# An optimized PyCBC search for gravitational waves from intermediate-mass
black hole mergers

Koustav Chandra  Department of Physics, Indian Institute of Technology Bombay,
Powai, Mumbai 400 076, India<EMAIL_ADDRESS>V. Villa-Ortega
IGFAE, Campus Sur, Universidade de Santiago de Compostela, 15782 Spain  T.
Dent  IGFAE, Campus Sur, Universidade de Santiago de Compostela, 15782 Spain
C. McIsaac  University of Portsmouth, Portsmouth, PO1 3FX, United Kingdom
Archana Pai  Department of Physics, Indian Institute of Technology Bombay,
Powai, Mumbai 400 076, India  I. W. Harry  University of Portsmouth,
Portsmouth, PO1 3FX, United Kingdom  G. S. Cabourn Davies  University of
Portsmouth, Portsmouth, PO1 3FX, United Kingdom  K. Soni  Inter-University
Centre for Astronomy and Astrophysics, Pune 411007, India

###### Abstract

The detection of intermediate-mass black holes i.e. those with mass $\sim
100$–$10^{5}$$\mathrm{M}_{\odot}$, is an emerging goal of gravitational-wave
(GW) astronomy with wide implications for cosmology and tests of strong-field
gravity. Current PyCBC-based searches for compact binary mergers, which
matched filter the detector data against a set of template waveforms, have so
far detected or confirmed several GW events. However, the sensitivity of these
searches to signals arising from mergers of IMBH binaries is not optimal.
Here, we present a new optimised PyCBC-based search for such signals. Our
search benefits from using a targeted template bank, stricter signal-noise
discriminators and a lower matched-filter frequency cut-off. In particular,
for a population of simulated signals with isotropically distributed spins, we
improve the sensitive volume-time product over previous PyCBC-based searches,
at an inverse false alarm rate of 100 years, by a factor of 1.5 to 3 depending
on the total binary mass. We deploy this new search on Advanced LIGO-Virgo
data from the first half of the third observing run. The search does not
identify any new significant IMBH binaries but does confirm the detection of
the short-duration GW signal GW190521 with a false alarm rate of 1 in 727
years.

intermediate-mass black hole — gravitational waves

##  I Introduction

What started as a trickle back in September 2015 (Abbott  _et al._ , 2016a)
has turned into a veritable deluge (Abbott  _et al._ , 2019a, 2020a) of
gravitational-wave (GW) detections at the end of the first half of the third
observing run (O3a) of advanced GW detectors. As a result, the gravitational
wave catalogues (Abbott  _et al._ , 2019a; Nitz  _et al._ , 2019a, b;
Venumadhav  _et al._ , 2020, 2019; Abbott  _et al._ , 2020a; Nitz  _et al._ ,
2021a) now list more than $50$ compact binary coalescences (CBCs). This rapid
surge in GW events is largely due to the upgrades of the Advanced LIGO (Aasi
_et al._ , 2015) and Advanced Virgo (Acernese  _et al._ , 2015) instruments in
the interim between the observing runs. The search algorithms, namely cWB
(Klimenko and Mitselmakher, 2004; Klimenko  _et al._ , 2005, 2006, 2011,
2016), GstLAL (Messick  _et al._ , 2017; Sachdev  _et al._ , 2019; Hanna  _et
al._ , 2020), PyCBC (Usman  _et al._ , 2016; Nitz  _et al._ , 2017; Davies
_et al._ , 2020), MBTA (Adams  _et al._ , 2016; Aubin  _et al._ , 2021) and
SPIIR (Chu, 2017) also have improved significantly enabling them to better
separate gravitational signal from the detector noise. As a consequence, the
second gravitational wave transient catalogue (GWTC-2) not only reports the
detection of a plethora of stellar mass compact binaries (Abbott  _et al._ ,
2020b, a) but also details the detection of a couple of relatively asymmetric-
mass compact binaries (Abbott  _et al._ , 2020c, d), and a signal, GW190521,
from a putative intermediate-mass black hole (IMBH) binary (Abbott  _et al._ ,
2020e, f).

The signal GW190521 is quite different from other reported GW events. The pre-
merger phase of the signal was barely observable within the detectors’
bandwidth, allowing for its multivalent interpretation (Abbott  _et al._ ,
2020e, f; Bustillo  _et al._ , 2021a; Gayathri  _et al._ , 2020; Palmese and
Conselice, 2021; Liu and Bromm, 2020; Bustillo  _et al._ , 2021b; Nitz and
Capano, 2021). If we assume that the signal is from a quasi-circular black
hole binary, then the heavier component of the binary has a high probability
of populating the pair-instability mass gap, and the remnant, with mass $\sim
142$ $\mathrm{M}_{\odot}$, is the first conclusively observed intermediate-
mass black hole (Abbott  _et al._ , 2020e, f).

The event was first identified on 21 May 2019 at 03:02:29 UTC by the low
latency matched-filter search for compact binaries, PyCBC-LIVE (Nitz  _et al._
, 2018; Dal Canton  _et al._ , 2020), and the weakly modelled transient
search, cWB, in its IMBH configuration. The two searches reported the event
with an inverse false alarm rate (IFAR) of 8.34 years and 28.0 years,
respectively. The event was also reported by two other low-latency searches,
namely GstLAL and SPIIR, though with lower statistical significance.

Low latency searches are designed to generate rapid alerts to enable prompt
follow-up of gravitational-wave triggers for potential electromagnetic or
other counterpart signals. Hence, the statistical significance estimated by
low-latency pipelines is limited due to the available amount of empirically
generated background. Therefore, most search pipelines re-scrutinise the
strain data with improved calibration, data quality vetoes, and signal-noise
discriminators, which are generally unavailable during low-latency searches.
Further, offline searches estimate the background over a larger amount of
data, and can thus provide a better estimate of a candidate’s statistical
significance. In particular, when such an analysis was carried out at the time
around GW190521, the search pipelines reported a maximum IFAR of 4900 years
(Abbott  _et al._ , 2020e; Szczepanczyk  _et al._ , 2020).

However, contrary to other searches, the offline PyCBC-based search, PyCBC-
broad, identified the event with an IFAR of less than a year. This is
primarily due to the strong disagreement between the event and the best-
matching template used in the search (Abbott  _et al._ , 2020g). This search
also suffered from an inherent “look-elsewhere effect” (or trials factor), as
it tries to find signals over a broad parameter space covering compact binary
coalescences from binary neutron stars up to IMBH binaries. The other PyCBC-
based search, namely PyCBC-BBH, failed to detect the signal due to its focus
on stellar-mass black hole binary (BBH).

Figure 1: Posterior probability distribution of the source frame total mass
$M_{T}$ and redshift $z$ for the 37 confident BBH events announced in GWTC-2
[red]. The contours enclose 90% of the posterior probability, inferred under
the default parameter estimation priors used in the GWTC-2 publications
(Abbott  _et al._ , 2020a). For several high-mass mergers, the redshift
extends to $z\sim 1$: note that the template masses required to detect such
signals scale as $(1+z)M_{T}$.

The two gravitational-wave transient catalogues to date also show some
interesting trends concerning binary masses. In the first LIGO-Virgo
catalogue, GWTC-1 (Abbott  _et al._ , 2019a), a lack of systems with
$m_{1}\gtrsim 45\mathrm{M}_{\odot}$ is evident. However, more recently GWTC-2
lists several systems in this range, indicating additional structure in the
BBH population distribution as discussed in Abbott  _et al._ (2020h). In Fig.
1 we show the inferred source total masses $M_{T}$ and redshifts $z$ for 37
confidently detected BBHs announced in GWTC-2. The lack of low-mass events at
high $z$ is due to a selection effect as the amplitude of emitted GW scales
with mass. Already, several high-mass BBHs are detectable at $z\sim 1$: thus,
the template masses required to detect such systems are significantly larger
than the source masses due to redshifting of the GW signal (Krolak and Schutz,
1987). Thus, even for (relatively heavy) stellar-mass BBH ($\gtrsim
50\mathrm{M}_{\odot}$), an effective IMBH binary search is required.

We expect these trends to continue during upcoming runs when GW
interferometers achieve higher global network sensitivity to BBH mergers
(Abbott  _et al._ , 2020i). The improvement will facilitate the detection of
potentially hundreds of BBHs per year, reaching out to larger redshifts (Mehta
_et al._ , 2021). Also, within the turn of the next decade, we will have more
sensitive detectors such as Cosmic Explorer (Reitze  _et al._ , 2019) and the
Einstein Telescope (Maggiore  _et al._ , 2020; Sathyaprakash  _et al._ , 2012)
that will help detect more BBH mergers at even further distances, possibly up
to $z\sim 20$ and higher. The launch of the Laser Interferometer Space Antenna
(LISA) will potentially allow us to look even deeper and for more massive BBHs
(Amaro-Seoane  _et al._ , 2017). Such binaries may be heavier than those
observed so far (Safarzadeh and Farr, 2019) and so would produce remnants in
the lower ($10^{2}\,\mathrm{M}_{\odot}$–$10^{3}\,\mathrm{M}_{\odot}$) to mid
($10^{3}\,\mathrm{M}_{\odot}$–$10^{4}\,\mathrm{M}_{\odot}$) IMBH mass range
(Mangiagli  _et al._ , 2019). Detecting such systems in multiband GW window
(Sesana, 2016; Jani  _et al._ , 2019) will help us to estimate better the
population distribution of low and mid mass range IMBHs, which is currently
lacking. It will also enable us to understand better the formation mechanism
of IMBH systems and to perform more detailed tests of general relativity in
the strong-field regime (Abbott  _et al._ , 2020j). And as mentioned above, GW
signals from high redshift binaries will have higher detector frame masses, up
to an order of magnitude or larger than the source masses. So, regardless of
whether we detect any more IMBHs, we still need to extend the target space of
current CBC searches and tune them to prevent missing these potential signals.

We make such an attempt in this work. Here, we propose a new PyCBC-based
search which is optimised to detect both GW signals from IMBH binaries and
highly redshifted heavy stellar-mass BBH mergers. We construct a bank of non-
precessing waveforms simulating BBH mergers with component detector frame
masses $m_{1,2}(1+z)\geq 40\mathrm{M}_{\odot}$, total detector frame masses
$M_{T}(1+z)\in[100,600]\mathrm{M}_{\odot}$ and mass-ratios $q\in[1,10]$.
Because of our choices in the target search space, our search is susceptible
to a larger number of noise triggers, requiring us to impose stricter noise
vetoes and discriminators (Cabero  _et al._ , 2019; Davis  _et al._ , 2020).
We find that, while keeping the basic structure of the PyCBC search algorithm,
our modifications increase the search sensitivity, in terms of sensitive
volume-time, for a simulated population of binaries, by an average factor of
$\sim 2$ at an IFAR of 100 years, compared to the PyCBC-broad search used in
Abbott  _et al._ (2020e).

We organise our paper as follows. Sec. II serves as an overview of the multi-
detector PyCBC analysis. Optimisations and changes to this analysis are
presented in Sec. III. In Sec. IV, we describe how these modifications combine
to improve the sensitivity of the PyCBC analysis to IMBH mergers. Because of
the changes made, the search now recovers the heavier mass black hole binary
mergers from the third observing run with higher significance, and we have
summarised these findings in Sec. V. Finally, in Sec. VI we conclude the paper
by indicating the future optimisation prospects in the upcoming observing
runs.

##  II Review of Existing PyCBC detection methods for CBC systems

The strain that an incident GW signal produces in the interferometric detector
is a weighted linear combination of the gravitational wave polarisation
$h_{+}(t)$ and $h_{\times}(t)$:

$s(t)=F_{+}(\alpha,\delta,\psi)h_{+}(t;\vec{\zeta},\vec{\kappa})+F_{\times}(\alpha,\delta,\psi)h_{\times}(t;\vec{\zeta},\vec{\kappa})~{},$
(1)

where the weights $F_{+/\times}$ represent the detector beam pattern
functions. These functions depend on the source’s sky location
$(\alpha,\delta)$ with respect to the detector and on the polarisation angle
$\psi$. If the signal is from a quasi-circular binary, then $\vec{\zeta}$ in
the above equation describes the intrinsic parameters of the binary, which
comprises of the individual component masses $m_{i}$ and the dimensionless
spin $\vec{\chi}_{i}$ of the binary. $\vec{\kappa}$, on the other hand,
consists of the luminosity distance $D_{L}$ to the source, the inclination
angle $\iota$ of the binary with respect to the observer and the merger time
and phase $(t_{c},\varphi_{c})$ of the signal.

Current PyCBC-based GW searches primarily target signals coming from mergers
of binaries consisting of a pair of neutron stars, a pair of black holes, or a
neutron star-black hole pair. So, in the subsequent subsections, we briefly
review the steps involved in detecting these well-modelled CBC signals.

###  II.1 Pre-processing of detector data

The calibrated detector output is an evenly spaced time-series data containing
information about strain due to different sources. This makes it amenable to
standard techniques of time series analysis. The key foundation of prevalent
gravitational wave time-series analysis is a linear model of the data $d(t)$:
$d(t)=s(t)+g(t)+n_{G}(t)$, where $s(t)$ is the GW signal strain, $n_{G}(t)$ is
the strain due to random (Gaussian) detector noise and $g(t)$ is the strain
due to non-Gaussian terrestrial transients, a.k.a. ‘glitches’.

For most of the time, the data $d(t)$ is just $n_{G}(t)$ which is usually
assumed to be additive, wide-sense stationary coloured Gaussian noise. This
presupposition allows one to fully describe the noise’s statistical properties
in terms of its power spectral density (PSD), $S_{n}(f)$. PyCBC-based searches
estimate the PSD via Welch’s method and use it to whiten the detector data so
that any excess power due to the presence of either $s(t)$ or $g(t)$ is more
prominent.

However, the PSD estimate can be significantly affected during periods of poor
detector performance. Therefore, the PyCBC toolkit (Nitz  _et al._ , 2021b)
uses data quality information to zero out flagged times of badly contaminated
data before evaluating PSD. Further, to reduce the number of false alarms
caused due to high-amplitude glitches, the search algorithm internally
identifies times of large deviation from Gaussian noise in the whitened strain
data and window them out using a procedure known as auto-gating (Usman  _et
al._ , 2016). The PyCBC algorithm also vetoes out flagged times of additional
glitches that can generate loud triggers but do not contaminate the
surrounding data to affect the performance of the PSD estimation. This data
wrangling process ensures better search performance but cannot completely
purge the data from all glitches $g(t)$.

###  II.2 Matched-Filtering

Most current CBC searches assume that the incident GW signal can be adequately
represented by the dominant harmonic of a quasi-circular non-precessing
binary. The form of such a signal is well-modelled in the framework of general
relativity. So, after the pre-processing step, PyCBC-based searches use
matched-filtering (Sathyaprakash and Dhurandhar, 1991) to find whether or not
there is a GW signal buried in the detector data (Allen  _et al._ , 2012;
Babak  _et al._ , 2013; Usman  _et al._ , 2016). As the parameters of the
incident signal are not known a priori, CBC searches construct and search over
a discrete bank of templates spanning the search space.

The detector response due to the dominant harmonic of a non-precessing quasi-
circular binary can be written as:

$\tilde{h}(f;\vec{\theta})=\frac{F}{D_{L}}\tilde{h}_{22}(f;\vec{\zeta})e^{i\phi}$
(2)

provided stationary phase approximation holds (Sathyaprakash and Dhurandhar,
1991; Finn and Chernoff, 1993). Here, $\tilde{h}_{22}$ is the geocentric
waveform, parameterised completely by $\vec{\zeta}$, which forms the set of
filter waveforms used in the search. $F$, on the other hand, describes the
effective antenna pattern function:

$F=\sqrt{F_{+}^{2}\Bigg{(}\frac{1+\cos^{2}\iota}{2}\Bigg{)}+F_{\times}^{2}\cos^{2}\iota}$
(3)

while

$\phi=\arctan{\Bigg{(}\frac{2F_{\times}\cos\iota}{F_{+}\big{(}1+\cos^{2}{\iota\big{)}}}\Bigg{)}}+\varphi_{c}+2\pi
f\Delta t$ (4)

represents the effective merger phase, with $\Delta t$ denoting the arrival
time of the signal to the detector relative to a geocentric time reference.

The above presupposition also allow us to decompose the template strain,
$\tilde{h}_{22}$, into two orthonormal components, $\hat{h}_{c}$ and
$\hat{h}_{s}$, with an overall effective amplitude. These can be used to
define the log likelihood ratio, $\ln\mathcal{L}$, between the signal and
noise hypothesis given $g(t)=0$. It also allows one to maximise the log
likelihood ratio over the effective template phase and amplitude, giving
(Finn, 1992):

$\ln\mathcal{L}_{\textrm{max}}(t;\vec{\zeta})=\frac{1}{2}\rho^{2}(t;\vec{\zeta})\,.$
(5)

Here, $\rho(t)$ denotes the matched-filter signal-to-noise ratio (SNR):

$\rho(t;\vec{\zeta})=\sqrt{\langle d|\hat{h}_{s}\rangle^{2}+\langle
d|\hat{h}_{c}\rangle^{2}},$ (6)

which is evaluated for each template independently in each detector. $\langle
d|h\rangle$ defines the noise-weighted inner product between the pre-processed
data and the template and is given as:

$\langle
d|h\rangle(t)=4\mathbb{R}e\int_{f_{\textrm{low}}}^{f_{\textrm{high}}}\frac{\tilde{d}(f)^{\ast}\tilde{h}(f)}{S_{n}(f)}e^{2i\pi
ft}\,df\,.$ (7)

Here, $f_{\textrm{low}}$ and $f_{\textrm{high}}$ represents the lower and
upper frequency cut-off of the matched-filter operation. Typically,
$f_{\textrm{low}}$ is set to the frequency from which the filter waveform is
generated, while $f_{\textrm{high}}$ is set either as the final frequency cut-
off of the template or the Nyquist frequency of the detector data, whichever
is smaller. A peak in this SNR time-series will correspond to an astrophysical
trigger provided there is no glitch in the data. Since we do not know a priori
the parameters describing the gravitational-wave in the data, current CBC
searches carry out this matched filter operation over all the templates in the
bank. The template which best describes any signal present in the data gives
the largest peak in the SNR time-series: hereafter, we will call such a filter
waveform the best-matched template.

###  II.3 Single Detector Noise Discriminators

Matched-filtering would have given the optimal detection statistic provided
there were no glitches in the data (Wainstein and Zubakov, 1970).
Unfortunately, this is not the case. Pre-processing of the calibrated detector
data eliminates loud glitches, but the relatively softer glitches still
pollute the detector data and form the majority of the single-detector
triggers. To reduce the effect of these glitches on the search, the PyCBC
toolkit uses several noise discriminators at the single detector level.

Firstly, the PyCBC toolkit discards trigger below some pre-determined SNR
threshold and clusters triggers within a fixed window of time — keeping only
the triggers with the largest SNR. It also tries to suppress loud glitches
$g(t)$ by performing two different signal consistency tests:
$\chi_{\mathrm{r}}^{2}$ (Allen, 2005) and $\chi_{\mathrm{sg}}^{2}$ (Nitz,
2018). The $\chi_{\textrm{r}}^{2}$ test checks if the morphology of the
candidate trigger in frequency domain is consistent with that of the best-
matched template while the $\chi_{\textrm{sg}}^{2}$ test is designed to down-
rank triggers with excess power at frequencies exceeding those allowed by the
best-matched template. In the presence of Gaussian noise, both
$\chi_{\mathrm{r}}^{2}$ and $\chi_{\mathrm{sg}}^{2}$ follow a normalised
$\chi^{2}$ distribution. However, these statistics produce large values in the
presence of glitches or when the signal at hand is not well-modelled by the
best-matched template. PyCBC-based searches use these test results to re-weigh
the trigger SNR (Babak  _et al._ , 2013; Nitz, 2018). They first calculate the
“reweighted SNR” for the triggers via

$\tilde{\rho}=\begin{cases}\rho\Big{[}\frac{1}{2}\big{(}1+(\chi^{2}_{\textrm{r}})^{3}\big{)}\Big{]}^{-1/6}&\mathrm{for\,}\chi^{2}_{\textrm{r}}>1\\\
\rho&\mathrm{for\,}\chi^{2}_{\textrm{r}}\leq 1\end{cases}$ (8)

and then further re-weigh it by calculating

$\hat{\rho}=\begin{cases}\tilde{\rho}(\chi^{2}_{\textrm{sg}})^{-1/2}&\text{if}~{}\chi_{\textrm{sg}}^{2}>4,\\\
\tilde{\rho}&\text{otherwise.}\end{cases}$ (9)

The above two amendments to the standard trigger SNR help reduce the apparent
loudness of the glitches and hence increase the false alarm rate (FAR) of
quieter short duration glitches.

The detector data also contains broadband non-stationary detector noise, which
affects the detector’s sensitivity in the order of tens of seconds. To
alleviate the effects of this noise, the PyCBC algorithm re-scales
$\hat{\rho}$ with an estimate of the short-term variation in the PSD,
v${}_{s}(t)$, (Mozzon  _et al._ , 2020). When combined with $\hat{\rho}$, this
gives the single detector statistic of the trigger:

$\breve{\rho}=\hat{\rho}\textrm{v}_{s}(t)^{-0.5}\,.$ (10)

###  II.4 Multi-detector Coincident Candidates

After generating single-detector triggers from each detector, templated
searches perform a coincidence test to identify candidate events. This
involves checking whether triggers from the same template are observed across
multiple detectors with time-delays consistent with the light travel time
between detectors.

Under the assumption that the noise is independent between detectors, this
coincidence test helps us to further separate signal triggers from the noise
background. We perform this test for all possible two or three detector
combinations. To determine the significance of the surviving multi-detector
candidates, PyCBC searches assigns them a ranking statistic based on the
relative rate densities of signal and noise events (Nitz  _et al._ , 2017;
Davies  _et al._ , 2020):

$\Lambda_{s}=-\ln A_{\\{a\\}}-\sum_{a}\ln
r_{a,i}(\breve{\rho}_{a})+\ln\frac{p(\vec{\Omega}|S)}{p(\vec{\Omega}|N)}+3\ln\frac{\sigma_{\mathrm{min}}}{\sigma_{\mathrm{ref}}}\,.$
(11)

The first two terms on the RHS estimate the rate of coincident noise triggers
in a combination of detectors labelled by ${\\{a\\}}$, representing the
allowed time window $A$ for coincidences in these detectors and the noise rate
estimate $r$ in each detector and each template $i$ at single-detector
statistic values $\breve{\rho}_{a}$. The noise models
$r_{a,i}(\breve{\rho}_{a})$ are obtained by fitting (detector- and template-
dependent) exponential functions to the observed distributions of single-
detector triggers. The probability densities $p(\vec{\Omega}|S)$ and
$p(\vec{\Omega}|N)$ describe the distributions over extrinsic parameters
$\vec{\Omega}$ – the differences in times-of-arrival, phase and the relative
amplitude of the recovered triggers – expected under the signal or noise
hypothesis respectively. The last term provides an estimate of network
sensitive volume based on the least sensitive detector involved in this
coincident event, compared to a constant reference sensitivity across detector
combinations. This term then provides a natural weighting in favour of more
sensitive detector combinations. Therefore the ranking statistic exploits the
information encapsulated in the relative phases, amplitudes, arrival times to
the different detectors, noise model and expected distribution of signal SNR.

###  II.5 Estimation of statistical significance

The final step in GW searches is the determination of the statistical
significance of a coincident candidate. PyCBC-based searches do it empirically
by first generating background triggers using the method of time-shifts: shift
the data from one of the detectors with respect to other detector(s) by a
duration greater than the light travel time between them and look for
artificial coincidences (Usman  _et al._ , 2016; Davies  _et al._ , 2020).
This set of coincidences form the search background, and PyCBC-based searches
assign a FAR to an apparent event by comparing its ranking statistics with
those of the simulated background triggers. The method, by construction,
guarantees that the background candidates thus produced can not be entirely
due to an astrophysical signal. By repeating this procedure, searches can
generate noise background worth more than $10^{4}$ years with just a few days
of data. To minimise background contamination due to signal triggers, the
PyCBC toolkit removes triggers from the background within a certain time
window around events with large IFAR 111IFAR = 1/FAR.

However, there can be chance coincidences between a signal and a noise
trigger. This can significantly contaminate the search background, especially
when one of them is loud. The PyCBC toolkit, therefore, hierarchically removes
loud triggers to minimise the impact of aforementioned astrophysical
contamination while still estimating an unbiased IFAR (Abbott  _et al._ ,
2016b).

Currently, PyCBC-based searches analyse data from all possible two and three
detector combinations. So it is possible to obtain coincidences of the same
event in different detector combinations. The PyCBC pipelines therefore only
keep the event with the highest-ranking statistics across detector
combinations within a given time-shift window to prevent double-counting.
Further, while calculating an event’s overall statistical significance, PyCBC
searches add the FAR from all contributing detector combinations at the
ranking statistic of the event, thus accounting for the multiple possible
detector combinations.

##  III New Methods for observing intermediate-mass black hole binaries

At present, two PyCBC-based searches are looking for GW signals from compact
binary coalescence as recently presented in Nitz  _et al._ (2019a, b); Abbott
_et al._ (2020e, a). The first of the two covers a broad range of parameters
ranging from binary neutron stars to intermediate-mass black hole (IMBH)
binaries, using a hybrid geometric-stochastic template bank Roy  _et al._
(2019); we will refer to this search as “PyCBC-broad”. The other search,
namely PyCBC-BBH, employs a subset of the templates used in PyCBC-broad and
targets specifically binaries having redshifted component masses greater than
5 $\mathrm{M}_{\odot}$ and mass-ratio $q\in[1,3]$. Thus, both these analyses
are not precisely intended to identify IMBH binary mergers, and their
sensitivities to such signals are correspondingly penalised. Further, both the
searches use template banks that are devoid of filter waveforms with a
duration less than 150 ms measured from $\sim 20$ Hz, which further limits
their sensitivity towards shorter duration signals (Abbott  _et al._ , 2019b;
Calderón Bustillo  _et al._ , 2018; Chandra  _et al._ , 2020; Abbott  _et al._
, 2020e).

This section introduces a new PyCBC-based search that is specifically designed
to look for short duration signals arising from putative IMBH binaries. Owing
to its construction, the search is also sensitive to highly redshifted
stellar-mass BBH mergers.

###  III.1 Search Space and Template Bank

The black hole mergers we are mostly targeting form the lower mass range
($10^{2}-10^{3}$) of IMBH binaries. Signals emitted by these systems are
extremely short-lived ($\lesssim 1$s) within the current detector bandwidth,
making them difficult to detect. However, since they are a result of CBC
mergers, they should share morphological resemblances with other observed GW
signals. Hence like most templated searches, we assume that these signals are
adequately described by the dominant harmonic of a quasi-circular, non-
precessing binary. This allows us to design and use a template bank that is
entirely parameterised by $\vec{\zeta}$.

In what follows, we discuss the salient features of our proposed template bank
and how we construct it.

####  III.1.1 Bounds on mass-spin space

For this work, we construct a bank of filter waveforms imitating BBHs with
detector frame (redshifted) total mass, $M_{T}(1+z)$, between or close to
$100~{}\mathrm{M}_{\odot}$ and $600~{}\mathrm{M}_{\odot}$. We limit our
templates to a mass ratio between $1\leq q=m_{1}/m_{2}\leq 10$ provided the
secondary component has a mass greater than $40~{}\mathrm{M}_{\odot}$.
Binaries outside our mass-ratio range will emit signals with significant
higher harmonics making quadrupolar templates ill-equipped at detecting them
(Harry  _et al._ , 2018; Mills and Fairhurst, 2020).

Since we are ignorant about the spin distribution of the IMBH population, we
allow $\chi_{1}$ and $\chi_{2}$ of the templates to take on any values between
$\pm 0.998$. We don’t allow our templates to have misaligned spins 222Due to
spin-spin and spin-orbit coupling, misaligned spins cause orbital precession
(Apostolatos  _et al._ , 1994). as it will violate our underlying assumption
of the signal.

Our search domain motivates us to choose the reduced-order representation of
spinning effective one-body model, SEOBNRv4 (Taracchini  _et al._ , 2014; Bohé
_et al._ , 2017) as the template bank approximant. Because of the restriction
in the waveform model, we bound the dimensionless spin between the specified
range and not between theoretical bounds of $\pm 1$.

Figure 2: PSDs estimated using data from each of the contributing detectors
used in the first half of the third observing run. The data is now publicly
available at the GWOSC website (Vallisneri  _et al._ , 2015; Abbott  _et al._
, 2019c). We use the harmonic mean of these PSDs to model the detector noise
while constructing the bank.

####  III.1.2 Choice of lower frequency cut

When constructing the bank and calculating the matched-filter SNR, we use a
lower frequency cut-off of 15 Hz. We make this choice to balance out a couple
of practical considerations. The quadrupolar GW frequency at merger scales
inversely with the binary’s detector frame total mass (Maggiore, 2007).
Therefore, particularly for heavier CBCs, a lower starting frequency for
matched filtering equates to better search sensitivity. However, as
illustrated in Fig 2, the noise PSD of the current advanced detectors
increases steeply below 15 Hz, indicating that a lower starting frequency
would not effectively improve the search performance. Furthermore, we observe
that lower values of the cut-off frequencies resulted in significantly higher
matched-filter SNRs caused by short-duration glitches (Soni  _et al._ , 2021).
Current signal-noise discriminators, such as $\chi_{\textrm{r}}^{2}$ and
$\chi_{\textrm{sg}}^{2}$, often fail to distinguish these transients from
astrophysical population appreciably, especially when the best-matched
templates are comparatively short-lived. So, we restrict the matched-filter
calculation to the aforementioned lower frequency cut-off to limit the SNR of
these artefacts. We set the higher frequency cut-off to the maximum frequency
of the template both while creating the bank and calculating the matched-
filter SNR.

Figure 3: KDE plot showing the distribution of noise triggers [red] with
$\rho>6$ in O3a LIGO-Livingston data while using a template bank without
duration threshold. We also show in blue the template duration distribution.
The dashed dotted represents the position of the proposed 70ms with respect to
the distribution of the noise triggers. The template duration in the negative
zone is a KDE artefact.

####  III.1.3 Template duration cut

The above choices in mass and spin space make our search susceptible to a
variety of glitches since short-duration CBC templates are well-mimicked by
glitches. To demonstrate this, we perform a search over $\sim 32$ days of O3a
science data using a template bank covering the specified target space and
obeying the frequency constraints. As can be seen in Fig. 3 the proportion of
the noise triggers increases with a decrease in template duration. After
comparing search sensitivity for representative stretches of data using
different settings, we empirically excluded any templates having a duration of
less than 70 ms (measured from 15 Hz) in the detector bandwidth.

Figure 4: The distribution of templates in the redshifted total mass and
effective spin space. In red are the templates for the bank used in this work,
and in light blue, we represent the subset of templates with redshifted total
mass greater than $100\mathrm{M}_{\odot}$, as used in the PyCBC-broad search
of (Abbott  _et al._ , 2020a). The density of the PyCBC-broad templates in the
comparatively lower total mass region is larger due to a higher mass ratio cut
of 98 and lower minimum component mass requirements. Despite that, the PyCBC-
broad bank has a coarser coverage over shorter-duration templates because of
the duration-cut of 150 ms (measured from $\sim 20$ Hz). Note that the PyCBC-
broad template bank has no templates beyond $M_{T}(1+z)=500\mathrm{M}_{\odot}$
as opposed to PyCBC-IMBH bank.

####  III.1.4 Stochastic template bank approach

Having selected the bounds of our template bank, we now seek to create the
bank efficiently. Generally, a template bank can be constructed in two ways —
geometrically (Owen, 1996; Owen and Sathyaprakash, 1999; Babak  _et al._ ,
2006; Cokelaer, 2007; Brown  _et al._ , 2012; Harry  _et al._ , 2014; Dal
Canton  _et al._ , 2014) or stochastically (Harry  _et al._ , 2008; Babak,
2008; Harry  _et al._ , 2009; Manca and Vallisneri, 2010), where a hybrid of
both methods may be applied to cover a large parameter space Roy  _et al._
(2017). The geometrical approach uses a quasi-regular lattice and is
particularly successful when applied to low-mass systems, for which the merger
and ringdown occur outside of the detector bandwidth. Since the post-inspiral
phase of the waveform is crucial for our target space, we use the stochastic
template placement scheme with a minimal match criterion of 0.99.

The basic idea of the stochastic template scheme is the following. We begin by
randomly selecting a potential template waveforms, $h_{T}$ for our bank
$\mathfrak{B}$. Initially, $\mathfrak{B}$ is empty, so we add $h_{T}$ directly
to it. If however there are any templates in the bank, we evaluate the match,
$\mathcal{M}(h_{T},h_{i})=\max_{\Delta\varphi_{c},\Delta
t_{c}}\langle\hat{h}_{T}|\hat{h}_{i}\rangle$, between the proposed template
and all templates $h_{i}\in\mathfrak{B}$. Or in other words, we evaluate the
effectualness or the fitting factor (FF) (Apostolatos, 1995) of
$\mathfrak{B}$:

$\text{FF}=\max_{h_{i}\in\mathfrak{B}}~{}\mathcal{M}(h_{T},h_{i})~{}~{}.$ (12)

If the FF of the new template is below the minimal match of 0.99, then the
bank $\mathfrak{B}$ is deemed ineffectual, and we add the new template $h_{T}$
to $\mathfrak{B}$. This generates a new seed bank
$\mathfrak{B}^{\prime}=\mathfrak{B}+h_{T}$ for the next iteration, and we
repeat this process until the rate of rejection of proposed templates reaches
a set limit.

Figure 5: Top: The effective fitting factor of 100 simulated signals as a
function of total-mass and effective-spin. Note that even though some
simulated points lie outside the bank limits, owing to the duration threshold,
they still have good $\textrm{FF}_{\textrm{eff}}$. Bottom: Plot showing the
fitting factor of 15,600 simulated non-precessing signals lying within the
target search space.

The seemingly high choice of minimal match value ensures an adequate number of
templates in the high-mass region of our search space where the signals lack
pre-merger power. Fig. 4 compares the proposed bank used in this work with
that of the one used by the PyCBC-broad in Abbott  _et al._ (2020e, a) in
terms of total mass and effective inspiral spin (Ajith  _et al._ , 2011;
Santamaria  _et al._ , 2010) 333The effective inspiral spin
$\chi_{\textrm{eff}}=\frac{m_{1}\chi_{1}+m_{2}\chi_{2}}{m_{1}+m_{2}}$ ranges
between $\pm 1$ and gives a measure of the alignedness of the out-of-plane
component spin with the direction of orbital angular momentum..

Before performing the search, as a final check, we evaluate the template
bank’s performance in terms of effective fitting factor (Buonanno  _et al._ ,
2003):

$\textrm{FF}_{\textrm{eff}}=\sqrt[3]{\frac{\sum_{i}\textrm{FF}(h_{i})\rho_{\textrm{opt}}^{3}(h_{i})}{\sum_{i}\rho_{\textrm{opt}}^{3}(h_{i})}},$
(13)

for a hundred different non-precessing simulated signals containing only the
dominant harmonic and lying within the search target space. Here,
$\rho_{\textrm{opt}}(h_{i})=\sqrt{\langle h_{i}|h_{i}\rangle}$ defines the SNR
recovered if the template is an exact replica of the incident signal. As can
be seen in Fig 5, the $\textrm{FF}_{\textrm{eff}}\gtrsim 0.99$ for all the
points. Additionally, we also calculate the recovered fitting factor of
approximately 15,600 non-precessing simulated quadrupolar harmonic signals
lying within our target space. The edge in the bottom panel plot is owing to
the duration threshold of 70 ms. Here too, we observe that all of the
injections have $\mathrm{FF}\geq 0.975$ signifying that the bank, summarised
in Table 1, meets the design expectations.

Parameter |
---|---
$M_{T}(1+z)$ | $(100\mathrm{M}_{\odot},~{}600\mathrm{M}_{\odot})$
$q=m_{1}/m_{2}$ | $(1,~{}10)$
$m_{i}$ | $(40\mathrm{M}_{\odot},~{}540\mathrm{M}_{\odot})$
$\chi_{\textrm{i,z}}$ | $(-0.998,~{}0.998)$
$f_{\textrm{low}}$ |  $15$ Hz
Minimum Match | 0.99
Minimum Template Duration | 70 ms
Waveform Model | SEOBNRv4_ROM
Number of templates | 630
Table 1: Summary of the Template Bank used for the search.

We note that applying the duration cut leads to only $\sim 1\%$ fewer
templates in the bank but improves the search sensitivity. We demonstrate this
in Sec. IV when discussing sensitivity computation. Also, as most of the power
in the waveforms comes from the merger-ringdown portion of the template, the
designed search is sensitive to a wide variety of short-duration signals
arising from mergers producing IMBHs (Bustillo  _et al._ , 2021a).

###  III.2 Improved Rejection of Instrumental Transients

As discussed in Sec. II, an important part of search algorithms for detecting
GW signals is reducing the number of false alarms caused due to glitches.

Figure 6: Top: Distribution of SNR and $\chi_{r}^{2}$ of single detector
triggers from the representative portion of LIGO-Livingston data from the
third observing run. Bottom: Distribution of SNR and short-term variation in
the PSD, v${}_{s}(t)$ from the representative portion of same LIGO-Livingston
data from the third observing run. In both the panels, the black dots
represent the background triggers which are coincidentally observed in
Livingston and Virgo data while the other coloured markers correspond to the
recovered injections. The dashed lines in the top panel are contours of
$\tilde{\rho}=5,7,9,11,13$ respectively.

Our search uses a lower duration threshold and starts matched-filtering from a
comparatively lower low-frequency cut-off. This makes it susceptible to more
glitches, as illustrated in Fig 3. There is also an absence of data quality
flags for Virgo data segments which seriously hampers the search performance,
especially since the search relies on data quality information. Hence, while
pre-processing the data, we choose to use an auto-gating threshold of
$50\sigma$ from Gaussian Noise to gate out loud $g(t)$. The threshold used is
half of that used in Nitz  _et al._ (2019a, b). We note that this can also
excise out signals of similar loudness but observed GW signals from recent BBH
mergers have so far not caused such large deviation from whitened detector
data.

Figure 7: Histogram of triggers close to auto-gated glitches in the Livingston
detector. Triggers are removed around the central time within a window of $\pm
0.5$ s around an auto-gate, but we see here that there is a significantly
increased trigger rate around auto gates which is not removed.

Even then, while performing the single detector analysis with our proposed
bank, we find many loud background triggers that our signal-noise
discriminator does not efficiently differentiate. As illustrated in the top
panel of Fig. 6, these triggers have a large $\tilde{\rho}$ even when having
relatively higher $\chi_{\textrm{r}}^{2}$ and hence are not efficiently
suppressed. Further, some background triggers also have large v${}_{s}(t)$
signifying that they are within data segments affected by non-stationary
broadband noise. So, we choose to discard any trigger whose $\chi_{r}^{2}$ or
v${}_{s}(t)$ are greater than 10. The choice is motivated by the clear
separation in the distribution of background triggers and the injection
population. We use the SEOBNRv4 waveform model to generate the quadrupolar
quasi-circular non-precessing injections, and we denote them in red. In blue,
we have the non-precessing injections containing the full symphony of a signal
and they are generated using the reduced-order representation of the
SEOBNRv4HM waveform model (Cotesta  _et al._ , 2018, 2020). We generate the
remaining orange marked injections with the NRSur7dq4 (Varma  _et al._ , 2019)
waveform model. They contain both the quadrupolar as well as higher-order
harmonics of a precessing binary. We provide additional details of these
injections in Sec. IV.

As can be seen, the above constraint rejects approximately $\sim 3\%$ of the
total injections used. But most of these injections have large single-detector
SNR($\gtrsim 30$). Such large SNR signals are difficult to observe given the
current detector sensitivity and the target source population.

In addition to these veto choices, we also remove triggers from a wider window
around auto-gated times of loud non-Gaussianity. During preliminary analysis
of O3a data, we noticed several instances where the loud glitch prompting the
auto-gate was correlated with nearby, lower frequency glitches that had
relatively high SNRs in IMBH templates. We can see the effect of this
correlation in the histogram of Fig 7, which shows an elevated relative rate
of triggers with high $\breve{\rho}$ in short-duration templates within a few
seconds of auto-gated glitches. This effect is mainly visible in both LIGO
detectors’ data, increasing up to two orders of magnitude, being much subtler
for Virgo data. As a preliminary approach to this issue, we veto all triggers
between 1 second before and 2.5 seconds after the central auto-gating times of
Advanced LIGO data. The tuning limits were chosen empirically and are subject
to future improvements. As a result of this refinement, we see additional
suppression of high-statistic background events that leads to an increase in
sensitive-volume-time, implying that a GW signal belonging to the target space
will be detected with an improved significance. We provide details of this
study in the next section.

Figure 8: Plot showing the sensitive volume-time, VT, that the search is
sensitive to before [dashed] and after [solid] the duration threshold on
filter waveforms. We assess the improvement using a representative population
of GWs from a simulated generically spinning BHs in a binary system injected
in $\sim 30$ days of O3a data. Figure 9: Plot showing the sensitive-VT before
[dashed] and after [solid] the removal of additional triggers around auto-
gated times.

##  IV Evaluating the Improved Search Technique

(a) Plot showing the ratio of sensitive-VT, between PyCBC-IMBH and PyCBC-broad
search.

(b) Plot showing the ratio of sensitive-VT, between PyCBC-IMBH and PyCBC-BBH
search.

Figure 10: Plots showing the improvement in sensitivity at different total
mass range at different IFAR. Both the plots show a significant increment in
VT, particularly for signals from relatively heavier binaries.

To motivate the various choices made and to quantify the benefit of our
restricted analysis as compared to previous PyCBC-based analysis, we resort to
an injection campaign: add simulated signals to real or simulated GW data as
part of the analysis pipeline without any physical actuation and then estimate
the sensitivity of the pipeline to the signals added. For our purpose, we
inject the simulated signals in $\sim 30$ days of O3a data, and we use the
sensitive volume-time product, VT, and the sensitive distance as the metrics
of the search sensitivity. We estimate these sensitivity metrics using a Monte
Carlo method with importance sampling (See Sec. 4 of Usman  _et al._ (2016)).

As mentioned in Sec. III.2, we use SEOBNRv4, SEOBNRv4HM and NRSur7dq4 as the
waveform model for our signals. The simulated binaries have $M_{T}(1+z)$ in
the range $[100,600]\mathrm{M}_{\odot}$ and $q$ between $[1,10]$ except when
using precessing injections during which we restrict to $q\leq 4$ binaries
owing to waveform constraints. The binary spins are isotropically distributed
in spin directions as allowed by respective waveform models, and we uniformly
distribute the simulated signals in $M_{T}(1+z)$ and $m_{1}/(m_{1}+m_{2})$
space. We also place them uniformly in distances between bounds of 0.5 Gpc and
11 Gpc and distribute them isotropically all over the sky and binary
orientation parameters.

Fig 8 compares the sensitivity between searches with and without the duration
threshold of filter waveforms discussed in Sec. III.1. As can be seen, the
search using the duration threshold of $70$ ms performs better than the search
not using it and the improvement in sensitive-VT ranges between a factor of
1.1 to 1.3 at an IFAR of 100 years depending on the total mass of the
injection.

The search also benefits from the improved gating setting discussed in Sec.
III.2. Due to this, we see that the search performance improves significantly,
especially for comparatively heavier BBHs (See Fig. 9).

Combined, all the proposed optimisations significantly improves the search
performance as compared to the already-existing PyCBC-broad search. We
illustrate this in Fig. 10(a) where one can see a clear increment in sensitive
VT between a factor of $1.50\pm 0.31$ and $2.77\pm 0.75$ at an IFAR of 100
years depending on the total mass of the system, demonstrating the algorithm’s
ability to distinguish high-mass signals from noisy transients.

Finally, we also compare the sensitivity of the PyCBC-IMBH search with that of
the PyCBC-BBH search used in Abbott  _et al._ (2020a) in Fig 10(b) for our set
of injections. We find that the sensitive VT at an IFAR of 100 years varies
between a factor of $1.12\pm 0.07$ for systems with a total mass between
$[100,200]\mathrm{M}_{\odot}$ to $12.61\pm 3.52$ for
$[450,600]\mathrm{M}_{\odot}$ systems, clearly demonstrating the improvement
due to detection optimisation for the IMBH binaries. For signals with
$M_{T}(1+z)>450\mathrm{M}_{\odot}$, the match between the template and signal
is quite poor in the PyCBC-BBH search resulting in high $\chi_{r}^{2}$ values,
which lead to the majority of even high-SNR signals being entirely missed.

Event Name | GPS Time (s) | $\textrm{IFAR}(\textrm{yr)}$ | $\Lambda_{s}$ | $\rho_{H}$ | $\rho_{L}$ | $\rho_{V}$ |  $m_{1}$ ($\mathrm{M}_{\odot}$) |  $m_{2}$ ($\mathrm{M}_{\odot}$) | $\chi_{\mathrm{eff}}{}$
---|---|---|---|---|---|---|---|---|---
GW$190521\\_074359$ | 1242459857.5 |  $>$ 43070.23 | 72.55 | 12.00 | 21.14 | - | 60.74 | 40.32 | 0.12
GW$190828\\_063405$ | 1251009263.8 |  $>$ 14260.16 | 47.92 | 10.04 | 11.20 | - | 60.38 | 40.36 | 0.63
GW$190519\\_153544$ | 1242315362.4 |  $>$ 9103.08 | 44.02 | 8.37 | 10.51 | - | 100.2 | 62.82 | 0.72
GW$190706\\_222641$ | 1246487219.3 |  $>$ 8873.62 | 34.81 | 8.73 | 8.36 | - | 149.40 | 44.49 | 0.81
GW$190727\\_060333$ | 1248242632.0 |  $>$ 8105.10 | 31.58 | 8.37 | 8.11 | - | 60.32 | 40.27 | 0.14
GW$190701\\_203306$ | 1246048404.6 |  $>$ 5191.03 | 28.64 | 6.01 | 8.76 | 5.85 | 67.68 | 47.02 | -0.48
GW$190915\\_235702$ | 1252627040.7 | 2612.10 | 27.87 | 8.41 | 7.50 | - | 73.87 | 49.39 | 0.75
GW$190517\\_055101$ | 1242107479.8 | 1153.60 | 26.45 | 6.62 | 7.42 | - | 58.43 | 48.41 | 0.99
GW$190602\\_175927$ | 1243533585.1 | 915.02 | 26.09 | 6.32 | 10.58 | - | 132.67 | 52.10 | 0.47
GW$190521$ | 1242442967.5 | 726.65 | 25.78 | 8.27 | 11.54 | - | 195.46 | 43.06 | 0.50
GW$190503\\_185404$ | 1240944862.3 | 397.78 | 27.31 | 9.00 | 7.66 | - | 60.32 | 40.27 | 0.15
GW$190421\\_213856$ | 1239917954.3 | 163.39 | 22.66 | 7.88 | 6.25 | - | 58.41 | 53.35 | 0.05
GW$190408\\_181802$ | 1238782700.3 | 62.66 | 24.01 | 6.70 | 8.09 | - | 82.52 | 40.07 | 0.98
GW$190513\\_205428$ | 1241816086.8 | 19.97 | 20.94 | 8.83 | 7.20 | - | 55.39 | 46.03 | 0.76
GW$190413\\_134308$ | 1239198206.7 | 7.10 | 20.32 | 5.46 | 7.50 | - | 79.54 | 56.15 | 0.04
GW$190803\\_022701$ | 1248834439.9 | 5.86 | 19.69 | 5.68 | 6.57 | - | 57.33 | 42.78 | -0.08
GW$190929\\_012149$ | 1253755327.5 | 3.02 | 19.01 | 6.04 | 6.79 | - | 123.03 | 40.67 | 0.15
GW$190413\\_052954$ | 1239168612.5 | 1.79 | 18.24 | 5.14 | 6.65 | - | 71.14 | 43.83 | 0.23
GW$190731\\_140936$ | 1248617394.6 | 1.56 | 17.09 | 5.61 | 6.00 | - | 58.41 | 53.35 | 0.05
Table 2:  Candidate events from the PyCBC-IMBH search for compact binary
mergers in O3a data. Candidates are sorted by IFAR evaluated for the entire
bank of templates. Finite background statistics limits the IFAR estimated for
the top six events, and hence we state their lower limits. We list the
parameters of the template associated with each candidate. The masses are
given in the detector frame while the SNR corresponds to the matched-filter
SNR defined in Eq. (6). Note that the listed parameters are not intended as a
rigorous estimation of the source parameters, and the reader should refer to
Abbott  _et al._ (2020a) for the same.

##  V Results

Using this optimised analysis, we perform a search on the O3a data collected
during the observation period between 1 April 2019 15:00 UTC and 1 October
2019 15:00 UTC. Table 2 summarises the search results and tabulates them in
the descending order of significance in terms of IFAR. We analysed the data
separately after sub-dividing them into five independent blocks of duration
$\sim 30$ days. The bulk of the events listed are known BBHs from below the
mass range of the template bank, meaning they have been found with reduced
significance in templates with around 100 $\mathrm{M}_{\odot}$. We only state
the lower limits in IFAR of the top six events due to finite background
statistics. Apart from the IFAR and event id, we also report the GPS time,
$\Lambda_{s}$, the parameters of the best-matched templates and the value of
matched-filter SNR of the signal in the corresponding detector. Among all the
signals reported, only GW$190701\\_203306$ is observed as a three-detector
event by this dedicated search.

###  V.1 Re-detection of GW190521

GW190521 was first reported in Abbott  _et al._ (2020e) where the dedicated
cWB-IMBH search recorded the event with IFAR 4900 years. However, the offline
PyCBC-broad and PyCBC-BBH search failed to detect this signal with enough
statistical significance, as mentioned before. Our optimised PyCBC-IMBH search
recovers the signal with a network SNR of 14.1 and IFAR 727 years which is
significantly larger than those reported in Abbott  _et al._ (2020e) for a
PyCBC-based search. This change is due to a culmination of all the
modifications that we have made for our analysis. However, the improvement in
IFAR is not a statistical statement about the search as a whole. The reader
should refer to Sec. IV for the same.

##  VI Conclusion

We construct and validate a new optimised PyCBC-based search that is capable
of detecting both highly redshifted BBH mergers and mergers producing low mass
range IMBH remnants. We test the analysis against previous PyCBC-based
searches using a set of generically spinning simulated BBHs which we inject at
different times in the GW data collected during the O3a run. We find that our
analysis can now better separate short-duration GW signals from instrumental
artefacts because of targeted usage of filter waveforms, optimisation of data
quality vetoes and stricter signal-noise discriminators. As a result, the
search sensitivity at an IFAR of 100 years, in terms of sensitive-VT improves
by a factor of $1.50\pm 0.31$ to $2.77\pm 0.75$ as compared to previous PyCBC-
based searches, with the largest increase seen for binaries with total masses
between $[450-600]\mathrm{M}_{\odot}$. We also report all the signals with an
IFAR$>1.5$ years in our search. However, none of these signals are new, and
they have already been reported in (Abbott  _et al._ , 2020a).

The main limitation of this new search is that it currently relies on
waveforms that model the dominant harmonic of a quasi-circular non-precessing
binary. A near-term development goal is to make the search capable of
detecting CBC signals with significant higher harmonic content and develop
newer signal-noise discriminators that can better separate a glitch from a
short-duration signal. These improvements will enable the search to detect
heavier, asymmetric binaries.

Also, advanced GW detectors are expected to observe thousands of BBH mergers
in the next few years, and the detection rates will go up by several orders of
magnitude with the advent of third-generation observatories like the Einstein
Telescope (Maggiore  _et al._ , 2020; Sathyaprakash  _et al._ , 2012) and
Cosmic Explorer (Reitze  _et al._ , 2019) and space-based observatories like
LISA (Sesana, 2016). Their functioning will enable us to detect GW signals
from even further BBH mergers whose detector frame masses can be several
orders of magnitude larger than their source mass. Some of these signals may
be due to mergers of IMBHs lying above the pair-instability mass-gap
(Mangiagli  _et al._ , 2019; Ezquiaga and Holz, 2021; Tanikawa  _et al._ ,
2021; Mehta  _et al._ , 2021), and detection of such signals will enable us to
understand the origins of these binaries better. Also, the detection of mass-
gap remnants or components will provide us with a better understanding of the
rate at which they are formed. Hence, there is a continuous need to expand the
target search space depending on the detector sensitivity to not miss out on
potential sources.

##  VII Acknowledgements

The authors would like to thank Shasvath Kapadia, Khun Sang Phukon, Tito Dal
Canton and Juan Calderon Bustillo for their detailed comments and useful
suggestions. The authors are grateful for the computational resources and data
provided by the LIGO Laboratory and supported by National Science Foundation
Grants No. PHY-0757058 and No. PHY-0823459. The open data is available in the
Gravitational Wave Open Science Center (https://www.gw-openscience.org/ ) a
service of LIGO Laboratory, the LIGO Scientific Collaboration and the Virgo
Collaboration. The authors also acknowledge the use of the IUCAA LDG cluster,
Sarathi, for computational/numerical work. We acknowledge the usage KC
acknowledges the MHRD, Government of India, for the fellowship support. VVO
and TD acknowledge financial support from Xunta de Galicia (Centro singular de
investigación de Galicia accreditation 2019-2022), by European Union ERDF, and
by the “María de Maeztu” Units of Excellence program MDM-2016-0692 and the
Spanish Research State Agency. AP’s research is supported by SERB-Power-
fellowship grant SPF/2021/000036, DST, India. GSCD and IWH acknowledge the
STFC for funding through grant ST/T000333/1. CM was supported by the STFC
through the DISCnet Centre for Doctoral Training. KS acknowledges the Inter-
University Centre of Astronomy and Astrophysics (IUCAA), India, for the
fellowship support. This document has LIGO DCC No LIGO-P2100177.

We want to thank all of the essential workers who put their health at risk
during this ongoing COVID-19 pandemic. Without their support, we would not
have completed this work. We offer condolences to people who have lost their
family members during this pandemic.

## References

  * Abbott  _et al._ (2016a) B. Abbott _et al._ (LIGO Scientific, Virgo), Phys. Rev. Lett. 116, 061102 (2016a), arXiv:1602.03837 [gr-qc] .
  * Abbott  _et al._ (2019a) B. Abbott _et al._ (LIGO Scientific, Virgo), Phys. Rev. X 9, 031040 (2019a), arXiv:1811.12907 [astro-ph.HE] .
  * Abbott  _et al._ (2020a) R. Abbott _et al._ , arXiv e-prints (2020a), arXiv:2010.14527 [gr-qc] .
  * Nitz  _et al._ (2019a) A. H. Nitz, C. Capano, A. B. Nielsen, S. Reyes, R. White, D. A. Brown, and B. Krishnan, Astrophys. J. 872, 195 (2019a), arXiv:1811.01921 [gr-qc] .
  * Nitz  _et al._ (2019b) A. H. Nitz, T. Dent, G. S. Davies, S. Kumar, C. D. Capano, I. Harry, S. Mozzon, L. Nuttall, A. Lundgren, and M. Tápai, Astrophys. J. 891, 123 (2019b), arXiv:1910.05331 [astro-ph.HE] .
  * Venumadhav  _et al._ (2020) T. Venumadhav, B. Zackay, J. Roulet, L. Dai, and M. Zaldarriaga, Phys. Rev. D 101, 083030 (2020), arXiv:1904.07214 [astro-ph.HE] .
  * Venumadhav  _et al._ (2019) T. Venumadhav, B. Zackay, J. Roulet, L. Dai, and M. Zaldarriaga, Phys. Rev. D 100, 023011 (2019), arXiv:1902.10341 [astro-ph.IM] .
  * Nitz  _et al._ (2021a) A. H. Nitz, C. D. Capano, S. Kumar, Y.-F. Wang, S. Kastha, M. Schäfer, R. Dhurkunde, and M. Cabero, (2021a), arXiv:2105.09151 [astro-ph.HE] .
  * Aasi  _et al._ (2015) J. Aasi _et al._ (LIGO Scientific), Class. Quant. Grav. 32, 074001 (2015), arXiv:1411.4547 [gr-qc] .
  * Acernese  _et al._ (2015) F. Acernese _et al._ (Virgo), Class. Quant. Grav. 32, 024001 (2015), arXiv:1408.3978 [gr-qc] .
  * Klimenko and Mitselmakher (2004) S. Klimenko and G. Mitselmakher, Class. Quant. Grav. 21, S1819 (2004).
  * Klimenko  _et al._ (2005) S. Klimenko, S. Mohanty, M. Rakhmanov, and G. Mitselmakher, Phys. Rev. D 72, 122002 (2005), arXiv:gr-qc/0508068 .
  * Klimenko  _et al._ (2006) S. Klimenko, S. Mohanty, M. Rakhmanov, and G. Mitselmakher, J. Phys. Conf. Ser. 32, 12 (2006).
  * Klimenko  _et al._ (2011) S. Klimenko, G. Vedovato, M. Drago, G. Mazzolo, G. Mitselmakher, C. Pankow, G. Prodi, V. Re, F. Salemi, and I. Yakushin, Phys. Rev. D 83, 102001 (2011), arXiv:1101.5408 [astro-ph.IM] .
  * Klimenko  _et al._ (2016) S. Klimenko _et al._ , Phys. Rev. D 93, 042004 (2016), arXiv:1511.05999 [gr-qc] .
  * Messick  _et al._ (2017) C. Messick _et al._ , Phys. Rev. D 95, 042001 (2017), arXiv:1604.04324 [astro-ph.IM] .
  * Sachdev  _et al._ (2019) S. Sachdev _et al._ , arXiv e-prints (2019), arXiv:1901.08580 [gr-qc] .
  * Hanna  _et al._ (2020) C. Hanna _et al._ , Phys. Rev. D 101, 022003 (2020), arXiv:1901.02227 [gr-qc] .
  * Usman  _et al._ (2016) S. A. Usman _et al._ , Class. Quant. Grav. 33, 215004 (2016), arXiv:1508.02357 [gr-qc] .
  * Nitz  _et al._ (2017) A. H. Nitz, T. Dent, T. Dal Canton, S. Fairhurst, and D. A. Brown, Astrophys. J. 849, 118 (2017), arXiv:1705.01513 [gr-qc] .
  * Davies  _et al._ (2020) G. S. Davies, T. Dent, M. Tápai, I. Harry, C. McIsaac, and A. H. Nitz, Phys. Rev. D 102, 022004 (2020), arXiv:2002.08291 [astro-ph.HE] .
  * Adams  _et al._ (2016) T. Adams, D. Buskulic, V. Germain, G. Guidi, F. Marion, M. Montani, B. Mours, F. Piergiovanni, and G. Wang, Class. Quant. Grav. 33, 175012 (2016), arXiv:1512.02864 [gr-qc] .
  * Aubin  _et al._ (2021) F. Aubin _et al._ , Class. Quant. Grav. 38, 095004 (2021), arXiv:2012.11512 [gr-qc] .
  * Chu (2017) Q. Chu,  _Low-latency detection and localization of gravitational waves from compact binary coalescences_ , Ph.D. thesis, The University of Western Australia (2017).
  * Abbott  _et al._ (2020b) B. Abbott _et al._ (LIGO Scientific, Virgo), Astrophys. J. Lett. 892, L3 (2020b), arXiv:2001.01761 [astro-ph.HE] .
  * Abbott  _et al._ (2020c) R. Abbott _et al._ (LIGO Scientific, Virgo), Phys. Rev. D 102, 043015 (2020c), arXiv:2004.08342 [astro-ph.HE] .
  * Abbott  _et al._ (2020d) R. Abbott _et al._ (LIGO Scientific, Virgo), Astrophys. J. Lett. 896, L44 (2020d), arXiv:2006.12611 [astro-ph.HE] .
  * Abbott  _et al._ (2020e) R. Abbott _et al._ (LIGO Scientific, Virgo), Phys. Rev. Lett. 125, 101102 (2020e), arXiv:2009.01075 [gr-qc] .
  * Abbott  _et al._ (2020f) R. Abbott _et al._ (LIGO Scientific, Virgo), Astrophys. J. Lett. 900, L13 (2020f), arXiv:2009.01190 [astro-ph.HE] .
  * Bustillo  _et al._ (2021a) J. C. Bustillo, N. Sanchis-Gual, A. Torres-Forné, and J. A. Font, Phys. Rev. Lett. 126, 201101 (2021a), arXiv:2009.01066 [gr-qc] .
  * Gayathri  _et al._ (2020) V. Gayathri, J. Healy, J. Lange, B. O’Brien, M. Szczepanczyk, I. Bartos, M. Campanelli, S. Klimenko, C. Lousto, and R. O’Shaughnessy, (2020), arXiv:2009.05461 [astro-ph.HE] .
  * Palmese and Conselice (2021) A. Palmese and C. J. Conselice, Phys. Rev. Lett. 126, 181103 (2021), arXiv:2009.10688 [astro-ph.GA] .
  * Liu and Bromm (2020) B. Liu and V. Bromm, Astrophys. J. Lett. 903, L40 (2020), arXiv:2009.11447 [astro-ph.GA] .
  * Bustillo  _et al._ (2021b) J. C. Bustillo, N. Sanchis-Gual, A. Torres-Forné, J. A. Font, A. Vajpeyi, R. Smith, C. Herdeiro, E. Radu, and S. H. W. Leong, Phys. Rev. Lett. 126, 081101 (2021b), arXiv:2009.05376 [gr-qc] .
  * Nitz and Capano (2021) A. H. Nitz and C. D. Capano, Astrophys. J. Lett. 907, L9 (2021), arXiv:2010.12558 [astro-ph.HE] .
  * Nitz  _et al._ (2018) A. H. Nitz, T. Dal Canton, D. Davis, and S. Reyes, Phys. Rev. D 98, 024050 (2018), arXiv:1805.11174 [gr-qc] .
  * Dal Canton  _et al._ (2020) T. Dal Canton, A. H. Nitz, B. Gadre, G. S. Davies, V. Villa-Ortega, T. Dent, I. Harry, and L. Xiao, arXiv e-prints (2020), arXiv:2008.07494 [astro-ph.HE] .
  * Szczepanczyk  _et al._ (2020) M. Szczepanczyk _et al._ , arXiv e-prints (2020), arXiv:2009.11336 [astro-ph.HE] .
  * Abbott  _et al._ (2020g) R. Abbott _et al._ , “Supplement: Gw190521: A binary black hole merger with a total mass of $150m_{\odot}$,”  (2020g).
  * Abbott  _et al._ (2020h) R. Abbott _et al._ (LIGO Scientific, Virgo), arXiv e-prints (2020h), arXiv:2010.14533 [astro-ph.HE] .
  * Krolak and Schutz (1987) A. Krolak and B. F. Schutz, Gen. Rel. Grav. 19, 1163 (1987).
  * Abbott  _et al._ (2020i) B. Abbott _et al._ (KAGRA, LIGO Scientific, Virgo), Living Rev. Rel. 23, 3 (2020i), arXiv:1304.0670 [gr-qc] .
  * Mehta  _et al._ (2021) A. K. Mehta, A. Buonanno, J. Gair, M. C. Miller, E. Farag, R. J. deBoer, M. Wiescher, and F. X. Timmes, (2021), arXiv:2105.06366 [gr-qc] .
  * Reitze  _et al._ (2019) D. Reitze _et al._ , Bull. Am. Astron. Soc. 51, 035 (2019), arXiv:1907.04833 [astro-ph.IM] .
  * Maggiore  _et al._ (2020) M. Maggiore _et al._ , JCAP 03, 050 (2020), arXiv:1912.02622 [astro-ph.CO] .
  * Sathyaprakash  _et al._ (2012) B. Sathyaprakash _et al._ , Class. Quant. Grav. 29, 124013 (2012), [Erratum: Class.Quant.Grav. 30, 079501 (2013)], arXiv:1206.0331 [gr-qc] .
  * Amaro-Seoane  _et al._ (2017) P. Amaro-Seoane _et al._ (LISA), (2017), arXiv:1702.00786 [astro-ph.IM] .
  * Safarzadeh and Farr (2019) M. Safarzadeh and W. M. Farr, Astrophys. J. Lett. 883, L24 (2019), arXiv:1909.01356 [astro-ph.HE] .
  * Mangiagli  _et al._ (2019) A. Mangiagli, M. Bonetti, A. Sesana, and M. Colpi, Astrophys. J. Lett. 883, L27 (2019), arXiv:1907.12562 [astro-ph.HE] .
  * Sesana (2016) A. Sesana, Phys. Rev. Lett. 116, 231102 (2016), arXiv:1602.06951 [gr-qc] .
  * Jani  _et al._ (2019) K. Jani, D. Shoemaker, and C. Cutler, Nature Astron. 4, 260 (2019), arXiv:1908.04985 [gr-qc] .
  * Abbott  _et al._ (2020j) R. Abbott _et al._ (LIGO Scientific, Virgo), arXiv e-prints (2020j), arXiv:2010.14529 [gr-qc] .
  * Cabero  _et al._ (2019) M. Cabero _et al._ , Class. Quant. Grav. 36, 15 (2019), arXiv:1901.05093 [physics.ins-det] .
  * Davis  _et al._ (2020) D. Davis, L. V. White, and P. R. Saulson, Class. Quant. Grav. 37, 145001 (2020), arXiv:2002.09429 [gr-qc] .
  * Nitz  _et al._ (2021b) A. Nitz, I. Harry, D. Brown, C. M. Biwer, J. Willis, T. D. Canton, C. Capano, L. Pekowsky, T. Dent, A. R. Williamson, G. S. Davies, S. De, M. Cabero, B. Machenschalk, P. Kumar, S. Reyes, D. Macleod, dfinstad, F. Pannarale, T. Massinger, S. Kumar, M. Tápai, L. Singer, S. Khan, S. Fairhurst, A. Nielsen, S. Singh, shasvath, and B. U. V. Gadre, “gwastro/pycbc: 1.18.0 release of pycbc,”  (2021b).
  * Sathyaprakash and Dhurandhar (1991) B. Sathyaprakash and S. Dhurandhar, Phys. Rev. D 44, 3819 (1991).
  * Allen  _et al._ (2012) B. Allen, W. G. Anderson, P. R. Brady, D. A. Brown, and J. D. Creighton, Phys. Rev. D 85, 122006 (2012), arXiv:gr-qc/0509116 .
  * Babak  _et al._ (2013) S. Babak _et al._ , Phys. Rev. D 87, 024033 (2013), arXiv:1208.3491 [gr-qc] .
  * Finn and Chernoff (1993) L. S. Finn and D. F. Chernoff, Phys. Rev. D 47, 2198 (1993), arXiv:gr-qc/9301003 .
  * Finn (1992) L. S. Finn, Phys. Rev. D 46, 5236 (1992), arXiv:gr-qc/9209010 .
  * Wainstein and Zubakov (1970) L. A. Wainstein and V. D. Zubakov,  _Extraction of Signals from Noise_ (1970).
  * Allen (2005) B. Allen, Phys. Rev. D 71, 062001 (2005), arXiv:gr-qc/0405045 .
  * Nitz (2018) A. H. Nitz, Class. Quant. Grav. 35, 035016 (2018), arXiv:1709.08974 [gr-qc] .
  * Mozzon  _et al._ (2020) S. Mozzon, L. Nuttall, A. Lundgren, T. Dent, S. Kumar, and A. Nitz, Class. Quant. Grav. 37, 215014 (2020), arXiv:2002.09407 [astro-ph.IM] .
  * Abbott  _et al._ (2016b) B. Abbott _et al._ (LIGO Scientific, Virgo), Phys. Rev. X 6, 041015 (2016b), [Erratum: Phys.Rev.X 8, 039903 (2018)], arXiv:1606.04856 [gr-qc] .
  * Roy  _et al._ (2019) S. Roy, A. S. Sengupta, and P. Ajith, Phys. Rev. D 99, 024048 (2019), arXiv:1711.08743 [gr-qc] .
  * Abbott  _et al._ (2019b) B. P. Abbott _et al._ (LIGO Scientific, Virgo), Phys. Rev. D 100, 064064 (2019b), arXiv:1906.08000 [gr-qc] .
  * Calderón Bustillo  _et al._ (2018) J. Calderón Bustillo, F. Salemi, T. Dal Canton, and K. P. Jani, Phys. Rev. D 97, 024016 (2018), arXiv:1711.02009 [gr-qc] .
  * Chandra  _et al._ (2020) K. Chandra, V. Gayathri, J. C. Bustillo, and A. Pai, Phys. Rev. D 102, 044035 (2020), arXiv:2002.10666 [astro-ph.CO] .
  * Harry  _et al._ (2018) I. Harry, J. Calderón Bustillo, and A. Nitz, Phys. Rev. D 97, 023004 (2018), arXiv:1709.09181 [gr-qc] .
  * Mills and Fairhurst (2020) C. Mills and S. Fairhurst, arXiv e-prints (2020), arXiv:2007.04313 [gr-qc] .
  * Apostolatos  _et al._ (1994) T. A. Apostolatos, C. Cutler, G. J. Sussman, and K. S. Thorne, Phys. Rev. D 49, 6274 (1994).
  * Taracchini  _et al._ (2014) A. Taracchini, A. Buonanno, Y. Pan, T. Hinderer, M. Boyle, D. A. Hemberger, L. E. Kidder, G. Lovelace, A. H. Mroué, H. P. Pfeiffer, and et al., Physical Review D 89 (2014), 10.1103/physrevd.89.061502.
  * Bohé  _et al._ (2017) A. Bohé _et al._ , Phys. Rev. D 95, 044028 (2017), arXiv:1611.03703 [gr-qc] .
  * Vallisneri  _et al._ (2015) M. Vallisneri, J. Kanner, R. Williams, A. Weinstein, and B. Stephens, J. Phys. Conf. Ser. 610, 012021 (2015), arXiv:1410.4839 [gr-qc] .
  * Abbott  _et al._ (2019c) R. Abbott _et al._ (LIGO Scientific, Virgo), (2019c), arXiv:1912.11716 [gr-qc] .
  * Maggiore (2007) M. Maggiore,  _Gravitational Waves. Vol. 1: Theory and Experiments_ , Oxford Master Series in Physics (Oxford University Press, 2007).
  * Soni  _et al._ (2021) S. Soni _et al._ , (2021), arXiv:2103.12104 [gr-qc] .
  * Owen (1996) B. J. Owen, Phys. Rev. D 53, 6749 (1996), arXiv:gr-qc/9511032 .
  * Owen and Sathyaprakash (1999) B. J. Owen and B. Sathyaprakash, Phys. Rev. D 60, 022002 (1999), arXiv:gr-qc/9808076 .
  * Babak  _et al._ (2006) S. Babak, R. Balasubramanian, D. Churches, T. Cokelaer, and B. S. Sathyaprakash, Class. Quant. Grav. 23, 5477 (2006), arXiv:gr-qc/0604037 .
  * Cokelaer (2007) T. Cokelaer, Phys. Rev. D 76, 102004 (2007), arXiv:0706.4437 [gr-qc] .
  * Brown  _et al._ (2012) D. A. Brown, I. Harry, A. Lundgren, and A. H. Nitz, Phys. Rev. D 86, 084017 (2012), arXiv:1207.6406 [gr-qc] .
  * Harry  _et al._ (2014) I. W. Harry, A. H. Nitz, D. A. Brown, A. P. Lundgren, E. Ochsner, and D. Keppel, Phys. Rev. D 89, 024010 (2014), arXiv:1307.3562 [gr-qc] .
  * Dal Canton  _et al._ (2014) T. Dal Canton _et al._ , Phys. Rev. D 90, 082004 (2014), arXiv:1405.6731 [gr-qc] .
  * Harry  _et al._ (2008) I. W. Harry, S. Fairhurst, and B. S. Sathyaprakash, Class. Quant. Grav. 25, 184027 (2008), arXiv:0804.3274 [gr-qc] .
  * Babak (2008) S. Babak, Class. Quant. Grav. 25, 195011 (2008), arXiv:0801.4070 [gr-qc] .
  * Harry  _et al._ (2009) I. W. Harry, B. Allen, and B. Sathyaprakash, Phys. Rev. D 80, 104014 (2009), arXiv:0908.2090 [gr-qc] .
  * Manca and Vallisneri (2010) G. M. Manca and M. Vallisneri, Phys. Rev. D 81, 024004 (2010), arXiv:0909.0563 [gr-qc] .
  * Roy  _et al._ (2017) S. Roy, A. S. Sengupta, and N. Thakor, Phys. Rev. D 95, 104045 (2017), arXiv:1702.06771 [gr-qc] .
  * Apostolatos (1995) T. A. Apostolatos, Phys. Rev. D 52, 605 (1995).
  * Ajith  _et al._ (2011) P. Ajith _et al._ , Phys. Rev. Lett. 106, 241101 (2011), arXiv:0909.2867 [gr-qc] .
  * Santamaria  _et al._ (2010) L. Santamaria _et al._ , Phys. Rev. D 82, 064016 (2010), arXiv:1005.3306 [gr-qc] .
  * Buonanno  _et al._ (2003) A. Buonanno, Y.-b. Chen, and M. Vallisneri, Phys. Rev. D 67, 104025 (2003), [Erratum: Phys.Rev.D 74, 029904 (2006)], arXiv:gr-qc/0211087 .
  * Cotesta  _et al._ (2018) R. Cotesta, A. Buonanno, A. Bohé, A. Taracchini, I. Hinder, and S. Ossokine, Phys. Rev. D 98, 084028 (2018), arXiv:1803.10701 [gr-qc] .
  * Cotesta  _et al._ (2020) R. Cotesta, S. Marsat, and M. Pürrer, Phys. Rev. D 101, 124040 (2020), arXiv:2003.12079 [gr-qc] .
  * Varma  _et al._ (2019) V. Varma, S. E. Field, M. A. Scheel, J. Blackman, D. Gerosa, L. C. Stein, L. E. Kidder, and H. P. Pfeiffer, Phys. Rev. Research. 1, 033015 (2019), arXiv:1905.09300 [gr-qc] .
  * Ezquiaga and Holz (2021) J. M. Ezquiaga and D. E. Holz, Astrophys. J. Lett. 909, L23 (2021), arXiv:2006.02211 [astro-ph.HE] .
  * Tanikawa  _et al._ (2021) A. Tanikawa, H. Susa, T. Yoshida, A. A. Trani, and T. Kinugawa, Astrophys. J. 910, 30 (2021), arXiv:2008.01890 [astro-ph.HE] .

  *[GW]: gravitational-wave
  *[IMBH]: intermediate-mass black hole
  *[O3a]: the first half of the third observing run
  *[CBCs]: compact binary coalescence
  *[GWTC-2]: second gravitational wave transient catalogue
  *[IFAR]: inverse false alarm rate
  *[BBH]: black hole binary
  *[BBHs]: black hole binary
  *[IMBHs]: intermediate-mass black hole
  *[CBC]: compact binary coalescence
  *[PSD]: power spectral density
  *[SNR]: signal-to-noise ratio
  *[FAR]: false alarm rate
  *[PSDs]: power spectral density
  *[SNRs]: signal-to-noise ratio
  *[GWs]: gravitational-wave