# New binary black hole mergers in the LIGO–Virgo O3b data

Ajit Kumar Mehta<EMAIL_ADDRESS>Department of Physics, University of
California at Santa Barbara, Santa Barbara, CA 93106, USA Seth Olsen
Department of Physics, Princeton University, Princeton, NJ 08540, USA Digvijay
Wadekar  School of Natural Sciences, Institute for Advanced Study, 1 Einstein
Drive, Princeton, NJ 08540, USA Javier Roulet  TAPIR, Walter Burke Institute
for Theoretical Physics, California Institute of Technology, Pasadena, CA
91125, USA Tejaswi Venumadhav  Department of Physics, University of California
at Santa Barbara, Santa Barbara, CA 93106, USA International Centre for
Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore
560089, India Jonathan Mushkin  Department of Particle Physics & Astrophysics,
Weizmann Institute of Science, Rehovot 76100, Israel Barak Zackay  Department
of Particle Physics & Astrophysics, Weizmann Institute of Science, Rehovot
76100, Israel Matias Zaldarriaga  School of Natural Sciences, Institute for
Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA

###### Abstract

We report the detection of 5 new candidate binary black hole (BBH) merger
signals in the publicly released data from the second half of the third
observing run (O3b) of advanced LIGO and advanced Virgo. The LIGO–Virgo–KAGRA
(LVK) collaboration reported 35 compact binary coalescences (CBCs) in their
analysis of the O3b data Abbott  _et al._ (2021), with 30 BBH mergers having
coincidence in the Hanford and Livingston detectors. We confirm 17 of these
for a total of 22 detections in our analysis of the Hanford–Livingston
coincident O3b data. We identify candidates using a search pipeline employing
aligned-spin quadrupole-only waveforms. Our pipeline is similar to the one
used in our O3a coincident analysis Olsen  _et al._ (2022), except for a few
improvements in the veto procedure and the ranking statistic, and we continue
to use an astrophysical probability of one half as our detection threshold,
following the approach of the LVK catalogs. Most of the new candidates
reported in this work are placed in the upper/lower-mass gap of the black hole
(BH) mass distribution. One BBH event also shows a sign of spin-orbit
precession with negatively aligned spins. We also identify a possible neutron
star-black hole (NSBH) merger. We expect these events to help inform the black
hole mass and spin distributions inferred in a full population analysis.

##  I Introduction

The Advanced LIGO and J Aasi  _et al._ (2015) and Advanced Virgo Acernese  _et
al._ (2015) detectors have now been joined by KAGRA Akutsu  _et al._ (2021) to
form the LIGO–Virgo–KAGRA (LVK) collaboration, which recently released data
from the second half of the third observing run (O3b) to the public Vallisneri
_et al._ (2015). The LVK detected gravitational waves (GW) from 35 compact
binary coalescence (CBC) events including two probable neutron star–black hole
(NSBH) mergers Abbott  _et al._ (2021). 32 of these were found to be
coincident in the Hanford–Livingston (HL) detectors, among which 30 were
reported to be binary black hole (BBH) signals. Nitz  _et al._ (2021)
independently produced the 4-OGC catalog, which included an additional 7 BBH
mergers that were not in the LVK catalog.

In this work, we report the detection of 5 new candidate BBH merger signals
from our coincident search of O3b HL data (excluding Virgo). Our search was
carried out with a pipeline that is very similar to the one used in Olsen  _et
al._ (2022) (see Venumadhav  _et al._ (2019) for an overview of the pipeline).
We show these detections in Fig. 1 alongside the 90 CBC signals detected by
LVK, additional events detected in 4-OGC, and the events previously detected
by our pipeline in O1-O3a with probability of astrophysical origin ($p_{\rm
astro}$) greater than one half Abbott  _et al._ (2016a, 2019); Nitz  _et al._
(2019, 2020); Abbott  _et al._ (2021a); The LIGO Scientific Collaboration  _et
al._ (2021); Venumadhav  _et al._ (2019, 2020); Olsen  _et al._ (2022).

Understanding the mass and spin distributions of the astrophysical BBH
population is one of the major goals of GW astronomy. As the number of events
in the catalog increases, statistically inferred measurements of the
population parameters become more and more precise Roulet  _et al._ (2021);
Abbott  _et al._ (2021b). These improved measurements help us to constrain BBH
formation channel rates, and they allow us to probe deeper into the
fundamental physics of black holes (BHs) and even cosmology Yang  _et al._
(2017); Perkins  _et al._ (2021); Abbott  _et al._ (2021); O’Brien  _et al._
(2019); Ezquiaga (2021).

One of the standard BBH formation channels consists of binary stars that
evolve in isolation. Stellar evolution models predict that, if massive enough,
stars can go through pulsational pair-instability (PPISN) and pair-instability
supernovae (PISN). In particular, the latter can completely destroy the stars,
leaving no remnant at the end of the evolution. The standard prediction is
that this will lead to an “upper mass gap” (UMG) in which the astrophysical
distribution drops sharply for BH masses between $\sim 45\,{\rm M_{\odot}}$
and $\sim 135\,{\rm M_{\odot}}$Fowler and Hoyle (1964); Barkat  _et al._
(1967); Bond  _et al._ (1984); Heger and Woosley (2002); Woosley  _et al._
(2007); Woosley (2017); Farmer  _et al._ (2019); Chen  _et al._ (2014);
Yoshida  _et al._ (2016); Belczynski, K.  _et al._ (2016). Local observations
of BHs also hint at the existence of an empirical “lower mass gap” (LMG)
between $\sim 2\,{\rm M_{\odot}}$ and $\sim 5\,{\rm M_{\odot}}$ corresponding
to the region between the maximum NS mass Alsing  _et al._ (2018) and the
lowest observed BH mass Bailyn  _et al._ (1998a); Özel  _et al._ (2010a); Farr
_et al._ (2011a); Belczynski  _et al._ (2012); Farah  _et al._ (2021); Liu
_et al._ (2021) (note that according to Alsing  _et al._ (2018), the maximum
mass of the NS can vary between $[2,2.6]\,{\rm M_{\odot}}$). Detecting BHs in
these gaps can have several implications, e.g., detecting a BH in the UMG
suggests an alternative to the isolated stellar evolution mechanism for its
formation, such as hierarchical mergers in dense stellar environments (the
“dynamical formation” channel) Santoliquido  _et al._ (2020); Di Carlo  _et
al._ (2020); Kremer  _et al._ (2020); Mapelli  _et al._ (2021); González  _et
al._ (2021); Fabj  _et al._ (2020); McKernan  _et al._ (2020); Tagawa  _et
al._ (2021, 2020); Yang  _et al._ (2019); Gröbner, M.  _et al._ (2020)) and/or
they can make us revisit the problem of stellar collapse Farmer  _et al._
(2019); Marchant and Moriya (2020); Mehta  _et al._ (2022). As we will see
later, among the new events presented here we do find sources whose
constituents lie in these gaps (see Table 1). Including such events in the
population analysis could impact the inferred BH mass distribution Abbott  _et
al._ (2021b); Roulet  _et al._ (2021).

Figure 1: The source-frame total mass and effective spin for the BBH events
detected so far from all the search pipelines across the first three observing
runs of LVK. Posterior contours enclose $50\%$ of the probability and the
median is represented by a dot. For parameter inference, we use the
IMRPhenomXPHM waveform approximant Pratten  _et al._ (2021) and a prior that
is uniform in detector-frame constituent masses and comoving volume-time
(redshifts based on Planck15 results Ade  _et al._ (2016)). Contours for the 5
new events are colored by their $p_{\rm astro}$ values, and the events
appearing in previous IAS, OGC and LVK catalogs up to 3-OGC and GWTC-3 Abbott
_et al._ (2016a); Venumadhav  _et al._ (2019); Abbott  _et al._ (2019);
Venumadhav  _et al._ (2020); Abbott  _et al._ (2021a); The LIGO Scientific
Collaboration  _et al._ (2021); Olsen  _et al._ (2022); Abbott  _et al._
(2021) are transparent gray. The additional (7) events reported in 4-OGC
catalog Nitz  _et al._ (2021) from O3b are shown with solid gray color. Though
our search only covers events with Hanford–Livingston coincidence triggers, we
include all BBH events declared in the LVK and OGC catalogs through O3b in
this figure. _Left panel:_ Results obtained with uniform prior on the
effective spin (default prior used in this work). _Right panel:_ Results with
isotropic priors on individual spins, as used in the GWTC-3 and 4-OGC
catalogs.

In addition to the masses, the BH spins can also be measured from GW signals.
The best measured parameter, however, is a particular combination of the
masses and spins called the effective spin:

$\displaystyle\chi_{\rm
eff}=\frac{m_{1}\chi_{1,z}+m_{2}\chi_{2,z}}{m_{1}+m_{2}}\,.$ (1)

where $m_{i}$ are the masses and $\chi_{i,z}$ are the dimensionless spins
projected on the orbital angular momentum. Together with the measurement of
the masses, measuring $\chi_{\rm eff}$ could give us more information about
the underlying formation channels. For example, as the total mass of the
binaries increases, highly spinning systems with $\chi_{\rm{eff}}<0$ (anti-
aligned) become increasingly difficult to form in the isolated binary
evolution channel even under a broad range of BH natal kicks Rodriguez  _et
al._ (2016). Similar to our previous work Olsen  _et al._ (2022), we employ a
spin prior which is uniform in $\chi_{\rm{eff}}$. This prior is also useful if
a reader wants to reweight these results to another prior of their choice,
e.g., a prior that is isotropic in the individual spins such as the one used
in the GWTC-3 Abbott  _et al._ (2021) and 4-OGC Nitz  _et al._ (2021) catalogs
. Though we use uniform in $\chi_{\rm{eff}}$ as our default spin prior for our
parameter estimation runs, we perform an additional set of parameter
estimation runs to compare against the isotropic spin prior results.

In this work, we follow-up on our previous study (Olsen  _et al._ (2022))
which looked for new events in the Hanford–Livingston (HL) data from the first
half of the third observing run (O3a), and analyze the data from the second
half of the third observing run (O3b) to complete an O3 catalog with a similar
pipeline (see Section II for a description of the changes). We detect 5 new
BBH candidate events under the criterion that the astrophysical probability
$p_{\rm astro}$ is at least one half (which is also the threshold used in the
GWTC-3 and 4-OGC catalogs). By simply summing the complements of the $p_{\rm
astro}$ values assigned to these events, we expect that roughly 2 of the 5
events may be noise transients rather than astrophysical signals (note,
however, that the estimates of $p_{\rm astro}$ depend on multiple factors
including the astrophysical prior used, and that the dependence is strongest
in the case of near-threshold detections such as these).

Our pipeline confirmed the detections of 17 out of the 30 HL coincident BBH
mergers reported in the GWTC-3 catalog (thus, in total, we detected 22
candidate CBC events in our coincident search of HL data from O3b). When we
investigated our pipeline’s performance on the remaining events in the LVK
catalog, we found that 6 of them were marginal in our catalog, i.e., recovered
with a $p_{\rm astro}$ lower than one half, while 6 were vetoed for failing
one or more of our signal consistency and excess power tests, and one event
was missed. Most of the marginally recovered events were detected by only one
of the LVK search pipelines, while three of the vetoed events show signs of
physical effects like spin-precession and higher harmonics that were not
modeled in our template bank. We also note that four of the vetoed events were
flagged as having data-quality issues in the GWTC-3 catalog paper. Finally, we
also checked that 4 of the 5 new candidates reported in this work were also
present in the list of GWTC-3 sub-threshold candidates LIGO Scientific
Collaboration and Collaboration (2021).

The new GW sources reported here could come from a range of astrophysical
scenarios. Two events have their primary (i.e. more massive) constituents
confidently placed in the upper mass gap, one of which is also significantly
precessing. One event has its secondary (i.e. less massive) constituent
confidently placed in the lower mass gap, i.e. $2\,{\rm M_{\odot}}\lesssim
m_{2}^{\rm{src}}\lesssim 5\,{\rm M_{\odot}}$. If we allow for the possibility
that the maximum mass of the NS can reach up to $\sim 2.6\,{\rm M_{\odot}}$
Alsing  _et al._ (2018), this event could also be a neutron star-black hole
(NSBH) signal at $90\%$ confidence (note however that we did not perform a
dedicated NSBH search). There is also a particular low-mass event which, under
uniform prior on effective spin, seems to have strongly anti-aligned spins
($\chi_{\rm{eff}}\leq-0.8$ at $90\%$ confidence; see the discussion in the
text for caveats).

We find that for at least two of the new events, detailed parameter estimation
shows some evidence for effects such as higher-order modes (HM) and spin-
precession, and also some information from the VIRGO data, which suggests that
their significance could be potentially improved by including these elements
in future improved searches (our current search of the Hanford–Livingston
coincident data uses aligned-spin templates that only have the fundamental
($\ell=|m|=2$) harmonic). As noted earlier, some loud events in the LVK
catalog that were vetoed by our pipeline also showed evidence for these
physical effects, which additionally motivates the development of improved
pipelines incorporating them.

The rest of the paper is organized as follows: in §II we review changes to the
IAS pipeline between the O3a and O3b analyses. In §III we discuss the BBH
mergers first reported in this work (see Table 1). In §IV we report our
results for events already included in GWTC-3 Abbott  _et al._ (2021) and
4-OGC Nitz  _et al._ (2021), noting differences (see Table 2). We summarize
the results in §V and discuss the astrophysical implications of the new
events. In Appendix A, we show the computation of the astrophysical
probability, $p_{\rm astro}$ and also discuss certain details of our veto
procedure.

Corner plots of posterior distributions for new events can be found in
Appendix B, with PE samples publicly available at
https://github.com/AjitMehta/new_BBH_mergers_O3b_IAS_pipeline.

##  II Changes to the O3a analysis pipeline

Our analysis pipeline is very similar to the version used in our recent
analysis of the Hanford–Livingston coincident O3a data Olsen  _et al._ (2022),
but we make changes to two components of the pipeline detailed below in this
section. Once we have the ranked lists of coincident foreground and background
candidates, we calculate the candidates’ $p_{\rm astro}$ values using the same
procedure as in Appendix A of Olsen  _et al._ (2022). Note that, unlike the
results reported in the previous IAS papers, we also report, for each event,
an overall inverse false-alarm rate (IFAR) combined across our template banks
(assuming an equal astrophysical rate density for each bank) in addition to
the IFAR computed within the respective bank.

###  II.1 Signal-consistency veto tests:

In the matched-filtering step of our pipeline, we collect and save triggers
above a particular threshold on the signal-to-noise ratio (SNR; we use
$\rho^{2}\gtrsim$ 15 for the template banks for the most massive BBHs, where
$\rho$ is the single-detector SNR; the exact threshold varies with the bank
and is typically higher for banks for less massive BBHs). In our previous
studies, we only performed our signal-consistency veto tests on the subset of
these triggers that passed a higher threshold on their SNR ($\rho^{2}\geq
30$). Ideally, one should perform the veto tests on all the candidates
irrespective of their SNR, but we need to pick a higher threshold as the veto
tests are computationally expensive (they take roughly a minute per trigger
per CPU in a single detector). This choice can lead to some spurious triggers
(i.e., ones that should ideally be vetoed) that are below the SNR threshold
entering our final ranked lists (this happens to both the coincident
foreground and background triggers).

To ameliorate this, we use the following procedure. We first construct our
ranked lists using the same $\rho^{2}$ veto threshold as before. We then
collect high-ranking candidates with SNR below the veto threshold (which had
been omitted from our veto tests before), and screen them through the veto
tests (we do this procedure on $\sim 10000$ top candidates from our background
and coincident lists). We make our final ranked candidate lists by removing
any candidates which failed at least one veto test. There is another slight
change we make to the order in which the veto procedure is applied to the
triggers in the pipeline compared to the O3a pipeline, which we discuss in
Appendix A.

###  II.2 Ranking statistic

Our statistic to rank the triggers performs two functions: $(i)$ it up-weights
triggers which have good coherence among multiple detectors, ($ii$) it down-
weights triggers in individual detectors based on the probability with which
similar triggers occur in the background (for a detailed discussion on the
ranking statistic used in the pipeline, see Appendix A and Ref. Wadekar  _et
al._ (2023a)). Corresponding to the second function, our ranking statistic
includes a term: $-2\log P(\rho^{2}|N)$ – this is the probability of obtaining
a trigger with squared SNR $\rho^{2}$ from the background for a given detector
(in our previous papers, we labelled this term as the rank function (denoted
by $\tilde{\rho}$), see section J of Ref. Venumadhav  _et al._ (2019)). We
measure $P(\rho^{2}|N)$ by constructing a histogram of the SNR values of
background triggers (obtained using timeslides) and correcting for the
incompleteness introduced by our cuts.

In the previous iterations of our search pipeline, we combined background
triggers from all templates in a given subbank to construct this histogram and
estimate the rank function. In reality, $\log P(\rho^{2}|N)$ can have
different values even for different templates in a given subbank, i.e., the
background can be strongly template-dependent, see e.g., Abbott  _et al._
(2016b); Nitz  _et al._ (2017); Wadekar  _et al._ (2023a). In order to
optimize our analysis, we follow the technique in Ref. Wadekar  _et al._
(2023a), where we first cluster the templates within each sub-bank based on
their sensitivity to glitches (as quantified empirically by the relative
fraction of loud and faint triggers belonging to each template). We then
separately construct the histograms of background triggers for each template
group, and estimate a rank function for triggers belonging to templates within
that group. A detailed discussion on this point will be provided in our
subsequent paper Wadekar  _et al._ (2023a).

We expect the senstivity of our pipeline to increase due to these two
improvements. We plan to quantify this increase in terms of the volume-time
($VT$) based on the performance of our pipeline on recovery of injected
signals in the data in a future paper.

Table 1: New events with $p_{\rm astro}>0.5$. The parameter values correspond to the median and $90\%$ uncertainties and $\ln\mathcal{L}_{\rm{max}}$ denotes the maximum log likelihood from parameter estimation (PE) runs. While our search templates only include aligned-spin (2,2) mode (based on the IMRPhenomD approximant), PE was done with IMRPhenomXPHM waveform which additionally includes effects of precession and higher-harmonics: (2,1), (3,3) and (4,4) modes. The PE also uses Virgo data when available, unlike the search. $\rho^{2}_{\rm{H,L}}$ denote the SNR of the triggers in the Hanford and Livingston detectors. The IFAR column shows the IFAR within the bank and the one combined across the chirp-mass banks assuming an equal astrophysical rate density for each chirp-mass bank. Event | Bank | PE | $\rho_{\rm H}^{2}$ | $\rho_{\rm L}^{2}$ | IFAR (yr) | $p_{\mathrm{astro}}$
---|---|---|---|---|---|---
$m_{1}^{\textrm{src}}{\scriptstyle(\rm M_{\odot})}$ | $m_{2}^{\textrm{src}}{\scriptstyle(\rm M_{\odot})}$ | $\chi_{\rm eff}$ | $z$ | $\ln\mathcal{L}_{\mathrm{max}}$ | within bank $|$ |  $|$ overall
GW200109_195634111This event’s significance could be potentially improved in future searches in which Virgo data is also included in the coincident analysis. | (5, 4) | $69_{-19}^{+24}$ | $48_{-17}^{+22}$ | $0.5_{-0.8}^{+0.3}$ | $1.0_{-0.4}^{+0.7}$ | $42.0$ | $30.6$ | $33.6$ | $2.9$ | $0.50$ | $0.77$
GW191228_085854 222This event has bi-modal posterior distributions in the intrinsic parameters. The values quoted here correspond to the first mode. See III.2 for further details. | (1, 0) | $9.7_{-1.5}^{+4.2}$ | $5.5_{-1.4}^{+0.9}$ | $-0.89_{-0.10}^{+0.42}$ | $0.14_{-0.04}^{+0.05}$ | $43.2$ | $26.9$ | $54.0$ | $1.7$ | $0.20$ | $0.65$
GW200225_075134 | (3, 1) | $51_{-11}^{+17}$ | $37_{-11}^{+13}$ | $-0.5_{-0.4}^{+0.9}$ | $0.6_{-0.3}^{+0.4}$ | $43.0$ | $20.0$ | $49.4$ | $0.92$ | $0.15$ | $0.60$
GW200316_235947 | (0, 0) | $6.4_{-1.4}^{+4.9}$ | $3.6_{-1.3}^{+1.0}$ | $-0.11_{-0.13}^{+0.34}$ | $0.17_{-0.05}^{+0.05}$ | $38.9$ | $36.7$ | $32.7$ | $0.59$ | $0.085$ | $0.51$
GW191122_214924333This event’s significance could be potentially improved in future searches that include the effects of precession and higher harmonics of GW radiation. | (4, 2) | $70_{-20}^{+50}$ | $27_{-14}^{+29}$ | $0.1_{-0.4}^{+0.4}$ | $0.6_{-0.3}^{+0.5}$ | $55.4$ | $16.8$ | $63.7$ | $0.42$ | $0.087$ | $0.51$

##  III Newly Reported BBH mergers

Table 1 lists some properties of the newly reported events: source-frame
masses ($m_{1}^{\rm{src}}$ and $m_{2}^{\rm{src}}$), effective spin
($\chi_{\rm{eff}}$), redshift ($z$), inverse false alarm rate (IFAR) and
estimated $p_{\rm astro}$.

We perform parameter estimation (PE) using a prior that is uniform in
detector-frame constituent masses, effective spin $\chi_{\rm eff}$, and
comoving volume-time ($VT$). The other extrinsic parameters have the standard
geometric priors used in GWTC-3 Abbott  _et al._ (2021). We compute redshifts
using a $\Lambda$ cold dark matter ($\Lambda$CDM) cosmology with Planck15
parameters Ade  _et al._ (2016). We use the phenomenological waveform
approximant IMRPhenomXPHM Pratten  _et al._ (2021), which includes the sub-
dominant (or higher-order) modes $21$, $33$ and $44$ in addition to the
dominant mode $22$, and models the effect of orbital precession due to in-
plane spins. We accelerate the likelihood evaluations using the relative
binning algorithm described in Zackay  _et al._ (2018) as implemented in the
PE package $\tt{cogwheel}$ Roulet  _et al._ (2022) (see Appendix B for more
details). We note that these details are the same as in our O3a search: Olsen
_et al._ (2022).

In the rest of this section, we will briefly comment on the properties of the
new events reported in this paper.

Figure 2: A closer look at one of our new events: GW$191122\\_214924$. Results
are shown with the precessing waveform model IMRPhenomXPHM Pratten  _et al._
(2021), and also with the non-precessing limit of this waveform (labelled as
IMRPhenomXPHM_Aligned). The latter yields much lower log-likelihood,
indicating that the signal has contributions from precession. Bayes factor
computation favors the precessing model over the non-precessing one by a
factor of $\sim 8$. Note that the posterior of $\chi_{1,\perp}$ in the case of
IMRPhemomXPHM_Aligned is the same as its prior as we have set the in-plane
spin components to zero during the likelihood evaluations in this case.

###  III.1 High-mass sources

#### GW200109_195634

This event is our most significant new detection, with $p_{\rm astro}=0.77$.
It has a primary mass ($m_{1}^{\mathrm{src}}=69^{+24}_{-19}\,{\rm M_{\odot}}$)
that lies in the UMG (see Fig. 7 below). We find that the best-fit waveform
that the PE explores has a higher value of $\rm{SNR}^{2}$ than the search by
$\Delta\rm{SNR}^{2}=2\ln\mathcal{L}_{\rm{max}}-\rho_{\rm{H}}^{2}-\rho_{\rm{L}}^{2}\approx
20$, where $\ln\mathcal{L}_{\rm{max}}$ is the maximum log likelihood achieved
within the posterior samples, and $\rho_{\rm{H,L}}$ represent the SNR
recovered by the search template in the Hanford and Livingston detectors. It
turns out that a significant fraction of the $\rm{SNR}^{2}$ difference
($\Delta\rm{SNR}^{2}\approx 15$) comes from the Virgo detector which is
included in the PE but not in our search. Including Virgo data in the future
coincident searches could thus raise the significance of this event. This is
also the most distant event among our new detections, with redshift
$z=1.0^{+0.7}_{-0.4}$.

#### GW200225_075134

This event, with $p_{\rm astro}=0.60$, has a primary mass measurement of
$m_{1}^{\mathrm{src}}=51^{+17}_{-11}\,{\rm M_{\odot}}$ (Fig. 8). It does not
pose an issue for the UMG.

#### GW191122_214924

This event is one of the least significant events in our list, with $p_{\rm
astro}=0.51$. However, as we show below, the significance of this event could
be improved in future searches which include the effect of orbital precession
in their templates. This event has a primary mass of
$m_{1}^{\mathrm{src}}=70^{+50}_{-20}\,{\rm M_{\odot}}$ (see Fig. 9), that lies
confidently within the UMG. The best-fit parameters indicate that the primary
BH has a large in-plane spin magnitude,
$\chi_{1,\perp}=\sqrt{\chi_{1,x}^{2}+\chi_{1,y}^{2}}\approx 0.75$, with the
effective spin being mildly negative ($\chi_{\rm{eff}}\sim-0.2$) (see Fig. 2).

The PE again uncovers a significantly higher $\rm{SNR}^{2}$ compared to the
search:
$\Delta\rm{SNR}^{2}=2\ln\mathcal{L}_{\rm{max}}-\rho_{\rm{H}}^{2}-\rho_{\rm{L}}^{2}\approx
30.2$. Recall that our search templates are based on the $\tt{IMRPhenomD}$
approximant Khan  _et al._ (2016), which only models the dominant
$(\ell,|m|)=(2,2)$ mode and does not incorporate precession. Indeed, a PE
using either $\tt{IMRPhenomD}$ or $\tt{IMRPhenomXAS}$ Pratten  _et al._
(2020)444$\tt{IMRPhenomXAS}$ is the most recent $(2,2)$ mode aligned-spin
phenomenological waveform. waveforms yields a very similar SNR to that
obtained by the search. It turns out that the above SNR difference between PE
and the search is mainly due to the lack of precession in the search
templates, i.e., using IMRPhenomXPHM waveforms with and without precession in
the PE gives $\Delta\rm{SNR}^{2}=22.71$ (Fig. 2). The remaining difference
(i.e., $\Delta\rm{SNR}^{2}\approx 8$) comes from the HM contribution. The
Bayes factor is $\sim 8$ in favor of the presence of orbital precession. These
properties are robust to the spin prior used. A future search with templates
that incorporate the effects of precession (and higher modes) could thus
further improve the significance of this event.

###  III.2 Low-mass sources

#### GW191228_085854

This event, with $p_{\rm astro}=0.65$, has a bi-modal posterior distribution
in the masses and effective spin under our default spin prior (see Fig. 12).
The first posterior mode occurs at the secondary mass,
$m_{2}^{\mathrm{src}}\sim 5.5\,{\rm M_{\odot}}$ and effective spin,
$\chi_{\rm{eff}}\sim-0.89$ while the second one occurs at
$m_{2}^{\mathrm{src}}\sim 3\,{\rm M_{\odot}}$ and $\chi_{\rm{eff}}\sim 0.0$.
Interestingly, the likelihoods of these two modes are very similar, which
suggests that the data seems to prefer both modes equally likely. Both these
solutions are, however, very interesting astrophysically. While the first
solution hints at a highly negatively spinning stellar mass BBH merger, the
second solution suggests at a significantly asymmetric ($1/q\gtrsim 5$) non-
spining BBH merger with the secondary mass confidently lying in the LMG.

On the other hand, a PE with LVK prior (i.e., isotropic prior on spins)
selects out only the second solution. This might be expected as this prior
does not have significant weight at high positive or negative effective spins.
In appendix C we discuss this event in further detail and also show similar
results (i.e., bi-modal phenomena) from known LVK events in the similar
parameter space region when analysed with our default spin prior. This brings
out to our attention the usefulness of using a generic prior so that at least
the results for other priors of choice can be obtained by properly reweighting
the generic result.

Figure 3: Sky localization for a new possible NSBH candidate, GW200316_235947.
The priors used were uniform in detector-frame constituent masses, effective
spin, and comoving $VT$. The probability contours enclose $50\%$ and $90\%$.
The $x$-axis represents right ascension in hours, and the $y$-axis represents
declination in degrees.

#### GW200316_235947

: This event is the most marginal event, with $p_{\rm astro}=0.51$. It has a
secondary mass of $m_{2}^{\mathrm{src}}=3.6^{+1.0}_{-1.3}\,{\rm M_{\odot}}$
(Fig. 10), placing its lighter constituent confidently in the LMG. This object
is also consistent with being a heavy NS at $90\%$ confidence, if we take the
maximum NS mass to be $\sim 2.6\,{\rm M_{\odot}}$. Based on the likelihood
comparison between the regions $m_{2}^{\rm{src}}\lesssim 2.6\,{\rm M_{\odot}}$
(NSBH) and $m_{2}^{\rm{src}}\gtrsim 2.6\,{\rm M_{\odot}}$ (BBH), the NSBH and
BBH solutions have comparable support from the data, so the priors may play a
deciding role in identifying the secondary object as a BH or NS. The NSBH
solution also has a slightly positive effective spin (see Fig. 10), which
makes it more interesting for EM followup. In Fig. 3 we show the sky
localization of this event. Although the sky localization is not very well
constrained, it would be worthwhile to do a follow-up search for an EM
counterpart.

##  IV Comparison to previously reported catalogs

In Table 2, we summarize our pipeline’s results for the O3b Hanford–Livingston
coincident events published in the GWTC-3 catalog Abbott  _et al._ (2021). We
also include the additional events as well as the significance reported by the
4-OGC catalog Nitz  _et al._ (2021). Our $p_{\rm astro}$ estimation is based
on the distribution of foreground and background triggers over the O3b run
(see Appendix A). We compute the inverse false-alarm rate independently for
each template bank. For a comparison of $p_{\rm astro}$ across different
search pipelines, see Section IV of Olsen  _et al._ (2022).

#### Confidently recovered events

The LVK collaboration has five main search pipelines: cWB Klimenko  _et al._
(2016), MBTA Andres  _et al._ (2022), GstLAL Sachdev  _et al._ (2019), PyCBC
and PyCBC_BBH Usman  _et al._ (2016). Whenever the estimated $p_{\rm astro}$
from any one of these pipelines crosses the threshold of one half, the event
is declared a confident detection. With this criterion, there were 32
Hanford–Livingston (HL) coincident events in Abbott  _et al._ (2021). However,
two of them (GW200115_042309 and GW191219_163120) were NSBH mergers. We did
not look for such signals in this work. Of the remaining 30 coincident BBH
mergers, our pipeline retained 17 with a significance comparable to or better
than the LVK catalog.

#### Candidates with low $p_{\rm astro}$

Our pipeline assigned $p_{\rm astro}<0.5$ to 6 of the LVK events. Five of
these events were detected confidently by only one of the LVK search
pipelines: GW191126_115259, GW200208_222617 and GW200308_173609 were detected
by only PyCBC_BBH, while GW200306_093714 and GW200322_091133 were detected by
only MBTA. Given that each individual pipeline differs in their analysis
choices, which can be especially important for near-threshold events like
these, it is not surprising that these signals were also considered marginal
by our pipeline. The remaining event, GW200202_154313, was detected by more
than one pipeline. However, this event also has a substantial SNR contribution
from the Virgo detector, which indicates that adding Virgo data to our
coincident search may improve its significance in our future analyses.

#### Vetoed candidates

We implement a series of signal consistency checks in order to reject triggers
that are likely to arise from glitches (noise transients) and consequently
improve our pipeline’s sensitivity. Noise fluctuations and the incompleteness
of our template bank can cause astrophysical signals to be vetoed, but the
tests are designed to gain more in true positive rate than the loss they
produce from false negatives due to these effects (in a statistical sense).

Six events from the GWTC-3 catalog were vetoed in our search: GW191103_012549,
GW191109_010717, GW191113_071753, GW191127_050227, GW200129_065458 and
GW200210_092254.

The events GW191109_010717 and GW200129_065458 had fairly high SNR and are
high-mass binaries with imprints of precession Abbott  _et al._ (2021). Our
search used a template bank that was built using the non-precessing
$\tt{IMRPhenomD}$ approximant, and the signal consistency tests compare the
data only to the best-fit waveform within the template bank – the absence of
precession and higher-harmonics in the template can make it more likely for
events that exhibit these phenomena to trigger the signal-consistency tests
555We note that some of the vetoed events here are restored in our search with
higher-harmonics Wadekar  _et al._ (2023b).. The data for two events was also
flagged for data-quality issues in the GWTC3 catalog.

Our pipeline vetoed GW191113_071753 since the residuals after subtracting the
best-fit template exhibited excess power beyond the expectation from Gaussian
noise in multiple frequency bands. In the GWTC3 analysis, this candidate was
marked as affected by transient, non-Gaussian detector noise. The best-fit
waveform in PE for this candidate has a significantly asymmetric mass ratio
$q\lesssim 0.2$, and the absence of higher modes in our template bank could
have also contributed to the failure of the excess power tests.

GW200210_092254 failed “split-tests” designed to check for consistency between
the SNR in different sub-ranges of frequency. This event also has a
significantly asymmetric mass ratio, but when we investigated further, we
found that our pipeline assigned a representative trigger to this event that
came from a different region of the template bank than would be implied from
the parameters from the inference runs. The template with the correct
parameters had a matched-filtering SNR in Hanford that fluctuated below the
collection threshold we used to define triggers666We set these thresholds to
reduce the large volume of trigger data that we would otherwise need to
analyze with the more costly coincidence-section of the pipeline.. In other
words, the actual trigger in the Livingston data could not find a coincident
one in the Hanford data due to this threshold, and thus the event was assigned
to a different bank in which it failed signal consistency tests. We can detect
such events by either lowering the SNR threshold for triggering, or performing
a targeted search for events with disparate detector-responses, such as in
Ref. Zackay  _et al._ (2021).

The other two events were straightforwardly vetoed in our search;
GW191127_050227 failed multiple excess power tests in a few specific bands in
a unit-second interval, while GW191103_012549 failed the split tests. We also
note that the data for GW191127_050227 was flagged as being affected by data-
quality issues in the GWTC3 catalog paper.

We further note that, two events GW191129_134029 and GW200202_154313 were
recovered with secondary triggers, i.e., their primary triggers were vetoed.
This is the reason we recover them with lower SNR, and thus the lower IFAR
compared to the LVK analysis (see Table 2).

#### Lost triggers

Our pipeline missed the event GW200220_061928. This is a high-mass BBH (87
${\rm M_{\odot}}+61\,{\rm M_{\odot}}$ at 6 Gpc) which was only found by PyCBC-
Broad, with all other LVK pipelines having no coincident triggers at this
time.

#### Search space excluded from this work

We did not perform a dedicated search for NSBH or BNS signals. We leave this
to future work.

Table 2: Hanford–Livingston coincident BBH events already reported in the GWTC-3 catalog Abbott  _et al._ (2021) as detected by our pipeline and the 4-OGC catalog Nitz  _et al._ (2021). Six events found by LVK in Hanford–Livingston coincidence were vetoed in our search: GW191103_012549, GW191109_010717, GW191113_071753, GW191127_050227, GW200129_065458 and GW200210_092254. The inverse false alarm rate (IFAR) values in the GWTC-3 column are taken from the $\tt{GWOSC}$ catalog, which corresponds to whichever LVK pipeline achieved the highest astrophysical probability for that event in the GWTC-3 analysis. The 4-OGC column was taken from the catalog summary data at $\tt{GitHub}$, as listed in the publication. The events in italics are the ones from the 4-OGC catalog Nitz  _et al._ (2021). Event Name | Bank | $\rho_{\rm H}^{2}$ | $\rho_{\rm L}^{2}$ | GWTC-3 | $p_{\rm astro}$ | IFAR (yr)
---|---|---|---|---|---|---
$\rho_{\rm Network}^{2}$777Note that the quoted $\rm{SNR}^{2}$ is from the parameter estimation runs for the events [$\tt{GWOSC}$]. The search $\rm{SNR}^{2}$ is generally lower and varies between the different pipelines used by the LVK. |  IAS $|$ |  $|$ GWTC-3 $|$ |  $|$ 4-OGC |  IAS 888The combined IFAR across the chirp-mass banks. $|$ |  $|$ GWTC-3 $|$ |  $|$ 4-OGC
GW191103_012549 | BBH_2 | $40.2$ | $43.9$ | $79.2$ | $--$ | $0.94$ | $--$ | Veto | $2.2$ | $--$
GW191105_143521 | BBH_1 | $31.0$ | $57.0$ | $94.1$ | $0.98$ | $0.99$ | $1.0$ | $106$ | $83.3$ | $316$
GW191109_010717 | BBH_5 | $84.8$ | $165.6$ | $299.3$ | $--$ | $0.99$ | $1.0$ | Veto | $>1000$ | $>1000$
GW191113_071753 | BBH_2 | $36.7$ | $28.9$ | $62.4$ | $--$ | $0.68$ | $--$ | Veto | $0.038$ | $--$
GW191126_115259 | BBH_2 | $33.3$ | $44.0$ | $68.9$ | $0.36$ | $0.70$ | $1.0$ | $0.034$ | $0.31$ | $4.9$
GW191127_050227 | BBH_2 | $48.4$ | $42.2$ | $84.6$ | $--$ | $0.74$ | $0.99$ | Veto | $4.0$ | $0.15$
GW191129_134029999 The primary triggers for these event were vetoed. We recover them with secondary triggers with much lower SNRs, which can happen rarely due to parameter choices in the clustering of single-detector triggers in the pipeline. | BBH_1 | $28.6$ | $51.1$ | $171.6$ | $0.68$ | $0.99$ | $1.0$ | $0.24$ | $>1000$ | $>1000$
GW191204_110529 | BBH_5 | $21.1$ | $49.4$ | $77.4$ | $0.62$ | $0.74$ | $0.99$ | $0.17$ | $0.30$ | $1.6$
GW191204_171526 | BBH_1 | $87.8$ | $183.3$ | $306.2$ | $1.00$ | $0.99$ | $1.0$ | $>1000$ | $>1000$ | $>1000$
GW191215_223052 | BBH_3 | $52.4$ | $64.9$ | $125.4$ | $1.00$ | $0.99$ | $1.0$ | $>1000$ | $>1000$ | $869$
GW191222_033537 | BBH_4 | $73.7$ | $66.7$ | $156.2$ | $0.99$ | $0.99$ | $1.0$ | $>1000$ | $>1000$ | $>1000$
GW191224_043228 | BBH_2 | $29.0$ | $50.0$ | $--$ | $0.44$ | $--$ | $0.87$ | $0.058$ | $--$ | $0.13$
GW191230_180458 | BBH_4 | $54.0$ | $44.8$ | $108.2$ | $1.00$ | $0.96$ | $1.0$ | $>1000$ | $20.0$ | $497$
GW200106_134123 | BBH_4 | $29.9$ | $28.7$ | $--$ | $0.34$ | $--$ | $0.69$ | $0.030$ | $--$ | $0.059$
GW200128_022011 | BBH_4 | $53.0$ | $45.9$ | $112.4$ | $1.00$ | $0.99$ | $1.0$ | $>1000$ | $233$ | $307$
GW200129_065458 | BBH_4 | $184.9$ | $334.5$ | $718.2$ | $--$ | $0.99$ | $1.0$ | Veto | $>1000$ | $>1000$
GW200129_114245 | BBH_4 | $22.5$ | $42.0$ | $--$ | $0.39$ | $--$ | $0.53$ | $0.041$ | $--$ | $0.037$
GW200202_154313${}^{\ref{primaryvetoed}}$ | BBH_1 | $28.0$ | $38.4$ | $116.6$ | $0.011$ | $0.99$ | $1.0$ | $<0.001$ | $>1000$ | $6.1$
GW200208_130117 | BBH_3 | $45.1$ | $51.8$ | $116.6$ | $1.00$ | $0.99$ | $1.0$ | $>1000$ | $>1000$ | $917$
GW200208_222617 | BBH_3 | $25.5$ | $33.5$ | $54.8$ | $0.14$ | $0.70$ | $--$ | $0.005$ | $0.21$ | $--$
GW200209_085452 | BBH_3 | $53.1$ | $34.3$ | $92.2$ | $0.95$ | $0.97$ | $0.99$ | $14.3$ | $21.7$ | $1.1$
GW200210_005122 | BBH_1 | $29.9$ | $34.6$ | $--$ | $--$ | $--$ | $0.74$ | Veto | $--$ | $0.042$
GW200210_092254 | BBH_1 | $24.7$ | $41.7$ | $70.6$ | $--$ | $0.54$ | $--$ | Veto | $0.83$ | $--$
GW200214_223306 | BBH_4 | $29.9$ | $25.8$ | $--$ | $0.12$ | $--$ | $0.72$ | $0.004$ | $--$ | $--$
GW200216_220804 | BBH_4 | $43.5$ | $29.1$ | $65.6$ | $0.64$ | $0.77$ | $0.78$ | $0.19$ | $2.9$ | $0.093$
GW200219_094415 | BBH_3 | $37.5$ | $67.4$ | $114.5$ | $1.00$ | $0.99$ | $1.0$ | $>1000$ | $>1000$ | $22.9$
GW200220_061928 | – | $--$ | $--$ | $51.8$ | $--$ | $0.62$ | $--$ | $--$ | $0.15$ | $--$
GW200220_124850 | BBH_4 | $38.0$ | $28.4$ | $72.2$ | $0.96$ | $0.83$ | $--$ | $21.1$ | $0.033$ | $--$
GW200224_222234 | BBH_4 | $157.5$ | $168.9$ | $400.0$ | $1.00$ | $0.99$ | $1.0$ | $>1000$ | $>1000$ | $>1000$
GW200225_060421 | BBH_2 | $90.7$ | $61.0$ | $156.2$ | $1.00$ | $0.99$ | $1.0$ | $>1000$ | $>1000$ | $>1000$
GW200305_084739 | BBH_3 | $18.0$ | $44.3$ | $--$ | $0.31$ | $--$ | $0.59$ | $0.024$ | $--$ | $0.019$
GW200306_093714 | BBH_3 | $31.2$ | $35.1$ | $60.8$ | $0.25$ | $0.81$ | $0.51$ | $0.016$ | $0.042$ | $0.018$
GW200308_173609 | BBH_3 | $22.7$ | $37.9$ | $50.4$ | $0.16$ | $0.86$ | $--$ | $0.006$ | $0.42$ | $--$
GW200311_115853 | BBH_3 | $155.2$ | $105.4$ | $316.8$ | $1.00$ | $0.99$ | $1.0$ | $>1000$ | $>1000$ | $817$
GW200316_215756 | BBH_2 | $30.8$ | $65.1$ | $106.1$ | $0.90$ | $0.99$ | $1.0$ | $3.2$ | $>1000$ | $22.4$
GW200318_191337 | BBH_4 | $22.4$ | $42.1$ | $--$ | $--$ | $--$ | $0.97$ | Veto | $--$ | $0.50$
GW200322_091133 | BBH_3 | $31.7$ | $29.2$ | $36.0$ | $0.054$ | $0.62$ | $--$ | $0.001$ | $0.007$ | $--$

##  V Discussion

Below we present a qualitative discussion of the astrophysical properties of
the new events, including where they could possibly contribute to constraints
from full population analyses. We plan to conduct a population analysis
involving these events in a separate work. We conclude with the summary of our
O3b search results and an outline of the major improvements for our upcoming
searches unifying O3a and O3b data.

###  V.1 Astrophysical implications of the new events

#### The lower mass gap (LMG)

The BH masses inferred from observations of low-mass X-ray binaries Bailyn
_et al._ (1998b); Özel  _et al._ (2010b); Farr  _et al._ (2011b) seem to be
concentrated above $\sim 5\,{\rm M_{\odot}}$. Separately, there are
observational upper limits on the known NS mass range ($\lesssim 2.6\,{\rm
M_{\odot}}$) Alsing  _et al._ (2018). Thus, there might be no way to form
compact objects between $\sim 2.6\,{\rm M_{\odot}}$ and $\sim 5\,{\rm
M_{\odot}}$. This is the basis for hypothesizing the LMG in the astrophysical
mass distribution. However, it is still unclear whether the existence of such
a gap is supported by any solid theoretical or observational evidence (as
opposed to, for example, an artifact of systematic effects in the EM
observations of x-ray binaries and GW observations of BBH, NSBH, and BNS
mergers).

As of now, we have already observed GW sources whose secondary constituents
confidently lie below $\sim 5\,{\rm M_{\odot}}$ Olsen  _et al._ (2022); Abbott
_et al._ (2021). Population analyses using catalogs that include the LVK O3b
events Abbott  _et al._ (2021b); Roulet  _et al._ (2021); Abbott  _et al._
(2023) also do not provide strong evidence for such a gap. Although a
substantial reduction in the merger rates above the maximum NS mass ($\sim
2.5\,{\rm M_{\odot}}$) is observed, there is no subsequent rise above $\sim
5\,{\rm M_{\odot}}$ (see figure 5 of Abbott  _et al._ (2023)). This indicates
that two distinct populations are required for modeling the observed compact
objects, but otherwise no such gap is discernible. The detection of more
events in this region of parameter space will help us gain a stronger
understanding of this question.

Here we present a new event, GW200316_235947, whose secondary constituent
might be either a BH in the LMG or a heavy NS. The NS scenario may be more
interesting from an astrophysical standpoint. A prior that includes the LMG as
a feature would indeed yield only the NSBH solution. This solution would also
have a positive effective spin and mass ratio $1/q\gtrsim 3.5$. The positive
spin makes it more favorable for an EM counterpart follow-up search, and we
show the sky localization for this event in Fig. 3. The BBH solution,
$m_{2}^{\rm{src}}\gtrsim 2.6\,{\rm M_{\odot}}$, has a slightly negative
effective spin with nearly equal mass ratio. Thus, this event looks
interesting under either of the potential solutions for the source
configuration. Since it has a low $p_{\rm astro}$, its impact on the
population analysis may be limited Roulet  _et al._ (2020). However, the
population analysis also recomputes $p_{\rm astro}$ under the various
astrophysical priors being tested, so there is a chance that it would become
more important in the case of other mass and spin priors.

Another event, GW191228_085854, might have its secondary constituent in the
LMG. We saw that, under our default (uniform) prior on the effective spin,
this event yielded bi-modal posterior distribution on the secondary mass where
the secondary mode lies confidently in the LMG. This solution was also
preferred by the isotropic spin prior (LVK prior). This solution also has a
high mass ratio, $1/q\gtrsim 5$ at $90\%$ confidence interval.

#### The upper mass gap (UMG)

The evolution of massive stars can go through pair-instability phases where
the stars are completely disrupted and no remnant is left behind. This
produces a gap in the predicted distribution of BH mass. The exact boundary of
such a gap is not well determined, as it depends on multiple uncertain factors
such as the rate of carbon-to-oxygen burning in the core
${}^{12}\rm{C}(\alpha,\gamma){}^{16}O$, angular momentum transport,
metallicity, wind loss, etc. Marchant and Moriya (2020); Farmer  _et al._
(2019); Mehta  _et al._ (2022).

Analyses thus far have not found any conclusive evidence for the UMG in the
observed BH mass distribution Abbott  _et al._ (2023); Roulet  _et al._
(2021). This either challenges the current theoretical models of stellar
evolution, or the gap might be filled by BBH formed via alternative mechanisms
such as hierarchical mergers Anagnostou  _et al._ (2020); Fragione  _et al._
(2020); Veske  _et al._ (2021); Fragione  _et al._ (2021). Since the
prediction of relative rates of mergers throughout parameter space is highly
uncertain, it is hard to tell at this time. As the number of observations in
this region of parameter space grows, the structures in the observed BH mass
distribution should be able to tell us whether such a gap really exists.

Here we present two new events, GW191122_214924 and GW200109_195634, whose
primary masses confidently lie between $\sim 45\,{\rm M_{\odot}}$ and $\sim
135\,{\rm M_{\odot}}$. Our measurement of the effective spin is consistent
with zero for both of these events. However, the higher likelihood region for
GW191122_214924 is concentrated around negative effective spin
($\chi_{\rm{eff}}\sim-0.2$), whereas for GW200109_195634 the high likelihood
region is at positive effective spin ($\chi_{\rm{eff}}\sim 0.5$). The Bayesian
evidence of GW191122_214924 also supports precession, and the maximum
likelihood spin parameters are far from aligned (significant in-plane
components). The spin properties make these events stand out among the
existing detections. The significance of these events will likely be improved
in future searches where HM and precession are included in the templates and
with Virgo data included in the coincident triggering.

#### Spin

GW signals also allow us to measure the spins of the binary constituents.
Specifically, a certain combination of these spins (namely, the effective
spin) can be measured more accurately Ajith (2011); Ng  _et al._ (2018). These
spin parameters encode crucial information about BBH formation channels. For
example, the isolated formation channel (under standard assumptions for
parameters like BH natal kicks) is highly unlikely to form anti-aligned or
misaligned BBH systems, especially if the total mass is high Rodriguez  _et
al._ (2016). The characteristics of BBH spins depend on many physical
processes that occur during the evolution of the progenitor stars, e.g., the
angular momentum transport Fuller  _et al._ (2019); Fuller and Ma (2019);
Belczynski, K.  _et al._ (2020), tides and mass transfer Gerosa  _et al._
(2018); Qin  _et al._ (2019); Bavera, Simone S.  _et al._ (2020), external
environments, BH natal kicks Rodriguez  _et al._ (2016), etc. It is expected
that BBH formed in isolated environments will have spins preferentially
aligned with the orbital angular momentum. On the other hand, BBH formed in
dense stellar environments (such as globular clusters) will have their spin
directions randomized by interactions, i.e., an isotropic spin distribution
Rodriguez  _et al._ (2016); Mandel and O’Shaughnessy (2010).

The GW detectors are slightly biased towards positively aligned
($\chi_{\rm{eff}}>0$) BBH systems due to selection effects.101010This is
because the $\chi_{\rm{eff}}>0$ systems are relatively louder for fixed mass
and distance. This means that we can observe these systems from a larger
volume of space. Thus, their fraction in the population of GW observations is
expected to be correspondingly larger than their fraction of the true
astrophysical population. This is consistent with what we see in Fig. 1. This
selection effect is indeed taken into consideration during the population
analysis, and thus the inference of astrophysical parameters is not expected
to be biased. However, it is not clear that the observation in Fig. 1 is
entirely due to selection effects. We know that the anti-aligned systems are
shorter in length and hence they could be more prone to being mistaken for
glitches. The waveform approximants in this regime might also not be very
faithful. One way to address these questions would be to do injection studies
where we inject astrophysical signals into the data and let the pipeline
discover them. We plan to do this in our next work.

There are some interesting spin properties among the new events reported here
which could be informative in the full population analysis. The high-mass
binary GW191122_214924 is likely to have precessing spins with slight anti-
alignment ($\chi_{\rm{eff}}\sim-0.2$). Another high-mass binary,
GW200109_195634, has its high likelihood region concentrated around a positive
effective spin of $\chi_{\rm{eff}}\sim 0.5$. On the other hand, the low-mass
binary GW191228_085854 may be a merger with a large negative
$\chi_{\rm{eff}}=-0.89^{+0.42}_{-0.10}$. If true, this may add valuable
information to the full population analysis as there is rarely such an event
in this parameter space.

###  V.2 Concluding remarks

In this work, we report 5 new candidate BBH mergers from the IAS pipeline’s
search of O3b Hanford–Livingston coincident data, based on the criteria that
the astrophysical probability is greater than one half (following the LVK
collaboration Abbott  _et al._ (2021)). We recovered 17 of the 30
Hanford–Livingston coincident BBH events with comparable or improved
significance. Our pipeline recovered 6 events with a significance lower than
one half; most of these events were detected by only one LVK pipeline. Thus,
in total, we present 22 confidently detected events in the Hanford–Livingston
coincident data from the second part of LVK’s third observing run (O3b). The
new events reported here, except GW200225_075134, are also present in the list
of GWTC-3 sub-threshold events released by the LVK collaboration LIGO
Scientific Collaboration and Collaboration (2021).

The new events declared here have interesting astrophysical properties. For
example, two events have their primary constituents sitting in the UMG, one of
which is also precessing with the primary spin’s in-plane magnitude inferred
to be $\chi_{1,\perp}\geq 0.7$. One event has its secondary constituent placed
confidently below the top of the LMG, with a possibility of being an NSBH
signal. We also have a low-mass binary which may have strongly anti-aligned
spins. As we can see from Fig. 1, at least three events lie in the sparsely
populated regions of the $\chi_{\rm{eff}}$–$M^{\rm{src}}_{\rm{tot}}$ plane.
These new events could statistically impact the inferred distributions of BBH
component masses and effective spin.

We expect roughly 2 of the newly reported events to be noise transients rather
than astrophysical signals, as suggested by summing the complements of the
$p_{\rm astro}$ values in Table 1. Nevertheless, we have shown that for at
least two events the $p_{\rm astro}$ may be improved in future searches that
include Virgo data in coincident analysis, and HM and precession in search
templates. The source properties, including significance ($p_{\rm astro}$),
become more sensitive to the prior choices for low-SNR events like ours. To
facilitate further analysis and comparisons between priors, we make our
posterior samples and other relevant information public at
https://github.com/AjitMehta/new_BBH_mergers_O3b_IAS_pipeline. These results
can be reweighted with other choices of priors to observe how the results
(like the number of events itself) may change. Our prior choices differ from
the other catalogs Abbott  _et al._ (2021); Nitz  _et al._ (2021) mainly in
the spins. We use a prior that is flat in the effective spin. Our motivation
lies in the fact that the effective spin is the best-measured spin parameter,
and hence we want to give equal weights to all physically possible values of
that parameter Zackay  _et al._ (2019). On the other hand, using an isotropic
spin prior will significantly down-weight large effective spins. A full
population analysis not only requires the PE samples, but also the $p_{\rm
astro}$ of each event Roulet  _et al._ (2020). For this reason, we also
provide a file with the full list of triggers, IAS_O3b_triggers.hdf, in the
Github repository.

The idea of this work was to complete the search on the full third observing
run (O3) data using the same pipeline that was used for our O3a search Olsen
_et al._ (2022). Nonetheless, we already made a few notable improvements in
our pipeline for this work, and we continue to plan to make improvements for
upcoming searches. In fact, we will soon release results from a search of the
full O3 data using templates that include higher harmonics Wadekar  _et al._
(2023b). We also plan to include Virgo detector data in our coincident
analysis in future work. Our next immediate task is to do an injection study,
which should enable us to assess the sensitivity of our pipeline in different
regions of the compact binary parameter space.

## Acknowledgements

We thank Horng Sheng Chia, Katerina Chatziioannou for helpful discussions. DW
gratefully acknowledges support from the Friends of the Institute for Advanced
Study Membership and the Keck foundation. TV acknowledges support from NSF
grants 2012086 and 2309360, the Alfred P. Sloan Foundation through grant
number FG-2023-20470, the BSF through award number 2022136 and the Hellman
Family Faculty Fellowship. BZ is supported by the Israel Science Foundation,
NSF-BSF and by a research grant from the Willner Family Leadership Institute
for the Weizmann Institute of Science. MZ is supported by NSF 2209991 and NSF-
BSF 2207583. This research was also supported in part by the National Science
Foundation under Grant No. NSF PHY-1748958. We also thank ICTS-TIFR for their
hospitality during the completion of a part of this work.

This research has made use of data, software and/or web tools obtained from
the Gravitational Wave Open Science Center (https://www.gw-openscience.org/),
a service of LIGO Laboratory, the LIGO Scientific Collaboration and the Virgo
Collaboration. LIGO Laboratory and Advanced LIGO are funded by the United
States National Science Foundation (NSF) as well as the Science and Technology
Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS),
and the State of Niedersachsen/Germany for support of the construction of
Advanced LIGO and construction and operation of the GEO600 detector.
Additional support for Advanced LIGO was provided by the Australian Research
Council. Virgo is funded, through the European Gravitational Observatory
(EGO), by the French Centre National de Recherche Scientifique (CNRS), the
Italian Istituto Nazionale di Fisica Nucleare (INFN) and the Dutch Nikhef,
with contributions by institutions from Belgium, Germany, Greece, Hungary,
Ireland, Japan, Monaco, Poland, Portugal, Spain.

##  Appendix A Vetoes and Estimation of $p_{\rm astro}$

Let us define “trigger” to mean a template and a segment of data for which the
quadrature sum of matched-filter SNR from each detector (let us call it an
incoherent score) passes a certain threshold. A typical event will produce
triggers above the follow-up threshold associated with multiple templates when
the data stream is match-filtered against the template bank (shown in Fig. 4).
Within a segment, we pick the trigger with the highest incoherent score as the
representative one for further follow-up. At the next stage, the triggers are
then assigned a coherent score (see Appendix D of Olsen  _et al._ (2022))
which incorporates information about the consistency of the phases, amplitudes
and arrival times between the detectors. These (coherent) scores can be used
to rank triggers. However, the different templates within a bank do not
represent the same amount of phase-space volume (or prior probability, see
figure 18 of Olsen  _et al._ (2022)). Triggers associated with templates from
low-probability regions of the bank should be down-weighted relative to those
from regions with larger probability in order to improve the search’s overall
sensitivity to the population Dent and Veitch (2014). We achieve this by using
an additional template prior (see section C of Olsen  _et al._ (2022)).
Finally, we combine these two pieces of information to compare the triggers
within a few milliseconds of each other across sub-banks or banks. The one
which has the highest value of
$\tilde{C}\equiv\log(\rm{coherent\,\,score})+\log(\rm{template\,\,prior\,\,density})$
is selected and the event is assigned to that trigger. Different events are
then ranked using a statistic which adds the rank function to $\tilde{C}$ to
account for the non-Gaussian tails from glitches (see subsection III.J of
Venumadhav  _et al._ (2019)). More specifically, the final ranking score
($\Sigma$) used to rank the events is

$\Sigma=\tilde{C}-\Big{[}\rho^{2}_{H}+\rho^{2}_{L}+2\log
P(\rho^{2}_{H}|N)+2\log P(\rho^{2}_{L}|N)\Big{]}$ (2)

where the quantity inside the square parenthesis becomes zero for the Gaussian
noise distributions. See section 4 of Wadekar  _et al._ (2023a) for further
details on the justification of the above equation.

Figure 4: We use the same template bank as in our O3a analysis Olsen  _et al._
(2022) (see Ref. Roulet  _et al._ (2019) for details on our bank construction
using geometric placement). The labeled numbers denote the different banks
(the first four banks are divided based on the chirp mass while the fifth bank
is divided using the mass of the primary). The colors denote the different
subbanks wherein the amplitude profiles remain the same while the phases of
the templates could vary.

Previously, as in Olsen  _et al._ (2022), we applied vetoes on individual
triggers before maximizing the statistic $\hat{C}$ over different template
banks when picking which bank to assign each trigger to. We found that this
procedure led to a slight overproduction of background triggers. Here we give
an argument for why that occurs. Say a candidate produced triggers in three
subbanks (or banks), and their scores are $\tilde{C}_{1}$, $\tilde{C}_{2}$ and
$\tilde{C}_{3}$. Suppose further that the trigger associated with
$\tilde{C}_{3}$ was vetoed out when we applied our signal-consistency tests.
If $\tilde{C}_{3}$ were the highest among the three scores, i.e., the “best-
fit” template was not a good match to the data, we would not want to keep this
candidate in our catalog. However, the maximization process would then pick
one of the remaining two lower scores $\tilde{C}_{1}$ and $\tilde{C}_{2}$, and
the candidate would enter the catalog. In this work, we switch the order: we
first maximize over the scores $\tilde{C}$ and then apply vetoes. This way all
the three triggers are removed if $\tilde{C}_{3}$ were the highest and got
vetoed. This procedure slightly improves our background. However, we also pay
the price of losing a few foreground triggers.

The astrophysical probability ($p_{\rm astro}$) of an event with ranking score
$\Sigma_{0}$ is defined as follows;

$p_{\rm astro}(\Sigma_{0})=\dfrac{\dfrac{dN}{d\Sigma}(\Sigma_{0}\mid
H_{S})}{\dfrac{dN}{d\Sigma}(\Sigma_{0}\mid
H_{S})+\dfrac{dN}{d\Sigma}(\Sigma_{0}\mid H_{N})}$ (3)

where $H_{S}$ denotes the signal hypothesis and $H_{N}$ the noise hypothesis.
Then, $dN/{d\Sigma}(\Sigma_{0}|H_{S})$ and $dN/{d\Sigma}(\Sigma_{0}|H_{N})$
denote the foreground and background trigger densities at the score
$\Sigma_{0}$, respectively. We compute $p_{\rm astro}$ following the same
procedure outlined in Appendix B of Olsen  _et al._ (2022). We measure the
foreground and background trigger distributions directly from the data. To
estimate the background, we generate an additional 2000 O3b runtimes worth of
noise realizations from the O3b data using timeslides, i.e., unphysical time
shifts between the data at the Hanford and Livingston detectors.

Figure 5: $p_{\rm astro}$ as a function of ranking score $\Sigma$ computed
based on the simple analytical model proposed in Eq. B4 of Olsen  _et al._
(2022). The smooth line represents the fit given in Eq. 4.

In Fig. 5 we show $p_{\rm astro}$ as a function of the ranking score $\Sigma$.
Using the same fitting ansatz as Olsen  _et al._ (2022), we find that

$p_{\rm
astro}(\Sigma)\approx\dfrac{1}{1+ae^{-\gamma\Sigma}},\,\,\,\,\,(a,\gamma)=(1.5,0.3)$
(4)

provides a good fit over the relevant range. Notice that the fit coefficients
are different from the ones in Olsen  _et al._ (2022), as we could have
expected.

##  Appendix B Posteriors for the new events

Here we present corner plots of the posteriors for a few selected parameters
for our new events: the source-frame constituent masses $m_{1}^{\rm{src}}$ and
$m_{2}^{\rm{src}}$, the effective spin $\chi_{\rm{eff}}$, and the redshift
$z$. The sampling prior used here is the same as in Ref. Olsen  _et al._
(2022), i.e., uniform in detector-frame constituent masses (as in GWTC-3 and
4-OGC), effective spin (for more details on the flat effective spin prior, see
Zackay  _et al._ (2019) or Olsen  _et al._ (2021)), and comoving $VT$ (using a
$\Lambda$CDM cosmology with Planck15 results Ade  _et al._ (2016)). These
samples are publicly available at
https://github.com/AjitMehta/new_BBH_mergers_O3b_IAS_pipeline. The posteriors
were generated using the same package $\tt{cogwheel}$ as in Olsen  _et al._
(2022) but with the most recent commit
https://github.com/jroulet/cogwheel/tree/c15d40ab29faf595e6dcd7951b15ccc92cdf1296
at the time when the analysis was conducted. The other details are also the
same, e.g., we use 8192 live points with a log-evidence tolerance value of 0.1
for the underlying $\tt{PyMultiNest}$ sampler Buchner, J.  _et al._ (2014).

Figure 6: Corner plot for the event GW$200109\\_195634$ with $p_{\rm
astro}=0.77$. The primary BH lies in UMG. This event has a noticeable
contribution from the Virgo detector as well. Our future searches where Virgo
data is included will thus improve its significance further. The redshift
observed is highest among our newly detected events. Figure 7: Corner plot for
the event GW191228_085854 with $p_{\rm astro}=0.65$. The effective spin is
highly negative. See appendix C for discussion. Figure 8: Corner plot for the
event GW$200225\\_075134$ with $p_{\rm astro}=0.60$. This event seems to be
consistent with a typical stellar BBH. Figure 9: Corner plot for the event
GW$191122\\_214924$ with $p_{\rm astro}=0.51$. The primary BH lies confidently
in UMG. There is also indication of precession, with a Bayesian evidence ratio
of $8$ in its favor against the non-precessing binary hypothesis. This event
too will become more secure in the future searches with HM and precession.
Figure 10: Corner plot for the event GW$200316\\_235947$ with $p_{\rm
astro}=0.51$. The secondary constituent confidently lies in LMG. It can also
be a heavy NS. The likelihood comparison between the regions
$m_{2}^{\rm{src}}\lesssim 2.6\,{\rm M_{\odot}}$ (NSBH) and
$m_{2}^{\rm{src}}\gtrsim 2.6\,{\rm M_{\odot}}$ (BBH) shows that both the NSBH
and BBH solutions are equally favorable. We show the sky localization for this
event in Fig. 3.

##  Appendix C Bi-modality in posteriors: GW191228_085854 and the LVK analog
GW200210_092254

One of the new events reported in this work, GW191228_085854, has a posterior
distribution that is bi-modal in several intrinsic parameters when we analyse
it with our default spin prior that is uniform in the effective spin (See Fig.
12 below, in which this prior is labelled as the “IAS prior”). Posteriors
obtained using the LVK collaboration’s default spin prior (isotropic in
individual spins), on the other hand, do not show any such feature and pick
out only the secondary mode of the result obtained using the IAS prior. The
first posterior mode suggests that this system is a BBH merger with large and
anti-aligned spins, while the second mode points to a BBH system with
significantly asymmetric masses, but zero effective spin.

The fact that the posterior, and consequently the astrophysical
interpretation, can differ depending on the prior choices is not new
(especially for low SNR events) but this event calls for further
investigation. We looked for analogs in the events within the LVK catalog, and
found similar (i.e., low total mass) events within. For example, see Fig. 11
for the event GW200210_092254. It can be seen to have very similar features in
the posteriors. Other low mass LVK events GW191113_071753 and GW190917_114630
also exhibit bi-modality in some of their intrinsic parameters. We leave
detailed investigations of such systems to future work.

Figure 11: Corner plot for the LVK event GW200210_092254. This event has very
similar features in the posteriors as GW191228_085854.

Figure 12: A closer look at our new event GW$191228\\_085854$. Left panel: The
results obtained with a prior uniform in effective spin (IAS prior) and
isotropic in the spins (LVK prior). Right panel: Same as the left panel but
with a cut in the posterior samples for the IAS prior, $\chi_{\rm{eff}}>-0.6$
(in other words, the zoomed-in version of the left panel plot near less
negative $\chi_{\rm{eff}}$). The bi-modal feature in the IAS prior result is
more clearly visible in the right panel plot. The LVK prior selectively picks
out the second mode. The median and $90\%$ confidence interval values quoted
in the left panel plot are for the IAS prior.

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