event was publicly
reported via GCN minutes after the event was observed (Abbott, R. and others 2019). Given the significance of the low-latency alert
with the 3-detector configuration, we employ both LHO-LLO and LHO-LLO-Virgo networks in cWB to estimate the significance
for this event: we find FARs of
15
.
87 yr
−
1
and
0
.
029 yr
−
1
for these configurations, respectively. The SNR reconstructed by cWB
for each network configuration is 12.3 and 14.5, respectively. As mentioned above in 3.1, we apply a trials factor of 2 to the
most significant result, obtaining a FAR of
0
.
058 yr
−
1
for the cWB search. The combined p-value of this event,
0
.
12
, is marginally
significant.
We then examined possible environmental or instrumental causes for the candidate signal. Excess vibrational noise could
have contributed to the signal in the LIGO Hanford detector, as discussed in Appendix B.1. Furthermore, the morphology of
200114_020818 is consistent with a well-studied class of glitches known as Tomtes (Buikema et al. 2020; Davis et al. 2021), which
occur multiple times per hour in LIGO Livingston. However, we are not currently able to exclude a putative morphologically similar
astrophysical signal, as there are no known instrumental auxiliary channels that couple to this glitch type. We undertake detailed
model-independent event reconstruction and parameter estimation (PE) studies, summarized in Appendix B. Although model inde-
pendent methods/algorithms produce mutually consistent reconstructions of the event, our analysis using the available quasi-circular
BBH merger waveforms does not support a consistent interpretation of the event as a binary merger signal present across the de-
tector network. We cannot conclusively rule out an astrophysical origin for the event, however it also appears consistent with an
instrumental artefact in LLO in coincidence with noise fluctuations in LHO and Virgo.
The third-ranked event was observed by the cWB pipeline on 14th February, 2020 at 22:45:26 UTC with a combined SNR of 13.1
in the two Advanced LIGO Detectors. The event has a
p
cWB
=
0
.
092
and thus a
̄
p
=
0
.
251
. In addition to its marginal significance,
the event has characteristics consistent with an instrumental noise transient. Excess noise due to fast scattered light (Soni et al. 2021)
is present in both LLO and LHO data. At Livingston, the excess noise extends up to 70 Hz and lasts many seconds before and after
the event. The Hanford scattering noise is weaker in amplitude but still overlaps completely with the duration of the event. Since it is
the most significant noise event obtained in the combined search with the cWB pipeline in its production configuration considering
only 2-detector events, we use 200214_224526 to establish a threshold of significance for inference of IMBH merger rates (for
which see Sect. 5). As 200214_224526 is likely caused by detector noise, any events with lower significance may be assumed to
have a high probability of noise origin. For completeness, we discuss some marginal events from the combined search in Appendix
A.
Article number, page 7 of 27
A&A proofs:
manuscript no. o3imbh
cWB
PyCBC
GstLAL
Combined
GWTC-2 Broad
GWTC-2 BBH
IMBH
GWTC-2 Broad
IMBH
IMBH
Event
FAR (yr
−
1
)
FAR (yr
−
1
)
FAR (yr
−
1
)
̄
p
GW190408_181802
9
.
5
×
10
−
4
<
2
.
5
×
10
−
5
<
7
.
9
×
10
−
5
1
.
6
×
10
−
2
<
1
.
0
×
10
−
5
<
1
.
0
×
10
−
5
<
1
.
0
×
10
−
4
GW190413_052954
-
-
7
.
2
×
10
−
2
5
.
6
×
10
−
1
-
5
.
4
×
10
+
3
7
.
1
×
10
−
1
GW190413_134308
-
-
4
.
4
×
10
−
2
1
.
4
×
10
−
1
3
.
8
×
10
−
1
1
.
2
×
10
+
3
2
.
7
×
10
−
1
GW190421_213856
3
.
0
×
10
−
1
1
.
9
×
10
+
0
6
.
6
×
10
−
3
6
.
1
×
10
−
3
7
.
7
×
10
−
4
1
.
8
×
10
+
0
1
.
4
×
10
−
2
GW190503_185404
1
.
8
×
10
−
3
3
.
7
×
10
−
2
<
7
.
9
×
10
−
5
2
.
5
×
10
−
3
<
1
.
0
×
10
−
5
1
.
7
×
10
−
1
4
.
0
×
10
−
3
GW190512_180714
8
.
8
×
10
−
3
3
.
8
×
10
−
5
<
5
.
7
×
10
−
5
4
.
0
×
10
+
1
<
1
.
0
×
10
−
5
<
1
.
0
×
10
−
5
<
1
.
0
×
10
−
4
GW190513_205428
-
3
.
7
×
10
−
4
<
5
.
7
×
10
−
5
5
.
0
×
10
−
2
<
1
.
0
×
10
−
5
2
.
1
×
10
−
1
1
.
1
×
10
−
1
GW190514_065416
-
-
5
.
3
×
10
−
1
1
.
1
×
10
+
0
-
7
.
6
×
10
+
2
9
.
2
×
10
−
1
GW190517_055101
8
.
0
×
10
−
3
1
.
8
×
10
−
2
<
5
.
7
×
10
−
5
8
.
7
×
10
−
4
9
.
6
×
10
−
4
2
.
7
×
10
−
2
1
.
9
×
10
−
3
GW190519_153544
3
.
1
×
10
−
4
<
1
.
8
×
10
−
5
<
5
.
7
×
10
−
5
<
1
.
1
×
10
−
4
<
1
.
0
×
10
−
5
3
.
9
×
10
−
3
2
.
5
×
10
−
4
GW190521
2
.
0
×
10
−
4
1
.
1
×
10
+
0
-
1
.
4
×
10
−
3
1
.
2
×
10
−
3
1
.
9
×
10
−
3
4
.
5
×
10
−
4
GW190521_074359
<
1
.
0
×
10
−
4
<
1
.
8
×
10
−
5
<
5
.
7
×
10
−
5
<
2
.
3
×
10
−
5
<
1
.
0
×
10
−
5
<
1
.
0
×
10
−
5
<
1
.
0
×
10
−
4
GW190602_175927
1
.
5
×
10
−
2
-
1
.
5
×
10
−
2
1
.
1
×
10
−
3
1
.
1
×
10
−
5
<
1
.
0
×
10
−
5
<
1
.
0
×
10
−
4
GW190701_203306
3
.
2
×
10
−
1
-
-
<
1
.
9
×
10
−
4
1
.
1
×
10
−
2
3
.
8
×
10
−
2
4
.
3
×
10
−
4
GW190706_222641
<
1
.
0
×
10
−
3
6
.
7
×
10
−
5
4
.
6
×
10
−
5
<
1
.
1
×
10
−
4
<
1
.
0
×
10
−
5
2
.
4
×
10
−
3
2
.
5
×
10
−
4
GW190727_060333
8
.
8
×
10
−
2
3
.
5
×
10
−
5
3
.
7
×
10
−
5
<
1
.
2
×
10
−
4
<
1
.
0
×
10
−
5
4
.
5
×
10
−
4
2
.
7
×
10
−
4
GW190731_140936
-
-
2
.
8
×
10
−
1
6
.
4
×
10
−
1
2
.
1
×
10
−
1
2
.
1
×
10
+
0
7
.
6
×
10
−
1
GW190803_022701
-
-
2
.
7
×
10
−
2
1
.
7
×
10
−
1
3
.
2
×
10
−
2
3
.
0
×
10
+
0
3
.
2
×
10
−
1
GW190828_063405
<
9
.
6
×
10
−
4
<
1
.
0
×
10
−
5
<
3
.
3
×
10
−
5
<
7
.
0
×
10
−
5
<
1
.
0
×
10
−
5
<
1
.
0
×
10
−
5
<
1
.
0
×
10
−
4
GW190915_235702
<
1
.
0
×
10
−
4
8
.
6
×
10
−
4
<
3
.
3
×
10
−
5
3
.
8
×
10
−
4
<
1
.
0
×
10
−
5
4
.
7
×
10
−
1
2
.
2
×
10
−
4
GW190929_012149
-
-
-
3
.
1
×
10
−
1
2
.
0
×
10
−
2
2
.
9
×
10
+
1
5
.
0
×
10
−
1
Table 2.
Candidate events from this search for IMBH mergers in O3a data, including binary black hole mergers outside the IMBH parameter space,
and comparison with previously obtained GWTC-2 results from the templated search algorithms (Abbott et al. 2020c). The cWB search algorithm
used here is unchanged over GWTC-2. Candidates are sorted by GPS time and the FAR is provided for each search algorithm. Templated methods
used in GWTC-2 comprise the PyCBC and GstLAL broad parameter space pipelines and the PyCBC BBH-focused pipeline, while the optimized
algorithms applied in this search are labelled “IMBH”. The event names encode the UTC date with the time of the event given after the underscore,
except for the individually published event GW190521. The GstLAL FAR values have been capped at
1
.
0
×
10
−
5
yr
−
1
and corresponding
̄
p
values
have also been capped. For PyCBC events with FAR estimates limited by finite background statistics, an upper limit is stated. The IMBH combined
search p-values
̄
p
for each event are calculated from Eq. (7) using p-values of the cWB, PyCBC-IMBH and GstLAL-IMBH searches.For details
of the search configurations and event parameters, refer to Abbott et al. (2020c).
4.2. Complete O3a search results including BBH
As noted earlier in 3, the template-based searches have high sensitivity to the known population of heavy stellar-mass BBH mergers,
which may be compared to searches deployed in GWTC-2 (Abbott et al. 2020c). Here we record the complete list of significant
events recovered by the combined IMBH search from O3a data in Table 2, and supply corresponding search results from GWTC-2
for comparison. Specifically, we show outputs from the PyCBC broad parameter space and focused BBH searches (Nitz et al. 2019)
and the GstLAL broad parameter space search (Sachdev et al. 2019).
For GW190521, the PyCBC IMBH search yields a FAR of
1
.
4
×
10
−
3
yr
−
1
, as compared to
1
.
1 yr
−
1
for the broad parameter
space analysis of Abbott et al. (2020b,c). This significant change is in part because the PyCBC IMBH search is optimized for
shorter duration signals, and does not consider potential signals of total mass significantly below 100
M
; the mass and spin values
of GW190521 are also likely not covered by the templates used in earlier PyCBC searches, which imposed a minimum duration
of
0
.
15
s. A similar change in statistical significance is also observed for GW190602_
175927
for the same reasons. However, the
IMBH search results assign lower significance to GW190519_
153544
and GW190706_
222641
as compared to the GWTC-2 results.
The GstLAL pipeline recovers the GW190521 event at a FAR of
1
.
9
×
10
−
3
yr
−
1
over all of O3 data. It was reported earlier (Abbott
et al. 2020b,c) at a FAR of
1
.
2
×
10
−
3
yr
−
1
over O3a. As described in 3.2.1, the GstLAL pipeline has employed a dedicated search
for IMBH binaries with better coverage for the heavier mass binaries than the catalog search. Also, the iDQ based data quality
information used to inform the calculation of the ranking statistics, now incorporates multi-detector triggers, as against the only
single detector triggers that were used before. Differences in the significance of the events found by the IMBH specific GstLAL
search presented here, with what was reported for O3a in Abbott et al. (2020c) can be attributed to the differences in the search
settings and the data spanning over all of O3.
5. Astrophysical Rates of IMBH Binary Coalescence
Improved detector sensitivity, updated search methods, and the detection of GW190521 allow us to obtain revised bounds on the
merger rate (strictly, rate density) of IMBH binaries. Due to the lack of knowledge of specific formation channels for IMBH binaries,
even more so than for stellar-mass BH binaries, and the sparse observational evidence of any IMBH population, we do not consider
any overall mass model for such a population. Instead, here we simulate a suite of IMBH binary waveforms for discrete points in
parameter space, including generically spinning component BHs, derived from NR simulations. A similar campaign was carried out
Article number, page 8 of 27
The LVK Collaboration (full author list in Appendix C): Search for intermediate mass black hole binaries in the third observing run of Advanced
LIGO and Advanced Virgo
in (Abbott et al. 2019) using NR waveforms for IMBH binaries having component BH spins aligned with the binary orbital axis,
injected into the O1 and O2 data.
5.1. Injection Set
Here, we report on the merger rate of IMBH binary sources based on NR simulations computed by the SXS (Mroué et al. 2013),
RIT (Healy et al. 2017), and GeorgiaTech (Jani et al. 2016) codes. These simulations include higher-order multipoles, which may
make important contributions to the detection of high-mass and low mass-ratio (
q
≤
1
/
4
) binaries (Calderón Bustillo et al. 2016).
Based on previous studies which measured the agreement between different NR codes (Abbott et al. 2019), we include the following
harmonic modes in our analysis:
(
`,
m
)
=
{
(2
,
±
1)
,
(2
,
±
2)
,
(3
,
±
2)
,
(3
,
±
3)
,
(4
,
±
2)
,
(4
,
±
3)
,
(4
,
±
4)
}
.
We consider 43 IMBH binary sources with fixed source frame masses and spins, shown in Table 3. These 43 sources include
a subset of 16 sources investigated in the O1-O2 IMBH binary search. This updated search includes sources with total mass up to
800 M
and expands the range of targeted mass ratio
q
to between
1
/
1
−
1
/
10
. We also further explore the effects of the component
spins on detection efficiency. Of the 43 targeted IMBH sources, 4 have spins aligned with the orbital axis, with effective total
spin (Ajith et al. 2011)
χ
e
ff
≡
(
χ
1
,
‖
+
q
χ
2
,
‖
)
/
(1
+
q
)
=
0
.
8
, where
χ
‖
denotes the BH spin resolved along the orbital axis, and 4 have
anti-aligned spins with
χ
e
ff
=
−
0
.
8
. A further 11 have precessing spins:
χ
p
,
0
, where
χ
p
is the effective spin-precession parameter
of (Hannam et al. 2014; Schmidt et al. 2015).
The simulated signals for each targeted source point are uniformly distributed in sky location
(
θ,φ
)
and inclination angle
cos(
ι
)
.
The source redshift
z
is uniformly distributed in comoving volume, according to the TT+lowP+lensing+ext cosmological parameters
given in Table IV of Ref. Ade et al. (2016), up to a maximum redshift
z
max
. The signals are added to the O3 strain data, i.e. injected,
with a uniform spacing in time approximately every 100 s over the full observing time,
T
0
=
363
.
38
days.
To avoid generating injections that are well outside any possible detection range,
z
max
is calculated for each IMBH source point
independently. We consider values of redshift
z
in increments of 0.05 and calculate a conservative upper bound on the optimal
three-detector network SNR, SNR
net
, for each
z
. To bound the optimal SNR in a single detector, we assume the source is face-on
cos(
ι
)
=
1
, located directly overhead the detector, and we estimate the detector’s PSD using
∼
8
hours of typical O3 data. For
precessing waveforms, the
ι
is set at 10 Hz. We determine the maximum redshift by requiring that SNR
net
(
z
max
)
∼
5
. This results a
range of
z
max
across all targeted sources from 0.05 for the
(400
+
400) M
anti-aligned spin source to 2.75 for the
(100
+
100) M
aligned-spin source, as in Table 3.
When generating the injection parameters, we impose an additional threshold SNR
net
>
5
to limit the number of simulations
injected into detection pipelines that have a negligibly small probability of detection. For this purpose, the SNR
net
is re-estimated,
taking into account the randomly selected source position and orientation. We thus assume simulated events with SNR
net
<
5
are
missed by the search pipelines; these events are, though, accounted for in the calculation of sensitive volume and merger rates.
As stated in Sect. 3, the searches process the remaining injections with the same configuration as used for results from O3 data.
This is necessary to obtain unbiased rate estimates. In the case of cWB, injections were processed with the most sensitive two-
detector configuration: thus, for consistency, we consider only events recovered in the corresponding offline two-detector search
results.
5.2. Sensitive Volume Time and Merger Rate
Here we calculate limits on the merger rate for points in the binary component mass and spin parameter space described in Table 3,
using the loudest-event method (Biswas et al. 2009; Abbott et al. 2016c).
To derive the upper limit on merger rate for a given point in source parameter space, we consider the sensitive volume-time,
〈
VT
〉
sen
, of our combined search to such sources at a p-value threshold of 0.251, which is determined by 200214_224526, the most
significant event due to noise in the combined search results. For mergers with given intrinsic parameters the expected number of
detected signals
N
is related to the merger rate
R
and to the sensitive volume-time as
〈
N
〉
=
R
〈
VT
〉
sen
. For each source point, we
estimate
〈
VT
〉
sen
, as a fraction of the total volume-time out to its maximum injection redshift
z
max
, by counting injected signals that
are detected with a combined p-value below the threshold and dividing by the total number of injections generated.
Then, taking a uniform prior on
R
and using the Poisson probability of zero detected signals as a likelihood, we obtain the
90%
credible upper limit
R
90%
=
2
.
3
/
〈
VT
〉
sen
. The only significant IMBH binary signal in the combined search results is GW190521.
However, there is only one mass-spin (marked with † in Table 3) point which is consistent with both its component mass and spin
χ
e
ff
–
χ
p
90% credible regions. Therefore, for that source point, we conservatively use the Poisson probability of having one IMBH
binary detection and thus take
R
90%
=
3
.
9
/
〈
VT
〉
sen
.
Injections with component masses (60+60)
M
were performed: however, since this parameter point is within the stellar-mass
BBH distribution characterized in Abbott et al. (2020d), to which several heavy BBH systems detected in O3a may contribute, we
do not quote an upper rate limit. We do, however, state search sensitivity for such systems in our data release products.
Table 3 summarises the sensitive volume-time and upper limit on the merger rate for our chosen set of injections. For simulated
non-spinning sources, the sensitive volume-time decreases with an increase in total mass but increases with increasing mass ratio
q
. There are multiple reasons for these trends. First, for a fixed mass ratio, the duration of a signal within the detector bandwidth
decreases with increased total mass, even though its overall intrinsic luminosity increases. This is evident if one compares the
sensitive volume-time obtained for
(80
+
40) M
,
(100
+
50) M
and
(133
+
67) M
systems. Second, the amplitude of a source
decreases with a decrease in the mass ratio for a fixed total mass. Hence the sensitivity drops with a decrease in mass ratio. Last, a
decrement in mass ratio also increases the contribution coming from sub-dominant emission multipoles. This significantly affects
the GstLAL and PyCBC searches that filter using dominant multipole templates only.
Article number, page 9 of 27
A&A proofs:
manuscript no. o3imbh
M
(M
)
q
χ
e
ff
χ
p
SIM ID
z
max
〈
VT
〉
sen
[
Gpc
3
yr
]
R
90%
[
Gpc
−
3
yr
−
1
]
120
1/2
0.00
0.00
SXS:BBH:0169, RIT:BBH:0117:n140, GT:0446
2.00
12.42
0.19
120
1/4
0.00
0.00
SXS:BBH:0182, RIT:BBH:0119:n140, GT:0454
1.35
5.08
0.45
120
1/5
0.00
0.00
SXS:BBH:0056, RIT:BBH:0120:n140, GT:0906
1.15
3.45
0.67
120
1/7
0.00
0.00
SXS:BBH:0298 RIT:BBH:Q10:n173, GT:0568
0.90
1.85
1.24
120
1/10
0.00
0.00
SXS:BBH:0154, RIT:BBH:0068:n100
0.70
0.91
2.52
150
1/2
0.00
0.00
SXS:BBH:0169, RIT:BBH:0117:n140, GT:0446
1.85
12.84
0.30
200
1
0.00
0.00
SXS:BBH:0180, RIT:BBH:0198:n140, GT:0905
1.85
16.04
0.14
200
1/2
0.00
0.00
SXS:BBH:0169, RIT:BBH:0117:n140, GT:0446
1.60
11.67
0.20
200
1/4
0.00
0.00
SXS:BBH:0182, RIT:BBH:0119:n140, GT:0454
1.15
4.80
0.48
200
1/7
0.00
0.00
SXS:BBH:0298 RIT:BBH:Q10:n173, GT:0568
0.80
1.74
1.32
220
1/10
0.00
0.00
SXS:BBH:0154, RIT:BBH:0068:n100
0.60
0.81
2.86
250
1/4
0.00
0.00
SXS:BBH:0182, RIT:BBH:0119:n140, GT:0454
1.00
3.90
0.59
300
1/2
0.00
0.00
SXS:BBH:0169, RIT:BBH:0117:n140, GT:0446
1.15
7.55
0.31
350
1/6
0.00
0.00
SXS:BBH:0181, RIT:BBH:0121:n140, GT:0604
0.60
1.13
2.03
400
1
0.00
0.00
SXS:BBH:0180, RIT:BBH:0198:n140, GT:0905
1.00
5.65
0.41
400
1/2
0.00
0.00
SXS:BBH:0169, RIT:BBH:0117:n140, GT:0446
0.85
4.06
0.57
400
1/3
0.00
0.00
SXS:BBH:0030, RIT:BBH:0102:n140, GT:0453
0.70
2.55
0.90
400
1/4
0.00
0.00
SXS:BBH:0182, RIT:BBH:0119:n140, GT:0454
0.60
1.70
1.36
400
1/7
0.00
0.00
SXS:BBH:0298 RIT:BBH:Q10:n173, GT:0568
0.45
0.68
3.38
440
1/10
0.00
0.00
RIT:BBH:Q10:n173, GT:0568
0.30
0.31
7.51
500
2/3
0.00
0.00
RIT:BBH:0115:n140, GT:0477
0.70
2.39
0.96
600
1
0.00
0.00
SXS:BBH:0180, RIT:BBH:0198:n140, GT:0905
0.55
1.09
2.12
600
1/2
0.00
0.00
SXS:BBH:0169, RIT:BBH:0117:n140, GT:0446
0.50
0.99
2.32
800
1
0.00
0.00
SXS:BBH:0180, RIT:BBH:0198:n140, GT:0905
0.35
0.20
11.76
200
1
0.80
0.00
SXS:BBH:0230, RIT:BBH:0063:n100
2.75
40.34
0.06
400
1
0.80
0.00
SXS:BBH:0230, RIT:BBH:0063:n100
1.55
20.07
0.11
600
1
0.80
0.00
SXS:BBH:0230, RIT:BBH:0063:n100
0.95
6.46
0.36
800
1
0.80
0.00
SXS:BBH:0230, RIT:BBH:0063:n100
0.65
1.36
1.70
200
1
-0.80
0.00
SXS:BBH:0154,RIT:BBH:0068:n100
1.45
11.40
0.20
400
1
-0.80
0.00
SXS:BBH:0154,RIT:BBH:0068:n100
0.75
2.33
0.99
600
1
-0.80
0.00
SXS:BBH:0154,RIT:BBH:0068:n100
0.40
0.29
7.88
800
1
-0.80
0.00
SXS:BBH:0154,RIT:BBH:0068:n100
0.25
0.06
38.27
200
1
0.51
0.42
GT:0803
2.15
27.72
0.08
200
1/2
0.14
0.42
GT:0872
1.90
15.45
0.15
200
1/4
0.26
0.42
GT:0875
1.55
9.20
0.25
200
1/7
0.32
0.42
GT:0888
1.15
4.30
0.54
400
1
0.51
0.42
GT:0803
1.20
11.79
0.20
400
1/2
0.14
0.42
GT:0872
1.05
6.45
0.36
400
1/4
0.26
0.42
GT:0875
0.90
4.28
0.54
400
1/7
0.32
0.42
GT:0888
0.70
2.12
1.08
600
1
0.51
0.42
GT:0803
0.70
3.02
0.76
600
1/2
0.14
0.42
GT:0872
0.60
1.73
1.33
800
1
0.51
0.42
GT:0803
0.45
0.22
10.28
Table 3.
Summary of the source frame parameters, sensitive volume-time and merger rate density upper limit at 90% confidence. For the upper
limit, we assume no detection except for the non-spinning system with total mass
M
T
=
150 M
and
q
=
1
/
2
marked with
†
, for which we have
assumed one detection. The source spin parameters are defined at a starting frequency of 16 Hz.
Concerning the dependence on spins, for more positive (negative) values of the effective inspiral spin of a system, keeping the
source frame component masses fixed, the duration of the merger signal within the detector bandwidth increases (decreases) as
compared to a non-spinning counterpart. Hence the sensitivity improves (degrades) for systems with positive (negative) effective
total spin (Abbott et al. 2019; Tiwari et al. 2018). All precessing systems used in this analysis have positive
χ
e
ff
: hence, the combined
search can observe them to a greater distance compared to their non-spinning counterpart.
Figure 1 shows this trend visually. The panels show the sensitive volume-time for non-precessing and precessing simulated
sources, respectively. Each circle corresponds to one class of IMBH binaries in the source frame. The IMBH binaries with aligned
and anti-aligned BH spins,
χ
1
,
2
are labeled and shown as displaced circles. In general, we find an increase in the sensitive volume-
time of the combined search compared to results in Abbott et al. (2019). This increase is due to an overall increase in the analysis
time, detector sensitivity, and the contributing searches’ sensitivity.
Figure 2 shows the 90% upper limit on merger rate,
R
90%
, in
Gpc
−
3
yr
−
1
for the targeted 43 IMBH binary sources in the
m
1
-
m
2
plane. As before the left panel shows the result for non-precessing simulated sources whereas the right panel shows the same for
precessing simulated sources. We set our most stringent upper limit 0.06
Gpc
−
3
yr
−
1
for equal-mass IMBH binaries with total mass
200 M
and spin
χ
1
,
2
=
0
.
8
which is
∼
3
.
5
times more stringent than the previous study (Abbott et al. 2019).
5.3. Updated GW190521 merger rate estimate
We re-estimate the merger rate of a GW190521-like population. As in Abbott et al. (2017a, 2016c, 2020b,e), we consider a simulated
signal to be detected if it is recovered with an FAR less than
100 yr
−
1
. This corresponds to a combined p-value threshold of 0.009.
We considered the maximum observed time (
T
a
=
0
.
874
yr) across the three pipelines as the analysis time of the combined search.
The population is generated by drawing the intrinsic parameters from the posterior distribution inferred using the
NRSur7dq4
Article number, page 10 of 27